LMFDB - Embedded newform 637.2.f.d.393.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.295");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			393.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.d.295.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-2.36603 - 4.09808i) q^{11} +0.732051 q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.13397 + 3.69615i) q^{17} +4.26795 q^{18} +(1.00000 - 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(-0.633975 - 1.09808i) q^{24} -2.00000 q^{25} +(6.23205 - 0.401924i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +(1.09808 - 1.90192i) q^{30} +6.19615 q^{31} +(-2.59808 + 4.50000i) q^{32} +(-1.73205 + 3.00000i) q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} +3.46410 q^{38} +(-2.63397 + 0.169873i) q^{39} +3.00000 q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +4.73205 q^{44} +(2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +0.928203 q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +3.12436 q^{51} +(2.00000 + 3.00000i) q^{52} +3.92820 q^{53} +(-3.46410 - 6.00000i) q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +(-2.59808 + 4.50000i) q^{58} +(5.36603 - 9.29423i) q^{59} +1.26795 q^{60} +(-7.59808 + 13.1603i) q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(2.76795 - 5.59808i) q^{65} -6.00000 q^{66} +(-2.09808 - 3.63397i) q^{67} +(-2.13397 - 3.69615i) q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(2.13397 - 3.69615i) q^{72} -7.19615 q^{73} +(-6.06218 + 10.5000i) q^{74} +(0.732051 + 1.26795i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +5.80385 q^{79} +(4.33013 + 7.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-4.50000 + 7.79423i) q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} -17.6603 q^{86} +(1.09808 - 1.90192i) q^{87} +(-4.09808 - 7.09808i) q^{88} +(-0.464102 - 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} +(0.803848 + 1.39230i) q^{94} +(1.73205 - 3.00000i) q^{95} +3.80385 q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} + 6 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^4 + 6 * q^6 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} + 24 q^{18} + 4 q^{19} + 6 q^{22} - 6 q^{23} - 6 q^{24} - 8 q^{25} + 18 q^{26} - 16 q^{27} + 6 q^{29} - 6 q^{30} + 4 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} - 14 q^{39} + 12 q^{40} - 10 q^{43} + 12 q^{44} + 12 q^{45} - 6 q^{46} - 24 q^{47} - 10 q^{48} - 36 q^{51} + 8 q^{52} - 12 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} + 12 q^{60} - 20 q^{61} + 18 q^{62} + 4 q^{64} + 18 q^{65} - 24 q^{66} + 2 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} + 44 q^{79} - 2 q^{81} - 18 q^{82} - 12 q^{83} + 6 q^{85} - 36 q^{86} - 6 q^{87} - 6 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} + 24 q^{94} + 36 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 + 6 * q^6 - 2 * q^9 + 6 * q^10 - 6 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 + 24 * q^18 + 4 * q^19 + 6 * q^22 - 6 * q^23 - 6 * q^24 - 8 * q^25 + 18 * q^26 - 16 * q^27 + 6 * q^29 - 6 * q^30 + 4 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 - 14 * q^39 + 12 * q^40 - 10 * q^43 + 12 * q^44 + 12 * q^45 - 6 * q^46 - 24 * q^47 - 10 * q^48 - 36 * q^51 + 8 * q^52 - 12 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 + 12 * q^60 - 20 * q^61 + 18 * q^62 + 4 * q^64 + 18 * q^65 - 24 * q^66 + 2 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 + 12 * q^72 - 8 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 + 44 * q^79 - 2 * q^81 - 18 * q^82 - 12 * q^83 + 6 * q^85 - 36 * q^86 - 6 * q^87 - 6 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 + 24 * q^94 + 36 * q^96 - 8 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	0.990839	+	0.135045i	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	−0.366025	−	0.633975i	−0.211325	−	0.366025i	0.740805	−	0.671721i	$-0.234444\pi$
$3$	−0.366025	−	0.633975i	−0.211325	−	0.366025i	−0.952129	+	0.305695i	$0.901111\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.73205			0.774597			0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205			0.774597			0.387298	+	0.921954i	$0.373408\pi$
$6$	0.633975	−	1.09808i	0.258819	−	0.448288i
$7$		0			0
$7$		0			0
$8$	1.73205			0.612372
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	−0.963580	−	0.267421i	$-0.913828\pi$
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	0.250196	−	0.968195i	$-0.419505\pi$
$12$	0.732051			0.211325
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$		0			0
$15$	−0.633975	−	1.09808i	−0.163692	−	0.283522i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−2.13397	+	3.69615i	−0.517565	+	0.896449i	0.482227	+	0.876046i	$0.339828\pi$
$17$	−2.13397	+	3.69615i	−0.517565	+	0.896449i	−0.999792	+	0.0204023i	$0.993505\pi$
$18$	4.26795			1.00597
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$		0			0
$22$	4.09808	−	7.09808i	0.873713	−	1.51331i
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$	−0.633975	−	1.09808i	−0.129410	−	0.224144i
$25$	−2.00000			−0.400000
$26$	6.23205	−	0.401924i	1.22221	−	0.0788237i
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	1.09808	−	1.90192i	0.200480	−	0.347242i
$31$	6.19615			1.11286			0.556431	−	0.830894i	$-0.312170\pi$
$31$	6.19615			1.11286			0.556431	+	0.830894i	$0.312170\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	−1.73205	+	3.00000i	−0.301511	+	0.522233i
$34$	−7.39230			−1.26777
$35$		0			0
$36$	1.23205	+	2.13397i	0.205342	+	0.355662i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	3.46410			0.561951
$39$	−2.63397	+	0.169873i	−0.421773	+	0.0272014i
$40$	3.00000			0.474342
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	0.994409	−	0.105601i	$-0.0336766\pi$
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	−0.588657	+	0.808383i	$0.700343\pi$
$42$		0			0
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	0.155958	+	0.987764i	$0.450153\pi$
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	−0.933408	+	0.358818i	$0.883180\pi$
$44$	4.73205			0.713384
$45$	2.13397	−	3.69615i	0.318114	−	0.550990i
$46$	1.09808	−	1.90192i	0.161903	−	0.280423i
$47$	0.928203			0.135392			0.0676962	−	0.997706i	$-0.478435\pi$
$47$	0.928203			0.135392			0.0676962	+	0.997706i	$0.478435\pi$
$48$	1.83013	−	3.16987i	0.264156	−	0.457532i
$49$		0			0
$50$	−1.73205	−	3.00000i	−0.244949	−	0.424264i
$51$	3.12436			0.437497
$52$	2.00000	+	3.00000i	0.277350	+	0.416025i
$53$	3.92820			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$54$	−3.46410	−	6.00000i	−0.471405	−	0.816497i
$55$	−4.09808	−	7.09808i	−0.552584	−	0.957104i
$56$		0			0
$57$	−1.46410			−0.193925
$58$	−2.59808	+	4.50000i	−0.341144	+	0.590879i
$59$	5.36603	−	9.29423i	0.698597	−	1.21001i	−0.270356	−	0.962760i	$-0.587141\pi$
$59$	5.36603	−	9.29423i	0.698597	−	1.21001i	0.968953	−	0.247245i	$-0.0795253\pi$
$60$	1.26795			0.163692
$61$	−7.59808	+	13.1603i	−0.972834	+	1.68500i	−0.285929	+	0.958251i	$0.592302\pi$
$61$	−7.59808	+	13.1603i	−0.972834	+	1.68500i	−0.686905	+	0.726747i	$0.741031\pi$
$62$	5.36603	+	9.29423i	0.681486	+	1.18037i
$63$		0			0
$64$	1.00000			0.125000
$65$	2.76795	−	5.59808i	0.343322	−	0.694356i
$66$	−6.00000			−0.738549
$67$	−2.09808	−	3.63397i	−0.256321	−	0.443961i	0.708933	−	0.705276i	$-0.249177\pi$
$67$	−2.09808	−	3.63397i	−0.256321	−	0.443961i	−0.965253	+	0.261316i	$0.915844\pi$
$68$	−2.13397	−	3.69615i	−0.258782	−	0.448224i
$69$	−0.464102	+	0.803848i	−0.0558713	+	0.0967719i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	2.13397	−	3.69615i	0.251491	−	0.435596i
$73$	−7.19615			−0.842246			−0.421123	−	0.907004i	$-0.638364\pi$
$73$	−7.19615			−0.842246			−0.421123	+	0.907004i	$0.638364\pi$
$74$	−6.06218	+	10.5000i	−0.704714	+	1.22060i
$75$	0.732051	+	1.26795i	0.0845299	+	0.146410i
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$		0			0
$78$	−2.53590	−	3.80385i	−0.287134	−	0.430701i
$79$	5.80385			0.652984			0.326492	−	0.945200i	$-0.394133\pi$
