LMFDB - Embedded newform 780.2.g.d.131.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [780,2,Mod(131,780)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(780, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("780.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	780.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.22833135766$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.10
Character	$\chi$	$=$	780.131
Dual form			780.2.g.d.131.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.885473 + 1.10270i) q^{2} +(-1.58822 + 0.691055i) q^{3} +(-0.431874 - 1.95281i) q^{4} -1.00000i q^{5} +(0.644303 - 2.36323i) q^{6} +2.86589i q^{7} +(2.53577 + 1.25294i) q^{8} +(2.04489 - 2.19509i) q^{9} +(1.10270 + 0.885473i) q^{10} -4.24800 q^{11} +(2.03541 + 2.80305i) q^{12} +1.00000 q^{13} +(-3.16020 - 2.53767i) q^{14} +(0.691055 + 1.58822i) q^{15} +(-3.62697 + 1.68674i) q^{16} -6.17427i q^{17} +(0.609829 + 4.19858i) q^{18} -2.87129i q^{19} +(-1.95281 + 0.431874i) q^{20} +(-1.98048 - 4.55166i) q^{21} +(3.76149 - 4.68425i) q^{22} +3.95180 q^{23} +(-4.89322 - 0.237585i) q^{24} -1.00000 q^{25} +(-0.885473 + 1.10270i) q^{26} +(-1.73080 + 4.89942i) q^{27} +(5.59654 - 1.23770i) q^{28} +10.2281i q^{29} +(-2.36323 - 0.644303i) q^{30} -7.95193i q^{31} +(1.35162 - 5.49301i) q^{32} +(6.74675 - 2.93560i) q^{33} +(6.80834 + 5.46715i) q^{34} +2.86589 q^{35} +(-5.16975 - 3.04528i) q^{36} +9.09015 q^{37} +(3.16615 + 2.54245i) q^{38} +(-1.58822 + 0.691055i) q^{39} +(1.25294 - 2.53577i) q^{40} -4.90666i q^{41} +(6.77276 + 1.84650i) q^{42} -0.365453i q^{43} +(1.83460 + 8.29555i) q^{44} +(-2.19509 - 2.04489i) q^{45} +(-3.49921 + 4.35763i) q^{46} +9.74823 q^{47} +(4.59479 - 5.18535i) q^{48} -1.21330 q^{49} +(0.885473 - 1.10270i) q^{50} +(4.26676 + 9.80610i) q^{51} +(-0.431874 - 1.95281i) q^{52} +11.9264i q^{53} +(-3.87000 - 6.24685i) q^{54} +4.24800i q^{55} +(-3.59078 + 7.26724i) q^{56} +(1.98422 + 4.56023i) q^{57} +(-11.2784 - 9.05667i) q^{58} +3.66920 q^{59} +(2.80305 - 2.03541i) q^{60} +8.03057 q^{61} +(8.76856 + 7.04122i) q^{62} +(6.29089 + 5.86041i) q^{63} +(4.86029 + 6.35434i) q^{64} -1.00000i q^{65} +(-2.73700 + 10.0390i) q^{66} +1.85359i q^{67} +(-12.0572 + 2.66651i) q^{68} +(-6.27633 + 2.73091i) q^{69} +(-2.53767 + 3.16020i) q^{70} +5.11426 q^{71} +(7.93569 - 3.00414i) q^{72} -14.0499 q^{73} +(-8.04908 + 10.0237i) q^{74} +(1.58822 - 0.691055i) q^{75} +(-5.60709 + 1.24003i) q^{76} -12.1743i q^{77} +(0.644303 - 2.36323i) q^{78} -1.80212i q^{79} +(1.68674 + 3.62697i) q^{80} +(-0.636882 - 8.97744i) q^{81} +(5.41056 + 4.34472i) q^{82} +16.1101 q^{83} +(-8.03322 + 5.83326i) q^{84} -6.17427 q^{85} +(0.402983 + 0.323599i) q^{86} +(-7.06815 - 16.2444i) q^{87} +(-10.7720 - 5.32248i) q^{88} -6.13592i q^{89} +(4.19858 - 0.609829i) q^{90} +2.86589i q^{91} +(-1.70668 - 7.71713i) q^{92} +(5.49522 + 12.6294i) q^{93} +(-8.63180 + 10.7493i) q^{94} -2.87129 q^{95} +(1.64930 + 9.65815i) q^{96} +9.93736 q^{97} +(1.07435 - 1.33790i) q^{98} +(-8.68667 + 9.32475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 6 q^{4} + 10 q^{6} + 12 q^{9} + 6 q^{10} - 20 q^{12} + 32 q^{13} - 6 q^{16} + 4 q^{18} + 20 q^{21} + 16 q^{22} + 10 q^{24} - 32 q^{25} + 16 q^{28} + 16 q^{33} + 28 q^{34} + 30 q^{36} - 24 q^{37}+ \cdots + 112 q^{97}+O(q^{100}) $ 32 * q + 6 * q^4 + 10 * q^6 + 12 * q^9 + 6 * q^10 - 20 * q^12 + 32 * q^13 - 6 * q^16 + 4 * q^18 + 20 * q^21 + 16 * q^22 + 10 * q^24 - 32 * q^25 + 16 * q^28 + 16 * q^33 + 28 * q^34 + 30 * q^36 - 24 * q^37 + 6 * q^40 + 20 * q^45 - 80 * q^46 - 16 * q^48 + 16 * q^49 + 6 * q^52 + 2 * q^54 - 64 * q^57 - 100 * q^58 + 14 * q^60 + 16 * q^61 + 126 * q^64 + 60 * q^66 - 4 * q^69 - 16 * q^70 - 16 * q^72 - 104 * q^73 + 20 * q^76 + 10 * q^78 - 72 * q^81 - 116 * q^82 + 20 * q^84 + 24 * q^85 - 14 * q^90 + 16 * q^93 + 28 * q^94 - 74 * q^96 + 112 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/780\mathbb{Z}\right)^\times$.

$n$	$157$	$301$	$391$	$521$
$\chi(n)$	$1$	$1$	$-1$	$-1$

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 $

$2$	−0.885473	+	1.10270i	−0.626124	+	0.779723i
$2$	−0.885473	+	1.10270i	−0.626124	+	0.779723i
$3$	−1.58822	+	0.691055i	−0.916959	+	0.398981i
$3$	−1.58822	+	0.691055i	−0.916959	+	0.398981i
$4$	−0.431874	−	1.95281i	−0.215937	−	0.976407i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.644303	−	2.36323i	0.263036	−	0.964786i
$7$			2.86589i			1.08320i	0.840635	+	0.541602i	$0.182182\pi$
$7$			2.86589i			1.08320i	−0.840635	+	0.541602i	$0.817818\pi$
$8$	2.53577	+	1.25294i	0.896531	+	0.442981i
$9$	2.04489	−	2.19509i	0.681629	−	0.731698i
$10$	1.10270	+	0.885473i	0.348703	+	0.280011i
$11$	−4.24800			−1.28082			−0.640409	−	0.768034i	$-0.721235\pi$
$11$	−4.24800			−1.28082			−0.640409	+	0.768034i	$0.721235\pi$
$12$	2.03541	+	2.80305i	0.587573	+	0.809171i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	−3.16020	−	2.53767i	−0.844599	−	0.678220i
$15$	0.691055	+	1.58822i	0.178430	+	0.410077i
$16$	−3.62697	+	1.68674i	−0.906742	+	0.421685i
$17$		−	6.17427i		−	1.49748i	−0.662863	−	0.748740i	$-0.730659\pi$
$17$		−	6.17427i		−	1.49748i	0.662863	−	0.748740i	$-0.269341\pi$
$18$	0.609829	+	4.19858i	0.143738	+	0.989616i
$19$		−	2.87129i		−	0.658718i	−0.944205	−	0.329359i	$-0.893167\pi$
$19$		−	2.87129i		−	0.658718i	0.944205	−	0.329359i	$-0.106833\pi$
$20$	−1.95281	+	0.431874i	−0.436663	+	0.0965700i
$21$	−1.98048	−	4.55166i	−0.432177	−	0.993253i
$22$	3.76149	−	4.68425i	0.801952	−	0.998685i
$23$	3.95180			0.824007			0.412004	−	0.911182i	$-0.364829\pi$
$23$	3.95180			0.824007			0.412004	+	0.911182i	$0.364829\pi$
$24$	−4.89322	−	0.237585i	−0.998823	−	0.0484968i
$25$	−1.00000			−0.200000
$26$	−0.885473	+	1.10270i	−0.173656	+	0.216256i
$27$	−1.73080	+	4.89942i	−0.333092	+	0.942894i
$28$	5.59654	−	1.23770i	1.05765	−	0.233904i
$29$			10.2281i			1.89930i	0.313311	+	0.949651i	$0.398562\pi$
$29$			10.2281i			1.89930i	−0.313311	+	0.949651i	$0.601438\pi$
$30$	−2.36323	−	0.644303i	−0.431465	−	0.117633i
$31$		−	7.95193i		−	1.42821i	−0.700039	−	0.714104i	$-0.746834\pi$
$31$		−	7.95193i		−	1.42821i	0.700039	−	0.714104i	$-0.253166\pi$
$32$	1.35162	−	5.49301i	0.238935	−	0.971035i
$33$	6.74675	−	2.93560i	1.17446	−	0.511022i
$34$	6.80834	+	5.46715i	1.16762	+	0.937609i
$35$	2.86589			0.484423
$36$	−5.16975	−	3.04528i	−0.861624	−	0.507546i
$37$	9.09015			1.49441			0.747206	−	0.664593i	$-0.231395\pi$
$37$	9.09015			1.49441			0.747206	+	0.664593i	$0.231395\pi$
$38$	3.16615	+	2.54245i	0.513618	+	0.412439i
$39$	−1.58822	+	0.691055i	−0.254319	+	0.110657i
$40$	1.25294	−	2.53577i	0.198107	−	0.400941i
$41$		−	4.90666i		−	0.766292i	−0.923688	−	0.383146i	$-0.874841\pi$
$41$		−	4.90666i		−	0.766292i	0.923688	−	0.383146i	$-0.125159\pi$
$42$	6.77276	+	1.84650i	1.04506	+	0.284921i
$43$		−	0.365453i		−	0.0557310i	−0.999612	−	0.0278655i	$-0.991129\pi$
$43$		−	0.365453i		−	0.0557310i	0.999612	−	0.0278655i	$-0.00887102\pi$
$44$	1.83460	+	8.29555i	0.276576	+	1.25060i
$45$	−2.19509	−	2.04489i	−0.327225	−	0.304834i
$46$	−3.49921	+	4.35763i	−0.515931	+	0.642498i
$47$	9.74823			1.42193			0.710963	−	0.703230i	$-0.248259\pi$
$47$	9.74823			1.42193			0.710963	+	0.703230i	$0.248259\pi$
$48$	4.59479	−	5.18535i	0.663201	−	0.748441i
$49$	−1.21330			−0.173329
$50$	0.885473	−	1.10270i	0.125225	−	0.155945i
$51$	4.26676	+	9.80610i	0.597466	+	1.37313i
$52$	−0.431874	−	1.95281i	−0.0598902	−	0.270807i
$53$			11.9264i			1.63821i	0.573640	+	0.819107i	$0.305531\pi$
$53$			11.9264i			1.63821i	−0.573640	+	0.819107i	$0.694469\pi$
$54$	−3.87000	−	6.24685i	−0.526640	−	0.850089i
$55$			4.24800i			0.572800i
$56$	−3.59078	+	7.26724i	−0.479838	+	0.971125i
$57$	1.98422	+	4.56023i	0.262816	+	0.604018i
$58$	−11.2784	−	9.05667i	−1.48093	−	1.18920i
$59$	3.66920			0.477689			0.238845	−	0.971058i	$-0.423231\pi$
$59$	3.66920			0.477689			0.238845	+	0.971058i	$0.423231\pi$
$60$	2.80305	−	2.03541i	0.361872	−	0.262771i
$61$	8.03057			1.02821			0.514105	−	0.857727i	$-0.328124\pi$
$61$	8.03057			1.02821			0.514105	+	0.857727i	$0.328124\pi$
$62$	8.76856	+	7.04122i	1.11361	+	0.894236i
$63$	6.29089	+	5.86041i	0.792578	+	0.738342i
$64$	4.86029	+	6.35434i	0.607536	+	0.794292i
$65$		−	1.00000i		−	0.124035i
$66$	−2.73700	+	10.0390i	−0.336901	+	1.23572i
$67$			1.85359i			0.226452i	0.993569	+	0.113226i	$0.0361184\pi$
