LMFDB - Embedded newform 690.2.w.a.103.12

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			103.12
Character	$\chi$	$=$	690.103
Dual form			690.2.w.a.67.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.212565 - 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(2.23554 - 0.0484830i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.261500 - 3.65625i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +O(q^{10})$	\(q+(0.212565 - 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(2.23554 - 0.0484830i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.261500 - 3.65625i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +(0.427824 - 2.19476i) q^{10} +(-0.378266 + 0.588594i) q^{11} +(0.977147 - 0.212565i) q^{12} +(0.0644295 - 0.00460809i) q^{13} +(-3.51711 - 1.03272i) q^{14} +(-1.76059 + 1.37852i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.623394 - 1.67138i) q^{17} +(-0.877679 - 0.479249i) q^{18} +(0.527703 - 1.15551i) q^{19} +(-2.05366 - 0.884576i) q^{20} +(1.98177 + 3.08369i) q^{21} +(0.494737 + 0.494737i) q^{22} +(-4.43994 - 1.81298i) q^{23} -1.00000i q^{24} +(4.99530 - 0.216772i) q^{25} +(0.00919270 - 0.0639366i) q^{26} +(0.349464 + 0.936950i) q^{27} +(-1.75673 + 3.21721i) q^{28} +(4.44318 - 2.02913i) q^{29} +(0.972780 + 2.01338i) q^{30} +(-0.205405 - 1.42862i) q^{31} +(0.877679 - 0.479249i) q^{32} +(-0.0499134 - 0.697881i) q^{33} +(-1.50068 - 0.964425i) q^{34} +(0.407329 - 8.18638i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-4.20780 - 7.70601i) q^{37} +(-1.01693 - 0.761264i) q^{38} +(-0.0488170 + 0.0423001i) q^{39} +(-1.30090 + 1.81870i) q^{40} +(-0.168450 + 0.0494614i) q^{41} +(3.43447 - 1.28099i) q^{42} +(-1.91963 - 2.56433i) 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} +(-0.977147 - 0.212565i) q^{48} +(-6.37104 - 0.916017i) q^{49} +(0.850010 - 4.92722i) q^{50} +(0.502570 + 1.71160i) q^{51} +(-0.0605214 - 0.0225733i) q^{52} +(11.7745 + 0.842129i) q^{53} +(0.989821 - 0.142315i) q^{54} +(-0.817094 + 1.33417i) q^{55} +(2.77027 + 2.40045i) q^{56} +(0.270022 + 1.24127i) q^{57} +(-1.03829 - 4.77296i) q^{58} +(-2.90025 - 2.51308i) q^{59} +(2.17415 - 0.522574i) q^{60} +(-6.39637 + 0.919659i) q^{61} +(-1.43964 - 0.102965i) q^{62} +(-3.43447 - 1.28099i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(0.143812 - 0.0134253i) q^{65} +(-0.692542 - 0.0995725i) q^{66} +(-2.90267 - 0.631438i) 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} +(0.599278 + 0.800541i) q^{72} +(1.15103 - 0.429313i) q^{73} +(-8.42433 + 2.47361i) q^{74} +(-3.86904 + 3.16711i) q^{75} +(-0.960030 + 0.831871i) q^{76} +(2.05313 + 1.53695i) q^{77} +(0.0309567 + 0.0566929i) q^{78} +(-10.9270 + 12.6104i) q^{79} +(1.50061 + 1.65776i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(0.0125244 + 0.175114i) q^{82} +(12.6326 - 6.89791i) q^{83} +(-0.521668 - 3.62828i) q^{84} +(1.31259 - 3.76667i) q^{85} +(-2.91377 + 1.33067i) q^{86} +(-2.34093 + 4.28710i) q^{87} +(-0.244507 - 0.655549i) q^{88} +(-2.23608 + 15.5523i) q^{89} +(-1.98532 - 1.02883i) q^{90} -0.236776i q^{91} +(3.28557 + 3.49357i) q^{92} +(1.02058 + 1.02058i) q^{93} +(-2.57534 - 4.00731i) q^{94} +(1.12368 - 2.60877i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(0.329640 + 0.179997i) q^{97} +(-2.24934 + 6.03073i) 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 $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	0.212565	−	0.977147i	0.150306	−	0.690947i
$2$	0.212565	−	0.977147i	0.150306	−	0.690947i
$3$	−0.800541	+	0.599278i	−0.462193	+	0.345993i
$3$	−0.800541	+	0.599278i	−0.462193	+	0.345993i
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	2.23554	−	0.0484830i	0.999765	−	0.0216823i
$5$	2.23554	−	0.0484830i	0.999765	−	0.0216823i
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	0.261500	−	3.65625i	0.0988378	−	1.38193i	−0.669939	−	0.742416i	$-0.733680\pi$
$7$	0.261500	−	3.65625i	0.0988378	−	1.38193i	0.768777	−	0.639517i	$-0.220866\pi$
$8$	−0.599278	+	0.800541i	−0.211877	+	0.283034i
$9$	0.281733	−	0.959493i	0.0939109	−	0.319831i
$10$	0.427824	−	2.19476i	0.135290	−	0.694044i
$11$	−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	$0.215456\pi$
$12$	0.977147	−	0.212565i	0.282078	−	0.0613623i
$13$	0.0644295	−	0.00460809i	0.0178695	−	0.00127805i	−0.0624016	−	0.998051i	$-0.519876\pi$
$13$	0.0644295	−	0.00460809i	0.0178695	−	0.00127805i	0.0802711	+	0.996773i	$0.474421\pi$
$14$	−3.51711	−	1.03272i	−0.939987	−	0.276005i
$15$	−1.76059	+	1.37852i	−0.454582	+	0.355933i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	0.623394	−	1.67138i	0.151195	−	0.405370i	−0.839167	−	0.543874i	$-0.816957\pi$
$17$	0.623394	−	1.67138i	0.151195	−	0.405370i	0.990362	+	0.138504i	$0.0442295\pi$
$18$	−0.877679	−	0.479249i	−0.206871	−	0.112960i
$19$	0.527703	−	1.15551i	0.121063	−	0.265092i	−0.839392	−	0.543527i	$-0.817089\pi$
$19$	0.527703	−	1.15551i	0.121063	−	0.265092i	0.960455	+	0.278435i	$0.0898158\pi$
$20$	−2.05366	−	0.884576i	−0.459213	−	0.197797i
$21$	1.98177	+	3.08369i	0.432457	+	0.672916i
$22$	0.494737	+	0.494737i	0.105478	+	0.105478i
$23$	−4.43994	−	1.81298i	−0.925792	−	0.378033i
$23$	−4.43994	−	1.81298i	−0.925792	−	0.378033i
$24$		−	1.00000i		−	0.204124i
$25$	4.99530	−	0.216772i	0.999060	−	0.0433543i
$26$	0.00919270	−	0.0639366i	0.00180284	−	0.0125390i
$27$	0.349464	+	0.936950i	0.0672544	+	0.180316i
$28$	−1.75673	+	3.21721i	−0.331991	+	0.607996i
$29$	4.44318	−	2.02913i	0.825077	−	0.376800i	0.0423023	−	0.999105i	$-0.486531\pi$
$29$	4.44318	−	2.02913i	0.825077	−	0.376800i	0.782775	+	0.622305i	$0.213803\pi$
$30$	0.972780	+	2.01338i	0.177604	+	0.367591i
$31$	−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	$0.995919\pi$
$32$	0.877679	−	0.479249i	0.155153	−	0.0847201i
$33$	−0.0499134	−	0.697881i	−0.00868881	−	0.121485i
$34$	−1.50068	−	0.964425i	−0.257364	−	0.165398i
$35$	0.407329	−	8.18638i	0.0688511	−	1.38375i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−4.20780	−	7.70601i	−0.691758	−	1.26686i	−0.953404	−	0.301696i	$-0.902447\pi$
$37$	−4.20780	−	7.70601i	−0.691758	−	1.26686i	0.261646	−	0.965164i	$-0.415735\pi$
$38$	−1.01693	−	0.761264i	−0.164968	−	0.123493i
$39$	−0.0488170	+	0.0423001i	−0.00781697	+	0.00677344i
$40$	−1.30090	+	1.81870i	−0.205690	+	0.287561i
$41$	−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	$0.413455\pi$
$42$	3.43447	−	1.28099i	0.529951	−	0.197661i
$43$	−1.91963	−	2.56433i	−0.292741	−	0.391056i	0.629925	−	0.776656i	$-0.283086\pi$
$43$	−1.91963	−	2.56433i	−0.292741	−	0.391056i	−0.922666	+	0.385600i	$0.873995\pi$
$44$	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	−0.417404	−	0.908721i	$-0.637060\pi$
$47$	3.36830	−	3.36830i	0.491317	−	0.491317i	0.908721	+	0.417404i	$0.137060\pi$
$48$	−0.977147	−	0.212565i	−0.141039	−	0.0306812i
$49$	−6.37104	−	0.916017i	−0.910148	−	0.130860i
$50$	0.850010	−	4.92722i	0.120209	−	0.696814i
$51$	0.502570	+	1.71160i	0.0703739	+	0.239672i
$52$	−0.0605214	−	0.0225733i	−0.00839281	−	0.00313036i
$53$	11.7745	+	0.842129i	1.61735	+	0.115675i	0.850439	−	0.526074i	$-0.176337\pi$
$53$	11.7745	+	0.842129i	1.61735	+	0.115675i	0.766914	+	0.641750i	$0.221791\pi$
$54$	0.989821	−	0.142315i	0.134698	−	0.0193666i
$55$	−0.817094	+	1.33417i	−0.110177	+	0.179899i
$56$	2.77027	+	2.40045i	0.370193	+	0.320774i
$57$	0.270022	+	1.24127i	0.0357653	+	0.164410i
$58$	−1.03829	−	4.77296i	−0.136335	−	0.626720i
$59$	−2.90025	−	2.51308i	−0.377580	−	0.327175i	0.445309	−	0.895377i	$-0.353094\pi$
$59$	−2.90025	−	2.51308i	−0.377580	−	0.327175i	−0.822889	+	0.568202i	$0.807639\pi$
$60$	2.17415	−	0.522574i	0.280681	−	0.0674640i
$61$	−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	$0.590308\pi$
$62$	−1.43964	−	0.102965i	−0.182834	−	0.0130766i
$63$	−3.43447	−	1.28099i	−0.432703	−	0.161390i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	0.143812	−	0.0134253i	0.0178376	−	0.00166521i
$66$	−0.692542	−	0.0995725i	−0.0852460	−	0.0122565i
$67$	−2.90267	−	0.631438i	−0.354618	−	0.0771424i	0.0317275	−	0.999497i	$-0.489899\pi$
$67$	−2.90267	−	0.631438i	−0.354618	−	0.0771424i	−0.386346	+	0.922354i	$0.626263\pi$
$68$	−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	$0.256242\pi$
$72$	0.599278	+	0.800541i	0.0706256	+	0.0943447i
$73$	1.15103	−	0.429313i	0.134718	−	0.0502473i	−0.281201	−	0.959649i	$-0.590733\pi$
$73$	1.15103	−	0.429313i	0.134718	−	0.0502473i	0.415919	+	0.909402i	$0.363460\pi$
$74$	−8.42433	+	2.47361i	−0.979309	+	0.287551i
$75$	−3.86904	+	3.16711i	−0.446758	+	0.365706i
$76$	−0.960030	+	0.831871i	−0.110123	+	0.0954222i
$77$	2.05313	+	1.53695i	0.233976	+	0.175152i
$78$	0.0309567	+	0.0566929i	0.00350515	+	0.00641921i
$79$	−10.9270	+	12.6104i	−1.22938	+	1.41878i	−0.354075	+	0.935217i	$0.615204\pi$
