LMFDB - Embedded newform 1350.2.q.d.1043.1

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			1043.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1350.1043
Dual form			1350.2.q.d.1007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-1.22474 - 0.328169i) q^{7} +(0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-1.22474 - 0.328169i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-3.00000 + 1.73205i) q^{11} +(1.22474 - 0.328169i) q^{13} +(0.633975 - 1.09808i) q^{14} +(0.500000 + 0.866025i) q^{16} -7.19615i q^{19} +(-0.896575 - 3.34607i) q^{22} +(2.12132 + 7.91688i) q^{23} +1.26795i q^{26} +(0.896575 + 0.896575i) q^{28} +(-3.63397 - 6.29423i) q^{29} +(5.09808 - 8.83013i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-1.55291 + 1.55291i) q^{37} +(6.95095 + 1.86250i) q^{38} +(1.50000 + 0.866025i) q^{41} +(1.67303 - 6.24384i) q^{43} +3.46410 q^{44} -8.19615 q^{46} +(1.55291 - 5.79555i) q^{47} +(-4.66987 - 2.69615i) q^{49} +(-1.22474 - 0.328169i) q^{52} +(-1.55291 + 1.55291i) q^{53} +(-1.09808 + 0.633975i) q^{56} +(7.02030 - 1.88108i) q^{58} +(6.23205 - 10.7942i) q^{59} +(2.00000 + 3.46410i) q^{61} +(7.20977 + 7.20977i) q^{62} -1.00000i q^{64} +(-3.22595 - 12.0394i) q^{67} -10.7321i q^{71} +(3.67423 + 3.67423i) q^{73} +(-1.09808 - 1.90192i) q^{74} +(-3.59808 + 6.23205i) q^{76} +(4.24264 - 1.13681i) q^{77} +(-8.66025 + 5.00000i) q^{79} +(-1.22474 + 1.22474i) q^{82} +(-6.57201 - 1.76097i) q^{83} +(5.59808 + 3.23205i) q^{86} +(-0.896575 + 3.34607i) q^{88} -8.66025 q^{89} -1.60770 q^{91} +(2.12132 - 7.91688i) q^{92} +(5.19615 + 3.00000i) q^{94} +(14.1607 + 3.79435i) q^{97} +(3.81294 - 3.81294i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times$.

$n$	$1001$	$1027$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.22474	−	0.328169i	−0.462910	−	0.124036i	0.0198238	−	0.999803i	$-0.493689\pi$
$7$	−1.22474	−	0.328169i	−0.462910	−	0.124036i	−0.482734	+	0.875767i	$0.660356\pi$
$8$	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
$13$	1.22474	−	0.328169i	0.339683	−	0.0910178i	−0.0849451	−	0.996386i	$-0.527071\pi$
$13$	1.22474	−	0.328169i	0.339683	−	0.0910178i	0.424628	+	0.905368i	$0.360405\pi$
$14$	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	$-0.250000\pi$
$17$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$18$		0			0
$19$		−	7.19615i		−	1.65091i	−0.564467	−	0.825455i	$-0.690918\pi$
$19$		−	7.19615i		−	1.65091i	0.564467	−	0.825455i	$-0.309082\pi$
$20$		0			0
$21$		0			0
$22$	−0.896575	−	3.34607i	−0.191151	−	0.713384i
$23$	2.12132	+	7.91688i	0.442326	+	1.65078i	0.722902	+	0.690951i	$0.242808\pi$
$23$	2.12132	+	7.91688i	0.442326	+	1.65078i	−0.280576	+	0.959832i	$0.590525\pi$
$24$		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	$-0.930891\pi$
$29$	−3.63397	−	6.29423i	−0.674812	−	1.16881i	0.301712	−	0.953399i	$-0.402442\pi$
$30$		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	$-0.201650\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.55291	+	1.55291i	−0.255298	+	0.255298i	−0.823138	−	0.567841i	$-0.807779\pi$
$37$	−1.55291	+	1.55291i	−0.255298	+	0.255298i	0.567841	+	0.823138i	$0.307779\pi$
$38$	6.95095	+	1.86250i	1.12759	+	0.302138i
$39$		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
$43$	1.67303	−	6.24384i	0.255135	−	0.952177i	−0.712880	−	0.701286i	$-0.752610\pi$
$43$	1.67303	−	6.24384i	0.255135	−	0.952177i	0.968015	−	0.250891i	$-0.0807237\pi$
$44$	3.46410			0.522233
$45$		0			0
$46$	−8.19615			−1.20846
$47$	1.55291	−	5.79555i	0.226516	−	0.845369i	−0.755276	−	0.655407i	$-0.772497\pi$
$47$	1.55291	−	5.79555i	0.226516	−	0.845369i	0.981792	−	0.189961i	$-0.0608363\pi$
$48$		0			0
$49$	−4.66987	−	2.69615i	−0.667125	−	0.385165i
$50$		0			0
$51$		0			0
$52$	−1.22474	−	0.328169i	−0.169842	−	0.0455089i
$53$	−1.55291	+	1.55291i	−0.213309	+	0.213309i	−0.805672	−	0.592362i	$-0.798195\pi$
$53$	−1.55291	+	1.55291i	−0.213309	+	0.213309i	0.592362	+	0.805672i	$0.298195\pi$
$54$		0			0
$55$		0			0
$56$	−1.09808	+	0.633975i	−0.146737	+	0.0847184i
$57$		0			0
$58$	7.02030	−	1.88108i	0.921811	−	0.246998i
$59$	6.23205	−	10.7942i	0.811344	−	1.40529i	−0.100580	−	0.994929i	$-0.532070\pi$
$59$	6.23205	−	10.7942i	0.811344	−	1.40529i	0.911924	−	0.410360i	$-0.134597\pi$
$60$		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
$67$	−3.22595	−	12.0394i	−0.394112	−	1.47085i	−0.823287	−	0.567625i	$-0.807862\pi$
$67$	−3.22595	−	12.0394i	−0.394112	−	1.47085i	0.429175	−	0.903221i	$-0.358804\pi$
$68$		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	$-0.151650\pi$
$73$	3.67423	+	3.67423i	0.430037	+	0.430037i	−0.458604	+	0.888641i	$0.651650\pi$
$74$	−1.09808	−	1.90192i	−0.127649	−	0.221094i
$75$		0			0
$76$	−3.59808	+	6.23205i	−0.412728	+	0.714865i
