LMFDB - Embedded newform 570.2.bb.a.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	570.71
Dual form			570.2.bb.a.281.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-0.939713 + 1.45497i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.385412 - 1.68863i) q^{6} +(-1.27478 - 2.20798i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.23388 - 2.73451i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.939713 + 1.45497i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.385412 - 1.68863i) q^{6} +(-1.27478 - 2.20798i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.23388 - 2.73451i) q^{9} +(0.342020 - 0.939693i) q^{10} +(2.48165 + 1.43278i) q^{11} +(0.215376 + 1.71861i) q^{12} +(-0.122235 + 0.0215533i) q^{13} +(1.95307 + 1.63882i) q^{14} +(-0.510537 - 1.65510i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.64588 - 4.52202i) q^{17} +(2.09473 + 2.14759i) q^{18} +(1.02793 - 4.23596i) q^{19} +1.00000i q^{20} +(4.41047 + 0.220101i) q^{21} +(-2.82202 - 0.497599i) q^{22} +(-0.0216324 - 0.0257805i) q^{23} +(-0.790186 - 1.54130i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(0.107492 - 0.0620603i) q^{26} +(5.13812 + 0.774392i) q^{27} +(-2.39580 - 0.871998i) q^{28} +(2.95506 + 1.07555i) q^{29} +(1.04582 + 1.38067i) q^{30} +(7.19374 - 4.15331i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.41669 + 2.26432i) q^{33} +(3.09325 + 3.68639i) q^{34} +(2.51082 + 0.442725i) q^{35} +(-2.70292 - 1.30163i) q^{36} +4.34953i q^{37} +(0.482846 + 4.33207i) q^{38} +(0.0835063 - 0.198102i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-1.16187 + 6.58931i) q^{41} +(-4.21976 + 1.30164i) q^{42} +(0.667517 + 0.560113i) q^{43} +(2.82202 - 0.497599i) q^{44} +(2.88788 + 0.812501i) q^{45} +(0.0291452 + 0.0168270i) q^{46} +(0.180872 - 0.496940i) q^{47} +(1.26969 + 1.17809i) q^{48} +(0.249892 - 0.432825i) q^{49} +(0.500000 + 0.866025i) q^{50} +(8.12607 + 1.85469i) q^{51} +(-0.0797832 + 0.0950820i) q^{52} +(2.52341 - 2.11740i) q^{53} +(-5.09311 + 1.02965i) q^{54} +(-2.69274 + 0.980079i) q^{55} +2.54955 q^{56} +(5.19724 + 5.47619i) q^{57} -3.14471 q^{58} +(7.78605 - 2.83389i) q^{59} +(-1.45497 - 0.939713i) q^{60} +(9.58449 - 8.04234i) q^{61} +(-5.33939 + 6.36324i) q^{62} +(-4.46481 + 6.21027i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0620603 - 0.107492i) q^{65} +(3.37588 - 3.63836i) q^{66} +(4.87885 - 13.4045i) q^{67} +(-4.16752 - 2.40612i) q^{68} +(0.0578380 - 0.00724825i) q^{69} +(-2.51082 + 0.442725i) q^{70} +(-6.84283 - 5.74181i) q^{71} +(2.98509 + 0.298682i) q^{72} +(-0.954037 + 5.41061i) q^{73} +(-1.48763 - 4.08722i) q^{74} +(1.59605 + 0.672783i) q^{75} +(-1.93538 - 3.90567i) q^{76} -7.30589i q^{77} +(-0.0107153 + 0.214716i) q^{78} +(3.19541 + 0.563438i) q^{79} +(0.642788 + 0.766044i) q^{80} +(-5.95508 + 6.74812i) q^{81} +(-1.16187 - 6.58931i) q^{82} +(0.676338 - 0.390484i) q^{83} +(3.52009 - 2.66638i) q^{84} +(4.52202 + 1.64588i) q^{85} +(-0.818830 - 0.298030i) q^{86} +(-4.34180 + 3.28881i) q^{87} +(-2.48165 + 1.43278i) q^{88} +(-1.05331 - 5.97362i) q^{89} +(-2.99161 + 0.224211i) q^{90} +(0.203412 + 0.242416i) q^{91} +(-0.0331427 - 0.00584396i) q^{92} +(-0.717106 + 14.3696i) q^{93} +0.528833i q^{94} +(2.58419 + 3.51026i) q^{95} +(-1.59605 - 0.672783i) q^{96} +(0.964701 + 2.65050i) q^{97} +(-0.0867865 + 0.492191i) q^{98} +(0.855892 - 8.55396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{7}{18}\right)$	$1$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−0.939713	+	1.45497i	−0.542543	+	0.840028i
$3$	−0.939713	+	1.45497i	−0.542543	+	0.840028i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−0.642788	+	0.766044i	−0.287463	+	0.342585i
$5$	−0.642788	+	0.766044i	−0.287463	+	0.342585i
$6$	0.385412	−	1.68863i	0.157344	−	0.689379i
$7$	−1.27478	−	2.20798i	−0.481820	−	0.834537i	0.517962	−	0.855404i	$-0.326691\pi$
$7$	−1.27478	−	2.20798i	−0.481820	−	0.834537i	−0.999782	+	0.0208667i	$0.993357\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−1.23388	−	2.73451i	−0.411294	−	0.911503i
$10$	0.342020	−	0.939693i	0.108156	−	0.297157i
$11$	2.48165	+	1.43278i	0.748244	+	0.431999i	0.825059	−	0.565046i	$-0.191142\pi$
$11$	2.48165	+	1.43278i	0.748244	+	0.431999i	−0.0768148	+	0.997045i	$0.524475\pi$
$12$	0.215376	+	1.71861i	0.0621736	+	0.496119i
$13$	−0.122235	+	0.0215533i	−0.0339019	+	0.00597782i	−0.190573	−	0.981673i	$-0.561035\pi$
$13$	−0.122235	+	0.0215533i	−0.0339019	+	0.00597782i	0.156672	+	0.987651i	$0.449924\pi$
$14$	1.95307	+	1.63882i	0.521980	+	0.437993i
$15$	−0.510537	−	1.65510i	−0.131820	−	0.427345i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−1.64588	−	4.52202i	−0.399185	−	1.09675i	−0.962682	−	0.270634i	$-0.912767\pi$
$17$	−1.64588	−	4.52202i	−0.399185	−	1.09675i	0.563497	−	0.826118i	$-0.309456\pi$
$18$	2.09473	+	2.14759i	0.493732	+	0.506191i
$19$	1.02793	−	4.23596i	0.235823	−	0.971796i
$19$	1.02793	−	4.23596i	0.235823	−	0.971796i
$20$			1.00000i			0.223607i
$21$	4.41047	+	0.220101i	0.962442	+	0.0480301i
$22$	−2.82202	−	0.497599i	−0.601657	−	0.106088i
$23$	−0.0216324	−	0.0257805i	−0.00451066	−	0.00537560i	0.763784	−	0.645471i	$-0.223339\pi$
$23$	−0.0216324	−	0.0257805i	−0.00451066	−	0.00537560i	−0.768295	+	0.640096i	$0.778895\pi$
$24$	−0.790186	−	1.54130i	−0.161296	−	0.314617i
$25$	−0.173648	−	0.984808i	−0.0347296	−	0.196962i
$26$	0.107492	−	0.0620603i	0.0210809	−	0.0121710i
$27$	5.13812	+	0.774392i	0.988832	+	0.149032i
$28$	−2.39580	−	0.871998i	−0.452763	−	0.164792i
$29$	2.95506	+	1.07555i	0.548741	+	0.199725i	0.601487	−	0.798883i	$-0.294575\pi$
$29$	2.95506	+	1.07555i	0.548741	+	0.199725i	−0.0527463	+	0.998608i	$0.516797\pi$
$30$	1.04582	+	1.38067i	0.190941	+	0.252075i
$31$	7.19374	−	4.15331i	1.29203	−	0.745956i	0.313020	−	0.949747i	$-0.398659\pi$
$31$	7.19374	−	4.15331i	1.29203	−	0.745956i	0.979015	+	0.203790i	$0.0653260\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−4.41669	+	2.26432i	−0.768846	+	0.394168i
$34$	3.09325	+	3.68639i	0.530487	+	0.632210i
$35$	2.51082	+	0.442725i	0.424406	+	0.0748342i
$36$	−2.70292	−	1.30163i	−0.450486	−	0.216939i
$37$			4.34953i			0.715058i	0.933902	+	0.357529i	$0.116381\pi$
$37$			4.34953i			0.715058i	−0.933902	+	0.357529i	$0.883619\pi$
$38$	0.482846	+	4.33207i	0.0783279	+	0.702755i
$39$	0.0835063	−	0.198102i	0.0133717	−	0.0317218i
$40$	−0.342020	−	0.939693i	−0.0540781	−	0.148578i
$41$	−1.16187	+	6.58931i	−0.181454	+	1.02908i	0.748973	+	0.662600i	$0.230547\pi$
$41$	−1.16187	+	6.58931i	−0.181454	+	1.02908i	−0.930427	+	0.366477i	$0.880564\pi$
$42$	−4.21976	+	1.30164i	−0.651123	+	0.200847i
$43$	0.667517	+	0.560113i	0.101795	+	0.0854164i	0.692265	−	0.721643i	$-0.256613\pi$
$43$	0.667517	+	0.560113i	0.101795	+	0.0854164i	−0.590470	+	0.807060i	$0.701057\pi$
$44$	2.82202	−	0.497599i	0.425436	−	0.0750159i
$45$	2.88788	+	0.812501i	0.430500	+	0.121120i
$46$	0.0291452	+	0.0168270i	0.00429723	+	0.00248101i
$47$	0.180872	−	0.496940i	0.0263828	−	0.0724862i	−0.925802	−	0.378009i	$-0.876609\pi$
$47$	0.180872	−	0.496940i	0.0263828	−	0.0724862i	0.952185	+	0.305523i	$0.0988311\pi$
$48$	1.26969	+	1.17809i	0.183264	+	0.170043i
$49$	0.249892	−	0.432825i	0.0356988	−	0.0618322i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	8.12607	+	1.85469i	1.13788	+	0.259709i
$52$	−0.0797832	+	0.0950820i	−0.0110639	+	0.0131855i
$53$	2.52341	−	2.11740i	0.346618	−	0.290847i	−0.452813	−	0.891606i	$-0.649579\pi$
$53$	2.52341	−	2.11740i	0.346618	−	0.290847i	0.799430	+	0.600759i	$0.205135\pi$
$54$	−5.09311	+	1.02965i	−0.693085	+	0.140118i
$55$	−2.69274	+	0.980079i	−0.363089	+	0.132154i
$56$	2.54955			0.340698
$57$	5.19724	+	5.47619i	0.688391	+	0.725340i
$58$	−3.14471			−0.412920
$59$	7.78605	−	2.83389i	1.01366	−	0.368941i	0.218821	−	0.975765i	$-0.429779\pi$
$59$	7.78605	−	2.83389i	1.01366	−	0.368941i	0.794836	+	0.606824i	$0.207557\pi$
$60$	−1.45497	−	0.939713i	−0.187836	−	0.121316i
$61$	9.58449	−	8.04234i	1.22717	−	1.02972i	0.228750	−	0.973485i	$-0.426536\pi$
$61$	9.58449	−	8.04234i	1.22717	−	1.02972i	0.998418	−	0.0562306i	$-0.0179082\pi$
$62$	−5.33939	+	6.36324i	−0.678104	+	0.808132i
$63$	−4.46481	+	6.21027i	−0.562513	+	0.782420i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.0620603	−	0.107492i	0.00769764	−	0.0133327i
$66$	3.37588	−	3.63836i	0.415542	−	0.447851i
$67$	4.87885	−	13.4045i	0.596047	−	1.63762i	−0.163028	−	0.986621i	$-0.552126\pi$
$67$	4.87885	−	13.4045i	0.596047	−	1.63762i	0.759075	−	0.651003i	$-0.225652\pi$
$68$	−4.16752	−	2.40612i	−0.505386	−	0.291785i
$69$	0.0578380	−	0.00724825i	0.00696288	−	0.000872587i
$70$	−2.51082	+	0.442725i	−0.300100	+	0.0529158i
$71$	−6.84283	−	5.74181i	−0.812094	−	0.681428i	0.139013	−	0.990291i	$-0.455607\pi$
$71$	−6.84283	−	5.74181i	−0.812094	−	0.681428i	−0.951107	+	0.308863i	$0.900052\pi$
$72$	2.98509	+	0.298682i	0.351797	+	0.0352001i
$73$	−0.954037	+	5.41061i	−0.111662	+	0.633264i	0.876687	+	0.481060i	$0.159748\pi$
$73$	−0.954037	+	5.41061i	−0.111662	+	0.633264i	−0.988349	+	0.152204i	$0.951363\pi$
$74$	−1.48763	−	4.08722i	−0.172933	−	0.475129i
$75$	1.59605	+	0.672783i	0.184296	+	0.0776863i
$76$	−1.93538	−	3.90567i	−0.222004	−	0.448012i
$77$		−	7.30589i		−	0.832583i
$78$	−0.0107153	+	0.214716i	−0.00121327	+	0.0243118i
$79$	3.19541	+	0.563438i	0.359512	+	0.0633917i	0.350487	−	0.936568i	$-0.386016\pi$
