LMFDB - Embedded newform 637.2.g.l.373.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(263,637)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("637.263"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.5
Root			$1.16700 - 2.02131i$ of defining polynomial
Character	$\chi$	$=$	637.373
Dual form			637.2.g.l.263.5

$q$-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} -0.428448 q^{3} +(-0.815580 + 1.41263i) q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 - 0.707051i) q^{6} +0.702849 q^{8} -2.81643 q^{9} -2.80714 q^{10} -4.39361 q^{11} +(0.349433 - 0.605236i) 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} +(-2.68344 - 4.64786i) q^{18} -3.24209 q^{19} +(-1.20145 - 2.08098i) q^{20} +(-4.18615 - 7.25062i) q^{22} +(2.21855 + 3.84264i) q^{23} -0.301134 q^{24} +(1.41494 + 2.45075i) q^{25} +(-6.51816 - 2.17223i) q^{26} +2.49204 q^{27} +(-0.0837807 + 0.145112i) q^{29} +1.20271 q^{30} +(2.62272 + 4.54268i) q^{31} +(-3.68150 + 6.37655i) q^{32} +1.88243 q^{33} -2.29184 q^{34} +(2.29702 - 3.97856i) q^{36} +(-3.52527 - 6.10595i) q^{37} +(-3.08900 - 5.35031i) q^{38} +(1.15575 - 1.02500i) q^{39} +(-0.517694 + 0.896672i) q^{40} +(2.58195 - 4.47206i) q^{41} +(-0.0113752 - 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} +(2.07449 - 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} +(5.84178 - 10.1183i) q^{47} +(-0.985780 - 1.70742i) q^{48} +(-2.69626 + 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(-1.17946 - 5.76175i) q^{52} +(0.0708929 + 0.122790i) q^{53} +(2.37436 + 4.11252i) q^{54} +(3.23618 - 5.60523i) q^{55} +1.38907 q^{57} -0.319298 q^{58} +(-2.67177 + 4.62764i) q^{59} +(0.514760 + 0.891591i) q^{60} -11.5457 q^{61} +(-4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(-1.06519 - 5.20354i) q^{65} +(1.79355 + 3.10651i) q^{66} +4.13546 q^{67} +(-0.980907 - 1.69898i) q^{68} +(-0.950533 - 1.64637i) q^{69} +(4.98486 + 8.63403i) q^{71} -1.97953 q^{72} +(7.62080 + 13.1996i) 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} +(-0.387251 + 0.670738i) q^{79} -6.77881 q^{80} +7.38159 q^{81} +9.84011 q^{82} +16.0186 q^{83} +(-0.885875 - 1.53438i) q^{85} +(0.0216761 - 0.0375441i) q^{86} +(0.0358956 - 0.0621731i) q^{87} -3.08805 q^{88} +(3.27880 + 5.67904i) q^{89} +7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +22.2637 q^{94} +(2.38801 - 4.13616i) q^{95} +(1.57733 - 2.73202i) q^{96} +(1.74583 + 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Character values

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

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

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 $

$2$	0.952780	+	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	$0.598030\pi$
$3$	−0.428448			−0.247364			−0.123682	−	0.992322i	$-0.539470\pi$
$3$	−0.428448			−0.247364			−0.123682	+	0.992322i	$0.539470\pi$
$4$	−0.815580	+	1.41263i	−0.407790	+	0.706313i
$5$	−0.736565	+	1.27577i	−0.329402	+	0.570541i	−0.982393	−	0.186825i	$-0.940180\pi$
$5$	−0.736565	+	1.27577i	−0.329402	+	0.570541i	0.652991	+	0.757365i	$0.273514\pi$
$6$	−0.408216	−	0.707051i	−0.166654	−	0.288653i
$7$		0			0
$7$		0			0
$8$	0.702849			0.248495
$9$	−2.81643			−0.938811
$10$	−2.80714			−0.887695
$11$	−4.39361			−1.32472			−0.662362	−	0.749184i	$-0.730446\pi$
$11$	−4.39361			−1.32472			−0.662362	+	0.749184i	$0.730446\pi$
$12$	0.349433	−	0.605236i	0.100873	−	0.174717i
$13$	−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	−0.929690	−	0.368343i	$-0.879925\pi$
$17$	−0.601356	+	1.04158i	−0.145850	+	0.252620i	0.783840	+	0.620963i	$0.213258\pi$
$18$	−2.68344	−	4.64786i	−0.632493	−	1.09551i
$19$	−3.24209			−0.743787			−0.371893	−	0.928275i	$-0.621291\pi$
$19$	−3.24209			−0.743787			−0.371893	+	0.928275i	$0.621291\pi$
$20$	−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	$0.680250\pi$
$24$	−0.301134			−0.0614687
$25$	1.41494	+	2.45075i	0.282989	+	0.490151i
$26$	−6.51816	−	2.17223i	−1.27832	−	0.426010i
$27$	2.49204			0.479593
$28$		0			0
$29$	−0.0837807	+	0.145112i	−0.0155577	+	0.0269467i	−0.873699	−	0.486466i	$-0.838286\pi$
$29$	−0.0837807	+	0.145112i	−0.0155577	+	0.0269467i	0.858142	+	0.513413i	$0.171619\pi$
$30$	1.20271			0.219584
$31$	2.62272	+	4.54268i	0.471054	+	0.815889i	0.999452	−	0.0331076i	$-0.0105404\pi$
$31$	2.62272	+	4.54268i	0.471054	+	0.815889i	−0.528398	+	0.848997i	$0.677207\pi$
$32$	−3.68150	+	6.37655i	−0.650803	+	1.12722i
$33$	1.88243			0.327690
$34$	−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	$-0.363439\pi$
$38$	−3.08900	−	5.35031i	−0.501102	−	0.867934i
$39$	1.15575	−	1.02500i	0.185068	−	0.164131i
$40$	−0.517694	+	0.896672i	−0.0818546	+	0.141776i
$41$	2.58195	−	4.47206i	0.403233	−	0.698419i	−0.590881	−	0.806758i	$-0.701220\pi$
$41$	2.58195	−	4.47206i	0.403233	−	0.698419i	0.994114	+	0.108339i	$0.0345533\pi$
$42$		0			0
$43$	−0.0113752	−	0.0197024i	−0.00173470	−	0.00300459i	0.865157	−	0.501502i	$-0.167219\pi$
$43$	−0.0113752	−	0.0197024i	−0.00173470	−	0.00300459i	−0.866891	+	0.498497i	$0.833886\pi$
$44$	3.58334	−	6.20653i	0.540209	−	0.935670i
$45$	2.07449	−	3.59311i	0.309246	−	0.535630i
$46$	−4.22758	+	7.32239i	−0.623323	+	1.07963i
$47$	5.84178	−	10.1183i	0.852111	−	1.47590i	−0.0271891	−	0.999630i	$-0.508656\pi$
$47$	5.84178	−	10.1183i	0.852111	−	1.47590i	0.879300	−	0.476269i	$-0.158011\pi$
$48$	−0.985780	−	1.70742i	−0.142285	−	0.246445i
$49$		0			0
$50$	−2.69626	+	4.67006i	−0.381309	+	0.660446i
$51$	0.257649	−	0.446262i	0.0360781	−	0.0624892i
$52$	−1.17946	−	5.76175i	−0.163561	−	0.799010i
$53$	0.0708929	+	0.122790i	0.00973788	+	0.0168665i	0.870853	−	0.491543i	$-0.163567\pi$
$53$	0.0708929	+	0.122790i	0.00973788	+	0.0168665i	−0.861115	+	0.508410i	$0.830234\pi$
$54$	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
$58$	−0.319298			−0.0419259
$59$	−2.67177	+	4.62764i	−0.347835	+	0.602468i	−0.985865	−	0.167544i	$-0.946416\pi$
$59$	−2.67177	+	4.62764i	−0.347835	+	0.602468i	0.638030	+	0.770012i	$0.279750\pi$
$60$	0.514760	+	0.891591i	0.0664553	+	0.115104i
$61$	−11.5457			−1.47828			−0.739141	−	0.673551i	$-0.764768\pi$
$61$	−11.5457			−1.47828			−0.739141	+	0.673551i	$0.764768\pi$
$62$	−4.99774	+	8.65635i	−0.634714	+	1.09936i
$63$		0			0
$64$	−4.82736			−0.603420
$65$	−1.06519	−	5.20354i	−0.132121	−	0.645420i
$66$	1.79355	+	3.10651i	0.220770	+	0.382385i
$67$	4.13546			0.505226			0.252613	−	0.967567i	$-0.418710\pi$
$67$	4.13546			0.505226			0.252613	+	0.967567i	$0.418710\pi$
$68$	−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	0.994018	+	0.109217i	$0.0348344\pi$
$71$	4.98486	+	8.63403i	0.591594	+	1.02467i	−0.402424	+	0.915453i	$0.631832\pi$
$72$	−1.97953			−0.233289
$73$	7.62080	+	13.1996i	0.891947	+	1.54490i	0.837539	+	0.546378i	$0.183994\pi$
$73$	7.62080	+	13.1996i	0.891947	+	1.54490i	0.0544080	+	0.998519i	$0.482673\pi$
$74$	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
$79$	−0.387251	+	0.670738i	−0.0435691	+	0.0754639i	−0.886988	−	0.461793i	$-0.847206\pi$
