LMFDB - Embedded newform 164.2.o.b.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(7,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("164.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.o (of order $40$, degree $16$, 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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	164.11
Dual form			164.2.o.b.15.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00855 + 0.991379i) q^{2} +(0.116266 - 0.280690i) q^{3} +(0.0343339 + 1.99971i) q^{4} +(0.922111 - 1.80974i) q^{5} +(0.395529 - 0.167826i) q^{6} +(0.274171 + 1.14200i) q^{7} +(-1.94784 + 2.05083i) q^{8} +(2.05605 + 2.05605i) q^{9} +O(q^{10})$	\(q+(1.00855 + 0.991379i) q^{2} +(0.116266 - 0.280690i) q^{3} +(0.0343339 + 1.99971i) q^{4} +(0.922111 - 1.80974i) q^{5} +(0.395529 - 0.167826i) q^{6} +(0.274171 + 1.14200i) q^{7} +(-1.94784 + 2.05083i) q^{8} +(2.05605 + 2.05605i) q^{9} +(2.72414 - 0.911051i) q^{10} +(0.0847682 - 0.0992508i) q^{11} +(0.565289 + 0.222860i) q^{12} +(-2.37552 - 3.87650i) q^{13} +(-0.855645 + 1.42357i) q^{14} +(-0.400767 - 0.469238i) q^{15} +(-3.99764 + 0.137316i) q^{16} +(0.0717643 + 0.911852i) q^{17} +(0.0352975 + 4.11195i) q^{18} +(-6.42437 - 3.93686i) q^{19} +(3.65062 + 1.78181i) q^{20} +(0.352426 + 0.0558188i) q^{21} +(0.183888 - 0.0160617i) q^{22} +(-1.18641 - 0.861977i) q^{23} +(0.349182 + 0.785180i) q^{24} +(0.514040 + 0.707515i) q^{25} +(1.44726 - 6.26468i) q^{26} +(1.65823 - 0.686862i) q^{27} +(-2.27426 + 0.587471i) q^{28} +(0.0293854 - 0.373377i) q^{29} +(0.0610004 - 0.870561i) q^{30} +(2.86096 - 8.80513i) q^{31} +(-4.16794 - 3.82469i) q^{32} +(-0.0180031 - 0.0353330i) q^{33} +(-0.831614 + 0.990791i) q^{34} +(2.31955 + 0.556875i) q^{35} +(-4.04090 + 4.18209i) q^{36} +(1.33919 + 4.12161i) q^{37} +(-2.57636 - 10.3395i) q^{38} +(-1.36429 + 0.216082i) q^{39} +(1.91536 + 5.41619i) q^{40} +(-6.31398 + 1.06474i) q^{41} +(0.300100 + 0.405683i) q^{42} +(0.623604 + 3.93728i) q^{43} +(0.201383 + 0.166104i) q^{44} +(5.61683 - 1.82502i) q^{45} +(-0.342003 - 2.04553i) q^{46} +(-1.80179 + 7.50499i) q^{47} +(-0.426245 + 1.13806i) q^{48} +(5.00804 - 2.55172i) q^{49} +(-0.182983 + 1.22317i) q^{50} +(0.264291 + 0.0858735i) q^{51} +(7.67030 - 4.88344i) q^{52} +(-3.50822 - 0.276103i) q^{53} +(2.35334 + 0.951203i) q^{54} +(-0.101453 - 0.244929i) q^{55} +(-2.87610 - 1.66216i) q^{56} +(-1.85197 + 1.34553i) q^{57} +(0.399795 - 0.347436i) q^{58} +(-2.06311 + 2.83963i) q^{59} +(0.924578 - 0.817527i) q^{60} +(0.586573 - 3.70347i) q^{61} +(11.6146 - 6.04409i) q^{62} +(-1.78431 + 2.91173i) q^{63} +(-0.411845 - 7.98939i) q^{64} +(-9.20598 + 0.724526i) q^{65} +(0.0168715 - 0.0534829i) q^{66} +(5.36295 - 4.58039i) q^{67} +(-1.82097 + 0.174815i) q^{68} +(-0.379887 + 0.232795i) q^{69} +(1.78730 + 2.86119i) q^{70} +(6.33090 + 5.40710i) q^{71} +(-8.22148 + 0.211764i) q^{72} +(-6.90701 + 6.90701i) q^{73} +(-2.73544 + 5.48449i) q^{74} +(0.258358 - 0.0620262i) q^{75} +(7.65198 - 12.9820i) q^{76} +(0.136586 + 0.0695940i) q^{77} +(-1.59017 - 1.13460i) q^{78} +(12.4208 + 5.14485i) q^{79} +(-3.43776 + 7.36133i) q^{80} +8.17778i q^{81} +(-7.42350 - 5.18571i) q^{82} +15.8828i q^{83} +(-0.0995209 + 0.706664i) q^{84} +(1.71639 + 0.710954i) q^{85} +(-3.27440 + 4.58916i) q^{86} +(-0.101387 - 0.0516591i) q^{87} +(0.0384322 + 0.367170i) q^{88} +(-5.88802 + 1.41359i) q^{89} +(7.47413 + 3.72779i) q^{90} +(3.77568 - 3.77568i) q^{91} +(1.68296 - 2.40206i) q^{92} +(-2.13888 - 1.82678i) q^{93} +(-9.25748 + 5.78288i) q^{94} +(-13.0487 + 7.99625i) q^{95} +(-1.55814 + 0.725219i) q^{96} +(1.29043 - 1.10213i) q^{97} +(7.58057 + 2.39133i) q^{98} +(0.378352 - 0.0297770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{3}{40}\right)$

Coefficient data

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

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

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

$2$	1.00855	+	0.991379i	0.713150	+	0.701011i
$2$	1.00855	+	0.991379i	0.713150	+	0.701011i
$3$	0.116266	−	0.280690i	0.0671260	−	0.162056i	−0.886756	−	0.462237i	$-0.847047\pi$
$3$	0.116266	−	0.280690i	0.0671260	−	0.162056i	0.953882	+	0.300181i	$0.0970469\pi$
$4$	0.0343339	+	1.99971i	0.0171670	+	0.999853i
$5$	0.922111	−	1.80974i	0.412380	−	0.809342i	−0.587619	−	0.809137i	$-0.699935\pi$
$5$	0.922111	−	1.80974i	0.412380	−	0.809342i	1.00000		0.000204875i	$-6.52137e-5\pi$
$6$	0.395529	−	0.167826i	0.161474	−	0.0685145i
$7$	0.274171	+	1.14200i	0.103627	+	0.431637i	0.999930	−	0.0118042i	$-0.00375747\pi$
$7$	0.274171	+	1.14200i	0.103627	+	0.431637i	−0.896303	+	0.443441i	$0.853757\pi$
$8$	−1.94784	+	2.05083i	−0.688665	+	0.725080i
$9$	2.05605	+	2.05605i	0.685350	+	0.685350i
$10$	2.72414	−	0.911051i	0.861447	−	0.288099i
$11$	0.0847682	−	0.0992508i	0.0255586	−	0.0299252i	−0.747479	−	0.664285i	$-0.768736\pi$
$11$	0.0847682	−	0.0992508i	0.0255586	−	0.0299252i	0.773038	+	0.634360i	$0.218736\pi$
$12$	0.565289	+	0.222860i	0.163185	+	0.0643340i
$13$	−2.37552	−	3.87650i	−0.658852	−	1.07515i	−0.991249	−	0.132009i	$-0.957857\pi$
$13$	−2.37552	−	3.87650i	−0.658852	−	1.07515i	0.332397	−	0.943140i	$-0.392143\pi$
$14$	−0.855645	+	1.42357i	−0.228681	+	0.380466i
$15$	−0.400767	−	0.469238i	−0.103478	−	0.121157i
$16$	−3.99764	+	0.137316i	−0.999411	+	0.0343289i
$17$	0.0717643	+	0.911852i	0.0174054	+	0.221157i	0.999468	+	0.0326034i	$0.0103798\pi$
$17$	0.0717643	+	0.911852i	0.0174054	+	0.221157i	−0.982063	+	0.188553i	$0.939620\pi$
$18$	0.0352975	+	4.11195i	0.00831969	+	0.969196i
$19$	−6.42437	−	3.93686i	−1.47385	−	0.903177i	−0.999742	−	0.0227115i	$-0.992770\pi$
$19$	−6.42437	−	3.93686i	−1.47385	−	0.903177i	−0.474110	−	0.880466i	$-0.657230\pi$
$20$	3.65062	+	1.78181i	0.816302	+	0.398426i
$21$	0.352426	+	0.0558188i	0.0769056	+	0.0121807i
$22$	0.183888	−	0.0160617i	0.0392050	−	0.00342436i
$23$	−1.18641	−	0.861977i	−0.247383	−	0.179735i	0.457183	−	0.889373i	$-0.348858\pi$
$23$	−1.18641	−	0.861977i	−0.247383	−	0.179735i	−0.704566	+	0.709638i	$0.748858\pi$
$24$	0.349182	+	0.785180i	0.0712765	+	0.160274i
$25$	0.514040	+	0.707515i	0.102808	+	0.141503i
$26$	1.44726	−	6.26468i	0.283831	−	1.22861i
$27$	1.65823	−	0.686862i	0.319127	−	0.132187i
$28$	−2.27426	+	0.587471i	−0.429795	+	0.111022i
$29$	0.0293854	−	0.373377i	0.00545674	−	0.0693344i	−0.993586	−	0.113079i	$-0.963929\pi$
$29$	0.0293854	−	0.373377i	0.00545674	−	0.0693344i	0.999043	+	0.0437444i	$0.0139287\pi$
$30$	0.0610004	−	0.870561i	0.0111371	−	0.158942i
$31$	2.86096	−	8.80513i	0.513844	−	1.58145i	−0.271532	−	0.962429i	$-0.587530\pi$
$31$	2.86096	−	8.80513i	0.513844	−	1.58145i	0.785376	−	0.619019i	$-0.212470\pi$
$32$	−4.16794	−	3.82469i	−0.736795	−	0.676116i
$33$	−0.0180031	−	0.0353330i	−0.00313393	−	0.00615069i
$34$	−0.831614	+	0.990791i	−0.142621	+	0.169919i
$35$	2.31955	+	0.556875i	0.392076	+	0.0941291i
$36$	−4.04090	+	4.18209i	−0.673484	+	0.697015i
$37$	1.33919	+	4.12161i	0.220162	+	0.677589i	0.998747	+	0.0500497i	$0.0159380\pi$
$37$	1.33919	+	4.12161i	0.220162	+	0.677589i	−0.778585	+	0.627540i	$0.784062\pi$
$38$	−2.57636	−	10.3395i	−0.417940	−	1.67729i
$39$	−1.36429	+	0.216082i	−0.218461	+	0.0346008i
$40$	1.91536	+	5.41619i	0.302845	+	0.856374i
$41$	−6.31398	+	1.06474i	−0.986078	+	0.166284i
$41$	−6.31398	+	1.06474i	−0.986078	+	0.166284i
$42$	0.300100	+	0.405683i	0.0463065	+	0.0625983i
$43$	0.623604	+	3.93728i	0.0950987	+	0.600430i	0.988506	+	0.151182i	$0.0483079\pi$
$43$	0.623604	+	3.93728i	0.0950987	+	0.600430i	−0.893407	+	0.449248i	$0.851692\pi$
$44$	0.201383	+	0.166104i	0.0303596	+	0.0250411i
$45$	5.61683	−	1.82502i	0.837308	−	0.272058i
$46$	−0.342003	−	2.04553i	−0.0504256	−	0.301596i
$47$	−1.80179	+	7.50499i	−0.262818	+	1.09472i	0.672272	+	0.740304i	$0.265319\pi$
$47$	−1.80179	+	7.50499i	−0.262818	+	1.09472i	−0.935090	+	0.354411i	$0.884681\pi$
$48$	−0.426245	+	1.13806i	−0.0615232	+	0.164265i
$49$	5.00804	−	2.55172i	0.715434	−	0.364532i
$50$	−0.182983	+	1.22317i	−0.0258777	+	0.172983i
$51$	0.264291	+	0.0858735i	0.0370082	+	0.0120247i
$52$	7.67030	−	4.88344i	1.06368	−	0.677212i
$53$	−3.50822	−	0.276103i	−0.481891	−	0.0379256i	−0.164812	−	0.986325i	$-0.552702\pi$
$53$	−3.50822	−	0.276103i	−0.481891	−	0.0379256i	−0.317078	+	0.948399i	$0.602702\pi$
$54$	2.35334	+	0.951203i	0.320250	+	0.129442i
$55$	−0.101453	−	0.244929i	−0.0136799	−	0.0330262i
$56$	−2.87610	−	1.66216i	−0.384335	−	0.222116i
$57$	−1.85197	+	1.34553i	−0.245299	+	0.178220i
$58$	0.399795	−	0.347436i	0.0524957	−	0.0456206i
$59$	−2.06311	+	2.83963i	−0.268594	+	0.369688i	−0.921915	−	0.387393i	$-0.873376\pi$
$59$	−2.06311	+	2.83963i	−0.268594	+	0.369688i	0.653320	+	0.757082i	$0.273376\pi$
$60$	0.924578	−	0.817527i	0.119363	−	0.105542i
$61$	0.586573	−	3.70347i	0.0751029	−	0.474181i	−0.921258	−	0.388951i	$-0.872837\pi$
$61$	0.586573	−	3.70347i	0.0751029	−	0.474181i	0.996361	−	0.0852300i	$-0.0271625\pi$
$62$	11.6146	−	6.04409i	1.47506	−	0.767600i
$63$	−1.78431	+	2.91173i	−0.224802	+	0.366843i
$64$	−0.411845	−	7.98939i	−0.0514807	−	0.998674i
$65$	−9.20598	+	0.724526i	−1.14186	+	0.0898664i
$66$	0.0168715	−	0.0534829i	0.00207674	−	0.00658329i
$67$	5.36295	−	4.58039i	0.655189	−	0.559584i	−0.258494	−	0.966013i	$-0.583226\pi$
$67$	5.36295	−	4.58039i	0.655189	−	0.559584i	0.913682	+	0.406429i	$0.133226\pi$
$68$	−1.82097	+	0.174815i	−0.220825	+	0.0211994i
$69$	−0.379887	+	0.232795i	−0.0457330	+	0.0280252i
$70$	1.78730	+	2.86119i	0.213624	+	0.341978i
$71$	6.33090	+	5.40710i	0.751340	+	0.641705i	0.940326	−	0.340275i	$-0.110520\pi$
