LMFDB - Embedded newform 900.2.k.n.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(307,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 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("900.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.k (of order $4$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.1
Root			$-0.0912546 - 1.41127i$ of defining polynomial
Character	$\chi$	$=$	900.307
Dual form			900.2.k.n.343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41127 + 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.86678 + 1.86678i) q^{7} +(-2.77552 + 0.544488i) q^{8} +O(q^{10})$	\(q+(-1.41127 + 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.86678 + 1.86678i) q^{7} +(-2.77552 + 0.544488i) q^{8} -0.728515i q^{11} +(3.12489 - 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(1.12489 + 1.12489i) q^{17} -3.73356 q^{19} +(0.0664803 + 1.02813i) q^{22} +(5.83347 + 5.83347i) q^{23} +(-4.12489 + 4.69521i) q^{26} +(-3.22164 + 4.18329i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(-5.36458 + 1.79480i) q^{32} +(-1.69016 - 1.48486i) q^{34} +(-3.12489 - 3.12489i) q^{37} +(5.26904 - 0.340704i) q^{38} +4.24977 q^{41} +(5.10495 + 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(-2.09991 + 2.09991i) q^{47} +0.0302761i q^{49} +(5.39285 - 7.00260i) q^{52} +(0.484862 - 0.484862i) q^{53} +(4.16485 - 6.19773i) q^{56} +(-0.240914 - 3.72578i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(-0.548448 - 8.48183i) q^{62} +(7.40707 - 3.02248i) q^{64} +(-5.10495 + 5.10495i) q^{67} +(2.52077 + 1.94130i) q^{68} +13.1240i q^{71} +(-3.96972 + 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(1.35998 + 1.35998i) q^{77} +7.11388 q^{79} +(-5.99756 + 0.387811i) q^{82} +(-3.55694 - 3.55694i) q^{83} +(-7.67030 - 6.73860i) q^{86} +(0.396668 + 2.02201i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(13.0723 + 10.0673i) q^{92} +(2.77191 - 3.15516i) q^{94} +(12.5298 + 12.5298i) q^{97} +(-0.00276283 - 0.0427276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8}+O(q^{10}) $ 12 * q - 12 * q^8	$ 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61} - 56 q^{62} - 16 q^{68} - 44 q^{73} + 8 q^{76} + 48 q^{77} - 16 q^{82} - 64 q^{86} - 60 q^{88} + 56 q^{92} + 20 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q - 12 * q^8 + 4 * q^13 + 12 * q^16 - 20 * q^17 - 12 * q^22 - 16 * q^26 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 40 * q^46 + 8 * q^52 + 4 * q^53 + 64 * q^56 + 20 * q^58 - 32 * q^61 - 56 * q^62 - 16 * q^68 - 44 * q^73 + 8 * q^76 + 48 * q^77 - 16 * q^82 - 64 * q^86 - 60 * q^88 + 56 * q^92 + 20 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.41127	+	0.0912546i	−0.997916	+	0.0645267i
$2$	−1.41127	+	0.0912546i	−0.997916	+	0.0645267i
$3$		0			0
$3$		0			0
$4$	1.98335	−	0.257569i	0.991673	−	0.128785i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.86678	+	1.86678i	−0.705576	+	0.705576i	−0.965602	−	0.260026i	$-0.916269\pi$
$7$	−1.86678	+	1.86678i	−0.705576	+	0.705576i	0.260026	+	0.965602i	$0.416269\pi$
$8$	−2.77552	+	0.544488i	−0.981296	+	0.192506i
$9$		0			0
$10$		0			0
$11$		−	0.728515i		−	0.219656i	−0.993951	−	0.109828i	$-0.964970\pi$
$11$		−	0.728515i		−	0.219656i	0.993951	−	0.109828i	$-0.0350299\pi$
$12$		0			0
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	−0.125417	−	0.992104i	$-0.540027\pi$
$13$	3.12489	−	3.12489i	0.866687	−	0.866687i	0.992104	+	0.125417i	$0.0400268\pi$
$14$	2.46417	−	2.80487i	0.658577	−	0.749634i
$15$		0			0
$16$	3.86732	−	1.02170i	0.966829	−	0.255424i
$17$	1.12489	+	1.12489i	0.272825	+	0.272825i	0.830236	−	0.557412i	$-0.188205\pi$
$17$	1.12489	+	1.12489i	0.272825	+	0.272825i	−0.557412	+	0.830236i	$0.688205\pi$
$18$		0			0
$19$	−3.73356			−0.856537			−0.428268	−	0.903652i	$-0.640876\pi$
$19$	−3.73356			−0.856537			−0.428268	+	0.903652i	$0.640876\pi$
$20$		0			0
$21$		0			0
$22$	0.0664803	+	1.02813i	0.0141737	+	0.219198i
$23$	5.83347	+	5.83347i	1.21636	+	1.21636i	0.968897	+	0.247466i	$0.0795978\pi$
$23$	5.83347	+	5.83347i	1.21636	+	1.21636i	0.247466	+	0.968897i	$0.420402\pi$
$24$		0			0
$25$		0			0
$26$	−4.12489	+	4.69521i	−0.808957	+	0.920806i
$27$		0			0
$28$	−3.22164	+	4.18329i	−0.608833	+	0.790568i
$29$			2.64002i			0.490240i	0.969493	+	0.245120i	$0.0788274\pi$
$29$			2.64002i			0.490240i	−0.969493	+	0.245120i	$0.921173\pi$
$30$		0			0
$31$			6.01008i			1.07944i	0.841844	+	0.539721i	$0.181470\pi$
$31$			6.01008i			1.07944i	−0.841844	+	0.539721i	$0.818530\pi$
$32$	−5.36458	+	1.79480i	−0.948333	+	0.317278i
$33$		0			0
$34$	−1.69016	−	1.48486i	−0.289861	−	0.254652i
$35$		0			0
$36$		0			0
$37$	−3.12489	−	3.12489i	−0.513728	−	0.513728i	0.401939	−	0.915667i	$-0.368337\pi$
$37$	−3.12489	−	3.12489i	−0.513728	−	0.513728i	−0.915667	+	0.401939i	$0.868337\pi$
$38$	5.26904	−	0.340704i	0.854752	−	0.0552695i
$39$		0			0
$40$		0			0
$41$	4.24977			0.663703			0.331851	−	0.943332i	$-0.392327\pi$
$41$	4.24977			0.663703			0.331851	+	0.943332i	$0.392327\pi$
$42$		0			0
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	0.979575	−	0.201077i	$-0.0644442\pi$
$43$	5.10495	+	5.10495i	0.778498	+	0.778498i	−0.201077	+	0.979575i	$0.564444\pi$
$44$	−0.187643	−	1.44490i	−0.0282882	−	0.217826i
$45$		0			0
$46$	−8.76491	−	7.70025i	−1.29232	−	1.13534i
$47$	−2.09991	+	2.09991i	−0.306304	+	0.306304i	−0.843474	−	0.537170i	$-0.819493\pi$
$47$	−2.09991	+	2.09991i	−0.306304	+	0.306304i	0.537170	+	0.843474i	$0.319493\pi$
$48$		0			0
$49$			0.0302761i			0.00432516i
$50$		0			0
$51$		0			0
$52$	5.39285	−	7.00260i	0.747854	−	0.971086i
$53$	0.484862	−	0.484862i	0.0666009	−	0.0666009i	−0.673022	−	0.739623i	$-0.735004\pi$
$53$	0.484862	−	0.484862i	0.0666009	−	0.0666009i	0.739623	+	0.673022i	$0.235004\pi$
$54$		0			0
$55$		0			0
$56$	4.16485	−	6.19773i	0.556552	−	0.828206i
$57$		0			0
$58$	−0.240914	−	3.72578i	−0.0316336	−	0.489218i
$59$	4.92834			0.641615			0.320808	−	0.947144i	$-0.396046\pi$
$59$	4.92834			0.641615			0.320808	+	0.947144i	$0.396046\pi$
$60$		0			0
$61$	2.31032			0.295807			0.147903	−	0.989002i	$-0.452748\pi$
$61$	2.31032			0.295807			0.147903	+	0.989002i	$0.452748\pi$
$62$	−0.548448	−	8.48183i	−0.0696529	−	1.07719i
$63$		0			0
$64$	7.40707	−	3.02248i	0.925883	−	0.377810i
$65$		0			0
$66$		0			0
$67$	−5.10495	+	5.10495i	−0.623669	+	0.623669i	−0.946468	−	0.322798i	$-0.895376\pi$
$67$	−5.10495	+	5.10495i	−0.623669	+	0.623669i	0.322798	+	0.946468i	$0.395376\pi$
$68$	2.52077	+	1.94130i	0.305688	+	0.235417i
$69$		0			0
$70$		0			0
$71$			13.1240i			1.55753i	0.627317	+	0.778764i	$0.284153\pi$
$71$			13.1240i			1.55753i	−0.627317	+	0.778764i	$0.715847\pi$
$72$		0			0
$73$	−3.96972	+	3.96972i	−0.464621	+	0.464621i	−0.900167	−	0.435546i	$-0.856555\pi$
