LMFDB - Embedded newform 637.2.f.d.393.1

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			393.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.d.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 1.50000i) q^{2} +(1.36603 + 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(2.36603 - 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 1.50000i) q^{2} +(1.36603 + 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(2.36603 - 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} -2.73205 q^{12} +(-3.59808 - 0.232051i) q^{13} +(-2.36603 - 4.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.86603 + 6.69615i) q^{17} +7.73205 q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(-2.36603 - 4.09808i) q^{24} -2.00000 q^{25} +(2.76795 + 5.59808i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} -4.19615 q^{31} +(2.59808 - 4.50000i) q^{32} +(1.73205 - 3.00000i) q^{33} +13.3923 q^{34} +(-2.23205 - 3.86603i) q^{36} +(3.50000 + 6.06218i) q^{37} -3.46410 q^{38} +(-4.36603 - 8.83013i) q^{39} +3.00000 q^{40} +(-2.59808 - 4.50000i) q^{41} +(0.0980762 - 0.169873i) q^{43} +1.26795 q^{44} +(3.86603 - 6.69615i) q^{45} +(-4.09808 + 7.09808i) q^{46} -12.9282 q^{47} +(-6.83013 + 11.8301i) q^{48} +(1.73205 + 3.00000i) q^{50} -21.1244 q^{51} +(2.00000 - 3.00000i) q^{52} -9.92820 q^{53} +(3.46410 + 6.00000i) q^{54} +(1.09808 + 1.90192i) q^{55} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} +(3.63397 - 6.29423i) q^{59} +4.73205 q^{60} +(-2.40192 + 4.16025i) q^{61} +(3.63397 + 6.29423i) q^{62} +1.00000 q^{64} +(6.23205 + 0.401924i) q^{65} -6.00000 q^{66} +(3.09808 + 5.36603i) q^{67} +(-3.86603 - 6.69615i) q^{68} +(6.46410 - 11.1962i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} +3.19615 q^{73} +(6.06218 - 10.5000i) q^{74} +(-2.73205 - 4.73205i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-9.46410 + 14.1962i) q^{78} +16.1962 q^{79} +(-4.33013 - 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(-4.50000 + 7.79423i) q^{82} +2.19615 q^{83} +(6.69615 - 11.5981i) q^{85} -0.339746 q^{86} +(-4.09808 + 7.09808i) q^{87} +(1.09808 + 1.90192i) q^{88} +(6.46410 + 11.1962i) q^{89} -13.3923 q^{90} +4.73205 q^{92} +(-5.73205 - 9.92820i) q^{93} +(11.1962 + 19.3923i) q^{94} +(-1.73205 + 3.00000i) q^{95} +14.1962 q^{96} +(3.19615 - 5.53590i) q^{97} +5.66025 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	$-0.956882\pi$
$2$	−0.866025	−	1.50000i	−0.612372	−	1.06066i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	1.36603	+	2.36603i	0.788675	+	1.36603i	0.926779	+	0.375608i	$0.122566\pi$
$3$	1.36603	+	2.36603i	0.788675	+	1.36603i	−0.138104	+	0.990418i	$0.544101\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.73205			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$	2.36603	−	4.09808i	0.965926	−	1.67303i
$7$		0			0
$7$		0			0
$8$	−1.73205			−0.612372
$9$	−2.23205	+	3.86603i	−0.744017	+	1.28868i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$	−2.73205			−0.788675
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$		0			0
$15$	−2.36603	−	4.09808i	−0.610905	−	1.05812i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	−3.86603	+	6.69615i	−0.937649	+	1.62406i	−0.167808	+	0.985820i	$0.553669\pi$
$17$	−3.86603	+	6.69615i	−0.937649	+	1.62406i	−0.769841	+	0.638236i	$0.779664\pi$
$18$	7.73205			1.82246
$19$	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
$22$	−1.09808	+	1.90192i	−0.234111	+	0.405492i
$23$	−2.36603	−	4.09808i	−0.493350	−	0.854508i	0.506620	−	0.862169i	$-0.330895\pi$
$23$	−2.36603	−	4.09808i	−0.493350	−	0.854508i	−0.999971	+	0.00766135i	$0.997561\pi$
$24$	−2.36603	−	4.09808i	−0.482963	−	0.836516i
$25$	−2.00000			−0.400000
$26$	2.76795	+	5.59808i	0.542839	+	1.09787i
$27$	−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	$0.743482\pi$
$30$	−4.09808	+	7.09808i	−0.748203	+	1.29593i
$31$	−4.19615			−0.753651			−0.376826	−	0.926284i	$-0.622984\pi$
$31$	−4.19615			−0.753651			−0.376826	+	0.926284i	$0.622984\pi$
$32$	2.59808	−	4.50000i	0.459279	−	0.795495i
$33$	1.73205	−	3.00000i	0.301511	−	0.522233i
$34$	13.3923			2.29676
$35$		0			0
$36$	−2.23205	−	3.86603i	−0.372008	−	0.644338i
$37$	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
$39$	−4.36603	−	8.83013i	−0.699124	−	1.41395i
$40$	3.00000			0.474342
$41$	−2.59808	−	4.50000i	−0.405751	−	0.702782i	0.588657	−	0.808383i	$-0.299657\pi$
$41$	−2.59808	−	4.50000i	−0.405751	−	0.702782i	−0.994409	+	0.105601i	$0.966323\pi$
$42$		0			0
$43$	0.0980762	−	0.169873i	0.0149565	−	0.0259054i	−0.858450	−	0.512897i	$-0.828572\pi$
$43$	0.0980762	−	0.169873i	0.0149565	−	0.0259054i	0.873407	+	0.486991i	$0.161906\pi$
$44$	1.26795			0.191151
$45$	3.86603	−	6.69615i	0.576313	−	0.998203i
$46$	−4.09808	+	7.09808i	−0.604228	+	1.04655i
$47$	−12.9282			−1.88577			−0.942886	−	0.333115i	$-0.891900\pi$
$47$	−12.9282			−1.88577			−0.942886	+	0.333115i	$0.891900\pi$
$48$	−6.83013	+	11.8301i	−0.985844	+	1.70753i
$49$		0			0
$50$	1.73205	+	3.00000i	0.244949	+	0.424264i
$51$	−21.1244			−2.95800
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$	−9.92820			−1.36374			−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820			−1.36374			−0.681872	+	0.731472i	$0.738834\pi$
$54$	3.46410	+	6.00000i	0.471405	+	0.816497i
$55$	1.09808	+	1.90192i	0.148065	+	0.256455i
$56$		0			0
$57$	5.46410			0.723738
$58$	2.59808	−	4.50000i	0.341144	−	0.590879i
$59$	3.63397	−	6.29423i	0.473103	−	0.819439i	−0.526423	−	0.850223i	$-0.676467\pi$
$59$	3.63397	−	6.29423i	0.473103	−	0.819439i	0.999526	+	0.0307841i	$0.00980044\pi$
$60$	4.73205			0.610905
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	−0.977822	−	0.209435i	$-0.932837\pi$
$61$	−2.40192	+	4.16025i	−0.307535	+	0.532666i	0.670288	+	0.742101i	$0.266171\pi$
$62$	3.63397	+	6.29423i	0.461515	+	0.799368i
$63$		0			0
$64$	1.00000			0.125000
$65$	6.23205	+	0.401924i	0.772991	+	0.0498525i
$66$	−6.00000			−0.738549
$67$	3.09808	+	5.36603i	0.378490	+	0.655564i	0.990843	−	0.135020i	$-0.0431100\pi$
$67$	3.09808	+	5.36603i	0.378490	+	0.655564i	−0.612353	+	0.790585i	$0.709777\pi$
$68$	−3.86603	−	6.69615i	−0.468824	−	0.812028i
$69$	6.46410	−	11.1962i	0.778186	−	1.34786i
$70$		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	$0.282538\pi$
$72$	3.86603	−	6.69615i	0.455615	−	0.789149i
$73$	3.19615			0.374081			0.187041	−	0.982352i	$-0.440110\pi$
$73$	3.19615			0.374081			0.187041	+	0.982352i	$0.440110\pi$
$74$	6.06218	−	10.5000i	0.704714	−	1.22060i
$75$	−2.73205	−	4.73205i	−0.315470	−	0.546410i
$76$	1.00000	+	1.73205i	0.114708	+	0.198680i
$77$		0			0
$78$	−9.46410	+	14.1962i	−1.07160	+	1.60740i
$79$	16.1962			1.82221			0.911105	−	0.412175i	$-0.135231\pi$
$79$	16.1962			1.82221			0.911105	+	0.412175i	$0.135231\pi$
$80$	−4.33013	−	7.50000i	−0.484123	−	0.838525i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	2.19615			0.241059			0.120530	−	0.992710i	$-0.461541\pi$
$83$	2.19615			0.241059			0.120530	+	0.992710i	$0.461541\pi$
$84$		0			0
$85$	6.69615	−	11.5981i	0.726300	−	1.25799i
$86$	−0.339746			−0.0366357
$87$	−4.09808	+	7.09808i	−0.439360	+	0.760994i
$88$	1.09808	+	1.90192i	0.117055	+	0.202746i
$89$	6.46410	+	11.1962i	0.685193	+	1.18679i	0.973376	+	0.229214i	$0.0736157\pi$
$89$	6.46410	+	11.1962i	0.685193	+	1.18679i	−0.288183	+	0.957575i	$0.593051\pi$
$90$	−13.3923			−1.41167
$91$		0			0
$92$	4.73205			0.493350
$93$	−5.73205	−	9.92820i	−0.594386	−	1.02951i
$94$	11.1962	+	19.3923i	1.15479	+	2.00016i
$95$	−1.73205	+	3.00000i	−0.177705	+	0.307794i
