LMFDB - Embedded newform 1350.2.q.a.557.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1350,2,Mod(143,1350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1350, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("1350.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1350 = 2 \cdot 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1350.q (of order $12$, degree $4$, not 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:	$10.7798042729$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 450)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.557
Dual form			1350.2.q.a.143.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.328169 + 1.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.328169 + 1.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(0.328169 + 1.22474i) q^{13} +(-0.633975 + 1.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +7.19615i q^{19} +(-3.34607 + 0.896575i) q^{22} +(-7.91688 + 2.12132i) q^{23} +1.26795i q^{26} +(-0.896575 + 0.896575i) q^{28} +(3.63397 + 6.29423i) q^{29} +(5.09808 - 8.83013i) q^{31} +(0.258819 + 0.965926i) q^{32} +(1.55291 + 1.55291i) q^{37} +(-1.86250 + 6.95095i) q^{38} +(1.50000 + 0.866025i) q^{41} +(6.24384 + 1.67303i) q^{43} -3.46410 q^{44} -8.19615 q^{46} +(-5.79555 - 1.55291i) q^{47} +(4.66987 + 2.69615i) q^{49} +(-0.328169 + 1.22474i) q^{52} +(-1.55291 - 1.55291i) q^{53} +(-1.09808 + 0.633975i) q^{56} +(1.88108 + 7.02030i) q^{58} +(-6.23205 + 10.7942i) q^{59} +(2.00000 + 3.46410i) q^{61} +(7.20977 - 7.20977i) q^{62} +1.00000i q^{64} +(-12.0394 + 3.22595i) q^{67} -10.7321i q^{71} +(-3.67423 + 3.67423i) q^{73} +(1.09808 + 1.90192i) q^{74} +(-3.59808 + 6.23205i) q^{76} +(-1.13681 - 4.24264i) q^{77} +(8.66025 - 5.00000i) q^{79} +(1.22474 + 1.22474i) q^{82} +(1.76097 - 6.57201i) q^{83} +(5.59808 + 3.23205i) q^{86} +(-3.34607 - 0.896575i) q^{88} +8.66025 q^{89} -1.60770 q^{91} +(-7.91688 - 2.12132i) q^{92} +(-5.19615 - 3.00000i) q^{94} +(3.79435 - 14.1607i) q^{97} +(3.81294 + 3.81294i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 24 q^{11} - 12 q^{14} + 4 q^{16} + 36 q^{29} + 20 q^{31} + 12 q^{41} - 24 q^{46} + 72 q^{49} + 12 q^{56} - 36 q^{59} + 16 q^{61} - 12 q^{74} - 8 q^{76} + 24 q^{86} - 96 q^{91}+O(q^{100}) $ 8 * q - 24 * q^11 - 12 * q^14 + 4 * q^16 + 36 * q^29 + 20 * q^31 + 12 * q^41 - 24 * q^46 + 72 * q^49 + 12 * q^56 - 36 * q^59 + 16 * q^61 - 12 * q^74 - 8 * q^76 + 24 * q^86 - 96 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−0.328169	+	1.22474i	−0.124036	+	0.462910i	−0.999803	−	0.0198238i	$-0.993689\pi$
$7$	−0.328169	+	1.22474i	−0.124036	+	0.462910i	0.875767	+	0.482734i	$0.160356\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$		0			0
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.878668	−	0.477432i	$-0.841568\pi$
$11$	−3.00000	+	1.73205i	−0.904534	+	0.522233i	−0.0258656	+	0.999665i	$0.508234\pi$
$12$		0			0
$13$	0.328169	+	1.22474i	0.0910178	+	0.339683i	0.996386	−	0.0849451i	$-0.0270715\pi$
$13$	0.328169	+	1.22474i	0.0910178	+	0.339683i	−0.905368	+	0.424628i	$0.860405\pi$
$14$	−0.633975	+	1.09808i	−0.169437	+	0.293473i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$17$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$18$		0			0
$19$			7.19615i			1.65091i	0.564467	+	0.825455i	$0.309082\pi$
$19$			7.19615i			1.65091i	−0.564467	+	0.825455i	$0.690918\pi$
$20$		0			0
$21$		0			0
$22$	−3.34607	+	0.896575i	−0.713384	+	0.191151i
$23$	−7.91688	+	2.12132i	−1.65078	+	0.442326i	−0.959832	−	0.280576i	$-0.909475\pi$
$23$	−7.91688	+	2.12132i	−1.65078	+	0.442326i	−0.690951	+	0.722902i	$0.742808\pi$
$24$		0			0
$25$		0			0
$26$			1.26795i			0.248665i
$27$		0			0
$28$	−0.896575	+	0.896575i	−0.169437	+	0.169437i
$29$	3.63397	+	6.29423i	0.674812	+	1.16881i	0.976524	+	0.215410i	$0.0691087\pi$
$29$	3.63397	+	6.29423i	0.674812	+	1.16881i	−0.301712	+	0.953399i	$0.597558\pi$
$30$		0			0
$31$	5.09808	−	8.83013i	0.915642	−	1.58594i	0.109682	−	0.993967i	$-0.465017\pi$
$31$	5.09808	−	8.83013i	0.915642	−	1.58594i	0.805959	−	0.591971i	$-0.201650\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.55291	+	1.55291i	0.255298	+	0.255298i	0.823138	−	0.567841i	$-0.192221\pi$
$37$	1.55291	+	1.55291i	0.255298	+	0.255298i	−0.567841	+	0.823138i	$0.692221\pi$
$38$	−1.86250	+	6.95095i	−0.302138	+	1.12759i
$39$		0			0
$40$		0			0
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	0.612536	−	0.790443i	$-0.290149\pi$
$41$	1.50000	+	0.866025i	0.234261	+	0.135250i	−0.378275	+	0.925693i	$0.623483\pi$
$42$		0			0
$43$	6.24384	+	1.67303i	0.952177	+	0.255135i	0.701286	−	0.712880i	$-0.252610\pi$
$43$	6.24384	+	1.67303i	0.952177	+	0.255135i	0.250891	+	0.968015i	$0.419276\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	−8.19615			−1.20846
$47$	−5.79555	−	1.55291i	−0.845369	−	0.226516i	−0.189961	−	0.981792i	$-0.560836\pi$
$47$	−5.79555	−	1.55291i	−0.845369	−	0.226516i	−0.655407	+	0.755276i	$0.727503\pi$
$48$		0			0
$49$	4.66987	+	2.69615i	0.667125	+	0.385165i
$50$		0			0
$51$		0			0
$52$	−0.328169	+	1.22474i	−0.0455089	+	0.169842i
$53$	−1.55291	−	1.55291i	−0.213309	−	0.213309i	0.592362	−	0.805672i	$-0.298195\pi$
$53$	−1.55291	−	1.55291i	−0.213309	−	0.213309i	−0.805672	+	0.592362i	$0.798195\pi$
$54$		0			0
$55$		0			0
$56$	−1.09808	+	0.633975i	−0.146737	+	0.0847184i
$57$		0			0
$58$	1.88108	+	7.02030i	0.246998	+	0.921811i
$59$	−6.23205	+	10.7942i	−0.811344	+	1.40529i	0.100580	+	0.994929i	$0.467930\pi$
$59$	−6.23205	+	10.7942i	−0.811344	+	1.40529i	−0.911924	+	0.410360i	$0.865403\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$	7.20977	−	7.20977i	0.915642	−	0.915642i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−12.0394	+	3.22595i	−1.47085	+	0.394112i	−0.903221	−	0.429175i	$-0.858804\pi$
$67$	−12.0394	+	3.22595i	−1.47085	+	0.394112i	−0.567625	+	0.823287i	$0.692138\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.7321i		−	1.27366i	−0.771004	−	0.636830i	$-0.780245\pi$
$71$		−	10.7321i		−	1.27366i	0.771004	−	0.636830i	$-0.219755\pi$
$72$		0			0
$73$	−3.67423	+	3.67423i	−0.430037	+	0.430037i	−0.888641	−	0.458604i	$-0.848350\pi$
$73$	−3.67423	+	3.67423i	−0.430037	+	0.430037i	0.458604	+	0.888641i	$0.348350\pi$
$74$	1.09808	+	1.90192i	0.127649	+	0.221094i
$75$		0			0
$76$	−3.59808	+	6.23205i	−0.412728	+	0.714865i
$77$	−1.13681	−	4.24264i	−0.129552	−	0.483494i
$78$		0			0
$79$	8.66025	−	5.00000i	0.974355	−	0.562544i	0.0737937	−	0.997274i	$-0.476489\pi$
$79$	8.66025	−	5.00000i	0.974355	−	0.562544i	0.900561	+	0.434730i	$0.143156\pi$
$80$		0			0
$81$		0			0
$82$	1.22474	+	1.22474i	0.135250	+	0.135250i
$83$	1.76097	−	6.57201i	0.193291	−	0.721372i	−0.799412	−	0.600784i	$-0.794855\pi$
