LMFDB - Embedded newform 43.8.g.a.10.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(9,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$300$
Relative dimension:	$25$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			10.11
Character	$\chi$	$=$	43.10
Dual form			43.8.g.a.13.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01772 - 4.45891i) q^{2} +(-55.9466 - 51.9109i) q^{3} +(96.4779 - 46.4613i) q^{4} +(-458.625 + 69.1265i) q^{5} +(-174.528 + 302.291i) q^{6} +(-360.749 - 624.835i) q^{7} +(-670.356 - 840.600i) q^{8} +(271.850 + 3627.59i) q^{9} +O(q^{10})$	\(q+(-1.01772 - 4.45891i) q^{2} +(-55.9466 - 51.9109i) q^{3} +(96.4779 - 46.4613i) q^{4} +(-458.625 + 69.1265i) q^{5} +(-174.528 + 302.291i) q^{6} +(-360.749 - 624.835i) q^{7} +(-670.356 - 840.600i) q^{8} +(271.850 + 3627.59i) q^{9} +(774.979 + 1974.61i) q^{10} +(-1319.86 - 635.613i) q^{11} +(-7809.46 - 2408.90i) q^{12} +(2675.86 - 6817.97i) q^{13} +(-2418.94 + 2244.45i) q^{14} +(29246.9 + 19940.2i) q^{15} +(5479.97 - 6871.66i) q^{16} +(16693.8 + 2516.18i) q^{17} +(15898.4 - 4904.01i) q^{18} +(-2274.66 + 30353.2i) q^{19} +(-41035.4 + 27977.5i) q^{20} +(-12253.1 + 53684.2i) q^{21} +(-1490.89 + 6532.02i) q^{22} +(30953.8 - 21103.9i) q^{23} +(-6132.12 + 81827.4i) q^{24} +(130904. - 40378.5i) q^{25} +(-33124.0 - 4992.64i) q^{26} +(69034.1 - 86566.0i) q^{27} +(-63834.9 - 43521.9i) q^{28} +(-156244. + 144973. i) q^{29} +(59146.4 - 150703. i) q^{30} +(-39818.1 - 12282.3i) q^{31} +(-160210. - 77153.0i) q^{32} +(40846.7 + 104076. i) q^{33} +(-5770.11 - 76996.8i) q^{34} +(208641. + 261627. i) q^{35} +(194770. + 337352. i) q^{36} +(86938.3 - 150582. i) q^{37} +(137657. - 20748.5i) q^{38} +(-503632. + 242536. i) q^{39} +(365549. + 339180. i) q^{40} +(-143940. - 630644. i) q^{41} +251843. q^{42} +(481674. + 199522. i) q^{43} -156869. q^{44} +(-375440. - 1.64491e6i) q^{45} +(-125603. - 116542. i) q^{46} +(-1.24734e6 + 600687. i) q^{47} +(-663299. + 99976.3i) q^{48} +(151492. - 262392. i) q^{49} +(-313267. - 542594. i) q^{50} +(-803343. - 1.00736e6i) q^{51} +(-58610.9 - 782108. i) q^{52} +(-124109. - 316224. i) q^{53} +(-456247. - 219717. i) q^{54} +(649259. + 200270. i) q^{55} +(-283406. + 722107. i) q^{56} +(1.70292e6 - 1.58008e6i) q^{57} +(805432. + 549134. i) q^{58} +(-1.52016e6 + 1.90622e6i) q^{59} +(3.74813e6 + 564939. i) q^{60} +(-2.34681e6 + 723895. i) q^{61} +(-14241.9 + 190045. i) q^{62} +(2.16857e6 - 1.47851e6i) q^{63} +(69369.8 - 303929. i) q^{64} +(-755911. + 3.31186e6i) q^{65} +(422493. - 288051. i) q^{66} +(-288787. + 3.85360e6i) q^{67} +(1.72749e6 - 532859. i) q^{68} +(-2.82728e6 - 426144. i) q^{69} +(954235. - 1.19657e6i) q^{70} +(4.07421e6 + 2.77775e6i) q^{71} +(2.86711e6 - 2.66029e6i) q^{72} +(836272. - 2.13079e6i) q^{73} +(-759908. - 234401. i) q^{74} +(-9.41971e6 - 4.53629e6i) q^{75} +(1.19080e6 + 3.03410e6i) q^{76} +(78985.9 + 1.05399e6i) q^{77} +(1.59400e6 + 1.99881e6i) q^{78} +(-1.88782e6 - 3.26980e6i) q^{79} +(-2.03823e6 + 3.53032e6i) q^{80} +(-489020. + 73707.9i) q^{81} +(-2.66549e6 + 1.28363e6i) q^{82} +(3.85378e6 + 3.57578e6i) q^{83} +(1.31209e6 + 5.74863e6i) q^{84} -7.83011e6 q^{85} +(399443. - 2.35080e6i) q^{86} +1.62670e7 q^{87} +(350482. + 1.53556e6i) q^{88} +(-2.20476e6 - 2.04572e6i) q^{89} +(-6.95240e6 + 3.34810e6i) q^{90} +(-5.22542e6 + 787606. i) q^{91} +(2.00584e6 - 3.47421e6i) q^{92} +(1.59011e6 + 2.75414e6i) q^{93} +(3.94785e6 + 4.95044e6i) q^{94} +(-1.05500e6 - 1.40780e7i) q^{95} +(4.95812e6 + 1.26331e7i) q^{96} +(-64404.7 - 31015.7i) q^{97} +(-1.32416e6 - 408449. i) q^{98} +(1.94694e6 - 4.96071e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) $ 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.01772	−	4.45891i	−0.0899543	−	0.394115i	0.909828	−	0.414986i	$-0.136213\pi$
$2$	−1.01772	−	4.45891i	−0.0899543	−	0.394115i	−0.999782	+	0.0208703i	$0.993356\pi$
$3$	−55.9466	−	51.9109i	−1.19633	−	1.11003i	−0.991348	−	0.131261i	$-0.958097\pi$
$3$	−55.9466	−	51.9109i	−1.19633	−	1.11003i	−0.204977	−	0.978767i	$-0.565712\pi$
$4$	96.4779	−	46.4613i	0.753734	−	0.362979i
$5$	−458.625	+	69.1265i	−1.64082	+	0.247315i	−0.903614	−	0.428348i	$-0.859096\pi$
$5$	−458.625	+	69.1265i	−1.64082	+	0.247315i	−0.737211	+	0.675662i	$0.763858\pi$
$6$	−174.528	+	302.291i	−0.329865	+	0.571342i
$7$	−360.749	−	624.835i	−0.397523	−	0.688529i	0.595897	−	0.803061i	$-0.296797\pi$
$7$	−360.749	−	624.835i	−0.397523	−	0.688529i	−0.993420	+	0.114532i	$0.963463\pi$
$8$	−670.356	−	840.600i	−0.462904	−	0.580463i
$9$	271.850	+	3627.59i	0.124303	+	1.65870i
$10$	774.979	+	1974.61i	0.245070	+	0.624428i
$11$	−1319.86	−	635.613i	−0.298989	−	0.143985i	0.278375	−	0.960472i	$-0.410204\pi$
$11$	−1319.86	−	635.613i	−0.298989	−	0.143985i	−0.577364	+	0.816487i	$0.695918\pi$
$12$	−7809.46	−	2408.90i	−1.30463	−	0.402424i
$13$	2675.86	−	6817.97i	0.337801	−	0.860703i	−0.656523	−	0.754306i	$-0.727973\pi$
$13$	2675.86	−	6817.97i	0.337801	−	0.860703i	0.994324	−	0.106397i	$-0.0339314\pi$
$14$	−2418.94	+	2244.45i	−0.235601	+	0.218606i
$15$	29246.9	+	19940.2i	2.23749	+	1.52549i
$16$	5479.97	−	6871.66i	0.334471	−	0.419413i
$17$	16693.8	+	2516.18i	0.824107	+	0.124214i	0.547539	−	0.836780i	$-0.315565\pi$
$17$	16693.8	+	2516.18i	0.824107	+	0.124214i	0.276568	+	0.960994i	$0.410803\pi$
$18$	15898.4	−	4904.01i	0.642540	−	0.198197i
$19$	−2274.66	+	30353.2i	−0.0760814	+	1.01524i	0.820294	+	0.571941i	$0.193810\pi$
$19$	−2274.66	+	30353.2i	−0.0760814	+	1.01524i	−0.896376	+	0.443295i	$0.853809\pi$
$20$	−41035.4	+	27977.5i	−1.14697	+	0.781994i
$21$	−12253.1	+	53684.2i	−0.288720	+	1.26497i
$22$	−1490.89	+	6532.02i	−0.0298515	+	0.130788i
$23$	30953.8	−	21103.9i	0.530476	−	0.361673i	−0.268267	−	0.963345i	$-0.586451\pi$
$23$	30953.8	−	21103.9i	0.530476	−	0.361673i	0.798743	+	0.601672i	$0.205499\pi$
$24$	−6132.12	+	81827.4i	−0.0905464	+	1.20826i
$25$	130904.	−	40378.5i	1.67557	−	0.516845i
$26$	−33124.0	−	4992.64i	−0.369603	−	0.0557087i
$27$	69034.1	−	86566.0i	0.674979	−	0.846397i
$28$	−63834.9	−	43521.9i	−0.549548	−	0.374675i
$29$	−156244.	+	144973.i	−1.18962	+	1.10381i	−0.197273	+	0.980349i	$0.563208\pi$
$29$	−156244.	+	144973.i	−1.18962	+	1.10381i	−0.992350	+	0.123460i	$0.960601\pi$
$30$	59146.4	−	150703.i	0.399949	−	1.01905i
$31$	−39818.1	−	12282.3i	−0.240057	−	0.0740478i	0.172392	−	0.985028i	$-0.444850\pi$
$31$	−39818.1	−	12282.3i	−0.240057	−	0.0740478i	−0.412449	+	0.910981i	$0.635327\pi$
$32$	−160210.	−	77153.0i	−0.864299	−	0.416225i
$33$	40846.7	+	104076.i	0.197860	+	0.504139i
$34$	−5770.11	−	76996.8i	−0.0251772	−	0.335967i
$35$	208641.	+	261627.i	0.822548	+	1.03144i
$36$	194770.	+	337352.i	0.695766	+	1.20510i
$37$	86938.3	−	150582.i	0.282166	−	0.488726i	−0.689752	−	0.724046i	$-0.742280\pi$
$37$	86938.3	−	150582.i	0.282166	−	0.488726i	0.971918	+	0.235320i	$0.0756137\pi$
$38$	137657.	−	20748.5i	0.406964	−	0.0613400i
$39$	−503632.	+	242536.i	−1.35952	+	0.654713i
$40$	365549.	+	339180.i	0.903101	+	0.837955i
$41$	−143940.	−	630644.i	−0.326166	−	1.42903i	−0.826373	−	0.563123i	$-0.809600\pi$
$41$	−143940.	−	630644.i	−0.326166	−	1.42903i	0.500207	−	0.865906i	$-0.333257\pi$
$42$	251843.			0.524514
$43$	481674.	+	199522.i	0.923875	+	0.382694i
$43$	481674.	+	199522.i	0.923875	+	0.382694i
$44$	−156869.			−0.277621
$45$	−375440.	−	1.64491e6i	−0.614181	−	2.69090i
$46$	−125603.	−	116542.i	−0.190259	−	0.176535i
$47$	−1.24734e6	+	600687.i	−1.75244	+	0.843929i	−0.775218	+	0.631694i	$0.782360\pi$
$47$	−1.24734e6	+	600687.i	−1.75244	+	0.843929i	−0.977219	+	0.212234i	$0.931926\pi$
$48$	−663299.	+	99976.3i	−0.865696	+	0.130483i
$49$	151492.	−	262392.i	0.183952	−	0.318614i
$50$	−313267.	−	542594.i	−0.354421	−	0.613875i
$51$	−803343.	−	1.00736e6i	−0.848018	−	1.06338i
$52$	−58610.9	−	782108.i	−0.0578051	−	0.771356i
$53$	−124109.	−	316224.i	−0.114508	−	0.291762i	0.862118	−	0.506708i	$-0.169138\pi$
$53$	−124109.	−	316224.i	−0.114508	−	0.291762i	−0.976626	+	0.214946i	$0.931042\pi$
$54$	−456247.	−	219717.i	−0.394296	−	0.189883i
$55$	649259.	+	200270.i	0.526198	+	0.162310i
$56$	−283406.	+	722107.i	−0.215651	+	0.549470i
$57$	1.70292e6	−	1.58008e6i	1.21796	−	1.13010i
$58$	805432.	+	549134.i	0.542040	+	0.369556i
$59$	−1.52016e6	+	1.90622e6i	−0.963624	+	1.20835i	0.0144087	+	0.999896i	$0.495413\pi$
$59$	−1.52016e6	+	1.90622e6i	−0.963624	+	1.20835i	−0.978033	+	0.208450i	$0.933158\pi$
$60$	3.74813e6	+	564939.i	2.24019	+	0.337654i
$61$	−2.34681e6	+	723895.i	−1.32380	+	0.408339i	−0.874493	−	0.485037i	$-0.838806\pi$
$61$	−2.34681e6	+	723895.i	−1.32380	+	0.408339i	−0.449309	+	0.893376i	$0.648330\pi$
$62$	−14241.9	+	190045.i	−0.00758923	+	0.101271i
$63$	2.16857e6	−	1.47851e6i	1.09265	−	0.744959i
$64$	69369.8	−	303929.i	0.0330781	−	0.144925i
$65$	−755911.	+	3.31186e6i	−0.341408	+	1.49581i
$66$	422493.	−	288051.i	0.180891	−	0.123329i
$67$	−288787.	+	3.85360e6i	−0.117305	+	1.56532i	0.559292	+	0.828971i	$0.311073\pi$
$67$	−288787.	+	3.85360e6i	−0.117305	+	1.56532i	−0.676597	+	0.736354i	$0.736546\pi$
$68$	1.72749e6	−	532859.i	0.666244	−	0.205509i
$69$	−2.82728e6	−	426144.i	−1.03609	−	0.156165i
$70$	954235.	−	1.19657e6i	0.332516	−	0.416962i
$71$	4.07421e6	+	2.77775e6i	1.35095	+	0.921062i	0.999883	−	0.0152887i	$-0.00486674\pi$
$71$	4.07421e6	+	2.77775e6i	1.35095	+	0.921062i	0.351066	+	0.936351i	$0.385819\pi$
$72$	2.86711e6	−	2.66029e6i	0.905276	−	0.839973i
$73$	836272.	−	2.13079e6i	0.251604	−	0.641077i	−0.748144	−	0.663537i	$-0.769055\pi$
$73$	836272.	−	2.13079e6i	0.251604	−	0.641077i	0.999748	+	0.0224602i	$0.00714989\pi$
$74$	−759908.	−	234401.i	−0.217997	−	0.0672431i
$75$	−9.41971e6	−	4.53629e6i	−2.57824	−	1.24161i
$76$	1.19080e6	+	3.03410e6i	0.311164	+	0.792834i
$77$	78985.9	+	1.05399e6i	0.0197166	+	0.263100i
$78$	1.59400e6	+	1.99881e6i	0.380327	+	0.476916i
$79$	−1.88782e6	−	3.26980e6i	−0.430789	−	0.746149i	0.566152	−	0.824301i	$-0.308432\pi$
$79$	−1.88782e6	−	3.26980e6i	−0.430789	−	0.746149i	−0.996941	+	0.0781516i	$0.975098\pi$
$80$	−2.03823e6	+	3.53032e6i	−0.445081	+	0.770903i
$81$	−489020.	+	73707.9i	−0.102242	+	0.0154105i
$82$	−2.66549e6	+	1.28363e6i	−0.533862	+	0.257094i
$83$	3.85378e6	+	3.57578e6i	0.739799	+	0.686433i	0.957128	−	0.289666i	$-0.0935441\pi$
$83$	3.85378e6	+	3.57578e6i	0.739799	+	0.686433i	−0.217329	+	0.976098i	$0.569735\pi$
