LMFDB - Embedded newform 180.2.k.e.127.6

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			127.6
Root			$1.41127 - 0.0912546i$ of defining polynomial
Character	$\chi$	$=$	180.127
Dual form			180.2.k.e.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41127 - 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +(2.77552 - 0.544488i) q^{8} +O(q^{10})$	\(q+(1.41127 - 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +(2.77552 - 0.544488i) q^{8} +(-1.69819 + 2.66761i) q^{10} -0.728515i q^{11} +(-3.12489 + 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(-1.12489 - 1.12489i) q^{17} -3.73356 q^{19} +(-2.15316 + 3.91968i) q^{20} +(-0.0664803 - 1.02813i) q^{22} +(-5.83347 - 5.83347i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(-4.12489 + 4.69521i) q^{26} +(3.22164 - 4.18329i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(5.36458 - 1.79480i) q^{32} +(-1.69016 - 1.48486i) q^{34} +(0.905130 + 5.83347i) q^{35} +(3.12489 + 3.12489i) q^{37} +(-5.26904 + 0.340704i) q^{38} +(-2.68099 + 5.72820i) q^{40} +4.24977 q^{41} +(-5.10495 - 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(2.09991 - 2.09991i) q^{47} +0.0302761i q^{49} +(-2.57308 - 6.58629i) q^{50} +(-5.39285 + 7.00260i) q^{52} +(-0.484862 + 0.484862i) q^{53} +(1.31488 + 0.961649i) q^{55} +(4.16485 - 6.19773i) q^{56} +(0.240914 + 3.72578i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(0.548448 + 8.48183i) q^{62} +(7.40707 - 3.02248i) q^{64} +(-1.51514 - 9.76491i) q^{65} +(5.10495 - 5.10495i) q^{67} +(-2.52077 - 1.94130i) q^{68} +(1.80971 + 8.14998i) q^{70} +13.1240i q^{71} +(3.96972 - 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(-1.35998 - 1.35998i) q^{77} +7.11388 q^{79} +(-3.26087 + 8.32867i) q^{80} +(5.99756 - 0.387811i) q^{82} +(3.55694 + 3.55694i) q^{83} +(3.51514 - 0.545414i) q^{85} +(-7.67030 - 6.73860i) q^{86} +(-0.396668 - 2.02201i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(-13.0723 - 10.0673i) q^{92} +(2.77191 - 3.15516i) q^{94} +(4.92834 - 6.73860i) q^{95} +(-12.5298 - 12.5298i) q^{97} +(0.00276283 + 0.0427276i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{8}+O(q^{10}) $ 12 * q + 12 * q^8	$ 12 q + 12 q^{8} - 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 $

$2$	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
$5$	−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	−0.260026	−	0.965602i	$-0.583731\pi$
$7$	1.86678	−	1.86678i	0.705576	−	0.705576i	0.965602	+	0.260026i	$0.0837311\pi$
$8$	2.77552	−	0.544488i	0.981296	−	0.192506i
$9$		0			0
$10$	−1.69819	+	2.66761i	−0.537013	+	0.843574i
$11$		−	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	−0.992104	−	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	$-0.640876\pi$
$19$	−3.73356			−0.856537			−0.428268	+	0.903652i	$0.640876\pi$
$20$	−2.15316	+	3.91968i	−0.481461	+	0.876467i
$21$		0			0
$22$	−0.0664803	−	1.02813i	−0.0141737	−	0.219198i
$23$	−5.83347	−	5.83347i	−1.21636	−	1.21636i	−0.968897	−	0.247466i	$-0.920402\pi$
$23$	−5.83347	−	5.83347i	−1.21636	−	1.21636i	−0.247466	−	0.968897i	$-0.579598\pi$
$24$		0			0
$25$	−1.51514	−	4.76491i	−0.303028	−	0.952982i
$26$	−4.12489	+	4.69521i	−0.808957	+	0.920806i
$27$		0			0
$28$	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
$35$	0.905130	+	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	$0.631663\pi$
$38$	−5.26904	+	0.340704i	−0.854752	+	0.0552695i
$39$		0			0
$40$	−2.68099	+	5.72820i	−0.423902	+	0.905708i
$41$	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	0.201077	−	0.979575i	$-0.435556\pi$
$43$	−5.10495	−	5.10495i	−0.778498	−	0.778498i	−0.979575	+	0.201077i	$0.935556\pi$
$44$	−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	−0.537170	−	0.843474i	$-0.680507\pi$
$47$	2.09991	−	2.09991i	0.306304	−	0.306304i	0.843474	+	0.537170i	$0.180507\pi$
$48$		0			0
$49$			0.0302761i			0.00432516i
$50$	−2.57308	−	6.58629i	−0.363889	−	0.931442i
$51$		0			0
$52$	−5.39285	+	7.00260i	−0.747854	+	0.971086i
$53$	−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
$58$	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
$65$	−1.51514	−	9.76491i	−0.187930	−	1.21119i
