LMFDB - Embedded newform 180.2.k.e.127.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [180,2,Mod(127,180)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(180, 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("180.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.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:	$1.43730723638$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			127.4
Root			$-0.0912546 + 1.41127i$ of defining polynomial
Character	$\chi$	$=$	180.127
Dual form			180.2.k.e.163.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0912546 + 1.41127i) q^{2} +(-1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(-1.86678 + 1.86678i) q^{7} +(0.544488 - 2.77552i) q^{8} +O(q^{10})$	\(q+(-0.0912546 + 1.41127i) q^{2} +(-1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(-1.86678 + 1.86678i) q^{7} +(0.544488 - 2.77552i) q^{8} +(-2.42670 - 2.02759i) q^{10} +0.728515i q^{11} +(-3.12489 + 3.12489i) q^{13} +(-2.46417 - 2.80487i) q^{14} +(3.86732 + 1.02170i) q^{16} +(-1.12489 - 1.12489i) q^{17} +3.73356 q^{19} +(3.08292 - 3.23969i) q^{20} +(-1.02813 - 0.0664803i) q^{22} +(5.83347 + 5.83347i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(-4.12489 - 4.69521i) q^{26} +(4.18329 - 3.22164i) q^{28} +2.64002i q^{29} -6.01008i q^{31} +(-1.79480 + 5.36458i) q^{32} +(1.69016 - 1.48486i) q^{34} +(-0.905130 - 5.83347i) q^{35} +(3.12489 + 3.12489i) q^{37} +(-0.340704 + 5.26904i) q^{38} +(4.29074 + 4.64646i) q^{40} +4.24977 q^{41} +(5.10495 + 5.10495i) q^{43} +(0.187643 - 1.44490i) q^{44} +(-8.76491 + 7.70025i) q^{46} +(-2.09991 + 2.09991i) q^{47} +0.0302761i q^{49} +(6.86282 - 1.70344i) q^{50} +(7.00260 - 5.39285i) q^{52} +(-0.484862 + 0.484862i) q^{53} +(-1.31488 - 0.961649i) q^{55} +(4.16485 + 6.19773i) q^{56} +(-3.72578 - 0.240914i) q^{58} -4.92834 q^{59} +2.31032 q^{61} +(8.48183 + 0.548448i) q^{62} +(-7.40707 - 3.02248i) q^{64} +(-1.51514 - 9.76491i) q^{65} +(-5.10495 + 5.10495i) q^{67} +(1.94130 + 2.52077i) q^{68} +(8.31518 - 0.745049i) q^{70} -13.1240i q^{71} +(3.96972 - 3.96972i) q^{73} +(-4.69521 + 4.12489i) q^{74} +(-7.40493 - 0.961649i) q^{76} +(-1.35998 - 1.35998i) q^{77} -7.11388 q^{79} +(-6.94894 + 5.63137i) q^{80} +(-0.387811 + 5.99756i) q^{82} +(-3.55694 - 3.55694i) q^{83} +(3.51514 - 0.545414i) q^{85} +(-7.67030 + 6.73860i) q^{86} +(2.02201 + 0.396668i) q^{88} +1.03028i q^{89} -11.6669i q^{91} +(-10.0673 - 13.0723i) q^{92} +(-2.77191 - 3.15516i) q^{94} +(-4.92834 + 6.73860i) q^{95} +(-12.5298 - 12.5298i) q^{97} +(-0.0427276 - 0.00276283i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^8	$ 12 q + 12 q^{8} - 8 q^{10} - 4 q^{13} + 12 q^{16} + 20 q^{17} - 20 q^{20} + 12 q^{22} - 20 q^{25} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{37} - 16 q^{38} - 8 q^{40} - 16 q^{41} - 40 q^{46} + 16 q^{50} - 8 q^{52} - 4 q^{53} + 64 q^{56} - 20 q^{58} - 32 q^{61} + 56 q^{62} - 20 q^{65} + 16 q^{68} + 44 q^{70} + 44 q^{73} + 8 q^{76} - 48 q^{77} - 4 q^{80} + 16 q^{82} + 44 q^{85} - 64 q^{86} + 60 q^{88} - 56 q^{92} - 20 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q + 12 * q^8 - 8 * q^10 - 4 * q^13 + 12 * q^16 + 20 * q^17 - 20 * q^20 + 12 * q^22 - 20 * q^25 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^37 - 16 * q^38 - 8 * q^40 - 16 * q^41 - 40 * q^46 + 16 * q^50 - 8 * q^52 - 4 * q^53 + 64 * q^56 - 20 * q^58 - 32 * q^61 + 56 * q^62 - 20 * q^65 + 16 * q^68 + 44 * q^70 + 44 * q^73 + 8 * q^76 - 48 * q^77 - 4 * q^80 + 16 * q^82 + 44 * q^85 - 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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−0.0912546	+	1.41127i	−0.0645267	+	0.997916i
$2$	−0.0912546	+	1.41127i	−0.0645267	+	0.997916i
$3$		0			0
$3$		0			0
$4$	−1.98335	−	0.257569i	−0.991673	−	0.128785i
$5$	−1.32001	+	1.80487i	−0.590327	+	0.807164i
$5$	−1.32001	+	1.80487i	−0.590327	+	0.807164i
$6$		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	$0.416269\pi$
$8$	0.544488	−	2.77552i	0.192506	−	0.981296i
$9$		0			0
$10$	−2.42670	−	2.02759i	−0.767390	−	0.641181i
$11$			0.728515i			0.219656i	0.993951	+	0.109828i	$0.0350299\pi$
$11$			0.728515i			0.219656i	−0.993951	+	0.109828i	$0.964970\pi$
$12$		0			0
$13$	−3.12489	+	3.12489i	−0.866687	+	0.866687i	−0.992104	−	0.125417i	$-0.959973\pi$
$13$	−3.12489	+	3.12489i	−0.866687	+	0.866687i	0.125417	+	0.992104i	$0.459973\pi$
$14$	−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	0.557412	−	0.830236i	$-0.311795\pi$
$17$	−1.12489	−	1.12489i	−0.272825	−	0.272825i	−0.830236	+	0.557412i	$0.811795\pi$
$18$		0			0
$19$	3.73356			0.856537			0.428268	−	0.903652i	$-0.359124\pi$
$19$	3.73356			0.856537			0.428268	+	0.903652i	$0.359124\pi$
$20$	3.08292	−	3.23969i	0.689362	−	0.724417i
$21$		0			0
$22$	−1.02813	−	0.0664803i	−0.219198	−	0.0141737i
$23$	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
$25$	−1.51514	−	4.76491i	−0.303028	−	0.952982i
$26$	−4.12489	−	4.69521i	−0.808957	−	0.920806i
$27$		0			0
$28$	4.18329	−	3.22164i	0.790568	−	0.608833i
$29$			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	$-0.818530\pi$
$31$		−	6.01008i		−	1.07944i	0.841844	−	0.539721i	$-0.181470\pi$
$32$	−1.79480	+	5.36458i	−0.317278	+	0.948333i
$33$		0			0
$34$	1.69016	−	1.48486i	0.289861	−	0.254652i
$35$	−0.905130	−	5.83347i	−0.152995	−	0.986036i
$36$		0			0
$37$	3.12489	+	3.12489i	0.513728	+	0.513728i	0.915667	−	0.401939i	$-0.131663\pi$
$37$	3.12489	+	3.12489i	0.513728	+	0.513728i	−0.401939	+	0.915667i	$0.631663\pi$
$38$	−0.340704	+	5.26904i	−0.0552695	+	0.854752i
$39$		0			0
$40$	4.29074	+	4.64646i	0.678426	+	0.734669i
$41$	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
