LMFDB - Embedded newform 637.2.r.e.116.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(116,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.116"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,4,0,0,0,0,2,0,0,20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			116.1
Root			$0.550552 + 0.147520i$ of defining polynomial
Character	$\chi$	$=$	637.116
Dual form			637.2.r.e.324.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.14878 + 1.24060i) q^{2} +(-0.837565 + 1.45071i) q^{3} +(2.07816 - 3.59948i) q^{4} +(0.584680 - 0.337565i) q^{5} -4.15633i q^{6} +5.35026i q^{8} +(0.0969683 + 0.167954i) q^{9} +(-0.837565 + 1.45071i) q^{10} +(-3.88083 - 2.24060i) q^{11} +(3.48119 + 6.02961i) q^{12} +(3.28726 + 1.48119i) q^{13} +1.13093i q^{15} +(-2.48119 - 4.29755i) q^{16} +(1.64363 - 2.84685i) q^{17} +(-0.416726 - 0.240597i) q^{18} +(-4.52007 + 2.60966i) q^{19} -2.80606i q^{20} +11.1187 q^{22} +(-2.38423 - 4.12960i) q^{23} +(-7.76166 - 4.48119i) q^{24} +(-2.27210 + 3.93539i) q^{25} +(-8.90115 + 0.895406i) q^{26} -5.35026 q^{27} -9.31265 q^{29} +(-1.40303 - 2.43012i) q^{30} +(-1.41813 - 0.818760i) q^{31} +(1.39614 + 0.806063i) q^{32} +(6.50089 - 3.75329i) q^{33} +8.15633i q^{34} +0.806063 q^{36} +(-1.25018 + 0.721791i) q^{37} +(6.47508 - 11.2152i) q^{38} +(-4.90207 + 3.52825i) q^{39} +(1.80606 + 3.12819i) q^{40} -7.92478i q^{41} -4.61213 q^{43} +(-16.1300 + 9.31265i) q^{44} +(0.113391 + 0.0654663i) q^{45} +(10.2463 + 5.91573i) q^{46} +(6.81481 - 3.93453i) q^{47} +8.31265 q^{48} -11.2750i q^{50} +(2.75329 + 4.76884i) q^{51} +(12.1630 - 8.75427i) q^{52} +(1.57816 - 2.73346i) q^{53} +(11.4965 - 6.63752i) q^{54} -3.02539 q^{55} -8.74306i q^{57} +(20.0108 - 11.5532i) q^{58} +(2.20334 + 1.27210i) q^{59} +(4.07077 + 2.35026i) q^{60} +(1.15633 + 2.00281i) q^{61} +4.06300 q^{62} +5.92478 q^{64} +(2.42200 - 0.243639i) q^{65} +(-9.31265 + 16.1300i) q^{66} +(-6.36551 - 3.67513i) q^{67} +(-6.83146 - 11.8324i) q^{68} +7.98778 q^{69} +7.75623i q^{71} +(-0.898598 + 0.518806i) q^{72} +(13.1152 + 7.57205i) q^{73} +(1.79090 - 3.10194i) q^{74} +(-3.80606 - 6.59230i) q^{75} +21.6932i q^{76} +(6.15633 - 13.6629i) q^{78} +(-7.33146 - 12.6985i) q^{79} +(-2.90141 - 1.67513i) q^{80} +(4.19029 - 7.25779i) q^{81} +(9.83146 + 17.0286i) q^{82} -1.45088i q^{83} -2.21933i q^{85} +(9.91043 - 5.72179i) q^{86} +(7.79995 - 13.5099i) q^{87} +(11.9878 - 20.7634i) q^{88} +(-6.74967 + 3.89692i) q^{89} -0.324869 q^{90} -19.8192 q^{92} +(2.37556 - 1.37153i) q^{93} +(-9.76234 + 16.9089i) q^{94} +(-1.76187 + 3.05164i) q^{95} +(-2.33872 + 1.35026i) q^{96} -17.9805i q^{97} -0.869067i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 2 q^{9} + 20 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} + 4 q^{38} + 8 q^{39} + 20 q^{40} - 52 q^{43}+ \cdots - 58 q^{95}+O(q^{100}) $ 12 * q + 4 * q^4 + 2 * q^9 + 20 * q^12 + 16 * q^13 - 8 * q^16 + 8 * q^17 + 48 * q^22 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 24 * q^27 - 28 * q^29 - 16 * q^30 + 8 * q^36 + 4 * q^38 + 8 * q^39 + 20 * q^40 - 52 * q^43 + 16 * q^48 - 8 * q^51 + 20 * q^52 - 2 * q^53 + 24 * q^55 - 28 * q^61 + 32 * q^62 - 16 * q^64 + 6 * q^65 - 28 * q^66 - 20 * q^68 - 8 * q^69 + 24 * q^74 - 44 * q^75 + 32 * q^78 - 26 * q^79 + 26 * q^81 + 56 * q^82 + 40 * q^87 + 40 * q^88 - 24 * q^90 - 72 * q^92 - 20 * q^94 - 58 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.14878	+	1.24060i	−1.51941	+	0.877235i	−0.519677	+	0.854363i	$0.673948\pi$
$2$	−2.14878	+	1.24060i	−1.51941	+	0.877235i	−0.999738	+	0.0228716i	$0.992719\pi$
$3$	−0.837565	+	1.45071i	−0.483569	+	0.837565i	−0.999822	−	0.0188705i	$-0.993993\pi$
$3$	−0.837565	+	1.45071i	−0.483569	+	0.837565i	0.516253	+	0.856436i	$0.327326\pi$
$4$	2.07816	−	3.59948i	1.03908	−	1.79974i
$5$	0.584680	−	0.337565i	0.261477	−	0.150964i	−0.363531	−	0.931582i	$-0.618429\pi$
$5$	0.584680	−	0.337565i	0.261477	−	0.150964i	0.625008	+	0.780618i	$0.285096\pi$
$6$		−	4.15633i		−	1.69681i
$7$		0			0
$7$		0			0
$8$			5.35026i			1.89160i
$9$	0.0969683	+	0.167954i	0.0323228	+	0.0559847i
$10$	−0.837565	+	1.45071i	−0.264861	+	0.458753i
$11$	−3.88083	−	2.24060i	−1.17011	−	0.675565i	−0.216407	−	0.976303i	$-0.569434\pi$
$11$	−3.88083	−	2.24060i	−1.17011	−	0.675565i	−0.953707	+	0.300738i	$0.902767\pi$
$12$	3.48119	+	6.02961i	1.00493	+	1.74060i
$13$	3.28726	+	1.48119i	0.911721	+	0.410809i
$13$	3.28726	+	1.48119i	0.911721	+	0.410809i
$14$		0			0
$15$			1.13093i			0.292006i
$16$	−2.48119	−	4.29755i	−0.620299	−	1.07439i
$17$	1.64363	−	2.84685i	0.398639	−	0.690462i	−0.594920	−	0.803785i	$-0.702816\pi$
$17$	1.64363	−	2.84685i	0.398639	−	0.690462i	0.993558	+	0.113323i	$0.0361495\pi$
$18$	−0.416726	−	0.240597i	−0.0982234	−	0.0567093i
$19$	−4.52007	+	2.60966i	−1.03698	+	0.598698i	−0.918975	−	0.394315i	$-0.870982\pi$
$19$	−4.52007	+	2.60966i	−1.03698	+	0.598698i	−0.118000	+	0.993014i	$0.537648\pi$
$20$		−	2.80606i		−	0.627455i
$21$		0			0
$22$	11.1187			2.37052
$23$	−2.38423	−	4.12960i	−0.497145	−	0.861081i	0.502849	−	0.864374i	$-0.332285\pi$
$23$	−2.38423	−	4.12960i	−0.497145	−	0.861081i	−0.999995	+	0.00329297i	$0.998952\pi$
$24$	−7.76166	−	4.48119i	−1.58434	−	0.914720i
$25$	−2.27210	+	3.93539i	−0.454420	+	0.787078i
$26$	−8.90115	+	0.895406i	−1.74566	+	0.175604i
$27$	−5.35026			−1.02966
$28$		0			0
$29$	−9.31265			−1.72932			−0.864658	−	0.502361i	$-0.832465\pi$
$29$	−9.31265			−1.72932			−0.864658	+	0.502361i	$0.832465\pi$
$30$	−1.40303	−	2.43012i	−0.256157	−	0.443678i
$31$	−1.41813	−	0.818760i	−0.254704	−	0.147054i	0.367212	−	0.930137i	$-0.380312\pi$
$31$	−1.41813	−	0.818760i	−0.254704	−	0.147054i	−0.621916	+	0.783084i	$0.713646\pi$
$32$	1.39614	+	0.806063i	0.246806	+	0.142493i
$33$	6.50089	−	3.75329i	1.13166	−	0.653365i
$34$			8.15633i			1.39880i
$35$		0			0
$36$	0.806063			0.134344
$37$	−1.25018	+	0.721791i	−0.205528	+	0.118662i	−0.599231	−	0.800576i	$-0.704527\pi$
$37$	−1.25018	+	0.721791i	−0.205528	+	0.118662i	0.393703	+	0.919238i	$0.371194\pi$
$38$	6.47508	−	11.2152i	1.05040	−	1.81934i
$39$	−4.90207	+	3.52825i	−0.784960	+	0.564972i
$40$	1.80606	+	3.12819i	0.285564	+	0.494611i
$41$		−	7.92478i		−	1.23764i	−0.785532	−	0.618821i	$-0.787611\pi$
$41$		−	7.92478i		−	1.23764i	0.785532	−	0.618821i	$-0.212389\pi$
$42$		0			0
$43$	−4.61213			−0.703343			−0.351671	−	0.936124i	$-0.614387\pi$
$43$	−4.61213			−0.703343			−0.351671	+	0.936124i	$0.614387\pi$
$44$	−16.1300	+	9.31265i	−2.43169	+	1.40393i
$45$	0.113391	+	0.0654663i	0.0169033	+	0.00975914i
$46$	10.2463	+	5.91573i	1.51074	+	0.872227i
$47$	6.81481	−	3.93453i	0.994043	−	0.573911i	0.0875623	−	0.996159i	$-0.472092\pi$
$47$	6.81481	−	3.93453i	0.994043	−	0.573911i	0.906480	+	0.422248i	$0.138759\pi$
$48$	8.31265			1.19983
$49$		0			0
$50$		−	11.2750i		−	1.59453i
$51$	2.75329	+	4.76884i	0.385538	+	0.667772i
$52$	12.1630	−	8.75427i	1.68670	−	1.21400i
$53$	1.57816	−	2.73346i	0.216777	−	0.375469i	−0.737044	−	0.675845i	$-0.763779\pi$
$53$	1.57816	−	2.73346i	0.216777	−	0.375469i	0.953821	+	0.300376i	$0.0971121\pi$
$54$	11.4965	−	6.63752i	1.56448	−	0.903252i
$55$	−3.02539			−0.407944
$56$		0			0
$57$		−	8.74306i		−	1.15805i
$58$	20.0108	−	11.5532i	2.62755	−	1.51702i
$59$	2.20334	+	1.27210i	0.286850	+	0.165613i	0.636521	−	0.771260i	$-0.280373\pi$
$59$	2.20334	+	1.27210i	0.286850	+	0.165613i	−0.349670	+	0.936873i	$0.613706\pi$
$60$	4.07077	+	2.35026i	0.525535	+	0.303417i
$61$	1.15633	+	2.00281i	0.148052	+	0.256434i	0.930508	−	0.366273i	$-0.119366\pi$
$61$	1.15633	+	2.00281i	0.148052	+	0.256434i	−0.782455	+	0.622707i	$0.786033\pi$
$62$	4.06300			0.516002
$63$		0			0
$64$	5.92478			0.740597
$65$	2.42200	−	0.243639i	0.300412	−	0.0302197i
$66$	−9.31265	+	16.1300i	−1.14631	+	1.98546i
$67$	−6.36551	−	3.67513i	−0.777671	−	0.448989i	0.0579331	−	0.998320i	$-0.481549\pi$
$67$	−6.36551	−	3.67513i	−0.777671	−	0.448989i	−0.835604	+	0.549332i	$0.814882\pi$
$68$	−6.83146	−	11.8324i	−0.828436	−	1.43489i
$69$	7.98778			0.961616
$70$		0			0
$71$			7.75623i			0.920496i	0.887791	+	0.460248i	$0.152239\pi$
$71$			7.75623i			0.920496i	−0.887791	+	0.460248i	$0.847761\pi$
