LMFDB - Embedded newform 180.2.n.c.59.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(59,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.8
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} + 7x^{4} + 36x^{2} + 81 $ x^8 + 4x^6 + 7x^4 + 36*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			59.4
Root			$0.178197 - 1.72286i$ of defining polynomial
Character	$\chi$	$=$	180.59
Dual form			180.2.n.c.119.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22474 - 0.707107i) q^{2} +(0.178197 - 1.72286i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-1.00000 - 2.23607i) q^{6} +(2.62769 + 4.55129i) q^{7} -2.82843i q^{8} +(-2.93649 - 0.614017i) q^{9} -3.16228 q^{10} +(-2.80588 - 2.03151i) q^{12} +(6.43649 + 3.71611i) q^{14} +(-2.27129 + 3.13707i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-4.03063 + 1.32440i) q^{18} +(-3.87298 + 2.23607i) q^{20} +(8.30948 - 3.71611i) q^{21} +(6.50275 + 3.75437i) q^{23} +(-4.87298 - 0.504017i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-1.58114 + 4.94975i) q^{27} +10.5107 q^{28} +(-0.627017 + 0.362008i) q^{29} +(-0.563508 + 5.44816i) q^{30} +(-4.89898 - 2.82843i) q^{32} -11.7514i q^{35} +(-4.00000 + 4.47214i) q^{36} +(-3.16228 + 5.47723i) q^{40} +(-7.06351 - 4.07812i) q^{41} +(7.54930 - 10.4270i) q^{42} +(-1.58114 - 2.73861i) q^{43} +(5.00000 + 4.47214i) q^{45} +10.6190 q^{46} +(-2.82852 + 1.63305i) q^{47} +(-6.32456 + 2.82843i) q^{48} +(-10.3095 + 17.8565i) q^{49} +(6.12372 + 3.53553i) q^{50} +(1.56351 + 7.18021i) q^{54} +(12.8730 - 7.43222i) q^{56} +(-0.511957 + 0.886735i) q^{58} +(3.16228 + 7.07107i) q^{60} +(-3.80948 - 6.59820i) q^{61} +(-4.92161 - 14.9783i) q^{63} -8.00000 q^{64} +(-2.11573 + 3.66455i) q^{67} +(7.62702 - 10.5343i) q^{69} +(-8.30948 - 14.3924i) q^{70} +(-1.73670 + 8.30565i) q^{72} +(7.90569 - 3.53553i) q^{75} +8.94427i q^{80} +(8.24597 + 3.60611i) q^{81} -11.5347 q^{82} +(-13.8512 + 7.99701i) q^{83} +(1.87298 - 18.1085i) q^{84} +(-3.87298 - 2.23607i) q^{86} +(0.511957 + 1.14477i) q^{87} -14.1404i q^{89} +(9.28600 + 1.94169i) q^{90} +(13.0055 - 7.50873i) q^{92} +(-2.30948 + 4.00013i) q^{94} +(-5.74597 + 7.93624i) q^{96} +29.1596i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{6} - 8 q^{9} + 36 q^{14} - 16 q^{16} + 20 q^{21} - 8 q^{24} + 20 q^{25} - 36 q^{29} - 20 q^{30} - 32 q^{36} - 72 q^{41} + 40 q^{45} - 8 q^{46} - 36 q^{49} + 28 q^{54} + 72 q^{56} + 16 q^{61}+ \cdots + 16 q^{96}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^6 - 8 * q^9 + 36 * q^14 - 16 * q^16 + 20 * q^21 - 8 * q^24 + 20 * q^25 - 36 * q^29 - 20 * q^30 - 32 * q^36 - 72 * q^41 + 40 * q^45 - 8 * q^46 - 36 * q^49 + 28 * q^54 + 72 * q^56 + 16 * q^61 - 64 * q^64 + 92 * q^69 - 20 * q^70 + 4 * q^81 - 16 * q^84 + 28 * q^94 + 16 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i
$3$	0.178197	−	1.72286i	0.102882	−	0.994694i
$3$	0.178197	−	1.72286i	0.102882	−	0.994694i
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−1.93649	−	1.11803i	−0.866025	−	0.500000i
$5$	−1.93649	−	1.11803i	−0.866025	−	0.500000i
$6$	−1.00000	−	2.23607i	−0.408248	−	0.912871i
$7$	2.62769	+	4.55129i	0.993172	+	1.72022i	0.597614	+	0.801784i	$0.296115\pi$
$7$	2.62769	+	4.55129i	0.993172	+	1.72022i	0.395558	+	0.918441i	$0.370551\pi$
$8$		−	2.82843i		−	1.00000i
$9$	−2.93649	−	0.614017i	−0.978831	−	0.204672i
$10$	−3.16228			−1.00000
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−2.80588	−	2.03151i	−0.809989	−	0.586445i
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$	6.43649	+	3.71611i	1.72022	+	0.993172i
$15$	−2.27129	+	3.13707i	−0.586445	+	0.809989i
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$	−4.03063	+	1.32440i	−0.950028	+	0.312164i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−3.87298	+	2.23607i	−0.866025	+	0.500000i
$21$	8.30948	−	3.71611i	1.81328	−	0.810922i
$22$		0			0
$23$	6.50275	+	3.75437i	1.35592	+	0.782839i	0.989071	−	0.147442i	$-0.0471040\pi$
$23$	6.50275	+	3.75437i	1.35592	+	0.782839i	0.366847	+	0.930281i	$0.380437\pi$
$24$	−4.87298	−	0.504017i	−0.994694	−	0.102882i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$		0			0
$27$	−1.58114	+	4.94975i	−0.304290	+	0.952579i
$28$	10.5107			1.98634
$29$	−0.627017	+	0.362008i	−0.116434	+	0.0672232i	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−0.627017	+	0.362008i	−0.116434	+	0.0672232i	0.440652	+	0.897678i	$0.354747\pi$
$30$	−0.563508	+	5.44816i	−0.102882	+	0.994694i
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	−4.89898	−	2.82843i	−0.866025	−	0.500000i
$33$		0			0
$34$		0			0
$35$		−	11.7514i		−	1.98634i
$36$	−4.00000	+	4.47214i	−0.666667	+	0.745356i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$		0			0
$40$	−3.16228	+	5.47723i	−0.500000	+	0.866025i
$41$	−7.06351	−	4.07812i	−1.10313	−	0.636895i	−0.166092	−	0.986110i	$-0.553115\pi$
$41$	−7.06351	−	4.07812i	−1.10313	−	0.636895i	−0.937043	+	0.349215i	$0.886448\pi$
$42$	7.54930	−	10.4270i	1.16488	−	1.60892i
$43$	−1.58114	−	2.73861i	−0.241121	−	0.417635i	0.719913	−	0.694065i	$-0.244182\pi$
$43$	−1.58114	−	2.73861i	−0.241121	−	0.417635i	−0.961034	+	0.276430i	$0.910849\pi$
$44$		0			0
$45$	5.00000	+	4.47214i	0.745356	+	0.666667i
$46$	10.6190			1.56568
$47$	−2.82852	+	1.63305i	−0.412582	+	0.238204i	−0.691898	−	0.721995i	$-0.743225\pi$
$47$	−2.82852	+	1.63305i	−0.412582	+	0.238204i	0.279317	+	0.960199i	$0.409892\pi$
$48$	−6.32456	+	2.82843i	−0.912871	+	0.408248i
$49$	−10.3095	+	17.8565i	−1.47278	+	2.55093i
$50$	6.12372	+	3.53553i	0.866025	+	0.500000i
$51$		0			0
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	1.56351	+	7.18021i	0.212767	+	0.977103i
$55$		0			0
$56$	12.8730	−	7.43222i	1.72022	−	0.993172i
$57$		0			0