$79$	5.80385			0.652984			0.326492	+	0.945200i	$0.394133\pi$
$80$	4.33013	+	7.50000i	0.484123	+	0.838525i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	−8.19615			−0.899645			−0.449822	−	0.893118i	$-0.648513\pi$
$83$	−8.19615			−0.899645			−0.449822	+	0.893118i	$0.648513\pi$
$84$		0			0
$85$	−3.69615	+	6.40192i	−0.400904	+	0.694386i
$86$	−17.6603			−1.90435
$87$	1.09808	−	1.90192i	0.117726	−	0.203908i
$88$	−4.09808	−	7.09808i	−0.436856	−	0.756657i
$89$	−0.464102	−	0.803848i	−0.0491947	−	0.0852077i	0.840379	−	0.541998i	$-0.182332\pi$
$89$	−0.464102	−	0.803848i	−0.0491947	−	0.0852077i	−0.889574	+	0.456791i	$0.848999\pi$
$90$	7.39230			0.779217
$91$		0			0
$92$	1.26795			0.132193
$93$	−2.26795	−	3.92820i	−0.235175	−	0.407336i
$94$	0.803848	+	1.39230i	0.0829105	+	0.143605i
$95$	1.73205	−	3.00000i	0.177705	−	0.307794i
$96$	3.80385			0.388229
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	0.225944	+	0.974140i	$0.427454\pi$
$97$	−7.19615	+	12.4641i	−0.730659	+	1.26554i	−0.956602	+	0.291397i	$0.905880\pi$
$98$		0			0
$99$	−11.6603			−1.17190
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−2.13397	−	3.69615i	−0.212338	−	0.367781i	0.740108	−	0.672489i	$-0.234775\pi$
$101$	−2.13397	−	3.69615i	−0.212338	−	0.367781i	−0.952446	+	0.304708i	$0.901441\pi$
$102$	2.70577	+	4.68653i	0.267911	+	0.464036i
$103$	−6.39230			−0.629853			−0.314926	−	0.949116i	$-0.601980\pi$
$103$	−6.39230			−0.629853			−0.314926	+	0.949116i	$0.601980\pi$
$104$	2.76795	−	5.59808i	0.271420	−	0.548937i
$105$		0			0
$106$	3.40192	+	5.89230i	0.330424	+	0.572311i
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.722991	−	0.690858i	$-0.757233\pi$
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.236805	−	0.971557i	$-0.576100\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	12.3923			1.18697			0.593484	−	0.804846i	$-0.297752\pi$
$109$	12.3923			1.18697			0.593484	+	0.804846i	$0.297752\pi$
$110$	7.09808	−	12.2942i	0.676775	−	1.17221i
$111$	2.56218	−	4.43782i	0.243191	−	0.421219i
$112$		0			0
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	−0.638137	−	0.769923i	$-0.720294\pi$
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	0.985841	+	0.167681i	$0.0536278\pi$
$114$	−1.26795	−	2.19615i	−0.118754	−	0.205689i
$115$	−1.09808	−	1.90192i	−0.102396	−	0.177355i
$116$	−3.00000			−0.278543
$117$	−4.92820	−	7.39230i	−0.455613	−	0.683419i
$118$	18.5885			1.71121
$119$		0			0
$120$	−1.09808	−	1.90192i	−0.100240	−	0.173621i
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	−26.3205			−2.38295
$123$	1.90192	−	3.29423i	0.171491	−	0.297031i
$124$	−3.09808	+	5.36603i	−0.278215	+	0.481883i
$125$	−12.1244			−1.08444
$126$		0			0
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	0.914204	−	0.405254i	$-0.132817\pi$
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	−0.808063	+	0.589097i	$0.799484\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	7.46410			0.657178
$130$	10.7942	−	0.696152i	0.946716	−	0.0610566i
$131$	−3.46410			−0.302660			−0.151330	−	0.988483i	$-0.548356\pi$
$131$	−3.46410			−0.302660			−0.151330	+	0.988483i	$0.548356\pi$
$132$	−1.73205	−	3.00000i	−0.150756	−	0.261116i
$133$		0			0
$134$	3.63397	−	6.29423i	0.313928	−	0.543739i
$135$	−6.92820			−0.596285
$136$	−3.69615	+	6.40192i	−0.316942	+	0.548960i
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.165200	+	0.986260i	$0.552827\pi$
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.771526	+	0.636198i	$0.780506\pi$
$138$	−1.60770			−0.136856
$139$	10.2942	−	17.8301i	0.873145	−	1.51233i	0.0144194	−	0.999896i	$-0.495410\pi$
$139$	10.2942	−	17.8301i	0.873145	−	1.51233i	0.858726	−	0.512436i	$-0.171257\pi$
$140$		0			0
$141$	−0.339746	−	0.588457i	−0.0286118	−	0.0495570i
$142$	−10.3923			−0.872103
$143$	−17.0263	+	1.09808i	−1.42381	+	0.0918257i
$144$	12.3205			1.02671
$145$	2.59808	+	4.50000i	0.215758	+	0.373705i
$146$	−6.23205	−	10.7942i	−0.515768	−	0.893337i
$147$		0			0
$148$	−7.00000			−0.575396
$149$	−0.232051	+	0.401924i	−0.0190103	+	0.0329269i	−0.875374	−	0.483446i	$-0.839385\pi$
$149$	−0.232051	+	0.401924i	−0.0190103	+	0.0329269i	0.856364	+	0.516373i	$0.172718\pi$
$150$	−1.26795	+	2.19615i	−0.103528	+	0.179315i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	1.73205	−	3.00000i	0.140488	−	0.243332i
$153$	5.25833	+	9.10770i	0.425111	+	0.736314i
$154$		0			0
$155$	10.7321			0.862019
$156$	1.16987	−	2.36603i	0.0936648	−	0.189434i
$157$	9.19615			0.733933			0.366966	−	0.930234i	$-0.380396\pi$
$157$	9.19615			0.733933			0.366966	+	0.930234i	$0.380396\pi$
$158$	5.02628	+	8.70577i	0.399869	+	0.692594i
$159$	−1.43782	−	2.49038i	−0.114027	−	0.197500i
$160$	−4.50000	+	7.79423i	−0.355756	+	0.616188i
$161$		0			0
$162$	3.86603	−	6.69615i	0.303744	−	0.526099i
$163$	−2.90192	+	5.02628i	−0.227296	+	0.393689i	−0.957006	−	0.290069i	$-0.906322\pi$
$163$	−2.90192	+	5.02628i	−0.227296	+	0.393689i	0.729710	+	0.683757i	$0.239655\pi$
$164$	−5.19615			−0.405751
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−7.09808	−	12.2942i	−0.550918	−	0.954217i
$167$	12.2942	+	21.2942i	0.951356	+	1.64780i	0.742495	+	0.669852i	$0.233642\pi$
$167$	12.2942	+	21.2942i	0.951356	+	1.64780i	0.208861	+	0.977945i	$0.433024\pi$
$168$		0			0
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$	−12.8038			−0.982010
$171$	−2.46410	−	4.26795i	−0.188435	−	0.326378i
$172$	−5.09808	−	8.83013i	−0.388725	−	0.673291i
$173$	7.73205	−	13.3923i	0.587857	−	1.01820i	−0.406656	−	0.913581i	$-0.633305\pi$
$173$	7.73205	−	13.3923i	0.587857	−	1.01820i	0.994513	−	0.104617i	$-0.0333615\pi$
$174$	3.80385			0.288369
$175$		0			0
$176$	11.8301	−	20.4904i	0.891729	−	1.54452i
$177$	−7.85641			−0.590524
$178$	0.803848	−	1.39230i	0.0602509	−	0.104358i
$179$	−3.46410	−	6.00000i	−0.258919	−	0.448461i	0.707034	−	0.707180i	$-0.250033\pi$
$179$	−3.46410	−	6.00000i	−0.258919	−	0.448461i	−0.965953	+	0.258719i	$0.916700\pi$
$180$	2.13397	+	3.69615i	0.159057	+	0.275495i
$181$	25.5885			1.90198			0.950988	−	0.309229i	$-0.100071\pi$
$181$	25.5885			1.90198			0.950988	+	0.309229i	$0.100071\pi$
$182$		0			0
$183$	11.1244			0.822336
$184$	−1.09808	−	1.90192i	−0.0809513	−	0.140212i
$185$	6.06218	+	10.5000i	0.445700	+	0.771975i
$186$	3.92820	−	6.80385i	0.288030	−	0.498882i
$187$	20.1962			1.47689
$188$	−0.464102	+	0.803848i	−0.0338481	+	0.0586266i
$189$		0			0
$190$	6.00000			0.435286
$191$	−0.633975	+	1.09808i	−0.0458728	+	0.0794540i	−0.888050	−	0.459747i	$-0.847940\pi$
$191$	−0.633975	+	1.09808i	−0.0458728	+	0.0794540i	0.842177	+	0.539201i	$0.181274\pi$
$192$	−0.366025	−	0.633975i	−0.0264156	−	0.0457532i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	−24.9282			−1.78974
$195$	−4.56218	+	0.294229i	−0.326704	+	0.0210702i
$196$		0			0
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$	−10.0981	−	17.4904i	−0.717639	−	1.24299i
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$	−3.46410			−0.244949
$201$	−1.53590	+	2.66025i	−0.108334	+	0.187640i
$202$	3.69615	−	6.40192i	0.260060	−	0.450438i
$203$		0			0
$204$	−1.56218	+	2.70577i	−0.109374	+	0.189442i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	−5.53590	−	9.58846i	−0.385704	−	0.668059i
$207$	−3.12436			−0.217158
$208$	17.9904	−	1.16025i	1.24741	−	0.0804491i
$209$	−9.46410			−0.654646
$210$		0			0
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	−1.96410	+	3.40192i	−0.134895	+	0.233645i
$213$	4.39230			0.300956
$214$	17.1962	−	29.7846i	1.17550	−	2.03603i
$215$	−8.83013	+	15.2942i	−0.602210	+	1.04306i
$216$	−6.92820			−0.471405
$217$		0			0
$218$	10.7321	+	18.5885i	0.726866	+	1.25897i
$219$	2.63397	+	4.56218i	0.177988	+	0.308283i
$220$	8.19615			0.552584
$221$	8.53590	+	12.8038i	0.574187	+	0.861280i
$222$	8.87564			0.595694
$223$	−5.00000	−	8.66025i	−0.334825	−	0.579934i	0.648626	−	0.761107i	$-0.275344\pi$
$223$	−5.00000	−	8.66025i	−0.334825	−	0.579934i	−0.983451	+	0.181173i	$0.942010\pi$
