LMFDB - Embedded newform 43.8.g.a.9.17

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			9.17
Character	$\chi$	$=$	43.9
Dual form			43.8.g.a.24.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.94589 + 7.45591i) q^{2} +(86.0795 + 12.9744i) q^{3} +(8.24571 - 36.1268i) q^{4} +(-256.150 - 174.640i) q^{5} +(415.083 + 718.945i) q^{6} +(380.244 - 658.602i) q^{7} +(1418.17 - 682.954i) q^{8} +(5151.52 + 1589.03i) q^{9} +O(q^{10})$	\(q+(5.94589 + 7.45591i) q^{2} +(86.0795 + 12.9744i) q^{3} +(8.24571 - 36.1268i) q^{4} +(-256.150 - 174.640i) q^{5} +(415.083 + 718.945i) q^{6} +(380.244 - 658.602i) q^{7} +(1418.17 - 682.954i) q^{8} +(5151.52 + 1589.03i) q^{9} +(-220.939 - 2948.23i) q^{10} +(1257.82 + 5510.88i) q^{11} +(1178.51 - 3002.80i) q^{12} +(551.467 - 7358.81i) q^{13} +(7171.36 - 1080.91i) q^{14} +(-19783.5 - 18356.4i) q^{15} +(9250.88 + 4454.99i) q^{16} +(-29858.1 + 20356.9i) q^{17} +(18782.7 + 47857.4i) q^{18} +(35496.0 - 10949.1i) q^{19} +(-8421.35 + 7813.87i) q^{20} +(41276.2 - 51758.7i) q^{21} +(-33609.7 + 42145.3i) q^{22} +(-41179.0 + 38208.5i) q^{23} +(130936. - 40388.5i) q^{24} +(6571.51 + 16743.9i) q^{25} +(58145.6 - 39643.0i) q^{26} +(251295. + 121017. i) q^{27} +(-20657.8 - 19167.6i) q^{28} +(-95217.0 + 14351.7i) q^{29} +(19233.1 - 256648. i) q^{30} +(-60890.0 + 155145. i) q^{31} +(-23044.4 - 100964. i) q^{32} +(36772.4 + 490694. i) q^{33} +(-329312. - 101579. i) q^{34} +(-212418. + 102295. i) q^{35} +(99884.6 - 173005. i) q^{36} +(-149122. - 258286. i) q^{37} +(292690. + 199553. i) q^{38} +(142946. - 626288. i) q^{39} +(-482536. - 72730.6i) q^{40} +(43417.1 + 54443.3i) q^{41} +631331. q^{42} +(159770. + 496278. i) q^{43} +209462. q^{44} +(-1.04205e6 - 1.30669e6i) q^{45} +(-529725. - 79843.2i) q^{46} +(33686.8 - 147592. i) q^{47} +(738511. + 503508. i) q^{48} +(122601. + 212351. i) q^{49} +(-85767.8 + 148554. i) q^{50} +(-2.83429e6 + 1.36492e6i) q^{51} +(-261303. - 80601.4i) q^{52} +(11384.2 + 151911. i) q^{53} +(591877. + 2.59318e6i) q^{54} +(640231. - 1.63128e6i) q^{55} +(89455.3 - 1.19370e6i) q^{56} +(3.19754e6 - 481951. i) q^{57} +(-673154. - 624596. i) q^{58} +(-2.46333e6 - 1.18628e6i) q^{59} +(-826286. + 563352. i) q^{60} +(317103. + 807965. i) q^{61} +(-1.51879e6 + 468486. i) q^{62} +(3.00537e6 - 2.78858e6i) q^{63} +(1.43519e6 - 1.79967e6i) q^{64} +(-1.42640e6 + 1.78865e6i) q^{65} +(-3.43992e6 + 3.19178e6i) q^{66} +(-116360. + 35892.4i) q^{67} +(489229. + 1.24653e6i) q^{68} +(-4.04040e6 + 2.75470e6i) q^{69} +(-2.02572e6 - 975534. i) q^{70} +(-333795. - 309717. i) q^{71} +(8.39096e6 - 1.26473e6i) q^{72} +(-31636.1 + 422154. i) q^{73} +(1.03910e6 - 2.64758e6i) q^{74} +(348430. + 1.52657e6i) q^{75} +(-102865. - 1.37264e6i) q^{76} +(4.10775e6 + 1.26707e6i) q^{77} +(5.51949e6 - 2.65805e6i) q^{78} +(2.06636e6 - 3.57905e6i) q^{79} +(-1.59160e6 - 2.75673e6i) q^{80} +(1.03197e7 + 7.03587e6i) q^{81} +(-147771. + 647427. i) q^{82} +(-3.82593e6 - 576666. i) q^{83} +(-1.52953e6 - 1.91796e6i) q^{84} +1.12033e7 q^{85} +(-2.75023e6 + 4.14205e6i) q^{86} -8.38244e6 q^{87} +(5.54748e6 + 6.95633e6i) q^{88} +(9.71511e6 + 1.46432e6i) q^{89} +(3.54665e6 - 1.55389e7i) q^{90} +(-4.63683e6 - 3.16134e6i) q^{91} +(1.04080e6 + 1.80272e6i) q^{92} +(-7.25430e6 + 1.25648e7i) q^{93} +(1.30073e6 - 626397. i) q^{94} +(-1.10045e7 - 3.39443e6i) q^{95} +(-673703. - 8.98994e6i) q^{96} +(477810. + 2.09342e6i) q^{97} +(-854297. + 2.17671e6i) q^{98} +(-2.27727e6 + 3.03881e7i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{21}\right)$

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 $

$2$	5.94589	+	7.45591i	0.525547	+	0.659015i	0.971777	−	0.235903i	$-0.0758049\pi$
$2$	5.94589	+	7.45591i	0.525547	+	0.659015i	−0.446229	+	0.894919i	$0.647233\pi$
$3$	86.0795	+	12.9744i	1.84067	+	0.277436i	0.974840	−	0.222905i	$-0.0715540\pi$
$3$	86.0795	+	12.9744i	1.84067	+	0.277436i	0.865828	+	0.500341i	$0.166792\pi$
$4$	8.24571	−	36.1268i	0.0644196	−	0.282241i
$5$	−256.150	−	174.640i	−0.916432	−	0.624813i	0.0105397	−	0.999944i	$-0.496645\pi$
$5$	−256.150	−	174.640i	−0.916432	−	0.624813i	−0.926971	+	0.375132i	$0.877597\pi$
$6$	415.083	+	718.945i	0.784523	+	1.35883i
$7$	380.244	−	658.602i	0.419005	−	0.725738i	−0.576835	−	0.816861i	$-0.695712\pi$
$7$	380.244	−	658.602i	0.419005	−	0.725738i	0.995840	+	0.0911232i	$0.0290457\pi$
$8$	1418.17	−	682.954i	0.979294	−	0.471603i
$9$	5151.52	+	1589.03i	2.35552	+	0.726581i
$10$	−220.939	−	2948.23i	−0.0698670	−	0.932311i
$11$	1257.82	+	5510.88i	0.284934	+	1.24838i	0.891381	+	0.453255i	$0.149737\pi$
$11$	1257.82	+	5510.88i	0.284934	+	1.24838i	−0.606447	+	0.795124i	$0.707406\pi$
$12$	1178.51	−	3002.80i	0.196879	−	0.501639i
$13$	551.467	−	7358.81i	0.0696174	−	0.928979i	−0.847611	−	0.530618i	$-0.821960\pi$
$13$	551.467	−	7358.81i	0.0696174	−	0.928979i	0.917229	−	0.398361i	$-0.130421\pi$
$14$	7171.36	−	1080.91i	0.698479	−	0.105279i
$15$	−19783.5	−	18356.4i	−1.51350	−	1.40432i
$16$	9250.88	+	4454.99i	0.564629	+	0.271911i
$17$	−29858.1	+	20356.9i	−1.47398	+	1.00494i	−0.482324	+	0.875993i	$0.660207\pi$
$17$	−29858.1	+	20356.9i	−1.47398	+	1.00494i	−0.991651	+	0.128947i	$0.958840\pi$
$18$	18782.7	+	47857.4i	0.759107	+	1.93417i
$19$	35496.0	−	10949.1i	1.18725	−	0.366218i	0.362644	−	0.931928i	$-0.381874\pi$
$19$	35496.0	−	10949.1i	1.18725	−	0.366218i	0.824604	+	0.565710i	$0.191398\pi$
$20$	−8421.35	+	7813.87i	−0.235384	+	0.218404i
$21$	41276.2	−	51758.7i	0.972595	−	1.21960i
$22$	−33609.7	+	42145.3i	−0.672954	+	0.843858i
$23$	−41179.0	+	38208.5i	−0.705713	+	0.654806i	−0.949046	−	0.315137i	$-0.897950\pi$
$23$	−41179.0	+	38208.5i	−0.705713	+	0.654806i	0.243333	+	0.969943i	$0.421759\pi$
$24$	130936.	−	40388.5i	1.93340	−	0.596374i
$25$	6571.51	+	16743.9i	0.0841153	+	0.214322i
$26$	58145.6	−	39643.0i	0.648799	−	0.442343i
$27$	251295.	+	121017.i	2.45703	+	1.18324i
$28$	−20657.8	−	19167.6i	−0.177841	−	0.165012i
$29$	−95217.0	+	14351.7i	−0.724973	+	0.109272i	−0.501153	−	0.865359i	$-0.667091\pi$
$29$	−95217.0	+	14351.7i	−0.724973	+	0.109272i	−0.223819	+	0.974631i	$0.571853\pi$
$30$	19233.1	−	256648.i	0.130055	−	1.73546i
$31$	−60890.0	+	155145.i	−0.367096	+	0.935347i	0.621317	+	0.783560i	$0.286598\pi$
$31$	−60890.0	+	155145.i	−0.367096	+	0.935347i	−0.988413	+	0.151787i	$0.951497\pi$
$32$	−23044.4	−	100964.i	−0.124320	−	0.544682i
$33$	36772.4	+	490694.i	0.178124	+	2.37690i
$34$	−329312.	−	101579.i	−1.43691	−	0.443229i
$35$	−212418.	+	102295.i	−0.837439	+	0.403289i
$36$	99884.6	−	173005.i	0.356812	−	0.618017i
$37$	−149122.	−	258286.i	−0.483988	−	0.838291i	0.515843	−	0.856683i	$-0.327479\pi$
$37$	−149122.	−	258286.i	−0.483988	−	0.838291i	−0.999831	+	0.0183918i	$0.994145\pi$
$38$	292690.	+	199553.i	0.865298	+	0.589950i
$39$	142946.	−	626288.i	0.385875	−	1.69063i
$40$	−482536.	−	72730.6i	−1.19212	−	0.179683i
$41$	43417.1	+	54443.3i	0.0983824	+	0.123368i	0.828586	−	0.559862i	$-0.189146\pi$
$41$	43417.1	+	54443.3i	0.0983824	+	0.123368i	−0.730203	+	0.683230i	$0.760575\pi$
$42$	631331.			1.31488
$43$	159770.	+	496278.i	0.306448	+	0.951887i
$43$	159770.	+	496278.i	0.306448	+	0.951887i
$44$	209462.			0.370699
$45$	−1.04205e6	−	1.30669e6i	−1.70469	−	2.13762i
$46$	−529725.	−	79843.2i	−0.802413	−	0.120944i
$47$	33686.8	−	147592.i	0.0473279	−	0.207357i	−0.945735	−	0.324938i	$-0.894657\pi$
$47$	33686.8	−	147592.i	0.0473279	−	0.207357i	0.993063	+	0.117580i	$0.0375138\pi$
$48$	738511.	+	503508.i	0.963857	+	0.657147i
$49$	122601.	+	212351.i	0.148870	+	0.257850i
$50$	−85767.8	+	148554.i	−0.0970351	+	0.168070i
$51$	−2.83429e6	+	1.36492e6i	−2.99191	+	1.44083i
$52$	−261303.	−	80601.4i	−0.257711	−	0.0794934i
$53$	11384.2	+	151911.i	0.0105036	+	0.140160i	0.999990	−	0.00446516i	$-0.00142131\pi$
$53$	11384.2	+	151911.i	0.0105036	+	0.140160i	−0.989486	+	0.144625i	$0.953802\pi$
$54$	591877.	+	2.59318e6i	0.511509	+	2.24107i
$55$	640231.	−	1.63128e6i	0.518880	−	1.32208i
$56$	89455.3	−	1.19370e6i	0.0680688	−	0.908315i
$57$	3.19754e6	−	481951.i	2.28693	−	0.344700i
$58$	−673154.	−	624596.i	−0.453019	−	0.420340i
$59$	−2.46333e6	−	1.18628e6i	−1.56150	−	0.751977i	−0.564213	−	0.825629i	$-0.690820\pi$
$59$	−2.46333e6	−	1.18628e6i	−1.56150	−	0.751977i	−0.997284	+	0.0736522i	$0.976535\pi$
$60$	−826286.	+	563352.i	−0.493857	+	0.336706i
$61$	317103.	+	807965.i	0.178873	+	0.455762i	0.991987	−	0.126344i	$-0.0403242\pi$
$61$	317103.	+	807965.i	0.178873	+	0.455762i	−0.813113	+	0.582106i	$0.802229\pi$
$62$	−1.51879e6	+	468486.i	−0.809334	+	0.249647i
$63$	3.00537e6	−	2.78858e6i	1.51428	−	1.40505i
$64$	1.43519e6	−	1.79967e6i	0.684353	−	0.858151i
$65$	−1.42640e6	+	1.78865e6i	−0.644238	+	0.807848i
$66$	−3.43992e6	+	3.19178e6i	−1.47280	+	1.36656i
$67$	−116360.	+	35892.4i	−0.0472654	+	0.0145794i	−0.318298	−	0.947991i	$-0.603111\pi$
$67$	−116360.	+	35892.4i	−0.0472654	+	0.0145794i	0.271032	+	0.962570i	$0.412635\pi$
$68$	489229.	+	1.24653e6i	0.188682	+	0.480754i
$69$	−4.04040e6	+	2.75470e6i	−1.48065	+	1.00949i
$70$	−2.02572e6	−	975534.i	−0.705888	−	0.339938i
$71$	−333795.	−	309717.i	−0.110682	−	0.102698i	0.622891	−	0.782309i	$-0.285958\pi$
$71$	−333795.	−	309717.i	−0.110682	−	0.102698i	−0.733573	+	0.679611i	$0.762149\pi$
$72$	8.39096e6	−	1.26473e6i	2.64940	−	0.399333i
$73$	−31636.1	+	422154.i	−0.00951814	+	0.127011i	−0.999939	−	0.0110730i	$-0.996475\pi$
$73$	−31636.1	+	422154.i	−0.00951814	+	0.127011i	0.990421	+	0.138084i	$0.0440943\pi$
$74$	1.03910e6	−	2.64758e6i	0.298088	−	0.759517i
$75$	348430.	+	1.52657e6i	0.0953677	+	0.417833i
$76$	−102865.	−	1.37264e6i	−0.0268795	−	0.358682i
$77$	4.10775e6	+	1.26707e6i	1.02538	+	0.316289i
$78$	5.51949e6	−	2.65805e6i	1.31695	−	0.634208i
$79$	2.06636e6	−	3.57905e6i	0.471533	−	0.816719i	−0.527937	−	0.849284i	$-0.677034\pi$
$79$	2.06636e6	−	3.57905e6i	0.471533	−	0.816719i	0.999470	+	0.0325646i	$0.0103675\pi$
