LMFDB - Embedded newform 2100.2.bo.g.1349.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1349,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2100.1349");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.bo (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 16 x^{16} + 87 x^{14} + 91 x^{12} - 1104 x^{10} + 819 x^{8} + 7047 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 16x^16 + 87x^14 + 91x^12 - 1104x^10 + 819x^8 + 7047x^6 - 11664x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1349.5
Root			$1.64368 + 0.546177i$ of defining polynomial
Character	$\chi$	$=$	2100.1349
Dual form			2100.2.bo.g.1949.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.348838 + 1.69656i) q^{3} +(-2.41433 + 1.08214i) q^{7} +(-2.75662 - 1.18365i) q^{9} +O(q^{10})$	\(q+(-0.348838 + 1.69656i) q^{3} +(-2.41433 + 1.08214i) q^{7} +(-2.75662 - 1.18365i) q^{9} +(1.17086 - 0.675999i) q^{11} +4.94296 q^{13} +(4.97280 - 2.87105i) q^{17} +(-2.84694 - 1.64368i) q^{19} +(-0.993697 - 4.47354i) q^{21} +(2.50270 - 4.33480i) q^{23} +(2.96974 - 4.26388i) q^{27} -5.68630i q^{29} +(-2.45160 + 1.41543i) q^{31} +(0.738430 + 2.22225i) q^{33} +(3.33498 + 1.92545i) q^{37} +(-1.72429 + 8.38603i) q^{39} -3.73802 q^{41} +4.06339i q^{43} +(4.92419 + 2.84298i) q^{47} +(4.65797 - 5.22526i) q^{49} +(3.13620 + 9.43818i) q^{51} +(0.730773 + 1.26574i) q^{53} +(3.78172 - 4.25662i) q^{57} +(4.34239 + 7.52123i) q^{59} +(1.65306 + 0.954394i) q^{61} +(7.93626 - 0.125326i) q^{63} +(-4.36371 + 2.51939i) q^{67} +(6.48121 + 5.75812i) q^{69} -3.38259i q^{71} +(8.16364 + 14.1398i) q^{73} +(-2.09533 + 2.89912i) q^{77} +(2.41693 - 4.18625i) q^{79} +(6.19796 + 6.52574i) q^{81} -16.6525i q^{83} +(9.64714 + 1.98359i) q^{87} +(8.08150 - 13.9976i) q^{89} +(-11.9339 + 5.34895i) q^{91} +(-1.54615 - 4.65303i) q^{93} +12.0577 q^{97} +(-4.02778 + 0.477584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{9}+O(q^{10}) $ 20 * q - 6 * q^9	$ 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) $ 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−0.348838	+	1.69656i	−0.201402	+	0.979509i
$3$	−0.348838	+	1.69656i	−0.201402	+	0.979509i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.41433	+	1.08214i	−0.912531	+	0.409009i
$7$	−2.41433	+	1.08214i	−0.912531	+	0.409009i
$8$		0			0
$9$	−2.75662	−	1.18365i	−0.918875	−	0.394549i
$10$		0			0
$11$	1.17086	−	0.675999i	0.353029	−	0.203821i	−0.312990	−	0.949757i	$-0.601331\pi$
$11$	1.17086	−	0.675999i	0.353029	−	0.203821i	0.666018	+	0.745935i	$0.267997\pi$
$12$		0			0
$13$	4.94296			1.37093			0.685466	−	0.728105i	$-0.259599\pi$
$13$	4.94296			1.37093			0.685466	+	0.728105i	$0.259599\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.97280	−	2.87105i	1.20608	−	0.696332i	0.244181	−	0.969730i	$-0.421481\pi$
$17$	4.97280	−	2.87105i	1.20608	−	0.696332i	0.961901	+	0.273398i	$0.0881477\pi$
$18$		0			0
$19$	−2.84694	−	1.64368i	−0.653133	−	0.377087i	0.136523	−	0.990637i	$-0.456407\pi$
$19$	−2.84694	−	1.64368i	−0.653133	−	0.377087i	−0.789656	+	0.613550i	$0.789741\pi$
$20$		0			0
$21$	−0.993697	−	4.47354i	−0.216842	−	0.976207i
$22$		0			0
$23$	2.50270	−	4.33480i	0.521849	−	0.903868i	−0.477828	−	0.878453i	$-0.658576\pi$
$23$	2.50270	−	4.33480i	0.521849	−	0.903868i	0.999677	−	0.0254150i	$-0.00809072\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.96974	−	4.26388i	0.571527	−	0.820583i
$28$		0			0
$29$		−	5.68630i		−	1.05592i	−0.849270	−	0.527959i	$-0.822957\pi$
$29$		−	5.68630i		−	1.05592i	0.849270	−	0.527959i	$-0.177043\pi$
$30$		0			0
$31$	−2.45160	+	1.41543i	−0.440320	+	0.254219i	−0.703733	−	0.710464i	$-0.748485\pi$
$31$	−2.45160	+	1.41543i	−0.440320	+	0.254219i	0.263414	+	0.964683i	$0.415152\pi$
$32$		0			0
$33$	0.738430	+	2.22225i	0.128544	+	0.386845i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.33498	+	1.92545i	0.548267	+	0.316542i	0.748423	−	0.663222i	$-0.230811\pi$
$37$	3.33498	+	1.92545i	0.548267	+	0.316542i	−0.200156	+	0.979764i	$0.564145\pi$
$38$		0			0
$39$	−1.72429	+	8.38603i	−0.276108	+	1.34284i
$40$		0			0
$41$	−3.73802			−0.583781			−0.291890	−	0.956452i	$-0.594284\pi$
$41$	−3.73802			−0.583781			−0.291890	+	0.956452i	$0.594284\pi$
$42$		0			0
$43$			4.06339i			0.619661i	0.950792	+	0.309830i	$0.100272\pi$
$43$			4.06339i			0.619661i	−0.950792	+	0.309830i	$0.899728\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.92419	+	2.84298i	0.718266	+	0.414691i	0.814114	−	0.580705i	$-0.197223\pi$
$47$	4.92419	+	2.84298i	0.718266	+	0.414691i	−0.0958478	+	0.995396i	$0.530556\pi$
$48$		0			0
$49$	4.65797	−	5.22526i	0.665424	−	0.746466i
$50$		0			0
$51$	3.13620	+	9.43818i	0.439156	+	1.32161i
$52$		0			0
$53$	0.730773	+	1.26574i	0.100379	+	0.173862i	0.911841	−	0.410544i	$-0.134661\pi$
$53$	0.730773	+	1.26574i	0.100379	+	0.173862i	−0.811462	+	0.584406i	$0.801328\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.78172	−	4.25662i	0.500902	−	0.563804i
$58$		0			0
$59$	4.34239	+	7.52123i	0.565330	+	0.979181i	0.997019	+	0.0771582i	$0.0245846\pi$
$59$	4.34239	+	7.52123i	0.565330	+	0.979181i	−0.431688	+	0.902023i	$0.642082\pi$
$60$		0			0
$61$	1.65306	+	0.954394i	0.211653	+	0.122198i	0.602079	−	0.798436i	$-0.294339\pi$
$61$	1.65306	+	0.954394i	0.211653	+	0.122198i	−0.390427	+	0.920634i	$0.627672\pi$
$62$		0			0
$63$	7.93626	−	0.125326i	0.999875	−	0.0157896i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.36371	+	2.51939i	−0.533113	+	0.307793i	−0.742283	−	0.670086i	$-0.766257\pi$
$67$	−4.36371	+	2.51939i	−0.533113	+	0.307793i	0.209170	+	0.977879i	$0.432924\pi$
$68$		0			0
$69$	6.48121	+	5.75812i	0.780246	+	0.693196i
$70$		0			0
$71$		−	3.38259i		−	0.401440i	−0.979649	−	0.200720i	$-0.935672\pi$
$71$		−	3.38259i		−	0.401440i	0.979649	−	0.200720i	$-0.0643281\pi$
$72$		0			0
$73$	8.16364	+	14.1398i	0.955481	+	1.65494i	0.733263	+	0.679945i	$0.237996\pi$
$73$	8.16364	+	14.1398i	0.955481	+	1.65494i	0.222218	+	0.974997i	$0.428670\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.09533	+	2.89912i	−0.238785	+	0.330385i
$78$		0			0
$79$	2.41693	−	4.18625i	0.271926	−	0.470990i	−0.697429	−	0.716654i	$-0.745673\pi$
$79$	2.41693	−	4.18625i	0.271926	−	0.470990i	0.969355	+	0.245664i	$0.0790059\pi$
$80$		0			0
$81$	6.19796	+	6.52574i	0.688662	+	0.725083i
$82$		0			0
$83$		−	16.6525i		−	1.82785i	−0.405879	−	0.913927i	$-0.633035\pi$