$66$		0			0
$67$	5.10495	−	5.10495i	0.623669	−	0.623669i	−0.322798	−	0.946468i	$-0.604624\pi$
$67$	5.10495	−	5.10495i	0.623669	−	0.623669i	0.946468	+	0.322798i	$0.104624\pi$
$68$	−2.52077	−	1.94130i	−0.305688	−	0.235417i
$69$		0			0
$70$	1.80971	+	8.14998i	0.216302	+	0.974109i
$71$			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	−0.435546	−	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	$-0.368945\pi$
$79$	7.11388			0.800375			0.400187	+	0.916433i	$0.368945\pi$
$80$	−3.26087	+	8.32867i	−0.364576	+	0.931174i
$81$		0			0
$82$	5.99756	−	0.387811i	0.662320	−	0.0428266i
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	0.874839	−	0.484414i	$-0.160967\pi$
$83$	3.55694	+	3.55694i	0.390425	+	0.390425i	−0.484414	+	0.874839i	$0.660967\pi$
$84$		0			0
$85$	3.51514	−	0.545414i	0.381270	−	0.0591585i
$86$	−7.67030	−	6.73860i	−0.827110	−	0.726642i
$87$		0			0
$88$	−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
$95$	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	$-0.606133\pi$
$98$	0.00276283	+	0.0427276i	0.000279088	+	0.00431614i
$99$		0			0
$100$	−4.23233	−	9.06021i	−0.423233	−	0.906021i
$101$	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	0.709886	−	0.704317i	$-0.248747\pi$
$103$	0.0565188	+	0.0565188i	0.00556896	+	0.00556896i	−0.704317	+	0.709886i	$0.748747\pi$
$104$	−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	−0.492373	−	0.870384i	$-0.663871\pi$
$107$	3.91017	−	3.91017i	0.378011	−	0.378011i	0.870384	+	0.492373i	$0.163871\pi$
$108$		0			0
$109$			15.7796i			1.51141i	0.654912	+	0.755705i	$0.272706\pi$
$109$			15.7796i			1.51141i	−0.654912	+	0.755705i	$0.727294\pi$
$110$	1.94340	+	1.23715i	0.185296	+	0.117958i
$111$		0			0
$112$	5.31214	−	9.12670i	0.501950	−	0.862392i
$113$	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
$118$	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
$125$	10.6001	+	3.55510i	0.948098	+	0.317978i
$126$		0			0
$127$	−11.2572	+	11.2572i	−0.998914	+	0.998914i	−0.999999	−	0.00108535i	$-0.999655\pi$
$127$	−11.2572	+	11.2572i	−0.998914	+	0.998914i	0.00108535	+	0.999999i	$0.499655\pi$
$128$	10.1775	−	4.94145i	0.899575	−	0.436767i
$129$		0			0
$130$	−3.02936	−	13.6426i	−0.265692	−	1.19654i
$131$		−	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	0.860045	−	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	$-0.695525\pi$
$139$	−13.5902			−1.15271			−0.576354	+	0.817200i	$0.695525\pi$
$140$	3.29771	+	11.3366i	0.278707	+	0.958122i
$141$		0			0
$142$	1.19762	+	18.5214i	0.100502	+	1.55428i
$143$	2.27653	+	2.27653i	0.190373	+	0.190373i
$144$		0			0
$145$	−4.76491	−	3.48486i	−0.395704	−	0.289402i
$146$	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
$155$	−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	$0.787714\pi$
$158$	10.0396	−	0.649175i	0.798707	−	0.0516456i
$159$		0			0
$160$	−3.84193	+	12.0515i	−0.303731	+	0.952758i
$161$	−21.7796			−1.71647
$162$		0			0
$163$	−4.28546	−	4.28546i	−0.335663	−	0.335663i	0.519069	−	0.854732i	$-0.326279\pi$
$163$	−4.28546	−	4.28546i	−0.335663	−	0.335663i	−0.854732	+	0.519069i	$0.826279\pi$
$164$	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	−0.855862	−	0.517203i	$-0.826973\pi$
$167$	−4.37644	+	4.37644i	−0.338659	+	0.338659i	0.517203	+	0.855862i	$0.326973\pi$
$168$		0			0
$169$		−	6.52982i		−	0.502294i
$170$	4.91102	−	1.09050i	0.376658	−	0.0836373i
$171$		0			0
$172$	−11.4398	−	8.81001i	−0.872274	−	0.671757i
$173$	−16.4049	+	16.4049i	−1.24724	+	1.24724i	−0.290312	+	0.956932i	$0.593759\pi$
$173$	−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
$178$	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
$185$	−9.76491	+	1.51514i	−0.717930	+	0.111395i
$186$		0			0
$187$	−0.819496	+	0.819496i	−0.0599275	+	0.0599275i
$188$	3.62398	−	4.70572i	0.264306	−	0.343200i
$189$		0			0
$190$	6.34027	−	9.95969i	0.459972	−	0.722552i
$191$		−	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	−0.672486	−	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	$-0.558897\pi$
$199$	−5.19059			−0.367951			−0.183975	+	0.982931i	$0.558897\pi$
$200$	−6.79974	−	12.4001i	−0.480814	−	0.876823i
$201$		0			0