$84$	1.31209e6	+	5.74863e6i	0.241538	+	1.05825i
$85$	−7.83011e6			−1.38293
$86$	399443.	−	2.35080e6i	0.0677190	−	0.398538i
$87$	1.62670e7			2.64843
$88$	350482.	+	1.53556e6i	0.0548248	+	0.240203i
$89$	−2.20476e6	−	2.04572e6i	−0.331510	−	0.307596i	0.496801	−	0.867864i	$-0.334508\pi$
$89$	−2.20476e6	−	2.04572e6i	−0.331510	−	0.307596i	−0.828312	+	0.560268i	$0.810698\pi$
$90$	−6.95240e6	+	3.34810e6i	−1.00528	+	0.484116i
$91$	−5.22542e6	+	787606.i	−0.726903	+	0.109563i
$92$	2.00584e6	−	3.47421e6i	0.268558	−	0.465157i
$93$	1.59011e6	+	2.75414e6i	0.204991	+	0.355055i
$94$	3.94785e6	+	4.95044e6i	0.490245	+	0.614747i
$95$	−1.05500e6	−	1.40780e7i	−0.126246	−	1.68464i
$96$	4.95812e6	+	1.26331e7i	0.571962	+	1.45734i
$97$	−64404.7	−	31015.7i	−0.00716501	−	0.00345049i	0.430298	−	0.902687i	$-0.358409\pi$
$97$	−64404.7	−	31015.7i	−0.00716501	−	0.00345049i	−0.437463	+	0.899237i	$0.644123\pi$
$98$	−1.32416e6	−	408449.i	−0.142118	−	0.0438375i
$99$	1.94694e6	−	4.96071e6i	0.201664	−	0.513832i
$100$	1.07533e7	−	9.97760e6i	1.07533	−	0.997760i
$101$	1.04747e7	+	7.14151e6i	1.01162	+	0.689708i	0.951235	−	0.308468i	$-0.0998161\pi$
$101$	1.04747e7	+	7.14151e6i	1.01162	+	0.689708i	0.0603808	+	0.998175i	$0.480768\pi$
$102$	−3.67415e6	+	4.60724e6i	−0.342812	+	0.429873i
$103$	−1.26002e7	−	1.89917e6i	−1.13618	−	0.171251i	−0.446098	−	0.894984i	$-0.647187\pi$
$103$	−1.26002e7	−	1.89917e6i	−1.13618	−	0.171251i	−0.690080	+	0.723733i	$0.742425\pi$
$104$	−7.52496e6	+	2.32114e6i	−0.655976	+	0.202342i
$105$	1.90855e6	−	2.54679e7i	0.160895	−	2.14699i
$106$	−1.28370e6	+	875215.i	−0.104687	+	0.0713747i
$107$	615703.	−	2.69757e6i	0.0485879	−	0.212877i	−0.944806	−	0.327629i	$-0.893750\pi$
$107$	615703.	−	2.69757e6i	0.0485879	−	0.212877i	0.993394	+	0.114752i	$0.0366074\pi$
$108$	2.63829e6	−	1.15591e7i	0.201530	−	0.882961i
$109$	1.35834e7	−	9.26099e6i	1.00465	−	0.684959i	0.0550700	−	0.998482i	$-0.482462\pi$
$109$	1.35834e7	−	9.26099e6i	1.00465	−	0.684959i	0.949580	+	0.313523i	$0.101509\pi$
$110$	232223.	−	3.09881e6i	0.0166353	−	0.221983i
$111$	−1.26807e7	+	3.91148e6i	−0.880063	+	0.271463i
$112$	−6.27055e6	−	945133.i	−0.421738	−	0.0635667i
$113$	2.01919e6	−	2.53199e6i	0.131645	−	0.165077i	−0.711640	−	0.702544i	$-0.752047\pi$
$113$	2.01919e6	−	2.53199e6i	0.131645	−	0.165077i	0.843285	+	0.537467i	$0.180619\pi$
$114$	−8.77852e6	−	5.98509e6i	−0.554951	−	0.378359i
$115$	−1.27373e7	+	1.18185e7i	−0.780972	+	0.724636i
$116$	−8.33842e6	+	2.12460e7i	−0.495999	+	1.26379i
$117$	2.54602e7	+	7.85344e6i	1.46964	+	0.453325i
$118$	1.00468e7	+	4.83827e6i	0.562910	+	0.271083i
$119$	−4.45006e6	−	1.13386e7i	−0.242076	−	0.616799i
$120$	−2.84411e6	−	3.79520e7i	−0.150249	−	2.00493i
$121$	−1.08120e7	−	1.35578e7i	−0.554827	−	0.695732i
$122$	5.61616e6	+	9.72748e6i	0.280014	+	0.484999i
$123$	−2.46843e7	+	4.27545e7i	−1.19606	+	2.07164i
$124$	−4.41222e6	+	665035.i	−0.207817	+	0.0313234i
$125$	−2.45981e7	+	1.18458e7i	−1.12646	+	0.542476i
$126$	−8.79953e6	−	8.16477e6i	−0.391889	−	0.363619i
$127$	−637560.	−	2.79333e6i	−0.0276190	−	0.121007i	0.959239	−	0.282595i	$-0.0911954\pi$
$127$	−637560.	−	2.79333e6i	−0.0276190	−	0.121007i	−0.986858	+	0.161589i	$0.948338\pi$
$128$	−2.41867e7			−1.01939
$129$	−1.65906e7	−	3.61667e7i	−0.680455	−	1.48335i
$130$	1.55366e7			0.620232
$131$	−4.94278e6	−	2.16557e7i	−0.192097	−	0.841633i	−0.975479	−	0.220093i	$-0.929364\pi$
$131$	−4.94278e6	−	2.16557e7i	−0.192097	−	0.841633i	0.783382	−	0.621541i	$-0.213493\pi$
$132$	8.77629e6	+	8.14321e6i	0.332125	+	0.308167i
$133$	1.97863e7	−	9.52860e6i	0.729264	−	0.351195i
$134$	1.74767e7	−	2.63419e6i	0.627471	−	0.0945760i
$135$	−2.56767e7	+	4.44734e7i	−0.898197	+	1.55572i
$136$	−9.07567e6	−	1.57195e7i	−0.309380	−	0.535862i
$137$	1.04075e7	+	1.30505e7i	0.345798	+	0.433617i	0.924068	−	0.382229i	$-0.124843\pi$
$137$	1.04075e7	+	1.30505e7i	0.345798	+	0.433617i	−0.578270	+	0.815846i	$0.696272\pi$
$138$	977233.	+	1.30403e7i	0.0316535	+	0.422386i
$139$	−2.10268e6	−	5.35753e6i	−0.0664080	−	0.169205i	0.893817	−	0.448431i	$-0.148017\pi$
$139$	−2.10268e6	−	5.35753e6i	−0.0664080	−	0.169205i	−0.960225	+	0.279227i	$0.909922\pi$
$140$	3.22848e7	+	1.55475e7i	0.994374	+	0.478865i
$141$	1.00967e8	+	3.11441e7i	3.03327	+	0.935639i
$142$	8.23934e6	−	2.09935e7i	0.241481	−	0.615284i
$143$	−7.86536e6	+	7.29798e6i	−0.224927	+	0.208702i
$144$	2.64173e7	+	1.80110e7i	0.737258	+	0.502654i
$145$	6.16357e7	−	7.72887e7i	1.67897	−	2.10537i
$146$	−1.03521e7	−	1.56032e6i	−0.275291	−	0.0414934i
$147$	−2.20965e7	+	6.81586e6i	−0.573736	+	0.176974i
$148$	1.39141e6	−	1.85671e7i	0.0352808	−	0.470790i
$149$	−5.39272e7	+	3.67669e7i	−1.33554	+	0.910553i	−0.999510	−	0.0312991i	$-0.990036\pi$
$149$	−5.39272e7	+	3.67669e7i	−1.33554	+	0.910553i	−0.336027	+	0.941853i	$0.609083\pi$
$150$	−1.06403e7	+	4.66183e7i	−0.257416	+	1.12781i
$151$	−2.66935e6	+	1.16952e7i	−0.0630938	+	0.276432i	−0.996628	−	0.0820574i	$-0.973851\pi$
$151$	−2.66935e6	+	1.16952e7i	−0.0630938	+	0.276432i	0.933534	+	0.358489i	$0.116708\pi$
$152$	2.70397e7	−	1.84354e7i	0.624525	−	0.425794i
$153$	−4.58946e6	+	6.12422e7i	−0.103596	+	1.38239i
$154$	4.61927e6	−	1.42486e6i	0.101918	−	0.0314376i
$155$	1.91106e7	+	2.88046e6i	0.412205	+	0.0621299i
$156$	−3.73208e7	+	4.67988e7i	−0.787073	+	0.986958i
$157$	3.04727e7	+	2.07759e7i	0.628437	+	0.428461i	0.835213	−	0.549927i	$-0.185344\pi$
$157$	3.04727e7	+	2.07759e7i	0.628437	+	0.428461i	−0.206775	+	0.978388i	$0.566297\pi$
$158$	−1.26585e7	+	1.17453e7i	−0.255318	+	0.236900i
$159$	−9.47198e6	+	2.41342e7i	−0.186875	+	0.476149i
$160$	7.88095e7	+	2.43095e7i	1.52110	+	0.469198i
$161$	−2.43530e7	−	1.17278e7i	−0.459898	−	0.221475i
$162$	826340.	+	2.10548e6i	0.0152706	+	0.0389089i
$163$	−497155.	−	6.63407e6i	−0.00899156	−	0.119984i	0.990902	−	0.134587i	$-0.0429707\pi$
$163$	−497155.	−	6.63407e6i	−0.00899156	−	0.119984i	−0.999893	+	0.0146027i	$0.995352\pi$
$164$	−4.31876e7	−	5.41556e7i	−0.764550	−	0.958715i
$165$	−2.59277e7	−	4.49080e7i	−0.449334	−	0.778270i
$166$	1.20220e7	−	2.08228e7i	0.203986	−	0.353314i
$167$	−6.51616e7	+	9.82153e6i	−1.08264	+	0.163182i	−0.666046	−	0.745911i	$-0.732014\pi$
$167$	−6.51616e7	+	9.82153e6i	−1.08264	+	0.163182i	−0.416594	+	0.909093i	$0.636776\pi$
$168$	5.33408e7	−	2.56876e7i	0.867915	−	0.417966i
$169$	6.67338e6	+	6.19199e6i	0.106351	+	0.0986794i
$170$	7.96883e6	+	3.49137e7i	0.124401	+	0.545036i
$171$	−1.10727e8			−1.69343
$172$	5.57409e7	−	3.12972e6i	0.835266	−	0.0468981i
$173$	−7.12346e7			−1.04600			−0.522998	−	0.852334i	$-0.675186\pi$
$173$	−7.12346e7			−1.04600			−0.522998	+	0.852334i	$0.675186\pi$
$174$	−1.65552e7	−	7.25329e7i	−0.238238	−	1.04379i
$175$	−7.24533e7	−	6.72268e7i	−1.02194	−	0.948221i
$176$	−1.16005e7	+	5.58652e6i	−0.160392	+	0.0772408i
$177$	1.84002e8	−	2.77338e7i	2.49411	−	0.375926i
$178$	−6.87786e6	+	1.19128e7i	−0.0914078	+	0.158323i
$179$	6.71484e6	+	1.16304e7i	0.0875085	+	0.151569i	0.906457	−	0.422297i	$-0.138776\pi$
$179$	6.71484e6	+	1.16304e7i	0.0875085	+	0.151569i	−0.818949	+	0.573866i	$0.805443\pi$
$180$	−1.12646e8	−	1.41254e8i	−1.43967	−	1.80529i
$181$	8.01831e6	+	1.06997e8i	0.100510	+	1.34121i	0.788297	+	0.615295i	$0.210963\pi$
$181$	8.01831e6	+	1.06997e8i	0.100510	+	1.34121i	−0.687787	+	0.725912i	$0.741418\pi$
$182$	8.82986e6	+	2.24981e7i	0.108569	+	0.276628i
$183$	1.68874e8	+	8.13254e7i	2.03697	+	0.980951i
$184$	−3.84900e7	−	1.18726e7i	−0.455497	−	0.140502i
$185$	−2.94629e7	+	7.50701e7i	−0.342116	+	0.871698i
$186$	1.06622e7	−	9.89307e6i	0.121493	−	0.112729i
$187$	−2.04342e7	−	1.39318e7i	−0.228513	−	0.155798i
$188$	−9.24320e7	+	1.15906e8i	−1.01454	+	1.27220i
$189$	−7.89935e7	−	1.19063e7i	−0.851089	−	0.128281i
$190$	−6.16987e7	+	1.90315e7i	−0.652587	+	0.201296i
$191$	8.77519e6	−	1.17097e8i	0.0911255	−	1.21599i	−0.744855	−	0.667226i	$-0.767481\pi$
$191$	8.77519e6	−	1.17097e8i	0.0911255	−	1.21599i	0.835981	−	0.548759i	$-0.184899\pi$
$192$	−1.96582e7	+	1.34027e7i	−0.200442	+	0.136659i
$193$	−585587.	+	2.56562e6i	−0.00586328	+	0.0256887i	−0.977775	−	0.209657i	$-0.932765\pi$
$193$	−585587.	+	2.56562e6i	−0.00586328	+	0.0256887i	0.971912	+	0.235346i	$0.0756223\pi$
$194$	−72750.3	+	318740.i	−0.000715367	+	0.00313423i
$195$	2.14212e8	−	1.46047e8i	2.06882	−	1.41050i
$196$	2.42456e6	−	3.23536e7i	0.0230005	−	0.306920i
$197$	5.01036e7	−	1.54549e7i	0.466914	−	0.144024i	−0.0523660	−	0.998628i	$-0.516676\pi$
$197$	5.01036e7	−	1.54549e7i	0.466914	−	0.144024i	0.519280	+	0.854604i	$0.326200\pi$
$198$	−2.41008e7	−	3.63261e6i	−0.220649	−	0.0332576i
$199$	−4.31946e7	+	5.41644e7i	−0.388548	+	0.487223i	−0.937183	−	0.348839i	$-0.886576\pi$
$199$	−4.31946e7	+	5.41644e7i	−0.388548	+	0.487223i	0.548635	+	0.836062i	$0.315148\pi$
$200$	−1.21694e8	−	8.29698e7i	−1.07564	−	0.733356i
$201$	2.16200e8	−	2.00604e8i	1.87789	−	1.74243i
$202$	2.11831e7	−	5.39736e7i	0.180825	−	0.460736i
$203$	1.46949e8	+	4.53277e7i	1.23291	+	0.380301i
$204$	−1.24308e8	−	5.98636e7i	−1.02517	−	0.493694i
$205$	1.09609e8	+	2.79279e8i	0.888602	+	2.26412i
$206$	4.35518e6	+	5.81159e7i	0.0347113	+	0.463190i
$207$	8.49711e7	+	1.06550e8i	0.665848	+	0.834947i
$208$	−3.21872e7	−	5.57499e7i	−0.248006	−	0.429558i
$209$	2.22951e7	−	3.86163e7i	0.168927	−	0.292589i
$210$	−1.15501e8	+	1.74090e7i	−0.860636	+	0.129720i
$211$	−6.42218e7	+	3.09276e7i	−0.470645	+	0.226651i	−0.654145	−	0.756369i	$-0.726972\pi$
$211$	−6.42218e7	+	3.09276e7i	−0.470645	+	0.226651i	0.183500	+	0.983020i	$0.441257\pi$
$212$	−2.66659e7	−	2.47423e7i	−0.192212	−	0.178347i
$213$	−8.37428e7	−	3.66901e8i	−0.593771	−	2.60148i
$214$	−1.26548e7			−0.0882690
$215$	−2.34700e8	−	5.82093e7i	−1.61056	−	0.399446i
$216$	−1.19045e8			−0.803752
$217$	6.68995e6	+	2.93106e7i	0.0444440	+	0.194722i
$218$	−5.51179e7	−	5.11420e7i	−0.360326	−	0.334333i
$219$	−1.57398e8	+	7.57986e7i	−1.01261	+	0.487649i
$220$	7.19440e7	−	1.08438e7i	0.455528	−	0.0686598i
$221$	6.18254e7	−	1.07085e8i	0.385296	−	0.667352i
$222$	3.03463e7	+	5.25614e7i	0.186153	+	0.322427i
$223$	−1.72196e8	−	2.15927e8i	−1.03981	−	1.30389i	−0.951452	−	0.307797i	$-0.900408\pi$
$223$	−1.72196e8	−	2.15927e8i	−1.03981	−	1.30389i	−0.0883614	−	0.996088i	$-0.528163\pi$
$224$	9.58759e6	+	1.27938e8i	0.0569956	+	0.760554i
$225$	1.82063e8	+	4.63888e8i	1.06557	+	2.71503i
