LMFDB - Embedded newform 637.2.k.h.569.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(459,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.459"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,-8,6] 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 $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.4
Root			$-1.08105 + 0.911778i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.h.459.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.823556i q^{2} +(-1.33015 + 2.30388i) q^{3} +1.32176 q^{4} +(2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +(-2.03858 - 3.53092i) q^{9} +(-1.30208 + 2.25527i) q^{10} +(-5.14653 - 2.97135i) q^{11} +(-1.75813 + 3.04517i) q^{12} +(-0.0766193 + 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +0.390549 q^{16} +2.69964 q^{17} +(2.90791 - 1.67888i) q^{18} +(-1.69485 + 0.978524i) q^{19} +(3.61956 + 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +2.72941 q^{23} +(-6.30261 - 3.63882i) q^{24} +(2.49941 + 4.32911i) q^{25} +(-2.96870 - 0.0631003i) q^{26} +2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +(-3.46391 - 5.99967i) q^{30} +(-0.997270 + 0.575774i) q^{31} +5.79294i q^{32} +(13.6913 - 7.90465i) q^{33} +2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} -6.50454i q^{37} +(-0.805869 - 1.39581i) q^{38} +(-8.20297 - 4.97135i) q^{39} +(-4.32519 + 7.49145i) q^{40} +(-3.23351 + 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +(-6.80245 - 3.92740i) q^{44} -12.8923i q^{45} +2.24783i q^{46} +(-0.394969 - 0.228035i) q^{47} +(-0.519487 + 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +(-3.59092 + 6.21965i) q^{51} +(-0.101272 + 4.76458i) q^{52} +(-0.199643 - 0.345792i) q^{53} +2.35994i q^{54} +(-9.39568 - 16.2738i) q^{55} -5.20632i q^{57} +(-4.27822 + 2.47003i) q^{58} -4.80586i q^{59} +(-9.62910 + 5.55936i) q^{60} +(0.578514 + 1.00201i) q^{61} +(-0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.90907 + 9.75026i) q^{65} +(6.50993 + 11.2755i) q^{66} +(5.43793 + 3.13959i) q^{67} +3.56827 q^{68} +(-3.63052 + 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +(9.65936 - 5.57684i) q^{72} +(7.19299 - 4.15288i) q^{73} +5.35685 q^{74} -13.2983 q^{75} +(-2.24018 + 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} +(3.95705 - 6.85381i) q^{79} +(1.06950 + 0.617476i) q^{80} +(2.30414 - 3.99089i) q^{81} +(-1.53747 - 2.66298i) q^{82} +6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} +(4.98630 + 2.87884i) q^{86} -15.9576 q^{87} +(8.12857 - 14.0791i) q^{88} +3.56136i q^{89} +10.6176 q^{90} +3.60762 q^{92} -3.06345i q^{93} +(0.187800 - 0.325279i) q^{94} -6.18837 q^{95} +(-13.3462 - 7.70546i) q^{96} +(-2.96831 - 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26}+ \cdots + 6 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9 + 12 * q^10 - 6 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^15 + 16 * q^16 + 8 * q^17 + 12 * q^18 - 12 * q^20 + 6 * q^22 + 24 * q^23 - 12 * q^24 + 10 * q^25 + 18 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 - 18 * q^31 + 30 * q^33 - 10 * q^36 - 2 * q^38 + 14 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 - 24 * q^44 - 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 - 28 * q^52 + 22 * q^53 - 6 * q^55 + 12 * q^58 - 66 * q^60 + 14 * q^61 - 4 * q^62 - 52 * q^64 - 18 * q^65 + 26 * q^66 + 24 * q^67 + 16 * q^68 + 4 * q^69 - 24 * q^71 - 60 * q^72 - 30 * q^73 - 12 * q^74 - 92 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 + 72 * q^80 + 2 * q^81 + 14 * q^82 - 48 * q^85 + 60 * q^86 + 4 * q^87 - 14 * q^88 + 24 * q^90 + 24 * q^92 + 4 * q^94 + 44 * q^95 - 6 * q^96 + 6 * q^97

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$			0.823556i			0.582342i	0.956671	+	0.291171i	$0.0940449\pi$
$2$			0.823556i			0.582342i	−0.956671	+	0.291171i	$0.905955\pi$
$3$	−1.33015	+	2.30388i	−0.767960	+	1.33015i	0.170707	+	0.985322i	$0.445395\pi$
$3$	−1.33015	+	2.30388i	−0.767960	+	1.33015i	−0.938667	+	0.344824i	$0.887939\pi$
$4$	1.32176			0.660878
$5$	2.73845	+	1.58105i	1.22467	+	0.707065i	0.965911	−	0.258876i	$-0.0833520\pi$
$5$	2.73845	+	1.58105i	1.22467	+	0.707065i	0.258762	+	0.965941i	$0.416685\pi$
$6$	−1.89737	−	1.09545i	−0.774600	−	0.447215i
$7$		0			0
$7$		0			0
$8$			2.73565i			0.967199i
$9$	−2.03858	−	3.53092i	−0.679526	−	1.17697i
$10$	−1.30208	+	2.25527i	−0.411754	+	0.713179i
$11$	−5.14653	−	2.97135i	−1.55174	−	0.895895i	−0.998001	−	0.0632025i	$-0.979869\pi$
$11$	−5.14653	−	2.97135i	−1.55174	−	0.895895i	−0.553735	−	0.832693i	$-0.686798\pi$
$12$	−1.75813	+	3.04517i	−0.507528	+	0.879064i
$13$	−0.0766193	+	3.60474i	−0.0212504	+	0.999774i
$13$	−0.0766193	+	3.60474i	−0.0212504	+	0.999774i
$14$		0			0
$15$	−7.28508	+	4.20604i	−1.88100	+	1.08600i
$16$	0.390549			0.0976372
$17$	2.69964			0.654760			0.327380	−	0.944893i	$-0.393834\pi$
$17$	2.69964			0.654760			0.327380	+	0.944893i	$0.393834\pi$
$18$	2.90791	−	1.67888i	0.685401	−	0.395716i
$19$	−1.69485	+	0.978524i	−0.388826	+	0.224489i	−0.681651	−	0.731677i	$-0.738738\pi$
$19$	−1.69485	+	0.978524i	−0.388826	+	0.224489i	0.292825	+	0.956166i	$0.405405\pi$
$20$	3.61956	+	2.08976i	0.809359	+	0.467284i
$21$		0			0
$22$	2.44707	−	4.23845i	0.521717	−	0.903641i
$23$	2.72941			0.569122			0.284561	−	0.958658i	$-0.408152\pi$
$23$	2.72941			0.569122			0.284561	+	0.958658i	$0.408152\pi$
$24$	−6.30261	−	3.63882i	−1.28652	−	0.742770i
$25$	2.49941	+	4.32911i	0.499883	+	0.865822i
$26$	−2.96870	−	0.0631003i	−0.582211	−	0.0123750i
$27$	2.86554			0.551474
$28$		0			0
$29$	2.99923	+	5.19481i	0.556942	+	0.964652i	0.997750	+	0.0670505i	$0.0213589\pi$
$29$	2.99923	+	5.19481i	0.556942	+	0.964652i	−0.440807	+	0.897602i	$0.645308\pi$
$30$	−3.46391	−	5.99967i	−0.632421	−	1.09539i
$31$	−0.997270	+	0.575774i	−0.179115	+	0.103412i	−0.586877	−	0.809676i	$-0.699643\pi$
$31$	−0.997270	+	0.575774i	−0.179115	+	0.103412i	0.407762	+	0.913088i	$0.366309\pi$
$32$			5.79294i			1.02406i
$33$	13.6913	−	7.90465i	2.38334	−	1.37602i
$34$			2.22331i			0.381294i
$35$		0			0
$36$	−2.69450	−	4.66701i	−0.449083	−	0.777835i
$37$		−	6.50454i		−	1.06934i	−0.845061	−	0.534670i	$-0.820436\pi$
$37$		−	6.50454i		−	1.06934i	0.845061	−	0.534670i	$-0.179564\pi$
$38$	−0.805869	−	1.39581i	−0.130729	−	0.226430i
$39$	−8.20297	−	4.97135i	−1.31353	−	0.796053i
$40$	−4.32519	+	7.49145i	−0.683873	+	1.18450i
$41$	−3.23351	+	1.86687i	−0.504990	+	0.291556i	−0.730772	−	0.682622i	$-0.760840\pi$
$41$	−3.23351	+	1.86687i	−0.504990	+	0.291556i	0.225782	+	0.974178i	$0.427506\pi$
$42$		0			0
$43$	3.49562	−	6.05460i	0.533078	−	0.923318i	−0.466176	−	0.884692i	$-0.654369\pi$
$43$	3.49562	−	6.05460i	0.533078	−	0.923318i	0.999254	−	0.0386258i	$-0.0122980\pi$
$44$	−6.80245	−	3.92740i	−1.02551	−	0.592077i
$45$		−	12.8923i		−	1.92188i
$46$			2.24783i			0.331424i
$47$	−0.394969	−	0.228035i	−0.0576121	−	0.0332624i	0.470917	−	0.882177i	$-0.343923\pi$
$47$	−0.394969	−	0.228035i	−0.0576121	−	0.0332624i	−0.528529	+	0.848915i	$0.677256\pi$
$48$	−0.519487	+	0.899778i	−0.0749815	+	0.129872i
$49$		0			0
$50$	−3.56527	+	2.05841i	−0.504205	+	0.291103i
$51$	−3.59092	+	6.21965i	−0.502829	+	0.870926i
$52$	−0.101272	+	4.76458i	−0.0140439	+	0.660729i
$53$	−0.199643	−	0.345792i	−0.0274231	−	0.0474982i	0.851988	−	0.523561i	$-0.175397\pi$
$53$	−0.199643	−	0.345792i	−0.0274231	−	0.0474982i	−0.879411	+	0.476063i	$0.842063\pi$
$54$			2.35994i			0.321146i
$55$	−9.39568	−	16.2738i	−1.26691	−	2.19436i
$56$		0			0
$57$		−	5.20632i		−	0.689594i
$58$	−4.27822	+	2.47003i	−0.561758	+	0.324331i
$59$		−	4.80586i		−	0.625670i	−0.949807	−	0.312835i	$-0.898721\pi$
$59$		−	4.80586i		−	0.625670i	0.949807	−	0.312835i	$-0.101279\pi$
$60$	−9.62910	+	5.55936i	−1.24311	+	0.717711i
$61$	0.578514	+	1.00201i	0.0740711	+	0.128295i	0.900682	−	0.434479i	$-0.143067\pi$
$61$	0.578514	+	1.00201i	0.0740711	+	0.128295i	−0.826611	+	0.562774i	$0.809734\pi$
$62$	−0.474182	−	0.821308i	−0.0602212	−	0.104306i
$63$		0			0
$64$	−3.98971			−0.498714
$65$	−5.90907	+	9.75026i	−0.732930	+	1.20937i
$66$	6.50993	+	11.2755i	0.801316	+	1.38792i
$67$	5.43793	+	3.13959i	0.664349	+	0.383562i	0.793932	−	0.608007i	$-0.208031\pi$
$67$	5.43793	+	3.13959i	0.664349	+	0.383562i	−0.129583	+	0.991569i	$0.541364\pi$
