LMFDB - Embedded newform 690.2.w.a.493.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.6
Character	$\chi$	$=$	690.493
Dual form			690.2.w.a.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(2.23599 - 0.0191781i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.197874 + 0.362379i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(2.23599 - 0.0191781i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.197874 + 0.362379i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-2.23166 - 0.140384i) q^{10} +(2.14545 + 1.85905i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(1.42292 + 0.776975i) q^{13} +(-0.171518 - 0.375572i) q^{14} +(0.494033 + 2.18081i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.178490 + 0.238435i) q^{17} +(0.936950 - 0.349464i) q^{18} +(0.324029 - 2.25367i) q^{19} +(2.21596 + 0.299231i) q^{20} +(-0.312036 + 0.270381i) q^{21} +(-2.00736 - 2.00736i) q^{22} +(-0.593093 + 4.75902i) q^{23} -1.00000i q^{24} +(4.99926 - 0.0857637i) q^{25} +(-1.36387 - 0.876506i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(0.144288 + 0.386851i) q^{28} +(-2.51402 + 0.361462i) q^{29} +(-0.337197 - 2.21050i) q^{30} +(5.05222 - 3.24687i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(-1.36051 + 2.49159i) q^{33} +(0.195045 - 0.225094i) q^{34} +(0.449393 + 0.806479i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.563033 - 1.50955i) q^{37} +(-0.483978 + 2.22481i) q^{38} +(-0.456755 + 1.55556i) q^{39} +(-2.18896 - 0.456553i) q^{40} +(0.810149 - 1.77398i) q^{41} +(0.330530 - 0.247432i) q^{42} +(-2.53575 + 0.551618i) q^{43} +(1.85905 + 2.14545i) q^{44} +(-2.02596 + 0.946307i) q^{45} +(0.931086 - 4.70458i) q^{46} +(-8.55701 + 8.55701i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(3.69232 - 5.74536i) q^{49} +(-4.99265 - 0.271098i) q^{50} +(-0.270927 - 0.123728i) q^{51} +(1.29787 + 0.971570i) q^{52} +(-0.215564 + 0.117707i) q^{53} +(0.540641 + 0.841254i) q^{54} +(4.83285 + 4.11565i) q^{55} +(-0.116323 - 0.396158i) q^{56} +(2.27104 - 0.162428i) q^{57} +(2.53340 - 0.181192i) q^{58} +(2.89074 + 9.84494i) q^{59} +(0.178643 + 2.22892i) q^{60} +(2.71054 + 4.21768i) q^{61} +(-5.27098 + 2.87817i) q^{62} +(-0.330530 - 0.247432i) q^{63} +(0.909632 + 0.415415i) q^{64} +(3.19654 + 1.71002i) q^{65} +(1.53479 - 2.38818i) q^{66} +(-0.678110 + 9.48121i) q^{67} +(-0.210606 + 0.210606i) q^{68} +(-4.77633 + 0.432063i) q^{69} +(-0.390714 - 0.836483i) q^{70} +(0.0645553 + 0.0745008i) q^{71} +(0.977147 - 0.212565i) q^{72} +(2.73613 - 2.04824i) q^{73} +(-0.669289 + 1.46554i) q^{74} +(1.14647 + 4.86679i) q^{75} +(0.641461 - 2.18462i) q^{76} +(-0.249150 + 1.14532i) q^{77} +(0.566564 - 1.51902i) q^{78} +(8.99504 - 2.64118i) q^{79} +(2.15082 + 0.611549i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.934638 + 1.71166i) q^{82} +(11.4503 + 4.27074i) q^{83} +(-0.347339 + 0.223221i) q^{84} +(-0.394529 + 0.536561i) q^{85} +(2.56864 - 0.369314i) q^{86} +(-0.887595 - 2.37973i) q^{87} +(-1.70125 - 2.27261i) q^{88} +(-2.18067 - 1.40143i) q^{89} +(2.08830 - 0.799366i) q^{90} +0.669381i q^{91} +(-1.26433 + 4.62617i) q^{92} +(4.24659 + 4.24659i) q^{93} +(9.14566 - 7.92476i) q^{94} +(0.681303 - 5.04539i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-8.48000 + 3.16288i) q^{97} +(-4.09278 + 5.46732i) q^{98} +(-2.72385 - 0.799794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	2.23599	−	0.0191781i	0.999963	−	0.00857669i
$5$	2.23599	−	0.0191781i	0.999963	−	0.00857669i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	0.197874	+	0.362379i	0.0747893	+	0.136966i	0.912398	−	0.409305i	$-0.134229\pi$
$7$	0.197874	+	0.362379i	0.0747893	+	0.136966i	−0.837608	+	0.546271i	$0.816047\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	−2.23166	−	0.140384i	−0.705712	−	0.0443934i
$11$	2.14545	+	1.85905i	0.646878	+	0.560523i	0.915297	−	0.402779i	$-0.131956\pi$
$11$	2.14545	+	1.85905i	0.646878	+	0.560523i	−0.268419	+	0.963302i	$0.586501\pi$
$12$	0.0713392	+	0.997452i	0.0205938	+	0.287940i
$13$	1.42292	+	0.776975i	0.394648	+	0.215494i	0.664304	−	0.747463i	$-0.268728\pi$
$13$	1.42292	+	0.776975i	0.394648	+	0.215494i	−0.269656	+	0.962957i	$0.586910\pi$
$14$	−0.171518	−	0.375572i	−0.0458401	−	0.100376i
$15$	0.494033	+	2.18081i	0.127559	+	0.563083i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−0.178490	+	0.238435i	−0.0432903	+	0.0578290i	−0.821664	−	0.569972i	$-0.806954\pi$
$17$	−0.178490	+	0.238435i	−0.0432903	+	0.0578290i	0.778374	+	0.627801i	$0.216045\pi$
$18$	0.936950	−	0.349464i	0.220841	−	0.0823695i
$19$	0.324029	−	2.25367i	0.0743373	−	0.517027i	−0.918298	−	0.395889i	$-0.870437\pi$
$19$	0.324029	−	2.25367i	0.0743373	−	0.517027i	0.992636	−	0.121138i	$-0.0386544\pi$
$20$	2.21596	+	0.299231i	0.495503	+	0.0669101i
$21$	−0.312036	+	0.270381i	−0.0680919	+	0.0590020i
$22$	−2.00736	−	2.00736i	−0.427971	−	0.427971i
$23$	−0.593093	+	4.75902i	−0.123668	+	0.992324i
$23$	−0.593093	+	4.75902i	−0.123668	+	0.992324i
$24$		−	1.00000i		−	0.204124i
$25$	4.99926	−	0.0857637i	0.999853	−	0.0171527i
$26$	−1.36387	−	0.876506i	−0.267477	−	0.171897i
$27$	−0.599278	−	0.800541i	−0.115331	−	0.154064i
$28$	0.144288	+	0.386851i	0.0272678	+	0.0731079i
$29$	−2.51402	+	0.361462i	−0.466842	+	0.0671217i	−0.371722	−	0.928344i	$-0.621233\pi$
$29$	−2.51402	+	0.361462i	−0.466842	+	0.0671217i	−0.0951199	+	0.995466i	$0.530323\pi$
$30$	−0.337197	−	2.21050i	−0.0615634	−	0.403580i
$31$	5.05222	−	3.24687i	0.907406	−	0.583154i	−0.00157191	−	0.999999i	$-0.500500\pi$
$31$	5.05222	−	3.24687i	0.907406	−	0.583154i	0.908978	+	0.416844i	$0.136864\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	−1.36051	+	2.49159i	−0.236835	+	0.433730i
$34$	0.195045	−	0.225094i	0.0334500	−	0.0386034i
$35$	0.449393	+	0.806479i	0.0759612	+	0.136320i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	0.563033	−	1.50955i	0.0925621	−	0.248169i	−0.882416	−	0.470470i	$-0.844084\pi$
$37$	0.563033	−	1.50955i	0.0925621	−	0.248169i	0.974978	+	0.222302i	$0.0713570\pi$
$38$	−0.483978	+	2.22481i	−0.0785116	+	0.360912i
$39$	−0.456755	+	1.55556i	−0.0731393	+	0.249090i
$40$	−2.18896	−	0.456553i	−0.346105	−	0.0721874i
$41$	0.810149	−	1.77398i	0.126524	−	0.277049i	−0.835760	−	0.549094i	$-0.814973\pi$
$41$	0.810149	−	1.77398i	0.126524	−	0.277049i	0.962284	+	0.272045i	$0.0877001\pi$
$42$	0.330530	−	0.247432i	0.0510019	−	0.0381795i
$43$	−2.53575	+	0.551618i	−0.386698	+	0.0841210i	−0.401711	−	0.915766i	$-0.631584\pi$
$43$	−2.53575	+	0.551618i	−0.386698	+	0.0841210i	0.0150136	+	0.999887i	$0.495221\pi$
$44$	1.85905	+	2.14545i	0.280262	+	0.323439i
$45$	−2.02596	+	0.946307i	−0.302012	+	0.141067i
$46$	0.931086	−	4.70458i	0.137281	−	0.693653i
$47$	−8.55701	+	8.55701i	−1.24817	+	1.24817i	−0.291640	+	0.956528i	$0.594201\pi$
$47$	−8.55701	+	8.55701i	−1.24817	+	1.24817i	−0.956528	+	0.291640i	$0.905799\pi$
$48$	−0.0713392	+	0.997452i	−0.0102969	+	0.143970i
$49$	3.69232	−	5.74536i	0.527474	−	0.820766i
$50$	−4.99265	−	0.271098i	−0.706067	−	0.0383391i
$51$	−0.270927	−	0.123728i	−0.0379374	−	0.0173254i
$52$	1.29787	+	0.971570i	0.179982	+	0.134733i
$53$	−0.215564	+	0.117707i	−0.0296100	+	0.0161683i	−0.493986	−	0.869470i	$-0.664461\pi$
$53$	−0.215564	+	0.117707i	−0.0296100	+	0.0161683i	0.464376	+	0.885638i	$0.346279\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	4.83285	+	4.11565i	0.651662	+	0.554954i
$56$	−0.116323	−	0.396158i	−0.0155443	−	0.0529389i
$57$	2.27104	−	0.162428i	0.300807	−	0.0215141i
$58$	2.53340	−	0.181192i	0.332652	−	0.0237917i
$59$	2.89074	+	9.84494i	0.376342	+	1.28170i	0.902269	+	0.431173i	$0.141900\pi$
$59$	2.89074	+	9.84494i	0.376342	+	1.28170i	−0.525928	+	0.850529i	$0.676282\pi$
$60$	0.178643	+	2.22892i	0.0230627	+	0.287752i
$61$	2.71054	+	4.21768i	0.347049	+	0.540019i	0.970269	−	0.242027i	$-0.0778124\pi$
$61$	2.71054	+	4.21768i	0.347049	+	0.540019i	−0.623220	+	0.782046i	$0.714176\pi$
$62$	−5.27098	+	2.87817i	−0.669415	+	0.365528i
$63$	−0.330530	−	0.247432i	−0.0416429	−	0.0311735i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	3.19654	+	1.71002i	0.396482	+	0.212102i
$66$	1.53479	−	2.38818i	0.188920	−	0.293965i
$67$	−0.678110	+	9.48121i	−0.0828443	+	1.15831i	0.770666	+	0.637239i	$0.219924\pi$
$67$	−0.678110	+	9.48121i	−0.0828443	+	1.15831i	−0.853511	+	0.521076i	$0.825531\pi$
$68$	−0.210606	+	0.210606i	−0.0255398	+	0.0255398i
$69$	−4.77633	+	0.432063i	−0.575002	+	0.0520143i
$70$	−0.390714	−	0.836483i	−0.0466993	−	0.0999789i
$71$	0.0645553	+	0.0745008i	0.00766131	+	0.00884162i	0.759567	−	0.650429i	$-0.225411\pi$
$71$	0.0645553	+	0.0745008i	0.00766131	+	0.00884162i	−0.751906	+	0.659270i	$0.770865\pi$
$72$	0.977147	−	0.212565i	0.115158	−	0.0250511i
$73$	2.73613	−	2.04824i	0.320239	−	0.239728i	−0.427048	−	0.904229i	$-0.640447\pi$
$73$	2.73613	−	2.04824i	0.320239	−	0.239728i	0.747288	+	0.664501i	$0.231356\pi$
$74$	−0.669289	+	1.46554i	−0.0778033	+	0.170365i
$75$	1.14647	+	4.86679i	0.132383	+	0.561968i
$76$	0.641461	−	2.18462i	0.0735806	−	0.250593i
$77$	−0.249150	+	1.14532i	−0.0283932	+	0.130522i
$78$	0.566564	−	1.51902i	0.0641507	−	0.171995i
$79$	8.99504	−	2.64118i	1.01202	−	0.297156i	0.266641	−	0.963796i	$-0.414086\pi$
$79$	8.99504	−	2.64118i	1.01202	−	0.297156i	0.745380	+	0.666640i	$0.232268\pi$
$80$	2.15082	+	0.611549i	0.240469	+	0.0683732i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−0.934638	+	1.71166i	−0.103214	+	0.189022i