$67$			1.85359i			0.226452i	−0.993569	+	0.113226i	$0.963882\pi$
$68$	−12.0572	+	2.66651i	−1.46215	+	0.323362i
$69$	−6.27633	+	2.73091i	−0.755581	+	0.328763i
$70$	−2.53767	+	3.16020i	−0.303309	+	0.377716i
$71$	5.11426			0.606951			0.303475	−	0.952839i	$-0.401853\pi$
$71$	5.11426			0.606951			0.303475	+	0.952839i	$0.401853\pi$
$72$	7.93569	−	3.00414i	0.935230	−	0.354042i
$73$	−14.0499			−1.64442			−0.822209	−	0.569186i	$-0.807259\pi$
$73$	−14.0499			−1.64442			−0.822209	+	0.569186i	$0.807259\pi$
$74$	−8.04908	+	10.0237i	−0.935687	+	1.16523i
$75$	1.58822	−	0.691055i	0.183392	−	0.0797962i
$76$	−5.60709	+	1.24003i	−0.643177	+	0.142242i
$77$		−	12.1743i		−	1.38739i
$78$	0.644303	−	2.36323i	0.0729530	−	0.267584i
$79$		−	1.80212i		−	0.202755i	−0.994848	−	0.101377i	$-0.967675\pi$
$79$		−	1.80212i		−	0.202755i	0.994848	−	0.101377i	$-0.0323249\pi$
$80$	1.68674	+	3.62697i	0.188583	+	0.405507i
$81$	−0.636882	−	8.97744i	−0.0707647	−	0.997493i
$82$	5.41056	+	4.34472i	0.597496	+	0.479794i
$83$	16.1101			1.76831			0.884155	−	0.467194i	$-0.154735\pi$
$83$	16.1101			1.76831			0.884155	+	0.467194i	$0.154735\pi$
$84$	−8.03322	+	5.83326i	−0.876496	+	0.636461i
$85$	−6.17427			−0.669694
$86$	0.402983	+	0.323599i	0.0434548	+	0.0348945i
$87$	−7.06815	−	16.2444i	−0.757785	−	1.74158i
$88$	−10.7720	−	5.32248i	−1.14829	−	0.567378i
$89$		−	6.13592i		−	0.650406i	−0.945644	−	0.325203i	$-0.894567\pi$
$89$		−	6.13592i		−	0.650406i	0.945644	−	0.325203i	$-0.105433\pi$
$90$	4.19858	−	0.609829i	0.442570	−	0.0642816i
$91$			2.86589i			0.300426i
$92$	−1.70668	−	7.71713i	−0.177934	−	0.804567i
$93$	5.49522	+	12.6294i	0.569828	+	1.30961i
$94$	−8.63180	+	10.7493i	−0.890302	+	1.10871i
$95$	−2.87129			−0.294588
$96$	1.64930	+	9.65815i	0.168330	+	0.985731i
$97$	9.93736			1.00899			0.504493	−	0.863416i	$-0.331679\pi$
$97$	9.93736			1.00899			0.504493	+	0.863416i	$0.331679\pi$
$98$	1.07435	−	1.33790i	0.108525	−	0.135149i
$99$	−8.68667	+	9.32475i	−0.873043	+	0.937173i
$100$	0.431874	+	1.95281i	0.0431874	+	0.195281i
$101$			1.71996i			0.171143i	0.996332	+	0.0855713i	$0.0272715\pi$
$101$			1.71996i			0.171143i	−0.996332	+	0.0855713i	$0.972728\pi$
$102$	−14.5912	−	3.97810i	−1.44475	−	0.393891i
$103$			5.54725i			0.546587i	0.961931	+	0.273293i	$0.0881130\pi$
$103$			5.54725i			0.546587i	−0.961931	+	0.273293i	$0.911887\pi$
$104$	2.53577	+	1.25294i	0.248653	+	0.122861i
$105$	−4.55166	+	1.98048i	−0.444196	+	0.193276i
$106$	−13.1512	−	10.5605i	−1.27735	−	1.02573i
$107$	−8.18510			−0.791283			−0.395642	−	0.918405i	$-0.629478\pi$
$107$	−8.18510			−0.791283			−0.395642	+	0.918405i	$0.629478\pi$
$108$	10.3152	+	1.26399i	0.992576	+	0.121628i
$109$	7.39835			0.708633			0.354317	−	0.935125i	$-0.384713\pi$
$109$	7.39835			0.708633			0.354317	+	0.935125i	$0.384713\pi$
$110$	−4.68425	−	3.76149i	−0.446625	−	0.358644i
$111$	−14.4372	+	6.28179i	−1.37031	+	0.596241i
$112$	−4.83401	−	10.3945i	−0.456771	−	0.982186i
$113$			1.06302i			0.100000i	0.998749	+	0.0500002i	$0.0159222\pi$
$113$			1.06302i			0.100000i	−0.998749	+	0.0500002i	$0.984078\pi$
$114$	−6.78552	−	1.84998i	−0.635522	−	0.173266i
$115$		−	3.95180i		−	0.368507i
$116$	19.9735	−	4.41723i	1.85449	−	0.410130i
$117$	2.04489	−	2.19509i	0.189050	−	0.202937i
$118$	−3.24898	+	4.04601i	−0.299093	+	0.372466i
$119$	17.6948			1.62208
$120$	−0.237585	+	4.89322i	−0.0216884	+	0.446687i
$121$	7.04547			0.640497
$122$	−7.11086	+	8.85527i	−0.643787	+	0.801719i
$123$	3.39077	+	7.79286i	0.305736	+	0.702659i
$124$	−15.5286	+	3.43423i	−1.39451	+	0.308403i
$125$			1.00000i			0.0894427i
$126$	−12.0327	+	1.74770i	−1.07195	+	0.155698i
$127$		−	10.0625i		−	0.892904i	−0.894808	−	0.446452i	$-0.852687\pi$
$127$		−	10.0625i		−	0.892904i	0.894808	−	0.446452i	$-0.147313\pi$
$128$	−11.3106	−	0.267179i	−0.999721	−	0.0236156i
$129$	0.252548	+	0.580419i	0.0222356	+	0.0511031i
$130$	1.10270	+	0.885473i	0.0967128	+	0.0776611i
$131$	16.0192			1.39960			0.699801	−	0.714338i	$-0.253272\pi$
$131$	16.0192			1.39960			0.699801	+	0.714338i	$0.253272\pi$
$132$	−8.64643	−	11.9073i	−0.752575	−	1.03640i
$133$	8.22878			0.713525
$134$	−2.04394	−	1.64130i	−0.176570	−	0.141787i
$135$	4.89942	+	1.73080i	0.421675	+	0.148963i
$136$	7.73599	−	15.6566i	0.663355	−	1.34254i
$137$		−	4.54576i		−	0.388370i	−0.980965	−	0.194185i	$-0.937794\pi$
$137$		−	4.54576i		−	0.388370i	0.980965	−	0.194185i	$-0.0622063\pi$
$138$	2.54616	−	9.33903i	0.216743	−	0.794991i
$139$		−	16.3247i		−	1.38464i	−0.721589	−	0.692321i	$-0.756588\pi$
$139$		−	16.3247i		−	1.38464i	0.721589	−	0.692321i	$-0.243412\pi$
$140$	−1.23770	−	5.59654i	−0.104605	−	0.472994i
$141$	−15.4823	+	6.73656i	−1.30385	+	0.567321i
$142$	−4.52854	+	5.63947i	−0.380027	+	0.473254i
$143$	−4.24800			−0.355235
$144$	−3.71418	+	11.4107i	−0.309515	+	0.950894i
$145$	10.2281			0.849393
$146$	12.4408	−	15.4928i	1.02961	−	1.28219i
$147$	1.92699	−	0.838459i	0.158936	−	0.0691549i
$148$	−3.92580	−	17.7514i	−0.322699	−	1.45915i
$149$		−	12.0625i		−	0.988199i	−0.869405	−	0.494100i	$-0.835498\pi$
$149$		−	12.0625i		−	0.988199i	0.869405	−	0.494100i	$-0.164502\pi$
$150$	−0.644303	+	2.36323i	−0.0526071	+	0.192957i
$151$		−	11.6403i		−	0.947273i	−0.880721	−	0.473636i	$-0.842941\pi$
$151$		−	11.6403i		−	0.947273i	0.880721	−	0.473636i	$-0.157059\pi$
$152$	3.59755	−	7.28093i	0.291799	−	0.590561i
$153$	−13.5531	−	12.6257i	−1.09570	−	1.02073i
$154$	13.4245	+	10.7800i	1.08178	+	0.868676i
$155$	−7.95193			−0.638714
$156$	2.03541	+	2.80305i	0.162964	+	0.224424i
$157$	−5.20474			−0.415383			−0.207692	−	0.978194i	$-0.566595\pi$
$157$	−5.20474			−0.415383			−0.207692	+	0.978194i	$0.566595\pi$
$158$	1.98719	+	1.59573i	0.158093	+	0.126950i
$159$	−8.24179	−	18.9417i	−0.653616	−	1.50218i
$160$	−5.49301	−	1.35162i	−0.434260	−	0.106855i
$161$			11.3254i			0.892567i
$162$	10.4633	+	7.24699i	0.822076	+	0.569378i
$163$		−	4.40608i		−	0.345111i	−0.985000	−	0.172556i	$-0.944798\pi$
$163$		−	4.40608i		−	0.345111i	0.985000	−	0.172556i	$-0.0552024\pi$
$164$	−9.58181	+	2.11906i	−0.748213	+	0.165471i
$165$	−2.93560	−	6.74675i	−0.228536	−	0.525234i
$166$	−14.2650	+	17.7645i	−1.10718	+	1.37879i
$167$	22.3785			1.73170			0.865849	−	0.500305i	$-0.166779\pi$
$167$	22.3785			1.73170			0.865849	+	0.500305i	$0.166779\pi$
$168$	0.680891	−	14.0234i	0.0525318	−	1.08193i
$169$	1.00000			0.0769231
$170$	5.46715	−	6.80834i	0.419311	−	0.522176i
$171$	−6.30274	−	5.87145i	−0.481983	−	0.449001i
$172$	−0.713661	+	0.157830i	−0.0544162	+	0.0120344i
$173$			9.57026i			0.727613i	0.931474	+	0.363807i	$0.118523\pi$
$173$			9.57026i			0.727613i	−0.931474	+	0.363807i	$0.881477\pi$
$174$	24.1713	+	6.58997i	1.83242	+	0.499584i
$175$		−	2.86589i		−	0.216641i
$176$	15.4073	−	7.16527i	1.16137	−	0.540102i
$177$	−5.82750	+	2.53562i	−0.438022	+	0.190589i
$178$	6.76605	+	5.43319i	0.507137	+	0.407235i
$179$	1.70286			0.127278			0.0636388	−	0.997973i	$-0.479729\pi$
$179$	1.70286			0.127278			0.0636388	+	0.997973i	$0.479729\pi$
$180$	−3.04528	+	5.16975i	−0.226982	+	0.385330i
$181$	−2.18927			−0.162727			−0.0813635	−	0.996684i	$-0.525927\pi$
$181$	−2.18927			−0.162727			−0.0813635	+	0.996684i	$0.525927\pi$
$182$	−3.16020	−	2.53767i	−0.234250	−	0.188104i
$183$	−12.7543	+	5.54957i	−0.942826	+	0.410236i
$184$	10.0209	+	4.95136i	0.738748	+	0.365019i
$185$		−	9.09015i		−	0.668321i
$186$	−18.7923	−	5.12345i	−1.37792	−	0.375670i
$187$			26.2283i			1.91800i
$188$	−4.21001	−	19.0365i	−0.307047	−	1.38838i
$189$	−14.0412	−	4.96027i	−1.02135	−	0.360807i
$190$	2.54245	−	3.16615i	0.184448	−	0.229697i
$191$	−14.3893			−1.04117			−0.520585	−	0.853810i	$-0.674286\pi$
$191$	−14.3893			−1.04117			−0.520585	+	0.853810i	$0.674286\pi$
$192$	−12.1104	−	6.73336i	−0.873993	−	0.485938i
$193$	15.6033			1.12315			0.561575	−	0.827426i	$-0.310196\pi$
$193$	15.6033			1.12315			0.561575	+	0.827426i	$0.310196\pi$
$194$	−8.79927	+	10.9579i	−0.631750	+	0.786730i
$195$	0.691055	+	1.58822i	0.0494875	+	0.113735i
$196$	0.523994	+	2.36935i	0.0374282	+	0.169240i
$197$		−	25.9412i		−	1.84823i	−0.382111	−	0.924116i	$-0.624803\pi$
$197$		−	25.9412i		−	1.84823i	0.382111	−	0.924116i	$-0.375197\pi$
$198$	−2.59055	−	17.8356i	−0.184102	−	1.26752i
$199$		−	7.25282i		−	0.514139i	−0.966393	−	0.257069i	$-0.917243\pi$
$199$		−	7.25282i		−	0.514139i	0.966393	−	0.257069i	$-0.0827569\pi$
