LMFDB - Embedded newform 637.2.e.o.508.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(79,637)]

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([2, 0]))

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

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

chi := DirichletCharacter("637.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.e (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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + \cdots + 1 $ x^12 - 2x^11 + 9x^10 - 6x^9 + 34x^8 - 18x^7 + 85x^6 - 2x^5 + 92x^4 - 26x^3 + 43x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.6
Root			$-0.833726 - 1.44406i$ of defining polynomial
Character	$\chi$	$=$	637.508
Dual form			637.2.e.o.79.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22392 + 2.11990i) q^{2} +(-0.333726 + 0.578030i) q^{3} +(-1.99598 + 3.45713i) q^{4} +(0.455143 + 0.788331i) q^{5} -1.63382 q^{6} -4.87599 q^{8} +(1.27725 + 2.21227i) q^{9} +O(q^{10})$	\(q+(1.22392 + 2.11990i) q^{2} +(-0.333726 + 0.578030i) q^{3} +(-1.99598 + 3.45713i) q^{4} +(0.455143 + 0.788331i) q^{5} -1.63382 q^{6} -4.87599 q^{8} +(1.27725 + 2.21227i) q^{9} +(-1.11412 + 1.92971i) q^{10} +(-1.83918 + 3.18556i) q^{11} +(-1.33222 - 2.30747i) q^{12} -1.00000 q^{13} -0.607572 q^{15} +(-1.97589 - 3.42234i) q^{16} +(3.59265 - 6.22266i) q^{17} +(-3.12652 + 5.41529i) q^{18} +(-0.989010 - 1.71302i) q^{19} -3.63382 q^{20} -9.00407 q^{22} +(0.298350 + 0.516758i) q^{23} +(1.62724 - 2.81847i) q^{24} +(2.08569 - 3.61252i) q^{25} +(-1.22392 - 2.11990i) q^{26} -3.70737 q^{27} -3.64900 q^{29} +(-0.743621 - 1.28799i) q^{30} +(-3.54416 + 6.13867i) q^{31} +(-0.0393239 + 0.0681110i) q^{32} +(-1.22757 - 2.12621i) q^{33} +17.5885 q^{34} -10.1975 q^{36} +(-0.355426 - 0.615615i) q^{37} +(2.42094 - 4.19320i) q^{38} +(0.333726 - 0.578030i) q^{39} +(-2.21927 - 3.84390i) q^{40} -5.27529 q^{41} +11.0790 q^{43} +(-7.34193 - 12.7166i) q^{44} +(-1.16267 + 2.01380i) q^{45} +(-0.730315 + 1.26494i) q^{46} +(6.05674 + 10.4906i) q^{47} +2.63762 q^{48} +10.2109 q^{50} +(2.39792 + 4.15332i) q^{51} +(1.99598 - 3.45713i) q^{52} +(5.72422 - 9.91463i) q^{53} +(-4.53753 - 7.85923i) q^{54} -3.34837 q^{55} +1.32023 q^{57} +(-4.46610 - 7.73550i) q^{58} +(4.79493 - 8.30506i) q^{59} +(1.21270 - 2.10046i) q^{60} +(3.49268 + 6.04950i) q^{61} -17.3511 q^{62} -8.09606 q^{64} +(-0.455143 - 0.788331i) q^{65} +(3.00489 - 5.20462i) q^{66} +(-0.614197 + 1.06382i) q^{67} +(14.3417 + 24.8406i) q^{68} -0.398269 q^{69} +11.3635 q^{71} +(-6.22788 - 10.7870i) q^{72} +(3.26709 - 5.65877i) q^{73} +(0.870027 - 1.50693i) q^{74} +(1.39210 + 2.41118i) q^{75} +7.89616 q^{76} +1.63382 q^{78} +(5.76021 + 9.97697i) q^{79} +(1.79862 - 3.11531i) q^{80} +(-2.59452 + 4.49384i) q^{81} +(-6.45655 - 11.1831i) q^{82} -7.16403 q^{83} +6.54069 q^{85} +(13.5599 + 23.4864i) q^{86} +(1.21777 - 2.10923i) q^{87} +(8.96784 - 15.5328i) q^{88} +(6.42451 + 11.1276i) q^{89} -5.69206 q^{90} -2.38200 q^{92} +(-2.36556 - 4.09727i) q^{93} +(-14.8260 + 25.6793i) q^{94} +(0.900282 - 1.55933i) q^{95} +(-0.0262468 - 0.0454608i) q^{96} -9.09062 q^{97} -9.39642 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	$ 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) $ 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.22392	+	2.11990i	0.865444	+	1.49899i	0.866605	+	0.498994i	$0.166297\pi$
$2$	1.22392	+	2.11990i	0.865444	+	1.49899i	−0.00116093	+	0.999999i	$0.500370\pi$
$3$	−0.333726	+	0.578030i	−0.192677	+	0.333726i	−0.946136	−	0.323768i	$-0.895050\pi$
$3$	−0.333726	+	0.578030i	−0.192677	+	0.333726i	0.753460	+	0.657494i	$0.228384\pi$
$4$	−1.99598	+	3.45713i	−0.997988	+	1.72857i
$5$	0.455143	+	0.788331i	0.203546	+	0.352552i	0.949669	−	0.313256i	$-0.101420\pi$
$5$	0.455143	+	0.788331i	0.203546	+	0.352552i	−0.746122	+	0.665809i	$0.768087\pi$
$6$	−1.63382			−0.667004
$7$		0			0
$7$		0			0
$8$	−4.87599			−1.72392
$9$	1.27725	+	2.21227i	0.425751	+	0.737423i
$10$	−1.11412	+	1.92971i	−0.352316	+	0.610229i
$11$	−1.83918	+	3.18556i	−0.554534	+	0.960482i	0.443405	+	0.896321i	$0.353770\pi$
$11$	−1.83918	+	3.18556i	−0.554534	+	0.960482i	−0.997940	+	0.0641605i	$0.979563\pi$
$12$	−1.33222	−	2.30747i	−0.384578	−	0.666109i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$	−0.607572			−0.156874
$16$	−1.97589	−	3.42234i	−0.493972	−	0.855584i
$17$	3.59265	−	6.22266i	0.871347	−	1.50922i	0.0107428	−	0.999942i	$-0.496580\pi$
$17$	3.59265	−	6.22266i	0.871347	−	1.50922i	0.860604	−	0.509275i	$-0.170086\pi$
$18$	−3.12652	+	5.41529i	−0.736928	+	1.27640i
$19$	−0.989010	−	1.71302i	−0.226894	−	0.392993i	0.729992	−	0.683456i	$-0.239524\pi$
$19$	−0.989010	−	1.71302i	−0.226894	−	0.392993i	−0.956886	+	0.290463i	$0.906191\pi$
$20$	−3.63382			−0.812547
$21$		0			0
$22$	−9.00407			−1.91967
$23$	0.298350	+	0.516758i	0.0622103	+	0.107751i	0.895453	−	0.445156i	$-0.146852\pi$
$23$	0.298350	+	0.516758i	0.0622103	+	0.107751i	−0.833243	+	0.552907i	$0.813518\pi$
$24$	1.62724	−	2.81847i	0.332160	−	0.575318i
$25$	2.08569	−	3.61252i	0.417138	−	0.722504i
$26$	−1.22392	−	2.11990i	−0.240031	−	0.415746i
$27$	−3.70737			−0.713483
$28$		0			0
$29$	−3.64900			−0.677602			−0.338801	−	0.940858i	$-0.610021\pi$
$29$	−3.64900			−0.677602			−0.338801	+	0.940858i	$0.610021\pi$
$30$	−0.743621	−	1.28799i	−0.135766	−	0.235154i
$31$	−3.54416	+	6.13867i	−0.636551	+	1.10254i	0.349634	+	0.936887i	$0.386306\pi$
$31$	−3.54416	+	6.13867i	−0.636551	+	1.10254i	−0.986184	+	0.165652i	$0.947027\pi$
$32$	−0.0393239	+	0.0681110i	−0.00695155	+	0.0120404i
$33$	−1.22757	−	2.12621i	−0.213692	−	0.370125i
$34$	17.5885			3.01641
$35$		0			0
$36$	−10.1975			−1.69958
$37$	−0.355426	−	0.615615i	−0.0584316	−	0.101207i	0.835330	−	0.549749i	$-0.185277\pi$
$37$	−0.355426	−	0.615615i	−0.0584316	−	0.101207i	−0.893762	+	0.448542i	$0.851943\pi$
$38$	2.42094	−	4.19320i	0.392729	−	0.680227i
$39$	0.333726	−	0.578030i	0.0534389	−	0.0925589i
$40$	−2.21927	−	3.84390i	−0.350898	−	0.607773i
$41$	−5.27529			−0.823863			−0.411931	−	0.911215i	$-0.635146\pi$
$41$	−5.27529			−0.823863			−0.411931	+	0.911215i	$0.635146\pi$
$42$		0			0
$43$	11.0790			1.68954			0.844768	−	0.535132i	$-0.179738\pi$
$43$	11.0790			1.68954			0.844768	+	0.535132i	$0.179738\pi$
$44$	−7.34193	−	12.7166i	−1.10684	−	1.91710i
$45$	−1.16267	+	2.01380i	−0.173320	+	0.300199i
$46$	−0.730315	+	1.26494i	−0.107679	+	0.186506i
$47$	6.05674	+	10.4906i	0.883467	+	1.53021i	0.847461	+	0.530858i	$0.178130\pi$
$47$	6.05674	+	10.4906i	0.883467	+	1.53021i	0.0360062	+	0.999352i	$0.488536\pi$
$48$	2.63762			0.380707
$49$		0			0
$50$	10.2109			1.44404
$51$	2.39792	+	4.15332i	0.335776	+	0.581582i
$52$	1.99598	−	3.45713i	0.276792	−	0.479418i
$53$	5.72422	−	9.91463i	0.786282	−	1.36188i	−0.141949	−	0.989874i	$-0.545337\pi$
$53$	5.72422	−	9.91463i	0.786282	−	1.36188i	0.928230	−	0.372006i	$-0.121330\pi$
$54$	−4.53753	−	7.85923i	−0.617480	−	1.06951i
$55$	−3.34837			−0.451494
$56$		0			0
$57$	1.32023			0.174869
$58$	−4.46610	−	7.73550i	−0.586427	−	1.01572i
$59$	4.79493	−	8.30506i	0.624247	−	1.08123i	−0.364439	−	0.931227i	$-0.618739\pi$
$59$	4.79493	−	8.30506i	0.624247	−	1.08123i	0.988686	−	0.150000i	$-0.0479273\pi$
$60$	1.21270	−	2.10046i	0.156559	−	0.271168i
$61$	3.49268	+	6.04950i	0.447192	+	0.774559i	0.998202	−	0.0599392i	$-0.0190907\pi$
$61$	3.49268	+	6.04950i	0.447192	+	0.774559i	−0.551010	+	0.834499i	$0.685757\pi$
$62$	−17.3511			−2.20360
$63$		0			0
$64$	−8.09606			−1.01201
$65$	−0.455143	−	0.788331i	−0.0564536	−	0.0977804i
$66$	3.00489	−	5.20462i	0.369877	−	0.640645i
$67$	−0.614197	+	1.06382i	−0.0750360	+	0.129966i	−0.901102	−	0.433607i	$-0.857241\pi$
$67$	−0.614197	+	1.06382i	−0.0750360	+	0.129966i	0.826066	+	0.563574i	$0.190574\pi$
$68$	14.3417	+	24.8406i	1.73919	+	3.01236i
$69$	−0.398269			−0.0479459
$70$		0			0
$71$	11.3635			1.34859			0.674297	−	0.738460i	$-0.264447\pi$
$71$	11.3635			1.34859			0.674297	+	0.738460i	$0.264447\pi$
$72$	−6.22788	−	10.7870i	−0.733963	−	1.27126i
$73$	3.26709	−	5.65877i	0.382384	−	0.662309i	−0.609018	−	0.793156i	$-0.708436\pi$