$83$	11.4503	+	4.27074i	1.25683	+	0.468775i	0.887623	−	0.460571i	$-0.152355\pi$
$83$	11.4503	+	4.27074i	1.25683	+	0.468775i	0.369211	+	0.929346i	$0.379628\pi$
$84$	−0.347339	+	0.223221i	−0.0378978	+	0.0243555i
$85$	−0.394529	+	0.536561i	−0.0427927	+	0.0581982i
$86$	2.56864	−	0.369314i	0.276983	−	0.0398242i
$87$	−0.887595	−	2.37973i	−0.0951601	−	0.255134i
$88$	−1.70125	−	2.27261i	−0.181354	−	0.242261i
$89$	−2.18067	−	1.40143i	−0.231151	−	0.148552i	0.419939	−	0.907552i	$-0.362051\pi$
$89$	−2.18067	−	1.40143i	−0.231151	−	0.148552i	−0.651090	+	0.759001i	$0.725688\pi$
$90$	2.08830	−	0.799366i	0.220127	−	0.0842606i
$91$			0.669381i			0.0701702i
$92$	−1.26433	+	4.62617i	−0.131816	+	0.482312i
$93$	4.24659	+	4.24659i	0.440351	+	0.440351i
$94$	9.14566	−	7.92476i	0.943303	−	0.817376i
$95$	0.681303	−	5.04539i	0.0699002	−	0.517646i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−8.48000	+	3.16288i	−0.861013	+	0.321141i	−0.740897	−	0.671619i	$-0.765599\pi$
$97$	−8.48000	+	3.16288i	−0.861013	+	0.321141i	−0.120116	+	0.992760i	$0.538327\pi$
$98$	−4.09278	+	5.46732i	−0.413434	+	0.552283i
$99$	−2.72385	−	0.799794i	−0.273757	−	0.0803823i
$100$	4.96058	+	0.626579i	0.496058	+	0.0626579i
$101$	0.00234615	+	0.00513735i	0.000233451	+	0.000511186i	0.909749	−	0.415159i	$-0.136274\pi$
$101$	0.00234615	+	0.00513735i	0.000233451	+	0.000511186i	−0.909515	+	0.415671i	$0.863547\pi$
$102$	0.261410	+	0.142741i	0.0258835	+	0.0141334i
$103$	−0.723934	−	10.1219i	−0.0713313	−	0.997342i	−0.899516	−	0.436887i	$-0.856081\pi$
$103$	−0.723934	−	10.1219i	−0.0713313	−	0.997342i	0.828185	−	0.560455i	$-0.189374\pi$
$104$	−1.22525	−	1.06168i	−0.120145	−	0.104107i
$105$	−0.692523	+	0.610552i	−0.0675833	+	0.0595838i
$106$	0.223412	−	0.102029i	0.0216997	−	0.00990990i
$107$	−5.50331	−	1.19717i	−0.532025	−	0.115735i	−0.0614754	−	0.998109i	$-0.519581\pi$
$107$	−5.50331	−	1.19717i	−0.532025	−	0.115735i	−0.470549	+	0.882374i	$0.655944\pi$
$108$	−0.479249	−	0.877679i	−0.0461158	−	0.0844547i
$109$	−2.57596	−	17.9162i	−0.246732	−	1.71606i	−0.616853	−	0.787078i	$-0.711593\pi$
$109$	−2.57596	−	17.9162i	−0.246732	−	1.71606i	0.370121	−	0.928984i	$-0.379316\pi$
$110$	−4.52693	−	4.44994i	−0.431626	−	0.424285i
$111$	1.59473	+	0.229288i	0.151365	+	0.0217631i
$112$	0.0877646	+	0.403447i	0.00829298	+	0.0381222i
$113$	−6.78091	−	0.484980i	−0.637894	−	0.0456231i	−0.251353	−	0.967895i	$-0.580876\pi$
$113$	−6.78091	−	0.484980i	−0.637894	−	0.0456231i	−0.386541	+	0.922272i	$0.626330\pi$
$114$	−2.27684			−0.213246
$115$	−1.23488	+	10.6525i	−0.115153	+	0.993348i
$116$	−2.53987			−0.235821
$117$	−1.61710	−	0.115658i	−0.149501	−	0.0106926i
$118$	−2.18104	−	10.0261i	−0.200781	−	0.922976i
$119$	−0.121722	−	0.0175010i	−0.0111583	−	0.00160432i
$120$	−0.0191781	−	2.23599i	−0.00175071	−	0.204117i
$121$	−0.418546	−	2.91105i	−0.0380496	−	0.264641i
$122$	−2.40275	−	4.40030i	−0.217535	−	0.398385i
$123$	1.90565	+	0.414548i	0.171826	+	0.0373785i
$124$	5.46288	−	2.49481i	0.490581	−	0.224041i
$125$	11.1766	−	0.287643i	0.999669	−	0.0257275i
$126$	0.312036	+	0.270381i	0.0277984	+	0.0240874i
$127$	0.274295	+	3.83515i	0.0243398	+	0.340314i	0.995001	+	0.0998638i	$0.0318407\pi$
$127$	0.274295	+	3.83515i	0.0243398	+	0.340314i	−0.970661	+	0.240451i	$0.922705\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	−1.07802	−	2.36054i	−0.0949147	−	0.207834i
$130$	−3.06640	−	1.93370i	−0.268941	−	0.169597i
$131$	−13.7618	−	4.04084i	−1.20238	−	0.353050i	−0.381615	−	0.924321i	$-0.624632\pi$
$131$	−13.7618	−	4.04084i	−1.20238	−	0.353050i	−0.820761	+	0.571272i	$0.806450\pi$
$132$	−1.70125	+	2.27261i	−0.148075	+	0.197805i
$133$	0.880799	−	0.328521i	0.0763749	−	0.0284864i
$134$	1.35276	−	9.40868i	0.116861	−	0.812786i
$135$	−1.35533	−	1.77851i	−0.116648	−	0.153069i
$136$	0.225094	−	0.195045i	0.0193017	−	0.0167250i
$137$	−14.5329	−	14.5329i	−1.24163	−	1.24163i	−0.959325	−	0.282304i	$-0.908901\pi$
$137$	−14.5329	−	14.5329i	−1.24163	−	1.24163i	−0.282304	−	0.959325i	$-0.591099\pi$
$138$	4.79498	−	0.0902227i	0.408176	−	0.00768027i
$139$		−	5.15359i		−	0.437122i	−0.975823	−	0.218561i	$-0.929864\pi$
$139$		−	5.15359i		−	0.437122i	0.975823	−	0.218561i	$-0.0701362\pi$
$140$	0.330045	+	0.862225i	0.0278939	+	0.0728714i
$141$	−10.1804	−	6.54253i	−0.857343	−	0.550981i
$142$	−0.0590760	−	0.0789163i	−0.00495755	−	0.00662251i
$143$	1.60838	+	4.31224i	0.134500	+	0.360608i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	−5.61438	+	0.856437i	−0.466249	+	0.0711232i
$146$	−2.87527	+	1.84783i	−0.237959	+	0.152927i
$147$	6.39892	+	2.38668i	0.527774	+	0.196850i
$148$	0.772134	−	1.41406i	0.0634690	−	0.116235i
$149$	13.3672	−	15.4266i	1.09508	−	1.26379i	0.132977	−	0.991119i	$-0.457546\pi$
$149$	13.3672	−	15.4266i	1.09508	−	1.26379i	0.962106	−	0.272675i	$-0.0879083\pi$
$150$	−0.796360	−	4.93617i	−0.0650225	−	0.403037i
$151$	−15.9223	+	4.67522i	−1.29574	+	0.380464i	−0.855681	−	0.517504i	$-0.826861\pi$
$151$	−15.9223	+	4.67522i	−1.29574	+	0.380464i	−0.440061	+	0.897968i	$0.645043\pi$
$152$	−0.795675	+	2.13329i	−0.0645378	+	0.173033i
$153$	0.0633110	−	0.291036i	0.00511839	−	0.0235289i
$154$	0.330221	−	1.12463i	0.0266100	−	0.0906253i
$155$	11.2344	−	7.35684i	0.902371	−	0.590915i
$156$	−0.673486	+	1.47473i	−0.0539220	+	0.118073i
$157$	8.74818	−	6.54881i	0.698181	−	0.522652i	−0.190208	−	0.981744i	$-0.560916\pi$
$157$	8.74818	−	6.54881i	0.698181	−	0.522652i	0.888389	+	0.459092i	$0.151825\pi$
$158$	−9.16054	+	1.99275i	−0.728773	+	0.158535i
$159$	−0.160838	−	0.185617i	−0.0127553	−	0.0147204i
$160$	−2.10171	−	0.763428i	−0.166155	−	0.0603543i
$161$	−1.84192	+	0.726760i	−0.145164	+	0.0572767i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	−0.433914	+	6.06691i	−0.0339868	+	0.475197i	0.951747	+	0.306884i	$0.0992865\pi$
$163$	−0.433914	+	6.06691i	−0.0339868	+	0.475197i	−0.985734	+	0.168313i	$0.946168\pi$
$164$	1.05437	−	1.64063i	0.0823321	−	0.128111i
$165$	−2.99430	+	5.59725i	−0.233106	+	0.435746i
$166$	−11.1165	−	5.07671i	−0.862804	−	0.394029i
$167$	−3.11016	−	2.32824i	−0.240672	−	0.180165i	0.472133	−	0.881528i	$-0.343484\pi$
$167$	−3.11016	−	2.32824i	−0.240672	−	0.180165i	−0.712804	+	0.701363i	$0.752575\pi$
$168$	0.362379	−	0.197874i	0.0279581	−	0.0152663i
$169$	−5.60731	−	8.72514i	−0.431331	−	0.671165i
$170$	0.431802	−	0.507048i	0.0331177	−	0.0388888i
$171$	0.641461	+	2.18462i	0.0490538	+	0.167062i
$172$	−2.58844	+	0.185129i	−0.197367	+	0.0141159i
$173$	3.02939	−	0.216666i	0.230320	−	0.0164728i	0.0442981	−	0.999018i	$-0.485895\pi$
$173$	3.02939	−	0.216666i	0.230320	−	0.0164728i	0.186022	+	0.982546i	$0.440440\pi$
$174$	0.715565	+	2.43699i	0.0542468	+	0.184748i
$175$	1.02030	+	1.79466i	0.0771276	+	0.135663i
$176$	1.53479	+	2.38818i	0.115689	+	0.180016i
$177$	−9.00548	+	4.91737i	−0.676894	+	0.369612i
$178$	2.07514	+	1.55343i	0.155538	+	0.116434i
$179$	0.378685	+	0.172940i	0.0283042	+	0.0129261i	0.429517	−	0.903059i	$-0.358684\pi$
$179$	0.378685	+	0.172940i	0.0283042	+	0.0129261i	−0.401213	+	0.915985i	$0.631411\pi$
$180$	−2.14001	+	0.648351i	−0.159507	+	0.0483252i
$181$	−6.52017	+	10.1456i	−0.484641	+	0.754115i	−0.994341	−	0.106237i	$-0.966120\pi$
$181$	−6.52017	+	10.1456i	−0.484641	+	0.754115i	0.509700	+	0.860352i	$0.329756\pi$
$182$	0.0477531	−	0.667675i	0.00353969	−	0.0494914i
$183$	−3.54513	+	3.54513i	−0.262063	+	0.262063i
$184$	1.59114	−	4.52419i	0.117300	−	0.333528i
$185$	1.22998	−	3.38613i	0.0904303	−	0.248953i
$186$	−3.93282	−	4.53872i	−0.288369	−	0.332795i
$187$	−0.826204	+	0.179730i	−0.0604180	+	0.0131431i
$188$	−9.68770	+	7.25212i	−0.706548	+	0.528915i
$189$	0.171518	−	0.375572i	0.0124761	−	0.0273188i
$190$	−1.03950	+	4.98393i	−0.0754133	+	0.361572i
$191$	1.64228	−	5.59309i	0.118831	−	0.404702i	−0.878497	−	0.477747i	$-0.841454\pi$
$191$	1.64228	−	5.59309i	0.118831	−	0.404702i	0.997329	+	0.0730451i	$0.0232717\pi$
$192$	−0.212565	+	0.977147i	−0.0153406	+	0.0705195i
$193$	5.99381	−	16.0700i	0.431444	−	1.15675i	−0.521407	−	0.853308i	$-0.674593\pi$
$193$	5.99381	−	16.0700i	0.431444	−	1.15675i	0.952851	−	0.303438i	$-0.0981345\pi$
$194$	8.68403	−	2.54986i	0.623477	−	0.183069i
$195$	−0.991465	+	3.48698i	−0.0710003	+	0.249708i
$196$	4.47239	−	5.16141i	0.319456	−	0.368672i
$197$	−1.67733	+	3.07181i	−0.119505	+	0.218857i	−0.930583	−	0.366081i	$-0.880699\pi$
$197$	−1.67733	+	3.07181i	−0.119505	+	0.218857i	0.811078	+	0.584938i	$0.198881\pi$
$198$	2.65985	+	0.992073i	0.189027	+	0.0705036i
$199$	−6.46522	+	4.15494i	−0.458307	+	0.294536i	−0.749350	−	0.662174i	$-0.769634\pi$
$199$	−6.46522	+	4.15494i	−0.458307	+	0.294536i	0.291043	+	0.956710i	$0.405998\pi$
$200$	−4.90325	−	0.978866i	−0.346712	−	0.0692163i
$201$	−9.40868	+	1.35276i	−0.663637	+	0.0954166i
$202$	−0.00197368	−	0.00529164i	−0.000138868	−	0.000372318i
$203$	−0.628445	−	0.839504i	−0.0441082	−	0.0589216i
$204$	−0.250561	−	0.161026i	−0.0175428	−	0.0112741i
$205$	1.77746	−	3.98213i	0.124143	−	0.278124i
$206$			10.1478i			0.707029i
$207$	−1.43747	−	4.57533i	−0.0999111	−	0.318008i
$208$	1.14639	+	1.14639i	0.0794876	+	0.0794876i
$209$	4.88486	−	4.23276i	0.337893	−	0.292786i
$210$	0.734315	−	0.559592i	0.0506725	−	0.0386155i
$211$	2.39699	−	16.6714i	0.165016	−	1.14771i	−0.723990	−	0.689811i	$-0.757694\pi$
$211$	2.39699	−	16.6714i	0.165016	−	1.14771i	0.889005	−	0.457897i	$-0.151397\pi$
$212$	−0.230121	+	0.0858307i	−0.0158048	+	0.00589488i
$213$	−0.0590760	+	0.0789163i	−0.00404782	+	0.00540726i
$214$	5.40388	+	1.58672i	0.369402	+	0.108466i
