LMFDB - Embedded newform 637.2.e.n.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.n.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	−0.753460	−	0.657494i	$-0.771616\pi$
$3$	0.333726	−	0.578030i	0.192677	−	0.333726i	0.946136	+	0.323768i	$0.104950\pi$
$4$	−1.99598	+	3.45713i	−0.997988	+	1.72857i
$5$	−0.455143	−	0.788331i	−0.203546	−	0.352552i	0.746122	−	0.665809i	$-0.231913\pi$
$5$	−0.455143	−	0.788331i	−0.203546	−	0.352552i	−0.949669	+	0.313256i	$0.898580\pi$
$6$	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	$0.503420\pi$
$17$	−3.59265	+	6.22266i	−0.871347	+	1.50922i	−0.860604	+	0.509275i	$0.829914\pi$
$18$	−3.12652	+	5.41529i	−0.736928	+	1.27640i
$19$	0.989010	+	1.71302i	0.226894	+	0.392993i	0.956886	−	0.290463i	$-0.0938094\pi$
$19$	0.989010	+	1.71302i	0.226894	+	0.392993i	−0.729992	+	0.683456i	$0.760476\pi$
$20$	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	$-0.613694\pi$
$31$	3.54416	−	6.13867i	0.636551	−	1.10254i	0.986184	−	0.165652i	$-0.0529727\pi$
$32$	−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	$-0.364854\pi$
$41$	5.27529			0.823863			0.411931	+	0.911215i	$0.364854\pi$
$42$		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	$-0.821870\pi$
$47$	−6.05674	−	10.4906i	−0.883467	−	1.53021i	−0.0360062	−	0.999352i	$-0.511464\pi$
$48$	−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	$0.381261\pi$
$59$	−4.79493	+	8.30506i	−0.624247	+	1.08123i	−0.988686	+	0.150000i	$0.952073\pi$
$60$	1.21270	−	2.10046i	0.156559	−	0.271168i
$61$	−3.49268	−	6.04950i	−0.447192	−	0.774559i	0.551010	−	0.834499i	$-0.314243\pi$
$61$	−3.49268	−	6.04950i	−0.447192	−	0.774559i	−0.998202	+	0.0599392i	$0.980909\pi$
$62$	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	−0.991403	−	0.130847i	$-0.958230\pi$
$73$	−3.26709	+	5.65877i	−0.382384	+	0.662309i	0.609018	+	0.793156i	$0.291564\pi$
$74$	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	$-0.371376\pi$
$83$	7.16403			0.786355			0.393177	+	0.919463i	$0.371376\pi$
$84$		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	$-0.928213\pi$
$89$	−6.42451	−	11.1276i	−0.680997	−	1.17952i	0.293680	−	0.955904i	$-0.405120\pi$
$90$	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	$-0.347309\pi$
$97$	9.09062			0.923012			0.461506	+	0.887137i	$0.347309\pi$
$98$		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	−0.684661	−	0.728861i	$-0.740050\pi$
$101$	2.90322	−	5.02853i	0.288882	−	0.500358i	0.973543	+	0.228504i	$0.0733833\pi$
$102$	−5.86975	+	10.1667i	−0.581192	+	1.00665i
$103$	−6.43411	−	11.1442i	−0.633971	−	1.09807i	−0.986732	−	0.162357i	$-0.948090\pi$
$103$	−6.43411	−	11.1442i	−0.633971	−	1.09807i	0.352761	−	0.935714i	$-0.385243\pi$
$104$	−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	$0.170666\pi$
$131$	9.98324	+	17.2915i	0.872240	+	1.51076i	0.0125654	+	0.999921i	$0.496000\pi$
$132$	−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	$-0.520958\pi$
$139$	−1.55138			−0.131586			−0.0657931	+	0.997833i	$0.520958\pi$
$140$		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	−0.999999	−	0.00161951i	$-0.999484\pi$
$157$	−6.24740	+	10.8208i	−0.498597	+	0.863595i	0.501402	+	0.865215i	$0.332818\pi$
$158$	−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	$-0.440193\pi$
$167$	4.82764			0.373574			0.186787	+	0.982400i	$0.440193\pi$
$168$		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	$0.153369\pi$
$173$	11.1062	+	19.2365i	0.844388	+	1.46252i	−0.0417636	+	0.999128i	$0.513298\pi$
$174$	−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	$-0.586635\pi$
$181$	−7.23332			−0.537649			−0.268824	+	0.963189i	$0.586635\pi$
$182$		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	−0.928922	−	0.370275i	$-0.879263\pi$
$199$	−2.02846	+	3.51339i	−0.143794	+	0.249058i	0.785129	+	0.619333i	$0.212597\pi$
$200$	−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	$-0.681483\pi$
$223$	−16.1205			−1.07951			−0.539755	+	0.841822i	$0.681483\pi$
$224$		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	−0.685339	−	0.728224i	$-0.740346\pi$