$83$	1.76097	−	6.57201i	0.193291	−	0.721372i	0.992703	−	0.120588i	$-0.0384781\pi$
$84$		0			0
$85$		0			0
$86$	5.59808	+	3.23205i	0.603656	+	0.348521i
$87$		0			0
$88$	−3.34607	−	0.896575i	−0.356692	−	0.0955753i
$89$	8.66025			0.917985			0.458993	−	0.888440i	$-0.348210\pi$
$89$	8.66025			0.917985			0.458993	+	0.888440i	$0.348210\pi$
$90$		0			0
$91$	−1.60770			−0.168532
$92$	−7.91688	−	2.12132i	−0.825391	−	0.221163i
$93$		0			0
$94$	−5.19615	−	3.00000i	−0.535942	−	0.309426i
$95$		0			0
$96$		0			0
$97$	3.79435	−	14.1607i	0.385258	−	1.43780i	−0.452501	−	0.891764i	$-0.649468\pi$
$97$	3.79435	−	14.1607i	0.385258	−	1.43780i	0.837760	−	0.546039i	$-0.183865\pi$
$98$	3.81294	+	3.81294i	0.385165	+	0.385165i
$99$		0			0
$100$		0			0
$101$	9.29423	−	5.36603i	0.924810	−	0.533939i	0.0396438	−	0.999214i	$-0.487378\pi$
$101$	9.29423	−	5.36603i	0.924810	−	0.533939i	0.885167	+	0.465274i	$0.154044\pi$
$102$		0			0
$103$	2.68973	+	10.0382i	0.265027	+	0.989093i	0.962234	+	0.272223i	$0.0877590\pi$
$103$	2.68973	+	10.0382i	0.265027	+	0.989093i	−0.697207	+	0.716869i	$0.745574\pi$
$104$	−0.633975	+	1.09808i	−0.0621663	+	0.107675i
$105$		0			0
$106$	−1.09808	−	1.90192i	−0.106655	−	0.184731i
$107$	0.568406	−	0.568406i	0.0549499	−	0.0549499i	−0.679098	−	0.734048i	$-0.737629\pi$
$107$	0.568406	−	0.568406i	0.0549499	−	0.0549499i	0.734048	+	0.679098i	$0.237629\pi$
$108$		0			0
$109$			12.1962i			1.16818i	0.811689	+	0.584090i	$0.198548\pi$
$109$			12.1962i			1.16818i	−0.811689	+	0.584090i	$0.801452\pi$
$110$		0			0
$111$		0			0
$112$	−1.22474	+	0.328169i	−0.115728	+	0.0310091i
$113$	−7.14042	+	1.91327i	−0.671714	+	0.179985i	−0.578527	−	0.815663i	$-0.696372\pi$
$113$	−7.14042	+	1.91327i	−0.671714	+	0.179985i	−0.0931872	+	0.995649i	$0.529706\pi$
$114$		0			0
$115$		0			0
$116$			7.26795i			0.674812i
$117$		0			0
$118$	−8.81345	+	8.81345i	−0.811344	+	0.811344i
$119$		0			0
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	1.03528	+	3.86370i	0.0937295	+	0.349803i
$123$		0			0
$124$	8.83013	−	5.09808i	0.792969	−	0.457821i
$125$		0			0
$126$		0			0
$127$	1.55291	+	1.55291i	0.137799	+	0.137799i	0.772641	−	0.634843i	$-0.218935\pi$
$127$	1.55291	+	1.55291i	0.137799	+	0.137799i	−0.634843	+	0.772641i	$0.718935\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$		0			0
$130$		0			0
$131$	6.00000	+	3.46410i	0.524222	+	0.302660i	0.738661	−	0.674078i	$-0.235459\pi$
$131$	6.00000	+	3.46410i	0.524222	+	0.302660i	−0.214438	+	0.976738i	$0.568792\pi$
$132$		0			0
$133$	−8.81345	−	2.36156i	−0.764223	−	0.204773i
$134$	−12.4641			−1.07673
$135$		0			0
$136$		0			0
$137$	−7.14042	−	1.91327i	−0.610047	−	0.163462i	−0.0594480	−	0.998231i	$-0.518934\pi$
$137$	−7.14042	−	1.91327i	−0.610047	−	0.163462i	−0.550599	+	0.834770i	$0.685601\pi$
$138$		0			0
$139$	−6.92820	−	4.00000i	−0.587643	−	0.339276i	0.176522	−	0.984297i	$-0.443515\pi$
$139$	−6.92820	−	4.00000i	−0.587643	−	0.339276i	−0.764165	+	0.645021i	$0.776849\pi$
$140$		0			0
$141$		0			0
$142$	2.77766	−	10.3664i	0.233096	−	0.869926i
$143$	−3.10583	−	3.10583i	−0.259722	−	0.259722i
$144$		0			0
$145$		0			0
$146$	−4.50000	+	2.59808i	−0.372423	+	0.215018i
$147$		0			0
$148$	0.568406	+	2.12132i	0.0467227	+	0.174371i
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	−0.216394	−	0.976306i	$-0.569430\pi$
$149$	9.00000	−	15.5885i	0.737309	−	1.27706i	0.953703	−	0.300750i	$-0.0972370\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	−5.08845	+	5.08845i	−0.412728	+	0.412728i
$153$		0			0
$154$		−	4.39230i		−	0.353942i
$155$		0			0
$156$		0			0
$157$	−7.58871	+	2.03339i	−0.605645	+	0.162282i	−0.548593	−	0.836089i	$-0.684837\pi$
$157$	−7.58871	+	2.03339i	−0.605645	+	0.162282i	−0.0570512	+	0.998371i	$0.518170\pi$
$158$	9.65926	−	2.58819i	0.768449	−	0.205905i
$159$		0			0
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$		0			0
$163$	14.3688	−	14.3688i	1.12545	−	1.12545i	0.134541	−	0.990908i	$-0.457044\pi$
$163$	14.3688	−	14.3688i	1.12545	−	1.12545i	0.990908	−	0.134541i	$-0.0429559\pi$
$164$	0.866025	+	1.50000i	0.0676252	+	0.117130i
$165$		0			0
$166$	3.40192	−	5.89230i	0.264040	−	0.457332i
$167$	1.13681	+	4.24264i	0.0879692	+	0.328305i	0.995860	−	0.0909015i	$-0.0289749\pi$
$167$	1.13681	+	4.24264i	0.0879692	+	0.328305i	−0.907891	+	0.419207i	$0.862308\pi$
$168$		0			0
$169$	9.86603	−	5.69615i	0.758925	−	0.438166i
$170$		0			0
$171$		0			0
$172$	4.57081	+	4.57081i	0.348521	+	0.348521i
$173$	1.13681	−	4.24264i	0.0864302	−	0.322562i	−0.909151	−	0.416467i	$-0.863268\pi$
$173$	1.13681	−	4.24264i	0.0864302	−	0.322562i	0.995581	+	0.0939047i	$0.0299349\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000	−	1.73205i	−0.226134	−	0.130558i
$177$		0			0
$178$	8.36516	+	2.24144i	0.626995	+	0.168003i
$179$	−4.85641			−0.362985			−0.181492	−	0.983392i	$-0.558093\pi$
$179$	−4.85641			−0.362985			−0.181492	+	0.983392i	$0.558093\pi$
$180$		0			0
$181$	8.39230			0.623795			0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230			0.623795			0.311898	+	0.950116i	$0.399035\pi$
$182$	−1.55291	−	0.416102i	−0.115110	−	0.0308435i
$183$		0			0
$184$	−7.09808	−	4.09808i	−0.523277	−	0.302114i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−4.24264	−	4.24264i	−0.309426	−	0.309426i
$189$		0			0
$190$		0			0
$191$	−3.00000	+	1.73205i	−0.217072	+	0.125327i	−0.604594	−	0.796534i	$-0.706665\pi$
$191$	−3.00000	+	1.73205i	−0.217072	+	0.125327i	0.387522	+	0.921861i	$0.373331\pi$
$192$		0			0
$193$	−6.45189	−	24.0788i	−0.464417	−	1.73323i	−0.658813	−	0.752306i	$-0.728941\pi$
$193$	−6.45189	−	24.0788i	−0.464417	−	1.73323i	0.194396	−	0.980923i	$-0.437725\pi$
$194$	7.33013	−	12.6962i	0.526272	−	0.911531i
$195$		0			0
$196$	2.69615	+	4.66987i	0.192582	+	0.333562i
$197$	−2.68973	+	2.68973i	−0.191635	+	0.191635i	−0.796402	−	0.604767i	$-0.793266\pi$
$197$	−2.68973	+	2.68973i	−0.191635	+	0.191635i	0.604767	+	0.796402i	$0.293266\pi$
$198$		0			0
$199$		−	0.392305i		−	0.0278098i	−0.999903	−	0.0139049i	$-0.995574\pi$
$199$		−	0.392305i		−	0.0278098i	0.999903	−	0.0139049i	$-0.00442620\pi$
$200$		0			0
$201$		0			0
$202$	10.3664	−	2.77766i	0.729375	−	0.195435i
$203$	−8.90138	+	2.38512i	−0.624755	+	0.167403i
$204$		0			0
$205$		0			0
$206$			10.3923i			0.724066i
$207$		0			0
$208$	−0.896575	+	0.896575i	−0.0621663	+	0.0621663i
$209$	−12.4641	−	21.5885i	−0.862160	−	1.49330i
$210$		0			0
$211$	4.59808	−	7.96410i	0.316545	−	0.548271i	−0.663220	−	0.748424i	$-0.730811\pi$
$211$	4.59808	−	7.96410i	0.316545	−	0.548271i	0.979765	+	0.200153i	$0.0641440\pi$
$212$	−0.568406	−	2.12132i	−0.0390383	−	0.145693i
$213$		0			0
$214$	0.696152	−	0.401924i	0.0475880	−	0.0274749i
$215$		0			0
$216$		0			0
$217$	9.14162	+	9.14162i	0.620574	+	0.620574i
