LMFDB - Embedded newform 2100.2.ce.d.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(157,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, 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:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.d.1993.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{3} +(0.728357 + 2.54352i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{3} +(0.728357 + 2.54352i) q^{7} +(0.866025 - 0.500000i) q^{9} +(2.14536 - 3.71588i) q^{11} +(-3.22938 - 3.22938i) q^{13} +(-0.923215 - 3.44549i) q^{17} +(-3.13437 - 5.42888i) q^{19} +(1.36185 + 2.26834i) q^{21} +(-2.79643 - 0.749302i) q^{23} +(0.707107 - 0.707107i) q^{27} +2.84333i q^{29} +(-1.34333 - 0.775572i) q^{31} +(1.11052 - 4.14453i) q^{33} +(1.47519 - 5.50550i) q^{37} +(-3.95516 - 2.28351i) q^{39} -10.7150i q^{41} +(-2.38553 + 2.38553i) q^{43} +(8.28905 + 2.22104i) q^{47} +(-5.93899 + 3.70518i) q^{49} +(-1.78351 - 3.08914i) q^{51} +(2.34836 + 8.76419i) q^{53} +(-4.43266 - 4.43266i) q^{57} +(-0.820799 + 1.42166i) q^{59} +(8.94331 - 5.16342i) q^{61} +(1.90254 + 1.83858i) q^{63} +(-4.46947 + 1.19759i) q^{67} -2.89508 q^{69} +11.7381 q^{71} +(8.97416 - 2.40462i) q^{73} +(11.0140 + 2.75029i) q^{77} +(6.68892 - 3.86185i) q^{79} +(0.500000 - 0.866025i) q^{81} +(3.32417 + 3.32417i) q^{83} +(0.735908 + 2.74645i) q^{87} +(-8.91203 - 15.4361i) q^{89} +(5.86185 - 10.5661i) q^{91} +(-1.49829 - 0.401465i) q^{93} +(0.100580 - 0.100580i) q^{97} -4.29073i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{11} + 8 q^{21} - 12 q^{31} - 8 q^{51} - 48 q^{61} + 64 q^{71} + 12 q^{81} + 116 q^{91}+O(q^{100}) $ 24 * q - 8 * q^11 + 8 * q^21 - 12 * q^31 - 8 * q^51 - 48 * q^61 + 64 * q^71 + 12 * q^81 + 116 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.728357	+	2.54352i	0.275293	+	0.961360i
$7$	0.728357	+	2.54352i	0.275293	+	0.961360i
$8$		0			0
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$		0			0
$11$	2.14536	−	3.71588i	0.646852	−	1.12038i	−0.337019	−	0.941498i	$-0.609419\pi$
$11$	2.14536	−	3.71588i	0.646852	−	1.12038i	0.983870	−	0.178882i	$-0.0572481\pi$
$12$		0			0
$13$	−3.22938	−	3.22938i	−0.895668	−	0.895668i	0.0993812	−	0.995049i	$-0.468314\pi$
$13$	−3.22938	−	3.22938i	−0.895668	−	0.895668i	−0.995049	+	0.0993812i	$0.968314\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.923215	−	3.44549i	−0.223913	−	0.835653i	−0.982837	−	0.184475i	$-0.940942\pi$
$17$	−0.923215	−	3.44549i	−0.223913	−	0.835653i	0.758925	−	0.651178i	$-0.225725\pi$
$18$		0			0
$19$	−3.13437	−	5.42888i	−0.719073	−	1.24547i	−0.961368	−	0.275268i	$-0.911233\pi$
$19$	−3.13437	−	5.42888i	−0.719073	−	1.24547i	0.242295	−	0.970203i	$-0.422100\pi$
$20$		0			0
$21$	1.36185	+	2.26834i	0.297180	+	0.494992i
$22$		0			0
$23$	−2.79643	−	0.749302i	−0.583097	−	0.156240i	−0.0448005	−	0.998996i	$-0.514265\pi$
$23$	−2.79643	−	0.749302i	−0.583097	−	0.156240i	−0.538296	+	0.842756i	$0.680932\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$		0			0
$29$			2.84333i			0.527993i	0.964524	+	0.263997i	$0.0850408\pi$
$29$			2.84333i			0.527993i	−0.964524	+	0.263997i	$0.914959\pi$
$30$		0			0
$31$	−1.34333	−	0.775572i	−0.241269	−	0.139297i	0.374491	−	0.927231i	$-0.377818\pi$
$31$	−1.34333	−	0.775572i	−0.241269	−	0.139297i	−0.615760	+	0.787934i	$0.711151\pi$
$32$		0			0
$33$	1.11052	−	4.14453i	0.193317	−	0.721469i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.47519	−	5.50550i	0.242520	−	0.905098i	−0.732093	−	0.681204i	$-0.761456\pi$
$37$	1.47519	−	5.50550i	0.242520	−	0.905098i	0.974614	−	0.223894i	$-0.0718769\pi$
$38$		0			0
$39$	−3.95516	−	2.28351i	−0.633333	−	0.365655i
$40$		0			0
$41$		−	10.7150i		−	1.67339i	−0.547665	−	0.836697i	$-0.684483\pi$
$41$		−	10.7150i		−	1.67339i	0.547665	−	0.836697i	$-0.315517\pi$
$42$		0			0
$43$	−2.38553	+	2.38553i	−0.363790	+	0.363790i	−0.865206	−	0.501416i	$-0.832813\pi$
$43$	−2.38553	+	2.38553i	−0.363790	+	0.363790i	0.501416	+	0.865206i	$0.332813\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	8.28905	+	2.22104i	1.20908	+	0.323973i	0.806402	−	0.591368i	$-0.201412\pi$
$47$	8.28905	+	2.22104i	1.20908	+	0.323973i	0.402681	+	0.915341i	$0.368079\pi$
$48$		0			0
$49$	−5.93899	+	3.70518i	−0.848428	+	0.529311i
$50$		0			0
$51$	−1.78351	−	3.08914i	−0.249742	−	0.432566i
$52$		0			0
$53$	2.34836	+	8.76419i	0.322572	+	1.20385i	0.916730	+	0.399506i	$0.130818\pi$
$53$	2.34836	+	8.76419i	0.322572	+	1.20385i	−0.594159	+	0.804348i	$0.702515\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.43266	−	4.43266i	−0.587120	−	0.587120i
