LMFDB - Embedded newform 420.2.bh.b.101.5

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			101.5
Root			$1.15038 + 1.29484i$ of defining polynomial
Character	$\chi$	$=$	420.101
Dual form			420.2.bh.b.341.5

$q$-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 $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

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

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	0.666018	−	0.745935i	$-0.267997\pi$
$11$	1.17086	+	0.675999i	0.353029	+	0.203821i	−0.312990	+	0.949757i	$0.601331\pi$
$12$		0			0
$13$			4.94296i			1.37093i	0.728105	+	0.685466i	$0.240401\pi$
$13$			4.94296i			1.37093i	−0.728105	+	0.685466i	$0.759599\pi$
$14$		0			0
$15$	1.15038	+	1.29484i	0.297027	+	0.334327i
$16$		0			0
$17$	2.87105	−	4.97280i	0.696332	−	1.20608i	−0.273398	−	0.961901i	$-0.588148\pi$
$17$	2.87105	−	4.97280i	0.696332	−	1.20608i	0.969730	−	0.244181i	$-0.0785190\pi$
$18$		0			0
$19$	2.84694	−	1.64368i	0.653133	−	0.377087i	−0.136523	−	0.990637i	$-0.543593\pi$
$19$	2.84694	−	1.64368i	0.653133	−	0.377087i	0.789656	+	0.613550i	$0.210259\pi$
$20$		0			0
$21$	−0.993697	+	4.47354i	−0.216842	+	0.976207i
$22$		0			0
$23$	−4.33480	+	2.50270i	−0.903868	+	0.521849i	−0.878453	−	0.477828i	$-0.841424\pi$
$23$	−4.33480	+	2.50270i	−0.903868	+	0.521849i	−0.0254150	+	0.999677i	$0.508091\pi$
$24$		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	$-0.822957\pi$
$29$		−	5.68630i		−	1.05592i	0.849270	−	0.527959i	$-0.177043\pi$
$30$		0			0
$31$	−2.45160	−	1.41543i	−0.440320	−	0.254219i	0.263414	−	0.964683i	$-0.415152\pi$
$31$	−2.45160	−	1.41543i	−0.440320	−	0.254219i	−0.703733	+	0.710464i	$0.748485\pi$
$32$		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	0.663222	−	0.748423i	$-0.269189\pi$
$37$	−1.92545	−	3.33498i	−0.316542	−	0.548267i	−0.979764	+	0.200156i	$0.935855\pi$
$38$		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	0.580705	−	0.814114i	$-0.302777\pi$
$47$	−2.84298	−	4.92419i	−0.414691	−	0.718266i	−0.995396	+	0.0958478i	$0.969444\pi$
$48$		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	0.584406	−	0.811462i	$-0.301328\pi$
$53$	1.26574	+	0.730773i	0.173862	+	0.100379i	−0.410544	+	0.911841i	$0.634661\pi$
$54$		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	0.431688	+	0.902023i	$0.357918\pi$
$59$	−4.34239	+	7.52123i	−0.565330	+	0.979181i	−0.997019	+	0.0771582i	$0.975415\pi$
$60$		0			0
$61$	1.65306	−	0.954394i	0.211653	−	0.122198i	−0.390427	−	0.920634i	$-0.627672\pi$
$61$	1.65306	−	0.954394i	0.211653	−	0.122198i	0.602079	+	0.798436i	$0.294339\pi$
$62$		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	−0.977879	−	0.209170i	$-0.932924\pi$
$67$	−2.51939	+	4.36371i	−0.307793	+	0.533113i	0.670086	+	0.742283i	$0.266257\pi$
$68$		0			0
$69$	−6.48121	+	5.75812i	−0.780246	+	0.693196i
$70$		0			0
$71$			3.38259i			0.401440i	0.979649	+	0.200720i	$0.0643281\pi$
$71$			3.38259i			0.401440i	−0.979649	+	0.200720i	$0.935672\pi$
$72$		0			0
$73$	14.1398	+	8.16364i	1.65494	+	0.955481i	0.974997	+	0.222218i	$0.0713298\pi$
$73$	14.1398	+	8.16364i	1.65494	+	0.955481i	0.679945	+	0.733263i	$0.262004\pi$
$74$		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	0.697429	−	0.716654i	$-0.254327\pi$
$79$	−2.41693	−	4.18625i	−0.271926	−	0.470990i	−0.969355	+	0.245664i	$0.920994\pi$
$80$		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	−0.875118	−	0.483909i	$-0.839216\pi$