$79$	3.19541	+	0.563438i	0.359512	+	0.0633917i	0.00902507	+	0.999959i	$0.497127\pi$
$80$	0.642788	+	0.766044i	0.0718658	+	0.0856464i
$81$	−5.95508	+	6.74812i	−0.661675	+	0.749791i
$82$	−1.16187	−	6.58931i	−0.128307	−	0.727667i
$83$	0.676338	−	0.390484i	0.0742377	−	0.0428612i	−0.462422	−	0.886660i	$-0.653019\pi$
$83$	0.676338	−	0.390484i	0.0742377	−	0.0428612i	0.536659	+	0.843799i	$0.319686\pi$
$84$	3.52009	−	2.66638i	0.384073	−	0.290926i
$85$	4.52202	+	1.64588i	0.490482	+	0.178521i
$86$	−0.818830	−	0.298030i	−0.0882967	−	0.0321374i
$87$	−4.34180	+	3.28881i	−0.465490	+	0.352598i
$88$	−2.48165	+	1.43278i	−0.264544	+	0.152735i
$89$	−1.05331	−	5.97362i	−0.111651	−	0.633203i	−0.988354	−	0.152171i	$-0.951373\pi$
$89$	−1.05331	−	5.97362i	−0.111651	−	0.633203i	0.876703	−	0.481031i	$-0.159738\pi$
$90$	−2.99161	+	0.224211i	−0.315343	+	0.0236340i
$91$	0.203412	+	0.242416i	0.0213233	+	0.0254121i
$92$	−0.0331427	−	0.00584396i	−0.00345537	−	0.000609274i
$93$	−0.717106	+	14.3696i	−0.0743604	+	1.49006i
$94$			0.528833i			0.0545450i
$95$	2.58419	+	3.51026i	0.265133	+	0.360145i
$96$	−1.59605	−	0.672783i	−0.162896	−	0.0686656i
$97$	0.964701	+	2.65050i	0.0979506	+	0.269117i	0.978984	−	0.203937i	$-0.0653738\pi$
$97$	0.964701	+	2.65050i	0.0979506	+	0.269117i	−0.881033	+	0.473054i	$0.843152\pi$
$98$	−0.0867865	+	0.492191i	−0.00876676	+	0.0497188i
$99$	0.855892	−	8.55396i	0.0860203	−	0.859705i
$100$	−0.766044	−	0.642788i	−0.0766044	−	0.0642788i
$101$	−13.9490	+	2.45959i	−1.38798	+	0.244738i	−0.817195	−	0.576361i	$-0.804472\pi$
$101$	−13.9490	+	2.45959i	−1.38798	+	0.244738i	−0.570785	+	0.821100i	$0.693361\pi$
$102$	−8.27035	+	1.03644i	−0.818887	+	0.102623i
$103$	0.537120	+	0.310107i	0.0529241	+	0.0305557i	0.526229	−	0.850343i	$-0.323606\pi$
$103$	0.537120	+	0.310107i	0.0529241	+	0.0305557i	−0.473305	+	0.880899i	$0.656939\pi$
$104$	0.0424518	−	0.116635i	0.00416274	−	0.0114370i
$105$	−3.00360	+	3.23713i	−0.293121	+	0.315912i
$106$	−1.64704	+	2.85276i	−0.159975	+	0.277085i
$107$	−2.28942	−	3.96540i	−0.221327	−	0.383350i	0.733884	−	0.679275i	$-0.237705\pi$
$107$	−2.28942	−	3.96540i	−0.221327	−	0.383350i	−0.955211	+	0.295925i	$0.904372\pi$
$108$	4.43380	−	2.70950i	0.426643	−	0.260722i
$109$	−8.86538	+	10.5653i	−0.849149	+	1.01198i	0.150577	+	0.988598i	$0.451887\pi$
$109$	−8.86538	+	10.5653i	−0.849149	+	1.01198i	−0.999727	+	0.0233786i	$0.992558\pi$
$110$	2.19514	−	1.84195i	0.209299	−	0.175623i
$111$	−6.32843	−	4.08730i	−0.600668	−	0.387950i
$112$	−2.39580	+	0.871998i	−0.226381	+	0.0823961i
$113$	−15.3929			−1.44804			−0.724020	−	0.689779i	$-0.757708\pi$
$113$	−15.3929			−1.44804			−0.724020	+	0.689779i	$0.757708\pi$
$114$	−6.75678	−	3.36838i	−0.632830	−	0.315477i
$115$	0.0336540			0.00313825
$116$	2.95506	−	1.07555i	0.274370	−	0.0998626i
$117$	0.209761	+	0.307659i	0.0193924	+	0.0284430i
$118$	−6.34725	+	5.32597i	−0.584312	+	0.490296i
$119$	−7.88639	+	9.39864i	−0.722945	+	0.861572i
$120$	1.68863	+	0.385412i	0.154150	+	0.0351831i
$121$	−1.39429	−	2.41498i	−0.126754	−	0.219544i
$122$	−6.25583	+	10.8354i	−0.566376	+	0.980992i
$123$	−8.49543	−	7.88255i	−0.766007	−	0.710745i
$124$	2.84103	−	7.80567i	0.255132	−	0.700970i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	2.07151	−	7.36280i	0.184545	−	0.655930i
$127$	21.1739	−	3.73353i	1.87888	−	0.331297i	0.887341	−	0.461114i	$-0.152550\pi$
$127$	21.1739	−	3.73353i	1.87888	−	0.331297i	0.991538	+	0.129817i	$0.0414389\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−1.44222	+	0.444872i	−0.126981	+	0.0391688i
$130$	−0.0215533	+	0.122235i	−0.00189035	+	0.0107207i
$131$	−4.97159	−	13.6593i	−0.434370	−	1.19342i	−0.943104	−	0.332498i	$-0.892108\pi$
$131$	−4.97159	−	13.6593i	−0.434370	−	1.19342i	0.508734	−	0.860924i	$-0.330114\pi$
$132$	−1.92790	+	4.57356i	−0.167802	+	0.398078i
$133$	−10.6633	+	3.13026i	−0.924624	+	0.271428i
$134$			14.2648i			1.23229i
$135$	−3.89594	+	3.43826i	−0.335309	+	0.295918i
$136$	4.73913	+	0.835636i	0.406377	+	0.0716552i
$137$	−12.9496	−	15.4328i	−1.10636	−	1.31851i	−0.943317	−	0.331893i	$-0.892313\pi$
$137$	−12.9496	−	15.4328i	−1.10636	−	1.31851i	−0.163046	−	0.986618i	$-0.552132\pi$
$138$	−0.0518709	+	0.0265929i	−0.00441555	+	0.00226374i
$139$	−1.76125	−	9.98854i	−0.149387	−	0.847217i	−0.963739	−	0.266846i	$-0.914019\pi$
$139$	−1.76125	−	9.98854i	−0.149387	−	0.847217i	0.814352	−	0.580371i	$-0.197092\pi$
$140$	2.20798	−	1.27478i	0.186608	−	0.107738i
$141$	0.553067	+	0.730144i	0.0465766	+	0.0614892i
$142$	8.39397	+	3.05515i	0.704406	+	0.256383i
$143$	−0.334225	−	0.121648i	−0.0279493	−	0.0101727i
$144$	−2.90723	+	0.740293i	−0.242269	+	0.0616911i
$145$	−2.72340	+	1.57235i	−0.226166	+	0.130577i
$146$	−0.954037	−	5.41061i	−0.0789567	−	0.447786i
$147$	0.394922	+	0.770317i	0.0325726	+	0.0635347i
$148$	2.79582	+	3.33193i	0.229815	+	0.273883i
$149$	13.7412	+	2.42295i	1.12572	+	0.198496i	0.705353	−	0.708856i	$-0.250789\pi$
$149$	13.7412	+	2.42295i	1.12572	+	0.198496i	0.420372	+	0.907352i	$0.361900\pi$
$150$	−1.72990	−	0.0863295i	−0.141246	−	0.00704877i
$151$		−	15.3948i		−	1.25281i	−0.779498	−	0.626404i	$-0.784526\pi$
$151$		−	15.3948i		−	1.25281i	0.779498	−	0.626404i	$-0.215474\pi$
$152$	3.15448	+	3.00819i	0.255862	+	0.243997i
$153$	−10.3347	+	10.0803i	−0.835510	+	0.814945i
$154$	2.49876	+	6.86529i	0.201356	+	0.553221i
$155$	−1.44243	+	8.18042i	−0.115859	+	0.657067i
$156$	−0.0633682	−	0.205432i	−0.00507352	−	0.0164477i
$157$	−6.67600	−	5.60183i	−0.532803	−	0.447074i	0.336265	−	0.941767i	$-0.390836\pi$
$157$	−6.67600	−	5.60183i	−0.532803	−	0.447074i	−0.869068	+	0.494693i	$0.835281\pi$
$158$	−3.19541	+	0.563438i	−0.254213	+	0.0448247i
$159$	0.709466	+	5.66124i	0.0562643	+	0.448965i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−0.0293462	+	0.0806281i	−0.00231281	+	0.00635438i
$162$	3.28795	−	8.37791i	0.258326	−	0.658231i
$163$	−5.24087	+	9.07746i	−0.410497	+	0.711002i	−0.994944	−	0.100430i	$-0.967978\pi$
$163$	−5.24087	+	9.07746i	−0.410497	+	0.711002i	0.584447	+	0.811432i	$0.301311\pi$
$164$	3.34548	+	5.79454i	0.261238	+	0.452478i
$165$	1.10442	−	4.83886i	0.0859789	−	0.376704i
$166$	−0.501996	+	0.598256i	−0.0389625	+	0.0464337i
$167$	15.2688	−	12.8120i	1.18153	−	0.991423i	0.181565	−	0.983379i	$-0.441884\pi$
$167$	15.2688	−	12.8120i	1.18153	−	0.991423i	0.999968	−	0.00804417i	$-0.00256057\pi$
$168$	−2.39585	+	3.70952i	−0.184844	+	0.286196i
$169$	−12.2015	+	4.44099i	−0.938579	+	0.341615i
$170$	−4.81224			−0.369082
$171$	−12.8516	+	2.41579i	−0.982787	+	0.184740i
$172$	0.871381			0.0664422
$173$	19.9461	−	7.25979i	1.51647	−	0.551952i	0.556210	−	0.831042i	$-0.312255\pi$
$173$	19.9461	−	7.25979i	1.51647	−	0.551952i	0.960265	+	0.279090i	$0.0900329\pi$
$174$	2.95512	−	4.57546i	0.224027	−	0.346865i
$175$	−1.95307	+	1.63882i	−0.147638	+	0.123883i
$176$	1.84195	−	2.19514i	0.138842	−	0.165465i
$177$	−3.19342	+	13.9915i	−0.240032	+	1.05167i
$178$	3.03289	+	5.25311i	0.227324	+	0.393738i
$179$	−7.11341	+	12.3208i	−0.531681	+	0.920899i	0.467635	+	0.883922i	$0.345106\pi$
$179$	−7.11341	+	12.3208i	−0.531681	+	0.920899i	−0.999316	+	0.0369775i	$0.988227\pi$
$180$	2.73451	−	1.23388i	0.203818	−	0.0919680i
$181$	−6.33245	+	17.3983i	−0.470688	+	1.29320i	0.446513	+	0.894777i	$0.352666\pi$
$181$	−6.33245	+	17.3983i	−0.470688	+	1.29320i	−0.917200	+	0.398426i	$0.869556\pi$
$182$	−0.274056	−	0.158226i	−0.0203144	−	0.0117285i
$183$	2.69471	+	21.5026i	0.199198	+	1.58952i
$184$	0.0331427	−	0.00584396i	0.00244331	−	0.000430822i
$185$	−3.33193	−	2.79582i	−0.244968	−	0.205553i
$186$	−4.24084	−	13.7483i	−0.310953	−	1.00807i
$187$	2.39456	−	13.5802i	0.175108	−	0.993086i
$188$	−0.180872	−	0.496940i	−0.0131914	−	0.0362431i
$189$	−4.84012	−	12.3320i	−0.352067	−	0.897024i
$190$	−3.62893	−	2.41472i	−0.263270	−	0.175182i
$191$			1.30985i			0.0947773i	0.998877	+	0.0473886i	$0.0150899\pi$
$191$			1.30985i			0.0947773i	−0.998877	+	0.0473886i	$0.984910\pi$
$192$	1.72990	+	0.0863295i	0.124845	+	0.00623029i
$193$	5.25261	+	0.926176i	0.378091	+	0.0666676i	0.359464	−	0.933159i	$-0.382959\pi$
$193$	5.25261	+	0.926176i	0.378091	+	0.0666676i	0.0186268	+	0.999827i	$0.494071\pi$
$194$	−1.81305	−	2.16070i	−0.130169	−	0.155129i
$195$	0.0980784	+	0.191307i	0.00702354	+	0.0136998i
$196$	−0.0867865	−	0.492191i	−0.00619904	−	0.0351565i
$197$	−4.46328	+	2.57687i	−0.317995	+	0.183595i	−0.650499	−	0.759507i	$-0.725440\pi$
$197$	−4.46328	+	2.57687i	−0.317995	+	0.183595i	0.332503	+	0.943102i	$0.392107\pi$
$198$	2.12135	+	8.33083i	0.150758	+	0.592046i
$199$	0.165479	+	0.0602294i	0.0117305	+	0.00426955i	0.347879	−	0.937540i	$-0.386902\pi$
$199$	0.165479	+	0.0602294i	0.0117305	+	0.00426955i	−0.336148	+	0.941809i	$0.609124\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	14.9185	+	19.6950i	1.05227	+	1.38918i
$202$	12.2666	−	7.08211i	0.863073	−	0.498295i
$203$	−1.39224	−	7.89579i	−0.0977162	−	0.554176i
$204$	7.41710	−	3.80256i	0.519301	−	0.266232i
$205$	−4.30087	−	5.12557i	−0.300385	−	0.357985i
$206$	−0.610791	−	0.107699i	−0.0425558	−	0.00750374i
$207$	−0.0438051	+	0.0909639i	−0.00304467	+	0.00632243i
$208$			0.124121i			0.00860622i
$209$	8.62015	−	9.03936i	0.596268	−	0.625265i
$210$	1.71530	−	4.06920i	0.118367	−	0.280802i
$211$	2.32962	+	6.40058i	0.160378	+	0.440634i	0.993689	−	0.112170i	$-0.0357801\pi$