$79$	−10.9270	+	12.6104i	−1.22938	+	1.41878i	−0.875308	+	0.483566i	$0.839341\pi$
$80$	1.50061	+	1.65776i	0.167773	+	0.185343i
$81$	−0.841254	−	0.540641i	−0.0934726	−	0.0600712i
$82$	0.0125244	+	0.175114i	0.00138309	+	0.0193381i
$83$	12.6326	−	6.89791i	1.38661	−	0.757144i	0.399428	−	0.916765i	$-0.369209\pi$
$83$	12.6326	−	6.89791i	1.38661	−	0.757144i	0.987179	+	0.159620i	$0.0510269\pi$
$84$	−0.521668	−	3.62828i	−0.0569186	−	0.395878i
$85$	1.31259	−	3.76667i	0.142370	−	0.408553i
$86$	−2.91377	+	1.33067i	−0.314200	+	0.143490i
$87$	−2.34093	+	4.28710i	−0.250974	+	0.459625i
$88$	−0.244507	−	0.655549i	−0.0260646	−	0.0698818i
$89$	−2.23608	+	15.5523i	−0.237024	+	1.64854i	0.429509	+	0.903063i	$0.358687\pi$
$89$	−2.23608	+	15.5523i	−0.237024	+	1.64854i	−0.666533	+	0.745475i	$0.732222\pi$
$90$	−1.98532	−	1.02883i	−0.209272	−	0.108448i
$91$		−	0.236776i		−	0.0248208i
$92$	3.28557	+	3.49357i	0.342545	+	0.364230i
$93$	1.02058	+	1.02058i	0.105829	+	0.105829i
$94$	−2.57534	−	4.00731i	−0.265626	−	0.413322i
$95$	1.12368	−	2.60877i	0.115287	−	0.267654i
$96$	−0.415415	+	0.909632i	−0.0423981	+	0.0928389i
$97$	0.329640	+	0.179997i	0.0334699	+	0.0182760i	0.495897	−	0.868381i	$-0.334839\pi$
$97$	0.329640	+	0.179997i	0.0334699	+	0.0182760i	−0.462427	+	0.886657i	$0.653021\pi$
$98$	−2.24934	+	6.03073i	−0.227218	+	0.609195i
$99$	0.458182	+	0.528770i	0.0460490	+	0.0531434i
$100$	−4.63393	−	1.87794i	−0.463393	−	0.187794i
$101$	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	$0.384998\pi$
$102$	1.77931	−	0.127259i	0.176178	−	0.0126005i
$103$	−0.123420	+	0.0268483i	−0.0121609	+	0.00264544i	−0.218642	−	0.975805i	$-0.570163\pi$
$103$	−0.123420	+	0.0268483i	−0.0121609	+	0.00264544i	0.206481	+	0.978451i	$0.433799\pi$
$104$	−0.0349222	+	0.0543400i	−0.00342440	+	0.00532848i
$105$	4.57983	+	6.79764i	0.446946	+	0.663382i
$106$	3.32574	−	11.3264i	0.323024	−	1.10012i
$107$	−8.36141	+	11.1695i	−0.808328	+	1.07980i	0.186915	+	0.982376i	$0.440151\pi$
$107$	−8.36141	+	11.1695i	−0.808328	+	1.07980i	−0.995243	+	0.0974237i	$0.968940\pi$
$108$	0.0713392	−	0.997452i	0.00686462	−	0.0959799i
$109$	5.36102	+	11.7390i	0.513492	+	1.12439i	0.971845	+	0.235621i	$0.0757124\pi$
$109$	5.36102	+	11.7390i	0.513492	+	1.12439i	−0.458353	+	0.888770i	$0.651560\pi$
$110$	1.12999	+	1.08202i	0.107740	+	0.103166i
$111$	7.98655	+	3.64734i	0.758050	+	0.346190i
$112$	2.93446	−	2.19671i	0.277280	−	0.207569i
$113$	−0.324425	+	1.49136i	−0.0305193	+	0.140295i	−0.989885	−	0.141869i	$-0.954689\pi$
$113$	−0.324425	+	1.49136i	−0.0305193	+	0.140295i	0.959366	+	0.282164i	$0.0910523\pi$
$114$	1.27030			0.118975
$115$	−10.0136	−	3.83774i	−0.933771	−	0.357871i
$116$	−4.88459			−0.453523
$117$	0.0137305	−	0.0631179i	0.00126938	−	0.00583525i
$118$	−3.07214	+	2.29978i	−0.282813	+	0.211711i
$119$	−5.94798	−	2.71635i	−0.545250	−	0.249007i
$120$	−0.0484830	−	2.23554i	−0.00442587	−	0.204076i
$121$	4.36621	+	9.56066i	0.396928	+	0.869151i
$122$	−0.461004	+	6.44568i	−0.0417373	+	0.583564i
$123$	0.105210	−	0.140544i	0.00948647	−	0.0126724i
$124$	−0.406629	+	1.38485i	−0.0365164	+	0.124363i
$125$	11.1567	−	0.726789i	0.997885	−	0.0650060i
$126$	−1.98177	+	3.08369i	−0.176550	+	0.274717i
$127$	−1.76792	+	0.384588i	−0.156878	+	0.0341267i	−0.290318	−	0.956930i	$-0.593761\pi$
$127$	−1.76792	+	0.384588i	−0.156878	+	0.0341267i	0.133440	+	0.991057i	$0.457398\pi$
$128$	−0.997452	+	0.0713392i	−0.0881631	+	0.00630555i
$129$	3.07349	+	0.902458i	0.270606	+	0.0794570i
$130$	0.0174508	−	0.143379i	0.00153054	−	0.0125751i
$131$	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	$0.588867\pi$
$132$	−0.244507	+	0.655549i	−0.0212816	+	0.0570582i
$133$	−4.08683	−	2.23158i	−0.354373	−	0.193502i
$134$	−1.23402	+	2.70212i	−0.106603	+	0.233427i
$135$	0.826668	+	2.07765i	0.0711483	+	0.178815i
$136$	0.964425	+	1.50068i	0.0826988	+	0.128682i
$137$	13.8113	+	13.8113i	1.17997	+	1.17997i	0.979750	+	0.200225i	$0.0641673\pi$
$137$	13.8113	+	13.8113i	1.17997	+	1.17997i	0.200225	+	0.979750i	$0.435833\pi$
$138$	−0.195271	−	4.79185i	−0.0166226	−	0.407910i
$139$		−	5.42731i		−	0.460338i	−0.973151	−	0.230169i	$-0.926072\pi$
$139$		−	5.42731i		−	0.460338i	0.973151	−	0.230169i	$-0.0739279\pi$
$140$	−3.77127	+	7.27738i	−0.318730	+	0.615051i
$141$	−0.677916	+	4.71501i	−0.0570908	+	0.397075i
$142$	−1.13877	−	3.05316i	−0.0955636	−	0.256216i
$143$	−0.0216592	+	0.0396659i	−0.00181124	+	0.00331703i
$144$	0.909632	−	0.415415i	0.0758027	−	0.0346179i
$145$	9.83453	−	4.75163i	0.816714	−	0.394601i
$146$	−0.174832	−	1.21598i	−0.0144692	−	0.100636i
$147$	5.64923	−	3.08471i	0.465940	−	0.254423i
$148$	0.626357	+	8.75761i	0.0514862	+	0.719871i
$149$	4.17879	+	2.68554i	0.342340	+	0.220008i	0.700501	−	0.713651i	$-0.252960\pi$
$149$	4.17879	+	2.68554i	0.342340	+	0.220008i	−0.358161	+	0.933660i	$0.616596\pi$
$150$	2.27230	+	4.45383i	0.185533	+	0.363654i
$151$	−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	$0.246529\pi$
$152$	0.608791	+	1.11492i	0.0493795	+	0.0904318i
$153$	−1.42805	−	1.06903i	−0.115451	−	0.0864256i
$154$	1.93825	−	1.67951i	0.156189	−	0.135339i
$155$	−0.528456	−	3.18379i	−0.0424466	−	0.255728i
$156$	0.0619776	−	0.0181983i	0.00496218	−	0.00145703i
$157$	12.5567	−	4.68341i	1.00214	−	0.373777i	0.205775	−	0.978599i	$-0.434029\pi$
$157$	12.5567	−	4.68341i	1.00214	−	0.373777i	0.796360	+	0.604822i	$0.206756\pi$
$158$	9.99953	+	13.3578i	0.795520	+	1.06269i
$159$	−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
$163$	9.31660	+	2.02670i	0.729732	+	0.158743i	0.562057	−	0.827099i	$-0.310010\pi$
$163$	9.31660	+	2.02670i	0.729732	+	0.158743i	0.167675	+	0.985842i	$0.446374\pi$
$164$	0.173775	+	0.0249850i	0.0135695	+	0.00195100i
$165$	−0.145419	−	1.55772i	−0.0113208	−	0.121268i
$166$	−4.05503	−	13.8101i	−0.314731	−	1.07188i
$167$	−11.0300	−	4.11399i	−0.853529	−	0.318350i	−0.115656	−	0.993289i	$-0.536897\pi$
$167$	−11.0300	−	4.11399i	−0.853529	−	0.318350i	−0.737873	+	0.674940i	$0.764170\pi$
$168$	−3.65625	−	0.261500i	−0.282086	−	0.0201752i
$169$	−12.8635	+	1.84950i	−0.989504	+	0.142269i
$170$	−3.40158	−	2.08326i	−0.260889	−	0.159778i
$171$	−0.960030	−	0.831871i	−0.0734154	−	0.0636148i
$172$	0.680898	+	3.13004i	0.0519180	+	0.238663i
$173$	−4.28778	−	19.7106i	−0.325994	−	1.49857i	−0.790203	−	0.612845i	$-0.790025\pi$
$173$	−4.28778	−	19.7106i	−0.325994	−	1.49857i	0.464209	−	0.885726i	$-0.346339\pi$
$174$	3.69153	+	3.19873i	0.279854	+	0.242495i
$175$	0.513701	−	18.3208i	0.0388321	−	1.38492i
$176$	−0.692542	+	0.0995725i	−0.0522023	+	0.00750556i
$177$	3.82780	+	0.273770i	0.287715	+	0.0205778i
$178$	14.7215	+	5.49085i	1.10343	+	0.411557i
$179$	−0.0765394	−	0.260669i	−0.00572082	−	0.0194833i	0.956583	−	0.291460i	$-0.0941409\pi$
$179$	−0.0765394	−	0.260669i	−0.00572082	−	0.0194833i	−0.962304	+	0.271976i	$0.912323\pi$
$180$	−1.42733	+	1.72126i	−0.106387	+	0.128295i
$181$	−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	$0.766742\pi$
$182$	−0.231364	−	0.0503303i	−0.0171499	−	0.00373073i
$183$	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
$187$	0.747958	+	0.999154i	0.0546961	+	0.0730654i
$188$	−4.46315	+	1.66467i	−0.325509	+	0.121409i
$189$	3.51711	−	1.03272i	0.255832	−	0.0751190i
$190$	−2.31030	−	1.65253i	−0.167607	−	0.119887i
$191$	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	$-0.0574267\pi$
$192$	0.800541	+	0.599278i	0.0577741	+	0.0432491i
$193$	4.61076	+	8.44398i	0.331890	+	0.607811i	0.989329	−	0.145696i	$-0.0465422\pi$
$193$	4.61076	+	8.44398i	0.331890	+	0.607811i	−0.657439	+	0.753507i	$0.728360\pi$
$194$	0.245954	−	0.283846i	0.0176585	−	0.0203789i
$195$	−0.107082	+	0.0969305i	−0.00766827	+	0.00694134i
$196$	5.41477	+	3.47986i	0.386769	+	0.248562i
$197$	0.781586	+	10.9280i	0.0556857	+	0.778588i	0.946190	+	0.323612i	$0.104897\pi$
$197$	0.781586	+	10.9280i	0.0556857	+	0.778588i	−0.890504	+	0.454975i	$0.849648\pi$
$198$	0.614080	−	0.335313i	0.0436407	−	0.0238296i
$199$	2.53453	+	17.6280i	0.179668	+	1.24962i	0.857532	+	0.514430i	$0.171997\pi$
$199$	2.53453	+	17.6280i	0.179668	+	1.24962i	−0.677864	+	0.735187i	$0.737094\pi$
$200$	−2.82004	+	4.12885i	−0.199407	+	0.291954i
$201$	2.70212	−	1.23402i	0.190593	−	0.0870408i
$202$	5.80574	−	10.6324i	0.408490	−	0.748094i
$203$	−6.25712	−	16.7760i	−0.439164	−	1.17744i
$204$	0.253869	−	1.76570i	0.0177744	−	0.123624i
$205$	−0.374179	+	0.118740i	−0.0261338	+	0.00829316i
$206$			0.126306i			0.00880017i
$207$	−2.99042	+	3.74932i	−0.207849	+	0.260596i
$208$	0.0456749	+	0.0456749i	0.00316699	+	0.00316699i
$209$	0.480513	+	0.747692i	0.0332378	+	0.0517190i
$210$	7.61581	−	3.03023i	0.525540	−	0.209105i
$211$	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	$0.0867084\pi$