$73$	3.26709	−	5.65877i	0.382384	−	0.662309i	0.991403	+	0.130847i	$0.0417697\pi$
$74$	0.870027	−	1.50693i	0.101139	−	0.175177i
$75$	1.39210	+	2.41118i	0.160745	+	0.278419i
$76$	7.89616			0.905752
$77$		0			0
$78$	1.63382			0.184994
$79$	5.76021	+	9.97697i	0.648074	+	1.12250i	0.983582	+	0.180460i	$0.0577586\pi$
$79$	5.76021	+	9.97697i	0.648074	+	1.12250i	−0.335508	+	0.942037i	$0.608908\pi$
$80$	1.79862	−	3.11531i	0.201092	−	0.348302i
$81$	−2.59452	+	4.49384i	−0.288280	+	0.499315i
$82$	−6.45655	−	11.1831i	−0.713007	−	1.23496i
$83$	−7.16403			−0.786355			−0.393177	−	0.919463i	$-0.628624\pi$
$83$	−7.16403			−0.786355			−0.393177	+	0.919463i	$0.628624\pi$
$84$		0			0
$85$	6.54069			0.709437
$86$	13.5599	+	23.4864i	1.46220	+	2.53260i
$87$	1.21777	−	2.10923i	0.130558	−	0.226133i
$88$	8.96784	−	15.5328i	0.955975	−	1.65580i
$89$	6.42451	+	11.1276i	0.680997	+	1.17952i	0.974677	+	0.223617i	$0.0717866\pi$
$89$	6.42451	+	11.1276i	0.680997	+	1.17952i	−0.293680	+	0.955904i	$0.594880\pi$
$90$	−5.69206			−0.599996
$91$		0			0
$92$	−2.38200			−0.248341
$93$	−2.36556	−	4.09727i	−0.245297	−	0.424867i
$94$	−14.8260	+	25.6793i	−1.52918	+	2.64862i
$95$	0.900282	−	1.55933i	0.0923670	−	0.159984i
$96$	−0.0262468	−	0.0454608i	−0.00267880	−	0.00463982i
$97$	−9.09062			−0.923012			−0.461506	−	0.887137i	$-0.652691\pi$
$97$	−9.09062			−0.923012			−0.461506	+	0.887137i	$0.652691\pi$
$98$		0			0
$99$	−9.39642			−0.944375
$100$	8.32597	+	14.4210i	0.832597	+	1.44210i
$101$	−2.90322	+	5.02853i	−0.288882	+	0.500358i	−0.973543	−	0.228504i	$-0.926617\pi$
$101$	−2.90322	+	5.02853i	−0.288882	+	0.500358i	0.684661	+	0.728861i	$0.259950\pi$
$102$	−5.86975	+	10.1667i	−0.581192	+	1.00665i
$103$	6.43411	+	11.1442i	0.633971	+	1.09807i	0.986732	+	0.162357i	$0.0519096\pi$
$103$	6.43411	+	11.1442i	0.633971	+	1.09807i	−0.352761	+	0.935714i	$0.614757\pi$
$104$	4.87599			0.478130
$105$		0			0
$106$	28.0240			2.72193
$107$	−2.22874	−	3.86029i	−0.215460	−	0.373188i	0.737955	−	0.674850i	$-0.235792\pi$
$107$	−2.22874	−	3.86029i	−0.215460	−	0.373188i	−0.953415	+	0.301662i	$0.902458\pi$
$108$	7.39981	−	12.8168i	0.712047	−	1.23330i
$109$	−0.439448	+	0.761146i	−0.0420915	+	0.0729046i	−0.886304	−	0.463105i	$-0.846735\pi$
$109$	−0.439448	+	0.761146i	−0.0420915	+	0.0729046i	0.844212	+	0.536009i	$0.180069\pi$
$110$	−4.09814	−	7.09819i	−0.390743	−	0.676786i
$111$	0.474459			0.0450336
$112$		0			0
$113$	−5.36723			−0.504906			−0.252453	−	0.967609i	$-0.581237\pi$
$113$	−5.36723			−0.504906			−0.252453	+	0.967609i	$0.581237\pi$
$114$	1.61586	+	2.79876i	0.151339	+	0.262128i
$115$	−0.271584	+	0.470397i	−0.0253253	+	0.0438648i
$116$	7.28332	−	12.6151i	0.676239	−	1.17128i
$117$	−1.27725	−	2.21227i	−0.118082	−	0.204524i
$118$	23.4745			2.16100
$119$		0			0
$120$	2.96252			0.270439
$121$	−1.26519	−	2.19137i	−0.115017	−	0.199215i
$122$	−8.54955	+	14.8083i	−0.774040	+	1.34068i
$123$	1.76050	−	3.04928i	0.158739	−	0.274944i
$124$	−14.1481	−	24.5053i	−1.27054	−	2.20064i
$125$	8.34858			0.746720
$126$		0			0
$127$	6.61029			0.586568			0.293284	−	0.956025i	$-0.405252\pi$
$127$	6.61029			0.586568			0.293284	+	0.956025i	$0.405252\pi$
$128$	−9.83031	−	17.0266i	−0.868885	−	1.50495i
$129$	−3.69736	+	6.40401i	−0.325534	+	0.563842i
$130$	1.11412	−	1.92971i	0.0977148	−	0.169247i
$131$	−9.98324	−	17.2915i	−0.872240	−	1.51076i	−0.859674	−	0.510843i	$-0.829334\pi$
$131$	−9.98324	−	17.2915i	−0.872240	−	1.51076i	−0.0125654	−	0.999921i	$-0.504000\pi$
$132$	9.80076			0.853047
$133$		0			0
$134$	−3.00692			−0.259758
$135$	−1.68738	−	2.92263i	−0.145227	−	0.251540i
$136$	−17.5178	+	30.3416i	−1.50213	+	2.60177i
$137$	−2.87726	+	4.98355i	−0.245821	+	0.425774i	−0.962362	−	0.271771i	$-0.912391\pi$
$137$	−2.87726	+	4.98355i	−0.245821	+	0.425774i	0.716541	+	0.697545i	$0.245724\pi$
$138$	−0.487450	−	0.844288i	−0.0414945	−	0.0718706i
$139$	1.55138			0.131586			0.0657931	−	0.997833i	$-0.479042\pi$
$139$	1.55138			0.131586			0.0657931	+	0.997833i	$0.479042\pi$
$140$		0			0
$141$	−8.08517			−0.680894
$142$	13.9080	+	24.0894i	1.16713	+	2.02153i
$143$	1.83918	−	3.18556i	0.153800	−	0.266390i
$144$	5.04742	−	8.74239i	0.420618	−	0.728532i
$145$	−1.66082	−	2.87662i	−0.137923	−	0.238890i
$146$	15.9947			1.32373
$147$		0			0
$148$	2.83768			0.233256
$149$	−7.46683	−	12.9329i	−0.611707	−	1.05951i	−0.990953	−	0.134211i	$-0.957150\pi$
$149$	−7.46683	−	12.9329i	−0.611707	−	1.05951i	0.379246	−	0.925296i	$-0.376183\pi$
$150$	−3.40764	+	5.90220i	−0.278233	+	0.481913i
$151$	3.95051	−	6.84248i	0.321488	−	0.556833i	−0.659307	−	0.751873i	$-0.729150\pi$
$151$	3.95051	−	6.84248i	0.321488	−	0.556833i	0.980795	+	0.195040i	$0.0624838\pi$
$152$	4.82240	+	8.35265i	0.391149	+	0.677489i
$153$	18.3549			1.48391
$154$		0			0
$155$	−6.45241			−0.518270
$156$	1.33222	+	2.30747i	0.106663	+	0.184745i
$157$	6.24740	−	10.8208i	0.498597	−	0.863595i	−0.501402	−	0.865215i	$-0.667182\pi$
$157$	6.24740	−	10.8208i	0.498597	−	0.863595i	0.999999	+	0.00161951i	$0.000515506\pi$
$158$	−14.1001	+	24.4221i	−1.12174	+	1.94292i
$159$	3.82064	+	6.61754i	0.302996	+	0.524805i
$160$	−0.0715920			−0.00565985
$161$		0			0
$162$	−12.7020			−0.997961
$163$	−3.50714	−	6.07454i	−0.274700	−	0.475795i	0.695359	−	0.718662i	$-0.255245\pi$
$163$	−3.50714	−	6.07454i	−0.274700	−	0.475795i	−0.970059	+	0.242868i	$0.921912\pi$
$164$	10.5294	−	18.2374i	0.822205	−	1.42410i
$165$	1.11744	−	1.93546i	0.0869923	−	0.150675i
$166$	−8.76823	−	15.1870i	−0.680546	−	1.17874i
$167$	−4.82764			−0.373574			−0.186787	−	0.982400i	$-0.559807\pi$
$167$	−4.82764			−0.373574			−0.186787	+	0.982400i	$0.559807\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	8.00530	+	13.8656i	0.613979	+	1.06344i
$171$	2.52643	−	4.37591i	0.193201	−	0.334634i
$172$	−22.1135	+	38.3017i	−1.68614	+	2.92047i
$173$	−11.1062	−	19.2365i	−0.844388	−	1.46252i	−0.886152	−	0.463395i	$-0.846631\pi$
$173$	−11.1062	−	19.2365i	−0.844388	−	1.46252i	0.0417636	−	0.999128i	$-0.486702\pi$
$174$	5.96180			0.451963
$175$		0			0
$176$	14.5361			1.09570
$177$	3.20038	+	5.54323i	0.240556	+	0.416654i
$178$	−15.7262	+	27.2386i	−1.17873	+	2.04162i
$179$	−2.28753	+	3.96211i	−0.170978	+	0.296142i	−0.938762	−	0.344566i	$-0.888026\pi$
$179$	−2.28753	+	3.96211i	−0.170978	+	0.296142i	0.767784	+	0.640709i	$0.221359\pi$
$180$	−4.64131	−	8.03899i	−0.345943	−	0.599191i
$181$	7.23332			0.537649			0.268824	−	0.963189i	$-0.413365\pi$
$181$	7.23332			0.537649			0.268824	+	0.963189i	$0.413365\pi$
$182$		0			0
$183$	−4.66239			−0.344654
$184$	−1.45475	−	2.51971i	−0.107246	−	0.185755i
$185$	0.323539	−	0.560386i	0.0237871	−	0.0412004i
$186$	5.79052	−	10.0295i	0.424582	−	0.735397i
$187$	13.2151	+	22.8892i	0.966384	+	1.67383i
$188$	−48.3565			−3.52676
$189$		0			0
$190$	4.40751			0.319754
$191$	−0.986209	−	1.70816i	−0.0713596	−	0.123598i	0.828138	−	0.560525i	$-0.189400\pi$
$191$	−0.986209	−	1.70816i	−0.0713596	−	0.123598i	−0.899497	+	0.436926i	$0.856067\pi$
$192$	2.70187	−	4.67977i	0.194990	−	0.337733i
$193$	12.6036	−	21.8301i	0.907230	−	1.57137i	0.0893339	−	0.996002i	$-0.471526\pi$
$193$	12.6036	−	21.8301i	0.907230	−	1.57137i	0.817896	−	0.575366i	$-0.195140\pi$
$194$	−11.1262	−	19.2712i	−0.798816	−	1.38359i
$195$	0.607572			0.0435091
$196$		0			0
$197$	−3.04497			−0.216945			−0.108473	−	0.994099i	$-0.534596\pi$
$197$	−3.04497			−0.216945			−0.108473	+	0.994099i	$0.534596\pi$
$198$	−11.5005	−	19.9194i	−0.817304	−	1.41561i
$199$	2.02846	−	3.51339i	0.143794	−	0.249058i	−0.785129	−	0.619333i	$-0.787403\pi$
$199$	2.02846	−	3.51339i	0.143794	−	0.249058i	0.928922	+	0.370275i	$0.120737\pi$
$200$	−10.1698	+	17.6146i	−0.719114	+	1.24554i
$201$	−0.409946	−	0.710048i	−0.0289154	−	0.0500829i
$202$	−14.2133			−1.00004
$203$		0			0
$204$	−19.1448			−1.34040
$205$	−2.40101	−	4.15868i	−0.167694	−	0.290455i
$206$	−15.7497	+	27.2793i	−1.09733	+	1.90064i
$207$	−0.762138	+	1.32006i	−0.0529722	+	0.0917506i
$208$	1.97589	+	3.42234i	0.137003	+	0.237296i
$209$	7.27588			0.503283
$210$		0			0