$72$	−0.898598	+	0.518806i	−0.105901	+	0.0611418i
$73$	13.1152	+	7.57205i	1.53502	+	0.886242i	0.999119	+	0.0419581i	$0.0133596\pi$
$73$	13.1152	+	7.57205i	1.53502	+	0.886242i	0.535896	+	0.844284i	$0.319974\pi$
$74$	1.79090	−	3.10194i	0.208188	−	0.360593i
$75$	−3.80606	−	6.59230i	−0.439486	−	0.761213i
$76$			21.6932i			2.48838i
$77$		0			0
$78$	6.15633	−	13.6629i	0.697067	−	1.54702i
$79$	−7.33146	−	12.6985i	−0.824853	−	1.42869i	−0.902031	−	0.431670i	$-0.857924\pi$
$79$	−7.33146	−	12.6985i	−0.824853	−	1.42869i	0.0771782	−	0.997017i	$-0.475409\pi$
$80$	−2.90141	−	1.67513i	−0.324388	−	0.187285i
$81$	4.19029	−	7.25779i	0.465588	−	0.806422i
$82$	9.83146	+	17.0286i	1.08570	+	1.88049i
$83$		−	1.45088i		−	0.159254i	−0.996825	−	0.0796272i	$-0.974627\pi$
$83$		−	1.45088i		−	0.159254i	0.996825	−	0.0796272i	$-0.0253730\pi$
$84$		0			0
$85$		−	2.21933i		−	0.240720i
$86$	9.91043	−	5.72179i	1.06867	−	0.616997i
$87$	7.79995	−	13.5099i	0.836243	−	1.44842i
$88$	11.9878	−	20.7634i	1.27790	−	2.21339i
$89$	−6.74967	+	3.89692i	−0.715463	+	0.413073i	−0.813081	−	0.582151i	$-0.802211\pi$
$89$	−6.74967	+	3.89692i	−0.715463	+	0.413073i	0.0976173	+	0.995224i	$0.468878\pi$
$90$	−0.324869			−0.0342442
$91$		0			0
$92$	−19.8192			−2.06630
$93$	2.37556	−	1.37153i	0.246334	−	0.142221i
$94$	−9.76234	+	16.9089i	−1.00691	+	1.74402i
$95$	−1.76187	+	3.05164i	−0.180764	+	0.313092i
$96$	−2.33872	+	1.35026i	−0.238695	+	0.137811i
$97$		−	17.9805i		−	1.82564i	−0.408360	−	0.912821i	$-0.633899\pi$
$97$		−	17.9805i		−	1.82564i	0.408360	−	0.912821i	$-0.366101\pi$
$98$		0			0
$99$		−	0.869067i		−	0.0873446i
$100$	9.44358	+	16.3568i	0.944358	+	1.63568i
$101$	−4.66902	+	8.08698i	−0.464585	+	0.804685i	−0.999183	−	0.0404219i	$-0.987130\pi$
$101$	−4.66902	+	8.08698i	−0.464585	+	0.804685i	0.534598	+	0.845107i	$0.320463\pi$
$102$	−11.8324	−	6.83146i	−1.17159	−	0.676415i
$103$	−3.11871	−	5.40177i	−0.307296	−	0.532252i	0.670474	−	0.741933i	$-0.266091\pi$
$103$	−3.11871	−	5.40177i	−0.307296	−	0.532252i	−0.977770	+	0.209681i	$0.932758\pi$
$104$	−7.92478	+	17.5877i	−0.777088	+	1.72461i
$105$		0			0
$106$			7.83146i			0.760658i
$107$	−3.62236	−	6.27411i	−0.350187	−	0.606541i	0.636095	−	0.771611i	$-0.280549\pi$
$107$	−3.62236	−	6.27411i	−0.350187	−	0.606541i	−0.986282	+	0.165069i	$0.947215\pi$
$108$	−11.1187	+	19.2582i	−1.06990	+	1.85312i
$109$	−4.15159	−	2.39692i	−0.397650	−	0.229584i	0.287819	−	0.957685i	$-0.407070\pi$
$109$	−4.15159	−	2.39692i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$110$	6.50089	−	3.75329i	0.619836	−	0.357862i
$111$		−	2.41819i		−	0.229524i
$112$		0			0
$113$	−9.34297			−0.878912			−0.439456	−	0.898264i	$-0.644829\pi$
$113$	−9.34297			−0.878912			−0.439456	+	0.898264i	$0.644829\pi$
$114$	10.8466	+	18.7869i	1.01588	+	1.75955i
$115$	−2.78802	−	1.60966i	−0.259984	−	0.150102i
$116$	−19.3532	+	33.5207i	−1.79690	+	3.11232i
$117$	0.0699872	+	0.695737i	0.00647032	+	0.0643209i
$118$	−6.31265			−0.581127
$119$		0			0
$120$	−6.05079			−0.552359
$121$	4.54055	+	7.86447i	0.412777	+	0.714951i
$122$	−4.96937	−	2.86907i	−0.449906	−	0.259753i
$123$	11.4965	+	6.63752i	1.03661	+	0.598485i
$124$	−5.89422	+	3.40303i	−0.529317	+	0.305601i
$125$			6.44358i			0.576332i
$126$		0			0
$127$	−1.38058			−0.122507			−0.0612533	−	0.998122i	$-0.519510\pi$
$127$	−1.38058			−0.122507			−0.0612533	+	0.998122i	$0.519510\pi$
$128$	−15.5233	+	8.96239i	−1.37208	+	0.792171i
$129$	3.86296	−	6.69084i	0.340114	−	0.589096i
$130$	−4.90207	+	3.52825i	−0.429940	+	0.309448i
$131$	−6.24965	−	10.8247i	−0.546034	−	0.945759i	−0.998541	−	0.0539980i	$-0.982804\pi$
$131$	−6.24965	−	10.8247i	−0.546034	−	0.945759i	0.452507	−	0.891761i	$-0.350530\pi$
$132$		−	31.1998i		−	2.71560i
$133$		0			0
$134$	18.2374			1.57547
$135$	−3.12819	+	1.80606i	−0.269232	+	0.155441i
$136$	15.2314	+	8.79384i	1.30608	+	0.754066i
$137$	−2.77661	−	1.60308i	−0.237222	−	0.136960i	0.376677	−	0.926345i	$-0.377067\pi$
$137$	−2.77661	−	1.60308i	−0.237222	−	0.136960i	−0.613899	+	0.789384i	$0.710400\pi$
$138$	−17.1640	+	9.90962i	−1.46109	+	0.843563i
$139$	−0.249646			−0.0211747			−0.0105874	−	0.999944i	$-0.503370\pi$
$139$	−0.249646			−0.0211747			−0.0105874	+	0.999944i	$0.503370\pi$
$140$		0			0
$141$			13.1817i			1.11010i
$142$	−9.62236	−	16.6664i	−0.807491	−	1.39861i
$143$	−9.43852	−	13.1137i	−0.789289	−	1.09662i
$144$	0.481194	−	0.833453i	0.0400995	−	0.0694544i
$145$	−5.44492	+	3.14363i	−0.452176	+	0.261064i
$146$	−37.5755			−3.10977
$147$		0			0
$148$			6.00000i			0.493197i
$149$	−3.49241	+	2.01634i	−0.286109	+	0.165185i	−0.636186	−	0.771536i	$-0.719489\pi$
$149$	−3.49241	+	2.01634i	−0.286109	+	0.165185i	0.350077	+	0.936721i	$0.386156\pi$
$150$	16.3568	+	9.44358i	1.33552	+	0.771065i
$151$	−1.35931	−	0.784795i	−0.110619	−	0.0638657i	0.443670	−	0.896190i	$-0.353676\pi$
$151$	−1.35931	−	0.784795i	−0.110619	−	0.0638657i	−0.554289	+	0.832325i	$0.687010\pi$
$152$	−13.9624	−	24.1836i	−1.13250	−	1.96155i
$153$	0.637519			0.0515404
$154$		0			0
$155$	−1.10554			−0.0887991
$156$	2.51257	+	24.9772i	0.201166	+	1.99978i
$157$	−1.44969	+	2.51094i	−0.115698	+	0.200395i	−0.918059	−	0.396445i	$-0.870244\pi$
$157$	−1.44969	+	2.51094i	−0.115698	+	0.200395i	0.802361	+	0.596840i	$0.203577\pi$
$158$	31.5073	+	18.1908i	2.50659	+	1.44718i
$159$	2.64363	+	4.57890i	0.209653	+	0.363130i
$160$	1.08840			0.0860453
$161$		0			0
$162$			20.7938i			1.63372i
$163$	14.9606	−	8.63752i	1.17181	−	0.676543i	0.217702	−	0.976015i	$-0.430144\pi$
$163$	14.9606	−	8.63752i	1.17181	−	0.676543i	0.954105	+	0.299473i	$0.0968107\pi$
$164$	−28.5251	−	16.4690i	−2.22744	−	1.28601i
$165$	2.53396	−	4.38895i	0.197269	−	0.341680i
$166$	1.79995	+	3.11761i	0.139704	+	0.241974i
$167$			16.2931i			1.26080i	0.776270	+	0.630400i	$0.217109\pi$
$167$			16.2931i			1.26080i	−0.776270	+	0.630400i	$0.782891\pi$
$168$		0			0
$169$	8.61213	+	9.73813i	0.662471	+	0.749087i
$170$	2.75329	+	4.76884i	0.211168	+	0.365754i
$171$	−0.876607	−	0.506109i	−0.0670358	−	0.0387032i
$172$	−9.58475	+	16.6013i	−0.730830	+	1.26584i
$173$	−1.08721	−	1.88311i	−0.0826592	−	0.143170i	0.821732	−	0.569874i	$-0.193008\pi$
$173$	−1.08721	−	1.88311i	−0.0826592	−	0.143170i	−0.904391	+	0.426704i	$0.859675\pi$
$174$			38.7064i			2.93432i
$175$		0			0
$176$			22.2374i			1.67621i
$177$	−3.69088	+	2.13093i	−0.277424	+	0.160171i
$178$	9.66902	−	16.7472i	0.724724	−	1.25526i
$179$	0.275746	−	0.477607i	0.0206102	−	0.0356980i	−0.855536	−	0.517743i	$-0.826772\pi$
$179$	0.275746	−	0.477607i	0.0206102	−	0.0356980i	0.876147	+	0.482045i	$0.160106\pi$
$180$	0.471290	−	0.272099i	0.0351278	−	0.0202811i
$181$	0.511511			0.0380203			0.0190102	−	0.999819i	$-0.493949\pi$
$181$	0.511511			0.0380203			0.0190102	+	0.999819i	$0.493949\pi$
$182$		0			0
$183$	−3.87399			−0.286374
$184$	22.0944	−	12.7562i	1.62882	−	0.940402i
$185$	−0.487304	+	0.844035i	−0.0358273	+	0.0620547i
$186$	−3.40303	+	5.89422i	−0.249522	+	0.432185i
$187$	−12.7573	+	7.36542i	−0.932905	+	0.538613i
$188$		−	32.7064i		−	2.38536i
$189$		0			0
$190$		−	8.74306i		−	0.634288i
$191$	8.27210	+	14.3277i	0.598548	+	1.03672i	0.993036	+	0.117814i	$0.0375888\pi$
$191$	8.27210	+	14.3277i	0.598548	+	1.03672i	−0.394488	+	0.918901i	$0.629078\pi$
$192$	−4.96239	+	8.59511i	−0.358130	+	0.620299i
$193$	−6.41802	−	3.70545i	−0.461979	−	0.266724i	0.250897	−	0.968014i	$-0.419275\pi$
$193$	−6.41802	−	3.70545i	−0.461979	−	0.266724i	−0.712876	+	0.701290i	$0.752608\pi$
$194$	22.3065	+	38.6361i	1.60152	+	2.77391i
$195$	−1.67513	+	3.71767i	−0.119959	+	0.266228i
$196$		0			0
$197$			7.14903i			0.509347i	0.967027	+	0.254674i	$0.0819681\pi$
$197$			7.14903i			0.509347i	−0.967027	+	0.254674i	$0.918032\pi$
$198$	1.07816	+	1.86743i	0.0766217	+	0.132713i
$199$	−2.55031	+	4.41726i	−0.180787	+	0.313131i	−0.942149	−	0.335195i	$-0.891198\pi$
$199$	−2.55031	+	4.41726i	−0.180787	+	0.313131i	0.761362	+	0.648327i	$0.224531\pi$
$200$	−21.0554	−	12.1563i	−1.48884	−	0.859582i
$201$	10.6631	−	6.15633i	0.752115	−	0.434234i
$202$		−	23.1695i		−	1.63020i
$203$		0			0
$204$	22.8872			1.60242
$205$	−2.67513	−	4.63346i	−0.186839	−	0.323615i