$50$	6.86282	−	1.70344i	0.970549	−	0.240903i
$51$		0			0
$52$	7.00260	−	5.39285i	0.971086	−	0.747854i
$53$	−0.484862	+	0.484862i	−0.0666009	+	0.0666009i	−0.739623	−	0.673022i	$-0.764996\pi$
$53$	−0.484862	+	0.484862i	−0.0666009	+	0.0666009i	0.673022	+	0.739623i	$0.264996\pi$
$54$		0			0
$55$	−1.31488	−	0.961649i	−0.177298	−	0.129669i
$56$	4.16485	+	6.19773i	0.556552	+	0.828206i
$57$		0			0
$58$	−3.72578	−	0.240914i	−0.489218	−	0.0316336i
$59$	−4.92834			−0.641615			−0.320808	−	0.947144i	$-0.603954\pi$
$59$	−4.92834			−0.641615			−0.320808	+	0.947144i	$0.603954\pi$
$60$		0			0
$61$	2.31032			0.295807			0.147903	−	0.989002i	$-0.452748\pi$
$61$	2.31032			0.295807			0.147903	+	0.989002i	$0.452748\pi$
$62$	8.48183	+	0.548448i	1.07719	+	0.0696529i
$63$		0			0
$64$	−7.40707	−	3.02248i	−0.925883	−	0.377810i
$65$	−1.51514	−	9.76491i	−0.187930	−	1.21119i
$66$		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	$0.395376\pi$
$68$	1.94130	+	2.52077i	0.235417	+	0.305688i
$69$		0			0
$70$	8.31518	−	0.745049i	0.993854	−	0.0890503i
$71$		−	13.1240i		−	1.55753i	−0.627317	−	0.778764i	$-0.715847\pi$
$71$		−	13.1240i		−	1.55753i	0.627317	−	0.778764i	$-0.284153\pi$
$72$		0			0
$73$	3.96972	−	3.96972i	0.464621	−	0.464621i	−0.435546	−	0.900167i	$-0.643445\pi$
$73$	3.96972	−	3.96972i	0.464621	−	0.464621i	0.900167	+	0.435546i	$0.143445\pi$
$74$	−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	$-0.631055\pi$
$79$	−7.11388			−0.800375			−0.400187	+	0.916433i	$0.631055\pi$
$80$	−6.94894	+	5.63137i	−0.776915	+	0.629606i
$81$		0			0
$82$	−0.387811	+	5.99756i	−0.0428266	+	0.662320i
$83$	−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
$85$	3.51514	−	0.545414i	0.381270	−	0.0591585i
$86$	−7.67030	+	6.73860i	−0.827110	+	0.726642i
$87$		0			0
$88$	2.02201	+	0.396668i	0.215547	+	0.0422849i
$89$			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
$92$	−10.0673	−	13.0723i	−1.04958	−	1.36288i
$93$		0			0
$94$	−2.77191	−	3.15516i	−0.285901	−	0.325430i
$95$	−4.92834	+	6.73860i	−0.505637	+	0.691366i
$96$		0			0
$97$	−12.5298	−	12.5298i	−1.27221	−	1.27221i	−0.944926	−	0.327284i	$-0.893867\pi$
$97$	−12.5298	−	12.5298i	−1.27221	−	1.27221i	−0.327284	−	0.944926i	$-0.606133\pi$
$98$	−0.0427276	−	0.00276283i	−0.00431614	−	0.000279088i
$99$		0			0
$100$	1.77775	+	9.84071i	0.177775	+	0.984071i
$101$	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	$0.727294\pi$
$110$	1.47713	−	1.76789i	0.140839	−	0.168562i
$111$		0			0
$112$	−9.12670	+	5.31214i	−0.862392	+	0.501950i
$113$	1.84484	−	1.84484i	0.173548	−	0.173548i	−0.614988	−	0.788536i	$-0.710839\pi$
$113$	1.84484	−	1.84484i	0.173548	−	0.173548i	0.788536	+	0.614988i	$0.210839\pi$
$114$		0			0
$115$	−18.2289	+	2.82843i	−1.69986	+	0.263752i
$116$	0.679988	−	5.23608i	0.0631353	−	0.486158i
$117$		0			0
$118$	0.449733	−	6.95520i	0.0414013	−	0.640278i
$119$	4.19982			0.384997
$120$		0			0
$121$	10.4693			0.951751
$122$	−0.210828	+	3.26048i	−0.0190874	+	0.295190i
$123$		0			0
$124$	−1.54801	+	11.9201i	−0.139016	+	1.07045i
$125$	10.6001	+	3.55510i	0.948098	+	0.317978i
$126$		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	$0.000345478\pi$
$128$	4.94145	−	10.1775i	0.436767	−	0.899575i
$129$		0			0
$130$	13.9192	−	1.24717i	1.22079	−	0.109384i
$131$			4.57511i			0.399729i	0.979824	+	0.199865i	$0.0640502\pi$
$131$			4.57511i			0.399729i	−0.979824	+	0.199865i	$0.935950\pi$
$132$		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	0.860045	−	0.510219i	$-0.170436\pi$
$137$	4.09461	+	4.09461i	0.349826	+	0.349826i	−0.510219	+	0.860045i	$0.670436\pi$
$138$		0			0
$139$	13.5902			1.15271			0.576354	−	0.817200i	$-0.304475\pi$
$139$	13.5902			1.15271			0.576354	+	0.817200i	$0.304475\pi$
$140$	0.292664	+	11.8029i	0.0247346	+	0.997528i
$141$		0			0
$142$	18.5214	+	1.19762i	1.55428	+	0.100502i
$143$	−2.27653	−	2.27653i	−0.190373	−	0.190373i
$144$		0			0
$145$	−4.76491	−	3.48486i	−0.395704	−	0.289402i
$146$	5.24008	+	5.96459i	0.433672	+	0.493633i
$147$		0			0
$148$	−5.39285	−	7.00260i	−0.443290	−	0.575610i
$149$		−	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	$0.286390\pi$
$151$			19.2471i			1.56631i	−0.621829	+	0.783153i	$0.713610\pi$
$152$	2.03288	−	10.3626i	0.164888	−	0.840516i
$153$		0			0
$154$	2.04339	−	1.79518i	0.164661	−	0.144660i
$155$	10.8474	+	7.93338i	0.871287	+	0.637224i
$156$		0			0
$157$	−2.09461	−	2.09461i	−0.167168	−	0.167168i	0.618565	−	0.785733i	$-0.287714\pi$
$157$	−2.09461	−	2.09461i	−0.167168	−	0.167168i	−0.785733	+	0.618565i	$0.787714\pi$
$158$	0.649175	−	10.0396i	0.0516456	−	0.798707i
$159$		0			0
$160$	−7.31324	−	10.3207i	−0.578162	−	0.815922i
$161$	−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
$170$	0.448952	+	5.01057i	0.0344331	+	0.384293i
$171$		0			0
$172$	−8.81001	−	11.4398i	−0.671757	−	0.872274i
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.290312	+	0.956932i	$0.593759\pi$
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.956932	+	0.290312i	$0.906241\pi$
$174$		0			0
$175$	11.7235	+	6.06660i	0.886210	+	0.458592i
$176$	−0.744321	+	2.81740i	−0.0561053	+	0.212369i
$177$		0			0
$178$	−1.45399	−	0.0940174i	−0.108981	−	0.00704690i
$179$	24.4156			1.82491			0.912455	−	0.409178i	$-0.134185\pi$
$179$	24.4156			1.82491			0.912455	+	0.409178i	$0.134185\pi$
$180$		0			0
$181$	11.2800			0.838439			0.419220	−	0.907885i	$-0.362304\pi$
$181$	11.2800			0.838439			0.419220	+	0.907885i	$0.362304\pi$
$182$	16.4652	+	1.06466i	1.22048	+	0.0789180i
$183$		0			0
$184$	19.3672	−	13.0147i	1.42777	−	0.959455i
$185$	−9.76491	+	1.51514i	−0.717930	+	0.111395i
$186$		0			0
$187$	0.819496	−	0.819496i	0.0599275	−	0.0599275i
$188$	4.70572	−	3.62398i	0.343200	−	0.264306i
