LMFDB - Embedded newform 637.2.f.k.393.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(295,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

//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: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 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			393.5
Root			$1.16700 - 2.02131i$ of defining polynomial
Character	$\chi$	$=$	637.393
Dual form			637.2.f.k.295.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.952780 + 1.65026i) q^{2} +(-0.214224 - 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} -1.47313 q^{5} +(0.408216 - 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +(-1.40357 - 2.43105i) q^{10} +(2.19681 + 3.80498i) q^{11} +0.698866 q^{12} +(2.69752 + 2.39236i) q^{13} +(0.315580 + 0.546600i) q^{15} +(2.30082 + 3.98514i) q^{16} +(0.601356 - 1.04158i) q^{17} +5.36688 q^{18} +(-1.62105 + 2.80773i) q^{19} +(1.20145 - 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} +(2.21855 + 3.84264i) q^{23} +(-0.150567 - 0.260790i) q^{24} -2.82989 q^{25} +(-1.37787 + 6.73101i) q^{26} -2.49204 q^{27} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 + 1.04158i) q^{30} +5.24543 q^{31} +(-3.68150 + 6.37655i) q^{32} +(0.941217 - 1.63024i) q^{33} +2.29184 q^{34} +(2.29702 + 3.97856i) q^{36} +(-3.52527 - 6.10595i) q^{37} -6.17800 q^{38} +(0.309802 - 1.51341i) q^{39} -1.03539 q^{40} +(-2.58195 - 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} -7.16668 q^{44} +(-2.07449 + 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} +11.6836 q^{47} +(0.985780 - 1.70742i) q^{48} +(-2.69626 - 4.67006i) q^{50} -0.515299 q^{51} +(-5.57955 + 1.85943i) q^{52} -0.141786 q^{53} +(-2.37436 - 4.11252i) q^{54} +(-3.23618 - 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 - 0.276520i) q^{58} +(2.67177 - 4.62764i) q^{59} -1.02952 q^{60} +(-5.77287 + 9.99891i) q^{61} +(4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(-3.97380 - 3.52425i) q^{65} +3.58709 q^{66} +(-2.06773 - 3.58141i) q^{67} +(0.980907 + 1.69898i) q^{68} +(0.950533 - 1.64637i) q^{69} +(4.98486 - 8.63403i) q^{71} +(0.989763 - 1.71432i) q^{72} +15.2416 q^{73} +(6.71762 - 11.6353i) q^{74} +(0.606229 + 1.05002i) q^{75} +(-2.64418 - 4.57986i) q^{76} +(2.79269 - 0.930689i) q^{78} +0.774501 q^{79} +(-3.38941 - 5.87062i) q^{80} +(-3.69080 - 6.39265i) q^{81} +(4.92006 - 8.52179i) q^{82} -16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} -0.0433522 q^{86} +(-0.0358956 + 0.0621731i) q^{87} +(1.54402 + 2.67433i) q^{88} +(-3.27880 - 5.67904i) q^{89} -7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +(11.1319 + 19.2809i) q^{94} +(2.38801 - 4.13616i) q^{95} +3.15466 q^{96} +(-1.74583 + 3.02387i) q^{97} +12.3743 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.952780	+	1.65026i	0.673717	+	1.16691i	0.976842	+	0.213962i	$0.0686367\pi$
$2$	0.952780	+	1.65026i	0.673717	+	1.16691i	−0.303125	+	0.952951i	$0.598030\pi$
$3$	−0.214224	−	0.371047i	−0.123682	−	0.214224i	0.797535	−	0.603273i	$-0.206137\pi$
$3$	−0.214224	−	0.371047i	−0.123682	−	0.214224i	−0.921217	+	0.389049i	$0.872804\pi$
$4$	−0.815580	+	1.41263i	−0.407790	+	0.706313i
$5$	−1.47313			−0.658804			−0.329402	−	0.944190i	$-0.606847\pi$
$5$	−1.47313			−0.658804			−0.329402	+	0.944190i	$0.606847\pi$
$6$	0.408216	−	0.707051i	0.166654	−	0.288653i
$7$		0			0
$7$		0			0
$8$	0.702849			0.248495
$9$	1.40822	−	2.43910i	0.469405	−	0.813034i
$10$	−1.40357	−	2.43105i	−0.443847	−	0.768766i
$11$	2.19681	+	3.80498i	0.662362	+	1.14725i	0.979993	+	0.199031i	$0.0637794\pi$
$11$	2.19681	+	3.80498i	0.662362	+	1.14725i	−0.317631	+	0.948214i	$0.602887\pi$
$12$	0.698866			0.201745
$13$	2.69752	+	2.39236i	0.748158	+	0.663520i
$13$	2.69752	+	2.39236i	0.748158	+	0.663520i
$14$		0			0
$15$	0.315580	+	0.546600i	0.0814823	+	0.141131i
$16$	2.30082	+	3.98514i	0.575205	+	0.996284i
$17$	0.601356	−	1.04158i	0.145850	−	0.252620i	−0.783840	−	0.620963i	$-0.786742\pi$
$17$	0.601356	−	1.04158i	0.145850	−	0.252620i	0.929690	+	0.368343i	$0.120075\pi$
$18$	5.36688			1.26499
$19$	−1.62105	+	2.80773i	−0.371893	+	0.644138i	−0.989857	−	0.142068i	$-0.954625\pi$
$19$	−1.62105	+	2.80773i	−0.371893	+	0.644138i	0.617963	+	0.786207i	$0.287958\pi$
$20$	1.20145	−	2.08098i	0.268653	−	0.465321i
$21$		0			0
$22$	−4.18615	+	7.25062i	−0.892490	+	1.54584i
$23$	2.21855	+	3.84264i	0.462600	+	0.801246i	0.999090	−	0.0426603i	$-0.0135833\pi$
$23$	2.21855	+	3.84264i	0.462600	+	0.801246i	−0.536490	+	0.843907i	$0.680250\pi$
$24$	−0.150567	−	0.260790i	−0.0307343	−	0.0532334i
$25$	−2.82989			−0.565978
$26$	−1.37787	+	6.73101i	−0.270223	+	1.32006i
$27$	−2.49204			−0.479593
$28$		0			0
$29$	−0.0837807	−	0.145112i	−0.0155577	−	0.0269467i	0.858142	−	0.513413i	$-0.171619\pi$
$29$	−0.0837807	−	0.145112i	−0.0155577	−	0.0269467i	−0.873699	+	0.486466i	$0.838286\pi$
$30$	−0.601356	+	1.04158i	−0.109792	+	0.190165i
$31$	5.24543			0.942108			0.471054	−	0.882104i	$-0.343874\pi$
$31$	5.24543			0.942108			0.471054	+	0.882104i	$0.343874\pi$
$32$	−3.68150	+	6.37655i	−0.650803	+	1.12722i
$33$	0.941217	−	1.63024i	0.163845	−	0.283788i
$34$	2.29184			0.393047
$35$		0			0
$36$	2.29702	+	3.97856i	0.382837	+	0.663094i
$37$	−3.52527	−	6.10595i	−0.579552	−	1.00381i	−0.995531	−	0.0944386i	$-0.969894\pi$
$37$	−3.52527	−	6.10595i	−0.579552	−	1.00381i	0.415979	−	0.909374i	$-0.363439\pi$
$38$	−6.17800			−1.00220
$39$	0.309802	−	1.51341i	0.0496080	−	0.242339i
$40$	−1.03539			−0.163709
$41$	−2.58195	−	4.47206i	−0.403233	−	0.698419i	0.590881	−	0.806758i	$-0.298780\pi$
$41$	−2.58195	−	4.47206i	−0.403233	−	0.698419i	−0.994114	+	0.108339i	$0.965447\pi$
$42$		0			0
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	−0.866891	−	0.498497i	$-0.833886\pi$
$43$	−0.0113752	+	0.0197024i	−0.00173470	+	0.00300459i	0.865157	+	0.501502i	$0.167219\pi$
$44$	−7.16668			−1.08042
$45$	−2.07449	+	3.59311i	−0.309246	+	0.535630i
$46$	−4.22758	+	7.32239i	−0.623323	+	1.07963i
$47$	11.6836			1.70422			0.852111	−	0.523362i	$-0.175322\pi$
$47$	11.6836			1.70422			0.852111	+	0.523362i	$0.175322\pi$
$48$	0.985780	−	1.70742i	0.142285	−	0.246445i
$49$		0			0
$50$	−2.69626	−	4.67006i	−0.381309	−	0.660446i
$51$	−0.515299			−0.0721563
$52$	−5.57955	+	1.85943i	−0.773744	+	0.257857i
$53$	−0.141786			−0.0194758			−0.00973788	−	0.999953i	$-0.503100\pi$
$53$	−0.141786			−0.0194758			−0.00973788	+	0.999953i	$0.503100\pi$
$54$	−2.37436	−	4.11252i	−0.323110	−	0.559643i
$55$	−3.23618	−	5.60523i	−0.436367	−	0.755809i
$56$		0			0
$57$	1.38907			0.183986
$58$	0.159649	−	0.276520i	0.0209630	−	0.0363089i
$59$	2.67177	−	4.62764i	0.347835	−	0.602468i	−0.638030	−	0.770012i	$-0.720250\pi$
$59$	2.67177	−	4.62764i	0.347835	−	0.602468i	0.985865	+	0.167544i	$0.0535837\pi$
$60$	−1.02952			−0.132911
$61$	−5.77287	+	9.99891i	−0.739141	+	1.28023i	0.213742	+	0.976890i	$0.431435\pi$
$61$	−5.77287	+	9.99891i	−0.739141	+	1.28023i	−0.952883	+	0.303339i	$0.901898\pi$
$62$	4.99774	+	8.65635i	0.634714	+	1.09936i
$63$		0			0
$64$	−4.82736			−0.603420
$65$	−3.97380	−	3.52425i	−0.492889	−	0.437130i
$66$	3.58709			0.441540
$67$	−2.06773	−	3.58141i	−0.252613	−	0.437539i	0.711631	−	0.702553i	$-0.247957\pi$
$67$	−2.06773	−	3.58141i	−0.252613	−	0.437539i	−0.964245	+	0.265014i	$0.914623\pi$
$68$	0.980907	+	1.69898i	0.118952	+	0.206032i
$69$	0.950533	−	1.64637i	0.114431	−	0.198200i
$70$		0			0
$71$	4.98486	−	8.63403i	0.591594	−	1.02467i	−0.402424	−	0.915453i	$-0.631832\pi$
$71$	4.98486	−	8.63403i	0.591594	−	1.02467i	0.994018	−	0.109217i	$-0.0348344\pi$
$72$	0.989763	−	1.71432i	0.116645	−	0.202035i
$73$	15.2416			1.78389			0.891947	−	0.452141i	$-0.149340\pi$
$73$	15.2416			1.78389			0.891947	+	0.452141i	$0.149340\pi$
$74$	6.71762	−	11.6353i	0.780908	−	1.35257i
$75$	0.606229	+	1.05002i	0.0700013	+	0.121246i
$76$	−2.64418	−	4.57986i	−0.303309	−	0.525346i
$77$		0			0
$78$	2.79269	−	0.930689i	0.316210	−	0.105380i
$79$	0.774501			0.0871382			0.0435691	−	0.999050i	$-0.486127\pi$