$215$	−5.65932	+	1.28204i	−0.385962	+	0.0874345i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	2.17630	+	1.18835i	0.147737	+	0.0806704i
$218$	1.29127	+	18.0543i	0.0874559	+	1.22279i
$219$	2.58304	+	2.23821i	0.174545	+	0.151244i
$220$	4.19794	+	4.76155i	0.283025	+	0.321023i
$221$	−0.439237	+	0.200593i	−0.0295462	+	0.0134933i
$222$	−1.57431	−	0.342471i	−0.105661	−	0.0229852i
$223$	−2.23405	−	4.09136i	−0.149603	−	0.273978i	0.792121	−	0.610364i	$-0.208977\pi$
$223$	−2.23405	−	4.09136i	−0.149603	−	0.273978i	−0.941724	+	0.336387i	$0.890795\pi$
$224$	−0.0587594	−	0.408681i	−0.00392603	−	0.0273061i
$225$	−4.51186	+	2.15478i	−0.300791	+	0.143652i
$226$	6.72903	+	0.967489i	0.447609	+	0.0643564i
$227$	−4.56410	−	20.9808i	−0.302930	−	1.39255i	−0.837045	−	0.547135i	$-0.815719\pi$
$227$	−4.56410	−	20.9808i	−0.302930	−	1.39255i	0.534115	−	0.845412i	$-0.320645\pi$
$228$	2.27104	+	0.162428i	0.150403	+	0.0107571i
$229$	−9.64469			−0.637339			−0.318670	−	0.947866i	$-0.603236\pi$
$229$	−9.64469			−0.637339			−0.318670	+	0.947866i	$0.603236\pi$
$230$	1.99167	−	10.5372i	0.131327	−	0.694804i
$231$	−1.17211			−0.0771191
$232$	2.53340	+	0.181192i	0.166326	+	0.0118959i
$233$	−0.112867	−	0.518841i	−0.00739416	−	0.0339904i	0.973302	−	0.229528i	$-0.0737184\pi$
$233$	−0.112867	−	0.518841i	−0.00739416	−	0.0339904i	−0.980696	+	0.195538i	$0.937355\pi$
$234$	1.60473	+	0.230726i	0.104905	+	0.0150830i
$235$	−18.9692	+	19.2975i	−1.23742	+	1.25883i
$236$	1.46023	+	10.1561i	0.0950529	+	0.661108i
$237$	4.49285	+	8.22805i	0.291842	+	0.534469i
$238$	0.120164	+	0.0261400i	0.00778906	+	0.00169441i
$239$	17.1202	−	7.81855i	1.10742	−	0.505740i	0.224123	−	0.974561i	$-0.428048\pi$
$239$	17.1202	−	7.81855i	1.10742	−	0.505740i	0.883293	+	0.468821i	$0.155321\pi$
$240$	−0.140384	+	2.23166i	−0.00906176	+	0.144053i
$241$	−7.43182	−	6.43971i	−0.478726	−	0.414818i	0.381785	−	0.924251i	$-0.375310\pi$
$241$	−7.43182	−	6.43971i	−0.478726	−	0.414818i	−0.860510	+	0.509433i	$0.829855\pi$
$242$	0.209808	+	2.93349i	0.0134869	+	0.188572i
$243$	0.877679	+	0.479249i	0.0563031	+	0.0307438i
$244$	2.08271	+	4.56050i	0.133332	+	0.291956i
$245$	8.14579	−	12.9174i	0.520416	−	0.825260i
$246$	−1.87122	−	0.549439i	−0.119304	−	0.0350310i
$247$	2.21211	−	2.95504i	0.140753	−	0.188025i
$248$	−5.62693	+	2.09874i	−0.357311	+	0.133270i
$249$	−1.73920	+	12.0964i	−0.110218	+	0.766580i
$250$	−11.1687	−	0.510423i	−0.706370	−	0.0322820i
$251$	−2.64381	+	2.29087i	−0.166876	+	0.144599i	−0.734295	−	0.678830i	$-0.762487\pi$
$251$	−2.64381	+	2.29087i	−0.166876	+	0.144599i	0.567420	+	0.823429i	$0.307942\pi$
$252$	−0.291952	−	0.291952i	−0.0183913	−	0.0183913i
$253$	−10.1197	+	9.10766i	−0.636219	+	0.572594i
$254$		−	3.84495i		−	0.241253i
$255$	−0.608162	−	0.271459i	−0.0380846	−	0.0169994i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	1.64385	+	2.19593i	0.102541	+	0.136978i	0.848876	−	0.528591i	$-0.177280\pi$
$257$	1.64385	+	2.19593i	0.102541	+	0.136978i	−0.746336	+	0.665570i	$0.768189\pi$
$258$	0.906878	+	2.43143i	0.0564597	+	0.151374i
$259$	0.658439	−	0.0946692i	0.0409134	−	0.00588246i
$260$	2.92064	+	2.14753i	0.181131	+	0.133184i
$261$	2.13668	−	1.37316i	0.132257	−	0.0849964i
$262$	13.4385	+	5.01230i	0.830233	+	0.309661i
$263$	9.12595	−	16.7129i	0.562730	−	1.03056i	−0.429131	−	0.903242i	$-0.641180\pi$
$263$	9.12595	−	16.7129i	0.562730	−	1.03056i	0.991862	−	0.127321i	$-0.0406379\pi$
$264$	1.85905	−	2.14545i	0.114416	−	0.132043i
$265$	−0.479740	+	0.267325i	−0.0294702	+	0.0164216i
$266$	−0.901991	+	0.264848i	−0.0553046	+	0.0162389i
$267$	0.905870	−	2.42873i	0.0554384	−	0.148636i
$268$	−2.02052	+	9.28820i	−0.123423	+	0.567367i
$269$	4.32232	−	14.7205i	0.263537	−	0.897523i	−0.716312	−	0.697780i	$-0.754171\pi$
$269$	4.32232	−	14.7205i	0.263537	−	0.897523i	0.979848	−	0.199743i	$-0.0640107\pi$
$270$	1.22500	+	1.87066i	0.0745511	+	0.113845i
$271$	−3.33464	+	7.30184i	−0.202565	+	0.443555i	−0.983464	−	0.181101i	$-0.942034\pi$
$271$	−3.33464	+	7.30184i	−0.202565	+	0.443555i	0.780899	+	0.624657i	$0.214761\pi$
$272$	−0.238435	+	0.178490i	−0.0144573	+	0.0108226i
$273$	−0.654083	+	0.142287i	−0.0395869	+	0.00861161i
$274$	13.4591	+	15.5326i	0.813094	+	0.938361i
$275$	10.8851	+	9.10986i	0.656398	+	0.549345i
$276$	−4.78920	−	0.252077i	−0.288276	−	0.0151733i
$277$	−9.50184	+	9.50184i	−0.570910	+	0.570910i	−0.932383	−	0.361473i	$-0.882274\pi$
$277$	−9.50184	+	9.50184i	−0.570910	+	0.570910i	0.361473	+	0.932383i	$0.382274\pi$
$278$	−0.367653	+	5.14046i	−0.0220504	+	0.308304i
$279$	−3.24687	+	5.05222i	−0.194385	+	0.302469i
$280$	−0.267693	−	0.883574i	−0.0159977	−	0.0528036i
$281$	2.69353	+	1.23010i	0.160683	+	0.0733813i	0.494133	−	0.869386i	$-0.335486\pi$
$281$	2.69353	+	1.23010i	0.160683	+	0.0733813i	−0.333450	+	0.942768i	$0.608213\pi$
$282$	9.68770	+	7.25212i	0.576894	+	0.431858i
$283$	22.2311	−	12.1391i	1.32150	−	0.721595i	0.345307	−	0.938490i	$-0.387775\pi$
$283$	22.2311	−	12.1391i	1.32150	−	0.721595i	0.976195	+	0.216895i	$0.0695930\pi$
$284$	0.0532957	+	0.0829297i	0.00316252	+	0.00492097i
$285$	5.07490	−	0.406741i	0.300611	−	0.0240933i
$286$	−1.29665	−	4.41600i	−0.0766728	−	0.261123i
$287$	0.803159	−	0.0574431i	0.0474090	−	0.00339076i
$288$	0.997452	−	0.0713392i	0.0587754	−	0.00420370i
$289$	4.76446	+	16.2263i	0.280262	+	0.954486i
$290$	5.66117	−	0.453729i	0.332436	−	0.0266439i
$291$	−4.89315	−	7.61389i	−0.286841	−	0.446334i
$292$	2.99977	−	1.63800i	0.175548	−	0.0958566i
$293$	3.16739	+	2.37108i	0.185041	+	0.138520i	0.687782	−	0.725917i	$-0.258584\pi$
$293$	3.16739	+	2.37108i	0.185041	+	0.138520i	−0.502742	+	0.864437i	$0.667675\pi$
$294$	−6.21236	−	2.83709i	−0.362312	−	0.165462i
$295$	6.65245	+	21.9577i	0.387321	+	1.27843i
$296$	−0.871044	+	1.35537i	−0.0506284	+	0.0787794i
$297$	0.202521	−	2.83161i	0.0117514	−	0.164307i
$298$	−14.4337	+	14.4337i	−0.836119	+	0.836119i
$299$	−4.54157	+	6.31090i	−0.262646	+	0.364969i
$300$	0.442189	+	4.98041i	0.0255298	+	0.287544i
$301$	−0.701653	−	0.809750i	−0.0404426	−	0.0466732i
$302$	16.2153	−	3.52742i	0.933086	−	0.202980i
$303$	−0.00452124	+	0.00338456i	−0.000259738	+	0.000194438i
$304$	0.945835	−	2.07109i	0.0542474	−	0.118785i
$305$	6.14161	+	9.37869i	0.351668	+	0.537022i
$306$	−0.0839119	+	0.285778i	−0.00479692	+	0.0163368i
$307$	2.66134	−	12.2340i	0.151891	−	0.698231i	−0.836707	−	0.547651i	$-0.815522\pi$
$307$	2.66134	−	12.2340i	0.151891	−	0.698231i	0.988598	−	0.150580i	$-0.0481141\pi$
$308$	−0.409610	+	1.09821i	−0.0233397	+	0.0625762i
$309$	9.73672	−	2.85896i	0.553903	−	0.162640i
$310$	−11.7306	+	6.53664i	−0.666255	+	0.371256i
$311$	7.82401	−	9.02938i	0.443659	−	0.512009i	−0.489240	−	0.872149i	$-0.662726\pi$
$311$	7.82401	−	9.02938i	0.443659	−	0.512009i	0.932898	+	0.360140i	$0.117271\pi$
$312$	0.776975	−	1.42292i	0.0439876	−	0.0805572i
$313$	10.4092	+	3.88241i	0.588360	+	0.219447i	0.625972	−	0.779845i	$-0.284702\pi$
$313$	10.4092	+	3.88241i	0.588360	+	0.219447i	−0.0376121	+	0.999292i	$0.511975\pi$
$314$	−9.19308	+	5.90804i	−0.518796	+	0.333410i
$315$	−0.743805	−	0.546915i	−0.0419087	−	0.0308151i
$316$	9.27936	−	1.33417i	0.522005	−	0.0750530i
$317$	−10.8693	−	29.1418i	−0.610482	−	1.63677i	−0.761447	−	0.648228i	$-0.775511\pi$
$317$	−10.8693	−	29.1418i	−0.610482	−	1.63677i	0.150964	−	0.988539i	$-0.451762\pi$
$318$	0.147187	+	0.196618i	0.00825381	+	0.0110258i
$319$	−6.06568	−	3.89818i	−0.339613	−	0.218256i
$320$	2.04189	+	0.911417i	0.114145	+	0.0509498i
$321$		−	5.63202i		−	0.314348i
$322$	1.88908	−	0.593507i	0.105274	−	0.0330749i
$323$	0.479518	+	0.479518i	0.0266811	+	0.0266811i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	7.18021	+	3.76227i	0.398286	+	0.208693i
$326$	0.865617	−	6.02050i	0.0479421	−	0.333445i
$327$	16.9592	−	6.32546i	0.937846	−	0.349799i
$328$	−1.16872	+	1.56123i	−0.0645318	+	0.0862044i
$329$	−4.79409	−	1.40767i	−0.264307	−	0.0776074i
$330$	3.38597	−	5.36938i	0.186392	−	0.295575i
$331$	11.1286	+	24.3683i	0.611685	+	1.33940i	0.921415	+	0.388579i	$0.127034\pi$
$331$	11.1286	+	24.3683i	0.611685	+	1.33940i	−0.309730	+	0.950824i	$0.600239\pi$
$332$	10.7260	+	5.85682i	0.588664	+	0.321435i
$333$	0.114937	+	1.60703i	0.00629851	+	0.0880646i
$334$	2.93615	+	2.54418i	0.160659	+	0.139212i
$335$	−1.33441	+	21.2129i	−0.0729067	+	1.15898i
$336$	−0.375572	+	0.171518i	−0.0204891	+	0.00935706i
$337$	−12.9363	−	2.81413i	−0.704687	−	0.153295i	−0.154078	−	0.988059i	$-0.549241\pi$
$337$	−12.9363	−	2.81413i	−0.704687	−	0.153295i	−0.550609	+	0.834763i	$0.685604\pi$
$338$	4.97058	+	9.10293i	0.270364	+	0.495134i
$339$	−0.967489	−	6.72903i	−0.0525468	−	0.365471i
$340$	−0.466874	+	0.474952i	−0.0253198	+	0.0257579i
$341$	16.8754	+	2.42631i	0.913853	+	0.131392i
$342$	−0.483978	−	2.22481i	−0.0261705	−	0.120304i
$343$	5.69543	+	0.407345i	0.307524	+	0.0219946i
$344$	2.59505			0.139916
$345$	−10.6715	+	1.05769i	−0.574535	+	0.0569440i
$346$	−3.03713			−0.163277
$347$	−29.2590	−	2.09264i	−1.57070	−	0.112339i	−0.741371	−	0.671095i	$-0.765824\pi$
$347$	−29.2590	−	2.09264i	−1.57070	−	0.112339i	−0.829332	+	0.558756i	$0.811279\pi$
$348$	−0.539889	−	2.48183i	−0.0289411	−	0.133040i
$349$	−11.1507	−	1.60323i	−0.596885	−	0.0858191i	−0.162750	−	0.986667i	$-0.552037\pi$
$349$	−11.1507	−	1.60323i	−0.596885	−	0.0858191i	−0.434134	+	0.900848i	$0.642946\pi$
$350$	−0.889673	−	1.86287i	−0.0475550	−	0.0995747i
$351$	−0.230726	−	1.60473i	−0.0123152	−	0.0856543i
