LMFDB - Embedded newform 164.2.o.b.15.13

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			15.13
Character	$\chi$	$=$	164.15
Dual form			164.2.o.b.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.652832 + 1.25452i) q^{2} +(-0.116266 - 0.280690i) q^{3} +(-1.14762 + 1.63798i) q^{4} +(0.922111 + 1.80974i) q^{5} +(0.276228 - 0.329100i) q^{6} +(-0.274171 + 1.14200i) q^{7} +(-2.80407 - 0.370385i) q^{8} +(2.05605 - 2.05605i) q^{9} +O(q^{10})$	\(q+(0.652832 + 1.25452i) q^{2} +(-0.116266 - 0.280690i) q^{3} +(-1.14762 + 1.63798i) q^{4} +(0.922111 + 1.80974i) q^{5} +(0.276228 - 0.329100i) q^{6} +(-0.274171 + 1.14200i) q^{7} +(-2.80407 - 0.370385i) q^{8} +(2.05605 - 2.05605i) q^{9} +(-1.66837 + 2.33826i) q^{10} +(-0.0847682 - 0.0992508i) q^{11} +(0.593192 + 0.131685i) q^{12} +(-2.37552 + 3.87650i) q^{13} +(-1.61165 + 0.401585i) q^{14} +(0.400767 - 0.469238i) q^{15} +(-1.36593 - 3.75955i) q^{16} +(0.0717643 - 0.911852i) q^{17} +(3.92161 + 1.23709i) q^{18} +(6.42437 - 3.93686i) q^{19} +(-4.02255 - 0.566504i) q^{20} +(0.352426 - 0.0558188i) q^{21} +(0.0691723 - 0.171137i) q^{22} +(1.18641 - 0.861977i) q^{23} +(0.222054 + 0.830137i) q^{24} +(0.514040 - 0.707515i) q^{25} +(-6.41395 - 0.449427i) q^{26} +(-1.65823 - 0.686862i) q^{27} +(-1.55593 - 1.75967i) q^{28} +(0.0293854 + 0.373377i) q^{29} +(0.850300 + 0.196435i) q^{30} +(-2.86096 - 8.80513i) q^{31} +(3.82469 - 4.16794i) q^{32} +(-0.0180031 + 0.0353330i) q^{33} +(1.19078 - 0.505257i) q^{34} +(-2.31955 + 0.556875i) q^{35} +(1.00820 + 5.72733i) q^{36} +(1.33919 - 4.12161i) q^{37} +(9.13289 + 5.48937i) 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} +(0.259852 - 0.0249461i) q^{44} +(5.61683 + 1.82502i) q^{45} +(1.85589 + 0.925643i) q^{46} +(1.80179 + 7.50499i) q^{47} +(-0.896457 + 0.820510i) q^{48} +(5.00804 + 2.55172i) q^{49} +(1.22317 + 0.182983i) q^{50} +(-0.264291 + 0.0858735i) q^{51} +(-3.62342 - 8.33981i) q^{52} +(-3.50822 + 0.276103i) q^{53} +(-0.220867 - 2.52868i) q^{54} +(0.101453 - 0.244929i) q^{55} +(1.19178 - 3.10071i) q^{56} +(-1.85197 - 1.34553i) q^{57} +(-0.449224 + 0.280617i) q^{58} +(2.06311 + 2.83963i) q^{59} +(0.308672 + 1.19495i) q^{60} +(0.586573 + 3.70347i) q^{61} +(9.17845 - 9.33739i) q^{62} +(1.78431 + 2.91173i) q^{63} +(7.72563 + 2.07717i) q^{64} +(-9.20598 - 0.724526i) q^{65} +(-0.0560788 + 0.000481387i) q^{66} +(-5.36295 - 4.58039i) q^{67} +(1.41123 + 1.16401i) q^{68} +(-0.379887 - 0.232795i) q^{69} +(-2.21289 - 2.54637i) q^{70} +(-6.33090 + 5.40710i) q^{71} +(-6.52684 + 5.00378i) q^{72} +(-6.90701 - 6.90701i) q^{73} +(6.04490 - 1.01068i) q^{74} +(-0.258358 - 0.0620262i) q^{75} +(-0.924256 + 15.0410i) q^{76} +(0.136586 - 0.0695940i) q^{77} +(0.619572 + 1.85259i) q^{78} +(-12.4208 + 5.14485i) q^{79} +(5.54428 - 5.93871i) q^{80} -8.17778i q^{81} +(-2.78624 - 8.61608i) q^{82} +15.8828i q^{83} +(-0.313021 + 0.641324i) q^{84} +(1.71639 - 0.710954i) q^{85} +(-5.34649 + 1.78806i) q^{86} +(0.101387 - 0.0516591i) q^{87} +(0.200935 + 0.309703i) q^{88} +(-5.88802 - 1.41359i) q^{89} +(1.37733 + 8.23784i) q^{90} +(-3.77568 - 3.77568i) q^{91} +(0.0503501 + 2.93253i) q^{92} +(-2.13888 + 1.82678i) q^{93} +(-8.23886 + 7.15987i) q^{94} +(13.0487 + 7.99625i) q^{95} +(-1.61458 - 0.588964i) q^{96} +(1.29043 + 1.10213i) q^{97} +(0.0682310 + 7.94851i) 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 $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{37}{40}\right)$

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 $

$2$	0.652832	+	1.25452i	0.461622	+	0.887077i
$2$	0.652832	+	1.25452i	0.461622	+	0.887077i
$3$	−0.116266	−	0.280690i	−0.0671260	−	0.162056i	0.886756	−	0.462237i	$-0.152953\pi$
$3$	−0.116266	−	0.280690i	−0.0671260	−	0.162056i	−0.953882	+	0.300181i	$0.902953\pi$
$4$	−1.14762	+	1.63798i	−0.573810	+	0.818988i
$5$	0.922111	+	1.80974i	0.412380	+	0.809342i	1.00000		0.000204875i	$6.52137e-5\pi$
$5$	0.922111	+	1.80974i	0.412380	+	0.809342i	−0.587619	+	0.809137i	$0.699935\pi$
$6$	0.276228	−	0.329100i	0.112770	−	0.134355i
$7$	−0.274171	+	1.14200i	−0.103627	+	0.431637i	−0.999930	−	0.0118042i	$-0.996243\pi$
$7$	−0.274171	+	1.14200i	−0.103627	+	0.431637i	0.896303	+	0.443441i	$0.146243\pi$
$8$	−2.80407	−	0.370385i	−0.991389	−	0.130951i
$9$	2.05605	−	2.05605i	0.685350	−	0.685350i
$10$	−1.66837	+	2.33826i	−0.527585	+	0.739423i
$11$	−0.0847682	−	0.0992508i	−0.0255586	−	0.0299252i	0.747479	−	0.664285i	$-0.231264\pi$
$11$	−0.0847682	−	0.0992508i	−0.0255586	−	0.0299252i	−0.773038	+	0.634360i	$0.781264\pi$
$12$	0.593192	+	0.131685i	0.171240	+	0.0380143i
$13$	−2.37552	+	3.87650i	−0.658852	+	1.07515i	0.332397	+	0.943140i	$0.392143\pi$
$13$	−2.37552	+	3.87650i	−0.658852	+	1.07515i	−0.991249	+	0.132009i	$0.957857\pi$
$14$	−1.61165	+	0.401585i	−0.430732	+	0.107328i
$15$	0.400767	−	0.469238i	0.103478	−	0.121157i
$16$	−1.36593	−	3.75955i	−0.341484	−	0.939888i
$17$	0.0717643	−	0.911852i	0.0174054	−	0.221157i	−0.982063	−	0.188553i	$-0.939620\pi$
$17$	0.0717643	−	0.911852i	0.0174054	−	0.221157i	0.999468	−	0.0326034i	$-0.0103798\pi$
$18$	3.92161	+	1.23709i	0.924331	+	0.291586i
$19$	6.42437	−	3.93686i	1.47385	−	0.903177i	0.474110	−	0.880466i	$-0.342770\pi$
$19$	6.42437	−	3.93686i	1.47385	−	0.903177i	0.999742	−	0.0227115i	$-0.00722993\pi$
$20$	−4.02255	−	0.566504i	−0.899470	−	0.126674i
$21$	0.352426	−	0.0558188i	0.0769056	−	0.0121807i
$22$	0.0691723	−	0.171137i	0.0147476	−	0.0364866i
$23$	1.18641	−	0.861977i	0.247383	−	0.179735i	−0.457183	−	0.889373i	$-0.651142\pi$
$23$	1.18641	−	0.861977i	0.247383	−	0.179735i	0.704566	+	0.709638i	$0.251142\pi$
$24$	0.222054	+	0.830137i	0.0453265	+	0.169451i
$25$	0.514040	−	0.707515i	0.102808	−	0.141503i
$26$	−6.41395	−	0.449427i	−1.25788	−	0.0881400i
$27$	−1.65823	−	0.686862i	−0.319127	−	0.132187i
$28$	−1.55593	−	1.75967i	−0.294044	−	0.332547i
$29$	0.0293854	+	0.373377i	0.00545674	+	0.0693344i	0.999043	−	0.0437444i	$-0.0139287\pi$
$29$	0.0293854	+	0.373377i	0.00545674	+	0.0693344i	−0.993586	+	0.113079i	$0.963929\pi$
$30$	0.850300	+	0.196435i	0.155243	+	0.0358640i
$31$	−2.86096	−	8.80513i	−0.513844	−	1.58145i	−0.785376	−	0.619019i	$-0.787530\pi$
$31$	−2.86096	−	8.80513i	−0.513844	−	1.58145i	0.271532	−	0.962429i	$-0.412470\pi$
$32$	3.82469	−	4.16794i	0.676116	−	0.736795i
$33$	−0.0180031	+	0.0353330i	−0.00313393	+	0.00615069i
$34$	1.19078	−	0.505257i	0.204218	−	0.0866508i
$35$	−2.31955	+	0.556875i	−0.392076	+	0.0941291i
$36$	1.00820	+	5.72733i	0.168033	+	0.954555i
$37$	1.33919	−	4.12161i	0.220162	−	0.677589i	−0.778585	−	0.627540i	$-0.784062\pi$
$37$	1.33919	−	4.12161i	0.220162	−	0.677589i	0.998747	−	0.0500497i	$-0.0159380\pi$
$38$	9.13289	+	5.48937i	1.48155	+	0.890493i
$39$	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	0.893407	+	0.449248i	$0.148308\pi$
$43$	−0.623604	+	3.93728i	−0.0950987	+	0.600430i	−0.988506	+	0.151182i	$0.951692\pi$
$44$	0.259852	−	0.0249461i	0.0391742	−	0.00376076i
$45$	5.61683	+	1.82502i	0.837308	+	0.272058i
$46$	1.85589	+	0.925643i	0.273636	+	0.136479i
$47$	1.80179	+	7.50499i	0.262818	+	1.09472i	0.935090	+	0.354411i	$0.115319\pi$
$47$	1.80179	+	7.50499i	0.262818	+	1.09472i	−0.672272	+	0.740304i	$0.734681\pi$
$48$	−0.896457	+	0.820510i	−0.129392	+	0.118430i
$49$	5.00804	+	2.55172i	0.715434	+	0.364532i
$50$	1.22317	+	0.182983i	0.172983	+	0.0258777i
$51$	−0.264291	+	0.0858735i	−0.0370082	+	0.0120247i
$52$	−3.62342	−	8.33981i	−0.502478	−	1.15652i
$53$	−3.50822	+	0.276103i	−0.481891	+	0.0379256i	−0.317078	−	0.948399i	$-0.602702\pi$
$53$	−3.50822	+	0.276103i	−0.481891	+	0.0379256i	−0.164812	+	0.986325i	$0.552702\pi$
$54$	−0.220867	−	2.52868i	−0.0300562	−	0.344110i
$55$	0.101453	−	0.244929i	0.0136799	−	0.0330262i
$56$	1.19178	−	3.10071i	0.159258	−	0.414350i
$57$	−1.85197	−	1.34553i	−0.245299	−	0.178220i
$58$	−0.449224	+	0.280617i	−0.0589860	+	0.0368468i
$59$	2.06311	+	2.83963i	0.268594	+	0.369688i	0.921915	−	0.387393i	$-0.126624\pi$
$59$	2.06311	+	2.83963i	0.268594	+	0.369688i	−0.653320	+	0.757082i	$0.726624\pi$
$60$	0.308672	+	1.19495i	0.0398494	+	0.154268i
$61$	0.586573	+	3.70347i	0.0751029	+	0.474181i	0.996361	+	0.0852300i	$0.0271625\pi$
$61$	0.586573	+	3.70347i	0.0751029	+	0.474181i	−0.921258	+	0.388951i	$0.872837\pi$
$62$	9.17845	−	9.33739i	1.16566	−	1.18585i
$63$	1.78431	+	2.91173i	0.224802	+	0.366843i
$64$	7.72563	+	2.07717i	0.965704	+	0.259646i
$65$	−9.20598	−	0.724526i	−1.14186	−	0.0898664i
$66$	−0.0560788		0.000481387i	−0.00690283		5.92547e-5i
$67$	−5.36295	−	4.58039i	−0.655189	−	0.559584i	0.258494	−	0.966013i	$-0.416774\pi$
$67$	−5.36295	−	4.58039i	−0.655189	−	0.559584i	−0.913682	+	0.406429i	$0.866774\pi$
$68$	1.41123	+	1.16401i	0.171137	+	0.141157i
$69$	−0.379887	−	0.232795i	−0.0457330	−	0.0280252i
$70$	−2.21289	−	2.54637i	−0.264491	−	0.304349i
$71$	−6.33090	+	5.40710i	−0.751340	+	0.641705i	−0.940326	−	0.340275i	$-0.889480\pi$
$71$	−6.33090	+	5.40710i	−0.751340	+	0.641705i	0.188986	+	0.981980i	$0.439480\pi$
$72$	−6.52684	+	5.00378i	−0.769196	+	0.589702i
$73$	−6.90701	−	6.90701i	−0.808404	−	0.808404i	0.175988	−	0.984392i	$-0.443688\pi$
$73$	−6.90701	−	6.90701i	−0.808404	−	0.808404i	−0.984392	+	0.175988i	$0.943688\pi$
$74$	6.04490	−	1.01068i	0.702705	−	0.117489i
