LMFDB - Embedded newform 43.8.g.a.9.3

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			9.3
Character	$\chi$	$=$	43.9
Dual form			43.8.g.a.24.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-11.9571 - 14.9937i) q^{2} +(22.8341 + 3.44169i) q^{3} +(-53.3566 + 233.771i) q^{4} +(-375.006 - 255.675i) q^{5} +(-221.425 - 383.520i) q^{6} +(97.1595 - 168.285i) q^{7} +(1931.43 - 930.128i) q^{8} +(-1580.29 - 487.454i) q^{9} +O(q^{10})$	\(q+(-11.9571 - 14.9937i) q^{2} +(22.8341 + 3.44169i) q^{3} +(-53.3566 + 233.771i) q^{4} +(-375.006 - 255.675i) q^{5} +(-221.425 - 383.520i) q^{6} +(97.1595 - 168.285i) q^{7} +(1931.43 - 930.128i) q^{8} +(-1580.29 - 487.454i) q^{9} +(650.465 + 8679.85i) q^{10} +(341.242 + 1495.08i) q^{11} +(-2022.92 + 5154.31i) q^{12} +(-530.539 + 7079.55i) q^{13} +(-3684.96 + 555.418i) q^{14} +(-7682.97 - 7128.76i) q^{15} +(-9387.64 - 4520.85i) q^{16} +(-1402.53 + 956.230i) q^{17} +(11586.9 + 29522.9i) q^{18} +(27686.2 - 8540.07i) q^{19} +(79778.3 - 74023.4i) q^{20} +(2797.74 - 3508.25i) q^{21} +(18336.5 - 22993.3i) q^{22} +(38198.8 - 35443.3i) q^{23} +(47303.7 - 14591.3i) q^{24} +(46717.6 + 119035. i) q^{25} +(112492. - 76696.0i) q^{26} +(-79907.7 - 38481.5i) q^{27} +(34156.0 + 31692.2i) q^{28} +(67958.2 - 10243.0i) q^{29} +(-15020.5 + 200435. i) q^{30} +(-87693.5 + 223439. i) q^{31} +(-16594.6 - 72705.7i) q^{32} +(2646.36 + 35313.3i) q^{33} +(31107.6 + 9595.42i) q^{34} +(-79461.7 + 38266.7i) q^{35} +(198271. - 343416. i) q^{36} +(-158938. - 275289. i) q^{37} +(-459094. - 313005. i) q^{38} +(-36480.0 + 159829. i) q^{39} +(-962108. - 145015. i) q^{40} +(416961. + 522853. i) q^{41} -86054.4 q^{42} +(110319. + 509557. i) q^{43} -367714. q^{44} +(467987. + 586837. i) q^{45} +(-988172. - 148943. i) q^{46} +(-93521.6 + 409745. i) q^{47} +(-198799. - 135539. i) q^{48} +(392892. + 680508. i) q^{49} +(1.22616e6 - 2.12377e6i) q^{50} +(-35316.6 + 17007.6i) q^{51} +(-1.62668e6 - 501766. i) q^{52} +(2888.29 + 38541.5i) q^{53} +(378482. + 1.65824e6i) q^{54} +(254286. - 647911. i) q^{55} +(31130.1 - 415402. i) q^{56} +(661583. - 99717.6i) q^{57} +(-966162. - 896467. i) q^{58} +(-1.77090e6 - 852819. i) q^{59} +(2.07643e6 - 1.41569e6i) q^{60} +(185527. + 472715. i) q^{61} +(4.39874e6 - 1.35683e6i) q^{62} +(-235571. + 218578. i) q^{63} +(-1.72325e6 + 2.16089e6i) q^{64} +(2.00902e6 - 2.51923e6i) q^{65} +(497834. - 461922. i) q^{66} +(-2.98687e6 + 921326. i) q^{67} +(-148704. - 378892. i) q^{68} +(994221. - 677848. i) q^{69} +(1.52389e6 + 733866. i) q^{70} +(-2.66957e6 - 2.47700e6i) q^{71} +(-3.50561e6 + 528386. i) q^{72} +(-312698. + 4.17267e6i) q^{73} +(-2.22716e6 + 5.67472e6i) q^{74} +(657075. + 2.87884e6i) q^{75} +(519174. + 6.92790e6i) q^{76} +(284755. + 87835.2i) q^{77} +(2.83263e6 - 1.36412e6i) q^{78} +(-2.34401e6 + 4.05994e6i) q^{79} +(2.36455e6 + 4.09553e6i) q^{80} +(1.29613e6 + 883690. i) q^{81} +(2.85386e6 - 1.25036e7i) q^{82} +(4.52040e6 + 681341. i) q^{83} +(670848. + 841217. i) q^{84} +770442. q^{85} +(6.32105e6 - 7.74690e6i) q^{86} +1.58702e6 q^{87} +(2.04970e6 + 2.57025e6i) q^{88} +(-1.01819e7 - 1.53467e6i) q^{89} +(3.20310e6 - 1.40337e7i) q^{90} +(1.13984e6 + 777128. i) q^{91} +(6.24745e6 + 1.08209e7i) q^{92} +(-2.77141e6 + 4.80022e6i) q^{93} +(7.26183e6 - 3.49711e6i) q^{94} +(-1.25660e7 - 3.87609e6i) q^{95} +(-128693. - 1.71728e6i) q^{96} +(-2.58712e6 - 1.13349e7i) q^{97} +(5.50550e6 - 1.40278e7i) q^{98} +(189522. - 2.52900e6i) 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 $

$2$	−11.9571	−	14.9937i	−1.05687	−	1.32527i	−0.943375	−	0.331729i	$-0.892368\pi$
$2$	−11.9571	−	14.9937i	−1.05687	−	1.32527i	−0.113491	−	0.993539i	$-0.536203\pi$
$3$	22.8341	+	3.44169i	0.488270	+	0.0735948i	0.388563	−	0.921422i	$-0.372972\pi$
$3$	22.8341	+	3.44169i	0.488270	+	0.0735948i	0.0997064	+	0.995017i	$0.468210\pi$
$4$	−53.3566	+	233.771i	−0.416849	+	1.82633i
$5$	−375.006	−	255.675i	−1.34166	−	0.914730i	−0.341974	−	0.939709i	$-0.611095\pi$
$5$	−375.006	−	255.675i	−1.34166	−	0.914730i	−0.999688	+	0.0249798i	$0.992048\pi$
$6$	−221.425	−	383.520i	−0.418503	−	0.724868i
$7$	97.1595	−	168.285i	0.107064	−	0.185440i	−0.807516	−	0.589846i	$-0.799188\pi$
$7$	97.1595	−	168.285i	0.107064	−	0.185440i	0.914579	+	0.404406i	$0.132522\pi$
$8$	1931.43	−	930.128i	1.33372	−	0.642285i
$9$	−1580.29	−	487.454i	−0.722582	−	0.222887i
$10$	650.465	+	8679.85i	0.205695	+	2.74481i
$11$	341.242	+	1495.08i	0.0773016	+	0.338681i	0.998759	−	0.0497982i	$-0.0158578\pi$
$11$	341.242	+	1495.08i	0.0773016	+	0.338681i	−0.921458	+	0.388479i	$0.873001\pi$
$12$	−2022.92	+	5154.31i	−0.337943	+	0.861065i
$13$	−530.539	+	7079.55i	−0.0669755	+	0.893726i	0.857988	+	0.513670i	$0.171714\pi$
$13$	−530.539	+	7079.55i	−0.0669755	+	0.893726i	−0.924964	+	0.380056i	$0.875905\pi$
$14$	−3684.96	+	555.418i	−0.358909	+	0.0540969i
$15$	−7682.97	−	7128.76i	−0.587773	−	0.545374i
$16$	−9387.64	−	4520.85i	−0.572976	−	0.275931i
$17$	−1402.53	+	956.230i	−0.0692375	+	0.0472053i	−0.597444	−	0.801911i	$-0.703817\pi$
$17$	−1402.53	+	956.230i	−0.0692375	+	0.0472053i	0.528207	+	0.849116i	$0.322865\pi$
$18$	11586.9	+	29522.9i	0.468287	+	1.19318i
$19$	27686.2	−	8540.07i	0.926033	−	0.285643i	0.205174	−	0.978725i	$-0.434224\pi$
$19$	27686.2	−	8540.07i	0.926033	−	0.285643i	0.720858	+	0.693082i	$0.243748\pi$
$20$	79778.3	−	74023.4i	2.22987	−	2.06902i
$21$	2797.74	−	3508.25i	0.0659233	−	0.0826652i
$22$	18336.5	−	22993.3i	0.367145	−	0.460385i
$23$	38198.8	−	35443.3i	0.654640	−	0.607417i	−0.281282	−	0.959625i	$-0.590760\pi$
$23$	38198.8	−	35443.3i	0.654640	−	0.607417i	0.935922	+	0.352208i	$0.114569\pi$
$24$	47303.7	−	14591.3i	0.698483	−	0.215454i
$25$	46717.6	+	119035.i	0.597985	+	1.52364i
$26$	112492.	−	76696.0i	1.25521	−	0.855788i
$27$	−79907.7	−	38481.5i	−0.781296	−	0.376252i
$28$	34156.0	+	31692.2i	0.294045	+	0.272834i
$29$	67958.2	−	10243.0i	0.517427	−	0.0779895i	0.114863	−	0.993381i	$-0.463357\pi$
$29$	67958.2	−	10243.0i	0.517427	−	0.0779895i	0.402564	+	0.915392i	$0.368119\pi$
$30$	−15020.5	+	200435.i	−0.101569	+	1.35534i
$31$	−87693.5	+	223439.i	−0.528690	+	1.34708i	0.378204	+	0.925722i	$0.376542\pi$
$31$	−87693.5	+	223439.i	−0.528690	+	1.34708i	−0.906894	+	0.421358i	$0.861553\pi$
$32$	−16594.6	−	72705.7i	−0.0895245	−	0.392233i
$33$	2646.36	+	35313.3i	0.0128189	+	0.171056i
$34$	31107.6	+	9595.42i	0.135735	+	0.0418686i
$35$	−79461.7	+	38266.7i	−0.313270	+	0.150863i
$36$	198271.	−	343416.i	0.708273	−	1.22677i
$37$	−158938.	−	275289.i	−0.515849	−	0.893476i	−0.999831	−	0.0183981i	$-0.994143\pi$
$37$	−158938.	−	275289.i	−0.515849	−	0.893476i	0.483982	−	0.875078i	$-0.339190\pi$
$38$	−459094.	−	313005.i	−1.35725	−	0.925355i
$39$	−36480.0	+	159829.i	−0.0984756	+	0.431450i
$40$	−962108.	−	145015.i	−2.37692	−	0.358263i
$41$	416961.	+	522853.i	0.944827	+	1.18478i	0.982646	+	0.185491i	$0.0593874\pi$
$41$	416961.	+	522853.i	0.944827	+	1.18478i	−0.0378194	+	0.999285i	$0.512041\pi$
$42$	−86054.4			−0.179226
$43$	110319.	+	509557.i	0.211598	+	0.977357i
$43$	110319.	+	509557.i	0.211598	+	0.977357i
$44$	−367714.			−0.650767
$45$	467987.	+	586837.i	0.765579	+	0.960006i
$46$	−988172.	−	148943.i	−1.49686	−	0.225615i
$47$	−93521.6	+	409745.i	−0.131392	+	0.575666i	0.865774	+	0.500435i	$0.166827\pi$
$47$	−93521.6	+	409745.i	−0.131392	+	0.575666i	−0.997166	+	0.0752312i	$0.976031\pi$
$48$	−198799.	−	135539.i	−0.259460	−	0.176897i
$49$	392892.	+	680508.i	0.477075	+	0.826318i
$50$	1.22616e6	−	2.12377e6i	1.38724	−	2.40278i
$51$	−35316.6	+	17007.6i	−0.0372806	+	0.0179534i
$52$	−1.62668e6	−	501766.i	−1.60432	−	0.494868i
$53$	2888.29	+	38541.5i	0.00266486	+	0.0355601i	0.998378	−	0.0569382i	$-0.0181338\pi$
$53$	2888.29	+	38541.5i	0.00266486	+	0.0355601i	−0.995713	+	0.0924983i	$0.970515\pi$
$54$	378482.	+	1.65824e6i	0.327090	+	1.43308i
$55$	254286.	−	647911.i	0.206088	−	0.525105i
$56$	31130.1	−	415402.i	0.0236877	−	0.316090i
$57$	661583.	−	99717.6i	0.473175	−	0.0713197i
$58$	−966162.	−	896467.i	−0.650207	−	0.603304i
$59$	−1.77090e6	−	852819.i	−1.12256	−	0.540599i	−0.221881	−	0.975074i	$-0.571220\pi$
$59$	−1.77090e6	−	852819.i	−1.12256	−	0.540599i	−0.900684	+	0.434475i	$0.856934\pi$
$60$	2.07643e6	−	1.41569e6i	1.24105	−	0.846132i
$61$	185527.	+	472715.i	0.104653	+	0.266652i	0.973603	−	0.228248i	$-0.0732998\pi$
$61$	185527.	+	472715.i	0.104653	+	0.266652i	−0.868950	+	0.494900i	$0.835205\pi$
$62$	4.39874e6	−	1.35683e6i	2.34400	−	0.723028i
$63$	−235571.	+	218578.i	−0.118694	+	0.110132i
$64$	−1.72325e6	+	2.16089e6i	−0.821710	+	1.03039i
$65$	2.00902e6	−	2.51923e6i	0.907376	−	1.13781i
$66$	497834.	−	461922.i	0.213148	−	0.197772i
$67$	−2.98687e6	+	921326.i	−1.21326	+	0.374241i	−0.834372	−	0.551201i	$-0.814170\pi$
$67$	−2.98687e6	+	921326.i	−1.21326	+	0.374241i	−0.378888	+	0.925443i	$0.623693\pi$
$68$	−148704.	−	378892.i	−0.0573511	−	0.146128i
$69$	994221.	−	677848.i	0.364343	−	0.248405i
$70$	1.52389e6	+	733866.i	0.531019	+	0.255725i
$71$	−2.66957e6	−	2.47700e6i	−0.885190	−	0.821337i	0.0996101	−	0.995027i	$-0.468240\pi$
$71$	−2.66957e6	−	2.47700e6i	−0.885190	−	0.821337i	−0.984800	+	0.173690i	$0.944431\pi$
$72$	−3.50561e6	+	528386.i	−1.10688	+	0.166835i
$73$	−312698.	+	4.17267e6i	−0.0940796	+	1.25540i	0.727818	+	0.685770i	$0.240534\pi$
$73$	−312698.	+	4.17267e6i	−0.0940796	+	1.25540i	−0.821898	+	0.569635i	$0.807085\pi$
$74$	−2.22716e6	+	5.67472e6i	−0.638912	+	1.62792i
$75$	657075.	+	2.87884e6i	0.179846	+	0.787957i
$76$	519174.	+	6.92790e6i	0.135664	+	1.81031i
$77$	284755.	+	87835.2i	0.0710810	+	0.0219256i
$78$	2.83263e6	−	1.36412e6i	0.675862	−	0.325478i
$79$	−2.34401e6	+	4.05994e6i	−0.534890	+	0.926457i	0.464278	+	0.885689i	$0.346314\pi$
$79$	−2.34401e6	+	4.05994e6i	−0.534890	+	0.926457i	−0.999169	+	0.0407677i	$0.987020\pi$
$80$	2.36455e6	+	4.09553e6i	0.516338	+	0.894324i
