LMFDB - Embedded newform 780.2.g.b.131.8

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 = [8,0,0,-2] 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:	$8$
Coefficient field:	8.0.342102016.5
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.8
Root			$-1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	780.131
Dual form			780.2.g.b.131.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.17915 + 0.780776i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(0.780776 + 1.84130i) q^{4} +1.00000i q^{5} +(0.179147 - 2.44293i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(-1.56155 + 2.56155i) q^{9} +(-0.780776 + 1.17915i) q^{10} -4.71659 q^{11} +(2.11862 - 2.74070i) q^{12} -1.00000 q^{13} +(-2.35829 + 3.56155i) q^{14} +(1.51022 - 0.848071i) q^{15} +(-2.78078 + 2.87529i) q^{16} -1.12311i q^{17} +(-3.84130 + 1.80122i) q^{18} -4.71659i q^{19} +(-1.84130 + 0.780776i) q^{20} +(4.56155 - 2.56155i) q^{21} +(-5.56155 - 3.68260i) q^{22} -7.73704 q^{23} +(4.63804 - 1.57752i) q^{24} -1.00000 q^{25} +(-1.17915 - 0.780776i) q^{26} +(5.19283 + 0.185917i) q^{27} +(-5.56155 + 2.35829i) q^{28} +8.00000i q^{29} +(2.44293 + 0.179147i) q^{30} -1.32431i q^{31} +(-5.52390 + 1.21922i) q^{32} +(4.00000 + 7.12311i) q^{33} +(0.876894 - 1.32431i) q^{34} -3.02045 q^{35} +(-5.93581 - 0.875288i) q^{36} +10.0000 q^{37} +(3.68260 - 5.56155i) q^{38} +(0.848071 + 1.51022i) q^{39} +(-2.78078 - 0.516994i) q^{40} +12.2462i q^{41} +(7.37874 + 0.541105i) q^{42} +9.80501i q^{43} +(-3.68260 - 8.68466i) q^{44} +(-2.56155 - 1.56155i) q^{45} +(-9.12311 - 6.04090i) q^{46} +5.66906 q^{47} +(6.70062 + 1.76115i) q^{48} -2.12311 q^{49} +(-1.17915 - 0.780776i) q^{50} +(-1.69614 + 0.952473i) q^{51} +(-0.780776 - 1.84130i) q^{52} -5.12311i q^{53} +(5.97795 + 4.27366i) q^{54} -4.71659i q^{55} +(-8.39919 - 1.56155i) q^{56} +(-7.12311 + 4.00000i) q^{57} +(-6.24621 + 9.43318i) q^{58} +10.7575 q^{59} +(2.74070 + 2.11862i) q^{60} +9.36932 q^{61} +(1.03399 - 1.56155i) q^{62} +(-7.73704 - 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} -1.00000i q^{65} +(-0.844964 + 11.5223i) q^{66} -5.66906i q^{67} +(2.06798 - 0.876894i) q^{68} +(6.56155 + 11.6847i) q^{69} +(-3.56155 - 2.35829i) q^{70} +2.06798 q^{71} +(-6.31579 - 5.66664i) q^{72} -6.00000 q^{73} +(11.7915 + 7.80776i) q^{74} +(0.848071 + 1.51022i) q^{75} +(8.68466 - 3.68260i) q^{76} -14.2462i q^{77} +(-0.179147 + 2.44293i) q^{78} +3.97292i q^{79} +(-2.87529 - 2.78078i) q^{80} +(-4.12311 - 8.00000i) q^{81} +(-9.56155 + 14.4401i) q^{82} -6.41273 q^{83} +(8.27814 + 6.39919i) q^{84} +1.12311 q^{85} +(-7.65552 + 11.5616i) q^{86} +(12.0818 - 6.78456i) q^{87} +(2.43845 - 13.1158i) q^{88} +3.12311i q^{89} +(-1.80122 - 3.84130i) q^{90} -3.02045i q^{91} +(-6.04090 - 14.2462i) q^{92} +(-2.00000 + 1.12311i) q^{93} +(6.68466 + 4.42627i) q^{94} +4.71659 q^{95} +(6.52596 + 7.30834i) q^{96} -16.2462 q^{97} +(-2.50345 - 1.65767i) q^{98} +(7.36520 - 12.0818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 8 q^{6} + 4 q^{9} + 2 q^{10} + 14 q^{12} - 8 q^{13} - 14 q^{16} - 16 q^{18} + 20 q^{21} - 28 q^{22} + 20 q^{24} - 8 q^{25} - 28 q^{28} + 6 q^{30} + 32 q^{33} + 40 q^{34} - 18 q^{36} + 80 q^{37}+ \cdots - 64 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 8 * q^6 + 4 * q^9 + 2 * q^10 + 14 * q^12 - 8 * q^13 - 14 * q^16 - 16 * q^18 + 20 * q^21 - 28 * q^22 + 20 * q^24 - 8 * q^25 - 28 * q^28 + 6 * q^30 + 32 * q^33 + 40 * q^34 - 18 * q^36 + 80 * q^37 - 14 * q^40 + 16 * q^42 - 4 * q^45 - 40 * q^46 + 10 * q^48 + 16 * q^49 + 2 * q^52 + 16 * q^54 - 24 * q^57 + 16 * q^58 - 4 * q^60 - 24 * q^61 - 2 * q^64 - 28 * q^66 + 36 * q^69 - 12 * q^70 - 24 * q^72 - 48 * q^73 + 20 * q^76 + 8 * q^78 - 60 * q^82 + 12 * q^84 - 24 * q^85 + 36 * q^88 + 18 * q^90 - 16 * q^93 + 4 * q^94 - 12 * q^96 - 64 * 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 $

$2$	1.17915	+	0.780776i	0.833783	+	0.552092i
$2$	1.17915	+	0.780776i	0.833783	+	0.552092i
$3$	−0.848071	−	1.51022i	−0.489634	−	0.871928i
$3$	−0.848071	−	1.51022i	−0.489634	−	0.871928i
$4$	0.780776	+	1.84130i	0.390388	+	0.920650i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.179147	−	2.44293i	0.0731366	−	0.997322i
$7$			3.02045i			1.14162i	0.821081	+	0.570811i	$0.193371\pi$
$7$			3.02045i			1.14162i	−0.821081	+	0.570811i	$0.806629\pi$
$8$	−0.516994	+	2.78078i	−0.182785	+	0.983153i
$9$	−1.56155	+	2.56155i	−0.520518	+	0.853851i
$10$	−0.780776	+	1.17915i	−0.246903	+	0.372879i
$11$	−4.71659			−1.42211			−0.711053	−	0.703139i	$-0.751781\pi$
$11$	−4.71659			−1.42211			−0.711053	+	0.703139i	$0.751781\pi$
$12$	2.11862	−	2.74070i	0.611594	−	0.791172i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−2.35829	+	3.56155i	−0.630281	+	0.951865i
$15$	1.51022	−	0.848071i	0.389938	−	0.218971i
$16$	−2.78078	+	2.87529i	−0.695194	+	0.718822i
$17$		−	1.12311i		−	0.272393i	−0.990682	−	0.136197i	$-0.956512\pi$
$17$		−	1.12311i		−	0.272393i	0.990682	−	0.136197i	$-0.0434879\pi$
$18$	−3.84130	+	1.80122i	−0.905403	+	0.424553i
$19$		−	4.71659i		−	1.08206i	−0.841003	−	0.541030i	$-0.818035\pi$
$19$		−	4.71659i		−	1.08206i	0.841003	−	0.541030i	$-0.181965\pi$
$20$	−1.84130	+	0.780776i	−0.411727	+	0.174587i
$21$	4.56155	−	2.56155i	0.995412	−	0.558977i
$22$	−5.56155	−	3.68260i	−1.18573	−	0.785133i
$23$	−7.73704			−1.61328			−0.806642	−	0.591041i	$-0.798717\pi$
$23$	−7.73704			−1.61328			−0.806642	+	0.591041i	$0.798717\pi$
$24$	4.63804	−	1.57752i	0.946736	−	0.322010i
$25$	−1.00000			−0.200000
$26$	−1.17915	−	0.780776i	−0.231250	−	0.153123i
$27$	5.19283	+	0.185917i	0.999360	+	0.0357798i
$28$	−5.56155	+	2.35829i	−1.05103	+	0.445676i
$29$			8.00000i			1.48556i	0.669534	+	0.742781i	$0.266494\pi$
$29$			8.00000i			1.48556i	−0.669534	+	0.742781i	$0.733506\pi$
$30$	2.44293	+	0.179147i	0.446016	+	0.0327077i
$31$		−	1.32431i		−	0.237853i	−0.992903	−	0.118926i	$-0.962055\pi$
$31$		−	1.32431i		−	0.237853i	0.992903	−	0.118926i	$-0.0379452\pi$
$32$	−5.52390	+	1.21922i	−0.976497	+	0.215530i
$33$	4.00000	+	7.12311i	0.696311	+	1.23997i
$34$	0.876894	−	1.32431i	0.150386	−	0.227117i
$35$	−3.02045			−0.510549
$36$	−5.93581	−	0.875288i	−0.989302	−	0.145881i
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$	3.68260	−	5.56155i	0.597397	−	0.902203i
$39$	0.848071	+	1.51022i	0.135800	+	0.241829i
$40$	−2.78078	−	0.516994i	−0.439679	−	0.0817439i
$41$			12.2462i			1.91254i	0.292490	+	0.956268i	$0.405516\pi$
$41$			12.2462i			1.91254i	−0.292490	+	0.956268i	$0.594484\pi$
$42$	7.37874	+	0.541105i	1.13856	+	0.0834943i
$43$			9.80501i			1.49525i	0.664121	+	0.747625i	$0.268806\pi$
$43$			9.80501i			1.49525i	−0.664121	+	0.747625i	$0.731194\pi$
$44$	−3.68260	−	8.68466i	−0.555173	−	1.30926i
$45$	−2.56155	−	1.56155i	−0.381854	−	0.232783i
$46$	−9.12311	−	6.04090i	−1.34513	−	0.890681i
$47$	5.66906			0.826918			0.413459	−	0.910523i	$-0.364321\pi$
$47$	5.66906			0.826918			0.413459	+	0.910523i	$0.364321\pi$
$48$	6.70062	+	1.76115i	0.967152	+	0.254200i
$49$	−2.12311			−0.303301
$50$	−1.17915	−	0.780776i	−0.166757	−	0.110418i
$51$	−1.69614	+	0.952473i	−0.237507	+	0.133373i
$52$	−0.780776	−	1.84130i	−0.108274	−	0.255342i
$53$		−	5.12311i		−	0.703713i	−0.936054	−	0.351856i	$-0.885551\pi$
$53$		−	5.12311i		−	0.703713i	0.936054	−	0.351856i	$-0.114449\pi$
$54$	5.97795	+	4.27366i	0.813495	+	0.581571i
$55$		−	4.71659i		−	0.635985i
$56$	−8.39919	−	1.56155i	−1.12239	−	0.208671i
$57$	−7.12311	+	4.00000i	−0.943478	+	0.529813i
$58$	−6.24621	+	9.43318i	−0.820168	+	1.23864i
$59$	10.7575			1.40051			0.700253	−	0.713895i	$-0.253071\pi$
$59$	10.7575			1.40051			0.700253	+	0.713895i	$0.253071\pi$
$60$	2.74070	+	2.11862i	0.353823	+	0.273513i
$61$	9.36932			1.19962			0.599809	−	0.800143i	$-0.295243\pi$
$61$	9.36932			1.19962			0.599809	+	0.800143i	$0.295243\pi$
$62$	1.03399	−	1.56155i	0.131317	−	0.198317i
$63$	−7.73704	−	4.71659i	−0.974775	−	0.594234i
$64$	−7.46543	−	2.87529i	−0.933179	−	0.359411i
$65$		−	1.00000i		−	0.124035i
$66$	−0.844964	+	11.5223i	−0.104008	+	1.41830i
$67$		−	5.66906i		−	0.692586i	−0.938126	−	0.346293i	$-0.887440\pi$
$67$		−	5.66906i		−	0.692586i	0.938126	−	0.346293i	$-0.112560\pi$
$68$	2.06798	−	0.876894i	0.250779	−	0.106339i
$69$	6.56155	+	11.6847i	0.789918	+	1.40667i
