LMFDB - Embedded newform 690.2.w.a.517.8

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			517.8
Character	$\chi$	$=$	690.517
Dual form			690.2.w.a.343.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.977147 + 0.212565i) q^{2} +(0.599278 + 0.800541i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.90687 + 1.16784i) q^{5} +(0.415415 + 0.909632i) q^{6} +(3.65625 + 0.261500i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-0.281733 + 0.959493i) q^{9} +O(q^{10})$	\(q+(0.977147 + 0.212565i) q^{2} +(0.599278 + 0.800541i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.90687 + 1.16784i) q^{5} +(0.415415 + 0.909632i) q^{6} +(3.65625 + 0.261500i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-0.281733 + 0.959493i) q^{9} +(-2.11153 + 0.735816i) q^{10} +(-0.378266 + 0.588594i) q^{11} +(0.212565 + 0.977147i) q^{12} +(-0.00460809 - 0.0644295i) q^{13} +(3.51711 + 1.03272i) q^{14} +(-2.07765 - 0.826668i) q^{15} +(0.654861 + 0.755750i) q^{16} +(1.67138 + 0.623394i) q^{17} +(-0.479249 + 0.877679i) q^{18} +(-0.527703 + 1.15551i) q^{19} +(-2.21969 + 0.270161i) q^{20} +(1.98177 + 3.08369i) q^{21} +(-0.494737 + 0.494737i) q^{22} +(-1.81298 + 4.43994i) q^{23} +1.00000i q^{24} +(2.27230 - 4.45383i) q^{25} +(0.00919270 - 0.0639366i) q^{26} +(-0.936950 + 0.349464i) q^{27} +(3.21721 + 1.75673i) q^{28} +(-4.44318 + 2.02913i) q^{29} +(-1.85445 - 1.24941i) q^{30} +(-0.205405 - 1.42862i) q^{31} +(0.479249 + 0.877679i) q^{32} +(-0.697881 + 0.0499134i) q^{33} +(1.50068 + 0.964425i) q^{34} +(-7.27738 + 3.77127i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(7.70601 - 4.20780i) q^{37} +(-0.761264 + 1.01693i) q^{38} +(0.0488170 - 0.0423001i) q^{39} +(-2.22639 - 0.207841i) q^{40} +(-0.168450 + 0.0494614i) q^{41} +(1.28099 + 3.43447i) q^{42} +(-2.56433 + 1.91963i) q^{43} +(-0.588594 + 0.378266i) q^{44} +(-0.583306 - 2.15865i) q^{45} +(-2.71533 + 3.95310i) q^{46} +(3.36830 + 3.36830i) q^{47} +(-0.212565 + 0.977147i) q^{48} +(6.37104 + 0.916017i) q^{49} +(3.16711 - 3.86904i) q^{50} +(0.502570 + 1.71160i) q^{51} +(0.0225733 - 0.0605214i) q^{52} +(0.842129 - 11.7745i) q^{53} +(-0.989821 + 0.142315i) q^{54} +(0.0339218 - 1.56413i) q^{55} +(2.77027 + 2.40045i) q^{56} +(-1.24127 + 0.270022i) q^{57} +(-4.77296 + 1.03829i) q^{58} +(2.90025 + 2.51308i) q^{59} +(-1.54648 - 1.61505i) q^{60} +(-6.39637 + 0.919659i) q^{61} +(0.102965 - 1.43964i) q^{62} +(-1.28099 + 3.43447i) q^{63} +(0.281733 + 0.959493i) q^{64} +(0.0840303 + 0.117477i) q^{65} +(-0.692542 - 0.0995725i) q^{66} +(0.631438 - 2.90267i) q^{67} +(1.26138 + 1.26138i) q^{68} +(-4.64084 + 1.20939i) q^{69} +(-7.91271 + 2.13816i) q^{70} +(2.74133 - 1.76174i) q^{71} +(-0.800541 + 0.599278i) q^{72} +(-0.429313 - 1.15103i) q^{73} +(8.42433 - 2.47361i) q^{74} +(4.92722 - 0.850010i) q^{75} +(-0.960030 + 0.831871i) q^{76} +(-1.53695 + 2.05313i) q^{77} +(0.0566929 - 0.0309567i) q^{78} +(10.9270 - 12.6104i) q^{79} +(-2.13133 - 0.676344i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(-0.175114 + 0.0125244i) q^{82} +(-6.89791 - 12.6326i) q^{83} +(0.521668 + 3.62828i) q^{84} +(-3.91513 + 0.763176i) q^{85} +(-2.91377 + 1.33067i) q^{86} +(-4.28710 - 2.34093i) q^{87} +(-0.655549 + 0.244507i) q^{88} +(2.23608 - 15.5523i) q^{89} +(-0.111122 - 2.23331i) q^{90} -0.236776i q^{91} +(-3.49357 + 3.28557i) q^{92} +(1.02058 - 1.02058i) q^{93} +(2.57534 + 4.00731i) q^{94} +(-0.343187 - 2.81967i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-0.179997 + 0.329640i) q^{97} +(6.03073 + 2.24934i) q^{98} +(-0.458182 - 0.528770i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$2$	0.977147	+	0.212565i	0.690947	+	0.150306i
$3$	0.599278	+	0.800541i	0.345993	+	0.462193i
$3$	0.599278	+	0.800541i	0.345993	+	0.462193i
$4$	0.909632	+	0.415415i	0.454816	+	0.207708i
$5$	−1.90687	+	1.16784i	−0.852778	+	0.522273i
$5$	−1.90687	+	1.16784i	−0.852778	+	0.522273i
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	3.65625	+	0.261500i	1.38193	+	0.0988378i	0.742416	−	0.669939i	$-0.233680\pi$
$7$	3.65625	+	0.261500i	1.38193	+	0.0988378i	0.639517	+	0.768777i	$0.279134\pi$
$8$	0.800541	+	0.599278i	0.283034	+	0.211877i
$9$	−0.281733	+	0.959493i	−0.0939109	+	0.319831i
$10$	−2.11153	+	0.735816i	−0.667726	+	0.232685i
$11$	−0.378266	+	0.588594i	−0.114052	+	0.177468i	−0.893587	−	0.448891i	$-0.851819\pi$
$11$	−0.378266	+	0.588594i	−0.114052	+	0.177468i	0.779535	+	0.626359i	$0.215456\pi$
$12$	0.212565	+	0.977147i	0.0613623	+	0.282078i
$13$	−0.00460809	−	0.0644295i	−0.00127805	−	0.0178695i	0.996773	−	0.0802711i	$-0.0255786\pi$
$13$	−0.00460809	−	0.0644295i	−0.00127805	−	0.0178695i	−0.998051	+	0.0624016i	$0.980124\pi$
$14$	3.51711	+	1.03272i	0.939987	+	0.276005i
$15$	−2.07765	−	0.826668i	−0.536446	−	0.213445i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	1.67138	+	0.623394i	0.405370	+	0.151195i	0.543874	−	0.839167i	$-0.316957\pi$
$17$	1.67138	+	0.623394i	0.405370	+	0.151195i	−0.138504	+	0.990362i	$0.544230\pi$
$18$	−0.479249	+	0.877679i	−0.112960	+	0.206871i
$19$	−0.527703	+	1.15551i	−0.121063	+	0.265092i	−0.960455	−	0.278435i	$-0.910184\pi$
$19$	−0.527703	+	1.15551i	−0.121063	+	0.265092i	0.839392	+	0.543527i	$0.182911\pi$
$20$	−2.21969	+	0.270161i	−0.496337	+	0.0604099i
$21$	1.98177	+	3.08369i	0.432457	+	0.672916i
$22$	−0.494737	+	0.494737i	−0.105478	+	0.105478i
$23$	−1.81298	+	4.43994i	−0.378033	+	0.925792i
$23$	−1.81298	+	4.43994i	−0.378033	+	0.925792i
$24$			1.00000i			0.204124i
$25$	2.27230	−	4.45383i	0.454461	−	0.890767i
$26$	0.00919270	−	0.0639366i	0.00180284	−	0.0125390i
$27$	−0.936950	+	0.349464i	−0.180316	+	0.0672544i
$28$	3.21721	+	1.75673i	0.607996	+	0.331991i
$29$	−4.44318	+	2.02913i	−0.825077	+	0.376800i	−0.782775	−	0.622305i	$-0.786197\pi$
$29$	−4.44318	+	2.02913i	−0.825077	+	0.376800i	−0.0423023	+	0.999105i	$0.513469\pi$
$30$	−1.85445	−	1.24941i	−0.338574	−	0.228110i
$31$	−0.205405	−	1.42862i	−0.0368919	−	0.256589i	0.963026	−	0.269409i	$-0.0868282\pi$
$31$	−0.205405	−	1.42862i	−0.0368919	−	0.256589i	−0.999918	+	0.0128201i	$0.995919\pi$
$32$	0.479249	+	0.877679i	0.0847201	+	0.155153i
$33$	−0.697881	+	0.0499134i	−0.121485	+	0.00868881i
$34$	1.50068	+	0.964425i	0.257364	+	0.165398i
$35$	−7.27738	+	3.77127i	−1.23010	+	0.637460i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	7.70601	−	4.20780i	1.26686	−	0.691758i	0.301696	−	0.953404i	$-0.402447\pi$
$37$	7.70601	−	4.20780i	1.26686	−	0.691758i	0.965164	+	0.261646i	$0.0842654\pi$
$38$	−0.761264	+	1.01693i	−0.123493	+	0.164968i
$39$	0.0488170	−	0.0423001i	0.00781697	−	0.00677344i
$40$	−2.22639	−	0.207841i	−0.352023	−	0.0328626i
$41$	−0.168450	+	0.0494614i	−0.0263075	+	0.00772457i	−0.294860	−	0.955541i	$-0.595273\pi$
$41$	−0.168450	+	0.0494614i	−0.0263075	+	0.00772457i	0.268552	+	0.963265i	$0.413455\pi$
$42$	1.28099	+	3.43447i	0.197661	+	0.529951i
$43$	−2.56433	+	1.91963i	−0.391056	+	0.292741i	−0.776656	−	0.629925i	$-0.783086\pi$
$43$	−2.56433	+	1.91963i	−0.391056	+	0.292741i	0.385600	+	0.922666i	$0.373995\pi$
$44$	−0.588594	+	0.378266i	−0.0887339	+	0.0570258i
$45$	−0.583306	−	2.15865i	−0.0869541	−	0.321792i
$46$	−2.71533	+	3.95310i	−0.400353	+	0.582853i
$47$	3.36830	+	3.36830i	0.491317	+	0.491317i	0.908721	−	0.417404i	$-0.137060\pi$
$47$	3.36830	+	3.36830i	0.491317	+	0.491317i	−0.417404	+	0.908721i	$0.637060\pi$
$48$	−0.212565	+	0.977147i	−0.0306812	+	0.141039i
$49$	6.37104	+	0.916017i	0.910148	+	0.130860i
$50$	3.16711	−	3.86904i	0.447896	−	0.547164i
$51$	0.502570	+	1.71160i	0.0703739	+	0.239672i
$52$	0.0225733	−	0.0605214i	0.00313036	−	0.00839281i
$53$	0.842129	−	11.7745i	0.115675	−	1.61735i	−0.526074	−	0.850439i	$-0.676337\pi$
$53$	0.842129	−	11.7745i	0.115675	−	1.61735i	0.641750	−	0.766914i	$-0.278209\pi$
$54$	−0.989821	+	0.142315i	−0.134698	+	0.0193666i
$55$	0.0339218	−	1.56413i	0.00457401	−	0.210907i
$56$	2.77027	+	2.40045i	0.370193	+	0.320774i
$57$	−1.24127	+	0.270022i	−0.164410	+	0.0357653i
$58$	−4.77296	+	1.03829i	−0.626720	+	0.136335i
$59$	2.90025	+	2.51308i	0.377580	+	0.327175i	0.822889	−	0.568202i	$-0.192361\pi$
$59$	2.90025	+	2.51308i	0.377580	+	0.327175i	−0.445309	+	0.895377i	$0.646906\pi$
$60$	−1.54648	−	1.61505i	−0.199650	−	0.208502i
$61$	−6.39637	+	0.919659i	−0.818971	+	0.117750i	−0.539051	−	0.842273i	$-0.681217\pi$
$61$	−6.39637	+	0.919659i	−0.818971	+	0.117750i	−0.279920	+	0.960023i	$0.590308\pi$
$62$	0.102965	−	1.43964i	0.0130766	−	0.182834i
$63$	−1.28099	+	3.43447i	−0.161390	+	0.432703i
$64$	0.281733	+	0.959493i	0.0352166	+	0.119937i
$65$	0.0840303	+	0.117477i	0.0104227	+	0.0145713i
$66$	−0.692542	−	0.0995725i	−0.0852460	−	0.0122565i
$67$	0.631438	−	2.90267i	0.0771424	−	0.354618i	−0.922354	−	0.386346i	$-0.873737\pi$
$67$	0.631438	−	2.90267i	0.0771424	−	0.354618i	0.999497	+	0.0317275i	$0.0101009\pi$
$68$	1.26138	+	1.26138i	0.152964	+	0.152964i
$69$	−4.64084	+	1.20939i	−0.558691	+	0.145593i
$70$	−7.91271	+	2.13816i	−0.945750	+	0.255559i
$71$	2.74133	−	1.76174i	0.325336	−	0.209080i	−0.367770	−	0.929917i	$-0.619878\pi$
$71$	2.74133	−	1.76174i	0.325336	−	0.209080i	0.693105	+	0.720836i	$0.256242\pi$
$72$	−0.800541	+	0.599278i	−0.0943447	+	0.0706256i
$73$	−0.429313	−	1.15103i	−0.0502473	−	0.134718i	0.909402	−	0.415919i	$-0.136540\pi$
$73$	−0.429313	−	1.15103i	−0.0502473	−	0.134718i	−0.959649	+	0.281201i	$0.909267\pi$
$74$	8.42433	−	2.47361i	0.979309	−	0.287551i
$75$	4.92722	−	0.850010i	0.568946	−	0.0981506i
$76$	−0.960030	+	0.831871i	−0.110123	+	0.0954222i
$77$	−1.53695	+	2.05313i	−0.175152	+	0.233976i