$89$	−8.08150	−	13.9976i	−0.856637	−	1.48374i	0.0184813	−	0.999829i	$-0.494117\pi$
$90$		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	$-0.790310\pi$
$97$		−	12.0577i		−	1.22427i	0.790751	−	0.612137i	$-0.209690\pi$
$98$		0			0
$99$	4.02778	+	0.477584i	0.404807	+	0.0479990i
$100$		0			0
$101$	9.01683	−	15.6176i	0.897208	−	1.55401i	0.0661605	−	0.997809i	$-0.478925\pi$
$101$	9.01683	−	15.6176i	0.897208	−	1.55401i	0.831048	−	0.556201i	$-0.187742\pi$
$102$		0			0
$103$	0.533615	−	0.308083i	0.0525787	−	0.0303563i	−0.473480	−	0.880804i	$-0.657002\pi$
$103$	0.533615	−	0.308083i	0.0525787	−	0.0303563i	0.526059	+	0.850448i	$0.323669\pi$
$104$		0			0
$105$	−4.37105	+	1.37620i	−0.426571	+	0.134304i
$106$		0			0
$107$	−15.3374	+	8.85503i	−1.48272	+	0.856048i	−0.999807	−	0.0196209i	$-0.993754\pi$
$107$	−15.3374	+	8.85503i	−1.48272	+	0.856048i	−0.482912	+	0.875669i	$0.660421\pi$
$108$		0			0
$109$	0.855282	−	1.48139i	0.0819211	−	0.141892i	−0.822154	−	0.569265i	$-0.807228\pi$
$109$	0.855282	−	1.48139i	0.0819211	−	0.141892i	0.904075	+	0.427374i	$0.140561\pi$
$110$		0			0
$111$	−4.43001	−	4.98632i	−0.420478	−	0.473280i
$112$		0			0
$113$			13.1214i			1.23436i	0.786822	+	0.617180i	$0.211725\pi$
$113$			13.1214i			1.23436i	−0.786822	+	0.617180i	$0.788275\pi$
$114$		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	0.601353	−	0.798984i	$-0.294629\pi$
$131$	−4.47822	−	7.75651i	−0.391264	−	0.677689i	−0.992617	+	0.121295i	$0.961295\pi$
$132$		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	0.947724	−	0.319092i	$-0.103378\pi$
$137$	13.4047	+	7.73923i	1.14524	+	0.661207i	0.197520	+	0.980299i	$0.436711\pi$
$138$		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
$143$	−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	−0.550307	−	0.834963i	$-0.685489\pi$
$149$	−1.24947	+	0.721384i	−0.102361	+	0.0590981i	0.447946	+	0.894061i	$0.352156\pi$
$150$		0			0
$151$	−8.12108	+	14.0661i	−0.660884	+	1.14468i	0.319500	+	0.947586i	$0.396485\pi$
$151$	−8.12108	+	14.0661i	−0.660884	+	1.14468i	−0.980384	+	0.197098i	$0.936848\pi$
$152$		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	0.973173	−	0.230073i	$-0.0738965\pi$
$157$	15.7942	+	9.11876i	1.26051	+	0.727756i	0.287338	+	0.957829i	$0.407230\pi$
$158$		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	0.739592	+	0.673055i	$0.235018\pi$
$163$	12.1630	+	21.0669i	0.952679	+	1.65009i	0.213087	+	0.977033i	$0.431648\pi$
$164$		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	−0.997124	−	0.0757927i	$-0.975851\pi$
$173$	−7.42089	−	12.8534i	−0.564200	−	0.977223i	0.432923	−	0.901431i	$-0.357482\pi$
$174$		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	0.823015	−	0.568020i	$-0.192291\pi$
$179$	9.93533	+	5.73617i	0.742602	+	0.428741i	−0.0804127	+	0.996762i	$0.525624\pi$
$180$		0			0
$181$			5.91099i			0.439361i	0.975572	+	0.219680i	$0.0705014\pi$
$181$			5.91099i			0.439361i	−0.975572	+	0.219680i	$0.929499\pi$
$182$		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	−0.130652	−	0.991428i	$-0.541707\pi$
$191$	9.15764	−	5.28716i	0.662623	−	0.382566i	0.793276	+	0.608862i	$0.208374\pi$
$192$		0			0
$193$	−6.03231	+	10.4483i	−0.434215	+	0.752082i	−0.997231	−	0.0743635i	$-0.976307\pi$
$193$	−6.03231	+	10.4483i	−0.434215	+	0.752082i	0.563016	+	0.826446i	$0.309641\pi$
$194$		0			0
$195$	−6.40037	+	5.68630i	−0.458340	+	0.407204i
$196$		0			0
$197$		−	17.2423i		−	1.22846i	−0.789126	−	0.614231i	$-0.789466\pi$