$79$	0.774501			0.0871382			0.0435691	+	0.999050i	$0.486127\pi$
$80$	−3.38941	−	5.87062i	−0.378947	−	0.656356i
$81$	−3.69080	−	6.39265i	−0.410088	−	0.710294i
$82$	4.92006	−	8.52179i	0.543329	−	0.941074i
$83$	−16.0186			−1.75827			−0.879136	−	0.476571i	$-0.841879\pi$
$83$	−16.0186			−1.75827			−0.879136	+	0.476571i	$0.841879\pi$
$84$		0			0
$85$	−0.885875	+	1.53438i	−0.0960866	+	0.166427i
$86$	−0.0433522			−0.00467479
$87$	−0.0358956	+	0.0621731i	−0.00384842	+	0.00666565i
$88$	1.54402	+	2.67433i	0.164593	+	0.285084i
$89$	−3.27880	−	5.67904i	−0.347552	−	0.601977i	0.638262	−	0.769819i	$-0.279654\pi$
$89$	−3.27880	−	5.67904i	−0.347552	−	0.601977i	−0.985814	+	0.167842i	$0.946320\pi$
$90$	−7.90611			−0.833378
$91$		0			0
$92$	−7.23762			−0.754574
$93$	−1.12370	−	1.94630i	−0.116522	−	0.201822i
$94$	11.1319	+	19.2809i	1.14816	+	1.98868i
$95$	2.38801	−	4.13616i	0.245005	−	0.424361i
$96$	3.15466			0.321971
$97$	−1.74583	+	3.02387i	−0.177262	+	0.307027i	−0.940942	−	0.338568i	$-0.890057\pi$
$97$	−1.74583	+	3.02387i	−0.177262	+	0.307027i	0.763680	+	0.645595i	$0.223391\pi$
$98$		0			0
$99$	12.3743			1.24367
$100$	2.30800	−	3.99757i	0.230800	−	0.399757i
$101$	−1.28890	−	2.23244i	−0.128250	−	0.222136i	0.794749	−	0.606939i	$-0.207603\pi$
$101$	−1.28890	−	2.23244i	−0.128250	−	0.222136i	−0.922999	+	0.384803i	$0.874269\pi$
$102$	−0.490966	−	0.850379i	−0.0486129	−	0.0842000i
$103$	−16.8635			−1.66161			−0.830803	−	0.556567i	$-0.812118\pi$
$103$	−16.8635			−1.66161			−0.830803	+	0.556567i	$0.812118\pi$
$104$	1.89595	+	1.68146i	0.185913	+	0.164881i
$105$		0			0
$106$	−0.135091	−	0.233984i	−0.0131212	−	0.0227265i
$107$	−4.34132	−	7.51939i	−0.419692	−	0.726927i	0.576217	−	0.817297i	$-0.304528\pi$
$107$	−4.34132	−	7.51939i	−0.419692	−	0.726927i	−0.995908	+	0.0903697i	$0.971195\pi$
$108$	2.03245	−	3.52031i	0.195573	−	0.338742i
$109$	−12.0405			−1.15327			−0.576637	−	0.817001i	$-0.695635\pi$
$109$	−12.0405			−1.15327			−0.576637	+	0.817001i	$0.695635\pi$
$110$	6.16674	−	10.6811i	0.587976	−	1.01840i
$111$	−1.51040	+	2.61608i	−0.143360	+	0.248307i
$112$		0			0
$113$	−4.68616	+	8.11667i	−0.440837	+	0.763552i	−0.997752	−	0.0670176i	$-0.978652\pi$
$113$	−4.68616	+	8.11667i	−0.440837	+	0.763552i	0.556915	+	0.830570i	$0.311985\pi$
$114$	1.32348	+	2.29233i	0.123955	+	0.214696i
$115$	−3.26821	−	5.66071i	−0.304763	−	0.527864i
$116$	0.273319			0.0253771
$117$	9.63390	−	3.21058i	0.890654	−	0.296818i
$118$	10.1824			0.937369
$119$		0			0
$120$	0.221805	+	0.384177i	0.0202479	+	0.0350704i
$121$	−4.15192	+	7.19134i	−0.377448	+	0.653758i
$122$	−22.0011			−1.99189
$123$	−1.10623	+	1.91605i	−0.0997453	+	0.172764i
$124$	−4.27807	+	7.40983i	−0.384182	+	0.665423i
$125$	11.5344			1.03167
$126$		0			0
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	−0.966764	−	0.255672i	$-0.917703\pi$
$127$	−7.94269	−	13.7571i	−0.704800	−	1.22075i	0.261964	−	0.965078i	$-0.415630\pi$
$128$	2.76359	+	4.78667i	0.244269	+	0.423086i
$129$	0.00974735			0.000858206
$130$	2.02978	−	9.91566i	0.178024	−	0.869661i
$131$	1.85745			0.162286			0.0811430	−	0.996702i	$-0.474143\pi$
$131$	1.85745			0.162286			0.0811430	+	0.996702i	$0.474143\pi$
$132$	1.53527	+	2.65917i	0.133628	+	0.231451i
$133$		0			0
$134$	3.94018	−	6.82459i	0.340380	−	0.589555i
$135$	3.67109			0.315957
$136$	0.422662	−	0.732072i	0.0362430	−	0.0627747i
$137$	6.40011	−	11.0853i	0.546798	−	0.947082i	−0.451693	−	0.892173i	$-0.649180\pi$
$137$	6.40011	−	11.0853i	0.546798	−	0.947082i	0.998491	−	0.0549088i	$-0.0174868\pi$
$138$	3.62260			0.308376
$139$	0.169365	−	0.293348i	0.0143653	−	0.0248815i	−0.858753	−	0.512389i	$-0.828761\pi$
$139$	0.169365	−	0.293348i	0.0143653	−	0.0248815i	0.873119	+	0.487508i	$0.162094\pi$
$140$		0			0
$141$	−2.50290	−	4.33514i	−0.210782	−	0.365085i
$142$	18.9979			1.59427
$143$	−3.17693	+	15.5196i	−0.265669	+	1.29781i
$144$	12.9602			1.08002
$145$	0.123420	+	0.213769i	0.0102495	+	0.0177526i
$146$	14.5219	+	25.1526i	1.20184	+	2.08165i
$147$		0			0
$148$	11.5006			0.945341
$149$	−1.96158	+	3.39756i	−0.160699	+	0.278339i	−0.935120	−	0.354332i	$-0.884708\pi$
$149$	−1.96158	+	3.39756i	−0.160699	+	0.278339i	0.774421	+	0.632671i	$0.218041\pi$
$150$	−1.15521	+	2.00088i	−0.0943222	+	0.163371i
$151$	−2.11879			−0.172424			−0.0862122	−	0.996277i	$-0.527476\pi$
$151$	−2.11879			−0.172424			−0.0862122	+	0.996277i	$0.527476\pi$
$152$	−1.13935	+	1.97341i	−0.0924135	+	0.160065i
$153$	−1.69368	−	2.93354i	−0.136926	−	0.237162i
$154$		0			0
$155$	−7.72721			−0.620664
$156$	1.88521	+	1.67194i	0.150937	+	0.133862i
$157$	−22.1128			−1.76479			−0.882397	−	0.470506i	$-0.844071\pi$
$157$	−22.1128			−1.76479			−0.882397	+	0.470506i	$0.844071\pi$
$158$	0.737929	+	1.27813i	0.0587065	+	0.101683i
$159$	0.0303739	+	0.0526091i	0.00240881	+	0.00417217i
$160$	5.42333	−	9.39348i	0.428752	−	0.742620i
$161$		0			0
$162$	7.03303	−	12.1816i	0.552567	−	0.957074i
$163$	−1.92607	+	3.33605i	−0.150861	+	0.261299i	−0.931544	−	0.363628i	$-0.881538\pi$
$163$	−1.92607	+	3.33605i	−0.150861	+	0.261299i	0.780683	+	0.624927i	$0.214871\pi$
$164$	8.42314			0.657736
$165$	−1.38653	+	2.40155i	−0.107942	+	0.186960i
$166$	−15.2622	−	26.4349i	−1.18458	−	2.05175i
$167$	−1.06947	−	1.85238i	−0.0827582	−	0.143341i	0.821676	−	0.569956i	$-0.193040\pi$
$167$	−1.06947	−	1.85238i	−0.0827582	−	0.143341i	−0.904434	+	0.426614i	$0.859706\pi$
$168$		0			0
$169$	1.55326	+	12.9069i	0.119482	+	0.992836i
$170$	−3.37618			−0.258941
$171$	4.56557	+	7.90779i	0.349138	+	0.604724i
$172$	−0.0185547	−	0.0321378i	−0.00141479	−	0.00245048i
$173$	8.30664	−	14.3875i	0.631542	−	1.09386i	−0.355695	−	0.934602i	$-0.615756\pi$
$173$	8.30664	−	14.3875i	0.631542	−	1.09386i	0.987237	−	0.159260i	$-0.0509110\pi$
$174$	−0.136803			−0.0103710
$175$		0			0
$176$	−10.1089	+	17.5091i	−0.761988	+	1.31980i
$177$	−2.28943			−0.172084
$178$	6.24795	−	10.8218i	0.468303	−	0.811125i
$179$	0.269748	+	0.467217i	0.0201619	+	0.0349214i	0.875930	−	0.482438i	$-0.160248\pi$
$179$	0.269748	+	0.467217i	0.0201619	+	0.0349214i	−0.855768	+	0.517359i	$0.826915\pi$
$180$	−3.38382	−	5.86094i	−0.252215	−	0.436849i
$181$	2.77164			0.206014			0.103007	−	0.994681i	$-0.467154\pi$
$181$	2.77164			0.206014			0.103007	+	0.994681i	$0.467154\pi$
$182$		0			0
$183$	4.94675			0.365674
$184$	1.55931	+	2.70080i	0.114954	+	0.199105i
$185$	5.19319	+	8.99486i	0.381811	+	0.661316i
$186$	2.14127	−	3.70879i	0.157006	−	0.271942i
$187$	5.28425			0.386423
$188$	−9.52887	+	16.5045i	−0.694964	+	1.20371i
$189$		0			0
$190$	9.10100			0.660256
$191$	10.1204	−	17.5290i	0.732284	−	1.26835i	−0.223621	−	0.974676i	$-0.571788\pi$
$191$	10.1204	−	17.5290i	0.732284	−	1.26835i	0.955905	−	0.293677i	$-0.0948790\pi$
$192$	1.03414	+	1.79118i	0.0746323	+	0.129267i
$193$	8.18856	+	14.1830i	0.589425	+	1.02091i	0.994308	+	0.106546i	$0.0339791\pi$
$193$	8.18856	+	14.1830i	0.589425	+	1.02091i	−0.404882	+	0.914369i	$0.632688\pi$
$194$	−6.65357			−0.477698
$195$	−0.456378	+	2.22944i	−0.0326819	+	0.159654i
$196$		0			0
$197$	−9.86676	−	17.0897i	−0.702977	−	1.21759i	−0.967417	−	0.253190i	$-0.918520\pi$
$197$	−9.86676	−	17.0897i	−0.702977	−	1.21759i	0.264439	−	0.964402i	$-0.414813\pi$
$198$	11.7900	+	20.4209i	0.837879	+	1.45125i
$199$	7.05873	−	12.2261i	0.500380	−	0.866683i	−0.499620	−	0.866245i	$-0.666527\pi$
$199$	7.05873	−	12.2261i	0.500380	−	0.866683i	1.00000		0.000438630i	$-0.000139620\pi$
$200$	−1.98898			−0.140642
$201$	−0.885913	+	1.53445i	−0.0624875	+	0.108232i
$202$	2.45607	−	4.25404i	0.172809	−	0.299313i
$203$		0			0
$204$	0.420267	−	0.727924i	0.0294246	−	0.0509649i
$205$	3.80354	+	6.58793i	0.265651	+	0.460121i
$206$	−16.0672	−	27.8291i	−1.11945	−	1.93895i
$207$	12.4968			0.868588
$208$	−3.32735	+	16.2544i	−0.230710	+	1.12704i
$209$	−14.2445			−0.985313
$210$		0			0
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	0.934597	−	0.355709i	$-0.115761\pi$
$211$	2.31317	+	4.00652i	0.159245	+	0.275820i	−0.775352	+	0.631530i	$0.782427\pi$