$200$	−2.53577	−	1.25294i	−0.179306	−	0.0885962i
$201$	−1.28093	−	2.94391i	−0.0903500	−	0.207647i
$202$	−1.89659	−	1.52298i	−0.133444	−	0.107156i
$203$	−29.3124			−2.05733
$204$	17.3068	−	12.5672i	1.21172	−	0.879880i
$205$	−4.90666			−0.342696
$206$	−6.11693	−	4.91194i	−0.426187	−	0.342231i
$207$	8.08098	−	8.67458i	0.561667	−	0.602925i
$208$	−3.62697	+	1.68674i	−0.251485	+	0.116954i
$209$			12.1972i			0.843699i
$210$	1.84650	−	6.77276i	0.127421	−	0.467365i
$211$			7.99477i			0.550383i	0.961389	+	0.275191i	$0.0887412\pi$
$211$			7.99477i			0.550383i	−0.961389	+	0.275191i	$0.911259\pi$
$212$	23.2900	−	5.15070i	1.59956	−	0.353751i
$213$	−8.12257	+	3.53423i	−0.556549	+	0.242162i
$214$	7.24769	−	9.02567i	0.495442	−	0.616982i
$215$	−0.365453			−0.0249237
$216$	−10.5276	+	10.2552i	−0.716312	+	0.697780i
$217$	22.7893			1.54704
$218$	−6.55104	+	8.15813i	−0.443692	+	0.552538i
$219$	22.3144	−	9.70926i	1.50786	−	0.656091i
$220$	8.29555	−	1.83460i	0.559286	−	0.123689i
$221$		−	6.17427i		−	0.415326i
$222$	5.85681	−	21.4821i	0.393084	−	1.44179i
$223$			12.3219i			0.825137i	0.910926	+	0.412569i	$0.135368\pi$
$223$			12.3219i			0.825137i	−0.910926	+	0.412569i	$0.864632\pi$
$224$	15.7423	+	3.87360i	1.05183	+	0.258816i
$225$	−2.04489	+	2.19509i	−0.136326	+	0.146340i
$226$	−1.17219	−	0.941274i	−0.0779726	−	0.0626126i
$227$	−19.7406			−1.31023			−0.655113	−	0.755531i	$-0.727379\pi$
$227$	−19.7406			−1.31023			−0.655113	+	0.755531i	$0.727379\pi$
$228$	8.04836	−	5.84425i	0.533016	−	0.387045i
$229$	−29.9806			−1.98118			−0.990588	−	0.136880i	$-0.956293\pi$
$229$	−29.9806			−1.98118			−0.990588	+	0.136880i	$0.956293\pi$
$230$	4.35763	+	3.49921i	0.287334	+	0.230731i
$231$	8.41309	+	19.3354i	0.553541	+	1.27218i
$232$	−12.8151	+	25.9360i	−0.841354	+	1.70278i
$233$			19.7267i			1.29234i	0.763195	+	0.646169i	$0.223630\pi$
$233$			19.7267i			1.29234i	−0.763195	+	0.646169i	$0.776370\pi$
$234$	0.609829	+	4.19858i	0.0398658	+	0.274470i
$235$		−	9.74823i		−	0.635904i
$236$	−1.58463	−	7.16527i	−0.103151	−	0.466419i
$237$	1.24537	+	2.86217i	0.0808952	+	0.185918i
$238$	−15.6682	+	19.5119i	−1.01562	+	1.26477i
$239$	−7.99750			−0.517315			−0.258658	−	0.965969i	$-0.583280\pi$
$239$	−7.99750			−0.517315			−0.258658	+	0.965969i	$0.583280\pi$
$240$	−5.18535	−	4.59479i	−0.334713	−	0.296593i
$241$	−10.6112			−0.683526			−0.341763	−	0.939786i	$-0.611024\pi$
$241$	−10.6112			−0.683526			−0.341763	+	0.939786i	$0.611024\pi$
$242$	−6.23857	+	7.76901i	−0.401031	+	0.499411i
$243$	7.21541	+	13.8180i	0.462869	+	0.886427i
$244$	−3.46820	−	15.6822i	−0.222029	−	1.00395i
$245$			1.21330i			0.0775150i
$246$	−11.5956	−	3.16138i	−0.739308	−	0.201562i
$247$		−	2.87129i		−	0.182696i
$248$	9.96328	−	20.1643i	0.632669	−	1.28043i
$249$	−25.5863	+	11.1329i	−1.62147	+	0.705522i
$250$	−1.10270	−	0.885473i	−0.0697406	−	0.0560022i
$251$	−1.26328			−0.0797374			−0.0398687	−	0.999205i	$-0.512694\pi$
$251$	−1.26328			−0.0797374			−0.0398687	+	0.999205i	$0.512694\pi$
$252$	8.72742	−	14.8159i	0.549776	−	0.933314i
$253$	−16.7872			−1.05540
$254$	11.0959	+	8.91009i	0.696218	+	0.559069i
$255$	9.80610	−	4.26676i	0.614082	−	0.267195i
$256$	10.3098	−	12.2355i	0.644363	−	0.764720i
$257$			3.52977i			0.220181i	0.993922	+	0.110090i	$0.0351141\pi$
$257$			3.52977i			0.220181i	−0.993922	+	0.110090i	$0.964886\pi$
$258$	−0.863650	−	0.235462i	−0.0537685	−	0.0146592i
$259$			26.0513i			1.61875i
$260$	−1.95281	+	0.431874i	−0.121108	+	0.0267837i
$261$	22.4515	+	20.9152i	1.38972	+	1.29462i
$262$	−14.1846	+	17.6643i	−0.876325	+	1.09130i
$263$	−20.0297			−1.23509			−0.617543	−	0.786537i	$-0.711872\pi$
$263$	−20.0297			−1.23509			−0.617543	+	0.786537i	$0.711872\pi$
$264$	20.7864	+	1.00926i	1.27931	+	0.0621156i
$265$	11.9264			0.732632
$266$	−7.28636	+	9.07383i	−0.446755	+	0.556352i
$267$	4.24026	+	9.74519i	0.259499	+	0.596396i
$268$	3.61971	−	0.800517i	0.221109	−	0.0488994i
$269$		−	0.156032i		−	0.00951341i	−0.999989	−	0.00475670i	$-0.998486\pi$
$269$		−	0.156032i		−	0.00951341i	0.999989	−	0.00475670i	$-0.00151411\pi$
$270$	−6.24685	+	3.87000i	−0.380171	+	0.235520i
$271$			5.40592i			0.328386i	0.986428	+	0.164193i	$0.0525020\pi$
$271$			5.40592i			0.328386i	−0.986428	+	0.164193i	$0.947498\pi$
$272$	10.4144	+	22.3939i	0.631466	+	1.35783i
$273$	−1.98048	−	4.55166i	−0.119864	−	0.275479i
$274$	5.01259	+	4.02515i	0.302822	+	0.243168i
$275$	4.24800			0.256164
$276$	8.04355	+	11.0771i	0.484165	+	0.666763i
$277$	−3.93265			−0.236290			−0.118145	−	0.992996i	$-0.537695\pi$
$277$	−3.93265			−0.236290			−0.118145	+	0.992996i	$0.537695\pi$
$278$	18.0012	+	14.4551i	1.07964	+	0.866958i
$279$	−17.4552	−	16.2608i	−1.04502	−	0.973508i
$280$	7.26724	+	3.59078i	0.434300	+	0.214590i
$281$		−	20.0451i		−	1.19579i	−0.801574	−	0.597896i	$-0.796004\pi$
$281$		−	20.0451i		−	1.19579i	0.801574	−	0.597896i	$-0.203996\pi$
$282$	6.28082	−	23.0373i	0.374017	−	1.37185i
$283$			8.25743i			0.490853i	0.969415	+	0.245427i	$0.0789281\pi$
$283$			8.25743i			0.490853i	−0.969415	+	0.245427i	$0.921072\pi$
$284$	−2.20872	−	9.98720i	−0.131063	−	0.592631i
$285$	4.56023	−	1.98422i	0.270125	−	0.117535i
$286$	3.76149	−	4.68425i	0.222421	−	0.276985i
$287$	14.0619			0.830050
$288$	−9.29376	−	14.1995i	−0.547640	−	0.836714i
$289$	−21.1216			−1.24245
$290$	−9.05667	+	11.2784i	−0.531826	+	0.662292i
$291$	−15.7827	+	6.86726i	−0.925199	+	0.402566i
$292$	6.06780	+	27.4369i	0.355091	+	1.60562i
$293$			0.770477i			0.0450117i	0.999747	+	0.0225059i	$0.00716444\pi$
$293$			0.770477i			0.0450117i	−0.999747	+	0.0225059i	$0.992836\pi$
$294$	−0.781735	+	2.86732i	−0.0455917	+	0.167225i
$295$		−	3.66920i		−	0.213629i
$296$	23.0506	+	11.3894i	1.33979	+	0.661996i
$297$	7.35242	−	20.8127i	0.426631	−	1.20768i
$298$	13.3013	+	10.6810i	0.770522	+	0.618735i
$299$	3.95180			0.228538
$300$	−2.03541	−	2.80305i	−0.117515	−	0.161834i
$301$	1.04735			0.0603680
$302$	12.8357	+	10.3072i	0.738611	+	0.593110i
$303$	−1.18859	−	2.73168i	−0.0682826	−	0.156931i
$304$	4.84311	+	10.4141i	0.277772	+	0.597288i
$305$		−	8.03057i		−	0.459829i
$306$	25.9232	−	3.76525i	1.48193	−	0.215245i
$307$		−	11.7703i		−	0.671765i	−0.941904	−	0.335882i	$-0.890966\pi$
$307$		−	11.7703i		−	0.671765i	0.941904	−	0.335882i	$-0.109034\pi$
$308$	−23.7741	+	5.25776i	−1.35465	+	0.299588i
$309$	−3.83346	−	8.81026i	−0.218078	−	0.501198i
$310$	7.04122	−	8.76856i	0.399914	−	0.498020i
$311$	−16.5939			−0.940952			−0.470476	−	0.882413i	$-0.655918\pi$
$311$	−16.5939			−0.940952			−0.470476	+	0.882413i	$0.655918\pi$
$312$	−4.89322	−	0.237585i	−0.277024	−	0.0134506i
$313$	24.4382			1.38133			0.690665	−	0.723175i	$-0.257318\pi$
$313$	24.4382			1.38133			0.690665	+	0.723175i	$0.257318\pi$
$314$	4.60866	−	5.73924i	0.260081	−	0.323884i
$315$	5.86041	−	6.29089i	0.330197	−	0.354452i
$316$	−3.51921	+	0.778291i	−0.197971	+	0.0437823i
$317$			4.48775i			0.252057i	0.992027	+	0.126029i	$0.0402231\pi$
$317$			4.48775i			0.252057i	−0.992027	+	0.126029i	$0.959777\pi$
$318$	28.1848	+	7.68421i	1.58053	+	0.430909i
$319$		−	43.4487i		−	2.43266i
$320$	6.35434	−	4.86029i	0.355218	−	0.271698i
$321$	12.9997	−	5.65635i	0.725575	−	0.315707i
$322$	−12.4885	−	10.0283i	−0.695956	−	0.558858i
$323$	−17.7281			−0.986418
$324$	−17.2562	+	5.12084i	−0.958679	+	0.284491i
$325$	−1.00000			−0.0554700
$326$	4.85857	+	3.90147i	0.269091	+	0.216082i
$327$	−11.7502	+	5.11267i	−0.649788	+	0.282731i
$328$	6.14775	−	12.4422i	0.339453	−	0.687005i
$329$			27.9373i			1.54023i
$330$	10.0390	+	2.73700i	0.552629	+	0.150667i
$331$		−	12.4242i		−	0.682898i	−0.939900	−	0.341449i	$-0.889082\pi$
$331$		−	12.4242i		−	0.682898i	0.939900	−	0.341449i	$-0.110918\pi$
$332$	−6.95753	−	31.4600i	−0.381844	−	1.72659i
$333$	18.5883	−	19.9537i	1.01863	−	1.09346i
$334$	−19.8155	+	24.6766i	−1.08426	+	1.35025i
$335$	1.85359			0.101272
$336$	14.8606	+	13.1682i	0.810714	+	0.718382i
$337$	−0.801900			−0.0436823			−0.0218411	−	0.999761i	$-0.506953\pi$
$337$	−0.801900			−0.0436823			−0.0218411	+	0.999761i	$0.506953\pi$
$338$	−0.885473	+	1.10270i	−0.0481634	+	0.0599787i
$339$	−0.734604	−	1.68831i	−0.0398982	−	0.0916963i
$340$	2.66651	+	12.0572i	0.144612	+	0.653894i
$341$			33.7798i			1.82928i
$342$	12.0553	−	1.75099i	0.651878	−	0.0946829i
$343$			16.5840i			0.895453i
