LMFDB - Embedded newform 1350.2.q.a.557.1

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			557.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.557
Dual form			1350.2.q.a.143.1

$q$-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	−0.875767	−	0.482734i	$-0.839644\pi$
$7$	0.328169	−	1.22474i	0.124036	−	0.462910i	0.999803	+	0.0198238i	$0.00631052\pi$
$8$	−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	0.905368	−	0.424628i	$-0.139595\pi$
$13$	−0.328169	−	1.22474i	−0.0910178	−	0.339683i	−0.996386	+	0.0849451i	$0.972929\pi$
$14$	−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	0.690951	−	0.722902i	$-0.257192\pi$
$23$	7.91688	−	2.12132i	1.65078	−	0.442326i	0.959832	+	0.280576i	$0.0905255\pi$
$24$		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	0.567841	−	0.823138i	$-0.307779\pi$
$37$	−1.55291	−	1.55291i	−0.255298	−	0.255298i	−0.823138	+	0.567841i	$0.807779\pi$
$38$	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	−0.250891	−	0.968015i	$-0.580724\pi$
$43$	−6.24384	−	1.67303i	−0.952177	−	0.255135i	−0.701286	+	0.712880i	$0.747390\pi$
$44$	−3.46410			−0.522233
$45$		0			0
$46$	−8.19615			−1.20846
$47$	5.79555	+	1.55291i	0.845369	+	0.226516i	0.655407	−	0.755276i	$-0.272497\pi$
$47$	5.79555	+	1.55291i	0.845369	+	0.226516i	0.189961	+	0.981792i	$0.439164\pi$
$48$		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	0.805672	−	0.592362i	$-0.201805\pi$
$53$	1.55291	+	1.55291i	0.213309	+	0.213309i	−0.592362	+	0.805672i	$0.701805\pi$
$54$		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	0.567625	−	0.823287i	$-0.307862\pi$
$67$	12.0394	−	3.22595i	1.47085	−	0.394112i	0.903221	+	0.429175i	$0.141196\pi$
$68$		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	−0.458604	−	0.888641i	$-0.651650\pi$
$73$	3.67423	−	3.67423i	0.430037	−	0.430037i	0.888641	+	0.458604i	$0.151650\pi$
$74$	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	$0.205145\pi$
$83$	−1.76097	+	6.57201i	−0.193291	+	0.721372i	−0.992703	+	0.120588i	$0.961522\pi$
$84$		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	$0.350532\pi$
$97$	−3.79435	+	14.1607i	−0.385258	+	1.43780i	−0.837760	+	0.546039i	$0.816135\pi$
$98$	−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	$-0.912241\pi$
$103$	−2.68973	−	10.0382i	−0.265027	−	0.989093i	0.697207	−	0.716869i	$-0.254426\pi$
$104$	−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	−0.734048	−	0.679098i	$-0.762371\pi$
$107$	−0.568406	+	0.568406i	−0.0549499	+	0.0549499i	0.679098	+	0.734048i	$0.262371\pi$
$108$		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	0.0931872	−	0.995649i	$-0.470294\pi$
$113$	7.14042	−	1.91327i	0.671714	−	0.179985i	0.578527	+	0.815663i	$0.303628\pi$
$114$		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	0.634843	−	0.772641i	$-0.281065\pi$
$127$	−1.55291	−	1.55291i	−0.137799	−	0.137799i	−0.772641	+	0.634843i	$0.781065\pi$
$128$	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	0.550599	−	0.834770i	$-0.314399\pi$
$137$	7.14042	+	1.91327i	0.610047	+	0.163462i	0.0594480	+	0.998231i	$0.481066\pi$
$138$		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	0.0570512	−	0.998371i	$-0.481830\pi$
$157$	7.58871	−	2.03339i	0.605645	−	0.162282i	0.548593	+	0.836089i	$0.315163\pi$