$73$	−3.96972	+	3.96972i	−0.464621	+	0.464621i	0.435546	+	0.900167i	$0.356555\pi$
$74$	4.69521	+	4.12489i	0.545807	+	0.479508i
$75$		0			0
$76$	−7.40493	+	0.961649i	−0.849404	+	0.110309i
$77$	1.35998	+	1.35998i	0.154984	+	0.154984i
$78$		0			0
$79$	7.11388			0.800375			0.400187	−	0.916433i	$-0.368945\pi$
$79$	7.11388			0.800375			0.400187	+	0.916433i	$0.368945\pi$
$80$		0			0
$81$		0			0
$82$	−5.99756	+	0.387811i	−0.662320	+	0.0428266i
$83$	−3.55694	−	3.55694i	−0.390425	−	0.390425i	0.484414	−	0.874839i	$-0.339033\pi$
$83$	−3.55694	−	3.55694i	−0.390425	−	0.390425i	−0.874839	+	0.484414i	$0.839033\pi$
$84$		0			0
$85$		0			0
$86$	−7.67030	−	6.73860i	−0.827110	−	0.726642i
$87$		0			0
$88$	0.396668	+	2.02201i	0.0422849	+	0.215547i
$89$			1.03028i			0.109209i	0.998508	+	0.0546045i	$0.0173898\pi$
$89$			1.03028i			0.109209i	−0.998508	+	0.0546045i	$0.982610\pi$
$90$		0			0
$91$			11.6669i			1.22303i
$92$	13.0723	+	10.0673i	1.36288	+	1.04958i
$93$		0			0
$94$	2.77191	−	3.15516i	0.285901	−	0.325430i
$95$		0			0
$96$		0			0
$97$	12.5298	+	12.5298i	1.27221	+	1.27221i	0.944926	+	0.327284i	$0.106133\pi$
$97$	12.5298	+	12.5298i	1.27221	+	1.27221i	0.327284	+	0.944926i	$0.393867\pi$
$98$	−0.00276283	−	0.0427276i	−0.000279088	−	0.00431614i
$99$		0			0
$100$		0			0
$101$	5.67030			0.564216			0.282108	−	0.959383i	$-0.408966\pi$
$101$	5.67030			0.564216			0.282108	+	0.959383i	$0.408966\pi$
$102$		0			0
$103$	−0.0565188	−	0.0565188i	−0.00556896	−	0.00556896i	0.704317	−	0.709886i	$-0.251253\pi$
$103$	−0.0565188	−	0.0565188i	−0.00556896	−	0.00556896i	−0.709886	+	0.704317i	$0.751253\pi$
$104$	−6.97173	+	10.3747i	−0.683635	+	1.01732i
$105$		0			0
$106$	−0.640023	+	0.728515i	−0.0621646	+	0.0707597i
$107$	−3.91017	+	3.91017i	−0.378011	+	0.378011i	−0.870384	−	0.492373i	$-0.836129\pi$
$107$	−3.91017	+	3.91017i	−0.378011	+	0.378011i	0.492373	+	0.870384i	$0.336129\pi$
$108$		0			0
$109$			15.7796i			1.51141i	0.654912	+	0.755705i	$0.272706\pi$
$109$			15.7796i			1.51141i	−0.654912	+	0.755705i	$0.727294\pi$
$110$		0			0
$111$		0			0
$112$	−5.31214	+	9.12670i	−0.501950	+	0.862392i
$113$	−1.84484	+	1.84484i	−0.173548	+	0.173548i	−0.788536	−	0.614988i	$-0.789161\pi$
$113$	−1.84484	+	1.84484i	−0.173548	+	0.173548i	0.614988	+	0.788536i	$0.289161\pi$
$114$		0			0
$115$		0			0
$116$	0.679988	+	5.23608i	0.0631353	+	0.486158i
$117$		0			0
$118$	−6.95520	+	0.449733i	−0.640278	+	0.0414013i
$119$	−4.19982			−0.384997
$120$		0			0
$121$	10.4693			0.951751
$122$	−3.26048	+	0.210828i	−0.295190	+	0.0190874i
$123$		0			0
$124$	1.54801	+	11.9201i	0.139016	+	1.07045i
$125$		0			0
$126$		0			0
$127$	11.2572	−	11.2572i	0.998914	−	0.998914i	−0.00108535	−	0.999999i	$-0.500345\pi$
$127$	11.2572	−	11.2572i	0.998914	−	0.998914i	0.999999	+	0.00108535i	$0.000345478\pi$
$128$	−10.1775	+	4.94145i	−0.899575	+	0.436767i
$129$		0			0
$130$		0			0
$131$		−	4.57511i		−	0.399729i	−0.979824	−	0.199865i	$-0.935950\pi$
$131$		−	4.57511i		−	0.399729i	0.979824	−	0.199865i	$-0.0640502\pi$
$132$		0			0
$133$	6.96972	−	6.96972i	0.604352	−	0.604352i
$134$	6.73860	−	7.67030i	0.582126	−	0.662613i
$135$		0			0
$136$	−3.73463	−	2.50966i	−0.320242	−	0.215202i
$137$	−4.09461	−	4.09461i	−0.349826	−	0.349826i	0.510219	−	0.860045i	$-0.329564\pi$
$137$	−4.09461	−	4.09461i	−0.349826	−	0.349826i	−0.860045	+	0.510219i	$0.829564\pi$
$138$		0			0
$139$	−13.5902			−1.15271			−0.576354	−	0.817200i	$-0.695525\pi$
$139$	−13.5902			−1.15271			−0.576354	+	0.817200i	$0.695525\pi$
$140$		0			0
$141$		0			0
$142$	−1.19762	−	18.5214i	−0.100502	−	1.55428i
$143$	−2.27653	−	2.27653i	−0.190373	−	0.190373i
$144$		0			0
$145$		0			0
$146$	5.24008	−	5.96459i	0.433672	−	0.493633i
$147$		0			0
$148$	−7.00260	−	5.39285i	−0.575610	−	0.443290i
$149$		−	5.67030i		−	0.464529i	−0.972653	−	0.232265i	$-0.925386\pi$
$149$		−	5.67030i		−	0.464529i	0.972653	−	0.232265i	$-0.0746135\pi$
$150$		0			0
$151$		−	19.2471i		−	1.56631i	−0.621829	−	0.783153i	$-0.713610\pi$
$151$		−	19.2471i		−	1.56631i	0.621829	−	0.783153i	$-0.286390\pi$
$152$	10.3626	−	2.03288i	0.840516	−	0.164888i
$153$		0			0
$154$	−2.04339	−	1.79518i	−0.164661	−	0.144660i
$155$		0			0
$156$		0			0
$157$	2.09461	+	2.09461i	0.167168	+	0.167168i	0.785733	−	0.618565i	$-0.212286\pi$
$157$	2.09461	+	2.09461i	0.167168	+	0.167168i	−0.618565	+	0.785733i	$0.712286\pi$
$158$	−10.0396	+	0.649175i	−0.798707	+	0.0516456i
$159$		0			0
$160$		0			0
$161$	−21.7796			−1.71647
$162$		0			0
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	0.854732	−	0.519069i	$-0.173721\pi$
$163$	4.28546	+	4.28546i	0.335663	+	0.335663i	−0.519069	+	0.854732i	$0.673721\pi$
$164$	8.42876	−	1.09461i	0.658176	−	0.0854746i
$165$		0			0
$166$	5.34438	+	4.69521i	0.414804	+	0.364419i
$167$	4.37644	−	4.37644i	0.338659	−	0.338659i	−0.517203	−	0.855862i	$-0.673027\pi$
$167$	4.37644	−	4.37644i	0.338659	−	0.338659i	0.855862	+	0.517203i	$0.173027\pi$
$168$		0			0
$169$		−	6.52982i		−	0.502294i
$170$		0			0
$171$		0			0
$172$	11.4398	+	8.81001i	0.872274	+	0.671757i
$173$	16.4049	−	16.4049i	1.24724	−	1.24724i	0.290312	−	0.956932i	$-0.406241\pi$
$173$	16.4049	−	16.4049i	1.24724	−	1.24724i	0.956932	−	0.290312i	$-0.0937590\pi$
$174$		0			0
$175$		0			0
$176$	−0.744321	−	2.81740i	−0.0561053	−	0.212369i
$177$		0			0
$178$	−0.0940174	−	1.45399i	−0.00704690	−	0.108981i
$179$	−24.4156			−1.82491			−0.912455	−	0.409178i	$-0.865815\pi$
$179$	−24.4156			−1.82491			−0.912455	+	0.409178i	$0.865815\pi$
$180$		0			0
$181$	11.2800			0.838439			0.419220	−	0.907885i	$-0.362304\pi$
$181$	11.2800			0.838439			0.419220	+	0.907885i	$0.362304\pi$
$182$	−1.06466	−	16.4652i	−0.0789180	−	1.22048i
$183$		0			0
$184$	−19.3672	−	13.0147i	−1.42777	−	0.959455i
$185$		0			0
$186$		0			0
$187$	0.819496	−	0.819496i	0.0599275	−	0.0599275i
$188$	−3.62398	+	4.70572i	−0.264306	+	0.343200i
$189$		0			0
$190$		0			0
$191$		−	3.26729i		−	0.236413i	−0.992989	−	0.118206i	$-0.962286\pi$
$191$		−	3.26729i		−	0.236413i	0.992989	−	0.118206i	$-0.0377144\pi$
$192$		0			0
$193$	−0.939448	+	0.939448i	−0.0676229	+	0.0676229i	−0.740109	−	0.672486i	$-0.765226\pi$
$193$	−0.939448	+	0.939448i	−0.0676229	+	0.0676229i	0.672486	+	0.740109i	$0.265226\pi$
$194$	−18.8263	−	16.5395i	−1.35165	−	1.18747i
$195$		0			0
$196$	0.00779818	+	0.0600479i	0.000557013	+	0.00428914i
$197$	−1.45459	−	1.45459i	−0.103635	−	0.103635i	0.653388	−	0.757023i	$-0.273347\pi$
$197$	−1.45459	−	1.45459i	−0.103635	−	0.103635i	−0.757023	+	0.653388i	$0.773347\pi$
$198$		0			0
$199$	−5.19059			−0.367951			−0.183975	−	0.982931i	$-0.558897\pi$
$199$	−5.19059			−0.367951			−0.183975	+	0.982931i	$0.558897\pi$
$200$		0			0
$201$		0			0
$202$	−8.00230	+	0.517441i	−0.563040	+	0.0364070i
$203$	−4.92834	−	4.92834i	−0.345902	−	0.345902i
$204$		0			0
