LMFDB - Embedded newform 637.2.g.e.263.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(263,637)]

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([4, 2]))

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

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

chi := DirichletCharacter("637.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not 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:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			263.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	637.263
Dual form			637.2.g.e.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 1.50000i) q^{2} +2.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +4.46410 q^{9} +O(q^{10})$	\(q+(-0.866025 + 1.50000i) q^{2} +2.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +4.46410 q^{9} +3.00000 q^{10} +1.26795 q^{11} +(-1.36603 - 2.36603i) 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} +(-3.86603 + 6.69615i) q^{18} +2.00000 q^{19} +(-0.866025 + 1.50000i) q^{20} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 + 4.09808i) q^{23} -4.73205 q^{24} +(1.00000 - 1.73205i) q^{25} +(-3.46410 + 5.19615i) q^{26} +4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +8.19615 q^{30} +(-2.09808 + 3.63397i) q^{31} +(2.59808 + 4.50000i) q^{32} +3.46410 q^{33} -13.3923 q^{34} +(-2.23205 - 3.86603i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(9.83013 + 0.633975i) q^{39} +(1.50000 + 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(0.0980762 - 0.169873i) q^{43} +(-0.633975 - 1.09808i) q^{44} +(-3.86603 - 6.69615i) q^{45} +(-4.09808 - 7.09808i) q^{46} +(-6.46410 - 11.1962i) q^{47} +(6.83013 - 11.8301i) q^{48} +(1.73205 + 3.00000i) q^{50} +(10.5622 + 18.2942i) q^{51} +(-1.59808 - 3.23205i) q^{52} +(4.96410 - 8.59808i) q^{53} +(-3.46410 + 6.00000i) q^{54} +(-1.09808 - 1.90192i) q^{55} +5.46410 q^{57} -5.19615 q^{58} +(-3.63397 - 6.29423i) q^{59} +(-2.36603 + 4.09808i) q^{60} -4.80385 q^{61} +(-3.63397 - 6.29423i) q^{62} +1.00000 q^{64} +(-2.76795 - 5.59808i) q^{65} +(-3.00000 + 5.19615i) q^{66} -6.19615 q^{67} +(3.86603 - 6.69615i) q^{68} +(-6.46410 + 11.1962i) q^{69} +(-3.00000 + 5.19615i) q^{71} -7.73205 q^{72} +(1.59808 - 2.76795i) 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} +(-8.09808 - 14.0263i) q^{79} -8.66025 q^{80} -2.46410 q^{81} -9.00000 q^{82} -2.19615 q^{83} +(6.69615 - 11.5981i) q^{85} +(0.169873 + 0.294229i) q^{86} +(4.09808 + 7.09808i) q^{87} -2.19615 q^{88} +(-6.46410 + 11.1962i) q^{89} +13.3923 q^{90} +4.73205 q^{92} +(-5.73205 + 9.92820i) q^{93} +22.3923 q^{94} +(-1.73205 - 3.00000i) q^{95} +(7.09808 + 12.2942i) q^{96} +(-3.19615 + 5.53590i) q^{97} +5.66025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 2 q^{4} - 6 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 2 * q^4 - 6 * q^6 + 4 * q^9	$ 4 q + 4 q^{3} - 2 q^{4} - 6 q^{6} + 4 q^{9} + 12 q^{10} + 12 q^{11} - 2 q^{12} + 4 q^{13} - 6 q^{15} + 10 q^{16} + 12 q^{17} - 12 q^{18} + 8 q^{19} + 6 q^{22} - 6 q^{23} - 12 q^{24} + 4 q^{25} + 16 q^{27} + 6 q^{29} + 12 q^{30} + 2 q^{31} - 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} + 6 q^{40} - 10 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 12 q^{47} + 10 q^{48} + 18 q^{51} + 4 q^{52} + 6 q^{53} + 6 q^{55} + 8 q^{57} - 18 q^{59} - 6 q^{60} - 40 q^{61} - 18 q^{62} + 4 q^{64} - 18 q^{65} - 12 q^{66} - 4 q^{67} + 12 q^{68} - 12 q^{69} - 12 q^{71} - 24 q^{72} - 4 q^{73} + 4 q^{75} - 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} - 36 q^{82} + 12 q^{83} + 6 q^{85} + 18 q^{86} + 6 q^{87} + 12 q^{88} - 12 q^{89} + 12 q^{90} + 12 q^{92} - 16 q^{93} + 48 q^{94} + 18 q^{96} + 8 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 2 * q^4 - 6 * q^6 + 4 * q^9 + 12 * q^10 + 12 * q^11 - 2 * q^12 + 4 * q^13 - 6 * q^15 + 10 * q^16 + 12 * q^17 - 12 * q^18 + 8 * q^19 + 6 * q^22 - 6 * q^23 - 12 * q^24 + 4 * q^25 + 16 * q^27 + 6 * q^29 + 12 * q^30 + 2 * q^31 - 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 + 6 * q^40 - 10 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 12 * q^47 + 10 * q^48 + 18 * q^51 + 4 * q^52 + 6 * q^53 + 6 * q^55 + 8 * q^57 - 18 * q^59 - 6 * q^60 - 40 * q^61 - 18 * q^62 + 4 * q^64 - 18 * q^65 - 12 * q^66 - 4 * q^67 + 12 * q^68 - 12 * q^69 - 12 * q^71 - 24 * q^72 - 4 * q^73 + 4 * q^75 - 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 - 36 * q^82 + 12 * q^83 + 6 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 12 * q^89 + 12 * q^90 + 12 * q^92 - 16 * q^93 + 48 * q^94 + 18 * q^96 + 8 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	0.378467	+	0.925615i	$0.376451\pi$
$2$	−0.866025	+	1.50000i	−0.612372	+	1.06066i	−0.990839	+	0.135045i	$0.956882\pi$
$3$	2.73205			1.57735			0.788675	−	0.614810i	$-0.210767\pi$
$3$	2.73205			1.57735			0.788675	+	0.614810i	$0.210767\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	0.604787	−	0.796387i	$-0.293258\pi$
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	−0.992085	+	0.125567i	$0.959925\pi$
$6$	−2.36603	+	4.09808i	−0.965926	+	1.67303i
$7$		0			0
$7$		0			0
$8$	−1.73205			−0.612372
$9$	4.46410			1.48803
$10$	3.00000			0.948683
$11$	1.26795			0.382301			0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795			0.382301			0.191151	+	0.981561i	$0.438778\pi$
$12$	−1.36603	−	2.36603i	−0.394338	−	0.683013i
$13$	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	0.769841	+	0.638236i	$0.220336\pi$
$17$	3.86603	+	6.69615i	0.937649	+	1.62406i	0.167808	+	0.985820i	$0.446331\pi$
$18$	−3.86603	+	6.69615i	−0.911231	+	1.57830i
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−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	−0.999971	−	0.00766135i	$-0.997561\pi$
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	0.506620	+	0.862169i	$0.330895\pi$
$24$	−4.73205			−0.965926
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$	−3.46410	+	5.19615i	−0.679366	+	1.01905i
$27$	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	$0.743482\pi$
$30$	8.19615			1.49641
$31$	−2.09808	+	3.63397i	−0.376826	+	0.652681i	−0.990598	−	0.136802i	$-0.956318\pi$
$31$	−2.09808	+	3.63397i	−0.376826	+	0.652681i	0.613773	+	0.789483i	$0.289651\pi$
$32$	2.59808	+	4.50000i	0.459279	+	0.795495i
$33$	3.46410			0.603023
$34$	−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	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−1.73205	+	3.00000i	−0.280976	+	0.486664i
$39$	9.83013	+	0.633975i	1.57408	+	0.101517i
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	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
$43$	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	$0.161906\pi$
$44$	−0.633975	−	1.09808i	−0.0955753	−	0.165541i
$45$	−3.86603	−	6.69615i	−0.576313	−	0.998203i
$46$	−4.09808	−	7.09808i	−0.604228	−	1.04655i
$47$	−6.46410	−	11.1962i	−0.942886	−	1.63313i	−0.759929	−	0.650006i	$-0.774766\pi$
$47$	−6.46410	−	11.1962i	−0.942886	−	1.63313i	−0.182957	−	0.983121i	$-0.558567\pi$
$48$	6.83013	−	11.8301i	0.985844	−	1.70753i
$49$		0			0
$50$	1.73205	+	3.00000i	0.244949	+	0.424264i
$51$	10.5622	+	18.2942i	1.47900	+	2.56170i