$352$	−1.36051	−	2.49159i	−0.0725155	−	0.132802i
$353$	−2.97630	−	0.647454i	−0.158412	−	0.0344605i	0.132660	−	0.991162i	$-0.457648\pi$
$353$	−2.97630	−	0.647454i	−0.158412	−	0.0344605i	−0.291072	+	0.956701i	$0.594012\pi$
$354$	9.33334	−	4.26239i	0.496061	−	0.226544i
$355$	0.145774	+	0.165345i	0.00773686	+	0.00877559i
$356$	−1.95903	−	1.69751i	−0.103828	−	0.0899679i
$357$	−0.00877287	−	0.122661i	−0.000464310	−	0.00649190i
$358$	−0.365383	−	0.199514i	−0.0193111	−	0.0105446i
$359$	12.5296	+	27.4360i	0.661287	+	1.44802i	0.881318	+	0.472524i	$0.156657\pi$
$359$	12.5296	+	27.4360i	0.661287	+	1.44802i	−0.220031	+	0.975493i	$0.570616\pi$
$360$	2.18081	−	0.494033i	0.114939	−	0.0260378i
$361$	13.2563	+	3.89241i	0.697702	+	0.204864i
$362$	7.22734	−	9.65459i	0.379860	−	0.507434i
$363$	2.75556	−	1.02777i	0.144629	−	0.0539439i
$364$	−0.0952628	+	0.662567i	−0.00499313	+	0.0347280i
$365$	6.07866	−	4.63231i	0.318172	−	0.242466i
$366$	3.78900	−	3.28319i	0.198054	−	0.171615i
$367$	−4.54422	−	4.54422i	−0.237207	−	0.237207i	0.578486	−	0.815692i	$-0.303644\pi$
$367$	−4.54422	−	4.54422i	−0.237207	−	0.237207i	−0.815692	+	0.578486i	$0.803644\pi$
$368$	−1.90984	+	4.39915i	−0.0995572	+	0.229322i
$369$			1.95021i			0.101524i
$370$	−1.46841	+	3.28976i	−0.0763392	+	0.171026i
$371$	−0.0853089	−	0.0548247i	−0.00442902	−	0.00284636i
$372$	3.59902	+	4.80772i	0.186600	+	0.249269i
$373$	0.915207	+	2.45376i	0.0473876	+	0.127051i	0.958488	−	0.285134i	$-0.0920383\pi$
$373$	0.915207	+	2.45376i	0.0473876	+	0.127051i	−0.911100	+	0.412186i	$0.864766\pi$
$374$	0.836921	−	0.120331i	0.0432762	−	0.00622217i
$375$	2.65683	+	10.8601i	0.137198	+	0.560812i
$376$	10.1804	−	6.54253i	0.525013	−	0.337405i
$377$	−3.85811	−	1.43900i	−0.198703	−	0.0741123i
$378$	−0.197874	+	0.362379i	−0.0101775	+	0.0186388i
$379$	−15.8684	+	18.3132i	−0.815107	+	0.940683i	−0.999107	−	0.0422428i	$-0.986550\pi$
$379$	−15.8684	+	18.3132i	−0.815107	+	0.940683i	0.184001	+	0.982926i	$0.441095\pi$
$380$	1.39240	−	4.89707i	0.0714287	−	0.251214i
$381$	−3.68920	+	1.08325i	−0.189003	+	0.0554964i
$382$	−2.03710	+	5.46168i	−0.104227	+	0.279444i
$383$	−8.17072	+	37.5602i	−0.417505	+	1.91924i	−0.0245024	+	0.999700i	$0.507800\pi$
$383$	−8.17072	+	37.5602i	−0.417505	+	1.91924i	−0.393002	+	0.919538i	$0.628563\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	−0.535130	+	2.56570i	−0.0272728	+	0.130760i
$386$	−7.12496	+	15.6015i	−0.362651	+	0.794095i
$387$	2.07745	−	1.55516i	0.105603	−	0.0790531i
$388$	−8.84381	+	1.92385i	−0.448976	+	0.0976688i
$389$	9.17514	+	10.5887i	0.465198	+	0.536867i	0.939070	−	0.343727i	$-0.111689\pi$
$389$	9.17514	+	10.5887i	0.465198	+	0.536867i	−0.473872	+	0.880594i	$0.657144\pi$
$390$	1.23770	−	3.40736i	0.0626732	−	0.172539i
$391$	−1.02886	−	0.990853i	−0.0520315	−	0.0501096i
$392$	−4.82921	+	4.82921i	−0.243912	+	0.243912i
$393$	1.02320	−	14.3063i	0.0516138	−	0.721656i
$394$	1.89220	−	2.94432i	0.0953277	−	0.148333i
$395$	20.0621	−	6.07815i	1.00943	−	0.305825i
$396$	−2.58230	−	1.17930i	−0.129765	−	0.0592619i
$397$	−0.223545	−	0.167344i	−0.0112194	−	0.00839873i	0.593653	−	0.804721i	$-0.297685\pi$
$397$	−0.223545	−	0.167344i	−0.0112194	−	0.00839873i	−0.604873	+	0.796322i	$0.706776\pi$
$398$	6.74516	−	3.68313i	0.338104	−	0.184619i
$399$	0.508240	+	0.790838i	0.0254438	+	0.0395914i
$400$	4.82092	+	1.32617i	0.241046	+	0.0663083i
$401$	3.01368	+	10.2636i	0.150496	+	0.512541i	0.999884	−	0.0152269i	$-0.00484707\pi$
$401$	3.01368	+	10.2636i	0.150496	+	0.512541i	−0.849388	+	0.527768i	$0.823029\pi$
$402$	9.48121	−	0.678110i	0.472880	−	0.0338210i
$403$	9.71167	−	0.694592i	0.483773	−	0.0346001i
$404$	0.00159115	+	0.00541896i	7.91626e−5	+	0.000269603i
$405$	1.44977	−	1.70240i	0.0720394	−	0.0845931i
$406$	0.566954	+	0.882198i	0.0281375	+	0.0437827i
$407$	4.01428	−	2.19197i	0.198981	−	0.108652i
$408$	0.238435	+	0.178490i	0.0118043	+	0.00883659i
$409$	−28.8602	−	13.1800i	−1.42705	−	0.651710i	−0.455865	−	0.890049i	$-0.650670\pi$
$409$	−28.8602	−	13.1800i	−1.42705	−	0.651710i	−0.971182	+	0.238339i	$0.923397\pi$
$410$	−2.05701	+	3.84518i	−0.101589	+	0.189900i
$411$	11.1116	−	17.2900i	0.548094	−	0.852851i
$412$	0.723934	−	10.1219i	0.0356657	−	0.498671i
$413$	−2.99560	+	2.99560i	−0.147404	+	0.147404i
$414$	1.10741	+	4.66622i	0.0544261	+	0.229332i
$415$	25.6846	+	9.32972i	1.26081	+	0.457978i
$416$	−1.06168	−	1.22525i	−0.0520533	−	0.0600727i
$417$	5.03581	−	1.09547i	0.246605	−	0.0536456i
$418$	−5.17438	+	3.87349i	−0.253087	+	0.189459i
$419$	−11.5244	+	25.2349i	−0.563003	+	1.23280i	0.387437	+	0.921896i	$0.373360\pi$
$419$	−11.5244	+	25.2349i	−0.563003	+	1.23280i	−0.950440	+	0.310908i	$0.899367\pi$
$420$	−0.772365	+	0.505781i	−0.0376875	+	0.0246796i
$421$	1.33407	−	4.54342i	0.0650185	−	0.221433i	−0.920574	−	0.390567i	$-0.872279\pi$
$421$	1.33407	−	4.54342i	0.0650185	−	0.221433i	0.985593	+	0.169134i	$0.0540972\pi$
$422$	−3.58021	+	16.4579i	−0.174282	+	0.801160i
$423$	4.22902	−	11.3384i	0.205622	−	0.551294i
$424$	0.235658	−	0.0691954i	0.0114446	−	0.00336043i
$425$	−0.871871	+	1.20731i	−0.0422920	+	0.0585631i
$426$	0.0645553	−	0.0745008i	0.00312772	−	0.00360958i
$427$	−0.992054	+	1.81681i	−0.0480088	+	0.0879216i
$428$	−5.27692	−	1.96819i	−0.255069	−	0.0951360i
$429$	−3.87181	+	2.48826i	−0.186933	+	0.120134i
$430$	5.73636	−	0.875043i	0.276632	−	0.0421983i
$431$	−6.13342	+	0.881853i	−0.295437	+	0.0424774i	−0.288439	−	0.957498i	$-0.593136\pi$
$431$	−6.13342	+	0.881853i	−0.295437	+	0.0424774i	−0.00699715	+	0.999976i	$0.502227\pi$
$432$	−0.349464	−	0.936950i	−0.0168136	−	0.0450790i
$433$	2.65125	+	3.54165i	0.127411	+	0.170201i	0.859711	−	0.510781i	$-0.170644\pi$
$433$	2.65125	+	3.54165i	0.127411	+	0.170201i	−0.732300	+	0.680983i	$0.761553\pi$
$434$	−2.08598	−	1.34058i	−0.100130	−	0.0643497i
$435$	−2.03029	−	5.30403i	−0.0973448	−	0.254309i
$436$		−	18.1004i		−	0.866854i
$437$	10.5331	+	2.87869i	0.503865	+	0.137707i
$438$	−2.41678	−	2.41678i	−0.115478	−	0.115478i
$439$	−1.22419	+	1.06076i	−0.0584272	+	0.0506274i	−0.683585	−	0.729871i	$-0.739580\pi$
$439$	−1.22419	+	1.06076i	−0.0584272	+	0.0506274i	0.625158	+	0.780498i	$0.285035\pi$
$440$	−3.84756	−	5.04889i	−0.183425	−	0.240697i
$441$	−0.971943	+	6.76001i	−0.0462830	+	0.321905i
$442$	0.452428	−	0.168747i	0.0215198	−	0.00802646i
$443$	17.6157	−	23.5318i	0.836948	−	1.11803i	−0.154559	−	0.987983i	$-0.549396\pi$
$443$	17.6157	−	23.5318i	0.836948	−	1.11803i	0.991508	−	0.130048i	$-0.0415133\pi$
$444$	1.54587	+	0.453909i	0.0733638	+	0.0215416i
$445$	−4.90283	−	3.09176i	−0.232416	−	0.146564i
$446$	1.93648	+	4.24031i	0.0916952	+	0.200784i
$447$	17.9154	+	9.78256i	0.847371	+	0.462699i
$448$	0.0294547	+	0.411831i	0.00139161	+	0.0194572i
$449$	−15.4064	−	13.3497i	−0.727071	−	0.630011i	0.210585	−	0.977576i	$-0.432463\pi$
$449$	−15.4064	−	13.3497i	−0.727071	−	0.630011i	−0.937656	+	0.347565i	$0.887009\pi$
$450$	4.65409	−	1.82742i	0.219396	−	0.0861454i
$451$	5.03604	−	2.29988i	0.237138	−	0.108297i
$452$	−6.64287	−	1.44507i	−0.312454	−	0.0679703i
$453$	−7.95292	−	14.5647i	−0.373661	−	0.684308i
$454$	3.05572	+	21.2530i	0.143412	+	0.997452i
$455$	0.0128374	+	1.49673i	0.000601827	+	0.0701676i
$456$	−2.25367	−	0.324029i	−0.105538	−	0.0151740i
$457$	6.19646	+	28.4847i	0.289858	+	1.33246i	0.859741	+	0.510730i	$0.170625\pi$
$457$	6.19646	+	28.4847i	0.289858	+	1.33246i	−0.569883	+	0.821726i	$0.693011\pi$
$458$	9.62012	+	0.688045i	0.449519	+	0.0321502i
$459$	0.297842			0.0139021
$460$	−2.73831	+	10.3683i	−0.127675	+	0.483424i
$461$	−10.9110			−0.508177			−0.254089	−	0.967181i	$-0.581775\pi$
$461$	−10.9110			−0.508177			−0.254089	+	0.967181i	$0.581775\pi$
$462$	1.16912	+	0.0836173i	0.0543925	+	0.00389023i
$463$	−2.97020	−	13.6538i	−0.138037	−	0.634545i	−0.993223	−	0.116224i	$-0.962921\pi$
$463$	−2.97020	−	13.6538i	−0.138037	−	0.634545i	0.855186	−	0.518321i	$-0.173443\pi$
$464$	−2.51402	−	0.361462i	−0.116710	−	0.0167804i
$465$	9.57676	+	9.41388i	0.444112	+	0.436558i
$466$	0.0755657	+	0.525571i	0.00350051	+	0.0243466i
$467$	−8.44187	−	15.4601i	−0.390643	−	0.715410i	0.606157	−	0.795345i	$-0.292710\pi$
$467$	−8.44187	−	15.4601i	−0.390643	−	0.715410i	−0.996800	+	0.0799355i	$0.974529\pi$
$468$	−1.58419	−	0.344618i	−0.0732290	−	0.0159300i
$469$	−3.56997	+	1.63035i	−0.164846	+	0.0752826i
$470$	20.2976	−	17.8950i	0.936258	−	0.825437i
$471$	8.25871	+	7.15621i	0.380541	+	0.329741i
$472$	−0.731980	−	10.2344i	−0.0336921	−	0.471078i
$473$	−6.46581	−	3.53060i	−0.297298	−	0.162337i
$474$	−3.89442	−	8.52760i	−0.178877	−	0.391686i
$475$	1.42662	−	11.2945i	0.0654579	−	0.518226i
$476$	−0.117993	−	0.0346458i	−0.00540819	−	0.00158799i
$477$	0.147187	−	0.196618i	0.00673921	−	0.00900253i
$478$	−17.6344	+	6.57729i	−0.806578	+	0.300838i
$479$	−1.66373	+	11.5715i	−0.0760178	+	0.528716i	0.915858	+	0.401503i	$0.131512\pi$
$479$	−1.66373	+	11.5715i	−0.0760178	+	0.528716i	−0.991875	+	0.127212i	$0.959397\pi$
$480$	0.299231	−	2.21596i	0.0136580	−	0.101144i
$481$	1.97404	−	1.71051i	0.0900084	−	0.0779927i
$482$	6.95348	+	6.95348i	0.316722	+	0.316722i
$483$	−1.10168	−	1.64535i	−0.0501282	−	0.0748659i
$484$		−	2.94099i		−	0.133681i
$485$	−18.9005	+	7.23477i	−0.858227	+	0.328514i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	16.3820	+	21.8838i	0.742339	+	0.991649i	0.999679	+	0.0253283i	$0.00806311\pi$
$487$	16.3820	+	21.8838i	0.742339	+	0.991649i	−0.257340	+	0.966321i	$0.582846\pi$
$488$	−1.75206	−	4.69746i	−0.0793121	−	0.212644i