$71$	6.33090	+	5.40710i	0.751340	+	0.641705i	−0.188986	+	0.981980i	$0.560520\pi$
$72$	−8.22148	+	0.211764i	−0.968910	+	0.0249566i
$73$	−6.90701	+	6.90701i	−0.808404	+	0.808404i	−0.984392	−	0.175988i	$-0.943688\pi$
$73$	−6.90701	+	6.90701i	−0.808404	+	0.808404i	0.175988	+	0.984392i	$0.443688\pi$
$74$	−2.73544	+	5.48449i	−0.317989	+	0.637559i
$75$	0.258358	−	0.0620262i	0.0298326	−	0.00716216i
$76$	7.65198	−	12.9820i	0.877743	−	1.48914i
$77$	0.136586	+	0.0695940i	0.0155654	+	0.00793097i
$78$	−1.59017	−	1.13460i	−0.180051	−	0.128468i
$79$	12.4208	+	5.14485i	1.39745	+	0.578841i	0.949087	−	0.315013i	$-0.102009\pi$
$79$	12.4208	+	5.14485i	1.39745	+	0.578841i	0.448358	+	0.893854i	$0.352009\pi$
$80$	−3.43776	+	7.36133i	−0.384354	+	0.823022i
$81$			8.17778i			0.908642i
$82$	−7.42350	−	5.18571i	−0.819789	−	0.572666i
$83$			15.8828i			1.74337i	0.490070	+	0.871683i	$0.336971\pi$
$83$			15.8828i			1.74337i	−0.490070	+	0.871683i	$0.663029\pi$
$84$	−0.0995209	+	0.706664i	−0.0108586	+	0.0771034i
$85$	1.71639	+	0.710954i	0.186169	+	0.0771137i
$86$	−3.27440	+	4.58916i	−0.353088	+	0.494862i
$87$	−0.101387	−	0.0516591i	−0.0108698	−	0.00553844i
$88$	0.0384322	+	0.367170i	0.00409688	+	0.0391405i
$89$	−5.88802	+	1.41359i	−0.624128	+	0.149840i	−0.533161	−	0.846014i	$-0.678996\pi$
$89$	−5.88802	+	1.41359i	−0.624128	+	0.149840i	−0.0909676	+	0.995854i	$0.528996\pi$
$90$	7.47413	+	3.72779i	0.787842	+	0.392944i
$91$	3.77568	−	3.77568i	0.395799	−	0.395799i
$92$	1.68296	−	2.40206i	0.175461	−	0.250432i
$93$	−2.13888	−	1.82678i	−0.221792	−	0.189428i
$94$	−9.25748	+	5.78288i	−0.954836	+	0.596458i
$95$	−13.0487	+	7.99625i	−1.33877	+	0.820398i
$96$	−1.55814	+	0.725219i	−0.159027	+	0.0740174i
$97$	1.29043	−	1.10213i	0.131024	−	0.111905i	−0.581522	−	0.813531i	$-0.697542\pi$
$97$	1.29043	−	1.10213i	0.131024	−	0.111905i	0.712545	+	0.701626i	$0.247542\pi$
$98$	7.58057	+	2.39133i	0.765753	+	0.241561i
$99$	0.378352	−	0.0297770i	0.0380259	−	0.00299270i
$100$	−1.39717	+	1.05222i	−0.139717	+	0.105222i
$101$	6.70906	−	10.9482i	0.667576	−	1.08939i	−0.322189	−	0.946675i	$-0.604419\pi$
$101$	6.70906	−	10.9482i	0.667576	−	1.08939i	0.989765	−	0.142710i	$-0.0455815\pi$
$102$	0.181417	+	0.348620i	0.0179630	+	0.0345186i
$103$	1.63715	−	10.3366i	0.161314	−	1.01849i	−0.765627	−	0.643285i	$-0.777571\pi$
$103$	1.63715	−	10.3366i	0.161314	−	1.01849i	0.926940	−	0.375209i	$-0.122429\pi$
$104$	12.5772	+	2.67900i	1.23330	+	0.262697i
$105$	0.425993	−	0.586329i	0.0415727	−	0.0572199i
$106$	−3.26448	−	3.75644i	−0.317074	−	0.364857i
$107$	2.54436	−	1.84859i	0.245973	−	0.178710i	−0.457967	−	0.888969i	$-0.651422\pi$
$107$	2.54436	−	1.84859i	0.245973	−	0.178710i	0.703940	+	0.710259i	$0.251422\pi$
$108$	1.43045	+	3.29239i	0.137646	+	0.316810i
$109$	2.98456	+	7.20537i	0.285869	+	0.690149i	0.999951	−	0.00991323i	$-0.00315553\pi$
$109$	2.98456	+	7.20537i	0.285869	+	0.690149i	−0.714082	+	0.700062i	$0.753156\pi$
$110$	0.140498	−	0.347601i	0.0133959	−	0.0331424i
$111$	1.31260	+	0.103304i	0.124586	+	0.00980515i
$112$	−1.25285	−	4.52768i	−0.118383	−	0.427825i
$113$	5.82404	+	1.89235i	0.547880	+	0.178017i	0.569861	−	0.821741i	$-0.306997\pi$
$113$	5.82404	+	1.89235i	0.547880	+	0.178017i	−0.0219807	+	0.999758i	$0.506997\pi$
$114$	−3.20173	−	0.478970i	−0.299870	−	0.0448596i
$115$	−2.65396	+	1.35226i	−0.247483	+	0.126099i
$116$	0.747653	+	0.0459427i	0.0694179	+	0.00426567i
$117$	3.08609	−	12.8545i	0.285309	−	1.18840i
$118$	−4.89590	+	0.818574i	−0.450704	+	0.0753558i
$119$	−1.02166	+	0.331959i	−0.0936557	+	0.0304306i
$120$	1.74296	+	0.0920931i	0.159110	+	0.00840691i
$121$	1.71811	+	10.8477i	0.156192	+	0.986159i
$122$	4.26313	−	3.15361i	0.385966	−	0.285515i
$123$	−0.435238	+	1.89606i	−0.0392441	+	0.170962i
$124$	17.7059	+	5.41876i	1.59004	+	0.486619i
$125$	11.7850	−	1.86656i	1.05408	−	0.166950i
$126$	−4.68619	+	1.16769i	−0.417479	+	0.104026i
$127$	−4.11029	−	12.6502i	−0.364729	−	1.12252i	−0.950150	−	0.311792i	$-0.899071\pi$
$127$	−4.11029	−	12.6502i	−0.364729	−	1.12252i	0.585421	−	0.810729i	$-0.300929\pi$
$128$	7.50515	−	8.46597i	0.663368	−	0.748293i
$129$	1.17766	+	0.282731i	0.103687	+	0.0248931i
$130$	−10.0029	−	8.39590i	−0.877316	−	0.736369i
$131$	−2.22786	−	4.37243i	−0.194649	−	0.382021i	0.772967	−	0.634446i	$-0.218772\pi$
$131$	−2.22786	−	4.37243i	−0.194649	−	0.382021i	−0.967616	+	0.252425i	$0.918772\pi$
$132$	0.0700375	−	0.0372140i	0.00609598	−	0.00323906i
$133$	2.73453	−	8.41603i	0.237114	−	0.729763i
$134$	9.94970	+	0.697178i	0.859523	+	0.0602270i
$135$	0.286028	−	3.63434i	0.0246174	−	0.312794i
$136$	−2.00984	−	1.62896i	−0.172343	−	0.139683i
$137$	−16.7988	+	6.95828i	−1.43522	+	0.594486i	−0.958634	−	0.284643i	$-0.908125\pi$
$137$	−16.7988	+	6.95828i	−1.43522	+	0.594486i	−0.476583	+	0.879129i	$0.658125\pi$
$138$	−0.613921	−	0.141827i	−0.0522605	−	0.0120731i
$139$	6.66167	+	9.16900i	0.565035	+	0.777704i	0.991956	−	0.126585i	$-0.0404016\pi$
$139$	6.66167	+	9.16900i	0.565035	+	0.777704i	−0.426920	+	0.904289i	$0.640402\pi$
$140$	−1.03395	+	4.65754i	−0.0873845	+	0.393634i
$141$	1.89709	+	1.37832i	0.159764	+	0.116075i
$142$	1.02452	+	11.7296i	0.0859761	+	0.984330i
$143$	−0.586115	−	0.0928315i	−0.0490134	−	0.00776296i
$144$	−8.50169	−	7.93703i	−0.708474	−	0.661419i
$145$	−0.648621	−	0.397475i	−0.0538650	−	0.0330085i
$146$	−13.8135	+	0.118577i	−1.14321	+	0.00981348i
$147$	−0.133981	−	1.70238i	−0.0110505	−	0.140410i
$148$	−8.19603	+	2.81950i	−0.673710	+	0.231762i
$149$	−6.90242	−	8.08170i	−0.565468	−	0.662078i	0.401832	−	0.915714i	$-0.368374\pi$
$149$	−6.90242	−	8.08170i	−0.565468	−	0.662078i	−0.967300	+	0.253635i	$0.918374\pi$
$150$	0.322057	+	0.193574i	0.0262959	+	0.0158053i
$151$	−8.95473	−	14.6128i	−0.728726	−	1.18917i	−0.975479	−	0.220094i	$-0.929364\pi$
$151$	−8.95473	−	14.6128i	−0.728726	−	1.18917i	0.246753	−	0.969078i	$-0.420636\pi$
$152$	20.5875	−	5.50695i	1.66987	−	0.446673i
$153$	−1.72726	+	2.02237i	−0.139641	+	0.163499i
$154$	0.0687592	+	0.205597i	0.00554078	+	0.0165675i
$155$	−13.2969	−	13.2969i	−1.06803	−	1.06803i
$156$	−0.478941	−	2.72075i	−0.0383460	−	0.217835i
$157$	−2.91000	−	12.1210i	−0.232243	−	0.967363i	−0.959659	−	0.281166i	$-0.909279\pi$
$157$	−2.91000	−	12.1210i	−0.232243	−	0.967363i	0.727416	−	0.686197i	$-0.240721\pi$
$158$	7.42643	+	17.5025i	0.590815	+	1.39243i
$159$	−0.485384	+	0.952620i	−0.0384935	+	0.0755477i
$160$	−10.7650	+	4.01612i	−0.851049	+	0.317502i
$161$	0.659102	−	1.59121i	0.0519445	−	0.125405i
$162$	−8.10728	+	8.24767i	−0.636968	+	0.647999i
$163$	−4.99983			−0.391617			−0.195808	−	0.980642i	$-0.562733\pi$
$163$	−4.99983			−0.391617			−0.195808	+	0.980642i	$0.562733\pi$
$164$	−2.34594	−	12.5895i	−0.183187	−	0.983078i
$165$	−0.0805446			−0.00627039
$166$	−15.7459	+	16.0186i	−1.22212	+	1.24328i
$167$	−4.89833	+	11.8256i	−0.379044	+	0.915094i	0.613101	+	0.790004i	$0.289922\pi$
$167$	−4.89833	+	11.8256i	−0.379044	+	0.915094i	−0.992145	+	0.125089i	$0.960078\pi$
$168$	−0.800944	+	0.614041i	−0.0617942	+	0.0473743i
$169$	−3.48229	+	6.83437i	−0.267868	+	0.525721i
$170$	1.02624	+	2.41863i	0.0787089	+	0.185500i
$171$	−5.11445	−	21.3032i	−0.391112	−	1.62910i
$172$	−7.85199	+	1.38221i	−0.598709	+	0.105392i
$173$	13.1582	+	13.1582i	1.00040	+	1.00040i	1.00000		0.000399927i	$0.000127301\pi$
$173$	13.1582	+	13.1582i	1.00040	+	1.00040i	0.000399927		1.00000i	$0.499873\pi$
$174$	−0.0510395	−	0.152613i	−0.00386929	−	0.0115696i
$175$	−0.667051	+	0.781016i	−0.0504243	+	0.0590393i
$176$	−0.325244	+	0.408409i	−0.0245162	+	0.0307850i
$177$	0.557187	+	0.909246i	0.0418807	+	0.0683431i
$178$	−7.33974	−	4.41159i	−0.550137	−	0.330663i
$179$	−1.42535	−	1.66887i	−0.106536	−	0.124737i	0.704576	−	0.709629i	$-0.251137\pi$
$179$	−1.42535	−	1.66887i	−0.106536	−	0.124737i	−0.811112	+	0.584891i	$0.801137\pi$
$180$	3.84235	+	11.1694i	0.286392	+	0.832514i
$181$	−0.440222	−	5.59356i	−0.0327215	−	0.415766i	−0.991363	−	0.131149i	$-0.958134\pi$
$181$	−0.440222	−	5.59356i	−0.0327215	−	0.415766i	0.958641	−	0.284617i	$-0.0918665\pi$
$182$	7.55109	−	0.0648194i	0.559724	−	0.00480474i
$183$	−0.971329	−	0.595231i	−0.0718027	−	0.0440008i
$184$	4.07871	−	0.754137i	0.300686	−	0.0555957i
$185$	8.69395	+	1.37699i	0.639192	+	0.101238i
$186$	−0.346133	−	3.96283i	−0.0253797	−	0.290569i
$187$	0.0965854	+	0.0701734i	0.00706302	+	0.00513159i
$188$	−15.0696	−	3.34537i	−1.09907	−	0.243986i
$189$	1.23904	+	1.70539i	0.0901267	+	0.124049i
$190$	−21.0875	−	4.87161i	−1.52985	−	0.353424i
$191$	23.5293	−	9.74614i	1.70252	−	0.705206i	0.702539	−	0.711645i	$-0.252050\pi$
$191$	23.5293	−	9.74614i	1.70252	−	0.705206i	0.999979	+	0.00643873i	$0.00204952\pi$
$192$	−2.29043	−	0.813290i	−0.165297	−	0.0586942i
$193$	1.64408	−	20.8900i	0.118344	−	1.50370i	−0.595479	−	0.803371i	$-0.703038\pi$
$193$	1.64408	−	20.8900i	0.118344	−	1.50370i	0.713823	−	0.700326i	$-0.246962\pi$
$194$	2.39409	+	0.167755i	0.171886	+	0.0120441i
$195$	−0.866971	+	2.66826i	−0.0620851	+	0.191078i
$196$	5.27464	+	9.92700i	0.376760	+	0.709071i
$197$	−0.592787	−	1.16341i	−0.0422343	−	0.0828895i	0.868925	−	0.494944i	$-0.164811\pi$
$197$	−0.592787	−	1.16341i	−0.0422343	−	0.0828895i	−0.911159	+	0.412054i	$0.864811\pi$
$198$	0.411107	+	0.345059i	0.0292161	+	0.0245223i
$199$	−7.24168	−	1.73857i	−0.513349	−	0.123244i	−0.0315092	−	0.999503i	$-0.510031\pi$
$199$	−7.24168	−	1.73857i	−0.513349	−	0.123244i	−0.481840	+	0.876259i	$0.660031\pi$
$200$	−2.45226	−	0.323915i	−0.173401	−	0.0229043i
$201$	−0.662144	−	2.03787i	−0.0467040	−	0.143740i
$202$	17.6202	−	4.39054i	1.23975	−	0.308917i