$58$	−0.511957	+	0.886735i	−0.0672232	+	0.116434i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	3.16228	+	7.07107i	0.408248	+	0.912871i
$61$	−3.80948	−	6.59820i	−0.487753	−	0.844813i	0.512148	−	0.858898i	$-0.328850\pi$
$61$	−3.80948	−	6.59820i	−0.487753	−	0.844813i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$		0			0
$63$	−4.92161	−	14.9783i	−0.620065	−	1.88708i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	−2.11573	+	3.66455i	−0.258478	+	0.447696i	−0.965834	−	0.259161i	$-0.916554\pi$
$67$	−2.11573	+	3.66455i	−0.258478	+	0.447696i	0.707357	+	0.706857i	$0.249887\pi$
$68$		0			0
$69$	7.62702	−	10.5343i	0.918185	−	1.26818i
$70$	−8.30948	−	14.3924i	−0.993172	−	1.72022i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$	−1.73670	+	8.30565i	−0.204672	+	0.978831i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$		0			0
$75$	7.90569	−	3.53553i	0.912871	−	0.408248i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$			8.94427i			1.00000i
$81$	8.24597	+	3.60611i	0.916219	+	0.400679i
$82$	−11.5347			−1.27379
$83$	−13.8512	+	7.99701i	−1.52037	+	0.877785i	−0.520658	+	0.853766i	$0.674313\pi$
$83$	−13.8512	+	7.99701i	−1.52037	+	0.877785i	−0.999711	+	0.0240199i	$0.992353\pi$
$84$	1.87298	−	18.1085i	0.204359	−	1.97580i
$85$		0			0
$86$	−3.87298	−	2.23607i	−0.417635	−	0.241121i
$87$	0.511957	+	1.14477i	0.0548875	+	0.122732i
$88$		0			0
$89$		−	14.1404i		−	1.49888i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$		−	14.1404i		−	1.49888i	0.662071	−	0.749441i	$-0.269678\pi$
$90$	9.28600	+	1.94169i	0.978831	+	0.204672i
$91$		0			0
$92$	13.0055	−	7.50873i	1.35592	−	0.782839i
$93$		0			0
$94$	−2.30948	+	4.00013i	−0.238204	+	0.412582i
$95$		0			0
$96$	−5.74597	+	7.93624i	−0.586445	+	0.809989i
$97$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$97$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$98$			29.1596i			2.94556i
$99$		0			0
$100$	10.0000			1.00000
$101$	−7.74597	+	4.47214i	−0.770752	+	0.444994i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−7.74597	+	4.47214i	−0.770752	+	0.444994i	0.0623905	+	0.998052i	$0.480128\pi$
$102$		0			0
$103$	7.90569	−	13.6931i	0.778971	−	1.34922i	−0.153564	−	0.988139i	$-0.549075\pi$
$103$	7.90569	−	13.6931i	0.778971	−	1.34922i	0.932535	−	0.361079i	$-0.117592\pi$
$104$		0			0
$105$	−20.2460	−	2.09406i	−1.97580	−	0.204359i
$106$		0			0
$107$			0.976550i			0.0944066i	0.998885	+	0.0472033i	$0.0150309\pi$
$107$			0.976550i			0.0944066i	−0.998885	+	0.0472033i	$0.984969\pi$
$108$	6.99208	+	7.68836i	0.672813	+	0.739813i
$109$	19.6190			1.87915			0.939577	−	0.342337i	$-0.111218\pi$
$109$	19.6190			1.87915			0.939577	+	0.342337i	$0.111218\pi$
$110$		0			0
$111$		0			0
$112$	10.5107	−	18.2051i	0.993172	−	1.72022i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$		0			0
$115$	−8.39502	−	14.5406i	−0.782839	−	1.35592i
$116$			1.44803i			0.134446i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	8.87298	+	6.42419i	0.809989	+	0.586445i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−9.33127	−	5.38741i	−0.844813	−	0.487753i
$123$	−8.28472	+	11.4427i	−0.747008	+	1.03176i
$124$		0			0
$125$		−	11.1803i		−	1.00000i
$126$	−16.6190	−	14.8644i	−1.48053	−	1.32423i
$127$	−14.7422			−1.30816			−0.654080	−	0.756426i	$-0.726944\pi$
$127$	−14.7422			−1.30816			−0.654080	+	0.756426i	$0.726944\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$	−5.00000	+	2.23607i	−0.440225	+	0.196875i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$		0			0
$134$			5.98419i			0.516955i
$135$	8.59585	−	7.81738i	0.739813	−	0.672813i
$136$		0			0
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$	1.89226	−	18.2950i	0.161080	−	1.55737i
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$	−20.3540	−	11.7514i	−1.72022	−	0.993172i
$141$	2.30948	+	5.16414i	0.194493	+	0.434899i
$142$		0			0
$143$		0			0
$144$	3.74597	+	11.4003i	0.312164	+	0.950028i
$145$	1.61895			0.134446
$146$		0			0
$147$	28.9272	+	20.9438i	2.38587	+	1.72741i
$148$		0			0
$149$	19.9365	+	11.5103i	1.63326	+	0.942964i	0.983078	+	0.183186i	$0.0586410\pi$
$149$	19.9365	+	11.5103i	1.63326	+	0.942964i	0.650183	+	0.759778i	$0.274692\pi$
$150$	7.18246	−	9.92030i	0.586445	−	0.809989i
$151$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$151$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$157$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$158$		0			0
$159$		0			0
$160$	6.32456	+	10.9545i	0.500000	+	0.866025i
$161$			39.4612i			3.10998i
$162$	12.6491	−	1.41421i	0.993808	−	0.111111i
$163$	22.1359			1.73382			0.866910	−	0.498464i	$-0.166102\pi$
$163$	22.1359			1.73382			0.866910	+	0.498464i	$0.166102\pi$
$164$	−14.1270	+	8.15624i	−1.10313	+	0.636895i
$165$		0			0
$166$	−11.3095	+	19.5886i	−0.877785	+	1.52037i
$167$	17.5255	+	10.1183i	1.35616	+	0.782980i	0.989104	−	0.147219i	$-0.0470322\pi$
$167$	17.5255	+	10.1183i	1.35616	+	0.782980i	0.367057	+	0.930199i	$0.380366\pi$
$168$	−10.5107	−	23.5027i	−0.810922	−	1.81328i
$169$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$170$		0			0
$171$		0			0
$172$	−6.32456			−0.482243
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	1.43649	+	1.04004i	0.108900	+	0.0788455i
$175$	−13.1384	+	22.7564i	−0.993172	+	1.72022i
$176$		0			0
$177$		0			0
$178$	−9.99879	−	17.3184i	−0.749441	−	1.29807i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	12.7460	−	4.18812i	0.950028	−	0.312164i
$181$	−24.2379			−1.80159			−0.900794	−	0.434246i	$-0.857015\pi$
$181$	−24.2379			−1.80159			−0.900794	+	0.434246i	$0.857015\pi$
$182$		0			0
$183$	−12.0466	+	5.38741i	−0.890512	+	0.398249i
$184$	10.6190	−	18.3926i	0.782839	−	1.35592i
$185$		0			0
$186$		0			0
$187$		0			0
$188$			6.53218i			0.476408i
$189$	−26.6825	+	5.81017i	−1.94086	+	0.422628i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	−1.42558	+	13.7829i	−0.102882	+	0.994694i