$489$	−6.02050	+	0.865617i	−0.272257	+	0.0391446i
$490$	−9.04655	+	12.3033i	−0.408682	+	0.555808i
$491$	−28.8062	+	18.5126i	−1.30001	+	0.835464i	−0.993213	−	0.116312i	$-0.962893\pi$
$491$	−28.8062	+	18.5126i	−1.30001	+	0.835464i	−0.306794	+	0.951776i	$0.599256\pi$
$492$	1.82725	+	0.681530i	0.0823789	+	0.0307258i
$493$	0.362543	−	0.663948i	0.0163281	−	0.0299027i
$494$	−2.41729	+	2.78970i	−0.108759	+	0.125514i
$495$	−6.10582	−	1.73609i	−0.274436	−	0.0780314i
$496$	5.76232	−	1.69197i	0.258736	−	0.0759717i
$497$	−0.0142237	+	0.0381352i	−0.000638020	+	0.00171060i
$498$	2.59772	−	11.9415i	0.116407	−	0.535113i
$499$	−0.827420	+	2.81793i	−0.0370404	+	0.126148i	−0.975938	−	0.218049i	$-0.930031\pi$
$499$	−0.827420	+	2.81793i	−0.0370404	+	0.126148i	0.938897	+	0.344197i	$0.111849\pi$
$500$	11.1038	+	1.30589i	0.496578	+	0.0584010i
$501$	1.61392	−	3.53399i	0.0721046	−	0.157887i
$502$	2.80050	−	2.09643i	0.124992	−	0.0935682i
$503$	−20.0778	+	4.36765i	−0.895224	+	0.194744i	−0.636564	−	0.771224i	$-0.719645\pi$
$503$	−20.0778	+	4.36765i	−0.895224	+	0.194744i	−0.258660	+	0.965968i	$0.583281\pi$
$504$	0.270381	+	0.312036i	0.0120437	+	0.0138992i
$505$	0.00534449	+	0.0114421i	0.000237826	+	0.000509165i
$506$	10.7436	−	8.36252i	0.477613	−	0.371759i
$507$	7.33383	−	7.33383i	0.325707	−	0.325707i
$508$	−0.274295	+	3.83515i	−0.0121699	+	0.170157i
$509$	21.9452	−	34.1474i	0.972703	−	1.51356i	0.118936	−	0.992902i	$-0.462052\pi$
$509$	21.9452	−	34.1474i	0.972703	−	1.51356i	0.853768	−	0.520654i	$-0.174312\pi$
$510$	0.587247	+	0.314153i	0.0260037	+	0.0139109i
$511$	1.28365	+	0.586221i	0.0567852	+	0.0259329i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	−1.99834	+	1.09118i	−0.0882288	+	0.0481766i
$514$	−1.48301	−	2.30760i	−0.0654126	−	0.101784i
$515$	−1.81282	−	22.6186i	−0.0798826	−	0.996694i
$516$	−0.731111	−	2.48993i	−0.0321854	−	0.109613i
$517$	−34.2665	+	2.45079i	−1.50704	+	0.107786i
$518$	−0.663515	+	0.0474555i	−0.0291532	+	0.00208508i
$519$	0.855659	+	2.91411i	0.0375593	+	0.127915i
$520$	−2.76000	−	2.35041i	−0.121034	−	0.103072i
$521$	17.3056	+	26.9280i	0.758170	+	1.17974i	0.978888	+	0.204398i	$0.0655237\pi$
$521$	17.3056	+	26.9280i	0.758170	+	1.17974i	−0.220718	+	0.975338i	$0.570840\pi$
$522$	−2.22919	+	1.21723i	−0.0975691	+	0.0532768i
$523$	−31.3845	−	23.4942i	−1.37235	−	1.02733i	−0.994854	−	0.101316i	$-0.967695\pi$
$523$	−31.3845	−	23.4942i	−1.37235	−	1.02733i	−0.377494	−	0.926012i	$-0.623214\pi$
$524$	−13.0467	−	5.95822i	−0.569947	−	0.260286i
$525$	−1.53676	+	1.37847i	−0.0670698	+	0.0601612i
$526$	−10.2950	+	16.0193i	−0.448883	+	0.698475i
$527$	−0.127606	+	1.78416i	−0.00555859	+	0.0777193i
$528$	−2.00736	+	2.00736i	−0.0873593	+	0.0873593i
$529$	−22.2965	−	5.64508i	−0.969412	−	0.245438i
$530$	0.497589	−	0.232419i	0.0216139	−	0.0100956i
$531$	−6.71924	−	7.75442i	−0.291590	−	0.336513i
$532$	0.918587	−	0.199826i	0.0398258	−	0.00866357i
$533$	2.53112	−	1.89477i	0.109635	−	0.0820716i
$534$	−1.07683	+	2.35792i	−0.0465988	+	0.102037i
$535$	−12.3283	−	2.57131i	−0.532998	−	0.111168i
$536$	2.67799	−	9.12039i	0.115672	−	0.393941i
$537$	−0.0884921	+	0.406792i	−0.00381872	+	0.0175544i
$538$	−5.36145	+	14.3746i	−0.231149	+	0.619734i
$539$	18.6026	−	5.46221i	0.801270	−	0.235274i
$540$	−1.08843	−	1.95329i	−0.0468384	−	0.0840561i
$541$	−12.8766	+	14.8603i	−0.553606	+	0.638896i	−0.961720	−	0.274036i	$-0.911641\pi$
$541$	−12.8766	+	14.8603i	−0.553606	+	0.638896i	0.408113	+	0.912931i	$0.366187\pi$
$542$	3.84705	−	7.04535i	0.165245	−	0.302624i
$543$	−11.2997	−	4.21457i	−0.484916	−	0.180864i
$544$	0.250561	−	0.161026i	0.0107427	−	0.00690392i
$545$	−6.10341	−	40.0110i	−0.261441	−	1.71388i
$546$	0.662567	−	0.0952628i	0.0283553	−	0.00407687i
$547$	−6.76293	−	18.1321i	−0.289162	−	0.775273i	−0.997583	−	0.0694833i	$-0.977865\pi$
$547$	−6.76293	−	18.1321i	−0.289162	−	0.775273i	0.708421	−	0.705790i	$-0.249408\pi$
$548$	−12.3167	−	16.4532i	−0.526144	−	0.702847i
$549$	−4.21768	−	2.71054i	−0.180006	−	0.115683i
$550$	−10.2075	−	9.86318i	−0.435249	−	0.420567i
$551$			5.78289i			0.246360i
$552$	4.75902	+	0.593093i	0.202557	+	0.0252437i
$553$	2.73699	+	2.73699i	0.116389	+	0.116389i
$554$	10.1555	−	8.79978i	0.431465	−	0.373867i
$555$	3.57020	+	0.482101i	0.151547	+	0.0204641i
$556$	0.733432	−	5.10113i	0.0311045	−	0.216336i
$557$	−5.48891	+	2.04726i	−0.232572	+	0.0867450i	−0.463048	−	0.886333i	$-0.653244\pi$
$557$	−5.48891	+	2.04726i	−0.232572	+	0.0867450i	0.230476	+	0.973078i	$0.425972\pi$
$558$	3.59902	−	4.80772i	0.152358	−	0.203527i
$559$	−4.03677	−	1.18530i	−0.170737	−	0.0501330i
$560$	0.203978	+	0.900419i	0.00861963	+	0.0380497i
$561$	−0.351245	−	0.769119i	−0.0148296	−	0.0324722i
$562$	−2.59892	−	1.41912i	−0.109629	−	0.0598618i
$563$	0.0814099	+	1.13826i	0.00343102	+	0.0479719i	0.998879	−	0.0473326i	$-0.0150721\pi$
$563$	0.0814099	+	1.13826i	0.00343102	+	0.0479719i	−0.995448	+	0.0953045i	$0.969618\pi$
$564$	−9.14566	−	7.92476i	−0.385102	−	0.333693i
$565$	−15.1713	−	0.954364i	−0.638262	−	0.0401504i
$566$	−23.0405	+	10.5222i	−0.968462	+	0.442282i
$567$	0.403447	+	0.0877646i	0.0169432	+	0.00368577i
$568$	−0.0472437	−	0.0865204i	−0.00198230	−	0.00363032i
$569$	−5.39013	−	37.4892i	−0.225966	−	1.57163i	−0.714849	−	0.699279i	$-0.753505\pi$
$569$	−5.39013	−	37.4892i	−0.225966	−	1.57163i	0.488883	−	0.872349i	$-0.337404\pi$
$570$	−5.09099	+	0.0436654i	−0.213238	+	0.00182894i
$571$	12.0294	+	1.72957i	0.503416	+	0.0723803i	0.389345	−	0.921092i	$-0.372702\pi$
$571$	12.0294	+	1.72957i	0.503416	+	0.0723803i	0.114072	+	0.993473i	$0.463611\pi$
$572$	0.978317	+	4.49725i	0.0409055	+	0.188039i
$573$	5.81437	+	0.415852i	0.242899	+	0.0173725i
$574$	−0.805211			−0.0336088
$575$	−2.55688	+	23.8424i	−0.106629	+	0.994299i
$576$	−1.00000			−0.0416667
$577$	14.8691	+	1.06346i	0.619010	+	0.0442725i	0.377323	−	0.926082i	$-0.376845\pi$
$577$	14.8691	+	1.06346i	0.619010	+	0.0442725i	0.241687	+	0.970354i	$0.422299\pi$
$578$	−3.59475	−	16.5248i	−0.149522	−	0.687342i
$579$	16.9769	+	2.44090i	0.705534	+	0.101440i
$580$	−5.67912	+	0.0487098i	−0.235813	+	0.00202257i
$581$	0.718088	+	4.99441i	0.0297913	+	0.207203i
$582$	4.33751	+	7.94356i	0.179796	+	0.329271i
$583$	−0.681304	−	0.148209i	−0.0282167	−	0.00613817i
$584$	−3.10898	+	1.41982i	−0.128651	+	0.0587527i
$585$	−3.61804	−	0.227596i	−0.149588	−	0.00940993i
$586$	−2.99017	−	2.59100i	−0.123523	−	0.107033i
$587$	−1.24714	−	17.4373i	−0.0514750	−	0.719715i	−0.956013	−	0.293323i	$-0.905239\pi$
$587$	−1.24714	−	17.4373i	−0.0514750	−	0.719715i	0.904538	−	0.426392i	$-0.140216\pi$
$588$	5.99413	+	3.27304i	0.247194	+	0.134978i
$589$	−5.68030	−	12.4381i	−0.234053	−	0.512504i
$590$	−5.06906	−	22.3763i	−0.208690	−	0.921220i
$591$	−3.35815	−	0.986042i	−0.138136	−	0.0405603i
$592$	0.965516	−	1.28978i	0.0396825	−	0.0530096i
$593$	−14.8372	+	5.53400i	−0.609292	+	0.227254i	−0.635122	−	0.772412i	$-0.719050\pi$
$593$	−14.8372	+	5.53400i	−0.609292	+	0.227254i	0.0258293	+	0.999666i	$0.491777\pi$
$594$	−0.404009	+	2.80994i	−0.0165767	+	0.115293i
$595$	−0.272505	−	0.0367977i	−0.0111716	−	0.00150856i
$596$	15.4266	−	13.3672i	0.631897	−	0.547542i
$597$	−5.43427	−	5.43427i	−0.222410	−	0.222410i
$598$	4.98021	−	5.97083i	0.203656	−	0.244165i
$599$			38.8039i			1.58549i	0.609556	+	0.792743i	$0.291348\pi$
$599$			38.8039i			1.58549i	−0.609556	+	0.792743i	$0.708652\pi$
$600$	−0.0857637	−	4.99926i	−0.00350129	−	0.204094i
$601$	−17.8523	−	11.4729i	−0.728208	−	0.467991i	0.123275	−	0.992373i	$-0.460660\pi$
$601$	−17.8523	−	11.4729i	−0.728208	−	0.467991i	−0.851484	+	0.524381i	$0.824297\pi$
$602$	0.642098	+	0.857742i	0.0261700	+	0.0349590i
$603$	−3.32181	−	8.90611i	−0.135274	−	0.362685i
$604$	−16.4256	+	2.36165i	−0.668349	+	0.0960941i
$605$	−0.991691	−	6.50104i	−0.0403180	−	0.264305i
$606$	0.00475117	−	0.00305339i	0.000193003	−	0.000124036i
$607$	42.6218	+	15.8971i	1.72997	+	0.645244i	0.999297	−	0.0374885i	$-0.0119357\pi$
$607$	42.6218	+	15.8971i	1.72997	+	0.645244i	0.730669	+	0.682732i	$0.239208\pi$
$608$	−1.09118	+	1.99834i	−0.0442530	+	0.0810433i
$609$	0.686733	−	0.792532i	0.0278278	−	0.0321150i
$610$	−5.45690	−	9.79294i	−0.220943	−	0.396504i
$611$	−18.8246	+	5.52739i	−0.761560	+	0.223614i
$612$	0.104085	−	0.279063i	0.00420740	−	0.0112805i
$613$	−1.71098	+	7.86523i	−0.0691057	+	0.317674i	−0.998704	−	0.0509014i	$-0.983791\pi$
$613$	−1.71098	+	7.86523i	−0.0691057	+	0.317674i	0.929598	+	0.368575i	$0.120154\pi$
$614$	−3.52732	+	12.0130i	−0.142351	+	0.484804i
$615$	4.26895	+	0.890377i	0.172141	+	0.0359035i
$616$	0.486912	−	1.06619i	0.0196182	−	0.0429579i
$617$	0.481894	−	0.360741i	0.0194003	−	0.0145229i	−0.589534	−	0.807744i	$-0.700688\pi$
$617$	0.481894	−	0.360741i	0.0194003	−	0.0145229i	0.608934	+	0.793221i	$0.291597\pi$
$618$	−9.91587	+	2.15706i	−0.398875	+	0.0867699i
$619$	9.50495	+	10.9693i	0.382036	+	0.440893i	0.913902	−	0.405936i	$-0.133054\pi$
$619$	9.50495	+	10.9693i	0.382036	+	0.440893i	−0.531865	+	0.846829i	$0.678509\pi$
$620$	12.1671	−	5.68313i	0.488641	−	0.228240i
$621$	4.16522	−	2.37718i	0.167144	−	0.0953928i
$622$	−8.44822	+	8.44822i	−0.338743	+	0.338743i
$623$	0.0763517	−	1.06754i	0.00305897	−	0.0427699i
$624$	−0.876506	+	1.36387i	−0.0350883	+	0.0545985i
$625$	24.9853	−	0.857511i	0.999412	−	0.0343004i
$626$	−10.1057	−	4.61510i	−0.403903	−	0.184457i
$627$	5.17438	+	3.87349i	0.206645	+	0.154692i
$628$	9.59113	−	5.23716i	0.382728	−	0.208985i