$75$	−0.258358	−	0.0620262i	−0.0298326	−	0.00716216i
$76$	−0.924256	+	15.0410i	−0.106019	+	1.72532i
$77$	0.136586	−	0.0695940i	0.0155654	−	0.00793097i
$78$	0.619572	+	1.85259i	0.0701527	+	0.209764i
$79$	−12.4208	+	5.14485i	−1.39745	+	0.578841i	−0.949087	−	0.315013i	$-0.897991\pi$
$79$	−12.4208	+	5.14485i	−1.39745	+	0.578841i	−0.448358	+	0.893854i	$0.647991\pi$
$80$	5.54428	−	5.93871i	0.619870	−	0.663968i
$81$		−	8.17778i		−	0.908642i
$82$	−2.78624	−	8.61608i	−0.307689	−	0.951487i
$83$			15.8828i			1.74337i	0.490070	+	0.871683i	$0.336971\pi$
$83$			15.8828i			1.74337i	−0.490070	+	0.871683i	$0.663029\pi$
$84$	−0.313021	+	0.641324i	−0.0341534	+	0.0699742i
$85$	1.71639	−	0.710954i	0.186169	−	0.0771137i
$86$	−5.34649	+	1.78806i	−0.576527	+	0.192812i
$87$	0.101387	−	0.0516591i	0.0108698	−	0.00553844i
$88$	0.200935	+	0.309703i	0.0214198	+	0.0330145i
$89$	−5.88802	−	1.41359i	−0.624128	−	0.149840i	−0.0909676	−	0.995854i	$-0.528996\pi$
$89$	−5.88802	−	1.41359i	−0.624128	−	0.149840i	−0.533161	+	0.846014i	$0.678996\pi$
$90$	1.37733	+	8.23784i	0.145184	+	0.868345i
$91$	−3.77568	−	3.77568i	−0.395799	−	0.395799i
$92$	0.0503501	+	2.93253i	0.00524936	+	0.305738i
$93$	−2.13888	+	1.82678i	−0.221792	+	0.189428i
$94$	−8.23886	+	7.15987i	−0.849774	+	0.738484i
$95$	13.0487	+	7.99625i	1.33877	+	0.820398i
$96$	−1.61458	−	0.588964i	−0.164787	−	0.0601109i
$97$	1.29043	+	1.10213i	0.131024	+	0.111905i	0.712545	−	0.701626i	$-0.247542\pi$
$97$	1.29043	+	1.10213i	0.131024	+	0.111905i	−0.581522	+	0.813531i	$0.697542\pi$
$98$	0.0682310	+	7.94851i	0.00689237	+	0.802921i
$99$	−0.378352	−	0.0297770i	−0.0380259	−	0.00299270i
$100$	0.568971	+	1.65394i	0.0568971	+	0.165394i
$101$	6.70906	+	10.9482i	0.667576	+	1.08939i	0.989765	+	0.142710i	$0.0455815\pi$
$101$	6.70906	+	10.9482i	0.667576	+	1.08939i	−0.322189	+	0.946675i	$0.604419\pi$
$102$	−0.280268	−	0.275497i	−0.0277506	−	0.0272782i
$103$	−1.63715	−	10.3366i	−0.161314	−	1.01849i	−0.926940	−	0.375209i	$-0.877571\pi$
$103$	−1.63715	−	10.3366i	−0.161314	−	1.01849i	0.765627	−	0.643285i	$-0.222429\pi$
$104$	8.09694	−	9.99013i	0.793970	−	0.979613i
$105$	0.425993	+	0.586329i	0.0415727	+	0.0572199i
$106$	−2.63665	−	4.22087i	−0.256094	−	0.409967i
$107$	−2.54436	−	1.84859i	−0.245973	−	0.178710i	0.457967	−	0.888969i	$-0.348578\pi$
$107$	−2.54436	−	1.84859i	−0.245973	−	0.178710i	−0.703940	+	0.710259i	$0.748578\pi$
$108$	3.02808	−	1.92789i	0.291377	−	0.185511i
$109$	2.98456	−	7.20537i	0.285869	−	0.690149i	−0.714082	−	0.700062i	$-0.753156\pi$
$109$	2.98456	−	7.20537i	0.285869	−	0.690149i	0.999951	+	0.00991323i	$0.00315553\pi$
$110$	0.373499	−	0.0326232i	0.0356117	−	0.00311050i
$111$	−1.31260	+	0.103304i	−0.124586	+	0.00980515i
$112$	4.66792	−	0.529143i	0.441077	−	0.0499993i
$113$	5.82404	−	1.89235i	0.547880	−	0.178017i	−0.0219807	−	0.999758i	$-0.506997\pi$
$113$	5.82404	−	1.89235i	0.547880	−	0.178017i	0.569861	+	0.821741i	$0.306997\pi$
$114$	0.478970	−	3.20173i	0.0448596	−	0.299870i
$115$	2.65396	+	1.35226i	0.247483	+	0.126099i
$116$	−0.645306	−	0.380363i	−0.0599152	−	0.0353158i
$117$	3.08609	+	12.8545i	0.285309	+	1.18840i
$118$	−2.21550	+	4.44201i	−0.203953	+	0.408920i
$119$	1.02166	+	0.331959i	0.0936557	+	0.0304306i
$120$	−1.29758	+	1.16734i	−0.118452	+	0.106563i
$121$	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
$126$	−2.48796	+	4.13932i	−0.221645	+	0.368760i
$127$	4.11029	−	12.6502i	0.364729	−	1.12252i	−0.585421	−	0.810729i	$-0.699071\pi$
$127$	4.11029	−	12.6502i	0.364729	−	1.12252i	0.950150	−	0.311792i	$-0.100929\pi$
$128$	2.43770	+	11.0480i	0.215464	+	0.976512i
$129$	1.17766	−	0.282731i	0.103687	−	0.0248931i
$130$	−5.10103	−	12.0220i	−0.447390	−	1.05440i
$131$	2.22786	−	4.37243i	0.194649	−	0.382021i	−0.772967	−	0.634446i	$-0.781228\pi$
$131$	2.22786	−	4.37243i	0.194649	−	0.382021i	0.967616	+	0.252425i	$0.0812283\pi$
$132$	−0.0372140	−	0.0700375i	−0.00323906	−	0.00609598i
$133$	2.73453	+	8.41603i	0.237114	+	0.729763i
$134$	2.24507	−	9.71814i	0.193944	−	0.839519i
$135$	−0.286028	−	3.63434i	−0.0246174	−	0.312794i
$136$	−0.538968	+	2.53032i	−0.0462161	+	0.216973i
$137$	−16.7988	−	6.95828i	−1.43522	−	0.594486i	−0.476583	−	0.879129i	$-0.658125\pi$
$137$	−16.7988	−	6.95828i	−1.43522	−	0.594486i	−0.958634	+	0.284643i	$0.908125\pi$
$138$	0.0440426	−	0.628550i	0.00374916	−	0.0535057i
$139$	−6.66167	+	9.16900i	−0.565035	+	0.777704i	−0.991956	−	0.126585i	$-0.959598\pi$
$139$	−6.66167	+	9.16900i	−0.565035	+	0.777704i	0.426920	+	0.904289i	$0.359598\pi$
$140$	1.74982	−	4.43845i	0.147887	−	0.375118i
$141$	1.89709	−	1.37832i	0.159764	−	0.116075i
$142$	−10.9163	−	4.41229i	−0.916077	−	0.370271i
$143$	0.586115	−	0.0928315i	0.0490134	−	0.00776296i
$144$	−10.5383	−	4.92140i	−0.878188	−	0.410117i
$145$	−0.648621	+	0.397475i	−0.0538650	+	0.0330085i
$146$	4.15583	−	13.1741i	0.343939	−	1.09029i
$147$	0.133981	−	1.70238i	0.0110505	−	0.140410i
$148$	5.21422	+	6.92362i	0.428606	+	0.569118i
$149$	−6.90242	+	8.08170i	−0.565468	+	0.662078i	−0.967300	−	0.253635i	$-0.918374\pi$
$149$	−6.90242	+	8.08170i	−0.565468	+	0.662078i	0.401832	+	0.915714i	$0.368374\pi$
$150$	−0.0908513	−	0.364606i	−0.00741798	−	0.0297700i
$151$	8.95473	−	14.6128i	0.728726	−	1.18917i	−0.246753	−	0.969078i	$-0.579364\pi$
$151$	8.95473	−	14.6128i	0.728726	−	1.18917i	0.975479	−	0.220094i	$-0.0706365\pi$
$152$	−19.4725	+	8.65975i	−1.57943	+	0.702398i
$153$	−1.72726	−	2.02237i	−0.139641	−	0.163499i
$154$	0.176474	+	0.125916i	0.0142207	+	0.0101466i
$155$	13.2969	−	13.2969i	1.06803	−	1.06803i
$156$	−1.91962	+	1.98669i	−0.153693	+	0.159063i
$157$	−2.91000	+	12.1210i	−0.232243	+	0.967363i	0.727416	+	0.686197i	$0.240721\pi$
$157$	−2.91000	+	12.1210i	−0.232243	+	0.967363i	−0.959659	+	0.281166i	$0.909279\pi$
$158$	−14.5630	−	12.2233i	−1.15857	−	0.972436i
$159$	0.485384	+	0.952620i	0.0384935	+	0.0755477i
$160$	11.0697	+	3.07841i	0.875136	+	0.243370i
$161$	0.659102	+	1.59121i	0.0519445	+	0.125405i
$162$	10.2592	−	5.33872i	0.806035	−	0.419449i
$163$	4.99983			0.391617			0.195808	−	0.980642i	$-0.437267\pi$
$163$	4.99983			0.391617			0.195808	+	0.980642i	$0.437267\pi$
$164$	8.99006	−	9.12024i	0.702006	−	0.712171i
$165$	−0.0805446			−0.00627039
$166$	−19.9253	+	10.3688i	−1.54650	+	0.804776i
$167$	4.89833	+	11.8256i	0.379044	+	0.915094i	0.992145	+	0.125089i	$0.0399218\pi$
$167$	4.89833	+	11.8256i	0.379044	+	0.915094i	−0.613101	+	0.790004i	$0.710078\pi$
$168$	−1.00890	+	0.0259867i	−0.0778384	+	0.00200492i
$169$	−3.48229	−	6.83437i	−0.267868	−	0.525721i
$170$	2.01242	+	1.68911i	0.154346	+	0.129549i
$171$	5.11445	−	21.3032i	0.391112	−	1.62910i
$172$	−5.73351	−	5.53995i	−0.437176	−	0.422417i
$173$	13.1582	−	13.1582i	1.00040	−	1.00040i	0.000399927	−	1.00000i	$-0.499873\pi$
$173$	13.1582	−	13.1582i	1.00040	−	1.00040i	1.00000		0.000399927i	$-0.000127301\pi$
$174$	0.130996	+	0.0934665i	0.00993075	+	0.00708568i
$175$	0.667051	+	0.781016i	0.0504243	+	0.0590393i
$176$	−0.257351	+	0.454260i	−0.0193985	+	0.0342412i
$177$	0.557187	−	0.909246i	0.0418807	−	0.0683431i
$178$	−2.07052	−	8.30945i	−0.155192	−	0.622819i
$179$	1.42535	−	1.66887i	0.106536	−	0.124737i	−0.704576	−	0.709629i	$-0.748863\pi$
$179$	1.42535	−	1.66887i	0.106536	−	0.124737i	0.811112	+	0.584891i	$0.198863\pi$
$180$	−9.43533	+	7.10581i	−0.703268	+	0.529636i
$181$	−0.440222	+	5.59356i	−0.0327215	+	0.415766i	0.958641	+	0.284617i	$0.0918665\pi$
$181$	−0.440222	+	5.59356i	−0.0327215	+	0.415766i	−0.991363	+	0.131149i	$0.958134\pi$
$182$	2.27177	−	7.20154i	0.168395	−	0.533814i
$183$	0.971329	−	0.595231i	0.0718027	−	0.0440008i
$184$	−3.64604	+	1.97762i	−0.268789	+	0.145792i
$185$	8.69395	−	1.37699i	0.639192	−	0.101238i
$186$	−3.68805	−	1.49068i	−0.270421	−	0.109302i
$187$	−0.0965854	+	0.0701734i	−0.00706302	+	0.00513159i
$188$	−14.3608	−	5.66159i	−1.04737	−	0.412914i
$189$	1.23904	−	1.70539i	0.0901267	−	0.124049i
$190$	−1.51282	+	21.5900i	−0.109751	+	1.56630i
$191$	−23.5293	−	9.74614i	−1.70252	−	0.705206i	−0.702539	−	0.711645i	$-0.747950\pi$
$191$	−23.5293	−	9.74614i	−1.70252	−	0.705206i	−0.999979	+	0.00643873i	$0.997950\pi$
$192$	−0.315184	−	2.41001i	−0.0227465	−	0.173927i
$193$	1.64408	+	20.8900i	0.118344	+	1.50370i	0.713823	+	0.700326i	$0.246962\pi$
$193$	1.64408	+	20.8900i	0.118344	+	1.50370i	−0.595479	+	0.803371i	$0.703038\pi$
$194$	−0.540208	+	2.33838i	−0.0387847	+	0.167886i
$195$	0.866971	+	2.66826i	0.0620851	+	0.191078i
$196$	−9.92700	+	5.27464i	−0.709071	+	0.376760i
$197$	−0.592787	+	1.16341i	−0.0422343	+	0.0828895i	−0.911159	−	0.412054i	$-0.864811\pi$
$197$	−0.592787	+	1.16341i	−0.0422343	+	0.0828895i	0.868925	+	0.494944i	$0.164811\pi$
$198$	−0.209645	−	0.494089i	−0.0148988	−	0.0351133i
$199$	7.24168	−	1.73857i	0.513349	−	0.123244i	0.0315092	−	0.999503i	$-0.489969\pi$
$199$	7.24168	−	1.73857i	0.513349	−	0.123244i	0.481840	+	0.876259i	$0.339969\pi$
$200$	−1.70346	+	1.79353i	−0.120453	+	0.126822i
$201$	−0.662144	+	2.03787i	−0.0467040	+	0.143740i
$202$	−9.35478	+	15.5639i	−0.658200	+	1.09508i
$203$	−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
$208$	17.8187	+	3.63586i	1.23551	+	0.252101i
$209$	−0.935319	−	0.303903i	−0.0646973	−	0.0210214i
$210$	−0.457458	+	0.917190i	−0.0315676	+	0.0632921i