$211$	2.32962	+	6.40058i	0.160378	+	0.440634i	−0.833311	+	0.552804i	$0.813558\pi$
$212$	0.572012	−	3.24404i	0.0392859	−	0.222802i
$213$	14.7845	−	4.56046i	1.01301	−	0.312478i
$214$	3.50760	+	2.94323i	0.239775	+	0.201195i
$215$	−0.858143	+	0.151314i	−0.0585248	+	0.0103195i
$216$	−3.23970	+	4.06255i	−0.220434	+	0.276422i
$217$	−18.3408	−	10.5891i	−1.24506	−	0.718834i
$218$	4.71717	−	12.9603i	0.319487	−	0.877784i
$219$	−6.97577	−	6.47252i	−0.471379	−	0.437372i
$220$	−1.43278	+	2.48165i	−0.0965979	+	0.167313i
$221$	0.298649	+	0.517275i	0.0200893	+	0.0347957i
$222$	7.34472	+	1.67636i	0.492945	+	0.112510i
$223$	−15.5624	+	18.5466i	−1.04214	+	1.24197i	−0.0725141	+	0.997367i	$0.523102\pi$
$223$	−15.5624	+	18.5466i	−1.04214	+	1.24197i	−0.969623	+	0.244603i	$0.921342\pi$
$224$	1.95307	−	1.63882i	0.130495	−	0.109498i
$225$	−2.47870	+	1.68998i	−0.165247	+	0.112665i
$226$	14.4646	−	5.26467i	0.962169	−	0.350201i
$227$	19.2221			1.27581			0.637907	−	0.770114i	$-0.279800\pi$
$227$	19.2221			1.27581			0.637907	+	0.770114i	$0.279800\pi$
$228$	7.50135	+	0.854286i	0.496789	+	0.0565765i
$229$	2.65614			0.175523			0.0877614	−	0.996142i	$-0.472029\pi$
$229$	2.65614			0.175523			0.0877614	+	0.996142i	$0.472029\pi$
$230$	−0.0316244	+	0.0115103i	−0.00208525	+	0.000758970i
$231$	10.6299	+	6.86544i	0.699393	+	0.451713i
$232$	−2.40899	+	2.02138i	−0.158158	+	0.132710i
$233$	−8.11482	+	9.67087i	−0.531620	+	0.633560i	−0.963287	−	0.268473i	$-0.913481\pi$
$233$	−8.11482	+	9.67087i	−0.531620	+	0.633560i	0.431668	+	0.902033i	$0.357925\pi$
$234$	−0.302336	−	0.217362i	−0.0197644	−	0.0142094i
$235$	0.264416	+	0.457983i	0.0172486	+	0.0298755i
$236$	4.14287	−	7.17566i	0.269678	−	0.467096i
$237$	−3.82256	+	4.11976i	−0.248302	+	0.267607i
$238$	4.19626	−	11.5291i	0.272003	−	0.747323i
$239$	5.50617	+	3.17899i	0.356165	+	0.205632i	0.667397	−	0.744702i	$-0.267408\pi$
$239$	5.50617	+	3.17899i	0.356165	+	0.205632i	−0.311232	+	0.950334i	$0.600742\pi$
$240$	−1.71861	+	0.215376i	−0.110936	+	0.0139024i
$241$	−0.586101	+	0.103345i	−0.0377541	+	0.00665707i	−0.192493	−	0.981298i	$-0.561657\pi$
$241$	−0.586101	+	0.103345i	−0.0377541	+	0.00665707i	0.154739	+	0.987955i	$0.450546\pi$
$242$	2.13617	+	1.79246i	0.137318	+	0.115224i
$243$	−4.22225	−	15.0058i	−0.270858	−	0.962619i
$244$	2.17263	−	12.3216i	0.139088	−	0.788808i
$245$	0.170936	+	0.469643i	0.0109207	+	0.0300044i
$246$	10.6791	+	4.50156i	0.680873	+	0.287009i
$247$	−0.0343500	+	0.539938i	−0.00218564	+	0.0343554i
$248$			8.30662i			0.527471i
$249$	−0.0674205	+	1.35099i	−0.00427260	+	0.0856158i
$250$	−0.984808	−	0.173648i	−0.0622847	−	0.0109825i
$251$	−5.69780	−	6.79037i	−0.359642	−	0.428605i	0.555637	−	0.831425i	$-0.312474\pi$
$251$	−5.69780	−	6.79037i	−0.359642	−	0.428605i	−0.915279	+	0.402820i	$0.868030\pi$
$252$	0.571639	+	7.62727i	0.0360099	+	0.480473i
$253$	−0.0167462	−	0.0949724i	−0.00105282	−	0.00597086i
$254$	−18.6200	+	10.7503i	−1.16832	+	0.674532i
$255$	−6.64411	+	5.03276i	−0.416071	+	0.315164i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	21.8270	+	7.94440i	1.36153	+	0.495558i	0.916528	−	0.399970i	$-0.130979\pi$
$257$	21.8270	+	7.94440i	1.36153	+	0.495558i	0.445006	+	0.895528i	$0.353202\pi$
$258$	1.20309	−	0.911312i	0.0749011	−	0.0567358i
$259$	9.60365	−	5.54467i	0.596742	−	0.344529i
$260$	−0.0215533	−	0.122235i	−0.00133668	−	0.00758069i
$261$	−0.705080	−	9.40774i	−0.0436433	−	0.582324i
$262$	9.34354	+	11.1352i	0.577246	+	0.687935i
$263$	7.98265	+	1.40756i	0.492231	+	0.0867937i	0.414254	−	0.910161i	$-0.364043\pi$
$263$	7.98265	+	1.40756i	0.492231	+	0.0867937i	0.0779776	+	0.996955i	$0.475154\pi$
$264$	0.247382	−	4.95712i	0.0152253	−	0.305090i
$265$			3.29408i			0.202354i
$266$	8.94960	−	6.58854i	0.548735	−	0.403969i
$267$	9.68125	+	4.08095i	0.592483	+	0.249750i
$268$	−4.87885	−	13.4045i	−0.298023	−	0.818812i
$269$	0.324223	−	1.83876i	0.0197682	−	0.112111i	−0.973327	−	0.229422i	$-0.926316\pi$
$269$	0.324223	−	1.83876i	0.0197682	−	0.112111i	0.993095	+	0.117311i	$0.0374274\pi$
$270$	2.48503	−	4.56340i	0.151234	−	0.277720i
$271$	18.4922	+	15.5168i	1.12332	+	0.942580i	0.998768	−	0.0496321i	$-0.0158049\pi$
$271$	18.4922	+	15.5168i	1.12332	+	0.942580i	0.124556	+	0.992213i	$0.460249\pi$
$272$	−4.73913	+	0.835636i	−0.287352	+	0.0506679i
$273$	−0.543857	+	0.0681561i	−0.0329157	+	0.00412500i
$274$	17.4470	+	10.0730i	1.05401	+	0.608534i
$275$	0.980079	−	2.69274i	0.0591010	−	0.162379i
$276$	0.0396474	−	0.0427301i	0.00238649	−	0.00257205i
$277$	5.61896	−	9.73233i	0.337611	−	0.584759i	−0.646372	−	0.763022i	$-0.723715\pi$
$277$	5.61896	−	9.73233i	0.337611	−	0.584759i	0.983983	+	0.178263i	$0.0570479\pi$
$278$	5.07131	+	8.78377i	0.304157	+	0.526816i
$279$	−20.2335	−	14.5467i	−1.21135	−	0.870886i
$280$	−1.63882	+	1.95307i	−0.0979383	+	0.116718i
$281$	−14.0640	+	11.8011i	−0.838987	+	0.703993i	−0.957336	−	0.288979i	$-0.906684\pi$
$281$	−14.0640	+	11.8011i	−0.838987	+	0.703993i	0.118349	+	0.992972i	$0.462240\pi$
$282$	−0.769437	−	0.496951i	−0.0458193	−	0.0295930i
$283$	17.0439	−	6.20346i	1.01315	−	0.368758i	0.218510	−	0.975835i	$-0.429880\pi$
$283$	17.0439	−	6.20346i	1.01315	−	0.368758i	0.794643	+	0.607077i	$0.207658\pi$
$284$	−8.93267			−0.530057
$285$	−7.53573	+	0.461288i	−0.446378	+	0.0273243i
$286$	0.355675			0.0210315
$287$	16.0302	−	5.83450i	0.946231	−	0.344400i
$288$	2.47870	−	1.68998i	0.146059	−	0.0995829i
$289$	−4.71702	+	3.95805i	−0.277472	+	0.232826i
$290$	2.02138	−	2.40899i	0.118699	−	0.141461i
$291$	−4.76294	−	1.08709i	−0.279208	−	0.0637264i
$292$	2.74704	+	4.75801i	0.160758	+	0.278442i
$293$	14.3166	−	24.7971i	0.836386	−	1.44866i	−0.0565114	−	0.998402i	$-0.517998\pi$
$293$	14.3166	−	24.7971i	0.836386	−	1.44866i	0.892897	−	0.450261i	$-0.148669\pi$
$294$	−0.634569	−	0.588790i	−0.0370088	−	0.0343389i
$295$	−2.83389	+	7.78605i	−0.164996	+	0.453321i
$296$	−3.76680	−	2.17476i	−0.218941	−	0.126406i
$297$	11.6415	+	9.28356i	0.675507	+	0.538687i
$298$	−13.7412	+	2.42295i	−0.796008	+	0.140358i
$299$	0.00319989	+	0.00268503i	0.000185054	+	0.000155279i
$300$	1.65510	−	0.510537i	0.0955572	−	0.0294759i
$301$	0.385782	−	2.18788i	0.0222361	−	0.126107i
$302$	5.26532	+	14.4664i	0.302985	+	0.832445i
$303$	9.52944	−	22.6067i	0.547452	−	1.29872i
$304$	−3.99311	−	1.74788i	−0.229020	−	0.100248i
$305$			12.5117i			0.716415i
$306$	6.26376	−	13.0071i	0.358075	−	0.743565i
$307$	−16.2465	−	2.86469i	−0.927236	−	0.163497i	−0.310416	−	0.950601i	$-0.600468\pi$
$307$	−16.2465	−	2.86469i	−0.927236	−	0.163497i	−0.616820	+	0.787104i	$0.711579\pi$
$308$	−4.69614	−	5.59664i	−0.267587	−	0.318898i
$309$	−0.955935	+	0.490084i	−0.0543812	+	0.0278799i
$310$	−1.44243	−	8.18042i	−0.0819245	−	0.464617i
$311$	3.35430	−	1.93660i	0.190205	−	0.109815i	−0.401874	−	0.915695i	$-0.631641\pi$
$311$	3.35430	−	1.93660i	0.190205	−	0.109815i	0.592078	+	0.805880i	$0.298308\pi$
$312$	0.129809	+	0.171370i	0.00734896	+	0.00970190i
$313$	18.4089	+	6.70030i	1.04053	+	0.378724i	0.805083	−	0.593162i	$-0.202121\pi$
$313$	18.4089	+	6.70030i	1.04053	+	0.378724i	0.235452	+	0.971886i	$0.424343\pi$
$314$	8.18932	+	2.98067i	0.462150	+	0.168209i
$315$	−1.88742	−	7.41213i	−0.106344	−	0.417626i
$316$	2.81000	−	1.62235i	0.158075	−	0.0912645i
$317$	1.68941	+	9.58113i	0.0948868	+	0.538130i	0.994782	+	0.102024i	$0.0325317\pi$
$317$	1.68941	+	9.58113i	0.0948868	+	0.538130i	−0.899895	+	0.436106i	$0.856357\pi$
$318$	−2.60294	−	5.07717i	−0.145965	−	0.284714i
$319$	5.79238	+	6.90309i	0.324311	+	0.386499i
$320$	0.984808	+	0.173648i	0.0550524	+	0.00970723i
$321$	7.92094	+	0.395290i	0.442104	+	0.0220629i
$322$		−	0.0858026i		−	0.00478159i
$323$	−20.8470	+	2.32357i	−1.15996	+	0.129287i
$324$	−0.224249	+	8.99721i	−0.0124583	+	0.499845i
$325$	0.0424518	+	0.116635i	0.00235480	+	0.00646976i
$326$	1.82014	−	10.3225i	0.100808	−	0.571711i
$327$	−7.04137	−	22.8273i	−0.389388	−	1.26235i
$328$	−5.12557	−	4.30087i	−0.283012	−	0.237476i
$329$	−1.32780	+	0.234128i	−0.0732042	+	0.0129079i
$330$	0.617172	+	4.92477i	0.0339742	+	0.271100i
$331$	−24.6939	−	14.2570i	−1.35730	−	0.783637i	−0.368040	−	0.929810i	$-0.619971\pi$
$331$	−24.6939	−	14.2570i	−1.35730	−	0.783637i	−0.989259	+	0.146173i	$0.953304\pi$
$332$	0.267107	−	0.733869i	0.0146594	−	0.0402763i
$333$	11.8938	−	5.36680i	0.651777	−	0.294099i
$334$	−9.96598	+	17.2616i	−0.545314	+	0.944511i
$335$	7.13240	+	12.3537i	0.389685	+	0.674954i
$336$	0.982627	−	4.30524i	0.0536067	−	0.234870i
$337$	−20.4878	+	24.4165i	−1.11604	+	1.33005i	−0.177804	+	0.984066i	$0.556899\pi$
$337$	−20.4878	+	24.4165i	−1.11604	+	1.33005i	−0.938241	+	0.345984i	$0.887545\pi$
$338$	9.94678	−	8.34634i	0.541033	−	0.453981i
$339$	14.4649	−	22.3962i	0.785624	−	1.21639i
$340$	4.52202	−	1.64588i	0.245241	−	0.0892605i
$341$	23.8031			1.28901
$342$	11.2503	−	6.66561i	0.608348	−	0.360435i
$343$	−19.1211			−1.03244
$344$	−0.818830	+	0.298030i	−0.0441484	+	0.0160687i
$345$	−0.0316251	+	0.0489656i	−0.00170264	+	0.00263622i
$346$	−16.2602	+	13.6439i	−0.874155	+	0.733503i
$347$	−11.8503	+	14.1226i	−0.636156	+	0.758142i	−0.983758	−	0.179501i	$-0.942552\pi$
$347$	−11.8503	+	14.1226i	−0.636156	+	0.758142i	0.347601	+	0.937642i	$0.386996\pi$
$348$	−1.21201	+	5.31023i	−0.0649704	+	0.284658i
$349$	7.89906	+	13.6816i	0.422827	+	0.732358i	0.996215	−	0.0869263i	$-0.0277045\pi$