$158$	−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	$0.542956\pi$
$163$	−14.3688	+	14.3688i	−1.12545	+	1.12545i	−0.990908	+	0.134541i	$0.957044\pi$
$164$	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	0.907891	−	0.419207i	$-0.137692\pi$
$167$	−1.13681	−	4.24264i	−0.0879692	−	0.328305i	−0.995860	+	0.0909015i	$0.971025\pi$
$168$		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	−0.995581	−	0.0939047i	$-0.970065\pi$
$173$	−1.13681	+	4.24264i	−0.0864302	+	0.322562i	0.909151	+	0.416467i	$0.136732\pi$
$174$		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	$0.271059\pi$
$193$	6.45189	+	24.0788i	0.464417	+	1.73323i	−0.194396	+	0.980923i	$0.562275\pi$
$194$	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	−0.604767	−	0.796402i	$-0.706734\pi$
$197$	2.68973	−	2.68973i	0.191635	−	0.191635i	0.796402	+	0.604767i	$0.206734\pi$
$198$		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	0.551565	−	0.834132i	$-0.314031\pi$
$223$	9.14162	+	2.44949i	0.612168	+	0.164030i	0.0606032	+	0.998162i	$0.480698\pi$
$224$	−1.26795			−0.0847184
$225$		0			0
$226$	−7.39230			−0.491729
$227$	−22.4058	−	6.00361i	−1.48712	−	0.398473i	−0.578358	−	0.815783i	$-0.696306\pi$
$227$	−22.4058	−	6.00361i	−1.48712	−	0.398473i	−0.908764	+	0.417310i	$0.862973\pi$
$228$		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	$-0.937338\pi$
$233$	−17.9551	−	17.9551i	−1.17628	−	1.17628i	−0.195590	−	0.980686i	$-0.562662\pi$
$234$		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	0.993094	−	0.117319i	$-0.0374301\pi$
$257$	1.19256	+	4.45069i	0.0743898	+	0.277627i	−0.918704	+	0.394946i	$0.870763\pi$
$258$		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	$0.277595\pi$
$263$	−4.81105	+	17.9551i	−0.296662	+	1.10716i	−0.939889	+	0.341481i	$0.889071\pi$
$264$		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	$0.361373\pi$
$277$	−6.60420	+	24.6472i	−0.396808	+	1.48091i	−0.818679	+	0.574251i	$0.805293\pi$
$278$	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	$0.0120147\pi$
$283$	2.56961	+	9.58991i	0.152747	+	0.570061i	−0.846540	+	0.532325i	$0.821319\pi$
$284$	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	−0.636062	−	0.771638i	$-0.719438\pi$
$293$	−13.7124	+	3.67423i	−0.801089	+	0.214651i	−0.165027	+	0.986289i	$0.552771\pi$
$294$		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	0.633743	−	0.773543i	$-0.281517\pi$
$307$	−2.44949	−	2.44949i	−0.139800	−	0.139800i	−0.773543	+	0.633743i	$0.781517\pi$
$308$	−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	0.348834	−	0.937184i	$-0.386578\pi$
$313$	3.22595	+	0.864390i	0.182341	+	0.0488582i	−0.166493	+	0.986043i	$0.553244\pi$
$314$	−7.85641			−0.443363
$315$		0			0
$316$	10.0000			0.562544
$317$	−23.7506	−	6.36396i	−1.33397	−	0.357436i	−0.479775	−	0.877392i	$-0.659282\pi$
$317$	−23.7506	−	6.36396i	−1.33397	−	0.357436i	−0.854193	+	0.519956i	$0.825948\pi$
$318$		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	−0.894312	−	0.447443i	$-0.852335\pi$
$337$	−26.5283	+	7.10823i	−1.44509	+	0.387210i	−0.550775	+	0.834653i	$0.685668\pi$
$338$	−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	$-0.740886\pi$
$347$	−8.48528	−	31.6675i	−0.455514	−	1.70000i	0.231059	−	0.972940i	$-0.425781\pi$
$348$		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	$0.214040\pi$