$205$		0			0
$206$	0.0849206	+	0.0746054i	0.00591670	+	0.00519801i
$207$		0			0
$208$	8.89224	−	15.2776i	0.616566	−	1.05931i
$209$			2.71995i			0.188143i
$210$		0			0
$211$			11.7800i			0.810967i	0.914102	+	0.405483i	$0.132897\pi$
$211$			11.7800i			0.810967i	−0.914102	+	0.405483i	$0.867103\pi$
$212$	0.836763	−	1.08653i	0.0574691	−	0.0746235i
$213$		0			0
$214$	5.16147	−	5.87511i	0.352831	−	0.401615i
$215$		0			0
$216$		0			0
$217$	−11.2195	−	11.2195i	−0.761629	−	0.761629i
$218$	−1.43996	−	22.2692i	−0.0975264	−	1.50826i
$219$		0			0
$220$		0			0
$221$	7.03028			0.472908
$222$		0			0
$223$	−3.32381	−	3.32381i	−0.222579	−	0.222579i	0.587005	−	0.809583i	$-0.300307\pi$
$223$	−3.32381	−	3.32381i	−0.222579	−	0.222579i	−0.809583	+	0.587005i	$0.800307\pi$
$224$	6.66399	−	13.3650i	0.445257	−	0.892984i
$225$		0			0
$226$	2.43521	−	2.77191i	0.161988	−	0.184385i
$227$	8.83851	−	8.83851i	0.586633	−	0.586633i	−0.350085	−	0.936718i	$-0.613847\pi$
$227$	8.83851	−	8.83851i	0.586633	−	0.586633i	0.936718	+	0.350085i	$0.113847\pi$
$228$		0			0
$229$		−	7.09083i		−	0.468575i	−0.972167	−	0.234288i	$-0.924724\pi$
$229$		−	7.09083i		−	0.468575i	0.972167	−	0.234288i	$-0.0752757\pi$
$230$		0			0
$231$		0			0
$232$	−1.43746	−	7.32745i	−0.0943739	−	0.481071i
$233$	−15.3747	+	15.3747i	−1.00723	+	1.00723i	−0.00725353	+	0.999974i	$0.502309\pi$
$233$	−15.3747	+	15.3747i	−1.00723	+	1.00723i	−0.999974	+	0.00725353i	$0.997691\pi$
$234$		0			0
$235$		0			0
$236$	9.77460	−	1.26939i	0.636272	−	0.0826301i
$237$		0			0
$238$	5.92707	−	0.383253i	0.384195	−	0.0248426i
$239$	0.706459			0.0456970			0.0228485	−	0.999739i	$-0.492726\pi$
$239$	0.706459			0.0456970			0.0228485	+	0.999739i	$0.492726\pi$
$240$		0			0
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$	−14.7749	+	0.955368i	−0.949768	+	0.0614134i
$243$		0			0
$244$	4.58217	−	0.595068i	0.293343	−	0.0380953i
$245$		0			0
$246$		0			0
$247$	−11.6669	+	11.6669i	−0.742349	+	0.742349i
$248$	−3.27242	−	16.6811i	−0.207799	−	1.05925i
$249$		0			0
$250$		0			0
$251$		−	28.6154i		−	1.80619i	−0.429440	−	0.903095i	$-0.641289\pi$
$251$		−	28.6154i		−	1.80619i	0.429440	−	0.903095i	$-0.358711\pi$
$252$		0			0
$253$	4.24977	−	4.24977i	0.267181	−	0.267181i
$254$	−14.8596	+	16.9142i	−0.932376	+	1.06129i
$255$		0			0
$256$	13.9123	−	7.90245i	0.869517	−	0.493903i
$257$	−3.90539	−	3.90539i	−0.243612	−	0.243612i	0.574731	−	0.818342i	$-0.305107\pi$
$257$	−3.90539	−	3.90539i	−0.243612	−	0.243612i	−0.818342	+	0.574731i	$0.805107\pi$
$258$		0			0
$259$	11.6669			0.724948
$260$		0			0
$261$		0			0
$262$	0.417500	+	6.45670i	0.0257932	+	0.398896i
$263$	−0.176615	−	0.176615i	−0.0108905	−	0.0108905i	0.701641	−	0.712531i	$-0.252451\pi$
$263$	−0.176615	−	0.176615i	−0.0108905	−	0.0108905i	−0.712531	+	0.701641i	$0.752451\pi$
$264$		0			0
$265$		0			0
$266$	−9.20012	+	10.4722i	−0.564095	+	0.642089i
$267$		0			0
$268$	−8.81001	+	11.4398i	−0.538157	+	0.698795i
$269$			5.38934i			0.328594i	0.986411	+	0.164297i	$0.0525355\pi$
$269$			5.38934i			0.328594i	−0.986411	+	0.164297i	$0.947465\pi$
$270$		0			0
$271$		−	15.4005i		−	0.935513i	−0.883857	−	0.467757i	$-0.845062\pi$
$271$		−	15.4005i		−	0.935513i	0.883857	−	0.467757i	$-0.154938\pi$
$272$	5.49958	+	3.20100i	0.333461	+	0.194089i
$273$		0			0
$274$	6.15224	+	5.40493i	0.371670	+	0.326524i
$275$		0			0
$276$		0			0
$277$	−8.59415	−	8.59415i	−0.516372	−	0.516372i	0.400099	−	0.916472i	$-0.368976\pi$
$277$	−8.59415	−	8.59415i	−0.516372	−	0.516372i	−0.916472	+	0.400099i	$0.868976\pi$
$278$	19.1794	−	1.24017i	1.15031	−	0.0743805i
$279$		0			0
$280$		0			0
$281$	20.7493			1.23780			0.618900	−	0.785470i	$-0.287579\pi$
$281$	20.7493			1.23780			0.618900	+	0.785470i	$0.287579\pi$
$282$		0			0
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.993849	−	0.110745i	$-0.964676\pi$
$283$	−18.5822	−	18.5822i	−1.10459	−	1.10459i	−0.110745	−	0.993849i	$-0.535324\pi$
$284$	3.38033	+	26.0294i	0.200586	+	1.54456i
$285$		0			0
$286$	3.42053	+	3.00504i	0.202260	+	0.177692i
$287$	−7.93338	+	7.93338i	−0.468293	+	0.468293i
$288$		0			0
$289$		−	14.4693i		−	0.851133i
$290$		0			0
$291$		0			0
$292$	−6.85085	+	8.89581i	−0.400916	+	0.520588i
$293$	6.23509	−	6.23509i	0.364258	−	0.364258i	−0.501120	−	0.865378i	$-0.667078\pi$
$293$	6.23509	−	6.23509i	0.364258	−	0.364258i	0.865378	+	0.501120i	$0.167078\pi$
$294$		0			0
$295$		0			0
$296$	10.3747	+	6.97173i	0.603015	+	0.405224i
$297$		0			0
$298$	0.517441	+	8.00230i	0.0299745	+	0.463561i
$299$	36.4578			2.10841
$300$		0			0
$301$	−19.0596			−1.09858
$302$	1.75639	+	27.1628i	0.101069	+	1.56304i
$303$		0			0
$304$	−14.4388	+	3.81456i	−0.828125	+	0.218780i
$305$		0			0
$306$		0			0
$307$	−0.905130	+	0.905130i	−0.0516585	+	0.0516585i	−0.732464	−	0.680806i	$-0.761630\pi$
$307$	−0.905130	+	0.905130i	−0.0516585	+	0.0516585i	0.680806	+	0.732464i	$0.261630\pi$
$308$	3.04759	+	2.34702i	0.173653	+	0.133734i
$309$		0			0
$310$		0			0
$311$			24.4377i			1.38573i	0.721066	+	0.692867i	$0.243653\pi$
$311$			24.4377i			1.38573i	−0.721066	+	0.692867i	$0.756347\pi$
$312$		0			0
$313$	−18.5904	+	18.5904i	−1.05079	+	1.05079i	−0.0521506	+	0.998639i	$0.516608\pi$
$313$	−18.5904	+	18.5904i	−1.05079	+	1.05079i	−0.998639	+	0.0521506i	$0.983392\pi$
$314$	−3.14719	−	2.76491i	−0.177606	−	0.156033i
$315$		0			0
$316$	14.1093	−	1.83232i	0.793710	−	0.103076i
$317$	19.3141	+	19.3141i	1.08479	+	1.08479i	0.996055	+	0.0887327i	$0.0282817\pi$
$317$	19.3141	+	19.3141i	1.08479	+	1.08479i	0.0887327	+	0.996055i	$0.471718\pi$
$318$		0			0
$319$	1.92330			0.107684
$320$		0			0
$321$		0			0
$322$	30.7368	−	1.98749i	1.71289	−	0.110758i
$323$	−4.19982	−	4.19982i	−0.233684	−	0.233684i
$324$		0			0
$325$		0			0
$326$	−6.43899	−	5.65685i	−0.356623	−	0.313304i
$327$		0			0
$328$	−11.7953	+	2.31395i	−0.651289	+	0.127766i
$329$		−	7.84014i		−	0.432241i
$330$		0			0
$331$		−	11.0294i		−	0.606231i	−0.952954	−	0.303115i	$-0.901973\pi$
$331$		−	11.0294i		−	0.606231i	0.952954	−	0.303115i	$-0.0980268\pi$
$332$	−7.97080	−	6.13849i	−0.437455	−	0.336893i
$333$		0			0
$334$	−5.77695	+	6.57569i	−0.316101	+	0.359806i
$335$		0			0
$336$		0			0
$337$	−13.6206	−	13.6206i	−0.741964	−	0.741964i	0.230992	−	0.972956i	$-0.425803\pi$
$337$	−13.6206	−	13.6206i	−0.741964	−	0.741964i	−0.972956	+	0.230992i	$0.925803\pi$
$338$	0.595876	+	9.21531i	0.0324114	+	0.501247i
$339$		0			0
$340$		0			0
$341$	4.37844			0.237106
$342$		0			0
$343$	−13.1240	−	13.1240i	−0.708628	−	0.708628i
$344$	−16.9485	−	11.3893i	−0.913802	−	0.614072i
$345$		0			0
$346$	−21.6547	+	24.6488i	−1.16416	+	1.32513i
$347$	17.7627	−	17.7627i	0.953549	−	0.953549i	−0.0454187	−	0.998968i	$-0.514462\pi$
$347$	17.7627	−	17.7627i	0.953549	−	0.953549i	0.998968	+	0.0454187i	$0.0144622\pi$