$81$	1.29613e6	+	883690.i	0.270990	+	0.184758i
$82$	2.85386e6	−	1.25036e7i	0.571589	−	2.50430i
$83$	4.52040e6	+	681341.i	0.867769	+	0.130795i	0.567813	−	0.823158i	$-0.307790\pi$
$83$	4.52040e6	+	681341.i	0.867769	+	0.130795i	0.299956	+	0.953953i	$0.403028\pi$
$84$	670848.	+	841217.i	0.123494	+	0.154857i
$85$	770442.			0.136073
$86$	6.32105e6	−	7.74690e6i	1.07163	−	1.31336i
$87$	1.58702e6			0.258383
$88$	2.04970e6	+	2.57025e6i	0.320628	+	0.402055i
$89$	−1.01819e7	−	1.53467e6i	−1.53095	−	0.230754i	−0.671128	−	0.741341i	$-0.734190\pi$
$89$	−1.01819e7	−	1.53467e6i	−1.53095	−	0.230754i	−0.859826	+	0.510587i	$0.829428\pi$
$90$	3.20310e6	−	1.40337e7i	0.463151	−	2.02920i
$91$	1.13984e6	+	777128.i	0.158562	+	0.108105i
$92$	6.24745e6	+	1.08209e7i	0.836460	+	1.44879i
$93$	−2.77141e6	+	4.80022e6i	−0.357282	+	0.618830i
$94$	7.26183e6	−	3.49711e6i	0.901776	−	0.434272i
$95$	−1.25660e7	−	3.87609e6i	−1.50371	−	0.463833i
$96$	−128693.	−	1.71728e6i	−0.0148458	−	0.198104i
$97$	−2.58712e6	−	1.13349e7i	−0.287816	−	1.26100i	−0.887515	−	0.460778i	$-0.847570\pi$
$97$	−2.58712e6	−	1.13349e7i	−0.287816	−	1.26100i	0.599699	−	0.800225i	$-0.295287\pi$
$98$	5.50550e6	−	1.40278e7i	0.590888	−	1.50556i
$99$	189522.	−	2.52900e6i	0.0196307	−	0.261954i
$100$	−3.03195e7	+	4.56993e6i	−3.03195	+	0.456993i
$101$	1.30825e7	+	1.21388e7i	1.26347	+	1.17233i	0.976764	+	0.214315i	$0.0687521\pi$
$101$	1.30825e7	+	1.21388e7i	1.26347	+	1.17233i	0.286710	+	0.958017i	$0.407438\pi$
$102$	677290.	+	326166.i	0.0631937	+	0.0304325i
$103$	1.39028e7	−	9.47877e6i	1.25364	−	0.854715i	0.259811	−	0.965660i	$-0.416340\pi$
$103$	1.39028e7	−	9.47877e6i	1.25364	−	0.854715i	0.993827	+	0.110944i	$0.0353875\pi$
$104$	5.56019e6	+	1.41671e7i	0.484700	+	1.23500i
$105$	−1.94614e6	+	600304.i	−0.164063	+	0.0506068i
$106$	543344.	−	504149.i	0.0443103	−	0.0411139i
$107$	−1.08849e7	+	1.36492e7i	−0.858974	+	1.07712i	0.137271	+	0.990534i	$0.456167\pi$
$107$	−1.08849e7	+	1.36492e7i	−0.858974	+	1.07712i	−0.996244	+	0.0865853i	$0.972404\pi$
$108$	1.32595e7	−	1.66268e7i	1.01284	−	1.27007i
$109$	−1.17105e7	+	1.08658e7i	−0.866131	+	0.803652i	−0.981856	−	0.189629i	$-0.939272\pi$
$109$	−1.17105e7	+	1.08658e7i	−0.866131	+	0.803652i	0.115724	+	0.993281i	$0.463081\pi$
$110$	−1.27551e7	+	3.93443e6i	−0.913713	+	0.281843i
$111$	−2.68175e6	−	6.83300e6i	−0.186118	−	0.474221i
$112$	−1.67289e6	+	1.14056e6i	−0.112513	+	0.0767104i
$113$	7.43817e6	+	3.58204e6i	0.484944	+	0.233537i	0.660348	−	0.750960i	$-0.270409\pi$
$113$	7.43817e6	+	3.58204e6i	0.484944	+	0.233537i	−0.175404	+	0.984497i	$0.556123\pi$
$114$	−9.40573e6	−	8.72724e6i	−0.594601	−	0.551709i
$115$	−2.33867e7	+	3.52498e6i	−1.43393	+	0.216130i
$116$	−1.23150e6	+	1.64332e7i	−0.0732537	+	0.977503i
$117$	4.28936e6	−	1.09291e7i	0.247595	−	0.630862i
$118$	8.38784e6	+	3.67495e7i	0.469962	+	2.05904i
$119$	24650.1	+	328932.i	0.00134092	+	0.0178934i
$120$	−2.14698e7	−	6.62255e6i	−1.13421	−	0.349858i
$121$	1.54385e7	−	7.43480e6i	0.792240	−	0.381523i
$122$	4.86939e6	−	8.43402e6i	0.242781	−	0.420509i
$123$	7.72144e6	+	1.33739e7i	0.374137	+	0.648024i
$124$	−4.75545e7	−	3.24221e7i	−2.23983	−	1.52709i
$125$	5.02444e6	−	2.20135e7i	0.230093	−	1.00810i
$126$	6.09403e6	+	918528.i	0.271399	+	0.0409068i
$127$	−1.73340e7	−	2.17361e7i	−0.750905	−	0.941606i	0.248731	−	0.968573i	$-0.419987\pi$
$127$	−1.73340e7	−	2.17361e7i	−0.750905	−	0.941606i	−0.999636	+	0.0269670i	$0.991415\pi$
$128$	4.34591e7			1.83166
$129$	765305.	+	1.20150e7i	0.0313885	+	0.492786i
$130$	−6.17945e7			−2.46688
$131$	4.94206e6	+	6.19714e6i	0.192069	+	0.240847i	0.868536	−	0.495626i	$-0.165061\pi$
$131$	4.94206e6	+	6.19714e6i	0.192069	+	0.240847i	−0.676467	+	0.736473i	$0.736490\pi$
$132$	−8.39641e6	−	1.26556e6i	−0.317750	−	0.0478930i
$133$	1.25281e6	−	5.48893e6i	0.0461748	−	0.202305i
$134$	4.95283e7	+	3.37678e7i	1.77822	+	1.21237i
$135$	2.01271e7	+	3.48612e7i	0.704066	+	1.21948i
$136$	−1.81948e6	+	3.15143e6i	−0.0620241	+	0.107429i
$137$	−1.94855e7	+	9.38371e6i	−0.647424	+	0.311783i	−0.728623	−	0.684915i	$-0.759839\pi$
$137$	−1.94855e7	+	9.38371e6i	−0.647424	+	0.311783i	0.0811988	+	0.996698i	$0.474125\pi$
$138$	−2.20514e7	−	6.80196e6i	−0.714265	−	0.220322i
$139$	−302861.	−	4.04140e6i	−0.00956516	−	0.127638i	0.990377	−	0.138396i	$-0.0441947\pi$
$139$	−302861.	−	4.04140e6i	−0.00956516	−	0.127638i	−0.999942	+	0.0107578i	$0.996576\pi$
$140$	−4.70583e6	−	2.06176e7i	−0.144940	−	0.635023i
$141$	−3.54569e6	+	9.03428e6i	−0.106521	+	0.271411i
$142$	−5.21912e6	+	6.96443e7i	−0.152964	+	2.04116i
$143$	−1.07655e7	+	1.62265e6i	−0.307865	+	0.0464032i
$144$	1.26315e7	+	1.17203e7i	0.352521	+	0.327092i
$145$	−2.81036e7	−	1.35340e7i	−0.765551	−	0.368670i
$146$	6.63027e7	−	4.52044e7i	1.76318	−	1.20211i
$147$	6.62923e6	+	1.68910e7i	0.172128	+	0.438576i
$148$	7.28349e7	−	2.24666e7i	1.84682	−	0.569667i
$149$	−2.12831e7	+	1.97478e7i	−0.527087	+	0.489065i	−0.898239	−	0.439507i	$-0.855153\pi$
$149$	−2.12831e7	+	1.97478e7i	−0.527087	+	0.489065i	0.371153	+	0.928572i	$0.378963\pi$
$150$	3.53077e7	−	4.42744e7i	0.854181	−	1.07111i
$151$	6.86162e6	−	8.60421e6i	0.162184	−	0.203372i	−0.694099	−	0.719880i	$-0.744197\pi$
$151$	6.86162e6	−	8.60421e6i	0.162184	−	0.203372i	0.856282	+	0.516508i	$0.172768\pi$
$152$	4.55307e7	−	4.22463e7i	1.05160	−	0.975745i
$153$	2.68252e6	−	827448.i	0.0605512	−	0.0186776i
$154$	−2.08786e6	−	5.31978e6i	−0.0460658	−	0.117374i
$155$	9.00133e7	−	6.13701e7i	1.94154	−	1.32372i
$156$	−3.54170e7	−	1.70559e7i	−0.746922	−	0.359699i
$157$	5.06323e7	+	4.69799e7i	1.04419	+	0.968865i	0.999546	−	0.0301385i	$-0.00959482\pi$
$157$	5.06323e7	+	4.69799e7i	1.04419	+	0.968865i	0.0446420	+	0.999003i	$0.485785\pi$
$158$	8.89011e7	−	1.33997e7i	1.79311	−	0.270268i
$159$	−66696.4	+	890001.i	−0.00131587	+	0.0175590i
$160$	−1.23659e7	+	3.15079e7i	−0.238675	+	0.608134i
$161$	−2.25321e6	−	9.87195e6i	−0.0425511	−	0.186428i
$162$	−2.24820e6	−	3.00002e7i	−0.0415464	−	0.554398i
$163$	3.49013e7	+	1.07656e7i	0.631225	+	0.194707i	0.593826	−	0.804593i	$-0.297617\pi$
$163$	3.49013e7	+	1.07656e7i	0.631225	+	0.194707i	0.0373989	+	0.999300i	$0.488093\pi$
$164$	−1.44475e8	+	6.95756e7i	−2.55764	+	1.23170i
$165$	8.03631e6	−	1.39193e7i	0.139272	−	0.241226i
$166$	−4.38350e7	−	7.59244e7i	−0.743777	−	1.28826i
$167$	8.64868e7	+	5.89657e7i	1.43695	+	0.979697i	0.996645	+	0.0818497i	$0.0260828\pi$
$167$	8.64868e7	+	5.89657e7i	1.43695	+	0.979697i	0.440307	+	0.897847i	$0.354870\pi$
$168$	2.14051e6	−	9.37820e6i	0.0348285	−	0.152594i
$169$	1.22090e7	+	1.84022e6i	0.194571	+	0.0293269i
$170$	−9.21223e6	−	1.15518e7i	−0.143811	−	0.180334i
$171$	−4.79151e7			−0.732800
$172$	−1.25006e8	−	1.39884e6i	−1.87318	−	0.0209613i
$173$	−6.28442e7			−0.922792			−0.461396	−	0.887194i	$-0.652651\pi$
$173$	−6.28442e7			−0.922792			−0.461396	+	0.887194i	$0.652651\pi$
$174$	−1.89761e7	−	2.37953e7i	−0.273076	−	0.342427i
$175$	2.45708e7	+	3.70345e6i	0.346566	+	0.0522365i
$176$	3.55558e6	−	1.55780e7i	0.0491604	−	0.215386i
$177$	−3.75017e7	−	2.55682e7i	−0.508329	−	0.346573i
$178$	9.87349e7	+	1.71014e8i	1.31220	+	2.27280i
$179$	2.42377e7	−	4.19809e7i	0.315868	−	0.547100i	−0.663754	−	0.747951i	$-0.731038\pi$
$179$	2.42377e7	−	4.19809e7i	0.315868	−	0.547100i	0.979622	+	0.200852i	$0.0643709\pi$
$180$	−1.62156e8	+	7.80900e7i	−2.07242	+	0.998026i
$181$	−4.58122e7	−	1.41312e7i	−0.574256	−	0.177135i	−0.00599396	−	0.999982i	$-0.501908\pi$
$181$	−4.58122e7	−	1.41312e7i	−0.574256	−	0.177135i	−0.568262	+	0.822847i	$0.692384\pi$
$182$	−1.97710e6	−	2.63825e7i	−0.0243096	−	0.324390i
$183$	2.60941e6	+	1.14326e7i	0.0314748	+	0.137900i
$184$	4.08115e7	−	1.03986e8i	0.482971	−	1.23059i
$185$	−1.07817e7	+	1.43871e8i	−0.125195	+	1.67060i
$186$	1.05111e8	−	1.58429e7i	1.19771	−	0.180526i
$187$	−1.90824e6	−	1.77059e6i	−0.0213397	−	0.0198004i
$188$	−9.07963e7	−	4.37252e7i	−0.996588	−	0.479932i
$189$	−1.42397e7	+	9.70844e6i	−0.153421	+	0.104600i
$190$	9.21354e7	+	2.34757e8i	0.974516	+	2.48303i
$191$	−1.30981e7	+	4.04024e6i	−0.136017	+	0.0419557i	−0.362016	−	0.932172i	$-0.617911\pi$
$191$	−1.30981e7	+	4.04024e6i	−0.136017	+	0.0419557i	0.225999	+	0.974127i	$0.427435\pi$
$192$	−4.67860e7	+	4.34111e7i	−0.477047	+	0.442635i
$193$	8.40662e7	−	1.05416e8i	0.841727	−	1.05549i	−0.155977	−	0.987761i	$-0.549853\pi$
$193$	8.40662e7	−	1.05416e8i	0.841727	−	1.05549i	0.997704	−	0.0677310i	$-0.0215760\pi$
$194$	−1.39018e8	+	1.74323e8i	−1.36698	+	1.71414i
$195$	5.45445e7	−	5.06099e7i	0.526781	−	0.488781i
$196$	−1.80046e8	+	5.55369e7i	−1.70800	+	0.526848i
$197$	−4.06233e7	−	1.03506e8i	−0.378567	−	0.964574i	−0.985478	−	0.169804i	$-0.945687\pi$
$197$	−4.06233e7	−	1.03506e8i	−0.378567	−	0.964574i	0.606910	−	0.794770i	$-0.292409\pi$
$198$	−4.01851e7	+	2.73978e7i	−0.367906	+	0.250834i
$199$	−7.11551e7	−	3.42665e7i	−0.640059	−	0.308236i	0.0855598	−	0.996333i	$-0.472732\pi$
$199$	−7.11551e7	−	3.42665e7i	−0.640059	−	0.308236i	−0.725619	+	0.688097i	$0.758446\pi$
$200$	2.00949e8	+	1.86454e8i	1.77616	+	1.64803i
$201$	−7.13733e7	+	1.07578e7i	−0.619940	+	0.0934410i
$202$	2.55769e7	−	3.41300e8i	0.218332	−	2.91344i
$203$	4.87903e6	−	1.24316e7i	0.0409352	−	0.104301i
$204$	−2.09150e6	−	9.16346e6i	−0.0172485	−	0.0755707i
$205$	−2.26827e7	−	3.02679e8i	−0.183889	−	2.45383i
$206$	−3.08358e8	−	9.51160e7i	−2.45765	−	0.758086i
$207$	−7.76420e7	+	3.73904e7i	−0.608416	+	0.292998i
$208$	3.69861e7	−	6.40619e7i	0.284982	−	0.493603i
$209$	2.22158e7	+	3.84789e7i	0.168326	+	0.291549i
$210$	3.22709e7	+	2.20019e7i	0.240460	+	0.163943i
$211$	−7.28177e6	+	3.19035e7i	−0.0533640	+	0.233803i	−0.994576	−	0.104014i	$-0.966831\pi$
$211$	−7.28177e6	+	3.19035e7i	−0.0533640	+	0.233803i	0.941212	+	0.337817i	$0.109688\pi$
$212$	−9.16398e6	−	1.38125e6i	−0.0660554	−	0.00995626i
$213$	−5.24321e7	−	6.57478e7i	−0.371765	−	0.466179i
$214$	3.34803e8			2.33529