$211$	16.4116			1.12982			0.564910	−	0.825152i	$-0.308911\pi$
$211$	16.4116			1.12982			0.564910	+	0.825152i	$0.308911\pi$
$212$	22.8508	+	39.5787i	1.56940	+	2.71828i
$213$	−3.79228	+	6.56842i	−0.259843	+	0.450061i
$214$	5.45561	−	9.44939i	0.372938	−	0.645947i
$215$	5.04255	+	8.73394i	0.343899	+	0.595650i
$216$	18.0771			1.22999
$217$		0			0
$218$	−2.15140			−0.145711
$219$	2.18063	+	3.77696i	0.147353	+	0.255223i
$220$	6.68326	−	11.5757i	0.450585	−	0.780436i
$221$	−3.59265	+	6.22266i	−0.241668	+	0.418581i
$222$	0.580701	+	1.00580i	0.0389741	+	0.0675051i
$223$	16.1205			1.07951			0.539755	−	0.841822i	$-0.318517\pi$
$223$	16.1205			1.07951			0.539755	+	0.841822i	$0.318517\pi$
$224$		0			0
$225$	10.6558			0.710388
$226$	−6.56907	−	11.3780i	−0.436968	−	0.756851i
$227$	−4.33902	+	7.51540i	−0.287991	+	0.498815i	−0.973330	−	0.229409i	$-0.926321\pi$
$227$	−4.33902	+	7.51540i	−0.287991	+	0.498815i	0.685339	+	0.728224i	$0.259654\pi$
$228$	−2.63515	+	4.56422i	−0.174517	+	0.302273i
$229$	−10.3796	−	17.9780i	−0.685902	−	1.18802i	−0.973152	−	0.230162i	$-0.926074\pi$
$229$	−10.3796	−	17.9780i	−0.685902	−	1.18802i	0.287250	−	0.957856i	$-0.407259\pi$
$230$	−1.32959			−0.0876707
$231$		0			0
$232$	17.7925			1.16813
$233$	4.92234	+	8.52574i	0.322473	+	0.558540i	0.980998	−	0.194019i	$-0.0621525\pi$
$233$	4.92234	+	8.52574i	0.322473	+	0.558540i	−0.658525	+	0.752559i	$0.728819\pi$
$234$	3.12652	−	5.41529i	0.204387	−	0.354009i
$235$	−5.51337	+	9.54944i	−0.359653	+	0.622937i
$236$	19.1411	+	33.1534i	1.24598	+	2.15810i
$237$	−7.68932			−0.499475
$238$		0			0
$239$	1.13539			0.0734424			0.0367212	−	0.999326i	$-0.488309\pi$
$239$	1.13539			0.0734424			0.0367212	+	0.999326i	$0.488309\pi$
$240$	1.20049	+	2.07932i	0.0774915	+	0.134219i
$241$	−10.9104	+	18.8974i	−0.702802	+	1.21729i	0.264677	+	0.964337i	$0.414735\pi$
$241$	−10.9104	+	18.8974i	−0.702802	+	1.21729i	−0.967479	+	0.252951i	$0.918599\pi$
$242$	3.09698	−	5.36413i	0.199081	−	0.344819i
$243$	−7.29276	−	12.6314i	−0.467831	−	0.810307i
$244$	−27.8852			−1.78517
$245$		0			0
$246$	8.61888			0.549519
$247$	0.989010	+	1.71302i	0.0629292	+	0.108997i
$248$	17.2813	−	29.9321i	1.09736	−	1.90069i
$249$	2.39082	−	4.14103i	0.151512	−	0.262427i
$250$	10.2180	+	17.6981i	0.646244	+	1.11933i
$251$	−9.44377			−0.596086			−0.298043	−	0.954552i	$-0.596334\pi$
$251$	−9.44377			−0.596086			−0.298043	+	0.954552i	$0.596334\pi$
$252$		0			0
$253$	−2.19488			−0.137991
$254$	8.09048	+	14.0131i	0.507642	+	0.879262i
$255$	−2.18280	+	3.78071i	−0.136692	+	0.236758i
$256$	15.9670	−	27.6557i	0.997939	−	1.72848i
$257$	−1.81376	−	3.14153i	−0.113139	−	0.195963i	0.803895	−	0.594771i	$-0.202757\pi$
$257$	−1.81376	−	3.14153i	−0.113139	−	0.195963i	−0.917034	+	0.398808i	$0.869424\pi$
$258$	−18.1011			−1.12693
$259$		0			0
$260$	3.63382			0.225360
$261$	−4.66070	−	8.07257i	−0.288490	−	0.499680i
$262$	24.4374	−	42.3269i	1.50975	−	2.61496i
$263$	−3.29792	+	5.71217i	−0.203359	+	0.352227i	−0.949608	−	0.313439i	$-0.898519\pi$
$263$	−3.29792	+	5.71217i	−0.203359	+	0.352227i	0.746250	+	0.665666i	$0.231852\pi$
$264$	5.98560	+	10.3674i	0.368388	+	0.638067i
$265$	10.4214			0.640179
$266$		0			0
$267$	−8.57610			−0.524849
$268$	−2.45184	−	4.24672i	−0.149770	−	0.259409i
$269$	11.7657	−	20.3787i	0.717365	−	1.24251i	−0.244675	−	0.969605i	$-0.578681\pi$
$269$	11.7657	−	20.3787i	0.717365	−	1.24251i	0.962040	−	0.272908i	$-0.0879853\pi$
$270$	4.13045	−	7.15415i	0.251371	−	0.435388i
$271$	1.34883	+	2.33625i	0.0819358	+	0.141917i	0.904081	−	0.427360i	$-0.140556\pi$
$271$	1.34883	+	2.33625i	0.0819358	+	0.141917i	−0.822146	+	0.569277i	$0.807223\pi$
$272$	−28.3947			−1.72168
$273$		0			0
$274$	−14.0862			−0.850976
$275$	7.67193	+	13.2882i	0.462635	+	0.801307i
$276$	0.794934	−	1.37687i	0.0478494	−	0.0828776i
$277$	12.3775	−	21.4384i	0.743690	−	1.28811i	−0.207115	−	0.978317i	$-0.566407\pi$
$277$	12.3775	−	21.4384i	0.743690	−	1.28811i	0.950804	−	0.309792i	$-0.100259\pi$
$278$	1.89877	+	3.28876i	0.113881	+	0.197247i
$279$	−18.1072			−1.08405
$280$		0			0
$281$	−4.05377			−0.241828			−0.120914	−	0.992663i	$-0.538582\pi$
$281$	−4.05377			−0.241828			−0.120914	+	0.992663i	$0.538582\pi$
$282$	−9.89562	−	17.1397i	−0.589276	−	1.02066i
$283$	6.46186	−	11.1923i	0.384118	−	0.665311i	−0.607529	−	0.794298i	$-0.707839\pi$
$283$	6.46186	−	11.1923i	0.384118	−	0.665311i	0.991646	+	0.128987i	$0.0411724\pi$
$284$	−22.6812	+	39.2850i	−1.34588	+	2.33113i
$285$	0.600895	+	1.04078i	0.0355939	+	0.0616505i
$286$	9.00407			0.532422
$287$		0			0
$288$	−0.200906			−0.0118385
$289$	−17.3143	−	29.9893i	−1.01849	−	1.76408i
$290$	4.06543	−	7.04152i	0.238730	−	0.413492i
$291$	3.03377	−	5.25465i	0.177843	−	0.308033i
$292$	13.0421	+	22.5895i	0.763230	+	1.32195i
$293$	23.5553			1.37611			0.688057	−	0.725656i	$-0.258464\pi$
$293$	23.5553			1.37611			0.688057	+	0.725656i	$0.258464\pi$
$294$		0			0
$295$	8.72952			0.508252
$296$	1.73305	+	3.00173i	0.100732	+	0.174472i
$297$	6.81852	−	11.8100i	0.395651	−	0.685287i
$298$	18.2777	−	31.6578i	1.05880	−	1.83389i
$299$	−0.298350	−	0.516758i	−0.0172540	−	0.0298849i
$300$	−11.1144			−0.641688
$301$		0			0
$302$	19.3405			1.11292
$303$	−1.93776	−	3.35630i	−0.111321	−	0.192814i
$304$	−3.90834	+	6.76945i	−0.224159	+	0.388255i
$305$	−3.17934	+	5.50678i	−0.182049	+	0.315317i
$306$	22.4650	+	38.9106i	1.28424	+	2.22437i
$307$	−19.9551			−1.13890			−0.569450	−	0.822026i	$-0.692844\pi$
$307$	−19.9551			−1.13890			−0.569450	+	0.822026i	$0.692844\pi$
$308$		0			0
$309$	−8.58891			−0.488606
$310$	−7.89725	−	13.6784i	−0.448534	−	0.776883i
$311$	3.24035	−	5.61245i	0.183743	−	0.318253i	−0.759409	−	0.650613i	$-0.774512\pi$
$311$	3.24035	−	5.61245i	0.183743	−	0.318253i	0.943152	+	0.332361i	$0.107845\pi$
$312$	−1.62724	+	2.81847i	−0.0921245	+	0.159564i
$313$	8.05771	+	13.9564i	0.455449	+	0.788860i	0.998714	−	0.0507010i	$-0.0161455\pi$
$313$	8.05771	+	13.9564i	0.455449	+	0.788860i	−0.543265	+	0.839561i	$0.682812\pi$
$314$	30.5854			1.72603
$315$		0			0
$316$	−45.9889			−2.58708
$317$	−7.26517	−	12.5836i	−0.408053	−	0.706768i	0.586619	−	0.809863i	$-0.300459\pi$
$317$	−7.26517	−	12.5836i	−0.408053	−	0.706768i	−0.994672	+	0.103095i	$0.967125\pi$
$318$	−9.35233	+	16.1987i	−0.524453	+	0.908379i
$319$	6.71118	−	11.6241i	0.375754	−	0.650825i
$320$	−3.68487	−	6.38238i	−0.205990	−	0.356786i
$321$	2.97515			0.166057
$322$		0			0
$323$	−14.2127			−0.790815
$324$	−10.3572	−	17.9392i	−0.575400	−	0.996622i
$325$	−2.08569	+	3.61252i	−0.115693	+	0.200387i
$326$	8.58493	−	14.8695i	0.475475	−	0.823547i
$327$	−0.293310	−	0.508028i	−0.0162201	−	0.0280940i
$328$	25.7223			1.42028
$329$		0			0
$330$	5.47062			0.301148
$331$	−10.5473	−	18.2684i	−0.579730	−	1.00412i	−0.995510	−	0.0946563i	$-0.969825\pi$
$331$	−10.5473	−	18.2684i	−0.579730	−	1.00412i	0.415780	−	0.909465i	$-0.363509\pi$
$332$	14.2992	−	24.7670i	0.784773	−	1.35927i
$333$	0.907938	−	1.57259i	0.0497547	−	0.0861776i
$334$	−5.90866	−	10.2341i	−0.323308	−	0.559985i
$335$	−1.11819			−0.0610932
$336$		0			0
$337$	−32.8693			−1.79050			−0.895251	−	0.445562i	$-0.853004\pi$
$337$	−32.8693			−1.79050			−0.895251	+	0.445562i	$0.853004\pi$
$338$	1.22392	+	2.11990i	0.0665726	+	0.115307i
$339$	1.79118	−	3.10242i	0.0972836	−	0.168500i
$340$	−13.0551	+	22.6120i	−0.708010	+	1.22631i
$341$	−13.0367	−	22.5803i	−0.705979	−	1.22279i
$342$	12.3686			0.668820
$343$		0			0
$344$	−54.0213			−2.91263
$345$	−0.181269	−	0.313967i	−0.00975921	−	0.0169034i
$346$	27.1862	−	47.0880i	1.46154	−	2.53146i
$347$	−7.95802	+	13.7837i	−0.427209	+	0.739948i	−0.996624	−	0.0821026i	$-0.973836\pi$
$347$	−7.95802	+	13.7837i	−0.427209	+	0.739948i	0.569415	+	0.822050i	$0.307170\pi$
$348$	4.86126	+	8.41995i	0.260591	+	0.451357i
$349$	29.6245			1.58576			0.792882	−	0.609375i	$-0.208580\pi$
$349$	29.6245			1.58576			0.792882	+	0.609375i	$0.208580\pi$
$350$		0			0
$351$	3.70737			0.197885
$352$	−0.144648	−	0.250537i	−0.00770975	−	0.0133537i
$353$	−14.3539	+	24.8617i	−0.763980	+	1.32325i	0.176804	+	0.984246i	$0.443424\pi$