$349$	7.89906	+	13.6816i	0.422827	+	0.732358i	−0.573388	+	0.819284i	$0.694371\pi$
$350$	1.27478	−	2.20798i	0.0681396	−	0.118021i
$351$	−0.644749	+	0.0160859i	−0.0344142	+	0.000858602i
$352$	−0.980079	+	2.69274i	−0.0522384	+	0.143524i
$353$	−2.78327	−	1.60692i	−0.148138	−	0.0855278i	0.424099	−	0.905616i	$-0.360591\pi$
$353$	−2.78327	−	1.60692i	−0.148138	−	0.0855278i	−0.572237	+	0.820088i	$0.693924\pi$
$354$	−1.78455	−	14.2399i	−0.0948476	−	0.756845i
$355$	8.79697	−	1.55114i	0.466895	−	0.0823261i
$356$	−4.64665	−	3.89900i	−0.246272	−	0.206647i
$357$	−6.26380	−	20.3065i	−0.331516	−	1.07473i
$358$	2.47046	−	14.0107i	0.130568	−	0.740488i
$359$	1.53552	+	4.21881i	0.0810418	+	0.222661i	0.973595	−	0.228281i	$-0.0733105\pi$
$359$	1.53552	+	4.21881i	0.0810418	+	0.222661i	−0.892553	+	0.450942i	$0.851088\pi$
$360$	−2.14759	+	2.09473i	−0.113188	+	0.110402i
$361$	−16.8867	−	8.70854i	−0.888775	−	0.458344i
$362$		−	18.5149i		−	0.973119i
$363$	4.82395	+	0.240736i	0.253192	+	0.0126354i
$364$	0.311645	+	0.0549513i	0.0163346	+	0.00288023i
$365$	−3.53153	−	4.20871i	−0.184849	−	0.220294i
$366$	−9.88653	−	19.2842i	−0.516777	−	1.00800i
$367$	−1.35880	−	7.70612i	−0.0709286	−	0.402256i	−0.999515	−	0.0311398i	$-0.990086\pi$
$367$	−1.35880	−	7.70612i	−0.0709286	−	0.402256i	0.928586	−	0.371116i	$-0.121025\pi$
$368$	−0.0291452	+	0.0168270i	−0.00151930	+	0.000877168i
$369$	19.4521	−	4.95327i	1.01264	−	0.257857i
$370$	4.08722	+	1.48763i	0.212484	+	0.0773380i
$371$	−7.89195	−	2.87243i	−0.409730	−	0.149129i
$372$	8.68727	+	11.4687i	0.450414	+	0.594625i
$373$	6.71803	−	3.87865i	0.347846	−	0.200829i	−0.315890	−	0.948796i	$-0.602303\pi$
$373$	6.71803	−	3.87865i	0.347846	−	0.200829i	0.663736	+	0.747967i	$0.268970\pi$
$374$	2.39456	+	13.5802i	0.123820	+	0.702218i
$375$	−1.54130	+	0.790186i	−0.0795924	+	0.0408050i
$376$	0.339927	+	0.405110i	0.0175304	+	0.0208919i
$377$	−0.384393	−	0.0677789i	−0.0197973	−	0.00349079i
$378$	8.76603	+	9.93290i	0.450876	+	0.510893i
$379$			9.76760i			0.501728i	0.968022	+	0.250864i	$0.0807147\pi$
$379$			9.76760i			0.501728i	−0.968022	+	0.250864i	$0.919285\pi$
$380$	4.23596	+	1.02793i	0.217300	+	0.0527317i
$381$	−14.4652	+	34.3158i	−0.741074	+	1.75805i
$382$	−0.447994	−	1.23085i	−0.0229214	−	0.0629760i
$383$	3.07426	−	17.4350i	0.157087	−	0.890886i	−0.799765	−	0.600313i	$-0.795043\pi$
$383$	3.07426	−	17.4350i	0.157087	−	0.890886i	0.956853	−	0.290573i	$-0.0938461\pi$
$384$	−1.65510	+	0.510537i	−0.0844614	+	0.0260532i
$385$	5.59664	+	4.69614i	0.285231	+	0.239337i
$386$	−5.25261	+	0.926176i	−0.267351	+	0.0471411i
$387$	0.707998	−	2.51644i	0.0359896	−	0.127918i
$388$	2.44271	+	1.41030i	0.124010	+	0.0715971i
$389$	−7.58730	+	20.8459i	−0.384691	+	1.05693i	0.584666	+	0.811274i	$0.301226\pi$
$389$	−7.58730	+	20.8459i	−0.384691	+	1.05693i	−0.969357	+	0.245656i	$0.920997\pi$
$390$	−0.157594	−	0.146225i	−0.00798011	−	0.00740440i
$391$	−0.0809755	+	0.140254i	−0.00409511	+	0.00709294i
$392$	0.249892	+	0.432825i	0.0126214	+	0.0218610i
$393$	24.5458	+	5.60233i	1.23817	+	0.282600i
$394$	3.31277	−	3.94800i	0.166895	−	0.198897i
$395$	−2.48559	+	2.08566i	−0.125064	+	0.104941i
$396$	−4.84273	−	7.10287i	−0.243356	−	0.356933i
$397$	−12.5032	+	4.55079i	−0.627517	+	0.228397i	−0.636150	−	0.771565i	$-0.719474\pi$
$397$	−12.5032	+	4.55079i	−0.627517	+	0.228397i	0.00863331	+	0.999963i	$0.497252\pi$
$398$	−0.176099			−0.00882704
$399$	5.46599	−	18.4563i	0.273642	−	0.923971i
$400$	−1.00000			−0.0500000
$401$	30.2987	−	11.0278i	1.51305	−	0.550704i	0.553647	−	0.832752i	$-0.313236\pi$
$401$	30.2987	−	11.0278i	1.51305	−	0.550704i	0.959400	+	0.282047i	$0.0910135\pi$
$402$	−20.7549	−	13.4048i	−1.03516	−	0.668572i
$403$	−0.789810	+	0.662729i	−0.0393432	+	0.0330129i
$404$	−9.10458	+	10.8504i	−0.452970	+	0.539828i
$405$	−1.34151	−	8.89946i	−0.0666600	−	0.442218i
$406$	4.00880	+	6.94344i	0.198953	+	0.344597i
$407$	−6.23191	+	10.7940i	−0.308904	+	0.535038i
$408$	−5.66925	+	6.11004i	−0.280669	+	0.302492i
$409$	0.507516	−	1.39439i	0.0250950	−	0.0689480i	−0.926513	−	0.376264i	$-0.877209\pi$
$409$	0.507516	−	1.39439i	0.0250950	−	0.0689480i	0.951608	+	0.307316i	$0.0994308\pi$
$410$	5.79454	+	3.34548i	0.286172	+	0.165221i
$411$	34.6232	−	4.33897i	1.70784	−	0.214026i
$412$	0.610791	−	0.107699i	0.0300915	−	0.00530594i
$413$	−16.1826	−	13.5788i	−0.796296	−	0.668171i
$414$	0.0100519	−	0.100460i	0.000494022	−	0.00493736i
$415$	−0.135614	+	0.769103i	−0.00665701	+	0.0377538i
$416$	−0.0424518	−	0.116635i	−0.00208137	−	0.00571852i
$417$	16.1881	+	6.82379i	0.792734	+	0.334162i
$418$	−5.00865	+	11.4425i	−0.244981	+	0.559670i
$419$			39.2663i			1.91828i	0.282925	+	0.959142i	$0.408695\pi$
$419$			39.2663i			1.91828i	−0.282925	+	0.959142i	$0.591305\pi$
$420$	−0.220101	+	4.41047i	−0.0107399	+	0.215209i
$421$	10.2012	+	1.79874i	0.497174	+	0.0876651i	0.416612	−	0.909084i	$-0.363217\pi$
$421$	10.2012	+	1.79874i	0.497174	+	0.0876651i	0.0805619	+	0.996750i	$0.474329\pi$
$422$	−4.37825	−	5.21780i	−0.213130	−	0.253998i
$423$	−1.58206	+	0.118570i	−0.0769225	+	0.00576509i
$424$	0.572012	+	3.24404i	0.0277793	+	0.157544i
$425$	−4.16752	+	2.40612i	−0.202154	+	0.116714i
$426$	−12.3331	+	9.34201i	−0.597540	+	0.452622i
$427$	−29.9754	−	10.9101i	−1.45061	−	0.527979i
$428$	−4.30271	−	1.56606i	−0.207979	−	0.0756983i
$429$	0.491070	−	0.371974i	0.0237091	−	0.0179591i
$430$	0.754638	−	0.435690i	0.0363919	−	0.0210109i
$431$	4.25940	+	24.1563i	0.205168	+	1.16357i	0.897175	+	0.441675i	$0.145616\pi$
$431$	4.25940	+	24.1563i	0.205168	+	1.16357i	−0.692007	+	0.721891i	$0.743273\pi$
$432$	1.65485	−	4.92559i	0.0796191	−	0.236983i
$433$	13.5304	+	16.1249i	0.650229	+	0.774912i	0.985948	−	0.167050i	$-0.0534240\pi$
$433$	13.5304	+	16.1249i	0.650229	+	0.774912i	−0.335720	+	0.941962i	$0.608980\pi$
$434$	20.8564	+	3.67755i	1.00114	+	0.176528i
$435$	0.271481	−	5.44002i	0.0130165	−	0.260829i
$436$			13.7921i			0.660521i
$437$	−0.131442	+	0.0651334i	−0.00628770	+	0.00311575i
$438$	8.76881	+	3.69633i	0.418990	+	0.176617i
$439$	9.30662	+	25.5697i	0.444181	+	1.22038i	0.936718	+	0.350085i	$0.113847\pi$
$439$	9.30662	+	25.5697i	0.444181	+	1.22038i	−0.492537	+	0.870291i	$0.663930\pi$
$440$	0.497599	−	2.82202i	0.0237221	−	0.134535i
$441$	−1.49190	−	0.149277i	−0.0710429	−	0.00710841i
$442$	−0.457557	−	0.383936i	−0.0217638	−	0.0182620i
$443$	−14.1917	+	2.50238i	−0.674268	+	0.118892i	−0.500290	−	0.865858i	$-0.666773\pi$
$443$	−14.1917	+	2.50238i	−0.674268	+	0.118892i	−0.173978	+	0.984750i	$0.555662\pi$
$444$	−7.47513	+	0.936782i	−0.354754	+	0.0444577i
$445$	5.25311	+	3.03289i	0.249021	+	0.143773i
$446$	8.28060	−	22.7507i	0.392098	−	1.07728i
$447$	−16.4381	+	17.7162i	−0.777496	+	0.837948i
$448$	−1.27478	+	2.20798i	−0.0602275	+	0.104317i
$449$	−16.5322	−	28.6347i	−0.780204	−	1.35135i	−0.931822	−	0.362915i	$-0.881782\pi$
$449$	−16.5322	−	28.6347i	−0.780204	−	1.35135i	0.151618	−	0.988439i	$-0.451552\pi$
$450$	1.75121	−	2.43583i	0.0825530	−	0.114826i
$451$	−12.3244	+	14.6876i	−0.580332	+	0.691613i
$452$	−11.7916	+	9.89435i	−0.554631	+	0.465391i
$453$	22.3989	+	14.4667i	1.05239	+	0.679703i
$454$	−18.0628	+	6.57434i	−0.847731	+	0.308549i
$455$	−0.316452			−0.0148355
$456$	−7.34114	+	1.76285i	−0.343781	+	0.0825528i
$457$	30.1507			1.41039			0.705194	−	0.709014i	$-0.250860\pi$
$457$	30.1507			1.41039			0.705194	+	0.709014i	$0.250860\pi$
$458$	−2.49596	+	0.908454i	−0.116628	+	0.0424493i
$459$	−4.95493	−	24.5093i	−0.231276	−	1.14400i
$460$	0.0257805	−	0.0216324i	0.00120202	−	0.00100861i
$461$	−4.94947	+	5.89855i	−0.230520	+	0.274723i	−0.868888	−	0.495008i	$-0.835165\pi$
$461$	−4.94947	+	5.89855i	−0.230520	+	0.274723i	0.638369	+	0.769731i	$0.279610\pi$
$462$	−12.3369	−	2.81577i	−0.573965	−	0.131002i
$463$	4.27169	+	7.39879i	0.198522	+	0.343851i	0.948050	−	0.318123i	$-0.103052\pi$
$463$	4.27169	+	7.39879i	0.198522	+	0.343851i	−0.749527	+	0.661974i	$0.769719\pi$
$464$	1.57235	−	2.72340i	0.0729947	−	0.126431i
$465$	−10.5468	−	9.78594i	−0.489097	−	0.453812i
$466$	4.31781	−	11.8631i	0.200019	−	0.549546i
$467$	−29.3299	−	16.9336i	−1.35723	−	0.783594i	−0.367976	−	0.929835i	$-0.619949\pi$
$467$	−29.3299	−	16.9336i	−1.35723	−	0.783594i	−0.989249	+	0.146241i	$0.953283\pi$
$468$	0.358445	+	0.100848i	0.0165691	+	0.00466171i
$469$	−35.8163	+	6.31539i	−1.65385	+	0.291618i
$470$	−0.405110	−	0.339927i	−0.0186863	−	0.0156797i
$471$	14.4240	−	4.44927i	0.664623	−	0.205012i
$472$	−1.43880	+	8.15986i	−0.0662263	+	0.375588i
$473$	0.854022	+	2.34641i	0.0392680	+	0.107888i
$474$	2.18298	−	5.17870i	0.100268	−	0.237866i
$475$	−4.35010	−	0.276747i	−0.199596	−	0.0126980i
$476$			12.2691i			0.562351i
$477$	−8.90363	−	4.28768i	−0.407669	−	0.196320i
$478$	−6.26139	−	1.10405i	−0.286389	−	0.0504982i
$479$	11.0621	+	13.1833i	0.505440	+	0.602361i	0.957074	−	0.289843i	$-0.0936031\pi$
$479$	11.0621	+	13.1833i	0.505440	+	0.602361i	−0.451634	+	0.892203i	$0.649159\pi$
$480$	1.54130	−	0.790186i	0.0703504	−	0.0360669i
$481$	−0.0937468	−	0.531664i	−0.00427448	−	0.0242418i
$482$	0.515409	−	0.297571i	0.0234762	−	0.0135540i
$483$	−0.0897345	−	0.118465i	−0.00408306	−	0.00539035i
$484$	−2.62041	−	0.953750i	−0.119109	−	0.0433523i
$485$	−2.65050	−	0.964701i	−0.120353	−	0.0438048i
$486$	9.09989	+	12.6567i	0.412779	+	0.574120i
$487$	−31.8458	+	18.3862i	−1.44307	+	0.833158i	−0.998054	−	0.0623628i	$-0.980136\pi$