$78$	0.0566929	−	0.0309567i	0.00641921	−	0.00350515i
$79$	10.9270	−	12.6104i	1.22938	−	1.41878i	0.354075	−	0.935217i	$-0.384796\pi$
$79$	10.9270	−	12.6104i	1.22938	−	1.41878i	0.875308	−	0.483566i	$-0.160659\pi$
$80$	−2.13133	−	0.676344i	−0.238290	−	0.0756176i
$81$	−0.841254	−	0.540641i	−0.0934726	−	0.0600712i
$82$	−0.175114	+	0.0125244i	−0.0193381	+	0.00138309i
$83$	−6.89791	−	12.6326i	−0.757144	−	1.38661i	−0.916765	−	0.399428i	$-0.869209\pi$
$83$	−6.89791	−	12.6326i	−0.757144	−	1.38661i	0.159620	−	0.987179i	$-0.448973\pi$
$84$	0.521668	+	3.62828i	0.0569186	+	0.395878i
$85$	−3.91513	+	0.763176i	−0.424656	+	0.0827780i
$86$	−2.91377	+	1.33067i	−0.314200	+	0.143490i
$87$	−4.28710	−	2.34093i	−0.459625	−	0.250974i
$88$	−0.655549	+	0.244507i	−0.0698818	+	0.0260646i
$89$	2.23608	−	15.5523i	0.237024	−	1.64854i	−0.429509	−	0.903063i	$-0.641313\pi$
$89$	2.23608	−	15.5523i	0.237024	−	1.64854i	0.666533	−	0.745475i	$-0.267778\pi$
$90$	−0.111122	−	2.23331i	−0.0117133	−	0.235411i
$91$		−	0.236776i		−	0.0248208i
$92$	−3.49357	+	3.28557i	−0.364230	+	0.342545i
$93$	1.02058	−	1.02058i	0.105829	−	0.105829i
$94$	2.57534	+	4.00731i	0.265626	+	0.413322i
$95$	−0.343187	−	2.81967i	−0.0352102	−	0.289292i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	−0.179997	+	0.329640i	−0.0182760	+	0.0334699i	−0.886657	−	0.462427i	$-0.846979\pi$
$97$	−0.179997	+	0.329640i	−0.0182760	+	0.0334699i	0.868381	+	0.495897i	$0.165161\pi$
$98$	6.03073	+	2.24934i	0.609195	+	0.227218i
$99$	−0.458182	−	0.528770i	−0.0460490	−	0.0531434i
$100$	3.91715	−	3.10740i	0.391715	−	0.310740i
$101$	11.6235	+	3.41298i	1.15658	+	0.339604i	0.803105	−	0.595838i	$-0.203180\pi$
$101$	11.6235	+	3.41298i	1.15658	+	0.339604i	0.353480	+	0.935442i	$0.384998\pi$
$102$	0.127259	+	1.77931i	0.0126005	+	0.176178i
$103$	0.0268483	+	0.123420i	0.00264544	+	0.0121609i	0.978451	−	0.206481i	$-0.0662011\pi$
$103$	0.0268483	+	0.123420i	0.00264544	+	0.0121609i	−0.975805	+	0.218642i	$0.929837\pi$
$104$	0.0349222	−	0.0543400i	0.00342440	−	0.00532848i
$105$	−7.38023	−	3.56581i	−0.720236	−	0.347988i
$106$	3.32574	−	11.3264i	0.323024	−	1.10012i
$107$	−11.1695	−	8.36141i	−1.07980	−	0.808328i	−0.0974237	−	0.995243i	$-0.531060\pi$
$107$	−11.1695	−	8.36141i	−1.07980	−	0.808328i	−0.982376	+	0.186915i	$0.940151\pi$
$108$	−0.997452	−	0.0713392i	−0.0959799	−	0.00686462i
$109$	−5.36102	−	11.7390i	−0.513492	−	1.12439i	−0.971845	−	0.235621i	$-0.924288\pi$
$109$	−5.36102	−	11.7390i	−0.513492	−	1.12439i	0.458353	−	0.888770i	$-0.348440\pi$
$110$	0.365626	−	1.52117i	0.0348610	−	0.145038i
$111$	7.98655	+	3.64734i	0.758050	+	0.346190i
$112$	2.19671	+	2.93446i	0.207569	+	0.277280i
$113$	1.49136	+	0.324425i	0.140295	+	0.0305193i	0.282164	−	0.959366i	$-0.408948\pi$
$113$	1.49136	+	0.324425i	0.140295	+	0.0305193i	−0.141869	+	0.989885i	$0.545311\pi$
$114$	−1.27030			−0.118975
$115$	−1.72801	−	10.5837i	−0.161138	−	0.986932i
$116$	−4.88459			−0.453523
$117$	0.0631179	+	0.0137305i	0.00583525	+	0.00126938i
$118$	2.29978	+	3.07214i	0.211711	+	0.282813i
$119$	5.94798	+	2.71635i	0.545250	+	0.249007i
$120$	−1.16784	−	1.90687i	−0.106609	−	0.174073i
$121$	4.36621	+	9.56066i	0.396928	+	0.869151i
$122$	−6.44568	−	0.461004i	−0.583564	−	0.0417373i
$123$	−0.140544	−	0.105210i	−0.0126724	−	0.00948647i
$124$	0.406629	−	1.38485i	0.0365164	−	0.124363i
$125$	0.868372	+	11.1466i	0.0776695	+	0.996979i
$126$	−1.98177	+	3.08369i	−0.176550	+	0.274717i
$127$	−0.384588	−	1.76792i	−0.0341267	−	0.156878i	0.956930	−	0.290318i	$-0.0937612\pi$
$127$	−0.384588	−	1.76792i	−0.0341267	−	0.156878i	−0.991057	+	0.133440i	$0.957398\pi$
$128$	0.0713392	+	0.997452i	0.00630555	+	0.0881631i
$129$	−3.07349	−	0.902458i	−0.270606	−	0.0794570i
$130$	0.0571384	+	0.132654i	0.00501137	+	0.0116346i
$131$	8.18520	+	9.44623i	0.715145	+	0.825321i	0.990714	−	0.135960i	$-0.0434120\pi$
$131$	8.18520	+	9.44623i	0.715145	+	0.825321i	−0.275570	+	0.961281i	$0.588867\pi$
$132$	−0.655549	−	0.244507i	−0.0570582	−	0.0212816i
$133$	−2.23158	+	4.08683i	−0.193502	+	0.354373i
$134$	1.23402	−	2.70212i	0.106603	−	0.233427i
$135$	1.37852	−	1.76059i	0.118644	−	0.151527i
$136$	0.964425	+	1.50068i	0.0826988	+	0.128682i
$137$	−13.8113	+	13.8113i	−1.17997	+	1.17997i	−0.200225	+	0.979750i	$0.564167\pi$
$137$	−13.8113	+	13.8113i	−1.17997	+	1.17997i	−0.979750	+	0.200225i	$0.935833\pi$
$138$	−4.79185	+	0.195271i	−0.407910	+	0.0166226i
$139$			5.42731i			0.460338i	0.973151	+	0.230169i	$0.0739279\pi$
$139$			5.42731i			0.460338i	−0.973151	+	0.230169i	$0.926072\pi$
$140$	−8.18638	+	0.407329i	−0.691876	+	0.0344256i
$141$	−0.677916	+	4.71501i	−0.0570908	+	0.397075i
$142$	3.05316	−	1.13877i	0.256216	−	0.0955636i
$143$	0.0396659	+	0.0216592i	0.00331703	+	0.00181124i
$144$	−0.909632	+	0.415415i	−0.0758027	+	0.0346179i
$145$	6.10286	−	9.05821i	0.506815	−	0.752243i
$146$	−0.174832	−	1.21598i	−0.0144692	−	0.100636i
$147$	3.08471	+	5.64923i	0.254423	+	0.465940i
$148$	8.75761	−	0.626357i	0.719871	−	0.0514862i
$149$	−4.17879	−	2.68554i	−0.342340	−	0.220008i	0.358161	−	0.933660i	$-0.383404\pi$
$149$	−4.17879	−	2.68554i	−0.342340	−	0.220008i	−0.700501	+	0.713651i	$0.747040\pi$
$150$	4.99530	+	0.216772i	0.407864	+	0.0176993i
$151$	−0.973027	+	1.12293i	−0.0791838	+	0.0913830i	−0.793959	−	0.607971i	$-0.791984\pi$
$151$	−0.973027	+	1.12293i	−0.0791838	+	0.0913830i	0.714775	+	0.699354i	$0.246529\pi$
$152$	−1.11492	+	0.608791i	−0.0904318	+	0.0493795i
$153$	−1.06903	+	1.42805i	−0.0864256	+	0.115451i
$154$	−1.93825	+	1.67951i	−0.156189	+	0.135339i
$155$	2.06008	+	2.48432i	0.165470	+	0.199545i
$156$	0.0619776	−	0.0181983i	0.00496218	−	0.00145703i
$157$	4.68341	+	12.5567i	0.373777	+	1.00214i	0.978599	+	0.205775i	$0.0659714\pi$
$157$	4.68341	+	12.5567i	0.373777	+	1.00214i	−0.604822	+	0.796360i	$0.706756\pi$
$158$	13.3578	−	9.99953i	1.06269	−	0.795520i
$159$	9.93065	−	6.38204i	0.787552	−	0.506129i
$160$	−1.93885	−	1.11393i	−0.153280	−	0.0880642i
$161$	−7.78977	+	15.7594i	−0.613920	+	1.24202i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	2.02670	−	9.31660i	0.158743	−	0.729732i	−0.827099	−	0.562057i	$-0.810010\pi$
$163$	2.02670	−	9.31660i	0.158743	−	0.729732i	0.985842	−	0.167675i	$-0.0536261\pi$
$164$	−0.173775	−	0.0249850i	−0.0135695	−	0.00195100i
$165$	1.27248	−	0.910190i	0.0990622	−	0.0708582i
$166$	−4.05503	−	13.8101i	−0.314731	−	1.07188i
$167$	4.11399	−	11.0300i	0.318350	−	0.853529i	−0.674940	−	0.737873i	$-0.735830\pi$
$167$	4.11399	−	11.0300i	0.318350	−	0.853529i	0.993289	−	0.115656i	$-0.0368969\pi$
$168$	−0.261500	+	3.65625i	−0.0201752	+	0.282086i
$169$	12.8635	−	1.84950i	0.989504	−	0.142269i
$170$	−3.98789	−	0.0864867i	−0.305857	−	0.00663322i
$171$	−0.960030	−	0.831871i	−0.0734154	−	0.0636148i
$172$	−3.13004	+	0.680898i	−0.238663	+	0.0519180i
$173$	−19.7106	+	4.28778i	−1.49857	+	0.325994i	−0.885726	−	0.464209i	$-0.846339\pi$
$173$	−19.7106	+	4.28778i	−1.49857	+	0.325994i	−0.612845	+	0.790203i	$0.709975\pi$
$174$	−3.69153	−	3.19873i	−0.279854	−	0.242495i
$175$	9.47279	−	15.6901i	0.716076	−	1.18606i
$176$	−0.692542	+	0.0995725i	−0.0522023	+	0.00750556i
$177$	−0.273770	+	3.82780i	−0.0205778	+	0.287715i
$178$	5.49085	−	14.7215i	0.411557	−	1.10343i
$179$	0.0765394	+	0.260669i	0.00572082	+	0.0194833i	0.962304	−	0.271976i	$-0.0876773\pi$
$179$	0.0765394	+	0.260669i	0.00572082	+	0.0194833i	−0.956583	+	0.291460i	$0.905859\pi$
$180$	0.366140	−	2.20589i	0.0272905	−	0.164417i
$181$	−17.0596	−	2.45280i	−1.26803	−	0.182315i	−0.524727	−	0.851270i	$-0.675833\pi$
$181$	−17.0596	−	2.45280i	−1.26803	−	0.182315i	−0.743303	+	0.668955i	$0.766742\pi$
$182$	0.0503303	−	0.231364i	0.00373073	−	0.0171499i
$183$	−4.56942	−	4.56942i	−0.337782	−	0.337782i
$184$	−4.11213	+	2.46788i	−0.303150	+	0.181934i
$185$	−9.78032	+	17.0231i	−0.719063	+	1.25156i
$186$	1.21419	−	0.780315i	0.0890290	−	0.0572155i
$187$	−0.999154	+	0.747958i	−0.0730654	+	0.0546961i
$188$	1.66467	+	4.46315i	0.121409	+	0.325509i
$189$	−3.51711	+	1.03272i	−0.255832	+	0.0751190i
$190$	0.264021	−	2.82819i	0.0191541	−	0.205178i
$191$	17.9855	−	15.5845i	1.30138	−	1.12765i	0.317613	−	0.948220i	$-0.397119\pi$
$191$	17.9855	−	15.5845i	1.30138	−	1.12765i	0.983770	−	0.179434i	$-0.0574267\pi$
$192$	−0.599278	+	0.800541i	−0.0432491	+	0.0577741i
$193$	8.44398	−	4.61076i	0.607811	−	0.331890i	−0.145696	−	0.989329i	$-0.546542\pi$
$193$	8.44398	−	4.61076i	0.607811	−	0.331890i	0.753507	+	0.657439i	$0.228360\pi$
$194$	−0.245954	+	0.283846i	−0.0176585	+	0.0203789i
$195$	−0.0436878	+	0.137671i	−0.00312855	+	0.00985884i
$196$	5.41477	+	3.47986i	0.386769	+	0.248562i
$197$	−10.9280	+	0.781586i	−0.778588	+	0.0556857i	−0.454975	−	0.890504i	$-0.650352\pi$
$197$	−10.9280	+	0.781586i	−0.778588	+	0.0556857i	−0.323612	+	0.946190i	$0.604897\pi$
$198$	−0.335313	−	0.614080i	−0.0238296	−	0.0436407i
$199$	−2.53453	−	17.6280i	−0.179668	−	1.24962i	−0.857532	−	0.514430i	$-0.828003\pi$
$199$	−2.53453	−	17.6280i	−0.179668	−	1.24962i	0.677864	−	0.735187i	$-0.262906\pi$
$200$	4.48816	−	2.20374i	0.317361	−	0.155828i
$201$	2.70212	−	1.23402i	0.190593	−	0.0870408i
$202$	10.6324	+	5.80574i	0.748094	+	0.408490i
$203$	−16.7760	+	6.25712i	−1.17744	+	0.439164i
$204$	−0.253869	+	1.76570i	−0.0177744	+	0.123624i
$205$	0.263449	−	0.291039i	0.0184001	−	0.0203270i
$206$			0.126306i			0.00880017i
$207$	−3.74932	−	2.99042i	−0.260596	−	0.207849i
$208$	0.0456749	−	0.0456749i	0.00316699	−	0.00316699i
$209$	−0.480513	−	0.747692i	−0.0332378	−	0.0517190i
$210$	−6.45360	−	5.05310i	−0.445341	−	0.348697i