$96$	14.1962			1.44889
$97$	3.19615	−	5.53590i	0.324520	−	0.562085i	−0.656895	−	0.753982i	$-0.728131\pi$
$97$	3.19615	−	5.53590i	0.324520	−	0.562085i	0.981415	+	0.191897i	$0.0614639\pi$
$98$		0			0
$99$	5.66025			0.568877
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	−3.86603	−	6.69615i	−0.384684	−	0.666292i	0.607041	−	0.794670i	$-0.292356\pi$
$101$	−3.86603	−	6.69615i	−0.384684	−	0.666292i	−0.991725	+	0.128378i	$0.959023\pi$
$102$	18.2942	+	31.6865i	1.81140	+	3.13743i
$103$	14.3923			1.41812			0.709058	−	0.705150i	$-0.249120\pi$
$103$	14.3923			1.41812			0.709058	+	0.705150i	$0.249120\pi$
$104$	6.23205	+	0.401924i	0.611103	+	0.0394119i
$105$		0			0
$106$	8.59808	+	14.8923i	0.835119	+	1.44647i
$107$	3.92820	+	6.80385i	0.379754	+	0.657753i	0.991026	−	0.133667i	$-0.0426754\pi$
$107$	3.92820	+	6.80385i	0.379754	+	0.657753i	−0.611273	+	0.791420i	$0.709342\pi$
$108$	2.00000	−	3.46410i	0.192450	−	0.333333i
$109$	−8.39230			−0.803837			−0.401919	−	0.915675i	$-0.631656\pi$
$109$	−8.39230			−0.803837			−0.401919	+	0.915675i	$0.631656\pi$
$110$	1.90192	−	3.29423i	0.181341	−	0.314092i
$111$	−9.56218	+	16.5622i	−0.907602	+	1.57201i
$112$		0			0
$113$	−6.69615	+	11.5981i	−0.629921	+	1.09106i	0.357646	+	0.933857i	$0.383579\pi$
$113$	−6.69615	+	11.5981i	−0.629921	+	1.09106i	−0.987567	+	0.157198i	$0.949754\pi$
$114$	−4.73205	−	8.19615i	−0.443197	−	0.767640i
$115$	4.09808	+	7.09808i	0.382148	+	0.661899i
$116$	−3.00000			−0.278543
$117$	8.92820	−	13.3923i	0.825413	−	1.23812i
$118$	−12.5885			−1.15886
$119$		0			0
$120$	4.09808	+	7.09808i	0.374101	+	0.647963i
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	8.32051			0.753303
$123$	7.09808	−	12.2942i	0.640012	−	1.10853i
$124$	2.09808	−	3.63397i	0.188413	−	0.326341i
$125$	12.1244			1.08444
$126$		0			0
$127$	−9.19615	−	15.9282i	−0.816027	−	1.41340i	−0.908588	−	0.417693i	$-0.862839\pi$
$127$	−9.19615	−	15.9282i	−0.816027	−	1.41340i	0.0925619	−	0.995707i	$-0.470494\pi$
$128$	−6.06218	−	10.5000i	−0.535826	−	0.928078i
$129$	0.535898			0.0471832
$130$	−4.79423	−	9.69615i	−0.420482	−	0.850409i
$131$	3.46410			0.302660			0.151330	−	0.988483i	$-0.451644\pi$
$131$	3.46410			0.302660			0.151330	+	0.988483i	$0.451644\pi$
$132$	1.73205	+	3.00000i	0.150756	+	0.261116i
$133$		0			0
$134$	5.36603	−	9.29423i	0.463554	−	0.802899i
$135$	6.92820			0.596285
$136$	6.69615	−	11.5981i	0.574190	−	0.994527i
$137$	−4.03590	+	6.99038i	−0.344810	+	0.597229i	−0.985319	−	0.170722i	$-0.945390\pi$
$137$	−4.03590	+	6.99038i	−0.344810	+	0.597229i	0.640509	+	0.767951i	$0.278723\pi$
$138$	−22.3923			−1.90616
$139$	−5.29423	+	9.16987i	−0.449051	+	0.777778i	−0.998324	−	0.0578639i	$-0.981571\pi$
$139$	−5.29423	+	9.16987i	−0.449051	+	0.777778i	0.549274	+	0.835642i	$0.314904\pi$
$140$		0			0
$141$	−17.6603	−	30.5885i	−1.48726	−	2.57601i
$142$	10.3923			0.872103
$143$	2.02628	+	4.09808i	0.169446	+	0.342698i
$144$	−22.3205			−1.86004
$145$	−2.59808	−	4.50000i	−0.215758	−	0.373705i
$146$	−2.76795	−	4.79423i	−0.229077	−	0.396773i
$147$		0			0
$148$	−7.00000			−0.575396
$149$	3.23205	−	5.59808i	0.264780	−	0.458612i	−0.702726	−	0.711461i	$-0.748034\pi$
$149$	3.23205	−	5.59808i	0.264780	−	0.458612i	0.967506	+	0.252848i	$0.0813674\pi$
$150$	−4.73205	+	8.19615i	−0.386370	+	0.669213i
$151$	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
$153$	−17.2583	−	29.8923i	−1.39525	−	2.41665i
$154$		0			0
$155$	7.26795			0.583776
$156$	9.83013	+	0.633975i	0.787040	+	0.0507586i
$157$	−1.19615			−0.0954634			−0.0477317	−	0.998860i	$-0.515199\pi$
$157$	−1.19615			−0.0954634			−0.0477317	+	0.998860i	$0.515199\pi$
$158$	−14.0263	−	24.2942i	−1.11587	−	1.93275i
$159$	−13.5622	−	23.4904i	−1.07555	−	1.86291i
$160$	−4.50000	+	7.79423i	−0.355756	+	0.616188i
$161$		0			0
$162$	2.13397	−	3.69615i	0.167661	−	0.290397i
$163$	−8.09808	+	14.0263i	−0.634290	+	1.09862i	0.352375	+	0.935859i	$0.385374\pi$
$163$	−8.09808	+	14.0263i	−0.634290	+	1.09862i	−0.986665	+	0.162764i	$0.947959\pi$
$164$	5.19615			0.405751
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−1.90192	−	3.29423i	−0.147618	−	0.255682i
$167$	−3.29423	−	5.70577i	−0.254915	−	0.441526i	0.709957	−	0.704245i	$-0.248714\pi$
$167$	−3.29423	−	5.70577i	−0.254915	−	0.441526i	−0.964872	+	0.262719i	$0.915381\pi$
$168$		0			0
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$	−23.1962			−1.77906
$171$	4.46410	+	7.73205i	0.341378	+	0.591285i
$172$	0.0980762	+	0.169873i	0.00747824	+	0.0129527i
$173$	4.26795	−	7.39230i	0.324486	−	0.562027i	−0.656922	−	0.753958i	$-0.728142\pi$
$173$	4.26795	−	7.39230i	0.324486	−	0.562027i	0.981408	+	0.191932i	$0.0614753\pi$
$174$	14.1962			1.07621
$175$		0			0
$176$	3.16987	−	5.49038i	0.238938	−	0.413853i
$177$	19.8564			1.49250
$178$	11.1962	−	19.3923i	0.839187	−	1.45351i
$179$	3.46410	+	6.00000i	0.258919	+	0.448461i	0.965953	−	0.258719i	$-0.0833004\pi$
$179$	3.46410	+	6.00000i	0.258919	+	0.448461i	−0.707034	+	0.707180i	$0.749967\pi$
$180$	3.86603	+	6.69615i	0.288157	+	0.499102i
$181$	−5.58846			−0.415387			−0.207693	−	0.978194i	$-0.566596\pi$
$181$	−5.58846			−0.415387			−0.207693	+	0.978194i	$0.566596\pi$
$182$		0			0
$183$	−13.1244			−0.970180
$184$	4.09808	+	7.09808i	0.302114	+	0.523277i
$185$	−6.06218	−	10.5000i	−0.445700	−	0.771975i
$186$	−9.92820	+	17.1962i	−0.727971	+	1.26088i
$187$	9.80385			0.716928
$188$	6.46410	−	11.1962i	0.471443	−	0.816563i
$189$		0			0
$190$	6.00000			0.435286
$191$	−2.36603	+	4.09808i	−0.171200	+	0.296526i	−0.938840	−	0.344355i	$-0.888098\pi$
$191$	−2.36603	+	4.09808i	−0.171200	+	0.296526i	0.767640	+	0.640881i	$0.221431\pi$
$192$	1.36603	+	2.36603i	0.0985844	+	0.170753i
$193$	−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	$0.890928\pi$
$194$	−11.0718			−0.794909
$195$	7.56218	+	15.2942i	0.541539	+	1.09524i
$196$		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	$0.973933\pi$
$198$	−4.90192	−	8.49038i	−0.348365	−	0.603385i
$199$	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
$201$	−8.46410	+	14.6603i	−0.597012	+	1.03405i
$202$	−6.69615	+	11.5981i	−0.471140	+	0.816038i
$203$		0			0
$204$	10.5622	−	18.2942i	0.739500	−	1.28085i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	−12.4641	−	21.5885i	−0.868415	−	1.50414i
$207$	21.1244			1.46824
$208$	−7.99038	−	16.1603i	−0.554033	−	1.12051i
$209$	−2.53590			−0.175412
$210$		0			0
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	0.895400	−	0.445263i	$-0.146890\pi$
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	−0.833309	+	0.552808i	$0.813556\pi$
$212$	4.96410	−	8.59808i	0.340936	−	0.590518i
$213$	−16.3923			−1.12318
$214$	6.80385	−	11.7846i	0.465101	−	0.805579i
$215$	−0.169873	+	0.294229i	−0.0115852	+	0.0200662i
$216$	6.92820			0.471405
$217$		0			0
$218$	7.26795	+	12.5885i	0.492248	+	0.852598i
$219$	4.36603	+	7.56218i	0.295029	+	0.511005i
$220$	−2.19615			−0.148065
$221$	15.4641	−	23.1962i	1.04023	−	1.56034i
$222$	33.1244			2.22316
$223$	−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
$225$	4.46410	−	7.73205i	0.297607	−	0.515470i
$226$	23.1962			1.54299
$227$	2.83013	−	4.90192i	0.187842	−	0.325352i	−0.756688	−	0.653776i	$-0.773184\pi$
$227$	2.83013	−	4.90192i	0.187842	−	0.325352i	0.944531	+	0.328424i	$0.106517\pi$
$228$	−2.73205	+	4.73205i	−0.180934	+	0.313388i
$229$	14.3923			0.951070			0.475535	−	0.879697i	$-0.342254\pi$
$229$	14.3923			0.951070			0.475535	+	0.879697i	$0.342254\pi$
$230$	7.09808	−	12.2942i	0.468033	−	0.810657i
$231$		0			0
