LMFDB - Embedded newform 420.2.bh.b.341.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(101,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))

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

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

chi := DirichletCharacter("420.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.29471584693248.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 2x^{8} - 4x^{7} + 13x^{6} - 36x^{5} + 39x^{4} - 36x^{3} + 54x^{2} - 162x + 243 $ x^10 - 2x^9 + 2x^8 - 4x^7 + 13x^6 - 36x^5 + 39x^4 - 36x^3 + 54x^2 - 162*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.5
Root			$1.15038 - 1.29484i$ of defining polynomial
Character	$\chi$	$=$	420.341
Dual form			420.2.bh.b.101.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.69656 + 0.348838i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.08214 - 2.41433i) q^{7} +(2.75662 + 1.18365i) q^{9} +O(q^{10})$	\(q+(1.69656 + 0.348838i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.08214 - 2.41433i) q^{7} +(2.75662 + 1.18365i) q^{9} +(1.17086 - 0.675999i) q^{11} -4.94296i q^{13} +(1.15038 - 1.29484i) q^{15} +(2.87105 + 4.97280i) q^{17} +(2.84694 + 1.64368i) q^{19} +(-0.993697 - 4.47354i) q^{21} +(-4.33480 - 2.50270i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(4.26388 + 2.96974i) q^{27} +5.68630i q^{29} +(-2.45160 + 1.41543i) q^{31} +(2.22225 - 0.738430i) q^{33} +(-2.63194 - 0.270008i) q^{35} +(-1.92545 + 3.33498i) q^{37} +(1.72429 - 8.38603i) q^{39} -3.73802 q^{41} +4.06339 q^{43} +(2.40338 - 1.79548i) q^{45} +(-2.84298 + 4.92419i) q^{47} +(-4.65797 + 5.22526i) q^{49} +(3.13620 + 9.43818i) q^{51} +(1.26574 - 0.730773i) q^{53} -1.35200i q^{55} +(4.25662 + 3.78172i) q^{57} +(-4.34239 - 7.52123i) q^{59} +(1.65306 + 0.954394i) q^{61} +(-0.125326 - 7.93626i) q^{63} +(-4.28073 - 2.47148i) q^{65} +(-2.51939 - 4.36371i) q^{67} +(-6.48121 - 5.75812i) q^{69} -3.38259i q^{71} +(14.1398 - 8.16364i) q^{73} +(-0.546177 - 1.64368i) q^{75} +(-2.89912 - 2.09533i) q^{77} +(-2.41693 + 4.18625i) q^{79} +(6.19796 + 6.52574i) q^{81} -16.6525 q^{83} +5.74210 q^{85} +(-1.98359 + 9.64714i) q^{87} +(-8.08150 + 13.9976i) q^{89} +(-11.9339 + 5.34895i) q^{91} +(-4.65303 + 1.54615i) q^{93} +(2.84694 - 1.64368i) q^{95} +12.0577i q^{97} +(4.02778 - 0.477584i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	$ 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) $ 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.69656	+	0.348838i	0.979509	+	0.201402i
$3$	1.69656	+	0.348838i	0.979509	+	0.201402i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	−1.08214	−	2.41433i	−0.409009	−	0.912531i
$7$	−1.08214	−	2.41433i	−0.409009	−	0.912531i
$8$		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
$13$		−	4.94296i		−	1.37093i	−0.728105	−	0.685466i	$-0.759599\pi$
$13$		−	4.94296i		−	1.37093i	0.728105	−	0.685466i	$-0.240401\pi$
$14$		0			0
$15$	1.15038	−	1.29484i	0.297027	−	0.334327i
$16$		0			0
$17$	2.87105	+	4.97280i	0.696332	+	1.20608i	0.969730	+	0.244181i	$0.0785190\pi$
$17$	2.87105	+	4.97280i	0.696332	+	1.20608i	−0.273398	+	0.961901i	$0.588148\pi$
$18$		0			0
$19$	2.84694	+	1.64368i	0.653133	+	0.377087i	0.789656	−	0.613550i	$-0.210259\pi$
$19$	2.84694	+	1.64368i	0.653133	+	0.377087i	−0.136523	+	0.990637i	$0.543593\pi$
$20$		0			0
$21$	−0.993697	−	4.47354i	−0.216842	−	0.976207i
$22$		0			0
$23$	−4.33480	−	2.50270i	−0.903868	−	0.521849i	−0.0254150	−	0.999677i	$-0.508091\pi$
$23$	−4.33480	−	2.50270i	−0.903868	−	0.521849i	−0.878453	+	0.477828i	$0.841424\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	4.26388	+	2.96974i	0.820583	+	0.571527i
$28$		0			0
$29$			5.68630i			1.05592i	0.849270	+	0.527959i	$0.177043\pi$
$29$			5.68630i			1.05592i	−0.849270	+	0.527959i	$0.822957\pi$
$30$		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
$33$	2.22225	−	0.738430i	0.386845	−	0.128544i
$34$		0			0
$35$	−2.63194	−	0.270008i	−0.444879	−	0.0456397i
$36$		0			0
$37$	−1.92545	+	3.33498i	−0.316542	+	0.548267i	−0.979764	−	0.200156i	$-0.935855\pi$
$37$	−1.92545	+	3.33498i	−0.316542	+	0.548267i	0.663222	+	0.748423i	$0.269189\pi$
$38$		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
$43$	4.06339			0.619661			0.309830	−	0.950792i	$-0.399728\pi$
$43$	4.06339			0.619661			0.309830	+	0.950792i	$0.399728\pi$
$44$		0			0
$45$	2.40338	−	1.79548i	0.358275	−	0.267655i
$46$		0			0
$47$	−2.84298	+	4.92419i	−0.414691	+	0.718266i	−0.995396	−	0.0958478i	$-0.969444\pi$
$47$	−2.84298	+	4.92419i	−0.414691	+	0.718266i	0.580705	+	0.814114i	$0.302777\pi$
$48$		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
$53$	1.26574	−	0.730773i	0.173862	−	0.100379i	−0.410544	−	0.911841i	$-0.634661\pi$
$53$	1.26574	−	0.730773i	0.173862	−	0.100379i	0.584406	+	0.811462i	$0.301328\pi$
$54$		0			0
$55$		−	1.35200i		−	0.182303i
$56$		0			0
$57$	4.25662	+	3.78172i	0.563804	+	0.500902i
$58$		0			0
$59$	−4.34239	−	7.52123i	−0.565330	−	0.979181i	−0.997019	−	0.0771582i	$-0.975415\pi$
$59$	−4.34239	−	7.52123i	−0.565330	−	0.979181i	0.431688	−	0.902023i	$-0.357918\pi$
$60$		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
$63$	−0.125326	−	7.93626i	−0.0157896	−	0.999875i
$64$		0			0
$65$	−4.28073	−	2.47148i	−0.530959	−	0.306550i
$66$		0			0
$67$	−2.51939	−	4.36371i	−0.307793	−	0.533113i	0.670086	−	0.742283i	$-0.266257\pi$
$67$	−2.51939	−	4.36371i	−0.307793	−	0.533113i	−0.977879	+	0.209170i	$0.932924\pi$
$68$		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
$73$	14.1398	−	8.16364i	1.65494	−	0.955481i	0.679945	−	0.733263i	$-0.262004\pi$
$73$	14.1398	−	8.16364i	1.65494	−	0.955481i	0.974997	−	0.222218i	$-0.0713298\pi$
$74$		0			0
$75$	−0.546177	−	1.64368i	−0.0630671	−	0.189796i
