LMFDB - Embedded newform 780.2.g.d.131.23

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			131.23
Character	$\chi$	$=$	780.131
Dual form			780.2.g.d.131.24

$q$-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} +(2.16835 - 1.13941i) 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} +(0.663591 - 3.39995i) 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} +(4.23121 - 0.311189i) 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} +(-3.16152 - 3.74230i) 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} +(1.13941 + 2.16835i) 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} +(3.40348 - 4.94129i) 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} +(3.26543 + 6.21424i) 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} +(-6.92606 + 0.172481i) 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} +(6.93515 + 2.42976i) 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} +(3.39995 + 0.663591i) 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} +(9.21114 - 4.84022i) 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} +(-2.43505 - 8.12838i) 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} +(2.16835 - 1.13941i) 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} +(9.74386 + 1.90178i) 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} +(0.311189 + 4.23121i) 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} +(-5.94264 + 7.79006i) 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
$6$	2.16835	−	1.13941i	0.885225	−	0.465163i
$7$			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	$-0.278765\pi$
$11$	4.24800			1.28082			0.640409	+	0.768034i	$0.278765\pi$
$12$	0.663591	−	3.39995i	0.191562	−	0.981480i
$13$	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	$0.269341\pi$
$17$			6.17427i			1.49748i	−0.662863	+	0.748740i	$0.730659\pi$
$18$	4.23121	−	0.311189i	0.997306	−	0.0733479i
$19$		−	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	$-0.635171\pi$
$23$	−3.95180			−0.824007			−0.412004	+	0.911182i	$0.635171\pi$
$24$	−3.16152	−	3.74230i	−0.645342	−	0.763894i
$25$	−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	$-0.601438\pi$
$29$		−	10.2281i		−	1.89930i	0.313311	−	0.949651i	$-0.398562\pi$
$30$	1.13941	+	2.16835i	0.208027	+	0.395885i
$31$		−	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
$36$	3.40348	−	4.94129i	0.567247	−	0.823548i
$37$	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	$0.125159\pi$
$41$			4.90666i			0.766292i	−0.923688	+	0.383146i	$0.874841\pi$
$42$	3.26543	+	6.21424i	0.503866	+	0.958878i
$43$		−	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	$-0.751741\pi$
$47$	−9.74823			−1.42193			−0.710963	+	0.703230i	$0.751741\pi$
$48$	−6.92606	+	0.172481i	−0.999690	+	0.0248955i
$49$	−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	$-0.694469\pi$
$53$		−	11.9264i		−	1.63821i	0.573640	−	0.819107i	$-0.305531\pi$
$54$	6.93515	+	2.42976i	0.943754	+	0.330649i
$55$			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	$-0.576769\pi$
$59$	−3.66920			−0.477689			−0.238845	+	0.971058i	$0.576769\pi$
$60$	3.39995	+	0.663591i	0.438931	+	0.0856692i
$61$	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
$66$	9.21114	−	4.84022i	1.13381	−	0.595790i
$67$			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	$-0.598147\pi$
$71$	−5.11426			−0.606951			−0.303475	+	0.952839i	$0.598147\pi$
$72$	−2.43505	−	8.12838i	−0.286973	−	0.957939i
$73$	−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
$78$	2.16835	−	1.13941i	0.245517	−	0.129013i
$79$		−	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	$-0.845265\pi$
$83$	−16.1101			−1.76831			−0.884155	+	0.467194i	$0.845265\pi$
$84$	9.74386	+	1.90178i	1.06314	+	0.207501i
$85$	−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	$0.105433\pi$
$89$			6.13592i			0.650406i	−0.945644	+	0.325203i	$0.894567\pi$
$90$	0.311189	+	4.23121i	0.0328022	+	0.446009i
$91$			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
$96$	−5.94264	+	7.79006i	−0.606518	+	0.795069i
