LMFDB - Embedded newform 637.2.f.j.295.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(295,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.295"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [12,2,-1,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$0.217953 + 0.377506i$ of defining polynomial
Character	$\chi$	$=$	637.295
Dual form			637.2.f.j.393.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.929081 + 1.60921i) q^{2} +(1.14703 - 1.98672i) q^{3} +(-0.726381 - 1.25813i) q^{4} +0.197362 q^{5} +(2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(-0.183365 + 0.317598i) q^{10} +(2.09137 - 3.62236i) q^{11} -3.33274 q^{12} +(2.72221 + 2.36423i) q^{13} +(0.226381 - 0.392104i) q^{15} +(2.39750 - 4.15260i) q^{16} +(0.420653 + 0.728592i) q^{17} +4.20455 q^{18} +(0.675876 + 1.17065i) q^{19} +(-0.143360 - 0.248307i) q^{20} +(3.88610 + 6.73092i) q^{22} +(2.05760 - 3.56386i) q^{23} +(-1.16637 + 2.02021i) q^{24} -4.96105 q^{25} +(-6.33370 + 2.18406i) q^{26} +1.69131 q^{27} +(4.11931 - 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +1.28070 q^{31} +(3.43809 + 5.95495i) q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 + 2.84683i) q^{36} +(-1.52242 + 2.63692i) q^{37} -2.51177 q^{38} +(7.81953 - 2.69642i) q^{39} -0.200689 q^{40} +(2.69848 - 4.67390i) q^{41} +(-2.66389 - 4.61399i) q^{43} -6.07652 q^{44} +(-0.223290 - 0.386750i) q^{45} +(3.82334 + 6.62223i) q^{46} +11.6641 q^{47} +(-5.50003 - 9.52634i) q^{48} +(4.60921 - 7.98339i) q^{50} +1.93001 q^{51} +(0.997141 - 5.14222i) q^{52} +4.64796 q^{53} +(-1.57136 + 2.72168i) q^{54} +(0.412757 - 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} +(3.02905 + 5.24648i) q^{59} -0.657756 q^{60} +(-5.68285 - 9.84298i) q^{61} +(-1.18987 + 2.06092i) q^{62} -3.18704 q^{64} +(0.537262 + 0.466609i) q^{65} +17.8300 q^{66} +(-6.69851 + 11.6022i) q^{67} +(0.611109 - 1.05847i) q^{68} +(-4.72026 - 8.17574i) q^{69} +(2.98520 + 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} -3.88547 q^{73} +(-2.82891 - 4.89982i) q^{74} +(-5.69049 + 9.85622i) q^{75} +(0.981887 - 1.70068i) q^{76} +(-2.92585 + 15.0885i) q^{78} -10.7334 q^{79} +(0.473177 - 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(5.01421 + 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 + 0.143797i) q^{85} +9.89987 q^{86} +(-9.44997 - 16.3678i) q^{87} +(-2.12662 + 3.68341i) q^{88} +(-5.99207 + 10.3786i) q^{89} +0.829819 q^{90} -5.97840 q^{92} +(1.46901 - 2.54439i) q^{93} +(-10.8369 + 18.7700i) q^{94} +(0.133392 + 0.231042i) q^{95} +15.7744 q^{96} +(9.73637 + 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.929081	+	1.60921i	−0.656959	+	1.13789i	0.324440	+	0.945906i	$0.394824\pi$
$2$	−0.929081	+	1.60921i	−0.656959	+	1.13789i	−0.981399	+	0.191980i	$0.938509\pi$
$3$	1.14703	−	1.98672i	0.662240	−	1.14703i	−0.317785	−	0.948163i	$-0.602939\pi$
$3$	1.14703	−	1.98672i	0.662240	−	1.14703i	0.980026	−	0.198871i	$-0.0637276\pi$
$4$	−0.726381	−	1.25813i	−0.363191	−	0.629065i
$5$	0.197362			0.0882631			0.0441315	−	0.999026i	$-0.485948\pi$
$5$	0.197362			0.0882631			0.0441315	+	0.999026i	$0.485948\pi$
$6$	2.13137	+	3.69165i	0.870130	+	1.50711i
$7$		0			0
$7$		0			0
$8$	−1.01686			−0.359513
$9$	−1.13137	−	1.95960i	−0.377125	−	0.653199i
$10$	−0.183365	+	0.317598i	−0.0579852	+	0.100433i
$11$	2.09137	−	3.62236i	0.630571	−	1.09218i	−0.356864	−	0.934156i	$-0.616154\pi$
$11$	2.09137	−	3.62236i	0.630571	−	1.09218i	0.987435	−	0.158025i	$-0.0505127\pi$
$12$	−3.33274			−0.962078
$13$	2.72221	+	2.36423i	0.755005	+	0.655719i
$13$	2.72221	+	2.36423i	0.755005	+	0.655719i
$14$		0			0
$15$	0.226381	−	0.392104i	0.0584514	−	0.101241i
$16$	2.39750	−	4.15260i	0.599376	−	1.03815i
$17$	0.420653	+	0.728592i	0.102023	+	0.176709i	0.912518	−	0.409036i	$-0.134135\pi$
$17$	0.420653	+	0.728592i	0.102023	+	0.176709i	−0.810495	+	0.585746i	$0.800802\pi$
$18$	4.20455			0.991022
$19$	0.675876	+	1.17065i	0.155057	+	0.268566i	0.933080	−	0.359670i	$-0.117111\pi$
$19$	0.675876	+	1.17065i	0.155057	+	0.268566i	−0.778023	+	0.628236i	$0.783777\pi$
$20$	−0.143360	−	0.248307i	−0.0320563	−	0.0555232i
$21$		0			0
$22$	3.88610	+	6.73092i	0.828519	+	1.43504i
$23$	2.05760	−	3.56386i	0.429038	−	0.743116i	−0.567750	−	0.823201i	$-0.692186\pi$
$23$	2.05760	−	3.56386i	0.429038	−	0.743116i	0.996788	+	0.0800850i	$0.0255192\pi$
$24$	−1.16637	+	2.02021i	−0.238084	+	0.412373i
$25$	−4.96105			−0.992210
$26$	−6.33370	+	2.18406i	−1.24214	+	0.428330i
$27$	1.69131			0.325492
$28$		0			0
$29$	4.11931	−	7.13485i	0.764936	−	1.32491i	−0.175344	−	0.984507i	$-0.556104\pi$
$29$	4.11931	−	7.13485i	0.764936	−	1.32491i	0.940280	−	0.340401i	$-0.110563\pi$
$30$	0.420653	+	0.728592i	0.0768003	+	0.133022i
$31$	1.28070			0.230020			0.115010	−	0.993364i	$-0.463310\pi$
$31$	1.28070			0.230020			0.115010	+	0.993364i	$0.463310\pi$
$32$	3.43809	+	5.95495i	0.607774	+	1.05270i
$33$	−4.79774	−	8.30993i	−0.835180	−	1.44657i
$34$	−1.56328			−0.268100
$35$		0			0
$36$	−1.64362	+	2.84683i	−0.273936	+	0.474471i
$37$	−1.52242	+	2.63692i	−0.250285	+	0.433506i	−0.963604	−	0.267333i	$-0.913858\pi$
$37$	−1.52242	+	2.63692i	−0.250285	+	0.433506i	0.713319	+	0.700839i	$0.247191\pi$
$38$	−2.51177			−0.407463
$39$	7.81953	−	2.69642i	1.25213	−	0.431773i
$40$	−0.200689			−0.0317317
$41$	2.69848	−	4.67390i	0.421431	−	0.729941i	−0.574648	−	0.818400i	$-0.694861\pi$
$41$	2.69848	−	4.67390i	0.421431	−	0.729941i	0.996080	+	0.0884599i	$0.0281945\pi$
$42$		0			0
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	0.588226	−	0.808697i	$-0.299827\pi$
$43$	−2.66389	−	4.61399i	−0.406239	−	0.703627i	−0.994465	+	0.105070i	$0.966493\pi$
$44$	−6.07652			−0.916070
$45$	−0.223290	−	0.386750i	−0.0332862	−	0.0576534i
$46$	3.82334	+	6.62223i	0.563721	+	0.976394i
$47$	11.6641			1.70138			0.850690	−	0.525668i	$-0.176185\pi$
$47$	11.6641			1.70138			0.850690	+	0.525668i	$0.176185\pi$
$48$	−5.50003	−	9.52634i	−0.793862	−	1.37501i
$49$		0			0
$50$	4.60921	−	7.98339i	0.651841	−	1.12902i
$51$	1.93001			0.270256
$52$	0.997141	−	5.14222i	0.138279	−	0.713098i
$53$	4.64796			0.638447			0.319223	−	0.947679i	$-0.396578\pi$
$53$	4.64796			0.638447			0.319223	+	0.947679i	$0.396578\pi$
$54$	−1.57136	+	2.72168i	−0.213835	+	0.370373i
$55$	0.412757	−	0.714916i	0.0556562	−	0.0963993i
$56$		0			0
$57$	3.10101			0.410739
$58$	7.65434	+	13.2577i	1.00506	+	1.74082i
$59$	3.02905	+	5.24648i	0.394349	+	0.683033i	0.993018	−	0.117964i	$-0.0376367\pi$
$59$	3.02905	+	5.24648i	0.394349	+	0.683033i	−0.598669	+	0.800997i	$0.704303\pi$
$60$	−0.657756			−0.0849160
$61$	−5.68285	−	9.84298i	−0.727614	−	1.26026i	−0.957889	−	0.287139i	$-0.907296\pi$
$61$	−5.68285	−	9.84298i	−0.727614	−	1.26026i	0.230275	−	0.973126i	$-0.426038\pi$
$62$	−1.18987	+	2.06092i	−0.151114	+	0.261737i
$63$		0			0
$64$	−3.18704			−0.398380
$65$	0.537262	+	0.466609i	0.0666391	+	0.0578758i
$66$	17.8300			2.19472
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	0.0885411	+	0.996073i	$0.471780\pi$
$67$	−6.69851	+	11.6022i	−0.818354	+	1.41743i	−0.906895	+	0.421357i	$0.861554\pi$
$68$	0.611109	−	1.05847i	0.0741078	−	0.128358i
$69$	−4.72026	−	8.17574i	−0.568253	−	0.984243i
$70$		0			0
$71$	2.98520	+	5.17051i	0.354278	+	0.613627i	0.986994	−	0.160757i	$-0.0513934\pi$
$71$	2.98520	+	5.17051i	0.354278	+	0.613627i	−0.632716	+	0.774384i	$0.718060\pi$
$72$	1.15044	+	1.99263i	0.135581	+	0.234833i
$73$	−3.88547			−0.454759			−0.227380	−	0.973806i	$-0.573016\pi$
$73$	−3.88547			−0.454759			−0.227380	+	0.973806i	$0.573016\pi$
$74$	−2.82891	−	4.89982i	−0.328854	−	0.569592i
$75$	−5.69049	+	9.85622i	−0.657081	+	1.13810i
$76$	0.981887	−	1.70068i	0.112630	−	0.195081i
$77$		0			0
$78$	−2.92585	+	15.0885i	−0.331287	+	1.70844i
$79$	−10.7334			−1.20760			−0.603799	−	0.797136i	$-0.706347\pi$
$79$	−10.7334			−1.20760			−0.603799	+	0.797136i	$0.706347\pi$
$80$	0.473177	−	0.819566i	0.0529028	−	0.0916303i
$81$	5.33411	−	9.23895i	0.592679	−	1.02655i
$82$	5.01421	+	8.68486i	0.553726	+	0.959082i
$83$	−3.07390			−0.337404			−0.168702	−	0.985667i	$-0.553958\pi$
$83$	−3.07390			−0.337404			−0.168702	+	0.985667i	$0.553958\pi$