$77$	4.24264	−	1.13681i	0.483494	−	0.129552i
$78$		0			0
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.900561	−	0.434730i	$-0.856844\pi$
$79$	−8.66025	+	5.00000i	−0.974355	+	0.562544i	−0.0737937	+	0.997274i	$0.523511\pi$
$80$		0			0
$81$		0			0
$82$	−1.22474	+	1.22474i	−0.135250	+	0.135250i
$83$	−6.57201	−	1.76097i	−0.721372	−	0.193291i	−0.120588	−	0.992703i	$-0.538478\pi$
$83$	−6.57201	−	1.76097i	−0.721372	−	0.193291i	−0.600784	+	0.799412i	$0.705145\pi$
$84$		0			0
$85$		0			0
$86$	5.59808	+	3.23205i	0.603656	+	0.348521i
$87$		0			0
$88$	−0.896575	+	3.34607i	−0.0955753	+	0.356692i
$89$	−8.66025			−0.917985			−0.458993	−	0.888440i	$-0.651790\pi$
$89$	−8.66025			−0.917985			−0.458993	+	0.888440i	$0.651790\pi$
$90$		0			0
$91$	−1.60770			−0.168532
$92$	2.12132	−	7.91688i	0.221163	−	0.825391i
$93$		0			0
$94$	5.19615	+	3.00000i	0.535942	+	0.309426i
$95$		0			0
$96$		0			0
$97$	14.1607	+	3.79435i	1.43780	+	0.385258i	0.891764	−	0.452501i	$-0.149468\pi$
$97$	14.1607	+	3.79435i	1.43780	+	0.385258i	0.546039	+	0.837760i	$0.316135\pi$
$98$	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
$103$	10.0382	−	2.68973i	0.989093	−	0.265027i	0.272223	−	0.962234i	$-0.412241\pi$
$103$	10.0382	−	2.68973i	0.989093	−	0.265027i	0.716869	+	0.697207i	$0.245574\pi$
$104$	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	$-0.237629\pi$
$107$	0.568406	+	0.568406i	0.0549499	+	0.0549499i	−0.679098	+	0.734048i	$0.737629\pi$
$108$		0			0
$109$		−	12.1962i		−	1.16818i	−0.811689	−	0.584090i	$-0.801452\pi$
$109$		−	12.1962i		−	1.16818i	0.811689	−	0.584090i	$-0.198548\pi$
$110$		0			0
$111$		0			0
$112$	−0.328169	−	1.22474i	−0.0310091	−	0.115728i
$113$	1.91327	+	7.14042i	0.179985	+	0.671714i	0.995649	+	0.0931872i	$0.0297055\pi$
$113$	1.91327	+	7.14042i	0.179985	+	0.671714i	−0.815663	+	0.578527i	$0.803628\pi$
$114$		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
$122$	−3.86370	+	1.03528i	−0.349803	+	0.0937295i
$123$		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	$-0.781065\pi$
$127$	−1.55291	+	1.55291i	−0.137799	+	0.137799i	0.634843	+	0.772641i	$0.281065\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		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
$133$	−2.36156	+	8.81345i	−0.204773	+	0.764223i
$134$	12.4641			1.07673
$135$		0			0
$136$		0			0
$137$	1.91327	−	7.14042i	0.163462	−	0.610047i	−0.834770	−	0.550599i	$-0.814399\pi$
$137$	1.91327	−	7.14042i	0.163462	−	0.610047i	0.998231	−	0.0594480i	$-0.0189340\pi$
$138$		0			0
$139$	6.92820	+	4.00000i	0.587643	+	0.339276i	0.764165	−	0.645021i	$-0.223151\pi$
$139$	6.92820	+	4.00000i	0.587643	+	0.339276i	−0.176522	+	0.984297i	$0.556485\pi$
$140$		0			0
$141$		0			0
$142$	10.3664	+	2.77766i	0.869926	+	0.233096i
$143$	−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
$148$	2.12132	−	0.568406i	0.174371	−	0.0467227i
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	0.216394	+	0.976306i	$0.430570\pi$
$149$	−9.00000	+	15.5885i	−0.737309	+	1.27706i	−0.953703	+	0.300750i	$0.902763\pi$
$150$		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
$157$	−2.03339	−	7.58871i	−0.162282	−	0.605645i	−0.998371	−	0.0570512i	$-0.981830\pi$
$157$	−2.03339	−	7.58871i	−0.162282	−	0.605645i	0.836089	−	0.548593i	$-0.184837\pi$
$158$	−2.58819	−	9.65926i	−0.205905	−	0.768449i
$159$		0			0
$160$		0			0
$161$		−	10.3923i		−	0.819028i
$162$		0			0
$163$	−14.3688	−	14.3688i	−1.12545	−	1.12545i	−0.990908	−	0.134541i	$-0.957044\pi$
$163$	−14.3688	−	14.3688i	−1.12545	−	1.12545i	−0.134541	−	0.990908i	$-0.542956\pi$
$164$	−0.866025	−	1.50000i	−0.0676252	−	0.117130i
$165$		0			0
$166$	3.40192	−	5.89230i	0.264040	−	0.457332i
$167$	−4.24264	+	1.13681i	−0.328305	+	0.0879692i	−0.419207	−	0.907891i	$-0.637692\pi$
$167$	−4.24264	+	1.13681i	−0.328305	+	0.0879692i	0.0909015	+	0.995860i	$0.471025\pi$
$168$		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
$173$	−4.24264	−	1.13681i	−0.322562	−	0.0864302i	0.0939047	−	0.995581i	$-0.470065\pi$
$173$	−4.24264	−	1.13681i	−0.322562	−	0.0864302i	−0.416467	+	0.909151i	$0.636732\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000	−	1.73205i	−0.226134	−	0.130558i
$177$		0			0
$178$	2.24144	−	8.36516i	0.168003	−	0.626995i
$179$	4.85641			0.362985			0.181492	−	0.983392i	$-0.441907\pi$
$179$	4.85641			0.362985			0.181492	+	0.983392i	$0.441907\pi$
$180$		0			0
$181$	8.39230			0.623795			0.311898	−	0.950116i	$-0.399035\pi$
$181$	8.39230			0.623795			0.311898	+	0.950116i	$0.399035\pi$
$182$	0.416102	−	1.55291i	0.0308435	−	0.115110i
$183$		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
$193$	−24.0788	+	6.45189i	−1.73323	+	0.464417i	−0.980923	−	0.194396i	$-0.937725\pi$
$193$	−24.0788	+	6.45189i	−1.73323	+	0.464417i	−0.752306	+	0.658813i	$0.771059\pi$
