LMFDB - Embedded newform 540.2.bb.a.59.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [540,2,Mod(59,540)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(540, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 5, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("540.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.bb (of order $18$, degree $6$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{18}]$

Embedding invariants

Embedding label			59.2
Character	$\chi$	$=$	540.59
Dual form			540.2.bb.a.119.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909039 - 1.08335i) q^{2} +(1.72763 + 0.123682i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.764780 + 2.10122i) q^{5} +(-1.43649 - 1.98406i) q^{6} +(-0.264032 - 1.49740i) q^{7} +(2.44949 - 1.41421i) q^{8} +(2.96941 + 0.427352i) q^{9} +O(q^{10})$	\(q+(-0.909039 - 1.08335i) q^{2} +(1.72763 + 0.123682i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.764780 + 2.10122i) q^{5} +(-1.43649 - 1.98406i) q^{6} +(-0.264032 - 1.49740i) q^{7} +(2.44949 - 1.41421i) q^{8} +(2.96941 + 0.427352i) q^{9} +(1.58114 - 2.73861i) q^{10} +(-0.843605 + 3.35981i) q^{12} +(-1.38219 + 1.64723i) q^{14} +(1.06137 + 3.72471i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(-2.23633 - 3.60539i) q^{18} +(-4.40419 + 0.776578i) q^{20} +(-0.270949 - 2.61961i) q^{21} +(9.44261 + 1.66499i) q^{23} +(4.40672 - 2.14028i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(5.07718 + 1.10557i) q^{27} +3.04100 q^{28} +(4.79648 + 5.71623i) q^{29} +(3.07034 - 4.53575i) q^{30} +(1.93476 + 5.31570i) q^{32} +(2.94444 - 1.69997i) q^{35} +(-1.87298 + 5.70017i) q^{36} +(4.84489 + 4.06535i) q^{40} +(-2.75601 + 3.28449i) q^{41} +(-2.59165 + 2.67486i) q^{42} +(-8.87217 - 3.22921i) q^{43} +(1.37298 + 6.56619i) q^{45} +(-6.77994 - 11.7432i) q^{46} +(-1.46287 + 0.257943i) q^{47} +(-6.32456 - 2.82843i) q^{48} +(4.40535 - 1.60342i) q^{49} +(6.96364 + 1.22788i) q^{50} +(-3.41763 - 6.50537i) q^{54} +(-2.76439 - 3.29447i) q^{56} +(1.83249 - 10.3925i) q^{58} +(-7.70486 + 0.796921i) q^{60} +(-2.10222 - 11.9223i) q^{61} +(-0.144101 - 4.55922i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-7.18941 - 6.03263i) q^{67} +(16.1074 + 4.04436i) q^{69} +(-4.51827 - 1.64452i) q^{70} +(7.87790 - 3.15258i) q^{72} +(-7.01471 + 5.07877i) q^{75} -8.94427i q^{80} +(8.63474 + 2.53796i) q^{81} +6.06358 q^{82} +(-11.5797 - 13.8002i) q^{83} +(5.25372 + 0.376116i) q^{84} +(4.56679 + 12.5471i) q^{86} +(7.57955 + 10.4688i) q^{87} +(-15.2075 + 8.78007i) q^{89} +(5.86539 - 7.45635i) q^{90} +(-6.55877 + 18.0201i) q^{92} +(1.60925 + 1.35032i) q^{94} +(2.68509 + 9.42286i) q^{96} +(-5.74170 - 3.31497i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{6}+O(q^{10}) $ 24 * q + 12 * q^6	$ 24 q + 12 q^{6} - 36 q^{14} + 36 q^{29} + 48 q^{36} - 144 q^{41} - 60 q^{45} + 24 q^{49} - 72 q^{56} - 48 q^{61} + 96 q^{64} + 192 q^{69} - 120 q^{70} + 48 q^{84} + 168 q^{94}+O(q^{100}) $ 24 * q + 12 * q^6 - 36 * q^14 + 36 * q^29 + 48 * q^36 - 144 * q^41 - 60 * q^45 + 24 * q^49 - 72 * q^56 - 48 * q^61 + 96 * q^64 + 192 * q^69 - 120 * q^70 + 48 * q^84 + 168 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−0.909039	−	1.08335i	−0.642788	−	0.766044i
$2$	−0.909039	−	1.08335i	−0.642788	−	0.766044i
$3$	1.72763	+	0.123682i	0.997447	+	0.0714077i
$3$	1.72763	+	0.123682i	0.997447	+	0.0714077i
$4$	−0.347296	+	1.96962i	−0.173648	+	0.984808i
$5$	0.764780	+	2.10122i	0.342020	+	0.939693i
$5$	0.764780	+	2.10122i	0.342020	+	0.939693i
$6$	−1.43649	−	1.98406i	−0.586445	−	0.809989i
$7$	−0.264032	−	1.49740i	−0.0997948	−	0.565964i	−0.993172	−	0.116657i	$-0.962782\pi$
$7$	−0.264032	−	1.49740i	−0.0997948	−	0.565964i	0.893377	−	0.449307i	$-0.148329\pi$
$8$	2.44949	−	1.41421i	0.866025	−	0.500000i
$9$	2.96941	+	0.427352i	0.989802	+	0.142451i
$10$	1.58114	−	2.73861i	0.500000	−	0.866025i
$11$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$11$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$12$	−0.843605	+	3.35981i	−0.243528	+	0.969894i
$13$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$13$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$14$	−1.38219	+	1.64723i	−0.369407	+	0.440242i
$15$	1.06137	+	3.72471i	0.274046	+	0.961717i
$16$	−3.75877	−	1.36808i	−0.939693	−	0.342020i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−2.23633	−	3.60539i	−0.527109	−	0.849798i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$	−4.40419	+	0.776578i	−0.984808	+	0.173648i
$21$	−0.270949	−	2.61961i	−0.0591258	−	0.571646i
$22$		0			0
$23$	9.44261	+	1.66499i	1.96892	+	0.347174i	0.989071	+	0.147442i	$0.0471040\pi$
$23$	9.44261	+	1.66499i	1.96892	+	0.347174i	0.979851	+	0.199732i	$0.0640071\pi$
$24$	4.40672	−	2.14028i	0.899518	−	0.436883i
$25$	−3.83022	+	3.21394i	−0.766044	+	0.642788i
$26$		0			0
$27$	5.07718	+	1.10557i	0.977103	+	0.212767i
$28$	3.04100			0.574695
$29$	4.79648	+	5.71623i	0.890685	+	1.06148i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	4.79648	+	5.71623i	0.890685	+	1.06148i	−0.107053	+	0.994253i	$0.534142\pi$
$30$	3.07034	−	4.53575i	0.560564	−	0.828111i
$31$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$31$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$32$	1.93476	+	5.31570i	0.342020	+	0.939693i
$33$		0			0
$34$		0			0
$35$	2.94444	−	1.69997i	0.497701	−	0.287348i
$36$	−1.87298	+	5.70017i	−0.312164	+	0.950028i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	4.84489	+	4.06535i	0.766044	+	0.642788i
$41$	−2.75601	+	3.28449i	−0.430417	+	0.512951i	−0.937043	−	0.349215i	$-0.886448\pi$
$41$	−2.75601	+	3.28449i	−0.430417	+	0.512951i	0.506626	+	0.862166i	$0.330893\pi$
$42$	−2.59165	+	2.67486i	−0.399901	+	0.412740i
$43$	−8.87217	−	3.22921i	−1.35299	−	0.492449i	−0.439112	−	0.898432i	$-0.644707\pi$
$43$	−8.87217	−	3.22921i	−1.35299	−	0.492449i	−0.913881	+	0.405983i	$0.866929\pi$
$44$		0			0
$45$	1.37298	+	6.56619i	0.204672	+	0.978831i
$46$	−6.77994	−	11.7432i	−0.999648	−	1.73144i
$47$	−1.46287	+	0.257943i	−0.213381	+	0.0376248i	−0.279317	−	0.960199i	$-0.590108\pi$
$47$	−1.46287	+	0.257943i	−0.213381	+	0.0376248i	0.0659356	+	0.997824i	$0.478997\pi$
$48$	−6.32456	−	2.82843i	−0.912871	−	0.408248i
$49$	4.40535	−	1.60342i	0.629336	−	0.229060i
$50$	6.96364	+	1.22788i	0.984808	+	0.173648i
$51$		0			0
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−3.41763	−	6.50537i	−0.465081	−	0.885268i