$79$	−0.387251	+	0.670738i	−0.0435691	+	0.0754639i	0.843418	+	0.537257i	$0.180540\pi$
$80$	−6.77881			−0.757894
$81$	7.38159			0.820177
$82$	9.84011			1.08666
$83$	16.0186			1.75827			0.879136	−	0.476571i	$-0.158121\pi$
$83$	16.0186			1.75827			0.879136	+	0.476571i	$0.158121\pi$
$84$		0			0
$85$	−0.885875	−	1.53438i	−0.0960866	−	0.166427i
$86$	0.0216761	−	0.0375441i	0.00233740	−	0.00404849i
$87$	0.0358956	−	0.0621731i	0.00384842	−	0.00666565i
$88$	−3.08805			−0.329187
$89$	3.27880	+	5.67904i	0.347552	+	0.601977i	0.985814	−	0.167842i	$-0.0536797\pi$
$89$	3.27880	+	5.67904i	0.347552	+	0.601977i	−0.638262	+	0.769819i	$0.720346\pi$
$90$	7.90611			0.833378
$91$		0			0
$92$	−7.23762			−0.754574
$93$	−1.12370	−	1.94630i	−0.116522	−	0.201822i
$94$	22.2637			2.29633
$95$	2.38801	−	4.13616i	0.245005	−	0.424361i
$96$	1.57733	−	2.73202i	0.160986	−	0.278835i
$97$	1.74583	+	3.02387i	0.177262	+	0.307027i	0.940942	−	0.338568i	$-0.109943\pi$
$97$	1.74583	+	3.02387i	0.177262	+	0.307027i	−0.763680	+	0.645595i	$0.776609\pi$
$98$		0			0
$99$	12.3743			1.24367
$100$	−4.61600			−0.461600
$101$	−2.57780			−0.256500			−0.128250	−	0.991742i	$-0.540936\pi$
$101$	−2.57780			−0.256500			−0.128250	+	0.991742i	$0.540936\pi$
$102$	0.981933			0.0972258
$103$	−8.43173	+	14.6042i	−0.830803	+	1.43899i	0.0665997	+	0.997780i	$0.478785\pi$
$103$	−8.43173	+	14.6042i	−0.830803	+	1.43899i	−0.897402	+	0.441213i	$0.854548\pi$
$104$	−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
$109$	6.02026	+	10.4274i	0.576637	+	0.998764i	0.995862	+	0.0908816i	$0.0289685\pi$
$109$	6.02026	+	10.4274i	0.576637	+	0.998764i	−0.419225	+	0.907882i	$0.637698\pi$
$110$	12.3335			1.17595
$111$	1.51040	+	2.61608i	0.143360	+	0.248307i
$112$		0			0
$113$	−4.68616	−	8.11667i	−0.440837	−	0.763552i	0.556915	−	0.830570i	$-0.311985\pi$
$113$	−4.68616	−	8.11667i	−0.440837	−	0.763552i	−0.997752	+	0.0670176i	$0.978652\pi$
$114$	1.32348	+	2.29233i	0.123955	+	0.214696i
$115$	−6.53643			−0.609525
$116$	−0.136660	−	0.236701i	−0.0126885	−	0.0219772i
$117$	7.59739	−	6.73791i	0.702379	−	0.622920i
$118$	−10.1824			−0.937369
$119$		0			0
$120$	0.221805	−	0.384177i	0.0202479	−	0.0350704i
$121$	8.30385			0.754895
$122$	−11.0006	−	19.0535i	−0.995944	−	1.72503i
$123$	−1.10623	+	1.91605i	−0.0997453	+	0.172764i
$124$	−8.55614			−0.768364
$125$	−11.5344			−1.03167
$126$		0			0
$127$	−7.94269	+	13.7571i	−0.704800	+	1.22075i	0.261964	+	0.965078i	$0.415630\pi$
$127$	−7.94269	+	13.7571i	−0.704800	+	1.22075i	−0.966764	+	0.255672i	$0.917703\pi$
$128$	2.76359	+	4.78667i	0.244269	+	0.423086i
$129$	0.00487367	+	0.00844145i	0.000429103	+	0.000743228i
$130$	7.57232	−	6.71567i	0.664136	−	0.589004i
$131$	0.928725	−	1.60860i	0.0811430	−	0.140544i	−0.822598	−	0.568623i	$-0.807476\pi$
$131$	0.928725	−	1.60860i	0.0811430	−	0.140544i	0.903741	+	0.428079i	$0.140810\pi$
$132$	−1.53527	+	2.65917i	−0.133628	+	0.231451i
$133$		0			0
$134$	3.94018	+	6.82459i	0.340380	+	0.589555i
$135$	−1.83555	+	3.17926i	−0.157979	+	0.273627i
$136$	−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	$-0.0174868\pi$
$138$	1.81130	−	3.13726i	0.154188	−	0.267061i
$139$	−0.169365	−	0.293348i	−0.0143653	−	0.0248815i	0.858753	−	0.512389i	$-0.171239\pi$
$139$	−0.169365	−	0.293348i	−0.0143653	−	0.0248815i	−0.873119	+	0.487508i	$0.837906\pi$
$140$		0			0
$141$	−2.50290	+	4.33514i	−0.210782	+	0.365085i
$142$	−9.49894	+	16.4527i	−0.797134	+	1.38068i
$143$	11.8519	−	10.5111i	0.991104	−	0.878982i
$144$	−6.48010	−	11.2239i	−0.540009	−	0.935322i
$145$	−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
$149$	3.92316			0.321398			0.160699	−	0.987003i	$-0.448625\pi$
$149$	3.92316			0.321398			0.160699	+	0.987003i	$0.448625\pi$
$150$	1.15521	−	2.00088i	0.0943222	−	0.163371i
$151$	1.05939	+	1.83492i	0.0862122	+	0.149324i	0.905907	−	0.423476i	$-0.139190\pi$
$151$	1.05939	+	1.83492i	0.0862122	+	0.149324i	−0.819695	+	0.572800i	$0.805857\pi$
$152$	−2.27870			−0.184827
$153$	1.69368	−	2.93354i	0.136926	−	0.237162i
$154$		0			0
$155$	−7.72721			−0.620664
$156$	0.505336	+	2.46861i	0.0404593	+	0.197647i
$157$	−11.0564	−	19.1502i	−0.882397	−	1.52836i	−0.848668	−	0.528925i	$-0.822595\pi$
$157$	−11.0564	−	19.1502i	−0.882397	−	1.52836i	−0.0337285	−	0.999431i	$-0.510738\pi$
$158$	−1.47586			−0.117413
$159$	−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
$163$	3.85214			0.301723			0.150861	−	0.988555i	$-0.451795\pi$
$163$	3.85214			0.301723			0.150861	+	0.988555i	$0.451795\pi$
$164$	4.21157	+	7.29465i	0.328868	+	0.569616i
$165$	−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	$-0.806960\pi$
$167$	1.06947	−	1.85238i	0.0827582	−	0.143341i	0.904434	+	0.426614i	$0.140294\pi$
$168$		0			0
$169$	1.55326	−	12.9069i	0.119482	−	0.992836i
$170$	1.68809	−	2.92385i	0.129470	−	0.224249i
$171$	9.13113			0.698275
$172$	0.0371095			0.00282957
$173$	16.6133			1.26308			0.631542	−	0.775342i	$-0.282422\pi$
$173$	16.6133			1.26308			0.631542	+	0.775342i	$0.282422\pi$
$174$	0.136803			0.0103710
$175$		0			0
$176$	−10.1089	−	17.5091i	−0.761988	−	1.31980i
$177$	1.14471	−	1.98270i	0.0860419	−	0.149029i
$178$	−6.24795	+	10.8218i	−0.468303	+	0.811125i
$179$	−0.539496			−0.0403238			−0.0201619	−	0.999797i	$-0.506418\pi$
$179$	−0.539496			−0.0403238			−0.0201619	+	0.999797i	$0.506418\pi$
$180$	3.38382	+	5.86094i	0.252215	+	0.436849i
$181$	−2.77164			−0.206014			−0.103007	−	0.994681i	$-0.532846\pi$
$181$	−2.77164			−0.206014			−0.103007	+	0.994681i	$0.532846\pi$
$182$		0			0
$183$	4.94675			0.365674
$184$	1.55931	+	2.70080i	0.114954	+	0.199105i
$185$	10.3864			0.763621
$186$	2.14127	−	3.70879i	0.157006	−	0.271942i
$187$	2.64213	−	4.57629i	0.193211	−	0.334652i
$188$	9.52887	+	16.5045i	0.694964	+	1.20371i
$189$		0			0
$190$	9.10100			0.660256
$191$	−20.2407			−1.46457			−0.732284	−	0.680999i	$-0.761546\pi$
$191$	−20.2407			−1.46457			−0.732284	+	0.680999i	$0.761546\pi$
$192$	2.06827			0.149265
$193$	−16.3771			−1.17885			−0.589425	−	0.807823i	$-0.700646\pi$
$193$	−16.3771			−1.17885			−0.589425	+	0.807823i	$0.700646\pi$
$194$	−3.32678	+	5.76216i	−0.238849	+	0.413699i
$195$	0.456378	+	2.22944i	0.0326819	+	0.159654i
$196$		0			0
$197$	−9.86676	+	17.0897i	−0.702977	+	1.21759i	0.264439	+	0.964402i	$0.414813\pi$
$197$	−9.86676	+	17.0897i	−0.702977	+	1.21759i	−0.967417	+	0.253190i	$0.918520\pi$
$198$	11.7900	+	20.4209i	0.837879	+	1.45125i
$199$	−7.05873	+	12.2261i	−0.500380	+	0.866683i	0.499620	+	0.866245i	$0.333473\pi$
$199$	−7.05873	+	12.2261i	−0.500380	+	0.866683i	−1.00000		0.000438630i	$0.999860\pi$
$200$	0.994491	+	1.72251i	0.0703212	+	0.121800i
$201$	−1.77183			−0.124975
$202$	−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
$206$	−32.1343			−2.23890
$207$	−6.24840	−	10.8225i	−0.434294	−	0.752219i
$208$	−15.7404	−	5.24562i	−1.09140	−	0.363718i
$209$	14.2445			0.985313
$210$		0			0
$211$	2.31317	−	4.00652i	0.159245	−	0.275820i	−0.775352	−	0.631530i	$-0.782427\pi$
$211$	2.31317	−	4.00652i	0.159245	−	0.275820i	0.934597	+	0.355709i	$0.115761\pi$
$212$	−0.231275			−0.0158840