$232$	−2.59808	−	4.50000i	−0.170572	−	0.295439i
$233$	−1.85641			−0.121617			−0.0608086	−	0.998149i	$-0.519368\pi$
$233$	−1.85641			−0.121617			−0.0608086	+	0.998149i	$0.519368\pi$
$234$	−27.8205	−	1.79423i	−1.81868	−	0.117292i
$235$	22.3923			1.46071
$236$	3.63397	+	6.29423i	0.236552	+	0.409719i
$237$	22.1244	+	38.3205i	1.43713	+	2.48918i
$238$		0			0
$239$	−15.8038			−1.02227			−0.511133	−	0.859502i	$-0.670774\pi$
$239$	−15.8038			−1.02227			−0.511133	+	0.859502i	$0.670774\pi$
$240$	11.8301	−	20.4904i	0.763631	−	1.32265i
$241$	−10.5981	+	18.3564i	−0.682682	+	1.18244i	0.291477	+	0.956578i	$0.405853\pi$
$241$	−10.5981	+	18.3564i	−0.682682	+	1.18244i	−0.974159	+	0.225862i	$0.927480\pi$
$242$	−16.2679			−1.04574
$243$	−9.36603	+	16.2224i	−0.600831	+	1.04067i
$244$	−2.40192	−	4.16025i	−0.153767	−	0.266333i
$245$		0			0
$246$	−24.5885			−1.56770
$247$	−4.00000	+	6.00000i	−0.254514	+	0.381771i
$248$	7.26795			0.461515
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	−10.5000	−	18.1865i	−0.664078	−	1.15022i
$251$	−0.803848	+	1.39230i	−0.0507384	+	0.0878815i	−0.890279	−	0.455415i	$-0.849491\pi$
$251$	−0.803848	+	1.39230i	−0.0507384	+	0.0878815i	0.839541	+	0.543297i	$0.182824\pi$
$252$		0			0
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−15.9282	+	27.5885i	−0.999424	+	1.73105i
$255$	36.5885			2.29126
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	3.06218	+	5.30385i	0.191013	+	0.330845i	0.945586	−	0.325371i	$-0.105489\pi$
$257$	3.06218	+	5.30385i	0.191013	+	0.330845i	−0.754573	+	0.656216i	$0.772156\pi$
$258$	−0.464102	−	0.803848i	−0.0288937	−	0.0500454i
$259$		0			0
$260$	−3.46410	+	5.19615i	−0.214834	+	0.322252i
$261$	−13.3923			−0.828963
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	0.845817	−	0.533473i	$-0.179113\pi$
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	−0.884910	+	0.465763i	$0.845780\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$	17.1962			1.05635
$266$		0			0
$267$	−17.6603	+	30.5885i	−1.08079	+	1.87198i
$268$	−6.19615			−0.378490
$269$	2.53590	−	4.39230i	0.154616	−	0.267804i	−0.778303	−	0.627889i	$-0.783919\pi$
$269$	2.53590	−	4.39230i	0.154616	−	0.267804i	0.932919	+	0.360086i	$0.117252\pi$
$270$	−6.00000	−	10.3923i	−0.365148	−	0.632456i
$271$	2.90192	+	5.02628i	0.176279	+	0.305325i	0.940603	−	0.339508i	$-0.110260\pi$
$271$	2.90192	+	5.02628i	0.176279	+	0.305325i	−0.764324	+	0.644832i	$0.776927\pi$
$272$	−38.6603			−2.34412
$273$		0			0
$274$	13.9808			0.844609
$275$	1.26795	+	2.19615i	0.0764602	+	0.132433i
$276$	6.46410	+	11.1962i	0.389093	+	0.673929i
$277$	−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	$0.996047\pi$
$278$	18.3397			1.09994
$279$	9.36603	−	16.2224i	0.560729	−	0.971212i
$280$		0			0
$281$	13.3923			0.798918			0.399459	−	0.916751i	$-0.369198\pi$
$281$	13.3923			0.798918			0.399459	+	0.916751i	$0.369198\pi$
$282$	−30.5885	+	52.9808i	−1.82152	+	3.15496i
$283$	5.09808	+	8.83013i	0.303049	+	0.524897i	0.976825	−	0.214039i	$-0.0686620\pi$
$283$	5.09808	+	8.83013i	0.303049	+	0.524897i	−0.673776	+	0.738936i	$0.735329\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−9.46410			−0.560605
$286$	4.39230	−	6.58846i	0.259722	−	0.389584i
$287$		0			0
$288$	11.5981	+	20.0885i	0.683423	+	1.18372i
$289$	−21.3923	−	37.0526i	−1.25837	−	2.17956i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	17.4641			1.02376
$292$	−1.59808	+	2.76795i	−0.0935203	+	0.161982i
$293$	−0.401924	+	0.696152i	−0.0234806	+	0.0406697i	−0.877527	−	0.479527i	$-0.840808\pi$
$293$	−0.401924	+	0.696152i	−0.0234806	+	0.0406697i	0.854046	+	0.520197i	$0.174141\pi$
$294$		0			0
$295$	−6.29423	+	10.9019i	−0.366464	+	0.634735i
$296$	−6.06218	−	10.5000i	−0.352357	−	0.610300i
$297$	2.53590	+	4.39230i	0.147148	+	0.254867i
$298$	−11.1962			−0.648576
$299$	7.56218	+	15.2942i	0.437332	+	0.884488i
$300$	5.46410			0.315470
$301$		0			0
$302$	−1.73205	−	3.00000i	−0.0996683	−	0.172631i
$303$	10.5622	−	18.2942i	0.606781	−	1.05098i
$304$	10.0000			0.573539
$305$	4.16025	−	7.20577i	0.238215	−	0.412601i
$306$	−29.8923	+	51.7750i	−1.70883	+	2.95978i
$307$	4.58846			0.261877			0.130939	−	0.991390i	$-0.458201\pi$
$307$	4.58846			0.261877			0.130939	+	0.991390i	$0.458201\pi$
$308$		0			0
$309$	19.6603	+	34.0526i	1.11843	+	1.93718i
$310$	−6.29423	−	10.9019i	−0.357488	−	0.619188i
$311$	−1.26795			−0.0718988			−0.0359494	−	0.999354i	$-0.511446\pi$
$311$	−1.26795			−0.0718988			−0.0359494	+	0.999354i	$0.511446\pi$
$312$	7.56218	+	15.2942i	0.428124	+	0.865865i
$313$	−28.7846			−1.62700			−0.813501	−	0.581563i	$-0.802441\pi$
$313$	−28.7846			−1.62700			−0.813501	+	0.581563i	$0.802441\pi$
$314$	1.03590	+	1.79423i	0.0584591	+	0.101254i
$315$		0			0
$316$	−8.09808	+	14.0263i	−0.455552	+	0.789040i
$317$	−6.46410			−0.363060			−0.181530	−	0.983385i	$-0.558105\pi$
$317$	−6.46410			−0.363060			−0.181530	+	0.983385i	$0.558105\pi$
$318$	−23.4904	+	40.6865i	−1.31728	+	2.28159i
$319$	1.90192	−	3.29423i	0.106487	−	0.184441i
$320$	−1.73205			−0.0968246
$321$	−10.7321	+	18.5885i	−0.599005	+	1.03751i
$322$		0			0
$323$	7.73205	+	13.3923i	0.430223	+	0.745168i
$324$	−2.46410			−0.136895
$325$	7.19615	+	0.464102i	0.399171	+	0.0257437i
$326$	28.0526			1.55369
$327$	−11.4641	−	19.8564i	−0.633966	−	1.09806i
$328$	4.50000	+	7.79423i	0.248471	+	0.430364i
$329$		0			0
$330$	10.3923			0.572078
$331$	−12.4904	+	21.6340i	−0.686533	+	1.18911i	0.286419	+	0.958105i	$0.407535\pi$
$331$	−12.4904	+	21.6340i	−0.686533	+	1.18911i	−0.972952	+	0.231006i	$0.925798\pi$
$332$	−1.09808	+	1.90192i	−0.0602648	+	0.104382i
$333$	−31.2487			−1.71242
$334$	−5.70577	+	9.88269i	−0.312206	+	0.540757i
$335$	−5.36603	−	9.29423i	−0.293177	−	0.507798i
$336$		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
$339$	−36.5885			−1.98721
$340$	6.69615	+	11.5981i	0.363150	+	0.628994i
$341$	2.66025	+	4.60770i	0.144061	+	0.249521i
$342$	7.73205	−	13.3923i	0.418101	−	0.724173i
$343$		0			0
$344$	−0.169873	+	0.294229i	−0.00915894	+	0.0158637i
$345$	−11.1962	+	19.3923i	−0.602781	+	1.04405i
$346$	−14.7846			−0.794826
$347$	−3.63397	+	6.29423i	−0.195082	+	0.337892i	−0.946927	−	0.321448i	$-0.895831\pi$
$347$	−3.63397	+	6.29423i	−0.195082	+	0.337892i	0.751845	+	0.659339i	$0.229164\pi$
$348$	−4.09808	−	7.09808i	−0.219680	−	0.380497i
$349$	−12.3923	−	21.4641i	−0.663345	−	1.14895i	−0.979731	−	0.200317i	$-0.935803\pi$
$349$	−12.3923	−	21.4641i	−0.663345	−	1.14895i	0.316386	−	0.948630i	$-0.397530\pi$
$350$		0			0
$351$	14.3923	+	0.928203i	0.768204	+	0.0495438i
$352$	−6.58846			−0.351166
$353$	10.3301	+	17.8923i	0.549817	+	0.952311i	0.998287	+	0.0585131i	$0.0186360\pi$
$353$	10.3301	+	17.8923i	0.549817	+	0.952311i	−0.448469	+	0.893798i	$0.648031\pi$
$354$	−17.1962	−	29.7846i	−0.913965	−	1.58303i
$355$	5.19615	−	9.00000i	0.275783	−	0.477670i
$356$	−12.9282			−0.685193
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	18.9282			0.998992			0.499496	−	0.866316i	$-0.333518\pi$
$359$	18.9282			0.998992			0.499496	+	0.866316i	$0.333518\pi$
$360$	−6.69615	+	11.5981i	−0.352918	+	0.611272i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	4.83975	+	8.38269i	0.254371	+	0.440584i
$363$	25.6603			1.34681
$364$		0			0
$365$	−5.53590			−0.289762
$366$	11.3660	+	19.6865i	0.594112	+	1.02903i
$367$	2.09808	+	3.63397i	0.109519	+	0.189692i	0.915575	−	0.402146i	$-0.131736\pi$
$367$	2.09808	+	3.63397i	0.109519	+	0.189692i	−0.806057	+	0.591838i	$0.798402\pi$
$368$	11.8301	−	20.4904i	0.616688	−	1.06813i
$369$	23.1962			1.20754