$80$	−1.59160e6	−	2.75673e6i	−0.347551	−	0.601975i
$81$	1.03197e7	+	7.03587e6i	2.15760	+	1.47102i
$82$	−147771.	+	647427.i	−0.0295965	+	0.129671i
$83$	−3.82593e6	−	576666.i	−0.734452	−	0.110701i	−0.228843	−	0.973463i	$-0.573494\pi$
$83$	−3.82593e6	−	576666.i	−0.734452	−	0.110701i	−0.505609	+	0.862762i	$0.668732\pi$
$84$	−1.52953e6	−	1.91796e6i	−0.281565	−	0.353072i
$85$	1.12033e7			1.97870
$86$	−2.75023e6	+	4.14205e6i	−0.466256	+	0.702215i
$87$	−8.38244e6			−1.36475
$88$	5.54748e6	+	6.95633e6i	0.867774	+	1.08815i
$89$	9.71511e6	+	1.46432e6i	1.46077	+	0.220176i	0.830857	−	0.556486i	$-0.187851\pi$
$89$	9.71511e6	+	1.46432e6i	1.46077	+	0.220176i	0.629917	+	0.776663i	$0.283089\pi$
$90$	3.54665e6	−	1.55389e7i	0.512826	−	2.24684i
$91$	−4.63683e6	−	3.16134e6i	−0.645025	−	0.439771i
$92$	1.04080e6	+	1.80272e6i	0.139351	+	0.241363i
$93$	−7.25430e6	+	1.25648e7i	−0.935202	+	1.61982i
$94$	1.30073e6	−	626397.i	0.161525	−	0.0777862i
$95$	−1.10045e7	−	3.39443e6i	−1.31685	−	0.406194i
$96$	−673703.	−	8.98994e6i	−0.0777176	−	1.03707i
$97$	477810.	+	2.09342e6i	0.0531562	+	0.232893i	0.994527	−	0.104482i	$-0.0333183\pi$
$97$	477810.	+	2.09342e6i	0.0531562	+	0.232893i	−0.941371	+	0.337374i	$0.890461\pi$
$98$	−854297.	+	2.17671e6i	−0.0916891	+	0.233620i
$99$	−2.27727e6	+	3.03881e7i	−0.235880	+	3.14761i
$100$	659092.	−	99342.1i	0.0659092	−	0.00993421i
$101$	−8.59353e6	−	7.97363e6i	−0.829940	−	0.770072i	0.145728	−	0.989325i	$-0.453448\pi$
$101$	−8.59353e6	−	7.97363e6i	−0.829940	−	0.770072i	−0.975668	+	0.219253i	$0.929638\pi$
$102$	−2.70291e7	−	1.30165e7i	−2.52191	−	1.21449i
$103$	−1.62352e7	+	1.10690e7i	−1.46395	+	0.998105i	−0.470679	+	0.882305i	$0.655991\pi$
$103$	−1.62352e7	+	1.10690e7i	−1.46395	+	0.998105i	−0.993272	+	0.115801i	$0.963057\pi$
$104$	−4.24366e6	−	1.08127e7i	−0.369934	−	0.942576i
$105$	−1.96121e7	+	6.04952e6i	−1.65334	+	0.509986i
$106$	−1.06495e6	+	988128.i	−0.0868477	+	0.0805829i
$107$	−9.47117e6	+	1.18765e7i	−0.747413	+	0.937226i	−0.999536	−	0.0304694i	$-0.990300\pi$
$107$	−9.47117e6	+	1.18765e7i	−0.747413	+	0.937226i	0.252123	+	0.967695i	$0.418871\pi$
$108$	6.44407e6	−	8.08061e6i	0.492240	−	0.617250i
$109$	1.15336e7	−	1.07016e7i	0.853044	−	0.791509i	−0.126663	−	0.991946i	$-0.540427\pi$
$109$	1.15336e7	−	1.07016e7i	0.853044	−	0.791509i	0.979707	+	0.200437i	$0.0642361\pi$
$110$	1.59694e7	−	4.92591e6i	1.14397	−	0.352868i
$111$	−9.48521e6	−	2.41679e7i	−0.658289	−	1.67729i
$112$	6.45165e6	−	4.39866e6i	0.433918	−	0.295841i
$113$	1.65829e7	+	7.98592e6i	1.08115	+	0.520656i	0.887685	−	0.460451i	$-0.152312\pi$
$113$	1.65829e7	+	7.98592e6i	1.08115	+	0.520656i	0.193468	+	0.981107i	$0.438027\pi$
$114$	2.26056e7	+	2.09749e7i	1.42905	+	1.32597i
$115$	1.72208e7	−	2.59561e6i	1.05587	−	0.159147i
$116$	−266652.	+	3.55823e6i	−0.0158614	+	0.211656i
$117$	1.45343e7	−	3.70327e7i	0.838963	−	2.13764i
$118$	−5.80192e6	−	2.54199e7i	−0.325076	−	1.42425i
$119$	2.05373e6	+	2.74051e7i	0.111720	+	1.49079i
$120$	−4.05929e7	−	1.25212e7i	−2.14445	−	0.661474i
$121$	−1.12303e7	+	5.40825e6i	−0.576294	+	0.277529i
$122$	−4.13865e6	+	7.16836e6i	−0.206348	+	0.357405i
$123$	3.03095e6	+	5.24977e6i	0.146863	+	0.254374i
$124$	5.10282e6	+	3.47905e6i	0.240345	+	0.163864i
$125$	−4.14865e6	+	1.81764e7i	−0.189986	+	0.832384i
$126$	3.86610e7	+	5.82720e6i	1.72177	+	0.259515i
$127$	−2.53150e6	−	3.17440e6i	−0.109664	−	0.137514i	0.723970	−	0.689831i	$-0.242315\pi$
$127$	−2.53150e6	−	3.17440e6i	−0.109664	−	0.137514i	−0.833634	+	0.552317i	$0.813744\pi$
$128$	8.69592e6			0.366505
$129$	7.31404e6	+	4.47923e7i	0.299981	+	1.83713i
$130$	−2.18173e7			−0.870962
$131$	5.57772e6	+	6.99423e6i	0.216774	+	0.271826i	0.878314	−	0.478084i	$-0.158668\pi$
$131$	5.57772e6	+	6.99423e6i	0.216774	+	0.271826i	−0.661540	+	0.749909i	$0.730097\pi$
$132$	1.80304e7	+	2.71765e6i	0.682334	+	0.102845i
$133$	6.28606e6	−	2.75410e7i	0.231685	−	1.01508i
$134$	−959476.	−	654160.i	−0.0344483	−	0.0234864i
$135$	−4.32348e7	−	7.48848e7i	−1.51239	−	2.61954i
$136$	−2.84410e7	+	4.92612e7i	−0.969523	+	1.67926i
$137$	2.74269e7	−	1.32081e7i	0.911286	−	0.438852i	0.0813339	−	0.996687i	$-0.474082\pi$
$137$	2.74269e7	−	1.32081e7i	0.911286	−	0.438852i	0.829952	+	0.557835i	$0.188368\pi$
$138$	−4.45626e7	−	1.37457e7i	−1.44342	−	0.445237i
$139$	−2.60727e6	−	3.47916e7i	−0.0823443	−	1.09881i	−0.873380	−	0.487039i	$-0.838077\pi$
$139$	−2.60727e6	−	3.47916e7i	−0.0823443	−	1.09881i	0.791036	−	0.611770i	$-0.209542\pi$
$140$	1.94406e6	+	8.51749e6i	0.0598772	+	0.262339i
$141$	4.81466e6	−	1.22676e7i	0.144643	−	0.368545i
$142$	324510.	−	4.33029e6i	0.00951084	−	0.126913i
$143$	4.12472e7	−	6.21701e6i	1.17955	−	0.177789i
$144$	4.05769e7	+	3.76499e7i	1.13243	+	1.05074i
$145$	2.68963e7	+	1.29526e7i	0.732662	+	0.352832i
$146$	−3.33564e6	+	2.27420e6i	−0.0887043	+	0.0604776i
$147$	7.79830e6	+	1.98697e7i	0.202483	+	0.515919i
$148$	−1.05607e7	+	3.25754e6i	−0.267778	+	0.0825987i
$149$	−1.44562e7	+	1.34134e7i	−0.358015	+	0.332189i	−0.838589	−	0.544765i	$-0.816619\pi$
$149$	−1.44562e7	+	1.34134e7i	−0.358015	+	0.332189i	0.480574	+	0.876954i	$0.340428\pi$
$150$	−9.31025e6	+	1.16747e7i	−0.225238	+	0.282440i
$151$	1.71372e7	−	2.14894e7i	0.405061	−	0.507931i	−0.536903	−	0.843644i	$-0.680406\pi$
$151$	1.71372e7	−	2.14894e7i	0.405061	−	0.507931i	0.941964	+	0.335713i	$0.108977\pi$
$152$	4.28616e7	−	3.97698e7i	0.989956	−	0.918545i
$153$	−1.86162e8	+	5.74234e7i	−4.20214	+	1.29619i
$154$	1.49770e7	+	3.81609e7i	0.330448	+	0.841969i
$155$	4.26916e7	−	2.91067e7i	0.920835	−	0.627815i
$156$	−2.14471e7	−	1.03284e7i	−0.452307	−	0.217819i
$157$	2.12458e7	+	1.97132e7i	0.438152	+	0.406545i	0.868164	−	0.496278i	$-0.165300\pi$
$157$	2.12458e7	+	1.97132e7i	0.438152	+	0.406545i	−0.430012	+	0.902823i	$0.641491\pi$
$158$	3.89714e7	−	5.87400e6i	0.786043	−	0.118477i
$159$	−991015.	+	1.32242e7i	−0.0195520	+	0.260903i
$160$	−1.17296e7	+	2.98865e7i	−0.226393	+	0.576840i
$161$	9.50614e6	+	4.16491e7i	0.179520	+	0.786530i
$162$	8.90113e6	+	1.18777e8i	0.164491	+	2.19498i
$163$	2.05417e7	+	6.33627e6i	0.371517	+	0.114598i	0.474891	−	0.880045i	$-0.342488\pi$
$163$	2.05417e7	+	6.33627e6i	0.371517	+	0.114598i	−0.103374	+	0.994643i	$0.532964\pi$
$164$	2.32487e6	−	1.11960e6i	0.0411571	−	0.0198202i
$165$	7.62757e7	−	1.32113e8i	1.32188	−	2.28956i
$166$	−1.84490e7	−	3.19546e7i	−0.313036	−	0.542194i
$167$	−3.74036e7	−	2.55013e7i	−0.621449	−	0.423697i	0.211243	−	0.977434i	$-0.432249\pi$
$167$	−3.74036e7	−	2.55013e7i	−0.621449	−	0.423697i	−0.832692	+	0.553737i	$0.813201\pi$
$168$	2.31878e7	−	1.01592e8i	0.377291	−	1.65302i
$169$	8.19965e6	+	1.23590e6i	0.130675	+	0.0196961i
$170$	6.66135e7	+	8.35307e7i	1.03990	+	1.30399i
$171$	2.00257e8			3.06267
$172$	1.92464e7	−	1.67983e6i	0.288403	−	0.0251718i
$173$	5.52132e7			0.810740			0.405370	−	0.914153i	$-0.367143\pi$
$173$	5.52132e7			0.810740			0.405370	+	0.914153i	$0.367143\pi$
$174$	−4.98410e7	−	6.24987e7i	−0.717241	−	0.899391i
$175$	1.35264e7	+	2.03877e6i	0.190787	+	0.0287564i
$176$	−1.29149e7	+	5.65841e7i	−0.178566	+	0.782348i
$177$	−1.96651e8	−	1.34075e8i	−2.66557	−	1.81736i
$178$	4.68471e7	+	8.11416e7i	0.622606	+	1.07838i
$179$	−1.09640e7	+	1.89903e7i	−0.142884	+	0.247483i	−0.928582	−	0.371128i	$-0.878971\pi$
$179$	−1.09640e7	+	1.89903e7i	−0.142884	+	0.247483i	0.785697	+	0.618611i	$0.212304\pi$
$180$	−5.57992e7	+	2.68715e7i	−0.713139	+	0.343430i
$181$	−4.43408e7	−	1.36773e7i	−0.555813	−	0.171446i	0.00410793	−	0.999992i	$-0.498692\pi$
$181$	−4.43408e7	−	1.36773e7i	−0.555813	−	0.171446i	−0.559921	+	0.828546i	$0.689169\pi$
$182$	−3.99944e6	−	5.33688e7i	−0.0491755	−	0.656202i
$183$	1.68132e7	+	7.36635e7i	0.202802	+	0.888532i
$184$	−3.23041e7	+	8.23095e7i	−0.382292	+	0.974065i
$185$	−6.90964e6	+	9.22027e7i	−0.0802332	+	1.07064i
$186$	−1.36815e8	+	2.06216e7i	−1.55898	+	0.234978i
$187$	−1.49740e8	−	1.38939e8i	−1.67453	−	1.55374i
$188$	−5.05425e6	−	2.43400e6i	−0.0554758	−	0.0267158i
$189$	1.75255e8	−	1.19487e8i	1.88823	−	1.28737i
$190$	−4.01228e7	−	1.02231e8i	−0.424378	−	1.08130i
$191$	1.38458e8	−	4.27085e7i	1.43781	−	0.443504i	0.524721	−	0.851274i	$-0.324170\pi$
$191$	1.38458e8	−	4.27085e7i	1.43781	−	0.443504i	0.913085	+	0.407770i	$0.133693\pi$
$192$	1.46890e8	−	1.36294e8i	1.49775	−	1.38971i
$193$	2.38770e6	−	2.99409e6i	0.0239073	−	0.0299788i	−0.769734	−	0.638365i	$-0.779611\pi$
$193$	2.38770e6	−	2.99409e6i	0.0239073	−	0.0299788i	0.793641	+	0.608386i	$0.208183\pi$
$194$	−1.27674e7	+	1.60098e7i	−0.125544	+	0.157427i
$195$	−1.45991e8	+	1.35460e8i	−1.40995	+	1.30825i
$196$	8.68249e6	−	2.67819e6i	0.0823661	−	0.0254066i
$197$	−2.50108e7	−	6.37266e7i	−0.233075	−	0.593867i	0.765707	−	0.643189i	$-0.222389\pi$
$197$	−2.50108e7	−	6.37266e7i	−0.233075	−	0.593867i	−0.998783	+	0.0493224i	$0.984294\pi$
$198$	−2.40111e8	+	1.63705e8i	−2.19829	+	1.49877i
$199$	−6.64922e7	−	3.20210e7i	−0.598116	−	0.288037i	0.110227	−	0.993906i	$-0.464842\pi$
$199$	−6.64922e7	−	3.20210e7i	−0.598116	−	0.288037i	−0.708342	+	0.705869i	$0.750557\pi$
$200$	2.07549e7	+	1.92577e7i	0.183449	+	0.170216i
$201$	−1.04819e7	+	1.57990e6i	−0.0910448	+	0.0137228i
$202$	8.35448e6	−	1.11483e8i	0.0713165	−	0.951652i
$203$	−2.67537e7	+	6.81672e7i	−0.224464	+	0.571925i
$204$	2.59395e7	+	1.13649e8i	0.213923	+	0.937256i
$205$	−1.61330e6	−	2.15281e7i	−0.0130791	−	0.174528i
$206$	−1.79062e8	−	5.52332e7i	−1.42714	−	0.440215i
$207$	−2.72849e8	+	1.31397e8i	−2.13809	+	1.02965i
$208$	3.78850e7	−	6.56187e7i	0.291908	−	0.505599i
$209$	1.04987e8	+	1.81842e8i	0.795467	+	1.37779i
$210$	−1.61716e8	−	1.10256e8i	−1.20499	−	0.821551i
$211$	1.73989e7	−	7.62294e7i	0.127506	−	0.558642i	−0.870305	−	0.492514i	$-0.836078\pi$
$211$	1.73989e7	−	7.62294e7i	0.127506	−	0.558642i	0.997811	−	0.0661286i	$-0.0210648\pi$
$212$	5.58195e6	+	841344.i	0.0402356	+	0.00606454i