$226$	−1.33449e7	−	6.42656e6i	−0.0769016	−	0.0370338i
$227$	5.93476e7	+	1.83063e7i	0.336754	+	0.103875i	0.458520	−	0.888684i	$-0.348380\pi$
$227$	5.93476e7	+	1.83063e7i	0.336754	+	0.103875i	−0.121766	+	0.992559i	$0.538856\pi$
$228$	9.08817e7	−	2.31563e8i	0.507814	−	1.29389i
$229$	−2.15548e8	+	1.99999e8i	−1.18610	+	1.10054i	−0.193248	+	0.981150i	$0.561902\pi$
$229$	−2.15548e8	+	1.99999e8i	−1.18610	+	1.10054i	−0.992848	+	0.119386i	$0.961907\pi$
$230$	6.56606e7	+	4.47666e7i	0.355842	+	0.242609i
$231$	5.02947e7	−	6.30676e7i	0.268461	−	0.336639i
$232$	2.26603e8	+	3.41549e7i	1.19140	+	0.179575i
$233$	−1.15874e8	+	3.57424e7i	−0.600123	+	0.185114i	−0.579908	−	0.814682i	$-0.696911\pi$
$233$	−1.15874e8	+	3.57424e7i	−0.600123	+	0.185114i	−0.0202156	+	0.999796i	$0.506435\pi$
$234$	9.10647e6	−	1.21517e8i	0.0464616	−	0.619987i
$235$	5.30537e8	−	3.61714e8i	2.66673	−	1.81814i
$236$	−5.80964e7	+	2.54537e8i	−0.287712	+	1.26055i
$237$	−6.41209e7	+	2.80932e8i	−0.312882	+	1.37083i
$238$	−4.60287e7	+	3.13819e7i	−0.221314	+	0.150890i
$239$	−2.47479e7	+	3.30238e8i	−0.117259	+	1.56471i	0.559704	+	0.828693i	$0.310915\pi$
$239$	−2.47479e7	+	3.30238e8i	−0.117259	+	1.56471i	−0.676962	+	0.736018i	$0.736704\pi$
$240$	2.97294e8	−	9.17032e7i	1.38819	−	0.428198i
$241$	−8.75455e7	−	1.31954e7i	−0.402878	−	0.0607241i	−0.0555223	−	0.998457i	$-0.517682\pi$
$241$	−8.75455e7	−	1.31954e7i	−0.402878	−	0.0607241i	−0.347356	+	0.937733i	$0.612920\pi$
$242$	−4.94496e7	+	6.20078e7i	−0.224289	+	0.281250i
$243$	−1.68888e8	−	1.15146e8i	−0.755051	−	0.514785i
$244$	−1.92782e8	+	1.78876e8i	−0.849576	+	0.788291i
$245$	−5.13398e7	+	1.30812e8i	−0.223035	+	0.568283i
$246$	2.15760e8	+	6.65531e7i	0.924055	+	0.285033i
$247$	2.00861e8	+	9.67294e7i	0.848117	+	0.408432i
$248$	1.63678e7	+	4.17046e7i	0.0681413	+	0.173621i
$249$	−2.99838e7	−	4.00106e8i	−0.123080	−	1.64239i
$250$	7.78533e7	+	9.76250e7i	0.315128	+	0.395158i
$251$	−1.40921e8	−	2.44082e8i	−0.562492	−	0.974265i	−0.997278	−	0.0737311i	$-0.976509\pi$
$251$	−1.40921e8	−	2.44082e8i	−0.562492	−	0.974265i	0.434786	−	0.900534i	$-0.356824\pi$
$252$	1.40526e8	−	2.43398e8i	0.553165	−	0.958111i
$253$	−5.42687e7	+	8.17968e6i	−0.210682	+	0.0317552i
$254$	−1.18064e7	+	5.68564e6i	−0.0452062	+	0.0217702i
$255$	4.38068e8	+	4.06468e8i	1.65444	+	1.53510i
$256$	1.57359e7	+	6.89433e7i	0.0586206	+	0.256834i
$257$	−2.32336e7			−0.0853788			−0.0426894	−	0.999088i	$-0.513593\pi$
$257$	−2.32336e7			−0.0853788			−0.0426894	+	0.999088i	$0.513593\pi$
$258$	−1.44379e8	+	1.10784e8i	−0.523403	+	0.401612i
$259$	−1.25452e8			−0.448670
$260$	8.09448e7	+	3.54642e8i	0.285616	+	1.25136i
$261$	−5.68376e8	−	5.27376e8i	−1.97877	−	1.83603i
$262$	−9.15305e7	+	4.40788e7i	−0.314421	+	0.151417i
$263$	2.61277e8	−	3.93811e7i	0.885637	−	0.133488i	0.309556	−	0.950881i	$-0.399819\pi$
$263$	2.61277e8	−	3.93811e7i	0.885637	−	0.133488i	0.576081	+	0.817393i	$0.304581\pi$
$264$	6.01041e7	−	1.04103e8i	0.201044	−	0.348218i
$265$	7.87787e7	+	1.36449e8i	0.260045	+	0.450411i
$266$	−6.26240e7	−	7.85280e7i	−0.204012	−	0.255823i
$267$	1.71539e7	+	2.28902e8i	0.0551534	+	0.735971i
$268$	1.51182e8	+	3.85204e8i	0.479763	+	1.22242i
$269$	−5.19963e7	−	2.50401e7i	−0.162869	−	0.0784338i	0.350673	−	0.936498i	$-0.385953\pi$
$269$	−5.19963e7	−	2.50401e7i	−0.162869	−	0.0784338i	−0.513543	+	0.858064i	$0.671667\pi$
$270$	2.24434e8	+	6.92288e7i	0.693931	+	0.214049i
$271$	−8.60856e7	+	2.19342e8i	−0.262747	+	0.669469i	−0.999981	−	0.00616900i	$-0.998036\pi$
$271$	−8.60856e7	+	2.19342e8i	−0.262747	+	0.669469i	0.737234	+	0.675638i	$0.236132\pi$
$272$	1.08772e8	−	1.00925e8i	0.327736	−	0.304095i
$273$	3.33230e8	+	2.27192e8i	0.991230	+	0.675809i
$274$	4.75993e7	−	5.96876e7i	0.139789	−	0.175290i
$275$	−1.98440e8	−	2.99101e7i	−0.575394	−	0.0867267i
$276$	−2.92569e8	+	9.02457e7i	−0.837620	+	0.258371i
$277$	4.53960e7	−	6.05768e8i	0.128333	−	1.71249i	−0.446972	−	0.894548i	$-0.647498\pi$
$277$	4.53960e7	−	6.05768e8i	0.128333	−	1.71249i	0.575305	−	0.817939i	$-0.304883\pi$
$278$	−2.17488e7	+	1.48281e7i	−0.0607126	+	0.0413931i
$279$	3.37304e7	−	1.47783e8i	0.0929837	−	0.407388i
$280$	8.00603e7	−	3.50767e8i	0.217954	−	0.954917i
$281$	−4.81543e8	+	3.28311e8i	−1.29468	+	0.882699i	−0.997398	−	0.0720896i	$-0.977033\pi$
$281$	−4.81543e8	+	3.28311e8i	−1.29468	+	0.882699i	−0.297284	+	0.954789i	$0.596081\pi$
$282$	3.61132e7	−	4.81897e8i	0.0958945	−	1.27962i
$283$	−1.06669e8	+	3.29030e7i	−0.279760	+	0.0862945i	−0.431460	−	0.902132i	$-0.642001\pi$
$283$	−1.06669e8	+	3.29030e7i	−0.279760	+	0.0862945i	0.151700	+	0.988427i	$0.451525\pi$
$284$	5.22129e8	+	7.86983e7i	1.35258	+	0.203869i
$285$	−6.71776e8	+	8.42380e8i	−1.71897	+	2.15552i
$286$	4.05457e7	+	2.76436e7i	0.102486	+	0.0698737i
$287$	−3.42122e8	+	3.17443e8i	−0.854269	+	0.792646i
$288$	2.36326e8	−	6.02149e8i	0.582959	−	1.48535i
$289$	−1.19757e8	−	3.69403e7i	−0.291850	−	0.0900239i
$290$	−4.07351e8	−	1.96170e8i	−0.980789	−	0.472323i
$291$	1.99317e6	+	5.07853e6i	0.00474155	+	0.0120813i
$292$	−1.83174e7	−	2.44428e8i	−0.0430549	−	0.574528i
$293$	−2.18285e8	−	2.73721e8i	−0.506977	−	0.635729i	0.460811	−	0.887499i	$-0.347559\pi$
$293$	−2.18285e8	−	2.73721e8i	−0.506977	−	0.635729i	−0.967787	+	0.251770i	$0.918987\pi$
$294$	5.28792e7	+	9.15895e7i	0.121358	+	0.210199i
$295$	5.65413e8	−	9.79324e8i	1.28230	−	2.22100i
$296$	−1.84858e8	+	2.78629e7i	−0.414303	+	0.0624462i
$297$	−1.46138e8	+	7.03764e7i	−0.323680	+	0.155876i
$298$	2.18823e8	+	2.03038e8i	0.479000	+	0.444447i
$299$	−6.10581e7	−	2.67513e8i	−0.132097	−	0.578756i
$300$	−1.11956e9			−2.39398
$301$	−4.90948e7	−	3.72944e8i	−0.103765	−	0.788244i
$302$	5.48644e7			0.114622
$303$	−2.15300e8	−	9.43292e8i	−0.444627	−	1.94804i
$304$	1.96112e8	+	1.81965e8i	0.400356	+	0.371476i
$305$	1.02626e9	−	4.94222e8i	2.07114	−	0.997408i
$306$	2.77744e8	−	4.18632e7i	0.554140	−	0.0835232i
$307$	−6.61344e6	+	1.14548e7i	−0.0130450	+	0.0225946i	−0.872474	−	0.488660i	$-0.837486\pi$
$307$	−6.61344e6	+	1.14548e7i	−0.0130450	+	0.0225946i	0.859429	+	0.511255i	$0.170819\pi$
$308$	5.65903e7	+	9.80173e7i	0.110361	+	0.191150i
$309$	6.06350e8	+	7.60338e8i	1.16915	+	1.46606i
$310$	−6.60547e6	−	8.81439e7i	−0.0125932	−	0.168045i
$311$	−1.08605e8	−	2.76721e8i	−0.204733	−	0.521652i	0.791219	−	0.611533i	$-0.209447\pi$
$311$	−1.08605e8	−	2.76721e8i	−0.204733	−	0.521652i	−0.995953	+	0.0898805i	$0.971351\pi$
$312$	5.41489e8	+	2.60767e8i	1.00937	+	0.486085i
$313$	6.99379e8	+	2.15730e8i	1.28916	+	0.397654i	0.862178	−	0.506605i	$-0.169100\pi$
$313$	6.99379e8	+	2.15730e8i	1.28916	+	0.397654i	0.426984	+	0.904259i	$0.359576\pi$
$314$	6.16254e7	−	1.57019e8i	0.112333	−	0.286219i
$315$	−8.92357e8	+	8.27987e8i	−1.60861	+	1.49258i
$316$	−3.34052e8	−	2.27753e8i	−0.595537	−	0.406030i
$317$	−1.12097e8	+	1.40565e8i	−0.197646	+	0.247840i	−0.870771	−	0.491688i	$-0.836380\pi$
$317$	−1.12097e8	+	1.40565e8i	−0.197646	+	0.247840i	0.673126	+	0.739528i	$0.264951\pi$
$318$	1.17252e8	+	1.76729e7i	0.204468	+	0.0308186i
$319$	2.98367e8	−	9.20339e7i	0.514616	−	0.158738i
$320$	−1.08051e7	+	1.44185e8i	−0.0184334	+	0.245977i
$321$	−1.74480e8	+	1.18958e8i	−0.294427	+	0.200737i
$322$	−2.75087e7	+	1.20523e8i	−0.0459171	+	0.201176i
$323$	−1.14347e8	+	5.00986e8i	−0.188806	+	0.827212i
$324$	−4.37550e7	+	2.98317e7i	−0.0714695	+	0.0487271i
$325$	7.49806e7	−	1.00055e9i	0.121159	−	1.61676i
$326$	−2.90748e7	+	8.96837e6i	−0.0464787	+	0.0143368i
$327$	−1.24069e9	−	1.87004e8i	−1.96221	−	0.295756i
$328$	−4.33628e8	+	5.43752e8i	−0.678514	+	0.850830i
$329$	8.25307e8	+	5.62685e8i	1.27770	+	0.871123i
$330$	−1.73854e8	+	1.61313e8i	−0.266309	+	0.247098i
$331$	−3.89561e8	+	9.92586e8i	−0.590443	+	1.50442i	0.253143	+	0.967429i	$0.418536\pi$
$331$	−3.89561e8	+	9.92586e8i	−0.590443	+	1.50442i	−0.843585	+	0.536995i	$0.819559\pi$
$332$	5.37940e8	+	1.65933e8i	0.806772	+	0.248856i
$333$	5.69882e8	+	2.74441e8i	0.845727	+	0.407281i
$334$	1.10109e8	+	2.80554e8i	0.161701	+	0.412006i
$335$	−1.33941e8	−	1.78732e9i	−0.194651	−	2.59744i
$336$	3.01753e8	+	3.78387e8i	0.433975	+	0.544187i
$337$	−2.14095e8	−	3.70823e8i	−0.304720	−	0.527791i	0.672479	−	0.740116i	$-0.265230\pi$
$337$	−2.14095e8	−	3.70823e8i	−0.304720	−	0.527791i	−0.977199	+	0.212325i	$0.931896\pi$
$338$	2.08179e7	−	3.60577e7i	0.0293244	−	0.0507913i
$339$	−2.44405e8	+	3.68381e7i	−0.340730	+	0.0513569i
$340$	−7.55433e8	+	3.63797e8i	−1.04236	+	0.501976i
$341$	4.47477e7	+	4.15198e7i	0.0611126	+	0.0567042i
$342$	1.12689e8	+	4.93723e8i	0.152332	+	0.667409i
$343$	−8.12787e8			−1.08754
$344$	−1.55175e8	−	5.38646e8i	−0.205526	−	0.713425i
$345$	1.32612e9			1.73866
$346$	7.24967e7	+	3.17629e8i	0.0940918	+	0.412243i
$347$	−5.77373e8	−	5.35724e8i	−0.741828	−	0.688316i	0.215763	−	0.976446i	$-0.430776\pi$
$347$	−5.77373e8	−	5.35724e8i	−0.741828	−	0.688316i	−0.957591	+	0.288130i	$0.906967\pi$
$348$	1.56940e9	−	7.55784e8i	1.99621	−	0.961326i
$349$	4.67029e8	−	7.03934e7i	0.588106	−	0.0886426i	0.151753	−	0.988418i	$-0.451508\pi$
$349$	4.67029e8	−	7.03934e7i	0.588106	−	0.0886426i	0.436353	+	0.899776i	$0.356270\pi$
$350$	−2.26021e8	+	3.91480e8i	−0.281781	+	0.488059i
$351$	−4.05479e8	−	7.02311e8i	−0.500488	−	0.866871i
$352$	1.62416e8	+	2.03663e8i	0.198485	+	0.248893i
$353$	−7.64086e7	−	1.01960e9i	−0.0924551	−	1.23373i	−0.829742	−	0.558148i	$-0.811512\pi$
$353$	−7.64086e7	−	1.01960e9i	−0.0924551	−	1.23373i	0.737287	−	0.675580i	$-0.236107\pi$
$354$	−3.10924e8	−	7.92221e8i	−0.372514	−	0.949150i
$355$	−2.06055e9	−	9.92308e8i	−2.44446	−	1.17719i
$356$	−3.07758e8	−	9.49307e7i	−0.361521	−	0.111515i
$357$	−3.39629e8	+	8.65361e8i	−0.395063	+	1.00660i
$358$	4.50253e7	−	4.17774e7i	0.0518640	−	0.0481227i
$359$	6.72252e8	+	4.58334e8i	0.766834	+	0.522819i	0.882411	−	0.470480i	$-0.155919\pi$
$359$	6.72252e8	+	4.58334e8i	0.766834	+	0.522819i	−0.115577	+	0.993299i	$0.536872\pi$
$360$	−1.13103e9	+	1.41827e9i	−1.27766	+	1.60214i
$361$	−3.22557e7	−	4.86176e6i	−0.0360853	−	0.00543899i
$362$	4.68929e8	−	1.44645e8i	0.519549	−	0.160260i
$363$	−9.89035e7	+	1.31978e9i	−0.108527	+	1.44820i
$364$	−4.67545e8	+	3.18766e8i	−0.508122	+	0.346432i
$365$	−2.36241e8	+	1.03504e9i	−0.254291	+	1.11412i
$366$	1.90757e8	−	8.35759e8i	0.203374	−	0.891041i
$367$	−5.62505e8	+	3.83509e8i	−0.594011	+	0.404990i	−0.822672	−	0.568516i	$-0.807518\pi$