$84$		0			0
$85$	0.0830210	+	0.143797i	0.00900489	+	0.0155969i
$86$	9.89987			1.06753
$87$	−9.44997	−	16.3678i	−1.01314	−	1.75482i
$88$	−2.12662	+	3.68341i	−0.226698	+	0.392653i
$89$	−5.99207	+	10.3786i	−0.635159	+	1.10013i	0.351323	+	0.936254i	$0.385732\pi$
$89$	−5.99207	+	10.3786i	−0.635159	+	1.10013i	−0.986482	+	0.163873i	$0.947601\pi$
$90$	0.829819			0.0874706
$91$		0			0
$92$	−5.97840			−0.623291
$93$	1.46901	−	2.54439i	0.152329	−	0.263841i
$94$	−10.8369	+	18.7700i	−1.11774	+	1.93598i
$95$	0.133392	+	0.231042i	0.0136858	+	0.0237045i
$96$	15.7744			1.60997
$97$	9.73637	+	16.8639i	0.988578	+	1.71227i	0.624807	+	0.780779i	$0.285178\pi$
$97$	9.73637	+	16.8639i	0.988578	+	1.71227i	0.363771	+	0.931488i	$0.381489\pi$
$98$		0			0
$99$	−9.46448			−0.951216
$100$	3.60361	+	6.24164i	0.360361	+	0.624164i
$101$	−8.46697	+	14.6652i	−0.842495	+	1.45924i	0.0452843	+	0.998974i	$0.485581\pi$
$101$	−8.46697	+	14.6652i	−0.842495	+	1.45924i	−0.887779	+	0.460270i	$0.847753\pi$
$102$	−1.79314	+	3.10580i	−0.177547	+	0.307520i
$103$	7.23425			0.712811			0.356406	−	0.934331i	$-0.384002\pi$
$103$	7.23425			0.712811			0.356406	+	0.934331i	$0.384002\pi$
$104$	−2.76809	−	2.40408i	−0.271434	−	0.235739i
$105$		0			0
$106$	−4.31833	+	7.47957i	−0.419434	+	0.726480i
$107$	4.92625	−	8.53251i	0.476238	−	0.824869i	−0.523391	−	0.852093i	$-0.675333\pi$
$107$	4.92625	−	8.53251i	0.476238	−	0.824869i	0.999629	+	0.0272237i	$0.00866664\pi$
$108$	−1.22853	−	2.12788i	−0.118216	−	0.204756i
$109$	−13.8159			−1.32332			−0.661662	−	0.749802i	$-0.730149\pi$
$109$	−13.8159			−1.32332			−0.661662	+	0.749802i	$0.730149\pi$
$110$	0.766969	+	1.32843i	0.0731277	+	0.126661i
$111$	3.49255	+	6.04927i	0.331498	+	0.574171i
$112$		0			0
$113$	2.13432	+	3.69675i	0.200780	+	0.347761i	0.948780	−	0.315938i	$-0.102319\pi$
$113$	2.13432	+	3.69675i	0.200780	+	0.347761i	−0.748000	+	0.663699i	$0.768986\pi$
$114$	−2.88109	+	4.99019i	−0.269839	+	0.467374i
$115$	0.406092	−	0.703371i	0.0378682	−	0.0655897i
$116$	−11.9687			−1.11127
$117$	1.55310	−	8.00926i	0.143584	−	0.740456i
$118$	−11.2569			−1.03629
$119$		0			0
$120$	−0.230197	+	0.398713i	−0.0210140	+	0.0363973i
$121$	−3.24765	−	5.62509i	−0.295240	−	0.511372i
$122$	21.1193			1.91205
$123$	−6.19049	−	10.7222i	−0.558178	−	0.966792i
$124$	−0.930276	−	1.61129i	−0.0835412	−	0.144698i
$125$	−1.96593			−0.175839
$126$		0			0
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	−0.813339	−	0.581791i	$-0.802352\pi$
$127$	1.09512	−	1.89680i	0.0971761	−	0.168314i	0.910515	+	0.413477i	$0.135686\pi$
$128$	−3.91516	+	6.78126i	−0.346055	+	0.599385i
$129$	−12.2223			−1.07611
$130$	−1.25003	+	0.431052i	−0.109635	+	0.0378057i
$131$	−2.27612			−0.198865			−0.0994326	−	0.995044i	$-0.531703\pi$
$131$	−2.27612			−0.198865			−0.0994326	+	0.995044i	$0.531703\pi$
$132$	−6.96998	+	12.0724i	−0.606659	+	1.05076i
$133$		0			0
$134$	−12.4469	−	21.5587i	−1.07525	−	1.86239i
$135$	0.333800			0.0287289
$136$	−0.427743	−	0.740873i	−0.0366787	−	0.0635293i
$137$	−6.72399	−	11.6463i	−0.574469	−	0.995010i	−0.996099	−	0.0882417i	$-0.971875\pi$
$137$	−6.72399	−	11.6463i	−0.574469	−	0.995010i	0.421630	−	0.906768i	$-0.361458\pi$
$138$	17.5420			1.49328
$139$	2.02270	+	3.50342i	0.171563	+	0.297156i	0.938966	−	0.344009i	$-0.111785\pi$
$139$	2.02270	+	3.50342i	0.171563	+	0.297156i	−0.767403	+	0.641165i	$0.778452\pi$
$140$		0			0
$141$	13.3791	−	23.1733i	1.12672	−	1.95154i
$142$	−11.0940			−0.930984
$143$	14.2572	−	4.91634i	1.19225	−	0.411125i
$144$	−10.8499			−0.904157
$145$	0.812996	−	1.40815i	0.0675156	−	0.116940i
$146$	3.60991	−	6.25255i	0.298758	−	0.517465i
$147$		0			0
$148$	4.42344			0.363605
$149$	−7.67596	−	13.2952i	−0.628840	−	1.08918i	−0.987785	−	0.155823i	$-0.950197\pi$
$149$	−7.67596	−	13.2952i	−0.628840	−	1.08918i	0.358945	−	0.933359i	$-0.383136\pi$
$150$	−10.5738	−	18.3144i	−0.863351	−	1.49537i
$151$	6.12108			0.498127			0.249063	−	0.968487i	$-0.419877\pi$
$151$	6.12108			0.498127			0.249063	+	0.968487i	$0.419877\pi$
$152$	−0.687268	−	1.19038i	−0.0557448	−	0.0965528i
$153$	0.951831	−	1.64862i	0.0769510	−	0.133283i
$154$		0			0
$155$	0.252762			0.0203023
$156$	−9.07241	−	7.87935i	−0.726374	−	0.630853i
$157$	−4.53668			−0.362067			−0.181033	−	0.983477i	$-0.557944\pi$
$157$	−4.53668			−0.362067			−0.181033	+	0.983477i	$0.557944\pi$
$158$	9.97217	−	17.2723i	0.793343	−	1.37411i
$159$	5.33137	−	9.23421i	0.422805	−	0.732320i
$160$	0.678549	+	1.17528i	0.0536440	+	0.0929142i
$161$		0			0
$162$	9.91163	+	17.1674i	0.778731	+	1.34880i
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	0.828128	−	0.560538i	$-0.189406\pi$
$163$	−0.911271	−	1.57837i	−0.0713762	−	0.123627i	−0.899505	+	0.436911i	$0.856072\pi$
$164$	−7.84049			−0.612240
$165$	−0.946893	−	1.64007i	−0.0737155	−	0.127679i
$166$	2.85590	−	4.94656i	0.221661	−	0.383928i
$167$	−5.35397	+	9.27336i	−0.414303	+	0.717594i	−0.995355	−	0.0962726i	$-0.969308\pi$
$167$	−5.35397	+	9.27336i	−0.414303	+	0.717594i	0.581052	+	0.813866i	$0.302641\pi$
$168$		0			0
$169$	1.82086	+	12.8718i	0.140066	+	0.990142i
$170$	−0.308533			−0.0236634
$171$	1.52934	−	2.64889i	0.116951	−	0.202566i
$172$	−3.87000	+	6.70303i	−0.295085	+	0.511102i
$173$	−6.74634	−	11.6850i	−0.512915	−	0.888395i	−0.999888	−	0.0149778i	$-0.995232\pi$
$173$	−6.74634	−	11.6850i	−0.512915	−	0.888395i	0.486973	−	0.873417i	$-0.338101\pi$
$174$	35.1191			2.66237
$175$		0			0
$176$	−10.0281	−	17.3692i	−0.755898	−	1.30925i
$177$	13.8977			1.04462
$178$	−11.1342	−	19.2851i	−0.834547	−	1.44548i
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	−0.992615	−	0.121309i	$-0.961291\pi$
$179$	−5.23458	+	9.06657i	−0.391251	+	0.677667i	0.601364	+	0.798975i	$0.294624\pi$
$180$	−0.324388	+	0.561857i	−0.0241785	+	0.0418783i
$181$	−12.5209			−0.930674			−0.465337	−	0.885133i	$-0.654067\pi$
$181$	−12.5209			−0.930674			−0.465337	+	0.885133i	$0.654067\pi$
$182$		0			0
$183$	−26.0737			−1.92742
$184$	−2.09228	+	3.62393i	−0.154245	+	0.267160i
$185$	−0.300469	+	0.520428i	−0.0220909	+	0.0382626i
$186$	2.72965	+	4.72789i	0.200148	+	0.346666i
$187$	3.51896			0.257332
$188$	−8.47256	−	14.6749i	−0.617925	−	1.07028i
$189$		0			0
$190$	−0.495729			−0.0359640
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	0.525135	−	0.851019i	$-0.324015\pi$
$191$	−6.55685	−	11.3568i	−0.474437	−	0.821749i	−0.999572	+	0.0292704i	$0.990682\pi$
$192$	−3.65565	+	6.33176i	−0.263823	+	0.456956i
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	−0.884160	−	0.467184i	$-0.845269\pi$
$193$	−0.520786	+	0.902028i	−0.0374870	+	0.0649294i	0.846673	+	0.532113i	$0.178602\pi$
$194$	−36.1835			−2.59782
$195$	1.54328	−	0.532172i	0.110517	−	0.0381096i
$196$		0			0
$197$	−0.739167	+	1.28027i	−0.0526635	+	0.0912158i	−0.891155	−	0.453698i	$-0.850104\pi$
$197$	−0.739167	+	1.28027i	−0.0526635	+	0.0912158i	0.838492	+	0.544914i	$0.183438\pi$
$198$	8.79326	−	15.2304i	0.624910	−	1.08238i
$199$	7.04993	+	12.2108i	0.499756	+	0.865603i	1.00000		0.000281618i	$-8.96419e-5\pi$
$199$	7.04993	+	12.2108i	0.499756	+	0.865603i	−0.500244	+	0.865885i	$0.666756\pi$
$200$	5.04467			0.356712
$201$	15.3668	+	26.6162i	1.08389	+	1.87736i
$202$	−15.7330	−	27.2503i	−1.10697	−	1.91733i
$203$		0			0
$204$	−1.40192	−	2.42820i	−0.0981543	−	0.170008i
$205$	0.532578	−	0.922451i	0.0371968	−	0.0644268i
$206$	−6.72120	+	11.6415i	−0.468288	+	0.811099i
$207$	−9.31164			−0.647204
$208$	16.3442	−	5.63600i	1.13327	−	0.390786i
$209$	5.65402			0.391097
$210$		0			0
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.0986067	+	0.995126i	$0.531439\pi$
$211$	−13.2346	+	22.9230i	−0.911108	+	1.57809i	−0.812501	+	0.582959i	$0.801895\pi$
$212$	−3.37619	−	5.84774i	−0.231878	−	0.401624i
$213$	13.6965			0.938468
$214$	9.15376	+	15.8548i	0.625738	+	1.08381i
$215$	−0.525751	−	0.910628i	−0.0358559	−	0.0621043i
$216$	−1.71981			−0.117019
$217$		0			0
$218$	12.8361	−	22.2328i	0.869370	−	1.50579i
$219$	−4.45676	+	7.71934i	−0.301160	+	0.521625i
$220$	−1.19928			−0.0808552
$221$	−0.577452	+	2.97790i	−0.0388436	+	0.200315i
$222$	−12.9794			−0.871122