$211$	−6.46703	−	26.9371i	−0.445209	−	1.85443i	−0.515483	−	0.856900i	$-0.672388\pi$
$211$	−6.46703	−	26.9371i	−0.445209	−	1.85443i	0.0702748	−	0.997528i	$-0.477612\pi$
$212$	3.57385	−	6.06324i	0.245453	−	0.416425i
$213$	2.25379	+	1.14836i	0.154427	+	0.0786844i
$214$	0.658041	−	4.39876i	0.0449828	−	0.300693i
$215$	−7.70050	+	2.50205i	−0.525170	+	0.170638i
$216$	4.39539	+	2.54019i	0.299069	+	0.172838i
$217$	10.8399	−	0.853118i	0.735860	−	0.0579134i
$218$	10.9877	−	0.959716i	0.744179	−	0.0650002i
$219$	−1.13568	+	2.74177i	−0.0767421	+	0.185272i
$220$	0.284758	+	0.447263i	0.0191984	+	0.0301545i
$221$	3.36432	+	2.44432i	0.226309	+	0.164423i
$222$	−0.986502	−	1.57923i	−0.0662097	−	0.105991i
$223$	10.0996	+	13.9009i	0.676317	+	0.930871i	0.999882	−	0.0153351i	$-0.00488151\pi$
$223$	10.0996	+	13.9009i	0.676317	+	0.930871i	−0.323565	+	0.946206i	$0.604882\pi$
$224$	3.71119	+	5.51054i	0.247964	+	0.368189i
$225$	−0.397795	−	2.51158i	−0.0265197	−	0.167439i
$226$	6.17610	+	6.07097i	0.410828	+	0.403835i
$227$	12.6114	+	20.5799i	0.837048	+	1.36594i	0.928964	+	0.370171i	$0.120701\pi$
$227$	12.6114	+	20.5799i	0.837048	+	1.36594i	−0.0919163	+	0.995767i	$0.529299\pi$
$228$	4.32931	−	1.48932i	0.286716	−	0.0986326i
$229$	1.26877	+	0.0998546i	0.0838428	+	0.00659857i	0.120311	−	0.992736i	$-0.461611\pi$
$229$	1.26877	+	0.0998546i	0.0838428	+	0.00659857i	−0.0364683	+	0.999335i	$0.511611\pi$
$230$	0.0361583	+	4.21223i	0.00238421	+	0.277746i
$231$	−0.0354146	−	0.0302469i	−0.00233011	−	0.00199010i
$232$	0.0558944	−	1.05786i	0.00366964	−	0.0694519i
$233$	−9.32814	−	5.71629i	−0.611107	−	0.374487i	0.182242	−	0.983254i	$-0.441664\pi$
$233$	−9.32814	−	5.71629i	−0.611107	−	0.374487i	−0.793349	+	0.608767i	$0.791664\pi$
$234$	−14.1115	+	12.2634i	−0.922495	+	0.801682i
$235$	−11.9207	+	10.1812i	−0.777618	+	0.664149i
$236$	−7.01892	+	0.120511i	−0.456893	+	0.00784462i
$237$	2.88822	+	2.88822i	0.187610	+	0.187610i
$238$	0.250527	+	1.49841i	0.0162393	+	0.0971273i
$239$	15.3801	+	3.69244i	0.994856	+	0.238844i	0.698015	−	0.716083i	$-0.254067\pi$
$239$	15.3801	+	3.69244i	0.994856	+	0.238844i	0.296841	+	0.954927i	$0.404067\pi$
$240$	−2.31155	−	0.865756i	−0.149210	−	0.0558843i
$241$	9.12337	−	4.64859i	0.587688	−	0.299442i	−0.134748	−	0.990880i	$-0.543022\pi$
$241$	9.12337	−	4.64859i	0.587688	−	0.299442i	0.722436	+	0.691438i	$0.243022\pi$
$242$	14.7303	−	4.92635i	0.946900	−	0.316678i
$243$	−7.27011	+	3.01138i	−0.466378	+	0.193180i
$244$	−6.73936	−	3.28939i	−0.431444	−	0.210582i
$245$			11.4162i			0.729357i
$246$	−2.09450	+	1.78382i	−0.133541	+	0.113732i
$247$			34.2562i			2.17967i
$248$	4.76105	+	25.7499i	0.302327	+	1.63512i
$249$	4.45815	−	1.84663i	0.282524	−	0.117025i
$250$	5.35200	+	16.0030i	0.338490	+	1.01212i
$251$	−23.8102	+	12.1319i	−1.50289	+	0.765760i	−0.995392	−	0.0958931i	$-0.969429\pi$
$251$	−23.8102	+	12.1319i	−1.50289	+	0.765760i	−0.507497	+	0.861653i	$0.669429\pi$
$252$	−6.81706	−	0.418902i	−0.429434	−	0.0263884i
$253$	−0.186122	−	0.0446838i	−0.0117014	−	0.00280925i
$254$	18.5532	−	3.10201i	1.16413	−	0.194638i
$255$	−0.399115	−	0.399115i	−0.0249935	−	0.0249935i
$256$	−12.2684	+	10.2706i	−0.766778	+	0.641912i
$257$	−7.78697	+	6.65070i	−0.485738	+	0.414859i	−0.858300	−	0.513148i	$-0.828479\pi$
$257$	−7.78697	+	6.65070i	−0.485738	+	0.414859i	0.372562	+	0.928007i	$0.378479\pi$
$258$	1.12350	+	1.29282i	0.0699463	+	0.0804872i
$259$	4.33973	+	2.65939i	0.269658	+	0.165247i
$260$	11.7517	−	14.2477i	0.728811	−	0.883604i
$261$	0.828101	+	0.707265i	0.0512581	+	0.0437786i
$262$	6.93970	−	0.0595712i	0.428736	−	0.00368032i
$263$	−4.37833	−	0.344582i	−0.269979	−	0.0212478i	−0.0572532	−	0.998360i	$-0.518234\pi$
$263$	−4.37833	−	0.344582i	−0.269979	−	0.0212478i	−0.212726	+	0.977112i	$0.568234\pi$
$264$	0.0635687	−	0.0924083i	0.00391238	−	0.00568733i
$265$	−3.73464	−	6.09438i	−0.229417	−	0.374375i
$266$	−8.77285	+	8.92477i	−0.537898	+	0.547213i
$267$	0.287794	+	1.81706i	0.0176127	+	0.111202i
$268$	13.6572	−	3.52784i	0.834247	−	0.215497i
$269$	−12.3379	−	16.9816i	−0.752253	−	1.03539i	−0.997819	−	0.0660079i	$-0.978974\pi$
$269$	−12.3379	−	16.9816i	−0.752253	−	1.03539i	0.245566	−	0.969380i	$-0.421026\pi$
$270$	4.37260	−	2.73144i	0.266108	−	0.166230i
$271$	−1.96179	−	1.42532i	−0.119170	−	0.0865822i	0.526604	−	0.850111i	$-0.323465\pi$
$271$	−1.96179	−	1.42532i	−0.119170	−	0.0865822i	−0.645774	+	0.763529i	$0.723465\pi$
$272$	−3.52618	+	0.975728i	−0.213806	+	0.0591622i
$273$	−0.620814	+	1.49878i	−0.0375734	+	0.0907102i
$274$	−2.23751	−	25.6169i	−0.135173	−	1.54758i
$275$	−0.113796	+	0.00895592i	−0.00686214	+	0.000540062i
$276$	0.817278	−	0.355085i	0.0491944	−	0.0213736i
$277$	−27.6665	+	8.98940i	−1.66232	+	0.540121i	−0.981357	−	0.192195i	$-0.938439\pi$
$277$	−27.6665	+	8.98940i	−1.66232	+	0.540121i	−0.680965	+	0.732316i	$0.738439\pi$
$278$	−15.8516	−	2.37135i	−0.950716	−	0.142224i
$279$	−23.9861	−	12.2215i	−1.43601	−	0.731683i
$280$	6.71045	−	0.702391i	0.401026	−	0.0419759i
$281$	1.54846	+	6.44979i	0.0923732	+	0.384762i	0.999335	−	0.0364498i	$-0.0116049\pi$
$281$	1.54846	+	6.44979i	0.0923732	+	0.384762i	−0.906962	+	0.421212i	$0.861605\pi$
$282$	2.96760	+	1.48012i	0.176718	+	0.0881398i
$283$	28.8363	+	9.36948i	1.71414	+	0.556958i	0.991014	−	0.133758i	$-0.0427046\pi$
$283$	28.8363	+	9.36948i	1.71414	+	0.556958i	0.723126	+	0.690716i	$0.242705\pi$
$284$	−1.59123	−	16.5752i	−0.0944223	−	0.983556i
$285$	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
$290$	−0.922079	−	0.554220i	−0.0541464	−	0.0325449i
$291$	0.159325	−	0.490352i	0.00933979	−	0.0287449i
$292$	19.2401	−	3.38689i	1.12594	−	0.198203i
$293$	8.43098	−	2.02410i	0.492543	−	0.118249i	0.0204374	−	0.999791i	$-0.493494\pi$
$293$	8.43098	−	2.02410i	0.492543	−	0.118249i	0.472105	+	0.881542i	$0.343494\pi$
$294$	2.22313	−	0.943290i	0.129656	−	0.0550138i
$295$	−3.23659	+	6.35216i	−0.188441	+	0.369837i
$296$	−5.28178	+	11.0613i	−0.306997	+	0.642924i
$297$	0.0723936	+	0.222805i	0.00420070	+	0.0129284i
$298$	−14.6447	−	3.38321i	−0.848347	−	0.195984i
$299$	0.523112	+	6.64676i	0.0302523	+	0.384392i
$300$	0.398094	−	0.352001i	0.0229840	−	0.0203228i
$301$	−4.32542	−	1.79165i	−0.249313	−	0.103269i
$302$	24.1779	+	1.69415i	1.39128	+	0.0974876i
$303$	2.29301	−	3.15606i	0.131730	−	0.181311i
$304$	−23.5761	−	18.7753i	−1.35218	−	1.07683i
$305$	−6.16145	+	4.47656i	−0.352804	+	0.256327i
$306$	1.40948	−	3.48714i	0.0805744	−	0.199347i
$307$	−25.8018	+	4.08660i	−1.47258	+	0.233234i	−0.840562	−	0.541716i	$-0.817775\pi$
$307$	−25.8018	+	4.08660i	−1.47258	+	0.233234i	−0.632022	+	0.774950i	$0.717775\pi$
$308$	−0.0427554	+	0.303592i	−0.00243622	+	0.0172988i
$309$	−2.71103	+	1.66132i	−0.154225	+	0.0945093i
$310$	25.3618	+	8.00054i	1.44046	+	0.454400i
$311$	1.17732	−	14.9593i	0.0667597	−	0.848262i	−0.868816	−	0.495135i	$-0.835118\pi$
$311$	1.17732	−	14.9593i	0.0667597	−	0.848262i	0.935576	−	0.353127i	$-0.114882\pi$
$312$	−3.74552	−	1.11122i	−0.212049	−	0.0629104i
$313$	18.8542	−	22.0755i	1.06570	−	1.24778i	0.0981356	−	0.995173i	$-0.468712\pi$
$313$	18.8542	−	22.0755i	1.06570	−	1.24778i	0.967569	−	0.252607i	$-0.0812879\pi$
$314$	−17.1058	+	4.26235i	−0.965334	+	0.240539i
$315$	−3.62415	+	5.91408i	−0.204198	+	0.333221i
$316$	5.82719	−	26.2493i	0.327805	−	1.47664i
$317$	−16.0995	−	18.8501i	−0.904239	−	1.05873i	−0.998005	−	0.0631332i	$-0.979891\pi$
$317$	−16.0995	−	18.8501i	−0.904239	−	1.05873i	0.0937665	−	0.995594i	$-0.470109\pi$
$318$	−0.878203	+	1.23082i	−0.0492472	+	0.0690211i
$319$	0.0345670	−	0.0345670i	0.00193538	−	0.00193538i
$320$	3.36474	+	15.8968i	0.188095	+	0.888658i
$321$	−0.223058	+	0.929104i	−0.0124499	+	0.0518575i
$322$	−1.56592	+	1.86565i	−0.0872653	+	0.103969i
$323$	−3.12879	−	6.14060i	−0.174091	−	0.341672i
$324$	13.3950	+	9.38499i	0.744167	+	0.521388i
$325$	1.52157	+	3.67340i	0.0844016	+	0.203763i
$326$	3.26405	+	6.27236i	0.180779	+	0.347394i
$327$	−2.36948			−0.131032
$328$	17.3105	+	5.32420i	0.955812	+	0.293980i
$329$	−9.06473			−0.499755
$330$	−0.0525821	−	0.101044i	−0.00289455	−	0.00556231i
$331$	1.84650	+	4.45785i	0.101493	+	0.245026i	0.966467	−	0.256791i	$-0.0826652\pi$
$331$	1.84650	+	4.45785i	0.101493	+	0.245026i	−0.864974	+	0.501817i	$0.832665\pi$
$332$	−26.0157	−	18.2275i	−1.42780	−	1.00036i
$333$	−5.72080	−	11.2277i	−0.313498	−	0.615274i
$334$	−11.6376	+	13.8652i	−0.636783	+	0.758669i
$335$	3.34411	−	13.9292i	0.182708	−	0.761034i
$336$	−0.691244	−	1.24872i	−0.0377104	−	0.0681231i
$337$	−17.2644	+	17.2644i	−0.940452	+	0.940452i	−0.998324	−	0.0578717i	$-0.981569\pi$
$337$	−17.2644	+	17.2644i	−0.940452	+	0.940452i	0.0578717	+	0.998324i	$0.481569\pi$
$338$	6.30048	−	8.83028i	0.342701	−	0.480304i
$339$	−1.20830	−	1.41474i	−0.0656257	−	0.0768379i
$340$	−0.805243	+	3.62732i	−0.0436705	+	0.196719i
$341$	−0.631398	+	1.03035i	−0.0341921	+	0.0557965i
$342$	30.0641	−	7.49126i	1.62568	−	0.405081i
$343$	−9.62637	+	11.2710i	−0.519775	+	0.608579i
$344$	3.20694	−	10.8094i	0.172907	−	0.582806i
$345$	0.0710016	−	0.902160i	0.00382260	−	0.0485707i
$346$	25.0973	+	7.91708i	1.34924	+	0.425625i
$347$	16.0423	−	9.83075i	0.861197	−	0.527742i	−0.0203743	−	0.999792i	$-0.506486\pi$