$367$	−5.62505e8	+	3.83509e8i	−0.594011	+	0.404990i	0.228661	+	0.973506i	$0.426565\pi$
$368$	2.46066e7	−	3.28353e8i	0.0257386	−	0.343458i
$369$	2.24859e9	−	6.93597e8i	2.32979	−	0.718646i
$370$	3.64716e8	+	5.49720e7i	0.374325	+	0.0564204i
$371$	−1.52816e8	+	1.91625e8i	−0.155367	+	0.194824i
$372$	2.81371e8	+	1.91836e8i	0.283387	+	0.193210i
$373$	4.43713e8	−	4.11705e8i	0.442712	−	0.410777i	−0.427066	−	0.904221i	$-0.640453\pi$
$373$	4.43713e8	−	4.11705e8i	0.442712	−	0.410777i	0.869778	+	0.493444i	$0.164262\pi$
$374$	−4.13244e7	+	1.05293e8i	−0.0408466	+	0.104075i
$375$	1.99111e9	+	6.14175e8i	1.94978	+	0.601427i
$376$	1.34110e9	+	6.45839e8i	1.30108	+	0.626566i
$377$	5.70335e8	+	1.45319e9i	0.548196	+	1.39678i
$378$	2.73036e7	+	3.64342e8i	0.0260016	+	0.346967i
$379$	1.06170e9	+	1.33132e9i	1.00176	+	1.25617i	0.966468	+	0.256788i	$0.0826643\pi$
$379$	1.06170e9	+	1.33132e9i	1.00176	+	1.25617i	0.0352907	+	0.999377i	$0.488764\pi$
$380$	−7.55865e8	−	1.30920e9i	−0.706645	−	1.22395i
$381$	−1.09335e8	+	1.89374e8i	−0.101280	+	0.175421i
$382$	−5.31054e8	+	8.00436e7i	−0.487436	+	0.0734691i
$383$	6.15264e8	−	2.96295e8i	0.559584	−	0.269482i	−0.132640	−	0.991164i	$-0.542345\pi$
$383$	6.15264e8	−	2.96295e8i	0.559584	−	0.269482i	0.692224	+	0.721683i	$0.256631\pi$
$384$	1.35316e9	+	1.25555e9i	1.21952	+	1.13155i
$385$	−1.09084e8	−	4.77927e8i	−0.0974199	−	0.426824i
$386$	1.20358e7			0.0106517
$387$	−5.92841e8	+	1.80155e9i	−0.519936	+	1.58001i
$388$	−7.65466e6			−0.00665296
$389$	−2.20279e8	−	9.65104e8i	−0.189736	−	0.831286i	−0.976755	−	0.214358i	$-0.931234\pi$
$389$	−2.20279e8	−	9.65104e8i	−0.189736	−	0.831286i	0.787020	−	0.616928i	$-0.211623\pi$
$390$	−8.69219e8	−	8.06518e8i	−0.741999	−	0.688474i
$391$	5.69836e8	−	2.74419e8i	0.482094	−	0.232164i
$392$	−3.22120e8	+	4.85518e7i	−0.270095	+	0.0407103i
$393$	−8.47635e8	+	1.46815e9i	−0.704426	+	1.22010i
$394$	−1.19903e8	−	2.07679e8i	−0.0987630	−	0.171063i
$395$	1.09183e9	+	1.36911e9i	0.891384	+	1.11776i
$396$	−4.26449e7	−	5.69056e8i	−0.0345091	−	0.460492i
$397$	−6.28472e8	−	1.60132e9i	−0.504103	−	1.28443i	−0.925909	−	0.377746i	$-0.876699\pi$
$397$	−6.28472e8	−	1.60132e9i	−0.504103	−	1.28443i	0.421807	−	0.906686i	$-0.361396\pi$
$398$	2.85474e8	+	1.37477e8i	0.226974	+	0.109305i
$399$	−1.60162e9	−	4.94033e8i	−1.26227	−	0.389360i
$400$	4.39882e8	−	1.12080e9i	0.343657	−	0.875625i
$401$	9.62678e8	−	8.93235e8i	0.745549	−	0.691768i	−0.212887	−	0.977077i	$-0.568287\pi$
$401$	9.62678e8	−	8.93235e8i	0.745549	−	0.691768i	0.958436	+	0.285309i	$0.0920962\pi$
$402$	−1.11451e9	−	7.59858e8i	−0.855641	−	0.583366i
$403$	−1.90288e8	+	2.38613e8i	−0.144825	+	0.181605i
$404$	1.34238e9	+	2.02331e8i	1.01284	+	0.152661i
$405$	2.19181e8	−	6.76085e7i	0.163950	−	0.0505718i
$406$	5.25598e7	−	7.01362e8i	0.0389774	−	0.520117i
$407$	−2.10458e8	+	1.43488e8i	−0.154734	+	0.105496i
$408$	−3.08261e8	+	1.35058e9i	−0.224703	+	0.984486i
$409$	−3.89934e8	+	1.70841e9i	−0.281812	+	1.23470i	0.613656	+	0.789573i	$0.289698\pi$
$409$	−3.89934e8	+	1.70841e9i	−0.281812	+	1.23470i	−0.895468	+	0.445126i	$0.853159\pi$
$410$	1.13373e9	−	7.72962e8i	0.812391	−	0.553879i
$411$	9.52028e7	−	1.27039e9i	0.0676399	−	0.902592i
$412$	−1.30388e9	+	4.02193e8i	−0.918536	+	0.283331i
$413$	1.73947e9	+	2.62183e8i	1.21504	+	0.183138i
$414$	3.88622e8	−	4.87316e8i	0.269170	−	0.337528i
$415$	−2.01462e9	−	1.37354e9i	−1.38364	−	0.943353i
$416$	−9.54725e8	+	8.85856e8i	−0.650207	+	0.603304i
$417$	−1.60476e8	+	4.08887e8i	−0.108376	+	0.276139i
$418$	−1.94877e8	−	6.01115e7i	−0.130510	−	0.0402569i
$419$	−2.33732e9	−	1.12560e9i	−1.55228	−	0.747538i	−0.555795	−	0.831320i	$-0.687586\pi$
$419$	−2.33732e9	−	1.12560e9i	−1.55228	−	0.747538i	−0.996484	+	0.0837815i	$0.973300\pi$
$420$	−9.99138e8	−	2.54576e9i	−0.658041	−	1.67666i
$421$	−1.40255e8	−	1.87157e9i	−0.0916075	−	1.22242i	−0.833738	−	0.552161i	$-0.813803\pi$
$421$	−1.40255e8	−	1.87157e9i	−0.0916075	−	1.22242i	0.742130	−	0.670256i	$-0.233816\pi$
$422$	2.03263e8	+	2.54884e8i	0.131663	+	0.165100i
$423$	−2.51813e9	−	4.36154e9i	−1.61766	−	2.80187i
$424$	−1.82620e8	+	3.16308e8i	−0.116351	+	0.201525i
$425$	2.28688e9	−	3.44692e8i	1.44505	−	0.217806i
$426$	−1.55075e9	+	7.46803e8i	−0.971872	+	0.468029i
$427$	1.29892e9	+	1.20522e9i	0.807395	+	0.749153i
$428$	−6.59309e7	−	2.88862e8i	−0.0406477	−	0.178089i
$429$	8.18885e8			0.500751
$430$	−2.06922e7	+	1.10574e9i	−0.0125507	+	0.670680i
$431$	−6.54742e8			−0.393912			−0.196956	−	0.980412i	$-0.563106\pi$
$431$	−6.54742e8			−0.393912			−0.196956	+	0.980412i	$0.563106\pi$
$432$	−2.16548e8	−	9.48758e8i	−0.129229	−	0.566190i
$433$	−8.13721e8	−	7.55022e8i	−0.481690	−	0.446943i	0.401569	−	0.915829i	$-0.368465\pi$
$433$	−8.13721e8	−	7.55022e8i	−0.481690	−	0.446943i	−0.883259	+	0.468886i	$0.844656\pi$
$434$	1.23885e8	−	5.96597e7i	0.0727450	−	0.0350322i
$435$	−7.46043e9	+	1.12448e9i	−4.34562	+	0.654996i
$436$	8.80218e8	−	1.52458e9i	0.508613	−	0.880944i
$437$	5.70162e8	+	9.87550e8i	0.326824	+	0.566075i
$438$	4.98165e8	+	6.24679e8i	0.283279	+	0.355220i
$439$	1.85043e8	+	2.46922e9i	0.104387	+	1.39295i	0.765874	+	0.642991i	$0.222307\pi$
$439$	1.85043e8	+	2.46922e9i	0.104387	+	1.39295i	−0.661487	+	0.749957i	$0.730074\pi$
$440$	−2.66888e8	−	6.80019e8i	−0.149364	−	0.380572i
$441$	9.93033e8	+	4.78220e8i	0.551352	+	0.265517i
$442$	−5.40402e8	−	1.66692e8i	−0.297673	−	0.0918198i
$443$	1.69867e7	−	4.32815e7i	0.00928317	−	0.0236531i	−0.926157	−	0.377138i	$-0.876908\pi$
$443$	1.69867e7	−	4.32815e7i	0.00928317	−	0.0236531i	0.935440	+	0.353485i	$0.115003\pi$
$444$	−1.04168e9	+	9.66535e8i	−0.564797	+	0.524055i
$445$	1.15257e9	+	7.85810e8i	0.620023	+	0.422725i
$446$	−7.87551e8	+	9.87557e8i	−0.420346	+	0.527097i
$447$	4.92565e9	+	7.42422e8i	2.60848	+	0.393164i
$448$	−2.14931e8	+	6.62973e7i	−0.112934	+	0.0348356i
$449$	−6.40447e6	+	8.54617e7i	−0.00333903	+	0.0445563i	−0.998624	−	0.0524333i	$-0.983302\pi$
$449$	−6.40447e6	+	8.54617e7i	−0.00333903	+	0.0445563i	0.995285	+	0.0969896i	$0.0309214\pi$
$450$	1.88315e9	−	1.28391e9i	0.974183	−	0.664186i
$451$	−2.10864e8	+	9.23855e8i	−0.108239	+	0.474226i
$452$	7.71681e7	−	3.38096e8i	0.0393055	−	0.172209i
$453$	7.56449e8	−	5.15738e8i	0.382328	−	0.260667i
$454$	2.12271e7	−	2.83256e8i	0.0106462	−	0.142064i
$455$	2.34206e9	−	7.22430e8i	1.16562	−	0.359547i
$456$	−2.46978e9	−	3.72259e8i	−1.21978	−	0.183852i
$457$	2.27847e8	−	2.85711e8i	0.111670	−	0.140030i	−0.722855	−	0.690999i	$-0.757171\pi$
$457$	2.27847e8	−	2.85711e8i	0.111670	−	0.140030i	0.834525	+	0.550970i	$0.185742\pi$
$458$	1.11115e9	+	7.57566e8i	0.540433	+	0.368461i
$459$	1.37026e9	−	1.27141e9i	0.661389	−	0.613680i
$460$	−6.79766e8	+	1.73202e9i	−0.325617	+	0.829659i
$461$	−1.31276e9	−	4.04933e8i	−0.624068	−	0.192500i	−0.0334367	−	0.999441i	$-0.510645\pi$
$461$	−1.31276e9	−	4.04933e8i	−0.624068	−	0.192500i	−0.590632	+	0.806941i	$0.701121\pi$
$462$	−3.32398e8	−	1.60075e8i	−0.156824	−	0.0755223i
$463$	1.08448e9	+	2.76322e9i	0.507797	+	1.29385i	0.923239	+	0.384226i	$0.125532\pi$
$463$	1.08448e9	+	2.76322e9i	0.507797	+	1.29385i	−0.415442	+	0.909620i	$0.636373\pi$
$464$	1.39995e8	+	1.86810e9i	0.0650577	+	0.868135i
$465$	−9.19646e8	−	1.15320e9i	−0.424165	−	0.531886i
$466$	2.77299e8	+	4.80296e8i	0.126940	+	0.219866i
$467$	1.78125e8	−	3.08521e8i	0.0809311	−	0.140177i	−0.822719	−	0.568448i	$-0.807544\pi$
$467$	1.78125e8	−	3.08521e8i	0.0809311	−	0.140177i	0.903650	+	0.428271i	$0.140877\pi$
$468$	2.82123e9	−	4.25232e8i	1.27227	−	0.191763i
$469$	2.51204e9	−	1.20974e9i	1.12440	−	0.541484i
$470$	−2.15279e9	−	1.99749e9i	−0.956442	−	0.887448i
$471$	−6.26347e8	−	2.74421e9i	−0.276212	−	1.21016i
$472$	2.62142e9			1.14747
$473$	−5.08925e8	−	5.69500e8i	−0.221126	−	0.247446i
$474$	1.31791e9			0.568409
$475$	9.27855e8	+	4.06520e9i	0.397240	+	1.74042i
$476$	−9.56137e8	−	8.87166e8i	−0.406346	−	0.377034i
$477$	1.11339e9	−	5.36180e8i	0.469713	−	0.226202i
$478$	1.49769e9	−	2.25740e8i	0.627225	−	0.0945389i
$479$	6.89202e8	−	1.19373e9i	0.286531	−	0.496287i	−0.686448	−	0.727179i	$-0.740831\pi$
$479$	6.89202e8	−	1.19373e9i	0.286531	−	0.496287i	0.972979	+	0.230892i	$0.0741644\pi$
$480$	−3.14719e9	−	5.45110e9i	−1.29891	−	2.24978i
$481$	−7.94027e8	−	9.95678e8i	−0.325332	−	0.407954i
$482$	3.02596e7	+	4.03786e8i	0.0123083	+	0.164243i
$483$	7.53668e8	+	1.92031e9i	0.304344	+	0.775457i
$484$	−1.67304e9	−	8.05692e8i	−0.670728	−	0.323006i
$485$	3.16816e7	+	9.77248e6i	0.0126099	+	0.00388963i
$486$	−3.41544e8	+	8.70241e8i	−0.134965	+	0.343885i
$487$	−1.77066e9	+	1.64293e9i	−0.694678	+	0.644567i	−0.946312	−	0.323255i	$-0.895223\pi$
$487$	−1.77066e9	+	1.64293e9i	−0.694678	+	0.644567i	0.251633	+	0.967823i	$0.419032\pi$
$488$	2.18170e9	+	1.48746e9i	0.849818	+	0.579396i
$489$	−3.16566e8	+	3.96962e8i	−0.122429	+	0.153521i
$490$	6.35526e8	+	9.57901e7i	0.244032	+	0.0367819i
$491$	2.44971e9	−	7.55634e8i	0.933961	−	0.288089i	0.209820	−	0.977740i	$-0.432712\pi$
$491$	2.44971e9	−	7.55634e8i	0.933961	−	0.288089i	0.724142	+	0.689651i	$0.242236\pi$
$492$	−3.95061e8	+	5.27173e9i	−0.149550	+	1.99561i
$493$	−2.97307e9	+	2.02701e9i	−1.11748	+	0.761888i
$494$	2.26888e8	−	9.94063e8i	0.0846775	−	0.370996i
$495$	−5.49996e8	+	2.40969e9i	−0.203817	+	0.892982i
$496$	−3.02602e8	+	2.06310e8i	−0.111349	+	0.0759163i
$497$	2.65869e8	−	3.54778e9i	0.0971451	−	1.29631i
$498$	−1.75352e9	+	5.40889e8i	−0.636221	+	0.196248i
$499$	−1.21936e9	−	1.83789e8i	−0.439320	−	0.0662169i	−0.0743418	−	0.997233i	$-0.523686\pi$
$499$	−1.21936e9	−	1.83789e8i	−0.439320	−	0.0662169i	−0.364979	+	0.931016i	$0.618924\pi$
$500$	−1.82280e9	+	2.28572e9i	−0.652145	+	0.817764i
$501$	4.15541e9	+	2.83311e9i	1.47633	+	1.00654i
$502$	−9.44920e8	+	8.76758e8i	−0.333374	+	0.309326i
$503$	7.93279e7	−	2.02124e8i	0.0277932	−	0.0708159i	−0.916304	−	0.400485i	$-0.868842\pi$
$503$	7.93279e7	−	2.02124e8i	0.0277932	−	0.0708159i	0.944097	+	0.329669i	$0.106937\pi$
$504$	−2.69655e9	−	8.31776e8i	−0.938214	−	0.289401i
$505$	−5.29761e9	−	2.55119e9i	−1.83046	−	0.881503i
$506$	9.17026e7	+	2.33654e8i	0.0314669	+	0.0801765i
$507$	−5.19213e7	−	6.92841e8i	−0.0176937	−	0.236105i
$508$	−1.91292e8	−	2.39873e8i	−0.0647403	−	0.0811818i
$509$	1.42722e9	+	2.47201e9i	0.479709	+	0.830880i	0.999729	−	0.0232741i	$-0.00740905\pi$