$55$		0			0
$56$	−2.76439	−	3.29447i	−0.369407	−	0.440242i
$57$		0			0
$58$	1.83249	−	10.3925i	0.240617	−	1.36461i
$59$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$59$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$60$	−7.70486	+	0.796921i	−0.994694	+	0.102882i
$61$	−2.10222	−	11.9223i	−0.269162	−	1.52649i	−0.756915	−	0.653513i	$-0.773295\pi$
$61$	−2.10222	−	11.9223i	−0.269162	−	1.52649i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$	−0.144101	−	4.55922i	−0.0181550	−	0.574408i
$64$	4.00000	−	6.92820i	0.500000	−	0.866025i
$65$		0			0
$66$		0			0
$67$	−7.18941	−	6.03263i	−0.878326	−	0.737003i	0.0875079	−	0.996164i	$-0.472110\pi$
$67$	−7.18941	−	6.03263i	−0.878326	−	0.737003i	−0.965834	+	0.259161i	$0.916554\pi$
$68$		0			0
$69$	16.1074	+	4.04436i	1.93910	+	0.486884i
$70$	−4.51827	−	1.64452i	−0.540037	−	0.196557i
$71$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$71$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$72$	7.87790	−	3.15258i	0.928419	−	0.371535i
$73$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$73$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$74$		0			0
$75$	−7.01471	+	5.07877i	−0.809989	+	0.586445i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$79$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$80$		−	8.94427i		−	1.00000i
$81$	8.63474	+	2.53796i	0.959416	+	0.281996i
$82$	6.06358			0.669610
$83$	−11.5797	−	13.8002i	−1.27104	−	1.51477i	−0.750384	−	0.661002i	$-0.770131\pi$
$83$	−11.5797	−	13.8002i	−1.27104	−	1.51477i	−0.520658	−	0.853766i	$-0.674313\pi$
$84$	5.25372	+	0.376116i	0.573228	+	0.0410376i
$85$		0			0
$86$	4.56679	+	12.5471i	0.492449	+	1.35299i
$87$	7.57955	+	10.4688i	0.812613	+	1.12237i
$88$		0			0
$89$	−15.2075	+	8.78007i	−1.61200	+	0.930686i	−0.623088	+	0.782152i	$0.714122\pi$
$89$	−15.2075	+	8.78007i	−1.61200	+	0.930686i	−0.988907	+	0.148534i	$0.952545\pi$
$90$	5.86539	−	7.45635i	0.618267	−	0.785968i
$91$		0			0
$92$	−6.55877	+	18.0201i	−0.683799	+	1.87872i
$93$		0			0
$94$	1.60925	+	1.35032i	0.165981	+	0.139275i
$95$		0			0
$96$	2.68509	+	9.42286i	0.274046	+	0.961717i
$97$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$97$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$98$	−5.74170	−	3.31497i	−0.579999	−	0.334863i
$99$		0			0
$100$	−5.00000	−	8.66025i	−0.500000	−	0.866025i
$101$	19.7558	−	3.48349i	1.96578	−	0.346620i	0.972055	−	0.234753i	$-0.0754280\pi$
$101$	19.7558	−	3.48349i	1.96578	−	0.346620i	0.993723	−	0.111867i	$-0.0356831\pi$
$102$		0			0
$103$	−17.7869	+	6.47389i	−1.75259	+	0.637892i	−0.999793	−	0.0203574i	$-0.993520\pi$
$103$	−17.7869	+	6.47389i	−1.75259	+	0.637892i	−0.752800	+	0.658249i	$0.771297\pi$
$104$		0			0
$105$	5.29715	−	2.57275i	0.516949	−	0.251074i
$106$		0			0
$107$		−	20.5207i		−	1.98381i	−0.126968	−	0.991907i	$-0.540525\pi$
$107$		−	20.5207i		−	1.98381i	0.126968	−	0.991907i	$-0.459475\pi$
$108$	−3.94083	+	9.61613i	−0.379206	+	0.925312i
$109$	10.4342			0.999416			0.499708	−	0.866194i	$-0.333441\pi$
$109$	10.4342			0.999416			0.499708	+	0.866194i	$0.333441\pi$
$110$		0			0
$111$		0			0
$112$	−1.05613	+	5.98960i	−0.0997948	+	0.565964i
$113$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$113$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$114$		0			0
$115$	3.72303	+	21.1143i	0.347174	+	1.96892i
$116$	−12.9246	+	7.46200i	−1.20002	+	0.692830i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	7.86737	+	7.62263i	0.718189	+	0.695848i
$121$	−8.42649	−	7.07066i	−0.766044	−	0.642788i
$122$	−11.0050	+	13.1153i	−0.996348	+	1.18740i
$123$	−5.16760	+	5.33351i	−0.465947	+	0.480907i
$124$		0			0
$125$	−9.68246	−	5.59017i	−0.866025	−	0.500000i
$126$	−4.80824	+	4.30062i	−0.428352	+	0.383130i
$127$	0.167160	+	0.289529i	0.0148330	+	0.0256915i	0.873347	−	0.487099i	$-0.161945\pi$
$127$	0.167160	+	0.289529i	0.0148330	+	0.0256915i	−0.858514	+	0.512791i	$0.828612\pi$
$128$	−11.1418	+	1.96460i	−0.984808	+	0.173648i
$129$	−14.9284	−	6.67619i	−1.31437	−	0.587806i
$130$		0			0
$131$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$131$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$132$		0			0
$133$		0			0
$134$			13.2725i			1.14657i
$135$	1.55989	+	11.5138i	0.134254	+	0.990947i
$136$		0			0
$137$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$137$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$138$	−10.2608	−	21.1264i	−0.873458	−	1.79840i
$139$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$139$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$140$	2.32570	+	6.38980i	0.196557	+	0.540037i
$141$	−2.55920	+	0.264700i	−0.215523	+	0.0222918i
$142$		0			0
$143$		0			0
$144$	−10.5767	−	5.66871i	−0.881389	−	0.472392i
$145$	−8.34277	+	14.4501i	−0.692830	+	1.20002i
$146$		0			0
$147$	7.80913	−	2.22525i	0.644086	−	0.183535i
$148$		0			0
$149$	−14.6934	+	17.5109i	−1.20373	+	1.43455i	−0.332896	+	0.942964i	$0.608026\pi$
$149$	−14.6934	+	17.5109i	−1.20373	+	1.43455i	−0.870831	+	0.491582i	$0.836419\pi$
$150$	11.8787	+	2.98259i	0.969894	+	0.243528i
$151$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$151$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$157$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$158$		0			0
$159$		0			0
$160$	−9.68978	+	8.13069i	−0.766044	+	0.642788i
$161$		−	14.5790i		−	1.14899i
$162$	−5.09981	−	11.6616i	−0.400679	−	0.916219i
$163$	−0.0452680			−0.00354566			−0.00177283	−	0.999998i	$-0.500564\pi$
$163$	−0.0452680			−0.00354566			−0.00177283	+	0.999998i	$0.500564\pi$
$164$	−5.51203	−	6.56898i	−0.430417	−	0.512951i
$165$		0			0
$166$	−4.42401	+	25.0898i	−0.343370	+	1.94735i
$167$	−1.76753	−	4.85626i	−0.136776	−	0.375788i	0.852328	−	0.523007i	$-0.175190\pi$
$167$	−1.76753	−	4.85626i	−0.136776	−	0.375788i	−0.989104	+	0.147219i	$0.952968\pi$
$168$	−4.36837	−	6.03353i	−0.337027	−	0.465497i
$169$	2.25743	+	12.8025i	0.173648	+	0.984808i
$170$		0			0
$171$		0			0
$172$	9.44157	−	16.3533i	0.719913	−	1.24693i
$173$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$173$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$174$	4.45122	−	17.7278i	0.337446	−	1.34394i
$175$	5.82385	+	4.88679i	0.440242	+	0.369407i
$176$		0			0
$177$		0			0
$178$	23.3361	+	8.49366i	1.74912	+	0.636627i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$	−13.4097	+	0.423834i	−0.999501	+	0.0315907i