$189$		0			0
$190$	−9.06022	−	7.57013i	−0.657298	−	0.549195i
$191$			3.26729i			0.236413i	0.992989	+	0.118206i	$0.0377144\pi$
$191$			3.26729i			0.236413i	−0.992989	+	0.118206i	$0.962286\pi$
$192$		0			0
$193$	0.939448	−	0.939448i	0.0676229	−	0.0676229i	−0.672486	−	0.740109i	$-0.734774\pi$
$193$	0.939448	−	0.939448i	0.0676229	−	0.0676229i	0.740109	+	0.672486i	$0.234774\pi$
$194$	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	0.757023	−	0.653388i	$-0.226653\pi$
$197$	1.45459	+	1.45459i	0.103635	+	0.103635i	−0.653388	+	0.757023i	$0.726653\pi$
$198$		0			0
$199$	5.19059			0.367951			0.183975	−	0.982931i	$-0.441103\pi$
$199$	5.19059			0.367951			0.183975	+	0.982931i	$0.441103\pi$
$200$	−14.0501	+	1.61087i	−0.993492	+	0.113906i
$201$		0			0
$202$	−0.517441	+	8.00230i	−0.0364070	+	0.563040i
$203$	−4.92834	−	4.92834i	−0.345902	−	0.345902i
$204$		0			0
$205$	−5.60975	+	7.67030i	−0.391802	+	0.535717i
$206$	0.0849206	−	0.0746054i	0.00591670	−	0.00519801i
$207$		0			0
$208$	−15.2776	+	8.89224i	−1.05931	+	0.616566i
$209$			2.71995i			0.188143i
$210$		0			0
$211$		−	11.7800i		−	0.810967i	−0.914102	−	0.405483i	$-0.867103\pi$
$211$		−	11.7800i		−	0.810967i	0.914102	−	0.405483i	$-0.132897\pi$
$212$	1.08653	−	0.836763i	0.0746235	−	0.0574691i
$213$		0			0
$214$	−5.16147	−	5.87511i	−0.352831	−	0.401615i
$215$	−15.9524	+	2.47520i	−1.08794	+	0.168807i
$216$		0			0
$217$	11.2195	+	11.2195i	0.761629	+	0.761629i
$218$	−22.2692	−	1.43996i	−1.50826	−	0.0975264i
$219$		0			0
$220$	2.36017	+	2.24595i	0.159122	+	0.151422i
$221$	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	$-0.0752757\pi$
$230$	−2.32819	−	25.9840i	−0.153516	−	1.71333i
$231$		0			0
$232$	7.32745	+	1.43746i	0.481071	+	0.0943739i
$233$	15.3747	−	15.3747i	1.00723	−	1.00723i	0.00725353	−	0.999974i	$-0.497691\pi$
$233$	15.3747	−	15.3747i	1.00723	−	1.00723i	0.999974	−	0.00725353i	$-0.00230889\pi$
$234$		0			0
$235$	−1.01817	−	6.56198i	−0.0664179	−	0.428057i
$236$	9.77460	+	1.26939i	0.636272	+	0.0826301i
$237$		0			0
$238$	−0.383253	+	5.92707i	−0.0248426	+	0.384195i
$239$	−0.706459			−0.0456970			−0.0228485	−	0.999739i	$-0.507274\pi$
$239$	−0.706459			−0.0456970			−0.0228485	+	0.999739i	$0.507274\pi$
$240$		0			0
$241$	−24.9991			−1.61033			−0.805166	−	0.593049i	$-0.797924\pi$
$241$	−24.9991			−1.61033			−0.805166	+	0.593049i	$0.797924\pi$
$242$	−0.955368	+	14.7749i	−0.0614134	+	0.949768i
$243$		0			0
$244$	−4.58217	−	0.595068i	−0.293343	−	0.0380953i
$245$	−0.0546445	−	0.0399648i	−0.00349111	−	0.00255326i
$246$		0			0
$247$	−11.6669	+	11.6669i	−0.742349	+	0.742349i
$248$	−16.6811	−	3.27242i	−1.05925	−	0.207799i
$249$		0			0
$250$	−5.98450	+	14.6351i	−0.378493	+	0.925604i
$251$			28.6154i			1.80619i	0.429440	+	0.903095i	$0.358711\pi$
$251$			28.6154i			1.80619i	−0.429440	+	0.903095i	$0.641289\pi$
$252$		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	0.818342	−	0.574731i	$-0.194893\pi$
$257$	3.90539	+	3.90539i	0.243612	+	0.243612i	−0.574731	+	0.818342i	$0.694893\pi$
$258$		0			0
$259$	−11.6669			−0.724948
$260$	0.489904	+	19.7574i	0.0303825	+	1.22530i
$261$		0			0
$262$	−6.45670	−	0.417500i	−0.398896	−	0.0257932i
$263$	−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
$265$	−0.235091	−	1.51514i	−0.0144415	−	0.0930742i
$266$	−9.20012	−	10.4722i	−0.564095	−	0.642089i
$267$		0			0
$268$	11.4398	−	8.81001i	0.698795	−	0.538157i
$269$			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	$0.154938\pi$
$271$			15.4005i			0.935513i	−0.883857	+	0.467757i	$0.845062\pi$
$272$	−3.20100	−	5.49958i	−0.194089	−	0.333461i
$273$		0			0
$274$	−6.15224	+	5.40493i	−0.371670	+	0.326524i
$275$	3.47131	−	1.10380i	0.209328	−	0.0665617i
$276$		0			0
$277$	8.59415	+	8.59415i	0.516372	+	0.516372i	0.916472	−	0.400099i	$-0.131024\pi$
$277$	8.59415	+	8.59415i	0.516372	+	0.516372i	−0.400099	+	0.916472i	$0.631024\pi$
$278$	−1.24017	+	19.1794i	−0.0743805	+	1.15031i
$279$		0			0
$280$	−16.6838	−	0.664043i	−0.997046	−	0.0396842i
$281$	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
$290$	5.35289	−	6.40655i	0.314332	−	0.376205i
$291$		0			0
$292$	−8.89581	+	6.85085i	−0.520588	+	0.400916i
$293$	−6.23509	+	6.23509i	−0.364258	+	0.364258i	−0.865378	−	0.501120i	$-0.832922\pi$
$293$	−6.23509	+	6.23509i	−0.364258	+	0.364258i	0.501120	+	0.865378i	$0.332922\pi$
$294$		0			0
$295$	6.50547	−	8.89503i	0.378763	−	0.517889i
$296$	10.3747	−	6.97173i	0.603015	−	0.405224i
$297$		0			0
$298$	8.00230	+	0.517441i	0.463561	+	0.0299745i
$299$	−36.4578			−2.10841
$300$		0			0
$301$	−19.0596			−1.09858
$302$	−27.1628	−	1.75639i	−1.56304	−	0.101069i
$303$		0			0
$304$	14.4388	+	3.81456i	0.828125	+	0.218780i
$305$	−3.04965	+	4.16984i	−0.174623	+	0.238764i
$306$		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	$0.261630\pi$
$308$	2.34702	+	3.04759i	0.133734	+	0.173653i
$309$		0			0
$310$	−12.1860	+	14.5847i	−0.692118	+	0.828354i
$311$		−	24.4377i		−	1.38573i	−0.721066	−	0.692867i	$-0.756347\pi$
$311$		−	24.4377i		−	1.38573i	0.721066	−	0.692867i	$-0.243653\pi$
$312$		0			0
$313$	18.5904	−	18.5904i	1.05079	−	1.05079i	0.0521506	−	0.998639i	$-0.483392\pi$
$313$	18.5904	−	18.5904i	1.05079	−	1.05079i	0.998639	−	0.0521506i	$-0.0166076\pi$
$314$	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	$-0.971718\pi$
$317$	−19.3141	−	19.3141i	−1.08479	−	1.08479i	−0.0887327	−	0.996055i	$-0.528282\pi$
$318$		0			0
$319$	−1.92330			−0.107684
$320$	15.2326	−	9.37911i	0.851529	−	0.524308i
$321$		0			0
$322$	1.98749	−	30.7368i	0.110758	−	1.71289i
$323$	−4.19982	−	4.19982i	−0.233684	−	0.233684i
$324$		0			0
$325$	19.6244	+	10.1552i	1.08857	+	0.563307i
$326$	−6.43899	+	5.65685i	−0.356623	+	0.313304i