$212$	−10.3606	−	5.65733i	−0.711571	−	0.388547i
$213$	−1.13877	+	3.05316i	−0.0780273	+	0.209199i
$214$	9.13693	+	10.5446i	0.624588	+	0.720813i
$215$	−4.41574	−	5.63959i	−0.301151	−	0.384617i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	−5.27712	+	0.377427i	−0.358234	+	0.0256214i
$218$	12.6103	−	2.74320i	0.854076	−	0.185793i
$219$	−0.664171	+	1.03347i	−0.0448805	+	0.0698355i
$220$	1.29749	−	0.874168i	0.0874766	−	0.0589364i
$221$	0.0324631	−	0.110559i	0.00218370	−	0.00743701i
$222$	5.26165	−	7.02874i	0.353139	−	0.471738i
$223$	0.676044	−	9.45233i	0.0452712	−	0.632975i	−0.923275	−	0.384140i	$-0.874498\pi$
$223$	0.676044	−	9.45233i	0.0452712	−	0.632975i	0.968546	−	0.248835i	$-0.0800475\pi$
$224$	−1.52274	−	3.33434i	−0.101742	−	0.222785i
$225$	1.19935	−	4.85403i	0.0799565	−	0.323602i
$226$	1.38831	+	0.634021i	0.0923492	+	0.0421744i
$227$	−7.73960	+	5.79379i	−0.513695	+	0.384547i	−0.824443	−	0.565945i	$-0.808511\pi$
$227$	−7.73960	+	5.79379i	−0.513695	+	0.384547i	0.310748	+	0.950492i	$0.399421\pi$
$228$	0.270022	−	1.24127i	0.0178827	−	0.0822052i
$229$	−10.2972			−0.680461			−0.340230	−	0.940342i	$-0.610505\pi$
$229$	−10.2972			−0.680461			−0.340230	+	0.940342i	$0.610505\pi$
$230$	−5.87857	+	8.96897i	−0.387622	+	0.591396i
$231$	−2.56468			−0.168743
$232$	−1.03829	+	4.77296i	−0.0681673	+	0.313360i
$233$	−3.81161	+	2.85333i	−0.249707	+	0.186928i	−0.716798	−	0.697281i	$-0.754393\pi$
$233$	−3.81161	+	2.85333i	−0.249707	+	0.186928i	0.467091	+	0.884209i	$0.345302\pi$
$234$	−0.0587569	−	0.0268334i	−0.00384106	−	0.00175415i
$235$	7.36667	−	7.69328i	0.480549	−	0.501854i
$236$	1.59419	+	3.49078i	0.103773	+	0.227231i
$237$	1.19036	−	16.6435i	0.0773225	−	1.08111i
$238$	−3.91861	+	5.23465i	−0.254006	+	0.339312i
$239$	0.804813	−	2.74094i	0.0520590	−	0.177297i	−0.929360	−	0.369176i	$-0.879640\pi$
$239$	0.804813	−	2.74094i	0.0520590	−	0.177297i	0.981419	+	0.191879i	$0.0614582\pi$
$240$	−2.19476	−	0.427824i	−0.141671	−	0.0276159i
$241$	−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	$0.770707\pi$
$242$	10.2703	−	2.23416i	0.660198	−	0.143617i
$243$	0.997452	−	0.0713392i	0.0639866	−	0.00457641i
$244$	6.20038	+	1.82060i	0.396939	+	0.116552i
$245$	−14.2871	−	1.73891i	−0.912771	−	0.111095i
$246$	−0.114968	−	0.132681i	−0.00733011	−	0.00845940i
$247$	0.0286749	−	0.0768805i	0.00182454	−	0.00489179i
$248$	1.26677	+	0.691707i	0.0804398	+	0.0439235i
$249$	−5.97914	+	13.0925i	−0.378913	+	0.829703i
$250$	1.66135	−	11.0562i	0.105073	−	0.699257i
$251$	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
$253$	2.74659	−	1.92753i	0.172677	−	0.121183i
$254$			1.80927i			0.113524i
$255$	1.20650	+	3.80198i	0.0755540	+	0.238089i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	4.13594	+	11.0889i	0.257993	+	0.691706i	0.999778	+	0.0210682i	$0.00670671\pi$
$257$	4.13594	+	11.0889i	0.257993	+	0.691706i	−0.741785	+	0.670638i	$0.766021\pi$
$258$	1.53515	−	2.81142i	0.0955743	−	0.175031i
$259$	−29.2754	+	13.3696i	−1.81909	+	0.830749i
$260$	−0.136393	−	0.0475294i	−0.00845871	−	0.00294765i
$261$	−0.695149	−	4.83487i	−0.0430287	−	0.299271i
$262$	10.9702	−	5.99021i	0.677744	−	0.370076i
$263$	−0.410085	−	5.73374i	−0.0252869	−	0.353558i	−0.994305	−	0.106569i	$-0.966013\pi$
$263$	−0.410085	−	5.73374i	−0.0252869	−	0.353558i	0.969018	−	0.246989i	$-0.0794411\pi$
$264$	0.588594	+	0.378266i	0.0362255	+	0.0232807i
$265$	26.3632	+	1.31175i	1.61948	+	0.0805803i
$266$	−3.04930	+	3.51908i	−0.186964	+	0.215769i
$267$	−7.53006	−	13.7903i	−0.460832	−	0.843951i
$268$	2.37806	+	1.78019i	0.145263	+	0.108742i
$269$	10.1700	−	8.81237i	0.620077	−	0.537299i	−0.287180	−	0.957877i	$-0.592718\pi$
$269$	10.1700	−	8.81237i	0.620077	−	0.537299i	0.907257	+	0.420577i	$0.138172\pi$
$270$	2.20589	−	0.366140i	0.134246	−	0.0222826i
$271$	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	$0.402236\pi$
$272$	1.67138	−	0.623394i	0.101343	−	0.0377988i
$273$	0.141894	+	0.189549i	0.00858783	+	0.0114720i
$274$	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	−0.313561	−	0.949568i	$-0.601522\pi$
$277$	10.5853	−	10.5853i	0.636007	−	0.636007i	0.949568	+	0.313561i	$0.101522\pi$
$278$	−5.30327	−	1.15366i	−0.318069	−	0.0691917i
$279$	−1.42862	−	0.205405i	−0.0855295	−	0.0122973i
$280$	6.30943	+	5.23200i	0.377061	+	0.312672i
$281$	−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	$0.973074\pi$
$282$	4.46315	+	1.66467i	0.265777	+	0.0991297i
$283$	−27.4103	−	1.96042i	−1.62937	−	0.116535i	−0.773526	−	0.633765i	$-0.781509\pi$
$283$	−27.4103	−	1.96042i	−1.62937	−	0.116535i	−0.855847	+	0.517230i	$0.826963\pi$
$284$	−3.22545	+	0.463750i	−0.191395	+	0.0275185i
$285$	0.663827	+	2.76182i	0.0393217	+	0.163596i
$286$	0.0341554	+	0.0295959i	0.00201965	+	0.00175004i
$287$	0.136794	+	0.628830i	0.00807467	+	0.0371186i
$288$	−0.212565	−	0.977147i	−0.0125255	−	0.0575789i
$289$	10.4428	+	9.04877i	0.614285	+	0.532281i
$290$	−2.55256	−	10.6198i	−0.149891	−	0.623617i
$291$	−0.371759	+	0.0534509i	−0.0217929	+	0.00313335i
$292$	−1.22536	−	0.0876394i	−0.0717087	−	0.00512871i
$293$	−24.8689	−	9.27561i	−1.45285	−	0.541887i	−0.505713	−	0.862702i	$-0.668771\pi$
$293$	−24.8689	−	9.27561i	−1.45285	−	0.541887i	−0.947142	+	0.320815i	$0.896043\pi$
$294$	−1.81339	−	6.17583i	−0.105759	−	0.360181i
$295$	−6.60547	−	5.47748i	−0.384585	−	0.318911i
$296$	8.69062	+	1.24952i	0.505132	+	0.0726270i
$297$	−0.683674	−	0.148724i	−0.0396708	−	0.00862985i
$298$	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
$302$	0.890439	+	1.18949i	0.0512390	+	0.0684473i
$303$	−11.3504	+	4.23350i	−0.652066	+	0.243208i
$304$	1.21885	−	0.357886i	0.0699056	−	0.0205261i
$305$	−14.2548	+	2.36605i	−0.816225	+	0.135480i
$306$	−1.34815	+	1.16818i	−0.0770685	+	0.0667802i
$307$	16.1358	+	12.0791i	0.920918	+	0.689391i	0.950682	−	0.310166i	$-0.100385\pi$
$307$	16.1358	+	12.0791i	0.920918	+	0.689391i	−0.0297643	+	0.999557i	$0.509476\pi$
$308$	−1.22912	−	2.25096i	−0.0700356	−	0.128261i
$309$	0.0827130	−	0.0954559i	0.00470538	−	0.00543029i
$310$	−3.22336	−	0.160385i	−0.183075	−	0.00910923i
$311$	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	$0.418642\pi$
$312$	−0.00460809	−	0.0644295i	−0.000260882	−	0.00364760i
$313$	−2.67974	+	1.46325i	−0.151468	+	0.0827078i	−0.553195	−	0.833051i	$-0.686592\pi$
$313$	−2.67974	+	1.46325i	−0.151468	+	0.0827078i	0.401727	+	0.915759i	$0.368410\pi$
$314$	−1.90726	−	13.2653i	−0.107633	−	0.748604i
$315$	−7.74002	−	2.69720i	−0.436101	−	0.151970i
$316$	15.1781	−	6.93161i	0.853835	−	0.389933i
$317$	−3.37483	+	6.18054i	−0.189549	+	0.347134i	−0.955120	−	0.296218i	$-0.904275\pi$
$317$	−3.37483	+	6.18054i	−0.189549	+	0.347134i	0.765571	+	0.643351i	$0.222456\pi$
$318$	4.12528	+	11.0603i	0.231334	+	0.620231i
$319$	−0.486371	+	3.38278i	−0.0272315	+	0.189399i
$320$	−0.676344	−	2.13133i	−0.0378088	−	0.119145i
$321$		−	13.9525i		−	0.778752i
$322$	13.7435	+	10.9617i	0.765893	+	0.610869i
$323$	−1.60233	−	1.60233i	−0.0891560	−	0.0891560i
$324$	0.540641	+	0.841254i	0.0300356	+	0.0467363i
$325$	0.320846	−	0.0369853i	0.0177973	−	0.00205157i
$326$	3.96077	−	8.67288i	0.219367	−	0.480346i
$327$	−11.3266	−	6.18481i	−0.626364	−	0.342021i
$328$	0.0613525	−	0.164492i	0.00338762	−	0.00908257i
$329$	−11.4345	−	13.1962i	−0.630406	−	0.727528i
$330$	−1.55303	−	0.189022i	−0.0854917	−	0.0104053i
$331$	−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	$0.788145\pi$
$332$	−14.3565	+	1.02680i	−0.787915	+	0.0563528i
$333$	−8.57933	+	1.86632i	−0.470145	+	0.102274i
$334$	−6.36457	+	9.90346i	−0.348254	+	0.541893i
$335$	−6.51967	−	1.27088i	−0.356207	−	0.0694354i
$336$	−1.03272	+	3.51711i	−0.0563393	+	0.191874i
$337$	6.68963	−	8.93629i	0.364407	−	0.486791i	−0.580440	−	0.814303i	$-0.697119\pi$
$337$	6.68963	−	8.93629i	0.364407	−	0.486791i	0.944847	+	0.327512i	$0.106210\pi$
$338$	−0.927112	+	12.9627i	−0.0504282	+	0.705079i
$339$	−0.634021	−	1.38831i	−0.0344353	−	0.0754028i
$340$	−2.75871	+	2.88102i	−0.149612	+	0.156245i
$341$	0.918578	+	0.419501i	0.0497438	+	0.0227172i
$342$	−1.01693	+	0.761264i	−0.0549892	+	0.0411644i
$343$	0.439026	−	2.01817i	0.0237052	−	0.108971i
$344$	3.20324			0.172707
$345$	10.3162	−	2.92865i	0.555403	−	0.157673i
$346$	−20.1716			−1.08443
$347$	−4.47341	+	20.5639i	−0.240145	+	1.10393i	0.686247	+	0.727368i	$0.259257\pi$
$347$	−4.47341	+	20.5639i	−0.240145	+	1.10393i	−0.926392	+	0.376560i	$0.877107\pi$
$348$	3.91031	−	2.92723i	0.209615	−	0.156916i
$349$	−0.360700	−	0.164726i	−0.0193078	−	0.00881760i	0.405738	−	0.913990i	$-0.367015\pi$
$349$	−0.360700	−	0.164726i	−0.0193078	−	0.00881760i	−0.425046	+	0.905172i	$0.639742\pi$
$350$	−17.7929	−	4.39632i	−0.951069	−	0.234993i
$351$	0.0268334	+	0.0587569i	0.00143226	+	0.00313621i