$509$	1.42722e9	+	2.47201e9i	0.479709	+	0.830880i	−0.520021	+	0.854154i	$0.674076\pi$
$510$	1.36657e9	−	2.36697e9i	0.456181	−	0.790129i
$511$	−1.63307e9	+	2.46146e8i	−0.541418	+	0.0816057i
$512$	−2.49791e9	+	1.20293e9i	−0.822492	+	0.396091i
$513$	2.47053e9	+	2.29232e9i	0.807940	+	0.749659i
$514$	2.36452e7	+	1.03596e8i	0.00768019	+	0.0336491i
$515$	5.91003e9			1.90662
$516$	−3.28098e9	−	2.71846e9i	−1.05131	−	0.871063i
$517$	2.02812e9			0.645472
$518$	1.27674e8	+	5.59377e8i	0.0403598	+	0.176828i
$519$	3.98534e9	+	3.69785e9i	1.25135	+	1.16108i
$520$	3.29068e9	−	1.58471e9i	1.02630	−	0.494240i
$521$	4.04750e9	−	6.10063e8i	1.25388	−	0.188992i	0.511682	−	0.859175i	$-0.329023\pi$
$521$	4.04750e9	−	6.10063e8i	1.25388	−	0.188992i	0.742195	+	0.670184i	$0.233785\pi$
$522$	−1.77308e9	+	3.07106e9i	−0.545608	+	0.945020i
$523$	1.52166e9	+	2.63559e9i	0.465116	+	0.805605i	0.999207	−	0.0398222i	$-0.0126792\pi$
$523$	1.52166e9	+	2.63559e9i	0.465116	+	0.805605i	−0.534090	+	0.845427i	$0.679346\pi$
$524$	−1.48302e9	−	1.85965e9i	−0.450286	−	0.564640i
$525$	5.63713e8	+	7.52223e9i	0.170020	+	2.26876i
$526$	−4.41503e8	−	1.12493e9i	−0.132277	−	0.337035i
$527$	−6.33810e8	−	3.05227e8i	−0.188635	−	0.0908418i
$528$	9.39011e8	+	2.89646e8i	0.277621	+	0.0856347i
$529$	−7.31162e8	+	1.86297e9i	−0.214743	+	0.547156i
$530$	5.28238e8	−	4.90133e8i	0.154122	−	0.143004i
$531$	−7.32824e9	−	4.99631e9i	−2.12407	−	1.44817i
$532$	1.46623e9	−	1.83860e9i	0.422194	−	0.529415i
$533$	−4.68488e9	−	7.06132e8i	−1.34015	−	0.201995i
$534$	1.00320e9	−	3.09445e8i	0.285096	−	0.0879405i
$535$	−9.59028e7	+	1.27973e9i	−0.0270765	+	0.361311i
$536$	3.43292e9	−	2.34053e9i	0.962913	−	0.656503i
$537$	2.28074e8	−	9.99257e8i	0.0635573	−	0.278463i
$538$	−5.87340e7	+	2.57331e8i	−0.0162612	+	0.0712448i
$539$	−3.66729e8	+	2.50031e8i	−0.100875	+	0.0687755i
$540$	−4.10945e8	+	5.48367e9i	−0.112307	+	1.49863i
$541$	−3.33308e9	+	1.02812e9i	−0.905015	+	0.279160i	−0.712119	−	0.702059i	$-0.752264\pi$
$541$	−3.33308e9	+	1.02812e9i	−0.905015	+	0.279160i	−0.192896	+	0.981219i	$0.561788\pi$
$542$	1.06564e9	+	1.60619e8i	0.287483	+	0.0433311i
$543$	5.10570e9	−	6.40235e9i	1.36854	−	1.71609i
$544$	−2.48038e9	−	1.69109e9i	−0.660574	−	0.450372i
$545$	−5.58949e9	+	5.18629e9i	−1.47906	+	1.37236i
$546$	6.73896e8	−	1.71706e9i	0.177182	−	0.451451i
$547$	2.04719e9	+	6.31473e8i	0.534812	+	0.164968i	0.550385	−	0.834911i	$-0.314481\pi$
$547$	2.04719e9	+	6.31473e8i	0.534812	+	0.164968i	−0.0155726	+	0.999879i	$0.504957\pi$
$548$	1.61043e9	+	7.75544e8i	0.418033	+	0.201314i
$549$	−3.26397e9	−	8.31646e9i	−0.841866	−	2.14504i
$550$	6.85898e7	+	9.15267e8i	0.0175788	+	0.234573i
$551$	−4.04499e9	−	5.07226e9i	−1.03012	−	1.29173i
$552$	1.53707e9	+	2.66228e9i	0.388961	+	0.673700i
$553$	−1.36206e9	+	2.35915e9i	−0.342497	+	0.593222i
$554$	−2.74726e9	+	4.14084e8i	−0.686462	+	0.103467i
$555$	5.54530e9	−	2.67048e9i	1.37689	−	0.663076i
$556$	−4.51780e8	−	4.19190e8i	−0.111472	−	0.103431i
$557$	−8.21154e8	−	3.59771e9i	−0.201341	−	0.882131i	−0.970122	−	0.242619i	$-0.921994\pi$
$557$	−8.21154e8	−	3.59771e9i	−0.201341	−	0.882131i	0.768781	−	0.639512i	$-0.220864\pi$
$558$	−6.93277e8			−0.168922
$559$	2.64923e9	−	2.75015e9i	0.641472	−	0.665908i
$560$	2.94116e9			0.707719
$561$	4.20012e8	+	1.84019e9i	0.100437	+	0.440041i
$562$	1.95398e9	+	1.81303e9i	0.464348	+	0.430852i
$563$	−3.46911e9	+	1.67064e9i	−0.819293	+	0.394551i	−0.796089	−	0.605180i	$-0.793101\pi$
$563$	−3.46911e9	+	1.67064e9i	−0.819293	+	0.394551i	−0.0232042	+	0.999731i	$0.507387\pi$
$564$	1.11880e10	−	1.68633e9i	2.62589	−	0.395790i
$565$	−7.51025e8	+	1.30081e9i	−0.175180	+	0.303421i
$566$	2.55270e8	+	4.42141e8i	0.0591756	+	0.102495i
$567$	2.22469e8	+	2.78967e8i	0.0512540	+	0.0642705i
$568$	−3.96195e8	−	5.28686e9i	−0.0907173	−	1.21054i
$569$	1.01143e9	+	2.57708e9i	0.230167	+	0.586455i	0.998567	−	0.0535144i	$-0.0170423\pi$
$569$	1.01143e9	+	2.57708e9i	0.230167	+	0.586455i	−0.768401	+	0.639969i	$0.778947\pi$
$570$	4.43977e9	+	2.13808e9i	1.00415	+	0.483573i
$571$	−6.49184e9	−	2.00247e9i	−1.45929	−	0.450131i	−0.539314	−	0.842105i	$-0.681316\pi$
$571$	−6.49184e9	−	2.00247e9i	−1.45929	−	0.450131i	−0.919976	+	0.391974i	$0.871792\pi$
$572$	−4.19759e8	+	1.06953e9i	−0.0937808	+	0.238950i
$573$	−6.56954e9	+	6.09564e9i	−1.45879	+	1.35356i
$574$	1.76363e9	+	1.20242e9i	0.389239	+	0.265379i
$575$	3.19982e9	−	4.01245e9i	0.701921	−	0.880181i
$576$	1.12139e9	+	1.69022e8i	0.244499	+	0.0368523i
$577$	6.94594e9	−	2.14254e9i	1.50527	−	0.464315i	0.571023	−	0.820934i	$-0.306547\pi$
$577$	6.94594e9	−	2.14254e9i	1.50527	−	0.464315i	0.934250	+	0.356618i	$0.116070\pi$
$578$	−4.28342e7	+	5.71582e8i	−0.00922663	+	0.123121i
$579$	1.65945e8	−	1.13140e8i	0.0355296	−	0.0242236i
$580$	2.35555e9	−	1.03203e10i	0.501295	−	2.19632i
$581$	8.44030e8	−	3.69794e9i	0.178542	−	0.782245i
$582$	2.06162e7	−	1.40559e7i	0.00433489	−	0.00295548i
$583$	−3.71893e7	+	4.96257e8i	−0.00777281	+	0.103721i
$584$	−2.35174e9	+	7.25415e8i	−0.488589	+	0.150710i
$585$	−1.22196e10	−	1.84180e9i	−2.52354	−	0.380362i
$586$	−9.98345e8	+	1.25188e9i	−0.204946	+	0.256994i
$587$	2.79017e9	+	1.90231e9i	0.569374	+	0.388193i	0.813512	−	0.581548i	$-0.197553\pi$
$587$	2.79017e9	+	1.90231e9i	0.569374	+	0.388193i	−0.244138	+	0.969740i	$0.578505\pi$
$588$	−1.81515e9	+	1.68421e9i	−0.368206	+	0.341646i
$589$	4.63379e8	−	1.18067e9i	0.0934399	−	0.238081i
$590$	−4.94214e9	−	1.52445e9i	−0.990680	−	0.305584i
$591$	−3.60540e9	−	1.73627e9i	−0.718452	−	0.345988i
$592$	−5.58327e8	−	1.42259e9i	−0.110602	−	0.281809i
$593$	−3.51032e8	−	4.68419e9i	−0.0691282	−	0.922451i	−0.918694	−	0.394969i	$-0.870755\pi$
$593$	−3.51032e8	−	4.68419e9i	−0.0691282	−	0.922451i	0.849566	−	0.527482i	$-0.176864\pi$
$594$	4.62529e8	+	5.79993e8i	0.0905495	+	0.113546i
$595$	2.82470e9	+	4.89253e9i	0.549748	+	0.952191i
$596$	−3.49454e9	+	6.05272e9i	−0.676127	+	1.17109i
$597$	5.22831e9	−	7.88041e8i	1.00566	−	0.151579i
$598$	−1.13068e9	+	5.44505e8i	−0.216214	+	0.104123i
$599$	−6.60892e9	−	6.13218e9i	−1.25643	−	1.16579i	−0.978737	−	0.205122i	$-0.934241\pi$
$599$	−6.60892e9	−	6.13218e9i	−1.25643	−	1.16579i	−0.277689	−	0.960671i	$-0.589568\pi$
$600$	2.50135e9	+	1.09591e10i	0.472765	+	2.07132i
$601$	−6.23677e9			−1.17192			−0.585962	−	0.810339i	$-0.699283\pi$
$601$	−6.23677e9			−1.17192			−0.585962	+	0.810339i	$0.699283\pi$
$602$	−1.61296e9	+	5.98460e8i	−0.301325	+	0.111802i
$603$	−1.40578e10			−2.61099
$604$	2.85841e8	+	1.25235e9i	0.0527831	+	0.231258i
$605$	5.89586e9	+	5.47056e9i	1.08244	+	1.00436i
$606$	−3.98694e9	+	1.92001e9i	−0.727755	+	0.350468i
$607$	2.13609e9	−	3.21963e8i	0.387667	−	0.0584314i	0.0476827	−	0.998863i	$-0.484816\pi$
$607$	2.13609e9	−	3.21963e8i	0.387667	−	0.0584314i	0.339984	+	0.940431i	$0.389578\pi$
$608$	2.70626e9	−	4.68739e9i	0.488323	−	0.845801i
$609$	−5.86829e9	−	1.01642e10i	−1.05281	−	1.82352i
$610$	−3.24814e9	−	4.07304e9i	−0.579402	−	0.726547i
$611$	7.57766e8	+	1.01117e10i	0.134397	+	1.79341i
$612$	2.40261e9	+	6.12175e9i	0.423695	+	1.07956i
$613$	−5.04310e9	−	2.42863e9i	−0.884272	−	0.425843i	−0.0640890	−	0.997944i	$-0.520414\pi$
$613$	−5.04310e9	−	2.42863e9i	−0.884272	−	0.425843i	−0.820183	+	0.572101i	$0.806128\pi$
$614$	5.78066e7	+	1.78310e7i	0.0100783	+	0.00310875i
$615$	8.36536e9	−	2.13146e10i	1.45018	−	3.69500i
$616$	8.33038e8	−	7.72946e8i	0.143593	−	0.133235i
$617$	2.30281e9	+	1.57003e9i	0.394693	+	0.269097i	0.744362	−	0.667776i	$-0.232754\pi$
$617$	2.30281e9	+	1.57003e9i	0.394693	+	0.269097i	−0.349669	+	0.936873i	$0.613706\pi$
$618$	2.77319e9	−	3.47747e9i	0.472628	−	0.592657i
$619$	3.99853e8	+	6.02681e7i	0.0677615	+	0.0102134i	0.182835	−	0.983144i	$-0.441472\pi$
$619$	3.99853e8	+	6.02681e7i	0.0677615	+	0.0102134i	−0.115074	+	0.993357i	$0.536711\pi$
$620$	1.97758e9	−	6.10003e8i	0.333245	−	0.102792i
$621$	3.09983e8	−	4.13643e9i	0.0519418	−	0.693115i
$622$	−1.12335e9	+	7.65884e8i	−0.187175	+	0.127613i
$623$	−4.82873e8	+	2.11560e9i	−0.0800064	+	0.350531i
$624$	−1.09326e9	+	4.78988e9i	−0.180126	+	0.789185i
$625$	1.61975e9	−	1.10433e9i	0.265380	−	0.180933i
$626$	2.50150e8	−	3.33802e9i	0.0407559	−	0.543849i
$627$	−3.25194e9	+	1.00309e9i	−0.526873	+	0.162519i
$628$	3.90522e9	+	5.88617e8i	0.629197	+	0.0948362i
$629$	1.83022e9	−	2.29502e9i	0.293242	−	0.367714i
$630$	4.60008e9	+	3.13628e9i	0.732949	+	0.499716i
$631$	5.89108e9	−	5.46613e9i	0.933453	−	0.866118i	−0.0577687	−	0.998330i	$-0.518399\pi$
$631$	5.89108e9	−	5.46613e9i	0.933453	−	0.866118i	0.991221	+	0.132212i	$0.0422081\pi$
$632$	−1.48308e9	+	3.77882e9i	−0.233698	+	0.595452i
$633$	5.19847e9	+	1.60352e9i	0.814634	+	0.251281i
$634$	7.40852e8	+	3.56775e8i	0.115457	+	0.0556010i
$635$	4.85494e8	+	1.23702e9i	0.0752447	+	0.191720i
$636$	2.07470e8	+	2.76850e9i	0.0319784	+	0.426721i
$637$	−1.38361e9	−	1.73499e9i	−0.212093	−	0.265956i
$638$	−7.14024e8	−	1.23673e9i	−0.108853	−	0.188539i
$639$	−8.96895e9	+	1.55347e10i	−1.35984	+	2.35532i
$640$	1.10926e10	−	1.67194e9i	1.67264	−	0.252111i
$641$	5.03258e8	−	2.42356e8i	0.0754723	−	0.0363456i	−0.395767	−	0.918351i	$-0.629521\pi$
$641$	5.03258e8	−	2.42356e8i	0.0754723	−	0.0363456i	0.471239	+	0.882005i	$0.343807\pi$
$642$	7.07995e8	+	6.56923e8i	0.105598	+	0.0979810i
$643$	1.23941e9	+	5.43020e9i	0.183855	+	0.805522i	0.979772	+	0.200116i	$0.0641320\pi$
$643$	1.23941e9	+	5.43020e9i	0.183855	+	0.805522i	−0.795917	+	0.605406i	$0.793011\pi$
$644$	−2.89441e9			−0.427032
$645$	1.01090e10	+	1.54401e10i	1.48336	+	2.26564i
$646$	2.35022e9			0.343001
$647$	−4.10544e8	−	1.79871e9i	−0.0595929	−	0.261094i	0.936352	−	0.351064i	$-0.114180\pi$
$647$	−4.10544e8	−	1.79871e9i	−0.0595929	−	0.261094i	−0.995944	+	0.0899701i	$0.971323\pi$
$648$	3.89776e8	+	3.61659e8i	0.0562733	+	0.0522140i
$649$	3.21802e9	−	1.54972e9i	0.462097	−	0.222534i
$650$	−4.53765e9	+	6.83941e8i	−0.648089	+	0.0976836i
$651$	1.14726e9	−	1.98711e9i	0.162977	−	0.282285i
$652$	−3.56192e8	−	6.16943e8i	−0.0503289	−	0.0871723i
$653$	−5.91558e9	−	7.41791e9i	−0.831384	−	1.04252i	−0.998399	−	0.0565679i	$-0.981984\pi$
$653$	−5.91558e9	−	7.41791e9i	−0.831384	−	1.04252i	0.167015	−	0.985954i	$-0.446587\pi$
$654$	4.28837e8	+	5.72244e9i	0.0599474	+	0.799943i
$655$	3.76386e9	+	9.59017e9i	0.523346	+	1.33346i
$656$	−5.12236e9	−	2.46680e9i	−0.708446	−	0.341170i