$348$		0			0
$349$		−	14.6888i		−	0.786271i	−0.919480	−	0.393136i	$-0.871390\pi$
$349$		−	14.6888i		−	0.786271i	0.919480	−	0.393136i	$-0.128610\pi$
$350$		0			0
$351$		0			0
$352$	1.30754	+	3.90818i	0.0696919	+	0.208307i
$353$	−18.4049	+	18.4049i	−0.979596	+	0.979596i	−0.999796	−	0.0202002i	$-0.993570\pi$
$353$	−18.4049	+	18.4049i	−0.979596	+	0.979596i	0.0202002	+	0.999796i	$0.493570\pi$
$354$		0			0
$355$		0			0
$356$	0.265367	+	2.04339i	0.0140644	+	0.108300i
$357$		0			0
$358$	34.4569	−	2.22804i	1.82111	−	0.117755i
$359$	−9.63060			−0.508284			−0.254142	−	0.967167i	$-0.581793\pi$
$359$	−9.63060			−0.508284			−0.254142	+	0.967167i	$0.581793\pi$
$360$		0			0
$361$	−5.06055			−0.266345
$362$	−15.9192	+	1.02936i	−0.836692	+	0.0541017i
$363$		0			0
$364$	3.00504	+	23.1396i	0.157507	+	1.21284i
$365$		0			0
$366$		0			0
$367$	15.4570	−	15.4570i	0.806850	−	0.806850i	−0.177306	−	0.984156i	$-0.556738\pi$
$367$	15.4570	−	15.4570i	0.806850	−	0.806850i	0.984156	+	0.177306i	$0.0567383\pi$
$368$	28.5199	+	16.5998i	1.48670	+	0.865326i
$369$		0			0
$370$		0			0
$371$			1.81026i			0.0939840i
$372$		0			0
$373$	−3.37466	+	3.37466i	−0.174733	+	0.174733i	−0.789055	−	0.614322i	$-0.789430\pi$
$373$	−3.37466	+	3.37466i	−0.174733	+	0.174733i	0.614322	+	0.789055i	$0.289430\pi$
$374$	−1.08174	+	1.23131i	−0.0559357	+	0.0636695i
$375$		0			0
$376$	4.68498	−	6.97173i	0.241609	−	0.359540i
$377$	8.24977	+	8.24977i	0.424885	+	0.424885i
$378$		0			0
$379$	5.89705			0.302911			0.151455	−	0.988464i	$-0.451604\pi$
$379$	5.89705			0.302911			0.151455	+	0.988464i	$0.451604\pi$
$380$		0			0
$381$		0			0
$382$	0.298155	+	4.61102i	0.0152549	+	0.235920i
$383$	0.642881	+	0.642881i	0.0328497	+	0.0328497i	0.723341	−	0.690491i	$-0.242606\pi$
$383$	0.642881	+	0.642881i	0.0328497	+	0.0328497i	−0.690491	+	0.723341i	$0.742606\pi$
$384$		0			0
$385$		0			0
$386$	1.24008	−	1.41154i	0.0631185	−	0.0718455i
$387$		0			0
$388$	28.0782	+	21.6237i	1.42546	+	1.09778i
$389$		−	18.8292i		−	0.954680i	−0.878719	−	0.477340i	$-0.841601\pi$
$389$		−	18.8292i		−	0.954680i	0.878719	−	0.477340i	$-0.158399\pi$
$390$		0			0
$391$			13.1240i			0.663708i
$392$	−0.0164850	−	0.0840320i	−0.000832616	−	0.00424426i
$393$		0			0
$394$	2.18555	+	1.92007i	0.110106	+	0.0967317i
$395$		0			0
$396$		0			0
$397$	24.3444	+	24.3444i	1.22181	+	1.22181i	0.966988	+	0.254821i	$0.0820166\pi$
$397$	24.3444	+	24.3444i	1.22181	+	1.22181i	0.254821	+	0.966988i	$0.417983\pi$
$398$	7.32530	−	0.473665i	0.367184	−	0.0237427i
$399$		0			0
$400$		0			0
$401$	−15.9394			−0.795978			−0.397989	−	0.917390i	$-0.630292\pi$
$401$	−15.9394			−0.795978			−0.397989	+	0.917390i	$0.630292\pi$
$402$		0			0
$403$	18.7808	+	18.7808i	0.935539	+	0.935539i
$404$	11.2462	−	1.46049i	0.559517	−	0.0726623i
$405$		0			0
$406$	7.40493	+	6.50547i	0.367501	+	0.322861i
$407$	−2.27653	+	2.27653i	−0.112843	+	0.112843i
$408$		0			0
$409$			23.4087i			1.15749i	0.815510	+	0.578743i	$0.196457\pi$
$409$			23.4087i			1.15749i	−0.815510	+	0.578743i	$0.803543\pi$
$410$		0			0
$411$		0			0
$412$	−0.126654	−	0.0975387i	−0.00623978	−	0.00480539i
$413$	−9.20012	+	9.20012i	−0.452708	+	0.452708i
$414$		0			0
$415$		0			0
$416$	−11.1552	+	22.3722i	−0.546927	+	1.09689i
$417$		0			0
$418$	−0.248208	−	3.83858i	−0.0121403	−	0.187751i
$419$	28.0361			1.36966			0.684828	−	0.728705i	$-0.259878\pi$
$419$	28.0361			1.36966			0.684828	+	0.728705i	$0.259878\pi$
$420$		0			0
$421$	17.4087			0.848449			0.424224	−	0.905557i	$-0.360547\pi$
$421$	17.4087			0.848449			0.424224	+	0.905557i	$0.360547\pi$
$422$	−1.07498	−	16.6247i	−0.0523290	−	0.809277i
$423$		0			0
$424$	−1.08174	+	1.60975i	−0.0525342	+	0.0781762i
$425$		0			0
$426$		0			0
$427$	−4.31286	+	4.31286i	−0.208714	+	0.208714i
$428$	−6.74808	+	8.76236i	−0.326181	+	0.423545i
$429$		0			0
$430$		0			0
$431$		−	31.1542i		−	1.50065i	−0.661071	−	0.750323i	$-0.729898\pi$
$431$		−	31.1542i		−	1.50065i	0.661071	−	0.750323i	$-0.270102\pi$
$432$		0			0
$433$	12.1589	−	12.1589i	0.584321	−	0.584321i	−0.351766	−	0.936088i	$-0.614419\pi$
$433$	12.1589	−	12.1589i	0.584321	−	0.584321i	0.936088	+	0.351766i	$0.114419\pi$
$434$	16.8575	+	14.8099i	0.809187	+	0.710896i
$435$		0			0
$436$	4.06433	+	31.2964i	0.194646	+	1.49882i
$437$	−21.7796	−	21.7796i	−1.04186	−	1.04186i
$438$		0			0
$439$	14.2967			0.682344			0.341172	−	0.940001i	$-0.389176\pi$
$439$	14.2967			0.682344			0.341172	+	0.940001i	$0.389176\pi$
$440$		0			0
$441$		0			0
$442$	−9.92159	+	0.641545i	−0.471922	+	0.0305152i
$443$	7.02825	+	7.02825i	0.333922	+	0.333922i	0.854074	−	0.520152i	$-0.174125\pi$
$443$	7.02825	+	7.02825i	0.333922	+	0.333922i	−0.520152	+	0.854074i	$0.674125\pi$
$444$		0			0
$445$		0			0
$446$	4.99409	+	4.38747i	0.236477	+	0.207753i
$447$		0			0
$448$	−8.18505	+	19.4696i	−0.386707	+	0.919854i
$449$			38.4608i			1.81508i	0.419969	+	0.907538i	$0.362041\pi$
$449$			38.4608i			1.81508i	−0.419969	+	0.907538i	$0.637959\pi$
$450$		0			0
$451$		−	3.09602i		−	0.145786i
$452$	−3.18378	+	4.13412i	−0.149752	+	0.194453i
$453$		0			0
$454$	−11.6669	+	13.2800i	−0.547557	+	0.623263i
$455$		0			0
$456$		0			0
$457$	−4.93945	−	4.93945i	−0.231058	−	0.231058i	0.582076	−	0.813134i	$-0.302240\pi$
$457$	−4.93945	−	4.93945i	−0.231058	−	0.231058i	−0.813134	+	0.582076i	$0.802240\pi$
$458$	0.647071	+	10.0070i	0.0302356	+	0.467599i
$459$		0			0
$460$		0			0
$461$	−27.1689			−1.26538			−0.632691	−	0.774404i	$-0.718050\pi$
$461$	−27.1689			−1.26538			−0.632691	+	0.774404i	$0.718050\pi$
$462$		0			0
$463$	−4.96280	−	4.96280i	−0.230641	−	0.230641i	0.582319	−	0.812960i	$-0.302145\pi$
$463$	−4.96280	−	4.96280i	−0.230641	−	0.230641i	−0.812960	+	0.582319i	$0.802145\pi$
$464$	2.69730	+	10.2098i	0.125219	+	0.473978i
$465$		0			0
$466$	20.2947	−	23.1007i	0.940135	−	1.07012i
$467$	−21.2340	+	21.2340i	−0.982591	+	0.982591i	−0.999851	−	0.0172604i	$-0.994506\pi$
$467$	−21.2340	+	21.2340i	−0.982591	+	0.982591i	0.0172604	+	0.999851i	$0.494506\pi$
$468$		0			0
$469$		−	19.0596i		−	0.880092i
$470$		0			0
$471$		0			0
$472$	−13.6787	+	2.68342i	−0.629614	+	0.123514i
$473$	3.71904	−	3.71904i	0.171001	−	0.171001i
$474$		0			0
$475$		0			0
$476$	−8.32970	+	1.08174i	−0.381791	+	0.0495817i
$477$		0			0
$478$	−0.997001	+	0.0644676i	−0.0456018	+	0.00294868i
$479$	−18.7808			−0.858118			−0.429059	−	0.903277i	$-0.641155\pi$
$479$	−18.7808			−0.858118			−0.429059	+	0.903277i	$0.641155\pi$
$480$		0			0
$481$	−19.5298			−0.890483
$482$	35.2804	−	2.28128i	1.60698	−	0.103909i
$483$		0			0
$484$	20.7642	−	2.69656i	0.943826	−	0.122571i
$485$		0			0
$486$		0			0
$487$	−2.97058	+	2.97058i	−0.134610	+	0.134610i	−0.771201	−	0.636591i	$-0.780344\pi$
$487$	−2.97058	+	2.97058i	−0.134610	+	0.134610i	0.636591	+	0.771201i	$0.280344\pi$