$83$		−	16.6525i		−	1.82785i	0.405879	−	0.913927i	$-0.366965\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.64714	+	1.98359i	1.03428	+	0.212664i
$88$		0			0
$89$	8.08150	−	13.9976i	0.856637	−	1.48374i	−0.0184813	−	0.999829i	$-0.505883\pi$
$89$	8.08150	−	13.9976i	0.856637	−	1.48374i	0.875118	−	0.483909i	$-0.160784\pi$
$90$		0			0
$91$	−11.9339	+	5.34895i	−1.25102	+	0.560723i
$92$		0			0
$93$	−1.54615	−	4.65303i	−0.160328	−	0.482497i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	12.0577			1.22427			0.612137	−	0.790751i	$-0.290310\pi$
$97$	12.0577			1.22427			0.612137	+	0.790751i	$0.290310\pi$
$98$		0			0
$99$	−4.02778	+	0.477584i	−0.404807	+	0.0479990i
$100$		0			0
$101$	9.01683	+	15.6176i	0.897208	+	1.55401i	0.831048	+	0.556201i	$0.187742\pi$
$101$	9.01683	+	15.6176i	0.897208	+	1.55401i	0.0661605	+	0.997809i	$0.478925\pi$
$102$		0			0
$103$	−0.308083	+	0.533615i	−0.0303563	+	0.0525787i	−0.880804	−	0.473480i	$-0.842998\pi$
$103$	−0.308083	+	0.533615i	−0.0303563	+	0.0525787i	0.850448	+	0.526059i	$0.176331\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.85503	+	15.3374i	−0.856048	+	1.48272i	0.0196209	+	0.999807i	$0.493754\pi$
$107$	−8.85503	+	15.3374i	−0.856048	+	1.48272i	−0.875669	+	0.482912i	$0.839579\pi$
$108$		0			0
$109$	−0.855282	−	1.48139i	−0.0819211	−	0.141892i	0.822154	−	0.569265i	$-0.192772\pi$
$109$	−0.855282	−	1.48139i	−0.0819211	−	0.141892i	−0.904075	+	0.427374i	$0.859439\pi$
$110$		0			0
$111$	−4.43001	+	4.98632i	−0.420478	+	0.473280i
$112$		0			0
$113$	13.1214			1.23436			0.617180	−	0.786822i	$-0.288275\pi$
$113$	13.1214			1.23436			0.617180	+	0.786822i	$0.288275\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−13.6259	−	5.85073i	−1.25971	−	0.540900i
$118$		0			0
$119$	−8.89912	+	12.3129i	−0.815781	+	1.12872i
$120$		0			0
$121$	−4.58605	+	7.94327i	−0.416914	+	0.722116i
$122$		0			0
$123$	1.30396	−	6.34177i	0.117574	−	0.571818i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			15.5324i			1.37828i	0.724629	+	0.689139i	$0.242011\pi$
$127$			15.5324i			1.37828i	−0.724629	+	0.689139i	$0.757989\pi$
$128$		0			0
$129$	−6.89377	−	1.41746i	−0.606963	−	0.124801i
$130$		0			0
$131$	−4.47822	+	7.75651i	−0.391264	+	0.677689i	−0.992617	−	0.121295i	$-0.961295\pi$
$131$	−4.47822	+	7.75651i	−0.391264	+	0.677689i	0.601353	+	0.798984i	$0.294629\pi$
$132$		0			0
$133$	8.65214	+	0.887614i	0.750235	+	0.0769659i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.73923	−	13.4047i	−0.661207	−	1.14524i	−0.980299	−	0.197520i	$-0.936711\pi$
$137$	−7.73923	−	13.4047i	−0.661207	−	1.14524i	0.319092	−	0.947724i	$-0.396622\pi$
$138$		0			0
$139$		−	20.1547i		−	1.70950i	−0.519044	−	0.854748i	$-0.673712\pi$
$139$		−	20.1547i		−	1.70950i	0.519044	−	0.854748i	$-0.326288\pi$
$140$		0			0
$141$	−6.54103	+	7.36243i	−0.550854	+	0.620029i
$142$		0			0
$143$	5.78754	−	3.34144i	0.483978	−	0.279425i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.24009	+	9.72528i	0.597152	+	0.802128i
$148$		0			0
$149$	1.24947	+	0.721384i	0.102361	+	0.0590981i	0.550307	−	0.834963i	$-0.314511\pi$
$149$	1.24947	+	0.721384i	0.102361	+	0.0590981i	−0.447946	+	0.894061i	$0.647844\pi$
$150$		0			0
$151$	−8.12108	−	14.0661i	−0.660884	−	1.14468i	−0.980384	−	0.197098i	$-0.936848\pi$
$151$	−8.12108	−	14.0661i	−0.660884	−	1.14468i	0.319500	−	0.947586i	$-0.396485\pi$
$152$		0			0
$153$	−17.1065	+	2.02836i	−1.38298	+	0.163983i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.11876	−	15.7942i	−0.727756	−	1.26051i	−0.957829	−	0.287338i	$-0.907230\pi$
$157$	−9.11876	−	15.7942i	−0.727756	−	1.26051i	0.230073	−	0.973173i	$-0.426103\pi$
$158$		0			0
$159$	−2.40232	+	0.798263i	−0.190516	+	0.0633064i
$160$		0			0
$161$	−1.35150	+	13.1739i	−0.106513	+	1.03825i
$162$		0			0
$163$	21.0669	+	12.1630i	1.65009	+	0.952679i	0.977033	+	0.213087i	$0.0683517\pi$
$163$	21.0669	+	12.1630i	1.65009	+	0.952679i	0.673055	+	0.739592i	$0.264982\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	12.5007i		−	0.967336i	−0.875252	−	0.483668i	$-0.839304\pi$
$167$		−	12.5007i		−	0.967336i	0.875252	−	0.483668i	$-0.160696\pi$
$168$		0			0
$169$	11.4329			0.879453
$170$		0			0
$171$	5.90241	+	7.90079i	0.451368	+	0.604188i
$172$		0			0
$173$	−12.8534	−	7.42089i	−0.977223	−	0.564200i	−0.0757927	−	0.997124i	$-0.524149\pi$
$173$	−12.8534	−	7.42089i	−0.977223	−	0.564200i	−0.901431	+	0.432923i	$0.857482\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−14.2750	+	4.74342i	−1.07297	+	0.356538i
$178$		0			0
$179$	−9.93533	+	5.73617i	−0.742602	+	0.428741i	−0.823015	−	0.568020i	$-0.807709\pi$
$179$	−9.93533	+	5.73617i	−0.742602	+	0.428741i	0.0804127	+	0.996762i	$0.474376\pi$
$180$		0			0
$181$		−	5.91099i		−	0.439361i	−0.975572	−	0.219680i	$-0.929499\pi$
$181$		−	5.91099i		−	0.439361i	0.975572	−	0.219680i	$-0.0705014\pi$
$182$		0			0
$183$	−2.19584	+	2.47158i	−0.162321	+	0.182705i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	3.88165	−	6.72322i	0.283854	−	0.491650i
$188$		0			0
$189$	−2.55584	+	13.5081i	−0.185910	+	0.982567i
$190$		0			0
$191$	9.15764	+	5.28716i	0.662623	+	0.382566i	0.793276	−	0.608862i	$-0.208374\pi$
$191$	9.15764	+	5.28716i	0.662623	+	0.382566i	−0.130652	+	0.991428i	$0.541707\pi$
$192$		0			0
$193$	10.4483	−	6.03231i	0.752082	−	0.434215i	−0.0743635	−	0.997231i	$-0.523693\pi$
$193$	10.4483	−	6.03231i	0.752082	−	0.434215i	0.826446	+	0.563016i	$0.190359\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.2423			1.22846			0.614231	−	0.789126i	$-0.289466\pi$
$197$	17.2423			1.22846			0.614231	+	0.789126i	$0.289466\pi$
$198$		0			0
$199$	−2.46400	+	1.42259i	−0.174668	+	0.100845i	−0.584785	−	0.811188i	$-0.698821\pi$
$199$	−2.46400	+	1.42259i	−0.174668	+	0.100845i	0.410117	+	0.912033i	$0.365488\pi$
$200$		0			0
$201$	−2.75207	−	8.28216i	−0.194116	−	0.584178i
$202$		0			0
$203$	6.15334	+	13.7286i	0.431880	+	0.963558i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−12.0299	+	8.98710i	−0.836134	+	0.624647i
$208$		0			0
$209$	−4.44451			−0.307433
$210$		0			0
$211$	22.4677			1.54674			0.773372	−	0.633953i	$-0.218569\pi$
$211$	22.4677			1.54674			0.773372	+	0.633953i	$0.218569\pi$
$212$		0			0
$213$	5.73877	+	1.17998i	0.393214	+	0.0808506i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.38727	−	6.07027i	0.297828	−	0.412077i