$657$	7.95695e9	+	2.45440e9i	1.09463	+	0.337649i
$658$	1.66903e9	−	4.25262e9i	0.228388	−	0.581924i
$659$	2.61043e9	−	2.42213e9i	0.355315	−	0.329684i	−0.482238	−	0.876040i	$-0.660176\pi$
$659$	2.61043e9	−	2.42213e9i	0.355315	−	0.329684i	0.837553	+	0.546356i	$0.183985\pi$
$660$	−4.58793e9	−	3.12800e9i	−0.621174	−	0.423509i
$661$	2.74576e9	−	3.44307e9i	0.369792	−	0.463704i	−0.561767	−	0.827296i	$-0.689878\pi$
$661$	2.74576e9	−	3.44307e9i	0.369792	−	0.463704i	0.931558	+	0.363592i	$0.118450\pi$
$662$	4.82231e9	+	7.26847e8i	0.646030	+	0.0973733i
$663$	−9.01778e9	+	2.78162e9i	−1.20172	+	0.370681i
$664$	4.22400e8	−	5.63653e9i	0.0559932	−	0.747178i
$665$	−8.41582e9	+	5.73781e9i	−1.10974	+	0.756607i
$666$	6.43727e8	−	2.82035e9i	0.0844388	−	0.369951i
$667$	−1.77683e9	+	7.78481e9i	−0.231849	+	1.01580i
$668$	−5.83033e9	+	3.97505e9i	−0.756790	+	0.515971i
$669$	−1.57517e9	+	2.10192e10i	−0.203393	+	2.71409i
$670$	−7.83317e9	+	2.41621e9i	−1.00618	+	0.310365i
$671$	3.55758e9	+	5.36219e8i	0.454597	+	0.0685194i
$672$	6.10495e9	−	7.65537e9i	0.776051	−	0.973137i
$673$	5.57117e9	+	3.79836e9i	0.704521	+	0.480334i	0.861818	−	0.507217i	$-0.169326\pi$
$673$	5.57117e9	+	3.79836e9i	0.704521	+	0.480334i	−0.157298	+	0.987551i	$0.550278\pi$
$674$	−1.43558e9	+	1.33202e9i	−0.180600	+	0.167572i
$675$	5.54142e9	−	1.41193e10i	0.693519	−	1.76706i
$676$	9.31521e8	+	2.87336e8i	0.115979	+	0.0357748i
$677$	9.54533e9	+	4.59679e9i	1.18231	+	0.569370i	0.918583	−	0.395228i	$-0.129334\pi$
$677$	9.54533e9	+	4.59679e9i	1.18231	+	0.569370i	0.263725	+	0.964598i	$0.415049\pi$
$678$	4.12993e8	+	1.05229e9i	0.0508907	+	0.129667i
$679$	3.85424e6	+	5.14312e7i	0.000472492	+	0.00630496i
$680$	5.24896e9	+	6.58199e9i	0.640165	+	0.802742i
$681$	−2.37000e9	−	4.10496e9i	−0.287564	−	0.498075i
$682$	1.39592e8	−	2.41781e8i	0.0168507	−	0.0291862i
$683$	2.98491e8	−	4.49903e7i	0.0358475	−	0.00540314i	−0.131094	−	0.991370i	$-0.541849\pi$
$683$	2.98491e8	−	4.49903e7i	0.0358475	−	0.00540314i	0.166942	+	0.985967i	$0.446611\pi$
$684$	−1.06827e10	+	5.14454e9i	−1.27640	+	0.614681i
$685$	−5.67525e9	−	5.26586e9i	−0.674634	−	0.625969i
$686$	8.27186e8	+	3.62414e9i	0.0978293	+	0.428618i
$687$	2.24413e10			2.64058
$688$	4.01060e9	−	2.21652e9i	0.469516	−	0.259485i
$689$	−2.48810e9			−0.289801
$690$	−1.34961e9	−	5.91304e9i	−0.156400	−	0.685234i
$691$	−6.55409e8	−	6.08130e8i	−0.0755682	−	0.0701170i	0.641485	−	0.767136i	$-0.278319\pi$
$691$	−6.55409e8	−	6.08130e8i	−0.0755682	−	0.0701170i	−0.717053	+	0.697019i	$0.754509\pi$
$692$	−6.87257e9	+	3.30965e9i	−0.788402	+	0.379674i
$693$	−3.80198e9	+	5.73057e8i	−0.433954	+	0.0654080i
$694$	−1.80114e9	+	3.11967e9i	−0.204545	+	0.354283i
$695$	1.33469e9	+	2.31174e9i	0.150811	+	0.261212i
$696$	−1.09047e10	−	1.36740e10i	−1.22597	−	1.53732i
$697$	−8.16094e8	−	1.08900e10i	−0.0912904	−	1.21819i
$698$	−7.89181e8	−	2.01080e9i	−0.0878381	−	0.223808i
$699$	8.33818e9	+	4.01546e9i	0.923424	+	0.444698i
$700$	−1.01136e10	−	3.11963e9i	−1.11445	−	0.343764i
$701$	2.51852e9	−	6.41709e9i	0.276142	−	0.703599i	−0.723766	−	0.690046i	$-0.757590\pi$
$701$	2.51852e9	−	6.41709e9i	0.276142	−	0.703599i	0.999908	−	0.0135535i	$-0.00431434\pi$
$702$	−2.71888e9	+	2.52275e9i	−0.296626	+	0.275229i
$703$	4.37288e9	+	2.98138e9i	0.474705	+	0.323648i
$704$	−2.84740e8	+	3.57052e8i	−0.0307570	+	0.0385680i
$705$	−4.84586e10	−	7.30396e9i	−5.20846	−	0.785049i
$706$	−4.46855e9	+	1.37837e9i	−0.477914	+	0.147417i
$707$	6.83542e8	−	9.12123e9i	0.0727440	−	0.970701i
$708$	1.64635e10	−	1.12246e10i	1.74344	−	1.18866i
$709$	−2.45070e9	+	1.07372e10i	−0.258243	+	1.13144i	0.664886	+	0.746945i	$0.268480\pi$
$709$	−2.45070e9	+	1.07372e10i	−0.258243	+	1.13144i	−0.923129	+	0.384491i	$0.874377\pi$
$710$	−2.32755e9	+	1.01977e10i	−0.244059	+	1.06929i
$711$	1.13483e10	−	7.73712e9i	1.18409	−	0.807301i
$712$	−2.41657e8	+	3.22468e9i	−0.0250910	+	0.334817i
$713$	−1.49172e9	+	4.60136e8i	−0.154126	+	0.0475415i
$714$	4.20421e9	+	6.33683e8i	0.432256	+	0.0651521i
$715$	3.10276e9	−	3.89074e9i	0.317451	−	0.398071i
$716$	1.18820e9	+	8.10101e8i	0.120974	+	0.0824790i
$717$	1.85275e10	−	1.71910e10i	1.87715	−	1.74174i
$718$	1.35951e9	−	3.46396e9i	0.137071	−	0.349251i
$719$	−7.31392e9	−	2.25604e9i	−0.733836	−	0.226358i	−0.0947579	−	0.995500i	$-0.530208\pi$
$719$	−7.31392e9	−	2.25604e9i	−0.733836	−	0.226358i	−0.639078	+	0.769142i	$0.720684\pi$
$720$	−1.33607e10	−	6.43415e9i	−1.33402	−	0.642433i
$721$	3.35883e9	+	8.55816e9i	0.333745	+	0.850368i
$722$	1.11490e7	+	1.48773e8i	0.00110244	+	0.0147110i
$723$	4.21289e9	+	5.28279e9i	0.414568	+	0.519852i
$724$	5.74480e9	+	9.95029e9i	0.562588	+	0.974430i
$725$	−1.45991e10	+	2.52864e10i	−1.42280	+	2.46436i
$726$	5.98542e9	−	9.02156e8i	0.580519	−	0.0874991i
$727$	9.42677e9	−	4.53970e9i	0.909898	−	0.438184i	0.0804442	−	0.996759i	$-0.474366\pi$
$727$	9.42677e9	−	4.53970e9i	0.909898	−	0.438184i	0.829454	+	0.558575i	$0.188652\pi$
$728$	4.16495e9	+	3.86451e9i	0.400083	+	0.371223i
$729$	3.71206e9	+	1.62636e10i	0.354869	+	1.55478i
$730$	4.85557e9			0.461966
$731$	7.53892e9	+	4.54276e9i	0.713836	+	0.430139i
$732$	2.00711e10			1.89139
$733$	−1.64094e9	−	7.18945e9i	−0.153897	−	0.674267i	−0.991730	−	0.128340i	$-0.959035\pi$
$733$	−1.64094e9	−	7.18945e9i	−0.153897	−	0.674267i	0.837833	−	0.545926i	$-0.183822\pi$
$734$	2.28250e9	+	2.11785e9i	0.213047	+	0.197678i
$735$	9.66283e9	−	4.65337e9i	0.897632	−	0.432277i
$736$	−6.58732e9	+	9.92879e8i	−0.609027	+	0.0917961i
$737$	2.83055e9	−	4.90266e9i	0.260457	−	0.451124i
$738$	−5.38111e9	−	9.32035e9i	−0.492804	−	0.853562i
$739$	−8.44562e9	−	1.05905e10i	−0.769797	−	0.965295i	0.230172	−	0.973150i	$-0.426071\pi$
$739$	−8.44562e9	−	1.05905e10i	−0.769797	−	0.965295i	−0.999969	+	0.00785504i	$0.997500\pi$
$740$	6.45342e8	+	8.61149e9i	0.0585436	+	0.781209i
$741$	−6.21617e9	−	1.58385e10i	−0.561253	−	1.43005i
$742$	1.00996e9	+	4.86371e8i	0.0907591	+	0.0437073i
$743$	−1.47414e10	−	4.54711e9i	−1.31849	−	0.406701i	−0.445870	−	0.895098i	$-0.647106\pi$
$743$	−1.47414e10	−	4.54711e9i	−1.31849	−	0.406701i	−0.872621	+	0.488397i	$0.837582\pi$
$744$	1.24920e9	−	3.18290e9i	0.111205	−	0.283346i
$745$	2.21908e10	−	2.05900e10i	1.96619	−	1.82436i
$746$	−2.28733e9	−	1.55948e9i	−0.201717	−	0.137528i
$747$	−1.19238e10	+	1.49520e10i	−1.04663	+	1.31243i
$748$	−2.61874e9	−	3.94711e8i	−0.228790	−	0.0344845i
$749$	−1.90765e9	+	5.88432e8i	−0.165887	+	0.0511694i
$750$	7.12168e8	−	9.50322e9i	0.0616408	−	0.822539i
$751$	−5.19626e9	+	3.54275e9i	−0.447663	+	0.305212i	−0.766087	−	0.642737i	$-0.777799\pi$
$751$	−5.19626e9	+	3.54275e9i	−0.447663	+	0.305212i	0.318424	+	0.947948i	$0.396846\pi$
$752$	−2.70766e9	+	1.18630e10i	−0.232184	+	1.01726i
$753$	−4.78646e9	+	2.09708e10i	−0.408537	+	1.78992i
$754$	5.89920e9	−	4.02201e9i	0.501180	−	0.341699i
$755$	4.15782e8	−	5.54823e9i	0.0351602	−	0.469180i
$756$	−8.17431e9	+	2.52144e9i	−0.688058	+	0.212238i
$757$	−1.52435e10	−	2.29759e9i	−1.27717	−	0.192503i	−0.524792	−	0.851231i	$-0.675857\pi$
$757$	−1.52435e10	−	2.29759e9i	−1.27717	−	0.192503i	−0.752381	+	0.658728i	$0.771095\pi$
$758$	4.85575e9	−	6.08892e9i	0.404962	−	0.507806i
$759$	3.46076e9	+	2.35951e9i	0.287293	+	0.195873i
$760$	−1.11267e10	+	1.03241e10i	−0.919431	+	0.853108i
$761$	−6.58915e8	+	1.67889e9i	−0.0541980	+	0.138094i	−0.955408	−	0.295287i	$-0.904585\pi$
$761$	−6.58915e8	+	1.67889e9i	−0.0541980	+	0.138094i	0.901210	+	0.433382i	$0.142680\pi$
$762$	9.55672e8	+	2.94786e8i	0.0782468	+	0.0241359i
$763$	−1.06868e10	−	5.14648e9i	−0.870985	−	0.419445i
$764$	−4.59386e9	−	1.17050e10i	−0.372693	−	0.949605i
$765$	−2.12862e9	−	2.84044e10i	−0.171903	−	2.29388i
$766$	−1.94732e9	−	2.44186e9i	−0.156544	−	0.196300i
$767$	8.92884e9	+	1.54652e10i	0.714515	+	1.23758i
$768$	2.69854e9	−	4.67400e9i	0.214963	−	0.372327i
$769$	1.28744e9	−	1.94050e8i	0.102090	−	0.0153876i	−0.0977985	−	0.995206i	$-0.531180\pi$
$769$	1.28744e9	−	1.94050e8i	0.102090	−	0.0153876i	0.199889	+	0.979819i	$0.435942\pi$
$770$	−2.02002e9	+	9.72789e8i	−0.159455	+	0.0767894i
$771$	1.29984e9	+	1.20607e9i	0.102141	+	0.0947729i
$772$	6.27060e7	+	2.74733e8i	0.00490511	+	0.0214907i
$773$	−8.60828e9			−0.670330			−0.335165	−	0.942160i	$-0.608792\pi$
$773$	−8.60828e9			−0.670330			−0.335165	+	0.942160i	$0.608792\pi$
$774$	8.63630e9	+	8.09951e8i	0.669475	+	0.0627864i
$775$	−5.70828e9			−0.440504
$776$	1.71023e7	+	7.49301e7i	0.00131383	+	0.00575626i
$777$	7.01859e9	+	6.51230e9i	0.536755	+	0.498036i
$778$	−4.07913e9	+	1.96440e9i	−0.310555	+	0.149555i
$779$	1.94695e10	−	2.93455e9i	1.47562	−	0.222413i
$780$	1.38812e10	−	2.40429e10i	1.04736	−	1.81408i
$781$	−3.61183e9	−	6.25587e9i	−0.271299	−	0.469904i
$782$	−1.80354e9	−	2.26157e9i	−0.134866	−	0.169116i
$783$	1.76359e9	+	2.35335e10i	0.131290	+	1.75194i
$784$	−9.72898e8	−	2.47890e9i	−0.0721043	−	0.183719i
$785$	−1.54117e10	−	7.42188e9i	−1.13712	−	0.547608i
$786$	7.40899e9	+	2.28537e9i	0.544227	+	0.167872i
$787$	−3.68658e9	+	9.39324e9i	−0.269595	+	0.686917i	0.730398	+	0.683022i	$0.239335\pi$
$787$	−3.68658e9	+	9.39324e9i	−0.269595	+	0.686917i	−0.999992	+	0.00389429i	$0.998760\pi$
$788$	4.11584e9	−	3.81894e9i	0.299651	−	0.278036i
$789$	−1.66619e10	−	1.13599e10i	−1.20769	−	0.823386i
$790$	4.99356e9	−	6.26173e9i	0.360343	−	0.451855i
$791$	−2.31050e9	−	3.48252e8i	−0.165992	−	0.0250193i
$792$	−5.47511e9	+	1.68885e9i	−0.391611	+	0.120796i
$793$	−1.34423e9	+	1.79375e10i	−0.0957233	+	1.27734i
$794$	−6.50053e9	+	4.43199e9i	−0.460868	+	0.314215i
$795$	2.67577e9	−	1.17233e10i	0.188870	−	0.827495i
$796$	−1.65078e9	+	7.23255e9i	−0.116010	+	0.508271i
$797$	−7.28388e9	+	4.96607e9i	−0.509634	+	0.347463i	−0.790678	−	0.612232i	$-0.790272\pi$
$797$	−7.28388e9	+	4.96607e9i	−0.509634	+	0.347463i	0.281044	+	0.959695i	$0.409319\pi$
$798$	−5.72857e8	+	7.64424e9i	−0.0399058	+	0.532506i
$799$	−2.23342e10	+	6.88920e9i	−1.54902	+	0.477810i
$800$	−2.40874e10	−	3.63059e9i	−1.66332	−	0.250705i
$801$	6.82167e9	−	8.55410e9i	0.469004	−	0.588113i
$802$	−4.96259e9	−	3.38343e9i	−0.339702	−	0.231605i
$803$	−2.45812e9	+	2.28080e9i	−0.167532	+	0.155447i
$804$	1.15382e10	−	2.93988e10i	0.782964	−	1.99496i
$805$	1.19796e10	+	3.69521e9i	0.809387	+	0.249663i
$806$	1.25761e9	+	6.05635e8i	0.0846008	+	0.0407416i
$807$	1.60916e9	+	4.10008e9i	0.107781	+	0.274622i
$808$	−1.01861e9	−	1.35924e10i	−0.0679308	−	0.906473i