$213$	−2.47145e7	−	3.09911e7i	−0.175236	−	0.219739i
$214$	−1.44864e8			−1.01045
$215$	4.57450e7	−	1.55024e8i	0.313913	−	1.06381i
$216$	4.39028e8			2.96417
$217$	7.90259e7	+	9.90953e7i	0.525001	+	0.658330i
$218$	1.48367e8	+	2.23628e7i	0.969931	+	0.146194i
$219$	−8.20041e6	+	3.59283e7i	−0.0527571	+	0.231144i
$220$	−5.36539e7	−	3.65806e7i	−0.339720	−	0.231617i
$221$	1.33337e8	+	2.30946e8i	0.830954	+	1.43925i
$222$	1.23796e8	−	2.14420e8i	0.759399	−	1.31532i
$223$	−6.78379e7	+	3.26690e7i	−0.409643	+	0.197274i	−0.627345	−	0.778742i	$-0.715858\pi$
$223$	−6.78379e7	+	3.26690e7i	−0.409643	+	0.197274i	0.217702	+	0.976015i	$0.430144\pi$
$224$	−7.52577e7	−	2.32139e7i	−0.447387	−	0.138000i
$225$	7.24659e6	+	9.66990e7i	0.0424126	+	0.565957i
$226$	3.90580e7	+	1.71124e8i	0.225077	+	0.986125i
$227$	−3.51733e7	+	8.96200e7i	−0.199582	+	0.508527i	−0.995266	−	0.0971844i	$-0.969016\pi$
$227$	−3.51733e7	+	8.96200e7i	−0.199582	+	0.508527i	0.795684	+	0.605712i	$0.207112\pi$
$228$	8.95460e6	−	1.19491e8i	0.0500351	−	0.667671i
$229$	−1.12548e8	+	1.69639e7i	−0.619319	+	0.0933473i	−0.451205	−	0.892420i	$-0.649006\pi$
$229$	−1.12548e8	+	1.69639e7i	−0.619319	+	0.0933473i	−0.168114	+	0.985768i	$0.553768\pi$
$230$	1.21745e8	+	1.12963e8i	0.659789	+	0.612195i
$231$	3.37154e8	+	1.62365e8i	1.79964	+	0.866662i
$232$	−1.25232e8	+	8.53820e7i	−0.658428	+	0.448909i
$233$	−1.27222e8	−	3.24155e8i	−0.658893	−	1.67883i	−0.731823	−	0.681495i	$-0.761330\pi$
$233$	−1.27222e8	−	3.24155e8i	−0.658893	−	1.67883i	0.0729300	−	0.997337i	$-0.476765\pi$
$234$	3.62532e8	−	1.11826e8i	1.84965	−	0.570543i
$235$	−3.44044e7	+	3.19226e7i	−0.172932	+	0.160458i
$236$	−6.31684e7	+	7.92107e7i	−0.312830	+	0.392276i
$237$	2.24308e8	−	2.81273e8i	1.09452	−	1.37249i
$238$	−1.92119e8	+	1.78260e8i	−0.923742	+	0.857107i
$239$	−7.22729e7	+	2.22932e7i	−0.342439	+	0.105628i	−0.461204	−	0.887294i	$-0.652583\pi$
$239$	−7.22729e7	+	2.22932e7i	−0.342439	+	0.105628i	0.118766	+	0.992922i	$0.462106\pi$
$240$	−1.01237e8	−	2.57948e8i	−0.472716	−	1.20446i
$241$	−5.11297e6	+	3.48596e6i	−0.0235295	+	0.0160422i	−0.575028	−	0.818134i	$-0.695009\pi$
$241$	−5.11297e6	+	3.48596e6i	−0.0235295	+	0.0160422i	0.551498	+	0.834176i	$0.314056\pi$
$242$	−1.07098e8	−	5.15756e7i	−0.485765	−	0.233932i
$243$	3.49877e8	+	3.24638e8i	1.56420	+	1.45137i
$244$	3.18039e7	−	4.79367e6i	0.140158	−	0.0211254i
$245$	5.68079e6	−	7.58048e7i	0.0246790	−	0.329318i
$246$	−2.11201e7	+	5.38130e7i	−0.0904528	+	0.230470i
$247$	−6.09972e7	−	2.67246e8i	−0.257556	−	1.12842i
$248$	1.96048e7	+	2.61607e8i	0.0816170	+	1.08910i
$249$	−3.21852e8	−	9.92783e7i	−1.32117	−	0.407527i
$250$	−1.60189e8	+	7.71430e7i	−0.648400	+	0.312253i
$251$	1.77848e8	−	3.08041e8i	0.709888	−	1.22956i	−0.255010	−	0.966938i	$-0.582079\pi$
$251$	1.77848e8	−	3.08041e8i	0.709888	−	1.22956i	0.964898	−	0.262624i	$-0.0845879\pi$
$252$	−7.59610e7	−	1.31568e8i	−0.299012	−	0.517904i
$253$	−2.62358e8	−	1.78873e8i	−1.01853	−	0.694421i
$254$	8.61601e6	−	3.77492e7i	0.0329905	−	0.144541i
$255$	9.64374e8	+	1.45356e8i	3.64213	+	0.548962i
$256$	−1.32000e8	−	1.65522e8i	−0.491737	−	0.616619i
$257$	7.59792e6			0.0279208			0.0139604	−	0.999903i	$-0.495556\pi$
$257$	7.59792e6			0.0279208			0.0139604	+	0.999903i	$0.495556\pi$
$258$	−2.90479e8	+	3.20863e8i	−1.05304	+	1.16319i
$259$	−2.26810e8			−0.811173
$260$	5.28567e7	+	6.62802e7i	0.186506	+	0.233871i
$261$	−5.13317e8	−	7.73701e7i	−1.78708	−	0.269359i
$262$	−1.89839e7	+	8.31738e7i	−0.0652125	+	0.285714i
$263$	3.89368e8	+	2.65467e8i	1.31982	+	0.899839i	0.998883	−	0.0472607i	$-0.0150491\pi$
$263$	3.89368e8	+	2.65467e8i	1.31982	+	0.899839i	0.320939	+	0.947100i	$0.396002\pi$
$264$	3.87271e8	+	6.70773e8i	1.29539	+	2.24368i
$265$	2.36138e7	−	4.09003e7i	0.0779481	−	0.135010i
$266$	2.42719e8	−	1.16888e8i	0.790713	−	0.380787i
$267$	8.17274e8	+	2.52096e8i	2.62771	+	0.810543i
$268$	337205.	+	4.49969e6i	0.00107010	+	0.0142794i
$269$	−6.90458e7	−	3.02509e8i	−0.216274	−	0.947558i	−0.960204	−	0.279300i	$-0.909897\pi$
$269$	−6.90458e7	−	3.02509e8i	−0.216274	−	0.947558i	0.743930	−	0.668258i	$-0.232960\pi$
$270$	3.01265e8	−	7.67611e8i	0.931485	−	2.37338i
$271$	−8.24064e6	+	1.09964e8i	−0.0251518	+	0.335627i	0.970406	+	0.241478i	$0.0776321\pi$
$271$	−8.24064e6	+	1.09964e8i	−0.0251518	+	0.335627i	−0.995558	+	0.0941491i	$0.969987\pi$
$272$	−3.66903e8	+	5.53017e7i	−1.10550	+	0.166628i
$273$	−3.58120e8	−	3.32287e8i	−1.06527	−	0.988425i
$274$	2.61556e8	+	1.25959e8i	0.768134	+	0.369914i
$275$	−8.40080e7	+	5.72757e7i	−0.243588	+	0.166076i
$276$	6.62026e7	+	1.68681e8i	0.189537	+	0.482931i
$277$	−3.04841e8	+	9.40311e7i	−0.861776	+	0.265823i	−0.693976	−	0.719998i	$-0.744143\pi$
$277$	−3.04841e8	+	9.40311e7i	−0.861776	+	0.265823i	−0.167800	+	0.985821i	$0.553666\pi$
$278$	2.43900e8	−	2.26306e8i	0.680856	−	0.631742i
$279$	−5.60207e8	+	7.02477e8i	−1.54431	+	1.93650i
$280$	−2.31382e8	+	2.90144e8i	−0.629907	+	0.789878i
$281$	1.91200e8	−	1.77408e8i	0.514063	−	0.476981i	−0.379959	−	0.925003i	$-0.624062\pi$
$281$	1.91200e8	−	1.77408e8i	0.514063	−	0.476981i	0.894022	+	0.448022i	$0.147871\pi$
$282$	1.20093e8	−	3.70438e7i	0.318894	−	0.0983658i
$283$	−1.26932e8	−	3.23417e8i	−0.332903	−	0.848223i	−0.995098	−	0.0988914i	$-0.968470\pi$
$283$	−1.26932e8	−	3.23417e8i	−0.332903	−	0.848223i	0.662195	−	0.749331i	$-0.269625\pi$
$284$	−1.39415e7	+	9.50513e6i	−0.0361155	+	0.0246232i
$285$	−9.03218e8	−	4.34967e8i	−2.31119	−	1.11301i
$286$	2.91605e8	+	2.70569e8i	0.737078	+	0.683908i
$287$	5.23655e7	−	7.89283e6i	0.130755	−	0.0197082i
$288$	4.17217e7	−	5.56737e8i	0.102917	−	1.37334i
$289$	3.27188e8	−	8.33660e8i	0.797360	−	2.03164i
$290$	6.33491e7	+	2.77550e8i	0.152527	+	0.668265i
$291$	1.39688e7	+	1.86400e8i	0.0332302	+	0.443426i
$292$	1.49902e7	+	4.62387e6i	0.0352345	+	0.0108684i
$293$	2.55321e8	−	1.22956e8i	0.592993	−	0.285570i	−0.113220	−	0.993570i	$-0.536116\pi$
$293$	2.55321e8	−	1.22956e8i	0.592993	−	0.285570i	0.706213	+	0.708000i	$0.250402\pi$
$294$	−1.01779e8	+	1.76287e8i	−0.233584	+	0.404579i
$295$	4.23812e8	+	7.34063e8i	0.961160	+	1.66478i
$296$	−3.87877e8	−	2.64450e8i	−0.869307	−	0.592684i
$297$	−3.50827e8	+	1.53707e9i	−0.777044	+	3.40445i
$298$	−1.85963e8	−	2.80295e7i	−0.407071	−	0.0613561i
$299$	2.58461e8	+	3.24099e8i	0.559172	+	0.701179i
$300$	5.80233e7			0.124073
$301$	3.87601e8	+	8.34818e7i	0.819224	+	0.176445i
$302$	2.62119e8			0.547613
$303$	−6.36274e8	−	7.97862e8i	−1.31400	−	1.64770i
$304$	3.77147e8	+	5.68458e7i	0.769934	+	0.116049i
$305$	5.98773e7	−	2.62340e8i	0.120841	−	0.529437i
$306$	−1.53504e9	−	1.04657e9i	−3.06263	−	2.08807i
$307$	6.56422e7	+	1.13696e8i	0.129479	+	0.224264i	0.923475	−	0.383659i	$-0.125336\pi$
$307$	6.56422e7	+	1.13696e8i	0.129479	+	0.224264i	−0.793996	+	0.607923i	$0.792003\pi$
$308$	7.96467e7	−	1.37952e8i	0.155325	−	0.269030i
$309$	−1.54113e9	+	7.42169e8i	−2.97156	+	1.43103i
$310$	4.70856e8	+	1.45240e8i	0.897682	+	0.276898i
$311$	−1.53245e7	−	2.04492e8i	−0.0288886	−	0.385491i	−0.992843	−	0.119425i	$-0.961895\pi$
$311$	−1.53245e7	−	2.04492e8i	−0.0288886	−	0.385491i	0.963955	−	0.266066i	$-0.0857240\pi$
$312$	−2.25004e8	−	9.85809e8i	−0.419421	−	1.83760i
$313$	3.31098e8	−	8.43625e8i	0.610312	−	1.55505i	−0.206685	−	0.978408i	$-0.566267\pi$
$313$	3.31098e8	−	8.43625e8i	0.610312	−	1.55505i	0.816997	−	0.576642i	$-0.195637\pi$
$314$	−2.06548e7	+	2.75619e8i	−0.0376502	+	0.502407i
$315$	−1.25683e9	+	1.89436e8i	−2.26562	+	0.341488i
$316$	−1.12261e8	−	1.04163e8i	−0.200136	−	0.185699i
$317$	9.53224e8	+	4.59048e8i	1.68069	+	0.809377i	0.996813	+	0.0797797i	$0.0254217\pi$
$317$	9.53224e8	+	4.59048e8i	1.68069	+	0.809377i	0.683877	+	0.729598i	$0.260293\pi$
$318$	−1.04491e8	+	7.12405e7i	−0.182214	+	0.124232i
$319$	−1.98856e8	−	5.06678e8i	−0.342983	−	0.873905i
$320$	−6.81921e8	+	2.10345e8i	−1.16335	+	0.358845i
$321$	−9.69364e8	+	8.99438e8i	−1.63576	+	1.51776i
$322$	−2.54009e8	+	3.18518e8i	−0.423989	+	0.531665i
$323$	−8.36953e8	+	1.04951e9i	−1.38195	+	1.73291i
$324$	3.39277e8	−	3.14803e8i	0.554175	−	0.514199i
$325$	1.26839e8	−	3.91248e7i	0.204957	−	0.0632208i
$326$	7.48958e7	+	1.90831e8i	0.119728	+	0.305062i
$327$	1.13165e9	−	7.71547e8i	1.78976	−	1.22024i
$328$	9.87551e7	+	4.75579e7i	0.154526	+	0.0744157i
$329$	−8.43949e7	−	7.83070e7i	−0.130656	−	0.121231i
$330$	1.43855e9	−	2.16827e8i	2.20357	−	0.332134i
$331$	2.37569e7	−	3.17014e8i	0.0360074	−	0.480485i	−0.949828	−	0.312771i	$-0.898743\pi$
$331$	2.37569e7	−	3.17014e8i	0.0360074	−	0.480485i	0.985836	−	0.167713i	$-0.0536384\pi$
$332$	−5.23806e7	+	1.33464e8i	−0.0785575	+	0.200161i
$333$	−3.57777e8	−	1.56752e9i	−0.530955	−	2.32627i
$334$	−3.22619e7	−	4.30506e8i	−0.0473781	−	0.632217i
$335$	3.60740e7	+	1.11274e7i	0.0524249	+	0.0161710i
$336$	6.12426e8	−	2.94929e8i	0.880777	−	0.424160i
$337$	−9.10244e7	+	1.57659e8i	−0.129555	+	0.224395i	−0.923504	−	0.383588i	$-0.874688\pi$
$337$	−9.10244e7	+	1.57659e8i	−0.129555	+	0.224395i	0.793949	+	0.607984i	$0.208021\pi$
$338$	3.95394e7	+	6.84843e7i	0.0556958	+	0.0964679i
$339$	1.32384e9	+	9.02579e8i	1.84560	+	1.25831i
$340$	9.23791e7	−	4.04739e8i	0.127467	−	0.558469i
$341$	−9.31576e8	−	1.40412e8i	−1.27227	−	0.191763i
$342$	1.19070e9	+	1.49309e9i	1.60958	+	2.01835i
$343$	8.12767e8			1.08752
$344$	5.65517e8	+	5.94691e8i	0.749016	+	0.787656i
$345$	1.51603e9			1.98766
$346$	3.28291e8	+	4.11664e8i	0.426082	+	0.534290i
$347$	−8.77599e8	−	1.32277e8i	−1.12757	−	0.169954i	−0.441340	−	0.897340i	$-0.645497\pi$
$347$	−8.77599e8	−	1.32277e8i	−1.12757	−	0.169954i	−0.686228	+	0.727386i	$0.740735\pi$
$348$	−6.91192e7	+	3.02831e8i	−0.0879167	+	0.385188i
$349$	1.07607e9	+	7.33651e8i	1.35504	+	0.923848i	0.999940	−	0.0109822i	$-0.00349582\pi$
$349$	1.07607e9	+	7.33651e8i	1.35504	+	0.923848i	0.355096	+	0.934830i	$0.384448\pi$
$350$	6.52253e7	+	1.12974e8i	0.0813164	+	0.140844i