$218$	−3.15660	+	11.7806i	−0.213792	+	0.797881i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−9.14162	−	2.44949i	−0.612168	−	0.164030i	−0.0606032	−	0.998162i	$-0.519302\pi$
$223$	−9.14162	−	2.44949i	−0.612168	−	0.164030i	−0.551565	+	0.834132i	$0.685969\pi$
$224$	−1.26795			−0.0847184
$225$		0			0
$226$	−7.39230			−0.491729
$227$	22.4058	+	6.00361i	1.48712	+	0.398473i	0.908764	−	0.417310i	$-0.137027\pi$
$227$	22.4058	+	6.00361i	1.48712	+	0.398473i	0.578358	+	0.815783i	$0.303694\pi$
$228$		0			0
$229$	−14.0263	−	8.09808i	−0.926883	−	0.535136i	−0.0410583	−	0.999157i	$-0.513073\pi$
$229$	−14.0263	−	8.09808i	−0.926883	−	0.535136i	−0.885824	+	0.464021i	$0.846406\pi$
$230$		0			0
$231$		0			0
$232$	−1.88108	+	7.02030i	−0.123499	+	0.460905i
$233$	17.9551	+	17.9551i	1.17628	+	1.17628i	0.980686	+	0.195590i	$0.0626622\pi$
$233$	17.9551	+	17.9551i	1.17628	+	1.17628i	0.195590	+	0.980686i	$0.437338\pi$
$234$		0			0
$235$		0			0
$236$	−10.7942	+	6.23205i	−0.702644	+	0.405672i
$237$		0			0
$238$		0			0
$239$	−7.09808	+	12.2942i	−0.459136	+	0.795248i	−0.998916	−	0.0465591i	$-0.985174\pi$
$239$	−7.09808	+	12.2942i	−0.459136	+	0.795248i	0.539779	+	0.841807i	$0.318508\pi$
$240$		0			0
$241$	5.69615	+	9.86603i	0.366921	+	0.635527i	0.989083	−	0.147363i	$-0.0470785\pi$
$241$	5.69615	+	9.86603i	0.366921	+	0.635527i	−0.622161	+	0.782889i	$0.713745\pi$
$242$	0.707107	−	0.707107i	0.0454545	−	0.0454545i
$243$		0			0
$244$			4.00000i			0.256074i
$245$		0			0
$246$		0			0
$247$	−8.81345	+	2.36156i	−0.560786	+	0.150262i
$248$	9.84873	−	2.63896i	0.625395	−	0.167574i
$249$		0			0
$250$		0			0
$251$		−	9.00000i		−	0.568075i	−0.958813	−	0.284037i	$-0.908326\pi$
$251$		−	9.00000i		−	0.568075i	0.958813	−	0.284037i	$-0.0916740\pi$
$252$		0			0
$253$	20.0764	−	20.0764i	1.26219	−	1.26219i
$254$	1.09808	+	1.90192i	0.0688994	+	0.119337i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.19256	−	4.45069i	−0.0743898	−	0.277627i	0.918704	−	0.394946i	$-0.129237\pi$
$257$	−1.19256	−	4.45069i	−0.0743898	−	0.277627i	−0.993094	+	0.117319i	$0.962570\pi$
$258$		0			0
$259$	−2.41154	+	1.39230i	−0.149846	+	0.0865136i
$260$		0			0
$261$		0			0
$262$	4.89898	+	4.89898i	0.302660	+	0.302660i
$263$	4.81105	−	17.9551i	0.296662	−	1.10716i	−0.643227	−	0.765676i	$-0.722405\pi$
$263$	4.81105	−	17.9551i	0.296662	−	1.10716i	0.939889	−	0.341481i	$-0.110929\pi$
$264$		0			0
$265$		0			0
$266$	−7.90192	−	4.56218i	−0.484498	−	0.279725i
$267$		0			0
$268$	−12.0394	−	3.22595i	−0.735423	−	0.197056i
$269$	28.0526			1.71039			0.855197	−	0.518303i	$-0.173436\pi$
$269$	28.0526			1.71039			0.855197	+	0.518303i	$0.173436\pi$
$270$		0			0
$271$	−4.58846			−0.278729			−0.139364	−	0.990241i	$-0.544506\pi$
$271$	−4.58846			−0.278729			−0.139364	+	0.990241i	$0.544506\pi$
$272$		0			0
$273$		0			0
$274$	−6.40192	−	3.69615i	−0.386754	−	0.223293i
$275$		0			0
$276$		0			0
$277$	6.60420	−	24.6472i	0.396808	−	1.48091i	−0.421871	−	0.906656i	$-0.638627\pi$
$277$	6.60420	−	24.6472i	0.396808	−	1.48091i	0.818679	−	0.574251i	$-0.194707\pi$
$278$	−5.65685	−	5.65685i	−0.339276	−	0.339276i
$279$		0			0
$280$		0			0
$281$	−9.00000	+	5.19615i	−0.536895	+	0.309976i	−0.743820	−	0.668380i	$-0.766988\pi$
$281$	−9.00000	+	5.19615i	−0.536895	+	0.309976i	0.206925	+	0.978357i	$0.433655\pi$
$282$		0			0
$283$	−2.56961	−	9.58991i	−0.152747	−	0.570061i	−0.999288	−	0.0377364i	$-0.987985\pi$
$283$	−2.56961	−	9.58991i	−0.152747	−	0.570061i	0.846540	−	0.532325i	$-0.178681\pi$
$284$	5.36603	−	9.29423i	0.318415	−	0.551511i
$285$		0			0
$286$	−2.19615	−	3.80385i	−0.129861	−	0.224926i
$287$	−1.55291	+	1.55291i	−0.0916656	+	0.0916656i
$288$		0			0
$289$			17.0000i			1.00000i
$290$		0			0
$291$		0			0
$292$	−5.01910	+	1.34486i	−0.293720	+	0.0787022i
$293$	13.7124	−	3.67423i	0.801089	−	0.214651i	0.165027	−	0.986289i	$-0.447229\pi$
$293$	13.7124	−	3.67423i	0.801089	−	0.214651i	0.636062	+	0.771638i	$0.280562\pi$
$294$		0			0
$295$		0			0
$296$			2.19615i			0.127649i
$297$		0			0
$298$	12.7279	−	12.7279i	0.737309	−	0.737309i
$299$	−5.19615	−	9.00000i	−0.300501	−	0.520483i
$300$		0			0
$301$	−4.09808	+	7.09808i	−0.236209	+	0.409126i
$302$	2.07055	+	7.72741i	0.119147	+	0.444662i
$303$		0			0
$304$	−6.23205	+	3.59808i	−0.357433	+	0.206364i
$305$		0			0
$306$		0			0
$307$	2.44949	+	2.44949i	0.139800	+	0.139800i	0.773543	−	0.633743i	$-0.218483\pi$
$307$	2.44949	+	2.44949i	0.139800	+	0.139800i	−0.633743	+	0.773543i	$0.718483\pi$
$308$	1.13681	−	4.24264i	0.0647759	−	0.241747i
$309$		0			0
$310$		0			0
$311$	−21.5885	−	12.4641i	−1.22417	−	0.706774i	−0.258365	−	0.966047i	$-0.583184\pi$
$311$	−21.5885	−	12.4641i	−1.22417	−	0.706774i	−0.965804	+	0.259273i	$0.916517\pi$
$312$		0			0
$313$	−3.22595	−	0.864390i	−0.182341	−	0.0488582i	0.166493	−	0.986043i	$-0.446756\pi$
$313$	−3.22595	−	0.864390i	−0.182341	−	0.0488582i	−0.348834	+	0.937184i	$0.613422\pi$
$314$	−7.85641			−0.443363
$315$		0			0
$316$	10.0000			0.562544
$317$	23.7506	+	6.36396i	1.33397	+	0.357436i	0.854193	−	0.519956i	$-0.174052\pi$
$317$	23.7506	+	6.36396i	1.33397	+	0.357436i	0.479775	+	0.877392i	$0.340718\pi$
$318$		0			0
$319$	−21.8038	−	12.5885i	−1.22078	−	0.704818i
$320$		0			0
$321$		0			0
$322$	2.68973	−	10.0382i	0.149893	−	0.559407i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	17.5981	−	10.1603i	0.974667	−	0.562724i
$327$		0			0
$328$	0.448288	+	1.67303i	0.0247525	+	0.0923778i
$329$	3.80385	−	6.58846i	0.209713	−	0.363233i
$330$		0			0
$331$	−8.79423	−	15.2321i	−0.483375	−	0.837229i	0.516443	−	0.856321i	$-0.327256\pi$
$331$	−8.79423	−	15.2321i	−0.483375	−	0.837229i	−0.999818	+	0.0190922i	$0.993922\pi$
$332$	4.81105	−	4.81105i	0.264040	−	0.264040i
$333$		0			0
$334$			4.39230i			0.240336i
$335$		0			0
$336$		0			0
$337$	26.5283	−	7.10823i	1.44509	−	0.387210i	0.550775	−	0.834653i	$-0.314332\pi$
$337$	26.5283	−	7.10823i	1.44509	−	0.387210i	0.894312	+	0.447443i	$0.147665\pi$
$338$	11.0041	−	2.94855i	0.598545	−	0.160380i
$339$		0			0
$340$		0			0
$341$			35.3205i			1.91271i
$342$		0			0
$343$	−11.1106	+	11.1106i	−0.599918	+	0.599918i
$344$	3.23205	+	5.59808i	0.174261	+	0.301828i
$345$		0			0
$346$	2.19615	−	3.80385i	0.118066	−	0.204496i
$347$	8.48528	+	31.6675i	0.455514	+	1.70000i	0.686573	+	0.727061i	$0.259114\pi$
$347$	8.48528	+	31.6675i	0.455514	+	1.70000i	−0.231059	+	0.972940i	$0.574219\pi$
$348$		0			0
$349$	1.73205	−	1.00000i	0.0927146	−	0.0535288i	−0.452926	−	0.891548i	$-0.649620\pi$
$349$	1.73205	−	1.00000i	0.0927146	−	0.0535288i	0.545640	+	0.838019i	$0.316286\pi$
$350$		0			0
$351$		0			0
$352$	−2.44949	−	2.44949i	−0.130558	−	0.130558i
$353$	3.88229	−	14.4889i	0.206633	−	0.771166i	−0.782312	−	0.622886i	$-0.785960\pi$