$809$	6.15050e9	+	7.71249e9i	0.408405	+	0.512123i	0.942913	−	0.333040i	$-0.108074\pi$
$809$	6.15050e9	+	7.71249e9i	0.408405	+	0.512123i	−0.534508	+	0.845163i	$0.679503\pi$
$810$	−5.24524e8	−	9.08503e8i	−0.0346791	−	0.0600660i
$811$	−6.04334e9	+	1.04674e10i	−0.397836	+	0.689072i	−0.993459	−	0.114192i	$-0.963572\pi$
$811$	−6.04334e9	+	1.04674e10i	−0.397836	+	0.689072i	0.595623	+	0.803264i	$0.296905\pi$
$812$	1.62833e10	−	2.45431e9i	1.06732	−	0.160873i
$813$	1.62025e10	−	7.80269e9i	1.05746	−	0.509246i
$814$	8.53987e8	+	7.92384e8i	0.0554965	+	0.0514932i
$815$	6.86598e8	+	3.00818e9i	0.0444274	+	0.194649i
$816$	−1.13245e10			−0.729633
$817$	−7.15178e9	+	1.41665e10i	−0.458814	+	0.908836i
$818$	8.01449e9			0.511964
$819$	−4.27764e9	−	1.87416e10i	−0.272089	−	1.19210i
$820$	2.35505e10	+	2.18517e10i	1.49160	+	1.38400i
$821$	9.86273e9	−	4.74964e9i	0.622008	−	0.299543i	−0.0962103	−	0.995361i	$-0.530672\pi$
$821$	9.86273e9	−	4.74964e9i	0.622008	−	0.299543i	0.718218	+	0.695818i	$0.244958\pi$
$822$	−5.76145e9	+	8.68399e8i	−0.361810	+	0.0545341i
$823$	−8.61673e9	+	1.49246e10i	−0.538819	+	0.933262i	0.460149	+	0.887842i	$0.347796\pi$
$823$	−8.61673e9	+	1.49246e10i	−0.538819	+	0.933262i	−0.998968	+	0.0454203i	$0.985537\pi$
$824$	6.85016e9	+	1.18648e10i	0.426536	+	0.738782i
$825$	9.54940e9	+	1.19746e10i	0.592090	+	0.742457i
$826$	−6.01238e8	−	8.02297e9i	−0.0371207	−	0.495342i
$827$	−8.75839e8	−	2.23160e9i	−0.0538462	−	0.137198i	0.901420	−	0.432947i	$-0.142526\pi$
$827$	−8.75839e8	−	2.23160e9i	−0.0538462	−	0.137198i	−0.955266	+	0.295749i	$0.904431\pi$
$828$	1.31483e10	+	6.33189e9i	0.804940	+	0.387639i
$829$	2.73740e10	+	8.44377e9i	1.66878	+	0.514749i	0.978050	−	0.208369i	$-0.0668154\pi$
$829$	2.73740e10	+	8.44377e9i	1.66878	+	0.514749i	0.690725	+	0.723118i	$0.257292\pi$
$830$	−4.07419e9	+	1.03809e10i	−0.247325	+	0.630174i
$831$	−3.39857e10	+	3.15341e10i	−2.05444	+	1.90624i
$832$	−1.88656e9	−	1.28623e9i	−0.113563	−	0.0774261i
$833$	3.18920e9	−	3.99913e9i	0.191172	−	0.239722i
$834$	1.98651e9	+	2.99418e8i	0.118579	+	0.0178730i
$835$	2.92058e10	−	9.00879e9i	1.73607	−	0.535505i
$836$	3.56824e8	−	4.76148e9i	0.0211218	−	0.281851i
$837$	−3.81203e9	+	2.59900e9i	−0.224708	+	0.153203i
$838$	−2.64019e9	+	1.15674e10i	−0.154982	+	0.679021i
$839$	3.30367e9	−	1.44743e10i	0.193121	−	0.846119i	−0.781793	−	0.623538i	$-0.785695\pi$
$839$	3.30367e9	−	1.44743e10i	0.193121	−	0.846119i	0.974914	−	0.222581i	$-0.0714482\pi$
$840$	−2.26877e10	+	1.54682e10i	−1.32073	+	0.900457i
$841$	2.10584e9	−	2.81005e10i	0.122079	−	1.62903i
$842$	−8.20243e9	+	2.53011e9i	−0.473533	+	0.146066i
$843$	4.39836e10	+	6.62946e9i	2.52868	+	0.381137i
$844$	−4.75905e9	+	5.96766e9i	−0.272472	+	0.341669i
$845$	−3.48860e9	−	2.37849e9i	−0.198908	−	0.135613i
$846$	−1.68849e10	+	1.56669e10i	−0.958745	+	0.889586i
$847$	−4.57099e9	+	1.16467e10i	−0.258475	+	0.658584i
$848$	−2.85309e9	−	8.80062e8i	−0.160668	−	0.0495596i
$849$	7.67578e9	+	3.69646e9i	0.430473	+	0.207305i
$850$	−3.86434e9	−	9.84619e9i	−0.215829	−	0.549923i
$851$	−4.86793e8	−	6.49580e9i	−0.0270764	−	0.361310i
$852$	−2.51260e10	−	3.15071e10i	−1.39183	−	1.74530i
$853$	−6.44830e9	−	1.11688e10i	−0.355732	−	0.616147i	0.631511	−	0.775367i	$-0.282435\pi$
$853$	−6.44830e9	−	1.11688e10i	−0.355732	−	0.616147i	−0.987243	+	0.159221i	$0.949102\pi$
$854$	4.05205e9	−	7.01835e9i	0.222624	−	0.385596i
$855$	5.07823e10	−	7.65419e9i	2.77863	−	0.418811i
$856$	−2.68032e9	+	1.29077e9i	−0.146059	+	0.0703382i
$857$	1.65898e10	+	1.53930e10i	0.900341	+	0.835395i	0.986980	−	0.160845i	$-0.0514220\pi$
$857$	1.65898e10	+	1.53930e10i	0.900341	+	0.835395i	−0.0866383	+	0.996240i	$0.527612\pi$
$858$	−8.33392e8	−	3.65133e9i	−0.0450447	−	0.197354i
$859$	2.93738e10			1.58119			0.790596	−	0.612338i	$-0.209771\pi$
$859$	2.93738e10			1.58119			0.790596	+	0.612338i	$0.209771\pi$
$860$	−2.53478e10	+	5.28854e9i	−1.35893	+	0.283525i
$861$	3.56193e10			1.90184
$862$	6.66341e8	+	2.91943e9i	0.0354341	+	0.155247i
$863$	−1.69743e10	−	1.57499e10i	−0.898991	−	0.834141i	0.0878007	−	0.996138i	$-0.472016\pi$
$863$	−1.69743e10	−	1.57499e10i	−0.898991	−	0.834141i	−0.986791	+	0.161997i	$0.948207\pi$
$864$	−1.77388e10	+	8.54254e9i	−0.935675	+	0.450598i
$865$	3.26699e10	−	4.92420e9i	1.71630	−	0.258690i
$866$	−2.53844e9	+	4.39670e9i	−0.132817	+	0.230046i
$867$	4.78242e9	+	8.28340e9i	0.249219	+	0.431660i
$868$	2.00724e9	+	2.51700e9i	0.104179	+	0.130636i
$869$	4.13337e8	+	5.51560e9i	0.0213666	+	0.285117i
$870$	1.26065e10	+	3.21210e10i	0.649051	+	1.65375i
$871$	2.55010e10	+	1.22806e10i	1.30765	+	0.629733i
$872$	−1.68905e10	−	5.21002e9i	−0.862649	−	0.266092i
$873$	9.50037e7	−	2.42065e8i	0.00483271	−	0.0123135i
$874$	3.82313e9	−	3.54735e9i	0.193700	−	0.179727i
$875$	1.62754e10	+	1.10964e10i	0.821304	+	0.559956i
$876$	−1.16637e10	+	1.46258e10i	−0.586234	+	0.735114i
$877$	−2.47461e10	−	3.72988e9i	−1.23882	−	0.186722i	−0.503233	−	0.864151i	$-0.667856\pi$
$877$	−2.47461e10	−	3.72988e9i	−1.23882	−	0.186722i	−0.735588	+	0.677429i	$0.763094\pi$
$878$	1.08217e10	−	3.33806e9i	0.539592	−	0.166442i
$879$	−1.99678e9	+	2.66451e10i	−0.0991673	+	1.32330i
$880$	4.93411e9	−	3.36402e9i	0.244073	−	0.166406i
$881$	6.74284e9	−	2.95423e10i	0.332221	−	1.45555i	−0.482600	−	0.875841i	$-0.660307\pi$
$881$	6.74284e9	−	2.95423e10i	0.332221	−	1.45555i	0.814820	−	0.579713i	$-0.196836\pi$
$882$	1.12171e9	−	4.91454e9i	0.0550479	−	0.241181i
$883$	−9.57429e9	+	6.52764e9i	−0.467998	+	0.319076i	−0.774256	−	0.632873i	$-0.781876\pi$
$883$	−9.57429e9	+	6.52764e9i	−0.467998	+	0.319076i	0.306257	+	0.951949i	$0.400923\pi$
$884$	9.89488e8	−	1.32038e10i	0.0481757	−	0.642860i
$885$	−8.24705e10	+	2.54388e10i	−3.99942	+	1.23366i
$886$	−2.10276e8	−	3.16940e7i	−0.0101571	−	0.00153094i
$887$	−1.39318e10	+	1.74699e10i	−0.670307	+	0.840539i	−0.994422	−	0.105479i	$-0.966362\pi$
$887$	−1.39318e10	+	1.74699e10i	−0.670307	+	0.840539i	0.324114	+	0.946018i	$0.394934\pi$
$888$	1.17886e10	+	8.03732e9i	0.564958	+	0.385182i
$889$	−1.51537e9	+	1.40606e9i	−0.0723375	+	0.0671194i
$890$	2.33086e9	−	5.93894e9i	0.110829	−	0.282387i
$891$	6.92289e8	+	2.13543e8i	0.0327880	+	0.0101138i
$892$	−2.66453e10	−	1.28317e10i	−1.25703	−	0.605352i
$893$	−1.53955e10	−	3.92271e10i	−0.723459	−	1.84334i
$894$	−1.70252e9	−	2.27186e10i	−0.0796914	−	1.06341i
$895$	−3.88356e9	−	4.86983e9i	−0.181071	−	0.227056i
$896$	8.72531e9	+	1.51127e10i	0.405231	+	0.701881i
$897$	−1.04708e10	+	1.81360e10i	−0.484404	+	0.839012i
$898$	3.87584e8	−	5.84188e7i	0.0178607	−	0.00269207i
$899$	8.00192e9	−	3.85352e9i	0.367312	−	0.176888i
$900$	3.91179e10	+	3.62961e10i	1.78866	+	1.65963i
$901$	−1.27617e9	−	5.59124e9i	−0.0581260	−	0.254666i
$902$	4.33398e9			0.196637
$903$	−1.66132e10	+	2.34135e10i	−0.750836	+	1.05818i
$904$	−3.48197e9			−0.156760
$905$	−1.10737e10	−	4.85171e10i	−0.496619	−	2.17583i
$906$	−3.06948e9	−	2.84806e9i	−0.137125	−	0.127233i
$907$	1.03568e10	−	4.98758e9i	0.460894	−	0.221955i	−0.189004	−	0.981976i	$-0.560526\pi$
$907$	1.03568e10	−	4.98758e9i	0.460894	−	0.221955i	0.649898	+	0.760022i	$0.274812\pi$
$908$	6.57627e9	−	9.91214e8i	0.291527	−	0.0439407i
$909$	−2.30589e10	+	3.99392e10i	−1.01828	+	1.76370i
$910$	−5.60481e9	−	9.70781e9i	−0.246556	−	0.427048i
$911$	−6.78113e9	−	8.50327e9i	−0.297158	−	0.372625i	0.610729	−	0.791840i	$-0.290877\pi$
$911$	−6.78113e9	−	8.50327e9i	−0.297158	−	0.372625i	−0.907887	+	0.419215i	$0.862305\pi$
$912$	−1.52582e9	−	2.03607e10i	−0.0666073	−	0.888813i
$913$	−2.81365e9	−	7.16906e9i	−0.122355	−	0.311756i
$914$	−1.50584e9	−	7.25175e8i	−0.0652330	−	0.0314146i
$915$	−8.30715e10	−	2.56242e10i	−3.58491	−	1.10580i
$916$	−1.15034e10	+	2.93102e10i	−0.494529	+	1.26004i
$917$	−1.17482e10	+	1.09007e10i	−0.503126	+	0.466833i
$918$	−7.06364e9	−	4.81591e9i	−0.301355	−	0.205461i
$919$	1.14934e9	−	1.44122e9i	0.0488476	−	0.0612530i	−0.756808	−	0.653638i	$-0.773242\pi$
$919$	1.14934e9	−	1.44122e9i	0.0488476	−	0.0612530i	0.805655	+	0.592385i	$0.201813\pi$
$920$	1.84732e10	+	2.78438e9i	0.782139	+	0.117888i
$921$	9.64629e8	−	2.97549e8i	0.0406866	−	0.0125502i
$922$	−4.69541e8	+	6.26558e9i	−0.0197294	+	0.263271i
$923$	2.98406e10	−	2.03450e10i	1.24911	−	0.851631i
$924$	1.92213e9	−	8.42139e9i	0.0801549	−	0.351182i
$925$	5.30030e9	−	2.32221e10i	0.220194	−	0.964731i
$926$	1.12173e10	−	7.64780e9i	0.464246	−	0.316518i
$927$	3.46405e9	−	4.62245e10i	0.142825	−	1.90587i
$928$	3.62168e10	−	1.11714e10i	1.48762	−	0.458871i
$929$	4.46651e10	+	6.73219e9i	1.82774	+	0.275487i	0.970792	−	0.239922i	$-0.0771219\pi$
$929$	4.46651e10	+	6.73219e9i	1.82774	+	0.275487i	0.856944	+	0.515409i	$0.172360\pi$
$930$	−4.20607e9	+	5.27424e9i	−0.171469	+	0.215016i
$931$	7.61985e9	+	5.19513e9i	0.309473	+	0.210995i
$932$	−9.51865e9	+	8.83202e9i	−0.385141	+	0.357359i
$933$	−8.28875e9	+	2.11194e10i	−0.334121	+	0.851326i
$934$	−1.55695e9	−	4.80255e8i	−0.0625259	−	0.0192867i
$935$	1.03347e10	+	4.97692e9i	0.413482	+	0.199122i
$936$	−1.04658e10	−	2.66665e10i	−0.417165	−	1.06292i
$937$	−4.95458e8	−	6.61142e9i	−0.0196751	−	0.262547i	−0.998363	−	0.0571935i	$-0.981785\pi$
$937$	−4.95458e8	−	6.61142e9i	−0.0196751	−	0.262547i	0.978688	−	0.205353i	$-0.0658343\pi$
$938$	−7.95065e9	−	9.96980e9i	−0.314552	−	0.394436i
$939$	−2.79292e10	−	4.83747e10i	−1.10085	−	1.90673i
$940$	3.43794e10	−	5.95469e10i	1.35005	−	2.33836i
$941$	−2.37394e10	+	3.57813e9i	−0.928764	+	0.139989i	−0.595966	−	0.803009i	$-0.703231\pi$
$941$	−2.37394e10	+	3.57813e9i	−0.928764	+	0.139989i	−0.332798	+	0.942998i	$0.607993\pi$
$942$	−1.15987e10	+	5.58565e9i	−0.452097	+	0.217719i
$943$	−1.77646e10	−	1.64831e10i	−0.689864	−	0.640100i
$944$	4.76848e9	+	2.08921e10i	0.184492	+	0.808313i
$945$	3.70514e10			1.42821
$946$	−2.02141e9	+	2.84884e9i	−0.0776309	+	0.109408i
$947$	−1.56095e10			−0.597260			−0.298630	−	0.954369i	$-0.596530\pi$
$947$	−1.56095e10			−0.597260			−0.298630	+	0.954369i	$0.596530\pi$
$948$	6.86622e9	+	3.00829e10i	0.261751	+	1.14681i
$949$	−1.22899e10	−	1.14034e10i	−0.466785	−	0.433113i
$950$	1.71821e10	−	8.27444e9i	0.650193	−	0.313117i
$951$	1.35683e10	−	2.04510e9i	0.511558	−	0.0771049i
$952$	−6.54807e9	+	1.13416e10i	−0.245971	+	0.426035i
$953$	2.16828e9	+	3.75558e9i	0.0811504	+	0.140557i	0.903744	−	0.428073i	$-0.140807\pi$