$327$		0			0
$328$	2.31395	−	11.7953i	0.127766	−	0.651289i
$329$		−	7.84014i		−	0.432241i
$330$		0			0
$331$			11.0294i			0.606231i	0.952954	+	0.303115i	$0.0980268\pi$
$331$			11.0294i			0.606231i	−0.952954	+	0.303115i	$0.901973\pi$
$332$	6.13849	+	7.97080i	0.336893	+	0.437455i
$333$		0			0
$334$	5.77695	+	6.57569i	0.316101	+	0.359806i
$335$	−2.47520	−	15.9524i	−0.135235	−	0.871572i
$336$		0			0
$337$	13.6206	+	13.6206i	0.741964	+	0.741964i	0.972956	−	0.230992i	$-0.0741971\pi$
$337$	13.6206	+	13.6206i	0.741964	+	0.741964i	−0.230992	+	0.972956i	$0.574197\pi$
$338$	9.21531	+	0.595876i	0.501247	+	0.0324114i
$339$		0			0
$340$	−7.11221	+	0.176354i	−0.385714	+	0.00956413i
$341$	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	$-0.128610\pi$
$350$	−9.63141	+	15.9913i	−0.514821	+	0.854772i
$351$		0			0
$352$	−3.90818	−	1.30754i	−0.208307	−	0.0696919i
$353$	18.4049	−	18.4049i	0.979596	−	0.979596i	−0.0202002	−	0.999796i	$-0.506430\pi$
$353$	18.4049	−	18.4049i	0.979596	−	0.979596i	0.999796	+	0.0202002i	$0.00643038\pi$
$354$		0			0
$355$	23.6871	+	17.3238i	1.25718	+	0.919451i
$356$	0.265367	−	2.04339i	0.0140644	−	0.108300i
$357$		0			0
$358$	−2.22804	+	34.4569i	−0.117755	+	1.82111i
$359$	9.63060			0.508284			0.254142	−	0.967167i	$-0.418207\pi$
$359$	9.63060			0.508284			0.254142	+	0.967167i	$0.418207\pi$
$360$		0			0
$361$	−5.06055			−0.266345
$362$	−1.02936	+	15.9192i	−0.0541017	+	0.836692i
$363$		0			0
$364$	−3.00504	+	23.1396i	−0.157507	+	1.21284i
$365$	1.92477	+	12.4049i	0.100747	+	0.649304i
$366$		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	$0.0567383\pi$
$368$	16.5998	+	28.5199i	0.865326	+	1.48670i
$369$		0			0
$370$	−1.24717	−	13.9192i	−0.0648373	−	0.723622i
$371$		−	1.81026i		−	0.0939840i
$372$		0			0
$373$	3.37466	−	3.37466i	0.174733	−	0.174733i	−0.614322	−	0.789055i	$-0.710570\pi$
$373$	3.37466	−	3.37466i	0.174733	−	0.174733i	0.789055	+	0.614322i	$0.210570\pi$
$374$	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	$-0.548396\pi$
$379$	−5.89705			−0.302911			−0.151455	+	0.988464i	$0.548396\pi$
$380$	11.5103	−	12.0956i	0.590463	−	0.620490i
$381$		0			0
$382$	−4.61102	−	0.298155i	−0.235920	−	0.0152549i
$383$	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
$385$	4.24977	−	0.659401i	0.216588	−	0.0336062i
$386$	1.24008	+	1.41154i	0.0631185	+	0.0718455i
$387$		0			0
$388$	21.6237	+	28.0782i	1.09778	+	1.42546i
$389$		−	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
$392$	0.0840320	+	0.0164850i	0.00424426	+	0.000832616i
$393$		0			0
$394$	−2.18555	+	1.92007i	−0.110106	+	0.0967317i
$395$	9.39041	−	12.8397i	0.472483	−	0.646034i
$396$		0			0
$397$	−24.3444	−	24.3444i	−1.22181	−	1.22181i	−0.966988	−	0.254821i	$-0.917983\pi$
$397$	−24.3444	−	24.3444i	−1.22181	−	1.22181i	−0.254821	−	0.966988i	$-0.582017\pi$
$398$	−0.473665	+	7.32530i	−0.0237427	+	0.367184i
$399$		0			0
$400$	−0.991227	−	19.9754i	−0.0495614	−	0.998771i
$401$	−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	$0.803543\pi$
$410$	−10.3129	−	8.61680i	−0.509319	−	0.425553i
$411$		0			0
$412$	0.0975387	+	0.126654i	0.00480539	+	0.00623978i
$413$	9.20012	−	9.20012i	0.452708	−	0.452708i
$414$		0			0
$415$	11.1150	−	1.72463i	0.545616	−	0.0846586i
$416$	−11.1552	−	22.3722i	−0.546927	−	1.09689i
$417$		0			0
$418$	−3.83858	−	0.248208i	−0.187751	−	0.0121403i
$419$	−28.0361			−1.36966			−0.684828	−	0.728705i	$-0.740122\pi$
$419$	−28.0361			−1.36966			−0.684828	+	0.728705i	$0.740122\pi$
$420$		0			0
$421$	17.4087			0.848449			0.424224	−	0.905557i	$-0.360547\pi$
$421$	17.4087			0.848449			0.424224	+	0.905557i	$0.360547\pi$
$422$	16.6247	+	1.07498i	0.809277	+	0.0523290i
$423$		0			0
$424$	1.08174	+	1.60975i	0.0525342	+	0.0781762i
$425$	−3.65562	+	7.06433i	−0.177324	+	0.342670i
$426$		0			0
$427$	−4.31286	+	4.31286i	−0.208714	+	0.208714i
$428$	8.76236	−	6.74808i	0.423545	−	0.326181i
$429$		0			0
$430$	−2.03743	−	22.7390i	−0.0982538	−	1.09657i
$431$			31.1542i			1.50065i	0.661071	+	0.750323i	$0.270102\pi$
$431$			31.1542i			1.50065i	−0.661071	+	0.750323i	$0.729898\pi$
$432$		0			0
$433$	−12.1589	+	12.1589i	−0.584321	+	0.584321i	−0.936088	−	0.351766i	$-0.885581\pi$
$433$	−12.1589	+	12.1589i	−0.584321	+	0.584321i	0.351766	+	0.936088i	$0.385581\pi$
$434$	−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	$-0.610824\pi$
$439$	−14.2967			−0.682344			−0.341172	+	0.940001i	$0.610824\pi$
$440$	−3.38501	+	3.12587i	−0.161374	+	0.149020i
$441$		0			0
$442$	−0.641545	+	9.92159i	−0.0305152	+	0.471922i
$443$	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
$445$	−1.85952	−	1.35998i	−0.0881496	−	0.0644691i
$446$	4.99409	−	4.38747i	0.236477	−	0.207753i
$447$		0			0
$448$	19.4696	−	8.18505i	0.919854	−	0.386707i
$449$			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
$452$	−4.13412	+	3.18378i	−0.194453	+	0.149752i
$453$		0			0
$454$	11.6669	+	13.2800i	0.547557	+	0.623263i
$455$	21.0573	+	15.4005i	0.987184	+	0.721986i
$456$		0			0
$457$	4.93945	+	4.93945i	0.231058	+	0.231058i	0.813134	−	0.582076i	$-0.197760\pi$
$457$	4.93945	+	4.93945i	0.231058	+	0.231058i	−0.582076	+	0.813134i	$0.697760\pi$
$458$	10.0070	+	0.647071i	0.467599	+	0.0302356i
$459$		0			0
$460$	36.8828	−	0.914542i	1.71967	−	0.0426407i
$461$	−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
$470$	9.35362	−	0.838094i	0.431450	−	0.0386584i
$471$		0			0
$472$	−2.68342	+	13.6787i	−0.123514	+	0.629614i
$473$	−3.71904	+	3.71904i	−0.171001	+	0.171001i
$474$		0			0
$475$	−5.65685	−	17.7901i	−0.259554	−	0.816264i
$476$	−8.32970	−	1.08174i	−0.381791	−	0.0495817i
$477$		0			0
$478$	0.0644676	−	0.997001i	0.00294868	−	0.0456018i