$223$	−0.364024	+	0.630508i	−0.0243769	+	0.0422219i	−0.877956	−	0.478740i	$-0.841093\pi$
$223$	−0.364024	+	0.630508i	−0.0243769	+	0.0422219i	0.853580	+	0.520962i	$0.174427\pi$
$224$		0			0
$225$	5.61280	+	9.72165i	0.374187	+	0.648110i
$226$	−7.93182			−0.527617
$227$	−1.42598	−	2.46986i	−0.0946454	−	0.163931i	0.814815	−	0.579721i	$-0.196838\pi$
$227$	−1.42598	−	2.46986i	−0.0946454	−	0.163931i	−0.909461	+	0.415790i	$0.863505\pi$
$228$	−2.25252	−	3.90147i	−0.149177	−	0.258381i
$229$	−3.17352			−0.209712			−0.104856	−	0.994487i	$-0.533438\pi$
$229$	−3.17352			−0.209712			−0.104856	+	0.994487i	$0.533438\pi$
$230$	0.754584	+	1.30698i	0.0497558	+	0.0861795i
$231$		0			0
$232$	−4.18874	+	7.25511i	−0.275004	+	0.476321i
$233$	13.4071			0.878327			0.439163	−	0.898407i	$-0.355275\pi$
$233$	13.4071			0.878327			0.439163	+	0.898407i	$0.355275\pi$
$234$	11.4457	+	9.94051i	0.748227	+	0.649832i
$235$	2.30205			0.150169
$236$	4.40050	−	7.62188i	0.286448	−	0.496142i
$237$	−12.3115	+	21.3242i	−0.799721	+	1.38516i
$238$		0			0
$239$	−15.5538			−1.00609			−0.503046	−	0.864259i	$-0.667788\pi$
$239$	−15.5538			−1.00609			−0.503046	+	0.864259i	$0.667788\pi$
$240$	−1.08550	−	1.88014i	−0.0700687	−	0.121363i
$241$	−3.78787	−	6.56078i	−0.243998	−	0.422617i	0.717851	−	0.696196i	$-0.245126\pi$
$241$	−3.78787	−	6.56078i	−0.243998	−	0.422617i	−0.961849	+	0.273579i	$0.911792\pi$
$242$	12.0693			0.775844
$243$	−9.69985	−	16.8006i	−0.622245	−	1.07776i
$244$	−8.25583	+	14.2995i	−0.528525	+	0.915433i
$245$		0			0
$246$	23.0059			1.46680
$247$	−0.927810	+	4.78468i	−0.0590351	+	0.304442i
$248$	−1.30229			−0.0826953
$249$	−3.52587	+	6.10698i	−0.223443	+	0.387014i
$250$	1.82651	−	3.16361i	0.115519	−	0.200084i
$251$	0.637382	+	1.10398i	0.0402312	+	0.0696825i	0.885440	−	0.464754i	$-0.153857\pi$
$251$	0.637382	+	1.10398i	0.0402312	+	0.0696825i	−0.845209	+	0.534436i	$0.820524\pi$
$252$		0			0
$253$	−8.60638	−	14.9067i	−0.541079	−	0.937176i
$254$	2.03491	+	3.52456i	0.127682	+	0.221151i
$255$	0.380912			0.0238536
$256$	−10.4620	−	18.1208i	−0.653878	−	1.13255i
$257$	−4.24010	+	7.34406i	−0.264490	+	0.458110i	−0.967430	−	0.253139i	$-0.918537\pi$
$257$	−4.24010	+	7.34406i	−0.264490	+	0.458110i	0.702940	+	0.711249i	$0.251870\pi$
$258$	11.3555	−	19.6683i	0.706962	−	1.22449i
$259$		0			0
$260$	0.196798	−	1.01488i	0.0122049	−	0.0629402i
$261$	−18.6419			−1.15390
$262$	2.11470	−	3.66276i	0.130646	−	0.226286i
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	−0.993009	−	0.118038i	$-0.962339\pi$
$263$	−6.39415	+	11.0750i	−0.394280	+	0.682913i	0.598729	+	0.800952i	$0.295673\pi$
$264$	4.87861	+	8.45000i	0.300258	+	0.520062i
$265$	0.917333			0.0563513
$266$		0			0
$267$	13.7462	+	23.8092i	0.841255	+	1.45710i
$268$	19.4627			1.18887
$269$	−2.35586	−	4.08047i	−0.143639	−	0.248790i	0.785225	−	0.619210i	$-0.212547\pi$
$269$	−2.35586	−	4.08047i	−0.143639	−	0.248790i	−0.928864	+	0.370420i	$0.879214\pi$
$270$	−0.310127	+	0.537156i	−0.0188737	+	0.0326903i
$271$	−9.00562	+	15.5982i	−0.547052	+	0.947522i	0.451422	+	0.892310i	$0.350917\pi$
$271$	−9.00562	+	15.5982i	−0.547052	+	0.947522i	−0.998475	+	0.0552119i	$0.982417\pi$
$272$	4.03407			0.244601
$273$		0			0
$274$	24.9885			1.50961
$275$	−10.3754	+	17.9707i	−0.625659	+	1.08367i
$276$	−6.85742	+	11.8774i	−0.412768	+	0.714936i
$277$	13.0604	+	22.6213i	0.784725	+	1.35918i	0.929163	+	0.369670i	$0.120529\pi$
$277$	13.0604	+	22.6213i	0.784725	+	1.35918i	−0.144438	+	0.989514i	$0.546137\pi$
$278$	−7.51700			−0.450840
$279$	−1.44895	−	2.50965i	−0.0867463	−	0.150249i
$280$		0			0
$281$	−3.66197			−0.218455			−0.109227	−	0.994017i	$-0.534838\pi$
$281$	−3.66197			−0.218455			−0.109227	+	0.994017i	$0.534838\pi$
$282$	24.8605	+	43.0596i	1.48042	+	2.56416i
$283$	3.82263	−	6.62099i	0.227232	−	0.393577i	−0.729755	−	0.683709i	$-0.760366\pi$
$283$	3.82263	−	6.62099i	0.227232	−	0.393577i	0.956987	+	0.290132i	$0.0936991\pi$
$284$	4.33678	−	7.51153i	0.257341	−	0.445727i
$285$	0.612022			0.0362531
$286$	−5.33465	+	27.5106i	−0.315445	+	1.62674i
$287$		0			0
$288$	7.77953	−	13.4745i	0.458413	−	0.793995i
$289$	8.14610	−	14.1095i	0.479183	−	0.829968i
$290$	1.51068	+	2.61657i	0.0887100	+	0.153650i
$291$	44.6718			2.61871
$292$	2.82233	+	4.88842i	0.165164	+	0.286073i
$293$	−8.57670	−	14.8553i	−0.501056	−	0.867855i	−0.999999	−	0.00122001i	$-0.999612\pi$
$293$	−8.57670	−	14.8553i	−0.501056	−	0.867855i	0.498943	−	0.866635i	$-0.333722\pi$
$294$		0			0
$295$	0.597821	+	1.03546i	0.0348065	+	0.0602866i
$296$	1.54809	−	2.68136i	0.0899807	−	0.155851i
$297$	3.53715	−	6.12652i	0.205246	−	0.355497i
$298$	28.5264			1.65249
$299$	14.0270	−	4.83695i	0.811201	−	0.279728i
$300$	16.5339			0.954583
$301$		0			0
$302$	−5.68698	+	9.85014i	−0.327249	+	0.566812i
$303$	19.4238	+	33.6430i	1.11587	+	1.93274i
$304$	6.48166			0.371749
$305$	−1.12158	−	1.94263i	−0.0642215	−	0.111235i
$306$	1.76866	+	3.06340i	0.101107	+	0.175123i
$307$	28.0696			1.60201			0.801007	−	0.598655i	$-0.204298\pi$
$307$	28.0696			1.60201			0.801007	+	0.598655i	$0.204298\pi$
$308$		0			0
$309$	8.29793	−	14.3724i	0.472052	−	0.817619i
$310$	−0.234836	+	0.406748i	−0.0133378	+	0.0231017i
$311$	23.5341			1.33450			0.667248	−	0.744836i	$-0.267472\pi$
$311$	23.5341			1.33450			0.667248	+	0.744836i	$0.267472\pi$
$312$	−7.95133	+	2.74187i	−0.450155	+	0.155228i
$313$	3.34860			0.189274			0.0946370	−	0.995512i	$-0.469831\pi$
$313$	3.34860			0.189274			0.0946370	+	0.995512i	$0.469831\pi$
$314$	4.21494	−	7.30050i	0.237863	−	0.411991i
$315$		0			0
$316$	7.79652	+	13.5040i	0.438588	+	0.759658i
$317$	−7.27834			−0.408793			−0.204396	−	0.978888i	$-0.565523\pi$
$317$	−7.27834			−0.408793			−0.204396	+	0.978888i	$0.565523\pi$
$318$	9.90655	+	17.1586i	0.555532	+	0.962209i
$319$	−17.2300	−	29.8432i	−0.964694	−	1.67090i
$320$	−0.629002			−0.0351623
$321$	−11.3011	−	19.5742i	−0.630768	−	1.09252i
$322$		0			0
$323$	−0.568618	+	0.984875i	−0.0316388	+	0.0547999i
$324$	−15.4984			−0.861021
$325$	−13.5050	−	11.7290i	−0.749123	−	0.650610i
$326$	3.38658			0.187565
$327$	−15.8473	+	27.4484i	−0.876359	+	1.51790i
$328$	−2.74396	+	4.75268i	−0.151510	+	0.262423i
$329$		0			0
$330$	3.51896			0.193712
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	0.992927	−	0.118728i	$-0.0378818\pi$
$331$	7.16168	+	12.4044i	0.393642	+	0.681807i	−0.599285	+	0.800536i	$0.704548\pi$
$332$	2.23282	+	3.86736i	0.122542	+	0.212249i
$333$	6.88973			0.377555
$334$	−9.94855	−	17.2314i	−0.544360	−	0.942860i
$335$	−1.32203	+	2.28983i	−0.0722304	+	0.125107i
$336$		0			0
$337$	17.1802			0.935868			0.467934	−	0.883764i	$-0.344999\pi$
$337$	17.1802			0.935868			0.467934	+	0.883764i	$0.344999\pi$
$338$	−22.4053	−	9.02883i	−1.21869	−	0.491104i
$339$	9.79255			0.531858
$340$	0.120610	−	0.208902i	0.00654098	−	0.0113293i
$341$	2.67841	−	4.63915i	0.145044	−	0.251224i
$342$	2.84175	+	4.92206i	0.153664	+	0.266155i
$343$		0			0
$344$	2.70879	+	4.69176i	0.146048	+	0.252963i
$345$	−0.931602	−	1.61358i	−0.0501558	−	0.0868723i
$346$	25.0716			1.34786
$347$	3.85139	+	6.67080i	0.206753	+	0.358107i	0.950690	−	0.310143i	$-0.100377\pi$
$347$	3.85139	+	6.67080i	0.206753	+	0.358107i	−0.743937	+	0.668250i	$0.767044\pi$
$348$	−13.7286	+	23.7786i	−0.735928	+	1.27466i
$349$	11.1850	−	19.3730i	0.598721	−	1.03702i	−0.394289	−	0.918986i	$-0.629009\pi$
$349$	11.1850	−	19.3730i	0.598721	−	1.03702i	0.993010	−	0.118029i	$-0.0376575\pi$
$350$		0			0
$351$	4.60409	+	3.99863i	0.245748	+	0.213431i
$352$	28.7613			1.53298
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	0.401450	+	0.915881i	$0.368506\pi$
$353$	−11.1311	+	19.2797i	−0.592451	+	1.02616i	−0.993901	+	0.110275i	$0.964827\pi$
$354$	−12.9121	+	22.3644i	−0.686270	+	1.18865i
$355$	0.589165	+	1.02046i	0.0312697	+	0.0541606i
$356$	17.4101			0.922735
$357$		0			0
$358$	−9.72670	−	16.8471i	−0.514072	−	0.890399i
$359$	−2.75842			−0.145584			−0.0727920	−	0.997347i	$-0.523191\pi$
$359$	−2.75842			−0.145584			−0.0727920	+	0.997347i	$0.523191\pi$
$360$	0.227054	+	0.393269i	0.0119668	+	0.0207271i
$361$	8.58638	−	14.8721i	0.451915	−	0.782740i