$68$	3.56827			0.432716
$69$	−3.63052	+	6.28825i	−0.437063	+	0.757016i
$70$		0			0
$71$	3.90335	+	2.25360i	0.463242	+	0.267453i	0.713406	−	0.700751i	$-0.247151\pi$
$71$	3.90335	+	2.25360i	0.463242	+	0.267453i	−0.250165	+	0.968203i	$0.580485\pi$
$72$	9.65936	−	5.57684i	1.13837	−	0.657236i
$73$	7.19299	−	4.15288i	0.841876	−	0.486057i	−0.0160254	−	0.999872i	$-0.505101\pi$
$73$	7.19299	−	4.15288i	0.841876	−	0.486057i	0.857901	+	0.513814i	$0.171768\pi$
$74$	5.35685			0.622721
$75$	−13.2983			−1.53556
$76$	−2.24018	+	1.29337i	−0.256966	+	0.148360i
$77$		0			0
$78$	4.09418	−	6.75560i	0.463575	−	0.764921i
$79$	3.95705	−	6.85381i	0.445203	−	0.771114i	−0.552864	−	0.833272i	$-0.686465\pi$
$79$	3.95705	−	6.85381i	0.445203	−	0.771114i	0.998066	+	0.0621581i	$0.0197983\pi$
$80$	1.06950	+	0.617476i	0.119574	+	0.0690359i
$81$	2.30414	−	3.99089i	0.256016	−	0.443432i
$82$	−1.53747	−	2.66298i	−0.169785	−	0.294077i
$83$			6.19795i			0.680313i	0.940369	+	0.340156i	$0.110480\pi$
$83$			6.19795i			0.680313i	−0.940369	+	0.340156i	$0.889520\pi$
$84$		0			0
$85$	7.39284	+	4.26826i	0.801866	+	0.462958i
$86$	4.98630	+	2.87884i	0.537687	+	0.310434i
$87$	−15.9576			−1.71084
$88$	8.12857	−	14.0791i	0.866509	−	1.50084i
$89$			3.56136i			0.377504i	0.982025	+	0.188752i	$0.0604442\pi$
$89$			3.56136i			0.377504i	−0.982025	+	0.188752i	$0.939556\pi$
$90$	10.6176			1.11919
$91$		0			0
$92$	3.60762			0.376120
$93$		−	3.06345i		−	0.317665i
$94$	0.187800	−	0.325279i	0.0193701	−	0.0335500i
$95$	−6.18837			−0.634913
$96$	−13.3462	−	7.70546i	−1.36215	−	0.786435i
$97$	−2.96831	−	1.71375i	−0.301386	−	0.174005i	0.341679	−	0.939817i	$-0.389004\pi$
$97$	−2.96831	−	1.71375i	−0.301386	−	0.174005i	−0.643065	+	0.765811i	$0.722338\pi$
$98$		0			0
$99$			24.2293i			2.43513i
$100$	3.30361	+	5.72203i	0.330361	+	0.572203i
$101$	−6.66474	+	11.5437i	−0.663167	+	1.14864i	0.316612	+	0.948555i	$0.397455\pi$
$101$	−6.66474	+	11.5437i	−0.663167	+	1.14864i	−0.979779	+	0.200084i	$0.935879\pi$
$102$	−5.12223	−	2.95732i	−0.507177	−	0.292819i
$103$	5.82248	−	10.0848i	0.573706	−	0.993688i	−0.422475	−	0.906375i	$-0.638839\pi$
$103$	5.82248	−	10.0848i	0.573706	−	0.993688i	0.996181	−	0.0873131i	$-0.0278281\pi$
$104$	−9.86130	−	0.209604i	−0.966981	−	0.0205533i
$105$		0			0
$106$	0.284779	−	0.164417i	0.0276602	−	0.0159696i
$107$	3.92966			0.379894			0.189947	−	0.981794i	$-0.439168\pi$
$107$	3.92966			0.379894			0.189947	+	0.981794i	$0.439168\pi$
$108$	3.78755			0.364457
$109$	9.74566	−	5.62666i	0.933465	−	0.538936i	0.0455595	−	0.998962i	$-0.485493\pi$
$109$	9.74566	−	5.62666i	0.933465	−	0.538936i	0.887906	+	0.460025i	$0.152160\pi$
$110$	13.4024	−	7.73787i	1.27787	−	0.737777i
$111$	14.9857	+	8.65199i	1.42238	+	0.821210i
$112$		0			0
$113$	2.88709	−	5.00059i	0.271595	−	0.470416i	−0.697676	−	0.716414i	$-0.745782\pi$
$113$	2.88709	−	5.00059i	0.271595	−	0.470416i	0.969270	+	0.245998i	$0.0791157\pi$
$114$	4.28770			0.401579
$115$	7.47437	+	4.31533i	0.696989	+	0.402407i
$116$	3.96424	+	6.86627i	0.368071	+	0.637517i
$117$	12.8842	−	7.07800i	1.19115	−	0.654361i
$118$	3.95790			0.364354
$119$		0			0
$120$	−11.5063	−	19.9294i	−1.05037	−	1.81930i
$121$	12.1578	+	21.0580i	1.10526	+	1.91436i
$122$	−0.825215	+	0.476438i	−0.0747115	+	0.0431347i
$123$		−	9.93284i		−	0.895614i
$124$	−1.31815	+	0.761033i	−0.118373	+	0.0683428i
$125$		−	0.00370455i		−	0.000331345i
$126$		0			0
$127$	3.06558	+	5.30975i	0.272027	+	0.471164i	0.969381	−	0.245563i	$-0.0789728\pi$
$127$	3.06558	+	5.30975i	0.272027	+	0.471164i	−0.697354	+	0.716727i	$0.745639\pi$
$128$			8.30013i			0.733635i
$129$	9.29938	+	16.1070i	0.818765	+	1.41814i
$130$	−8.02989	−	4.86645i	−0.704268	−	0.426816i
$131$	−5.11084	+	8.85224i	−0.446537	+	0.773424i	−0.998158	−	0.0606707i	$-0.980676\pi$
$131$	−5.11084	+	8.85224i	−0.446537	+	0.773424i	0.551621	+	0.834095i	$0.314009\pi$
$132$	18.0965	−	10.4480i	1.57510	−	0.909383i
$133$		0			0
$134$	−2.58563	+	4.47844i	−0.223364	+	0.386878i
$135$	7.84715	+	4.53056i	0.675375	+	0.389928i
$136$			7.38528i			0.633283i
$137$			19.9475i			1.70423i	0.523353	+	0.852116i	$0.324681\pi$
$137$			19.9475i			1.70423i	−0.523353	+	0.852116i	$0.675319\pi$
$138$	−5.17872	−	2.98994i	−0.440842	−	0.254520i
$139$	10.1637	−	17.6041i	0.862077	−	1.49316i	−0.00784365	−	0.999969i	$-0.502497\pi$
$139$	10.1637	−	17.6041i	0.862077	−	1.49316i	0.869921	−	0.493192i	$-0.164170\pi$
$140$		0			0
$141$	1.05073	−	0.606641i	0.0884877	−	0.0510884i
$142$	−1.85596	+	3.21462i	−0.155749	+	0.269765i
$143$	11.1053	−	18.3242i	0.928668	−	1.53235i
$144$	−0.796164	−	1.37900i	−0.0663470	−	0.114916i
$145$			18.9677i			1.57518i
$146$	3.42013	+	5.92383i	0.283052	+	0.490260i
$147$		0			0
$148$		−	8.59741i		−	0.706703i
$149$	9.28046	−	5.35808i	0.760285	−	0.438951i	−0.0691132	−	0.997609i	$-0.522017\pi$
$149$	9.28046	−	5.35808i	0.760285	−	0.438951i	0.829398	+	0.558658i	$0.188684\pi$
$150$		−	10.9519i		−	0.894221i
$151$	−7.57267	+	4.37208i	−0.616255	+	0.355795i	−0.775409	−	0.631459i	$-0.782456\pi$
$151$	−7.57267	+	4.37208i	−0.616255	+	0.355795i	0.159155	+	0.987254i	$0.449123\pi$
$152$	−2.67690	−	4.63653i	−0.217125	−	0.376072i
$153$	−5.50343	−	9.53222i	−0.444926	−	0.770634i
$154$		0			0
$155$	−3.64130			−0.292476
$156$	−10.8423	−	6.57091i	−0.868080	−	0.526094i
$157$	−3.25367	−	5.63552i	−0.259671	−	0.449763i	0.706483	−	0.707730i	$-0.250281\pi$
$157$	−3.25367	−	5.63552i	−0.259671	−	0.449763i	−0.966154	+	0.257967i	$0.916947\pi$
$158$	5.64449	+	3.25885i	0.449052	+	0.259260i
$159$	1.06222			0.0842393
$160$	−9.15891	+	15.8637i	−0.724075	+	1.25414i
$161$		0			0
$162$	3.28672	+	1.89759i	0.258229	+	0.149089i
$163$	−2.26264	+	1.30634i	−0.177224	+	0.102320i	−0.585988	−	0.810320i	$-0.699293\pi$
$163$	−2.26264	+	1.30634i	−0.177224	+	0.102320i	0.408764	+	0.912640i	$0.365960\pi$
$164$	−4.27392	+	2.46755i	−0.333737	+	0.192683i
$165$	49.9905			3.89175
$166$	−5.10436			−0.396175
$167$	−3.36558	+	1.94312i	−0.260436	+	0.150363i	−0.624534	−	0.780998i	$-0.714711\pi$
$167$	−3.36558	+	1.94312i	−0.260436	+	0.150363i	0.364097	+	0.931361i	$0.381378\pi$
$168$		0			0
$169$	−12.9883	−	0.552385i	−0.999097	−	0.0424911i
$170$	−3.51515	+	6.08842i	−0.269600	+	0.466961i
$171$	6.91018	+	3.98959i	0.528434	+	0.305092i
$172$	4.62036	−	8.00270i	0.352299	−	0.610200i
$173$	6.98838	+	12.1042i	0.531317	+	0.920267i	0.999332	+	0.0365470i	$0.0116358\pi$
$173$	6.98838	+	12.1042i	0.531317	+	0.920267i	−0.468015	+	0.883720i	$0.655031\pi$
$174$		−	13.1420i		−	0.996293i
$175$		0			0
$176$	−2.00997	−	1.16046i	−0.151507	−	0.0874727i
$177$	11.0721	+	6.39250i	0.832232	+	0.480490i
$178$	−2.93298			−0.219836
$179$	−12.6422	+	21.8968i	−0.944919	+	1.63665i	−0.189005	+	0.981976i	$0.560526\pi$
$179$	−12.6422	+	21.8968i	−0.944919	+	1.63665i	−0.755914	+	0.654671i	$0.772807\pi$
$180$		−	17.0405i		−	1.27013i
$181$	−0.864474			−0.0642559			−0.0321279	−	0.999484i	$-0.510228\pi$
$181$	−0.864474			−0.0642559			−0.0321279	+	0.999484i	$0.510228\pi$
$182$		0			0
$183$	−3.07803			−0.227535
$184$			7.46673i			0.550454i
$185$	10.2840	−	17.8124i	0.756093	−	1.30959i
$186$	2.52293			0.184990
$187$	−13.8938	−	8.02158i	−1.01601	−	0.586596i
$188$	−0.522052	−	0.301407i	−0.0380746	−	0.0219824i
$189$		0			0
$190$		−	5.09647i		−	0.369737i
$191$	−7.33382	−	12.7026i	−0.530657	−	0.919125i	−0.999360	−	0.0357690i	$-0.988612\pi$
$191$	−7.33382	−	12.7026i	−0.530657	−	0.919125i	0.468703	−	0.883356i	$-0.344721\pi$
$192$	5.30690	−	9.19182i	0.382993	−	0.663363i
$193$	−14.2859	−	8.24794i	−1.02832	−	0.593700i	−0.111816	−	0.993729i	$-0.535667\pi$
$193$	−14.2859	−	8.24794i	−1.02832	−	0.593700i	−0.916503	+	0.400029i	$0.869000\pi$
$194$	1.41137	−	2.44457i	0.101331	−	0.175510i
$195$	−14.6035	−	26.5831i	−1.04578	−	1.90365i
$196$		0			0
$197$	9.53510	−	5.50509i	0.679348	−	0.392222i	−0.120262	−	0.992742i	$-0.538373\pi$
$197$	9.53510	−	5.50509i	0.679348	−	0.392222i	0.799609	+	0.600521i	$0.205040\pi$
$198$	−19.9542			−1.41808
$199$	21.2117			1.50366			0.751829	−	0.659358i	$-0.229172\pi$
$199$	21.2117			1.50366			0.751829	+	0.659358i	$0.229172\pi$
$200$	−11.8429	+	6.83753i	−0.837423	+	0.483486i
$201$	−14.4665	+	8.35223i	−1.02039	+	0.589121i