$213$	−2.13575	−	3.69923i	−0.146339	−	0.253467i
$214$	8.27265	−	14.3287i	0.565507	−	0.979487i
$215$	0.0335143			0.00228565
$216$	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
$220$	5.27873	+	9.14303i	0.355892	+	0.616423i
$221$	−0.869656	−	4.24834i	−0.0584994	−	0.285774i
$222$	−2.87815	+	4.98510i	−0.193169	+	0.334578i
$223$	−10.6761	+	18.4916i	−0.714926	+	1.23829i	0.248061	+	0.968744i	$0.420207\pi$
$223$	−10.6761	+	18.4916i	−0.714926	+	1.23829i	−0.962988	+	0.269545i	$0.913127\pi$
$224$		0			0
$225$	−3.98509	−	6.90239i	−0.265673	−	0.460159i
$226$	8.92976	−	15.4668i	0.593999	−	1.02884i
$227$	−5.22451	+	9.04911i	−0.346763	+	0.600611i	−0.985672	−	0.168671i	$-0.946052\pi$
$227$	−5.22451	+	9.04911i	−0.346763	+	0.600611i	0.638910	+	0.769282i	$0.279386\pi$
$228$	−1.13289	+	1.96223i	−0.0750278	+	0.129952i
$229$	7.22901	−	12.5210i	0.477706	−	0.827412i	−0.521967	−	0.852966i	$-0.674802\pi$
$229$	7.22901	−	12.5210i	0.477706	−	0.827412i	0.999673	+	0.0255538i	$0.00813493\pi$
$230$	−6.22778	−	10.7868i	−0.410648	−	0.711262i
$231$		0			0
$232$	−0.0588852	+	0.101992i	−0.00386600	+	0.00669611i
$233$	4.64413	−	8.04388i	0.304247	−	0.526972i	−0.672846	−	0.739783i	$-0.734928\pi$
$233$	4.64413	−	8.04388i	0.304247	−	0.526972i	0.977093	+	0.212811i	$0.0682617\pi$
$234$	18.3580	+	6.11795i	1.20010	+	0.399943i
$235$	8.60570	+	14.9055i	0.561374	+	0.972328i
$236$	−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	$0.281007\pi$
$240$	2.90437			0.187476
$241$	3.65552	−	6.33155i	0.235473	−	0.407851i	−0.723937	−	0.689866i	$-0.757669\pi$
$241$	3.65552	−	6.33155i	0.235473	−	0.407851i	0.959410	+	0.282015i	$0.0910028\pi$
$242$	7.91174	+	13.7035i	0.508586	+	0.880897i
$243$	−10.6387			−0.682475
$244$	9.41648	−	16.3098i	0.602828	−	1.04413i
$245$		0			0
$246$	−4.21597			−0.268801
$247$	8.74562	−	7.75624i	0.556470	−	0.493518i
$248$	1.84337	+	3.19282i	0.117054	+	0.202744i
$249$	−6.86314			−0.434934
$250$	−10.9898	−	19.0349i	−0.695055	−	1.20387i
$251$	−5.93191	−	10.2744i	−0.374419	−	0.648512i	0.615821	−	0.787886i	$-0.288824\pi$
$251$	−5.93191	−	10.2744i	−0.374419	−	0.648512i	−0.990240	+	0.139374i	$0.955491\pi$
$252$		0			0
$253$	−9.74746	−	16.8831i	−0.612817	−	1.06143i
$254$	−30.2706			−1.89934
$255$	0.379551	+	0.657402i	0.0237684	+	0.0411681i
$256$	−10.0935	+	17.4825i	−0.630846	+	1.09266i
$257$	−7.58608	−	13.1395i	−0.473206	−	0.819618i	0.526323	−	0.850285i	$-0.323570\pi$
$257$	−7.58608	−	13.1395i	−0.473206	−	0.819618i	−0.999530	+	0.0306670i	$0.990237\pi$
$258$	−0.00928708	+	0.0160857i	−0.000578188	+	0.00100145i
$259$		0			0
$260$	8.21940	+	2.73919i	0.509745	+	0.169877i
$261$	0.235963	−	0.408699i	0.0146057	−	0.0252979i
$262$	3.53948			0.218670
$263$	17.1964			1.06037			0.530187	−	0.847880i	$-0.322122\pi$
$263$	17.1964			1.06037			0.530187	+	0.847880i	$0.322122\pi$
$264$	1.32307			0.0814291
$265$	−0.208869			−0.0128307
$266$		0			0
$267$	−1.40479	−	2.43317i	−0.0859719	−	0.148908i
$268$	−3.37279	+	5.84185i	−0.206026	+	0.356848i
$269$	9.46102	−	16.3870i	0.576849	−	0.999131i	−0.418989	−	0.907991i	$-0.637616\pi$
$269$	9.46102	−	16.3870i	0.576849	−	0.999131i	0.995838	−	0.0911401i	$-0.0290511\pi$
$270$	−6.99549			−0.425732
$271$	16.0667	+	27.8283i	0.975982	+	1.69045i	0.676657	+	0.736298i	$0.263428\pi$
$271$	16.0667	+	27.8283i	0.975982	+	1.69045i	0.299324	+	0.954151i	$0.403239\pi$
$272$	−5.53444			−0.335575
$273$		0			0
$274$	24.3916			1.47355
$275$	−6.21672	−	10.7677i	−0.374882	−	0.649315i
$276$	3.10094			0.186655
$277$	−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	$0.980174\pi$
$278$	0.322734	−	0.558992i	0.0193563	−	0.0335261i
$279$	−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	$0.639480\pi$
$282$	−9.53883			−0.568029
$283$	11.4289			0.679378			0.339689	−	0.940538i	$-0.389678\pi$
$283$	11.4289			0.679378			0.339689	+	0.940538i	$0.389678\pi$
$284$	−16.2622			−0.964983
$285$	−1.02314	+	1.77213i	−0.0606055	+	0.104972i
$286$	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
$291$	−0.747997	−	1.29557i	−0.0438483	−	0.0759476i
$292$	−24.8615			−1.45491
$293$	−6.60231	−	11.4355i	−0.385711	−	0.668071i	0.606156	−	0.795345i	$-0.292711\pi$
$293$	−6.60231	−	11.4355i	−0.385711	−	0.668071i	−0.991868	+	0.127274i	$0.959377\pi$
$294$		0			0
$295$	−3.93586	−	6.81712i	−0.229155	−	0.396908i
$296$	−2.47773	−	4.29156i	−0.144015	−	0.249442i
$297$	−10.9490			−0.635328
$298$	3.73791	+	6.47425i	0.216531	+	0.375043i
$299$	−15.1776	−	5.05805i	−0.877741	−	0.292515i
$300$	1.97771			0.114183
$301$		0			0
$302$	−2.01874	+	3.49656i	−0.116165	+	0.201204i
$303$	1.10445			0.0634490
$304$	−7.45947	−	12.9202i	−0.427830	−	0.741023i
$305$	8.50420	−	14.7297i	0.486949	−	0.843420i
$306$	6.45481			0.368997
$307$	6.65903			0.380051			0.190026	−	0.981779i	$-0.439143\pi$
$307$	6.65903			0.380051			0.190026	+	0.981779i	$0.439143\pi$
$308$		0			0
$309$	3.61255	−	6.25713i	0.205511	−	0.355955i
$310$	−7.36233	−	12.7519i	−0.418152	−	0.724261i
$311$	−1.02298	−	1.77186i	−0.0580081	−	0.100473i	0.835563	−	0.549395i	$-0.185142\pi$
$311$	−1.02298	−	1.77186i	−0.0580081	−	0.100473i	−0.893571	+	0.448922i	$0.851808\pi$
$312$	0.812315	−	0.720419i	0.0459883	−	0.0407857i
$313$	4.70883	−	8.15594i	0.266159	−	0.461001i	−0.701708	−	0.712465i	$-0.747579\pi$
$313$	4.70883	−	8.15594i	0.266159	−	0.461001i	0.967867	+	0.251464i	$0.0809120\pi$
$314$	21.0686	−	36.4919i	1.18897	−	2.05936i
$315$		0			0
$316$	−0.631667	−	1.09408i	−0.0355341	−	0.0615468i
$317$	16.6856	−	28.9004i	0.937159	−	1.62321i	0.166421	−	0.986055i	$-0.446779\pi$
$317$	16.6856	−	28.9004i	0.937159	−	1.62321i	0.770738	−	0.637153i	$-0.219888\pi$
$318$	0.0578792	−	0.100250i	0.00324571	−	0.00562173i
$319$	0.368100	−	0.637568i	0.0206097	−	0.0356970i
$320$	3.55567	−	6.15860i	0.198768	−	0.344276i
$321$	1.86003	+	3.22167i	0.103817	+	0.179816i
$322$		0			0
$323$	1.94965	−	3.37689i	0.108481	−	0.187895i
$324$	−6.02027	+	10.4274i	−0.334460	+	0.579301i
$325$	−9.67992	−	3.22592i	−0.536946	−	0.178942i
$326$	3.67024	+	6.35704i	0.203276	+	0.352084i
$327$	−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
$331$	19.0660			1.04796			0.523980	−	0.851731i	$-0.324447\pi$
$331$	19.0660			1.04796			0.523980	+	0.851731i	$0.324447\pi$
$332$	−13.0645	+	22.6283i	−0.717005	+	1.24189i
$333$	9.92870	+	17.1970i	0.544089	+	0.942390i
$334$	4.07589			0.223023
$335$	−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	$0.824670\pi$
$338$	22.7797	−	9.73412i	1.23905	−	0.529466i
$339$	2.00777	+	3.47757i	0.109047	+	0.188876i
$340$	2.89001			0.156733
$341$	−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
$345$	2.80052			0.150775
$346$	15.8288	+	27.4163i	0.850961	+	1.47391i
$347$	−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	−0.342877	−	0.939380i	$-0.611401\pi$
$349$	11.9952	−	20.7763i	0.642089	−	1.11213i	0.984966	−	0.172750i	$-0.0552652\pi$
$350$		0			0
$351$	−6.72233	+	5.96184i	−0.358811	+	0.318219i
$352$	16.1751	−	28.0161i	0.862135	−	1.49326i
$353$	−12.7934			−0.680922			−0.340461	−	0.940259i	$-0.610583\pi$