$488$	−6.41236	+	1.25794i	−0.290274	+	0.0569444i
$489$		0			0
$490$		0			0
$491$			29.5480i			1.33348i	0.745290	+	0.666741i	$0.232311\pi$
$491$			29.5480i			1.33348i	−0.745290	+	0.666741i	$0.767689\pi$
$492$		0			0
$493$	−2.96972	+	2.96972i	−0.133750	+	0.133750i
$494$	15.4005	−	17.5298i	0.692901	−	0.788704i
$495$		0			0
$496$	6.14048	+	23.2429i	0.275716	+	1.04364i
$497$	−24.4995	−	24.4995i	−1.09895	−	1.09895i
$498$		0			0
$499$	15.0473			0.673608			0.336804	−	0.941575i	$-0.390654\pi$
$499$	15.0473			0.673608			0.336804	+	0.941575i	$0.390654\pi$
$500$		0			0
$501$		0			0
$502$	2.61129	+	40.3840i	0.116548	+	1.80243i
$503$	13.4136	+	13.4136i	0.598084	+	0.598084i	0.939802	−	0.341719i	$-0.111009\pi$
$503$	13.4136	+	13.4136i	0.598084	+	0.598084i	−0.341719	+	0.939802i	$0.611009\pi$
$504$		0			0
$505$		0			0
$506$	−5.60975	+	6.38537i	−0.249384	+	0.283864i
$507$		0			0
$508$	19.4274	−	25.2264i	0.861951	−	1.11924i
$509$		−	41.4187i		−	1.83585i	−0.396752	−	0.917926i	$-0.629863\pi$
$509$		−	41.4187i		−	1.83585i	0.396752	−	0.917926i	$-0.370137\pi$
$510$		0			0
$511$		−	14.8212i		−	0.655651i
$512$	−18.9128	+	12.4220i	−0.835835	+	0.548981i
$513$		0			0
$514$	5.86793	+	5.15516i	0.258823	+	0.227384i
$515$		0			0
$516$		0			0
$517$	1.52982	+	1.52982i	0.0672813	+	0.0672813i
$518$	−16.4652	+	1.06466i	−0.723437	+	0.0467785i
$519$		0			0
$520$		0			0
$521$	−30.8392			−1.35109			−0.675545	−	0.737318i	$-0.736092\pi$
$521$	−30.8392			−1.35109			−0.675545	+	0.737318i	$0.736092\pi$
$522$		0			0
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	0.974259	−	0.225430i	$-0.0723787\pi$
$523$	17.1251	+	17.1251i	0.748829	+	0.748829i	−0.225430	+	0.974259i	$0.572379\pi$
$524$	−1.17841	−	9.07402i	−0.0514789	−	0.396400i
$525$		0			0
$526$	0.265367	+	0.233133i	0.0115706	+	0.0101651i
$527$	−6.76066	+	6.76066i	−0.294499	+	0.294499i
$528$		0			0
$529$			45.0587i			1.95907i
$530$		0			0
$531$		0			0
$532$	12.0282	−	15.6186i	0.521488	−	0.677150i
$533$	13.2800	−	13.2800i	0.575223	−	0.575223i
$534$		0			0
$535$		0			0
$536$	11.3893	−	16.9485i	0.491944	−	0.732064i
$537$		0			0
$538$	−0.491802	−	7.60579i	−0.0212031	−	0.327909i
$539$	0.0220566			0.000950045
$540$		0			0
$541$	−22.3397			−0.960458			−0.480229	−	0.877143i	$-0.659446\pi$
$541$	−22.3397			−0.960458			−0.480229	+	0.877143i	$0.659446\pi$
$542$	1.40537	+	21.7342i	0.0603656	+	0.933564i
$543$		0			0
$544$	−8.05348	−	4.01560i	−0.345290	−	0.172167i
$545$		0			0
$546$		0			0
$547$	25.3428	−	25.3428i	1.08358	−	1.08358i	0.0874075	−	0.996173i	$-0.472142\pi$
$547$	25.3428	−	25.3428i	1.08358	−	1.08358i	0.996173	−	0.0874075i	$-0.0278582\pi$
$548$	−9.17567	−	7.06638i	−0.391965	−	0.301861i
$549$		0			0
$550$		0			0
$551$		−	9.85668i		−	0.419909i
$552$		0			0
$553$	−13.2800	+	13.2800i	−0.564725	+	0.564725i
$554$	12.9129	+	11.3444i	0.548616	+	0.481977i
$555$		0			0
$556$	−26.9541	+	3.50042i	−1.14311	+	0.148451i
$557$	21.1055	+	21.1055i	0.894269	+	0.894269i	0.994922	−	0.100653i	$-0.0320931\pi$
$557$	21.1055	+	21.1055i	0.894269	+	0.894269i	−0.100653	+	0.994922i	$0.532093\pi$
$558$		0			0
$559$	31.9048			1.34943
$560$		0			0
$561$		0			0
$562$	−29.2828	+	1.89347i	−1.23522	+	0.0798712i
$563$	10.2955	+	10.2955i	0.433905	+	0.433905i	0.889955	−	0.456049i	$-0.150736\pi$
$563$	10.2955	+	10.2955i	0.433905	+	0.433905i	−0.456049	+	0.889955i	$0.650736\pi$
$564$		0			0
$565$		0			0
$566$	27.9201	+	24.5287i	1.17357	+	1.03102i
$567$		0			0
$568$	−7.14584	−	36.4259i	−0.299833	−	1.52840i
$569$			28.3179i			1.18715i	0.804780	+	0.593574i	$0.202283\pi$
$569$			28.3179i			1.18715i	−0.804780	+	0.593574i	$0.797717\pi$
$570$		0			0
$571$		−	27.2387i		−	1.13990i	−0.821678	−	0.569952i	$-0.806962\pi$
$571$		−	27.2387i		−	1.13990i	0.821678	−	0.569952i	$-0.193038\pi$
$572$	−5.10150	−	3.92878i	−0.213304	−	0.164270i
$573$		0			0
$574$	10.4722	−	11.9201i	0.437099	−	0.497534i
$575$		0			0
$576$		0			0
$577$	−4.81078	−	4.81078i	−0.200275	−	0.200275i	0.599843	−	0.800118i	$-0.295230\pi$
$577$	−4.81078	−	4.81078i	−0.200275	−	0.200275i	−0.800118	+	0.599843i	$0.795230\pi$
$578$	1.32039	+	20.4200i	0.0549208	+	0.849359i
$579$		0			0
$580$		0			0
$581$	13.2800			0.550949
$582$		0			0
$583$	−0.353229	−	0.353229i	−0.0146293	−	0.0146293i
$584$	8.85660	−	13.1795i	0.366489	−	0.545373i
$585$		0			0
$586$	−8.23039	+	9.36835i	−0.339994	+	0.387003i
$587$	4.84271	−	4.84271i	0.199880	−	0.199880i	−0.600069	−	0.799948i	$-0.704860\pi$
$587$	4.84271	−	4.84271i	0.199880	−	0.199880i	0.799948	+	0.600069i	$0.204860\pi$
$588$		0			0
$589$		−	22.4390i		−	0.924582i
$590$		0			0
$591$		0			0
$592$	−15.2776	−	8.89224i	−0.627906	−	0.365469i
$593$	18.8439	−	18.8439i	0.773827	−	0.773827i	−0.204946	−	0.978773i	$-0.565702\pi$
$593$	18.8439	−	18.8439i	0.773827	−	0.773827i	0.978773	+	0.204946i	$0.0657019\pi$
$594$		0			0
$595$		0			0
$596$	−1.46049	−	11.2462i	−0.0598241	−	0.460661i
$597$		0			0
$598$	−51.4517	+	3.32695i	−2.10402	+	0.136049i
$599$	30.2765			1.23706			0.618532	−	0.785760i	$-0.287728\pi$
$599$	30.2765			1.23706			0.618532	+	0.785760i	$0.287728\pi$
$600$		0			0
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$	26.8982	−	1.73928i	1.09629	−	0.0708877i
$603$		0			0
$604$	−4.95745	−	38.1736i	−0.201716	−	1.55326i
$605$		0			0
$606$		0			0
$607$	−19.5438	+	19.5438i	−0.793258	+	0.793258i	−0.982022	−	0.188764i	$-0.939552\pi$
$607$	−19.5438	+	19.5438i	−0.793258	+	0.793258i	0.188764	+	0.982022i	$0.439552\pi$
$608$	20.0290	−	6.70097i	0.812282	−	0.271760i
$609$		0			0
$610$		0			0
$611$			13.1240i			0.530939i
$612$		0			0
$613$	−23.4040	+	23.4040i	−0.945279	+	0.945279i	−0.998579	−	0.0532993i	$-0.983026\pi$
$613$	−23.4040	+	23.4040i	−0.945279	+	0.945279i	0.0532993	+	0.998579i	$0.483026\pi$
$614$	1.19478	−	1.35998i	0.0482175	−	0.0548842i
$615$		0			0
$616$	−4.51514	−	3.03416i	−0.181920	−	0.122250i
$617$	−17.9348	−	17.9348i	−0.722026	−	0.722026i	0.246992	−	0.969018i	$-0.420558\pi$
$617$	−17.9348	−	17.9348i	−0.722026	−	0.722026i	−0.969018	+	0.246992i	$0.920558\pi$
$618$		0			0
$619$	−38.9056			−1.56375			−0.781875	−	0.623435i	$-0.785736\pi$
$619$	−38.9056			−1.56375			−0.781875	+	0.623435i	$0.785736\pi$
$620$		0			0
$621$		0			0
$622$	−2.23005	−	34.4881i	−0.0894169	−	1.38285i
$623$	−1.92330	−	1.92330i	−0.0770553	−	0.0770553i
$624$		0			0
$625$		0			0
$626$	24.5395	−	27.9324i	0.980796	−	1.11640i
$627$		0			0
$628$	4.69384	+	3.61483i	0.187305	+	0.144247i
$629$		−	7.03028i		−	0.280315i
$630$		0			0
$631$		−	12.7707i		−	0.508395i	−0.967152	−	0.254198i	$-0.918189\pi$
$631$		−	12.7707i		−	0.508395i	0.967152	−	0.254198i	$-0.0818113\pi$
$632$	−19.7448	+	3.87342i	−0.785404	+	0.154077i
$633$		0			0
$634$	−29.0198	−	25.4948i	−1.15253	−	1.01253i
$635$		0			0
$636$		0			0
$637$	0.0946093	+	0.0946093i	0.00374856	+	0.00374856i