$629$	0.259434	+	0.403687i	0.0103443	+	0.0160961i
$630$	0.702894	+	0.598584i	0.0280040	+	0.0238481i
$631$	2.46139	+	8.38271i	0.0979862	+	0.333710i	0.993867	−	0.110585i	$-0.0352723\pi$
$631$	2.46139	+	8.38271i	0.0979862	+	0.333710i	−0.895880	+	0.444295i	$0.853454\pi$
$632$	−9.35090	+	0.668789i	−0.371959	+	0.0266030i
$633$	16.7999	−	1.20156i	0.667738	−	0.0477576i
$634$	8.76268	+	29.8430i	0.348011	+	1.18522i
$635$	0.686871	+	8.57008i	0.0272576	+	0.340093i
$636$	−0.132785	−	0.206617i	−0.00526527	−	0.00819292i
$637$	9.71790	−	5.30638i	0.385037	−	0.210246i
$638$	5.77214	+	4.32097i	0.228521	+	0.171069i
$639$	−0.0896703	−	0.0409511i	−0.00354730	−	0.00162000i
$640$	−1.97167	−	1.05476i	−0.0779371	−	0.0416931i
$641$	18.9736	−	29.5235i	0.749412	−	1.16611i	−0.231723	−	0.972782i	$-0.574436\pi$
$641$	18.9736	−	29.5235i	0.749412	−	1.16611i	0.981135	−	0.193325i	$-0.0619273\pi$
$642$	−0.401783	+	5.61767i	−0.0158571	+	0.221712i
$643$	2.24665	−	2.24665i	0.0885994	−	0.0885994i	−0.661418	−	0.750017i	$-0.730045\pi$
$643$	2.24665	−	2.24665i	0.0885994	−	0.0885994i	0.750017	+	0.661418i	$0.230045\pi$
$644$	−1.92660	+	0.457230i	−0.0759189	+	0.0180174i
$645$	−2.45572	−	5.25747i	−0.0966937	−	0.207012i
$646$	−0.444088	−	0.512505i	−0.0174724	−	0.0201642i
$647$	20.2088	−	4.39616i	0.794491	−	0.172831i	0.203038	−	0.979171i	$-0.434918\pi$
$647$	20.2088	−	4.39616i	0.794491	−	0.172831i	0.591453	+	0.806340i	$0.298555\pi$
$648$	−0.800541	+	0.599278i	−0.0314482	+	0.0235419i
$649$	−12.1003	+	26.4959i	−0.474977	+	1.04005i
$650$	−6.89352	−	4.26492i	−0.270386	−	0.167284i
$651$	−0.698586	+	2.37916i	−0.0273797	+	0.0932468i
$652$	−1.29291	+	5.94341i	−0.0506343	+	0.232762i
$653$	11.6748	−	31.3015i	0.456872	−	1.22492i	−0.480625	−	0.876926i	$-0.659590\pi$
$653$	11.6748	−	31.3015i	0.456872	−	1.22492i	0.937497	−	0.347994i	$-0.113137\pi$
$654$	−17.3673	+	5.09949i	−0.679113	+	0.199406i
$655$	−30.8487	−	8.77133i	−1.20536	−	0.342724i
$656$	1.27712	−	1.47387i	0.0498631	−	0.0575451i
$657$	−1.63800	+	2.99977i	−0.0639044	+	0.117032i
$658$	4.68145	+	1.74609i	0.182502	+	0.0680697i
$659$	−11.3677	+	7.30559i	−0.442824	+	0.284586i	−0.742991	−	0.669301i	$-0.766594\pi$
$659$	−11.3677	+	7.30559i	−0.442824	+	0.284586i	0.300168	+	0.953886i	$0.402957\pi$
$660$	−3.76039	+	5.11415i	−0.146373	+	0.199068i
$661$	−4.65136	+	0.668764i	−0.180917	+	0.0260119i	−0.232178	−	0.972673i	$-0.574585\pi$
$661$	−4.65136	+	0.668764i	−0.180917	+	0.0260119i	0.0512609	+	0.998685i	$0.483676\pi$
$662$	−9.36186	−	25.1001i	−0.363859	−	0.975544i
$663$	−0.289375	−	0.386560i	−0.0112384	−	0.0150127i
$664$	−10.2808	−	6.60708i	−0.398973	−	0.256404i
$665$	1.96315	−	0.751460i	0.0761278	−	0.0291404i
$666$		−	1.61113i		−	0.0624302i
$667$	−0.229154	−	12.1786i	−0.00887289	−	0.471559i
$668$	−2.74716	−	2.74716i	−0.106291	−	0.106291i
$669$	3.52298	−	3.05268i	0.136206	−	0.118023i
$670$	2.84432	−	21.0636i	0.109886	−	0.813759i
$671$	−2.02553	+	14.0879i	−0.0781946	+	0.543855i
$672$	0.386851	−	0.144288i	0.0149231	−	0.00556602i
$673$	22.2853	−	29.7697i	0.859037	−	1.14754i	−0.128742	−	0.991678i	$-0.541094\pi$
$673$	22.2853	−	29.7697i	0.859037	−	1.14754i	0.987779	−	0.155860i	$-0.0498150\pi$
$674$	12.7026	+	3.72983i	0.489287	+	0.143668i
$675$	−3.06460	−	3.95072i	−0.117957	−	0.152063i
$676$	−4.30852	−	9.43433i	−0.165712	−	0.362859i
$677$	29.0611	+	15.8686i	1.11691	+	0.609878i	0.928173	−	0.372150i	$-0.121379\pi$
$677$	29.0611	+	15.8686i	1.11691	+	0.609878i	0.188735	+	0.982028i	$0.439561\pi$
$678$	0.484980	+	6.78091i	0.0186255	+	0.260419i
$679$	−2.82413	−	2.44712i	−0.108380	−	0.0939119i
$680$	0.499567	−	0.440435i	0.0191575	−	0.0168899i
$681$	19.5312	−	8.91959i	0.748437	−	0.341800i
$682$	−16.6593	−	3.62401i	−0.637917	−	0.138770i
$683$	−12.3352	−	22.5903i	−0.471995	−	0.864394i	−0.999886	−	0.0150823i	$-0.995199\pi$
$683$	−12.3352	−	22.5903i	−0.471995	−	0.864394i	0.527891	−	0.849312i	$-0.322983\pi$
$684$	0.324029	+	2.25367i	0.0123895	+	0.0861712i
$685$	−32.7741	−	32.2166i	−1.25223	−	1.23093i
$686$	−5.65186	−	0.812615i	−0.215789	−	0.0310258i
$687$	−2.05013	−	9.42428i	−0.0782172	−	0.359559i
$688$	−2.58844	−	0.185129i	−0.0986834	−	0.00705797i
$689$	−0.398186			−0.0151697
$690$	10.7198	−	0.293695i	0.408095	−	0.0111808i
$691$	19.7711			0.752127			0.376064	−	0.926594i	$-0.377277\pi$
$691$	19.7711			0.752127			0.376064	+	0.926594i	$0.377277\pi$
$692$	3.02939	+	0.216666i	0.115160	+	0.00823642i
$693$	−0.249150	−	1.14532i	−0.00946441	−	0.0435072i
$694$	29.0351	+	4.17462i	1.10216	+	0.158466i
$695$	−0.0988358	−	11.5234i	−0.00374906	−	0.437106i
$696$	0.361462	+	2.51402i	0.0137012	+	0.0952937i
$697$	0.278375	+	0.509806i	0.0105442	+	0.0193103i
$698$	11.0079	+	2.39463i	0.416657	+	0.0906381i
$699$	0.482993	−	0.220575i	0.0182685	−	0.00834292i
$700$	0.754511	+	1.92159i	0.0285178	+	0.0726294i
$701$	38.2691	+	33.1603i	1.44540	+	1.25245i	0.914236	+	0.405182i	$0.132792\pi$
$701$	38.2691	+	33.1603i	1.44540	+	1.25245i	0.531167	+	0.847267i	$0.321754\pi$
$702$	0.115658	+	1.61710i	0.00436522	+	0.0610337i
$703$	−3.21959	−	1.75803i	−0.121429	−	0.0663053i
$704$	1.17930	+	2.58230i	0.0444464	+	0.0973241i
$705$	−22.8887	−	14.4338i	−0.862037	−	0.543607i
$706$	2.92253	+	0.858131i	0.109991	+	0.0322962i
$707$	−0.00139743	+	0.00186674i	−5.25556e−5	+	7.02061e-5i
$708$	−9.61364	+	3.58570i	−0.361303	+	0.134759i
$709$	−5.85829	+	40.7453i	−0.220013	+	1.53022i	0.517968	+	0.855400i	$0.326689\pi$
$709$	−5.85829	+	40.7453i	−0.220013	+	1.53022i	−0.737980	+	0.674822i	$0.764220\pi$
$710$	−0.133607	−	0.175323i	−0.00501417	−	0.00657975i
$711$	−7.08499	+	6.13918i	−0.265708	+	0.230237i
$712$	1.83294	+	1.83294i	0.0686924	+	0.0686924i
$713$	12.4555	+	25.9693i	0.466460	+	0.972558i
$714$			0.122974i			0.00460219i
$715$	3.67902	+	9.61127i	0.137588	+	0.359441i
$716$	0.350219	+	0.225072i	0.0130883	+	0.00841133i
$717$	11.2790	+	15.0670i	0.421224	+	0.562689i
$718$	−10.5404	−	28.2599i	−0.393365	−	1.05465i
$719$	−10.1755	+	1.46301i	−0.379480	+	0.0545610i	−0.329416	−	0.944185i	$-0.606852\pi$
$719$	−10.1755	+	1.46301i	−0.379480	+	0.0545610i	−0.0500645	+	0.998746i	$0.515943\pi$
$720$	−2.21050	+	0.337197i	−0.0823804	+	0.0125666i
$721$	3.52472	−	2.26520i	0.131267	−	0.0843605i
$722$	−12.9449	−	4.82819i	−0.481759	−	0.179687i
$723$	4.71279	−	8.63084i	0.175271	−	0.320984i
$724$	−7.89767	+	9.11440i	−0.293515	+	0.338734i
$725$	−12.5373	+	2.02265i	−0.465622	+	0.0751195i
$726$	−2.82186	+	0.828571i	−0.104729	+	0.0307512i
$727$	8.70106	−	23.3284i	0.322704	−	0.865204i	−0.669750	−	0.742587i	$-0.733599\pi$
$727$	8.70106	−	23.3284i	0.322704	−	0.865204i	0.992454	−	0.122617i	$-0.0391286\pi$
$728$	0.142287	−	0.654083i	0.00527351	−	0.0242419i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	−6.39364	+	4.18686i	−0.236639	+	0.154963i
$731$	0.321081	−	0.703070i	0.0118756	−	0.0260040i
$732$	−4.01357	+	3.00452i	−0.148346	+	0.111050i
$733$	−8.19628	+	1.78299i	−0.302736	+	0.0658563i	−0.361368	−	0.932423i	$-0.617690\pi$
$733$	−8.19628	+	1.78299i	−0.302736	+	0.0658563i	0.0586312	+	0.998280i	$0.481326\pi$
$734$	4.20846	+	4.85683i	0.155337	+	0.179269i
$735$	14.3537	+	5.21385i	0.529443	+	0.192316i
$736$	2.21880	−	4.25169i	0.0817862	−	0.156720i
$737$	−19.0809	+	19.0809i	−0.702852	+	0.702852i
$738$	0.139127	−	1.94525i	0.00512133	−	0.0716055i
$739$	−0.0773273	+	0.120324i	−0.00284453	+	0.00442617i	−0.842673	−	0.538426i	$-0.819019\pi$
$739$	−0.0773273	+	0.120324i	−0.00284453	+	0.00442617i	0.839828	+	0.542852i	$0.182656\pi$
$740$	1.69936	−	3.17662i	0.0624698	−	0.116775i
$741$	3.35772	+	1.53342i	0.123349	+	0.0563317i
$742$	0.0811804	+	0.0607709i	0.00298022	+	0.00223097i
$743$	−29.5004	+	16.1084i	−1.08226	+	0.590961i	−0.918453	−	0.395531i	$-0.870561\pi$
$743$	−29.5004	+	16.1084i	−1.08226	+	0.590961i	−0.163811	+	0.986492i	$0.552379\pi$
$744$	−3.24687	−	5.05222i	−0.119036	−	0.185223i
$745$	29.5930	−	34.7499i	1.08420	−	1.27314i
$746$	−0.737825	−	2.51280i	−0.0270137	−	0.0920002i
$747$	−12.1897	+	0.871824i	−0.445997	+	0.0318984i
$748$	−0.843373	+	0.0603192i	−0.0308368	+	0.00220549i
$749$	−0.655131	−	2.23117i	−0.0239380	−	0.0815252i
$750$	−1.87532	−	11.0219i	−0.0684769	−	0.402464i
$751$	25.0142	+	38.9229i	0.912781	+	1.42032i	0.907371	+	0.420330i	$0.138086\pi$
$751$	25.0142	+	38.9229i	0.912781	+	1.42032i	0.00541008	+	0.999985i	$0.498278\pi$
$752$	−10.6212	+	5.79960i	−0.387315	+	0.211490i
$753$	−2.80050	−	2.09643i	−0.102056	−	0.0763981i
$754$	3.74562	+	1.71057i	0.136407	+	0.0622952i
$755$	−35.5125	+	10.7591i	−1.29243	+	0.391563i
$756$	0.223221	−	0.347339i	0.00811849	−	0.0126326i
$757$	−3.86772	+	54.0778i	−0.140575	+	1.96549i	0.100361	+	0.994951i	$0.468000\pi$
$757$	−3.86772	+	54.0778i	−0.140575	+	1.96549i	−0.240936	+	0.970541i	$0.577454\pi$
$758$	17.1344	−	17.1344i	0.622351	−	0.622351i
$759$	−11.0506	−	7.95244i	−0.401112	−	0.288655i
$760$	−1.73821	+	4.78526i	−0.0630514	+	0.173580i
$761$	16.2690	+	18.7755i	0.589753	+	0.680611i	0.969672	−	0.244409i	$-0.0785939\pi$
$761$	16.2690	+	18.7755i	0.589753	+	0.680611i	−0.379920	+	0.925019i	$0.624048\pi$
$762$	3.75708	−	0.817302i	0.136105	−	0.0296077i
$763$	5.98274	−	4.47862i	0.216590	−	0.162137i
$764$	2.42155	−	5.30244i	0.0876084	−	0.191836i
$765$	0.135981	−	0.651966i	0.00491640	−	0.0235719i
$766$	10.8294	−	36.8816i	0.391283	−	1.33259i
$767$	−3.53598	+	16.2546i	−0.127677	+	0.586921i
$768$	−0.349464	+	0.936950i	−0.0126102	+	0.0338093i
$769$	15.7464	−	4.62357i	0.567831	−	0.166730i	0.0147992	−	0.999890i	$-0.495289\pi$