$215$	8.89105e7	−	2.19293e8i	0.610124	−	1.50484i
$216$	−1.90129e8			−1.28369
$217$	2.90813e7	+	3.64668e7i	0.193199	+	0.242264i
$218$	3.02942e8	+	4.56611e7i	1.98044	+	0.298503i
$219$	−2.15012e7	+	9.42029e7i	−0.138327	+	0.606052i
$220$	1.37895e8	+	9.40151e7i	0.873109	+	0.595276i
$221$	−6.02559e6	−	1.04366e7i	−0.0375514	−	0.0650410i
$222$	−7.03859e7	+	1.21912e8i	−0.431768	+	0.747844i
$223$	−4.44074e7	+	2.13855e7i	−0.268157	+	0.129137i	−0.563131	−	0.826368i	$-0.690403\pi$
$223$	−4.44074e7	+	2.13855e7i	−0.268157	+	0.129137i	0.294974	+	0.955505i	$0.404689\pi$
$224$	−1.38476e7	−	4.27143e6i	−0.0823203	−	0.0253925i
$225$	−1.58034e7	−	2.10881e8i	−0.0924934	−	1.23424i
$226$	−3.52308e7	−	1.54356e8i	−0.203022	−	0.889498i
$227$	2.75124e7	−	7.01005e7i	0.156113	−	0.397769i	−0.831323	−	0.555790i	$-0.812416\pi$
$227$	2.75124e7	−	7.01005e7i	0.156113	−	0.397769i	0.987436	+	0.158021i	$0.0505113\pi$
$228$	−1.19888e7	+	1.59979e8i	−0.0669890	+	0.893906i
$229$	1.36190e8	−	2.05274e7i	0.749413	−	0.112956i	0.236780	−	0.971563i	$-0.423908\pi$
$229$	1.36190e8	−	2.05274e7i	0.749413	−	0.112956i	0.512634	+	0.858608i	$0.328670\pi$
$230$	3.32489e8	+	3.08505e8i	1.80190	+	1.67192i
$231$	6.19982e6	+	2.98568e6i	0.0330931	+	0.0159368i
$232$	1.21729e8	−	8.29936e7i	0.640010	−	0.436351i
$233$	9.06296e7	+	2.30920e8i	0.469380	+	1.19596i	0.948094	+	0.317990i	$0.103008\pi$
$233$	9.06296e7	+	2.30920e8i	0.469380	+	1.19596i	−0.478714	+	0.877971i	$0.658897\pi$
$234$	−2.15156e8	+	6.63668e7i	−1.09774	+	0.338607i
$235$	1.39832e8	−	1.29746e8i	0.702863	−	0.652161i
$236$	2.93853e8	−	3.68480e8i	1.45525	−	1.82483i
$237$	−6.74964e7	+	8.46379e7i	−0.329353	+	0.412996i
$238$	4.63717e6	−	4.30266e6i	0.0222963	−	0.0206880i
$239$	−1.07359e8	+	3.31157e7i	−0.508679	+	0.156907i	−0.538462	−	0.842650i	$-0.680995\pi$
$239$	−1.07359e8	+	3.31157e7i	−0.508679	+	0.156907i	0.0297829	+	0.999556i	$0.490518\pi$
$240$	3.98970e7	+	1.01656e8i	0.186295	+	0.474671i
$241$	−2.08920e8	+	1.42439e8i	−0.961436	+	0.655496i	−0.938878	−	0.344250i	$-0.888133\pi$
$241$	−2.08920e8	+	1.42439e8i	−0.961436	+	0.655496i	−0.0225576	+	0.999746i	$0.507181\pi$
$242$	−2.96075e8	−	1.42582e8i	−1.34291	−	0.646712i
$243$	1.68743e8	+	1.56570e8i	0.754402	+	0.699983i
$244$	−1.20406e8	+	1.81483e7i	−0.530620	+	0.0799781i
$245$	2.66521e7	−	3.55647e8i	0.115784	−	1.54503i
$246$	1.08199e8	−	2.75686e8i	0.463393	−	1.18071i
$247$	4.57713e7	+	2.00537e8i	0.193265	+	0.846750i
$248$	3.84533e7	+	5.13124e8i	0.160086	+	2.13620i
$249$	1.00874e8	+	3.11156e7i	0.414079	+	0.127727i
$250$	−3.90142e8	+	1.87882e8i	−1.57918	+	0.760494i
$251$	−1.99490e8	+	3.45527e8i	−0.796276	+	1.37919i	0.125749	+	0.992062i	$0.459867\pi$
$251$	−1.99490e8	+	3.45527e8i	−0.796276	+	1.37919i	−0.922026	+	0.387129i	$0.873467\pi$
$252$	−3.85279e7	−	6.67322e7i	−0.151661	−	0.262684i
$253$	6.60257e7	+	4.50155e7i	0.256325	+	0.174759i
$254$	−1.18641e8	+	5.19801e8i	−0.454273	+	1.99030i
$255$	1.75923e7	+	2.65162e6i	0.0664405	+	0.0100143i
$256$	−2.99067e8	−	3.75018e8i	−1.11411	−	1.39705i
$257$	−1.08408e8			−0.398379			−0.199189	−	0.979961i	$-0.563831\pi$
$257$	−1.08408e8			−0.398379			−0.199189	+	0.979961i	$0.563831\pi$
$258$	1.70998e8	−	1.55139e8i	0.619900	−	0.562407i
$259$	−6.17694e7			−0.220915
$260$	4.81728e8	+	6.04067e8i	1.69979	+	2.13147i
$261$	−1.12386e8	−	1.69395e7i	−0.391266	−	0.0589738i
$262$	3.38255e7	−	1.48199e8i	0.116196	−	0.509087i
$263$	4.17531e7	+	2.84668e7i	0.141529	+	0.0964925i	0.632014	−	0.774957i	$-0.282228\pi$
$263$	4.17531e7	+	2.84668e7i	0.141529	+	0.0964925i	−0.490486	+	0.871449i	$0.663181\pi$
$264$	3.79572e7	+	6.57437e7i	0.126964	+	0.219908i
$265$	8.77096e6	−	1.51917e7i	0.0289525	−	0.0501473i
$266$	−9.72794e7	+	4.68473e7i	−0.316909	+	0.152615i
$267$	−2.27212e8	−	7.00856e7i	−0.730536	−	0.225341i
$268$	−5.60099e7	−	7.47401e8i	−0.177743	−	2.37182i
$269$	−1.09499e8	−	4.79747e8i	−0.342987	−	1.50272i	−0.792734	−	0.609568i	$-0.791343\pi$
$269$	−1.09499e8	−	4.79747e8i	−0.342987	−	1.50272i	0.449747	−	0.893156i	$-0.351514\pi$
$270$	2.82037e8	−	7.18618e8i	0.872032	−	2.22190i
$271$	−3.00053e6	+	4.00393e7i	−0.00915810	+	0.122206i	−0.999909	−	0.0134865i	$-0.995707\pi$
$271$	−3.00053e6	+	4.00393e7i	−0.00915810	+	0.122206i	0.990751	+	0.135693i	$0.0433260\pi$
$272$	1.74894e7	−	2.63611e6i	0.0526969	−	0.00794278i
$273$	2.33525e7	+	2.16680e7i	0.0694648	+	0.0644539i
$274$	3.73686e8	+	1.79958e8i	1.09744	+	0.528498i
$275$	−1.62024e8	+	1.10466e8i	−0.469803	+	0.320306i
$276$	1.05413e8	+	2.68587e8i	0.301795	+	0.768960i
$277$	5.34584e8	−	1.64897e8i	1.51125	−	0.466160i	0.575198	−	0.818015i	$-0.304925\pi$
$277$	5.34584e8	−	1.64897e8i	1.51125	−	0.466160i	0.936055	+	0.351855i	$0.114449\pi$
$278$	−5.69742e7	+	5.28644e7i	−0.159046	+	0.147573i
$279$	2.47497e8	−	3.10352e8i	0.682269	−	0.855538i
$280$	−1.17882e8	+	1.47819e8i	−0.320918	+	0.402418i
$281$	−2.78620e8	+	2.58521e8i	−0.749100	+	0.695063i	−0.959235	−	0.282609i	$-0.908800\pi$
$281$	−2.78620e8	+	2.58521e8i	−0.749100	+	0.695063i	0.210135	+	0.977672i	$0.432610\pi$
$282$	1.77853e8	−	5.48605e7i	0.472270	−	0.145676i
$283$	3.57888e7	+	9.11883e7i	0.0938630	+	0.239159i	0.970093	−	0.242735i	$-0.0780444\pi$
$283$	3.57888e7	+	9.11883e7i	0.0938630	+	0.239159i	−0.876230	+	0.481894i	$0.839949\pi$
$284$	7.21488e8	−	4.91902e8i	1.86902	−	1.27428i
$285$	−2.73593e8	−	1.31755e8i	−0.700080	−	0.337141i
$286$	1.53054e8	+	1.42013e8i	0.386868	+	0.358961i
$287$	1.28500e8	−	1.93683e7i	0.320861	−	0.0483620i
$288$	−9.21645e6	+	1.22985e8i	−0.0227347	+	0.303374i
$289$	−1.48861e8	+	3.79291e8i	−0.362776	+	0.924337i
$290$	1.33112e8	+	5.83204e8i	0.320498	+	1.40419i
$291$	−2.00633e7	−	2.67726e8i	−0.0477284	−	0.636891i
$292$	−9.58763e8	−	2.95739e8i	−2.25357	−	0.695135i
$293$	−2.96535e8	+	1.42804e8i	−0.688714	+	0.331667i	−0.745299	−	0.666730i	$-0.767693\pi$
$293$	−2.96535e8	+	1.42804e8i	−0.688714	+	0.331667i	0.0565846	+	0.998398i	$0.481979\pi$
$294$	1.73992e8	−	3.01364e8i	0.399314	−	0.691632i
$295$	4.46053e8	+	7.72586e8i	1.01160	+	1.75214i
$296$	−5.63032e8	−	3.83869e8i	−1.26186	−	0.860324i
$297$	3.02651e7	−	1.32600e8i	0.0670339	−	0.293695i
$298$	5.50575e8	+	8.29859e7i	1.20520	+	0.181655i
$299$	2.30657e8	+	2.89235e8i	0.499019	+	0.625750i
$300$	−7.08047e8			−1.51404
$301$	9.64694e7	+	3.09432e7i	0.203895	+	0.0654007i
$302$	−2.11054e8			−0.440929
$303$	2.56950e8	+	3.22205e8i	0.530639	+	0.665400i
$304$	−2.98517e8	−	4.49942e7i	−0.609413	−	0.0918542i
$305$	5.12876e7	−	2.24706e8i	0.103505	−	0.453486i
$306$	−4.44816e7	−	3.03270e7i	−0.0887473	−	0.0605069i
$307$	1.73794e8	+	3.01020e8i	0.342807	+	0.593760i	0.984953	−	0.172823i	$-0.0552889\pi$
$307$	1.73794e8	+	3.01020e8i	0.342807	+	0.593760i	−0.642146	+	0.766583i	$0.721956\pi$
$308$	−3.57269e7	+	6.18807e7i	−0.0696735	+	0.120678i
$309$	3.50081e8	−	1.68590e8i	0.675015	−	0.325070i
$310$	−1.99646e9	−	6.15826e8i	−3.80623	−	1.17407i
$311$	−6.10509e7	−	8.14668e8i	−0.115088	−	1.53575i	−0.693773	−	0.720194i	$-0.744053\pi$
$311$	−6.10509e7	−	8.14668e8i	−0.115088	−	1.53575i	0.578684	−	0.815552i	$-0.303566\pi$
$312$	7.82032e7	+	3.42631e8i	0.145775	+	0.638682i
$313$	−2.77222e8	+	7.06350e8i	−0.511002	+	1.30201i	0.409869	+	0.912144i	$0.365574\pi$
$313$	−2.77222e8	+	7.06350e8i	−0.511002	+	1.30201i	−0.920871	+	0.389867i	$0.872521\pi$
$314$	9.89883e7	−	1.32091e9i	0.180439	−	2.40779i
$315$	1.44225e8	−	2.17385e7i	0.259989	−	0.0391870i
$316$	−8.24027e8	−	7.64586e8i	−1.46905	−	1.36308i
$317$	−7.83516e7	−	3.77321e7i	−0.138147	−	0.0665279i	0.363533	−	0.931581i	$-0.381570\pi$
$317$	−7.83516e7	−	3.77321e7i	−0.138147	−	0.0665279i	−0.501680	+	0.865053i	$0.667285\pi$
$318$	1.41419e7	−	9.64178e6i	0.0246611	−	0.0168137i
$319$	3.85044e7	+	9.81076e7i	0.0664114	+	0.169214i
$320$	1.19871e9	−	3.69754e8i	2.04499	−	0.630795i
$321$	−2.95522e8	+	2.74205e8i	−0.498681	+	0.462708i
$322$	−1.21075e8	+	1.51824e8i	−0.202097	+	0.253422i
$323$	−3.06646e7	+	3.84521e7i	−0.0506323	+	0.0634909i
$324$	−2.75738e8	+	2.55848e8i	−0.450391	+	0.417901i
$325$	−8.67497e8	+	2.67587e8i	−1.40177	+	0.432388i
$326$	−2.55901e8	−	6.52024e8i	−0.409081	−	1.04232i
$327$	−3.04796e8	+	2.07806e8i	−0.482050	+	0.328656i
$328$	1.29165e9	+	6.22027e8i	2.02110	+	0.973309i
$329$	5.98675e7	+	5.55489e7i	0.0926841	+	0.0859983i
$330$	−3.04793e8	+	4.59401e7i	−0.466880	+	0.0703709i
$331$	−5.28939e7	+	7.05820e8i	−0.0801692	+	1.06978i	0.801525	+	0.597962i	$0.204023\pi$
$331$	−5.28939e7	+	7.05820e8i	−0.0801692	+	1.06978i	−0.881694	+	0.471822i	$0.843597\pi$
$332$	−4.00471e8	+	1.02038e9i	−0.600604	+	1.53031i
$333$	1.16977e8	+	5.12511e8i	0.173599	+	0.760585i
$334$	−1.50015e8	−	2.00181e9i	−0.220304	−	2.93975i
$335$	1.35565e9	+	4.18163e8i	1.97011	+	0.607700i
$336$	−4.21244e7	+	2.02861e7i	−0.0605824	+	0.0291749i
$337$	−2.02780e8	+	3.51225e8i	−0.288616	+	0.499897i	−0.973480	−	0.228774i	$-0.926528\pi$
$337$	−2.02780e8	+	3.51225e8i	−0.288616	+	0.499897i	0.684864	+	0.728671i	$0.259862\pi$
$338$	−1.18393e8	−	2.05062e8i	−0.166770	−	0.288853i
$339$	1.57516e8	+	1.07392e8i	0.219596	+	0.149718i
$340$	−4.11082e7	+	1.80107e8i	−0.0567221	+	0.248516i
$341$	−3.63985e8	−	5.48618e7i	−0.497099	−	0.0749256i
$342$	5.72924e8	+	7.18424e8i	0.774472	+	0.971157i
$343$	3.12723e8			0.418437
$344$	6.87027e8	+	8.81563e8i	0.909954	+	1.16761i
$345$	−5.46147e8			−0.716049
$346$	7.51432e8	+	9.42266e8i	0.975267	+	1.22295i
$347$	−7.01271e8	−	1.05700e8i	−0.901016	−	0.135806i	−0.317833	−	0.948147i	$-0.602955\pi$
$347$	−7.01271e8	−	1.05700e8i	−0.901016	−	0.135806i	−0.583183	+	0.812341i	$0.698193\pi$
$348$	−8.46779e7	+	3.70998e8i	−0.107707	+	0.471894i
$349$	−4.60217e8	−	3.13771e8i	−0.579527	−	0.395115i	0.237778	−	0.971319i	$-0.423581\pi$
$349$	−4.60217e8	−	3.13771e8i	−0.579527	−	0.395115i	−0.817306	+	0.576205i	$0.804533\pi$
$350$	−2.38267e8	−	4.12690e8i	−0.297047	−	0.514500i
$351$	3.14826e8	−	5.45295e8i	0.388594	−	0.673065i