$638$	−2.71428	+	0.175510i	−0.107460	+	0.00694849i
$639$		0			0
$640$		0			0
$641$	16.4683			0.650461			0.325230	−	0.945635i	$-0.394558\pi$
$641$	16.4683			0.650461			0.325230	+	0.945635i	$0.394558\pi$
$642$		0			0
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	0.584751	−	0.811213i	$-0.301192\pi$
$643$	−5.74249	−	5.74249i	−0.226462	−	0.226462i	−0.811213	+	0.584751i	$0.801192\pi$
$644$	−43.1964	+	5.60975i	−1.70218	+	0.221055i
$645$		0			0
$646$	6.31032	+	5.54382i	0.248276	+	0.218119i
$647$	−4.61663	+	4.61663i	−0.181498	+	0.181498i	−0.792009	−	0.610510i	$-0.790964\pi$
$647$	−4.61663	+	4.61663i	−0.181498	+	0.181498i	0.610510	+	0.792009i	$0.290964\pi$
$648$		0			0
$649$		−	3.59037i		−	0.140934i
$650$		0			0
$651$		0			0
$652$	9.60334	+	7.39574i	0.376096	+	0.289640i
$653$	14.4655	−	14.4655i	0.566078	−	0.566078i	−0.364949	−	0.931027i	$-0.618914\pi$
$653$	14.4655	−	14.4655i	0.566078	−	0.566078i	0.931027	+	0.364949i	$0.118914\pi$
$654$		0			0
$655$		0			0
$656$	16.4352	−	4.34198i	0.641687	−	0.169526i
$657$		0			0
$658$	0.715449	+	11.0645i	0.0278911	+	0.431340i
$659$	−35.5474			−1.38473			−0.692364	−	0.721548i	$-0.743431\pi$
$659$	−35.5474			−1.38473			−0.692364	+	0.721548i	$0.743431\pi$
$660$		0			0
$661$	15.1883			0.590756			0.295378	−	0.955380i	$-0.404554\pi$
$661$	15.1883			0.590756			0.295378	+	0.955380i	$0.404554\pi$
$662$	1.00648	+	15.5654i	0.0391181	+	0.604967i
$663$		0			0
$664$	11.8091	+	7.93567i	0.458282	+	0.307964i
$665$		0			0
$666$		0			0
$667$	−15.4005	+	15.4005i	−0.596310	+	0.596310i
$668$	7.55275	−	9.80722i	0.292225	−	0.379453i
$669$		0			0
$670$		0			0
$671$		−	1.68311i		−	0.0649756i
$672$		0			0
$673$	20.3700	−	20.3700i	0.785204	−	0.785204i	−0.195500	−	0.980704i	$-0.562633\pi$
$673$	20.3700	−	20.3700i	0.785204	−	0.785204i	0.980704	+	0.195500i	$0.0626328\pi$
$674$	20.4653	+	17.9794i	0.788294	+	0.692541i
$675$		0			0
$676$	−1.68188	−	12.9509i	−0.0646876	−	0.498111i
$677$	9.06433	+	9.06433i	0.348371	+	0.348371i	0.859502	−	0.511132i	$-0.170774\pi$
$677$	9.06433	+	9.06433i	0.348371	+	0.348371i	−0.511132	+	0.859502i	$0.670774\pi$
$678$		0			0
$679$	−46.7808			−1.79528
$680$		0			0
$681$		0			0
$682$	−6.17914	+	0.399552i	−0.236612	+	0.0152997i
$683$	−24.8545	−	24.8545i	−0.951030	−	0.951030i	0.0478253	−	0.998856i	$-0.484771\pi$
$683$	−24.8545	−	24.8545i	−0.951030	−	0.951030i	−0.998856	+	0.0478253i	$0.984771\pi$
$684$		0			0
$685$		0			0
$686$	19.7190	+	17.3238i	0.752876	+	0.661425i
$687$		0			0
$688$	24.9582	+	14.5268i	0.951522	+	0.553827i
$689$		−	3.03028i		−	0.115444i
$690$		0			0
$691$			40.8979i			1.55583i	0.628371	+	0.777914i	$0.283722\pi$
$691$			40.8979i			1.55583i	−0.628371	+	0.777914i	$0.716278\pi$
$692$	28.3112	−	36.7620i	1.07623	−	1.39748i
$693$		0			0
$694$	−23.4469	+	26.6888i	−0.890033	+	1.01309i
$695$		0			0
$696$		0			0
$697$	4.78051	+	4.78051i	0.181075	+	0.181075i
$698$	1.34042	+	20.7298i	0.0507355	+	0.784633i
$699$		0			0
$700$		0			0
$701$	43.1396			1.62936			0.814679	−	0.579912i	$-0.196913\pi$
$701$	43.1396			1.62936			0.814679	+	0.579912i	$0.196913\pi$
$702$		0			0
$703$	11.6669	+	11.6669i	0.440027	+	0.440027i
$704$	−2.20192	−	5.39616i	−0.0829880	−	0.203375i
$705$		0			0
$706$	24.2947	−	27.6538i	0.914344	−	1.04076i
$707$	−10.5852	+	10.5852i	−0.398097	+	0.398097i
$708$		0			0
$709$		−	18.4702i		−	0.693662i	−0.937928	−	0.346831i	$-0.887258\pi$
$709$		−	18.4702i		−	0.693662i	0.937928	−	0.346831i	$-0.112742\pi$
$710$		0			0
$711$		0			0
$712$	−0.560973	−	2.85956i	−0.0210233	−	0.107166i
$713$	−35.0596	+	35.0596i	−1.31299	+	1.31299i
$714$		0			0
$715$		0			0
$716$	−48.4246	+	6.28871i	−1.80971	+	0.235020i
$717$		0			0
$718$	13.5913	−	0.878837i	0.507225	−	0.0327979i
$719$	−33.3725			−1.24458			−0.622292	−	0.782785i	$-0.713799\pi$
$719$	−33.3725			−1.24458			−0.622292	+	0.782785i	$0.713799\pi$
$720$		0			0
$721$	0.211016			0.00785865
$722$	7.14179	−	0.461799i	0.265790	−	0.0171864i
$723$		0			0
$724$	22.3722	−	2.90539i	0.831457	−	0.107978i
$725$		0			0
$726$		0			0
$727$	23.2774	−	23.2774i	0.863309	−	0.863309i	−0.128412	−	0.991721i	$-0.540988\pi$
$727$	23.2774	−	23.2774i	0.863309	−	0.863309i	0.991721	+	0.128412i	$0.0409879\pi$
$728$	−6.35251	−	32.3819i	−0.235440	−	1.20015i
$729$		0			0
$730$		0			0
$731$			11.4850i			0.424787i
$732$		0			0
$733$	16.2157	−	16.2157i	0.598941	−	0.598941i	−0.341090	−	0.940031i	$-0.610796\pi$
$733$	16.2157	−	16.2157i	0.598941	−	0.598941i	0.940031	+	0.341090i	$0.110796\pi$
$734$	−20.4034	+	23.2245i	−0.753105	+	0.857231i
$735$		0			0
$736$	−41.7640	−	20.8242i	−1.53944	−	0.767591i
$737$	3.71904	+	3.71904i	0.136992	+	0.136992i
$738$		0			0
$739$	14.3408			0.527535			0.263768	−	0.964586i	$-0.415035\pi$
$739$	14.3408			0.527535			0.263768	+	0.964586i	$0.415035\pi$
$740$		0			0
$741$		0			0
$742$	−0.165194	−	2.55476i	−0.00606448	−	0.0937881i
$743$	−11.6034	−	11.6034i	−0.425686	−	0.425686i	0.461470	−	0.887156i	$-0.347322\pi$
$743$	−11.6034	−	11.6034i	−0.425686	−	0.425686i	−0.887156	+	0.461470i	$0.847322\pi$
$744$		0			0
$745$		0			0
$746$	4.45459	−	5.07049i	0.163094	−	0.185644i
$747$		0			0
$748$	1.41427	−	1.83642i	0.0517107	−	0.0671462i
$749$		−	14.5988i		−	0.533430i
$750$		0			0
$751$			35.1721i			1.28345i	0.766936	+	0.641724i	$0.221780\pi$
$751$			35.1721i			1.28345i	−0.766936	+	0.641724i	$0.778220\pi$
$752$	−5.97555	+	10.2665i	−0.217906	+	0.374381i
$753$		0			0
$754$	−12.3955	−	10.8898i	−0.451416	−	0.396583i
$755$		0			0
$756$		0			0
$757$	15.7455	+	15.7455i	0.572281	+	0.572281i	0.932765	−	0.360484i	$-0.117389\pi$
$757$	15.7455	+	15.7455i	0.572281	+	0.572281i	−0.360484	+	0.932765i	$0.617389\pi$
$758$	−8.32230	+	0.538132i	−0.302280	+	0.0195459i
$759$		0			0
$760$		0			0
$761$	24.4002			0.884508			0.442254	−	0.896890i	$-0.354179\pi$
$761$	24.4002			0.884508			0.442254	+	0.896890i	$0.354179\pi$
$762$		0			0
$763$	−29.4570	−	29.4570i	−1.06641	−	1.06641i
$764$	−0.841553	−	6.48016i	−0.0304463	−	0.234444i
$765$		0			0
$766$	−0.965943	−	0.848611i	−0.0349009	−	0.0306616i
$767$	15.4005	−	15.4005i	0.556080	−	0.556080i
$768$		0			0
$769$		−	15.9688i		−	0.575850i	−0.957653	−	0.287925i	$-0.907035\pi$
$769$		−	15.9688i		−	0.575850i	0.957653	−	0.287925i	$-0.0929654\pi$
$770$		0			0
$771$		0			0
$772$	−1.62128	+	2.10522i	−0.0583510	+	0.0757686i
$773$	−2.84392	+	2.84392i	−0.102289	+	0.102289i	−0.756399	−	0.654110i	$-0.773043\pi$
$773$	−2.84392	+	2.84392i	−0.102289	+	0.102289i	0.654110	+	0.756399i	$0.273043\pi$
$774$		0			0
$775$		0			0
$776$	−41.5991	−	27.9545i	−1.49332	−	1.00351i
$777$		0			0
$778$	1.71825	+	26.5731i	0.0616024	+	0.952691i
$779$	−15.8668			−0.568486
$780$		0			0
$781$	9.56101			0.342120
$782$	−1.19762	−	18.5214i	−0.0428269	−	0.662324i
$783$		0			0