$97$	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	$-0.972728\pi$
$101$		−	1.71996i		−	0.171143i	0.996332	−	0.0855713i	$-0.0272715\pi$
$102$	7.03504	+	13.3880i	0.696573	+	1.32561i
$103$			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	$-0.370522\pi$
$107$	8.18510			0.791283			0.395642	+	0.918405i	$0.370522\pi$
$108$	8.82018	−	5.49586i	0.848722	−	0.528840i
$109$	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	$-0.984078\pi$
$113$		−	1.06302i		−	0.100000i	0.998749	−	0.0500002i	$-0.0159222\pi$
$114$	−3.27158	−	6.22595i	−0.306411	−	0.583114i
$115$		−	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
$120$	3.74230	−	3.16152i	0.341624	−	0.288606i
$121$	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
$126$	0.891832	+	12.1262i	0.0794507	+	1.08029i
$127$		−	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	$-0.746728\pi$
$131$	−16.0192			−1.39960			−0.699801	+	0.714338i	$0.746728\pi$
$132$	2.81893	−	14.4430i	0.245356	−	1.25710i
$133$	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	$0.0622063\pi$
$137$			4.54576i			0.388370i	−0.980965	+	0.194185i	$0.937794\pi$
$138$	−8.56888	+	4.50273i	−0.729432	+	0.383298i
$139$		−	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
$144$	−11.1193	−	4.51235i	−0.926608	−	0.376029i
$145$	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	$0.164502\pi$
$149$			12.0625i			0.988199i	−0.869405	+	0.494100i	$0.835498\pi$
$150$	−2.16835	+	1.13941i	−0.177045	+	0.0930326i
$151$		−	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
$156$	0.663591	−	3.39995i	0.0531298	−	0.272214i
$157$	−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
$162$	9.33544	+	8.65157i	0.733461	+	0.679731i
$163$		−	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	$-0.833221\pi$
$167$	−22.3785			−1.73170			−0.865849	+	0.500305i	$0.833221\pi$
$168$	10.7250	−	9.06054i	0.827452	−	0.699036i
$169$	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	$-0.881477\pi$
$173$		−	9.57026i		−	0.727613i	0.931474	−	0.363807i	$-0.118523\pi$
$174$	−11.6540	−	22.1780i	−0.883485	−	1.68131i
$175$		−	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	$-0.520271\pi$
$179$	−1.70286			−0.127278			−0.0636388	+	0.997973i	$0.520271\pi$
$180$	4.94129	+	3.40348i	0.368302	+	0.253680i
$181$	−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
$186$	−9.06053	−	17.2426i	−0.664350	−	1.26429i
$187$			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	$-0.325714\pi$
$191$	14.3893			1.04117			0.520585	+	0.853810i	$0.325714\pi$
$192$	3.32801	+	13.4508i	0.240178	+	0.970729i
$193$	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	$0.375197\pi$
$197$			25.9412i			1.84823i	−0.382111	+	0.924116i	$0.624803\pi$
$198$	17.9742	−	1.32193i	1.27737	−	0.0939454i
$199$		−	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
$204$	20.9922	+	4.09719i	1.46975	+	0.286861i
$205$	−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
$210$	−6.21424	+	3.26543i	−0.428823	+	0.225336i
$211$			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
$216$	1.74977	−	14.5924i	0.119057	−	0.992887i
$217$	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
$222$	19.7106	−	10.3574i	1.32289	−	0.695145i
$223$			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	$-0.272621\pi$
$227$	19.7406			1.31023			0.655113	+	0.755531i	$0.272621\pi$
$228$	−9.76222	−	1.90536i	−0.646519	−	0.126185i
$229$	−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	$-0.776370\pi$
$233$		−	19.7267i		−	1.29234i	0.763195	−	0.646169i	$-0.223630\pi$
$234$	4.23121	−	0.311189i	0.276603	−	0.0203431i
$235$		−	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	$-0.416720\pi$
$239$	7.99750			0.517315			0.258658	+	0.965969i	$0.416720\pi$
$240$	−0.172481	−	6.92606i	−0.0111336	−	0.447075i
$241$	−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
$246$	5.59071	+	10.6394i	0.356451	+	0.678341i
$247$		−	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	$-0.487306\pi$
$251$	1.26328			0.0797374			0.0398687	+	0.999205i	$0.487306\pi$
$252$	14.1612	+	9.75398i	0.892070	+	0.614443i