$487$	−31.8458	+	18.3862i	−1.44307	+	0.833158i	−0.445019	+	0.895521i	$0.646803\pi$
$488$	2.17263	+	12.3216i	0.0983502	+	0.557772i
$489$	−8.28253	−	16.1555i	−0.374549	−	0.730578i
$490$	−0.321255	−	0.382857i	−0.0145128	−	0.0172957i
$491$	−19.1764	−	3.38131i	−0.865417	−	0.152596i	−0.276720	−	0.960950i	$-0.589248\pi$
$491$	−19.1764	−	3.38131i	−0.865417	−	0.152596i	−0.588697	+	0.808354i	$0.700359\pi$
$492$	−11.5747	−	0.577627i	−0.521827	−	0.0260414i
$493$		−	15.1331i		−	0.681560i
$494$	−0.152391	−	0.519124i	−0.00685641	−	0.0233565i
$495$	6.00256	+	6.15403i	0.269795	+	0.276603i
$496$	−2.84103	−	7.80567i	−0.127566	−	0.350485i
$497$	−3.95472	+	22.4283i	−0.177393	+	1.00605i
$498$	−0.398713	−	1.29258i	−0.0178667	−	0.0579218i
$499$	18.8052	+	15.7794i	0.841837	+	0.706385i	0.957976	−	0.286848i	$-0.0926075\pi$
$499$	18.8052	+	15.7794i	0.841837	+	0.706385i	−0.116139	+	0.993233i	$0.537052\pi$
$500$	0.984808	−	0.173648i	0.0440419	−	0.00776578i
$501$	4.29286	+	34.2552i	0.191791	+	1.53041i
$502$	7.67662	+	4.43210i	0.342625	+	0.197814i
$503$	10.4660	−	28.7550i	0.466654	−	1.28212i	−0.453741	−	0.891134i	$-0.649911\pi$
$503$	10.4660	−	28.7550i	0.466654	−	1.28212i	0.920395	−	0.390989i	$-0.127867\pi$
$504$	−3.14584	−	6.97177i	−0.140127	−	0.310547i
$505$	7.08211	−	12.2666i	0.315150	−	0.545855i
$506$	0.0482187	+	0.0835173i	0.00214358	+	0.00371280i
$507$	5.00441	−	21.9261i	0.222254	−	0.973773i
$508$	13.8203	−	16.4704i	0.613176	−	0.730754i
$509$	21.8504	−	18.3346i	0.968500	−	0.812668i	−0.0138150	−	0.999905i	$-0.504398\pi$
$509$	21.8504	−	18.3346i	0.968500	−	0.812668i	0.982315	+	0.187237i	$0.0599532\pi$
$510$	4.52212	−	7.00167i	0.200243	−	0.310039i
$511$	13.1627	−	4.79083i	0.582283	−	0.211934i
$512$	1.00000			0.0441942
$513$	8.56192	−	20.9689i	0.378018	−	0.925798i
$514$	−23.2279			−1.02454
$515$	−0.582810	+	0.212125i	−0.0256817	+	0.00934736i
$516$	−0.818848	+	1.26783i	−0.0360478	+	0.0558133i
$517$	1.16086	−	0.974081i	0.0510548	−	0.0428400i
$518$	−7.12809	+	8.49493i	−0.313190	+	0.373246i
$519$	−8.18082	+	35.8431i	−0.359098	+	1.57334i
$520$	0.0620603	+	0.107492i	0.00272153	+	0.00471382i
$521$	−20.1824	+	34.9570i	−0.884208	+	1.53149i	−0.0375900	+	0.999293i	$0.511968\pi$
$521$	−20.1824	+	34.9570i	−0.884208	+	1.53149i	−0.846618	+	0.532201i	$0.821365\pi$
$522$	3.88019	+	8.59923i	0.169831	+	0.376378i
$523$	11.1821	−	30.7225i	0.488959	−	1.34340i	−0.412665	−	0.910883i	$-0.635402\pi$
$523$	11.1821	−	30.7225i	0.488959	−	1.34340i	0.901624	−	0.432520i	$-0.142376\pi$
$524$	−12.5885	−	7.26798i	−0.549932	−	0.317503i
$525$	−0.549112	−	4.38168i	−0.0239652	−	0.191232i
$526$	−7.98265	+	1.40756i	−0.348060	+	0.0613724i
$527$	−30.6214	−	25.6944i	−1.33389	−	1.11927i
$528$	1.46297	+	4.74278i	0.0636677	+	0.206403i
$529$	3.99371	−	22.6495i	0.173640	−	0.984759i
$530$	−1.12664	−	3.09543i	−0.0489382	−	0.134457i
$531$	−17.3564	−	17.7943i	−0.753202	−	0.772209i
$532$	−6.15646	+	9.25214i	−0.266916	+	0.401131i
$533$		−	0.830486i		−	0.0359724i
$534$	−10.4932	−	0.523655i	−0.454084	−	0.0226608i
$535$	4.50928	+	0.795109i	0.194953	+	0.0343755i
$536$	9.16924	+	10.9275i	0.396051	+	0.471995i
$537$	−11.2418	−	21.9278i	−0.485121	−	0.946255i
$538$	0.324223	+	1.83876i	0.0139783	+	0.0792746i
$539$	1.24029	−	0.716080i	0.0534229	−	0.0308437i
$540$	−0.774392	+	5.13812i	−0.0333245	+	0.221110i
$541$	−33.7550	−	12.2858i	−1.45124	−	0.528208i	−0.508303	−	0.861178i	$-0.669727\pi$
$541$	−33.7550	−	12.2858i	−1.45124	−	0.528208i	−0.942937	+	0.332970i	$0.891949\pi$
$542$	−22.6841	−	8.25633i	−0.974365	−	0.354640i
$543$	−19.3633	−	25.5629i	−0.830959	−	1.09701i
$544$	4.16752	−	2.40612i	0.178681	−	0.103161i
$545$	−2.39497	−	13.5826i	−0.102589	−	0.581813i
$546$	0.487748	−	0.250056i	0.0208737	−	0.0107014i
$547$	7.12822	+	8.49509i	0.304781	+	0.363224i	0.896596	−	0.442850i	$-0.146033\pi$
$547$	7.12822	+	8.49509i	0.304781	+	0.363224i	−0.591815	+	0.806074i	$0.701588\pi$
$548$	−19.8400	−	3.49833i	−0.847523	−	0.149441i
$549$	−33.8180	−	16.2856i	−1.44332	−	0.695051i
$550$			2.86556i			0.122188i
$551$	7.59359	−	11.4119i	0.323498	−	0.486164i
$552$	−0.0226418	+	0.0537133i	−0.000963701	+	0.00228619i
$553$	−2.82938	−	7.77366i	−0.120317	−	0.330569i
$554$	−1.95145	+	11.0672i	−0.0829090	+	0.470200i
$555$	7.19889	−	2.22059i	0.305576	−	0.0942589i
$556$	−7.76970	−	6.51955i	−0.329509	−	0.276491i
$557$	−6.22494	+	1.09763i	−0.263759	+	0.0465079i	−0.303964	−	0.952684i	$-0.598310\pi$
$557$	−6.22494	+	1.09763i	−0.263759	+	0.0465079i	0.0402045	+	0.999191i	$0.487199\pi$
$558$	23.9885	+	6.74914i	1.01551	+	0.285714i
$559$	−0.0936662	−	0.0540782i	−0.00396166	−	0.00228726i
$560$	0.871998	−	2.39580i	0.0368486	−	0.101241i
$561$	17.5087	+	16.2456i	0.739216	+	0.685888i
$562$	9.17961	−	15.8996i	0.387218	−	0.670682i
$563$	2.02139	+	3.50114i	0.0851913	+	0.147556i	0.905473	−	0.424404i	$-0.139517\pi$
$563$	2.02139	+	3.50114i	0.0851913	+	0.147556i	−0.820281	+	0.571960i	$0.806183\pi$
$564$	0.893001	+	0.203818i	0.0376021	+	0.00858230i
$565$	9.89435	−	11.7916i	0.416258	−	0.496077i
$566$	−13.8943	+	11.6587i	−0.584021	+	0.490052i
$567$	22.4911	+	4.54634i	0.944536	+	0.190928i
$568$	8.39397	−	3.05515i	0.352203	−	0.128191i
$569$	−24.6520			−1.03346			−0.516732	−	0.856147i	$-0.672852\pi$
$569$	−24.6520			−1.03346			−0.516732	+	0.856147i	$0.672852\pi$
$570$	6.92350	−	3.01084i	0.289993	−	0.126110i
$571$	22.3759			0.936403			0.468201	−	0.883622i	$-0.344902\pi$
$571$	22.3759			0.936403			0.468201	+	0.883622i	$0.344902\pi$
$572$	−0.334225	+	0.121648i	−0.0139747	+	0.00508636i
$573$	−1.90579	−	1.23088i	−0.0796155	−	0.0514208i
$574$	−13.0679	+	10.9653i	−0.545444	+	0.457682i
$575$	−0.0216324	+	0.0257805i	−0.000902132	+	0.00107512i
$576$	−1.75121	+	2.43583i	−0.0729672	+	0.101493i
$577$	14.7394	+	25.5293i	0.613608	+	1.06280i	0.990627	+	0.136595i	$0.0436158\pi$
$577$	14.7394	+	25.5293i	0.613608	+	1.06280i	−0.377019	+	0.926206i	$0.623051\pi$
$578$	3.07882	−	5.33267i	0.128062	−	0.221810i
$579$	−6.28350	+	6.77205i	−0.261133	+	0.281437i
$580$	−1.07555	+	2.95506i	−0.0446599	+	0.122702i
$581$	−1.72436	−	0.995559i	−0.0715384	−	0.0413027i
$582$	4.84750	−	0.607488i	0.200935	−	0.0251812i
$583$	9.29598	−	1.63913i	0.385000	−	0.0678859i
$584$	−4.20871	−	3.53153i	−0.174158	−	0.146136i
$585$	−0.370512	−	0.0370727i	−0.0153188	−	0.00153277i
$586$	−4.97211	+	28.1982i	−0.205396	+	1.16486i
$587$	−2.44951	−	6.72998i	−0.101102	−	0.277776i	0.878821	−	0.477152i	$-0.158331\pi$
$587$	−2.44951	−	6.72998i	−0.101102	−	0.277776i	−0.979923	+	0.199376i	$0.936109\pi$
$588$	0.797678	+	0.336246i	0.0328957	+	0.0138666i
$589$	−10.1986	−	34.7417i	−0.420226	−	1.43151i
$590$		−	8.28574i		−	0.341119i
$591$	0.444921	−	8.91546i	0.0183016	−	0.366733i
$592$	4.28345	+	0.755287i	0.176049	+	0.0310421i
$593$	−24.7796	−	29.5312i	−1.01758	−	1.21270i	−0.976937	−	0.213527i	$-0.931505\pi$
$593$	−24.7796	−	29.5312i	−1.01758	−	1.21270i	−0.0406392	−	0.999174i	$-0.512939\pi$
$594$	−14.1146	−	4.74208i	−0.579128	−	0.194570i
$595$	−2.13050	−	12.0827i	−0.0873419	−	0.495341i
$596$	12.0838	−	6.97660i	0.494973	−	0.285773i
$597$	−0.243134	+	0.184169i	−0.00995083	+	0.00753752i
$598$	−0.00392524	−	0.00142867i	−0.000160515	−	5.84227e-5i
$599$	−2.50285	−	0.910961i	−0.102264	−	0.0372209i	0.290382	−	0.956911i	$-0.406218\pi$
$599$	−2.50285	−	0.910961i	−0.102264	−	0.0372209i	−0.392645	+	0.919690i	$0.628440\pi$
$600$	−1.38067	+	1.04582i	−0.0563656	+	0.0426956i
$601$	−15.3065	+	8.83723i	−0.624366	+	0.360478i	−0.778567	−	0.627562i	$-0.784053\pi$
$601$	−15.3065	+	8.83723i	−0.624366	+	0.360478i	0.154201	+	0.988040i	$0.450720\pi$
$602$	0.385782	+	2.18788i	0.0157233	+	0.0891713i
$603$	−42.6747	+	3.19833i	−1.73785	+	0.130246i
$604$	−9.89557	−	11.7931i	−0.402645	−	0.479854i
$605$	2.74621	+	0.484231i	0.111649	+	0.0196868i
$606$	−1.22279	+	24.5026i	−0.0496724	+	0.995352i
$607$			33.6213i			1.36465i	0.731050	+	0.682324i	$0.239031\pi$
$607$			33.6213i			1.36465i	−0.731050	+	0.682324i	$0.760969\pi$
$608$	4.35010	+	0.276747i	0.176420	+	0.0112236i
$609$	12.7965	+	5.39410i	0.518538	+	0.218580i
$610$	−4.27924	−	11.7571i	−0.173261	−	0.476032i
$611$	−0.0113981	+	0.0646419i	−0.000461118	+	0.00261513i
$612$	−1.43733	+	14.3650i	−0.0581006	+	0.580670i
$613$	28.8639	+	24.2197i	1.16580	+	0.978223i	0.999969	−	0.00793046i	$-0.00252437\pi$
$613$	28.8639	+	24.2197i	1.16580	+	0.978223i	0.165833	+	0.986154i	$0.446969\pi$
$614$	16.2465	−	2.86469i	0.655655	−	0.115610i
$615$	11.4991	−	1.44107i	0.463690	−	0.0581096i
$616$	6.32709	+	3.65294i	0.254926	+	0.147181i
$617$	−1.98816	+	5.46244i	−0.0800405	+	0.219909i	−0.973258	−	0.229716i	$-0.926220\pi$
$617$	−1.98816	+	5.46244i	−0.0800405	+	0.219909i	0.893217	+	0.449625i	$0.148443\pi$
$618$	0.730667	−	0.787477i	0.0293917	−	0.0316770i
$619$	19.4490	−	33.6866i	0.781720	−	1.35398i	−0.149219	−	0.988804i	$-0.547676\pi$
$619$	19.4490	−	33.6866i	0.781720	−	1.35398i	0.930939	−	0.365175i	$-0.118991\pi$
$620$	4.15331	+	7.19374i	0.166801	+	0.288908i
$621$	−0.0911856	−	0.149215i	−0.00365915	−	0.00598780i
$622$	−2.48965	+	2.96705i	−0.0998259	+	0.118968i
$623$	−11.8469	+	9.94071i	−0.474635	+	0.398266i
$624$	−0.180592	−	0.116638i	−0.00722947	−	0.00466925i
$625$	−0.939693	+	0.342020i	−0.0375877	+	0.0136808i
$626$	−19.5904			−0.782989
$627$	5.05154	+	21.0365i	0.201739	+	0.840116i