$352$	−0.0499134	+	0.697881i	−0.00266039	+	0.0371972i
$353$	0.455955	−	0.609085i	0.0242681	−	0.0324183i	−0.788243	−	0.615364i	$-0.789009\pi$
$353$	0.455955	−	0.609085i	0.0242681	−	0.0324183i	0.812511	+	0.582946i	$0.198100\pi$
$354$	1.08117	−	3.68213i	0.0574636	−	0.195703i
$355$	6.04294	−	4.07136i	0.320726	−	0.216085i
$356$	8.49466	−	13.2179i	0.450216	−	0.700550i
$357$	6.38945	−	1.38994i	0.338166	−	0.0735634i
$358$	−0.270982	+	0.0193810i	−0.0143218	+	0.00102432i
$359$	−34.2969	−	10.0705i	−1.81012	−	0.531500i	−0.811519	−	0.584326i	$-0.801359\pi$
$359$	−34.2969	−	10.0705i	−1.81012	−	0.531500i	−0.998604	+	0.0528266i	$0.983177\pi$
$360$	1.37852	+	1.76059i	0.0726546	+	0.0927912i
$361$	11.3856	+	13.1397i	0.599243	+	0.691564i
$362$	−6.02302	+	16.1484i	−0.316563	+	0.848739i
$363$	−9.22482	−	5.03713i	−0.484177	−	0.264381i
$364$	−0.0983601	+	0.215379i	−0.00515547	+	0.0112889i
$365$	2.55237	−	1.01555i	0.133597	−	0.0531565i
$366$	−3.49370	−	5.43630i	−0.182619	−	0.284160i
$367$	6.36237	+	6.36237i	0.332113	+	0.332113i	0.853389	−	0.521275i	$-0.174544\pi$
$367$	6.36237	+	6.36237i	0.332113	+	0.332113i	−0.521275	+	0.853389i	$0.674544\pi$
$368$	−1.53738	−	4.54274i	−0.0801416	−	0.236807i
$369$			0.175562i			0.00913937i
$370$	−18.7130	+	5.93829i	−0.972844	+	0.308717i
$371$	6.15807	−	42.8303i	0.319711	−	2.22364i
$372$	−0.504387	−	1.35231i	−0.0261513	−	0.0701142i
$373$	10.4928	−	19.2162i	0.543297	−	0.994975i	−0.451419	−	0.892312i	$-0.649082\pi$
$373$	10.4928	−	19.2162i	0.543297	−	0.994975i	0.994716	−	0.102663i	$-0.0327363\pi$
$374$	1.13531	−	0.518479i	0.0587055	−	0.0268099i
$375$	−8.49584	+	7.26778i	−0.438723	+	0.375307i
$376$	0.677916	+	4.71501i	0.0349608	+	0.243158i
$377$	0.276921	−	0.151211i	0.0142622	−	0.00778774i
$378$	−0.261500	−	3.65625i	−0.0134501	−	0.188057i
$379$	−6.42622	−	4.12988i	−0.330093	−	0.212138i	0.365087	−	0.930973i	$-0.381039\pi$
$379$	−6.42622	−	4.12988i	−0.330093	−	0.212138i	−0.695180	+	0.718835i	$0.744675\pi$
$380$	−2.10586	+	1.90623i	−0.108028	+	0.0977874i
$381$	1.18482	−	1.36736i	0.0607002	−	0.0700517i
$382$	−11.4053	−	20.8872i	−0.583544	−	1.06868i
$383$	18.5950	+	13.9200i	0.950159	+	0.711280i	0.957421	−	0.288694i	$-0.0932209\pi$
$383$	18.5950	+	13.9200i	0.950159	+	0.711280i	−0.00726281	+	0.999974i	$0.502312\pi$
$384$	0.755750	−	0.654861i	0.0385667	−	0.0334182i
$385$	4.66438	+	3.33639i	0.237719	+	0.170038i
$386$	9.23110	−	2.71050i	0.469851	−	0.137961i
$387$	−3.00128	+	1.11942i	−0.152563	+	0.0569032i
$388$	−0.225078	−	0.300669i	−0.0114266	−	0.0152641i
$389$	6.99937	−	4.49822i	0.354882	−	0.228069i	−0.351037	−	0.936362i	$-0.614171\pi$
$389$	6.99937	−	4.49822i	0.354882	−	0.228069i	0.705919	+	0.708293i	$0.250534\pi$
$390$	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
$393$	−12.2135	−	2.65689i	−0.616090	−	0.134022i
$394$	10.8444	+	1.55919i	0.546333	+	0.0785508i
$395$	−23.8164	+	28.7209i	−1.19833	+	1.44511i
$396$	−0.197118	−	0.671322i	−0.00990555	−	0.0337352i
$397$	−12.4419	−	4.64059i	−0.624441	−	0.232904i	0.0172701	−	0.999851i	$-0.494502\pi$
$397$	−12.4419	−	4.64059i	−0.624441	−	0.232904i	−0.641711	+	0.766946i	$0.721775\pi$
$398$	17.7639	+	1.27050i	0.890425	+	0.0636844i
$399$	4.60901	−	0.662676i	0.230739	−	0.0331753i
$400$	3.43505	+	3.63324i	0.171753	+	0.181662i
$401$	−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	$0.875767\pi$
$402$	−0.631438	−	2.90267i	−0.0314933	−	0.144772i
$403$	−0.0198174	−	0.0910991i	−0.000987175	−	0.00453797i
$404$	−9.15534	−	7.93314i	−0.455495	−	0.394689i
$405$	−1.90687	−	1.16784i	−0.0947531	−	0.0580304i
$406$	−17.7227	+	2.54813i	−0.879561	+	0.126462i
$407$	6.12738	+	0.438239i	0.303723	+	0.0217227i
$408$	−1.67138	−	0.623394i	−0.0827458	−	0.0308626i
$409$	−9.70664	−	33.0578i	−0.479962	−	1.63460i	−0.742620	−	0.669713i	$-0.766417\pi$
$409$	−9.70664	−	33.0578i	−0.479962	−	1.63460i	0.262658	−	0.964889i	$-0.415401\pi$
$410$	0.0364889	+	0.390868i	0.00180206	+	0.0193036i
$411$	−19.3333	−	2.77970i	−0.953639	−	0.137113i
$412$	0.123420	+	0.0268483i	0.00608045	+	0.00132272i
$413$	−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
$417$	3.25246	+	4.34478i	0.159274	+	0.212765i
$418$	0.832746	−	0.310598i	0.0407309	−	0.0151918i
$419$	−9.86966	+	2.89799i	−0.482164	+	0.141576i	−0.513777	−	0.857924i	$-0.671754\pi$
$419$	−9.86966	+	2.89799i	−0.482164	+	0.141576i	0.0316123	+	0.999500i	$0.489936\pi$
$420$	−1.34212	−	8.08588i	−0.0654888	−	0.394551i
$421$	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	$-0.0506380\pi$
$422$	−3.61333	−	2.70490i	−0.175894	−	0.131673i
$423$	−2.28290	−	4.18082i	−0.110998	−	0.203278i
$424$	−7.73036	+	8.92131i	−0.375419	+	0.433257i
$425$	2.75173	−	8.48419i	0.133479	−	0.411544i
$426$	2.74133	+	1.76174i	0.132818	+	0.0853567i
$427$	1.68985	+	23.6272i	0.0817776	+	1.14340i
$428$	12.2458	−	6.68671i	0.591923	−	0.323214i
$429$	−0.00643179	−	0.0447341i	−0.000310530	−	0.00215978i
$430$	−6.44934	+	3.11605i	−0.311015	+	0.150269i
$431$	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	$0.0664073\pi$
$432$	−0.479249	+	0.877679i	−0.0230579	+	0.0422274i
$433$	−12.7551	−	34.1977i	−0.612970	−	1.64344i	−0.756657	−	0.653812i	$-0.773169\pi$
$433$	−12.7551	−	34.1977i	−0.612970	−	1.64344i	0.143688	−	0.989623i	$-0.454104\pi$
$434$	−0.752931	+	5.23675i	−0.0361419	+	0.251372i
$435$	−5.02541	+	9.69749i	−0.240950	+	0.464959i
$436$		−	12.9052i		−	0.618047i
$437$	−4.43789	+	4.17367i	−0.212293	+	0.199654i
$438$	0.868673	+	0.868673i	0.0415068	+	0.0415068i
$439$	0.142542	+	0.221800i	0.00680316	+	0.0105859i	0.844638	−	0.535337i	$-0.179815\pi$
$439$	0.142542	+	0.221800i	0.00680316	+	0.0105859i	−0.837835	+	0.545923i	$0.816179\pi$
$440$	−0.578389	−	1.45365i	−0.0275736	−	0.0693002i
$441$	−2.67384	+	5.85489i	−0.127326	+	0.278804i
$442$	−0.101132	−	0.0552222i	−0.00481036	−	0.00262665i
$443$	7.80841	−	20.9351i	0.370989	−	0.994659i	−0.608570	−	0.793500i	$-0.708257\pi$
$443$	7.80841	−	20.9351i	0.370989	−	0.994659i	0.979559	−	0.201159i	$-0.0644707\pi$
$444$	−5.74967	−	6.63547i	−0.272867	−	0.314905i
$445$	−4.24483	+	34.8762i	−0.201224	+	1.65329i
$446$	−9.09261	−	2.66983i	−0.430548	−	0.126420i
$447$	−4.95468	+	0.354366i	−0.234348	+	0.0167609i
$448$	−3.58182	+	0.779177i	−0.169225	+	0.0368127i
$449$	14.5325	−	22.6130i	0.685830	−	1.06717i	−0.307464	−	0.951560i	$-0.599481\pi$
$449$	14.5325	−	22.6130i	0.685830	−	1.06717i	0.993294	−	0.115613i	$-0.0368831\pi$
$450$	−4.48816	−	2.20374i	−0.211574	−	0.103885i
$451$	0.0346063	−	0.117858i	0.00162955	−	0.00554973i
$452$	0.914639	−	1.22181i	0.0430210	−	0.0574693i
$453$	0.106000	−	1.48207i	0.00498029	−	0.0696336i
$454$	4.01621	+	8.79428i	0.188490	+	0.412736i
$455$	−0.0114796	−	0.529322i	−0.000538171	−	0.0248150i
$456$	−1.15551	−	0.527703i	−0.0541116	−	0.0247119i
$457$	18.8351	−	14.0998i	0.881068	−	0.659559i	−0.0598449	−	0.998208i	$-0.519061\pi$
$457$	18.8351	−	14.0998i	0.881068	−	0.659559i	0.940913	+	0.338648i	$0.109970\pi$
$458$	−2.18884	+	10.0619i	−0.102278	+	0.470162i
$459$	1.78386			0.0832633
$460$	7.51442	+	7.65072i	0.350361	+	0.356717i
$461$	18.2160			0.848402			0.424201	−	0.905568i	$-0.360555\pi$
$461$	18.2160			0.848402			0.424201	+	0.905568i	$0.360555\pi$
$462$	−0.545162	+	2.50607i	−0.0253632	+	0.116593i
$463$	−15.2423	+	11.4102i	−0.708369	+	0.530278i	−0.891618	−	0.452788i	$-0.850429\pi$
$463$	−15.2423	+	11.4102i	−0.708369	+	0.530278i	0.183249	+	0.983066i	$0.441338\pi$
$464$	4.44318	+	2.02913i	0.206269	+	0.0942001i
$465$	2.33103	+	2.23206i	0.108099	+	0.103510i
$466$	1.97791	+	4.33102i	0.0916249	+	0.200631i
$467$	−0.135175	+	1.88999i	−0.00625514	+	0.0874582i	−0.999621	−	0.0275415i	$-0.991232\pi$
$467$	−0.135175	+	1.88999i	−0.00625514	+	0.0874582i	0.993366	+	0.115000i	$0.0366867\pi$
$468$	−0.0387098	+	0.0517102i	−0.00178936	+	0.00239031i
$469$	−3.06775	+	10.4478i	−0.141655	+	0.482434i
$470$	−5.95157	−	8.83364i	−0.274525	−	0.407466i
$471$	−7.24551	+	11.2742i	−0.333855	+	0.519489i
$472$	3.74988	−	0.815736i	0.172602	−	0.0375473i
$473$	2.23548	−	0.159885i	0.102788	−	0.00735151i
$474$	−16.0101	−	4.70098i	−0.735367	−	0.215923i
$475$	2.38555	−	5.88650i	0.109457	−	0.270091i
$476$	4.28206	+	4.94176i	0.196268	+	0.226505i
$477$	4.12528	−	11.0603i	0.188884	−	0.506416i
$478$	−2.50723	−	1.36905i	−0.114678	−	0.0626188i
$479$	3.13799	−	6.87123i	0.143378	−	0.313955i	−0.824295	−	0.566160i	$-0.808428\pi$
$479$	3.13799	−	6.87123i	0.143378	−	0.313955i	0.967674	+	0.252205i	$0.0811558\pi$
$480$	−0.884576	+	2.05366i	−0.0403752	+	0.0937364i
$481$	−0.306616	−	0.477104i	−0.0139805	−	0.0217541i
$482$	21.1040	+	21.1040i	0.961262	+	0.961262i
$483$	−3.20825	−	17.2843i	−0.145981	−	0.786464i
$484$		−	10.5105i		−	0.477749i
$485$	0.745652	+	0.386410i	0.0338583	+	0.0175460i