$479$	18.7808			0.858118			0.429059	−	0.903277i	$-0.358845\pi$
$479$	18.7808			0.858118			0.429059	+	0.903277i	$0.358845\pi$
$480$		0			0
$481$	−19.5298			−0.890483
$482$	2.28128	−	35.2804i	0.103909	−	1.60698i
$483$		0			0
$484$	−20.7642	−	2.69656i	−0.943826	−	0.122571i
$485$	39.1542	−	6.07523i	1.77790	−	0.275862i
$486$		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	$0.280344\pi$
$488$	1.25794	−	6.41236i	0.0569444	−	0.290274i
$489$		0			0
$490$	0.0613875	−	0.0734710i	0.00277321	−	0.00331908i
$491$		−	29.5480i		−	1.33348i	−0.745290	−	0.666741i	$-0.767689\pi$
$491$		−	29.5480i		−	1.33348i	0.745290	−	0.666741i	$-0.232311\pi$
$492$		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	$-0.609346\pi$
$499$	−15.0473			−0.673608			−0.336804	+	0.941575i	$0.609346\pi$
$500$	−20.1079	−	9.78124i	−0.899252	−	0.437430i
$501$		0			0
$502$	−40.3840	−	2.61129i	−1.80243	−	0.116548i
$503$	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
$505$	−7.48486	+	10.2342i	−0.333072	+	0.455415i
$506$	−5.60975	−	6.38537i	−0.249384	−	0.283864i
$507$		0			0
$508$	−25.2264	+	19.4274i	−1.11924	+	0.861951i
$509$		−	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
$512$	−12.4220	+	18.9128i	−0.548981	+	0.835835i
$513$		0			0
$514$	−5.86793	+	5.15516i	−0.258823	+	0.227384i
$515$	0.176615	−	0.0274038i	0.00778257	−	0.00120756i
$516$		0			0
$517$	−1.52982	−	1.52982i	−0.0672813	−	0.0672813i
$518$	1.06466	−	16.4652i	0.0467785	−	0.723437i
$519$		0			0
$520$	−27.9277	−	1.11157i	−1.22471	−	0.0487457i
$521$	−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
$530$	2.15972	−	0.193513i	0.0938121	−	0.00840566i
$531$		0			0
$532$	15.6186	−	12.0282i	0.677150	−	0.521488i
$533$	−13.2800	+	13.2800i	−0.575223	+	0.575223i
$534$		0			0
$535$	−1.89589	−	12.2188i	−0.0819666	−	0.528266i
$536$	11.3893	+	16.9485i	0.491944	+	0.732064i
$537$		0			0
$538$	−7.60579	−	0.491802i	−0.327909	−	0.0212031i
$539$	−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	$0.659446\pi$
$542$	−21.7342	−	1.40537i	−0.933564	−	0.0603656i
$543$		0			0
$544$	8.05348	−	4.01560i	0.345290	−	0.172167i
$545$	−28.4802	−	20.8292i	−1.21996	−	0.892227i
$546$		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	$-0.0278582\pi$
$548$	−7.06638	−	9.17567i	−0.301861	−	0.391965i
$549$		0			0
$550$	1.24098	+	4.99967i	0.0529158	+	0.213187i
$551$			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	0.100653	−	0.994922i	$-0.467907\pi$
$557$	−21.1055	−	21.1055i	−0.894269	−	0.894269i	−0.994922	+	0.100653i	$0.967907\pi$
$558$		0			0
$559$	−31.9048			−1.34943
$560$	2.45961	−	23.4846i	0.103938	−	0.992407i
$561$		0			0
$562$	−1.89347	+	29.2828i	−0.0798712	+	1.23522i
$563$	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
$565$	0.894492	+	5.76491i	0.0376316	+	0.242532i
$566$	27.9201	−	24.5287i	1.17357	−	1.03102i
$567$		0			0
$568$	−36.4259	−	7.14584i	−1.52840	−	0.299833i
$569$			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	$0.193038\pi$
$571$			27.2387i			1.13990i	−0.821678	+	0.569952i	$0.806962\pi$
$572$	3.92878	+	5.10150i	0.164270	+	0.213304i
$573$		0			0
$574$	−10.4722	−	11.9201i	−0.437099	−	0.497534i
$575$	18.9574	−	36.6345i	0.790580	−	1.52776i
$576$		0			0
$577$	4.81078	+	4.81078i	0.200275	+	0.200275i	0.800118	−	0.599843i	$-0.204770\pi$
$577$	4.81078	+	4.81078i	0.200275	+	0.200275i	−0.599843	+	0.800118i	$0.704770\pi$
$578$	20.4200	+	1.32039i	0.849359	+	0.0549208i
$579$		0			0
$580$	8.55287	+	8.13898i	0.355138	+	0.337953i
$581$	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
$590$	11.9596	+	9.99266i	0.492369	+	0.411391i
$591$		0			0
$592$	8.89224	+	15.2776i	0.365469	+	0.627906i
$593$	−18.8439	+	18.8439i	−0.773827	+	0.773827i	−0.978773	−	0.204946i	$-0.934298\pi$
$593$	−18.8439	+	18.8439i	−0.773827	+	0.773827i	0.204946	+	0.978773i	$0.434298\pi$
$594$		0			0
$595$	−5.54382	+	7.58015i	−0.227274	+	0.310756i
$596$	−1.46049	+	11.2462i	−0.0598241	+	0.460661i
$597$		0			0
$598$	3.32695	−	51.4517i	0.136049	−	2.10402i
$599$	−30.2765			−1.23706			−0.618532	−	0.785760i	$-0.712272\pi$
$599$	−30.2765			−1.23706			−0.618532	+	0.785760i	$0.712272\pi$
$600$		0			0
$601$	30.1505			1.22986			0.614932	−	0.788581i	$-0.289184\pi$
$601$	30.1505			1.22986			0.614932	+	0.788581i	$0.289184\pi$
$602$	1.73928	−	26.8982i	0.0708877	−	1.09629i
$603$		0			0
$604$	4.95745	−	38.1736i	0.201716	−	1.55326i
$605$	−13.8196	+	18.8957i	−0.561845	+	0.768220i
$606$		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	$0.439552\pi$
$608$	−6.70097	+	20.0290i	−0.271760	+	0.812282i
$609$		0			0
$610$	−5.60646	−	4.68439i	−0.226999	−	0.189665i
$611$		−	13.1240i		−	0.530939i
$612$		0			0
$613$	23.4040	−	23.4040i	0.945279	−	0.945279i	−0.0532993	−	0.998579i	$-0.516974\pi$
$613$	23.4040	−	23.4040i	0.945279	−	0.945279i	0.998579	+	0.0532993i	$0.0169737\pi$
$614$	−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	0.969018	−	0.246992i	$-0.0794421\pi$
$617$	17.9348	+	17.9348i	0.722026	+	0.722026i	−0.246992	+	0.969018i	$0.579442\pi$
$618$		0			0
$619$	38.9056			1.56375			0.781875	−	0.623435i	$-0.214264\pi$
$619$	38.9056			1.56375			0.781875	+	0.623435i	$0.214264\pi$
$620$	−19.4708	−	18.5286i	−0.781967	−	0.744126i
$621$		0			0
$622$	34.4881	+	2.23005i	1.38285	+	0.0894169i
$623$	−1.92330	−	1.92330i	−0.0770553	−	0.0770553i
$624$		0			0
$625$	−20.4087	+	14.4390i	−0.816349	+	0.577560i
$626$	24.5395	+	27.9324i	0.980796	+	1.11640i
$627$		0			0
$628$	3.61483	+	4.69384i	0.144247	+	0.187305i
$629$		−	7.03028i		−	0.280315i
$630$		0			0
$631$			12.7707i			0.508395i	0.967152	+	0.254198i	$0.0818113\pi$
$631$			12.7707i			0.508395i	−0.967152	+	0.254198i	$0.918189\pi$
$632$	−3.87342	+	19.7448i	−0.154077	+	0.785404i
$633$		0			0