$370$	−10.5000	+	18.1865i	−0.545869	+	0.945473i
$371$		0			0
$372$	11.4641			0.594386
$373$	5.69615	−	9.86603i	0.294936	−	0.510843i	−0.680034	−	0.733180i	$-0.738035\pi$
$373$	5.69615	−	9.86603i	0.294936	−	0.510843i	0.974970	+	0.222337i	$0.0713685\pi$
$374$	−8.49038	−	14.7058i	−0.439027	−	0.760417i
$375$	16.5622	+	28.6865i	0.855267	+	1.48137i
$376$	22.3923			1.15479
$377$	−4.79423	−	9.69615i	−0.246915	−	0.499377i
$378$		0			0
$379$	−13.2942	−	23.0263i	−0.682879	−	1.18278i	−0.974098	−	0.226124i	$-0.927394\pi$
$379$	−13.2942	−	23.0263i	−0.682879	−	1.18278i	0.291220	−	0.956656i	$-0.405939\pi$
$380$	−1.73205	−	3.00000i	−0.0888523	−	0.153897i
$381$	25.1244	−	43.5167i	1.28716	−	2.22943i
$382$	8.19615			0.419352
$383$	−5.83013	+	10.0981i	−0.297906	+	0.515988i	−0.975657	−	0.219304i	$-0.929621\pi$
$383$	−5.83013	+	10.0981i	−0.297906	+	0.515988i	0.677751	+	0.735291i	$0.262955\pi$
$384$	16.5622	−	28.6865i	0.845185	−	1.46390i
$385$		0			0
$386$	−4.33013	+	7.50000i	−0.220398	+	0.381740i
$387$	0.437822	+	0.758330i	0.0222558	+	0.0385481i
$388$	3.19615	+	5.53590i	0.162260	+	0.281043i
$389$	−23.5359			−1.19332			−0.596659	−	0.802495i	$-0.703505\pi$
$389$	−23.5359			−1.19332			−0.596659	+	0.802495i	$0.703505\pi$
$390$	16.3923	−	24.5885i	0.830057	−	1.24508i
$391$	36.5885			1.85036
$392$		0			0
$393$	4.73205	+	8.19615i	0.238700	+	0.413441i
$394$	−10.3923	+	18.0000i	−0.523557	+	0.906827i
$395$	−28.0526			−1.41148
$396$	−2.83013	+	4.90192i	−0.142219	+	0.246331i
$397$	−9.39230	+	16.2679i	−0.471386	+	0.816465i	−0.999464	−	0.0327309i	$-0.989580\pi$
$397$	−9.39230	+	16.2679i	−0.471386	+	0.816465i	0.528078	+	0.849196i	$0.322913\pi$
$398$	−3.46410			−0.173640
$399$		0			0
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$	5.42820	+	9.40192i	0.271072	+	0.469510i	0.969136	−	0.246525i	$-0.0792887\pi$
$401$	5.42820	+	9.40192i	0.271072	+	0.469510i	−0.698065	+	0.716034i	$0.745955\pi$
$402$	29.3205			1.46237
$403$	15.0981	+	0.973721i	0.752089	+	0.0485045i
$404$	7.73205			0.384684
$405$	−2.13397	−	3.69615i	−0.106038	−	0.183663i
$406$		0			0
$407$	4.43782	−	7.68653i	0.219975	−	0.381007i
$408$	36.5885			1.81140
$409$	−8.40192	+	14.5526i	−0.415448	+	0.719578i	−0.995475	−	0.0950195i	$-0.969709\pi$
$409$	−8.40192	+	14.5526i	−0.415448	+	0.719578i	0.580027	+	0.814597i	$0.303042\pi$
$410$	7.79423	−	13.5000i	0.384930	−	0.666717i
$411$	−22.0526			−1.08777
$412$	−7.19615	+	12.4641i	−0.354529	+	0.614062i
$413$		0			0
$414$	−18.2942	−	31.6865i	−0.899112	−	1.55731i
$415$	−3.80385			−0.186724
$416$	−10.3923	+	15.5885i	−0.509525	+	0.764287i
$417$	−28.9282			−1.41662
$418$	2.19615	+	3.80385i	0.107417	+	0.186052i
$419$	−16.0981	−	27.8827i	−0.786442	−	1.36216i	−0.928134	−	0.372247i	$-0.878587\pi$
$419$	−16.0981	−	27.8827i	−0.786442	−	1.36216i	0.141691	−	0.989911i	$-0.454746\pi$
$420$		0			0
$421$	−32.1769			−1.56821			−0.784103	−	0.620630i	$-0.786877\pi$
$421$	−32.1769			−1.56821			−0.784103	+	0.620630i	$0.786877\pi$
$422$	1.56218	−	2.70577i	0.0760456	−	0.131715i
$423$	28.8564	−	49.9808i	1.40305	−	2.43015i
$424$	17.1962			0.835119
$425$	7.73205	−	13.3923i	0.375060	−	0.649622i
$426$	14.1962	+	24.5885i	0.687806	+	1.19131i
$427$		0			0
$428$	−7.85641			−0.379754
$429$	−6.92820	+	10.3923i	−0.334497	+	0.501745i
$430$	0.588457			0.0283779
$431$	−0.339746	−	0.588457i	−0.0163650	−	0.0283450i	0.857727	−	0.514106i	$-0.171876\pi$
$431$	−0.339746	−	0.588457i	−0.0163650	−	0.0283450i	−0.874092	+	0.485761i	$0.838543\pi$
$432$	−10.0000	−	17.3205i	−0.481125	−	0.833333i
$433$	−6.79423	+	11.7679i	−0.326510	+	0.565532i	−0.981817	−	0.189831i	$-0.939206\pi$
$433$	−6.79423	+	11.7679i	−0.326510	+	0.565532i	0.655307	+	0.755363i	$0.272539\pi$
$434$		0			0
$435$	7.09808	−	12.2942i	0.340327	−	0.589463i
$436$	4.19615	−	7.26795i	0.200959	−	0.348072i
$437$	−9.46410			−0.452729
$438$	7.56218	−	13.0981i	0.361335	−	0.625850i
$439$	7.29423	+	12.6340i	0.348135	+	0.602987i	0.985918	−	0.167229i	$-0.0534819\pi$
$439$	7.29423	+	12.6340i	0.348135	+	0.602987i	−0.637784	+	0.770216i	$0.720149\pi$
$440$	−1.90192	−	3.29423i	−0.0906707	−	0.157046i
$441$		0			0
$442$	−48.1865	−	3.10770i	−2.29200	−	0.147818i
$443$	23.3205			1.10799			0.553995	−	0.832520i	$-0.313103\pi$
$443$	23.3205			1.10799			0.553995	+	0.832520i	$0.313103\pi$
$444$	−9.56218	−	16.5622i	−0.453801	−	0.786006i
$445$	−11.1962	−	19.3923i	−0.530749	−	0.919283i
$446$	−8.66025	+	15.0000i	−0.410075	+	0.710271i
$447$	17.6603			0.835301
$448$		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	$0.0752847\pi$
$450$	−15.4641			−0.728985
$451$	−3.29423	+	5.70577i	−0.155119	+	0.268674i
$452$	−6.69615	−	11.5981i	−0.314961	−	0.545528i
$453$	2.73205	+	4.73205i	0.128363	+	0.222331i
$454$	−9.80385			−0.460117
$455$		0			0
$456$	−9.46410			−0.443197
$457$	−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	$0.916159\pi$
$458$	−12.4641	−	21.5885i	−0.582409	−	1.00876i
$459$	15.4641	−	26.7846i	0.721802	−	1.25020i
$460$	−8.19615			−0.382148
$461$	−7.79423	+	13.5000i	−0.363013	+	0.628758i	−0.988455	−	0.151513i	$-0.951585\pi$
$461$	−7.79423	+	13.5000i	−0.363013	+	0.628758i	0.625442	+	0.780271i	$0.284919\pi$
$462$		0			0
$463$	−4.58846			−0.213244			−0.106622	−	0.994300i	$-0.534003\pi$
$463$	−4.58846			−0.213244			−0.106622	+	0.994300i	$0.534003\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$	9.92820	+	17.1962i	0.460409	+	0.797452i
$466$	1.60770	+	2.78461i	0.0744750	+	0.128995i
$467$	−25.5167			−1.18077			−0.590385	−	0.807122i	$-0.701024\pi$
$467$	−25.5167			−1.18077			−0.590385	+	0.807122i	$0.701024\pi$
$468$	7.13397	+	14.4282i	0.329768	+	0.666944i
$469$		0			0
$470$	−19.3923	−	33.5885i	−0.894500	−	1.54932i
$471$	−1.63397	−	2.83013i	−0.0752896	−	0.130405i
$472$	−6.29423	+	10.9019i	−0.289715	+	0.501802i
$473$	−0.248711			−0.0114358
$474$	38.3205	−	66.3731i	1.76012	−	3.04862i
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	22.1603	−	38.3827i	1.01465	−	1.75742i
$478$	13.6865	+	23.7058i	0.626007	+	1.08428i
$479$	0.633975	+	1.09808i	0.0289670	+	0.0501724i	0.880146	−	0.474704i	$-0.157445\pi$
$479$	0.633975	+	1.09808i	0.0289670	+	0.0501724i	−0.851178	+	0.524876i	$0.824112\pi$
$480$	−24.5885			−1.12230
$481$	−11.1865	−	22.6244i	−0.510062	−	1.03158i
$482$	36.7128			1.67222
$483$		0			0
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	−5.53590	+	9.58846i	−0.251372	+	0.435389i
$486$	32.4449			1.47173
$487$	−20.3923	+	35.3205i	−0.924064	+	1.60052i	−0.131003	+	0.991382i	$0.541820\pi$
$487$	−20.3923	+	35.3205i	−0.924064	+	1.60052i	−0.793060	+	0.609143i	$0.791514\pi$
$488$	4.16025	−	7.20577i	0.188326	−	0.326190i
$489$	−44.2487			−2.00100
$490$		0			0
$491$	−3.80385	−	6.58846i	−0.171665	−	0.297333i	0.767337	−	0.641244i	$-0.221581\pi$
$491$	−3.80385	−	6.58846i	−0.171665	−	0.297333i	−0.939002	+	0.343911i	$0.888248\pi$
$492$	7.09808	+	12.2942i	0.320006	+	0.554267i
$493$	−23.1962			−1.04470
$494$	12.4641	+	0.803848i	0.560786	+	0.0361668i
$495$	−9.80385			−0.440650
$496$	−10.4904	−	18.1699i	−0.471032	−	0.815851i
$497$		0			0
$498$	5.19615	−	9.00000i	0.232845	−	0.403300i
$499$	−38.9808			−1.74502			−0.872509	−	0.488598i	$-0.837509\pi$
$499$	−38.9808			−1.74502			−0.872509	+	0.488598i	$0.837509\pi$
$500$	−6.06218	+	10.5000i	−0.271109	+	0.469574i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	2.78461			0.124283
$503$	−9.29423	+	16.0981i	−0.414409	+	0.717778i	−0.995366	−	0.0961565i	$-0.969345\pi$
$503$	−9.29423	+	16.0981i	−0.414409	+	0.717778i	0.580957	+	0.813934i	$0.302678\pi$
$504$		0			0