$194$	−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	$-0.293266\pi$
$197$	−2.68973	−	2.68973i	−0.191635	−	0.191635i	−0.796402	+	0.604767i	$0.793266\pi$
$198$		0			0
$199$			0.392305i			0.0278098i	0.999903	+	0.0139049i	$0.00442620\pi$
$199$			0.392305i			0.0278098i	−0.999903	+	0.0139049i	$0.995574\pi$
$200$		0			0
$201$		0			0
$202$	2.77766	+	10.3664i	0.195435	+	0.729375i
$203$	2.38512	+	8.90138i	0.167403	+	0.624755i
$204$		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	$0.0641440\pi$
$212$	2.12132	−	0.568406i	0.145693	−	0.0390383i
$213$		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
$218$	11.7806	+	3.15660i	0.797881	+	0.213792i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−2.44949	+	9.14162i	−0.164030	+	0.612168i	0.834132	+	0.551565i	$0.185969\pi$
$223$	−2.44949	+	9.14162i	−0.164030	+	0.612168i	−0.998162	+	0.0606032i	$0.980698\pi$
$224$	1.26795			0.0847184
$225$		0			0
$226$	−7.39230			−0.491729
$227$	−6.00361	+	22.4058i	−0.398473	+	1.48712i	0.417310	+	0.908764i	$0.362973\pi$
$227$	−6.00361	+	22.4058i	−0.398473	+	1.48712i	−0.815783	+	0.578358i	$0.803694\pi$
$228$		0			0
$229$	14.0263	+	8.09808i	0.926883	+	0.535136i	0.885824	−	0.464021i	$-0.153594\pi$
$229$	14.0263	+	8.09808i	0.926883	+	0.535136i	0.0410583	+	0.999157i	$0.486927\pi$
$230$		0			0
$231$		0			0
$232$	−7.02030	−	1.88108i	−0.460905	−	0.123499i
$233$	17.9551	−	17.9551i	1.17628	−	1.17628i	0.195590	−	0.980686i	$-0.437338\pi$
$233$	17.9551	−	17.9551i	1.17628	−	1.17628i	0.980686	−	0.195590i	$-0.0626622\pi$
$234$		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	−0.539779	−	0.841807i	$-0.681492\pi$
$239$	7.09808	−	12.2942i	0.459136	−	0.795248i	0.998916	+	0.0465591i	$0.0148256\pi$
$240$		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
$247$	−2.36156	−	8.81345i	−0.150262	−	0.560786i
$248$	−2.63896	−	9.84873i	−0.167574	−	0.625395i
$249$		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
$257$	4.45069	−	1.19256i	0.277627	−	0.0743898i	−0.117319	−	0.993094i	$-0.537430\pi$
$257$	4.45069	−	1.19256i	0.277627	−	0.0743898i	0.394946	+	0.918704i	$0.370763\pi$
$258$		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
$263$	−17.9551	−	4.81105i	−1.10716	−	0.296662i	−0.341481	−	0.939889i	$-0.610929\pi$
$263$	−17.9551	−	4.81105i	−1.10716	−	0.296662i	−0.765676	+	0.643227i	$0.777595\pi$
$264$		0			0
$265$		0			0
$266$	−7.90192	−	4.56218i	−0.484498	−	0.279725i
$267$		0			0
$268$	−3.22595	+	12.0394i	−0.197056	+	0.735423i
$269$	−28.0526			−1.71039			−0.855197	−	0.518303i	$-0.826564\pi$
$269$	−28.0526			−1.71039			−0.855197	+	0.518303i	$0.826564\pi$
$270$		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
$277$	24.6472	+	6.60420i	1.48091	+	0.396808i	0.906656	−	0.421871i	$-0.138627\pi$
$277$	24.6472	+	6.60420i	1.48091	+	0.396808i	0.574251	+	0.818679i	$0.305293\pi$
$278$	−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
$283$	−9.58991	+	2.56961i	−0.570061	+	0.152747i	−0.532325	−	0.846540i	$-0.678681\pi$
$283$	−9.58991	+	2.56961i	−0.570061	+	0.152747i	−0.0377364	+	0.999288i	$0.512015\pi$
$284$	−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
$292$	−1.34486	−	5.01910i	−0.0787022	−	0.293720i
$293$	−3.67423	−	13.7124i	−0.214651	−	0.801089i	−0.986289	−	0.165027i	$-0.947229\pi$
$293$	−3.67423	−	13.7124i	−0.214651	−	0.801089i	0.771638	−	0.636062i	$-0.219438\pi$
$294$		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
$302$	−7.72741	+	2.07055i	−0.444662	+	0.119147i
$303$		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	$-0.781517\pi$
$307$	−2.44949	+	2.44949i	−0.139800	+	0.139800i	0.633743	+	0.773543i	$0.281517\pi$
$308$	−4.24264	−	1.13681i	−0.241747	−	0.0647759i
$309$		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
$313$	−0.864390	+	3.22595i	−0.0488582	+	0.182341i	−0.986043	−	0.166493i	$-0.946756\pi$
$313$	−0.864390	+	3.22595i	−0.0488582	+	0.182341i	0.937184	+	0.348834i	$0.113422\pi$
$314$	7.85641			0.443363
$315$		0			0
$316$	10.0000			0.562544
$317$	−6.36396	+	23.7506i	−0.357436	+	1.33397i	0.519956	+	0.854193i	$0.325948\pi$
$317$	−6.36396	+	23.7506i	−0.357436	+	1.33397i	−0.877392	+	0.479775i	$0.840718\pi$
$318$		0			0
$319$	21.8038	+	12.5885i	1.22078	+	0.704818i
$320$		0			0
$321$		0			0
$322$	10.0382	+	2.68973i	0.559407	+	0.149893i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	17.5981	−	10.1603i	0.974667	−	0.562724i
$327$		0			0
$328$	1.67303	−	0.448288i	0.0923778	−	0.0247525i
$329$	−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
$337$	7.10823	+	26.5283i	0.387210	+	1.44509i	0.834653	+	0.550775i	$0.185668\pi$
$337$	7.10823	+	26.5283i	0.387210	+	1.44509i	−0.447443	+	0.894312i	$0.647665\pi$
$338$	−2.94855	−	11.0041i	−0.160380	−	0.598545i
$339$		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