$193$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$193$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$194$		0			0
$195$		0			0
$196$	20.6190	+	35.7131i	1.47278	+	2.55093i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	12.2474	−	7.07107i	0.866025	−	0.500000i
$201$	5.93649	+	4.29812i	0.418728	+	0.303166i
$202$	−6.32456	+	10.9545i	−0.444994	+	0.770752i
$203$	−3.29521	−	1.90249i	−0.231278	−	0.133529i
$204$		0			0
$205$	9.11895	+	15.7945i	0.636895	+	1.10313i
$206$		−	22.3607i		−	1.55794i
$207$	−16.7900	−	15.0175i	−1.16699	−	1.04379i
$208$		0			0
$209$		0			0
$210$	−26.2769	+	11.7514i	−1.81328	+	0.810922i
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$		0			0
$213$		0			0
$214$	0.690525	+	1.19602i	0.0472033	+	0.0817585i
$215$			7.07107i			0.482243i
$216$	14.0000	+	4.47214i	0.952579	+	0.304290i
$217$		0			0
$218$	24.0282	−	13.8727i	1.62740	−	0.939577i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	13.6504	+	23.6432i	0.914098	+	1.58326i	0.808217	+	0.588885i	$0.200433\pi$
$223$	13.6504	+	23.6432i	0.914098	+	1.58326i	0.105881	+	0.994379i	$0.466234\pi$
$224$		−	29.7289i		−	1.98634i
$225$	−4.68246	−	14.2504i	−0.312164	−	0.950028i
$226$		0			0
$227$	−8.57321	+	4.94975i	−0.569024	+	0.328526i	−0.756760	−	0.653693i	$-0.773219\pi$
$227$	−8.57321	+	4.94975i	−0.569024	+	0.328526i	0.187735	+	0.982220i	$0.439885\pi$
$228$		0			0
$229$	15.1190	−	26.1868i	0.999088	−	1.73047i	0.462573	−	0.886581i	$-0.346926\pi$
$229$	15.1190	−	26.1868i	0.999088	−	1.73047i	0.536515	−	0.843891i	$-0.319740\pi$
$230$	−20.5635	−	11.8723i	−1.35592	−	0.782839i
$231$		0			0
$232$	1.02391	+	1.77347i	0.0672232	+	0.116434i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	7.30320			0.476408
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$239$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$240$	15.4097	+	1.59384i	0.994694	+	0.102882i
$241$	−12.8095	−	22.1867i	−0.825131	−	1.42917i	−0.901819	−	0.432113i	$-0.857768\pi$
$241$	−12.8095	−	22.1867i	−0.825131	−	1.42917i	0.0766885	−	0.997055i	$-0.475565\pi$
$242$		−	15.5563i		−	1.00000i
$243$	7.68223	−	13.5640i	0.492815	−	0.870134i
$244$	−15.2379			−0.975507
$245$	39.9284	−	23.0527i	2.55093	−	1.47278i
$246$	−2.05544	+	19.8726i	−0.131050	+	1.26703i
$247$		0			0
$248$		0			0
$249$	11.3095	+	25.2888i	0.716709	+	1.60261i
$250$	−7.90569	−	13.6931i	−0.500000	−	0.866025i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−30.8647	−	6.45378i	−1.94429	−	0.406550i
$253$		0			0
$254$	−18.0554	+	10.4243i	−1.13290	+	0.654080i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$257$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$258$	−4.54259	+	6.27415i	−0.282809	+	0.390611i
$259$		0			0
$260$		0			0
$261$	2.06351	−	0.678035i	0.127728	−	0.0419693i
$262$		0			0
$263$	13.4722	−	7.77817i	0.830731	−	0.479623i	−0.0233719	−	0.999727i	$-0.507440\pi$
$263$	13.4722	−	7.77817i	0.830731	−	0.479623i	0.854103	+	0.520104i	$0.174107\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−24.3620	−	2.51978i	−1.49093	−	0.154208i
$268$	4.23146	+	7.32910i	0.258478	+	0.447696i
$269$		−	9.60427i		−	0.585583i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$		−	9.60427i		−	0.585583i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$	5.00000	−	15.6525i	0.304290	−	0.952579i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−10.6190	−	23.7447i	−0.639186	−	1.42926i
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$		0			0
$279$		0			0
$280$	−33.2379			−1.98634
$281$	−4.55544	+	2.63009i	−0.271755	+	0.156898i	−0.629685	−	0.776851i	$-0.716816\pi$
$281$	−4.55544	+	2.63009i	−0.271755	+	0.156898i	0.357930	+	0.933748i	$0.383483\pi$
$282$	6.48012	+	4.69171i	0.385885	+	0.279387i
$283$	8.90697	−	15.4273i	0.529465	−	0.917060i	−0.469945	−	0.882696i	$-0.655726\pi$
$283$	8.90697	−	15.4273i	0.529465	−	0.917060i	0.999409	−	0.0343638i	$-0.0109405\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	42.8641i		−	2.53019i
$288$	12.6491	+	11.3137i	0.745356	+	0.666667i
$289$	−17.0000			−1.00000
$290$	1.98280	−	1.14477i	0.116434	−	0.0672232i
$291$		0			0
$292$		0			0
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$	50.2379	+	5.19615i	2.92993	+	0.303046i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	32.5562			1.88593
$299$		0			0
$300$	1.78197	−	17.2286i	0.102882	−	0.994694i
$301$	8.30948	−	14.3924i	0.478950	−	0.829566i
$302$		0			0
$303$	6.32456	+	14.1421i	0.363336	+	0.812444i
$304$		0			0
$305$			17.0365i			0.975507i
$306$		0			0
$307$	13.7183			0.782944			0.391472	−	0.920190i	$-0.371966\pi$
$307$	13.7183			0.782944			0.391472	+	0.920190i	$0.371966\pi$
$308$		0			0
$309$	−22.1825	−	16.0605i	−1.26192	−	0.913648i
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$		0			0
$315$	−7.21554	+	34.5078i	−0.406550	+	1.94429i
$316$		0			0
$317$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$317$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$318$		0			0
$319$		0			0
$320$	15.4919	+	8.94427i	0.866025	+	0.500000i
$321$	1.68246	+	0.174018i	0.0939057	+	0.00971275i
$322$	27.9033	+	48.3299i	1.55499	+	2.69332i
$323$		0			0
$324$	14.4919	−	10.6763i	0.805107	−	0.593129i
$325$		0			0
$326$	27.1109	−	15.6525i	1.50153	−	0.866910i
$327$	3.49604	−	33.8007i	0.193331	−	1.86918i
$328$	−11.5347	+	19.9786i	−0.636895	+	1.10313i
$329$	−14.8649	−	8.58226i	−0.819529	−	0.473156i
$330$		0			0
$331$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$331$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$332$			31.9880i			1.75557i
$333$		0			0
$334$	28.6190			1.56596
$335$	8.19419	−	4.73092i	0.447696	−	0.258478i
$336$	−29.4919	−	21.3526i	−1.60892	−	1.16488i