$505$	6.69615	+	11.5981i	0.297975	+	0.516108i
$506$	10.3923			0.461994
$507$	13.6603	+	32.7846i	0.606673	+	1.45602i
$508$	18.3923			0.816027
$509$	6.86603	+	11.8923i	0.304331	+	0.527117i	0.977112	−	0.212725i	$-0.0682337\pi$
$509$	6.86603	+	11.8923i	0.304331	+	0.527117i	−0.672781	+	0.739842i	$0.734900\pi$
$510$	−31.6865	−	54.8827i	−1.40310	−	2.43025i
$511$		0			0
$512$	8.66025			0.382733
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	5.30385	−	9.18653i	0.233943	−	0.405201i
$515$	−24.9282			−1.09847
$516$	−0.267949	+	0.464102i	−0.0117958	+	0.0204309i
$517$	8.19615	+	14.1962i	0.360466	+	0.624346i
$518$		0			0
$519$	23.3205			1.02366
$520$	−10.7942	−	0.696152i	−0.473358	−	0.0305283i
$521$	24.1244			1.05691			0.528454	−	0.848962i	$-0.322772\pi$
$521$	24.1244			1.05691			0.528454	+	0.848962i	$0.322772\pi$
$522$	11.5981	+	20.0885i	0.507634	+	0.879248i
$523$	−14.5885	−	25.2679i	−0.637909	−	1.10489i	−0.985891	−	0.167389i	$-0.946466\pi$
$523$	−14.5885	−	25.2679i	−0.637909	−	1.10489i	0.347982	−	0.937501i	$-0.386867\pi$
$524$	−1.73205	+	3.00000i	−0.0756650	+	0.131056i
$525$		0			0
$526$	−1.09808	+	1.90192i	−0.0478784	+	0.0829278i
$527$	16.2224	−	28.0981i	0.706660	−	1.22397i
$528$	17.3205			0.753778
$529$	0.303848	−	0.526279i	0.0132108	−	0.0228817i
$530$	−14.8923	−	25.7942i	−0.646880	−	1.12043i
$531$	16.2224	+	28.0981i	0.703994	+	1.21935i
$532$		0			0
$533$	8.30385	+	16.7942i	0.359680	+	0.727439i
$534$	61.1769			2.64738
$535$	−6.80385	−	11.7846i	−0.294156	−	0.509493i
$536$	−5.36603	−	9.29423i	−0.231777	−	0.401450i
$537$	−9.46410	+	16.3923i	−0.408406	+	0.707380i
$538$	−8.78461			−0.378731
$539$		0			0
$540$	−3.46410	+	6.00000i	−0.149071	+	0.258199i
$541$	−14.6077			−0.628034			−0.314017	−	0.949417i	$-0.601675\pi$
$541$	−14.6077			−0.628034			−0.314017	+	0.949417i	$0.601675\pi$
$542$	5.02628	−	8.70577i	0.215897	−	0.373945i
$543$	−7.63397	−	13.2224i	−0.327605	−	0.567429i
$544$	20.0885	+	34.7942i	0.861285	+	1.49179i
$545$	14.5359			0.622649
$546$		0			0
$547$	17.8038			0.761238			0.380619	−	0.924732i	$-0.375711\pi$
$547$	17.8038			0.761238			0.380619	+	0.924732i	$0.375711\pi$
$548$	−4.03590	−	6.99038i	−0.172405	−	0.298614i
$549$	−10.7224	−	18.5718i	−0.457622	−	0.792625i
$550$	2.19615	−	3.80385i	0.0936443	−	0.162197i
$551$	6.00000			0.255609
$552$	−11.1962	+	19.3923i	−0.476540	+	0.825391i
$553$		0			0
$554$	29.4449			1.25099
$555$	16.5622	−	28.6865i	0.703025	−	1.21768i
$556$	−5.29423	−	9.16987i	−0.224525	−	0.388889i
$557$	−21.8205	−	37.7942i	−0.924565	−	1.60139i	−0.792260	−	0.610184i	$-0.791096\pi$
$557$	−21.8205	−	37.7942i	−0.924565	−	1.60139i	−0.132305	−	0.991209i	$-0.542238\pi$
$558$	−32.4449			−1.37350
$559$	−0.392305	+	0.588457i	−0.0165927	+	0.0248891i
$560$		0			0
$561$	13.3923	+	23.1962i	0.565424	+	0.979342i
$562$	−11.5981	−	20.0885i	−0.489235	−	0.847380i
$563$	14.0263	−	24.2942i	0.591137	−	1.02388i	−0.402942	−	0.915225i	$-0.632013\pi$
$563$	14.0263	−	24.2942i	0.591137	−	1.02388i	0.994080	−	0.108654i	$-0.0346542\pi$
$564$	35.3205			1.48726
$565$	11.5981	−	20.0885i	0.487935	−	0.845128i
$566$	8.83013	−	15.2942i	0.371158	−	0.642864i
$567$		0			0
$568$	5.19615	−	9.00000i	0.218026	−	0.377632i
$569$	−21.4641	−	37.1769i	−0.899822	−	1.55854i	−0.827721	−	0.561140i	$-0.810363\pi$
$569$	−21.4641	−	37.1769i	−0.899822	−	1.55854i	−0.0721010	−	0.997397i	$-0.522970\pi$
$570$	8.19615	+	14.1962i	0.343299	+	0.594611i
$571$	16.7846			0.702414			0.351207	−	0.936298i	$-0.385771\pi$
$571$	16.7846			0.702414			0.351207	+	0.936298i	$0.385771\pi$
$572$	−4.56218	−	0.294229i	−0.190754	−	0.0123023i
$573$	−12.9282			−0.540083
$574$		0			0
$575$	4.73205	+	8.19615i	0.197340	+	0.341803i
$576$	−2.23205	+	3.86603i	−0.0930021	+	0.161084i
$577$	−43.1962			−1.79828			−0.899140	−	0.437662i	$-0.855807\pi$
$577$	−43.1962			−1.79828			−0.899140	+	0.437662i	$0.855807\pi$
$578$	−37.0526	+	64.1769i	−1.54118	+	2.66941i
$579$	6.83013	−	11.8301i	0.283850	−	0.491643i
$580$	5.19615			0.215758
$581$		0			0
$582$	−15.1244	−	26.1962i	−0.626925	−	1.08587i
$583$	6.29423	+	10.9019i	0.260680	+	0.451512i
$584$	−5.53590			−0.229077
$585$	−15.4641	+	23.1962i	−0.639362	+	0.959043i
$586$	1.39230			0.0575156
$587$	8.19615	+	14.1962i	0.338291	+	0.585938i	0.984111	−	0.177552i	$-0.0568177\pi$
$587$	8.19615	+	14.1962i	0.338291	+	0.585938i	−0.645820	+	0.763490i	$0.723484\pi$
$588$		0			0
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$	21.8038			0.897650
$591$	16.3923	−	28.3923i	0.674289	−	1.16790i
$592$	−17.5000	+	30.3109i	−0.719246	+	1.24577i
$593$	17.4449			0.716375			0.358187	−	0.933650i	$-0.383395\pi$
$593$	17.4449			0.716375			0.358187	+	0.933650i	$0.383395\pi$
$594$	4.39230	−	7.60770i	0.180218	−	0.312148i
$595$		0			0
$596$	3.23205	+	5.59808i	0.132390	+	0.229306i
$597$	5.46410			0.223631
$598$	16.3923	−	24.5885i	0.670331	−	1.00550i
$599$	43.8564			1.79192			0.895962	−	0.444131i	$-0.146487\pi$
$599$	43.8564			1.79192			0.895962	+	0.444131i	$0.146487\pi$
$600$	4.73205	+	8.19615i	0.193185	+	0.334607i
$601$	−14.9904	−	25.9641i	−0.611470	−	1.05910i	−0.990993	−	0.133915i	$-0.957245\pi$
$601$	−14.9904	−	25.9641i	−0.611470	−	1.05910i	0.379522	−	0.925183i	$-0.376088\pi$
$602$		0			0
$603$	−27.6603			−1.12641
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	−8.13397	+	14.0885i	−0.330693	+	0.572777i
$606$	−36.5885			−1.48630
$607$	−7.19615	+	12.4641i	−0.292083	+	0.505902i	−0.974302	−	0.225245i	$-0.927682\pi$
$607$	−7.19615	+	12.4641i	−0.292083	+	0.505902i	0.682219	+	0.731148i	$0.261015\pi$
$608$	−5.19615	−	9.00000i	−0.210732	−	0.364998i
$609$		0			0
$610$	−14.4115			−0.583506
$611$	46.5167	+	3.00000i	1.88186	+	0.121367i
$612$	34.5167			1.39525
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	0.829737	−	0.558154i	$-0.188490\pi$
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	−0.898244	+	0.439497i	$0.855157\pi$
$614$	−3.97372	−	6.88269i	−0.160366	−	0.277763i
$615$	−12.2942	+	21.2942i	−0.495751	+	0.858666i
$616$		0			0
$617$	−24.6962	+	42.7750i	−0.994230	+	1.72206i	−0.404214	+	0.914664i	$0.632455\pi$
$617$	−24.6962	+	42.7750i	−0.994230	+	1.72206i	−0.590016	+	0.807392i	$0.700878\pi$
$618$	34.0526	−	58.9808i	1.36979	−	2.37255i
$619$	−35.3731			−1.42176			−0.710882	−	0.703311i	$-0.751704\pi$
$619$	−35.3731			−1.42176			−0.710882	+	0.703311i	$0.751704\pi$
$620$	−3.63397	+	6.29423i	−0.145944	+	0.252782i
$621$	9.46410	+	16.3923i	0.379781	+	0.657801i
$622$	1.09808	+	1.90192i	0.0440288	+	0.0762602i
$623$		0			0
$624$	27.3205	−	40.9808i	1.09370	−	1.64054i
$625$	−11.0000			−0.440000
$626$	24.9282	+	43.1769i	0.996331	+	1.72570i
$627$	−3.46410	−	6.00000i	−0.138343	−	0.239617i
$628$	0.598076	−	1.03590i	0.0238658	−	0.0413368i
$629$	−54.1244			−2.15808
$630$		0			0
$631$	6.39230	−	11.0718i	0.254474	−	0.440761i	−0.710279	−	0.703920i	$-0.751431\pi$
$631$	6.39230	−	11.0718i	0.254474	−	0.440761i	0.964752	+	0.263159i	$0.0847645\pi$
$632$	−28.0526			−1.11587
$633$	−2.46410	+	4.26795i	−0.0979392	+	0.169636i
$634$	5.59808	+	9.69615i	0.222328	+	0.385083i
$635$	15.9282	+	27.5885i	0.632091	+	1.09481i
$636$	27.1244			1.07555
$637$		0			0
$638$	−6.58846			−0.260840
$639$	−13.3923	−	23.1962i	−0.529791	−	0.917626i
$640$	10.5000	+	18.1865i	0.415049	+	0.718886i
$641$	−14.4282	+	24.9904i	−0.569880	+	0.987061i	0.426698	+	0.904394i	$0.359677\pi$
$641$	−14.4282	+	24.9904i	−0.569880	+	0.987061i	−0.996577	+	0.0826663i	$0.973656\pi$
$642$	37.1769			1.46726
$643$	−0.392305	+	0.679492i	−0.0154710	+	0.0267965i	−0.873657	−	0.486542i	$-0.838258\pi$