$52$	−1.59808	−	3.23205i	−0.221613	−	0.448205i
$53$	4.96410	−	8.59808i	0.681872	−	1.18104i	−0.292537	−	0.956254i	$-0.594500\pi$
$53$	4.96410	−	8.59808i	0.681872	−	1.18104i	0.974409	−	0.224782i	$-0.0721671\pi$
$54$	−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
$58$	−5.19615			−0.682288
$59$	−3.63397	−	6.29423i	−0.473103	−	0.819439i	0.526423	−	0.850223i	$-0.323533\pi$
$59$	−3.63397	−	6.29423i	−0.473103	−	0.819439i	−0.999526	+	0.0307841i	$0.990200\pi$
$60$	−2.36603	+	4.09808i	−0.305453	+	0.529059i
$61$	−4.80385			−0.615070			−0.307535	−	0.951537i	$-0.599504\pi$
$61$	−4.80385			−0.615070			−0.307535	+	0.951537i	$0.599504\pi$
$62$	−3.63397	−	6.29423i	−0.461515	−	0.799368i
$63$		0			0
$64$	1.00000			0.125000
$65$	−2.76795	−	5.59808i	−0.343322	−	0.694356i
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	−6.19615			−0.756980			−0.378490	−	0.925605i	$-0.623557\pi$
$67$	−6.19615			−0.756980			−0.378490	+	0.925605i	$0.623557\pi$
$68$	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	$0.282538\pi$
$72$	−7.73205			−0.911231
$73$	1.59808	−	2.76795i	0.187041	−	0.323964i	−0.757222	−	0.653158i	$-0.773444\pi$
$73$	1.59808	−	2.76795i	0.187041	−	0.323964i	0.944262	+	0.329194i	$0.106777\pi$
$74$	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
$79$	−8.09808	−	14.0263i	−0.911105	−	1.57808i	−0.812506	−	0.582952i	$-0.801897\pi$
$79$	−8.09808	−	14.0263i	−0.911105	−	1.57808i	−0.0985985	−	0.995127i	$-0.531436\pi$
$80$	−8.66025			−0.968246
$81$	−2.46410			−0.273789
$82$	−9.00000			−0.993884
$83$	−2.19615			−0.241059			−0.120530	−	0.992710i	$-0.538459\pi$
$83$	−2.19615			−0.241059			−0.120530	+	0.992710i	$0.538459\pi$
$84$		0			0
$85$	6.69615	−	11.5981i	0.726300	−	1.25799i
$86$	0.169873	+	0.294229i	0.0183179	+	0.0317275i
$87$	4.09808	+	7.09808i	0.439360	+	0.760994i
$88$	−2.19615			−0.234111
$89$	−6.46410	+	11.1962i	−0.685193	+	1.18679i	0.288183	+	0.957575i	$0.406949\pi$
$89$	−6.46410	+	11.1962i	−0.685193	+	1.18679i	−0.973376	+	0.229214i	$0.926384\pi$
$90$	13.3923			1.41167
$91$		0			0
$92$	4.73205			0.493350
$93$	−5.73205	+	9.92820i	−0.594386	+	1.02951i
$94$	22.3923			2.30959
$95$	−1.73205	−	3.00000i	−0.177705	−	0.307794i
$96$	7.09808	+	12.2942i	0.724444	+	1.25477i
$97$	−3.19615	+	5.53590i	−0.324520	+	0.562085i	−0.981415	−	0.191897i	$-0.938536\pi$
$97$	−3.19615	+	5.53590i	−0.324520	+	0.562085i	0.656895	+	0.753982i	$0.271869\pi$
$98$		0			0
$99$	5.66025			0.568877
$100$	−2.00000			−0.200000
$101$	−7.73205			−0.769368			−0.384684	−	0.923048i	$-0.625690\pi$
$101$	−7.73205			−0.769368			−0.384684	+	0.923048i	$0.625690\pi$
$102$	−36.5885			−3.62280
$103$	7.19615	+	12.4641i	0.709058	+	1.22812i	0.965207	+	0.261487i	$0.0842129\pi$
$103$	7.19615	+	12.4641i	0.709058	+	1.22812i	−0.256149	+	0.966637i	$0.582454\pi$
$104$	−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	−0.611273	−	0.791420i	$-0.709342\pi$
$107$	3.92820	−	6.80385i	0.379754	−	0.657753i	0.991026	+	0.133667i	$0.0426754\pi$
$108$	−2.00000	−	3.46410i	−0.192450	−	0.333333i
$109$	4.19615	−	7.26795i	0.401919	−	0.696143i	−0.592039	−	0.805909i	$-0.701677\pi$
$109$	4.19615	−	7.26795i	0.401919	−	0.696143i	0.993957	+	0.109766i	$0.0350102\pi$
$110$	3.80385			0.362683
$111$	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
$115$	8.19615			0.764295
$116$	1.50000	−	2.59808i	0.139272	−	0.241225i
$117$	16.0622	+	1.03590i	1.48495	+	0.0957688i
$118$	12.5885			1.15886
$119$		0			0
$120$	4.09808	+	7.09808i	0.374101	+	0.647963i
$121$	−9.39230			−0.853846
$122$	4.16025	−	7.20577i	0.376652	−	0.652380i
$123$	7.09808	+	12.2942i	0.640012	+	1.10853i
$124$	4.19615			0.376826
$125$	−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
$129$	0.267949	−	0.464102i	0.0235916	−	0.0408619i
$130$	10.7942	+	0.696152i	0.946716	+	0.0610566i
$131$	1.73205	+	3.00000i	0.151330	+	0.262111i	0.931717	−	0.363186i	$-0.118311\pi$
$131$	1.73205	+	3.00000i	0.151330	+	0.262111i	−0.780387	+	0.625297i	$0.784978\pi$
$132$	−1.73205	−	3.00000i	−0.150756	−	0.261116i
$133$		0			0
$134$	5.36603	−	9.29423i	0.463554	−	0.802899i
$135$	−3.46410	−	6.00000i	−0.298142	−	0.516398i
$136$	−6.69615	−	11.5981i	−0.574190	−	0.994527i
$137$	−4.03590	−	6.99038i	−0.344810	−	0.597229i	0.640509	−	0.767951i	$-0.278723\pi$
$137$	−4.03590	−	6.99038i	−0.344810	−	0.597229i	−0.985319	+	0.170722i	$0.945390\pi$
$138$	−11.1962	−	19.3923i	−0.953080	−	1.65078i
$139$	5.29423	−	9.16987i	0.449051	−	0.777778i	−0.549274	−	0.835642i	$-0.685096\pi$
$139$	5.29423	−	9.16987i	0.449051	−	0.777778i	0.998324	+	0.0578639i	$0.0184290\pi$
$140$		0			0
$141$	−17.6603	−	30.5885i	−1.48726	−	2.57601i
$142$	−5.19615	−	9.00000i	−0.436051	−	0.755263i
$143$	4.56218	+	0.294229i	0.381508	+	0.0246046i
$144$	11.1603	−	19.3301i	0.930021	−	1.61084i
$145$	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
$149$	−6.46410			−0.529560			−0.264780	−	0.964309i	$-0.585299\pi$
$149$	−6.46410			−0.529560			−0.264780	+	0.964309i	$0.585299\pi$
$150$	4.73205	+	8.19615i	0.386370	+	0.669213i
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$	−3.46410			−0.280976
$153$	17.2583	+	29.8923i	1.39525	+	2.41665i
$154$		0			0
$155$	7.26795			0.583776
$156$	−4.36603	−	8.83013i	−0.349562	−	0.706976i
$157$	−0.598076	+	1.03590i	−0.0477317	+	0.0826737i	−0.888904	−	0.458093i	$-0.848533\pi$
$157$	−0.598076	+	1.03590i	−0.0477317	+	0.0826737i	0.841172	+	0.540767i	$0.181866\pi$
$158$	28.0526			2.23174
$159$	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
$163$	16.1962			1.26858			0.634290	−	0.773095i	$-0.281292\pi$
$163$	16.1962			1.26858			0.634290	+	0.773095i	$0.281292\pi$
$164$	2.59808	−	4.50000i	0.202876	−	0.351391i
$165$	−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	0.964872	−	0.262719i	$-0.0846192\pi$
$167$	3.29423	+	5.70577i	0.254915	+	0.441526i	−0.709957	+	0.704245i	$0.751286\pi$
$168$		0			0
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$	11.5981	+	20.0885i	0.889532	+	1.54071i
$171$	8.92820			0.682757
$172$	−0.196152			−0.0149565
$173$	8.53590			0.648972			0.324486	−	0.945890i	$-0.394809\pi$
$173$	8.53590			0.648972			0.324486	+	0.945890i	$0.394809\pi$
$174$	−14.1962			−1.07621
$175$		0			0
$176$	3.16987	−	5.49038i	0.238938	−	0.413853i
$177$	−9.92820	−	17.1962i	−0.746249	−	1.29254i
$178$	−11.1962	−	19.3923i	−0.839187	−	1.45351i
$179$	−6.92820			−0.517838			−0.258919	−	0.965899i	$-0.583366\pi$
$179$	−6.92820			−0.517838			−0.258919	+	0.965899i	$0.583366\pi$
$180$	−3.86603	+	6.69615i	−0.288157	+	0.499102i
$181$	5.58846			0.415387			0.207693	−	0.978194i	$-0.433404\pi$
$181$	5.58846			0.415387			0.207693	+	0.978194i	$0.433404\pi$
$182$		0			0
$183$	−13.1244			−0.970180
$184$	4.09808	−	7.09808i	0.302114	−	0.523277i
$185$	−12.1244			−0.891400
$186$	−9.92820	−	17.1962i	−0.727971	−	1.26088i
$187$	4.90192	+	8.49038i	0.358464	+	0.620878i
$188$	−6.46410	+	11.1962i	−0.471443	+	0.816563i
$189$		0			0
$190$	6.00000			0.435286
$191$	4.73205			0.342399			0.171200	−	0.985236i	$-0.445236\pi$
$191$	4.73205			0.342399			0.171200	+	0.985236i	$0.445236\pi$
$192$	2.73205			0.197169