$486$	0.142315	−	0.989821i	0.00645553	−	0.0448992i
$487$	13.7693	+	36.9168i	0.623945	+	1.67286i	0.734179	+	0.678956i	$0.237567\pi$
$487$	13.7693	+	36.9168i	0.623945	+	1.67286i	−0.110233	+	0.993906i	$0.535160\pi$
$488$	3.09698	−	5.67169i	0.140193	−	0.256745i
$489$	−8.67288	+	3.96077i	−0.392201	+	0.179112i
$490$	−4.73612	+	13.5910i	−0.213956	+	0.613979i
$491$	−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	$-0.176407\pi$
$492$	−0.154087	+	0.0841377i	−0.00694676	+	0.00379322i
$493$	−0.621607	−	8.69120i	−0.0279958	−	0.391432i
$494$	−0.0690282	−	0.0443618i	−0.00310573	−	0.00199593i
$495$	1.04992	+	1.15987i	0.0471905	+	0.0521325i
$496$	0.945171	−	1.09079i	0.0424394	−	0.0489777i
$497$	−5.72452	−	10.4837i	−0.256780	−	0.470257i
$498$	11.5223	+	8.62551i	0.516328	+	0.386518i
$499$	32.2157	−	27.9151i	1.44217	−	1.24965i	0.525037	−	0.851079i	$-0.324051\pi$
$499$	32.2157	−	27.9151i	1.44217	−	1.24965i	0.917137	−	0.398572i	$-0.130494\pi$
$500$	−10.4504	−	3.97355i	−0.467356	−	0.177702i
$501$	11.2954	−	3.31663i	0.504642	−	0.148176i
$502$	24.0761	−	8.97993i	1.07457	−	0.400794i
$503$	23.6215	+	31.5546i	1.05323	+	1.40695i	0.908700	+	0.417449i	$0.137076\pi$
$503$	23.6215	+	31.5546i	1.05323	+	1.40695i	0.144529	+	0.989501i	$0.453833\pi$
$504$	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
$508$	1.76792	+	0.384588i	0.0784389	+	0.0170633i
$509$	18.5355	+	2.66500i	0.821571	+	0.118124i	0.540266	−	0.841494i	$-0.318324\pi$
$509$	18.5355	+	2.66500i	0.821571	+	0.118124i	0.281305	+	0.959618i	$0.409233\pi$
$510$	3.97155	−	0.370759i	0.175863	−	0.0164175i
$511$	−1.26868	−	4.32073i	−0.0561231	−	0.191138i
$512$	0.936950	+	0.349464i	0.0414077	+	0.0154443i
$513$	1.26707	+	0.0906223i	0.0559423	+	0.00400107i
$514$	11.7146	−	1.68431i	0.516710	−	0.0742917i
$515$	−0.274608	+	0.0660043i	−0.0121007	+	0.00290850i
$516$	−2.42085	−	2.09768i	−0.106572	−	0.0923451i
$517$	0.708447	+	3.25668i	0.0311574	+	0.143228i
$518$	6.84116	+	31.4483i	0.300583	+	1.38176i
$519$	15.2447	+	13.2096i	0.669167	+	0.579837i
$520$	−0.0754355	+	0.123173i	−0.00330807	+	0.00540147i
$521$	−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	$0.548846\pi$
$522$	−4.87214	−	0.348463i	−0.213248	−	0.0152518i
$523$	5.75761	+	2.14748i	0.251763	+	0.0939026i	0.472177	−	0.881504i	$-0.343468\pi$
$523$	5.75761	+	2.14748i	0.251763	+	0.0939026i	−0.220414	+	0.975406i	$0.570741\pi$
$524$	−3.52142	−	11.9928i	−0.153834	−	0.523910i
$525$	10.5680	+	14.9744i	0.461224	+	0.653535i
$526$	−5.68988	−	0.818081i	−0.248091	−	0.0356700i
$527$	−2.51583	−	0.547285i	−0.109591	−	0.0238401i
$528$	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
$532$	2.79048	+	3.72765i	0.120983	+	0.161614i
$533$	−0.0106252	+	0.00396301i	−0.000460230	+	0.000171657i
$534$	−15.0757	+	4.42664i	−0.652391	+	0.191559i
$535$	−18.1508	+	25.3754i	−0.784725	+	1.09707i
$536$	2.24500	−	1.94530i	0.0969692	−	0.0840243i
$537$	0.217486	+	0.162808i	0.00938522	+	0.00702569i
$538$	−6.44918	−	11.8108i	−0.278044	−	0.509200i
$539$	2.94911	−	3.40346i	0.127027	−	0.146597i
$540$	0.111122	−	2.23331i	0.00478194	−	0.0961062i
$541$	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	$0.456902\pi$
$542$	−0.0505800	−	0.707201i	−0.00217260	−	0.0303769i
$543$	15.1268	−	8.25987i	0.649154	−	0.354465i
$544$	−0.253869	−	1.76570i	−0.0108846	−	0.0757037i
$545$	12.5539	+	25.9831i	0.537751	+	1.11299i
$546$	0.215379	−	0.0983601i	0.00921735	−	0.00420942i
$547$	6.14671	−	11.2569i	0.262814	−	0.481309i	−0.712634	−	0.701536i	$-0.752498\pi$
$547$	6.14671	−	11.2569i	0.262814	−	0.481309i	0.975449	+	0.220227i	$0.0706798\pi$
$548$	−6.82576	−	18.3006i	−0.291582	−	0.781761i
$549$	−0.919659	+	6.39637i	−0.0392501	+	0.272990i
$550$	2.57860	+	2.36411i	0.109952	+	0.100806i
$551$		−	6.20490i		−	0.264338i
$552$	−1.81298	+	4.43994i	−0.0771657	+	0.188977i
$553$	43.2494	+	43.2494i	1.83915	+	1.83915i
$554$	−8.09330	−	12.5934i	−0.343851	−	0.535043i
$555$	18.0311	+	7.76656i	0.765378	+	0.329672i
$556$	−2.25458	+	4.93685i	−0.0956157	+	0.209369i
$557$	−35.6325	−	19.4568i	−1.50980	−	0.824413i	−0.510430	−	0.859919i	$-0.670514\pi$
$557$	−35.6325	−	19.4568i	−1.50980	−	0.824413i	−0.999369	+	0.0355066i	$0.988696\pi$
$558$	−0.504387	+	1.35231i	−0.0213524	+	0.0572480i
$559$	−0.135498	−	0.156373i	−0.00573094	−	0.00661385i
$560$	6.45360	−	5.05310i	0.272714	−	0.213532i
$561$	−1.19754	−	0.351630i	−0.0505602	−	0.0148458i
$562$	−6.67671	+	0.477528i	−0.281640	+	0.0201433i
$563$	3.54629	−	0.771449i	0.149458	−	0.0325127i	−0.137214	−	0.990541i	$-0.543815\pi$
$563$	3.54629	−	0.771449i	0.149458	−	0.0325127i	0.286672	+	0.958029i	$0.407451\pi$
$564$	2.57534	−	4.00731i	0.108441	−	0.168738i
$565$	−0.652960	+	3.34972i	−0.0274702	+	0.140924i
$566$	−7.74210	+	26.3672i	−0.325425	+	1.10829i
$567$	−2.19671	+	2.93446i	−0.0922530	+	0.123236i
$568$	−0.232467	+	3.25032i	−0.00975411	+	0.136380i
$569$	−2.05531	−	4.50051i	−0.0861632	−	0.188671i	0.861646	−	0.507511i	$-0.169434\pi$
$569$	−2.05531	−	4.50051i	−0.0861632	−	0.188671i	−0.947809	+	0.318839i	$0.896707\pi$
$570$	2.83981	−	0.0615880i	0.118947	−	0.00257964i
$571$	−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	$0.791948\pi$
$572$	0.0361798	−	0.0270838i	0.00151275	−	0.00113243i
$573$	−5.05867	+	23.2543i	−0.211329	+	0.971463i
$574$	0.643537			0.0268607
$575$	−22.5718	−	8.09394i	−0.941311	−	0.337541i
$576$	−1.00000			−0.0416667
$577$	−4.49327	+	20.6552i	−0.187057	+	0.859889i	0.783947	+	0.620827i	$0.213203\pi$
$577$	−4.49327	+	20.6552i	−0.187057	+	0.859889i	−0.971005	+	0.239061i	$0.923160\pi$
$578$	11.0618	−	8.28073i	0.460109	−	0.344433i
$579$	−8.75140	−	3.99663i	−0.363696	−	0.166094i
$580$	−10.9197	+	0.236819i	−0.453416	+	0.00983339i
$581$	−21.9171	−	47.9917i	−0.909274	−	1.99103i
$582$	−0.0267937	+	0.374625i	−0.00111064	+	0.0155287i
$583$	−4.94957	+	6.61186i	−0.204990	+	0.273835i
$584$	−0.346105	+	1.17873i	−0.0143219	+	0.0487761i
$585$	0.0276349	−	0.141768i	0.00114256	−	0.00586141i
$586$	−14.3499	+	22.3289i	−0.592789	+	0.922397i
$587$	−2.09649	+	0.456064i	−0.0865315	+	0.0188238i	−0.255623	−	0.966777i	$-0.582280\pi$
$587$	−2.09649	+	0.456064i	−0.0865315	+	0.0188238i	0.169091	+	0.985600i	$0.445917\pi$
$588$	−6.42015	+	0.459178i	−0.264763	+	0.0189362i
$589$	−1.75918	−	0.516542i	−0.0724857	−	0.0212837i
$590$	−6.75640	+	5.29019i	−0.278157	+	0.217794i
$591$	−7.17460	−	8.27993i	−0.295123	−	0.340591i
$592$	3.06829	−	8.22640i	0.126106	−	0.338103i
$593$	−23.1745	−	12.6542i	−0.951662	−	0.519647i	−0.0731260	−	0.997323i	$-0.523298\pi$
$593$	−23.1745	−	12.6542i	−0.951662	−	0.519647i	−0.878536	+	0.477676i	$0.841479\pi$
$594$	−0.290651	+	0.636436i	−0.0119255	+	0.0261133i
$595$	−13.4287	−	5.78414i	−0.550521	−	0.237127i
$596$	−2.68554	−	4.17879i	−0.110004	−	0.171170i
$597$	−12.5931	−	12.5931i	−0.515400	−	0.515400i
$598$	−0.156731	+	0.267209i	−0.00640921	+	0.0109270i
$599$			16.4009i			0.670124i	0.942196	+	0.335062i	$0.108757\pi$
$599$			16.4009i			0.670124i	−0.942196	+	0.335062i	$0.891243\pi$
$600$	−0.216772	−	4.99530i	−0.00884966	−	0.203932i
$601$	−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	$0.942017\pi$
$602$	4.10333	+	11.0015i	0.167239	+	0.448386i
$603$	−1.42364	+	2.60720i	−0.0579750	+	0.106173i
$604$	1.35158	−	0.617246i	0.0549950	−	0.0251154i
$605$	10.2244	+	21.1616i	0.415680	+	0.860340i
$606$	1.72404	+	11.9909i	0.0700342	+	0.487099i
$607$	−30.7800	+	16.8071i	−1.24932	+	0.682181i	−0.961316	−	0.275448i	$-0.911174\pi$
$607$	−30.7800	+	16.8071i	−1.24932	+	0.682181i	−0.288005	+	0.957629i	$0.592992\pi$
$608$	−0.0906223	−	1.26707i	−0.00367522	−	0.0513863i
$609$	15.0626	+	9.68012i	0.610366	+	0.392258i
$610$	−0.718088	+	14.4319i	−0.0290745	+	0.584332i
$611$	0.201496	−	0.232539i	0.00815168	−	0.00940753i
$612$	0.854911	+	1.56565i	0.0345577	+	0.0632878i
$613$	9.82285	+	7.35330i	0.396741	+	0.296997i	0.778958	−	0.627076i	$-0.215748\pi$
$613$	9.82285	+	7.35330i	0.396741	+	0.296997i	−0.382217	+	0.924073i	$0.624839\pi$
$614$	15.2330	−	13.1994i	0.614752	−	0.532686i
$615$	0.228388	−	0.319293i	0.00920948	−	0.0128752i
$616$	−2.46079	+	0.722553i	−0.0991481	+	0.0291125i
$617$	−31.2881	+	11.6698i	−1.25961	+	0.469810i	−0.888542	−	0.458795i	$-0.848281\pi$
$617$	−31.2881	+	11.6698i	−1.25961	+	0.469810i	−0.371068	+	0.928606i	$0.621008\pi$
$618$	−0.0756925	−	0.101113i	−0.00304480	−	0.00406737i
$619$	4.65009	−	2.98843i	0.186903	−	0.120115i	−0.443843	−	0.896104i	$-0.646385\pi$
$619$	4.65009	−	2.98843i	0.186903	−	0.120115i	0.630746	+	0.775989i	$0.282749\pi$
$620$	−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
$623$	56.2783	+	12.2426i	2.25474	+	0.490489i
$624$	−0.0639366	−	0.00919270i	−0.00255951	−	0.000368002i
$625$	24.9060	−	2.16568i	0.996241	−	0.0866271i