$347$	−31.6675	+	8.48528i	−1.70000	+	0.455514i	−0.972940	−	0.231059i	$-0.925781\pi$
$347$	−31.6675	+	8.48528i	−1.70000	+	0.455514i	−0.727061	+	0.686573i	$0.759114\pi$
$348$		0			0
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$		0			0
$351$		0			0
$352$	2.44949	−	2.44949i	0.130558	−	0.130558i
$353$	−14.4889	−	3.88229i	−0.771166	−	0.206633i	−0.148279	−	0.988946i	$-0.547373\pi$
$353$	−14.4889	−	3.88229i	−0.771166	−	0.206633i	−0.622886	+	0.782312i	$0.714040\pi$
$354$		0			0
$355$		0			0
$356$	7.50000	+	4.33013i	0.397499	+	0.229496i
$357$		0			0
$358$	−1.25693	+	4.69093i	−0.0664308	+	0.247923i
$359$	0.679492			0.0358622			0.0179311	−	0.999839i	$-0.494292\pi$
$359$	0.679492			0.0358622			0.0179311	+	0.999839i	$0.494292\pi$
$360$		0			0
$361$	−32.7846			−1.72551
$362$	−2.17209	+	8.10634i	−0.114162	+	0.426060i
$363$		0			0
$364$	1.39230	+	0.803848i	0.0729766	+	0.0421331i
$365$		0			0
$366$		0			0
$367$	−30.7709	−	8.24504i	−1.60623	−	0.430388i	−0.659313	−	0.751868i	$-0.729153\pi$
$367$	−30.7709	−	8.24504i	−1.60623	−	0.430388i	−0.946916	+	0.321481i	$0.895819\pi$
$368$	−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
$373$	10.9348	−	2.92996i	0.566181	−	0.151708i	0.0356365	−	0.999365i	$-0.488654\pi$
$373$	10.9348	−	2.92996i	0.566181	−	0.151708i	0.530545	+	0.847657i	$0.321987\pi$
$374$		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	$0.175464\pi$
$379$			20.3923i			1.04748i	−0.851877	+	0.523741i	$0.824536\pi$
$380$		0			0
$381$		0			0
$382$	−0.896575	−	3.34607i	−0.0458728	−	0.171200i
$383$	−9.46979	−	35.3417i	−0.483884	−	1.80588i	−0.585036	−	0.811007i	$-0.698920\pi$
$383$	−9.46979	−	35.3417i	−0.483884	−	1.80588i	0.101152	−	0.994871i	$-0.467747\pi$
$384$		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	0.967158	−	0.254177i	$-0.0818045\pi$
$389$	5.19615	+	9.00000i	0.263455	+	0.456318i	−0.703702	+	0.710495i	$0.748471\pi$
$390$		0			0
$391$		0			0
$392$	−5.20857	+	1.39563i	−0.263072	+	0.0704900i
$393$		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	$-0.818715\pi$
$397$	−6.03579	+	6.03579i	−0.302928	+	0.302928i	0.539231	+	0.842158i	$0.318715\pi$
$398$	−0.378937	−	0.101536i	−0.0189944	−	0.00508954i
$399$		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
$403$	3.34607	−	12.4877i	0.166679	−	0.622056i
$404$	−10.7321			−0.533939
$405$		0			0
$406$	−9.21539			−0.457352
$407$	1.96902	−	7.34847i	0.0976005	−	0.364250i
$408$		0			0
$409$	0.526279	+	0.303848i	0.0260228	+	0.0150243i	0.512955	−	0.858416i	$-0.328551\pi$
$409$	0.526279	+	0.303848i	0.0260228	+	0.0150243i	−0.486932	+	0.873440i	$0.661884\pi$
$410$		0			0
$411$		0			0
$412$	−10.0382	−	2.68973i	−0.494546	−	0.132513i
$413$	−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
$418$	−24.0788	+	6.45189i	−1.17773	+	0.315572i
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	−0.734919	−	0.678155i	$-0.762780\pi$
$419$	4.50000	−	7.79423i	0.219839	−	0.380773i	0.954759	+	0.297382i	$0.0961133\pi$
$420$		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
$427$	−1.31268	−	4.89898i	−0.0635249	−	0.237078i
$428$	−0.208051	−	0.776457i	−0.0100565	−	0.0375315i
$429$		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	0.998629	+	0.0523546i	$0.0166726\pi$
$433$	21.8695	+	21.8695i	1.05098	+	1.05098i	0.0523546	+	0.998629i	$0.483327\pi$
$434$	−6.46410	−	11.1962i	−0.310287	−	0.537433i
$435$		0			0
$436$	−6.09808	+	10.5622i	−0.292045	+	0.505837i
$437$	56.9710	−	15.2653i	2.72529	−	0.730240i
$438$		0			0
$439$	28.2224	−	16.2942i	1.34698	−	0.777681i	0.359162	−	0.933275i	$-0.383063\pi$
$439$	28.2224	−	16.2942i	1.34698	−	0.777681i	0.987821	+	0.155594i	$0.0497292\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.0382	+	2.68973i	0.476929	+	0.127793i	0.489272	−	0.872131i	$-0.337262\pi$
$443$	10.0382	+	2.68973i	0.476929	+	0.127793i	−0.0123433	+	0.999924i	$0.503929\pi$
$444$		0			0
$445$		0			0
$446$	−8.19615	−	4.73205i	−0.388099	−	0.224069i
$447$		0			0
$448$	−0.328169	+	1.22474i	−0.0155045	+	0.0578638i
$449$	−5.87564			−0.277289			−0.138644	−	0.990342i	$-0.544275\pi$
$449$	−5.87564			−0.277289			−0.138644	+	0.990342i	$0.544275\pi$
$450$		0			0
$451$	−6.00000			−0.282529
$452$	1.91327	−	7.14042i	0.0899926	−	0.335857i
$453$		0			0
$454$	−20.0885	−	11.5981i	−0.942798	−	0.544325i
$455$		0			0
$456$		0			0
$457$	−3.46618	−	0.928761i	−0.162141	−	0.0434456i	0.176835	−	0.984240i	$-0.443414\pi$
$457$	−3.46618	−	0.928761i	−0.162141	−	0.0434456i	−0.338976	+	0.940795i	$0.610081\pi$
$458$	−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
$463$	7.91688	−	2.12132i	0.367928	−	0.0985861i	−0.0701175	−	0.997539i	$-0.522337\pi$
$463$	7.91688	−	2.12132i	0.367928	−	0.0985861i	0.438046	+	0.898953i	$0.355671\pi$