$202$	−9.50686	−	5.48879i	−0.668901	−	0.386190i
$203$		0			0
$204$	−4.74632	+	8.22086i	−0.332309	+	0.575576i
$205$	−11.8064			−0.824597
$206$	8.30542	+	4.79514i	0.578666	+	0.334093i
$207$	−5.56412	−	9.63734i	−0.386733	−	0.669842i
$208$	−0.0299236	+	1.40783i	−0.00207483	+	0.0976152i
$209$	11.6301			0.804474
$210$		0			0
$211$	8.96788	+	15.5328i	0.617375	+	1.06932i	0.989963	+	0.141327i	$0.0451370\pi$
$211$	8.96788	+	15.5328i	0.617375	+	1.06932i	−0.372588	+	0.927997i	$0.621530\pi$
$212$	−0.263879	−	0.457052i	−0.0181233	−	0.0313905i
$213$	−10.3840	+	5.99523i	−0.711503	+	0.410786i
$214$			3.23629i			0.221228i
$215$	19.1452	−	11.0535i	1.30569	−	0.753842i
$216$			7.83913i			0.533385i
$217$		0			0
$218$	4.63387	+	8.02610i	0.313845	+	0.543596i
$219$			22.0957i			1.49309i
$220$	−12.4188	−	21.5100i	−0.837275	−	1.45020i
$221$	−0.206845	+	9.73150i	−0.0139139	+	0.654612i
$222$	−7.12540	+	12.3415i	−0.478225	+	0.828311i
$223$	−13.8834	+	8.01558i	−0.929700	+	0.536763i	−0.886717	−	0.462313i	$-0.847020\pi$
$223$	−13.8834	+	8.01558i	−0.929700	+	0.536763i	−0.0429835	+	0.999076i	$0.513686\pi$
$224$		0			0
$225$	10.1905	−	17.6505i	0.679366	−	1.17670i
$226$	4.11826	+	2.37768i	0.273943	+	0.158161i
$227$			16.3750i			1.08685i	0.839458	+	0.543424i	$0.182873\pi$
$227$			16.3750i			1.08685i	−0.839458	+	0.543424i	$0.817127\pi$
$228$		−	6.88148i		−	0.455737i
$229$	−23.3917	−	13.5052i	−1.54577	−	0.892449i	−0.998458	−	0.0555193i	$-0.982319\pi$
$229$	−23.3917	−	13.5052i	−1.54577	−	0.892449i	−0.547310	−	0.836930i	$-0.684348\pi$
$230$	−3.55392	+	6.15556i	−0.234338	+	0.405886i
$231$		0			0
$232$	−14.2112	+	8.20484i	−0.933011	+	0.538674i
$233$	5.78406	−	10.0183i	0.378926	−	0.656320i	−0.611980	−	0.790873i	$-0.709627\pi$
$233$	5.78406	−	10.0183i	0.378926	−	0.656320i	0.990906	+	0.134554i	$0.0429601\pi$
$234$	5.82913	+	10.6109i	0.381062	+	0.693655i
$235$	−0.721069	−	1.24893i	−0.0470374	−	0.0814711i
$236$		−	6.35217i		−	0.413491i
$237$	10.5269	+	18.2331i	0.683796	+	1.18437i
$238$		0			0
$239$		−	14.6731i		−	0.949122i	−0.880223	−	0.474561i	$-0.842607\pi$
$239$		−	14.6731i		−	0.949122i	0.880223	−	0.474561i	$-0.157393\pi$
$240$	−2.84518	+	1.64267i	−0.183656	+	0.106034i
$241$		−	14.3467i		−	0.924151i	−0.886841	−	0.462076i	$-0.847105\pi$
$241$		−	14.3467i		−	0.924151i	0.886841	−	0.462076i	$-0.152895\pi$
$242$	−17.3424	+	10.0126i	−1.11481	+	0.643637i
$243$	10.4280	+	18.0618i	0.668956	+	1.15867i
$244$	0.764654	+	1.32442i	0.0489519	+	0.0847872i
$245$		0			0
$246$	8.18025			0.521554
$247$	−3.39746	−	6.18447i	−0.216175	−	0.393509i
$248$	−1.57512	−	2.72818i	−0.100020	−	0.173240i
$249$	−14.2793	−	8.24417i	−0.904916	−	0.522453i
$250$	0.00305091			0.000192956
$251$	4.30726	−	7.46040i	0.271872	−	0.470896i	−0.697469	−	0.716615i	$-0.745691\pi$
$251$	4.30726	−	7.46040i	0.271872	−	0.470896i	0.969341	+	0.245719i	$0.0790239\pi$
$252$		0			0
$253$	−14.0470	−	8.11004i	−0.883128	−	0.509874i
$254$	−4.37287	+	2.52468i	−0.274378	+	0.158412i
$255$	−19.6671	+	11.3548i	−1.23160	+	0.711066i
$256$	−14.8151			−0.925941
$257$	−10.3639			−0.646485			−0.323243	−	0.946316i	$-0.604773\pi$
$257$	−10.3639			−0.646485			−0.323243	+	0.946316i	$0.604773\pi$
$258$	−13.2650	+	7.65856i	−0.825844	+	0.476801i
$259$		0			0
$260$	−7.81035	+	12.8875i	−0.484377	+	0.799247i
$261$	12.2283	−	21.1800i	0.756913	−	1.31101i
$262$	−7.29032	−	4.20907i	−0.450397	−	0.260037i
$263$	11.0413	−	19.1241i	0.680835	−	1.17924i	−0.293891	−	0.955839i	$-0.594950\pi$
$263$	11.0413	−	19.1241i	0.680835	−	1.17924i	0.974726	−	0.223403i	$-0.0717165\pi$
$264$	21.6244	+	37.4545i	1.33089	+	2.30517i
$265$		−	1.26258i		−	0.0775596i
$266$		0			0
$267$	−8.20495	−	4.73713i	−0.502135	−	0.289908i
$268$	7.18761	+	4.14977i	0.439053	+	0.253488i
$269$	12.9399			0.788960			0.394480	−	0.918905i	$-0.370925\pi$
$269$	12.9399			0.788960			0.394480	+	0.918905i	$0.370925\pi$
$270$	−3.73117	+	6.46257i	−0.227072	+	0.393299i
$271$		−	17.6749i		−	1.07367i	−0.843686	−	0.536837i	$-0.819619\pi$
$271$		−	17.6749i		−	1.07367i	0.843686	−	0.536837i	$-0.180381\pi$
$272$	1.05434			0.0639289
$273$		0			0
$274$	−16.4279			−0.992446
$275$		−	29.7065i		−	1.79137i
$276$	−4.79866	+	8.31152i	−0.288845	+	0.500295i
$277$	18.0150			1.08242			0.541209	−	0.840888i	$-0.317967\pi$
$277$	18.0150			1.08242			0.541209	+	0.840888i	$0.317967\pi$
$278$	14.4980	+	8.37041i	0.869530	+	0.502024i
$279$	4.06602	+	2.34752i	0.243426	+	0.140542i
$280$		0			0
$281$			2.44178i			0.145665i	0.997344	+	0.0728323i	$0.0232038\pi$
$281$			2.44178i			0.145665i	−0.997344	+	0.0728323i	$0.976796\pi$
$282$	0.499603	+	0.865337i	0.0297509	+	0.0515301i
$283$	−14.3620	+	24.8757i	−0.853732	+	1.47871i	0.0240853	+	0.999710i	$0.492333\pi$
$283$	−14.3620	+	24.8757i	−0.853732	+	1.47871i	−0.877817	+	0.478996i	$0.841001\pi$
$284$	5.15927	+	2.97871i	0.306146	+	0.176754i
$285$	8.23143	−	14.2573i	0.487588	−	0.844527i
$286$	15.0910	+	9.14580i	0.892350	+	0.540802i
$287$		0			0
$288$	20.4544	−	11.8094i	1.20529	−	0.695873i
$289$	−9.71193			−0.571290
$290$	−15.6209			−0.917292
$291$	7.89657	−	4.55909i	0.462905	−	0.267258i
$292$	9.50738	−	5.48909i	0.556377	−	0.321225i
$293$	25.4013	+	14.6654i	1.48396	+	0.856763i	0.999834	−	0.0182359i	$-0.00580499\pi$
$293$	25.4013	+	14.6654i	1.48396	+	0.856763i	0.484124	+	0.874999i	$0.339138\pi$
$294$		0			0
$295$	7.59829	−	13.1606i	0.442390	−	0.766241i
$296$	17.7942			1.03426
$297$	−14.7476	−	8.51453i	−0.855742	−	0.494063i
$298$	4.41267	+	7.64298i	0.255619	+	0.442746i
$299$	−0.209126	+	9.83882i	−0.0120941	+	0.568994i
$300$	−17.5772			−1.01482
$301$		0			0
$302$	−3.60065	−	6.23651i	−0.207194	−	0.358871i
$303$	−17.7302	−	30.7096i	−1.01857	−	1.76422i
$304$	−0.661923	+	0.382161i	−0.0379639	+	0.0219185i
$305$			3.65863i			0.209492i
$306$	7.85032	−	4.53238i	0.448773	−	0.259099i
$307$		−	7.06910i		−	0.403455i	−0.979442	−	0.201728i	$-0.935344\pi$
$307$		−	7.06910i		−	0.403455i	0.979442	−	0.201728i	$-0.0646555\pi$
$308$		0			0
$309$	15.4895	+	26.8286i	0.881166	+	1.52623i
$310$		−	2.99882i		−	0.170321i
$311$	−11.1343	−	19.2852i	−0.631368	−	1.09356i	−0.987272	−	0.159039i	$-0.949160\pi$
$311$	−11.1343	−	19.2852i	−0.631368	−	1.09356i	0.355904	−	0.934522i	$-0.384173\pi$
$312$	13.5999	−	22.4405i	0.769941	−	1.27044i
$313$	14.0420	−	24.3214i	0.793700	−	1.37473i	−0.129961	−	0.991519i	$-0.541485\pi$
$313$	14.0420	−	24.3214i	0.793700	−	1.37473i	0.923661	−	0.383210i	$-0.125181\pi$
$314$	4.64117	−	2.67958i	0.261916	−	0.151217i
$315$		0			0
$316$	5.23025	−	9.05906i	0.294225	−	0.509612i
$317$	16.9009	+	9.75774i	0.949249	+	0.548049i	0.892848	−	0.450359i	$-0.148704\pi$
$317$	16.9009	+	9.75774i	0.949249	+	0.548049i	0.0564015	+	0.998408i	$0.482037\pi$
$318$			0.874796i			0.0490561i
$319$		−	35.6470i		−	1.99585i
$320$	−10.9256	−	6.30792i	−0.610762	−	0.352624i
$321$	−5.22702	+	9.05346i	−0.291744	+	0.505315i
$322$		0			0
$323$	−4.57550	+	2.64167i	−0.254588	+	0.146986i
$324$	3.04551	−	5.27498i	0.169195	−	0.293054i
$325$	−15.7968	+	8.67804i	−0.876250	+	0.481371i
$326$	−1.07584	−	1.86341i	−0.0595853	−	0.103205i
$327$			29.9371i			1.65553i
$328$	−5.10711	−	8.84577i	−0.281993	−	0.488426i
$329$		0			0
$330$			41.1700i			2.26633i
$331$	−13.5367	+	7.81539i	−0.744042	+	0.429573i	−0.823537	−	0.567263i	$-0.808002\pi$
$331$	−13.5367	+	7.81539i	−0.744042	+	0.429573i	0.0794953	+	0.996835i	$0.474669\pi$
$332$			8.19217i			0.449604i
$333$	−22.9670	+	13.2600i	−1.25858	+	0.726644i
$334$	−1.60027	−	2.77174i	−0.0875627	−	0.151663i
$335$	9.92767	+	17.1952i	0.542407	+	0.939476i
$336$		0			0
$337$	21.7501			1.18480			0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501			1.18480			0.592401	+	0.805643i	$0.298180\pi$
$338$	0.454920	−	10.6966i	0.0247444	−	0.581816i
$339$	7.68050	+	13.3030i	0.417148	+	0.722521i
$340$	9.77153	+	5.64160i	0.529936	+	0.305959i
$341$	6.84330			0.370586
$342$	−3.28565	+	5.69092i	−0.177668	+	0.307730i
$343$		0			0
$344$	16.5633	+	9.56281i	0.893032	+	0.515592i
$345$	−19.8840	+	11.4800i	−1.07052	+	0.618065i
$346$	−9.96851	+	5.75532i	−0.535910	+	0.309408i
$347$	−15.9590			−0.856726			−0.428363	−	0.903607i	$-0.640909\pi$
$347$	−15.9590			−0.856726			−0.428363	+	0.903607i	$0.640909\pi$
$348$	−21.0921			−1.13065