$626$	0.860190	+	2.92954i	0.0343801	+	0.117088i
$627$	−0.832746	−	0.310598i	−0.0332567	−	0.0124041i
$628$	−13.3676	−	0.956066i	−0.533423	−	0.0381512i
$629$	−15.5028	+	2.22897i	−0.618137	+	0.0888747i
$630$	−4.28082	+	6.98980i	−0.170552	+	0.278480i
$631$	−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	$0.896687\pi$
$632$	−3.54686	−	16.3047i	−0.141087	−	0.648564i
$633$	0.959436	+	4.41045i	0.0381341	+	0.175300i
$634$	5.32192	+	4.61147i	0.211361	+	0.183145i
$635$	−3.93362	+	0.945477i	−0.156101	+	0.0375201i
$636$	11.6844	−	1.67997i	0.463318	−	0.0666150i
$637$	−0.414704	−	0.0296602i	−0.0164312	−	0.00117518i
$638$	3.20209	+	1.19432i	0.126772	+	0.0472835i
$639$	−0.918060	−	3.12662i	−0.0363179	−	0.123687i
$640$	−2.22639	+	0.207841i	−0.0880057	+	0.00821565i
$641$	−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	$0.642827\pi$
$642$	−13.6336	−	2.96581i	−0.538076	−	0.117051i
$643$	−21.8816	+	21.8816i	−0.862928	+	0.862928i	−0.991677	−	0.128749i	$-0.958904\pi$
$643$	−21.8816	+	21.8816i	−0.862928	+	0.862928i	0.128749	+	0.991677i	$0.458904\pi$
$644$	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
$647$	−16.7595	−	22.3881i	−0.658886	−	0.880168i	0.339282	−	0.940685i	$-0.389816\pi$
$647$	−16.7595	−	22.3881i	−0.658886	−	0.880168i	−0.998167	+	0.0605168i	$0.980725\pi$
$648$	0.936950	−	0.349464i	0.0368069	−	0.0137282i
$649$	2.57625	−	0.756456i	0.101127	−	0.0296935i
$650$	0.0320606	−	0.321375i	0.00125752	−	0.0126054i
$651$	3.99837	−	3.46461i	0.156709	−	0.135789i
$652$	−7.63275	−	5.71381i	−0.298922	−	0.223770i
$653$	19.2168	+	35.1929i	0.752011	+	1.37721i	0.920199	+	0.391451i	$0.128027\pi$
$653$	19.2168	+	35.1929i	0.752011	+	1.37721i	−0.168187	+	0.985755i	$0.553791\pi$
$654$	−8.45111	+	9.75311i	−0.330465	+	0.381377i
$655$	18.7563	+	20.7206i	0.732871	+	0.809621i
$656$	−0.147692	−	0.0949157i	−0.00576639	−	0.00370584i
$657$	−0.0876394	−	1.22536i	−0.00341914	−	0.0478058i
$658$	−15.3252	+	8.36818i	−0.597437	+	0.326225i
$659$	5.16449	+	35.9198i	0.201180	+	1.39924i	0.800790	+	0.598945i	$0.204413\pi$
$659$	5.16449	+	35.9198i	0.201180	+	1.39924i	−0.599610	+	0.800292i	$0.704678\pi$
$660$	−0.514823	+	1.47736i	−0.0200395	+	0.0575063i
$661$	−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	$0.561983\pi$
$662$	−10.1271	+	18.5465i	−0.393602	+	0.720828i
$663$	0.0402676	+	0.107962i	0.00156386	+	0.00419288i
$664$	−2.04836	+	14.2467i	−0.0794919	+	0.552878i
$665$	−9.24448	−	4.79065i	−0.358485	−	0.185773i
$666$			8.77998i			0.340217i
$667$	−23.4062	+	0.953819i	−0.906293	+	0.0369320i
$668$	8.32425	+	8.32425i	0.322075	+	0.322075i
$669$	5.12337	+	7.97212i	0.198081	+	0.308220i
$670$	−2.62769	+	6.10053i	−0.101516	+	0.235684i
$671$	1.87823	−	4.11274i	0.0725081	−	0.158771i
$672$	3.21721	+	1.75673i	0.124107	+	0.0677673i
$673$	8.36853	−	22.4369i	0.322583	−	0.864879i	−0.669895	−	0.742456i	$-0.733661\pi$
$673$	8.36853	−	22.4369i	0.322583	−	0.864879i	0.992478	−	0.122423i	$-0.0390664\pi$
$674$	−7.31009	−	8.43629i	−0.281574	−	0.324954i
$675$	1.94878	+	4.60459i	0.0750087	+	0.177231i
$676$	12.4694	+	3.66135i	0.479593	+	0.140821i
$677$	−14.7689	+	1.05630i	−0.567616	+	0.0405967i	−0.352199	−	0.935925i	$-0.614566\pi$
$677$	−14.7689	+	1.05630i	−0.567616	+	0.0405967i	−0.215418	+	0.976522i	$0.569111\pi$
$678$	−1.49136	+	0.324425i	−0.0572752	+	0.0124595i
$679$	0.744316	−	1.15818i	0.0285642	−	0.0444468i
$680$	2.22877	+	3.30806i	0.0854695	+	0.126858i
$681$	2.72378	−	9.27634i	0.104375	−	0.355470i
$682$	0.605171	−	0.808414i	0.0231732	−	0.0309558i
$683$	−0.320589	+	4.48242i	−0.0122670	+	0.171515i	0.987625	+	0.156833i	$0.0501283\pi$
$683$	−0.320589	+	4.48242i	−0.0122670	+	0.171515i	−0.999892	+	0.0146825i	$0.995326\pi$
$684$	0.527703	+	1.15551i	0.0201772	+	0.0441819i
$685$	31.5452	+	30.2060i	1.20528	+	1.15411i
$686$	−1.87873	−	0.857986i	−0.0717301	−	0.0327581i
$687$	8.24337	−	6.17091i	0.314504	−	0.235435i
$688$	0.680898	−	3.13004i	0.0259590	−	0.119332i
$689$	0.762506			0.0290492
$690$	−0.668860	−	10.7029i	−0.0254631	−	0.407453i
$691$	18.9763			0.721893			0.360946	−	0.932587i	$-0.382454\pi$
$691$	18.9763			0.721893			0.360946	+	0.932587i	$0.382454\pi$
$692$	−4.28778	+	19.7106i	−0.162997	+	0.749285i
$693$	2.05313	−	1.53695i	0.0779920	−	0.0583841i
$694$	19.1431	+	8.74235i	0.726661	+	0.331855i
$695$	−0.263132	−	12.1330i	−0.00998116	−	0.460230i
$696$	−2.02913	−	4.44318i	−0.0769140	−	0.168418i
$697$	−0.0223418	+	0.312378i	−0.000846254	+	0.0118322i
$698$	−0.237634	+	0.317442i	−0.00899458	+	0.0120154i
$699$	1.34141	−	4.56842i	0.0507368	−	0.172794i
$700$	−8.07799	+	16.4517i	−0.305319	+	0.621817i
$701$	−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	$0.308742\pi$
$702$	0.0631179	−	0.0137305i	0.00238223	−	0.000518223i
$703$	−11.1248	+	0.795662i	−0.419580	+	0.0300090i
$704$	0.671322	+	0.197118i	0.0253014	+	0.00742916i
$705$	−1.28691	+	10.5735i	−0.0484679	+	0.398220i
$706$	−0.498245	−	0.575006i	−0.0187517	−	0.0216406i
$707$	15.5183	−	41.6061i	0.583624	−	1.56476i
$708$	−3.36816	−	1.83916i	−0.126583	−	0.0691197i
$709$	16.2772	−	35.6421i	0.611304	−	1.33857i	−0.310375	−	0.950614i	$-0.600455\pi$
$709$	16.2772	−	35.6421i	0.611304	−	1.33857i	0.921679	−	0.387954i	$-0.126818\pi$
$710$	−2.69380	−	6.77027i	−0.101096	−	0.254084i
$711$	9.02112	+	14.0371i	0.338318	+	0.526434i
$712$	−11.1102	−	11.1102i	−0.416373	−	0.416373i
$713$	−1.67809	+	6.71541i	−0.0628448	+	0.251494i
$714$		−	6.53889i		−	0.244712i
$715$	−0.0464970	+	0.0897250i	−0.00173889	+	0.00335552i
$716$	−0.0386632	+	0.268909i	−0.00144491	+	0.0100496i
$717$	0.998298	+	2.67654i	0.0372821	+	0.0999573i
$718$	−17.1307	+	31.3725i	−0.639311	+	1.17081i
$719$	3.74740	−	1.71138i	0.139754	−	0.0638237i	−0.344310	−	0.938856i	$-0.611887\pi$
$719$	3.74740	−	1.71138i	0.139754	−	0.0638237i	0.484065	+	0.875032i	$0.339160\pi$
$720$	2.01338	−	0.972780i	0.0750343	−	0.0362534i
$721$	0.0658899	+	0.458274i	0.00245387	+	0.0170670i
$722$	15.2596	−	8.33238i	0.567904	−	0.310099i
$723$	−2.12916	−	29.7695i	−0.0791843	−	1.10714i
$724$	14.4990	+	9.31796i	0.538852	+	0.346299i
$725$	21.7551	−	11.0993i	0.807966	−	0.412217i
$726$	−6.88289	+	7.94328i	−0.255448	+	0.294803i
$727$	11.2212	+	20.5500i	0.416170	+	0.762159i	0.998717	−	0.0506382i	$-0.0161255\pi$
$727$	11.2212	+	20.5500i	0.416170	+	0.762159i	−0.582547	+	0.812797i	$0.697944\pi$
$728$	0.189549	+	0.141894i	0.00702514	+	0.00525895i
$729$	−0.755750	+	0.654861i	−0.0279907	+	0.0242541i
$730$	−0.449799	−	2.70991i	−0.0166478	−	0.100298i
$731$	−5.48266	+	1.60985i	−0.202784	+	0.0595426i
$732$	−6.05470	+	2.25829i	−0.223788	+	0.0834687i
$733$	0.678273	+	0.906067i	0.0250526	+	0.0334664i	0.812893	−	0.582414i	$-0.197892\pi$
$733$	0.678273	+	0.906067i	0.0250526	+	0.0334664i	−0.787840	+	0.615880i	$0.788801\pi$
$734$	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
$738$	0.171549	+	0.0373183i	0.00631482	+	0.00137370i
$739$	−2.49066	−	0.358102i	−0.0916203	−	0.0131730i	0.0963522	−	0.995347i	$-0.469282\pi$
$739$	−2.49066	−	0.358102i	−0.0916203	−	0.0131730i	−0.187972	+	0.982174i	$0.560192\pi$
$740$	1.82484	+	19.5476i	0.0670825	+	0.718586i
$741$	0.0231173	+	0.0787303i	0.000849235	+	0.00289223i
$742$	−40.5425	−	15.1216i	−1.48836	−	0.555131i
$743$	4.01829	+	0.287394i	0.147417	+	0.0105435i	0.144853	−	0.989453i	$-0.453729\pi$
$743$	4.01829	+	0.287394i	0.147417	+	0.0105435i	0.00256430	+	0.999997i	$0.499184\pi$
$744$	−1.42862	+	0.205405i	−0.0523759	+	0.00753052i
$745$	9.47206	+	5.80105i	0.347030	+	0.212534i
$746$	−16.5466	−	14.3377i	−0.605814	−	0.524941i
$747$	−3.05949	−	14.0642i	−0.111941	−	0.514584i
$748$	−0.265302	−	1.21958i	−0.00970042	−	0.0445921i
$749$	38.6521	+	33.4922i	1.41232	+	1.22378i
$750$	5.29577	+	9.84657i	0.193374	+	0.359546i
$751$	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	$0.351666\pi$
$752$	4.75136	+	0.339824i	0.173264	+	0.0123921i
$753$	−24.0761	−	8.97993i	−0.877383	−	0.327247i
$754$	−0.0888910	−	0.302735i	−0.00323722	−	0.0110250i
$755$	−2.12080	+	2.55754i	−0.0771838	+	0.0930784i
$756$	−3.62828	−	0.521668i	−0.131959	−	0.0189729i
$757$	−49.9521	−	10.8664i	−1.81554	−	0.394946i	−0.829104	−	0.559095i	$-0.811149\pi$
$757$	−49.9521	−	10.8664i	−1.81554	−	0.394946i	−0.986436	+	0.164148i	$0.947512\pi$
$758$	−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	$0.233097\pi$
$762$	−1.08426	−	1.44840i	−0.0392784	−	0.0524698i
$763$	44.3226	−	16.5315i	1.60459	−	0.598480i
$764$	−22.8342	+	6.70472i	−0.826112	+	0.242568i
$765$	−3.24430	−	2.32061i	−0.117298	−	0.0839020i
$766$	17.5546	−	15.2111i	0.634272	−	0.549600i
$767$	−0.198442	−	0.148552i	−0.00716533	−	0.00536390i
$768$	−0.479249	−	0.877679i	−0.0172934	−	0.0316705i
$769$	34.0656	−	39.3138i	1.22844	−	1.41769i	0.352120	−	0.935955i	$-0.385461\pi$