$337$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$337$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$338$	−15.9217	−	9.19239i	−0.866025	−	0.500000i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−71.5727			−3.86456
$344$	−7.74597	+	4.47214i	−0.417635	+	0.241121i
$345$	−26.5474	+	11.8723i	−1.42926	+	0.639186i
$346$		0			0
$347$	−20.8207	−	12.0208i	−1.11771	−	0.645311i	−0.176896	−	0.984230i	$-0.556606\pi$
$347$	−20.8207	−	12.0208i	−1.11771	−	0.645311i	−0.940816	+	0.338918i	$0.889939\pi$
$348$	2.49476	+	0.258035i	0.133733	+	0.0138321i
$349$	18.1190	+	31.3829i	0.969885	+	1.67989i	0.695874	+	0.718164i	$0.255017\pi$
$349$	18.1190	+	31.3829i	0.969885	+	1.67989i	0.274011	+	0.961727i	$0.411649\pi$
$350$			37.1611i			1.98634i
$351$		0			0
$352$		0			0
$353$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$353$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$354$		0			0
$355$		0			0
$356$	−24.4919	−	14.1404i	−1.29807	−	0.749441i
$357$		0			0
$358$		0			0
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	12.6491	−	14.1421i	0.666667	−	0.745356i
$361$	19.0000			1.00000
$362$	−29.6852	+	17.1388i	−1.56022	+	0.900794i
$363$	−15.4324	−	11.1733i	−0.809989	−	0.586445i
$364$		0			0
$365$		0			0
$366$	−10.9446	+	15.1164i	−0.572081	+	0.790149i
$367$	−1.58114	−	2.73861i	−0.0825348	−	0.142954i	0.821803	−	0.569771i	$-0.192968\pi$
$367$	−1.58114	−	2.73861i	−0.0825348	−	0.142954i	−0.904338	+	0.426817i	$0.859635\pi$
$368$		−	30.0349i		−	1.56568i
$369$	18.2379	+	16.3125i	0.949427	+	0.849193i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$	−19.2622	−	1.99230i	−0.994694	−	0.102882i
$376$	4.61895	+	8.00026i	0.238204	+	0.412582i
$377$		0			0
$378$	−28.5708	+	25.9833i	−1.46952	+	1.33644i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	−2.62702	+	25.3988i	−0.134586	+	1.30122i
$382$		0			0
$383$	23.2702	+	13.4350i	1.18905	+	0.686498i	0.958091	−	0.286466i	$-0.0924804\pi$
$383$	23.2702	+	13.4350i	1.18905	+	0.686498i	0.230959	+	0.972964i	$0.425814\pi$
$384$	8.00000	+	17.8885i	0.408248	+	0.912871i
$385$		0			0
$386$		0			0
$387$	2.96145	+	9.01276i	0.150539	+	0.458144i
$388$		0			0
$389$	−31.5554	+	18.2185i	−1.59992	+	0.923717i	−0.608424	+	0.793612i	$0.708198\pi$
$389$	−31.5554	+	18.2185i	−1.59992	+	0.923717i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$		0			0
$392$	50.5059	+	29.1596i	2.55093	+	1.47278i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	10.0000	−	17.3205i	0.500000	−	0.866025i
$401$	30.9839	+	17.8885i	1.54726	+	0.893311i	0.998350	+	0.0574304i	$0.0182907\pi$
$401$	30.9839	+	17.8885i	1.54726	+	0.893311i	0.548911	+	0.835881i	$0.315043\pi$
$402$	10.3099	+	1.06636i	0.514212	+	0.0531854i
$403$		0			0
$404$			17.8885i			0.889988i
$405$	−11.9365	−	16.2025i	−0.593129	−	0.805107i
$406$	−5.38105			−0.267057
$407$		0			0
$408$		0			0
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$	22.3368	+	12.8961i	1.10313	+	0.636895i
$411$		0			0
$412$	−15.8114	−	27.3861i	−0.778971	−	1.34922i
$413$		0			0
$414$	−31.1825	−	6.52021i	−1.53253	−	0.320451i
$415$	35.7637			1.75557
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$419$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$420$	−23.8730	+	32.9730i	−1.16488	+	1.60892i
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	0.751935	−	0.659237i	$-0.229121\pi$
$421$	−4.00000	−	6.92820i	−0.194948	−	0.337660i	−0.946883	+	0.321577i	$0.895787\pi$
$422$		0			0
$423$	9.30864	−	3.05867i	0.452601	−	0.148717i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	20.0202	−	34.6760i	0.968846	−	1.67809i
$428$	1.69143	+	0.976550i	0.0817585	+	0.0472033i
$429$		0			0
$430$	5.00000	+	8.66025i	0.241121	+	0.417635i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	20.3087	−	4.42227i	0.977103	−	0.212767i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	0.288492	−	2.78922i	0.0138321	−	0.133733i
$436$	19.6190	−	33.9810i	0.939577	−	1.62740i
$437$		0			0
$438$		0			0
$439$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$439$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$440$		0			0
$441$	41.2379	−	46.1054i	1.96371	−	2.19549i
$442$		0			0
$443$	−24.8739	+	14.3610i	−1.18180	+	0.682310i	−0.956429	−	0.291964i	$-0.905691\pi$
$443$	−24.8739	+	14.3610i	−1.18180	+	0.682310i	−0.225367	+	0.974274i	$0.572358\pi$
$444$		0			0
$445$	−15.8095	+	27.3828i	−0.749441	+	1.29807i
$446$	33.4365	+	19.3046i	1.58326	+	0.914098i
$447$	23.3833	−	32.2967i	1.10599	−	1.52758i
$448$	−21.0215	−	36.4103i	−0.993172	−	1.72022i
$449$		−	22.3607i		−	1.05527i	−0.849473	−	0.527633i	$-0.823080\pi$
$449$		−	22.3607i		−	1.05527i	0.849473	−	0.527633i	$-0.176920\pi$
$450$	−15.8114	−	14.1421i	−0.745356	−	0.666667i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	−7.00000	+	12.1244i	−0.328526	+	0.569024i
$455$		0			0
$456$		0			0
$457$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$457$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$458$		−	42.7628i		−	1.99818i
$459$		0			0
$460$	−33.5801			−1.56568
$461$	−27.6270	+	15.9505i	−1.28672	+	0.742887i	−0.978068	−	0.208288i	$-0.933211\pi$
$461$	−27.6270	+	15.9505i	−1.28672	+	0.742887i	−0.308651	+	0.951175i	$0.599877\pi$
$462$		0			0
$463$	−20.5548	+	35.6020i	−0.955263	+	1.65456i	−0.221497	+	0.975161i	$0.571094\pi$
$463$	−20.5548	+	35.6020i	−0.955263	+	1.65456i	−0.733766	+	0.679403i	$0.762239\pi$
$464$	2.50807	+	1.44803i	0.116434	+	0.0672232i
$465$		0			0
$466$		0			0
$467$			32.5269i			1.50517i	0.658497	+	0.752583i	$0.271192\pi$
$467$			32.5269i			1.50517i	−0.658497	+	0.752583i	$0.728808\pi$
$468$		0			0
$469$	−22.2379			−1.02685
$470$	8.94456	−	5.16414i	0.412582	−	0.238204i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	20.0000	−	8.94427i	0.912871	−	0.408248i
$481$		0			0
$482$	−31.3767	−	18.1153i	−1.42917	−	0.825131i