$203$	0.434455	−	0.0688109i	0.0304928	−	0.00482958i
$204$	−0.162647	+	0.531453i	−0.0113876	+	0.0372092i
$205$	−3.89529	+	12.4085i	−0.272059	+	0.866647i
$206$	11.8986	−	8.80189i	0.829016	−	0.613257i
$207$	−0.667050	−	4.21159i	−0.0463632	−	0.292725i
$208$	10.0288	+	15.1707i	0.695372	+	1.05190i
$209$	−0.935319	+	0.303903i	−0.0646973	+	0.0210214i
$210$	1.01091	−	0.169020i	0.0697594	−	0.0116635i
$211$	6.46703	−	26.9371i	0.445209	−	1.85443i	−0.0702748	−	0.997528i	$-0.522388\pi$
$211$	6.46703	−	26.9371i	0.445209	−	1.85443i	0.515483	−	0.856900i	$-0.327612\pi$
$212$	0.431673	−	7.02488i	0.0296474	−	0.482471i
$213$	2.25379	−	1.14836i	0.154427	−	0.0786844i
$214$	4.39876	+	0.658041i	0.300693	+	0.0449828i
$215$	7.70050	+	2.50205i	0.525170	+	0.170638i
$216$	−1.82133	+	4.73865i	−0.123926	+	0.322424i
$217$	10.8399	+	0.853118i	0.735860	+	0.0579134i
$218$	−4.13318	+	10.2258i	−0.279934	+	0.692578i
$219$	1.13568	+	2.74177i	0.0767421	+	0.185272i
$220$	0.486303	−	0.211285i	0.0327865	−	0.0142449i
$221$	3.36432	−	2.44432i	0.226309	−	0.164423i
$222$	1.22140	+	1.40547i	0.0819752	+	0.0943289i
$223$	−10.0996	+	13.9009i	−0.676317	+	0.930871i	−0.999882	−	0.0153351i	$-0.995118\pi$
$223$	−10.0996	+	13.9009i	−0.676317	+	0.930871i	0.323565	+	0.946206i	$0.395118\pi$
$224$	3.22509	−	5.80843i	0.215485	−	0.388092i
$225$	−0.397795	+	2.51158i	−0.0265197	+	0.167439i
$226$	3.99779	+	7.68236i	0.265929	+	0.511023i
$227$	−12.6114	+	20.5799i	−0.837048	+	1.36594i	0.0919163	+	0.995767i	$0.470701\pi$
$227$	−12.6114	+	20.5799i	−0.837048	+	1.36594i	−0.928964	+	0.370171i	$0.879299\pi$
$228$	−2.75426	−	3.65720i	−0.182405	−	0.242204i
$229$	1.26877	−	0.0998546i	0.0838428	−	0.00659857i	−0.0364683	−	0.999335i	$-0.511611\pi$
$229$	1.26877	−	0.0998546i	0.0838428	−	0.00659857i	0.120311	+	0.992736i	$0.461611\pi$
$230$	−4.01724	−	1.26726i	−0.264889	−	0.0835608i
$231$	0.0354146	−	0.0302469i	0.00233011	−	0.00199010i
$232$	0.708497	+	0.787543i	0.0465151	+	0.0517048i
$233$	−9.32814	+	5.71629i	−0.611107	+	0.374487i	−0.793349	−	0.608767i	$-0.791664\pi$
$233$	−9.32814	+	5.71629i	−0.611107	+	0.374487i	0.182242	+	0.983254i	$0.441664\pi$
$234$	15.8561	−	9.90487i	1.03655	−	0.647502i
$235$	11.9207	+	10.1812i	0.777618	+	0.664149i
$236$	−5.74926	−	4.02812i	−0.374245	−	0.262208i
$237$	2.88822	−	2.88822i	0.187610	−	0.187610i
$238$	−1.35949	−	0.678060i	−0.0881228	−	0.0439521i
$239$	−15.3801	+	3.69244i	−0.994856	+	0.238844i	−0.698015	−	0.716083i	$-0.745933\pi$
$239$	−15.3801	+	3.69244i	−0.994856	+	0.238844i	−0.296841	+	0.954927i	$0.595933\pi$
$240$	1.66656	+	1.82081i	0.107576	+	0.117533i
$241$	9.12337	+	4.64859i	0.587688	+	0.299442i	0.722436	−	0.691438i	$-0.243022\pi$
$241$	9.12337	+	4.64859i	0.587688	+	0.299442i	−0.134748	+	0.990880i	$0.543022\pi$
$242$	−9.02143	+	12.6438i	−0.579920	+	0.812772i
$243$	7.27011	+	3.01138i	0.466378	+	0.193180i
$244$	7.42599	+	1.04582i	0.475401	+	0.0669516i
$245$		−	11.4162i		−	0.729357i
$246$	−2.31867	+	1.48078i	−0.147833	+	0.0944112i
$247$			34.2562i			2.17967i
$248$	12.4852	+	23.0183i	0.792810	+	1.46167i
$249$	4.45815	+	1.84663i	0.282524	+	0.117025i
$250$	13.7362	+	9.80090i	0.868754	+	0.619863i
$251$	23.8102	+	12.1319i	1.50289	+	0.765760i	0.995392	−	0.0958931i	$-0.0305707\pi$
$251$	23.8102	+	12.1319i	1.50289	+	0.765760i	0.507497	+	0.861653i	$0.330571\pi$
$252$	−5.88386	−	3.46812i	−0.370649	−	0.218471i
$253$	−0.186122	+	0.0446838i	−0.0117014	+	0.00280925i
$254$	8.39570	−	16.8332i	0.526793	−	1.05621i
$255$	0.399115	−	0.399115i	0.0249935	−	0.0249935i
$256$	15.9623	−	1.09788i	0.997643	−	0.0686173i
$257$	−7.78697	−	6.65070i	−0.485738	−	0.414859i	0.372562	−	0.928007i	$-0.378479\pi$
$257$	−7.78697	−	6.65070i	−0.485738	−	0.414859i	−0.858300	+	0.513148i	$0.828479\pi$
$258$	0.907430	+	1.45265i	0.0564942	+	0.0904383i
$259$	−4.33973	+	2.65939i	−0.269658	+	0.165247i
$260$	−1.76492	−	18.3844i	−0.109455	−	1.14015i
$261$	0.828101	−	0.707265i	0.0512581	−	0.0437786i
$262$	2.08783	−	6.61845i	0.128987	−	0.408889i
$263$	4.37833	−	0.344582i	0.269979	−	0.0212478i	0.0572532	−	0.998360i	$-0.481766\pi$
$263$	4.37833	−	0.344582i	0.269979	−	0.0212478i	0.212726	+	0.977112i	$0.431766\pi$
$264$	0.107529	+	0.0319017i	0.00661797	+	0.00196342i
$265$	−3.73464	+	6.09438i	−0.229417	+	0.374375i
$266$	11.1014	−	5.77700i	0.680670	−	0.354211i
$267$	−0.287794	+	1.81706i	−0.0176127	+	0.111202i
$268$	9.34357	+	10.5671i	0.570749	+	0.645486i
$269$	−12.3379	+	16.9816i	−0.752253	+	1.03539i	0.245566	+	0.969380i	$0.421026\pi$
$269$	−12.3379	+	16.9816i	−0.752253	+	1.03539i	−0.997819	+	0.0660079i	$0.978974\pi$
$270$	3.89148	−	3.38184i	0.236828	−	0.205812i
$271$	1.96179	−	1.42532i	0.119170	−	0.0865822i	−0.526604	−	0.850111i	$-0.676535\pi$
$271$	1.96179	−	1.42532i	0.119170	−	0.0865822i	0.645774	+	0.763529i	$0.276535\pi$
$272$	−0.412099	−	3.63540i	−0.0249872	−	0.220429i
$273$	−0.620814	−	1.49878i	−0.0375734	−	0.0907102i
$274$	−23.8407	−	9.63621i	−1.44027	−	0.582145i
$275$	0.113796	+	0.00895592i	0.00686214	+	0.000540062i
$276$	−0.478564	−	0.751668i	−0.0288062	−	0.0452451i
$277$	−27.6665	−	8.98940i	−1.66232	−	0.540121i	−0.680965	−	0.732316i	$-0.738439\pi$
$277$	−27.6665	−	8.98940i	−1.66232	−	0.540121i	−0.981357	+	0.192195i	$0.938439\pi$
$278$	−2.37135	+	15.8516i	−0.142224	+	0.950716i
$279$	23.9861	−	12.2215i	1.43601	−	0.731683i
$280$	−5.66017	+	3.67231i	−0.338260	+	0.219463i
$281$	1.54846	−	6.44979i	0.0923732	−	0.384762i	−0.906962	−	0.421212i	$-0.861605\pi$
$281$	1.54846	−	6.44979i	0.0923732	−	0.384762i	0.999335	+	0.0364498i	$0.0116049\pi$
$282$	0.546869	+	3.27083i	0.0325656	+	0.194775i
$283$	−28.8363	+	9.36948i	−1.71414	+	0.556958i	−0.991014	−	0.133758i	$-0.957295\pi$
$283$	−28.8363	+	9.36948i	−1.71414	+	0.556958i	−0.723126	+	0.690716i	$0.757295\pi$
$284$	−10.5952	+	12.8456i	−0.628712	+	0.762245i
$285$	0.727353	+	4.59232i	0.0430846	+	0.272026i
$286$	−0.499093	−	0.674687i	−0.0295120	−	0.0398951i
$287$	−2.94704	−	6.91867i	−0.173958	−	0.408396i
$288$	−0.705741	−	16.4333i	−0.0415862	−	0.968339i
$289$	15.9644	−	2.52851i	0.939081	−	0.148736i
$290$	−0.260116	−	1.04390i	−0.0152745	−	0.0613000i
$291$	−0.159325	−	0.490352i	−0.00933979	−	0.0287449i
$292$	−14.0491	−	13.5748i	−0.822163	−	0.794407i
$293$	8.43098	+	2.02410i	0.492543	+	0.118249i	0.472105	−	0.881542i	$-0.343494\pi$
$293$	8.43098	+	2.02410i	0.492543	+	0.118249i	0.0204374	+	0.999791i	$0.493494\pi$
$294$	1.55258	−	1.84976i	0.0905485	−	0.107880i
$295$	3.23659	+	6.35216i	0.188441	+	0.369837i
$296$	−11.0613	−	5.28178i	−0.642924	−	0.306997i
$297$	0.0723936	−	0.222805i	0.00420070	−	0.0129284i
$298$	1.05061	−	14.9937i	0.0608603	−	0.868561i
$299$	−0.523112	+	6.64676i	−0.0302523	+	0.384392i
$300$	0.132904	+	0.514509i	0.00767324	+	0.0297052i
$301$	−4.32542	+	1.79165i	−0.249313	+	0.103269i
$302$	5.45556	−	23.6152i	0.313932	−	1.35890i
$303$	−2.29301	−	3.15606i	−0.131730	−	0.181311i
$304$	26.2229	+	14.8560i	1.50399	+	0.852049i
$305$	−6.16145	−	4.47656i	−0.352804	−	0.256327i
$306$	−3.74696	+	0.327277i	−0.214199	+	0.0187092i
$307$	25.8018	+	4.08660i	1.47258	+	0.233234i	0.840562	−	0.541716i	$-0.182225\pi$
$307$	25.8018	+	4.08660i	1.47258	+	0.233234i	0.632022	+	0.774950i	$0.282225\pi$
$308$	−0.134478	+	0.275521i	−0.00766259	+	0.0156993i
$309$	−2.71103	−	1.66132i	−0.154225	−	0.0945093i
$310$	−0.228276	−	26.5929i	−0.0129652	−	1.51037i
$311$	−1.17732	−	14.9593i	−0.0667597	−	0.848262i	−0.935576	−	0.353127i	$-0.885118\pi$
$311$	−1.17732	−	14.9593i	−0.0667597	−	0.848262i	0.868816	−	0.495135i	$-0.164882\pi$
$312$	2.21426	−	3.21882i	0.125358	−	0.182230i
$313$	18.8542	+	22.0755i	1.06570	+	1.24778i	0.967569	+	0.252607i	$0.0812879\pi$
$313$	18.8542	+	22.0755i	1.06570	+	1.24778i	0.0981356	+	0.995173i	$0.468712\pi$
$314$	9.08167	−	15.1095i	0.512508	−	0.852681i
$315$	3.62415	+	5.91408i	0.204198	+	0.333221i
$316$	−9.86173	+	25.0145i	−0.554766	+	1.40718i
$317$	−16.0995	+	18.8501i	−0.904239	+	1.05873i	0.0937665	+	0.995594i	$0.470109\pi$
$317$	−16.0995	+	18.8501i	−0.904239	+	1.05873i	−0.998005	+	0.0631332i	$0.979891\pi$
$318$	−1.43394	+	0.479562i	−0.0804114	+	0.0268925i
$319$	−0.0345670	−	0.0345670i	−0.00193538	−	0.00193538i
$320$	−14.8385	−	6.62177i	−0.829499	−	0.370168i
$321$	−0.223058	−	0.929104i	−0.0124499	−	0.0518575i
$322$	2.24223	−	0.951393i	0.124955	−	0.0530191i
$323$	3.12879	−	6.14060i	0.174091	−	0.341672i
$324$	−16.3531	+	0.280775i	−0.908508	+	0.0155986i
$325$	1.52157	−	3.67340i	0.0844016	−	0.203763i
$326$	−5.04256	−	4.95673i	−0.279282	−	0.274528i
$327$	2.36948			0.131032
$328$	10.1150	−	15.0229i	0.558509	−	0.829499i
$329$	−9.06473			−0.499755
$330$	−0.0812330	−	0.0798502i	−0.00447173	−	0.00439561i
$331$	−1.84650	+	4.45785i	−0.101493	+	0.245026i	−0.966467	−	0.256791i	$-0.917335\pi$
$331$	−1.84650	+	4.45785i	−0.101493	+	0.245026i	0.864974	+	0.501817i	$0.167335\pi$
$332$	−31.7610	+	0.545320i	−1.74311	+	0.0299283i
$333$	−5.72080	+	11.2277i	−0.313498	+	0.615274i
$334$	−16.6639	+	7.07059i	−0.911807	+	0.386885i
$335$	−3.34411	−	13.9292i	−0.182708	−	0.761034i
$336$	−1.41654	−	0.174750i	−0.0772784	−	0.00953339i
$337$	−17.2644	−	17.2644i	−0.940452	−	0.940452i	0.0578717	−	0.998324i	$-0.481569\pi$
$337$	−17.2644	−	17.2644i	−0.940452	−	0.940452i	−0.998324	+	0.0578717i	$0.981569\pi$
$338$	−10.2875	+	3.44052i	−0.559567	+	0.187140i
$339$	1.20830	−	1.41474i	0.0656257	−	0.0768379i
$340$	−1.36277	+	3.45669i	−0.0739064	+	0.187465i
$341$	−0.631398	−	1.03035i	−0.0341921	−	0.0557965i
$342$	15.9614	−	26.5557i	0.863094	−	1.43597i
$343$	9.62637	+	11.2710i	0.519775	+	0.608579i
$344$	−9.28939	−	6.39028i	−0.500850	−	0.344541i
