LMFDB - Embedded newform 690.2.m.g.601.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (of order $11$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			601.1
Character	$\chi$	$=$	690.601
Dual form			690.2.m.g.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-2.43922 + 1.56759i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-2.43922 + 1.56759i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.841254 + 0.540641i) q^{10} +(-0.314571 + 2.18789i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(3.10077 + 1.99274i) q^{13} +(1.89877 + 2.19130i) q^{14} +(0.415415 + 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(5.05307 + 1.48372i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(6.48142 - 1.90312i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.412642 + 2.86999i) q^{21} +2.21039 q^{22} +(-0.0513676 - 4.79556i) q^{23} +1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(1.53117 - 3.35280i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(1.89877 - 2.19130i) q^{28} +(0.668051 + 0.196157i) q^{29} +(0.841254 - 0.540641i) q^{30} +(2.94169 + 6.44141i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.85950 + 1.19503i) q^{33} +(0.749487 - 5.21280i) q^{34} +(0.412642 - 2.86999i) q^{35} +(0.841254 + 0.540641i) q^{36} +(2.74949 + 3.17307i) q^{37} +(-2.80615 - 6.14461i) q^{38} +(3.10077 - 1.99274i) q^{39} +(-0.959493 - 0.281733i) q^{40} +(-5.15699 + 5.95149i) q^{41} +(2.78205 - 0.816884i) q^{42} +(-4.08164 + 8.93754i) q^{43} +(-0.314571 - 2.18789i) q^{44} +1.00000 q^{45} +(-4.73943 + 0.733324i) q^{46} -6.60033 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.584533 - 1.27995i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(3.44876 - 3.98008i) q^{51} +(-3.53658 - 1.03843i) q^{52} +(7.40426 - 4.75843i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-1.44750 - 1.67050i) q^{55} +(-2.43922 - 1.56759i) q^{56} +(0.961343 - 6.68629i) q^{57} +(0.0990873 - 0.689167i) q^{58} +(3.98705 + 2.56232i) q^{59} +(-0.654861 - 0.755750i) q^{60} +(5.67397 + 12.4243i) q^{61} +(5.95720 - 3.82846i) q^{62} +(2.78205 + 0.816884i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-3.53658 + 1.03843i) q^{65} +(0.918230 - 2.01064i) q^{66} +(-1.92613 - 13.3966i) q^{67} -5.26640 q^{68} +(-4.38353 - 1.94542i) q^{69} -2.89950 q^{70} +(-0.532089 - 3.70076i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-8.25168 + 2.42291i) q^{73} +(2.74949 - 3.17307i) q^{74} +(-0.959493 - 0.281733i) q^{75} +(-5.68271 + 3.65205i) q^{76} +(-2.66241 - 5.82986i) q^{77} +(-2.41374 - 2.78561i) q^{78} +(10.3240 + 6.63482i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(6.62482 + 4.25752i) q^{82} +(-10.2066 - 11.7791i) q^{83} +(-1.20450 - 2.63748i) q^{84} +(-4.43038 + 2.84723i) q^{85} +(9.42744 + 2.76815i) q^{86} +(0.455950 - 0.526194i) q^{87} +(-2.12085 + 0.622739i) q^{88} +(3.02461 - 6.62297i) q^{89} +(-0.142315 - 0.989821i) q^{90} -10.6872 q^{91} +(1.40035 + 4.58683i) q^{92} +7.08133 q^{93} +(0.939324 + 6.53314i) q^{94} +(-2.80615 + 6.14461i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(4.62111 - 5.33304i) q^{97} +(-1.35011 - 0.396428i) q^{98} +(1.85950 - 1.19503i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	−2.43922	+	1.56759i	−0.921937	+	0.592493i	−0.913219	−	0.407469i	$-0.866411\pi$
$7$	−2.43922	+	1.56759i	−0.921937	+	0.592493i	−0.00871785	+	0.999962i	$0.502775\pi$
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	0.841254	+	0.540641i	0.266028	+	0.170966i
$11$	−0.314571	+	2.18789i	−0.0948469	+	0.659674i	0.885826	+	0.464018i	$0.153593\pi$
$11$	−0.314571	+	2.18789i	−0.0948469	+	0.659674i	−0.980673	+	0.195656i	$0.937316\pi$
$12$	−0.142315	+	0.989821i	−0.0410828	+	0.285737i
$13$	3.10077	+	1.99274i	0.859998	+	0.552687i	0.894678	−	0.446711i	$-0.147405\pi$
$13$	3.10077	+	1.99274i	0.859998	+	0.552687i	−0.0346802	+	0.999398i	$0.511041\pi$
$14$	1.89877	+	2.19130i	0.507467	+	0.585649i
$15$	0.415415	+	0.909632i	0.107260	+	0.234866i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	5.05307	+	1.48372i	1.22555	+	0.359854i	0.829569	−	0.558404i	$-0.188586\pi$
$17$	5.05307	+	1.48372i	1.22555	+	0.359854i	0.395982	+	0.918258i	$0.370404\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	6.48142	−	1.90312i	1.48694	−	0.436605i	0.565376	−	0.824833i	$-0.308731\pi$
$19$	6.48142	−	1.90312i	1.48694	−	0.436605i	0.921563	+	0.388228i	$0.126913\pi$
$20$	0.415415	−	0.909632i	0.0928896	−	0.203400i
$21$	0.412642	+	2.86999i	0.0900459	+	0.626283i
$22$	2.21039			0.471257
$23$	−0.0513676	−	4.79556i	−0.0107109	−	0.999943i
$23$	−0.0513676	−	4.79556i	−0.0107109	−	0.999943i
$24$	1.00000			0.204124
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	1.53117	−	3.35280i	0.300288	−	0.657539i
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$	1.89877	−	2.19130i	0.358834	−	0.414116i
$29$	0.668051	+	0.196157i	0.124054	+	0.0364255i	0.343170	−	0.939273i	$-0.388499\pi$
$29$	0.668051	+	0.196157i	0.124054	+	0.0364255i	−0.219116	+	0.975699i	$0.570317\pi$
$30$	0.841254	−	0.540641i	0.153591	−	0.0987071i
$31$	2.94169	+	6.44141i	0.528343	+	1.15691i	0.966183	+	0.257858i	$0.0830166\pi$
$31$	2.94169	+	6.44141i	0.528343	+	1.15691i	−0.437839	+	0.899053i	$0.644256\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	1.85950	+	1.19503i	0.323697	+	0.208028i
$34$	0.749487	−	5.21280i	0.128536	−	0.893987i
$35$	0.412642	−	2.86999i	0.0697492	−	0.485117i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	2.74949	+	3.17307i	0.452013	+	0.521650i	0.935321	−	0.353800i	$-0.115111\pi$
$37$	2.74949	+	3.17307i	0.452013	+	0.521650i	−0.483309	+	0.875450i	$0.660565\pi$
$38$	−2.80615	−	6.14461i	−0.455217	−	0.996787i
$39$	3.10077	−	1.99274i	0.496520	−	0.319094i
$40$	−0.959493	−	0.281733i	−0.151709	−	0.0445458i
$41$	−5.15699	+	5.95149i	−0.805387	+	0.929466i	−0.998664	−	0.0516784i	$-0.983543\pi$
$41$	−5.15699	+	5.95149i	−0.805387	+	0.929466i	0.193277	+	0.981144i	$0.438088\pi$
$42$	2.78205	−	0.816884i	0.429280	−	0.126048i
$43$	−4.08164	+	8.93754i	−0.622444	+	1.36296i	0.291285	+	0.956636i	$0.405917\pi$
$43$	−4.08164	+	8.93754i	−0.622444	+	1.36296i	−0.913729	+	0.406325i	$0.866810\pi$
$44$	−0.314571	−	2.18789i	−0.0474234	−	0.329837i
$45$	1.00000			0.149071
$46$	−4.73943	+	0.733324i	−0.698791	+	0.108123i
$47$	−6.60033			−0.962756			−0.481378	−	0.876513i	$-0.659864\pi$
$47$	−6.60033			−0.962756			−0.481378	+	0.876513i	$0.659864\pi$
$48$	−0.142315	−	0.989821i	−0.0205414	−	0.142868i
$49$	0.584533	−	1.27995i	0.0835047	−	0.182850i
$50$	−0.959493	+	0.281733i	−0.135693	+	0.0398430i
$51$	3.44876	−	3.98008i	0.482923	−	0.557323i
$52$	−3.53658	−	1.03843i	−0.490436	−	0.144005i
$53$	7.40426	−	4.75843i	1.01705	−	0.653620i	0.0778437	−	0.996966i	$-0.475196\pi$
$53$	7.40426	−	4.75843i	1.01705	−	0.653620i	0.939209	+	0.343345i	$0.111560\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−1.44750	−	1.67050i	−0.195181	−	0.225250i
$56$	−2.43922	−	1.56759i	−0.325954	−	0.209478i
$57$	0.961343	−	6.68629i	0.127333	−	0.885621i
$58$	0.0990873	−	0.689167i	0.0130108	−	0.0904921i
$59$	3.98705	+	2.56232i	0.519069	+	0.333586i	0.773804	−	0.633425i	$-0.218352\pi$
$59$	3.98705	+	2.56232i	0.519069	+	0.333586i	−0.254734	+	0.967011i	$0.581988\pi$
$60$	−0.654861	−	0.755750i	−0.0845422	−	0.0975669i
$61$	5.67397	+	12.4243i	0.726478	+	1.59076i	0.804598	+	0.593820i	$0.202381\pi$
$61$	5.67397	+	12.4243i	0.726478	+	1.59076i	−0.0781201	+	0.996944i	$0.524892\pi$
$62$	5.95720	−	3.82846i	0.756565	−	0.486215i
$63$	2.78205	+	0.816884i	0.350505	+	0.102918i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−3.53658	+	1.03843i	−0.438659	+	0.128802i
$66$	0.918230	−	2.01064i	0.113026	−	0.247493i
$67$	−1.92613	−	13.3966i	−0.235315	−	1.63665i	−0.674515	−	0.738261i	$-0.735647\pi$
$67$	−1.92613	−	13.3966i	−0.235315	−	1.63665i	0.439200	−	0.898389i	$-0.355262\pi$
$68$	−5.26640			−0.638645
$69$	−4.38353	−	1.94542i	−0.527715	−	0.234201i
$70$	−2.89950			−0.346557
$71$	−0.532089	−	3.70076i	−0.0631474	−	0.439200i	−0.996728	−	0.0808315i	$-0.974242\pi$
$71$	−0.532089	−	3.70076i	−0.0631474	−	0.439200i	0.933580	−	0.358368i	$-0.116667\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	−8.25168	+	2.42291i	−0.965787	+	0.283581i	−0.726345	−	0.687330i	$-0.758783\pi$
$73$	−8.25168	+	2.42291i	−0.965787	+	0.283581i	−0.239442	+	0.970911i	$0.576964\pi$
$74$	2.74949	−	3.17307i	0.319621	−	0.368862i
$75$	−0.959493	−	0.281733i	−0.110793	−	0.0325317i
$76$	−5.68271	+	3.65205i	−0.651851	+	0.418919i
$77$	−2.66241	−	5.82986i	−0.303410	−	0.664374i
$78$	−2.41374	−	2.78561i	−0.273303	−	0.315408i
$79$	10.3240	+	6.63482i	1.16154	+	0.746475i	0.971904	−	0.235379i	$-0.0756333\pi$
$79$	10.3240	+	6.63482i	1.16154	+	0.746475i	0.189635	+	0.981855i	$0.439270\pi$
$80$	−0.142315	+	0.989821i	−0.0159113	+	0.110665i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	6.62482	+	4.25752i	0.731589	+	0.470164i
$83$	−10.2066	−	11.7791i	−1.12032	−	1.29292i	−0.951628	−	0.307252i	$-0.900591\pi$
$83$	−10.2066	−	11.7791i	−1.12032	−	1.29292i	−0.168693	−	0.985669i	$-0.553955\pi$
$84$	−1.20450	−	2.63748i	−0.131421	−	0.287773i
$85$	−4.43038	+	2.84723i	−0.480542	+	0.308826i
$86$	9.42744	+	2.76815i	1.01659	+	0.298497i
$87$	0.455950	−	0.526194i	0.0488829	−	0.0564139i
$88$	−2.12085	+	0.622739i	−0.226084	+	0.0663842i
$89$	3.02461	−	6.62297i	0.320608	−	0.702033i	−0.678873	−	0.734256i	$-0.737531\pi$