$769$	34.0656	−	39.3138i	1.22844	−	1.41769i	0.876317	−	0.481736i	$-0.159994\pi$
$770$	4.25162	−	3.84858i	0.153218	−	0.138693i
$771$	−9.95631	−	6.39853i	−0.358568	−	0.230438i
$772$	−0.686341	−	9.59630i	−0.0247019	−	0.345378i
$773$	−39.6303	+	21.6398i	−1.42540	+	0.778329i	−0.992399	−	0.123063i	$-0.960728\pi$
$773$	−39.6303	+	21.6398i	−1.42540	+	0.778329i	−0.433004	+	0.901392i	$0.642546\pi$
$774$	0.455869	+	3.17064i	0.0163859	+	0.113966i
$775$	−1.33575	−	7.09188i	−0.0479814	−	0.254748i
$776$	−0.341641	+	0.156022i	−0.0122642	+	0.00560088i
$777$	15.4241	−	28.2471i	0.553335	−	1.01336i
$778$	−2.90760	−	7.79558i	−0.104243	−	0.279485i
$779$	−0.0317385	+	0.220746i	−0.00113715	+	0.00790905i
$780$	0.137671	−	0.0436878i	0.00492942	−	0.00156428i
$781$			2.27994i			0.0815826i
$782$	4.91442	+	7.00269i	0.175739	+	0.250416i
$783$	3.45393	+	3.45393i	0.123433	+	0.123433i
$784$	−3.47986	−	5.41477i	−0.124281	−	0.193385i
$785$	27.8440	−	11.0788i	0.993795	−	0.395418i
$786$	−5.19234	+	11.3696i	−0.185204	+	0.405541i
$787$	−45.3414	−	24.7583i	−1.61625	−	0.882537i	−0.995103	−	0.0988390i	$-0.968487\pi$
$787$	−45.3414	−	24.7583i	−1.61625	−	0.882537i	−0.621142	−	0.783698i	$-0.713331\pi$
$788$	3.82870	−	10.2651i	0.136392	−	0.365680i
$789$	3.76439	+	4.34434i	0.134016	+	0.154663i
$790$	23.0020	+	29.3771i	0.818375	+	1.04519i
$791$	5.36793	+	1.57617i	0.190862	+	0.0560421i
$792$	−0.697881	+	0.0499134i	−0.0247981	+	0.00177360i
$793$	−0.407877	+	0.0887282i	−0.0144841	+	0.00315083i
$794$	−7.17925	+	11.1711i	−0.254782	+	0.396449i
$795$	−21.8910	+	14.7488i	−0.776392	+	0.523086i
$796$	5.01746	−	17.0879i	0.177839	−	0.605664i
$797$	−20.4077	+	27.2615i	−0.722877	+	0.965651i	0.277111	+	0.960838i	$0.410623\pi$
$797$	−20.4077	+	27.2615i	−0.722877	+	0.965651i	−0.999988	+	0.00481328i	$0.998468\pi$
$798$	0.332184	−	4.64454i	0.0117592	−	0.164415i
$799$	−3.52994	−	7.72950i	−0.124880	−	0.273450i
$800$	4.28038	−	2.58425i	0.151334	−	0.0913670i
$801$	14.2923	+	6.52709i	0.504994	+	0.230623i
$802$	−14.4204	+	10.7949i	−0.509201	+	0.381183i
$803$	−0.182706	+	0.839886i	−0.00644755	+	0.0296389i
$804$	−2.97056			−0.104764
$805$	−16.6503	+	35.6086i	−0.586846	+	1.25504i
$806$	−0.0932297			−0.00328387
$807$	−2.86046	+	13.1493i	−0.100693	+	0.462878i
$808$	−9.69795	+	7.25980i	−0.341173	+	0.255399i
$809$	−10.5605	−	4.82284i	−0.371289	−	0.169562i	0.221027	−	0.975268i	$-0.429059\pi$
$809$	−10.5605	−	4.82284i	−0.371289	−	0.169562i	−0.592316	+	0.805706i	$0.701786\pi$
$810$	−1.54648	+	1.61505i	−0.0543379	+	0.0567471i
$811$	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	$0.785637\pi$
$812$	−1.27732	+	17.8593i	−0.0448252	+	0.626738i
$813$	−0.424892	+	0.567590i	−0.0149016	+	0.0199062i
$814$	1.73069	−	5.89420i	0.0606607	−	0.206591i
$815$	20.9259	+	4.07908i	0.733002	+	0.142884i
$816$	−0.964425	+	1.50068i	−0.0337616	+	0.0525341i
$817$	−3.97609	+	0.864946i	−0.139106	+	0.0302606i
$818$	−34.3656	+	2.45788i	−1.20156	+	0.0859376i
$819$	−0.227184	−	0.0667074i	−0.00793847	−	0.00233094i
$820$	0.389692	+	0.0474299i	0.0136086	+	0.00165633i
$821$	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	$0.738097\pi$
$822$	−6.82576	+	18.3006i	−0.238076	+	0.638305i
$823$	41.0163	+	22.3966i	1.42974	+	0.780697i	0.992912	−	0.118849i	$-0.0379205\pi$
$823$	41.0163	+	22.3966i	1.42974	+	0.780697i	0.436827	+	0.899546i	$0.356102\pi$
$824$	0.0524695	−	0.114892i	0.00182786	−	0.00400246i
$825$	−0.400613	−	3.47530i	−0.0139476	−	0.120994i
$826$	7.60519	+	11.8339i	0.264618	+	0.411754i
$827$	17.8799	+	17.8799i	0.621746	+	0.621746i	0.945978	−	0.324231i	$-0.105106\pi$
$827$	17.8799	+	17.8799i	0.621746	+	0.621746i	−0.324231	+	0.945978i	$0.605106\pi$
$828$	4.27771	−	2.16823i	0.148661	−	0.0753513i
$829$			23.7220i			0.823899i	0.911207	+	0.411950i	$0.135152\pi$
$829$			23.7220i			0.823899i	−0.911207	+	0.411950i	$0.864848\pi$
$830$	−9.73474	−	30.6766i	−0.337898	−	1.06480i
$831$	−2.13043	+	14.8175i	−0.0739037	+	0.514012i
$832$	−0.0225733	−	0.0605214i	−0.000782589	−	0.00209820i
$833$	−5.50268	+	10.0774i	−0.190657	+	0.349161i
$834$	4.93685	−	2.25458i	0.170949	−	0.0780699i
$835$	−24.8575	−	8.66222i	−0.860231	−	0.299768i
$836$	−0.126487	−	0.879737i	−0.00437465	−	0.0304263i
$837$	1.26677	−	0.691707i	0.0437859	−	0.0239089i
$838$	0.733818	+	10.2601i	0.0253493	+	0.354430i
$839$	32.9960	+	21.2053i	1.13915	+	0.732087i	0.967450	−	0.253062i	$-0.0814378\pi$
$839$	32.9960	+	21.2053i	1.13915	+	0.732087i	0.171700	+	0.985149i	$0.445074\pi$
$840$	−8.18638	−	0.407329i	−0.282457	−	0.0140542i
$841$	−3.36650	+	3.88515i	−0.116086	+	0.133971i
$842$	−16.7157	−	30.6124i	−0.576059	−	1.05497i
$843$	5.35864	+	4.01142i	0.184561	+	0.138161i
$844$	−3.41116	+	2.95578i	−0.117417	+	0.101742i
$845$	−28.6673	+	4.75830i	−0.986186	+	0.163690i
$846$	−4.57054	+	1.34203i	−0.157138	+	0.0461400i
$847$	36.0979	−	13.4638i	1.24034	−	0.462623i
$848$	7.07422	+	9.45006i	0.242930	+	0.324516i
$849$	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
$853$	−28.6707	−	6.23693i	−0.981666	−	0.213548i	−0.307031	−	0.951700i	$-0.599335\pi$
$853$	−28.6707	−	6.23693i	−0.981666	−	0.213548i	−0.674635	+	0.738151i	$0.735699\pi$
$854$	23.4465	+	3.37109i	0.802321	+	0.115356i
$855$	−2.18652	−	1.81314i	−0.0747774	−	0.0620080i
$856$	−3.93087	−	13.3873i	−0.134354	−	0.457569i
$857$	6.58517	+	2.45614i	0.224945	+	0.0839002i	0.459410	−	0.888224i	$-0.348061\pi$
$857$	6.58517	+	2.45614i	0.224945	+	0.0839002i	−0.234465	+	0.972125i	$0.575334\pi$
$858$	−0.0450790	−	0.00322411i	−0.00153897	−	0.000110069i
$859$	−17.4096	+	2.50312i	−0.594007	+	0.0854053i	−0.432760	−	0.901509i	$-0.642460\pi$
$859$	−17.4096	+	2.50312i	−0.594007	+	0.0854053i	−0.161246	+	0.986914i	$0.551551\pi$
$860$	1.67393	+	6.96432i	0.0570805	+	0.237481i
$861$	−0.486352	−	0.421427i	−0.0165748	−	0.0143622i
$862$	−7.09491	−	32.6148i	−0.241653	−	1.11086i
$863$	9.82534	+	45.1664i	0.334458	+	1.53748i	0.770433	+	0.637521i	$0.220040\pi$
$863$	9.82534	+	45.1664i	0.334458	+	1.53748i	−0.435974	+	0.899959i	$0.643596\pi$
$864$	0.755750	+	0.654861i	0.0257111	+	0.0222788i
$865$	−10.5411	−	43.8560i	−0.358410	−	1.49115i
$866$	−36.1274	+	5.19434i	−1.22766	+	0.176511i
$867$	−13.7827	−	0.985755i	−0.468083	−	0.0334780i
$868$	4.95703	+	1.84888i	0.168253	+	0.0627549i
$869$	−3.28910	−	11.2017i	−0.111575	−	0.379990i
$870$	8.40765	+	6.97191i	0.285046	+	0.236370i
$871$	−0.189928	−	0.0273075i	−0.00643545	−	0.000925278i
$872$	−12.6103	−	2.74320i	−0.427038	−	0.0928964i
$873$	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
$877$	−9.62430	−	12.8566i	−0.324990	−	0.434135i	0.608056	−	0.793894i	$-0.291950\pi$
$877$	−9.62430	−	12.8566i	−0.324990	−	0.434135i	−0.933045	+	0.359759i	$0.882859\pi$
$878$	0.247030	−	0.0921376i	0.00833687	−	0.00310949i
$879$	25.4672	−	7.47785i	0.858988	−	0.252222i
$880$	−1.54338	+	0.256175i	−0.0520273	+	0.00863566i
$881$	−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	$0.974427\pi$
$882$	5.15273	+	3.85728i	0.173501	+	0.129881i
$883$	−26.1434	−	47.8781i	−0.879795	−	1.61122i	−0.788192	−	0.615429i	$-0.788983\pi$
$883$	−26.1434	−	47.8781i	−0.879795	−	1.61122i	−0.0916032	−	0.995796i	$-0.529199\pi$
$884$	−0.0754574	+	0.0870824i	−0.00253791	+	0.00292890i
$885$	8.57049	+	0.426441i	0.288094	+	0.0143346i
$886$	−18.7969	−	12.0800i	−0.631495	−	0.405837i
$887$	3.61480	+	50.5415i	0.121373	+	1.69702i	0.585038	+	0.811006i	$0.301080\pi$
$887$	3.61480	+	50.5415i	0.121373	+	1.69702i	−0.463665	+	0.886011i	$0.653466\pi$
$888$	−7.70601	+	4.20780i	−0.258597	+	0.141204i
$889$	0.943838	+	6.56454i	0.0316553	+	0.220168i
$890$	33.1768	+	11.5613i	1.11209	+	0.387535i
$891$	0.636436	−	0.290651i	0.0213214	−	0.00973716i
$892$	−4.54159	+	8.31730i	−0.152064	+	0.278484i
$893$	−2.11463	−	5.66956i	−0.0707636	−	0.189724i
$894$	−0.706926	+	4.91678i	−0.0236431	+	0.164442i
$895$	−0.183745	−	0.579026i	−0.00614192	−	0.0193547i
$896$			3.66559i			0.122459i
$897$	0.293434	−	0.0993058i	0.00979748	−	0.00331573i
$898$	−19.0071	−	19.0071i	−0.634275	−	0.634275i
$899$	−3.81152	−	5.93084i	−0.127121	−	0.197805i
$900$	−3.10740	+	3.91715i	−0.103580	+	0.130572i
$901$	8.74767	−	19.1547i	0.291427	−	0.638137i
$902$	−0.107809	−	0.0588680i	−0.00358964	−	0.00196009i
$903$	4.10333	−	11.0015i	0.136550	−	0.366105i
$904$	−0.999471	−	1.15345i	−0.0332419	−	0.0383632i
$905$	−38.2564	−	4.65624i	−1.27169	−	0.154779i
$906$	−1.42567	−	0.418613i	−0.0473646	−	0.0139075i
$907$	9.27323	−	0.663235i	0.307913	−	0.0220223i	0.0834720	−	0.996510i	$-0.473399\pi$
$907$	9.27323	−	0.663235i	0.307913	−	0.0220223i	0.224441	+	0.974488i	$0.427945\pi$
$908$	9.44701	−	2.05507i	0.313510	−	0.0682000i
$909$	6.54946	−	10.1912i	0.217232	−	0.338019i
$910$	−0.519665	−	0.101298i	−0.0172267	−	0.00335800i
$911$	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	$-0.0270162\pi$