$483$	67.9861	+	7.03186i	3.09347	+	0.319961i
$484$	−11.0000	−	19.0526i	−0.500000	−	0.866025i
$485$		0			0
$486$	−0.182458	−	22.0447i	−0.00827648	−	0.999966i
$487$	22.1359			1.00308			0.501538	−	0.865136i	$-0.332768\pi$
$487$	22.1359			1.00308			0.501538	+	0.865136i	$0.332768\pi$
$488$	−18.6625	+	10.7748i	−0.844813	+	0.487753i
$489$	3.94456	−	38.1371i	0.178379	−	1.72462i
$490$	32.6014	−	56.4673i	1.47278	−	2.55093i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	11.5347	+	25.7923i	0.520023	+	1.16281i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	31.7331	+	22.9753i	1.42199	+	1.02955i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	−19.3649	−	11.1803i	−0.866025	−	0.500000i
$501$	20.5554	−	28.3908i	0.918349	−	1.26841i
$502$		0			0
$503$			13.7045i			0.611052i	0.952184	+	0.305526i	$0.0988323\pi$
$503$			13.7045i			0.611052i	−0.952184	+	0.305526i	$0.901168\pi$
$504$	−42.3649	+	13.9204i	−1.88708	+	0.620065i
$505$	20.0000			0.889988
$506$		0			0
$507$	−20.5548	+	9.19239i	−0.912871	+	0.408248i
$508$	−14.7422	+	25.5343i	−0.654080	+	1.13290i
$509$	23.8649	+	13.7784i	1.05779	+	0.610718i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	23.8649	+	13.7784i	1.05779	+	0.610718i	0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			1.00000i
$513$		0			0
$514$		0			0
$515$	−30.6186	+	17.6777i	−1.34922	+	0.778971i
$516$	−1.12702	+	10.8963i	−0.0496141	+	0.479684i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	45.3173i		−	1.98539i	−0.120656	−	0.992694i	$-0.538500\pi$
$521$		−	45.3173i		−	1.98539i	0.120656	−	0.992694i	$-0.461500\pi$
$522$	2.04783	−	2.28954i	0.0896310	−	0.100210i
$523$	−8.32712			−0.364119			−0.182060	−	0.983287i	$-0.558276\pi$
$523$	−8.32712			−0.364119			−0.182060	+	0.983287i	$0.558276\pi$
$524$		0			0
$525$	36.8649	+	26.6908i	1.60892	+	1.16488i
$526$	11.0000	−	19.0526i	0.479623	−	0.830731i
$527$		0			0
$528$		0			0
$529$	16.6905	+	28.9088i	0.725675	+	1.25691i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−31.6190	+	14.1404i	−1.36829	+	0.611916i
$535$	1.09182	−	1.89108i	0.0472033	−	0.0817585i
$536$	10.3649	+	5.98419i	0.447696	+	0.258478i
$537$		0			0
$538$	−6.79124	−	11.7628i	−0.292791	−	0.507129i
$539$		0			0
$540$	−4.94425	−	22.7058i	−0.212767	−	0.977103i
$541$	−42.2379			−1.81595			−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−42.2379			−1.81595			−0.907975	+	0.419025i	$0.862372\pi$
$542$		0			0
$543$	−4.31912	+	41.7585i	−0.185351	+	1.79203i
$544$		0			0
$545$	−37.9919	−	21.9347i	−1.62740	−	0.939577i
$546$		0			0
$547$	−19.4177	−	33.6325i	−0.830242	−	1.43802i	−0.897846	−	0.440309i	$-0.854869\pi$
$547$	−19.4177	−	33.6325i	−0.830242	−	1.43802i	0.0676046	−	0.997712i	$-0.478464\pi$
$548$		0			0
$549$	7.13508	+	21.7147i	0.304518	+	0.926759i
$550$		0			0
$551$		0			0
$552$	−29.7955	−	21.5725i	−1.26818	−	0.918185i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	−40.7079	+	23.5027i	−1.72022	+	0.993172i
$561$		0			0
$562$	−3.71950	+	6.44237i	−0.156898	+	0.271755i
$563$	−36.1880	−	20.8931i	−1.52514	−	0.880541i	−0.999556	−	0.0298010i	$-0.990513\pi$
$563$	−36.1880	−	20.8931i	−1.52514	−	0.880541i	−0.525586	−	0.850740i	$-0.676154\pi$
$564$	11.2540	+	1.16402i	0.473880	+	0.0490139i
$565$		0			0
$566$		−	25.1927i		−	1.05893i
$567$	5.25537	+	47.0055i	0.220705	+	1.97404i
$568$		0			0
$569$	27.1109	−	15.6525i	1.13655	−	0.656186i	0.190974	−	0.981595i	$-0.438835\pi$
$569$	27.1109	−	15.6525i	1.13655	−	0.656186i	0.945573	+	0.325409i	$0.105502\pi$
$570$		0			0
$571$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$571$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$	−30.3095	−	52.4976i	−1.26509	−	2.19121i
$575$			37.5437i			1.56568i
$576$	23.4919	+	4.91213i	0.978831	+	0.204672i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−20.8207	+	12.0208i	−0.866025	+	0.500000i
$579$		0			0
$580$	1.61895	−	2.80410i	0.0672232	−	0.116434i
$581$	−72.7933	−	42.0273i	−3.01998	−	1.74358i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	39.8622	−	23.0145i	1.64529	−	0.949909i	0.666382	−	0.745611i	$-0.267842\pi$
$587$	39.8622	−	23.0145i	1.64529	−	0.949909i	0.978909	−	0.204298i	$-0.0654911\pi$
$588$	65.2028	−	29.1596i	2.68892	−	1.20252i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$	39.8730	−	23.0207i	1.63326	−	0.942964i
$597$		0			0
$598$		0			0
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	−10.0000	−	22.3607i	−0.408248	−	0.912871i
$601$	14.0000	+	24.2487i	0.571072	+	0.989126i	0.996456	+	0.0841128i	$0.0268056\pi$
$601$	14.0000	+	24.2487i	0.571072	+	0.989126i	−0.425384	+	0.905013i	$0.639861\pi$
$602$		−	23.5027i		−	0.957900i
$603$	8.46292	−	9.46183i	0.344637	−	0.385316i
$604$		0			0
$605$	−21.3014	+	12.2984i	−0.866025	+	0.500000i
$606$	17.7460	+	12.8484i	0.720881	+	0.521929i
$607$	−24.1611	+	41.8483i	−0.980670	+	1.69857i	−0.320882	+	0.947119i	$0.603979\pi$
$607$	−24.1611	+	41.8483i	−0.980670	+	1.69857i	−0.659788	+	0.751452i	$0.729354\pi$
$608$		0			0
$609$	−3.86492	+	5.33816i	−0.156614	+	0.216313i
$610$	12.0466	+	20.8654i	0.487753	+	0.844813i
$611$		0			0
$612$		0			0
$613$		0			0		1.00000			$0$
$613$		0			0		−1.00000			$\pi$
$614$	16.8014	−	9.70030i	0.678050	−	0.391472i
$615$	28.8367	−	12.8961i	1.16281	−	0.520023i
$616$		0			0
$617$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$617$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$618$	−38.5243	−	3.98461i	−1.54968	−	0.160284i
$619$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$619$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$620$		0			0
$621$	−28.8649	+	26.2508i	−1.15831	+	1.05341i
$622$		0			0
$623$	64.3571	−	37.1566i	2.57841	−	1.48865i
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	15.5635	+	47.3654i	0.620065	+	1.88708i
$631$		0			0		1.00000			$0$