$784$	0.0309330	+	0.117087i	0.00110475	+	0.00418169i
$785$		0			0
$786$		0			0
$787$	7.49452	−	7.49452i	0.267151	−	0.267151i	−0.560800	−	0.827951i	$-0.689506\pi$
$787$	7.49452	−	7.49452i	0.267151	−	0.267151i	0.827951	+	0.560800i	$0.189506\pi$
$788$	−3.25960	−	2.51029i	−0.116119	−	0.0894254i
$789$		0			0
$790$		0			0
$791$		−	6.88781i		−	0.244902i
$792$		0			0
$793$	7.21949	−	7.21949i	0.256372	−	0.256372i
$794$	−36.5779	−	32.1349i	−1.29810	−	1.14042i
$795$		0			0
$796$	−10.2947	+	1.33693i	−0.364887	+	0.0473864i
$797$	26.1552	+	26.1552i	0.926463	+	0.926463i	0.997475	−	0.0710121i	$-0.0226229\pi$
$797$	26.1552	+	26.1552i	0.926463	+	0.926463i	−0.0710121	+	0.997475i	$0.522623\pi$
$798$		0			0
$799$	−4.72432			−0.167134
$800$		0			0
$801$		0			0
$802$	22.4948	−	1.45455i	0.794319	−	0.0513619i
$803$	2.89200	+	2.89200i	0.102057	+	0.102057i
$804$		0			0
$805$		0			0
$806$	−28.2186	−	24.7909i	−0.993957	−	0.873222i
$807$		0			0
$808$	−15.7381	+	3.08741i	−0.553663	+	0.108615i
$809$			23.7115i			0.833651i	0.908987	+	0.416826i	$0.136857\pi$
$809$			23.7115i			0.833651i	−0.908987	+	0.416826i	$0.863143\pi$
$810$		0			0
$811$		−	26.0077i		−	0.913255i	−0.889658	−	0.456628i	$-0.849057\pi$
$811$		−	26.0077i		−	0.913255i	0.889658	−	0.456628i	$-0.150943\pi$
$812$	−11.0440	−	8.50521i	−0.387568	−	0.298474i
$813$		0			0
$814$	3.00504	−	3.42053i	0.105327	−	0.119889i
$815$		0			0
$816$		0			0
$817$	−19.0596	−	19.0596i	−0.666812	−	0.666812i
$818$	−2.13615	−	33.0359i	−0.0746888	−	1.15507i
$819$		0			0
$820$		0			0
$821$	−33.0790			−1.15447			−0.577233	−	0.816580i	$-0.695867\pi$
$821$	−33.0790			−1.15447			−0.577233	+	0.816580i	$0.695867\pi$
$822$		0			0
$823$	17.9737	+	17.9737i	0.626525	+	0.626525i	0.947192	−	0.320667i	$-0.103907\pi$
$823$	17.9737	+	17.9737i	0.626525	+	0.626525i	−0.320667	+	0.947192i	$0.603907\pi$
$824$	0.187643	+	0.126095i	0.00653685	+	0.00439274i
$825$		0			0
$826$	12.1443	−	13.8234i	0.422553	−	0.480977i
$827$	18.8665	−	18.8665i	0.656051	−	0.656051i	−0.298392	−	0.954443i	$-0.596450\pi$
$827$	18.8665	−	18.8665i	0.656051	−	0.656051i	0.954443	+	0.298392i	$0.0964504\pi$
$828$		0			0
$829$			3.28005i			0.113921i	0.998376	+	0.0569604i	$0.0181409\pi$
$829$			3.28005i			0.113921i	−0.998376	+	0.0569604i	$0.981859\pi$
$830$		0			0
$831$		0			0
$832$	13.7013	−	32.5911i	0.475008	−	1.12989i
$833$	−0.0340571	+	0.0340571i	−0.00118001	+	0.00118001i
$834$		0			0
$835$		0			0
$836$	0.700576	+	5.39461i	0.0242299	+	0.186576i
$837$		0			0
$838$	−39.5665	+	2.55843i	−1.36680	+	0.0883794i
$839$	54.8854			1.89486			0.947428	−	0.319969i	$-0.103673\pi$
$839$	54.8854			1.89486			0.947428	+	0.319969i	$0.103673\pi$
$840$		0			0
$841$	22.0303			0.759665
$842$	−24.5683	+	1.58862i	−0.846681	+	0.0547476i
$843$		0			0
$844$	3.03416	+	23.3638i	0.104440	+	0.804214i
$845$		0			0
$846$		0			0
$847$	−19.5438	+	19.5438i	−0.671533	+	0.671533i
$848$	1.37973	−	2.37050i	0.0473802	−	0.0814032i
$849$		0			0
$850$		0			0
$851$		−	36.4578i		−	1.24976i
$852$		0			0
$853$	17.9348	−	17.9348i	0.614074	−	0.614074i	−0.329931	−	0.944005i	$-0.607025\pi$
$853$	17.9348	−	17.9348i	0.614074	−	0.614074i	0.944005	+	0.329931i	$0.107025\pi$
$854$	5.69303	−	6.48016i	0.194811	−	0.221747i
$855$		0			0
$856$	8.72373	−	12.9818i	0.298171	−	0.443709i
$857$	−9.00378	−	9.00378i	−0.307563	−	0.307563i	0.536400	−	0.843964i	$-0.319784\pi$
$857$	−9.00378	−	9.00378i	−0.307563	−	0.307563i	−0.843964	+	0.536400i	$0.819784\pi$
$858$		0			0
$859$	24.6779			0.841998			0.420999	−	0.907061i	$-0.361680\pi$
$859$	24.6779			0.841998			0.420999	+	0.907061i	$0.361680\pi$
$860$		0			0
$861$		0			0
$862$	2.84297	+	43.9669i	0.0968318	+	1.49752i
$863$	−40.4811	−	40.4811i	−1.37799	−	1.37799i	−0.848009	−	0.529982i	$-0.822198\pi$
$863$	−40.4811	−	40.4811i	−1.37799	−	1.37799i	−0.529982	−	0.848009i	$-0.677802\pi$
$864$		0			0
$865$		0			0
$866$	−16.0499	+	18.2691i	−0.545399	+	0.620808i
$867$		0			0
$868$	−25.1419	−	19.3623i	−0.853373	−	0.657201i
$869$		−	5.18257i		−	0.175807i
$870$		0			0
$871$			31.9048i			1.08105i
$872$	−8.59179	−	43.7966i	−0.290955	−	1.48314i
$873$		0			0
$874$	32.7243	+	28.7493i	1.10692	+	0.972460i
$875$		0			0
$876$		0			0
$877$	1.59507	+	1.59507i	0.0538616	+	0.0538616i	0.733525	−	0.679663i	$-0.237874\pi$
$877$	1.59507	+	1.59507i	0.0538616	+	0.0538616i	−0.679663	+	0.733525i	$0.737874\pi$
$878$	−20.1764	+	1.30464i	−0.680922	+	0.0440294i
$879$		0			0
$880$		0			0
$881$	−33.2876			−1.12149			−0.560744	−	0.827989i	$-0.689485\pi$
$881$	−33.2876			−1.12149			−0.560744	+	0.827989i	$0.689485\pi$
$882$		0			0
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	0.00956956	−	0.999954i	$-0.496954\pi$
$883$	−29.4296	−	29.4296i	−0.990385	−	0.990385i	−0.999954	+	0.00956956i	$0.996954\pi$
$884$	13.9435	−	1.81078i	0.468969	−	0.0609032i
$885$		0			0
$886$	−10.5601	−	9.27737i	−0.354773	−	0.311679i
$887$	30.9776	−	30.9776i	1.04013	−	1.04013i	0.0409656	−	0.999161i	$-0.486957\pi$
$887$	30.9776	−	30.9776i	1.04013	−	1.04013i	0.999161	−	0.0409656i	$-0.0130434\pi$
$888$		0			0
$889$			42.0294i			1.40962i
$890$		0			0
$891$		0			0
$892$	−7.44837	−	5.73615i	−0.249390	−	0.192061i
$893$	7.84014	−	7.84014i	0.262360	−	0.262360i
$894$		0			0
$895$		0			0
$896$	9.77460	−	28.2238i	0.326546	−	0.942890i
$897$		0			0
$898$	−3.50972	−	54.2784i	−0.117121	−	1.81129i
$899$	−15.8668			−0.529186
$900$		0			0
$901$	1.09083			0.0363408
$902$	0.282526	+	4.36931i	0.00940709	+	0.145482i
$903$		0			0
$904$	4.11590	−	6.12489i	0.136893	−	0.203711i
$905$		0			0
$906$		0			0
$907$	−28.6790	+	28.6790i	−0.952271	+	0.952271i	−0.998912	−	0.0466405i	$-0.985148\pi$
$907$	−28.6790	+	28.6790i	−0.952271	+	0.952271i	0.0466405	+	0.998912i	$0.485148\pi$
$908$	15.2533	−	19.8063i	0.506198	−	0.657297i
$909$		0			0
$910$		0			0
$911$			31.8607i			1.05559i	0.849371	+	0.527796i	$0.176981\pi$
$911$			31.8607i			1.05559i	−0.849371	+	0.527796i	$0.823019\pi$
$912$		0			0
$913$	−2.59129	+	2.59129i	−0.0857591	+	0.0857591i
$914$	7.42162	+	6.52013i	0.245485	+	0.215667i
$915$		0			0
$916$	−1.82638	−	14.0636i	−0.0603452	−	0.464673i
$917$	8.54072	+	8.54072i	0.282039	+	0.282039i
$918$		0			0
$919$	−55.4206			−1.82816			−0.914079	−	0.405536i	$-0.867085\pi$
$919$	−55.4206			−1.82816			−0.914079	+	0.405536i	$0.867085\pi$
$920$		0			0
$921$		0			0
$922$	38.3426	−	2.47929i	1.26275	−	0.0816510i
$923$	41.0109	+	41.0109i	1.34989	+	1.34989i
$924$		0			0
$925$		0			0
$926$	7.45671	+	6.55096i	0.245043	+	0.215278i
$927$		0			0
$928$	−4.73830	−	14.1626i	−0.155542	−	0.464911i
$929$		−	46.9603i		−	1.54072i	−0.637610	−	0.770359i	$-0.720077\pi$
$929$		−	46.9603i		−	1.54072i	0.637610	−	0.770359i	$-0.279923\pi$
$930$		0			0
$931$		−	0.113038i		−	0.00370466i
$932$	−26.5332	+	34.4533i	−0.869124	+	1.12855i
$933$		0			0