$253$	−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	$-0.964886\pi$
$257$		−	3.52977i		−	0.220181i	0.993922	−	0.110090i	$-0.0351141\pi$
$258$	−0.416401	−	0.792429i	−0.0259240	−	0.0493345i
$259$			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	$-0.288128\pi$
$263$	20.0297			1.23509			0.617543	+	0.786537i	$0.288128\pi$
$264$	−13.4301	−	15.8973i	−0.826566	−	0.978410i
$265$	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	$0.00151411\pi$
$269$			0.156032i			0.00951341i	−0.999989	+	0.00475670i	$0.998486\pi$
$270$	−2.42976	+	6.93515i	−0.147871	+	0.422060i
$271$			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
$276$	−2.62238	+	13.4359i	−0.157849	+	0.808747i
$277$	−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	$0.203996\pi$
$281$			20.0451i			1.19579i	−0.801574	+	0.597896i	$0.796004\pi$
$282$	−21.1376	+	11.1073i	−1.25872	+	0.661427i
$283$			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
$288$	−14.8216	+	8.26563i	−0.873370	+	0.487057i
$289$	−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	$-0.992836\pi$
$293$		−	0.770477i		−	0.0450117i	0.999747	−	0.0225059i	$-0.00716444\pi$
$294$	−2.63086	+	1.38245i	−0.153435	+	0.0806262i
$295$		−	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
$300$	−0.663591	+	3.39995i	−0.0383124	+	0.196296i
$301$	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
$306$	1.92136	+	26.1247i	0.109837	+	1.49345i
$307$		−	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	$-0.344082\pi$
$311$	16.5939			0.940952			0.470476	+	0.882413i	$0.344082\pi$
$312$	−3.16152	−	3.74230i	−0.178986	−	0.211866i
$313$	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	$-0.959777\pi$
$317$		−	4.48775i		−	0.252057i	0.992027	−	0.126029i	$-0.0402231\pi$
$318$	−13.5891	−	25.8606i	−0.762037	−	1.45019i
$319$		−	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
$324$	17.8063	−	2.63341i	0.989240	−	0.146301i
$325$	−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
$330$	4.84022	+	9.21114i	0.266445	+	0.507057i
$331$		−	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
$336$	−0.494311	−	19.8493i	−0.0269669	−	1.08287i
$337$	−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
$342$	−0.893512	−	12.1490i	−0.0483156	−	0.656944i
$343$			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	$-0.606464\pi$
$347$	−12.2298			−0.656532			−0.328266	+	0.944585i	$0.606464\pi$
$348$	−34.7748	−	6.78724i	−1.86413	−	0.363834i
$349$	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	$0.0531548\pi$
$353$			6.24582i			0.332431i	−0.986089	+	0.166216i	$0.946845\pi$
$354$	−7.95611	+	4.18073i	−0.422862	+	0.222203i
$355$		−	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	$-0.637511\pi$
$359$	−15.8661			−0.837382			−0.418691	+	0.908129i	$0.637511\pi$
$360$	8.12838	−	2.43505i	0.428403	−	0.128338i
$361$	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
$366$	17.4131	−	9.15013i	0.910197	−	0.478285i
$367$		−	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
$372$	−27.0361	−	5.27683i	−1.40176	−	0.273591i
$373$	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
$378$	−6.96343	+	19.8753i	−0.358160	+	1.02228i
$379$		−	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	$-0.472587\pi$
$383$	3.36662			0.172026			0.0860130	+	0.996294i	$0.472587\pi$
$384$	17.7790	+	8.24055i	0.907281	+	0.420524i
$385$	−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	$-0.911865\pi$
$389$		−	10.7830i		−	0.546720i	0.961912	−	0.273360i	$-0.0881350\pi$
$390$	1.13941	+	2.16835i	0.0576964	+	0.109799i
$391$		−	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
$396$	14.4580	−	20.9906i	0.726540	−	1.05482i
$397$	−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	$-0.885846\pi$
$401$		−	14.0571i		−	0.701976i	0.936380	−	0.350988i	$-0.114154\pi$
$402$	2.11200	+	4.01923i	0.105337	+	0.200461i
$403$		−	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
$408$	23.1060	−	19.5201i	1.14392	−	0.966387i
$409$	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
$414$	−16.7209	+	1.22976i	−0.821788	+	0.0604392i