$212$	0.115638	−	0.200290i	0.00794202	−	0.0137560i
$213$	−4.27150			−0.292678
$214$	8.27265	−	14.3287i	0.565507	−	0.979487i
$215$	0.0167571	−	0.0290242i	0.00114283	−	0.00197943i
$216$	−1.75152			−0.119176
$217$		0			0
$218$	−11.4720	−	19.8700i	−0.776980	−	1.34577i
$219$	−3.26511	−	5.65534i	−0.220636	−	0.382152i
$220$	10.5575			0.711784
$221$	4.11400	−	1.37103i	0.276737	−	0.0922251i
$222$	−5.75630			−0.386337
$223$	10.6761	+	18.4916i	0.714926	+	1.23829i	0.962988	+	0.269545i	$0.0868732\pi$
$223$	10.6761	+	18.4916i	0.714926	+	1.23829i	−0.248061	+	0.968744i	$0.579793\pi$
$224$		0			0
$225$	−3.98509	+	6.90239i	−0.265673	+	0.460159i
$226$	−17.8595			−1.18800
$227$	5.22451	−	9.04911i	0.346763	−	0.600611i	−0.638910	−	0.769282i	$-0.720614\pi$
$227$	5.22451	−	9.04911i	0.346763	−	0.600611i	0.985672	+	0.168671i	$0.0539476\pi$
$228$	−1.13289	+	1.96223i	−0.0750278	+	0.129952i
$229$	14.4580			0.955413			0.477706	−	0.878520i	$-0.341468\pi$
$229$	14.4580			0.955413			0.477706	+	0.878520i	$0.341468\pi$
$230$	6.22778	−	10.7868i	0.410648	−	0.711262i
$231$		0			0
$232$	−0.0588852	−	0.101992i	−0.00386600	−	0.00669611i
$233$	−9.28827			−0.608495			−0.304247	−	0.952593i	$-0.598405\pi$
$233$	−9.28827			−0.608495			−0.304247	+	0.952593i	$0.598405\pi$
$234$	14.4773	+	12.8395i	0.946410	+	0.839344i
$235$	−17.2114			−1.12275
$236$	4.35808	+	7.54842i	0.283687	+	0.491360i
$237$	−0.165917	−	0.287376i	−0.0107774	−	0.0186671i
$238$		0			0
$239$	19.6332			1.26997			0.634983	−	0.772526i	$-0.281007\pi$
$239$	19.6332			1.26997			0.634983	+	0.772526i	$0.281007\pi$
$240$	−1.45218	+	2.51525i	−0.0937380	+	0.162359i
$241$	−3.65552	+	6.33155i	−0.235473	+	0.407851i	−0.959410	−	0.282015i	$-0.908997\pi$
$241$	−3.65552	+	6.33155i	−0.235473	+	0.407851i	0.723937	+	0.689866i	$0.242331\pi$
$242$	−15.8235			−1.01717
$243$	−5.31937	+	9.21341i	−0.341238	+	0.591041i
$244$	−9.41648	−	16.3098i	−0.602828	−	1.04413i
$245$		0			0
$246$	−4.21597			−0.268801
$247$	−11.0899	+	3.69581i	−0.705634	+	0.235159i
$248$	3.68675			0.234109
$249$	3.43157	+	5.94365i	0.217467	+	0.376664i
$250$	10.9898	+	19.0349i	0.695055	+	1.20387i
$251$	5.93191	−	10.2744i	0.374419	−	0.648512i	−0.615821	−	0.787886i	$-0.711176\pi$
$251$	5.93191	−	10.2744i	0.374419	−	0.648512i	0.990240	+	0.139374i	$0.0445089\pi$
$252$		0			0
$253$	−9.74746	+	16.8831i	−0.612817	+	1.06143i
$254$	15.1353	−	26.2151i	0.949672	−	1.64488i
$255$	0.759102			0.0475368
$256$	−10.0935	+	17.4825i	−0.630846	+	1.09266i
$257$	7.58608	+	13.1395i	0.473206	+	0.819618i	0.999530	−	0.0306670i	$-0.00976315\pi$
$257$	7.58608	+	13.1395i	0.473206	+	0.819618i	−0.526323	+	0.850285i	$0.676430\pi$
$258$	0.00928708	+	0.0160857i	0.000578188	+	0.00100145i
$259$		0			0
$260$	8.21940	−	2.73919i	0.509745	−	0.169877i
$261$	−0.471925			−0.0292115
$262$	1.76974	+	3.06528i	0.109335	+	0.189374i
$263$	−8.59820	−	14.8925i	−0.530187	−	0.918312i	−0.999380	−	0.0352156i	$-0.988788\pi$
$263$	−8.59820	−	14.8925i	−0.530187	−	0.918312i	0.469192	−	0.883096i	$-0.344545\pi$
$264$	0.661533	−	1.14581i	0.0407145	−	0.0705196i
$265$	0.208869			0.0128307
$266$		0			0
$267$	−1.40479	+	2.43317i	−0.0859719	+	0.148908i
$268$	6.74559			0.412052
$269$	−9.46102	+	16.3870i	−0.576849	+	0.999131i	0.418989	+	0.907991i	$0.362384\pi$
$269$	−9.46102	+	16.3870i	−0.576849	+	0.999131i	−0.995838	+	0.0911401i	$0.970949\pi$
$270$	3.49774	+	6.05827i	0.212866	+	0.368695i
$271$	−16.0667	−	27.8283i	−0.975982	−	1.69045i	−0.676657	−	0.736298i	$-0.736572\pi$
$271$	−16.0667	−	27.8283i	−0.975982	−	1.69045i	−0.299324	−	0.954151i	$-0.596761\pi$
$272$	5.53444			0.335575
$273$		0			0
$274$	24.3916			1.47355
$275$	−6.21672	−	10.7677i	−0.374882	−	0.649315i
$276$	1.55047	+	2.68549i	0.0933273	+	0.161648i
$277$	−9.20269	+	15.9395i	−0.552936	+	0.957714i	0.445125	+	0.895469i	$0.353159\pi$
$277$	−9.20269	+	15.9395i	−0.552936	+	0.957714i	−0.998061	+	0.0622450i	$0.980174\pi$
$278$	0.645469			0.0387126
$279$	7.38671	−	12.7942i	0.442231	−	0.765966i
$280$		0			0
$281$	−14.2252			−0.848603			−0.424302	−	0.905521i	$-0.639480\pi$
$281$	−14.2252			−0.848603			−0.424302	+	0.905521i	$0.639480\pi$
$282$	4.76942	−	8.26087i	0.284015	−	0.491928i
$283$	5.71446	+	9.89773i	0.339689	+	0.588359i	0.984374	−	0.176089i	$-0.0563448\pi$
$283$	5.71446	+	9.89773i	0.339689	+	0.588359i	−0.644685	+	0.764448i	$0.723011\pi$
$284$	8.13109	+	14.0835i	0.482492	+	0.835700i
$285$	−2.04628			−0.121211
$286$	−28.6383	+	9.54396i	−1.69342	+	0.564346i
$287$		0			0
$288$	10.3687	+	17.9591i	0.610981	+	1.05825i
$289$	7.77674	+	13.4697i	0.457455	+	0.792336i
$290$	−0.235184	+	0.407351i	−0.0138105	+	0.0239205i
$291$	1.49599			0.0876967
$292$	−12.4307	+	21.5307i	−0.727453	+	1.25999i
$293$	6.60231	−	11.4355i	0.385711	−	0.668071i	−0.606156	−	0.795345i	$-0.707289\pi$
$293$	6.60231	−	11.4355i	0.385711	−	0.668071i	0.991868	+	0.127274i	$0.0406228\pi$
$294$		0			0
$295$	−3.93586	+	6.81712i	−0.229155	+	0.396908i
$296$	−2.47773	−	4.29156i	−0.144015	−	0.249442i
$297$	−5.47452	−	9.48215i	−0.317664	−	0.550210i
$298$	−7.47582			−0.433062
$299$	−3.20838	+	15.6732i	−0.185545	+	0.906404i
$300$	−1.97771			−0.114183
$301$		0			0
$302$	−2.01874	−	3.49656i	−0.116165	−	0.201204i
$303$	−0.552225	+	0.956482i	−0.0317245	+	0.0549484i
$304$	−14.9189			−0.855660
$305$	8.50420	−	14.7297i	0.486949	−	0.843420i
$306$	3.22740	−	5.59003i	0.184498	−	0.319561i
$307$	−6.65903			−0.380051			−0.190026	−	0.981779i	$-0.560857\pi$
$307$	−6.65903			−0.380051			−0.190026	+	0.981779i	$0.560857\pi$
$308$		0			0
$309$	3.61255	+	6.25713i	0.205511	+	0.355955i
$310$	−7.36233	−	12.7519i	−0.418152	−	0.724261i
$311$	−2.04597			−0.116016			−0.0580081	−	0.998316i	$-0.518475\pi$
$311$	−2.04597			−0.116016			−0.0580081	+	0.998316i	$0.518475\pi$
$312$	0.217744	−	1.06370i	0.0123273	−	0.0602199i
$313$	9.41767			0.532318			0.266159	−	0.963929i	$-0.414245\pi$
$313$	9.41767			0.532318			0.266159	+	0.963929i	$0.414245\pi$
$314$	−21.0686	−	36.4919i	−1.18897	−	2.05936i
$315$		0			0
$316$	−0.631667	+	1.09408i	−0.0355341	+	0.0615468i
$317$	−33.3713			−1.87432			−0.937159	−	0.348902i	$-0.886555\pi$
$317$	−33.3713			−1.87432			−0.937159	+	0.348902i	$0.886555\pi$
$318$	−0.0578792	+	0.100250i	−0.00324571	+	0.00562173i
$319$	0.368100	−	0.637568i	0.0206097	−	0.0356970i
$320$	7.11133			0.397536
$321$	−1.86003	+	3.22167i	−0.103817	+	0.179816i
$322$		0			0
$323$	1.94965	+	3.37689i	0.108481	+	0.187895i
$324$	12.0405			0.668919
$325$	−7.63369	−	6.77010i	−0.423441	−	0.375538i
$326$	−7.34048			−0.406551
$327$	2.57937	+	4.46760i	0.142639	+	0.247059i
$328$	−1.81472	−	3.14318i	−0.100201	−	0.173553i
$329$		0			0
$330$	−5.28425			−0.290888
$331$	−9.53298	+	16.5116i	−0.523980	+	0.907560i	0.475631	+	0.879645i	$0.342220\pi$
$331$	−9.53298	+	16.5116i	−0.523980	+	0.907560i	−0.999610	+	0.0279144i	$0.991113\pi$
$332$	13.0645	−	22.6283i	0.717005	−	1.24189i
$333$	−19.8574			−1.08818
$334$	2.03794	−	3.52982i	0.111511	−	0.193143i
$335$	3.04603	+	5.27588i	0.166423	+	0.288252i
$336$		0			0
$337$	−31.2849			−1.70420			−0.852098	−	0.523382i	$-0.824670\pi$
$337$	−31.2849			−1.70420			−0.852098	+	0.523382i	$0.824670\pi$
$338$	−19.8198	+	14.8607i	−1.07806	+	0.808316i
$339$	4.01555			0.218095
$340$	−1.44500	−	2.50282i	−0.0783663	−	0.135734i
$341$	11.5232	+	19.9588i	0.624017	+	1.08083i
$342$	−8.69996	+	15.0688i	−0.470440	+	0.814826i
$343$		0			0
$344$	−0.00799504	+	0.0138478i	−0.000431064	+	0.000746624i
$345$	−1.40026	+	2.42532i	−0.0753874	+	0.130575i
$346$	31.6576			1.70192
$347$	−5.83759	+	10.1110i	−0.313378	+	0.542787i	−0.979091	−	0.203420i	$-0.934794\pi$
$347$	−5.83759	+	10.1110i	−0.313378	+	0.542787i	0.665713	+	0.746208i	$0.268128\pi$
$348$	−0.0585515	−	0.101414i	−0.00313869	−	0.00543637i
$349$	−11.9952	−	20.7763i	−0.642089	−	1.11213i	−0.984966	−	0.172750i	$-0.944735\pi$
$349$	−11.9952	−	20.7763i	−0.642089	−	1.11213i	0.342877	−	0.939380i	$-0.388599\pi$
$350$		0			0
$351$	−6.72233	−	5.96184i	−0.358811	−	0.318219i
$352$	−32.3502			−1.72427