$353$	−12.7934			−0.680922			−0.340461	+	0.940259i	$0.610583\pi$
$354$	4.36264			0.231872
$355$	−14.6867			−0.779488
$356$	−10.6965			−0.566912
$357$		0			0
$358$	−0.514021	−	0.890310i	−0.0271668	−	0.0470544i
$359$	−6.16986	+	10.6865i	−0.325633	+	0.564012i	−0.981640	−	0.190742i	$-0.938911\pi$
$359$	−6.16986	+	10.6865i	−0.325633	+	0.564012i	0.656008	+	0.754754i	$0.272244\pi$
$360$	1.45805	−	2.52542i	0.0768460	−	0.133101i
$361$	−8.48884			−0.446781
$362$	−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
$367$	−2.03077			−0.106005			−0.0530026	−	0.998594i	$-0.516879\pi$
$367$	−2.03077			−0.106005			−0.0530026	+	0.998594i	$0.516879\pi$
$368$	−10.2090	+	17.6825i	−0.532179	+	0.921762i
$369$	−7.27188	+	12.5953i	−0.378559	+	0.655684i
$370$	9.89593	+	17.1403i	0.514465	+	0.891079i
$371$		0			0
$372$	3.66586			0.190066
$373$	−3.87400			−0.200588			−0.100294	−	0.994958i	$-0.531978\pi$
$373$	−3.87400			−0.200588			−0.100294	+	0.994958i	$0.531978\pi$
$374$	10.0695			0.520679
$375$	4.94190			0.255199
$376$	4.10588	−	7.11160i	0.211745	−	0.366753i
$377$	−0.121160	−	0.591877i	−0.00624007	−	0.0304832i
$378$		0			0
$379$	7.28396	−	12.6162i	0.374152	−	0.648050i	−0.616048	−	0.787709i	$-0.711267\pi$
$379$	7.28396	−	12.6162i	0.374152	−	0.648050i	0.990200	+	0.139659i	$0.0446006\pi$
$380$	3.89523	+	6.74673i	0.199821	+	0.346100i
$381$	3.40303	−	5.89422i	0.174342	−	0.301970i
$382$	−19.2850	−	33.4025i	−0.986705	−	1.70902i
$383$	26.7818			1.36849			0.684243	−	0.729254i	$-0.260133\pi$
$383$	26.7818			1.36849			0.684243	+	0.729254i	$0.260133\pi$
$384$	−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
$388$	−5.69545			−0.289143
$389$	−6.00738	−	10.4051i	−0.304586	−	0.527559i	0.672583	−	0.740022i	$-0.265185\pi$
$389$	−6.00738	−	10.4051i	−0.304586	−	0.527559i	−0.977169	+	0.212463i	$0.931852\pi$
$390$	−3.24434	+	2.87731i	−0.164284	+	0.145698i
$391$	−5.33655			−0.269881
$392$		0			0
$393$	−0.397910	+	0.689200i	−0.0200719	+	0.0347655i
$394$	−37.6034			−1.89443
$395$	−0.570470	−	0.988084i	−0.0287035	−	0.0497159i
$396$	−10.0922	+	17.4803i	−0.507154	+	0.878417i
$397$	1.65765			0.0831951			0.0415975	−	0.999134i	$-0.486755\pi$
$397$	1.65765			0.0831951			0.0415975	+	0.999134i	$0.486755\pi$
$398$	−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	$0.662449\pi$
$402$	−1.68816	−	2.92398i	−0.0841978	−	0.145835i
$403$	−17.9425	−	5.97951i	−0.893782	−	0.297861i
$404$	2.10240	−	3.64146i	0.104598	−	0.181169i
$405$	−5.43702	+	9.41720i	−0.270168	+	0.467944i
$406$		0			0
$407$	15.4887	+	26.8272i	0.767746	+	1.32978i
$408$	0.181089	−	0.313655i	0.00896522	−	0.0155282i
$409$	7.43293	−	12.8742i	0.367535	−	0.636589i	−0.621645	−	0.783299i	$-0.713535\pi$
$409$	7.43293	−	12.8742i	0.367535	−	0.636589i	0.989180	+	0.146710i	$0.0468685\pi$
$410$	−7.24788	+	12.5537i	−0.357947	+	0.619983i
$411$	−2.74211	+	4.74948i	−0.135258	+	0.234274i
$412$	−13.7535	−	23.8217i	−0.677586	−	1.17361i
$413$		0			0
$414$	11.9067	−	20.6230i	0.585182	−	1.01357i
$415$	−11.7988	+	20.4360i	−0.579178	+	1.00317i
$416$	−5.32404	−	26.0083i	−0.261032	−	1.27516i
$417$	0.0725639	+	0.125684i	0.00355347	+	0.00615479i
$418$	13.5719	+	23.5072i	0.663822	+	1.14977i
$419$	−11.8087	+	20.4533i	−0.576895	+	0.999211i	0.418938	+	0.908015i	$0.362402\pi$
$419$	−11.8087	+	20.4533i	−0.576895	+	0.999211i	−0.995833	+	0.0911962i	$0.970931\pi$
$420$		0			0
$421$	26.0822			1.27117			0.635585	−	0.772031i	$-0.280759\pi$
$421$	26.0822			1.27117			0.635585	+	0.772031i	$0.280759\pi$
$422$	8.81576			0.429144
$423$	−16.4530	+	28.4974i	−0.799971	+	1.38559i
$424$	0.0498269	+	0.0863028i	0.00241981	+	0.00419123i
$425$	−3.40354			−0.165096
$426$	4.06980	−	7.04910i	0.197182	−	0.341530i
$427$		0			0
$428$	14.1628			0.684584
$429$	−5.07791	+	4.50345i	−0.245164	+	0.217429i
$430$	0.0319317	+	0.0553074i	0.00153988	+	0.00266716i
$431$	−13.3172			−0.641466			−0.320733	−	0.947170i	$-0.603929\pi$
$431$	−13.3172			−0.641466			−0.320733	+	0.947170i	$0.603929\pi$
$432$	5.73373	+	9.93110i	0.275864	+	0.477810i
$433$	10.2110	+	17.6860i	0.490711	+	0.849937i	0.999943	−	0.0106929i	$-0.00340371\pi$
$433$	10.2110	+	17.6860i	0.490711	+	0.849937i	−0.509232	+	0.860629i	$0.670070\pi$
$434$		0			0
$435$	0.0528790	+	0.0915890i	0.00253535	+	0.00439136i
$436$	−19.6400			−0.940586
$437$	−7.19275	−	12.4582i	−0.344076	−	0.595957i
$438$	6.22187	−	10.7766i	0.297292	−	0.514925i
$439$	−4.88537	−	8.46171i	−0.233166	−	0.403855i	0.725572	−	0.688146i	$-0.241575\pi$
$439$	−4.88537	−	8.46171i	−0.233166	−	0.403855i	−0.958738	+	0.284291i	$0.908242\pi$
$440$	2.27455	−	3.93963i	0.108435	−	0.187814i
$441$		0			0
$442$	6.18229	−	5.48290i	0.294061	−	0.260795i
$443$	−10.5819	+	18.3285i	−0.502763	+	0.870811i	0.497232	+	0.867618i	$0.334350\pi$
$443$	−10.5819	+	18.3285i	−0.502763	+	0.870811i	−0.999995	+	0.00319331i	$0.998984\pi$
$444$	−4.92739			−0.233844
$445$	−9.66019			−0.457937
$446$	−40.6880			−1.92663
$447$	−1.68087			−0.0795023
$448$		0			0
$449$	9.07320	+	15.7152i	0.428191	+	0.741648i	0.996712	−	0.0810200i	$-0.0258178\pi$
$449$	9.07320	+	15.7152i	0.428191	+	0.741648i	−0.568522	+	0.822668i	$0.692484\pi$
$450$	7.59384	−	13.1529i	0.357977	−	0.620034i
$451$	−11.3441	+	19.6485i	−0.534172	+	0.925213i
$452$	15.2877			0.719075
$453$	−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	$0.694849\pi$
$458$	27.5506			1.28736
$459$	−1.49860	+	2.59565i	−0.0699487	+	0.121155i
$460$	5.33098	−	9.23352i	0.248558	−	0.430515i
$461$	−14.8873	−	25.7855i	−0.693370	−	1.20095i	−0.970727	−	0.240185i	$-0.922792\pi$
$461$	−14.8873	−	25.7855i	−0.693370	−	1.20095i	0.277357	−	0.960767i	$-0.410542\pi$
$462$		0			0
$463$	17.7067			0.822900			0.411450	−	0.911432i	$-0.365023\pi$
$463$	17.7067			0.822900			0.411450	+	0.911432i	$0.365023\pi$
$464$	−0.771057			−0.0357954
$465$	3.31070			0.153530
$466$	17.6994			0.819907
$467$	−2.91461	+	5.04825i	−0.134872	+	0.233605i	−0.925549	−	0.378629i	$-0.876396\pi$
$467$	−2.91461	+	5.04825i	−0.134872	+	0.233605i	0.790677	+	0.612234i	$0.209729\pi$
$468$	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
$473$	0.0499782	+	0.0865648i	0.00229800	+	0.00398025i
$474$	0.632328			0.0290438
$475$	−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
$479$	−14.4913			−0.662125			−0.331062	−	0.943609i	$-0.607407\pi$
$479$	−14.4913			−0.662125			−0.331062	+	0.943609i	$0.607407\pi$
$480$	2.32361	+	4.02461i	0.106058	+	0.183698i
$481$	24.1171	+	8.03724i	1.09965	+	0.366467i
$482$	13.9316			0.634569
$483$		0			0
$484$	−6.77245	+	11.7302i	−0.307839	+	0.533192i
$485$	−5.14367			−0.233562
$486$	−10.1364	−	17.5567i	−0.459795	−	0.796389i
$487$	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	$0.0332675\pi$
$488$	−8.11491			−0.367345
$489$	−1.65044			−0.0746354
$490$		0			0
$491$	18.1505	−	31.4375i	0.819119	−	1.41876i	−0.0872134	−	0.996190i	$-0.527796\pi$
$491$	18.1505	−	31.4375i	0.819119	−	1.41876i	0.906332	−	0.422566i	$-0.138870\pi$
$492$	−1.80444	−	3.12537i	−0.0813503	−	0.140903i
$493$	−0.100764	−	0.174528i	−0.00453818	−	0.00786036i
$494$	21.1325	+	7.04258i	0.950796	+	0.316861i