$362$	11.6330	−	20.1489i	0.611415	−	1.05900i
$363$	−14.9006			−0.782081
$364$		0			0
$365$	−0.766844			−0.0401385
$366$	24.2246	−	41.9582i	1.26624	−	2.19319i
$367$	−7.07485	+	12.2540i	−0.369304	+	0.639654i	−0.989457	−	0.144827i	$-0.953737\pi$
$367$	−7.07485	+	12.2540i	−0.369304	+	0.639654i	0.620153	+	0.784481i	$0.287071\pi$
$368$	−9.86618	−	17.0887i	−0.514310	−	0.890812i
$369$	−12.2119			−0.635729
$370$	−0.558320	−	0.967039i	−0.0290257	−	0.0502740i
$371$		0			0
$372$	−4.26823			−0.221298
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	0.923890	−	0.382657i	$-0.124991\pi$
$373$	2.52142	+	4.36723i	0.130554	+	0.226127i	−0.793336	+	0.608784i	$0.791658\pi$
$374$	−3.26940	+	5.66276i	−0.169056	+	0.292814i
$375$	−2.25499	+	3.90576i	−0.116447	+	0.201693i
$376$	−11.8607			−0.611668
$377$	28.0820	−	9.68358i	1.44630	−	0.498730i
$378$		0			0
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	−0.777657	−	0.628688i	$-0.783592\pi$
$379$	3.02982	−	5.24780i	0.155631	−	0.269561i	0.933289	+	0.359127i	$0.116925\pi$
$380$	0.193787	−	0.335650i	0.00994109	−	0.0172185i
$381$	−2.51228	−	4.35139i	−0.128708	−	0.222929i
$382$	24.3674			1.24674
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	0.802168	−	0.597098i	$-0.203680\pi$
$383$	−2.27052	−	3.93266i	−0.116018	−	0.200950i	−0.918186	+	0.396149i	$0.870346\pi$
$384$	8.98165	+	15.5567i	0.458343	+	0.793873i
$385$		0			0
$386$	−0.967705	−	1.67611i	−0.0492549	−	0.0853120i
$387$	−6.02771	+	10.4403i	−0.306406	+	0.530710i
$388$	14.1446	−	24.4992i	0.718085	−	1.24376i
$389$	4.50765			0.228547			0.114273	−	0.993449i	$-0.463546\pi$
$389$	4.50765			0.228547			0.114273	+	0.993449i	$0.463546\pi$
$390$	−0.577452	+	2.97790i	−0.0292404	+	0.150792i
$391$	3.46213			0.175088
$392$		0			0
$393$	−2.61078	+	4.52201i	−0.131697	+	0.228105i
$394$	−1.37349	−	2.37896i	−0.0691955	−	0.119850i
$395$	−2.11836			−0.106586
$396$	6.87482	+	11.9075i	0.345473	+	0.598376i
$397$	2.00174	+	3.46712i	0.100465	+	0.174010i	0.911876	−	0.410465i	$-0.134634\pi$
$397$	2.00174	+	3.46712i	0.100465	+	0.174010i	−0.811412	+	0.584475i	$0.801300\pi$
$398$	−26.1998			−1.31328
$399$		0			0
$400$	−11.8941	+	20.6012i	−0.594706	+	1.03006i
$401$	−6.30674	+	10.9236i	−0.314944	+	0.545498i	−0.979426	−	0.201806i	$-0.935319\pi$
$401$	−6.30674	+	10.9236i	−0.314944	+	0.545498i	0.664482	+	0.747304i	$0.268652\pi$
$402$	−57.1081			−2.84829
$403$	3.48633	+	3.02786i	0.173667	+	0.150829i
$404$	24.6010			1.22394
$405$	1.05275	−	1.82342i	0.0523116	−	0.0906064i
$406$		0			0
$407$	6.36790	+	11.0295i	0.315645	+	0.546713i
$408$	−1.96254			−0.0971604
$409$	10.3476	+	17.9226i	0.511657	+	0.886216i	0.999909	+	0.0135128i	$0.00430140\pi$
$409$	10.3476	+	17.9226i	0.511657	+	0.886216i	−0.488252	+	0.872703i	$0.662365\pi$
$410$	0.989615	+	1.71406i	0.0488736	+	0.0846516i
$411$	−30.8506			−1.52175
$412$	−5.25482	−	9.10162i	−0.258886	−	0.448404i
$413$		0			0
$414$	8.65126	−	14.9844i	0.425186	−	0.736444i
$415$	−0.606672			−0.0297803
$416$	−4.71965	+	24.3391i	−0.231400	+	1.19332i
$417$	9.28042			0.454464
$418$	−5.25304	+	9.09854i	−0.256935	+	0.445024i
$419$	−10.9088	+	18.8945i	−0.532928	+	0.923058i	0.466333	+	0.884609i	$0.345575\pi$
$419$	−10.9088	+	18.8945i	−0.532928	+	0.923058i	−0.999261	+	0.0384484i	$0.987758\pi$
$420$		0			0
$421$	9.42727			0.459457			0.229728	−	0.973255i	$-0.426216\pi$
$421$	9.42727			0.459457			0.229728	+	0.973255i	$0.426216\pi$
$422$	−24.5920	−	42.5947i	−1.19712	−	2.07348i
$423$	−13.1964	−	22.8569i	−0.641632	−	1.11134i
$424$	−4.72631			−0.229530
$425$	−2.08688	−	3.61458i	−0.101228	−	0.175333i
$426$	−12.7251	+	22.0406i	−0.616535	+	1.06787i
$427$		0			0
$428$	−14.3133			−0.691861
$429$	6.58611	−	33.9643i	0.317980	−	1.63981i
$430$	1.95386			0.0942235
$431$	−10.2138	+	17.6908i	−0.491980	+	0.852134i	−0.999957	−	0.00923613i	$-0.997060\pi$
$431$	−10.2138	+	17.6908i	−0.491980	+	0.852134i	0.507977	+	0.861370i	$0.330393\pi$
$432$	4.05491	−	7.02332i	0.195092	−	0.337909i
$433$	13.1743	+	22.8186i	0.633117	+	1.09659i	0.986911	+	0.161267i	$0.0515581\pi$
$433$	13.1743	+	22.8186i	0.633117	+	1.09659i	−0.353794	+	0.935323i	$0.615109\pi$
$434$		0			0
$435$	−1.86507	−	3.23039i	−0.0894231	−	0.154885i
$436$	10.0356	+	17.3822i	0.480619	+	0.832457i
$437$	5.56272			0.266101
$438$	−8.28138	−	14.3438i	−0.395700	−	0.685372i
$439$	12.5655	−	21.7641i	0.599720	−	1.03875i	−0.393142	−	0.919478i	$-0.628612\pi$
$439$	12.5655	−	21.7641i	0.599720	−	1.03875i	0.992862	−	0.119267i	$-0.0380546\pi$
$440$	−0.419714	+	0.726967i	−0.0200091	+	0.0346568i
$441$		0			0
$442$	−4.25558	−	3.69595i	−0.202417	−	0.175799i
$443$	18.5199			0.879907			0.439953	−	0.898021i	$-0.354995\pi$
$443$	18.5199			0.879907			0.439953	+	0.898021i	$0.354995\pi$
$444$	5.07384	−	8.78815i	0.240794	−	0.417067i
$445$	−1.18261	+	2.04834i	−0.0560611	+	0.0971006i
$446$	−0.676415	−	1.17159i	−0.0320292	−	0.0554762i
$447$	−35.2184			−1.66577
$448$		0			0
$449$	−5.82155	−	10.0832i	−0.274736	−	0.475856i	0.695333	−	0.718688i	$-0.255257\pi$
$449$	−5.82155	−	10.0832i	−0.274736	−	0.475856i	−0.970068	+	0.242832i	$0.921924\pi$
$450$	−20.8590			−0.983301
$451$	−11.2870	−	19.5497i	−0.531485	−	0.920559i
$452$	3.10066	−	5.37050i	0.145843	−	0.252607i
$453$	7.02109	−	12.1609i	0.329880	−	0.571368i
$454$	5.29939			0.248713
$455$		0			0
$456$	−3.15328			−0.147666
$457$	−10.2592	+	17.7695i	−0.479906	+	0.831222i	−0.999734	−	0.0230490i	$-0.992663\pi$
$457$	−10.2592	+	17.7695i	−0.479906	+	0.831222i	0.519828	+	0.854271i	$0.325996\pi$
$458$	2.94845	−	5.10687i	0.137772	−	0.238629i
$459$	0.711453	+	1.23227i	0.0332078	+	0.0575176i
$460$	−1.17991			−0.0550136
$461$	1.02038	+	1.76734i	0.0475236	+	0.0823134i	0.888809	−	0.458278i	$-0.151534\pi$
$461$	1.02038	+	1.76734i	0.0475236	+	0.0823134i	−0.841285	+	0.540592i	$0.818200\pi$
$462$		0			0
$463$	3.03155			0.140888			0.0704441	−	0.997516i	$-0.477558\pi$
$463$	3.03155			0.140888			0.0704441	+	0.997516i	$0.477558\pi$
$464$	−19.7521	−	34.2116i	−0.916968	−	1.58824i
$465$	0.289926	−	0.502167i	0.0134450	−	0.0232874i
$466$	−12.4563	+	21.5749i	−0.577025	+	0.999436i
$467$	12.9274			0.598210			0.299105	−	0.954220i	$-0.403312\pi$
$467$	12.9274			0.598210			0.299105	+	0.954220i	$0.403312\pi$
$468$	−11.2048	+	3.86378i	−0.517943	+	0.178603i
$469$		0			0
$470$	−2.13879	+	3.70449i	−0.0986549	+	0.170875i
$471$	−5.20373	+	9.01312i	−0.239775	+	0.415303i
$472$	−3.08011	−	5.33491i	−0.141774	−	0.245559i
$473$	−22.2847			−1.02465
$474$	−22.8768	−	39.6238i	−1.05077	−	1.81998i
$475$	−3.35305	−	5.80766i	−0.153849	−	0.266474i
$476$		0			0
$477$	−5.25858	−	9.10814i	−0.240774	−	0.417033i
$478$	14.4507	−	25.0294i	0.660962	−	1.14482i
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	−0.0576873	−	0.998335i	$-0.518373\pi$
$479$	18.2911	−	31.6810i	0.835740	−	1.44754i	0.893427	−	0.449209i	$-0.148294\pi$
$480$	3.11328			0.142101
$481$	−10.3786	+	3.57888i	−0.473225	+	0.163183i
$482$	14.0769			0.641187
$483$		0			0
$484$	−4.71806	+	8.17191i	−0.214457	+	0.371451i
$485$	1.92159	+	3.32829i	0.0872550	+	0.151130i
$486$	36.0478			1.63516
$487$	−18.3748	−	31.8261i	−0.832642	−	1.44218i	−0.895936	−	0.444183i	$-0.853494\pi$
$487$	−18.3748	−	31.8261i	−0.832642	−	1.44218i	0.0632939	−	0.997995i	$-0.479839\pi$
$488$	5.77864	+	10.0089i	0.261587	+	0.453081i
$489$	−4.18103			−0.189073
$490$		0			0
$491$	4.09899	−	7.09965i	0.184985	−	0.320403i	−0.758587	−	0.651572i	$-0.774110\pi$
$491$	4.09899	−	7.09965i	0.184985	−	0.320403i	0.943571	+	0.331169i	$0.107443\pi$
$492$	−8.99331	+	15.5769i	−0.405450	+	0.702260i
$493$	6.93119			0.312165
$494$	−6.83757	−	5.93840i	−0.307637	−	0.267181i
$495$	−1.86793			−0.0839572
$496$	3.07048	−	5.31823i	0.137869	−	0.238795i
$497$		0			0
$498$	−6.55163	−	11.3478i	−0.293585	−	0.508505i
$499$	−43.2532			−1.93628			−0.968141	−	0.250407i	$-0.919436\pi$
$499$	−43.2532			−1.93628			−0.968141	+	0.250407i	$0.919436\pi$
$500$	1.42802	+	2.47340i	0.0638629	+	0.110614i
$501$	12.2824	+	21.2737i	0.548736	+	0.950439i
$502$	−2.36872			−0.105721
$503$	0.00909609	+	0.0157549i	0.000405575	+	0.000702476i	0.866228	−	0.499649i	$-0.166538\pi$