$76$		0			0
$77$	−2.89912	−	2.09533i	−0.330385	−	0.238785i
$78$		0			0
$79$	−2.41693	+	4.18625i	−0.271926	+	0.470990i	−0.969355	−	0.245664i	$-0.920994\pi$
$79$	−2.41693	+	4.18625i	−0.271926	+	0.470990i	0.697429	+	0.716654i	$0.254327\pi$
$80$		0			0
$81$	6.19796	+	6.52574i	0.688662	+	0.725083i
$82$		0			0
$83$	−16.6525			−1.82785			−0.913927	−	0.405879i	$-0.866965\pi$
$83$	−16.6525			−1.82785			−0.913927	+	0.405879i	$0.866965\pi$
$84$		0			0
$85$	5.74210			0.622818
$86$		0			0
$87$	−1.98359	+	9.64714i	−0.212664	+	1.03428i
$88$		0			0
$89$	−8.08150	+	13.9976i	−0.856637	+	1.48374i	0.0184813	+	0.999829i	$0.494117\pi$
$89$	−8.08150	+	13.9976i	−0.856637	+	1.48374i	−0.875118	+	0.483909i	$0.839216\pi$
$90$		0			0
$91$	−11.9339	+	5.34895i	−1.25102	+	0.560723i
$92$		0			0
$93$	−4.65303	+	1.54615i	−0.482497	+	0.160328i
$94$		0			0
$95$	2.84694	−	1.64368i	0.292090	−	0.168638i
$96$		0			0
$97$			12.0577i			1.22427i	0.790751	+	0.612137i	$0.209690\pi$
$97$			12.0577i			1.22427i	−0.790751	+	0.612137i	$0.790310\pi$
$98$		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
$103$	0.533615	+	0.308083i	0.0525787	+	0.0303563i	0.526059	−	0.850448i	$-0.323669\pi$
$103$	0.533615	+	0.308083i	0.0525787	+	0.0303563i	−0.473480	+	0.880804i	$0.657002\pi$
$104$		0			0
$105$	−4.37105	−	1.37620i	−0.426571	−	0.134304i
$106$		0			0
$107$	−15.3374	−	8.85503i	−1.48272	−	0.856048i	−0.482912	−	0.875669i	$-0.660421\pi$
$107$	−15.3374	−	8.85503i	−1.48272	−	0.856048i	−0.999807	+	0.0196209i	$0.993754\pi$
$108$		0			0
$109$	0.855282	+	1.48139i	0.0819211	+	0.141892i	0.904075	−	0.427374i	$-0.140561\pi$
$109$	0.855282	+	1.48139i	0.0819211	+	0.141892i	−0.822154	+	0.569265i	$0.807228\pi$
$110$		0			0
$111$	−4.43001	+	4.98632i	−0.420478	+	0.473280i
$112$		0			0
$113$		−	13.1214i		−	1.23436i	−0.786822	−	0.617180i	$-0.788275\pi$
$113$		−	13.1214i		−	1.23436i	0.786822	−	0.617180i	$-0.211725\pi$
$114$		0			0
$115$	−4.33480	+	2.50270i	−0.404222	+	0.233378i
$116$		0			0
$117$	5.85073	−	13.6259i	0.540900	−	1.25971i
$118$		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
$123$	−6.34177	−	1.30396i	−0.571818	−	0.117574i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−15.5324			−1.37828			−0.689139	−	0.724629i	$-0.742011\pi$
$127$	−15.5324			−1.37828			−0.689139	+	0.724629i	$0.742011\pi$
$128$		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
$133$	0.887614	−	8.65214i	0.0769659	−	0.750235i
$134$		0			0
$135$	4.70381	−	2.20775i	0.404839	−	0.190013i
$136$		0			0
$137$	13.4047	−	7.73923i	1.14524	−	0.661207i	0.197520	−	0.980299i	$-0.436711\pi$
$137$	13.4047	−	7.73923i	1.14524	−	0.661207i	0.947724	+	0.319092i	$0.103378\pi$
$138$		0			0
$139$			20.1547i			1.70950i	0.519044	+	0.854748i	$0.326288\pi$
$139$			20.1547i			1.70950i	−0.519044	+	0.854748i	$0.673712\pi$
$140$		0			0
$141$	−6.54103	+	7.36243i	−0.550854	+	0.620029i
$142$		0			0
$143$	−3.34144	−	5.78754i	−0.279425	−	0.483978i
$144$		0			0
$145$	4.92448	+	2.84315i	0.408955	+	0.236111i
$146$		0			0
$147$	−9.72528	+	7.24009i	−0.802128	+	0.597152i
$148$		0			0
$149$	−1.24947	−	0.721384i	−0.102361	−	0.0590981i	0.447946	−	0.894061i	$-0.352156\pi$
$149$	−1.24947	−	0.721384i	−0.102361	−	0.0590981i	−0.550307	+	0.834963i	$0.685489\pi$
$150$		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
$153$	2.02836	+	17.1065i	0.163983	+	1.38298i
$154$		0			0
$155$			2.83086i			0.227380i
$156$		0			0
$157$	15.7942	−	9.11876i	1.26051	−	0.727756i	0.287338	−	0.957829i	$-0.407230\pi$
$157$	15.7942	−	9.11876i	1.26051	−	0.727756i	0.973173	+	0.230073i	$0.0738965\pi$
$158$		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
$163$	12.1630	−	21.0669i	0.952679	−	1.65009i	0.213087	−	0.977033i	$-0.431648\pi$
$163$	12.1630	−	21.0669i	0.952679	−	1.65009i	0.739592	−	0.673055i	$-0.235018\pi$
$164$		0			0
$165$	0.471628	−	2.29374i	0.0367162	−	0.178568i
$166$		0			0
$167$	12.5007			0.967336			0.483668	−	0.875252i	$-0.339304\pi$
$167$	12.5007			0.967336			0.483668	+	0.875252i	$0.339304\pi$
$168$		0			0
$169$	−11.4329			−0.879453
$170$		0			0
$171$	5.90241	+	7.90079i	0.451368	+	0.604188i
$172$		0			0
$173$	−7.42089	+	12.8534i	−0.564200	+	0.977223i	0.432923	+	0.901431i	$0.357482\pi$
$173$	−7.42089	+	12.8534i	−0.564200	+	0.977223i	−0.997124	+	0.0757927i	$0.975851\pi$
$174$		0			0
$175$	−1.54980	+	2.14432i	−0.117154	+	0.162095i
$176$		0			0
$177$	−4.74342	−	14.2750i	−0.356538	−	1.07297i
$178$		0			0
$179$	9.93533	−	5.73617i	0.742602	−	0.428741i	−0.0804127	−	0.996762i	$-0.525624\pi$
$179$	9.93533	−	5.73617i	0.742602	−	0.428741i	0.823015	+	0.568020i	$0.192291\pi$
$180$		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
$183$	2.47158	+	2.19584i	0.182705	+	0.162321i
$184$		0			0
$185$	1.92545	+	3.33498i	0.141562	+	0.245192i
$186$		0			0
$187$	6.72322	+	3.88165i	0.491650	+	0.283854i
$188$		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
$193$	−6.03231	−	10.4483i	−0.434215	−	0.752082i	0.563016	−	0.826446i	$-0.309641\pi$
$193$	−6.03231	−	10.4483i	−0.434215	−	0.752082i	−0.997231	+	0.0743635i	$0.976307\pi$
$194$		0			0
$195$	−6.40037	−	5.68630i	−0.458340	−	0.407204i
$196$		0			0
$197$			17.2423i			1.22846i	0.789126	+	0.614231i	$0.210534\pi$
$197$			17.2423i			1.22846i	−0.789126	+	0.614231i	$0.789466\pi$
$198$		0			0
$199$	2.46400	−	1.42259i	0.174668	−	0.100845i	−0.410117	−	0.912033i	$-0.634512\pi$
$199$	2.46400	−	1.42259i	0.174668	−	0.100845i	0.584785	+	0.811188i	$0.301179\pi$
$200$		0			0
$201$	−2.75207	−	8.28216i	−0.194116	−	0.584178i
$202$		0			0
$203$	13.7286	−	6.15334i	0.963558	−	0.431880i
$204$		0			0
$205$	−1.86901	+	3.23722i	−0.130537	+	0.226097i
$206$		0			0
$207$	−8.98710	−	12.0299i	−0.624647	−	0.836134i
$208$		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