$193$	5.00000			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$193$	5.00000			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$194$	−5.53590	−	9.58846i	−0.397454	−	0.688411i
$195$	−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	$-0.189250\pi$
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	−0.899291	+	0.437351i	$0.855917\pi$
$200$	−1.73205	+	3.00000i	−0.122474	+	0.212132i
$201$	−16.9282			−1.19402
$202$	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
$206$	−24.9282			−1.73683
$207$	−10.5622	+	18.2942i	−0.734122	+	1.27154i
$208$	10.0000	−	15.0000i	0.693375	−	1.04006i
$209$	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	$0.813556\pi$
$212$	−9.92820			−0.681872
$213$	−8.19615	+	14.1962i	−0.561591	+	0.972704i
$214$	6.80385	+	11.7846i	0.465101	+	0.805579i
$215$	−0.339746			−0.0231705
$216$	−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
$220$	−1.09808	+	1.90192i	−0.0740323	+	0.128228i
$221$	12.3564	+	24.9904i	0.831182	+	1.68103i
$222$	16.5622	+	28.6865i	1.11158	+	1.92531i
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$		0			0
$225$	4.46410	−	7.73205i	0.297607	−	0.515470i
$226$	−11.5981	−	20.0885i	−0.771493	−	1.33626i
$227$	−2.83013	−	4.90192i	−0.187842	−	0.325352i	0.756688	−	0.653776i	$-0.226816\pi$
$227$	−2.83013	−	4.90192i	−0.187842	−	0.325352i	−0.944531	+	0.328424i	$0.893483\pi$
$228$	−2.73205	−	4.73205i	−0.180934	−	0.313388i
$229$	7.19615	+	12.4641i	0.475535	+	0.823651i	0.999607	−	0.0280229i	$-0.00892112\pi$
$229$	7.19615	+	12.4641i	0.475535	+	0.823651i	−0.524072	+	0.851674i	$0.675588\pi$
$230$	−7.09808	+	12.2942i	−0.468033	+	0.810657i
$231$		0			0
$232$	−2.59808	−	4.50000i	−0.170572	−	0.295439i
$233$	0.928203	+	1.60770i	0.0608086	+	0.105324i	0.894827	−	0.446413i	$-0.147299\pi$
$233$	0.928203	+	1.60770i	0.0608086	+	0.105324i	−0.834018	+	0.551737i	$0.813965\pi$
$234$	−15.4641	+	23.1962i	−1.01092	+	1.51638i
$235$	−11.1962	+	19.3923i	−0.730356	+	1.26501i
$236$	−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	$0.670774\pi$
$240$	−23.6603			−1.52726
$241$	10.5981	+	18.3564i	0.682682	+	1.18244i	0.974159	+	0.225862i	$0.0725199\pi$
$241$	10.5981	+	18.3564i	0.682682	+	1.18244i	−0.291477	+	0.956578i	$0.594147\pi$
$242$	8.13397	−	14.0885i	0.522872	−	0.905640i
$243$	−18.7321			−1.20166
$244$	2.40192	+	4.16025i	0.153767	+	0.266333i
$245$		0			0
$246$	−24.5885			−1.56770
$247$	7.19615	+	0.464102i	0.457880	+	0.0295301i
$248$	3.63397	−	6.29423i	0.230758	−	0.399684i
$249$	−6.00000			−0.380235
$250$	10.5000	−	18.1865i	0.664078	−	1.15022i
$251$	0.803848	−	1.39230i	0.0507384	−	0.0878815i	−0.839541	−	0.543297i	$-0.817176\pi$
$251$	0.803848	−	1.39230i	0.0507384	−	0.0878815i	0.890279	+	0.455415i	$0.150509\pi$
$252$		0			0
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	31.8564			1.99885
$255$	18.2942	−	31.6865i	1.14563	−	1.98429i
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	−3.06218	+	5.30385i	−0.191013	+	0.330845i	−0.945586	−	0.325371i	$-0.894511\pi$
$257$	−3.06218	+	5.30385i	−0.191013	+	0.330845i	0.754573	+	0.656216i	$0.227844\pi$
$258$	0.464102	+	0.803848i	0.0288937	+	0.0500454i
$259$		0			0
$260$	−3.46410	+	5.19615i	−0.214834	+	0.322252i
$261$	6.69615	+	11.5981i	0.414481	+	0.717903i
$262$	−6.00000			−0.370681
$263$	1.26795			0.0781851			0.0390925	−	0.999236i	$-0.487553\pi$
$263$	1.26795			0.0781851			0.0390925	+	0.999236i	$0.487553\pi$
$264$	−6.00000			−0.369274
$265$	−17.1962			−1.05635
$266$		0			0
$267$	−17.6603	+	30.5885i	−1.08079	+	1.87198i
$268$	3.09808	+	5.36603i	0.189245	+	0.327782i
$269$	−2.53590	−	4.39230i	−0.154616	−	0.267804i	0.778303	−	0.627889i	$-0.216081\pi$
$269$	−2.53590	−	4.39230i	−0.154616	−	0.267804i	−0.932919	+	0.360086i	$0.882748\pi$
$270$	12.0000			0.730297
$271$	−2.90192	+	5.02628i	−0.176279	+	0.305325i	−0.940603	−	0.339508i	$-0.889740\pi$
$271$	−2.90192	+	5.02628i	−0.176279	+	0.305325i	0.764324	+	0.644832i	$0.223073\pi$
$272$	38.6603			2.34412
$273$		0			0
$274$	13.9808			0.844609
$275$	1.26795	−	2.19615i	0.0764602	−	0.132433i
$276$	12.9282			0.778186
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	−0.999923	−	0.0124177i	$-0.996047\pi$
$277$	−8.50000	−	14.7224i	−0.510716	−	0.884585i	0.489207	−	0.872167i	$-0.337286\pi$
$278$	9.16987	+	15.8827i	0.549972	+	0.952580i
$279$	−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	$0.369198\pi$
$282$	61.1769			3.64303
$283$	10.1962			0.606098			0.303049	−	0.952975i	$-0.401995\pi$
$283$	10.1962			0.606098			0.303049	+	0.952975i	$0.401995\pi$
$284$	6.00000			0.356034
$285$	−4.73205	−	8.19615i	−0.280302	−	0.485498i
$286$	−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
$291$	−8.73205	+	15.1244i	−0.511882	+	0.886605i
$292$	−3.19615			−0.187041
$293$	0.401924	−	0.696152i	0.0234806	−	0.0406697i	−0.854046	−	0.520197i	$-0.825859\pi$
$293$	0.401924	−	0.696152i	0.0234806	−	0.0406697i	0.877527	+	0.479527i	$0.159192\pi$
$294$		0			0
$295$	−6.29423	+	10.9019i	−0.366464	+	0.634735i
$296$	−6.06218	+	10.5000i	−0.352357	+	0.610300i
$297$	5.07180			0.294295
$298$	5.59808	−	9.69615i	0.324288	−	0.561683i
$299$	−9.46410	+	14.1962i	−0.547323	+	0.820985i
$300$	−5.46410			−0.315470
$301$		0			0
$302$	−1.73205	−	3.00000i	−0.0996683	−	0.172631i
$303$	−21.1244			−1.21356
$304$	5.00000	−	8.66025i	0.286770	−	0.496700i
$305$	4.16025	+	7.20577i	0.238215	+	0.412601i
$306$	−59.7846			−3.41766
$307$	−4.58846			−0.261877			−0.130939	−	0.991390i	$-0.541799\pi$
$307$	−4.58846			−0.261877			−0.130939	+	0.991390i	$0.541799\pi$
$308$		0			0
$309$	19.6603	+	34.0526i	1.11843	+	1.93718i
$310$	−6.29423	+	10.9019i	−0.357488	+	0.619188i
$311$	−0.633975	+	1.09808i	−0.0359494	+	0.0622662i	−0.883440	−	0.468544i	$-0.844779\pi$
$311$	−0.633975	+	1.09808i	−0.0359494	+	0.0622662i	0.847491	+	0.530810i	$0.178112\pi$
$312$	−17.0263	−	1.09808i	−0.963923	−	0.0621663i
$313$	−14.3923	−	24.9282i	−0.813501	−	1.40903i	−0.910399	−	0.413731i	$-0.864225\pi$
$313$	−14.3923	−	24.9282i	−0.813501	−	1.40903i	0.0968980	−	0.995294i	$-0.469108\pi$
$314$	−1.03590	−	1.79423i	−0.0584591	−	0.101254i
$315$		0			0
$316$	−8.09808	+	14.0263i	−0.455552	+	0.789040i
$317$	3.23205	+	5.59808i	0.181530	+	0.314419i	0.942402	−	0.334483i	$-0.108562\pi$
$317$	3.23205	+	5.59808i	0.181530	+	0.314419i	−0.760872	+	0.648902i	$0.775228\pi$
$318$	23.4904	+	40.6865i	1.31728	+	2.28159i
$319$	1.90192	+	3.29423i	0.106487	+	0.184441i
$320$	−0.866025	−	1.50000i	−0.0484123	−	0.0838525i
$321$	10.7321	−	18.5885i	0.599005	−	1.03751i
$322$		0			0
$323$	7.73205	+	13.3923i	0.430223	+	0.745168i
$324$	1.23205	+	2.13397i	0.0684473	+	0.118554i
$325$	4.00000	−	6.00000i	0.221880	−	0.332820i
$326$	−14.0263	+	24.2942i	−0.776844	+	1.34553i
$327$	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
$331$	24.9808			1.37307			0.686533	−	0.727098i	$-0.259132\pi$
$331$	24.9808			1.37307			0.686533	+	0.727098i	$0.259132\pi$
$332$	1.09808	+	1.90192i	0.0602648	+	0.104382i
$333$	15.6244	−	27.0622i	0.856209	−	1.48300i
$334$	−11.4115			−0.624412
$335$	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	$0.403145\pi$
$338$	−13.6699	+	17.8923i	−0.743543	+	0.973213i
$339$	−18.2942	+	31.6865i	−0.993606	+	1.72098i
$340$	−13.3923			−0.726300