$58$		0			0
$59$	−0.820799	+	1.42166i	−0.106859	+	0.185085i	−0.914496	−	0.404595i	$-0.867413\pi$
$59$	−0.820799	+	1.42166i	−0.106859	+	0.185085i	0.807637	+	0.589680i	$0.200746\pi$
$60$		0			0
$61$	8.94331	−	5.16342i	1.14507	−	0.661108i	0.197391	−	0.980325i	$-0.436753\pi$
$61$	8.94331	−	5.16342i	1.14507	−	0.661108i	0.947682	+	0.319216i	$0.103420\pi$
$62$		0			0
$63$	1.90254	+	1.83858i	0.239697	+	0.231639i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.46947	+	1.19759i	−0.546032	+	0.146309i	−0.521282	−	0.853385i	$-0.674546\pi$
$67$	−4.46947	+	1.19759i	−0.546032	+	0.146309i	−0.0247507	+	0.999694i	$0.507879\pi$
$68$		0			0
$69$	−2.89508			−0.348527
$70$		0			0
$71$	11.7381			1.39306			0.696530	−	0.717528i	$-0.254726\pi$
$71$	11.7381			1.39306			0.696530	+	0.717528i	$0.254726\pi$
$72$		0			0
$73$	8.97416	−	2.40462i	1.05035	−	0.281439i	0.307951	−	0.951402i	$-0.400357\pi$
$73$	8.97416	−	2.40462i	1.05035	−	0.281439i	0.742394	+	0.669963i	$0.233690\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.0140	+	2.75029i	1.25516	+	0.313425i
$78$		0			0
$79$	6.68892	−	3.86185i	0.752562	−	0.434492i	−0.0740567	−	0.997254i	$-0.523595\pi$
$79$	6.68892	−	3.86185i	0.752562	−	0.434492i	0.826619	+	0.562762i	$0.190261\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	3.32417	+	3.32417i	0.364875	+	0.364875i	0.865604	−	0.500729i	$-0.166935\pi$
$83$	3.32417	+	3.32417i	0.364875	+	0.364875i	−0.500729	+	0.865604i	$0.666935\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.735908	+	2.74645i	0.0788976	+	0.294450i
$88$		0			0
$89$	−8.91203	−	15.4361i	−0.944674	−	1.63622i	−0.756403	−	0.654105i	$-0.773045\pi$
$89$	−8.91203	−	15.4361i	−0.944674	−	1.63622i	−0.188270	−	0.982117i	$-0.560288\pi$
$90$		0			0
$91$	5.86185	−	10.5661i	0.614489	−	1.10763i
$92$		0			0
$93$	−1.49829	−	0.401465i	−0.155365	−	0.0416300i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.100580	−	0.100580i	0.0102123	−	0.0102123i	−0.701982	−	0.712194i	$-0.747701\pi$
$97$	0.100580	−	0.100580i	0.0102123	−	0.0102123i	0.712194	+	0.701982i	$0.247701\pi$
$98$		0			0
$99$		−	4.29073i		−	0.431235i
$100$		0			0
$101$	7.57834	+	4.37535i	0.754073	+	0.435364i	0.827164	−	0.561961i	$-0.189953\pi$
$101$	7.57834	+	4.37535i	0.754073	+	0.435364i	−0.0730910	+	0.997325i	$0.523286\pi$
$102$		0			0
$103$	0.851703	−	3.17860i	0.0839208	−	0.313197i	−0.911187	−	0.411993i	$-0.864833\pi$
$103$	0.851703	−	3.17860i	0.0839208	−	0.313197i	0.995108	+	0.0987966i	$0.0314993\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.43903	+	12.8346i	−0.332463	+	1.24077i	0.574130	+	0.818764i	$0.305341\pi$
$107$	−3.43903	+	12.8346i	−0.332463	+	1.24077i	−0.906593	+	0.422006i	$0.861326\pi$
$108$		0			0
$109$	−12.3886	−	7.15258i	−1.18662	−	0.685093i	−0.229080	−	0.973408i	$-0.573572\pi$
$109$	−12.3886	−	7.15258i	−1.18662	−	0.685093i	−0.957536	+	0.288315i	$0.906905\pi$
$110$		0			0
$111$		−	5.69971i		−	0.540993i
$112$		0			0
$113$	−9.12116	+	9.12116i	−0.858047	+	0.858047i	−0.991108	−	0.133061i	$-0.957519\pi$
$113$	−9.12116	+	9.12116i	−0.858047	+	0.858047i	0.133061	+	0.991108i	$0.457519\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−4.41141	−	1.18203i	−0.407835	−	0.109279i
$118$		0			0
$119$	8.09123	−	4.85776i	0.741722	−	0.445310i
$120$		0			0
$121$	−3.70518	−	6.41756i	−0.336835	−	0.583414i
$122$		0			0
$123$	−2.77323	−	10.3499i	−0.250054	−	0.933215i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−10.6203	−	10.6203i	−0.942403	−	0.942403i	0.0560260	−	0.998429i	$-0.482157\pi$
$127$	−10.6203	−	10.6203i	−0.942403	−	0.942403i	−0.998429	+	0.0560260i	$0.982157\pi$
$128$		0			0
$129$	−1.68682	+	2.92166i	−0.148517	+	0.257238i
$130$		0			0
$131$	−2.84333	+	1.64160i	−0.248423	+	0.143427i	−0.619042	−	0.785358i	$-0.712479\pi$
$131$	−2.84333	+	1.64160i	−0.248423	+	0.143427i	0.370619	+	0.928785i	$0.379146\pi$
$132$		0			0
$133$	11.5255	−	11.9265i	0.999390	−	1.03416i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.0060	+	4.28878i	−1.36748	+	0.366415i	−0.866558	−	0.499077i	$-0.833673\pi$
$137$	−16.0060	+	4.28878i	−1.36748	+	0.366415i	−0.500923	+	0.865492i	$0.667006\pi$
$138$		0			0
$139$	−0.478566			−0.0405914			−0.0202957	−	0.999794i	$-0.506461\pi$
$139$	−0.478566			−0.0405914			−0.0202957	+	0.999794i	$0.506461\pi$
$140$		0			0
$141$	8.58146			0.722689
$142$		0			0
$143$	−18.9282	+	5.07179i	−1.58285	+	0.424124i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−4.77766	+	5.11605i	−0.394054	+	0.421965i
$148$		0			0
$149$	−8.41389	+	4.85776i	−0.689292	+	0.397963i	−0.803347	−	0.595511i	$-0.796949\pi$