$353$	−6.39668	−	11.0794i	−0.340461	−	0.589696i	0.644057	−	0.764977i	$-0.277250\pi$
$353$	−6.39668	−	11.0794i	−0.340461	−	0.589696i	−0.984518	+	0.175282i	$0.943916\pi$
$354$	−2.18132	−	3.77816i	−0.115936	−	0.200807i
$355$	−7.34334	+	12.7190i	−0.389744	+	0.675057i
$356$	10.6965			0.566912
$357$		0			0
$358$	−0.514021	+	0.890310i	−0.0271668	+	0.0470544i
$359$	12.3397			0.651265			0.325633	−	0.945496i	$-0.394423\pi$
$359$	12.3397			0.651265			0.325633	+	0.945496i	$0.394423\pi$
$360$	−1.45805	+	2.52542i	−0.0768460	+	0.133101i
$361$	4.24442	+	7.35155i	0.223390	+	0.386924i
$362$	2.64076	+	4.57393i	0.138795	+	0.240401i
$363$	3.55776			0.186734
$364$		0			0
$365$	−22.4528			−1.17524
$366$	4.71316	+	8.16344i	0.246361	+	0.426710i
$367$	−1.01538	−	1.75870i	−0.0530026	−	0.0918032i	0.838307	−	0.545199i	$-0.183546\pi$
$367$	−1.01538	−	1.75870i	−0.0530026	−	0.0918032i	−0.891309	+	0.453396i	$0.850212\pi$
$368$	−10.2090	+	17.6825i	−0.532179	+	0.921762i
$369$	−14.5438			−0.757118
$370$	−9.89593	+	17.1403i	−0.514465	+	0.891079i
$371$		0			0
$372$	3.66586			0.190066
$373$	1.93700	−	3.35498i	0.100294	−	0.173714i	−0.811512	−	0.584336i	$-0.801355\pi$
$373$	1.93700	−	3.35498i	0.100294	−	0.173714i	0.911806	+	0.410622i	$0.134688\pi$
$374$	5.03473	+	8.72040i	0.260340	+	0.450921i
$375$	−2.47095	−	4.27981i	−0.127599	−	0.221009i
$376$	8.21177			0.423490
$377$	0.121160	−	0.591877i	0.00624007	−	0.0304832i
$378$		0			0
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	0.990200	−	0.139659i	$-0.0446006\pi$
$379$	7.28396	+	12.6162i	0.374152	+	0.648050i	−0.616048	+	0.787709i	$0.711267\pi$
$380$	3.89523	+	6.74673i	0.199821	+	0.346100i
$381$	−3.40303	+	5.89422i	−0.174342	+	0.301970i
$382$	38.5699			1.97341
$383$	13.3909	−	23.1937i	0.684243	−	1.18514i	−0.289430	−	0.957199i	$-0.593466\pi$
$383$	13.3909	−	23.1937i	0.684243	−	1.18514i	0.973674	−	0.227945i	$-0.0732008\pi$
$384$	1.18405	−	2.05084i	0.0604234	−	0.104656i
$385$		0			0
$386$	−15.6038	+	27.0266i	−0.794212	+	1.37562i
$387$	0.0320375	+	0.0554905i	0.00162856	+	0.00282074i
$388$	−2.84773	−	4.93241i	−0.144571	−	0.250405i
$389$	12.0148			0.609173			0.304586	−	0.952485i	$-0.401482\pi$
$389$	12.0148			0.609173			0.304586	+	0.952485i	$0.401482\pi$
$390$	−4.11400	+	1.37103i	−0.208320	+	0.0694246i
$391$	5.33655			0.269881
$392$		0			0
$393$	−0.397910	−	0.689200i	−0.0200719	−	0.0347655i
$394$	18.8017	−	32.5655i	0.947216	−	1.64063i
$395$	−1.14094			−0.0574070
$396$	−10.0922	+	17.4803i	−0.507154	+	0.878417i
$397$	0.828825	−	1.43557i	0.0415975	−	0.0720491i	−0.844477	−	0.535592i	$-0.820089\pi$
$397$	0.828825	−	1.43557i	0.0415975	−	0.0720491i	0.886075	+	0.463543i	$0.153422\pi$
$398$	26.9017			1.34846
$399$		0			0
$400$	−6.51106	−	11.2775i	−0.325553	−	0.563874i
$401$	10.2414	+	17.7386i	0.511430	+	0.885823i	0.999912	+	0.0132488i	$0.00421735\pi$
$401$	10.2414	+	17.7386i	0.511430	+	0.885823i	−0.488482	+	0.872574i	$0.662449\pi$
$402$	−3.37632			−0.168396
$403$	14.1497	+	12.5489i	0.704846	+	0.625108i
$404$	4.20479			0.209196
$405$	5.43702	+	9.41720i	0.270168	+	0.467944i
$406$		0			0
$407$	15.4887	−	26.8272i	0.767746	−	1.32978i
$408$	−0.362177			−0.0179304
$409$	−7.43293	+	12.8742i	−0.367535	+	0.636589i	−0.989180	−	0.146710i	$-0.953131\pi$
$409$	−7.43293	+	12.8742i	−0.367535	+	0.636589i	0.621645	+	0.783299i	$0.286465\pi$
$410$	−7.24788	+	12.5537i	−0.357947	+	0.619983i
$411$	−5.48422			−0.270517
$412$	13.7535	−	23.8217i	0.677586	−	1.17361i
$413$		0			0
$414$	11.9067	+	20.6230i	0.585182	+	1.01357i
$415$	23.5975			1.15836
$416$	−25.1859	+	8.39342i	−1.23484	+	0.411521i
$417$	−0.145128			−0.00710693
$418$	−13.5719	−	23.5072i	−0.663822	−	1.14977i
$419$	11.8087	+	20.4533i	0.576895	+	0.999211i	0.995833	+	0.0911962i	$0.0290690\pi$
$419$	11.8087	+	20.4533i	0.576895	+	0.999211i	−0.418938	+	0.908015i	$0.637598\pi$
$420$		0			0
$421$	26.0822			1.27117			0.635585	−	0.772031i	$-0.280759\pi$
$421$	26.0822			1.27117			0.635585	+	0.772031i	$0.280759\pi$
$422$	−4.40788	+	7.63467i	−0.214572	+	0.371650i
$423$	16.4530	−	28.4974i	0.799971	−	1.38559i
$424$	−0.0996539			−0.00483962
$425$	−1.70177	+	2.94755i	−0.0825479	+	0.142977i
$426$	−4.06980	−	7.04910i	−0.197182	−	0.341530i
$427$		0			0
$428$	14.1628			0.684584
$429$	6.43906	−	2.14587i	0.310881	−	0.103604i
$430$	0.0638635			0.00307977
$431$	6.65859	+	11.5330i	0.320733	+	0.555526i	0.980640	−	0.195822i	$-0.0627374\pi$
$431$	6.65859	+	11.5330i	0.320733	+	0.555526i	−0.659906	+	0.751348i	$0.729404\pi$
$432$	−5.73373	−	9.93110i	−0.275864	−	0.477810i
$433$	−10.2110	+	17.6860i	−0.490711	+	0.849937i	−0.999943	−	0.0106929i	$-0.996596\pi$
$433$	−10.2110	+	17.6860i	−0.490711	+	0.849937i	0.509232	+	0.860629i	$0.329930\pi$
$434$		0			0
$435$	0.0528790	−	0.0915890i	0.00253535	−	0.00439136i
$436$	9.82001	−	17.0087i	0.470293	−	0.814571i
$437$	−14.3855			−0.688152
$438$	6.22187	−	10.7766i	0.297292	−	0.514925i
$439$	4.88537	+	8.46171i	0.233166	+	0.403855i	0.958738	−	0.284291i	$-0.0917581\pi$
$439$	4.88537	+	8.46171i	0.233166	+	0.403855i	−0.725572	+	0.688146i	$0.758425\pi$
$440$	−2.27455	−	3.93963i	−0.108435	−	0.187814i
$441$		0			0
$442$	6.18229	+	5.48290i	0.294061	+	0.260795i
$443$	21.1639			1.00553			0.502763	−	0.864424i	$-0.332317\pi$
$443$	21.1639			1.00553			0.502763	+	0.864424i	$0.332317\pi$
$444$	−2.46370	−	4.26725i	−0.116922	−	0.202514i
$445$	4.83010	+	8.36597i	0.228968	+	0.396585i
$446$	−20.3440	+	35.2368i	−0.963317	+	1.66851i
$447$	1.68087			0.0795023
$448$		0			0
$449$	9.07320	−	15.7152i	0.428191	−	0.741648i	−0.568522	−	0.822668i	$-0.692484\pi$
$449$	9.07320	−	15.7152i	0.428191	−	0.741648i	0.996712	+	0.0810200i	$0.0258178\pi$
$450$	−15.1877			−0.715954
$451$	11.3441	−	19.6485i	0.534172	−	0.925213i
$452$	−7.64387	−	13.2396i	−0.359538	−	0.622737i
$453$	0.453895	+	0.786168i	0.0213258	+	0.0369374i
$454$	19.9112			0.934480
$455$		0			0
$456$	0.976304			0.0457196
$457$	9.00991	+	15.6056i	0.421466	+	0.730000i	0.996083	−	0.0884220i	$-0.0281824\pi$
$457$	9.00991	+	15.6056i	0.421466	+	0.730000i	−0.574617	+	0.818422i	$0.694849\pi$
$458$	13.7753	+	23.8595i	0.643678	+	1.11488i
$459$	−1.49860	+	2.59565i	−0.0699487	+	0.121155i
$460$	10.6620			0.497116
$461$	14.8873	−	25.7855i	0.693370	−	1.20095i	−0.277357	−	0.960767i	$-0.589458\pi$
$461$	14.8873	−	25.7855i	0.693370	−	1.20095i	0.970727	−	0.240185i	$-0.0772082\pi$
$462$		0			0
$463$	17.7067			0.822900			0.411450	−	0.911432i	$-0.365023\pi$
$463$	17.7067			0.822900			0.411450	+	0.911432i	$0.365023\pi$
$464$	0.385529	−	0.667755i	0.0178977	−	0.0309997i
$465$	1.65535	+	2.86715i	0.0767651	+	0.132961i
$466$	−8.84968	−	15.3281i	−0.409953	−	0.710060i
$467$	−5.82922			−0.269744			−0.134872	−	0.990863i	$-0.543062\pi$
$467$	−5.82922			−0.269744			−0.134872	+	0.990863i	$0.543062\pi$
$468$	−3.32186	+	16.2276i	−0.153553	+	0.750120i
$469$		0			0
$470$	−16.3987	−	28.4033i	−0.756414	−	1.31015i
$471$	4.73709	+	8.20488i	0.218274	+	0.378061i
$472$	1.87785	−	3.25253i	0.0864350	−	0.149710i
$473$	−0.0999564			−0.00459600
$474$	0.316164	−	0.547612i	0.0145219	−	0.0251527i
$475$	4.58738	−	7.94557i	0.210483	−	0.364568i
$476$		0			0
$477$	−0.199665	+	0.345830i	−0.00914203	+	0.0158345i
$478$	18.7061	+	32.4000i	0.855598	+	1.48194i
$479$	−7.24565	−	12.5498i	−0.331062	−	0.573417i	0.651658	−	0.758513i	$-0.274074\pi$
$479$	−7.24565	−	12.5498i	−0.331062	−	0.573417i	−0.982720	+	0.185096i	$0.940740\pi$
$480$	−4.64722			−0.212116
$481$	5.09811	−	24.9047i	0.232454	−	1.13556i
$482$	−13.9316			−0.634569
$483$		0			0
$484$	−6.77245	−	11.7302i	−0.307839	−	0.533192i
$485$	2.57183	−	4.45455i	0.116781	−	0.202271i
$486$	−20.2727			−0.919591
$487$	8.98006	−	15.5539i	0.406926	−	0.704816i	−0.587618	−	0.809139i	$-0.699934\pi$
$487$	8.98006	−	15.5539i	0.406926	−	0.704816i	0.994543	+	0.104323i	$0.0332675\pi$
$488$	−4.05746	+	7.02772i	−0.183672	+	0.318130i
$489$	1.65044			0.0746354
$490$		0			0
$491$	18.1505	+	31.4375i	0.819119	+	1.41876i	0.906332	+	0.422566i	$0.138870\pi$