$349$	5.90375	−	3.40853i	0.316021	−	0.182455i	−0.333597	−	0.942716i	$-0.608262\pi$
$349$	5.90375	−	3.40853i	0.316021	−	0.182455i	0.649617	+	0.760261i	$0.274929\pi$
$350$		0			0
$351$	−0.219556	+	10.3295i	−0.0117190	+	0.551349i
$352$	17.2128	−	29.8135i	0.917448	−	1.58907i
$353$	−12.1272	−	7.00163i	−0.645465	−	0.372659i	0.141252	−	0.989974i	$-0.454887\pi$
$353$	−12.1272	−	7.00163i	−0.645465	−	0.372659i	−0.786716	+	0.617314i	$0.788221\pi$
$354$	−5.26458	+	9.11852i	−0.279809	+	0.484644i
$355$	7.12608	+	12.3427i	0.378213	+	0.655085i
$356$			4.70725i			0.249484i
$357$		0			0
$358$	−18.0333	−	10.4115i	−0.953088	−	0.550266i
$359$	−4.68947	−	2.70747i	−0.247501	−	0.142895i	0.371119	−	0.928586i	$-0.378974\pi$
$359$	−4.68947	−	2.70747i	−0.247501	−	0.142895i	−0.618619	+	0.785691i	$0.712308\pi$
$360$	35.2689			1.85884
$361$	−7.58498	+	13.1376i	−0.399210	+	0.691451i
$362$		−	0.711943i		−	0.0374189i
$363$	−64.6867			−3.39517
$364$		0			0
$365$	26.2636			1.37470
$366$		−	2.53493i		−	0.132503i
$367$	−15.0159	+	26.0083i	−0.783822	+	1.35762i	0.145878	+	0.989303i	$0.453399\pi$
$367$	−15.0159	+	26.0083i	−0.783822	+	1.35762i	−0.929700	+	0.368317i	$0.879934\pi$
$368$	1.06597			0.0555675
$369$	13.1835	+	7.61152i	0.686307	+	0.396240i
$370$	14.6695	+	8.46943i	0.762630	+	0.440305i
$371$		0			0
$372$		−	4.04914i		−	0.209938i
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	−0.997959	−	0.0638526i	$-0.979661\pi$
$373$	−10.7049	−	18.5414i	−0.554278	−	0.960037i	0.443682	−	0.896184i	$-0.353672\pi$
$374$	6.60622	−	11.4423i	0.341599	−	0.591668i
$375$	0.00853484	+	0.00492759i	0.000440737	+	0.000254460i
$376$	0.623826	−	1.08050i	0.0321713	−	0.0557224i
$377$	−18.9557	+	10.4134i	−0.976270	+	0.536317i
$378$		0			0
$379$	−8.20693	+	4.73827i	−0.421562	+	0.243389i	−0.695745	−	0.718289i	$-0.744926\pi$
$379$	−8.20693	+	4.73827i	−0.421562	+	0.243389i	0.274184	+	0.961677i	$0.411592\pi$
$380$	−8.17951			−0.419600
$381$	−16.3107			−0.835622
$382$	10.4613	−	6.03982i	0.535245	−	0.309024i
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	−0.375007	−	0.927022i	$-0.622360\pi$
$383$	4.70304	−	2.71530i	0.240314	−	0.138746i	0.615321	+	0.788277i	$0.289026\pi$
$384$	−19.1225	−	11.0404i	−0.975842	−	0.563402i
$385$		0			0
$386$	6.79264	−	11.7652i	0.345736	−	0.598833i
$387$	−28.5044			−1.44896
$388$	−3.92338	−	2.26516i	−0.199179	−	0.114996i
$389$	−5.32109	−	9.21640i	−0.269790	−	0.467290i	0.699018	−	0.715105i	$-0.253621\pi$
$389$	−5.32109	−	9.21640i	−0.269790	−	0.467290i	−0.968807	+	0.247815i	$0.920288\pi$
$390$	21.8926	−	12.0268i	1.10858	−	0.609001i
$391$	7.36845			0.372638
$392$		0			0
$393$	−13.5963	−	23.5495i	−0.685845	−	1.18792i
$394$	4.53375	+	7.85269i	0.228407	+	0.395613i
$395$	21.6724	−	12.5126i	1.09046	−	0.629575i
$396$			32.0252i			1.60933i
$397$	−32.2035	+	18.5927i	−1.61625	+	0.933140i	−0.628367	+	0.777917i	$0.716276\pi$
$397$	−32.2035	+	18.5927i	−1.61625	+	0.933140i	−0.987879	+	0.155223i	$0.950390\pi$
$398$			17.4690i			0.875644i
$399$		0			0
$400$	0.976143	+	1.69073i	0.0488072	+	0.0845365i
$401$		−	0.896610i		−	0.0447746i	−0.999749	−	0.0223873i	$-0.992873\pi$
$401$		−	0.896610i		−	0.0447746i	0.999749	−	0.0223873i	$-0.00712669\pi$
$402$	−6.87853	−	11.9140i	−0.343070	−	0.594214i
$403$	−1.99910	−	3.63901i	−0.0995825	−	0.181272i
$404$	−8.80916	+	15.2579i	−0.438272	+	0.759110i
$405$	12.6196	−	7.28590i	0.627071	−	0.362039i
$406$		0			0
$407$	−19.3273	+	33.4758i	−0.958016	+	1.65933i
$408$	−17.0148	−	9.82350i	−0.842359	−	0.486336i
$409$		−	24.5773i		−	1.21527i	−0.794217	−	0.607635i	$-0.792119\pi$
$409$		−	24.5773i		−	1.21527i	0.794217	−	0.607635i	$-0.207881\pi$
$410$		−	9.72326i		−	0.480198i
$411$	−45.9567	−	26.5331i	−2.26688	−	1.30878i
$412$	7.69589	−	13.3297i	0.379149	−	0.656706i
$413$		0			0
$414$	7.93689	−	4.58237i	0.390077	−	0.225211i
$415$	−9.79924	+	16.9728i	−0.481026	+	0.833161i
$416$	−20.8820	−	0.443851i	−1.02383	−	0.0217616i
$417$	27.0385	+	46.8321i	1.32408	+	2.29338i
$418$			9.57807i			0.468479i
$419$	3.82279	+	6.62126i	0.186755	+	0.323470i	0.944167	−	0.329468i	$-0.106869\pi$
$419$	3.82279	+	6.62126i	0.186755	+	0.323470i	−0.757411	+	0.652938i	$0.773536\pi$
$420$		0			0
$421$			25.0780i			1.22223i	0.791544	+	0.611113i	$0.209278\pi$
$421$			25.0780i			1.22223i	−0.791544	+	0.611113i	$0.790722\pi$
$422$	−12.7922	+	7.38555i	−0.622712	+	0.359523i
$423$			1.85947i			0.0904106i
$424$	0.945966	−	0.546154i	0.0459402	−	0.0265236i
$425$	6.74753	+	11.6871i	0.327303	+	0.566906i
$426$	−4.93741	−	8.55184i	−0.239218	−	0.414338i
$427$		0			0
$428$	5.19405			0.251064
$429$	27.4452	+	49.9591i	1.32507	+	2.41205i
$430$	9.10317	+	15.7671i	0.438994	+	0.760359i
$431$	−6.71520	−	3.87702i	−0.323460	−	0.186750i	0.329474	−	0.944165i	$-0.393129\pi$
$431$	−6.71520	−	3.87702i	−0.323460	−	0.186750i	−0.652934	+	0.757415i	$0.726462\pi$
$432$	1.11913			0.0538444
$433$	17.9880	−	31.1561i	0.864448	−	1.49727i	−0.00314644	−	0.999995i	$-0.501002\pi$
$433$	17.9880	−	31.1561i	0.864448	−	1.49727i	0.867594	−	0.497273i	$-0.165665\pi$
$434$		0			0
$435$	−43.6992	−	25.2298i	−2.09522	−	1.20967i
$436$	12.8814	−	7.43707i	0.616907	−	0.356171i
$437$	−4.62596	+	2.67080i	−0.221290	+	0.127762i
$438$	−18.1971			−0.869489
$439$	28.2350			1.34758			0.673792	−	0.738921i	$-0.264664\pi$
$439$	28.2350			1.34758			0.673792	+	0.738921i	$0.264664\pi$
$440$	44.5194	−	25.7033i	2.12238	−	1.22536i
$441$		0			0
$442$	−8.01444	−	0.170348i	−0.381208	−	0.00810264i
$443$	−14.3959	+	24.9344i	−0.683970	+	1.18467i	0.289790	+	0.957090i	$0.406415\pi$
$443$	−14.3959	+	24.9344i	−0.683970	+	1.18467i	−0.973759	+	0.227580i	$0.926919\pi$
$444$	19.8074	+	11.4358i	0.940018	+	0.542720i
$445$	−5.63068	+	9.75262i	−0.266920	+	0.462319i
$446$	−6.60128	−	11.4337i	−0.312579	−	0.541404i
$447$			28.5081i			1.34839i
$448$		0			0
$449$	−25.2795	−	14.5951i	−1.19301	−	0.688785i	−0.234023	−	0.972231i	$-0.575189\pi$
$449$	−25.2795	−	14.5951i	−1.19301	−	0.688785i	−0.958988	+	0.283446i	$0.908522\pi$
$450$	14.5361	+	8.39244i	0.685240	+	0.395624i
$451$	22.1885			1.04482
$452$	3.81603	−	6.60955i	0.179491	−	0.310887i
$453$		−	23.2620i		−	1.09295i
$454$	−13.4858			−0.632918
$455$		0			0
$456$	14.2427			0.666974
$457$		−	31.6848i		−	1.48215i	−0.671420	−	0.741077i	$-0.734316\pi$
$457$		−	31.6848i		−	1.48215i	0.671420	−	0.741077i	$-0.265684\pi$
$458$	11.1223	−	19.2644i	0.519711	−	0.900165i
$459$	7.73594			0.361083
$460$	9.87929	+	5.70381i	0.460624	+	0.265942i
$461$	−19.1407	−	11.0509i	−0.891471	−	0.514691i	−0.0170480	−	0.999855i	$-0.505427\pi$
$461$	−19.1407	−	11.0509i	−0.891471	−	0.514691i	−0.874424	+	0.485163i	$0.838760\pi$
$462$		0			0
$463$		−	38.8811i		−	1.80696i	−0.428632	−	0.903479i	$-0.641004\pi$
$463$		−	38.8811i		−	1.80696i	0.428632	−	0.903479i	$-0.358996\pi$
$464$	1.17134	+	2.02883i	0.0543783	+	0.0941860i
$465$	4.84346	−	8.38913i	0.224610	−	0.389036i
$466$	8.25062	+	4.76350i	0.382202	+	0.220665i
$467$	6.64116	−	11.5028i	0.307316	−	0.532287i	−0.670458	−	0.741947i	$-0.733902\pi$
$467$	6.64116	−	11.5028i	0.307316	−	0.532287i	0.977774	+	0.209660i	$0.0672358\pi$
$468$	17.0298	−	9.35538i	0.787203	−	0.432453i
$469$		0			0
$470$	1.02856	−	0.593841i	0.0474440	−	0.0273918i
$471$	17.3114			0.797668
$472$	13.1472			0.605147
$473$	−35.9807	+	20.7734i	−1.65439	+	0.955164i
$474$	−15.0160	+	8.66949i	−0.689708	+	0.398203i
$475$	−8.47228	−	4.89147i	−0.388735	−	0.224436i
$476$		0			0
$477$	−0.813975	+	1.40985i	−0.0372694	+	0.0645524i
$478$	12.0841			0.552714
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	0.362947	−	0.931810i	$-0.381770\pi$
$479$	−5.74618	−	3.31756i	−0.262550	−	0.151583i	−0.625497	+	0.780226i	$0.715104\pi$
$480$	−24.3654	−	42.2021i	−1.11212	−	1.92625i
$481$	23.4472	+	0.498373i	1.06910	+	0.0227239i
$482$	11.8153			0.538172
$483$		0			0
$484$	16.0697	+	27.8335i	0.730439	+	1.26516i
$485$	−5.41905	−	9.38607i	−0.246066	−	0.426200i
$486$	−14.8749	+	8.58804i	−0.674740	+	0.389561i
$487$		−	33.4701i		−	1.51668i	−0.651861	−	0.758338i	$-0.726012\pi$
$487$		−	33.4701i		−	1.51668i	0.651861	−	0.758338i	$-0.273988\pi$
$488$	−2.74116	+	1.58261i	−0.124087	+	0.0716415i
$489$		−	6.95047i		−	0.314311i
$490$		0			0