$464$	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	$-0.416482\pi$
$467$	−15.2653	−	15.2653i	−0.706396	−	0.706396i	−0.965775	+	0.259380i	$0.916482\pi$
$468$		0			0
$469$			15.8038i			0.729754i
$470$		0			0
$471$		0			0
$472$	−3.22595	−	12.0394i	−0.148486	−	0.554158i
$473$	5.79555	+	21.6293i	0.266480	+	0.994517i
$474$		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	0.517202	−	0.855863i	$-0.326974\pi$
$479$	−10.5622	−	18.2942i	−0.482598	−	0.835885i	−0.999800	+	0.0199786i	$0.993640\pi$
$480$		0			0
$481$	−1.39230	+	2.41154i	−0.0634836	+	0.109957i
$482$	−11.0041	+	2.94855i	−0.501224	+	0.134303i
$483$		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	$-0.916537\pi$
$487$	−15.5935	+	15.5935i	−0.706610	+	0.706610i	0.259211	+	0.965821i	$0.416537\pi$
$488$	3.86370	+	1.03528i	0.174902	+	0.0468648i
$489$		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
$497$	−3.52193	+	13.1440i	−0.157980	+	0.589590i
$498$		0			0
$499$	16.9641	+	9.79423i	0.759417	+	0.438450i	0.829087	−	0.559120i	$-0.188861\pi$
$499$	16.9641	+	9.79423i	0.759417	+	0.438450i	−0.0696691	+	0.997570i	$0.522194\pi$
$500$		0			0
$501$		0			0
$502$	8.69333	+	2.32937i	0.388002	+	0.103965i
$503$	25.8719	−	25.8719i	1.15357	−	1.15357i	0.167742	−	0.985831i	$-0.446352\pi$
$503$	25.8719	−	25.8719i	1.15357	−	1.15357i	0.985831	−	0.167742i	$-0.0536476\pi$
$504$		0			0
$505$		0			0
$506$	24.5885	−	14.1962i	1.09309	−	0.631096i
$507$		0			0
$508$	2.12132	−	0.568406i	0.0941184	−	0.0252189i
$509$	10.3923	−	18.0000i	0.460631	−	0.797836i	−0.538362	−	0.842714i	$-0.680957\pi$
$509$	10.3923	−	18.0000i	0.460631	−	0.797836i	0.998992	+	0.0448779i	$0.0142899\pi$
$510$		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
$517$	5.37945	+	20.0764i	0.236588	+	0.882959i
$518$	0.720710	+	2.68973i	0.0316662	+	0.118180i
$519$		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	$-0.105390\pi$
$523$	14.1929	+	14.1929i	0.620612	+	0.620612i	−0.325076	+	0.945688i	$0.605390\pi$
$524$	−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
$533$	2.12132	+	0.568406i	0.0918846	+	0.0246204i
$534$		0			0
$535$		0			0
$536$	−10.7942	−	6.23205i	−0.466240	−	0.269184i
$537$		0			0
$538$	7.26054	−	27.0967i	0.313024	−	1.16822i
$539$	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	$0.414168\pi$
$542$	1.18758	−	4.43211i	0.0510109	−	0.190375i
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	21.4213	+	5.73981i	0.915907	+	0.245416i	0.685835	−	0.727757i	$-0.259437\pi$
$547$	21.4213	+	5.73981i	0.915907	+	0.245416i	0.230072	+	0.973174i	$0.426104\pi$
$548$	−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
$553$	12.2474	−	3.28169i	0.520814	−	0.139552i
$554$	−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	$-0.362895\pi$
$557$	−11.5911	−	11.5911i	−0.491131	−	0.491131i	−0.908662	+	0.417531i	$0.862895\pi$
$558$		0			0
$559$		−	8.19615i		−	0.346660i
$560$		0			0
$561$		0			0
$562$	−2.68973	−	10.0382i	−0.113459	−	0.423436i
$563$	8.69333	+	32.4440i	0.366380	+	1.36735i	0.865540	+	0.500840i	$0.166975\pi$
$563$	8.69333	+	32.4440i	0.366380	+	1.36735i	−0.499160	+	0.866510i	$0.666358\pi$
$564$		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	0.958419	−	0.285364i	$-0.0921146\pi$
$569$	5.53590	+	9.58846i	0.232077	+	0.401969i	−0.726342	+	0.687333i	$0.758781\pi$
$570$		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	$0.225641\pi$
$572$	4.24264	−	1.13681i	0.177394	−	0.0475325i
$573$		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	$-0.594726\pi$
$577$	15.9217	−	15.9217i	0.662828	−	0.662828i	0.956046	+	0.293217i	$0.0947260\pi$
$578$	16.4207	+	4.39992i	0.683013	+	0.183013i
$579$		0			0
$580$		0			0
$581$	7.47114	+	4.31347i	0.309955	+	0.178953i
$582$		0			0
$583$	1.96902	−	7.34847i	0.0815483	−	0.304342i
$584$	5.19615			0.215018
$585$		0			0
$586$	14.1962			0.586438
$587$	4.24264	−	15.8338i	0.175113	−	0.653529i	−0.821420	−	0.570324i	$-0.806818\pi$
$587$	4.24264	−	15.8338i	0.175113	−	0.653529i	0.996532	−	0.0832050i	$-0.0265156\pi$
$588$		0			0
$589$	−63.5429	−	36.6865i	−2.61824	−	1.51164i
$590$		0			0
$591$		0			0
$592$	−2.12132	−	0.568406i	−0.0871857	−	0.0233613i
$593$	−14.8492	+	14.8492i	−0.609785	+	0.609785i	−0.942890	−	0.333105i	$-0.891904\pi$
$593$	−14.8492	+	14.8492i	−0.609785	+	0.609785i	0.333105	+	0.942890i	$0.391904\pi$
$594$		0			0
$595$		0			0
$596$	15.5885	−	9.00000i	0.638528	−	0.368654i
$597$		0			0
$598$	−10.0382	+	2.68973i	−0.410492	+	0.109991i
$599$	5.36603	−	9.29423i	0.219250	−	0.379752i	−0.735329	−	0.677710i	$-0.762972\pi$
$599$	5.36603	−	9.29423i	0.219250	−	0.379752i	0.954579	+	0.297958i	$0.0963057\pi$
$600$		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
$607$	−4.50644	−	16.8183i	−0.182911	−	0.682632i	−0.995068	−	0.0991937i	$-0.968374\pi$