$181$	−3.64899	−	6.32023i	−0.271227	−	0.469779i	0.697949	−	0.716147i	$-0.254096\pi$
$181$	−3.64899	−	6.32023i	−0.271227	−	0.469779i	−0.969176	+	0.246368i	$0.920763\pi$
$182$		0			0
$183$	−2.15729	−	20.8573i	−0.159472	−	1.54182i
$184$	25.4842	−	9.27550i	1.87872	−	0.683799i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		−	2.97087i		−	0.216673i
$189$	0.314939	−	7.89447i	0.0229085	−	0.574238i
$190$		0			0
$191$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$191$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$192$	7.76741	−	11.4746i	0.560564	−	0.828111i
$193$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$193$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$194$		0			0
$195$		0			0
$196$	1.62815	+	9.23371i	0.116297	+	0.659551i
$197$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$197$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$198$		0			0
$199$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$199$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$200$	−4.83690	+	13.2893i	−0.342020	+	0.939693i
$201$	−11.6745	−	11.3113i	−0.823456	−	0.797841i
$202$	−21.7327	−	18.2359i	−1.52910	−	1.28307i
$203$	7.29305	−	8.69152i	0.511872	−	0.610025i
$204$		0			0
$205$	−9.00917	−	3.27907i	−0.629228	−	0.229020i
$206$	23.1825	+	13.3844i	1.61520	+	0.932535i
$207$	27.3274	+	8.97935i	1.89939	+	0.624108i
$208$		0			0
$209$		0			0
$210$	−7.60250	−	3.39994i	−0.524622	−	0.234618i
$211$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$211$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$212$		0			0
$213$		0			0
$214$	−22.2311	+	18.6541i	−1.51969	+	1.27517i
$215$		−	21.1120i		−	1.43983i
$216$	14.0000	−	4.47214i	0.952579	−	0.304290i
$217$		0			0
$218$	−9.48510	−	11.3039i	−0.642412	−	0.765597i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	3.73557	+	21.1854i	0.250152	+	1.41868i	0.808217	+	0.588885i	$0.200433\pi$
$223$	3.73557	+	21.1854i	0.250152	+	1.41868i	−0.558065	+	0.829797i	$0.688456\pi$
$224$	7.44890	−	4.30062i	0.497701	−	0.287348i
$225$	−12.7470	+	7.90663i	−0.849798	+	0.527109i
$226$		0			0
$227$	−10.1229	+	27.8123i	−0.671878	+	1.84597i	−0.159525	+	0.987194i	$0.550996\pi$
$227$	−10.1229	+	27.8123i	−0.671878	+	1.84597i	−0.512352	+	0.858775i	$0.671226\pi$
$228$		0			0
$229$	−18.3805	−	15.4231i	−1.21462	−	1.01919i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−18.3805	−	15.4231i	−1.21462	−	1.01919i	−0.215532	−	0.976497i	$-0.569149\pi$
$230$	19.4898	−	23.2271i	1.28512	−	1.53155i
$231$		0			0
$232$	19.8329	+	7.21859i	1.30209	+	0.473923i
$233$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$233$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$234$		0			0
$235$	−1.66077	−	2.87653i	−0.108336	−	0.187644i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$239$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$240$	1.10624	−	15.4524i	0.0714077	−	0.997447i
$241$	16.6406	−	13.9631i	1.07191	−	0.899442i	0.0766885	−	0.997055i	$-0.475565\pi$
$241$	16.6406	−	13.9631i	1.07191	−	0.899442i	0.995224	+	0.0976134i	$0.0311209\pi$
$242$			15.5563i			1.00000i
$243$	14.6037	+	5.45262i	0.936830	+	0.349786i
$244$	24.2124			1.55004
$245$	6.73825	+	8.03034i	0.430491	+	0.513039i
$246$	10.4756	+	0.749953i	0.667901	+	0.0478153i
$247$		0			0
$248$		0			0
$249$	−18.2987	−	25.2738i	−1.15963	−	1.60166i
$250$	2.74562	+	15.5712i	0.173648	+	0.984808i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	9.02997	+	1.29958i	0.568834	+	0.0818657i
$253$		0			0
$254$	0.161707	−	0.444285i	0.0101464	−	0.0278769i
$255$		0			0
$256$	12.2567	+	10.2846i	0.766044	+	0.642788i
$257$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$257$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$258$	6.33786	+	22.2416i	0.394578	+	1.38470i
$259$		0			0
$260$		0			0
$261$	11.7999	+	19.0236i	0.730393	+	1.17753i
$262$		0			0
$263$	16.6131	−	2.92933i	1.02440	−	0.180630i	0.363889	−	0.931442i	$-0.381449\pi$
$263$	16.6131	−	2.92933i	1.02440	−	0.180630i	0.660516	+	0.750812i	$0.270338\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−27.3589	+	13.2878i	−1.67434	+	0.813201i
$268$	14.3788	−	12.0653i	0.878326	−	0.737003i
$269$		−	29.2206i		−	1.78161i	−0.454381	−	0.890807i	$-0.650140\pi$
$269$		−	29.2206i		−	1.78161i	0.454381	−	0.890807i	$-0.349860\pi$
$270$	11.0554	−	12.1564i	0.672813	−	0.739813i
$271$		0			0		1.00000			$0$
$271$		0			0		−1.00000			$\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−13.5599	+	30.3208i	−0.816209	+	1.82510i
$277$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$277$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$278$		0			0
$279$		0			0
$280$	4.80824	−	8.32812i	0.287348	−	0.497701i
$281$	11.4650	−	31.4997i	0.683942	−	1.87911i	0.326012	−	0.945366i	$-0.394295\pi$
$281$	11.4650	−	31.4997i	0.683942	−	1.87911i	0.357930	−	0.933748i	$-0.383483\pi$
$282$	2.61317	+	2.53188i	0.155612	+	0.150771i
$283$	−24.5080	−	20.5647i	−1.45685	−	1.22244i	−0.927385	−	0.374110i	$-0.877948\pi$
$283$	−24.5080	−	20.5647i	−1.45685	−	1.22244i	−0.529465	−	0.848332i	$-0.677607\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.64587	+	3.25965i	0.333265	+	0.192411i
$288$	3.47340	+	16.6113i	0.204672	+	0.978831i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	23.2384	−	4.09756i	1.36461	−	0.240617i
$291$		0			0
$292$		0			0
$293$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$293$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$294$	−9.50953	−	6.43719i	−0.554607	−	0.375424i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	32.3272			1.87267
$299$		0			0
$300$	−7.56703	−	15.5801i	−0.436883	−	0.899518i
$301$	−2.49288	+	14.1378i	−0.143687	+	0.814890i
$302$		0			0
$303$	34.5616	−	3.57474i	1.98551	−	0.205363i
$304$		0			0
$305$	23.4436	−	13.5352i	1.34238	−	0.775021i
$306$		0			0
$307$	5.10927	−	8.84952i	0.291602	−	0.505069i	−0.682587	−	0.730804i	$-0.739145\pi$
$307$	5.10927	−	8.84952i	0.291602	−	0.505069i	0.974189	+	0.225736i	$0.0724785\pi$
$308$		0			0
$309$	−31.5298	+	8.98458i	−1.79367	+	0.511115i
$310$		0			0
$311$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$311$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$312$		0			0
$313$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$313$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$314$		0			0
$315$	9.46971	−	3.78959i	0.533558	−	0.213519i
$316$		0			0