$415$		−	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	$-0.487553\pi$
$419$	1.60040			0.0781848			0.0390924	+	0.999236i	$0.487553\pi$
$420$	−1.90178	+	9.74386i	−0.0927971	+	0.475452i
$421$	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
$426$	−11.0895	+	5.82725i	−0.537288	+	0.282331i
$427$			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	$-0.751238\pi$
$431$	−29.4738			−1.41970			−0.709851	+	0.704352i	$0.751238\pi$
$432$	−14.5416	−	14.8506i	−0.699633	−	0.714502i
$433$	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
$438$	−30.4651	+	16.0086i	−1.45568	+	0.764923i
$439$			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	$-0.257876\pi$
$443$	29.0202			1.37879			0.689396	+	0.724385i	$0.257876\pi$
$444$	6.03214	−	30.9060i	0.286273	−	1.46674i
$445$	−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	$-0.887081\pi$
$449$		−	14.7205i		−	0.694702i	0.937735	−	0.347351i	$-0.112919\pi$
$450$	−4.23121	+	0.311189i	−0.199461	+	0.0146696i
$451$			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
$456$	−10.7452	+	9.07761i	−0.503191	+	0.425098i
$457$	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	$0.307511\pi$
$461$			35.3265i			1.64532i	−0.568534	+	0.822660i	$0.692489\pi$
$462$	13.8715	+	26.3981i	0.645361	+	1.22815i
$463$			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	$-0.405460\pi$
$467$	12.6488			0.585315			0.292657	+	0.956217i	$0.405460\pi$
$468$	3.40348	−	4.94129i	0.157326	−	0.228411i
$469$	−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
$474$	−2.05336	−	3.90763i	−0.0943140	−	0.179484i
$475$			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	$-0.613878\pi$
$479$	−15.3279			−0.700349			−0.350175	+	0.936684i	$0.613878\pi$
$480$	−7.79006	−	5.94264i	−0.355566	−	0.271243i
$481$	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
$486$	8.84802	+	20.1919i	0.401354	+	0.915923i
$487$			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	$-0.799320\pi$
$491$	−35.7975			−1.61552			−0.807759	+	0.589513i	$0.799320\pi$
$492$	16.6824	+	3.25602i	0.752101	+	0.146793i
$493$	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
$498$	−34.9323	+	18.3560i	−1.56535	+	0.822553i
$499$		−	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	$-0.742532\pi$
$503$	−30.9647			−1.38065			−0.690323	+	0.723501i	$0.742532\pi$
$504$	23.2950	−	6.97857i	1.03764	−	0.310850i
$505$	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	$-0.975929\pi$
$509$		−	3.40890i		−	0.151097i	0.997142	−	0.0755484i	$-0.0240708\pi$
$510$	−13.3880	+	7.03504i	−0.592830	+	0.311517i
$511$		−	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
$516$	−1.24252	−	0.242511i	−0.0546989	−	0.0106760i
$517$	−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	$0.0307765\pi$
$521$			4.40697i			0.193073i	−0.995329	+	0.0965365i	$0.969224\pi$
$522$	−3.18286	−	43.2771i	−0.139310	−	1.89419i
$523$			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
$528$	−29.4219	+	0.732698i	−1.28042	+	0.0318866i
$529$	−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
$534$	6.99134	+	13.3048i	0.302545	+	0.575755i
$535$			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
$540$	5.49586	+	8.82018i	0.236504	+	0.379560i
$541$	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
$546$	3.26543	+	6.21424i	0.139747	+	0.265945i
$547$		−	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
$552$	12.4937	+	14.7888i	0.531766	+	0.629454i
$553$	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	$0.216665\pi$
$557$			29.7048i			1.25863i	−0.777150	+	0.629316i	$0.783335\pi$
$558$	−2.47455	−	33.6463i	−0.104756	−	1.42436i
$559$		−	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	$-0.524430\pi$
$563$	−3.63856			−0.153347			−0.0766735	+	0.997056i	$0.524430\pi$
$564$	−6.46883	+	33.1435i	−0.272387	+	1.39559i
$565$	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	$0.174669\pi$
$569$			24.8848i			1.04322i	−0.853183	+	0.521612i	$0.825331\pi$
$570$	6.22595	−	3.27158i	0.260776	−	0.137031i
$571$			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