$634$	29.0198	−	25.4948i	1.15253	−	1.01253i
$635$	5.45818	+	35.1774i	0.216601	+	1.39597i
$636$		0			0
$637$	−0.0946093	−	0.0946093i	−0.00374856	−	0.00374856i
$638$	0.175510	−	2.71428i	0.00694849	−	0.107460i
$639$		0			0
$640$	11.8464	+	22.3531i	0.468269	+	0.883586i
$641$	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
$650$	−16.1225	+	26.7686i	−0.632375	+	1.04995i
$651$		0			0
$652$	−7.39574	−	9.60334i	−0.289640	−	0.376096i
$653$	−14.4655	+	14.4655i	−0.566078	+	0.566078i	−0.931027	−	0.364949i	$-0.881086\pi$
$653$	−14.4655	+	14.4655i	−0.566078	+	0.566078i	0.364949	+	0.931027i	$0.381086\pi$
$654$		0			0
$655$	−8.25750	−	6.03920i	−0.322647	−	0.235971i
$656$	16.4352	+	4.34198i	0.641687	+	0.169526i
$657$		0			0
$658$	11.0645	+	0.715449i	0.431340	+	0.0278911i
$659$	35.5474			1.38473			0.692364	−	0.721548i	$-0.256569\pi$
$659$	35.5474			1.38473			0.692364	+	0.721548i	$0.256569\pi$
$660$		0			0
$661$	15.1883			0.590756			0.295378	−	0.955380i	$-0.404554\pi$
$661$	15.1883			0.590756			0.295378	+	0.955380i	$0.404554\pi$
$662$	−15.5654	−	1.00648i	−0.604967	−	0.0391181i
$663$		0			0
$664$	−11.8091	+	7.93567i	−0.458282	+	0.307964i
$665$	−3.37935	−	21.7796i	−0.131046	−	0.844576i
$666$		0			0
$667$	−15.4005	+	15.4005i	−0.596310	+	0.596310i
$668$	−9.80722	+	7.55275i	−0.379453	+	0.292225i
$669$		0			0
$670$	22.7390	−	2.03743i	0.878482	−	0.0787129i
$671$			1.68311i			0.0649756i
$672$		0			0
$673$	−20.3700	+	20.3700i	−0.785204	+	0.785204i	−0.980704	−	0.195500i	$-0.937367\pi$
$673$	−20.3700	+	20.3700i	−0.785204	+	0.785204i	0.195500	+	0.980704i	$0.437367\pi$
$674$	−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	0.511132	−	0.859502i	$-0.329226\pi$
$677$	−9.06433	−	9.06433i	−0.348371	−	0.348371i	−0.859502	+	0.511132i	$0.829226\pi$
$678$		0			0
$679$	46.7808			1.79528
$680$	0.400140	−	10.0533i	0.0153447	−	0.385527i
$681$		0			0
$682$	−0.399552	+	6.17914i	−0.0152997	+	0.236612i
$683$	−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
$685$	−12.7952	+	1.98532i	−0.488879	+	0.0758552i
$686$	19.7190	−	17.3238i	0.752876	−	0.661425i
$687$		0			0
$688$	14.5268	+	24.9582i	0.553827	+	0.951522i
$689$		−	3.03028i		−	0.115444i
$690$		0			0
$691$		−	40.8979i		−	1.55583i	−0.628371	−	0.777914i	$-0.716278\pi$
$691$		−	40.8979i		−	1.55583i	0.628371	−	0.777914i	$-0.283722\pi$
$692$	36.7620	−	28.3112i	1.39748	−	1.07623i
$693$		0			0
$694$	23.4469	+	26.6888i	0.890033	+	1.01309i
$695$	−17.9393	+	24.5287i	−0.680475	+	0.930425i
$696$		0			0
$697$	−4.78051	−	4.78051i	−0.181075	−	0.181075i
$698$	20.7298	+	1.34042i	0.784633	+	0.0507355i
$699$		0			0
$700$	−21.6891	−	15.0518i	−0.819771	−	0.568903i
$701$	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	$-0.112742\pi$
$710$	−26.6100	+	31.8479i	−0.998657	+	1.19523i
$711$		0			0
$712$	2.85956	+	0.560973i	0.107166	+	0.0210233i
$713$	35.0596	−	35.0596i	1.31299	−	1.31299i
$714$		0			0
$715$	7.11388	−	1.10380i	0.266044	−	0.0412798i
$716$	−48.4246	−	6.28871i	−1.80971	−	0.235020i
$717$		0			0
$718$	−0.878837	+	13.5913i	−0.0327979	+	0.507225i
$719$	33.3725			1.24458			0.622292	−	0.782785i	$-0.286201\pi$
$719$	33.3725			1.24458			0.622292	+	0.782785i	$0.286201\pi$
$720$		0			0
$721$	0.211016			0.00785865
$722$	0.461799	−	7.14179i	0.0171864	−	0.265790i
$723$		0			0
$724$	−22.3722	−	2.90539i	−0.831457	−	0.107978i
$725$	12.5795	−	4.00000i	0.467190	−	0.148556i
$726$		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	$0.0409879\pi$
$728$	−32.3819	−	6.35251i	−1.20015	−	0.235440i
$729$		0			0
$730$	−17.6823	+	1.58435i	−0.654452	+	0.0586396i
$731$		−	11.4850i		−	0.424787i
$732$		0			0
$733$	−16.2157	+	16.2157i	−0.598941	+	0.598941i	−0.940031	−	0.341090i	$-0.889204\pi$
$733$	−16.2157	+	16.2157i	−0.598941	+	0.598941i	0.341090	+	0.940031i	$0.389204\pi$
$734$	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	$-0.584965\pi$
$739$	−14.3408			−0.527535			−0.263768	+	0.964586i	$0.584965\pi$
$740$	19.7574	−	0.489904i	0.726298	−	0.0180092i
$741$		0			0
$742$	2.55476	+	0.165194i	0.0937881	+	0.00606448i
$743$	−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
$745$	10.2342	+	7.48486i	0.374951	+	0.274224i
$746$	4.45459	+	5.07049i	0.163094	+	0.185644i
$747$		0			0
$748$	−1.83642	+	1.41427i	−0.0671462	+	0.0517107i
$749$		−	14.5988i		−	0.533430i
$750$		0			0
$751$		−	35.1721i		−	1.28345i	−0.766936	−	0.641724i	$-0.778220\pi$
$751$		−	35.1721i		−	1.28345i	0.766936	−	0.641724i	$-0.221780\pi$
$752$	−10.2665	+	5.97555i	−0.374381	+	0.217906i
$753$		0			0
$754$	12.3955	−	10.8898i	0.451416	−	0.396583i
$755$	−34.7386	−	25.4064i	−1.26427	−	0.924633i
$756$		0			0
$757$	−15.7455	−	15.7455i	−0.572281	−	0.572281i	0.360484	−	0.932765i	$-0.382611\pi$
$757$	−15.7455	−	15.7455i	−0.572281	−	0.572281i	−0.932765	+	0.360484i	$0.882611\pi$
$758$	0.538132	−	8.32230i	0.0195459	−	0.302280i
$759$		0			0
$760$	16.0197	+	17.3478i	0.581096	+	0.629271i
$761$	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	$-0.0929654\pi$
$770$	0.542779	+	6.05773i	0.0195604	+	0.218305i
$771$		0			0
$772$	−2.10522	+	1.62128i	−0.0757686	+	0.0583510i
$773$	2.84392	−	2.84392i	0.102289	−	0.102289i	−0.654110	−	0.756399i	$-0.726957\pi$
$773$	2.84392	−	2.84392i	0.102289	−	0.102289i	0.756399	+	0.654110i	$0.226957\pi$
$774$		0			0
$775$	−28.6375	+	9.10611i	−1.02869	+	0.327101i
$776$	−41.5991	+	27.9545i	−1.49332	+	1.00351i
$777$		0			0
$778$	26.5731	+	1.71825i	0.952691	+	0.0616024i
$779$	15.8668			0.568486
$780$		0			0
$781$	9.56101			0.342120
$782$	18.5214	+	1.19762i	0.662324	+	0.0428269i
$783$		0			0
$784$	−0.0309330	+	0.117087i	−0.00110475	+	0.00418169i
$785$	6.54541	−	1.01560i	0.233616	−	0.0362482i