$211$	1.87502	−	4.10572i	0.129082	−	0.282649i	−0.834046	−	0.551695i	$-0.813981\pi$
$211$	1.87502	−	4.10572i	0.129082	−	0.282649i	0.963127	+	0.269046i	$0.0867084\pi$
$212$	5.65733	−	10.3606i	0.388547	−	0.711571i
$213$	3.05316	+	1.13877i	0.209199	+	0.0780273i
$214$	−9.13693	−	10.5446i	−0.624588	−	0.720813i
$215$	2.64802	−	6.65521i	0.180593	−	0.453881i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	−0.377427	−	5.27712i	−0.0256214	−	0.358234i
$218$	−2.74320	−	12.6103i	−0.185793	−	0.854076i
$219$	0.664171	−	1.03347i	0.0448805	−	0.0698355i
$220$	0.680618	−	1.40869i	0.0458873	−	0.0949737i
$221$	0.0324631	−	0.110559i	0.00218370	−	0.00743701i
$222$	7.02874	+	5.26165i	0.471738	+	0.353139i
$223$	−9.45233	−	0.676044i	−0.632975	−	0.0452712i	−0.248835	−	0.968546i	$-0.580048\pi$
$223$	−9.45233	−	0.676044i	−0.632975	−	0.0452712i	−0.384140	+	0.923275i	$0.625502\pi$
$224$	1.52274	+	3.33434i	0.101742	+	0.222785i
$225$	3.63324	+	3.43505i	0.242216	+	0.229003i
$226$	1.38831	+	0.634021i	0.0923492	+	0.0421744i
$227$	−5.79379	−	7.73960i	−0.384547	−	0.513695i	0.565945	−	0.824443i	$-0.308511\pi$
$227$	−5.79379	−	7.73960i	−0.384547	−	0.513695i	−0.950492	+	0.310748i	$0.899421\pi$
$228$	−1.24127	−	0.270022i	−0.0822052	−	0.0178827i
$229$	10.2972			0.680461			0.340230	−	0.940342i	$-0.389495\pi$
$229$	10.2972			0.680461			0.340230	+	0.940342i	$0.389495\pi$
$230$	0.561196	−	10.7091i	0.0370042	−	0.706138i
$231$	−2.56468			−0.168743
$232$	−4.77296	−	1.03829i	−0.313360	−	0.0681673i
$233$	2.85333	+	3.81161i	0.186928	+	0.249707i	0.884209	−	0.467091i	$-0.154698\pi$
$233$	2.85333	+	3.81161i	0.186928	+	0.249707i	−0.697281	+	0.716798i	$0.745607\pi$
$234$	0.0587569	+	0.0268334i	0.00384106	+	0.00175415i
$235$	−10.3565	−	2.48928i	−0.675586	−	0.162383i
$236$	1.59419	+	3.49078i	0.103773	+	0.227231i
$237$	16.6435	+	1.19036i	1.08111	+	0.0773225i
$238$	5.23465	+	3.91861i	0.339312	+	0.254006i
$239$	−0.804813	+	2.74094i	−0.0520590	+	0.177297i	−0.981419	−	0.191879i	$-0.938542\pi$
$239$	−0.804813	+	2.74094i	−0.0520590	+	0.177297i	0.929360	+	0.369176i	$0.120360\pi$
$240$	−0.735816	−	2.11153i	−0.0474967	−	0.136299i
$241$	−16.1357	+	25.1077i	−1.03939	+	1.61733i	−0.287816	+	0.957686i	$0.592929\pi$
$241$	−16.1357	+	25.1077i	−1.03939	+	1.61733i	−0.751579	+	0.659644i	$0.770707\pi$
$242$	2.23416	+	10.2703i	0.143617	+	0.660198i
$243$	−0.0713392	−	0.997452i	−0.00457641	−	0.0639866i
$244$	−6.20038	−	1.82060i	−0.396939	−	0.116552i
$245$	−13.2185	+	5.69362i	−0.844499	+	0.363752i
$246$	−0.114968	−	0.132681i	−0.00733011	−	0.00845940i
$247$	0.0768805	+	0.0286749i	0.00489179	+	0.00182454i
$248$	0.691707	−	1.26677i	0.0439235	−	0.0804398i
$249$	5.97914	−	13.0925i	0.378913	−	0.829703i
$250$	−1.52085	+	11.0764i	−0.0961868	+	0.700534i
$251$	13.8925	+	21.6171i	0.876884	+	1.36446i	0.930652	+	0.365905i	$0.119241\pi$
$251$	13.8925	+	21.6171i	0.876884	+	1.36446i	−0.0537676	+	0.998553i	$0.517123\pi$
$252$	−2.59196	+	2.59196i	−0.163278	+	0.163278i
$253$	−1.92753	−	2.74659i	−0.121183	−	0.172677i
$254$		−	1.80927i		−	0.113524i
$255$	−2.95721	−	2.67687i	−0.185187	−	0.167632i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−11.0889	+	4.13594i	−0.691706	+	0.257993i	−0.670638	−	0.741785i	$-0.733979\pi$
$257$	−11.0889	+	4.13594i	−0.691706	+	0.257993i	−0.0210682	+	0.999778i	$0.506707\pi$
$258$	−2.81142	−	1.53515i	−0.175031	−	0.0955743i
$259$	29.2754	−	13.3696i	1.81909	−	0.830749i
$260$	0.0276349	+	0.141768i	0.00171384	+	0.00879211i
$261$	−0.695149	−	4.83487i	−0.0430287	−	0.299271i
$262$	5.99021	+	10.9702i	0.370076	+	0.677744i
$263$	−5.73374	+	0.410085i	−0.353558	+	0.0252869i	−0.246989	−	0.969018i	$-0.579441\pi$
$263$	−5.73374	+	0.410085i	−0.353558	+	0.0252869i	−0.106569	+	0.994305i	$0.533987\pi$
$264$	−0.588594	−	0.378266i	−0.0362255	−	0.0232807i
$265$	12.1449	+	23.4359i	0.746055	+	1.43966i
$266$	−3.04930	+	3.51908i	−0.186964	+	0.215769i
$267$	13.7903	−	7.53006i	0.843951	−	0.460832i
$268$	1.78019	−	2.37806i	0.108742	−	0.145263i
$269$	−10.1700	+	8.81237i	−0.620077	+	0.537299i	−0.907257	−	0.420577i	$-0.861828\pi$
$269$	−10.1700	+	8.81237i	−0.620077	+	0.537299i	0.287180	+	0.957877i	$0.407282\pi$
$270$	1.72126	−	1.42733i	0.104753	−	0.0868644i
$271$	0.680288	−	0.199751i	0.0413245	−	0.0121340i	−0.261005	−	0.965337i	$-0.584054\pi$
$271$	0.680288	−	0.199751i	0.0413245	−	0.0121340i	0.302329	+	0.953203i	$0.402236\pi$
$272$	0.623394	+	1.67138i	0.0377988	+	0.101343i
$273$	0.189549	−	0.141894i	0.0114720	−	0.00858783i
$274$	−16.4314	+	10.5598i	−0.992658	+	0.637943i
$275$	1.76196	+	3.02220i	0.106250	+	0.182246i
$276$	−4.72385	−	0.827773i	−0.284343	−	0.0498261i
$277$	10.5853	+	10.5853i	0.636007	+	0.636007i	0.949568	−	0.313561i	$-0.101522\pi$
$277$	10.5853	+	10.5853i	0.636007	+	0.636007i	−0.313561	+	0.949568i	$0.601522\pi$
$278$	−1.15366	+	5.30327i	−0.0691917	+	0.318069i
$279$	1.42862	+	0.205405i	0.0855295	+	0.0122973i
$280$	−8.08588	−	1.34212i	−0.483224	−	0.0802070i
$281$	−1.88585	−	6.42262i	−0.112500	−	0.383141i	0.883924	−	0.467631i	$-0.154892\pi$
$281$	−1.88585	−	6.42262i	−0.112500	−	0.383141i	−0.996424	+	0.0844893i	$0.973074\pi$
$282$	−1.66467	+	4.46315i	−0.0991297	+	0.265777i
$283$	−1.96042	+	27.4103i	−0.116535	+	1.62937i	0.517230	+	0.855847i	$0.326963\pi$
$283$	−1.96042	+	27.4103i	−0.116535	+	1.62937i	−0.633765	+	0.773526i	$0.718491\pi$
$284$	3.22545	−	0.463750i	0.191395	−	0.0275185i
$285$	2.05160	−	1.96450i	0.121526	−	0.116367i
$286$	0.0341554	+	0.0295959i	0.00201965	+	0.00175004i
$287$	−0.628830	+	0.136794i	−0.0371186	+	0.00807467i
$288$	−0.977147	+	0.212565i	−0.0575789	+	0.0125255i
$289$	−10.4428	−	9.04877i	−0.614285	−	0.532281i
$290$	7.88885	−	7.55394i	0.463249	−	0.443583i
$291$	−0.371759	+	0.0534509i	−0.0217929	+	0.00313335i
$292$	0.0876394	−	1.22536i	0.00512871	−	0.0717087i
$293$	−9.27561	+	24.8689i	−0.541887	+	1.45285i	0.320815	+	0.947142i	$0.396043\pi$
$293$	−9.27561	+	24.8689i	−0.541887	+	1.45285i	−0.862702	+	0.505713i	$0.831229\pi$
$294$	1.81339	+	6.17583i	0.105759	+	0.360181i
$295$	−8.46527	−	1.40509i	−0.492867	−	0.0818077i
$296$	8.69062	+	1.24952i	0.505132	+	0.0726270i
$297$	0.148724	−	0.683674i	0.00862985	−	0.0396708i
$298$	−3.51244	−	3.51244i	−0.203470	−	0.203470i
$299$	0.294418	+	0.0963500i	0.0170266	+	0.00557206i
$300$	4.83506	+	1.27364i	0.279152	+	0.0735339i
$301$	−9.87781	+	6.34808i	−0.569347	+	0.365897i
$302$	−1.18949	+	0.890439i	−0.0684473	+	0.0512390i
$303$	4.23350	+	11.3504i	0.243208	+	0.652066i
$304$	−1.21885	+	0.357886i	−0.0699056	+	0.0205261i
$305$	11.1230	−	9.22360i	0.636903	−	0.528142i
$306$	−1.34815	+	1.16818i	−0.0770685	+	0.0667802i
$307$	−12.0791	+	16.1358i	−0.689391	+	0.920918i	−0.999557	−	0.0297643i	$-0.990524\pi$
$307$	−12.0791	+	16.1358i	−0.689391	+	0.920918i	0.310166	+	0.950682i	$0.399615\pi$
$308$	−2.25096	+	1.22912i	−0.128261	+	0.0700356i
$309$	−0.0827130	+	0.0954559i	−0.00470538	+	0.00543029i
$310$	1.48492	+	2.86545i	0.0843381	+	0.162747i
$311$	21.8311	+	14.0300i	1.23793	+	0.795567i	0.985106	−	0.171946i	$-0.0550055\pi$
$311$	21.8311	+	14.0300i	1.23793	+	0.795567i	0.252820	+	0.967513i	$0.418642\pi$
$312$	0.0644295	−	0.00460809i	0.00364760	−	0.000260882i
$313$	1.46325	+	2.67974i	0.0827078	+	0.151468i	0.915759	−	0.401727i	$-0.131590\pi$
$313$	1.46325	+	2.67974i	0.0827078	+	0.151468i	−0.833051	+	0.553195i	$0.813408\pi$
$314$	1.90726	+	13.2653i	0.107633	+	0.748604i
$315$	−1.56823	−	8.04509i	−0.0883595	−	0.453289i
$316$	15.1781	−	6.93161i	0.853835	−	0.389933i
$317$	−6.18054	−	3.37483i	−0.347134	−	0.189549i	0.296218	−	0.955120i	$-0.404275\pi$
$317$	−6.18054	−	3.37483i	−0.347134	−	0.189549i	−0.643351	+	0.765571i	$0.722456\pi$
$318$	11.0603	−	4.12528i	0.620231	−	0.231334i
$319$	0.486371	−	3.38278i	0.0272315	−	0.189399i
$320$	−1.65776	−	1.50061i	−0.0926716	−	0.0838866i
$321$		−	13.9525i		−	0.778752i
$322$	−10.9617	+	13.7435i	−0.610869	+	0.765893i
$323$	−1.60233	+	1.60233i	−0.0891560	+	0.0891560i
$324$	−0.540641	−	0.841254i	−0.0300356	−	0.0467363i
$325$	−0.297429	−	0.125880i	−0.0164984	−	0.00698256i
$326$	3.96077	−	8.67288i	0.219367	−	0.480346i
$327$	6.18481	−	11.3266i	0.342021	−	0.626364i
$328$	−0.164492	−	0.0613525i	−0.00908257	−	0.00338762i
$329$	11.4345	+	13.1962i	0.630406	+	0.727528i
$330$	1.43687	−	0.618905i	0.0790972	−	0.0340696i
$331$	−20.2753	−	5.95336i	−1.11443	−	0.327226i	−0.327860	−	0.944726i	$-0.606327\pi$
$331$	−20.2753	−	5.95336i	−1.11443	−	0.327226i	−0.786571	+	0.617500i	$0.788145\pi$
$332$	−1.02680	−	14.3565i	−0.0563528	−	0.787915i
$333$	1.86632	+	8.57933i	0.102274	+	0.470145i
$334$	6.36457	−	9.90346i	0.348254	−	0.541893i
$335$	2.18579	+	6.27244i	0.119422	+	0.342700i
$336$	−1.03272	+	3.51711i	−0.0563393	+	0.191874i
$337$	8.93629	+	6.68963i	0.486791	+	0.364407i	0.814303	−	0.580440i	$-0.197119\pi$
$337$	8.93629	+	6.68963i	0.486791	+	0.364407i	−0.327512	+	0.944847i	$0.606210\pi$
$338$	12.9627	+	0.927112i	0.705079	+	0.0504282i
$339$	0.634021	+	1.38831i	0.0344353	+	0.0754028i
$340$	−3.87837	−	0.932196i	−0.210334	−	0.0505554i
$341$	0.918578	+	0.419501i	0.0497438	+	0.0227172i
$342$	−0.761264	−	1.01693i	−0.0411644	−	0.0549892i
$343$	−2.01817	−	0.439026i	−0.108971	−	0.0237052i
$344$	−3.20324			−0.172707
$345$	7.43710	−	7.72590i	0.400400	−	0.415949i
$346$	−20.1716			−1.08443
$347$	−20.5639	−	4.47341i	−1.10393	−	0.240145i	−0.376560	−	0.926392i	$-0.622893\pi$
$347$	−20.5639	−	4.47341i	−1.10393	−	0.240145i	−0.727368	+	0.686247i	$0.759257\pi$
$348$	−2.92723	−	3.91031i	−0.156916	−	0.209615i