$149$	−8.41389	+	4.85776i	−0.689292	+	0.397963i	0.114055	+	0.993474i	$0.463616\pi$
$150$		0			0
$151$	10.2196	−	17.7009i	0.831660	−	1.44048i	−0.0650611	−	0.997881i	$-0.520724\pi$
$151$	10.2196	−	17.7009i	0.831660	−	1.44048i	0.896721	−	0.442596i	$-0.145942\pi$
$152$		0			0
$153$	−2.52227	−	2.52227i	−0.203914	−	0.203914i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.36407	+	8.82282i	0.188673	+	0.704138i	0.993814	+	0.111055i	$0.0354229\pi$
$157$	2.36407	+	8.82282i	0.188673	+	0.704138i	−0.805141	+	0.593083i	$0.797910\pi$
$158$		0			0
$159$	4.53668	+	7.85776i	0.359782	+	0.623161i
$160$		0			0
$161$	−0.130935	−	7.65855i	−0.0103192	−	0.603578i
$162$		0			0
$163$	10.0382	+	2.68973i	0.786252	+	0.210676i	0.629539	−	0.776969i	$-0.283244\pi$
$163$	10.0382	+	2.68973i	0.786252	+	0.210676i	0.156713	+	0.987644i	$0.449910\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.0521	−	16.0521i	1.24215	−	1.24215i	0.283040	−	0.959108i	$-0.408657\pi$
$167$	16.0521	−	16.0521i	1.24215	−	1.24215i	0.959108	−	0.283040i	$-0.0913430\pi$
$168$		0			0
$169$			7.85776i			0.604443i
$170$		0			0
$171$	−5.42888	−	3.13437i	−0.415157	−	0.239691i
$172$		0			0
$173$	−5.99500	+	22.3737i	−0.455792	+	1.70104i	0.229958	+	0.973201i	$0.426141\pi$
$173$	−5.99500	+	22.3737i	−0.455792	+	1.70104i	−0.685750	+	0.727837i	$0.740526\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.424877	+	1.58566i	−0.0319357	+	0.119186i
$178$		0			0
$179$	5.19615	+	3.00000i	0.388379	+	0.224231i	0.681457	−	0.731858i	$-0.261346\pi$
$179$	5.19615	+	3.00000i	0.388379	+	0.224231i	−0.293079	+	0.956088i	$0.594680\pi$
$180$		0			0
$181$			18.9871i			1.41130i	0.708561	+	0.705650i	$0.249345\pi$
$181$			18.9871i			1.41130i	−0.708561	+	0.705650i	$0.750655\pi$
$182$		0			0
$183$	7.30218	−	7.30218i	0.539793	−	0.539793i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−14.7836	−	3.96127i	−1.08109	−	0.289677i
$188$		0			0
$189$	2.31357	+	1.28351i	0.168287	+	0.0933620i
$190$		0			0
$191$	−6.56703	−	11.3744i	−0.475174	−	0.823025i	0.524422	−	0.851458i	$-0.324281\pi$
$191$	−6.56703	−	11.3744i	−0.475174	−	0.823025i	−0.999596	+	0.0284336i	$0.990948\pi$
$192$		0			0
$193$	−2.32495	−	8.67682i	−0.167353	−	0.624571i	−0.997728	−	0.0673662i	$-0.978540\pi$
$193$	−2.32495	−	8.67682i	−0.167353	−	0.624571i	0.830375	−	0.557205i	$-0.188126\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.53033	+	7.53033i	0.536514	+	0.536514i	0.922503	−	0.385989i	$-0.126140\pi$
$197$	7.53033	+	7.53033i	0.536514	+	0.536514i	−0.385989	+	0.922503i	$0.626140\pi$
$198$		0			0
$199$	−0.0327307	+	0.0566912i	−0.00232021	+	0.00401873i	−0.867183	−	0.497989i	$-0.834072\pi$
$199$	−0.0327307	+	0.0566912i	−0.00232021	+	0.00401873i	0.864863	+	0.502008i	$0.167405\pi$
$200$		0			0
$201$	−4.00721	+	2.31357i	−0.282647	+	0.163186i
$202$		0			0
$203$	−7.23207	+	2.07096i	−0.507592	+	0.145353i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.79643	+	0.749302i	−0.194366	+	0.0520801i
$208$		0			0
$209$	−26.8974			−1.86053
$210$		0			0
$211$	−19.5733			−1.34748			−0.673740	−	0.738968i	$-0.735313\pi$
$211$	−19.5733			−1.34748			−0.673740	+	0.738968i	$0.735313\pi$
$212$		0			0
$213$	11.3382	−	3.03805i	0.776878	−	0.208164i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.994260	−	3.98168i	0.0674947	−	0.270294i
$218$		0			0
$219$	8.04601	−	4.64536i	0.543699	−	0.313905i
$220$		0			0
$221$	−8.14536	+	14.1082i	−0.547917	+	0.949019i
$222$		0			0
$223$	−9.67793	−	9.67793i	−0.648082	−	0.648082i	0.304447	−	0.952529i	$-0.401528\pi$
$223$	−9.67793	−	9.67793i	−0.648082	−	0.648082i	−0.952529	+	0.304447i	$0.901528\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.93184	+	10.9418i	0.194593	+	0.726232i	0.992372	+	0.123281i	$0.0393417\pi$
$227$	2.93184	+	10.9418i	0.194593	+	0.726232i	−0.797779	+	0.602951i	$0.793992\pi$
$228$		0			0
$229$	−1.04693	−	1.81334i	−0.0691833	−	0.119829i	0.829359	−	0.558716i	$-0.188706\pi$
$229$	−1.04693	−	1.81334i	−0.0691833	−	0.119829i	−0.898542	+	0.438888i	$0.855373\pi$
$230$		0			0
$231$	11.3505	−	0.194056i	0.746811	−	0.0127680i
$232$		0			0
$233$	23.8710	+	6.39622i	1.56384	+	0.419030i	0.933878	−	0.357593i	$-0.116402\pi$
$233$	23.8710	+	6.39622i	1.56384	+	0.419030i	0.629965	+	0.776623i	$0.283069\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	5.46148	−	5.46148i	0.354761	−	0.354761i
$238$		0			0
$239$		−	21.4022i		−	1.38439i	−0.721710	−	0.692196i	$-0.756643\pi$
$239$		−	21.4022i		−	1.38439i	0.721710	−	0.692196i	$-0.243357\pi$
$240$		0			0