$206$	13.4028	+	7.73813i	0.933820	+	0.539141i
$207$	0.462389	−	0.800881i	0.0321382	−	0.0556650i
$208$	−1.79081	−	17.8023i	−0.124170	−	1.23437i
$209$	23.3888			1.61784
$210$		0			0
$211$	0.193937			0.0133511			0.00667557	−	0.999978i	$-0.497875\pi$
$211$	0.193937			0.0133511			0.00667557	+	0.999978i	$0.497875\pi$
$212$	−6.55936	−	11.3611i	−0.450498	−	0.780286i
$213$	−11.2520	−	6.49635i	−0.770975	−	0.445123i
$214$	15.5673	+	8.98778i	1.06416	+	0.614392i
$215$	−2.69662	+	1.55689i	−0.183908	+	0.106179i
$216$		−	28.6253i		−	1.94771i
$217$		0			0
$218$	11.8945			0.805594
$219$	−21.9696	+	12.6842i	−1.48457	+	0.857117i
$220$	−6.28726	+	10.8898i	−0.423887	+	0.734194i
$221$	9.61977	−	6.92379i	0.647096	−	0.465745i
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$			5.83875i			0.390992i	0.980705	+	0.195496i	$0.0626316\pi$
$223$			5.83875i			0.390992i	−0.980705	+	0.195496i	$0.937368\pi$
$224$		0			0
$225$	−0.881286			−0.0587524
$226$	20.0760	−	11.5909i	1.33543	−	0.771012i
$227$	3.19334	+	1.84367i	0.211949	+	0.122369i	0.602217	−	0.798332i	$-0.294284\pi$
$227$	3.19334	+	1.84367i	0.211949	+	0.122369i	−0.390268	+	0.920701i	$0.627618\pi$
$228$	−31.4705	−	18.1695i	−2.08418	−	1.20330i
$229$	−4.89913	+	2.82852i	−0.323744	+	0.186914i	−0.653060	−	0.757306i	$-0.726515\pi$
$229$	−4.89913	+	2.82852i	−0.323744	+	0.186914i	0.329316	+	0.944220i	$0.393182\pi$
$230$	7.98778			0.526699
$231$		0			0
$232$		−	49.8251i		−	3.27118i
$233$	5.16291	+	8.94243i	0.338234	+	0.585838i	0.984101	−	0.177612i	$-0.0568373\pi$
$233$	5.16291	+	8.94243i	0.338234	+	0.585838i	−0.645867	+	0.763450i	$0.723504\pi$
$234$	−1.01352	−	1.40816i	−0.0662556	−	0.0920542i
$235$	2.65633	−	4.60089i	0.173280	−	0.300129i
$236$	9.15780	−	5.28726i	0.596122	−	0.344171i
$237$	24.5623			1.59549
$238$		0			0
$239$		−	22.2882i		−	1.44170i	−0.693089	−	0.720852i	$-0.743751\pi$
$239$		−	22.2882i		−	1.44170i	0.693089	−	0.720852i	$-0.256249\pi$
$240$	4.86024	−	2.80606i	0.313727	−	0.181131i
$241$	−25.4840	−	14.7132i	−1.64157	−	0.947762i	−0.980275	−	0.197637i	$-0.936673\pi$
$241$	−25.4840	−	14.7132i	−1.64157	−	0.947762i	−0.661296	−	0.750125i	$-0.729993\pi$
$242$	−19.5133	−	11.2660i	−1.25436	−	0.724205i
$243$	−1.00611	−	1.74263i	−0.0645419	−	0.111790i
$244$	9.61213			0.615353
$245$		0			0
$246$	−32.9380			−2.10005
$247$	−18.7241	+	1.88354i	−1.19138	+	0.119847i
$248$	4.38058	−	7.58739i	0.278167	−	0.481799i
$249$	2.10480	+	1.21520i	0.133386	+	0.0770105i
$250$	−7.99389	−	13.8458i	−0.505578	−	0.875687i
$251$	−21.5247			−1.35863			−0.679313	−	0.733849i	$-0.737722\pi$
$251$	−21.5247			−1.35863			−0.679313	+	0.733849i	$0.737722\pi$
$252$		0			0
$253$			21.3684i			1.34342i
$254$	2.96656	−	1.71274i	0.186138	−	0.107467i
$255$	3.21959	+	1.85883i	0.201619	+	0.116405i
$256$	16.3127	−	28.2543i	1.01954	−	1.76590i
$257$	−0.330979	−	0.573272i	−0.0206459	−	0.0357597i	0.855518	−	0.517773i	$-0.173239\pi$
$257$	−0.330979	−	0.573272i	−0.0206459	−	0.0357597i	−0.876164	+	0.482014i	$0.839906\pi$
$258$			19.1695i			1.19344i
$259$		0			0
$260$	4.15633	−	9.22425i	0.257764	−	0.572064i
$261$	−0.903032	−	1.56410i	−0.0558963	−	0.0968152i
$262$	26.8582	+	15.5066i	1.65930	+	0.958000i
$263$	−2.59332	+	4.49176i	−0.159911	+	0.276974i	−0.934836	−	0.355079i	$-0.884454\pi$
$263$	−2.59332	+	4.49176i	−0.159911	+	0.276974i	0.774925	+	0.632053i	$0.217787\pi$
$264$	20.0811	+	34.7815i	1.23591	+	2.14065i
$265$		−	2.13093i		−	0.130902i
$266$		0			0
$267$		−	13.0557i		−	0.798996i
$268$	−26.4571	+	15.2750i	−1.61613	+	0.933072i
$269$	−13.6253	+	23.5997i	−0.830749	+	1.43890i	0.0666957	+	0.997773i	$0.478754\pi$
$269$	−13.6253	+	23.5997i	−0.830749	+	1.43890i	−0.897445	+	0.441127i	$0.854579\pi$
$270$	4.48119	−	7.76166i	0.272717	−	0.472359i
$271$	−16.2476	+	9.38058i	−0.986974	+	0.569830i	−0.904368	−	0.426753i	$-0.859657\pi$
$271$	−16.2476	+	9.38058i	−0.986974	+	0.569830i	−0.0826055	+	0.996582i	$0.526324\pi$
$272$	−16.3127			−0.989100
$273$		0			0
$274$	7.95509			0.480585
$275$	17.6353	−	10.1817i	1.06345	−	0.613981i
$276$	16.5999	−	28.7519i	0.999197	−	1.73066i
$277$	7.71203	−	13.3576i	0.463371	−	0.802583i	−0.535755	−	0.844373i	$-0.679973\pi$
$277$	7.71203	−	13.3576i	0.463371	−	0.802583i	0.999126	+	0.0417908i	$0.0133063\pi$
$278$	0.536434	−	0.309711i	0.0321732	−	0.0185752i
$279$		−	0.317575i		−	0.0190127i
$280$		0			0
$281$		−	24.8446i		−	1.48211i	−0.671446	−	0.741053i	$-0.734327\pi$
$281$		−	24.8446i		−	1.48211i	0.671446	−	0.741053i	$-0.265673\pi$
$282$	−16.3532	−	28.3246i	−0.973819	−	1.68670i
$283$	11.4436	−	19.8209i	0.680250	−	1.17823i	−0.294654	−	0.955604i	$-0.595204\pi$
$283$	11.4436	−	19.8209i	0.680250	−	1.17823i	0.974904	−	0.222624i	$-0.0714623\pi$
$284$	27.9184	+	16.1187i	1.65665	+	0.956470i
$285$	−2.95135	−	5.11190i	−0.174823	−	0.302803i
$286$	36.5501	+	16.4690i	2.16125	+	0.973831i
$287$		0			0
$288$			0.312650i			0.0184231i
$289$	3.09697	+	5.36411i	0.182175	+	0.315536i
$290$	7.79995	−	13.5099i	0.458029	−	0.793330i
$291$	26.0844	+	15.0598i	1.52909	+	0.882823i
$292$	54.5110	−	31.4719i	3.19001	−	1.84175i
$293$			25.2193i			1.47333i	0.676258	+	0.736664i	$0.263600\pi$
$293$			25.2193i			1.47333i	−0.676258	+	0.736664i	$0.736400\pi$
$294$		0			0
$295$	1.71767			0.100006
$296$	−3.86177	−	6.68879i	−0.224461	−	0.388778i
$297$	20.7634	+	11.9878i	1.20482	+	0.695602i
$298$	5.00294	−	8.66535i	0.289813	−	0.501970i
$299$	−1.72082	−	17.1066i	−0.0995179	−	0.989298i
$300$	−31.6385			−1.82665
$301$		0			0
$302$	3.89446			0.224101
$303$	−7.82122	−	13.5468i	−0.449317	−	0.778241i
$304$	22.4304	+	12.9502i	1.28647	+	0.742743i
$305$	1.35216	+	0.780671i	0.0774245	+	0.0447011i
$306$	−1.36989	+	0.790905i	−0.0783112	+	0.0452130i
$307$			7.24965i			0.413759i	0.978366	+	0.206880i	$0.0663308\pi$
$307$			7.24965i			0.413759i	−0.978366	+	0.206880i	$0.933669\pi$
$308$		0			0
$309$	10.4485			0.594395
$310$	2.37556	−	1.37153i	0.134923	−	0.0778977i
$311$	−10.1199	+	17.5282i	−0.573847	+	0.993932i	0.422319	+	0.906447i	$0.361216\pi$
$311$	−10.1199	+	17.5282i	−0.573847	+	0.993932i	−0.996166	+	0.0874846i	$0.972117\pi$
$312$	−18.8770	−	26.2274i	−1.06870	−	1.48483i
$313$	16.5684	+	28.6973i	0.936502	+	1.62207i	0.771934	+	0.635703i	$0.219290\pi$
$313$	16.5684	+	28.6973i	0.936502	+	1.62207i	0.164568	+	0.986366i	$0.447377\pi$
$314$		−	7.19394i		−	0.405977i
$315$		0			0
$316$	−60.9438			−3.42836
$317$	14.7338	−	8.50659i	0.827535	−	0.477778i	−0.0254730	−	0.999676i	$-0.508109\pi$
$317$	14.7338	−	8.50659i	0.827535	−	0.477778i	0.853008	+	0.521898i	$0.174776\pi$
$318$	−11.3611	−	6.55936i	−0.637101	−	0.367830i
$319$	36.1408	+	20.8659i	2.02350	+	1.16827i
$320$	3.46410	−	2.00000i	0.193649	−	0.111803i
$321$	12.1359			0.677357
$322$		0			0
$323$			17.1573i			0.954657i
$324$	−17.4162	−	30.1658i	−0.967567	−	1.67588i
$325$	−13.2981	+	9.57122i	−0.737643	+	0.530916i
$326$	−21.4314	+	37.1202i	−1.18697	+	2.05590i
$327$	6.95446	−	4.01516i	0.384582	−	0.222039i
$328$	42.3996			2.34113
$329$		0			0
$330$			12.5745i			0.692204i
$331$	−9.38458	+	5.41819i	−0.515823	+	0.297811i	−0.735224	−	0.677824i	$-0.762923\pi$
$331$	−9.38458	+	5.41819i	−0.515823	+	0.297811i	0.219401	+	0.975635i	$0.429590\pi$
$332$	−5.22241	−	3.01516i	−0.286617	−	0.165478i
$333$	−0.242456	−	0.139982i	−0.0132865	−	0.00767095i
$334$	−20.2132	−	35.0103i	−1.10602	−	1.91568i
$335$	−4.96239			−0.271124
$336$		0			0
$337$	−2.96968			−0.161769			−0.0808845	−	0.996723i	$-0.525774\pi$
$337$	−2.96968			−0.161769			−0.0808845	+	0.996723i	$0.525774\pi$
$338$	−30.5866	−	10.2409i	−1.66369	−	0.557032i
$339$	7.82535	−	13.5539i	0.425014	−	0.736147i
$340$	−7.98844	−	4.61213i	−0.433234	−	0.250128i
$341$	3.66902	+	6.35493i	0.198689	+	0.344139i
$342$	2.51151			0.135807
$343$		0			0
$344$		−	24.6761i		−	1.33045i
$345$	4.67030	−	2.69640i	0.251440	−	0.145169i
$346$	4.67235	+	2.69758i	0.251187	+	0.145023i
$347$	−15.3684	+	26.6188i	−0.825017	+	1.42897i	0.0768897	+	0.997040i	$0.475501\pi$
$347$	−15.3684	+	26.6188i	−0.825017	+	1.42897i	−0.901906	+	0.431931i	$0.857832\pi$
$348$	−32.4191	−	56.1516i	−1.73785	−	3.01004i
$349$			2.00492i			0.107321i	0.998559	+	0.0536606i	$0.0170889\pi$