$227$	4.33902	−	7.51540i	0.287991	−	0.498815i	0.973330	+	0.229409i	$0.0736794\pi$
$228$	−2.63515	+	4.56422i	−0.174517	+	0.302273i
$229$	10.3796	+	17.9780i	0.685902	+	1.18802i	0.973152	+	0.230162i	$0.0739256\pi$
$229$	10.3796	+	17.9780i	0.685902	+	1.18802i	−0.287250	+	0.957856i	$0.592741\pi$
$230$	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	$-0.585265\pi$
$241$	10.9104	−	18.8974i	0.702802	−	1.21729i	0.967479	−	0.252951i	$-0.0814012\pi$
$242$	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	$-0.403666\pi$
$251$	9.44377			0.596086			0.298043	+	0.954552i	$0.403666\pi$
$252$		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	0.917034	−	0.398808i	$-0.130576\pi$
$257$	1.81376	+	3.14153i	0.113139	+	0.195963i	−0.803895	+	0.594771i	$0.797243\pi$
$258$	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	$0.421319\pi$
$269$	−11.7657	+	20.3787i	−0.717365	+	1.24251i	−0.962040	+	0.272908i	$0.912015\pi$
$270$	4.13045	−	7.15415i	0.251371	−	0.435388i
$271$	−1.34883	−	2.33625i	−0.0819358	−	0.141917i	0.822146	−	0.569277i	$-0.192777\pi$
$271$	−1.34883	−	2.33625i	−0.0819358	−	0.141917i	−0.904081	+	0.427360i	$0.859444\pi$
$272$	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	−0.991646	−	0.128987i	$-0.958828\pi$
$283$	−6.46186	+	11.1923i	−0.384118	+	0.665311i	0.607529	+	0.794298i	$0.292161\pi$
$284$	−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	$-0.741536\pi$
$293$	−23.5553			−1.37611			−0.688057	+	0.725656i	$0.741536\pi$
$294$		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	$-0.307156\pi$
$307$	19.9551			1.13890			0.569450	+	0.822026i	$0.307156\pi$
$308$		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	−0.943152	−	0.332361i	$-0.892155\pi$
$311$	−3.24035	+	5.61245i	−0.183743	+	0.318253i	0.759409	+	0.650613i	$0.225488\pi$
$312$	−1.62724	+	2.81847i	−0.0921245	+	0.159564i
$313$	−8.05771	−	13.9564i	−0.455449	−	0.788860i	0.543265	−	0.839561i	$-0.317188\pi$
$313$	−8.05771	−	13.9564i	−0.455449	−	0.788860i	−0.998714	+	0.0507010i	$0.983854\pi$
$314$	−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	$-0.791420\pi$
$349$	−29.6245			−1.58576			−0.792882	+	0.609375i	$0.791420\pi$
$350$		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	$-0.556576\pi$
$353$	14.3539	−	24.8617i	0.763980	−	1.32325i	0.940784	−	0.339006i	$-0.110091\pi$
$354$	−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	−0.705830	−	0.708381i	$-0.749426\pi$
$367$	4.99163	−	8.64575i	0.260561	−	0.451305i	0.966391	+	0.257076i	$0.0827592\pi$
$368$	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	0.970157	−	0.242477i	$-0.0779599\pi$
$383$	5.38356	+	9.32461i	0.275087	+	0.476465i	−0.695070	+	0.718942i	$0.744627\pi$
$384$	−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	$-0.935521\pi$
$397$	−13.2303	−	22.9155i	−0.664007	−	1.15009i	0.315546	−	0.948910i	$-0.397812\pi$
$398$	−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	−0.979621	−	0.200856i	$-0.935628\pi$
$409$	−6.38796	+	11.0643i	−0.315864	+	0.547093i	0.663757	+	0.747949i	$0.268961\pi$
$410$	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	$-0.397296\pi$
$419$	12.9811			0.634170			0.317085	+	0.948397i	$0.397296\pi$
$420$		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	$-0.571548\pi$
$433$	−9.27593			−0.445773			−0.222886	+	0.974844i	$0.571548\pi$
$434$		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	$0.158016\pi$
$439$	17.8539	+	30.9238i	0.852119	+	1.47591i	−0.0271736	+	0.999631i	$0.508651\pi$
$440$	−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	$-0.632495\pi$
$461$	−17.3627			−0.808661			−0.404331	+	0.914613i	$0.632495\pi$
$462$		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	$-0.859930\pi$
$467$	−17.7479	−	30.7403i	−0.821275	−	1.42249i	0.0834584	−	0.996511i	$-0.473403\pi$
$468$	−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	$-0.648376\pi$
$479$	12.0135	−	20.8080i	0.548911	−	0.950742i	0.998349	−	0.0574308i	$-0.0182909\pi$
$480$	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	$-0.170630\pi$