$503$	0.00909609	+	0.0157549i	0.000405575	+	0.000702476i	−0.865823	+	0.500351i	$0.833204\pi$
$504$		0			0
$505$	−1.67106	+	2.89436i	−0.0743612	+	0.128797i
$506$	31.9841			1.42187
$507$	27.6614	+	11.1469i	1.22848	+	0.495052i
$508$	−3.18190			−0.141174
$509$	21.5503	−	37.3262i	0.955200	−	1.65446i	0.221292	−	0.975208i	$-0.428973\pi$
$509$	21.5503	−	37.3262i	0.955200	−	1.65446i	0.733909	−	0.679248i	$-0.237694\pi$
$510$	−0.353897	+	0.612968i	−0.0156708	+	0.0271427i
$511$		0			0
$512$	23.2197			1.02617
$513$	1.14311	+	1.97993i	0.0504697	+	0.0874161i
$514$	−7.87878	−	13.6464i	−0.347518	−	0.601919i
$515$	1.42777			0.0629149
$516$	8.87804	+	15.3772i	0.390834	+	0.676944i
$517$	24.3939	−	42.2514i	1.07284	−	1.85822i
$518$		0			0
$519$	−30.9531			−1.35869
$520$	−0.546317	−	0.474474i	−0.0239576	−	0.0208071i
$521$	−20.9540			−0.918012			−0.459006	−	0.888433i	$-0.651794\pi$
$521$	−20.9540			−0.918012			−0.459006	+	0.888433i	$0.651794\pi$
$522$	17.3198	−	29.9988i	0.758068	−	1.31301i
$523$	−17.3701	+	30.0860i	−0.759543	+	1.31557i	0.183541	+	0.983012i	$0.441244\pi$
$523$	−17.3701	+	30.0860i	−0.759543	+	1.31557i	−0.943084	+	0.332555i	$0.892089\pi$
$524$	1.65333	+	2.86365i	0.0722260	+	0.125099i
$525$		0			0
$526$	−11.8814	−	20.5791i	−0.518052	−	0.897292i
$527$	0.538730	+	0.933107i	0.0234674	+	0.0406468i
$528$	−46.0104			−2.00235
$529$	3.03260	+	5.25262i	0.131852	+	0.228375i
$530$	−0.852276	+	1.47619i	−0.0370205	+	0.0641214i
$531$	6.85398	−	11.8714i	0.297438	−	0.515177i
$532$		0			0
$533$	18.3960	−	6.34352i	0.796819	−	0.274769i
$534$	−51.0854			−2.21068
$535$	0.972255	−	1.68400i	0.0420343	−	0.0728055i
$536$	6.81142	−	11.7977i	0.294209	−	0.509584i
$537$	12.0085	+	20.7993i	0.518205	+	0.897557i
$538$	8.75513			0.377460
$539$		0			0
$540$	−0.242466	−	0.419964i	−0.0104341	−	0.0180724i
$541$	−3.29846			−0.141812			−0.0709059	−	0.997483i	$-0.522589\pi$
$541$	−3.29846			−0.141812			−0.0709059	+	0.997483i	$0.522589\pi$
$542$	−16.7339	−	28.9839i	−0.718782	−	1.24497i
$543$	−14.3619	+	24.8756i	−0.616330	+	1.06752i
$544$	−2.89249	+	5.00993i	−0.124014	+	0.214799i
$545$	−2.72674			−0.116801
$546$		0			0
$547$	21.9417			0.938161			0.469080	−	0.883155i	$-0.344585\pi$
$547$	21.9417			0.938161			0.469080	+	0.883155i	$0.344585\pi$
$548$	−9.76836	+	16.9193i	−0.417284	+	0.722756i
$549$	−12.8589	+	22.2722i	−0.548803	+	0.950554i
$550$	−19.2791	−	33.3924i	−0.822065	−	1.42386i
$551$	11.1366			0.474434
$552$	4.79983	+	8.31354i	0.204294	+	0.353848i
$553$		0			0
$554$	−48.5368			−2.06213
$555$	0.689297	+	1.19390i	0.0292590	+	0.0506781i
$556$	2.93850	−	5.08963i	0.124620	−	0.215848i
$557$	7.14329	−	12.3725i	0.302671	−	0.524241i	−0.674069	−	0.738668i	$-0.735455\pi$
$557$	7.14329	−	12.3725i	0.302671	−	0.524241i	0.976740	+	0.214427i	$0.0687884\pi$
$558$	5.38476			0.227955
$559$	3.65686	−	18.8583i	0.154669	−	0.797621i
$560$		0			0
$561$	4.03637	−	6.99119i	0.170416	−	0.295168i
$562$	3.40226	−	5.89289i	0.143516	−	0.248577i
$563$	3.39392	+	5.87844i	0.143037	+	0.247747i	0.928639	−	0.370985i	$-0.120980\pi$
$563$	3.39392	+	5.87844i	0.143037	+	0.247747i	−0.785602	+	0.618732i	$0.787647\pi$
$564$	−38.8733			−1.63686
$565$	0.421234	+	0.729599i	0.0177215	+	0.0306945i
$566$	7.10307	+	12.3029i	0.298564	+	0.517128i
$567$		0			0
$568$	−3.03552	−	5.25767i	−0.127367	−	0.220607i
$569$	8.66061	−	15.0006i	0.363072	−	0.628859i	−0.625393	−	0.780310i	$-0.715061\pi$
$569$	8.66061	−	15.0006i	0.363072	−	0.628859i	0.988465	+	0.151451i	$0.0483947\pi$
$570$	−0.568618	+	0.984875i	−0.0238168	+	0.0412519i
$571$	−13.0116			−0.544520			−0.272260	−	0.962224i	$-0.587771\pi$
$571$	−13.0116			−0.544520			−0.272260	+	0.962224i	$0.587771\pi$
$572$	−16.5416	−	14.3663i	−0.691638	−	0.600685i
$573$	−30.0837			−1.25676
$574$		0			0
$575$	−10.2078	+	17.6805i	−0.425696	+	0.737327i
$576$	3.60574	+	6.24532i	0.150239	+	0.260222i
$577$	0.731535			0.0304542			0.0152271	−	0.999884i	$-0.495153\pi$
$577$	0.731535			0.0304542			0.0152271	+	0.999884i	$0.495153\pi$
$578$	15.1368	+	26.2177i	0.629607	+	1.09051i
$579$	1.19472	+	2.06931i	0.0496508	+	0.0859978i
$580$	−2.36218			−0.0980842
$581$		0			0
$582$	−41.5037	+	71.8865i	−1.72038	+	2.97979i
$583$	9.72061	−	16.8366i	0.402586	−	0.697300i
$584$	3.95096			0.163492
$585$	0.306522	−	1.58073i	0.0126731	−	0.0653550i
$586$	31.8738			1.31669
$587$	−4.26142	+	7.38099i	−0.175888	+	0.304646i	−0.940468	−	0.339882i	$-0.889613\pi$
$587$	−4.26142	+	7.38099i	−0.175888	+	0.304646i	0.764581	+	0.644528i	$0.222946\pi$
$588$		0			0
$589$	0.865594	+	1.49925i	0.0356662	+	0.0617756i
$590$	−2.22170			−0.0914657
$591$	1.69570	+	2.93704i	0.0697517	+	0.120814i
$592$	7.30004	+	12.6440i	0.300030	+	0.519667i
$593$	31.3093			1.28572			0.642860	−	0.765984i	$-0.277748\pi$
$593$	31.3093			1.28572			0.642860	+	0.765984i	$0.277748\pi$
$594$	6.57259	+	11.3841i	0.269677	+	0.467093i
$595$		0			0
$596$	−11.1514	+	19.3147i	−0.456777	+	0.791161i
$597$	32.3460			1.32383
$598$	−5.24850	+	27.0663i	−0.214627	+	1.10683i
$599$	−0.750232			−0.0306537			−0.0153268	−	0.999883i	$-0.504879\pi$
$599$	−0.750232			−0.0306537			−0.0153268	+	0.999883i	$0.504879\pi$
$600$	5.78641	−	10.0224i	0.236229	−	0.409161i
$601$	−4.77652	+	8.27318i	−0.194838	+	0.337470i	−0.946848	−	0.321683i	$-0.895752\pi$
$601$	−4.77652	+	8.27318i	−0.194838	+	0.337470i	0.752009	+	0.659153i	$0.229085\pi$
$602$		0			0
$603$	30.3141			1.23449
$604$	−4.44624	−	7.70111i	−0.180915	−	0.313354i
$605$	−0.640963	−	1.11018i	−0.0260588	−	0.0451352i
$606$	−72.1851			−2.93232
$607$	11.1197	+	19.2599i	0.451336	+	0.781737i	0.998469	−	0.0553087i	$-0.0176143\pi$
$607$	11.1197	+	19.2599i	0.451336	+	0.781737i	−0.547133	+	0.837045i	$0.684281\pi$
$608$	−4.64745	+	8.04961i	−0.188479	+	0.326455i
$609$		0			0
$610$	4.16815			0.168764
$611$	31.7521	+	27.5765i	1.28455	+	1.11563i
$612$	−2.76557			−0.111791
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	−0.770228	−	0.637769i	$-0.779857\pi$
$613$	4.13993	−	7.17057i	0.167210	−	0.289617i	0.937438	+	0.348152i	$0.113191\pi$
$614$	−26.0789	+	45.1699i	−1.05246	+	1.82291i
$615$	−1.22177	−	2.11617i	−0.0492665	−	0.0853321i
$616$		0			0
$617$	−10.1656	−	17.6073i	−0.409252	−	0.708845i	0.585554	−	0.810633i	$-0.300877\pi$
$617$	−10.1656	−	17.6073i	−0.409252	−	0.708845i	−0.994806	+	0.101789i	$0.967543\pi$
$618$	15.4189	+	26.7063i	0.620238	+	1.07428i
$619$	−5.34097			−0.214672			−0.107336	−	0.994223i	$-0.534232\pi$
$619$	−5.34097			−0.214672			−0.107336	+	0.994223i	$0.534232\pi$
$620$	−0.183601	−	0.318007i	−0.00737361	−	0.0127715i
$621$	3.48003	−	6.02758i	0.139649	−	0.241879i
$622$	−21.8651	+	37.8714i	−0.876709	+	1.51850i
$623$		0			0
$624$	7.55018	−	38.9360i	0.302249	−	1.55869i
$625$	24.4172			0.976690
$626$	−3.11112	+	5.38862i	−0.124345	+	0.215372i
$627$	6.48536	−	11.2330i	0.259000	−	0.448601i
$628$	3.29536	+	5.70773i	0.131499	+	0.227763i
$629$	−2.56165			−0.102140
$630$		0			0
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	0.794463	−	0.607312i	$-0.207752\pi$
$631$	−3.23331	−	5.60026i	−0.128716	−	0.222943i	−0.923179	+	0.384369i	$0.874419\pi$
$632$	10.9143			0.434147
$633$	30.3611	+	52.5870i	1.20675	+	2.09014i
$634$	6.76217	−	11.7124i	0.268560	−	0.465160i
$635$	0.216135	−	0.374357i	0.00857707	−	0.0148559i
$636$	−15.4904			−0.614236
$637$		0			0
$638$	64.0322			2.53506
$639$	6.75475	−	11.6996i	0.267214	−	0.462828i
$640$	−0.772706	+	1.33837i	−0.0305439	+	0.0529035i
$641$	−11.6644	−	20.2034i	−0.460717	−	0.797985i	0.538280	−	0.842766i	$-0.319074\pi$
$641$	−11.6644	−	20.2034i	−0.460717	−	0.797985i	−0.998997	+	0.0447808i	$0.985741\pi$
$642$	41.9987			1.65756
$643$	−1.79439	−	3.10797i	−0.0707637	−	0.122566i	0.828472	−	0.560030i	$-0.189210\pi$
$643$	−1.79439	−	3.10797i	−0.0707637	−	0.122566i	−0.899236	+	0.437463i	$0.855877\pi$
$644$		0			0
$645$	−2.41222			−0.0949810
$646$	−1.05658	−	1.83006i	−0.0415707	−	0.0720026i
$647$	−19.8262	+	34.3400i	−0.779448	+	1.35004i	0.152812	+	0.988255i	$0.451167\pi$
$647$	−19.8262	+	34.3400i	−0.779448	+	1.35004i	−0.932260	+	0.361788i	$0.882166\pi$
$648$	−5.42402	+	9.39467i	−0.213076	+	0.369058i