$224$		0			0
$225$	−2.46410	+	4.26795i	−0.164273	+	0.284530i
$226$	12.8038			0.851699
$227$	−5.83013	+	10.0981i	−0.386959	+	0.670233i	−0.992039	−	0.125932i	$-0.959808\pi$
$227$	−5.83013	+	10.0981i	−0.386959	+	0.670233i	0.605080	+	0.796165i	$0.293141\pi$
$228$	0.732051	−	1.26795i	0.0484812	−	0.0839720i
$229$	−6.39230			−0.422415			−0.211208	−	0.977441i	$-0.567740\pi$
$229$	−6.39230			−0.422415			−0.211208	+	0.977441i	$0.567740\pi$
$230$	1.90192	−	3.29423i	0.125409	−	0.217215i
$231$		0			0
$232$	2.59808	+	4.50000i	0.170572	+	0.295439i
$233$	25.8564			1.69391			0.846955	−	0.531665i	$-0.178433\pi$
$233$	25.8564			1.69391			0.846955	+	0.531665i	$0.178433\pi$
$234$	6.82051	−	13.7942i	0.445871	−	0.901757i
$235$	1.60770			0.104874
$236$	5.36603	+	9.29423i	0.349299	+	0.605003i
$237$	−2.12436	−	3.67949i	−0.137992	−	0.239009i
$238$		0			0
$239$	−26.1962			−1.69449			−0.847244	−	0.531204i	$-0.821740\pi$
$239$	−26.1962			−1.69449			−0.847244	+	0.531204i	$0.821740\pi$
$240$	3.16987	−	5.49038i	0.204614	−	0.354403i
$241$	−5.40192	+	9.35641i	−0.347969	+	0.602699i	−0.985888	−	0.167404i	$-0.946462\pi$
$241$	−5.40192	+	9.35641i	−0.347969	+	0.602699i	0.637920	+	0.770103i	$0.279795\pi$
$242$	−19.7321			−1.26842
$243$	−7.63397	+	13.2224i	−0.489720	+	0.848219i
$244$	−7.59808	−	13.1603i	−0.486417	−	0.842499i
$245$		0			0
$246$	6.58846			0.420065
$247$	−4.00000	−	6.00000i	−0.254514	−	0.381771i
$248$	10.7321			0.681486
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−10.5000	−	18.1865i	−0.664078	−	1.15022i
$251$	−11.1962	+	19.3923i	−0.706695	+	1.22403i	0.259382	+	0.965775i	$0.416481\pi$
$251$	−11.1962	+	19.3923i	−0.706695	+	1.22403i	−0.966076	+	0.258256i	$0.916852\pi$
$252$		0			0
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−2.07180	+	3.58846i	−0.129996	+	0.225160i
$255$	5.41154			0.338884
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−9.06218	−	15.6962i	−0.565283	−	0.979099i	−0.997023	−	0.0771011i	$-0.975434\pi$
$257$	−9.06218	−	15.6962i	−0.565283	−	0.979099i	0.431740	−	0.901998i	$-0.357900\pi$
$258$	6.46410	+	11.1962i	0.402437	+	0.697042i
$259$		0			0
$260$	3.46410	+	5.19615i	0.214834	+	0.322252i
$261$	7.39230			0.457572
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	0.783811	−	0.620999i	$-0.213273\pi$
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	−0.929707	+	0.368301i	$0.879940\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$	6.80385			0.417957
$266$		0			0
$267$	−0.339746	+	0.588457i	−0.0207921	+	0.0360130i
$268$	4.19615			0.256321
$269$	9.46410	−	16.3923i	0.577036	−	0.999456i	−0.418781	−	0.908087i	$-0.637542\pi$
$269$	9.46410	−	16.3923i	0.577036	−	0.999456i	0.995817	−	0.0913690i	$-0.0291243\pi$
$270$	−6.00000	−	10.3923i	−0.365148	−	0.632456i
$271$	8.09808	+	14.0263i	0.491923	+	0.852036i	0.999957	−	0.00930143i	$-0.00296078\pi$
$271$	8.09808	+	14.0263i	0.491923	+	0.852036i	−0.508034	+	0.861337i	$0.669627\pi$
$272$	−21.3397			−1.29391
$273$		0			0
$274$	−37.9808			−2.29450
$275$	4.73205	+	8.19615i	0.285353	+	0.494247i
$276$	−0.464102	−	0.803848i	−0.0279356	−	0.0483859i
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	35.6603			2.13876
$279$	7.63397	−	13.2224i	0.457034	−	0.791606i
$280$		0			0
$281$	−7.39230			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$282$	0.588457	−	1.01924i	0.0350421	−	0.0606947i
$283$	−0.0980762	−	0.169873i	−0.00583003	−	0.0100979i	0.863096	−	0.505040i	$-0.168522\pi$
$283$	−0.0980762	−	0.169873i	−0.00583003	−	0.0100979i	−0.868926	+	0.494943i	$0.835189\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−2.53590			−0.150214
$286$	−16.3923	−	24.5885i	−0.969297	−	1.45395i
$287$		0			0
$288$	6.40192	+	11.0885i	0.377237	+	0.653394i
$289$	−0.607695	−	1.05256i	−0.0357468	−	0.0619152i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	10.5359			0.617625
$292$	3.59808	−	6.23205i	0.210561	−	0.364703i
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	−0.981924	−	0.189277i	$-0.939386\pi$
$293$	−5.59808	+	9.69615i	−0.327043	+	0.566455i	0.654881	+	0.755732i	$0.272719\pi$
$294$		0			0
$295$	9.29423	−	16.0981i	0.541131	−	0.937266i
$296$	6.06218	+	10.5000i	0.352357	+	0.610300i
$297$	9.46410	+	16.3923i	0.549163	+	0.951178i
$298$	−0.803848			−0.0465656
$299$	−4.56218	+	0.294229i	−0.263838	+	0.0170157i
$300$	−1.46410			−0.0845299
$301$		0			0
$302$	1.73205	+	3.00000i	0.0996683	+	0.172631i
$303$	−1.56218	+	2.70577i	−0.0897448	+	0.155443i
$304$	10.0000			0.573539
$305$	−13.1603	+	22.7942i	−0.753554	+	1.30519i
$306$	−9.10770	+	15.7750i	−0.520652	+	0.901796i
$307$	−26.5885			−1.51748			−0.758742	−	0.651392i	$-0.774186\pi$
$307$	−26.5885			−1.51748			−0.758742	+	0.651392i	$0.774186\pi$
$308$		0			0
$309$	2.33975	+	4.05256i	0.133103	+	0.230542i
$310$	9.29423	+	16.0981i	0.527877	+	0.914309i
$311$	−4.73205			−0.268330			−0.134165	−	0.990959i	$-0.542835\pi$
$311$	−4.73205			−0.268330			−0.134165	+	0.990959i	$0.542835\pi$
$312$	−4.56218	+	0.294229i	−0.258282	+	0.0166574i
$313$	12.7846			0.722629			0.361314	−	0.932444i	$-0.382328\pi$
$313$	12.7846			0.722629			0.361314	+	0.932444i	$0.382328\pi$
$314$	7.96410	+	13.7942i	0.449440	+	0.778453i
$315$		0			0
$316$	−2.90192	+	5.02628i	−0.163246	+	0.282750i
$317$	0.464102			0.0260665			0.0130333	−	0.999915i	$-0.495851\pi$
$317$	0.464102			0.0260665			0.0130333	+	0.999915i	$0.495851\pi$
$318$	2.49038	−	4.31347i	0.139654	−	0.241887i
$319$	7.09808	−	12.2942i	0.397416	−	0.688345i
$320$	1.73205			0.0968246
$321$	−7.26795	+	12.5885i	−0.405657	+	0.702619i
$322$		0			0
$323$	4.26795	+	7.39230i	0.237475	+	0.411319i
$324$	4.46410			0.248006
$325$	−3.19615	+	6.46410i	−0.177291	+	0.358564i
$326$	−10.0526			−0.556760
$327$	−4.53590	−	7.85641i	−0.250836	−	0.434460i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$	−10.3923			−0.572078
$331$	13.4904	−	23.3660i	0.741498	−	1.28431i	−0.210315	−	0.977634i	$-0.567449\pi$
$331$	13.4904	−	23.3660i	0.741498	−	1.28431i	0.951813	−	0.306679i	$-0.0992179\pi$
$332$	4.09808	−	7.09808i	0.224911	−	0.389558i
$333$	17.2487			0.945224
$334$	−21.2942	+	36.8827i	−1.16517	+	2.01813i
$335$	−3.63397	−	6.29423i	−0.198545	−	0.343890i
$336$		0			0
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	8.66025	−	20.7846i	0.471056	−	1.13053i
$339$	−5.41154			−0.293915
$340$	−3.69615	−	6.40192i	−0.200452	−	0.347193i
$341$	−14.6603	−	25.3923i	−0.793897	−	1.37507i
$342$	4.26795	−	7.39230i	0.230784	−	0.399730i
$343$		0			0
$344$	−8.83013	+	15.2942i	−0.476089	+	0.824610i
$345$	−0.803848	+	1.39230i	−0.0432777	+	0.0749592i
$346$	26.7846			1.43995
$347$	−5.36603	+	9.29423i	−0.288063	+	0.498940i	−0.973347	−	0.229336i	$-0.926345\pi$
$347$	−5.36603	+	9.29423i	−0.288063	+	0.498940i	0.685284	+	0.728276i	$0.259678\pi$
$348$	1.09808	+	1.90192i	0.0588631	+	0.101954i
$349$	8.39230	+	14.5359i	0.449230	+	0.778089i	0.998336	−	0.0576637i	$-0.0183651\pi$
$349$	8.39230	+	14.5359i	0.449230	+	0.778089i	−0.549106	+	0.835753i	$0.685032\pi$
$350$		0			0
$351$	−6.39230	+	12.9282i	−0.341196	+	0.690056i
$352$	24.5885			1.31057
$353$	1.66987	+	2.89230i	0.0888784	+	0.153942i	0.907037	−	0.421050i	$-0.138338\pi$
$353$	1.66987	+	2.89230i	0.0888784	+	0.153942i	−0.818159	+	0.574992i	$0.805005\pi$
$354$	−6.80385	−	11.7846i	−0.361620	−	0.626345i
$355$	−5.19615	+	9.00000i	−0.275783	+	0.477670i
$356$	0.928203			0.0491947
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	5.07180			0.267679			0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180			0.267679			0.133840	+	0.991003i	$0.457269\pi$
$360$	3.69615	−	6.40192i	0.194804	−	0.337411i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	22.1603	+	38.3827i	1.16472	+	2.01735i
$363$	8.33975			0.437723
$364$		0			0
$365$	−12.4641			−0.652401
$366$	9.63397	+	16.6865i	0.503576	+	0.872219i
$367$	−3.09808	−	5.36603i	−0.161718	−	0.280104i	0.773767	−	0.633471i	$-0.218370\pi$
$367$	−3.09808	−	5.36603i	−0.161718	−	0.280104i	−0.935485	+	0.353366i	$0.885037\pi$