$607$	−4.50644	−	16.8183i	−0.182911	−	0.682632i	0.812157	−	0.583438i	$-0.198293\pi$
$608$	1.86250	+	6.95095i	0.0755344	+	0.281898i
$609$		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	$-0.225524\pi$
$613$	2.68973	+	2.68973i	0.108637	+	0.108637i	−0.650699	+	0.759336i	$0.725524\pi$
$614$	−1.73205	−	3.00000i	−0.0698999	−	0.121070i
$615$		0			0
$616$	2.19615	−	3.80385i	0.0884855	−	0.153261i
$617$	28.7697	−	7.70882i	1.15823	−	0.310346i	0.371969	−	0.928245i	$-0.378683\pi$
$617$	28.7697	−	7.70882i	1.15823	−	0.310346i	0.786257	+	0.617900i	$0.212016\pi$
$618$		0			0
$619$	14.2128	−	8.20577i	0.571261	−	0.329818i	−0.186392	−	0.982476i	$-0.559679\pi$
$619$	14.2128	−	8.20577i	0.571261	−	0.329818i	0.757653	+	0.652658i	$0.226346\pi$
$620$		0			0
$621$		0			0
$622$	17.6269	−	17.6269i	0.706774	−	0.706774i
$623$	10.6066	+	2.84203i	0.424945	+	0.113864i
$624$		0			0
$625$		0			0
$626$	−2.89230	−	1.66987i	−0.115600	−	0.0667415i
$627$		0			0
$628$	−2.03339	+	7.58871i	−0.0811410	+	0.302822i
$629$		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	$0.198485\pi$
$632$	−2.58819	+	9.65926i	−0.102953	+	0.384225i
$633$		0			0
$634$	−21.2942	−	12.2942i	−0.845702	−	0.488266i
$635$		0			0
$636$		0			0
$637$	−6.60420	−	1.76959i	−0.261668	−	0.0701137i
$638$	−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
$643$	16.0418	−	4.29839i	0.632627	−	0.169512i	0.0717654	−	0.997422i	$-0.477137\pi$
$643$	16.0418	−	4.29839i	0.632627	−	0.169512i	0.560861	+	0.827910i	$0.310470\pi$
$644$	−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	$-0.226177\pi$
$647$	2.68973	+	2.68973i	0.105744	+	0.105744i	−0.652255	+	0.757999i	$0.726177\pi$
$648$		0			0
$649$			43.1769i			1.69484i
$650$		0			0
$651$		0			0
$652$	5.25933	+	19.6281i	0.205971	+	0.768696i
$653$	−0.568406	−	2.12132i	−0.0222434	−	0.0830137i	0.953912	−	0.300087i	$-0.0970157\pi$
$653$	−0.568406	−	2.12132i	−0.0222434	−	0.0830137i	−0.976155	+	0.217073i	$0.930349\pi$
$654$		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	0.997041	−	0.0768747i	$-0.0244941\pi$
$659$	11.0885	+	19.2058i	0.431945	+	0.748151i	−0.565096	+	0.825025i	$0.691161\pi$
$660$		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	$0.315506\pi$
$662$	16.9891	−	4.55223i	0.660302	−	0.176927i
$663$		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
$668$	4.24264	+	1.13681i	0.164153	+	0.0439846i
$669$		0			0
$670$		0			0
$671$	−12.0000	−	6.92820i	−0.463255	−	0.267460i
$672$		0			0
$673$	−0.416102	+	1.55291i	−0.0160396	+	0.0598604i	−0.973482	−	0.228765i	$-0.926531\pi$
$673$	−0.416102	+	1.55291i	−0.0160396	+	0.0598604i	0.957442	+	0.288625i	$0.0931981\pi$
$674$	−27.4641			−1.05788
$675$		0			0
$676$	11.3923			0.438166
$677$	1.70522	−	6.36396i	0.0655369	−	0.244587i	−0.925384	−	0.379030i	$-0.876258\pi$
$677$	1.70522	−	6.36396i	0.0655369	−	0.244587i	0.990921	+	0.134443i	$0.0429245\pi$
$678$		0			0
$679$	−16.0981	−	9.29423i	−0.617787	−	0.356680i
$680$		0			0
$681$		0			0
$682$	−34.1170	−	9.14162i	−1.30641	−	0.350051i
$683$	27.9933	−	27.9933i	1.07113	−	1.07113i	0.0738643	−	0.997268i	$-0.476467\pi$
$683$	27.9933	−	27.9933i	1.07113	−	1.07113i	0.997268	−	0.0738643i	$-0.0235332\pi$
$684$		0			0
$685$		0			0
$686$	−13.6077	+	7.85641i	−0.519544	+	0.299959i
$687$		0			0
$688$	6.24384	−	1.67303i	0.238044	−	0.0637838i
$689$	−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
$698$	−0.517638	−	1.93185i	−0.0195929	−	0.0731217i
$699$		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
$707$	−13.1440	+	3.52193i	−0.494332	+	0.132456i
$708$		0			0
$709$	22.3468	−	12.9019i	0.839251	−	0.484542i	−0.0177584	−	0.999842i	$-0.505653\pi$
$709$	22.3468	−	12.9019i	0.839251	−	0.484542i	0.857010	+	0.515300i	$0.172320\pi$
$710$		0			0
$711$		0			0
$712$	−6.12372	+	6.12372i	−0.229496	+	0.229496i
$713$	80.7217	+	21.6293i	3.02305	+	0.810024i
$714$		0			0
$715$		0			0
$716$	−4.20577	−	2.42820i	−0.157177	−	0.0907462i
$717$		0			0
$718$	−0.175865	+	0.656339i	−0.00656324	+	0.0244943i
$719$	39.1244			1.45909			0.729546	−	0.683932i	$-0.239731\pi$
$719$	39.1244			1.45909			0.729546	+	0.683932i	$0.239731\pi$
$720$		0			0
$721$	−13.1769			−0.490734
$722$	8.48528	−	31.6675i	0.315789	−	1.17854i
$723$		0			0
$724$	−7.26795	−	4.19615i	−0.270111	−	0.155949i
$725$		0			0
$726$		0			0
$727$	−6.69213	−	1.79315i	−0.248197	−	0.0665043i	0.132575	−	0.991173i	$-0.457675\pi$
$727$	−6.69213	−	1.79315i	−0.248197	−	0.0665043i	−0.380773	+	0.924669i	$0.624342\pi$
$728$	−1.13681	+	1.13681i	−0.0421331	+	0.0421331i
$729$		0			0
$730$		0			0
$731$		0			0
$732$		0			0
$733$	33.2204	−	8.90138i	1.22702	−	0.328780i	0.413604	−	0.910457i	$-0.364270\pi$
$733$	33.2204	−	8.90138i	1.22702	−	0.328780i	0.813420	+	0.581677i	$0.197603\pi$
$734$	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	$-0.931630\pi$