$649$	25.3395			0.994661
$650$	31.4218	−	10.8352i	1.23246	−	0.424993i
$651$		0			0
$652$	−1.32386	+	2.29299i	−0.0518464	+	0.0898005i
$653$	−9.06777	+	15.7058i	−0.354849	+	0.614617i	−0.987092	−	0.160153i	$-0.948801\pi$
$653$	−9.06777	+	15.7058i	−0.354849	+	0.614617i	0.632243	+	0.774770i	$0.282135\pi$
$654$	−29.4469	−	51.0035i	−1.15146	−	1.99439i
$655$	−0.449219			−0.0175525
$656$	−12.9392	−	22.4114i	−0.505192	−	0.875017i
$657$	4.39592	+	7.61395i	0.171501	+	0.297048i
$658$		0			0
$659$	−6.74052	−	11.6749i	−0.262573	−	0.454791i	0.704352	−	0.709851i	$-0.251238\pi$
$659$	−6.74052	−	11.6749i	−0.262573	−	0.454791i	−0.966925	+	0.255061i	$0.917905\pi$
$660$	−1.37561	+	2.38263i	−0.0535456	+	0.0927437i
$661$	5.15611	−	8.93064i	0.200549	−	0.347362i	−0.748156	−	0.663523i	$-0.769061\pi$
$661$	5.15611	−	8.93064i	0.200549	−	0.347362i	0.948706	+	0.316161i	$0.102394\pi$
$662$	−26.6151			−1.03443
$663$	5.25390	+	4.56299i	0.204044	+	0.177212i
$664$	3.12571			0.121301
$665$		0			0
$666$	−6.40111	+	11.0870i	−0.248038	+	0.429614i
$667$	−16.9517	−	29.3613i	−0.656374	−	1.13687i
$668$	15.5561			0.601884
$669$	0.835096	+	1.44643i	0.0322867	+	0.0559222i
$670$	−2.45655	−	4.25487i	−0.0949049	−	0.164380i
$671$	−47.5397			−1.83525
$672$		0			0
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	−0.763257	−	0.646095i	$-0.776401\pi$
$673$	4.61528	−	7.99390i	0.177906	−	0.308142i	0.941163	+	0.337953i	$0.109734\pi$
$674$	−15.9618	+	27.6467i	−0.614827	+	1.06491i
$675$	−8.39066			−0.322956
$676$	14.8718	−	11.6407i	0.571993	−	0.447721i
$677$	21.0934			0.810687			0.405343	−	0.914165i	$-0.367152\pi$
$677$	21.0934			0.810687			0.405343	+	0.914165i	$0.367152\pi$
$678$	−9.09807	+	15.7583i	−0.349409	+	0.605194i
$679$		0			0
$680$	−0.0844203	−	0.146220i	−0.00323737	−	0.00560729i
$681$	−6.54258			−0.250712
$682$	4.97693	+	8.62029i	0.190576	+	0.330088i
$683$	19.1106	+	33.1005i	0.731246	+	1.26656i	0.956351	+	0.292221i	$0.0943944\pi$
$683$	19.1106	+	33.1005i	0.731246	+	1.26656i	−0.225104	+	0.974335i	$0.572272\pi$
$684$	−4.44353			−0.169902
$685$	−1.32706	−	2.29854i	−0.0507044	−	0.0878226i
$686$		0			0
$687$	−3.64013	+	6.30490i	−0.138880	+	0.240547i
$688$	−25.5467			−0.973960
$689$	12.6527	+	10.9888i	0.482031	+	0.418642i
$690$	3.46213			0.131801
$691$	−13.1161	+	22.7178i	−0.498960	+	0.864224i	−0.999999	−	0.00120019i	$-0.999618\pi$
$691$	−13.1161	+	22.7178i	−0.498960	+	0.864224i	0.501039	+	0.865425i	$0.332951\pi$
$692$	−9.80084	+	16.9755i	−0.372572	+	0.645313i
$693$		0			0
$694$	−14.3130			−0.543314
$695$	0.399204	+	0.691442i	0.0151427	+	0.0262279i
$696$	9.60925	+	16.6437i	0.364238	+	0.630878i
$697$	4.54049			0.171983
$698$	20.7836	+	35.9982i	0.786670	+	1.36255i
$699$	15.3784	−	26.6361i	0.581664	−	1.00747i
$700$		0			0
$701$	−46.7346			−1.76514			−0.882570	−	0.470180i	$-0.844189\pi$
$701$	−46.7346			−1.76514			−0.882570	+	0.470180i	$0.844189\pi$
$702$	−10.7122	+	3.69392i	−0.404307	+	0.139418i
$703$	−4.11588			−0.155233
$704$	−6.66528	+	11.5446i	−0.251207	+	0.435104i
$705$	2.64053	−	4.57353i	0.0994480	−	0.172249i
$706$	−20.6835	−	35.8248i	−0.778433	−	1.34828i
$707$		0			0
$708$	−10.0950	−	17.4851i	−0.379395	−	0.657131i
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.838745	+	0.544524i	$0.183290\pi$
$709$	23.7232	+	41.0898i	0.890944	+	1.54316i	0.0521988	+	0.998637i	$0.483377\pi$
$710$	−2.18953			−0.0821715
$711$	12.1435	+	21.0331i	0.455415	+	0.788802i
$712$	6.09307	−	10.5535i	0.228348	−	0.395510i
$713$	2.63516	−	4.56423i	0.0986876	−	0.170932i
$714$		0			0
$715$	2.81384	−	0.970301i	0.105232	−	0.0362872i
$716$	15.2092			0.568395
$717$	−17.8408	+	30.9011i	−0.666275	+	1.15402i
$718$	2.56280	−	4.43890i	0.0956428	−	0.165658i
$719$	−24.6190	−	42.6413i	−0.918133	−	1.59025i	−0.802249	−	0.596990i	$-0.796363\pi$
$719$	−24.6190	−	42.6413i	−0.918133	−	1.59025i	−0.115884	−	0.993263i	$-0.536970\pi$
$720$	−2.14136			−0.0798037
$721$		0			0
$722$	15.9549	+	27.6347i	0.593779	+	1.02846i
$723$	−17.3793			−0.646342
$724$	9.09498	+	15.7530i	0.338012	+	0.585454i
$725$	−20.4361	+	35.3963i	−0.758977	+	1.31459i
$726$	13.8439	−	23.9783i	0.513795	−	0.889919i
$727$	32.0495			1.18865			0.594325	−	0.804225i	$-0.297419\pi$
$727$	32.0495			1.18865			0.594325	+	0.804225i	$0.297419\pi$
$728$		0			0
$729$	−12.4996			−0.462947
$730$	0.712460	−	1.23402i	0.0263693	−	0.0456730i
$731$	2.24114	−	3.88178i	0.0828917	−	0.143573i
$732$	18.9394	+	32.8041i	0.700022	+	1.21247i
$733$	−28.2010			−1.04163			−0.520813	−	0.853670i	$-0.674371\pi$
$733$	−28.2010			−1.04163			−0.520813	+	0.853670i	$0.674371\pi$
$734$	−13.1462	−	22.7699i	−0.485236	−	0.840453i
$735$		0			0
$736$	28.2968			1.04303
$737$	28.0181	+	48.5288i	1.03206	+	1.78758i
$738$	11.3459	−	19.6516i	0.417648	−	0.723387i
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	−0.148180	−	0.988960i	$-0.547342\pi$
$739$	21.2685	−	36.8381i	0.782375	−	1.35511i	0.930555	−	0.366153i	$-0.119325\pi$
$740$	0.873021			0.0320929
$741$	8.44160	+	7.33149i	0.310110	+	0.269329i
$742$		0			0
$743$	−7.95711	+	13.7821i	−0.291918	+	0.505617i	−0.974263	−	0.225413i	$-0.927627\pi$
$743$	−7.95711	+	13.7821i	−0.291918	+	0.505617i	0.682345	+	0.731030i	$0.260960\pi$
$744$	−1.49377	+	2.58728i	−0.0547641	+	0.0948543i
$745$	−1.51495	−	2.62396i	−0.0555033	−	0.0961346i
$746$	−9.37042			−0.343075
$747$	3.47773	+	6.02360i	0.127243	+	0.220392i
$748$	−2.55611	−	4.42731i	−0.0934605	−	0.161878i
$749$		0			0
$750$	−4.19014	−	7.25754i	−0.153002	−	0.265008i
$751$	−9.09981	+	15.7613i	−0.332057	+	0.575139i	−0.982915	−	0.184060i	$-0.941076\pi$
$751$	−9.09981	+	15.7613i	−0.332057	+	0.575139i	0.650858	+	0.759199i	$0.274409\pi$
$752$	27.9646	−	48.4362i	1.01977	−	1.76629i
$753$	2.92440			0.106571
$754$	−10.5075	+	54.1868i	−0.382661	+	1.97337i
$755$	1.20807			0.0439662
$756$		0			0
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	−0.0926649	−	0.995697i	$-0.529539\pi$
$757$	22.4502	−	38.8849i	0.815967	−	1.41330i	0.908632	−	0.417598i	$-0.137128\pi$
$758$	5.62989	+	9.75126i	0.204487	+	0.354182i
$759$	−39.4872			−1.43330
$760$	−0.135641	−	0.234937i	−0.00492021	−	0.00852205i
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	0.519631	−	0.854391i	$-0.326069\pi$
$761$	−13.2444	−	22.9399i	−0.480108	−	0.831572i	−0.999740	+	0.0228184i	$0.992736\pi$
$762$	9.33644			0.338223
$763$		0			0
$764$	−9.52554	+	16.4987i	−0.344622	+	0.596903i
$765$	0.187856	−	0.325375i	0.00679193	−	0.0117640i
$766$	8.43800			0.304877
$767$	−4.15814	+	21.4434i	−0.150142	+	0.774276i
$768$	−48.0013			−1.73210
$769$	6.98127	−	12.0919i	0.251751	−	0.436045i	−0.712257	−	0.701919i	$-0.752327\pi$
$769$	6.98127	−	12.0919i	0.251751	−	0.436045i	0.964008	+	0.265873i	$0.0856603\pi$
$770$		0			0
$771$	9.72707	+	16.8478i	0.350312	+	0.606758i
$772$	1.51316			0.0544597
$773$	6.40564	+	11.0949i	0.230395	+	0.399056i	0.957924	−	0.287021i	$-0.0926648\pi$
$773$	6.40564	+	11.0949i	0.230395	+	0.399056i	−0.727529	+	0.686077i	$0.759332\pi$
$774$	−11.2005	−	19.3998i	−0.402592	−	0.697310i
$775$	−6.35361			−0.228228
$776$	−9.90048	−	17.1481i	−0.355406	−	0.615582i
$777$		0			0
$778$	−4.18797	+	7.25378i	−0.150146	+	0.260061i
$779$	7.29534			0.261383
$780$	−1.79055	−	1.55509i	−0.0641120	−	0.0556810i
$781$	24.9726			0.893590
$782$	−3.21660	+	5.57132i	−0.115025	+	0.199230i
$783$	6.96701	−	12.0672i	0.248981	−	0.431247i
$784$		0			0
$785$	−0.895370			−0.0319571
$786$	−4.85125	−	8.40262i	−0.173039	−	0.299712i
$787$	−13.6599	−	23.6597i	−0.486924	−	0.843377i	0.512963	−	0.858411i	$-0.328548\pi$
$787$	−13.6599	−	23.6597i	−0.486924	−	0.843377i	−0.999887	+	0.0150334i	$0.995215\pi$
$788$	2.14767			0.0765075
$789$	14.6686	+	25.4068i	0.522217	+	0.904506i
$790$	1.96813	−	3.40890i	0.0700229	−	0.121283i
$791$		0			0
$792$	9.62401			0.341974
$793$	7.80114	−	40.2302i	0.277027	−	1.42862i
$794$	−7.43912			−0.264005
$795$	1.05221	−	1.82248i	0.0373181	−	0.0646369i
$796$	10.2419	−	17.7394i	0.363013	−	0.628758i
$797$	−14.7002	−	25.4614i	−0.520707	−	0.901891i	−0.999710	−	0.0240775i	$-0.992335\pi$
$797$	−14.7002	−	25.4614i	−0.520707	−	0.901891i	0.479003	−	0.877813i	$-0.340998\pi$