$491$	18.1505	+	31.4375i	0.819119	+	1.41876i	−0.0872134	+	0.996190i	$0.527796\pi$
$492$	−1.80444	−	3.12537i	−0.0813503	−	0.140903i
$493$	−0.201528			−0.00907637
$494$	−16.6653	−	14.7800i	−0.749807	−	0.664983i
$495$	−18.2290			−0.819332
$496$	12.0688	+	20.9038i	0.541905	+	0.938607i
$497$		0			0
$498$	−6.53906	+	11.3260i	−0.293022	+	0.507530i
$499$	23.7076			1.06130			0.530649	−	0.847591i	$-0.321948\pi$
$499$	23.7076			1.06130			0.530649	+	0.847591i	$0.321948\pi$
$500$	−9.40726	+	16.2938i	−0.420705	+	0.728683i
$501$	−0.458213	+	0.793648i	−0.0204714	+	0.0354576i
$502$	22.6072			1.00901
$503$	−13.8876	+	24.0540i	−0.619217	+	1.07252i	0.370411	+	0.928868i	$0.379217\pi$
$503$	−13.8876	+	24.0540i	−0.619217	+	1.07252i	−0.989629	+	0.143648i	$0.954117\pi$
$504$		0			0
$505$	1.89871	+	3.28867i	0.0844916	+	0.146344i
$506$	−37.1487			−1.65146
$507$	4.45630	−	3.34129i	0.197911	−	0.148392i
$508$	25.9116			1.14964
$509$	−4.35208	−	7.53802i	−0.192902	−	0.334117i	0.753308	−	0.657667i	$-0.228457\pi$
$509$	−4.35208	−	7.53802i	−0.192902	−	0.334117i	−0.946211	+	0.323551i	$0.895123\pi$
$510$	0.723257	+	1.25272i	0.0320264	+	0.0554713i
$511$		0			0
$512$	−27.4134			−1.21151
$513$	4.03971	−	6.99698i	0.178357	−	0.308924i
$514$	−14.4557	+	25.0380i	−0.637615	+	1.10438i
$515$	24.8421			1.09467
$516$	−0.00794974	+	0.0137693i	−0.000349968	+	0.000606162i
$517$	25.6665	+	44.4557i	1.12881	+	1.95516i
$518$		0			0
$519$	−7.11792			−0.312442
$520$	−2.79298	−	2.47702i	−0.122480	−	0.108624i
$521$	−8.57146			−0.375523			−0.187761	−	0.982215i	$-0.560123\pi$
$521$	−8.57146			−0.375523			−0.187761	+	0.982215i	$0.560123\pi$
$522$	−0.449641	−	0.778801i	−0.0196803	−	0.0340872i
$523$	−14.9746	−	25.9369i	−0.654796	−	1.13414i	−0.981945	−	0.189167i	$-0.939421\pi$
$523$	−14.9746	−	25.9369i	−0.654796	−	1.13414i	0.327149	−	0.944973i	$-0.393912\pi$
$524$	−1.51490	+	2.62388i	−0.0661786	+	0.114625i
$525$		0			0
$526$	16.3844	−	28.3786i	0.714393	−	1.23736i
$527$	3.15437	−	5.46353i	0.137407	−	0.237995i
$528$	8.66228			0.376977
$529$	1.65606	−	2.86838i	0.0720027	−	0.124712i
$530$	0.199006	+	0.344689i	0.00864427	+	0.0149723i
$531$	−7.52486	−	13.0334i	−0.326551	−	0.565603i
$532$		0			0
$533$	3.73391	−	18.2404i	0.161734	−	0.790081i
$534$	−5.35383			−0.231683
$535$	6.39534	+	11.0770i	0.276494	+	0.478902i
$536$	−1.45330	−	2.51719i	−0.0627730	−	0.108726i
$537$	0.115573	−	0.200178i	0.00498734	−	0.00863832i
$538$	−36.0571			−1.55453
$539$		0			0
$540$	−2.99407	+	5.18588i	−0.128844	+	0.223165i
$541$	10.4819			0.450652			0.225326	−	0.974283i	$-0.427655\pi$
$541$	10.4819			0.450652			0.225326	+	0.974283i	$0.427655\pi$
$542$	30.6160	−	53.0285i	1.31507	−	2.27777i
$543$	−0.593751	−	1.02841i	−0.0254803	−	0.0441331i
$544$	4.42778	+	7.66914i	0.189840	+	0.328812i
$545$	17.7373			0.759781
$546$		0			0
$547$	15.2216			0.650829			0.325415	−	0.945571i	$-0.394496\pi$
$547$	15.2216			0.650829			0.325415	+	0.945571i	$0.394496\pi$
$548$	10.4396	+	18.0819i	0.445957	+	0.772421i
$549$	16.2589	+	28.1613i	0.693914	+	1.20189i
$550$	11.8463	−	20.5184i	0.505129	−	0.874909i
$551$	0.543250			0.0231432
$552$	0.668081	−	1.15715i	0.0284354	−	0.0492516i
$553$		0			0
$554$	−35.0726			−1.49009
$555$	2.22501	−	3.85383i	0.0944464	−	0.163586i
$556$	0.276261	+	0.478497i	0.0117161	+	0.0202928i
$557$	−5.92986	−	10.2708i	−0.251256	−	0.435189i	0.712616	−	0.701555i	$-0.247510\pi$
$557$	−5.92986	−	10.2708i	−0.251256	−	0.435189i	−0.963872	+	0.266366i	$0.914177\pi$
$558$	28.1516			1.19175
$559$	−0.0778200	+	0.0259342i	−0.00329144	+	0.00109690i
$560$		0			0
$561$	−1.13201	−	1.96070i	−0.0477936	−	0.0827809i
$562$	−13.5535	−	23.4753i	−0.571719	−	0.990246i
$563$	−3.84675	+	6.66276i	−0.162121	+	0.280802i	−0.935629	−	0.352985i	$-0.885167\pi$
$563$	−3.84675	+	6.66276i	−0.162121	+	0.280802i	0.773508	+	0.633786i	$0.218500\pi$
$564$	8.16524			0.343819
$565$	6.90332	−	11.9569i	0.290425	−	0.503031i
$566$	−10.8892	+	18.8607i	−0.457709	+	0.792775i
$567$		0			0
$568$	3.50360	−	6.06841i	0.147008	−	0.254625i
$569$	−18.7098	−	32.4063i	−0.784355	−	1.35854i	−0.929384	−	0.369115i	$-0.879661\pi$
$569$	−18.7098	−	32.4063i	−0.784355	−	1.35854i	0.145029	−	0.989427i	$-0.453673\pi$
$570$	−1.94965	−	3.37689i	−0.0816619	−	0.141443i
$571$	14.1657			0.592816			0.296408	−	0.955061i	$-0.404211\pi$
$571$	14.1657			0.592816			0.296408	+	0.955061i	$0.404211\pi$
$572$	−19.3323	−	17.1453i	−0.808324	−	0.716879i
$573$	−8.67209			−0.362282
$574$		0			0
$575$	−6.27825	−	10.8742i	−0.261821	−	0.453488i
$576$	−6.79797	+	11.7744i	−0.283249	+	0.490601i
$577$	−14.9755			−0.623439			−0.311720	−	0.950174i	$-0.600905\pi$
$577$	−14.9755			−0.623439			−0.311720	+	0.950174i	$0.600905\pi$
$578$	−14.8190	+	25.6673i	−0.616391	+	1.06762i
$579$	3.50837	−	6.07667i	0.145803	−	0.252538i
$580$	−0.402635			−0.0167185
$581$		0			0
$582$	1.42535	+	2.46878i	0.0590828	+	0.102334i
$583$	−0.311476	−	0.539492i	−0.0129000	−	0.0223435i
$584$	10.7125			0.443288
$585$	−14.1920	+	4.72960i	−0.586766	+	0.195545i
$586$	25.1622			1.03944
$587$	6.58821	+	11.4111i	0.271925	+	0.470987i	0.969355	−	0.245666i	$-0.0790066\pi$
$587$	6.58821	+	11.4111i	0.271925	+	0.470987i	−0.697430	+	0.716653i	$0.745673\pi$
$588$		0			0
$589$	−8.50309	+	14.7278i	−0.350364	+	0.606848i
$590$	−15.0001			−0.617542
$591$	−4.22739	+	7.32205i	−0.173892	+	0.301189i
$592$	16.2220	−	28.0974i	0.666722	−	1.15480i
$593$	−44.1327			−1.81231			−0.906156	−	0.422943i	$-0.860997\pi$
$593$	−44.1327			−1.81231			−0.906156	+	0.422943i	$0.860997\pi$
$594$	10.4320	−	18.0688i	0.428032	−	0.741372i
$595$		0			0
$596$	−3.19965	−	5.54195i	−0.131063	−	0.227007i
$597$	−6.04859			−0.247552
$598$	−28.9218	+	9.63843i	−1.18270	+	0.394145i
$599$	−6.02698			−0.246256			−0.123128	−	0.992391i	$-0.539293\pi$
$599$	−6.02698			−0.246256			−0.123128	+	0.992391i	$0.539293\pi$
$600$	0.426087	+	0.738005i	0.0173949	+	0.0301289i
$601$	−1.86260	−	3.22612i	−0.0759770	−	0.131596i	0.825534	−	0.564353i	$-0.190874\pi$
$601$	−1.86260	−	3.22612i	−0.0759770	−	0.131596i	−0.901511	+	0.432757i	$0.857541\pi$
$602$		0			0
$603$	−11.6472			−0.474312
$604$	1.72804	−	2.99305i	0.0703129	−	0.121786i
$605$	6.11632	−	10.5938i	0.248664	−	0.430698i
$606$	−2.10460			−0.0854934
$607$	3.00825	−	5.21045i	0.122101	−	0.211486i	−0.798495	−	0.602002i	$-0.794370\pi$
$607$	3.00825	−	5.21045i	0.122101	−	0.211486i	0.920596	+	0.390516i	$0.127703\pi$
$608$	−11.9358	−	20.6733i	−0.484059	−	0.838415i
$609$		0			0
$610$	32.4105			1.31226
$611$	31.5167	+	27.9512i	1.27503	+	1.13079i
$612$	5.52532			0.223348
$613$	−4.90413	−	8.49420i	−0.198076	−	0.343077i	0.749829	−	0.661632i	$-0.230136\pi$
$613$	−4.90413	−	8.49420i	−0.198076	−	0.343077i	−0.947904	+	0.318555i	$0.896803\pi$
$614$	−6.34459	−	10.9892i	−0.256047	−	0.443486i
$615$	1.62962	−	2.82258i	0.0657126	−	0.113818i
$616$		0			0
$617$	−16.8838	+	29.2436i	−0.679716	+	1.17730i	0.295350	+	0.955389i	$0.404564\pi$
$617$	−16.8838	+	29.2436i	−0.679716	+	1.17730i	−0.975066	+	0.221914i	$0.928770\pi$
$618$	−6.88394	+	11.9233i	−0.276913	+	0.479627i
$619$	4.09343			0.164529			0.0822644	−	0.996611i	$-0.473785\pi$
$619$	4.09343			0.164529			0.0822644	+	0.996611i	$0.473785\pi$
$620$	6.30215	−	10.9156i	0.253100	−	0.438383i
$621$	−5.52871	−	9.57601i	−0.221860	−	0.384272i
$622$	−1.94936	−	3.37639i	−0.0781621	−	0.135381i
$623$		0			0
$624$	6.74393	−	2.24747i	0.269973	−	0.0899709i
$625$	−2.84229			−0.113692
$626$	8.97297	+	15.5416i	0.358632	+	0.621169i
$627$	3.05151	+	5.28537i	0.121866	+	0.211077i
$628$	18.0347	−	31.2371i	0.719665	−	1.24650i
$629$	−8.47978			−0.338111
$630$		0			0
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	−0.466340	−	0.884605i	$-0.654428\pi$
$631$	13.3868	−	23.1866i	0.532921	−	0.923046i	0.999261	−	0.0384402i	$-0.0122389\pi$
$632$	0.544357			0.0216534
$633$	0.991071	−	1.71659i	0.0393915	−	0.0682282i
$634$	−31.7955	−	55.0714i	−1.26276	−	2.18717i
$635$	11.7006	+	20.2661i	0.464325	+	0.804234i
$636$	−0.0990892			−0.00392914
$637$		0			0
$638$	1.40287			0.0555403