$491$	−18.6643	−	32.3276i	−0.842310	−	1.45892i	−0.887937	−	0.459966i	$-0.847862\pi$
$491$	−18.6643	−	32.3276i	−0.842310	−	1.45892i	0.0456264	−	0.998959i	$-0.485472\pi$
$492$		−	13.1288i		−	0.591891i
$493$	8.09684	+	14.0241i	0.364663	+	0.631615i
$494$	5.09326	−	2.79800i	0.229157	−	0.125888i
$495$	−38.3076	+	66.3507i	−1.72180	+	2.98224i
$496$	−0.389483	+	0.224868i	−0.0174883	+	0.0100969i
$497$		0			0
$498$	6.78954	−	11.7598i	0.304246	−	0.526970i
$499$	29.5598	+	17.0663i	1.32328	+	0.763994i	0.984250	−	0.176783i	$-0.0565690\pi$
$499$	29.5598	+	17.0663i	1.32328	+	0.763994i	0.339027	+	0.940777i	$0.389902\pi$
$500$		−	0.00489651i		−	0.000218979i
$501$		−	10.3385i		−	0.461891i
$502$	6.14405	+	3.54727i	0.274223	+	0.158322i
$503$	−7.65447	+	13.2579i	−0.341296	+	0.591142i	−0.984674	−	0.174407i	$-0.944199\pi$
$503$	−7.65447	+	13.2579i	−0.341296	+	0.591142i	0.643378	+	0.765549i	$0.277533\pi$
$504$		0			0
$505$	−36.5022	+	21.0745i	−1.62433	+	0.937805i
$506$	6.67907	−	11.5685i	0.296921	−	0.514282i
$507$	18.5489	−	29.1886i	0.823786	−	1.29631i
$508$	4.05195	+	7.01819i	0.179776	+	0.311382i
$509$		−	18.4970i		−	0.819866i	−0.912116	−	0.409933i	$-0.865552\pi$
$509$		−	18.4970i		−	0.819866i	0.912116	−	0.409933i	$-0.134448\pi$
$510$	−9.35133	−	16.1970i	−0.414084	−	0.717214i
$511$		0			0
$512$			4.39924i			0.194421i
$513$	−4.85668	+	2.80400i	−0.214427	+	0.123800i
$514$		−	8.53529i		−	0.376476i
$515$	31.8892	−	18.4112i	1.40520	−	0.811295i
$516$	12.2915	+	21.2895i	0.541104	+	0.937219i
$517$	1.35515	+	2.34718i	0.0595992	+	0.103229i
$518$		0			0
$519$	−37.1823			−1.63212
$520$	−26.6733	−	16.1652i	−1.16970	−	0.708890i
$521$	−11.7932	−	20.4265i	−0.516671	−	0.894901i	−0.999813	−	0.0193585i	$-0.993838\pi$
$521$	−11.7932	−	20.4265i	−0.516671	−	0.894901i	0.483141	−	0.875542i	$-0.339496\pi$
$522$	17.4430	+	10.0707i	0.763457	+	0.440782i
$523$	12.3059			0.538099			0.269049	−	0.963126i	$-0.413291\pi$
$523$	12.3059			0.538099			0.269049	+	0.963126i	$0.413291\pi$
$524$	−6.75529	+	11.7005i	−0.295106	+	0.511139i
$525$		0			0
$526$	15.7498	+	9.09312i	0.686722	+	0.396479i
$527$	−2.69227	+	1.55438i	−0.117277	+	0.0677101i
$528$	5.34711	−	3.08715i	0.232703	−	0.134351i
$529$	−15.5503			−0.676100
$530$	1.03980			0.0451662
$531$	−16.9691	+	9.79712i	−0.736397	+	0.425159i
$532$		0			0
$533$	−6.48183	−	11.7990i	−0.280759	−	0.511072i
$534$	3.90129	−	6.75724i	0.168825	−	0.292414i
$535$	10.7612	+	6.21297i	0.465246	+	0.268610i
$536$	−8.58883	+	14.8763i	−0.370981	+	0.642558i
$537$	−33.6318	−	58.2520i	−1.45132	−	2.51376i
$538$			10.6567i			0.459444i
$539$		0			0
$540$	10.3720	+	5.98829i	0.446341	+	0.257695i
$541$	−16.8365	−	9.72054i	−0.723857	−	0.417919i	0.0923139	−	0.995730i	$-0.470574\pi$
$541$	−16.8365	−	9.72054i	−0.723857	−	0.417919i	−0.816170	+	0.577811i	$0.803907\pi$
$542$	14.5563			0.625245
$543$	1.14988	−	1.99165i	0.0493460	−	0.0854697i
$544$			15.6389i			0.670511i
$545$	35.5841			1.52425
$546$		0			0
$547$	40.2163			1.71953			0.859763	−	0.510693i	$-0.170611\pi$
$547$	40.2163			1.71953			0.859763	+	0.510693i	$0.170611\pi$
$548$			26.3658i			1.12629i
$549$	2.35869	−	4.08537i	0.100666	−	0.174359i
$550$	24.4650			1.04319
$551$	−10.1665	−	5.86963i	−0.433107	−	0.250055i
$552$	−17.2024	−	9.93184i	−0.732185	−	0.422727i
$553$		0			0
$554$			14.8364i			0.630337i
$555$	27.3584	+	47.3861i	1.16130	+	2.01143i
$556$	13.4340	−	23.2683i	0.569727	−	0.986797i
$557$	−6.89702	−	3.98199i	−0.292236	−	0.168722i	0.346714	−	0.937971i	$-0.387297\pi$
$557$	−6.89702	−	3.98199i	−0.292236	−	0.168722i	−0.638950	+	0.769248i	$0.720631\pi$
$558$	−1.93331	+	3.34860i	−0.0818437	+	0.141757i
$559$	21.5574	+	13.0647i	0.911781	+	0.552578i
$560$		0			0
$561$	36.9615	−	21.3397i	1.56052	−	0.900965i
$562$	−2.01095			−0.0848266
$563$	1.42396			0.0600128			0.0300064	−	0.999550i	$-0.490447\pi$
$563$	1.42396			0.0600128			0.0300064	+	0.999550i	$0.490447\pi$
$564$	1.38881	−	0.801831i	0.0584795	−	0.0337632i
$565$	15.8123	−	9.12924i	0.665229	−	0.384070i
$566$	−20.4865	−	11.8279i	−0.861113	−	0.497164i
$567$		0			0
$568$	−6.16506	+	10.6782i	−0.258680	+	0.448047i
$569$	18.5189			0.776353			0.388177	−	0.921585i	$-0.373105\pi$
$569$	18.5189			0.776353			0.388177	+	0.921585i	$0.373105\pi$
$570$	11.7417	+	6.77904i	0.491804	+	0.283943i
$571$	2.17883	+	3.77384i	0.0911812	+	0.157930i	0.908008	−	0.418952i	$-0.137602\pi$
$571$	2.17883	+	3.77384i	0.0911812	+	0.157930i	−0.816827	+	0.576882i	$0.804269\pi$
$572$	14.6784	−	24.2201i	0.613736	−	1.01269i
$573$	39.0202			1.63009
$574$		0			0
$575$	6.82194	+	11.8159i	0.284494	+	0.492759i
$576$	8.13334	+	14.0874i	0.338889	+	0.586973i
$577$	8.28280	−	4.78208i	0.344818	−	0.199081i	−0.317583	−	0.948231i	$-0.602871\pi$
$577$	8.28280	−	4.78208i	0.344818	−	0.199081i	0.662400	+	0.749150i	$0.269538\pi$
$578$		−	7.99832i		−	0.332686i
$579$	38.0046	−	21.9419i	1.57942	−	0.911876i
$580$			25.0706i			1.04100i
$581$		0			0
$582$	3.75466	+	6.50327i	0.155636	+	0.269569i
$583$			2.37284i			0.0982728i
$584$	11.3608	+	19.6775i	0.470114	+	0.814262i
$585$	46.4735	+	0.987801i	1.92144	+	0.0408406i
$586$	−12.0778	+	20.9194i	−0.498929	+	0.864171i
$587$	−2.04428	+	1.18027i	−0.0843765	+	0.0487148i	−0.541595	−	0.840640i	$-0.682179\pi$
$587$	−2.04428	+	1.18027i	−0.0843765	+	0.0487148i	0.457218	+	0.889355i	$0.348846\pi$
$588$		0			0
$589$	1.12682	−	1.95171i	0.0464297	−	0.0804186i
$590$	10.8385	+	6.25762i	0.446214	+	0.257622i
$591$			29.2903i			1.20484i
$592$		−	2.54034i		−	0.104407i
$593$	−35.0127	−	20.2146i	−1.43780	−	0.830114i	−0.440103	−	0.897947i	$-0.645058\pi$
$593$	−35.0127	−	20.2146i	−1.43780	−	0.830114i	−0.997697	+	0.0678337i	$0.978391\pi$
$594$	7.01219	−	12.1455i	0.287714	−	0.498335i
$595$		0			0
$596$	12.2665	−	7.08207i	0.502455	−	0.290093i
$597$	−28.2147	+	48.8693i	−1.15475	+	2.00009i
$598$	−8.10282	−	0.172227i	−0.331349	−	0.00704288i
$599$	19.2936	+	33.4176i	0.788316	+	1.36540i	0.926998	+	0.375067i	$0.122380\pi$
$599$	19.2936	+	33.4176i	0.788316	+	1.36540i	−0.138681	+	0.990337i	$0.544286\pi$
$600$		−	36.3796i		−	1.48519i
$601$	−4.08115	−	7.06877i	−0.166474	−	0.288341i	0.770704	−	0.637193i	$-0.219905\pi$
$601$	−4.08115	−	7.06877i	−0.166474	−	0.288341i	−0.937178	+	0.348852i	$0.886571\pi$
$602$		0			0
$603$		−	25.6012i		−	1.04256i
$604$	−10.0092	+	5.77882i	−0.407269	+	0.235137i
$605$			76.8883i			3.12595i
$606$	25.2910	−	14.6018i	1.02738	−	0.593157i
$607$	−3.79263	−	6.56902i	−0.153938	−	0.266628i	0.778734	−	0.627354i	$-0.215862\pi$
$607$	−3.79263	−	6.56902i	−0.153938	−	0.266628i	−0.932672	+	0.360726i	$0.882529\pi$
$608$	−5.66853	−	9.81819i	−0.229889	−	0.398180i
$609$		0			0
$610$	−3.01308			−0.121996
$611$	0.852270	−	1.40629i	0.0344792	−	0.0568923i
$612$	−7.27419	−	12.5993i	−0.294042	−	0.509295i
$613$	13.4908	+	7.78892i	0.544889	+	0.314592i	0.747058	−	0.664759i	$-0.231466\pi$
$613$	13.4908	+	7.78892i	0.544889	+	0.314592i	−0.202169	+	0.979351i	$0.564799\pi$
$614$	5.82180			0.234949
$615$	15.7043	−	27.2006i	0.633258	−	1.09683i
$616$		0			0
$617$	20.6709	+	11.9343i	0.832177	+	0.480458i	0.854598	−	0.519291i	$-0.173804\pi$
$617$	20.6709	+	11.9343i	0.832177	+	0.480458i	−0.0224202	+	0.999749i	$0.507137\pi$
$618$	−22.0948	+	12.7565i	−0.888785	+	0.513140i
$619$	−16.8843	+	9.74814i	−0.678636	+	0.391811i	−0.799341	−	0.600878i	$-0.794818\pi$
$619$	−16.8843	+	9.74814i	−0.678636	+	0.391811i	0.120705	+	0.992688i	$0.461485\pi$
$620$	−4.81291			−0.193291
$621$	7.82126			0.313856
$622$	15.8824	−	9.16972i	0.636827	−	0.367672i
$623$		0			0
$624$	−3.20366	−	1.94155i	−0.128249	−	0.0777244i
$625$	12.5029	−	21.6557i	0.500117	−	0.866228i
$626$	20.0301	+	11.5644i	0.800562	+	0.462205i
$627$	−15.4698	+	26.7945i	−0.617804	+	1.07007i
$628$	−4.30055	−	7.44878i	−0.171611	−	0.297239i
$629$		−	17.5599i		−	0.700161i
$630$		0			0
$631$	−22.2239	−	12.8309i	−0.884718	−	0.510792i	−0.0125066	−	0.999922i	$-0.503981\pi$
$631$	−22.2239	−	12.8309i	−0.884718	−	0.510792i	−0.872211	+	0.489130i	$0.837314\pi$
$632$	18.7496	+	10.8251i	0.745820	+	0.430600i
$633$	−47.7144			−1.89648
$634$	−8.03604	+	13.9188i	−0.319152	+	0.552788i
$635$			19.3873i			0.769362i
$636$	1.40399			0.0556719
$637$		0			0
$638$	29.3573			1.16227
$639$		−	18.3765i		−	0.726964i