$202$	8.00230	−	0.517441i	0.563040	−	0.0364070i
$203$	4.92834	+	4.92834i	0.345902	+	0.345902i
$204$		0			0
$205$	−5.60975	+	7.67030i	−0.391802	+	0.535717i
$206$	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
$215$	15.9524	−	2.47520i	1.08794	−	0.168807i
$216$		0			0
$217$	11.2195	+	11.2195i	0.761629	+	0.761629i
$218$	1.43996	+	22.2692i	0.0975264	+	1.50826i
$219$		0			0
$220$	2.85555	+	1.56861i	0.192521	+	0.105756i
$221$	7.03028			0.472908
$222$		0			0
$223$	3.32381	+	3.32381i	0.222579	+	0.222579i	0.809583	−	0.587005i	$-0.199693\pi$
$223$	3.32381	+	3.32381i	0.222579	+	0.222579i	−0.587005	+	0.809583i	$0.699693\pi$
$224$	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	−0.936718	−	0.350085i	$-0.886153\pi$
$227$	−8.83851	+	8.83851i	−0.586633	+	0.586633i	0.350085	+	0.936718i	$0.386153\pi$
$228$		0			0
$229$		−	7.09083i		−	0.468575i	−0.972167	−	0.234288i	$-0.924724\pi$
$229$		−	7.09083i		−	0.468575i	0.972167	−	0.234288i	$-0.0752757\pi$
$230$	25.4678	−	5.65514i	1.67929	−	0.372889i
$231$		0			0
$232$	1.43746	+	7.32745i	0.0943739	+	0.481071i
$233$	15.3747	−	15.3747i	1.00723	−	1.00723i	0.00725353	−	0.999974i	$-0.497691\pi$
$233$	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
$238$	−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
$245$	−0.0546445	−	0.0399648i	−0.00349111	−	0.00255326i
$246$		0			0
$247$	11.6669	−	11.6669i	0.742349	−	0.742349i
$248$	3.27242	+	16.6811i	0.207799	+	1.05925i
$249$		0			0
$250$	15.2839	+	4.04989i	0.966640	+	0.256138i
$251$		−	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	0.818342	−	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
$260$	−5.52018	−	18.9769i	−0.342347	−	1.17690i
$261$		0			0
$262$	−0.417500	−	6.45670i	−0.0257932	−	0.398896i
$263$	0.176615	+	0.176615i	0.0108905	+	0.0108905i	0.712531	−	0.701641i	$-0.247549\pi$
$263$	0.176615	+	0.176615i	0.0108905	+	0.0108905i	−0.701641	+	0.712531i	$0.747549\pi$
$264$		0			0
$265$	−0.235091	−	1.51514i	−0.0144415	−	0.0930742i
$266$	−9.20012	+	10.4722i	−0.564095	+	0.642089i
$267$		0			0
$268$	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
$275$	−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	$0.631024\pi$
$278$	−19.1794	+	1.24017i	−1.15031	+	0.0743805i
$279$		0			0
$280$	5.68846	+	15.6981i	0.339951	+	0.938141i
$281$	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	$0.0353238\pi$
$283$	18.5822	+	18.5822i	1.10459	+	1.10459i	0.110745	+	0.993849i	$0.464676\pi$
$284$	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
$290$	−7.04256	−	4.48325i	−0.413554	−	0.263265i
$291$		0			0
$292$	6.85085	−	8.89581i	0.400916	−	0.520588i
$293$	−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
$298$	−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
$305$	−3.04965	+	4.16984i	−0.174623	+	0.238764i
$306$		0			0
$307$	0.905130	−	0.905130i	0.0516585	−	0.0516585i	−0.680806	−	0.732464i	$-0.738370\pi$
$307$	0.905130	−	0.905130i	0.0516585	−	0.0516585i	0.732464	+	0.680806i	$0.238370\pi$
$308$	−3.04759	−	2.34702i	−0.173653	−	0.133734i
$309$		0			0
$310$	−16.0326	−	10.2062i	−0.910590	−	0.579675i
$311$			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	$-0.483392\pi$
$313$	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
$320$	−4.32222	+	17.3585i	−0.241620	+	0.970371i
$321$		0			0
$322$	−30.7368	+	1.98749i	−1.71289	+	0.110758i
$323$	4.19982	+	4.19982i	0.233684	+	0.233684i
$324$		0			0
$325$	19.6244	+	10.1552i	1.08857	+	0.563307i
$326$	−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
$335$	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	$0.574197\pi$
$338$	−0.595876	−	9.21531i	−0.0324114	−	0.501247i
$339$		0			0
$340$	6.83125	−	1.98714i	0.370477	−	0.107768i
$341$	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	−0.998968	−	0.0454187i	$-0.985538\pi$
$347$	−17.7627	+	17.7627i	−0.953549	+	0.953549i	0.0454187	+	0.998968i	$0.485538\pi$
$348$		0			0
$349$		−	14.6888i		−	0.786271i	−0.919480	−	0.393136i	$-0.871390\pi$
$349$		−	14.6888i		−	0.786271i	0.919480	−	0.393136i	$-0.128610\pi$
$350$	−17.0985	−	7.49177i	−0.913955	−	0.400452i
$351$		0			0
$352$	−1.30754	−	3.90818i	−0.0696919	−	0.208307i