$197$		−	17.2423i		−	1.22846i	0.789126	−	0.614231i	$-0.210534\pi$
$198$		0			0
$199$	2.46400	+	1.42259i	0.174668	+	0.100845i	0.584785	−	0.811188i	$-0.301179\pi$
$199$	2.46400	+	1.42259i	0.174668	+	0.100845i	−0.410117	+	0.912033i	$0.634512\pi$
$200$		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	$0.0565294\pi$
$223$			5.27620i			0.353321i	−0.984272	+	0.176660i	$0.943471\pi$
$224$		0			0
$225$	−0.353244	+	2.97913i	−0.0235496	+	0.198609i
$226$		0			0
$227$	6.24055	−	10.8090i	0.414200	−	0.717416i	−0.581144	−	0.813801i	$-0.697395\pi$
$227$	6.24055	−	10.8090i	0.414200	−	0.717416i	0.995344	+	0.0963851i	$0.0307280\pi$
$228$		0			0
$229$	−14.0882	+	8.13380i	−0.930971	+	0.537496i	−0.887119	−	0.461542i	$-0.847297\pi$
$229$	−14.0882	+	8.13380i	−0.930971	+	0.537496i	−0.0438526	+	0.999038i	$0.513963\pi$
$230$		0			0
$231$	−4.18759	+	4.56617i	−0.275523	+	0.300432i
$232$		0			0
$233$	7.64788	−	4.41551i	0.501029	−	0.289269i	−0.228109	−	0.973636i	$-0.573254\pi$
$233$	7.64788	−	4.41551i	0.501029	−	0.289269i	0.729139	+	0.684366i	$0.239921\pi$
$234$		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	$0.130603\pi$
$239$			12.3333i			0.797773i	−0.917000	+	0.398886i	$0.869397\pi$
$240$		0			0
$241$	6.88815	+	3.97688i	0.443705	+	0.256173i	0.705168	−	0.709040i	$-0.250872\pi$
$241$	6.88815	+	3.97688i	0.443705	+	0.256173i	−0.261463	+	0.965214i	$0.584205\pi$
$242$		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	0.874247	+	0.485482i	$0.161356\pi$
$257$	13.7478	+	23.8118i	0.857563	+	1.48534i	−0.0166841	+	0.999861i	$0.505311\pi$
$258$		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	0.912890	−	0.408206i	$-0.133845\pi$
$263$	16.4738	+	9.51115i	1.01582	+	0.586483i	0.102928	+	0.994689i	$0.467179\pi$
$264$		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	−0.697421	−	0.716662i	$-0.745669\pi$
$269$	4.46010	−	7.72512i	0.271937	−	0.471009i	0.969358	+	0.245653i	$0.0790024\pi$
$270$		0			0
$271$	6.53123	−	3.77081i	0.396744	−	0.229060i	−0.288334	−	0.957530i	$-0.593101\pi$
$271$	6.53123	−	3.77081i	0.396744	−	0.229060i	0.685078	+	0.728470i	$0.259768\pi$
$272$		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	−0.838096	−	0.545523i	$-0.816331\pi$
$277$	0.888562	−	1.53903i	0.0533885	−	0.0924716i	0.891485	+	0.453051i	$0.149664\pi$
$278$		0			0
$279$	−8.43350	−	0.999983i	−0.504900	−	0.0598674i
$280$		0			0
$281$			25.3819i			1.51416i	0.653324	+	0.757079i	$0.273374\pi$
$281$			25.3819i			1.51416i	−0.653324	+	0.757079i	$0.726626\pi$
$282$		0			0
$283$	−13.9774	−	8.06987i	−0.830872	−	0.479704i	0.0232795	−	0.999729i	$-0.492589\pi$
$283$	−13.9774	−	8.06987i	−0.830872	−	0.479704i	−0.854151	+	0.520025i	$0.825923\pi$
$284$		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	$-0.890456\pi$
$307$		−	11.8231i		−	0.674777i	0.941365	−	0.337389i	$-0.109544\pi$
$308$		0			0
$309$	0.797839	−	0.708826i	0.0453875	−	0.0403237i
$310$		0			0
$311$	−11.1689	+	19.3451i	−0.633331	+	1.09696i	0.353535	+	0.935421i	$0.384980\pi$
$311$	−11.1689	+	19.3451i	−0.633331	+	1.09696i	−0.986866	+	0.161540i	$0.948354\pi$
$312$		0			0
$313$	−11.5250	+	6.65398i	−0.651433	+	0.376105i	−0.789005	−	0.614387i	$-0.789404\pi$
$313$	−11.5250	+	6.65398i	−0.651433	+	0.376105i	0.137572	+	0.990492i	$0.456070\pi$
$314$		0			0
$315$	−6.93567	+	3.85960i	−0.390781	+	0.217464i
$316$		0			0
$317$	−29.3395	+	16.9392i	−1.64787	+	0.951400i	−0.669958	+	0.742399i	$0.733688\pi$