$769$	15.7464	−	4.62357i	0.567831	−	0.166730i	0.553032	+	0.833160i	$0.313471\pi$
$770$	0.716802	−	2.52099i	0.0258317	−	0.0908502i
$771$	−1.79632	+	2.07306i	−0.0646928	+	0.0746594i
$772$	8.21981	−	15.0535i	0.295837	−	0.541786i
$773$	6.54617	+	2.44160i	0.235450	+	0.0878181i	0.464419	−	0.885615i	$-0.346263\pi$
$773$	6.54617	+	2.44160i	0.235450	+	0.0878181i	−0.228970	+	0.973433i	$0.573536\pi$
$774$	−2.18310	+	1.40299i	−0.0784698	+	0.0504295i
$775$	24.9789	−	16.6652i	0.897270	−	0.598633i
$776$	8.95852	−	1.28804i	0.321592	−	0.0462380i
$777$	0.232467	+	0.623268i	0.00833971	+	0.0223596i
$778$	−8.39638	−	11.2162i	−0.301025	−	0.402122i
$779$	−3.73545	−	2.40063i	−0.133836	−	0.0860114i
$780$	−1.47762	+	3.31039i	−0.0529073	+	0.118531i
$781$			0.279849i			0.0100138i
$782$	0.955548	+	1.06173i	0.0341703	+	0.0379672i
$783$	1.79596	+	1.79596i	0.0641824	+	0.0641824i
$784$	5.16141	−	4.47239i	0.184336	−	0.159728i
$785$	19.4352	−	14.8108i	0.693673	−	0.528621i
$786$	−2.04119	+	14.1968i	−0.0728070	+	0.506384i
$787$	39.7557	−	14.8281i	1.41714	−	0.528564i	0.479920	−	0.877312i	$-0.340666\pi$
$787$	39.7557	−	14.8281i	1.41714	−	0.528564i	0.937217	+	0.348748i	$0.113393\pi$
$788$	−2.09742	+	2.80183i	−0.0747177	+	0.0998111i
$789$	18.2708	+	5.36480i	0.650459	+	0.190992i
$790$	−20.4446	+	4.63145i	−0.727387	+	0.164780i
$791$	−1.16602	−	2.55322i	−0.0414588	−	0.0907821i
$792$	2.49159	+	1.36051i	0.0885348	+	0.0483437i
$793$	0.579857	+	8.10747i	0.0205913	+	0.287905i
$794$	0.211037	+	0.182865i	0.00748943	+	0.00648962i
$795$	−0.363192	−	0.411953i	−0.0128811	−	0.0146105i
$796$	−6.99072	+	3.19256i	−0.247780	+	0.113157i
$797$	−42.5133	−	9.24820i	−1.50590	−	0.327588i	−0.617466	−	0.786597i	$-0.711841\pi$
$797$	−42.5133	−	9.24820i	−1.50590	−	0.327588i	−0.888431	+	0.459009i	$0.848204\pi$
$798$	−0.450528	−	0.825080i	−0.0159485	−	0.0292075i
$799$	−0.512949	−	3.56764i	−0.0181468	−	0.126214i
$800$	−4.71403	−	1.66671i	−0.166666	−	0.0589270i
$801$	2.56579	+	0.368904i	0.0906576	+	0.0130346i
$802$	−2.27380	−	10.4525i	−0.0802906	−	0.369090i
$803$	9.67800	+	0.692184i	0.341529	+	0.0244266i
$804$	−9.50543			−0.335231
$805$	−4.10458	+	1.66035i	−0.144667	+	0.0585197i
$806$	−9.73647			−0.342953
$807$	15.3028	+	1.09448i	0.538685	+	0.0385275i
$808$	−0.00120051	−	0.00551866i	−4.22338e−5	−	0.000194146i
$809$	4.31973	+	0.621083i	0.151874	+	0.0218361i	0.217832	−	0.975986i	$-0.430101\pi$
$809$	4.31973	+	0.621083i	0.151874	+	0.0218361i	−0.0659586	+	0.997822i	$0.521011\pi$
$810$	−1.56752	+	1.59464i	−0.0550770	+	0.0560300i
$811$	−7.04809	−	49.0205i	−0.247492	−	1.72134i	−0.612612	−	0.790384i	$-0.709881\pi$
$811$	−7.04809	−	49.0205i	−0.247492	−	1.72134i	0.365120	−	0.930960i	$-0.381028\pi$
$812$	−0.502574	−	0.920396i	−0.0176369	−	0.0322996i
$813$	−7.84380	−	1.70632i	−0.275094	−	0.0598431i
$814$	−4.16043	+	1.90000i	−0.145823	+	0.0665951i
$815$	−0.853875	+	13.5739i	−0.0299099	+	0.475471i
$816$	−0.225094	−	0.195045i	−0.00787988	−	0.00682795i
$817$	0.421510	+	5.89348i	0.0147468	+	0.206187i
$818$	27.8465	+	15.2053i	0.973628	+	0.531641i
$819$	−0.278071	−	0.608890i	−0.00971658	−	0.0212763i
$820$	2.32608	−	3.68864i	0.0812303	−	0.128813i
$821$	33.4791	+	9.83036i	1.16843	+	0.343082i	0.807703	−	0.589590i	$-0.200710\pi$
$821$	33.4791	+	9.83036i	1.16843	+	0.343082i	0.360727	+	0.932672i	$0.382529\pi$
$822$	−12.3167	+	16.4532i	−0.429595	+	0.573872i
$823$	−14.0569	+	5.24295i	−0.489992	+	0.182758i	−0.582302	−	0.812973i	$-0.697848\pi$
$823$	−14.0569	+	5.24295i	−0.489992	+	0.182758i	0.0923094	+	0.995730i	$0.470575\pi$
$824$	−1.44418	+	10.0445i	−0.0503104	+	0.349916i
$825$	−6.58787	+	12.5728i	−0.229360	+	0.437729i
$826$	3.20167	−	2.77426i	0.111400	−	0.0965289i
$827$	11.9076	+	11.9076i	0.414067	+	0.414067i	0.883153	−	0.469085i	$-0.155416\pi$
$827$	11.9076	+	11.9076i	0.414067	+	0.414067i	−0.469085	+	0.883153i	$0.655416\pi$
$828$	−0.771702	−	4.73334i	−0.0268185	−	0.164495i
$829$			33.5573i			1.16549i	0.812654	+	0.582746i	$0.198022\pi$
$829$			33.5573i			1.16549i	−0.812654	+	0.582746i	$0.801978\pi$
$830$	−24.9536	−	11.1383i	−0.866152	−	0.386615i
$831$	−11.3045	−	7.26493i	−0.392147	−	0.252018i
$832$	0.971570	+	1.29787i	0.0336831	+	0.0449954i
$833$	0.710853	+	1.90587i	0.0246296	+	0.0660345i
$834$	−5.10113	+	0.733432i	−0.176638	+	0.0253967i
$835$	−6.99893	−	5.14626i	−0.242208	−	0.178094i
$836$	5.43752	−	3.49448i	0.188061	−	0.120859i
$837$	−5.62693	−	2.09874i	−0.194495	−	0.0725430i
$838$	13.2953	−	24.3484i	0.459277	−	0.841103i
$839$	−7.15452	+	8.25676i	−0.247001	+	0.285055i	−0.865689	−	0.500582i	$-0.833119\pi$
$839$	−7.15452	+	8.25676i	−0.247001	+	0.285055i	0.618687	+	0.785637i	$0.287665\pi$
$840$	0.806479	−	0.449393i	0.0278262	−	0.0155055i
$841$	−21.6357	+	6.35280i	−0.746057	+	0.219062i
$842$	−1.65479	+	4.43667i	−0.0570279	+	0.152898i
$843$	−0.629432	+	2.89345i	−0.0216788	+	0.0996558i
$844$	4.74518	−	16.1606i	0.163336	−	0.556271i
$845$	−12.7052	−	19.4018i	−0.437072	−	0.667441i
$846$	−5.02712	+	11.0079i	−0.172836	+	0.378458i
$847$	0.972084	−	0.727693i	0.0334012	−	0.0250038i
$848$	−0.239994	+	0.0522075i	−0.00824142	+	0.00179281i
$849$	16.5872	+	19.1427i	0.569273	+	0.656976i
$850$	0.955778	−	1.14203i	0.0327829	−	0.0391714i
$851$	6.85005	+	3.57479i	0.234817	+	0.122542i
$852$	−0.0697057	+	0.0697057i	−0.00238808	+	0.00238808i
$853$	−1.85071	+	25.8763i	−0.0633671	+	0.885988i	0.861998	+	0.506912i	$0.169213\pi$
$853$	−1.85071	+	25.8763i	−0.0633671	+	0.885988i	−0.925365	+	0.379077i	$0.876242\pi$
$854$	1.11914	−	1.74141i	0.0382960	−	0.0595898i
$855$	1.47619	+	4.87247i	0.0504848	+	0.166635i
$856$	5.12306	+	2.33962i	0.175103	+	0.0799667i
$857$	−6.39738	−	4.78902i	−0.218530	−	0.163590i	0.484404	−	0.874844i	$-0.339036\pi$
$857$	−6.39738	−	4.78902i	−0.218530	−	0.163590i	−0.702934	+	0.711255i	$0.748127\pi$
$858$	4.03946	−	2.20571i	0.137905	−	0.0753017i
$859$	−26.6256	−	41.4303i	−0.908455	−	1.41358i	−0.910466	−	0.413585i	$-0.864277\pi$
$859$	−26.6256	−	41.4303i	−0.908455	−	1.41358i	0.00201107	−	0.999998i	$-0.499360\pi$
$860$	−5.78417	+	0.463587i	−0.197238	+	0.0158082i
$861$	0.226854	+	0.772594i	0.00773117	+	0.0263299i
$862$	6.18070	−	0.442053i	0.210516	−	0.0150564i
$863$	−37.0634	+	2.65082i	−1.26165	+	0.0902351i	−0.686086	−	0.727521i	$-0.740673\pi$
$863$	−37.0634	+	2.65082i	−1.26165	+	0.0902351i	−0.575566	+	0.817756i	$0.695218\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	6.76952	−	0.542561i	0.230171	−	0.0184476i
$866$	−2.39184	−	3.72177i	−0.0812779	−	0.126471i
$867$	−14.8427	+	8.10472i	−0.504084	+	0.275251i
$868$	1.98503	+	1.48597i	0.0673762	+	0.0504372i
$869$	24.2085	+	11.0556i	0.821217	+	0.375037i
$870$	1.64673	+	5.43535i	0.0558294	+	0.184276i
$871$	−8.33157	+	12.9642i	−0.282304	+	0.439274i
$872$	−1.29127	+	18.0543i	−0.0437280	+	0.611397i
$873$	6.39977	−	6.39977i	0.216599	−	0.216599i
$874$	−10.3009	−	3.62278i	−0.348432	−	0.122542i
$875$	2.31580	+	3.99326i	0.0782883	+	0.134997i
$876$	2.23821	+	2.58304i	0.0756222	+	0.0872727i
$877$	51.8207	−	11.2729i	1.74986	−	0.380659i	0.780279	−	0.625432i	$-0.215077\pi$
$877$	51.8207	−	11.2729i	1.74986	−	0.380659i	0.969580	+	0.244773i	$0.0787134\pi$
$878$	1.29674	−	0.970728i	0.0437629	−	0.0327605i
$879$	−1.64361	+	3.59901i	−0.0554377	+	0.121392i
$880$	3.47758	+	5.31051i	0.117229	+	0.179017i
$881$	−14.0451	+	47.8332i	−0.473191	+	1.61154i	0.284328	+	0.958727i	$0.408230\pi$
$881$	−14.0451	+	47.8332i	−0.473191	+	1.61154i	−0.757519	+	0.652813i	$0.773589\pi$
$882$	1.45172	−	6.67345i	0.0488820	−	0.224707i
$883$	16.0674	−	43.0783i	0.540711	−	1.44970i	−0.323333	−	0.946285i	$-0.604803\pi$
$883$	16.0674	−	43.0783i	0.540711	−	1.44970i	0.864044	−	0.503416i	$-0.167924\pi$
$884$	−0.463313	+	0.136041i	−0.0155829	+	0.00457555i
$885$	−20.0418	+	11.1679i	−0.673699	+	0.375404i
$886$	−19.2496	+	22.2152i	−0.646702	+	0.746334i
$887$	18.4920	−	33.8655i	0.620900	−	1.13709i	−0.358186	−	0.933650i	$-0.616605\pi$
$887$	18.4920	−	33.8655i	0.620900	−	1.13709i	0.979087	−	0.203444i	$-0.0652134\pi$
$888$	−1.50955	−	0.563033i	−0.0506572	−	0.0188942i
$889$	−1.33550	+	0.858274i	−0.0447913	+	0.0287856i
$890$	4.66977	+	3.43365i	0.156531	+	0.115096i
$891$	2.80994	−	0.404009i	0.0941367	−	0.0135348i
$892$	−1.62905	−	4.36765i	−0.0545446	−	0.146240i
$893$	16.5120	+	22.0574i	0.552551	+	0.738122i
$894$	−17.1719	−	11.0357i	−0.574314	−	0.369089i
$895$	0.850051	+	0.379428i	0.0284141	+	0.0126829i
$896$		−	0.412883i		−	0.0137935i
$897$	−7.13206	−	3.09630i	−0.238132	−	0.103382i
$898$	14.4148	+	14.4148i	0.481027	+	0.481027i
$899$	−11.5278	+	9.98887i	−0.384473	+	0.333148i
$900$	−4.77260	+	1.49075i	−0.159087	+	0.0496915i
$901$	0.0104106	−	0.0724075i	0.000346828	−	0.00241224i
$902$	−5.18728	+	1.93476i	−0.172718	+	0.0644203i
$903$	0.642098	−	0.857742i	0.0213677	−	0.0285439i
$904$	6.52285	+	1.91528i	0.216947	+	0.0637013i
$905$	−14.3844	+	22.8104i	−0.478155	+	0.758244i
$906$	6.89362	+	15.0949i	0.229025	+	0.501495i
$907$	−10.3692	−	5.66202i	−0.344304	−	0.188004i	0.297787	−	0.954632i	$-0.403751\pi$
$907$	−10.3692	−	5.66202i	−0.344304	−	0.188004i	−0.642092	+	0.766628i	$0.721933\pi$
$908$	−1.53176	−	21.4168i	−0.0508333	−	0.710742i
$909$	−0.00426827	−	0.00369848i	−0.000141570	−	0.000122671i
$910$	0.0939705	−	1.49383i	0.00311509	−	0.0495199i
$911$	−33.5620	+	15.3273i	−1.11196	+	0.507815i	−0.884766	−	0.466035i	$-0.845682\pi$
$911$	−33.5620	+	15.3273i	−1.11196	+	0.507815i	−0.227193	+	0.973850i	$0.572955\pi$