$347$	16.0423	−	9.83075i	0.861197	−	0.527742i	0.881572	+	0.472050i	$0.156486\pi$
$348$	−0.0317371	+	0.225354i	−0.00170128	+	0.0120802i
$349$	−18.8469	+	2.98506i	−1.00885	+	0.159787i	−0.638921	−	0.769272i	$-0.720619\pi$
$349$	−18.8469	+	2.98506i	−1.00885	+	0.159787i	−0.369932	+	0.929059i	$0.620619\pi$
$350$	−0.544325	+	1.34670i	−0.0290954	+	0.0719841i
$351$	6.60179	−	4.79648i	0.352377	−	0.256017i
$352$	−0.737884	−	0.0262948i	−0.0393293	−	0.00140151i
$353$	−8.68675	+	11.9563i	−0.462349	+	0.636369i	−0.974994	−	0.222232i	$-0.928666\pi$
$353$	−8.68675	+	11.9563i	−0.462349	+	0.636369i	0.512645	+	0.858601i	$0.328666\pi$
$354$	1.50441	+	0.105415i	0.0799587	+	0.00560272i
$355$	−15.6233	−	6.47137i	−0.829197	−	0.343465i
$356$	9.07263	−	8.02217i	0.480849	−	0.425174i
$357$	−0.0256069	−	0.325366i	−0.00135526	−	0.0172202i
$358$	3.02414	+	0.698633i	0.159831	+	0.0369239i
$359$	0.813248	+	2.50292i	0.0429216	+	0.132099i	0.970221	−	0.242221i	$-0.0778760\pi$
$359$	0.813248	+	2.50292i	0.0429216	+	0.132099i	−0.927299	+	0.374320i	$0.877876\pi$
$360$	−15.0740	−	7.19787i	−0.794472	−	0.379361i
$361$	17.1479	−	33.6546i	0.902519	−	1.77129i
$362$	−7.30460	+	3.09939i	−0.383921	+	0.162900i
$363$	−3.24461	+	0.778962i	−0.170298	+	0.0408849i
$364$	10.5175	−	1.85143i	0.551269	−	0.0970413i
$365$	6.13089	−	18.8689i	0.320905	−	0.987645i
$366$	1.38084	+	0.829962i	0.0721778	+	0.0433828i
$367$	17.7622	+	2.81325i	0.927178	+	0.146851i	0.601721	−	0.798706i	$-0.294482\pi$
$367$	17.7622	+	2.81325i	0.927178	+	0.146851i	0.325457	+	0.945557i	$0.394482\pi$
$368$	−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
$372$	−0.537594	−	5.59988i	−0.0278729	−	0.290340i
$373$	12.1681	+	3.95365i	0.630040	+	0.204712i	0.606593	−	0.795013i	$-0.292536\pi$
$373$	12.1681	+	3.95365i	0.630040	+	0.204712i	0.0234471	+	0.999725i	$0.492536\pi$
$374$	−0.151088	−	0.0753565i	−0.00781256	−	0.00389659i
$375$	−0.846266	−	3.52495i	−0.0437010	−	0.182028i
$376$	−2.27261	−	21.7119i	−0.117201	−	1.11970i
$377$	−1.51720	−	0.773054i	−0.0781400	−	0.0398143i
$378$	2.94832	+	0.441060i	0.151645	+	0.0226857i
$379$	18.1870	−	5.90930i	0.934201	−	0.303540i	0.197922	−	0.980218i	$-0.436581\pi$
$379$	18.1870	−	5.90930i	0.934201	−	0.303540i	0.736279	+	0.676678i	$0.236581\pi$
$380$	−28.0726	+	12.1968i	−1.44009	+	0.625682i
$381$	−4.02866	+	0.317063i	−0.206395	+	0.0162436i
$382$	−3.13397	−	35.8804i	−0.160348	−	1.83580i
$383$	−5.46420	+	13.1917i	−0.279208	+	0.674067i	−0.999814	−	0.0192774i	$-0.993863\pi$
$383$	−5.46420	+	13.1917i	−0.279208	+	0.674067i	0.720607	+	0.693344i	$0.243863\pi$
$384$	2.81763	−	1.96874i	0.143787	−	0.100467i
$385$	0.251895	+	0.183012i	0.0128377	+	0.00932716i
$386$	−25.1336	+	15.7002i	−1.27926	+	0.799119i
$387$	6.81309	+	9.37741i	0.346329	+	0.476681i
$388$	−3.28620	+	0.848867i	−0.166831	+	0.0430947i
$389$	4.63862	+	29.2871i	0.235187	+	1.48491i	0.768966	+	0.639290i	$0.220772\pi$
$389$	4.63862	+	29.2871i	0.235187	+	1.48491i	−0.533778	+	0.845625i	$0.679228\pi$
$390$	−2.78139	+	2.82956i	−0.140841	+	0.143280i
$391$	−0.700853	−	1.14369i	−0.0354437	−	0.0578388i
$392$	−13.0978	−	9.01012i	−0.661538	−	0.455080i
$393$	−1.48632	−	0.116976i	−0.0749749	−	0.00590065i
$394$	−1.84651	+	0.0158506i	−0.0930256	+	0.000798543i
$395$	−20.7642	−	17.7343i	−1.04476	−	0.892309i
$396$	0.482979	−	0.585560i	0.0242706	−	0.0294255i
$397$	−4.33299	−	2.65526i	−0.217467	−	0.133264i	0.409499	−	0.912310i	$-0.365703\pi$
$397$	−4.33299	−	2.65526i	−0.217467	−	0.133264i	−0.626966	+	0.779047i	$0.715703\pi$
$398$	6.90867	+	7.94981i	0.346300	+	0.398488i
$399$	2.04436	−	1.74605i	0.102346	−	0.0874119i
$400$	−3.36208	−	0.966140i	−0.168104	−	0.0483070i
$401$	14.6854	+	14.6854i	0.733352	+	0.733352i	0.971282	−	0.237930i	$-0.0764689\pi$
$401$	14.6854	+	14.6854i	0.733352	+	0.733352i	−0.237930	+	0.971282i	$0.576469\pi$
$402$	−2.98881	+	0.499716i	−0.149068	+	0.0249236i
$403$	40.9294	+	9.82628i	2.03884	+	0.489482i
$404$	−25.6323	−	1.57508i	−1.27526	−	0.0783634i
$405$	14.7997	−	7.54082i	0.735403	−	0.374706i
$406$	−0.197302	−	0.589953i	−0.00979192	−	0.0292789i
$407$	−0.522595	+	0.216466i	−0.0259041	+	0.0107298i
$408$	0.772898	−	0.142906i	0.0382642	−	0.00707489i
$409$			27.4521i			1.35742i	0.734406	+	0.678710i	$0.237461\pi$
$409$			27.4521i			1.35742i	−0.734406	+	0.678710i	$0.762539\pi$
$410$	13.0237	−	12.9874i	0.643194	−	0.641400i
$411$			5.52426i			0.272491i
$412$	18.8099	+	9.18086i	0.926698	+	0.452308i
$413$	−3.80852	+	1.57754i	−0.187405	+	0.0776256i
$414$	5.71897	−	1.91263i	0.281072	−	0.0940008i
$415$	−28.7438	+	14.6457i	−1.41098	+	0.718930i
$416$	7.07139	+	24.7275i	0.346704	+	1.21236i
$417$	3.34817	+	0.803824i	0.163961	+	0.0393634i
$418$	−0.229354	−	1.37177i	−0.0112181	−	0.0670955i
$419$	−12.7939	−	12.7939i	−0.625024	−	0.625024i	0.321788	−	0.946812i	$-0.395716\pi$
$419$	−12.7939	−	12.7939i	−0.625024	−	0.625024i	−0.946812	+	0.321788i	$0.895716\pi$
$420$	−1.44927	+	0.0248833i	−0.0707173	+	0.00121418i
$421$	16.4615	−	14.0595i	0.802285	−	0.685216i	−0.150584	−	0.988597i	$-0.548115\pi$
$421$	16.4615	−	14.0595i	0.802285	−	0.685216i	0.952869	+	0.303381i	$0.0981154\pi$
$422$	29.5712	−	25.6984i	1.43950	−	1.25098i
$423$	19.1352	+	11.7261i	0.930386	+	0.570141i
$424$	9.93955	+	0.525178i	0.482707	+	0.0255049i
$425$	−0.608260	−	0.519503i	−0.0295049	−	0.0251996i
$426$	0.0307062	+	3.57710i	0.00148772	+	0.173311i
$427$	−4.39020	−	0.345517i	−0.212457	−	0.0167207i
$428$	5.94791	−	2.04613i	0.287503	−	0.0989034i
$429$	−0.0942019	−	0.153723i	−0.00454811	−	0.00742184i
$430$	−8.16599	−	8.02699i	−0.393799	−	0.387096i
$431$	−3.09781	−	19.5588i	−0.149216	−	0.942116i	−0.942729	−	0.333561i	$-0.891750\pi$
$431$	−3.09781	−	19.5588i	−0.149216	−	0.942116i	0.793512	−	0.608555i	$-0.208250\pi$
$432$	−0.317257	+	7.17241i	−0.0152640	+	0.345083i
$433$	1.17648	+	1.61928i	0.0565379	+	0.0778177i	0.836350	−	0.548196i	$-0.184685\pi$
$433$	1.17648	+	1.61928i	0.0565379	+	0.0778177i	−0.779812	+	0.626014i	$0.784685\pi$
$434$	8.14688	+	13.0419i	0.391063	+	0.626030i
$435$	0.186980	+	0.135849i	0.00896498	+	0.00651344i
$436$	8.37708	+	13.1577i	0.401189	+	0.630138i
$437$	4.22845	−	10.2084i	0.202274	−	0.488333i
$438$	−4.18101	+	0.365189i	−0.199776	+	0.0174494i
$439$	26.9232	−	2.11890i	1.28497	−	0.101130i	0.582495	−	0.812835i	$-0.302077\pi$
$439$	26.9232	−	2.11890i	1.28497	−	0.101130i	0.702478	+	0.711705i	$0.252077\pi$
$440$	−0.375199	+	0.649222i	−0.0178869	+	0.0309504i
$441$	15.5433	−	5.05031i	0.740155	−	0.240491i
$442$	−0.870104	+	5.81632i	−0.0413866	+	0.276654i
$443$	−26.0781	−	13.2875i	−1.23901	−	0.631306i	−0.293206	−	0.956049i	$-0.594722\pi$
$443$	−26.0781	−	13.2875i	−1.23901	−	0.631306i	−0.945802	+	0.324743i	$0.894722\pi$
$444$	1.33716	−	2.26856i	0.0634586	−	0.107661i
$445$	−2.87117	−	11.9593i	−0.136107	−	0.566925i
$446$	−10.8455	+	21.7450i	−0.513551	+	1.02966i
$447$	3.07096	+	0.997817i	0.145252	+	0.0471951i
$448$	−4.49028	+	8.25321i	−0.212146	+	0.389927i
$449$	−2.60051	+	16.4190i	−0.122726	+	0.774860i	0.847167	+	0.531327i	$0.178306\pi$
$449$	−2.60051	+	16.4190i	−0.122726	+	0.774860i	−0.969893	+	0.243533i	$0.921694\pi$
$450$	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
$454$	−17.5847	+	29.2564i	−0.825292	+	1.37307i
$455$	3.35142	−	10.3146i	0.157117	−	0.483557i
$456$	4.69469	+	4.45892i	0.219849	+	0.208808i
$457$	20.5689	−	4.93816i	0.962173	−	0.230997i	0.278215	−	0.960519i	$-0.410257\pi$
$457$	20.5689	−	4.93816i	0.962173	−	0.230997i	0.683958	+	0.729521i	$0.260257\pi$
$458$	0.703026	+	1.65688i	0.0328503	+	0.0774211i
$459$	−0.745318	+	1.46277i	−0.0347885	+	0.0682762i
$460$	−5.26070	+	2.79524i	−0.245282	+	0.130329i
$461$	−1.31576	−	4.04949i	−0.0612810	−	0.188603i	0.915729	−	0.401796i	$-0.131614\pi$
$461$	−1.31576	−	4.04949i	−0.0612810	−	0.188603i	−0.977010	+	0.213192i	$0.931614\pi$
$462$	0.0148254	−	0.0641743i	0.000689742	−	0.00298566i
$463$	1.07808	+	13.6983i	0.0501025	+	0.636612i	0.969787	+	0.243954i	$0.0784445\pi$
$463$	1.07808	+	13.6983i	0.0501025	+	0.636612i	−0.919684	+	0.392658i	$0.871555\pi$
$464$	1.36359	−	0.620485i	0.0633032	−	0.0288053i
$465$	−5.27828	−	2.18634i	−0.244775	−	0.101389i
$466$	1.08147	−	15.4341i	0.0500981	−	0.714970i
$467$	−1.44939	+	1.99492i	−0.0670700	+	0.0923139i	−0.841234	−	0.540671i	$-0.818170\pi$
$467$	−1.44939	+	1.99492i	−0.0670700	+	0.0923139i	0.774164	+	0.632985i	$0.218170\pi$
$468$	−24.5970	−	9.69713i	−1.13700	−	0.448250i
$469$	6.70120	−	4.86870i	0.309433	−	0.224816i
$470$	−20.5547	−	8.30804i	−0.948117	−	0.383221i
$471$	3.74058	−	0.592450i	0.172357	−	0.0272987i
$472$	−4.73336	−	8.72667i	−0.217870	−	0.401678i
$473$	0.443640	−	0.271863i	0.0203986	−	0.0125003i
$474$	−1.73779	+	5.50883i	−0.0798195	+	0.253029i
$475$	0.516995	−	6.56904i	0.0237214	−	0.301408i
$476$	−1.71622	+	1.29250i	−0.0786629	+	0.0592416i
$477$	−6.64539	+	7.78076i	−0.304272	+	0.356256i
$478$	5.40841	+	21.7051i	0.247375	+	0.992770i
$479$	−11.8355	+	19.3137i	−0.540776	+	0.882466i	−0.999983	−	0.00586355i	$-0.998134\pi$
$479$	−11.8355	+	19.3137i	−0.540776	+	0.882466i	0.459207	+	0.888329i	$0.348134\pi$
$480$	−0.422946	−	3.46507i	−0.0193048	−	0.158158i
$481$	12.7962	+	14.9824i	0.583455	+	0.683138i
$482$	11.7878	+	8.41066i	0.536918	+	0.383095i
$483$	0.370007	−	0.370007i	0.0168359	−	0.0168359i