$218$		0			0
$219$	−26.8368	+	8.91758i	−1.81347	+	0.602594i
$220$		0			0
$221$	24.5804	−	14.1915i	1.65346	−	0.954623i
$222$		0			0
$223$	5.27620			0.353321			0.176660	−	0.984272i	$-0.443471\pi$
$223$	5.27620			0.353321			0.176660	+	0.984272i	$0.443471\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.8090	−	6.24055i	0.717416	−	0.414200i	−0.0963851	−	0.995344i	$-0.530728\pi$
$227$	10.8090	−	6.24055i	0.717416	−	0.414200i	0.813801	+	0.581144i	$0.197395\pi$
$228$		0			0
$229$	14.0882	+	8.13380i	0.930971	+	0.537496i	0.887119	−	0.461542i	$-0.152703\pi$
$229$	14.0882	+	8.13380i	0.930971	+	0.537496i	0.0438526	+	0.999038i	$0.486037\pi$
$230$		0			0
$231$	−4.18759	−	4.56617i	−0.275523	−	0.300432i
$232$		0			0
$233$	−4.41551	+	7.64788i	−0.289269	+	0.501029i	−0.973636	−	0.228109i	$-0.926746\pi$
$233$	−4.41551	+	7.64788i	−0.289269	+	0.501029i	0.684366	+	0.729139i	$0.260079\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.25911	+	5.56079i	0.406573	+	0.361212i
$238$		0			0
$239$			12.3333i			0.797773i	0.917000	+	0.398886i	$0.130603\pi$
$239$			12.3333i			0.797773i	−0.917000	+	0.398886i	$0.869397\pi$
$240$		0			0
$241$	6.88815	−	3.97688i	0.443705	−	0.256173i	−0.261463	−	0.965214i	$-0.584205\pi$
$241$	6.88815	−	3.97688i	0.443705	−	0.256173i	0.705168	+	0.709040i	$0.250872\pi$
$242$		0			0
$243$	−13.2334	+	8.23878i	−0.848922	+	0.528518i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−14.0723	−	8.12466i	−0.895401	−	0.516960i
$248$		0			0
$249$	28.2520	+	5.80903i	1.79040	+	0.368133i
$250$		0			0
$251$	−7.64756			−0.482710			−0.241355	−	0.970437i	$-0.577592\pi$
$251$	−7.64756			−0.482710			−0.241355	+	0.970437i	$0.577592\pi$
$252$		0			0
$253$		−	6.76728i		−	0.425455i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−23.8118	−	13.7478i	−1.48534	−	0.857563i	−0.485482	−	0.874247i	$-0.661356\pi$
$257$	−23.8118	−	13.7478i	−1.48534	−	0.857563i	−0.999861	+	0.0166841i	$0.994689\pi$
$258$		0			0
$259$	−10.1353	−	1.03977i	−0.629779	−	0.0646084i
$260$		0			0
$261$	−6.73057	+	15.6750i	−0.416612	+	0.970257i
$262$		0			0
$263$	9.51115	+	16.4738i	0.586483	+	1.01582i	0.994689	+	0.102928i	$0.0328212\pi$
$263$	9.51115	+	16.4738i	0.586483	+	1.01582i	−0.408206	+	0.912890i	$0.633845\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	20.9286	+	18.5936i	1.28081	+	1.13791i
$268$		0			0
$269$	−4.46010	−	7.72512i	−0.271937	−	0.471009i	0.697421	−	0.716662i	$-0.254331\pi$
$269$	−4.46010	−	7.72512i	−0.271937	−	0.471009i	−0.969358	+	0.245653i	$0.920998\pi$
$270$		0			0
$271$	6.53123	+	3.77081i	0.396744	+	0.229060i	0.685078	−	0.728470i	$-0.259768\pi$
$271$	6.53123	+	3.77081i	0.396744	+	0.229060i	−0.288334	+	0.957530i	$0.593101\pi$
$272$		0			0
$273$	−4.91181	−	22.1125i	−0.297276	−	1.33831i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.53903	−	0.888562i	0.0924716	−	0.0533885i	−0.453051	−	0.891485i	$-0.649664\pi$
$277$	1.53903	−	0.888562i	0.0924716	−	0.0533885i	0.545523	+	0.838096i	$0.316331\pi$
$278$		0			0
$279$	8.43350	−	0.999983i	0.504900	−	0.0598674i
$280$		0			0
$281$		−	25.3819i		−	1.51416i	−0.653324	−	0.757079i	$-0.726626\pi$
$281$		−	25.3819i		−	1.51416i	0.653324	−	0.757079i	$-0.273374\pi$
$282$		0			0
$283$	−8.06987	−	13.9774i	−0.479704	−	0.830872i	0.520025	−	0.854151i	$-0.325923\pi$
$283$	−8.06987	−	13.9774i	−0.479704	−	0.830872i	−0.999729	+	0.0232795i	$0.992589\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.02481	−	4.04504i	0.532718	−	0.238771i
$288$		0			0
$289$	7.98584	−	13.8319i	0.469755	−	0.813640i
$290$		0			0
$291$	−4.20618	+	20.4566i	−0.246571	+	1.19919i
$292$		0			0
$293$			19.5542i			1.14237i	0.820821	+	0.571186i	$0.193516\pi$
$293$			19.5542i			1.14237i	−0.820821	+	0.571186i	$0.806484\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.594790	−	6.99996i	0.0345132	−	0.406179i
$298$		0			0
$299$	12.3707	−	21.4268i	0.715419	−	1.23914i
$300$		0			0
$301$	−4.39713	−	9.81035i	−0.253447	−	0.565459i
$302$		0			0
$303$	−29.6416	+	9.84957i	−1.70287	+	0.565843i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	11.8231			0.674777			0.337389	−	0.941365i	$-0.390456\pi$
$307$	11.8231			0.674777			0.337389	+	0.941365i	$0.390456\pi$
$308$		0			0
$309$	−0.797839	−	0.708826i	−0.0453875	−	0.0403237i
$310$		0			0
$311$	−11.1689	−	19.3451i	−0.633331	−	1.09696i	−0.986866	−	0.161540i	$-0.948354\pi$
$311$	−11.1689	−	19.3451i	−0.633331	−	1.09696i	0.353535	−	0.935421i	$-0.384980\pi$
$312$		0			0
$313$	6.65398	−	11.5250i	0.376105	−	0.651433i	−0.614387	−	0.789005i	$-0.710596\pi$
$313$	6.65398	−	11.5250i	0.376105	−	0.651433i	0.990492	+	0.137572i	$0.0439298\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−16.9392	+	29.3395i	−0.951400	+	1.64787i	−0.209001	+	0.977915i	$0.567021\pi$
$317$	−16.9392	+	29.3395i	−0.951400	+	1.64787i	−0.742399	+	0.669958i	$0.766312\pi$
$318$		0			0
$319$	−3.84393	−	6.65788i	−0.215219	−	0.372770i
$320$		0			0
$321$	−22.9318	−	20.3733i	−1.27993	−	1.13713i
$322$		0			0
$323$	−18.8764			−1.05031
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.81162	−	0.934271i	0.155483	−	0.0516653i
$328$		0			0
$329$	−14.9651	−	1.53525i	−0.825052	−	0.0846413i
$330$		0			0
$331$	0.989824	−	1.71443i	0.0544057	−	0.0942334i	−0.837540	−	0.546376i	$-0.816007\pi$
$331$	0.989824	−	1.71443i	0.0544057	−	0.0942334i	0.891946	+	0.452143i	$0.149340\pi$
$332$		0			0
$333$	−6.91423	−	9.25518i	−0.378897	−	0.507181i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			12.0217i			0.654862i	0.944875	+	0.327431i	$0.106183\pi$
$337$			12.0217i			0.654862i	−0.944875	+	0.327431i	$0.893817\pi$
$338$		0			0
$339$	−4.57724	+	22.2613i	−0.248602	+	1.20907i
$340$		0			0
$341$	−1.91366	+	3.31455i	−0.103630	+	0.179493i
$342$		0			0
$343$	−5.59143	+	17.6560i	−0.301909	+	0.953337i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.33186	+	12.6992i	0.393595	+	0.681726i	0.992921	−	0.118779i	$-0.0378980\pi$
$347$	7.33186	+	12.6992i	0.393595	+	0.681726i	−0.599326	+	0.800505i	$0.704565\pi$
$348$		0			0
$349$		−	25.0573i		−	1.34129i	−0.741780	−	0.670644i	$-0.766018\pi$
$349$		−	25.0573i		−	1.34129i	0.741780	−	0.670644i	$-0.233982\pi$
$350$		0			0
$351$	14.6793	−	21.0762i	0.783525	−	1.12496i
$352$		0			0
$353$	−6.72669	+	3.88365i	−0.358025	+	0.206706i	−0.668214	−	0.743969i	$-0.732941\pi$