$352$	1.03038e8	−	4.96206e7i	0.125921	−	0.0606404i
$353$	−9.59529e8	−	2.95976e8i	−1.16104	−	0.358133i	−0.346392	−	0.938090i	$-0.612593\pi$
$353$	−9.59529e8	−	2.95976e8i	−1.16104	−	0.358133i	−0.814647	+	0.579957i	$0.803069\pi$
$354$	6.50484e7	+	8.68011e8i	0.0779337	+	1.03995i
$355$	3.67798e8	+	1.61143e9i	0.436325	+	1.91167i
$356$	9.02031e8	−	2.29834e9i	1.05961	−	2.69984i
$357$	−569220.	+	7.59571e6i	−0.000662127	+	0.00883547i
$358$	−9.19261e8	+	1.38556e8i	−1.05888	+	0.159601i
$359$	2.61369e8	+	2.42515e8i	0.298143	+	0.276636i	0.815032	−	0.579416i	$-0.196720\pi$
$359$	2.61369e8	+	2.42515e8i	0.298143	+	0.276636i	−0.516889	+	0.856052i	$0.672910\pi$
$360$	1.44972e9	+	6.98148e8i	1.63767	+	0.788658i
$361$	−4.49568e7	+	3.06510e7i	−0.0502945	+	0.0342902i
$362$	3.35901e8	+	8.55861e8i	0.372161	+	0.948251i
$363$	3.78113e8	−	1.16632e8i	0.414905	−	0.127981i
$364$	−2.42488e8	+	2.24996e8i	−0.263533	+	0.244523i
$365$	1.18411e9	−	1.48483e9i	1.27458	−	1.59827i
$366$	1.40215e8	−	1.75825e8i	0.149490	−	0.187454i
$367$	−1.06960e9	+	9.92440e8i	−1.12951	+	1.04803i	−0.131113	+	0.991367i	$0.541855\pi$
$367$	−1.06960e9	+	9.92440e8i	−1.12951	+	1.04803i	−0.998393	+	0.0566612i	$0.981955\pi$
$368$	−5.18831e8	+	1.60038e8i	−0.542698	+	0.167400i
$369$	−4.04052e8	−	1.02951e9i	−0.418644	−	1.06669i
$370$	2.28608e9	−	1.55862e9i	2.34631	−	1.59969i
$371$	6.76659e6	+	3.25862e6i	0.00687956	+	0.00331302i
$372$	−9.74278e8	−	9.03998e8i	−0.981257	−	0.910474i
$373$	4.95193e8	−	7.46383e7i	0.494076	−	0.0744699i	0.102722	−	0.994710i	$-0.467245\pi$
$373$	4.95193e8	−	7.46383e7i	0.494076	−	0.0744699i	0.391354	+	0.920240i	$0.372007\pi$
$374$	−3.73070e6	+	4.97827e7i	−0.00368757	+	0.0492071i
$375$	1.90492e8	−	4.85366e8i	0.186538	−	0.475292i
$376$	2.00485e8	+	8.78381e8i	0.194502	+	0.852168i
$377$	3.64617e7	+	4.86548e8i	0.0350463	+	0.467661i
$378$	3.15830e8	+	9.74207e7i	0.300768	+	0.0927748i
$379$	1.79424e9	−	8.64060e8i	1.69295	−	0.815279i	0.697862	−	0.716232i	$-0.254135\pi$
$379$	1.79424e9	−	8.64060e8i	1.69295	−	0.815279i	0.995083	−	0.0990476i	$-0.0315796\pi$
$380$	1.57660e9	−	2.73074e9i	1.47393	−	2.55293i
$381$	−3.20997e8	−	5.55983e8i	−0.297347	−	0.515020i
$382$	2.17194e8	+	1.48080e8i	0.199354	+	0.135917i
$383$	−5.73846e6	+	2.51418e7i	−0.00521915	+	0.0228666i	−0.977470	−	0.211072i	$-0.932304\pi$
$383$	−5.73846e6	+	2.51418e7i	−0.00521915	+	0.0228666i	0.972251	+	0.233939i	$0.0751616\pi$
$384$	9.92349e8	+	1.49573e8i	0.894345	+	0.134801i
$385$	−8.43275e7	−	1.05743e8i	−0.0753107	−	0.0944366i
$386$	−2.58576e9			−2.28840
$387$	7.40495e7	−	8.59021e8i	0.0649432	−	0.753383i
$388$	2.78781e9			2.42299
$389$	−7.72417e8	−	9.68580e8i	−0.665316	−	0.834280i	0.328594	−	0.944471i	$-0.393425\pi$
$389$	−7.72417e8	−	9.68580e8i	−0.665316	−	0.834280i	−0.993910	+	0.110191i	$0.964854\pi$
$390$	−1.41102e9	−	2.12678e8i	−1.20450	−	0.181550i
$391$	−1.96831e7	+	8.62372e7i	−0.0166523	+	0.0729585i
$392$	1.39180e9	+	9.48915e8i	1.16702	+	0.795658i
$393$	9.15188e7	+	1.58515e8i	0.0760565	+	0.131734i
$394$	−1.06621e9	+	1.84673e9i	−0.878224	+	1.52113i
$395$	1.91704e9	−	9.23199e8i	1.56510	−	0.753712i
$396$	5.81093e8	+	1.79243e8i	0.470232	+	0.145047i
$397$	−1.15153e8	−	1.53661e9i	−0.0923654	−	1.23253i	−0.830168	−	0.557514i	$-0.811755\pi$
$397$	−1.15153e8	−	1.53661e9i	−0.0923654	−	1.23253i	0.737802	−	0.675017i	$-0.235864\pi$
$398$	3.37025e8	+	1.47660e9i	0.267961	+	1.17401i
$399$	4.74981e7	−	1.21023e8i	0.0374344	−	0.0953813i
$400$	9.95691e7	−	1.32866e9i	0.0777884	−	1.03801i
$401$	−2.04446e9	+	3.08153e8i	−1.58334	+	0.238650i	−0.880973	−	0.473167i	$-0.843111\pi$
$401$	−2.04446e9	+	3.08153e8i	−1.58334	+	0.238650i	−0.702365	+	0.711817i	$0.747872\pi$
$402$	1.01472e9	+	9.41518e8i	0.779028	+	0.722832i
$403$	−1.53533e9	−	7.39374e8i	−1.16851	−	0.562725i
$404$	−3.53573e9	+	2.41062e9i	−2.66775	+	1.81884i
$405$	−2.60121e8	−	6.62778e8i	−0.194573	−	0.495764i
$406$	−2.44734e8	+	7.54904e7i	−0.181490	+	0.0559823i
$407$	3.57343e8	−	3.31566e8i	0.262727	−	0.243775i
$408$	−5.23924e7	+	6.56980e7i	−0.0381907	+	0.0478896i
$409$	−5.15647e8	+	6.46601e8i	−0.372667	+	0.467310i	−0.932434	−	0.361340i	$-0.882319\pi$
$409$	−5.15647e8	+	6.46601e8i	−0.372667	+	0.467310i	0.559767	+	0.828650i	$0.310891\pi$
$410$	−4.26706e9	+	3.95926e9i	−3.05763	+	2.83707i
$411$	−4.77229e8	+	1.47206e8i	−0.339063	+	0.104587i
$412$	1.47405e9	+	3.75582e9i	1.03842	+	2.64585i
$413$	−3.15576e8	+	2.15156e8i	−0.220434	+	0.150290i
$414$	1.48899e9	+	7.17061e8i	1.03131	+	0.496655i
$415$	−1.52098e9	−	1.41126e9i	−1.04461	−	0.969256i
$416$	5.23528e8	−	7.89092e7i	0.356544	−	0.0537404i
$417$	6.99368e6	−	9.33242e7i	0.00472313	−	0.0630258i
$418$	3.11305e8	−	7.93192e8i	0.208482	−	0.531204i
$419$	4.26741e8	+	1.86968e9i	0.283410	+	1.24170i	0.893389	+	0.449284i	$0.148321\pi$
$419$	4.26741e8	+	1.86968e9i	0.283410	+	1.24170i	−0.609979	+	0.792418i	$0.708822\pi$
$420$	−3.64941e7	−	4.86980e8i	−0.0240353	−	0.320729i
$421$	−1.70203e9	−	5.25006e8i	−1.11168	−	0.342907i	−0.316081	−	0.948732i	$-0.602367\pi$
$421$	−1.70203e9	−	5.25006e8i	−1.11168	−	0.342907i	−0.795598	+	0.605825i	$0.792843\pi$
$422$	5.65420e8	−	2.72292e8i	0.366250	−	0.176377i
$423$	3.47522e8	−	6.01927e8i	0.223250	−	0.386680i
$424$	4.14271e7	+	7.17538e7i	0.0263939	+	0.0457156i
$425$	−1.79347e8	−	1.22277e8i	−0.113327	−	0.0772651i
$426$	−3.58868e8	+	1.57230e9i	−0.224906	+	0.985378i
$427$	9.75767e7	+	1.47073e7i	0.0606524	+	0.00914189i
$428$	−2.61000e9	−	3.27284e9i	−1.60912	−	2.01777i
$429$	−2.51406e8			−0.153736
$430$	−4.35112e9	+	1.28900e9i	−2.63913	+	0.781833i
$431$	2.67851e9			1.61147			0.805737	−	0.592273i	$-0.201769\pi$
$431$	2.67851e9			1.61147			0.805737	+	0.592273i	$0.201769\pi$
$432$	5.76176e8	+	7.22502e8i	0.343845	+	0.431167i
$433$	2.59836e9	+	3.91639e8i	1.53812	+	0.231835i	0.862746	−	0.505637i	$-0.168743\pi$
$433$	2.59836e9	+	3.91639e8i	1.53812	+	0.231835i	0.675378	+	0.737472i	$0.263981\pi$
$434$	1.99045e8	−	8.72071e8i	0.116879	−	0.512080i
$435$	−5.95141e8	−	4.05760e8i	−0.346663	−	0.236351i
$436$	−1.91527e9	−	3.31734e9i	−1.10669	−	1.91685i
$437$	7.54893e8	−	1.30751e9i	0.432713	−	0.749481i
$438$	1.66954e9	−	8.04009e8i	0.949375	−	0.457195i
$439$	−2.30333e9	−	7.10482e8i	−1.29936	−	0.400799i	−0.433531	−	0.901139i	$-0.642732\pi$
$439$	−2.30333e9	−	7.10482e8i	−1.29936	−	0.400799i	−0.865829	+	0.500339i	$0.833209\pi$
$440$	−1.11504e8	−	1.48791e9i	−0.0624030	−	0.832710i
$441$	−2.89165e8	−	1.26691e9i	−0.160550	−	0.703416i
$442$	−8.44351e7	+	2.15137e8i	−0.0465099	+	0.118505i
$443$	−1.02755e8	+	1.37117e9i	−0.0561552	+	0.749338i	0.896064	+	0.443924i	$0.146414\pi$
$443$	−1.02755e8	+	1.37117e9i	−0.0561552	+	0.749338i	−0.952220	+	0.305414i	$0.901205\pi$
$444$	1.74044e9	−	2.62330e8i	0.943669	−	0.142235i
$445$	3.42588e9	+	3.17876e9i	1.84295	+	1.71000i
$446$	8.51630e8	+	4.10124e8i	0.454547	+	0.218898i
$447$	−5.53945e8	+	3.77673e8i	−0.293353	+	0.200005i
$448$	1.96215e8	+	4.99948e8i	0.103100	+	0.262695i
$449$	−2.19204e9	+	6.76154e8i	−1.14284	+	0.352520i	−0.807669	−	0.589637i	$-0.799271\pi$
$449$	−2.19204e9	+	6.76154e8i	−1.14284	+	0.352520i	−0.335173	+	0.942157i	$0.608795\pi$
$450$	−2.97293e9	+	2.75847e9i	−1.53794	+	1.42700i
$451$	−6.39422e8	+	8.01810e8i	−0.328224	+	0.411579i
$452$	−1.23425e9	+	1.54770e9i	−0.628664	+	0.788320i
$453$	1.86292e8	−	1.72854e8i	0.0941566	−	0.0873645i
$454$	−1.38003e9	+	4.25684e8i	−0.692140	+	0.213497i
$455$	−2.28754e8	−	5.82855e8i	−0.113849	−	0.290082i
$456$	1.18505e9	−	8.07954e8i	0.585275	−	0.399034i
$457$	2.57324e9	+	1.23921e9i	1.26117	+	0.607347i	0.940483	−	0.339839i	$-0.110373\pi$
$457$	2.57324e9	+	1.23921e9i	1.26117	+	0.607347i	0.320685	+	0.947186i	$0.396087\pi$
$458$	−1.93622e9	−	1.79655e9i	−0.941726	−	0.873794i
$459$	1.48870e8	−	2.24386e7i	0.0718561	−	0.0108306i
$460$	4.23800e8	−	5.65521e9i	0.203006	−	2.70892i
$461$	1.11772e9	−	2.84790e9i	0.531348	−	1.35385i	−0.373308	−	0.927708i	$-0.621776\pi$
$461$	1.11772e9	−	2.84790e9i	0.531348	−	1.35385i	0.904655	−	0.426144i	$-0.140128\pi$
$462$	−2.93654e7	−	1.28658e8i	−0.0138544	−	0.0607003i
$463$	−1.17085e8	−	1.56239e9i	−0.0548237	−	0.731571i	−0.955106	−	0.296264i	$-0.904259\pi$
$463$	−1.17085e8	−	1.56239e9i	−0.0548237	−	0.731571i	0.900282	−	0.435306i	$-0.143360\pi$
$464$	−6.84274e8	−	2.11071e8i	−0.317993	−	0.0980878i
$465$	2.26659e9	−	1.09153e9i	1.04541	−	0.503444i
$466$	2.37869e9	−	4.12001e9i	1.08890	−	1.88602i
$467$	−1.41500e9	−	2.45086e9i	−0.642907	−	1.11355i	−0.984781	−	0.173802i	$-0.944395\pi$
$467$	−1.41500e9	−	2.45086e9i	−0.642907	−	1.11355i	0.341873	−	0.939746i	$-0.388939\pi$
$468$	2.32604e9	+	1.58587e9i	1.04895	+	0.715165i
$469$	−1.35157e8	+	5.92161e8i	−0.0604969	+	0.265054i
$470$	−3.61735e9	−	5.45228e8i	−1.60712	−	0.242234i
$471$	9.94453e8	+	1.24700e9i	0.438542	+	0.549914i
$472$	−4.21360e9			−1.84440
$473$	−7.24183e8	+	3.38819e8i	−0.314655	+	0.147215i
$474$	2.07609e9			0.895412
$475$	2.31000e9	+	2.89665e9i	0.988972	+	1.24013i
$476$	−7.82099e7	−	1.17883e7i	−0.0332382	−	0.00500985i
$477$	1.42229e7	−	6.23145e7i	0.00600030	−	0.0262890i
$478$	1.78022e9	+	1.21373e9i	0.745550	+	0.508307i
$479$	1.10869e9	+	1.92031e9i	0.460932	+	0.798357i	0.999008	−	0.0445394i	$-0.0141820\pi$
$479$	1.10869e9	+	1.92031e9i	0.460932	+	0.798357i	−0.538076	+	0.842896i	$0.680849\pi$
$480$	−3.90806e8	+	6.76895e8i	−0.161293	+	0.279368i
$481$	2.03325e9	−	9.79160e8i	0.833072	−	0.401186i
$482$	4.63376e9	+	1.42933e9i	1.88482	+	0.581389i
$483$	−1.74738e7	−	2.33172e8i	−0.00705623	−	0.0941589i
$484$	9.14290e8	+	4.00577e9i	0.366543	+	1.60593i
$485$	−1.92786e9	+	4.91211e9i	−0.767326	+	1.95511i
$486$	3.29899e8	−	4.40220e9i	0.130363	−	1.73957i
$487$	2.67531e9	−	4.03238e8i	1.04960	−	0.158201i	0.398478	−	0.917178i	$-0.369538\pi$
$487$	2.67531e9	−	4.03238e8i	1.04960	−	0.158201i	0.651118	+	0.758977i	$0.274300\pi$
$488$	7.98018e8	+	7.40453e8i	0.310845	+	0.288422i