$912$	−0.761264	+	1.01693i	−0.0252080	+	0.0336739i
$913$	−0.718412	+	10.0447i	−0.0237760	+	0.332432i
$914$	−9.77386	−	21.4018i	−0.323290	−	0.707907i
$915$	9.99360	−	10.4367i	0.330378	−	0.345026i
$916$	9.36670	+	4.27763i	0.309484	+	0.141337i
$917$	36.6782	−	27.4570i	1.21122	−	0.906709i
$918$	0.379186	−	1.74309i	0.0125150	−	0.0575305i
$919$	4.39797			0.145076			0.0725378	−	0.997366i	$-0.476890\pi$
$919$	4.39797			0.145076			0.0725378	+	0.997366i	$0.476890\pi$
$920$	9.07318	−	5.71641i	0.299134	−	0.188464i
$921$	−20.1561			−0.664166
$922$	3.87208	−	17.7997i	0.127520	−	0.586201i
$923$	0.168504	−	0.126141i	0.00554638	−	0.00415197i
$924$	2.33291	+	1.06541i	0.0767472	+	0.0350493i
$925$	−22.6897	−	37.5817i	−0.746031	−	1.23568i
$926$	7.90949	+	17.3194i	0.259922	+	0.569149i
$927$	−0.00901058	+	0.125984i	−0.000295946	+	0.00413787i
$928$	2.92723	−	3.91031i	0.0960909	−	0.128362i
$929$	−10.2410	+	34.8775i	−0.335995	+	1.14429i	0.602246	+	0.798310i	$0.294273\pi$
$929$	−10.2410	+	34.8775i	−0.335995	+	1.14429i	−0.938241	+	0.345983i	$0.887546\pi$
$930$	2.67655	−	1.80330i	0.0877675	−	0.0591324i
$931$	−4.42048	+	6.87840i	−0.144875	+	0.225430i
$932$	4.65247	−	1.01208i	0.152397	−	0.0331519i
$933$	−25.8845	+	1.85130i	−0.847421	+	0.0606088i
$934$	1.81806	+	0.533831i	0.0594888	+	0.0174675i
$935$	1.72053	+	2.19739i	0.0562674	+	0.0718623i
$936$	0.0423001	+	0.0488170i	0.00138262	+	0.00159563i
$937$	11.2629	−	30.1971i	0.367944	−	0.986495i	−0.612635	−	0.790366i	$-0.709890\pi$
$937$	11.2629	−	30.1971i	0.367944	−	0.986495i	0.980578	−	0.196129i	$-0.0628370\pi$
$938$	9.55692	+	5.21847i	0.312045	+	0.170389i
$939$	1.26835	−	2.77730i	0.0413911	−	0.0906338i
$940$	−9.89686	+	3.93783i	−0.322800	+	0.128438i
$941$	−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
$943$	0.837581	+	0.0857914i	0.0272754	+	0.00279375i
$944$		−	3.83758i		−	0.124903i
$945$	7.81257	−	2.47920i	0.254143	−	0.0806484i
$946$	0.318955	−	2.21838i	0.0103701	−	0.0721257i
$947$	−6.17521	−	16.5564i	−0.200667	−	0.538010i	0.797169	−	0.603756i	$-0.206330\pi$
$947$	−6.17521	−	16.5564i	−0.200667	−	0.538010i	−0.997836	+	0.0657461i	$0.979057\pi$
$948$	−7.99674	+	14.6449i	−0.259722	+	0.475645i
$949$	0.0721822	−	0.0329645i	0.00234313	−	0.00107007i
$950$	−5.24489	−	3.58230i	−0.170167	−	0.116225i
$951$	−1.00217	−	6.97024i	−0.0324975	−	0.226025i
$952$	5.73904	−	3.13375i	0.186003	−	0.101566i
$953$	1.90565	+	26.6445i	0.0617301	+	0.863100i	0.930129	+	0.367234i	$0.119695\pi$
$953$	1.90565	+	26.6445i	0.0617301	+	0.863100i	−0.868399	+	0.495867i	$0.834850\pi$
$954$	−9.93065	−	6.38204i	−0.321517	−	0.206626i
$955$	39.4517	−	35.7118i	1.27663	−	1.15561i
$956$	−1.87071	+	2.15892i	−0.0605031	+	0.0698243i
$957$	−1.63787	−	2.99953i	−0.0529447	−	0.0969609i
$958$	−6.04718	−	4.52686i	−0.195375	−	0.146256i
$959$	54.1090	−	46.8858i	1.74727	−	1.51402i
$960$	1.81870	+	1.30090i	0.0586982	+	0.0419863i
$961$	27.7455	−	8.14682i	0.895016	−	0.262800i
$962$	−0.531377	+	0.198193i	−0.0171323	+	0.00639001i
$963$	8.36141	+	11.1695i	0.269443	+	0.359933i
$964$	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	−0.686987	−	0.726669i	$-0.741067\pi$
$967$	1.23397	−	1.23397i	0.0396818	−	0.0396818i	0.726669	+	0.686987i	$0.241067\pi$
$968$	−10.2703	−	2.23416i	−0.330099	−	0.0718087i
$969$	2.24297	+	0.322491i	0.0720546	+	0.0103599i
$970$	0.536079	−	0.646474i	0.0172124	−	0.0207570i
$971$	−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	$-0.320416\pi$
$972$	−0.936950	−	0.349464i	−0.0300527	−	0.0112091i
$973$	−19.8436	−	1.41924i	−0.636156	−	0.0454988i
$974$	39.0001	−	5.60736i	1.24964	−	0.179671i
$975$	−0.234686	+	0.221884i	−0.00751596	+	0.00710597i
$976$	−4.88376	−	4.23180i	−0.156325	−	0.135457i
$977$	−2.43751	−	11.2050i	−0.0779828	−	0.358481i	0.921576	−	0.388199i	$-0.126903\pi$
$977$	−2.43751	−	11.2050i	−0.0779828	−	0.358481i	−0.999558	+	0.0297180i	$0.990539\pi$
$978$	2.02670	+	9.31660i	0.0648068	+	0.297912i
$979$	−8.30815	−	7.19905i	−0.265529	−	0.230083i
$980$	12.2737	+	7.51686i	0.392068	+	0.240117i
$981$	12.7739	−	1.83660i	0.407838	−	0.0586382i
$982$	−17.6769	−	1.26428i	−0.564093	−	0.0403448i
$983$	−7.84113	−	2.92459i	−0.250093	−	0.0932799i	0.221291	−	0.975208i	$-0.428973\pi$
$983$	−7.84113	−	2.92459i	−0.250093	−	0.0932799i	−0.471384	+	0.881928i	$0.656246\pi$
$984$	0.0494614	+	0.168450i	0.00157677	+	0.00536999i
$985$	2.27709	+	24.3921i	0.0725541	+	0.777197i
$986$	−8.62471	−	1.24005i	−0.274667	−	0.0394911i
$987$	17.0620	+	3.71161i	0.543089	+	0.118142i
$988$	−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	$0.274790\pi$
$992$	−0.864947	−	1.15543i	−0.0274621	−	0.0366851i
$993$	19.7989	−	7.38461i	0.628300	−	0.234344i
$994$	−11.4609	+	3.36523i	−0.363518	+	0.106739i
$995$	6.52070	+	39.2853i	0.206720	+	1.24543i
$996$	10.8776	−	9.42552i	0.344671	−	0.298659i
$997$	−38.3343	−	28.6967i	−1.21406	−	0.908834i	−0.216339	−	0.976318i	$-0.569412\pi$
$997$	−38.3343	−	28.6967i	−1.21406	−	0.908834i	−0.997720	+	0.0674846i	$0.978503\pi$
$998$	−20.4292	−	37.4133i	−0.646675	−	1.18430i
$999$	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.103.12	yes	240
5.2	odd	4	inner	690.2.w.a.517.8	yes	240
23.21	odd	22	inner	690.2.w.a.343.8	yes	240
115.67	even	44	inner	690.2.w.a.67.12	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.67.12	✓	240	115.67	even	44	inner
690.2.w.a.103.12	yes	240	1.1	even	1	trivial
690.2.w.a.343.8	yes	240	23.21	odd	22	inner
690.2.w.a.517.8	yes	240	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.212565 - 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(2.23554 - 0.0484830i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.261500 - 3.65625i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +O(q^{10})\)	\(q+(0.212565 - 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(2.23554 - 0.0484830i) q^{5} +(0.415415 + 0.909632i) q^{6} +(0.261500 - 3.65625i) q^{7} +(-0.599278 + 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +(0.427824 - 2.19476i) q^{10} +(-0.378266 + 0.588594i) q^{11} +(0.977147 - 0.212565i) q^{12} +(0.0644295 - 0.00460809i) q^{13} +(-3.51711 - 1.03272i) q^{14} +(-1.76059 + 1.37852i) q^{15} +(0.654861 + 0.755750i) q^{16} +(0.623394 - 1.67138i) q^{17} +(-0.877679 - 0.479249i) q^{18} +(0.527703 - 1.15551i) q^{19} +(-2.05366 - 0.884576i) q^{20} +(1.98177 + 3.08369i) q^{21} +(0.494737 + 0.494737i) q^{22} +(-4.43994 - 1.81298i) q^{23} -1.00000i q^{24} +(4.99530 - 0.216772i) q^{25} +(0.00919270 - 0.0639366i) q^{26} +(0.349464 + 0.936950i) q^{27} +(-1.75673 + 3.21721i) q^{28} +(4.44318 - 2.02913i) q^{29} +(0.972780 + 2.01338i) q^{30} +(-0.205405 - 1.42862i) q^{31} +(0.877679 - 0.479249i) q^{32} +(-0.0499134 - 0.697881i) q^{33} +(-1.50068 - 0.964425i) q^{34} +(0.407329 - 8.18638i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-4.20780 - 7.70601i) q^{37} +(-1.01693 - 0.761264i) q^{38} +(-0.0488170 + 0.0423001i) q^{39} +(-1.30090 + 1.81870i) q^{40} +(-0.168450 + 0.0494614i) q^{41} +(3.43447 - 1.28099i) q^{42} +(-1.91963 - 2.56433i) 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} +(-0.977147 - 0.212565i) q^{48} +(-6.37104 - 0.916017i) q^{49} +(0.850010 - 4.92722i) q^{50} +(0.502570 + 1.71160i) q^{51} +(-0.0605214 - 0.0225733i) q^{52} +(11.7745 + 0.842129i) q^{53} +(0.989821 - 0.142315i) q^{54} +(-0.817094 + 1.33417i) q^{55} +(2.77027 + 2.40045i) q^{56} +(0.270022 + 1.24127i) q^{57} +(-1.03829 - 4.77296i) q^{58} +(-2.90025 - 2.51308i) q^{59} +(2.17415 - 0.522574i) q^{60} +(-6.39637 + 0.919659i) q^{61} +(-1.43964 - 0.102965i) q^{62} +(-3.43447 - 1.28099i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(0.143812 - 0.0134253i) q^{65} +(-0.692542 - 0.0995725i) q^{66} +(-2.90267 - 0.631438i) 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} +(0.599278 + 0.800541i) q^{72} +(1.15103 - 0.429313i) q^{73} +(-8.42433 + 2.47361i) q^{74} +(-3.86904 + 3.16711i) q^{75} +(-0.960030 + 0.831871i) q^{76} +(2.05313 + 1.53695i) q^{77} +(0.0309567 + 0.0566929i) q^{78} +(-10.9270 + 12.6104i) q^{79} +(1.50061 + 1.65776i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(0.0125244 + 0.175114i) q^{82} +(12.6326 - 6.89791i) q^{83} +(-0.521668 - 3.62828i) q^{84} +(1.31259 - 3.76667i) q^{85} +(-2.91377 + 1.33067i) q^{86} +(-2.34093 + 4.28710i) q^{87} +(-0.244507 - 0.655549i) q^{88} +(-2.23608 + 15.5523i) q^{89} +(-1.98532 - 1.02883i) q^{90} -0.236776i q^{91} +(3.28557 + 3.49357i) q^{92} +(1.02058 + 1.02058i) q^{93} +(-2.57534 - 4.00731i) q^{94} +(1.12368 - 2.60877i) q^{95} +(-0.415415 + 0.909632i) q^{96} +(0.329640 + 0.179997i) q^{97} +(-2.24934 + 6.03073i) 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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