$89$	3.02461	−	6.62297i	0.320608	−	0.702033i	0.999481	+	0.0322226i	$0.0102586\pi$
$90$	−0.142315	−	0.989821i	−0.0150013	−	0.104336i
$91$	−10.6872			−1.12033
$92$	1.40035	+	4.58683i	0.145997	+	0.478210i
$93$	7.08133			0.734300
$94$	0.939324	+	6.53314i	0.0968839	+	0.673842i
$95$	−2.80615	+	6.14461i	−0.287905	+	0.630423i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	4.62111	−	5.33304i	0.469202	−	0.541488i	−0.470987	−	0.882140i	$-0.656102\pi$
$97$	4.62111	−	5.33304i	0.469202	−	0.541488i	0.940190	+	0.340652i	$0.110648\pi$
$98$	−1.35011	−	0.396428i	−0.136382	−	0.0400452i
$99$	1.85950	−	1.19503i	0.186887	−	0.120105i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	6.16785	+	7.11808i	0.613724	+	0.708275i	0.974503	−	0.224376i	$-0.0720345\pi$
$101$	6.16785	+	7.11808i	0.613724	+	0.708275i	−0.360779	+	0.932651i	$0.617489\pi$
$102$	−4.43038	−	2.84723i	−0.438673	−	0.281918i
$103$	−2.03617	+	14.1619i	−0.200630	+	1.39541i	0.601792	+	0.798653i	$0.294453\pi$
$103$	−2.03617	+	14.1619i	−0.200630	+	1.39541i	−0.802422	+	0.596757i	$0.796456\pi$
$104$	−0.524557	+	3.64837i	−0.0514370	+	0.357752i
$105$	−2.43922	−	1.56759i	−0.238043	−	0.152981i
$106$	−5.76373	−	6.65170i	−0.559823	−	0.646070i
$107$	1.63415	+	3.57829i	0.157979	+	0.345926i	0.972026	−	0.234873i	$-0.0754674\pi$
$107$	1.63415	+	3.57829i	0.157979	+	0.345926i	−0.814047	+	0.580799i	$0.802740\pi$
$108$	0.841254	−	0.540641i	0.0809497	−	0.0520232i
$109$	2.58550	+	0.759171i	0.247646	+	0.0727154i	0.403200	−	0.915112i	$-0.367898\pi$
$109$	2.58550	+	0.759171i	0.247646	+	0.0727154i	−0.155554	+	0.987827i	$0.549716\pi$
$110$	−1.44750	+	1.67050i	−0.138014	+	0.159276i
$111$	4.02851	−	1.18288i	0.382369	−	0.112274i
$112$	−1.20450	+	2.63748i	−0.113814	+	0.249218i
$113$	−2.25986	−	15.7177i	−0.212589	−	1.47859i	−0.764465	−	0.644666i	$-0.776997\pi$
$113$	−2.25986	−	15.7177i	−0.212589	−	1.47859i	0.551875	−	0.833927i	$-0.313912\pi$
$114$	−6.75505			−0.632668
$115$	3.65788	+	3.10160i	0.341099	+	0.289226i
$116$	−0.696254			−0.0646456
$117$	−0.524557	−	3.64837i	−0.0484953	−	0.337292i
$118$	1.96882	−	4.31112i	0.181245	−	0.396871i
$119$	−14.6514	+	4.30204i	−1.34309	+	0.394367i
$120$	−0.654861	+	0.755750i	−0.0597803	+	0.0689902i
$121$	5.86650	+	1.72256i	0.533319	+	0.156596i
$122$	11.4903	−	7.38438i	1.04028	−	0.668550i
$123$	3.27137	+	7.16330i	0.294969	+	0.645893i
$124$	−4.63729	−	5.35171i	−0.416441	−	0.480598i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	0.412642	−	2.86999i	0.0367611	−	0.255679i
$127$	−0.133262	+	0.926858i	−0.0118251	+	0.0822453i	−0.994879	−	0.101069i	$-0.967774\pi$
$127$	−0.133262	+	0.926858i	−0.0118251	+	0.0822453i	0.983054	+	0.183315i	$0.0586827\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	6.43430	+	7.42557i	0.566508	+	0.653785i
$130$	1.53117	+	3.35280i	0.134293	+	0.294060i
$131$	−9.02052	+	5.79714i	−0.788127	+	0.506498i	−0.871722	−	0.490002i	$-0.836996\pi$
$131$	−9.02052	+	5.79714i	−0.788127	+	0.506498i	0.0835948	+	0.996500i	$0.473360\pi$
$132$	−2.12085	−	0.622739i	−0.184597	−	0.0542025i
$133$	−12.8263	+	14.8023i	−1.11218	+	1.28352i
$134$	−12.9861	+	3.81306i	−1.12183	+	0.329398i
$135$	0.415415	−	0.909632i	0.0357532	−	0.0782887i
$136$	0.749487	+	5.21280i	0.0642680	+	0.446994i
$137$	6.03780			0.515844			0.257922	−	0.966166i	$-0.416962\pi$
$137$	6.03780			0.515844			0.257922	+	0.966166i	$0.416962\pi$
$138$	−1.30178	+	4.61577i	−0.110815	+	0.392921i
$139$	6.35489			0.539015			0.269507	−	0.962998i	$-0.413139\pi$
$139$	6.35489			0.539015			0.269507	+	0.962998i	$0.413139\pi$
$140$	0.412642	+	2.86999i	0.0348746	+	0.242558i
$141$	−2.74187	+	6.00387i	−0.230907	+	0.505617i
$142$	−3.58737	+	1.05335i	−0.301045	+	0.0883949i
$143$	−5.33532	+	6.15728i	−0.446162	+	0.514898i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−0.585726	+	0.376423i	−0.0486419	+	0.0312603i
$146$	3.57259	+	7.82288i	0.295670	+	0.647426i
$147$	−0.921459	−	1.06342i	−0.0760006	−	0.0877094i
$148$	−3.53207	−	2.26992i	−0.290334	−	0.186587i
$149$	2.41926	−	16.8263i	0.198194	−	1.37847i	−0.611328	−	0.791378i	$-0.709364\pi$
$149$	2.41926	−	16.8263i	0.198194	−	1.37847i	0.809521	−	0.587090i	$-0.199727\pi$
$150$	−0.142315	+	0.989821i	−0.0116200	+	0.0808186i
$151$	−3.20417	−	2.05919i	−0.260751	−	0.167575i	0.403733	−	0.914877i	$-0.367712\pi$
$151$	−3.20417	−	2.05919i	−0.260751	−	0.167575i	−0.664484	+	0.747302i	$0.731349\pi$
$152$	4.42361	+	5.10512i	0.358803	+	0.414080i
$153$	−2.18774	−	4.79049i	−0.176868	−	0.387288i
$154$	−5.39162	+	3.46498i	−0.434469	+	0.279216i
$155$	−6.79449	−	1.99504i	−0.545746	−	0.160246i
$156$	−2.41374	+	2.78561i	−0.193254	+	0.223027i
$157$	0.768766	−	0.225730i	0.0613542	−	0.0180152i	−0.250911	−	0.968010i	$-0.580730\pi$
$157$	0.768766	−	0.225730i	0.0613542	−	0.0180152i	0.312266	+	0.949995i	$0.398912\pi$
$158$	5.09803	−	11.1631i	0.405577	−	0.888091i
$159$	−1.25258	−	8.71187i	−0.0993359	−	0.690896i
$160$	1.00000			0.0790569
$161$	7.64276	+	11.6169i	0.602334	+	0.915538i
$162$	1.00000			0.0785674
$163$	−3.05758	−	21.2659i	−0.239488	−	1.66568i	−0.654653	−	0.755929i	$-0.727185\pi$
$163$	−3.05758	−	21.2659i	−0.239488	−	1.66568i	0.415166	−	0.909746i	$-0.363724\pi$
$164$	3.27137	−	7.16330i	0.255451	−	0.559360i
$165$	−2.12085	+	0.622739i	−0.165108	+	0.0484802i
$166$	−10.2066	+	11.7791i	−0.792187	+	0.914233i
$167$	−19.2613	−	5.65564i	−1.49049	−	0.437646i	−0.567790	−	0.823173i	$-0.692201\pi$
$167$	−19.2613	−	5.65564i	−1.49049	−	0.437646i	−0.922697	+	0.385527i	$0.874020\pi$
$168$	−2.43922	+	1.56759i	−0.188190	+	0.120942i
$169$	0.243339	+	0.532837i	0.0187184	+	0.0409875i
$170$	3.44876	+	3.98008i	0.264508	+	0.305258i
$171$	−5.68271	−	3.65205i	−0.434567	−	0.279280i
$172$	1.39831	−	9.72543i	0.106620	−	0.741557i
$173$	−1.65396	+	11.5035i	−0.125748	+	0.874599i	0.825110	+	0.564972i	$0.191113\pi$
$173$	−1.65396	+	11.5035i	−0.125748	+	0.874599i	−0.950858	+	0.309626i	$0.899796\pi$
$174$	−0.585726	−	0.376423i	−0.0444038	−	0.0285366i
$175$	1.89877	+	2.19130i	0.143533	+	0.165646i
$176$	0.918230	+	2.01064i	0.0692142	+	0.151558i
$177$	3.98705	−	2.56232i	0.299685	−	0.192596i
$178$	−6.98600	−	2.05128i	−0.523623	−	0.153750i
$179$	0.751879	−	0.867714i	0.0561981	−	0.0648560i	−0.726955	−	0.686686i	$-0.759065\pi$
$179$	0.751879	−	0.867714i	0.0561981	−	0.0648560i	0.783153	+	0.621830i	$0.213610\pi$
$180$	−0.959493	+	0.281733i	−0.0715164	+	0.0209991i
$181$	−7.04894	+	15.4350i	−0.523943	+	1.14728i	0.443982	+	0.896036i	$0.353566\pi$
$181$	−7.04894	+	15.4350i	−0.523943	+	1.14728i	−0.967925	+	0.251240i	$0.919162\pi$
$182$	1.52095	+	10.5785i	0.112740	+	0.784127i
$183$	13.6586			1.00967
$184$	4.34085	−	2.03887i	0.320012	−	0.150308i
$185$	−4.19858			−0.308686
$186$	−1.00778	−	7.00926i	−0.0738939	−	0.513944i
$187$	−4.83577	+	10.5888i	−0.353626	+	0.774333i
$188$	6.33297	−	1.85953i	0.461879	−	0.135620i
$189$	1.89877	−	2.19130i	0.138115	−	0.159393i
$190$	6.48142	+	1.90312i	0.470212	+	0.138067i
$191$	−9.70457	+	6.23675i	−0.702198	+	0.451275i	−0.842404	−	0.538847i	$-0.818860\pi$
$191$	−9.70457	+	6.23675i	−0.702198	+	0.451275i	0.140205	+	0.990122i	$0.455224\pi$
$192$	0.415415	+	0.909632i	0.0299800	+	0.0656470i
$193$	3.36454	+	3.88289i	0.242185	+	0.279497i	0.863809	−	0.503819i	$-0.168072\pi$
$193$	3.36454	+	3.88289i	0.242185	+	0.279497i	−0.621624	+	0.783316i	$0.713527\pi$
$194$	−5.93641	−	3.81510i	−0.426209	−	0.273908i
$195$	−0.524557	+	3.64837i	−0.0375643	+	0.261265i
$196$	−0.200252	+	1.39278i	−0.0143037	+	0.0994846i
$197$	11.4395	+	7.35170i	0.815028	+	0.523787i	0.880488	−	0.474069i	$-0.157215\pi$
$197$	11.4395	+	7.35170i	0.815028	+	0.523787i	−0.0654600	+	0.997855i	$0.520851\pi$
$198$	−1.44750	−	1.67050i	−0.102869	−	0.118717i
$199$	−1.39511	−	3.05487i	−0.0988968	−	0.216554i	0.853716	−	0.520738i	$-0.174343\pi$
$199$	−1.39511	−	3.05487i	−0.0988968	−	0.216554i	−0.952613	+	0.304185i	$0.901616\pi$
$200$	0.841254	−	0.540641i	0.0594856	−	0.0382291i
$201$	−12.9861	−	3.81306i	−0.915968	−	0.268952i
$202$	6.16785	−	7.11808i	0.433968	−	0.500826i
$203$	−1.93701	+	0.568759i	−0.135952	+	0.0399190i
$204$	−2.18774	+	4.79049i	−0.153173	+	0.335401i
$205$	−1.12072	−	7.79479i	−0.0782746	−	0.544412i
$206$	14.3075			0.996850
$207$	−3.59060	+	3.17924i	−0.249564	+	0.220973i
$208$	3.68589			0.255570
$209$	2.12495	+	14.7793i	0.146986	+	1.02231i
$210$	−1.20450	+	2.63748i	−0.0831181	+	0.182003i
$211$	−17.3198	+	5.08554i	−1.19234	+	0.350103i	−0.816920	−	0.576751i	$-0.804320\pi$
$211$	−17.3198	+	5.08554i	−1.19234	+	0.350103i	−0.375421	+	0.926854i	$0.622502\pi$
$212$	−5.76373	+	6.65170i	−0.395855	+	0.456840i
$213$	−3.58737	−	1.05335i	−0.245802	−	0.0721741i
$214$	3.30931	−	2.12676i	0.226219	−	0.145382i
$215$	−4.08164	−	8.93754i	−0.278365	−	0.609535i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	−17.2729	−	11.1006i	−1.17256	−	0.753559i
$218$	0.383489	−	2.66722i	0.0259732	−	0.180647i
$219$	−1.22391	+	8.51251i	−0.0827045	+	0.575222i
$220$	1.85950	+	1.19503i	0.125367	+	0.0805688i
$221$	12.7117	+	14.6701i	0.855084	+	0.986820i
$222$	−1.74415	−	3.81916i	−0.117060	−	0.256325i
$223$	17.4841	−	11.2363i	1.17082	−	0.752441i	0.197144	−	0.980374i	$-0.436833\pi$
$223$	17.4841	−	11.2363i	1.17082	−	0.752441i	0.973677	+	0.227933i	$0.0731968\pi$
$224$	2.78205	+	0.816884i	0.185884	+	0.0545803i
$225$	−0.654861	+	0.755750i	−0.0436574	+	0.0503833i