$353$	−6.72669	+	3.88365i	−0.358025	+	0.206706i	0.310189	+	0.950675i	$0.399608\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−17.7852	−	19.3931i	−0.941293	−	1.02639i
$358$		0			0
$359$	3.86952	+	2.23407i	0.204225	+	0.117910i	0.598625	−	0.801030i	$-0.295714\pi$
$359$	3.86952	+	2.23407i	0.204225	+	0.117910i	−0.394399	+	0.918939i	$0.629047\pi$
$360$		0			0
$361$	−4.09662	−	7.09555i	−0.215612	−	0.373450i
$362$		0			0
$363$	−11.8764	−	10.5514i	−0.623352	−	0.553806i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.842240	−	1.45880i	−0.0439646	−	0.0761489i	0.843206	−	0.537591i	$-0.180666\pi$
$367$	−0.842240	−	1.45880i	−0.0439646	−	0.0761489i	−0.887170	+	0.461442i	$0.847332\pi$
$368$		0			0
$369$	10.3043	+	4.42450i	0.536421	+	0.230330i
$370$		0			0
$371$	−3.13402	−	2.26511i	−0.162710	−	0.117599i
$372$		0			0
$373$	−11.9914	−	6.92322i	−0.620890	−	0.358471i	0.156325	−	0.987706i	$-0.450035\pi$
$373$	−11.9914	−	6.92322i	−0.620890	−	0.358471i	−0.777215	+	0.629235i	$0.783368\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	28.1072i		−	1.44759i
$378$		0			0
$379$	2.15603			0.110748			0.0553739	−	0.998466i	$-0.482365\pi$
$379$	2.15603			0.110748			0.0553739	+	0.998466i	$0.482365\pi$
$380$		0			0
$381$	−26.3516	−	5.41829i	−1.35004	−	0.277587i
$382$		0			0
$383$	−3.23197	−	1.86598i	−0.165146	−	0.0953471i	0.415149	−	0.909753i	$-0.363729\pi$
$383$	−3.23197	−	1.86598i	−0.165146	−	0.0953471i	−0.580295	+	0.814406i	$0.697063\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.80962	−	11.2012i	0.244487	−	0.569391i
$388$		0			0
$389$	11.9512	−	6.90001i	0.605948	−	0.349844i	−0.165430	−	0.986222i	$-0.552901\pi$
$389$	11.9512	−	6.90001i	0.605948	−	0.349844i	0.771378	+	0.636377i	$0.219568\pi$
$390$		0			0
$391$		−	28.7415i		−	1.45352i
$392$		0			0
$393$	−11.5972	−	10.3033i	−0.585001	−	0.519734i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−8.17565	+	14.1606i	−0.410324	+	0.710702i	−0.994925	−	0.100619i	$-0.967918\pi$
$397$	−8.17565	+	14.1606i	−0.410324	+	0.710702i	0.584601	+	0.811321i	$0.301251\pi$
$398$		0			0
$399$	−4.52408	+	14.3692i	−0.226487	+	0.719361i
$400$		0			0
$401$	−11.9669	−	6.90910i	−0.597599	−	0.345024i	0.170497	−	0.985358i	$-0.445463\pi$
$401$	−11.9669	−	6.90910i	−0.597599	−	0.345024i	−0.768096	+	0.640334i	$0.778796\pi$
$402$		0			0
$403$	−12.1182	+	6.99642i	−0.603648	+	0.348516i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	5.20641			0.258072
$408$		0			0
$409$	8.26987	−	4.77461i	0.408919	−	0.236089i	−0.281406	−	0.959589i	$-0.590801\pi$
$409$	8.26987	−	4.77461i	0.408919	−	0.236089i	0.690325	+	0.723499i	$0.257467\pi$
$410$		0			0
$411$	25.4417	−	8.45398i	1.25494	−	0.417004i
$412$		0			0
$413$	−18.6229	−	13.4597i	−0.916375	−	0.662307i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	34.1936	+	7.03070i	1.67447	+	0.344295i
$418$		0			0
$419$	−9.71886			−0.474797			−0.237399	−	0.971412i	$-0.576295\pi$
$419$	−9.71886			−0.474797			−0.237399	+	0.971412i	$0.576295\pi$
$420$		0			0
$421$	34.8713			1.69953			0.849763	−	0.527165i	$-0.176745\pi$
$421$	34.8713			1.69953			0.849763	+	0.527165i	$0.176745\pi$
$422$		0			0
$423$	−10.2090	−	13.6655i	−0.496381	−	0.664441i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.02381	−	0.515388i	−0.243119	−	0.0249414i
$428$		0			0
$429$	3.65003	+	10.9845i	0.176225	+	0.530338i
$430$		0			0
$431$	−1.57279	+	0.908052i	−0.0757587	+	0.0437393i	−0.537401	−	0.843327i	$-0.680594\pi$
$431$	−1.57279	+	0.908052i	−0.0757587	+	0.0437393i	0.461642	+	0.887066i	$0.347260\pi$
$432$		0			0
$433$	10.6773			0.513117			0.256558	−	0.966529i	$-0.417411\pi$
$433$	10.6773			0.513117			0.256558	+	0.966529i	$0.417411\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−14.2501	+	8.22728i	−0.681673	+	0.393564i
$438$		0			0
$439$	−26.6759	−	15.4013i	−1.27317	−	0.735066i	−0.297588	−	0.954694i	$-0.596182\pi$
$439$	−26.6759	−	15.4013i	−1.27317	−	0.735066i	−0.975584	+	0.219628i	$0.929516\pi$
$440$		0			0
$441$	−19.0251	+	8.89069i	−0.905959	+	0.423366i
$442$		0			0
$443$	8.26640	−	14.3178i	0.392749	−	0.680260i	−0.600062	−	0.799953i	$-0.704858\pi$
$443$	8.26640	−	14.3178i	0.392749	−	0.680260i	0.992811	+	0.119693i	$0.0381909\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−1.65974	+	1.86816i	−0.0785028	+	0.0883610i
$448$		0			0
$449$		−	2.59098i		−	0.122276i	−0.998129	−	0.0611380i	$-0.980527\pi$
$449$		−	2.59098i		−	0.122276i	0.998129	−	0.0611380i	$-0.0194730\pi$
$450$		0			0
$451$	−4.37671	+	2.52690i	−0.206091	+	0.118987i
$452$		0			0
$453$	26.6969	−	8.87110i	1.25433	−	0.416800i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−19.2040	−	11.0874i	−0.898323	−	0.518647i	−0.0216672	−	0.999765i	$-0.506897\pi$
$457$	−19.2040	−	11.0874i	−0.898323	−	0.518647i	−0.876656	+	0.481118i	$0.840231\pi$
$458$		0			0
$459$	2.52615	−	29.7297i	0.117910	−	1.38766i
$460$		0			0
$461$	−30.5304			−1.42194			−0.710971	−	0.703221i	$-0.751744\pi$
$461$	−30.5304			−1.42194			−0.710971	+	0.703221i	$0.751744\pi$
$462$		0			0
$463$			3.54824i			0.164901i	0.996595	+	0.0824504i	$0.0262746\pi$
$463$			3.54824i			0.164901i	−0.996595	+	0.0824504i	$0.973725\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	29.7157	+	17.1564i	1.37508	+	0.793901i	0.991562	−	0.129633i	$-0.0413799\pi$
$467$	29.7157	+	17.1564i	1.37508	+	0.793901i	0.383515	+	0.923534i	$0.374713\pi$
$468$		0			0
$469$	7.80912	−	10.8048i	0.360592	−	0.498918i
$470$		0			0
$471$	29.9767	−	9.96092i	1.38125	−	0.458975i
$472$		0			0
$473$	2.74684	+	4.75767i	0.126300	+	0.218758i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.516282	−	4.35414i	−0.0236389	−	0.199362i
$478$		0			0
$479$	9.78624	+	16.9503i	0.447145	+	0.774477i	0.998199	−	0.0599923i	$-0.0191076\pi$
$479$	9.78624	+	16.9503i	0.447145	+	0.774477i	−0.551054	+	0.834469i	$0.685774\pi$
$480$		0			0
$481$	16.4847	+	9.51743i	0.751637	+	0.433958i
$482$		0			0
$483$	−21.8788	−	6.88844i	−0.995521	−	0.313435i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−21.8468	+	12.6133i	−0.989973	+	0.571561i	−0.905266	−	0.424844i	$-0.860329\pi$
$487$	−21.8468	+	12.6133i	−0.989973	+	0.571561i	−0.0847071	+	0.996406i	$0.526995\pi$
$488$		0			0
$489$	−27.9842	+	31.4984i	−1.26549	+	1.42441i
$490$		0			0
$491$		−	38.6556i		−	1.74450i	−0.489057	−	0.872252i	$-0.662659\pi$
$491$		−	38.6556i		−	1.74450i	0.489057	−	0.872252i	$-0.337341\pi$
$492$		0			0