$353$	−3.88229	+	14.4889i	−0.206633	+	0.771166i	−0.988946	+	0.148279i	$0.952627\pi$
$354$		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	$-0.604181\pi$
$367$	8.24504	−	30.7709i	0.430388	−	1.60623i	0.751868	−	0.659313i	$-0.229153\pi$
$368$	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	$-0.988654\pi$
$373$	−2.92996	−	10.9348i	−0.151708	−	0.566181i	0.847657	−	0.530545i	$-0.178013\pi$
$374$		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	−0.994871	−	0.101152i	$-0.967747\pi$
$383$	−35.3417	+	9.46979i	−1.80588	+	0.483884i	−0.811007	+	0.585036i	$0.801080\pi$
$384$		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	0.539231	−	0.842158i	$-0.318715\pi$
$397$	−6.03579	−	6.03579i	−0.302928	−	0.302928i	−0.842158	+	0.539231i	$0.818715\pi$
$398$	−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	$-0.483327\pi$
$433$	21.8695	−	21.8695i	1.05098	−	1.05098i	0.998629	−	0.0523546i	$-0.0166726\pi$
$434$	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	−0.872131	−	0.489272i	$-0.837262\pi$
$443$	2.68973	−	10.0382i	0.127793	−	0.476929i	0.999924	+	0.0123433i	$0.00392908\pi$
$444$		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	−0.940795	−	0.338976i	$-0.889919\pi$
$457$	0.928761	−	3.46618i	0.0434456	−	0.162141i	0.984240	+	0.176835i	$0.0565860\pi$
$458$	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	0.898953	−	0.438046i	$-0.144329\pi$
$463$	−2.12132	−	7.91688i	−0.0985861	−	0.367928i	−0.997539	+	0.0701175i	$0.977663\pi$
$464$	−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	−0.259380	−	0.965775i	$-0.583518\pi$
$467$	15.2653	−	15.2653i	0.706396	−	0.706396i	0.965775	+	0.259380i	$0.0835181\pi$
$468$		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	0.259211	−	0.965821i	$-0.416537\pi$
$487$	−15.5935	−	15.5935i	−0.706610	−	0.706610i	−0.965821	+	0.259211i	$0.916537\pi$
$488$	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	$-0.946352\pi$
$503$	−25.8719	−	25.8719i	−1.15357	−	1.15357i	−0.167742	−	0.985831i	$-0.553648\pi$
$504$		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	−0.325076	−	0.945688i	$-0.605390\pi$
$523$	14.1929	−	14.1929i	0.620612	−	0.620612i	0.945688	+	0.325076i	$0.105390\pi$
$524$	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	$0.240563\pi$
$547$	−5.73981	+	21.4213i	−0.245416	+	0.915907i	−0.973174	+	0.230072i	$0.926104\pi$
$548$	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	−0.417531	−	0.908662i	$-0.637105\pi$
$557$	11.5911	−	11.5911i	0.491131	−	0.491131i	0.908662	+	0.417531i	$0.137105\pi$
$558$		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	0.500840	−	0.865540i	$-0.333025\pi$
$563$	32.4440	−	8.69333i	1.36735	−	0.366380i	0.866510	+	0.499160i	$0.166358\pi$
$564$		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	0.956046	−	0.293217i	$-0.0947260\pi$
$577$	15.9217	+	15.9217i	0.662828	+	0.662828i	−0.293217	+	0.956046i	$0.594726\pi$
$578$	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	0.570324	−	0.821420i	$-0.306818\pi$
$587$	15.8338	+	4.24264i	0.653529	+	0.175113i	0.0832050	+	0.996532i	$0.473484\pi$
$588$		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	0.942890	−	0.333105i	$-0.108096\pi$
$593$	14.8492	+	14.8492i	0.609785	+	0.609785i	−0.333105	+	0.942890i	$0.608096\pi$