$353$	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
$358$	−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
$365$	1.92477	+	12.4049i	0.100747	+	0.649304i
$366$		0			0
$367$	−15.4570	+	15.4570i	−0.806850	+	0.806850i	−0.984156	−	0.177306i	$-0.943262\pi$
$367$	−15.4570	+	15.4570i	−0.806850	+	0.806850i	0.177306	+	0.984156i	$0.443262\pi$
$368$	−28.5199	−	16.5998i	−1.48670	−	0.865326i
$369$		0			0
$370$	−13.6426	+	3.02936i	−0.709246	+	0.157489i
$371$			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	$-0.451604\pi$
$379$	5.89705			0.302911			0.151455	+	0.988464i	$0.451604\pi$
$380$	8.03894	−	14.6344i	0.412389	−	0.750727i
$381$		0			0
$382$	−0.298155	−	4.61102i	−0.0152549	−	0.235920i
$383$	−0.642881	−	0.642881i	−0.0328497	−	0.0328497i	0.690491	−	0.723341i	$-0.257394\pi$
$383$	−0.642881	−	0.642881i	−0.0328497	−	0.0328497i	−0.723341	+	0.690491i	$0.757394\pi$
$384$		0			0
$385$	4.24977	−	0.659401i	0.216588	−	0.0336062i
$386$	1.24008	−	1.41154i	0.0631185	−	0.0718455i
$387$		0			0
$388$	−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
$395$	−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	$-0.582017\pi$
$398$	−7.32530	+	0.473665i	−0.367184	+	0.0237427i
$399$		0			0
$400$	−10.7278	−	16.8794i	−0.536390	−	0.843970i
$401$	−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	$0.803543\pi$
$410$	−7.21690	+	11.3368i	−0.356417	+	0.559882i
$411$		0			0
$412$	0.126654	+	0.0975387i	0.00623978	+	0.00480539i
$413$	9.20012	−	9.20012i	0.452708	−	0.452708i
$414$		0			0
$415$	−11.1150	+	1.72463i	−0.545616	+	0.0846586i
$416$	−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
$425$	−3.65562	+	7.06433i	−0.177324	+	0.342670i
$426$		0			0
$427$	4.31286	−	4.31286i	0.208714	−	0.208714i
$428$	6.74808	−	8.76236i	0.326181	−	0.423545i
$429$		0			0
$430$	22.2872	−	4.94889i	1.07478	−	0.238657i
$431$		−	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	−0.936088	−	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	$-0.389176\pi$
$439$	14.2967			0.682344			0.341172	+	0.940001i	$0.389176\pi$
$440$	4.17308	+	1.95314i	0.198944	+	0.0931125i
$441$		0			0
$442$	9.92159	−	0.641545i	0.471922	−	0.0305152i
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	0.520152	−	0.854074i	$-0.325875\pi$
$443$	−7.02825	−	7.02825i	−0.333922	−	0.333922i	−0.854074	+	0.520152i	$0.825875\pi$
$444$		0			0
$445$	−1.85952	−	1.35998i	−0.0881496	−	0.0644691i
$446$	4.99409	+	4.38747i	0.236477	+	0.207753i
$447$		0			0
$448$	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
$455$	−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	$0.697760\pi$
$458$	−0.647071	−	10.0070i	−0.0302356	−	0.467599i
$459$		0			0
$460$	35.4257	−	10.3050i	1.65173	−	0.480471i
$461$	−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	0.812960	−	0.582319i	$-0.197855\pi$
$463$	4.96280	+	4.96280i	0.230641	+	0.230641i	−0.582319	+	0.812960i	$0.697855\pi$
$464$	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	−0.0172604	−	0.999851i	$-0.505494\pi$
$467$	21.2340	−	21.2340i	0.982591	−	0.982591i	0.999851	+	0.0172604i	$0.00549442\pi$
$468$		0			0
$469$		−	19.0596i		−	0.880092i
$470$	2.03572	+	9.16779i	0.0939006	+	0.422879i
$471$		0			0
$472$	13.6787	−	2.68342i	0.629614	−	0.123514i
$473$	−3.71904	+	3.71904i	−0.171001	+	0.171001i
$474$		0			0
$475$	5.65685	+	17.7901i	0.259554	+	0.816264i
$476$	−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
$485$	39.1542	−	6.07523i	1.77790	−	0.275862i
$486$		0			0
$487$	2.97058	−	2.97058i	0.134610	−	0.134610i	−0.636591	−	0.771201i	$-0.719656\pi$
$487$	2.97058	−	2.97058i	0.134610	−	0.134610i	0.771201	+	0.636591i	$0.219656\pi$
$488$	6.41236	−	1.25794i	0.290274	−	0.0569444i
$489$		0			0
$490$	−0.0807649	−	0.0514144i	−0.00364859	−	0.00232267i
$491$			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	$0.390654\pi$
$500$	21.9393	+	4.32075i	0.981154	+	0.193230i
$501$		0			0
$502$	−2.61129	−	40.3840i	−0.116548	−	1.80243i
$503$	−13.4136	−	13.4136i	−0.598084	−	0.598084i	0.341719	−	0.939802i	$-0.388991\pi$
$503$	−13.4136	−	13.4136i	−0.598084	−	0.598084i	−0.939802	+	0.341719i	$0.888991\pi$
$504$		0			0