$70$	−3.56155	−	2.35829i	−0.425687	−	0.281870i
$71$	2.06798			0.245423			0.122712	−	0.992442i	$-0.460841\pi$
$71$	2.06798			0.245423			0.122712	+	0.992442i	$0.460841\pi$
$72$	−6.31579	−	5.66664i	−0.744323	−	0.667819i
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	11.7915	+	7.80776i	1.37073	+	0.907634i
$75$	0.848071	+	1.51022i	0.0979267	+	0.174386i
$76$	8.68466	−	3.68260i	0.996199	−	0.422423i
$77$		−	14.2462i		−	1.62351i
$78$	−0.179147	+	2.44293i	−0.0202844	+	0.276607i
$79$			3.97292i			0.446988i	0.974705	+	0.223494i	$0.0717464\pi$
$79$			3.97292i			0.446988i	−0.974705	+	0.223494i	$0.928254\pi$
$80$	−2.87529	−	2.78078i	−0.321467	−	0.310900i
$81$	−4.12311	−	8.00000i	−0.458123	−	0.888889i
$82$	−9.56155	+	14.4401i	−1.05590	+	1.59464i
$83$	−6.41273			−0.703889			−0.351944	−	0.936021i	$-0.614479\pi$
$83$	−6.41273			−0.703889			−0.351944	+	0.936021i	$0.614479\pi$
$84$	8.27814	+	6.39919i	0.903219	+	0.698209i
$85$	1.12311			0.121818
$86$	−7.65552	+	11.5616i	−0.825516	+	1.24671i
$87$	12.0818	−	6.78456i	1.29530	−	0.727382i
$88$	2.43845	−	13.1158i	0.259939	−	1.39815i
$89$			3.12311i			0.331049i	0.986206	+	0.165524i	$0.0529316\pi$
$89$			3.12311i			0.331049i	−0.986206	+	0.165524i	$0.947068\pi$
$90$	−1.80122	−	3.84130i	−0.189866	−	0.404909i
$91$		−	3.02045i		−	0.316629i
$92$	−6.04090	−	14.2462i	−0.629807	−	1.48527i
$93$	−2.00000	+	1.12311i	−0.207390	+	0.116461i
$94$	6.68466	+	4.42627i	0.689470	+	0.456535i
$95$	4.71659			0.483912
$96$	6.52596	+	7.30834i	0.666053	+	0.745904i
$97$	−16.2462			−1.64955			−0.824776	−	0.565459i	$-0.808699\pi$
$97$	−16.2462			−1.64955			−0.824776	+	0.565459i	$0.808699\pi$
$98$	−2.50345	−	1.65767i	−0.252887	−	0.167450i
$99$	7.36520	−	12.0818i	0.740231	−	1.21427i
$100$	−0.780776	−	1.84130i	−0.0780776	−	0.184130i
$101$			4.00000i			0.398015i	0.979998	+	0.199007i	$0.0637718\pi$
$101$			4.00000i			0.398015i	−0.979998	+	0.199007i	$0.936228\pi$
$102$	−2.74367	−	0.201201i	−0.271664	−	0.0199219i
$103$		−	15.1022i		−	1.48807i	−0.668142	−	0.744034i	$-0.732910\pi$
$103$		−	15.1022i		−	1.48807i	0.668142	−	0.744034i	$-0.267090\pi$
$104$	0.516994	−	2.78078i	0.0506954	−	0.272678i
$105$	2.56155	+	4.56155i	0.249982	+	0.445162i
$106$	4.00000	−	6.04090i	0.388514	−	0.586744i
$107$	−1.69614			−0.163972			−0.0819861	−	0.996633i	$-0.526126\pi$
$107$	−1.69614			−0.163972			−0.0819861	+	0.996633i	$0.526126\pi$
$108$	3.71211	+	9.70671i	0.357198	+	0.934029i
$109$	9.36932			0.897418			0.448709	−	0.893678i	$-0.351884\pi$
$109$	9.36932			0.897418			0.448709	+	0.893678i	$0.351884\pi$
$110$	3.68260	−	5.56155i	0.351122	−	0.530273i
$111$	−8.48071	−	15.1022i	−0.804953	−	1.43344i
$112$	−8.68466	−	8.39919i	−0.820623	−	0.793649i
$113$		−	5.12311i		−	0.481941i	−0.970532	−	0.240971i	$-0.922534\pi$
$113$		−	5.12311i		−	0.481941i	0.970532	−	0.240971i	$-0.0774657\pi$
$114$	−11.5223	−	0.844964i	−1.07916	−	0.0791381i
$115$		−	7.73704i		−	0.721482i
$116$	−14.7304	+	6.24621i	−1.36768	+	0.579946i
$117$	1.56155	−	2.56155i	0.144366	−	0.236816i
$118$	12.6847	+	8.39919i	1.16772	+	0.773208i
$119$	3.39228			0.310970
$120$	1.57752	+	4.63804i	0.144007	+	0.423393i
$121$	11.2462			1.02238
$122$	11.0478	+	7.31534i	1.00022	+	0.662300i
$123$	18.4945	−	10.3857i	1.66759	−	0.936443i
$124$	2.43845	−	1.03399i	0.218979	−	0.0928548i
$125$		−	1.00000i		−	0.0894427i
$126$	−5.44050	−	11.6024i	−0.484679	−	1.03363i
$127$			15.1022i			1.34011i	0.742313	+	0.670054i	$0.233729\pi$
$127$			15.1022i			1.34011i	−0.742313	+	0.670054i	$0.766271\pi$
$128$	−6.55789	−	9.21922i	−0.579641	−	0.814872i
$129$	14.8078	−	8.31534i	1.30375	−	0.732125i
$130$	0.780776	−	1.17915i	0.0684786	−	0.103418i
$131$	11.3381			0.990616			0.495308	−	0.868717i	$-0.335055\pi$
$131$	11.3381			0.990616			0.495308	+	0.868717i	$0.335055\pi$
$132$	−9.99267	+	12.9268i	−0.869751	+	1.12513i
$133$	14.2462			1.23530
$134$	4.42627	−	6.68466i	0.382371	−	0.577467i
$135$	−0.185917	+	5.19283i	−0.0160012	+	0.446927i
$136$	3.12311	+	0.580639i	0.267804	+	0.0497894i
$137$			8.24621i			0.704521i	0.935902	+	0.352261i	$0.114587\pi$
$137$			8.24621i			0.704521i	−0.935902	+	0.352261i	$0.885413\pi$
$138$	−1.38607	+	18.9010i	−0.117990	+	1.60896i
$139$			22.8393i			1.93720i	0.248620	+	0.968601i	$0.420023\pi$
$139$			22.8393i			1.93720i	−0.248620	+	0.968601i	$0.579977\pi$
$140$	−2.35829	−	5.56155i	−0.199312	−	0.470037i
$141$	−4.80776	−	8.56155i	−0.404887	−	0.721013i
$142$	2.43845	+	1.61463i	0.204630	+	0.135496i
$143$	4.71659			0.394421
$144$	−3.02287	−	11.6130i	−0.251906	−	0.967752i
$145$	−8.00000			−0.664364
$146$	−7.07488	−	4.68466i	−0.585522	−	0.387705i
$147$	1.80054	+	3.20636i	0.148506	+	0.264457i
$148$	7.80776	+	18.4130i	0.641794	+	1.51354i
$149$		−	10.0000i		−	0.819232i	−0.912258	−	0.409616i	$-0.865663\pi$
$149$		−	10.0000i		−	0.819232i	0.912258	−	0.409616i	$-0.134337\pi$
$150$	−0.179147	+	2.44293i	−0.0146273	+	0.199464i
$151$			5.46026i			0.444349i	0.975007	+	0.222175i	$0.0713155\pi$
$151$			5.46026i			0.444349i	−0.975007	+	0.222175i	$0.928684\pi$
$152$	13.1158	+	2.43845i	1.06383	+	0.197784i
$153$	2.87689	+	1.75379i	0.232583	+	0.141785i
$154$	11.1231	−	16.7984i	0.896325	−	1.35365i
$155$	1.32431			0.106371
$156$	−2.11862	+	2.74070i	−0.169626	+	0.219432i
$157$	8.24621			0.658119			0.329060	−	0.944309i	$-0.393268\pi$
$157$	8.24621			0.658119			0.329060	+	0.944309i	$0.393268\pi$
$158$	−3.10196	+	4.68466i	−0.246779	+	0.372691i
$159$	−7.73704	+	4.34475i	−0.613587	+	0.344561i
$160$	−1.21922	−	5.52390i	−0.0963881	−	0.436703i
$161$		−	23.3693i		−	1.84176i
$162$	1.38446	−	12.6524i	0.108774	−	0.994067i
$163$		−	9.06134i		−	0.709739i	−0.934916	−	0.354870i	$-0.884525\pi$
$163$		−	9.06134i		−	0.709739i	0.934916	−	0.354870i	$-0.115475\pi$
$164$	−22.5490	+	9.56155i	−1.76078	+	0.746632i
$165$	−7.12311	+	4.00000i	−0.554533	+	0.311400i
$166$	−7.56155	−	5.00691i	−0.586890	−	0.388611i
$167$	−11.7100			−0.906144			−0.453072	−	0.891474i	$-0.649672\pi$
$167$	−11.7100			−0.906144			−0.453072	+	0.891474i	$0.649672\pi$
$168$	4.76481	+	14.0090i	0.367613	+	1.08082i
$169$	1.00000			0.0769231
$170$	1.32431	+	0.876894i	0.101570	+	0.0672547i
$171$	12.0818	+	7.36520i	0.923918	+	0.563231i
$172$	−18.0540	+	7.65552i	−1.37660	+	0.583728i
$173$		−	11.3693i		−	0.864393i	−0.901779	−	0.432197i	$-0.857739\pi$
$173$		−	11.3693i		−	0.864393i	0.901779	−	0.432197i	$-0.142261\pi$
$174$	19.5434	+	1.43318i	1.48158	+	0.108649i
$175$		−	3.02045i		−	0.228324i
$176$	13.1158	−	13.5616i	0.988639	−	1.02224i
$177$	−9.12311	−	16.2462i	−0.685735	−	1.22114i
$178$	−2.43845	+	3.68260i	−0.182769	+	0.276023i
$179$	−5.29723			−0.395933			−0.197967	−	0.980209i	$-0.563434\pi$
$179$	−5.29723			−0.395933			−0.197967	+	0.980209i	$0.563434\pi$
$180$	0.875288	−	5.93581i	0.0652401	−	0.442429i
$181$	8.24621			0.612936			0.306468	−	0.951881i	$-0.400853\pi$
$181$	8.24621			0.612936			0.306468	+	0.951881i	$0.400853\pi$
$182$	2.35829	−	3.56155i	0.174808	−	0.264000i
$183$	−7.94584	−	14.1498i	−0.587373	−	1.04598i
$184$	4.00000	−	21.5150i	0.294884	−	1.58610i
$185$			10.0000i			0.735215i
$186$	−3.23519	−	0.237246i	−0.237216	−	0.0173957i
$187$			5.29723i			0.387372i
$188$	4.42627	+	10.4384i	0.322819	+	0.761302i
$189$	−0.561553	+	15.6847i	−0.0408470	+	1.14089i
$190$	5.56155	+	3.68260i	0.403477	+	0.267164i
$191$	−11.3381			−0.820398			−0.410199	−	0.911996i	$-0.634541\pi$
$191$	−11.3381			−0.820398			−0.410199	+	0.911996i	$0.634541\pi$
$192$	1.98889	+	13.7129i	0.143535	+	0.989645i
$193$	2.00000			0.143963			0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000			0.143963			0.0719816	+	0.997406i	$0.477068\pi$
$194$	−19.1567	−	12.6847i	−1.37537	−	0.910705i
$195$	−1.51022	+	0.848071i	−0.108149	+	0.0607316i
$196$	−1.65767	−	3.90928i	−0.118405	−	0.279234i
$197$		−	12.2462i		−	0.872506i	−0.899824	−	0.436253i	$-0.856305\pi$
$197$		−	12.2462i		−	0.872506i	0.899824	−	0.436253i	$-0.143695\pi$
$198$	18.1178	−	8.49563i	1.28758	−	0.603758i
$199$			16.0547i			1.13809i	0.822307	+	0.569044i	$0.192687\pi$
$199$			16.0547i			1.13809i	−0.822307	+	0.569044i	$0.807313\pi$
$200$	0.516994	−	2.78078i	0.0365570	−	0.196631i
$201$	−8.56155	+	4.80776i	−0.603885	+	0.339114i
$202$	−3.12311	+	4.71659i	−0.219741	+	0.331858i
$203$	−24.1636			−1.69595