$349$	0.360700	+	0.164726i	0.0193078	+	0.00881760i	0.425046	−	0.905172i	$-0.360258\pi$
$349$	0.360700	+	0.164726i	0.0193078	+	0.00881760i	−0.405738	+	0.913990i	$0.632985\pi$
$350$	12.5915	−	13.3180i	0.673043	−	0.711875i
$351$	0.0268334	+	0.0587569i	0.00143226	+	0.00313621i
$352$	−0.697881	−	0.0499134i	−0.0371972	−	0.00266039i
$353$	−0.609085	−	0.455955i	−0.0324183	−	0.0242681i	0.582946	−	0.812511i	$-0.301900\pi$
$353$	−0.609085	−	0.455955i	−0.0324183	−	0.0242681i	−0.615364	+	0.788243i	$0.710991\pi$
$354$	−1.08117	+	3.68213i	−0.0574636	+	0.195703i
$355$	−3.16992	+	6.56084i	−0.168242	+	0.348213i
$356$	8.49466	−	13.2179i	0.450216	−	0.700550i
$357$	1.38994	+	6.38945i	0.0735634	+	0.338166i
$358$	0.0193810	+	0.270982i	0.00102432	+	0.0143218i
$359$	34.2969	+	10.0705i	1.81012	+	0.531500i	0.998604	−	0.0528266i	$-0.0168231\pi$
$359$	34.2969	+	10.0705i	1.81012	+	0.531500i	0.811519	+	0.584326i	$0.198641\pi$
$360$	0.826668	−	2.07765i	0.0435692	−	0.109502i
$361$	11.3856	+	13.1397i	0.599243	+	0.691564i
$362$	−16.1484	−	6.02302i	−0.848739	−	0.316563i
$363$	−5.03713	+	9.22482i	−0.264381	+	0.484177i
$364$	0.0983601	−	0.215379i	0.00515547	−	0.0112889i
$365$	2.16286	+	1.69350i	0.113209	+	0.0886419i
$366$	−3.49370	−	5.43630i	−0.182619	−	0.284160i
$367$	−6.36237	+	6.36237i	−0.332113	+	0.332113i	−0.853389	−	0.521275i	$-0.825456\pi$
$367$	−6.36237	+	6.36237i	−0.332113	+	0.332113i	0.521275	+	0.853389i	$0.325456\pi$
$368$	−4.54274	+	1.53738i	−0.236807	+	0.0801416i
$369$		−	0.175562i		−	0.00913937i
$370$	−13.1753	+	14.5551i	−0.684953	+	0.756684i
$371$	6.15807	−	42.8303i	0.319711	−	2.22364i
$372$	1.35231	−	0.504387i	0.0701142	−	0.0261513i
$373$	−19.2162	−	10.4928i	−0.994975	−	0.543297i	−0.102663	−	0.994716i	$-0.532736\pi$
$373$	−19.2162	−	10.4928i	−0.994975	−	0.543297i	−0.892312	+	0.451419i	$0.850918\pi$
$374$	−1.13531	+	0.518479i	−0.0587055	+	0.0268099i
$375$	−8.40289	+	7.37506i	−0.433923	+	0.380846i
$376$	0.677916	+	4.71501i	0.0349608	+	0.243158i
$377$	0.151211	+	0.276921i	0.00778774	+	0.0142622i
$378$	−3.65625	+	0.261500i	−0.188057	+	0.0134501i
$379$	6.42622	+	4.12988i	0.330093	+	0.212138i	0.695180	−	0.718835i	$-0.255325\pi$
$379$	6.42622	+	4.12988i	0.330093	+	0.212138i	−0.365087	+	0.930973i	$0.618961\pi$
$380$	0.859161	−	2.70743i	0.0440741	−	0.138888i
$381$	1.18482	−	1.36736i	0.0607002	−	0.0700517i
$382$	20.8872	−	11.4053i	1.06868	−	0.583544i
$383$	13.9200	−	18.5950i	0.711280	−	0.950159i	−0.288694	−	0.957421i	$-0.593221\pi$
$383$	13.9200	−	18.5950i	0.711280	−	0.950159i	0.999974	+	0.00726281i	$0.00231184\pi$
$384$	−0.755750	+	0.654861i	−0.0385667	+	0.0334182i
$385$	0.533046	−	5.70997i	0.0271665	−	0.291007i
$386$	9.23110	−	2.71050i	0.469851	−	0.137961i
$387$	−1.11942	−	3.00128i	−0.0569032	−	0.152563i
$388$	−0.300669	+	0.225078i	−0.0152641	+	0.0114266i
$389$	−6.99937	+	4.49822i	−0.354882	+	0.228069i	−0.705919	−	0.708293i	$-0.749466\pi$
$389$	−6.99937	+	4.49822i	−0.354882	+	0.228069i	0.351037	+	0.936362i	$0.385829\pi$
$390$	−0.0719536	+	0.125238i	−0.00364351	+	0.00634170i
$391$	−5.79802	+	6.29064i	−0.293219	+	0.318132i
$392$	4.55133	+	4.55133i	0.229877	+	0.229877i
$393$	−2.65689	+	12.2135i	−0.134022	+	0.616090i
$394$	−10.8444	−	1.55919i	−0.546333	−	0.0785508i
$395$	−6.10941	+	36.8074i	−0.307398	+	1.85198i
$396$	−0.197118	−	0.671322i	−0.00990555	−	0.0337352i
$397$	4.64059	−	12.4419i	0.232904	−	0.624441i	−0.766946	−	0.641711i	$-0.778225\pi$
$397$	4.64059	−	12.4419i	0.232904	−	0.624441i	0.999851	+	0.0172701i	$0.00549752\pi$
$398$	1.27050	−	17.7639i	0.0636844	−	0.890425i
$399$	−4.60901	+	0.662676i	−0.230739	+	0.0331753i
$400$	4.85403	−	1.19935i	0.242701	−	0.0599674i
$401$	−13.6135	−	11.7962i	−0.679826	−	0.589073i	0.244972	−	0.969530i	$-0.421221\pi$
$401$	−13.6135	−	11.7962i	−0.679826	−	0.589073i	−0.924799	+	0.380457i	$0.875767\pi$
$402$	2.90267	−	0.631438i	0.144772	−	0.0314933i
$403$	−0.0910991	+	0.0198174i	−0.00453797	+	0.000987175i
$404$	9.15534	+	7.93314i	0.455495	+	0.394689i
$405$	2.23554	+	0.0484830i	0.111085	+	0.00240914i
$406$	−17.7227	+	2.54813i	−0.879561	+	0.126462i
$407$	−0.438239	+	6.12738i	−0.0217227	+	0.303723i
$408$	−0.623394	+	1.67138i	−0.0308626	+	0.0827458i
$409$	9.70664	+	33.0578i	0.479962	+	1.63460i	0.742620	+	0.669713i	$0.233583\pi$
$409$	9.70664	+	33.0578i	0.479962	+	1.63460i	−0.262658	+	0.964889i	$0.584599\pi$
$410$	0.319293	−	0.228388i	0.0157688	−	0.0112793i
$411$	−19.3333	−	2.77970i	−0.953639	−	0.137113i
$412$	−0.0268483	+	0.123420i	−0.00132272	+	0.00608045i
$413$	9.94687	+	9.94687i	0.489453	+	0.489453i
$414$	−3.02797	−	3.71906i	−0.148817	−	0.182782i
$415$	27.9062	+	16.0330i	1.36986	+	0.787031i
$416$	0.0543400	−	0.0349222i	0.00266424	−	0.00171220i
$417$	−4.34478	+	3.25246i	−0.212765	+	0.159274i
$418$	−0.310598	−	0.832746i	−0.0151918	−	0.0407309i
$419$	9.86966	−	2.89799i	0.482164	−	0.141576i	−0.0316123	−	0.999500i	$-0.510064\pi$
$419$	9.86966	−	2.89799i	0.482164	−	0.141576i	0.513777	+	0.857924i	$0.328246\pi$
$420$	−5.23200	−	6.30943i	−0.255295	−	0.307869i
$421$	26.3597	−	22.8408i	1.28469	−	1.11319i	0.297319	−	0.954778i	$-0.403907\pi$
$421$	26.3597	−	22.8408i	1.28469	−	1.11319i	0.987373	−	0.158414i	$-0.0506380\pi$
$422$	2.70490	−	3.61333i	0.131673	−	0.175894i
$423$	−4.18082	+	2.28290i	−0.203278	+	0.110998i
$424$	7.73036	−	8.92131i	0.375419	−	0.433257i
$425$	6.57438	−	6.02752i	0.318904	−	0.292378i
$426$	2.74133	+	1.76174i	0.132818	+	0.0853567i
$427$	−23.6272	+	1.68985i	−1.14340	+	0.0817776i
$428$	−6.68671	−	12.2458i	−0.323214	−	0.591923i
$429$	0.00643179	+	0.0447341i	0.000310530	+	0.00215978i
$430$	4.00217	−	5.94024i	0.193002	−	0.286464i
$431$	30.3613	−	13.8655i	1.46245	−	0.667879i	0.484134	−	0.874994i	$-0.339135\pi$
$431$	30.3613	−	13.8655i	1.46245	−	0.667879i	0.978317	+	0.207115i	$0.0664073\pi$
$432$	−0.877679	−	0.479249i	−0.0422274	−	0.0230579i
$433$	−34.1977	+	12.7551i	−1.64344	+	0.612970i	−0.989623	−	0.143688i	$-0.954104\pi$
$433$	−34.1977	+	12.7551i	−1.64344	+	0.612970i	−0.653812	+	0.756657i	$0.726831\pi$
$434$	0.752931	−	5.23675i	0.0361419	−	0.251372i
$435$	10.9088	−	0.542787i	0.523036	−	0.0260246i
$436$		−	12.9052i		−	0.618047i
$437$	−4.17367	−	4.43789i	−0.199654	−	0.212293i
$438$	0.868673	−	0.868673i	0.0415068	−	0.0415068i
$439$	−0.142542	−	0.221800i	−0.00680316	−	0.0105859i	0.837835	−	0.545923i	$-0.183821\pi$
$439$	−0.142542	−	0.221800i	−0.00680316	−	0.0105859i	−0.844638	+	0.535337i	$0.820185\pi$
$440$	0.964502	−	1.23182i	0.0459808	−	0.0587247i
$441$	−2.67384	+	5.85489i	−0.127326	+	0.278804i
$442$	0.0552222	−	0.101132i	0.00262665	−	0.00481036i
$443$	−20.9351	−	7.80841i	−0.994659	−	0.370989i	−0.201159	−	0.979559i	$-0.564471\pi$
$443$	−20.9351	−	7.80841i	−0.994659	−	0.370989i	−0.793500	+	0.608570i	$0.791743\pi$
$444$	5.74967	+	6.63547i	0.272867	+	0.314905i
$445$	13.8986	+	32.2675i	0.658859	+	1.52963i
$446$	−9.09261	−	2.66983i	−0.430548	−	0.126420i
$447$	−0.354366	−	4.95468i	−0.0167609	−	0.234348i
$448$	0.779177	+	3.58182i	0.0368127	+	0.169225i
$449$	−14.5325	+	22.6130i	−0.685830	+	1.06717i	0.307464	+	0.951560i	$0.400519\pi$
$449$	−14.5325	+	22.6130i	−0.685830	+	1.06717i	−0.993294	+	0.115613i	$0.963117\pi$
$450$	2.82004	+	4.12885i	0.132938	+	0.194636i
$451$	0.0346063	−	0.117858i	0.00162955	−	0.00554973i
$452$	1.22181	+	0.914639i	0.0574693	+	0.0430210i
$453$	−1.48207	−	0.106000i	−0.0696336	−	0.00498029i
$454$	−4.01621	−	8.79428i	−0.188490	−	0.412736i
$455$	0.276516	+	0.451500i	0.0129633	+	0.0211666i
$456$	−1.15551	−	0.527703i	−0.0541116	−	0.0247119i
$457$	14.0998	+	18.8351i	0.659559	+	0.881068i	0.998208	−	0.0598449i	$-0.0190606\pi$
$457$	14.0998	+	18.8351i	0.659559	+	0.881068i	−0.338648	+	0.940913i	$0.609970\pi$
$458$	10.0619	+	2.18884i	0.470162	+	0.102278i
$459$	−1.78386			−0.0832633
$460$	2.82476	−	10.3451i	0.131705	−	0.482342i
$461$	18.2160			0.848402			0.424201	−	0.905568i	$-0.360555\pi$
$461$	18.2160			0.848402			0.424201	+	0.905568i	$0.360555\pi$
$462$	−2.50607	−	0.545162i	−0.116593	−	0.0253632i
$463$	11.4102	+	15.2423i	0.530278	+	0.708369i	0.983066	−	0.183249i	$-0.0586616\pi$
$463$	11.4102	+	15.2423i	0.530278	+	0.708369i	−0.452788	+	0.891618i	$0.649571\pi$
$464$	−4.44318	−	2.02913i	−0.206269	−	0.0942001i
$465$	−0.754239	+	3.13798i	−0.0349770	+	0.145520i
$466$	1.97791	+	4.33102i	0.0916249	+	0.200631i
$467$	−1.88999	−	0.135175i	−0.0874582	−	0.00625514i	0.0275415	−	0.999621i	$-0.491232\pi$
$467$	−1.88999	−	0.135175i	−0.0874582	−	0.00625514i	−0.115000	+	0.993366i	$0.536687\pi$
$468$	0.0517102	+	0.0387098i	0.00239031	+	0.00178936i
$469$	3.06775	−	10.4478i	0.141655	−	0.482434i
$470$	−9.59073	−	4.63383i	−0.442387	−	0.213743i
$471$	−7.24551	+	11.2742i	−0.333855	+	0.519489i
$472$	0.815736	+	3.74988i	0.0375473	+	0.172602i
$473$	−0.159885	−	2.23548i	−0.00735151	−	0.102788i
$474$	16.0101	+	4.70098i	0.735367	+	0.215923i
$475$	3.94734	+	4.97596i	0.181116	+	0.228313i
$476$	4.28206	+	4.94176i	0.196268	+	0.226505i
$477$	11.0603	+	4.12528i	0.506416	+	0.188884i
$478$	−1.36905	+	2.50723i	−0.0626188	+	0.114678i
$479$	−3.13799	+	6.87123i	−0.143378	+	0.313955i	−0.967674	−	0.252205i	$-0.918844\pi$
$479$	−3.13799	+	6.87123i	−0.143378	+	0.313955i	0.824295	+	0.566160i	$0.191572\pi$
$480$	−0.270161	−	2.21969i	−0.0123311	−	0.101314i
$481$	−0.306616	−	0.477104i	−0.0139805	−	0.0217541i
$482$	−21.1040	+	21.1040i	−0.961262	+	0.961262i
$483$	−17.2843	+	3.20825i	−0.786464	+	0.145981i
$484$			10.5105i			0.477749i
$485$	−0.0417355	−	0.838789i	−0.00189511	−	0.0380875i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	−36.9168	+	13.7693i	−1.67286	+	0.623945i	−0.993906	−	0.110233i	$-0.964840\pi$