$241$	22.4877	+	12.9833i	1.44856	+	0.836328i	0.998396	−	0.0566174i	$-0.0180315\pi$
$241$	22.4877	+	12.9833i	1.44856	+	0.836328i	0.450166	+	0.892945i	$0.351365\pi$
$242$		0			0
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.40985	+	27.6539i	−0.471478	+	1.75958i
$248$		0			0
$249$	4.07126	+	2.35054i	0.258006	+	0.148960i
$250$		0			0
$251$		−	2.18432i		−	0.137873i	−0.997621	−	0.0689365i	$-0.978039\pi$
$251$		−	2.18432i		−	0.137873i	0.997621	−	0.0689365i	$-0.0219606\pi$
$252$		0			0
$253$	−8.78369	+	8.78369i	−0.552226	+	0.552226i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.04741	+	0.548601i	0.127714	+	0.0342208i	0.322110	−	0.946702i	$-0.395608\pi$
$257$	2.04741	+	0.548601i	0.127714	+	0.0342208i	−0.194396	+	0.980923i	$0.562275\pi$
$258$		0			0
$259$	15.0778	−	0.257780i	0.936890	−	0.0160177i
$260$		0			0
$261$	1.42166	+	2.46240i	0.0879988	+	0.152418i
$262$		0			0
$263$	6.73759	+	25.1450i	0.415458	+	1.55051i	0.783917	+	0.620865i	$0.213219\pi$
$263$	6.73759	+	25.1450i	0.415458	+	1.55051i	−0.368460	+	0.929644i	$0.620115\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−12.6035	−	12.6035i	−0.771323	−	0.771323i
$268$		0			0
$269$	−2.89508	+	5.01443i	−0.176516	+	0.305735i	−0.940685	−	0.339281i	$-0.889816\pi$
$269$	−2.89508	+	5.01443i	−0.176516	+	0.305735i	0.764169	+	0.645016i	$0.223149\pi$
$270$		0			0
$271$	−5.07112	+	2.92781i	−0.308049	+	0.177852i	−0.646053	−	0.763293i	$-0.723581\pi$
$271$	−5.07112	+	2.92781i	−0.308049	+	0.177852i	0.338004	+	0.941145i	$0.390248\pi$
$272$		0			0
$273$	2.92740	−	11.7233i	0.177174	−	0.709524i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	7.57756	−	2.03040i	0.455291	−	0.121995i	−0.0238829	−	0.999715i	$-0.507603\pi$
$277$	7.57756	−	2.03040i	0.455291	−	0.121995i	0.479174	+	0.877720i	$0.340936\pi$
$278$		0			0
$279$	−1.55114			−0.0928645
$280$		0			0
$281$	−0.313341			−0.0186923			−0.00934617	−	0.999956i	$-0.502975\pi$
$281$	−0.313341			−0.0186923			−0.00934617	+	0.999956i	$0.502975\pi$
$282$		0			0
$283$	6.50853	−	1.74396i	0.386892	−	0.103667i	−0.0601295	−	0.998191i	$-0.519151\pi$
$283$	6.50853	−	1.74396i	0.386892	−	0.103667i	0.447022	+	0.894523i	$0.352485\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	27.2537	−	7.80431i	1.60874	−	0.460674i
$288$		0			0
$289$	3.70338	−	2.13815i	0.217846	−	0.125774i
$290$		0			0
$291$	0.0711205	−	0.123184i	0.00416916	−	0.00722119i
$292$		0			0
$293$	−8.70685	−	8.70685i	−0.508659	−	0.508659i	0.405455	−	0.914115i	$-0.367113\pi$
$293$	−8.70685	−	8.70685i	−0.508659	−	0.508659i	−0.914115	+	0.405455i	$0.867113\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−1.11052	−	4.14453i	−0.0644391	−	0.240490i
$298$		0			0
$299$	6.61096	+	11.4505i	0.382322	+	0.662201i
$300$		0			0
$301$	−7.80516	−	4.33013i	−0.449882	−	0.249584i
$302$		0			0
$303$	8.45253	+	2.26485i	0.485585	+	0.130112i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	22.2469	−	22.2469i	1.26970	−	1.26970i	0.323451	−	0.946245i	$-0.395157\pi$
$307$	22.2469	−	22.2469i	1.26970	−	1.26970i	0.946245	−	0.323451i	$-0.104843\pi$
$308$		0			0
$309$		−	3.29073i		−	0.187203i
$310$		0			0
$311$	2.56391	+	1.48027i	0.145386	+	0.0839385i	0.570928	−	0.821000i	$-0.306583\pi$
$311$	2.56391	+	1.48027i	0.145386	+	0.0839385i	−0.425543	+	0.904938i	$0.639917\pi$
$312$		0			0
$313$	1.36934	−	5.11045i	0.0773998	−	0.288860i	−0.916367	−	0.400339i	$-0.868892\pi$
$313$	1.36934	−	5.11045i	0.0773998	−	0.288860i	0.993767	+	0.111479i	$0.0355589\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.27900	+	19.7015i	−0.296498	+	1.10655i	0.643522	+	0.765428i	$0.277473\pi$
$317$	−5.27900	+	19.7015i	−0.296498	+	1.10655i	−0.940020	+	0.341119i	$0.889194\pi$
$318$		0			0
$319$	10.5655	+	6.09998i	0.591553	+	0.341533i
$320$		0			0
$321$			13.2874i			0.741630i
$322$		0			0
$323$	−15.8114	+	15.8114i	−0.879772	+	0.879772i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−13.8177	−	3.70245i	−0.764122	−	0.204746i
$328$		0			0
$329$	0.388112	+	22.7011i	0.0213973	+	1.25155i
$330$		0			0
$331$	2.91036	+	5.04089i	0.159968	+	0.277072i	0.934857	−	0.355025i	$-0.115528\pi$
$331$	2.91036	+	5.04089i	0.159968	+	0.277072i	−0.774889	+	0.632097i	$0.782194\pi$
$332$		0			0
$333$	−1.47519	−	5.50550i	−0.0808401	−	0.301699i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−20.2904	−	20.2904i	−1.10529	−	1.10529i	−0.993761	−	0.111526i	$-0.964426\pi$
$337$	−20.2904	−	20.2904i	−1.10529	−	1.10529i	−0.111526	−	0.993761i	$-0.535574\pi$
$338$		0			0
$339$	−6.44964	+	11.1711i	−0.350296	+	0.606731i
$340$		0			0