$204$	−3.07810	−	2.37944i	−0.215510	−	0.166594i
$205$	−12.2462			−0.855312
$206$	11.7915	−	17.8078i	0.821551	−	1.24073i
$207$	12.0818	−	19.8188i	0.839743	−	1.37750i
$208$	2.78078	−	2.87529i	0.192812	−	0.199365i
$209$			22.2462i			1.53880i
$210$	−0.541105	+	7.37874i	−0.0373398	+	0.509182i
$211$			16.7984i			1.15645i	0.815878	+	0.578224i	$0.196254\pi$
$211$			16.7984i			1.15645i	−0.815878	+	0.578224i	$0.803746\pi$
$212$	9.43318	−	4.00000i	0.647873	−	0.274721i
$213$	−1.75379	−	3.12311i	−0.120168	−	0.213992i
$214$	−2.00000	−	1.32431i	−0.136717	−	0.0905278i
$215$	−9.80501			−0.668696
$216$	−3.20165	+	14.3440i	−0.217845	+	0.975983i
$217$	4.00000			0.271538
$218$	11.0478	+	7.31534i	0.748252	+	0.495457i
$219$	5.08842	+	9.06134i	0.343844	+	0.612309i
$220$	8.68466	−	3.68260i	0.585520	−	0.248281i
$221$			1.12311i			0.0755483i
$222$	1.79147	−	24.4293i	0.120236	−	1.63959i
$223$			6.41273i			0.429428i	0.976677	+	0.214714i	$0.0688820\pi$
$223$			6.41273i			0.429428i	−0.976677	+	0.214714i	$0.931118\pi$
$224$	−3.68260	−	16.6847i	−0.246054	−	1.11479i
$225$	1.56155	−	2.56155i	0.104104	−	0.170770i
$226$	4.00000	−	6.04090i	0.266076	−	0.401834i
$227$	−1.11550			−0.0740385			−0.0370192	−	0.999315i	$-0.511786\pi$
$227$	−1.11550			−0.0740385			−0.0370192	+	0.999315i	$0.511786\pi$
$228$	−12.9268	−	9.99267i	−0.856095	−	0.661781i
$229$	−16.2462			−1.07358			−0.536790	−	0.843716i	$-0.680363\pi$
$229$	−16.2462			−1.07358			−0.536790	+	0.843716i	$0.680363\pi$
$230$	6.04090	−	9.12311i	0.398325	−	0.601560i
$231$	−21.5150	+	12.0818i	−1.41558	+	0.794924i
$232$	−22.2462	−	4.13595i	−1.46054	−	0.271538i
$233$		−	9.12311i		−	0.597675i	−0.954304	−	0.298837i	$-0.903401\pi$
$233$		−	9.12311i		−	0.597675i	0.954304	−	0.298837i	$-0.0965988\pi$
$234$	3.84130	−	1.80122i	0.251114	−	0.117750i
$235$			5.66906i			0.369809i
$236$	8.39919	+	19.8078i	0.546741	+	1.28938i
$237$	6.00000	−	3.36932i	0.389742	−	0.218861i
$238$	4.00000	+	2.64861i	0.259281	+	0.171684i
$239$	5.46026			0.353195			0.176597	−	0.984283i	$-0.443491\pi$
$239$	5.46026			0.353195			0.176597	+	0.984283i	$0.443491\pi$
$240$	−1.76115	+	6.70062i	−0.113682	+	0.432523i
$241$	12.8769			0.829474			0.414737	−	0.909941i	$-0.363874\pi$
$241$	12.8769			0.829474			0.414737	+	0.909941i	$0.363874\pi$
$242$	13.2609	+	8.78078i	0.852445	+	0.564450i
$243$	−8.58511	+	13.0114i	−0.550735	+	0.834680i
$244$	7.31534	+	17.2517i	0.468317	+	1.10443i
$245$		−	2.12311i		−	0.135640i
$246$	29.9166	+	2.19387i	1.90741	+	0.139876i
$247$			4.71659i			0.300109i
$248$	3.68260	+	0.684658i	0.233845	+	0.0434759i
$249$	5.43845	+	9.68466i	0.344648	+	0.613740i
$250$	0.780776	−	1.17915i	0.0493806	−	0.0745758i
$251$	−13.9867			−0.882835			−0.441418	−	0.897302i	$-0.645524\pi$
$251$	−13.9867			−0.882835			−0.441418	+	0.897302i	$0.645524\pi$
$252$	2.64376	−	17.9288i	0.166541	−	1.12941i
$253$	36.4924			2.29426
$254$	−11.7915	+	17.8078i	−0.739863	+	1.11736i
$255$	−0.952473	−	1.69614i	−0.0596462	−	0.106216i
$256$	−0.534565	−	15.9911i	−0.0334103	−	0.999442i
$257$			17.1231i			1.06811i	0.845450	+	0.534055i	$0.179332\pi$
$257$			17.1231i			1.06811i	−0.845450	+	0.534055i	$0.820668\pi$
$258$	23.9530	+	1.75654i	1.49125	+	0.109357i
$259$			30.2045i			1.87682i
$260$	1.84130	−	0.780776i	0.114193	−	0.0484217i
$261$	−20.4924	−	12.4924i	−1.26845	−	0.773262i
$262$	13.3693	+	8.85254i	0.825959	+	0.546912i
$263$	19.0752			1.17622			0.588112	−	0.808779i	$-0.299871\pi$
$263$	19.0752			1.17622			0.588112	+	0.808779i	$0.299871\pi$
$264$	−21.8757	+	7.44050i	−1.34636	+	0.457931i
$265$	5.12311			0.314710
$266$	16.7984	+	11.1231i	1.02997	+	0.682001i
$267$	4.71659	−	2.64861i	0.288651	−	0.162093i
$268$	10.4384	−	4.42627i	0.637630	−	0.270377i
$269$		−	10.8769i		−	0.663176i	−0.943424	−	0.331588i	$-0.892416\pi$
$269$		−	10.8769i		−	0.663176i	0.943424	−	0.331588i	$-0.107584\pi$
$270$	−4.27366	+	5.97795i	−0.260087	+	0.363806i
$271$		−	1.32431i		−	0.0804459i	−0.999191	−	0.0402230i	$-0.987193\pi$
$271$		−	1.32431i		−	0.0804459i	0.999191	−	0.0402230i	$-0.0128068\pi$
$272$	3.22925	+	3.12311i	0.195802	+	0.189366i
$273$	−4.56155	+	2.56155i	−0.276078	+	0.155032i
$274$	−6.43845	+	9.72350i	−0.388961	+	0.587418i
$275$	4.71659			0.284421
$276$	−16.3919	+	21.2049i	−0.986674	+	1.27638i
$277$	−18.0000			−1.08152			−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000			−1.08152			−0.540758	+	0.841178i	$0.681862\pi$
$278$	−17.8324	+	26.9309i	−1.06951	+	1.61521i
$279$	3.39228	+	2.06798i	0.203091	+	0.123806i
$280$	1.56155	−	8.39919i	0.0933206	−	0.501948i
$281$			8.24621i			0.491928i	0.969279	+	0.245964i	$0.0791045\pi$
$281$			8.24621i			0.491928i	−0.969279	+	0.245964i	$0.920896\pi$
$282$	1.01560	−	13.8491i	0.0604779	−	0.824703i
$283$			10.5487i			0.627054i	0.949579	+	0.313527i	$0.101511\pi$
$283$			10.5487i			0.627054i	−0.949579	+	0.313527i	$0.898489\pi$
$284$	1.61463	+	3.80776i	0.0958104	+	0.225949i
$285$	−4.00000	−	7.12311i	−0.236940	−	0.421936i
$286$	5.56155	+	3.68260i	0.328862	+	0.217757i
$287$	−36.9890			−2.18339
$288$	5.50276	−	16.0536i	0.324253	−	0.945970i
$289$	15.7386			0.925802
$290$	−9.43318	−	6.24621i	−0.553935	−	0.366790i
$291$	13.7779	+	24.5354i	0.807677	+	1.43829i
$292$	−4.68466	−	11.0478i	−0.274149	−	0.646524i
$293$		−	16.2462i		−	0.949114i	−0.880225	−	0.474557i	$-0.842608\pi$
$293$		−	16.2462i		−	0.949114i	0.880225	−	0.474557i	$-0.157392\pi$
$294$	−0.380349	+	5.18660i	−0.0221824	+	0.302489i
$295$			10.7575i			0.626325i
$296$	−5.16994	+	27.8078i	−0.300497	+	1.61629i
$297$	−24.4924	−	0.876894i	−1.42119	−	0.0508826i
$298$	7.80776	−	11.7915i	0.452292	−	0.683062i
$299$	7.73704			0.447444
$300$	−2.11862	+	2.74070i	−0.122319	+	0.158234i
$301$	−29.6155			−1.70701
$302$	−4.26324	+	6.43845i	−0.245322	+	0.370491i
$303$	6.04090	−	3.39228i	0.347040	−	0.194882i
$304$	13.5616	+	13.1158i	0.777808	+	0.752242i
$305$			9.36932i			0.536486i
$306$	2.02297	+	4.31419i	0.115645	+	0.246626i
$307$		−	9.06134i		−	0.517158i	−0.965990	−	0.258579i	$-0.916746\pi$
$307$		−	9.06134i		−	0.517158i	0.965990	−	0.258579i	$-0.0832543\pi$
$308$	26.2316	−	11.1231i	1.49468	−	0.633798i
$309$	−22.8078	+	12.8078i	−1.29749	+	0.728608i
$310$	1.56155	+	1.03399i	0.0886902	+	0.0587265i
$311$	20.7713			1.17783			0.588916	−	0.808194i	$-0.299555\pi$
$311$	20.7713			1.17783			0.588916	+	0.808194i	$0.299555\pi$
$312$	−4.63804	+	1.57752i	−0.262577	+	0.0893094i
$313$	24.2462			1.37048			0.685238	−	0.728319i	$-0.259698\pi$
$313$	24.2462			1.37048			0.685238	+	0.728319i	$0.259698\pi$
$314$	9.72350	+	6.43845i	0.548729	+	0.363343i
$315$	4.71659	−	7.73704i	0.265750	−	0.435933i
$316$	−7.31534	+	3.10196i	−0.411520	+	0.174499i
$317$			0.246211i			0.0138286i	0.999976	+	0.00691430i	$0.00220091\pi$
$317$			0.246211i			0.0138286i	−0.999976	+	0.00691430i	$0.997799\pi$
$318$	−12.5154	−	0.917790i	−0.701828	−	0.0514671i
$319$		−	37.7327i		−	2.11263i
$320$	2.87529	−	7.46543i	0.160734	−	0.417330i
$321$	1.43845	+	2.56155i	0.0802863	+	0.142972i
$322$	18.2462	−	27.5559i	1.01682	−	1.53563i
$323$	−5.29723			−0.294746
$324$	11.5112	−	13.8381i	0.639510	−	0.768783i
$325$	1.00000			0.0554700
$326$	7.07488	−	10.6847i	0.391842	−	0.591768i
$327$	−7.94584	−	14.1498i	−0.439406	−	0.782484i
$328$	−34.0540	−	6.33122i	−1.88032	−	0.349583i
$329$			17.1231i			0.944027i
$330$	−11.5223	−	0.844964i	−0.634282	−	0.0465137i
$331$		−	18.7033i		−	1.02803i	−0.857782	−	0.514014i	$-0.828158\pi$
$331$		−	18.7033i		−	1.02803i	0.857782	−	0.514014i	$-0.171842\pi$
$332$	−5.00691	−	11.8078i	−0.274790	−	0.648035i
$333$	−15.6155	+	25.6155i	−0.855726	+	1.40372i
$334$	−13.8078	−	9.14286i	−0.755527	−	0.500275i
$335$	5.66906			0.309734
$336$	−5.31946	+	20.2389i	−0.290200	+	1.10412i
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	1.17915	+	0.780776i	0.0641372	+	0.0424686i
$339$	−7.73704	+	4.34475i	−0.420218	+	0.235975i
$340$	0.876894	+	2.06798i	0.0475563	+	0.112152i
$341$			6.24621i			0.338251i
$342$	8.49563	+	18.1178i	0.459391	+	0.979700i
$343$			14.7304i			0.795367i
$344$	−27.2655	−	5.06913i	−1.47006	−	0.273309i
$345$	−11.6847	+	6.56155i	−0.629081	+	0.353262i
$346$	8.87689	−	13.4061i	0.477225	−	0.720716i
$347$	27.3471			1.46807			0.734034	−	0.679113i	$-0.237635\pi$
$347$	27.3471			1.46807			0.734034	+	0.679113i	$0.237635\pi$