$640$	−13.1229	+	22.7295i	−0.518728	+	0.898463i
$641$	1.10604			0.0436860			0.0218430	−	0.999761i	$-0.493047\pi$
$641$	1.10604			0.0436860			0.0218430	+	0.999761i	$0.493047\pi$
$642$	−7.45603	−	4.30474i	−0.294266	−	0.169895i
$643$	10.9437	+	6.31833i	0.431576	+	0.249171i	0.700018	−	0.714125i	$-0.253175\pi$
$643$	10.9437	+	6.31833i	0.431576	+	0.249171i	−0.268442	+	0.963296i	$0.586509\pi$
$644$		0			0
$645$			58.8110i			2.31568i
$646$	−2.17556	−	3.76818i	−0.0855962	−	0.148257i
$647$	12.8574	−	22.2697i	0.505477	−	0.875512i	−0.494503	−	0.869176i	$-0.664650\pi$
$647$	12.8574	−	22.2697i	0.505477	−	0.875512i	0.999980	−	0.00633579i	$-0.00201676\pi$
$648$	10.9177	+	6.30332i	0.428887	+	0.247618i
$649$	−14.2799	+	24.7335i	−0.560535	+	0.970875i
$650$	−7.14685	−	13.0096i	−0.280323	−	0.510277i
$651$		0			0
$652$	−2.99066	+	1.72666i	−0.117123	+	0.0676211i
$653$	25.2607			0.988527			0.494263	−	0.869312i	$-0.335438\pi$
$653$	25.2607			0.988527			0.494263	+	0.869312i	$0.335438\pi$
$654$	−24.6549			−0.964083
$655$	−27.9916	+	16.1610i	−1.09372	+	0.631461i
$656$	−1.26285	+	0.729104i	−0.0493058	+	0.0284667i
$657$	−29.3269	−	16.9319i	−1.14415	−	0.660577i
$658$		0			0
$659$	−11.4882	+	19.8982i	−0.447517	+	0.775123i	−0.998224	−	0.0595764i	$-0.981025\pi$
$659$	−11.4882	+	19.8982i	−0.447517	+	0.775123i	0.550707	+	0.834699i	$0.314358\pi$
$660$	66.0752			2.57197
$661$	−26.3554	−	15.2163i	−1.02511	−	0.591845i	−0.109528	−	0.993984i	$-0.534934\pi$
$661$	−26.3554	−	15.2163i	−1.02511	−	0.591845i	−0.915579	+	0.402138i	$0.868267\pi$
$662$	−6.43641	−	11.1482i	−0.250158	−	0.433287i
$663$	−22.1451	−	13.4209i	−0.860044	−	0.521223i
$664$	−16.9554			−0.657998
$665$		0			0
$666$	−10.9204	−	18.9146i	−0.423155	−	0.732926i
$667$	8.18613	+	14.1788i	0.316968	+	0.549005i
$668$	−4.44847	+	2.56833i	−0.172117	+	0.0993715i
$669$		−	42.6475i		−	1.64885i
$670$	−14.1612	+	8.17600i	−0.547096	+	0.315866i
$671$		−	6.87586i		−	0.265440i
$672$		0			0
$673$	5.41933	+	9.38656i	0.208900	+	0.361825i	0.951368	−	0.308056i	$-0.0996784\pi$
$673$	5.41933	+	9.38656i	0.208900	+	0.361825i	−0.742468	+	0.669881i	$0.766345\pi$
$674$			17.9124i			0.689960i
$675$	7.16218	+	12.4053i	0.275672	+	0.477479i
$676$	−17.1673	−	0.730117i	−0.660281	−	0.0280814i
$677$	9.06044	−	15.6931i	0.348221	−	0.603137i	−0.637712	−	0.770275i	$-0.720119\pi$
$677$	9.06044	−	15.6931i	0.348221	−	0.603137i	0.985934	+	0.167138i	$0.0534525\pi$
$678$	−10.9558	+	6.32532i	−0.420754	+	0.242923i
$679$		0			0
$680$	−11.6765	+	20.2242i	−0.447772	+	0.775564i
$681$	−37.7261	−	21.7812i	−1.44567	−	0.834656i
$682$			5.63584i			0.215808i
$683$		−	37.8352i		−	1.44772i	−0.689946	−	0.723861i	$-0.742366\pi$
$683$		−	37.8352i		−	1.44772i	0.689946	−	0.723861i	$-0.257634\pi$
$684$	9.13357	+	5.27327i	0.349231	+	0.201628i
$685$	−31.5380	+	54.6254i	−1.20500	+	2.08713i
$686$		0			0
$687$	62.2288	−	35.9278i	2.37418	−	1.37073i
$688$	1.36521	−	2.36462i	0.0520482	−	0.0901502i
$689$	1.26179	−	0.693166i	0.0480702	−	0.0264075i
$690$	−9.45446	−	16.3756i	−0.359925	−	0.623408i
$691$			30.0261i			1.14225i	0.820864	+	0.571124i	$0.193492\pi$
$691$			30.0261i			1.14225i	−0.820864	+	0.571124i	$0.806508\pi$
$692$	9.23693	+	15.9988i	0.351135	+	0.608184i
$693$		0			0
$694$		−	13.1432i		−	0.498907i
$695$	55.6658	−	32.1387i	2.11152	−	1.21909i
$696$		−	43.6545i		−	1.65472i
$697$	−8.72934	+	5.03988i	−0.330647	+	0.190899i
$698$	2.80712	+	4.86207i	0.106251	+	0.184032i
$699$	15.3873	+	26.6516i	0.582001	+	1.00805i
$700$		0			0
$701$	0.116177			0.00438796			0.00219398	−	0.999998i	$-0.499302\pi$
$701$	0.116177			0.00438796			0.00219398	+	0.999998i	$0.499302\pi$
$702$	−8.50695	−	0.180816i	−0.321074	−	0.00682448i
$703$	6.36485	+	11.0242i	0.240055	+	0.415787i
$704$	20.5332	+	11.8548i	0.773873	+	0.446796i
$705$	3.83651			0.144491
$706$	5.76624	−	9.98741i	0.217015	−	0.375881i
$707$		0			0
$708$	14.6347	+	8.44932i	0.550004	+	0.317545i
$709$	−5.82829	+	3.36497i	−0.218886	+	0.126374i	−0.605434	−	0.795895i	$-0.707001\pi$
$709$	−5.82829	+	3.36497i	−0.218886	+	0.126374i	0.386548	+	0.922269i	$0.373667\pi$
$710$	−10.1649	+	5.86873i	−0.381483	+	0.220249i
$711$	−32.2670			−1.21011
$712$	−9.74265			−0.365121
$713$	−2.72196	+	1.57153i	−0.101938	+	0.0588541i
$714$		0			0
$715$	59.3826	−	32.6221i	2.22078	−	1.22000i
$716$	−16.7098	+	28.9423i	−0.624476	+	1.08162i
$717$	33.8050	+	19.5173i	1.26247	+	0.728888i
$718$	2.22975	−	3.86204i	0.0832136	−	0.144130i
$719$	23.4039	+	40.5367i	0.872818	+	1.51177i	0.859069	+	0.511860i	$0.171043\pi$
$719$	23.4039	+	40.5367i	0.872818	+	1.51177i	0.0137492	+	0.999905i	$0.495623\pi$
$720$		−	5.03509i		−	0.187647i
$721$		0			0
$722$	−10.8195	−	6.24666i	−0.402661	−	0.232476i
$723$	33.0530	+	19.0832i	1.22926	+	0.709711i
$724$	−1.14262			−0.0424653
$725$	−14.9926	+	25.9680i	−0.556812	+	0.964426i
$726$		−	53.2731i		−	1.97715i
$727$	13.3362			0.494611			0.247305	−	0.968938i	$-0.420455\pi$
$727$	13.3362			0.494611			0.247305	+	0.968938i	$0.420455\pi$
$728$		0			0
$729$	−41.6582			−1.54290
$730$			21.6295i			0.800544i
$731$	9.43694	−	16.3453i	0.349038	−	0.604551i
$732$	−4.06840			−0.150373
$733$	−25.5142	−	14.7306i	−0.942387	−	0.544087i	−0.0516792	−	0.998664i	$-0.516457\pi$
$733$	−25.5142	−	14.7306i	−0.942387	−	0.544087i	−0.890708	+	0.454576i	$0.849791\pi$
$734$	−21.4193	−	12.3664i	−0.790599	−	0.456453i
$735$		0			0
$736$			15.8113i			0.582814i
$737$	−18.6576	−	32.3160i	−0.687263	−	1.19037i
$738$	−6.26851	+	10.8574i	−0.230747	+	0.399666i
$739$	10.4184	+	6.01509i	0.383249	+	0.221269i	0.679231	−	0.733925i	$-0.262314\pi$
$739$	10.4184	+	6.01509i	0.383249	+	0.221269i	−0.295982	+	0.955193i	$0.595647\pi$
$740$	13.5929	−	23.5436i	0.499685	−	0.865480i
$741$	18.7674	+	0.398904i	0.689438	+	0.0146541i
$742$		0			0
$743$	−18.9509	+	10.9413i	−0.695242	+	0.401398i	−0.805573	−	0.592497i	$-0.798142\pi$
$743$	−18.9509	+	10.9413i	−0.695242	+	0.401398i	0.110331	+	0.993895i	$0.464809\pi$
$744$	8.38055			0.307246
$745$	33.8855			1.24147
$746$	15.2699	−	8.81607i	0.559070	−	0.322779i
$747$	21.8844	−	12.6350i	0.800710	−	0.462290i
$748$	−18.3642	−	10.6026i	−0.671461	−	0.387668i
$749$		0			0
$750$	−0.00405815	+	0.00702892i	−0.000148183	+	0.000256660i
$751$	−34.7492			−1.26802			−0.634008	−	0.773327i	$-0.718591\pi$
$751$	−34.7492			−1.26802			−0.634008	+	0.773327i	$0.718591\pi$
$752$	−0.154255	−	0.0890590i	−0.00562509	−	0.00324765i
$753$	11.4586	+	19.8468i	0.417574	+	0.723259i
$754$	−8.57602	−	15.6111i	−0.312320	−	0.568523i
$755$	−27.6498			−1.00628
$756$		0			0
$757$	−21.9632	−	38.0413i	−0.798265	−	1.38264i	−0.920745	−	0.390164i	$-0.872418\pi$
$757$	−21.9632	−	38.0413i	−0.798265	−	1.38264i	0.122481	−	0.992471i	$-0.460915\pi$
$758$	−3.90223	−	6.75887i	−0.141736	−	0.245493i
$759$	37.3691	−	21.5751i	1.35641	−	0.783126i
$760$		−	16.9292i		−	0.614087i
$761$	−0.122449	+	0.0706957i	−0.00443876	+	0.00256272i	−0.502218	−	0.864741i	$-0.667482\pi$
$761$	−0.122449	+	0.0706957i	−0.00443876	+	0.00256272i	0.497779	+	0.867304i	$0.334149\pi$
$762$		−	13.4328i		−	0.486618i
$763$		0			0
$764$	−9.69352	−	16.7897i	−0.350699	−	0.607429i
$765$		−	34.8047i		−	1.25837i
$766$	2.23620	+	3.87322i	0.0807973	+	0.139945i
$767$	17.3239	+	0.368222i	0.625529	+	0.0132957i
$768$	19.7062	−	34.1321i	0.711086	−	1.23164i
$769$	11.8200	−	6.82429i	0.426241	−	0.246090i	−0.271503	−	0.962438i	$-0.587521\pi$
$769$	11.8200	−	6.82429i	0.426241	−	0.246090i	0.697744	+	0.716347i	$0.254187\pi$
$770$		0			0
$771$	13.7856	−	23.8773i	0.496475	−	0.859920i
$772$	−18.8824	−	10.9018i	−0.679593	−	0.392363i
$773$		−	17.5894i		−	0.632646i	−0.948652	−	0.316323i	$-0.897552\pi$
$773$		−	17.5894i		−	0.632646i	0.948652	−	0.316323i	$-0.102448\pi$
$774$		−	23.4750i		−	0.843790i
$775$	−4.98518	−	2.87820i	−0.179073	−	0.103388i
$776$	4.68824	−	8.12026i	0.168298	−	0.291500i
$777$		0			0
$778$	7.59022	−	4.38221i	0.272123	−	0.157110i
$779$	3.65356	−	6.32814i	0.130902	−	0.226729i
$780$	−19.3023	−	35.1363i	−0.691132	−	1.25808i
$781$	−13.3924	−	23.1964i	−0.479219	−	0.830032i
$782$			6.06833i			0.217003i
$783$	8.59441	+	14.8860i	0.307139	+	0.531981i
$784$		0			0
$785$		−	20.5768i		−	0.734418i
$786$	19.3944	−	11.1973i	0.691774	−	0.399396i