$317$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$317$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$318$		0			0
$319$		0			0
$320$	17.6168	+	3.10631i	0.984808	+	0.173648i
$321$	2.53804	−	35.4522i	0.141659	−	1.97875i
$322$	−15.7942	+	13.2529i	−0.880174	+	0.738553i
$323$		0			0
$324$	−7.99763	+	16.1257i	−0.444313	+	0.895872i
$325$		0			0
$326$	0.0411503	+	0.0490411i	0.00227911	+	0.00271613i
$327$	18.0264	+	1.29052i	0.996865	+	0.0713660i
$328$	−2.10586	+	11.9429i	−0.116277	+	0.659437i
$329$	0.772488	+	2.12239i	0.0425886	+	0.117011i
$330$		0			0
$331$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$331$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$332$	31.2027	−	18.0149i	1.71247	−	0.988695i
$333$		0			0
$334$	−3.65427	+	6.32939i	−0.199953	+	0.346329i
$335$	7.17755	−	19.7201i	0.392151	−	1.07743i
$336$	−2.56540	+	10.2172i	−0.139954	+	0.557393i
$337$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$337$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$338$	11.8175	−	14.0836i	0.642788	−	0.766044i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−8.88586	−	15.3908i	−0.479792	−	0.831023i
$344$	−26.2991	+	4.63724i	−1.41795	+	0.250023i
$345$	3.82055	+	36.9382i	0.205692	+	1.98869i
$346$		0			0
$347$	−12.4349	−	2.19260i	−0.667539	−	0.117705i	−0.170399	−	0.985375i	$-0.554505\pi$
$347$	−12.4349	−	2.19260i	−0.667539	−	0.117705i	−0.497140	+	0.867670i	$0.665617\pi$
$348$	−23.2518	+	11.2930i	−1.24643	+	0.605371i
$349$	28.4700	−	23.8892i	1.52396	−	1.27876i	0.695874	−	0.718164i	$-0.255017\pi$
$349$	28.4700	−	23.8892i	1.52396	−	1.27876i	0.828091	−	0.560594i	$-0.189427\pi$
$350$		−	10.7516i		−	0.574695i
$351$		0			0
$352$		0			0
$353$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$353$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$354$		0			0
$355$		0			0
$356$	−12.0118	−	33.0023i	−0.636627	−	1.74912i
$357$		0			0
$358$		0			0
$359$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$359$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$360$	12.6491	+	14.1421i	0.666667	+	0.745356i
$361$	−9.50000	+	16.4545i	−0.500000	+	0.866025i
$362$	−3.52996	+	9.69847i	−0.185530	+	0.509740i
$363$	−13.6833	−	13.2577i	−0.718189	−	0.695848i
$364$		0			0
$365$		0			0
$366$	−20.6347	+	21.2972i	−1.07859	+	1.11322i
$367$	−2.97157	−	1.08156i	−0.155115	−	0.0564571i	0.263296	−	0.964715i	$-0.415190\pi$
$367$	−2.97157	−	1.08156i	−0.155115	−	0.0564571i	−0.418411	+	0.908258i	$0.637413\pi$
$368$	−33.2148	−	19.1766i	−1.73144	−	0.999648i
$369$	−9.58736	+	8.57519i	−0.499098	+	0.446407i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$373$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$374$		0			0
$375$	−16.0363	−	10.8553i	−0.828111	−	0.560564i
$376$	−3.21849	+	2.70064i	−0.165981	+	0.139275i
$377$		0			0
$378$	−8.83877	+	6.83519i	−0.454617	+	0.351564i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$	0.252980	+	0.520873i	0.0129606	+	0.0266851i
$382$		0			0
$383$	13.0250	+	35.7859i	0.665546	+	1.82857i	0.549803	+	0.835294i	$0.314703\pi$
$383$	13.0250	+	35.7859i	0.665546	+	1.82857i	0.115743	+	0.993279i	$0.463075\pi$
$384$	−19.4919	+	2.01607i	−0.994694	+	0.102882i
$385$		0			0
$386$		0			0
$387$	−24.9651	−	13.3804i	−1.26905	−	0.680162i
$388$		0			0
$389$	−13.4783	+	37.0313i	−0.683376	+	1.87756i	−0.300300	+	0.953845i	$0.597087\pi$
$389$	−13.4783	+	37.0313i	−0.683376	+	1.87756i	−0.383076	+	0.923717i	$0.625135\pi$
$390$		0			0
$391$		0			0
$392$	8.52329	−	10.1577i	0.430491	−	0.513039i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$397$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$398$		0			0
$399$		0			0
$400$	18.7939	−	6.84040i	0.939693	−	0.342020i
$401$	−32.9684	−	5.81322i	−1.64636	−	0.290298i	−0.727865	−	0.685721i	$-0.759487\pi$
$401$	−32.9684	−	5.81322i	−1.64636	−	0.290298i	−0.918499	+	0.395423i	$0.870598\pi$
$402$	−1.64157	+	22.9300i	−0.0818741	+	1.14365i
$403$		0			0
$404$			40.1212i			1.99610i
$405$	1.27087	+	20.0844i	0.0631499	+	0.998004i
$406$	−16.0456			−0.796332
$407$		0			0
$408$		0			0
$409$	−5.70553	+	32.3577i	−0.282120	+	1.59998i	0.433273	+	0.901263i	$0.357359\pi$
$409$	−5.70553	+	32.3577i	−0.282120	+	1.59998i	−0.715394	+	0.698722i	$0.753753\pi$
$410$	4.63730	+	12.7409i	0.229020	+	0.629228i
$411$		0			0
$412$	−6.57376	−	37.2817i	−0.323866	−	1.83674i
$413$		0			0
$414$	−15.1139	−	37.7677i	−0.742808	−	1.85618i
$415$	20.1412	−	34.8857i	0.988695	−	1.71247i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$419$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$420$	3.22764	+	11.3269i	0.157493	+	0.552694i
$421$	36.5135	+	13.2898i	1.77956	+	0.647706i	0.999765	+	0.0216699i	$0.00689828\pi$
$421$	36.5135	+	13.2898i	1.77956	+	0.647706i	0.779794	+	0.626037i	$0.215324\pi$
$422$		0			0
$423$	−4.45408	+	0.140778i	−0.216565	+	0.00684485i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−17.2974	+	6.29574i	−0.837080	+	0.304672i
$428$	40.4179	+	7.12677i	1.95367	+	0.344486i
$429$		0			0
$430$	−22.8717	+	19.1916i	−1.10297	+	0.925502i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	−17.5714	−	11.1016i	−0.845406	−	0.534124i
$433$		0			0		1.00000			$0$
$433$		0			0		−1.00000			$\pi$
$434$		0			0
$435$	−16.2004	+	23.9326i	−0.776751	+	1.14748i
$436$	−3.62376	+	20.5514i	−0.173547	+	0.984233i
$437$		0			0
$438$		0			0
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	13.7665	−	2.87856i	0.655548	−	0.137074i
$442$		0			0
$443$	−12.8309	+	35.2527i	−0.609617	+	1.67491i	0.121446	+	0.992598i	$0.461247\pi$
$443$	−12.8309	+	35.2527i	−0.609617	+	1.67491i	−0.731063	+	0.682310i	$0.760975\pi$
$444$		0			0
$445$	−30.0793	−	25.2395i	−1.42589	−	1.19647i
$446$	19.5555	−	23.3053i	0.925979	−	1.10354i
$447$	−27.5504	+	28.4350i	−1.30309	+	1.34493i
$448$	−11.4304	−	4.16033i	−0.540037	−	0.196557i
$449$	−17.3175	−	9.99829i	−0.817265	−	0.471848i	0.0322072	−	0.999481i	$-0.489746\pi$
$449$	−17.3175	−	9.99829i	−0.817265	−	0.471848i	−0.849473	+	0.527633i	$0.823080\pi$
$450$	20.1531	+	6.62200i	0.950028	+	0.312164i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	39.3326	−	14.3159i	1.84597	−	0.671878i
$455$		0			0
$456$		0			0
$457$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$457$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$458$			33.9328i			1.58557i
$459$		0			0
$460$	−42.8801			−1.99930