$505$	−7.48486	+	10.2342i	−0.333072	+	0.455415i
$506$	−5.60975	+	6.38537i	−0.249384	+	0.283864i
$507$		0			0
$508$	−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
$515$	−0.176615	+	0.0274038i	−0.00778257	+	0.00120756i
$516$		0			0
$517$	−1.52982	−	1.52982i	−0.0672813	−	0.0672813i
$518$	16.4652	−	1.06466i	0.723437	−	0.0467785i
$519$		0			0
$520$	−9.52218	−	26.2778i	−0.417575	−	1.15236i
$521$	−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	0.225430	−	0.974259i	$-0.427621\pi$
$523$	−17.1251	−	17.1251i	−0.748829	−	0.748829i	−0.974259	+	0.225430i	$0.927621\pi$
$524$	−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
$530$	−0.470039	−	2.11681i	−0.0204172	−	0.0919484i
$531$		0			0
$532$	−12.0282	+	15.6186i	−0.521488	+	0.677150i
$533$	−13.2800	+	13.2800i	−0.575223	+	0.575223i
$534$		0			0
$535$	1.89589	+	12.2188i	0.0819666	+	0.528266i
$536$	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
$545$	−28.4802	−	20.8292i	−1.21996	−	0.892227i
$546$		0			0
$547$	−25.3428	+	25.3428i	−1.08358	+	1.08358i	−0.0874075	+	0.996173i	$0.527858\pi$
$547$	−25.3428	+	25.3428i	−1.08358	+	1.08358i	−0.996173	+	0.0874075i	$0.972142\pi$
$548$	9.17567	+	7.06638i	0.391965	+	0.301861i
$549$		0			0
$550$	−4.79821	+	1.87453i	−0.204597	+	0.0799302i
$551$		−	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
$560$	9.46046	+	21.6351i	0.399777	+	0.914250i
$561$		0			0
$562$	29.2828	−	1.89347i	1.23522	−	0.0798712i
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	0.456049	−	0.889955i	$-0.349264\pi$
$563$	−10.2955	−	10.2955i	−0.433905	−	0.433905i	−0.889955	+	0.456049i	$0.849264\pi$
$564$		0			0
$565$	0.894492	+	5.76491i	0.0376316	+	0.242532i
$566$	27.9201	+	24.5287i	1.17357	+	1.03102i
$567$		0			0
$568$	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
$575$	−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	$0.704770\pi$
$578$	−1.32039	−	20.4200i	−0.0549208	−	0.849359i
$579$		0			0
$580$	−10.3481	−	5.68439i	−0.429679	−	0.236032i
$581$	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	−0.799948	−	0.600069i	$-0.795140\pi$
$587$	−4.84271	+	4.84271i	−0.199880	+	0.199880i	0.600069	+	0.799948i	$0.295140\pi$
$588$		0			0
$589$		−	22.4390i		−	0.924582i
$590$	−8.36923	+	13.1469i	−0.344556	+	0.541250i
$591$		0			0
$592$	15.2776	+	8.89224i	0.627906	+	0.365469i
$593$	−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
$598$	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
$605$	−13.8196	+	18.8957i	−0.561845	+	0.768220i
$606$		0			0
$607$	19.5438	−	19.5438i	0.793258	−	0.793258i	−0.188764	−	0.982022i	$-0.560448\pi$
$607$	19.5438	−	19.5438i	0.793258	−	0.793258i	0.982022	+	0.188764i	$0.0604482\pi$
$608$	−20.0290	+	6.70097i	−0.812282	+	0.271760i
$609$		0			0
$610$	−3.92336	+	6.16305i	−0.158852	+	0.249535i
$611$			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	$-0.785736\pi$
$619$	−38.9056			−1.56375			−0.781875	+	0.623435i	$0.785736\pi$
$620$	−23.5576	−	12.9407i	−0.946097	−	0.519710i
$621$		0			0
$622$	2.23005	+	34.4881i	0.0894169	+	1.38285i
$623$	1.92330	+	1.92330i	0.0770553	+	0.0770553i
$624$		0			0
$625$	−20.4087	+	14.4390i	−0.816349	+	0.577560i
$626$	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
$635$	−5.45818	−	35.1774i	−0.216601	−	1.39597i
$636$		0			0
$637$	−0.0946093	−	0.0946093i	−0.00374856	−	0.00374856i
$638$	2.71428	−	0.175510i	0.107460	−	0.00694849i
$639$		0			0
$640$	−4.51576	+	24.8919i	−0.178501	+	0.983940i
$641$	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	0.811213	−	0.584751i	$-0.198808\pi$
$643$	5.74249	+	5.74249i	0.226462	+	0.226462i	−0.584751	+	0.811213i	$0.698808\pi$
$644$	−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	−0.610510	−	0.792009i	$-0.709036\pi$
$647$	4.61663	−	4.61663i	0.181498	−	0.181498i	0.792009	+	0.610510i	$0.209036\pi$
$648$		0			0
$649$		−	3.59037i		−	0.140934i
$650$	28.6220	+	12.5408i	1.12265	+	0.491891i
$651$		0			0
$652$	−9.60334	−	7.39574i	−0.376096	−	0.289640i
$653$	−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
$658$	−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
$665$	−3.37935	−	21.7796i	−0.131046	−	0.844576i
$666$		0			0
$667$	15.4005	−	15.4005i	0.596310	−	0.596310i