$341$	−5.76386	+	3.32777i	−0.312131	+	0.180209i
$342$		0			0
$343$	−13.7499	−	12.4073i	−0.742425	−	0.669929i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	31.8854	−	8.54368i	1.71170	−	0.458649i	0.735860	−	0.677134i	$-0.236778\pi$
$347$	31.8854	−	8.54368i	1.71170	−	0.458649i	0.975840	+	0.218485i	$0.0701115\pi$
$348$		0			0
$349$	12.3566			0.661431			0.330716	−	0.943730i	$-0.392710\pi$
$349$	12.3566			0.661431			0.330716	+	0.943730i	$0.392710\pi$
$350$		0			0
$351$	−4.56703			−0.243770
$352$		0			0
$353$	0.649324	−	0.173986i	0.0345600	−	0.00926034i	−0.241498	−	0.970401i	$-0.577639\pi$
$353$	0.649324	−	0.173986i	0.0345600	−	0.00926034i	0.276058	+	0.961141i	$0.410972\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.55825	−	6.78640i	0.347099	−	0.359174i
$358$		0			0
$359$	24.7577	−	14.2939i	1.30666	−	0.754401i	0.325123	−	0.945672i	$-0.394594\pi$
$359$	24.7577	−	14.2939i	1.30666	−	0.754401i	0.981537	+	0.191271i	$0.0612609\pi$
$360$		0			0
$361$	−10.1485	+	17.5777i	−0.534131	+	0.925142i
$362$		0			0
$363$	−5.23992	−	5.23992i	−0.275024	−	0.275024i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−0.671865	−	2.50744i	−0.0350711	−	0.130887i	0.946171	−	0.323668i	$-0.104916\pi$
$367$	−0.671865	−	2.50744i	−0.0350711	−	0.130887i	−0.981242	+	0.192781i	$0.938249\pi$
$368$		0			0
$369$	−5.35748	−	9.27942i	−0.278899	−	0.483068i
$370$		0			0
$371$	−20.5815	+	12.3566i	−1.06854	+	0.641520i
$372$		0			0
$373$	4.99370	+	1.33806i	0.258564	+	0.0692820i	0.385772	−	0.922594i	$-0.373935\pi$
$373$	4.99370	+	1.33806i	0.258564	+	0.0692820i	−0.127208	+	0.991876i	$0.540602\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.18219	−	9.18219i	0.472907	−	0.472907i
$378$		0			0
$379$			8.44740i			0.433914i	0.976181	+	0.216957i	$0.0696131\pi$
$379$			8.44740i			0.433914i	−0.976181	+	0.216957i	$0.930387\pi$
$380$		0			0
$381$	−13.0072	−	7.50972i	−0.666380	−	0.384735i
$382$		0			0
$383$	−2.22104	+	8.28905i	−0.113490	+	0.423551i	−0.999170	−	0.0407465i	$-0.987026\pi$
$383$	−2.22104	+	8.28905i	−0.113490	+	0.423551i	0.885679	+	0.464297i	$0.153693\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−0.873164	+	3.25869i	−0.0443854	+	0.165649i
$388$		0			0
$389$	15.0903	+	8.71239i	0.765109	+	0.441736i	0.831127	−	0.556083i	$-0.187696\pi$
$389$	15.0903	+	8.71239i	0.765109	+	0.441736i	−0.0660180	+	0.997818i	$0.521029\pi$
$390$		0			0
$391$			10.3268i			0.522251i
$392$		0			0
$393$	−2.32157	+	2.32157i	−0.117108	+	0.117108i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−9.20526	−	2.46654i	−0.461999	−	0.123792i	0.0203095	−	0.999794i	$-0.493535\pi$
$397$	−9.20526	−	2.46654i	−0.461999	−	0.123792i	−0.482308	+	0.876002i	$0.660202\pi$
$398$		0			0
$399$	8.04601	−	14.5031i	0.402804	−	0.726064i
$400$		0			0
$401$	5.42479	+	9.39601i	0.270901	+	0.469214i	0.969093	−	0.246696i	$-0.0793451\pi$
$401$	5.42479	+	9.39601i	0.270901	+	0.469214i	−0.698192	+	0.715911i	$0.746012\pi$
$402$		0			0
$403$	1.83350	+	6.84273i	0.0913334	+	0.340861i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.2929	−	17.2929i	−0.857179	−	0.857179i
$408$		0			0
$409$	−16.2986	+	28.2299i	−0.805912	+	1.39588i	0.109761	+	0.993958i	$0.464991\pi$
$409$	−16.2986	+	28.2299i	−0.805912	+	1.39588i	−0.915673	+	0.401923i	$0.868342\pi$
$410$		0			0
$411$	−14.3505	+	8.28529i	−0.707860	+	0.408683i
$412$		0			0
$413$	−4.21387	−	1.05224i	−0.207351	−	0.0517773i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.462259	+	0.123862i	−0.0226369	+	0.00606555i
$418$		0			0
$419$	22.6179			1.10496			0.552479	−	0.833527i	$-0.313682\pi$
$419$	22.6179			1.10496			0.552479	+	0.833527i	$0.313682\pi$
$420$		0			0
$421$	−12.0370			−0.586649			−0.293325	−	0.956013i	$-0.594762\pi$
$421$	−12.0370			−0.586649			−0.293325	+	0.956013i	$0.594762\pi$
$422$		0			0
$423$	8.28905	−	2.22104i	0.403028	−	0.107991i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	19.6472	+	18.9867i	0.950794	+	0.918830i
$428$		0			0
$429$	−16.9705	+	9.79794i	−0.819345	+	0.473049i
$430$		0			0
$431$	−17.0144	+	29.4699i	−0.819556	+	1.41951i	0.0864534	+	0.996256i	$0.472447\pi$
$431$	−17.0144	+	29.4699i	−0.819556	+	1.41951i	−0.906010	+	0.423257i	$0.860887\pi$
$432$		0			0
$433$	−22.6580	−	22.6580i	−1.08888	−	1.08888i	−0.995645	−	0.0932307i	$-0.970281\pi$
$433$	−22.6580	−	22.6580i	−1.08888	−	1.08888i	−0.0932307	−	0.995645i	$-0.529719\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.69717	+	17.5301i	0.224696	+	0.838578i
$438$		0			0
$439$	−1.99698	−	3.45887i	−0.0953106	−	0.165083i	0.814428	−	0.580265i	$-0.197051\pi$