$353$	3.88229	−	14.4889i	0.206633	−	0.771166i	0.988946	−	0.148279i	$-0.0473735\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	+	4.33013i	0.397499	+	0.229496i
$357$		0			0
$358$	−4.69093	−	1.25693i	−0.247923	−	0.0664308i
$359$	−0.679492			−0.0358622			−0.0179311	−	0.999839i	$-0.505708\pi$
$359$	−0.679492			−0.0358622			−0.0179311	+	0.999839i	$0.505708\pi$
$360$		0			0
$361$	−32.7846			−1.72551
$362$	8.10634	+	2.17209i	0.426060	+	0.114162i
$363$		0			0
$364$	−1.39230	−	0.803848i	−0.0729766	−	0.0421331i
$365$		0			0
$366$		0			0
$367$	−8.24504	+	30.7709i	−0.430388	+	1.60623i	0.321481	+	0.946916i	$0.395819\pi$
$367$	−8.24504	+	30.7709i	−0.430388	+	1.60623i	−0.751868	+	0.659313i	$0.770847\pi$
$368$	−5.79555	−	5.79555i	−0.302114	−	0.302114i
$369$		0			0
$370$		0			0
$371$	2.41154	−	1.39230i	0.125201	−	0.0722849i
$372$		0			0
$373$	2.92996	+	10.9348i	0.151708	+	0.566181i	0.999365	+	0.0356365i	$0.0113458\pi$
$373$	2.92996	+	10.9348i	0.151708	+	0.566181i	−0.847657	+	0.530545i	$0.821987\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	−6.51626	+	6.51626i	−0.335605	+	0.335605i
$378$		0			0
$379$		−	20.3923i		−	1.04748i	−0.851877	−	0.523741i	$-0.824536\pi$
$379$		−	20.3923i		−	1.04748i	0.851877	−	0.523741i	$-0.175464\pi$
$380$		0			0
$381$		0			0
$382$	−3.34607	+	0.896575i	−0.171200	+	0.0458728i
$383$	35.3417	−	9.46979i	1.80588	−	0.483884i	0.811007	−	0.585036i	$-0.198920\pi$
$383$	35.3417	−	9.46979i	1.80588	−	0.483884i	0.994871	+	0.101152i	$0.0322529\pi$
$384$		0			0
$385$		0			0
$386$		−	24.9282i		−	1.26881i
$387$		0			0
$388$	10.3664	−	10.3664i	0.526272	−	0.526272i
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	0.703702	−	0.710495i	$-0.251529\pi$
$389$	−5.19615	−	9.00000i	−0.263455	−	0.456318i	−0.967158	+	0.254177i	$0.918196\pi$
$390$		0			0
$391$		0			0
$392$	1.39563	+	5.20857i	0.0704900	+	0.263072i
$393$		0			0
$394$	−3.29423	+	1.90192i	−0.165961	+	0.0958175i
$395$		0			0
$396$		0			0
$397$	6.03579	+	6.03579i	0.302928	+	0.302928i	0.842158	−	0.539231i	$-0.181285\pi$
$397$	6.03579	+	6.03579i	0.302928	+	0.302928i	−0.539231	+	0.842158i	$0.681285\pi$
$398$	0.101536	−	0.378937i	0.00508954	−	0.0189944i
$399$		0			0
$400$		0			0
$401$	−9.00000	−	5.19615i	−0.449439	−	0.259483i	0.258154	−	0.966104i	$-0.416886\pi$
$401$	−9.00000	−	5.19615i	−0.449439	−	0.259483i	−0.707593	+	0.706620i	$0.750219\pi$
$402$		0			0
$403$	12.4877	+	3.34607i	0.622056	+	0.166679i
$404$	10.7321			0.533939
$405$		0			0
$406$	−9.21539			−0.457352
$407$	−7.34847	−	1.96902i	−0.364250	−	0.0976005i
$408$		0			0
$409$	−0.526279	−	0.303848i	−0.0260228	−	0.0150243i	0.486932	−	0.873440i	$-0.338116\pi$
$409$	−0.526279	−	0.303848i	−0.0260228	−	0.0150243i	−0.512955	+	0.858416i	$0.671449\pi$
$410$		0			0
$411$		0			0
$412$	−2.68973	+	10.0382i	−0.132513	+	0.494546i
$413$	−11.1750	−	11.1750i	−0.549886	−	0.549886i
$414$		0			0
$415$		0			0
$416$	−1.09808	+	0.633975i	−0.0538376	+	0.0310832i
$417$		0			0
$418$	−6.45189	−	24.0788i	−0.315572	−	1.17773i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$		0			0
$421$	4.29423	+	7.43782i	0.209288	+	0.362497i	0.951490	−	0.307678i	$-0.0995521\pi$
$421$	4.29423	+	7.43782i	0.209288	+	0.362497i	−0.742203	+	0.670176i	$0.766219\pi$
$422$	6.50266	−	6.50266i	0.316545	−	0.316545i
$423$		0			0
$424$		−	2.19615i		−	0.106655i
$425$		0			0
$426$		0			0
$427$	−4.89898	+	1.31268i	−0.237078	+	0.0635249i
$428$	0.776457	−	0.208051i	0.0375315	−	0.0100565i
$429$		0			0
$430$		0			0
$431$		−	3.12436i		−	0.150495i	−0.997165	−	0.0752475i	$-0.976025\pi$
$431$		−	3.12436i		−	0.150495i	0.997165	−	0.0752475i	$-0.0239747\pi$
$432$		0			0
$433$	−21.8695	+	21.8695i	−1.05098	+	1.05098i	−0.0523546	+	0.998629i	$0.516673\pi$
$433$	−21.8695	+	21.8695i	−1.05098	+	1.05098i	−0.998629	+	0.0523546i	$0.983327\pi$
$434$	6.46410	+	11.1962i	0.310287	+	0.537433i
$435$		0			0
$436$	−6.09808	+	10.5622i	−0.292045	+	0.505837i
$437$	−15.2653	−	56.9710i	−0.730240	−	2.72529i
$438$		0			0
$439$	−28.2224	+	16.2942i	−1.34698	+	0.777681i	−0.987821	−	0.155594i	$-0.950271\pi$
$439$	−28.2224	+	16.2942i	−1.34698	+	0.777681i	−0.359162	+	0.933275i	$0.616937\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.68973	+	10.0382i	−0.127793	+	0.476929i	−0.999924	−	0.0123433i	$-0.996071\pi$
$443$	−2.68973	+	10.0382i	−0.127793	+	0.476929i	0.872131	+	0.489272i	$0.162738\pi$
$444$		0			0
$445$		0			0
$446$	−8.19615	−	4.73205i	−0.388099	−	0.224069i
$447$		0			0
$448$	−1.22474	−	0.328169i	−0.0578638	−	0.0155045i
$449$	5.87564			0.277289			0.138644	−	0.990342i	$-0.455725\pi$
$449$	5.87564			0.277289			0.138644	+	0.990342i	$0.455725\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	−7.14042	−	1.91327i	−0.335857	−	0.0899926i
$453$		0			0
$454$	20.0885	+	11.5981i	0.942798	+	0.544325i
$455$		0			0
$456$		0			0
$457$	−0.928761	+	3.46618i	−0.0434456	+	0.162141i	−0.984240	−	0.176835i	$-0.943414\pi$
$457$	−0.928761	+	3.46618i	−0.0434456	+	0.162141i	0.940795	+	0.338976i	$0.110081\pi$
$458$	−11.4524	−	11.4524i	−0.535136	−	0.535136i
$459$		0			0
$460$		0			0
$461$	24.2942	−	14.0263i	1.13150	−	0.653269i	0.187185	−	0.982325i	$-0.440064\pi$
$461$	24.2942	−	14.0263i	1.13150	−	0.653269i	0.944310	+	0.329056i	$0.106730\pi$
$462$		0			0
$463$	2.12132	+	7.91688i	0.0985861	+	0.367928i	0.997539	−	0.0701175i	$-0.0223374\pi$
$463$	2.12132	+	7.91688i	0.0985861	+	0.367928i	−0.898953	+	0.438046i	$0.855671\pi$
$464$	−3.63397	+	6.29423i	−0.168703	+	0.292202i
$465$		0			0
$466$	12.6962	+	21.9904i	0.588138	+	1.01868i
$467$	−15.2653	+	15.2653i	−0.706396	+	0.706396i	−0.965775	−	0.259380i	$-0.916482\pi$
$467$	−15.2653	+	15.2653i	−0.706396	+	0.706396i	0.259380	+	0.965775i	$0.416482\pi$
$468$		0			0
$469$		−	15.8038i		−	0.729754i
$470$		0			0
$471$		0			0
$472$	−12.0394	+	3.22595i	−0.554158	+	0.148486i
$473$	−21.6293	+	5.79555i	−0.994517	+	0.266480i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$	−10.0382	+	10.0382i	−0.459136	+	0.459136i
$479$	10.5622	+	18.2942i	0.482598	+	0.835885i	0.999800	−	0.0199786i	$-0.00635981\pi$
$479$	10.5622	+	18.2942i	0.482598	+	0.835885i	−0.517202	+	0.855863i	$0.673026\pi$
$480$		0			0
$481$	−1.39230	+	2.41154i	−0.0634836	+	0.109957i
$482$	2.94855	+	11.0041i	0.134303	+	0.501224i
$483$		0			0
$484$	0.866025	−	0.500000i	0.0393648	−	0.0227273i
$485$		0			0
$486$		0			0
$487$	15.5935	+	15.5935i	0.706610	+	0.706610i	0.965821	−	0.259211i	$-0.0834625\pi$
$487$	15.5935	+	15.5935i	0.706610	+	0.706610i	−0.259211	+	0.965821i	$0.583463\pi$
$488$	−1.03528	+	3.86370i	−0.0468648	+	0.174902i
$489$		0			0
$490$		0			0
$491$	31.7942	+	18.3564i	1.43485	+	0.828413i	0.997486	−	0.0708697i	$-0.0225774\pi$