$628$	−8.71489			−0.347762
$629$	19.6687	−	7.15881i	0.784241	−	0.285440i
$630$	4.30869	+	6.31959i	0.171662	+	0.251778i
$631$	−31.0227	+	26.0311i	−1.23499	+	1.03628i	−0.237095	+	0.971486i	$0.576195\pi$
$631$	−31.0227	+	26.0311i	−1.23499	+	1.03628i	−0.997898	+	0.0647965i	$0.979360\pi$
$632$	−2.08566	+	2.48559i	−0.0829630	+	0.0988715i
$633$	−11.5018	−	2.62517i	−0.457157	−	0.104341i
$634$	−4.86447	−	8.42550i	−0.193193	−	0.334620i
$635$	−10.7503	+	18.6200i	−0.426611	+	0.738912i
$636$	4.18246	+	3.88072i	0.165845	+	0.153881i
$637$	−0.0212167	+	0.0582924i	−0.000840637	+	0.00230963i
$638$	−7.80405	−	4.50567i	−0.308965	−	0.178381i
$639$	−7.25781	+	25.7965i	−0.287114	+	1.02049i
$640$	−0.984808	+	0.173648i	−0.0389279	+	0.00686405i
$641$	−26.5062	−	22.2414i	−1.04693	−	0.878481i	−0.0541653	−	0.998532i	$-0.517250\pi$
$641$	−26.5062	−	22.2414i	−1.04693	−	0.878481i	−0.992768	+	0.120051i	$0.961694\pi$
$642$	−7.57845	+	2.33767i	−0.299097	+	0.0922605i
$643$	−1.81071	+	10.2690i	−0.0714073	+	0.404971i	0.928063	+	0.372423i	$0.121473\pi$
$643$	−1.81071	+	10.2690i	−0.0714073	+	0.404971i	−0.999470	+	0.0325473i	$0.989638\pi$
$644$	0.0293462	+	0.0806281i	0.00115640	+	0.00317719i
$645$	0.586250	−	1.39076i	0.0230836	−	0.0547613i
$646$	18.7950	−	9.31352i	0.739481	−	0.366436i
$647$			22.5286i			0.885691i	0.896598	+	0.442846i	$0.146031\pi$
$647$			22.5286i			0.885691i	−0.896598	+	0.442846i	$0.853969\pi$
$648$	−2.86650	−	8.53131i	−0.112607	−	0.335141i
$649$	23.3826	+	4.12298i	0.917846	+	0.161841i
$650$	−0.0797832	−	0.0950820i	−0.00312936	−	0.00372942i
$651$	32.6419	−	16.7347i	1.27934	−	0.655884i
$652$	1.82014	+	10.3225i	0.0712820	+	0.404261i
$653$	−24.9063	+	14.3797i	−0.974659	+	0.562720i	−0.900653	−	0.434538i	$-0.856912\pi$
$653$	−24.9063	+	14.3797i	−0.974659	+	0.562720i	−0.0740057	+	0.997258i	$0.523578\pi$
$654$	14.4241	+	19.0423i	0.564027	+	0.744614i
$655$	13.6593	+	4.97159i	0.533715	+	0.194256i
$656$	6.28744	+	2.28844i	0.245483	+	0.0893487i
$657$	15.9725	−	4.06723i	0.623148	−	0.158678i
$658$	1.16765	−	0.674144i	0.0455198	−	0.0262809i
$659$	7.79061	+	44.1828i	0.303479	+	1.72112i	0.630578	+	0.776126i	$0.282818\pi$
$659$	7.79061	+	44.1828i	0.303479	+	1.72112i	−0.327099	+	0.944990i	$0.606071\pi$
$660$	−2.26432	−	4.41669i	−0.0881386	−	0.171919i
$661$	20.4442	+	24.3644i	0.795186	+	0.947666i	0.999512	−	0.0312373i	$-0.00994476\pi$
$661$	20.4442	+	24.3644i	0.795186	+	0.947666i	−0.204326	+	0.978903i	$0.565500\pi$
$662$	28.0809	+	4.95141i	1.09139	+	0.192442i
$663$	−1.03327	−	0.0515644i	−0.0401287	−	0.00200260i
$664$			0.780968i			0.0303074i
$665$	4.45631	−	10.1806i	0.172808	−	0.394788i
$666$	−9.34098	+	9.11106i	−0.361956	+	0.353047i
$667$	−0.0361967	−	0.0994495i	−0.00140154	−	0.00385070i
$668$	3.46115	−	19.6291i	0.133916	−	0.759474i
$669$	−12.3605	−	40.0713i	−0.477886	−	1.54925i
$670$	−10.9275	−	9.16924i	−0.422165	−	0.354239i
$671$	35.3082	−	6.22579i	1.36306	−	0.240344i
$672$	0.549112	+	4.38168i	0.0211824	+	0.169027i
$673$	10.0872	+	5.82387i	0.388834	+	0.224494i	0.681655	−	0.731674i	$-0.261261\pi$
$673$	10.0872	+	5.82387i	0.388834	+	0.224494i	−0.292821	+	0.956167i	$0.594594\pi$
$674$	10.9014	−	29.9512i	0.419905	−	1.15368i
$675$	−0.129599	−	5.19454i	−0.00498827	−	0.199938i
$676$	−6.49230	+	11.2450i	−0.249704	+	0.432500i
$677$	−11.5366	−	19.9820i	−0.443388	−	0.767971i	0.554550	−	0.832150i	$-0.312890\pi$
$677$	−11.5366	−	19.9820i	−0.443388	−	0.767971i	−0.997938	+	0.0641794i	$0.979557\pi$
$678$	−5.93259	+	25.9928i	−0.227840	+	0.998248i
$679$	4.62245	−	5.50883i	0.177394	−	0.211409i
$680$	−3.68639	+	3.09325i	−0.141367	+	0.118621i
$681$	−18.0632	+	27.9676i	−0.692184	+	1.07172i
$682$	−22.3676	+	8.14114i	−0.856500	+	0.311740i
$683$	13.3250			0.509865			0.254933	−	0.966959i	$-0.417947\pi$
$683$	13.3250			0.509865			0.254933	+	0.966959i	$0.417947\pi$
$684$	−8.29207	+	10.1115i	−0.317055	+	0.386621i
$685$	20.1461			0.769742
$686$	17.9679	−	6.53980i	0.686019	−	0.249691i
$687$	−2.49601	+	3.86461i	−0.0952287	+	0.147444i
$688$	0.667517	−	0.560113i	0.0254488	−	0.0213541i
$689$	−0.262813	+	0.313208i	−0.0100124	+	0.0119323i
$690$	0.0129706	−	0.0568290i	0.000493784	−	0.00216344i
$691$	−18.1605	−	31.4550i	−0.690860	−	1.19660i	−0.971557	−	0.236807i	$-0.923899\pi$
$691$	−18.1605	−	31.4550i	−0.690860	−	1.19660i	0.280697	−	0.959796i	$-0.409434\pi$
$692$	10.6131	−	18.3824i	0.403450	−	0.698795i
$693$	−19.9780	+	9.01460i	−0.758902	+	0.342436i
$694$	6.30540	−	17.3239i	0.239350	−	0.657608i
$695$	8.78377	+	5.07131i	0.333187	+	0.192366i
$696$	−0.677294	−	5.40452i	−0.0256727	−	0.204858i
$697$	31.7093	−	5.59121i	1.20108	−	0.211782i
$698$	−12.1021	−	10.1548i	−0.458070	−	0.384366i
$699$	−6.44523	−	20.8947i	−0.243781	−	0.790309i
$700$	−0.442725	+	2.51082i	−0.0167334	+	0.0949000i
$701$	0.524743	+	1.44172i	0.0198193	+	0.0544530i	0.949208	−	0.314650i	$-0.101887\pi$
$701$	0.524743	+	1.44172i	0.0198193	+	0.0544530i	−0.929388	+	0.369103i	$0.879665\pi$
$702$	0.600365	−	0.235633i	0.0226593	−	0.00889340i
$703$	18.4244	+	4.47101i	0.694890	+	0.168627i
$704$		−	2.86556i		−	0.108000i
$705$	−0.914827	−	0.0456539i	−0.0344544	−	0.00171942i
$706$	3.16502	+	0.558078i	0.119117	+	0.0210035i
$707$	23.2126	+	27.6637i	0.873000	+	1.04040i
$708$	6.54727	+	12.7708i	0.246062	+	0.479957i
$709$	0.958102	+	5.43367i	0.0359823	+	0.204066i	0.997499	−	0.0706808i	$-0.0225172\pi$
$709$	0.958102	+	5.43367i	0.0359823	+	0.204066i	−0.961517	+	0.274746i	$0.911406\pi$
$710$	−7.73592	+	4.46634i	−0.290324	+	0.167619i
$711$	−2.40203	−	9.43310i	−0.0900833	−	0.353769i
$712$	5.69996	+	2.07462i	0.213615	+	0.0777495i
$713$	−0.262692	−	0.0956121i	−0.00983789	−	0.00358070i
$714$	12.8313	+	16.9395i	0.480199	+	0.633945i
$715$	0.308024	−	0.177838i	0.0115194	−	0.00665075i
$716$	2.47046	+	14.0107i	0.0923255	+	0.523604i
$717$	−9.79956	+	5.02398i	−0.365971	+	0.187624i
$718$	−2.88584	−	3.43921i	−0.107699	−	0.128350i
$719$	49.2510	+	8.68427i	1.83675	+	0.323869i	0.981073	−	0.193639i	$-0.0620291\pi$
$719$	49.2510	+	8.68427i	1.83675	+	0.323869i	0.855678	+	0.517508i	$0.173140\pi$
$720$	1.30163	−	2.70292i	0.0485090	−	0.100732i
$721$		−	1.58127i		−	0.0588894i
$722$	18.8468	+	2.40775i	0.701406	+	0.0896073i
$723$	0.400402	−	0.949875i	0.0148911	−	0.0353262i
$724$	6.33245	+	17.3983i	0.235344	+	0.646602i
$725$	0.546073	−	3.09693i	0.0202806	−	0.115017i
$726$	−4.61537	+	1.42367i	−0.171293	+	0.0528374i
$727$	−3.30979	−	2.77725i	−0.122753	−	0.103002i	0.579344	−	0.815083i	$-0.303309\pi$
$727$	−3.30979	−	2.77725i	−0.122753	−	0.103002i	−0.702098	+	0.712081i	$0.747753\pi$
$728$	−0.311645	+	0.0549513i	−0.0115503	+	0.00203663i
$729$	25.8006	+	7.95784i	0.955579	+	0.294735i
$730$	4.75801	+	2.74704i	0.176102	+	0.101673i
$731$	1.43419	−	3.94041i	0.0530455	−	0.145741i
$732$	15.8859	+	14.7398i	0.587159	+	0.544800i
$733$	23.4749	−	40.6597i	0.867064	−	1.50180i	0.00208117	−	0.999998i	$-0.499338\pi$
$733$	23.4749	−	40.6597i	0.867064	−	1.50180i	0.864983	−	0.501801i	$-0.167329\pi$
$734$	3.91250	+	6.77664i	0.144413	+	0.250131i
$735$	−0.843948	−	0.192622i	−0.0311295	−	0.00710499i
$736$	0.0216324	−	0.0257805i	0.000797380	−	0.000950280i
$737$	31.3133	−	26.2750i	1.15344	−	0.967852i
$738$	−16.5849	+	11.3076i	−0.610499	+	0.416237i
$739$	15.6505	−	5.69631i	0.575712	−	0.209542i	−0.0377215	−	0.999288i	$-0.512010\pi$
$739$	15.6505	−	5.69631i	0.575712	−	0.209542i	0.613434	+	0.789746i	$0.289788\pi$
$740$	−4.34953			−0.159892
$741$	−0.753315	−	0.557365i	−0.0276737	−	0.0204753i
$742$	8.39844			0.308316
$743$	31.4254	−	11.4379i	1.15289	−	0.419617i	0.306336	−	0.951923i	$-0.400897\pi$
$743$	31.4254	−	11.4379i	1.15289	−	0.419617i	0.846552	+	0.532307i	$0.178675\pi$
$744$	−12.0859	−	7.80583i	−0.443090	−	0.286176i
$745$	−10.6888	+	8.96894i	−0.391606	+	0.328597i
$746$	−4.98630	+	5.94244i	−0.182562	+	0.217568i
$747$	−1.90230	−	1.36764i	−0.0696016	−	0.0500394i
$748$	−6.89487	−	11.9423i	−0.252102	−	0.436653i
$749$	−5.83701	+	10.1100i	−0.213280	+	0.369411i
$750$	1.17809	−	1.26969i	0.0430177	−	0.0463624i
$751$	−9.04353	+	24.8469i	−0.330003	+	0.906676i	0.658107	+	0.752925i	$0.271358\pi$
$751$	−9.04353	+	24.8469i	−0.330003	+	0.906676i	−0.988110	+	0.153751i	$0.950865\pi$
$752$	−0.457983	−	0.264416i	−0.0167009	−	0.00964228i
$753$	15.2341	−	1.90913i	0.555161	−	0.0695727i
$754$	0.384393	−	0.0677789i	0.0139988	−	0.00246836i
$755$	11.7931	+	9.89557i	0.429194	+	0.360137i
$756$	−11.6346	−	6.33572i	−0.423147	−	0.230428i
$757$	5.13089	−	29.0987i	0.186485	−	1.05761i	−0.737547	−	0.675296i	$-0.764016\pi$
$757$	5.13089	−	29.0987i	0.186485	−	1.05761i	0.924032	−	0.382315i	$-0.124873\pi$
$758$	−3.34072	−	9.17854i	−0.121340	−	0.333380i
$759$	0.153919	+	0.0648815i	0.00558689	+	0.00235505i
$760$	−4.33207	+	0.482846i	−0.157141	+	0.0175146i
$761$		−	39.4635i		−	1.43055i	−0.698842	−	0.715276i	$-0.746301\pi$
$761$		−	39.4635i		−	1.43055i	0.698842	−	0.715276i	$-0.253699\pi$
$762$	1.85613	−	37.1937i	0.0672405	−	1.34739i
$763$	34.6294	+	6.10610i	1.25367	+	0.221056i
$764$	0.841954	+	1.00340i	0.0304608	+	0.0363018i
$765$	−1.07896	−	14.3963i	−0.0390098	−	0.520501i
$766$	3.07426	+	17.4350i	0.111077	+	0.629952i
$767$	−0.890648	+	0.514216i	−0.0321595	+	0.0185673i
$768$	1.38067	−	1.04582i	0.0498206	−	0.0377380i
$769$	−36.5496	−	13.3030i	−1.31801	−	0.479717i	−0.415191	−	0.909734i	$-0.636285\pi$