$341$	−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
$345$	22.3923			1.20556
$346$	−7.39230	+	12.8038i	−0.397413	+	0.688339i
$347$	−3.63397	−	6.29423i	−0.195082	−	0.337892i	0.751845	−	0.659339i	$-0.229164\pi$
$347$	−3.63397	−	6.29423i	−0.195082	−	0.337892i	−0.946927	+	0.321448i	$0.895831\pi$
$348$	4.09808	−	7.09808i	0.219680	−	0.380497i
$349$	12.3923	+	21.4641i	0.663345	+	1.14895i	0.979731	+	0.200317i	$0.0641971\pi$
$349$	12.3923	+	21.4641i	0.663345	+	1.14895i	−0.316386	+	0.948630i	$0.602470\pi$
$350$		0			0
$351$	14.3923	+	0.928203i	0.768204	+	0.0495438i
$352$	3.29423	+	5.70577i	0.175583	+	0.304119i
$353$	20.6603			1.09963			0.549817	−	0.835285i	$-0.314697\pi$
$353$	20.6603			1.09963			0.549817	+	0.835285i	$0.314697\pi$
$354$	34.3923			1.82793
$355$	10.3923			0.551566
$356$	12.9282			0.685193
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	−9.46410	−	16.3923i	−0.499496	−	0.865153i	0.500504	−	0.865734i	$-0.333148\pi$
$359$	−9.46410	−	16.3923i	−0.499496	−	0.865153i	−1.00000		0.000581665i	$0.999815\pi$
$360$	6.69615	+	11.5981i	0.352918	+	0.611272i
$361$	−15.0000			−0.789474
$362$	−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
$367$	4.19615			0.219037			0.109519	−	0.993985i	$-0.465069\pi$
$367$	4.19615			0.219037			0.109519	+	0.993985i	$0.465069\pi$
$368$	11.8301	+	20.4904i	0.616688	+	1.06813i
$369$	11.5981	+	20.0885i	0.603772	+	1.04576i
$370$	10.5000	−	18.1865i	0.545869	−	0.945473i
$371$		0			0
$372$	11.4641			0.594386
$373$	−11.3923			−0.589871			−0.294936	−	0.955517i	$-0.595298\pi$
$373$	−11.3923			−0.589871			−0.294936	+	0.955517i	$0.595298\pi$
$374$	−16.9808			−0.878054
$375$	−33.1244			−1.71053
$376$	11.1962	+	19.3923i	0.577397	+	1.00008i
$377$	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
$382$	−4.09808	+	7.09808i	−0.209676	+	0.363169i
$383$	−11.6603			−0.595811			−0.297906	−	0.954595i	$-0.596288\pi$
$383$	−11.6603			−0.595811			−0.297906	+	0.954595i	$0.596288\pi$
$384$	−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
$388$	6.39230			0.324520
$389$	11.7679	−	20.3827i	0.596659	−	1.03344i	−0.396652	−	0.917969i	$-0.629828\pi$
$389$	11.7679	−	20.3827i	0.596659	−	1.03344i	0.993310	−	0.115474i	$-0.0368387\pi$
$390$	29.4904	+	1.90192i	1.49330	+	0.0963077i
$391$	−36.5885			−1.85036
$392$		0			0
$393$	4.73205	+	8.19615i	0.238700	+	0.413441i
$394$	20.7846			1.04711
$395$	−14.0263	+	24.2942i	−0.705739	+	1.22238i
$396$	−2.83013	−	4.90192i	−0.142219	−	0.246331i
$397$	−18.7846			−0.942773			−0.471386	−	0.881927i	$-0.656246\pi$
$397$	−18.7846			−0.942773			−0.471386	+	0.881927i	$0.656246\pi$
$398$	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	−0.698065	−	0.716034i	$-0.745955\pi$
$401$	5.42820	−	9.40192i	0.271072	−	0.469510i	0.969136	+	0.246525i	$0.0792887\pi$
$402$	14.6603	−	25.3923i	0.731187	−	1.26645i
$403$	−8.39230	+	12.5885i	−0.418050	+	0.627076i
$404$	3.86603	+	6.69615i	0.192342	+	0.333146i
$405$	2.13397	+	3.69615i	0.106038	+	0.183663i
$406$		0			0
$407$	4.43782	−	7.68653i	0.219975	−	0.381007i
$408$	−18.2942	−	31.6865i	−0.905699	−	1.56872i
$409$	8.40192	+	14.5526i	0.415448	+	0.719578i	0.995475	−	0.0950195i	$-0.0302913\pi$
$409$	8.40192	+	14.5526i	0.415448	+	0.719578i	−0.580027	+	0.814597i	$0.696958\pi$
$410$	7.79423	+	13.5000i	0.384930	+	0.666717i
$411$	−11.0263	−	19.0981i	−0.543886	−	0.942039i
$412$	7.19615	−	12.4641i	0.354529	−	0.614062i
$413$		0			0
$414$	−18.2942	−	31.6865i	−0.899112	−	1.55731i
$415$	1.90192	+	3.29423i	0.0933618	+	0.161707i
$416$	8.30385	+	16.7942i	0.407130	+	0.823405i
$417$	14.4641	−	25.0526i	0.708310	−	1.22683i
$418$	−2.19615	+	3.80385i	−0.107417	+	0.186052i
$419$	16.0981	+	27.8827i	0.786442	+	1.36216i	0.928134	+	0.372247i	$0.121413\pi$
$419$	16.0981	+	27.8827i	0.786442	+	1.36216i	−0.141691	+	0.989911i	$0.545254\pi$
$420$		0			0
$421$	−32.1769			−1.56821			−0.784103	−	0.620630i	$-0.786877\pi$
$421$	−32.1769			−1.56821			−0.784103	+	0.620630i	$0.786877\pi$
$422$	−3.12436			−0.152091
$423$	−28.8564	−	49.9808i	−1.40305	−	2.43015i
$424$	−8.59808	+	14.8923i	−0.417559	+	0.723234i
$425$	15.4641			0.750119
$426$	−14.1962	−	24.5885i	−0.687806	−	1.19131i
$427$		0			0
$428$	−7.85641			−0.379754
$429$	12.4641	+	0.803848i	0.601772	+	0.0388101i
$430$	0.294229	−	0.509619i	0.0141890	−	0.0245760i
$431$	0.679492			0.0327300			0.0163650	−	0.999866i	$-0.494791\pi$
$431$	0.679492			0.0327300			0.0163650	+	0.999866i	$0.494791\pi$
$432$	10.0000	−	17.3205i	0.481125	−	0.833333i
$433$	6.79423	−	11.7679i	0.326510	−	0.565532i	−0.655307	−	0.755363i	$-0.727461\pi$
$433$	6.79423	−	11.7679i	0.326510	−	0.565532i	0.981817	+	0.189831i	$0.0607941\pi$
$434$		0			0
$435$	7.09808	−	12.2942i	0.340327	−	0.589463i
$436$	−8.39230			−0.401919
$437$	−4.73205	+	8.19615i	−0.226365	+	0.392075i
$438$	7.56218	+	13.0981i	0.361335	+	0.625850i
$439$	−7.29423	+	12.6340i	−0.348135	+	0.602987i	−0.985918	−	0.167229i	$-0.946518\pi$
$439$	−7.29423	+	12.6340i	−0.348135	+	0.602987i	0.637784	+	0.770216i	$0.279851\pi$
$440$	1.90192	+	3.29423i	0.0906707	+	0.157046i
$441$		0			0
$442$	−48.1865	−	3.10770i	−2.29200	−	0.147818i
$443$	−11.6603	−	20.1962i	−0.553995	−	0.959548i	−0.997981	−	0.0635142i	$-0.979769\pi$
$443$	−11.6603	−	20.1962i	−0.553995	−	0.959548i	0.443986	−	0.896034i	$-0.353564\pi$
$444$	−19.1244			−0.907602
$445$	22.3923			1.06150
$446$	−17.3205			−0.820150
$447$	−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	$0.0752847\pi$
$450$	7.73205	+	13.3923i	0.364492	+	0.631319i
$451$	3.29423	+	5.70577i	0.155119	+	0.268674i
$452$	13.3923			0.629921
$453$	−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	−0.965512	−	0.260358i	$-0.916159\pi$
$457$	−5.50000	+	9.52628i	−0.257279	+	0.445621i	0.708233	+	0.705979i	$0.249493\pi$
$458$	−24.9282			−1.16482
$459$	15.4641	+	26.7846i	0.721802	+	1.25020i
$460$	−4.09808	−	7.09808i	−0.191074	−	0.330950i
$461$	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
$463$	−4.58846			−0.213244			−0.106622	−	0.994300i	$-0.534003\pi$
$463$	−4.58846			−0.213244			−0.106622	+	0.994300i	$0.534003\pi$
$464$	15.0000			0.696358
$465$	19.8564			0.920819
$466$	−3.21539			−0.148950
$467$	−12.7583	−	22.0981i	−0.590385	−	1.02258i	−0.994180	−	0.107728i	$-0.965643\pi$
$467$	−12.7583	−	22.0981i	−0.590385	−	1.02258i	0.403795	−	0.914849i	$-0.367691\pi$
$468$	−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
$473$	0.124356	−	0.215390i	0.00571788	−	0.00990366i
$474$	76.6410			3.52024
$475$	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
$479$	1.26795			0.0579341			0.0289670	−	0.999580i	$-0.490778\pi$
$479$	1.26795			0.0579341			0.0289670	+	0.999580i	$0.490778\pi$
$480$	12.2942	−	21.2942i	0.561152	−	0.971944i
$481$	14.0000	−	21.0000i	0.638345	−	0.957518i
$482$	−36.7128			−1.67222
$483$		0			0
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	11.0718			0.502744
$486$	16.2224	−	28.0981i	0.735864	−	1.27455i
$487$	−20.3923	−	35.3205i	−0.924064	−	1.60052i	−0.793060	−	0.609143i	$-0.791514\pi$
$487$	−20.3923	−	35.3205i	−0.924064	−	1.60052i	−0.131003	−	0.991382i	$-0.541820\pi$
$488$	8.32051			0.376652
$489$	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