$353$	−14.3539	+	24.8617i	−0.763980	+	1.32325i	−0.940784	+	0.339006i	$0.889909\pi$
$354$	−7.83405	+	13.5690i	−0.416375	+	0.721182i
$355$	5.17200	+	8.95817i	0.274501	+	0.475450i
$356$	−51.2927			−2.71851
$357$		0			0
$358$	−11.1990			−0.591887
$359$	−13.6466	−	23.6365i	−0.720238	−	1.24749i	−0.960904	−	0.276881i	$-0.910699\pi$
$359$	−13.6466	−	23.6365i	−0.720238	−	1.24749i	0.240666	−	0.970608i	$-0.422634\pi$
$360$	5.66915	−	9.81926i	0.298791	−	0.517521i
$361$	7.54372	−	13.0661i	0.397038	−	0.687690i
$362$	8.85303	+	15.3339i	0.465305	+	0.805932i
$363$	1.68890			0.0886443
$364$		0			0
$365$	5.94798			0.311332
$366$	−5.70641	−	9.88379i	−0.298279	−	0.516634i
$367$	−4.99163	+	8.64575i	−0.260561	+	0.451305i	−0.966391	−	0.257076i	$-0.917241\pi$
$367$	−4.99163	+	8.64575i	−0.260561	+	0.451305i	0.705830	+	0.708381i	$0.250574\pi$
$368$	1.17901	−	2.04211i	0.0614603	−	0.106452i
$369$	−6.73789	−	11.6704i	−0.350761	−	0.607535i
$370$	1.58395			0.0823455
$371$		0			0
$372$	18.8864			0.979214
$373$	−2.34304	−	4.05827i	−0.121318	−	0.210129i	0.798970	−	0.601371i	$-0.205379\pi$
$373$	−2.34304	−	4.05827i	−0.121318	−	0.210129i	−0.920288	+	0.391242i	$0.872045\pi$
$374$	−32.3485	+	56.0293i	−1.67270	+	2.89721i
$375$	−2.78614	+	4.82573i	−0.143875	+	0.249200i
$376$	−29.5326	−	51.1520i	−1.52303	−	2.63796i
$377$	3.64900			0.187933
$378$		0			0
$379$	−2.45019			−0.125858			−0.0629288	−	0.998018i	$-0.520044\pi$
$379$	−2.45019			−0.125858			−0.0629288	+	0.998018i	$0.520044\pi$
$380$	3.59388	+	6.22479i	0.184362	+	0.319325i
$381$	−2.20602	+	3.82094i	−0.113018	+	0.195753i
$382$	2.41409	−	4.18132i	0.123515	−	0.213935i
$383$	−5.38356	−	9.32461i	−0.275087	−	0.476465i	0.695070	−	0.718942i	$-0.255373\pi$
$383$	−5.38356	−	9.32461i	−0.275087	−	0.476465i	−0.970157	+	0.242477i	$0.922040\pi$
$384$	13.1225			0.669656
$385$		0			0
$386$	61.7035			3.14063
$387$	14.1507	+	24.5098i	0.719322	+	1.24590i
$388$	18.1447	−	31.4275i	0.921155	−	1.59549i
$389$	−7.01860	+	12.1566i	−0.355857	+	0.616362i	−0.987264	−	0.159089i	$-0.949144\pi$
$389$	−7.01860	+	12.1566i	−0.355857	+	0.616362i	0.631407	+	0.775451i	$0.282478\pi$
$390$	0.743621	+	1.28799i	0.0376547	+	0.0652199i
$391$	4.28748			0.216827
$392$		0			0
$393$	13.3267			0.672241
$394$	−3.72681	−	6.45503i	−0.187754	−	0.325200i
$395$	−5.24344	+	9.08190i	−0.263826	+	0.456960i
$396$	18.7550	−	32.4846i	0.942475	−	1.63241i
$397$	13.2303	+	22.9155i	0.664007	+	1.15009i	0.979553	+	0.201184i	$0.0644790\pi$
$397$	13.2303	+	22.9155i	0.664007	+	1.15009i	−0.315546	+	0.948910i	$0.602188\pi$
$398$	9.93070			0.497781
$399$		0			0
$400$	−16.4843			−0.824217
$401$	9.50779	+	16.4680i	0.474796	+	0.822371i	0.999583	−	0.0288621i	$-0.00918838\pi$
$401$	9.50779	+	16.4680i	0.474796	+	0.822371i	−0.524787	+	0.851234i	$0.675855\pi$
$402$	1.00349	−	1.73809i	0.0500493	−	0.0866880i
$403$	3.54416	−	6.13867i	0.176547	−	0.305789i
$404$	−11.5895	−	20.0737i	−0.576601	−	0.998701i
$405$	−4.72351			−0.234713
$406$		0			0
$407$	2.61477			0.129609
$408$	−11.6923	−	20.2516i	−0.578853	−	1.00260i
$409$	6.38796	−	11.0643i	0.315864	−	0.547093i	−0.663757	−	0.747949i	$-0.731039\pi$
$409$	6.38796	−	11.0643i	0.315864	−	0.547093i	0.979621	+	0.200856i	$0.0643723\pi$
$410$	5.87731	−	10.1798i	0.290260	−	0.502745i
$411$	−1.92043	−	3.32628i	−0.0947278	−	0.164073i
$412$	−51.3693			−2.53078
$413$		0			0
$414$	−3.73119			−0.183378
$415$	−3.26066	−	5.64763i	−0.160060	−	0.277231i
$416$	0.0393239	−	0.0681110i	0.00192801	−	0.00333942i
$417$	−0.517735	+	0.896744i	−0.0253536	+	0.0439137i
$418$	8.90512	+	15.4241i	0.435564	+	0.754418i
$419$	−12.9811			−0.634170			−0.317085	−	0.948397i	$-0.602704\pi$
$419$	−12.9811			−0.634170			−0.317085	+	0.948397i	$0.602704\pi$
$420$		0			0
$421$	−11.6737			−0.568943			−0.284472	−	0.958684i	$-0.591818\pi$
$421$	−11.6737			−0.568943			−0.284472	+	0.958684i	$0.591818\pi$
$422$	20.0865	+	34.7909i	0.977797	+	1.69359i
$423$	−15.4720	+	26.7983i	−0.752275	+	1.30298i
$424$	−27.9112	+	48.3437i	−1.35549	+	2.34778i
$425$	−14.9863	−	25.9571i	−0.726944	−	1.25910i
$426$	−18.5658			−0.899517
$427$		0			0
$428$	17.7940			0.860107
$429$	1.22757	+	2.12621i	0.0592674	+	0.102654i
$430$	−12.3434	+	21.3794i	−0.595250	+	1.03100i
$431$	0.233842	−	0.405026i	0.0112638	−	0.0195094i	−0.860339	−	0.509723i	$-0.829748\pi$
$431$	0.233842	−	0.405026i	0.0112638	−	0.0195094i	0.871602	+	0.490214i	$0.163081\pi$
$432$	7.32533	+	12.6879i	0.352440	+	0.610445i
$433$	9.27593			0.445773			0.222886	−	0.974844i	$-0.428452\pi$
$433$	9.27593			0.445773			0.222886	+	0.974844i	$0.428452\pi$
$434$		0			0
$435$	2.21703			0.106298
$436$	−1.75426	−	3.03846i	−0.0840136	−	0.145516i
$437$	0.590143	−	1.02216i	0.0282303	−	0.0488964i
$438$	−5.33784	+	9.24541i	−0.255052	+	0.441763i
$439$	−17.8539	−	30.9238i	−0.852119	−	1.47591i	−0.879292	−	0.476282i	$-0.841984\pi$
$439$	−17.8539	−	30.9238i	−0.852119	−	1.47591i	0.0271736	−	0.999631i	$-0.491349\pi$
$440$	16.3266			0.778340
$441$		0			0
$442$	−17.5885			−0.836601
$443$	18.1729	+	31.4764i	0.863421	+	1.49549i	0.868606	+	0.495503i	$0.165016\pi$
$443$	18.1729	+	31.4764i	0.863421	+	1.49549i	−0.00518509	+	0.999987i	$0.501650\pi$
$444$	−0.947008	+	1.64027i	−0.0449430	+	0.0778436i
$445$	−5.84814	+	10.1293i	−0.277229	+	0.480174i
$446$	19.7303	+	34.1738i	0.934255	+	1.61818i
$447$	9.96750			0.471447
$448$		0			0
$449$	−40.4910			−1.91089			−0.955444	−	0.295171i	$-0.904623\pi$
$449$	−40.4910			−1.91089			−0.955444	+	0.295171i	$0.904623\pi$
$450$	13.0419	+	22.5892i	0.614801	+	1.06487i
$451$	9.70223	−	16.8048i	0.456860	−	0.791305i
$452$	10.7129	−	18.5552i	0.503890	−	0.872764i
$453$	2.63677	+	4.56702i	0.123886	+	0.214578i
$454$	−21.2425			−0.996960
$455$		0			0
$456$	−6.43744			−0.301461
$457$	−2.50994	−	4.34734i	−0.117410	−	0.203360i	0.801331	−	0.598222i	$-0.204126\pi$
$457$	−2.50994	−	4.34734i	−0.117410	−	0.203360i	−0.918741	+	0.394862i	$0.870793\pi$
$458$	25.4076	−	44.0073i	1.18722	−	2.05633i
$459$	−13.3193	+	23.0697i	−0.621691	+	1.07680i
$460$	−1.08415	−	1.87780i	−0.0505488	−	0.0875530i
$461$	17.3627			0.808661			0.404331	−	0.914613i	$-0.367505\pi$
$461$	17.3627			0.808661			0.404331	+	0.914613i	$0.367505\pi$
$462$		0			0
$463$	35.4306			1.64660			0.823301	−	0.567606i	$-0.192130\pi$
$463$	35.4306			1.64660			0.823301	+	0.567606i	$0.192130\pi$
$464$	7.21001	+	12.4881i	0.334716	+	0.579746i
$465$	2.15334	−	3.72969i	0.0998585	−	0.172960i
$466$	−12.0491	+	20.8697i	−0.558165	+	0.966770i
$467$	17.7479	+	30.7403i	0.821275	+	1.42249i	0.904733	+	0.425978i	$0.140070\pi$
$467$	17.7479	+	30.7403i	0.821275	+	1.42249i	−0.0834584	+	0.996511i	$0.526597\pi$
$468$	10.1975			0.471378
$469$		0			0
$470$	−26.9918			−1.24504
$471$	4.16984	+	7.22237i	0.192136	+	0.332789i
$472$	−23.3800	+	40.4954i	−1.07615	+	1.86395i
$473$	−20.3764	+	35.2929i	−0.936906	+	1.62277i
$474$	−9.41114	−	16.3006i	−0.432268	−	0.748710i
$475$	−8.25107			−0.378585
$476$		0			0
$477$	29.2451			1.33904
$478$	1.38963	+	2.40691i	0.0635603	+	0.110090i
$479$	−12.0135	+	20.8080i	−0.548911	+	0.950742i	0.449438	+	0.893311i	$0.351624\pi$
$479$	−12.0135	+	20.8080i	−0.548911	+	0.950742i	−0.998349	+	0.0574308i	$0.981709\pi$
$480$	0.0238921	−	0.0413823i	0.00109052	−	0.00188884i
$481$	0.355426	+	0.615615i	0.0162060	+	0.0280696i
$482$	−53.4140			−2.43294
$483$		0			0
$484$	10.1011			0.459142
$485$	−4.13753	−	7.16642i	−0.187876	−	0.325410i
$486$	17.8516	−	30.9198i	0.809763	−	1.40255i
$487$	−10.4038	+	18.0199i	−0.471440	+	0.816558i	−0.999466	−	0.0326699i	$-0.989599\pi$
$487$	−10.4038	+	18.0199i	−0.471440	+	0.816558i	0.528026	+	0.849228i	$0.322932\pi$
$488$	−17.0303	−	29.4973i	−0.770925	−	1.33528i
$489$	4.68169			0.211713
$490$		0			0
$491$	−36.2195			−1.63456			−0.817281	−	0.576240i	$-0.804519\pi$
$491$	−36.2195			−1.63456			−0.817281	+	0.576240i	$0.804519\pi$
$492$	7.02784	+	12.1726i	0.316839	+	0.548782i
$493$	−13.1096	+	22.7065i	−0.590427	+	1.02265i
$494$	−2.42094	+	4.19320i	−0.108923	+	0.188661i
$495$	−4.27671	−	7.40749i	−0.192224	−	0.332942i
$496$	28.0115			1.25775
$497$		0			0