$317$	−29.3395	+	16.9392i	−1.64787	+	0.951400i	−0.977915	+	0.209001i	$0.932979\pi$
$318$		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	0.891946	−	0.452143i	$-0.149340\pi$
$331$	0.989824	+	1.71443i	0.0544057	+	0.0942334i	−0.837540	+	0.546376i	$0.816007\pi$
$332$		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	0.118779	−	0.992921i	$-0.462102\pi$
$347$	−12.6992	−	7.33186i	−0.681726	−	0.393595i	−0.800505	+	0.599326i	$0.795435\pi$
$348$		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
$353$	3.88365	−	6.72669i	0.206706	−	0.358025i	−0.743969	−	0.668214i	$-0.767059\pi$
$353$	3.88365	−	6.72669i	0.206706	−	0.358025i	0.950675	+	0.310189i	$0.100392\pi$
$354$		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	−0.598625	−	0.801030i	$-0.704286\pi$
$359$	−3.86952	+	2.23407i	−0.204225	+	0.117910i	0.394399	+	0.918939i	$0.370953\pi$
$360$		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	0.537591	−	0.843206i	$-0.319334\pi$
$367$	1.45880	+	0.842240i	0.0761489	+	0.0439646i	−0.461442	+	0.887170i	$0.652668\pi$
$368$		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	0.629235	−	0.777215i	$-0.283368\pi$
$373$	−6.92322	−	11.9914i	−0.358471	−	0.620890i	−0.987706	+	0.156325i	$0.950035\pi$
$374$		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	0.814406	−	0.580295i	$-0.197063\pi$
$383$	−1.86598	−	3.23197i	−0.0953471	−	0.165146i	−0.909753	+	0.415149i	$0.863729\pi$
$384$		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	0.165430	−	0.986222i	$-0.447099\pi$
$389$	−11.9512	−	6.90001i	−0.605948	−	0.349844i	−0.771378	+	0.636377i	$0.780432\pi$
$390$		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	−0.811321	−	0.584601i	$-0.801251\pi$
$397$	−14.1606	+	8.17565i	−0.710702	+	0.410324i	0.100619	+	0.994925i	$0.467918\pi$
$398$		0			0
$399$	4.52408	+	14.3692i	0.226487	+	0.719361i
$400$		0			0
$401$	−11.9669	+	6.90910i	−0.597599	+	0.345024i	−0.768096	−	0.640334i	$-0.778796\pi$
$401$	−11.9669	+	6.90910i	−0.597599	+	0.345024i	0.170497	+	0.985358i	$0.445463\pi$
$402$		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	0.281406	−	0.959589i	$-0.409199\pi$
$409$	−8.26987	−	4.77461i	−0.408919	−	0.236089i	−0.690325	+	0.723499i	$0.742533\pi$
$410$		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	0.461642	−	0.887066i	$-0.347260\pi$
$431$	−1.57279	−	0.908052i	−0.0757587	−	0.0437393i	−0.537401	+	0.843327i	$0.680594\pi$
$432$		0			0
$433$			10.6773i			0.513117i	0.966529	+	0.256558i	$0.0825886\pi$
$433$			10.6773i			0.513117i	−0.966529	+	0.256558i	$0.917411\pi$
$434$		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	0.297588	−	0.954694i	$-0.403818\pi$
$439$	26.6759	−	15.4013i	1.27317	−	0.735066i	0.975584	+	0.219628i	$0.0704845\pi$
$440$		0			0
$441$	−19.0251	−	8.89069i	−0.905959	−	0.423366i
$442$		0			0
$443$	−14.3178	+	8.26640i	−0.680260	+	0.392749i	−0.799953	−	0.600062i	$-0.795142\pi$
$443$	−14.3178	+	8.26640i	−0.680260	+	0.392749i	0.119693	+	0.992811i	$0.461809\pi$
$444$		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	$-0.980527\pi$
$449$		−	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
$453$	−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	0.999765	+	0.0216672i	$0.00689744\pi$
$457$	11.0874	+	19.2040i	0.518647	+	0.898323i	−0.481118	+	0.876656i	$0.659769\pi$
$458$		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	−0.923534	−	0.383515i	$-0.874713\pi$