$493$	−11.5981	+	20.0885i	−0.522351	+	0.904739i
$494$	−6.92820	+	10.3923i	−0.311715	+	0.467572i
$495$	−4.90192	−	8.49038i	−0.220325	−	0.381614i
$496$	10.4904	+	18.1699i	0.471032	+	0.815851i
$497$		0			0
$498$	5.19615	−	9.00000i	0.232845	−	0.403300i
$499$	19.4904	+	33.7583i	0.872509	+	1.51123i	0.859393	+	0.511316i	$0.170842\pi$
$499$	19.4904	+	33.7583i	0.872509	+	1.51123i	0.0131168	+	0.999914i	$0.495825\pi$
$500$	6.06218	+	10.5000i	0.271109	+	0.469574i
$501$	9.00000	+	15.5885i	0.402090	+	0.696441i
$502$	1.39230	+	2.41154i	0.0621416	+	0.107632i
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	−0.580957	−	0.813934i	$-0.697322\pi$
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	0.995366	+	0.0961565i	$0.0306549\pi$
$504$		0			0
$505$	6.69615	+	11.5981i	0.297975	+	0.516108i
$506$	−5.19615	−	9.00000i	−0.230997	−	0.400099i
$507$	35.2224	+	4.56218i	1.56428	+	0.202613i
$508$	−9.19615	+	15.9282i	−0.408013	+	0.706700i
$509$	−6.86603	+	11.8923i	−0.304331	+	0.527117i	−0.977112	−	0.212725i	$-0.931766\pi$
$509$	−6.86603	+	11.8923i	−0.304331	+	0.527117i	0.672781	+	0.739842i	$0.265100\pi$
$510$	31.6865	+	54.8827i	1.40310	+	2.43025i
$511$		0			0
$512$	8.66025			0.382733
$513$	8.00000			0.353209
$514$	−5.30385	−	9.18653i	−0.233943	−	0.405201i
$515$	12.4641	−	21.5885i	0.549234	−	0.951301i
$516$	−0.535898			−0.0235916
$517$	−8.19615	−	14.1962i	−0.360466	−	0.624346i
$518$		0			0
$519$	23.3205			1.02366
$520$	4.79423	+	9.69615i	0.210241	+	0.425204i
$521$	12.0622	−	20.8923i	0.528454	−	0.915308i	−0.470996	−	0.882135i	$-0.656105\pi$
$521$	12.0622	−	20.8923i	0.528454	−	0.915308i	0.999450	−	0.0331732i	$-0.0105613\pi$
$522$	−23.1962			−1.01527
$523$	14.5885	−	25.2679i	0.637909	−	1.10489i	−0.347982	−	0.937501i	$-0.613133\pi$
$523$	14.5885	−	25.2679i	0.637909	−	1.10489i	0.985891	−	0.167389i	$-0.0535336\pi$
$524$	1.73205	−	3.00000i	0.0756650	−	0.131056i
$525$		0			0
$526$	−1.09808	+	1.90192i	−0.0478784	+	0.0829278i
$527$	−32.4449			−1.41332
$528$	8.66025	−	15.0000i	0.376889	−	0.652791i
$529$	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
$534$	−30.5885	−	52.9808i	−1.32369	−	2.29270i
$535$	−13.6077			−0.588312
$536$	10.7321			0.463554
$537$	−18.9282			−0.816812
$538$	8.78461			0.378731
$539$		0			0
$540$	−3.46410	+	6.00000i	−0.149071	+	0.258199i
$541$	7.30385	+	12.6506i	0.314017	+	0.543893i	0.979228	−	0.202762i	$-0.0649918\pi$
$541$	7.30385	+	12.6506i	0.314017	+	0.543893i	−0.665211	+	0.746655i	$0.731658\pi$
$542$	−5.02628	−	8.70577i	−0.215897	−	0.373945i
$543$	15.2679			0.655210
$544$	−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
$549$	−21.4449			−0.915244
$550$	2.19615	+	3.80385i	0.0936443	+	0.162197i
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$	11.1962	−	19.3923i	0.476540	−	0.825391i
$553$		0			0
$554$	29.4449			1.25099
$555$	−33.1244			−1.40605
$556$	−10.5885			−0.449051
$557$	43.6410			1.84913			0.924565	−	0.381025i	$-0.124429\pi$
$557$	43.6410			1.84913			0.924565	+	0.381025i	$0.124429\pi$
$558$	−16.2224	−	28.0981i	−0.686750	−	1.18949i
$559$	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	−0.994080	−	0.108654i	$-0.965346\pi$
$563$	−14.0263	−	24.2942i	−0.591137	−	1.02388i	0.402942	−	0.915225i	$-0.367987\pi$
$564$	−17.6603	+	30.5885i	−0.743631	+	1.28801i
$565$	23.1962			0.975869
$566$	−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	−0.0721010	+	0.997397i	$0.522970\pi$
$569$	−21.4641	+	37.1769i	−0.899822	+	1.55854i	−0.827721	+	0.561140i	$0.810363\pi$
$570$	16.3923			0.686598
$571$	−8.39230	+	14.5359i	−0.351207	+	0.608308i	−0.986461	−	0.163995i	$-0.947562\pi$
$571$	−8.39230	+	14.5359i	−0.351207	+	0.608308i	0.635254	+	0.772303i	$0.280895\pi$
$572$	−2.02628	−	4.09808i	−0.0847230	−	0.171349i
$573$	12.9282			0.540083
$574$		0			0
$575$	4.73205	+	8.19615i	0.197340	+	0.341803i
$576$	4.46410			0.186004
$577$	−21.5981	+	37.4090i	−0.899140	+	1.55736i	−0.0705436	+	0.997509i	$0.522473\pi$
$577$	−21.5981	+	37.4090i	−0.899140	+	1.55736i	−0.828596	+	0.559847i	$0.810860\pi$
$578$	−37.0526	−	64.1769i	−1.54118	−	2.66941i
$579$	13.6603			0.567701
$580$	−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
$584$	−2.76795	+	4.79423i	−0.114539	+	0.198387i
$585$	−12.3564	−	24.9904i	−0.510875	−	1.03323i
$586$	0.696152	+	1.20577i	0.0287578	+	0.0498100i
$587$	−8.19615	−	14.1962i	−0.338291	−	0.585938i	0.645820	−	0.763490i	$-0.276516\pi$
$587$	−8.19615	−	14.1962i	−0.338291	−	0.585938i	−0.984111	+	0.177552i	$0.943182\pi$
$588$		0			0
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$	−10.9019	−	18.8827i	−0.448825	−	0.777388i
$591$	−16.3923	−	28.3923i	−0.674289	−	1.16790i
$592$	−17.5000	−	30.3109i	−0.719246	−	1.24577i
$593$	8.72243	+	15.1077i	0.358187	+	0.620399i	0.987658	−	0.156626i	$-0.0500616\pi$
$593$	8.72243	+	15.1077i	0.358187	+	0.620399i	−0.629471	+	0.777024i	$0.716728\pi$
$594$	−4.39230	+	7.60770i	−0.180218	+	0.312148i
$595$		0			0
$596$	3.23205	+	5.59808i	0.132390	+	0.229306i
$597$	−2.73205	−	4.73205i	−0.111815	−	0.193670i
$598$	−13.0981	−	26.4904i	−0.535620	−	1.08327i
$599$	−21.9282	+	37.9808i	−0.895962	+	1.55185i	−0.0633527	+	0.997991i	$0.520179\pi$
$599$	−21.9282	+	37.9808i	−0.895962	+	1.55185i	−0.832609	+	0.553861i	$0.813154\pi$
$600$	−4.73205	+	8.19615i	−0.193185	+	0.334607i
$601$	14.9904	+	25.9641i	0.611470	+	1.05910i	0.990993	+	0.133915i	$0.0427550\pi$
$601$	14.9904	+	25.9641i	0.611470	+	1.05910i	−0.379522	+	0.925183i	$0.623912\pi$
$602$		0			0
$603$	−27.6603			−1.12641
$604$	2.00000			0.0813788
$605$	8.13397	+	14.0885i	0.330693	+	0.572777i
$606$	18.2942	−	31.6865i	0.743152	−	1.28718i
$607$	−14.3923			−0.584166			−0.292083	−	0.956393i	$-0.594348\pi$
$607$	−14.3923			−0.584166			−0.292083	+	0.956393i	$0.594348\pi$
$608$	5.19615	+	9.00000i	0.210732	+	0.364998i
$609$		0			0
$610$	−14.4115			−0.583506
$611$	−20.6603	−	41.7846i	−0.835824	−	1.69042i
$612$	17.2583	−	29.8923i	0.697627	−	1.20832i
$613$	3.39230			0.137014			0.0685070	−	0.997651i	$-0.478176\pi$
$613$	3.39230			0.137014			0.0685070	+	0.997651i	$0.478176\pi$
$614$	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	$0.700878\pi$
$618$	−68.1051			−2.73959
$619$	−17.6865	+	30.6340i	−0.710882	+	1.23128i	0.253645	+	0.967297i	$0.418371\pi$
$619$	−17.6865	+	30.6340i	−0.710882	+	1.23128i	−0.964527	+	0.263986i	$0.914963\pi$
$620$	−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
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$	49.8564			1.99266
$627$	6.92820			0.276686
$628$	1.19615			0.0477317
$629$	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	$0.0847645\pi$
$632$	14.0263	+	24.2942i	0.557935	+	0.966373i
$633$	2.46410	+	4.26795i	0.0979392	+	0.169636i
$634$	−11.1962			−0.444656
$635$	−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
$640$	21.0000			0.830098
$641$	−14.4282	−	24.9904i	−0.569880	−	0.987061i	−0.996577	−	0.0826663i	$-0.973656\pi$
$641$	−14.4282	−	24.9904i	−0.569880	−	0.987061i	0.426698	−	0.904394i	$-0.359677\pi$
$642$	18.5885	+	32.1962i	0.733628	+	1.27068i
$643$	0.392305	−	0.679492i	0.0154710	−	0.0267965i	−0.858186	−	0.513338i	$-0.828409\pi$
$643$	0.392305	−	0.679492i	0.0154710	−	0.0267965i	0.873657	+	0.486542i	$0.161742\pi$