$498$	11.7047			0.524502
$499$	20.0914	+	34.7994i	0.899416	+	1.55783i	0.828243	+	0.560370i	$0.189341\pi$
$499$	20.0914	+	34.7994i	0.899416	+	1.55783i	0.0711731	+	0.997464i	$0.477326\pi$
$500$	−16.6636	+	28.8621i	−0.745217	+	1.29075i
$501$	1.61111	−	2.79052i	0.0719790	−	0.124671i
$502$	−11.5585	−	20.0198i	−0.515879	−	0.893529i
$503$	−38.5636			−1.71946			−0.859732	−	0.510745i	$-0.829370\pi$
$503$	−38.5636			−1.71946			−0.859732	+	0.510745i	$0.829370\pi$
$504$		0			0
$505$	−5.28553			−0.235203
$506$	−2.68637	−	4.65292i	−0.119424	−	0.206848i
$507$	−0.333726	+	0.578030i	−0.0148213	+	0.0256712i
$508$	−13.1940	+	22.8526i	−0.585388	+	1.01392i
$509$	2.16989	+	3.75835i	0.0961785	+	0.166586i	0.910100	−	0.414389i	$-0.136005\pi$
$509$	2.16989	+	3.75835i	0.0961785	+	0.166586i	−0.813921	+	0.580975i	$0.802671\pi$
$510$	−10.6863			−0.473197
$511$		0			0
$512$	38.8484			1.71687
$513$	3.66662	+	6.35078i	0.161885	+	0.280394i
$514$	4.43981	−	7.68998i	0.195832	−	0.339190i
$515$	−5.85688	+	10.1444i	−0.258085	+	0.447016i
$516$	−14.7597	−	25.5645i	−0.649758	−	1.12541i
$517$	−44.5578			−1.95965
$518$		0			0
$519$	14.8257			0.650776
$520$	2.21927	+	3.84390i	0.0973216	+	0.168566i
$521$	6.89219	−	11.9376i	0.301952	−	0.522997i	−0.674626	−	0.738160i	$-0.735695\pi$
$521$	6.89219	−	11.9376i	0.301952	−	0.522997i	0.976578	+	0.215163i	$0.0690283\pi$
$522$	11.4087	−	19.7604i	0.499344	−	0.864890i
$523$	−14.7417	−	25.5334i	−0.644609	−	1.11650i	−0.984392	−	0.175992i	$-0.943687\pi$
$523$	−14.7417	−	25.5334i	−0.644609	−	1.11650i	0.339782	−	0.940504i	$-0.389647\pi$
$524$	79.7052			3.48194
$525$		0			0
$526$	−16.1456			−0.703982
$527$	25.4659	+	44.1083i	1.10931	+	1.92139i
$528$	−4.85106	+	8.40228i	−0.211115	+	0.365662i
$529$	11.3220	−	19.6102i	0.492260	−	0.852619i
$530$	12.7549	+	22.0922i	0.554039	+	0.959624i
$531$	24.4974			1.06310
$532$		0			0
$533$	5.27529			0.228498
$534$	−10.4965	−	18.1804i	−0.454227	−	0.786745i
$535$	2.02879	−	3.51397i	0.0877122	−	0.151922i
$536$	2.99482	−	5.18717i	0.129356	−	0.224052i
$537$	−1.52681	−	2.64452i	−0.0658869	−	0.114119i
$538$	57.6011			2.48336
$539$		0			0
$540$	13.4719			0.579738
$541$	−11.6260	−	20.1368i	−0.499840	−	0.865747i	0.500160	−	0.865933i	$-0.333274\pi$
$541$	−11.6260	−	20.1368i	−0.499840	−	0.865747i	−1.00000		0.000185310i	$0.999941\pi$
$542$	−3.30174	+	5.71878i	−0.141822	+	0.245643i
$543$	−2.41395	+	4.18108i	−0.103592	+	0.179427i
$544$	0.282554	+	0.489399i	0.0121144	+	0.0209828i
$545$	−0.800047			−0.0342703
$546$		0			0
$547$	1.18365			0.0506093			0.0253046	−	0.999680i	$-0.491944\pi$
$547$	1.18365			0.0506093			0.0253046	+	0.999680i	$0.491944\pi$
$548$	−11.4859	−	19.8941i	−0.490652	−	0.849834i
$549$	−8.92209	+	15.4535i	−0.380785	+	0.659540i
$550$	−18.7797	+	32.5274i	−0.800769	+	1.38697i
$551$	3.60890	+	6.25079i	0.153744	+	0.266293i
$552$	1.94195			0.0826550
$553$		0			0
$554$	60.5962			2.57449
$555$	0.215947	+	0.374031i	0.00916642	+	0.0158767i
$556$	−3.09651	+	5.36332i	−0.131321	+	0.227455i
$557$	3.21412	−	5.56702i	0.136187	−	0.235882i	−0.789864	−	0.613283i	$-0.789849\pi$
$557$	3.21412	−	5.56702i	0.136187	−	0.235882i	0.926050	+	0.377401i	$0.123182\pi$
$558$	−22.1618	−	38.3854i	−0.938184	−	1.62498i
$559$	−11.0790			−0.468593
$560$		0			0
$561$	−17.6409			−0.744798
$562$	−4.96150	−	8.59357i	−0.209288	−	0.362498i
$563$	5.72813	−	9.92141i	0.241412	−	0.418138i	−0.719705	−	0.694280i	$-0.755723\pi$
$563$	5.72813	−	9.92141i	0.241412	−	0.418138i	0.961117	+	0.276142i	$0.0890562\pi$
$564$	16.1378	−	27.9515i	0.679524	−	1.17697i
$565$	−2.44286	−	4.23115i	−0.102772	−	0.178006i
$566$	31.6353			1.32973
$567$		0			0
$568$	−55.4081			−2.32487
$569$	−19.1668	−	33.1978i	−0.803512	−	1.39172i	−0.917291	−	0.398218i	$-0.869629\pi$
$569$	−19.1668	−	33.1978i	−0.803512	−	1.39172i	0.113779	−	0.993506i	$-0.463705\pi$
$570$	−1.47090	+	2.54767i	−0.0616092	+	0.106710i
$571$	−3.12928	+	5.42008i	−0.130956	+	0.226823i	−0.924046	−	0.382282i	$-0.875138\pi$
$571$	−3.12928	+	5.42008i	−0.130956	+	0.226823i	0.793089	+	0.609106i	$0.208471\pi$
$572$	7.34193	+	12.7166i	0.306981	+	0.531707i
$573$	1.31649			0.0549973
$574$		0			0
$575$	2.48906			0.103801
$576$	−10.3407	−	17.9107i	−0.430864	−	0.746278i
$577$	0.0225966	−	0.0391384i	0.000940708	−	0.00162935i	−0.865555	−	0.500814i	$-0.833034\pi$
$577$	0.0225966	−	0.0391384i	0.000940708	−	0.00162935i	0.866495	+	0.499185i	$0.166367\pi$
$578$	42.3828	−	73.4092i	1.76289	−	3.05342i
$579$	8.41232	+	14.5706i	0.349604	+	0.605532i
$580$	13.2598			0.550583
$581$		0			0
$582$	14.8524			0.615653
$583$	21.0558	+	36.4696i	0.872041	+	1.51042i
$584$	−15.9303	+	27.5921i	−0.659201	+	1.14177i
$585$	1.16267	−	2.01380i	0.0480704	−	0.0832603i
$586$	28.8299	+	49.9348i	1.19095	+	2.06279i
$587$	−2.71409			−0.112023			−0.0560113	−	0.998430i	$-0.517838\pi$
$587$	−2.71409			−0.112023			−0.0560113	+	0.998430i	$0.517838\pi$
$588$		0			0
$589$	14.0209			0.577719
$590$	10.6843	+	18.5057i	0.439864	+	0.761867i
$591$	1.01619	−	1.76009i	0.0418003	−	0.0724003i
$592$	−1.40456	+	2.43277i	−0.0577271	+	0.0999863i
$593$	3.39307	+	5.87698i	0.139337	+	0.241339i	0.927246	−	0.374453i	$-0.122170\pi$
$593$	3.39307	+	5.87698i	0.139337	+	0.241339i	−0.787909	+	0.615792i	$0.788836\pi$
$594$	33.3814			1.36965
$595$		0			0
$596$	59.6145			2.44190
$597$	1.35390	+	2.34502i	0.0554113	+	0.0959752i
$598$	0.730315	−	1.26494i	0.0298648	−	0.0517274i
$599$	13.4169	−	23.2387i	0.548198	−	0.949507i	−0.450200	−	0.892928i	$-0.648647\pi$
$599$	13.4169	−	23.2387i	0.548198	−	0.949507i	0.998398	−	0.0565794i	$-0.0180194\pi$
$600$	−6.78785	−	11.7569i	−0.277113	−	0.479974i
$601$	−12.3356			−0.503178			−0.251589	−	0.967834i	$-0.580953\pi$
$601$	−12.3356			−0.503178			−0.251589	+	0.967834i	$0.580953\pi$
$602$		0			0
$603$	−3.13794			−0.127787
$604$	15.7702	+	27.3148i	0.641682	+	1.11143i
$605$	1.15168	−	1.99477i	0.0468225	−	0.0810990i
$606$	4.74334	−	8.21571i	0.192685	−	0.333740i
$607$	−8.72982	−	15.1205i	−0.354332	−	0.613722i	0.632671	−	0.774421i	$-0.281958\pi$
$607$	−8.72982	−	15.1205i	−0.354332	−	0.613722i	−0.987003	+	0.160699i	$0.948625\pi$
$608$	0.155567			0.00630907
$609$		0			0
$610$	−15.5651			−0.630211
$611$	−6.05674	−	10.4906i	−0.245030	−	0.424404i
$612$	−36.6360	+	63.4554i	−1.48092	+	2.56503i
$613$	−0.525132	+	0.909556i	−0.0212099	+	0.0367366i	−0.876436	−	0.481519i	$-0.840085\pi$
$613$	−0.525132	+	0.909556i	−0.0212099	+	0.0367366i	0.855226	+	0.518256i	$0.173418\pi$
$614$	−24.4236	−	42.3028i	−0.985654	−	1.70720i
$615$	3.20512			0.129243
$616$		0			0
$617$	10.5872			0.426223			0.213111	−	0.977028i	$-0.431640\pi$
$617$	10.5872			0.426223			0.213111	+	0.977028i	$0.431640\pi$
$618$	−10.5122	−	18.2076i	−0.422861	−	0.732417i
$619$	0.619027	−	1.07219i	0.0248808	−	0.0430948i	−0.853317	−	0.521393i	$-0.825413\pi$
$619$	0.619027	−	1.07219i	0.0248808	−	0.0430948i	0.878198	+	0.478298i	$0.158746\pi$
$620$	12.8789	−	22.3068i	0.517227	−	0.895864i
$621$	−1.10609	−	1.91581i	−0.0443860	−	0.0768788i
$622$	15.8637			0.636078
$623$		0			0
$624$	−2.63762			−0.105589
$625$	−6.62865	−	11.4812i	−0.265146	−	0.459246i
$626$	−19.7240	+	34.1630i	−0.788331	+	1.36543i
$627$	−2.42815	+	4.20568i	−0.0969709	+	0.167959i
$628$	24.9393	+	43.1962i	0.995187	+	1.72371i
$629$	−5.10769			−0.203657
$630$		0			0
$631$	−21.2658			−0.846577			−0.423289	−	0.905995i	$-0.639124\pi$
$631$	−21.2658			−0.846577			−0.423289	+	0.905995i	$0.639124\pi$
$632$	−28.0867	−	48.6476i	−1.11723	−	1.93510i
$633$	−5.47697	+	9.48640i	−0.217690	+	0.377050i
$634$	17.7840	−	30.8028i	0.706294	−	1.22334i
$635$	3.00863	+	5.21109i	0.119394	+	0.206796i
$636$	−30.5036			−1.20955
$637$		0			0
$638$	32.8559			1.30078
$639$	14.5140	+	25.1390i	0.574166	+	0.994484i
$640$	8.94840	−	15.4991i	0.353717	−	0.612655i
$641$	−5.52532	+	9.57013i	−0.218237	+	0.377998i	−0.954269	−	0.298949i	$-0.903364\pi$
$641$	−5.52532	+	9.57013i	−0.218237	+	0.377998i	0.736032	+	0.676947i	$0.236697\pi$
$642$	3.64135	+	6.30701i	0.143713	+	0.248918i
$643$	−6.50321			−0.256461			−0.128231	−	0.991744i	$-0.540930\pi$