$787$		−	2.96845i		−	0.105814i	−0.998599	−	0.0529069i	$-0.983151\pi$
$787$		−	2.96845i		−	0.105814i	0.998599	−	0.0529069i	$-0.0168487\pi$
$788$	12.6031	−	7.27639i	0.448966	−	0.259210i
$789$	29.3731	+	50.8756i	1.04571	+	1.81122i
$790$	10.3048	+	17.8484i	0.366628	+	0.635018i
$791$		0			0
$792$	−66.2829			−2.35526
$793$	−3.65633	+	2.00862i	−0.129840	+	0.0713280i
$794$	−15.3121	−	26.5214i	−0.543407	−	0.941208i
$795$	2.90883	+	1.67941i	0.103166	+	0.0595627i
$796$	28.0367			0.993735
$797$	4.72611	−	8.18586i	0.167407	−	0.289958i	−0.770100	−	0.637923i	$-0.779794\pi$
$797$	4.72611	−	8.18586i	0.167407	−	0.289958i	0.937508	+	0.347965i	$0.113127\pi$
$798$		0			0
$799$	−1.06628	−	0.615614i	−0.0377221	−	0.0217789i
$800$	−25.0783	+	14.4790i	−0.886652	+	0.511909i
$801$	12.5749	−	7.26011i	0.444312	−	0.256523i
$802$	0.738409			0.0260741
$803$	−49.3586			−1.74183
$804$	−19.1212	+	11.0396i	−0.674351	+	0.389337i
$805$		0			0
$806$	2.99693	−	1.64637i	0.105562	−	0.0579911i
$807$	−17.2120	+	29.8120i	−0.605890	+	1.04943i
$808$	−31.5795	−	18.2324i	−1.11096	−	0.641414i
$809$	0.581273	−	1.00679i	0.0204365	−	0.0353970i	−0.855626	−	0.517594i	$-0.826828\pi$
$809$	0.581273	−	1.00679i	0.0204365	−	0.0353970i	0.876063	+	0.482197i	$0.160161\pi$
$810$	6.00035	+	10.3929i	0.210831	+	0.365170i
$811$			19.5561i			0.686706i	0.939206	+	0.343353i	$0.111563\pi$
$811$			19.5561i			0.686706i	−0.939206	+	0.343353i	$0.888437\pi$
$812$		0			0
$813$	40.7209	+	23.5102i	1.42814	+	0.824538i
$814$	−27.5692	−	15.9171i	−0.966299	−	0.557893i
$815$	−8.26151			−0.289388
$816$	−1.40243	+	2.42908i	−0.0490949	+	0.0850348i
$817$			13.6822i			0.478680i
$818$	20.2408			0.707702
$819$		0			0
$820$	−15.6052			−0.544958
$821$			12.6189i			0.440403i	0.975454	+	0.220201i	$0.0706714\pi$
$821$			12.6189i			0.440403i	−0.975454	+	0.220201i	$0.929329\pi$
$822$	21.8515	−	37.8479i	0.762159	−	1.32010i
$823$	6.56808			0.228949			0.114474	−	0.993426i	$-0.463482\pi$
$823$	6.56808			0.228949			0.114474	+	0.993426i	$0.463482\pi$
$824$	27.5886	+	15.9283i	0.961094	+	0.554888i
$825$	68.4403	+	39.5140i	2.38278	+	1.37570i
$826$		0			0
$827$		−	17.3050i		−	0.601754i	−0.953663	−	0.300877i	$-0.902721\pi$
$827$		−	17.3050i		−	0.601754i	0.953663	−	0.300877i	$-0.0972794\pi$
$828$	−7.35441	−	12.7382i	−0.255583	−	0.442683i
$829$	−1.87837	+	3.25343i	−0.0652385	+	0.112996i	−0.896800	−	0.442437i	$-0.854114\pi$
$829$	−1.87837	+	3.25343i	−0.0652385	+	0.112996i	0.831561	+	0.555433i	$0.187447\pi$
$830$	−13.9780	−	8.07022i	−0.485185	−	0.280122i
$831$	−23.9626	+	41.5044i	−0.831253	+	1.43977i
$832$	0.305689	−	14.3819i	0.0105979	−	0.498602i
$833$		0			0
$834$	−38.5688	+	22.2677i	−1.33553	+	0.771068i
$835$	−12.2886			−0.425266
$836$	15.3722			0.531659
$837$	−2.85772	+	1.64991i	−0.0987773	+	0.0570291i
$838$	−5.45298	+	3.14828i	−0.188370	+	0.108756i
$839$	−40.1340	−	23.1714i	−1.38558	−	0.799965i	−0.392766	−	0.919638i	$-0.628482\pi$
$839$	−40.1340	−	23.1714i	−1.38558	−	0.799965i	−0.992813	+	0.119674i	$0.961815\pi$
$840$		0			0
$841$	−3.49071	+	6.04609i	−0.120369	+	0.208486i
$842$	−20.6531			−0.711753
$843$	−5.62558	−	3.24793i	−0.193755	−	0.111865i
$844$	11.8534	+	20.5306i	0.408009	+	0.706693i
$845$	−34.6944	−	22.0477i	−1.19352	−	0.758465i
$846$	−1.53138			−0.0526499
$847$		0			0
$848$	−0.0779704	−	0.135049i	−0.00267751	−	0.00463759i
$849$	−38.2071	−	66.1766i	−1.31126	−	2.27118i
$850$	−9.62495	+	5.55697i	−0.330133	+	0.190602i
$851$		−	17.7536i		−	0.608585i
$852$	−13.7252	+	7.92423i	−0.470216	+	0.271479i
$853$		−	15.3103i		−	0.524215i	−0.965039	−	0.262107i	$-0.915583\pi$
$853$		−	15.3103i		−	0.524215i	0.965039	−	0.262107i	$-0.0844174\pi$
$854$		0			0
$855$	12.6155	+	21.8506i	0.431440	+	0.747275i
$856$			10.7502i			0.367433i
$857$	1.29624	+	2.24515i	0.0442787	+	0.0766929i	0.887315	−	0.461163i	$-0.152568\pi$
$857$	1.29624	+	2.24515i	0.0442787	+	0.0766929i	−0.843037	+	0.537856i	$0.819234\pi$
$858$	−41.1441	+	22.6026i	−1.40464	+	0.771642i
$859$	6.88689	−	11.9284i	0.234978	−	0.406993i	−0.724289	−	0.689497i	$-0.757832\pi$
$859$	6.88689	−	11.9284i	0.234978	−	0.406993i	0.959266	+	0.282504i	$0.0911650\pi$
$860$	25.3053	−	14.6100i	0.862903	−	0.498197i
$861$		0			0
$862$	3.19294	−	5.53034i	0.108752	−	0.188364i
$863$	−25.7723	−	14.8796i	−0.877298	−	0.506508i	−0.00753143	−	0.999972i	$-0.502397\pi$
$863$	−25.7723	−	14.8796i	−0.877298	−	0.506508i	−0.869767	+	0.493463i	$0.835731\pi$
$864$			16.5999i			0.564741i
$865$			44.1958i			1.50270i
$866$	25.6588	+	14.8141i	0.871922	+	0.503404i
$867$	12.9183	−	22.3751i	0.438728	−	0.759899i
$868$		0			0
$869$	−40.7301	+	23.5155i	−1.38167	+	0.797710i
$870$	20.7781	−	35.9888i	0.704444	−	1.22013i
$871$	−11.7340	+	19.3618i	−0.397593	+	0.656048i
$872$	15.3926	+	26.6607i	0.521259	+	0.902847i
$873$			13.9745i			0.472965i
$874$	−2.19955	−	3.80974i	−0.0744009	−	0.128866i
$875$		0			0
$876$			29.2051i			0.986750i
$877$	1.24995	−	0.721660i	0.0422079	−	0.0243687i	−0.478748	−	0.877953i	$-0.658909\pi$
$877$	1.24995	−	0.721660i	0.0422079	−	0.0243687i	0.520955	+	0.853584i	$0.325576\pi$
$878$			23.2531i			0.784755i
$879$	−67.5748	+	39.0143i	−2.27924	+	1.31592i
$880$	−3.66947	−	6.35571i	−0.123698	−	0.214251i
$881$	−17.9402	−	31.0733i	−0.604420	−	1.04689i	−0.992143	−	0.125110i	$-0.960072\pi$
$881$	−17.9402	−	31.0733i	−0.604420	−	1.04689i	0.387723	−	0.921776i	$-0.373262\pi$
$882$		0			0
$883$	10.5626			0.355458			0.177729	−	0.984079i	$-0.443125\pi$
$883$	10.5626			0.355458			0.177729	+	0.984079i	$0.443125\pi$
$884$	−0.273398	+	12.8627i	−0.00919537	+	0.432618i
$885$	20.2137	+	35.0111i	0.679475	+	1.17689i
$886$	−20.5349	−	11.8558i	−0.689883	−	0.398304i
$887$	12.2280			0.410577			0.205288	−	0.978702i	$-0.434187\pi$
$887$	12.2280			0.410577			0.205288	+	0.978702i	$0.434187\pi$
$888$	−23.6688	+	40.9956i	−0.794274	+	1.37572i
$889$		0			0
$890$	−8.03183	−	4.63718i	−0.269228	−	0.155439i
$891$	−23.7166	+	13.6928i	−0.794537	+	0.458726i
$892$	−18.3504	+	10.5946i	−0.614418	+	0.354735i
$893$	0.892553			0.0298681
$894$	−23.4780			−0.785222
$895$	−69.2399	+	39.9757i	−2.31443	+	1.33624i
$896$		0			0
$897$	−22.3893	−	13.5689i	−0.747557	−	0.453051i
$898$	12.0199	−	20.8190i	0.401109	−	0.694741i
$899$	−5.98208	−	3.45375i	−0.199513	−	0.115189i
$900$	13.4693	−	23.3296i	0.448978	−	0.777653i
$901$	−0.538965	−	0.933515i	−0.0179555	−	0.0310999i
$902$			18.2735i			0.608440i
$903$		0			0
$904$	13.6799	+	7.89807i	0.454985	+	0.262686i
$905$	−2.36732	−	1.36677i	−0.0786924	−	0.0454331i
$906$	19.1576			0.636468
$907$	2.26278	−	3.91924i	0.0751343	−	0.130136i	−0.826010	−	0.563655i	$-0.809395\pi$
$907$	2.26278	−	3.91924i	0.0751343	−	0.130136i	0.901145	+	0.433519i	$0.142728\pi$
$908$			21.6438i			0.718274i
$909$	54.3464			1.80256
$910$		0			0
$911$	−57.2723			−1.89751			−0.948757	−	0.316006i	$-0.897658\pi$
$911$	−57.2723			−1.89751			−0.948757	+	0.316006i	$0.897658\pi$
$912$		−	2.03332i		−	0.0673300i
$913$	18.4163	−	31.8979i	0.609489	−	1.05567i
$914$	26.0942			0.863120
$915$	−8.42904	−	4.86651i	−0.278655	−	0.160882i
$916$	−30.9181	−	17.8506i	−1.02156	−	0.589800i
$917$		0			0
$918$			6.37098i			0.210274i
$919$	20.3775	+	35.2949i	0.672193	+	1.16427i	0.977281	+	0.211948i	$0.0679809\pi$
$919$	20.3775	+	35.2949i	0.672193	+	1.16427i	−0.305088	+	0.952324i	$0.598686\pi$
$920$	−11.8052	+	20.4473i	−0.389207	+	0.674127i
$921$	16.2864	+	9.40294i	0.536654	+	0.309837i
$922$	9.10103	−	15.7634i	0.299726	−	0.519141i
$923$	−8.42270	+	13.8979i	−0.277236	+	0.457454i
$924$		0			0
$925$	28.1589	−	16.2575i	0.925858	−	0.534545i
$926$	32.0208			1.05227
$927$	−47.4783			−1.55939
$928$	−30.0932	+	17.3743i	−0.987859	+	0.570341i
$929$	−45.2751	+	26.1396i	−1.48543	+	0.857611i	−0.999862	−	0.0165897i	$-0.994719\pi$
$929$	−45.2751	+	26.1396i	−1.48543	+	0.857611i	−0.485564	+	0.874201i	$0.661386\pi$
$930$	6.90891	+	3.98886i	0.226552	+	0.130800i
$931$		0			0
$932$	7.64511	−	13.2417i	0.250424	−	0.433747i
$933$	59.2410			1.93946
$934$	9.47322	+	5.46937i	0.309973	+	0.178963i
$935$	−25.3650	−	43.9334i	−0.829523	−	1.43678i
$936$	19.3629	+	35.2468i	0.632897	+	1.15208i
$937$	−6.38634			−0.208633			−0.104316	−	0.994544i	$-0.533265\pi$
$937$	−6.38634			−0.208633			−0.104316	+	0.994544i	$0.533265\pi$