$213$	1.17998	−	5.73877i	0.0808506	−	0.393214i
$214$		0			0
$215$	2.03169	−	3.51900i	0.138560	−	0.239994i
$216$		0			0
$217$	6.07027	+	4.38727i	0.412077	+	0.297828i
$218$		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
$223$		−	5.27620i		−	0.353321i	−0.984272	−	0.176660i	$-0.943471\pi$
$223$		−	5.27620i		−	0.353321i	0.984272	−	0.176660i	$-0.0565294\pi$
$224$		0			0
$225$	−0.353244	−	2.97913i	−0.0235496	−	0.198609i
$226$		0			0
$227$	6.24055	+	10.8090i	0.414200	+	0.717416i	0.995344	−	0.0963851i	$-0.0307280\pi$
$227$	6.24055	+	10.8090i	0.414200	+	0.717416i	−0.581144	+	0.813801i	$0.697395\pi$
$228$		0			0
$229$	−14.0882	−	8.13380i	−0.930971	−	0.537496i	−0.0438526	−	0.999038i	$-0.513963\pi$
$229$	−14.0882	−	8.13380i	−0.930971	−	0.537496i	−0.887119	+	0.461542i	$0.847297\pi$
$230$		0			0
$231$	−4.18759	−	4.56617i	−0.275523	−	0.300432i
$232$		0			0
$233$	7.64788	+	4.41551i	0.501029	+	0.289269i	0.729139	−	0.684366i	$-0.239921\pi$
$233$	7.64788	+	4.41551i	0.501029	+	0.289269i	−0.228109	+	0.973636i	$0.573254\pi$
$234$		0			0
$235$	2.84298	+	4.92419i	0.185456	+	0.321219i
$236$		0			0
$237$	−5.56079	+	6.25911i	−0.361212	+	0.406573i
$238$		0			0
$239$		−	12.3333i		−	0.797773i	−0.917000	−	0.398886i	$-0.869397\pi$
$239$		−	12.3333i		−	0.797773i	0.917000	−	0.398886i	$-0.130603\pi$
$240$		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
$243$	8.23878	+	13.2334i	0.528518	+	0.848922i
$244$		0			0
$245$	2.19622	+	6.64655i	0.140312	+	0.424632i
$246$		0			0
$247$	8.12466	−	14.0723i	0.516960	−	0.895401i
$248$		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
$253$	−6.76728			−0.425455
$254$		0			0
$255$	9.74181	+	2.00306i	0.610056	+	0.125436i
$256$		0			0
$257$	13.7478	−	23.8118i	0.857563	−	1.48534i	−0.0166841	−	0.999861i	$-0.505311\pi$
$257$	13.7478	−	23.8118i	0.857563	−	1.48534i	0.874247	−	0.485482i	$-0.161356\pi$
$258$		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
$263$	16.4738	−	9.51115i	1.01582	−	0.586483i	0.102928	−	0.994689i	$-0.467179\pi$
$263$	16.4738	−	9.51115i	1.01582	−	0.586483i	0.912890	+	0.408206i	$0.133845\pi$
$264$		0			0
$265$		−	1.46155i		−	0.0897821i
$266$		0			0
$267$	−18.5936	+	20.9286i	−1.13791	+	1.28081i
$268$		0			0
$269$	4.46010	+	7.72512i	0.271937	+	0.471009i	0.969358	−	0.245653i	$-0.0790024\pi$
$269$	4.46010	+	7.72512i	0.271937	+	0.471009i	−0.697421	+	0.716662i	$0.745669\pi$
$270$		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
$273$	−22.1125	+	4.91181i	−1.33831	+	0.297276i
$274$		0			0
$275$	−1.17086	−	0.675999i	−0.0706058	−	0.0407643i
$276$		0			0
$277$	0.888562	+	1.53903i	0.0533885	+	0.0924716i	0.891485	−	0.453051i	$-0.149664\pi$
$277$	0.888562	+	1.53903i	0.0533885	+	0.0924716i	−0.838096	+	0.545523i	$0.816331\pi$
$278$		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
$283$	−13.9774	+	8.06987i	−0.830872	+	0.479704i	−0.854151	−	0.520025i	$-0.825923\pi$
$283$	−13.9774	+	8.06987i	−0.830872	+	0.479704i	0.0232795	+	0.999729i	$0.492589\pi$
$284$		0			0
$285$	5.40338	−	1.79548i	0.320069	−	0.106355i
$286$		0			0
$287$	4.04504	+	9.02481i	0.238771	+	0.532718i
$288$		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
$293$	19.5542			1.14237			0.571186	−	0.820821i	$-0.306484\pi$
$293$	19.5542			1.14237			0.571186	+	0.820821i	$0.306484\pi$
$294$		0			0
$295$	−8.68477			−0.505647
$296$		0			0
$297$	6.99996	+	0.594790i	0.406179	+	0.0345132i
$298$		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
$303$	9.84957	+	29.6416i	0.565843	+	1.70287i
$304$		0			0
$305$	1.65306	−	0.954394i	0.0946539	−	0.0546485i
$306$		0			0
$307$			11.8231i			0.674777i	0.941365	+	0.337389i	$0.109544\pi$
$307$			11.8231i			0.674777i	−0.941365	+	0.337389i	$0.890456\pi$
$308$		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
$313$	−11.5250	−	6.65398i	−0.651433	−	0.376105i	0.137572	−	0.990492i	$-0.456070\pi$
$313$	−11.5250	−	6.65398i	−0.651433	−	0.376105i	−0.789005	+	0.614387i	$0.789404\pi$
$314$		0			0
$315$	−6.93567	−	3.85960i	−0.390781	−	0.217464i
$316$		0			0
$317$	−29.3395	−	16.9392i	−1.64787	−	0.951400i	−0.977915	−	0.209001i	$-0.932979\pi$
$317$	−29.3395	−	16.9392i	−1.64787	−	0.951400i	−0.669958	−	0.742399i	$-0.733688\pi$
$318$		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
$323$			18.8764i			1.05031i
$324$		0			0
$325$	−4.28073	+	2.47148i	−0.237452	+	0.137093i
$326$		0			0
$327$	0.934271	+	2.81162i	0.0516653	+	0.155483i
$328$		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
$333$	−9.25518	+	6.91423i	−0.507181	+	0.378897i
$334$		0			0
$335$	−5.03878			−0.275298
$336$		0			0
$337$	−12.0217			−0.654862			−0.327431	−	0.944875i	$-0.606183\pi$
$337$	−12.0217			−0.654862			−0.327431	+	0.944875i	$0.606183\pi$
$338$		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
$343$	17.6560	+	5.59143i	0.953337	+	0.301909i
$344$		0			0
$345$	−8.22728	+	2.73383i	−0.442942	+	0.147185i
$346$		0			0
$347$	−12.6992	+	7.33186i	−0.681726	+	0.393595i	−0.800505	−	0.599326i	$-0.795435\pi$
$347$	−12.6992	+	7.33186i	−0.681726	+	0.393595i	0.118779	+	0.992921i	$0.462102\pi$
$348$		0			0
$349$			25.0573i			1.34129i	0.741780	+	0.670644i	$0.233982\pi$
$349$			25.0573i			1.34129i	−0.741780	+	0.670644i	$0.766018\pi$
$350$		0			0
$351$	14.6793	−	21.0762i	0.783525	−	1.12496i
$352$		0			0
$353$	3.88365	+	6.72669i	0.206706	+	0.358025i	0.950675	−	0.310189i	$-0.100392\pi$
$353$	3.88365	+	6.72669i	0.206706	+	0.358025i	−0.743969	+	0.668214i	$0.767059\pi$
$354$		0			0
$355$	−2.92941	−	1.69130i	−0.155477	−	0.0897647i
$356$		0			0
$357$	19.3931	−	17.7852i	1.02639	−	0.941293i
$358$		0			0
$359$	−3.86952	−	2.23407i	−0.204225	−	0.117910i	0.394399	−	0.918939i	$-0.370953\pi$
$359$	−3.86952	−	2.23407i	−0.204225	−	0.117910i	−0.598625	+	0.801030i	$0.704286\pi$