$491$	31.7942	+	18.3564i	1.43485	+	0.828413i	0.437368	+	0.899283i	$0.355911\pi$
$492$		0			0
$493$		0			0
$494$	−9.12436			−0.410524
$495$		0			0
$496$	10.1962			0.457821
$497$	13.1440	+	3.52193i	0.589590	+	0.157980i
$498$		0			0
$499$	−16.9641	−	9.79423i	−0.759417	−	0.438450i	0.0696691	−	0.997570i	$-0.477806\pi$
$499$	−16.9641	−	9.79423i	−0.759417	−	0.438450i	−0.829087	+	0.559120i	$0.811139\pi$
$500$		0			0
$501$		0			0
$502$	2.32937	−	8.69333i	0.103965	−	0.388002i
$503$	25.8719	+	25.8719i	1.15357	+	1.15357i	0.985831	+	0.167742i	$0.0536476\pi$
$503$	25.8719	+	25.8719i	1.15357	+	1.15357i	0.167742	+	0.985831i	$0.446352\pi$
$504$		0			0
$505$		0			0
$506$	24.5885	−	14.1962i	1.09309	−	0.631096i
$507$		0			0
$508$	0.568406	+	2.12132i	0.0252189	+	0.0941184i
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	−0.998992	−	0.0448779i	$-0.985710\pi$
$509$	−10.3923	+	18.0000i	−0.460631	+	0.797836i	0.538362	+	0.842714i	$0.319043\pi$
$510$		0			0
$511$	−3.29423	−	5.70577i	−0.145728	−	0.252408i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	4.60770i		−	0.203237i
$515$		0			0
$516$		0			0
$517$	20.0764	−	5.37945i	0.882959	−	0.236588i
$518$	−2.68973	+	0.720710i	−0.118180	+	0.0316662i
$519$		0			0
$520$		0			0
$521$			38.7846i			1.69918i	0.527440	+	0.849592i	$0.323152\pi$
$521$			38.7846i			1.69918i	−0.527440	+	0.849592i	$0.676848\pi$
$522$		0			0
$523$	−14.1929	+	14.1929i	−0.620612	+	0.620612i	−0.945688	−	0.325076i	$-0.894610\pi$
$523$	−14.1929	+	14.1929i	−0.620612	+	0.620612i	0.325076	+	0.945688i	$0.394610\pi$
$524$	3.46410	+	6.00000i	0.151330	+	0.262111i
$525$		0			0
$526$	9.29423	−	16.0981i	0.405248	−	0.701909i
$527$		0			0
$528$		0			0
$529$	38.2583	−	22.0885i	1.66341	−	0.960368i
$530$		0			0
$531$		0			0
$532$	−6.45189	−	6.45189i	−0.279725	−	0.279725i
$533$	−0.568406	+	2.12132i	−0.0246204	+	0.0918846i
$534$		0			0
$535$		0			0
$536$	−10.7942	−	6.23205i	−0.466240	−	0.269184i
$537$		0			0
$538$	27.0967	+	7.26054i	1.16822	+	0.313024i
$539$	−18.6795			−0.804583
$540$		0			0
$541$	12.3923			0.532787			0.266393	−	0.963864i	$-0.414168\pi$
$541$	12.3923			0.532787			0.266393	+	0.963864i	$0.414168\pi$
$542$	−4.43211	−	1.18758i	−0.190375	−	0.0510109i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	5.73981	−	21.4213i	0.245416	−	0.915907i	−0.727757	−	0.685835i	$-0.759437\pi$
$547$	5.73981	−	21.4213i	0.245416	−	0.915907i	0.973174	−	0.230072i	$-0.0738961\pi$
$548$	−5.22715	−	5.22715i	−0.223293	−	0.223293i
$549$		0			0
$550$		0			0
$551$	−45.2942	+	26.1506i	−1.92960	+	1.11405i
$552$		0			0
$553$	3.28169	+	12.2474i	0.139552	+	0.520814i
$554$	12.7583	−	22.0981i	0.542050	−	0.938857i
$555$		0			0
$556$	−4.00000	−	6.92820i	−0.169638	−	0.293821i
$557$	−11.5911	+	11.5911i	−0.491131	+	0.491131i	−0.908662	−	0.417531i	$-0.862895\pi$
$557$	−11.5911	+	11.5911i	−0.491131	+	0.491131i	0.417531	+	0.908662i	$0.362895\pi$
$558$		0			0
$559$			8.19615i			0.346660i
$560$		0			0
$561$		0			0
$562$	−10.0382	+	2.68973i	−0.423436	+	0.113459i
$563$	−32.4440	+	8.69333i	−1.36735	+	0.366380i	−0.866510	−	0.499160i	$-0.833642\pi$
$563$	−32.4440	+	8.69333i	−1.36735	+	0.366380i	−0.500840	+	0.865540i	$0.666975\pi$
$564$		0			0
$565$		0			0
$566$		−	9.92820i		−	0.417314i
$567$		0			0
$568$	7.58871	−	7.58871i	0.318415	−	0.318415i
$569$	−5.53590	−	9.58846i	−0.232077	−	0.401969i	0.726342	−	0.687333i	$-0.241219\pi$
$569$	−5.53590	−	9.58846i	−0.232077	−	0.401969i	−0.958419	+	0.285364i	$0.907885\pi$
$570$		0			0
$571$	−4.40192	+	7.62436i	−0.184215	+	0.319069i	−0.943312	−	0.331908i	$-0.892308\pi$
$571$	−4.40192	+	7.62436i	−0.184215	+	0.319069i	0.759097	+	0.650978i	$0.225641\pi$
$572$	−1.13681	−	4.24264i	−0.0475325	−	0.177394i
$573$		0			0
$574$	−1.90192	+	1.09808i	−0.0793848	+	0.0458328i
$575$		0			0
$576$		0			0
$577$	−15.9217	−	15.9217i	−0.662828	−	0.662828i	0.293217	−	0.956046i	$-0.405274\pi$
$577$	−15.9217	−	15.9217i	−0.662828	−	0.662828i	−0.956046	+	0.293217i	$0.905274\pi$
$578$	−4.39992	+	16.4207i	−0.183013	+	0.683013i
$579$		0			0
$580$		0			0
$581$	7.47114	+	4.31347i	0.309955	+	0.178953i
$582$		0			0
$583$	7.34847	+	1.96902i	0.304342	+	0.0815483i
$584$	−5.19615			−0.215018
$585$		0			0
$586$	14.1962			0.586438
$587$	−15.8338	−	4.24264i	−0.653529	−	0.175113i	−0.0832050	−	0.996532i	$-0.526516\pi$
$587$	−15.8338	−	4.24264i	−0.653529	−	0.175113i	−0.570324	+	0.821420i	$0.693182\pi$
$588$		0			0
$589$	63.5429	+	36.6865i	2.61824	+	1.51164i
$590$		0			0
$591$		0			0
$592$	−0.568406	+	2.12132i	−0.0233613	+	0.0871857i
$593$	−14.8492	−	14.8492i	−0.609785	−	0.609785i	0.333105	−	0.942890i	$-0.391904\pi$
$593$	−14.8492	−	14.8492i	−0.609785	−	0.609785i	−0.942890	+	0.333105i	$0.891904\pi$
$594$		0			0
$595$		0			0
$596$	15.5885	−	9.00000i	0.638528	−	0.368654i
$597$		0			0
$598$	−2.68973	−	10.0382i	−0.109991	−	0.410492i
$599$	−5.36603	+	9.29423i	−0.219250	+	0.379752i	−0.954579	−	0.297958i	$-0.903694\pi$
$599$	−5.36603	+	9.29423i	−0.219250	+	0.379752i	0.735329	+	0.677710i	$0.237028\pi$
$600$		0			0
$601$	−6.39230	−	11.0718i	−0.260748	−	0.451628i	0.705693	−	0.708518i	$-0.250636\pi$
$601$	−6.39230	−	11.0718i	−0.260748	−	0.451628i	−0.966441	+	0.256890i	$0.917302\pi$
$602$	−5.79555	+	5.79555i	−0.236209	+	0.236209i
$603$		0			0
$604$			8.00000i			0.325515i
$605$		0			0
$606$		0			0
$607$	−16.8183	+	4.50644i	−0.682632	+	0.182911i	−0.583438	−	0.812157i	$-0.698293\pi$
$607$	−16.8183	+	4.50644i	−0.682632	+	0.182911i	−0.0991937	+	0.995068i	$0.531626\pi$
$608$	−6.95095	+	1.86250i	−0.281898	+	0.0755344i
$609$		0			0
$610$		0			0
$611$		−	7.60770i		−	0.307774i
$612$		0			0
$613$	−2.68973	+	2.68973i	−0.108637	+	0.108637i	−0.759336	−	0.650699i	$-0.774476\pi$
$613$	−2.68973	+	2.68973i	−0.108637	+	0.108637i	0.650699	+	0.759336i	$0.274476\pi$
$614$	1.73205	+	3.00000i	0.0698999	+	0.121070i
$615$		0			0
$616$	2.19615	−	3.80385i	0.0884855	−	0.153261i
$617$	−7.70882	−	28.7697i	−0.310346	−	1.15823i	−0.928245	−	0.371969i	$-0.878683\pi$
$617$	−7.70882	−	28.7697i	−0.310346	−	1.15823i	0.617900	−	0.786257i	$-0.287984\pi$
$618$		0			0
$619$	−14.2128	+	8.20577i	−0.571261	+	0.329818i	−0.757653	−	0.652658i	$-0.773654\pi$
$619$	−14.2128	+	8.20577i	−0.571261	+	0.329818i	0.186392	+	0.982476i	$0.440321\pi$
$620$		0			0
$621$		0			0
$622$	−17.6269	−	17.6269i	−0.706774	−	0.706774i
$623$	−2.84203	+	10.6066i	−0.113864	+	0.424945i
$624$		0			0
$625$		0			0
$626$	−2.89230	−	1.66987i	−0.115600	−	0.0667415i
$627$		0			0
$628$	−7.58871	−	2.03339i	−0.302822	−	0.0811410i
$629$		0			0
$630$		0			0
$631$	40.7846			1.62361			0.811805	−	0.583929i	$-0.198485\pi$
$631$	40.7846			1.62361			0.811805	+	0.583929i	$0.198485\pi$
$632$	9.65926	+	2.58819i	0.384225	+	0.102953i
$633$		0			0
$634$	21.2942	+	12.2942i	0.845702	+	0.488266i