$489$	7.59887e8	+	3.65942e8i	0.293879	+	0.141525i
$490$	−5.65114e9	+	3.85288e9i	−2.16995	+	1.47945i
$491$	−1.42285e8	−	3.62536e8i	−0.0542467	−	0.138218i	0.901181	−	0.433442i	$-0.142701\pi$
$491$	−1.42285e8	−	3.62536e8i	−0.0542467	−	0.138218i	−0.955428	+	0.295224i	$0.904606\pi$
$492$	−3.53842e9	+	1.09146e9i	−1.33947	+	0.413171i
$493$	−8.55188e7	+	7.93498e7i	−0.0321438	+	0.0298251i
$494$	2.45950e9	−	3.08412e9i	0.917915	−	1.15103i
$495$	−7.17672e8	+	8.99932e8i	−0.265955	+	0.333497i
$496$	1.83337e9	−	1.70112e9i	0.674628	−	0.625963i
$497$	−6.76216e8	+	2.08585e8i	−0.247080	+	0.0762141i
$498$	−7.39625e8	−	1.88453e9i	−0.268354	−	0.683756i
$499$	−1.74284e9	+	1.18825e9i	−0.627922	+	0.428110i	−0.835027	−	0.550209i	$-0.814548\pi$
$499$	−1.74284e9	+	1.18825e9i	−0.627922	+	0.428110i	0.207105	+	0.978319i	$0.433596\pi$
$500$	4.87803e9	+	2.34913e9i	1.74522	+	0.840452i
$501$	1.77191e9	+	1.64409e9i	0.629519	+	0.584108i
$502$	7.56605e9	−	1.14040e9i	2.66936	−	0.402341i
$503$	−1.89388e8	+	2.52721e9i	−0.0663537	+	0.885429i	0.860366	+	0.509676i	$0.170235\pi$
$503$	−1.89388e8	+	2.52721e9i	−0.0663537	+	0.885429i	−0.926720	+	0.375753i	$0.877384\pi$
$504$	−2.51684e8	+	6.41280e8i	−0.0875686	+	0.223121i
$505$	−1.80244e9	−	7.89699e9i	−0.622788	−	2.72861i
$506$	−1.14524e8	−	1.52822e9i	−0.0392981	−	0.524397i
$507$	2.72449e8	+	8.40394e7i	0.0928448	+	0.0286388i
$508$	6.00615e9	−	2.89241e9i	2.03270	−	0.978897i
$509$	3.02526e8	−	5.23990e8i	0.101683	−	0.176121i	−0.810695	−	0.585469i	$-0.800910\pi$
$509$	3.02526e8	−	5.23990e8i	0.101683	−	0.176121i	0.912378	+	0.409348i	$0.134244\pi$
$510$	−1.70595e8	−	2.95480e8i	−0.0569471	−	0.0986353i
$511$	6.71817e8	+	4.58037e8i	0.222729	+	0.151854i
$512$	−8.09113e8	+	3.54495e9i	−0.266418	+	1.16726i
$513$	−2.54098e9	−	3.82991e8i	−0.830980	−	0.125250i
$514$	1.29624e9	+	1.62544e9i	0.421033	+	0.527959i
$515$	−7.63711e9			−2.46379
$516$	−2.84958e9	−	4.62172e8i	−0.913076	−	0.148091i
$517$	−6.44515e8			−0.205124
$518$	7.38581e8	+	9.26152e8i	0.233477	+	0.292771i
$519$	−1.43499e9	−	2.16290e8i	−0.450571	−	0.0679127i
$520$	1.53707e9	−	6.73436e9i	0.479384	−	2.10032i
$521$	−2.13497e9	−	1.45560e9i	−0.661394	−	0.450931i	0.185535	−	0.982638i	$-0.440598\pi$
$521$	−2.13497e9	−	1.45560e9i	−0.661394	−	0.450931i	−0.846928	+	0.531707i	$0.821551\pi$
$522$	1.08983e9	+	1.88763e9i	0.335359	+	0.580860i
$523$	1.96314e9	−	3.40026e9i	0.600062	−	1.03934i	−0.392750	−	0.919645i	$-0.628476\pi$
$523$	1.96314e9	−	3.40026e9i	0.600062	−	1.03934i	0.992811	−	0.119692i	$-0.0381906\pi$
$524$	−1.71240e9	+	8.24649e8i	−0.519932	+	0.250386i
$525$	5.48306e8	+	1.69130e8i	0.165373	+	0.0510110i
$526$	−7.24227e7	−	9.66414e8i	−0.0216982	−	0.289543i
$527$	−9.06665e7	−	3.97236e8i	−0.0269842	−	0.118226i
$528$	1.34803e8	−	3.43472e8i	0.0398548	−	0.101548i
$529$	−5.15225e7	+	6.87521e8i	−0.0151322	+	0.201925i
$530$	−3.32655e8	+	5.01397e7i	−0.0970575	+	0.0146291i
$531$	2.38281e9	+	2.21093e9i	0.690652	+	0.640832i
$532$	1.21631e9	+	5.85742e8i	0.350229	+	0.168661i
$533$	−3.92278e9	+	2.67451e9i	−1.12214	+	0.765065i
$534$	1.66595e9	+	4.24477e9i	0.473442	+	1.20631i
$535$	7.57164e9	−	2.33554e9i	2.13772	−	0.659401i
$536$	−4.91198e9	+	4.55765e9i	−1.37778	+	1.27839i
$537$	6.97932e8	−	8.75178e8i	0.194492	−	0.243886i
$538$	−5.88389e9	+	7.37817e9i	−1.62902	+	2.04273i
$539$	−8.83343e8	+	8.19623e8i	−0.242979	+	0.225452i
$540$	−9.22344e9	+	2.84505e9i	−2.52066	+	0.777522i
$541$	1.83183e9	+	4.66743e9i	0.497388	+	1.26732i	0.930602	+	0.366033i	$0.119284\pi$
$541$	1.83183e9	+	4.66743e9i	0.497388	+	1.26732i	−0.433214	+	0.901291i	$0.642620\pi$
$542$	6.36215e8	−	4.33764e8i	0.171635	−	0.117019i
$543$	−9.97445e8	−	4.80344e8i	−0.267356	−	0.128752i
$544$	9.27979e7	+	8.61038e7i	0.0247139	+	0.0229312i
$545$	7.16962e9	−	1.08065e9i	1.89718	−	0.285954i
$546$	4.56552e7	−	6.09227e8i	0.0120037	−	0.160179i
$547$	−1.76517e9	+	4.49759e9i	−0.461139	+	1.17496i	0.491505	+	0.870875i	$0.336447\pi$
$547$	−1.76517e9	+	4.49759e9i	−0.461139	+	1.17496i	−0.952644	+	0.304088i	$0.901648\pi$
$548$	−1.15396e9	−	5.05582e9i	−0.299542	−	1.31238i
$549$	−6.27590e7	−	8.37461e8i	−0.0161872	−	0.216004i
$550$	3.59363e9	+	1.10849e9i	0.921010	+	0.284094i
$551$	1.79403e9	−	8.63959e8i	0.456877	−	0.220020i
$552$	1.28978e9	−	2.23397e9i	0.326385	−	0.565315i
$553$	4.55486e8	+	7.88924e8i	0.114535	+	0.198380i
$554$	−8.86448e9	−	6.04370e9i	−2.21498	−	1.51015i
$555$	−7.41351e8	+	3.24807e9i	−0.184076	+	0.806492i
$556$	9.60921e8	+	1.44836e8i	0.237097	+	0.0357366i
$557$	−6.84467e8	−	8.58295e8i	−0.167826	−	0.210447i	0.690805	−	0.723041i	$-0.257256\pi$
$557$	−6.84467e8	−	8.58295e8i	−0.167826	−	0.210447i	−0.858631	+	0.512594i	$0.828685\pi$
$558$	−7.61266e9			−1.85488
$559$	−3.66596e9	+	5.10671e8i	−0.887661	+	0.123652i
$560$	9.18956e8			0.221124
$561$	−3.74792e7	−	4.69975e7i	−0.00896233	−	0.0112384i
$562$	7.20767e9	+	1.08638e9i	1.71284	+	0.258170i
$563$	8.83552e8	−	3.87109e9i	0.208666	−	0.914227i	−0.756789	−	0.653659i	$-0.773233\pi$
$563$	8.83552e8	−	3.87109e9i	0.208666	−	0.914227i	0.965455	−	0.260568i	$-0.0839099\pi$
$564$	−1.92276e9	−	1.31092e9i	−0.451283	−	0.307680i
$565$	−1.87352e9	−	3.24504e9i	−0.437008	−	0.756920i
$566$	9.39321e8	−	1.62695e9i	0.217749	−	0.377153i
$567$	2.74644e8	−	1.32261e8i	0.0632745	−	0.0304714i
$568$	−7.46001e9	−	2.30111e9i	−1.70813	−	0.526888i
$569$	−3.58623e8	−	4.78549e9i	−0.0816103	−	1.08901i	−0.876226	−	0.481901i	$-0.839947\pi$
$569$	−3.58623e8	−	4.78549e9i	−0.0816103	−	1.08901i	0.794616	−	0.607113i	$-0.207672\pi$
$570$	1.29587e9	+	5.67757e9i	0.293089	+	1.28411i
$571$	−2.25562e8	+	5.74722e8i	−0.0507037	+	0.129191i	−0.953982	−	0.299865i	$-0.903058\pi$
$571$	−2.25562e8	+	5.74722e8i	−0.0507037	+	0.129191i	0.903278	+	0.429056i	$0.141154\pi$
$572$	1.95087e8	−	2.60325e9i	0.0435854	−	0.581607i
$573$	−3.12990e8	+	4.71756e7i	−0.0695006	+	0.0104755i
$574$	−1.82689e9	−	1.69510e9i	−0.403200	−	0.374115i
$575$	6.00354e9	+	2.89115e9i	1.31695	+	0.634210i
$576$	3.77656e9	−	2.57482e9i	0.823413	−	0.561394i
$577$	1.46820e9	+	3.74092e9i	0.318178	+	0.810705i	0.997072	+	0.0764682i	$0.0243644\pi$
$577$	1.46820e9	+	3.74092e9i	0.318178	+	0.810705i	−0.678894	+	0.734236i	$0.737540\pi$
$578$	7.46692e9	−	2.30324e9i	1.60840	−	0.496126i
$579$	2.28239e9	−	2.11774e9i	0.488668	−	0.453418i
$580$	4.66336e9	−	5.84767e9i	0.992433	−	1.24447i
$581$	5.53860e8	−	6.94518e8i	0.117161	−	0.146915i
$582$	−3.77431e9	+	3.50205e9i	−0.793609	+	0.736362i
$583$	−5.66370e7	+	1.74702e7i	−0.0118375	+	0.00365139i
$584$	3.27716e9	+	8.35007e9i	0.680852	+	1.73478i
$585$	−4.40283e9	+	3.00180e9i	−0.909257	+	0.619921i
$586$	5.68684e9	+	2.73864e9i	1.16743	+	0.562203i
$587$	−2.47280e9	−	2.29442e9i	−0.504609	−	0.468209i	0.386311	−	0.922369i	$-0.373749\pi$
$587$	−2.47280e9	−	2.29442e9i	−0.504609	−	0.468209i	−0.890920	+	0.454159i	$0.849940\pi$
$588$	−4.30234e9	+	6.48473e8i	−0.872738	+	0.131544i
$589$	−5.19714e8	+	6.93510e9i	−0.104800	+	1.39846i
$590$	6.25043e9	−	1.59258e10i	1.25293	−	3.19242i
$591$	−5.71360e8	−	2.50329e9i	−0.113855	−	0.498833i
$592$	2.47514e8	+	3.30285e9i	0.0490314	+	0.654279i
$593$	−3.08519e9	−	9.51655e8i	−0.607562	−	0.187408i	−0.0243168	−	0.999704i	$-0.507741\pi$
$593$	−3.08519e9	−	9.51655e8i	−0.607562	−	0.187408i	−0.583245	+	0.812296i	$0.698217\pi$
$594$	−2.35005e9	+	1.13172e9i	−0.460070	+	0.221558i
$595$	7.48557e7	−	1.29654e8i	0.0145685	−	0.0252334i
$596$	−3.48086e9	−	6.02903e9i	−0.673480	−	1.16650i
$597$	−1.50683e9	−	1.02734e9i	−0.289837	−	0.197607i
$598$	1.57871e9	−	6.91680e9i	0.301890	−	1.32267i
$599$	−3.37553e9	−	5.08780e8i	−0.641724	−	0.0967244i	−0.179885	−	0.983688i	$-0.557572\pi$
$599$	−3.37553e9	−	5.08780e8i	−0.641724	−	0.0967244i	−0.461840	+	0.886963i	$0.652811\pi$
$600$	3.94678e9	+	4.94911e9i	0.745957	+	0.935400i
$601$	−1.21795e6			−0.000228859			−0.000114430	−	1.00000i	$-0.500036\pi$
$601$	−1.21795e6			−0.000228859			−0.000114430		1.00000i	$0.500036\pi$
$602$	−6.89539e8	−	1.81642e9i	−0.128816	−	0.339336i
$603$	5.16921e9			0.960093
$604$	1.64530e9	+	2.06314e9i	0.303819	+	0.380977i
$605$	−7.69042e9	−	1.15914e9i	−1.41191	−	0.212811i
$606$	1.75867e9	−	7.70525e9i	0.321019	−	1.40648i
$607$	−4.91513e9	−	3.35108e9i	−0.892021	−	0.608169i	0.0281858	−	0.999603i	$-0.491027\pi$
$607$	−4.91513e9	−	3.35108e9i	−0.892021	−	0.608169i	−0.920206	+	0.391433i	$0.871979\pi$
$608$	−1.08035e9	−	1.87123e9i	−0.194941	−	0.337648i
$609$	1.54194e8	−	2.67072e8i	0.0276635	−	0.0479145i
$610$	−3.98242e9	+	1.91783e9i	−0.710382	+	0.342102i
$611$	−2.85119e9	−	8.79477e8i	−0.505688	−	0.155984i
$612$	5.03028e7	+	6.71244e8i	0.00887079	+	0.118372i
$613$	−5.21859e8	−	2.28641e9i	−0.0915042	−	0.400906i	0.908346	−	0.418220i	$-0.137346\pi$
$613$	−5.21859e8	−	2.28641e9i	−0.0915042	−	0.400906i	−0.999850	+	0.0173135i	$0.994489\pi$
$614$	2.43533e9	−	6.20513e9i	0.424589	−	1.08184i
$615$	5.23789e8	−	6.98948e9i	0.0908016	−	1.21166i
$616$	6.31683e8	−	9.52108e7i	0.108885	−	0.0164117i
$617$	3.38477e9	+	3.14061e9i	0.580138	+	0.538290i	0.914726	−	0.404075i	$-0.132407\pi$
$617$	3.38477e9	+	3.14061e9i	0.580138	+	0.538290i	−0.334588	+	0.942365i	$0.608597\pi$
$618$	−6.71373e9	−	3.23316e9i	−1.14421	−	0.551021i
$619$	3.36446e9	−	2.29385e9i	0.570162	−	0.388730i	−0.243646	−	0.969864i	$-0.578343\pi$
$619$	3.36446e9	−	2.29385e9i	0.570162	−	0.388730i	0.813807	+	0.581135i	$0.197391\pi$
$620$	9.54371e9	+	2.43170e10i	1.60822	+	4.09769i
$621$	−4.41629e9	+	1.36225e9i	−0.740010	+	0.228263i
$622$	−1.14849e10	+	1.06564e10i	−1.91364	+	1.77560i
$623$	−1.24753e9	+	1.56435e9i	−0.206701	+	0.259194i
$624$	1.06503e9	−	1.33550e9i	0.175475	−	0.220038i
$625$	−1.89191e8	+	1.75543e8i	−0.0309970	+	0.0287610i
$626$	1.39056e10	−	4.28930e9i	2.26558	−	0.698837i
$627$	3.74846e8	+	9.55092e8i	0.0607318	+	0.154742i
$628$	−1.36841e10	+	9.32965e9i	−2.20474	+	1.50316i
$629$	4.86156e8	+	2.34120e8i	0.0778929	+	0.0375113i