$360$		0			0
$361$	−4.09662	−	7.09555i	−0.215612	−	0.373450i
$362$		0			0
$363$	−10.5514	+	11.8764i	−0.553806	+	0.623352i
$364$		0			0
$365$		−	16.3273i		−	0.854608i
$366$		0			0
$367$	1.45880	−	0.842240i	0.0761489	−	0.0439646i	−0.461442	−	0.887170i	$-0.652668\pi$
$367$	1.45880	−	0.842240i	0.0761489	−	0.0439646i	0.537591	+	0.843206i	$0.319334\pi$
$368$		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
$373$	−6.92322	+	11.9914i	−0.358471	+	0.620890i	−0.987706	−	0.156325i	$-0.950035\pi$
$373$	−6.92322	+	11.9914i	−0.358471	+	0.620890i	0.629235	+	0.777215i	$0.283368\pi$
$374$		0			0
$375$	−1.69656	−	0.348838i	−0.0876099	−	0.0180139i
$376$		0			0
$377$	28.1072			1.44759
$378$		0			0
$379$	−2.15603			−0.110748			−0.0553739	−	0.998466i	$-0.517635\pi$
$379$	−2.15603			−0.110748			−0.0553739	+	0.998466i	$0.517635\pi$
$380$		0			0
$381$	−26.3516	−	5.41829i	−1.35004	−	0.277587i
$382$		0			0
$383$	−1.86598	+	3.23197i	−0.0953471	+	0.165146i	−0.909753	−	0.415149i	$-0.863729\pi$
$383$	−1.86598	+	3.23197i	−0.0953471	+	0.165146i	0.814406	+	0.580295i	$0.197063\pi$
$384$		0			0
$385$	−3.26417	+	1.46304i	−0.166357	+	0.0745636i
$386$		0			0
$387$	11.2012	+	4.80962i	0.569391	+	0.244487i
$388$		0			0
$389$	−11.9512	+	6.90001i	−0.605948	+	0.349844i	−0.771378	−	0.636377i	$-0.780432\pi$
$389$	−11.9512	+	6.90001i	−0.605948	+	0.349844i	0.165430	+	0.986222i	$0.447099\pi$
$390$		0			0
$391$		−	28.7415i		−	1.45352i
$392$		0			0
$393$	−10.3033	+	11.5972i	−0.519734	+	0.585001i
$394$		0			0
$395$	2.41693	+	4.18625i	0.121609	+	0.210633i
$396$		0			0
$397$	−14.1606	−	8.17565i	−0.710702	−	0.410324i	0.100619	−	0.994925i	$-0.467918\pi$
$397$	−14.1606	−	8.17565i	−0.710702	−	0.410324i	−0.811321	+	0.584601i	$0.801251\pi$
$398$		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
$403$	6.99642	+	12.1182i	0.348516	+	0.603648i
$404$		0			0
$405$	8.75044	−	2.10472i	0.434813	−	0.104584i
$406$		0			0
$407$			5.20641i			0.258072i
$408$		0			0
$409$	−8.26987	+	4.77461i	−0.408919	+	0.236089i	−0.690325	−	0.723499i	$-0.742533\pi$
$409$	−8.26987	+	4.77461i	−0.408919	+	0.236089i	0.281406	+	0.959589i	$0.409199\pi$
$410$		0			0
$411$	25.4417	−	8.45398i	1.25494	−	0.417004i
$412$		0			0
$413$	−13.4597	+	18.6229i	−0.662307	+	0.916375i
$414$		0			0
$415$	−8.32627	+	14.4215i	−0.408721	+	0.707925i
$416$		0			0
$417$	−7.03070	+	34.1936i	−0.344295	+	1.67447i
$418$		0			0
$419$	9.71886			0.474797			0.237399	−	0.971412i	$-0.423705\pi$
$419$	9.71886			0.474797			0.237399	+	0.971412i	$0.423705\pi$
$420$		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
$423$	−13.6655	+	10.2090i	−0.664441	+	0.496381i
$424$		0			0
$425$	2.87105	−	4.97280i	0.139266	−	0.241216i
$426$		0			0
$427$	0.515388	−	5.02381i	0.0249414	−	0.243119i
$428$		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
$433$		−	10.6773i		−	0.513117i	−0.966529	−	0.256558i	$-0.917411\pi$
$433$		−	10.6773i		−	0.513117i	0.966529	−	0.256558i	$-0.0825886\pi$
$434$		0			0
$435$	7.36287	+	6.54141i	0.353022	+	0.313637i
$436$		0			0
$437$	−8.22728	−	14.2501i	−0.393564	−	0.681673i
$438$		0			0
$439$	26.6759	+	15.4013i	1.27317	+	0.735066i	0.975584	−	0.219628i	$-0.0704845\pi$
$439$	26.6759	+	15.4013i	1.27317	+	0.735066i	0.297588	+	0.954694i	$0.403818\pi$
$440$		0			0
$441$	−19.0251	+	8.89069i	−0.905959	+	0.423366i
$442$		0			0
$443$	−14.3178	−	8.26640i	−0.680260	−	0.392749i	0.119693	−	0.992811i	$-0.461809\pi$
$443$	−14.3178	−	8.26640i	−0.680260	−	0.392749i	−0.799953	+	0.600062i	$0.795142\pi$
$444$		0			0
$445$	8.08150	+	13.9976i	0.383100	+	0.663548i
$446$		0			0
$447$	−1.86816	−	1.65974i	−0.0883610	−	0.0785028i
$448$		0			0
$449$			2.59098i			0.122276i	0.998129	+	0.0611380i	$0.0194730\pi$
$449$			2.59098i			0.122276i	−0.998129	+	0.0611380i	$0.980527\pi$
$450$		0			0
$451$	−4.37671	+	2.52690i	−0.206091	+	0.118987i
$452$		0			0
$453$	−8.87110	−	26.6969i	−0.416800	−	1.25433i
$454$		0			0
$455$	−1.33464	+	13.0096i	−0.0625689	+	0.609898i
$456$		0			0
$457$	11.0874	−	19.2040i	0.518647	−	0.898323i	−0.481118	−	0.876656i	$-0.659769\pi$
$457$	11.0874	−	19.2040i	0.518647	−	0.898323i	0.999765	−	0.0216672i	$-0.00689744\pi$
$458$		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
$463$	3.54824			0.164901			0.0824504	−	0.996595i	$-0.473725\pi$
$463$	3.54824			0.164901			0.0824504	+	0.996595i	$0.473725\pi$
$464$		0			0
$465$	−0.987510	+	4.80272i	−0.0457947	+	0.222721i
$466$		0			0
$467$	−17.1564	+	29.7157i	−0.793901	+	1.37508i	0.129633	+	0.991562i	$0.458620\pi$
$467$	−17.1564	+	29.7157i	−0.793901	+	1.37508i	−0.923534	+	0.383515i	$0.874713\pi$
$468$		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
$473$	4.75767	−	2.74684i	0.218758	−	0.126300i
$474$		0			0
$475$		−	3.28736i		−	0.150835i
$476$		0			0
$477$	4.35414	−	0.516282i	0.199362	−	0.0236389i
$478$		0			0
$479$	−9.78624	−	16.9503i	−0.447145	−	0.774477i	0.551054	−	0.834469i	$-0.314226\pi$
$479$	−9.78624	−	16.9503i	−0.447145	−	0.774477i	−0.998199	+	0.0599923i	$0.980892\pi$
$480$		0			0
$481$	16.4847	+	9.51743i	0.751637	+	0.433958i
$482$		0			0
$483$	−6.88844	+	21.8788i	−0.313435	+	0.995521i
$484$		0			0
$485$	10.4423	+	6.02885i	0.474160	+	0.273756i
$486$		0			0
$487$	−12.6133	−	21.8468i	−0.571561	−	0.989973i	−0.996406	−	0.0847071i	$-0.973005\pi$
$487$	−12.6133	−	21.8468i	−0.571561	−	0.989973i	0.424844	−	0.905266i	$-0.360329\pi$
$488$		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
$493$	−28.2768	+	16.3256i	−1.27352	+	0.735269i
$494$		0			0
$495$	1.60029	−	3.72695i	0.0719276	−	0.167514i
$496$		0			0
$497$	−8.16669	+	3.66042i	−0.366326	+	0.164192i
$498$		0			0
$499$	−2.80910	+	4.86551i	−0.125753	+	0.217810i	−0.922027	−	0.387126i	$-0.873468\pi$