$349$			2.00492i			0.107321i	−0.998559	+	0.0536606i	$0.982911\pi$
$350$		0			0
$351$	−17.5877	−	7.92478i	−0.938761	−	0.422993i
$352$	−3.61213	−	6.25639i	−0.192527	−	0.333467i
$353$	14.9429	+	8.62729i	0.795330	+	0.459184i	0.841836	−	0.539734i	$-0.181475\pi$
$353$	14.9429	+	8.62729i	0.795330	+	0.459184i	−0.0465055	+	0.998918i	$0.514809\pi$
$354$	5.28726	−	9.15780i	0.281015	−	0.486732i
$355$	2.61824	+	4.53492i	0.138962	+	0.240688i
$356$			32.3938i			1.71687i
$357$		0			0
$358$			1.36836i			0.0723201i
$359$	−6.15441	+	3.55325i	−0.324817	+	0.187533i	−0.653538	−	0.756894i	$-0.726716\pi$
$359$	−6.15441	+	3.55325i	−0.324817	+	0.187533i	0.328721	+	0.944427i	$0.393383\pi$
$360$	−0.350262	+	0.606671i	−0.0184604	+	0.0319744i
$361$	4.12070	−	7.13726i	0.216879	−	0.375645i
$362$	−1.09912	+	0.634580i	−0.0577687	+	0.0333528i
$363$	−15.2120			−0.798425
$364$		0			0
$365$	10.2243			0.535162
$366$	8.32435	−	4.80606i	0.435121	−	0.251217i
$367$	13.6314	−	23.6103i	0.711554	−	1.23245i	−0.252720	−	0.967539i	$-0.581325\pi$
$367$	13.6314	−	23.6103i	0.711554	−	1.23245i	0.964274	−	0.264908i	$-0.0853415\pi$
$368$	−11.8315	+	20.4927i	−0.616757	+	1.06825i
$369$	1.33100	−	0.768452i	0.0692890	−	0.0400040i
$370$		−	2.41819i		−	0.125716i
$371$		0			0
$372$		−	11.4010i		−	0.591117i
$373$	2.95945	+	5.12592i	0.153234	+	0.265410i	0.932415	−	0.361390i	$-0.117698\pi$
$373$	2.95945	+	5.12592i	0.153234	+	0.265410i	−0.779180	+	0.626800i	$0.784364\pi$
$374$	18.2750	−	31.6533i	0.944980	−	1.63675i
$375$	−9.34774	−	5.39692i	−0.482715	−	0.278696i
$376$	21.0508	+	36.4610i	1.08561	+	1.88033i
$377$	−30.6131	−	13.7938i	−1.57665	−	0.710419i
$378$		0			0
$379$			28.9706i			1.48812i	0.668112	+	0.744061i	$0.267103\pi$
$379$			28.9706i			1.48812i	−0.668112	+	0.744061i	$0.732897\pi$
$380$	7.32288	+	12.6836i	0.375656	+	0.650655i
$381$	1.15633	−	2.00281i	0.0592403	−	0.102607i
$382$	−35.5498	−	20.5247i	−1.81889	−	1.05013i
$383$	−20.1128	+	11.6121i	−1.02772	+	0.593352i	−0.916329	−	0.400425i	$-0.868862\pi$
$383$	−20.1128	+	11.6121i	−1.02772	+	0.593352i	−0.111386	+	0.993777i	$0.535529\pi$
$384$		−	30.0263i		−	1.53228i
$385$		0			0
$386$	18.3879			0.935918
$387$	−0.447230	−	0.774625i	−0.0227340	−	0.0393764i
$388$	−64.7205	−	37.3664i	−3.28568	−	1.89699i
$389$	8.06594	−	13.9706i	0.408960	−	0.708339i	−0.585814	−	0.810446i	$-0.699225\pi$
$389$	8.06594	−	13.9706i	0.408960	−	0.708339i	0.994773	+	0.102107i	$0.0325584\pi$
$390$	−1.01264	−	10.0666i	−0.0512772	−	0.509742i
$391$	−15.6751			−0.792725
$392$		0			0
$393$	20.9380			1.05618
$394$	−8.86907	−	15.3617i	−0.446817	−	0.773910i
$395$	−8.57312	−	4.94969i	−0.431360	−	0.249046i
$396$	−3.12819	−	1.80606i	−0.157198	−	0.0907581i
$397$	20.8329	−	12.0279i	1.04557	−	0.603661i	0.124165	−	0.992262i	$-0.460375\pi$
$397$	20.8329	−	12.0279i	1.04557	−	0.603661i	0.921406	+	0.388601i	$0.127041\pi$
$398$		−	12.6556i		−	0.634369i
$399$		0			0
$400$	22.5501			1.12750
$401$	2.40387	−	1.38787i	0.120043	−	0.0693071i	−0.438776	−	0.898596i	$-0.644588\pi$
$401$	2.40387	−	1.38787i	0.120043	−	0.0693071i	0.558819	+	0.829289i	$0.311255\pi$
$402$	−15.2750	+	26.4571i	−0.761850	+	1.31956i
$403$	−3.44903	−	4.79201i	−0.171808	−	0.238707i
$404$	19.4060	+	33.6121i	0.965483	+	1.67227i
$405$		−	5.65799i		−	0.281148i
$406$		0			0
$407$	6.46898			0.320655
$408$	−25.5146	+	14.7308i	−1.26316	+	0.729285i
$409$	−17.4339	−	10.0655i	−0.862051	−	0.497705i	0.00264770	−	0.999996i	$-0.499157\pi$
$409$	−17.4339	−	10.0655i	−0.862051	−	0.497705i	−0.864699	+	0.502291i	$0.832491\pi$
$410$	11.4965	+	6.63752i	0.567773	+	0.327804i
$411$	4.65119	−	2.68536i	0.229426	−	0.132459i
$412$	−25.9248			−1.27722
$413$		0			0
$414$			2.29455i			0.112771i
$415$	−0.489766	−	0.848300i	−0.0240417	−	0.0416414i
$416$	3.39554	+	4.71770i	0.166480	+	0.231304i
$417$	0.209095	−	0.362163i	0.0102394	−	0.0177352i
$418$	−50.2574	+	29.0161i	−2.45817	+	1.41922i
$419$	−0.385503			−0.0188331			−0.00941654	−	0.999956i	$-0.502997\pi$
$419$	−0.385503			−0.0188331			−0.00941654	+	0.999956i	$0.502997\pi$
$420$		0			0
$421$		−	15.6810i		−	0.764246i	−0.924112	−	0.382123i	$-0.875193\pi$
$421$		−	15.6810i		−	0.764246i	0.924112	−	0.382123i	$-0.124807\pi$
$422$	−0.416726	+	0.240597i	−0.0202859	+	0.0117121i
$423$	1.32164	+	0.763050i	0.0642604	+	0.0371008i
$424$	14.6247	+	8.44358i	0.710239	+	0.410057i
$425$	7.46898	+	12.9366i	0.362299	+	0.627519i
$426$	32.2374			1.56191
$427$		0			0
$428$	−30.1114			−1.45549
$429$	26.9295	−	2.70895i	1.30017	−	0.130790i
$430$	3.86296	−	6.69084i	0.186288	−	0.322661i
$431$	1.33100	+	0.768452i	0.0641119	+	0.0370150i	0.531713	−	0.846924i	$-0.321548\pi$
$431$	1.33100	+	0.768452i	0.0641119	+	0.0370150i	−0.467601	+	0.883939i	$0.654882\pi$
$432$	13.2750	+	22.9930i	0.638696	+	1.10625i
$433$	26.0362			1.25122			0.625610	−	0.780136i	$-0.284850\pi$
$433$	26.0362			1.25122			0.625610	+	0.780136i	$0.284850\pi$
$434$		0			0
$435$		−	10.5320i		−	0.504970i
$436$	−17.2554	+	9.96239i	−0.826382	+	0.477112i
$437$	21.5537	+	12.4441i	1.03106	+	0.595280i
$438$	31.4719	−	54.5110i	1.50379	−	2.60463i
$439$	9.56230	+	16.5624i	0.456384	+	0.790479i	0.998767	−	0.0496519i	$-0.0158112\pi$
$439$	9.56230	+	16.5624i	0.456384	+	0.790479i	−0.542383	+	0.840131i	$0.682478\pi$
$440$		−	16.1866i		−	0.771668i
$441$		0			0
$442$	−12.0811	+	26.8119i	−0.574639	+	1.27531i
$443$	6.30900	+	10.9275i	0.299750	+	0.519182i	0.976079	−	0.217418i	$-0.0697635\pi$
$443$	6.30900	+	10.9275i	0.299750	+	0.519182i	−0.676329	+	0.736600i	$0.736430\pi$
$444$	−8.70424	−	5.02539i	−0.413085	−	0.238495i
$445$	−2.63093	+	4.55691i	−0.124718	+	0.216018i
$446$	−7.24354	−	12.5462i	−0.342991	−	0.594079i
$447$		−	6.75528i		−	0.319514i
$448$		0			0
$449$		−	1.02302i		−	0.0482794i	−0.999709	−	0.0241397i	$-0.992315\pi$
$449$		−	1.02302i		−	0.0482794i	0.999709	−	0.0241397i	$-0.00768466\pi$
$450$	1.89369	−	1.09332i	0.0892693	−	0.0515397i
$451$	−17.7562	+	30.7547i	−0.836108	+	1.44818i
$452$	−19.4162	+	33.6299i	−0.913261	+	1.58182i
$453$	2.27701	−	1.31464i	0.106983	−	0.0617669i
$454$	−9.14903			−0.429385
$455$		0			0
$456$	46.7777			2.19056
$457$	−24.7094	+	14.2660i	−1.15586	+	0.667335i	−0.950308	−	0.311312i	$-0.899232\pi$
$457$	−24.7094	+	14.2660i	−1.15586	+	0.667335i	−0.205550	+	0.978647i	$0.565898\pi$
$458$	7.01810	−	12.1557i	0.327934	−	0.567999i
$459$	−8.79384	+	15.2314i	−0.410462	+	0.710940i
$460$	−11.5879	+	6.69029i	−0.540290	+	0.311936i
$461$		−	25.3503i		−	1.18068i	−0.807155	−	0.590340i	$-0.798994\pi$
$461$		−	25.3503i		−	1.18068i	0.807155	−	0.590340i	$-0.201006\pi$
$462$		0			0
$463$			39.6810i			1.84413i	0.387032	+	0.922066i	$0.373500\pi$
$463$			39.6810i			1.84413i	−0.387032	+	0.922066i	$0.626500\pi$
$464$	23.1065	+	40.0216i	1.07269	+	1.85796i
$465$	0.925962	−	1.60381i	0.0429405	−	0.0743751i
$466$	−22.1879	−	12.8102i	−1.02783	−	0.593421i
$467$	0.975792	+	1.69012i	0.0451543	+	0.0782095i	0.887719	−	0.460385i	$-0.152289\pi$
$467$	0.975792	+	1.69012i	0.0451543	+	0.0782095i	−0.842565	+	0.538595i	$0.818955\pi$
$468$	2.64974	+	1.19394i	0.122484	+	0.0551897i
$469$		0			0
$470$			13.1817i			0.608027i
$471$	−2.42842	−	4.20615i	−0.111896	−	0.193809i
$472$	−6.80606	+	11.7884i	−0.313274	+	0.542607i
$473$	17.8989	+	10.3339i	0.822991	+	0.475154i
$474$	−52.7789	+	30.4719i	−2.42422	+	1.39962i
$475$		−	23.7177i		−	1.08824i
$476$		0			0
$477$	0.612127			0.0280274
$478$	27.6507	+	47.8924i	1.26471	+	2.19055i
$479$	22.6351	+	13.0684i	1.03423	+	0.597111i	0.918192	−	0.396135i	$-0.129649\pi$
$479$	22.6351	+	13.0684i	1.03423	+	0.597111i	0.116034	+	0.993245i	$0.462982\pi$
$480$	−0.911603	+	1.57894i	−0.0416088	+	0.0720686i
$481$	−5.17878	+	0.520956i	−0.236132	+	0.0237535i
$482$	73.0127			3.32564
$483$		0			0
$484$	37.7440			1.71564
$485$	−6.06959	−	10.5128i	−0.275606	−	0.477363i
$486$	4.32381	+	2.49635i	0.196132	+	0.113237i
$487$	−18.1540	−	10.4812i	−0.822634	−	0.474948i	0.0286896	−	0.999588i	$-0.490867\pi$
$487$	−18.1540	−	10.4812i	−0.822634	−	0.474948i	−0.851324	+	0.524640i	$0.824200\pi$
$488$	−10.7156	+	6.18664i	−0.485071	+	0.280056i
$489$			28.9380i			1.30862i
$490$		0			0