$439$	−1.99698	−	3.45887i	−0.0953106	−	0.165083i	−0.909738	+	0.415182i	$0.863718\pi$
$440$		0			0
$441$	−3.29073	+	6.17828i	−0.156701	+	0.294204i
$442$		0			0
$443$	−13.0831	−	3.50559i	−0.621595	−	0.166556i	−0.0657421	−	0.997837i	$-0.520941\pi$
$443$	−13.0831	−	3.50559i	−0.621595	−	0.166556i	−0.555853	+	0.831281i	$0.687608\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−6.86991	+	6.86991i	−0.324936	+	0.324936i
$448$		0			0
$449$			28.8496i			1.36150i	0.732518	+	0.680748i	$0.238345\pi$
$449$			28.8496i			1.36150i	−0.732518	+	0.680748i	$0.761655\pi$
$450$		0			0
$451$	−39.8155	−	22.9875i	−1.87484	−	1.08244i
$452$		0			0
$453$	5.29006	−	19.7428i	0.248549	−	0.927596i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.68047	+	21.1998i	−0.265721	+	0.991685i	0.696086	+	0.717958i	$0.254923\pi$
$457$	−5.68047	+	21.1998i	−0.265721	+	0.991685i	−0.961808	+	0.273727i	$0.911744\pi$
$458$		0			0
$459$	−3.08914	−	1.78351i	−0.144189	−	0.0832473i
$460$		0			0
$461$			6.11282i			0.284702i	0.989816	+	0.142351i	$0.0454662\pi$
$461$			6.11282i			0.284702i	−0.989816	+	0.142351i	$0.954534\pi$
$462$		0			0
$463$	27.0346	−	27.0346i	1.25640	−	1.25640i	0.303607	−	0.952797i	$-0.401809\pi$
$463$	27.0346	−	27.0346i	1.25640	−	1.25640i	0.952797	−	0.303607i	$-0.0981909\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.89037	−	2.65012i	−0.457672	−	0.122633i	0.0226152	−	0.999744i	$-0.492801\pi$
$467$	−9.89037	−	2.65012i	−0.457672	−	0.122633i	−0.480287	+	0.877112i	$0.659467\pi$
$468$		0			0
$469$	−6.30146	−	10.4959i	−0.290974	−	0.484656i
$470$		0			0
$471$	4.56703	+	7.91033i	0.210438	+	0.364489i
$472$		0			0
$473$	3.74651	+	13.9822i	0.172265	+	0.642901i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.41583	+	6.41583i	0.293761	+	0.293761i
$478$		0			0
$479$	11.3744	−	19.7011i	0.519711	−	0.900166i	−0.480027	−	0.877254i	$-0.659373\pi$
$479$	11.3744	−	19.7011i	0.519711	−	0.900166i	0.999737	−	0.0229118i	$-0.00729368\pi$
$480$		0			0
$481$	−22.5433	+	13.0154i	−1.02789	+	0.593450i
$482$		0			0
$483$	−2.10865	−	7.36370i	−0.0959470	−	0.335060i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−37.1047	+	9.94217i	−1.68137	+	0.450523i	−0.968141	−	0.250405i	$-0.919436\pi$
$487$	−37.1047	+	9.94217i	−1.68137	+	0.450523i	−0.713233	+	0.700927i	$0.752770\pi$
$488$		0			0
$489$	10.3923			0.469956
$490$		0			0
$491$	−5.47626			−0.247140			−0.123570	−	0.992336i	$-0.539434\pi$
$491$	−5.47626			−0.247140			−0.123570	+	0.992336i	$0.539434\pi$
$492$		0			0
$493$	9.79665	−	2.62501i	0.441219	−	0.118224i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	8.54954	+	29.8562i	0.383499	+	1.33923i
$498$		0			0
$499$	10.2370	−	5.91036i	0.458273	−	0.264584i	−0.253045	−	0.967455i	$-0.581432\pi$
$499$	10.2370	−	5.91036i	0.458273	−	0.264584i	0.711318	+	0.702871i	$0.248099\pi$
$500$		0			0
$501$	11.3505	−	19.6597i	0.507105	−	0.878331i
$502$		0			0
$503$	−12.7279	−	12.7279i	−0.567510	−	0.567510i	0.363920	−	0.931430i	$-0.381438\pi$
$503$	−12.7279	−	12.7279i	−0.567510	−	0.567510i	−0.931430	+	0.363920i	$0.881438\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	2.03374	+	7.59001i	0.0903215	+	0.337084i
$508$		0			0
$509$	8.41389	+	14.5733i	0.372939	+	0.645949i	0.990016	−	0.140953i	$-0.0450168\pi$
$509$	8.41389	+	14.5733i	0.372939	+	0.645949i	−0.617077	+	0.786903i	$0.711683\pi$
$510$		0			0
$511$	12.6526	+	21.0745i	0.559717	+	0.932282i
$512$		0			0
$513$	−6.05513	−	1.62247i	−0.267340	−	0.0716337i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	26.0362	−	26.0362i	1.14507	−	1.14507i
$518$		0			0
$519$			23.1629i			1.01674i
$520$		0			0
$521$	31.5444	+	18.2122i	1.38199	+	0.797890i	0.992395	−	0.123098i	$-0.0392829\pi$
$521$	31.5444	+	18.2122i	1.38199	+	0.797890i	0.389592	+	0.920988i	$0.372616\pi$
$522$		0			0
$523$	1.03901	−	3.87764i	0.0454328	−	0.169557i	−0.939482	−	0.342599i	$-0.888693\pi$
$523$	1.03901	−	3.87764i	0.0454328	−	0.169557i	0.984915	+	0.173042i	$0.0553595\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.43204	+	5.34444i	−0.0623806	+	0.232808i
$528$		0			0
$529$	−12.6600	−	7.30925i	−0.550434	−	0.317793i
$530$		0			0
$531$			1.64160i			0.0712392i
$532$		0			0
$533$	−34.6026	+	34.6026i	−1.49881	+	1.49881i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.79555	+	1.55291i	0.250097	+	0.0670132i
$538$		0			0
$539$	1.02670	+	30.0176i	0.0442230	+	1.29295i
$540$		0			0
$541$	14.9248	+	25.8505i	0.641667	+	1.11140i	0.985061	+	0.172208i	$0.0550901\pi$
$541$	14.9248	+	25.8505i	0.641667	+	1.11140i	−0.343394	+	0.939191i	$0.611577\pi$