$368$	3.16987	−	5.49038i	0.165241	−	0.286206i
$369$	12.8038			0.666542
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$		0			0
$372$	4.53590			0.235175
$373$	−4.69615	+	8.13397i	−0.243158	+	0.421161i	−0.961612	−	0.274413i	$-0.911517\pi$
$373$	−4.69615	+	8.13397i	−0.243158	+	0.421161i	0.718454	+	0.695574i	$0.244850\pi$
$374$	17.4904	+	30.2942i	0.904406	+	1.56648i
$375$	4.43782	+	7.68653i	0.229168	+	0.396931i
$376$	1.60770			0.0829105
$377$	10.7942	−	0.696152i	0.555931	−	0.0358537i
$378$		0			0
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	0.918914	−	0.394458i	$-0.129068\pi$
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	−0.801067	+	0.598574i	$0.795734\pi$
$380$	1.73205	+	3.00000i	0.0888523	+	0.153897i
$381$	0.875644	−	1.51666i	0.0448606	−	0.0777009i
$382$	−2.19615			−0.112365
$383$	2.83013	−	4.90192i	0.144613	−	0.250477i	−0.784616	−	0.619982i	$-0.787140\pi$
$383$	2.83013	−	4.90192i	0.144613	−	0.250477i	0.929228	+	0.369506i	$0.120473\pi$
$384$	4.43782	−	7.68653i	0.226467	−	0.392252i
$385$		0			0
$386$	4.33013	−	7.50000i	0.220398	−	0.381740i
$387$	12.5622	+	21.7583i	0.638571	+	1.10604i
$388$	−7.19615	−	12.4641i	−0.365329	−	0.632769i
$389$	−30.4641			−1.54459			−0.772296	−	0.635263i	$-0.780892\pi$
$389$	−30.4641			−1.54459			−0.772296	+	0.635263i	$0.780892\pi$
$390$	−4.39230	−	6.58846i	−0.222413	−	0.333620i
$391$	5.41154			0.273673
$392$		0			0
$393$	1.26795	+	2.19615i	0.0639596	+	0.110781i
$394$	10.3923	−	18.0000i	0.523557	−	0.906827i
$395$	10.0526			0.505799
$396$	5.83013	−	10.0981i	0.292975	−	0.507447i
$397$	11.3923	−	19.7321i	0.571763	−	0.990323i	−0.424622	−	0.905371i	$-0.639593\pi$
$397$	11.3923	−	19.7321i	0.571763	−	0.990323i	0.996385	−	0.0849523i	$-0.0270738\pi$
$398$	3.46410			0.173640
$399$		0			0
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$	−8.42820	−	14.5981i	−0.420884	−	0.728993i	0.575142	−	0.818054i	$-0.304947\pi$
$401$	−8.42820	−	14.5981i	−0.420884	−	0.728993i	−0.996026	+	0.0890606i	$0.971614\pi$
$402$	−5.32051			−0.265363
$403$	9.90192	−	20.0263i	0.493250	−	0.997580i
$404$	4.26795			0.212338
$405$	−3.86603	−	6.69615i	−0.192104	−	0.332734i
$406$		0			0
$407$	16.5622	−	28.6865i	0.820957	−	1.42194i
$408$	5.41154			0.267911
$409$	−13.5981	+	23.5526i	−0.672382	+	1.16460i	0.304845	+	0.952402i	$0.401395\pi$
$409$	−13.5981	+	23.5526i	−0.672382	+	1.16460i	−0.977227	+	0.212197i	$0.931938\pi$
$410$	−7.79423	+	13.5000i	−0.384930	+	0.666717i
$411$	16.0526			0.791814
$412$	3.19615	−	5.53590i	0.157463	−	0.272734i
$413$		0			0
$414$	−2.70577	−	4.68653i	−0.132981	−	0.230331i
$415$	−14.1962			−0.696862
$416$	10.3923	+	15.5885i	0.509525	+	0.764287i
$417$	−15.0718			−0.738069
$418$	−8.19615	−	14.1962i	−0.400887	−	0.694357i
$419$	−10.9019	−	18.8827i	−0.532594	−	0.922480i	−0.999276	−	0.0380543i	$-0.987884\pi$
$419$	−10.9019	−	18.8827i	−0.532594	−	0.922480i	0.466682	−	0.884425i	$-0.345449\pi$
$420$		0			0
$421$	30.1769			1.47073			0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769			1.47073			0.735366	+	0.677670i	$0.237010\pi$
$422$	−10.5622	+	18.2942i	−0.514159	+	0.890549i
$423$	1.14359	−	1.98076i	0.0556034	−	0.0963079i
$424$	6.80385			0.330424
$425$	4.26795	−	7.39230i	0.207026	−	0.358579i
$426$	3.80385	+	6.58846i	0.184297	+	0.319212i
$427$		0			0
$428$	19.8564			0.959796
$429$	6.92820	+	10.3923i	0.334497	+	0.501745i
$430$	−30.5885			−1.47511
$431$	−17.6603	−	30.5885i	−0.850665	−	1.47339i	−0.880610	−	0.473843i	$-0.842867\pi$
$431$	−17.6603	−	30.5885i	−0.850665	−	1.47339i	0.0299451	−	0.999552i	$-0.490467\pi$
$432$	−10.0000	−	17.3205i	−0.481125	−	0.833333i
$433$	8.79423	−	15.2321i	0.422624	−	0.732006i	−0.573572	−	0.819155i	$-0.694443\pi$
$433$	8.79423	−	15.2321i	0.422624	−	0.732006i	0.996195	+	0.0871498i	$0.0277759\pi$
$434$		0			0
$435$	1.90192	−	3.29423i	0.0911903	−	0.157946i
$436$	−6.19615	+	10.7321i	−0.296742	+	0.513972i
$437$	−2.53590			−0.121308
$438$	−4.56218	+	7.90192i	−0.217989	+	0.377569i
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	0.597349	−	0.801982i	$-0.296221\pi$
$439$	−8.29423	−	14.3660i	−0.395862	−	0.685653i	−0.993211	+	0.116329i	$0.962887\pi$
$440$	−7.09808	−	12.2942i	−0.338388	−	0.586104i
$441$		0			0
$442$	−11.8135	+	23.8923i	−0.561909	+	1.13644i
$443$	−11.3205			−0.537854			−0.268927	−	0.963161i	$-0.586669\pi$
$443$	−11.3205			−0.537854			−0.268927	+	0.963161i	$0.586669\pi$
$444$	2.56218	+	4.43782i	0.121596	+	0.210610i
$445$	−0.803848	−	1.39230i	−0.0381060	−	0.0660016i
$446$	8.66025	−	15.0000i	0.410075	−	0.710271i
$447$	0.339746			0.0160694
$448$		0			0
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	−0.689003	−	0.724758i	$-0.741951\pi$
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	0.972161	+	0.234315i	$0.0752847\pi$
$450$	−8.53590			−0.402386
$451$	12.2942	−	21.2942i	0.578913	−	1.00271i
$452$	3.69615	+	6.40192i	0.173852	+	0.301121i
$453$	−0.732051	−	1.26795i	−0.0343947	−	0.0595734i
$454$	−20.1962			−0.947852
$455$		0			0
$456$	−2.53590			−0.118754
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$	−5.53590	−	9.58846i	−0.258676	−	0.448039i
$459$	8.53590	−	14.7846i	0.398422	−	0.690086i
$460$	2.19615			0.102396
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	−0.625442	−	0.780271i	$-0.715081\pi$
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	0.988455	+	0.151513i	$0.0484146\pi$
$462$		0			0
$463$	26.5885			1.23567			0.617835	−	0.786308i	$-0.288010\pi$
$463$	26.5885			1.23567			0.617835	+	0.786308i	$0.288010\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$	−3.92820	−	6.80385i	−0.182166	−	0.315521i
$466$	22.3923	+	38.7846i	1.03730	+	1.79666i
$467$	19.5167			0.903123			0.451562	−	0.892240i	$-0.350867\pi$
$467$	19.5167			0.903123			0.451562	+	0.892240i	$0.350867\pi$
$468$	8.86603	−	0.571797i	0.409832	−	0.0264313i
$469$		0			0
$470$	1.39230	+	2.41154i	0.0642222	+	0.111236i
$471$	−3.36603	−	5.83013i	−0.155098	−	0.268638i
$472$	9.29423	−	16.0981i	0.427802	−	0.740974i
$473$	48.2487			2.21848
$474$	3.67949	−	6.37307i	0.169005	−	0.292725i
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	4.83975	−	8.38269i	0.221597	−	0.383817i
$478$	−22.6865	−	39.2942i	−1.03766	−	1.79728i
$479$	2.36603	+	4.09808i	0.108106	+	0.187246i	0.915003	−	0.403447i	$-0.132188\pi$
$479$	2.36603	+	4.09808i	0.108106	+	0.187246i	−0.806897	+	0.590693i	$0.798855\pi$
$480$	6.58846			0.300721
$481$	25.1865	−	1.62436i	1.14841	−	0.0740642i
$482$	−18.7128			−0.852345
$483$		0			0
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	−12.4641	+	21.5885i	−0.565966	+	0.980281i
$486$	−26.4449			−1.19956
$487$	0.392305	−	0.679492i	0.0177770	−	0.0307907i	−0.857000	−	0.515316i	$-0.827674\pi$
$487$	0.392305	−	0.679492i	0.0177770	−	0.0307907i	0.874777	+	0.484526i	$0.161008\pi$
$488$	−13.1603	+	22.7942i	−0.595737	+	1.03185i
$489$	4.24871			0.192133
$490$		0			0
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	−0.985285	−	0.170920i	$-0.945326\pi$
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	0.344622	−	0.938742i	$-0.388007\pi$
$492$	1.90192	+	3.29423i	0.0857453	+	0.148515i
$493$	−12.8038			−0.576656
$494$	5.53590	−	11.1962i	0.249072	−	0.503739i
$495$	−20.1962			−0.907750
$496$	15.4904	+	26.8301i	0.695539	+	1.20471i
$497$		0			0
$498$	−5.19615	+	9.00000i	−0.232845	+	0.403300i
$499$	12.9808			0.581099			0.290549	−	0.956860i	$-0.406162\pi$
$499$	12.9808			0.581099			0.290549	+	0.956860i	$0.406162\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	−38.7846			−1.73104
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	−0.690898	−	0.722952i	$-0.742785\pi$
$503$	6.29423	−	10.9019i	0.280646	−	0.486093i	0.971544	+	0.236859i	$0.0761181\pi$
$504$		0			0
$505$	−3.69615	−	6.40192i	−0.164477	−	0.284882i
$506$	−10.3923			−0.461994
$507$	−3.66025	+	8.78461i	−0.162558	+	0.390138i
$508$	−2.39230			−0.106141
$509$	5.13397	+	8.89230i	0.227559	+	0.394144i	0.957084	−	0.289810i	$-0.0935921\pi$
$509$	5.13397	+	8.89230i	0.227559	+	0.394144i	−0.729525	+	0.683954i	$0.760259\pi$