$643$	−6.50321			−0.256461			−0.128231	+	0.991744i	$0.540930\pi$
$644$		0			0
$645$	−6.73131			−0.265045
$646$	−17.3952	−	30.1294i	−0.684407	−	1.18543i
$647$	−0.446970	+	0.774175i	−0.0175722	+	0.0304360i	−0.874678	−	0.484705i	$-0.838927\pi$
$647$	−0.446970	+	0.774175i	−0.0175722	+	0.0304360i	0.857106	+	0.515141i	$0.172260\pi$
$648$	12.6509	−	21.9119i	0.496972	−	0.860781i
$649$	17.6375	+	30.5491i	0.692333	+	1.19916i
$650$	−10.2109			−0.400504
$651$		0			0
$652$	28.0006			1.09659
$653$	19.2739	+	33.3833i	0.754244	+	1.30639i	0.945749	+	0.324898i	$0.105330\pi$
$653$	19.2739	+	33.3833i	0.754244	+	1.30639i	−0.191505	+	0.981492i	$0.561337\pi$
$654$	0.717979	−	1.24358i	0.0280752	−	0.0486276i
$655$	9.08761	−	15.7402i	0.355082	−	0.615020i
$656$	10.4234	+	18.0538i	0.406965	+	0.704884i
$657$	16.6916			0.651203
$658$		0			0
$659$	−10.8013			−0.420759			−0.210380	−	0.977620i	$-0.567470\pi$
$659$	−10.8013			−0.420759			−0.210380	+	0.977620i	$0.567470\pi$
$660$	4.46075	+	7.72625i	0.173634	+	0.300744i
$661$	20.3169	−	35.1900i	0.790237	−	1.36873i	−0.135583	−	0.990766i	$-0.543291\pi$
$661$	20.3169	−	35.1900i	0.790237	−	1.36873i	0.925820	−	0.377965i	$-0.123376\pi$
$662$	25.8181	−	44.7182i	1.00345	−	1.73802i
$663$	−2.39792	−	4.15332i	−0.0931276	−	0.161302i
$664$	34.9318			1.35562
$665$		0			0
$666$	4.44498			0.172240
$667$	−1.08868	−	1.88565i	−0.0421538	−	0.0730126i
$668$	9.63586	−	16.6898i	0.372822	−	0.645747i
$669$	−5.37983	+	9.31814i	−0.207996	+	0.360260i
$670$	−1.36858	−	2.37045i	−0.0528728	−	0.0915783i
$671$	−25.6947			−0.991934
$672$		0			0
$673$	32.3136			1.24560			0.622799	−	0.782382i	$-0.285995\pi$
$673$	32.3136			1.24560			0.622799	+	0.782382i	$0.285995\pi$
$674$	−40.2294	−	69.6794i	−1.54958	−	2.68395i
$675$	−7.73241	+	13.3929i	−0.297621	+	0.515494i
$676$	−1.99598	+	3.45713i	−0.0767683	+	0.132967i
$677$	−12.6079	−	21.8376i	−0.484562	−	0.839285i	0.515281	−	0.857021i	$-0.327688\pi$
$677$	−12.6079	−	21.8376i	−0.484562	−	0.839285i	−0.999843	+	0.0177358i	$0.994354\pi$
$678$	8.76908			0.336774
$679$		0			0
$680$	−31.8923			−1.22302
$681$	−2.89608	−	5.01617i	−0.110978	−	0.192220i
$682$	31.9119	−	55.2731i	1.22197	−	2.11651i
$683$	3.14365	−	5.44497i	0.120289	−	0.208346i	−0.799593	−	0.600542i	$-0.794951\pi$
$683$	3.14365	−	5.44497i	0.120289	−	0.208346i	0.919881	+	0.392197i	$0.128285\pi$
$684$	10.0854	+	17.4684i	0.385625	+	0.667922i
$685$	−5.23826			−0.200143
$686$		0			0
$687$	13.8557			0.528629
$688$	−21.8909	−	37.9162i	−0.834583	−	1.44554i
$689$	−5.72422	+	9.91463i	−0.218075	+	0.377717i
$690$	0.443719	−	0.768544i	0.0168921	−	0.0292580i
$691$	8.57653	+	14.8550i	0.326267	+	0.565110i	0.981768	−	0.190084i	$-0.0608759\pi$
$691$	8.57653	+	14.8550i	0.326267	+	0.565110i	−0.655501	+	0.755194i	$0.727543\pi$
$692$	88.6707			3.37076
$693$		0			0
$694$	−38.9600			−1.47890
$695$	0.706100	+	1.22300i	0.0267839	+	0.0463910i
$696$	−5.93781	+	10.2846i	−0.225072	+	0.389837i
$697$	−18.9523	+	32.8264i	−0.717870	+	1.24339i
$698$	36.2581	+	62.8009i	1.37239	+	2.37705i
$699$	−6.57085			−0.248532
$700$		0			0
$701$	−23.6620			−0.893702			−0.446851	−	0.894609i	$-0.647455\pi$
$701$	−23.6620			−0.893702			−0.446851	+	0.894609i	$0.647455\pi$
$702$	4.53753	+	7.85923i	0.171258	+	0.296628i
$703$	−0.703039	+	1.21770i	−0.0265156	+	0.0459264i
$704$	14.8901	−	25.7905i	0.561193	−	0.972015i
$705$	−3.67991	−	6.37379i	−0.138593	−	0.240051i
$706$	−70.2722			−2.64473
$707$		0			0
$708$	−25.5516			−0.960286
$709$	10.7515	+	18.6222i	0.403782	+	0.699370i	0.994179	−	0.107742i	$-0.0343622\pi$
$709$	10.7515	+	18.6222i	0.403782	+	0.699370i	−0.590397	+	0.807113i	$0.701029\pi$
$710$	−12.6603	+	21.9282i	−0.475131	+	0.822951i
$711$	−14.7145	+	25.4863i	−0.551837	+	0.955810i
$712$	−31.3259	−	54.2580i	−1.17399	−	2.03340i
$713$	−4.22961			−0.158400
$714$		0			0
$715$	3.34837			0.125222
$716$	−9.13170	−	15.8166i	−0.341268	−	0.591093i
$717$	−0.378909	+	0.656290i	−0.0141506	+	0.0245096i
$718$	33.4047	−	57.8586i	1.24665	−	2.15927i
$719$	−6.43464	−	11.1451i	−0.239971	−	0.415643i	0.720734	−	0.693211i	$-0.243805\pi$
$719$	−6.43464	−	11.1451i	−0.239971	−	0.415643i	−0.960706	+	0.277569i	$0.910471\pi$
$720$	9.18919			0.342461
$721$		0			0
$722$	36.9317			1.37446
$723$	−7.28217	−	12.6131i	−0.270827	−	0.469086i
$724$	−14.4375	+	25.0065i	−0.536567	+	0.929361i
$725$	−7.61068	+	13.1821i	−0.282654	+	0.489570i
$726$	2.06708	+	3.58030i	0.0767167	+	0.132877i
$727$	16.4329			0.609463			0.304732	−	0.952438i	$-0.401433\pi$
$727$	16.4329			0.609463			0.304732	+	0.952438i	$0.401433\pi$
$728$		0			0
$729$	−5.83198			−0.215999
$730$	7.27987	+	12.6091i	0.269440	+	0.466684i
$731$	39.8031	−	68.9411i	1.47217	−	2.54988i
$732$	9.30602	−	16.1185i	0.343960	−	0.595757i
$733$	10.8611	+	18.8120i	0.401164	+	0.694836i	0.993867	−	0.110585i	$-0.0352724\pi$
$733$	10.8611	+	18.8120i	0.401164	+	0.694836i	−0.592703	+	0.805421i	$0.701939\pi$
$734$	−24.4375			−0.902004
$735$		0			0
$736$	−0.0469292			−0.00172983
$737$	−2.25924	−	3.91312i	−0.0832201	−	0.144142i
$738$	16.4933	−	28.5673i	0.607128	−	1.05158i
$739$	−0.790007	+	1.36833i	−0.0290609	+	0.0503349i	−0.880190	−	0.474621i	$-0.842585\pi$
$739$	−0.790007	+	1.36833i	−0.0290609	+	0.0503349i	0.851129	+	0.524956i	$0.175918\pi$
$740$	1.29155	+	2.23703i	0.0474784	+	0.0822350i
$741$	−1.32023			−0.0485000
$742$		0			0
$743$	45.9718			1.68654			0.843271	−	0.537489i	$-0.180627\pi$
$743$	45.9718			1.68654			0.843271	+	0.537489i	$0.180627\pi$
$744$	11.5344	+	19.9782i	0.422873	+	0.732438i
$745$	6.79696	−	11.7727i	0.249021	−	0.431317i
$746$	5.73541	−	9.93402i	0.209988	−	0.363710i
$747$	−9.15029	−	15.8488i	−0.334792	−	0.579876i
$748$	−105.508			−3.85776
$749$		0			0
$750$	−13.6401			−0.498065
$751$	3.21143	+	5.56236i	0.117187	+	0.202973i	0.918652	−	0.395068i	$-0.129279\pi$
$751$	3.21143	+	5.56236i	0.117187	+	0.202973i	−0.801465	+	0.598042i	$0.795946\pi$
$752$	23.9349	−	41.4564i	0.872815	−	1.51176i
$753$	3.15163	−	5.45878i	0.114852	−	0.198929i
$754$	4.46610	+	7.73550i	0.162646	+	0.281710i
$755$	7.19219			0.261750
$756$		0			0
$757$	−6.10016			−0.221714			−0.110857	−	0.993836i	$-0.535360\pi$
$757$	−6.10016			−0.221714			−0.110857	+	0.993836i	$0.535360\pi$
$758$	−2.99884	−	5.19414i	−0.108923	−	0.188660i
$759$	0.732489	−	1.26871i	0.0265877	−	0.0460512i
$760$	−4.38977	+	7.60330i	−0.159234	+	0.275801i
$761$	9.19742	+	15.9304i	0.333406	+	0.577476i	0.983177	−	0.182653i	$-0.0584686\pi$
$761$	9.19742	+	15.9304i	0.333406	+	0.577476i	−0.649771	+	0.760130i	$0.725135\pi$
$762$	−10.8000			−0.391243
$763$		0			0
$764$	7.87380			0.284864
$765$	8.35412	+	14.4698i	0.302044	+	0.523155i
$766$	13.1781	−	22.8252i	0.476146	−	0.824708i
$767$	−4.79493	+	8.30506i	−0.173135	+	0.299878i
$768$	10.6572	+	18.4588i	0.384559	+	0.666076i
$769$	24.1850			0.872133			0.436066	−	0.899914i	$-0.356371\pi$
$769$	24.1850			0.872133			0.436066	+	0.899914i	$0.356371\pi$
$770$		0			0
$771$	2.42120			0.0871973
$772$	50.3131	+	87.1449i	1.81081	+	3.13641i
$773$	−5.38005	+	9.31852i	−0.193507	+	0.335164i	−0.946410	−	0.322967i	$-0.895320\pi$
$773$	−5.38005	+	9.31852i	−0.193507	+	0.335164i	0.752903	+	0.658131i	$0.228653\pi$
$774$	−34.6388	+	59.9962i	−1.24507	+	2.15652i
$775$	14.7841	+	25.6067i	0.531059	+	0.919821i
$776$	44.3258			1.59120
$777$		0			0
$778$	−34.3609			−1.23190
$779$	5.21732	+	9.03666i	0.186930	+	0.323772i
$780$	−1.21270	+	2.10046i	−0.0434216	+	0.0752084i
$781$	−20.8995	+	36.1989i	−0.747842	+	1.29530i
$782$	5.24754	+	9.08901i	0.187652	+	0.325022i
$783$	13.5282			0.483458
$784$		0			0
$785$	11.3738			0.405950
$786$	16.3108	+	28.2511i	0.581787	+	1.00768i
$787$	−7.36739	+	12.7607i	−0.262619	+	0.454869i	−0.966937	−	0.255015i	$-0.917920\pi$
$787$	−7.36739	+	12.7607i	−0.262619	+	0.454869i	0.704318	+	0.709884i	$0.251253\pi$
$788$	6.07769	−	10.5269i	0.216509	−	0.375004i
$789$	−2.20120	−	3.81259i	−0.0783649	−	0.135732i
$790$	−25.6703			−0.913307
$791$		0			0
$792$	45.8168			1.62803
$793$	−3.49268	−	6.04950i	−0.124029	−	0.214824i
$794$	−32.3856	+	56.0936i	−1.14932	+	1.99069i
$795$	−3.47787	+	6.02385i	−0.123347	+	0.213644i