$461$	−14.6361	−	17.4426i	−0.681671	−	0.812383i	0.308651	−	0.951175i	$-0.400123\pi$
$461$	−14.6361	−	17.4426i	−0.681671	−	0.812383i	−0.990322	+	0.138792i	$0.955678\pi$
$462$		0			0
$463$	−1.65523	+	9.38729i	−0.0769252	+	0.436264i	0.921884	+	0.387467i	$0.126650\pi$
$463$	−1.65523	+	9.38729i	−0.0769252	+	0.436264i	−0.998809	+	0.0487972i	$0.984461\pi$
$464$	−10.2086	−	28.0480i	−0.473923	−	1.30209i
$465$		0			0
$466$		0			0
$467$	−7.26081	+	4.19203i	−0.335990	+	0.193984i	−0.658497	−	0.752583i	$-0.728808\pi$
$467$	−7.26081	+	4.19203i	−0.335990	+	0.193984i	0.322507	+	0.946567i	$0.395474\pi$
$468$		0			0
$469$	−7.13503	+	12.3582i	−0.329465	+	0.570650i
$470$	−1.60659	+	4.41407i	−0.0741065	+	0.203606i
$471$		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		0.984808	−	0.173648i	$-0.0555556\pi$
$479$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$480$	−17.7460	+	12.8484i	−0.809989	+	0.586445i
$481$		0			0
$482$	−30.2538	−	5.33457i	−1.37802	−	0.242983i
$483$	1.80315	−	25.1871i	0.0820463	−	1.14605i
$484$	16.8530	−	14.1413i	0.766044	−	0.642788i
$485$		0			0
$486$	−7.36826	−	20.7776i	−0.334231	−	0.942491i
$487$	22.1359			1.00308			0.501538	−	0.865136i	$-0.332768\pi$
$487$	22.1359			1.00308			0.501538	+	0.865136i	$0.332768\pi$
$488$	−22.0101	−	26.2306i	−0.996348	−	1.18740i
$489$	−0.0782063	−	0.00559882i	−0.00353661	−	0.000253187i
$490$	2.57434	−	14.5998i	0.116297	−	0.659551i
$491$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$491$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$492$	−8.71028	−	12.0305i	−0.392690	−	0.542377i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−10.7462	+	42.7988i	−0.481549	+	1.91786i
$499$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$499$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$500$	14.3732	−	17.1293i	0.642788	−	0.766044i
$501$	−2.45301	−	8.60842i	−0.109592	−	0.384596i
$502$		0			0
$503$	38.4874	+	22.2207i	1.71607	+	0.990772i	0.925803	+	0.378005i	$0.123390\pi$
$503$	38.4874	+	22.2207i	1.71607	+	0.990772i	0.790264	+	0.612767i	$0.209943\pi$
$504$	−6.80069	−	10.9640i	−0.302927	−	0.488375i
$505$	22.4284	+	38.8472i	0.998052	+	1.72868i
$506$		0			0
$507$	2.31656	+	22.3972i	0.102882	+	0.994694i
$508$	−0.628315	+	0.228688i	−0.0278769	+	0.0101464i
$509$	39.3649	+	6.94110i	1.74482	+	0.307659i	0.952972	−	0.303059i	$-0.0980078\pi$
$509$	39.3649	+	6.94110i	1.74482	+	0.307659i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$		0			0
$515$	−27.2061	−	32.4230i	−1.19884	−	1.42873i
$516$	18.3341	−	27.0846i	0.807115	−	1.19233i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	33.1303	−	19.1278i	1.45147	−	0.838004i	0.452901	−	0.891561i	$-0.350389\pi$
$521$	33.1303	−	19.1278i	1.45147	−	0.838004i	0.998565	+	0.0535562i	$0.0170556\pi$
$522$	9.88267	−	30.0766i	0.432553	−	1.31642i
$523$	−21.4224	+	37.1046i	−0.936735	+	1.62247i	−0.165224	+	0.986256i	$0.552835\pi$
$523$	−21.4224	+	37.1046i	−0.936735	+	1.62247i	−0.771511	+	0.636216i	$0.780499\pi$
$524$		0			0
$525$	9.45705	+	9.16287i	0.412740	+	0.399901i
$526$	−18.2754	−	15.3349i	−0.796846	−	0.668633i
$527$		0			0
$528$		0			0
$529$	64.7779	+	23.5772i	2.81643	+	1.02510i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	39.2657	+	17.5601i	1.69919	+	0.759902i
$535$	43.1185	−	15.6938i	1.86417	−	0.678504i
$536$	−26.1418	−	4.60951i	−1.12915	−	0.199100i
$537$		0			0
$538$	−31.6562	+	26.5627i	−1.36480	+	1.14520i
$539$		0			0
$540$	−23.2194	−	0.926308i	−0.999205	−	0.0398620i
$541$	−26.5310			−1.14065			−0.570327	−	0.821417i	$-0.693184\pi$
$541$	−26.5310			−1.14065			−0.570327	+	0.821417i	$0.693184\pi$
$542$		0			0
$543$	−5.52240	−	11.3703i	−0.236989	−	0.487948i
$544$		0			0
$545$	7.97988	+	21.9245i	0.341820	+	0.939144i
$546$		0			0
$547$	−4.78849	−	27.1569i	−0.204741	−	1.16115i	−0.897846	−	0.440309i	$-0.854869\pi$
$547$	−4.78849	−	27.1569i	−0.204741	−	1.16115i	0.693105	−	0.720836i	$-0.256242\pi$
$548$		0			0
$549$	−1.14733	−	36.3005i	−0.0489669	−	1.54927i
$550$		0			0
$551$		0			0
$552$	45.1745	−	12.8727i	1.92276	−	0.547898i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$557$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$		0			0
$560$	−13.3932	+	2.36158i	−0.565964	+	0.0997948i
$561$		0			0
$562$	−44.5473	+	16.2139i	−1.87911	+	0.683942i
$563$	31.0938	+	5.48267i	1.31045	+	0.231067i	0.784860	−	0.619673i	$-0.212735\pi$
$563$	31.0938	+	5.48267i	1.31045	+	0.231067i	0.525586	+	0.850740i	$0.323846\pi$
$564$	0.367442	−	5.13256i	0.0154721	−	0.216120i
$565$		0			0
$566$			45.2448i			1.90178i
$567$	1.52050	−	13.5998i	0.0638550	−	0.571137i
$568$		0			0
$569$	30.1014	+	35.8734i	1.26191	+	1.50389i	0.777252	+	0.629190i	$0.216613\pi$
$569$	30.1014	+	35.8734i	1.26191	+	1.50389i	0.484663	+	0.874701i	$0.338942\pi$
$570$		0			0
$571$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$571$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$572$		0			0
$573$		0			0
$574$	−1.60098	−	9.07960i	−0.0668236	−	0.378975i
$575$	−41.5185	+	23.9707i	−1.73144	+	0.999648i
$576$	14.8384	−	18.8632i	0.618267	−	0.785968i
$577$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$577$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$578$	8.22272	−	22.5917i	0.342020	−	0.939693i
$579$		0			0
$580$	−25.5637	−	21.4505i	−1.06148	−	0.890685i
$581$	−17.6070	+	20.9832i	−0.730461	+	0.870530i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.81581	+	1.20181i	−0.281319	+	0.0496041i	−0.312527	−	0.949909i	$-0.601176\pi$
$587$	−6.81581	+	1.20181i	−0.281319	+	0.0496041i	0.0312085	+	0.999513i	$0.490064\pi$
$588$	1.67080	+	16.1538i	0.0689027	+	0.666172i
$589$		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
$596$	−29.3867	−	35.0217i	−1.20373	−	1.43455i
$597$		0			0
$598$		0			0
$599$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$599$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$600$	−10.0000	+	22.3607i	−0.408248	+	0.912871i
$601$	−3.62175	−	20.5400i	−0.147734	−	0.837844i	−0.965131	−	0.261768i	$-0.915694\pi$
$601$	−3.62175	−	20.5400i	−0.147734	−	0.837844i	0.817396	−	0.576076i	$-0.195417\pi$
$602$	17.5823	−	10.1512i	0.716602	−	0.413730i
$603$	−18.7702	−	20.9857i	−0.764382	−	0.854605i
$604$		0			0
$605$	8.41258	−	23.1134i	0.342020	−	0.939693i
$606$	−35.2905	−	34.1927i	−1.43358	−	1.38899i
$607$	33.1042	+	27.7777i	1.34366	+	1.12746i	0.980670	+	0.195667i	$0.0626873\pi$
$607$	33.1042	+	27.7777i	1.34366	+	1.12746i	0.362986	+	0.931794i	$0.381757\pi$