$953$	2.16828e9	+	3.75558e9i	0.0811504	+	0.140557i	−0.822594	+	0.568629i	$0.807474\pi$
$954$	−3.52389e9	−	4.41882e9i	−0.131402	−	0.164773i
$955$	4.06998e9	+	5.43101e10i	0.151210	+	2.01776i
$956$	1.29557e10	+	3.30105e10i	0.479575	+	1.22194i
$957$	−2.14702e10	−	1.03395e10i	−0.791851	−	0.381335i
$958$	−6.02416e9	−	1.85821e9i	−0.221369	−	0.0682833i
$959$	4.39996e9	−	1.12109e10i	0.161095	−	0.410465i
$960$	8.08925e9	−	7.50573e9i	0.295093	−	0.273806i
$961$	−2.12974e10	−	1.45203e10i	−0.774094	−	0.527769i
$962$	−3.63154e9	+	4.55381e9i	−0.131516	+	0.164916i
$963$	9.95305e9	+	1.50018e9i	0.359140	+	0.0541317i
$964$	−9.05928e9	+	2.79442e9i	−0.325705	+	0.100467i
$965$	9.12118e7	−	1.21714e9i	0.00326742	−	0.0436007i
$966$	7.79549e9	−	5.31487e9i	0.278242	−	0.189702i
$967$	1.81735e9	−	7.96234e9i	0.0646318	−	0.283171i	−0.932276	−	0.361747i	$-0.882180\pi$
$967$	1.81735e9	−	7.96234e9i	0.0646318	−	0.283171i	0.996908	+	0.0785766i	$0.0250375\pi$
$968$	−4.14882e9	+	1.81772e10i	−0.147015	+	0.644113i
$969$	3.24039e10	−	2.20926e10i	1.14410	−	0.780035i
$970$	1.13317e7	−	1.51211e8i	0.000398652	−	0.00531964i
$971$	1.46364e10	−	4.51472e9i	0.513057	−	0.158257i	−0.0274066	−	0.999624i	$-0.508725\pi$
$971$	1.46364e10	−	4.51472e9i	0.513057	−	0.158257i	0.540464	+	0.841367i	$0.318249\pi$
$972$	−2.16438e10	−	3.26227e9i	−0.755964	−	0.113943i
$973$	−2.58904e9	+	3.24655e9i	−0.0901038	+	0.112987i
$974$	9.12771e9	+	6.22317e9i	0.316523	+	0.215802i
$975$	−5.61341e10	+	5.20848e10i	−1.93959	+	1.79968i
$976$	−7.88608e9	+	2.00934e10i	−0.271510	+	0.691797i
$977$	1.26484e10	+	3.90151e9i	0.433914	+	0.133845i	0.504014	−	0.863695i	$-0.331856\pi$
$977$	1.26484e10	+	3.90151e9i	0.433914	+	0.133845i	−0.0701005	+	0.997540i	$0.522332\pi$
$978$	2.09219e9	+	1.00755e9i	0.0715179	+	0.0344412i
$979$	1.60970e9	+	4.10145e9i	0.0548284	+	0.139700i
$980$	1.12452e9	+	1.50057e10i	0.0381661	+	0.509291i
$981$	3.72877e10	+	4.67573e10i	1.26103	+	1.58128i
$982$	−5.86241e9	−	1.01540e10i	−0.197554	−	0.342174i
$983$	−2.27710e9	+	3.94405e9i	−0.0764618	+	0.132436i	−0.901721	−	0.432318i	$-0.857696\pi$
$983$	−2.27710e9	+	3.94405e9i	−0.0764618	+	0.132436i	0.825259	+	0.564754i	$0.191029\pi$
$984$	5.24867e10	−	7.91109e9i	1.75617	−	0.264700i
$985$	−2.19104e10	+	1.05515e10i	−0.730506	+	0.351793i
$986$	1.20640e10	+	1.11937e10i	0.400794	+	0.371883i
$987$	−1.69637e10	−	7.43227e10i	−0.561577	−	2.46043i
$988$	2.38728e10			0.787506
$989$	1.91203e10	−	3.98924e9i	0.628504	−	0.131130i
$990$	1.13043e10			0.370272
$991$	5.70436e9	+	2.49924e10i	0.186187	+	0.815738i	0.978603	+	0.205757i	$0.0659657\pi$
$991$	5.70436e9	+	2.49924e10i	0.186187	+	0.815738i	−0.792416	+	0.609981i	$0.791177\pi$
$992$	5.43164e9	+	5.03982e9i	0.176661	+	0.163917i
$993$	7.33206e10	−	3.53094e10i	2.37631	−	1.14437i
$994$	−1.60898e10	+	2.42515e9i	−0.519635	+	0.0783224i
$995$	1.60659e10	−	2.78270e10i	0.517041	−	0.895542i
$996$	−2.14822e10	−	3.72083e10i	−0.688924	−	1.19325i
$997$	−2.03463e9	−	2.55134e9i	−0.0650207	−	0.0815333i	0.748258	−	0.663408i	$-0.230891\pi$
$997$	−2.03463e9	−	2.55134e9i	−0.0650207	−	0.0815333i	−0.813278	+	0.581875i	$0.802319\pi$
$998$	4.21466e8	+	5.62407e9i	0.0134216	+	0.179099i
$999$	−7.03354e9	−	1.79212e10i	−0.223200	−	0.568705i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.10.11	✓	300
43.13	even	21	inner	43.8.g.a.13.11	yes	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.10.11	✓	300	1.1	even	1	trivial
43.8.g.a.13.11	yes	300	43.13	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01772 - 4.45891i) q^{2} +(-55.9466 - 51.9109i) q^{3} +(96.4779 - 46.4613i) q^{4} +(-458.625 + 69.1265i) q^{5} +(-174.528 + 302.291i) q^{6} +(-360.749 - 624.835i) q^{7} +(-670.356 - 840.600i) q^{8} +(271.850 + 3627.59i) q^{9} +O(q^{10})\)	\(q+(-1.01772 - 4.45891i) q^{2} +(-55.9466 - 51.9109i) q^{3} +(96.4779 - 46.4613i) q^{4} +(-458.625 + 69.1265i) q^{5} +(-174.528 + 302.291i) q^{6} +(-360.749 - 624.835i) q^{7} +(-670.356 - 840.600i) q^{8} +(271.850 + 3627.59i) q^{9} +(774.979 + 1974.61i) q^{10} +(-1319.86 - 635.613i) q^{11} +(-7809.46 - 2408.90i) q^{12} +(2675.86 - 6817.97i) q^{13} +(-2418.94 + 2244.45i) q^{14} +(29246.9 + 19940.2i) q^{15} +(5479.97 - 6871.66i) q^{16} +(16693.8 + 2516.18i) q^{17} +(15898.4 - 4904.01i) q^{18} +(-2274.66 + 30353.2i) q^{19} +(-41035.4 + 27977.5i) q^{20} +(-12253.1 + 53684.2i) q^{21} +(-1490.89 + 6532.02i) q^{22} +(30953.8 - 21103.9i) q^{23} +(-6132.12 + 81827.4i) q^{24} +(130904. - 40378.5i) q^{25} +(-33124.0 - 4992.64i) q^{26} +(69034.1 - 86566.0i) q^{27} +(-63834.9 - 43521.9i) q^{28} +(-156244. + 144973. i) q^{29} +(59146.4 - 150703. i) q^{30} +(-39818.1 - 12282.3i) q^{31} +(-160210. - 77153.0i) q^{32} +(40846.7 + 104076. i) q^{33} +(-5770.11 - 76996.8i) q^{34} +(208641. + 261627. i) q^{35} +(194770. + 337352. i) q^{36} +(86938.3 - 150582. i) q^{37} +(137657. - 20748.5i) q^{38} +(-503632. + 242536. i) q^{39} +(365549. + 339180. i) q^{40} +(-143940. - 630644. i) q^{41} +251843. q^{42} +(481674. + 199522. i) q^{43} -156869. q^{44} +(-375440. - 1.64491e6i) q^{45} +(-125603. - 116542. i) q^{46} +(-1.24734e6 + 600687. i) q^{47} +(-663299. + 99976.3i) q^{48} +(151492. - 262392. i) q^{49} +(-313267. - 542594. i) q^{50} +(-803343. - 1.00736e6i) q^{51} +(-58610.9 - 782108. i) q^{52} +(-124109. - 316224. i) q^{53} +(-456247. - 219717. i) q^{54} +(649259. + 200270. i) q^{55} +(-283406. + 722107. i) q^{56} +(1.70292e6 - 1.58008e6i) q^{57} +(805432. + 549134. i) q^{58} +(-1.52016e6 + 1.90622e6i) q^{59} +(3.74813e6 + 564939. i) q^{60} +(-2.34681e6 + 723895. i) q^{61} +(-14241.9 + 190045. i) q^{62} +(2.16857e6 - 1.47851e6i) q^{63} +(69369.8 - 303929. i) q^{64} +(-755911. + 3.31186e6i) q^{65} +(422493. - 288051. i) q^{66} +(-288787. + 3.85360e6i) q^{67} +(1.72749e6 - 532859. i) q^{68} +(-2.82728e6 - 426144. i) q^{69} +(954235. - 1.19657e6i) q^{70} +(4.07421e6 + 2.77775e6i) q^{71} +(2.86711e6 - 2.66029e6i) q^{72} +(836272. - 2.13079e6i) q^{73} +(-759908. - 234401. i) q^{74} +(-9.41971e6 - 4.53629e6i) q^{75} +(1.19080e6 + 3.03410e6i) q^{76} +(78985.9 + 1.05399e6i) q^{77} +(1.59400e6 + 1.99881e6i) q^{78} +(-1.88782e6 - 3.26980e6i) q^{79} +(-2.03823e6 + 3.53032e6i) q^{80} +(-489020. + 73707.9i) q^{81} +(-2.66549e6 + 1.28363e6i) q^{82} +(3.85378e6 + 3.57578e6i) q^{83} +(1.31209e6 + 5.74863e6i) q^{84} -7.83011e6 q^{85} +(399443. - 2.35080e6i) q^{86} +1.62670e7 q^{87} +(350482. + 1.53556e6i) q^{88} +(-2.20476e6 - 2.04572e6i) q^{89} +(-6.95240e6 + 3.34810e6i) q^{90} +(-5.22542e6 + 787606. i) q^{91} +(2.00584e6 - 3.47421e6i) q^{92} +(1.59011e6 + 2.75414e6i) q^{93} +(3.94785e6 + 4.95044e6i) q^{94} +(-1.05500e6 - 1.40780e7i) q^{95} +(4.95812e6 + 1.26331e7i) q^{96} +(-64404.7 - 31015.7i) q^{97} +(-1.32416e6 - 408449. i) q^{98} +(1.94694e6 - 4.96071e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9}+O(q^{10}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9	\( 300 q - 40 q^{2} - 12 q^{3} - 3028 q^{4} + 235 q^{5} + 1274 q^{6} - 4122 q^{7} + 762 q^{8} + 8097 q^{9} - 1681 q^{10} + 4580 q^{11} + 9330 q^{12} - 20444 q^{13} - 45798 q^{14} + 50477 q^{15} - 74504 q^{16} - 25312 q^{17} + 2046 q^{18} + 4046 q^{19} + 140781 q^{20} + 100555 q^{21} + 95810 q^{22} + 1648 q^{23} - 292592 q^{24} + 419068 q^{25} + 393435 q^{26} + 274140 q^{27} + 233644 q^{28} + 605697 q^{29} - 1216016 q^{30} + 358580 q^{31} - 19194 q^{32} + 1280291 q^{33} + 1137255 q^{34} + 652739 q^{35} - 8980975 q^{36} - 2360047 q^{37} - 308490 q^{38} + 536339 q^{39} + 3057993 q^{40} - 1376320 q^{41} + 8417790 q^{42} + 7173000 q^{43} - 3856780 q^{44} + 2761486 q^{45} - 7073993 q^{46} + 1437090 q^{47} - 9543469 q^{48} - 16053170 q^{49} - 3046893 q^{50} + 2972901 q^{51} + 17415142 q^{52} + 3320604 q^{53} + 6000486 q^{54} + 13427750 q^{55} - 5450793 q^{56} + 3333100 q^{57} - 7876190 q^{58} - 7084765 q^{59} + 7356443 q^{60} + 3354606 q^{61} - 719427 q^{62} + 14716815 q^{63} - 16086234 q^{64} - 19914646 q^{65} - 8293345 q^{66} + 13025470 q^{67} - 22191927 q^{68} - 33964295 q^{69} + 8094727 q^{70} + 30843495 q^{71} + 93841607 q^{72} - 3067637 q^{73} + 18179570 q^{74} - 41508571 q^{75} - 19751872 q^{76} - 15169179 q^{77} - 69509396 q^{78} - 12090149 q^{79} - 69662530 q^{80} + 3387954 q^{81} + 39226888 q^{82} + 16408777 q^{83} + 98603231 q^{84} - 13423424 q^{85} + 111906660 q^{86} + 49022010 q^{87} + 76213954 q^{88} - 12540205 q^{89} - 92608607 q^{90} - 59091937 q^{91} - 50489370 q^{92} - 52218334 q^{93} - 3441600 q^{94} - 79947551 q^{95} - 23449784 q^{96} - 116467587 q^{97} + 73909552 q^{98} - 20061115 q^{99}+O(q^{100}) \) 300 * q - 40 * q^2 - 12 * q^3 - 3028 * q^4 + 235 * q^5 + 1274 * q^6 - 4122 * q^7 + 762 * q^8 + 8097 * q^9 - 1681 * q^10 + 4580 * q^11 + 9330 * q^12 - 20444 * q^13 - 45798 * q^14 + 50477 * q^15 - 74504 * q^16 - 25312 * q^17 + 2046 * q^18 + 4046 * q^19 + 140781 * q^20 + 100555 * q^21 + 95810 * q^22 + 1648 * q^23 - 292592 * q^24 + 419068 * q^25 + 393435 * q^26 + 274140 * q^27 + 233644 * q^28 + 605697 * q^29 - 1216016 * q^30 + 358580 * q^31 - 19194 * q^32 + 1280291 * q^33 + 1137255 * q^34 + 652739 * q^35 - 8980975 * q^36 - 2360047 * q^37 - 308490 * q^38 + 536339 * q^39 + 3057993 * q^40 - 1376320 * q^41 + 8417790 * q^42 + 7173000 * q^43 - 3856780 * q^44 + 2761486 * q^45 - 7073993 * q^46 + 1437090 * q^47 - 9543469 * q^48 - 16053170 * q^49 - 3046893 * q^50 + 2972901 * q^51 + 17415142 * q^52 + 3320604 * q^53 + 6000486 * q^54 + 13427750 * q^55 - 5450793 * q^56 + 3333100 * q^57 - 7876190 * q^58 - 7084765 * q^59 + 7356443 * q^60 + 3354606 * q^61 - 719427 * q^62 + 14716815 * q^63 - 16086234 * q^64 - 19914646 * q^65 - 8293345 * q^66 + 13025470 * q^67 - 22191927 * q^68 - 33964295 * q^69 + 8094727 * q^70 + 30843495 * q^71 + 93841607 * q^72 - 3067637 * q^73 + 18179570 * q^74 - 41508571 * q^75 - 19751872 * q^76 - 15169179 * q^77 - 69509396 * q^78 - 12090149 * q^79 - 69662530 * q^80 + 3387954 * q^81 + 39226888 * q^82 + 16408777 * q^83 + 98603231 * q^84 - 13423424 * q^85 + 111906660 * q^86 + 49022010 * q^87 + 76213954 * q^88 - 12540205 * q^89 - 92608607 * q^90 - 59091937 * q^91 - 50489370 * q^92 - 52218334 * q^93 - 3441600 * q^94 - 79947551 * q^95 - 23449784 * q^96 - 116467587 * q^97 + 73909552 * q^98 - 20061115 * q^99

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