$467$	−17.1564	−	29.7157i	−0.793901	−	1.37508i	0.129633	−	0.991562i	$-0.458620\pi$
$468$		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	−0.998199	−	0.0599923i	$-0.980892\pi$
$479$	−9.78624	+	16.9503i	−0.447145	+	0.774477i	0.551054	+	0.834469i	$0.314226\pi$
$480$		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	0.424844	+	0.905266i	$0.360329\pi$
$487$	−12.6133	+	21.8468i	−0.571561	+	0.989973i	−0.996406	+	0.0847071i	$0.973005\pi$
$488$		0			0
$489$	27.9842	+	31.4984i	1.26549	+	1.42441i
$490$		0			0
$491$			38.6556i			1.74450i	0.489057	+	0.872252i	$0.337341\pi$
$491$			38.6556i			1.74450i	−0.489057	+	0.872252i	$0.662659\pi$
$492$		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	0.796274	−	0.604936i	$-0.206801\pi$
$499$	−2.80910	−	4.86551i	−0.125753	−	0.217810i	−0.922027	+	0.387126i	$0.873468\pi$
$500$		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	0.976445	+	0.215767i	$0.0692253\pi$
$509$	15.2306	+	26.3801i	0.675082	+	1.16928i	−0.301362	+	0.953510i	$0.597441\pi$
$510$		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	−0.999210	−	0.0397366i	$-0.987348\pi$
$521$	−10.6182	+	18.3913i	−0.465192	+	0.805737i	0.534018	+	0.845473i	$0.320681\pi$
$522$		0			0
$523$	−10.7227	+	6.19077i	−0.468872	+	0.270704i	−0.715768	−	0.698339i	$-0.753923\pi$
$523$	−10.7227	+	6.19077i	−0.468872	+	0.270704i	0.246895	+	0.969042i	$0.420590\pi$
$524$		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	0.677721	−	0.735319i	$-0.262968\pi$
$541$	−6.93001	−	12.0031i	−0.297944	−	0.516055i	−0.975665	+	0.219264i	$0.929634\pi$
$542$		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	0.562438	−	0.826840i	$-0.309864\pi$
$557$	3.01129	+	1.73857i	0.127593	+	0.0736656i	−0.434845	+	0.900505i	$0.643197\pi$
$558$		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	−0.964648	−	0.263541i	$-0.915110\pi$
$563$	−6.02897	+	10.4425i	−0.254091	+	0.440098i	0.710557	+	0.703639i	$0.248443\pi$
$564$		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	−0.726628	−	0.687031i	$-0.758913\pi$
$569$	−11.8065	+	6.81650i	−0.494955	+	0.285762i	0.231673	+	0.972794i	$0.425580\pi$
$570$		0			0
$571$	22.0474	−	38.1873i	0.922657	−	1.59809i	0.127369	−	0.991855i	$-0.459347\pi$
$571$	22.0474	−	38.1873i	0.922657	−	1.59809i	0.795287	−	0.606233i	$-0.207320\pi$
$572$		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	0.368504	−	0.929626i	$-0.379870\pi$
$577$	−6.06103	−	3.49934i	−0.252324	−	0.145679i	−0.620828	+	0.783947i	$0.713203\pi$
$578$		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	0.505451	−	0.862855i	$-0.331326\pi$
$593$	−12.0426	−	20.8583i	−0.494529	−	0.856549i	−0.999980	+	0.00630583i	$0.997993\pi$
$594$		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	0.391134	−	0.920334i	$-0.372083\pi$
$599$	−5.14773	−	2.97205i	−0.210331	−	0.121434i	−0.601465	+	0.798899i	$0.705416\pi$
$600$		0			0
$601$			46.9992i			1.91714i	0.284863	+	0.958568i	$0.408052\pi$
$601$			46.9992i			1.91714i	−0.284863	+	0.958568i	$0.591948\pi$
$602$		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	−0.664521	−	0.747270i	$-0.731364\pi$
$607$	−8.61387	+	4.97322i	−0.349626	+	0.201857i	0.314894	+	0.949127i	$0.398031\pi$
$608$		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	−0.324014	−	0.946052i	$-0.605033\pi$
$613$	16.2739	−	28.1873i	0.657298	−	1.13847i	0.981312	−	0.192421i	$-0.0616340\pi$
$614$		0			0
$615$	−4.30015	−	4.84015i	−0.173399	−	0.195174i
$616$		0			0