$344$	0.457890	−	0.926705i	0.0246878	−	0.0499646i
$345$	2.73091	+	6.27633i	0.147027	+	0.337906i
$346$	−10.5531	−	8.47421i	−0.567337	−	0.455576i
$347$	12.2298			0.656532			0.328266	−	0.944585i	$-0.393536\pi$
$347$	12.2298			0.656532			0.328266	+	0.944585i	$0.393536\pi$
$348$	−28.6697	+	20.8183i	−1.53686	+	1.11598i
$349$	10.5505			0.564754			0.282377	−	0.959304i	$-0.408877\pi$
$349$	10.5505			0.564754			0.282377	+	0.959304i	$0.408877\pi$
$350$	3.16020	+	2.53767i	0.168920	+	0.135644i
$351$	−1.73080	+	4.89942i	−0.0923832	+	0.261512i
$352$	−5.74169	+	23.3343i	−0.306033	+	1.24372i
$353$		−	6.24582i		−	0.332431i	−0.986089	−	0.166216i	$-0.946845\pi$
$353$		−	6.24582i		−	0.332431i	0.986089	−	0.166216i	$-0.0531548\pi$
$354$	2.36408	−	8.67118i	0.125649	−	0.460868i
$355$		−	5.11426i		−	0.271437i
$356$	−11.9823	+	2.64994i	−0.635061	+	0.140447i
$357$	−28.1032	+	12.2281i	−1.48738	+	0.647177i
$358$	−1.50783	+	1.87773i	−0.0796915	+	0.0992413i
$359$	15.8661			0.837382			0.418691	−	0.908129i	$-0.362489\pi$
$359$	15.8661			0.837382			0.418691	+	0.908129i	$0.362489\pi$
$360$	−3.00414	−	7.93569i	−0.158332	−	0.418247i
$361$	10.7557			0.566091
$362$	1.93854	−	2.41410i	0.101887	−	0.126882i
$363$	−11.1898	+	4.86881i	−0.587310	+	0.255546i
$364$	5.59654	−	1.23770i	0.293339	−	0.0648732i
$365$			14.0499i			0.735406i
$366$	5.17412	−	18.9781i	0.270456	−	0.992002i
$367$		−	12.0162i		−	0.627242i	−0.949548	−	0.313621i	$-0.898458\pi$
$367$		−	12.0162i		−	0.627242i	0.949548	−	0.313621i	$-0.101542\pi$
$368$	−14.3331	+	6.66566i	−0.747162	+	0.347472i
$369$	−10.7706	−	10.0336i	−0.560695	−	0.522327i
$370$	10.0237	+	8.04908i	0.521106	+	0.418452i
$371$	−34.1797			−1.77452
$372$	22.2897	−	16.1855i	1.15566	−	0.839177i
$373$	1.95896			0.101431			0.0507154	−	0.998713i	$-0.483850\pi$
$373$	1.95896			0.101431			0.0507154	+	0.998713i	$0.483850\pi$
$374$	−28.9218	−	23.2244i	−1.49551	−	1.20091i
$375$	−0.691055	−	1.58822i	−0.0356859	−	0.0820153i
$376$	24.7193	+	12.2139i	1.27480	+	0.629886i
$377$			10.2281i			0.526771i
$378$	17.9028	−	11.0910i	0.920819	−	0.570458i
$379$		−	7.23188i		−	0.371477i	−0.982599	−	0.185738i	$-0.940532\pi$
$379$		−	7.23188i		−	0.371477i	0.982599	−	0.185738i	$-0.0594677\pi$
$380$	1.24003	+	5.60709i	0.0636124	+	0.287638i
$381$	6.95375	+	15.9815i	0.356251	+	0.818756i
$382$	12.7413	−	15.8670i	0.651902	−	0.811825i
$383$	−3.36662			−0.172026			−0.0860130	−	0.996294i	$-0.527413\pi$
$383$	−3.36662			−0.172026			−0.0860130	+	0.996294i	$0.527413\pi$
$384$	18.1483	−	7.39187i	0.926126	−	0.377215i
$385$	−12.1743			−0.620458
$386$	−13.8163	+	17.2057i	−0.703231	+	0.875746i
$387$	−0.802203	−	0.747309i	−0.0407783	−	0.0379879i
$388$	−4.29169	−	19.4058i	−0.217878	−	0.985181i
$389$			10.7830i			0.546720i	0.961912	+	0.273360i	$0.0881350\pi$
$389$			10.7830i			0.546720i	−0.961912	+	0.273360i	$0.911865\pi$
$390$	−2.36323	−	0.644303i	−0.119667	−	0.0326256i
$391$		−	24.3995i		−	1.23394i
$392$	−3.07666	−	1.52019i	−0.155395	−	0.0767814i
$393$	−25.4420	+	11.0701i	−1.28338	+	0.558414i
$394$	28.6052	+	22.9702i	1.44111	+	1.15722i
$395$	−1.80212			−0.0906747
$396$	21.9611	+	12.9363i	1.10358	+	0.650075i
$397$	−6.94070			−0.348344			−0.174172	−	0.984715i	$-0.555725\pi$
$397$	−6.94070			−0.348344			−0.174172	+	0.984715i	$0.555725\pi$
$398$	7.99765	+	6.42218i	0.400886	+	0.321915i
$399$	−13.0691	+	5.68654i	−0.654274	+	0.284683i
$400$	3.62697	−	1.68674i	0.181348	−	0.0843370i
$401$			14.0571i			0.701976i	0.936380	+	0.350988i	$0.114154\pi$
$401$			14.0571i			0.701976i	−0.936380	+	0.350988i	$0.885846\pi$
$402$	4.38046	+	1.19427i	0.218478	+	0.0595649i
$403$		−	7.95193i		−	0.396114i
$404$	3.35877	−	0.742807i	0.167105	−	0.0369560i
$405$	−8.97744	+	0.636882i	−0.446092	+	0.0316469i
$406$	25.9554	−	32.3227i	1.28814	−	1.60415i
$407$	−38.6149			−1.91407
$408$	−1.46691	+	30.2120i	−0.0726230	+	1.49572i
$409$	18.1904			0.899460			0.449730	−	0.893165i	$-0.351520\pi$
$409$	18.1904			0.899460			0.449730	+	0.893165i	$0.351520\pi$
$410$	4.34472	−	5.41056i	0.214570	−	0.267208i
$411$	3.14137	+	7.21967i	0.154952	+	0.356120i
$412$	10.8328	−	2.39572i	0.533692	−	0.118028i
$413$			10.5155i			0.517434i
$414$	2.40992	+	16.5920i	0.118441	+	0.815451i
$415$		−	16.1101i		−	0.790812i
$416$	1.35162	−	5.49301i	0.0662687	−	0.269317i
$417$	11.2813	+	25.9272i	0.552446	+	1.26966i
$418$	−13.4498	−	10.8003i	−0.657852	−	0.528260i
$419$	−1.60040			−0.0781848			−0.0390924	−	0.999236i	$-0.512447\pi$
$419$	−1.60040			−0.0781848			−0.0390924	+	0.999236i	$0.512447\pi$
$420$	5.83326	+	8.03322i	0.284634	+	0.391981i
$421$	19.1787			0.934715			0.467357	−	0.884068i	$-0.345206\pi$
$421$	19.1787			0.934715			0.467357	+	0.884068i	$0.345206\pi$
$422$	−8.81580	−	7.07916i	−0.429146	−	0.344608i
$423$	19.9340	−	21.3983i	0.969225	−	1.04042i
$424$	−14.9430	+	30.2426i	−0.725698	+	1.46871i
$425$			6.17427i			0.299496i
$426$	3.29513	−	12.0862i	0.159650	−	0.585578i
$427$			23.0147i			1.11376i
$428$	3.53493	+	15.9840i	0.170868	+	0.772615i
$429$	6.74675	−	2.93560i	0.325736	−	0.141732i
$430$	0.323599	−	0.402983i	0.0156053	−	0.0194336i
$431$	29.4738			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$431$	29.4738			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$432$	−1.98651	−	20.6895i	−0.0955758	−	0.995422i
$433$	5.58729			0.268508			0.134254	−	0.990947i	$-0.457136\pi$
$433$	5.58729			0.268508			0.134254	+	0.990947i	$0.457136\pi$
$434$	−20.1793	+	25.1297i	−0.968639	+	1.20626i
$435$	−16.2444	+	7.06815i	−0.778859	+	0.338892i
$436$	−3.19516	−	14.4476i	−0.153020	−	0.691915i
$437$		−	11.3467i		−	0.542788i
$438$	−9.05240	+	33.2032i	−0.432541	+	1.58651i
$439$			8.86949i			0.423318i	0.977344	+	0.211659i	$0.0678865\pi$
$439$			8.86949i			0.423318i	−0.977344	+	0.211659i	$0.932113\pi$
$440$	−5.32248	+	10.7720i	−0.253739	+	0.513533i
$441$	−2.48107	+	2.66331i	−0.118146	+	0.126824i
$442$	6.80834	+	5.46715i	0.323840	+	0.260046i
$443$	−29.0202			−1.37879			−0.689396	−	0.724385i	$-0.742124\pi$
$443$	−29.0202			−1.37879			−0.689396	+	0.724385i	$0.742124\pi$
$444$	18.5022	+	25.4801i	0.878076	+	1.20923i
$445$	−6.13592			−0.290870
$446$	−13.5873	−	10.9107i	−0.643379	−	0.516638i
$447$	8.33586	+	19.1579i	0.394272	+	0.906138i
$448$	−18.2108	+	13.9290i	−0.860380	+	0.658085i
$449$			14.7205i			0.694702i	0.937735	+	0.347351i	$0.112919\pi$
$449$			14.7205i			0.694702i	−0.937735	+	0.347351i	$0.887081\pi$
$450$	−0.609829	−	4.19858i	−0.0287476	−	0.197923i
$451$			20.8435i			0.981482i
$452$	2.07588	−	0.459090i	0.0976411	−	0.0215938i
$453$	8.04407	+	18.4873i	0.377944	+	0.868610i
$454$	17.4797	−	21.7678i	0.820364	−	1.02161i
$455$	2.86589			0.134355
$456$	−0.682173	+	14.0498i	−0.0319457	+	0.657943i
$457$	9.67137			0.452407			0.226204	−	0.974080i	$-0.427369\pi$
$457$	9.67137			0.452407			0.226204	+	0.974080i	$0.427369\pi$
$458$	26.5470	−	33.0595i	1.24046	−	1.54477i
$459$	30.2504	+	10.6864i	1.41197	+	0.498799i
$460$	−7.71713	+	1.70668i	−0.359813	+	0.0795744i
$461$		−	35.3265i		−	1.64532i	−0.568534	−	0.822660i	$-0.692489\pi$
$461$		−	35.3265i		−	1.64532i	0.568534	−	0.822660i	$-0.307511\pi$
$462$	−28.7706	−	7.84392i	−1.33853	−	0.364932i
$463$			15.5886i			0.724463i	0.932088	+	0.362231i	$0.117985\pi$
$463$			15.5886i			0.724463i	−0.932088	+	0.362231i	$0.882015\pi$
$464$	−17.2521	−	37.0968i	−0.800907	−	1.72218i
$465$	12.6294	−	5.49522i	0.585675	−	0.254835i
$466$	−21.7525	−	17.4674i	−1.00767	−	0.809164i
$467$	−12.6488			−0.585315			−0.292657	−	0.956217i	$-0.594540\pi$
$467$	−12.6488			−0.585315			−0.292657	+	0.956217i	$0.594540\pi$
$468$	−5.16975	−	3.04528i	−0.238972	−	0.140768i
$469$	−5.31217			−0.245293
$470$	10.7493	+	8.63180i	0.495830	+	0.398155i
$471$	8.26627	−	3.59676i	0.380890	−	0.165730i
$472$	9.30426	+	4.59729i	0.428263	+	0.211607i
$473$			1.55244i			0.0713813i
$474$	−4.25884	−	1.16111i	−0.195615	−	0.0533317i
$475$			2.87129i			0.131744i
$476$	−7.64191	−	34.5546i	−0.350266	−	1.58381i
$477$	26.1795	+	24.3881i	1.19868	+	1.11665i
$478$	7.08157	−	8.81881i	0.323904	−	0.403363i
$479$	15.3279			0.700349			0.350175	−	0.936684i	$-0.386122\pi$
$479$	15.3279			0.700349			0.350175	+	0.936684i	$0.386122\pi$
$480$	9.65815	−	1.64930i	0.440832	−	0.0752797i
$481$	9.09015			0.414475
$482$	9.39591	−	11.7009i	0.427972	−	0.532961i
$483$	−7.82648	−	17.9872i	−0.356117	−	0.818448i
$484$	−3.04276	−	13.7585i	−0.138307	−	0.625386i