$630$	−2.05045e9	−	1.90254e9i	−0.326707	−	0.303140i
$631$	−8.01186e9	+	1.20759e9i	−1.26949	+	0.191345i	−0.749028	−	0.662538i	$-0.769479\pi$
$631$	−8.01186e9	+	1.20759e9i	−1.26949	+	0.191345i	−0.520465	+	0.853883i	$0.674241\pi$
$632$	−7.51025e8	+	1.00217e10i	−0.118344	+	1.57919i
$633$	−2.76075e8	+	7.03427e8i	−0.0432627	+	0.110232i
$634$	3.71111e8	+	1.62595e9i	0.0578352	+	0.253392i
$635$	9.42968e8	+	1.25830e10i	0.146147	+	1.95019i
$636$	−2.04497e8	−	6.30791e7i	−0.0315201	−	0.00972267i
$637$	−5.02614e9	+	2.42046e9i	−0.770454	+	0.371031i
$638$	1.01060e9	−	1.75040e9i	0.154065	−	0.266849i
$639$	3.01126e9	+	5.21565e9i	0.456557	+	0.790780i
$640$	−1.62974e10	−	1.11114e10i	−2.45747	−	1.67548i
$641$	−2.09672e9	+	9.18635e9i	−0.314440	+	1.37765i	0.532709	+	0.846298i	$0.321174\pi$
$641$	−2.09672e9	+	9.18635e9i	−0.314440	+	1.37765i	−0.847150	+	0.531354i	$0.821683\pi$
$642$	7.64493e9	+	1.15229e9i	1.14025	+	0.171865i
$643$	−8.73133e8	−	1.09487e9i	−0.129521	−	0.162415i	0.712842	−	0.701325i	$-0.247408\pi$
$643$	−8.73133e8	−	1.09487e9i	−0.129521	−	0.162415i	−0.842363	+	0.538910i	$0.818836\pi$
$644$	2.42800e9			0.358218
$645$	2.78493e9	−	4.70135e9i	0.408653	−	0.689864i
$646$	9.43198e8			0.137654
$647$	3.48457e9	+	4.36952e9i	0.505807	+	0.634262i	0.967528	−	0.252763i	$-0.0813394\pi$
$647$	3.48457e9	+	4.36952e9i	0.505807	+	0.634262i	−0.461721	+	0.887025i	$0.652768\pi$
$648$	3.32534e9	+	5.01214e8i	0.480091	+	0.0723621i
$649$	6.70728e8	−	2.93865e9i	0.0963142	−	0.421980i
$650$	1.43849e10	+	9.80743e9i	2.05451	+	1.40074i
$651$	5.38538e8	+	9.32775e8i	0.0765037	+	0.132508i
$652$	−4.37890e9	+	7.58447e9i	−0.618726	+	1.07166i
$653$	3.70482e9	−	1.78415e9i	0.520680	−	0.250746i	−0.155036	−	0.987909i	$-0.549549\pi$
$653$	3.70482e9	−	1.78415e9i	0.520680	−	0.250746i	0.675715	+	0.737163i	$0.263835\pi$
$654$	6.76026e9	+	2.08526e9i	0.945020	+	0.291500i
$655$	−2.68848e8	−	3.58752e9i	−0.0373819	−	0.498827i
$656$	−1.55054e9	−	6.79338e9i	−0.214447	−	0.939555i
$657$	2.52814e9	−	6.44158e9i	0.347794	−	0.886164i
$658$	1.17043e8	−	1.56184e9i	0.0160161	−	0.213720i
$659$	1.81129e9	−	2.73008e8i	0.246541	−	0.0371601i	−0.0246092	−	0.999697i	$-0.507834\pi$
$659$	1.81129e9	−	2.73008e8i	0.246541	−	0.0371601i	0.271150	+	0.962537i	$0.412596\pi$
$660$	2.82513e9	+	2.62134e9i	0.382503	+	0.354911i
$661$	6.43127e9	+	3.09713e9i	0.866146	+	0.417114i	0.813545	−	0.581501i	$-0.197535\pi$
$661$	6.43127e9	+	3.09713e9i	0.866146	+	0.417114i	0.0526011	+	0.998616i	$0.483249\pi$
$662$	1.12153e10	−	7.64647e9i	1.50248	−	1.02437i
$663$	−1.01669e8	−	2.59049e8i	−0.0135485	−	0.0345211i
$664$	9.36459e9	−	2.88859e9i	1.24137	−	0.382911i
$665$	−1.87319e9	+	1.73807e9i	−0.247006	+	0.229188i
$666$	6.28572e9	−	7.88205e9i	0.824509	−	1.03390i
$667$	2.23287e9	−	2.79993e9i	0.291356	−	0.365349i
$668$	−1.83991e10	+	1.70719e10i	−2.38824	+	2.21597i
$669$	−1.08761e9	+	3.35482e8i	−0.140437	+	0.0433189i
$670$	−9.93982e9	−	2.53262e10i	−1.27678	−	3.25319i
$671$	−6.43438e8	+	4.38688e8i	−0.0822200	+	0.0560567i
$672$	−3.01497e8	−	1.45193e8i	−0.0383258	−	0.0184567i
$673$	−9.39799e9	−	8.72006e9i	−1.18845	−	1.10272i	−0.992517	−	0.122107i	$-0.961035\pi$
$673$	−9.39799e9	−	8.72006e9i	−1.18845	−	1.10272i	−0.195936	−	0.980617i	$-0.562775\pi$
$674$	7.69082e9	−	1.15920e9i	0.967526	−	0.145831i
$675$	8.47533e8	−	1.13095e10i	0.106070	−	1.41541i
$676$	−1.08162e9	+	2.75593e9i	−0.134667	+	0.343127i
$677$	2.44320e9	+	1.07044e10i	0.302621	+	1.32587i	0.866154	+	0.499777i	$0.166585\pi$
$677$	2.44320e9	+	1.07044e10i	0.302621	+	1.32587i	−0.563533	+	0.826093i	$0.690558\pi$
$678$	−2.73218e8	−	3.64584e9i	−0.0336671	−	0.449256i
$679$	−2.15886e9	−	6.65919e8i	−0.264655	−	0.0816352i
$680$	1.48806e9	−	7.16610e8i	0.181484	−	0.0873980i
$681$	8.69486e8	−	1.50599e9i	0.105499	−	0.182729i
$682$	3.52961e9	+	6.11346e9i	0.426070	+	0.737975i
$683$	−3.05260e9	−	2.08123e9i	−0.366605	−	0.249947i	0.365980	−	0.930623i	$-0.380734\pi$
$683$	−3.05260e9	−	2.08123e9i	−0.366605	−	0.249947i	−0.732585	+	0.680676i	$0.761686\pi$
$684$	2.55659e9	−	1.12011e10i	0.305467	−	1.33834i
$685$	9.70635e9	+	1.46300e9i	1.15382	+	0.173911i
$686$	−3.73925e9	−	4.68887e9i	−0.442232	−	0.554541i
$687$	3.18043e9			0.374229
$688$	1.26799e9	−	5.28228e9i	0.148442	−	0.618389i
$689$	−2.74389e8			−0.0319595
$690$	6.53032e9	+	8.18876e9i	0.756768	+	0.948957i
$691$	−5.31303e9	−	8.00811e8i	−0.612589	−	0.0923329i	−0.164583	−	0.986363i	$-0.552628\pi$
$691$	−5.31303e9	−	8.00811e8i	−0.612589	−	0.0923329i	−0.448006	+	0.894030i	$0.647866\pi$
$692$	3.35315e9	−	1.46911e10i	0.384664	−	1.68533i
$693$	−4.07179e8	−	2.77610e8i	−0.0464749	−	0.0316861i
$694$	6.80032e9	+	1.17785e10i	0.772273	+	1.33762i
$695$	−9.19710e8	+	1.59298e9i	−0.103921	+	0.179997i
$696$	3.06522e9	−	1.47613e9i	0.344611	−	0.165956i
$697$	−1.08477e9	−	3.34607e8i	−0.121345	−	0.0374300i
$698$	7.98267e8	+	1.06521e10i	0.0888493	+	1.18561i
$699$	1.27469e9	+	5.58478e9i	0.141167	+	0.618495i
$700$	−2.17677e9	+	5.54633e9i	−0.239867	+	0.611171i
$701$	−3.41909e8	+	4.56246e9i	−0.0374885	+	0.500249i	0.946581	+	0.322466i	$0.104512\pi$
$701$	−3.41909e8	+	4.56246e9i	−0.0374885	+	0.500249i	−0.984070	+	0.177783i	$0.943107\pi$
$702$	−1.19404e10	+	1.79972e9i	−1.30268	+	0.196348i
$703$	−6.75139e9	−	6.26437e9i	−0.732908	−	0.680039i
$704$	−3.81875e9	−	1.83901e9i	−0.412493	−	0.198646i
$705$	3.63949e9	−	2.48137e9i	0.391182	−	0.266704i
$706$	7.03539e9	+	1.79259e10i	0.752440	+	1.91719i
$707$	3.31387e9	−	1.02219e9i	0.352669	−	0.108784i
$708$	7.97807e9	−	7.40257e9i	0.844854	−	0.783910i
$709$	3.33401e9	−	4.18072e9i	0.351322	−	0.440544i	−0.574500	−	0.818505i	$-0.694803\pi$
$709$	3.33401e9	−	4.18072e9i	0.351322	−	0.440544i	0.925821	+	0.377961i	$0.123375\pi$
$710$	1.97635e10	−	2.47826e10i	2.07233	−	2.59862i
$711$	5.68324e9	−	5.27328e9i	0.592997	−	0.550221i
$712$	−2.10930e10	+	6.50633e9i	−2.19007	+	0.675548i
$713$	4.56964e9	+	1.16433e10i	0.472138	+	1.20299i
$714$	1.20694e8	−	8.22878e7i	0.0124091	−	0.00846041i
$715$	4.45201e9	+	2.14398e9i	0.455497	+	0.219356i
$716$	8.52067e9	+	7.90602e9i	0.867517	+	0.804938i
$717$	−2.56541e9	+	3.86674e8i	−0.259920	+	0.0391767i
$718$	5.10988e8	−	6.81867e9i	0.0515200	−	0.687486i
$719$	−3.60983e9	+	9.19770e9i	−0.362189	+	0.922843i	0.627371	+	0.778721i	$0.284131\pi$
$719$	−3.60983e9	+	9.19770e9i	−0.362189	+	0.922843i	−0.989560	+	0.144122i	$0.953964\pi$
$720$	−1.74029e9	−	7.62472e9i	−0.173763	−	0.761308i
$721$	−2.44347e8	−	3.26059e9i	−0.0242792	−	0.323983i
$722$	9.97124e8	+	3.07572e8i	0.0985982	+	0.0304135i
$723$	−5.26073e9	+	2.53343e9i	−0.517681	+	0.249302i
$724$	5.74784e9	−	9.95555e9i	0.562885	−	0.974945i
$725$	4.39412e9	+	7.61084e9i	0.428242	+	0.741736i
$726$	−6.26988e9	−	4.27473e9i	−0.608108	−	0.414601i
$727$	4.38262e8	−	1.92015e9i	0.0423022	−	0.185338i	−0.949363	−	0.314183i	$-0.898270\pi$
$727$	4.38262e8	−	1.92015e9i	0.0423022	−	0.185338i	0.991665	+	0.128844i	$0.0411267\pi$
$728$	2.92435e9	+	4.40774e8i	0.280911	+	0.0423405i
$729$	1.17516e9	+	1.47361e9i	0.112344	+	0.140875i
$730$	−3.64215e10			−3.46520
$731$	−6.41980e8	−	6.09179e8i	−0.0607870	−	0.0576812i
$732$	−2.81182e9			−0.264972
$733$	6.53838e9	+	8.19887e9i	0.613206	+	0.768936i	0.987371	−	0.158426i	$-0.0506421\pi$
$733$	6.53838e9	+	8.19887e9i	0.613206	+	0.768936i	−0.374165	+	0.927362i	$0.622071\pi$
$734$	2.76696e10	+	4.17052e9i	2.58266	+	0.389273i
$735$	1.83260e9	−	8.02915e9i	0.170240	−	0.745872i
$736$	−3.21083e9	−	2.18910e9i	−0.296855	−	0.202392i
$737$	−2.39670e9	−	4.15121e9i	−0.220535	−	0.381978i
$738$	−1.06048e10	+	1.83681e10i	−0.971195	+	1.68216i
$739$	−1.01420e10	+	4.88415e9i	−0.924421	+	0.445178i	−0.834647	−	0.550785i	$-0.814329\pi$
$739$	−1.01420e10	+	4.88415e9i	−0.924421	+	0.445178i	−0.0897734	+	0.995962i	$0.528614\pi$
$740$	−3.30577e10	−	1.01969e10i	−2.99889	−	0.925036i
$741$	3.54960e8	+	4.73662e9i	0.0320491	+	0.427666i
$742$	−3.20499e7	−	1.40420e8i	−0.00288013	−	0.0126187i
$743$	−3.05256e9	+	7.77781e9i	−0.273026	+	0.695659i	0.726934	+	0.686707i	$0.240945\pi$
$743$	−3.05256e9	+	7.77781e9i	−0.273026	+	0.695659i	−0.999960	+	0.00895151i	$0.997151\pi$
$744$	−8.87965e8	+	1.18491e10i	−0.0790479	+	1.05482i
$745$	1.30303e10	−	1.96400e9i	1.15453	−	0.174018i
$746$	−7.04016e9	−	6.53231e9i	−0.620864	−	0.576078i
$747$	−6.81141e9	−	3.28020e9i	−0.597881	−	0.287924i
$748$	5.15730e8	−	3.51619e8i	0.0450575	−	0.0307197i
$749$	1.23939e9	+	3.15791e9i	0.107776	+	0.274608i
$750$	−9.55517e9	+	2.94738e9i	−0.827035	+	0.255106i
$751$	−1.79395e9	+	1.66454e9i	−0.154551	+	0.143402i	−0.753658	−	0.657266i	$-0.771713\pi$
$751$	−1.79395e9	+	1.66454e9i	−0.154551	+	0.143402i	0.599108	+	0.800669i	$0.295522\pi$
$752$	2.73034e9	−	3.42374e9i	0.234129	−	0.293588i
$753$	−5.74438e9	+	7.20323e9i	−0.490299	+	0.614815i
$754$	6.85918e9	−	6.36439e9i	0.582737	−	0.540700i
$755$	−4.77303e9	+	1.47228e9i	−0.403626	+	0.124502i
$756$	−1.50977e9	−	3.84683e9i	−0.127082	−	0.323800i
$757$	1.34555e10	−	9.17379e9i	1.12736	−	0.768622i	0.151814	−	0.988409i	$-0.451488\pi$
$757$	1.34555e10	−	9.17379e9i	1.12736	−	0.768622i	0.975548	+	0.219787i	$0.0705361\pi$
$758$	−3.44093e10	−	1.65706e10i	−2.86968	−	1.38197i
$759$	1.35271e9	+	1.25513e9i	0.112294	+	0.104194i
$760$	−2.78756e10	+	4.20157e9i	−2.30344	+	0.347187i
$761$	−2.79432e7	+	3.72877e8i	−0.00229843	+	0.0306704i	−0.998235	−	0.0593861i	$-0.981086\pi$
$761$	−2.79432e7	+	3.72877e8i	−0.00229843	+	0.0306704i	0.995937	+	0.0900564i	$0.0287047\pi$
$762$	−4.49806e9	+	1.14609e10i	−0.368284	+	0.938372i
$763$	6.90761e8	+	3.02642e9i	0.0562979	+	0.246657i
$764$	−2.45617e8	−	3.27754e9i	−0.0199266	−	0.265901i
$765$	−1.21752e9	−	3.75555e8i	−0.0983242	−	0.0303290i
$766$	4.45584e8	−	2.14582e8i	0.0358203	−	0.0172501i
$767$	6.97711e9	−	1.20847e10i	0.558331	−	0.967058i
$768$	−5.53824e9	−	9.59251e9i	−0.441171	−	0.764131i
$769$	1.54575e10	+	1.05387e10i	1.22574	+	0.835693i	0.990670	−	0.136286i	$-0.0435165\pi$