$668$	−7.55275	+	9.80722i	−0.292225	+	0.379453i
$669$		0			0
$670$	4.94889	+	22.2872i	0.191192	+	0.861030i
$671$		−	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
$680$	9.45938	−	3.42776i	0.362751	−	0.131449i
$681$		0			0
$682$	6.17914	−	0.399552i	0.236612	−	0.0152997i
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	0.998856	−	0.0478253i	$-0.0152291\pi$
$683$	24.8545	+	24.8545i	0.951030	+	0.951030i	−0.0478253	+	0.998856i	$0.515229\pi$
$684$		0			0
$685$	−12.7952	+	1.98532i	−0.488879	+	0.0758552i
$686$	19.7190	+	17.3238i	0.752876	+	0.661425i
$687$		0			0
$688$	−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
$695$	17.9393	−	24.5287i	0.680475	−	0.930425i
$696$		0			0
$697$	−4.78051	−	4.78051i	−0.181075	−	0.181075i
$698$	−1.34042	−	20.7298i	−0.0507355	−	0.784633i
$699$		0			0
$700$	−24.8142	−	9.01257i	−0.937890	−	0.340643i
$701$	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	$-0.112742\pi$
$710$	−35.0097	−	22.2869i	−1.31389	−	0.836413i
$711$		0			0
$712$	0.560973	+	2.85956i	0.0210233	+	0.107166i
$713$	35.0596	−	35.0596i	1.31299	−	1.31299i
$714$		0			0
$715$	−7.11388	+	1.10380i	−0.266044	+	0.0412798i
$716$	−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
$725$	12.5795	−	4.00000i	0.467190	−	0.148556i
$726$		0			0
$727$	−23.2774	+	23.2774i	−0.863309	+	0.863309i	−0.991721	−	0.128412i	$-0.959012\pi$
$727$	−23.2774	+	23.2774i	−0.863309	+	0.863309i	0.128412	+	0.991721i	$0.459012\pi$
$728$	6.35251	+	32.3819i	0.235440	+	1.20015i
$729$		0			0
$730$	3.84837	+	17.3310i	0.142434	+	0.641450i
$731$			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	$-0.415035\pi$
$739$	14.3408			0.527535			0.263768	+	0.964586i	$0.415035\pi$
$740$	−18.9769	+	5.52018i	−0.697606	+	0.202926i
$741$		0			0
$742$	0.165194	+	2.55476i	0.00606448	+	0.0937881i
$743$	11.6034	+	11.6034i	0.425686	+	0.425686i	0.887156	−	0.461470i	$-0.152678\pi$
$743$	11.6034	+	11.6034i	0.425686	+	0.425686i	−0.461470	+	0.887156i	$0.652678\pi$
$744$		0			0
$745$	10.2342	+	7.48486i	0.374951	+	0.274224i
$746$	4.45459	−	5.07049i	0.163094	−	0.185644i
$747$		0			0
$748$	−1.41427	+	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
$755$	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	$0.882611\pi$
$758$	8.32230	−	0.538132i	0.302280	−	0.0195459i
$759$		0			0
$760$	10.0096	−	21.3866i	0.363088	−	0.775772i
$761$	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	$-0.0929654\pi$
$770$	5.93739	−	1.31840i	0.213969	−	0.0475119i
$771$		0			0
$772$	1.62128	−	2.10522i	0.0583510	−	0.0757686i
$773$	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
$778$	−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
$785$	6.54541	−	1.01560i	0.233616	−	0.0362482i
$786$		0			0
$787$	−7.49452	+	7.49452i	−0.267151	+	0.267151i	−0.827951	−	0.560800i	$-0.810494\pi$
$787$	−7.49452	+	7.49452i	−0.267151	+	0.267151i	0.560800	+	0.827951i	$0.310494\pi$
$788$	3.25960	+	2.51029i	0.116119	+	0.0894254i
$789$		0			0
$790$	−12.0807	+	18.9771i	−0.429812	+	0.675175i
$791$		−	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
$800$	−16.6801	−	22.8424i	−0.589731	−	0.807600i
$801$		0			0
$802$	−22.4948	+	1.45455i	−0.794319	+	0.0513619i
$803$	−2.89200	−	2.89200i	−0.102057	−	0.102057i
$804$		0			0
$805$	28.7493	−	39.3094i	1.01328	−	1.38547i
$806$	−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
$815$	13.3916	−	2.07786i	0.469086	−	0.0727841i
$816$		0			0
$817$	19.0596	+	19.0596i	0.666812	+	0.666812i
$818$	2.13615	+	33.0359i	0.0746888	+	1.15507i
$819$		0			0
$820$	−9.15043	+	16.6577i	−0.319547	+	0.581714i
$821$	−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	0.320667	−	0.947192i	$-0.396093\pi$
$823$	−17.9737	−	17.9737i	−0.626525	−	0.626525i	−0.947192	+	0.320667i	$0.896093\pi$
$824$	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	−0.954443	−	0.298392i	$-0.903550\pi$
$827$	−18.8665	+	18.8665i	−0.656051	+	0.656051i	0.298392	+	0.954443i	$0.403550\pi$
$828$		0			0
$829$			3.28005i			0.113921i	0.998376	+	0.0569604i	$0.0181409\pi$
$829$			3.28005i			0.113921i	−0.998376	+	0.0569604i	$0.981859\pi$
$830$	−15.5289	+	3.44820i	−0.539016	+	0.119689i