$608$		0			0
$609$	13.6747	−	14.1137i	0.554126	−	0.571917i
$610$	−35.9745	−	13.0936i	−1.45656	−	0.530146i
$611$		0			0
$612$		0			0
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	−14.2317	+	2.50943i	−0.574343	+	0.101272i
$615$	−15.1589	−	6.77929i	−0.611268	−	0.273367i
$616$		0			0
$617$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$617$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$618$	38.3953	+	25.9905i	1.54448	+	1.04549i
$619$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$619$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$620$		0			0
$621$	46.1011	+	18.8929i	1.84997	+	0.758145i
$622$		0			0
$623$	17.1626	+	20.4535i	0.687604	+	0.819454i
$624$		0			0
$625$	4.34120	−	24.6202i	0.173648	−	0.984808i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−12.7138	−	6.81413i	−0.506530	−	0.271481i
$631$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$631$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.480523	+	0.572664i	−0.0190690	+	0.0227255i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−12.6491	−	21.9089i	−0.500000	−	0.866025i
$641$	41.4826	−	7.31450i	1.63846	−	0.288905i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	41.4826	−	7.31450i	1.63846	−	0.288905i	0.915602	+	0.402087i	$0.131715\pi$
$642$	−40.7143	+	29.4779i	−1.60687	+	1.16340i
$643$	20.7754	−	7.56162i	0.819301	−	0.298201i	0.101841	−	0.994801i	$-0.467527\pi$
$643$	20.7754	−	7.56162i	0.819301	−	0.298201i	0.717460	+	0.696600i	$0.245305\pi$
$644$	28.7150	+	5.06323i	1.13153	+	0.199519i
$645$	2.61117	−	36.4737i	0.102815	−	1.43615i
$646$		0			0
$647$		−	43.5211i		−	1.71099i	−0.517812	−	0.855495i	$-0.673253\pi$
$647$		−	43.5211i		−	1.71099i	0.517812	−	0.855495i	$-0.326747\pi$
$648$	24.7399	−	5.99465i	0.971876	−	0.235492i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.0157214	−	0.0891605i	0.000615698	−	0.00349179i
$653$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$653$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$654$	−14.9887	−	20.7021i	−0.586103	−	0.809516i
$655$		0			0
$656$	14.8527	−	8.57519i	0.579899	−	0.334805i
$657$		0			0
$658$	1.59707	−	2.76621i	0.0622604	−	0.107838i
$659$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$659$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$660$		0			0
$661$	−38.9586	−	32.6902i	−1.51531	−	1.27150i	−0.852515	−	0.522702i	$-0.824924\pi$
$661$	−38.9586	−	32.6902i	−1.51531	−	1.27150i	−0.662799	−	0.748798i	$-0.730632\pi$
$662$		0			0
$663$		0			0
$664$	−47.8809	−	17.4272i	−1.85814	−	0.676307i
$665$		0			0
$666$		0			0
$667$	35.7739	+	61.9622i	1.38517	+	2.39919i
$668$	10.1788	−	1.79480i	0.393830	−	0.0694429i
$669$	3.83342	+	37.0626i	0.148209	+	1.43292i
$670$	−27.8885	+	10.1506i	−1.07743	+	0.392151i
$671$		0			0
$672$	13.4008	−	6.50859i	0.516949	−	0.251074i
$673$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$673$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$674$		0			0
$675$	−22.9999	+	12.0832i	−0.885268	+	0.465081i
$676$	−26.0000			−1.00000
$677$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$677$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−20.9284	+	46.7974i	−0.801979	+	1.79328i
$682$		0			0
$683$	−40.3289	+	23.2839i	−1.54314	+	0.890934i	−0.544505	+	0.838757i	$0.683283\pi$
$683$	−40.3289	+	23.2839i	−1.54314	+	0.890934i	−0.998638	+	0.0521768i	$0.983384\pi$
$684$		0			0
$685$		0			0
$686$	−8.59600	+	23.6173i	−0.328197	+	0.901713i
$687$	−29.8472	−	28.9187i	−1.13874	−	1.10332i
$688$	28.9306	+	24.2757i	1.10297	+	0.925502i
$689$		0			0
$690$	36.5440	−	37.7173i	1.39121	−	1.43587i
$691$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$691$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$692$		0			0
$693$		0			0
$694$	8.92843	+	15.4645i	0.338918	+	0.587024i
$695$		0			0
$696$	33.3711	+	14.9240i	1.26493	+	0.565693i
$697$		0			0
$698$	−51.7607	−	9.12681i	−1.95917	−	0.345455i
$699$		0			0
$700$	−11.6477	+	9.77359i	−0.440242	+	0.369407i
$701$			47.9831i			1.81230i	0.422961	+	0.906148i	$0.360991\pi$
$701$			47.9831i			1.81230i	−0.422961	+	0.906148i	$0.639009\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	−2.51341	−	5.17499i	−0.0946606	−	0.194901i
$706$		0			0
$707$	−10.4323	−	28.6626i	−0.392349	−	1.07797i
$708$		0			0
$709$	−3.12397	−	17.7169i	−0.117323	−	0.665373i	−0.985574	−	0.169247i	$-0.945866\pi$
$709$	−3.12397	−	17.7169i	−0.117323	−	0.665373i	0.868250	−	0.496126i	$-0.165245\pi$
$710$		0			0
$711$		0			0
$712$	−24.8338	+	43.0134i	−0.930686	+	1.61200i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	3.82235	−	26.5592i	0.142451	−	0.989802i
$721$	14.3903	+	24.9248i	0.535923	+	0.928247i
$722$	26.4618	−	4.66594i	0.984808	−	0.173648i
$723$	30.4757	−	22.0649i	1.13340	−	0.820603i
$724$	13.7157	−	4.99211i	0.509740	−	0.185530i
$725$	−36.7432	−	6.47882i	−1.36461	−	0.240617i
$726$	−1.92404	+	26.8756i	−0.0714077	+	0.997447i
$727$	39.8096	−	33.4042i	1.47646	−	1.23889i	0.566585	−	0.824003i	$-0.308264\pi$
$727$	39.8096	−	33.4042i	1.47646	−	1.23889i	0.909871	−	0.414891i	$-0.136180\pi$
$728$		0			0
$729$	24.5554	+	11.2263i	0.909461	+	0.415790i
$730$		0			0
$731$		0			0
$732$	41.8301	+	2.99464i	1.54609	+	0.110685i
$733$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$733$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$734$	1.52956	+	4.20243i	0.0564571	+	0.155115i
$735$	10.6480	+	14.7068i	0.392757	+	0.542470i
$736$	9.41859	+	53.4155i	0.347174	+	1.96892i
$737$		0			0
$738$	18.0052	+	2.59128i	0.662781	+	0.0953865i
$739$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$739$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−32.8296	+	39.1248i	−1.20440	+	1.43535i	−0.334305	+	0.942465i	$0.608502\pi$
$743$	−32.8296	+	39.1248i	−1.20440	+	1.43535i	−0.870095	+	0.492883i	$0.835943\pi$
$744$		0			0
$745$	−48.0313	−	17.4820i	−1.75973	−	0.640490i
$746$		0			0
$747$	−28.4874	−	45.9270i	−1.04230	−	1.68038i
$748$		0			0
$749$	−30.7277	+	5.41813i	−1.12277	+	0.197974i
$750$	2.81754	+	27.2408i	0.102882	+	0.994694i
$751$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$751$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$752$	5.85147	+	1.03177i	0.213381	+	0.0376248i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	15.4397	+	3.36203i	0.561536	+	0.122276i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.140146	−	0.385048i	−0.00508029	−	0.0139580i	0.937127	−	0.348990i	$-0.113475\pi$