$345$	0.0710016	+	0.902160i	0.00382260	+	0.0485707i
$346$	0.225895	+	26.3154i	0.0121442	+	1.41473i
$347$	−16.0423	−	9.83075i	−0.861197	−	0.527742i	0.0203743	−	0.999792i	$-0.493514\pi$
$347$	−16.0423	−	9.83075i	−0.861197	−	0.527742i	−0.881572	+	0.472050i	$0.843514\pi$
$348$	0.0998220	−	0.204517i	0.00535102	−	0.0109633i
$349$	−18.8469	−	2.98506i	−1.00885	−	0.159787i	−0.369932	−	0.929059i	$-0.620619\pi$
$349$	−18.8469	−	2.98506i	−1.00885	−	0.159787i	−0.638921	+	0.769272i	$0.720619\pi$
$350$	−1.44704	+	0.126391i	−0.0773473	+	0.00675589i
$351$	−6.60179	−	4.79648i	−0.352377	−	0.256017i
$352$	−0.732913	+	0.0894594i	−0.0390644	+	0.00476820i
$353$	−8.68675	−	11.9563i	−0.462349	−	0.636369i	0.512645	−	0.858601i	$-0.328666\pi$
$353$	−8.68675	−	11.9563i	−0.462349	−	0.636369i	−0.974994	+	0.222232i	$0.928666\pi$
$354$	−0.339459	+	1.46940i	−0.0180420	+	0.0780978i
$355$	15.6233	−	6.47137i	0.829197	−	0.343465i
$356$	−3.02892	−	11.7258i	−0.160532	−	0.621464i
$357$	−0.0256069	+	0.325366i	−0.00135526	+	0.0172202i
$358$	0.216952	−	3.09620i	0.0114662	−	0.163639i
$359$	−0.813248	+	2.50292i	−0.0429216	+	0.132099i	−0.970221	−	0.242221i	$-0.922124\pi$
$359$	−0.813248	+	2.50292i	−0.0429216	+	0.132099i	0.927299	+	0.374320i	$0.122124\pi$
$360$	−7.19787	+	15.0740i	−0.379361	+	0.794472i
$361$	17.1479	+	33.6546i	0.902519	+	1.77129i
$362$	5.10135	−	6.07779i	0.268121	−	0.319442i
$363$	3.24461	+	0.778962i	0.170298	+	0.0408849i
$364$	7.67989	+	7.42062i	0.402536	+	0.388946i
$365$	6.13089	+	18.8689i	0.320905	+	0.987645i
$366$	−0.389531	−	1.56327i	−0.0203611	−	0.0817137i
$367$	−17.7622	+	2.81325i	−0.927178	+	0.146851i	−0.601721	−	0.798706i	$-0.705518\pi$
$367$	−17.7622	+	2.81325i	−0.927178	+	0.146851i	−0.325457	+	0.945557i	$0.605518\pi$
$368$	4.86120	+	3.28296i	0.253408	+	0.171136i
$369$	−15.1710	−	10.7927i	−0.789772	−	0.561846i
$370$	7.40314	+	10.0078i	0.384871	+	0.520279i
$371$	−0.646541	−	4.08210i	−0.0335667	−	0.211932i
$372$	3.57958	−	4.33985i	0.185593	−	0.225011i
$373$	12.1681	−	3.95365i	0.630040	−	0.204712i	0.0234471	−	0.999725i	$-0.492536\pi$
$373$	12.1681	−	3.95365i	0.630040	−	0.204712i	0.606593	+	0.795013i	$0.292536\pi$
$374$	0.0278424	+	0.166526i	0.00143970	+	0.00861085i
$375$	0.846266	−	3.52495i	0.0437010	−	0.182028i
$376$	−11.8819	−	18.3137i	−0.612762	−	0.944456i
$377$	−1.51720	+	0.773054i	−0.0781400	+	0.0398143i
$378$	−0.441060	+	2.94832i	−0.0226857	+	0.151645i
$379$	−18.1870	−	5.90930i	−0.934201	−	0.303540i	−0.197922	−	0.980218i	$-0.563419\pi$
$379$	−18.1870	−	5.90930i	−0.934201	−	0.303540i	−0.736279	+	0.676678i	$0.763419\pi$
$380$	−16.4382	−	25.8190i	−0.843259	−	1.32449i
$381$	−4.02866	−	0.317063i	−0.206395	−	0.0162436i
$382$	33.3925	+	13.4970i	1.70851	+	0.690566i
$383$	5.46420	+	13.1917i	0.279208	+	0.674067i	0.999814	−	0.0192774i	$-0.00613657\pi$
$383$	5.46420	+	13.1917i	0.279208	+	0.674067i	−0.720607	+	0.693344i	$0.756137\pi$
$384$	−1.50372	−	3.09092i	−0.0767365	−	0.157733i
$385$	0.251895	−	0.183012i	0.0128377	−	0.00932716i
$386$	22.3681	−	19.4387i	1.13850	−	0.989402i
$387$	−6.81309	+	9.37741i	−0.346329	+	0.476681i
$388$	2.24825	+	2.54264i	0.114137	+	0.129083i
$389$	4.63862	−	29.2871i	0.235187	−	1.48491i	−0.533778	−	0.845625i	$-0.679228\pi$
$389$	4.63862	−	29.2871i	0.235187	−	1.48491i	0.768966	−	0.639290i	$-0.220772\pi$
$390$	−3.51964	+	1.83157i	−0.178224	+	0.0927452i
$391$	0.700853	−	1.14369i	0.0354437	−	0.0578388i
$392$	−4.52169	+	15.2410i	−0.228380	+	0.769787i
$393$	−1.48632	+	0.116976i	−0.0749749	+	0.00590065i
$394$	0.555527	−	1.76103i	0.0279870	−	0.0887194i
$395$	20.7642	−	17.7343i	1.04476	−	0.892309i
$396$	0.0725355	+	0.755571i	0.00364505	+	0.0379689i
$397$	−4.33299	+	2.65526i	−0.217467	+	0.133264i	−0.626966	−	0.779047i	$-0.715703\pi$
$397$	−4.33299	+	2.65526i	−0.217467	+	0.133264i	0.409499	+	0.912310i	$0.365703\pi$
$398$	−5.57999	−	8.93269i	−0.279700	−	0.447755i
$399$	−2.04436	−	1.74605i	−0.102346	−	0.0874119i
$400$	−2.15210	−	2.75781i	−0.107605	−	0.137890i
$401$	14.6854	−	14.6854i	0.733352	−	0.733352i	−0.237930	−	0.971282i	$-0.576469\pi$
$401$	14.6854	−	14.6854i	0.733352	−	0.733352i	0.971282	+	0.237930i	$0.0764689\pi$
$402$	1.35250	−	2.71172i	0.0674565	−	0.135248i
$403$	−40.9294	+	9.82628i	−2.03884	+	0.489482i
$404$	22.1235	+	13.0402i	1.10068	+	0.648776i
$405$	14.7997	+	7.54082i	0.735403	+	0.374706i
$406$	0.506386	+	0.361311i	0.0251315	+	0.0179316i
$407$	0.522595	+	0.216466i	0.0259041	+	0.0107298i
$408$	−0.690909	+	0.374750i	−0.0342051	+	0.0185529i
$409$		−	27.4521i		−	1.35742i	−0.734406	−	0.678710i	$-0.762539\pi$
$409$		−	27.4521i		−	1.35742i	0.734406	−	0.678710i	$-0.237461\pi$
$410$	−16.2301	+	8.65284i	−0.801548	+	0.427333i
$411$			5.52426i			0.272491i
$412$	20.7263	+	2.91893i	1.02111	+	0.143805i
$413$	−3.80852	−	1.57754i	−0.187405	−	0.0776256i
$414$	3.50253	−	4.90888i	0.172140	−	0.241258i
$415$	28.7438	+	14.6457i	1.41098	+	0.718930i
$416$	−4.92538	+	25.2427i	−0.241487	+	1.23762i
$417$	3.34817	−	0.803824i	0.163961	−	0.0393634i
$418$	−1.24460	−	0.620755i	−0.0608752	−	0.0303621i
$419$	12.7939	−	12.7939i	0.625024	−	0.625024i	−0.321788	−	0.946812i	$-0.604284\pi$
$419$	12.7939	−	12.7939i	0.625024	−	0.625024i	0.946812	+	0.321788i	$0.104284\pi$
$420$	1.18711	+	0.831730i	0.0579251	+	0.0405843i
$421$	16.4615	+	14.0595i	0.802285	+	0.685216i	0.952869	−	0.303381i	$-0.0981154\pi$
$421$	16.4615	+	14.0595i	0.802285	+	0.685216i	−0.150584	+	0.988597i	$0.548115\pi$
$422$	33.2272	−	20.7561i	1.61747	−	1.01039i
$423$	−19.1352	+	11.7261i	−0.930386	+	0.570141i
$424$	7.39968	−	6.65697i	0.359360	−	0.323291i
$425$	−0.608260	+	0.519503i	−0.0295049	+	0.0251996i
$426$	3.41151	+	1.07618i	0.165288	+	0.0521411i
$427$	4.39020	−	0.345517i	0.212457	−	0.0167207i
$428$	3.78399	+	5.02451i	0.182906	+	0.242869i
$429$	−0.0942019	+	0.153723i	−0.00454811	+	0.00742184i
$430$	5.28584	+	10.1576i	0.254906	+	0.489841i
$431$	3.09781	−	19.5588i	0.149216	−	0.942116i	−0.793512	−	0.608555i	$-0.791750\pi$
$431$	3.09781	−	19.5588i	0.149216	−	0.942116i	0.942729	−	0.333561i	$-0.108250\pi$
$432$	−6.53470	+	2.97353i	−0.314401	+	0.143064i
$433$	1.17648	−	1.61928i	0.0565379	−	0.0778177i	−0.779812	−	0.626014i	$-0.784685\pi$
$433$	1.17648	−	1.61928i	0.0565379	−	0.0778177i	0.836350	+	0.548196i	$0.184685\pi$
$434$	10.0868	+	11.6069i	0.484181	+	0.557147i
$435$	−0.186980	+	0.135849i	−0.00896498	+	0.00651344i
$436$	−14.3061	+	6.21563i	−0.685140	+	0.297675i
$437$	4.22845	+	10.2084i	0.202274	+	0.488333i
$438$	−1.57275	+	3.89110i	−0.0751490	+	0.185924i
$439$	−26.9232	−	2.11890i	−1.28497	−	0.101130i	−0.582495	−	0.812835i	$-0.697923\pi$
$439$	−26.9232	−	2.11890i	−1.28497	−	0.101130i	−0.702478	+	0.711705i	$0.747923\pi$
$440$	0.699923	+	0.269019i	0.0333675	+	0.0128250i
$441$	15.5433	+	5.05031i	0.740155	+	0.240491i
$442$	5.81632	+	0.870104i	0.276654	+	0.0413866i
$443$	26.0781	−	13.2875i	1.23901	−	0.631306i	0.293206	−	0.956049i	$-0.405278\pi$
$443$	26.0781	−	13.2875i	1.23901	−	0.631306i	0.945802	+	0.324743i	$0.105278\pi$
$444$	−0.161510	+	2.62836i	−0.00766494	+	0.124736i
$445$	−2.87117	+	11.9593i	−0.136107	+	0.566925i
$446$	−23.9669	+	4.00717i	−1.13487	+	0.189745i
$447$	−3.07096	+	0.997817i	−0.145252	+	0.0471951i
$448$	9.01101	−	2.66079i	0.425730	−	0.125710i
$449$	−2.60051	−	16.4190i	−0.122726	−	0.774860i	−0.969893	−	0.243533i	$-0.921694\pi$
$449$	−2.60051	−	16.4190i	−0.122726	−	0.774860i	0.847167	−	0.531327i	$-0.178306\pi$
$450$	−2.89112	+	2.13868i	−0.136289	+	0.100818i
$451$	−0.429549	+	0.716923i	−0.0202267	+	0.0337586i
$452$	−3.58417	+	11.7113i	−0.168585	+	0.550855i
$453$	−5.14279	+	0.814538i	−0.241629	+	0.0382703i
$454$	−33.1217	+	8.25314i	−1.55448	+	0.387339i
$455$	−3.35142	−	10.3146i	−0.157117	−	0.483557i
$456$	0.847870	−	6.41897i	0.0397051	−	0.300596i
$457$	20.5689	+	4.93816i	0.962173	+	0.230997i	0.683958	−	0.729521i	$-0.260257\pi$
$457$	20.5689	+	4.93816i	0.962173	+	0.230997i	0.278215	+	0.960519i	$0.410257\pi$
$458$	1.37861	+	1.15713i	0.0644182	+	0.0540690i
$459$	0.745318	+	1.46277i	0.0347885	+	0.0682762i
$460$	−2.79524	−	5.26070i	−0.130329	−	0.245282i
$461$	−1.31576	+	4.04949i	−0.0612810	+	0.188603i	−0.977010	−	0.213192i	$-0.931614\pi$
$461$	−1.31576	+	4.04949i	−0.0612810	+	0.188603i	0.915729	+	0.401796i	$0.131614\pi$
$462$	0.0657034	+	0.00460385i	0.00305680	+	0.000214191i
$463$	−1.07808	+	13.6983i	−0.0501025	+	0.636612i	0.919684	+	0.392658i	$0.128445\pi$
$463$	−1.07808	+	13.6983i	−0.0501025	+	0.636612i	−0.969787	+	0.243954i	$0.921555\pi$
$464$	−0.0662019	+	1.49666i	−0.00307335	+	0.0694809i
$465$	−5.27828	+	2.18634i	−0.244775	+	0.101389i
$466$	−15.0749	−	3.48258i	−0.698330	−	0.161327i
$467$	1.44939	+	1.99492i	0.0670700	+	0.0923139i	0.841234	−	0.540671i	$-0.181830\pi$
$467$	1.44939	+	1.99492i	0.0670700	+	0.0923139i	−0.774164	+	0.632985i	$0.781830\pi$
$468$	25.8111	+	5.72993i	1.19312	+	0.264866i
$469$	6.70120	+	4.86870i	0.309433	+	0.224816i
$470$	1.92911	+	22.0861i	0.0889832	+	1.01876i
$471$	−3.74058	−	0.592450i	−0.172357	−	0.0272987i
$472$	−1.80500	−	9.76225i	−0.0830819	−	0.449344i
$473$	0.443640	+	0.271863i	0.0203986	+	0.0125003i
$474$	5.77622	−	0.0495837i	0.265311	−	0.00227746i
$475$	−0.516995	−	6.56904i	−0.0237214	−	0.301408i
$476$	−0.698897	−	2.03163i	−0.0320339	−	0.0931195i
$477$	−6.64539	−	7.78076i	−0.304272	−	0.356256i
$478$	−19.1722	−	11.5235i	−0.876914	−	0.527074i
$479$	11.8355	+	19.3137i	0.540776	+	0.882466i	0.999983	−	0.00586355i	$-0.00186644\pi$
$479$	11.8355	+	19.3137i	0.540776	+	0.882466i	−0.459207	+	0.888329i	$0.651866\pi$
$480$	−0.124316	+	3.48857i	−0.00567424	+	0.159231i