$351$	1.02912e9	−	1.78249e9i	1.27026	−	2.20015i
$352$	5.27416e8	−	2.53990e8i	0.644546	−	0.310397i
$353$	−9.36781e8	−	2.88959e8i	−1.13351	−	0.349643i	−0.329443	−	0.944176i	$-0.606861\pi$
$353$	−9.36781e8	−	2.88959e8i	−1.13351	−	0.349643i	−0.804071	+	0.594533i	$0.797337\pi$
$354$	−1.69619e8	−	2.26341e9i	−0.203218	−	2.71176i
$355$	3.14127e7	+	1.37628e8i	0.0372655	+	0.163271i
$356$	1.33009e8	−	3.38902e8i	0.156245	−	0.398106i
$357$	−1.78781e8	+	2.38567e9i	−0.207961	+	2.77505i
$358$	−2.06780e8	+	3.11671e7i	−0.238187	+	0.0359010i
$359$	9.76443e8	+	9.06007e8i	1.11382	+	1.03348i	0.999197	+	0.0400688i	$0.0127577\pi$
$359$	9.76443e8	+	9.06007e8i	1.11382	+	1.03348i	0.114627	+	0.993409i	$0.463433\pi$
$360$	−2.37022e9	−	1.14144e9i	−2.67750	−	1.28942i
$361$	4.01532e8	−	2.73760e8i	0.449205	−	0.306263i
$362$	−1.61669e8	−	4.11925e8i	−0.179121	−	0.456392i
$363$	−1.03687e9	+	3.19833e8i	−1.13776	+	0.350953i
$364$	−1.52443e8	+	1.41447e8i	−0.165674	+	0.153723i
$365$	8.18287e7	−	1.02610e8i	0.0880807	−	0.110450i
$366$	−4.49258e8	+	5.63352e8i	−0.478975	+	0.600615i
$367$	−9.75154e8	+	9.04811e8i	−1.02977	+	0.955491i	−0.999030	−	0.0440364i	$-0.985978\pi$
$367$	−9.75154e8	+	9.04811e8i	−1.02977	+	0.955491i	−0.0307443	+	0.999527i	$0.509788\pi$
$368$	−5.51161e8	+	1.70011e8i	−0.576515	+	0.177831i
$369$	1.37152e8	+	3.49457e8i	0.142105	+	0.362077i
$370$	−7.28539e8	+	4.96709e8i	−0.747733	+	0.509796i
$371$	1.04378e8	+	5.02658e7i	0.106121	+	0.0511050i
$372$	3.94110e8	+	3.65681e8i	0.396933	+	0.368300i
$373$	1.94877e9	−	2.93730e8i	1.94437	−	0.293067i	0.944957	−	0.327195i	$-0.106103\pi$
$373$	1.94877e9	−	2.93730e8i	1.94437	−	0.293067i	0.999417	+	0.0341273i	$0.0108652\pi$
$374$	1.45575e8	−	1.94257e9i	0.143892	−	1.92011i
$375$	−5.92942e8	+	1.51079e9i	−0.580635	+	1.47943i
$376$	−5.30247e7	−	2.32317e8i	−0.0514424	−	0.225384i
$377$	5.31021e7	+	7.08599e8i	0.0510408	+	0.681092i
$378$	1.93293e9	+	5.96231e8i	1.84075	+	0.567797i
$379$	−1.30257e9	+	6.27284e8i	−1.22903	+	0.591871i	−0.931813	−	0.362938i	$-0.881774\pi$
$379$	−1.30257e9	+	6.27284e8i	−1.22903	+	0.591871i	−0.297219	+	0.954809i	$0.596059\pi$
$380$	−2.13370e8	+	3.69567e8i	−0.199476	+	0.345502i
$381$	−1.76724e8	−	3.06095e8i	−0.163704	−	0.283543i
$382$	1.14168e9	+	7.78387e8i	1.04791	+	0.714454i
$383$	2.92603e8	−	1.28198e9i	0.266123	−	1.16596i	−0.648359	−	0.761335i	$-0.724544\pi$
$383$	2.92603e8	−	1.28198e9i	0.266123	−	1.16596i	0.914482	−	0.404627i	$-0.132598\pi$
$384$	7.48540e8	+	1.12824e8i	0.674615	+	0.101682i
$385$	−8.30920e8	−	1.04194e9i	−0.742073	−	0.930531i
$386$	3.65207e7			0.0323209
$387$	3.44570e7	+	2.81046e9i	0.0302196	+	2.46485i
$388$	7.95686e7			0.0691561
$389$	−8.71492e8	−	1.09282e9i	−0.750654	−	0.941290i	0.248976	−	0.968510i	$-0.419906\pi$
$389$	−8.71492e8	−	1.09282e9i	−0.750654	−	0.941290i	−0.999629	+	0.0272195i	$0.991335\pi$
$390$	−1.87802e9	−	2.83066e8i	−1.60315	−	0.241636i
$391$	4.51719e8	−	1.97911e9i	0.382164	−	1.67437i
$392$	3.18895e8	+	2.17419e8i	0.267391	+	0.182304i
$393$	3.89381e8	+	6.74428e8i	0.323594	+	0.560482i
$394$	3.26428e8	−	5.65390e8i	0.268875	−	0.465705i
$395$	−1.15435e9	+	5.55904e8i	−0.942424	+	0.453848i
$396$	1.07905e9	+	3.32842e8i	0.873188	+	0.269343i
$397$	8.37921e7	+	1.11813e9i	0.0672104	+	0.896860i	0.924294	+	0.381682i	$0.124655\pi$
$397$	8.37921e7	+	1.11813e9i	0.0672104	+	0.896860i	−0.857083	+	0.515178i	$0.827726\pi$
$398$	−1.56610e8	−	6.86153e8i	−0.124517	−	0.545545i
$399$	8.98430e8	−	2.28916e9i	0.708074	−	1.80414i
$400$	−1.38018e7	+	1.84172e8i	−0.0107827	+	0.143885i
$401$	−8.18911e8	+	1.23431e8i	−0.634207	+	0.0955914i	−0.458274	−	0.888811i	$-0.651532\pi$
$401$	−8.18911e8	+	1.23431e8i	−0.634207	+	0.0955914i	−0.175933	+	0.984402i	$0.556294\pi$
$402$	−7.41039e7	−	6.87584e7i	−0.0568919	−	0.0527879i
$403$	1.10811e9	+	5.33636e8i	0.843361	+	0.406141i
$404$	−3.58922e8	+	2.44709e8i	−0.270810	+	0.184635i
$405$	−1.41465e9	−	3.60448e9i	−1.05818	−	2.69619i
$406$	−6.67322e8	+	2.05842e8i	−0.494874	+	0.152648i
$407$	1.23582e9	−	1.14667e9i	0.908601	−	0.843058i
$408$	−3.08732e9	+	3.87138e9i	−2.25046	+	2.82199i
$409$	1.21549e8	−	1.52418e8i	0.0878456	−	0.110155i	−0.735966	−	0.677018i	$-0.763272\pi$
$409$	1.21549e8	−	1.52418e8i	0.0878456	−	0.110155i	0.823812	+	0.566863i	$0.191843\pi$
$410$	1.50919e8	−	1.40032e8i	0.108143	−	0.100342i
$411$	2.53226e9	−	7.81099e8i	1.79913	−	0.554958i
$412$	2.66016e8	+	6.77797e8i	0.187399	+	0.477484i
$413$	−1.71795e9	+	1.17128e9i	−1.20001	+	0.818155i
$414$	−2.60201e9	−	1.25306e9i	−1.80222	−	0.867904i
$415$	8.79304e8	+	8.15875e8i	0.603908	+	0.560345i
$416$	−7.55685e8	+	1.13901e8i	−0.514653	+	0.0775714i
$417$	2.26967e8	−	3.02867e9i	0.153281	−	2.04539i
$418$	−7.31559e8	+	1.86398e9i	−0.489928	+	1.24832i
$419$	−5.27469e8	−	2.31099e9i	−0.350306	−	1.53479i	−0.776476	−	0.630147i	$-0.782994\pi$
$419$	−5.27469e8	−	2.31099e9i	−0.350306	−	1.53479i	0.426170	−	0.904643i	$-0.359863\pi$
$420$	5.68346e7	+	7.58405e8i	0.0374317	+	0.499492i
$421$	1.07139e9	+	3.30480e8i	0.699778	+	0.215853i	0.624174	−	0.781285i	$-0.285436\pi$
$421$	1.07139e9	+	3.30480e8i	0.699778	+	0.215853i	0.0756034	+	0.997138i	$0.475912\pi$
$422$	6.71811e8	−	3.23527e8i	0.435165	−	0.209564i
$423$	4.08066e8	−	7.06791e8i	0.262144	−	0.454046i
$424$	1.19893e8	+	2.07661e8i	0.0763861	+	0.132305i
$425$	−5.37067e8	−	3.66166e8i	−0.339365	−	0.231375i
$426$	8.41165e7	−	3.68539e8i	0.0527167	−	0.230967i
$427$	6.52703e8	+	9.83792e7i	0.405712	+	0.0611513i
$428$	3.50963e8	+	4.40093e8i	0.216375	+	0.271326i
$429$	3.63120e9			2.22049
$430$	1.42784e9	−	5.80686e8i	0.866044	−	0.352210i
$431$	3.03348e8			0.182503			0.0912517	−	0.995828i	$-0.470913\pi$
$431$	3.03348e8			0.182503			0.0912517	+	0.995828i	$0.470913\pi$
$432$	1.78557e9	+	2.23903e9i	1.06557	+	1.33619i
$433$	2.51574e8	+	3.79187e7i	0.148922	+	0.0224463i	0.223080	−	0.974800i	$-0.428389\pi$
$433$	2.51574e8	+	3.79187e7i	0.148922	+	0.0224463i	−0.0741583	+	0.997246i	$0.523627\pi$
$434$	−2.68966e8	+	1.17842e9i	−0.157937	+	0.691967i
$435$	2.14717e9	+	1.46391e9i	1.25070	+	0.852713i
$436$	−2.91512e8	−	5.04914e8i	−0.168443	−	0.291753i
$437$	−1.04334e9	+	1.80712e9i	−0.598055	+	1.03586i
$438$	−3.16637e8	+	1.52484e8i	−0.180054	+	0.0867094i
$439$	−2.12980e9	−	6.56956e8i	−1.20147	−	0.370604i	−0.371511	−	0.928429i	$-0.621160\pi$
$439$	−2.12980e9	−	6.56956e8i	−1.20147	−	0.370604i	−0.829959	+	0.557824i	$0.811636\pi$
$440$	−2.06135e8	−	2.75068e9i	−0.115363	−	1.53942i
$441$	2.94148e8	+	1.28875e9i	0.163317	+	0.715537i
$442$	−9.29107e8	+	2.36733e9i	−0.511785	+	1.30401i
$443$	2.17111e8	−	2.89715e9i	0.118650	−	1.58328i	−0.547077	−	0.837083i	$-0.684259\pi$
$443$	2.17111e8	−	2.89715e9i	0.118650	−	1.58328i	0.665727	−	0.746195i	$-0.268122\pi$
$444$	−9.51322e8	+	1.43389e8i	−0.515807	+	0.0777454i
$445$	−2.23280e9	−	2.07174e9i	−1.20113	−	1.11449i
$446$	−6.46934e8	−	3.11547e8i	−0.345293	−	0.166284i
$447$	−1.41841e9	+	9.67056e8i	−0.751148	+	0.512124i
$448$	−6.39545e8	−	1.62953e9i	−0.336046	−	0.856230i
$449$	−1.26329e9	+	3.89673e8i	−0.658628	+	0.203160i	−0.606013	−	0.795455i	$-0.707232\pi$
$449$	−1.26329e9	+	3.89673e8i	−0.658628	+	0.203160i	−0.0526154	+	0.998615i	$0.516756\pi$
$450$	−6.77891e8	+	6.28991e8i	−0.350684	+	0.325387i
$451$	−2.45420e8	+	3.07746e8i	−0.125977	+	0.157970i
$452$	4.25244e8	−	5.33240e8i	0.216598	−	0.271605i
$453$	1.75398e9	−	1.62745e9i	0.886502	−	0.822554i
$454$	−8.77334e8	+	2.70622e8i	−0.440017	+	0.135727i
$455$	6.35629e8	+	1.61956e9i	0.316347	+	0.806040i
$456$	4.20550e9	−	2.86726e9i	2.07702	−	1.41609i
$457$	−8.49227e8	−	4.08966e8i	−0.416215	−	0.200438i	0.214043	−	0.976824i	$-0.431337\pi$
$457$	−8.49227e8	−	4.08966e8i	−0.416215	−	0.200438i	−0.630258	+	0.776386i	$0.717051\pi$
$458$	−7.95680e8	−	7.38283e8i	−0.386999	−	0.359082i
$459$	−9.96671e9	+	1.50224e9i	−4.81069	+	0.725095i
$460$	4.82262e7	−	6.43534e8i	0.0231010	−	0.308262i
$461$	−1.38027e8	+	3.51688e8i	−0.0656163	+	0.167188i	−0.959921	−	0.280271i	$-0.909576\pi$
$461$	−1.38027e8	+	3.51688e8i	−0.0656163	+	0.167188i	0.894305	+	0.447459i	$0.147671\pi$
$462$	7.94103e8	+	3.47919e9i	0.374653	+	1.64146i
$463$	−1.77351e7	−	2.36659e8i	−0.00830426	−	0.110813i	0.991511	−	0.130021i	$-0.0415045\pi$
$463$	−1.77351e7	−	2.36659e8i	−0.00830426	−	0.110813i	−0.999816	+	0.0192083i	$0.993885\pi$
$464$	−9.44778e8	−	2.91425e8i	−0.439053	−	0.135430i
$465$	4.05252e9	−	1.95159e9i	1.86913	−	0.900126i
$466$	1.66043e9	−	2.87594e9i	0.760096	−	1.31653i
$467$	−5.83746e8	−	1.01108e9i	−0.265225	−	0.459383i	0.702398	−	0.711785i	$-0.252113\pi$
$467$	−5.83746e8	−	1.01108e9i	−0.265225	−	0.459383i	−0.967623	+	0.252402i	$0.918780\pi$
$468$	−1.21803e9	−	8.30439e8i	−0.549285	−	0.374496i
$469$	−2.06065e7	+	9.02830e7i	−0.00922358	+	0.0404111i
$470$	−4.42576e8	−	6.67076e7i	−0.196628	−	0.0296369i
$471$	1.57306e9	+	1.97256e9i	0.693701	+	0.869874i
$472$	−4.30360e9			−1.88380
$473$	−2.53397e9	+	1.50470e9i	−1.10100	+	0.653788i
$474$	3.43085e9			1.47971
$475$	4.16593e8	+	5.22391e8i	0.178354	+	0.223649i
$476$	1.00700e9	+	1.51780e8i	0.427960	+	0.0645046i
$477$	−1.82746e8	+	8.00664e8i	−0.0770965	+	0.337782i
$478$	−5.95943e8	−	4.06307e8i	−0.249578	−	0.170160i
$479$	1.63020e9	+	2.82359e9i	0.677745	+	1.17389i	0.975658	+	0.219296i	$0.0703760\pi$
$479$	1.63020e9	+	2.82359e9i	0.677745	+	1.17389i	−0.297913	+	0.954593i	$0.596291\pi$
$480$	−1.39744e9	+	2.42043e9i	−0.576751	+	0.998962i
$481$	−1.98291e9	+	9.54921e8i	−0.812449	+	0.391255i
$482$	−5.63922e7	−	1.73947e7i	−0.0229379	−	0.00707541i
$483$	2.77912e8	+	3.70847e9i	0.112226	+	1.49755i
$484$	1.02781e8	+	4.50312e8i	0.0412053	+	0.180532i
$485$	2.43205e8	−	6.19676e8i	0.0968002	−	0.246643i
$486$	−3.40144e8	+	4.53891e9i	−0.134411	+	1.79359i
$487$	−3.18944e9	+	4.80731e8i	−1.25131	+	0.188604i	−0.741068	−	0.671430i	$-0.765681\pi$
$487$	−3.18944e9	+	4.80731e8i	−1.25131	+	0.188604i	−0.510237	+	0.860034i	$0.670442\pi$