$484$	15.7966	+	15.2633i	0.718028	+	0.693788i
$485$	−0.804658	+	3.35164i	−0.0365376	+	0.152190i
$486$	−8.52398	−	7.15455i	−0.386656	−	0.324537i
$487$	−11.6528	−	22.8699i	−0.528038	−	1.03633i	−0.988861	−	0.148840i	$-0.952446\pi$
$487$	−11.6528	−	22.8699i	−0.528038	−	1.03633i	0.460824	−	0.887492i	$-0.347554\pi$
$488$	−0.273082	−	10.6021i	−0.0123618	−	0.479933i
$489$	−0.581308	−	1.40340i	−0.0262876	−	0.0634640i
$490$	−14.3219	+	7.45289i	−0.646996	+	0.336687i
$491$	39.8567			1.79871			0.899354	−	0.437222i	$-0.144038\pi$
$491$	39.8567			1.79871			0.899354	+	0.437222i	$0.144038\pi$
$492$	−3.60519	−	1.46305i	−0.162535	−	0.0659594i
$493$	0.342574			0.0154287
$494$	−42.9749	+	22.3635i	−1.93353	+	1.00618i
$495$	−0.294994	−	0.712179i	−0.0132590	−	0.0320101i
$496$	−29.1955	+	22.7832i	−1.31091	+	1.02299i
$497$	−4.43919	−	8.71239i	−0.199125	−	0.390804i
$498$	5.22704	+	4.38728i	0.234229	+	0.196599i
$499$	−4.20733	+	17.5248i	−0.188346	+	0.784517i	0.795567	+	0.605866i	$0.207173\pi$
$499$	−4.20733	+	17.5248i	−0.188346	+	0.784517i	−0.983913	+	0.178651i	$0.942827\pi$
$500$	−16.5821	+	17.1615i	−0.741574	+	0.767484i
$501$	2.74982	−	2.74982i	0.122853	−	0.122853i
$502$	−30.7638	−	21.9502i	−1.37305	−	0.979686i
$503$	−15.2453	−	17.8500i	−0.679754	−	0.795890i	0.308087	−	0.951358i	$-0.400311\pi$
$503$	−15.2453	−	17.8500i	−0.679754	−	0.795890i	−0.987841	+	0.155468i	$0.950311\pi$
$504$	−3.92487	−	8.82558i	−0.174828	−	0.393122i
$505$	−13.6269	+	22.2371i	−0.606390	+	0.989539i
$506$	−0.0654496	−	0.262664i	−0.00290959	−	0.0116768i
$507$	−1.51347	+	1.77205i	−0.0672155	+	0.0786993i
$508$	16.0036	+	21.2502i	0.710046	+	0.942823i
$509$	−0.833446	+	10.5899i	−0.0369418	+	0.469391i	0.950427	+	0.310949i	$0.100647\pi$
$509$	−0.833446	+	10.5899i	−0.0369418	+	0.469391i	−0.987368	+	0.158441i	$0.949353\pi$
$510$	0.240141	−	0.761251i	0.0106336	−	0.0337088i
$511$	9.78153	−	5.99413i	0.432710	−	0.265165i
$512$	−20.8939	−	8.68599i	−0.923387	−	0.383870i
$513$	−13.3572	+	2.11557i	−0.589733	+	0.0934046i
$514$	−13.4270	−	5.42709i	−0.592239	−	0.239379i
$515$	17.1969	−	12.4943i	0.757787	−	0.550565i
$516$	−0.888399	+	2.25344i	−0.0391096	+	0.0992024i
$517$	0.592142	−	0.815013i	0.0260424	−	0.0358442i
$518$	−0.503133	+	7.18040i	−0.0221064	+	0.315489i
$519$	−5.22322	−	2.16353i	−0.229274	−	0.0949684i
$520$	25.5459	+	5.44138i	1.12026	+	0.238620i
$521$	1.10151	+	13.9960i	0.0482581	+	0.613177i	0.972732	+	0.231932i	$0.0745046\pi$
$521$	1.10151	+	13.9960i	0.0482581	+	0.613177i	−0.924474	+	0.381245i	$0.875495\pi$
$522$	−0.346664	+	1.50059i	−0.0151731	+	0.0656791i
$523$	−2.37882	−	7.32126i	−0.104019	−	0.320136i	0.885480	−	0.464677i	$-0.153830\pi$
$523$	−2.37882	−	7.32126i	−0.104019	−	0.320136i	−0.989499	+	0.144541i	$0.953830\pi$
$524$	4.60519	+	8.66707i	0.201179	+	0.378623i
$525$	0.141668	−	0.278040i	0.00618291	−	0.0121346i
$526$	−2.42603	−	5.71764i	−0.105780	−	0.249301i
$527$	−8.23429	+	1.97688i	−0.358691	+	0.0861142i
$528$	0.157427	+	0.0194209i	0.00685115	+	0.000845186i
$529$	−6.44283	+	19.8290i	−0.280123	+	0.862130i
$530$	5.20740	−	8.66377i	0.226195	−	0.376330i
$531$	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
$536$	13.3416	+	14.8301i	0.576269	+	0.640563i
$537$	−0.634155	−	0.206049i	−0.0273658	−	0.00889169i
$538$	13.2492	−	26.5642i	0.571212	−	1.14526i
$539$	−0.171262	−	0.713357i	−0.00737677	−	0.0307265i
$540$	6.28121	+	3.70233i	0.270300	+	0.159323i
$541$	−20.7913	−	10.5937i	−0.893890	−	0.455460i	−0.0542025	−	0.998530i	$-0.517262\pi$
$541$	−20.7913	−	10.5937i	−0.893890	−	0.455460i	−0.839687	+	0.543070i	$0.817262\pi$
$542$	0.507372	−	3.39159i	0.0217935	−	0.145681i
$543$	1.62124	−	0.526772i	0.0695739	−	0.0226059i
$544$	−3.52607	−	3.78666i	−0.151179	−	0.162352i
$545$	15.7920	−	1.24285i	0.676454	−	0.0532381i
$546$	−2.28553	+	0.199629i	−0.0978116	+	0.00854334i
$547$	−5.78327	+	13.9620i	−0.247275	+	0.596974i	−0.997971	−	0.0636739i	$-0.979718\pi$
$547$	−5.78327	+	13.9620i	−0.247275	+	0.596974i	0.750696	+	0.660648i	$0.229718\pi$
$548$	30.6761	−	19.5305i	1.31042	−	0.834303i
$549$	8.82055	+	6.40851i	0.376452	+	0.273508i
$550$	−0.0855248	−	0.136912i	−0.00364679	−	0.00583794i
$551$	1.65872	+	2.28303i	0.0706637	+	0.0972602i
$552$	0.979005	+	0.793477i	0.0416692	+	0.0337726i
$553$	−2.47003	−	15.5951i	−0.105036	−	0.663173i
$554$	−29.3390	−	28.8395i	−1.24649	−	1.22527i
$555$	−1.39731	−	2.28021i	−0.0593127	−	0.0967895i
$556$	−7.37354	−	21.4342i	−0.312708	−	0.909012i
$557$	37.7765	+	2.97307i	1.60064	+	0.125973i	0.847102	−	0.531431i	$-0.178345\pi$
$557$	37.7765	+	2.97307i	1.60064	+	0.125973i	0.753539	+	0.657404i	$0.228345\pi$
$558$	−0.326793	−	38.0695i	−0.0138343	−	1.61161i
$559$	−13.7815	−	11.7705i	−0.582895	−	0.497840i
$560$	5.26196	+	7.95982i	0.222358	+	0.336364i
$561$	0.0309265	+	0.0189518i	0.00130572	+	0.000800145i
$562$	−7.08048	+	6.15319i	−0.298672	+	0.259557i
$563$	−1.60877	+	1.37402i	−0.0678016	+	0.0579080i	−0.682703	−	0.730696i	$-0.739196\pi$
$563$	−1.60877	+	1.37402i	−0.0678016	+	0.0579080i	0.614902	+	0.788604i	$0.289196\pi$
$564$	0.0805107	+	4.68917i	0.00339011	+	0.197450i
$565$	8.79508	+	8.79508i	0.370012	+	0.370012i
$566$	7.07110	+	42.2923i	0.297220	+	1.77768i
$567$	9.33906	+	2.24211i	0.392204	+	0.0941598i
$568$	19.7550	−	12.8170i	0.828902	−	0.537791i
$569$	21.8953	−	11.1562i	0.917899	−	0.467693i	0.0698182	−	0.997560i	$-0.477758\pi$
$569$	21.8953	−	11.1562i	0.917899	−	0.467693i	0.848081	+	0.529867i	$0.177758\pi$
$570$	6.23598	−	2.08554i	0.261197	−	0.0873537i
$571$	−17.9499	+	7.43507i	−0.751178	+	0.311148i	−0.725222	−	0.688515i	$-0.758263\pi$
$571$	−17.9499	+	7.43507i	−0.751178	+	0.311148i	−0.0259559	+	0.999663i	$0.508263\pi$
$572$	−0.520582	+	1.06658i	−0.0217666	+	0.0445959i
$573$			7.73757i			0.323242i
$574$	10.6035	−	0.819619i	0.442582	−	0.0342102i
$575$		−	1.28249i		−	0.0534837i
$576$	20.1551	−	11.6135i	0.839794	−	0.483897i
$577$	14.5203	−	6.01449i	0.604487	−	0.250387i	−0.0593824	−	0.998235i	$-0.518913\pi$
$577$	14.5203	−	6.01449i	0.604487	−	0.250387i	0.663869	+	0.747849i	$0.268913\pi$
$578$	7.25000	+	21.6783i	0.301560	+	0.901697i
$579$	5.67247	−	2.89027i	0.235740	−	0.120115i
$580$	0.0933153	−	1.51858i	0.00387470	−	0.0630554i
$581$	−18.1383	−	4.35461i	−0.752502	−	0.180660i
$582$	0.719166	−	0.120242i	0.0298104	−	0.00498418i
$583$	0.324789	+	0.324789i	0.0134514	+	0.0134514i
$584$	16.8095	+	21.9260i	0.695582	+	0.907304i
$585$	−20.4176	+	17.4383i	−0.844165	+	0.720985i
$586$	8.04327	+	9.25540i	0.332265	+	0.382337i
$587$	32.7606	+	20.0757i	1.35217	+	0.828613i	0.994450	−	0.105214i	$-0.0335528\pi$
$587$	32.7606	+	20.0757i	1.35217	+	0.828613i	0.357724	+	0.933827i	$0.383553\pi$
$588$	2.63471	+	2.17315i	0.108653	+	0.0896191i
$589$	−53.0444	−	45.3042i	−2.18566	−	1.86673i
$590$	−10.0818	+	0.0865436i	−0.415063	+	0.00356295i
$591$	0.395478	+	0.0311248i	0.0162678	+	0.00128030i
$592$	−17.3247	+	0.595087i	−0.712040	+	0.0244579i
$593$	9.50204	+	15.5059i	0.390202	+	0.636752i	0.986070	−	0.166330i	$-0.0531918\pi$
$593$	9.50204	+	15.5059i	0.390202	+	0.636752i	−0.595868	+	0.803082i	$0.703192\pi$
$594$	−0.232251	+	0.236273i	−0.00952938	+	0.00969440i
$595$	0.341327	+	2.15505i	0.0139930	+	0.0883485i
$596$	−5.31627	−	20.5807i	−0.217763	−	0.843019i
$597$	−1.32996	−	1.83053i	−0.0544316	−	0.0749186i
$598$	−7.99697	+	4.99547i	−0.327020	+	0.204280i
$599$	32.0475	+	23.2838i	1.30942	+	0.951352i	1.00000		0.000428024i	$0.000136244\pi$
$599$	32.0475	+	23.2838i	1.30942	+	0.951352i	0.309424	+	0.950924i	$0.399864\pi$
$600$	0.701479	+	0.269617i	0.0286378	+	0.0110071i
$601$	−4.81587	+	11.6265i	−0.196443	+	0.474256i	−0.991151	−	0.132736i	$-0.957624\pi$
$601$	−4.81587	+	11.6265i	−0.196443	+	0.474256i	0.794708	+	0.606992i	$0.207624\pi$
$602$	−0.576122	−	6.59595i	−0.0234810	−	0.268831i
$603$	−20.4440	+	1.60898i	−0.832545	+	0.0655227i
$604$	13.6588	+	31.4376i	0.555768	+	1.27918i
$605$	21.2159	−	6.89348i	0.862550	−	0.280260i
$606$	5.45628	+	0.816243i	0.221646	+	0.0331576i
$607$	−12.4418	−	6.33944i	−0.504999	−	0.257310i	0.182880	−	0.983135i	$-0.441458\pi$
$607$	−12.4418	−	6.33944i	−0.504999	−	0.257310i	−0.687879	+	0.725825i	$0.741458\pi$
$608$	8.16263	−	41.8337i	0.331038	−	1.69658i
$609$	0.0311976	+	0.129947i	0.00126419	+	0.00526574i
$610$	−9.63831	−	4.80720i	−0.390244	−	0.194638i
$611$	−33.3733	−	10.8436i	−1.35014	−	0.438687i
$612$	5.29483	−	0.508309i	0.214031	−	0.0205472i
$613$	−3.64910	+	23.0395i	−0.147386	+	0.930558i	0.797538	+	0.603269i	$0.206135\pi$
$613$	−3.64910	+	23.0395i	−0.147386	+	0.930558i	−0.944924	+	0.327290i	$0.893865\pi$
$614$	−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	0.406680	−	0.913571i	$-0.366686\pi$
$617$	12.6966	+	2.01095i	0.511148	+	0.0809578i	0.104467	+	0.994528i	$0.466686\pi$
$618$	−3.85400	−	2.31647i	−0.155031	−	0.0931819i
$619$	8.19755	−	25.2295i	0.329487	−	1.01406i	−0.639887	−	0.768469i	$-0.721019\pi$
$619$	8.19755	−	25.2295i	0.329487	−	1.01406i	0.969374	−	0.245589i	$-0.0789813\pi$
$620$	6.52022	+	37.0399i	0.261858	+	1.48756i
$621$	−2.55940	+	0.614457i	−0.102705	+	0.0246573i
$622$	19.5352	−	8.28892i	0.783291	−	0.332355i
$623$	3.22865	−	6.33658i	0.129353	−	0.253870i
$624$	−1.05116	−	5.42426i	−0.0420799	−	0.217144i
$625$	6.13785	+	18.8904i	0.245514	+	0.755614i