$831$		0			0
$832$	−13.7013	+	32.5911i	−0.475008	+	1.12989i
$833$	0.0340571	−	0.0340571i	0.00118001	−	0.00118001i
$834$		0			0
$835$	−2.12197	−	13.6759i	−0.0734337	−	0.473273i
$836$	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
$845$	11.7855	+	8.61944i	0.405433	+	0.296518i
$846$		0			0
$847$	19.5438	−	19.5438i	0.671533	−	0.671533i
$848$	−1.37973	+	2.37050i	−0.0473802	+	0.0814032i
$849$		0			0
$850$	−4.51440	+	10.3032i	−0.154843	+	0.353398i
$851$		−	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	$-0.361680\pi$
$859$	24.6779			0.841998			0.420999	+	0.907061i	$0.361680\pi$
$860$	31.0016	−	9.01801i	1.05714	−	0.307512i
$861$		0			0
$862$	−2.84297	−	43.9669i	−0.0968318	−	1.49752i
$863$	40.4811	+	40.4811i	1.37799	+	1.37799i	0.848009	+	0.529982i	$0.177802\pi$
$863$	40.4811	+	40.4811i	1.37799	+	1.37799i	0.529982	+	0.848009i	$0.322198\pi$
$864$		0			0
$865$	−7.95413	−	51.2635i	−0.270448	−	1.74301i
$866$	−16.0499	+	18.2691i	−0.545399	+	0.620808i
$867$		0			0
$868$	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
$875$	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	$0.762126\pi$
$878$	20.1764	−	1.30464i	0.680922	−	0.0440294i
$879$		0			0
$880$	6.06756	+	2.37559i	0.204537	+	0.0800812i
$881$	−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	0.999954	−	0.00956956i	$-0.00304613\pi$
$883$	29.4296	+	29.4296i	0.990385	+	0.990385i	−0.00956956	+	0.999954i	$0.503046\pi$
$884$	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	$0.513043\pi$
$887$	−30.9776	+	30.9776i	−1.04013	+	1.04013i	−0.999161	+	0.0409656i	$0.986957\pi$
$888$		0			0
$889$			42.0294i			1.40962i
$890$	−2.74838	−	1.74960i	−0.0921259	−	0.0586467i
$891$		0			0
$892$	7.44837	+	5.73615i	0.249390	+	0.192061i
$893$	−7.84014	+	7.84014i	−0.262360	+	0.262360i
$894$		0			0
$895$	32.2289	−	44.0671i	1.07729	−	1.47300i
$896$	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
$905$	−14.8898	+	20.3591i	−0.494954	+	0.676758i
$906$		0			0
$907$	28.6790	−	28.6790i	0.952271	−	0.952271i	−0.0466405	−	0.998912i	$-0.514852\pi$
$907$	28.6790	−	28.6790i	0.952271	−	0.952271i	0.998912	+	0.0466405i	$0.0148515\pi$
$908$	−15.2533	+	19.8063i	−0.506198	+	0.657297i
$909$		0			0
$910$	−31.1229	−	19.8126i	−1.03171	−	0.656782i
$911$			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	$0.867085\pi$
$920$	49.0548	−	17.7758i	1.61729	−	0.586051i
$921$		0			0
$922$	−38.3426	+	2.47929i	−1.26275	+	0.0816510i
$923$	−41.0109	−	41.0109i	−1.34989	−	1.34989i
$924$		0			0
$925$	10.1552	−	19.6244i	0.333900	−	0.645247i
$926$	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
$935$	−0.397342	−	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	$0.672248\pi$
$938$	−1.73928	−	26.8982i	−0.0567895	−	0.878258i
$939$		0			0
$940$	3.70954	+	12.7524i	0.120992	+	0.415938i
$941$	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	−0.150003	−	0.988685i	$-0.547928\pi$
$947$	25.8091	−	25.8091i	0.838682	−	0.838682i	0.988685	+	0.150003i	$0.0479284\pi$
$948$		0			0
$949$			24.8099i			0.805362i
$950$	9.60675	+	24.5903i	0.311684	+	0.797815i
$951$		0			0
$952$	−11.6567	+	2.28675i	−0.377796	+	0.0741141i
$953$	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
$958$	−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
$965$	0.455503	+	2.93567i	0.0146631	+	0.0945025i
$966$		0			0
$967$	11.7235	−	11.7235i	0.377001	−	0.377001i	−0.493018	−	0.870019i	$-0.664106\pi$
$967$	11.7235	−	11.7235i	0.377001	−	0.377001i	0.870019	+	0.493018i	$0.164106\pi$
$968$	29.0577	−	5.70039i	0.933950	−	0.183217i
$969$		0			0
$970$	54.7027	−	12.1468i	1.75640	−	0.390009i
$971$			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	0.893646	−	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
$980$	−0.118673	−	0.0651893i	−0.00379086	−	0.00208239i
$981$		0			0
$982$	2.69639	+	41.7001i	0.0860452	+	1.33070i
$983$	−13.9381	−	13.9381i	−0.444557	−	0.444557i	0.448983	−	0.893540i	$-0.351786\pi$
$983$	−13.9381	−	13.9381i	−0.444557	−	0.444557i	−0.893540	+	0.448983i	$0.851786\pi$
$984$		0			0
$985$	−4.54541	+	0.705273i	−0.144829	+	0.0224719i
$986$	3.92007	−	4.46207i	0.124840	−	0.142101i
$987$		0			0