$786$		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	$0.189506\pi$
$788$	−2.51029	−	3.25960i	−0.0894254	−	0.116119i
$789$		0			0
$790$	17.2633	+	14.4240i	0.614199	+	0.513185i
$791$			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	0.0710121	−	0.997475i	$-0.477377\pi$
$797$	−26.1552	−	26.1552i	−0.926463	−	0.926463i	−0.997475	+	0.0710121i	$0.977377\pi$
$798$		0			0
$799$	4.72432			0.167134
$800$	28.2811	+	0.423963i	0.999888	+	0.0149894i
$801$		0			0
$802$	1.45455	−	22.4948i	0.0513619	−	0.794319i
$803$	2.89200	+	2.89200i	0.102057	+	0.102057i
$804$		0			0
$805$	28.7493	−	39.3094i	1.01328	−	1.38547i
$806$	−28.2186	+	24.7909i	−0.993957	+	0.873222i
$807$		0			0
$808$	3.08741	−	15.7381i	0.108615	−	0.553663i
$809$			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	$0.150943\pi$
$811$			26.0077i			0.913255i	−0.889658	+	0.456628i	$0.849057\pi$
$812$	8.50521	+	11.0440i	0.298474	+	0.387568i
$813$		0			0
$814$	−3.00504	−	3.42053i	−0.105327	−	0.119889i
$815$	−13.3916	+	2.07786i	−0.469086	+	0.0727841i
$816$		0			0
$817$	19.0596	+	19.0596i	0.666812	+	0.666812i
$818$	−33.0359	−	2.13615i	−1.15507	−	0.0746888i
$819$		0			0
$820$	13.1017	−	13.7680i	0.457531	−	0.480798i
$821$	−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	$0.981859\pi$
$830$	1.41961	+	15.8437i	0.0492753	+	0.549941i
$831$		0			0
$832$	32.5911	−	13.7013i	1.12989	−	0.475008i
$833$	0.0340571	−	0.0340571i	0.00118001	−	0.00118001i
$834$		0			0
$835$	2.12197	+	13.6759i	0.0734337	+	0.473273i
$836$	0.700576	−	5.39461i	0.0242299	−	0.186576i
$837$		0			0
$838$	2.55843	−	39.5665i	0.0883794	−	1.36680i
$839$	−54.8854			−1.89486			−0.947428	−	0.319969i	$-0.896327\pi$
$839$	−54.8854			−1.89486			−0.947428	+	0.319969i	$0.896327\pi$
$840$		0			0
$841$	22.0303			0.759665
$842$	−1.58862	+	24.5683i	−0.0547476	+	0.846681i
$843$		0			0
$844$	−3.03416	+	23.3638i	−0.104440	+	0.804214i
$845$	11.7855	+	8.61944i	0.405433	+	0.296518i
$846$		0			0
$847$	−19.5438	+	19.5438i	−0.671533	+	0.671533i
$848$	−2.37050	+	1.37973i	−0.0814032	+	0.0473802i
$849$		0			0
$850$	−9.63606	−	5.80371i	−0.330514	−	0.199065i
$851$			36.4578i			1.24976i
$852$		0			0
$853$	−17.9348	+	17.9348i	−0.614074	+	0.614074i	−0.944005	−	0.329931i	$-0.892975\pi$
$853$	−17.9348	+	17.9348i	−0.614074	+	0.614074i	0.329931	+	0.944005i	$0.392975\pi$
$854$	−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	0.843964	−	0.536400i	$-0.180216\pi$
$857$	9.00378	+	9.00378i	0.307563	+	0.307563i	−0.536400	+	0.843964i	$0.680216\pi$
$858$		0			0
$859$	−24.6779			−0.841998			−0.420999	−	0.907061i	$-0.638320\pi$
$859$	−24.6779			−0.841998			−0.420999	+	0.907061i	$0.638320\pi$
$860$	32.2766	−	0.800329i	1.10062	−	0.0272910i
$861$		0			0
$862$	−43.9669	−	2.84297i	−1.49752	−	0.0968318i
$863$	−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
$865$	−7.95413	−	51.2635i	−0.270448	−	1.74301i
$866$	−16.0499	−	18.2691i	−0.545399	−	0.620808i
$867$		0			0
$868$	−19.3623	−	25.1419i	−0.657201	−	0.853373i
$869$		−	5.18257i		−	0.175807i
$870$		0			0
$871$		−	31.9048i		−	1.08105i
$872$	43.7966	+	8.59179i	1.48314	+	0.290955i
$873$		0			0
$874$	−32.7243	+	28.7493i	−1.10692	+	0.972460i
$875$	−26.4246	+	13.1514i	−0.893313	+	0.444598i
$876$		0			0
$877$	−1.59507	−	1.59507i	−0.0538616	−	0.0538616i	0.679663	−	0.733525i	$-0.262126\pi$
$877$	−1.59507	−	1.59507i	−0.0538616	−	0.0538616i	−0.733525	+	0.679663i	$0.762126\pi$
$878$	1.30464	−	20.1764i	0.0440294	−	0.680922i
$879$		0			0
$880$	−4.10254	−	5.06241i	−0.138296	−	0.170654i
$881$	−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
$890$	2.08898	−	2.50017i	0.0700227	−	0.0838059i
$891$		0			0
$892$	5.73615	+	7.44837i	0.192061	+	0.249390i
$893$	−7.84014	+	7.84014i	−0.262360	+	0.262360i
$894$		0			0
$895$	−32.2289	+	44.0671i	−1.07729	+	1.47300i
$896$	9.77460	+	28.2238i	0.326546	+	0.942890i
$897$		0			0
$898$	−54.2784	−	3.50972i	−1.81129	−	0.117121i
$899$	15.8668			0.529186
$900$		0			0
$901$	1.09083			0.0363408
$902$	−4.36931	−	0.282526i	−0.145482	−	0.00940709i
$903$		0			0
$904$	−4.11590	−	6.12489i	−0.136893	−	0.203711i
$905$	−14.8898	+	20.3591i	−0.494954	+	0.676758i
$906$		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	$0.485148\pi$
$908$	−19.8063	+	15.2533i	−0.657297	+	0.506198i
$909$		0			0
$910$	−23.6558	+	28.3122i	−0.784181	+	0.938539i
$911$		−	31.8607i		−	1.05559i	−0.849371	−	0.527796i	$-0.823019\pi$
$911$		−	31.8607i		−	1.05559i	0.849371	−	0.527796i	$-0.176981\pi$
$912$		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	$-0.132915\pi$
$919$	55.4206			1.82816			0.914079	+	0.405536i	$0.132915\pi$
$920$	−2.07506	+	52.1349i	−0.0684127	+	1.71884i
$921$		0			0
$922$	2.47929	−	38.3426i	0.0816510	−	1.26275i
$923$	41.0109	+	41.0109i	1.34989	+	1.34989i
$924$		0			0
$925$	10.1552	−	19.6244i	0.333900	−	0.645247i
$926$	7.45671	−	6.55096i	0.245043	−	0.215278i
$927$		0			0
$928$	−14.1626	−	4.73830i	−0.464911	−	0.155542i
$929$		−	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
$932$	−34.4533	+	26.5332i	−1.12855	+	0.869124i
$933$		0			0
$934$	−28.0291	−	31.9045i	−0.917140	−	1.04395i
$935$	0.397342	+	2.56083i	0.0129945	+	0.0837481i
$936$		0			0
$937$	10.4693	+	10.4693i	0.342016	+	0.342016i	0.857125	−	0.515109i	$-0.172248\pi$
$937$	10.4693	+	10.4693i	0.342016	+	0.342016i	−0.515109	+	0.857125i	$0.672248\pi$
$938$	26.8982	+	1.73928i	0.878258	+	0.0567895i
$939$		0			0
$940$	0.329214	+	13.2769i	0.0107378	+	0.433046i
$941$	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
$950$	25.6227	−	6.35990i	0.831311	−	0.206343i
$951$		0			0
$952$	2.28675	−	11.6567i	0.0741141	−	0.377796i
$953$	7.78429	−	7.78429i	0.252158	−	0.252158i	−0.569697	−	0.821855i	$-0.692939\pi$