$510$	4.68653	+	8.11731i	0.207523	+	0.359441i
$511$		0			0
$512$	−8.66025			−0.382733
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	15.6962	−	27.1865i	0.692328	−	1.19915i
$515$	−11.0718			−0.487882
$516$	−3.73205	+	6.46410i	−0.164294	+	0.284566i
$517$	−2.19615	−	3.80385i	−0.0965867	−	0.167293i
$518$		0			0
$519$	−11.3205			−0.496915
$520$	4.79423	−	9.69615i	0.210241	−	0.425204i
$521$	−0.124356			−0.00544812			−0.00272406	−	0.999996i	$-0.500867\pi$
$521$	−0.124356			−0.00544812			−0.00272406	+	0.999996i	$0.500867\pi$
$522$	6.40192	+	11.0885i	0.280205	+	0.485329i
$523$	16.5885	+	28.7321i	0.725363	+	1.25636i	0.958825	+	0.283999i	$0.0916612\pi$
$523$	16.5885	+	28.7321i	0.725363	+	1.25636i	−0.233462	+	0.972366i	$0.575005\pi$
$524$	1.73205	−	3.00000i	0.0756650	−	0.131056i
$525$		0			0
$526$	4.09808	−	7.09808i	0.178685	−	0.309491i
$527$	−13.2224	+	22.9019i	−0.575978	+	0.997623i
$528$	−17.3205			−0.753778
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	5.89230	+	10.2058i	0.255945	+	0.443310i
$531$	−13.2224	−	22.9019i	−0.573805	−	0.993859i
$532$		0			0
$533$	18.6962	−	1.20577i	0.809820	−	0.0522278i
$534$	−1.17691			−0.0509301
$535$	−17.1962	−	29.7846i	−0.743455	−	1.28770i
$536$	−3.63397	−	6.29423i	−0.156964	−	0.271869i
$537$	−2.53590	+	4.39230i	−0.109432	+	0.189542i
$538$	32.7846			1.41344
$539$		0			0
$540$	3.46410	−	6.00000i	0.149071	−	0.258199i
$541$	−35.3923			−1.52163			−0.760817	−	0.648966i	$-0.775202\pi$
$541$	−35.3923			−1.52163			−0.760817	+	0.648966i	$0.775202\pi$
$542$	−14.0263	+	24.2942i	−0.602480	+	1.04353i
$543$	−9.36603	−	16.2224i	−0.401935	−	0.696171i
$544$	−11.0885	−	19.2058i	−0.475414	−	0.823441i
$545$	21.4641			0.919421
$546$		0			0
$547$	28.1962			1.20558			0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962			1.20558			0.602790	+	0.797900i	$0.294056\pi$
$548$	−10.9641	−	18.9904i	−0.468363	−	0.811229i
$549$	18.7224	+	32.4282i	0.799054	+	1.38400i
$550$	−8.19615	+	14.1962i	−0.349485	+	0.605326i
$551$	6.00000			0.255609
$552$	−0.803848	+	1.39230i	−0.0342140	+	0.0592604i
$553$		0			0
$554$	−29.4449			−1.25099
$555$	4.43782	−	7.68653i	0.188375	−	0.326275i
$556$	10.2942	+	17.8301i	0.436573	+	0.756166i
$557$	12.8205	+	22.2058i	0.543222	+	0.940889i	0.998716	+	0.0506499i	$0.0161293\pi$
$557$	12.8205	+	22.2058i	0.543222	+	0.940889i	−0.455494	+	0.890239i	$0.650537\pi$
$558$	26.4449			1.11950
$559$	20.3923	+	30.5885i	0.862503	+	1.29375i
$560$		0			0
$561$	−7.39230	−	12.8038i	−0.312103	−	0.540579i
$562$	−6.40192	−	11.0885i	−0.270049	−	0.467738i
$563$	−5.02628	+	8.70577i	−0.211832	+	0.366905i	−0.952288	−	0.305201i	$-0.901276\pi$
$563$	−5.02628	+	8.70577i	−0.211832	+	0.366905i	0.740456	+	0.672105i	$0.234610\pi$
$564$	0.679492			0.0286118
$565$	6.40192	−	11.0885i	0.269331	−	0.466495i
$566$	0.169873	−	0.294229i	0.00714029	−	0.0123674i
$567$		0			0
$568$	−5.19615	+	9.00000i	−0.218026	+	0.377632i
$569$	−14.5359	−	25.1769i	−0.609377	−	1.05547i	−0.991343	−	0.131295i	$-0.958086\pi$
$569$	−14.5359	−	25.1769i	−0.609377	−	1.05547i	0.381967	−	0.924176i	$-0.375247\pi$
$570$	−2.19615	−	3.80385i	−0.0919867	−	0.159326i
$571$	−24.7846			−1.03720			−0.518602	−	0.855016i	$-0.673547\pi$
$571$	−24.7846			−1.03720			−0.518602	+	0.855016i	$0.673547\pi$
$572$	7.56218	−	15.2942i	0.316191	−	0.639484i
$573$	0.928203			0.0387762
$574$		0			0
$575$	1.26795	+	2.19615i	0.0528771	+	0.0915859i
$576$	1.23205	−	2.13397i	0.0513355	−	0.0889156i
$577$	−32.8038			−1.36564			−0.682821	−	0.730586i	$-0.739247\pi$
$577$	−32.8038			−1.36564			−0.682821	+	0.730586i	$0.739247\pi$
$578$	1.05256	−	1.82309i	0.0437807	−	0.0758304i
$579$	−1.83013	+	3.16987i	−0.0760575	+	0.131735i
$580$	−5.19615			−0.215758
$581$		0			0
$582$	9.12436	+	15.8038i	0.378217	+	0.655091i
$583$	−9.29423	−	16.0981i	−0.384928	−	0.666714i
$584$	−12.4641			−0.515768
$585$	−8.53590	−	12.8038i	−0.352916	−	0.529374i
$586$	−19.3923			−0.801089
$587$	−2.19615	−	3.80385i	−0.0906449	−	0.157002i	0.817138	−	0.576442i	$-0.195559\pi$
$587$	−2.19615	−	3.80385i	−0.0906449	−	0.157002i	−0.907783	+	0.419441i	$0.862226\pi$
$588$		0			0
$589$	6.19615	−	10.7321i	0.255308	−	0.442206i
$590$	32.1962			1.32549
$591$	−4.39230	+	7.60770i	−0.180675	+	0.312939i
$592$	−17.5000	+	30.3109i	−0.719246	+	1.24577i
$593$	−41.4449			−1.70194			−0.850968	−	0.525217i	$-0.823984\pi$
$593$	−41.4449			−1.70194			−0.850968	+	0.525217i	$0.823984\pi$
$594$	−16.3923	+	28.3923i	−0.672584	+	1.16495i
$595$		0			0
$596$	−0.232051	−	0.401924i	−0.00950517	−	0.0164634i
$597$	−1.46410			−0.0599217
$598$	−4.39230	−	6.58846i	−0.179615	−	0.269422i
$599$	16.1436			0.659609			0.329805	−	0.944049i	$-0.393017\pi$
$599$	16.1436			0.659609			0.329805	+	0.944049i	$0.393017\pi$
$600$	1.26795	+	2.19615i	0.0517638	+	0.0896575i
$601$	10.9904	+	19.0359i	0.448307	+	0.776490i	0.998276	−	0.0586946i	$-0.0186938\pi$
$601$	10.9904	+	19.0359i	0.448307	+	0.776490i	−0.549969	+	0.835185i	$0.685360\pi$
$602$		0			0
$603$	−10.3397			−0.421067
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	−9.86603	+	17.0885i	−0.401111	+	0.694745i
$606$	−5.41154			−0.219829
$607$	3.19615	−	5.53590i	0.129728	−	0.224695i	−0.793843	−	0.608122i	$-0.791923\pi$
$607$	3.19615	−	5.53590i	0.129728	−	0.224695i	0.923571	+	0.383427i	$0.125256\pi$
$608$	5.19615	+	9.00000i	0.210732	+	0.364998i
$609$		0			0
$610$	−45.5885			−1.84582
$611$	1.48334	−	3.00000i	0.0600095	−	0.121367i
$612$	−10.5167			−0.425111
$613$	8.69615	+	15.0622i	0.351234	+	0.608356i	0.986466	−	0.163966i	$-0.0524287\pi$
$613$	8.69615	+	15.0622i	0.351234	+	0.608356i	−0.635232	+	0.772322i	$0.719095\pi$
$614$	−23.0263	−	39.8827i	−0.929265	−	1.60953i
$615$	3.29423	−	5.70577i	0.132836	−	0.230079i
$616$		0			0
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	0.420097	+	0.907479i	$0.361996\pi$
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	−0.995949	+	0.0899245i	$0.971337\pi$
$618$	−4.05256	+	7.01924i	−0.163018	+	0.282355i
$619$	37.3731			1.50215			0.751075	−	0.660217i	$-0.229536\pi$
$619$	37.3731			1.50215			0.751075	+	0.660217i	$0.229536\pi$
$620$	−5.36603	+	9.29423i	−0.215505	+	0.373265i
$621$	2.53590	+	4.39230i	0.101762	+	0.176257i
$622$	−4.09808	−	7.09808i	−0.164318	−	0.284607i
$623$		0			0
$624$	−7.32051	−	10.9808i	−0.293055	−	0.439582i
$625$	−11.0000			−0.440000
$626$	11.0718	+	19.1769i	0.442518	+	0.766464i
$627$	3.46410	+	6.00000i	0.138343	+	0.239617i
$628$	−4.59808	+	7.96410i	−0.183483	+	0.317802i
$629$	−29.8756			−1.19122
$630$		0			0
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	0.423313	+	0.905984i	$0.360867\pi$
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	−0.996261	+	0.0863924i	$0.972466\pi$
$632$	10.0526			0.399869
$633$	4.46410	−	7.73205i	0.177432	−	0.307321i
$634$	0.401924	+	0.696152i	0.0159624	+	0.0276477i
$635$	2.07180	+	3.58846i	0.0822167	+	0.142404i
$636$	2.87564			0.114027
$637$		0			0
$638$	24.5885			0.973466
$639$	7.39230	+	12.8038i	0.292435	+	0.506512i
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	−0.571797	+	0.990381i	−0.0225846	+	0.0391177i	−0.877097	−	0.480314i	$-0.840523\pi$
$641$	−0.571797	+	0.990381i	−0.0225846	+	0.0391177i	0.854512	+	0.519431i	$0.173856\pi$
$642$	−25.1769			−0.993654
$643$	20.3923	−	35.3205i	0.804194	−	1.39290i	−0.112640	−	0.993636i	$-0.535931\pi$
$643$	20.3923	−	35.3205i	0.804194	−	1.39290i	0.916834	−	0.399269i	$-0.130736\pi$
$644$		0			0
$645$	12.9282			0.509048
$646$	−7.39230	+	12.8038i	−0.290846	+	0.503761i
$647$	−22.5167	−	39.0000i	−0.885221	−	1.53325i	−0.845460	−	0.534039i	$-0.820674\pi$
$647$	−22.5167	−	39.0000i	−0.885221	−	1.53325i	−0.0397614	−	0.999209i	$-0.512660\pi$
$648$	−3.86603	−	6.69615i	−0.151872	−	0.263050i
$649$	−50.7846			−1.99347
$650$	−12.4641	+	0.803848i	−0.488882	+	0.0315295i
$651$		0			0
$652$	−2.90192	−	5.02628i	−0.113648	−	0.196844i
$653$	5.07180	+	8.78461i	0.198475	+	0.343768i	0.948034	−	0.318169i	$-0.103068\pi$