$499$	−2.80910	+	4.86551i	−0.125753	+	0.217810i	0.796274	+	0.604936i	$0.206801\pi$
$500$		0			0
$501$	21.2082	+	4.36073i	0.947514	+	0.194823i
$502$		0			0
$503$	25.8655			1.15329			0.576644	−	0.816996i	$-0.304362\pi$
$503$	25.8655			1.15329			0.576644	+	0.816996i	$0.304362\pi$
$504$		0			0
$505$	18.0337			0.802487
$506$		0			0
$507$	−19.3966	−	3.98822i	−0.861432	−	0.177123i
$508$		0			0
$509$	15.2306	−	26.3801i	0.675082	−	1.16928i	−0.301362	−	0.953510i	$-0.597441\pi$
$509$	15.2306	−	26.3801i	0.675082	−	1.16928i	0.976445	−	0.215767i	$-0.0692253\pi$
$510$		0			0
$511$	−35.0109	−	25.3040i	−1.54879	−	1.11939i
$512$		0			0
$513$	7.25769	+	15.4631i	0.320435	+	0.682714i
$514$		0			0
$515$	0.533615	−	0.308083i	0.0235139	−	0.0135758i
$516$		0			0
$517$			7.68740i			0.338092i
$518$		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
$523$	−10.7227	−	6.19077i	−0.468872	−	0.270704i	0.246895	−	0.969042i	$-0.420590\pi$
$523$	−10.7227	−	6.19077i	−0.468872	−	0.270704i	−0.715768	+	0.698339i	$0.753923\pi$
$524$		0			0
$525$	−3.37735	+	3.09734i	−0.147400	+	0.135179i
$526$		0			0
$527$	−14.0773	−	8.12754i	−0.613217	−	0.354041i
$528$		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
$533$			18.4769i			0.800323i
$534$		0			0
$535$	−15.3374	+	8.85503i	−0.663092	+	0.382836i
$536$		0			0
$537$	18.8569	−	6.26593i	0.813734	−	0.270395i
$538$		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
$543$	2.06198	−	10.0283i	0.0884879	−	0.430358i
$544$		0			0
$545$	1.71056			0.0732725
$546$		0			0
$547$	17.7100			0.757226			0.378613	−	0.925555i	$-0.376401\pi$
$547$	17.7100			0.757226			0.378613	+	0.925555i	$0.376401\pi$
$548$		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
$553$	12.7224	+	1.30518i	0.541013	+	0.0555020i
$554$		0			0
$555$	2.10327	+	6.32966i	0.0892790	+	0.268679i
$556$		0			0
$557$	3.01129	−	1.73857i	0.127593	−	0.0736656i	−0.434845	−	0.900505i	$-0.643197\pi$
$557$	3.01129	−	1.73857i	0.127593	−	0.0736656i	0.562438	+	0.826840i	$0.309864\pi$
$558$		0			0
$559$		−	20.0852i		−	0.849512i
$560$		0			0
$561$	10.0523	+	8.93076i	0.424407	+	0.377057i
$562$		0			0
$563$	−6.02897	−	10.4425i	−0.254091	−	0.440098i	0.710557	−	0.703639i	$-0.248443\pi$
$563$	−6.02897	−	10.4425i	−0.254091	−	0.440098i	−0.964648	+	0.263541i	$0.915110\pi$
$564$		0			0
$565$	−11.3635	−	6.56071i	−0.478065	−	0.276011i
$566$		0			0
$567$	9.04826	−	22.0256i	0.379991	−	0.924990i
$568$		0			0
$569$	−11.8065	−	6.81650i	−0.494955	−	0.285762i	0.231673	−	0.972794i	$-0.425580\pi$
$569$	−11.8065	−	6.81650i	−0.494955	−	0.285762i	−0.726628	+	0.687031i	$0.758913\pi$
$570$		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
$573$	13.6921	+	12.1645i	0.571996	+	0.508180i
$574$		0			0
$575$			5.00540i			0.208739i
$576$		0			0
$577$	−6.06103	+	3.49934i	−0.252324	+	0.145679i	−0.620828	−	0.783947i	$-0.713203\pi$
$577$	−6.06103	+	3.49934i	−0.252324	+	0.145679i	0.368504	+	0.929626i	$0.379870\pi$
$578$		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
$583$	0.988003	−	1.71127i	0.0409189	−	0.0708736i
$584$		0			0
$585$	−8.87501	−	11.8798i	−0.366936	−	0.491170i
$586$		0			0
$587$	29.9161			1.23477			0.617385	−	0.786661i	$-0.288192\pi$
$587$	29.9161			1.23477			0.617385	+	0.786661i	$0.288192\pi$
$588$		0			0
$589$	−9.30607			−0.383450
$590$		0			0
$591$	−6.01476	+	29.2525i	−0.247414	+	1.20329i
$592$		0			0
$593$	−12.0426	+	20.8583i	−0.494529	+	0.856549i	−0.999980	−	0.00630583i	$-0.997993\pi$
$593$	−12.0426	+	20.8583i	−0.494529	+	0.856549i	0.505451	+	0.862855i	$0.331326\pi$
$594$		0			0
$595$	−6.21372	−	13.8633i	−0.254738	−	0.568340i
$596$		0			0
$597$	4.67657	−	1.55397i	0.191399	−	0.0635999i
$598$		0			0
$599$	−5.14773	+	2.97205i	−0.210331	+	0.121434i	−0.601465	−	0.798899i	$-0.705416\pi$
$599$	−5.14773	+	2.97205i	−0.210331	+	0.121434i	0.391134	+	0.920334i	$0.372083\pi$
$600$		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
$603$	−1.77992	−	15.0112i	−0.0724839	−	0.611303i
$604$		0			0
$605$	4.58605	+	7.94327i	0.186450	+	0.322940i
$606$		0			0
$607$	−8.61387	−	4.97322i	−0.349626	−	0.201857i	0.314894	−	0.949127i	$-0.398031\pi$
$607$	−8.61387	−	4.97322i	−0.349626	−	0.201857i	−0.664521	+	0.747270i	$0.731364\pi$
$608$		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
$613$	16.2739	+	28.1873i	0.657298	+	1.13847i	0.981312	+	0.192421i	$0.0616340\pi$
$613$	16.2739	+	28.1873i	0.657298	+	1.13847i	−0.324014	+	0.946052i	$0.605033\pi$
$614$		0			0
$615$	−4.30015	+	4.84015i	−0.173399	+	0.195174i
$616$		0			0
$617$		−	7.69843i		−	0.309927i	−0.987920	−	0.154964i	$-0.950474\pi$
$617$		−	7.69843i		−	0.309927i	0.987920	−	0.154964i	$-0.0495260\pi$
$618$		0			0
$619$	2.76170	−	1.59447i	0.111002	−	0.0640872i	−0.443471	−	0.896289i	$-0.646253\pi$
$619$	2.76170	−	1.59447i	0.111002	−	0.0640872i	0.554473	+	0.832202i	$0.312920\pi$
$620$		0			0
$621$	−11.0507	−	23.5444i	−0.443448	−	0.944805i
$622$		0			0
$623$	42.5400	+	4.36414i	1.70433	+	0.174845i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	7.54037	+	1.55041i	0.301133	+	0.0619175i
$628$		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
$633$	38.1179	+	7.83760i	1.51505	+	0.311516i
$634$		0			0
$635$	−7.76620	+	13.4515i	−0.308192	+	0.533805i
$636$		0			0
$637$	25.8283	+	23.0242i	1.02335	+	0.912251i
$638$		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
$643$		−	29.0919i		−	1.14727i	−0.819110	−	0.573637i	$-0.805532\pi$
$643$		−	29.0919i		−	1.14727i	0.819110	−	0.573637i	$-0.194468\pi$
$644$		0			0
$645$	4.67445	−	5.26145i	0.184056	−	0.207170i
$646$		0			0
$647$	−21.5999	−	37.4122i	−0.849181	−	1.47082i	−0.881940	−	0.471361i	$-0.843763\pi$
$647$	−21.5999	−	37.4122i	−0.849181	−	1.47082i	0.0327597	−	0.999463i	$-0.489570\pi$
$648$		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