$485$		−	9.93736i		−	0.451232i
$486$	−21.6261	−	4.27909i	−0.980981	−	0.194104i
$487$			23.9704i			1.08620i	0.839667	+	0.543101i	$0.182750\pi$
$487$			23.9704i			1.08620i	−0.839667	+	0.543101i	$0.817250\pi$
$488$	20.3637	+	10.0618i	0.921822	+	0.455477i
$489$	3.04485	+	6.99783i	0.137693	+	0.316453i
$490$	−1.33790	−	1.07435i	−0.0604403	−	0.0485340i
$491$	35.7975			1.61552			0.807759	−	0.589513i	$-0.200680\pi$
$491$	35.7975			1.61552			0.807759	+	0.589513i	$0.200680\pi$
$492$	13.7536	−	9.98709i	0.620061	−	0.450253i
$493$	63.1508			2.84417
$494$	3.16615	+	2.54245i	0.142452	+	0.114390i
$495$	9.32475	+	8.68667i	0.419117	+	0.390437i
$496$	13.4128	+	28.8414i	0.602254	+	1.29502i
$497$			14.6569i			0.657451i
$498$	10.3798	−	38.0719i	0.465129	−	1.70604i
$499$		−	22.4553i		−	1.00524i	−0.864509	−	0.502618i	$-0.832370\pi$
$499$		−	22.4553i		−	1.00524i	0.864509	−	0.502618i	$-0.167630\pi$
$500$	1.95281	−	0.431874i	0.0873325	−	0.0193140i
$501$	−35.5419	+	15.4648i	−1.58790	+	0.690914i
$502$	1.11860	−	1.39301i	0.0499255	−	0.0621731i
$503$	30.9647			1.38065			0.690323	−	0.723501i	$-0.257468\pi$
$503$	30.9647			1.38065			0.690323	+	0.723501i	$0.257468\pi$
$504$	8.60953	+	22.7428i	0.383499	+	1.01304i
$505$	1.71996			0.0765373
$506$	14.8646	−	18.5112i	0.660814	−	0.822923i
$507$	−1.58822	+	0.691055i	−0.0705353	+	0.0306908i
$508$	−19.6502	+	4.34574i	−0.871838	+	0.192811i
$509$			3.40890i			0.151097i	0.997142	+	0.0755484i	$0.0240708\pi$
$509$			3.40890i			0.151097i	−0.997142	+	0.0755484i	$0.975929\pi$
$510$	−3.97810	+	14.5912i	−0.176153	+	0.646111i
$511$		−	40.2654i		−	1.78124i
$512$	4.36299	+	22.2028i	0.192819	+	0.981234i
$513$	14.0676	+	4.96962i	0.621101	+	0.219414i
$514$	−3.89226	−	3.12552i	−0.171680	−	0.137861i
$515$	5.54725			0.244441
$516$	1.02438	−	0.743847i	0.0450959	−	0.0327461i
$517$	−41.4104			−1.82123
$518$	−28.7267	−	23.0678i	−1.26218	−	1.01354i
$519$	−6.61358	−	15.1997i	−0.290304	−	0.667192i
$520$	1.25294	−	2.53577i	0.0549450	−	0.111201i
$521$		−	4.40697i		−	0.193073i	−0.995329	−	0.0965365i	$-0.969224\pi$
$521$		−	4.40697i		−	0.193073i	0.995329	−	0.0965365i	$-0.0307765\pi$
$522$	−42.9433	+	6.23736i	−1.87958	+	0.273002i
$523$			25.4812i			1.11422i	0.830440	+	0.557108i	$0.188089\pi$
$523$			25.4812i			1.11422i	−0.830440	+	0.557108i	$0.811911\pi$
$524$	−6.91827	−	31.2825i	−0.302226	−	1.36658i
$525$	1.98048	+	4.55166i	0.0864354	+	0.198651i
$526$	17.7358	−	22.0867i	0.773317	−	0.963025i
$527$	−49.0974			−2.13872
$528$	−19.5187	+	22.0273i	−0.849441	+	0.958617i
$529$	−7.38328			−0.321012
$530$	−10.5605	+	13.1512i	−0.458718	+	0.571250i
$531$	7.50310	−	8.05424i	0.325607	−	0.349524i
$532$	−3.55380	−	16.0693i	−0.154077	−	0.696691i
$533$		−	4.90666i		−	0.212531i
$534$	−14.5006	−	3.95339i	−0.627503	−	0.171080i
$535$			8.18510i			0.353873i
$536$	−2.32243	+	4.70028i	−0.100314	+	0.203021i
$537$	−2.70451	+	1.17677i	−0.116708	+	0.0507813i
$538$	0.172055	+	0.138162i	0.00741783	+	0.00595658i
$539$	5.15410			0.222003
$540$	1.26399	−	10.3152i	0.0543936	−	0.443893i
$541$	8.98846			0.386444			0.193222	−	0.981155i	$-0.438106\pi$
$541$	8.98846			0.386444			0.193222	+	0.981155i	$0.438106\pi$
$542$	−5.96108	−	4.78679i	−0.256050	−	0.205610i
$543$	3.47704	−	1.51291i	0.149214	−	0.0649250i
$544$	−33.9153	−	8.34528i	−1.45411	−	0.357801i
$545$		−	7.39835i		−	0.316911i
$546$	6.77276	+	1.84650i	0.289847	+	0.0790229i
$547$		−	32.3627i		−	1.38373i	−0.722026	−	0.691866i	$-0.756789\pi$
$547$		−	32.3627i		−	1.38373i	0.722026	−	0.691866i	$-0.243211\pi$
$548$	−8.87703	+	1.96320i	−0.379208	+	0.0838636i
$549$	16.4216	−	17.6279i	0.700857	−	0.752339i
$550$	−3.76149	+	4.68425i	−0.160390	+	0.199737i
$551$	29.3677			1.25110
$552$	−19.3370	−	0.938887i	−0.823038	−	0.0399617i
$553$	5.16468			0.219625
$554$	3.48226	−	4.33651i	0.147947	−	0.184241i
$555$	6.28179	+	14.4372i	0.266647	+	0.612823i
$556$	−31.8791	+	7.05022i	−1.35197	+	0.298996i
$557$		−	29.7048i		−	1.25863i	−0.777150	−	0.629316i	$-0.783335\pi$
$557$		−	29.7048i		−	1.25863i	0.777150	−	0.629316i	$-0.216665\pi$
$558$	33.3868	−	4.84932i	1.41338	−	0.205288i
$559$		−	0.365453i		−	0.0154570i
$560$	−10.3945	+	4.83401i	−0.439247	+	0.204274i
$561$	−18.1252	−	41.6563i	−0.765246	−	1.75873i
$562$	22.1037	+	17.7494i	0.932386	+	0.748714i
$563$	3.63856			0.153347			0.0766735	−	0.997056i	$-0.475570\pi$
$563$	3.63856			0.153347			0.0766735	+	0.997056i	$0.475570\pi$
$564$	19.8417	+	27.3248i	0.835485	+	1.15058i
$565$	1.06302			0.0447215
$566$	−9.10543	−	7.31174i	−0.382730	−	0.307335i
$567$	25.7283	−	1.82523i	1.08049	−	0.0766525i
$568$	12.9686	+	6.40786i	0.544150	+	0.268868i
$569$		−	24.8848i		−	1.04322i	−0.853183	−	0.521612i	$-0.825331\pi$
$569$		−	24.8848i		−	1.04322i	0.853183	−	0.521612i	$-0.174669\pi$
$570$	−1.84998	+	6.78552i	−0.0774871	+	0.284214i
$571$			8.09283i			0.338674i	0.985558	+	0.169337i	$0.0541627\pi$
$571$			8.09283i			0.338674i	−0.985558	+	0.169337i	$0.945837\pi$
$572$	1.83460	+	8.29555i	0.0767085	+	0.346854i
$573$	22.8533	−	9.94377i	0.954711	−	0.415407i
$574$	−12.4515	+	15.5060i	−0.519714	+	0.647210i
$575$	−3.95180			−0.164801
$576$	23.8871	+	2.32511i	0.995296	+	0.0968794i
$577$	−43.9533			−1.82980			−0.914900	−	0.403681i	$-0.867730\pi$
$577$	−43.9533			−1.82980			−0.914900	+	0.403681i	$0.867730\pi$
$578$	18.7026	−	23.2907i	0.777927	−	0.968767i
$579$	−24.7815	+	10.7827i	−1.02988	+	0.448115i
$580$	−4.41723	−	19.9735i	−0.183416	−	0.829354i
$581$			46.1696i			1.91544i
$582$	6.40267	−	23.4843i	0.265399	−	0.973456i
$583$		−	50.6632i		−	2.09826i
$584$	−35.6274	−	17.6037i	−1.47427	−	0.728446i
$585$	−2.19509	−	2.04489i	−0.0907560	−	0.0845456i
$586$	−0.849601	−	0.682236i	−0.0350967	−	0.0281829i
$587$	−40.9366			−1.68963			−0.844817	−	0.535055i	$-0.820291\pi$
$587$	−40.9366			−1.68963			−0.844817	+	0.535055i	$0.820291\pi$
$588$	−2.46957	−	3.40095i	−0.101843	−	0.140253i
$589$	−22.8323			−0.940787
$590$	4.04601	+	3.24898i	0.166572	+	0.133758i
$591$	17.9268	+	41.2003i	0.737409	+	1.69475i
$592$	−32.9697	+	15.3327i	−1.35505	+	0.630171i
$593$		−	11.7674i		−	0.483230i	−0.970372	−	0.241615i	$-0.922323\pi$
$593$		−	11.7674i		−	0.483230i	0.970372	−	0.241615i	$-0.0776771\pi$
$594$	16.4397	+	26.5366i	0.674530	+	1.08881i
$595$		−	17.6948i		−	0.725414i
$596$	−23.5558	+	5.20949i	−0.964885	+	0.213389i
$597$	5.01210	+	11.5191i	0.205132	+	0.471444i
$598$	−3.49921	+	4.35763i	−0.143093	+	0.178197i
$599$	−21.5307			−0.879720			−0.439860	−	0.898066i	$-0.644972\pi$
$599$	−21.5307			−0.879720			−0.439860	+	0.898066i	$0.644972\pi$
$600$	4.89322	+	0.237585i	0.199765	+	0.00969935i
$601$	40.9258			1.66940			0.834699	−	0.550706i	$-0.185642\pi$
$601$	40.9258			1.66940			0.834699	+	0.550706i	$0.185642\pi$
$602$	−0.927397	+	1.15490i	−0.0377979	+	0.0470703i
$603$	4.06880	+	3.79038i	0.165694	+	0.154356i
$604$	−22.7313	+	5.02714i	−0.924924	+	0.204551i
$605$		−	7.04547i		−	0.286439i
$606$	4.06467	+	1.10818i	0.165116	+	0.0450166i
$607$			19.5238i			0.792445i	0.918154	+	0.396223i	$0.129679\pi$
$607$			19.5238i			0.792445i	−0.918154	+	0.396223i	$0.870321\pi$
$608$	−15.7720	−	3.88089i	−0.639639	−	0.157391i
$609$	46.5546	−	20.2565i	1.88649	−	0.820835i
$610$	8.85527	+	7.11086i	0.358540	+	0.287910i
$611$	9.74823			0.394371
$612$	−18.8024	+	31.9194i	−0.760041	+	1.29027i
$613$	−21.4800			−0.867570			−0.433785	−	0.901016i	$-0.642822\pi$
$613$	−21.4800			−0.867570			−0.433785	+	0.901016i	$0.642822\pi$
$614$	12.9790	+	10.4223i	0.523791	+	0.420608i
$615$	7.79286	−	3.39077i	0.314239	−	0.136729i
$616$	15.2536	−	30.8712i	0.614586	−	1.24384i
$617$			2.91455i			0.117335i	0.998278	+	0.0586677i	$0.0186852\pi$
$617$			2.91455i			0.117335i	−0.998278	+	0.0586677i	$0.981315\pi$
$618$	13.1095	+	3.57411i	0.527340	+	0.143772i
$619$			29.9890i			1.20536i	0.797983	+	0.602680i	$0.205901\pi$
$619$			29.9890i			1.20536i	−0.797983	+	0.602680i	$0.794099\pi$
$620$	3.43423	+	15.5286i	0.137922	+	0.623645i
$621$	−6.83977	+	19.3615i	−0.274470	+	0.776952i
$622$	14.6934	−	18.2980i	0.589153	−	0.733682i
$623$	17.5848			0.704522
$624$	4.59479	−	5.18535i	0.183939	−	0.207580i
$625$	1.00000			0.0400000
$626$	−21.6394	+	26.9479i	−0.864884	+	1.07706i
$627$	−8.42894	−	19.3719i	−0.336620	−	0.773637i
$628$	2.24779	+	10.1639i	0.0896967	+	0.405583i
$629$		−	56.1251i		−	2.23785i