$653$	5.07180	+	8.78461i	0.198475	+	0.343768i	−0.749559	+	0.661937i	$0.769735\pi$
$654$	7.85641	−	13.6077i	0.307210	−	0.532103i
$655$	−6.00000			−0.234439
$656$	−12.9904	+	22.5000i	−0.507189	+	0.878477i
$657$	−8.86603	+	15.3564i	−0.345897	+	0.599110i
$658$		0			0
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	−0.930554	−	0.366156i	$-0.880674\pi$
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	0.782377	+	0.622805i	$0.214007\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−11.4019	−	19.7487i	−0.443483	−	0.768136i	0.554462	−	0.832209i	$-0.312924\pi$
$661$	−11.4019	−	19.7487i	−0.443483	−	0.768136i	−0.997945	+	0.0640734i	$0.979591\pi$
$662$	46.7321			1.81629
$663$	4.99296	−	10.0981i	0.193910	−	0.392177i
$664$	−14.1962			−0.550918
$665$		0			0
$666$	14.9378	+	25.8731i	0.578829	+	1.00256i
$667$	1.90192	−	3.29423i	0.0736428	−	0.127553i
$668$	−24.5885			−0.951356
$669$	−3.66025	+	6.33975i	−0.141514	+	0.245109i
$670$	6.29423	−	10.9019i	0.243167	−	0.421178i
$671$	71.9090			2.77601
$672$		0			0
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	0.635974	−	0.771711i	$-0.280599\pi$
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	−0.986308	+	0.164914i	$0.947265\pi$
$674$	9.52628	+	16.5000i	0.366939	+	0.635556i
$675$	8.00000			0.307920
$676$	12.8923	−	1.66987i	0.495858	−	0.0642259i
$677$	36.9282			1.41927			0.709633	−	0.704571i	$-0.248861\pi$
$677$	36.9282			1.41927			0.709633	+	0.704571i	$0.248861\pi$
$678$	−4.68653	−	8.11731i	−0.179985	−	0.311744i
$679$		0			0
$680$	−6.40192	+	11.0885i	−0.245503	+	0.425223i
$681$	8.53590			0.327096
$682$	25.3923	−	43.9808i	0.972322	−	1.68411i
$683$	−4.26795	+	7.39230i	−0.163309	+	0.282859i	−0.936053	−	0.351858i	$-0.885550\pi$
$683$	−4.26795	+	7.39230i	−0.163309	+	0.282859i	0.772745	+	0.634717i	$0.218883\pi$
$684$	4.92820			0.188435
$685$	−18.9904	+	32.8923i	−0.725585	+	1.25675i
$686$		0			0
$687$	2.33975	+	4.05256i	0.0892669	+	0.154615i
$688$	−50.9808			−1.94362
$689$	6.27757	−	12.6962i	0.239156	−	0.483685i
$690$	−2.78461			−0.106008
$691$	−10.1962	−	17.6603i	−0.387880	−	0.671828i	0.604284	−	0.796769i	$-0.293459\pi$
$691$	−10.1962	−	17.6603i	−0.387880	−	0.671828i	−0.992164	+	0.124941i	$0.960126\pi$
$692$	7.73205	+	13.3923i	0.293928	+	0.509099i
$693$		0			0
$694$	−18.5885			−0.705608
$695$	17.8301	−	30.8827i	0.676335	−	1.17145i
$696$	1.90192	−	3.29423i	0.0720922	−	0.124867i
$697$	−22.1769			−0.840011
$698$	−14.5359	+	25.1769i	−0.550192	+	0.952960i
$699$	−9.46410	−	16.3923i	−0.357965	−	0.620014i
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	−24.9282	+	1.60770i	−0.940854	+	0.0606785i
$703$	14.0000			0.528020
$704$	−2.36603	−	4.09808i	−0.0891729	−	0.154452i
$705$	−0.588457	−	1.01924i	−0.0221626	−	0.0383867i
$706$	−2.89230	+	5.00962i	−0.108853	+	0.188539i
$707$		0			0
$708$	3.92820	−	6.80385i	0.147631	−	0.255704i
$709$	16.0885	−	27.8660i	0.604215	−	1.04653i	−0.387960	−	0.921676i	$-0.626820\pi$
$709$	16.0885	−	27.8660i	0.604215	−	1.04653i	0.992175	−	0.124854i	$-0.0398464\pi$
$710$	−18.0000			−0.675528
$711$	7.15064	−	12.3853i	0.268170	−	0.464484i
$712$	−0.803848	−	1.39230i	−0.0301255	−	0.0521788i
$713$	−3.92820	−	6.80385i	−0.147112	−	0.254806i
$714$		0			0
$715$	−29.4904	+	1.90192i	−1.10288	+	0.0711279i
$716$	6.92820			0.258919
$717$	9.58846	+	16.6077i	0.358087	+	0.620226i
$718$	4.39230	+	7.60770i	0.163919	+	0.283917i
$719$	−5.36603	+	9.29423i	−0.200119	+	0.346616i	−0.948567	−	0.316578i	$-0.897466\pi$
$719$	−5.36603	+	9.29423i	−0.200119	+	0.346616i	0.748448	+	0.663194i	$0.230800\pi$
$720$	21.3397			0.795285
$721$		0			0
$722$	−12.9904	+	22.5000i	−0.483452	+	0.837363i
$723$	7.90897			0.294138
$724$	−12.7942	+	22.1603i	−0.475494	+	0.823579i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	7.22243	+	12.5096i	0.268050	+	0.464276i
$727$	−21.1769			−0.785408			−0.392704	−	0.919665i	$-0.628460\pi$
$727$	−21.1769			−0.785408			−0.392704	+	0.919665i	$0.628460\pi$
$728$		0			0
$729$	−2.21539			−0.0820515
$730$	−10.7942	−	18.6962i	−0.399512	−	0.691976i
$731$	−21.7583	−	37.6865i	−0.804761	−	1.39389i
$732$	−5.56218	+	9.63397i	−0.205584	+	0.356082i
$733$	7.58846			0.280286			0.140143	−	0.990131i	$-0.455244\pi$
$733$	7.58846			0.280286			0.140143	+	0.990131i	$0.455244\pi$
$734$	5.36603	−	9.29423i	0.198064	−	0.343056i
$735$		0			0
$736$	6.58846			0.242854
$737$	−9.92820	+	17.1962i	−0.365710	+	0.633428i
$738$	11.0885	+	19.2058i	0.408172	+	0.706974i
$739$	0.392305	+	0.679492i	0.0144312	+	0.0249955i	0.873151	−	0.487450i	$-0.162073\pi$
$739$	0.392305	+	0.679492i	0.0144312	+	0.0249955i	−0.858720	+	0.512446i	$0.828740\pi$
$740$	−12.1244			−0.445700
$741$	−2.33975	+	4.73205i	−0.0859527	+	0.173836i
$742$		0			0
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	0.999707	+	0.0241941i	$0.00770196\pi$
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	−0.478901	+	0.877869i	$0.658965\pi$
$744$	−3.92820	−	6.80385i	−0.144015	−	0.249441i
$745$	−0.401924	+	0.696152i	−0.0147253	+	0.0255051i
$746$	−16.2679			−0.595612
$747$	−10.0981	+	17.4904i	−0.369469	+	0.639940i
$748$	−10.0981	+	17.4904i	−0.369222	+	0.639512i
$749$		0			0
$750$	−7.68653	+	13.3135i	−0.280673	+	0.486139i
$751$	−23.0981	−	40.0070i	−0.842861	−	1.45988i	−0.887466	−	0.460873i	$-0.847536\pi$
$751$	−23.0981	−	40.0070i	−0.842861	−	1.45988i	0.0446053	−	0.999005i	$-0.485797\pi$
$752$	2.32051	+	4.01924i	0.0846202	+	0.146567i
$753$	16.3923			0.597369
$754$	10.3923	+	15.5885i	0.378465	+	0.567698i
$755$	3.46410			0.126072
$756$		0			0
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	−3.97372	+	6.88269i	−0.144332	+	0.249990i
$759$	4.39230			0.159431
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	3.33975	−	5.78461i	0.121066	−	0.209692i	−0.799123	−	0.601168i	$-0.794702\pi$
$761$	3.33975	−	5.78461i	0.121066	−	0.209692i	0.920188	+	0.391476i	$0.128035\pi$
$762$	3.03332			0.109886
$763$		0			0
$764$	−0.633975	−	1.09808i	−0.0229364	−	0.0397270i
$765$	9.10770	+	15.7750i	0.329289	+	0.570346i
$766$	9.80385			0.354227
$767$	−21.4641	−	32.1962i	−0.775024	−	1.16254i
$768$	13.9090			0.501897
$769$	−23.5885	−	40.8564i	−0.850622	−	1.47332i	−0.880648	−	0.473771i	$-0.842893\pi$
$769$	−23.5885	−	40.8564i	−0.850622	−	1.47332i	0.0300268	−	0.999549i	$-0.490441\pi$
$770$		0			0
$771$	−6.63397	+	11.4904i	−0.238917	+	0.413816i
$772$	5.00000			0.179954
$773$	0.464102	−	0.803848i	0.0166926	−	0.0289124i	−0.857558	−	0.514387i	$-0.828020\pi$
$773$	0.464102	−	0.803848i	0.0166926	−	0.0289124i	0.874251	+	0.485474i	$0.161353\pi$
$774$	−21.7583	+	37.6865i	−0.782087	+	1.35461i
$775$	−12.3923			−0.445145
$776$	−12.4641	+	21.5885i	−0.447435	+	0.774980i
$777$		0			0
$778$	−26.3827	−	45.6962i	−0.945865	−	1.63829i
$779$	10.3923			0.372343
$780$	2.02628	−	4.09808i	0.0725524	−	0.146735i
$781$	28.3923			1.01596
$782$	4.68653	+	8.11731i	0.167590	+	0.290275i
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$		0			0
$785$	15.9282			0.568502
$786$	−2.19615	+	3.80385i	−0.0783342	+	0.135679i
$787$	−19.4904	+	33.7583i	−0.694757	+	1.20335i	0.275505	+	0.961300i	$0.411155\pi$
$787$	−19.4904	+	33.7583i	−0.694757	+	1.20335i	−0.970263	+	0.242055i	$0.922179\pi$
$788$	12.0000			0.427482
$789$	−1.73205	+	3.00000i	−0.0616626	+	0.106803i
$790$	8.70577	+	15.0788i	0.309737	+	0.536481i
$791$		0			0
$792$	−20.1962			−0.717639
$793$	30.3923	+	45.5885i	1.07926	+	1.61889i
$794$	39.4641			1.40053
$795$	−2.49038	−	4.31347i	−0.0883247	−	0.152983i
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	−6.80385	+	11.7846i	−0.241005	+	0.417432i	−0.961001	−	0.276546i	$-0.910810\pi$
$797$	−6.80385	+	11.7846i	−0.241005	+	0.417432i	0.719996	+	0.693978i	$0.244144\pi$
$798$		0			0
$799$	−1.98076	+	3.43078i	−0.0700743	+	0.121372i
$800$	5.19615	−	9.00000i	0.183712	−	0.318198i
$801$	−2.28719			−0.0808138
$802$	14.5981	−	25.2846i	0.515476	−	0.892831i
$803$	17.0263	+	29.4904i	0.600844	+	1.04069i
$804$	−1.53590	−	2.66025i	−0.0541670	−	0.0938199i
$805$		0			0