$653$	−6.27142	−	3.62080i	−0.245420	−	0.141693i	0.372246	−	0.928134i	$-0.378588\pi$
$653$	−6.27142	−	3.62080i	−0.245420	−	0.141693i	−0.617665	+	0.786441i	$0.711921\pi$
$654$		0			0
$655$	4.47822	+	7.75651i	0.174979	+	0.303072i
$656$		0			0
$657$	48.6411	−	5.76750i	1.89767	−	0.225012i
$658$		0			0
$659$		−	5.29324i		−	0.206196i	−0.994671	−	0.103098i	$-0.967125\pi$
$659$		−	5.29324i		−	0.206196i	0.994671	−	0.103098i	$-0.0328755\pi$
$660$		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
$663$	46.6526	−	15.5021i	1.81184	−	0.602053i
$664$		0			0
$665$	−7.04916	−	5.09477i	−0.273355	−	0.197567i
$666$		0			0
$667$	14.2311	−	24.6490i	0.551030	−	0.954411i
$668$		0			0
$669$	1.84054	−	8.95139i	0.0711593	−	0.346081i
$670$		0			0
$671$	2.58068			0.0996259
$672$		0			0
$673$	−21.8855			−0.843625			−0.421812	−	0.906683i	$-0.638606\pi$
$673$	−21.8855			−0.843625			−0.421812	+	0.906683i	$0.638606\pi$
$674$		0			0
$675$	0.439934	−	5.17750i	0.0169331	−	0.199282i
$676$		0			0
$677$	−6.87236	+	11.9033i	−0.264126	+	0.457480i	−0.967334	−	0.253504i	$-0.918417\pi$
$677$	−6.87236	+	11.9033i	−0.264126	+	0.457480i	0.703208	+	0.710984i	$0.251750\pi$
$678$		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
$683$	−37.1547	+	21.4513i	−1.42169	+	0.820811i	−0.996443	−	0.0842682i	$-0.973145\pi$
$683$	−37.1547	+	21.4513i	−1.42169	+	0.820811i	−0.425243	+	0.905079i	$0.639811\pi$
$684$		0			0
$685$		−	15.4785i		−	0.591401i
$686$		0			0
$687$	−21.0640	−	18.7139i	−0.803642	−	0.713982i
$688$		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
$693$	−5.51164	−	9.20757i	−0.209370	−	0.349767i
$694$		0			0
$695$	17.4544	+	10.0773i	0.662085	+	0.382255i
$696$		0			0
$697$	−10.7320	−	18.5884i	−0.406505	−	0.704087i
$698$		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
$703$	−10.9633	+	6.32966i	−0.413488	+	0.238728i
$704$		0			0
$705$	3.10554	+	9.34591i	0.116961	+	0.351987i
$706$		0			0
$707$	27.9486	−	38.6700i	1.05112	−	1.45433i
$708$		0			0
$709$	22.8069	−	39.5026i	0.856529	−	1.48355i	−0.0186897	−	0.999825i	$-0.505949\pi$
$709$	22.8069	−	39.5026i	0.856529	−	1.48355i	0.875219	−	0.483727i	$-0.160717\pi$
$710$		0			0
$711$	−11.6176	+	8.67913i	−0.435695	+	0.325493i
$712$		0			0
$713$	14.1696			0.530655
$714$		0			0
$715$	−6.68287			−0.249925
$716$		0			0
$717$	4.30231	−	20.9241i	0.160673	−	0.781426i
$718$		0			0
$719$	−9.50850	+	16.4692i	−0.354607	+	0.614198i	−0.987051	−	0.160409i	$-0.948719\pi$
$719$	−9.50850	+	16.4692i	−0.354607	+	0.614198i	0.632443	+	0.774607i	$0.282052\pi$
$720$		0			0
$721$	0.166370	−	1.62171i	0.00619593	−	0.0603956i
$722$		0			0
$723$	13.0734	−	4.34416i	0.486207	−	0.161561i
$724$		0			0
$725$	4.92448	−	2.84315i	0.182890	−	0.105592i
$726$		0			0
$727$			34.0540i			1.26299i	0.775379	+	0.631496i	$0.217559\pi$
$727$			34.0540i			1.26299i	−0.775379	+	0.631496i	$0.782441\pi$
$728$		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
$733$	−6.71837	−	3.87885i	−0.248148	−	0.143269i	0.370768	−	0.928726i	$-0.379095\pi$
$733$	−6.71837	−	3.87885i	−0.248148	−	0.143269i	−0.618916	+	0.785457i	$0.712428\pi$
$734$		0			0
$735$	1.40746	+	12.0424i	0.0519148	+	0.444190i
$736$		0			0
$737$	−5.89973	−	3.40621i	−0.217319	−	0.125469i
$738$		0			0
$739$	4.19659	+	7.26871i	0.154374	+	0.267384i	0.932831	−	0.360314i	$-0.117331\pi$
$739$	4.19659	+	7.26871i	0.154374	+	0.267384i	−0.778457	+	0.627698i	$0.783997\pi$
$740$		0			0
$741$	18.6929	−	21.0403i	0.686702	−	0.772936i
$742$		0			0
$743$		−	14.7540i		−	0.541273i	−0.962682	−	0.270636i	$-0.912766\pi$
$743$		−	14.7540i		−	0.541273i	0.962682	−	0.270636i	$-0.0872341\pi$
$744$		0			0
$745$	−1.24947	+	0.721384i	−0.0457772	+	0.0264295i
$746$		0			0
$747$	−45.9048	−	19.7107i	−1.67957	−	0.721178i
$748$		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
$753$	−12.9745	−	2.66776i	−0.472818	−	0.0972185i
$754$		0			0
$755$	−16.2422			−0.591113
$756$		0			0
$757$	−11.8681			−0.431354			−0.215677	−	0.976465i	$-0.569196\pi$
$757$	−11.8681			−0.431354			−0.215677	+	0.976465i	$0.569196\pi$
$758$		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
$763$	2.65104	−	3.66800i	0.0959739	−	0.132790i
$764$		0			0
$765$	15.8288	+	6.79662i	0.572292	+	0.245732i
$766$		0			0
$767$	−37.1772	+	21.4643i	−1.34239	+	0.775029i
$768$		0			0
$769$		−	6.25608i		−	0.225600i	−0.993618	−	0.112800i	$-0.964018\pi$
$769$		−	6.25608i		−	0.225600i	0.993618	−	0.112800i	$-0.0359820\pi$
$770$		0			0
$771$	31.6304	−	35.6025i	1.13914	−	1.28219i
$772$		0			0
$773$	−10.0161	−	17.3483i	−0.360253	−	0.623977i	0.627749	−	0.778416i	$-0.283976\pi$
$773$	−10.0161	−	17.3483i	−0.360253	−	0.623977i	−0.988002	+	0.154439i	$0.950643\pi$
$774$		0			0
$775$	2.45160	+	1.41543i	0.0880639	+	0.0508437i
$776$		0			0
$777$	16.8325	+	5.29962i	0.603862	+	0.190123i
$778$		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
$783$	−16.8868	+	24.2457i	−0.603486	+	0.866469i
$784$		0			0
$785$		−	18.2375i		−	0.650925i
$786$		0			0
$787$	−1.27835	+	0.738053i	−0.0455681	+	0.0263088i	−0.522611	−	0.852571i	$-0.675042\pi$
$787$	−1.27835	+	0.738053i	−0.0455681	+	0.0263088i	0.477043	+	0.878880i	$0.341709\pi$
$788$		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
$793$	4.71754	−	8.17101i	0.167525	−	0.290161i
$794$		0			0
$795$	0.509842	−	2.47960i	0.0180822	−	0.0879423i
$796$		0			0
$797$	−22.9470			−0.812823			−0.406411	−	0.913690i	$-0.633220\pi$
$797$	−22.9470			−0.812823			−0.406411	+	0.913690i	$0.633220\pi$
$798$		0			0
$799$	−32.6493			−1.15505
$800$		0			0
$801$	−38.8458	+	29.0204i	−1.37255	+	1.02538i
$802$		0			0
$803$	11.0372	−	19.1170i	0.389495	−	0.674625i
$804$		0			0
$805$	10.7332	+	7.75737i	0.378295	+	0.273412i
$806$		0			0
$807$	4.87201	+	14.6620i	0.171503	+	0.516126i