$769$	−36.5496	−	13.3030i	−1.31801	−	0.479717i	−0.902821	+	0.430017i	$0.858508\pi$
$770$	−6.86529	−	2.49876i	−0.247408	−	0.0900491i
$771$	−32.0700	+	24.2923i	−1.15497	+	0.874865i
$772$	4.61907	−	2.66682i	0.166244	−	0.0959809i
$773$	5.78489	+	32.8077i	0.208068	+	1.18001i	0.892539	+	0.450971i	$0.148922\pi$
$773$	5.78489	+	32.8077i	0.208068	+	1.18001i	−0.684471	+	0.729040i	$0.739967\pi$
$774$	0.195374	+	2.60683i	0.00702256	+	0.0937006i
$775$	−5.33939	−	6.36324i	−0.191797	−	0.228574i
$776$	−2.77775	−	0.489792i	−0.0997153	−	0.0175825i
$777$	−0.957337	+	19.1834i	−0.0343443	+	0.688202i
$778$		−	22.1838i		−	0.795327i
$779$	26.7177	+	11.6950i	0.957262	+	0.419017i
$780$	0.198102	+	0.0835063i	0.00709320	+	0.00299001i
$781$	−8.75472	−	24.0534i	−0.313269	−	0.860698i
$782$	0.0281225	−	0.159491i	0.00100566	−	0.00570337i
$783$	14.3506	+	7.81470i	0.512847	+	0.279275i
$784$	−0.382857	−	0.321255i	−0.0136734	−	0.0114734i
$785$	8.58250	−	1.51333i	0.306322	−	0.0540129i
$786$	−24.9816	+	3.13069i	−0.891065	+	0.111668i
$787$	−35.4504	−	20.4673i	−1.26367	−	0.729581i	−0.289888	−	0.957060i	$-0.593618\pi$
$787$	−35.4504	−	20.4673i	−1.26367	−	0.729581i	−0.973783	+	0.227480i	$0.926951\pi$
$788$	−1.76269	+	4.84294i	−0.0627931	+	0.172523i
$789$	−9.54935	+	10.2918i	−0.339966	+	0.366399i
$790$	1.62235	−	2.81000i	0.0577208	−	0.0999753i
$791$	19.6225	+	33.9871i	0.697695	+	1.20844i
$792$	6.98000	+	5.01820i	0.248024	+	0.178314i
$793$	−0.998221	+	1.18963i	−0.0354479	+	0.0422451i
$794$	10.1927	−	8.55268i	0.361725	−	0.303523i
$795$	−4.79280	−	3.09549i	−0.169983	−	0.109786i
$796$	0.165479	−	0.0602294i	0.00586524	−	0.00213477i
$797$	19.6931			0.697567			0.348783	−	0.937203i	$-0.386595\pi$
$797$	19.6931			0.697567			0.348783	+	0.937203i	$0.386595\pi$
$798$	1.17608	+	19.2127i	0.0416327	+	0.680123i
$799$	−2.54487			−0.0900310
$800$	0.939693	−	0.342020i	0.0332232	−	0.0120922i
$801$	−15.0353	+	10.2510i	−0.531245	+	0.362202i
$802$	−24.6998	+	20.7256i	−0.872179	+	0.731845i
$803$	−10.1198	+	12.0603i	−0.357120	+	0.425599i
$804$	24.0879	+	5.49782i	0.849516	+	0.193893i
$805$	−0.0429013	−	0.0743073i	−0.00151207	−	0.00261899i
$806$	0.515512	−	0.892892i	0.0181581	−	0.0314508i
$807$	2.37067	+	2.19964i	0.0834514	+	0.0774311i
$808$	4.84445	−	13.3100i	0.170427	−	0.468244i
$809$	−12.4432	−	7.18408i	−0.437479	−	0.252579i	0.265048	−	0.964235i	$-0.414612\pi$
$809$	−12.4432	−	7.18408i	−0.437479	−	0.252579i	−0.702528	+	0.711656i	$0.747945\pi$
$810$	4.30440	+	7.90393i	0.151241	+	0.277716i
$811$	−7.37989	+	1.30127i	−0.259143	+	0.0456939i	−0.301710	−	0.953400i	$-0.597557\pi$
$811$	−7.37989	+	1.30127i	−0.259143	+	0.0456939i	0.0425671	+	0.999094i	$0.486446\pi$
$812$	−6.14183	−	5.15361i	−0.215536	−	0.180856i
$813$	−39.9539	+	12.3243i	−1.40125	+	0.432232i
$814$	2.16432	−	12.2745i	0.0758594	−	0.430220i
$815$	−3.58497	−	9.84962i	−0.125576	−	0.345017i
$816$	3.23759	−	7.68055i	0.113338	−	0.268873i
$817$	3.05878	−	2.25182i	0.107013	−	0.0787811i
$818$			1.48388i			0.0518825i
$819$	0.411904	−	0.855344i	0.0143931	−	0.0298881i
$820$	−6.58931	−	1.16187i	−0.230109	−	0.0405744i
$821$	9.40997	+	11.2144i	0.328410	+	0.391384i	0.904832	−	0.425768i	$-0.139996\pi$
$821$	9.40997	+	11.2144i	0.328410	+	0.391384i	−0.576422	+	0.817152i	$0.695552\pi$
$822$	−31.0511	+	15.9191i	−1.08303	+	0.555244i
$823$	−2.17257	−	12.3213i	−0.0757310	−	0.429492i	−0.998974	−	0.0452764i	$-0.985583\pi$
$823$	−2.17257	−	12.3213i	−0.0757310	−	0.429492i	0.923244	−	0.384215i	$-0.125528\pi$
$824$	−0.537120	+	0.310107i	−0.0187115	+	0.0108031i
$825$	2.99687	+	3.95639i	0.104338	+	0.137744i
$826$	19.8509	+	7.22515i	0.690703	+	0.251395i
$827$	20.0108	+	7.28333i	0.695844	+	0.253266i	0.665635	−	0.746277i	$-0.268161\pi$
$827$	20.0108	+	7.28333i	0.695844	+	0.253266i	0.0302084	+	0.999544i	$0.490383\pi$
$828$	0.0249138	+	0.0978398i	0.000865815	+	0.00340017i
$829$	−20.8494	+	12.0374i	−0.724130	+	0.418076i	−0.816271	−	0.577669i	$-0.803962\pi$
$829$	−20.8494	+	12.0374i	−0.724130	+	0.418076i	0.0921411	+	0.995746i	$0.470629\pi$
$830$	−0.135614	−	0.769103i	−0.00470722	−	0.0266960i
$831$	8.88005	+	17.3210i	0.308045	+	0.600860i
$832$	0.0797832	+	0.0950820i	0.00276599	+	0.00329637i
$833$	−2.36854	−	0.417637i	−0.0820650	−	0.0144703i
$834$	−17.5457	−	0.875607i	−0.607558	−	0.0303198i
$835$			19.9320i			0.689774i
$836$	0.793034	−	12.4655i	0.0274276	−	0.431128i
$837$	40.1786	−	15.7694i	1.38878	−	0.545072i
$838$	−13.4299	−	36.8983i	−0.463927	−	1.27463i
$839$	2.70216	−	15.3247i	0.0932890	−	0.529068i	−0.901969	−	0.431800i	$-0.857878\pi$
$839$	2.70216	−	15.3247i	0.0932890	−	0.529068i	0.995258	−	0.0972680i	$-0.0310104\pi$
$840$	−1.30164	−	4.21976i	−0.0449109	−	0.145596i
$841$	−14.6397	−	12.2842i	−0.504818	−	0.423593i
$842$	−10.2012	+	1.79874i	−0.351555	+	0.0619886i
$843$	−3.95413	−	31.5523i	−0.136187	−	1.08672i
$844$	5.89880	+	3.40568i	0.203045	+	0.117228i
$845$	4.44099	−	12.2015i	0.152775	−	0.419745i
$846$	1.44610	−	0.652517i	0.0497179	−	0.0224340i
$847$	−3.55481	+	6.15711i	−0.122145	+	0.211561i
$848$	−1.64704	−	2.85276i	−0.0565596	−	0.0979642i
$849$	−6.99048	+	30.6278i	−0.239913	+	1.05114i
$850$	3.09325	−	3.68639i	0.106097	−	0.126442i
$851$	0.112133	−	0.0940906i	0.00384386	−	0.00322538i
$852$	8.39415	−	12.9968i	0.287579	−	0.445262i
$853$	32.0889	−	11.6794i	1.09870	−	0.399895i	0.271864	−	0.962336i	$-0.412360\pi$
$853$	32.0889	−	11.6794i	1.09870	−	0.399895i	0.826837	+	0.562441i	$0.190138\pi$
$854$	31.8991			1.09157
$855$	6.41026	−	11.3977i	0.219226	−	0.389795i
$856$	4.57885			0.156502
$857$	−14.2401	+	5.18299i	−0.486434	+	0.177048i	−0.573582	−	0.819148i	$-0.694447\pi$
$857$	−14.2401	+	5.18299i	−0.486434	+	0.177048i	0.0871484	+	0.996195i	$0.472225\pi$
$858$	−0.334232	+	0.517497i	−0.0114105	+	0.0176671i
$859$	14.5952	−	12.2469i	0.497983	−	0.417858i	−0.358894	−	0.933378i	$-0.616846\pi$
$859$	14.5952	−	12.2469i	0.497983	−	0.417858i	0.856877	+	0.515521i	$0.172402\pi$
$860$	−0.560113	+	0.667517i	−0.0190997	+	0.0227621i
$861$	−6.57472	+	28.8062i	−0.224066	+	0.981712i
$862$	−12.2645	−	21.2427i	−0.417729	−	0.723528i
$863$	−0.904537	+	1.56670i	−0.0307908	+	0.0533313i	−0.881010	−	0.473097i	$-0.843136\pi$
$863$	−0.904537	+	1.56670i	−0.0307908	+	0.0533313i	0.850219	+	0.526429i	$0.176469\pi$
$864$	0.129599	+	5.19454i	0.00440905	+	0.176722i
$865$	−7.25979	+	19.9461i	−0.246840	+	0.678188i
$866$	−18.2294	−	10.5248i	−0.619461	−	0.357646i
$867$	−1.32620	−	10.5826i	−0.0450403	−	0.359402i
$868$	−20.8564	+	3.67755i	−0.707913	+	0.124824i
$869$	7.12260	+	5.97657i	0.241618	+	0.202741i
$870$	1.60549	+	5.20480i	0.0544312	+	0.176459i
$871$	−0.307454	+	1.74366i	−0.0104177	+	0.0590816i
$872$	−4.71717	−	12.9603i	−0.159744	−	0.438892i
$873$	6.05748	−	5.90838i	0.205015	−	0.199968i
$874$	0.101238	−	0.106161i	0.00342442	−	0.00359095i
$875$		−	2.54955i		−	0.0861906i
$876$	−9.50420	−	0.474301i	−0.321117	−	0.0160252i
$877$	16.4599	+	2.90233i	0.555813	+	0.0980048i	0.444497	−	0.895780i	$-0.353382\pi$
$877$	16.4599	+	2.90233i	0.555813	+	0.0980048i	0.111316	+	0.993785i	$0.464493\pi$
$878$	−17.4907	−	20.8446i	−0.590283	−	0.703472i
$879$	22.6256	+	44.1324i	0.763141	+	1.48855i
$880$	0.497599	+	2.82202i	0.0167741	+	0.0951304i
$881$	0.141911	−	0.0819325i	0.00478111	−	0.00276038i	−0.497608	−	0.867402i	$-0.665788\pi$
$881$	0.141911	−	0.0819325i	0.00478111	−	0.00276038i	0.502389	+	0.864642i	$0.332455\pi$
$882$	1.45298	−	0.369986i	0.0489245	−	0.0124581i
$883$	−25.3637	−	9.23162i	−0.853556	−	0.310669i	−0.122066	−	0.992522i	$-0.538952\pi$
$883$	−25.3637	−	9.23162i	−0.853556	−	0.310669i	−0.731489	+	0.681853i	$0.761174\pi$
$884$	0.561277	+	0.204288i	0.0188778	+	0.00687095i
$885$	−8.66544	−	11.4399i	−0.291285	−	0.384547i
$886$	12.4800	−	7.20531i	0.419273	−	0.242067i
$887$	2.30939	+	13.0972i	0.0775417	+	0.439761i	0.998718	+	0.0506158i	$0.0161184\pi$
$887$	2.30939	+	13.0972i	0.0775417	+	0.439761i	−0.921177	+	0.389145i	$0.872770\pi$
$888$	6.70393	−	3.43693i	0.224969	−	0.115336i
$889$	−35.2355	−	41.9921i	−1.18176	−	1.40837i
$890$	−5.97362	−	1.05331i	−0.200236	−	0.0353070i
$891$	−24.4470	+	8.21412i	−0.819004	+	0.275184i
$892$			24.2108i			0.810639i
$893$	−1.91910	−	1.27698i	−0.0642201	−	0.0427327i
$894$	9.38748	−	22.2700i	0.313964	−	0.744819i
$895$	−4.86586	−	13.3688i	−0.162648	−	0.446871i
$896$	0.442725	−	2.51082i	0.0147904	−	0.0838806i
$897$	−0.00691361	+	0.00213259i	−0.000230839	+	7.12052e-5i
$898$	25.3289	+	21.2534i	0.845235	+	0.709236i
$899$	25.7250	−	4.53602i	0.857978	−	0.151285i
$900$	−0.812501	+	2.88788i	−0.0270834	+	0.0962626i
$901$	−13.7282	−	7.92596i	−0.457351	−	0.264052i
$902$	6.55767	−	18.0170i	0.218346	−	0.599902i
$903$	2.82078	+	2.61728i	0.0938696	+	0.0870976i
$904$	7.69644	−	13.3306i	0.255980	−	0.443370i
$905$	−9.25743	−	16.0343i	−0.307727	−	0.532999i
$906$	−25.9960	−	5.93332i	−0.863660	−	0.197121i
$907$	9.80440	−	11.6844i	0.325550	−	0.387975i	−0.578301	−	0.815824i	$-0.696284\pi$
$907$	9.80440	−	11.6844i	0.325550	−	0.387975i	0.903850	+	0.427849i	$0.140728\pi$
$908$	14.7250	−	12.3557i	0.488665	−	0.410039i
$909$	23.9372	+	35.1089i	0.793947	+	1.16449i
$910$	0.297368	−	0.108233i	0.00985765	−	0.00358789i
$911$	−39.0945			−1.29526			−0.647630	−	0.761955i	$-0.724240\pi$
$911$	−39.0945			−1.29526			−0.647630	+	0.761955i	$0.724240\pi$
$912$	6.29549	−	4.16735i	0.208464	−	0.137995i
$913$	2.23791			0.0740639