$739$		−	11.5885i		−	0.426288i	0.977021	−	0.213144i	$-0.0683704\pi$
$740$		0			0
$741$		0			0
$742$	0.720710	+	2.68973i	0.0264581	+	0.0987430i
$743$	10.1905	+	38.0315i	0.373853	+	1.39524i	0.855013	+	0.518606i	$0.173549\pi$
$743$	10.1905	+	38.0315i	0.373853	+	1.39524i	−0.481160	+	0.876633i	$0.659784\pi$
$744$		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	$0.0440890\pi$
$752$	5.79555	−	1.55291i	0.211342	−	0.0566290i
$753$		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	$-0.662866\pi$
$757$	10.5187	−	10.5187i	0.382308	−	0.382308i	0.871933	+	0.489625i	$0.162866\pi$
$758$	−19.6975	−	5.27792i	−0.715444	−	0.191703i
$759$		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
$763$	−4.00240	+	14.9372i	−0.144897	+	0.540762i
$764$	3.46410			0.125327
$765$		0			0
$766$	36.5885			1.32199
$767$	4.09034	−	15.2653i	0.147693	−	0.551200i
$768$		0			0
$769$	−28.9186	−	16.6962i	−1.04283	−	0.602079i	−0.122197	−	0.992506i	$-0.538994\pi$
$769$	−28.9186	−	16.6962i	−1.04283	−	0.602079i	−0.920634	+	0.390427i	$0.872327\pi$
$770$		0			0
$771$		0			0
$772$	24.0788	+	6.45189i	0.866615	+	0.232209i
$773$	6.51626	−	6.51626i	0.234374	−	0.234374i	−0.580142	−	0.814516i	$-0.697003\pi$
$773$	6.51626	−	6.51626i	0.234374	−	0.234374i	0.814516	+	0.580142i	$0.197003\pi$
$774$		0			0
$775$		0			0
$776$	12.6962	−	7.33013i	0.455765	−	0.263136i
$777$		0			0
$778$	−10.0382	+	2.68973i	−0.359887	+	0.0964314i
$779$	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
$787$	−4.48288	−	16.7303i	−0.159797	−	0.596372i	−0.998647	−	0.0520081i	$-0.983438\pi$
$787$	−4.48288	−	16.7303i	−0.159797	−	0.596372i	0.838849	−	0.544364i	$-0.183229\pi$
$788$	0.984508	+	3.67423i	0.0350717	+	0.130889i
$789$		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
$797$	10.6066	−	2.84203i	0.375705	−	0.100670i	−0.0660248	−	0.997818i	$-0.521032\pi$
$797$	10.6066	−	2.84203i	0.375705	−	0.100670i	0.441730	+	0.897148i	$0.354365\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$	7.34847	−	7.34847i	0.259483	−	0.259483i
$803$	−17.3867	−	4.65874i	−0.613562	−	0.164403i
$804$		0			0
$805$		0			0
$806$	11.1962	+	6.46410i	0.394368	+	0.227688i
$807$		0			0
$808$	2.77766	−	10.3664i	0.0977177	−	0.364687i
$809$	−1.73205			−0.0608957			−0.0304478	−	0.999536i	$-0.509693\pi$
$809$	−1.73205			−0.0608957			−0.0304478	+	0.999536i	$0.509693\pi$
$810$		0			0
$811$	−38.3731			−1.34746			−0.673730	−	0.738977i	$-0.735309\pi$
$811$	−38.3731			−1.34746			−0.673730	+	0.738977i	$0.735309\pi$
$812$	2.38512	−	8.90138i	0.0837013	−	0.312377i
$813$		0			0
$814$	6.58846	+	3.80385i	0.230925	+	0.133325i
$815$		0			0
$816$		0			0
$817$	−44.9316	−	12.0394i	−1.57196	−	0.421205i
$818$	−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
$823$	−27.6651	+	7.41284i	−0.964345	+	0.258395i	−0.706438	−	0.707775i	$-0.749699\pi$
$823$	−27.6651	+	7.41284i	−0.964345	+	0.258395i	−0.257906	+	0.966170i	$0.583033\pi$
$824$	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	$-0.187638\pi$
$827$	7.91688	+	7.91688i	0.275297	+	0.275297i	−0.555931	+	0.831228i	$0.687638\pi$
$828$		0			0
$829$		−	2.58846i		−	0.0899008i	−0.998989	−	0.0449504i	$-0.985687\pi$
$829$		−	2.58846i		−	0.0899008i	0.998989	−	0.0449504i	$-0.0143130\pi$
$830$		0			0
$831$		0			0
$832$	−0.328169	−	1.22474i	−0.0113772	−	0.0424604i
$833$		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	$-0.983561\pi$
$839$	−15.7583	−	27.2942i	−0.544038	−	0.942301i	0.454629	−	0.890681i	$-0.349772\pi$
$840$		0			0
$841$	−11.9115	+	20.6314i	−0.410743	+	0.711427i
$842$	−8.29581	+	2.22286i	−0.285893	+	0.0766047i
$843$		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
$848$	−2.12132	−	0.568406i	−0.0728464	−	0.0195191i
$849$		0			0
$850$		0			0
$851$	−15.5885	−	9.00000i	−0.534365	−	0.308516i
$852$		0			0
$853$	13.8004	−	51.5037i	0.472515	−	1.76345i	−0.158169	−	0.987412i	$-0.550559\pi$
$853$	13.8004	−	51.5037i	0.472515	−	1.76345i	0.630684	−	0.776040i	$-0.282774\pi$
$854$	5.07180			0.173553
$855$		0			0
$856$	0.803848			0.0274749
$857$	−0.0557471	+	0.208051i	−0.00190429	+	0.00710689i	−0.966871	−	0.255264i	$-0.917838\pi$
$857$	−0.0557471	+	0.208051i	−0.00190429	+	0.00710689i	0.964967	+	0.262371i	$0.0845043\pi$
$858$		0			0
$859$	−9.01666	−	5.20577i	−0.307644	−	0.177619i	0.338227	−	0.941064i	$-0.390173\pi$
$859$	−9.01666	−	5.20577i	−0.307644	−	0.177619i	−0.645872	+	0.763446i	$0.723506\pi$
$860$		0			0
$861$		0			0
$862$	3.01790	+	0.808643i	0.102790	+	0.0275425i
$863$	3.52193	−	3.52193i	0.119888	−	0.119888i	−0.644617	−	0.764505i	$-0.722983\pi$
$863$	3.52193	−	3.52193i	0.119888	−	0.119888i	0.764505	+	0.644617i	$0.222983\pi$
$864$		0			0
$865$		0			0
$866$	−26.7846	+	15.4641i	−0.910178	+	0.525492i
$867$		0			0
$868$	12.4877	−	3.34607i	0.423860	−	0.113573i