$491$	2.95651			0.133425			0.0667127	−	0.997772i	$-0.478749\pi$
$491$	2.95651			0.133425			0.0667127	+	0.997772i	$0.478749\pi$
$492$	47.7833	−	27.5877i	2.15424	−	1.24375i
$493$	−15.3065	+	26.5117i	−0.689372	+	1.19403i
$494$	37.8971	−	27.2763i	1.70507	−	1.22722i
$495$	−0.293367	−	0.508127i	−0.0131859	−	0.0228386i
$496$			8.12601i			0.364869i
$497$		0			0
$498$	−6.03032			−0.270225
$499$	2.47205	−	1.42724i	0.110664	−	0.0638920i	−0.443646	−	0.896202i	$-0.646315\pi$
$499$	2.47205	−	1.42724i	0.110664	−	0.0638920i	0.554311	+	0.832310i	$0.312982\pi$
$500$	23.1936	+	13.3908i	1.03725	+	0.598855i
$501$	−23.6366	−	13.6466i	−1.05600	−	0.609684i
$502$	46.2518	−	26.7035i	2.06432	−	1.19183i
$503$	23.8641			1.06405			0.532025	−	0.846729i	$-0.321431\pi$
$503$	23.8641			1.06405			0.532025	+	0.846729i	$0.321431\pi$
$504$		0			0
$505$			6.30440i			0.280542i
$506$	−26.5095	−	45.9158i	−1.17849	−	2.04121i
$507$	−21.3404	+	4.33734i	−0.947760	+	0.192628i
$508$	−2.86907	+	4.96937i	−0.127294	+	0.220480i
$509$	9.69506	−	5.59745i	0.429726	−	0.248102i	−0.269504	−	0.962999i	$-0.586860\pi$
$509$	9.69506	−	5.59745i	0.429726	−	0.248102i	0.699230	+	0.714897i	$0.253526\pi$
$510$	−9.22425			−0.408457
$511$		0			0
$512$			45.1002i			1.99316i
$513$	24.1836	−	13.9624i	1.06773	−	0.616455i
$514$	1.42240	+	0.821222i	0.0627393	+	0.0362226i
$515$	−3.64690	−	2.10554i	−0.160702	−	0.0927812i
$516$	−16.0557	−	27.8093i	−0.706813	−	1.22424i
$517$	−35.2628			−1.55086
$518$		0			0
$519$	3.64244			0.159886
$520$	1.30353	+	12.9583i	0.0571637	+	0.568259i
$521$	13.2447	−	22.9405i	0.580262	−	1.00504i	−0.415186	−	0.909736i	$-0.636284\pi$
$521$	13.2447	−	22.9405i	0.580262	−	1.00504i	0.995448	−	0.0953065i	$-0.0303831\pi$
$522$	3.88083	+	2.24060i	0.169859	+	0.0980683i
$523$	6.47627	+	11.2172i	0.283188	+	0.490495i	0.972168	−	0.234285i	$-0.0752748\pi$
$523$	6.47627	+	11.2172i	0.283188	+	0.490495i	−0.688981	+	0.724780i	$0.741941\pi$
$524$	−51.9511			−2.26950
$525$		0			0
$526$		−	12.8691i		−	0.561118i
$527$	−4.66177	+	2.69147i	−0.203070	+	0.117242i
$528$	−32.2600	−	18.6253i	−1.40393	−	0.810562i
$529$	0.130933	−	0.226782i	0.00569272	−	0.00986008i
$530$	2.64363	+	4.57890i	0.114832	+	0.198895i
$531$			0.493413i			0.0214123i
$532$		0			0
$533$	11.7381	−	26.0508i	0.508435	−	1.12838i
$534$	16.1969	+	28.0538i	0.700907	+	1.21401i
$535$	−4.23585	−	2.44557i	−0.183132	−	0.105731i
$536$	19.6629	−	34.0572i	0.849308	−	1.47105i
$537$	0.461911	+	0.800053i	0.0199329	+	0.0345249i
$538$		−	67.6140i		−	2.91505i
$539$		0			0
$540$			15.0132i			0.646064i
$541$	−24.3295	+	14.0467i	−1.04601	+	0.603913i	−0.921529	−	0.388309i	$-0.873059\pi$
$541$	−24.3295	+	14.0467i	−1.04601	+	0.603913i	−0.124479	+	0.992222i	$0.539726\pi$
$542$	23.2750	−	40.3136i	0.999749	−	1.73162i
$543$	−0.428424	+	0.742053i	−0.0183854	+	0.0318445i
$544$	4.58948	−	2.64974i	0.196772	−	0.113607i
$545$	−3.23647			−0.138635
$546$		0			0
$547$	14.8192			0.633625			0.316812	−	0.948488i	$-0.397387\pi$
$547$	14.8192			0.633625			0.316812	+	0.948488i	$0.397387\pi$
$548$	−11.5405	+	6.66291i	−0.492986	+	0.284625i
$549$	−0.224254	+	0.388419i	−0.00957092	+	0.0165773i
$550$	−25.2628	+	43.7565i	−1.07721	+	1.86578i
$551$	42.0938	−	24.3029i	1.79326	−	1.03534i
$552$			42.7367i			1.81900i
$553$		0			0
$554$			38.2701i			1.62594i
$555$	−0.816297	−	1.41387i	−0.0346499	−	0.0600154i
$556$	−0.518806	+	0.898598i	−0.0220023	+	0.0381090i
$557$	−15.9244	−	9.19394i	−0.674737	−	0.389560i	0.123132	−	0.992390i	$-0.460706\pi$
$557$	−15.9244	−	9.19394i	−0.674737	−	0.389560i	−0.797869	+	0.602831i	$0.794039\pi$
$558$	0.393983	+	0.682398i	0.0166786	+	0.0288882i
$559$	−15.1612	−	6.83146i	−0.641253	−	0.288940i
$560$		0			0
$561$		−	24.6761i		−	1.04183i
$562$	30.8222	+	53.3856i	1.30016	+	2.25193i
$563$	−7.66784	+	13.2811i	−0.323161	+	0.559731i	−0.981138	−	0.193307i	$-0.938079\pi$
$563$	−7.66784	+	13.2811i	−0.323161	+	0.559731i	0.657978	+	0.753037i	$0.271412\pi$
$564$	47.4474	+	27.3938i	1.99789	+	1.15349i
$565$	−5.46265	+	3.15386i	−0.229815	+	0.132684i
$566$			56.7875i			2.38696i
$567$		0			0
$568$	−41.4979			−1.74121
$569$	0.661250	+	1.14532i	0.0277210	+	0.0480142i	0.879553	−	0.475801i	$-0.157842\pi$
$569$	0.661250	+	1.14532i	0.0277210	+	0.0480142i	−0.851832	+	0.523815i	$0.824508\pi$
$570$	12.6836	+	7.32288i	0.531258	+	0.306722i
$571$	−18.9587	+	32.8375i	−0.793399	+	1.37421i	0.130452	+	0.991455i	$0.458357\pi$
$571$	−18.9587	+	32.8375i	−0.793399	+	1.37421i	−0.923851	+	0.382752i	$0.874976\pi$
$572$	−66.8173	+	6.72144i	−2.79377	+	0.281038i
$573$	−27.7137			−1.15776
$574$		0			0
$575$	21.6688			0.903651
$576$	0.574515	+	0.995090i	0.0239381	+	0.0414621i
$577$	−11.1394	−	6.43136i	−0.463741	−	0.267741i	0.249875	−	0.968278i	$-0.419611\pi$
$577$	−11.1394	−	6.43136i	−0.463741	−	0.267741i	−0.713616	+	0.700537i	$0.752944\pi$
$578$	−13.3094	−	7.68418i	−0.553598	−	0.319620i
$579$	10.7510	−	6.20711i	0.446798	−	0.257959i
$580$			26.1319i			1.08507i
$581$		0			0
$582$	−74.7328			−3.09777
$583$	−12.2492	+	7.07205i	−0.507308	+	0.292895i
$584$	−40.5125	+	70.1697i	−1.67642	+	2.90364i
$585$	0.275777	+	0.383159i	0.0114020	+	0.0158417i
$586$	−31.2870	−	54.1907i	−1.29246	−	2.23860i
$587$			31.0240i			1.28050i	0.768168	+	0.640248i	$0.221169\pi$
$587$			31.0240i			1.28050i	−0.768168	+	0.640248i	$0.778831\pi$
$588$		0			0
$589$	8.54675			0.352163
$590$	−3.69088	+	2.13093i	−0.151951	+	0.0877291i
$591$	−10.3711	−	5.98778i	−0.426612	−	0.246304i
$592$	6.20388	+	3.58181i	0.254978	+	0.147211i
$593$	−9.88295	+	5.70593i	−0.405844	+	0.234314i	−0.689003	−	0.724759i	$-0.741951\pi$
$593$	−9.88295	+	5.70593i	−0.405844	+	0.234314i	0.283158	+	0.959073i	$0.408618\pi$
$594$	−59.4880			−2.44082
$595$		0			0
$596$			16.7612i			0.686564i
$597$	−4.27210	−	7.39949i	−0.174845	−	0.302841i
$598$	24.9200	+	34.6233i	1.01906	+	1.41585i
$599$	−3.68664	+	6.38545i	−0.150632	+	0.260902i	−0.931460	−	0.363844i	$-0.881464\pi$
$599$	−3.68664	+	6.38545i	−0.150632	+	0.260902i	0.780828	+	0.624746i	$0.214798\pi$
$600$	35.2705	−	20.3634i	1.43991	−	0.831334i
$601$	17.2144			0.702190			0.351095	−	0.936340i	$-0.385809\pi$
$601$	17.2144			0.702190			0.351095	+	0.936340i	$0.385809\pi$
$602$		0			0
$603$		−	1.42548i		−	0.0580502i
$604$	−5.64972	+	3.26187i	−0.229884	+	0.132723i
$605$	5.30954	+	3.06547i	0.215864	+	0.124629i
$606$	33.6121	+	19.4060i	1.36540	+	0.788314i
$607$	−16.2132	−	28.0821i	−0.658074	−	1.13982i	−0.981114	−	0.193433i	$-0.938038\pi$
$607$	−16.2132	−	28.0821i	−0.658074	−	1.13982i	0.323039	−	0.946386i	$-0.395295\pi$
$608$	−8.41422			−0.341242
$609$		0			0
$610$	−3.87399			−0.156853
$611$	28.2299	−	2.83977i	1.14206	−	0.114885i
$612$	1.32487	−	2.29474i	0.0535547	−	0.0927594i
$613$	−30.9163	−	17.8496i	−1.24870	−	0.720937i	−0.277849	−	0.960625i	$-0.589622\pi$
$613$	−30.9163	−	17.8496i	−1.24870	−	0.720937i	−0.970850	+	0.239688i	$0.922955\pi$
$614$	−8.99389	−	15.5779i	−0.362964	−	0.628672i
$615$	8.96239			0.361398
$616$		0			0
$617$		−	20.3733i		−	0.820198i	−0.912041	−	0.410099i	$-0.865494\pi$
$617$		−	20.3733i		−	0.820198i	0.912041	−	0.410099i	$-0.134506\pi$
$618$	−22.4515	+	12.9624i	−0.903132	+	0.521424i
$619$	34.6512	+	20.0059i	1.39275	+	0.804104i	0.993619	−	0.112790i	$-0.0359787\pi$
$619$	34.6512	+	20.0059i	1.39275	+	0.804104i	0.399130	+	0.916894i	$0.369312\pi$
$620$	−2.29749	+	3.97937i	−0.0922695	+	0.159815i
$621$	12.7562	+	22.0944i	0.511890	+	0.886620i
$622$		−	50.2189i		−	2.01359i
$623$		0			0
$624$	27.3258	+	12.3127i	1.09391	+	0.492900i
$625$	−9.18536	−	15.9095i	−0.367415	−	0.636381i
$626$	−71.2036	−	41.1094i	−2.84587	−	1.64306i
$627$	−19.5897	+	33.9303i	−0.782336	+	1.35505i
$628$	6.02539	+	10.4363i	0.240439	+	0.416453i
$629$			4.74543i			0.189213i
$630$		0			0
$631$		−	16.3879i		−	0.652391i	−0.945302	−	0.326195i	$-0.894233\pi$
$631$		−	16.3879i		−	0.652391i	0.945302	−	0.326195i	$-0.105767\pi$
$632$	67.9401	−	39.2252i	2.70251	−	1.56030i
$633$	−0.162435	+	0.281345i	−0.00645619	+	0.0111825i
$634$	−21.1065	+	36.5575i	−0.838246	+	1.45188i
$635$	−0.807198	+	0.466036i	−0.0320327	+	0.0184941i
$636$	21.9756			0.871388
$637$		0			0
$638$	−103.545			−4.09937