$487$	−36.9168	+	13.7693i	−1.67286	+	0.623945i	−0.678956	+	0.734179i	$0.737567\pi$
$488$	−5.67169	−	3.09698i	−0.256745	−	0.140193i
$489$	8.67288	−	3.96077i	0.392201	−	0.179112i
$490$	−14.1267	+	2.75371i	−0.638178	+	0.124400i
$491$	−2.52212	−	17.5417i	−0.113821	−	0.791646i	−0.964143	−	0.265382i	$-0.914502\pi$
$491$	−2.52212	−	17.5417i	−0.113821	−	0.791646i	0.850322	−	0.526263i	$-0.176407\pi$
$492$	−0.0841377	−	0.154087i	−0.00379322	−	0.00694676i
$493$	−8.69120	+	0.621607i	−0.391432	+	0.0279958i
$494$	0.0690282	+	0.0443618i	0.00310573	+	0.00199593i
$495$	1.49121	+	0.473213i	0.0670250	+	0.0212693i
$496$	0.945171	−	1.09079i	0.0424394	−	0.0489777i
$497$	10.4837	−	5.72452i	0.470257	−	0.256780i
$498$	8.62551	−	11.5223i	0.386518	−	0.516328i
$499$	−32.2157	+	27.9151i	−1.44217	+	1.24965i	−0.525037	+	0.851079i	$0.675949\pi$
$499$	−32.2157	+	27.9151i	−1.44217	+	1.24965i	−0.917137	+	0.398572i	$0.869506\pi$
$500$	−3.84055	+	10.5000i	−0.171755	+	0.469575i
$501$	11.2954	−	3.31663i	0.504642	−	0.148176i
$502$	8.97993	+	24.0761i	0.400794	+	1.07457i
$503$	31.5546	−	23.6215i	1.40695	−	1.05323i	0.417449	−	0.908700i	$-0.362924\pi$
$503$	31.5546	−	23.6215i	1.40695	−	1.05323i	0.989501	−	0.144529i	$-0.0461666\pi$
$504$	−3.08369	+	1.98177i	−0.137359	+	0.0882749i
$505$	−26.1504	+	7.06631i	−1.16368	+	0.314447i
$506$	−1.29965	−	3.09355i	−0.0577766	−	0.137525i
$507$	9.18944	+	9.18944i	0.408117	+	0.408117i
$508$	0.384588	−	1.76792i	0.0170633	−	0.0784389i
$509$	−18.5355	−	2.66500i	−0.821571	−	0.118124i	−0.281305	−	0.959618i	$-0.590767\pi$
$509$	−18.5355	−	2.66500i	−0.821571	−	0.118124i	−0.540266	+	0.841494i	$0.681676\pi$
$510$	−2.32061	−	3.24430i	−0.102759	−	0.143660i
$511$	−1.26868	−	4.32073i	−0.0561231	−	0.191138i
$512$	−0.349464	+	0.936950i	−0.0154443	+	0.0414077i
$513$	0.0906223	−	1.26707i	0.00400107	−	0.0559423i
$514$	−11.7146	+	1.68431i	−0.516710	+	0.0742917i
$515$	−0.195331	−	0.203991i	−0.00860729	−	0.00898891i
$516$	−2.42085	−	2.09768i	−0.106572	−	0.0923451i
$517$	−3.25668	+	0.708447i	−0.143228	+	0.0311574i
$518$	31.4483	−	6.84116i	1.38176	−	0.300583i
$519$	−15.2447	−	13.2096i	−0.669167	−	0.579837i
$520$	−0.00313171	+	0.144403i	−0.000137335	+	0.00633248i
$521$	−13.1916	+	1.89667i	−0.577937	+	0.0830947i	−0.425083	−	0.905154i	$-0.639755\pi$
$521$	−13.1916	+	1.89667i	−0.577937	+	0.0830947i	−0.152853	+	0.988249i	$0.548846\pi$
$522$	0.348463	−	4.87214i	0.0152518	−	0.213248i
$523$	2.14748	−	5.75761i	0.0939026	−	0.251763i	−0.881504	−	0.472177i	$-0.843468\pi$
$523$	2.14748	−	5.75761i	0.0939026	−	0.251763i	0.975406	+	0.220414i	$0.0707410\pi$
$524$	3.52142	+	11.9928i	0.153834	+	0.523910i
$525$	18.2374	−	1.81938i	0.795946	−	0.0794042i
$526$	−5.68988	−	0.818081i	−0.248091	−	0.0356700i
$527$	0.547285	−	2.51583i	0.0238401	−	0.109591i
$528$	−0.494737	−	0.494737i	−0.0215306	−	0.0215306i
$529$	−16.4262	−	16.0991i	−0.714182	−	0.699960i
$530$	6.88568	+	25.4819i	0.299095	+	1.10686i
$531$	−3.22838	+	2.07475i	−0.140100	+	0.0900366i
$532$	−3.72765	+	2.79048i	−0.161614	+	0.120983i
$533$	0.00396301	+	0.0106252i	0.000171657	+	0.000460230i
$534$	15.0757	−	4.42664i	0.652391	−	0.191559i
$535$	31.0636	+	2.89990i	1.34300	+	0.125374i
$536$	2.24500	−	1.94530i	0.0969692	−	0.0840243i
$537$	−0.162808	+	0.217486i	−0.00702569	+	0.00938522i
$538$	−11.8108	+	6.44918i	−0.509200	+	0.278044i
$539$	−2.94911	+	3.40346i	−0.127027	+	0.146597i
$540$	1.98532	−	1.02883i	0.0854347	−	0.0442737i
$541$	25.4077	+	16.3286i	1.09236	+	0.702019i	0.957381	−	0.288828i	$-0.0932657\pi$
$541$	25.4077	+	16.3286i	1.09236	+	0.702019i	0.134983	+	0.990848i	$0.456902\pi$
$542$	0.707201	−	0.0505800i	0.0303769	−	0.00217260i
$543$	−8.25987	−	15.1268i	−0.354465	−	0.649154i
$544$	0.253869	+	1.76570i	0.0108846	+	0.0757037i
$545$	23.9320	+	16.1239i	1.02513	+	0.690673i
$546$	0.215379	−	0.0983601i	0.00921735	−	0.00420942i
$547$	11.2569	+	6.14671i	0.481309	+	0.262814i	0.701536	−	0.712634i	$-0.252498\pi$
$547$	11.2569	+	6.14671i	0.481309	+	0.262814i	−0.220227	+	0.975449i	$0.570680\pi$
$548$	−18.3006	+	6.82576i	−0.781761	+	0.291582i
$549$	0.919659	−	6.39637i	0.0392501	−	0.272990i
$550$	1.07928	+	3.32767i	0.0460208	+	0.141892i
$551$		−	6.20490i		−	0.264338i
$552$	−4.43994	−	1.81298i	−0.188977	−	0.0771657i
$553$	43.2494	−	43.2494i	1.83915	−	1.83915i
$554$	8.09330	+	12.5934i	0.343851	+	0.535043i
$555$	−19.4888	+	2.37201i	−0.827254	+	0.100686i
$556$	−2.25458	+	4.93685i	−0.0956157	+	0.209369i
$557$	19.4568	−	35.6325i	0.824413	−	1.50980i	−0.0355066	−	0.999369i	$-0.511304\pi$
$557$	19.4568	−	35.6325i	0.824413	−	1.50980i	0.859919	−	0.510430i	$-0.170514\pi$
$558$	1.35231	+	0.504387i	0.0572480	+	0.0213524i
$559$	0.135498	+	0.156373i	0.00573094	+	0.00661385i
$560$	−7.61581	−	3.03023i	−0.321827	−	0.128050i
$561$	−1.19754	−	0.351630i	−0.0505602	−	0.0148458i
$562$	−0.477528	−	6.67671i	−0.0201433	−	0.281640i
$563$	−0.771449	−	3.54629i	−0.0325127	−	0.149458i	0.958029	−	0.286672i	$-0.0925490\pi$
$563$	−0.771449	−	3.54629i	−0.0325127	−	0.149458i	−0.990541	+	0.137214i	$0.956185\pi$
$564$	−2.57534	+	4.00731i	−0.108441	+	0.168738i
$565$	−3.22270	+	1.12303i	−0.135580	+	0.0472461i
$566$	−7.74210	+	26.3672i	−0.325425	+	1.10829i
$567$	−2.93446	−	2.19671i	−0.123236	−	0.0922530i
$568$	3.25032	+	0.232467i	0.136380	+	0.00975411i
$569$	2.05531	+	4.50051i	0.0861632	+	0.188671i	0.947809	−	0.318839i	$-0.103293\pi$
$569$	2.05531	+	4.50051i	0.0861632	+	0.188671i	−0.861646	+	0.507511i	$0.830566\pi$
$570$	2.42230	−	1.48351i	0.101459	−	0.0621373i
$571$	−20.4125	−	9.32207i	−0.854236	−	0.390116i	−0.0603456	−	0.998178i	$-0.519220\pi$
$571$	−20.4125	−	9.32207i	−0.854236	−	0.390116i	−0.793890	+	0.608061i	$0.791948\pi$
$572$	0.0270838	+	0.0361798i	0.00113243	+	0.00151275i
$573$	23.2543	+	5.05867i	0.971463	+	0.211329i
$574$	−0.643537			−0.0268607
$575$	15.6551	+	18.1636i	0.652863	+	0.757476i
$576$	−1.00000			−0.0416667
$577$	−20.6552	−	4.49327i	−0.859889	−	0.187057i	−0.239061	−	0.971005i	$-0.576840\pi$
$577$	−20.6552	−	4.49327i	−0.859889	−	0.187057i	−0.620827	+	0.783947i	$0.713203\pi$
$578$	−8.28073	−	11.0618i	−0.344433	−	0.460109i
$579$	8.75140	+	3.99663i	0.363696	+	0.166094i
$580$	9.31427	−	5.70441i	0.386754	−	0.236863i
$581$	−21.9171	−	47.9917i	−0.909274	−	1.99103i
$582$	−0.374625	−	0.0267937i	−0.0155287	−	0.00111064i
$583$	6.61186	+	4.94957i	0.273835	+	0.204990i
$584$	0.346105	−	1.17873i	0.0143219	−	0.0487761i
$585$	−0.136393	+	0.0475294i	−0.00563914	+	0.00196510i
$586$	−14.3499	+	22.3289i	−0.592789	+	0.922397i
$587$	−0.456064	−	2.09649i	−0.0188238	−	0.0865315i	0.966777	−	0.255623i	$-0.0822804\pi$
$587$	−0.456064	−	2.09649i	−0.0188238	−	0.0865315i	−0.985600	+	0.169091i	$0.945917\pi$
$588$	0.459178	+	6.42015i	0.0189362	+	0.264763i
$589$	1.75918	+	0.516542i	0.0724857	+	0.0212837i
$590$	−7.97314	−	3.17240i	−0.328249	−	0.130606i
$591$	−7.17460	−	8.27993i	−0.295123	−	0.340591i
$592$	8.22640	+	3.06829i	0.338103	+	0.126106i
$593$	−12.6542	+	23.1745i	−0.519647	+	0.951662i	0.477676	+	0.878536i	$0.341479\pi$
$593$	−12.6542	+	23.1745i	−0.519647	+	0.951662i	−0.997323	+	0.0731260i	$0.976702\pi$
$594$	0.290651	−	0.636436i	0.0119255	−	0.0261133i
$595$	−14.5143	+	1.76655i	−0.595028	+	0.0724217i
$596$	−2.68554	−	4.17879i	−0.110004	−	0.171170i
$597$	12.5931	−	12.5931i	0.515400	−	0.515400i
$598$	0.267209	+	0.156731i	0.0109270	+	0.00640921i
$599$		−	16.4009i		−	0.670124i	−0.942196	−	0.335062i	$-0.891243\pi$
$599$		−	16.4009i		−	0.670124i	0.942196	−	0.335062i	$-0.108757\pi$
$600$	4.45383	+	2.27230i	0.181827	+	0.0927664i
$601$	−2.22779	+	15.4946i	−0.0908735	+	0.632039i	0.892581	+	0.450886i	$0.148892\pi$
$601$	−2.22779	+	15.4946i	−0.0908735	+	0.632039i	−0.983455	+	0.181153i	$0.942017\pi$
$602$	−11.0015	+	4.10333i	−0.448386	+	0.167239i
$603$	2.60720	+	1.42364i	0.106173	+	0.0579750i
$604$	−1.35158	+	0.617246i	−0.0549950	+	0.0251154i
$605$	−19.4911	−	13.1319i	−0.792426	−	0.533888i
$606$	1.72404	+	11.9909i	0.0700342	+	0.487099i
$607$	−16.8071	−	30.7800i	−0.682181	−	1.24932i	−0.957629	−	0.288005i	$-0.907008\pi$
$607$	−16.8071	−	30.7800i	−0.682181	−	1.24932i	0.275448	−	0.961316i	$-0.411174\pi$
$608$	−1.26707	+	0.0906223i	−0.0513863	+	0.00367522i
$609$	−15.0626	−	9.68012i	−0.610366	−	0.392258i
$610$	12.8294	−	6.64844i	0.519449	−	0.269187i
$611$	0.201496	−	0.232539i	0.00815168	−	0.00940753i
$612$	−1.56565	+	0.854911i	−0.0632878	+	0.0345577i
$613$	7.35330	−	9.82285i	0.296997	−	0.396741i	−0.627076	−	0.778958i	$-0.715748\pi$
$613$	7.35330	−	9.82285i	0.296997	−	0.396741i	0.924073	+	0.382217i	$0.124839\pi$
$614$	−15.2330	+	13.1994i	−0.614752	+	0.532686i
$615$	0.390868	+	0.0364889i	0.0157613	+	0.00147138i
$616$	−2.46079	+	0.722553i	−0.0991481	+	0.0291125i
$617$	−11.6698	−	31.2881i	−0.469810	−	1.25961i	−0.928606	−	0.371068i	$-0.878992\pi$
$617$	−11.6698	−	31.2881i	−0.469810	−	1.25961i	0.458795	−	0.888542i	$-0.348281\pi$
$618$	−0.101113	+	0.0756925i	−0.00406737	+	0.00304480i
$619$	−4.65009	+	2.98843i	−0.186903	+	0.120115i	−0.630746	−	0.775989i	$-0.717251\pi$
$619$	−4.65009	+	2.98843i	−0.186903	+	0.120115i	0.443843	+	0.896104i	$0.353615\pi$
$620$	0.841895	+	3.11561i	0.0338113	+	0.125126i
$621$	0.147073	−	4.79358i	0.00590186	−	0.192360i
$622$	18.3499	+	18.3499i	0.735763	+	0.735763i
$623$	12.2426	−	56.2783i	0.490489	−	2.25474i
$624$	0.0639366	+	0.00919270i	0.00255951	+	0.000368002i
$625$	−14.6733	−	20.2409i	−0.586931	−	0.809637i
$626$	0.860190	+	2.92954i	0.0343801	+	0.117088i
$627$	0.310598	−	0.832746i	0.0124041	−	0.0332567i