$495$	−9.11449	+	15.7868i	−0.409666	+	0.709562i
$496$	−12.0688	+	20.9038i	−0.541905	+	0.938607i
$497$		0			0
$498$	−6.53906	−	11.3260i	−0.293022	−	0.507530i
$499$	−11.8538	+	20.5314i	−0.530649	+	0.919112i	0.468711	+	0.883352i	$0.344719\pi$
$499$	−11.8538	+	20.5314i	−0.530649	+	0.919112i	−0.999360	+	0.0357602i	$0.988615\pi$
$500$	9.40726	−	16.2938i	0.420705	−	0.728683i
$501$	−0.458213	+	0.793648i	−0.0204714	+	0.0354576i
$502$	11.3036	−	19.5784i	0.504505	−	0.873828i
$503$	13.8876	+	24.0540i	0.619217	+	1.07252i	0.989629	+	0.143648i	$0.0458834\pi$
$503$	13.8876	+	24.0540i	0.619217	+	1.07252i	−0.370411	+	0.928868i	$0.620783\pi$
$504$		0			0
$505$	1.89871	−	3.28867i	0.0844916	−	0.146344i
$506$	18.5744	−	32.1717i	0.825731	−	1.43021i
$507$	−0.665491	+	5.52992i	−0.0295555	+	0.245592i
$508$	−12.9558	−	22.4401i	−0.574820	−	0.995618i
$509$	4.35208	+	7.53802i	0.192902	+	0.334117i	0.946211	−	0.323551i	$-0.104877\pi$
$509$	4.35208	+	7.53802i	0.192902	+	0.334117i	−0.753308	+	0.657667i	$0.771543\pi$
$510$	−0.723257	+	1.25272i	−0.0320264	+	0.0554713i
$511$		0			0
$512$	−27.4134			−1.21151
$513$	−8.07941			−0.356715
$514$	14.4557	−	25.0380i	0.637615	−	1.10438i
$515$	−12.4210	−	21.5139i	−0.547336	−	0.948014i
$516$	−0.0158995			−0.000699935
$517$	−25.6665	+	44.4557i	−1.12881	+	1.95516i
$518$		0			0
$519$	−7.11792			−0.312442
$520$	−0.748668	−	3.65730i	−0.0328313	−	0.160383i
$521$	−4.28573	−	7.42310i	−0.187761	−	0.325212i	0.756742	−	0.653713i	$-0.226790\pi$
$521$	−4.28573	−	7.42310i	−0.187761	−	0.325212i	−0.944504	+	0.328501i	$0.893456\pi$
$522$	0.899282			0.0393605
$523$	14.9746	+	25.9369i	0.654796	+	1.13414i	0.981945	+	0.189167i	$0.0605787\pi$
$523$	14.9746	+	25.9369i	0.654796	+	1.13414i	−0.327149	+	0.944973i	$0.606088\pi$
$524$	1.51490	+	2.62388i	0.0661786	+	0.114625i
$525$		0			0
$526$	16.3844	+	28.3786i	0.714393	+	1.23736i
$527$	−6.30874			−0.274813
$528$	4.33114	+	7.50175i	0.188489	+	0.326472i
$529$	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
$534$	2.67692	−	4.63656i	0.115842	−	0.200643i
$535$	12.7907			0.552989
$536$	2.90660			0.125546
$537$	0.231146			0.00997467
$538$	36.0571			1.55453
$539$		0			0
$540$	−2.99407	−	5.18588i	−0.128844	−	0.223165i
$541$	−5.24095	+	9.07760i	−0.225326	+	0.390276i	−0.956417	−	0.292003i	$-0.905678\pi$
$541$	−5.24095	+	9.07760i	−0.225326	+	0.390276i	0.731091	+	0.682280i	$0.239011\pi$
$542$	−30.6160	+	53.0285i	−1.31507	+	2.27777i
$543$	1.18750			0.0509606
$544$	−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
$549$	32.5178			1.38783
$550$	11.8463	−	20.5184i	0.505129	−	0.874909i
$551$	0.271625	−	0.470468i	0.0115716	−	0.0200426i
$552$	−0.668081	−	1.15715i	−0.0284354	−	0.0492516i
$553$		0			0
$554$	−35.0726			−1.49009
$555$	−4.45002			−0.188893
$556$	0.552521			0.0234321
$557$	11.8597			0.502513			0.251256	−	0.967921i	$-0.419156\pi$
$557$	11.8597			0.502513			0.251256	+	0.967921i	$0.419156\pi$
$558$	14.0758	−	24.3800i	0.595877	−	1.03209i
$559$	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	−0.773508	−	0.633786i	$-0.781500\pi$
$563$	3.84675	−	6.66276i	0.162121	−	0.280802i	0.935629	+	0.352985i	$0.114833\pi$
$564$	−4.08262	−	7.07131i	−0.171909	−	0.297756i
$565$	13.8066			0.580850
$566$	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	$-0.453673\pi$
$570$	−3.89930			−0.163324
$571$	−7.08285	−	12.2679i	−0.296408	−	0.513394i	0.678903	−	0.734228i	$-0.262456\pi$
$571$	−7.08285	−	12.2679i	−0.296408	−	0.513394i	−0.975311	+	0.220834i	$0.929122\pi$
$572$	5.18208	+	25.3149i	0.216674	+	1.05847i
$573$	8.67209			0.362282
$574$		0			0
$575$	−6.27825	+	10.8742i	−0.261821	+	0.453488i
$576$	13.5959			0.566498
$577$	−7.48776	−	12.9692i	−0.311720	−	0.539914i	0.667015	−	0.745044i	$-0.267572\pi$
$577$	−7.48776	−	12.9692i	−0.311720	−	0.539914i	−0.978735	+	0.205130i	$0.934238\pi$
$578$	−14.8190	+	25.6673i	−0.616391	+	1.06762i
$579$	7.01674			0.291606
$580$	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
$584$	5.35627	+	9.27732i	0.221644	+	0.383898i
$585$	3.00004	+	14.6554i	0.124036	+	0.605927i
$586$	12.5811	−	21.7911i	0.519720	−	0.900182i
$587$	−6.58821	+	11.4111i	−0.271925	+	0.470987i	−0.969355	−	0.245666i	$-0.920993\pi$
$587$	−6.58821	+	11.4111i	−0.271925	+	0.470987i	0.697430	+	0.716653i	$0.254327\pi$
$588$		0			0
$589$	−8.50309	−	14.7278i	−0.350364	−	0.606848i
$590$	7.50003	−	12.9904i	0.308771	−	0.534807i
$591$	4.22739	−	7.32205i	0.173892	−	0.301189i
$592$	16.2220	−	28.0974i	0.666722	−	1.15480i
$593$	−22.0663	+	38.2200i	−0.906156	+	1.56951i	−0.0867989	+	0.996226i	$0.527664\pi$
$593$	−22.0663	+	38.2200i	−0.906156	+	1.56951i	−0.819357	+	0.573283i	$0.805670\pi$
$594$	−10.4320	−	18.0688i	−0.428032	−	0.741372i
$595$		0			0
$596$	−3.19965	+	5.54195i	−0.131063	+	0.227007i
$597$	3.02429	−	5.23823i	0.123776	−	0.214387i
$598$	−6.11376	−	29.8662i	−0.250010	−	1.22132i
$599$	3.01349	+	5.21952i	0.123128	+	0.213264i	0.921000	−	0.389564i	$-0.127374\pi$
$599$	3.01349	+	5.21952i	0.123128	+	0.213264i	−0.797872	+	0.602827i	$0.794041\pi$
$600$	−0.426087	−	0.738005i	−0.0173949	−	0.0301289i
$601$	1.86260	−	3.22612i	0.0759770	−	0.131596i	−0.825534	−	0.564353i	$-0.809126\pi$
$601$	1.86260	−	3.22612i	0.0759770	−	0.131596i	0.901511	+	0.432757i	$0.142459\pi$
$602$		0			0
$603$	−11.6472			−0.474312
$604$	−3.45608			−0.140626
$605$	−6.11632	+	10.5938i	−0.248664	+	0.430698i
$606$	1.05230	+	1.82263i	0.0427467	+	0.0740394i
$607$	6.01651			0.244203			0.122101	−	0.992518i	$-0.461037\pi$
$607$	6.01651			0.244203			0.122101	+	0.992518i	$0.461037\pi$
$608$	11.9358	−	20.6733i	0.484059	−	0.838415i
$609$		0			0
$610$	32.4105			1.31226
$611$	8.44814	+	41.2698i	0.341775	+	1.66960i
$612$	2.76266	+	4.78506i	0.111674	+	0.193425i
$613$	9.80825			0.396152			0.198076	−	0.980187i	$-0.436531\pi$
$613$	9.80825			0.396152			0.198076	+	0.980187i	$0.436531\pi$
$614$	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	−0.975066	−	0.221914i	$-0.928770\pi$
$617$	−16.8838	−	29.2436i	−0.679716	−	1.17730i	0.295350	−	0.955389i	$-0.404564\pi$
$618$	13.7679			0.553825
$619$	2.04671	+	3.54501i	0.0822644	+	0.142486i	0.904222	−	0.427062i	$-0.140451\pi$
$619$	2.04671	+	3.54501i	0.0822644	+	0.142486i	−0.821958	+	0.569548i	$0.807118\pi$
$620$	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
$625$	1.42115	−	2.46150i	0.0568459	−	0.0984599i
$626$	17.9459			0.717264
$627$	−6.10302			−0.243731
$628$	36.0695			1.43933
$629$	8.47978			0.338111
$630$		0			0
$631$	13.3868	+	23.1866i	0.532921	+	0.923046i	0.999261	+	0.0384402i	$0.0122389\pi$
$631$	13.3868	+	23.1866i	0.532921	+	0.923046i	−0.466340	+	0.884605i	$0.654428\pi$
$632$	−0.272179	+	0.471427i	−0.0108267	+	0.0187524i
$633$	−0.991071	+	1.71659i	−0.0393915	+	0.0682282i
$634$	63.5910			2.52552
$635$	−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
$640$	−8.14224			−0.321850
$641$	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	$0.0471273\pi$
$642$	−3.54440	+	6.13908i	−0.139886	+	0.242290i
$643$	−1.96695	−	3.40686i	−0.0775690	−	0.134353i	0.824632	−	0.565670i	$-0.191382\pi$