$226$	−15.2361	+	4.47371i	−1.01349	+	0.297587i
$227$	6.11149	−	13.3823i	0.405634	−	0.888214i	−0.591034	−	0.806647i	$-0.701280\pi$
$227$	6.11149	−	13.3823i	0.405634	−	0.888214i	0.996668	−	0.0815674i	$-0.0259926\pi$
$228$	0.961343	+	6.68629i	0.0636665	+	0.442810i
$229$	−9.76080			−0.645012			−0.322506	−	0.946567i	$-0.604525\pi$
$229$	−9.76080			−0.645012			−0.322506	+	0.946567i	$0.604525\pi$
$230$	2.54946	−	4.06205i	0.168106	−	0.267844i
$231$	−6.40903			−0.421683
$232$	0.0990873	+	0.689167i	0.00650540	+	0.0452461i
$233$	0.0249406	−	0.0546123i	0.00163391	−	0.00357777i	−0.908813	−	0.417203i	$-0.863010\pi$
$233$	0.0249406	−	0.0546123i	0.00163391	−	0.00357777i	0.910447	+	0.413625i	$0.135738\pi$
$234$	−3.53658	+	1.03843i	−0.231194	+	0.0678846i
$235$	4.32229	−	4.98819i	0.281955	−	0.325394i
$236$	−4.54743	−	1.33525i	−0.296013	−	0.0869172i
$237$	10.3240	−	6.63482i	0.670614	−	0.430978i
$238$	6.34336	+	13.8900i	0.411179	+	0.900356i
$239$	−0.0158106	−	0.0182464i	−0.00102270	−	0.00118026i	0.755238	−	0.655451i	$-0.227521\pi$
$239$	−0.0158106	−	0.0182464i	−0.00102270	−	0.00118026i	−0.756261	+	0.654270i	$0.772976\pi$
$240$	0.841254	+	0.540641i	0.0543027	+	0.0348982i
$241$	2.97735	−	20.7080i	0.191788	−	1.33392i	−0.635483	−	0.772115i	$-0.719199\pi$
$241$	2.97735	−	20.7080i	0.191788	−	1.33392i	0.827272	−	0.561802i	$-0.189892\pi$
$242$	0.870137	−	6.05194i	0.0559345	−	0.389033i
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$	−8.94446	−	10.3225i	−0.572610	−	0.660827i
$245$	0.584533	+	1.27995i	0.0373444	+	0.0817729i
$246$	6.62482	−	4.25752i	0.422383	−	0.271449i
$247$	23.8898	+	7.01468i	1.52007	+	0.446333i
$248$	−4.63729	+	5.35171i	−0.294468	+	0.339834i
$249$	−14.9546	+	4.39107i	−0.947709	+	0.278272i
$250$	0.415415	−	0.909632i	0.0262732	−	0.0575302i
$251$	−2.76285	−	19.2160i	−0.174390	−	1.21291i	−0.869474	−	0.493978i	$-0.835542\pi$
$251$	−2.76285	−	19.2160i	−0.174390	−	1.21291i	0.695085	−	0.718928i	$-0.255367\pi$
$252$	−2.89950			−0.182651
$253$	10.5083	+	1.39616i	0.660653	+	0.0877757i
$254$	0.936389			0.0587543
$255$	0.749487	+	5.21280i	0.0469347	+	0.326438i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	16.2704	−	4.77741i	1.01492	−	0.298007i	0.268354	−	0.963320i	$-0.413520\pi$
$257$	16.2704	−	4.77741i	1.01492	−	0.298007i	0.746564	+	0.665314i	$0.231702\pi$
$258$	6.43430	−	7.42557i	0.400582	−	0.462296i
$259$	−11.6807	−	3.42975i	−0.725801	−	0.213114i
$260$	3.10077	−	1.99274i	0.192301	−	0.123585i
$261$	−0.289234	−	0.633335i	−0.0179032	−	0.0392025i
$262$	7.02189	+	8.10369i	0.433814	+	0.500648i
$263$	−23.1266	−	14.8626i	−1.42605	−	0.916466i	−0.999930	−	0.0117991i	$-0.996244\pi$
$263$	−23.1266	−	14.8626i	−1.42605	−	0.916466i	−0.426119	−	0.904667i	$-0.640119\pi$
$264$	−0.314571	+	2.18789i	−0.0193605	+	0.134655i
$265$	−1.25258	+	8.71187i	−0.0769452	+	0.535166i
$266$	16.4770	+	10.5891i	1.01027	+	0.649261i
$267$	−4.76800	−	5.50256i	−0.291797	−	0.336751i
$268$	5.62236	+	12.3112i	0.343440	+	0.752029i
$269$	−11.2504	+	7.23017i	−0.685947	+	0.440831i	−0.836643	−	0.547749i	$-0.815485\pi$
$269$	−11.2504	+	7.23017i	−0.685947	+	0.440831i	0.150696	+	0.988580i	$0.451849\pi$
$270$	−0.959493	−	0.281733i	−0.0583929	−	0.0171457i
$271$	4.13034	−	4.76667i	0.250901	−	0.289555i	−0.616302	−	0.787510i	$-0.711370\pi$
$271$	4.13034	−	4.76667i	0.250901	−	0.289555i	0.867203	+	0.497955i	$0.165916\pi$
$272$	5.05307	−	1.48372i	0.306388	−	0.0899635i
$273$	−4.43964	+	9.72145i	−0.268699	+	0.588369i
$274$	−0.859269	−	5.97635i	−0.0519104	−	0.361044i
$275$	2.21039			0.133292
$276$	4.75405	+	0.631634i	0.286160	+	0.0380199i
$277$	−28.2535			−1.69759			−0.848795	−	0.528721i	$-0.822672\pi$
$277$	−28.2535			−1.69759			−0.848795	+	0.528721i	$0.822672\pi$
$278$	−0.904395	−	6.29020i	−0.0542420	−	0.377261i
$279$	2.94169	−	6.44141i	0.176114	−	0.385637i
$280$	2.78205	−	0.816884i	0.166259	−	0.0488181i
$281$	−8.11581	+	9.36614i	−0.484149	+	0.558737i	−0.944293	−	0.329107i	$-0.893252\pi$
$281$	−8.11581	+	9.36614i	−0.484149	+	0.558737i	0.460144	+	0.887844i	$0.347798\pi$
$282$	6.33297	+	1.85953i	0.377123	+	0.110733i
$283$	10.6487	−	6.84353i	0.633002	−	0.406806i	−0.184418	−	0.982848i	$-0.559040\pi$
$283$	10.6487	−	6.84353i	0.633002	−	0.406806i	0.817420	+	0.576042i	$0.195404\pi$
$284$	1.55316	+	3.40095i	0.0921631	+	0.201809i
$285$	4.42361	+	5.10512i	0.262032	+	0.302401i
$286$	6.85391	+	4.40474i	0.405280	+	0.260458i
$287$	3.24953	−	22.6010i	0.191814	−	1.33409i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	9.03083	+	5.80376i	0.531225	+	0.341398i
$290$	0.455950	+	0.526194i	0.0267743	+	0.0308992i
$291$	−2.93143	−	6.41893i	−0.171843	−	0.376284i
$292$	7.23482	−	4.64954i	0.423386	−	0.272094i
$293$	23.4300	+	6.87966i	1.36879	+	0.401914i	0.881854	−	0.471522i	$-0.156295\pi$
$293$	23.4300	+	6.87966i	1.36879	+	0.401914i	0.486939	+	0.873436i	$0.338113\pi$
$294$	−0.921459	+	1.06342i	−0.0537406	+	0.0620199i
$295$	−4.54743	+	1.33525i	−0.264762	+	0.0777411i
$296$	−1.74415	+	3.81916i	−0.101377	+	0.221984i
$297$	−0.314571	−	2.18789i	−0.0182533	−	0.126954i
$298$	−16.9994			−0.984747
$299$	9.39703	−	14.9723i	0.543444	−	0.865868i
$300$	1.00000			0.0577350
$301$	−4.05439	−	28.1989i	−0.233691	−	1.62536i
$302$	−1.58223	+	3.46461i	−0.0910473	+	0.199366i
$303$	9.03705	−	2.65352i	0.519165	−	0.152441i
$304$	4.42361	−	5.10512i	0.253712	−	0.292799i
$305$	−13.1053	−	3.84806i	−0.750407	−	0.220339i
$306$	−4.43038	+	2.84723i	−0.253268	+	0.162765i
$307$	−9.72017	−	21.2842i	−0.554759	−	1.21475i	−0.954524	−	0.298135i	$-0.903635\pi$
$307$	−9.72017	−	21.2842i	−0.554759	−	1.21475i	0.399764	−	0.916618i	$-0.369092\pi$
$308$	4.19702	+	4.84362i	0.239148	+	0.275991i
$309$	12.0362	+	7.73521i	0.684717	+	0.440041i
$310$	−1.00778	+	7.00926i	−0.0572380	+	0.398099i
$311$	1.06778	−	7.42659i	0.0605484	−	0.421124i	−0.936892	−	0.349619i	$-0.886311\pi$
$311$	1.06778	−	7.42659i	0.0605484	−	0.421124i	0.997440	−	0.0715043i	$-0.0227800\pi$
$312$	3.10077	+	1.99274i	0.175546	+	0.112817i
$313$	9.11203	+	10.5158i	0.515043	+	0.594391i	0.952383	−	0.304905i	$-0.0986249\pi$
$313$	9.11203	+	10.5158i	0.515043	+	0.594391i	−0.437340	+	0.899296i	$0.644079\pi$
$314$	−0.332839	−	0.728816i	−0.0187832	−	0.0411295i
$315$	−2.43922	+	1.56759i	−0.137434	+	0.0883236i
$316$	−11.7750	−	3.45746i	−0.662397	−	0.194497i
$317$	−13.6964	+	15.8065i	−0.769267	+	0.887781i	−0.996286	−	0.0861093i	$-0.972557\pi$
$317$	−13.6964	+	15.8065i	−0.769267	+	0.887781i	0.227019	+	0.973890i	$0.427102\pi$
$318$	−8.44494	+	2.47966i	−0.473568	+	0.139052i
$319$	−0.639321	+	1.39992i	−0.0357951	+	0.0783804i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	3.93378			0.219562
$322$	10.4110	−	9.21822i	0.580180	−	0.513711i
$323$	35.5748			1.97943
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	1.53117	−	3.35280i	0.0849342	−	0.185980i
$326$	−20.6143	+	6.05291i	−1.14172	+	0.335240i
$327$	1.76462	−	2.03648i	0.0975838	−	0.112618i
$328$	−7.55595	−	2.21863i	−0.417208	−	0.122503i
$329$	16.0996	−	10.3466i	0.887601	−	0.570426i
$330$	0.918230	+	2.01064i	0.0505469	+	0.110682i
$331$	−1.32199	−	1.52566i	−0.0726634	−	0.0838580i	0.718254	−	0.695781i	$-0.244942\pi$
$331$	−1.32199	−	1.52566i	−0.0726634	−	0.0838580i	−0.790917	+	0.611923i	$0.790396\pi$
$332$	13.1117	+	8.42639i	0.719599	+	0.462458i
$333$	0.597520	−	4.15584i	0.0327439	−	0.227739i
$334$	−2.85690	+	19.8702i	−0.156322	+	1.08725i
$335$	11.3858	+	7.31720i	0.622072	+	0.399782i
$336$	1.89877	+	2.19130i	0.103586	+	0.119545i
$337$	8.16127	+	17.8707i	0.444573	+	0.973479i	0.990736	+	0.135800i	$0.0433605\pi$
$337$	8.16127	+	17.8707i	0.444573	+	0.973479i	−0.546163	+	0.837679i	$0.683912\pi$
$338$	0.492783	−	0.316692i	0.0268039	−	0.0172258i
$339$	−15.2361	−	4.47371i	−0.827509	−	0.242979i
$340$	3.44876	−	3.98008i	0.187035	−	0.215850i
$341$	−15.0185	+	4.40982i	−0.813296	+	0.238805i
$342$	−2.80615	+	6.14461i	−0.151739	+	0.332262i
$343$	−2.30786	−	16.0515i	−0.124613	−	0.866702i
$344$	−9.82544			−0.529752
$345$	4.34085	−	2.03887i	0.233704	−	0.109769i
$346$	11.6218			0.624794
$347$	0.509957	+	3.54683i	0.0273759	+	0.190404i	0.998920	−	0.0464531i	$-0.0147918\pi$
$347$	0.509957	+	3.54683i	0.0273759	+	0.190404i	−0.971545	+	0.236857i	$0.923883\pi$
$348$	−0.289234	+	0.633335i	−0.0155046	+	0.0339503i
$349$	12.4031	−	3.64187i	0.663921	−	0.194945i	0.0676269	−	0.997711i	$-0.478457\pi$
$349$	12.4031	−	3.64187i	0.663921	−	0.194945i	0.596294	+	0.802766i	$0.296639\pi$
$350$	1.89877	−	2.19130i	0.101493	−	0.117130i
$351$	−3.53658	−	1.03843i	−0.188769	−	0.0554275i
$352$	1.85950	−	1.19503i	0.0991117	−	0.0636952i
$353$	−5.08835	−	11.1419i	−0.270825	−	0.593025i	0.724535	−	0.689238i	$-0.242054\pi$
$353$	−5.08835	−	11.1419i	−0.270825	−	0.593025i	−0.995361	+	0.0962128i	$0.969327\pi$
$354$	−3.10366	−	3.58181i	−0.164957	−	0.190371i
$355$	3.14529	+	2.02136i	0.166935	+	0.107282i
$356$	−1.03618	+	7.20682i	−0.0549177	+	0.381961i
$357$	−2.17314	+	15.1145i	−0.115015	+	0.799945i
$358$	−0.965886	−	0.620737i	−0.0510487	−	0.0328070i
$359$	13.3082	+	15.3585i	0.702380	+	0.810590i	0.989072	−	0.147433i	$-0.0471011\pi$
$359$	13.3082	+	15.3585i	0.702380	+	0.810590i	−0.286692	+	0.958023i	$0.592556\pi$
$360$	0.415415	+	0.909632i	0.0218943	+	0.0479418i
$361$	22.4031	−	14.3976i	1.17911	−	0.757769i
$362$	16.2811	+	4.78056i	0.855714	+	0.251260i
$363$	4.00393	−	4.62078i	0.210152	−	0.242528i