$626$	40.0027	+	9.24136i	1.59883	+	0.369359i
$627$	0.0234427	+	0.297868i	0.000936212	+	0.0118957i
$628$	−16.5144	−	18.6769i	−0.658996	−	0.745288i
$629$	−3.66220	−	1.51693i	−0.146021	−	0.0604840i
$630$	−9.78527	−	0.685657i	−0.389855	−	0.0273172i
$631$	−12.0127	+	16.5340i	−0.478217	+	0.658210i	−0.978161	−	0.207848i	$-0.933354\pi$
$631$	−12.0127	+	16.5340i	−0.478217	+	0.658210i	0.499944	+	0.866058i	$0.333354\pi$
$632$	36.7343	−	9.82607i	1.46121	−	0.390860i
$633$	−6.80908	+	4.94709i	−0.270637	+	0.196629i
$634$	13.1375	−	32.5030i	0.521756	−	1.29086i
$635$	26.6837	−	4.22629i	1.05891	−	0.167715i
$636$	−2.11741	−	0.298198i	−0.0839606	−	0.0118243i
$637$	−21.7885	+	13.3520i	−0.863292	+	0.529026i
$638$	0.0659314	+	0.0207984i	0.00261025	+	0.000823418i
$639$	−1.89938	+	24.1339i	−0.0751384	+	0.954724i
$640$	−17.7462	+	14.5991i	−0.701479	+	0.577079i
$641$	27.6577	−	32.3830i	1.09241	−	1.27905i	0.134837	−	0.990868i	$-0.456949\pi$
$641$	27.6577	−	32.3830i	1.09241	−	1.27905i	0.957575	−	0.288183i	$-0.0930510\pi$
$642$	−1.31120	+	0.326719i	−0.0517488	+	0.0128946i
$643$	2.49973	−	4.07919i	0.0985798	−	0.160868i	−0.799548	−	0.600602i	$-0.794928\pi$
$643$	2.49973	−	4.07919i	0.0985798	−	0.160868i	0.898128	+	0.439735i	$0.144928\pi$
$644$	−3.36277	−	0.746515i	−0.132512	−	0.0294168i
$645$	1.59760	+	1.87055i	0.0629055	+	0.0736529i
$646$	5.66091	−	7.93390i	0.222725	−	0.312155i
$647$	28.0505	−	28.0505i	1.10278	−	1.10278i	0.108705	−	0.994074i	$-0.465330\pi$
$647$	28.0505	−	28.0505i	1.10278	−	1.10278i	0.994074	−	0.108705i	$-0.0346703\pi$
$648$	−3.02892	+	22.9311i	−0.118987	+	0.900818i
$649$	0.106949	−	0.445476i	0.00419813	−	0.0174865i
$650$	−3.61501	+	4.30695i	−0.141792	+	0.168932i
$651$	−1.49977	−	2.94346i	−0.0587805	−	0.115363i
$652$	−5.73790	+	8.18960i	−0.224714	+	0.320729i
$653$	−18.4480	−	44.5374i	−0.721926	−	1.74288i	−0.667791	−	0.744349i	$-0.732760\pi$
$653$	−18.4480	−	44.5374i	−0.721926	−	1.74288i	−0.0541347	−	0.998534i	$-0.517240\pi$
$654$	−1.54687	−	2.97255i	−0.0604874	−	0.116236i
$655$	9.96731			0.389455
$656$	4.62155	+	25.1921i	0.180441	+	0.983586i
$657$	−28.4023			−1.10808
$658$	−5.91775	−	11.3718i	−0.230698	−	0.443321i
$659$	−5.22152	−	12.6059i	−0.203402	−	0.491055i	0.788956	−	0.614450i	$-0.210622\pi$
$659$	−5.22152	−	12.6059i	−0.203402	−	0.491055i	−0.992358	+	0.123395i	$0.960622\pi$
$660$	0.0924346	−	0.131930i	0.00359801	−	0.00513537i
$661$	−8.04929	−	15.7976i	−0.313081	−	0.614456i	0.679823	−	0.733376i	$-0.262057\pi$
$661$	−8.04929	−	15.7976i	−0.313081	−	0.614456i	−0.992904	+	0.118920i	$0.962057\pi$
$662$	−4.38699	+	5.22669i	−0.170505	+	0.203141i
$663$	0.294942	−	1.22852i	0.0114546	−	0.0477118i
$664$	5.88275	−	44.5366i	0.228295	−	1.72835i
$665$	−12.7093	+	12.7093i	−0.492846	+	0.492846i
$666$	10.3506	−	14.5066i	0.401078	−	0.562121i
$667$	0.356706	+	0.417648i	0.0138117	+	0.0161714i
$668$	−24.9915	−	5.54797i	−0.966951	−	0.214657i
$669$	2.72760	−	4.45104i	0.105455	−	0.172087i
$670$	19.6575	−	4.89820i	0.759437	−	0.189234i
$671$	0.317850	−	0.372155i	0.0122705	−	0.0143669i
$672$	1.11527	−	1.68238i	0.0430225	−	0.0648992i
$673$	−2.35035	+	29.8640i	−0.0905992	+	1.15117i	0.768669	+	0.639647i	$0.220919\pi$
$673$	−2.35035	+	29.8640i	−0.0905992	+	1.15117i	−0.859268	+	0.511526i	$0.829081\pi$
$674$	−32.9292	−	10.3877i	−1.26839	−	0.400120i
$675$	−1.33836	+	0.820149i	−0.0515136	+	0.0315676i
$676$	15.1909	+	2.13936i	0.584265	+	0.0822832i
$677$	−7.34411	+	1.16319i	−0.282257	+	0.0447051i	−0.295958	−	0.955201i	$-0.595639\pi$
$677$	−7.34411	+	1.16319i	−0.282257	+	0.0447051i	0.0137008	+	0.999906i	$0.495639\pi$
$678$	0.985992	−	2.43941i	0.0378668	−	0.0936851i
$679$	−1.61244	+	1.17151i	−0.0618798	+	0.0449583i
$680$	−5.07622	+	1.35784i	−0.194664	+	0.0520707i
$681$	4.31031	−	5.93263i	0.165171	−	0.227339i
$682$	−1.70478	−	0.119455i	−0.0652796	−	0.00457416i
$683$	−33.4642	−	13.8613i	−1.28047	−	0.530389i	−0.364340	−	0.931266i	$-0.618705\pi$
$683$	−33.4642	−	13.8613i	−1.28047	−	0.530389i	−0.916132	+	0.400877i	$0.868705\pi$
$684$	29.0247	+	32.8254i	1.10979	+	1.25511i
$685$	−2.89762	−	36.8178i	−0.110713	−	1.40674i
$686$	−20.4241	−	4.71834i	−0.779796	−	0.180147i
$687$	−0.119486	−	0.367741i	−0.00455869	−	0.0140302i
$688$	15.6542	−	3.03360i	0.596811	−	0.115655i
$689$	7.26354	−	14.2555i	0.276719	−	0.543091i
$690$	1.17813	−	0.499887i	0.0448505	−	0.0190304i
$691$	−7.84909	+	1.88440i	−0.298593	+	0.0716859i	−0.379974	−	0.924997i	$-0.624067\pi$
$691$	−7.84909	+	1.88440i	−0.298593	+	0.0716859i	0.0813807	+	0.996683i	$0.474067\pi$
$692$	6.45221	+	36.6535i	0.245276	+	1.39336i
$693$	0.137739	−	0.423916i	0.00523226	−	0.0161032i
$694$	22.8058	+	13.7075i	0.865696	+	0.520331i
$695$	−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
$700$	−2.04481	+	0.196303i	−0.0772865	+	0.00741957i
$701$	15.9918	+	5.19606i	0.604003	+	0.196253i	0.595025	−	0.803707i	$-0.297142\pi$
$701$	15.9918	+	5.19606i	0.604003	+	0.196253i	0.00897818	+	0.999960i	$0.497142\pi$
$702$	10.3271	+	5.15075i	0.389772	+	0.194403i
$703$	−7.62274	−	31.7510i	−0.287497	−	1.19751i
$704$	−0.448727	−	0.942853i	−0.0169120	−	0.0355351i
$705$	4.24373	+	2.16229i	0.159828	+	0.0814364i
$706$	−20.6703	−	3.09222i	−0.777938	−	0.116377i
$707$	−14.3423	+	4.66010i	−0.539398	+	0.175261i
$708$	0.849885	+	1.95613i	0.0319406	+	0.0735158i
$709$	−33.4973	+	2.63630i	−1.25802	+	0.0990083i	−0.689880	−	0.723924i	$-0.742337\pi$
$709$	−33.4973	+	2.63630i	−1.25802	+	0.0990083i	−0.568139	+	0.822932i	$0.692337\pi$
$710$	−2.08093	−	23.8244i	−0.0780961	−	0.894112i
$711$	−14.9597	+	36.1158i	−0.561031	+	1.35445i
$712$	15.9868	+	6.14463i	0.599132	+	0.230280i
$713$	−10.9841	−	7.98041i	−0.411357	−	0.298869i
$714$	0.391460	−	0.244534i	0.0146500	−	0.00915144i
$715$	0.708464	+	0.975117i	0.0264951	+	0.0364673i
$716$	1.09781	+	4.24993i	0.0410271	+	0.158827i
$717$	−0.751747	−	4.74634i	−0.0280745	−	0.177255i
$718$	−2.60904	+	2.65422i	−0.0973684	+	0.0990545i
$719$	11.1696	+	18.2272i	0.416556	+	0.679758i	0.990248	−	0.139313i	$-0.0444894\pi$
$719$	11.1696	+	18.2272i	0.416556	+	0.679758i	−0.573692	+	0.819071i	$0.694489\pi$
$720$	−0.810970	−	23.6096i	−0.0302231	−	0.879879i
$721$	12.2533	+	0.964354i	0.456336	+	0.0359144i
$722$	53.4148	−	0.458519i	1.98789	−	0.0170643i
$723$	−2.36555	−	2.02037i	−0.0879756	−	0.0751383i
$724$	−8.65690	−	7.14035i	−0.321731	−	0.265369i
$725$	0.279275	+	0.171140i	0.0103720	+	0.00635599i
$726$	−3.09541	−	3.56188i	−0.114881	−	0.132194i
$727$	−30.3591	+	25.9291i	−1.12596	+	0.961658i	−0.999540	−	0.0303193i	$-0.990348\pi$
$727$	−30.3591	+	25.9291i	−1.12596	+	0.961658i	−0.126417	+	0.991977i	$0.540348\pi$
$728$	9.18883	+	11.9857i	0.340561	+	0.444221i
$729$	−15.6572	−	15.6572i	−0.579895	−	0.579895i
$730$	27.6738	−	4.62695i	1.02425	−	0.171251i
$731$	3.54546	+	0.851191i	0.131134	+	0.0314824i
$732$	−0.139742	+	2.27411i	−0.00516503	+	0.0840537i
$733$	−19.5528	+	9.96267i	−0.722201	+	0.367980i	−0.776137	−	0.630565i	$-0.782823\pi$
$733$	−19.5528	+	9.96267i	−0.722201	+	0.367980i	0.0539359	+	0.998544i	$0.482823\pi$
$734$	8.06645	+	24.1195i	0.297738	+	0.890268i
$735$	3.20443	−	1.32732i	0.118197	−	0.0489588i
$736$	0.944979	−	8.24168i	0.0348324	−	0.303792i
$737$			0.920549i			0.0339089i
$738$	−23.4438	−	11.9865i	−0.862977	−	0.441227i
$739$			5.96203i			0.219317i	0.993969	+	0.109658i	$0.0349757\pi$
$739$			5.96203i			0.219317i	−0.993969	+	0.109658i	$0.965024\pi$
$740$	−7.72189	+	15.8208i	−0.283862	+	0.581582i
$741$	9.61537	−	3.98282i	0.353229	−	0.146312i
$742$	5.54314	−	1.85383i	0.203495	−	0.0680562i
$743$	−5.88472	+	2.99841i	−0.215889	+	0.110001i	−0.558591	−	0.829443i	$-0.688658\pi$
$743$	−5.88472	+	2.99841i	−0.215889	+	0.110001i	0.342702	+	0.939444i	$0.388658\pi$
$744$	6.67418	−	4.33020i	0.244687	−	0.158753i
$745$	−20.9906	−	5.03940i	−0.769036	−	0.184629i
$746$	2.98380	+	17.8461i	0.109245	+	0.653393i
$747$	32.6559	+	32.6559i	1.19482	+	1.19482i
$748$	−0.00409899	−	0.238737i	−0.000149874	−	0.00872909i
$749$	2.80869	−	2.39885i	0.102627	−	0.0876519i
$750$	3.86964	−	3.36285i	0.141299	−	0.122794i
$751$	18.6109	+	11.4048i	0.679122	+	0.416166i	0.818838	−	0.574025i	$-0.194619\pi$
$751$	18.6109	+	11.4048i	0.679122	+	0.416166i	−0.139716	+	0.990192i	$0.544619\pi$
$752$	25.7543	−	17.0252i	0.939161	−	0.620847i
$753$	6.17362	+	5.27277i	0.224979	+	0.192150i
$754$	−0.0206708	−	2.40803i	−0.000752787	−	0.0876953i
$755$	34.7027	+	2.73116i	1.26296	+	0.0993971i
$756$	1.37144	+	3.98665i	0.0498789	+	0.144993i
$757$	−14.4608	−	23.5979i	−0.525588	−	0.857681i	0.474153	−	0.880442i	$-0.342754\pi$
$757$	−14.4608	−	23.5979i	−0.525588	−	0.857681i	−0.999741	+	0.0227611i	$0.992754\pi$
$758$	19.2863	+	18.9580i	0.700511	+	0.688587i
$759$	0.00909723	+	0.0574376i	0.000330209	+	0.00208485i
$760$	−33.6278	−	27.2551i	−1.21981	−	0.988646i
$761$	14.4672	+	19.9124i	0.524435	+	0.721822i	0.986270	−	0.165143i	$-0.0528087\pi$
$761$	14.4672	+	19.9124i	0.524435	+	0.721822i	−0.461835	+	0.886966i	$0.652809\pi$
$762$	−3.02780	−	4.84703i	−0.109686	−	0.175589i
$763$	7.41028	+	5.38389i	0.268270	+	0.194910i
$764$	42.9666	−	27.3555i	1.55448	−	0.989688i
$765$	2.06724	−	4.99075i	0.0747411	−	0.180441i
$766$	−20.1165	+	1.75707i	−0.726837	+	0.0634855i
$767$	−15.9088	+	1.25205i	−0.574434	+	0.0452089i