$639$	−14.0395	−	24.3172i	−0.555395	−	0.961972i
$640$	−4.07112	−	7.05139i	−0.160925	−	0.278731i
$641$	9.28610	−	16.0840i	0.366779	−	0.635279i	−0.622281	−	0.782794i	$-0.713794\pi$
$641$	9.28610	−	16.0840i	0.366779	−	0.635279i	0.989060	+	0.147514i	$0.0471273\pi$
$642$	−7.08880			−0.279773
$643$	1.96695	−	3.40686i	0.0775690	−	0.134353i	−0.824632	−	0.565670i	$-0.808618\pi$
$643$	1.96695	−	3.40686i	0.0775690	−	0.134353i	0.902201	+	0.431317i	$0.141951\pi$
$644$		0			0
$645$	−0.0143591			−0.000565389
$646$	−3.71518	+	6.43487i	−0.146172	+	0.253177i
$647$	0.0985378	+	0.170672i	0.00387392	+	0.00670983i	0.867956	−	0.496641i	$-0.165434\pi$
$647$	0.0985378	+	0.170672i	0.00387392	+	0.00670983i	−0.864082	+	0.503351i	$0.832100\pi$
$648$	−2.59407	−	4.49306i	−0.101905	−	0.176504i
$649$	23.4775			0.921571
$650$	3.89922	−	19.0480i	0.152940	−	0.747125i
$651$		0			0
$652$	−3.14172	−	5.44163i	−0.123039	−	0.213110i
$653$	7.23363	+	12.5290i	0.283074	+	0.490298i	0.972140	−	0.234400i	$-0.0753125\pi$
$653$	7.23363	+	12.5290i	0.283074	+	0.490298i	−0.689066	+	0.724698i	$0.741979\pi$
$654$	−4.91514	+	8.51327i	−0.192197	+	0.332895i
$655$	−2.73626			−0.106915
$656$	11.8812	−	20.5788i	0.463883	−	0.803468i
$657$	21.4635	−	37.1758i	0.837369	−	1.45037i
$658$		0			0
$659$	11.7066	−	20.2764i	0.456024	−	0.789857i	−0.542722	−	0.839912i	$-0.682606\pi$
$659$	11.7066	−	20.2764i	0.456024	−	0.789857i	0.998746	+	0.0500552i	$0.0159397\pi$
$660$	−2.26166	−	3.91731i	−0.0880349	−	0.152481i
$661$	2.02409	+	3.50582i	0.0787278	+	0.136361i	0.902701	−	0.430268i	$-0.141581\pi$
$661$	2.02409	+	3.50582i	0.0787278	+	0.136361i	−0.823973	+	0.566628i	$0.808248\pi$
$662$	−36.3313			−1.41206
$663$	−1.39003	−	1.23278i	−0.0539843	−	0.0478771i
$664$	−11.2587			−0.436921
$665$		0			0
$666$	−18.9197	−	32.7699i	−0.733125	−	1.26981i
$667$	0.371744	−	0.643879i	0.0143940	−	0.0249311i
$668$	3.48896			0.134992
$669$	4.57416	−	7.92268i	0.176847	−	0.306309i
$670$	−5.80440	+	10.0535i	−0.224243	+	0.388401i
$671$	−50.7276			−1.95832
$672$		0			0
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	0.787133	−	0.616783i	$-0.211564\pi$
$673$	−3.64704	−	6.31685i	−0.140583	−	0.243497i	−0.927716	+	0.373286i	$0.878231\pi$
$674$	−29.8076	−	51.6283i	−1.14815	−	1.98865i
$675$	7.05218			0.271439
$676$	−19.4994	−	8.33241i	−0.749976	−	0.320477i
$677$	−15.7511			−0.605362			−0.302681	−	0.953092i	$-0.597882\pi$
$677$	−15.7511			−0.605362			−0.302681	+	0.953092i	$0.597882\pi$
$678$	3.82593	+	6.62671i	0.146934	+	0.254497i
$679$		0			0
$680$	−0.622636	+	1.07844i	−0.0238770	+	0.0413562i
$681$	−4.47686			−0.171553
$682$	−21.9582	+	38.0327i	−0.840822	+	1.45635i
$683$	−20.7427	+	35.9274i	−0.793697	+	1.37472i	0.129967	+	0.991518i	$0.458513\pi$
$683$	−20.7427	+	35.9274i	−0.793697	+	1.37472i	−0.923664	+	0.383204i	$0.874820\pi$
$684$	−14.8943			−0.569499
$685$	−9.42819	+	16.3301i	−0.360233	+	0.623941i
$686$		0			0
$687$	−3.09725	−	5.36460i	−0.118168	−	0.204672i
$688$	−0.104689			−0.00399123
$689$	−0.382470	−	0.339202i	−0.0145710	−	0.0129226i
$690$	−5.33655			−0.203159
$691$	23.4108	+	40.5487i	0.890589	+	1.54255i	0.839171	+	0.543868i	$0.183041\pi$
$691$	23.4108	+	40.5487i	0.890589	+	1.54255i	0.0514184	+	0.998677i	$0.483626\pi$
$692$	13.5494	+	23.4683i	0.515073	+	0.892132i
$693$		0			0
$694$	−22.2478			−0.844514
$695$	−0.249496	+	0.432140i	−0.00946392	+	0.0163920i
$696$	−0.0252292	+	0.0436983i	−0.000956311	+	0.00165638i
$697$	−6.21068			−0.235246
$698$	22.8576	−	39.5905i	0.865172	−	1.49852i
$699$	1.98977	+	3.44638i	0.0752600	+	0.130354i
$700$		0			0
$701$	29.8626			1.12790			0.563948	−	0.825810i	$-0.309282\pi$
$701$	29.8626			1.12790			0.563948	+	0.825810i	$0.309282\pi$
$702$	3.43371	−	16.7739i	0.129597	−	0.633091i
$703$	22.8585			0.862126
$704$	−10.6048	−	18.3680i	−0.399683	−	0.692271i
$705$	3.68709	+	6.38623i	0.138864	+	0.240519i
$706$	12.1893	−	21.1124i	0.458749	−	0.794576i
$707$		0			0
$708$	1.86721	−	3.23410i	0.0701740	−	0.121545i
$709$	−13.4666	+	23.3249i	−0.505750	+	0.875984i	0.494228	+	0.869332i	$0.335451\pi$
$709$	−13.4666	+	23.3249i	−0.505750	+	0.875984i	−0.999978	+	0.00665185i	$0.997883\pi$
$710$	−27.9864			−1.05031
$711$	1.09067	−	1.88909i	0.0409031	−	0.0708463i
$712$	−2.30450	−	3.99151i	−0.0863647	−	0.149588i
$713$	11.6373	+	20.1563i	0.435819	+	0.754861i
$714$		0			0
$715$	4.68004	−	22.8623i	0.175023	−	0.855003i
$716$	−0.880004			−0.0328873
$717$	−4.20590	−	7.28483i	−0.157072	−	0.272057i
$718$	11.7570	+	20.3638i	0.438769	+	0.759969i
$719$	7.24938	−	12.5563i	0.270356	−	0.468271i	−0.698597	−	0.715516i	$-0.746192\pi$
$719$	7.24938	−	12.5563i	0.270356	−	0.468271i	0.968953	+	0.247245i	$0.0795252\pi$
$720$	−19.0921			−0.711519
$721$		0			0
$722$	−8.08799	+	14.0088i	−0.301004	+	0.521354i
$723$	3.13240			0.116495
$724$	−2.26049	+	3.91528i	−0.0840105	+	0.145510i
$725$	0.237090	+	0.410652i	0.00880530	+	0.0152512i
$726$	3.38977	+	5.87125i	0.125806	+	0.217902i
$727$	−6.26424			−0.232328			−0.116164	−	0.993230i	$-0.537060\pi$
$727$	−6.26424			−0.232328			−0.116164	+	0.993230i	$0.537060\pi$
$728$		0			0
$729$	−17.5866			−0.651357
$730$	−21.3926	−	37.0531i	−0.791776	−	1.37140i
$731$	0.0136811	+	0.0236963i	0.000506013	+	0.000876440i
$732$	−4.03447	+	6.98790i	−0.149118	+	0.258280i
$733$	−11.9838			−0.442631			−0.221316	−	0.975202i	$-0.571035\pi$
$733$	−11.9838			−0.442631			−0.221316	+	0.975202i	$0.571035\pi$
$734$	1.93487	−	3.35130i	0.0714175	−	0.123699i
$735$		0			0
$736$	−32.6704			−1.20425
$737$	9.08480	−	15.7353i	0.334643	−	0.579619i
$738$	−13.8570	−	24.0010i	−0.510084	−	0.883491i
$739$	−6.76269	−	11.7133i	−0.248770	−	0.430882i	0.714415	−	0.699722i	$-0.246693\pi$
$739$	−6.76269	−	11.7133i	−0.248770	−	0.430882i	−0.963185	+	0.268840i	$0.913360\pi$
$740$	−16.9418			−0.622794
$741$	3.74704	+	3.32314i	0.137651	+	0.122079i
$742$		0			0
$743$	19.2299	+	33.3072i	0.705477	+	1.22192i	0.966519	+	0.256594i	$0.0826003\pi$
$743$	19.2299	+	33.3072i	0.705477	+	1.22192i	−0.261043	+	0.965327i	$0.584066\pi$
$744$	−0.789789	−	1.36795i	−0.0289551	−	0.0501516i
$745$	2.88966	−	5.00504i	0.105869	−	0.183371i
$746$	7.38214			0.270279
$747$	−22.5577	+	39.0710i	−0.825342	+	1.42953i
$748$	−4.30973	+	7.46466i	−0.157579	+	0.272935i
$749$		0			0
$750$	4.70855	−	8.15544i	0.171932	−	0.297795i
$751$	−5.85573	−	10.1424i	−0.213679	−	0.370102i	0.739184	−	0.673503i	$-0.235211\pi$
$751$	−5.85573	−	10.1424i	−0.213679	−	0.370102i	−0.952863	+	0.303401i	$0.901878\pi$
$752$	26.8817	+	46.5605i	0.980276	+	1.69789i
$753$	−5.08302			−0.185236
$754$	1.09219	−	0.363983i	0.0397753	−	0.0132555i
$755$	3.12125			0.113594
$756$		0			0
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	0.768877	−	0.639396i	$-0.220816\pi$
$757$	−4.65791	−	8.06773i	−0.169295	−	0.293227i	−0.938172	+	0.346169i	$0.887482\pi$
$758$	−13.8800	+	24.0409i	−0.504145	+	0.873205i
$759$	8.35255			0.303178
$760$	1.67841	−	2.90709i	0.0608824	−	0.105451i
$761$	21.9691	−	38.0515i	0.796378	−	1.37937i	−0.125582	−	0.992083i	$-0.540080\pi$
$761$	21.9691	−	38.0515i	0.796378	−	1.37937i	0.921960	−	0.387284i	$-0.126587\pi$
$762$	−12.9693			−0.469830
$763$		0			0
$764$	16.5079	+	28.5926i	0.597236	+	1.03444i
$765$	2.49501	+	4.32148i	0.0902072	+	0.156243i
$766$	51.0344			1.84395
$767$	18.2781	−	6.09134i	0.659985	−	0.219946i
$768$	8.64911			0.312098
$769$	−12.6771	−	21.9573i	−0.457147	−	0.791802i	0.541662	−	0.840597i	$-0.317795\pi$
$769$	−12.6771	−	21.9573i	−0.457147	−	0.791802i	−0.998809	+	0.0487946i	$0.984462\pi$
$770$		0			0
$771$	3.25024	−	5.62957i	0.117054	−	0.202744i
$772$	−26.7137			−0.961447
$773$	11.5542	−	20.0125i	0.415576	−	0.719798i	−0.579913	−	0.814678i	$-0.696913\pi$
$773$	11.5542	−	20.0125i	0.415576	−	0.719798i	0.995489	+	0.0948801i	$0.0302468\pi$
$774$	−0.0610493	+	0.105741i	−0.00219437	+	0.00380076i
$775$	−14.8440			−0.533212
$776$	−1.22705	+	2.12532i	−0.0440487	+	0.0762946i
$777$		0			0
$778$	11.4474	+	19.8275i	0.410410	+	0.710851i
$779$	16.7418			0.599838