$914$	−28.3324	+	10.3121i	−0.937151	+	0.341095i
$915$	−18.2041	−	11.7574i	−0.601809	−	0.388686i
$916$	2.03472	−	1.70733i	0.0672291	−	0.0564119i
$917$	−23.8218	+	28.3898i	−0.786667	+	0.937513i
$918$	13.0388	+	21.3365i	0.430344	+	0.704210i
$919$	−20.5436	−	35.5826i	−0.677671	−	1.17376i	−0.975680	−	0.219198i	$-0.929656\pi$
$919$	−20.5436	−	35.5826i	−0.677671	−	1.17376i	0.298009	−	0.954563i	$-0.403677\pi$
$920$	−0.0168270	+	0.0291452i	−0.000554770	+	0.000960889i
$921$	19.4351	−	20.9462i	0.640407	−	0.690200i
$922$	2.63356	−	7.23564i	0.0867316	−	0.238293i
$923$	0.960188	+	0.554365i	0.0316050	+	0.0182471i
$924$	12.5560	−	1.57351i	0.413061	−	0.0517647i
$925$	4.28345	−	0.755287i	0.140839	−	0.0248337i
$926$	−6.54461	−	5.49158i	−0.215069	−	0.180465i
$927$	0.185247	−	1.85140i	0.00608430	−	0.0608078i
$928$	−0.546073	+	3.09693i	−0.0179257	+	0.101662i
$929$	−13.4409	−	36.9285i	−0.440980	−	1.21158i	−0.938848	−	0.344331i	$-0.888106\pi$
$929$	−13.4409	−	36.9285i	−0.440980	−	1.21158i	0.497868	−	0.867253i	$-0.334116\pi$
$930$	13.2577	+	5.58855i	0.434739	+	0.183256i
$931$	−1.57656	−	1.50345i	−0.0516697	−	0.0492735i
$932$			12.6244i			0.413527i
$933$	−0.334372	+	6.70026i	−0.0109469	+	0.219357i
$934$	33.3527	+	5.88098i	1.09133	+	0.192432i
$935$	8.86388	+	10.5636i	0.289880	+	0.345465i
$936$	−0.371321	+	0.0278293i	−0.0121370	+	0.000909629i
$937$	−5.14239	−	29.1639i	−0.167995	−	0.952745i	−0.945923	−	0.324392i	$-0.894840\pi$
$937$	−5.14239	−	29.1639i	−0.167995	−	0.952745i	0.777928	−	0.628353i	$-0.216271\pi$
$938$	31.4964	−	18.1844i	1.02839	−	0.593743i
$939$	−27.0479	+	20.4881i	−0.882673	+	0.668604i
$940$	0.496940	+	0.180872i	0.0162084	+	0.00589938i
$941$	−7.25449	−	2.64042i	−0.236490	−	0.0860752i	0.221057	−	0.975261i	$-0.429049\pi$
$941$	−7.25449	−	2.64042i	−0.236490	−	0.0860752i	−0.457546	+	0.889186i	$0.651272\pi$
$942$	−12.0324	+	9.11425i	−0.392037	+	0.296958i
$943$	0.195009	−	0.112589i	0.00635038	−	0.00366639i
$944$	−1.43880	−	8.15986i	−0.0468291	−	0.265581i
$945$	12.5581	+	4.21913i	0.408514	+	0.137248i
$946$	−1.60504	−	1.91281i	−0.0521842	−	0.0621907i
$947$	39.1696	+	6.90666i	1.27284	+	0.224436i	0.768938	−	0.639324i	$-0.220786\pi$
$947$	39.1696	+	6.90666i	1.27284	+	0.224436i	0.503903	+	0.863760i	$0.331897\pi$
$948$	−0.280114	+	5.61301i	−0.00909768	+	0.182302i
$949$		−	0.681929i		−	0.0221364i
$950$	4.18241	−	1.22777i	0.135695	−	0.0398340i
$951$	−15.5278	−	6.54546i	−0.503524	−	0.212251i
$952$	−4.19626	−	11.5291i	−0.136002	−	0.373661i
$953$	−9.63127	+	54.6216i	−0.311987	+	1.76937i	0.276650	+	0.960971i	$0.410776\pi$
$953$	−9.63127	+	54.6216i	−0.311987	+	1.76937i	−0.588637	+	0.808397i	$0.700335\pi$
$954$	9.83315	+	0.983885i	0.318360	+	0.0318544i
$955$	−1.00340	−	0.841954i	−0.0324693	−	0.0272450i
$956$	6.26139	−	1.10405i	0.202508	−	0.0357076i
$957$	−15.4870	+	1.94082i	−0.500622	+	0.0627379i
$958$	−14.9039	−	8.60479i	−0.481524	−	0.278008i
$959$	−17.5673	+	48.2659i	−0.567279	+	1.55859i
$960$	−1.17809	+	1.26969i	−0.0380227	+	0.0409790i
$961$	19.0000	−	32.9089i	0.612902	−	1.06158i
$962$	0.269933	+	0.467538i	0.00870299	+	0.0150740i
$963$	−8.01854	+	11.1533i	−0.258394	+	0.359409i
$964$	−0.382550	+	0.455906i	−0.0123211	+	0.0146837i
$965$	−4.08580	+	3.42840i	−0.131527	+	0.110364i
$966$	0.124840	+	0.0806298i	0.00401667	+	0.00259422i
$967$	46.3985	−	16.8877i	1.49208	−	0.543071i	0.538080	−	0.842893i	$-0.319150\pi$
$967$	46.3985	−	16.8877i	1.49208	−	0.543071i	0.953995	+	0.299822i	$0.0969274\pi$
$968$	2.78858			0.0896283
$969$	16.2094	−	32.5152i	0.520722	−	1.04454i
$970$	2.82060			0.0905640
$971$	11.7248	−	4.26749i	0.376267	−	0.136950i	−0.146962	−	0.989142i	$-0.546949\pi$
$971$	11.7248	−	4.26749i	0.376267	−	0.136950i	0.523229	+	0.852192i	$0.324727\pi$
$972$	−12.8799	−	8.78106i	−0.413124	−	0.281653i
$973$	−19.8093	+	16.6219i	−0.635056	+	0.532875i
$974$	23.6368	−	28.1693i	0.757373	−	0.902602i
$975$	−0.209593	−	0.0478376i	−0.00671236	−	0.00153203i
$976$	−6.25583	−	10.8354i	−0.200244	−	0.346833i
$977$	−13.3964	+	23.2033i	−0.428589	+	0.742339i	−0.996748	−	0.0805804i	$-0.974323\pi$
$977$	−13.3964	+	23.2033i	−0.428589	+	0.742339i	0.568159	+	0.822919i	$0.307656\pi$
$978$	13.3085	+	12.3484i	0.425560	+	0.394859i
$979$	5.94493	−	16.3336i	0.190001	−	0.522023i
$980$	0.432825	+	0.249892i	0.0138261	+	0.00798250i
$981$	39.8299	+	11.2061i	1.27167	+	0.357783i
$982$	19.1764	−	3.38131i	0.611942	−	0.107902i
$983$	15.6507	+	13.1325i	0.499180	+	0.418861i	0.857302	−	0.514813i	$-0.172139\pi$
$983$	15.6507	+	13.1325i	0.499180	+	0.418861i	−0.358123	+	0.933674i	$0.616583\pi$
$984$	11.0742	−	3.41598i	0.353033	−	0.108897i
$985$	0.894939	−	5.07545i	0.0285151	−	0.161717i
$986$	5.17582	+	14.2204i	0.164832	+	0.452871i
$987$	0.907105	−	2.15193i	0.0288735	−	0.0684966i
$988$	0.320752	+	0.435696i	0.0102045	+	0.0138613i
$989$		−	0.0293255i		−	0.000932495i
$990$	−7.74536	−	3.72990i	−0.246164	−	0.118544i
$991$	−14.4523	−	2.54833i	−0.459092	−	0.0809503i	−0.0606809	−	0.998157i	$-0.519327\pi$
$991$	−14.4523	−	2.54833i	−0.459092	−	0.0809503i	−0.398411	+	0.917207i	$0.630438\pi$
$992$	5.33939	+	6.36324i	0.169526	+	0.202033i
$993$	43.9487	−	22.5314i	1.39467	−	0.715012i
$994$	−3.95472	−	22.4283i	−0.125436	−	0.711383i
$995$	−0.152506	+	0.0880494i	−0.00483477	+	0.00279135i
$996$	0.816755	+	1.07826i	0.0258799	+	0.0341659i
$997$	24.7320	+	9.00171i	0.783270	+	0.285087i	0.702535	−	0.711649i	$-0.252051\pi$
$997$	24.7320	+	9.00171i	0.783270	+	0.285087i	0.0807343	+	0.996736i	$0.474273\pi$
$998$	−23.0680	−	8.39607i	−0.730205	−	0.265773i
$999$	−3.36824	+	22.3484i	−0.106566	+	0.707072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.a.71.5	✓	84
3.2	odd	2		570.2.bb.b.71.7	yes	84
19.15	odd	18		570.2.bb.b.281.7	yes	84
57.53	even	18	inner	570.2.bb.a.281.5	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.71.5	✓	84	1.1	even	1	trivial
570.2.bb.a.281.5	yes	84	57.53	even	18	inner
570.2.bb.b.71.7	yes	84	3.2	odd	2
570.2.bb.b.281.7	yes	84	19.15	odd	18

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.939713 + 1.45497i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.385412 - 1.68863i) q^{6} +(-1.27478 - 2.20798i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.23388 - 2.73451i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-0.939713 + 1.45497i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-0.642788 + 0.766044i) q^{5} +(0.385412 - 1.68863i) q^{6} +(-1.27478 - 2.20798i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.23388 - 2.73451i) q^{9} +(0.342020 - 0.939693i) q^{10} +(2.48165 + 1.43278i) q^{11} +(0.215376 + 1.71861i) q^{12} +(-0.122235 + 0.0215533i) q^{13} +(1.95307 + 1.63882i) q^{14} +(-0.510537 - 1.65510i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.64588 - 4.52202i) q^{17} +(2.09473 + 2.14759i) q^{18} +(1.02793 - 4.23596i) q^{19} +1.00000i q^{20} +(4.41047 + 0.220101i) q^{21} +(-2.82202 - 0.497599i) q^{22} +(-0.0216324 - 0.0257805i) q^{23} +(-0.790186 - 1.54130i) q^{24} +(-0.173648 - 0.984808i) q^{25} +(0.107492 - 0.0620603i) q^{26} +(5.13812 + 0.774392i) q^{27} +(-2.39580 - 0.871998i) q^{28} +(2.95506 + 1.07555i) q^{29} +(1.04582 + 1.38067i) q^{30} +(7.19374 - 4.15331i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.41669 + 2.26432i) q^{33} +(3.09325 + 3.68639i) q^{34} +(2.51082 + 0.442725i) q^{35} +(-2.70292 - 1.30163i) q^{36} +4.34953i q^{37} +(0.482846 + 4.33207i) q^{38} +(0.0835063 - 0.198102i) q^{39} +(-0.342020 - 0.939693i) q^{40} +(-1.16187 + 6.58931i) q^{41} +(-4.21976 + 1.30164i) q^{42} +(0.667517 + 0.560113i) q^{43} +(2.82202 - 0.497599i) q^{44} +(2.88788 + 0.812501i) q^{45} +(0.0291452 + 0.0168270i) q^{46} +(0.180872 - 0.496940i) q^{47} +(1.26969 + 1.17809i) q^{48} +(0.249892 - 0.432825i) q^{49} +(0.500000 + 0.866025i) q^{50} +(8.12607 + 1.85469i) q^{51} +(-0.0797832 + 0.0950820i) q^{52} +(2.52341 - 2.11740i) q^{53} +(-5.09311 + 1.02965i) q^{54} +(-2.69274 + 0.980079i) q^{55} +2.54955 q^{56} +(5.19724 + 5.47619i) q^{57} -3.14471 q^{58} +(7.78605 - 2.83389i) q^{59} +(-1.45497 - 0.939713i) q^{60} +(9.58449 - 8.04234i) q^{61} +(-5.33939 + 6.36324i) q^{62} +(-4.46481 + 6.21027i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.0620603 - 0.107492i) q^{65} +(3.37588 - 3.63836i) q^{66} +(4.87885 - 13.4045i) q^{67} +(-4.16752 - 2.40612i) q^{68} +(0.0578380 - 0.00724825i) q^{69} +(-2.51082 + 0.442725i) q^{70} +(-6.84283 - 5.74181i) q^{71} +(2.98509 + 0.298682i) q^{72} +(-0.954037 + 5.41061i) q^{73} +(-1.48763 - 4.08722i) q^{74} +(1.59605 + 0.672783i) q^{75} +(-1.93538 - 3.90567i) q^{76} -7.30589i q^{77} +(-0.0107153 + 0.214716i) q^{78} +(3.19541 + 0.563438i) q^{79} +(0.642788 + 0.766044i) q^{80} +(-5.95508 + 6.74812i) q^{81} +(-1.16187 - 6.58931i) q^{82} +(0.676338 - 0.390484i) q^{83} +(3.52009 - 2.66638i) q^{84} +(4.52202 + 1.64588i) q^{85} +(-0.818830 - 0.298030i) q^{86} +(-4.34180 + 3.28881i) q^{87} +(-2.48165 + 1.43278i) q^{88} +(-1.05331 - 5.97362i) q^{89} +(-2.99161 + 0.224211i) q^{90} +(0.203412 + 0.242416i) q^{91} +(-0.0331427 - 0.00584396i) q^{92} +(-0.717106 + 14.3696i) q^{93} +0.528833i q^{94} +(2.58419 + 3.51026i) q^{95} +(-1.59605 - 0.672783i) q^{96} +(0.964701 + 2.65050i) q^{97} +(-0.0867865 + 0.492191i) q^{98} +(0.855892 - 8.55396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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