$481$	12.7962	−	14.9824i	0.583455	−	0.683138i
$482$	4.59283	+	13.7330i	0.209198	+	0.625523i
$483$	−0.370007	−	0.370007i	−0.0168359	−	0.0168359i
$484$	−21.6333	+	3.80817i	−0.983332	+	0.173099i
$485$	−0.804658	−	3.35164i	−0.0365376	−	0.152190i
$486$	4.34683	+	10.2446i	0.197176	+	0.464702i
$487$	11.6528	−	22.8699i	0.528038	−	1.03633i	−0.460824	−	0.887492i	$-0.652446\pi$
$487$	11.6528	−	22.8699i	0.528038	−	1.03633i	0.988861	−	0.148840i	$-0.0475540\pi$
$488$	6.45266	+	8.41673i	0.292098	+	0.381008i
$489$	−0.581308	+	1.40340i	−0.0262876	+	0.0634640i
$490$	11.3178	−	11.5138i	0.511288	−	0.520141i
$491$	−39.8567			−1.79871			−0.899354	−	0.437222i	$-0.855962\pi$
$491$	−39.8567			−1.79871			−0.899354	+	0.437222i	$0.855962\pi$
$492$	−3.80651	−	0.805248i	−0.171611	−	0.0363034i
$493$	0.342574			0.0154287
$494$	−33.9609	+	34.5490i	−1.52797	+	1.55443i
$495$	0.294994	−	0.712179i	0.0132590	−	0.0320101i
$496$	−10.2280	+	35.5926i	−0.459252	+	1.59816i
$497$	−4.43919	+	8.71239i	−0.199125	+	0.390804i
$498$	2.66555	+	6.28212i	0.119446	+	0.281509i
$499$	4.20733	+	17.5248i	0.188346	+	0.784517i	0.983913	+	0.178651i	$0.0571733\pi$
$499$	4.20733	+	17.5248i	0.188346	+	0.784517i	−0.795567	+	0.605866i	$0.792827\pi$
$500$	4.13720	+	23.5025i	0.185021	+	1.05106i
$501$	2.74982	+	2.74982i	0.122853	+	0.122853i
$502$	11.9864	+	35.8406i	0.534980	+	1.59964i
$503$	15.2453	−	17.8500i	0.679754	−	0.795890i	−0.308087	−	0.951358i	$-0.599689\pi$
$503$	15.2453	−	17.8500i	0.679754	−	0.795890i	0.987841	+	0.155468i	$0.0496886\pi$
$504$	−2.49593	−	9.33091i	−0.111177	−	0.415632i
$505$	−13.6269	−	22.2371i	−0.606390	−	0.989539i
$506$	−0.232011	−	0.139451i	−0.0103141	−	0.00619937i
$507$	1.51347	+	1.77205i	0.0672155	+	0.0786993i
$508$	25.1555	−	8.65370i	1.11609	−	0.383946i
$509$	−0.833446	−	10.5899i	−0.0369418	−	0.469391i	−0.987368	−	0.158441i	$-0.949353\pi$
$509$	−0.833446	−	10.5899i	−0.0369418	−	0.469391i	0.950427	−	0.310949i	$-0.100647\pi$
$510$	0.798201	−	0.00685185i	0.0353449	−	0.000303405i
$511$	−9.78153	−	5.99413i	−0.432710	−	0.265165i
$512$	17.1871	+	14.7174i	0.759571	+	0.650424i
$513$	−13.3572	−	2.11557i	−0.589733	−	0.0934046i
$514$	−1.26016	−	14.4274i	−0.0555832	−	0.636365i
$515$	−17.1969	−	12.4943i	−0.757787	−	0.550565i
$516$	−0.524945	+	2.36468i	−0.0231094	+	0.104099i
$517$	0.592142	+	0.815013i	0.0260424	+	0.0358442i
$518$	−7.01329	−	1.62020i	−0.308146	−	0.0711875i
$519$	5.22322	−	2.16353i	0.229274	−	0.0949684i
$520$	16.4459	−	20.2912i	0.721200	−	0.889828i
$521$	1.10151	−	13.9960i	0.0482581	−	0.613177i	−0.924474	−	0.381245i	$-0.875495\pi$
$521$	1.10151	−	13.9960i	0.0482581	−	0.613177i	0.972732	−	0.231932i	$-0.0745046\pi$
$522$	1.53635	+	0.107652i	0.0672440	+	0.00471181i
$523$	2.37882	−	7.32126i	0.104019	−	0.320136i	−0.885480	−	0.464677i	$-0.846170\pi$
$523$	2.37882	−	7.32126i	0.104019	−	0.320136i	0.989499	+	0.144541i	$0.0461705\pi$
$524$	8.66707	−	4.60519i	0.378623	−	0.201179i
$525$	0.141668	+	0.278040i	0.00618291	+	0.0121346i
$526$	4.75736	+	3.99306i	0.207431	+	0.174106i
$527$	8.23429	+	1.97688i	0.358691	+	0.0861142i
$528$	0.0768216	+	0.138777i	0.00334323	+	0.00603948i
$529$	−6.44283	−	19.8290i	−0.280123	−	0.862130i
$530$	−9.80840	+	2.44402i	−0.426050	+	0.106162i
$531$	−10.0803	+	1.59656i	−0.437447	+	0.0692849i
$532$	16.9235	+	5.17931i	0.733726	+	0.224551i
$533$	19.1265	+	21.9469i	0.828459	+	0.950624i
$534$	−2.09165	+	1.54728i	−0.0905144	+	0.0669572i
$535$	−0.999287	−	6.30925i	−0.0432029	−	0.272773i
$536$	−1.05254	+	19.9204i	−0.0454627	+	0.860430i
$537$	−0.634155	+	0.206049i	−0.0273658	+	0.00889169i
$538$	−29.2786	+	4.89525i	−1.26229	+	0.211049i
$539$	0.171262	−	0.713357i	0.00737677	−	0.0307265i
$540$	7.27742	+	0.447191i	0.313170	+	0.0192441i
$541$	−20.7913	+	10.5937i	−0.893890	+	0.455460i	−0.839687	−	0.543070i	$-0.817262\pi$
$541$	−20.7913	+	10.5937i	−0.893890	+	0.455460i	−0.0542025	+	0.998530i	$0.517262\pi$
$542$	3.39159	+	0.507372i	0.145681	+	0.0217935i
$543$	−1.62124	−	0.526772i	−0.0695739	−	0.0226059i
$544$	3.18844	−	4.07502i	0.136703	−	0.174715i
$545$	15.7920	+	1.24285i	0.676454	+	0.0532381i
$546$	0.859738	−	2.12705i	0.0367934	−	0.0910294i
$547$	5.78327	+	13.9620i	0.247275	+	0.596974i	0.997971	−	0.0636739i	$-0.0202818\pi$
$547$	5.78327	+	13.9620i	0.247275	+	0.596974i	−0.750696	+	0.660648i	$0.770282\pi$
$548$	−14.4913	−	33.3537i	−0.619037	−	1.42480i
$549$	8.82055	−	6.40851i	0.376452	−	0.273508i
$550$	0.105890	+	0.121847i	0.00451515	+	0.00519558i
$551$	−1.65872	+	2.28303i	−0.0706637	+	0.0972602i
$552$	0.262534	−	1.23253i	0.0111742	−	0.0524600i
$553$	−2.47003	+	15.5951i	−0.105036	+	0.663173i
$554$	−18.9911	−	36.4943i	−0.806854	−	1.55049i
$555$	1.39731	−	2.28021i	0.0593127	−	0.0967895i
$556$	−18.1066	+	13.6362i	−0.767890	+	0.578303i
$557$	37.7765	−	2.97307i	1.60064	−	0.125973i	0.753539	−	0.657404i	$-0.228345\pi$
$557$	37.7765	−	2.97307i	1.60064	−	0.125973i	0.847102	+	0.531431i	$0.178345\pi$
$558$	36.3073	+	11.4533i	1.53701	+	0.484858i
$559$	13.7815	−	11.7705i	0.582895	−	0.497840i
$560$	−9.34921	−	1.90768i	−0.395076	−	0.0806141i
$561$	0.0309265	−	0.0189518i	0.00130572	−	0.000800145i
$562$	7.95588	−	4.96981i	0.335598	−	0.209639i
$563$	1.60877	+	1.37402i	0.0678016	+	0.0579080i	0.682703	−	0.730696i	$-0.260804\pi$
$563$	1.60877	+	1.37402i	0.0678016	+	0.0579080i	−0.614902	+	0.788604i	$0.710804\pi$
$564$	−2.69109	+	3.84094i	−0.113315	+	0.161733i
$565$	8.79508	−	8.79508i	0.370012	−	0.370012i
$566$	−38.3715	−	19.1381i	−1.61287	−	0.804436i
$567$	−9.33906	+	2.24211i	−0.392204	+	0.0941598i
$568$	−23.4207	+	2.45147i	−0.982709	+	0.102861i
$569$	21.8953	+	11.1562i	0.917899	+	0.467693i	0.848081	−	0.529867i	$-0.177758\pi$
$569$	21.8953	+	11.1562i	0.917899	+	0.467693i	0.0698182	+	0.997560i	$0.477758\pi$
$570$	−3.81917	+	5.35266i	−0.159967	+	0.224198i
$571$	17.9499	+	7.43507i	0.751178	+	0.311148i	0.725222	−	0.688515i	$-0.241737\pi$
$571$	17.9499	+	7.43507i	0.751178	+	0.311148i	0.0259559	+	0.999663i	$0.491737\pi$
$572$	0.165512	−	1.17524i	0.00692040	−	0.0491394i
$573$		−	7.73757i		−	0.323242i
$574$	3.88680	−	9.89945i	0.162232	−	0.413195i
$575$		−	1.28249i		−	0.0534837i
$576$	15.5798	−	17.2734i	0.649159	−	0.719724i
$577$	14.5203	+	6.01449i	0.604487	+	0.250387i	0.663869	−	0.747849i	$-0.268913\pi$
$577$	14.5203	+	6.01449i	0.604487	+	0.250387i	−0.0593824	+	0.998235i	$0.518913\pi$
$578$	18.6075	+	13.2766i	0.773971	+	0.552235i
$579$	−5.67247	−	2.89027i	−0.235740	−	0.120115i
$580$	0.772564	−	1.31070i	0.0320790	−	0.0544237i
$581$	−18.1383	+	4.35461i	−0.752502	+	0.180660i
$582$	0.325438	−	0.652494i	0.0134898	−	0.0270467i
$583$	−0.324789	+	0.324789i	−0.0134514	+	0.0134514i
$584$	−0.711390	−	27.6189i	−0.0294375	−	1.14288i
$585$	−20.4176	−	17.4383i	−0.844165	−	0.720985i
$586$	6.49639	+	10.3997i	0.268363	+	0.429607i
$587$	−32.7606	+	20.0757i	−1.35217	+	0.828613i	−0.994450	−	0.105214i	$-0.966447\pi$
$587$	−32.7606	+	20.0757i	−1.35217	+	0.828613i	−0.357724	+	0.933827i	$0.616447\pi$
$588$	3.39967	−	0.326371i	0.140200	−	0.0134593i
$589$	−53.0444	+	45.3042i	−2.18566	+	1.86673i
$590$	−3.03315	+	9.61514i	−0.124873	+	0.395849i
$591$	−0.395478	+	0.0311248i	−0.0162678	+	0.00128030i
$592$	−5.91958	−	16.2928i	−0.243293	−	0.669632i
$593$	9.50204	−	15.5059i	0.390202	−	0.636752i	−0.595868	−	0.803082i	$-0.703192\pi$
$593$	9.50204	−	15.5059i	0.390202	−	0.636752i	0.986070	+	0.166330i	$0.0531918\pi$
$594$	0.293896	−	0.152939i	0.0120587	−	0.00627518i
$595$	−0.341327	+	2.15505i	−0.0139930	+	0.0883485i
$596$	15.9240	−	14.0803i	0.652273	−	0.576751i
$597$	−1.32996	+	1.83053i	−0.0544316	+	0.0749186i
$598$	−7.11705	+	6.18497i	−0.291038	+	0.252922i
$599$	−32.0475	+	23.2838i	−1.30942	+	0.951352i	−0.309424	+	0.950924i	$0.600136\pi$
$599$	−32.0475	+	23.2838i	−1.30942	+	0.951352i	−1.00000		0.000428024i	$0.999864\pi$
$600$	−0.376034	+	0.650666i	−0.0153515	+	0.0265633i
$601$	−4.81587	−	11.6265i	−0.196443	−	0.474256i	0.794708	−	0.606992i	$-0.207624\pi$
$601$	−4.81587	−	11.6265i	−0.196443	−	0.474256i	−0.991151	+	0.132736i	$0.957624\pi$
$602$	−6.13859	−	2.48117i	−0.250190	−	0.101125i
$603$	20.4440	+	1.60898i	0.832545	+	0.0655227i
$604$	28.9138	−	18.4085i	1.17649	−	0.749033i
$605$	21.2159	+	6.89348i	0.862550	+	0.280260i
$606$	0.816243	−	5.45628i	0.0331576	−	0.221646i
$607$	12.4418	−	6.33944i	0.504999	−	0.257310i	−0.182880	−	0.983135i	$-0.558542\pi$
$607$	12.4418	−	6.33944i	0.504999	−	0.257310i	0.687879	+	0.725825i	$0.258542\pi$
$608$	11.7191	+	40.9798i	0.475274	+	1.66195i
$609$	0.0311976	−	0.129947i	0.00126419	−	0.00526574i
$610$	−1.77615	−	10.6232i	−0.0719141	−	0.430119i
$611$	33.3733	−	10.8436i	1.35014	−	0.438687i
$612$	−4.10344	−	3.38458i	−0.165872	−	0.136814i
$613$	−3.64910	−	23.0395i	−0.147386	−	0.930558i	−0.944924	−	0.327290i	$-0.893865\pi$
$613$	−3.64910	−	23.0395i	−0.147386	−	0.930558i	0.797538	−	0.603269i	$-0.206135\pi$
$614$	21.9709	+	29.7009i	0.886674	+	1.19863i
$615$	3.03005	+	2.53605i	0.122183	+	0.102263i
$616$	−0.408773	+	0.144557i	−0.0164699	+	0.00582437i
$617$	12.6966	−	2.01095i	0.511148	−	0.0809578i	0.104467	−	0.994528i	$-0.466686\pi$
$617$	12.6966	−	2.01095i	0.511148	−	0.0809578i	0.406680	+	0.913571i	$0.366686\pi$
$618$	−1.08720	−	4.36318i	−0.0437337	−	0.175513i
$619$	−8.19755	−	25.2295i	−0.329487	−	1.01406i	−0.969374	−	0.245589i	$-0.921019\pi$
$619$	−8.19755	−	25.2295i	−0.329487	−	1.01406i	0.639887	−	0.768469i	$-0.278981\pi$
$620$	26.1334	−	27.0464i	1.04954	−	1.08621i
$621$	−2.55940	−	0.614457i	−0.102705	−	0.0246573i
$622$	13.6429	−	16.2543i	0.547031	−	0.651738i