$594$		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	0.0991937	−	0.995068i	$-0.468374\pi$
$607$	16.8183	−	4.50644i	0.682632	−	0.182911i	0.583438	+	0.812157i	$0.301707\pi$
$608$	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	−0.650699	−	0.759336i	$-0.725524\pi$
$613$	2.68973	−	2.68973i	0.108637	−	0.108637i	0.759336	+	0.650699i	$0.225524\pi$
$614$	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	$0.121317\pi$
$617$	7.70882	+	28.7697i	0.310346	+	1.15823i	−0.617900	+	0.786257i	$0.712016\pi$
$618$		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	$-0.977137\pi$
$643$	−4.29839	−	16.0418i	−0.169512	−	0.632627i	0.827910	−	0.560861i	$-0.189530\pi$
$644$	5.19615	−	9.00000i	0.204757	−	0.354650i
$645$		0			0
$646$		0			0
$647$	−2.68973	+	2.68973i	−0.105744	+	0.105744i	−0.757999	−	0.652255i	$-0.773823\pi$
$647$	−2.68973	+	2.68973i	−0.105744	+	0.105744i	0.652255	+	0.757999i	$0.273823\pi$
$648$		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	−0.300087	−	0.953912i	$-0.597016\pi$
$653$	−2.12132	+	0.568406i	−0.0830137	+	0.0222434i	0.217073	+	0.976155i	$0.430349\pi$
$654$		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	0.288625	−	0.957442i	$-0.406802\pi$
$673$	1.55291	+	0.416102i	0.0598604	+	0.0160396i	−0.228765	+	0.973482i	$0.573469\pi$
$674$	27.4641			1.05788
$675$		0			0
$676$	11.3923			0.438166
$677$	6.36396	+	1.70522i	0.244587	+	0.0655369i	0.379030	−	0.925384i	$-0.376258\pi$
$677$	6.36396	+	1.70522i	0.244587	+	0.0655369i	−0.134443	+	0.990921i	$0.542924\pi$
$678$		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	$-0.976467\pi$
$683$	−27.9933	−	27.9933i	−1.07113	−	1.07113i	−0.0738643	−	0.997268i	$-0.523533\pi$
$684$		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	−0.924669	−	0.380773i	$-0.875658\pi$
$727$	1.79315	−	6.69213i	0.0665043	−	0.248197i	0.991173	+	0.132575i	$0.0423247\pi$
$728$	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	$-0.864270\pi$
$733$	−8.90138	−	33.2204i	−0.328780	−	1.22702i	0.581677	−	0.813420i	$-0.302397\pi$
$734$	−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	0.518606	−	0.855013i	$-0.326451\pi$
$743$	38.0315	−	10.1905i	1.39524	−	0.373853i	0.876633	+	0.481160i	$0.159784\pi$
$744$		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	0.871933	−	0.489625i	$-0.162866\pi$
$757$	10.5187	+	10.5187i	0.382308	+	0.382308i	−0.489625	+	0.871933i	$0.662866\pi$
$758$	−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	0.580142	−	0.814516i	$-0.302997\pi$
$773$	−6.51626	−	6.51626i	−0.234374	−	0.234374i	−0.814516	+	0.580142i	$0.802997\pi$
$774$		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	0.0520081	−	0.998647i	$-0.483438\pi$
$787$	16.7303	−	4.48288i	0.596372	−	0.159797i	0.544364	+	0.838849i	$0.316771\pi$
$788$	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	0.997818	−	0.0660248i	$-0.0210316\pi$
$797$	2.84203	+	10.6066i	0.100670	+	0.375705i	−0.897148	+	0.441730i	$0.854365\pi$
$798$		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	$0.0830326\pi$
$823$	7.41284	+	27.6651i	0.258395	+	0.964345i	−0.707775	+	0.706438i	$0.750301\pi$
$824$	−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	−0.831228	−	0.555931i	$-0.812362\pi$
$827$	−7.91688	+	7.91688i	−0.275297	+	0.275297i	0.555931	+	0.831228i	$0.312362\pi$