$493$	−16.3256	−	28.2768i	−0.735269	−	1.27352i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.66042	+	8.16669i	0.164192	+	0.366326i
$498$		0			0
$499$	2.80910	−	4.86551i	0.125753	−	0.217810i	−0.796274	−	0.604936i	$-0.793199\pi$
$499$	2.80910	−	4.86551i	0.125753	−	0.217810i	0.922027	+	0.387126i	$0.126532\pi$
$500$		0			0
$501$	21.2082	+	4.36073i	0.947514	+	0.194823i
$502$		0			0
$503$			25.8655i			1.15329i	0.816996	+	0.576644i	$0.195638\pi$
$503$			25.8655i			1.15329i	−0.816996	+	0.576644i	$0.804362\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−3.98822	+	19.3966i	−0.177123	+	0.861432i
$508$		0			0
$509$	−15.2306	+	26.3801i	−0.675082	+	1.16928i	0.301362	+	0.953510i	$0.402559\pi$
$509$	−15.2306	+	26.3801i	−0.675082	+	1.16928i	−0.976445	+	0.215767i	$0.930775\pi$
$510$		0			0
$511$	−35.0109	−	25.3040i	−1.54879	−	1.11939i
$512$		0			0
$513$	−15.4631	+	7.25769i	−0.682714	+	0.320435i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	7.68740			0.338092
$518$		0			0
$519$	17.0737	−	19.2178i	0.749453	−	0.843568i
$520$		0			0
$521$	−10.6182	−	18.3913i	−0.465192	−	0.805737i	0.534018	−	0.845473i	$-0.320681\pi$
$521$	−10.6182	−	18.3913i	−0.465192	−	0.805737i	−0.999210	+	0.0397366i	$0.987348\pi$
$522$		0			0
$523$	6.19077	−	10.7227i	0.270704	−	0.468872i	−0.698339	−	0.715768i	$-0.746077\pi$
$523$	6.19077	−	10.7227i	0.270704	−	0.468872i	0.969042	+	0.246895i	$0.0794103\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.12754	+	14.0773i	−0.354041	+	0.613217i
$528$		0			0
$529$	−1.02699	−	1.77880i	−0.0446518	−	0.0773392i
$530$		0			0
$531$	−3.06784	−	25.8731i	−0.133133	−	1.12280i
$532$		0			0
$533$	−18.4769			−0.800323
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−6.26593	−	18.8569i	−0.270395	−	0.813734i
$538$		0			0
$539$	1.92158	−	9.26685i	0.0827682	−	0.399151i
$540$		0			0
$541$	−6.93001	+	12.0031i	−0.297944	+	0.516055i	−0.975665	−	0.219264i	$-0.929634\pi$
$541$	−6.93001	+	12.0031i	−0.297944	+	0.516055i	0.677721	+	0.735319i	$0.262968\pi$
$542$		0			0
$543$	10.0283	+	2.06198i	0.430358	+	0.0884879i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	17.7100i		−	0.757226i	−0.925555	−	0.378613i	$-0.876401\pi$
$547$		−	17.7100i		−	0.757226i	0.925555	−	0.378613i	$-0.123599\pi$
$548$		0			0
$549$	−3.42720	−	4.58755i	−0.146269	−	0.195792i
$550$		0			0
$551$	−9.34646	+	16.1885i	−0.398173	+	0.689655i
$552$		0			0
$553$	−1.30518	+	12.7224i	−0.0555020	+	0.541013i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.73857	−	3.01129i	−0.0736656	−	0.127593i	0.826840	−	0.562438i	$-0.190136\pi$
$557$	−1.73857	−	3.01129i	−0.0736656	−	0.127593i	−0.900505	+	0.434845i	$0.856803\pi$
$558$		0			0
$559$			20.0852i			0.849512i
$560$		0			0
$561$	10.0523	+	8.93076i	0.424407	+	0.377057i
$562$		0			0
$563$	10.4425	−	6.02897i	0.440098	−	0.254091i	−0.263541	−	0.964648i	$-0.584890\pi$
$563$	10.4425	−	6.02897i	0.440098	−	0.254091i	0.703639	+	0.710557i	$0.251557\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−22.0256	−	9.04826i	−0.924990	−	0.379991i
$568$		0			0
$569$	11.8065	+	6.81650i	0.494955	+	0.285762i	0.726628	−	0.687031i	$-0.241087\pi$
$569$	11.8065	+	6.81650i	0.494955	+	0.285762i	−0.231673	+	0.972794i	$0.574420\pi$
$570$		0			0
$571$	22.0474	+	38.1873i	0.922657	+	1.59809i	0.795287	+	0.606233i	$0.207320\pi$
$571$	22.0474	+	38.1873i	0.922657	+	1.59809i	0.127369	+	0.991855i	$0.459347\pi$
$572$		0			0
$573$	−12.1645	+	13.6921i	−0.508180	+	0.571996i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.49934	+	6.06103i	0.145679	+	0.252324i	0.929626	−	0.368504i	$-0.120130\pi$
$577$	3.49934	+	6.06103i	0.145679	+	0.252324i	−0.783947	+	0.620828i	$0.786797\pi$
$578$		0			0
$579$	6.58942	+	19.8304i	0.273847	+	0.824123i
$580$		0			0
$581$	18.0203	+	40.2047i	0.747608	+	1.66797i
$582$		0			0
$583$	1.71127	+	0.988003i	0.0708736	+	0.0409189i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	29.9161i		−	1.23477i	−0.786661	−	0.617385i	$-0.788192\pi$
$587$		−	29.9161i		−	1.23477i	0.786661	−	0.617385i	$-0.211808\pi$
$588$		0			0
$589$	9.30607			0.383450
$590$		0			0
$591$	−6.01476	+	29.2525i	−0.247414	+	1.20329i
$592$		0			0
$593$	−20.8583	−	12.0426i	−0.856549	−	0.494529i	0.00630583	−	0.999980i	$-0.497993\pi$
$593$	−20.8583	−	12.0426i	−0.856549	−	0.494529i	−0.862855	+	0.505451i	$0.831326\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.55397	−	4.67657i	−0.0635999	−	0.191399i
$598$		0			0
$599$	5.14773	−	2.97205i	0.210331	−	0.121434i	−0.391134	−	0.920334i	$-0.627917\pi$
$599$	5.14773	−	2.97205i	0.210331	−	0.121434i	0.601465	+	0.798899i	$0.294584\pi$
$600$		0			0
$601$		−	46.9992i		−	1.91714i	−0.284863	−	0.958568i	$-0.591948\pi$
$601$		−	46.9992i		−	1.91714i	0.284863	−	0.958568i	$-0.408052\pi$
$602$		0			0
$603$	15.0112	−	1.77992i	0.611303	−	0.0724839i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−4.97322	+	8.61387i	−0.201857	+	0.349626i	−0.949127	−	0.314894i	$-0.898031\pi$
$607$	−4.97322	+	8.61387i	−0.201857	+	0.349626i	0.747270	+	0.664521i	$0.231364\pi$
$608$		0			0
$609$	−25.4379	+	5.65046i	−1.03079	+	0.228968i
$610$		0			0
$611$	24.3401	+	14.0528i	0.984694	+	0.568513i
$612$		0			0
$613$	−28.1873	+	16.2739i	−1.13847	+	0.657298i	−0.946052	−	0.324014i	$-0.894967\pi$
$613$	−28.1873	+	16.2739i	−1.13847	+	0.657298i	−0.192421	+	0.981312i	$0.561634\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.69843			−0.309927			−0.154964	−	0.987920i	$-0.549526\pi$
$617$	−7.69843			−0.309927			−0.154964	+	0.987920i	$0.549526\pi$
$618$		0			0
$619$	−2.76170	+	1.59447i	−0.111002	+	0.0640872i	−0.554473	−	0.832202i	$-0.687080\pi$
$619$	−2.76170	+	1.59447i	−0.111002	+	0.0640872i	0.443471	+	0.896289i	$0.353747\pi$
$620$		0			0
$621$	−11.0507	−	23.5444i	−0.443448	−	0.944805i
$622$		0			0
$623$	−4.36414	+	42.5400i	−0.174845	+	1.70433i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.55041	−	7.54037i	0.0619175	−	0.301133i
$628$		0			0
$629$	22.1122			0.881673
$630$		0			0
$631$	7.97461			0.317464			0.158732	−	0.987322i	$-0.449259\pi$
$631$	7.97461			0.317464			0.158732	+	0.987322i	$0.449259\pi$
$632$		0			0
$633$	−7.83760	+	38.1179i	−0.311516	+	1.51505i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	23.0242	−	25.8283i	0.912251	−	1.02335i
$638$		0			0
$639$	−4.00380	+	9.32454i	−0.158388	+	0.368873i
$640$		0			0