$364$	10.2543	−	3.01094i	0.537473	−	0.157816i
$365$	3.57259	−	7.82288i	0.186998	−	0.409468i
$366$	−1.94382	−	13.5195i	−0.101605	−	0.706678i
$367$	30.8211			1.60885			0.804424	−	0.594056i	$-0.202474\pi$
$367$	30.8211			1.60885			0.804424	+	0.594056i	$0.202474\pi$
$368$	−2.63589	−	4.00651i	−0.137405	−	0.208854i
$369$	7.87494			0.409953
$370$	0.597520	+	4.15584i	0.0310636	+	0.216052i
$371$	−10.6013	+	23.2137i	−0.550393	+	1.20519i
$372$	−6.79449	+	1.99504i	−0.352278	+	0.103438i
$373$	−1.70346	+	1.96590i	−0.0882018	+	0.101790i	−0.798135	−	0.602479i	$-0.794180\pi$
$373$	−1.70346	+	1.96590i	−0.0882018	+	0.101790i	0.709933	+	0.704269i	$0.248725\pi$
$374$	11.1693	+	3.27959i	0.577549	+	0.169584i
$375$	0.841254	−	0.540641i	0.0434421	−	0.0279186i
$376$	−2.74187	−	6.00387i	−0.141401	−	0.309626i
$377$	1.68058	+	1.93949i	0.0865542	+	0.0998889i
$378$	−2.43922	−	1.56759i	−0.125460	−	0.0806281i
$379$	4.76761	−	33.1595i	0.244896	−	1.70329i	−0.381982	−	0.924170i	$-0.624758\pi$
$379$	4.76761	−	33.1595i	0.244896	−	1.70329i	0.626878	−	0.779118i	$-0.284333\pi$
$380$	0.961343	−	6.68629i	0.0493159	−	0.342999i
$381$	0.787740	+	0.506250i	0.0403572	+	0.0259360i
$382$	7.55437	+	8.71821i	0.386515	+	0.446063i
$383$	5.98163	+	13.0979i	0.305647	+	0.669274i	0.998665	−	0.0516462i	$-0.0164468\pi$
$383$	5.98163	+	13.0979i	0.305647	+	0.669274i	−0.693018	+	0.720920i	$0.743720\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	6.14942	+	1.80563i	0.313404	+	0.0920236i
$386$	3.36454	−	3.88289i	0.171251	−	0.197634i
$387$	9.42744	−	2.76815i	0.479224	−	0.140713i
$388$	−2.93143	+	6.41893i	−0.148821	+	0.325872i
$389$	1.35503	+	9.42441i	0.0687026	+	0.477837i	0.994906	+	0.100812i	$0.0321439\pi$
$389$	1.35503	+	9.42441i	0.0687026	+	0.477837i	−0.926203	+	0.377025i	$0.876947\pi$
$390$	3.68589			0.186642
$391$	6.85568	−	24.3085i	0.346707	−	1.22933i
$392$	1.40711			0.0710696
$393$	1.52600	+	10.6136i	0.0769766	+	0.535384i
$394$	5.64886	−	12.3693i	0.284586	−	0.623155i
$395$	−11.7750	+	3.45746i	−0.592466	+	0.173964i
$396$	−1.44750	+	1.67050i	−0.0727395	+	0.0839459i
$397$	−33.3718	−	9.79885i	−1.67488	−	0.491790i	−0.699932	−	0.714209i	$-0.746786\pi$
$397$	−33.3718	−	9.79885i	−1.67488	−	0.491790i	−0.974951	+	0.222419i	$0.928605\pi$
$398$	−2.82523	+	1.81566i	−0.141616	+	0.0910110i
$399$	8.13643	+	17.8163i	0.407331	+	0.891930i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	19.2427	+	12.3665i	0.960933	+	0.617554i	0.924256	−	0.381773i	$-0.124686\pi$
$401$	19.2427	+	12.3665i	0.960933	+	0.617554i	0.0366766	+	0.999327i	$0.488323\pi$
$402$	−1.92613	+	13.3966i	−0.0960668	+	0.668160i
$403$	−3.71456	+	25.8353i	−0.185035	+	1.28695i
$404$	−7.92340	−	5.09206i	−0.394204	−	0.253339i
$405$	−0.654861	−	0.755750i	−0.0325403	−	0.0375535i
$406$	0.838636	+	1.83636i	0.0416208	+	0.0911368i
$407$	−7.80726	+	5.01742i	−0.386991	+	0.248704i
$408$	5.05307	+	1.48372i	0.250164	+	0.0734549i
$409$	23.0521	−	26.6035i	1.13985	−	1.31546i	0.197706	−	0.980261i	$-0.436651\pi$
$409$	23.0521	−	26.6035i	1.13985	−	1.31546i	0.942147	−	0.335199i	$-0.108804\pi$
$410$	−7.55595	+	2.21863i	−0.373162	+	0.109570i
$411$	2.50819	−	5.49218i	0.123720	−	0.270909i
$412$	−2.03617	−	14.1619i	−0.100315	−	0.697705i
$413$	−13.7419			−0.676196
$414$	3.65788	+	3.10160i	0.179775	+	0.152435i
$415$	15.5859			0.765083
$416$	−0.524557	−	3.64837i	−0.0257185	−	0.178876i
$417$	2.63992	−	5.78061i	0.129277	−	0.283078i
$418$	14.3265	−	4.20663i	0.700731	−	0.205753i
$419$	1.78806	−	2.06354i	0.0873526	−	0.100810i	−0.710390	−	0.703808i	$-0.751482\pi$
$419$	1.78806	−	2.06354i	0.0873526	−	0.100810i	0.797743	+	0.602997i	$0.206027\pi$
$420$	2.78205	+	0.816884i	0.135750	+	0.0398599i
$421$	13.5379	−	8.70028i	0.659797	−	0.424026i	−0.167438	−	0.985883i	$-0.553549\pi$
$421$	13.5379	−	8.70028i	0.659797	−	0.424026i	0.827234	+	0.561857i	$0.189913\pi$
$422$	7.49863	+	16.4197i	0.365028	+	0.799299i
$423$	4.32229	+	4.98819i	0.210157	+	0.242534i
$424$	7.40426	+	4.75843i	0.359582	+	0.231090i
$425$	0.749487	−	5.21280i	0.0363555	−	0.252858i
$426$	−0.532089	+	3.70076i	−0.0257798	+	0.179302i
$427$	−33.3162	−	21.4110i	−1.61228	−	1.03615i
$428$	−2.57608	−	2.97295i	−0.124519	−	0.143703i
$429$	3.38449	+	7.41100i	0.163405	+	0.357807i
$430$	−8.26569	+	5.31204i	−0.398607	+	0.256169i
$431$	13.6696	+	4.01375i	0.658440	+	0.193335i	0.593849	−	0.804576i	$-0.297608\pi$
$431$	13.6696	+	4.01375i	0.658440	+	0.193335i	0.0645908	+	0.997912i	$0.479426\pi$
$432$	−0.654861	+	0.755750i	−0.0315070	+	0.0363610i
$433$	20.2023	−	5.93194i	0.970862	−	0.285071i	0.242415	−	0.970173i	$-0.422061\pi$
$433$	20.2023	−	5.93194i	0.970862	−	0.285071i	0.728447	+	0.685102i	$0.240242\pi$
$434$	−8.52944	+	18.6769i	−0.409426	+	0.896518i
$435$	0.0990873	+	0.689167i	0.00475087	+	0.0330430i
$436$	−2.69465			−0.129050
$437$	−9.45944	−	30.9843i	−0.452506	−	1.48218i
$438$	8.60005			0.410926
$439$	1.49133	+	10.3724i	0.0711771	+	0.495048i	0.993961	+	0.109731i	$0.0349988\pi$
$439$	1.49133	+	10.3724i	0.0711771	+	0.495048i	−0.922784	+	0.385317i	$0.874092\pi$
$440$	0.918230	−	2.01064i	0.0437749	−	0.0958536i
$441$	−1.35011	+	0.396428i	−0.0642909	+	0.0188775i
$442$	12.7117	−	14.6701i	0.604636	−	0.697787i
$443$	−34.8554	−	10.2345i	−1.65603	−	0.486255i	−0.685670	−	0.727912i	$-0.740491\pi$
$443$	−34.8554	−	10.2345i	−1.65603	−	0.486255i	−0.970362	+	0.241657i	$0.922309\pi$
$444$	−3.53207	+	2.26992i	−0.167625	+	0.107726i
$445$	3.02461	+	6.62297i	0.143380	+	0.313959i
$446$	−13.6102	−	15.7070i	−0.644462	−	0.743749i
$447$	−14.3008	−	9.19056i	−0.676404	−	0.434698i
$448$	0.412642	−	2.86999i	0.0194955	−	0.135594i
$449$	1.26640	−	8.80798i	0.0597649	−	0.415674i	−0.937873	−	0.346979i	$-0.887207\pi$
$449$	1.26640	−	8.80798i	0.0597649	−	0.415674i	0.997638	−	0.0686949i	$-0.0218835\pi$
$450$	0.841254	+	0.540641i	0.0396571	+	0.0254861i
$451$	−11.3990	−	13.1551i	−0.536756	−	0.619450i
$452$	6.59649	+	14.4443i	0.310273	+	0.679403i
$453$	−3.20417	+	2.05919i	−0.150545	+	0.0967493i
$454$	−14.1158	−	4.14478i	−0.662489	−	0.194524i
$455$	6.99865	−	8.07687i	0.328102	−	0.378650i
$456$	6.48142	−	1.90312i	0.303520	−	0.0891216i
$457$	−2.41360	+	5.28505i	−0.112904	+	0.247224i	−0.957646	−	0.287949i	$-0.907027\pi$
$457$	−2.41360	+	5.28505i	−0.112904	+	0.247224i	0.844742	+	0.535174i	$0.179754\pi$
$458$	1.38911	+	9.66145i	0.0649087	+	0.451450i
$459$	−5.26640			−0.245815
$460$	−4.38353	−	1.94542i	−0.204383	−	0.0907057i
$461$	7.43479			0.346273			0.173136	−	0.984898i	$-0.444610\pi$
$461$	7.43479			0.346273			0.173136	+	0.984898i	$0.444610\pi$
$462$	0.912100	+	6.34380i	0.0424347	+	0.295140i
$463$	−8.11811	+	17.7762i	−0.377281	+	0.826129i	0.621797	+	0.783179i	$0.286403\pi$
$463$	−8.11811	+	17.7762i	−0.377281	+	0.826129i	−0.999077	+	0.0429505i	$0.986324\pi$
$464$	0.668051	−	0.196157i	0.0310135	−	0.00910638i
$465$	−4.63729	+	5.35171i	−0.215049	+	0.248180i
$466$	−0.0576058	−	0.0169146i	−0.00266854	−	0.000783554i
$467$	−18.5626	+	11.9294i	−0.858974	+	0.552029i	−0.894362	−	0.447345i	$-0.852370\pi$
$467$	−18.5626	+	11.9294i	−0.858974	+	0.552029i	0.0353880	+	0.999374i	$0.488733\pi$
$468$	1.53117	+	3.35280i	0.0707785	+	0.154983i
$469$	25.6985	+	29.6577i	1.18665	+	1.36947i
$470$	−5.55255	−	3.56841i	−0.256120	−	0.164598i
$471$	0.114026	−	0.793065i	0.00525402	−	0.0365425i
$472$	−0.674489	+	4.69117i	−0.0310459	+	0.215929i
$473$	−18.2704	−	11.7417i	−0.840074	−	0.539883i
$474$	−8.03654	−	9.27466i	−0.369131	−	0.425999i
$475$	−2.80615	−	6.14461i	−0.128755	−	0.281934i
$476$	12.8459	−	8.25555i	0.588790	−	0.378392i
$477$	−8.44494	−	2.47966i	−0.386667	−	0.113536i
$478$	−0.0158106	+	0.0182464i	−0.000723159	+	0.000834570i
$479$	−21.5591	+	6.33031i	−0.985058	+	0.289239i	−0.734311	−	0.678813i	$-0.762495\pi$
$479$	−21.5591	+	6.33031i	−0.985058	+	0.289239i	−0.250747	+	0.968053i	$0.580676\pi$
$480$	0.415415	−	0.909632i	0.0189610	−	0.0415188i
$481$	2.20239	+	15.3180i	0.100420	+	0.698440i
$482$	−20.9209			−0.952921
$483$	13.7420	−	2.12627i	0.625282	−	0.0967487i
$484$	−6.11417			−0.277917
$485$	1.00426	+	6.98480i	0.0456012	+	0.317163i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	−2.80615	+	0.823960i	−0.127159	+	0.0373372i	−0.344693	−	0.938716i	$-0.612017\pi$
$487$	−2.80615	+	0.823960i	−0.127159	+	0.0373372i	0.217534	+	0.976053i	$0.430199\pi$
$488$	−8.94446	+	10.3225i	−0.404897	+	0.467275i
$489$	−20.6143	−	6.05291i	−0.932212	−	0.273722i
$490$	1.18373	−	0.760739i	0.0534756	−	0.0343667i
$491$	−3.82992	−	8.38636i	−0.172842	−	0.378471i	0.803309	−	0.595562i	$-0.203071\pi$
$491$	−3.82992	−	8.38636i	−0.172842	−	0.378471i	−0.976151	+	0.217091i	$0.930343\pi$
$492$	−5.15699	−	5.95149i	−0.232495	−	0.268314i
$493$	3.08467	+	1.98240i	0.138927	+	0.0892827i
$494$	3.54340	−	24.6449i	0.159425	−	1.10883i
$495$	−0.314571	+	2.18789i	−0.0141389	+	0.0983385i
$496$	5.95720	+	3.82846i	0.267486	+	0.171903i
$497$	7.09915	+	8.19286i	0.318440	+	0.367500i
$498$	6.47463	+	14.1775i	0.290135	+	0.635307i
$499$	22.5629	−	14.5003i	1.01006	−	0.649124i	0.0726486	−	0.997358i	$-0.476855\pi$
$499$	22.5629	−	14.5003i	1.01006	−	0.649124i	0.937408	+	0.348234i	$0.113218\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	−13.1460	+	15.1713i	−0.587320	+	0.677803i
$502$	−18.6273	+	5.46946i	−0.831375	+	0.244114i
$503$	10.8946	−	23.8559i	0.485767	−	1.06368i	−0.495071	−	0.868853i	$-0.664858\pi$