$934$	28.0291	−	31.9045i	0.917140	−	1.04395i
$935$		0			0
$936$		0			0
$937$	−10.4693	−	10.4693i	−0.342016	−	0.342016i	0.515109	−	0.857125i	$-0.327752\pi$
$937$	−10.4693	−	10.4693i	−0.342016	−	0.342016i	−0.857125	+	0.515109i	$0.827752\pi$
$938$	1.73928	+	26.8982i	0.0567895	+	0.878258i
$939$		0			0
$940$		0			0
$941$	41.1084			1.34009			0.670047	−	0.742318i	$-0.266274\pi$
$941$	41.1084			1.34009			0.670047	+	0.742318i	$0.266274\pi$
$942$		0			0
$943$	24.7909	+	24.7909i	0.807303	+	0.807303i
$944$	19.0594	−	5.03527i	0.620332	−	0.163884i
$945$		0			0
$946$	−4.90917	+	5.58793i	−0.159611	+	0.181679i
$947$	−25.8091	+	25.8091i	−0.838682	+	0.838682i	−0.988685	−	0.150003i	$-0.952072\pi$
$947$	−25.8091	+	25.8091i	−0.838682	+	0.838682i	0.150003	+	0.988685i	$0.452072\pi$
$948$		0			0
$949$			24.8099i			0.805362i
$950$		0			0
$951$		0			0
$952$	11.6567	−	2.28675i	0.377796	−	0.0741141i
$953$	−7.78429	+	7.78429i	−0.252158	+	0.252158i	−0.821855	−	0.569697i	$-0.807061\pi$
$953$	−7.78429	+	7.78429i	−0.252158	+	0.252158i	0.569697	+	0.821855i	$0.307061\pi$
$954$		0			0
$955$		0			0
$956$	1.40115	−	0.181962i	0.0453165	−	0.00588507i
$957$		0			0
$958$	26.5047	−	1.71384i	0.856329	−	0.0553715i
$959$	15.2875			0.493658
$960$		0			0
$961$	−5.12110			−0.165197
$962$	27.5618	−	1.78219i	0.888627	−	0.0574600i
$963$		0			0
$964$	−49.5818	+	6.43899i	−1.59692	+	0.207386i
$965$		0			0
$966$		0			0
$967$	−11.7235	+	11.7235i	−0.377001	+	0.377001i	−0.870019	−	0.493018i	$-0.835894\pi$
$967$	−11.7235	+	11.7235i	−0.377001	+	0.377001i	0.493018	+	0.870019i	$0.335894\pi$
$968$	−29.0577	+	5.70039i	−0.933950	+	0.183217i
$969$		0			0
$970$		0			0
$971$			12.9748i			0.416380i	0.978088	+	0.208190i	$0.0667572\pi$
$971$			12.9748i			0.416380i	−0.978088	+	0.208190i	$0.933243\pi$
$972$		0			0
$973$	25.3700	−	25.3700i	0.813324	−	0.813324i
$974$	3.92120	−	4.46336i	0.125643	−	0.143015i
$975$		0			0
$976$	8.93475	−	2.36045i	0.285994	−	0.0755561i
$977$	−13.9054	−	13.9054i	−0.444873	−	0.444873i	0.448773	−	0.893646i	$-0.351861\pi$
$977$	−13.9054	−	13.9054i	−0.444873	−	0.444873i	−0.893646	+	0.448773i	$0.851861\pi$
$978$		0			0
$979$	0.750572			0.0239884
$980$		0			0
$981$		0			0
$982$	−2.69639	−	41.7001i	−0.0860452	−	1.33070i
$983$	13.9381	+	13.9381i	0.444557	+	0.444557i	0.893540	−	0.448983i	$-0.148214\pi$
$983$	13.9381	+	13.9381i	0.444557	+	0.444557i	−0.448983	+	0.893540i	$0.648214\pi$
$984$		0			0
$985$		0			0
$986$	3.92007	−	4.46207i	0.124840	−	0.142101i
$987$		0			0
$988$	−20.1345	+	26.1446i	−0.640565	+	0.831771i
$989$			59.5592i			1.89387i
$990$		0			0
$991$			52.9621i			1.68240i	0.540726	+	0.841199i	$0.318150\pi$
$991$			52.9621i			1.68240i	−0.540726	+	0.841199i	$0.681850\pi$
$992$	−10.7869	−	32.2416i	−0.342484	−	1.02367i
$993$		0			0
$994$	36.8111	+	32.3397i	1.16758	+	1.02575i
$995$		0			0
$996$		0			0
$997$	−1.53452	−	1.53452i	−0.0485986	−	0.0485986i	0.682390	−	0.730988i	$-0.260941\pi$
$997$	−1.53452	−	1.53452i	−0.0485986	−	0.0485986i	−0.730988	+	0.682390i	$0.760941\pi$
$998$	−21.2357	+	1.37313i	−0.672204	+	0.0434657i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.k.n.307.1		12
3.2	odd	2		300.2.j.d.7.6		12
4.3	odd	2	inner	900.2.k.n.307.3		12
5.2	odd	4		180.2.k.e.163.4		12
5.3	odd	4	inner	900.2.k.n.343.3		12
5.4	even	2		180.2.k.e.127.6		12
12.11	even	2		300.2.j.d.7.4		12
15.2	even	4		60.2.j.a.43.3	yes	12
15.8	even	4		300.2.j.d.43.4		12
15.14	odd	2		60.2.j.a.7.1	✓	12
20.3	even	4	inner	900.2.k.n.343.1		12
20.7	even	4		180.2.k.e.163.6		12
20.19	odd	2		180.2.k.e.127.4		12
60.23	odd	4		300.2.j.d.43.6		12
60.47	odd	4		60.2.j.a.43.1	yes	12
60.59	even	2		60.2.j.a.7.3	yes	12
120.29	odd	2		960.2.w.g.127.4		12
120.59	even	2		960.2.w.g.127.1		12
120.77	even	4		960.2.w.g.703.1		12
120.107	odd	4		960.2.w.g.703.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	15.14	odd	2
60.2.j.a.7.3	yes	12	60.59	even	2
60.2.j.a.43.1	yes	12	60.47	odd	4
60.2.j.a.43.3	yes	12	15.2	even	4
180.2.k.e.127.4		12	20.19	odd	2
180.2.k.e.127.6		12	5.4	even	2
180.2.k.e.163.4		12	5.2	odd	4
180.2.k.e.163.6		12	20.7	even	4
300.2.j.d.7.4		12	12.11	even	2
300.2.j.d.7.6		12	3.2	odd	2
300.2.j.d.43.4		12	15.8	even	4
300.2.j.d.43.6		12	60.23	odd	4
900.2.k.n.307.1		12	1.1	even	1	trivial
900.2.k.n.307.3		12	4.3	odd	2	inner
900.2.k.n.343.1		12	20.3	even	4	inner
900.2.k.n.343.3		12	5.3	odd	4	inner
960.2.w.g.127.1		12	120.59	even	2
960.2.w.g.127.4		12	120.29	odd	2
960.2.w.g.703.1		12	120.77	even	4
960.2.w.g.703.4		12	120.107	odd	4

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41127 + 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.86678 + 1.86678i) q^{7} +(-2.77552 + 0.544488i) q^{8} +O(q^{10})\)	\(q+(-1.41127 + 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.86678 + 1.86678i) q^{7} +(-2.77552 + 0.544488i) q^{8} -0.728515i q^{11} +(3.12489 - 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(1.12489 + 1.12489i) q^{17} -3.73356 q^{19} +(0.0664803 + 1.02813i) q^{22} +(5.83347 + 5.83347i) q^{23} +(-4.12489 + 4.69521i) q^{26} +(-3.22164 + 4.18329i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(-5.36458 + 1.79480i) q^{32} +(-1.69016 - 1.48486i) q^{34} +(-3.12489 - 3.12489i) q^{37} +(5.26904 - 0.340704i) q^{38} +4.24977 q^{41} +(5.10495 + 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(-2.09991 + 2.09991i) q^{47} +0.0302761i q^{49} +(5.39285 - 7.00260i) q^{52} +(0.484862 - 0.484862i) q^{53} +(4.16485 - 6.19773i) q^{56} +(-0.240914 - 3.72578i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(-0.548448 - 8.48183i) q^{62} +(7.40707 - 3.02248i) q^{64} +(-5.10495 + 5.10495i) q^{67} +(2.52077 + 1.94130i) q^{68} +13.1240i q^{71} +(-3.96972 + 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(1.35998 + 1.35998i) q^{77} +7.11388 q^{79} +(-5.99756 + 0.387811i) q^{82} +(-3.55694 - 3.55694i) q^{83} +(-7.67030 - 6.73860i) q^{86} +(0.396668 + 2.02201i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(13.0723 + 10.0673i) q^{92} +(2.77191 - 3.15516i) q^{94} +(12.5298 + 12.5298i) q^{97} +(-0.00276283 - 0.0427276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8}+O(q^{10}) \) 12 * q - 12 * q^8	\( 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61} - 56 q^{62} - 16 q^{68} - 44 q^{73} + 8 q^{76} + 48 q^{77} - 16 q^{82} - 64 q^{86} - 60 q^{88} + 56 q^{92} + 20 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q - 12 * q^8 + 4 * q^13 + 12 * q^16 - 20 * q^17 - 12 * q^22 - 16 * q^26 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 40 * q^46 + 8 * q^52 + 4 * q^53 + 64 * q^56 + 20 * q^58 - 32 * q^61 - 56 * q^62 - 16 * q^68 - 44 * q^73 + 8 * q^76 + 48 * q^77 - 16 * q^82 - 64 * q^86 - 60 * q^88 + 56 * q^92 + 20 * q^97 + 24 * q^98

Introduction

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