$542$		0			0
$543$	4.91422	+	18.3401i	0.210889	+	0.787050i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−17.4023	−	17.4023i	−0.744067	−	0.744067i	0.229291	−	0.973358i	$-0.426359\pi$
$547$	−17.4023	−	17.4023i	−0.744067	−	0.744067i	−0.973358	+	0.229291i	$0.926359\pi$
$548$		0			0
$549$	5.16342	−	8.94331i	0.220369	−	0.381691i
$550$		0			0
$551$	15.4361	−	8.91203i	0.657600	−	0.379665i
$552$		0			0
$553$	14.6946	+	14.2006i	0.624879	+	0.603871i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−24.9195	+	6.67716i	−1.05587	+	0.282920i	−0.744677	−	0.667426i	$-0.767396\pi$
$557$	−24.9195	+	6.67716i	−1.05587	+	0.282920i	−0.311196	+	0.950346i	$0.600730\pi$
$558$		0			0
$559$	15.4075			0.651670
$560$		0			0
$561$	−15.3052			−0.646184
$562$		0			0
$563$	10.7826	−	2.88918i	0.454430	−	0.121764i	−0.0243413	−	0.999704i	$-0.507749\pi$
$563$	10.7826	−	2.88918i	0.454430	−	0.121764i	0.478772	+	0.877939i	$0.341082\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.56693	+	0.640985i	0.107801	+	0.0269188i
$568$		0			0
$569$	14.8189	−	8.55572i	0.621243	−	0.358675i	−0.156110	−	0.987740i	$-0.549895\pi$
$569$	14.8189	−	8.55572i	0.621243	−	0.358675i	0.777353	+	0.629065i	$0.216562\pi$
$570$		0			0
$571$	−4.56294	+	7.90324i	−0.190953	+	0.330740i	−0.945566	−	0.325429i	$-0.894491\pi$
$571$	−4.56294	+	7.90324i	−0.190953	+	0.330740i	0.754613	+	0.656170i	$0.227824\pi$
$572$		0			0
$573$	−9.28718	−	9.28718i	−0.387978	−	0.387978i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−4.43836	−	16.5642i	−0.184771	−	0.689575i	−0.994679	−	0.103019i	$-0.967150\pi$
$577$	−4.43836	−	16.5642i	−0.184771	−	0.689575i	0.809908	−	0.586557i	$-0.199517\pi$
$578$		0			0
$579$	−4.49145	−	7.77942i	−0.186658	−	0.323302i
$580$		0			0
$581$	−6.03392	+	10.8763i	−0.250329	+	0.451224i
$582$		0			0
$583$	37.6048	+	10.0762i	1.55743	+	0.417312i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.8269	−	30.8269i	1.27236	−	1.27236i	0.327520	−	0.944844i	$-0.393787\pi$
$587$	30.8269	−	30.8269i	1.27236	−	1.27236i	0.944844	−	0.327520i	$-0.106213\pi$
$588$		0			0
$589$			9.72370i			0.400658i
$590$		0			0
$591$	9.22273	+	5.32475i	0.379373	+	0.219031i
$592$		0			0
$593$	−8.09652	+	30.2166i	−0.332484	+	1.24085i	0.574087	+	0.818794i	$0.305357\pi$
$593$	−8.09652	+	30.2166i	−0.332484	+	1.24085i	−0.906571	+	0.422053i	$0.861309\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−0.0169426	+	0.0632308i	−0.000693416	+	0.00258786i
$598$		0			0
$599$	3.23190	+	1.86594i	0.132052	+	0.0762403i	0.564571	−	0.825385i	$-0.309042\pi$
$599$	3.23190	+	1.86594i	0.132052	+	0.0762403i	−0.432519	+	0.901625i	$0.642375\pi$
$600$		0			0
$601$			12.0089i			0.489854i	0.969542	+	0.244927i	$0.0787639\pi$
$601$			12.0089i			0.489854i	−0.969542	+	0.244927i	$0.921236\pi$
$602$		0			0
$603$	−3.27188	+	3.27188i	−0.133241	+	0.133241i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	11.5614	+	3.09786i	0.469261	+	0.125738i	0.485698	−	0.874127i	$-0.338565\pi$
$607$	11.5614	+	3.09786i	0.469261	+	0.125738i	−0.0164366	+	0.999865i	$0.505232\pi$
$608$		0			0
$609$	−6.44964	+	3.87219i	−0.261352	+	0.156909i
$610$		0			0
$611$	−19.5959	−	33.9411i	−0.792765	−	1.37311i
$612$		0			0
$613$	−0.665794	−	2.48478i	−0.0268912	−	0.100359i	0.951176	−	0.308649i	$-0.0998769\pi$
$613$	−0.665794	−	2.48478i	−0.0268912	−	0.100359i	−0.978067	+	0.208290i	$0.933210\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−30.2339	−	30.2339i	−1.21717	−	1.21717i	−0.968618	−	0.248555i	$-0.920044\pi$
$617$	−30.2339	−	30.2339i	−1.21717	−	1.21717i	−0.248555	−	0.968618i	$-0.579956\pi$
$618$		0			0
$619$	10.9215	−	18.9166i	0.438972	−	0.760323i	−0.558638	−	0.829412i	$-0.688676\pi$
$619$	10.9215	−	18.9166i	0.438972	−	0.760323i	0.997611	+	0.0690889i	$0.0220092\pi$
$620$		0			0
$621$	−2.50721	+	1.44754i	−0.100611	+	0.0580878i
$622$		0			0
$623$	32.7709	−	33.9109i	1.31294	−	1.35861i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−25.9809	+	6.96157i	−1.03758	+	0.278018i
$628$		0			0
$629$	−20.3310			−0.810652
$630$		0			0
$631$	46.5651			1.85373			0.926864	−	0.375398i	$-0.122494\pi$
$631$	46.5651			1.85373			0.926864	+	0.375398i	$0.122494\pi$
$632$		0			0
$633$	−18.9063	+	5.06594i	−0.751459	+	0.201353i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	31.1447	+	7.21383i	1.23400	+	0.285822i
$638$		0			0
$639$	10.1655	−	5.86906i	0.402142	−	0.232177i
$640$		0			0
$641$	−20.7124	+	35.8749i	−0.818090	+	1.41697i	0.0889971	+	0.996032i	$0.471634\pi$
$641$	−20.7124	+	35.8749i	−0.818090	+	1.41697i	−0.907087	+	0.420942i	$0.861700\pi$