$488$	1.00151e9	+	9.29264e8i	0.390108	+	0.361968i
$489$	1.68601e9	+	8.11939e8i	0.652047	+	0.314009i
$490$	5.98971e8	−	4.08372e8i	0.229996	−	0.156808i
$491$	−3.69212e8	−	9.40737e8i	−0.140764	−	0.358660i	0.843055	−	0.537827i	$-0.180755\pi$
$491$	−3.69212e8	−	9.40737e8i	−0.140764	−	0.358660i	−0.983819	+	0.179168i	$0.942660\pi$
$492$	2.14650e8	−	6.62107e7i	0.0812555	−	0.0250640i
$493$	2.55084e9	−	2.36683e9i	0.958780	−	0.889618i
$494$	1.62988e9	−	2.04381e9i	0.608291	−	0.762773i
$495$	5.89032e9	−	7.38622e9i	2.18283	−	2.73719i
$496$	−1.25446e9	+	1.16397e9i	−0.461604	+	0.428306i
$497$	−3.30903e8	+	1.02070e8i	−0.120908	+	0.0372951i
$498$	−1.17349e9	−	2.99000e9i	−0.425771	−	1.08485i
$499$	−1.24899e9	+	8.51548e8i	−0.449995	+	0.306801i	−0.767028	−	0.641613i	$-0.778266\pi$
$499$	−1.24899e9	+	8.51548e8i	−0.449995	+	0.306801i	0.317034	+	0.948414i	$0.397313\pi$
$500$	6.22448e8	+	2.99755e8i	0.222694	+	0.107244i
$501$	−2.88882e9	−	2.68043e9i	−1.02633	−	0.952298i
$502$	3.35419e9	−	5.05562e8i	1.18338	−	0.178366i
$503$	−3.84133e8	+	5.12590e9i	−0.134584	+	1.79590i	0.366415	+	0.930452i	$0.380585\pi$
$503$	−3.84133e8	+	5.12590e9i	−0.134584	+	1.79590i	−0.500999	+	0.865448i	$0.667034\pi$
$504$	2.35765e9	−	6.00720e9i	0.820301	−	2.09009i
$505$	8.08718e8	+	3.54323e9i	0.279433	+	1.22428i
$506$	−2.26294e8	−	3.01968e9i	−0.0776507	−	1.03618i
$507$	6.89787e8	+	2.12771e8i	0.235065	+	0.0725078i
$508$	−1.35555e8	+	6.52798e7i	−0.0458767	+	0.0220931i
$509$	−5.20686e7	+	9.01855e7i	−0.0175010	+	0.0303127i	−0.874643	−	0.484767i	$-0.838904\pi$
$509$	−5.20686e7	+	9.01855e7i	−0.0175010	+	0.0303127i	0.857142	+	0.515080i	$0.172238\pi$
$510$	4.65030e9	+	8.05455e9i	1.55233	+	2.68872i
$511$	2.66002e8	+	1.81357e8i	0.0881884	+	0.0601258i
$512$	6.96947e8	−	3.05352e9i	0.229485	−	1.00544i
$513$	1.02450e10	+	1.54418e9i	3.35043	+	0.504996i
$514$	4.51763e7	+	5.66493e7i	0.0146737	+	0.0184003i
$515$	6.09173e9			1.96524
$516$	1.67851e9	+	1.05112e8i	0.537837	+	0.0336804i
$517$	8.55732e8			0.272346
$518$	−1.34859e9	−	1.69108e9i	−0.426309	−	0.534575i
$519$	4.75273e9	+	7.16358e8i	1.49230	+	0.224929i
$520$	−8.01314e8	+	3.51079e9i	−0.249914	+	1.09495i
$521$	−1.48688e9	−	1.01374e9i	−0.460620	−	0.314045i	0.310683	−	0.950514i	$-0.399442\pi$
$521$	−1.48688e9	−	1.01374e9i	−0.460620	−	0.314045i	−0.771303	+	0.636468i	$0.780395\pi$
$522$	−2.47526e9	−	4.28728e9i	−0.761683	−	1.31927i
$523$	1.22788e9	−	2.12675e9i	0.375318	−	0.650071i	−0.615056	−	0.788483i	$-0.710867\pi$
$523$	1.22788e9	−	2.12675e9i	0.375318	−	0.650071i	0.990375	+	0.138413i	$0.0442000\pi$
$524$	2.98672e8	−	1.43833e8i	0.0906848	−	0.0436715i
$525$	1.13789e9	+	3.50993e8i	0.343197	+	0.105862i
$526$	3.35844e8	+	4.48153e9i	0.100621	+	1.34269i
$527$	−1.34022e9	−	5.87187e9i	−0.398876	−	1.74759i
$528$	−1.84586e9	+	4.70317e9i	−0.545732	+	1.39050i
$529$	−1.86246e7	+	2.48528e8i	−0.00547006	+	0.0729929i
$530$	4.45354e8	−	6.71263e7i	0.129939	−	0.0195852i
$531$	−1.08049e10	−	1.00254e10i	−3.13176	−	2.90585i
$532$	−9.43137e8	−	4.54191e8i	−0.271571	−	0.130782i
$533$	4.24581e8	−	2.89475e8i	0.121455	−	0.0828066i
$534$	2.97982e9	+	7.59245e9i	0.846828	+	2.15768i
$535$	4.50016e9	−	1.38811e9i	1.27054	−	0.391911i
$536$	−1.40506e8	+	1.30370e8i	−0.0394110	+	0.0365681i
$537$	−1.19017e9	+	1.49242e9i	−0.331663	+	0.415893i
$538$	1.84494e9	−	2.31349e9i	0.510793	−	0.640514i
$539$	−1.01603e9	+	9.42738e8i	−0.279477	+	0.259317i
$540$	−3.06185e9	+	9.44457e8i	−0.836770	+	0.258109i
$541$	−1.15057e9	−	2.93160e9i	−0.312408	−	0.796003i	−0.997703	−	0.0677373i	$-0.978422\pi$
$541$	−1.15057e9	−	2.93160e9i	−0.312408	−	0.796003i	0.685295	−	0.728265i	$-0.259673\pi$
$542$	−8.68877e8	+	5.92390e8i	−0.234402	+	0.159812i
$543$	−3.63938e9	−	1.75263e9i	−0.975503	−	0.469777i
$544$	2.74338e9	+	2.54548e9i	0.730617	+	0.677913i
$545$	−4.82326e9	+	7.26990e8i	−1.27630	+	0.192371i
$546$	3.48158e8	−	4.64585e9i	0.0915382	−	1.22149i
$547$	−2.25029e9	+	5.73364e9i	−0.587872	+	1.49787i	0.258894	+	0.965906i	$0.416642\pi$
$547$	−2.25029e9	+	5.73364e9i	−0.587872	+	1.49787i	−0.846765	+	0.531967i	$0.821453\pi$
$548$	−2.51012e8	−	1.09976e9i	−0.0651573	−	0.285473i
$549$	3.49678e8	+	4.66613e9i	0.0901914	+	1.20352i
$550$	−9.26544e8	−	2.85801e8i	−0.237463	−	0.0732478i
$551$	−3.22269e9	+	1.55196e9i	−0.820705	+	0.395231i
$552$	−3.84864e9	+	6.66604e9i	−0.973914	+	1.68687i
$553$	−1.57144e9	−	2.72182e9i	−0.395149	−	0.684419i
$554$	−2.51364e9	−	1.71377e9i	−0.628085	−	0.428221i
$555$	−1.79105e9	+	7.84712e9i	−0.444717	+	1.94843i
$556$	−1.27841e9	−	1.92689e8i	−0.315433	−	0.0475439i
$557$	1.25683e9	+	1.57602e9i	0.308166	+	0.386428i	0.911664	−	0.410937i	$-0.134798\pi$
$557$	1.25683e9	+	1.57602e9i	0.308166	+	0.386428i	−0.603498	+	0.797364i	$0.706227\pi$
$558$	−8.56853e9			−2.08779
$559$	3.74013e9	−	9.02039e8i	0.905618	−	0.218416i
$560$	−2.42078e9			−0.582501
$561$	−1.10869e10	−	1.39026e10i	−2.65120	−	3.32449i
$562$	2.45959e9	+	3.70724e8i	0.584502	+	0.0880996i
$563$	−1.47376e9	+	6.45697e9i	−0.348055	+	1.52493i	0.433536	+	0.901136i	$0.357266\pi$
$563$	−1.47376e9	+	6.45697e9i	−0.348055	+	1.52493i	−0.781590	+	0.623792i	$0.785591\pi$
$564$	−4.03488e8	−	2.75093e8i	−0.0947007	−	0.0645659i
$565$	−2.85306e9	−	4.94165e9i	−0.665490	−	1.15266i
$566$	1.65664e9	−	2.86939e9i	0.384035	−	0.665169i
$567$	8.55784e9	−	4.12124e9i	1.97162	−	0.949483i
$568$	−6.84900e8	−	2.11264e8i	−0.156822	−	0.0483733i
$569$	3.42220e8	+	4.56661e9i	0.0778776	+	1.03920i	0.890073	+	0.455818i	$0.150653\pi$
$569$	3.42220e8	+	4.56661e9i	0.0778776	+	1.03920i	−0.812195	+	0.583386i	$0.801728\pi$
$570$	−2.12736e9	−	9.32058e9i	−0.481149	−	2.10805i
$571$	−2.57786e9	+	6.56828e9i	−0.579473	+	1.47647i	0.277302	+	0.960783i	$0.410560\pi$
$571$	−2.57786e9	+	6.56828e9i	−0.579473	+	1.47647i	−0.856775	+	0.515690i	$0.827536\pi$
$572$	1.15511e8	−	1.54139e9i	0.0258071	−	0.344372i
$573$	1.24725e10	−	1.87993e9i	2.76957	−	0.417445i
$574$	3.70208e8	+	3.43503e8i	0.0817060	+	0.0758121i
$575$	−9.10369e8	−	4.38411e8i	−0.199701	−	0.0961709i
$576$	1.02532e10	−	6.99048e9i	2.23552	−	1.52415i
$577$	−3.76911e8	−	9.60353e8i	−0.0816814	−	0.208121i	0.884198	−	0.467112i	$-0.154705\pi$
$577$	−3.76911e8	−	9.60353e8i	−0.0816814	−	0.208121i	−0.965880	+	0.258991i	$0.916610\pi$
$578$	8.16111e9	−	2.51737e9i	1.75793	−	0.542250i
$579$	2.44379e8	−	2.26751e8i	0.0523226	−	0.0485482i
$580$	6.89714e8	−	8.64874e8i	0.146781	−	0.184058i
$581$	−1.83458e9	+	2.30049e9i	−0.388079	+	0.486636i
$582$	−1.30673e9	+	1.21246e9i	−0.274760	+	0.254940i
$583$	−8.22847e8	+	2.53815e8i	−0.171980	+	0.0530489i
$584$	2.43446e8	+	6.20291e8i	0.0505776	+	0.128870i
$585$	−1.01904e10	+	6.94768e9i	−2.10448	+	1.43481i
$586$	2.43486e9	+	1.17257e9i	0.499841	+	0.240711i
$587$	3.08198e9	+	2.85966e9i	0.628921	+	0.583554i	0.928872	−	0.370401i	$-0.120780\pi$
$587$	3.08198e9	+	2.85966e9i	0.628921	+	0.583554i	−0.299951	+	0.953955i	$0.596970\pi$
$588$	7.82133e8	−	1.17888e8i	0.158657	−	0.0239137i
$589$	−4.62657e8	+	6.17372e9i	−0.0932943	+	1.24493i
$590$	−2.95317e9	+	7.52456e9i	−0.591979	+	1.50834i
$591$	−1.32611e9	−	5.81006e9i	−0.264255	−	1.15778i
$592$	−2.28844e8	−	3.05371e9i	−0.0453329	−	0.604925i
$593$	2.53694e9	+	7.82542e8i	0.499595	+	0.154105i	0.534303	−	0.845293i	$-0.320574\pi$
$593$	2.53694e9	+	7.82542e8i	0.499595	+	0.154105i	−0.0347081	+	0.999397i	$0.511050\pi$
$594$	−1.35463e10	+	6.52353e9i	−2.65196	+	1.27712i
$595$	4.25998e9	−	7.37850e9i	0.829084	−	1.43601i
$596$	3.65381e8	+	6.32858e8i	0.0706942	+	0.122446i
$597$	−5.30817e9	−	3.61905e9i	−1.02102	−	0.696120i
$598$	−8.79677e8	+	3.85411e9i	−0.168217	+	0.737005i
$599$	2.81776e9	+	4.24708e8i	0.535685	+	0.0807415i	0.411313	−	0.911494i	$-0.365070\pi$
$599$	2.81776e9	+	4.24708e8i	0.535685	+	0.0807415i	0.124372	+	0.992236i	$0.460308\pi$
$600$	1.53671e9	+	1.92698e9i	0.290444	+	0.364206i
$601$	−4.37885e9			−0.822810			−0.411405	−	0.911453i	$-0.634962\pi$
$601$	−4.37885e9			−0.822810			−0.411405	+	0.911453i	$0.634962\pi$
$602$	1.68220e9	+	3.38629e9i	0.314261	+	0.632611i
$603$	−6.56467e8			−0.121928
$604$	−6.35035e8	−	7.96309e8i	−0.117265	−	0.147046i
$605$	3.82116e9	+	5.75947e8i	0.701538	+	0.105740i
$606$	2.16557e9	−	9.48800e9i	0.395293	−	1.73189i
$607$	−1.51012e9	−	1.02958e9i	−0.274063	−	0.186853i	0.418487	−	0.908223i	$-0.362560\pi$
$607$	−1.51012e9	−	1.02958e9i	−0.274063	−	0.186853i	−0.692550	+	0.721370i	$0.743513\pi$
$608$	−1.92345e9	−	3.33151e9i	−0.347071	−	0.601144i
$609$	−3.18737e9	+	5.52069e9i	−0.571837	+	0.990451i
$610$	2.31200e9	−	1.11340e9i	0.412414	−	0.198608i
$611$	−1.06752e9	−	3.29287e8i	−0.189336	−	0.0584023i
$612$	5.39486e8	+	7.19894e9i	0.0951371	+	1.26952i
$613$	2.31736e9	+	1.01530e10i	0.406332	+	1.78026i	0.600853	+	0.799359i	$0.294828\pi$
$613$	2.31736e9	+	1.01530e10i	0.406332	+	1.78026i	−0.194521	+	0.980898i	$0.562315\pi$
$614$	−4.57403e8	+	1.16544e9i	−0.0797462	+	0.203190i
$615$	1.40441e8	−	1.87406e9i	0.0243462	−	0.324878i
$616$	6.69084e9	−	1.00848e9i	1.15332	−	0.173834i
$617$	1.02049e9	+	9.46880e8i	0.174909	+	0.162292i	0.762770	−	0.646670i	$-0.223839\pi$
$617$	1.02049e9	+	9.46880e8i	0.174909	+	0.162292i	−0.587860	+	0.808962i	$0.700030\pi$
$618$	−1.46969e10	−	7.07766e9i	−2.50476	−	1.20623i
$619$	4.60345e8	−	3.13858e8i	0.0780128	−	0.0531882i	−0.523686	−	0.851912i	$-0.675443\pi$
$619$	4.60345e8	−	3.13858e8i	0.0780128	−	0.0531882i	0.601698	+	0.798723i	$0.294491\pi$
$620$	−6.99509e8	−	1.78232e9i	−0.117875	−	0.300341i
$621$	−1.49720e10	+	4.61824e9i	−2.50875	+	0.773848i
$622$	1.43355e9	−	1.33014e9i	0.238862	−	0.221632i
$623$	4.65851e9	−	5.84159e9i	0.771861	−	0.967883i
$624$	4.11249e9	−	5.15690e9i	0.677577	−	0.849654i
$625$	5.26715e9	−	4.88720e9i	0.862969	−	0.800719i
$626$	8.25866e9	−	2.54746e9i	1.34555	−	0.415047i
$627$	6.67791e9	+	1.70150e10i	1.08194	+	2.75674i
$628$	8.87363e8	−	6.04994e8i	0.142969	−	0.0974748i