$631$		0			0		−1.00000			$\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	28.5482	+	16.4823i	1.13290	+	0.654080i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	25.2982			1.00000
$641$	30.3014	−	17.4945i	1.19683	−	0.690992i	0.236986	−	0.971513i	$-0.423841\pi$
$641$	30.3014	−	17.4945i	1.19683	−	0.690992i	0.959848	+	0.280521i	$0.0905072\pi$
$642$	2.18363	−	0.976550i	0.0861811	−	0.0385413i
$643$	23.1372	−	40.0748i	0.912443	−	1.58040i	0.101841	−	0.994801i	$-0.467527\pi$
$643$	23.1372	−	40.0748i	0.912443	−	1.58040i	0.810602	−	0.585597i	$-0.199140\pi$
$644$	68.3488	+	39.4612i	2.69332	+	1.55499i
$645$	12.1825	+	1.26004i	0.479684	+	0.0496141i
$646$		0			0
$647$			50.2716i			1.97638i	0.153234	+	0.988190i	$0.451031\pi$
$647$			50.2716i			1.97638i	−0.153234	+	0.988190i	$0.548969\pi$
$648$	10.1996	−	23.3231i	0.400679	−	0.916219i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	22.1359	−	38.3406i	0.866910	−	1.50153i
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	−19.6190	−	43.8693i	−0.767162	−	1.71543i
$655$		0			0
$656$			32.6249i			1.27379i
$657$		0			0
$658$	−24.2743			−0.946311
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$		0			0
$663$		0			0
$664$	22.6190	+	39.1772i	0.877785	+	1.52037i
$665$		0			0
$666$		0			0
$667$	−5.43645			−0.210500
$668$	35.0509	−	20.2367i	1.35616	−	0.782980i
$669$	43.1663	−	19.3046i	1.66891	−	0.746358i
$670$	6.69052	−	11.5883i	0.258478	−	0.447696i
$671$		0			0
$672$	−51.2187	−	5.29760i	−1.97580	−	0.204359i
$673$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$673$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$674$		0			0
$675$	−25.3859	+	5.52784i	−0.977103	+	0.212767i
$676$	−26.0000			−1.00000
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	7.00000	+	15.6525i	0.268241	+	0.599804i
$682$		0			0
$683$		−	43.8406i		−	1.67751i	−0.544505	−	0.838757i	$-0.683283\pi$
$683$		−	43.8406i		−	1.67751i	0.544505	−	0.838757i	$-0.316717\pi$
$684$		0			0
$685$		0			0
$686$	−87.6583	+	50.6095i	−3.34681	+	1.93228i
$687$	−42.4220	−	30.7142i	−1.61850	−	1.17182i
$688$	−6.32456	+	10.9545i	−0.241121	+	0.417635i
$689$		0			0
$690$	−24.1187	+	33.3124i	−0.918185	+	1.26818i
$691$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$691$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$692$		0			0
$693$		0			0
$694$	−34.0000			−1.29062
$695$		0			0
$696$	3.23790	−	1.44803i	0.122732	−	0.0548875i
$697$		0			0
$698$	44.3822	+	25.6241i	1.67989	+	0.969885i
$699$		0			0
$700$	26.2769	+	45.5129i	0.993172	+	1.72022i
$701$			52.7496i			1.99232i	0.0875323	+	0.996162i	$0.472102\pi$
$701$			52.7496i			1.99232i	−0.0875323	+	0.996162i	$0.527898\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	1.30141	−	12.5824i	0.0490139	−	0.473880i
$706$		0			0
$707$	−40.7079	−	23.5027i	−1.53098	−	0.883912i
$708$		0			0
$709$	0.118950	+	0.206028i	0.00446726	+	0.00773753i	0.868250	−	0.496126i	$-0.165245\pi$
$709$	0.118950	+	0.206028i	0.00446726	+	0.00773753i	−0.863783	+	0.503864i	$0.831911\pi$
$710$		0			0
$711$		0			0
$712$	−39.9952			−1.49888
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	5.49193	−	26.2648i	0.204672	−	0.978831i
$721$	83.0948			3.09461
$722$	23.2702	−	13.4350i	0.866025	−	0.500000i
$723$	−40.5071	+	18.1153i	−1.50648	+	0.673716i
$724$	−24.2379	+	41.9813i	−0.900794	+	1.56022i
$725$	−3.13508	−	1.81004i	−0.116434	−	0.0672232i
$726$	−26.8014	−	2.77209i	−0.994694	−	0.102882i
$727$	−11.6026	−	20.0962i	−0.430315	−	0.745328i	0.566585	−	0.824003i	$-0.308264\pi$
$727$	−11.6026	−	20.0962i	−0.430315	−	0.745328i	−0.996900	+	0.0786754i	$0.974931\pi$
$728$		0			0
$729$	−22.0000	−	15.6525i	−0.814815	−	0.579721i
$730$		0			0
$731$		0			0
$732$	−2.71535	+	26.2528i	−0.100362	+	0.970330i
$733$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$733$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$734$	−3.87298	−	2.23607i	−0.142954	−	0.0825348i
$735$	−32.6014	−	72.8990i	−1.20252	−	2.68892i
$736$	−21.2379	−	36.7851i	−0.782839	−	1.35592i
$737$		0			0
$738$	33.8714	+	7.08248i	1.24682	+	0.260710i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−47.2107	−	27.2571i	−1.73199	−	0.999966i	−0.870095	−	0.492883i	$-0.835943\pi$
$743$	−47.2107	−	27.2571i	−1.73199	−	0.999966i	−0.861897	−	0.507083i	$-0.830724\pi$
$744$		0			0
$745$	−25.7379	−	44.5794i	−0.942964	−	1.63326i
$746$		0			0
$747$	45.5843	−	14.9783i	1.66784	−	0.548026i
$748$		0			0
$749$	−4.44456	+	2.56607i	−0.162401	+	0.0937620i
$750$	−25.0000	+	11.1803i	−0.912871	+	0.408248i
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$	11.3141	+	6.53218i	0.412582	+	0.238204i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−16.6190	+	52.0255i	−0.604425	+	1.89215i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	16.0081	+	9.24226i	0.580292	+	0.335032i	0.761249	−	0.648459i	$-0.224586\pi$
$761$	16.0081	+	9.24226i	0.580292	+	0.335032i	−0.180957	+	0.983491i	$0.557920\pi$
$762$	14.7422	+	32.9646i	0.534054	+	1.19418i
$763$	51.5525	+	89.2915i	1.86632	+	3.23257i
$764$		0			0
$765$		0			0
$766$	38.0000			1.37300
$767$		0			0
$768$	22.4471	+	16.2520i	0.809989	+	0.586445i
$769$	−19.7379	+	34.1870i	−0.711767	+	1.23282i	0.252426	+	0.967616i	$0.418771\pi$
$769$	−19.7379	+	34.1870i	−0.711767	+	1.23282i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0			−	1.00000i	$-0.5\pi$
$773$		0			0				1.00000i	$0.5\pi$
$774$	10.0000	+	8.94427i	0.359443	+	0.321495i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−25.7649	+	44.6261i	−0.923717	+	1.59992i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.800449	−	3.67596i	−0.0286057	−	0.131368i
$784$	82.4758			2.94556
$785$		0			0
$786$		0			0
$787$	−20.5548	+	35.6020i	−0.732700	+	1.26907i	0.223026	+	0.974813i	$0.428407\pi$
$787$	−20.5548	+	35.6020i	−0.732700	+	1.26907i	−0.955725	+	0.294260i	$0.904927\pi$