$643$	−0.392305	+	0.679492i	−0.0154710	+	0.0267965i	0.858186	+	0.513338i	$0.171591\pi$
$644$		0			0
$645$	−0.928203			−0.0365480
$646$	13.3923	−	23.1962i	0.526913	−	0.912640i
$647$	22.5167	+	39.0000i	0.885221	+	1.53325i	0.845460	+	0.534039i	$0.179326\pi$
$647$	22.5167	+	39.0000i	0.885221	+	1.53325i	0.0397614	+	0.999209i	$0.487340\pi$
$648$	−2.13397	−	3.69615i	−0.0838304	−	0.145199i
$649$	−9.21539			−0.361736
$650$	−5.53590	−	11.1962i	−0.217136	−	0.439149i
$651$		0			0
$652$	−8.09808	−	14.0263i	−0.317145	−	0.549311i
$653$	18.9282	+	32.7846i	0.740718	+	1.28296i	0.952169	+	0.305572i	$0.0988478\pi$
$653$	18.9282	+	32.7846i	0.740718	+	1.28296i	−0.211451	+	0.977389i	$0.567819\pi$
$654$	−19.8564	+	34.3923i	−0.776447	+	1.34485i
$655$	−6.00000			−0.234439
$656$	12.9904	−	22.5000i	0.507189	−	0.878477i
$657$	−7.13397	+	12.3564i	−0.278323	+	0.482069i
$658$		0			0
$659$	−14.1962	+	24.5885i	−0.553004	+	0.957830i	0.445052	+	0.895505i	$0.353185\pi$
$659$	−14.1962	+	24.5885i	−0.553004	+	0.957830i	−0.998056	+	0.0623257i	$0.980148\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−16.5981	−	28.7487i	−0.645590	−	1.11820i	−0.984165	−	0.177256i	$-0.943278\pi$
$661$	−16.5981	−	28.7487i	−0.645590	−	1.11820i	0.338574	−	0.940940i	$-0.390055\pi$
$662$	43.2679			1.68166
$663$	76.0070	+	4.90192i	2.95187	+	0.190375i
$664$	−3.80385			−0.147618
$665$		0			0
$666$	27.0622	+	46.8731i	1.04864	+	1.81629i
$667$	7.09808	−	12.2942i	0.274839	−	0.476034i
$668$	6.58846			0.254915
$669$	13.6603	−	23.6603i	0.528136	−	0.914758i
$670$	−9.29423	+	16.0981i	−0.359067	+	0.621923i
$671$	6.09103			0.235142
$672$		0			0
$673$	22.0885	+	38.2583i	0.851447	+	1.47475i	0.879902	+	0.475155i	$0.157608\pi$
$673$	22.0885	+	38.2583i	0.851447	+	1.47475i	−0.0284546	+	0.999595i	$0.509059\pi$
$674$	−9.52628	−	16.5000i	−0.366939	−	0.635556i
$675$	8.00000			0.307920
$676$	−7.89230	+	10.3301i	−0.303550	+	0.397313i
$677$	23.0718			0.886721			0.443361	−	0.896343i	$-0.353786\pi$
$677$	23.0718			0.886721			0.443361	+	0.896343i	$0.353786\pi$
$678$	31.6865	+	54.8827i	1.21691	+	2.10776i
$679$		0			0
$680$	−11.5981	+	20.0885i	−0.444766	+	0.770357i
$681$	15.4641			0.592586
$682$	4.60770	−	7.98076i	0.176438	−	0.305599i
$683$	−7.73205	+	13.3923i	−0.295859	+	0.512442i	−0.975184	−	0.221395i	$-0.928939\pi$
$683$	−7.73205	+	13.3923i	−0.295859	+	0.512442i	0.679326	+	0.733837i	$0.262272\pi$
$684$	−8.92820			−0.341378
$685$	6.99038	−	12.1077i	0.267089	−	0.462611i
$686$		0			0
$687$	19.6603	+	34.0526i	0.750085	+	1.29919i
$688$	0.980762			0.0373912
$689$	35.7224	+	2.30385i	1.36092	+	0.0877696i
$690$	38.7846			1.47650
$691$	0.196152	+	0.339746i	0.00746199	+	0.0129245i	0.869732	−	0.493524i	$-0.164291\pi$
$691$	0.196152	+	0.339746i	0.00746199	+	0.0129245i	−0.862270	+	0.506448i	$0.830958\pi$
$692$	4.26795	+	7.39230i	0.162243	+	0.281013i
$693$		0			0
$694$	12.5885			0.477851
$695$	9.16987	−	15.8827i	0.347833	−	0.602465i
$696$	7.09808	−	12.2942i	0.269052	−	0.466012i
$697$	40.1769			1.52181
$698$	−21.4641	+	37.1769i	−0.812428	+	1.40717i
$699$	−2.53590	−	4.39230i	−0.0959165	−	0.166132i
$700$		0			0
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	−11.0718	−	22.3923i	−0.417878	−	0.845143i
$703$	14.0000			0.528020
$704$	−0.633975	−	1.09808i	−0.0238938	−	0.0413853i
$705$	30.5885	+	52.9808i	1.15203	+	1.99537i
$706$	17.8923	−	30.9904i	0.673386	−	1.16634i
$707$		0			0
$708$	−9.92820	+	17.1962i	−0.373125	+	0.646271i
$709$	−15.0885	+	26.1340i	−0.566659	+	0.981482i	0.430234	+	0.902717i	$0.358431\pi$
$709$	−15.0885	+	26.1340i	−0.566659	+	0.981482i	−0.996893	+	0.0787648i	$0.974902\pi$
$710$	−18.0000			−0.675528
$711$	−36.1506	+	62.6147i	−1.35575	+	2.34824i
$712$	−11.1962	−	19.3923i	−0.419594	−	0.726757i
$713$	9.92820	+	17.1962i	0.371814	+	0.644001i
$714$		0			0
$715$	−3.50962	−	7.09808i	−0.131252	−	0.265453i
$716$	−6.92820			−0.258919
$717$	−21.5885	−	37.3923i	−0.806236	−	1.39644i
$718$	−16.3923	−	28.3923i	−0.611755	−	1.05959i
$719$	−3.63397	+	6.29423i	−0.135524	+	0.234735i	−0.925798	−	0.378019i	$-0.876605\pi$
$719$	−3.63397	+	6.29423i	−0.135524	+	0.234735i	0.790273	+	0.612755i	$0.209939\pi$
$720$	38.6603			1.44078
$721$		0			0
$722$	12.9904	−	22.5000i	0.483452	−	0.837363i
$723$	−57.9090			−2.15366
$724$	2.79423	−	4.83975i	0.103847	−	0.179868i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−22.2224	−	38.4904i	−0.824752	−	1.42851i
$727$	41.1769			1.52717			0.763584	−	0.645709i	$-0.223438\pi$
$727$	41.1769			1.52717			0.763584	+	0.645709i	$0.223438\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	4.79423	+	8.30385i	0.177442	+	0.307339i
$731$	0.758330	+	1.31347i	0.0280479	+	0.0485803i
$732$	6.56218	−	11.3660i	0.242545	−	0.420100i
$733$	−23.5885			−0.871260			−0.435630	−	0.900126i	$-0.643474\pi$
$733$	−23.5885			−0.871260			−0.435630	+	0.900126i	$0.643474\pi$
$734$	3.63397	−	6.29423i	0.134132	−	0.232324i
$735$		0			0
$736$	−24.5885			−0.906343
$737$	3.92820	−	6.80385i	0.144697	−	0.250623i
$738$	−20.0885	−	34.7942i	−0.739466	−	1.28079i
$739$	−20.3923	−	35.3205i	−0.750143	−	1.29929i	−0.947753	−	0.319005i	$-0.896651\pi$
$739$	−20.3923	−	35.3205i	−0.750143	−	1.29929i	0.197610	−	0.980281i	$-0.436682\pi$
$740$	12.1244			0.445700
$741$	−19.6603	−	1.26795i	−0.722237	−	0.0465793i
$742$		0			0
$743$	3.80385	+	6.58846i	0.139550	+	0.241707i	0.927326	−	0.374254i	$-0.122101\pi$
$743$	3.80385	+	6.58846i	0.139550	+	0.241707i	−0.787777	+	0.615961i	$0.788768\pi$
$744$	9.92820	+	17.1962i	0.363986	+	0.630442i
$745$	−5.59808	+	9.69615i	−0.205098	+	0.355240i
$746$	−19.7321			−0.722442
$747$	−4.90192	+	8.49038i	−0.179352	+	0.310647i
$748$	−4.90192	+	8.49038i	−0.179232	+	0.310439i
$749$		0			0
$750$	28.6865	−	49.6865i	1.04748	−	1.81430i
$751$	−17.9019	−	31.0070i	−0.653250	−	1.13146i	−0.982329	−	0.187161i	$-0.940072\pi$
$751$	−17.9019	−	31.0070i	−0.653250	−	1.13146i	0.329079	−	0.944302i	$-0.393262\pi$
$752$	−32.3205	−	55.9808i	−1.17861	−	2.04141i
$753$	−4.39230			−0.160064
$754$	−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	$0.739424\pi$
$758$	−23.0263	+	39.8827i	−0.836352	+	1.44860i
$759$	−16.3923			−0.595003
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	20.6603	−	35.7846i	0.748934	−	1.29719i	−0.199401	−	0.979918i	$-0.563900\pi$
$761$	20.6603	−	35.7846i	0.748934	−	1.29719i	0.948334	−	0.317273i	$-0.102767\pi$
$762$	−87.0333			−3.15288
$763$		0			0
$764$	−2.36603	−	4.09808i	−0.0855998	−	0.148263i
$765$	29.8923	+	51.7750i	1.08076	+	1.87193i
$766$	20.1962			0.729717
$767$	−14.5359	+	21.8038i	−0.524861	+	0.787291i
$768$	−51.9090			−1.87310
$769$	7.58846	+	13.1436i	0.273647	+	0.473970i	0.969793	−	0.243930i	$-0.0784367\pi$
$769$	7.58846	+	13.1436i	0.273647	+	0.473970i	−0.696146	+	0.717900i	$0.745103\pi$
$770$		0			0
$771$	−8.36603	+	14.4904i	−0.301295	+	0.521858i
$772$	5.00000			0.179954
$773$	−6.46410	+	11.1962i	−0.232498	+	0.402698i	−0.958542	−	0.284950i	$-0.908023\pi$
$773$	−6.46410	+	11.1962i	−0.232498	+	0.402698i	0.726045	+	0.687647i	$0.241356\pi$
$774$	0.758330	−	1.31347i	0.0272576	−	0.0472116i
$775$	8.39230			0.301460
$776$	−5.53590	+	9.58846i	−0.198727	+	0.344206i
$777$		0			0
$778$	20.3827	+	35.3038i	0.730755	+	1.26570i
$779$	−10.3923			−0.372343
$780$	−17.0263	−	1.09808i	−0.609639	−	0.0393174i
$781$	7.60770			0.272225
$782$	−31.6865	−	54.8827i	−1.13311	−	1.96260i
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$		0			0
$785$	2.07180			0.0739456
$786$	8.19615	−	14.1962i	0.292347	−	0.506360i
$787$	6.49038	−	11.2417i	0.231357	−	0.400722i	−0.726851	−	0.686796i	$-0.759017\pi$