$806$	38.6147	−	2.49038i	1.36015	−	0.0877199i
$807$	−13.8564			−0.487769
$808$	−3.69615	−	6.40192i	−0.130030	−	0.225219i
$809$	−7.96410	−	13.7942i	−0.280003	−	0.484979i	0.691382	−	0.722489i	$-0.257002\pi$
$809$	−7.96410	−	13.7942i	−0.280003	−	0.484979i	−0.971385	+	0.237510i	$0.923669\pi$
$810$	6.69615	−	11.5981i	0.235279	−	0.407515i
$811$	−14.5885			−0.512270			−0.256135	−	0.966641i	$-0.582449\pi$
$811$	−14.5885			−0.512270			−0.256135	+	0.966641i	$0.582449\pi$
$812$		0			0
$813$	5.92820	−	10.2679i	0.207911	−	0.360113i
$814$	57.3731			2.01092
$815$	−5.02628	+	8.70577i	−0.176063	+	0.304950i
$816$	7.81089	+	13.5289i	0.273436	+	0.473605i
$817$	10.1962	+	17.6603i	0.356718	+	0.617854i
$818$	−47.1051			−1.64699
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−15.9282	−	27.5885i	−0.555898	−	0.962844i	−0.997833	−	0.0657967i	$-0.979041\pi$
$821$	−15.9282	−	27.5885i	−0.555898	−	0.962844i	0.441935	−	0.897047i	$-0.354292\pi$
$822$	13.9019	+	24.0788i	0.484885	+	0.839846i
$823$	−10.5885	+	18.3397i	−0.369090	+	0.639283i	−0.989424	−	0.145055i	$-0.953664\pi$
$823$	−10.5885	+	18.3397i	−0.369090	+	0.639283i	0.620333	+	0.784338i	$0.286997\pi$
$824$	−11.0718			−0.385704
$825$	3.46410	−	6.00000i	0.120605	−	0.208893i
$826$		0			0
$827$	34.9808			1.21640			0.608200	−	0.793784i	$-0.291892\pi$
$827$	34.9808			1.21640			0.608200	+	0.793784i	$0.291892\pi$
$828$	1.56218	−	2.70577i	0.0542894	−	0.0940321i
$829$	−15.7942	−	27.3564i	−0.548556	−	0.950127i	−0.998374	−	0.0570068i	$-0.981844\pi$
$829$	−15.7942	−	27.3564i	−0.548556	−	0.950127i	0.449818	−	0.893120i	$-0.351489\pi$
$830$	−12.2942	−	21.2942i	−0.426739	−	0.739133i
$831$	12.4449			0.431708
$832$	1.59808	−	3.23205i	0.0554033	−	0.112051i
$833$		0			0
$834$	−13.0526	−	22.6077i	−0.451973	−	0.782840i
$835$	21.2942	+	36.8827i	0.736917	+	1.27638i
$836$	4.73205	−	8.19615i	0.163661	−	0.283470i
$837$	−24.7846			−0.856681
$838$	18.8827	−	32.7058i	0.652292	−	1.12980i
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	26.1340	+	45.2654i	0.900636	+	1.55995i
$843$	2.70577	+	4.68653i	0.0931917	+	0.161413i
$844$	−12.1962			−0.419809
$845$	−13.6699	−	17.8923i	−0.470258	−	0.615514i
$846$	3.96152			0.136200
$847$		0			0
$848$	9.82051	+	17.0096i	0.337238	+	0.584113i
$849$	−0.0717968	+	0.124356i	−0.00246406	+	0.00426787i
$850$	14.7846			0.507108
$851$	4.43782	−	7.68653i	0.152127	−	0.263491i
$852$	−2.19615	+	3.80385i	−0.0752389	+	0.130318i
$853$	25.5885			0.876132			0.438066	−	0.898943i	$-0.355664\pi$
$853$	25.5885			0.876132			0.438066	+	0.898943i	$0.355664\pi$
$854$		0			0
$855$	−4.26795	−	7.39230i	−0.145961	−	0.252811i
$856$	−17.1962	−	29.7846i	−0.587752	−	1.01802i
$857$	5.87564			0.200708			0.100354	−	0.994952i	$-0.468002\pi$
$857$	5.87564			0.200708			0.100354	+	0.994952i	$0.468002\pi$
$858$	−9.58846	+	19.3923i	−0.327345	+	0.662042i
$859$	18.1962			0.620845			0.310422	−	0.950599i	$-0.399530\pi$
$859$	18.1962			0.620845			0.310422	+	0.950599i	$0.399530\pi$
$860$	−8.83013	−	15.2942i	−0.301105	−	0.521529i
$861$		0			0
$862$	30.5885	−	52.9808i	1.04185	−	1.80453i
$863$	−37.5167			−1.27708			−0.638541	−	0.769588i	$-0.720462\pi$
$863$	−37.5167			−1.27708			−0.638541	+	0.769588i	$0.720462\pi$
$864$	10.3923	−	18.0000i	0.353553	−	0.612372i
$865$	13.3923	−	23.1962i	0.455352	−	0.788693i
$866$	30.4641			1.03521
$867$	−0.444864	+	0.770527i	−0.0151084	+	0.0261685i
$868$		0			0
$869$	−13.7321	−	23.7846i	−0.465828	−	0.806838i
$870$	6.58846			0.223370
$871$	−15.0981	+	0.973721i	−0.511579	+	0.0329933i
$872$	21.4641			0.726866
$873$	17.7321	+	30.7128i	0.600139	+	1.03947i
$874$	−2.19615	−	3.80385i	−0.0742860	−	0.128667i
$875$		0			0
$876$	−5.26795			−0.177988
$877$	10.8923	−	18.8660i	0.367807	−	0.637060i	−0.621415	−	0.783481i	$-0.713442\pi$
$877$	10.8923	−	18.8660i	0.367807	−	0.637060i	0.989222	+	0.146421i	$0.0467754\pi$
$878$	14.3660	−	24.8827i	0.484830	−	0.839750i
$879$	8.19615			0.276449
$880$	20.4904	−	35.4904i	0.690731	−	1.19638i
$881$	−19.7942	−	34.2846i	−0.666885	−	1.15508i	−0.978771	−	0.204958i	$-0.934294\pi$
$881$	−19.7942	−	34.2846i	−0.666885	−	1.15508i	0.311886	−	0.950119i	$-0.399039\pi$
$882$		0			0
$883$	45.7654			1.54013			0.770064	−	0.637967i	$-0.220224\pi$
$883$	45.7654			1.54013			0.770064	+	0.637967i	$0.220224\pi$
$884$	−15.3564	+	0.990381i	−0.516492	+	0.0333101i
$885$	−13.6077			−0.457418
$886$	−9.80385	−	16.9808i	−0.329367	−	0.570480i
$887$	−11.6603	−	20.1962i	−0.391513	−	0.678120i	0.601136	−	0.799147i	$-0.294715\pi$
$887$	−11.6603	−	20.1962i	−0.391513	−	0.678120i	−0.992649	+	0.121026i	$0.961382\pi$
$888$	4.43782	−	7.68653i	0.148924	−	0.257943i
$889$		0			0
$890$	1.39230	−	2.41154i	0.0466702	−	0.0808351i
$891$	−10.5622	+	18.2942i	−0.353846	+	0.612880i
$892$	10.0000			0.334825
$893$	0.928203	−	1.60770i	0.0310611	−	0.0537995i
$894$	0.294229	+	0.509619i	0.00984048	+	0.0170442i
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$		0			0
$897$	1.85641	+	2.78461i	0.0619836	+	0.0929754i
$898$	20.7846			0.693591
$899$	9.29423	+	16.0981i	0.309980	+	0.536901i
$900$	−2.46410	−	4.26795i	−0.0821367	−	0.142265i
$901$	−8.38269	+	14.5192i	−0.279268	+	0.483706i
$902$	42.5885			1.41804
$903$		0			0
$904$	6.40192	−	11.0885i	0.212925	−	0.368797i
$905$	44.3205			1.47326
$906$	1.26795	−	2.19615i	0.0421248	−	0.0729623i
$907$	−7.29423	−	12.6340i	−0.242201	−	0.419504i	0.719140	−	0.694865i	$-0.244536\pi$
$907$	−7.29423	−	12.6340i	−0.242201	−	0.419504i	−0.961341	+	0.275361i	$0.911203\pi$
$908$	−5.83013	−	10.0981i	−0.193480	−	0.335116i
$909$	−10.5167			−0.348816
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−3.66025	−	6.33975i	−0.121203	−	0.209930i
$913$	19.3923	+	33.5885i	0.641792	+	1.11162i
$914$	9.52628	−	16.5000i	0.315101	−	0.545771i
$915$	19.2679			0.636979
$916$	3.19615	−	5.53590i	0.105604	−	0.182911i
$917$		0			0
$918$	29.5692			0.975930
$919$	−21.7846	+	37.7321i	−0.718608	+	1.24467i	0.242943	+	0.970040i	$0.421887\pi$
$919$	−21.7846	+	37.7321i	−0.718608	+	1.24467i	−0.961551	+	0.274625i	$0.911446\pi$
$920$	−1.90192	−	3.29423i	−0.0627046	−	0.108608i
$921$	9.73205	+	16.8564i	0.320682	+	0.555437i
$922$	27.0000			0.889198
$923$	12.0000	+	18.0000i	0.394985	+	0.592477i
$924$		0			0
$925$	−7.00000	−	12.1244i	−0.230159	−	0.398646i
$926$	23.0263	+	39.8827i	0.756690	+	1.31063i
$927$	−7.87564	+	13.6410i	−0.258670	+	0.448030i
$928$	−15.5885			−0.511716
$929$	3.74167	−	6.48076i	0.122760	−	0.212627i	−0.798095	−	0.602532i	$-0.794159\pi$
$929$	3.74167	−	6.48076i	0.122760	−	0.212627i	0.920855	+	0.389905i	$0.127492\pi$
$930$	6.80385	−	11.7846i	0.223107	−	0.386433i
$931$		0			0
$932$	−12.9282	+	22.3923i	−0.423477	+	0.733484i
$933$	1.73205	+	3.00000i	0.0567048	+	0.0982156i
$934$	16.9019	+	29.2750i	0.553048	+	0.957907i
$935$	34.9808			1.14399
$936$	−8.53590	−	12.8038i	−0.279005	−	0.418507i
$937$	40.8038			1.33300			0.666502	−	0.745503i	$-0.267791\pi$
$937$	40.8038			1.33300			0.666502	+	0.745503i	$0.267791\pi$
$938$		0			0
$939$	−4.67949	−	8.10512i	−0.152709	−	0.264501i
$940$	−0.803848	+	1.39230i	−0.0262186	+	0.0454120i
$941$	55.8564			1.82087			0.910433	−	0.413656i	$-0.135748\pi$
$941$	55.8564			1.82087			0.910433	+	0.413656i	$0.135748\pi$
$942$	5.83013	−	10.0981i	0.189956	−	0.329013i
$943$	3.29423	−	5.70577i	0.107275	−	0.185805i
$944$	53.6603			1.74649
$945$		0			0
$946$	41.7846	+	72.3731i	1.35853	+	2.35305i
$947$	5.36603	+	9.29423i	0.174372	+	0.302022i	0.939944	−	0.341329i	$-0.110877\pi$
$947$	5.36603	+	9.29423i	0.174372	+	0.302022i	−0.765572	+	0.643351i	$0.777544\pi$
$948$	4.24871			0.137992
$949$	−11.5000	+	23.2583i	−0.373306	+	0.754997i
$950$	−6.92820			−0.224781
$951$	−0.169873	−	0.294229i	−0.00550851	−	0.00954102i
$952$		0			0
$953$	−18.5885	+	32.1962i	−0.602139	+	1.04294i	0.390357	+	0.920663i	$0.372351\pi$
$953$	−18.5885	+	32.1962i	−0.602139	+	1.04294i	−0.992497	+	0.122272i	$0.960982\pi$
$954$	16.7654			0.542799
$955$	−1.09808	+	1.90192i	−0.0355329	+	0.0615448i