$761$	−0.140146	−	0.385048i	−0.00508029	−	0.0139580i	−0.942207	+	0.335032i	$0.891253\pi$
$762$	0.334319	−	0.747560i	0.0121111	−	0.0270813i
$763$	−2.75497	−	15.6242i	−0.0997365	−	0.565634i
$764$		0			0
$765$		0			0
$766$	26.9284	−	46.6414i	0.972964	−	1.68522i
$767$		0			0
$768$	19.9030	+	19.2839i	0.718189	+	0.695848i
$769$	−24.1384	−	20.2545i	−0.870452	−	0.730396i	0.0937409	−	0.995597i	$-0.470117\pi$
$769$	−24.1384	−	20.2545i	−0.870452	−	0.730396i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$773$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$774$	8.19859	+	39.2092i	0.294692	+	1.40934i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	52.3702	−	19.0612i	1.87756	−	0.683376i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	18.0329	+	34.3251i	0.644444	+	1.22668i
$784$	−18.7523			−0.669726
$785$		0			0
$786$		0			0
$787$	7.13861	−	40.4851i	0.254464	−	1.44314i	−0.542981	−	0.839745i	$-0.682704\pi$
$787$	7.13861	−	40.4851i	0.254464	−	1.44314i	0.797445	−	0.603392i	$-0.206184\pi$
$788$		0			0
$789$	29.0635	−	3.00607i	1.03469	−	0.107019i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$797$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$798$		0			0
$799$		0			0
$800$	−24.4949	−	14.1421i	−0.866025	−	0.500000i
$801$	−48.9095	+	19.5726i	−1.72813	+	0.691565i
$802$	23.6718	+	41.0008i	0.835881	+	1.44779i
$803$		0			0
$804$	26.3335	−	19.0659i	0.928712	−	0.672403i
$805$	30.6336	−	11.1497i	1.07969	−	0.392976i
$806$		0			0
$807$	3.61406	−	50.4824i	0.127221	−	1.77707i
$808$	43.4653	−	36.4717i	1.52910	−	1.28307i
$809$		−	17.8885i		−	0.628928i	−0.949269	−	0.314464i	$-0.898175\pi$
$809$		−	17.8885i		−	0.628928i	0.949269	−	0.314464i	$-0.101825\pi$
$810$	20.6032	−	19.6343i	0.723924	−	0.689880i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$	14.5861	+	17.3830i	0.511872	+	0.610025i
$813$		0			0
$814$		0			0
$815$	−0.0346200	−	0.0951178i	−0.00121269	−	0.00333183i
$816$		0			0
$817$		0			0
$818$	40.2413	−	23.2333i	1.40700	−	0.812333i
$819$		0			0
$820$	9.58736	−	16.6058i	0.334805	−	0.579899i
$821$	−18.0268	+	49.5282i	−0.629139	+	1.72855i	0.0542853	+	0.998525i	$0.482712\pi$
$821$	−18.0268	+	49.5282i	−0.629139	+	1.72855i	−0.683425	+	0.730021i	$0.739510\pi$
$822$		0			0
$823$	25.8323	+	21.6759i	0.900459	+	0.755575i	0.970280	−	0.241985i	$-0.0777984\pi$
$823$	25.8323	+	21.6759i	0.900459	+	0.755575i	−0.0698210	+	0.997560i	$0.522243\pi$
$824$	−34.4133	+	41.0122i	−1.19884	+	1.42873i
$825$		0			0
$826$		0			0
$827$	45.3466	+	26.1809i	1.57686	+	0.910399i	0.995294	+	0.0968967i	$0.0308916\pi$
$827$	45.3466	+	26.1809i	1.57686	+	0.910399i	0.581562	+	0.813502i	$0.302442\pi$
$828$	−27.1766	+	50.7060i	−0.944451	+	1.76216i
$829$	−11.4684	−	19.8639i	−0.398315	−	0.689902i	0.595203	−	0.803576i	$-0.297072\pi$
$829$	−11.4684	−	19.8639i	−0.398315	−	0.689902i	−0.993518	+	0.113673i	$0.963738\pi$
$830$	−56.1026	+	9.89239i	−1.94735	+	0.343370i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	8.85227	−	7.42794i	0.306346	−	0.257054i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$839$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$840$	9.33690	−	13.7932i	0.322154	−	0.475911i
$841$	−4.63319	+	26.2761i	−0.159765	+	0.906074i
$842$	−18.7947	−	51.6379i	−0.647706	−	1.77956i
$843$	23.7031	−	53.0018i	0.816379	−	1.82548i
$844$		0			0
$845$	−25.1744	+	14.5344i	−0.866025	+	0.500000i
$846$	4.20144	+	4.69736i	0.144449	+	0.161498i
$847$	−8.36275	+	14.4847i	−0.287348	+	0.497701i
$848$		0			0
$849$	−39.7973	−	38.5593i	−1.36584	−	1.32335i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$853$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$854$	22.5445	+	13.0161i	0.771457	+	0.445401i
$855$		0			0
$856$	−29.0207	−	50.2653i	−0.991907	−	1.71803i
$857$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$857$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$858$		0			0
$859$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$859$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$860$	41.5825	+	7.33211i	1.41795	+	0.250023i
$861$	9.35082	+	6.32975i	0.318675	+	0.215717i
$862$		0			0
$863$			51.2413i			1.74427i	0.489262	+	0.872137i	$0.337266\pi$
$863$			51.2413i			1.74427i	−0.489262	+	0.872137i	$0.662734\pi$
$864$	3.94624	+	29.1278i	0.134254	+	0.990947i
$865$		0			0
$866$		0			0
$867$	12.8640	+	26.4862i	0.436883	+	0.899518i
$868$		0			0
$869$		0			0
$870$	40.6542	−	4.20490i	1.37831	−	0.142559i
$871$		0			0
$872$	25.5585	−	14.7562i	0.865520	−	0.499708i
$873$		0			0
$874$		0			0
$875$	−5.81424	+	15.9745i	−0.196557	+	0.540037i
$876$		0			0
$877$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$877$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	18.9774	+	10.9566i	0.639365	+	0.369137i	0.784370	−	0.620294i	$-0.212987\pi$
$881$	18.9774	+	10.9566i	0.639365	+	0.369137i	−0.145005	+	0.989431i	$0.546320\pi$
$882$	−15.6328	−	12.2972i	−0.526383	−	0.414069i
$883$	−26.2048	−	45.3881i	−0.881862	−	1.52743i	−0.849268	−	0.527962i	$-0.822956\pi$
$883$	−26.2048	−	45.3881i	−0.881862	−	1.52743i	−0.0325942	−	0.999469i	$-0.510377\pi$
$884$		0			0
$885$		0			0
$886$	49.8549	−	18.1457i	1.67491	−	0.609617i
$887$	−50.0385	−	8.82314i	−1.68013	−	0.296252i	−0.749443	−	0.662069i	$-0.769679\pi$
$887$	−50.0385	−	8.82314i	−1.68013	−	0.296252i	−0.930687	+	0.365817i	$0.880790\pi$
$888$		0			0
$889$	0.389405	−	0.326750i	0.0130602	−	0.0109588i
$890$			55.5301i			1.86137i
$891$		0			0
$892$	−43.0245			−1.44057
$893$		0			0
$894$	55.8495	+	3.99829i	1.86789	+	0.133723i
$895$		0			0
$896$	5.88360	+	16.1651i	0.196557	+	0.540037i
$897$		0			0
$898$	4.91067	+	27.8498i	0.163871	+	0.929360i
$899$		0			0
$900$	−11.1460	−	27.8526i	−0.371535	−	0.928419i
$901$		0			0
$902$		0			0
$903$	−6.05535	+	24.1166i	−0.201510	+	0.802549i
$904$		0			0
$905$	10.4895	−	12.5009i	0.348683	−	0.415544i
$906$		0			0
$907$	51.6913	+	18.8141i	1.71638	+	0.624712i	0.997516	−	0.0704373i	$-0.0224395\pi$
$907$	51.6913	+	18.8141i	1.71638	+	0.624712i	0.718866	+	0.695149i	$0.244662\pi$
$908$	−51.2640	−	29.5973i	−1.70125	−	0.982220i
$909$	60.1517	−	1.90118i	1.99511	−	0.0630583i
$910$		0			0
$911$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$911$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	42.1759	−	20.4842i	1.39429	−	0.677187i