$798$		0			0
$799$	4.90652	+	8.49835i	0.173580	+	0.300650i
$800$	−17.0565	−	29.5428i	−0.603040	−	1.04450i
$801$	27.1171			0.958136
$802$	−11.7189	−	20.2978i	−0.413810	−	0.716740i
$803$	−8.12594	+	14.0745i	−0.286758	+	0.496680i
$804$	22.3244	−	38.6669i	0.787320	−	1.36368i
$805$		0			0
$806$	−8.11157	+	2.79713i	−0.285718	+	0.0985246i
$807$	−10.8090			−0.380495
$808$	8.60968	−	14.9124i	0.302888	−	0.524617i
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	−0.808329	−	0.588731i	$-0.799628\pi$
$809$	3.00617	−	5.20683i	0.105691	−	0.183063i	0.914020	+	0.405668i	$0.132961\pi$
$810$	1.95618	+	3.38821i	0.0687332	+	0.119049i
$811$	−8.44807			−0.296652			−0.148326	−	0.988939i	$-0.547388\pi$
$811$	−8.44807			−0.296652			−0.148326	+	0.988939i	$0.547388\pi$
$812$		0			0
$813$	20.6595	+	35.7833i	0.724560	+	1.25497i
$814$	−23.6652			−0.829464
$815$	−0.179850	−	0.311510i	−0.00629989	−	0.0109117i
$816$	4.62721	−	8.01456i	0.161985	−	0.280566i
$817$	3.60092	−	6.23697i	0.125980	−	0.218204i
$818$	−38.4551			−1.34455
$819$		0			0
$820$	−1.54742			−0.0540382
$821$	17.1318	−	29.6731i	0.597903	−	1.03560i	−0.395228	−	0.918583i	$-0.629334\pi$
$821$	17.1318	−	29.6731i	0.597903	−	1.03560i	0.993130	−	0.117014i	$-0.0373324\pi$
$822$	28.6627	−	49.6452i	0.999725	−	1.73157i
$823$	3.11866	+	5.40168i	0.108710	+	0.188291i	0.915248	−	0.402891i	$-0.131995\pi$
$823$	3.11866	+	5.40168i	0.108710	+	0.188291i	−0.806538	+	0.591182i	$0.798661\pi$
$824$	−7.35618			−0.256265
$825$	23.8018	+	41.2260i	0.828673	+	1.43530i
$826$		0			0
$827$	19.5232			0.678889			0.339445	−	0.940626i	$-0.389761\pi$
$827$	19.5232			0.678889			0.339445	+	0.940626i	$0.389761\pi$
$828$	6.76380	+	11.7152i	0.235058	+	0.407133i
$829$	16.3383	−	28.2988i	0.567453	−	0.982857i	−0.429364	−	0.903131i	$-0.641262\pi$
$829$	16.3383	−	28.2988i	0.567453	−	0.982857i	0.996817	−	0.0797254i	$-0.0254043\pi$
$830$	0.563647	−	0.976265i	0.0195645	−	0.0338866i
$831$	59.9230			2.07871
$832$	−8.67580	−	7.53489i	−0.300779	−	0.261225i
$833$		0			0
$834$	−8.62225	+	14.9342i	−0.298564	+	0.517128i
$835$	−1.05667	+	1.83021i	−0.0365677	+	0.0633370i
$836$	−4.10698	−	7.11349i	−0.142043	−	0.246025i
$837$	2.16606			0.0748698
$838$	−20.2702	−	35.1091i	−0.700223	−	1.21282i
$839$	12.3713	+	21.4278i	0.427106	+	0.739769i	0.996615	−	0.0822161i	$-0.0261998\pi$
$839$	12.3713	+	21.4278i	0.427106	+	0.739769i	−0.569508	+	0.821985i	$0.692866\pi$
$840$		0			0
$841$	−19.4374	−	33.6665i	−0.670255	−	1.16092i
$842$	−8.75869	+	15.1705i	−0.301844	+	0.522810i
$843$	−4.20040	+	7.27531i	−0.144669	+	0.250575i
$844$	38.4535			1.32362
$845$	0.359368	+	2.54042i	0.0123626	+	0.0873930i
$846$	49.0422			1.68610
$847$		0			0
$848$	11.1435	−	19.3011i	0.382670	−	0.662803i
$849$	−8.76938	−	15.1890i	−0.300964	−	0.521285i
$850$	7.75551			0.266012
$851$	6.26507	+	10.8514i	0.214764	+	0.371982i
$852$	−9.94888	−	17.2320i	−0.340843	−	0.590357i
$853$	−18.2245			−0.623994			−0.311997	−	0.950083i	$-0.600998\pi$
$853$	−18.2245			−0.623994			−0.311997	+	0.950083i	$0.600998\pi$
$854$		0			0
$855$	0.301833	−	0.522791i	0.0103225	−	0.0178791i
$856$	−5.00928	+	8.67633i	−0.171214	+	0.296551i
$857$	−2.54679			−0.0869967			−0.0434984	−	0.999053i	$-0.513850\pi$
$857$	−2.54679			−0.0869967			−0.0434984	+	0.999053i	$0.513850\pi$
$858$	48.5369	+	42.1541i	1.65702	+	1.43912i
$859$	−54.0090			−1.84276			−0.921382	−	0.388657i	$-0.872939\pi$
$859$	−54.0090			−1.84276			−0.921382	+	0.388657i	$0.872939\pi$
$860$	−0.763792	+	1.32293i	−0.0260451	+	0.0451114i
$861$		0			0
$862$	−18.9788	−	32.8723i	−0.646421	−	1.11963i
$863$	1.24309			0.0423153			0.0211576	−	0.999776i	$-0.493265\pi$
$863$	1.24309			0.0423153			0.0211576	+	0.999776i	$0.493265\pi$
$864$	5.81487	+	10.0716i	0.197826	+	0.342644i
$865$	−1.33147	−	2.30618i	−0.0452715	−	0.0784125i
$866$	−48.9600			−1.66373
$867$	−18.6877	−	32.3681i	−0.634668	−	1.09928i
$868$		0			0
$869$	−22.4474	+	38.8801i	−0.761477	+	1.31892i
$870$	6.93119			0.234989
$871$	−45.6649	+	15.7467i	−1.54730	+	0.533557i
$872$	14.0488			0.475752
$873$	22.0309	−	38.1587i	0.745634	−	1.29148i
$874$	−5.16821	+	8.95161i	−0.174817	+	0.302793i
$875$		0			0
$876$	12.9492			0.437514
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	0.859170	−	0.511690i	$-0.170981\pi$
$877$	−0.401330	−	0.695125i	−0.0135520	−	0.0234727i	−0.872722	+	0.488218i	$0.837647\pi$
$878$	23.3488	+	40.4412i	0.787983	+	1.36483i
$879$	−39.3511			−1.32728
$880$	−1.97917	−	3.42803i	−0.0667179	−	0.115559i
$881$	−18.5318	+	32.0980i	−0.624352	+	1.08141i	0.364314	+	0.931276i	$0.381304\pi$
$881$	−18.5318	+	32.0980i	−0.624352	+	1.08141i	−0.988666	+	0.150133i	$0.952030\pi$
$882$		0			0
$883$	−22.8671			−0.769539			−0.384770	−	0.923013i	$-0.625719\pi$
$883$	−22.8671			−0.769539			−0.384770	+	0.923013i	$0.625719\pi$
$884$	4.16603	−	1.43658i	0.140119	−	0.0483174i
$885$	2.74288			0.0922010
$886$	−17.2065	+	29.8025i	−0.578063	+	1.00123i
$887$	−24.6287	+	42.6581i	−0.826950	+	1.43232i	0.0734699	+	0.997297i	$0.476593\pi$
$887$	−24.6287	+	42.6581i	−0.826950	+	1.43232i	−0.900420	+	0.435022i	$0.856741\pi$
$888$	−3.55141	−	6.15123i	−0.119178	−	0.206422i
$889$		0			0
$890$	−2.19748	−	3.80614i	−0.0736597	−	0.127582i
$891$	−22.3112	−	38.6441i	−0.747452	−	1.29463i
$892$	1.05768			0.0354138
$893$	7.88347	+	13.6546i	0.263810	+	0.456932i
$894$	32.7207	−	56.6739i	1.09434	−	1.89546i
$895$	−1.03311	+	1.78940i	−0.0345330	+	0.0598130i
$896$		0			0
$897$	6.47975	−	33.4159i	0.216353	−	1.11572i
$898$	21.6347			0.721961
$899$	5.27559	−	9.13760i	0.175951	−	0.304756i
$900$	8.15406	−	14.1233i	0.271802	−	0.470775i
$901$	1.95518	+	3.38647i	0.0651365	+	0.112820i
$902$	41.9462			1.39666
$903$		0			0
$904$	−2.17029	−	3.75906i	−0.0721829	−	0.125024i
$905$	−2.47116			−0.0821442
$906$	13.0463	+	22.5969i	0.433435	+	0.750731i
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	−0.821488	−	0.570226i	$-0.806855\pi$
$907$	2.50228	−	4.33407i	0.0830867	−	0.143910i	0.904574	+	0.426316i	$0.140189\pi$
$908$	−2.07161	+	3.58813i	−0.0687487	+	0.119076i
$909$	38.3172			1.27090
$910$		0			0
$911$	49.0582			1.62537			0.812685	−	0.582703i	$-0.198005\pi$
$911$	49.0582			1.62537			0.812685	+	0.582703i	$0.198005\pi$
$912$	7.43468	−	12.8772i	0.246187	−	0.426408i
$913$	−6.42866	+	11.1348i	−0.212757	+	0.368507i
$914$	−19.0633	−	33.0186i	−0.630557	−	1.09216i
$915$	−5.14596			−0.170120
$916$	2.30518	+	3.99270i	0.0761654	+	0.131922i
$917$		0			0
$918$	−2.64399			−0.0872646
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	0.511611	−	0.859217i	$-0.329049\pi$
$919$	−14.8028	−	25.6392i	−0.488299	−	0.845758i	−0.999909	+	0.0134590i	$0.995716\pi$
$920$	−0.412937	+	0.715227i	−0.0136141	+	0.0235803i
$921$	32.1967	−	55.7664i	1.06092	−	1.83756i
$922$	−3.79205			−0.124884
$923$	−4.09794	+	21.1329i	−0.134885	+	0.695598i
$924$		0			0
$925$	7.55282	−	13.0819i	0.248335	−	0.430129i
$926$	−2.81656	+	4.87842i	−0.0925578	+	0.160315i
$927$	−8.18464	−	14.1762i	−0.268819	−	0.465608i
$928$	56.6502			1.85963
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	0.970411	−	0.241460i	$-0.0776261\pi$
$929$	8.41525	+	14.5756i	0.276095	+	0.478211i	−0.694316	+	0.719671i	$0.744293\pi$
$930$	0.538730	+	0.933107i	0.0176656	+	0.0305978i
$931$		0			0
$932$	−9.73865	−	16.8678i	−0.319000	−	0.552524i
$933$	26.9944	−	46.7557i	0.883757	−	1.53071i
$934$	−12.0106	+	20.8030i	−0.392999	+	0.680695i
$935$	0.694510			0.0227129
$936$	−1.57927	+	8.14426i	−0.0516202	+	0.266203i
$937$	−44.0131			−1.43784			−0.718922	−	0.695091i	$-0.755364\pi$
$937$	−44.0131			−1.43784			−0.718922	+	0.695091i	$0.755364\pi$
$938$		0			0
$939$	3.84096	−	6.65273i	0.125345	−	0.217104i
$940$	−1.67216	−	2.89627i	−0.0545400	−	0.0944660i
$941$	−53.0675			−1.72995			−0.864976	−	0.501814i	$-0.832666\pi$
$941$	−53.0675			−1.72995			−0.864976	+	0.501814i	$0.832666\pi$
$942$	−9.66937	−	16.7478i	−0.315045	−	0.545674i
$943$	−11.1048	−	19.2340i	−0.361620	−	0.626345i
$944$	29.0487			0.945453
$945$		0			0
$946$	20.7043	−	35.8609i	0.673154	−	1.16594i
$947$	13.9409	−	24.1463i	0.453017	−	0.784649i	−0.545555	−	0.838075i	$-0.683681\pi$