$956$	13.0981	−	22.6865i	0.423622	−	0.733735i
$957$	−10.3923			−0.335936
$958$	−4.09808	+	7.09808i	−0.132403	+	0.229328i
$959$		0			0
$960$	−0.633975	−	1.09808i	−0.0204614	−	0.0354403i
$961$	7.39230			0.238461
$962$	24.2487	+	36.3731i	0.781810	+	1.17271i
$963$	−48.9282			−1.57669
$964$	−5.40192	−	9.35641i	−0.173984	−	0.301350i
$965$	−4.33013	−	7.50000i	−0.139392	−	0.241434i
$966$		0			0
$967$	3.01924			0.0970921			0.0485461	−	0.998821i	$-0.484541\pi$
$967$	3.01924			0.0970921			0.0485461	+	0.998821i	$0.484541\pi$
$968$	−9.86603	+	17.0885i	−0.317106	+	0.549244i
$969$	3.12436	−	5.41154i	0.100369	−	0.173844i
$970$	−43.1769			−1.38633
$971$	8.32051	−	14.4115i	0.267018	−	0.462488i	−0.701072	−	0.713090i	$-0.747295\pi$
$971$	8.32051	−	14.4115i	0.267018	−	0.462488i	0.968090	+	0.250602i	$0.0806284\pi$
$972$	−7.63397	−	13.2224i	−0.244860	−	0.424110i
$973$		0			0
$974$	1.35898			0.0435447
$975$	5.26795	−	0.339746i	0.168709	−	0.0108806i
$976$	−75.9808			−2.43208
$977$	18.8205	+	32.5981i	0.602121	+	1.04290i	0.992499	+	0.122250i	$0.0390110\pi$
$977$	18.8205	+	32.5981i	0.602121	+	1.04290i	−0.390378	+	0.920655i	$0.627656\pi$
$978$	3.67949	+	6.37307i	0.117657	+	0.203788i
$979$	−2.19615	+	3.80385i	−0.0701893	+	0.121571i
$980$		0			0
$981$	15.2679	−	26.4449i	0.487468	−	0.844320i
$982$	24.5885	−	42.5885i	0.784649	−	1.35905i
$983$	−17.3205			−0.552438			−0.276219	−	0.961095i	$-0.589082\pi$
$983$	−17.3205			−0.552438			−0.276219	+	0.961095i	$0.589082\pi$
$984$	3.29423	−	5.70577i	0.105016	−	0.181893i
$985$	−10.3923	−	18.0000i	−0.331126	−	0.573528i
$986$	−11.0885	−	19.2058i	−0.353128	−	0.611636i
$987$		0			0
$988$	7.19615	−	0.464102i	0.228940	−	0.0147650i
$989$	12.9282			0.411093
$990$	−17.4904	−	30.2942i	−0.555881	−	0.962814i
$991$	16.4904	+	28.5622i	0.523834	+	0.907307i	0.999615	+	0.0277436i	$0.00883220\pi$
$991$	16.4904	+	28.5622i	0.523834	+	0.907307i	−0.475781	+	0.879564i	$0.657834\pi$
$992$	−16.0981	+	27.8827i	−0.511114	+	0.885276i
$993$	−19.7513			−0.626788
$994$		0			0
$995$	1.73205	−	3.00000i	0.0549097	−	0.0951064i
$996$	−6.00000			−0.190117
$997$	−7.59808	+	13.1603i	−0.240633	+	0.416789i	−0.960895	−	0.276913i	$-0.910689\pi$
$997$	−7.59808	+	13.1603i	−0.240633	+	0.416789i	0.720261	+	0.693703i	$0.244022\pi$
$998$	11.2417	+	19.4711i	0.355849	+	0.616348i
$999$	−14.0000	−	24.2487i	−0.442940	−	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.d.393.2		4
7.2	even	3		637.2.g.d.263.2		4
7.3	odd	6		637.2.h.d.471.1		4
7.4	even	3		637.2.h.e.471.1		4
7.5	odd	6		637.2.g.e.263.2		4
7.6	odd	2		91.2.f.b.29.2	yes	4
13.3	even	3		8281.2.a.r.1.1		2
13.9	even	3	inner	637.2.f.d.295.2		4
13.10	even	6		8281.2.a.t.1.2		2
21.20	even	2		819.2.o.b.757.1		4
28.27	even	2		1456.2.s.o.1121.1		4
91.9	even	3		637.2.h.e.165.1		4
91.41	even	12		1183.2.c.e.337.3		4
91.48	odd	6		91.2.f.b.22.2	✓	4
91.55	odd	6		1183.2.a.f.1.1		2
91.61	odd	6		637.2.h.d.165.1		4
91.62	odd	6		1183.2.a.e.1.2		2
91.74	even	3		637.2.g.d.373.2		4
91.76	even	12		1183.2.c.e.337.1		4
91.87	odd	6		637.2.g.e.373.2		4
273.230	even	6		819.2.o.b.568.1		4
364.139	even	6		1456.2.s.o.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.2	✓	4	91.48	odd	6
91.2.f.b.29.2	yes	4	7.6	odd	2
637.2.f.d.295.2		4	13.9	even	3	inner
637.2.f.d.393.2		4	1.1	even	1	trivial
637.2.g.d.263.2		4	7.2	even	3
637.2.g.d.373.2		4	91.74	even	3
637.2.g.e.263.2		4	7.5	odd	6
637.2.g.e.373.2		4	91.87	odd	6
637.2.h.d.165.1		4	91.61	odd	6
637.2.h.d.471.1		4	7.3	odd	6
637.2.h.e.165.1		4	91.9	even	3
637.2.h.e.471.1		4	7.4	even	3
819.2.o.b.568.1		4	273.230	even	6
819.2.o.b.757.1		4	21.20	even	2
1183.2.a.e.1.2		2	91.62	odd	6
1183.2.a.f.1.1		2	91.55	odd	6
1183.2.c.e.337.1		4	91.76	even	12
1183.2.c.e.337.3		4	91.41	even	12
1456.2.s.o.113.1		4	364.139	even	6
1456.2.s.o.1121.1		4	28.27	even	2
8281.2.a.r.1.1		2	13.3	even	3
8281.2.a.t.1.2		2	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(0.633975 - 1.09808i) q^{6} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-2.36603 - 4.09808i) q^{11} +0.732051 q^{12} +(1.59808 - 3.23205i) q^{13} +(-0.633975 - 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-2.13397 + 3.69615i) q^{17} +4.26795 q^{18} +(1.00000 - 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +(4.09808 - 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(-0.633975 - 1.09808i) q^{24} -2.00000 q^{25} +(6.23205 - 0.401924i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +(1.09808 - 1.90192i) q^{30} +6.19615 q^{31} +(-2.59808 + 4.50000i) q^{32} +(-1.73205 + 3.00000i) q^{33} -7.39230 q^{34} +(1.23205 + 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} +3.46410 q^{38} +(-2.63397 + 0.169873i) q^{39} +3.00000 q^{40} +(2.59808 + 4.50000i) q^{41} +(-5.09808 + 8.83013i) q^{43} +4.73205 q^{44} +(2.13397 - 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} +0.928203 q^{47} +(1.83013 - 3.16987i) q^{48} +(-1.73205 - 3.00000i) q^{50} +3.12436 q^{51} +(2.00000 + 3.00000i) q^{52} +3.92820 q^{53} +(-3.46410 - 6.00000i) q^{54} +(-4.09808 - 7.09808i) q^{55} -1.46410 q^{57} +(-2.59808 + 4.50000i) q^{58} +(5.36603 - 9.29423i) q^{59} +1.26795 q^{60} +(-7.59808 + 13.1603i) q^{61} +(5.36603 + 9.29423i) q^{62} +1.00000 q^{64} +(2.76795 - 5.59808i) q^{65} -6.00000 q^{66} +(-2.09808 - 3.63397i) q^{67} +(-2.13397 - 3.69615i) q^{68} +(-0.464102 + 0.803848i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(2.13397 - 3.69615i) q^{72} -7.19615 q^{73} +(-6.06218 + 10.5000i) q^{74} +(0.732051 + 1.26795i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-2.53590 - 3.80385i) q^{78} +5.80385 q^{79} +(4.33013 + 7.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-4.50000 + 7.79423i) q^{82} -8.19615 q^{83} +(-3.69615 + 6.40192i) q^{85} -17.6603 q^{86} +(1.09808 - 1.90192i) q^{87} +(-4.09808 - 7.09808i) q^{88} +(-0.464102 - 0.803848i) q^{89} +7.39230 q^{90} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} +(0.803848 + 1.39230i) q^{94} +(1.73205 - 3.00000i) q^{95} +3.80385 q^{96} +(-7.19615 + 12.4641i) q^{97} -11.6603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} + 6 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^4 + 6 * q^6 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{4} + 6 q^{6} - 2 q^{9} + 6 q^{10} - 6 q^{11} - 4 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} + 24 q^{18} + 4 q^{19} + 6 q^{22} - 6 q^{23} - 6 q^{24} - 8 q^{25} + 18 q^{26} - 16 q^{27} + 6 q^{29} - 6 q^{30} + 4 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} - 14 q^{39} + 12 q^{40} - 10 q^{43} + 12 q^{44} + 12 q^{45} - 6 q^{46} - 24 q^{47} - 10 q^{48} - 36 q^{51} + 8 q^{52} - 12 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} + 12 q^{60} - 20 q^{61} + 18 q^{62} + 4 q^{64} + 18 q^{65} - 24 q^{66} + 2 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} + 12 q^{72} - 8 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} + 44 q^{79} - 2 q^{81} - 18 q^{82} - 12 q^{83} + 6 q^{85} - 36 q^{86} - 6 q^{87} - 6 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} + 24 q^{94} + 36 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 + 6 * q^6 - 2 * q^9 + 6 * q^10 - 6 * q^11 - 4 * q^12 - 4 * q^13 - 6 * q^15 + 10 * q^16 - 12 * q^17 + 24 * q^18 + 4 * q^19 + 6 * q^22 - 6 * q^23 - 6 * q^24 - 8 * q^25 + 18 * q^26 - 16 * q^27 + 6 * q^29 - 6 * q^30 + 4 * q^31 + 12 * q^34 - 2 * q^36 + 14 * q^37 - 14 * q^39 + 12 * q^40 - 10 * q^43 + 12 * q^44 + 12 * q^45 - 6 * q^46 - 24 * q^47 - 10 * q^48 - 36 * q^51 + 8 * q^52 - 12 * q^53 - 6 * q^55 + 8 * q^57 + 18 * q^59 + 12 * q^60 - 20 * q^61 + 18 * q^62 + 4 * q^64 + 18 * q^65 - 24 * q^66 + 2 * q^67 - 12 * q^68 + 12 * q^69 - 12 * q^71 + 12 * q^72 - 8 * q^73 - 4 * q^75 + 4 * q^76 - 24 * q^78 + 44 * q^79 - 2 * q^81 - 18 * q^82 - 12 * q^83 + 6 * q^85 - 36 * q^86 - 6 * q^87 - 6 * q^88 + 12 * q^89 - 12 * q^90 + 12 * q^92 - 16 * q^93 + 24 * q^94 + 36 * q^96 - 8 * q^97 - 12 * q^99

Introduction

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