$869$	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
$877$	5.97142	+	22.2856i	0.201641	+	0.752533i	0.990447	+	0.137892i	$0.0440325\pi$
$877$	5.97142	+	22.2856i	0.201641	+	0.752533i	−0.788807	+	0.614641i	$0.789301\pi$
$878$	8.43451	+	31.4780i	0.284651	+	1.06233i
$879$		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	$-0.240055\pi$
$883$	1.31268	+	1.31268i	0.0441751	+	0.0441751i	−0.684674	+	0.728849i	$0.740055\pi$
$884$		0			0
$885$		0			0
$886$	−5.19615	+	9.00000i	−0.174568	+	0.302361i
$887$	−10.0382	+	2.68973i	−0.337050	+	0.0903122i	−0.423374	−	0.905955i	$-0.639154\pi$
$887$	−10.0382	+	2.68973i	−0.337050	+	0.0903122i	0.0863246	+	0.996267i	$0.472488\pi$
$888$		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
$893$	−41.7057	−	11.1750i	−1.39563	−	0.373957i
$894$		0			0
$895$		0			0
$896$	−1.09808	−	0.633975i	−0.0366842	−	0.0211796i
$897$		0			0
$898$	1.52073	−	5.67544i	0.0507474	−	0.189392i
$899$	−74.1051			−2.47154
$900$		0			0
$901$		0			0
$902$	1.55291	−	5.79555i	0.0517064	−	0.192971i
$903$		0			0
$904$	6.40192	+	3.69615i	0.212925	+	0.122932i
$905$		0			0
$906$		0			0
$907$	−31.8756	−	8.54103i	−1.05841	−	0.283600i	−0.312687	−	0.949856i	$-0.601229\pi$
$907$	−31.8756	−	8.54103i	−1.05841	−	0.283600i	−0.745723	+	0.666256i	$0.767896\pi$
$908$	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
$913$	22.7661	−	6.10016i	0.753449	−	0.201886i
$914$	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	$0.149329\pi$
$919$			27.4115i			0.904223i	−0.891961	+	0.452112i	$0.850671\pi$
$920$		0			0
$921$		0			0
$922$	7.26054	+	27.0967i	0.239113	+	0.892382i
$923$	−3.52193	−	13.1440i	−0.115926	−	0.432641i
$924$		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	0.898009	−	0.439977i	$-0.145013\pi$
$929$	2.07180	+	3.58846i	0.0679734	+	0.117733i	−0.830036	+	0.557710i	$0.811680\pi$
$930$		0			0
$931$	−19.4019	+	33.6051i	−0.635872	+	1.10136i
$932$	−24.5271	+	6.57201i	−0.803411	+	0.215273i
$933$		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	$-0.681610\pi$
$937$	9.22955	−	9.22955i	0.301516	−	0.301516i	0.841607	+	0.540091i	$0.181610\pi$
$938$	−15.2653	−	4.09034i	−0.498431	−	0.133554i
$939$		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
$943$	−3.67423	+	13.7124i	−0.119650	+	0.446538i
$944$	12.4641			0.405672
$945$		0			0
$946$	−22.3923			−0.728037
$947$	−7.86113	+	29.3381i	−0.255452	+	0.953361i	0.712386	+	0.701788i	$0.247615\pi$
$947$	−7.86113	+	29.3381i	−0.255452	+	0.953361i	−0.967838	+	0.251573i	$0.919052\pi$
$948$		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	$-0.977002\pi$
$953$	−28.5617	+	28.5617i	−0.925203	+	0.925203i	0.0721877	+	0.997391i	$0.477002\pi$
$954$		0			0
$955$		0			0
$956$	−12.2942	+	7.09808i	−0.397624	+	0.229568i
$957$		0			0
$958$	20.4046	−	5.46739i	0.659241	−	0.176643i
$959$	−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
$967$	10.7589	+	40.1528i	0.345983	+	1.29123i	0.891460	+	0.453100i	$0.149682\pi$
$967$	10.7589	+	40.1528i	0.345983	+	1.29123i	−0.545476	+	0.838126i	$0.683651\pi$
$968$	−0.258819	−	0.965926i	−0.00831876	−	0.0310460i
$969$		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
$977$	−15.6257	+	4.18689i	−0.499910	+	0.133951i	−0.499958	−	0.866049i	$-0.666651\pi$
$977$	−15.6257	+	4.18689i	−0.499910	+	0.133951i	4.80066e−5		1.00000i	$0.499985\pi$
$978$		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
$983$	−18.5235	−	4.96335i	−0.590807	−	0.158306i	−0.0489851	−	0.998800i	$-0.515599\pi$
$983$	−18.5235	−	4.96335i	−0.590807	−	0.158306i	−0.541822	+	0.840493i	$0.682265\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−2.36156	+	8.81345i	−0.0751311	+	0.280393i
$989$	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	$0.323336\pi$
$992$	−2.63896	+	9.84873i	−0.0837870	+	0.312697i
$993$		0			0
$994$	−11.7846	−	6.80385i	−0.373785	−	0.215805i
$995$		0			0
$996$		0			0
$997$	−31.0991	−	8.33298i	−0.984918	−	0.263908i	−0.269804	−	0.962915i	$-0.586959\pi$
$997$	−31.0991	−	8.33298i	−0.984918	−	0.263908i	−0.715115	+	0.699007i	$0.753625\pi$
$998$	−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.d.1043.1		8
3.2	odd	2		450.2.p.c.293.2	yes	8
5.2	odd	4		1350.2.q.a.557.1		8
5.3	odd	4		1350.2.q.a.557.2		8
5.4	even	2	inner	1350.2.q.d.1043.2		8
9.2	odd	6		1350.2.q.a.143.1		8
9.7	even	3		450.2.p.e.443.2	yes	8
15.2	even	4		450.2.p.e.257.2	yes	8
15.8	even	4		450.2.p.e.257.1	yes	8
15.14	odd	2		450.2.p.c.293.1	✓	8
45.2	even	12	inner	1350.2.q.d.1007.1		8
45.7	odd	12		450.2.p.c.407.2	yes	8
45.29	odd	6		1350.2.q.a.143.2		8
45.34	even	6		450.2.p.e.443.1	yes	8
45.38	even	12	inner	1350.2.q.d.1007.2		8
45.43	odd	12		450.2.p.c.407.1	yes	8

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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