$576$	−4.00964	+	23.6627i	−0.167068	+	0.985945i
$577$	−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
$582$	21.5477	−	11.3227i	0.893180	−	0.469343i
$583$		−	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	$-0.179709\pi$
$587$	40.9366			1.68963			0.844817	+	0.535055i	$0.179709\pi$
$588$	−0.805136	+	4.12517i	−0.0332033	+	0.170119i
$589$	−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	$0.0776771\pi$
$593$			11.7674i			0.483230i	−0.970372	+	0.241615i	$0.922323\pi$
$594$	29.4605	+	10.3216i	1.20878	+	0.423502i
$595$		−	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	$-0.355028\pi$
$599$	21.5307			0.879720			0.439860	+	0.898066i	$0.355028\pi$
$600$	3.16152	+	3.74230i	0.129068	+	0.152779i
$601$	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
$606$	−1.95975	−	3.72948i	−0.0796092	−	0.151500i
$607$			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
$612$	30.5089	+	21.0140i	1.23325	+	0.849441i
$613$	−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	$-0.981315\pi$
$617$		−	2.91455i		−	0.117335i	0.998278	−	0.0586677i	$-0.0186852\pi$
$618$	6.32061	+	12.0284i	0.254252	+	0.483852i
$619$			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
$624$	−6.92606	+	0.172481i	−0.277264	+	0.00690476i
$625$	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
$630$	−12.1262	+	0.891832i	−0.483118	+	0.0355314i
$631$		−	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
$636$	−40.5491	−	7.91424i	−1.60788	−	0.313820i
$637$	−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	$-0.778860\pi$
$641$		−	32.4160i		−	1.28036i	0.768226	−	0.640178i	$-0.221140\pi$
$642$	17.7482	−	9.32620i	0.700464	−	0.368076i
$643$			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	$-0.735826\pi$
$647$	−34.3353			−1.34986			−0.674930	+	0.737881i	$0.735826\pi$
$648$	12.8632	−	21.9668i	0.505313	−	0.862936i
$649$	−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	$0.0171976\pi$
$653$			2.75989i			0.108003i	−0.998541	+	0.0540015i	$0.982802\pi$
$654$	16.0422	−	8.42977i	0.627300	−	0.329630i
$655$		−	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	$-0.481529\pi$
$659$	2.97758			0.115990			0.0579950	+	0.998317i	$0.481529\pi$
$660$	14.4430	+	2.81893i	0.562192	+	0.109727i
$661$	−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
$666$	38.4624	−	2.82875i	1.49039	−	0.109612i
$667$			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
$672$	−22.3254	−	17.0309i	−0.861222	−	0.656983i
$673$	−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	$0.172372\pi$
$677$			26.8227i			1.03088i	−0.856925	+	0.515440i	$0.827628\pi$
$678$	−1.21122	−	2.30500i	−0.0465165	−	0.0885228i
$679$			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	$-0.416183\pi$
$683$	13.6048			0.520573			0.260286	+	0.965531i	$0.416183\pi$
$684$	−14.1878	−	9.77236i	−0.542486	−	0.373656i
$685$	−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
$690$	−4.50273	−	8.56888i	−0.171416	−	0.326212i
$691$			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
$696$	−38.2765	+	32.3361i	−1.45087	+	1.22570i
$697$	−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	$0.258777\pi$
$701$			38.4614i			1.45267i	−0.687342	+	0.726334i	$0.741223\pi$
$702$	6.93515	+	2.42976i	0.261750	+	0.0917055i
$703$		−	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
$708$	−2.43485	+	12.4751i	−0.0915072	+	0.468843i
$709$	−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
$714$	−38.3684	+	20.1616i	−1.43590	+	0.754530i
$715$			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	$-0.548319\pi$
$719$	−8.10953			−0.302434			−0.151217	+	0.988501i	$0.548319\pi$
$720$	4.51235	−	11.1193i	0.168165	−	0.414392i
$721$	−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
$726$	15.2770	−	8.02769i	0.566984	−	0.297936i
$727$			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
$732$	5.32901	−	27.3035i	0.196966	−	1.00917i
$733$	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
$738$	1.52690	+	20.7611i	0.0562059	+	0.764228i
$739$			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	$-0.632215\pi$