$787$	6.49038	−	11.2417i	0.231357	−	0.400722i	0.958208	+	0.286073i	$0.0923501\pi$
$788$	12.0000			0.427482
$789$	1.73205	−	3.00000i	0.0616626	−	0.106803i
$790$	24.2942	+	42.0788i	0.864350	+	1.49710i
$791$		0			0
$792$	−9.80385			−0.348365
$793$	9.60770	−	14.4115i	0.341179	−	0.511769i
$794$	32.5359			1.15466
$795$	23.4904	+	40.6865i	0.833118	+	1.44300i
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	−17.1962	+	29.7846i	−0.609119	+	1.05503i	0.382267	+	0.924052i	$0.375143\pi$
$797$	−17.1962	+	29.7846i	−0.609119	+	1.05503i	−0.991386	+	0.130973i	$0.958190\pi$
$798$		0			0
$799$	49.9808	−	86.5692i	1.76819	−	3.06260i
$800$	−5.19615	+	9.00000i	−0.183712	+	0.318198i
$801$	−57.7128			−2.03918
$802$	9.40192	−	16.2846i	0.331993	−	0.575030i
$803$	−2.02628	−	3.50962i	−0.0715058	−	0.123852i
$804$	−8.46410	−	14.6603i	−0.298506	−	0.517027i
$805$		0			0
$806$	−11.6147	−	23.4904i	−0.409112	−	0.827413i
$807$	13.8564			0.487769
$808$	6.69615	+	11.5981i	0.235570	+	0.408019i
$809$	−1.03590	−	1.79423i	−0.0364202	−	0.0630817i	0.847241	−	0.531209i	$-0.178262\pi$
$809$	−1.03590	−	1.79423i	−0.0364202	−	0.0630817i	−0.883661	+	0.468127i	$0.844929\pi$
$810$	−3.69615	+	6.40192i	−0.129870	+	0.224941i
$811$	16.5885			0.582500			0.291250	−	0.956647i	$-0.405929\pi$
$811$	16.5885			0.582500			0.291250	+	0.956647i	$0.405929\pi$
$812$		0			0
$813$	−7.92820	+	13.7321i	−0.278054	+	0.481604i
$814$	−15.3731			−0.538826
$815$	14.0263	−	24.2942i	0.491319	−	0.850990i
$816$	−52.8109	−	91.4711i	−1.84875	−	3.20213i
$817$	−0.196152	−	0.339746i	−0.00686250	−	0.0118862i
$818$	29.1051			1.01764
$819$		0			0
$820$	−9.00000			−0.314294
$821$	−2.07180	−	3.58846i	−0.0723062	−	0.125238i	0.827605	−	0.561310i	$-0.189703\pi$
$821$	−2.07180	−	3.58846i	−0.0723062	−	0.125238i	−0.899912	+	0.436072i	$0.856369\pi$
$822$	19.0981	+	33.0788i	0.666122	+	1.15376i
$823$	20.5885	−	35.6603i	0.717669	−	1.24304i	−0.244253	−	0.969712i	$-0.578543\pi$
$823$	20.5885	−	35.6603i	0.717669	−	1.24304i	0.961921	−	0.273327i	$-0.0881240\pi$
$824$	−24.9282			−0.868415
$825$	−3.46410	+	6.00000i	−0.120605	+	0.208893i
$826$		0			0
$827$	−16.9808			−0.590479			−0.295239	−	0.955423i	$-0.595399\pi$
$827$	−16.9808			−0.590479			−0.295239	+	0.955423i	$0.595399\pi$
$828$	−10.5622	+	18.2942i	−0.367061	+	0.635768i
$829$	−0.205771	−	0.356406i	−0.00714673	−	0.0123785i	0.862430	−	0.506176i	$-0.168942\pi$
$829$	−0.205771	−	0.356406i	−0.00714673	−	0.0123785i	−0.869577	+	0.493798i	$0.835608\pi$
$830$	3.29423	+	5.70577i	0.114344	+	0.198050i
$831$	−46.4449			−1.61115
$832$	−3.59808	−	0.232051i	−0.124741	−	0.00804491i
$833$		0			0
$834$	25.0526	+	43.3923i	0.867499	+	1.50255i
$835$	5.70577	+	9.88269i	0.197456	+	0.342004i
$836$	1.26795	−	2.19615i	0.0438529	−	0.0759555i
$837$	16.7846			0.580161
$838$	−27.8827	+	48.2942i	−0.963191	+	1.66830i
$839$	−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
$842$	27.8660	+	48.2654i	0.960327	+	1.66333i
$843$	18.2942	+	31.6865i	0.630087	+	1.09134i
$844$	−1.80385			−0.0620910
$845$	−22.3301	−	2.89230i	−0.768180	−	0.0994983i
$846$	−99.9615			−3.43675
$847$		0			0
$848$	−24.8205	−	42.9904i	−0.852340	−	1.47630i
$849$	−13.9282	+	24.1244i	−0.478015	+	0.827946i
$850$	−26.7846			−0.918705
$851$	16.5622	−	28.6865i	0.567744	−	0.983362i
$852$	8.19615	−	14.1962i	0.280796	−	0.486352i
$853$	−5.58846			−0.191345			−0.0956726	−	0.995413i	$-0.530500\pi$
$853$	−5.58846			−0.191345			−0.0956726	+	0.995413i	$0.530500\pi$
$854$		0			0
$855$	−7.73205	−	13.3923i	−0.264431	−	0.458007i
$856$	−6.80385	−	11.7846i	−0.232551	−	0.402790i
$857$	30.1244			1.02903			0.514514	−	0.857482i	$-0.327972\pi$
$857$	30.1244			1.02903			0.514514	+	0.857482i	$0.327972\pi$
$858$	21.5885	+	1.39230i	0.737018	+	0.0475325i
$859$	7.80385			0.266264			0.133132	−	0.991098i	$-0.457497\pi$
$859$	7.80385			0.266264			0.133132	+	0.991098i	$0.457497\pi$
$860$	−0.169873	−	0.294229i	−0.00579262	−	0.0100331i
$861$		0			0
$862$	−0.588457	+	1.01924i	−0.0200429	+	0.0347154i
$863$	7.51666			0.255870			0.127935	−	0.991783i	$-0.459165\pi$
$863$	7.51666			0.255870			0.127935	+	0.991783i	$0.459165\pi$
$864$	−10.3923	+	18.0000i	−0.353553	+	0.612372i
$865$	−7.39230	+	12.8038i	−0.251346	+	0.435344i
$866$	23.5359			0.799782
$867$	58.4449	−	101.229i	1.98489	−	3.43793i
$868$		0			0
$869$	−10.2679	−	17.7846i	−0.348316	−	0.603302i
$870$	−24.5885			−0.833627
$871$	−9.90192	−	20.0263i	−0.335514	−	0.678565i
$872$	14.5359			0.492248
$873$	14.2679	+	24.7128i	0.482897	+	0.836402i
$874$	8.19615	+	14.1962i	0.277239	+	0.480192i
$875$		0			0
$876$	−8.73205			−0.295029
$877$	−9.89230	+	17.1340i	−0.334039	+	0.578573i	−0.983300	−	0.181993i	$-0.941745\pi$
$877$	−9.89230	+	17.1340i	−0.334039	+	0.578573i	0.649260	+	0.760566i	$0.275079\pi$
$878$	12.6340	−	21.8827i	0.426376	−	0.738505i
$879$	−2.19615			−0.0740744
$880$	−5.49038	+	9.50962i	−0.185081	+	0.320569i
$881$	−4.20577	−	7.28461i	−0.141696	−	0.245425i	0.786439	−	0.617667i	$-0.211922\pi$
$881$	−4.20577	−	7.28461i	−0.141696	−	0.245425i	−0.928135	+	0.372243i	$0.878589\pi$
$882$		0			0
$883$	−47.7654			−1.60743			−0.803716	−	0.595013i	$-0.797147\pi$
$883$	−47.7654			−1.60743			−0.803716	+	0.595013i	$0.797147\pi$
$884$	12.3564	+	24.9904i	0.415591	+	0.840517i
$885$	−34.3923			−1.15608
$886$	−20.1962	−	34.9808i	−0.678503	−	1.17520i
$887$	5.66025	+	9.80385i	0.190053	+	0.329181i	0.945267	−	0.326296i	$-0.105801\pi$
$887$	5.66025	+	9.80385i	0.190053	+	0.329181i	−0.755215	+	0.655477i	$0.772467\pi$
$888$	16.5622	−	28.6865i	0.555790	−	0.962657i
$889$		0			0
$890$	−19.3923	+	33.5885i	−0.650032	+	1.12589i
$891$	1.56218	−	2.70577i	0.0523349	−	0.0906468i
$892$	10.0000			0.334825
$893$	−12.9282	+	22.3923i	−0.432626	+	0.749330i
$894$	−15.2942	−	26.4904i	−0.511516	−	0.885971i
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$		0			0
$897$	−25.8564	+	38.7846i	−0.863320	+	1.29498i
$898$	−20.7846			−0.693591
$899$	−6.29423	−	10.9019i	−0.209924	−	0.363600i
$900$	4.46410	+	7.73205i	0.148803	+	0.257735i
$901$	38.3827	−	66.4808i	1.27871	−	2.21480i
$902$	11.4115			0.379963
$903$		0			0
$904$	11.5981	−	20.0885i	0.385746	−	0.668132i
$905$	9.67949			0.321757
$906$	4.73205	−	8.19615i	0.157212	−	0.272299i
$907$	8.29423	+	14.3660i	0.275405	+	0.477016i	0.970237	−	0.242156i	$-0.0778546\pi$
$907$	8.29423	+	14.3660i	0.275405	+	0.477016i	−0.694832	+	0.719172i	$0.744521\pi$
$908$	2.83013	+	4.90192i	0.0939211	+	0.162676i
$909$	34.5167			1.14485
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	13.6603	+	23.6603i	0.452336	+	0.783469i
$913$	−1.39230	−	2.41154i	−0.0460786	−	0.0798104i
$914$	−9.52628	+	16.5000i	−0.315101	+	0.545771i
$915$	22.7321			0.751498
$916$	−7.19615	+	12.4641i	−0.237768	+	0.411826i
$917$		0			0
$918$	−53.5692			−1.76805
$919$	19.7846	−	34.2679i	0.652634	−	1.13040i	−0.329847	−	0.944034i	$-0.606997\pi$
$919$	19.7846	−	34.2679i	0.652634	−	1.13040i	0.982481	−	0.186361i	$-0.0596694\pi$
$920$	−7.09808	−	12.2942i	−0.234017	−	0.405329i
$921$	6.26795	+	10.8564i	0.206536	+	0.357731i
$922$	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
$926$	3.97372	+	6.88269i	0.130585	+	0.226179i
$927$	−32.1244	+	55.6410i	−1.05510	+	1.82749i
$928$	15.5885			0.511716
$929$	26.2583	−	45.4808i	0.861508	−	1.49218i	−0.00896546	−	0.999960i	$-0.502854\pi$
$929$	26.2583	−	45.4808i	0.861508	−	1.49218i	0.870473	−	0.492216i	$-0.163813\pi$
$930$	17.1962	−	29.7846i	0.563884	−	0.976676i
$931$		0			0
$932$	0.928203	−	1.60770i	0.0304043	−	0.0526618i