$641$	−23.7774	+	13.7279i	−0.939152	+	0.542219i	−0.889694	−	0.456557i	$-0.849083\pi$
$641$	−23.7774	+	13.7279i	−0.939152	+	0.542219i	−0.0494573	+	0.998776i	$0.515749\pi$
$642$		0			0
$643$	29.0919			1.14727			0.573637	−	0.819110i	$-0.305532\pi$
$643$	29.0919			1.14727			0.573637	+	0.819110i	$0.305532\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−37.4122	+	21.5999i	−1.47082	+	0.849181i	−0.999463	−	0.0327597i	$-0.989570\pi$
$647$	−37.4122	+	21.5999i	−1.47082	+	0.849181i	−0.471361	+	0.881940i	$0.656237\pi$
$648$		0			0
$649$	10.1687	+	5.87089i	0.399156	+	0.230453i
$650$		0			0
$651$	8.76813	+	9.56081i	0.343650	+	0.374718i
$652$		0			0
$653$	3.62080	−	6.27142i	0.141693	−	0.245420i	−0.786441	−	0.617665i	$-0.788079\pi$
$653$	3.62080	−	6.27142i	0.141693	−	0.245420i	0.928134	+	0.372246i	$0.121412\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.76750	−	48.6411i	−0.225012	−	1.89767i
$658$		0			0
$659$			5.29324i			0.206196i	0.994671	+	0.103098i	$0.0328755\pi$
$659$			5.29324i			0.206196i	−0.994671	+	0.103098i	$0.967125\pi$
$660$		0			0
$661$	43.2638	−	24.9783i	1.68276	−	0.971545i	0.722954	−	0.690896i	$-0.242784\pi$
$661$	43.2638	−	24.9783i	1.68276	−	0.971545i	0.959810	−	0.280649i	$-0.0905497\pi$
$662$		0			0
$663$	15.5021	+	46.6526i	0.602053	+	1.81184i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.6490	−	14.2311i	−0.954411	−	0.551030i
$668$		0			0
$669$	−1.84054	+	8.95139i	−0.0711593	+	0.346081i
$670$		0			0
$671$	2.58068			0.0996259
$672$		0			0
$673$		−	21.8855i		−	0.843625i	−0.906683	−	0.421812i	$-0.861394\pi$
$673$		−	21.8855i		−	0.843625i	0.906683	−	0.421812i	$-0.138606\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	11.9033	+	6.87236i	0.457480	+	0.264126i	0.710984	−	0.703208i	$-0.248250\pi$
$677$	11.9033	+	6.87236i	0.457480	+	0.264126i	−0.253504	+	0.967334i	$0.581583\pi$
$678$		0			0
$679$	−29.1113	+	13.0481i	−1.11719	+	0.500739i
$680$		0			0
$681$	6.81690	+	20.5150i	0.261224	+	0.786135i
$682$		0			0
$683$	−21.4513	−	37.1547i	−0.820811	−	1.42169i	−0.905079	−	0.425243i	$-0.860189\pi$
$683$	−21.4513	−	37.1547i	−0.820811	−	1.42169i	0.0842682	−	0.996443i	$-0.473145\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−18.7139	+	21.0640i	−0.713982	+	0.803642i
$688$		0			0
$689$	3.61218	+	6.25649i	0.137613	+	0.238353i
$690$		0			0
$691$	−20.5494	−	11.8642i	−0.781735	−	0.451335i	0.0553098	−	0.998469i	$-0.482385\pi$
$691$	−20.5494	−	11.8642i	−0.781735	−	0.451335i	−0.837045	+	0.547134i	$0.815719\pi$
$692$		0			0
$693$	9.20757	−	5.51164i	0.349767	−	0.209370i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−18.5884	+	10.7320i	−0.704087	+	0.406505i
$698$		0			0
$699$	−11.4348	−	10.1590i	−0.432503	−	0.384250i
$700$		0			0
$701$			21.2721i			0.803436i	0.915763	+	0.401718i	$0.131587\pi$
$701$			21.2721i			0.803436i	−0.915763	+	0.401718i	$0.868413\pi$
$702$		0			0
$703$	−6.32966	−	10.9633i	−0.238728	−	0.413488i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−38.6700	−	27.9486i	−1.45433	−	1.05112i
$708$		0			0
$709$	−22.8069	+	39.5026i	−0.856529	+	1.48355i	0.0186897	+	0.999825i	$0.494051\pi$
$709$	−22.8069	+	39.5026i	−0.856529	+	1.48355i	−0.875219	+	0.483727i	$0.839283\pi$
$710$		0			0
$711$	−11.6176	+	8.67913i	−0.435695	+	0.325493i
$712$		0			0
$713$			14.1696i			0.530655i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−20.9241	−	4.30231i	−0.781426	−	0.160673i
$718$		0			0
$719$	9.50850	−	16.4692i	0.354607	−	0.614198i	−0.632443	−	0.774607i	$-0.717948\pi$
$719$	9.50850	−	16.4692i	0.354607	−	0.614198i	0.987051	+	0.160409i	$0.0512812\pi$
$720$		0			0
$721$	0.166370	−	1.62171i	0.00619593	−	0.0603956i
$722$		0			0
$723$	4.34416	+	13.0734i	0.161561	+	0.486207i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	34.0540			1.26299			0.631496	−	0.775379i	$-0.282441\pi$
$727$	34.0540			1.26299			0.631496	+	0.775379i	$0.282441\pi$
$728$		0			0
$729$	−9.36126	−	25.3252i	−0.346714	−	0.937971i
$730$		0			0
$731$	11.6662	+	20.2064i	0.431489	+	0.747361i
$732$		0			0
$733$	3.87885	−	6.71837i	0.143269	−	0.248148i	−0.785457	−	0.618916i	$-0.787572\pi$
$733$	3.87885	−	6.71837i	0.143269	−	0.248148i	0.928726	+	0.370768i	$0.120905\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.40621	+	5.89973i	−0.125469	+	0.217319i
$738$		0			0
$739$	−4.19659	−	7.26871i	−0.154374	−	0.267384i	0.778457	−	0.627698i	$-0.216003\pi$
$739$	−4.19659	−	7.26871i	−0.154374	−	0.267384i	−0.932831	+	0.360314i	$0.882669\pi$
$740$		0			0
$741$	18.6929	−	21.0403i	0.686702	−	0.772936i
$742$		0			0
$743$	14.7540			0.541273			0.270636	−	0.962682i	$-0.412766\pi$
$743$	14.7540			0.541273			0.270636	+	0.962682i	$0.412766\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−19.7107	+	45.9048i	−0.721178	+	1.67957i
$748$		0			0
$749$	4.78186	−	46.6118i	0.174725	−	1.70316i
$750$		0			0
$751$	−20.6067	+	35.6918i	−0.751948	+	1.30241i	0.194929	+	0.980817i	$0.437552\pi$
$751$	−20.6067	+	35.6918i	−0.751948	+	1.30241i	−0.946877	+	0.321595i	$0.895781\pi$
$752$		0			0
$753$	2.66776	−	12.9745i	0.0972185	−	0.472818i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			11.8681i			0.431354i	0.976465	+	0.215677i	$0.0691958\pi$
$757$			11.8681i			0.431354i	−0.976465	+	0.215677i	$0.930804\pi$
$758$		0			0
$759$	11.4811	+	2.36068i	0.416737	+	0.0856874i
$760$		0			0
$761$	17.7705	−	30.7795i	0.644181	−	1.11575i	−0.340309	−	0.940314i	$-0.610532\pi$
$761$	17.7705	−	30.7795i	0.644181	−	1.11575i	0.984490	−	0.175441i	$-0.0561351\pi$
$762$		0			0
$763$	3.66800	+	2.65104i	0.132790	+	0.0959739i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	21.4643	+	37.1772i	0.775029	+	1.34239i
$768$		0			0
$769$			6.25608i			0.225600i	0.993618	+	0.112800i	$0.0359820\pi$
$769$			6.25608i			0.225600i	−0.993618	+	0.112800i	$0.964018\pi$
$770$		0			0
$771$	31.6304	−	35.6025i	1.13914	−	1.28219i
$772$		0			0
$773$	17.3483	−	10.0161i	0.623977	−	0.360253i	−0.154439	−	0.988002i	$-0.549357\pi$
$773$	17.3483	−	10.0161i	0.623977	−	0.360253i	0.778416	+	0.627749i	$0.216024\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	5.29962	−	16.8325i	0.190123	−	0.603862i
$778$		0			0
$779$	10.6419	+	6.14412i	0.381286	+	0.220136i
$780$		0			0
$781$	−2.28663	−	3.96056i	−0.0818220	−	0.141720i
$782$		0			0
$783$	−24.2457	−	16.8868i	−0.866469	−	0.603486i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	0.738053	+	1.27835i	0.0263088	+	0.0455681i	0.878880	−	0.477043i	$-0.158291\pi$