$780$	−2.77716	−	2.46298i	−0.0994381	−	0.0881889i
$781$	43.8031			1.56740
$782$	5.08456	+	8.80672i	0.181824	+	0.314928i
$783$	0.208785	+	0.361626i	0.00746135	+	0.0129234i
$784$		0			0
$785$	32.5750			1.16265
$786$	0.758241	−	1.31331i	0.0270456	−	0.0468443i
$787$	12.3346	−	21.3642i	0.439682	−	0.761551i	−0.557983	−	0.829852i	$-0.688425\pi$
$787$	12.3346	−	21.3642i	0.439682	−	0.761551i	0.997665	+	0.0683012i	$0.0217579\pi$
$788$	32.1885			1.14667
$789$	−3.68388	+	6.38066i	−0.131149	+	0.227158i
$790$	−1.08707	−	1.88285i	−0.0386761	−	0.0669889i
$791$		0			0
$792$	8.69727			0.309044
$793$	−39.4934	+	13.1615i	−1.40245	+	0.467379i
$794$	3.15875			0.112100
$795$	−0.0447447	−	0.0775000i	−0.00158693	−	0.00274864i
$796$	11.5139	+	19.9427i	0.408100	+	0.706849i
$797$	−5.65686	+	9.79797i	−0.200376	+	0.347062i	−0.948650	−	0.316329i	$-0.897550\pi$
$797$	−5.65686	+	9.79797i	−0.200376	+	0.347062i	0.748273	+	0.663390i	$0.230883\pi$
$798$		0			0
$799$	7.02597	−	12.1693i	0.248561	−	0.430520i
$800$	10.4182	−	18.0449i	0.368340	−	0.637984i
$801$	−18.4690			−0.652571
$802$	−19.5156	+	33.8019i	−0.689118	+	1.19359i
$803$	33.4828	+	57.9940i	1.18158	+	2.04656i
$804$	−1.44507	−	2.50293i	−0.0509635	−	0.0882714i
$805$		0			0
$806$	−7.22754	+	35.3071i	−0.254579	+	1.24364i
$807$	8.10710			0.285384
$808$	−0.905900	−	1.56906i	−0.0318694	−	0.0551995i
$809$	−8.18540	−	14.1775i	−0.287783	−	0.498455i	0.685497	−	0.728075i	$-0.259585\pi$
$809$	−8.18540	−	14.1775i	−0.287783	−	0.498455i	−0.973280	+	0.229620i	$0.926252\pi$
$810$	−10.3606	+	17.9450i	−0.364033	+	0.630524i
$811$	−29.0412			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$811$	−29.0412			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$812$		0			0
$813$	−6.88373	+	11.9230i	−0.241423	+	0.418157i
$814$	59.0293			2.06898
$815$	2.83735	−	4.91443i	0.0993880	−	0.172145i
$816$	−1.18561	−	2.05354i	−0.0415046	−	0.0718881i
$817$	−0.0368794	−	0.0638770i	−0.00129025	−	0.00223477i
$818$	−28.3278			−0.990458
$819$		0			0
$820$	−12.4084			−0.433319
$821$	6.87589	+	11.9094i	0.239970	+	0.415640i	0.960705	−	0.277570i	$-0.0895290\pi$
$821$	6.87589	+	11.9094i	0.239970	+	0.415640i	−0.720735	+	0.693210i	$0.756196\pi$
$822$	−5.22526	−	9.05041i	−0.182252	−	0.315669i
$823$	14.5577	−	25.2146i	0.507448	−	0.878926i	−0.492515	−	0.870304i	$-0.663922\pi$
$823$	14.5577	−	25.2146i	0.507448	−	0.878926i	0.999963	−	0.00862197i	$-0.00274449\pi$
$824$	−11.8525			−0.412900
$825$	−2.66354	+	4.61338i	−0.0927325	+	0.160617i
$826$		0			0
$827$	−22.9118			−0.796722			−0.398361	−	0.917229i	$-0.630421\pi$
$827$	−22.9118			−0.796722			−0.398361	+	0.917229i	$0.630421\pi$
$828$	−10.1921	+	17.6533i	−0.354201	+	0.613494i
$829$	11.6914	+	20.2502i	0.406061	+	0.703317i	0.994444	−	0.105264i	$-0.0335689\pi$
$829$	11.6914	+	20.2502i	0.406061	+	0.703317i	−0.588384	+	0.808582i	$0.700236\pi$
$830$	22.4832	+	38.9421i	0.780404	+	1.35170i
$831$	7.88574			0.273553
$832$	−13.0219	−	11.5488i	−0.451454	−	0.400382i
$833$		0			0
$834$	−0.138275	−	0.239499i	−0.00478806	−	0.00829317i
$835$	1.57547	+	2.72880i	0.0545214	+	0.0944339i
$836$	11.6175	−	20.1221i	0.401801	−	0.695939i
$837$	−13.0718			−0.451828
$838$	−22.5023	+	38.9751i	−0.777328	+	1.34637i
$839$	−0.367168	+	0.635954i	−0.0126761	+	0.0219556i	−0.872294	−	0.488982i	$-0.837368\pi$
$839$	−0.367168	+	0.635954i	−0.0126761	+	0.0219556i	0.859618	+	0.510938i	$0.170702\pi$
$840$		0			0
$841$	14.4860	−	25.0904i	0.499516	−	0.865187i
$842$	24.8506	+	43.0426i	0.856409	+	1.48334i
$843$	3.04737	+	5.27820i	0.104957	+	0.181791i
$844$	−7.54629			−0.259754
$845$	−2.28816	−	19.0135i	−0.0787150	−	0.654084i
$846$	62.7042			2.15582
$847$		0			0
$848$	−0.326223	−	0.565035i	−0.0112026	−	0.0194034i
$849$	2.44834	−	4.24066i	0.0840270	−	0.145539i
$850$	−6.48565			−0.222456
$851$	15.6420	−	27.0927i	0.536201	−	0.928727i
$852$	3.48375	−	6.03403i	0.119351	−	0.206722i
$853$	54.3567			1.86114			0.930569	−	0.366118i	$-0.119313\pi$
$853$	54.3567			1.86114			0.930569	+	0.366118i	$0.119313\pi$
$854$		0			0
$855$	−6.72567	−	11.6492i	−0.230013	−	0.398395i
$856$	−3.05129	−	5.28500i	−0.104291	−	0.180637i
$857$	−21.0211			−0.718067			−0.359034	−	0.933325i	$-0.616894\pi$
$857$	−21.0211			−0.718067			−0.359034	+	0.933325i	$0.616894\pi$
$858$	9.67626	+	8.58160i	0.330342	+	0.292971i
$859$	−51.3629			−1.75248			−0.876240	−	0.481875i	$-0.839956\pi$
$859$	−51.3629			−1.75248			−0.876240	+	0.481875i	$0.839956\pi$
$860$	0.0273336	+	0.0473431i	0.000932066	+	0.00161439i
$861$		0			0
$862$	−12.6884	+	21.9769i	−0.432167	+	0.748535i
$863$	7.11319			0.242136			0.121068	−	0.992644i	$-0.461368\pi$
$863$	7.11319			0.242136			0.121068	+	0.992644i	$0.461368\pi$
$864$	9.17443	−	15.8906i	0.312121	−	0.540609i
$865$	−12.2368	+	21.1947i	−0.416062	+	0.720641i
$866$	−38.9155			−1.32240
$867$	3.33193	−	5.77107i	0.113158	−	0.195996i
$868$		0			0
$869$	1.70143	+	2.94696i	0.0577171	+	0.0999689i
$870$	0.201528			0.00683244
$871$	2.99027	−	14.6077i	0.101321	−	0.494962i
$872$	−8.46267			−0.286582
$873$	4.91701	+	8.51652i	0.166416	+	0.288240i
$874$	−13.7062	−	23.7399i	−0.463620	−	0.803013i
$875$		0			0
$876$	10.6518			0.359892
$877$	−0.256238	+	0.443818i	−0.00865255	+	0.0149867i	−0.870319	−	0.492488i	$-0.836088\pi$
$877$	−0.256238	+	0.443818i	−0.00865255	+	0.0149867i	0.861667	+	0.507475i	$0.169421\pi$
$878$	−9.30937	+	16.1243i	−0.314176	+	0.544169i
$879$	−5.65749			−0.190822
$880$	14.8917	−	25.7933i	0.502000	−	0.869490i
$881$	18.5464	+	32.1232i	0.624843	+	1.08226i	0.988571	+	0.150754i	$0.0481702\pi$
$881$	18.5464	+	32.1232i	0.624843	+	1.08226i	−0.363729	+	0.931505i	$0.618497\pi$
$882$		0			0
$883$	−15.5667			−0.523860			−0.261930	−	0.965087i	$-0.584359\pi$
$883$	−15.5667			−0.523860			−0.261930	+	0.965087i	$0.584359\pi$
$884$	−1.41855	+	6.92972i	−0.0477109	+	0.233072i
$885$	3.37262			0.113369
$886$	20.1645	+	34.9260i	0.677440	+	1.17336i
$887$	−13.7900	−	23.8849i	−0.463022	−	0.801977i	0.536088	−	0.844162i	$-0.319901\pi$
$887$	−13.7900	−	23.8849i	−0.463022	−	0.801977i	−0.999110	+	0.0421849i	$0.986568\pi$
$888$	−1.06158	+	1.83871i	−0.0356243	+	0.0617030i
$889$		0			0
$890$	−9.20404	+	15.9419i	−0.308520	+	0.534372i
$891$	16.2159	−	28.0868i	0.543254	−	0.940944i
$892$	−34.8289			−1.16616
$893$	−18.9396	+	32.8043i	−0.633789	+	1.09775i
$894$	1.60150	+	2.77388i	0.0535621	+	0.0927723i
$895$	−0.397374	−	0.688272i	−0.0132827	−	0.0230064i
$896$		0			0
$897$	6.50279	−	2.16711i	0.217122	−	0.0723577i
$898$	34.5791			1.15392
$899$	−0.439466	−	0.761178i	−0.0146570	−	0.0253867i
$900$	−6.50032	−	11.2589i	−0.216677	−	0.375296i
$901$	−0.0852637	+	0.147681i	−0.00284054	+	0.00491997i
$902$	43.2337			1.43952
$903$		0			0
$904$	−3.29366	+	5.70479i	−0.109546	+	0.189738i
$905$	−4.08298			−0.135723
$906$	−0.864923	+	1.49809i	−0.0287352	+	0.0497707i
$907$	22.5236	+	39.0119i	0.747882	+	1.29537i	0.948836	+	0.315769i	$0.102263\pi$
$907$	22.5236	+	39.0119i	0.747882	+	1.29537i	−0.200954	+	0.979601i	$0.564404\pi$
$908$	8.52200	+	14.7605i	0.282813	+	0.489846i
$909$	−7.26019			−0.240805
$910$		0			0
$911$	35.4678			1.17510			0.587550	−	0.809188i	$-0.300093\pi$
$911$	35.4678			1.17510			0.587550	+	0.809188i	$0.300093\pi$
$912$	3.19599	+	5.53562i	0.105830	+	0.183303i
$913$	−35.1898	−	60.9505i	−1.16461	−	2.01717i
$914$	−17.1689	+	29.7375i	−0.567898	+	0.983627i
$915$	−7.28720			−0.240908
$916$	−11.7917	+	20.4238i	−0.389608	+	0.674820i
$917$		0			0
$918$	−5.71135			−0.188503
$919$	−8.68622	+	15.0450i	−0.286532	+	0.496288i	−0.972980	−	0.230891i	$-0.925836\pi$
$919$	−8.68622	+	15.0450i	−0.286532	+	0.496288i	0.686447	+	0.727179i	$0.259169\pi$
$920$	−2.29706	−	3.97862i	−0.0757318	−	0.131171i
$921$	1.42652	+	2.47081i	0.0470056	+	0.0814160i
$922$	56.7372			1.86854
$923$	34.1024	−	11.3649i	1.12250	−	0.374081i
$924$		0			0
$925$	9.97613	+	17.2792i	0.328013	+	0.568136i
$926$	16.8706	+	29.2207i	0.554402	+	0.960252i
$927$	−23.7474	+	41.1317i	−0.779967	+	1.35094i
$928$	1.23375			0.0405000