$348$	21.9256	+	16.9490i	1.17534	+	0.908561i
$349$	−18.4924			−0.989877			−0.494938	−	0.868928i	$-0.664809\pi$
$349$	−18.4924			−0.989877			−0.494938	+	0.868928i	$0.664809\pi$
$350$	2.35829	−	3.56155i	0.126056	−	0.190373i
$351$	−5.19283	−	0.185917i	−0.277173	−	0.00992352i
$352$	26.0540	−	5.75058i	1.38868	−	0.306507i
$353$		−	14.0000i		−	0.745145i	−0.928003	−	0.372572i	$-0.878476\pi$
$353$		−	14.0000i		−	0.745145i	0.928003	−	0.372572i	$-0.121524\pi$
$354$	1.92717	−	26.2798i	0.102428	−	1.39675i
$355$			2.06798i			0.109757i
$356$	−5.75058	+	2.43845i	−0.304780	+	0.129237i
$357$	−2.87689	−	5.12311i	−0.152261	−	0.271144i
$358$	−6.24621	−	4.13595i	−0.330123	−	0.218592i
$359$	1.32431			0.0698942			0.0349471	−	0.999389i	$-0.488874\pi$
$359$	1.32431			0.0698942			0.0349471	+	0.999389i	$0.488874\pi$
$360$	5.66664	−	6.31579i	0.298658	−	0.332871i
$361$	−3.24621			−0.170853
$362$	9.72350	+	6.43845i	0.511056	+	0.338397i
$363$	−9.53758	−	16.9843i	−0.500593	−	0.891444i
$364$	5.56155	−	2.35829i	0.291505	−	0.123608i
$365$		−	6.00000i		−	0.314054i
$366$	1.67849	−	22.8886i	0.0877359	−	1.19641i
$367$		−	21.8868i		−	1.14248i	−0.820782	−	0.571241i	$-0.806462\pi$
$367$		−	21.8868i		−	1.14248i	0.820782	−	0.571241i	$-0.193538\pi$
$368$	21.5150	−	22.2462i	1.12155	−	1.15966i
$369$	−31.3693	−	19.1231i	−1.63302	−	0.995509i
$370$	−7.80776	+	11.7915i	−0.405906	+	0.613009i
$371$	15.4741			0.803374
$372$	−3.62953	−	2.80571i	−0.188182	−	0.145469i
$373$	−20.7386			−1.07381			−0.536903	−	0.843644i	$-0.680406\pi$
$373$	−20.7386			−1.07381			−0.536903	+	0.843644i	$0.680406\pi$
$374$	−4.13595	+	6.24621i	−0.213865	+	0.322984i
$375$	−1.51022	+	0.848071i	−0.0779876	+	0.0437942i
$376$	−2.93087	+	15.7644i	−0.151148	+	0.812986i
$377$		−	8.00000i		−	0.412021i
$378$	−12.9084	+	18.0561i	−0.663935	+	0.928704i
$379$			2.06798i			0.106225i	0.998589	+	0.0531124i	$0.0169142\pi$
$379$			2.06798i			0.106225i	−0.998589	+	0.0531124i	$0.983086\pi$
$380$	3.68260	+	8.68466i	0.188913	+	0.445514i
$381$	22.8078	−	12.8078i	1.16848	−	0.656162i
$382$	−13.3693	−	8.85254i	−0.684034	−	0.452935i
$383$	6.41273			0.327675			0.163838	−	0.986487i	$-0.447613\pi$
$383$	6.41273			0.327675			0.163838	+	0.986487i	$0.447613\pi$
$384$	−8.36154	+	17.7224i	−0.426698	+	0.904394i
$385$	14.2462			0.726054
$386$	2.35829	+	1.56155i	0.120034	+	0.0794809i
$387$	−25.1161	−	15.3110i	−1.27672	−	0.778304i
$388$	−12.6847	−	29.9142i	−0.643966	−	1.51866i
$389$			11.3693i			0.576447i	0.957563	+	0.288224i	$0.0930646\pi$
$389$			11.3693i			0.576447i	−0.957563	+	0.288224i	$0.906935\pi$
$390$	−2.44293	−	0.179147i	−0.123703	−	0.00907147i
$391$			8.68951i			0.439447i
$392$	1.09763	−	5.90388i	0.0554388	−	0.298191i
$393$	−9.61553	−	17.1231i	−0.485039	−	0.863746i
$394$	9.56155	−	14.4401i	0.481704	−	0.727481i
$395$	−3.97292			−0.199899
$396$	27.9968	+	4.12837i	1.40689	+	0.207459i
$397$	18.0000			0.903394			0.451697	−	0.892171i	$-0.350819\pi$
$397$	18.0000			0.903394			0.451697	+	0.892171i	$0.350819\pi$
$398$	−12.5351	+	18.9309i	−0.628330	+	0.948919i
$399$	−12.0818	−	21.5150i	−0.604846	−	1.07710i
$400$	2.78078	−	2.87529i	0.139039	−	0.143764i
$401$		−	11.6155i		−	0.580052i	−0.957019	−	0.290026i	$-0.906336\pi$
$401$		−	11.6155i		−	0.580052i	0.957019	−	0.290026i	$-0.0936639\pi$
$402$	−13.8491	−	1.01560i	−0.690731	−	0.0506534i
$403$			1.32431i			0.0659684i
$404$	−7.36520	+	3.12311i	−0.366433	+	0.155380i
$405$	8.00000	−	4.12311i	0.397523	−	0.204879i
$406$	−28.4924	−	18.8664i	−1.41406	−	0.936322i
$407$	−47.1659			−2.33793
$408$	−1.77172	−	5.20901i	−0.0877132	−	0.257884i
$409$	−37.3693			−1.84779			−0.923897	−	0.382642i	$-0.875014\pi$
$409$	−37.3693			−1.84779			−0.923897	+	0.382642i	$0.875014\pi$
$410$	−14.4401	−	9.56155i	−0.713145	−	0.472211i
$411$	12.4536	−	6.99337i	0.614292	−	0.344957i
$412$	27.8078	−	11.7915i	1.36999	−	0.580924i
$413$			32.4924i			1.59885i
$414$	29.7203	−	13.9361i	1.46067	−	0.684924i
$415$		−	6.41273i		−	0.314789i
$416$	5.52390	−	1.21922i	0.270832	−	0.0597774i
$417$	34.4924	−	19.3693i	1.68910	−	0.948520i
$418$	−17.3693	+	26.2316i	−0.849561	+	1.28303i
$419$	14.7304			0.719627			0.359814	−	0.933024i	$-0.382840\pi$
$419$	14.7304			0.719627			0.359814	+	0.933024i	$0.382840\pi$
$420$	−6.39919	+	8.27814i	−0.312249	+	0.403932i
$421$	27.6155			1.34590			0.672949	−	0.739689i	$-0.265027\pi$
$421$	27.6155			1.34590			0.672949	+	0.739689i	$0.265027\pi$
$422$	−13.1158	+	19.8078i	−0.638466	+	0.964227i
$423$	−8.85254	+	14.5216i	−0.430425	+	0.706064i
$424$	14.2462	+	2.64861i	0.691857	+	0.128628i
$425$			1.12311i			0.0544786i
$426$	0.370472	−	5.05192i	0.0179494	−	0.244766i
$427$			28.2995i			1.36951i
$428$	−1.32431	−	3.12311i	−0.0640128	−	0.150961i
$429$	−4.00000	−	7.12311i	−0.193122	−	0.343907i
$430$	−11.5616	−	7.65552i	−0.557548	−	0.369182i
$431$	−35.6647			−1.71791			−0.858955	−	0.512051i	$-0.828886\pi$
$431$	−35.6647			−1.71791			−0.858955	+	0.512051i	$0.828886\pi$
$432$	−14.9747	+	14.4139i	−0.720468	+	0.693488i
$433$	−16.7386			−0.804407			−0.402204	−	0.915550i	$-0.631756\pi$
$433$	−16.7386			−0.804407			−0.402204	+	0.915550i	$0.631756\pi$
$434$	4.71659	+	3.12311i	0.226404	+	0.149914i
$435$	6.78456	+	12.0818i	0.325295	+	0.579278i
$436$	7.31534	+	17.2517i	0.350341	+	0.826208i
$437$			36.4924i			1.74567i
$438$	−1.07488	+	14.6576i	−0.0513599	+	0.700366i
$439$			20.1907i			0.963648i	0.876268	+	0.481824i	$0.160026\pi$
$439$			20.1907i			0.963648i	−0.876268	+	0.481824i	$0.839974\pi$
$440$	13.1158	+	2.43845i	0.625270	+	0.116248i
$441$	3.31534	−	5.43845i	0.157873	−	0.258974i
$442$	−0.876894	+	1.32431i	−0.0417096	+	0.0629909i
$443$	3.60109			0.171093			0.0855464	−	0.996334i	$-0.472736\pi$
$443$	3.60109			0.171093			0.0855464	+	0.996334i	$0.472736\pi$
$444$	21.1862	−	27.4070i	1.00545	−	1.30068i
$445$	−3.12311			−0.148049
$446$	−5.00691	+	7.56155i	−0.237084	+	0.358050i
$447$	−15.1022	+	8.48071i	−0.714311	+	0.401124i
$448$	8.68466	−	22.5490i	0.410312	−	1.06534i
$449$			11.7538i			0.554696i	0.960770	+	0.277348i	$0.0894554\pi$
$449$			11.7538i			0.554696i	−0.960770	+	0.277348i	$0.910545\pi$
$450$	3.84130	−	1.80122i	0.181081	−	0.0849105i
$451$		−	57.7603i		−	2.71983i
$452$	9.43318	−	4.00000i	0.443699	−	0.188144i
$453$	8.24621	−	4.63068i	0.387441	−	0.217568i
$454$	−1.31534	−	0.870958i	−0.0617320	−	0.0408761i
$455$	3.02045			0.141601
$456$	−7.44050	−	21.8757i	−0.348434	−	1.02443i
$457$	−34.4924			−1.61349			−0.806744	−	0.590901i	$-0.798772\pi$
$457$	−34.4924			−1.61349			−0.806744	+	0.590901i	$0.798772\pi$
$458$	−19.1567	−	12.6847i	−0.895133	−	0.592715i
$459$	0.208805	−	5.83209i	0.00974616	−	0.272219i
$460$	14.2462	−	6.04090i	0.664233	−	0.281658i
$461$			11.1231i			0.518055i	0.965870	+	0.259027i	$0.0834020\pi$
$461$			11.1231i			0.518055i	−0.965870	+	0.259027i	$0.916598\pi$
$462$	−34.8025	−	2.55217i	−1.61916	−	0.118738i
$463$		−	10.9663i		−	0.509647i	−0.966988	−	0.254823i	$-0.917983\pi$
$463$		−	10.9663i		−	0.509647i	0.966988	−	0.254823i	$-0.0820173\pi$
$464$	−23.0023	−	22.2462i	−1.06786	−	1.03275i
$465$	−1.12311	−	2.00000i	−0.0520828	−	0.0927478i
$466$	7.12311	−	10.7575i	0.329971	−	0.498331i
$467$	33.3880			1.54501			0.772505	−	0.635008i	$-0.219003\pi$
$467$	33.3880			1.54501			0.772505	+	0.635008i	$0.219003\pi$
$468$	5.93581	+	0.875288i	0.274383	+	0.0404602i
$469$	17.1231			0.790672
$470$	−4.42627	+	6.68466i	−0.204169	+	0.308340i
$471$	−6.99337	−	12.4536i	−0.322237	−	0.573833i
$472$	−5.56155	+	29.9142i	−0.255991	+	1.37691i
$473$		−	46.2462i		−	2.12640i
$474$	9.70557	+	0.711738i	0.445791	+	0.0326912i
$475$			4.71659i			0.216412i
$476$	2.64861	+	6.24621i	0.121399	+	0.286295i
$477$	13.1231	+	8.00000i	0.600866	+	0.366295i
$478$	6.43845	+	4.26324i	0.294488	+	0.194996i
$479$	−2.48558			−0.113569			−0.0567846	−	0.998386i	$-0.518085\pi$
$479$	−2.48558			−0.113569			−0.0567846	+	0.998386i	$0.518085\pi$
$480$	−7.30834	+	6.52596i	−0.333579	+	0.297868i
$481$	−10.0000			−0.455961
$482$	15.1838	+	10.0540i	0.691601	+	0.457946i
$483$	−35.2929	+	19.8188i	−1.60588	+	0.901788i
$484$	8.78078	+	20.7077i	0.399126	+	0.941257i
$485$		−	16.2462i		−	0.737702i
$486$	−20.2821	+	8.63928i	−0.920014	+	0.391886i
$487$			18.4945i			0.838067i	0.907971	+	0.419033i	$0.137631\pi$
$487$			18.4945i			0.838067i	−0.907971	+	0.419033i	$0.862369\pi$