$503$	10.8946	−	23.8559i	0.485767	−	1.06368i	0.980837	−	0.194828i	$-0.0624148\pi$
$504$	0.412642	+	2.86999i	0.0183805	+	0.127839i
$505$	−9.41856			−0.419121
$506$	−0.113543	−	10.6001i	−0.00504758	−	0.471230i
$507$	0.585772			0.0260151
$508$	−0.133262	−	0.926858i	−0.00591255	−	0.0411227i
$509$	−3.37260	+	7.38497i	−0.149488	+	0.327333i	−0.969531	−	0.244969i	$-0.921222\pi$
$509$	−3.37260	+	7.38497i	−0.149488	+	0.327333i	0.820043	+	0.572302i	$0.193949\pi$
$510$	5.05307	−	1.48372i	0.223754	−	0.0657001i
$511$	16.3295	−	18.8453i	0.722375	−	0.833665i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	−5.68271	+	3.65205i	−0.250898	+	0.161242i
$514$	−7.04430	−	15.4249i	−0.310711	−	0.680362i
$515$	−9.36941	−	10.8129i	−0.412866	−	0.476472i
$516$	−8.26569	−	5.31204i	−0.363877	−	0.233849i
$517$	2.07627	−	14.4408i	0.0913144	−	0.635106i
$518$	−1.73251	+	12.0499i	−0.0761221	+	0.529441i
$519$	9.77692	+	6.28324i	0.429159	+	0.275804i
$520$	−2.41374	−	2.78561i	−0.105850	−	0.122157i
$521$	11.0146	+	24.1186i	0.482559	+	1.05666i	0.981752	+	0.190165i	$0.0609024\pi$
$521$	11.0146	+	24.1186i	0.482559	+	1.05666i	−0.499193	+	0.866491i	$0.666370\pi$
$522$	−0.585726	+	0.376423i	−0.0256365	+	0.0164756i
$523$	25.8689	+	7.59579i	1.13117	+	0.332141i	0.793167	−	0.609005i	$-0.208431\pi$
$523$	25.8689	+	7.59579i	1.13117	+	0.332141i	0.338001	+	0.941146i	$0.390249\pi$
$524$	7.02189	−	8.10369i	0.306753	−	0.354011i
$525$	2.78205	−	0.816884i	0.121419	−	0.0356517i
$526$	−11.4200	+	25.0064i	−0.497937	+	1.09033i
$527$	5.30737	+	36.9135i	0.231192	+	1.60798i
$528$	2.21039			0.0961949
$529$	−22.9947	+	0.492672i	−0.999771	+	0.0214205i
$530$	8.80146			0.382311
$531$	−0.674489	−	4.69117i	−0.0292703	−	0.203580i
$532$	8.13643	−	17.8163i	0.352759	−	0.772434i
$533$	−27.8504	+	8.17762i	−1.20633	+	0.354212i
$534$	−4.76800	+	5.50256i	−0.206331	+	0.238119i
$535$	−3.77443	−	1.10827i	−0.163183	−	0.0479148i
$536$	11.3858	−	7.31720i	0.491791	−	0.316055i
$537$	−0.476959	−	1.04439i	−0.0205823	−	0.0450690i
$538$	8.75767	+	10.1069i	0.377570	+	0.435739i
$539$	2.61651	+	1.68153i	0.112701	+	0.0724287i
$540$	−0.142315	+	0.989821i	−0.00612426	+	0.0425951i
$541$	−0.673798	+	4.68637i	−0.0289688	+	0.201483i	−0.999166	−	0.0408345i	$-0.986998\pi$
$541$	−0.673798	+	4.68637i	−0.0289688	+	0.201483i	0.970197	+	0.242317i	$0.0779075\pi$
$542$	−5.30596	−	3.40994i	−0.227911	−	0.146469i
$543$	11.1120	+	12.8239i	0.476859	+	0.550325i
$544$	−2.18774	−	4.79049i	−0.0937987	−	0.205390i
$545$	−2.26689	+	1.45684i	−0.0971027	+	0.0624041i
$546$	10.2543	+	3.01094i	0.438845	+	0.128856i
$547$	−21.6602	+	24.9972i	−0.926122	+	1.06880i	0.0713296	+	0.997453i	$0.477276\pi$
$547$	−21.6602	+	24.9972i	−0.926122	+	1.06880i	−0.997451	+	0.0713488i	$0.977270\pi$
$548$	−5.79323	+	1.70105i	−0.247475	+	0.0726651i
$549$	5.67397	−	12.4243i	0.242159	−	0.530255i
$550$	−0.314571	−	2.18789i	−0.0134134	−	0.0932921i
$551$	4.70323			0.200364
$552$	−0.0513676	−	4.79556i	−0.00218635	−	0.204112i
$553$	−35.5831			−1.51315
$554$	4.02090	+	27.9660i	0.170832	+	1.18816i
$555$	−1.74415	+	3.81916i	−0.0740352	+	0.162114i
$556$	−6.09747	+	1.79038i	−0.258590	+	0.0759290i
$557$	6.30560	−	7.27705i	0.267177	−	0.308339i	−0.606269	−	0.795260i	$-0.707335\pi$
$557$	6.30560	−	7.27705i	0.267177	−	0.308339i	0.873446	+	0.486921i	$0.161880\pi$
$558$	−6.79449	−	1.99504i	−0.287634	−	0.0844569i
$559$	−30.4664	+	19.5796i	−1.28859	+	0.828128i
$560$	−1.20450	−	2.63748i	−0.0508993	−	0.111454i
$561$	7.62311	+	8.79753i	0.321848	+	0.371432i
$562$	10.4258	+	6.70026i	0.439786	+	0.282633i
$563$	1.04557	−	7.27212i	0.0440657	−	0.306483i	−0.955854	−	0.293841i	$-0.905066\pi$
$563$	1.04557	−	7.27212i	0.0440657	−	0.306483i	0.999920	−	0.0126427i	$-0.00402442\pi$
$564$	0.939324	−	6.53314i	0.0395527	−	0.275095i
$565$	13.3585	+	8.58499i	0.561996	+	0.361173i
$566$	−8.28935	−	9.56642i	−0.348427	−	0.402107i
$567$	−1.20450	−	2.63748i	−0.0505841	−	0.110764i
$568$	3.14529	−	2.02136i	0.131974	−	0.0848143i
$569$	−27.9530	−	8.20773i	−1.17185	−	0.344086i	−0.362822	−	0.931858i	$-0.618187\pi$
$569$	−27.9530	−	8.20773i	−1.17185	−	0.344086i	−0.809026	+	0.587772i	$0.800005\pi$
$570$	4.42361	−	5.10512i	0.185285	−	0.213830i
$571$	−28.4437	+	8.35183i	−1.19033	+	0.349513i	−0.816149	−	0.577841i	$-0.803895\pi$
$571$	−28.4437	+	8.35183i	−1.19033	+	0.349513i	−0.374184	+	0.927355i	$0.622077\pi$
$572$	3.38449	−	7.41100i	0.141513	−	0.309870i
$573$	1.64172	+	11.4184i	0.0685839	+	0.477012i
$574$	−22.8334			−0.953048
$575$	−4.73943	+	0.733324i	−0.197648	+	0.0305817i
$576$	1.00000			0.0416667
$577$	1.18980	+	8.27524i	0.0495320	+	0.344503i	0.999484	+	0.0321079i	$0.0102220\pi$
$577$	1.18980	+	8.27524i	0.0495320	+	0.344503i	−0.949952	+	0.312395i	$0.898869\pi$
$578$	4.45947	−	9.76487i	0.185489	−	0.406165i
$579$	4.92968	−	1.44749i	0.204871	−	0.0601554i
$580$	0.455950	−	0.526194i	0.0189323	−	0.0218490i
$581$	43.3609	+	12.7319i	1.79891	+	0.528208i
$582$	−5.93641	+	3.81510i	−0.246072	+	0.158141i
$583$	8.08176	+	17.6966i	0.334712	+	0.732918i
$584$	−5.63183	−	6.49948i	−0.233047	−	0.268950i
$585$	3.10077	+	1.99274i	0.128201	+	0.0823897i
$586$	3.47520	−	24.1706i	0.143559	−	0.998477i
$587$	2.59458	−	18.0457i	0.107090	−	0.744827i	−0.863545	−	0.504271i	$-0.831761\pi$
$587$	2.59458	−	18.0457i	0.107090	−	0.744827i	0.970635	−	0.240556i	$-0.0773297\pi$
$588$	1.18373	+	0.760739i	0.0488163	+	0.0313724i
$589$	31.3251	+	36.1511i	1.29073	+	1.48958i
$590$	1.96882	+	4.31112i	0.0810552	+	0.177486i
$591$	11.4395	−	7.35170i	0.470557	−	0.302408i
$592$	4.02851	+	1.18288i	0.165571	+	0.0486159i
$593$	−1.41807	+	1.63653i	−0.0582330	+	0.0672044i	−0.784119	−	0.620611i	$-0.786885\pi$
$593$	−1.41807	+	1.63653i	−0.0582330	+	0.0672044i	0.725886	+	0.687815i	$0.241430\pi$
$594$	−2.12085	+	0.622739i	−0.0870197	+	0.0255513i
$595$	6.34336	−	13.8900i	0.260052	−	0.569435i
$596$	2.41926	+	16.8263i	0.0990969	+	0.689234i
$597$	−3.35836			−0.137448
$598$	−16.1572	−	7.17060i	−0.660717	−	0.293228i
$599$	−1.54621			−0.0631766			−0.0315883	−	0.999501i	$-0.510057\pi$
$599$	−1.54621			−0.0631766			−0.0315883	+	0.999501i	$0.510057\pi$
$600$	−0.142315	−	0.989821i	−0.00580998	−	0.0404093i
$601$	3.99622	−	8.75051i	0.163009	−	0.356941i	−0.810447	−	0.585811i	$-0.800776\pi$
$601$	3.99622	−	8.75051i	0.163009	−	0.356941i	0.973457	+	0.228871i	$0.0735032\pi$
$602$	−27.3349	+	8.02625i	−1.11409	+	0.327125i
$603$	−8.86309	+	10.2286i	−0.360933	+	0.416539i
$604$	3.65452	+	1.07306i	0.148700	+	0.0436623i
$605$	−5.14357	+	3.30557i	−0.209116	+	0.134391i
$606$	−3.91261	−	8.56743i	−0.158939	−	0.348028i
$607$	5.38798	+	6.21806i	0.218691	+	0.252383i	0.854485	−	0.519476i	$-0.173873\pi$
$607$	5.38798	+	6.21806i	0.218691	+	0.252383i	−0.635794	+	0.771859i	$0.719327\pi$
$608$	−5.68271	−	3.65205i	−0.230464	−	0.148110i
$609$	−0.287304	+	1.99824i	−0.0116421	+	0.0809728i
$610$	−1.94382	+	13.5195i	−0.0787028	+	0.547390i
$611$	−20.4661	−	13.1527i	−0.827969	−	0.532103i
$612$	3.44876	+	3.98008i	0.139408	+	0.160885i
$613$	−9.49313	−	20.7870i	−0.383424	−	0.839581i	−0.998685	−	0.0512579i	$-0.983677\pi$
$613$	−9.49313	−	20.7870i	−0.383424	−	0.839581i	0.615262	−	0.788323i	$-0.289050\pi$
$614$	−19.6842	+	12.6503i	−0.794391	+	0.510524i
$615$	−7.55595	−	2.21863i	−0.304685	−	0.0894637i
$616$	4.19702	−	4.84362i	0.169103	−	0.195155i
$617$	−14.7060	+	4.31809i	−0.592043	+	0.173840i	−0.564011	−	0.825767i	$-0.690742\pi$
$617$	−14.7060	+	4.31809i	−0.592043	+	0.173840i	−0.0280325	+	0.999607i	$0.508924\pi$
$618$	5.94355	−	13.0146i	0.239084	−	0.523522i
$619$	−3.59594	−	25.0103i	−0.144533	−	1.00525i	−0.924977	−	0.380023i	$-0.875916\pi$
$619$	−3.59594	−	25.0103i	−0.144533	−	1.00525i	0.780444	−	0.625225i	$-0.214993\pi$
$620$	7.08133			0.284393
$621$	1.40035	+	4.58683i	0.0561942	+	0.184063i
$622$	−7.50296			−0.300841
$623$	3.00442	+	20.8962i	0.120369	+	0.837188i
$624$	1.53117	−	3.35280i	0.0612960	−	0.134219i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	9.11203	−	10.5158i	0.364190	−	0.420298i
$627$	14.3265	+	4.20663i	0.572144	+	0.167997i
$628$	−0.674030	+	0.433173i	−0.0268967	+	0.0172855i
$629$	9.18541	+	20.1132i	0.366246	+	0.801967i
$630$	1.89877	+	2.19130i	0.0756488	+	0.0873033i
$631$	−18.8714	−	12.1279i	−0.751257	−	0.482804i	0.108125	−	0.994137i	$-0.465515\pi$
$631$	−18.8714	−	12.1279i	−0.751257	−	0.482804i	−0.859382	+	0.511334i	$0.829152\pi$
$632$	−1.74651	+	12.1472i	−0.0694723	+	0.483191i
$633$	−2.56892	+	17.8672i	−0.102105	+	0.710158i
$634$	17.5948	+	11.3075i	0.698779	+	0.449078i
$635$	−0.613204	−	0.707675i	−0.0243343	−	0.0280832i
$636$	3.65626	+	8.00609i	0.144980	+	0.317462i
$637$	4.36311	−	2.80400i	0.172873	−	0.111098i
$638$	1.47665	+	0.433585i	0.0584613	+	0.0171658i
$639$	−2.44840	+	2.82561i	−0.0968574	+	0.111779i
$640$	−0.959493	+	0.281733i	−0.0379273	+	0.0111365i
$641$	11.3786	−	24.9156i	0.449427	−	0.984107i	−0.540345	−	0.841444i	$-0.681706\pi$
$641$	11.3786	−	24.9156i	0.449427	−	0.984107i	0.989771	−	0.142663i	$-0.0455666\pi$
$642$	−0.559835	−	3.89374i	−0.0220949	−	0.153674i
$643$	−10.9521			−0.431908			−0.215954	−	0.976403i	$-0.569286\pi$
$643$	−10.9521			−0.431908			−0.215954	+	0.976403i	$0.569286\pi$
$644$	−10.6060	−	8.99309i	−0.417936	−	0.354378i
$645$	−9.82544			−0.386876
$646$	−5.06282	−	35.2127i	−0.199194	−	1.38542i
$647$	−10.2543	+	22.4537i	−0.403136	+	0.882746i	0.593806	+	0.804608i	$0.297625\pi$