$933$	−1.73205	−	3.00000i	−0.0567048	−	0.0982156i
$934$	22.0981	+	38.2750i	0.723071	+	1.25240i
$935$	−16.9808			−0.555330
$936$	−15.4641	+	23.1962i	−0.505460	+	0.758190i
$937$	51.1962			1.67251			0.836253	−	0.548344i	$-0.184742\pi$
$937$	51.1962			1.67251			0.836253	+	0.548344i	$0.184742\pi$
$938$		0			0
$939$	−39.3205	−	68.1051i	−1.28318	−	2.22253i
$940$	−11.1962	+	19.3923i	−0.365178	+	0.632507i
$941$	28.1436			0.917455			0.458727	−	0.888577i	$-0.348305\pi$
$941$	28.1436			0.917455			0.458727	+	0.888577i	$0.348305\pi$
$942$	−2.83013	+	4.90192i	−0.0922105	+	0.159713i
$943$	−12.2942	+	21.2942i	−0.400355	+	0.693435i
$944$	36.3397			1.18276
$945$		0			0
$946$	0.215390	+	0.373067i	0.00700294	+	0.0121295i
$947$	3.63397	+	6.29423i	0.118088	+	0.204535i	0.919010	−	0.394234i	$-0.128990\pi$
$947$	3.63397	+	6.29423i	0.118088	+	0.204535i	−0.800922	+	0.598769i	$0.795657\pi$
$948$	−44.2487			−1.43713
$949$	−11.5000	−	0.741670i	−0.373306	−	0.0240756i
$950$	6.92820			0.224781
$951$	−8.83013	−	15.2942i	−0.286336	−	0.495949i
$952$		0			0
$953$	12.5885	−	21.8038i	0.407780	−	0.706296i	−0.586861	−	0.809688i	$-0.699636\pi$
$953$	12.5885	−	21.8038i	0.407780	−	0.706296i	0.994641	+	0.103392i	$0.0329697\pi$
$954$	−76.7654			−2.48537
$955$	4.09808	−	7.09808i	0.132611	−	0.229688i
$956$	7.90192	−	13.6865i	0.255566	−	0.442654i
$957$	10.3923			0.335936
$958$	1.09808	−	1.90192i	0.0354772	−	0.0614484i
$959$		0			0
$960$	−2.36603	−	4.09808i	−0.0763631	−	0.132265i
$961$	−13.3923			−0.432010
$962$	−24.2487	+	36.3731i	−0.781810	+	1.17271i
$963$	−35.0718			−1.13017
$964$	−10.5981	−	18.3564i	−0.341341	−	0.591220i
$965$	4.33013	+	7.50000i	0.139392	+	0.241434i
$966$		0			0
$967$	54.9808			1.76806			0.884031	−	0.467428i	$-0.154819\pi$
$967$	54.9808			1.76806			0.884031	+	0.467428i	$0.154819\pi$
$968$	−8.13397	+	14.0885i	−0.261436	+	0.452820i
$969$	−21.1244	+	36.5885i	−0.678612	+	1.17539i
$970$	19.1769			0.615734
$971$	−26.3205	+	45.5885i	−0.844665	+	1.46300i	0.0412463	+	0.999149i	$0.486867\pi$
$971$	−26.3205	+	45.5885i	−0.844665	+	1.46300i	−0.885912	+	0.463854i	$0.846466\pi$
$972$	−9.36603	−	16.2224i	−0.300415	−	0.520335i
$973$		0			0
$974$	70.6410			2.26348
$975$	8.73205	+	17.6603i	0.279649	+	0.565581i
$976$	−24.0192			−0.768837
$977$	−15.8205	−	27.4019i	−0.506143	−	0.876665i	−0.999975	−	0.00710779i	$-0.997738\pi$
$977$	−15.8205	−	27.4019i	−0.506143	−	0.876665i	0.493832	−	0.869557i	$-0.335596\pi$
$978$	38.3205	+	66.3731i	1.22535	+	2.12238i
$979$	8.19615	−	14.1962i	0.261950	−	0.453711i
$980$		0			0
$981$	18.7321	−	32.4449i	0.598068	−	1.03588i
$982$	−6.58846	+	11.4115i	−0.210246	+	0.364157i
$983$	17.3205			0.552438			0.276219	−	0.961095i	$-0.410918\pi$
$983$	17.3205			0.552438			0.276219	+	0.961095i	$0.410918\pi$
$984$	−12.2942	+	21.2942i	−0.391926	+	0.678835i
$985$	10.3923	+	18.0000i	0.331126	+	0.573528i
$986$	20.0885	+	34.7942i	0.639747	+	1.10807i
$987$		0			0
$988$	−3.19615	−	6.46410i	−0.101683	−	0.205650i
$989$	−0.928203			−0.0295151
$990$	8.49038	+	14.7058i	0.269842	+	0.467380i
$991$	−9.49038	−	16.4378i	−0.301472	−	0.522165i	0.674998	−	0.737820i	$-0.264145\pi$
$991$	−9.49038	−	16.4378i	−0.301472	−	0.522165i	−0.976470	+	0.215655i	$0.930811\pi$
$992$	−10.9019	+	18.8827i	−0.346136	+	0.599526i
$993$	−68.2487			−2.16581
$994$		0			0
$995$	−1.73205	+	3.00000i	−0.0549097	+	0.0951064i
$996$	−6.00000			−0.190117
$997$	−2.40192	+	4.16025i	−0.0760697	+	0.131757i	−0.901551	−	0.432673i	$-0.857570\pi$
$997$	−2.40192	+	4.16025i	−0.0760697	+	0.131757i	0.825481	+	0.564430i	$0.190904\pi$
$998$	33.7583	+	58.4711i	1.06860	+	1.85087i
$999$	−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.393.1		4
7.2	even	3		637.2.g.d.263.1		4
7.3	odd	6		637.2.h.d.471.2		4
7.4	even	3		637.2.h.e.471.2		4
7.5	odd	6		637.2.g.e.263.1		4
7.6	odd	2		91.2.f.b.29.1	yes	4
13.3	even	3		8281.2.a.r.1.2		2
13.9	even	3	inner	637.2.f.d.295.1		4
13.10	even	6		8281.2.a.t.1.1		2
21.20	even	2		819.2.o.b.757.2		4
28.27	even	2		1456.2.s.o.1121.2		4
91.9	even	3		637.2.h.e.165.2		4
91.41	even	12		1183.2.c.e.337.2		4
91.48	odd	6		91.2.f.b.22.1	✓	4
91.55	odd	6		1183.2.a.f.1.2		2
91.61	odd	6		637.2.h.d.165.2		4
91.62	odd	6		1183.2.a.e.1.1		2
91.74	even	3		637.2.g.d.373.1		4
91.76	even	12		1183.2.c.e.337.4		4
91.87	odd	6		637.2.g.e.373.1		4
273.230	even	6		819.2.o.b.568.2		4
364.139	even	6		1456.2.s.o.113.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.b.22.1	✓	4	91.48	odd	6
91.2.f.b.29.1	yes	4	7.6	odd	2
637.2.f.d.295.1		4	13.9	even	3	inner
637.2.f.d.393.1		4	1.1	even	1	trivial
637.2.g.d.263.1		4	7.2	even	3
637.2.g.d.373.1		4	91.74	even	3
637.2.g.e.263.1		4	7.5	odd	6
637.2.g.e.373.1		4	91.87	odd	6
637.2.h.d.165.2		4	91.61	odd	6
637.2.h.d.471.2		4	7.3	odd	6
637.2.h.e.165.2		4	91.9	even	3
637.2.h.e.471.2		4	7.4	even	3
819.2.o.b.568.2		4	273.230	even	6
819.2.o.b.757.2		4	21.20	even	2
1183.2.a.e.1.1		2	91.62	odd	6
1183.2.a.f.1.2		2	91.55	odd	6
1183.2.c.e.337.2		4	91.41	even	12
1183.2.c.e.337.4		4	91.76	even	12
1456.2.s.o.113.2		4	364.139	even	6
1456.2.s.o.1121.2		4	28.27	even	2
8281.2.a.r.1.2		2	13.3	even	3
8281.2.a.t.1.1		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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{2} +(1.36603 + 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(2.36603 - 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 1.50000i) q^{2} +(1.36603 + 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(2.36603 - 4.09808i) q^{6} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} -2.73205 q^{12} +(-3.59808 - 0.232051i) q^{13} +(-2.36603 - 4.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.86603 + 6.69615i) q^{17} +7.73205 q^{18} +(1.00000 - 1.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(-2.36603 - 4.09808i) q^{24} -2.00000 q^{25} +(2.76795 + 5.59808i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} -4.19615 q^{31} +(2.59808 - 4.50000i) q^{32} +(1.73205 - 3.00000i) q^{33} +13.3923 q^{34} +(-2.23205 - 3.86603i) q^{36} +(3.50000 + 6.06218i) q^{37} -3.46410 q^{38} +(-4.36603 - 8.83013i) q^{39} +3.00000 q^{40} +(-2.59808 - 4.50000i) q^{41} +(0.0980762 - 0.169873i) q^{43} +1.26795 q^{44} +(3.86603 - 6.69615i) q^{45} +(-4.09808 + 7.09808i) q^{46} -12.9282 q^{47} +(-6.83013 + 11.8301i) q^{48} +(1.73205 + 3.00000i) q^{50} -21.1244 q^{51} +(2.00000 - 3.00000i) q^{52} -9.92820 q^{53} +(3.46410 + 6.00000i) q^{54} +(1.09808 + 1.90192i) q^{55} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} +(3.63397 - 6.29423i) q^{59} +4.73205 q^{60} +(-2.40192 + 4.16025i) q^{61} +(3.63397 + 6.29423i) q^{62} +1.00000 q^{64} +(6.23205 + 0.401924i) q^{65} -6.00000 q^{66} +(3.09808 + 5.36603i) q^{67} +(-3.86603 - 6.69615i) q^{68} +(6.46410 - 11.1962i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} +3.19615 q^{73} +(6.06218 - 10.5000i) q^{74} +(-2.73205 - 4.73205i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-9.46410 + 14.1962i) q^{78} +16.1962 q^{79} +(-4.33013 - 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(-4.50000 + 7.79423i) q^{82} +2.19615 q^{83} +(6.69615 - 11.5981i) q^{85} -0.339746 q^{86} +(-4.09808 + 7.09808i) q^{87} +(1.09808 + 1.90192i) q^{88} +(6.46410 + 11.1962i) q^{89} -13.3923 q^{90} +4.73205 q^{92} +(-5.73205 - 9.92820i) q^{93} +(11.1962 + 19.3923i) q^{94} +(-1.73205 + 3.00000i) q^{95} +14.1962 q^{96} +(3.19615 - 5.53590i) q^{97} +5.66025 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

L-functions

Modular forms

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