$488$	−4.84388	+	26.0540i	−0.219272	+	1.17941i
$489$	−13.6847	+	7.68466i	−0.618842	+	0.347512i
$490$	1.65767	−	2.50345i	0.0748859	−	0.113095i
$491$	27.5559			1.24358			0.621789	−	0.783184i	$-0.286406\pi$
$491$	27.5559			1.24358			0.621789	+	0.783184i	$0.286406\pi$
$492$	33.5632	+	25.9451i	1.51315	+	1.16970i
$493$	8.98485			0.404657
$494$	−3.68260	+	5.56155i	−0.165688	+	0.250226i
$495$	12.0818	+	7.36520i	0.543036	+	0.331041i
$496$	3.80776	+	3.68260i	0.170974	+	0.165354i
$497$			6.24621i			0.280181i
$498$	−1.14882	+	15.6658i	−0.0514800	+	0.702004i
$499$		−	10.0138i		−	0.448280i	−0.974557	−	0.224140i	$-0.928043\pi$
$499$		−	10.0138i		−	0.448280i	0.974557	−	0.224140i	$-0.0719573\pi$
$500$	1.84130	−	0.780776i	0.0823455	−	0.0349174i
$501$	9.93087	+	17.6847i	0.443679	+	0.790092i
$502$	−16.4924	−	10.9205i	−0.736093	−	0.487406i
$503$	−8.48071			−0.378136			−0.189068	−	0.981964i	$-0.560547\pi$
$503$	−8.48071			−0.378136			−0.189068	+	0.981964i	$0.560547\pi$
$504$	17.1158	−	19.0765i	0.762397	−	0.849736i
$505$	−4.00000			−0.177998
$506$	43.0299	+	28.4924i	1.91291	+	1.26664i
$507$	−0.848071	−	1.51022i	−0.0376641	−	0.0670714i
$508$	−27.8078	+	11.7915i	−1.23377	+	0.523162i
$509$			0.876894i			0.0388677i	0.999811	+	0.0194338i	$0.00618637\pi$
$509$			0.876894i			0.0388677i	−0.999811	+	0.0194338i	$0.993814\pi$
$510$	0.201201	−	2.74367i	0.00890934	−	0.121492i
$511$		−	18.1227i		−	0.801700i
$512$	11.8551	−	19.2732i	0.523927	−	0.851763i
$513$	0.876894	−	24.4924i	0.0387158	−	1.08137i
$514$	−13.3693	+	20.1907i	−0.589695	+	0.890572i
$515$	15.1022			0.665484
$516$	26.8726	+	20.7731i	1.18300	+	0.914486i
$517$	−26.7386			−1.17596
$518$	−23.5829	+	35.6155i	−1.03618	+	1.56486i
$519$	−17.1702	+	9.64198i	−0.753689	+	0.423236i
$520$	2.78078	+	0.516994i	0.121945	+	0.0226717i
$521$			24.0000i			1.05146i	0.850652	+	0.525730i	$0.176208\pi$
$521$			24.0000i			1.05146i	−0.850652	+	0.525730i	$0.823792\pi$
$522$	−14.4098	−	30.7304i	−0.630700	−	1.34503i
$523$			16.5896i			0.725412i	0.931904	+	0.362706i	$0.118147\pi$
$523$			16.5896i			0.725412i	−0.931904	+	0.362706i	$0.881853\pi$
$524$	8.85254	+	20.8769i	0.386725	+	0.912011i
$525$	−4.56155	+	2.56155i	−0.199082	+	0.111795i
$526$	22.4924	+	14.8934i	0.980716	+	0.649385i
$527$	−1.48734			−0.0647894
$528$	−31.6041	−	8.30661i	−1.37539	−	0.361499i
$529$	36.8617			1.60268
$530$	6.04090	+	4.00000i	0.262400	+	0.173749i
$531$	−16.7984	+	27.5559i	−0.728988	+	1.19582i
$532$	11.1231	+	26.2316i	0.482248	+	1.13728i
$533$		−	12.2462i		−	0.530442i
$534$	7.62953	+	0.559496i	0.330162	+	0.0242117i
$535$		−	1.69614i		−	0.0733306i
$536$	15.7644	+	2.93087i	0.680918	+	0.126594i
$537$	4.49242	+	8.00000i	0.193862	+	0.345225i
$538$	8.49242	−	12.8255i	0.366134	−	0.552945i
$539$	10.0138			0.431326
$540$	−9.70671	+	3.71211i	−0.417710	+	0.159744i
$541$	−8.24621			−0.354532			−0.177266	−	0.984163i	$-0.556725\pi$
$541$	−8.24621			−0.354532			−0.177266	+	0.984163i	$0.556725\pi$
$542$	1.03399	−	1.56155i	0.0444136	−	0.0670744i
$543$	−6.99337	−	12.4536i	−0.300114	−	0.534436i
$544$	1.36932	+	6.20393i	0.0587090	+	0.265991i
$545$			9.36932i			0.401337i
$546$	−7.37874	−	0.541105i	−0.315781	−	0.0231572i
$547$			30.5763i			1.30735i	0.756776	+	0.653674i	$0.226773\pi$
$547$			30.5763i			1.30735i	−0.756776	+	0.653674i	$0.773227\pi$
$548$	−15.1838	+	6.43845i	−0.648618	+	0.275037i
$549$	−14.6307	+	24.0000i	−0.624422	+	1.02430i
$550$	5.56155	+	3.68260i	0.237145	+	0.157027i
$551$	37.7327			1.60747
$552$	−35.8847	+	12.2053i	−1.52735	+	0.519493i
$553$	−12.0000			−0.510292
$554$	−21.2247	−	14.0540i	−0.901749	−	0.597096i
$555$	15.1022	−	8.48071i	0.641054	−	0.359986i
$556$	−42.0540	+	17.8324i	−1.78349	+	0.756261i
$557$		−	11.7538i		−	0.498024i	−0.968500	−	0.249012i	$-0.919894\pi$
$557$		−	11.7538i		−	0.498024i	0.968500	−	0.249012i	$-0.0801059\pi$
$558$	2.38537	+	5.08706i	0.100981	+	0.215352i
$559$		−	9.80501i		−	0.414708i
$560$	8.39919	−	8.68466i	0.354931	−	0.366994i
$561$	8.00000	−	4.49242i	0.337760	−	0.189670i
$562$	−6.43845	+	9.72350i	−0.271590	+	0.410161i
$563$	21.7238			0.915548			0.457774	−	0.889069i	$-0.348647\pi$
$563$	21.7238			0.915548			0.457774	+	0.889069i	$0.348647\pi$
$564$	12.0106	−	15.5372i	0.505738	−	0.654234i
$565$	5.12311			0.215531
$566$	−8.23616	+	12.4384i	−0.346192	+	0.522827i
$567$	24.1636	−	12.4536i	1.01478	−	0.523003i
$568$	−1.06913	+	5.75058i	−0.0448597	+	0.241289i
$569$		−	12.6307i		−	0.529506i	−0.964316	−	0.264753i	$-0.914710\pi$
$569$		−	12.6307i		−	0.529506i	0.964316	−	0.264753i	$-0.0852904\pi$
$570$	0.844964	−	11.5223i	0.0353916	−	0.482616i
$571$			12.9885i			0.543551i	0.962361	+	0.271776i	$0.0876109\pi$
$571$			12.9885i			0.543551i	−0.962361	+	0.271776i	$0.912389\pi$
$572$	3.68260	+	8.68466i	0.153977	+	0.363124i
$573$	9.61553	+	17.1231i	0.401694	+	0.715328i
$574$	−43.6155	−	28.8802i	−1.82048	−	1.20544i
$575$	7.73704			0.322657
$576$	19.0229	−	14.6332i	0.792620	−	0.609716i
$577$	−3.75379			−0.156272			−0.0781361	−	0.996943i	$-0.524897\pi$
$577$	−3.75379			−0.156272			−0.0781361	+	0.996943i	$0.524897\pi$
$578$	18.5582	+	12.2884i	0.771918	+	0.511128i
$579$	−1.69614	−	3.02045i	−0.0704892	−	0.125526i
$580$	−6.24621	−	14.7304i	−0.259360	−	0.611647i
$581$		−	19.3693i		−	0.803575i
$582$	−2.91046	+	39.6884i	−0.120643	+	1.64514i
$583$			24.1636i			1.00075i
$584$	3.10196	−	16.6847i	0.128360	−	0.690416i
$585$	2.56155	+	1.56155i	0.105907	+	0.0645623i
$586$	12.6847	−	19.1567i	0.523998	−	0.791355i
$587$	17.7509			0.732656			0.366328	−	0.930486i	$-0.380615\pi$
$587$	17.7509			0.732656			0.366328	+	0.930486i	$0.380615\pi$
$588$	−4.49806	+	5.81880i	−0.185497	+	0.239963i
$589$	−6.24621			−0.257371
$590$	−8.39919	+	12.6847i	−0.345789	+	0.522219i
$591$	−18.4945	+	10.3857i	−0.760763	+	0.427209i
$592$	−27.8078	+	28.7529i	−1.14289	+	1.18174i
$593$		−	34.9848i		−	1.43666i	−0.695705	−	0.718328i	$-0.744908\pi$
$593$		−	34.9848i		−	1.43666i	0.695705	−	0.718328i	$-0.255092\pi$
$594$	−28.1955	−	20.1571i	−1.15688	−	0.827056i
$595$			3.39228i			0.139070i
$596$	18.4130	−	7.80776i	0.754226	−	0.319818i
$597$	24.2462	−	13.6155i	0.992331	−	0.557246i
$598$	9.12311	+	6.04090i	0.373072	+	0.247031i
$599$	33.5968			1.37273			0.686363	−	0.727259i	$-0.259206\pi$
$599$	33.5968			1.37273			0.686363	+	0.727259i	$0.259206\pi$
$600$	−4.63804	+	1.57752i	−0.189347	+	0.0644019i
$601$	25.8617			1.05492			0.527461	−	0.849579i	$-0.323144\pi$
$601$	25.8617			1.05492			0.527461	+	0.849579i	$0.323144\pi$
$602$	−34.9211	−	23.1231i	−1.42328	−	0.942427i
$603$	14.5216	+	8.85254i	0.591365	+	0.360503i
$604$	−10.0540	+	4.26324i	−0.409090	+	0.173469i
$605$			11.2462i			0.457224i
$606$	9.77172	+	0.716589i	0.396949	+	0.0291094i
$607$			28.3453i			1.15050i	0.817977	+	0.575250i	$0.195095\pi$
$607$			28.3453i			1.15050i	−0.817977	+	0.575250i	$0.804905\pi$
$608$	5.75058	+	26.0540i	0.233217	+	1.05663i
$609$	20.4924	+	36.4924i	0.830395	+	1.47875i
$610$	−7.31534	+	11.0478i	−0.296190	+	0.447313i
$611$	−5.66906			−0.229346
$612$	−0.983041	+	6.66654i	−0.0397371	+	0.269479i
$613$	−2.49242			−0.100668			−0.0503340	−	0.998732i	$-0.516029\pi$
$613$	−2.49242			−0.100668			−0.0503340	+	0.998732i	$0.516029\pi$
$614$	7.07488	−	10.6847i	0.285519	−	0.431198i
$615$	10.3857	+	18.4945i	0.418790	+	0.745771i
$616$	39.6155	+	7.36520i	1.59616	+	0.296752i
$617$		−	8.24621i		−	0.331980i	−0.986127	−	0.165990i	$-0.946918\pi$
$617$		−	8.24621i		−	0.331980i	0.986127	−	0.165990i	$-0.0530819\pi$
$618$	−36.8937	−	2.70552i	−1.48408	−	0.108832i
$619$			45.0979i			1.81264i	0.422594	+	0.906319i	$0.361120\pi$
$619$			45.0979i			1.81264i	−0.422594	+	0.906319i	$0.638880\pi$
$620$	1.03399	+	2.43845i	0.0415259	+	0.0979304i
$621$	−40.1771	−	1.43845i	−1.61225	−	0.0577229i
$622$	24.4924	+	16.2177i	0.982057	+	0.650272i
$623$	−9.43318			−0.377932
$624$	−6.70062	−	1.76115i	−0.268240	−	0.0705023i
$625$	1.00000			0.0400000
$626$	28.5899	+	18.9309i	1.14268	+	0.756630i
$627$	33.5968	−	18.8664i	1.34173	−	0.753450i
$628$	6.43845	+	15.1838i	0.256922	+	0.605898i
$629$		−	11.2311i		−	0.447812i
$630$	11.6024	−	5.44050i	0.462253	−	0.216755i
$631$		−	26.9752i		−	1.07387i	−0.843625	−	0.536933i	$-0.819583\pi$
$631$		−	26.9752i		−	1.07387i	0.843625	−	0.536933i	$-0.180417\pi$