$647$	−10.2543	+	22.4537i	−0.403136	+	0.882746i	−0.996943	+	0.0781376i	$0.975103\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−6.86029	+	7.91720i	−0.269290	+	0.310777i
$650$	−3.53658	−	1.03843i	−0.138716	−	0.0407308i
$651$	−17.2729	+	11.1006i	−0.676978	+	0.435067i
$652$	8.92502	+	19.5431i	0.349531	+	0.765366i
$653$	−8.22939	−	9.49722i	−0.322041	−	0.371655i	0.571527	−	0.820583i	$-0.306351\pi$
$653$	−8.22939	−	9.49722i	−0.322041	−	0.371655i	−0.893568	+	0.448928i	$0.851806\pi$
$654$	−2.26689	−	1.45684i	−0.0886422	−	0.0569669i
$655$	1.52600	−	10.6136i	0.0596258	−	0.414707i
$656$	−1.12072	+	7.79479i	−0.0437568	+	0.304335i
$657$	7.23482	+	4.64954i	0.282257	+	0.181396i
$658$	−12.5325	−	14.4633i	−0.488568	−	0.563837i
$659$	18.9003	+	41.3858i	0.736250	+	1.61216i	0.789626	+	0.613589i	$0.210275\pi$
$659$	18.9003	+	41.3858i	0.736250	+	1.61216i	−0.0533752	+	0.998575i	$0.516998\pi$
$660$	1.85950	−	1.19503i	0.0723809	−	0.0465164i
$661$	2.20197	+	0.646558i	0.0856468	+	0.0251482i	0.324275	−	0.945963i	$-0.394880\pi$
$661$	2.20197	+	0.646558i	0.0856468	+	0.0251482i	−0.238628	+	0.971111i	$0.576698\pi$
$662$	−1.32199	+	1.52566i	−0.0513808	+	0.0592965i
$663$	18.6251	−	5.46881i	0.723338	−	0.212391i
$664$	6.47463	−	14.1775i	0.251264	−	0.550192i
$665$	−2.78742	−	19.3869i	−0.108091	−	0.751792i
$666$	−4.19858			−0.162692
$667$	0.906368	−	3.21375i	0.0350947	−	0.124437i
$668$	20.0745			0.776705
$669$	−2.95778	−	20.5718i	−0.114354	−	0.795353i
$670$	5.62236	−	12.3112i	0.217211	−	0.475625i
$671$	−28.9678	+	8.50572i	−1.11829	+	0.328360i
$672$	1.89877	−	2.19130i	0.0732466	−	0.0845311i
$673$	−12.0666	−	3.54308i	−0.465134	−	0.136576i	0.0407641	−	0.999169i	$-0.487021\pi$
$673$	−12.0666	−	3.54308i	−0.465134	−	0.136576i	−0.505898	+	0.862593i	$0.668839\pi$
$674$	16.5273	−	10.6215i	0.636609	−	0.409124i
$675$	0.415415	+	0.909632i	0.0159893	+	0.0350118i
$676$	−0.383599	−	0.442697i	−0.0147538	−	0.0170268i
$677$	−11.5788	−	7.44124i	−0.445009	−	0.285990i	0.298883	−	0.954290i	$-0.403386\pi$
$677$	−11.5788	−	7.44124i	−0.445009	−	0.285990i	−0.743892	+	0.668300i	$0.767022\pi$
$678$	−2.25986	+	15.7177i	−0.0867893	+	0.603633i
$679$	−2.91186	+	20.2524i	−0.111747	+	0.777217i
$680$	−4.43038	−	2.84723i	−0.169897	−	0.109186i
$681$	−9.63416	−	11.1184i	−0.369182	−	0.426058i
$682$	6.50229	+	14.2380i	0.248986	+	0.545202i
$683$	13.9648	−	8.97462i	0.534347	−	0.343404i	−0.245477	−	0.969402i	$-0.578945\pi$
$683$	13.9648	−	8.97462i	0.534347	−	0.343404i	0.779825	+	0.625998i	$0.215308\pi$
$684$	6.48142	+	1.90312i	0.247823	+	0.0727675i
$685$	−3.95392	+	4.56307i	−0.151072	+	0.174346i
$686$	−15.5597	+	4.56874i	−0.594073	+	0.174435i
$687$	−4.05478	+	8.87874i	−0.154700	+	0.338745i
$688$	1.39831	+	9.72543i	0.0533099	+	0.370779i
$689$	32.4412			1.23591
$690$	−2.63589	−	4.00651i	−0.100346	−	0.152525i
$691$	24.8273			0.944473			0.472237	−	0.881472i	$-0.343447\pi$
$691$	24.8273			0.944473			0.472237	+	0.881472i	$0.343447\pi$
$692$	−1.65396	−	11.5035i	−0.0628741	−	0.437299i
$693$	−2.66241	+	5.82986i	−0.101137	+	0.221458i
$694$	3.43816	−	1.00953i	0.130511	−	0.0383214i
$695$	−4.16157	+	4.80270i	−0.157857	+	0.182177i
$696$	0.668051	+	0.196157i	0.0253224	+	0.00743533i
$697$	−34.8890	+	22.4218i	−1.32151	+	0.849286i
$698$	−5.36994	−	11.7585i	−0.203255	−	0.445067i
$699$	−0.0393164	−	0.0453735i	−0.00148708	−	0.00171618i
$700$	−2.43922	−	1.56759i	−0.0921937	−	0.0592493i
$701$	4.83004	−	33.5937i	0.182428	−	1.26881i	−0.668571	−	0.743648i	$-0.733094\pi$
$701$	4.83004	−	33.5937i	0.182428	−	1.26881i	0.850999	−	0.525167i	$-0.175997\pi$
$702$	−0.524557	+	3.64837i	−0.0197981	+	0.137699i
$703$	23.8593	+	15.3334i	0.899871	+	0.578312i
$704$	−1.44750	−	1.67050i	−0.0545546	−	0.0629594i
$705$	−2.74187	−	6.00387i	−0.103265	−	0.226119i
$706$	−10.3044	+	6.62222i	−0.387810	+	0.249230i
$707$	−26.2029	−	7.69387i	−0.985462	−	0.289358i
$708$	−3.10366	+	3.58181i	−0.116643	+	0.134613i
$709$	−20.1005	+	5.90203i	−0.754889	+	0.221655i	−0.636463	−	0.771308i	$-0.719603\pi$
$709$	−20.1005	+	5.90203i	−0.754889	+	0.221655i	−0.118426	+	0.992963i	$0.537785\pi$
$710$	1.55316	−	3.40095i	0.0582891	−	0.127635i
$711$	−1.74651	−	12.1472i	−0.0654991	−	0.455556i
$712$	7.28093			0.272864
$713$	30.7390	−	14.4379i	1.15119	−	0.540705i
$714$	15.2699			0.571463
$715$	−1.15948	−	8.06433i	−0.0433619	−	0.301589i
$716$	−0.476959	+	1.04439i	−0.0178248	+	0.0390309i
$717$	−0.0231655	+	0.00680199i	−0.000865130	+	0.000254025i
$718$	13.3082	−	15.3585i	0.496658	−	0.573173i
$719$	8.94128	+	2.62540i	0.333453	+	0.0979107i	0.444173	−	0.895941i	$-0.353497\pi$
$719$	8.94128	+	2.62540i	0.333453	+	0.0979107i	−0.110720	+	0.993852i	$0.535316\pi$
$720$	0.841254	−	0.540641i	0.0313517	−	0.0201485i
$721$	−17.2333	−	37.7357i	−0.641802	−	1.40535i
$722$	−17.4394	−	20.1261i	−0.649026	−	0.749016i
$723$	−17.5998	−	11.3107i	−0.654543	−	0.420649i
$724$	2.41486	−	16.7957i	0.0897475	−	0.624207i
$725$	0.0990873	−	0.689167i	0.00368001	−	0.0255950i
$726$	−5.14357	−	3.30557i	−0.190896	−	0.122681i
$727$	1.02393	+	1.18168i	0.0379756	+	0.0438261i	0.774420	−	0.632672i	$-0.218042\pi$
$727$	1.02393	+	1.18168i	0.0379756	+	0.0438261i	−0.736444	+	0.676498i	$0.763497\pi$
$728$	−4.43964	−	9.72145i	−0.164544	−	0.360301i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−8.25168	−	2.42291i	−0.305409	−	0.0896760i
$731$	−33.8856	+	39.1060i	−1.25330	+	1.44639i
$732$	−13.1053	+	3.84806i	−0.484386	+	0.142228i
$733$	7.30727	−	16.0007i	0.269900	−	0.590999i	−0.725347	−	0.688384i	$-0.758321\pi$
$733$	7.30727	−	16.0007i	0.269900	−	0.590999i	0.995247	+	0.0973849i	$0.0310478\pi$
$734$	−4.38630	−	30.5074i	−0.161901	−	1.12605i
$735$	1.40711			0.0519019
$736$	−3.59060	+	3.17924i	−0.132351	+	0.117188i
$737$	29.9161			1.10198
$738$	−1.12072	−	7.79479i	−0.0412543	−	0.286930i
$739$	−13.4091	+	29.3618i	−0.493262	+	1.08009i	0.485339	+	0.874326i	$0.338696\pi$
$739$	−13.4091	+	29.3618i	−0.493262	+	1.08009i	−0.978601	+	0.205767i	$0.934031\pi$
$740$	4.02851	−	1.18288i	0.148091	−	0.0434834i
$741$	16.3050	−	18.8169i	0.598977	−	0.691257i
$742$	24.4861	+	7.18977i	0.898913	+	0.263945i
$743$	22.3565	−	14.3677i	0.820182	−	0.527099i	−0.0619623	−	0.998078i	$-0.519736\pi$
$743$	22.3565	−	14.3677i	0.820182	−	0.527099i	0.882144	+	0.470980i	$0.156099\pi$
$744$	2.94169	+	6.44141i	0.107848	+	0.236153i
$745$	11.1322	+	12.8473i	0.407853	+	0.470688i
$746$	2.18831	+	1.40634i	0.0801199	+	0.0514899i
$747$	−2.21811	+	15.4273i	−0.0811564	+	0.564455i
$748$	1.65666	−	11.5223i	0.0605735	−	0.421298i
$749$	−9.59533	−	6.16655i	−0.350606	−	0.225321i
$750$	−0.654861	−	0.755750i	−0.0239121	−	0.0275961i
$751$	5.70896	+	12.5009i	0.208323	+	0.456163i	0.984735	−	0.174063i	$-0.0556895\pi$
$751$	5.70896	+	12.5009i	0.208323	+	0.456163i	−0.776412	+	0.630226i	$0.782962\pi$
$752$	−5.55255	+	3.56841i	−0.202481	+	0.130126i
$753$	−18.6273	−	5.46946i	−0.678815	−	0.199318i
$754$	1.68058	−	1.93949i	0.0612031	−	0.0706321i
$755$	3.65452	−	1.07306i	0.133001	−	0.0390528i
$756$	−1.20450	+	2.63748i	−0.0438071	+	0.0959242i
$757$	−1.72827	−	12.0204i	−0.0628151	−	0.436888i	−0.996824	−	0.0796383i	$-0.974623\pi$
$757$	−1.72827	−	12.0204i	−0.0628151	−	0.436888i	0.934009	−	0.357250i	$-0.116286\pi$
$758$	−33.5005			−1.21679
$759$	5.63530	−	8.97872i	0.204549	−	0.325907i
$760$	−6.75505			−0.245031
$761$	2.71954	+	18.9148i	0.0985833	+	0.685662i	0.977846	+	0.209325i	$0.0671266\pi$
$761$	2.71954	+	18.9148i	0.0985833	+	0.685662i	−0.879263	+	0.476337i	$0.841964\pi$
$762$	0.388990	−	0.851769i	0.0140916	−	0.0308563i
$763$	−7.49666	+	2.20122i	−0.271397	+	0.0796894i
$764$	7.55437	−	8.71821i	0.273308	−	0.315414i
$765$	5.05307	+	1.48372i	0.182694	+	0.0536439i
$766$	12.1134	−	7.78478i	0.437673	−	0.281275i
$767$	7.25686	+	15.8903i	0.262030	+	0.573766i
$768$	−0.654861	−	0.755750i	−0.0236303	−	0.0272708i
$769$	−26.8701	−	17.2683i	−0.968960	−	0.622713i	−0.0424959	−	0.999097i	$-0.513531\pi$
$769$	−26.8701	−	17.2683i	−0.968960	−	0.622713i	−0.926464	+	0.376384i	$0.877167\pi$
$770$	0.912100	−	6.34380i	0.0328698	−	0.228615i
$771$	2.41327	−	16.7847i	0.0869118	−	0.604485i
$772$	−4.32219	−	2.77770i	−0.155559	−	0.0999718i
$773$	−20.0033	−	23.0851i	−0.719470	−	0.830313i	0.271773	−	0.962361i	$-0.412390\pi$
$773$	−20.0033	−	23.0851i	−0.719470	−	0.830313i	−0.991243	+	0.132048i	$0.957845\pi$
$774$	−4.08164	−	8.93754i	−0.146711	−	0.321253i
$775$	5.95720	−	3.82846i	0.213989	−	0.137522i
$776$	6.77078	+	1.98808i	0.243057	+	0.0713679i
$777$	−7.97213	+	9.20033i	−0.285999	+	0.330060i
$778$	9.13565	−	2.68247i	0.327529	−	0.0961711i
$779$	−22.0983	+	48.3884i	−0.791752	+	1.73370i
$780$	−0.524557	−	3.64837i	−0.0187821	−	0.130633i
$781$	8.26425			0.295718
$782$	−25.0368	−	3.32644i	−0.895313	−	0.118953i
$783$	−0.696254			−0.0248821
$784$	−0.200252	−	1.39278i	−0.00715186	−	0.0497423i
$785$	−0.332839	+	0.728816i	−0.0118795	+	0.0260126i
$786$	10.2884	−	3.02094i	0.366974	−	0.107753i
$787$	−26.0757	+	30.0930i	−0.929499	+	1.07270i	0.0676854	+	0.997707i	$0.478439\pi$
$787$	−26.0757	+	30.0930i	−0.929499	+	1.07270i	−0.997184	+	0.0749920i	$0.976107\pi$
$788$	−13.0473	−	3.83103i	−0.464791	−	0.136475i
$789$	−23.1266	+	14.8626i	−0.823330	+	0.529122i
$790$	5.09803	+	11.1631i	0.181380	+	0.397166i
$791$	30.1511	+	34.7962i	1.07205	+	1.23721i
$792$	1.85950	+	1.19503i	0.0660744	+	0.0424635i
$793$	−7.16469	+	49.8315i	−0.254426	+	1.76957i