$644$		0			0
$645$	−0.928203			−0.0365480
$646$	−26.7846			−1.05383
$647$	45.0333			1.77044			0.885221	−	0.465170i	$-0.154007\pi$
$647$	45.0333			1.77044			0.885221	+	0.465170i	$0.154007\pi$
$648$	4.26795			0.167661
$649$	−4.60770	−	7.98076i	−0.180868	−	0.313272i
$650$	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	−0.211451	−	0.977389i	$-0.567819\pi$
$653$	18.9282	−	32.7846i	0.740718	−	1.28296i	0.952169	−	0.305572i	$-0.0988478\pi$
$654$	19.8564	+	34.3923i	0.776447	+	1.34485i
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$	25.9808			1.01438
$657$	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
$661$	−33.1962			−1.29118			−0.645590	−	0.763684i	$-0.723389\pi$
$661$	−33.1962			−1.29118			−0.645590	+	0.763684i	$0.723389\pi$
$662$	−21.6340	+	37.4711i	−0.840828	+	1.45636i
$663$	33.7583	+	68.2750i	1.31106	+	2.65158i
$664$	3.80385			0.147618
$665$		0			0
$666$	27.0622	+	46.8731i	1.04864	+	1.81629i
$667$	−14.1962			−0.549677
$668$	3.29423	−	5.70577i	0.127458	−	0.220763i
$669$	13.6603	+	23.6603i	0.528136	+	0.914758i
$670$	−18.5885			−0.718135
$671$	−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
$675$	4.00000	−	6.92820i	0.153960	−	0.266667i
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	11.5359	+	19.9808i	0.443361	+	0.767923i	0.997936	−	0.0642101i	$-0.0204528\pi$
$677$	11.5359	+	19.9808i	0.443361	+	0.767923i	−0.554576	+	0.832133i	$0.687119\pi$
$678$	−31.6865	−	54.8827i	−1.21691	−	2.10776i
$679$		0			0
$680$	−11.5981	+	20.0885i	−0.444766	+	0.770357i
$681$	−7.73205	−	13.3923i	−0.296293	−	0.513194i
$682$	−4.60770	−	7.98076i	−0.176438	−	0.305599i
$683$	−7.73205	−	13.3923i	−0.295859	−	0.512442i	0.679326	−	0.733837i	$-0.262272\pi$
$683$	−7.73205	−	13.3923i	−0.295859	−	0.512442i	−0.975184	+	0.221395i	$0.928939\pi$
$684$	−4.46410	−	7.73205i	−0.170689	−	0.295642i
$685$	−6.99038	+	12.1077i	−0.267089	+	0.462611i
$686$		0			0
$687$	19.6603	+	34.0526i	0.750085	+	1.29919i
$688$	−0.490381	−	0.849365i	−0.0186956	−	0.0323817i
$689$	19.8564	−	29.7846i	0.756469	−	1.13470i
$690$	−19.3923	+	33.5885i	−0.738252	+	1.27869i
$691$	−0.196152	+	0.339746i	−0.00746199	+	0.0129245i	−0.869732	−	0.493524i	$-0.835709\pi$
$691$	−0.196152	+	0.339746i	−0.00746199	+	0.0129245i	0.862270	+	0.506448i	$0.169042\pi$
$692$	−4.26795	−	7.39230i	−0.162243	−	0.281013i
$693$		0			0
$694$	12.5885			0.477851
$695$	−18.3397			−0.695666
$696$	−7.09808	−	12.2942i	−0.269052	−	0.466012i
$697$	−20.0885	+	34.7942i	−0.760905	+	1.31793i
$698$	−42.9282			−1.62486
$699$	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	$0.371606\pi$
$702$	−13.8564	+	20.7846i	−0.522976	+	0.784465i
$703$	7.00000	−	12.1244i	0.264010	−	0.457279i
$704$	1.26795			0.0477876
$705$	−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
$709$	30.1769			1.13332			0.566659	−	0.823952i	$-0.308236\pi$
$709$	30.1769			1.13332			0.566659	+	0.823952i	$0.308236\pi$
$710$	−9.00000	+	15.5885i	−0.337764	+	0.585024i
$711$	−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
$716$	3.46410	+	6.00000i	0.129460	+	0.224231i
$717$	−43.1769			−1.61247
$718$	32.7846			1.22351
$719$	−7.26795			−0.271049			−0.135524	−	0.990774i	$-0.543272\pi$
$719$	−7.26795			−0.271049			−0.135524	+	0.990774i	$0.543272\pi$
$720$	−38.6603			−1.44078
$721$		0			0
$722$	12.9904	−	22.5000i	0.483452	−	0.837363i
$723$	28.9545	+	50.1506i	1.07683	+	1.86512i
$724$	−2.79423	−	4.83975i	−0.103847	−	0.179868i
$725$	6.00000			0.222834
$726$	22.2224	−	38.4904i	0.824752	−	1.42851i
$727$	−41.1769			−1.52717			−0.763584	−	0.645709i	$-0.776562\pi$
$727$	−41.1769			−1.52717			−0.763584	+	0.645709i	$0.776562\pi$
$728$		0			0
$729$	−43.7846			−1.62165
$730$	4.79423	−	8.30385i	0.177442	−	0.307339i
$731$	1.51666			0.0560957
$732$	6.56218	+	11.3660i	0.242545	+	0.420100i
$733$	−11.7942	−	20.4282i	−0.435630	−	0.754533i	0.561717	−	0.827329i	$-0.310141\pi$
$733$	−11.7942	−	20.4282i	−0.435630	−	0.754533i	−0.997347	+	0.0727965i	$0.976808\pi$
$734$	−3.63397	+	6.29423i	−0.134132	+	0.232324i
$735$		0			0
$736$	−24.5885			−0.906343
$737$	−7.85641			−0.289394
$738$	−40.1769			−1.47893
$739$	40.7846			1.50029			0.750143	−	0.661276i	$-0.229985\pi$
$739$	40.7846			1.50029			0.750143	+	0.661276i	$0.229985\pi$
$740$	6.06218	+	10.5000i	0.222850	+	0.385988i
$741$	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
$746$	9.86603	−	17.0885i	0.361221	−	0.625653i
$747$	−9.80385			−0.358704
$748$	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	0.329079	+	0.944302i	$0.393262\pi$
$751$	−17.9019	+	31.0070i	−0.653250	+	1.13146i	−0.982329	+	0.187161i	$0.940072\pi$
$752$	−64.6410			−2.35722
$753$	2.19615	−	3.80385i	0.0800322	−	0.138620i
$754$	−18.6962	−	1.20577i	−0.680874	−	0.0439116i
$755$	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	$0.739424\pi$
$758$	46.0526			1.67270
$759$	−8.19615	+	14.1962i	−0.297501	+	0.515288i
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	41.3205			1.49787			0.748934	−	0.662645i	$-0.230566\pi$
$761$	41.3205			1.49787			0.748934	+	0.662645i	$0.230566\pi$
$762$	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
$766$	10.0981	−	17.4904i	0.364858	−	0.631953i
$767$	−11.6147	−	23.4904i	−0.419384	−	0.848189i
$768$	−25.9545	−	44.9545i	−0.936552	−	1.62216i
$769$	−7.58846	−	13.1436i	−0.273647	−	0.473970i	0.696146	−	0.717900i	$-0.254897\pi$
$769$	−7.58846	−	13.1436i	−0.273647	−	0.473970i	−0.969793	+	0.243930i	$0.921563\pi$
$770$		0			0
$771$	−8.36603	+	14.4904i	−0.301295	+	0.521858i
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	6.46410	+	11.1962i	0.232498	+	0.402698i	0.958542	−	0.284950i	$-0.0919769\pi$
$773$	6.46410	+	11.1962i	0.232498	+	0.402698i	−0.726045	+	0.687647i	$0.758644\pi$
$774$	0.758330	+	1.31347i	0.0272576	+	0.0472116i
$775$	4.19615	+	7.26795i	0.150730	+	0.261072i
$776$	5.53590	−	9.58846i	0.198727	−	0.344206i
$777$		0			0
$778$	20.3827	+	35.3038i	0.730755	+	1.26570i
$779$	5.19615	+	9.00000i	0.186171	+	0.322458i
$780$	−9.46410	+	14.1962i	−0.338869	+	0.508304i
$781$	−3.80385	+	6.58846i	−0.136112	+	0.235754i
$782$	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
$786$	−16.3923			−0.584694
$787$	−6.49038	−	11.2417i	−0.231357	−	0.400722i	0.726851	−	0.686796i	$-0.240983\pi$
$787$	−6.49038	−	11.2417i	−0.231357	−	0.400722i	−0.958208	+	0.286073i	$0.907650\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$	3.46410			0.123325
$790$	−24.2942	−	42.0788i	−0.864350	−	1.49710i
$791$		0			0
$792$	−9.80385			−0.348365
$793$	−17.2846	−	1.11474i	−0.613794	−	0.0395855i
$794$	16.2679	−	28.1769i	0.577328	−	0.999961i
$795$	−46.9808			−1.66624
$796$	−1.00000	+	1.73205i	−0.0354441	+	0.0613909i
$797$	17.1962	−	29.7846i	0.609119	−	1.05503i	−0.382267	−	0.924052i	$-0.624857\pi$
$797$	17.1962	−	29.7846i	0.609119	−	1.05503i	0.991386	−	0.130973i	$-0.0418101\pi$
$798$		0			0
$799$	49.9808	−	86.5692i	1.76819	−	3.06260i
$800$	10.3923			0.367423
$801$	−28.8564	+	49.9808i	−1.01959	+	1.76598i
$802$	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
$807$	−6.92820	−	12.0000i	−0.243884	−	0.422420i
$808$	13.3923			0.471140
$809$	2.07180			0.0728405			0.0364202	−	0.999337i	$-0.488405\pi$