$503$	38.5636			1.71946			0.859732	+	0.510745i	$0.170630\pi$
$504$		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	0.813921	−	0.580975i	$-0.197329\pi$
$509$	−2.16989	−	3.75835i	−0.0961785	−	0.166586i	−0.910100	+	0.414389i	$0.863995\pi$
$510$	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	−0.976578	−	0.215163i	$-0.930972\pi$
$521$	−6.89219	+	11.9376i	−0.301952	+	0.522997i	0.674626	+	0.738160i	$0.264305\pi$
$522$	11.4087	−	19.7604i	0.499344	−	0.864890i
$523$	14.7417	+	25.5334i	0.644609	+	1.11650i	0.984392	+	0.175992i	$0.0563132\pi$
$523$	14.7417	+	25.5334i	0.644609	+	1.11650i	−0.339782	+	0.940504i	$0.610353\pi$
$524$	−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	−0.961117	−	0.276142i	$-0.910944\pi$
$563$	−5.72813	+	9.92141i	−0.241412	+	0.418138i	0.719705	+	0.694280i	$0.244277\pi$
$564$	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	−0.866495	−	0.499185i	$-0.833633\pi$
$577$	−0.0225966	+	0.0391384i	−0.000940708	+	0.00162935i	0.865555	+	0.500814i	$0.166966\pi$
$578$	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	$-0.482162\pi$
$587$	2.71409			0.112023			0.0560113	+	0.998430i	$0.482162\pi$
$588$		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	0.787909	−	0.615792i	$-0.211164\pi$
$593$	−3.39307	−	5.87698i	−0.139337	−	0.241339i	−0.927246	+	0.374453i	$0.877830\pi$
$594$	−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	$-0.419047\pi$
$601$	12.3356			0.503178			0.251589	+	0.967834i	$0.419047\pi$
$602$		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	0.987003	−	0.160699i	$-0.0513748\pi$
$607$	8.72982	+	15.1205i	0.354332	+	0.613722i	−0.632671	+	0.774421i	$0.718042\pi$
$608$	−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	−0.878198	−	0.478298i	$-0.841254\pi$
$619$	−0.619027	+	1.07219i	−0.0248808	+	0.0430948i	0.853317	+	0.521393i	$0.174587\pi$
$620$	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	$-0.459070\pi$
$643$	6.50321			0.256461			0.128231	+	0.991744i	$0.459070\pi$
$644$		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	−0.857106	−	0.515141i	$-0.827740\pi$
$647$	0.446970	−	0.774175i	0.0175722	−	0.0304360i	0.874678	+	0.484705i	$0.161073\pi$
$648$	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	$0.456709\pi$
$661$	−20.3169	+	35.1900i	−0.790237	+	1.36873i	−0.925820	+	0.377965i	$0.876624\pi$
$662$	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	0.999843	−	0.0177358i	$-0.00564578\pi$
$677$	12.6079	+	21.8376i	0.484562	+	0.839285i	−0.515281	+	0.857021i	$0.672312\pi$
$678$	−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	0.655501	−	0.755194i	$-0.272457\pi$
$691$	−8.57653	−	14.8550i	−0.326267	−	0.565110i	−0.981768	+	0.190084i	$0.939124\pi$
$692$	−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	0.960706	−	0.277569i	$-0.0895286\pi$
$719$	6.43464	+	11.1451i	0.239971	+	0.415643i	−0.720734	+	0.693211i	$0.756195\pi$
$720$	−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	$-0.598567\pi$
$727$	−16.4329			−0.609463			−0.304732	+	0.952438i	$0.598567\pi$
$728$		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	0.592703	−	0.805421i	$-0.298061\pi$
$733$	−10.8611	−	18.8120i	−0.401164	−	0.694836i	−0.993867	+	0.110585i	$0.964728\pi$
$734$	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	0.649771	−	0.760130i	$-0.274865\pi$
$761$	−9.19742	−	15.9304i	−0.333406	−	0.577476i	−0.983177	+	0.182653i	$0.941531\pi$
$762$	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	$-0.643629\pi$
$769$	−24.1850			−0.872133			−0.436066	+	0.899914i	$0.643629\pi$
$770$		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	−0.752903	−	0.658131i	$-0.771347\pi$
$773$	5.38005	−	9.31852i	0.193507	−	0.335164i	0.946410	+	0.322967i	$0.104680\pi$
$774$	−34.6388	+	59.9962i	−1.24507	+	2.15652i
$775$	−14.7841	−	25.6067i	−0.531059	−	0.919821i

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

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L-functions

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