$988$	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
$995$	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	$0.739059\pi$
$998$	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	180.2.k.e.127.6		12
3.2	odd	2		60.2.j.a.7.1	✓	12
4.3	odd	2	inner	180.2.k.e.127.4		12
5.2	odd	4		900.2.k.n.343.3		12
5.3	odd	4	inner	180.2.k.e.163.4		12
5.4	even	2		900.2.k.n.307.1		12
12.11	even	2		60.2.j.a.7.3	yes	12
15.2	even	4		300.2.j.d.43.4		12
15.8	even	4		60.2.j.a.43.3	yes	12
15.14	odd	2		300.2.j.d.7.6		12
20.3	even	4	inner	180.2.k.e.163.6		12
20.7	even	4		900.2.k.n.343.1		12
20.19	odd	2		900.2.k.n.307.3		12
24.5	odd	2		960.2.w.g.127.4		12
24.11	even	2		960.2.w.g.127.1		12
60.23	odd	4		60.2.j.a.43.1	yes	12
60.47	odd	4		300.2.j.d.43.6		12
60.59	even	2		300.2.j.d.7.4		12
120.53	even	4		960.2.w.g.703.1		12
120.83	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	3.2	odd	2
60.2.j.a.7.3	yes	12	12.11	even	2
60.2.j.a.43.1	yes	12	60.23	odd	4
60.2.j.a.43.3	yes	12	15.8	even	4
180.2.k.e.127.4		12	4.3	odd	2	inner
180.2.k.e.127.6		12	1.1	even	1	trivial
180.2.k.e.163.4		12	5.3	odd	4	inner
180.2.k.e.163.6		12	20.3	even	4	inner
300.2.j.d.7.4		12	60.59	even	2
300.2.j.d.7.6		12	15.14	odd	2
300.2.j.d.43.4		12	15.2	even	4
300.2.j.d.43.6		12	60.47	odd	4
900.2.k.n.307.1		12	5.4	even	2
900.2.k.n.307.3		12	20.19	odd	2
900.2.k.n.343.1		12	20.7	even	4
900.2.k.n.343.3		12	5.2	odd	4
960.2.w.g.127.1		12	24.11	even	2
960.2.w.g.127.4		12	24.5	odd	2
960.2.w.g.703.1		12	120.53	even	4
960.2.w.g.703.4		12	120.83	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41127 - 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +(2.77552 - 0.544488i) q^{8} +O(q^{10})\)	\(q+(1.41127 - 0.0912546i) q^{2} +(1.98335 - 0.257569i) q^{4} +(-1.32001 + 1.80487i) q^{5} +(1.86678 - 1.86678i) q^{7} +(2.77552 - 0.544488i) q^{8} +(-1.69819 + 2.66761i) q^{10} -0.728515i q^{11} +(-3.12489 + 3.12489i) q^{13} +(2.46417 - 2.80487i) q^{14} +(3.86732 - 1.02170i) q^{16} +(-1.12489 - 1.12489i) q^{17} -3.73356 q^{19} +(-2.15316 + 3.91968i) q^{20} +(-0.0664803 - 1.02813i) q^{22} +(-5.83347 - 5.83347i) q^{23} +(-1.51514 - 4.76491i) q^{25} +(-4.12489 + 4.69521i) q^{26} +(3.22164 - 4.18329i) q^{28} +2.64002i q^{29} +6.01008i q^{31} +(5.36458 - 1.79480i) q^{32} +(-1.69016 - 1.48486i) q^{34} +(0.905130 + 5.83347i) q^{35} +(3.12489 + 3.12489i) q^{37} +(-5.26904 + 0.340704i) q^{38} +(-2.68099 + 5.72820i) q^{40} +4.24977 q^{41} +(-5.10495 - 5.10495i) q^{43} +(-0.187643 - 1.44490i) q^{44} +(-8.76491 - 7.70025i) q^{46} +(2.09991 - 2.09991i) q^{47} +0.0302761i q^{49} +(-2.57308 - 6.58629i) q^{50} +(-5.39285 + 7.00260i) q^{52} +(-0.484862 + 0.484862i) q^{53} +(1.31488 + 0.961649i) q^{55} +(4.16485 - 6.19773i) q^{56} +(0.240914 + 3.72578i) q^{58} +4.92834 q^{59} +2.31032 q^{61} +(0.548448 + 8.48183i) q^{62} +(7.40707 - 3.02248i) q^{64} +(-1.51514 - 9.76491i) q^{65} +(5.10495 - 5.10495i) q^{67} +(-2.52077 - 1.94130i) q^{68} +(1.80971 + 8.14998i) q^{70} +13.1240i q^{71} +(3.96972 - 3.96972i) q^{73} +(4.69521 + 4.12489i) q^{74} +(-7.40493 + 0.961649i) q^{76} +(-1.35998 - 1.35998i) q^{77} +7.11388 q^{79} +(-3.26087 + 8.32867i) q^{80} +(5.99756 - 0.387811i) q^{82} +(3.55694 + 3.55694i) q^{83} +(3.51514 - 0.545414i) q^{85} +(-7.67030 - 6.73860i) q^{86} +(-0.396668 - 2.02201i) q^{88} +1.03028i q^{89} +11.6669i q^{91} +(-13.0723 - 10.0673i) q^{92} +(2.77191 - 3.15516i) q^{94} +(4.92834 - 6.73860i) q^{95} +(-12.5298 - 12.5298i) q^{97} +(0.00276283 + 0.0427276i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{8}+O(q^{10}) \) 12 * q + 12 * q^8	\( 12 q + 12 q^{8} - 8 q^{10} - 4 q^{13} + 12 q^{16} + 20 q^{17} - 20 q^{20} + 12 q^{22} - 20 q^{25} - 16 q^{26} - 4 q^{28} - 20 q^{32} + 4 q^{37} - 16 q^{38} - 8 q^{40} - 16 q^{41} - 40 q^{46} + 16 q^{50} - 8 q^{52} - 4 q^{53} + 64 q^{56} - 20 q^{58} - 32 q^{61} + 56 q^{62} - 20 q^{65} + 16 q^{68} + 44 q^{70} + 44 q^{73} + 8 q^{76} - 48 q^{77} - 4 q^{80} + 16 q^{82} + 44 q^{85} - 64 q^{86} + 60 q^{88} - 56 q^{92} - 20 q^{97} - 24 q^{98}+O(q^{100}) \) 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

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