$808$		0			0
$809$	19.5613	−	11.2937i	0.687739	−	0.397066i	−0.115026	−	0.993363i	$-0.536695\pi$
$809$	19.5613	−	11.2937i	0.687739	−	0.397066i	0.802764	+	0.596296i	$0.203362\pi$
$810$		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
$813$	9.76522	+	8.67573i	0.342481	+	0.304271i
$814$		0			0
$815$	−12.1630	−	21.0669i	−0.426051	−	0.737942i
$816$		0			0
$817$	11.5682	+	6.67892i	0.404721	+	0.233666i
$818$		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
$823$	10.2841	+	17.8125i	0.358480	+	0.620906i	0.987707	−	0.156316i	$-0.0499618\pi$
$823$	10.2841	+	17.8125i	0.358480	+	0.620906i	−0.629227	+	0.777222i	$0.716628\pi$
$824$		0			0
$825$	−1.75063	−	1.55531i	−0.0609490	−	0.0541491i
$826$		0			0
$827$			24.0587i			0.836603i	0.908308	+	0.418301i	$0.137374\pi$
$827$			24.0587i			0.836603i	−0.908308	+	0.418301i	$0.862626\pi$
$828$		0			0
$829$	−39.3074	+	22.6941i	−1.36520	+	0.788200i	−0.990311	−	0.138869i	$-0.955653\pi$
$829$	−39.3074	+	22.6941i	−1.36520	+	0.788200i	−0.374891	+	0.927069i	$0.622320\pi$
$830$		0			0
$831$	0.970625	+	2.92103i	0.0336706	+	0.101329i
$832$		0			0
$833$	−39.3574	−	8.16117i	−1.36365	−	0.282768i
$834$		0			0
$835$	6.25037	−	10.8260i	0.216303	−	0.374647i
$836$		0			0
$837$	−14.6568	−	1.24539i	−0.506612	−	0.0430471i
$838$		0			0
$839$	39.8758			1.37666			0.688332	−	0.725395i	$-0.258343\pi$
$839$	39.8758			1.37666			0.688332	+	0.725395i	$0.258343\pi$
$840$		0			0
$841$	−3.33396			−0.114964
$842$		0			0
$843$	8.85416	−	43.0619i	0.304954	−	1.48313i
$844$		0			0
$845$	−5.71645	+	9.90117i	−0.196652	+	0.340611i
$846$		0			0
$847$	24.1404	+	2.47654i	0.829474	+	0.0850949i
$848$		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
$853$		−	16.9504i		−	0.580372i	−0.956970	−	0.290186i	$-0.906283\pi$
$853$		−	16.9504i		−	0.580372i	0.956970	−	0.290186i	$-0.0937172\pi$
$854$		0			0
$855$	9.79349	−	1.16124i	0.334930	−	0.0397136i
$856$		0			0
$857$	−0.315644	−	0.546711i	−0.0107822	−	0.0186753i	0.860584	−	0.509309i	$-0.170099\pi$
$857$	−0.315644	−	0.546711i	−0.0107822	−	0.0186753i	−0.871366	+	0.490633i	$0.836765\pi$
$858$		0			0
$859$	−5.59642	−	3.23109i	−0.190947	−	0.110243i	0.401479	−	0.915868i	$-0.368496\pi$
$859$	−5.59642	−	3.23109i	−0.190947	−	0.110243i	−0.592426	+	0.805625i	$0.701830\pi$
$860$		0			0
$861$	3.71446	+	16.7222i	0.126588	+	0.569891i
$862$		0			0
$863$	−6.31821	−	3.64782i	−0.215074	−	0.124173i	0.388593	−	0.921409i	$-0.372961\pi$
$863$	−6.31821	−	3.64782i	−0.215074	−	0.124173i	−0.603667	+	0.797236i	$0.706295\pi$
$864$		0			0
$865$	7.42089	+	12.8534i	0.252318	+	0.437028i
$866$		0			0
$867$	−18.3735	+	20.6808i	−0.623998	+	0.702358i
$868$		0			0
$869$			6.53538i			0.221698i
$870$		0			0
$871$	−21.5697	+	12.4533i	−0.730861	+	0.421963i
$872$		0			0
$873$	−14.2721	+	33.2386i	−0.483037	+	1.12496i
$874$		0			0
$875$	1.08214	+	2.41433i	0.0365828	+	0.0816192i
$876$		0			0
$877$	−14.8442	+	25.7109i	−0.501253	+	0.868196i	0.498746	+	0.866748i	$0.333794\pi$
$877$	−14.8442	+	25.7109i	−0.501253	+	0.868196i	−0.999999	+	0.00144772i	$0.999539\pi$
$878$		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
$883$	−29.9462			−1.00777			−0.503884	−	0.863771i	$-0.668096\pi$
$883$	−29.9462			−1.00777			−0.503884	+	0.863771i	$0.668096\pi$
$884$		0			0
$885$	−14.7342	−	3.02957i	−0.495286	−	0.101838i
$886$		0			0
$887$	−5.89821	+	10.2160i	−0.198043	+	0.343020i	−0.947894	−	0.318587i	$-0.896792\pi$
$887$	−5.89821	+	10.2160i	−0.198043	+	0.343020i	0.749851	+	0.661607i	$0.230125\pi$
$888$		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
$893$	−16.1876	+	9.34591i	−0.541697	+	0.312749i
$894$		0			0
$895$		−	11.4723i		−	0.383478i
$896$		0			0
$897$	−28.4622	+	32.0364i	−0.950324	+	1.06966i
$898$		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
$903$	−4.03778	−	18.1777i	−0.134369	−	0.604917i
$904$		0			0
$905$	−5.11907	−	2.95550i	−0.170164	−	0.0982440i
$906$		0			0
$907$	14.2455	+	24.6739i	0.473014	+	0.819284i	0.999523	−	0.0308855i	$-0.00983273\pi$
$907$	14.2455	+	24.6739i	0.473014	+	0.819284i	−0.526509	+	0.850169i	$0.676499\pi$
$908$		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
$913$	−19.4979	+	11.2571i	−0.645285	+	0.372555i
$914$		0			0
$915$	3.13744	−	1.04254i	0.103721	−	0.0344652i
$916$		0			0
$917$	23.5728	+	2.41831i	0.778442	+	0.0798597i
$918$		0			0
$919$	2.83403	−	4.90869i	0.0934861	−	0.161923i	−0.815490	−	0.578772i	$-0.803532\pi$
$919$	2.83403	−	4.90869i	0.0934861	−	0.161923i	0.908976	+	0.416849i	$0.136866\pi$
$920$		0			0
$921$	−4.12433	+	20.0585i	−0.135901	+	0.660950i
$922$		0			0
$923$	−16.7200			−0.550346
$924$		0			0
$925$	3.85090			0.126617
$926$		0			0
$927$	1.10632	+	1.48088i	0.0363362	+	0.0486385i
$928$		0			0
$929$	8.51159	−	14.7425i	0.279256	−	0.483686i	−0.691944	−	0.721951i	$-0.743245\pi$
$929$	8.51159	−	14.7425i	0.279256	−	0.483686i	0.971200	+	0.238265i	$0.0765788\pi$
$930$		0			0
$931$	−21.8496	+	7.21979i	−0.716092	+	0.236619i
$932$		0			0
$933$	−12.2004	−	36.7163i	−0.399424	−	1.20204i
$934$		0			0
$935$	6.72322	−	3.88165i	0.219873	−	0.126944i
$936$		0			0
$937$			11.1936i			0.365678i	0.983143	+	0.182839i	$0.0585287\pi$
$937$			11.1936i			0.365678i	−0.983143	+	0.182839i	$0.941471\pi$
$938$		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
$943$	16.2036	+	9.35513i	0.527661	+	0.304645i
$944$		0			0
$945$	−10.4204	−	8.96746i	−0.338976	−	0.291711i
$946$		0			0
$947$	24.7743	+	14.3035i	0.805057	+	0.464800i	0.845236	−	0.534393i	$-0.179460\pi$
$947$	24.7743	+	14.3035i	0.805057	+	0.464800i	−0.0401795	+	0.999192i	$0.512793\pi$
$948$		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
$953$		−	45.2210i		−	1.46485i	−0.680846	−	0.732426i	$-0.738388\pi$
$953$		−	45.2210i		−	1.46485i	0.680846	−	0.732426i	$-0.261612\pi$