$743$	−21.9986			−0.807049			−0.403524	+	0.914969i	$0.632215\pi$
$744$	−29.7585	+	25.1401i	−1.09100	+	0.921682i
$745$	−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
$750$	−1.13941	−	2.16835i	−0.0416055	−	0.0791769i
$751$		−	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
$756$	15.7505	+	25.2776i	0.572841	+	0.919338i
$757$	−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	$0.0565126\pi$
$761$			9.74392i			0.353217i	−0.984281	+	0.176608i	$0.943487\pi$
$762$	−11.4654	−	21.8190i	−0.415346	−	0.790421i
$763$			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
$768$	24.8297	−	12.3080i	0.895963	−	0.444128i
$769$	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	$-0.752020\pi$
$773$		−	39.0689i		−	1.40521i	0.711580	−	0.702605i	$-0.247980\pi$
$774$	−0.113725	−	1.54631i	−0.00408775	−	0.0555809i
$775$			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
$780$	3.39995	+	0.663591i	0.121738	+	0.0237604i
$781$	−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
$786$	−34.7352	+	18.2525i	−1.23896	+	0.651043i
$787$		−	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
$792$	−10.3441	−	34.5293i	−0.367560	−	1.22695i
$793$	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	$-0.954213\pi$
$797$		−	8.09375i		−	0.286695i	0.989672	−	0.143348i	$-0.0457867\pi$
$798$	17.8429	−	9.37597i	0.631631	−	0.331906i
$799$		−	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
$804$	6.30211	+	1.23002i	0.222258	+	0.0433796i
$805$	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	$-0.848127\pi$
$809$		−	26.1234i		−	0.918448i	0.888320	−	0.459224i	$-0.151873\pi$
$810$	−8.65157	+	9.33544i	−0.303985	+	0.328014i
$811$			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
$816$	−1.06494	−	42.7634i	−0.0372805	−	1.49702i
$817$	−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	$-0.892472\pi$
$821$		−	18.9925i		−	0.662843i	0.943483	−	0.331421i	$-0.107528\pi$
$822$	5.17949	+	9.85680i	0.180656	+	0.343795i
$823$			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	$-0.540384\pi$
$827$	−7.27740			−0.253060			−0.126530	+	0.991963i	$0.540384\pi$
$828$	−13.4499	+	19.5270i	−0.467415	+	0.678610i
$829$	−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
$834$	−18.6006	−	35.3976i	−0.644085	−	1.22572i
$835$		−	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	$-0.559360\pi$
$839$	−10.7407			−0.370811			−0.185405	+	0.982662i	$0.559360\pi$
$840$	9.06054	+	10.7250i	0.312618	+	0.370048i
$841$	−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
$846$	−41.2468	+	3.03354i	−1.41810	+	0.104295i
$847$			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
$852$	−3.39378	+	17.3882i	−0.116269	+	0.595711i
$853$	−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	$-0.835626\pi$
$857$		−	28.9086i		−	0.987499i	0.869604	−	0.493749i	$-0.164374\pi$
$858$	9.21114	−	4.84022i	0.314463	−	0.165242i
$859$			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	$-0.339302\pi$
$863$	28.4177			0.967349			0.483674	+	0.875248i	$0.339302\pi$
$864$	−29.2519	+	2.88512i	−0.995171	+	0.0981536i
$865$	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
$870$	22.1780	−	11.6540i	0.751904	−	0.395107i
$871$			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
$876$	−9.32339	+	47.7690i	−0.315008	+	1.61396i
$877$	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	$0.0832545\pi$
$881$			15.3502i			0.517160i	−0.965990	+	0.258580i	$0.916745\pi$
$882$	−5.13374	+	0.377566i	−0.172862	+	0.0127133i
$883$		−	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	$-0.707094\pi$
$887$	−36.0766			−1.21134			−0.605668	+	0.795718i	$0.707094\pi$
$888$	−28.7386	−	34.0181i	−0.964406	−	1.14157i
$889$	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
$894$	13.7442	+	26.1557i	0.459674	+	0.874779i
$895$		−	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
$900$	−3.40348	+	4.94129i	−0.113449	+	0.164710i
$901$	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
$906$	−13.2631	−	25.2402i	−0.440636	−	0.838549i
$907$			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	$-0.537777\pi$