$643$	−1.96695	−	3.40686i	−0.0775690	−	0.134353i	−0.902201	+	0.431317i	$0.858049\pi$
$644$		0			0
$645$	−0.0143591			−0.000565389
$646$	7.43035			0.292343
$647$	0.197076			0.00774784			0.00387392	−	0.999992i	$-0.498767\pi$
$647$	0.197076			0.00774784			0.00387392	+	0.999992i	$0.498767\pi$
$648$	5.18814			0.203809
$649$	11.7387	−	20.3321i	0.460785	−	0.798104i
$650$	−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
$655$	1.36813	+	2.36967i	0.0534573	+	0.0925908i
$656$	23.7624			0.927765
$657$	−21.4635	−	37.1758i	−0.837369	−	1.45037i
$658$		0			0
$659$	11.7066	+	20.2764i	0.456024	+	0.789857i	0.998746	−	0.0500552i	$-0.0159397\pi$
$659$	11.7066	+	20.2764i	0.456024	+	0.789857i	−0.542722	+	0.839912i	$0.682606\pi$
$660$	−2.26166	−	3.91731i	−0.0880349	−	0.152481i
$661$	4.04817			0.157456			0.0787278	−	0.996896i	$-0.474914\pi$
$661$	4.04817			0.157456			0.0787278	+	0.996896i	$0.474914\pi$
$662$	18.1657	+	31.4638i	0.706028	+	1.22288i
$663$	0.372602	+	1.82019i	0.0144707	+	0.0706904i
$664$	11.2587			0.436921
$665$		0			0
$666$	−18.9197	+	32.7699i	−0.733125	+	1.26981i
$667$	−0.743487			−0.0287879
$668$	1.74448	+	3.02153i	0.0674959	+	0.116906i
$669$	4.57416	−	7.92268i	0.176847	−	0.306309i
$670$	−11.6088			−0.448487
$671$	50.7276			1.95832
$672$		0			0
$673$	−3.64704	+	6.31685i	−0.140583	+	0.243497i	−0.927716	−	0.373286i	$-0.878231\pi$
$673$	−3.64704	+	6.31685i	−0.140583	+	0.243497i	0.787133	+	0.616783i	$0.211564\pi$
$674$	−29.8076	−	51.6283i	−1.14815	−	1.98865i
$675$	3.52609	+	6.10737i	0.135719	+	0.235073i
$676$	16.9658	+	12.7208i	0.652529	+	0.489260i
$677$	−7.87553	+	13.6408i	−0.302681	+	0.524259i	−0.976742	−	0.214416i	$-0.931215\pi$
$677$	−7.87553	+	13.6408i	−0.302681	+	0.524259i	0.674061	+	0.738676i	$0.264548\pi$
$678$	−3.82593	+	6.62671i	−0.146934	+	0.254497i
$679$		0			0
$680$	−0.622636	−	1.07844i	−0.0238770	−	0.0413562i
$681$	2.23843	−	3.87707i	0.0857767	−	0.148570i
$682$	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	$0.874820\pi$
$684$	−7.44717	+	12.8989i	−0.284750	+	0.493201i
$685$	9.42819	+	16.3301i	0.360233	+	0.623941i
$686$		0			0
$687$	−3.09725	+	5.36460i	−0.118168	+	0.204672i
$688$	0.0523445	−	0.0906634i	0.00199562	−	0.00345651i
$689$	−0.484993	−	0.161628i	−0.0184767	−	0.00615754i
$690$	2.66828	+	4.62159i	0.101580	+	0.175941i
$691$	−23.4108	−	40.5487i	−0.890589	−	1.54255i	−0.839171	−	0.543868i	$-0.816959\pi$
$691$	−23.4108	−	40.5487i	−0.890589	−	1.54255i	−0.0514184	−	0.998677i	$-0.516374\pi$
$692$	−13.5494	+	23.4683i	−0.515073	+	0.892132i
$693$		0			0
$694$	−22.2478			−0.844514
$695$	0.498992			0.0189278
$696$	0.0252292	−	0.0436983i	0.000956311	−	0.00165638i
$697$	3.10534	+	5.37860i	0.117623	+	0.203729i
$698$	45.7152			1.73034
$699$	−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	$0.309282\pi$
$702$	−16.2435	−	5.41329i	−0.613072	−	0.204311i
$703$	11.4293	+	19.7961i	0.431063	+	0.746623i
$704$	21.2096			0.799366
$705$	−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
$709$	26.9332			1.01150			0.505750	−	0.862680i	$-0.331216\pi$
$709$	26.9332			1.01150			0.505750	+	0.862680i	$0.331216\pi$
$710$	−13.9932	−	24.2369i	−0.525155	−	0.909595i
$711$	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
$716$	0.440002	−	0.762105i	0.0164436	−	0.0284812i
$717$	−8.41180			−0.314144
$718$	−23.5141			−0.877537
$719$	14.4988			0.540713			0.270356	−	0.962760i	$-0.412859\pi$
$719$	14.4988			0.540713			0.270356	+	0.962760i	$0.412859\pi$
$720$	19.0921			0.711519
$721$		0			0
$722$	−8.08799	−	14.0088i	−0.301004	−	0.521354i
$723$	−1.56620	+	2.71274i	−0.0582476	+	0.100888i
$724$	2.26049	−	3.91528i	0.0840105	−	0.145510i
$725$	−0.474180			−0.0176106
$726$	−3.38977	−	5.87125i	−0.125806	−	0.217902i
$727$	6.26424			0.232328			0.116164	−	0.993230i	$-0.462940\pi$
$727$	6.26424			0.232328			0.116164	+	0.993230i	$0.462940\pi$
$728$		0			0
$729$	−17.5866			−0.651357
$730$	−21.3926	−	37.0531i	−0.791776	−	1.37140i
$731$	0.0273621			0.00101203
$732$	−4.03447	+	6.98790i	−0.149118	+	0.258280i
$733$	−5.99189	+	10.3783i	−0.221316	+	0.383330i	−0.955208	−	0.295936i	$-0.904368\pi$
$733$	−5.99189	+	10.3783i	−0.221316	+	0.383330i	0.733892	+	0.679266i	$0.237702\pi$
$734$	−1.93487	−	3.35130i	−0.0714175	−	0.123699i
$735$		0			0
$736$	−32.6704			−1.20425
$737$	−18.1696			−0.669286
$738$	−27.7140			−1.02017
$739$	13.5254			0.497539			0.248770	−	0.968563i	$-0.419974\pi$
$739$	13.5254			0.497539			0.248770	+	0.968563i	$0.419974\pi$
$740$	−8.47091	+	14.6721i	−0.311397	+	0.539355i
$741$	−3.74704	+	3.32314i	−0.137651	+	0.122079i
$742$		0			0
$743$	19.2299	−	33.3072i	0.705477	−	1.22192i	−0.261043	−	0.965327i	$-0.584066\pi$
$743$	19.2299	−	33.3072i	0.705477	−	1.22192i	0.966519	−	0.256594i	$-0.0826003\pi$
$744$	−0.789789	−	1.36795i	−0.0289551	−	0.0501516i
$745$	−2.88966	+	5.00504i	−0.105869	+	0.183371i
$746$	−3.69107	−	6.39312i	−0.135140	−	0.234069i
$747$	−45.1154			−1.65068
$748$	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	$0.901878\pi$
$752$	53.7635			1.96055
$753$	2.54151	+	4.40203i	0.0926178	+	0.160419i
$754$	0.861315	−	0.763875i	0.0313672	−	0.0278187i
$755$	−3.12125			−0.113594
$756$		0			0
$757$	−4.65791	+	8.06773i	−0.169295	+	0.293227i	−0.938172	−	0.346169i	$-0.887482\pi$
$757$	−4.65791	+	8.06773i	−0.169295	+	0.293227i	0.768877	+	0.639396i	$0.220816\pi$
$758$	27.7600			1.00829
$759$	4.17627	+	7.23352i	0.151589	+	0.262560i
$760$	1.67841	−	2.90709i	0.0608824	−	0.105451i
$761$	43.9381			1.59276			0.796378	−	0.604799i	$-0.206747\pi$
$761$	43.9381			1.59276			0.796378	+	0.604799i	$0.206747\pi$
$762$	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
$766$	25.5172	+	44.1971i	0.921973	+	1.59690i
$767$	−3.86381	−	18.8750i	−0.139514	−	0.681537i
$768$	4.32455	−	7.49035i	0.156049	−	0.270285i
$769$	12.6771	−	21.9573i	0.457147	−	0.791802i	−0.541662	−	0.840597i	$-0.682205\pi$
$769$	12.6771	−	21.9573i	0.457147	−	0.791802i	0.998809	+	0.0487946i	$0.0155380\pi$
$770$		0			0
$771$	3.25024	+	5.62957i	0.117054	+	0.202744i
$772$	13.3568	−	23.1347i	0.480723	−	0.832637i
$773$	−11.5542	+	20.0125i	−0.415576	+	0.719798i	−0.995489	−	0.0948801i	$-0.969753\pi$
$773$	−11.5542	+	20.0125i	−0.415576	+	0.719798i	0.579913	+	0.814678i	$0.303087\pi$
$774$	−0.0610493	+	0.105741i	−0.00219437	+	0.00380076i
$775$	−7.42200	+	12.8553i	−0.266606	+	0.461775i
$776$	1.22705	+	2.12532i	0.0440487	+	0.0762946i
$777$		0			0
$778$	11.4474	−	19.8275i	0.410410	−	0.710851i
$779$	−8.37091	+	14.4988i	−0.299919	+	0.519475i
$780$	−3.52158	−	1.17360i	−0.126093	−	0.0420215i
$781$	−21.9015	−	37.9346i	−0.783699	−	1.35741i
$782$	−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
$786$	−1.51648			−0.0540911
$787$	−12.3346	+	21.3642i	−0.439682	+	0.761551i	−0.997665	−	0.0683012i	$-0.978242\pi$
$787$	−12.3346	+	21.3642i	−0.439682	+	0.761551i	0.557983	+	0.829852i	$0.311575\pi$
$788$	−16.0943	−	27.8761i	−0.573334	−	0.993044i
$789$	−7.36775			−0.262299
$790$	1.08707	−	1.88285i	0.0386761	−	0.0669889i
$791$		0			0
$792$	8.69727			0.309044