$630$	1.74770	+	12.0327i	0.0696301	+	0.479393i
$631$		−	6.63487i		−	0.264130i	−0.991241	−	0.132065i	$-0.957839\pi$
$631$		−	6.63487i		−	0.264130i	0.991241	−	0.132065i	$-0.0421607\pi$
$632$	2.25795	−	4.56978i	0.0898165	−	0.181776i
$633$	−5.52483	−	12.6975i	−0.219592	−	0.504679i
$634$	−4.94862	−	3.97378i	−0.196535	−	0.157819i
$635$	−10.0625			−0.399319
$636$	−33.4303	+	24.2751i	−1.32560	+	0.962571i
$637$	−1.21330			−0.0480728
$638$	47.9107	+	38.4727i	1.89680	+	1.52315i
$639$	10.4581	−	11.2263i	0.413715	−	0.444105i
$640$	−0.267179	+	11.3106i	−0.0105612	+	0.447089i
$641$			32.4160i			1.28036i	0.768226	+	0.640178i	$0.221140\pi$
$641$			32.4160i			1.28036i	−0.768226	+	0.640178i	$0.778860\pi$
$642$	−5.27369	+	19.3433i	−0.208136	+	0.763419i
$643$			34.2105i			1.34913i	0.738216	+	0.674565i	$0.235669\pi$
$643$			34.2105i			1.34913i	−0.738216	+	0.674565i	$0.764331\pi$
$644$	22.1164	−	4.89115i	0.871509	−	0.192738i
$645$	0.580419	−	0.252548i	0.0228540	−	0.00994406i
$646$	15.6978	−	19.5487i	0.617620	−	0.769133i
$647$	34.3353			1.34986			0.674930	−	0.737881i	$-0.264174\pi$
$647$	34.3353			1.34986			0.674930	+	0.737881i	$0.264174\pi$
$648$	9.63319	−	23.5627i	0.378428	−	0.925631i
$649$	−15.5868			−0.611833
$650$	0.885473	−	1.10270i	0.0347311	−	0.0432513i
$651$	−36.1945	+	15.7487i	−1.41857	+	0.617239i
$652$	−8.60427	+	1.90288i	−0.336969	+	0.0745223i
$653$		−	2.75989i		−	0.108003i	−0.998541	−	0.0540015i	$-0.982802\pi$
$653$		−	2.75989i		−	0.108003i	0.998541	−	0.0540015i	$-0.0171976\pi$
$654$	4.76678	−	17.4840i	0.186396	−	0.683680i
$655$		−	16.0192i		−	0.625921i
$656$	8.27627	+	17.7963i	0.323134	+	0.694830i
$657$	−28.7305	+	30.8409i	−1.12088	+	1.20322i
$658$	−30.8063	−	24.7377i	−1.20096	−	0.964378i
$659$	−2.97758			−0.115990			−0.0579950	−	0.998317i	$-0.518471\pi$
$659$	−2.97758			−0.115990			−0.0579950	+	0.998317i	$0.518471\pi$
$660$	−11.9073	+	8.64643i	−0.463493	+	0.336562i
$661$	−22.3337			−0.868680			−0.434340	−	0.900749i	$-0.643018\pi$
$661$	−22.3337			−0.868680			−0.434340	+	0.900749i	$0.643018\pi$
$662$	13.7001	+	11.0013i	0.532471	+	0.427579i
$663$	4.26676	+	9.80610i	0.165707	+	0.380837i
$664$	40.8515	+	20.1849i	1.58534	+	0.783327i
$665$		−	8.22878i		−	0.319098i
$666$	5.54344	+	38.1658i	0.214804	+	1.47889i
$667$			40.4192i			1.56504i
$668$	−9.66469	−	43.7010i	−0.373938	−	1.69084i
$669$	−8.51513	−	19.5699i	−0.329214	−	0.756617i
$670$	−1.64130	+	2.04394i	−0.0634091	+	0.0789644i
$671$	−34.1138			−1.31695
$672$	−27.6792	+	4.72669i	−1.06775	+	0.182336i
$673$	−0.389594			−0.0150177			−0.00750887	−	0.999972i	$-0.502390\pi$
$673$	−0.389594			−0.0150177			−0.00750887	+	0.999972i	$0.502390\pi$
$674$	0.710061	−	0.884251i	0.0273505	−	0.0340601i
$675$	1.73080	−	4.89942i	0.0666184	−	0.188579i
$676$	−0.431874	−	1.95281i	−0.0166106	−	0.0751083i
$677$		−	26.8227i		−	1.03088i	−0.856925	−	0.515440i	$-0.827628\pi$
$677$		−	26.8227i		−	1.03088i	0.856925	−	0.515440i	$-0.172372\pi$
$678$	2.51216	+	0.684906i	0.0964790	+	0.0263037i
$679$			28.4793i			1.09294i
$680$	−15.6566	−	7.73599i	−0.600401	−	0.296662i
$681$	31.3523	−	13.6418i	1.20142	−	0.522755i
$682$	−37.2488	−	29.9111i	−1.42633	−	1.14535i
$683$	−13.6048			−0.520573			−0.260286	−	0.965531i	$-0.583817\pi$
$683$	−13.6048			−0.520573			−0.260286	+	0.965531i	$0.583817\pi$
$684$	−8.74386	+	14.8438i	−0.334330	+	0.567568i
$685$	−4.54576			−0.173685
$686$	−18.2871	−	14.6847i	−0.698205	−	0.560665i
$687$	47.6158	−	20.7183i	1.81666	−	0.790451i
$688$	0.616424	+	1.32549i	0.0235009	+	0.0505337i
$689$			11.9264i			0.454359i
$690$	−9.33903	−	2.54616i	−0.355531	−	0.0969306i
$691$			25.8210i			0.982279i	0.871081	+	0.491139i	$0.163419\pi$
$691$			25.8210i			0.982279i	−0.871081	+	0.491139i	$0.836581\pi$
$692$	18.6889	−	4.13315i	0.710447	−	0.157119i
$693$	−26.7237	−	24.8950i	−1.01515	−	0.945683i
$694$	−10.8292	+	13.4858i	−0.411071	+	0.511914i
$695$	−16.3247			−0.619231
$696$	2.43003	−	50.0481i	0.0921100	−	1.89707i
$697$	−30.2951			−1.14751
$698$	−9.34216	+	11.6340i	−0.353606	+	0.440352i
$699$	−13.6322	−	31.3303i	−0.515618	−	1.18502i
$700$	−5.59654	+	1.23770i	−0.211529	+	0.0467808i
$701$		−	38.4614i		−	1.45267i	−0.687342	−	0.726334i	$-0.741223\pi$
$701$		−	38.4614i		−	1.45267i	0.687342	−	0.726334i	$-0.258777\pi$
$702$	−3.87000	−	6.24685i	−0.146064	−	0.235772i
$703$		−	26.1004i		−	0.984396i
$704$	−20.6465	−	26.9932i	−0.778144	−	1.01734i
$705$	6.73656	+	15.4823i	0.253714	+	0.583098i
$706$	6.88723	+	5.53050i	0.259204	+	0.208143i
$707$	−4.92921			−0.185382
$708$	7.46834	+	10.2850i	0.280677	+	0.386532i
$709$	−30.7167			−1.15359			−0.576794	−	0.816890i	$-0.695697\pi$
$709$	−30.7167			−1.15359			−0.576794	+	0.816890i	$0.695697\pi$
$710$	5.63947	+	4.52854i	0.211646	+	0.169953i
$711$	−3.95583	−	3.68514i	−0.148355	−	0.138203i
$712$	7.68793	−	15.5593i	0.288117	−	0.583109i
$713$		−	31.4244i		−	1.17685i
$714$	11.4008	−	41.8169i	0.426664	−	1.56496i
$715$			4.24800i			0.158866i
$716$	−0.735421	−	3.32536i	−0.0274840	−	0.124275i
$717$	12.7018	−	5.52671i	0.474357	−	0.206399i
$718$	−14.0490	+	17.4955i	−0.524305	+	0.652926i
$719$	8.10953			0.302434			0.151217	−	0.988501i	$-0.451681\pi$
$719$	8.10953			0.302434			0.151217	+	0.988501i	$0.451681\pi$
$720$	11.4107	+	3.71418i	0.425253	+	0.138419i
$721$	−15.8978			−0.592065
$722$	−9.52390	+	11.8603i	−0.354443	+	0.441394i
$723$	16.8529	−	7.33290i	0.626765	−	0.272714i
$724$	0.945489	+	4.27524i	0.0351388	+	0.158888i
$725$		−	10.2281i		−	0.379860i
$726$	4.53942	−	16.6501i	0.168474	−	0.617943i
$727$			6.79526i			0.252022i	0.992029	+	0.126011i	$0.0402175\pi$
$727$			6.79526i			0.252022i	−0.992029	+	0.126011i	$0.959783\pi$
$728$	−3.59078	+	7.26724i	−0.133083	+	0.269342i
$729$	−21.0087	−	16.9598i	−0.778099	−	0.628142i
$730$	−15.4928	−	12.4408i	−0.573413	−	0.460455i
$731$	−2.25640			−0.0834561
$732$	16.3455	+	22.5101i	0.604148	+	0.831997i
$733$	33.5035			1.23748			0.618740	−	0.785596i	$-0.287643\pi$
$733$	33.5035			1.23748			0.618740	+	0.785596i	$0.287643\pi$
$734$	13.2502	+	10.6400i	0.489075	+	0.392731i
$735$	−0.838459	−	1.92699i	−0.0309270	−	0.0710781i
$736$	5.34134	−	21.7073i	0.196884	−	0.800140i
$737$		−	7.87404i		−	0.290044i
$738$	20.6010	−	2.99223i	0.758335	−	0.110145i
$739$			17.3045i			0.636557i	0.947997	+	0.318278i	$0.103105\pi$
$739$			17.3045i			0.636557i	−0.947997	+	0.318278i	$0.896895\pi$
$740$	−17.7514	+	3.92580i	−0.652554	+	0.144315i
$741$	1.98422	+	4.56023i	0.0728920	+	0.167524i
$742$	30.2652	−	37.6897i	1.11107	−	1.38363i
$743$	21.9986			0.807049			0.403524	−	0.914969i	$-0.367785\pi$
$743$	21.9986			0.807049			0.403524	+	0.914969i	$0.367785\pi$
$744$	−1.88926	+	38.9105i	−0.0692635	+	1.42653i
$745$	−12.0625			−0.441936
$746$	−1.73460	+	2.16013i	−0.0635083	+	0.0790880i
$747$	32.9433	−	35.3631i	1.20533	−	1.29387i
$748$	51.2190	−	11.3273i	1.87275	−	0.414168i
$749$		−	23.4576i		−	0.857121i
$750$	2.36323	+	0.644303i	0.0862931	+	0.0235266i
$751$		−	35.8032i		−	1.30648i	−0.757151	−	0.653239i	$-0.773410\pi$
$751$		−	35.8032i		−	1.30648i	0.757151	−	0.653239i	$-0.226590\pi$
$752$	−35.3565	+	16.4427i	−1.28932	+	0.599605i
$753$	2.00636	−	0.872995i	0.0731160	−	0.0318137i
$754$	−11.2784	−	9.05667i	−0.410736	−	0.329824i
$755$	−11.6403			−0.423633
$756$	−3.62246	+	29.5620i	−0.131748	+	1.07516i
$757$	−13.9799			−0.508107			−0.254054	−	0.967190i	$-0.581764\pi$
$757$	−13.9799			−0.508107			−0.254054	+	0.967190i	$0.581764\pi$
$758$	7.97456	+	6.40363i	0.289649	+	0.232590i
$759$	26.6618	−	11.6009i	0.967763	−	0.421086i
$760$	−7.28093	−	3.59755i	−0.264107	−	0.130497i
$761$		−	9.74392i		−	0.353217i	−0.984281	−	0.176608i	$-0.943487\pi$
$761$		−	9.74392i		−	0.353217i	0.984281	−	0.176608i	$-0.0565126\pi$
$762$	−23.7801	−	6.48331i	−0.861461	−	0.234866i
$763$			21.2028i			0.767594i
$764$	6.21435	+	28.0996i	0.224827	+	1.01661i
$765$	−12.6257	+	13.5531i	−0.456483	+	0.490014i
$766$	2.98105	−	3.71235i	0.107710	−	0.134133i
$767$	3.66920			0.132487
$768$	−7.91883	+	26.5573i	−0.285746	+	0.958305i
$769$	19.4459			0.701235			0.350618	−	0.936519i	$-0.385972\pi$
$769$	19.4459			0.701235			0.350618	+	0.936519i	$0.385972\pi$
$770$	10.7800	−	13.4245i	0.388484	−	0.483786i
$771$	−2.43926	−	5.60605i	−0.0878479	−	0.201897i
$772$	−6.73866	−	30.4703i	−0.242530	−	1.09665i
$773$			39.0689i			1.40521i	0.711580	+	0.702605i	$0.247980\pi$