$628$	−0.956066	+	13.3676i	−0.0381512	+	0.533423i
$629$	15.5028	−	2.22897i	0.618137	−	0.0888747i
$630$	0.177719	−	8.19458i	0.00708049	−	0.326480i
$631$	−19.2673	−	16.6952i	−0.767021	−	0.664627i	0.180768	−	0.983526i	$-0.442142\pi$
$631$	−19.2673	−	16.6952i	−0.767021	−	0.664627i	−0.947789	+	0.318899i	$0.896687\pi$
$632$	16.3047	−	3.54686i	0.648564	−	0.141087i
$633$	4.41045	−	0.959436i	0.175300	−	0.0381341i
$634$	−5.32192	−	4.61147i	−0.211361	−	0.183145i
$635$	2.79801	+	2.92206i	0.111036	+	0.115958i
$636$	11.6844	−	1.67997i	0.463318	−	0.0666150i
$637$	0.0296602	−	0.414704i	0.00117518	−	0.0164312i
$638$	1.19432	−	3.20209i	0.0472835	−	0.126772i
$639$	0.918060	+	3.12662i	0.0363179	+	0.123687i
$640$	−1.30090	−	1.81870i	−0.0514225	−	0.0718904i
$641$	−15.0941	−	2.17021i	−0.596182	−	0.0857181i	−0.162383	−	0.986728i	$-0.551918\pi$
$641$	−15.0941	−	2.17021i	−0.596182	−	0.0857181i	−0.433799	+	0.901010i	$0.642827\pi$
$642$	2.96581	−	13.6336i	0.117051	−	0.538076i
$643$	21.8816	+	21.8816i	0.862928	+	0.862928i	0.991677	−	0.128749i	$-0.0410963\pi$
$643$	21.8816	+	21.8816i	0.862928	+	0.862928i	−0.128749	+	0.991677i	$0.541096\pi$
$644$	−13.6325	+	11.0993i	−0.537197	+	0.437374i
$645$	6.91467	−	1.86847i	0.272265	−	0.0735709i
$646$	−1.90631	+	1.22511i	−0.0750028	+	0.0482014i
$647$	22.3881	−	16.7595i	0.880168	−	0.658886i	−0.0605168	−	0.998167i	$-0.519275\pi$
$647$	22.3881	−	16.7595i	0.880168	−	0.658886i	0.940685	+	0.339282i	$0.110184\pi$
$648$	−0.349464	−	0.936950i	−0.0137282	−	0.0368069i
$649$	−2.57625	+	0.756456i	−0.101127	+	0.0296935i
$650$	−0.263874	−	0.186226i	−0.0103500	−	0.00730439i
$651$	3.99837	−	3.46461i	0.156709	−	0.135789i
$652$	5.71381	−	7.63275i	0.223770	−	0.298922i
$653$	35.1929	−	19.2168i	1.37721	−	0.752011i	0.391451	−	0.920199i	$-0.371973\pi$
$653$	35.1929	−	19.2168i	1.37721	−	0.752011i	0.985755	+	0.168187i	$0.0537914\pi$
$654$	8.45111	−	9.75311i	0.330465	−	0.381377i
$655$	−26.6398	−	8.45373i	−1.04090	−	0.330314i
$656$	−0.147692	−	0.0949157i	−0.00576639	−	0.00370584i
$657$	1.22536	−	0.0876394i	0.0478058	−	0.00341914i
$658$	8.36818	+	15.3252i	0.326225	+	0.597437i
$659$	−5.16449	−	35.9198i	−0.201180	−	1.39924i	−0.800790	−	0.598945i	$-0.795587\pi$
$659$	−5.16449	−	35.9198i	−0.201180	−	1.39924i	0.599610	−	0.800292i	$-0.295322\pi$
$660$	1.53559	−	0.299333i	0.0597728	−	0.0116515i
$661$	−27.2956	+	12.4655i	−1.06168	+	0.484852i	−0.868180	−	0.496249i	$-0.834710\pi$
$661$	−27.2956	+	12.4655i	−1.06168	+	0.484852i	−0.193497	+	0.981101i	$0.561983\pi$
$662$	−18.5465	−	10.1271i	−0.720828	−	0.393602i
$663$	0.107962	−	0.0402676i	0.00419288	−	0.00156386i
$664$	2.04836	−	14.2467i	0.0794919	−	0.552878i
$665$	−0.517431	−	10.3992i	−0.0200651	−	0.403263i
$666$			8.77998i			0.340217i
$667$	−0.953819	−	23.4062i	−0.0369320	−	0.906293i
$668$	8.32425	−	8.32425i	0.322075	−	0.322075i
$669$	−5.12337	−	7.97212i	−0.198081	−	0.308220i
$670$	0.802531	+	6.59372i	0.0310045	+	0.254738i
$671$	1.87823	−	4.11274i	0.0725081	−	0.158771i
$672$	−1.75673	+	3.21721i	−0.0677673	+	0.124107i
$673$	−22.4369	−	8.36853i	−0.864879	−	0.322583i	−0.122423	−	0.992478i	$-0.539066\pi$
$673$	−22.4369	−	8.36853i	−0.864879	−	0.322583i	−0.742456	+	0.669895i	$0.766339\pi$
$674$	7.31009	+	8.43629i	0.281574	+	0.324954i
$675$	−0.572580	+	4.96711i	−0.0220386	+	0.191184i
$676$	12.4694	+	3.66135i	0.479593	+	0.140821i
$677$	−1.05630	−	14.7689i	−0.0405967	−	0.567616i	−0.976522	−	0.215418i	$-0.930889\pi$
$677$	−1.05630	−	14.7689i	−0.0405967	−	0.567616i	0.935925	−	0.352199i	$-0.114566\pi$
$678$	0.324425	+	1.49136i	0.0124595	+	0.0572752i
$679$	−0.744316	+	1.15818i	−0.0285642	+	0.0444468i
$680$	−3.59158	−	1.73530i	−0.137731	−	0.0665457i
$681$	2.72378	−	9.27634i	0.104375	−	0.355470i
$682$	0.808414	+	0.605171i	0.0309558	+	0.0231732i
$683$	4.48242	+	0.320589i	0.171515	+	0.0122670i	0.156833	−	0.987625i	$-0.449872\pi$
$683$	4.48242	+	0.320589i	0.171515	+	0.0122670i	0.0146825	+	0.999892i	$0.495326\pi$
$684$	−0.527703	−	1.15551i	−0.0201772	−	0.0441819i
$685$	10.2069	−	42.4656i	0.389987	−	1.62253i
$686$	−1.87873	−	0.857986i	−0.0717301	−	0.0327581i
$687$	6.17091	+	8.24337i	0.235435	+	0.314504i
$688$	−3.13004	−	0.680898i	−0.119332	−	0.0259590i
$689$	−0.762506			−0.0290492
$690$	8.90940	−	5.96847i	0.339175	−	0.227216i
$691$	18.9763			0.721893			0.360946	−	0.932587i	$-0.382454\pi$
$691$	18.9763			0.721893			0.360946	+	0.932587i	$0.382454\pi$
$692$	−19.7106	−	4.28778i	−0.749285	−	0.162997i
$693$	−1.53695	−	2.05313i	−0.0583841	−	0.0779920i
$694$	−19.1431	−	8.74235i	−0.726661	−	0.331855i
$695$	−6.33822	−	10.3492i	−0.240422	−	0.392566i
$696$	−2.02913	−	4.44318i	−0.0769140	−	0.168418i
$697$	−0.312378	−	0.0223418i	−0.0118322	−	0.000846254i
$698$	0.317442	+	0.237634i	0.0120154	+	0.00899458i
$699$	−1.34141	+	4.56842i	−0.0507368	+	0.172794i
$700$	15.1347	−	10.3371i	0.572037	−	0.390706i
$701$	−11.1153	+	17.2958i	−0.419820	+	0.653252i	−0.985167	−	0.171601i	$-0.945106\pi$
$701$	−11.1153	+	17.2958i	−0.419820	+	0.653252i	0.565347	+	0.824853i	$0.308742\pi$
$702$	0.0137305	+	0.0631179i	0.000518223	+	0.00238223i
$703$	0.795662	+	11.1248i	0.0300090	+	0.419580i
$704$	−0.671322	−	0.197118i	−0.0253014	−	0.00742916i
$705$	−4.21367	−	9.78260i	−0.158696	−	0.368434i
$706$	−0.498245	−	0.575006i	−0.0187517	−	0.0216406i
$707$	41.6061	+	15.5183i	1.56476	+	0.583624i
$708$	−1.83916	+	3.36816i	−0.0691197	+	0.126583i
$709$	−16.2772	+	35.6421i	−0.611304	+	1.33857i	0.310375	+	0.950614i	$0.399545\pi$
$709$	−16.2772	+	35.6421i	−0.611304	+	1.33857i	−0.921679	+	0.387954i	$0.873182\pi$
$710$	−4.49208	+	5.73709i	−0.168585	+	0.215309i
$711$	9.02112	+	14.0371i	0.338318	+	0.526434i
$712$	11.1102	−	11.1102i	0.416373	−	0.416373i
$713$	6.71541	+	1.67809i	0.251494	+	0.0628448i
$714$			6.53889i			0.244712i
$715$	−0.100932	+	0.00502207i	−0.00377465	+	0.000187815i
$716$	−0.0386632	+	0.268909i	−0.00144491	+	0.0100496i
$717$	−2.67654	+	0.998298i	−0.0999573	+	0.0372821i
$718$	31.3725	+	17.1307i	1.17081	+	0.639311i
$719$	−3.74740	+	1.71138i	−0.139754	+	0.0638237i	−0.484065	−	0.875032i	$-0.660840\pi$
$719$	−3.74740	+	1.71138i	−0.139754	+	0.0638237i	0.344310	+	0.938856i	$0.388113\pi$
$720$	1.24941	−	1.85445i	0.0465628	−	0.0691111i
$721$	0.0658899	+	0.458274i	0.00245387	+	0.0170670i
$722$	8.33238	+	15.2596i	0.310099	+	0.567904i
$723$	−29.7695	+	2.12916i	−1.10714	+	0.0791843i
$724$	−14.4990	−	9.31796i	−0.538852	−	0.346299i
$725$	−1.05884	+	24.4000i	−0.0393243	+	0.906193i
$726$	−6.88289	+	7.94328i	−0.255448	+	0.294803i
$727$	−20.5500	+	11.2212i	−0.762159	+	0.416170i	−0.812797	−	0.582547i	$-0.802056\pi$
$727$	−20.5500	+	11.2212i	−0.762159	+	0.416170i	0.0506382	+	0.998717i	$0.483874\pi$
$728$	0.141894	−	0.189549i	0.00525895	−	0.00702514i
$729$	0.755750	−	0.654861i	0.0279907	−	0.0242541i
$730$	1.75346	+	2.11455i	0.0648983	+	0.0782630i
$731$	−5.48266	+	1.60985i	−0.202784	+	0.0595426i
$732$	−2.25829	−	6.05470i	−0.0834687	−	0.223788i
$733$	0.906067	−	0.678273i	0.0334664	−	0.0250526i	−0.582414	−	0.812893i	$-0.697892\pi$
$733$	0.906067	−	0.678273i	0.0334664	−	0.0250526i	0.615880	+	0.787840i	$0.288801\pi$
$734$	−7.56939	+	4.86455i	−0.279391	+	0.179554i
$735$	−12.4795	−	7.16989i	−0.460314	−	0.264465i
$736$	−4.76571	+	0.536620i	−0.175667	+	0.0197801i
$737$	1.46965	+	1.46965i	0.0541351	+	0.0541351i
$738$	0.0373183	−	0.171549i	0.00137370	−	0.00631482i
$739$	2.49066	+	0.358102i	0.0916203	+	0.0131730i	0.187972	−	0.982174i	$-0.439808\pi$
$739$	2.49066	+	0.358102i	0.0916203	+	0.0131730i	−0.0963522	+	0.995347i	$0.530718\pi$
$740$	−15.9681	+	11.4219i	−0.587001	+	0.419876i
$741$	0.0231173	+	0.0787303i	0.000849235	+	0.00289223i
$742$	15.1216	−	40.5425i	0.555131	−	1.48836i
$743$	0.287394	−	4.01829i	0.0105435	−	0.147417i	−0.989453	−	0.144853i	$-0.953729\pi$
$743$	0.287394	−	4.01829i	0.0105435	−	0.147417i	0.999997	−	0.00256430i	$-0.000816244\pi$
$744$	1.42862	−	0.205405i	0.0523759	−	0.00753052i
$745$	11.1047	+	0.240831i	0.406844	+	0.00882338i
$746$	−16.5466	−	14.3377i	−0.605814	−	0.524941i
$747$	14.0642	−	3.05949i	0.514584	−	0.111941i
$748$	−1.21958	+	0.265302i	−0.0445921	+	0.00970042i
$749$	−38.6521	−	33.4922i	−1.41232	−	1.22378i
$750$	−9.77854	+	5.42035i	−0.357062	+	0.197923i
$751$	17.2305	−	2.47738i	0.628751	−	0.0904007i	0.179429	−	0.983771i	$-0.442575\pi$
$751$	17.2305	−	2.47738i	0.628751	−	0.0904007i	0.449321	+	0.893370i	$0.351666\pi$
$752$	−0.339824	+	4.75136i	−0.0123921	+	0.173264i
$753$	−8.97993	+	24.0761i	−0.327247	+	0.877383i
$754$	0.0888910	+	0.302735i	0.00323722	+	0.0110250i
$755$	0.544031	−	3.27763i	0.0197993	−	0.119285i
$756$	−3.62828	−	0.521668i	−0.131959	−	0.0189729i
$757$	10.8664	−	49.9521i	0.394946	−	1.81554i	−0.164148	−	0.986436i	$-0.552488\pi$
$757$	10.8664	−	49.9521i	0.394946	−	1.81554i	0.559095	−	0.829104i	$-0.311149\pi$
$758$	5.40149	+	5.40149i	0.196191	+	0.196191i
$759$	1.04363	−	3.18904i	0.0378815	−	0.115755i
$760$	1.41503	−	2.46293i	0.0513286	−	0.0893398i
$761$	12.2594	−	7.87863i	0.444402	−	0.285600i	−0.299240	−	0.954178i	$-0.596733\pi$
$761$	12.2594	−	7.87863i	0.444402	−	0.285600i	0.743642	+	0.668578i	$0.233097\pi$
$762$	1.44840	−	1.08426i	0.0524698	−	0.0392784i
$763$	−16.5315	−	44.3226i	−0.598480	−	1.60459i
$764$	22.8342	−	6.70472i	0.826112	−	0.242568i
$765$	0.370759	−	3.97155i	0.0134048	−	0.143592i
$766$	17.5546	−	15.2111i	0.634272	−	0.549600i
$767$	0.148552	−	0.198442i	0.00536390	−	0.00716533i
$768$	−0.877679	+	0.479249i	−0.0316705	+	0.0172934i
$769$	−34.0656	+	39.3138i	−1.22844	+	1.41769i	−0.352120	+	0.935955i	$0.614539\pi$