$828$		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	−0.776040	−	0.630684i	$-0.782774\pi$
$853$	−51.5037	−	13.8004i	−1.76345	−	0.472515i	−0.987412	+	0.158169i	$0.949441\pi$
$854$	−5.07180			−0.173553
$855$		0			0
$856$	0.803848			0.0274749
$857$	−0.208051	−	0.0557471i	−0.00710689	−	0.00190429i	0.255264	−	0.966871i	$-0.417838\pi$
$857$	−0.208051	−	0.0557471i	−0.00710689	−	0.00190429i	−0.262371	+	0.964967i	$0.584504\pi$
$858$		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	0.644617	−	0.764505i	$-0.277017\pi$
$863$	−3.52193	−	3.52193i	−0.119888	−	0.119888i	−0.764505	+	0.644617i	$0.777017\pi$
$864$		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	−0.614641	−	0.788807i	$-0.710699\pi$
$877$	−22.2856	+	5.97142i	−0.752533	+	0.201641i	−0.137892	+	0.990447i	$0.544033\pi$
$878$	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	−0.684674	−	0.728849i	$-0.740055\pi$
$883$	1.31268	−	1.31268i	0.0441751	−	0.0441751i	0.728849	+	0.684674i	$0.240055\pi$
$884$		0			0
$885$		0			0
$886$	−5.19615	+	9.00000i	−0.174568	+	0.302361i
$887$	−2.68973	−	10.0382i	−0.0903122	−	0.337050i	0.905955	−	0.423374i	$-0.139154\pi$
$887$	−2.68973	−	10.0382i	−0.0903122	−	0.337050i	−0.996267	+	0.0863246i	$0.972488\pi$
$888$		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	$-0.732104\pi$
$907$	8.54103	−	31.8756i	0.283600	−	1.05841i	0.949856	−	0.312687i	$-0.101229\pi$
$908$	−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	0.841607	−	0.540091i	$-0.181610\pi$
$937$	9.22955	+	9.22955i	0.301516	+	0.301516i	−0.540091	+	0.841607i	$0.681610\pi$
$938$	−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	−0.251573	−	0.967838i	$-0.580948\pi$
$947$	−29.3381	−	7.86113i	−0.953361	−	0.255452i	−0.701788	+	0.712386i	$0.747615\pi$
$948$		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	0.997391	−	0.0721877i	$-0.0229981\pi$
$953$	28.5617	+	28.5617i	0.925203	+	0.925203i	−0.0721877	+	0.997391i	$0.522998\pi$
$954$		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	−0.838126	−	0.545476i	$-0.816349\pi$
$967$	−40.1528	+	10.7589i	−1.29123	+	0.345983i	−0.453100	+	0.891460i	$0.649682\pi$
$968$	−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	0.866049	−	0.499958i	$-0.166651\pi$
$977$	−4.18689	−	15.6257i	−0.133951	−	0.499910i	−1.00000		4.80066e-5i	$0.999985\pi$
$978$		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	$0.182265\pi$
$983$	−4.96335	+	18.5235i	−0.158306	+	0.590807i	−0.998800	+	0.0489851i	$0.984401\pi$
$984$		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	$-0.746375\pi$
$997$	8.33298	−	31.0991i	0.263908	−	0.984918i	0.962915	−	0.269804i	$-0.0869588\pi$
$998$	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.557.1		8
3.2	odd	2		450.2.p.e.257.2	yes	8
5.2	odd	4		1350.2.q.d.1043.2		8
5.3	odd	4		1350.2.q.d.1043.1		8
5.4	even	2	inner	1350.2.q.a.557.2		8
9.2	odd	6		1350.2.q.d.1007.1		8
9.7	even	3		450.2.p.c.407.2	yes	8
15.2	even	4		450.2.p.c.293.1	✓	8
15.8	even	4		450.2.p.c.293.2	yes	8
15.14	odd	2		450.2.p.e.257.1	yes	8
45.2	even	12	inner	1350.2.q.a.143.2		8
45.7	odd	12		450.2.p.e.443.1	yes	8
45.29	odd	6		1350.2.q.d.1007.2		8
45.34	even	6		450.2.p.c.407.1	yes	8
45.38	even	12	inner	1350.2.q.a.143.1		8
45.43	odd	12		450.2.p.e.443.2	yes	8

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