$773$			39.0689i			1.40521i	−0.711580	+	0.702605i	$0.752020\pi$
$774$	1.53438	−	0.222864i	0.0551523	−	0.00801067i
$775$			7.95193i			0.285642i
$776$	25.1989	+	12.4509i	0.904587	+	0.446961i
$777$	−18.0029	−	41.3752i	−0.645851	−	1.48433i
$778$	−11.8904	−	9.54806i	−0.426290	−	0.342314i
$779$	−14.0884			−0.504771
$780$	2.80305	−	2.03541i	0.100365	−	0.0728795i
$781$	−21.7254			−0.777394
$782$	26.9052	+	21.6051i	0.962128	+	0.772597i
$783$	−50.1115	−	17.7027i	−1.79084	−	0.632643i
$784$	4.40061	−	2.04653i	0.157165	−	0.0730902i
$785$			5.20474i			0.185765i
$786$	10.3212	−	37.8571i	0.368145	−	1.35032i
$787$		−	11.4804i		−	0.409233i	−0.978842	−	0.204617i	$-0.934405\pi$
$787$		−	11.4804i		−	0.409233i	0.978842	−	0.204617i	$-0.0655948\pi$
$788$	−50.6583	+	11.2033i	−1.80463	+	0.399102i
$789$	31.8116	−	13.8416i	1.13252	−	0.492776i
$790$	1.59573	−	1.98719i	0.0567736	−	0.0707012i
$791$	−3.04649			−0.108321
$792$	−33.7108	+	12.7616i	−1.19786	+	0.453463i
$793$	8.03057			0.285174
$794$	6.14580	−	7.65348i	0.218106	−	0.271612i
$795$	−18.9417	+	8.24179i	−0.671794	+	0.292306i
$796$	−14.1634	+	3.13231i	−0.502009	+	0.111022i
$797$			8.09375i			0.286695i	0.989672	+	0.143348i	$0.0457867\pi$
$797$			8.09375i			0.286695i	−0.989672	+	0.143348i	$0.954213\pi$
$798$	5.30183	−	19.4465i	0.187683	−	0.688399i
$799$		−	60.1882i		−	2.12931i
$800$	−1.35162	+	5.49301i	−0.0477871	+	0.194207i
$801$	−13.4689	−	12.5472i	−0.475901	−	0.443335i
$802$	−15.5007	−	12.4471i	−0.547347	−	0.439524i
$803$	59.6840			2.10620
$804$	−5.19570	+	3.77282i	−0.183238	+	0.133057i
$805$	11.3254			0.399168
$806$	8.76856	+	7.04122i	0.308859	+	0.248016i
$807$	0.107826	+	0.247812i	0.00379567	+	0.00872341i
$808$	−2.15501	+	4.36143i	−0.0758129	+	0.153435i
$809$			26.1234i			0.918448i	0.888320	+	0.459224i	$0.151873\pi$
$809$			26.1234i			0.918448i	−0.888320	+	0.459224i	$0.848127\pi$
$810$	7.24699	−	10.4633i	0.254633	−	0.367644i
$811$			31.4381i			1.10394i	0.833864	+	0.551970i	$0.186124\pi$
$811$			31.4381i			1.10394i	−0.833864	+	0.551970i	$0.813876\pi$
$812$	12.6593	+	57.2417i	0.444254	+	2.00879i
$813$	−3.73579	−	8.58579i	−0.131020	−	0.301117i
$814$	34.1925	−	42.5805i	1.19845	−	1.49245i
$815$	−4.40608			−0.154338
$816$	−32.0158	−	28.3695i	−1.12078	−	0.993131i
$817$	−1.04932			−0.0367110
$818$	−16.1072	+	20.0585i	−0.563173	+	0.701330i
$819$	6.29089	+	5.86041i	0.219822	+	0.204779i
$820$	2.11906	+	9.58181i	0.0740009	+	0.334611i
$821$			18.9925i			0.662843i	0.943483	+	0.331421i	$0.107528\pi$
$821$			18.9925i			0.662843i	−0.943483	+	0.331421i	$0.892472\pi$
$822$	−10.7427	−	2.92885i	−0.374694	−	0.102155i
$823$			23.1485i			0.806907i	0.915000	+	0.403453i	$0.132190\pi$
$823$			23.1485i			0.806907i	−0.915000	+	0.403453i	$0.867810\pi$
$824$	−6.95037	+	14.0666i	−0.242128	+	0.490032i
$825$	−6.74675	+	2.93560i	−0.234892	+	0.102204i
$826$	−11.5954	−	9.31120i	−0.403456	−	0.323978i
$827$	7.27740			0.253060			0.126530	−	0.991963i	$-0.459616\pi$
$827$	7.27740			0.253060			0.126530	+	0.991963i	$0.459616\pi$
$828$	−20.4298	−	12.0343i	−0.709985	−	0.418222i
$829$	−10.7495			−0.373344			−0.186672	−	0.982422i	$-0.559770\pi$
$829$	−10.7495			−0.373344			−0.186672	+	0.982422i	$0.559770\pi$
$830$	17.7645	+	14.2650i	0.616615	+	0.495147i
$831$	6.24591	−	2.71768i	0.216668	−	0.0942752i
$832$	4.86029	+	6.35434i	0.168500	+	0.220297i
$833$			7.49126i			0.259557i
$834$	−38.5791	−	10.5181i	−1.33588	−	0.364210i
$835$		−	22.3785i		−	0.774439i
$836$	23.8189	−	5.26766i	0.823793	−	0.182186i
$837$	38.9599	+	13.7632i	1.34665	+	0.475725i
$838$	1.41711	−	1.76476i	0.0489534	−	0.0609625i
$839$	10.7407			0.370811			0.185405	−	0.982662i	$-0.440640\pi$
$839$	10.7407			0.370811			0.185405	+	0.982662i	$0.440640\pi$
$840$	−14.0234	−	0.680891i	−0.483853	−	0.0234930i
$841$	−75.6130			−2.60735
$842$	−16.9823	+	21.1483i	−0.585247	+	0.728819i
$843$	13.8523	+	31.8361i	0.477098	+	1.09649i
$844$	15.6123	−	3.45274i	0.537398	−	0.118848i
$845$		−	1.00000i		−	0.0344010i
$846$	5.94475	+	40.9288i	0.204385	+	1.40716i
$847$			20.1915i			0.693789i
$848$	−20.1167	−	43.2566i	−0.690811	−	1.48544i
$849$	−5.70634	−	13.1146i	−0.195841	−	0.450093i
$850$	−6.80834	−	5.46715i	−0.233524	−	0.187522i
$851$	35.9225			1.23141
$852$	10.4096	+	14.3355i	0.356628	+	0.491127i
$853$	−24.3418			−0.833446			−0.416723	−	0.909034i	$-0.636821\pi$
$853$	−24.3418			−0.833446			−0.416723	+	0.909034i	$0.636821\pi$
$854$	−25.3782	−	20.3789i	−0.868424	−	0.697352i
$855$	−5.87145	+	6.30274i	−0.200799	+	0.215549i
$856$	−20.7556	−	10.2554i	−0.709410	−	0.350523i
$857$			28.9086i			0.987499i	0.869604	+	0.493749i	$0.164374\pi$
$857$			28.9086i			0.987499i	−0.869604	+	0.493749i	$0.835626\pi$
$858$	−2.73700	+	10.0390i	−0.0934396	+	0.342726i
$859$			12.3604i			0.421731i	0.977515	+	0.210866i	$0.0676282\pi$
$859$			12.3604i			0.421731i	−0.977515	+	0.210866i	$0.932372\pi$
$860$	0.157830	+	0.713661i	0.00538195	+	0.0243357i
$861$	−22.3335	+	9.71757i	−0.761122	+	0.331174i
$862$	−26.0982	+	32.5006i	−0.888910	+	1.10698i
$863$	−28.4177			−0.967349			−0.483674	−	0.875248i	$-0.660698\pi$
$863$	−28.4177			−0.967349			−0.483674	+	0.875248i	$0.660698\pi$
$864$	24.5732	+	16.1295i	0.835996	+	0.548735i
$865$	9.57026			0.325399
$866$	−4.94739	+	6.16108i	−0.168119	+	0.209362i
$867$	33.5458	−	14.5962i	1.13928	−	0.495713i
$868$	−9.84212	−	44.5033i	−0.334063	−	1.51054i
$869$			7.65541i			0.259692i
$870$	6.58997	−	24.1713i	0.223421	−	0.819483i
$871$			1.85359i			0.0628065i
$872$	18.7605	+	9.26968i	0.635312	+	0.313911i
$873$	20.3208	−	21.8134i	0.687754	−	0.738273i
$874$	12.5120	+	10.0472i	0.423225	+	0.339853i
$875$	−2.86589			−0.0968846
$876$	−28.5974	−	39.3826i	−0.966216	−	1.33062i
$877$	54.6464			1.84528			0.922638	−	0.385666i	$-0.126028\pi$
$877$	54.6464			1.84528			0.922638	+	0.385666i	$0.126028\pi$
$878$	−9.78034	−	7.85369i	−0.330071	−	0.265049i
$879$	−0.532442	−	1.22369i	−0.0179588	−	0.0412739i
$880$	−7.16527	−	15.4073i	−0.241541	−	0.519382i
$881$		−	15.3502i		−	0.517160i	−0.965990	−	0.258580i	$-0.916745\pi$
$881$		−	15.3502i		−	0.517160i	0.965990	−	0.258580i	$-0.0832545\pi$
$882$	−0.739907	−	5.09415i	−0.0249140	−	0.171529i
$883$		−	22.3268i		−	0.751356i	−0.926750	−	0.375678i	$-0.877410\pi$
$883$		−	22.3268i		−	0.751356i	0.926750	−	0.375678i	$-0.122590\pi$
$884$	−12.0572	+	2.66651i	−0.405528	+	0.0896844i
$885$	2.53562	+	5.82750i	0.0852339	+	0.195889i
$886$	25.6966	−	32.0005i	0.863295	−	1.07508i
$887$	36.0766			1.21134			0.605668	−	0.795718i	$-0.292906\pi$
$887$	36.0766			1.21134			0.605668	+	0.795718i	$0.292906\pi$
$888$	−44.4801	−	2.15968i	−1.49265	−	0.0724741i
$889$	28.8380			0.967196
$890$	5.43319	−	6.76605i	0.182121	−	0.226798i
$891$	2.70547	+	38.1361i	0.0906367	+	1.27761i
$892$	24.0624	−	5.32153i	0.805670	−	0.178178i
$893$		−	27.9900i		−	0.936648i
$894$	−28.5065	−	7.77191i	−0.953401	−	0.259932i
$895$		−	1.70286i		−	0.0569203i
$896$	0.765706	−	32.4148i	0.0255804	−	1.08290i
$897$	−6.27633	+	2.73091i	−0.209560	+	0.0911825i
$898$	−16.2322	−	13.0346i	−0.541676	−	0.434970i
$899$	81.3327			2.71260
$900$	5.16975	+	3.04528i	0.172325	+	0.101509i
$901$	73.6367			2.45320
$902$	−22.9840	−	18.4564i	−0.765284	−	0.614529i
$903$	−1.66342	+	0.723774i	−0.0553550	+	0.0240857i
$904$	−1.33190	+	2.69557i	−0.0442983	+	0.0896534i
$905$			2.18927i			0.0727738i
$906$	−27.5087	−	7.49987i	−0.913915	−	0.249166i
$907$			48.3901i			1.60677i	0.595462	+	0.803383i	$0.296969\pi$
$907$			48.3901i			1.60677i	−0.595462	+	0.803383i	$0.703031\pi$
$908$	8.52544	+	38.5496i	0.282927	+	1.27931i
$909$	3.77548	+	3.51712i	0.125225	+	0.116656i
$910$	−2.53767	+	3.16020i	−0.0841228	+	0.104760i
$911$	7.14733			0.236802			0.118401	−	0.992966i	$-0.462223\pi$
$911$	7.14733			0.236802			0.118401	+	0.992966i	$0.462223\pi$
$912$	−14.8886	−	13.1930i	−0.493012	−	0.436863i
$913$	−68.4355			−2.26488
$914$	−8.56373	+	10.6646i	−0.283263	+	0.352753i
$915$	5.54957	+	12.7543i	0.183463	+	0.421645i
$916$	12.9479	+	58.5466i	0.427809	+	1.93443i
$917$			45.9091i			1.51605i
$918$	−38.5698	+	23.8944i	−1.27299	+	0.788633i
$919$			41.8313i			1.37989i	0.723864	+	0.689943i	$0.242364\pi$
$919$			41.8313i			1.37989i	−0.723864	+	0.689943i	$0.757636\pi$
$920$	4.95136	−	10.0209i	0.163242	−	0.330378i
$921$	8.13391	+	18.6938i	0.268021	+	0.615981i
$922$	38.9544	+	31.2807i	1.28289	+	1.03017i
$923$	5.11426			0.168338