$629$	9.71038e9	+	4.67627e9i	1.55582	+	0.749243i
$630$	−8.88536e9	−	8.24441e9i	−1.41574	−	1.31361i
$631$	−2.80093e9	+	4.22172e8i	−0.443813	+	0.0668940i	−0.367147	−	0.930163i	$-0.619665\pi$
$631$	−2.80093e9	+	4.22172e8i	−0.443813	+	0.0668940i	−0.0766655	+	0.997057i	$0.524427\pi$
$632$	4.86128e8	−	6.48693e9i	0.0766022	−	1.02218i
$633$	2.48672e9	−	6.33605e9i	0.389685	−	0.992901i
$634$	2.24514e9	+	9.83660e9i	0.349889	+	1.53297i
$635$	9.40661e7	+	1.25523e9i	0.0145789	+	0.194542i
$636$	4.69576e8	+	1.44845e8i	0.0723779	+	0.0223256i
$637$	1.63026e9	−	7.85092e8i	0.249902	−	0.120346i
$638$	2.59536e9	−	4.49530e9i	0.395663	−	0.685309i
$639$	−1.22740e9	−	2.12592e9i	−0.186094	−	0.322325i
$640$	−2.22746e9	−	1.51866e9i	−0.335877	−	0.228997i
$641$	−4.34582e7	+	1.90403e8i	−0.00651731	+	0.0285542i	−0.978082	−	0.208220i	$-0.933233\pi$
$641$	−4.34582e7	+	1.90403e8i	−0.00651731	+	0.0285542i	0.971565	+	0.236774i	$0.0760902\pi$
$642$	−1.24699e10	−	1.87953e9i	−1.85990	−	0.280334i
$643$	−3.38362e9	−	4.24293e9i	−0.501931	−	0.629401i	0.464733	−	0.885451i	$-0.346150\pi$
$643$	−3.38362e9	−	4.24293e9i	−0.501931	−	0.629401i	−0.966664	+	0.256050i	$0.917579\pi$
$644$	1.58303e9			0.233555
$645$	5.94906e9	−	1.27509e10i	0.872949	−	1.87103i
$646$	−1.28014e10			−1.86829
$647$	4.30183e9	+	5.39433e9i	0.624437	+	0.783019i	0.988961	−	0.148175i	$-0.0473399\pi$
$647$	4.30183e9	+	5.39433e9i	0.624437	+	0.783019i	−0.364525	+	0.931194i	$0.618768\pi$
$648$	1.94403e10	+	2.93015e9i	2.80666	+	0.423036i
$649$	3.43900e9	−	1.50673e10i	0.493829	−	2.16360i
$650$	1.04588e9	+	7.13072e8i	0.149378	+	0.101844i
$651$	5.51681e9	+	9.55539e9i	0.783708	+	1.35742i
$652$	3.98290e8	−	6.89858e8i	0.0562772	−	0.0974750i
$653$	−1.27569e10	+	6.14338e9i	−1.79286	+	0.863398i	−0.852944	+	0.522002i	$0.825185\pi$
$653$	−1.27569e10	+	6.14338e9i	−1.79286	+	0.863398i	−0.939920	+	0.341396i	$0.889100\pi$
$654$	1.24813e10	+	3.84996e9i	1.74476	+	0.538188i
$655$	−2.07258e8	−	2.76567e9i	−0.0288182	−	0.384553i
$656$	1.59102e8	+	6.97071e8i	0.0220045	+	0.0964082i
$657$	−8.33789e8	+	2.12446e9i	−0.114704	+	0.292260i
$658$	8.20473e7	−	1.09484e9i	0.0112273	−	0.149817i
$659$	2.21932e9	−	3.34508e8i	0.302079	−	0.0455311i	0.00374621	−	0.999993i	$-0.498808\pi$
$659$	2.21932e9	−	3.34508e8i	0.302079	−	0.0455311i	0.298333	+	0.954462i	$0.403569\pi$
$660$	−4.14389e9	−	3.84497e9i	−0.561053	−	0.520582i
$661$	−6.79304e9	−	3.27135e9i	−0.914869	−	0.440578i	−0.0836323	−	0.996497i	$-0.526652\pi$
$661$	−6.79304e9	−	3.27135e9i	−0.914869	−	0.440578i	−0.831236	+	0.555919i	$0.812366\pi$
$662$	2.50488e9	−	1.70780e9i	0.335570	−	0.228788i
$663$	8.48118e9	+	2.16097e10i	1.13021	+	2.87973i
$664$	−5.81965e9	+	1.79513e9i	−0.771452	+	0.237961i
$665$	−6.41995e9	+	5.95685e9i	−0.846557	+	0.785490i
$666$	9.56001e9	−	1.19879e10i	1.25400	−	1.57247i
$667$	3.37259e9	−	4.22909e9i	0.440071	−	0.551831i
$668$	−1.22970e9	+	1.14100e9i	−0.159618	+	0.148104i
$669$	−6.26332e9	+	1.93198e9i	−0.808748	+	0.249466i
$670$	1.31528e8	+	3.35127e8i	0.0168949	+	0.0430474i
$671$	−4.05374e9	+	2.76379e9i	−0.517996	+	0.353164i
$672$	−6.17696e9	−	2.97467e9i	−0.785204	−	0.378134i
$673$	1.02305e10	+	9.49248e9i	1.29373	+	1.20040i	0.966853	+	0.255334i	$0.0821854\pi$
$673$	1.02305e10	+	9.49248e9i	1.29373	+	1.20040i	0.326873	+	0.945068i	$0.394005\pi$
$674$	−1.71671e9	+	2.58753e8i	−0.215967	+	0.0325518i
$675$	−3.74918e8	+	5.00293e9i	−0.0469216	+	0.626125i
$676$	1.12261e8	−	2.86036e8i	0.0139771	−	0.0356129i
$677$	−2.40511e9	−	1.05375e10i	−0.297903	−	1.30520i	−0.873243	−	0.487285i	$-0.837987\pi$
$677$	−2.40511e9	−	1.05375e10i	−0.297903	−	1.30520i	0.575340	−	0.817915i	$-0.304870\pi$
$678$	1.14186e9	+	1.52371e10i	0.140705	+	1.87757i
$679$	1.56042e9	+	4.81324e8i	0.191292	+	0.0590057i
$680$	1.58882e10	−	7.65134e9i	1.93773	−	0.933160i
$681$	−4.19046e9	+	7.25810e9i	−0.508449	+	0.880659i
$682$	−4.49214e9	−	7.78062e9i	−0.542261	−	0.939223i
$683$	7.88179e9	+	5.37372e9i	0.946570	+	0.645360i	0.935028	−	0.354573i	$-0.115374\pi$
$683$	7.88179e9	+	5.37372e9i	0.946570	+	0.645360i	0.0115415	+	0.999933i	$0.496326\pi$
$684$	1.65126e9	−	7.23463e9i	0.197296	−	0.864411i
$685$	−9.33208e9	−	1.40658e9i	−1.10933	−	0.167205i
$686$	4.83262e9	+	6.05991e9i	0.571542	+	0.716691i
$687$	−9.90820e9			−1.16586
$688$	−7.32899e8	+	5.30279e9i	−0.0857994	+	0.620790i
$689$	1.12417e9			0.130937
$690$	9.01416e9	+	1.13034e10i	1.04461	+	1.30990i
$691$	1.51743e10	+	2.28715e9i	1.74958	+	0.263707i	0.944277	−	0.329152i	$-0.106763\pi$
$691$	1.51743e10	+	2.28715e9i	1.74958	+	0.263707i	0.805306	+	0.592859i	$0.202001\pi$
$692$	4.55272e8	−	1.99468e9i	0.0522276	−	0.228824i
$693$	1.91477e10	+	1.30547e10i	2.18550	+	1.49005i
$694$	−4.23186e9	−	7.32980e9i	−0.480588	−	0.832404i
$695$	−5.40816e9	+	9.36721e9i	−0.611087	+	1.05843i
$696$	−1.18877e10	+	5.72483e9i	−1.33649	+	0.643621i
$697$	−2.40465e9	−	7.41735e8i	−0.268990	−	0.0829725i
$698$	9.28147e8	+	1.23853e10i	0.103305	+	1.37851i
$699$	−6.74545e9	−	2.95538e10i	−0.747035	−	3.27297i
$700$	1.85189e8	−	4.71853e8i	0.0204066	−	0.0519953i
$701$	5.94821e8	−	7.93733e9i	0.0652188	−	0.870285i	−0.864646	−	0.502382i	$-0.832457\pi$
$701$	5.94821e8	−	7.93733e9i	0.0652188	−	0.870285i	0.929864	−	0.367902i	$-0.119924\pi$
$702$	1.94092e10	−	2.92546e9i	2.11752	−	0.319164i
$703$	−8.12121e9	−	7.53538e9i	−0.881611	−	0.818015i
$704$	1.17230e10	+	5.64550e9i	1.26629	+	0.609815i
$705$	−3.37569e9	+	2.30151e9i	−0.362828	+	0.247372i
$706$	−3.41555e9	−	8.70267e9i	−0.365295	−	0.930757i
$707$	−8.51908e9	+	2.62779e9i	−0.906619	+	0.279655i
$708$	−6.46522e9	+	5.99885e9i	−0.684647	+	0.635260i
$709$	9.81460e8	−	1.23071e9i	0.103422	−	0.129686i	−0.727427	−	0.686185i	$-0.759284\pi$
$709$	9.81460e8	−	1.23071e9i	0.103422	−	0.129686i	0.830849	+	0.556498i	$0.187855\pi$
$710$	−8.39366e8	+	1.05253e9i	−0.0880131	+	0.110365i
$711$	1.63321e10	−	1.51540e10i	1.70412	−	1.58119i
$712$	1.47777e10	−	4.55833e9i	1.53436	−	0.473288i
$713$	−3.42048e9	−	8.71524e9i	−0.353406	−	0.900464i
$714$	−1.88503e10	+	1.28519e10i	−1.93810	+	1.32137i
$715$	−1.16512e10	−	5.61093e9i	−1.19207	−	0.574069i
$716$	5.95651e8	+	5.52684e8i	0.0606452	+	0.0562705i
$717$	−6.51046e9	+	9.81294e8i	−0.659621	+	0.0994219i
$718$	−9.49282e8	+	1.26673e10i	−0.0957105	+	1.27717i
$719$	9.24039e8	−	2.35441e9i	0.0927127	−	0.236228i	−0.876994	−	0.480502i	$-0.840454\pi$
$719$	9.24039e8	−	2.35441e9i	0.0927127	−	0.236228i	0.969706	+	0.244274i	$0.0785496\pi$
$720$	−3.81861e9	−	1.67304e10i	−0.381278	−	1.67049i
$721$	1.11671e9	+	1.49014e10i	0.110960	+	1.48066i
$722$	4.42859e9	+	1.36604e9i	0.437910	+	0.135077i
$723$	−4.85350e8	+	2.33732e8i	−0.0477608	+	0.0230004i
$724$	−8.59741e8	+	1.48911e9i	−0.0841943	+	0.145829i
$725$	−8.66023e8	−	1.50000e9i	−0.0844008	−	0.146186i
$726$	−8.54976e9	−	5.82913e9i	−0.829232	−	0.565361i
$727$	1.30890e9	−	5.73465e9i	0.126338	−	0.553524i	−0.871650	−	0.490128i	$-0.836950\pi$
$727$	1.30890e9	−	5.73465e9i	0.126338	−	0.553524i	0.997988	−	0.0633954i	$-0.0201929\pi$
$728$	−8.73487e9	−	1.31657e9i	−0.839067	−	0.126469i
$729$	8.87422e9	+	1.11279e10i	0.848367	+	1.06382i
$730$	1.25159e9			0.119079
$731$	−1.48731e10	−	1.15655e10i	−1.40829	−	1.09510i
$732$	2.79986e9			0.263845
$733$	3.58545e9	+	4.49601e9i	0.336263	+	0.421661i	0.921000	−	0.389562i	$-0.127374\pi$
$733$	3.58545e9	+	4.49601e9i	0.336263	+	0.421661i	−0.584737	+	0.811223i	$0.698802\pi$
$734$	−1.25443e10	−	1.89076e9i	−1.17088	−	0.176481i
$735$	1.47252e9	−	6.45154e9i	0.136791	−	0.599319i
$736$	4.80664e9	+	3.27711e9i	0.444395	+	0.302983i
$737$	−3.44160e8	−	5.96102e8i	−0.0316682	−	0.0548510i
$738$	−1.79003e9	+	3.10042e9i	−0.163932	+	0.283938i
$739$	−5.05358e9	+	2.43368e9i	−0.460621	+	0.221823i	−0.649779	−	0.760123i	$-0.725139\pi$
$739$	−5.05358e9	+	2.43368e9i	−0.460621	+	0.221823i	0.189158	+	0.981947i	$0.439424\pi$
$740$	3.27402e9	+	1.00990e9i	0.297009	+	0.0916152i
$741$	−1.78325e9	−	2.37959e10i	−0.161009	−	2.14851i
$742$	2.45843e8	+	1.07711e9i	0.0220924	+	0.0967932i
$743$	−2.66443e9	+	6.78886e9i	−0.238311	+	0.607206i	−0.999128	−	0.0417607i	$-0.986703\pi$
$743$	−2.66443e9	+	6.78886e9i	−0.238311	+	0.607206i	0.760817	+	0.648967i	$0.224799\pi$
$744$	−1.70663e9	+	2.27734e10i	−0.151927	+	2.02732i
$745$	6.04547e9	−	9.11208e8i	0.535652	−	0.0807366i
$746$	1.37772e10	+	1.27834e10i	1.21500	+	1.12735i
$747$	−1.87930e10	−	9.05023e9i	−1.64958	−	0.794397i
$748$	−6.25414e9	+	4.26400e9i	−0.546401	+	0.372530i
$749$	4.22051e9	+	1.07537e10i	0.367010	+	0.935127i
$750$	−1.47899e10	+	4.56208e9i	−1.28012	+	0.394865i
$751$	−7.04711e9	+	6.53876e9i	−0.607116	+	0.563321i	−0.922672	−	0.385586i	$-0.873999\pi$
$751$	−7.04711e9	+	6.53876e9i	−0.607116	+	0.563321i	0.315556	+	0.948907i	$0.397809\pi$
$752$	9.69152e8	−	1.21528e9i	0.0831055	−	0.104211i
$753$	1.93057e10	−	2.42086e10i	1.64779	−	2.06627i
$754$	−4.96751e9	+	4.60917e9i	−0.422026	+	0.391582i
$755$	−8.14262e9	+	2.51167e9i	−0.688573	+	0.212397i
$756$	−2.87158e9	−	7.31668e9i	−0.241710	−	0.615868i
$757$	−6.46500e9	+	4.40776e9i	−0.541668	+	0.369303i	−0.803031	−	0.595938i	$-0.796780\pi$
$757$	−6.46500e9	+	4.40776e9i	−0.541668	+	0.369303i	0.261363	+	0.965241i	$0.415828\pi$
$758$	−1.24219e10	−	5.98207e9i	−1.03597	−	0.498895i
$759$	−2.02629e10	−	1.88012e10i	−1.68212	−	1.56078i
$760$	−1.79244e10	+	2.70167e9i	−1.48115	+	0.223247i
$761$	1.16687e9	−	1.55707e10i	0.0959786	−	1.28075i	−0.716431	−	0.697658i	$-0.754225\pi$
$761$	1.16687e9	−	1.55707e10i	0.0959786	−	1.28075i	0.812409	−	0.583087i	$-0.198156\pi$
$762$	1.23144e9	−	3.13765e9i	0.100825	−	0.256899i
$763$	−2.66252e9	−	1.16652e10i	−0.216998	−	0.950732i
$764$	−4.01242e8	−	5.35420e9i	−0.0325521	−	0.434378i
$765$	5.77139e10	+	1.78024e10i	4.66085	+	1.43768i
$766$	1.12981e10	−	5.44087e9i	0.908246	−	0.437388i
$767$	−1.00881e10	+	1.74730e10i	−0.807279	+	1.39825i
$768$	−9.21492e9	−	1.59607e10i	−0.734052	−	1.27142i