$617$			7.69843i			0.309927i	0.987920	+	0.154964i	$0.0495260\pi$
$617$			7.69843i			0.309927i	−0.987920	+	0.154964i	$0.950474\pi$
$618$		0			0
$619$	2.76170	+	1.59447i	0.111002	+	0.0640872i	0.554473	−	0.832202i	$-0.312920\pi$
$619$	2.76170	+	1.59447i	0.111002	+	0.0640872i	−0.443471	+	0.896289i	$0.646253\pi$
$620$		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	−0.0494573	−	0.998776i	$-0.515749\pi$
$641$	−23.7774	−	13.7279i	−0.939152	−	0.542219i	−0.889694	+	0.456557i	$0.849083\pi$
$642$		0			0
$643$			29.0919i			1.14727i	0.819110	+	0.573637i	$0.194468\pi$
$643$			29.0919i			1.14727i	−0.819110	+	0.573637i	$0.805532\pi$
$644$		0			0
$645$	4.67445	+	5.26145i	0.184056	+	0.207170i
$646$		0			0
$647$	−21.5999	+	37.4122i	−0.849181	+	1.47082i	0.0327597	+	0.999463i	$0.489570\pi$
$647$	−21.5999	+	37.4122i	−0.849181	+	1.47082i	−0.881940	+	0.471361i	$0.843763\pi$
$648$		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	−0.617665	−	0.786441i	$-0.711921\pi$
$653$	−6.27142	+	3.62080i	−0.245420	+	0.141693i	0.372246	+	0.928134i	$0.378588\pi$
$654$		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	$0.0328755\pi$
$659$			5.29324i			0.206196i	−0.994671	+	0.103098i	$0.967125\pi$
$660$		0			0
$661$	43.2638	+	24.9783i	1.68276	+	0.971545i	0.959810	+	0.280649i	$0.0905497\pi$
$661$	43.2638	+	24.9783i	1.68276	+	0.971545i	0.722954	+	0.690896i	$0.242784\pi$
$662$		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	0.703208	−	0.710984i	$-0.251750\pi$
$677$	−6.87236	−	11.9033i	−0.264126	−	0.457480i	−0.967334	+	0.253504i	$0.918417\pi$
$678$		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	−0.425243	−	0.905079i	$-0.639811\pi$
$683$	−37.1547	−	21.4513i	−1.42169	−	0.820811i	−0.996443	+	0.0842682i	$0.973145\pi$
$684$		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	−0.837045	−	0.547134i	$-0.815719\pi$
$691$	−20.5494	+	11.8642i	−0.781735	+	0.451335i	0.0553098	+	0.998469i	$0.482385\pi$
$692$		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	$-0.868413\pi$
$701$		−	21.2721i		−	0.803436i	0.915763	−	0.401718i	$-0.131587\pi$
$702$		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	0.875219	+	0.483727i	$0.160717\pi$
$709$	22.8069	+	39.5026i	0.856529	+	1.48355i	−0.0186897	+	0.999825i	$0.505949\pi$
$710$		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	0.632443	−	0.774607i	$-0.282052\pi$
$719$	−9.50850	−	16.4692i	−0.354607	−	0.614198i	−0.987051	+	0.160409i	$0.948719\pi$
$720$		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	$-0.782441\pi$
$727$		−	34.0540i		−	1.26299i	0.775379	−	0.631496i	$-0.217559\pi$
$728$		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	−0.618916	−	0.785457i	$-0.712428\pi$
$733$	−6.71837	+	3.87885i	−0.248148	+	0.143269i	0.370768	+	0.928726i	$0.379095\pi$
$734$		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	−0.778457	−	0.627698i	$-0.783997\pi$
$739$	4.19659	−	7.26871i	0.154374	−	0.267384i	0.932831	+	0.360314i	$0.117331\pi$
$740$		0			0
$741$	18.6929	+	21.0403i	0.686702	+	0.772936i
$742$		0			0
$743$			14.7540i			0.541273i	0.962682	+	0.270636i	$0.0872341\pi$
$743$			14.7540i			0.541273i	−0.962682	+	0.270636i	$0.912766\pi$
$744$		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	−0.946877	−	0.321595i	$-0.895781\pi$
$751$	−20.6067	−	35.6918i	−0.751948	−	1.30241i	0.194929	−	0.980817i	$-0.437552\pi$
$752$		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	0.984490	+	0.175441i	$0.0561351\pi$