$809$	2.07180			0.0728405			0.0364202	+	0.999337i	$0.488405\pi$
$810$	−7.39230			−0.259739
$811$	−16.5885			−0.582500			−0.291250	−	0.956647i	$-0.594071\pi$
$811$	−16.5885			−0.582500			−0.291250	+	0.956647i	$0.594071\pi$
$812$		0			0
$813$	−7.92820	+	13.7321i	−0.278054	+	0.481604i
$814$	7.68653	+	13.3135i	0.269413	+	0.466637i
$815$	−14.0263	−	24.2942i	−0.491319	−	0.850990i
$816$	105.622			3.69750
$817$	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	−0.899912	−	0.436072i	$-0.856369\pi$
$821$	−2.07180	+	3.58846i	−0.0723062	+	0.125238i	0.827605	+	0.561310i	$0.189703\pi$
$822$	38.1962			1.33224
$823$	20.5885	+	35.6603i	0.717669	+	1.24304i	0.961921	+	0.273327i	$0.0881240\pi$
$823$	20.5885	+	35.6603i	0.717669	+	1.24304i	−0.244253	+	0.969712i	$0.578543\pi$
$824$	−12.4641	−	21.5885i	−0.434208	−	0.752070i
$825$	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	$0.595399\pi$
$828$	21.1244			0.734122
$829$	−0.411543			−0.0142935			−0.00714673	−	0.999974i	$-0.502275\pi$
$829$	−0.411543			−0.0142935			−0.00714673	+	0.999974i	$0.502275\pi$
$830$	−6.58846			−0.228689
$831$	−23.2224	−	40.2224i	−0.805577	−	1.39530i
$832$	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
$837$	−8.39230	+	14.5359i	−0.290080	+	0.502434i
$838$	−55.7654			−1.92638
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	−0.667803	−	0.744338i	$-0.732765\pi$
$839$	9.00000	−	15.5885i	0.310715	−	0.538173i	0.978517	+	0.206165i	$0.0660984\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	27.8660	−	48.2654i	0.960327	−	1.66333i
$843$	36.5885			1.26017
$844$	0.901924	−	1.56218i	0.0310455	−	0.0537724i
$845$	−8.66025	−	20.7846i	−0.297922	−	0.715012i
$846$	99.9615			3.43675
$847$		0			0
$848$	−24.8205	−	42.9904i	−0.852340	−	1.47630i
$849$	27.8564			0.956029
$850$	−13.3923	+	23.1962i	−0.459352	+	0.795621i
$851$	16.5622	+	28.6865i	0.567744	+	0.983362i
$852$	16.3923			0.561591
$853$	5.58846			0.191345			0.0956726	−	0.995413i	$-0.469500\pi$
$853$	5.58846			0.191345			0.0956726	+	0.995413i	$0.469500\pi$
$854$		0			0
$855$	−7.73205	−	13.3923i	−0.264431	−	0.458007i
$856$	−6.80385	+	11.7846i	−0.232551	+	0.402790i
$857$	15.0622	−	26.0885i	0.514514	−	0.891165i	−0.485344	−	0.874323i	$-0.661306\pi$
$857$	15.0622	−	26.0885i	0.514514	−	0.891165i	0.999858	−	0.0168414i	$-0.00536105\pi$
$858$	−12.0000	+	18.0000i	−0.409673	+	0.614510i
$859$	3.90192	+	6.75833i	0.133132	+	0.230591i	0.924882	−	0.380254i	$-0.124163\pi$
$859$	3.90192	+	6.75833i	0.133132	+	0.230591i	−0.791750	+	0.610845i	$0.790830\pi$
$860$	0.169873	+	0.294229i	0.00579262	+	0.0100331i
$861$		0			0
$862$	−0.588457	+	1.01924i	−0.0200429	+	0.0347154i
$863$	−3.75833	−	6.50962i	−0.127935	−	0.221590i	0.794941	−	0.606686i	$-0.207502\pi$
$863$	−3.75833	−	6.50962i	−0.127935	−	0.221590i	−0.922876	+	0.385096i	$0.874168\pi$
$864$	10.3923	+	18.0000i	0.353553	+	0.612372i
$865$	−7.39230	−	12.8038i	−0.251346	−	0.435344i
$866$	11.7679	+	20.3827i	0.399891	+	0.692632i
$867$	−58.4449	+	101.229i	−1.98489	+	3.43793i
$868$		0			0
$869$	−10.2679	−	17.7846i	−0.348316	−	0.603302i
$870$	12.2942	+	21.2942i	0.416813	+	0.721942i
$871$	−22.2942	−	1.43782i	−0.755411	−	0.0487187i
$872$	−7.26795	+	12.5885i	−0.246124	+	0.426299i
$873$	−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
$877$	19.7846			0.668079			0.334039	−	0.942559i	$-0.391588\pi$
$877$	19.7846			0.668079			0.334039	+	0.942559i	$0.391588\pi$
$878$	−12.6340	−	21.8827i	−0.426376	−	0.738505i
$879$	1.09808	−	1.90192i	0.0370372	−	0.0641503i
$880$	−10.9808			−0.370161
$881$	4.20577	+	7.28461i	0.141696	+	0.245425i	0.928135	−	0.372243i	$-0.121411\pi$
$881$	4.20577	+	7.28461i	0.141696	+	0.245425i	−0.786439	+	0.617667i	$0.788078\pi$
$882$		0			0
$883$	−47.7654			−1.60743			−0.803716	−	0.595013i	$-0.797147\pi$
$883$	−47.7654			−1.60743			−0.803716	+	0.595013i	$0.797147\pi$
$884$	15.4641	−	23.1962i	0.520114	−	0.780171i
$885$	−17.1962	+	29.7846i	−0.578042	+	1.00120i
$886$	40.3923			1.35701
$887$	−5.66025	+	9.80385i	−0.190053	+	0.329181i	−0.945267	−	0.326296i	$-0.894199\pi$
$887$	−5.66025	+	9.80385i	−0.190053	+	0.329181i	0.755215	+	0.655477i	$0.227533\pi$
$888$	−16.5622	+	28.6865i	−0.555790	+	0.962657i
$889$		0			0
$890$	−19.3923	+	33.5885i	−0.650032	+	1.12589i
$891$	−3.12436			−0.104670
$892$	5.00000	−	8.66025i	0.167412	−	0.289967i
$893$	−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
$898$	10.3923	+	18.0000i	0.346796	+	0.600668i
$899$	−12.5885			−0.419849
$900$	−8.92820			−0.297607
$901$	76.7654			2.55743
$902$	−11.4115			−0.379963
$903$		0			0
$904$	11.5981	−	20.0885i	0.385746	−	0.668132i
$905$	−4.83975	−	8.38269i	−0.160879	−	0.278650i
$906$	−4.73205	−	8.19615i	−0.157212	−	0.272299i
$907$	−16.5885			−0.550811			−0.275405	−	0.961328i	$-0.588812\pi$
$907$	−16.5885			−0.550811			−0.275405	+	0.961328i	$0.588812\pi$
$908$	−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
$913$	−2.78461			−0.0921571
$914$	−9.52628	−	16.5000i	−0.315101	−	0.545771i
$915$	11.3660	+	19.6865i	0.375749	+	0.650817i
$916$	7.19615	−	12.4641i	0.237768	−	0.411826i
$917$		0			0
$918$	−53.5692			−1.76805
$919$	−39.5692			−1.30527			−0.652634	−	0.757673i	$-0.726336\pi$
$919$	−39.5692			−1.30527			−0.652634	+	0.757673i	$0.726336\pi$
$920$	−14.1962			−0.468033
$921$	−12.5359			−0.413072
$922$	13.5000	+	23.3827i	0.444599	+	0.770068i
$923$	−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
$928$	−7.79423	+	13.5000i	−0.255858	+	0.443159i
$929$	52.5167			1.72302			0.861508	−	0.507744i	$-0.169520\pi$
$929$	52.5167			1.72302			0.861508	+	0.507744i	$0.169520\pi$
$930$	−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
$934$	44.1962			1.44614
$935$	8.49038	−	14.7058i	0.277665	−	0.480930i
$936$	−27.8205	−	1.79423i	−0.909342	−	0.0586462i
$937$	−51.1962			−1.67251			−0.836253	−	0.548344i	$-0.815258\pi$
$937$	−51.1962			−1.67251			−0.836253	+	0.548344i	$0.815258\pi$
$938$		0			0
$939$	−39.3205	−	68.1051i	−1.28318	−	2.22253i
$940$	22.3923			0.730356
$941$	14.0718	−	24.3731i	0.458727	−	0.794539i	−0.540167	−	0.841558i	$-0.681639\pi$
$941$	14.0718	−	24.3731i	0.458727	−	0.794539i	0.998894	+	0.0470189i	$0.0149721\pi$
$942$	−2.83013	−	4.90192i	−0.0922105	−	0.159713i
$943$	−24.5885			−0.800710
$944$	−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	−0.800922	−	0.598769i	$-0.795657\pi$
$947$	3.63397	−	6.29423i	0.118088	−	0.204535i	0.919010	+	0.394234i	$0.128990\pi$
$948$	−22.1244	+	38.3205i	−0.718566	+	1.24459i
$949$	6.39230	−	9.58846i	0.207503	−	0.311254i
$950$	3.46410	+	6.00000i	0.112390	+	0.194666i
$951$	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	$0.0329697\pi$
$954$	38.3827	+	66.4808i	1.24269	+	2.15239i
$955$	−4.09808	−	7.09808i	−0.132611	−	0.229688i
$956$	7.90192	+	13.6865i	0.255566	+	0.442654i
$957$	5.19615	+	9.00000i	0.167968	+	0.290929i
$958$	−1.09808	+	1.90192i	−0.0354772	+	0.0614484i
$959$		0			0
$960$	−2.36603	−	4.09808i	−0.0763631	−	0.132265i
$961$	6.69615	+	11.5981i	0.216005	+	0.374131i
$962$	19.3756	+	39.1865i	0.624696	+	1.26342i
$963$	17.5359	−	30.3731i	0.565086	−	0.978758i
$964$	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	$0.154819\pi$