$623$	−3.22865	−	6.33658i	−0.129353	−	0.253870i
$624$	5.42426	−	1.05116i	0.217144	−	0.0420799i
$625$	6.13785	−	18.8904i	0.245514	−	0.755614i
$626$	−2.86979	+	40.9559i	−0.114700	+	1.63693i
$627$	−0.0234427	+	0.297868i	−0.000936212	+	0.0118957i
$628$	24.1386	−	6.23531i	0.963234	−	0.248816i
$629$	−3.66220	+	1.51693i	−0.146021	+	0.0604840i
$630$	−2.20797	+	9.55754i	−0.0879676	+	0.380782i
$631$	12.0127	+	16.5340i	0.478217	+	0.658210i	0.978161	−	0.207848i	$-0.0666460\pi$
$631$	12.0127	+	16.5340i	0.478217	+	0.658210i	−0.499944	+	0.866058i	$0.666646\pi$
$632$	−34.7449	+	15.4516i	−1.38208	+	0.614632i
$633$	−6.80908	−	4.94709i	−0.270637	−	0.196629i
$634$	−34.9247	+	3.05049i	−1.38704	+	0.121151i
$635$	−26.6837	−	4.22629i	−1.05891	−	0.167715i
$636$	−1.92162	−	0.937918i	−0.0761974	−	0.0371909i
$637$	−21.7885	−	13.3520i	−0.863292	−	0.529026i
$638$	−0.000593433	−	0.0691315i	−2.34942e−5	−	0.00273694i
$639$	1.89938	+	24.1339i	0.0751384	+	0.954724i
$640$	−8.40066	−	21.3890i	−0.332065	−	0.845473i
$641$	27.6577	+	32.3830i	1.09241	+	1.27905i	0.957575	+	0.288183i	$0.0930510\pi$
$641$	27.6577	+	32.3830i	1.09241	+	1.27905i	0.134837	+	0.990868i	$0.456949\pi$
$642$	0.696130	−	1.15818i	0.0274741	−	0.0457097i
$643$	−2.49973	−	4.07919i	−0.0985798	−	0.160868i	0.799548	−	0.600602i	$-0.205072\pi$
$643$	−2.49973	−	4.07919i	−0.0985798	−	0.160868i	−0.898128	+	0.439735i	$0.855072\pi$
$644$	3.20459	+	1.26338i	0.126278	+	0.0497840i
$645$	1.59760	−	1.87055i	0.0629055	−	0.0736529i
$646$	9.24320	−	3.09126i	0.363669	−	0.121624i
$647$	−28.0505	−	28.0505i	−1.10278	−	1.10278i	−0.994074	−	0.108705i	$-0.965330\pi$
$647$	−28.0505	−	28.0505i	−1.10278	−	1.10278i	−0.108705	−	0.994074i	$-0.534670\pi$
$648$	−16.7713	−	15.9290i	−0.658838	−	0.625750i
$649$	0.106949	+	0.445476i	0.00419813	+	0.0174865i
$650$	5.17631	−	2.19634i	0.203031	−	0.0861475i
$651$	1.49977	−	2.94346i	0.0587805	−	0.115363i
$652$	−0.171664	−	9.99818i	−0.00672287	−	0.391559i
$653$	−18.4480	+	44.5374i	−0.721926	+	1.74288i	−0.0541347	+	0.998534i	$0.517240\pi$
$653$	−18.4480	+	44.5374i	−0.721926	+	1.74288i	−0.667791	+	0.744349i	$0.732760\pi$
$654$	2.38973	+	2.34905i	0.0934457	+	0.0918551i
$655$	−9.96731			−0.389455
$656$	25.0948	−	5.12344i	0.979788	−	0.200037i
$657$	−28.4023			−1.10808
$658$	−9.14221	−	8.98659i	−0.356400	−	0.350334i
$659$	5.22152	−	12.6059i	0.203402	−	0.491055i	−0.788956	−	0.614450i	$-0.789378\pi$
$659$	5.22152	−	12.6059i	0.203402	−	0.491055i	0.992358	+	0.123395i	$0.0393781\pi$
$660$	−0.00276541	−	0.161065i	−0.000107644	−	0.00626946i
$661$	−8.04929	+	15.7976i	−0.313081	+	0.614456i	−0.992904	−	0.118920i	$-0.962057\pi$
$661$	−8.04929	+	15.7976i	−0.313081	+	0.614456i	0.679823	+	0.733376i	$0.262057\pi$
$662$	−6.28170	+	2.66537i	−0.244145	+	0.103592i
$663$	−0.294942	−	1.22852i	−0.0114546	−	0.0477118i
$664$	−32.5730	−	30.9372i	−1.26408	−	1.20060i
$665$	−12.7093	−	12.7093i	−0.492846	−	0.492846i
$666$	−16.9006	+	5.65218i	−0.654885	+	0.219018i
$667$	−0.356706	+	0.417648i	−0.0138117	+	0.0161714i
$668$	−23.8159	−	9.38920i	−0.921466	−	0.363279i
$669$	2.72760	+	4.45104i	0.105455	+	0.172087i
$670$	10.4364	−	17.3635i	0.403195	−	0.670812i
$671$	−0.317850	−	0.372155i	−0.0122705	−	0.0143669i
$672$	−1.25540	−	1.58057i	−0.0484281	−	0.0609718i
$673$	−2.35035	−	29.8640i	−0.0905992	−	1.15117i	−0.859268	−	0.511526i	$-0.829081\pi$
$673$	−2.35035	−	29.8640i	−0.0905992	−	1.15117i	0.768669	−	0.639647i	$-0.220919\pi$
$674$	−0.296389	−	34.5275i	−0.0114165	−	1.32995i
$675$	1.33836	+	0.820149i	0.0515136	+	0.0315676i
$676$	−13.7863	−	6.72890i	−0.530242	−	0.258804i
$677$	−7.34411	−	1.16319i	−0.282257	−	0.0447051i	0.0137008	−	0.999906i	$-0.495639\pi$
$677$	−7.34411	−	1.16319i	−0.282257	−	0.0447051i	−0.295958	+	0.955201i	$0.595639\pi$
$678$	2.62116	−	0.228945i	0.100665	−	0.00879259i
$679$	1.61244	+	1.17151i	0.0618798	+	0.0449583i
$680$	−4.80131	+	2.13522i	−0.184122	+	0.0818818i
$681$	4.31031	+	5.93263i	0.165171	+	0.227339i
$682$	0.384671	−	1.66511i	0.0147298	−	0.0637603i
$683$	33.4642	−	13.8613i	1.28047	−	0.530389i	0.364340	−	0.931266i	$-0.381295\pi$
$683$	33.4642	−	13.8613i	1.28047	−	0.530389i	0.916132	+	0.400877i	$0.131295\pi$
$684$	42.4246	−	10.9588i	1.62214	−	0.419021i
$685$	−2.89762	+	36.8178i	−0.110713	+	1.40674i
$686$	−1.46522	+	20.9108i	−0.0559424	+	0.798376i
$687$	0.119486	−	0.367741i	0.00455869	−	0.0140302i
$688$	−3.03360	−	15.6542i	−0.115655	−	0.596811i
$689$	7.26354	+	14.2555i	0.276719	+	0.543091i
$690$	−0.822775	+	0.980260i	−0.0313225	+	0.0373179i
$691$	7.84909	+	1.88440i	0.298593	+	0.0716859i	0.379974	−	0.924997i	$-0.375933\pi$
$691$	7.84909	+	1.88440i	0.298593	+	0.0716859i	−0.0813807	+	0.996683i	$0.525933\pi$
$692$	−25.8608	+	26.7643i	−0.983079	+	1.01743i
$693$	0.137739	+	0.423916i	0.00523226	+	0.0161032i
$694$	−6.43344	−	25.8188i	−0.244210	−	0.980069i
$695$	22.7363	−	3.60108i	0.862439	−	0.136597i
$696$	0.303429	−	0.107304i	0.0115015	−	0.00406734i
$697$	−1.42400	−	5.68101i	−0.0539378	−	0.215183i
$698$	−16.0487	−	21.6950i	−0.607452	−	0.821169i
$699$	0.519964	+	3.28292i	0.0196668	+	0.124172i
$700$	−1.58470	−	1.30709i	−0.0598962	−	0.0494033i
$701$	15.9918	−	5.19606i	0.604003	−	0.196253i	0.00897818	−	0.999960i	$-0.497142\pi$
$701$	15.9918	−	5.19606i	0.604003	−	0.196253i	0.595025	+	0.803707i	$0.297142\pi$
$702$	−1.90308	−	11.3824i	−0.0718272	−	0.429599i
$703$	7.62274	−	31.7510i	0.287497	−	1.19751i
$704$	−0.827865	−	0.636370i	−0.0312013	−	0.0239841i
$705$	4.24373	−	2.16229i	0.159828	−	0.0814364i
$706$	3.09222	−	20.6703i	0.116377	−	0.777938i
$707$	14.3423	+	4.66010i	0.539398	+	0.175261i
$708$	−1.79909	+	1.14543i	−0.0676141	+	0.0430478i
$709$	−33.4973	−	2.63630i	−1.25802	−	0.0990083i	−0.568139	−	0.822932i	$-0.692337\pi$
$709$	−33.4973	−	2.63630i	−1.25802	−	0.0990083i	−0.689880	+	0.723924i	$0.742337\pi$
$710$	22.1724	+	8.96191i	0.832115	+	0.336334i
$711$	14.9597	+	36.1158i	0.561031	+	1.35445i
$712$	8.56987	−	14.8288i	0.321170	−	0.555732i
$713$	−10.9841	+	7.98041i	−0.411357	+	0.298869i
$714$	−0.348387	+	0.302761i	−0.0130380	+	0.0113305i
$715$	−0.708464	+	0.975117i	−0.0264951	+	0.0364673i
$716$	3.28832	−	2.90758i	0.122890	−	0.108661i
$717$	−0.751747	+	4.74634i	−0.0280745	+	0.177255i
$718$	−3.30154	+	1.71807i	−0.123212	+	0.0641180i
$719$	−11.1696	+	18.2272i	−0.416556	+	0.679758i	−0.990248	−	0.139313i	$-0.955511\pi$
$719$	−11.1696	+	18.2272i	−0.416556	+	0.679758i	0.573692	+	0.819071i	$0.305511\pi$
$720$	−22.2035	+	8.06706i	−0.827475	+	0.300641i
$721$	12.2533	−	0.964354i	0.456336	−	0.0359144i
$722$	−16.0700	+	50.9422i	−0.598064	+	1.89587i
$723$	2.36555	−	2.02037i	0.0879756	−	0.0751383i
$724$	11.1703	−	1.07236i	0.415143	−	0.0398541i
$725$	0.279275	−	0.171140i	0.0103720	−	0.00635599i
$726$	2.50009	+	4.00226i	0.0927872	+	0.148538i
$727$	30.3591	+	25.9291i	1.12596	+	0.961658i	0.999540	−	0.0303193i	$-0.00965240\pi$
$727$	30.3591	+	25.9291i	1.12596	+	0.961658i	0.126417	+	0.991977i	$0.459652\pi$
$728$	0.388878	+	15.0977i	0.0144128	+	0.559559i
$729$	−15.6572	+	15.6572i	−0.579895	+	0.579895i
$730$	−12.5230	+	25.1082i	−0.463497	+	0.929298i
$731$	−3.54546	+	0.851191i	−0.131134	+	0.0314824i
$732$	1.15694	−	1.96281i	0.0427617	−	0.0725475i
$733$	−19.5528	−	9.96267i	−0.722201	−	0.367980i	0.0539359	−	0.998544i	$-0.482823\pi$
$733$	−19.5528	−	9.96267i	−0.722201	−	0.367980i	−0.776137	+	0.630565i	$0.782823\pi$
$734$	−20.7030	−	14.7718i	−0.764161	−	0.545236i
$735$	−3.20443	−	1.32732i	−0.118197	−	0.0489588i
$736$	1.64809	+	8.13032i	0.0607494	+	0.299687i
$737$		−	0.920549i		−	0.0339089i
$738$	−4.60101	−	25.9252i	−0.169365	−	0.954319i
$739$			5.96203i			0.219317i	0.993969	+	0.109658i	$0.0349757\pi$
$739$			5.96203i			0.219317i	−0.993969	+	0.109658i	$0.965024\pi$
$740$	−2.45507	+	17.4326i	−0.0902502	+	0.640836i
$741$	9.61537	+	3.98282i	0.353229	+	0.146312i
$742$	3.39484	−	4.75796i	0.124629	−	0.174670i
$743$	5.88472	+	2.99841i	0.215889	+	0.110001i	0.558591	−	0.829443i	$-0.311342\pi$
$743$	5.88472	+	2.99841i	0.215889	+	0.110001i	−0.342702	+	0.939444i	$0.611342\pi$
$744$	7.91261	−	0.828223i	0.290090	−	0.0303641i
$745$	−20.9906	+	5.03940i	−0.769036	+	0.184629i
$746$	16.1917	+	8.07575i	0.592819	+	0.295674i
$747$	−32.6559	+	32.6559i	−1.19482	+	1.19482i
$748$	−0.137010	+	0.195552i	−0.00500958	+	0.00715008i
$749$	2.80869	+	2.39885i	0.102627	+	0.0876519i
$750$	4.34806	−	2.71611i	0.158769	−	0.0991782i
$751$	−18.6109	+	11.4048i	−0.679122	+	0.416166i	−0.818838	−	0.574025i	$-0.805381\pi$
$751$	−18.6109	+	11.4048i	−0.679122	+	0.416166i	0.139716	+	0.990192i	$0.455381\pi$
$752$	6.17236	−	30.2497i	0.225083	−	1.10309i
$753$	6.17362	−	5.27277i	0.224979	−	0.192150i
$754$	−2.29656	−	0.724463i	−0.0836358	−	0.0263834i
$755$	−34.7027	+	2.73116i	−1.26296	+	0.0993971i
$756$	−3.36773	+	2.53626i	−0.122483	+	0.0922430i
$757$	−14.4608	+	23.5979i	−0.525588	+	0.857681i	−0.999741	−	0.0227611i	$-0.992754\pi$
$757$	−14.4608	+	23.5979i	−0.525588	+	0.857681i	0.474153	+	0.880442i	$0.342754\pi$
$758$	−12.4840	−	23.9900i	−0.453441	−	0.871355i
$759$	−0.00909723	+	0.0574376i	−0.000330209	+	0.00208485i
$760$	9.01777	−	42.3361i	0.327109	−	1.53569i
$761$	14.4672	−	19.9124i	0.524435	−	0.721822i	−0.461835	−	0.886966i	$-0.652809\pi$
$761$	14.4672	−	19.9124i	0.524435	−	0.721822i	0.986270	+	0.165143i	$0.0528087\pi$
$762$	−3.74876	−	4.31370i	−0.135803	−	0.156269i
$763$	−7.41028	+	5.38389i	−0.268270	+	0.194910i
$764$	20.2973	+	46.7170i	0.734329	+	1.69016i
$765$	2.06724	+	4.99075i	0.0747411	+	0.180441i
$766$	−7.56712	+	18.7216i	−0.273411	+	0.676439i
$767$	15.9088	+	1.25205i	0.574434	+	0.0452089i