$769$	1.54575e10	+	1.05387e10i	1.22574	+	0.835693i	0.235067	+	0.971979i	$0.424469\pi$
$770$	−5.77173e8	+	2.52876e9i	−0.0455605	+	0.199614i
$771$	−2.47540e9	−	3.73107e8i	−0.194516	−	0.0293186i
$772$	2.01576e10	+	2.52768e10i	1.57681	+	1.97725i
$773$	1.90280e10			1.48172			0.740859	−	0.671660i	$-0.234419\pi$
$773$	1.90280e10			1.48172			0.740859	+	0.671660i	$0.234419\pi$
$774$	−1.37653e10	+	9.16111e9i	−1.06707	+	0.710157i
$775$	−3.06938e10			−2.36862
$776$	−1.55397e10	−	1.94862e10i	−1.19379	−	1.49696i
$777$	−1.41045e9	−	2.12591e8i	−0.107866	−	0.0162582i
$778$	−5.28675e9	+	2.31628e10i	−0.402495	+	1.76344i
$779$	1.60093e10	+	1.09149e10i	1.21336	+	0.827257i
$780$	8.92081e9	+	1.54513e10i	0.673090	+	1.16583i
$781$	2.79234e9	−	4.83647e9i	0.209744	−	0.363287i
$782$	1.52837e9	−	7.36023e8i	0.114289	−	0.0550386i
$783$	−5.82455e9	−	1.79664e9i	−0.433607	−	0.133750i
$784$	−6.11850e8	−	8.16457e9i	−0.0453460	−	0.605100i
$785$	−6.97583e9	−	3.05631e10i	−0.514698	−	2.25504i
$786$	1.28243e9	−	3.26758e9i	0.0942010	−	0.240020i
$787$	8.66351e8	−	1.15606e10i	0.0633552	−	0.845416i	−0.871502	−	0.490392i	$-0.836854\pi$
$787$	8.66351e8	−	1.15606e10i	0.0633552	−	0.845416i	0.934857	−	0.355024i	$-0.115527\pi$
$788$	2.63643e10	−	3.97378e9i	1.91944	−	0.289309i
$789$	8.55422e8	+	7.93716e8i	0.0620027	+	0.0575301i
$790$	−3.67644e10	−	1.77048e10i	−2.65297	−	1.27760i
$791$	1.32549e9	−	9.03706e8i	0.0952269	−	0.0649246i
$792$	−1.98624e9	−	5.06086e9i	−0.142067	−	0.361981i
$793$	−3.44504e9	+	1.06265e9i	−0.245323	+	0.0756721i
$794$	−2.16626e10	+	2.01000e10i	−1.53582	+	1.42503i
$795$	2.52562e8	−	3.16703e8i	0.0178272	−	0.0223546i
$796$	1.18071e10	−	1.48056e10i	0.829750	−	1.04047i
$797$	9.55704e9	−	8.86764e9i	0.668682	−	0.620446i	−0.270966	−	0.962589i	$-0.587343\pi$
$797$	9.55704e9	−	8.86764e9i	0.668682	−	0.620446i	0.939648	+	0.342143i	$0.111153\pi$
$798$	−2.38252e9	+	7.34910e8i	−0.165969	+	0.0511946i
$799$	−2.60643e8	−	6.64108e8i	−0.0180773	−	0.0460601i
$800$	7.87923e9	−	5.37197e9i	0.544088	−	0.370953i
$801$	1.53422e10	+	7.38841e9i	1.05481	+	0.507969i
$802$	2.90661e10	+	2.69694e10i	1.98965	+	1.84613i
$803$	−6.34518e9	+	9.56382e8i	−0.432454	+	0.0651819i
$804$	1.29338e9	−	1.72590e10i	0.0877669	−	1.17117i
$805$	−1.67904e9	+	4.27813e9i	−0.113442	+	0.289047i
$806$	7.27206e9	+	3.18610e10i	0.489198	+	2.14332i
$807$	−8.49175e8	−	1.13315e10i	−0.0568774	−	0.758977i
$808$	3.65586e10	+	1.12768e10i	2.43809	+	0.752052i
$809$	−1.51880e10	+	7.31417e9i	−1.00851	+	0.485674i	−0.863819	−	0.503802i	$-0.831934\pi$
$809$	−1.51880e10	+	7.31417e9i	−1.00851	+	0.485674i	−0.144694	+	0.989476i	$0.546220\pi$
$810$	−6.82720e9	+	1.18251e10i	−0.451383	+	0.781818i
$811$	−9.71265e9	−	1.68228e10i	−0.639389	−	1.10745i	−0.985567	−	0.169285i	$-0.945854\pi$
$811$	−9.71265e9	−	1.68228e10i	−0.639389	−	1.10745i	0.346179	−	0.938169i	$-0.387479\pi$
$812$	2.64581e9	+	1.80388e9i	0.173425	+	0.118239i
$813$	−2.06317e8	+	9.03935e8i	−0.0134654	+	0.0589957i
$814$	−9.24417e9	−	1.39333e9i	−0.600734	−	0.0905461i
$815$	−1.03357e10	−	1.29605e10i	−0.668786	−	0.838632i
$816$	4.08429e8			0.0263148
$817$	7.40598e9	+	1.31656e10i	0.475122	+	0.844623i
$818$	1.58606e10			1.01317
$819$	−1.42246e9	−	1.78370e9i	−0.0904784	−	0.113456i
$820$	7.19678e10	+	1.08474e10i	4.55816	+	0.687033i
$821$	−6.16671e7	+	2.70181e8i	−0.00388913	+	0.0170394i	−0.976835	−	0.213993i	$-0.931353\pi$
$821$	−6.16671e7	+	2.70181e8i	−0.00388913	+	0.0170394i	0.972946	+	0.231032i	$0.0742103\pi$
$822$	7.91342e9	+	5.39528e9i	0.496950	+	0.338815i
$823$	1.34754e10	+	2.33401e10i	0.842640	+	1.45949i	0.887655	+	0.460508i	$0.152333\pi$
$823$	1.34754e10	+	2.33401e10i	0.842640	+	1.45949i	−0.0450156	+	0.998986i	$0.514334\pi$
$824$	1.80358e10	−	3.12390e10i	1.12303	−	1.94514i
$825$	−4.07987e9	+	1.96476e9i	−0.252963	+	0.121821i
$826$	6.99936e9	+	2.15902e9i	0.432143	+	0.133299i
$827$	−6.97612e8	−	9.30899e9i	−0.0428889	−	0.572312i	−0.976709	−	0.214569i	$-0.931165\pi$
$827$	−6.97612e8	−	9.30899e9i	−0.0428889	−	0.572312i	0.933820	−	0.357743i	$-0.116454\pi$
$828$	−4.59807e9	−	2.01455e10i	−0.281494	−	1.23331i
$829$	1.36721e9	−	3.48358e9i	0.0833476	−	0.212366i	−0.883124	−	0.469139i	$-0.844564\pi$
$829$	1.36721e9	−	3.48358e9i	0.0833476	−	0.212366i	0.966472	+	0.256773i	$0.0826594\pi$
$830$	−2.97358e9	+	3.96796e10i	−0.180512	+	2.40876i
$831$	1.27743e10	−	1.92541e9i	0.772205	−	0.116391i
$832$	−1.43839e10	−	1.33463e10i	−0.865853	−	0.803394i
$833$	−1.20177e9	−	5.78740e8i	−0.0720381	−	0.0346917i
$834$	−1.48290e9	+	1.01102e9i	−0.0885177	+	0.0603504i
$835$	−1.73570e10	−	4.42250e10i	−1.03175	−	2.62884i
$836$	−1.01806e10	+	3.14030e9i	−0.602631	+	0.185887i
$837$	1.56057e10	−	1.44799e10i	0.919906	−	0.853548i
$838$	2.29308e10	−	2.87543e10i	1.34606	−	1.68791i
$839$	8.71419e9	−	1.09273e10i	0.509402	−	0.638769i	−0.458919	−	0.888478i	$-0.651763\pi$
$839$	8.71419e9	−	1.09273e10i	0.509402	−	0.638769i	0.968321	+	0.249708i	$0.0803348\pi$
$840$	−3.20047e9	+	2.96960e9i	−0.186310	+	0.172871i
$841$	−1.19701e10	+	3.69229e9i	−0.693925	+	0.214048i
$842$	1.24795e10	+	3.17972e10i	0.720451	+	1.83568i
$843$	−7.25178e9	+	4.94418e9i	−0.416916	+	0.284248i
$844$	−7.06957e9	−	3.40453e9i	−0.404757	−	0.194921i
$845$	−4.10797e9	−	3.81164e9i	−0.234222	−	0.217327i
$846$	−1.31805e10	+	1.98663e9i	−0.748401	+	0.112803i
$847$	2.48832e8	−	3.32043e9i	0.0140707	−	0.187760i
$848$	1.47126e8	−	3.74871e8i	0.00828523	−	0.0211104i
$849$	5.03363e8	+	2.20538e9i	0.0282296	+	0.123682i
$850$	3.11086e8	+	4.15115e9i	0.0173746	+	0.231848i
$851$	−1.58284e10	−	4.88242e9i	−0.880407	−	0.271570i
$852$	1.81675e10	−	8.74901e9i	1.00637	−	0.484641i
$853$	1.64833e10	−	2.85498e10i	0.909330	−	1.57501i	0.0943322	−	0.995541i	$-0.469928\pi$
$853$	1.64833e10	−	2.85498e10i	0.909330	−	1.57501i	0.814997	−	0.579464i	$-0.196738\pi$
$854$	−9.46214e8	−	1.63889e9i	−0.0519861	−	0.0900425i
$855$	1.79684e10	+	1.22507e10i	0.983170	+	0.670314i
$856$	−8.32787e9	+	3.64868e10i	−0.453812	+	1.98828i
$857$	−1.25223e10	−	1.88744e9i	−0.679598	−	0.102433i	−0.199833	−	0.979830i	$-0.564040\pi$
$857$	−1.25223e10	−	1.88744e9i	−0.679598	−	0.102433i	−0.479765	+	0.877397i	$0.659278\pi$
$858$	3.00608e9	+	3.76951e9i	0.162478	+	0.203741i
$859$	−1.00416e10			−0.540538			−0.270269	−	0.962785i	$-0.587113\pi$
$859$	−1.00416e10			−0.540538			−0.270269	+	0.962785i	$0.587113\pi$
$860$	4.65202e10	+	3.24854e10i	2.49401	+	1.74158i
$861$	3.00085e9			0.160226
$862$	−3.20272e10	−	4.01608e10i	−1.70311	−	2.13564i
$863$	−2.96304e10	−	4.46607e9i	−1.56928	−	0.236531i	−0.693937	−	0.720036i	$-0.744125\pi$
$863$	−2.96304e10	−	4.46607e9i	−1.56928	−	0.236531i	−0.875342	+	0.483505i	$0.839364\pi$
$864$	−1.47179e9	+	6.44834e9i	−0.0776333	+	0.340134i
$865$	2.35669e10	+	1.60677e10i	1.23807	+	0.844105i
$866$	−2.51966e10	−	4.36419e10i	−1.31835	−	2.28344i
$867$	−4.70451e9	+	8.14844e9i	−0.245159	+	0.424627i
$868$	−1.00765e10	+	4.85261e9i	−0.522989	+	0.251858i
$869$	−6.86982e9	−	2.11906e9i	−0.355121	−	0.109540i
$870$	1.03230e9	+	1.37751e10i	0.0531481	+	0.709212i
$871$	−4.93793e9	−	2.16345e10i	−0.253210	−	1.10939i
$872$	−1.25115e10	+	3.18788e10i	−0.639002	+	1.62815i
$873$	−1.43685e9	+	1.91735e10i	−0.0730908	+	0.975329i
$874$	−2.86307e10	+	4.31539e9i	−1.45058	+	0.218640i
$875$	−3.21638e9	−	2.98436e9i	−0.162308	−	0.150599i
$876$	−2.08747e10	−	1.00527e10i	−1.04919	−	0.505264i
$877$	1.32663e10	−	9.04484e9i	0.664130	−	0.452796i	−0.183758	−	0.982971i	$-0.558826\pi$
$877$	1.32663e10	−	9.04484e9i	0.664130	−	0.452796i	0.847888	+	0.530176i	$0.177874\pi$
$878$	1.68883e10	+	4.30306e10i	0.842083	+	2.14559i
$879$	−7.26260e9	+	2.24021e9i	−0.360687	+	0.111257i
$880$	−5.31626e9	+	4.93277e9i	−0.262976	+	0.244006i
$881$	−1.07269e10	+	1.34511e10i	−0.528517	+	0.662739i	−0.972393	−	0.233349i	$-0.925032\pi$
$881$	−1.07269e10	+	1.34511e10i	−0.528517	+	0.662739i	0.443876	+	0.896088i	$0.353603\pi$
$882$	−1.55382e10	+	1.94842e10i	−0.762535	+	0.956188i
$883$	2.09699e10	−	1.94573e10i	1.02503	−	0.951085i	0.0262062	−	0.999657i	$-0.491657\pi$
$883$	2.09699e10	−	1.94573e10i	1.02503	−	0.951085i	0.998820	+	0.0485715i	$0.0154669\pi$
$884$	2.76128e9	−	8.51742e8i	0.134440	−	0.0414692i
$885$	7.52622e9	+	1.91765e10i	0.364985	+	0.929967i
$886$	2.17875e10	−	1.48545e10i	1.05242	−	0.717530i
$887$	7.38207e9	+	3.55502e9i	0.355177	+	0.171044i	0.602960	−	0.797771i	$-0.293988\pi$
$887$	7.38207e9	+	3.55502e9i	0.355177	+	0.171044i	−0.247783	+	0.968816i	$0.579702\pi$
$888$	−1.15352e10	−	1.07031e10i	−0.552814	−	0.512937i
$889$	−5.34203e9	+	8.05181e8i	−0.255006	+	0.0384359i
$890$	6.69775e9	−	8.93753e10i	0.318467	−	4.24964i
$891$	−8.78891e8	+	2.23938e9i	−0.0416259	+	0.106061i
$892$	−2.62987e9	−	1.15222e10i	−0.124067	−	0.543574i
$893$	9.09990e8	+	1.21430e10i	0.0427618	+	0.570617i
$894$	1.22863e10	+	3.78982e9i	0.575095	+	0.177393i
$895$	−1.98227e10	+	9.54613e9i	−0.924237	+	0.445089i
$896$	4.22246e9	−	7.31352e9i	0.196105	−	0.339663i
$897$	4.27139e9	+	7.39826e9i	0.197604	+	0.342260i
$898$	3.63484e10	+	2.47819e10i	1.67501	+	1.14200i
$899$	−3.67079e9	+	1.60828e10i	−0.168500	+	0.738248i
$900$	5.01411e10	+	7.55755e9i	2.29269	+	0.345567i
$901$	−4.09054e7	−	5.12938e7i	−0.00186314	−	0.00233630i
$902$	1.96677e10			0.892341
$903$	2.09630e9	+	1.03858e9i	0.0947427	+	0.0469388i
$904$	1.76981e10			0.796776
$905$	1.35668e10	+	1.70123e10i	0.608428	+	0.762944i
$906$	−4.81923e9	−	7.26381e8i	−0.215292	−	0.0324501i
$907$	−4.71714e9	+	2.06671e10i	−0.209920	+	0.919718i	0.754699	+	0.656071i	$0.227783\pi$
$907$	−4.71714e9	+	2.06671e10i	−0.209920	+	0.919718i	−0.964619	+	0.263648i	$0.915074\pi$
$908$	1.49195e10	+	1.01719e10i	0.661383	+	0.450923i
$909$	−1.47570e10	−	2.55599e10i	−0.651666	−	1.12872i
$910$	−6.00393e9	+	1.03991e10i	−0.264113	+	0.457458i
$911$	−2.70025e10	+	1.30037e10i	−1.18328	+	0.569840i	−0.918867	−	0.394568i	$-0.870894\pi$