$794$	−4.94981	+	34.4267i	−0.175662	+	1.22176i
$795$	7.40426	+	4.75843i	0.262602	+	0.168764i
$796$	2.19926	+	2.53808i	0.0779505	+	0.0899597i
$797$	7.02322	+	15.3787i	0.248775	+	0.544741i	0.992284	−	0.123984i	$-0.0395673\pi$
$797$	7.02322	+	15.3787i	0.248775	+	0.544741i	−0.743509	+	0.668726i	$0.766840\pi$
$798$	16.4770	−	10.5891i	0.583280	−	0.374851i
$799$	−33.3519	−	9.79301i	−1.17991	−	0.346452i
$800$	−0.654861	+	0.755750i	−0.0231528	+	0.0267198i
$801$	−6.98600	+	2.05128i	−0.246838	+	0.0724782i
$802$	9.50212	−	20.8067i	0.335531	−	0.734711i
$803$	−2.70533	−	18.8160i	−0.0954690	−	0.664001i
$804$	13.5343			0.477319
$805$	−13.7844	−	1.83142i	−0.485836	−	0.0645492i
$806$	26.1010			0.919369
$807$	1.90322	+	13.2372i	0.0669967	+	0.465972i
$808$	−3.91261	+	8.56743i	−0.137645	+	0.301401i
$809$	33.3007	−	9.77797i	1.17079	−	0.343775i	0.362174	−	0.932111i	$-0.382035\pi$
$809$	33.3007	−	9.77797i	1.17079	−	0.343775i	0.808617	+	0.588335i	$0.200217\pi$
$810$	−0.654861	+	0.755750i	−0.0230095	+	0.0265543i
$811$	36.9331	+	10.8445i	1.29689	+	0.380803i	0.856102	−	0.516806i	$-0.172879\pi$
$811$	36.9331	+	10.8445i	1.29689	+	0.380803i	0.440793	+	0.897609i	$0.354697\pi$
$812$	1.69831	−	1.09144i	0.0595991	−	0.0383020i
$813$	−2.62011	−	5.73724i	−0.0918913	−	0.201214i
$814$	6.07744	+	7.01374i	0.213014	+	0.245831i
$815$	18.0740	+	11.6155i	0.633104	+	0.406871i
$816$	0.749487	−	5.21280i	0.0262373	−	0.182484i
$817$	−9.44562	+	65.6958i	−0.330461	+	2.29840i
$818$	−29.6134	−	19.0314i	−1.03541	−	0.665417i
$819$	6.99865	+	8.07687i	0.244553	+	0.282229i
$820$	3.27137	+	7.16330i	0.114241	+	0.250153i
$821$	41.5757	−	26.7191i	1.45100	−	0.932502i	0.451817	−	0.892111i	$-0.350776\pi$
$821$	41.5757	−	26.7191i	1.45100	−	0.932502i	0.999184	−	0.0403910i	$-0.0128604\pi$
$822$	−5.79323	−	1.70105i	−0.202062	−	0.0593308i
$823$	26.4487	−	30.5234i	0.921943	−	1.06398i	−0.0758196	−	0.997122i	$-0.524157\pi$
$823$	26.4487	−	30.5234i	0.921943	−	1.06398i	0.997763	−	0.0668574i	$-0.0212972\pi$
$824$	−13.7279	+	4.03089i	−0.478235	+	0.140423i
$825$	0.918230	−	2.01064i	0.0319687	−	0.0700016i
$826$	1.95568	+	13.6021i	0.0680469	+	0.473276i
$827$	−52.3588			−1.82070			−0.910348	−	0.413844i	$-0.864186\pi$
$827$	−52.3588			−1.82070			−0.910348	+	0.413844i	$0.864186\pi$
$828$	2.54946	−	4.06205i	0.0885999	−	0.141166i
$829$	−35.1818			−1.22191			−0.610956	−	0.791664i	$-0.709215\pi$
$829$	−35.1818			−1.22191			−0.610956	+	0.791664i	$0.709215\pi$
$830$	−2.21811	−	15.4273i	−0.0769917	−	0.535489i
$831$	−11.7369	+	25.7003i	−0.407150	+	0.891535i
$832$	−3.53658	+	1.03843i	−0.122609	+	0.0360012i
$833$	4.85277	−	5.60040i	0.168139	−	0.194042i
$834$	−6.09747	−	1.79038i	−0.211138	−	0.0619957i
$835$	16.8877	−	10.8531i	0.584424	−	0.375587i
$836$	−6.20268	−	13.5820i	−0.214524	−	0.469743i
$837$	−4.63729	−	5.35171i	−0.160288	−	0.184982i
$838$	−2.29700	−	1.47619i	−0.0793485	−	0.0509942i
$839$	0.478880	−	3.33068i	0.0165328	−	0.114988i	−0.979884	−	0.199568i	$-0.936046\pi$
$839$	0.478880	−	3.33068i	0.0165328	−	0.114988i	0.996417	+	0.0845806i	$0.0269551\pi$
$840$	0.412642	−	2.86999i	0.0142375	−	0.0990240i
$841$	−23.9885	−	15.4165i	−0.827191	−	0.531603i
$842$	−10.5384	−	12.1619i	−0.363176	−	0.419128i
$843$	5.14831	+	11.2732i	0.177317	+	0.388271i
$844$	15.1854	−	9.75908i	0.522704	−	0.335921i
$845$	−0.562044	−	0.165031i	−0.0193349	−	0.00567724i
$846$	4.32229	−	4.98819i	0.148604	−	0.171498i
$847$	−17.0099	+	4.99457i	−0.584468	+	0.171615i
$848$	3.65626	−	8.00609i	0.125556	−	0.274930i
$849$	−1.80145	−	12.5293i	−0.0618255	−	0.430006i
$850$	−5.26640			−0.180636
$851$	15.0754	−	13.3483i	0.516779	−	0.457574i
$852$	3.73882			0.128090
$853$	−6.28671	−	43.7250i	−0.215253	−	1.49712i	−0.755243	−	0.655445i	$-0.772481\pi$
$853$	−6.28671	−	43.7250i	−0.215253	−	1.49712i	0.539990	−	0.841671i	$-0.318428\pi$
$854$	−16.4517	+	36.0242i	−0.562965	+	1.23272i
$855$	6.48142	−	1.90312i	0.221660	−	0.0650852i
$856$	−2.57608	+	2.97295i	−0.0880485	+	0.101613i
$857$	42.6750	+	12.5305i	1.45775	+	0.428034i	0.912096	−	0.409977i	$-0.134463\pi$
$857$	42.6750	+	12.5305i	1.45775	+	0.428034i	0.545654	+	0.838011i	$0.316281\pi$
$858$	6.85391	−	4.40474i	0.233989	−	0.150375i
$859$	−10.3441	−	22.6505i	−0.352937	−	0.772824i	−0.999947	−	0.0103421i	$-0.996708\pi$
$859$	−10.3441	−	22.6505i	−0.352937	−	0.772824i	0.647010	−	0.762482i	$-0.276019\pi$
$860$	6.43430	+	7.42557i	0.219408	+	0.253210i
$861$	−19.2087	−	12.3447i	−0.654630	−	0.420705i
$862$	2.02751	−	14.1016i	0.0690573	−	0.480304i
$863$	−2.03709	+	14.1683i	−0.0693435	+	0.482294i	0.925325	+	0.379174i	$0.123792\pi$
$863$	−2.03709	+	14.1683i	−0.0693435	+	0.482294i	−0.994669	+	0.103120i	$0.967117\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	−7.61069	−	8.78320i	−0.258771	−	0.298638i
$866$	−8.74665	−	19.1525i	−0.297223	−	0.650828i
$867$	9.03083	−	5.80376i	0.306703	−	0.197106i
$868$	19.7006	+	5.78463i	0.668683	+	0.196343i
$869$	−17.7639	+	20.5006i	−0.602599	+	0.695436i
$870$	0.668051	−	0.196157i	0.0226491	−	0.00665036i
$871$	20.7234	−	45.3779i	0.702185	−	1.53757i
$872$	0.383489	+	2.66722i	0.0129866	+	0.0903236i
$873$	−7.05662			−0.238831
$874$	−29.3227	+	13.7727i	−0.991854	+	0.465868i
$875$	−2.89950			−0.0980210
$876$	−1.22391	−	8.51251i	−0.0413522	−	0.287611i
$877$	14.4618	−	31.6670i	0.488341	−	1.06932i	−0.491744	−	0.870740i	$-0.663640\pi$
$877$	14.4618	−	31.6670i	0.488341	−	1.06932i	0.980085	−	0.198578i	$-0.0636324\pi$
$878$	10.0546	−	2.95229i	0.339326	−	0.0996350i
$879$	15.9911	−	18.4547i	0.539367	−	0.622463i
$880$	−2.12085	−	0.622739i	−0.0714940	−	0.0209925i
$881$	32.2088	−	20.6993i	1.08514	−	0.697378i	0.129402	−	0.991592i	$-0.458694\pi$
$881$	32.2088	−	20.6993i	1.08514	−	0.697378i	0.955740	+	0.294214i	$0.0950578\pi$
$882$	0.584533	+	1.27995i	0.0196823	+	0.0430981i
$883$	10.6343	+	12.2726i	0.357873	+	0.413007i	0.905926	−	0.423436i	$-0.139176\pi$
$883$	10.6343	+	12.2726i	0.357873	+	0.413007i	−0.548053	+	0.836444i	$0.684631\pi$
$884$	−16.3299	−	10.4946i	−0.549233	−	0.352971i
$885$	−0.674489	+	4.69117i	−0.0226727	+	0.157692i
$886$	−5.16986	+	35.9572i	−0.173685	+	1.20801i
$887$	49.0090	+	31.4961i	1.64556	+	1.05754i	0.935458	+	0.353439i	$0.114988\pi$
$887$	49.0090	+	31.4961i	1.64556	+	1.05754i	0.710102	+	0.704099i	$0.248649\pi$
$888$	2.74949	+	3.17307i	0.0922667	+	0.106481i
$889$	−1.12788	−	2.46971i	−0.0378278	−	0.0828313i
$890$	6.12511	−	3.93637i	0.205314	−	0.131947i
$891$	−2.12085	−	0.622739i	−0.0710513	−	0.0208625i
$892$	−13.6102	+	15.7070i	−0.455704	+	0.525910i
$893$	−42.7795	+	12.5612i	−1.43156	+	0.420344i
$894$	−7.06180	+	15.4632i	−0.236182	+	0.517166i
$895$	0.163399	+	1.13646i	0.00546182	+	0.0379878i
$896$	−2.89950			−0.0968655
$897$	−9.71558	−	14.7675i	−0.324394	−	0.493074i
$898$	−8.89855			−0.296949
$899$	0.701670	+	4.88022i	0.0234020	+	0.162765i
$900$	0.415415	−	0.909632i	0.0138472	−	0.0303211i
$901$	44.4744	−	13.0589i	1.48166	−	0.435054i
$902$	−11.3990	+	13.1551i	−0.379544	+	0.438017i
$903$	−27.3349	−	8.02625i	−0.909648	−	0.267097i
$904$	13.3585	−	8.58499i	0.444297	−	0.285532i
$905$	−7.04894	−	15.4350i	−0.234315	−	0.513077i
$906$	2.49423	+	2.87850i	0.0828654	+	0.0956317i
$907$	15.1439	+	9.73240i	0.502845	+	0.323159i	0.767353	−	0.641224i	$-0.221573\pi$
$907$	15.1439	+	9.73240i	0.502845	+	0.323159i	−0.264508	+	0.964383i	$0.585210\pi$
$908$	−2.09370	+	14.5620i	−0.0694820	+	0.483258i
$909$	1.34040	−	9.32270i	0.0444583	−	0.309214i
$910$	−8.99068	−	5.77796i	−0.298038	−	0.191537i
$911$	5.91523	+	6.82655i	0.195980	+	0.226174i	0.845231	−	0.534401i	$-0.179463\pi$
$911$	5.91523	+	6.82655i	0.195980	+	0.226174i	−0.649251	+	0.760575i	$0.724917\pi$
$912$	−2.80615	−	6.14461i	−0.0929208	−	0.203468i
$913$	28.9820	−	18.6256i	0.959165	−	0.616418i
$914$	5.57475	+	1.63689i	0.184396	+	0.0541437i
$915$	−8.94446	+	10.3225i	−0.295695	+	0.341250i
$916$	9.36542	−	2.74994i	0.309442	−	0.0908604i
$917$	12.9155	−	28.2809i	0.426506	−	0.933919i
$918$	0.749487	+	5.21280i	0.0247368	+	0.172048i
$919$	23.2148			0.765785			0.382892	−	0.923793i	$-0.374928\pi$
$919$	23.2148			0.765785			0.382892	+	0.923793i	$0.374928\pi$
$920$	−1.30178	+	4.61577i	−0.0429183	+	0.152178i
$921$	−23.3987			−0.771013
$922$	−1.05808	−	7.35912i	−0.0348461	−	0.242360i
$923$	5.72478	−	12.5355i	0.188433	−	0.412611i
$924$	6.14942	−	1.80563i	0.202301	−	0.0594010i
$925$	2.74949	−	3.17307i	0.0904025	−	0.104330i
$926$	18.7506	+	5.50567i	0.616182	+	0.180927i
$927$	12.0362	−	7.73521i	0.395322	−	0.254058i
$928$	−0.289234	−	0.633335i	−0.00949459	−	0.0207902i
$929$	14.0811	+	16.2505i	0.461987	+	0.533161i	0.938165	−	0.346188i	$-0.112524\pi$
$929$	14.0811	+	16.2505i	0.461987	+	0.533161i	−0.476179	+	0.879348i	$0.657978\pi$
$930$	5.95720	+	3.82846i	0.195344	+	0.125540i
$931$	1.35271	−	9.40832i	0.0443334	−	0.308345i
$932$	−0.00854427	+	0.0594267i	−0.000279877	+	0.00194659i
$933$	−6.31190	−	4.05641i	−0.206642	−	0.132801i
$934$	14.4497	+	16.6759i	0.472810	+	0.545652i
$935$	−4.83577	−	10.5888i	−0.158146	−	0.346292i
$936$	3.10077	−	1.99274i	0.101352	−	0.0651348i
$937$	46.3689	+	13.6151i	1.51481	+	0.444788i	0.930361	−	0.366645i	$-0.119494\pi$
$937$	46.3689	+	13.6151i	1.51481	+	0.444788i	0.584446	+	0.811432i	$0.301312\pi$
$938$	25.6985	−	29.6577i	0.839087	−	0.968358i
$939$	13.3508	−	3.92016i	0.435688	−	0.127929i
$940$	−2.74187	+	6.00387i	−0.0894301	+	0.195825i