$768$	1.54770	−	4.60810i	0.0558479	−	0.166280i
$769$	40.1606	+	13.0490i	1.44823	+	0.470557i	0.924452	−	0.381299i	$-0.124523\pi$
$769$	40.1606	+	13.0490i	1.44823	+	0.470557i	0.523775	+	0.851857i	$0.324523\pi$
$770$	0.435482	+	0.0651468i	0.0156937	+	0.00234773i
$771$	−2.77214	+	1.41248i	−0.0998362	+	0.0508691i
$772$	41.8303	+	2.57044i	1.50551	+	0.0925122i
$773$	5.90112	−	24.5799i	0.212249	−	0.884079i	−0.759961	−	0.649968i	$-0.774782\pi$
$773$	5.90112	−	24.5799i	0.212249	−	0.884079i	0.972210	−	0.234111i	$-0.0752179\pi$
$774$	−16.1679	+	2.70321i	−0.581143	+	0.0971647i
$775$	7.70042	−	2.50202i	0.276607	−	0.0898751i
$776$	−0.253261	+	4.79324i	−0.00909156	+	0.172067i
$777$	0.241903	+	1.52732i	0.00867822	+	0.0547921i
$778$	33.7129	−	24.9388i	1.20867	−	0.894099i
$779$	44.7551	+	18.0170i	1.60352	+	0.645526i
$780$	−5.36550	−	1.64207i	−0.192116	−	0.0587957i
$781$	1.07332	−	0.169997i	0.0384064	−	0.00608297i
$782$	1.84067	−	0.458652i	0.0658223	−	0.0164014i
$783$	−0.207731	−	0.639329i	−0.00742369	−	0.0228478i
$784$	−19.6700	+	10.8886i	−0.702499	+	0.388877i
$785$	−24.6193	−	5.91057i	−0.878701	−	0.210957i
$786$	−1.61499	−	1.35553i	−0.0576048	−	0.0483502i
$787$	−5.27600	−	10.3547i	−0.188069	−	0.369106i	0.777649	−	0.628698i	$-0.216412\pi$
$787$	−5.27600	−	10.3547i	−0.188069	−	0.369106i	−0.965718	+	0.259592i	$0.916412\pi$
$788$	2.30612	−	1.22534i	0.0821523	−	0.0436510i
$789$	0.412328	−	1.26902i	0.0146793	−	0.0451782i
$790$	38.5231	+	2.69932i	1.37059	+	0.0960376i
$791$	−0.564284	+	7.16991i	−0.0200636	+	0.254933i
$792$	−0.675902	+	0.833939i	−0.0240171	+	0.0296327i
$793$	−15.7499	+	6.52384i	−0.559297	+	0.231668i
$794$	−7.00240	−	1.61768i	−0.248506	−	0.0574094i
$795$	1.27642	+	1.75684i	0.0452700	+	0.0623088i
$796$	3.22800	−	14.5409i	0.114413	−	0.515389i
$797$	2.99527	+	2.17619i	0.106098	+	0.0770847i	0.639569	−	0.768734i	$-0.279113\pi$
$797$	2.99527	+	2.17619i	0.106098	+	0.0770847i	−0.533471	+	0.845818i	$0.679113\pi$
$798$	−0.330837	−	3.78771i	−0.0117115	−	0.134084i
$799$	−6.97274	−	1.10437i	−0.246678	−	0.0390700i
$800$	0.563539	−	4.91493i	0.0199241	−	0.173769i
$801$	−15.0125	−	9.19965i	−0.530440	−	0.325054i
$802$	29.3697	−	0.252113i	1.03708	−	0.00890240i
$803$	0.100031	+	1.27102i	0.00353003	+	0.0448533i
$804$	4.05240	−	1.39406i	0.142917	−	0.0491647i
$805$	−2.27192	−	2.66008i	−0.0800748	−	0.0937555i
$806$	−51.0208	−	30.6663i	−1.79713	−	1.08017i
$807$	3.33210	+	5.43749i	0.117295	+	0.191409i
$808$	9.38475	+	35.0845i	0.330154	+	1.23427i
$809$	15.0042	−	17.5677i	0.527520	−	0.617646i	−0.431111	−	0.902299i	$-0.641878\pi$
$809$	15.0042	−	17.5677i	0.527520	−	0.617646i	0.958631	+	0.284653i	$0.0918782\pi$
$810$	7.45037	+	22.2774i	0.261779	+	0.782747i
$811$	15.3741	+	15.3741i	0.539859	+	0.539859i	0.923487	−	0.383629i	$-0.125326\pi$
$811$	15.3741	+	15.3741i	0.539859	+	0.539859i	−0.383629	+	0.923487i	$0.625326\pi$
$812$	0.152518	+	0.866420i	0.00535234	+	0.0304054i
$813$	−0.171985	−	0.716370i	−0.00603179	−	0.0251242i
$814$	0.312461	+	0.736405i	0.0109518	+	0.0258110i
$815$	−4.61039	+	9.04841i	−0.161495	+	0.316952i
$816$	−1.06833	−	0.307000i	−0.0373992	−	0.0107472i
$817$	11.4943	−	27.7496i	0.402133	−	0.970835i
$818$	27.2155	−	27.6868i	0.951567	−	0.968045i
$819$	15.5260			0.542522
$820$	−24.9471	−	7.36340i	−0.871189	−	0.257141i
$821$	−25.3798			−0.885761			−0.442880	−	0.896581i	$-0.646043\pi$
$821$	−25.3798			−0.885761			−0.442880	+	0.896581i	$0.646043\pi$
$822$	−5.47663	+	5.57147i	−0.191020	+	0.194327i
$823$	15.0356	−	36.2991i	0.524108	−	1.26531i	−0.411223	−	0.911535i	$-0.634898\pi$
$823$	15.0356	−	36.2991i	0.524108	−	1.26531i	0.935331	−	0.353774i	$-0.115102\pi$
$824$	18.0097	+	23.4915i	0.627398	+	0.818366i
$825$	0.0157444	−	0.0309000i	0.000548148	−	0.00107580i
$826$	−2.27713	−	5.36671i	−0.0792314	−	0.186732i
$827$	11.3988	+	47.4794i	0.396375	+	1.65102i	0.712033	+	0.702146i	$0.247775\pi$
$827$	11.3988	+	47.4794i	0.396375	+	1.65102i	−0.315658	+	0.948873i	$0.602225\pi$
$828$	8.39903	−	1.47850i	0.291886	−	0.0513815i
$829$	−9.69216	−	9.69216i	−0.336623	−	0.336623i	0.518472	−	0.855095i	$-0.326501\pi$
$829$	−9.69216	−	9.69216i	−0.336623	−	0.336623i	−0.855095	+	0.518472i	$0.826501\pi$
$830$	14.4701	+	43.2670i	0.502263	+	1.50182i
$831$	−5.73990	+	6.72056i	−0.199115	+	0.233134i
$832$	−29.9926	+	20.5755i	−1.03980	+	0.713328i
$833$	2.68619	+	4.38347i	0.0930711	+	0.151878i
$834$	4.17368	+	2.50861i	0.144523	+	0.0868661i
$835$	16.8845	+	19.7693i	0.584314	+	0.684143i
$836$	−0.639831	−	1.85993i	−0.0221290	−	0.0643269i
$837$	−1.30377	−	16.5660i	−0.0450650	−	0.572606i
$838$	25.5869	−	0.219641i	0.883884	−	0.00758737i
$839$	0.542094	+	0.332196i	0.0187152	+	0.0114687i	0.531825	−	0.846854i	$-0.321507\pi$
$839$	0.542094	+	0.332196i	0.0187152	+	0.0114687i	−0.513110	+	0.858323i	$0.671507\pi$
$840$	0.372698	+	2.01572i	0.0128593	+	0.0695489i
$841$	28.5044	+	4.51466i	0.982911	+	0.155678i
$842$	2.66395	+	30.4992i	0.0918058	+	1.05107i
$843$	−1.63036	−	1.18452i	−0.0561525	−	0.0407972i
$844$	54.0883	+	12.0073i	1.86180	+	0.413308i
$845$	9.15741	+	12.6041i	0.315025	+	0.433594i
$846$	−30.9237	−	7.14396i	−1.06318	−	0.245614i
$847$	−11.9171	+	4.93623i	−0.409477	+	0.169611i
$848$	14.0625	+	0.622027i	0.482909	+	0.0213605i
$849$	−0.722750	+	9.18341i	−0.0248047	+	0.315174i
$850$	−1.12848	−	0.0790731i	−0.0387066	−	0.00271218i
$851$	1.96390	−	6.04427i	0.0673218	−	0.207195i
$852$	2.37376	+	4.46748i	0.0813238	+	0.153053i
$853$	−0.573733	−	1.12601i	−0.0196442	−	0.0385540i	0.880976	−	0.473161i	$-0.156887\pi$
$853$	−0.573733	−	1.12601i	−0.0196442	−	0.0385540i	−0.900620	+	0.434607i	$0.856887\pi$
$854$	4.77027	+	4.00389i	0.163235	+	0.137010i
$855$	−43.2695	−	10.3881i	−1.47978	−	0.355265i
$856$	−1.16486	+	8.81882i	−0.0398142	+	0.301421i
$857$	10.9780	+	33.7868i	0.375001	+	1.15413i	0.943478	+	0.331435i	$0.107533\pi$
$857$	10.9780	+	33.7868i	0.375001	+	1.15413i	−0.568477	+	0.822699i	$0.692467\pi$
$858$	−0.247405	+	0.0616475i	−0.00844628	+	0.00210461i
$859$	15.5005	−	2.45504i	0.528870	−	0.0837648i	0.113711	−	0.993514i	$-0.463726\pi$
$859$	15.5005	−	2.45504i	0.528870	−	0.0837648i	0.415159	+	0.909749i	$0.363726\pi$
$860$	−4.73896	+	15.4846i	−0.161597	+	0.528022i
$861$	−2.28464	+	0.0228018i	−0.0778604	+	0.000777085i
$862$	22.5145	−	16.6549i	0.766847	−	0.567268i
$863$	−2.51213	−	15.8609i	−0.0855138	−	0.539913i	−0.992837	−	0.119479i	$-0.961878\pi$
$863$	−2.51213	−	15.8609i	−0.0855138	−	0.539913i	0.907323	−	0.420434i	$-0.138122\pi$
$864$	−9.53844	−	3.47942i	−0.324504	−	0.118372i
$865$	35.9463	−	11.6797i	1.22221	−	0.397121i
$866$	2.79185	−	0.466786i	0.0948711	−	0.0158620i
$867$	1.14638	−	4.77502i	0.0389331	−	0.162168i
$868$	−1.33381	+	21.7059i	−0.0452724	+	0.736746i
$869$	1.56352	−	0.796652i	0.0530387	−	0.0270246i
$870$	−0.323255	−	0.0483580i	−0.0109594	−	0.00163949i
$871$	−30.4957	−	9.90867i	−1.03331	−	0.335742i
$872$	−20.5905	−	7.91406i	−0.697281	−	0.268004i
$873$	4.91924	+	0.387152i	0.166491	+	0.0131031i
$874$	−5.85579	+	14.4876i	−0.198075	+	0.490051i
$875$	5.36273	+	12.9468i	0.181293	+	0.437681i
$876$	−5.44375	+	2.36516i	−0.183927	+	0.0799114i
$877$	−9.05934	+	6.58199i	−0.305912	+	0.222258i	−0.730140	−	0.683297i	$-0.760545\pi$
$877$	−9.05934	+	6.58199i	−0.305912	+	0.222258i	0.424228	+	0.905555i	$0.360545\pi$
$878$	−25.0527	−	28.8281i	−0.845486	−	0.972901i
$879$	1.54838	−	2.13116i	0.0522254	−	0.0718821i
$880$	0.439205	+	0.965207i	0.0148056	+	0.0325371i
$881$	−2.54746	+	16.0840i	−0.0858261	+	0.541885i	0.906886	+	0.421376i	$0.138453\pi$
$881$	−2.54746	+	16.0840i	−0.0858261	+	0.541885i	−0.992712	+	0.120509i	$0.961547\pi$
$882$	10.6693	+	20.5027i	0.359255	+	0.690363i
$883$	1.85331	−	3.02432i	0.0623688	−	0.101777i	−0.819936	−	0.572455i	$-0.805991\pi$
$883$	1.85331	−	3.02432i	0.0623688	−	0.101777i	0.882305	+	0.470679i	$0.155991\pi$
$884$	5.00343	+	6.64372i	0.168284	+	0.223453i
$885$	2.15929	−	0.169940i	0.0725838	−	0.00571247i
$886$	39.4739	+	12.4523i	1.32615	+	0.418342i
$887$	−2.00151	+	1.70945i	−0.0672041	+	0.0573977i	−0.682416	−	0.730964i	$-0.739071\pi$
$887$	−2.00151	+	1.70945i	−0.0672041	+	0.0573977i	0.615212	+	0.788362i	$0.289071\pi$
$888$	−2.76859	+	2.49070i	−0.0929077	+	0.0835825i
$889$	13.3196	−	8.16228i	0.446726	−	0.273754i
$890$	−14.7519	+	9.21508i	−0.494485	+	0.308890i
$891$	0.811651	+	0.693216i	0.0271913	+	0.0232236i
$892$	−28.1444	−	19.7189i	−0.942344	−	0.660237i
$893$	41.1214	−	41.1214i	1.37608	−	1.37608i
$894$	−4.08643	−	2.03815i	−0.136671	−	0.0681658i
$895$	−4.33457	+	1.04064i	−0.144889	+	0.0347847i
$896$	11.7259	+	6.24979i	0.391734	+	0.208791i
$897$	1.80486	+	0.919622i	0.0602625	+	0.0307053i
$898$	13.6547	−	19.1374i	0.455664	−	0.638624i
$899$	−3.20357	−	1.32696i	−0.106845	−	0.0442566i
$900$	−5.03608	−	0.709241i	−0.167869	−	0.0236414i
$901$		−	3.21879i		−	0.107233i
$902$	−1.14396	+	0.297205i	−0.0380898	+	0.00989584i
$903$			1.42241i			0.0473348i
$904$	−15.2252	+	8.25816i	−0.506382	+	0.274662i
$905$	−10.5288	−	4.36119i	−0.349990	−	0.144971i
$906$	−5.99426	−	4.27696i	−0.199146	−	0.142092i
$907$	−16.4070	−	8.35979i	−0.544786	−	0.277582i	0.159862	−	0.987139i	$-0.448895\pi$
$907$	−16.4070	−	8.35979i	−0.544786	−	0.277582i	−0.704648	+	0.709557i	$0.748895\pi$
$908$	−41.5868	−	24.5125i	−1.38011	−	0.813475i
$909$	36.3042	−	8.71586i	1.20413	−	0.289087i
$910$	6.84564	−	13.7253i	0.226931	−	0.454990i
$911$	31.6959	−	31.6959i	1.05013	−	1.05013i	0.0514574	−	0.998675i	$-0.483613\pi$
$911$	31.6959	−	31.6959i	1.05013	−	1.05013i	0.998675	−	0.0514574i	$-0.0163866\pi$
$912$	7.21875	−	5.63327i	0.239037	−	0.186536i