$632$	−11.0478	−	2.05398i	−0.439458	−	0.0817028i
$633$	25.3693	−	14.2462i	1.00834	−	0.566236i
$634$	−0.192236	+	0.290319i	−0.00763466	+	0.0115301i
$635$	−15.1022			−0.599314
$636$	−14.0409	−	10.8539i	−0.556758	−	0.430386i
$637$	2.12311			0.0841205
$638$	29.4608	−	44.4924i	1.16636	−	1.76147i
$639$	−3.22925	+	5.29723i	−0.127747	+	0.209555i
$640$	9.21922	−	6.55789i	0.364422	−	0.259223i
$641$		−	19.3693i		−	0.765042i	−0.923947	−	0.382521i	$-0.875056\pi$
$641$		−	19.3693i		−	0.765042i	0.923947	−	0.382521i	$-0.124944\pi$
$642$	−0.303859	+	4.14355i	−0.0119924	+	0.163533i
$643$		−	13.9410i		−	0.549778i	−0.961476	−	0.274889i	$-0.911359\pi$
$643$		−	13.9410i		−	0.549778i	0.961476	−	0.274889i	$-0.0886411\pi$
$644$	43.0299	−	18.2462i	1.69562	−	0.719001i
$645$	8.31534	+	14.8078i	0.327416	+	0.583055i
$646$	−6.24621	−	4.13595i	−0.245754	−	0.162727i
$647$	−28.5083			−1.12078			−0.560389	−	0.828229i	$-0.689348\pi$
$647$	−28.5083			−1.12078			−0.560389	+	0.828229i	$0.689348\pi$
$648$	24.3778	−	7.32948i	0.957652	−	0.287929i
$649$	−50.7386			−1.99167
$650$	1.17915	+	0.780776i	0.0462500	+	0.0306246i
$651$	−3.39228	−	6.04090i	−0.132954	−	0.236761i
$652$	16.6847	−	7.07488i	0.653422	−	0.277074i
$653$			1.61553i			0.0632205i	0.999500	+	0.0316103i	$0.0100635\pi$
$653$			1.61553i			0.0632205i	−0.999500	+	0.0316103i	$0.989936\pi$
$654$	1.67849	−	22.8886i	0.0656340	−	0.895014i
$655$			11.3381i			0.443017i
$656$	−35.2114	−	34.0540i	−1.37477	−	1.32958i
$657$	9.36932	−	15.3693i	0.365532	−	0.599614i
$658$	−13.3693	+	20.1907i	−0.521190	+	0.787114i
$659$	−9.43318			−0.367464			−0.183732	−	0.982976i	$-0.558818\pi$
$659$	−9.43318			−0.367464			−0.183732	+	0.982976i	$0.558818\pi$
$660$	−12.9268	−	9.99267i	−0.503173	−	0.388964i
$661$	−45.3693			−1.76466			−0.882331	−	0.470629i	$-0.844027\pi$
$661$	−45.3693			−1.76466			−0.882331	+	0.470629i	$0.844027\pi$
$662$	14.6031	−	22.0540i	0.567566	−	0.857152i
$663$	1.69614	−	0.952473i	0.0658727	−	0.0369910i
$664$	3.31534	−	17.8324i	0.128660	−	0.692030i
$665$			14.2462i			0.552444i
$666$	−38.4130	+	18.0122i	−1.48847	+	0.697960i
$667$		−	61.8963i		−	2.39663i
$668$	−9.14286	−	21.5616i	−0.353748	−	0.834242i
$669$	9.68466	−	5.43845i	0.374431	−	0.210263i
$670$	6.68466	+	4.42627i	0.258251	+	0.171002i
$671$	−44.1912			−1.70598
$672$	−22.0745	+	19.7113i	−0.851541	+	0.760381i
$673$	−24.2462			−0.934623			−0.467311	−	0.884093i	$-0.654777\pi$
$673$	−24.2462			−0.934623			−0.467311	+	0.884093i	$0.654777\pi$
$674$	−21.2247	−	14.0540i	−0.817543	−	0.541339i
$675$	−5.19283	−	0.185917i	−0.199872	−	0.00715595i
$676$	0.780776	+	1.84130i	0.0300299	+	0.0708193i
$677$			46.1080i			1.77207i	0.463616	+	0.886036i	$0.346552\pi$
$677$			46.1080i			1.77207i	−0.463616	+	0.886036i	$0.653448\pi$
$678$	−12.5154	−	0.917790i	−0.480651	−	0.0352475i
$679$		−	49.0708i		−	1.88317i
$680$	−0.580639	+	3.12311i	−0.0222665	+	0.119766i
$681$	0.946025	+	1.68466i	0.0362517	+	0.0645563i
$682$	−4.87689	+	7.36520i	−0.186746	+	0.282028i
$683$	4.92539			0.188465			0.0942325	−	0.995550i	$-0.469960\pi$
$683$	4.92539			0.188465			0.0942325	+	0.995550i	$0.469960\pi$
$684$	−4.12837	+	27.9968i	−0.157852	+	1.07048i
$685$	−8.24621			−0.315072
$686$	−11.5012	+	17.3693i	−0.439116	+	0.663164i
$687$	13.7779	+	24.5354i	0.525661	+	0.936085i
$688$	−28.1922	−	27.2655i	−1.07482	−	1.03949i
$689$			5.12311i			0.195175i
$690$	−18.9010	−	1.38607i	−0.719550	−	0.0527667i
$691$			0.163030i			0.00620194i	0.999995	+	0.00310097i	$0.000987071\pi$
$691$			0.163030i			0.00620194i	−0.999995	+	0.00310097i	$0.999013\pi$
$692$	20.9343	−	8.87689i	0.795804	−	0.337449i
$693$	36.4924	+	22.2462i	1.38623	+	0.845064i
$694$	32.2462	+	21.3519i	1.22405	+	0.810509i
$695$	−22.8393			−0.866343
$696$	12.6201	+	37.1043i	0.478365	+	1.40644i
$697$	13.7538			0.520962
$698$	−21.8053	−	14.4384i	−0.825342	−	0.546503i
$699$	−13.7779	+	7.73704i	−0.521129	+	0.292642i
$700$	5.56155	−	2.35829i	0.210207	−	0.0891352i
$701$		−	21.6155i		−	0.816407i	−0.912891	−	0.408204i	$-0.866155\pi$
$701$		−	21.6155i		−	0.816407i	0.912891	−	0.408204i	$-0.133845\pi$
$702$	−5.97795	−	4.27366i	−0.225623	−	0.161299i
$703$		−	47.1659i		−	1.77890i
$704$	35.2114	+	13.5616i	1.32708	+	0.511120i
$705$	8.56155	−	4.80776i	0.322447	−	0.181071i
$706$	10.9309	−	16.5081i	0.411389	−	0.621289i
$707$	−12.0818			−0.454383
$708$	22.7911	−	29.4830i	0.856540	−	1.10804i
$709$	26.0000			0.976450			0.488225	−	0.872718i	$-0.337644\pi$
$709$	26.0000			0.976450			0.488225	+	0.872718i	$0.337644\pi$
$710$	−1.61463	+	2.43845i	−0.0605958	+	0.0915133i
$711$	−10.1768	−	6.20393i	−0.381662	−	0.232665i
$712$	−8.68466	−	1.61463i	−0.325471	−	0.0605107i
$713$			10.2462i			0.383724i
$714$	0.607718	−	8.28711i	0.0227433	−	0.310137i
$715$			4.71659i			0.176390i
$716$	−4.13595	−	9.75379i	−0.154568	−	0.364516i
$717$	−4.63068	−	8.24621i	−0.172936	−	0.307960i
$718$	1.56155	+	1.03399i	0.0582766	+	0.0385881i
$719$	18.8664			0.703596			0.351798	−	0.936076i	$-0.385570\pi$
$719$	18.8664			0.703596			0.351798	+	0.936076i	$0.385570\pi$
$720$	11.6130	−	3.02287i	0.432792	−	0.112656i
$721$	45.6155			1.69881
$722$	−3.82776	−	2.53457i	−0.142455	−	0.0943267i
$723$	−10.9205	−	19.4470i	−0.406138	−	0.723242i
$724$	6.43845	+	15.1838i	0.239283	+	0.564300i
$725$		−	8.00000i		−	0.297113i
$726$	2.01473	−	27.4737i	0.0747736	−	1.01964i
$727$			9.80501i			0.363648i	0.983331	+	0.181824i	$0.0582001\pi$
$727$			9.80501i			0.363648i	−0.983331	+	0.181824i	$0.941800\pi$
$728$	8.39919	+	1.56155i	0.311295	+	0.0578750i
$729$	26.9309	+	1.93087i	0.997440	+	0.0715137i
$730$	4.68466	−	7.07488i	0.173387	−	0.261853i
$731$	11.0121			0.407296
$732$	19.8500	−	25.6785i	0.733679	−	0.949104i
$733$	15.7538			0.581879			0.290940	−	0.956741i	$-0.406032\pi$
$733$	15.7538			0.581879			0.290940	+	0.956741i	$0.406032\pi$
$734$	17.0887	−	25.8078i	0.630755	−	0.952582i
$735$	−3.20636	+	1.80054i	−0.118269	+	0.0664140i
$736$	42.7386	−	9.43318i	1.57537	−	0.347712i
$737$			26.7386i			0.984930i
$738$	−22.0582	−	47.0414i	−0.811973	−	1.73162i
$739$		−	0.906698i		−	0.0333534i	−0.999861	−	0.0166767i	$-0.994691\pi$
$739$		−	0.906698i		−	0.0333534i	0.999861	−	0.0166767i	$-0.00530861\pi$
$740$	−18.4130	+	7.80776i	−0.676876	+	0.287019i
$741$	7.12311	−	4.00000i	0.261674	−	0.146944i
$742$	18.2462	+	12.0818i	0.669839	+	0.443537i
$743$	1.11550			0.0409238			0.0204619	−	0.999791i	$-0.493486\pi$
$743$	1.11550			0.0409238			0.0204619	+	0.999791i	$0.493486\pi$
$744$	−2.08912	−	6.14219i	−0.0765908	−	0.225184i
$745$	10.0000			0.366372
$746$	−24.4539	−	16.1922i	−0.895321	−	0.592840i
$747$	10.0138	−	16.4265i	0.366386	−	0.601016i
$748$	−9.75379	+	4.13595i	−0.356634	+	0.151225i
$749$		−	5.12311i		−	0.187194i
$750$	−2.44293	−	0.179147i	−0.0892032	−	0.00654153i
$751$		−	31.5288i		−	1.15050i	−0.817977	−	0.575251i	$-0.804904\pi$
$751$		−	31.5288i		−	1.15050i	0.817977	−	0.575251i	$-0.195096\pi$
$752$	−15.7644	+	16.3002i	−0.574868	+	0.594407i
$753$	11.8617	+	21.1231i	0.432266	+	0.769769i
$754$	6.24621	−	9.43318i	0.227474	−	0.343536i
$755$	−5.46026			−0.198719
$756$	−29.3186	+	11.2122i	−1.06631	+	0.407785i
$757$	36.2462			1.31739			0.658695	−	0.752410i	$-0.271109\pi$
$757$	36.2462			1.31739			0.658695	+	0.752410i	$0.271109\pi$
$758$	−1.61463	+	2.43845i	−0.0586459	+	0.0885684i
$759$	−30.9481	−	55.1117i	−1.12335	−	2.00043i
$760$	−2.43845	+	13.1158i	−0.0884518	+	0.475759i
$761$			24.8769i			0.901787i	0.892578	+	0.450893i	$0.148895\pi$
$761$			24.8769i			0.901787i	−0.892578	+	0.450893i	$0.851105\pi$
$762$	36.8937	+	2.70552i	1.33652	+	0.0980108i
$763$			28.2995i			1.02451i
$764$	−8.85254	−	20.8769i	−0.320274	−	0.755300i
$765$	−1.75379	+	2.87689i	−0.0634084	+	0.104014i
$766$	7.56155	+	5.00691i	0.273210	+	0.180907i
$767$	−10.7575			−0.388430
$768$	−23.6967	+	14.3689i	−0.855083	+	0.518492i
$769$	28.2462			1.01858			0.509292	−	0.860594i	$-0.329907\pi$
$769$	28.2462			1.01858			0.509292	+	0.860594i	$0.329907\pi$
$770$	16.7984	+	11.1231i	0.605372	+	0.400849i
$771$	25.8597	−	14.5216i	0.931315	−	0.522983i
$772$	1.56155	+	3.68260i	0.0562015	+	0.132540i
$773$		−	2.00000i		−	0.0719350i	−0.999353	−	0.0359675i	$-0.988549\pi$
$773$		−	2.00000i		−	0.0719350i	0.999353	−	0.0359675i	$-0.0114513\pi$