$929$	−5.38001	+	9.31845i	−0.176512	+	0.305729i	−0.940684	−	0.339285i	$-0.889815\pi$
$929$	−5.38001	+	9.31845i	−0.176512	+	0.305729i	0.764171	+	0.645013i	$0.223148\pi$
$930$	−3.15437	+	5.46353i	−0.103436	+	0.179156i
$931$		0			0
$932$	7.57532	−	13.1208i	0.248138	−	0.429788i
$933$	0.438295	+	0.759149i	0.0143491	+	0.0248534i
$934$	−5.55396	−	9.61975i	−0.181731	−	0.314768i
$935$	−7.78439			−0.254577
$936$	6.77117	−	2.25655i	0.221323	−	0.0737577i
$937$	−10.9816			−0.358755			−0.179377	−	0.983780i	$-0.557408\pi$
$937$	−10.9816			−0.358755			−0.179377	+	0.983780i	$0.557408\pi$
$938$		0			0
$939$	−2.01749	−	3.49439i	−0.0658383	−	0.114035i
$940$	14.0373	−	24.3132i	0.457845	−	0.793011i
$941$	8.17795			0.266594			0.133297	−	0.991076i	$-0.457444\pi$
$941$	8.17795			0.266594			0.133297	+	0.991076i	$0.457444\pi$
$942$	−9.02681	+	15.6349i	−0.294109	+	0.509412i
$943$	11.4564	−	19.8430i	0.373071	−	0.646177i
$944$	24.5890			0.800305
$945$		0			0
$946$	−0.0952365	−	0.164954i	−0.00309640	−	0.00536313i
$947$	2.29689	+	3.97833i	0.0746389	+	0.129278i	0.900929	−	0.433966i	$-0.142886\pi$
$947$	2.29689	+	3.97833i	0.0746389	+	0.129278i	−0.826290	+	0.563244i	$0.809553\pi$
$948$	0.541273			0.0175797
$949$	41.1145	+	36.4633i	1.33463	+	1.18365i
$950$	17.4831			0.567225
$951$	7.14892	+	12.3823i	0.231820	+	0.401524i
$952$		0			0
$953$	−10.5714	+	18.3102i	−0.342442	+	0.593126i	−0.984886	−	0.173206i	$-0.944587\pi$
$953$	−10.5714	+	18.3102i	−0.342442	+	0.593126i	0.642444	+	0.766333i	$0.277921\pi$
$954$	−0.760947			−0.0246366
$955$	−14.9086	+	25.8225i	−0.482432	+	0.835596i
$956$	−16.0124	+	27.7344i	−0.517879	+	0.896993i
$957$	−0.315423			−0.0101962
$958$	13.8070	−	23.9145i	0.446085	−	0.772641i
$959$		0			0
$960$	−1.52342	−	2.63864i	−0.0491681	−	0.0851616i
$961$	−3.48542			−0.112433
$962$	45.9566	−	15.3154i	1.48170	−	0.493790i
$963$	−24.4541			−0.788022
$964$	−5.96274	−	10.3278i	−0.192047	−	0.332635i
$965$	−12.0628	−	20.8934i	−0.388316	−	0.672582i
$966$		0			0
$967$	−32.0750			−1.03146			−0.515731	−	0.856750i	$-0.672480\pi$
$967$	−32.0750			−1.03146			−0.515731	+	0.856750i	$0.672480\pi$
$968$	−2.91817	+	5.05442i	−0.0937936	+	0.162455i
$969$	0.835323	−	1.44682i	0.0268344	−	0.0464786i
$970$	9.80157			0.314710
$971$	26.0417	−	45.1056i	0.835719	−	1.44751i	−0.0577245	−	0.998333i	$-0.518384\pi$
$971$	26.0417	−	45.1056i	0.835719	−	1.44751i	0.893444	−	0.449175i	$-0.148282\pi$
$972$	−8.67673	−	15.0285i	−0.278306	−	0.482041i
$973$		0			0
$974$	34.2241			1.09661
$975$	−0.876705	+	4.28277i	−0.0280770	+	0.137158i
$976$	−53.1294			−1.70063
$977$	−9.62898	−	16.6779i	−0.308058	−	0.533573i	0.669879	−	0.742470i	$-0.266346\pi$
$977$	−9.62898	−	16.6779i	−0.308058	−	0.533573i	−0.977938	+	0.208897i	$0.933013\pi$
$978$	1.57251	+	2.72366i	0.0502832	+	0.0870930i
$979$	14.4058	−	24.9515i	0.460410	−	0.797454i
$980$		0			0
$981$	−16.9557	+	29.3681i	−0.541353	+	0.937650i
$982$	−34.5868	+	59.9061i	−1.10371	+	1.91168i
$983$	−16.0731			−0.512653			−0.256327	−	0.966590i	$-0.582512\pi$
$983$	−16.0731			−0.512653			−0.256327	+	0.966590i	$0.582512\pi$
$984$	−0.777512	+	1.34669i	−0.0247862	+	0.0429309i
$985$	14.5350	+	25.1754i	0.463124	+	0.802155i
$986$	−0.192012	−	0.332574i	−0.00611490	−	0.0105913i
$987$		0			0
$988$	3.82391	−	18.6801i	0.121655	−	0.594294i
$989$	−0.100946			−0.00320989
$990$	−17.3682	−	30.0826i	−0.551998	−	0.956088i
$991$	−10.7132	−	18.5559i	−0.340317	−	0.589447i	0.644174	−	0.764879i	$-0.277201\pi$
$991$	−10.7132	−	18.5559i	−0.340317	−	0.589447i	−0.984492	+	0.175432i	$0.943868\pi$
$992$	−19.3111	+	33.4478i	−0.613127	+	1.06197i
$993$	8.16876			0.259228
$994$		0			0
$995$	−10.3984	+	18.0106i	−0.329652	+	0.570974i
$996$	−11.1949			−0.354723
$997$	8.47687	−	14.6824i	0.268465	−	0.464996i	−0.700000	−	0.714142i	$-0.746817\pi$
$997$	8.47687	−	14.6824i	0.268465	−	0.464996i	0.968466	+	0.249147i	$0.0801502\pi$
$998$	22.5881	+	39.1238i	0.715015	+	1.23844i
$999$	8.78511	+	15.2163i	0.277949	+	0.481421i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.f.k.393.5		12
7.2	even	3		91.2.g.b.81.5	yes	12
7.3	odd	6		637.2.h.l.471.2		12
7.4	even	3		91.2.h.b.16.2	yes	12
7.5	odd	6		637.2.g.l.263.5		12
7.6	odd	2		637.2.f.j.393.5		12
13.3	even	3		8281.2.a.bz.1.2		6
13.9	even	3	inner	637.2.f.k.295.5		12
13.10	even	6		8281.2.a.ce.1.5		6
21.2	odd	6		819.2.n.d.172.2		12
21.11	odd	6		819.2.s.d.289.5		12
91.9	even	3		91.2.h.b.74.2	yes	12
91.16	even	3		1183.2.e.h.508.5		12
91.23	even	6		1183.2.e.g.508.2		12
91.48	odd	6		637.2.f.j.295.5		12
91.55	odd	6		8281.2.a.ca.1.2		6
91.61	odd	6		637.2.h.l.165.2		12
91.62	odd	6		8281.2.a.cf.1.5		6
91.74	even	3		91.2.g.b.9.5	✓	12
91.81	even	3		1183.2.e.h.170.5		12
91.87	odd	6		637.2.g.l.373.5		12
91.88	even	6		1183.2.e.g.170.2		12
273.74	odd	6		819.2.n.d.100.2		12
273.191	odd	6		819.2.s.d.802.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.5	✓	12	91.74	even	3
91.2.g.b.81.5	yes	12	7.2	even	3
91.2.h.b.16.2	yes	12	7.4	even	3
91.2.h.b.74.2	yes	12	91.9	even	3
637.2.f.j.295.5		12	91.48	odd	6
637.2.f.j.393.5		12	7.6	odd	2
637.2.f.k.295.5		12	13.9	even	3	inner
637.2.f.k.393.5		12	1.1	even	1	trivial
637.2.g.l.263.5		12	7.5	odd	6
637.2.g.l.373.5		12	91.87	odd	6
637.2.h.l.165.2		12	91.61	odd	6
637.2.h.l.471.2		12	7.3	odd	6
819.2.n.d.100.2		12	273.74	odd	6
819.2.n.d.172.2		12	21.2	odd	6
819.2.s.d.289.5		12	21.11	odd	6
819.2.s.d.802.5		12	273.191	odd	6
1183.2.e.g.170.2		12	91.88	even	6
1183.2.e.g.508.2		12	91.23	even	6
1183.2.e.h.170.5		12	91.81	even	3
1183.2.e.h.508.5		12	91.16	even	3
8281.2.a.bz.1.2		6	13.3	even	3
8281.2.a.ca.1.2		6	91.55	odd	6
8281.2.a.ce.1.5		6	13.10	even	6
8281.2.a.cf.1.5		6	91.62	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.952780 + 1.65026i) q^{2} +(-0.214224 - 0.371047i) q^{3} +(-0.815580 + 1.41263i) q^{4} -1.47313 q^{5} +(0.408216 - 0.707051i) q^{6} +0.702849 q^{8} +(1.40822 - 2.43910i) q^{9} +(-1.40357 - 2.43105i) q^{10} +(2.19681 + 3.80498i) q^{11} +0.698866 q^{12} +(2.69752 + 2.39236i) q^{13} +(0.315580 + 0.546600i) q^{15} +(2.30082 + 3.98514i) q^{16} +(0.601356 - 1.04158i) q^{17} +5.36688 q^{18} +(-1.62105 + 2.80773i) q^{19} +(1.20145 - 2.08098i) q^{20} +(-4.18615 + 7.25062i) q^{22} +(2.21855 + 3.84264i) q^{23} +(-0.150567 - 0.260790i) q^{24} -2.82989 q^{25} +(-1.37787 + 6.73101i) q^{26} -2.49204 q^{27} +(-0.0837807 - 0.145112i) q^{29} +(-0.601356 + 1.04158i) q^{30} +5.24543 q^{31} +(-3.68150 + 6.37655i) q^{32} +(0.941217 - 1.63024i) q^{33} +2.29184 q^{34} +(2.29702 + 3.97856i) q^{36} +(-3.52527 - 6.10595i) q^{37} -6.17800 q^{38} +(0.309802 - 1.51341i) q^{39} -1.03539 q^{40} +(-2.58195 - 4.47206i) q^{41} +(-0.0113752 + 0.0197024i) q^{43} -7.16668 q^{44} +(-2.07449 + 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} +11.6836 q^{47} +(0.985780 - 1.70742i) q^{48} +(-2.69626 - 4.67006i) q^{50} -0.515299 q^{51} +(-5.57955 + 1.85943i) q^{52} -0.141786 q^{53} +(-2.37436 - 4.11252i) q^{54} +(-3.23618 - 5.60523i) q^{55} +1.38907 q^{57} +(0.159649 - 0.276520i) q^{58} +(2.67177 - 4.62764i) q^{59} -1.02952 q^{60} +(-5.77287 + 9.99891i) q^{61} +(4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(-3.97380 - 3.52425i) q^{65} +3.58709 q^{66} +(-2.06773 - 3.58141i) q^{67} +(0.980907 + 1.69898i) q^{68} +(0.950533 - 1.64637i) q^{69} +(4.98486 - 8.63403i) q^{71} +(0.989763 - 1.71432i) q^{72} +15.2416 q^{73} +(6.71762 - 11.6353i) q^{74} +(0.606229 + 1.05002i) q^{75} +(-2.64418 - 4.57986i) q^{76} +(2.79269 - 0.930689i) q^{78} +0.774501 q^{79} +(-3.38941 - 5.87062i) q^{80} +(-3.69080 - 6.39265i) q^{81} +(4.92006 - 8.52179i) q^{82} -16.0186 q^{83} +(-0.885875 + 1.53438i) q^{85} -0.0433522 q^{86} +(-0.0358956 + 0.0621731i) q^{87} +(1.54402 + 2.67433i) q^{88} +(-3.27880 - 5.67904i) q^{89} -7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +(11.1319 + 19.2809i) q^{94} +(2.38801 - 4.13616i) q^{95} +3.15466 q^{96} +(-1.74583 + 3.02387i) q^{97} +12.3743 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

Properties

Related objects

Downloads

Learn more