$639$	−1.30269	+	0.752109i	−0.0515336	+	0.0297530i
$640$	−6.05079	+	10.4803i	−0.239178	+	0.414269i
$641$	−4.11942	+	7.13505i	−0.162707	+	0.281817i	−0.935839	−	0.352428i	$-0.885356\pi$
$641$	−4.11942	+	7.13505i	−0.162707	+	0.281817i	0.773131	+	0.634246i	$0.218689\pi$
$642$	−26.0773	+	15.0557i	−1.02919	+	0.594201i
$643$			30.4847i			1.20220i	0.799174	+	0.601100i	$0.205271\pi$
$643$			30.4847i			1.20220i	−0.799174	+	0.601100i	$0.794729\pi$
$644$		0			0
$645$		−	5.21600i		−	0.205380i
$646$	−21.2853	−	36.8672i	−0.837458	−	1.45052i
$647$	14.4194	−	24.9751i	0.566884	−	0.981872i	−0.429988	−	0.902835i	$-0.641482\pi$
$647$	14.4194	−	24.9751i	0.566884	−	0.981872i	0.996872	−	0.0790373i	$-0.0251846\pi$
$648$	38.8311	+	22.4191i	1.52543	+	0.880707i
$649$	−5.70052	−	9.87360i	−0.223765	−	0.387573i
$650$	16.7005	−	37.0640i	0.655048	−	1.45377i
$651$		0			0
$652$		−	71.8007i		−	2.81193i
$653$	−10.7259	−	18.5778i	−0.419738	−	0.727007i	0.576175	−	0.817326i	$-0.304545\pi$
$653$	−10.7259	−	18.5778i	−0.419738	−	0.727007i	−0.995913	+	0.0903194i	$0.971211\pi$
$654$	−9.96239	+	17.2554i	−0.389560	+	0.674738i
$655$	−7.30809	−	4.21933i	−0.285551	−	0.164863i
$656$	−34.0572	+	19.6629i	−1.32971	+	0.767708i
$657$			2.93700i			0.114583i
$658$		0			0
$659$	−50.6589			−1.97339			−0.986696	−	0.162575i	$-0.948020\pi$
$659$	−50.6589			−1.97339			−0.986696	+	0.162575i	$0.948020\pi$
$660$	−10.5320	−	18.2419i	−0.409957	−	0.710066i
$661$	13.4647	+	7.77385i	0.523717	+	0.302368i	0.738454	−	0.674304i	$-0.235556\pi$
$661$	13.4647	+	7.77385i	0.523717	+	0.302368i	−0.214737	+	0.976672i	$0.568890\pi$
$662$	13.4436	−	23.2850i	0.522500	−	0.904996i
$663$	1.98720	+	19.7546i	0.0771765	+	0.767204i
$664$	7.76257			0.301246
$665$		0			0
$666$	0.694644			0.0269169
$667$	22.2035	+	38.4575i	0.859722	+	1.48908i
$668$	58.6469	+	33.8598i	2.26912	+	1.31007i
$669$	−8.47031	−	4.89034i	−0.327481	−	0.189071i
$670$	10.6631	−	6.15633i	0.411950	−	0.237840i
$671$		−	10.3634i		−	0.400076i
$672$		0			0
$673$	26.8700			1.03576			0.517882	−	0.855452i	$-0.326721\pi$
$673$	26.8700			1.03576			0.517882	+	0.855452i	$0.326721\pi$
$674$	6.38119	−	3.68418i	0.245794	−	0.141909i
$675$	12.1563	−	21.0554i	0.467897	−	0.810422i
$676$	52.9497	−	10.7618i	2.03653	−	0.413915i
$677$	−8.18783	−	14.1817i	−0.314684	−	0.545048i	0.664686	−	0.747122i	$-0.268565\pi$
$677$	−8.18783	−	14.1817i	−0.314684	−	0.545048i	−0.979370	+	0.202074i	$0.935232\pi$
$678$			38.8324i			1.49135i
$679$		0			0
$680$	11.8740			0.455347
$681$	−5.34926	+	3.08840i	−0.204984	+	0.118348i
$682$	−15.7678	−	9.10356i	−0.603781	−	0.348593i
$683$	13.6821	+	7.89938i	0.523532	+	0.302262i	0.738379	−	0.674386i	$-0.235592\pi$
$683$	13.6821	+	7.89938i	0.523532	+	0.302262i	−0.214846	+	0.976648i	$0.568925\pi$
$684$	−3.64346	+	2.10356i	−0.139311	+	0.0804314i
$685$	−2.16457			−0.0827041
$686$		0			0
$687$		−	9.47627i		−	0.361542i
$688$	11.4436	+	19.8209i	0.436283	+	0.755663i
$689$	9.23661	−	6.64801i	0.351887	−	0.253269i
$690$	−6.69029	+	11.5879i	−0.254695	+	0.441145i
$691$	−6.55423	+	3.78409i	−0.249335	+	0.143953i	−0.619460	−	0.785029i	$-0.712648\pi$
$691$	−6.55423	+	3.78409i	−0.249335	+	0.143953i	0.370125	+	0.928982i	$0.379315\pi$
$692$	−9.03761			−0.343558
$693$		0			0
$694$		−	76.2638i		−	2.89493i
$695$	−0.145963	+	0.0842720i	−0.00553671	+	0.00319662i
$696$	72.2816	+	41.7318i	2.73983	+	1.58184i
$697$	−22.5606	−	13.0254i	−0.854545	−	0.493372i
$698$	−2.48730	−	4.30814i	−0.0941458	−	0.163065i
$699$	−17.2971			−0.654237
$700$		0			0
$701$	−32.6629			−1.23366			−0.616831	−	0.787096i	$-0.711584\pi$
$701$	−32.6629			−1.23366			−0.616831	+	0.787096i	$0.711584\pi$
$702$	47.6235	−	4.79066i	1.79743	−	0.180812i
$703$	3.76727	−	6.52510i	0.142085	−	0.246099i
$704$	−22.9930	−	13.2750i	−0.866583	−	0.500322i
$705$	4.44969	+	7.70709i	0.167585	+	0.290266i
$706$	−42.8119			−1.61125
$707$		0			0
$708$			17.7137i			0.665722i
$709$	21.6692	−	12.5107i	0.813803	−	0.469850i	−0.0344715	−	0.999406i	$-0.510975\pi$
$709$	21.6692	−	12.5107i	0.813803	−	0.469850i	0.848275	+	0.529556i	$0.177641\pi$
$710$	−11.2520	−	6.49635i	−0.422281	−	0.243804i
$711$	1.42184	−	2.46269i	0.0533231	−	0.0923583i
$712$	−20.8496	−	36.1125i	−0.781370	−	1.35337i
$713$			7.80843i			0.292428i
$714$		0			0
$715$	−9.94525	−	4.48119i	−0.371931	−	0.167587i
$716$	−1.14609	−	1.98509i	−0.0428314	−	0.0741862i
$717$	32.3336	+	18.6678i	1.20752	+	0.697163i
$718$	8.81630	−	15.2703i	0.329021	−	0.569882i
$719$	−0.925962	−	1.60381i	−0.0345326	−	0.0598121i	0.848243	−	0.529608i	$-0.177661\pi$
$719$	−0.925962	−	1.60381i	−0.0345326	−	0.0598121i	−0.882775	+	0.469796i	$0.844328\pi$
$720$		−	0.649738i		−	0.0242143i
$721$		0			0
$722$			20.4485i			0.761015i
$723$	42.6891	−	24.6466i	1.58763	−	0.916616i
$724$	1.06300	−	1.84118i	0.0395062	−	0.0684268i
$725$	21.1593	−	36.6489i	0.785835	−	1.36111i
$726$	32.6873	−	18.8720i	1.21314	−	0.700406i
$727$	−10.8265			−0.401534			−0.200767	−	0.979639i	$-0.564343\pi$
$727$	−10.8265			−0.401534			−0.200767	+	0.979639i	$0.564343\pi$
$728$		0			0
$729$	28.5125			1.05602
$730$	−21.9696	+	12.6842i	−0.813133	+	0.469463i
$731$	−7.58062	+	13.1300i	−0.280380	+	0.485632i
$732$	−8.05079	+	13.9444i	−0.297566	+	0.515399i
$733$	20.2879	−	11.7132i	0.749350	−	0.432638i	−0.0761088	−	0.997100i	$-0.524250\pi$
$733$	20.2879	−	11.7132i	0.749350	−	0.432638i	0.825459	+	0.564462i	$0.190916\pi$
$734$			67.6444i			2.49680i
$735$		0			0
$736$		−	7.68735i		−	0.283359i
$737$	16.4690	+	28.5251i	0.606643	+	1.05074i
$738$	−1.90668	+	3.30246i	−0.0701858	+	0.121565i
$739$	−0.416726	−	0.240597i	−0.0153295	−	0.00885051i	0.492316	−	0.870417i	$-0.336151\pi$
$739$	−0.416726	−	0.240597i	−0.0153295	−	0.00885051i	−0.507645	+	0.861566i	$0.669484\pi$
$740$	2.02539	+	3.50808i	0.0744549	+	0.128960i
$741$	12.9502	−	28.7407i	0.475736	−	1.05582i
$742$		0			0
$743$		−	13.7889i		−	0.505866i	−0.967484	−	0.252933i	$-0.918605\pi$
$743$		−	13.7889i		−	0.505866i	0.967484	−	0.252933i	$-0.0813953\pi$
$744$	7.33804	+	12.7099i	0.269026	+	0.465966i
$745$	−1.36130	+	2.35783i	−0.0498740	+	0.0863843i
$746$	−12.7184	−	7.34297i	−0.465653	−	0.268845i
$747$	0.243681	−	0.140689i	0.00891581	−	0.00514754i
$748$			61.2262i			2.23865i
$749$		0			0
$750$	26.7816			0.977927
$751$	−13.2308	−	22.9165i	−0.482800	−	0.836235i	0.517005	−	0.855983i	$-0.327047\pi$
$751$	−13.2308	−	22.9165i	−0.482800	−	0.836235i	−0.999805	+	0.0197480i	$0.993714\pi$
$752$	−33.8177	−	19.5247i	−1.23321	−	0.711992i
$753$	18.0283	−	31.2260i	0.656989	−	1.13794i
$754$	82.8933	−	8.33860i	3.01880	−	0.303674i
$755$	−1.05968			−0.0385657
$756$		0			0
$757$	−21.1114			−0.767308			−0.383654	−	0.923477i	$-0.625334\pi$
$757$	−21.1114			−0.767308			−0.383654	+	0.923477i	$0.625334\pi$
$758$	−35.9409	−	62.2514i	−1.30543	−	2.26107i
$759$	−30.9992	−	17.8974i	−1.12520	−	0.649634i
$760$	−16.3271	−	9.42644i	−0.592245	−	0.341933i
$761$	−24.7031	+	14.2623i	−0.895487	+	0.517010i	−0.875733	−	0.482795i	$-0.839621\pi$
$761$	−24.7031	+	14.2623i	−0.895487	+	0.517010i	−0.0197536	+	0.999805i	$0.506288\pi$
$762$			5.73813i			0.207871i
$763$		0			0
$764$	68.7631			2.48776
$765$	0.372745	−	0.215205i	0.0134766	−	0.00778074i
$766$	28.8119	−	49.9037i	1.04102	−	1.80310i
$767$	5.35872	+	7.44529i	0.193492	+	0.268834i
$768$	27.3258	+	47.3297i	0.986036	+	1.70786i
$769$		−	25.8388i		−	0.931769i	−0.884845	−	0.465885i	$-0.845736\pi$
$769$		−	25.8388i		−	0.931769i	0.884845	−	0.465885i	$-0.154264\pi$
$770$		0			0
$771$	1.10886			0.0399348
$772$	−26.6754	+	15.4010i	−0.960069	+	0.554296i
$773$	23.7300	+	13.7005i	0.853509	+	0.492774i	0.861833	−	0.507192i	$-0.169316\pi$
$773$	23.7300	+	13.7005i	0.853509	+	0.492774i	−0.00832435	+	0.999965i	$0.502650\pi$
$774$	1.92200	+	1.10966i	0.0690847	+	0.0398861i
$775$	6.44428	−	3.72061i	0.231485	−	0.133648i
$776$	96.2003			3.45339
$777$		0			0
$778$			40.0263i			1.43501i
$779$	20.6810	+	35.8206i	0.740974	+	1.28340i
$780$	9.90048	+	13.7555i	0.354494	+	0.492527i
$781$	17.3786	−	30.1006i	0.621855	−	1.07708i
$782$	33.6824	−	19.4465i	1.20448	−	0.695406i
$783$	49.8251			1.78060
$784$		0			0
$785$			1.95746i			0.0698649i
$786$	−44.9910	+	25.9756i	−1.60478	+	0.926518i