$913$	1.57638	+	1.34636i	0.0521707	+	0.0445579i
$914$	15.8491	+	25.3720i	0.524243	+	0.839230i
$915$	−1.97289	+	1.20899i	−0.0652217	+	0.0399679i
$916$	0.243242	+	2.53374i	0.00803693	+	0.0837172i
$917$	4.38251	−	3.74302i	0.144723	−	0.123605i
$918$	−0.698471	+	2.21416i	−0.0230530	+	0.0730783i
$919$	−24.0266	+	1.89093i	−0.792564	+	0.0623761i	−0.468276	−	0.883582i	$-0.655125\pi$
$919$	−24.0266	+	1.89093i	−0.792564	+	0.0623761i	−0.324288	+	0.945958i	$0.605125\pi$
$920$	2.39622	−	8.07681i	0.0790011	−	0.266285i
$921$	4.14692	−	6.76716i	0.136646	−	0.222986i
$922$	−5.34158	+	2.77968i	−0.175916	+	0.0915439i
$923$	5.92144	−	37.3865i	0.194906	−	1.23059i
$924$	0.0617008	+	0.0697802i	0.00202981	+	0.00229560i
$925$	−2.22771	+	3.06618i	−0.0732465	+	0.100815i
$926$	−14.6675	+	12.7466i	−0.482003	+	0.418878i
$927$	24.6186	−	17.8865i	0.808581	−	0.587469i
$928$	−1.55053	+	1.44382i	−0.0508986	+	0.0473959i
$929$	5.55638	+	13.4143i	0.182299	+	0.440108i	0.988440	−	0.151615i	$-0.0484475\pi$
$929$	5.55638	+	13.4143i	0.182299	+	0.440108i	−0.806141	+	0.591724i	$0.798448\pi$
$930$	−7.49089	−	3.02776i	−0.245636	−	0.0992841i
$931$	−42.2193	−	3.32273i	−1.38368	−	0.108898i
$932$	−11.7512	−	18.4573i	−0.384922	−	0.604588i
$933$	−4.33580	−	1.40879i	−0.141948	−	0.0461216i
$934$	−0.515941	+	3.44887i	−0.0168821	+	0.112851i
$935$	0.216058	−	0.110087i	0.00706586	−	0.00360024i
$936$	20.3512	+	31.3675i	0.665201	+	1.02528i
$937$	−2.04042	+	8.49895i	−0.0666575	+	0.277649i	−0.995738	−	0.0922296i	$-0.970601\pi$
$937$	−2.04042	+	8.49895i	−0.0666575	+	0.277649i	0.929080	+	0.369878i	$0.120601\pi$
$938$	1.93174	+	11.5537i	0.0630735	+	0.377243i
$939$	8.38846	−	2.72558i	0.273747	−	0.0889458i
$940$	−19.9501	+	24.1874i	−0.650702	+	0.788905i
$941$	−0.700766	−	4.42446i	−0.0228443	−	0.144233i	0.973630	−	0.228134i	$-0.0732623\pi$
$941$	−0.700766	−	4.42446i	−0.0228443	−	0.144233i	−0.996474	+	0.0839002i	$0.973262\pi$
$942$	−3.18521	−	4.30585i	−0.103780	−	0.140292i
$943$	8.40874	+	4.17929i	0.273826	+	0.136096i
$944$	7.85766	−	11.6351i	0.255745	−	0.378691i
$945$	4.22885	−	0.669784i	0.137564	−	0.0217881i
$946$	0.177912	+	0.714002i	0.00578443	+	0.0232142i
$947$	−6.20996	−	19.1123i	−0.201797	−	0.621066i	−0.999830	−	0.0184527i	$-0.994126\pi$
$947$	−6.20996	−	19.1123i	−0.201797	−	0.621066i	0.798033	−	0.602614i	$-0.205874\pi$
$948$	5.87474	+	5.67642i	0.190803	+	0.184361i
$949$	43.1828	+	10.3673i	1.40177	+	0.336536i
$950$	5.99100	−	7.13773i	0.194374	−	0.231578i
$951$	3.41922	+	6.71059i	0.110876	+	0.217606i
$952$	1.30924	−	2.74186i	0.0424328	−	0.0888643i
$953$	−15.8667	+	48.8327i	−0.513973	+	1.58185i	0.271169	+	0.962532i	$0.412590\pi$
$953$	−15.8667	+	48.8327i	−0.513973	+	1.58185i	−0.785143	+	0.619315i	$0.787410\pi$
$954$	1.01149	−	14.4354i	0.0327482	−	0.467362i
$955$	4.05857	−	51.5690i	0.131332	−	1.66873i
$956$	−7.91184	−	30.6289i	−0.255887	−	0.990610i
$957$	−0.0137216	+	0.00568366i	−0.000443555	+	0.000183727i
$958$	−7.21060	+	31.2122i	−0.232964	+	1.00842i
$959$	−12.5521	−	17.2765i	−0.405329	−	0.557888i
$960$	−3.58387	+	3.39514i	−0.115669	+	0.109578i
$961$	−44.2657	−	32.1609i	−1.42793	−	1.03745i
$962$	27.7588	−	2.42458i	0.894978	−	0.0781717i
$963$	9.03213	+	1.43055i	0.291056	+	0.0460988i
$964$	−8.98257	+	18.4037i	−0.289309	+	0.592742i
$965$	−36.2896	−	22.2383i	−1.16820	−	0.715876i
$966$	−0.00635213	−	0.739986i	−0.000204376	−	0.0238087i
$967$	−1.86495	−	23.6964i	−0.0599726	−	0.762024i	−0.951221	−	0.308509i	$-0.900170\pi$
$967$	−1.86495	−	23.6964i	−0.0599726	−	0.762024i	0.891249	−	0.453515i	$-0.149830\pi$
$968$	−25.5935	−	17.6061i	−0.822608	−	0.565881i
$969$	−1.35983	−	1.59216i	−0.0436842	−	0.0511476i
$970$	2.51121	−	4.17801i	0.0806302	−	0.134148i
$971$	−17.8532	−	29.1338i	−0.572937	−	0.934948i	−0.999535	−	0.0305066i	$-0.990288\pi$
$971$	−17.8532	−	29.1338i	−0.572937	−	0.934948i	0.426598	−	0.904442i	$-0.359712\pi$
$972$	−5.77226	+	14.6415i	−0.185145	+	0.469625i
$973$	−8.64460	+	10.1215i	−0.277133	+	0.324481i
$974$	34.4251	−	11.5130i	1.10305	−	0.368900i
$975$	−0.854179	−	0.854179i	−0.0273556	−	0.0273556i
$976$	−1.83636	+	14.8857i	−0.0587805	+	0.476480i
$977$	0.974186	+	4.05778i	0.0311670	+	0.129820i	0.985784	−	0.168015i	$-0.0537356\pi$
$977$	0.974186	+	4.05778i	0.0311670	+	0.129820i	−0.954618	+	0.297835i	$0.903736\pi$
$978$	−1.97758	+	0.839099i	−0.0632360	+	0.0268314i
$979$	−0.358817	+	0.704218i	−0.0114678	+	0.0225069i
$980$	22.8291	−	0.391965i	0.729250	−	0.0125209i
$981$	−8.67820	+	20.9510i	−0.277073	+	0.668914i
$982$	−40.1973	−	39.5131i	−1.28275	−	1.26091i
$983$	−34.8359			−1.11109			−0.555546	−	0.831486i	$-0.687491\pi$
$983$	−34.8359			−1.11109			−0.555546	+	0.831486i	$0.687491\pi$
$984$	−3.04074	−	4.58583i	−0.0969352	−	0.146191i
$985$	−2.65209			−0.0845026
$986$	0.345502	+	0.339620i	0.0110030	+	0.0108157i
$987$	−1.05392	+	2.54438i	−0.0335465	+	0.0809885i
$988$	−68.5023	+	1.17615i	−2.17935	+	0.0374183i
$989$	2.65399	−	5.20876i	0.0843921	−	0.165629i
$990$	1.00355	−	0.425815i	0.0318951	−	0.0135333i
$991$	−1.78348	−	7.42875i	−0.0566543	−	0.235982i	0.936858	−	0.349711i	$-0.113720\pi$
$991$	−1.78348	−	7.42875i	−0.0566543	−	0.235982i	−0.993512	+	0.113729i	$0.963720\pi$
$992$	−45.6012	+	25.7570i	−1.44784	+	0.817785i
$993$	1.03659	+	1.03659i	0.0328952	+	0.0328952i
$994$	−13.1144	+	4.38594i	−0.415964	+	0.139114i
$995$	−9.82401	+	11.5024i	−0.311442	+	0.364652i
$996$	−3.53964	+	8.97838i	−0.112158	+	0.284491i
$997$	−31.0349	−	50.6444i	−0.982886	−	1.60392i	−0.781016	−	0.624512i	$-0.785298\pi$
$997$	−31.0349	−	50.6444i	−0.982886	−	1.60392i	−0.201870	−	0.979412i	$-0.564702\pi$
$998$	−13.1304	+	21.8456i	−0.415636	+	0.691511i
$999$	5.05167	+	5.91475i	0.159828	+	0.187134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.o.b.11.15	yes	288
4.3	odd	2	inner	164.2.o.b.11.13	✓	288
41.15	odd	40	inner	164.2.o.b.15.13	yes	288
164.15	even	40	inner	164.2.o.b.15.15	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.b.11.13	✓	288	4.3	odd	2	inner
164.2.o.b.11.15	yes	288	1.1	even	1	trivial
164.2.o.b.15.13	yes	288	41.15	odd	40	inner
164.2.o.b.15.15	yes	288	164.15	even	40	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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00855 + 0.991379i) q^{2} +(0.116266 - 0.280690i) q^{3} +(0.0343339 + 1.99971i) q^{4} +(0.922111 - 1.80974i) q^{5} +(0.395529 - 0.167826i) q^{6} +(0.274171 + 1.14200i) q^{7} +(-1.94784 + 2.05083i) q^{8} +(2.05605 + 2.05605i) q^{9} +O(q^{10})\)	\(q+(1.00855 + 0.991379i) q^{2} +(0.116266 - 0.280690i) q^{3} +(0.0343339 + 1.99971i) q^{4} +(0.922111 - 1.80974i) q^{5} +(0.395529 - 0.167826i) q^{6} +(0.274171 + 1.14200i) q^{7} +(-1.94784 + 2.05083i) q^{8} +(2.05605 + 2.05605i) q^{9} +(2.72414 - 0.911051i) q^{10} +(0.0847682 - 0.0992508i) q^{11} +(0.565289 + 0.222860i) q^{12} +(-2.37552 - 3.87650i) q^{13} +(-0.855645 + 1.42357i) q^{14} +(-0.400767 - 0.469238i) q^{15} +(-3.99764 + 0.137316i) q^{16} +(0.0717643 + 0.911852i) q^{17} +(0.0352975 + 4.11195i) q^{18} +(-6.42437 - 3.93686i) q^{19} +(3.65062 + 1.78181i) q^{20} +(0.352426 + 0.0558188i) q^{21} +(0.183888 - 0.0160617i) q^{22} +(-1.18641 - 0.861977i) q^{23} +(0.349182 + 0.785180i) q^{24} +(0.514040 + 0.707515i) q^{25} +(1.44726 - 6.26468i) q^{26} +(1.65823 - 0.686862i) q^{27} +(-2.27426 + 0.587471i) q^{28} +(0.0293854 - 0.373377i) q^{29} +(0.0610004 - 0.870561i) q^{30} +(2.86096 - 8.80513i) q^{31} +(-4.16794 - 3.82469i) q^{32} +(-0.0180031 - 0.0353330i) q^{33} +(-0.831614 + 0.990791i) q^{34} +(2.31955 + 0.556875i) q^{35} +(-4.04090 + 4.18209i) q^{36} +(1.33919 + 4.12161i) q^{37} +(-2.57636 - 10.3395i) q^{38} +(-1.36429 + 0.216082i) q^{39} +(1.91536 + 5.41619i) q^{40} +(-6.31398 + 1.06474i) q^{41} +(0.300100 + 0.405683i) q^{42} +(0.623604 + 3.93728i) q^{43} +(0.201383 + 0.166104i) q^{44} +(5.61683 - 1.82502i) q^{45} +(-0.342003 - 2.04553i) q^{46} +(-1.80179 + 7.50499i) q^{47} +(-0.426245 + 1.13806i) q^{48} +(5.00804 - 2.55172i) q^{49} +(-0.182983 + 1.22317i) q^{50} +(0.264291 + 0.0858735i) q^{51} +(7.67030 - 4.88344i) q^{52} +(-3.50822 - 0.276103i) q^{53} +(2.35334 + 0.951203i) q^{54} +(-0.101453 - 0.244929i) q^{55} +(-2.87610 - 1.66216i) q^{56} +(-1.85197 + 1.34553i) q^{57} +(0.399795 - 0.347436i) q^{58} +(-2.06311 + 2.83963i) q^{59} +(0.924578 - 0.817527i) q^{60} +(0.586573 - 3.70347i) q^{61} +(11.6146 - 6.04409i) q^{62} +(-1.78431 + 2.91173i) q^{63} +(-0.411845 - 7.98939i) q^{64} +(-9.20598 + 0.724526i) q^{65} +(0.0168715 - 0.0534829i) q^{66} +(5.36295 - 4.58039i) q^{67} +(-1.82097 + 0.174815i) q^{68} +(-0.379887 + 0.232795i) q^{69} +(1.78730 + 2.86119i) q^{70} +(6.33090 + 5.40710i) q^{71} +(-8.22148 + 0.211764i) q^{72} +(-6.90701 + 6.90701i) q^{73} +(-2.73544 + 5.48449i) q^{74} +(0.258358 - 0.0620262i) q^{75} +(7.65198 - 12.9820i) q^{76} +(0.136586 + 0.0695940i) q^{77} +(-1.59017 - 1.13460i) q^{78} +(12.4208 + 5.14485i) q^{79} +(-3.43776 + 7.36133i) q^{80} +8.17778i q^{81} +(-7.42350 - 5.18571i) q^{82} +15.8828i q^{83} +(-0.0995209 + 0.706664i) q^{84} +(1.71639 + 0.710954i) q^{85} +(-3.27440 + 4.58916i) q^{86} +(-0.101387 - 0.0516591i) q^{87} +(0.0384322 + 0.367170i) q^{88} +(-5.88802 + 1.41359i) q^{89} +(7.47413 + 3.72779i) q^{90} +(3.77568 - 3.77568i) q^{91} +(1.68296 - 2.40206i) q^{92} +(-2.13888 - 1.82678i) q^{93} +(-9.25748 + 5.78288i) q^{94} +(-13.0487 + 7.99625i) q^{95} +(-1.55814 + 0.725219i) q^{96} +(1.29043 - 1.10213i) q^{97} +(7.58057 + 2.39133i) q^{98} +(0.378352 - 0.0297770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

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