$768$	4.30925	+	2.24951i	0.155497	+	0.0811723i
$769$	40.1606	−	13.0490i	1.44823	−	0.470557i	0.523775	−	0.851857i	$-0.324523\pi$
$769$	40.1606	−	13.0490i	1.44823	−	0.470557i	0.924452	+	0.381299i	$0.124523\pi$
$770$	−0.0651468	+	0.435482i	−0.00234773	+	0.0156937i
$771$	2.77214	+	1.41248i	0.0998362	+	0.0508691i
$772$	−36.1042	−	21.2809i	−1.29942	−	0.765915i
$773$	5.90112	+	24.5799i	0.212249	+	0.884079i	0.972210	+	0.234111i	$0.0752179\pi$
$773$	5.90112	+	24.5799i	0.212249	+	0.884079i	−0.759961	+	0.649968i	$0.774782\pi$
$774$	−7.31631	+	14.6690i	−0.262979	+	0.527266i
$775$	−7.70042	−	2.50202i	−0.276607	−	0.0898751i
$776$	−3.21025	−	3.56842i	−0.115241	−	0.128099i
$777$	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
$782$	0.977236	−	1.62587i	0.0349459	−	0.0581409i
$783$	0.207731	−	0.639329i	0.00742369	−	0.0228478i
$784$	2.75268	−	22.3135i	0.0983101	−	0.796910i
$785$	−24.6193	+	5.91057i	−0.878701	+	0.210957i
$786$	−0.823569	−	1.94098i	−0.0293757	−	0.0692324i
$787$	5.27600	−	10.3547i	0.188069	−	0.369106i	−0.777649	−	0.628698i	$-0.783588\pi$
$787$	5.27600	−	10.3547i	0.188069	−	0.369106i	0.965718	+	0.259592i	$0.0835881\pi$
$788$	−1.22534	−	2.30612i	−0.0436510	−	0.0821523i
$789$	0.412328	+	1.26902i	0.0146793	+	0.0451782i
$790$	8.69243	−	37.6265i	0.309263	−	1.33869i
$791$	0.564284	+	7.16991i	0.0200636	+	0.254933i
$792$	1.04990	+	0.223633i	0.0373065	+	0.00794644i
$793$	−15.7499	−	6.52384i	−0.559297	−	0.231668i
$794$	0.502351	−	7.16925i	0.0178278	−	0.254427i
$795$	−1.27642	+	1.75684i	−0.0452700	+	0.0623088i
$796$	−5.46296	+	13.8569i	−0.193629	+	0.491146i
$797$	2.99527	−	2.17619i	0.106098	−	0.0770847i	−0.533471	−	0.845818i	$-0.679113\pi$
$797$	2.99527	−	2.17619i	0.106098	−	0.0770847i	0.639569	+	0.768734i	$0.279113\pi$
$798$	3.52507	+	1.42481i	0.124786	+	0.0504377i
$799$	6.97274	−	1.10437i	0.246678	−	0.0390700i
$800$	−0.982839	−	4.84852i	−0.0347486	−	0.171421i
$801$	−15.0125	+	9.19965i	−0.530440	+	0.325054i
$802$	−8.83595	+	28.0101i	−0.312008	+	0.989071i
$803$	−0.100031	+	1.27102i	−0.00353003	+	0.0448533i
$804$	−2.57809	−	3.42328i	−0.0909223	−	0.120730i
$805$	−2.27192	+	2.66008i	−0.0800748	+	0.0937555i
$806$	14.3928	+	57.7615i	0.506965	+	2.03456i
$807$	−3.33210	+	5.43749i	−0.117295	+	0.191409i
$808$	−14.7576	−	33.1844i	−0.519172	−	1.16742i
$809$	15.0042	+	17.5677i	0.527520	+	0.617646i	0.958631	−	0.284653i	$-0.0918782\pi$
$809$	15.0042	+	17.5677i	0.527520	+	0.617646i	−0.431111	+	0.902299i	$0.641878\pi$
$810$	19.1218	+	13.6436i	0.671871	+	0.479386i
$811$	−15.3741	+	15.3741i	−0.539859	+	0.539859i	−0.923487	−	0.383629i	$-0.874674\pi$
$811$	−15.3741	+	15.3741i	−0.539859	+	0.539859i	0.383629	+	0.923487i	$0.374674\pi$
$812$	0.611300	−	0.632658i	0.0214524	−	0.0222020i
$813$	−0.171985	+	0.716370i	−0.00603179	+	0.0251242i
$814$	−0.612726	−	0.514287i	−0.0214760	−	0.0180258i
$815$	4.61039	+	9.04841i	0.161495	+	0.316952i
$816$	0.683850	+	0.876319i	0.0239395	+	0.0306773i
$817$	11.4943	+	27.7496i	0.402133	+	0.970835i
$818$	−34.4391	+	17.9216i	−1.20414	+	0.626615i
$819$	−15.5260			−0.542522
$820$	24.7951	+	7.85985i	0.865884	+	0.274478i
$821$	−25.3798			−0.885761			−0.442880	−	0.896581i	$-0.646043\pi$
$821$	−25.3798			−0.885761			−0.442880	+	0.896581i	$0.646043\pi$
$822$	−6.93027	+	3.60641i	−0.241721	+	0.125788i
$823$	−15.0356	−	36.2991i	−0.524108	−	1.26531i	−0.935331	−	0.353774i	$-0.884898\pi$
$823$	−15.0356	−	36.2991i	−0.524108	−	1.26531i	0.411223	−	0.911535i	$-0.365102\pi$
$824$	0.762185	+	29.5909i	0.0265520	+	1.03085i
$825$	0.0157444	+	0.0309000i	0.000548148	+	0.00107580i
$826$	−4.46537	−	3.74798i	−0.155370	−	0.130409i
$827$	−11.3988	+	47.4794i	−0.396375	+	1.65102i	0.315658	+	0.948873i	$0.397775\pi$
$827$	−11.3988	+	47.4794i	−0.396375	+	1.65102i	−0.712033	+	0.702146i	$0.752225\pi$
$828$	6.13296	+	5.92591i	0.213135	+	0.205940i
$829$	−9.69216	+	9.69216i	−0.336623	+	0.336623i	−0.855095	−	0.518472i	$-0.826501\pi$
$829$	−9.69216	+	9.69216i	−0.336623	+	0.336623i	0.518472	+	0.855095i	$0.326501\pi$
$830$	−37.1382	−	26.4984i	−1.28909	−	0.919773i
$831$	5.73990	+	6.72056i	0.199115	+	0.233134i
$832$	−26.4046	+	25.0141i	−0.915414	+	0.867207i
$833$	2.68619	−	4.38347i	0.0930711	−	0.151878i
$834$	1.17738	+	4.72509i	0.0407694	+	0.163617i
$835$	−16.8845	+	19.7693i	−0.584314	+	0.684143i
$836$	1.57118	−	1.18326i	0.0543403	−	0.0409240i
$837$	−1.30377	+	16.5660i	−0.0450650	+	0.572606i
$838$	7.69789	−	24.4024i	0.265919	−	0.842969i
$839$	−0.542094	+	0.332196i	−0.0187152	+	0.0114687i	−0.531825	−	0.846854i	$-0.678493\pi$
$839$	−0.542094	+	0.332196i	−0.0187152	+	0.0114687i	0.513110	+	0.858323i	$0.328493\pi$
$840$	−0.977348	−	1.80189i	−0.0337217	−	0.0621711i
$841$	28.5044	−	4.51466i	0.982911	−	0.155678i
$842$	28.3844	+	11.4728i	0.978192	+	0.395378i
$843$	1.63036	−	1.18452i	0.0561525	−	0.0407972i
$844$	51.5441	+	20.3207i	1.77422	+	0.699469i
$845$	9.15741	−	12.6041i	0.315025	−	0.433594i
$846$	−2.21847	+	31.6606i	−0.0762724	+	1.08851i
$847$	11.9171	+	4.93623i	0.409477	+	0.169611i
$848$	5.83002	+	12.8122i	0.200204	+	0.439972i
$849$	−0.722750	−	9.18341i	−0.0248047	−	0.315174i
$850$	0.254633	−	1.10222i	0.00873384	−	0.0378058i
$851$	−1.96390	−	6.04427i	−0.0673218	−	0.207195i
$852$	−4.46748	+	2.37376i	−0.153053	+	0.0813238i
$853$	−0.573733	+	1.12601i	−0.0196442	+	0.0385540i	−0.900620	−	0.434607i	$-0.856887\pi$
$853$	−0.573733	+	1.12601i	−0.0196442	+	0.0385540i	0.880976	+	0.473161i	$0.156887\pi$
$854$	−2.43261	−	5.73315i	−0.0832422	−	0.196184i
$855$	43.2695	−	10.3881i	1.47978	−	0.355265i
$856$	6.44989	+	6.12597i	0.220453	+	0.209381i
$857$	10.9780	−	33.7868i	0.375001	−	1.15413i	−0.568477	−	0.822699i	$-0.692467\pi$
$857$	10.9780	−	33.7868i	0.375001	−	1.15413i	0.943478	−	0.331435i	$-0.107533\pi$
$858$	0.131351	−	0.218533i	0.00448423	−	0.00746060i
$859$	−15.5005	−	2.45504i	−0.528870	−	0.0837648i	−0.113711	−	0.993514i	$-0.536274\pi$
$859$	−15.5005	−	2.45504i	−0.528870	−	0.0837648i	−0.415159	+	0.909749i	$0.636274\pi$
$860$	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	−0.907323	−	0.420434i	$-0.861878\pi$
$863$	2.51213	−	15.8609i	0.0855138	−	0.539913i	0.992837	−	0.119479i	$-0.0381223\pi$
$864$	−9.20502	+	4.28437i	−0.313161	+	0.145757i
$865$	35.9463	+	11.6797i	1.22221	+	0.397121i
$866$	−1.26337	+	2.53303i	−0.0429311	+	0.0860758i
$867$	−1.14638	−	4.77502i	−0.0389331	−	0.162168i
$868$	−11.0427	+	18.7345i	−0.374814	+	0.635892i
$869$	1.56352	+	0.796652i	0.0530387	+	0.0270246i
$870$	−0.0483580	+	0.323255i	−0.00163949	+	0.0109594i
$871$	30.4957	−	9.90867i	1.03331	−	0.335742i
$872$	−11.0377	+	19.0989i	−0.373783	+	0.646771i
$873$	4.91924	−	0.387152i	0.166491	−	0.0131031i
$874$	15.5670	−	1.35970i	0.526563	−	0.0459926i
$875$	−5.36273	+	12.9468i	−0.181293	+	0.437681i
$876$	−3.18763	−	5.00673i	−0.107700	−	0.169162i
$877$	−9.05934	−	6.58199i	−0.305912	−	0.222258i	0.424228	−	0.905555i	$-0.360545\pi$
$877$	−9.05934	−	6.58199i	−0.305912	−	0.222258i	−0.730140	+	0.683297i	$0.760545\pi$
$878$	20.2345	+	32.3923i	0.682882	+	1.09319i
$879$	−1.54838	−	2.13116i	−0.0522254	−	0.0718821i
$880$	−1.05940	−	0.0468605i	−0.0357124	−	0.00157967i
$881$	−2.54746	−	16.0840i	−0.0858261	−	0.541885i	−0.992712	−	0.120509i	$-0.961547\pi$
$881$	−2.54746	−	16.0840i	−0.0858261	−	0.541885i	0.906886	−	0.421376i	$-0.138453\pi$
$882$	16.4828	+	16.2023i	0.555006	+	0.545559i
$883$	−1.85331	−	3.02432i	−0.0623688	−	0.101777i	0.819936	−	0.572455i	$-0.194009\pi$
$883$	−1.85331	−	3.02432i	−0.0623688	−	0.101777i	−0.882305	+	0.470679i	$0.844009\pi$
$884$	−7.86470	+	2.70552i	−0.264519	+	0.0909966i
$885$	2.15929	+	0.169940i	0.0725838	+	0.00571247i
$886$	−0.355296	−	41.3899i	−0.0119364	−	1.39052i
$887$	2.00151	+	1.70945i	0.0672041	+	0.0573977i	0.682416	−	0.730964i	$-0.260929\pi$
$887$	2.00151	+	1.70945i	0.0672041	+	0.0573977i	−0.615212	+	0.788362i	$0.710929\pi$
$888$	3.71888	+	0.196495i	0.124797	+	0.00659394i
$889$	13.3196	+	8.16228i	0.446726	+	0.273754i
$890$	13.1287	−	11.4093i	0.440076	−	0.382442i
$891$	−0.811651	+	0.693216i	−0.0271913	+	0.0232236i
$892$	−34.3598	+	0.589940i	−1.15045	+	0.0197526i
$893$	41.1214	+	41.1214i	1.37608	+	1.37608i
$894$	0.753047	+	4.50398i	0.0251857	+	0.150636i
$895$	4.33457	+	1.04064i	0.144889	+	0.0347847i
$896$	−13.2852	−	0.245172i	−0.443827	−	0.00819063i
$897$	1.80486	−	0.919622i	0.0602625	−	0.0307053i
$898$	−22.2956	+	7.45646i	−0.744013	+	0.248825i
$899$	3.20357	−	1.32696i	0.106845	−	0.0442566i
$900$	4.57043	+	2.23076i	0.152348	+	0.0743587i
$901$			3.21879i			0.107233i
$902$	−0.618968	+	1.00691i	−0.0206094	+	0.0335263i
$903$			1.42241i			0.0473348i
$904$	−17.0319	+	3.14914i	−0.566473	+	0.104739i
$905$	−10.5288	+	4.36119i	−0.349990	+	0.144971i
$906$	−2.33553	−	6.98347i	−0.0775927	−	0.232010i
$907$	16.4070	−	8.35979i	0.544786	−	0.277582i	−0.159862	−	0.987139i	$-0.551105\pi$
$907$	16.4070	−	8.35979i	0.544786	−	0.277582i	0.704648	+	0.709557i	$0.251105\pi$
$908$	−48.1825	−	2.96078i	−1.59899	−	0.0982568i
$909$	36.3042	+	8.71586i	1.20413	+	0.289087i
$910$	15.1278	−	2.52930i	0.501481	−	0.0838455i
$911$	−31.6959	−	31.6959i	−1.05013	−	1.05013i	−0.998675	−	0.0514574i	$-0.983613\pi$
$911$	−31.6959	−	31.6959i	−1.05013	−	1.05013i	−0.0514574	−	0.998675i	$-0.516387\pi$