$916$	36.7611	−	30.8462i	1.21462	−	1.01919i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$	38.9797	+	46.4542i	1.28512	+	1.53155i
$921$	9.92145	−	14.6568i	0.326923	−	0.482957i
$922$	−5.59169	+	31.7120i	−0.184152	+	1.04438i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	11.6744	−	6.74021i	0.383644	−	0.221497i
$927$	−55.5831	+	11.6224i	−1.82559	+	0.381728i
$928$	−21.1057	+	36.5562i	−0.692830	+	1.20002i
$929$	2.25055	−	6.18333i	0.0738381	−	0.202869i	−0.897283	−	0.441456i	$-0.854462\pi$
$929$	2.25055	−	6.18333i	0.0738381	−	0.202869i	0.971121	+	0.238587i	$0.0766843\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	11.1418	+	4.05528i	0.364571	+	0.132693i
$935$		0			0
$936$		0			0
$937$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$937$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$938$	19.8743	−	3.50438i	0.648920	−	0.114422i
$939$		0			0
$940$	6.24244	−	2.27206i	0.203606	−	0.0741065i
$941$	−60.3250	−	10.6369i	−1.96654	−	0.346754i	−0.992971	−	0.118359i	$-0.962237\pi$
$941$	−60.3250	−	10.6369i	−1.96654	−	0.346754i	−0.973568	−	0.228395i	$-0.926652\pi$
$942$		0			0
$943$	−31.4926	+	26.4254i	−1.02554	+	0.860531i
$944$		0			0
$945$	16.8289	−	5.37578i	0.547443	−	0.174874i
$946$		0			0
$947$	26.0239	+	31.0141i	0.845664	+	1.00782i	0.999804	+	0.0197743i	$0.00629477\pi$
$947$	26.0239	+	31.0141i	0.845664	+	1.00782i	−0.154140	+	0.988049i	$0.549261\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$953$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	30.0511	+	7.54543i	0.969894	+	0.243528i
$961$	−29.1305	−	10.6026i	−0.939693	−	0.342020i
$962$		0			0
$963$	8.76958	−	60.9344i	0.282596	−	1.96358i
$964$	21.7227	+	37.6248i	0.699641	+	1.21181i
$965$		0			0
$966$	−28.9256	+	20.9426i	−0.930665	+	0.673817i
$967$	−49.8964	+	18.1608i	−1.60456	+	0.584012i	−0.980354	−	0.197247i	$-0.936800\pi$
$967$	−49.8964	+	18.1608i	−1.60456	+	0.584012i	−0.624207	+	0.781259i	$0.714578\pi$
$968$	−30.6400	−	5.40266i	−0.984808	−	0.173648i
$969$		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
$974$	−20.1224	−	23.9810i	−0.644764	−	0.768400i
$975$		0			0
$976$	−8.40889	+	47.6892i	−0.269162	+	1.52649i
$977$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$977$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$978$	0.0650271	+	0.0898143i	0.00207934	+	0.00287195i
$979$		0			0
$980$	−18.1569	+	10.4829i	−0.579999	+	0.334863i
$981$	30.9834	+	4.45908i	0.989224	+	0.142368i
$982$		0			0
$983$	18.7298	−	51.4597i	0.597388	−	1.64131i	−0.159069	−	0.987267i	$-0.550849\pi$
$983$	18.7298	−	51.4597i	0.597388	−	1.64131i	0.756457	−	0.654043i	$-0.226928\pi$
$984$	−5.11526	+	20.3725i	−0.163069	+	0.649451i
$985$		0			0
$986$		0			0
$987$	1.07207	+	3.76225i	0.0341244	+	0.119754i
$988$		0			0
$989$	−78.3999	−	45.2642i	−2.49297	−	1.43932i
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	56.1348	−	27.2638i	1.77870	−	0.863887i
$997$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$997$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.bb.a.59.2	✓	24
4.3	odd	2	inner	540.2.bb.a.59.3	yes	24
5.4	even	2	inner	540.2.bb.a.59.3	yes	24
20.19	odd	2	CM	540.2.bb.a.59.2	✓	24
27.11	odd	18	inner	540.2.bb.a.119.2	yes	24
108.11	even	18	inner	540.2.bb.a.119.3	yes	24
135.119	odd	18	inner	540.2.bb.a.119.3	yes	24
540.119	even	18	inner	540.2.bb.a.119.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.bb.a.59.2	✓	24	1.1	even	1	trivial
540.2.bb.a.59.2	✓	24	20.19	odd	2	CM
540.2.bb.a.59.3	yes	24	4.3	odd	2	inner
540.2.bb.a.59.3	yes	24	5.4	even	2	inner
540.2.bb.a.119.2	yes	24	27.11	odd	18	inner
540.2.bb.a.119.2	yes	24	540.119	even	18	inner
540.2.bb.a.119.3	yes	24	108.11	even	18	inner
540.2.bb.a.119.3	yes	24	135.119	odd	18	inner

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909039 - 1.08335i) q^{2} +(1.72763 + 0.123682i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.764780 + 2.10122i) q^{5} +(-1.43649 - 1.98406i) q^{6} +(-0.264032 - 1.49740i) q^{7} +(2.44949 - 1.41421i) q^{8} +(2.96941 + 0.427352i) q^{9} +O(q^{10})\)	\(q+(-0.909039 - 1.08335i) q^{2} +(1.72763 + 0.123682i) q^{3} +(-0.347296 + 1.96962i) q^{4} +(0.764780 + 2.10122i) q^{5} +(-1.43649 - 1.98406i) q^{6} +(-0.264032 - 1.49740i) q^{7} +(2.44949 - 1.41421i) q^{8} +(2.96941 + 0.427352i) q^{9} +(1.58114 - 2.73861i) q^{10} +(-0.843605 + 3.35981i) q^{12} +(-1.38219 + 1.64723i) q^{14} +(1.06137 + 3.72471i) q^{15} +(-3.75877 - 1.36808i) q^{16} +(-2.23633 - 3.60539i) q^{18} +(-4.40419 + 0.776578i) q^{20} +(-0.270949 - 2.61961i) q^{21} +(9.44261 + 1.66499i) q^{23} +(4.40672 - 2.14028i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(5.07718 + 1.10557i) q^{27} +3.04100 q^{28} +(4.79648 + 5.71623i) q^{29} +(3.07034 - 4.53575i) q^{30} +(1.93476 + 5.31570i) q^{32} +(2.94444 - 1.69997i) q^{35} +(-1.87298 + 5.70017i) q^{36} +(4.84489 + 4.06535i) q^{40} +(-2.75601 + 3.28449i) q^{41} +(-2.59165 + 2.67486i) q^{42} +(-8.87217 - 3.22921i) q^{43} +(1.37298 + 6.56619i) q^{45} +(-6.77994 - 11.7432i) q^{46} +(-1.46287 + 0.257943i) q^{47} +(-6.32456 - 2.82843i) q^{48} +(4.40535 - 1.60342i) q^{49} +(6.96364 + 1.22788i) q^{50} +(-3.41763 - 6.50537i) q^{54} +(-2.76439 - 3.29447i) q^{56} +(1.83249 - 10.3925i) q^{58} +(-7.70486 + 0.796921i) q^{60} +(-2.10222 - 11.9223i) q^{61} +(-0.144101 - 4.55922i) q^{63} +(4.00000 - 6.92820i) q^{64} +(-7.18941 - 6.03263i) q^{67} +(16.1074 + 4.04436i) q^{69} +(-4.51827 - 1.64452i) q^{70} +(7.87790 - 3.15258i) q^{72} +(-7.01471 + 5.07877i) q^{75} -8.94427i q^{80} +(8.63474 + 2.53796i) q^{81} +6.06358 q^{82} +(-11.5797 - 13.8002i) q^{83} +(5.25372 + 0.376116i) q^{84} +(4.56679 + 12.5471i) q^{86} +(7.57955 + 10.4688i) q^{87} +(-15.2075 + 8.78007i) q^{89} +(5.86539 - 7.45635i) q^{90} +(-6.55877 + 18.0201i) q^{92} +(1.60925 + 1.35032i) q^{94} +(2.68509 + 9.42286i) q^{96} +(-5.74170 - 3.31497i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{6}+O(q^{10}) \) 24 * q + 12 * q^6	\( 24 q + 12 q^{6} - 36 q^{14} + 36 q^{29} + 48 q^{36} - 144 q^{41} - 60 q^{45} + 24 q^{49} - 72 q^{56} - 48 q^{61} + 96 q^{64} + 192 q^{69} - 120 q^{70} + 48 q^{84} + 168 q^{94}+O(q^{100}) \) 24 * q + 12 * q^6 - 36 * q^14 + 36 * q^29 + 48 * q^36 - 144 * q^41 - 60 * q^45 + 24 * q^49 - 72 * q^56 - 48 * q^61 + 96 * q^64 + 192 * q^69 - 120 * q^70 + 48 * q^84 + 168 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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