$769$	1.90196e10	+	1.29673e10i	1.50820	+	1.02827i	0.984302	+	0.176493i	$0.0564752\pi$
$769$	1.90196e10	+	1.29673e10i	1.50820	+	1.02827i	0.523898	+	0.851781i	$0.324477\pi$
$770$	2.82806e9	−	1.23905e10i	0.223239	−	0.978075i
$771$	6.54025e8	+	9.85784e7i	0.0513930	+	0.00774625i
$772$	−8.84785e7	−	1.10949e8i	−0.00692114	−	0.00867883i
$773$	−1.13523e10			−0.884007			−0.442004	−	0.897013i	$-0.645732\pi$
$773$	−1.13523e10			−0.884007			−0.442004	+	0.897013i	$0.645732\pi$
$774$	−2.07497e10	+	1.69676e10i	−1.60849	+	1.31531i
$775$	−2.99788e9			−0.231344
$776$	2.10733e9	+	2.64251e9i	0.161889	+	0.203002i
$777$	−1.95237e10	−	2.94273e9i	−1.49310	−	0.225049i
$778$	2.96614e9	−	1.29955e10i	0.225821	−	0.989385i
$779$	2.13724e9	+	1.45714e9i	0.161984	+	0.110439i
$780$	3.68994e9	+	6.39116e9i	0.278412	+	0.482223i
$781$	1.28696e9	−	2.22907e9i	0.0966685	−	0.167435i
$782$	1.74419e10	−	8.39958e9i	1.30428	−	0.628108i
$783$	−2.56643e10	−	7.91640e9i	−1.91057	−	0.589334i
$784$	1.88145e8	+	2.51062e9i	0.0139440	+	0.186069i
$785$	−1.99940e9	−	8.75993e9i	−0.147521	−	0.646334i
$786$	−2.71326e9	+	6.91326e9i	−0.199302	+	0.507813i
$787$	1.20685e9	−	1.61044e10i	0.0882558	−	1.17769i	−0.760655	−	0.649156i	$-0.775122\pi$
$787$	1.20685e9	−	1.61044e10i	0.0882558	−	1.17769i	0.848911	−	0.528536i	$-0.177259\pi$
$788$	−2.50847e9	+	3.78091e8i	−0.182628	+	0.0275268i
$789$	3.00724e10	+	2.79031e10i	2.17971	+	2.02247i
$790$	−1.10084e10	−	5.30136e9i	−0.794381	−	0.382554i
$791$	1.15651e10	−	7.88495e9i	0.830868	−	0.566476i
$792$	1.75241e10	+	4.46507e10i	1.25342	+	3.19367i
$793$	6.12053e9	−	1.88793e9i	0.435846	−	0.134441i
$794$	−7.83844e9	+	7.27301e9i	−0.555722	+	0.515635i
$795$	2.56332e9	−	3.21431e9i	0.180933	−	0.226883i
$796$	−1.70509e9	+	2.13812e9i	−0.119826	+	0.150257i
$797$	4.47066e9	−	4.14817e9i	0.312801	−	0.290237i	−0.508111	−	0.861292i	$-0.669656\pi$
$797$	4.47066e9	−	4.14817e9i	0.312801	−	0.290237i	0.820912	+	0.571055i	$0.193466\pi$
$798$	2.24097e10	−	6.91249e9i	1.56108	−	0.481531i
$799$	1.99868e9	+	5.09256e9i	0.138621	+	0.353201i
$800$	1.53910e9	−	1.04934e9i	0.106280	−	0.0724606i
$801$	4.77207e10	+	2.29811e10i	3.28090	+	1.58000i
$802$	−5.78944e9	−	5.37181e9i	−0.396302	−	0.367714i
$803$	−2.36623e9	+	3.56652e8i	−0.161270	+	0.0243075i
$804$	−2.93543e7	+	3.91706e8i	−0.00199194	+	0.0265806i
$805$	4.83862e9	−	1.23286e10i	0.326916	−	0.832967i
$806$	2.60994e9	+	1.14349e10i	0.175573	+	0.769234i
$807$	−2.01855e9	−	2.69357e10i	−0.135202	−	1.80414i
$808$	−1.76327e10	−	5.43897e9i	−1.17592	−	0.362724i
$809$	6.95632e9	−	3.34999e9i	0.461913	−	0.222445i	−0.188430	−	0.982087i	$-0.560340\pi$
$809$	6.95632e9	−	3.34999e9i	0.461913	−	0.222445i	0.650342	+	0.759641i	$0.274625\pi$
$810$	1.84633e10	−	3.19794e10i	1.22071	−	2.11433i
$811$	−6.70615e8	−	1.16154e9i	−0.0441469	−	0.0764647i	0.843108	−	0.537745i	$-0.180724\pi$
$811$	−6.70615e8	−	1.16154e9i	−0.0441469	−	0.0764647i	−0.887255	+	0.461280i	$0.847390\pi$
$812$	2.24206e9	+	1.52861e9i	0.146961	+	0.100196i
$813$	−2.13606e9	+	9.35870e9i	−0.139411	+	0.610800i
$814$	1.58975e10	+	2.39616e9i	1.03310	+	0.155715i
$815$	−4.15519e9	−	5.21044e9i	−0.268868	−	0.337150i
$816$	−3.23004e10			−2.08109
$817$	1.11050e10	+	1.58666e10i	0.712428	+	1.01790i
$818$	1.85913e9			0.118761
$819$	−1.88633e10	−	2.36538e10i	−1.19984	−	1.50455i
$820$	−7.91043e8	−	1.19231e8i	−0.0501016	−	0.00755160i
$821$	5.10322e9	−	2.23587e10i	0.321843	−	1.41008i	−0.512428	−	0.858730i	$-0.671254\pi$
$821$	5.10322e9	−	2.23587e10i	0.321843	−	1.41008i	0.834271	−	0.551355i	$-0.185889\pi$
$822$	2.08803e10	+	1.42360e10i	1.31125	+	0.893997i
$823$	5.25286e9	+	9.09822e9i	0.328470	+	0.568927i	0.982209	−	0.187793i	$-0.0601335\pi$
$823$	5.25286e9	+	9.09822e9i	0.328470	+	0.568927i	−0.653738	+	0.756721i	$0.726800\pi$
$824$	−1.54646e10	+	2.67855e10i	−0.962929	+	1.66784i
$825$	−7.97449e9	+	3.84031e9i	−0.494441	+	0.238110i
$826$	−1.89477e10	−	5.84459e9i	−1.16984	−	0.360848i
$827$	2.04745e9	+	2.73213e10i	0.125876	+	1.67970i	0.600588	+	0.799558i	$0.294933\pi$
$827$	2.04745e9	+	2.73213e10i	0.125876	+	1.67970i	−0.474712	+	0.880141i	$0.657448\pi$
$828$	2.49713e9	+	1.09406e10i	0.152874	+	0.669786i
$829$	−3.70638e9	+	9.44370e9i	−0.225948	+	0.575707i	−0.998223	−	0.0595814i	$-0.981023\pi$
$829$	−3.70638e9	+	9.44370e9i	−0.225948	+	0.575707i	0.772275	+	0.635288i	$0.219119\pi$
$830$	−8.54845e8	+	1.14071e10i	−0.0518936	+	0.692472i
$831$	−2.74606e10	+	4.13902e9i	−1.65999	+	0.250204i
$832$	−1.24520e10	−	1.15538e10i	−0.749562	−	0.695492i
$833$	−7.98342e9	−	3.84461e9i	−0.478555	−	0.230460i
$834$	2.39310e10	−	1.63159e10i	1.42850	−	0.973934i
$835$	5.12738e9	+	1.30644e10i	0.304785	+	0.776578i
$836$	7.43507e9	−	2.29342e9i	0.440112	−	0.135757i
$837$	−3.40766e10	+	3.16185e10i	−2.00871	+	1.86381i
$838$	1.40943e10	−	1.76736e10i	0.827348	−	1.03746i
$839$	−1.76804e9	+	2.21706e9i	−0.103354	+	0.129602i	−0.830818	−	0.556544i	$-0.812127\pi$
$839$	−1.76804e9	+	2.21706e9i	−0.103354	+	0.129602i	0.727465	+	0.686145i	$0.240699\pi$
$840$	−2.36817e10	+	2.19734e10i	−1.37859	+	1.27914i
$841$	−7.62320e9	+	2.35145e9i	−0.441928	+	0.136317i
$842$	3.90633e9	+	9.95318e9i	0.225516	+	0.574605i
$843$	1.87602e10	−	1.27905e10i	1.07855	−	0.735344i
$844$	−2.61046e9	−	1.25713e9i	−0.149458	−	0.0719751i
$845$	−1.88451e9	−	1.74857e9i	−0.107448	−	0.0996973i
$846$	7.69608e9	−	1.16000e9i	0.436992	−	0.0658659i
$847$	−7.08388e8	+	9.45278e9i	−0.0400571	+	0.534524i
$848$	−5.71450e8	+	1.45603e9i	−0.0321805	+	0.0819946i
$849$	−6.73008e9	−	2.94864e10i	−0.377436	−	1.65366i
$850$	−4.63239e8	−	6.18150e9i	−0.0258726	−	0.345245i
$851$	1.60094e10	+	4.93825e9i	0.890475	+	0.274675i
$852$	−1.32340e9	+	6.37315e8i	−0.0733081	+	0.0353033i
$853$	1.38227e9	−	2.39417e9i	0.0762558	−	0.132079i	−0.825376	−	0.564584i	$-0.809037\pi$
$853$	1.38227e9	−	2.39417e9i	0.0762558	−	0.132079i	0.901632	+	0.432505i	$0.142370\pi$
$854$	3.14739e9	+	5.45145e9i	0.172921	+	0.299508i
$855$	−5.12958e10	−	3.49729e10i	−2.80673	−	1.91360i
$856$	−5.32063e9	+	2.33112e10i	−0.289938	+	1.27030i
$857$	7.23168e9	+	1.09000e9i	0.392470	+	0.0591553i	0.342313	−	0.939586i	$-0.388790\pi$
$857$	7.23168e9	+	1.09000e9i	0.392470	+	0.0591553i	0.0501571	+	0.998741i	$0.484028\pi$
$858$	2.15907e10	+	2.70739e10i	1.16697	+	1.46334i
$859$	2.99818e9			0.161392			0.0806960	−	0.996739i	$-0.474286\pi$
$859$	2.99818e9			0.161392			0.0806960	+	0.996739i	$0.474286\pi$
$860$	−5.22333e9	−	2.93091e9i	−0.280029	−	0.157129i
$861$	4.61001e9			0.246145
$862$	1.80367e9	+	2.26174e9i	0.0959141	+	0.120272i
$863$	1.09276e10	+	1.64706e9i	0.578742	+	0.0872314i	0.431889	−	0.901927i	$-0.357847\pi$
$863$	1.09276e10	+	1.64706e9i	0.578742	+	0.0872314i	0.146854	+	0.989158i	$0.453085\pi$
$864$	6.42746e9	−	2.81606e10i	0.339033	−	1.48540i
$865$	−1.41429e10	−	9.64246e9i	−0.742988	−	0.506561i
$866$	1.21311e9	+	2.10117e9i	0.0634729	+	0.109938i
$867$	3.89804e10	−	6.75160e10i	2.03133	−	3.51836i
$868$	4.23162e9	−	2.03784e9i	0.219628	−	0.105767i
$869$	2.23228e10	+	6.88568e9i	1.15393	+	0.355941i
$870$	1.85201e9	+	2.47133e10i	0.0953511	+	1.27237i
$871$	1.99957e8	+	8.76068e8i	0.0102535	+	0.0449236i
$872$	9.04787e9	−	2.30536e10i	0.462103	−	1.17742i
$873$	−8.65070e8	+	1.15436e10i	−0.0440049	+	0.587205i
$874$	−1.96773e10	+	2.96588e9i	−0.996955	+	0.150267i
$875$	1.03935e10	+	9.64378e9i	0.524487	+	0.486653i
$876$	1.23036e9	+	5.92510e8i	0.0618397	+	0.0297804i
$877$	−4.42912e9	+	3.01972e9i	−0.221727	+	0.151171i	−0.669090	−	0.743182i	$-0.733316\pi$
$877$	−4.42912e9	+	3.01972e9i	−0.221727	+	0.151171i	0.447362	+	0.894353i	$0.352363\pi$
$878$	−7.76534e9	−	1.97858e10i	−0.387195	−	0.986557i
$879$	2.35732e10	−	7.27136e9i	1.17073	−	0.361123i
$880$	1.31900e10	−	1.22386e10i	0.652464	−	0.605398i
$881$	−1.29155e10	+	1.61956e10i	−0.636350	+	0.797958i	−0.990541	−	0.137215i	$-0.956185\pi$
$881$	−1.29155e10	+	1.61956e10i	−0.636350	+	0.797958i	0.354191	+	0.935173i	$0.384756\pi$
$882$	−7.85980e9	+	9.85587e9i	−0.385719	+	0.483677i
$883$	2.83588e8	−	2.63131e8i	0.0138620	−	0.0128620i	−0.673211	−	0.739450i	$-0.735086\pi$
$883$	2.83588e8	−	2.63131e8i	0.0138620	−	0.0128620i	0.687073	+	0.726588i	$0.258895\pi$
$884$	9.44280e9	−	2.91272e9i	0.459746	−	0.141813i
$885$	2.69575e10	+	6.86865e10i	1.30731	+	3.33097i
$886$	2.28918e10	−	1.56073e10i	1.10576	−	0.753895i
$887$	−7.31935e9	−	3.52481e9i	−0.352160	−	0.169591i	0.249437	−	0.968391i	$-0.419754\pi$
$887$	−7.31935e9	−	3.52481e9i	−0.352160	−	0.169591i	−0.601597	+	0.798800i	$0.705469\pi$
$888$	−2.99572e10	−	2.77962e10i	−1.43567	−	1.33211i
$889$	−3.05325e9	+	4.60203e8i	−0.145749	+	0.0219682i
$890$	2.17069e9	−	2.89659e10i	0.103213	−	1.37728i
$891$	−2.57934e10	+	6.57206e10i	−1.22162	+	3.11264i
$892$	6.20856e8	+	2.72015e9i	0.0292896	+	0.128326i
$893$	−4.20243e8	−	5.60775e9i	−0.0197479	−	0.263517i
$894$	−1.56440e10	−	4.82553e9i	−0.732261	−	0.225873i
$895$	6.12491e9	−	2.94960e9i	0.285574	−	0.137525i
$896$	3.30657e9	−	5.72714e9i	0.153568	−	0.265987i
$897$	1.80432e10	+	3.12517e10i	0.834717	+	1.44577i
$898$	−1.04167e10	−	7.10201e9i	−0.480025	−	0.327276i
$899$	3.57118e9	−	1.56463e10i	0.163928	−	0.718214i
$900$	3.55318e9	+	5.35556e8i	0.162468	+	0.0244881i
$901$	−3.43235e9	−	4.30404e9i	−0.156335	−	0.196037i
$902$	−3.75376e9			−0.170312
$903$	3.22814e10	+	1.22150e10i	1.45897	+	0.552059i
$904$	2.89714e10			1.30431
$905$	8.96931e9	+	1.12472e10i	0.402243	+	0.504397i
$906$	2.25631e10	+	3.40083e9i	1.00797	+	0.151928i
$907$	−7.97226e9	+	3.49288e10i	−0.354778	+	1.55438i	0.411218	+	0.911537i	$0.365103\pi$
$907$	−7.97226e9	+	3.49288e10i	−0.354778	+	1.55438i	−0.765996	+	0.642845i	$0.777754\pi$
$908$	2.94766e9	+	2.00968e9i	0.130670	+	0.0890894i
$909$	−3.15993e10	−	5.47317e10i	−1.39542	−	2.41694i
$910$	−8.29589e9	+	1.43689e10i	−0.364937	+	0.632090i
$911$	1.65423e9	−	7.96635e8i	0.0724905	−	0.0349096i	−0.397287	−	0.917694i	$-0.630048\pi$