$796$	8.09750	+	14.0253i	0.287008	+	0.497113i
$797$	−32.5732			−1.15380			−0.576901	−	0.816814i	$-0.695738\pi$
$797$	−32.5732			−1.15380			−0.576901	+	0.816814i	$0.695738\pi$
$798$		0			0
$799$	87.0392			3.07922
$800$	0.164035	+	0.284117i	0.00579951	+	0.0100450i
$801$	−16.4115	+	28.4255i	−0.579871	+	1.00437i
$802$	−23.2736	+	40.3111i	−0.821820	+	1.42343i
$803$	12.0176	+	20.8150i	0.424091	+	0.734546i
$804$	3.27297			0.115429
$805$		0			0
$806$	17.3511			0.611168
$807$	7.85301	+	13.6018i	0.276439	+	0.478806i
$808$	14.1561	−	24.5191i	0.498010	−	0.862578i
$809$	11.8463	−	20.5184i	0.416493	−	0.721388i	−0.579090	−	0.815263i	$-0.696592\pi$
$809$	11.8463	−	20.5184i	0.416493	−	0.721388i	0.995584	+	0.0938754i	$0.0299255\pi$
$810$	−5.78121	−	10.0134i	−0.203131	−	0.351833i
$811$	−45.8568			−1.61025			−0.805125	−	0.593105i	$-0.797902\pi$
$811$	−45.8568			−1.61025			−0.805125	+	0.593105i	$0.797902\pi$
$812$		0			0
$813$	−1.80056			−0.0631485
$814$	3.20028	+	5.54304i	0.112170	+	0.194284i
$815$	3.19250	−	5.52957i	0.111828	−	0.193692i
$816$	9.47605	−	16.4130i	0.331728	−	0.574570i
$817$	−10.9573	−	18.9786i	−0.383346	−	0.663976i
$818$	31.2735			1.09345
$819$		0			0
$820$	19.1695			0.669427
$821$	−6.64616	−	11.5115i	−0.231953	−	0.401754i	0.726430	−	0.687240i	$-0.241178\pi$
$821$	−6.64616	−	11.5115i	−0.231953	−	0.401754i	−0.958383	+	0.285487i	$0.907845\pi$
$822$	4.70092	−	8.14223i	0.163963	−	0.283993i
$823$	2.06516	−	3.57697i	0.0719871	−	0.124685i	−0.827785	−	0.561045i	$-0.810399\pi$
$823$	2.06516	−	3.57697i	0.0719871	−	0.124685i	0.899772	+	0.436360i	$0.143733\pi$
$824$	−31.3726	−	54.3390i	−1.09292	−	1.89299i
$825$	−10.2413			−0.356556
$826$		0			0
$827$	−4.67317			−0.162502			−0.0812510	−	0.996694i	$-0.525892\pi$
$827$	−4.67317			−0.162502			−0.0812510	+	0.996694i	$0.525892\pi$
$828$	−3.04242	−	5.26962i	−0.105731	−	0.183132i
$829$	0.874856	−	1.51529i	0.0303850	−	0.0526284i	−0.850433	−	0.526083i	$-0.823660\pi$
$829$	0.874856	−	1.51529i	0.0303850	−	0.0526284i	0.880818	+	0.473455i	$0.156993\pi$
$830$	7.98160	−	13.8245i	0.277045	−	0.479857i
$831$	8.26136	+	14.3091i	0.286583	+	0.496377i
$832$	8.09606			0.280681
$833$		0			0
$834$	−2.53467			−0.0877685
$835$	−2.19727	−	3.80578i	−0.0760396	−	0.131704i
$836$	−14.5225	+	25.1537i	−0.502271	+	0.869958i
$837$	13.1395	−	22.7583i	0.454168	−	0.786642i
$838$	−15.8879	−	27.5187i	−0.548839	−	0.950617i
$839$	15.4495			0.533374			0.266687	−	0.963783i	$-0.414071\pi$
$839$	15.4495			0.533374			0.266687	+	0.963783i	$0.414071\pi$
$840$		0			0
$841$	−15.6848			−0.540855
$842$	−14.2878	−	24.7471i	−0.492389	−	0.852842i
$843$	1.35285	−	2.34320i	0.0465945	−	0.0807041i
$844$	−32.7571	+	56.7370i	−1.12755	+	1.95297i
$845$	0.455143	+	0.788331i	0.0156574	+	0.0271194i
$846$	−75.7462			−2.60421
$847$		0			0
$848$	−45.2416			−1.55360
$849$	4.31298	+	7.47029i	0.148021	+	0.256380i
$850$	36.6842	−	63.5389i	1.25826	−	2.17937i
$851$	0.212083	−	0.367338i	0.00727010	−	0.0125922i
$852$	−15.1386	−	26.2208i	−0.518640	−	0.898310i
$853$	0.602575			0.0206318			0.0103159	−	0.999947i	$-0.496716\pi$
$853$	0.602575			0.0206318			0.0103159	+	0.999947i	$0.496716\pi$
$854$		0			0
$855$	4.59956			0.157302
$856$	10.8673	+	18.8227i	0.371437	+	0.643347i
$857$	−21.5820	+	37.3810i	−0.737226	+	1.27691i	0.216514	+	0.976279i	$0.430531\pi$
$857$	−21.5820	+	37.3810i	−0.737226	+	1.27691i	−0.953740	+	0.300633i	$0.902802\pi$
$858$	−3.00489	+	5.20462i	−0.102585	+	0.177683i
$859$	18.9704	+	32.8577i	0.647261	+	1.12109i	0.983774	+	0.179410i	$0.0574189\pi$
$859$	18.9704	+	32.8577i	0.647261	+	1.12109i	−0.336513	+	0.941679i	$0.609248\pi$
$860$	−40.2592			−1.37283
$861$		0			0
$862$	1.14482			0.0389927
$863$	−16.9533	−	29.3640i	−0.577098	−	0.999563i	−0.995810	−	0.0914443i	$-0.970852\pi$
$863$	−16.9533	−	29.3640i	−0.577098	−	0.999563i	0.418712	−	0.908119i	$-0.362482\pi$
$864$	0.145788	−	0.252512i	0.00495981	−	0.00859065i
$865$	10.1098	−	17.5107i	0.343744	−	0.595382i
$866$	11.3530	+	19.6640i	0.385792	+	0.668211i
$867$	23.1130			0.784957
$868$		0			0
$869$	−42.3763			−1.43752
$870$	2.71347	+	4.69988i	0.0919954	+	0.159341i
$871$	0.614197	−	1.06382i	0.0208113	−	0.0360462i
$872$	2.14274	−	3.71134i	0.0725625	−	0.125682i
$873$	−11.6110	−	20.1109i	−0.392974	−	0.680651i
$874$	2.88916			0.0977272
$875$		0			0
$876$	−17.4099			−0.588226
$877$	−3.25518	−	5.63814i	−0.109920	−	0.190386i	0.805818	−	0.592163i	$-0.201726\pi$
$877$	−3.25518	−	5.63814i	−0.109920	−	0.190386i	−0.915738	+	0.401777i	$0.868393\pi$
$878$	43.7035	−	75.6967i	1.47492	−	2.55464i
$879$	−7.86101	+	13.6157i	−0.265145	+	0.459245i
$880$	6.61599	+	11.4592i	0.223025	+	0.386291i
$881$	24.5160			0.825966			0.412983	−	0.910739i	$-0.364487\pi$
$881$	24.5160			0.825966			0.412983	+	0.910739i	$0.364487\pi$
$882$		0			0
$883$	−28.7175			−0.966419			−0.483210	−	0.875505i	$-0.660529\pi$
$883$	−28.7175			−0.966419			−0.483210	+	0.875505i	$0.660529\pi$
$884$	−14.3417	−	24.8406i	−0.482364	−	0.835478i
$885$	−2.91327	+	5.04592i	−0.0979283	+	0.169617i
$886$	−44.4845	+	77.0494i	−1.49449	+	2.58853i
$887$	3.47221	+	6.01405i	0.116585	+	0.201932i	0.918412	−	0.395624i	$-0.129472\pi$
$887$	3.47221	+	6.01405i	0.116585	+	0.201932i	−0.801827	+	0.597556i	$0.796138\pi$
$888$	−2.31346			−0.0776345
$889$		0			0
$890$	−28.6307			−0.959704
$891$	−9.54359	−	16.5300i	−0.319722	−	0.553775i
$892$	−32.1761	+	55.7307i	−1.07734	+	1.86600i
$893$	11.9804	−	20.7506i	0.400908	−	0.694392i
$894$	12.1995	+	21.1301i	0.408011	+	0.706695i
$895$	−4.16461			−0.139208
$896$		0			0
$897$	0.398269			0.0132978
$898$	−49.5579	−	85.8368i	−1.65377	−	2.86441i
$899$	12.9327	−	22.4000i	0.431328	−	0.747082i
$900$	−21.2688	+	36.8386i	−0.708959	+	1.22795i
$901$	−41.1303	−	71.2397i	−1.37025	−	2.37334i
$902$	47.4991			1.58155
$903$		0			0
$904$	26.1705			0.870419
$905$	3.29220	+	5.70225i	0.109436	+	0.189549i
$906$	−6.45441	+	11.1794i	−0.214434	+	0.371410i
$907$	−0.114774	+	0.198795i	−0.00381102	+	0.00660088i	−0.867925	−	0.496696i	$-0.834546\pi$
$907$	−0.114774	+	0.198795i	−0.00381102	+	0.00660088i	0.864114	+	0.503297i	$0.167880\pi$
$908$	−17.3212	−	30.0011i	−0.574823	−	0.995622i
$909$	−14.8326			−0.491967
$910$		0			0
$911$	−26.6727			−0.883706			−0.441853	−	0.897087i	$-0.645679\pi$
$911$	−26.6727			−0.883706			−0.441853	+	0.897087i	$0.645679\pi$
$912$	−2.60863	−	4.51828i	−0.0863804	−	0.149615i
$913$	13.1760	−	22.8214i	0.436061	−	0.755280i
$914$	6.14395	−	10.6416i	0.203224	−	0.351994i
$915$	−2.12206	−	3.67551i	−0.0701530	−	0.121509i
$916$	82.8696			2.73809
$917$		0			0
$918$	−65.2071			−2.15216
$919$	21.6165	+	37.4409i	0.713064	+	1.23506i	0.963702	+	0.266982i	$0.0860263\pi$
$919$	21.6165	+	37.4409i	0.713064	+	1.23506i	−0.250638	+	0.968081i	$0.580640\pi$
$920$	1.32424	−	2.29365i	0.0436589	−	0.0756195i
$921$	6.65954	−	11.5347i	0.219439	−	0.380080i
$922$	21.2506	+	36.8071i	0.699851	+	1.21218i
$923$	−11.3635			−0.374033
$924$		0			0
$925$	−2.96523			−0.0974961
$926$	43.3644	+	75.1093i	1.42504	+	2.46824i
$927$	−16.4360	+	28.4680i	−0.539828	+	0.935010i
$928$	0.143493	−	0.248537i	0.00471039	−	0.00815863i
$929$	−11.9246	−	20.6540i	−0.391233	−	0.677635i	0.601380	−	0.798963i	$-0.294618\pi$
$929$	−11.9246	−	20.6540i	−0.391233	−	0.677635i	−0.992612	+	0.121329i	$0.961285\pi$
$930$	10.5421			0.345688
$931$		0			0
$932$	−39.2995			−1.28730
$933$	2.16277	+	3.74604i	0.0708061	+	0.122640i
$934$	−43.4441	+	75.2474i	−1.42154	+	2.46217i
$935$	−12.0295	+	20.8357i	−0.393407	+	0.681402i
$936$	6.22788	+	10.7870i	0.203565	+	0.352584i
$937$	27.2033			0.888694			0.444347	−	0.895855i	$-0.353436\pi$
$937$	27.2033			0.888694			0.444347	+	0.895855i	$0.353436\pi$
$938$		0			0
$939$	−10.7563			−0.351017
$940$	−22.0091	−	38.1209i	−0.717858	−	1.24337i
$941$	6.72573	−	11.6493i	0.219253	−	0.379757i	−0.735327	−	0.677712i	$-0.762971\pi$
$941$	6.72573	−	11.6493i	0.219253	−	0.379757i	0.954580	+	0.297956i	$0.0963048\pi$
$942$	−10.2071	+	17.6793i	−0.332566	+	0.576021i
$943$	−1.57388	−	2.72605i	−0.0512527	−	0.0887723i
$944$	−37.8970			−1.23344