$787$	0.738053	+	1.27835i	0.0263088	+	0.0455681i	−0.852571	+	0.522611i	$0.824958\pi$
$788$		0			0
$789$	−31.2666	+	10.3895i	−1.11312	+	0.369878i
$790$		0			0
$791$	−31.6794	+	14.1991i	−1.12639	+	0.504863i
$792$		0			0
$793$	8.17101	+	4.71754i	0.290161	+	0.167525i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			22.9470i			0.812823i	0.913690	+	0.406411i	$0.133220\pi$
$797$			22.9470i			0.812823i	−0.913690	+	0.406411i	$0.866780\pi$
$798$		0			0
$799$	32.6493			1.15505
$800$		0			0
$801$	−38.8458	+	29.0204i	−1.37255	+	1.02538i
$802$		0			0
$803$	19.1170	+	11.0372i	0.674625	+	0.389495i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	14.6620	−	4.87201i	0.516126	−	0.171503i
$808$		0			0
$809$	−19.5613	+	11.2937i	−0.687739	+	0.397066i	−0.802764	−	0.596296i	$-0.796638\pi$
$809$	−19.5613	+	11.2937i	−0.687739	+	0.397066i	0.115026	+	0.993363i	$0.463305\pi$
$810$		0			0
$811$			41.9366i			1.47259i	0.676659	+	0.736296i	$0.263427\pi$
$811$			41.9366i			1.47259i	−0.676659	+	0.736296i	$0.736573\pi$
$812$		0			0
$813$	−8.67573	+	9.76522i	−0.304271	+	0.342481i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	6.67892	−	11.5682i	0.233666	−	0.404721i
$818$		0			0
$819$	39.2287	−	0.619483i	1.37076	−	0.0216465i
$820$		0			0
$821$	0.447025	+	0.258090i	0.0156013	+	0.00900741i	0.507780	−	0.861487i	$-0.330466\pi$
$821$	0.447025	+	0.258090i	0.0156013	+	0.00900741i	−0.492179	+	0.870494i	$0.663799\pi$
$822$		0			0
$823$	−17.8125	+	10.2841i	−0.620906	+	0.358480i	−0.777222	−	0.629227i	$-0.783372\pi$
$823$	−17.8125	+	10.2841i	−0.620906	+	0.358480i	0.156316	+	0.987707i	$0.450038\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	24.0587			0.836603			0.418301	−	0.908308i	$-0.362626\pi$
$827$	24.0587			0.836603			0.418301	+	0.908308i	$0.362626\pi$
$828$		0			0
$829$	39.3074	−	22.6941i	1.36520	−	0.788200i	0.374891	−	0.927069i	$-0.377680\pi$
$829$	39.3074	−	22.6941i	1.36520	−	0.788200i	0.990311	+	0.138869i	$0.0443468\pi$
$830$		0			0
$831$	0.970625	+	2.92103i	0.0336706	+	0.101329i
$832$		0			0
$833$	8.16117	−	39.3574i	0.282768	−	1.36365i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.24539	+	14.6568i	−0.0430471	+	0.506612i
$838$		0			0
$839$	−39.8758			−1.37666			−0.688332	−	0.725395i	$-0.741657\pi$
$839$	−39.8758			−1.37666			−0.688332	+	0.725395i	$0.741657\pi$
$840$		0			0
$841$	−3.33396			−0.114964
$842$		0			0
$843$	43.0619	+	8.85416i	1.48313	+	0.304954i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	2.47654	−	24.1404i	0.0850949	−	0.829474i
$848$		0			0
$849$	26.5286	−	8.81516i	0.910459	−	0.302535i
$850$		0			0
$851$	16.6929	−	9.63764i	0.572225	−	0.330374i
$852$		0			0
$853$	16.9504			0.580372			0.290186	−	0.956970i	$-0.406283\pi$
$853$	16.9504			0.580372			0.290186	+	0.956970i	$0.406283\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.546711	+	0.315644i	−0.0186753	+	0.0107822i	−0.509309	−	0.860584i	$-0.670099\pi$
$857$	−0.546711	+	0.315644i	−0.0186753	+	0.0107822i	0.490633	+	0.871366i	$0.336765\pi$
$858$		0			0
$859$	5.59642	+	3.23109i	0.190947	+	0.110243i	0.592426	−	0.805625i	$-0.298170\pi$
$859$	5.59642	+	3.23109i	0.190947	+	0.110243i	−0.401479	+	0.915868i	$0.631504\pi$
$860$		0			0
$861$	3.71446	+	16.7222i	0.126588	+	0.569891i
$862$		0			0
$863$	3.64782	−	6.31821i	0.124173	−	0.215074i	−0.797236	−	0.603667i	$-0.793705\pi$
$863$	3.64782	−	6.31821i	0.124173	−	0.215074i	0.921409	+	0.388593i	$0.127039\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	20.6808	+	18.3735i	0.702358	+	0.623998i
$868$		0			0
$869$		−	6.53538i		−	0.221698i
$870$		0			0
$871$	−21.5697	+	12.4533i	−0.730861	+	0.421963i
$872$		0			0
$873$	−33.2386	−	14.2721i	−1.12496	−	0.483037i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.7109	+	14.8442i	0.868196	+	0.501253i	0.866748	−	0.498746i	$-0.166206\pi$
$877$	25.7109	+	14.8442i	0.868196	+	0.501253i	0.00144772	+	0.999999i	$0.499539\pi$
$878$		0			0
$879$	−33.1749	−	6.82126i	−1.11896	−	0.230075i
$880$		0			0
$881$	−21.6272			−0.728638			−0.364319	−	0.931274i	$-0.618698\pi$
$881$	−21.6272			−0.728638			−0.364319	+	0.931274i	$0.618698\pi$
$882$		0			0
$883$		−	29.9462i		−	1.00777i	−0.863771	−	0.503884i	$-0.831904\pi$
$883$		−	29.9462i		−	1.00777i	0.863771	−	0.503884i	$-0.168096\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.2160	+	5.89821i	0.343020	+	0.198043i	0.661607	−	0.749851i	$-0.269875\pi$
$887$	10.2160	+	5.89821i	0.343020	+	0.198043i	−0.318587	+	0.947894i	$0.603208\pi$
$888$		0			0
$889$	−16.8082	−	37.5003i	−0.563728	−	1.25772i
$890$		0			0
$891$	11.6684	+	3.45095i	0.390905	+	0.115611i
$892$		0			0
$893$	−9.34591	−	16.1876i	−0.312749	−	0.541697i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	32.0364	+	28.4622i	1.06966	+	0.950324i
$898$		0			0
$899$	8.04855	+	13.9405i	0.268434	+	0.464942i
$900$		0			0
$901$	7.26798	+	4.19617i	0.242131	+	0.139795i
$902$		0			0
$903$	18.1777	−	4.03778i	0.604917	−	0.134369i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	24.6739	−	14.2455i	0.819284	−	0.473014i	−0.0308855	−	0.999523i	$-0.509833\pi$
$907$	24.6739	−	14.2455i	0.819284	−	0.473014i	0.850169	+	0.526509i	$0.176499\pi$
$908$		0			0
$909$	−6.37028	−	53.7246i	−0.211289	−	1.78193i
$910$		0			0
$911$		−	14.4884i		−	0.480023i	−0.970770	−	0.240011i	$-0.922849\pi$
$911$		−	14.4884i		−	0.480023i	0.970770	−	0.240011i	$-0.0771511\pi$
$912$		0			0
$913$	−11.2571	−	19.4979i	−0.372555	−	0.645285i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.41831	−	23.5728i	0.0798597	−	0.778442i
$918$		0			0
$919$	−2.83403	+	4.90869i	−0.0934861	+	0.161923i	−0.908976	−	0.416849i	$-0.863134\pi$
$919$	−2.83403	+	4.90869i	−0.0934861	+	0.161923i	0.815490	+	0.578772i	$0.196468\pi$
$920$		0			0
$921$	−4.12433	+	20.0585i	−0.135901	+	0.660950i
$922$		0			0
$923$		−	16.7200i		−	0.550346i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.48088	−	1.10632i	0.0486385	−	0.0363362i
$928$		0			0
$929$	−8.51159	+	14.7425i	−0.279256	+	0.483686i	−0.971200	−	0.238265i	$-0.923421\pi$
$929$	−8.51159	+	14.7425i	−0.279256	+	0.483686i	0.691944	+	0.721951i	$0.256755\pi$
$930$		0			0
$931$	−21.8496	+	7.21979i	−0.716092	+	0.236619i
$932$		0			0
$933$	36.7163	−	12.2004i	1.20204	−	0.399424i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	11.1936			0.365678			0.182839	−	0.983143i	$-0.441471\pi$