$774$	−17.6610	−	37.6640i	−0.634812	−	1.35380i
$775$			1.32431i			0.0475705i
$776$	8.39919	−	45.1771i	0.301513	−	1.62176i
$777$	45.6155	−	25.6155i	1.63645	−	0.918952i
$778$	−8.87689	+	13.4061i	−0.318252	+	0.480632i
$779$	57.7603			2.06948
$780$	−2.74070	−	2.11862i	−0.0981328	−	0.0758589i
$781$	−9.75379			−0.349018
$782$	−6.78456	+	10.2462i	−0.242616	+	0.366404i
$783$	−1.48734	+	41.5426i	−0.0531531	+	1.48461i
$784$	5.90388	−	6.10454i	0.210853	−	0.218019i
$785$			8.24621i			0.294320i
$786$	2.03119	−	27.6982i	0.0724503	−	0.987964i
$787$			3.02045i			0.107667i	0.998550	+	0.0538337i	$0.0171441\pi$
$787$			3.02045i			0.107667i	−0.998550	+	0.0538337i	$0.982856\pi$
$788$	22.5490	−	9.56155i	0.803273	−	0.340616i
$789$	−16.1771	−	28.8078i	−0.575919	−	1.02558i
$790$	−4.68466	−	3.10196i	−0.166673	−	0.110363i
$791$	15.4741			0.550195
$792$	29.7890	+	26.7272i	1.05851	+	0.949709i
$793$	−9.36932			−0.332714
$794$	21.2247	+	14.0540i	0.753235	+	0.498757i
$795$	−4.34475	−	7.73704i	−0.154093	−	0.274404i
$796$	−29.5616	+	12.5351i	−1.04778	+	0.444296i
$797$			7.86174i			0.278477i	0.990259	+	0.139239i	$0.0444655\pi$
$797$			7.86174i			0.278477i	−0.990259	+	0.139239i	$0.955535\pi$
$798$	2.55217	−	34.8025i	0.0903458	−	1.23199i
$799$		−	6.36696i		−	0.225247i
$800$	5.52390	−	1.21922i	0.195299	−	0.0431061i
$801$	−8.00000	−	4.87689i	−0.282666	−	0.172317i
$802$	9.06913	−	13.6964i	0.320242	−	0.483637i
$803$	28.2995			0.998669
$804$	−15.5372	−	12.0106i	−0.547955	−	0.423581i
$805$	23.3693			0.823660
$806$	−1.03399	+	1.56155i	−0.0364207	+	0.0550034i
$807$	−16.4265	+	9.22437i	−0.578242	+	0.324713i
$808$	−11.1231	−	2.06798i	−0.391309	−	0.0727511i
$809$			29.7538i			1.04609i	0.852306	+	0.523044i	$0.175204\pi$
$809$			29.7538i			1.04609i	−0.852306	+	0.523044i	$0.824796\pi$
$810$	12.6524	+	1.38446i	0.444560	+	0.0486451i
$811$			9.27015i			0.325519i	0.986666	+	0.162759i	$0.0520395\pi$
$811$			9.27015i			0.325519i	−0.986666	+	0.162759i	$0.947961\pi$
$812$	−18.8664	−	44.4924i	−0.662079	−	1.56138i
$813$	−2.00000	+	1.12311i	−0.0701431	+	0.0393890i
$814$	−55.6155	−	36.8260i	−1.94932	−	1.29075i
$815$	9.06134			0.317405
$816$	1.97796	−	7.52551i	0.0692423	−	0.263445i
$817$	46.2462			1.61795
$818$	−44.0639	−	29.1771i	−1.54066	−	1.02015i
$819$	7.73704	+	4.71659i	0.270354	+	0.164811i
$820$	−9.56155	−	22.5490i	−0.333904	−	0.787444i
$821$		−	31.7538i		−	1.10821i	−0.832445	−	0.554107i	$-0.813060\pi$
$821$		−	31.7538i		−	1.10821i	0.832445	−	0.554107i	$-0.186940\pi$
$822$	20.1449	+	1.47729i	0.702635	+	0.0515263i
$823$		−	21.8868i		−	0.762926i	−0.924384	−	0.381463i	$-0.875420\pi$
$823$		−	21.8868i		−	0.762926i	0.924384	−	0.381463i	$-0.124580\pi$
$824$	41.9960	+	7.80776i	1.46300	+	0.271996i
$825$	−4.00000	−	7.12311i	−0.139262	−	0.247995i
$826$	−25.3693	+	38.3134i	−0.882711	+	1.33309i
$827$	−10.9663			−0.381335			−0.190668	−	0.981655i	$-0.561065\pi$
$827$	−10.9663			−0.381335			−0.190668	+	0.981655i	$0.561065\pi$
$828$	45.9256	+	6.77214i	1.59602	+	0.235348i
$829$	−25.8617			−0.898215			−0.449108	−	0.893478i	$-0.648258\pi$
$829$	−25.8617			−0.898215			−0.449108	+	0.893478i	$0.648258\pi$
$830$	5.00691	−	7.56155i	0.173792	−	0.262465i
$831$	15.2653	+	27.1840i	0.529546	+	0.943004i
$832$	7.46543	+	2.87529i	0.258817	+	0.0996827i
$833$			2.38447i			0.0826171i
$834$	55.7948	+	4.09159i	1.93201	+	0.141680i
$835$		−	11.7100i		−	0.405240i
$836$	−40.9620	+	17.3693i	−1.41670	+	0.600730i
$837$	0.246211	−	6.87689i	0.00851031	−	0.237700i
$838$	17.3693	+	11.5012i	0.600013	+	0.397301i
$839$	54.9487			1.89704			0.948520	−	0.316717i	$-0.102581\pi$
$839$	54.9487			1.89704			0.948520	+	0.316717i	$0.102581\pi$
$840$	−14.0090	+	4.76481i	−0.483355	+	0.164402i
$841$	−35.0000			−1.20690
$842$	32.5628	+	21.5616i	1.12219	+	0.743060i
$843$	12.4536	−	6.99337i	0.428926	−	0.240864i
$844$	−30.9309	+	13.1158i	−1.06468	+	0.451464i
$845$			1.00000i			0.0344010i
$846$	−21.7766	+	10.2113i	−0.748694	+	0.351070i
$847$			33.9686i			1.16717i
$848$	14.7304	+	14.2462i	0.505844	+	0.489217i
$849$	15.9309	−	8.94602i	0.546746	−	0.307027i
$850$	−0.876894	+	1.32431i	−0.0300772	+	0.0454234i
$851$	−77.3704			−2.65222
$852$	4.38126	−	5.66770i	0.150099	−	0.194172i
$853$	0.738634			0.0252903			0.0126452	−	0.999920i	$-0.495975\pi$
$853$	0.738634			0.0252903			0.0126452	+	0.999920i	$0.495975\pi$
$854$	−22.0956	+	33.3693i	−0.756096	+	1.14187i
$855$	−7.36520	+	12.0818i	−0.251885	+	0.413189i
$856$	0.876894	−	4.71659i	0.0299716	−	0.161210i
$857$		−	29.6155i		−	1.01165i	−0.862637	−	0.505824i	$-0.831189\pi$
$857$		−	29.6155i		−	1.01165i	0.862637	−	0.505824i	$-0.168811\pi$
$858$	0.844964	−	11.5223i	0.0288466	−	0.393365i
$859$		−	17.5420i		−	0.598527i	−0.954171	−	0.299263i	$-0.903259\pi$
$859$		−	17.5420i		−	0.598527i	0.954171	−	0.299263i	$-0.0967410\pi$
$860$	−7.65552	−	18.0540i	−0.261051	−	0.615635i
$861$	31.3693	+	55.8617i	1.06906	+	1.90376i
$862$	−42.0540	−	27.8462i	−1.43236	−	0.948445i
$863$	−24.5354			−0.835195			−0.417598	−	0.908632i	$-0.637128\pi$
$863$	−24.5354			−0.835195			−0.417598	+	0.908632i	$0.637128\pi$
$864$	−28.9113	+	5.30423i	−0.983584	+	0.180453i
$865$	11.3693			0.386568
$866$	−19.7373	−	13.0691i	−0.670701	−	0.444107i
$867$	−13.3475	−	23.7689i	−0.453304	−	0.807233i
$868$	3.12311	+	7.36520i	0.106005	+	0.249991i
$869$		−	18.7386i		−	0.635665i
$870$	−1.43318	+	19.5434i	−0.0485893	+	0.662585i
$871$			5.66906i			0.192089i
$872$	−4.84388	+	26.0540i	−0.164034	+	0.882299i
$873$	25.3693	−	41.6155i	0.858621	−	1.40847i
$874$	−28.4924	+	43.0299i	−0.963771	+	1.45551i
$875$	3.02045			0.102110
$876$	−12.7117	+	16.4442i	−0.429490	+	0.555598i
$877$	18.0000			0.607817			0.303908	−	0.952701i	$-0.401708\pi$
$877$	18.0000			0.607817			0.303908	+	0.952701i	$0.401708\pi$
$878$	−15.7644	+	23.8078i	−0.532022	+	0.803473i
$879$	−24.5354	+	13.7779i	−0.827559	+	0.464718i
$880$	13.5616	+	13.1158i	0.457160	+	0.442133i
$881$		−	3.36932i		−	0.113515i	−0.998388	−	0.0567576i	$-0.981924\pi$
$881$		−	3.36932i		−	0.113515i	0.998388	−	0.0567576i	$-0.0180762\pi$
$882$	8.15549	−	3.82419i	0.274610	−	0.128767i
$883$			19.6558i			0.661470i	0.943724	+	0.330735i	$0.107297\pi$
$883$			19.6558i			0.661470i	−0.943724	+	0.330735i	$0.892703\pi$
$884$	−2.06798	+	0.876894i	−0.0695535	+	0.0294931i
$885$	16.2462	−	9.12311i	0.546110	−	0.306670i
$886$	4.24621	+	2.81164i	0.142654	+	0.0944590i
$887$	−27.3471			−0.918224			−0.459112	−	0.888378i	$-0.651832\pi$
$887$	−27.3471			−0.918224			−0.459112	+	0.888378i	$0.651832\pi$
$888$	46.3804	−	15.7752i	1.55643	−	0.529380i
$889$	−45.6155			−1.52990
$890$	−3.68260	−	2.43845i	−0.123441	−	0.0817369i
$891$	19.4470	+	37.7327i	0.651499	+	1.26409i
$892$	−11.8078	+	5.00691i	−0.395353	+	0.167644i
$893$		−	26.7386i		−	0.894774i
$894$	−24.4293	−	1.79147i	−0.817038	−	0.0599158i
$895$		−	5.29723i		−	0.177067i
$896$	27.8462	−	19.8078i	0.930276	−	0.661731i
$897$	−6.56155	−	11.6847i	−0.219084	−	0.390139i
$898$	−9.17708	+	13.8594i	−0.306243	+	0.462496i
$899$	10.5945			0.353345
$900$	5.93581	+	0.875288i	0.197860	+	0.0291763i
$901$	−5.75379			−0.191686
$902$	45.0979	−	68.1080i	1.50160	−	2.26775i
$903$	25.1161	+	44.7261i	0.835810	+	1.48839i
$904$	14.2462	+	2.64861i	0.473822	+	0.0880916i
$905$			8.24621i			0.274113i
$906$	13.3390	+	0.978190i	0.443159	+	0.0324982i
$907$		−	35.8735i		−	1.19116i	−0.803295	−	0.595581i	$-0.796922\pi$
$907$		−	35.8735i		−	1.19116i	0.803295	−	0.595581i	$-0.203078\pi$
$908$	−0.870958	−	2.05398i	−0.0289038	−	0.0681636i
$909$	−10.2462	−	6.24621i	−0.339845	−	0.207174i
$910$	3.56155	+	2.35829i	0.118064	+	0.0781767i
$911$	−2.23100			−0.0739165			−0.0369582	−	0.999317i	$-0.511767\pi$
$911$	−2.23100			−0.0739165			−0.0369582	+	0.999317i	$0.511767\pi$
$912$	8.30661	−	31.6041i	0.275059	−	1.04652i
$913$	30.2462			1.00100
$914$	−40.6716	−	26.9309i	−1.34530	−	0.890794i
$915$	14.1498	−	7.94584i	0.467777	−	0.262681i
$916$	−12.6847	−	29.9142i	−0.419113	−	0.988392i
$917$			34.2462i			1.13091i
$918$	4.79977	−	6.71386i	0.158416	−	0.221591i
$919$			25.8139i			0.851524i	0.904835	+	0.425762i	$0.139994\pi$
$919$			25.8139i			0.851524i	−0.904835	+	0.425762i	$0.860006\pi$
$920$	21.5150	+	4.00000i	0.709328	+	0.131876i
$921$	−13.6847	+	7.68466i	−0.450925	+	0.253218i
$922$	−8.68466	+	13.1158i	−0.286014	+	0.431945i