$945$		0			0
$946$	−99.7564			−3.24336
$947$	−7.51705	−	13.0199i	−0.244271	−	0.423090i	0.717655	−	0.696399i	$-0.245215\pi$
$947$	−7.51705	−	13.0199i	−0.244271	−	0.423090i	−0.961926	+	0.273308i	$0.911882\pi$
$948$	15.3477	−	26.5830i	0.498470	−	0.863375i
$949$	−3.26709	+	5.65877i	−0.106054	+	0.183691i
$950$	−10.0987	−	17.4914i	−0.327644	−	0.567497i
$951$	9.69830			0.314489
$952$		0			0
$953$	28.3775			0.919237			0.459618	−	0.888116i	$-0.347986\pi$
$953$	28.3775			0.919237			0.459618	+	0.888116i	$0.347986\pi$
$954$	35.7938	+	61.9966i	1.15887	+	2.00722i
$955$	0.897732	−	1.55492i	0.0290499	−	0.0503160i
$956$	−2.26621	+	3.92520i	−0.0732946	+	0.126950i
$957$	4.47939	+	7.75852i	0.144798	+	0.250797i
$958$	−58.8144			−1.90021
$959$		0			0
$960$	4.91894			0.158758
$961$	−9.62220	−	16.6661i	−0.310394	−	0.537618i
$962$	−0.870027	+	1.50693i	−0.0280508	+	0.0485854i
$963$	5.69333	−	9.86113i	0.183465	−	0.317771i
$964$	−43.5539	−	75.4375i	−1.40278	−	2.42968i
$965$	22.9458			0.738653
$966$		0			0
$967$	−52.0994			−1.67540			−0.837701	−	0.546129i	$-0.816101\pi$
$967$	−52.0994			−1.67540			−0.837701	+	0.546129i	$0.816101\pi$
$968$	6.16904	+	10.6851i	0.198280	+	0.343432i
$969$	4.74314	−	8.21536i	0.152372	−	0.263915i
$970$	10.1280	−	17.5423i	0.325192	−	0.563249i
$971$	−10.4209	−	18.0495i	−0.334423	−	0.579237i	0.648951	−	0.760830i	$-0.275208\pi$
$971$	−10.4209	−	18.0495i	−0.334423	−	0.579237i	−0.983374	+	0.181593i	$0.941875\pi$
$972$	58.2247			1.86756
$973$		0			0
$974$	−50.9337			−1.63202
$975$	−1.39210	−	2.41118i	−0.0445828	−	0.0772196i
$976$	13.8023	−	23.9063i	0.441800	−	0.765221i
$977$	−17.3151	+	29.9907i	−0.553960	+	0.959486i	0.444024	+	0.896015i	$0.353550\pi$
$977$	−17.3151	+	29.9907i	−0.553960	+	0.959486i	−0.997984	+	0.0634713i	$0.979783\pi$
$978$	5.73002	+	9.92469i	0.183226	+	0.317357i
$979$	−47.2634			−1.51054
$980$		0			0
$981$	−2.24515			−0.0716820
$982$	−44.3298	−	76.7815i	−1.41462	−	2.45020i
$983$	−29.4314	+	50.9767i	−0.938717	+	1.62590i	−0.170848	+	0.985297i	$0.554651\pi$
$983$	−29.4314	+	50.9767i	−0.938717	+	1.62590i	−0.767869	+	0.640607i	$0.778683\pi$
$984$	−8.58419	+	14.8683i	−0.273654	+	0.473983i
$985$	−1.38590	−	2.40045i	−0.0441584	−	0.0764846i
$986$	−64.1806			−2.04393
$987$		0			0
$988$	−7.89616			−0.251210
$989$	3.30543	+	5.72517i	0.105107	+	0.182050i
$990$	10.4687	−	18.1324i	0.332718	−	0.576285i
$991$	14.6874	−	25.4392i	0.466559	−	0.808104i	−0.532711	−	0.846297i	$-0.678827\pi$
$991$	14.6874	−	25.4392i	0.466559	−	0.808104i	0.999270	+	0.0381929i	$0.0121601\pi$
$992$	−0.278741	−	0.482793i	−0.00885003	−	0.0153287i
$993$	14.0796			0.446802
$994$		0			0
$995$	3.69295			0.117075
$996$	9.54405	+	16.5308i	0.302415	+	0.523798i
$997$	−3.75303	+	6.50044i	−0.118860	+	0.205871i	−0.919316	−	0.393520i	$-0.871257\pi$
$997$	−3.75303	+	6.50044i	−0.118860	+	0.205871i	0.800456	+	0.599391i	$0.204591\pi$
$998$	−49.1807	+	85.1835i	−1.55679	+	2.69644i
$999$	1.31769	+	2.28231i	0.0416899	+	0.0722091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.e.o.508.6		12
7.2	even	3	inner	637.2.e.o.79.6		12
7.3	odd	6		637.2.a.n.1.1	yes	6
7.4	even	3		637.2.a.m.1.1	✓	6
7.5	odd	6		637.2.e.n.79.6		12
7.6	odd	2		637.2.e.n.508.6		12
21.11	odd	6		5733.2.a.bu.1.6		6
21.17	even	6		5733.2.a.br.1.6		6
91.25	even	6		8281.2.a.cc.1.6		6
91.38	odd	6		8281.2.a.cd.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.1	✓	6	7.4	even	3
637.2.a.n.1.1	yes	6	7.3	odd	6
637.2.e.n.79.6		12	7.5	odd	6
637.2.e.n.508.6		12	7.6	odd	2
637.2.e.o.79.6		12	7.2	even	3	inner
637.2.e.o.508.6		12	1.1	even	1	trivial
5733.2.a.br.1.6		6	21.17	even	6
5733.2.a.bu.1.6		6	21.11	odd	6
8281.2.a.cc.1.6		6	91.25	even	6
8281.2.a.cd.1.6		6	91.38	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22392 + 2.11990i) q^{2} +(-0.333726 + 0.578030i) q^{3} +(-1.99598 + 3.45713i) q^{4} +(0.455143 + 0.788331i) q^{5} -1.63382 q^{6} -4.87599 q^{8} +(1.27725 + 2.21227i) q^{9} +O(q^{10})\)	\(q+(1.22392 + 2.11990i) q^{2} +(-0.333726 + 0.578030i) q^{3} +(-1.99598 + 3.45713i) q^{4} +(0.455143 + 0.788331i) q^{5} -1.63382 q^{6} -4.87599 q^{8} +(1.27725 + 2.21227i) q^{9} +(-1.11412 + 1.92971i) q^{10} +(-1.83918 + 3.18556i) q^{11} +(-1.33222 - 2.30747i) q^{12} -1.00000 q^{13} -0.607572 q^{15} +(-1.97589 - 3.42234i) q^{16} +(3.59265 - 6.22266i) q^{17} +(-3.12652 + 5.41529i) q^{18} +(-0.989010 - 1.71302i) q^{19} -3.63382 q^{20} -9.00407 q^{22} +(0.298350 + 0.516758i) q^{23} +(1.62724 - 2.81847i) q^{24} +(2.08569 - 3.61252i) q^{25} +(-1.22392 - 2.11990i) q^{26} -3.70737 q^{27} -3.64900 q^{29} +(-0.743621 - 1.28799i) q^{30} +(-3.54416 + 6.13867i) q^{31} +(-0.0393239 + 0.0681110i) q^{32} +(-1.22757 - 2.12621i) q^{33} +17.5885 q^{34} -10.1975 q^{36} +(-0.355426 - 0.615615i) q^{37} +(2.42094 - 4.19320i) q^{38} +(0.333726 - 0.578030i) q^{39} +(-2.21927 - 3.84390i) q^{40} -5.27529 q^{41} +11.0790 q^{43} +(-7.34193 - 12.7166i) q^{44} +(-1.16267 + 2.01380i) q^{45} +(-0.730315 + 1.26494i) q^{46} +(6.05674 + 10.4906i) q^{47} +2.63762 q^{48} +10.2109 q^{50} +(2.39792 + 4.15332i) q^{51} +(1.99598 - 3.45713i) q^{52} +(5.72422 - 9.91463i) q^{53} +(-4.53753 - 7.85923i) q^{54} -3.34837 q^{55} +1.32023 q^{57} +(-4.46610 - 7.73550i) q^{58} +(4.79493 - 8.30506i) q^{59} +(1.21270 - 2.10046i) q^{60} +(3.49268 + 6.04950i) q^{61} -17.3511 q^{62} -8.09606 q^{64} +(-0.455143 - 0.788331i) q^{65} +(3.00489 - 5.20462i) q^{66} +(-0.614197 + 1.06382i) q^{67} +(14.3417 + 24.8406i) q^{68} -0.398269 q^{69} +11.3635 q^{71} +(-6.22788 - 10.7870i) q^{72} +(3.26709 - 5.65877i) q^{73} +(0.870027 - 1.50693i) q^{74} +(1.39210 + 2.41118i) q^{75} +7.89616 q^{76} +1.63382 q^{78} +(5.76021 + 9.97697i) q^{79} +(1.79862 - 3.11531i) q^{80} +(-2.59452 + 4.49384i) q^{81} +(-6.45655 - 11.1831i) q^{82} -7.16403 q^{83} +6.54069 q^{85} +(13.5599 + 23.4864i) q^{86} +(1.21777 - 2.10923i) q^{87} +(8.96784 - 15.5328i) q^{88} +(6.42451 + 11.1276i) q^{89} -5.69206 q^{90} -2.38200 q^{92} +(-2.36556 - 4.09727i) q^{93} +(-14.8260 + 25.6793i) q^{94} +(0.900282 - 1.55933i) q^{95} +(-0.0262468 - 0.0454608i) q^{96} -9.09062 q^{97} -9.39642 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9	\( 12 q + 8 q^{3} - 4 q^{4} + 6 q^{5} - 8 q^{6} - 6 q^{9} + 4 q^{10} - 4 q^{11} - 4 q^{12} - 12 q^{13} + 24 q^{15} + 16 q^{17} + 4 q^{18} + 2 q^{19} - 32 q^{20} - 24 q^{22} + 6 q^{23} + 12 q^{24} + 4 q^{25} - 40 q^{27} - 12 q^{29} + 6 q^{31} + 20 q^{32} + 4 q^{33} - 48 q^{36} + 8 q^{38} - 8 q^{39} + 4 q^{40} + 16 q^{41} + 4 q^{43} + 4 q^{44} + 14 q^{45} - 8 q^{46} + 30 q^{47} + 16 q^{48} + 16 q^{50} + 4 q^{51} + 4 q^{52} + 14 q^{53} - 48 q^{54} + 16 q^{55} + 8 q^{57} + 8 q^{58} + 24 q^{59} - 12 q^{60} - 56 q^{62} - 40 q^{64} - 6 q^{65} - 4 q^{66} - 16 q^{67} + 28 q^{68} + 40 q^{69} + 16 q^{71} - 28 q^{72} - 6 q^{73} + 12 q^{74} + 12 q^{75} + 32 q^{76} + 8 q^{78} + 22 q^{79} - 28 q^{80} - 46 q^{81} - 40 q^{82} - 100 q^{83} - 16 q^{85} + 16 q^{86} - 16 q^{87} + 44 q^{88} + 26 q^{89} + 80 q^{90} + 40 q^{92} - 16 q^{93} - 32 q^{94} + 6 q^{95} - 20 q^{96} + 28 q^{97} + 24 q^{99}+O(q^{100}) \) 12 * q + 8 * q^3 - 4 * q^4 + 6 * q^5 - 8 * q^6 - 6 * q^9 + 4 * q^10 - 4 * q^11 - 4 * q^12 - 12 * q^13 + 24 * q^15 + 16 * q^17 + 4 * q^18 + 2 * q^19 - 32 * q^20 - 24 * q^22 + 6 * q^23 + 12 * q^24 + 4 * q^25 - 40 * q^27 - 12 * q^29 + 6 * q^31 + 20 * q^32 + 4 * q^33 - 48 * q^36 + 8 * q^38 - 8 * q^39 + 4 * q^40 + 16 * q^41 + 4 * q^43 + 4 * q^44 + 14 * q^45 - 8 * q^46 + 30 * q^47 + 16 * q^48 + 16 * q^50 + 4 * q^51 + 4 * q^52 + 14 * q^53 - 48 * q^54 + 16 * q^55 + 8 * q^57 + 8 * q^58 + 24 * q^59 - 12 * q^60 - 56 * q^62 - 40 * q^64 - 6 * q^65 - 4 * q^66 - 16 * q^67 + 28 * q^68 + 40 * q^69 + 16 * q^71 - 28 * q^72 - 6 * q^73 + 12 * q^74 + 12 * q^75 + 32 * q^76 + 8 * q^78 + 22 * q^79 - 28 * q^80 - 46 * q^81 - 40 * q^82 - 100 * q^83 - 16 * q^85 + 16 * q^86 - 16 * q^87 + 44 * q^88 + 26 * q^89 + 80 * q^90 + 40 * q^92 - 16 * q^93 - 32 * q^94 + 6 * q^95 - 20 * q^96 + 28 * q^97 + 24 * q^99

Introduction

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