$911$	−7.14733			−0.236802			−0.118401	+	0.992966i	$0.537777\pi$
$912$	0.495242	+	19.8867i	0.0163991	+	0.658514i
$913$	−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
$918$	−15.0020	+	42.8195i	−0.495141	+	1.41325i
$919$			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
$924$	41.3919	+	8.07873i	1.36169	+	0.265771i
$925$	−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	$-0.940040\pi$
$929$		−	11.4151i		−	0.374517i	0.982311	−	0.187258i	$-0.0599601\pi$
$930$	17.2426	−	9.06053i	0.565406	−	0.297106i
$931$			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
$936$	−2.43505	−	8.12838i	−0.0795920	−	0.265684i
$937$	−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	$0.238256\pi$
$941$			41.7523i			1.36109i	−0.732708	+	0.680543i	$0.761744\pi$
$942$	−11.2857	+	5.93034i	−0.367708	+	0.193221i
$943$		−	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	$-0.272350\pi$
$947$	40.3596			1.31151			0.655756	+	0.754973i	$0.272350\pi$
$948$	−6.12713	−	1.19587i	−0.199000	−	0.0388401i
$949$	−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	$0.235966\pi$
$953$			41.6911i			1.35051i	−0.737586	+	0.675253i	$0.764034\pi$
$954$	−3.71136	−	50.4631i	−0.120160	−	1.63380i
$955$			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
$960$	−13.4508	+	3.32801i	−0.434123	+	0.107411i
$961$	−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
$966$	−12.9043	−	24.5574i	−0.415189	−	0.790123i
$967$			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	$-0.470171\pi$
$971$	5.83157			0.187144			0.0935720	+	0.995613i	$0.470171\pi$
$972$	30.1002	+	8.12271i	0.965464	+	0.260536i
$973$	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	$-0.852113\pi$
$977$		−	28.0105i		−	0.896134i	0.894000	−	0.448067i	$-0.147887\pi$
$978$	−5.02035	−	9.55393i	−0.160533	−	0.305501i
$979$			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	$-0.245476\pi$
$983$	44.9653			1.43417			0.717085	+	0.696986i	$0.245476\pi$
$984$	18.3622	−	15.5125i	0.585366	−	0.494520i
$985$	−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
$990$	1.32193	+	17.9742i	0.0420137	+	0.571257i
$991$			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
$996$	−10.6905	+	54.7734i	−0.338741	+	1.73556i
$997$	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.131.23	yes	32
3.2	odd	2	inner	780.2.g.d.131.10	yes	32
4.3	odd	2	inner	780.2.g.d.131.9	✓	32
12.11	even	2	inner	780.2.g.d.131.24	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.d.131.9	✓	32	4.3	odd	2	inner
780.2.g.d.131.10	yes	32	3.2	odd	2	inner
780.2.g.d.131.23	yes	32	1.1	even	1	trivial
780.2.g.d.131.24	yes	32	12.11	even	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} +(2.16835 - 1.13941i) 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} +(0.663591 - 3.39995i) 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} +(4.23121 - 0.311189i) 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} +(-3.16152 - 3.74230i) 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} +(1.13941 + 2.16835i) 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} +(3.40348 - 4.94129i) 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} +(3.26543 + 6.21424i) 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} +(-6.92606 + 0.172481i) 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} +(6.93515 + 2.42976i) 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} +(3.39995 + 0.663591i) 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} +(9.21114 - 4.84022i) 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} +(-2.43505 - 8.12838i) 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} +(2.16835 - 1.13941i) 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} +(9.74386 + 1.90178i) 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} +(0.311189 + 4.23121i) 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} +(-5.94264 + 7.79006i) 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

Fields

Representations

Groups

Database

Properties

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