$635$		0			0
$636$		0			0
$637$	−1.76959	+	6.60420i	−0.0701137	+	0.261668i
$638$	−17.8028	−	17.8028i	−0.704818	−	0.704818i
$639$		0			0
$640$		0			0
$641$	0.911543	−	0.526279i	0.0360038	−	0.0207868i	−0.481890	−	0.876232i	$-0.660050\pi$
$641$	0.911543	−	0.526279i	0.0360038	−	0.0207868i	0.517894	+	0.855445i	$0.326716\pi$
$642$		0			0
$643$	4.29839	+	16.0418i	0.169512	+	0.632627i	0.997422	+	0.0717654i	$0.0228633\pi$
$643$	4.29839	+	16.0418i	0.169512	+	0.632627i	−0.827910	+	0.560861i	$0.810470\pi$
$644$	5.19615	−	9.00000i	0.204757	−	0.354650i
$645$		0			0
$646$		0			0
$647$	2.68973	−	2.68973i	0.105744	−	0.105744i	−0.652255	−	0.757999i	$-0.726177\pi$
$647$	2.68973	−	2.68973i	0.105744	−	0.105744i	0.757999	+	0.652255i	$0.226177\pi$
$648$		0			0
$649$		−	43.1769i		−	1.69484i
$650$		0			0
$651$		0			0
$652$	19.6281	−	5.25933i	0.768696	−	0.205971i
$653$	2.12132	−	0.568406i	0.0830137	−	0.0222434i	−0.217073	−	0.976155i	$-0.569651\pi$
$653$	2.12132	−	0.568406i	0.0830137	−	0.0222434i	0.300087	+	0.953912i	$0.402984\pi$
$654$		0			0
$655$		0			0
$656$			1.73205i			0.0676252i
$657$		0			0
$658$	5.37945	−	5.37945i	0.209713	−	0.209713i
$659$	−11.0885	−	19.2058i	−0.431945	−	0.748151i	0.565096	−	0.825025i	$-0.308839\pi$
$659$	−11.0885	−	19.2058i	−0.431945	−	0.748151i	−0.997041	+	0.0768747i	$0.975506\pi$
$660$		0			0
$661$	−11.5885	+	20.0718i	−0.450739	+	0.780702i	−0.998432	−	0.0559768i	$-0.982173\pi$
$661$	−11.5885	+	20.0718i	−0.450739	+	0.780702i	0.547693	+	0.836679i	$0.315506\pi$
$662$	−4.55223	−	16.9891i	−0.176927	−	0.660302i
$663$		0			0
$664$	5.89230	−	3.40192i	0.228666	−	0.132020i
$665$		0			0
$666$		0			0
$667$	−42.1218	−	42.1218i	−1.63096	−	1.63096i
$668$	−1.13681	+	4.24264i	−0.0439846	+	0.164153i
$669$		0			0
$670$		0			0
$671$	−12.0000	−	6.92820i	−0.463255	−	0.267460i
$672$		0			0
$673$	−1.55291	−	0.416102i	−0.0598604	−	0.0160396i	0.228765	−	0.973482i	$-0.426531\pi$
$673$	−1.55291	−	0.416102i	−0.0598604	−	0.0160396i	−0.288625	+	0.957442i	$0.593198\pi$
$674$	27.4641			1.05788
$675$		0			0
$676$	11.3923			0.438166
$677$	−6.36396	−	1.70522i	−0.244587	−	0.0655369i	0.134443	−	0.990921i	$-0.457076\pi$
$677$	−6.36396	−	1.70522i	−0.244587	−	0.0655369i	−0.379030	+	0.925384i	$0.623742\pi$
$678$		0			0
$679$	16.0981	+	9.29423i	0.617787	+	0.356680i
$680$		0			0
$681$		0			0
$682$	−9.14162	+	34.1170i	−0.350051	+	1.30641i
$683$	27.9933	+	27.9933i	1.07113	+	1.07113i	0.997268	+	0.0738643i	$0.0235332\pi$
$683$	27.9933	+	27.9933i	1.07113	+	1.07113i	0.0738643	+	0.997268i	$0.476467\pi$
$684$		0			0
$685$		0			0
$686$	−13.6077	+	7.85641i	−0.519544	+	0.299959i
$687$		0			0
$688$	1.67303	+	6.24384i	0.0637838	+	0.238044i
$689$	1.39230	−	2.41154i	0.0530426	−	0.0918725i
$690$		0			0
$691$	−6.20577	−	10.7487i	−0.236079	−	0.408900i	0.723507	−	0.690317i	$-0.242529\pi$
$691$	−6.20577	−	10.7487i	−0.236079	−	0.408900i	−0.959586	+	0.281417i	$0.909196\pi$
$692$	3.10583	−	3.10583i	0.118066	−	0.118066i
$693$		0			0
$694$			32.7846i			1.24449i
$695$		0			0
$696$		0			0
$697$		0			0
$698$	1.93185	−	0.517638i	0.0731217	−	0.0195929i
$699$		0			0
$700$		0			0
$701$		−	21.4641i		−	0.810688i	−0.914164	−	0.405344i	$-0.867152\pi$
$701$		−	21.4641i		−	0.810688i	0.914164	−	0.405344i	$-0.132848\pi$
$702$		0			0
$703$	−11.1750	+	11.1750i	−0.421473	+	0.421473i
$704$	−1.73205	−	3.00000i	−0.0652791	−	0.113067i
$705$		0			0
$706$	7.50000	−	12.9904i	0.282266	−	0.488899i
$707$	3.52193	+	13.1440i	0.132456	+	0.494332i
$708$		0			0
$709$	−22.3468	+	12.9019i	−0.839251	+	0.484542i	−0.857010	−	0.515300i	$-0.827680\pi$
$709$	−22.3468	+	12.9019i	−0.839251	+	0.484542i	0.0177584	+	0.999842i	$0.494347\pi$
$710$		0			0
$711$		0			0
$712$	6.12372	+	6.12372i	0.229496	+	0.229496i
$713$	−21.6293	+	80.7217i	−0.810024	+	3.02305i
$714$		0			0
$715$		0			0
$716$	−4.20577	−	2.42820i	−0.157177	−	0.0907462i
$717$		0			0
$718$	−0.656339	−	0.175865i	−0.0244943	−	0.00656324i
$719$	−39.1244			−1.45909			−0.729546	−	0.683932i	$-0.760269\pi$
$719$	−39.1244			−1.45909			−0.729546	+	0.683932i	$0.760269\pi$
$720$		0			0
$721$	−13.1769			−0.490734
$722$	−31.6675	−	8.48528i	−1.17854	−	0.315789i
$723$		0			0
$724$	7.26795	+	4.19615i	0.270111	+	0.155949i
$725$		0			0
$726$		0			0
$727$	−1.79315	+	6.69213i	−0.0665043	+	0.248197i	−0.991173	−	0.132575i	$-0.957675\pi$
$727$	−1.79315	+	6.69213i	−0.0665043	+	0.248197i	0.924669	+	0.380773i	$0.124342\pi$
$728$	−1.13681	−	1.13681i	−0.0421331	−	0.0421331i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	8.90138	+	33.2204i	0.328780	+	1.22702i	0.910457	+	0.413604i	$0.135730\pi$
$733$	8.90138	+	33.2204i	0.328780	+	1.22702i	−0.581677	+	0.813420i	$0.697603\pi$
$734$	−15.9282	+	27.5885i	−0.587921	+	1.01831i
$735$		0			0
$736$	−4.09808	−	7.09808i	−0.151057	−	0.261639i
$737$	30.5307	−	30.5307i	1.12461	−	1.12461i
$738$		0			0
$739$			11.5885i			0.426288i	0.977021	+	0.213144i	$0.0683704\pi$
$739$			11.5885i			0.426288i	−0.977021	+	0.213144i	$0.931630\pi$
$740$		0			0
$741$		0			0
$742$	2.68973	−	0.720710i	0.0987430	−	0.0264581i
$743$	−38.0315	+	10.1905i	−1.39524	+	0.373853i	−0.876633	−	0.481160i	$-0.840216\pi$
$743$	−38.0315	+	10.1905i	−1.39524	+	0.373853i	−0.518606	+	0.855013i	$0.673549\pi$
$744$		0			0
$745$		0			0
$746$			11.3205i			0.414473i
$747$		0			0
$748$		0			0
$749$	0.509619	+	0.882686i	0.0186211	+	0.0322526i
$750$		0			0
$751$	10.2942	−	17.8301i	0.375642	−	0.650631i	−0.614781	−	0.788698i	$-0.710756\pi$
$751$	10.2942	−	17.8301i	0.375642	−	0.650631i	0.990423	+	0.138067i	$0.0440890\pi$
$752$	−1.55291	−	5.79555i	−0.0566290	−	0.211342i
$753$		0			0
$754$	−7.98076	+	4.60770i	−0.290642	+	0.167802i
$755$		0			0
$756$		0			0
$757$	−10.5187	−	10.5187i	−0.382308	−	0.382308i	0.489625	−	0.871933i	$-0.337134\pi$
$757$	−10.5187	−	10.5187i	−0.382308	−	0.382308i	−0.871933	+	0.489625i	$0.837134\pi$
$758$	5.27792	−	19.6975i	0.191703	−	0.715444i
$759$		0			0
$760$		0			0
$761$	9.91154	+	5.72243i	0.359293	+	0.207438i	0.668771	−	0.743469i	$-0.266821\pi$
$761$	9.91154	+	5.72243i	0.359293	+	0.207438i	−0.309478	+	0.950907i	$0.600154\pi$
$762$		0			0
$763$	−14.9372	−	4.00240i	−0.540762	−	0.144897i
$764$	−3.46410			−0.125327
$765$		0			0
$766$	36.5885			1.32199
$767$	−15.2653	−	4.09034i	−0.551200	−	0.147693i
$768$		0			0
$769$	28.9186	+	16.6962i	1.04283	+	0.602079i	0.920634	−	0.390427i	$-0.127673\pi$
$769$	28.9186	+	16.6962i	1.04283	+	0.602079i	0.122197	+	0.992506i	$0.461006\pi$
$770$		0			0
$771$		0			0
$772$	6.45189	−	24.0788i	0.232209	−	0.866615i
$773$	6.51626	+	6.51626i	0.234374	+	0.234374i	0.814516	−	0.580142i	$-0.197003\pi$
$773$	6.51626	+	6.51626i	0.234374	+	0.234374i	−0.580142	+	0.814516i	$0.697003\pi$
$774$		0			0