$912$	−2.52894	+	8.80049i	−0.0837415	+	0.291413i
$913$	1.57638	−	1.34636i	0.0521707	−	0.0445579i
$914$	19.6230	+	22.5802i	0.649073	+	0.746888i
$915$	1.97289	+	1.20899i	0.0652217	+	0.0399679i
$916$	−1.61963	+	1.96362i	−0.0535140	+	0.0648800i
$917$	4.38251	+	3.74302i	0.144723	+	0.123605i
$918$	−2.32163	+	0.0199292i	−0.0766253	+	0.000657761i
$919$	24.0266	+	1.89093i	0.792564	+	0.0623761i	0.468276	−	0.883582i	$-0.344875\pi$
$919$	24.0266	+	1.89093i	0.792564	+	0.0623761i	0.324288	+	0.945958i	$0.394875\pi$
$920$	−6.94103	−	4.77482i	−0.228839	−	0.157421i
$921$	4.14692	+	6.76716i	0.136646	+	0.222986i
$922$	4.22118	−	4.29427i	0.139017	−	0.141424i
$923$	−5.92144	−	37.3865i	−0.194906	−	1.23059i
$924$	0.0901862	−	0.0232963i	0.00296691	−	0.000766391i
$925$	−2.22771	−	3.06618i	−0.0732465	−	0.100815i
$926$	−16.4809	+	10.2951i	−0.541595	+	0.338319i
$927$	−24.6186	−	17.8865i	−0.808581	−	0.587469i
$928$	1.66860	+	1.30558i	0.0547746	+	0.0428576i
$929$	5.55638	−	13.4143i	0.182299	−	0.440108i	−0.806141	−	0.591724i	$-0.798448\pi$
$929$	5.55638	−	13.4143i	0.182299	−	0.440108i	0.988440	+	0.151615i	$0.0484475\pi$
$930$	−0.703039	−	8.04900i	−0.0230535	−	0.263937i
$931$	42.2193	−	3.32273i	1.38368	−	0.108898i
$932$	20.0683	−	8.71914i	0.657359	−	0.285605i
$933$	−4.33580	+	1.40879i	−0.141948	+	0.0461216i
$934$	−3.44887	−	0.515941i	−0.112851	−	0.0168821i
$935$	−0.216058	−	0.110087i	−0.00706586	−	0.00360024i
$936$	−3.89251	−	37.1879i	−0.127231	−	1.21553i
$937$	−2.04042	−	8.49895i	−0.0666575	−	0.277649i	0.929080	−	0.369878i	$-0.120601\pi$
$937$	−2.04042	−	8.49895i	−0.0666575	−	0.277649i	−0.995738	+	0.0922296i	$0.970601\pi$
$938$	10.4826	+	5.22831i	0.342270	+	0.170710i
$939$	−8.38846	−	2.72558i	−0.273747	−	0.0889458i
$940$	−2.99618	−	31.2099i	−0.0977247	−	1.01796i
$941$	−0.700766	+	4.42446i	−0.0228443	+	0.144233i	−0.996474	−	0.0839002i	$-0.973262\pi$
$941$	−0.700766	+	4.42446i	−0.0228443	+	0.144233i	0.973630	+	0.228134i	$0.0732623\pi$
$942$	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
$946$	0.630679	+	0.379073i	0.0205051	+	0.0123247i
$947$	6.20996	−	19.1123i	0.201797	−	0.621066i	−0.798033	−	0.602614i	$-0.794126\pi$
$947$	6.20996	−	19.1123i	0.201797	−	0.621066i	0.999830	−	0.0184527i	$-0.00587402\pi$
$948$	−8.04541	+	1.41625i	−0.261303	+	0.0459978i
$949$	43.1828	−	10.3673i	1.40177	−	0.336536i
$950$	8.57848	−	3.63990i	0.278323	−	0.118094i
$951$	−3.41922	+	6.71059i	−0.110876	+	0.217606i
$952$	−2.74186	−	1.30924i	−0.0888643	−	0.0424328i
$953$	−15.8667	−	48.8327i	−0.513973	−	1.58185i	−0.785143	−	0.619315i	$-0.787410\pi$
$953$	−15.8667	−	48.8327i	−0.513973	−	1.58185i	0.271169	−	0.962532i	$-0.412590\pi$
$954$	−14.0994	−	3.25722i	−0.456485	−	0.105457i
$955$	−4.05857	−	51.5690i	−0.131332	−	1.66873i
$956$	−23.6987	+	20.9547i	−0.766469	+	0.677725i
$957$	−0.0137216	−	0.00568366i	−0.000443555	−	0.000183727i
$958$	−31.9559	−	2.23916i	−1.03245	−	0.0723439i
$959$	12.5521	−	17.2765i	0.405329	−	0.557888i
$960$	4.07087	−	2.79270i	0.131387	−	0.0901340i
$961$	−44.2657	+	32.1609i	−1.42793	+	1.03745i
$962$	−10.4419	+	25.8340i	−0.336660	+	0.832921i
$963$	−9.03213	+	1.43055i	−0.291056	+	0.0460988i
$964$	−2.85589	+	20.2787i	−0.0919819	+	0.653132i
$965$	−36.2896	+	22.2383i	−1.16820	+	0.715876i
$966$	0.705731	+	0.222627i	0.0227065	+	0.00716291i
$967$	1.86495	−	23.6964i	0.0599726	−	0.762024i	−0.891249	−	0.453515i	$-0.850170\pi$
$967$	1.86495	−	23.6964i	0.0599726	−	0.762024i	0.951221	−	0.308509i	$-0.0998301\pi$
$968$	−8.83555	+	29.7815i	−0.283985	+	0.957213i
$969$	−1.35983	+	1.59216i	−0.0436842	+	0.0511476i
$970$	−4.73000	+	1.17860i	−0.151871	+	0.0378427i
$971$	17.8532	−	29.1338i	0.572937	−	0.934948i	−0.426598	−	0.904442i	$-0.640288\pi$
$971$	17.8532	−	29.1338i	0.572937	−	0.934948i	0.999535	−	0.0305066i	$-0.00971206\pi$
$972$	3.41076	−	15.3642i	0.109400	−	0.492807i
$973$	−8.64460	−	10.1215i	−0.277133	−	0.324481i
$974$	21.0833	−	29.5488i	0.675552	−	0.946803i
$975$	0.854179	−	0.854179i	0.0273556	−	0.0273556i
$976$	13.1222	−	7.26395i	0.420031	−	0.232513i
$977$	0.974186	−	4.05778i	0.0311670	−	0.129820i	−0.954618	−	0.297835i	$-0.903736\pi$
$977$	0.974186	−	4.05778i	0.0311670	−	0.129820i	0.985784	+	0.168015i	$0.0537356\pi$
$978$	1.38109	−	1.64544i	0.0441625	−	0.0526155i
$979$	0.358817	+	0.704218i	0.0114678	+	0.0225069i
$980$	−18.6995	−	13.1015i	−0.597335	−	0.418513i
$981$	−8.67820	−	20.9510i	−0.277073	−	0.668914i
$982$	26.0197	+	50.0009i	0.830323	+	1.59559i
$983$	34.8359			1.11109			0.555546	−	0.831486i	$-0.312509\pi$
$983$	34.8359			1.11109			0.555546	+	0.831486i	$0.312509\pi$
$984$	−0.518165	−	5.47790i	−0.0165185	−	0.174629i
$985$	−2.65209			−0.0845026
$986$	0.223643	+	0.429764i	0.00712224	+	0.0136865i
$987$	1.05392	+	2.54438i	0.0335465	+	0.0809885i
$988$	−56.1109	−	39.3131i	−1.78512	−	1.25072i
$989$	2.65399	+	5.20876i	0.0843921	+	0.165629i
$990$	0.700858	−	0.835008i	0.0222747	−	0.0265383i
$991$	1.78348	−	7.42875i	0.0566543	−	0.235982i	−0.936858	−	0.349711i	$-0.886280\pi$
$991$	1.78348	−	7.42875i	0.0566543	−	0.235982i	0.993512	+	0.113729i	$0.0362797\pi$
$992$	−47.6416	−	21.7526i	−1.51262	−	0.690646i
$993$	1.03659	−	1.03659i	0.0328952	−	0.0328952i
$994$	8.03179	−	11.2568i	0.254753	−	0.357043i
$995$	9.82401	+	11.5024i	0.311442	+	0.364652i
$996$	−2.09153	+	9.42157i	−0.0662728	+	0.298534i
$997$	−31.0349	+	50.6444i	−0.982886	+	1.60392i	−0.201870	+	0.979412i	$0.564702\pi$
$997$	−31.0349	+	50.6444i	−0.982886	+	1.60392i	−0.781016	+	0.624512i	$0.785298\pi$
$998$	−24.7318	+	6.16258i	−0.782872	+	0.195073i
$999$	−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.15.13	yes	288
4.3	odd	2	inner	164.2.o.b.15.15	yes	288
41.11	odd	40	inner	164.2.o.b.11.15	yes	288
164.11	even	40	inner	164.2.o.b.11.13	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.b.11.13	✓	288	164.11	even	40	inner
164.2.o.b.11.15	yes	288	41.11	odd	40	inner
164.2.o.b.15.13	yes	288	1.1	even	1	trivial
164.2.o.b.15.15	yes	288	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(0.652832 + 1.25452i) q^{2} +(-0.116266 - 0.280690i) q^{3} +(-1.14762 + 1.63798i) q^{4} +(0.922111 + 1.80974i) q^{5} +(0.276228 - 0.329100i) q^{6} +(-0.274171 + 1.14200i) q^{7} +(-2.80407 - 0.370385i) q^{8} +(2.05605 - 2.05605i) q^{9} +O(q^{10})\)	\(q+(0.652832 + 1.25452i) q^{2} +(-0.116266 - 0.280690i) q^{3} +(-1.14762 + 1.63798i) q^{4} +(0.922111 + 1.80974i) q^{5} +(0.276228 - 0.329100i) q^{6} +(-0.274171 + 1.14200i) q^{7} +(-2.80407 - 0.370385i) q^{8} +(2.05605 - 2.05605i) q^{9} +(-1.66837 + 2.33826i) q^{10} +(-0.0847682 - 0.0992508i) q^{11} +(0.593192 + 0.131685i) q^{12} +(-2.37552 + 3.87650i) q^{13} +(-1.61165 + 0.401585i) q^{14} +(0.400767 - 0.469238i) q^{15} +(-1.36593 - 3.75955i) q^{16} +(0.0717643 - 0.911852i) q^{17} +(3.92161 + 1.23709i) q^{18} +(6.42437 - 3.93686i) q^{19} +(-4.02255 - 0.566504i) q^{20} +(0.352426 - 0.0558188i) q^{21} +(0.0691723 - 0.171137i) q^{22} +(1.18641 - 0.861977i) q^{23} +(0.222054 + 0.830137i) q^{24} +(0.514040 - 0.707515i) q^{25} +(-6.41395 - 0.449427i) q^{26} +(-1.65823 - 0.686862i) q^{27} +(-1.55593 - 1.75967i) q^{28} +(0.0293854 + 0.373377i) q^{29} +(0.850300 + 0.196435i) q^{30} +(-2.86096 - 8.80513i) q^{31} +(3.82469 - 4.16794i) q^{32} +(-0.0180031 + 0.0353330i) q^{33} +(1.19078 - 0.505257i) q^{34} +(-2.31955 + 0.556875i) q^{35} +(1.00820 + 5.72733i) q^{36} +(1.33919 - 4.12161i) q^{37} +(9.13289 + 5.48937i) 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} +(0.259852 - 0.0249461i) q^{44} +(5.61683 + 1.82502i) q^{45} +(1.85589 + 0.925643i) q^{46} +(1.80179 + 7.50499i) q^{47} +(-0.896457 + 0.820510i) q^{48} +(5.00804 + 2.55172i) q^{49} +(1.22317 + 0.182983i) q^{50} +(-0.264291 + 0.0858735i) q^{51} +(-3.62342 - 8.33981i) q^{52} +(-3.50822 + 0.276103i) q^{53} +(-0.220867 - 2.52868i) q^{54} +(0.101453 - 0.244929i) q^{55} +(1.19178 - 3.10071i) q^{56} +(-1.85197 - 1.34553i) q^{57} +(-0.449224 + 0.280617i) q^{58} +(2.06311 + 2.83963i) q^{59} +(0.308672 + 1.19495i) q^{60} +(0.586573 + 3.70347i) q^{61} +(9.17845 - 9.33739i) q^{62} +(1.78431 + 2.91173i) q^{63} +(7.72563 + 2.07717i) q^{64} +(-9.20598 - 0.724526i) q^{65} +(-0.0560788 + 0.000481387i) q^{66} +(-5.36295 - 4.58039i) q^{67} +(1.41123 + 1.16401i) q^{68} +(-0.379887 - 0.232795i) q^{69} +(-2.21289 - 2.54637i) q^{70} +(-6.33090 + 5.40710i) q^{71} +(-6.52684 + 5.00378i) q^{72} +(-6.90701 - 6.90701i) q^{73} +(6.04490 - 1.01068i) q^{74} +(-0.258358 - 0.0620262i) q^{75} +(-0.924256 + 15.0410i) q^{76} +(0.136586 - 0.0695940i) q^{77} +(0.619572 + 1.85259i) q^{78} +(-12.4208 + 5.14485i) q^{79} +(5.54428 - 5.93871i) q^{80} -8.17778i q^{81} +(-2.78624 - 8.61608i) q^{82} +15.8828i q^{83} +(-0.313021 + 0.641324i) q^{84} +(1.71639 - 0.710954i) q^{85} +(-5.34649 + 1.78806i) q^{86} +(0.101387 - 0.0516591i) q^{87} +(0.200935 + 0.309703i) q^{88} +(-5.88802 - 1.41359i) q^{89} +(1.37733 + 8.23784i) q^{90} +(-3.77568 - 3.77568i) q^{91} +(0.0503501 + 2.93253i) q^{92} +(-2.13888 + 1.82678i) q^{93} +(-8.23886 + 7.15987i) q^{94} +(13.0487 + 7.99625i) q^{95} +(-1.61458 - 0.588964i) q^{96} +(1.29043 + 1.10213i) q^{97} +(0.0682310 + 7.94851i) 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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