$788$		0			0
$789$	−11.0000	−	24.5967i	−0.391610	−	0.875667i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		0			0
$799$		0			0
$800$		−	28.2843i		−	1.00000i
$801$	−8.68246	+	41.5232i	−0.306780	+	1.46715i
$802$	50.5964			1.78662
$803$		0			0
$804$	13.3810	−	5.98419i	0.471913	−	0.211046i
$805$	44.1190	−	76.4163i	1.55499	−	2.69332i
$806$		0			0
$807$	−16.5468	−	1.71145i	−0.582475	−	0.0602460i
$808$	12.6491	+	21.9089i	0.444994	+	0.770752i
$809$			17.8885i			0.628928i	0.949269	+	0.314464i	$0.101825\pi$
$809$			17.8885i			0.628928i	−0.949269	+	0.314464i	$0.898175\pi$
$810$	−26.0760	−	11.4035i	−0.916219	−	0.400679i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	−6.59041	+	3.80498i	−0.231278	+	0.133529i
$813$		0			0
$814$		0			0
$815$	−42.8661	−	24.7487i	−1.50153	−	0.866910i
$816$		0			0
$817$		0			0
$818$		−	5.65685i		−	0.197787i
$819$		0			0
$820$	36.4758			1.27379
$821$	22.4446	−	12.9584i	0.783320	−	0.452250i	−0.0542853	−	0.998525i	$-0.517288\pi$
$821$	22.4446	−	12.9584i	0.783320	−	0.452250i	0.837606	+	0.546275i	$0.183955\pi$
$822$		0			0
$823$	19.9297	−	34.5192i	0.694705	−	1.20326i	−0.275575	−	0.961280i	$-0.588868\pi$
$823$	19.9297	−	34.5192i	0.694705	−	1.20326i	0.970280	−	0.241985i	$-0.0777984\pi$
$824$	−38.7298	−	22.3607i	−1.34922	−	0.778971i
$825$		0			0
$826$		0			0
$827$			24.8157i			0.862928i	0.902130	+	0.431464i	$0.142003\pi$
$827$			24.8157i			0.862928i	−0.902130	+	0.431464i	$0.857997\pi$
$828$	−42.8010	+	14.0637i	−1.48744	+	0.488748i
$829$	−16.3810			−0.568937			−0.284469	−	0.958685i	$-0.591817\pi$
$829$	−16.3810			−0.568937			−0.284469	+	0.958685i	$0.591817\pi$
$830$	43.8014	−	25.2888i	1.52037	−	0.877785i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−22.6253	−	39.1881i	−0.782980	−	1.35616i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	−5.92289	+	57.2642i	−0.204359	+	1.97580i
$841$	−14.2379	+	24.6608i	−0.490962	+	0.850371i
$842$	−9.79796	−	5.65685i	−0.337660	−	0.194948i
$843$	3.71950	+	8.31706i	0.128106	+	0.286455i
$844$		0			0
$845$			29.0689i			1.00000i
$846$	9.23790	−	10.3283i	0.317606	−	0.355094i
$847$	57.8091			1.98634
$848$		0			0
$849$	−24.9919	−	18.0946i	−0.857721	−	0.621004i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$853$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$854$		−	56.6257i		−	1.93769i
$855$		0			0
$856$	2.76210			0.0944066
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$		0			0
$859$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$859$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$860$	12.2474	+	7.07107i	0.417635	+	0.241121i
$861$	−73.8488	−	7.63825i	−2.51676	−	0.260311i
$862$		0			0
$863$		−	37.2072i		−	1.26655i	−0.773928	−	0.633274i	$-0.781711\pi$
$863$		−	37.2072i		−	1.26655i	0.773928	−	0.633274i	$-0.218289\pi$
$864$	21.7460	−	19.7766i	0.739813	−	0.672813i
$865$		0			0
$866$		0			0
$867$	−3.02935	+	29.2886i	−0.102882	+	0.994694i
$868$		0			0
$869$		0			0
$870$	−1.61895	−	3.62008i	−0.0548875	−	0.122732i
$871$		0			0
$872$		−	55.4908i		−	1.87915i
$873$		0			0
$874$		0			0
$875$	50.8849	−	29.3784i	1.72022	−	0.993172i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	18.6766i		−	0.629230i	−0.949219	−	0.314615i	$-0.898125\pi$
$881$		−	18.6766i		−	0.629230i	0.949219	−	0.314615i	$-0.101875\pi$
$882$	17.9045	−	85.6269i	0.602875	−	2.88321i
$883$	−58.8330			−1.97989			−0.989944	−	0.141457i	$-0.954821\pi$
$883$	−58.8330			−1.97989			−0.989944	+	0.141457i	$0.954821\pi$
$884$		0			0
$885$		0			0
$886$	−20.3095	+	35.1770i	−0.682310	+	1.18180i
$887$	45.3156	+	26.1630i	1.52155	+	0.878466i	0.999676	+	0.0254417i	$0.00809921\pi$
$887$	45.3156	+	26.1630i	1.52155	+	0.878466i	0.521871	+	0.853024i	$0.325234\pi$
$888$		0			0
$889$	−38.7379	−	67.0960i	−1.29923	−	2.25033i
$890$			44.7159i			1.49888i
$891$		0			0
$892$	54.6016			1.82820
$893$		0			0
$894$	5.80141	−	56.0897i	0.194028	−	1.87592i
$895$		0			0
$896$	−51.4919	−	29.7289i	−1.72022	−	0.993172i
$897$		0			0
$898$	−15.8114	−	27.3861i	−0.527633	−	0.913887i
$899$		0			0
$900$	−29.3649	−	6.14017i	−0.978831	−	0.204672i
$901$		0			0
$902$		0			0
$903$	−23.3154	−	16.8807i	−0.775889	−	0.561756i
$904$		0			0
$905$	46.9365	+	27.0988i	1.56022	+	0.900794i
$906$		0			0
$907$	16.8579	+	29.1988i	0.559759	+	0.969530i	0.997516	+	0.0704373i	$0.0224395\pi$
$907$	16.8579	+	29.1988i	0.559759	+	0.969530i	−0.437758	+	0.899093i	$0.644227\pi$
$908$			19.7990i			0.657053i
$909$	25.4919	−	8.37624i	0.845514	−	0.277822i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	29.3515	+	3.03585i	0.970330	+	0.100362i
$916$	−30.2379	−	52.3736i	−0.999088	−	1.73047i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	−41.1270	+	23.7447i	−1.35592	+	0.782839i
$921$	2.44456	−	23.6347i	0.0805509	−	0.778790i
$922$	−22.5574	+	39.0705i	−0.742887	+	1.28672i
$923$		0			0
$924$		0			0
$925$		0			0
$926$			58.1378i			1.91053i
$927$	−31.6228	+	35.3553i	−1.03863	+	1.16122i
$928$	4.09566			0.134446
$929$	−42.6028	+	24.5967i	−1.39775	+	0.806993i	−0.994157	−	0.107944i	$-0.965573\pi$
$929$	−42.6028	+	24.5967i	−1.39775	+	0.806993i	−0.403596	+	0.914937i	$0.632240\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	23.0000	+	39.8372i	0.752583	+	1.30351i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	−27.2358	+	15.7246i	−0.889279	+	0.513425i
$939$		0			0
$940$	7.30320	−	12.6495i	0.238204	−	0.412582i
$941$	50.8649	+	29.3669i	1.65815	+	0.957333i	0.973568	+	0.228395i	$0.0733479\pi$
$941$	50.8649	+	29.3669i	1.65815	+	0.957333i	0.684580	+	0.728937i	$0.259985\pi$
$942$		0			0
$943$	−30.6215	−	53.0380i	−0.997173	−	1.72715i
$944$		0			0
$945$	58.1663	+	18.5806i	1.89215	+	0.604425i
$946$		0			0
$947$	19.2169	−	11.0949i	0.624465	−	0.360535i	−0.154140	−	0.988049i	$-0.549261\pi$