$947$	13.9409	−	24.1463i	0.453017	−	0.784649i	0.998572	+	0.0534265i	$0.0170143\pi$
$948$	35.7715			1.16180
$949$	−10.5771	−	9.18613i	−0.343346	−	0.298194i
$950$	12.4610			0.404289
$951$	−8.34851	+	14.4600i	−0.270719	+	0.468899i
$952$		0			0
$953$	18.1784	+	31.4859i	0.588856	+	1.01993i	0.994383	+	0.105845i	$0.0337548\pi$
$953$	18.1784	+	31.4859i	0.588856	+	1.01993i	−0.405527	+	0.914083i	$0.632912\pi$
$954$	19.5426			0.632715
$955$	−1.29407	−	2.24140i	−0.0418753	−	0.0725301i
$956$	11.2980	+	19.5687i	0.365403	+	0.632897i
$957$	−79.0535			−2.55544
$958$	33.9877	+	58.8685i	1.09809	+	1.90195i
$959$		0			0
$960$	−0.721486	+	1.24965i	−0.0232859	+	0.0403323i
$961$	−29.3598			−0.947091
$962$	3.88339	−	20.0265i	0.125206	−	0.645681i
$963$	−22.2937			−0.718405
$964$	−5.50287	+	9.53126i	−0.177236	+	0.306981i
$965$	−0.102784	+	0.178026i	−0.00330872	+	0.00573087i
$966$		0			0
$967$	−15.2681			−0.490988			−0.245494	−	0.969398i	$-0.578950\pi$
$967$	−15.2681			−0.490988			−0.245494	+	0.969398i	$0.578950\pi$
$968$	3.30239	+	5.71990i	0.106143	+	0.183845i
$969$	1.30445	+	2.25937i	0.0419049	+	0.0725815i
$970$	−7.14125			−0.229292
$971$	−18.4460	−	31.9494i	−0.591961	−	1.02531i	−0.993968	−	0.109669i	$-0.965021\pi$
$971$	−18.4460	−	31.9494i	−0.591961	−	1.02531i	0.402008	−	0.915636i	$-0.368313\pi$
$972$	−14.0916	+	24.4073i	−0.451987	+	0.782865i
$973$		0			0
$974$	68.2867			2.18805
$975$	−38.7931	+	13.3771i	−1.24237	+	0.428410i
$976$	−54.4986			−1.74446
$977$	0.221957	−	0.384441i	0.00710104	−	0.0122994i	−0.862453	−	0.506137i	$-0.831073\pi$
$977$	0.221957	−	0.384441i	0.00710104	−	0.0122994i	0.869554	+	0.493838i	$0.164406\pi$
$978$	3.88452	−	6.72818i	0.124213	−	0.215144i
$979$	25.0633	+	43.4109i	0.801026	+	1.38742i
$980$		0			0
$981$	15.6310	+	27.0736i	0.499058	+	0.864394i
$982$	7.61658	+	13.1923i	0.243055	+	0.420983i
$983$	−45.5603			−1.45315			−0.726575	−	0.687088i	$-0.758889\pi$
$983$	−45.5603			−1.45315			−0.726575	+	0.687088i	$0.758889\pi$
$984$	6.29483	+	10.9030i	0.200672	+	0.347574i
$985$	−0.145884	+	0.252678i	−0.00464824	+	0.00805099i
$986$	−6.43964	+	11.1538i	−0.205080	+	0.355209i
$987$		0			0
$988$	6.69369	−	2.30820i	0.212955	−	0.0734336i
$989$	−21.9248			−0.697169
$990$	1.73546	−	3.00590i	0.0551565	−	0.0955338i
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	0.0277842	+	0.999614i	$0.491155\pi$
$991$	−26.8148	+	46.4445i	−0.851799	+	1.47536i	−0.879583	+	0.475745i	$0.842178\pi$
$992$	4.40316	+	7.62650i	0.139801	+	0.242142i
$993$	32.8588			1.04274
$994$		0			0
$995$	1.39139	+	2.40996i	0.0441100	+	0.0764008i
$996$	10.2445			0.324609
$997$	14.5426	+	25.1886i	0.460569	+	0.797730i	0.998989	−	0.0449470i	$-0.0143119\pi$
$997$	14.5426	+	25.1886i	0.460569	+	0.797730i	−0.538420	+	0.842677i	$0.680979\pi$
$998$	40.1857	−	69.6038i	1.27206	−	2.20327i
$999$	−2.57489	+	4.45984i	−0.0814658	+	0.141103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.j.295.1		12
7.2	even	3		637.2.h.l.165.6		12
7.3	odd	6		91.2.g.b.9.1	✓	12
7.4	even	3		637.2.g.l.373.1		12
7.5	odd	6		91.2.h.b.74.6	yes	12
7.6	odd	2		637.2.f.k.295.1		12
13.3	even	3	inner	637.2.f.j.393.1		12
13.4	even	6		8281.2.a.cf.1.1		6
13.9	even	3		8281.2.a.ca.1.6		6
21.5	even	6		819.2.s.d.802.1		12
21.17	even	6		819.2.n.d.100.6		12
91.3	odd	6		91.2.h.b.16.6	yes	12
91.16	even	3		637.2.g.l.263.1		12
91.17	odd	6		1183.2.e.g.170.6		12
91.48	odd	6		8281.2.a.bz.1.6		6
91.55	odd	6		637.2.f.k.393.1		12
91.61	odd	6		1183.2.e.h.508.1		12
91.68	odd	6		91.2.g.b.81.1	yes	12
91.69	odd	6		8281.2.a.ce.1.1		6
91.81	even	3		637.2.h.l.471.6		12
91.82	odd	6		1183.2.e.g.508.6		12
91.87	odd	6		1183.2.e.h.170.1		12
273.68	even	6		819.2.n.d.172.6		12
273.185	even	6		819.2.s.d.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.1	✓	12	7.3	odd	6
91.2.g.b.81.1	yes	12	91.68	odd	6
91.2.h.b.16.6	yes	12	91.3	odd	6
91.2.h.b.74.6	yes	12	7.5	odd	6
637.2.f.j.295.1		12	1.1	even	1	trivial
637.2.f.j.393.1		12	13.3	even	3	inner
637.2.f.k.295.1		12	7.6	odd	2
637.2.f.k.393.1		12	91.55	odd	6
637.2.g.l.263.1		12	91.16	even	3
637.2.g.l.373.1		12	7.4	even	3
637.2.h.l.165.6		12	7.2	even	3
637.2.h.l.471.6		12	91.81	even	3
819.2.n.d.100.6		12	21.17	even	6
819.2.n.d.172.6		12	273.68	even	6
819.2.s.d.289.1		12	273.185	even	6
819.2.s.d.802.1		12	21.5	even	6
1183.2.e.g.170.6		12	91.17	odd	6
1183.2.e.g.508.6		12	91.82	odd	6
1183.2.e.h.170.1		12	91.87	odd	6
1183.2.e.h.508.1		12	91.61	odd	6
8281.2.a.bz.1.6		6	91.48	odd	6
8281.2.a.ca.1.6		6	13.9	even	3
8281.2.a.ce.1.1		6	91.69	odd	6
8281.2.a.cf.1.1		6	13.4	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.929081 + 1.60921i) q^{2} +(1.14703 - 1.98672i) q^{3} +(-0.726381 - 1.25813i) q^{4} +0.197362 q^{5} +(2.13137 + 3.69165i) q^{6} -1.01686 q^{8} +(-1.13137 - 1.95960i) q^{9} +(-0.183365 + 0.317598i) q^{10} +(2.09137 - 3.62236i) q^{11} -3.33274 q^{12} +(2.72221 + 2.36423i) q^{13} +(0.226381 - 0.392104i) q^{15} +(2.39750 - 4.15260i) q^{16} +(0.420653 + 0.728592i) q^{17} +4.20455 q^{18} +(0.675876 + 1.17065i) q^{19} +(-0.143360 - 0.248307i) q^{20} +(3.88610 + 6.73092i) q^{22} +(2.05760 - 3.56386i) q^{23} +(-1.16637 + 2.02021i) q^{24} -4.96105 q^{25} +(-6.33370 + 2.18406i) q^{26} +1.69131 q^{27} +(4.11931 - 7.13485i) q^{29} +(0.420653 + 0.728592i) q^{30} +1.28070 q^{31} +(3.43809 + 5.95495i) q^{32} +(-4.79774 - 8.30993i) q^{33} -1.56328 q^{34} +(-1.64362 + 2.84683i) q^{36} +(-1.52242 + 2.63692i) q^{37} -2.51177 q^{38} +(7.81953 - 2.69642i) q^{39} -0.200689 q^{40} +(2.69848 - 4.67390i) q^{41} +(-2.66389 - 4.61399i) q^{43} -6.07652 q^{44} +(-0.223290 - 0.386750i) q^{45} +(3.82334 + 6.62223i) q^{46} +11.6641 q^{47} +(-5.50003 - 9.52634i) q^{48} +(4.60921 - 7.98339i) q^{50} +1.93001 q^{51} +(0.997141 - 5.14222i) q^{52} +4.64796 q^{53} +(-1.57136 + 2.72168i) q^{54} +(0.412757 - 0.714916i) q^{55} +3.10101 q^{57} +(7.65434 + 13.2577i) q^{58} +(3.02905 + 5.24648i) q^{59} -0.657756 q^{60} +(-5.68285 - 9.84298i) q^{61} +(-1.18987 + 2.06092i) q^{62} -3.18704 q^{64} +(0.537262 + 0.466609i) q^{65} +17.8300 q^{66} +(-6.69851 + 11.6022i) q^{67} +(0.611109 - 1.05847i) q^{68} +(-4.72026 - 8.17574i) q^{69} +(2.98520 + 5.17051i) q^{71} +(1.15044 + 1.99263i) q^{72} -3.88547 q^{73} +(-2.82891 - 4.89982i) q^{74} +(-5.69049 + 9.85622i) q^{75} +(0.981887 - 1.70068i) q^{76} +(-2.92585 + 15.0885i) q^{78} -10.7334 q^{79} +(0.473177 - 0.819566i) q^{80} +(5.33411 - 9.23895i) q^{81} +(5.01421 + 8.68486i) q^{82} -3.07390 q^{83} +(0.0830210 + 0.143797i) q^{85} +9.89987 q^{86} +(-9.44997 - 16.3678i) q^{87} +(-2.12662 + 3.68341i) q^{88} +(-5.99207 + 10.3786i) q^{89} +0.829819 q^{90} -5.97840 q^{92} +(1.46901 - 2.54439i) q^{93} +(-10.8369 + 18.7700i) q^{94} +(0.133392 + 0.231042i) q^{95} +15.7744 q^{96} +(9.73637 + 16.8639i) q^{97} -9.46448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - q^{3} - 4 q^{4} + 2 q^{5} + 9 q^{6} - 6 q^{8} + 3 q^{9} - 4 q^{10} + 4 q^{11} + 10 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} - 6 q^{18} + q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - q^3 - 4 * q^4 + 2 * q^5 + 9 * q^6 - 6 * q^8 + 3 * q^9 - 4 * q^10 + 4 * q^11 + 10 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 - 6 * q^18 + q^19 + q^20 - 5 * q^22 - q^23 + 11 * q^24 - 14 * q^25 - 11 * q^26 + 8 * q^27 + 3 * q^29 - 5 * q^30 + 32 * q^31 + 8 * q^32 - 16 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 - 34 * q^38 + 43 * q^39 - 10 * q^40 + 8 * q^41 - 11 * q^43 - 42 * q^44 + 7 * q^45 + 16 * q^46 - 2 * q^47 - 21 * q^48 + 6 * q^50 + 40 * q^51 + 16 * q^52 + 4 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 - 8 * q^58 - 13 * q^59 - 40 * q^60 + 5 * q^61 - 5 * q^62 - 30 * q^64 - 14 * q^65 + 36 * q^66 - 11 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 + 25 * q^72 - 60 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 - 14 * q^79 + 7 * q^80 - 6 * q^81 - q^82 + 54 * q^83 - q^85 + 14 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 - 45 * q^94 - 6 * q^95 + 38 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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