$775$		0			0
$776$	12.6962	−	7.33013i	0.455765	−	0.263136i
$777$		0			0
$778$	−2.68973	−	10.0382i	−0.0964314	−	0.359887i
$779$	−6.23205	+	10.7942i	−0.223286	+	0.386743i
$780$		0			0
$781$	18.5885	+	32.1962i	0.665147	+	1.15207i
$782$		0			0
$783$		0			0
$784$			5.39230i			0.192582i
$785$		0			0
$786$		0			0
$787$	−16.7303	+	4.48288i	−0.596372	+	0.159797i	−0.544364	−	0.838849i	$-0.683229\pi$
$787$	−16.7303	+	4.48288i	−0.596372	+	0.159797i	−0.0520081	+	0.998647i	$0.516562\pi$
$788$	−3.67423	+	0.984508i	−0.130889	+	0.0350717i
$789$		0			0
$790$		0			0
$791$		−	9.37307i		−	0.333268i
$792$		0			0
$793$	−3.58630	+	3.58630i	−0.127353	+	0.127353i
$794$	4.26795	+	7.39230i	0.151464	+	0.262343i
$795$		0			0
$796$	0.196152	−	0.339746i	0.00695244	−	0.0120420i
$797$	−2.84203	−	10.6066i	−0.100670	−	0.375705i	0.897148	−	0.441730i	$-0.145635\pi$
$797$	−2.84203	−	10.6066i	−0.100670	−	0.375705i	−0.997818	+	0.0660248i	$0.978968\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	−7.34847	−	7.34847i	−0.259483	−	0.259483i
$803$	4.65874	−	17.3867i	0.164403	−	0.613562i
$804$		0			0
$805$		0			0
$806$	11.1962	+	6.46410i	0.394368	+	0.227688i
$807$		0			0
$808$	10.3664	+	2.77766i	0.364687	+	0.0977177i
$809$	1.73205			0.0608957			0.0304478	−	0.999536i	$-0.490307\pi$
$809$	1.73205			0.0608957			0.0304478	+	0.999536i	$0.490307\pi$
$810$		0			0
$811$	−38.3731			−1.34746			−0.673730	−	0.738977i	$-0.735309\pi$
$811$	−38.3731			−1.34746			−0.673730	+	0.738977i	$0.735309\pi$
$812$	−8.90138	−	2.38512i	−0.312377	−	0.0837013i
$813$		0			0
$814$	−6.58846	−	3.80385i	−0.230925	−	0.133325i
$815$		0			0
$816$		0			0
$817$	−12.0394	+	44.9316i	−0.421205	+	1.57196i
$818$	−0.429705	−	0.429705i	−0.0150243	−	0.0150243i
$819$		0			0
$820$		0			0
$821$	18.5885	−	10.7321i	0.648742	−	0.374551i	−0.139232	−	0.990260i	$-0.544463\pi$
$821$	18.5885	−	10.7321i	0.648742	−	0.374551i	0.787974	+	0.615709i	$0.211130\pi$
$822$		0			0
$823$	−7.41284	−	27.6651i	−0.258395	−	0.964345i	−0.966170	−	0.257906i	$-0.916967\pi$
$823$	−7.41284	−	27.6651i	−0.258395	−	0.964345i	0.707775	−	0.706438i	$-0.249699\pi$
$824$	−5.19615	+	9.00000i	−0.181017	+	0.313530i
$825$		0			0
$826$	−7.90192	−	13.6865i	−0.274943	−	0.476215i
$827$	7.91688	−	7.91688i	0.275297	−	0.275297i	−0.555931	−	0.831228i	$-0.687638\pi$
$827$	7.91688	−	7.91688i	0.275297	−	0.275297i	0.831228	+	0.555931i	$0.187638\pi$
$828$		0			0
$829$			2.58846i			0.0899008i	0.998989	+	0.0449504i	$0.0143130\pi$
$829$			2.58846i			0.0899008i	−0.998989	+	0.0449504i	$0.985687\pi$
$830$		0			0
$831$		0			0
$832$	−1.22474	+	0.328169i	−0.0424604	+	0.0113772i
$833$		0			0
$834$		0			0
$835$		0			0
$836$		−	24.9282i		−	0.862160i
$837$		0			0
$838$	−6.36396	+	6.36396i	−0.219839	+	0.219839i
$839$	15.7583	+	27.2942i	0.544038	+	0.942301i	0.998667	+	0.0516204i	$0.0164386\pi$
$839$	15.7583	+	27.2942i	0.544038	+	0.942301i	−0.454629	+	0.890681i	$0.650228\pi$
$840$		0			0
$841$	−11.9115	+	20.6314i	−0.410743	+	0.711427i
$842$	2.22286	+	8.29581i	0.0766047	+	0.285893i
$843$		0			0
$844$	7.96410	−	4.59808i	0.274136	−	0.158272i
$845$		0			0
$846$		0			0
$847$	0.896575	+	0.896575i	0.0308067	+	0.0308067i
$848$	0.568406	−	2.12132i	0.0195191	−	0.0728464i
$849$		0			0
$850$		0			0
$851$	−15.5885	−	9.00000i	−0.534365	−	0.308516i
$852$		0			0
$853$	51.5037	+	13.8004i	1.76345	+	0.472515i	0.987412	−	0.158169i	$-0.0505590\pi$
$853$	51.5037	+	13.8004i	1.76345	+	0.472515i	0.776040	+	0.630684i	$0.217226\pi$
$854$	−5.07180			−0.173553
$855$		0			0
$856$	0.803848			0.0274749
$857$	0.208051	+	0.0557471i	0.00710689	+	0.00190429i	0.262371	−	0.964967i	$-0.415496\pi$
$857$	0.208051	+	0.0557471i	0.00710689	+	0.00190429i	−0.255264	+	0.966871i	$0.582162\pi$
$858$		0			0
$859$	9.01666	+	5.20577i	0.307644	+	0.177619i	0.645872	−	0.763446i	$-0.276494\pi$
$859$	9.01666	+	5.20577i	0.307644	+	0.177619i	−0.338227	+	0.941064i	$0.609827\pi$
$860$		0			0
$861$		0			0
$862$	0.808643	−	3.01790i	0.0275425	−	0.102790i
$863$	3.52193	+	3.52193i	0.119888	+	0.119888i	0.764505	−	0.644617i	$-0.222983\pi$
$863$	3.52193	+	3.52193i	0.119888	+	0.119888i	−0.644617	+	0.764505i	$0.722983\pi$
$864$		0			0
$865$		0			0
$866$	−26.7846	+	15.4641i	−0.910178	+	0.525492i
$867$		0			0
$868$	3.34607	+	12.4877i	0.113573	+	0.423860i
$869$	−17.3205	+	30.0000i	−0.587558	+	1.01768i
$870$		0			0
$871$	−7.90192	−	13.6865i	−0.267746	−	0.463750i
$872$	−8.62398	+	8.62398i	−0.292045	+	0.292045i
$873$		0			0
$874$		−	58.9808i		−	1.99505i
$875$		0			0
$876$		0			0
$877$	22.2856	−	5.97142i	0.752533	−	0.201641i	0.137892	−	0.990447i	$-0.455967\pi$
$877$	22.2856	−	5.97142i	0.752533	−	0.201641i	0.614641	+	0.788807i	$0.289301\pi$
$878$	−31.4780	+	8.43451i	−1.06233	+	0.284651i
$879$		0			0
$880$		0			0
$881$			53.3205i			1.79641i	0.439573	+	0.898207i	$0.355130\pi$
$881$			53.3205i			1.79641i	−0.439573	+	0.898207i	$0.644870\pi$
$882$		0			0
$883$	−1.31268	+	1.31268i	−0.0441751	+	0.0441751i	−0.728849	−	0.684674i	$-0.759945\pi$
$883$	−1.31268	+	1.31268i	−0.0441751	+	0.0441751i	0.684674	+	0.728849i	$0.259945\pi$
$884$		0			0
$885$		0			0
$886$	−5.19615	+	9.00000i	−0.174568	+	0.302361i
$887$	2.68973	+	10.0382i	0.0903122	+	0.337050i	0.996267	−	0.0863246i	$-0.0275122\pi$
$887$	2.68973	+	10.0382i	0.0903122	+	0.337050i	−0.905955	+	0.423374i	$0.860846\pi$
$888$		0			0
$889$	−2.41154	+	1.39230i	−0.0808805	+	0.0466964i
$890$		0			0
$891$		0			0
$892$	−6.69213	−	6.69213i	−0.224069	−	0.224069i
$893$	11.1750	−	41.7057i	0.373957	−	1.39563i
$894$		0			0
$895$		0			0
$896$	−1.09808	−	0.633975i	−0.0366842	−	0.0211796i
$897$		0			0
$898$	5.67544	+	1.52073i	0.189392	+	0.0507474i
$899$	74.1051			2.47154
$900$		0			0
$901$		0			0
$902$	−5.79555	−	1.55291i	−0.192971	−	0.0517064i
$903$		0			0
$904$	−6.40192	−	3.69615i	−0.212925	−	0.122932i
$905$		0			0
$906$		0			0
$907$	−8.54103	+	31.8756i	−0.283600	+	1.05841i	0.666256	+	0.745723i	$0.267896\pi$
$907$	−8.54103	+	31.8756i	−0.283600	+	1.05841i	−0.949856	+	0.312687i	$0.898771\pi$
$908$	16.4022	+	16.4022i	0.544325	+	0.544325i
$909$		0			0
$910$		0			0
$911$	12.8827	−	7.43782i	0.426822	−	0.246426i	−0.271170	−	0.962532i	$-0.587410\pi$
$911$	12.8827	−	7.43782i	0.426822	−	0.246426i	0.697992	+	0.716106i	$0.254077\pi$
$912$		0			0
$913$	6.10016	+	22.7661i	0.201886	+	0.753449i
$914$	−1.79423	+	3.10770i	−0.0593478	+	0.102793i
$915$		0			0
$916$	−8.09808	−	14.0263i	−0.267568	−	0.463441i
$917$	−6.21166	+	6.21166i	−0.205127	+	0.205127i
$918$		0			0
$919$		−	27.4115i		−	0.904223i	−0.891961	−	0.452112i	$-0.850671\pi$
$919$		−	27.4115i		−	0.904223i	0.891961	−	0.452112i	$-0.149329\pi$
$920$		0			0
$921$		0			0
$922$	27.0967	−	7.26054i	0.892382	−	0.239113i
$923$	13.1440	−	3.52193i	0.432641	−	0.115926i