$911$	−2.70025e10	+	1.30037e10i	−1.18328	+	0.569840i	−0.264418	+	0.964408i	$0.585180\pi$
$912$	−6.66151e9	−	2.05480e9i	−0.290798	−	0.0896992i
$913$	5.23893e8	+	6.99087e9i	0.0227822	+	0.304007i
$914$	−1.21881e10	−	5.33996e10i	−0.527989	−	2.31327i
$915$	1.94447e9	−	4.95443e9i	0.0839127	−	0.213806i
$916$	−2.46795e9	+	3.29325e10i	−0.106097	+	1.41576i
$917$	1.52305e9	−	2.29564e8i	0.0652263	−	0.00983129i
$918$	−2.11649e9	−	1.96382e9i	−0.0902957	−	0.0837822i
$919$	1.53183e9	+	7.37688e8i	0.0651036	+	0.0313522i	0.466152	−	0.884705i	$-0.345640\pi$
$919$	1.53183e9	+	7.37688e8i	0.0651036	+	0.0313522i	−0.401049	+	0.916057i	$0.631354\pi$
$920$	−4.18912e10	+	2.85609e10i	−1.77364	+	1.20925i
$921$	2.93241e9	+	7.47166e9i	0.123685	+	0.315144i
$922$	−5.60651e10	+	1.72938e10i	−2.35578	+	0.726662i
$923$	1.89523e10	−	1.75852e10i	0.793336	−	0.736108i
$924$	−1.02877e9	+	1.29003e9i	−0.0429007	+	0.0537958i
$925$	2.53437e10	−	3.17800e10i	1.05287	−	1.32025i
$926$	−2.20260e10	+	2.04372e10i	−0.911586	+	0.845828i
$927$	−2.65909e10	+	8.20219e9i	−1.09636	+	0.338182i
$928$	−1.87247e9	−	4.77097e9i	−0.0769124	−	0.195970i
$929$	−2.46401e10	+	1.67994e10i	−1.00830	+	0.687445i	−0.950449	−	0.310881i	$-0.899376\pi$
$929$	−2.46401e10	+	1.67994e10i	−1.00830	+	0.687445i	−0.0578474	+	0.998325i	$0.518424\pi$
$930$	−4.34679e10	−	2.09330e10i	−1.77206	−	0.853379i
$931$	1.66893e10	+	1.54854e10i	0.677819	+	0.628924i
$932$	−5.88181e10	+	8.86541e9i	−2.37988	+	0.358710i
$933$	1.40979e9	−	1.88123e10i	0.0568288	−	0.758328i
$934$	−1.98281e10	+	5.05212e10i	−0.796283	+	2.02890i
$935$	2.62907e8	+	1.15187e9i	0.0105187	+	0.0460854i
$936$	−1.88087e9	−	2.50985e10i	−0.0749711	−	1.00042i
$937$	4.92060e9	+	1.51781e9i	0.195402	+	0.0602736i	0.390912	−	0.920428i	$-0.372160\pi$
$937$	4.92060e9	+	1.51781e9i	0.195402	+	0.0602736i	−0.195509	+	0.980702i	$0.562636\pi$
$938$	1.04948e10	−	5.05401e9i	0.415205	−	0.199952i
$939$	−8.76115e9	+	1.51748e10i	−0.345328	+	0.598126i
$940$	2.28697e10	+	3.96115e10i	0.898077	+	1.55551i
$941$	−2.11583e10	−	1.44255e10i	−0.827783	−	0.564373i	0.0736533	−	0.997284i	$-0.476534\pi$
$941$	−2.11583e10	−	1.44255e10i	−0.827783	−	0.564373i	−0.901437	+	0.432911i	$0.857487\pi$
$942$	6.80646e9	−	2.98210e10i	0.265304	−	1.16237i
$943$	3.44591e10	+	5.19387e9i	1.33817	+	0.201697i
$944$	1.27691e10	+	1.60119e10i	0.494035	+	0.619500i
$945$	7.82216e9			0.301520
$946$	1.37393e10	+	6.80690e9i	0.527648	+	0.261415i
$947$	2.24417e10			0.858679			0.429340	−	0.903143i	$-0.358746\pi$
$947$	2.24417e10			0.858679			0.429340	+	0.903143i	$0.358746\pi$
$948$	−1.61845e10	−	2.02947e10i	−0.616977	−	0.773665i
$949$	−2.93747e10	−	4.42753e9i	−1.11569	−	0.168163i
$950$	1.58106e10	−	6.92708e10i	0.598296	−	2.62131i
$951$	−1.65923e9	−	1.13124e9i	−0.0625567	−	0.0426504i
$952$	3.53559e8	+	6.12382e8i	0.0132811	+	0.0230035i
$953$	−3.01348e9	+	5.21949e9i	−0.112783	+	0.195345i	−0.916891	−	0.399137i	$-0.869310\pi$
$953$	−3.01348e9	+	5.21949e9i	−0.112783	+	0.195345i	0.804109	+	0.594483i	$0.202643\pi$
$954$	−1.10439e9	+	5.31846e8i	−0.0411815	+	0.0198320i
$955$	5.94487e9	+	1.83375e9i	0.220867	+	0.0681284i
$956$	−2.01320e9	−	2.68642e10i	−0.0745218	−	0.994425i
$957$	5.41558e8	+	2.37272e9i	0.0199734	+	0.0875094i
$958$	1.55358e10	−	3.95847e10i	0.570894	−	1.45461i
$959$	−3.14060e8	+	4.19083e9i	−0.0114987	+	0.153439i
$960$	2.86441e10	−	4.31741e9i	1.04493	−	0.157498i
$961$	−2.20668e10	−	2.04750e10i	−0.802061	−	0.744204i
$962$	−3.89929e10	−	1.87780e10i	−1.41212	−	0.680043i
$963$	2.38546e10	−	1.62638e10i	0.860754	−	0.586852i
$964$	−2.21508e10	−	5.64394e10i	−0.796381	−	2.02914i
$965$	−5.84775e10	+	1.80379e10i	−2.09480	+	0.646161i
$966$	−3.28717e9	+	3.05005e9i	−0.117328	+	0.108865i
$967$	2.09892e10	−	2.63196e10i	0.746454	−	0.936023i	−0.253052	−	0.967453i	$-0.581434\pi$
$967$	2.09892e10	−	2.63196e10i	0.746454	−	0.936023i	0.999506	+	0.0314293i	$0.0100059\pi$
$968$	2.29031e10	−	2.87196e10i	0.811579	−	1.01769i
$969$	−8.32538e8	+	7.72482e8i	−0.0293948	+	0.0272744i
$970$	9.67023e10	−	2.98287e10i	3.40201	−	1.04938i
$971$	4.84473e9	+	1.23442e10i	0.169825	+	0.432708i	0.990295	−	0.138982i	$-0.0443831\pi$
$971$	4.84473e9	+	1.23442e10i	0.169825	+	0.432708i	−0.820469	+	0.571690i	$0.806288\pi$
$972$	−4.56051e10	+	3.10930e10i	−1.59287	+	1.08600i
$973$	−7.09534e8	−	3.41694e8i	−0.0246933	−	0.0118916i
$974$	−3.80349e10	−	3.52912e10i	−1.31894	−	1.22380i
$975$	−2.07295e10	+	3.12447e9i	−0.716262	+	0.107959i
$976$	3.95413e8	−	5.27642e9i	0.0136137	−	0.181662i
$977$	5.04791e9	−	1.28619e10i	0.173173	−	0.441238i	−0.817766	−	0.575551i	$-0.804788\pi$
$977$	5.04791e9	−	1.28619e10i	0.173173	−	0.441238i	0.990939	+	0.134313i	$0.0428827\pi$
$978$	−3.59920e9	−	1.57691e10i	−0.123032	−	0.539040i
$979$	−1.18003e9	−	1.57464e10i	−0.0401933	−	0.536342i
$980$	8.17178e10	+	2.52066e10i	2.77348	+	0.855506i
$981$	2.38026e10	−	1.14627e10i	0.804974	−	0.387655i
$982$	−3.73444e9	+	6.46824e9i	−0.125845	+	0.217970i
$983$	1.88263e10	+	3.26081e10i	0.632160	+	1.09493i	0.987109	+	0.160048i	$0.0511650\pi$
$983$	1.88263e10	+	3.26081e10i	0.632160	+	1.09493i	−0.354949	+	0.934886i	$0.615502\pi$
$984$	2.73529e10	+	1.86489e10i	0.915210	+	0.623979i
$985$	−1.12300e10	+	4.92019e10i	−0.374415	+	1.64042i
$986$	2.21230e9	+	3.33451e8i	0.0734979	+	0.0110780i
$987$	1.17584e9	+	1.47445e9i	0.0389258	+	0.0488114i
$988$	−4.93219e10			−1.62701
$989$	2.22744e10	+	1.55544e10i	0.732184	+	0.511288i
$990$	2.20746e10			0.723051
$991$	2.13816e9	+	2.68116e9i	0.0697882	+	0.0875116i	0.815500	−	0.578757i	$-0.196462\pi$
$991$	2.13816e9	+	2.68116e9i	0.0697882	+	0.0875116i	−0.745712	+	0.666268i	$0.767891\pi$
$992$	1.77006e10	+	2.66793e9i	0.575700	+	0.0867728i
$993$	−3.63700e9	+	1.59347e10i	−0.117875	+	0.516443i
$994$	1.12130e10	+	7.64491e9i	0.362135	+	0.246899i
$995$	1.79225e10	+	3.10427e10i	0.576790	+	0.999030i
$996$	−1.26562e10	+	2.19213e10i	−0.405880	+	0.703004i
$997$	−2.68836e9	+	1.29465e9i	−0.0859121	+	0.0413731i	−0.476346	−	0.879258i	$-0.658039\pi$
$997$	−2.68836e9	+	1.29465e9i	−0.0859121	+	0.0413731i	0.390434	+	0.920631i	$0.372325\pi$
$998$	3.86555e10	+	1.19236e10i	1.23099	+	0.379710i
$999$	2.10685e9	+	2.81139e10i	0.0668580	+	0.892159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.g.a.9.3	✓	300
43.24	even	21	inner	43.8.g.a.24.3	yes	300

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.g.a.9.3	✓	300	1.1	even	1	trivial
43.8.g.a.24.3	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)

\(f(q)\)	\(=\)	\(q+(-11.9571 - 14.9937i) q^{2} +(22.8341 + 3.44169i) q^{3} +(-53.3566 + 233.771i) q^{4} +(-375.006 - 255.675i) q^{5} +(-221.425 - 383.520i) q^{6} +(97.1595 - 168.285i) q^{7} +(1931.43 - 930.128i) q^{8} +(-1580.29 - 487.454i) q^{9} +O(q^{10})\)	\(q+(-11.9571 - 14.9937i) q^{2} +(22.8341 + 3.44169i) q^{3} +(-53.3566 + 233.771i) q^{4} +(-375.006 - 255.675i) q^{5} +(-221.425 - 383.520i) q^{6} +(97.1595 - 168.285i) q^{7} +(1931.43 - 930.128i) q^{8} +(-1580.29 - 487.454i) q^{9} +(650.465 + 8679.85i) q^{10} +(341.242 + 1495.08i) q^{11} +(-2022.92 + 5154.31i) q^{12} +(-530.539 + 7079.55i) q^{13} +(-3684.96 + 555.418i) q^{14} +(-7682.97 - 7128.76i) q^{15} +(-9387.64 - 4520.85i) q^{16} +(-1402.53 + 956.230i) q^{17} +(11586.9 + 29522.9i) q^{18} +(27686.2 - 8540.07i) q^{19} +(79778.3 - 74023.4i) q^{20} +(2797.74 - 3508.25i) q^{21} +(18336.5 - 22993.3i) q^{22} +(38198.8 - 35443.3i) q^{23} +(47303.7 - 14591.3i) q^{24} +(46717.6 + 119035. i) q^{25} +(112492. - 76696.0i) q^{26} +(-79907.7 - 38481.5i) q^{27} +(34156.0 + 31692.2i) q^{28} +(67958.2 - 10243.0i) q^{29} +(-15020.5 + 200435. i) q^{30} +(-87693.5 + 223439. i) q^{31} +(-16594.6 - 72705.7i) q^{32} +(2646.36 + 35313.3i) q^{33} +(31107.6 + 9595.42i) q^{34} +(-79461.7 + 38266.7i) q^{35} +(198271. - 343416. i) q^{36} +(-158938. - 275289. i) q^{37} +(-459094. - 313005. i) q^{38} +(-36480.0 + 159829. i) q^{39} +(-962108. - 145015. i) q^{40} +(416961. + 522853. i) q^{41} -86054.4 q^{42} +(110319. + 509557. i) q^{43} -367714. q^{44} +(467987. + 586837. i) q^{45} +(-988172. - 148943. i) q^{46} +(-93521.6 + 409745. i) q^{47} +(-198799. - 135539. i) q^{48} +(392892. + 680508. i) q^{49} +(1.22616e6 - 2.12377e6i) q^{50} +(-35316.6 + 17007.6i) q^{51} +(-1.62668e6 - 501766. i) q^{52} +(2888.29 + 38541.5i) q^{53} +(378482. + 1.65824e6i) q^{54} +(254286. - 647911. i) q^{55} +(31130.1 - 415402. i) q^{56} +(661583. - 99717.6i) q^{57} +(-966162. - 896467. i) q^{58} +(-1.77090e6 - 852819. i) q^{59} +(2.07643e6 - 1.41569e6i) q^{60} +(185527. + 472715. i) q^{61} +(4.39874e6 - 1.35683e6i) q^{62} +(-235571. + 218578. i) q^{63} +(-1.72325e6 + 2.16089e6i) q^{64} +(2.00902e6 - 2.51923e6i) q^{65} +(497834. - 461922. i) q^{66} +(-2.98687e6 + 921326. i) q^{67} +(-148704. - 378892. i) q^{68} +(994221. - 677848. i) q^{69} +(1.52389e6 + 733866. i) q^{70} +(-2.66957e6 - 2.47700e6i) q^{71} +(-3.50561e6 + 528386. i) q^{72} +(-312698. + 4.17267e6i) q^{73} +(-2.22716e6 + 5.67472e6i) q^{74} +(657075. + 2.87884e6i) q^{75} +(519174. + 6.92790e6i) q^{76} +(284755. + 87835.2i) q^{77} +(2.83263e6 - 1.36412e6i) q^{78} +(-2.34401e6 + 4.05994e6i) q^{79} +(2.36455e6 + 4.09553e6i) q^{80} +(1.29613e6 + 883690. i) q^{81} +(2.85386e6 - 1.25036e7i) q^{82} +(4.52040e6 + 681341. i) q^{83} +(670848. + 841217. i) q^{84} +770442. q^{85} +(6.32105e6 - 7.74690e6i) q^{86} +1.58702e6 q^{87} +(2.04970e6 + 2.57025e6i) q^{88} +(-1.01819e7 - 1.53467e6i) q^{89} +(3.20310e6 - 1.40337e7i) q^{90} +(1.13984e6 + 777128. i) q^{91} +(6.24745e6 + 1.08209e7i) q^{92} +(-2.77141e6 + 4.80022e6i) q^{93} +(7.26183e6 - 3.49711e6i) q^{94} +(-1.25660e7 - 3.87609e6i) q^{95} +(-128693. - 1.71728e6i) q^{96} +(-2.58712e6 - 1.13349e7i) q^{97} +(5.50550e6 - 1.40278e7i) q^{98} +(189522. - 2.52900e6i) 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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