$937$	11.1936			0.365678			0.182839	+	0.983143i	$0.441471\pi$
$938$		0			0
$939$	17.2317	+	15.3092i	0.562336	+	0.499598i
$940$		0			0
$941$	11.0101	+	19.0700i	0.358919	+	0.621665i	0.987780	−	0.155852i	$-0.0498122\pi$
$941$	11.0101	+	19.0700i	0.358919	+	0.621665i	−0.628862	+	0.777517i	$0.716479\pi$
$942$		0			0
$943$	−9.35513	+	16.2036i	−0.304645	+	0.527661i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.3035	−	24.7743i	0.464800	−	0.805057i	−0.534393	−	0.845236i	$-0.679460\pi$
$947$	14.3035	−	24.7743i	0.464800	−	0.805057i	0.999192	+	0.0401795i	$0.0127930\pi$
$948$		0			0
$949$	40.3526	+	69.8927i	1.30990	+	2.26881i
$950$		0			0
$951$	−43.8672	−	38.9731i	−1.42249	−	1.26379i
$952$		0			0
$953$	45.2210			1.46485			0.732426	−	0.680846i	$-0.238388\pi$
$953$	45.2210			1.46485			0.732426	+	0.680846i	$0.238388\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	12.6364	−	4.19893i	0.408477	−	0.135732i
$958$		0			0
$959$	33.1908	+	23.9886i	1.07179	+	0.774631i
$960$		0			0
$961$	−11.4931	+	19.9067i	−0.370746	+	0.642150i
$962$		0			0
$963$	42.5640	−	31.7981i	1.37161	−	1.02468i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			54.5961i			1.75569i	0.478943	+	0.877846i	$0.341020\pi$
$967$			54.5961i			1.75569i	−0.478943	+	0.877846i	$0.658980\pi$
$968$		0			0
$969$	6.58479	−	32.0249i	0.211534	−	1.02879i
$970$		0			0
$971$	12.1591	−	21.0603i	0.390206	−	0.675856i	−0.602271	−	0.798292i	$-0.705737\pi$
$971$	12.1591	−	21.0603i	0.390206	−	0.675856i	0.992476	+	0.122436i	$0.0390706\pi$
$972$		0			0
$973$	21.8101	+	48.6600i	0.699198	+	1.55997i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.58898	−	7.94835i	−0.146815	−	0.254290i	0.783234	−	0.621727i	$-0.213569\pi$
$977$	−4.58898	−	7.94835i	−0.146815	−	0.254290i	−0.930048	+	0.367437i	$0.880235\pi$
$978$		0			0
$979$		−	21.8523i		−	0.698403i
$980$		0			0
$981$	0.604246	+	5.09599i	0.0192921	+	0.162703i
$982$		0			0
$983$	−14.3720	+	8.29768i	−0.458396	+	0.264655i	−0.711369	−	0.702818i	$-0.751925\pi$
$983$	−14.3720	+	8.29768i	−0.458396	+	0.264655i	0.252974	+	0.967473i	$0.418591\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	7.82504	−	24.8536i	0.249074	−	0.791099i
$988$		0			0
$989$	17.6140	+	10.1694i	0.560092	+	0.323369i
$990$		0			0
$991$	−9.44914	−	16.3664i	−0.300162	−	0.519895i	0.676011	−	0.736892i	$-0.263707\pi$
$991$	−9.44914	−	16.3664i	−0.300162	−	0.519895i	−0.976172	+	0.216996i	$0.930374\pi$
$992$		0			0
$993$	2.56334	+	2.27735i	0.0813450	+	0.0722696i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.37103	−	12.7670i	−0.233443	−	0.404335i	0.725376	−	0.688353i	$-0.241666\pi$
$997$	−7.37103	−	12.7670i	−0.233443	−	0.404335i	−0.958819	+	0.284018i	$0.908333\pi$
$998$		0			0
$999$	18.1139	−	8.50184i	0.573099	−	0.268986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bo.g.1349.5		20
3.2	odd	2		2100.2.bo.h.1349.9		20
5.2	odd	4		420.2.bh.b.341.5	yes	10
5.3	odd	4		2100.2.bi.j.1601.1		10
5.4	even	2	inner	2100.2.bo.g.1349.6		20
7.3	odd	6		2100.2.bo.h.1949.2		20
15.2	even	4		420.2.bh.a.341.4	yes	10
15.8	even	4		2100.2.bi.k.1601.2		10
15.14	odd	2		2100.2.bo.h.1349.2		20
21.17	even	6	inner	2100.2.bo.g.1949.6		20
35.2	odd	12		2940.2.d.a.881.4		10
35.3	even	12		2100.2.bi.k.101.2		10
35.12	even	12		2940.2.d.b.881.7		10
35.17	even	12		420.2.bh.a.101.4	✓	10
35.24	odd	6		2100.2.bo.h.1949.9		20
105.2	even	12		2940.2.d.b.881.8		10
105.17	odd	12		420.2.bh.b.101.5	yes	10
105.38	odd	12		2100.2.bi.j.101.1		10
105.47	odd	12		2940.2.d.a.881.3		10
105.59	even	6	inner	2100.2.bo.g.1949.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.4	✓	10	35.17	even	12
420.2.bh.a.341.4	yes	10	15.2	even	4
420.2.bh.b.101.5	yes	10	105.17	odd	12
420.2.bh.b.341.5	yes	10	5.2	odd	4
2100.2.bi.j.101.1		10	105.38	odd	12
2100.2.bi.j.1601.1		10	5.3	odd	4
2100.2.bi.k.101.2		10	35.3	even	12
2100.2.bi.k.1601.2		10	15.8	even	4
2100.2.bo.g.1349.5		20	1.1	even	1	trivial
2100.2.bo.g.1349.6		20	5.4	even	2	inner
2100.2.bo.g.1949.5		20	105.59	even	6	inner
2100.2.bo.g.1949.6		20	21.17	even	6	inner
2100.2.bo.h.1349.2		20	15.14	odd	2
2100.2.bo.h.1349.9		20	3.2	odd	2
2100.2.bo.h.1949.2		20	7.3	odd	6
2100.2.bo.h.1949.9		20	35.24	odd	6
2940.2.d.a.881.3		10	105.47	odd	12
2940.2.d.a.881.4		10	35.2	odd	12
2940.2.d.b.881.7		10	35.12	even	12
2940.2.d.b.881.8		10	105.2	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.bo (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.348838 + 1.69656i) q^{3} +(-2.41433 + 1.08214i) q^{7} +(-2.75662 - 1.18365i) q^{9} +O(q^{10})\)	\(q+(-0.348838 + 1.69656i) q^{3} +(-2.41433 + 1.08214i) q^{7} +(-2.75662 - 1.18365i) q^{9} +(1.17086 - 0.675999i) q^{11} +4.94296 q^{13} +(4.97280 - 2.87105i) q^{17} +(-2.84694 - 1.64368i) q^{19} +(-0.993697 - 4.47354i) q^{21} +(2.50270 - 4.33480i) q^{23} +(2.96974 - 4.26388i) q^{27} -5.68630i q^{29} +(-2.45160 + 1.41543i) q^{31} +(0.738430 + 2.22225i) q^{33} +(3.33498 + 1.92545i) q^{37} +(-1.72429 + 8.38603i) q^{39} -3.73802 q^{41} +4.06339i q^{43} +(4.92419 + 2.84298i) q^{47} +(4.65797 - 5.22526i) q^{49} +(3.13620 + 9.43818i) q^{51} +(0.730773 + 1.26574i) q^{53} +(3.78172 - 4.25662i) q^{57} +(4.34239 + 7.52123i) q^{59} +(1.65306 + 0.954394i) q^{61} +(7.93626 - 0.125326i) q^{63} +(-4.36371 + 2.51939i) q^{67} +(6.48121 + 5.75812i) q^{69} -3.38259i q^{71} +(8.16364 + 14.1398i) q^{73} +(-2.09533 + 2.89912i) q^{77} +(2.41693 - 4.18625i) q^{79} +(6.19796 + 6.52574i) q^{81} -16.6525i q^{83} +(9.64714 + 1.98359i) q^{87} +(8.08150 - 13.9976i) q^{89} +(-11.9339 + 5.34895i) q^{91} +(-1.54615 - 4.65303i) q^{93} +12.0577 q^{97} +(-4.02778 + 0.477584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{9}+O(q^{10}) \) 20 * q - 6 * q^9	\( 20 q - 6 q^{9} + 12 q^{11} - 6 q^{19} + 24 q^{21} + 30 q^{31} + 42 q^{39} + 16 q^{41} + 26 q^{49} + 80 q^{51} + 84 q^{61} - 28 q^{69} - 2 q^{79} - 26 q^{81} + 56 q^{89} - 22 q^{91} - 72 q^{99}+O(q^{100}) \) 20 * q - 6 * q^9 + 12 * q^11 - 6 * q^19 + 24 * q^21 + 30 * q^31 + 42 * q^39 + 16 * q^41 + 26 * q^49 + 80 * q^51 + 84 * q^61 - 28 * q^69 - 2 * q^79 - 26 * q^81 + 56 * q^89 - 22 * q^91 - 72 * q^99

Introduction

L-functions

Modular forms

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Database

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