$924$	34.1251	−	24.7797i	1.12263	−	0.815192i
$925$	−9.09015			−0.298882
$926$	−17.1895	−	13.8033i	−0.564880	−	0.453604i
$927$	12.1767	+	11.3435i	0.399937	+	0.372569i
$928$	56.1827	+	13.8245i	1.84429	+	0.453810i
$929$			11.4151i			0.374517i	0.982311	+	0.187258i	$0.0599601\pi$
$929$			11.4151i			0.374517i	−0.982311	+	0.187258i	$0.940040\pi$
$930$	−5.12345	+	18.7923i	−0.168005	+	0.616223i
$931$			3.48374i			0.114175i
$932$	38.5225	−	8.51944i	1.26185	−	0.279064i
$933$	26.3547	−	11.4673i	0.862815	−	0.375422i
$934$	11.2001	−	13.9477i	0.366480	−	0.456384i
$935$	26.2283			0.857757
$936$	7.93569	−	3.00414i	0.259386	−	0.0981935i
$937$	−23.8854			−0.780301			−0.390150	−	0.920751i	$-0.627577\pi$
$937$	−23.8854			−0.780301			−0.390150	+	0.920751i	$0.627577\pi$
$938$	4.70379	−	5.85771i	0.153584	−	0.191261i
$939$	−38.8133	+	16.8882i	−1.26662	+	0.551124i
$940$	−19.0365	+	4.21001i	−0.620902	+	0.137315i
$941$		−	41.7523i		−	1.36109i	−0.732708	−	0.680543i	$-0.761744\pi$
$941$		−	41.7523i		−	1.36109i	0.732708	−	0.680543i	$-0.238256\pi$
$942$	−3.35343	+	12.3000i	−0.109261	+	0.400756i
$943$		−	19.3902i		−	0.631430i
$944$	−13.3081	+	6.18899i	−0.433141	+	0.201435i
$945$	−4.96027	+	14.0412i	−0.161358	+	0.456760i
$946$	−1.71187	−	1.37465i	−0.0556577	−	0.0446936i
$947$	−40.3596			−1.31151			−0.655756	−	0.754973i	$-0.727650\pi$
$947$	−40.3596			−1.31151			−0.655756	+	0.754973i	$0.727650\pi$
$948$	5.05144	−	3.66807i	0.164063	−	0.119133i
$949$	−14.0499			−0.456079
$950$	−3.16615	−	2.54245i	−0.102724	−	0.0824879i
$951$	−3.10128	−	7.12754i	−0.100566	−	0.231126i
$952$	44.8699	+	22.1705i	1.45424	+	0.718549i
$953$		−	41.6911i		−	1.35051i	−0.737586	−	0.675253i	$-0.764034\pi$
$953$		−	41.6911i		−	1.35051i	0.737586	−	0.675253i	$-0.235966\pi$
$954$	−50.0739	+	7.27305i	−1.62120	+	0.235474i
$955$			14.3893i			0.465625i
$956$	3.45391	+	15.6176i	0.111708	+	0.505110i
$957$	30.0255	+	69.0061i	0.970585	+	2.23065i
$958$	−13.5724	+	16.9020i	−0.438505	+	0.546079i
$959$	13.0276			0.420684
$960$	−6.73336	+	12.1104i	−0.217318	+	0.390862i
$961$	−32.2332			−1.03978
$962$	−8.04908	+	10.0237i	−0.259513	+	0.323176i
$963$	−16.7376	+	17.9671i	−0.539362	+	0.578981i
$964$	4.58269	+	20.7216i	0.147599	+	0.667399i
$965$		−	15.6033i		−	0.502288i
$966$	26.7646	+	7.29700i	0.861136	+	0.234777i
$967$			7.31899i			0.235363i	0.993051	+	0.117681i	$0.0375462\pi$
$967$			7.31899i			0.235363i	−0.993051	+	0.117681i	$0.962454\pi$
$968$	17.8657	+	8.82754i	0.574226	+	0.283728i
$969$	28.1561	−	12.2511i	0.904505	−	0.393562i
$970$	10.9579	+	8.79927i	0.351836	+	0.282527i
$971$	−5.83157			−0.187144			−0.0935720	−	0.995613i	$-0.529829\pi$
$971$	−5.83157			−0.187144			−0.0935720	+	0.995613i	$0.529829\pi$
$972$	23.8679	−	20.0580i	0.765563	−	0.643361i
$973$	46.7847			1.49985
$974$	−26.4320	−	21.2251i	−0.846937	−	0.680097i
$975$	1.58822	−	0.691055i	0.0508638	−	0.0221315i
$976$	−29.1266	+	13.5455i	−0.932321	+	0.433581i
$977$			28.0105i			0.896134i	0.894000	+	0.448067i	$0.147887\pi$
$977$			28.0105i			0.896134i	−0.894000	+	0.448067i	$0.852113\pi$
$978$	−10.4126	−	2.83885i	−0.332958	−	0.0907766i
$979$			26.0653i			0.833052i
$980$	2.36935	−	0.523994i	0.0756863	−	0.0167384i
$981$	15.1288	−	16.2401i	0.483025	−	0.518506i
$982$	−31.6977	+	39.4737i	−1.01151	+	1.25966i
$983$	−44.9653			−1.43417			−0.717085	−	0.696986i	$-0.754524\pi$
$983$	−44.9653			−1.43417			−0.717085	+	0.696986i	$0.754524\pi$
$984$	−1.16575	+	24.0094i	−0.0371627	+	0.765391i
$985$	−25.9412			−0.826555
$986$	−55.9183	+	69.6361i	−1.78080	+	2.21766i
$987$	−19.3062	−	44.3706i	−0.614524	−	1.41233i
$988$	−5.60709	+	1.24003i	−0.178385	+	0.0394508i
$989$		−	1.44420i		−	0.0459228i
$990$	−17.8356	+	2.59055i	−0.566852	+	0.0823331i
$991$			7.61258i			0.241822i	0.992663	+	0.120911i	$0.0385815\pi$
$991$			7.61258i			0.241822i	−0.992663	+	0.120911i	$0.961419\pi$
$992$	−43.6800	−	10.7480i	−1.38684	−	0.341250i
$993$	8.58583	+	19.7324i	0.272463	+	0.626190i
$994$	−16.1621	−	12.9783i	−0.512630	−	0.411646i
$995$	−7.25282			−0.229930
$996$	32.7907	+	45.1573i	1.03901	+	1.43086i
$997$	51.5640			1.63305			0.816524	−	0.577312i	$-0.195898\pi$
$997$	51.5640			1.63305			0.816524	+	0.577312i	$0.195898\pi$
$998$	24.7613	+	19.8835i	0.783806	+	0.629403i
$999$	−15.7332	+	44.5365i	−0.497777	+	1.40907i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.g.d.131.10	yes	32
3.2	odd	2	inner	780.2.g.d.131.23	yes	32
4.3	odd	2	inner	780.2.g.d.131.24	yes	32
12.11	even	2	inner	780.2.g.d.131.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.d.131.9	✓	32	12.11	even	2	inner
780.2.g.d.131.10	yes	32	1.1	even	1	trivial
780.2.g.d.131.23	yes	32	3.2	odd	2	inner
780.2.g.d.131.24	yes	32	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 780 = 2^{2} \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	780.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.885473 + 1.10270i) q^{2} +(-1.58822 + 0.691055i) q^{3} +(-0.431874 - 1.95281i) q^{4} -1.00000i q^{5} +(0.644303 - 2.36323i) q^{6} +2.86589i q^{7} +(2.53577 + 1.25294i) q^{8} +(2.04489 - 2.19509i) q^{9} +(1.10270 + 0.885473i) q^{10} -4.24800 q^{11} +(2.03541 + 2.80305i) q^{12} +1.00000 q^{13} +(-3.16020 - 2.53767i) q^{14} +(0.691055 + 1.58822i) q^{15} +(-3.62697 + 1.68674i) q^{16} -6.17427i q^{17} +(0.609829 + 4.19858i) q^{18} -2.87129i q^{19} +(-1.95281 + 0.431874i) q^{20} +(-1.98048 - 4.55166i) q^{21} +(3.76149 - 4.68425i) q^{22} +3.95180 q^{23} +(-4.89322 - 0.237585i) q^{24} -1.00000 q^{25} +(-0.885473 + 1.10270i) q^{26} +(-1.73080 + 4.89942i) q^{27} +(5.59654 - 1.23770i) q^{28} +10.2281i q^{29} +(-2.36323 - 0.644303i) q^{30} -7.95193i q^{31} +(1.35162 - 5.49301i) q^{32} +(6.74675 - 2.93560i) q^{33} +(6.80834 + 5.46715i) q^{34} +2.86589 q^{35} +(-5.16975 - 3.04528i) q^{36} +9.09015 q^{37} +(3.16615 + 2.54245i) q^{38} +(-1.58822 + 0.691055i) q^{39} +(1.25294 - 2.53577i) q^{40} -4.90666i q^{41} +(6.77276 + 1.84650i) q^{42} -0.365453i q^{43} +(1.83460 + 8.29555i) q^{44} +(-2.19509 - 2.04489i) q^{45} +(-3.49921 + 4.35763i) q^{46} +9.74823 q^{47} +(4.59479 - 5.18535i) q^{48} -1.21330 q^{49} +(0.885473 - 1.10270i) q^{50} +(4.26676 + 9.80610i) q^{51} +(-0.431874 - 1.95281i) q^{52} +11.9264i q^{53} +(-3.87000 - 6.24685i) q^{54} +4.24800i q^{55} +(-3.59078 + 7.26724i) q^{56} +(1.98422 + 4.56023i) q^{57} +(-11.2784 - 9.05667i) q^{58} +3.66920 q^{59} +(2.80305 - 2.03541i) q^{60} +8.03057 q^{61} +(8.76856 + 7.04122i) q^{62} +(6.29089 + 5.86041i) q^{63} +(4.86029 + 6.35434i) q^{64} -1.00000i q^{65} +(-2.73700 + 10.0390i) q^{66} +1.85359i q^{67} +(-12.0572 + 2.66651i) q^{68} +(-6.27633 + 2.73091i) q^{69} +(-2.53767 + 3.16020i) q^{70} +5.11426 q^{71} +(7.93569 - 3.00414i) q^{72} -14.0499 q^{73} +(-8.04908 + 10.0237i) q^{74} +(1.58822 - 0.691055i) q^{75} +(-5.60709 + 1.24003i) q^{76} -12.1743i q^{77} +(0.644303 - 2.36323i) q^{78} -1.80212i q^{79} +(1.68674 + 3.62697i) q^{80} +(-0.636882 - 8.97744i) q^{81} +(5.41056 + 4.34472i) q^{82} +16.1101 q^{83} +(-8.03322 + 5.83326i) q^{84} -6.17427 q^{85} +(0.402983 + 0.323599i) q^{86} +(-7.06815 - 16.2444i) q^{87} +(-10.7720 - 5.32248i) q^{88} -6.13592i q^{89} +(4.19858 - 0.609829i) q^{90} +2.86589i q^{91} +(-1.70668 - 7.71713i) q^{92} +(5.49522 + 12.6294i) q^{93} +(-8.63180 + 10.7493i) q^{94} -2.87129 q^{95} +(1.64930 + 9.65815i) q^{96} +9.93736 q^{97} +(1.07435 - 1.33790i) q^{98} +(-8.68667 + 9.32475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 6 q^{4} + 10 q^{6} + 12 q^{9} + 6 q^{10} - 20 q^{12} + 32 q^{13} - 6 q^{16} + 4 q^{18} + 20 q^{21} + 16 q^{22} + 10 q^{24} - 32 q^{25} + 16 q^{28} + 16 q^{33} + 28 q^{34} + 30 q^{36} - 24 q^{37}+ \cdots + 112 q^{97}+O(q^{100}) \) 32 * q + 6 * q^4 + 10 * q^6 + 12 * q^9 + 6 * q^10 - 20 * q^12 + 32 * q^13 - 6 * q^16 + 4 * q^18 + 20 * q^21 + 16 * q^22 + 10 * q^24 - 32 * q^25 + 16 * q^28 + 16 * q^33 + 28 * q^34 + 30 * q^36 - 24 * q^37 + 6 * q^40 + 20 * q^45 - 80 * q^46 - 16 * q^48 + 16 * q^49 + 6 * q^52 + 2 * q^54 - 64 * q^57 - 100 * q^58 + 14 * q^60 + 16 * q^61 + 126 * q^64 + 60 * q^66 - 4 * q^69 - 16 * q^70 - 16 * q^72 - 104 * q^73 + 20 * q^76 + 10 * q^78 - 72 * q^81 - 116 * q^82 + 20 * q^84 + 24 * q^85 - 14 * q^90 + 16 * q^93 + 28 * q^94 - 74 * q^96 + 112 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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