$968$	16.2679			0.522872
$969$	21.1244	+	36.5885i	0.678612	+	1.17539i
$970$	−9.58846	+	16.6077i	−0.307867	+	0.533241i
$971$	−52.6410			−1.68933			−0.844665	−	0.535295i	$-0.820201\pi$
$971$	−52.6410			−1.68933			−0.844665	+	0.535295i	$0.820201\pi$
$972$	9.36603	+	16.2224i	0.300415	+	0.520335i
$973$		0			0
$974$	70.6410			2.26348
$975$	10.9282	−	16.3923i	0.349983	−	0.524974i
$976$	−12.0096	+	20.8013i	−0.384419	+	0.665832i
$977$	31.6410			1.01229			0.506143	−	0.862450i	$-0.331071\pi$
$977$	31.6410			1.01229			0.506143	+	0.862450i	$0.331071\pi$
$978$	−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
$982$	13.1769			0.420492
$983$	8.66025	−	15.0000i	0.276219	−	0.478426i	−0.694223	−	0.719760i	$-0.744252\pi$
$983$	8.66025	−	15.0000i	0.276219	−	0.478426i	0.970442	+	0.241334i	$0.0775851\pi$
$984$	−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
$989$	0.464102	+	0.803848i	0.0147576	+	0.0255609i
$990$	16.9808			0.539684
$991$	18.9808			0.602944			0.301472	−	0.953475i	$-0.402522\pi$
$991$	18.9808			0.602944			0.301472	+	0.953475i	$0.402522\pi$
$992$	−21.8038			−0.692273
$993$	68.2487			2.16581
$994$		0			0
$995$	−1.73205	+	3.00000i	−0.0549097	+	0.0951064i
$996$	3.00000	+	5.19615i	0.0950586	+	0.164646i
$997$	2.40192	+	4.16025i	0.0760697	+	0.131757i	0.901551	−	0.432673i	$-0.142430\pi$
$997$	2.40192	+	4.16025i	0.0760697	+	0.131757i	−0.825481	+	0.564430i	$0.809096\pi$
$998$	−67.5167			−2.13720
$999$	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.g.e.263.1		4
7.2	even	3		637.2.h.d.471.2		4
7.3	odd	6		637.2.f.d.393.1		4
7.4	even	3		91.2.f.b.29.1	yes	4
7.5	odd	6		637.2.h.e.471.2		4
7.6	odd	2		637.2.g.d.263.1		4
13.9	even	3		637.2.h.d.165.2		4
21.11	odd	6		819.2.o.b.757.2		4
28.11	odd	6		1456.2.s.o.1121.2		4
91.3	odd	6		8281.2.a.r.1.2		2
91.9	even	3	inner	637.2.g.e.373.1		4
91.10	odd	6		8281.2.a.t.1.1		2
91.11	odd	12		1183.2.c.e.337.4		4
91.48	odd	6		637.2.h.e.165.2		4
91.61	odd	6		637.2.g.d.373.1		4
91.67	odd	12		1183.2.c.e.337.2		4
91.74	even	3		91.2.f.b.22.1	✓	4
91.81	even	3		1183.2.a.f.1.2		2
91.87	odd	6		637.2.f.d.295.1		4
91.88	even	6		1183.2.a.e.1.1		2
273.74	odd	6		819.2.o.b.568.2		4
364.347	odd	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	91.74	even	3
91.2.f.b.29.1	yes	4	7.4	even	3
637.2.f.d.295.1		4	91.87	odd	6
637.2.f.d.393.1		4	7.3	odd	6
637.2.g.d.263.1		4	7.6	odd	2
637.2.g.d.373.1		4	91.61	odd	6
637.2.g.e.263.1		4	1.1	even	1	trivial
637.2.g.e.373.1		4	91.9	even	3	inner
637.2.h.d.165.2		4	13.9	even	3
637.2.h.d.471.2		4	7.2	even	3
637.2.h.e.165.2		4	91.48	odd	6
637.2.h.e.471.2		4	7.5	odd	6
819.2.o.b.568.2		4	273.74	odd	6
819.2.o.b.757.2		4	21.11	odd	6
1183.2.a.e.1.1		2	91.88	even	6
1183.2.a.f.1.2		2	91.81	even	3
1183.2.c.e.337.2		4	91.67	odd	12
1183.2.c.e.337.4		4	91.11	odd	12
1456.2.s.o.113.2		4	364.347	odd	6
1456.2.s.o.1121.2		4	28.11	odd	6
8281.2.a.r.1.2		2	91.3	odd	6
8281.2.a.t.1.1		2	91.10	odd	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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 1.50000i) q^{2} +2.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +4.46410 q^{9} +O(q^{10})\)	\(q+(-0.866025 + 1.50000i) q^{2} +2.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 1.50000i) q^{5} +(-2.36603 + 4.09808i) q^{6} -1.73205 q^{8} +4.46410 q^{9} +3.00000 q^{10} +1.26795 q^{11} +(-1.36603 - 2.36603i) 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} +(-3.86603 + 6.69615i) q^{18} +2.00000 q^{19} +(-0.866025 + 1.50000i) q^{20} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 + 4.09808i) q^{23} -4.73205 q^{24} +(1.00000 - 1.73205i) q^{25} +(-3.46410 + 5.19615i) q^{26} +4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +8.19615 q^{30} +(-2.09808 + 3.63397i) q^{31} +(2.59808 + 4.50000i) q^{32} +3.46410 q^{33} -13.3923 q^{34} +(-2.23205 - 3.86603i) q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.73205 + 3.00000i) q^{38} +(9.83013 + 0.633975i) q^{39} +(1.50000 + 2.59808i) q^{40} +(2.59808 + 4.50000i) q^{41} +(0.0980762 - 0.169873i) q^{43} +(-0.633975 - 1.09808i) q^{44} +(-3.86603 - 6.69615i) q^{45} +(-4.09808 - 7.09808i) q^{46} +(-6.46410 - 11.1962i) q^{47} +(6.83013 - 11.8301i) q^{48} +(1.73205 + 3.00000i) q^{50} +(10.5622 + 18.2942i) q^{51} +(-1.59808 - 3.23205i) q^{52} +(4.96410 - 8.59808i) q^{53} +(-3.46410 + 6.00000i) q^{54} +(-1.09808 - 1.90192i) q^{55} +5.46410 q^{57} -5.19615 q^{58} +(-3.63397 - 6.29423i) q^{59} +(-2.36603 + 4.09808i) q^{60} -4.80385 q^{61} +(-3.63397 - 6.29423i) q^{62} +1.00000 q^{64} +(-2.76795 - 5.59808i) q^{65} +(-3.00000 + 5.19615i) q^{66} -6.19615 q^{67} +(3.86603 - 6.69615i) q^{68} +(-6.46410 + 11.1962i) q^{69} +(-3.00000 + 5.19615i) q^{71} -7.73205 q^{72} +(1.59808 - 2.76795i) 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} +(-8.09808 - 14.0263i) q^{79} -8.66025 q^{80} -2.46410 q^{81} -9.00000 q^{82} -2.19615 q^{83} +(6.69615 - 11.5981i) q^{85} +(0.169873 + 0.294229i) q^{86} +(4.09808 + 7.09808i) q^{87} -2.19615 q^{88} +(-6.46410 + 11.1962i) q^{89} +13.3923 q^{90} +4.73205 q^{92} +(-5.73205 + 9.92820i) q^{93} +22.3923 q^{94} +(-1.73205 - 3.00000i) q^{95} +(7.09808 + 12.2942i) q^{96} +(-3.19615 + 5.53590i) q^{97} +5.66025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 2 q^{4} - 6 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 2 * q^4 - 6 * q^6 + 4 * q^9	\( 4 q + 4 q^{3} - 2 q^{4} - 6 q^{6} + 4 q^{9} + 12 q^{10} + 12 q^{11} - 2 q^{12} + 4 q^{13} - 6 q^{15} + 10 q^{16} + 12 q^{17} - 12 q^{18} + 8 q^{19} + 6 q^{22} - 6 q^{23} - 12 q^{24} + 4 q^{25} + 16 q^{27} + 6 q^{29} + 12 q^{30} + 2 q^{31} - 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} + 6 q^{40} - 10 q^{43} - 6 q^{44} - 12 q^{45} - 6 q^{46} - 12 q^{47} + 10 q^{48} + 18 q^{51} + 4 q^{52} + 6 q^{53} + 6 q^{55} + 8 q^{57} - 18 q^{59} - 6 q^{60} - 40 q^{61} - 18 q^{62} + 4 q^{64} - 18 q^{65} - 12 q^{66} - 4 q^{67} + 12 q^{68} - 12 q^{69} - 12 q^{71} - 24 q^{72} - 4 q^{73} + 4 q^{75} - 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} - 36 q^{82} + 12 q^{83} + 6 q^{85} + 18 q^{86} + 6 q^{87} + 12 q^{88} - 12 q^{89} + 12 q^{90} + 12 q^{92} - 16 q^{93} + 48 q^{94} + 18 q^{96} + 8 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 2 * q^4 - 6 * q^6 + 4 * q^9 + 12 * q^10 + 12 * q^11 - 2 * q^12 + 4 * q^13 - 6 * q^15 + 10 * q^16 + 12 * q^17 - 12 * q^18 + 8 * q^19 + 6 * q^22 - 6 * q^23 - 12 * q^24 + 4 * q^25 + 16 * q^27 + 6 * q^29 + 12 * q^30 + 2 * q^31 - 12 * q^34 - 2 * q^36 + 14 * q^37 + 22 * q^39 + 6 * q^40 - 10 * q^43 - 6 * q^44 - 12 * q^45 - 6 * q^46 - 12 * q^47 + 10 * q^48 + 18 * q^51 + 4 * q^52 + 6 * q^53 + 6 * q^55 + 8 * q^57 - 18 * q^59 - 6 * q^60 - 40 * q^61 - 18 * q^62 + 4 * q^64 - 18 * q^65 - 12 * q^66 - 4 * q^67 + 12 * q^68 - 12 * q^69 - 12 * q^71 - 24 * q^72 - 4 * q^73 + 4 * q^75 - 4 * q^76 - 24 * q^78 - 22 * q^79 + 4 * q^81 - 36 * q^82 + 12 * q^83 + 6 * q^85 + 18 * q^86 + 6 * q^87 + 12 * q^88 - 12 * q^89 + 12 * q^90 + 12 * q^92 - 16 * q^93 + 48 * q^94 + 18 * q^96 + 8 * q^97 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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