$761$	17.7705	+	30.7795i	0.644181	+	1.11575i	−0.340309	+	0.940314i	$0.610532\pi$
$762$		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	$0.0359820\pi$
$769$			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
$773$	−10.0161	+	17.3483i	−0.360253	+	0.623977i	−0.988002	−	0.154439i	$-0.950643\pi$
$773$	−10.0161	+	17.3483i	−0.360253	+	0.623977i	0.627749	+	0.778416i	$0.283976\pi$
$774$		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	0.477043	−	0.878880i	$-0.341709\pi$
$787$	−1.27835	−	0.738053i	−0.0455681	−	0.0263088i	−0.522611	+	0.852571i	$0.675042\pi$
$788$		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	0.802764	−	0.596296i	$-0.203362\pi$
$809$	19.5613	+	11.2937i	0.687739	+	0.397066i	−0.115026	+	0.993363i	$0.536695\pi$
$810$		0			0
$811$		−	41.9366i		−	1.47259i	−0.676659	−	0.736296i	$-0.736573\pi$
$811$		−	41.9366i		−	1.47259i	0.676659	−	0.736296i	$-0.263427\pi$
$812$		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	−0.492179	−	0.870494i	$-0.663799\pi$
$821$	0.447025	−	0.258090i	0.0156013	−	0.00900741i	0.507780	+	0.861487i	$0.330466\pi$
$822$		0			0
$823$	10.2841	−	17.8125i	0.358480	−	0.620906i	−0.629227	−	0.777222i	$-0.716628\pi$
$823$	10.2841	−	17.8125i	0.358480	−	0.620906i	0.987707	+	0.156316i	$0.0499618\pi$
$824$		0			0
$825$	−1.75063	+	1.55531i	−0.0609490	+	0.0541491i
$826$		0			0
$827$		−	24.0587i		−	0.836603i	−0.908308	−	0.418301i	$-0.862626\pi$
$827$		−	24.0587i		−	0.836603i	0.908308	−	0.418301i	$-0.137374\pi$
$828$		0			0
$829$	−39.3074	−	22.6941i	−1.36520	−	0.788200i	−0.374891	−	0.927069i	$-0.622320\pi$
$829$	−39.3074	−	22.6941i	−1.36520	−	0.788200i	−0.990311	+	0.138869i	$0.955653\pi$
$830$		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	$0.0937172\pi$
$853$			16.9504i			0.580372i	−0.956970	+	0.290186i	$0.906283\pi$
$854$		0			0
$855$	9.79349	+	1.16124i	0.334930	+	0.0397136i
$856$		0			0
$857$	−0.315644	+	0.546711i	−0.0107822	+	0.0186753i	−0.871366	−	0.490633i	$-0.836765\pi$
$857$	−0.315644	+	0.546711i	−0.0107822	+	0.0186753i	0.860584	+	0.509309i	$0.170099\pi$
$858$		0			0
$859$	−5.59642	+	3.23109i	−0.190947	+	0.110243i	−0.592426	−	0.805625i	$-0.701830\pi$
$859$	−5.59642	+	3.23109i	−0.190947	+	0.110243i	0.401479	+	0.915868i	$0.368496\pi$
$860$		0			0
$861$	3.71446	−	16.7222i	0.126588	−	0.569891i
$862$		0			0
$863$	−6.31821	+	3.64782i	−0.215074	+	0.124173i	−0.603667	−	0.797236i	$-0.706295\pi$
$863$	−6.31821	+	3.64782i	−0.215074	+	0.124173i	0.388593	+	0.921409i	$0.372961\pi$
$864$		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	−0.999999	−	0.00144772i	$-0.999539\pi$
$877$	−14.8442	−	25.7109i	−0.501253	−	0.868196i	0.498746	−	0.866748i	$-0.333794\pi$
$878$		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	0.749851	−	0.661607i	$-0.230125\pi$
$887$	−5.89821	−	10.2160i	−0.198043	−	0.343020i	−0.947894	+	0.318587i	$0.896792\pi$
$888$		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	−0.526509	−	0.850169i	$-0.676499\pi$
$907$	14.2455	−	24.6739i	0.473014	−	0.819284i	0.999523	+	0.0308855i	$0.00983273\pi$
$908$		0			0
$909$	6.37028	−	53.7246i	0.211289	−	1.78193i
$910$		0			0
$911$			14.4884i			0.480023i	0.970770	+	0.240011i	$0.0771511\pi$
$911$			14.4884i			0.480023i	−0.970770	+	0.240011i	$0.922849\pi$
$912$		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	0.908976	−	0.416849i	$-0.136866\pi$
$919$	2.83403	+	4.90869i	0.0934861	+	0.161923i	−0.815490	+	0.578772i	$0.803532\pi$