$953$	7.78429	−	7.78429i	0.252158	−	0.252158i	0.821855	+	0.569697i	$0.192939\pi$
$954$		0			0
$955$	−5.89705	−	4.31286i	−0.190824	−	0.139561i
$956$	1.40115	+	0.181962i	0.0453165	+	0.00588507i
$957$		0			0
$958$	−1.71384	+	26.5047i	−0.0553715	+	0.856329i
$959$	−15.2875			−0.493658
$960$		0			0
$961$	−5.12110			−0.165197
$962$	1.78219	−	27.5618i	0.0574600	−	0.888627i
$963$		0			0
$964$	49.5818	+	6.43899i	1.59692	+	0.207386i
$965$	0.455503	+	2.93567i	0.0146631	+	0.0945025i
$966$		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	$0.335894\pi$
$968$	5.70039	−	29.0577i	0.183217	−	0.933950i
$969$		0			0
$970$	5.00077	+	55.8115i	0.160565	+	1.79200i
$971$		−	12.9748i		−	0.416380i	−0.978088	−	0.208190i	$-0.933243\pi$
$971$		−	12.9748i		−	0.416380i	0.978088	−	0.208190i	$-0.0667572\pi$
$972$		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	0.893646	−	0.448773i	$-0.148139\pi$
$977$	13.9054	+	13.9054i	0.444873	+	0.444873i	−0.448773	+	0.893646i	$0.648139\pi$
$978$		0			0
$979$	−0.750572			−0.0239884
$980$	0.0980853	+	0.0933387i	0.00313322	+	0.00298160i
$981$		0			0
$982$	41.7001	+	2.69639i	1.33070	+	0.0860452i
$983$	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
$985$	−4.54541	+	0.705273i	−0.144829	+	0.0224719i
$986$	3.92007	+	4.46207i	0.124840	+	0.142101i
$987$		0			0
$988$	26.1446	−	20.1345i	0.831771	−	0.640565i
$989$			59.5592i			1.89387i
$990$		0			0
$991$		−	52.9621i		−	1.68240i	−0.540726	−	0.841199i	$-0.681850\pi$
$991$		−	52.9621i		−	1.68240i	0.540726	−	0.841199i	$-0.318150\pi$
$992$	32.2416	+	10.7869i	1.02367	+	0.342484i
$993$		0			0
$994$	−36.8111	+	32.3397i	−1.16758	+	1.02575i
$995$	−6.85164	+	9.36835i	−0.217211	+	0.296997i
$996$		0			0
$997$	1.53452	+	1.53452i	0.0485986	+	0.0485986i	0.730988	−	0.682390i	$-0.239059\pi$
$997$	1.53452	+	1.53452i	0.0485986	+	0.0485986i	−0.682390	+	0.730988i	$0.739059\pi$
$998$	1.37313	−	21.2357i	0.0434657	−	0.672204i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.j.a.7.1	✓	12	12.11	even	2
60.2.j.a.7.3	yes	12	3.2	odd	2
60.2.j.a.43.1	yes	12	15.8	even	4
60.2.j.a.43.3	yes	12	60.23	odd	4
180.2.k.e.127.4		12	1.1	even	1	trivial
180.2.k.e.127.6		12	4.3	odd	2	inner
180.2.k.e.163.4		12	20.3	even	4	inner
180.2.k.e.163.6		12	5.3	odd	4	inner
300.2.j.d.7.4		12	15.14	odd	2
300.2.j.d.7.6		12	60.59	even	2
300.2.j.d.43.4		12	60.47	odd	4
300.2.j.d.43.6		12	15.2	even	4
900.2.k.n.307.1		12	20.19	odd	2
900.2.k.n.307.3		12	5.4	even	2
900.2.k.n.343.1		12	5.2	odd	4
900.2.k.n.343.3		12	20.7	even	4
960.2.w.g.127.1		12	24.5	odd	2
960.2.w.g.127.4		12	24.11	even	2
960.2.w.g.703.1		12	120.83	odd	4
960.2.w.g.703.4		12	120.53	even	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0912546 + 1.41127i) q^{2} +(-1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(-1.86678 + 1.86678i) q^{7} +(0.544488 - 2.77552i) q^{8} +O(q^{10})\)	\(q+(-0.0912546 + 1.41127i) q^{2} +(-1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(-1.86678 + 1.86678i) q^{7} +(0.544488 - 2.77552i) q^{8} +(-2.42670 - 2.02759i) q^{10} +0.728515i q^{11} +(-3.12489 + 3.12489i) q^{13} +(-2.46417 - 2.80487i) q^{14} +(3.86732 + 1.02170i) q^{16} +(-1.12489 - 1.12489i) q^{17} +3.73356 q^{19} +(3.08292 - 3.23969i) q^{20} +(-1.02813 - 0.0664803i) q^{22} +(5.83347 + 5.83347i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(-4.12489 - 4.69521i) q^{26} +(4.18329 - 3.22164i) q^{28} +2.64002i q^{29} -6.01008i q^{31} +(-1.79480 + 5.36458i) q^{32} +(1.69016 - 1.48486i) q^{34} +(-0.905130 - 5.83347i) q^{35} +(3.12489 + 3.12489i) q^{37} +(-0.340704 + 5.26904i) q^{38} +(4.29074 + 4.64646i) q^{40} +4.24977 q^{41} +(5.10495 + 5.10495i) q^{43} +(0.187643 - 1.44490i) q^{44} +(-8.76491 + 7.70025i) q^{46} +(-2.09991 + 2.09991i) q^{47} +0.0302761i q^{49} +(6.86282 - 1.70344i) q^{50} +(7.00260 - 5.39285i) q^{52} +(-0.484862 + 0.484862i) q^{53} +(-1.31488 - 0.961649i) q^{55} +(4.16485 + 6.19773i) q^{56} +(-3.72578 - 0.240914i) q^{58} -4.92834 q^{59} +2.31032 q^{61} +(8.48183 + 0.548448i) q^{62} +(-7.40707 - 3.02248i) q^{64} +(-1.51514 - 9.76491i) q^{65} +(-5.10495 + 5.10495i) q^{67} +(1.94130 + 2.52077i) q^{68} +(8.31518 - 0.745049i) q^{70} -13.1240i q^{71} +(3.96972 - 3.96972i) q^{73} +(-4.69521 + 4.12489i) q^{74} +(-7.40493 - 0.961649i) q^{76} +(-1.35998 - 1.35998i) q^{77} -7.11388 q^{79} +(-6.94894 + 5.63137i) q^{80} +(-0.387811 + 5.99756i) q^{82} +(-3.55694 - 3.55694i) q^{83} +(3.51514 - 0.545414i) q^{85} +(-7.67030 + 6.73860i) q^{86} +(2.02201 + 0.396668i) q^{88} +1.03028i q^{89} -11.6669i q^{91} +(-10.0673 - 13.0723i) q^{92} +(-2.77191 - 3.15516i) q^{94} +(-4.92834 + 6.73860i) q^{95} +(-12.5298 - 12.5298i) q^{97} +(-0.0427276 - 0.00276283i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^8	\( 12 q + 12 q^{8} - 8 q^{10} - 4 q^{13} + 12 q^{16} + 20 q^{17} - 20 q^{20} + 12 q^{22} - 20 q^{25} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{37} - 16 q^{38} - 8 q^{40} - 16 q^{41} - 40 q^{46} + 16 q^{50} - 8 q^{52} - 4 q^{53} + 64 q^{56} - 20 q^{58} - 32 q^{61} + 56 q^{62} - 20 q^{65} + 16 q^{68} + 44 q^{70} + 44 q^{73} + 8 q^{76} - 48 q^{77} - 4 q^{80} + 16 q^{82} + 44 q^{85} - 64 q^{86} + 60 q^{88} - 56 q^{92} - 20 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q + 12 * q^8 - 8 * q^10 - 4 * q^13 + 12 * q^16 + 20 * q^17 - 20 * q^20 + 12 * q^22 - 20 * q^25 - 16 * q^26 - 4 * q^28 - 20 * q^32 + 4 * q^37 - 16 * q^38 - 8 * q^40 - 16 * q^41 - 40 * q^46 + 16 * q^50 - 8 * q^52 - 4 * q^53 + 64 * q^56 - 20 * q^58 - 32 * q^61 + 56 * q^62 - 20 * q^65 + 16 * q^68 + 44 * q^70 + 44 * q^73 + 8 * q^76 - 48 * q^77 - 4 * q^80 + 16 * q^82 + 44 * q^85 - 64 * q^86 + 60 * q^88 - 56 * q^92 - 20 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more