$954$		0			0
$955$	9.15764	−	5.28716i	0.296334	−	0.171089i
$956$		0			0
$957$	4.19893	+	12.6364i	0.135732	+	0.408477i
$958$		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
$963$	−31.7981	−	42.5640i	−1.02468	−	1.37161i
$964$		0			0
$965$	−12.0646			−0.388374
$966$		0			0
$967$	−54.5961			−1.75569			−0.877846	−	0.478943i	$-0.841020\pi$
$967$	−54.5961			−1.75569			−0.877846	+	0.478943i	$0.841020\pi$
$968$		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
$973$	48.6600	−	21.8101i	1.55997	−	0.699198i
$974$		0			0
$975$	−8.12466	+	2.69973i	−0.260197	+	0.0864607i
$976$		0			0
$977$	7.94835	−	4.58898i	0.254290	−	0.146815i	−0.367437	−	0.930048i	$-0.619765\pi$
$977$	7.94835	−	4.58898i	0.254290	−	0.146815i	0.621727	+	0.783234i	$0.286431\pi$
$978$		0			0
$979$			21.8523i			0.698403i
$980$		0			0
$981$	0.604246	+	5.09599i	0.0192921	+	0.162703i
$982$		0			0
$983$	8.29768	+	14.3720i	0.264655	+	0.458396i	0.967473	−	0.252974i	$-0.0814086\pi$
$983$	8.29768	+	14.3720i	0.264655	+	0.458396i	−0.702818	+	0.711369i	$0.748075\pi$
$984$		0			0
$985$	14.9323	+	8.62114i	0.475781	+	0.274692i
$986$		0			0
$987$	24.8536	+	7.82504i	0.791099	+	0.249074i
$988$		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
$993$	2.27735	−	2.56334i	0.0722696	−	0.0813450i
$994$		0			0
$995$		−	2.84518i		−	0.0901983i
$996$		0			0
$997$	12.7670	−	7.37103i	0.404335	−	0.233443i	−0.284018	−	0.958819i	$-0.591667\pi$
$997$	12.7670	−	7.37103i	0.404335	−	0.233443i	0.688353	+	0.725376i	$0.258334\pi$
$998$		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	420.2.bh.b.341.5	yes	10
3.2	odd	2		420.2.bh.a.341.4	yes	10
5.2	odd	4		2100.2.bo.g.1349.6		20
5.3	odd	4		2100.2.bo.g.1349.5		20
5.4	even	2		2100.2.bi.j.1601.1		10
7.2	even	3		2940.2.d.a.881.4		10
7.3	odd	6		420.2.bh.a.101.4	✓	10
7.5	odd	6		2940.2.d.b.881.7		10
15.2	even	4		2100.2.bo.h.1349.2		20
15.8	even	4		2100.2.bo.h.1349.9		20
15.14	odd	2		2100.2.bi.k.1601.2		10
21.2	odd	6		2940.2.d.b.881.8		10
21.5	even	6		2940.2.d.a.881.3		10
21.17	even	6	inner	420.2.bh.b.101.5	yes	10
35.3	even	12		2100.2.bo.h.1949.2		20
35.17	even	12		2100.2.bo.h.1949.9		20
35.24	odd	6		2100.2.bi.k.101.2		10
105.17	odd	12		2100.2.bo.g.1949.5		20
105.38	odd	12		2100.2.bo.g.1949.6		20
105.59	even	6		2100.2.bi.j.101.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.4	✓	10	7.3	odd	6
420.2.bh.a.341.4	yes	10	3.2	odd	2
420.2.bh.b.101.5	yes	10	21.17	even	6	inner
420.2.bh.b.341.5	yes	10	1.1	even	1	trivial
2100.2.bi.j.101.1		10	105.59	even	6
2100.2.bi.j.1601.1		10	5.4	even	2
2100.2.bi.k.101.2		10	35.24	odd	6
2100.2.bi.k.1601.2		10	15.14	odd	2
2100.2.bo.g.1349.5		20	5.3	odd	4
2100.2.bo.g.1349.6		20	5.2	odd	4
2100.2.bo.g.1949.5		20	105.17	odd	12
2100.2.bo.g.1949.6		20	105.38	odd	12
2100.2.bo.h.1349.2		20	15.2	even	4
2100.2.bo.h.1349.9		20	15.8	even	4
2100.2.bo.h.1949.2		20	35.3	even	12
2100.2.bo.h.1949.9		20	35.17	even	12
2940.2.d.a.881.3		10	21.5	even	6
2940.2.d.a.881.4		10	7.2	even	3
2940.2.d.b.881.7		10	7.5	odd	6
2940.2.d.b.881.8		10	21.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.69656 + 0.348838i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.08214 - 2.41433i) q^{7} +(2.75662 + 1.18365i) q^{9} +O(q^{10})\)	\(q+(1.69656 + 0.348838i) q^{3} +(0.500000 - 0.866025i) q^{5} +(-1.08214 - 2.41433i) q^{7} +(2.75662 + 1.18365i) q^{9} +(1.17086 - 0.675999i) q^{11} -4.94296i q^{13} +(1.15038 - 1.29484i) q^{15} +(2.87105 + 4.97280i) q^{17} +(2.84694 + 1.64368i) q^{19} +(-0.993697 - 4.47354i) q^{21} +(-4.33480 - 2.50270i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(4.26388 + 2.96974i) q^{27} +5.68630i q^{29} +(-2.45160 + 1.41543i) q^{31} +(2.22225 - 0.738430i) q^{33} +(-2.63194 - 0.270008i) q^{35} +(-1.92545 + 3.33498i) q^{37} +(1.72429 - 8.38603i) q^{39} -3.73802 q^{41} +4.06339 q^{43} +(2.40338 - 1.79548i) q^{45} +(-2.84298 + 4.92419i) q^{47} +(-4.65797 + 5.22526i) q^{49} +(3.13620 + 9.43818i) q^{51} +(1.26574 - 0.730773i) q^{53} -1.35200i q^{55} +(4.25662 + 3.78172i) q^{57} +(-4.34239 - 7.52123i) q^{59} +(1.65306 + 0.954394i) q^{61} +(-0.125326 - 7.93626i) q^{63} +(-4.28073 - 2.47148i) q^{65} +(-2.51939 - 4.36371i) q^{67} +(-6.48121 - 5.75812i) q^{69} -3.38259i q^{71} +(14.1398 - 8.16364i) q^{73} +(-0.546177 - 1.64368i) q^{75} +(-2.89912 - 2.09533i) q^{77} +(-2.41693 + 4.18625i) q^{79} +(6.19796 + 6.52574i) q^{81} -16.6525 q^{83} +5.74210 q^{85} +(-1.98359 + 9.64714i) q^{87} +(-8.08150 + 13.9976i) q^{89} +(-11.9339 + 5.34895i) q^{91} +(-4.65303 + 1.54615i) q^{93} +(2.84694 - 1.64368i) q^{95} +12.0577i q^{97} +(4.02778 - 0.477584i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9	\( 10 q + q^{3} + 5 q^{5} - 5 q^{7} + 3 q^{9} + 6 q^{11} + 2 q^{15} - 6 q^{17} + 3 q^{19} + 12 q^{21} - 24 q^{23} - 5 q^{25} - 8 q^{27} + 15 q^{31} - 4 q^{33} - q^{35} - q^{37} - 21 q^{39} + 8 q^{41} - 26 q^{43} + 3 q^{45} - 14 q^{47} - 13 q^{49} + 40 q^{51} + 24 q^{53} + 18 q^{57} + 42 q^{61} - 49 q^{63} - 9 q^{65} + 7 q^{67} + 14 q^{69} - 3 q^{73} + q^{75} + 26 q^{77} + q^{79} - 13 q^{81} + 8 q^{83} - 12 q^{85} + 8 q^{87} - 28 q^{89} - 11 q^{91} + 25 q^{93} + 3 q^{95} + 36 q^{99}+O(q^{100}) \) 10 * q + q^3 + 5 * q^5 - 5 * q^7 + 3 * q^9 + 6 * q^11 + 2 * q^15 - 6 * q^17 + 3 * q^19 + 12 * q^21 - 24 * q^23 - 5 * q^25 - 8 * q^27 + 15 * q^31 - 4 * q^33 - q^35 - q^37 - 21 * q^39 + 8 * q^41 - 26 * q^43 + 3 * q^45 - 14 * q^47 - 13 * q^49 + 40 * q^51 + 24 * q^53 + 18 * q^57 + 42 * q^61 - 49 * q^63 - 9 * q^65 + 7 * q^67 + 14 * q^69 - 3 * q^73 + q^75 + 26 * q^77 + q^79 - 13 * q^81 + 8 * q^83 - 12 * q^85 + 8 * q^87 - 28 * q^89 - 11 * q^91 + 25 * q^93 + 3 * q^95 + 36 * q^99

Introduction

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