$920$		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	0.971200	−	0.238265i	$-0.0765788\pi$
$929$	8.51159	+	14.7425i	0.279256	+	0.483686i	−0.691944	+	0.721951i	$0.743245\pi$
$930$		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	$-0.941471\pi$
$937$		−	11.1936i		−	0.365678i	0.983143	−	0.182839i	$-0.0585287\pi$
$938$		0			0
$939$	−17.2317	+	15.3092i	−0.562336	+	0.499598i
$940$		0			0
$941$	11.0101	−	19.0700i	0.358919	−	0.621665i	−0.628862	−	0.777517i	$-0.716479\pi$
$941$	11.0101	−	19.0700i	0.358919	−	0.621665i	0.987780	+	0.155852i	$0.0498122\pi$
$942$		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	−0.0401795	−	0.999192i	$-0.512793\pi$
$947$	24.7743	−	14.3035i	0.805057	−	0.464800i	0.845236	+	0.534393i	$0.179460\pi$
$948$		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	$0.261612\pi$
$953$			45.2210i			1.46485i	−0.680846	+	0.732426i	$0.738388\pi$
$954$		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	0.992476	−	0.122436i	$-0.0390706\pi$
$971$	12.1591	+	21.0603i	0.390206	+	0.675856i	−0.602271	+	0.798292i	$0.705737\pi$
$972$		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	0.621727	−	0.783234i	$-0.286431\pi$
$977$	7.94835	+	4.58898i	0.254290	+	0.146815i	−0.367437	+	0.930048i	$0.619765\pi$
$978$		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	−0.702818	−	0.711369i	$-0.748075\pi$
$983$	8.29768	−	14.3720i	0.264655	−	0.458396i	0.967473	+	0.252974i	$0.0814086\pi$
$984$		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	−0.976172	−	0.216996i	$-0.930374\pi$
$991$	−9.44914	+	16.3664i	−0.300162	+	0.519895i	0.676011	+	0.736892i	$0.263707\pi$
$992$		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	0.688353	−	0.725376i	$-0.258334\pi$
$997$	12.7670	+	7.37103i	0.404335	+	0.233443i	−0.284018	+	0.958819i	$0.591667\pi$
$998$		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.101.5	yes	10
3.2	odd	2		420.2.bh.a.101.4	✓	10
5.2	odd	4		2100.2.bo.g.1949.5		20
5.3	odd	4		2100.2.bo.g.1949.6		20
5.4	even	2		2100.2.bi.j.101.1		10
7.3	odd	6		2940.2.d.b.881.8		10
7.4	even	3		2940.2.d.a.881.3		10
7.5	odd	6		420.2.bh.a.341.4	yes	10
15.2	even	4		2100.2.bo.h.1949.9		20
15.8	even	4		2100.2.bo.h.1949.2		20
15.14	odd	2		2100.2.bi.k.101.2		10
21.5	even	6	inner	420.2.bh.b.341.5	yes	10
21.11	odd	6		2940.2.d.b.881.7		10
21.17	even	6		2940.2.d.a.881.4		10
35.12	even	12		2100.2.bo.h.1349.2		20
35.19	odd	6		2100.2.bi.k.1601.2		10
35.33	even	12		2100.2.bo.h.1349.9		20
105.47	odd	12		2100.2.bo.g.1349.6		20
105.68	odd	12		2100.2.bo.g.1349.5		20
105.89	even	6		2100.2.bi.j.1601.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bh.a.101.4	✓	10	3.2	odd	2
420.2.bh.a.341.4	yes	10	7.5	odd	6
420.2.bh.b.101.5	yes	10	1.1	even	1	trivial
420.2.bh.b.341.5	yes	10	21.5	even	6	inner
2100.2.bi.j.101.1		10	5.4	even	2
2100.2.bi.j.1601.1		10	105.89	even	6
2100.2.bi.k.101.2		10	15.14	odd	2
2100.2.bi.k.1601.2		10	35.19	odd	6
2100.2.bo.g.1349.5		20	105.68	odd	12
2100.2.bo.g.1349.6		20	105.47	odd	12
2100.2.bo.g.1949.5		20	5.2	odd	4
2100.2.bo.g.1949.6		20	5.3	odd	4
2100.2.bo.h.1349.2		20	35.12	even	12
2100.2.bo.h.1349.9		20	35.33	even	12
2100.2.bo.h.1949.2		20	15.8	even	4
2100.2.bo.h.1949.9		20	15.2	even	4
2940.2.d.a.881.3		10	7.4	even	3
2940.2.d.a.881.4		10	21.17	even	6
2940.2.d.b.881.7		10	21.11	odd	6
2940.2.d.b.881.8		10	7.3	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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more