$793$	31.1449	−	27.6215i	1.10599	−	0.980870i
$794$	1.57938	+	2.73556i	0.0560500	+	0.0970814i
$795$	0.0894893			0.00317386
$796$	−11.5139	−	19.9427i	−0.408100	−	0.706849i
$797$	5.65686	+	9.79797i	0.200376	+	0.347062i	0.948650	−	0.316329i	$-0.102450\pi$
$797$	5.65686	+	9.79797i	0.200376	+	0.347062i	−0.748273	+	0.663390i	$0.769117\pi$
$798$		0			0
$799$	7.02597	+	12.1693i	0.248561	+	0.430520i
$800$	−20.8365			−0.736680
$801$	−9.23451	−	15.9946i	−0.326285	−	0.565143i
$802$	−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
$807$	−4.05355	+	7.02096i	−0.142692	+	0.247149i
$808$	−1.81180			−0.0637389
$809$	16.3708			0.575566			0.287783	−	0.957696i	$-0.407082\pi$
$809$	16.3708			0.575566			0.287783	+	0.957696i	$0.407082\pi$
$810$	−20.7211			−0.728067
$811$	29.0412			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$811$	29.0412			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$812$		0			0
$813$	−6.88373	−	11.9230i	−0.241423	−	0.418157i
$814$	−29.5146	+	51.1209i	−1.03449	+	1.79179i
$815$	−2.83735	+	4.91443i	−0.0993880	+	0.172145i
$816$	2.37122			0.0830093
$817$	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	$0.756196\pi$
$822$	−10.4505			−0.364504
$823$	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	$-0.00274449\pi$
$824$	−5.92623	+	10.2645i	−0.206450	+	0.357582i
$825$	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	$0.630421\pi$
$828$	20.3843			0.708402
$829$	23.3829			0.812121			0.406061	−	0.913846i	$-0.366902\pi$
$829$	23.3829			0.812121			0.406061	+	0.913846i	$0.366902\pi$
$830$	−44.9665			−1.56081
$831$	3.94287	−	6.82925i	0.136777	−	0.236904i
$832$	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
$837$	6.53591	+	11.3205i	0.225914	+	0.391295i
$838$	−45.0045			−1.55466
$839$	0.367168	+	0.635954i	0.0126761	+	0.0219556i	0.872294	−	0.488982i	$-0.162632\pi$
$839$	0.367168	+	0.635954i	0.0126761	+	0.0219556i	−0.859618	+	0.510938i	$0.829298\pi$
$840$		0			0
$841$	14.4860	+	25.0904i	0.499516	+	0.865187i
$842$	24.8506	+	43.0426i	0.856409	+	1.48334i
$843$	6.09475			0.209914
$844$	3.77314	+	6.53528i	0.129877	+	0.224954i
$845$	15.3221	+	11.4884i	0.527096	+	0.395211i
$846$	−62.7042			−2.15582
$847$		0			0
$848$	−0.326223	+	0.565035i	−0.0112026	+	0.0194034i
$849$	−4.89669			−0.168054
$850$	−3.24282	−	5.61674i	−0.111228	−	0.192652i
$851$	15.6420	−	27.0927i	0.536201	−	0.928727i
$852$	6.96750			0.238702
$853$	−54.3567			−1.86114			−0.930569	−	0.366118i	$-0.880687\pi$
$853$	−54.3567			−1.86114			−0.930569	+	0.366118i	$0.880687\pi$
$854$		0			0
$855$	−6.72567	+	11.6492i	−0.230013	+	0.398395i
$856$	−3.05129	−	5.28500i	−0.104291	−	0.180637i
$857$	−10.5106	−	18.2048i	−0.359034	−	0.621864i	0.628766	−	0.777595i	$-0.283560\pi$
$857$	−10.5106	−	18.2048i	−0.359034	−	0.621864i	−0.987800	+	0.155730i	$0.950227\pi$
$858$	−12.2700	−	4.08909i	−0.418891	−	0.139599i
$859$	−25.6814	+	44.4816i	−0.876240	+	1.51769i	−0.0208035	+	0.999784i	$0.506622\pi$
$859$	−25.6814	+	44.4816i	−0.876240	+	1.51769i	−0.855436	+	0.517908i	$0.826711\pi$
$860$	−0.0273336	+	0.0473431i	−0.000932066	+	0.00161439i
$861$		0			0
$862$	−12.6884	−	21.9769i	−0.432167	−	0.748535i
$863$	−3.55660	+	6.16021i	−0.121068	+	0.209696i	−0.920189	−	0.391474i	$-0.871965\pi$
$863$	−3.55660	+	6.16021i	−0.121068	+	0.209696i	0.799121	+	0.601170i	$0.205299\pi$
$864$	−9.17443	+	15.8906i	−0.312121	+	0.540609i
$865$	−12.2368	+	21.1947i	−0.416062	+	0.720641i
$866$	−19.4577	+	33.7018i	−0.661201	+	1.14523i
$867$	−3.33193	−	5.77107i	−0.113158	−	0.195996i
$868$		0			0
$869$	1.70143	−	2.94696i	0.0577171	−	0.0999689i
$870$	−0.100764	+	0.174528i	−0.00341622	+	0.00591707i
$871$	−11.1555	+	9.89349i	−0.377989	+	0.335228i
$872$	4.23133	+	7.32888i	0.143291	+	0.248187i
$873$	−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
$877$	0.512476			0.0173051			0.00865255	−	0.999963i	$-0.497246\pi$
$877$	0.512476			0.0173051			0.00865255	+	0.999963i	$0.497246\pi$
$878$	9.30937	−	16.1243i	0.314176	−	0.544169i
$879$	2.82874	+	4.89953i	0.0954112	+	0.165257i
$880$	29.7835			1.00400
$881$	−18.5464	+	32.1232i	−0.624843	+	1.08226i	0.363729	+	0.931505i	$0.381503\pi$
$881$	−18.5464	+	32.1232i	−0.624843	+	1.08226i	−0.988571	+	0.150754i	$0.951830\pi$
$882$		0			0
$883$	−15.5667			−0.523860			−0.261930	−	0.965087i	$-0.584359\pi$
$883$	−15.5667			−0.523860			−0.261930	+	0.965087i	$0.584359\pi$
$884$	6.71059	+	2.23636i	0.225701	+	0.0752169i
$885$	1.68631	+	2.92078i	0.0566847	+	0.0981809i
$886$	−40.3290			−1.35488
$887$	13.7900	+	23.8849i	0.463022	+	0.801977i	0.999110	−	0.0421849i	$-0.0134319\pi$
$887$	13.7900	+	23.8849i	0.463022	+	0.801977i	−0.536088	+	0.844162i	$0.680099\pi$
$888$	1.06158	+	1.83871i	0.0356243	+	0.0617030i
$889$		0			0
$890$	−9.20404	−	15.9419i	−0.308520	−	0.534372i
$891$	−32.4319			−1.08651
$892$	−17.4145	−	30.1627i	−0.583079	−	1.00992i
$893$	−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
$898$	−17.2895	+	29.9463i	−0.576959	+	0.999323i
$899$	−0.878932			−0.0293140
$900$	13.0006			0.433355
$901$	−0.170527			−0.00568109
$902$	−43.2337			−1.43952
$903$		0			0
$904$	−3.29366	−	5.70479i	−0.109546	−	0.189738i
$905$	2.04149	−	3.53597i	0.0678615	−	0.117539i
$906$	0.864923	−	1.49809i	0.0287352	−	0.0497707i
$907$	−45.0471			−1.49576			−0.747882	−	0.663831i	$-0.768929\pi$
$907$	−45.0471			−1.49576			−0.747882	+	0.663831i	$0.768929\pi$
$908$	−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
$913$	−70.3796			−2.32923
$914$	−17.1689	+	29.7375i	−0.567898	+	0.983627i
$915$	−3.64360	+	6.31090i	−0.120454	+	0.208632i
$916$	11.7917	+	20.4238i	0.389608	+	0.674820i
$917$		0			0
$918$	−5.71135			−0.188503
$919$	17.3724			0.573064			0.286532	−	0.958071i	$-0.407497\pi$
$919$	17.3724			0.573064			0.286532	+	0.958071i	$0.407497\pi$
$920$	−4.59412			−0.151464
$921$	−2.85305			−0.0940111
$922$	28.3686	−	49.1359i	0.934271	−	1.61820i
$923$	−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
$928$	−0.616877	−	1.06846i	−0.0202500	−	0.0350740i
$929$	−10.7600			−0.353025			−0.176512	−	0.984298i	$-0.556482\pi$
$929$	−10.7600			−0.353025			−0.176512	+	0.984298i	$0.556482\pi$
$930$	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
$934$	−11.1079			−0.363463
$935$	3.89219	+	6.74148i	0.127288	+	0.220470i
$936$	5.33982	−	4.73573i	0.174537	−	0.154792i
$937$	10.9816			0.358755			0.179377	−	0.983780i	$-0.442592\pi$
$937$	10.9816			0.358755			0.179377	+	0.983780i	$0.442592\pi$
$938$		0			0
$939$	−2.01749	+	3.49439i	−0.0658383	+	0.114035i
$940$	−28.0745			−0.915690
$941$	4.08897	+	7.08231i	0.133297	+	0.230877i	0.924946	−	0.380100i	$-0.124110\pi$
$941$	4.08897	+	7.08231i	0.133297	+	0.230877i	−0.791649	+	0.610976i	$0.790777\pi$
$942$	−9.02681	+	15.6349i	−0.294109	+	0.509412i
$943$	22.9127			0.746141
$944$	−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	$0.809553\pi$
$948$	0.270636	+	0.468756i	0.00878986	+	0.0152245i
$949$	−52.1354	−	17.3746i	−1.69239	−	0.564003i
$950$	8.74153	−	15.1408i	0.283613	−	0.491231i
$951$	−7.14892	+	12.3823i	−0.231820	+	0.401524i