$769$	−34.0656	+	39.3138i	−1.22844	+	1.41769i	−0.876317	+	0.481736i	$0.840006\pi$
$770$	1.73461	−	5.46617i	0.0625108	−	0.196987i
$771$	−9.95631	−	6.39853i	−0.358568	−	0.230438i
$772$	9.59630	−	0.686341i	0.345378	−	0.0247019i
$773$	21.6398	+	39.6303i	0.778329	+	1.42540i	0.901392	+	0.433004i	$0.142546\pi$
$773$	21.6398	+	39.6303i	0.778329	+	1.42540i	−0.123063	+	0.992399i	$0.539272\pi$
$774$	−0.455869	−	3.17064i	−0.0163859	−	0.113966i
$775$	−6.82960	−	2.33143i	−0.245326	−	0.0837474i
$776$	−0.341641	+	0.156022i	−0.0122642	+	0.00560088i
$777$	28.2471	+	15.4241i	1.01336	+	0.553335i
$778$	−7.79558	+	2.90760i	−0.279485	+	0.104243i
$779$	0.0317385	−	0.220746i	0.00113715	−	0.00790905i
$780$	−0.0969305	+	0.107082i	−0.00347067	+	0.00383413i
$781$			2.27994i			0.0815826i
$782$	−7.00269	+	4.91442i	−0.250416	+	0.175739i
$783$	3.45393	−	3.45393i	0.123433	−	0.123433i
$784$	3.47986	+	5.41477i	0.124281	+	0.193385i
$785$	−23.5949	−	18.4746i	−0.842138	−	0.659385i
$786$	−5.19234	+	11.3696i	−0.185204	+	0.405541i
$787$	24.7583	−	45.3414i	0.882537	−	1.61625i	0.0988390	−	0.995103i	$-0.468487\pi$
$787$	24.7583	−	45.3414i	0.882537	−	1.61625i	0.783698	−	0.621142i	$-0.213331\pi$
$788$	−10.2651	−	3.82870i	−0.365680	−	0.136392i
$789$	−3.76439	−	4.34434i	−0.134016	−	0.154663i
$790$	−13.7938	+	34.6676i	−0.490760	+	1.23342i
$791$	5.36793	+	1.57617i	0.190862	+	0.0560421i
$792$	−0.0499134	−	0.697881i	−0.00177360	−	0.0247981i
$793$	0.0887282	+	0.407877i	0.00315083	+	0.0144841i
$794$	7.17925	−	11.1711i	0.254782	−	0.396449i
$795$	−11.4833	+	23.7671i	−0.407269	+	0.842933i
$796$	5.01746	−	17.0879i	0.177839	−	0.605664i
$797$	−27.2615	−	20.4077i	−0.965651	−	0.722877i	−0.00481328	−	0.999988i	$-0.501532\pi$
$797$	−27.2615	−	20.4077i	−0.965651	−	0.722877i	−0.960838	+	0.277111i	$0.910623\pi$
$798$	−4.64454	−	0.332184i	−0.164415	−	0.0117592i
$799$	3.52994	+	7.72950i	0.124880	+	0.273450i
$800$	4.99804	−	0.140141i	0.176707	−	0.00495474i
$801$	14.2923	+	6.52709i	0.504994	+	0.230623i
$802$	−10.7949	−	14.4204i	−0.381183	−	0.509201i
$803$	0.839886	+	0.182706i	0.0296389	+	0.00644755i
$804$	2.97056			0.104764
$805$	−3.55042	−	39.1484i	−0.125136	−	1.37980i
$806$	−0.0932297			−0.00328387
$807$	−13.1493	−	2.86046i	−0.462878	−	0.100693i
$808$	7.25980	+	9.69795i	0.255399	+	0.341173i
$809$	10.5605	+	4.82284i	0.371289	+	0.169562i	0.592316	−	0.805706i	$-0.298214\pi$
$809$	10.5605	+	4.82284i	0.371289	+	0.169562i	−0.221027	+	0.975268i	$0.570941\pi$
$810$	2.17415	+	0.522574i	0.0763918	+	0.0183614i
$811$	5.73993	+	12.5687i	0.201556	+	0.441347i	0.983237	−	0.182332i	$-0.0583646\pi$
$811$	5.73993	+	12.5687i	0.201556	+	0.441347i	−0.781681	+	0.623679i	$0.785637\pi$
$812$	−17.8593	−	1.27732i	−0.626738	−	0.0448252i
$813$	0.567590	+	0.424892i	0.0199062	+	0.0149016i
$814$	−1.73069	+	5.89420i	−0.0606607	+	0.206591i
$815$	7.01563	+	20.1324i	0.245747	+	0.705207i
$816$	−0.964425	+	1.50068i	−0.0337616	+	0.0525341i
$817$	−0.864946	−	3.97609i	−0.0302606	−	0.139106i
$818$	2.45788	+	34.3656i	0.0859376	+	1.20156i
$819$	0.227184	+	0.0667074i	0.00793847	+	0.00233094i
$820$	0.360544	−	0.155298i	0.0125907	−	0.00542322i
$821$	4.07475	+	4.70252i	0.142210	+	0.164119i	0.822386	−	0.568930i	$-0.192642\pi$
$821$	4.07475	+	4.70252i	0.142210	+	0.164119i	−0.680176	+	0.733048i	$0.738097\pi$
$822$	−18.3006	−	6.82576i	−0.638305	−	0.238076i
$823$	22.3966	−	41.0163i	0.780697	−	1.42974i	−0.118849	−	0.992912i	$-0.537921\pi$
$823$	22.3966	−	41.0163i	0.780697	−	1.42974i	0.899546	−	0.436827i	$-0.143898\pi$
$824$	−0.0524695	+	0.114892i	−0.00182786	+	0.00400246i
$825$	−1.36349	+	3.22166i	−0.0474707	+	0.112164i
$826$	7.60519	+	11.8339i	0.264618	+	0.411754i
$827$	−17.8799	+	17.8799i	−0.621746	+	0.621746i	−0.945978	−	0.324231i	$-0.894894\pi$
$827$	−17.8799	+	17.8799i	−0.621746	+	0.621746i	0.324231	+	0.945978i	$0.394894\pi$
$828$	−2.16823	−	4.27771i	−0.0753513	−	0.148661i
$829$		−	23.7220i		−	0.823899i	−0.911207	−	0.411950i	$-0.864848\pi$
$829$		−	23.7220i		−	0.823899i	0.911207	−	0.411950i	$-0.135152\pi$
$830$	23.8604	+	21.5985i	0.828208	+	0.749696i
$831$	−2.13043	+	14.8175i	−0.0739037	+	0.514012i
$832$	0.0605214	−	0.0225733i	0.00209820	−	0.000782589i
$833$	10.0774	+	5.50268i	0.349161	+	0.190657i
$834$	−4.93685	+	2.25458i	−0.170949	+	0.0780699i
$835$	5.03645	+	25.8373i	0.174294	+	0.894136i
$836$	−0.126487	−	0.879737i	−0.00437465	−	0.0304263i
$837$	0.691707	+	1.26677i	0.0239089	+	0.0437859i
$838$	10.2601	−	0.733818i	0.354430	−	0.0253493i
$839$	−32.9960	−	21.2053i	−1.13915	−	0.732087i	−0.171700	−	0.985149i	$-0.554926\pi$
$839$	−32.9960	−	21.2053i	−1.13915	−	0.732087i	−0.967450	+	0.253062i	$0.918562\pi$
$840$	−3.77127	−	7.27738i	−0.130121	−	0.251094i
$841$	−3.36650	+	3.88515i	−0.116086	+	0.133971i
$842$	30.6124	−	16.7157i	1.05497	−	0.576059i
$843$	4.01142	−	5.35864i	0.138161	−	0.184561i
$844$	3.41116	−	2.95578i	0.117417	−	0.101742i
$845$	−22.3692	+	18.5493i	−0.769524	+	0.638116i
$846$	−4.57054	+	1.34203i	−0.157138	+	0.0461400i
$847$	13.4638	+	36.0979i	0.462623	+	1.24034i
$848$	9.45006	−	7.07422i	0.324516	−	0.242930i
$849$	−23.1179	+	14.8570i	−0.793404	+	0.509890i
$850$	7.70538	−	4.49229i	0.264292	−	0.154084i
$851$	4.71152	+	41.8429i	0.161509	+	1.43436i
$852$	2.30419	+	2.30419i	0.0789403	+	0.0789403i
$853$	−6.23693	+	28.6707i	−0.213548	+	0.981666i	0.738151	+	0.674635i	$0.235699\pi$
$853$	−6.23693	+	28.6707i	−0.213548	+	0.981666i	−0.951700	+	0.307031i	$0.900665\pi$
$854$	−23.4465	−	3.37109i	−0.802321	−	0.115356i
$855$	2.80214	+	0.465109i	0.0958313	+	0.0159064i
$856$	−3.93087	−	13.3873i	−0.134354	−	0.457569i
$857$	−2.45614	+	6.58517i	−0.0839002	+	0.224945i	−0.972125	−	0.234465i	$-0.924666\pi$
$857$	−2.45614	+	6.58517i	−0.0839002	+	0.224945i	0.888224	+	0.459410i	$0.151939\pi$
$858$	−0.00322411	+	0.0450790i	−0.000110069	+	0.00153897i
$859$	17.4096	−	2.50312i	0.594007	−	0.0854053i	0.161246	−	0.986914i	$-0.448449\pi$
$859$	17.4096	−	2.50312i	0.594007	−	0.0854053i	0.432760	+	0.901509i	$0.357540\pi$
$860$	5.17340	−	4.95376i	0.176411	−	0.168922i
$861$	−0.486352	−	0.421427i	−0.0165748	−	0.0143622i
$862$	32.6148	−	7.09491i	1.11086	−	0.241653i
$863$	45.1664	−	9.82534i	1.53748	−	0.334458i	0.637521	−	0.770433i	$-0.279960\pi$
$863$	45.1664	−	9.82534i	1.53748	−	0.334458i	0.899959	+	0.435974i	$0.143596\pi$
$864$	−0.755750	−	0.654861i	−0.0257111	−	0.0222788i
$865$	32.5781	−	31.1951i	1.10769	−	1.06066i
$866$	−36.1274	+	5.19434i	−1.22766	+	0.176511i
$867$	0.985755	−	13.7827i	0.0334780	−	0.468083i
$868$	1.84888	−	4.95703i	0.0627549	−	0.168253i
$869$	3.28910	+	11.2017i	0.111575	+	0.379990i
$870$	10.7749	+	1.78845i	0.365302	+	0.0606340i
$871$	−0.189928	−	0.0273075i	−0.00643545	−	0.000925278i
$872$	2.74320	−	12.6103i	0.0928964	−	0.427038i
$873$	−0.265577	−	0.265577i	−0.00898840	−	0.00898840i
$874$	−3.13495	−	5.22364i	−0.106041	−	0.176692i
$875$	0.260155	+	40.9817i	0.00879483	+	1.38543i
$876$	1.03347	−	0.664171i	0.0349177	−	0.0224403i
$877$	12.8566	−	9.62430i	0.434135	−	0.324990i	−0.359759	−	0.933045i	$-0.617141\pi$
$877$	12.8566	−	9.62430i	0.434135	−	0.324990i	0.793894	+	0.608056i	$0.208050\pi$
$878$	−0.0921376	−	0.247030i	−0.00310949	−	0.00833687i
$879$	−25.4672	+	7.47785i	−0.858988	+	0.252222i
$880$	1.20430	−	0.998649i	0.0405970	−	0.0336644i
$881$	−36.1542	+	31.3278i	−1.21807	+	1.05546i	−0.221292	+	0.975208i	$0.571027\pi$
$881$	−36.1542	+	31.3278i	−1.21807	+	1.05546i	−0.996775	+	0.0802530i	$0.974427\pi$
$882$	−3.85728	+	5.15273i	−0.129881	+	0.173501i
$883$	−47.8781	+	26.1434i	−1.61122	+	0.879795i	−0.615429	+	0.788192i	$0.711017\pi$
$883$	−47.8781	+	26.1434i	−1.61122	+	0.879795i	−0.995796	+	0.0916032i	$0.970801\pi$
$884$	0.0754574	−	0.0870824i	0.00253791	−	0.00292890i
$885$	−3.94821	−	7.61884i	−0.132718	−	0.256104i
$886$	−18.7969	−	12.0800i	−0.631495	−	0.405837i
$887$	−50.5415	+	3.61480i	−1.69702	+	0.121373i	−0.886011	−	0.463665i	$-0.846534\pi$
$887$	−50.5415	+	3.61480i	−1.69702	+	0.121373i	−0.811006	+	0.585038i	$0.801080\pi$
$888$	4.20780	+	7.70601i	0.141204	+	0.258597i
$889$	−0.943838	−	6.56454i	−0.0316553	−	0.220168i
$890$	6.72205	+	34.4845i	0.225324	+	1.15592i
$891$	0.636436	−	0.290651i	0.0213214	−	0.00973716i
$892$	−8.31730	−	4.54159i	−0.278484	−	0.152064i
$893$	−5.66956	+	2.11463i	−0.189724	+	0.0707636i
$894$	0.706926	−	4.91678i	0.0236431	−	0.164442i
$895$	−0.450370	−	0.407677i	−0.0150542	−	0.0136271i
$896$			3.66559i			0.122459i
$897$	0.0993058	+	0.293434i	0.00331573	+	0.00979748i
$898$	−19.0071	+	19.0071i	−0.634275	+	0.634275i
$899$	3.81152	+	5.93084i	0.127121	+	0.197805i
$900$	1.87794	+	4.63393i	0.0625980	+	0.154464i
$901$	8.74767	−	19.1547i	0.291427	−	0.638137i
$902$	0.0588680	−	0.107809i	0.00196009	−	0.00358964i
$903$	−11.0015	−	4.10333i	−0.366105	−	0.136550i
$904$	0.999471	+	1.15345i	0.0332419	+	0.0383632i
$905$	35.3949	−	15.2457i	1.17657	−	0.506784i
$906$	−1.42567	−	0.418613i	−0.0473646	−	0.0139075i
$907$	0.663235	+	9.27323i	0.0220223	+	0.307913i	0.996510	+	0.0834720i	$0.0266009\pi$
$907$	0.663235	+	9.27323i	0.0220223	+	0.307913i	−0.974488	+	0.224441i	$0.927945\pi$
$908$	−2.05507	−	9.44701i	−0.0682000	−	0.313510i
$909$	−6.54946	+	10.1912i	−0.217232	+	0.338019i
$910$	0.174223	+	0.499959i	0.00577544	+	0.0165735i
$911$	6.15747	−	20.9704i	0.204006	−	0.694781i	−0.792394	−	0.610009i	$-0.791166\pi$
$911$	6.15747	−	20.9704i	0.204006	−	0.694781i	0.996400	−	0.0847719i	$-0.0270162\pi$
$912$	−1.01693	−	0.761264i	−0.0336739	−	0.0252080i
$913$	10.0447	+	0.718412i	0.332432	+	0.0237760i