$787$	−26.8676	−	15.5120i	−0.957725	−	0.552943i	−0.0622528	−	0.998060i	$-0.519828\pi$
$787$	−26.8676	−	15.5120i	−0.957725	−	0.552943i	−0.895472	+	0.445118i	$0.853162\pi$
$788$	25.7328	+	14.8568i	0.916694	+	0.529253i
$789$	−4.34415	−	7.52429i	−0.154656	−	0.267872i
$790$	24.5623			0.873887
$791$		0			0
$792$	4.64974			0.165221
$793$	0.834582	+	8.29651i	0.0296369	+	0.294618i
$794$	−29.8434	+	51.6904i	−1.05910	+	1.83442i
$795$	3.09136	+	1.78480i	0.109639	+	0.0633002i
$796$	10.5999	+	18.3596i	0.375704	+	0.650738i
$797$	−16.1378			−0.571629			−0.285815	−	0.958285i	$-0.592264\pi$
$797$	−16.1378			−0.571629			−0.285815	+	0.958285i	$0.592264\pi$
$798$		0			0
$799$		−	25.8677i		−	0.915132i
$800$	−6.34435	+	3.66291i	−0.224307	+	0.129503i
$801$	−1.30901	−	0.755756i	−0.0462515	−	0.0267033i
$802$	−3.44358	+	5.96446i	−0.121597	+	0.210612i
$803$	−33.9318	−	58.7717i	−1.19743	−	2.07401i
$804$		−	51.1754i		−	1.80482i
$805$		0			0
$806$	13.3561	+	6.01810i	0.470450	+	0.211978i
$807$	−22.8242	−	39.5326i	−0.803449	−	1.39161i
$808$	−43.2675	−	24.9805i	−1.52214	−	0.878810i
$809$	5.17513	−	8.96359i	0.181948	−	0.315143i	−0.760596	−	0.649226i	$-0.775093\pi$
$809$	5.17513	−	8.96359i	0.181948	−	0.315143i	0.942544	+	0.334083i	$0.108426\pi$
$810$	7.01928	+	12.1578i	0.246632	+	0.427180i
$811$		−	46.3752i		−	1.62845i	−0.580547	−	0.814227i	$-0.697161\pi$
$811$		−	46.3752i		−	1.62845i	0.580547	−	0.814227i	$-0.302839\pi$
$812$		0			0
$813$		−	31.4274i		−	1.10221i
$814$	−13.9004	+	8.02539i	−0.487208	+	0.281290i
$815$	5.83146	−	10.1004i	0.204267	−	0.353801i
$816$	13.6629	−	23.6649i	0.478298	−	0.828436i
$817$	20.8471	−	12.0361i	0.729349	−	0.421090i
$818$	49.9488			1.74642
$819$		0			0
$820$	−22.2374			−0.776565
$821$	−48.0980	+	27.7694i	−1.67863	+	0.969159i	−0.716098	+	0.698000i	$0.754074\pi$
$821$	−48.0980	+	27.7694i	−1.67863	+	0.969159i	−0.962534	+	0.271159i	$0.912593\pi$
$822$	−6.66291	+	11.5405i	−0.232396	+	0.402521i
$823$	−10.4162	+	18.0414i	−0.363086	+	0.628884i	−0.988467	−	0.151436i	$-0.951610\pi$
$823$	−10.4162	+	18.0414i	−0.363086	+	0.628884i	0.625381	+	0.780320i	$0.284944\pi$
$824$	28.9009	−	16.6859i	1.00681	−	0.581282i
$825$			34.1114i			1.18761i
$826$		0			0
$827$			2.47295i			0.0859927i	0.999075	+	0.0429964i	$0.0136904\pi$
$827$			2.47295i			0.0859927i	−0.999075	+	0.0429964i	$0.986310\pi$
$828$	−1.92184	−	3.32872i	−0.0667885	−	0.115681i
$829$	−17.2811	+	29.9318i	−0.600199	+	1.03958i	0.392591	+	0.919713i	$0.371579\pi$
$829$	−17.2811	+	29.9318i	−0.600199	+	1.03958i	−0.992791	+	0.119862i	$0.961755\pi$
$830$	2.10480	+	1.21520i	0.0730585	+	0.0421804i
$831$	12.9187	+	22.3758i	0.448144	+	0.776208i
$832$	19.4763	+	8.77575i	0.675218	+	0.304244i
$833$		0			0
$834$			1.03761i			0.0359295i
$835$	5.50000	+	9.52628i	0.190335	+	0.329670i
$836$	48.6058	−	84.1877i	1.68107	−	2.91169i
$837$	7.58739	+	4.38058i	0.262258	+	0.151415i
$838$	0.828361	−	0.478255i	0.0286153	−	0.0165210i
$839$		−	39.9149i		−	1.37802i	−0.724754	−	0.689008i	$-0.758046\pi$
$839$		−	39.9149i		−	1.37802i	0.724754	−	0.689008i	$-0.241954\pi$
$840$		0			0
$841$	57.7255			1.99053
$842$	19.4538	+	33.6950i	0.670423	+	1.16121i
$843$	36.0423	+	20.8090i	1.24136	+	0.716700i
$844$	0.403032	−	0.698071i	0.0138729	−	0.0240286i
$845$	8.32260	+	2.78654i	0.286306	+	0.0958599i
$846$	−3.78655			−0.130184
$847$		0			0
$848$	−15.6629			−0.537867
$849$	19.1695	+	33.2025i	0.657896	+	1.13951i
$850$	−32.0983	−	18.5320i	−1.10096	−	0.635642i
$851$	5.96142	+	3.44183i	0.204355	+	0.117984i
$852$	−46.7670	+	27.0010i	−1.60221	+	0.925037i
$853$		−	32.6507i		−	1.11794i	−0.829188	−	0.558969i	$-0.811197\pi$
$853$		−	32.6507i		−	1.11794i	0.829188	−	0.558969i	$-0.188803\pi$
$854$		0			0
$855$	−0.683380			−0.0233711
$856$	33.5681	−	19.3806i	1.14734	−	0.662415i
$857$	−3.81828	+	6.61346i	−0.130430	+	0.225911i	−0.923842	−	0.382773i	$-0.874969\pi$
$857$	−3.81828	+	6.61346i	−0.130430	+	0.225911i	0.793412	+	0.608684i	$0.208302\pi$
$858$	−54.5047	+	39.2296i	−1.86076	+	1.33928i
$859$	4.48119	+	7.76166i	0.152896	+	0.264824i	0.932291	−	0.361709i	$-0.117807\pi$
$859$	4.48119	+	7.76166i	0.152896	+	0.264824i	−0.779395	+	0.626533i	$0.784473\pi$
$860$			12.9419i			0.441316i
$861$		0			0
$862$	−3.81336			−0.129883
$863$	40.5318	−	23.4010i	1.37972	−	0.796581i	0.387593	−	0.921830i	$-0.373306\pi$
$863$	40.5318	−	23.4010i	1.37972	−	0.796581i	0.992125	+	0.125250i	$0.0399732\pi$
$864$	−7.46973	−	4.31265i	−0.254125	−	0.146719i
$865$	−1.27134	−	0.734010i	−0.0432270	−	0.0249571i
$866$	−55.9460	+	32.3004i	−1.90112	+	1.09761i
$867$	−10.3757			−0.352376
$868$		0			0
$869$			65.7074i			2.22897i
$870$	13.0659	+	22.6309i	0.442977	+	0.767259i
$871$	−15.4815	−	21.5097i	−0.524571	−	0.728827i
$872$	12.8242	−	22.2121i	0.434281	−	0.752197i
$873$	3.01989	−	1.74354i	0.102208	−	0.0590098i
$874$	−61.7523			−2.08880
$875$		0			0
$876$			105.439i			3.56246i
$877$	−8.95522	+	5.17030i	−0.302396	+	0.174589i	−0.643519	−	0.765430i	$-0.722526\pi$
$877$	−8.95522	+	5.17030i	−0.302396	+	0.174589i	0.341123	+	0.940019i	$0.389193\pi$
$878$	−41.0945	−	23.7259i	−1.38687	−	0.800711i
$879$	−36.5858	−	21.1228i	−1.23401	−	0.712456i
$880$	7.50659	+	13.0018i	0.253047	+	0.438290i
$881$	−15.1538			−0.510543			−0.255272	−	0.966869i	$-0.582165\pi$
$881$	−15.1538			−0.510543			−0.255272	+	0.966869i	$0.582165\pi$
$882$		0			0
$883$	51.5983			1.73642			0.868211	−	0.496196i	$-0.165270\pi$
$883$	51.5983			1.73642			0.868211	+	0.496196i	$0.165270\pi$
$884$	−4.93063	−	49.0150i	−0.165835	−	1.64855i
$885$	−1.43866	+	2.49183i	−0.0483600	+	0.0837619i
$886$	−27.1133	−	15.6539i	−0.910889	−	0.525902i
$887$	−2.09332	−	3.62574i	−0.0702868	−	0.121740i	0.828740	−	0.559634i	$-0.189058\pi$
$887$	−2.09332	−	3.62574i	−0.0702868	−	0.121740i	−0.899027	+	0.437893i	$0.855725\pi$
$888$	12.9380			0.434169
$889$		0			0
$890$		−	13.0557i		−	0.437628i
$891$	−32.5236	+	18.7775i	−1.08958	+	0.629070i
$892$	21.0165	+	12.1339i	0.703684	+	0.406272i
$893$	−20.5356	+	35.5687i	−0.687199	+	1.19026i
$894$	8.38058	+	14.5156i	0.280288	+	0.485474i
$895$		−	0.372330i		−	0.0124456i
$896$		0			0
$897$	26.2579	+	11.8315i	0.876726	+	0.395041i
$898$	1.26916	+	2.19825i	0.0423524	+	0.0733565i
$899$	13.2066	+	7.62482i	0.440464	+	0.254302i
$900$	−1.83146	+	3.17217i	−0.0610485	+	0.105739i
$901$	−5.18783	−	8.98558i	−0.172832	−	0.299353i
$902$		−	88.1133i		−	2.93385i
$903$		0			0
$904$		−	49.9873i		−	1.66255i
$905$	0.299071	−	0.172669i	0.00994145	−	0.00573970i
$906$	−3.26187	+	5.64972i	−0.108368	+	0.187699i
$907$	−4.80242	+	8.31803i	−0.159462	+	0.276196i	−0.934675	−	0.355504i	$-0.884309\pi$
$907$	−4.80242	+	8.31803i	−0.159462	+	0.276196i	0.775213	+	0.631700i	$0.217642\pi$
$908$	13.2726	−	7.66291i	0.440465	−	0.254303i
$909$	−1.81099			−0.0600667
$910$		0			0
$911$	−1.82653			−0.0605157			−0.0302578	−	0.999542i	$-0.509633\pi$
$911$	−1.82653			−0.0605157			−0.0302578	+	0.999542i	$0.509633\pi$
$912$	−37.5738	+	21.6932i	−1.24419	+	0.718335i
$913$	−3.25083	+	5.63060i	−0.107587	+	0.186346i
$914$	35.3967	−	61.3089i	1.17082	−	2.02792i
$915$	−2.26505	+	1.30773i	−0.0748802	+	0.0432321i
$916$			23.5125i			0.776874i
$917$		0			0
$918$		−	43.6385i		−	1.44028i
$919$	−7.89209	−	13.6695i	−0.260336	−	0.450915i	0.705995	−	0.708217i	$-0.250500\pi$
$919$	−7.89209	−	13.6695i	−0.260336	−	0.450915i	−0.966331	+	0.257301i	$0.917167\pi$
$920$	8.61213	−	14.9166i	0.283933	−	0.491787i
$921$	−10.5171	−	6.07205i	−0.346550	−	0.200081i
$922$	31.4495	+	54.4721i	1.03573	+	1.79394i
$923$	−11.4885	+	25.4967i	−0.378148	+	0.839235i
$924$		0			0
$925$		−	6.55993i		−	0.215689i
$926$	−49.2281	−	85.2657i	−1.61774	−	2.80200i
$927$	0.604833	−	1.04760i	0.0198653	−	0.0344077i
$928$	−13.0018	−	7.50659i	−0.426805	−	0.246416i
$929$	14.5502	−	8.40057i	0.477377	−	0.275614i	−0.241946	−	0.970290i	$-0.577786\pi$
$929$	14.5502	−	8.40057i	0.477377	−	0.275614i	0.719323	+	0.694676i	$0.244452\pi$
$930$			4.59498i			0.150675i
$931$		0			0
$932$	42.9175			1.40581
$933$	−16.9522	−	29.3620i	−0.554989	−	0.961268i
$934$	−4.19352	−	2.42113i	−0.137216	−	0.0792218i
$935$	−4.97262	+	8.61284i	−0.162622	+	0.281670i