$947$	19.2169	−	11.0949i	0.624465	−	0.360535i	0.778605	+	0.627514i	$0.215927\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	18.1703	−	25.0966i	0.586445	−	0.809989i
$961$	−15.5000	−	26.8468i	−0.500000	−	0.866025i
$962$		0			0
$963$	0.599618	−	2.86763i	0.0193224	−	0.0924081i
$964$	−51.2379			−1.65026
$965$		0			0
$966$	88.2379	−	39.4612i	2.83901	−	1.26964i
$967$	−9.93089	+	17.2008i	−0.319356	+	0.553141i	−0.980354	−	0.197247i	$-0.936800\pi$
$967$	−9.93089	+	17.2008i	−0.319356	+	0.553141i	0.660998	+	0.750388i	$0.270133\pi$
$968$	−26.9444	−	15.5563i	−0.866025	−	0.500000i
$969$		0			0
$970$		0			0
$971$		0			0			−	1.00000i	$-0.5\pi$
$971$		0			0				1.00000i	$0.5\pi$
$972$	−15.8114	−	26.8701i	−0.507151	−	0.861858i
$973$		0			0
$974$	27.1109	−	15.6525i	0.868689	−	0.501538i
$975$		0			0
$976$	−15.2379	+	26.3928i	−0.487753	+	0.844813i
$977$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$977$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$978$	−22.1359	−	49.4975i	−0.707829	−	1.58275i
$979$		0			0
$980$		−	92.2107i		−	2.94556i
$981$	−57.6109	−	12.0464i	−1.83937	−	0.384611i
$982$		0			0
$983$	17.8168	−	10.2865i	0.568268	−	0.328090i	−0.188189	−	0.982133i	$-0.560262\pi$
$983$	17.8168	−	10.2865i	0.568268	−	0.328090i	0.756457	+	0.654043i	$0.226928\pi$
$984$	32.3649	+	23.4327i	1.03176	+	0.747008i
$985$		0			0
$986$		0			0
$987$	−17.4349	+	24.0808i	−0.554960	+	0.766501i
$988$		0			0
$989$		−	23.7447i		−	0.755037i
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	55.1109	+	5.70017i	1.74626	+	0.180617i
$997$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$997$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.c.59.4	yes	8
3.2	odd	2		540.2.n.c.179.2		8
4.3	odd	2	inner	180.2.n.c.59.1	✓	8
5.2	odd	4		900.2.r.a.851.3		8
5.3	odd	4		900.2.r.a.851.2		8
5.4	even	2	inner	180.2.n.c.59.1	✓	8
9.2	odd	6	inner	180.2.n.c.119.4	yes	8
9.7	even	3		540.2.n.c.359.2		8
12.11	even	2		540.2.n.c.179.4		8
15.14	odd	2		540.2.n.c.179.4		8
20.3	even	4		900.2.r.a.851.3		8
20.7	even	4		900.2.r.a.851.2		8
20.19	odd	2	CM	180.2.n.c.59.4	yes	8
36.7	odd	6		540.2.n.c.359.4		8
36.11	even	6	inner	180.2.n.c.119.1	yes	8
45.2	even	12		900.2.r.a.551.2		8
45.29	odd	6	inner	180.2.n.c.119.1	yes	8
45.34	even	6		540.2.n.c.359.4		8
45.38	even	12		900.2.r.a.551.3		8
60.59	even	2		540.2.n.c.179.2		8
180.47	odd	12		900.2.r.a.551.3		8
180.79	odd	6		540.2.n.c.359.2		8
180.83	odd	12		900.2.r.a.551.2		8
180.119	even	6	inner	180.2.n.c.119.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.c.59.1	✓	8	4.3	odd	2	inner
180.2.n.c.59.1	✓	8	5.4	even	2	inner
180.2.n.c.59.4	yes	8	1.1	even	1	trivial
180.2.n.c.59.4	yes	8	20.19	odd	2	CM
180.2.n.c.119.1	yes	8	36.11	even	6	inner
180.2.n.c.119.1	yes	8	45.29	odd	6	inner
180.2.n.c.119.4	yes	8	9.2	odd	6	inner
180.2.n.c.119.4	yes	8	180.119	even	6	inner
540.2.n.c.179.2		8	3.2	odd	2
540.2.n.c.179.2		8	60.59	even	2
540.2.n.c.179.4		8	12.11	even	2
540.2.n.c.179.4		8	15.14	odd	2
540.2.n.c.359.2		8	9.7	even	3
540.2.n.c.359.2		8	180.79	odd	6
540.2.n.c.359.4		8	36.7	odd	6
540.2.n.c.359.4		8	45.34	even	6
900.2.r.a.551.2		8	45.2	even	12
900.2.r.a.551.2		8	180.83	odd	12
900.2.r.a.551.3		8	45.38	even	12
900.2.r.a.551.3		8	180.47	odd	12
900.2.r.a.851.2		8	5.3	odd	4
900.2.r.a.851.2		8	20.7	even	4
900.2.r.a.851.3		8	5.2	odd	4
900.2.r.a.851.3		8	20.3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.178197 - 1.72286i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-1.93649 - 1.11803i) q^{5} +(-1.00000 - 2.23607i) q^{6} +(2.62769 + 4.55129i) q^{7} -2.82843i q^{8} +(-2.93649 - 0.614017i) q^{9} -3.16228 q^{10} +(-2.80588 - 2.03151i) q^{12} +(6.43649 + 3.71611i) q^{14} +(-2.27129 + 3.13707i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(-4.03063 + 1.32440i) q^{18} +(-3.87298 + 2.23607i) q^{20} +(8.30948 - 3.71611i) q^{21} +(6.50275 + 3.75437i) q^{23} +(-4.87298 - 0.504017i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-1.58114 + 4.94975i) q^{27} +10.5107 q^{28} +(-0.627017 + 0.362008i) q^{29} +(-0.563508 + 5.44816i) q^{30} +(-4.89898 - 2.82843i) q^{32} -11.7514i q^{35} +(-4.00000 + 4.47214i) q^{36} +(-3.16228 + 5.47723i) q^{40} +(-7.06351 - 4.07812i) q^{41} +(7.54930 - 10.4270i) q^{42} +(-1.58114 - 2.73861i) q^{43} +(5.00000 + 4.47214i) q^{45} +10.6190 q^{46} +(-2.82852 + 1.63305i) q^{47} +(-6.32456 + 2.82843i) q^{48} +(-10.3095 + 17.8565i) q^{49} +(6.12372 + 3.53553i) q^{50} +(1.56351 + 7.18021i) q^{54} +(12.8730 - 7.43222i) q^{56} +(-0.511957 + 0.886735i) q^{58} +(3.16228 + 7.07107i) q^{60} +(-3.80948 - 6.59820i) q^{61} +(-4.92161 - 14.9783i) q^{63} -8.00000 q^{64} +(-2.11573 + 3.66455i) q^{67} +(7.62702 - 10.5343i) q^{69} +(-8.30948 - 14.3924i) q^{70} +(-1.73670 + 8.30565i) q^{72} +(7.90569 - 3.53553i) q^{75} +8.94427i q^{80} +(8.24597 + 3.60611i) q^{81} -11.5347 q^{82} +(-13.8512 + 7.99701i) q^{83} +(1.87298 - 18.1085i) q^{84} +(-3.87298 - 2.23607i) q^{86} +(0.511957 + 1.14477i) q^{87} -14.1404i q^{89} +(9.28600 + 1.94169i) q^{90} +(13.0055 - 7.50873i) q^{92} +(-2.30948 + 4.00013i) q^{94} +(-5.74597 + 7.93624i) q^{96} +29.1596i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{6} - 8 q^{9} + 36 q^{14} - 16 q^{16} + 20 q^{21} - 8 q^{24} + 20 q^{25} - 36 q^{29} - 20 q^{30} - 32 q^{36} - 72 q^{41} + 40 q^{45} - 8 q^{46} - 36 q^{49} + 28 q^{54} + 72 q^{56} + 16 q^{61}+ \cdots + 16 q^{96}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^6 - 8 * q^9 + 36 * q^14 - 16 * q^16 + 20 * q^21 - 8 * q^24 + 20 * q^25 - 36 * q^29 - 20 * q^30 - 32 * q^36 - 72 * q^41 + 40 * q^45 - 8 * q^46 - 36 * q^49 + 28 * q^54 + 72 * q^56 + 16 * q^61 - 64 * q^64 + 92 * q^69 - 20 * q^70 + 4 * q^81 - 16 * q^84 + 28 * q^94 + 16 * q^96

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