$923$	−2.06798			−0.0680682
$924$	−39.0446	−	30.1824i	−1.28447	−	0.992926i
$925$	−10.0000			−0.328798
$926$	8.56222	−	12.9309i	0.281372	−	0.424935i
$927$	38.6852	+	23.5829i	1.27059	+	0.774566i
$928$	−9.75379	−	44.1912i	−0.320184	−	1.45065i
$929$			39.7538i			1.30428i	0.758099	+	0.652140i	$0.226128\pi$
$929$			39.7538i			1.30428i	−0.758099	+	0.652140i	$0.773872\pi$
$930$	0.237246	−	3.23519i	0.00777960	−	0.106086i
$931$			10.0138i			0.328190i
$932$	16.7984	−	7.12311i	0.550249	−	0.233325i
$933$	−17.6155	−	31.3693i	−0.576707	−	1.02699i
$934$	39.3693	+	26.0685i	1.28820	+	0.852988i
$935$	−5.29723			−0.173238
$936$	6.31579	+	5.66664i	0.206438	+	0.185220i
$937$	30.0000			0.980057			0.490029	−	0.871706i	$-0.336986\pi$
$937$	30.0000			0.980057			0.490029	+	0.871706i	$0.336986\pi$
$938$	20.1907	+	13.3693i	0.659249	+	0.436524i
$939$	−20.5625	−	36.6172i	−0.671032	−	1.19496i
$940$	−10.4384	+	4.42627i	−0.340465	+	0.144369i
$941$		−	16.3845i		−	0.534119i	−0.963680	−	0.267059i	$-0.913948\pi$
$941$		−	16.3845i		−	0.534119i	0.963680	−	0.267059i	$-0.0860519\pi$
$942$	1.47729	−	20.1449i	0.0481326	−	0.656357i
$943$		−	94.7494i		−	3.08546i
$944$	−29.9142	+	30.9309i	−0.973623	+	1.00671i
$945$	−15.6847	−	0.561553i	−0.510222	−	0.0182673i
$946$	36.1080	−	54.5311i	1.17397	−	1.77296i
$947$	−19.6558			−0.638728			−0.319364	−	0.947632i	$-0.603469\pi$
$947$	−19.6558			−0.638728			−0.319364	+	0.947632i	$0.603469\pi$
$948$	10.8886	+	8.41712i	0.353645	+	0.273375i
$949$	6.00000			0.194768
$950$	−3.68260	+	5.56155i	−0.119479	+	0.180441i
$951$	0.371834	−	0.208805i	0.0120575	−	0.00677095i
$952$	−1.75379	+	9.43318i	−0.0568406	+	0.305731i
$953$			43.3693i			1.40487i	0.711748	+	0.702435i	$0.247904\pi$
$953$			43.3693i			1.40487i	−0.711748	+	0.702435i	$0.752096\pi$
$954$	9.22786	+	19.6794i	0.298763	+	0.637144i
$955$		−	11.3381i		−	0.366893i
$956$	4.26324	+	10.0540i	0.137883	+	0.325169i
$957$	−56.9848	+	32.0000i	−1.84206	+	1.03441i
$958$	−2.93087	−	1.94069i	−0.0946921	−	0.0627007i
$959$	−24.9073			−0.804297
$960$	−13.7129	+	1.98889i	−0.442583	+	0.0641910i
$961$	29.2462			0.943426
$962$	−11.7915	−	7.80776i	−0.380172	−	0.251732i
$963$	2.64861	−	4.34475i	0.0853504	−	0.140008i
$964$	10.0540	+	23.7102i	0.323817	+	0.763655i
$965$			2.00000i			0.0643823i
$966$	−57.0896	−	4.18655i	−1.83683	−	0.134700i
$967$		−	17.3332i		−	0.557400i	−0.960378	−	0.278700i	$-0.910097\pi$
$967$		−	17.3332i		−	0.557400i	0.960378	−	0.278700i	$-0.0899034\pi$
$968$	−5.81422	+	31.2732i	−0.186876	+	1.00516i
$969$	4.49242	+	8.00000i	0.144317	+	0.256997i
$970$	12.6847	−	19.1567i	0.407280	−	0.615084i
$971$	−26.3946			−0.847043			−0.423521	−	0.905886i	$-0.639206\pi$
$971$	−26.3946			−0.847043			−0.423521	+	0.905886i	$0.639206\pi$
$972$	−30.6609	−	5.64879i	−0.983449	−	0.181185i
$973$	−68.9848			−2.21155
$974$	−14.4401	+	21.8078i	−0.462690	+	0.698766i
$975$	−0.848071	−	1.51022i	−0.0271600	−	0.0483659i
$976$	−26.0540	+	26.9395i	−0.833967	+	0.862312i
$977$			61.2311i			1.95896i	0.201553	+	0.979478i	$0.435401\pi$
$977$			61.2311i			1.95896i	−0.201553	+	0.979478i	$0.564599\pi$
$978$	−22.1362	−	1.62331i	−0.707838	−	0.0519079i
$979$		−	14.7304i		−	0.470786i
$980$	3.90928	−	1.65767i	0.124877	−	0.0529524i
$981$	−14.6307	+	24.0000i	−0.467122	+	0.766261i
$982$	32.4924	+	21.5150i	1.03687	+	0.686570i
$983$	34.7123			1.10715			0.553575	−	0.832800i	$-0.313263\pi$
$983$	34.7123			1.10715			0.553575	+	0.832800i	$0.313263\pi$
$984$	19.3186	+	56.7984i	0.615855	+	1.81067i
$985$	12.2462			0.390197
$986$	10.5945	+	7.01515i	0.337396	+	0.223408i
$987$	25.8597	−	14.5216i	0.823124	−	0.462228i
$988$	−8.68466	+	3.68260i	−0.276296	+	0.117159i
$989$		−	75.8617i		−	2.41226i
$990$	8.49563	+	18.1178i	0.270009	+	0.575823i
$991$		−	15.6371i		−	0.496729i	−0.968667	−	0.248364i	$-0.920107\pi$
$991$		−	15.6371i		−	0.496729i	0.968667	−	0.248364i	$-0.0798931\pi$
$992$	1.61463	+	7.31534i	0.0512644	+	0.232262i
$993$	−28.2462	+	15.8617i	−0.896366	+	0.503357i
$994$	−4.87689	+	7.36520i	−0.154686	+	0.233610i
$995$	−16.0547			−0.508969
$996$	−13.5862	+	17.5754i	−0.430494	+	0.556897i
$997$	51.4773			1.63030			0.815151	−	0.579249i	$-0.196654\pi$
$997$	51.4773			1.63030			0.815151	+	0.579249i	$0.196654\pi$
$998$	7.81855	−	11.8078i	0.247492	−	0.373768i
$999$	51.9283	+	1.85917i	1.64294	+	0.0588216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	780.2.g.b.131.8	yes	8
3.2	odd	2	inner	780.2.g.b.131.1	✓	8
4.3	odd	2	inner	780.2.g.b.131.2	yes	8
12.11	even	2	inner	780.2.g.b.131.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.g.b.131.1	✓	8	3.2	odd	2	inner
780.2.g.b.131.2	yes	8	4.3	odd	2	inner
780.2.g.b.131.7	yes	8	12.11	even	2	inner
780.2.g.b.131.8	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(1.17915 + 0.780776i) q^{2} +(-0.848071 - 1.51022i) q^{3} +(0.780776 + 1.84130i) q^{4} +1.00000i q^{5} +(0.179147 - 2.44293i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(-1.56155 + 2.56155i) q^{9} +(-0.780776 + 1.17915i) q^{10} -4.71659 q^{11} +(2.11862 - 2.74070i) q^{12} -1.00000 q^{13} +(-2.35829 + 3.56155i) q^{14} +(1.51022 - 0.848071i) q^{15} +(-2.78078 + 2.87529i) q^{16} -1.12311i q^{17} +(-3.84130 + 1.80122i) q^{18} -4.71659i q^{19} +(-1.84130 + 0.780776i) q^{20} +(4.56155 - 2.56155i) q^{21} +(-5.56155 - 3.68260i) q^{22} -7.73704 q^{23} +(4.63804 - 1.57752i) q^{24} -1.00000 q^{25} +(-1.17915 - 0.780776i) q^{26} +(5.19283 + 0.185917i) q^{27} +(-5.56155 + 2.35829i) q^{28} +8.00000i q^{29} +(2.44293 + 0.179147i) q^{30} -1.32431i q^{31} +(-5.52390 + 1.21922i) q^{32} +(4.00000 + 7.12311i) q^{33} +(0.876894 - 1.32431i) q^{34} -3.02045 q^{35} +(-5.93581 - 0.875288i) q^{36} +10.0000 q^{37} +(3.68260 - 5.56155i) q^{38} +(0.848071 + 1.51022i) q^{39} +(-2.78078 - 0.516994i) q^{40} +12.2462i q^{41} +(7.37874 + 0.541105i) q^{42} +9.80501i q^{43} +(-3.68260 - 8.68466i) q^{44} +(-2.56155 - 1.56155i) q^{45} +(-9.12311 - 6.04090i) q^{46} +5.66906 q^{47} +(6.70062 + 1.76115i) q^{48} -2.12311 q^{49} +(-1.17915 - 0.780776i) q^{50} +(-1.69614 + 0.952473i) q^{51} +(-0.780776 - 1.84130i) q^{52} -5.12311i q^{53} +(5.97795 + 4.27366i) q^{54} -4.71659i q^{55} +(-8.39919 - 1.56155i) q^{56} +(-7.12311 + 4.00000i) q^{57} +(-6.24621 + 9.43318i) q^{58} +10.7575 q^{59} +(2.74070 + 2.11862i) q^{60} +9.36932 q^{61} +(1.03399 - 1.56155i) q^{62} +(-7.73704 - 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} -1.00000i q^{65} +(-0.844964 + 11.5223i) q^{66} -5.66906i q^{67} +(2.06798 - 0.876894i) q^{68} +(6.56155 + 11.6847i) q^{69} +(-3.56155 - 2.35829i) q^{70} +2.06798 q^{71} +(-6.31579 - 5.66664i) q^{72} -6.00000 q^{73} +(11.7915 + 7.80776i) q^{74} +(0.848071 + 1.51022i) q^{75} +(8.68466 - 3.68260i) q^{76} -14.2462i q^{77} +(-0.179147 + 2.44293i) q^{78} +3.97292i q^{79} +(-2.87529 - 2.78078i) q^{80} +(-4.12311 - 8.00000i) q^{81} +(-9.56155 + 14.4401i) q^{82} -6.41273 q^{83} +(8.27814 + 6.39919i) q^{84} +1.12311 q^{85} +(-7.65552 + 11.5616i) q^{86} +(12.0818 - 6.78456i) q^{87} +(2.43845 - 13.1158i) q^{88} +3.12311i q^{89} +(-1.80122 - 3.84130i) q^{90} -3.02045i q^{91} +(-6.04090 - 14.2462i) q^{92} +(-2.00000 + 1.12311i) q^{93} +(6.68466 + 4.42627i) q^{94} +4.71659 q^{95} +(6.52596 + 7.30834i) q^{96} -16.2462 q^{97} +(-2.50345 - 1.65767i) q^{98} +(7.36520 - 12.0818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 8 q^{6} + 4 q^{9} + 2 q^{10} + 14 q^{12} - 8 q^{13} - 14 q^{16} - 16 q^{18} + 20 q^{21} - 28 q^{22} + 20 q^{24} - 8 q^{25} - 28 q^{28} + 6 q^{30} + 32 q^{33} + 40 q^{34} - 18 q^{36} + 80 q^{37}+ \cdots - 64 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 8 * q^6 + 4 * q^9 + 2 * q^10 + 14 * q^12 - 8 * q^13 - 14 * q^16 - 16 * q^18 + 20 * q^21 - 28 * q^22 + 20 * q^24 - 8 * q^25 - 28 * q^28 + 6 * q^30 + 32 * q^33 + 40 * q^34 - 18 * q^36 + 80 * q^37 - 14 * q^40 + 16 * q^42 - 4 * q^45 - 40 * q^46 + 10 * q^48 + 16 * q^49 + 2 * q^52 + 16 * q^54 - 24 * q^57 + 16 * q^58 - 4 * q^60 - 24 * q^61 - 2 * q^64 - 28 * q^66 + 36 * q^69 - 12 * q^70 - 24 * q^72 - 48 * q^73 + 20 * q^76 + 8 * q^78 - 60 * q^82 + 12 * q^84 - 24 * q^85 + 36 * q^88 + 18 * q^90 - 16 * q^93 + 4 * q^94 - 12 * q^96 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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