$912$	2.22481	+	0.483978i	0.0736709	+	0.0160261i
$913$	16.6266	+	30.4493i	0.550259	+	1.00772i
$914$	−4.14860	−	28.8541i	−0.137223	−	0.954410i
$915$	−7.85887	+	7.99484i	−0.259806	+	0.264301i
$916$	−9.54652	−	1.37258i	−0.315426	−	0.0453514i
$917$	−1.25879	−	5.78657i	−0.0415689	−	0.191089i
$918$	−0.297084	−	0.0212478i	−0.00980522	−	0.000701283i
$919$	23.4689			0.774169			0.387084	−	0.922044i	$-0.373482\pi$
$919$	23.4689			0.774169			0.387084	+	0.922044i	$0.373482\pi$
$920$	3.47100	−	10.1465i	0.114436	−	0.334521i
$921$	12.5201			0.412552
$922$	10.8832	+	0.778384i	0.358420	+	0.0256347i
$923$	0.0339720	+	0.156167i	0.00111820	+	0.00514030i
$924$	−1.16018	−	0.166809i	−0.0381671	−	0.00548760i
$925$	2.68529	−	7.59493i	0.0882917	−	0.249720i
$926$	1.98858	+	13.8309i	0.0653488	+	0.454511i
$927$	4.86331	+	8.90649i	0.159732	+	0.292527i
$928$	2.48183	+	0.539889i	0.0814700	+	0.0177227i
$929$	−41.2774	+	18.8508i	−1.35427	+	0.618473i	−0.954519	−	0.298151i	$-0.903630\pi$
$929$	−41.2774	+	18.8508i	−1.35427	+	0.618473i	−0.399749	+	0.916625i	$0.630903\pi$
$930$	−8.88078	−	10.0731i	−0.291212	−	0.330310i
$931$	−11.7517	−	10.1829i	−0.385147	−	0.333732i
$932$	−0.0378794	−	0.529623i	−0.00124078	−	0.0173484i
$933$	10.4861	+	5.72587i	0.343301	+	0.187457i
$934$	7.31745	+	16.0230i	0.239434	+	0.524288i
$935$	−1.84393	+	0.417718i	−0.0603031	+	0.0136608i
$936$	1.55556	+	0.456755i	0.0508452	+	0.0149295i
$937$	−29.9547	+	40.0148i	−0.978578	+	1.30723i	−0.0270607	+	0.999634i	$0.508615\pi$
$937$	−29.9547	+	40.0148i	−0.978578	+	1.30723i	−0.951518	+	0.307594i	$0.900476\pi$
$938$	3.67718	−	1.37152i	0.120064	−	0.0447817i
$939$	−1.58106	+	10.9965i	−0.0515960	+	0.358858i
$940$	−21.5225	+	16.4014i	−0.701986	+	0.534956i
$941$	41.0947	−	35.6088i	1.33965	−	1.16081i	0.366557	−	0.930396i	$-0.380536\pi$
$941$	41.0947	−	35.6088i	1.33965	−	1.16081i	0.973092	−	0.230417i	$-0.0740090\pi$
$942$	−7.72715	−	7.72715i	−0.251764	−	0.251764i
$943$	7.96190	+	4.90764i	0.259275	+	0.159815i
$944$			10.2606i			0.333953i
$945$	0.376309	−	0.843062i	0.0122413	−	0.0274248i
$946$	6.19746	+	3.98287i	0.201497	+	0.129494i
$947$	−15.1870	−	20.2874i	−0.493510	−	0.659252i	0.482774	−	0.875745i	$-0.339629\pi$
$947$	−15.1870	−	20.2874i	−0.493510	−	0.659252i	−0.976284	+	0.216493i	$0.930538\pi$
$948$	3.27615	+	8.78370i	0.106404	+	0.285281i
$949$	5.48473	−	0.788585i	0.178042	−	0.0255986i
$950$	−2.22873	+	11.1639i	−0.0723094	+	0.362206i
$951$	26.1654	−	16.8155i	0.848471	−	0.545279i
$952$	0.115221	+	0.0429750i	0.00373432	+	0.00139283i
$953$	−14.3130	+	26.2123i	−0.463644	+	0.849101i	0.536343	+	0.844000i	$0.319805\pi$
$953$	−14.3130	+	26.2123i	−0.463644	+	0.849101i	−0.999987	+	0.00510064i	$0.998376\pi$
$954$	−0.160838	+	0.185617i	−0.00520733	+	0.00600958i
$955$	3.56485	−	12.5376i	0.115356	−	0.405706i
$956$	18.0587	−	5.30251i	0.584059	−	0.171495i
$957$	2.51974	−	6.75568i	0.0814516	−	0.218380i
$958$	2.48499	−	11.4233i	0.0802865	−	0.369071i
$959$	2.39073	−	8.14209i	0.0772008	−	0.262922i
$960$	−0.456553	+	2.18896i	−0.0147352	+	0.0706485i
$961$	2.10495	−	4.60919i	0.0679015	−	0.148684i
$962$	−2.09104	+	1.56533i	−0.0674177	+	0.0504682i
$963$	5.50331	−	1.19717i	0.177342	−	0.0385783i
$964$	−6.43971	−	7.43182i	−0.207409	−	0.239363i
$965$	13.0939	−	36.0473i	0.421507	−	1.16040i
$966$	0.981496	+	1.71975i	0.0315791	+	0.0553320i
$967$	15.0174	−	15.0174i	0.482928	−	0.482928i	−0.423138	−	0.906065i	$-0.639071\pi$
$967$	15.0174	−	15.0174i	0.482928	−	0.482928i	0.906065	+	0.423138i	$0.139071\pi$
$968$	−0.209808	+	2.93349i	−0.00674347	+	0.0942860i
$969$	−0.366631	+	0.570488i	−0.0117779	+	0.0183267i
$970$	19.3685	−	5.86799i	0.621884	−	0.188410i
$971$	11.1273	+	5.08166i	0.357091	+	0.163078i	0.585880	−	0.810398i	$-0.300749\pi$
$971$	11.1273	+	5.08166i	0.357091	+	0.163078i	−0.228788	+	0.973476i	$0.573476\pi$
$972$	0.800541	+	0.599278i	0.0256774	+	0.0192218i
$973$	1.86755	−	1.01976i	0.0598709	−	0.0326920i
$974$	−14.7791	−	22.9967i	−0.473553	−	0.736862i
$975$	−2.15003	+	7.81585i	−0.0688560	+	0.250308i
$976$	1.41249	+	4.81048i	0.0452126	+	0.153980i
$977$	−1.62470	+	0.116201i	−0.0519788	+	0.00371760i	−0.0973044	−	0.995255i	$-0.531022\pi$
$977$	−1.62470	+	0.116201i	−0.0519788	+	0.00371760i	0.0453256	+	0.998972i	$0.485567\pi$
$978$	6.06691	−	0.433914i	0.193999	−	0.0138750i
$979$	−2.07320	−	7.06067i	−0.0662598	−	0.225660i
$980$	9.90121	−	11.6266i	0.316283	−	0.371399i
$981$	9.78584	+	15.2271i	0.312438	+	0.486163i
$982$	30.0535	−	16.4105i	0.959046	−	0.523679i
$983$	−0.649426	−	0.486154i	−0.0207135	−	0.0155059i	0.588871	−	0.808227i	$-0.299573\pi$
$983$	−0.649426	−	0.486154i	−0.0207135	−	0.0155059i	−0.609584	+	0.792721i	$0.708664\pi$
$984$	−1.77398	−	0.810149i	−0.0565523	−	0.0258266i
$985$	−3.69158	+	6.90069i	−0.117624	+	0.219874i
$986$	−0.408985	+	0.636393i	−0.0130247	+	0.0202669i
$987$	0.356445	−	4.98375i	0.0113458	−	0.158634i
$988$	2.61014	−	2.61014i	0.0830397	−	0.0830397i
$989$	−1.12123	−	12.3948i	−0.0356529	−	0.394132i
$990$	5.96641	+	2.16725i	0.189625	+	0.0688797i
$991$	21.1857	+	24.4496i	0.672987	+	0.776668i	0.984841	−	0.173462i	$-0.0554954\pi$
$991$	21.1857	+	24.4496i	0.672987	+	0.776668i	−0.311854	+	0.950130i	$0.600950\pi$
$992$	−5.86834	+	1.27658i	−0.186320	+	0.0405314i
$993$	−21.4459	+	16.0542i	−0.680564	+	0.509464i
$994$	0.0169080	−	0.0370234i	0.000536289	−	0.00117431i
$995$	−14.3765	+	9.41439i	−0.455764	+	0.298456i
$996$	−3.44300	+	11.7258i	−0.109096	+	0.371546i
$997$	−11.7794	+	54.1492i	−0.373059	+	1.71492i	0.282060	+	0.959397i	$0.408982\pi$
$997$	−11.7794	+	54.1492i	−0.373059	+	1.71492i	−0.655119	+	0.755526i	$0.727381\pi$
$998$	1.02634	−	2.75173i	0.0324882	−	0.0871044i
$999$	−1.54587	+	0.453909i	−0.0489092	+	0.0143610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.493.6	yes	240
5.2	odd	4	inner	690.2.w.a.217.11	yes	240
23.7	odd	22	inner	690.2.w.a.283.11	yes	240
115.7	even	44	inner	690.2.w.a.7.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.6	✓	240	115.7	even	44	inner
690.2.w.a.217.11	yes	240	5.2	odd	4	inner
690.2.w.a.283.11	yes	240	23.7	odd	22	inner
690.2.w.a.493.6	yes	240	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.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(2.23599 - 0.0191781i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.197874 + 0.362379i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(2.23599 - 0.0191781i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(0.197874 + 0.362379i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(-2.23166 - 0.140384i) q^{10} +(2.14545 + 1.85905i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(1.42292 + 0.776975i) q^{13} +(-0.171518 - 0.375572i) q^{14} +(0.494033 + 2.18081i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-0.178490 + 0.238435i) q^{17} +(0.936950 - 0.349464i) q^{18} +(0.324029 - 2.25367i) q^{19} +(2.21596 + 0.299231i) q^{20} +(-0.312036 + 0.270381i) q^{21} +(-2.00736 - 2.00736i) q^{22} +(-0.593093 + 4.75902i) q^{23} -1.00000i q^{24} +(4.99926 - 0.0857637i) q^{25} +(-1.36387 - 0.876506i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(0.144288 + 0.386851i) q^{28} +(-2.51402 + 0.361462i) q^{29} +(-0.337197 - 2.21050i) q^{30} +(5.05222 - 3.24687i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(-1.36051 + 2.49159i) q^{33} +(0.195045 - 0.225094i) q^{34} +(0.449393 + 0.806479i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.563033 - 1.50955i) q^{37} +(-0.483978 + 2.22481i) q^{38} +(-0.456755 + 1.55556i) q^{39} +(-2.18896 - 0.456553i) q^{40} +(0.810149 - 1.77398i) q^{41} +(0.330530 - 0.247432i) q^{42} +(-2.53575 + 0.551618i) q^{43} +(1.85905 + 2.14545i) q^{44} +(-2.02596 + 0.946307i) q^{45} +(0.931086 - 4.70458i) q^{46} +(-8.55701 + 8.55701i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(3.69232 - 5.74536i) q^{49} +(-4.99265 - 0.271098i) q^{50} +(-0.270927 - 0.123728i) q^{51} +(1.29787 + 0.971570i) q^{52} +(-0.215564 + 0.117707i) q^{53} +(0.540641 + 0.841254i) q^{54} +(4.83285 + 4.11565i) q^{55} +(-0.116323 - 0.396158i) q^{56} +(2.27104 - 0.162428i) q^{57} +(2.53340 - 0.181192i) q^{58} +(2.89074 + 9.84494i) q^{59} +(0.178643 + 2.22892i) q^{60} +(2.71054 + 4.21768i) q^{61} +(-5.27098 + 2.87817i) q^{62} +(-0.330530 - 0.247432i) q^{63} +(0.909632 + 0.415415i) q^{64} +(3.19654 + 1.71002i) q^{65} +(1.53479 - 2.38818i) q^{66} +(-0.678110 + 9.48121i) q^{67} +(-0.210606 + 0.210606i) q^{68} +(-4.77633 + 0.432063i) q^{69} +(-0.390714 - 0.836483i) q^{70} +(0.0645553 + 0.0745008i) q^{71} +(0.977147 - 0.212565i) q^{72} +(2.73613 - 2.04824i) q^{73} +(-0.669289 + 1.46554i) q^{74} +(1.14647 + 4.86679i) q^{75} +(0.641461 - 2.18462i) q^{76} +(-0.249150 + 1.14532i) q^{77} +(0.566564 - 1.51902i) q^{78} +(8.99504 - 2.64118i) q^{79} +(2.15082 + 0.611549i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-0.934638 + 1.71166i) q^{82} +(11.4503 + 4.27074i) q^{83} +(-0.347339 + 0.223221i) q^{84} +(-0.394529 + 0.536561i) q^{85} +(2.56864 - 0.369314i) q^{86} +(-0.887595 - 2.37973i) q^{87} +(-1.70125 - 2.27261i) q^{88} +(-2.18067 - 1.40143i) q^{89} +(2.08830 - 0.799366i) q^{90} +0.669381i q^{91} +(-1.26433 + 4.62617i) q^{92} +(4.24659 + 4.24659i) q^{93} +(9.14566 - 7.92476i) q^{94} +(0.681303 - 5.04539i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-8.48000 + 3.16288i) q^{97} +(-4.09278 + 5.46732i) q^{98} +(-2.72385 - 0.799794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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