$924$		0			0
$925$		0			0
$926$			8.19615i			0.269342i
$927$		0			0
$928$	−5.13922	+	5.13922i	−0.168703	+	0.168703i
$929$	−2.07180	−	3.58846i	−0.0679734	−	0.117733i	0.830036	−	0.557710i	$-0.188320\pi$
$929$	−2.07180	−	3.58846i	−0.0679734	−	0.117733i	−0.898009	+	0.439977i	$0.854987\pi$
$930$		0			0
$931$	−19.4019	+	33.6051i	−0.635872	+	1.10136i
$932$	6.57201	+	24.5271i	0.215273	+	0.803411i
$933$		0			0
$934$	−18.6962	+	10.7942i	−0.611757	+	0.353198i
$935$		0			0
$936$		0			0
$937$	−9.22955	−	9.22955i	−0.301516	−	0.301516i	0.540091	−	0.841607i	$-0.318390\pi$
$937$	−9.22955	−	9.22955i	−0.301516	−	0.301516i	−0.841607	+	0.540091i	$0.818390\pi$
$938$	4.09034	−	15.2653i	0.133554	−	0.498431i
$939$		0			0
$940$		0			0
$941$	36.8827	+	21.2942i	1.20234	+	0.694172i	0.961075	−	0.276287i	$-0.0891040\pi$
$941$	36.8827	+	21.2942i	1.20234	+	0.694172i	0.241266	+	0.970459i	$0.422437\pi$
$942$		0			0
$943$	−13.7124	−	3.67423i	−0.446538	−	0.119650i
$944$	−12.4641			−0.405672
$945$		0			0
$946$	−22.3923			−0.728037
$947$	29.3381	+	7.86113i	0.953361	+	0.255452i	0.701788	−	0.712386i	$-0.252385\pi$
$947$	29.3381	+	7.86113i	0.953361	+	0.255452i	0.251573	+	0.967838i	$0.419052\pi$
$948$		0			0
$949$	−5.70577	−	3.29423i	−0.185217	−	0.106935i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−28.5617	−	28.5617i	−0.925203	−	0.925203i	0.0721877	−	0.997391i	$-0.477002\pi$
$953$	−28.5617	−	28.5617i	−0.925203	−	0.925203i	−0.997391	+	0.0721877i	$0.977002\pi$
$954$		0			0
$955$		0			0
$956$	−12.2942	+	7.09808i	−0.397624	+	0.229568i
$957$		0			0
$958$	5.46739	+	20.4046i	0.176643	+	0.659241i
$959$	4.68653	−	8.11731i	0.151336	−	0.262122i
$960$		0			0
$961$	−36.4808	−	63.1865i	−1.17680	−	2.03828i
$962$	−1.96902	+	1.96902i	−0.0634836	+	0.0634836i
$963$		0			0
$964$			11.3923i			0.366921i
$965$		0			0
$966$		0			0
$967$	40.1528	−	10.7589i	1.29123	−	0.345983i	0.453100	−	0.891460i	$-0.350318\pi$
$967$	40.1528	−	10.7589i	1.29123	−	0.345983i	0.838126	+	0.545476i	$0.183651\pi$
$968$	0.965926	−	0.258819i	0.0310460	−	0.00831876i
$969$		0			0
$970$		0			0
$971$		−	36.0333i		−	1.15636i	−0.815908	−	0.578182i	$-0.803762\pi$
$971$		−	36.0333i		−	1.15636i	0.815908	−	0.578182i	$-0.196238\pi$
$972$		0			0
$973$	7.17260	−	7.17260i	0.229943	−	0.229943i
$974$	11.0263	+	19.0981i	0.353305	+	0.611942i
$975$		0			0
$976$	−2.00000	+	3.46410i	−0.0640184	+	0.110883i
$977$	4.18689	+	15.6257i	0.133951	+	0.499910i	1.00000		4.80066e-5i	$-1.52810e-5\pi$
$977$	4.18689	+	15.6257i	0.133951	+	0.499910i	−0.866049	+	0.499958i	$0.833349\pi$
$978$		0			0
$979$	−25.9808	+	15.0000i	−0.830349	+	0.479402i
$980$		0			0
$981$		0			0
$982$	25.9599	+	25.9599i	0.828413	+	0.828413i
$983$	4.96335	−	18.5235i	0.158306	−	0.590807i	−0.840493	−	0.541822i	$-0.817735\pi$
$983$	4.96335	−	18.5235i	0.158306	−	0.590807i	0.998800	−	0.0489851i	$-0.0155987\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−8.81345	−	2.36156i	−0.280393	−	0.0751311i
$989$	−52.9808			−1.68469
$990$		0			0
$991$	33.1769			1.05390			0.526950	−	0.849896i	$-0.323336\pi$
$991$	33.1769			1.05390			0.526950	+	0.849896i	$0.323336\pi$
$992$	9.84873	+	2.63896i	0.312697	+	0.0837870i
$993$		0			0
$994$	11.7846	+	6.80385i	0.373785	+	0.215805i
$995$		0			0
$996$		0			0
$997$	−8.33298	+	31.0991i	−0.263908	+	0.984918i	0.699007	+	0.715115i	$0.253625\pi$
$997$	−8.33298	+	31.0991i	−0.263908	+	0.984918i	−0.962915	+	0.269804i	$0.913041\pi$
$998$	−13.8511	−	13.8511i	−0.438450	−	0.438450i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1350.2.q.a.557.2		8
3.2	odd	2		450.2.p.e.257.1	yes	8
5.2	odd	4		1350.2.q.d.1043.1		8
5.3	odd	4		1350.2.q.d.1043.2		8
5.4	even	2	inner	1350.2.q.a.557.1		8
9.2	odd	6		1350.2.q.d.1007.2		8
9.7	even	3		450.2.p.c.407.1	yes	8
15.2	even	4		450.2.p.c.293.2	yes	8
15.8	even	4		450.2.p.c.293.1	✓	8
15.14	odd	2		450.2.p.e.257.2	yes	8
45.2	even	12	inner	1350.2.q.a.143.1		8
45.7	odd	12		450.2.p.e.443.2	yes	8
45.29	odd	6		1350.2.q.d.1007.1		8
45.34	even	6		450.2.p.c.407.2	yes	8
45.38	even	12	inner	1350.2.q.a.143.2		8
45.43	odd	12		450.2.p.e.443.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
450.2.p.c.293.1	✓	8	15.8	even	4
450.2.p.c.293.2	yes	8	15.2	even	4
450.2.p.c.407.1	yes	8	9.7	even	3
450.2.p.c.407.2	yes	8	45.34	even	6
450.2.p.e.257.1	yes	8	3.2	odd	2
450.2.p.e.257.2	yes	8	15.14	odd	2
450.2.p.e.443.1	yes	8	45.43	odd	12
450.2.p.e.443.2	yes	8	45.7	odd	12
1350.2.q.a.143.1		8	45.2	even	12	inner
1350.2.q.a.143.2		8	45.38	even	12	inner
1350.2.q.a.557.1		8	5.4	even	2	inner
1350.2.q.a.557.2		8	1.1	even	1	trivial
1350.2.q.d.1007.1		8	45.29	odd	6
1350.2.q.d.1007.2		8	9.2	odd	6
1350.2.q.d.1043.1		8	5.2	odd	4
1350.2.q.d.1043.2		8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1350.q (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.328169 + 1.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(-0.328169 + 1.22474i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(0.328169 + 1.22474i) q^{13} +(-0.633975 + 1.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} +7.19615i q^{19} +(-3.34607 + 0.896575i) q^{22} +(-7.91688 + 2.12132i) q^{23} +1.26795i q^{26} +(-0.896575 + 0.896575i) q^{28} +(3.63397 + 6.29423i) q^{29} +(5.09808 - 8.83013i) q^{31} +(0.258819 + 0.965926i) q^{32} +(1.55291 + 1.55291i) q^{37} +(-1.86250 + 6.95095i) q^{38} +(1.50000 + 0.866025i) q^{41} +(6.24384 + 1.67303i) q^{43} -3.46410 q^{44} -8.19615 q^{46} +(-5.79555 - 1.55291i) q^{47} +(4.66987 + 2.69615i) q^{49} +(-0.328169 + 1.22474i) q^{52} +(-1.55291 - 1.55291i) q^{53} +(-1.09808 + 0.633975i) q^{56} +(1.88108 + 7.02030i) q^{58} +(-6.23205 + 10.7942i) q^{59} +(2.00000 + 3.46410i) q^{61} +(7.20977 - 7.20977i) q^{62} +1.00000i q^{64} +(-12.0394 + 3.22595i) q^{67} -10.7321i q^{71} +(-3.67423 + 3.67423i) q^{73} +(1.09808 + 1.90192i) q^{74} +(-3.59808 + 6.23205i) q^{76} +(-1.13681 - 4.24264i) q^{77} +(8.66025 - 5.00000i) q^{79} +(1.22474 + 1.22474i) q^{82} +(1.76097 - 6.57201i) q^{83} +(5.59808 + 3.23205i) q^{86} +(-3.34607 - 0.896575i) q^{88} +8.66025 q^{89} -1.60770 q^{91} +(-7.91688 - 2.12132i) q^{92} +(-5.19615 - 3.00000i) q^{94} +(3.79435 - 14.1607i) q^{97} +(3.81294 + 3.81294i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 24 q^{11} - 12 q^{14} + 4 q^{16} + 36 q^{29} + 20 q^{31} + 12 q^{41} - 24 q^{46} + 72 q^{49} + 12 q^{56} - 36 q^{59} + 16 q^{61} - 12 q^{74} - 8 q^{76} + 24 q^{86} - 96 q^{91}+O(q^{100}) \) 8 * q - 24 * q^11 - 12 * q^14 + 4 * q^16 + 36 * q^29 + 20 * q^31 + 12 * q^41 - 24 * q^46 + 72 * q^49 + 12 * q^56 - 36 * q^59 + 16 * q^61 - 12 * q^74 - 8 * q^76 + 24 * q^86 - 96 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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