$952$		0			0
$953$	−10.5714	−	18.3102i	−0.342442	−	0.593126i	0.642444	−	0.766333i	$-0.277921\pi$
$953$	−10.5714	−	18.3102i	−0.342442	−	0.593126i	−0.984886	+	0.173206i	$0.944587\pi$
$954$	0.380474	−	0.659000i	0.0123183	−	0.0213359i
$955$	14.9086	−	25.8225i	0.482432	−	0.835596i
$956$	−16.0124	+	27.7344i	−0.517879	+	0.896993i
$957$	−0.157712	+	0.273165i	−0.00509809	+	0.00883016i
$958$	−13.8070	−	23.9145i	−0.446085	−	0.772641i
$959$		0			0
$960$	−1.52342	+	2.63864i	−0.0491681	+	0.0851616i
$961$	1.74271	−	3.01846i	0.0562164	−	0.0973697i
$962$	9.71476	+	47.4573i	0.313216	+	1.53009i
$963$	12.2270	+	21.1779i	0.394011	+	0.682447i
$964$	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	$0.672480\pi$
$968$	5.83635			0.187587
$969$	−0.835323	+	1.44682i	−0.0268344	+	0.0464786i
$970$	−4.90079	−	8.48841i	−0.157355	−	0.272546i
$971$	52.0835			1.67144			0.835719	−	0.549157i	$-0.185051\pi$
$971$	52.0835			1.67144			0.835719	+	0.549157i	$0.185051\pi$
$972$	8.67673	−	15.0285i	0.278306	−	0.482041i
$973$		0			0
$974$	34.2241			1.09661
$975$	4.14734	+	1.38214i	0.132821	+	0.0442638i
$976$	−26.5647	−	46.0114i	−0.850315	−	1.47279i
$977$	19.2580			0.616117			0.308058	−	0.951367i	$-0.400321\pi$
$977$	19.2580			0.616117			0.308058	+	0.951367i	$0.400321\pi$
$978$	−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
$982$	69.1736			2.20742
$983$	−8.03657	−	13.9197i	−0.256327	−	0.443971i	0.708928	−	0.705280i	$-0.249179\pi$
$983$	−8.03657	−	13.9197i	−0.256327	−	0.443971i	−0.965255	+	0.261310i	$0.915846\pi$
$984$	−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
$989$	0.0504729	−	0.0874216i	0.00160494	−	0.00277985i
$990$	−34.7364			−1.10400
$991$	21.4265			0.680635			0.340317	−	0.940311i	$-0.389466\pi$
$991$	21.4265			0.680635			0.340317	+	0.940311i	$0.389466\pi$
$992$	−38.6221			−1.22625
$993$	−8.16876			−0.259228
$994$		0			0
$995$	−10.3984	−	18.0106i	−0.329652	−	0.570974i
$996$	5.59743	−	9.69504i	0.177362	−	0.307199i
$997$	−8.47687	+	14.6824i	−0.268465	+	0.464996i	−0.968466	−	0.249147i	$-0.919850\pi$
$997$	−8.47687	+	14.6824i	−0.268465	+	0.464996i	0.700000	+	0.714142i	$0.253183\pi$
$998$	−45.1763			−1.43003
$999$	−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.g.l.373.5		12
7.2	even	3		637.2.f.j.295.5		12
7.3	odd	6		91.2.h.b.74.2	yes	12
7.4	even	3		637.2.h.l.165.2		12
7.5	odd	6		637.2.f.k.295.5		12
7.6	odd	2		91.2.g.b.9.5	✓	12
13.3	even	3		637.2.h.l.471.2		12
21.17	even	6		819.2.s.d.802.5		12
21.20	even	2		819.2.n.d.100.2		12
91.3	odd	6		91.2.g.b.81.5	yes	12
91.9	even	3		8281.2.a.ca.1.2		6
91.16	even	3		637.2.f.j.393.5		12
91.17	odd	6		1183.2.e.g.508.2		12
91.30	even	6		8281.2.a.cf.1.5		6
91.48	odd	6		1183.2.e.h.170.5		12
91.55	odd	6		91.2.h.b.16.2	yes	12
91.61	odd	6		8281.2.a.bz.1.2		6
91.68	odd	6		637.2.f.k.393.5		12
91.69	odd	6		1183.2.e.g.170.2		12
91.81	even	3	inner	637.2.g.l.263.5		12
91.82	odd	6		8281.2.a.ce.1.5		6
91.87	odd	6		1183.2.e.h.508.5		12
273.146	even	6		819.2.s.d.289.5		12
273.185	even	6		819.2.n.d.172.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.5	✓	12	7.6	odd	2
91.2.g.b.81.5	yes	12	91.3	odd	6
91.2.h.b.16.2	yes	12	91.55	odd	6
91.2.h.b.74.2	yes	12	7.3	odd	6
637.2.f.j.295.5		12	7.2	even	3
637.2.f.j.393.5		12	91.16	even	3
637.2.f.k.295.5		12	7.5	odd	6
637.2.f.k.393.5		12	91.68	odd	6
637.2.g.l.263.5		12	91.81	even	3	inner
637.2.g.l.373.5		12	1.1	even	1	trivial
637.2.h.l.165.2		12	7.4	even	3
637.2.h.l.471.2		12	13.3	even	3
819.2.n.d.100.2		12	21.20	even	2
819.2.n.d.172.2		12	273.185	even	6
819.2.s.d.289.5		12	273.146	even	6
819.2.s.d.802.5		12	21.17	even	6
1183.2.e.g.170.2		12	91.69	odd	6
1183.2.e.g.508.2		12	91.17	odd	6
1183.2.e.h.170.5		12	91.48	odd	6
1183.2.e.h.508.5		12	91.87	odd	6
8281.2.a.bz.1.2		6	91.61	odd	6
8281.2.a.ca.1.2		6	91.9	even	3
8281.2.a.ce.1.5		6	91.82	odd	6
8281.2.a.cf.1.5		6	91.30	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.952780 + 1.65026i) q^{2} -0.428448 q^{3} +(-0.815580 + 1.41263i) q^{4} +(-0.736565 + 1.27577i) q^{5} +(-0.408216 - 0.707051i) q^{6} +0.702849 q^{8} -2.81643 q^{9} -2.80714 q^{10} -4.39361 q^{11} +(0.349433 - 0.605236i) 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} +(-2.68344 - 4.64786i) q^{18} -3.24209 q^{19} +(-1.20145 - 2.08098i) q^{20} +(-4.18615 - 7.25062i) q^{22} +(2.21855 + 3.84264i) q^{23} -0.301134 q^{24} +(1.41494 + 2.45075i) q^{25} +(-6.51816 - 2.17223i) q^{26} +2.49204 q^{27} +(-0.0837807 + 0.145112i) q^{29} +1.20271 q^{30} +(2.62272 + 4.54268i) q^{31} +(-3.68150 + 6.37655i) q^{32} +1.88243 q^{33} -2.29184 q^{34} +(2.29702 - 3.97856i) q^{36} +(-3.52527 - 6.10595i) q^{37} +(-3.08900 - 5.35031i) q^{38} +(1.15575 - 1.02500i) q^{39} +(-0.517694 + 0.896672i) q^{40} +(2.58195 - 4.47206i) q^{41} +(-0.0113752 - 0.0197024i) q^{43} +(3.58334 - 6.20653i) q^{44} +(2.07449 - 3.59311i) q^{45} +(-4.22758 + 7.32239i) q^{46} +(5.84178 - 10.1183i) q^{47} +(-0.985780 - 1.70742i) q^{48} +(-2.69626 + 4.67006i) q^{50} +(0.257649 - 0.446262i) q^{51} +(-1.17946 - 5.76175i) q^{52} +(0.0708929 + 0.122790i) q^{53} +(2.37436 + 4.11252i) q^{54} +(3.23618 - 5.60523i) q^{55} +1.38907 q^{57} -0.319298 q^{58} +(-2.67177 + 4.62764i) q^{59} +(0.514760 + 0.891591i) q^{60} -11.5457 q^{61} +(-4.99774 + 8.65635i) q^{62} -4.82736 q^{64} +(-1.06519 - 5.20354i) q^{65} +(1.79355 + 3.10651i) q^{66} +4.13546 q^{67} +(-0.980907 - 1.69898i) q^{68} +(-0.950533 - 1.64637i) q^{69} +(4.98486 + 8.63403i) q^{71} -1.97953 q^{72} +(7.62080 + 13.1996i) 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} +(-0.387251 + 0.670738i) q^{79} -6.77881 q^{80} +7.38159 q^{81} +9.84011 q^{82} +16.0186 q^{83} +(-0.885875 - 1.53438i) q^{85} +(0.0216761 - 0.0375441i) q^{86} +(0.0358956 - 0.0621731i) q^{87} -3.08805 q^{88} +(3.27880 + 5.67904i) q^{89} +7.90611 q^{90} -7.23762 q^{92} +(-1.12370 - 1.94630i) q^{93} +22.2637 q^{94} +(2.38801 - 4.13616i) q^{95} +(1.57733 - 2.73202i) q^{96} +(1.74583 + 3.02387i) q^{97} +12.3743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 2 * q^3 - 4 * q^4 - q^5 + 9 * q^6 - 6 * q^8 - 6 * q^9 + 8 * q^10 - 8 * q^11 - 5 * q^12 + 2 * q^13 - 2 * q^15 + 8 * q^16 - 5 * q^17 + 3 * q^18 - 2 * q^19 + q^20 - 5 * q^22 - q^23 - 22 * q^24 + 7 * q^25 - 5 * q^26 + 8 * q^27 + 3 * q^29 + 10 * q^30 - 16 * q^31 + 8 * q^32 + 32 * q^33 - 32 * q^34 - 21 * q^36 - 13 * q^37 + 17 * q^38 - 23 * q^39 + 5 * q^40 + 8 * q^41 - 11 * q^43 + 21 * q^44 + 7 * q^45 + 16 * q^46 + q^47 - 21 * q^48 + 6 * q^50 - 20 * q^51 + 25 * q^52 - 2 * q^53 + 18 * q^54 - 9 * q^55 + 42 * q^57 + 16 * q^58 - 13 * q^59 + 20 * q^60 - 10 * q^61 - 5 * q^62 - 30 * q^64 + 19 * q^65 - 18 * q^66 + 22 * q^67 - 29 * q^68 - 23 * q^69 + 6 * q^71 - 50 * q^72 + 30 * q^73 - 3 * q^74 + 3 * q^75 + 9 * q^76 + 16 * q^78 + 7 * q^79 - 14 * q^80 + 12 * q^81 + 2 * q^82 + 54 * q^83 - q^85 - 7 * q^86 - 16 * q^87 - 4 * q^89 + 16 * q^90 + 54 * q^92 - 7 * q^93 + 90 * q^94 - 6 * q^95 - 19 * q^96 + 35 * q^97 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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