$914$	9.77386	+	21.4018i	0.323290	+	0.707907i
$915$	14.0496	+	3.37695i	0.464467	+	0.111638i
$916$	9.36670	+	4.27763i	0.309484	+	0.141337i
$917$	27.4570	+	36.6782i	0.906709	+	1.21122i
$918$	−1.74309	−	0.379186i	−0.0575305	−	0.0125150i
$919$	−4.39797			−0.145076			−0.0725378	−	0.997366i	$-0.523110\pi$
$919$	−4.39797			−0.145076			−0.0725378	+	0.997366i	$0.523110\pi$
$920$	4.95921	−	9.50822i	0.163500	−	0.313477i
$921$	−20.1561			−0.664166
$922$	17.7997	+	3.87208i	0.586201	+	0.127520i
$923$	−0.126141	−	0.168504i	−0.00415197	−	0.00554638i
$924$	−2.33291	−	1.06541i	−0.0767472	−	0.0350493i
$925$	−1.23044	−	43.8827i	−0.0404566	−	1.44285i
$926$	7.90949	+	17.3194i	0.259922	+	0.569149i
$927$	−0.125984	−	0.00901058i	−0.00413787	−	0.000295946i
$928$	−3.91031	−	2.92723i	−0.128362	−	0.0960909i
$929$	10.2410	−	34.8775i	0.335995	−	1.14429i	−0.602246	−	0.798310i	$-0.705727\pi$
$929$	10.2410	−	34.8775i	0.335995	−	1.14429i	0.938241	−	0.345983i	$-0.112454\pi$
$930$	−1.40403	+	2.90594i	−0.0460399	+	0.0952896i
$931$	−4.42048	+	6.87840i	−0.144875	+	0.225430i
$932$	1.01208	+	4.65247i	0.0331519	+	0.152397i
$933$	1.85130	+	25.8845i	0.0606088	+	0.847421i
$934$	−1.81806	−	0.533831i	−0.0594888	−	0.0174675i
$935$	1.03176	−	2.59311i	0.0337423	−	0.0848037i
$936$	0.0423001	+	0.0488170i	0.00138262	+	0.00159563i
$937$	30.1971	+	11.2629i	0.986495	+	0.367944i	0.790366	−	0.612635i	$-0.209890\pi$
$937$	30.1971	+	11.2629i	0.986495	+	0.367944i	0.196129	+	0.980578i	$0.437163\pi$
$938$	5.21847	−	9.55692i	0.170389	−	0.312045i
$939$	−1.26835	+	2.77730i	−0.0413911	+	0.0906338i
$940$	−8.38656	−	6.56659i	−0.273539	−	0.214178i
$941$	−2.32779	−	3.62211i	−0.0758838	−	0.118077i	0.801237	−	0.598347i	$-0.204175\pi$
$941$	−2.32779	−	3.62211i	−0.0758838	−	0.118077i	−0.877121	+	0.480269i	$0.840539\pi$
$942$	−9.47643	+	9.47643i	−0.308759	+	0.308759i
$943$	0.0857914	−	0.837581i	0.00279375	−	0.0272754i
$944$			3.83758i			0.124903i
$945$	5.50062	−	6.07667i	0.178935	−	0.197674i
$946$	0.318955	−	2.21838i	0.0103701	−	0.0721257i
$947$	16.5564	−	6.17521i	0.538010	−	0.200667i	−0.0657461	−	0.997836i	$-0.520943\pi$
$947$	16.5564	−	6.17521i	0.538010	−	0.200667i	0.603756	+	0.797169i	$0.293670\pi$
$948$	14.6449	+	7.99674i	0.475645	+	0.259722i
$949$	−0.0721822	+	0.0329645i	−0.00234313	+	0.00107007i
$950$	2.79941	+	5.70132i	0.0908249	+	0.184975i
$951$	−1.00217	−	6.97024i	−0.0324975	−	0.226025i
$952$	3.13375	+	5.73904i	0.101566	+	0.186003i
$953$	26.6445	−	1.90565i	0.863100	−	0.0617301i	0.367234	−	0.930129i	$-0.380305\pi$
$953$	26.6445	−	1.90565i	0.863100	−	0.0617301i	0.495867	+	0.868399i	$0.334850\pi$
$954$	9.93065	+	6.38204i	0.321517	+	0.206626i
$955$	−16.0958	+	50.7217i	−0.520847	+	1.64132i
$956$	−1.87071	+	2.15892i	−0.0605031	+	0.0698243i
$957$	2.99953	−	1.63787i	0.0969609	−	0.0529447i
$958$	−4.52686	+	6.04718i	−0.146256	+	0.195375i
$959$	−54.1090	+	46.8858i	−1.74727	+	1.51402i
$960$	0.207841	−	2.22639i	0.00670805	−	0.0718564i
$961$	27.7455	−	8.14682i	0.895016	−	0.262800i
$962$	−0.198193	−	0.531377i	−0.00639001	−	0.0171323i
$963$	11.1695	−	8.36141i	0.359933	−	0.269443i
$964$	−25.1077	+	16.1357i	−0.808665	+	0.519697i
$965$	−10.7169	+	18.6533i	−0.344991	+	0.600472i
$966$	−17.5713	−	0.539111i	−0.565347	−	0.0173456i
$967$	1.23397	+	1.23397i	0.0396818	+	0.0396818i	0.726669	−	0.686987i	$-0.241067\pi$
$967$	1.23397	+	1.23397i	0.0396818	+	0.0396818i	−0.686987	+	0.726669i	$0.741067\pi$
$968$	−2.23416	+	10.2703i	−0.0718087	+	0.330099i
$969$	−2.24297	−	0.322491i	−0.0720546	−	0.0103599i
$970$	0.137516	−	0.828492i	0.00441536	−	0.0266013i
$971$	−11.5909	−	39.4751i	−0.371971	−	1.26682i	−0.906694	−	0.421789i	$-0.861402\pi$
$971$	−11.5909	−	39.4751i	−0.371971	−	1.26682i	0.534723	−	0.845027i	$-0.320416\pi$
$972$	0.349464	−	0.936950i	0.0112091	−	0.0300527i
$973$	−1.41924	+	19.8436i	−0.0454988	+	0.636156i
$974$	−39.0001	+	5.60736i	−1.24964	+	0.179671i
$975$	−0.0774708	−	0.313541i	−0.00248105	−	0.0100414i
$976$	−4.88376	−	4.23180i	−0.156325	−	0.135457i
$977$	11.2050	−	2.43751i	0.358481	−	0.0779828i	−0.0297180	−	0.999558i	$-0.509461\pi$
$977$	11.2050	−	2.43751i	0.358481	−	0.0779828i	0.388199	+	0.921576i	$0.373097\pi$
$978$	9.31660	−	2.02670i	0.297912	−	0.0648068i
$979$	8.30815	+	7.19905i	0.265529	+	0.230083i
$980$	−14.3892	−	0.312063i	−0.459646	−	0.00996850i
$981$	12.7739	−	1.83660i	0.407838	−	0.0586382i
$982$	1.26428	−	17.6769i	0.0403448	−	0.564093i
$983$	−2.92459	+	7.84113i	−0.0932799	+	0.250093i	−0.975208	−	0.221291i	$-0.928973\pi$
$983$	−2.92459	+	7.84113i	−0.0932799	+	0.250093i	0.881928	+	0.471384i	$0.156246\pi$
$984$	−0.0494614	−	0.168450i	−0.00157677	−	0.00536999i
$985$	19.9255	−	14.2525i	0.634879	−	0.454123i
$986$	−8.62471	−	1.24005i	−0.274667	−	0.0394911i
$987$	−3.71161	+	17.0620i	−0.118142	+	0.543089i
$988$	0.0580210	+	0.0580210i	0.00184589	+	0.00184589i
$989$	−3.87397	−	14.8657i	−0.123185	−	0.472703i
$990$	1.35654	+	0.779379i	0.0431138	+	0.0247703i
$991$	7.19793	−	4.62583i	0.228650	−	0.146944i	−0.421300	−	0.906921i	$-0.638426\pi$
$991$	7.19793	−	4.62583i	0.228650	−	0.146944i	0.649950	+	0.759977i	$0.274790\pi$
$992$	1.15543	−	0.864947i	0.0366851	−	0.0274621i
$993$	−7.38461	−	19.7989i	−0.234344	−	0.628300i
$994$	11.4609	−	3.36523i	0.363518	−	0.106739i
$995$	25.4197	+	30.6544i	0.805859	+	0.971810i
$996$	10.8776	−	9.42552i	0.344671	−	0.298659i
$997$	28.6967	−	38.3343i	0.908834	−	1.21406i	−0.0674846	−	0.997720i	$-0.521497\pi$
$997$	28.6967	−	38.3343i	0.908834	−	1.21406i	0.976318	−	0.216339i	$-0.0694117\pi$
$998$	−37.4133	+	20.4292i	−1.18430	+	0.646675i
$999$	−5.74967	+	6.63547i	−0.181911	+	0.209937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.517.8	yes	240
5.3	odd	4	inner	690.2.w.a.103.12	yes	240
23.21	odd	22	inner	690.2.w.a.67.12	✓	240
115.113	even	44	inner	690.2.w.a.343.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.67.12	✓	240	23.21	odd	22	inner
690.2.w.a.103.12	yes	240	5.3	odd	4	inner
690.2.w.a.343.8	yes	240	115.113	even	44	inner
690.2.w.a.517.8	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)

\(f(q)\)	\(=\)	\(q+(0.977147 + 0.212565i) q^{2} +(0.599278 + 0.800541i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.90687 + 1.16784i) q^{5} +(0.415415 + 0.909632i) q^{6} +(3.65625 + 0.261500i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-0.281733 + 0.959493i) q^{9} +O(q^{10})\)	\(q+(0.977147 + 0.212565i) q^{2} +(0.599278 + 0.800541i) q^{3} +(0.909632 + 0.415415i) q^{4} +(-1.90687 + 1.16784i) q^{5} +(0.415415 + 0.909632i) q^{6} +(3.65625 + 0.261500i) q^{7} +(0.800541 + 0.599278i) q^{8} +(-0.281733 + 0.959493i) q^{9} +(-2.11153 + 0.735816i) q^{10} +(-0.378266 + 0.588594i) q^{11} +(0.212565 + 0.977147i) q^{12} +(-0.00460809 - 0.0644295i) q^{13} +(3.51711 + 1.03272i) q^{14} +(-2.07765 - 0.826668i) q^{15} +(0.654861 + 0.755750i) q^{16} +(1.67138 + 0.623394i) q^{17} +(-0.479249 + 0.877679i) q^{18} +(-0.527703 + 1.15551i) q^{19} +(-2.21969 + 0.270161i) q^{20} +(1.98177 + 3.08369i) q^{21} +(-0.494737 + 0.494737i) q^{22} +(-1.81298 + 4.43994i) q^{23} +1.00000i q^{24} +(2.27230 - 4.45383i) q^{25} +(0.00919270 - 0.0639366i) q^{26} +(-0.936950 + 0.349464i) q^{27} +(3.21721 + 1.75673i) q^{28} +(-4.44318 + 2.02913i) q^{29} +(-1.85445 - 1.24941i) q^{30} +(-0.205405 - 1.42862i) q^{31} +(0.479249 + 0.877679i) q^{32} +(-0.697881 + 0.0499134i) q^{33} +(1.50068 + 0.964425i) q^{34} +(-7.27738 + 3.77127i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(7.70601 - 4.20780i) q^{37} +(-0.761264 + 1.01693i) q^{38} +(0.0488170 - 0.0423001i) q^{39} +(-2.22639 - 0.207841i) q^{40} +(-0.168450 + 0.0494614i) q^{41} +(1.28099 + 3.43447i) q^{42} +(-2.56433 + 1.91963i) q^{43} +(-0.588594 + 0.378266i) q^{44} +(-0.583306 - 2.15865i) q^{45} +(-2.71533 + 3.95310i) q^{46} +(3.36830 + 3.36830i) q^{47} +(-0.212565 + 0.977147i) q^{48} +(6.37104 + 0.916017i) q^{49} +(3.16711 - 3.86904i) q^{50} +(0.502570 + 1.71160i) q^{51} +(0.0225733 - 0.0605214i) q^{52} +(0.842129 - 11.7745i) q^{53} +(-0.989821 + 0.142315i) q^{54} +(0.0339218 - 1.56413i) q^{55} +(2.77027 + 2.40045i) q^{56} +(-1.24127 + 0.270022i) q^{57} +(-4.77296 + 1.03829i) q^{58} +(2.90025 + 2.51308i) q^{59} +(-1.54648 - 1.61505i) q^{60} +(-6.39637 + 0.919659i) q^{61} +(0.102965 - 1.43964i) q^{62} +(-1.28099 + 3.43447i) q^{63} +(0.281733 + 0.959493i) q^{64} +(0.0840303 + 0.117477i) q^{65} +(-0.692542 - 0.0995725i) q^{66} +(0.631438 - 2.90267i) q^{67} +(1.26138 + 1.26138i) q^{68} +(-4.64084 + 1.20939i) q^{69} +(-7.91271 + 2.13816i) q^{70} +(2.74133 - 1.76174i) q^{71} +(-0.800541 + 0.599278i) q^{72} +(-0.429313 - 1.15103i) q^{73} +(8.42433 - 2.47361i) q^{74} +(4.92722 - 0.850010i) q^{75} +(-0.960030 + 0.831871i) q^{76} +(-1.53695 + 2.05313i) q^{77} +(0.0566929 - 0.0309567i) q^{78} +(10.9270 - 12.6104i) q^{79} +(-2.13133 - 0.676344i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(-0.175114 + 0.0125244i) q^{82} +(-6.89791 - 12.6326i) q^{83} +(0.521668 + 3.62828i) q^{84} +(-3.91513 + 0.763176i) q^{85} +(-2.91377 + 1.33067i) q^{86} +(-4.28710 - 2.34093i) q^{87} +(-0.655549 + 0.244507i) q^{88} +(2.23608 - 15.5523i) q^{89} +(-0.111122 - 2.23331i) q^{90} -0.236776i q^{91} +(-3.49357 + 3.28557i) q^{92} +(1.02058 - 1.02058i) q^{93} +(2.57534 + 4.00731i) q^{94} +(-0.343187 - 2.81967i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(-0.179997 + 0.329640i) q^{97} +(6.03073 + 2.24934i) q^{98} +(-0.458182 - 0.528770i) 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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