$941$	1.58062	+	10.9934i	0.0515267	+	0.358376i	0.999230	+	0.0392246i	$0.0124888\pi$
$941$	1.58062	+	10.9934i	0.0515267	+	0.358376i	−0.947704	+	0.319151i	$0.896602\pi$
$942$	−0.801221			−0.0261052
$943$	28.8056	+	24.4249i	0.938039	+	0.795385i
$944$	4.73941			0.154255
$945$	0.412642	+	2.86999i	0.0134232	+	0.0933607i
$946$	−9.02201	+	19.7555i	−0.293331	+	0.642305i
$947$	−21.0156	+	6.17073i	−0.682915	+	0.200522i	−0.604746	−	0.796418i	$-0.706725\pi$
$947$	−21.0156	+	6.17073i	−0.682915	+	0.200522i	−0.0781686	+	0.996940i	$0.524907\pi$
$948$	−8.03654	+	9.27466i	−0.261015	+	0.301227i
$949$	−30.4148	−	8.93059i	−0.987306	−	0.289899i
$950$	−5.68271	+	3.65205i	−0.184371	+	0.118488i
$951$	8.68840	+	19.0249i	0.281741	+	0.616926i
$952$	−9.99968	−	11.5402i	−0.324091	−	0.374021i
$953$	−3.70877	−	2.38348i	−0.120139	−	0.0772085i	0.479191	−	0.877710i	$-0.340930\pi$
$953$	−3.70877	−	2.38348i	−0.120139	−	0.0772085i	−0.599330	+	0.800502i	$0.704566\pi$
$954$	−1.25258	+	8.71187i	−0.0405537	+	0.282057i
$955$	1.64172	−	11.4184i	0.0531249	−	0.369492i
$956$	0.0203107	+	0.0130529i	0.000656896	+	0.000422162i
$957$	1.00783	+	1.16309i	0.0325784	+	0.0375975i
$958$	9.33405	+	20.4387i	0.301569	+	0.660345i
$959$	−14.7275	+	9.46479i	−0.475576	+	0.305634i
$960$	−0.959493	−	0.281733i	−0.0309675	−	0.00909288i
$961$	−12.5375	+	14.4690i	−0.404435	+	0.466743i
$962$	14.8486	−	4.35995i	0.478739	−	0.140570i
$963$	1.63415	−	3.57829i	0.0526598	−	0.115309i
$964$	2.97735	+	20.7080i	0.0958941	+	0.666958i
$965$	−5.13780			−0.165392
$966$	−4.06032	−	13.2995i	−0.130639	−	0.427905i
$967$	−21.7774			−0.700314			−0.350157	−	0.936691i	$-0.613872\pi$
$967$	−21.7774			−0.700314			−0.350157	+	0.936691i	$0.613872\pi$
$968$	0.870137	+	6.05194i	0.0279673	+	0.194517i
$969$	14.7783	−	32.3600i	0.474747	−	1.03955i
$970$	6.77078	−	1.98808i	0.217397	−	0.0638334i
$971$	28.6468	−	33.0602i	0.919321	−	1.06095i	−0.0786261	−	0.996904i	$-0.525053\pi$
$971$	28.6468	−	33.0602i	0.919321	−	1.06095i	0.997947	−	0.0640484i	$-0.0204012\pi$
$972$	−0.959493	−	0.281733i	−0.0307758	−	0.00903658i
$973$	−15.5009	+	9.96185i	−0.496937	+	0.319362i
$974$	1.21493	+	2.66032i	0.0389289	+	0.0852423i
$975$	−2.41374	−	2.78561i	−0.0773017	−	0.0892109i
$976$	11.4903	+	7.38438i	0.367796	+	0.236368i
$977$	0.752347	−	5.23269i	0.0240697	−	0.167409i	−0.974241	−	0.225509i	$-0.927595\pi$
$977$	0.752347	−	5.23269i	0.0240697	−	0.167409i	0.998311	+	0.0581008i	$0.0185045\pi$
$978$	−3.05758	+	21.2659i	−0.0977705	+	0.680009i
$979$	13.5389	+	8.70091i	0.432705	+	0.278082i
$980$	−0.921459	−	1.06342i	−0.0294349	−	0.0339697i
$981$	−1.11940	−	2.45114i	−0.0357397	−	0.0782589i
$982$	−7.75594	+	4.98444i	−0.247502	+	0.159060i
$983$	32.6013	+	9.57260i	1.03982	+	0.305318i	0.756697	−	0.653765i	$-0.226812\pi$
$983$	32.6013	+	9.57260i	1.03982	+	0.305318i	0.283122	+	0.959084i	$0.408630\pi$
$984$	−5.15699	+	5.95149i	−0.164399	+	0.189726i
$985$	−13.0473	+	3.83103i	−0.415721	+	0.122067i
$986$	1.52322	−	3.33540i	0.0485093	−	0.106221i
$987$	−2.72357	−	18.9429i	−0.0866922	−	0.602958i
$988$	−24.8983			−0.792122
$989$	43.0701	+	19.1146i	1.36955	+	0.607809i
$990$	2.21039			0.0702508
$991$	−1.06980	−	7.44065i	−0.0339834	−	0.236360i	0.965749	−	0.259477i	$-0.0835501\pi$
$991$	−1.06980	−	7.44065i	−0.0339834	−	0.236360i	−0.999733	+	0.0231168i	$0.992641\pi$
$992$	2.94169	−	6.44141i	0.0933988	−	0.204515i
$993$	−1.93697	+	0.568745i	−0.0614678	+	0.0180486i
$994$	7.09915	−	8.19286i	0.225171	−	0.259862i
$995$	3.22232	+	0.946158i	0.102154	+	0.0299952i
$996$	13.1117	−	8.42639i	0.415461	−	0.267000i
$997$	−1.58680	−	3.47461i	−0.0502545	−	0.110042i	0.882839	−	0.469675i	$-0.155629\pi$
$997$	−1.58680	−	3.47461i	−0.0502545	−	0.110042i	−0.933094	+	0.359633i	$0.882902\pi$
$998$	−17.5638	−	20.2697i	−0.555972	−	0.641626i
$999$	−3.53207	−	2.26992i	−0.111750	−	0.0718172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.g.601.1	yes	30
23.8	even	11	inner	690.2.m.g.31.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.g.31.1	✓	30	23.8	even	11	inner
690.2.m.g.601.1	yes	30	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-2.43922 + 1.56759i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(0.415415 - 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(-2.43922 + 1.56759i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.841254 + 0.540641i) q^{10} +(-0.314571 + 2.18789i) q^{11} +(-0.142315 + 0.989821i) q^{12} +(3.10077 + 1.99274i) q^{13} +(1.89877 + 2.19130i) q^{14} +(0.415415 + 0.909632i) q^{15} +(0.841254 - 0.540641i) q^{16} +(5.05307 + 1.48372i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(6.48142 - 1.90312i) q^{19} +(0.415415 - 0.909632i) q^{20} +(0.412642 + 2.86999i) q^{21} +2.21039 q^{22} +(-0.0513676 - 4.79556i) q^{23} +1.00000 q^{24} +(-0.142315 - 0.989821i) q^{25} +(1.53117 - 3.35280i) q^{26} +(-0.959493 + 0.281733i) q^{27} +(1.89877 - 2.19130i) q^{28} +(0.668051 + 0.196157i) q^{29} +(0.841254 - 0.540641i) q^{30} +(2.94169 + 6.44141i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(1.85950 + 1.19503i) q^{33} +(0.749487 - 5.21280i) q^{34} +(0.412642 - 2.86999i) q^{35} +(0.841254 + 0.540641i) q^{36} +(2.74949 + 3.17307i) q^{37} +(-2.80615 - 6.14461i) q^{38} +(3.10077 - 1.99274i) q^{39} +(-0.959493 - 0.281733i) q^{40} +(-5.15699 + 5.95149i) q^{41} +(2.78205 - 0.816884i) q^{42} +(-4.08164 + 8.93754i) q^{43} +(-0.314571 - 2.18789i) q^{44} +1.00000 q^{45} +(-4.73943 + 0.733324i) q^{46} -6.60033 q^{47} +(-0.142315 - 0.989821i) q^{48} +(0.584533 - 1.27995i) q^{49} +(-0.959493 + 0.281733i) q^{50} +(3.44876 - 3.98008i) q^{51} +(-3.53658 - 1.03843i) q^{52} +(7.40426 - 4.75843i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-1.44750 - 1.67050i) q^{55} +(-2.43922 - 1.56759i) q^{56} +(0.961343 - 6.68629i) q^{57} +(0.0990873 - 0.689167i) q^{58} +(3.98705 + 2.56232i) q^{59} +(-0.654861 - 0.755750i) q^{60} +(5.67397 + 12.4243i) q^{61} +(5.95720 - 3.82846i) q^{62} +(2.78205 + 0.816884i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-3.53658 + 1.03843i) q^{65} +(0.918230 - 2.01064i) q^{66} +(-1.92613 - 13.3966i) q^{67} -5.26640 q^{68} +(-4.38353 - 1.94542i) q^{69} -2.89950 q^{70} +(-0.532089 - 3.70076i) q^{71} +(0.415415 - 0.909632i) q^{72} +(-8.25168 + 2.42291i) q^{73} +(2.74949 - 3.17307i) q^{74} +(-0.959493 - 0.281733i) q^{75} +(-5.68271 + 3.65205i) q^{76} +(-2.66241 - 5.82986i) q^{77} +(-2.41374 - 2.78561i) q^{78} +(10.3240 + 6.63482i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(6.62482 + 4.25752i) q^{82} +(-10.2066 - 11.7791i) q^{83} +(-1.20450 - 2.63748i) q^{84} +(-4.43038 + 2.84723i) q^{85} +(9.42744 + 2.76815i) q^{86} +(0.455950 - 0.526194i) q^{87} +(-2.12085 + 0.622739i) q^{88} +(3.02461 - 6.62297i) q^{89} +(-0.142315 - 0.989821i) q^{90} -10.6872 q^{91} +(1.40035 + 4.58683i) q^{92} +7.08133 q^{93} +(0.939324 + 6.53314i) q^{94} +(-2.80615 + 6.14461i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(4.62111 - 5.33304i) q^{97} +(-1.35011 - 0.396428i) q^{98} +(1.85950 - 1.19503i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9	\( 30 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 8 q^{7} - 3 q^{8} - 3 q^{9} - 3 q^{10} + 8 q^{11} - 3 q^{12} - 5 q^{13} - 8 q^{14} - 3 q^{15} - 3 q^{16} + 4 q^{17} - 3 q^{18} + 6 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} + q^{23} + 30 q^{24} - 3 q^{25} - 5 q^{26} - 3 q^{27} - 8 q^{28} - 10 q^{29} - 3 q^{30} - 10 q^{31} - 3 q^{32} - 14 q^{33} - 7 q^{34} + 3 q^{35} - 3 q^{36} - 12 q^{37} - 5 q^{38} - 5 q^{39} - 3 q^{40} + 5 q^{41} + 3 q^{42} + 2 q^{43} + 8 q^{44} + 30 q^{45} - 21 q^{46} + 96 q^{47} - 3 q^{48} - 43 q^{49} - 3 q^{50} + 15 q^{51} - 16 q^{52} + 12 q^{53} - 3 q^{54} + 8 q^{55} - 8 q^{56} + 17 q^{57} + q^{58} - 9 q^{59} - 3 q^{60} + q^{61} - 32 q^{62} + 3 q^{63} - 3 q^{64} - 16 q^{65} - 3 q^{66} - 28 q^{67} + 4 q^{68} + 23 q^{69} + 14 q^{70} + 3 q^{71} - 3 q^{72} - 27 q^{73} - 12 q^{74} - 3 q^{75} - 16 q^{76} + 47 q^{77} + 6 q^{78} + 2 q^{79} - 3 q^{80} - 3 q^{81} + 27 q^{82} + 11 q^{83} + 3 q^{84} - 7 q^{85} + 2 q^{86} - 32 q^{87} - 3 q^{88} + 25 q^{89} - 3 q^{90} - 90 q^{91} - 10 q^{92} + 56 q^{93} - 25 q^{94} - 5 q^{95} - 3 q^{96} - 7 q^{97} - 32 q^{98} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 8 * q^7 - 3 * q^8 - 3 * q^9 - 3 * q^10 + 8 * q^11 - 3 * q^12 - 5 * q^13 - 8 * q^14 - 3 * q^15 - 3 * q^16 + 4 * q^17 - 3 * q^18 + 6 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 + q^23 + 30 * q^24 - 3 * q^25 - 5 * q^26 - 3 * q^27 - 8 * q^28 - 10 * q^29 - 3 * q^30 - 10 * q^31 - 3 * q^32 - 14 * q^33 - 7 * q^34 + 3 * q^35 - 3 * q^36 - 12 * q^37 - 5 * q^38 - 5 * q^39 - 3 * q^40 + 5 * q^41 + 3 * q^42 + 2 * q^43 + 8 * q^44 + 30 * q^45 - 21 * q^46 + 96 * q^47 - 3 * q^48 - 43 * q^49 - 3 * q^50 + 15 * q^51 - 16 * q^52 + 12 * q^53 - 3 * q^54 + 8 * q^55 - 8 * q^56 + 17 * q^57 + q^58 - 9 * q^59 - 3 * q^60 + q^61 - 32 * q^62 + 3 * q^63 - 3 * q^64 - 16 * q^65 - 3 * q^66 - 28 * q^67 + 4 * q^68 + 23 * q^69 + 14 * q^70 + 3 * q^71 - 3 * q^72 - 27 * q^73 - 12 * q^74 - 3 * q^75 - 16 * q^76 + 47 * q^77 + 6 * q^78 + 2 * q^79 - 3 * q^80 - 3 * q^81 + 27 * q^82 + 11 * q^83 + 3 * q^84 - 7 * q^85 + 2 * q^86 - 32 * q^87 - 3 * q^88 + 25 * q^89 - 3 * q^90 - 90 * q^91 - 10 * q^92 + 56 * q^93 - 25 * q^94 - 5 * q^95 - 3 * q^96 - 7 * q^97 - 32 * q^98 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more