$936$	−3.72237	+	0.374450i	−0.121670	+	0.0122393i
$937$	−38.3004			−1.25122			−0.625610	−	0.780136i	$-0.715150\pi$
$937$	−38.3004			−1.25122			−0.625610	+	0.780136i	$0.715150\pi$
$938$		0			0
$939$	−55.5085			−1.81145
$940$	−11.0406	−	19.1228i	−0.360103	−	0.623717i
$941$	−39.1873	−	22.6248i	−1.27747	−	0.737548i	−0.301088	−	0.953596i	$-0.597350\pi$
$941$	−39.1873	−	22.6248i	−1.27747	−	0.737548i	−0.976383	+	0.216048i	$0.930683\pi$
$942$	10.4363	+	6.02539i	0.340033	+	0.196318i
$943$	−32.7262	+	18.8945i	−1.06571	+	0.615288i
$944$		−	12.6253i		−	0.410919i
$945$		0			0
$946$	−51.2809			−1.66729
$947$	4.10212	−	2.36836i	0.133301	−	0.0769614i	−0.431867	−	0.901938i	$-0.642145\pi$
$947$	4.10212	−	2.36836i	0.133301	−	0.0769614i	0.565168	+	0.824976i	$0.308812\pi$
$948$	51.0444	−	88.4116i	1.65785	−	2.87147i
$949$	31.8973	+	44.3174i	1.03543	+	1.43860i
$950$	29.4241	+	50.9640i	0.954643	+	1.65349i
$951$			28.4993i			0.924153i
$952$		0			0
$953$	−44.8007			−1.45124			−0.725618	−	0.688098i	$-0.758446\pi$
$953$	−44.8007			−1.45124			−0.725618	+	0.688098i	$0.758446\pi$
$954$	−1.31532	+	0.759403i	−0.0425852	+	0.0245866i
$955$	9.67307	+	5.58475i	0.313013	+	0.180718i
$956$	−80.2260	−	46.3185i	−2.59470	−	1.49805i
$957$	−60.5406	+	34.9531i	−1.95700	+	1.12987i
$958$	−64.8505			−2.09522
$959$		0			0
$960$			6.70052i			0.216258i
$961$	−14.1593	−	24.5246i	−0.456750	−	0.791115i
$962$	10.4817	−	7.54419i	0.337945	−	0.243235i
$963$	0.702508	−	1.21678i	0.0226380	−	0.0392102i
$964$	−105.920	+	61.1529i	−3.41145	+	1.96960i
$965$	−5.00332			−0.161063
$966$		0			0
$967$			40.6843i			1.30832i	0.756356	+	0.654160i	$0.226978\pi$
$967$			40.6843i			1.30832i	−0.756356	+	0.654160i	$0.773022\pi$
$968$	−42.0769	+	24.2931i	−1.35240	+	0.780811i
$969$	−24.8902	−	14.3703i	−0.799587	−	0.461642i
$970$	26.0844	+	15.0598i	0.837520	+	0.483542i
$971$	20.7054	+	35.8629i	0.664469	+	1.15089i	0.979429	+	0.201790i	$0.0646758\pi$
$971$	20.7054	+	35.8629i	0.664469	+	1.15089i	−0.314959	+	0.949105i	$0.601991\pi$
$972$	−8.36344			−0.268257
$973$		0			0
$974$	52.0118			1.66656
$975$	−2.74704	−	27.3081i	−0.0879757	−	0.874559i
$976$	5.73813	−	9.93874i	0.183673	−	0.318131i
$977$	43.8271	+	25.3036i	1.40215	+	0.809534i	0.994613	−	0.103653i	$-0.0330532\pi$
$977$	43.8271	+	25.3036i	1.40215	+	0.809534i	0.407540	+	0.913187i	$0.366387\pi$
$978$	−35.9003	−	62.1812i	−1.14797	−	1.98834i
$979$	34.9257			1.11623
$980$		0			0
$981$		−	0.929702i		−	0.0296831i
$982$	−6.35288	+	3.66784i	−0.202729	+	0.117045i
$983$	−21.2567	−	12.2726i	−0.677984	−	0.391434i	0.121111	−	0.992639i	$-0.461354\pi$
$983$	−21.2567	−	12.2726i	−0.677984	−	0.391434i	−0.799095	+	0.601205i	$0.794688\pi$
$984$	−35.5125	+	61.5094i	−1.13210	+	1.96085i
$985$	2.41327	+	4.17990i	0.0768930	+	0.133183i
$986$		−	75.9570i		−	2.41896i
$987$		0			0
$988$	−32.1319	+	71.3112i	−1.02225	+	2.26871i
$989$	10.9964	+	19.0462i	0.349664	+	0.605635i
$990$	1.26076	+	0.727901i	0.0400696	+	0.0231342i
$991$	15.8271	−	27.4133i	0.502764	−	0.870814i	−0.497230	−	0.867619i	$-0.665650\pi$
$991$	15.8271	−	27.4133i	0.502764	−	0.870814i	0.999995	−	0.00319506i	$-0.00101702\pi$
$992$	−1.31994	−	2.28621i	−0.0419083	−	0.0725873i
$993$		−	18.1524i		−	0.576048i
$994$		0			0
$995$			3.44358i			0.109169i
$996$	8.74822	−	5.05079i	0.277198	−	0.160040i
$997$	14.5926	−	25.2751i	0.462153	−	0.800472i	−0.536915	−	0.843636i	$-0.680411\pi$
$997$	14.5926	−	25.2751i	0.462153	−	0.800472i	0.999068	+	0.0431642i	$0.0137439\pi$
$998$	−3.54126	+	6.13364i	−0.112097	+	0.194157i
$999$	6.68879	−	3.86177i	0.211624	−	0.122181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.r.e.116.1		12
7.2	even	3	inner	637.2.r.e.324.6		12
7.3	odd	6		637.2.c.d.246.1		6
7.4	even	3		91.2.c.a.64.1	✓	6
7.5	odd	6		637.2.r.d.324.6		12
7.6	odd	2		637.2.r.d.116.1		12
13.12	even	2	inner	637.2.r.e.116.6		12
21.11	odd	6		819.2.c.b.64.6		6
28.11	odd	6		1456.2.k.c.337.2		6
91.12	odd	6		637.2.r.d.324.1		12
91.18	odd	12		1183.2.a.h.1.1		3
91.25	even	6		91.2.c.a.64.6	yes	6
91.31	even	12		8281.2.a.be.1.1		3
91.38	odd	6		637.2.c.d.246.6		6
91.51	even	6	inner	637.2.r.e.324.1		12
91.60	odd	12		1183.2.a.j.1.3		3
91.73	even	12		8281.2.a.bi.1.3		3
91.90	odd	2		637.2.r.d.116.6		12
273.116	odd	6		819.2.c.b.64.1		6
364.207	odd	6		1456.2.k.c.337.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.c.a.64.1	✓	6	7.4	even	3
91.2.c.a.64.6	yes	6	91.25	even	6
637.2.c.d.246.1		6	7.3	odd	6
637.2.c.d.246.6		6	91.38	odd	6
637.2.r.d.116.1		12	7.6	odd	2
637.2.r.d.116.6		12	91.90	odd	2
637.2.r.d.324.1		12	91.12	odd	6
637.2.r.d.324.6		12	7.5	odd	6
637.2.r.e.116.1		12	1.1	even	1	trivial
637.2.r.e.116.6		12	13.12	even	2	inner
637.2.r.e.324.1		12	91.51	even	6	inner
637.2.r.e.324.6		12	7.2	even	3	inner
819.2.c.b.64.1		6	273.116	odd	6
819.2.c.b.64.6		6	21.11	odd	6
1183.2.a.h.1.1		3	91.18	odd	12
1183.2.a.j.1.3		3	91.60	odd	12
1456.2.k.c.337.1		6	364.207	odd	6
1456.2.k.c.337.2		6	28.11	odd	6
8281.2.a.be.1.1		3	91.31	even	12
8281.2.a.bi.1.3		3	91.73	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.14878 + 1.24060i) q^{2} +(-0.837565 + 1.45071i) q^{3} +(2.07816 - 3.59948i) q^{4} +(0.584680 - 0.337565i) q^{5} -4.15633i q^{6} +5.35026i q^{8} +(0.0969683 + 0.167954i) q^{9} +(-0.837565 + 1.45071i) q^{10} +(-3.88083 - 2.24060i) q^{11} +(3.48119 + 6.02961i) q^{12} +(3.28726 + 1.48119i) q^{13} +1.13093i q^{15} +(-2.48119 - 4.29755i) q^{16} +(1.64363 - 2.84685i) q^{17} +(-0.416726 - 0.240597i) q^{18} +(-4.52007 + 2.60966i) q^{19} -2.80606i q^{20} +11.1187 q^{22} +(-2.38423 - 4.12960i) q^{23} +(-7.76166 - 4.48119i) q^{24} +(-2.27210 + 3.93539i) q^{25} +(-8.90115 + 0.895406i) q^{26} -5.35026 q^{27} -9.31265 q^{29} +(-1.40303 - 2.43012i) q^{30} +(-1.41813 - 0.818760i) q^{31} +(1.39614 + 0.806063i) q^{32} +(6.50089 - 3.75329i) q^{33} +8.15633i q^{34} +0.806063 q^{36} +(-1.25018 + 0.721791i) q^{37} +(6.47508 - 11.2152i) q^{38} +(-4.90207 + 3.52825i) q^{39} +(1.80606 + 3.12819i) q^{40} -7.92478i q^{41} -4.61213 q^{43} +(-16.1300 + 9.31265i) q^{44} +(0.113391 + 0.0654663i) q^{45} +(10.2463 + 5.91573i) q^{46} +(6.81481 - 3.93453i) q^{47} +8.31265 q^{48} -11.2750i q^{50} +(2.75329 + 4.76884i) q^{51} +(12.1630 - 8.75427i) q^{52} +(1.57816 - 2.73346i) q^{53} +(11.4965 - 6.63752i) q^{54} -3.02539 q^{55} -8.74306i q^{57} +(20.0108 - 11.5532i) q^{58} +(2.20334 + 1.27210i) q^{59} +(4.07077 + 2.35026i) q^{60} +(1.15633 + 2.00281i) q^{61} +4.06300 q^{62} +5.92478 q^{64} +(2.42200 - 0.243639i) q^{65} +(-9.31265 + 16.1300i) q^{66} +(-6.36551 - 3.67513i) q^{67} +(-6.83146 - 11.8324i) q^{68} +7.98778 q^{69} +7.75623i q^{71} +(-0.898598 + 0.518806i) q^{72} +(13.1152 + 7.57205i) q^{73} +(1.79090 - 3.10194i) q^{74} +(-3.80606 - 6.59230i) q^{75} +21.6932i q^{76} +(6.15633 - 13.6629i) q^{78} +(-7.33146 - 12.6985i) q^{79} +(-2.90141 - 1.67513i) q^{80} +(4.19029 - 7.25779i) q^{81} +(9.83146 + 17.0286i) q^{82} -1.45088i q^{83} -2.21933i q^{85} +(9.91043 - 5.72179i) q^{86} +(7.79995 - 13.5099i) q^{87} +(11.9878 - 20.7634i) q^{88} +(-6.74967 + 3.89692i) q^{89} -0.324869 q^{90} -19.8192 q^{92} +(2.37556 - 1.37153i) q^{93} +(-9.76234 + 16.9089i) q^{94} +(-1.76187 + 3.05164i) q^{95} +(-2.33872 + 1.35026i) q^{96} -17.9805i q^{97} -0.869067i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 2 q^{9} + 20 q^{12} + 16 q^{13} - 8 q^{16} + 8 q^{17} + 48 q^{22} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 24 q^{27} - 28 q^{29} - 16 q^{30} + 8 q^{36} + 4 q^{38} + 8 q^{39} + 20 q^{40} - 52 q^{43}+ \cdots - 58 q^{95}+O(q^{100}) \) 12 * q + 4 * q^4 + 2 * q^9 + 20 * q^12 + 16 * q^13 - 8 * q^16 + 8 * q^17 + 48 * q^22 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 24 * q^27 - 28 * q^29 - 16 * q^30 + 8 * q^36 + 4 * q^38 + 8 * q^39 + 20 * q^40 - 52 * q^43 + 16 * q^48 - 8 * q^51 + 20 * q^52 - 2 * q^53 + 24 * q^55 - 28 * q^61 + 32 * q^62 - 16 * q^64 + 6 * q^65 - 28 * q^66 - 20 * q^68 - 8 * q^69 + 24 * q^74 - 44 * q^75 + 32 * q^78 - 26 * q^79 + 26 * q^81 + 56 * q^82 + 40 * q^87 + 40 * q^88 - 24 * q^90 - 72 * q^92 - 20 * q^94 - 58 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more