$911$	1.65423e9	−	7.96635e8i	0.0724905	−	0.0349096i	0.469778	+	0.882785i	$0.344334\pi$
$912$	3.17271e10	+	9.78652e9i	1.38500	+	0.427215i
$913$	−1.63440e9	−	2.18096e10i	−0.0710741	−	0.948418i
$914$	−2.00020e9	−	8.76343e9i	−0.0866484	−	0.379632i
$915$	8.55791e9	−	2.18052e10i	0.369312	−	0.940992i
$916$	−3.15188e8	+	4.20589e9i	−0.0135499	+	0.180811i
$917$	6.72730e9	−	1.01398e9i	0.288103	−	0.0434246i
$918$	−7.04615e10	−	6.53787e10i	−3.00609	−	2.78925i
$919$	2.75099e10	+	1.32481e10i	1.16919	+	0.563051i	0.914743	−	0.404036i	$-0.132393\pi$
$919$	2.75099e10	+	1.32481e10i	1.16919	+	0.563051i	0.254445	+	0.967087i	$0.418107\pi$
$920$	2.26493e10	−	1.54420e10i	0.958952	−	0.653803i
$921$	4.17532e9	+	1.06385e10i	0.176109	+	0.448718i
$922$	−3.44284e9	+	1.06198e9i	−0.144664	+	0.0446228i
$923$	−2.46322e9	+	2.28554e9i	−0.103109	+	0.0956715i
$924$	8.64580e9	−	1.08415e10i	0.360540	−	0.452103i
$925$	3.34477e9	−	4.19421e9i	0.138954	−	0.174243i
$926$	1.65906e9	−	1.53938e9i	0.0686630	−	0.0637099i
$927$	−1.01225e11	+	3.12237e10i	−4.17357	+	1.28737i
$928$	3.64323e9	+	9.28279e9i	0.149647	+	0.381294i
$929$	−3.31678e10	+	2.26134e10i	−1.35725	+	0.925360i	−0.999963	−	0.00863301i	$-0.997252\pi$
$929$	−3.31678e10	+	2.26134e10i	−1.35725	+	0.925360i	−0.357291	+	0.933993i	$0.616300\pi$
$930$	3.86467e10	+	1.86113e10i	1.57551	+	0.758727i
$931$	6.67688e9	+	6.19524e9i	0.271175	+	0.251614i
$932$	−1.27597e10	+	1.92322e9i	−0.516281	+	0.0778168i
$933$	1.33403e9	−	1.78014e10i	0.0537749	−	0.717576i
$934$	4.06761e9	−	1.03641e10i	0.163352	−	0.416215i
$935$	1.40917e10	+	6.17400e10i	0.563799	+	2.47016i
$936$	−4.67960e9	−	6.24450e10i	−0.186528	−	2.48904i
$937$	5.03308e9	+	1.55250e9i	0.199869	+	0.0616514i	0.393073	−	0.919507i	$-0.371412\pi$
$937$	5.03308e9	+	1.55250e9i	0.199869	+	0.0616514i	−0.193204	+	0.981159i	$0.561888\pi$
$938$	−7.95666e8	+	3.83172e8i	−0.0314790	+	0.0151595i
$939$	3.94463e10	−	6.83231e10i	1.55481	−	2.69301i
$940$	8.69573e8	+	1.50614e9i	0.0341475	+	0.0591452i
$941$	−1.59614e10	−	1.08823e10i	−0.624463	−	0.425752i	0.209318	−	0.977848i	$-0.432876\pi$
$941$	−1.59614e10	−	1.08823e10i	−0.624463	−	0.425752i	−0.833781	+	0.552096i	$0.813828\pi$
$942$	−5.35395e9	+	2.34572e10i	−0.208687	+	0.914320i
$943$	−3.86807e9	−	5.83018e8i	−0.150212	−	0.0226408i
$944$	−1.75031e10	−	2.19483e10i	−0.677196	−	0.849176i
$945$	−6.57590e10			−2.53480
$946$	−2.62856e10	−	9.94622e9i	−1.00948	−	0.381979i
$947$	2.35246e10			0.900114			0.450057	−	0.893000i	$-0.351404\pi$
$947$	2.35246e10			0.900114			0.450057	+	0.893000i	$0.351404\pi$
$948$	−8.31193e9	−	1.04228e10i	−0.316864	−	0.397334i
$949$	3.08910e9	+	4.65608e8i	0.117328	+	0.0176843i
$950$	−1.41788e9	+	6.21215e9i	−0.0536547	+	0.235077i
$951$	7.60972e10	+	5.18822e10i	2.86904	+	1.95608i
$952$	2.16290e10	+	3.74625e10i	0.812470	+	1.40724i
$953$	1.06136e10	−	1.83834e10i	0.397227	−	0.688018i	−0.596155	−	0.802869i	$-0.703306\pi$
$953$	1.06136e10	−	1.83834e10i	0.397227	−	0.688018i	0.993383	+	0.114851i	$0.0366391\pi$
$954$	−7.05627e9	+	3.39812e9i	−0.263121	+	0.126712i
$955$	−4.29246e10	−	1.32405e10i	−1.59476	−	0.491918i
$956$	2.09442e8	+	2.79482e9i	0.00775286	+	0.103455i
$957$	−1.05436e10	−	4.61946e10i	−0.388864	−	1.70373i
$958$	−1.13594e10	+	2.89433e10i	−0.417424	+	1.06358i
$959$	1.73003e9	−	2.30857e10i	0.0633417	−	0.845236i
$960$	−6.14285e10	+	9.25886e9i	−2.24089	+	0.337760i
$961$	−1.94282e8	−	1.80268e8i	−0.00706157	−	0.00655218i
$962$	−1.89100e10	−	9.10657e9i	−0.684823	−	0.329794i
$963$	−6.76630e10	+	4.61318e10i	−2.44151	+	1.66460i
$964$	8.37767e7	+	2.13460e8i	0.00301199	+	0.00767443i
$965$	−1.13450e9	+	3.49947e8i	−0.0406405	+	0.0125359i
$966$	−2.59976e10	+	2.41222e10i	−0.927926	+	0.860989i
$967$	−2.28557e10	+	2.86602e10i	−0.812835	+	1.01926i	0.186487	+	0.982457i	$0.440290\pi$
$967$	−2.28557e10	+	2.86602e10i	−0.812835	+	1.01926i	−0.999322	+	0.0368059i	$0.988282\pi$
$968$	−1.22329e10	+	1.53396e10i	−0.433478	+	0.543564i
$969$	−8.56612e10	+	7.94820e10i	−3.02448	+	2.80631i
$970$	6.06632e9	−	1.87121e9i	0.213415	−	0.0658297i
$971$	−2.04708e10	−	5.21588e10i	−0.717576	−	1.82835i	−0.534303	−	0.845293i	$-0.679426\pi$
$971$	−2.04708e10	−	5.21588e10i	−0.717576	−	1.82835i	−0.183273	−	0.983062i	$-0.558669\pi$
$972$	1.46131e10	−	9.96306e9i	0.510401	−	0.347985i
$973$	−2.39052e10	−	1.15121e10i	−0.831950	−	0.400646i
$974$	−2.25483e10	−	2.09218e10i	−0.781913	−	0.725509i
$975$	1.14259e10	−	1.72218e9i	0.394798	−	0.0595062i
$976$	−6.65994e8	+	8.88708e9i	−0.0229296	+	0.305974i
$977$	−8.94573e8	+	2.27933e9i	−0.0306891	+	0.0781947i	−0.945397	−	0.325921i	$-0.894326\pi$
$977$	−8.94573e8	+	2.27933e9i	−0.0306891	+	0.0781947i	0.914708	+	0.404116i	$0.132421\pi$
$978$	3.97107e9	+	1.73984e10i	0.135744	+	0.594735i
$979$	4.15021e9	+	5.53807e10i	0.141361	+	1.88634i
$980$	−2.69175e9	−	8.30294e8i	−0.0913572	−	0.0281800i
$981$	7.64206e10	−	3.68022e10i	2.58445	−	1.24461i
$982$	4.81875e9	−	8.34632e9i	0.162384	−	0.281258i
$983$	−1.23924e9	−	2.14642e9i	−0.0416119	−	0.0720738i	0.844469	−	0.535604i	$-0.179916\pi$
$983$	−1.23924e9	−	2.14642e9i	−0.0416119	−	0.0720738i	−0.886081	+	0.463530i	$0.846583\pi$
$984$	7.88376e9	+	5.37505e9i	0.263785	+	0.179846i
$985$	−4.72270e9	+	2.06915e10i	−0.157458	+	0.689867i
$986$	3.28139e10	+	4.94590e9i	1.09016	+	0.164315i
$987$	−6.24869e9	−	7.83560e9i	−0.206861	−	0.259396i
$988$	−1.01577e10			−0.335079
$989$	−2.55412e10	−	1.43317e10i	−0.839566	−	0.471096i
$990$	9.00941e10			2.95103
$991$	−9.49652e9	−	1.19083e10i	−0.309961	−	0.388678i	0.602313	−	0.798260i	$-0.294246\pi$
$991$	−9.49652e9	−	1.19083e10i	−0.309961	−	0.388678i	−0.912273	+	0.409582i	$0.865675\pi$
$992$	1.70673e10	+	2.57248e9i	0.555103	+	0.0836684i
$993$	6.15804e9	−	2.69801e10i	0.199582	−	0.874424i
$994$	−2.72854e9	−	1.86029e9i	−0.0881207	−	0.0600797i
$995$	1.14399e10	+	1.98144e10i	0.368163	+	0.637677i
$996$	−6.24051e9	+	1.08089e10i	−0.200130	+	0.346636i
$997$	3.21073e10	−	1.54621e10i	1.02606	−	0.494123i	0.156355	−	0.987701i	$-0.450026\pi$
$997$	3.21073e10	−	1.54621e10i	1.02606	−	0.494123i	0.869702	+	0.493578i	$0.164311\pi$
$998$	−1.37754e10	−	4.24915e9i	−0.438680	−	0.135315i
$999$	−6.21641e9	−	8.29522e10i	−0.197270	−	2.63238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.9.17	✓	300
43.24	even	21	inner	43.8.g.a.24.17	yes	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.17	✓	300	1.1	even	1	trivial
43.8.g.a.24.17	yes	300	43.24	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)

\(f(q)\)	\(=\)	\(q+(5.94589 + 7.45591i) q^{2} +(86.0795 + 12.9744i) q^{3} +(8.24571 - 36.1268i) q^{4} +(-256.150 - 174.640i) q^{5} +(415.083 + 718.945i) q^{6} +(380.244 - 658.602i) q^{7} +(1418.17 - 682.954i) q^{8} +(5151.52 + 1589.03i) q^{9} +O(q^{10})\)	\(q+(5.94589 + 7.45591i) q^{2} +(86.0795 + 12.9744i) q^{3} +(8.24571 - 36.1268i) q^{4} +(-256.150 - 174.640i) q^{5} +(415.083 + 718.945i) q^{6} +(380.244 - 658.602i) q^{7} +(1418.17 - 682.954i) q^{8} +(5151.52 + 1589.03i) q^{9} +(-220.939 - 2948.23i) q^{10} +(1257.82 + 5510.88i) q^{11} +(1178.51 - 3002.80i) q^{12} +(551.467 - 7358.81i) q^{13} +(7171.36 - 1080.91i) q^{14} +(-19783.5 - 18356.4i) q^{15} +(9250.88 + 4454.99i) q^{16} +(-29858.1 + 20356.9i) q^{17} +(18782.7 + 47857.4i) q^{18} +(35496.0 - 10949.1i) q^{19} +(-8421.35 + 7813.87i) q^{20} +(41276.2 - 51758.7i) q^{21} +(-33609.7 + 42145.3i) q^{22} +(-41179.0 + 38208.5i) q^{23} +(130936. - 40388.5i) q^{24} +(6571.51 + 16743.9i) q^{25} +(58145.6 - 39643.0i) q^{26} +(251295. + 121017. i) q^{27} +(-20657.8 - 19167.6i) q^{28} +(-95217.0 + 14351.7i) q^{29} +(19233.1 - 256648. i) q^{30} +(-60890.0 + 155145. i) q^{31} +(-23044.4 - 100964. i) q^{32} +(36772.4 + 490694. i) q^{33} +(-329312. - 101579. i) q^{34} +(-212418. + 102295. i) q^{35} +(99884.6 - 173005. i) q^{36} +(-149122. - 258286. i) q^{37} +(292690. + 199553. i) q^{38} +(142946. - 626288. i) q^{39} +(-482536. - 72730.6i) q^{40} +(43417.1 + 54443.3i) q^{41} +631331. q^{42} +(159770. + 496278. i) q^{43} +209462. q^{44} +(-1.04205e6 - 1.30669e6i) q^{45} +(-529725. - 79843.2i) q^{46} +(33686.8 - 147592. i) q^{47} +(738511. + 503508. i) q^{48} +(122601. + 212351. i) q^{49} +(-85767.8 + 148554. i) q^{50} +(-2.83429e6 + 1.36492e6i) q^{51} +(-261303. - 80601.4i) q^{52} +(11384.2 + 151911. i) q^{53} +(591877. + 2.59318e6i) q^{54} +(640231. - 1.63128e6i) q^{55} +(89455.3 - 1.19370e6i) q^{56} +(3.19754e6 - 481951. i) q^{57} +(-673154. - 624596. i) q^{58} +(-2.46333e6 - 1.18628e6i) q^{59} +(-826286. + 563352. i) q^{60} +(317103. + 807965. i) q^{61} +(-1.51879e6 + 468486. i) q^{62} +(3.00537e6 - 2.78858e6i) q^{63} +(1.43519e6 - 1.79967e6i) q^{64} +(-1.42640e6 + 1.78865e6i) q^{65} +(-3.43992e6 + 3.19178e6i) q^{66} +(-116360. + 35892.4i) q^{67} +(489229. + 1.24653e6i) q^{68} +(-4.04040e6 + 2.75470e6i) q^{69} +(-2.02572e6 - 975534. i) q^{70} +(-333795. - 309717. i) q^{71} +(8.39096e6 - 1.26473e6i) q^{72} +(-31636.1 + 422154. i) q^{73} +(1.03910e6 - 2.64758e6i) q^{74} +(348430. + 1.52657e6i) q^{75} +(-102865. - 1.37264e6i) q^{76} +(4.10775e6 + 1.26707e6i) q^{77} +(5.51949e6 - 2.65805e6i) q^{78} +(2.06636e6 - 3.57905e6i) q^{79} +(-1.59160e6 - 2.75673e6i) q^{80} +(1.03197e7 + 7.03587e6i) q^{81} +(-147771. + 647427. i) q^{82} +(-3.82593e6 - 576666. i) q^{83} +(-1.52953e6 - 1.91796e6i) q^{84} +1.12033e7 q^{85} +(-2.75023e6 + 4.14205e6i) q^{86} -8.38244e6 q^{87} +(5.54748e6 + 6.95633e6i) q^{88} +(9.71511e6 + 1.46432e6i) q^{89} +(3.54665e6 - 1.55389e7i) q^{90} +(-4.63683e6 - 3.16134e6i) q^{91} +(1.04080e6 + 1.80272e6i) q^{92} +(-7.25430e6 + 1.25648e7i) q^{93} +(1.30073e6 - 626397. i) q^{94} +(-1.10045e7 - 3.39443e6i) q^{95} +(-673703. - 8.98994e6i) q^{96} +(477810. + 2.09342e6i) q^{97} +(-854297. + 2.17671e6i) q^{98} +(-2.27727e6 + 3.03881e7i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more