$938$		0			0
$939$	37.3558	+	64.7021i	1.21906	+	2.11147i
$940$	−0.953077	−	1.65078i	−0.0310859	−	0.0538424i
$941$	−21.9720	+	12.6855i	−0.716266	+	0.413536i	−0.813377	−	0.581737i	$-0.802373\pi$
$941$	−21.9720	+	12.6855i	−0.716266	+	0.413536i	0.0971107	+	0.995274i	$0.469040\pi$
$942$			14.2569i			0.464516i
$943$	−8.82560	+	5.09546i	−0.287401	+	0.165931i
$944$		−	1.87692i		−	0.0610887i
$945$		0			0
$946$	−17.1081	−	29.6321i	−0.556232	−	0.963422i
$947$			27.2061i			0.884080i	0.896995	+	0.442040i	$0.145745\pi$
$947$			27.2061i			0.884080i	−0.896995	+	0.442040i	$0.854255\pi$
$948$	13.9140	+	24.0997i	0.451905	+	0.782723i
$949$	14.4189	+	26.2470i	0.468057	+	0.852015i
$950$	4.02840	−	6.97740i	0.130699	−	0.226377i
$951$	−44.9613	+	25.9584i	−1.45797	+	0.841760i
$952$		0			0
$953$	13.2939	−	23.0258i	0.430633	−	0.745878i	−0.566295	−	0.824203i	$-0.691624\pi$
$953$	13.2939	−	23.0258i	0.430633	−	0.745878i	0.996928	+	0.0783248i	$0.0249571\pi$
$954$	−1.16109	−	0.670354i	−0.0375916	−	0.0217035i
$955$		−	46.3805i		−	1.50084i
$956$		−	19.3942i		−	0.627254i
$957$	82.1264	+	47.4157i	2.65477	+	1.53273i
$958$	2.73220	−	4.73230i	0.0882732	−	0.152894i
$959$		0			0
$960$	29.0654	−	16.7809i	0.938082	−	0.541602i
$961$	−14.8370	+	25.6984i	−0.478612	+	0.828980i
$962$	−0.410438	+	19.3100i	−0.0132331	+	0.622581i
$963$	−8.01091	−	13.8753i	−0.258148	−	0.447125i
$964$		−	18.9628i		−	0.610751i
$965$	−26.0808	−	45.1732i	−0.839569	−	1.45418i
$966$		0			0
$967$			35.2467i			1.13346i	0.823904	+	0.566729i	$0.191791\pi$
$967$			35.2467i			1.13346i	−0.823904	+	0.566729i	$0.808209\pi$
$968$	−57.6073	+	33.2596i	−1.85157	+	1.06900i
$969$		−	14.0552i		−	0.451518i
$970$	7.72995	−	4.46289i	0.248194	−	0.143295i
$971$	−18.4891	−	32.0241i	−0.593344	−	1.02770i	−0.993778	−	0.111377i	$-0.964474\pi$
$971$	−18.4891	−	32.0241i	−0.593344	−	1.02770i	0.400434	−	0.916326i	$-0.368859\pi$
$972$	13.7833	+	23.8733i	0.442098	+	0.765737i
$973$		0			0
$974$	27.5645			0.883224
$975$	1.01891	−	47.9370i	0.0326312	−	1.53521i
$976$	0.225938	+	0.391336i	0.00723209	+	0.0125264i
$977$	21.4363	+	12.3762i	0.685807	+	0.395951i	0.802039	−	0.597271i	$-0.203748\pi$
$977$	21.4363	+	12.3762i	0.685807	+	0.395951i	−0.116232	+	0.993222i	$0.537082\pi$
$978$	5.72410			0.183036
$979$	10.5820	−	18.3286i	0.338204	−	0.585786i
$980$		0			0
$981$	−39.7346	−	22.9408i	−1.26863	−	0.732442i
$982$	26.6236	−	15.3711i	0.849593	−	0.490513i
$983$	3.94679	−	2.27868i	0.125883	−	0.0726786i	−0.435736	−	0.900074i	$-0.643512\pi$
$983$	3.94679	−	2.27868i	0.125883	−	0.0726786i	0.561619	+	0.827396i	$0.310179\pi$
$984$	27.1728			0.866237
$985$	34.8152			1.10930
$986$	−11.5497	+	6.66820i	−0.367816	+	0.212359i
$987$		0			0
$988$	−4.49062	−	8.17436i	−0.142866	−	0.260061i
$989$	9.54101	−	16.5255i	0.303386	−	0.525481i
$990$	−54.6436	−	31.5485i	−1.73669	−	1.00268i
$991$	13.5982	−	23.5527i	0.431960	−	0.748176i	−0.565082	−	0.825034i	$-0.691156\pi$
$991$	13.5982	−	23.5527i	0.431960	−	0.748176i	0.997042	+	0.0768584i	$0.0244890\pi$
$992$	−3.33543	−	5.77713i	−0.105900	−	0.183424i
$993$		−	41.5824i		−	1.31958i
$994$		0			0
$995$	58.0873	+	33.5367i	1.84149	+	1.06319i
$996$	−18.8738	−	10.8968i	−0.598039	−	0.345278i
$997$	−30.2274			−0.957312			−0.478656	−	0.878002i	$-0.658876\pi$
$997$	−30.2274			−0.957312			−0.478656	+	0.878002i	$0.658876\pi$
$998$	−14.0551	+	24.3441i	−0.444906	+	0.770600i
$999$		−	18.6390i		−	0.589713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.h.569.4		12
7.2	even	3		91.2.q.a.36.4	✓	12
7.3	odd	6		637.2.u.i.361.3		12
7.4	even	3		637.2.u.h.361.3		12
7.5	odd	6		637.2.q.h.491.4		12
7.6	odd	2		637.2.k.g.569.4		12
13.4	even	6		637.2.u.h.30.3		12
21.2	odd	6		819.2.ct.a.127.3		12
28.23	odd	6		1456.2.cc.c.673.6		12
91.2	odd	12		1183.2.a.m.1.5		6
91.4	even	6	inner	637.2.k.h.459.3		12
91.16	even	3		1183.2.c.i.337.8		12
91.17	odd	6		637.2.k.g.459.3		12
91.23	even	6		1183.2.c.i.337.5		12
91.30	even	6		91.2.q.a.43.4	yes	12
91.37	odd	12		1183.2.a.p.1.2		6
91.54	even	12		8281.2.a.by.1.5		6
91.69	odd	6		637.2.u.i.30.3		12
91.82	odd	6		637.2.q.h.589.4		12
91.89	even	12		8281.2.a.ch.1.2		6
273.212	odd	6		819.2.ct.a.316.3		12
364.303	odd	6		1456.2.cc.c.225.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	7.2	even	3
91.2.q.a.43.4	yes	12	91.30	even	6
637.2.k.g.459.3		12	91.17	odd	6
637.2.k.g.569.4		12	7.6	odd	2
637.2.k.h.459.3		12	91.4	even	6	inner
637.2.k.h.569.4		12	1.1	even	1	trivial
637.2.q.h.491.4		12	7.5	odd	6
637.2.q.h.589.4		12	91.82	odd	6
637.2.u.h.30.3		12	13.4	even	6
637.2.u.h.361.3		12	7.4	even	3
637.2.u.i.30.3		12	91.69	odd	6
637.2.u.i.361.3		12	7.3	odd	6
819.2.ct.a.127.3		12	21.2	odd	6
819.2.ct.a.316.3		12	273.212	odd	6
1183.2.a.m.1.5		6	91.2	odd	12
1183.2.a.p.1.2		6	91.37	odd	12
1183.2.c.i.337.5		12	91.23	even	6
1183.2.c.i.337.8		12	91.16	even	3
1456.2.cc.c.225.6		12	364.303	odd	6
1456.2.cc.c.673.6		12	28.23	odd	6
8281.2.a.by.1.5		6	91.54	even	12
8281.2.a.ch.1.2		6	91.89	even	12

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.823556i q^{2} +(-1.33015 + 2.30388i) q^{3} +1.32176 q^{4} +(2.73845 + 1.58105i) q^{5} +(-1.89737 - 1.09545i) q^{6} +2.73565i q^{8} +(-2.03858 - 3.53092i) q^{9} +(-1.30208 + 2.25527i) q^{10} +(-5.14653 - 2.97135i) q^{11} +(-1.75813 + 3.04517i) q^{12} +(-0.0766193 + 3.60474i) q^{13} +(-7.28508 + 4.20604i) q^{15} +0.390549 q^{16} +2.69964 q^{17} +(2.90791 - 1.67888i) q^{18} +(-1.69485 + 0.978524i) q^{19} +(3.61956 + 2.08976i) q^{20} +(2.44707 - 4.23845i) q^{22} +2.72941 q^{23} +(-6.30261 - 3.63882i) q^{24} +(2.49941 + 4.32911i) q^{25} +(-2.96870 - 0.0631003i) q^{26} +2.86554 q^{27} +(2.99923 + 5.19481i) q^{29} +(-3.46391 - 5.99967i) q^{30} +(-0.997270 + 0.575774i) q^{31} +5.79294i q^{32} +(13.6913 - 7.90465i) q^{33} +2.22331i q^{34} +(-2.69450 - 4.66701i) q^{36} -6.50454i q^{37} +(-0.805869 - 1.39581i) q^{38} +(-8.20297 - 4.97135i) q^{39} +(-4.32519 + 7.49145i) q^{40} +(-3.23351 + 1.86687i) q^{41} +(3.49562 - 6.05460i) q^{43} +(-6.80245 - 3.92740i) q^{44} -12.8923i q^{45} +2.24783i q^{46} +(-0.394969 - 0.228035i) q^{47} +(-0.519487 + 0.899778i) q^{48} +(-3.56527 + 2.05841i) q^{50} +(-3.59092 + 6.21965i) q^{51} +(-0.101272 + 4.76458i) q^{52} +(-0.199643 - 0.345792i) q^{53} +2.35994i q^{54} +(-9.39568 - 16.2738i) q^{55} -5.20632i q^{57} +(-4.27822 + 2.47003i) q^{58} -4.80586i q^{59} +(-9.62910 + 5.55936i) q^{60} +(0.578514 + 1.00201i) q^{61} +(-0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(-5.90907 + 9.75026i) q^{65} +(6.50993 + 11.2755i) q^{66} +(5.43793 + 3.13959i) q^{67} +3.56827 q^{68} +(-3.63052 + 6.28825i) q^{69} +(3.90335 + 2.25360i) q^{71} +(9.65936 - 5.57684i) q^{72} +(7.19299 - 4.15288i) q^{73} +5.35685 q^{74} -13.2983 q^{75} +(-2.24018 + 1.29337i) q^{76} +(4.09418 - 6.75560i) q^{78} +(3.95705 - 6.85381i) q^{79} +(1.06950 + 0.617476i) q^{80} +(2.30414 - 3.99089i) q^{81} +(-1.53747 - 2.66298i) q^{82} +6.19795i q^{83} +(7.39284 + 4.26826i) q^{85} +(4.98630 + 2.87884i) q^{86} -15.9576 q^{87} +(8.12857 - 14.0791i) q^{88} +3.56136i q^{89} +10.6176 q^{90} +3.60762 q^{92} -3.06345i q^{93} +(0.187800 - 0.325279i) q^{94} -6.18837 q^{95} +(-13.3462 - 7.70546i) q^{96} +(-2.96831 - 1.71375i) q^{97} +24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26}+ \cdots + 6 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9 + 12 * q^10 - 6 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^15 + 16 * q^16 + 8 * q^17 + 12 * q^18 - 12 * q^20 + 6 * q^22 + 24 * q^23 - 12 * q^24 + 10 * q^25 + 18 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 - 18 * q^31 + 30 * q^33 - 10 * q^36 - 2 * q^38 + 14 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 - 24 * q^44 - 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 - 28 * q^52 + 22 * q^53 - 6 * q^55 + 12 * q^58 - 66 * q^60 + 14 * q^61 - 4 * q^62 - 52 * q^64 - 18 * q^65 + 26 * q^66 + 24 * q^67 + 16 * q^68 + 4 * q^69 - 24 * q^71 - 60 * q^72 - 30 * q^73 - 12 * q^74 - 92 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 + 72 * q^80 + 2 * q^81 + 14 * q^82 - 48 * q^85 + 60 * q^86 + 4 * q^87 - 14 * q^88 + 24 * q^90 + 24 * q^92 + 4 * q^94 + 44 * q^95 - 6 * q^96 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more