$642$		0			0
$643$	27.2798	+	27.2798i	1.07581	+	1.07581i	0.996880	+	0.0789320i	$0.0251510\pi$
$643$	27.2798	+	27.2798i	1.07581	+	1.07581i	0.0789320	+	0.996880i	$0.474849\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.76026	+	25.2296i	0.265773	+	0.991879i	0.961775	+	0.273839i	$0.0882937\pi$
$647$	6.76026	+	25.2296i	0.265773	+	0.991879i	−0.696002	+	0.718040i	$0.745040\pi$
$648$		0			0
$649$	3.52182	+	6.09998i	0.138244	+	0.239445i
$650$		0			0
$651$	−0.0701533	−	4.10334i	−0.00274952	−	0.160823i
$652$		0			0
$653$	13.5844	+	3.63993i	0.531599	+	0.142441i	0.514626	−	0.857414i	$-0.327931\pi$
$653$	13.5844	+	3.63993i	0.531599	+	0.142441i	0.0169724	+	0.999856i	$0.494597\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.56954	−	6.56954i	0.256302	−	0.256302i
$658$		0			0
$659$			3.71552i			0.144736i	0.997378	+	0.0723680i	$0.0230556\pi$
$659$			3.71552i			0.144736i	−0.997378	+	0.0723680i	$0.976944\pi$
$660$		0			0
$661$	−31.1300	−	17.9729i	−1.21082	−	0.699065i	−0.247878	−	0.968791i	$-0.579733\pi$
$661$	−31.1300	−	17.9729i	−1.21082	−	0.699065i	−0.962937	+	0.269727i	$0.913067\pi$
$662$		0			0
$663$	−4.21635	+	15.7356i	−0.163750	+	0.611121i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.13051	−	7.95119i	0.0824938	−	0.307871i
$668$		0			0
$669$	−11.8530	−	6.84333i	−0.458263	−	0.264578i
$670$		0			0
$671$		−	44.3097i		−	1.71056i
$672$		0			0
$673$	−31.6052	+	31.6052i	−1.21829	+	1.21829i	−0.250061	+	0.968230i	$0.580451\pi$
$673$	−31.6052	+	31.6052i	−1.21829	+	1.21829i	−0.968230	+	0.250061i	$0.919549\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.4183	+	5.20311i	0.746305	+	0.199972i	0.611878	−	0.790952i	$-0.290414\pi$
$677$	19.4183	+	5.20311i	0.746305	+	0.199972i	0.134426	+	0.990924i	$0.457081\pi$
$678$		0			0
$679$	0.329084	+	0.182568i	0.0126291	+	0.00700633i
$680$		0			0
$681$	5.66389	+	9.81014i	0.217041	+	0.375925i
$682$		0			0
$683$	−1.25769	−	4.69375i	−0.0481241	−	0.179601i	0.937680	−	0.347499i	$-0.112969\pi$
$683$	−1.25769	−	4.69375i	−0.0481241	−	0.179601i	−0.985804	+	0.167897i	$0.946302\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1.48059	−	1.48059i	−0.0564879	−	0.0564879i
$688$		0			0
$689$	20.7191	−	35.8866i	0.789337	−	1.36717i
$690$		0			0
$691$	−38.9310	+	22.4768i	−1.48101	+	0.855059i	−0.999768	−	0.0215304i	$-0.993146\pi$
$691$	−38.9310	+	22.4768i	−1.48101	+	0.855059i	−0.481238	+	0.876590i	$0.659813\pi$
$692$		0			0
$693$	10.9136	−	3.12518i	0.414572	−	0.118716i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−36.9182	+	9.89221i	−1.39838	+	0.374694i
$698$		0			0
$699$	24.7131			0.934736
$700$		0			0
$701$	−30.2455			−1.14236			−0.571179	−	0.820826i	$-0.693514\pi$
$701$	−30.2455			−1.14236			−0.571179	+	0.820826i	$0.693514\pi$
$702$		0			0
$703$	−34.5125	+	9.24759i	−1.30166	+	0.348779i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.60907	+	22.4625i	−0.210951	+	0.844788i
$708$		0			0
$709$	−30.0324	+	17.3392i	−1.12789	+	0.651189i	−0.943404	−	0.331646i	$-0.892396\pi$
$709$	−30.0324	+	17.3392i	−1.12789	+	0.651189i	−0.184488	+	0.982835i	$0.559063\pi$
$710$		0			0
$711$	3.86185	−	6.68892i	0.144831	−	0.250854i
$712$		0			0
$713$	3.17540	+	3.17540i	0.118920	+	0.118920i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−5.53929	−	20.6729i	−0.206869	−	0.772044i
$718$		0			0
$719$	−7.75441	−	13.4310i	−0.289191	−	0.500893i	0.684426	−	0.729082i	$-0.260053\pi$
$719$	−7.75441	−	13.4310i	−0.289191	−	0.500893i	−0.973617	+	0.228189i	$0.926720\pi$
$720$		0			0
$721$	8.70518	−	0.148829i	0.324198	−	0.00554269i
$722$		0			0
$723$	25.0818	+	6.72065i	0.932802	+	0.249944i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−12.8475	+	12.8475i	−0.476489	+	0.476489i	−0.904007	−	0.427518i	$-0.859388\pi$
$727$	−12.8475	+	12.8475i	−0.476489	+	0.476489i	0.427518	+	0.904007i	$0.359388\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	10.4217	+	6.01695i	0.385459	+	0.222545i
$732$		0			0
$733$	3.99011	−	14.8913i	0.147378	−	0.550023i	−0.852260	−	0.523119i	$-0.824768\pi$
$733$	3.99011	−	14.8913i	0.147378	−	0.550023i	0.999638	−	0.0269041i	$-0.00856486\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.13854	+	19.1773i	−0.189280	+	0.706404i
$738$		0			0
$739$	34.8911	+	20.1444i	1.28349	+	0.741024i	0.977485	−	0.211006i	$-0.0676740\pi$
$739$	34.8911	+	20.1444i	1.28349	+	0.741024i	0.306006	+	0.952030i	$0.401007\pi$
$740$		0			0
$741$			28.6295i			1.05173i
$742$		0			0
$743$	−7.23914	+	7.23914i	−0.265578	+	0.265578i	−0.827316	−	0.561737i	$-0.810133\pi$
$743$	−7.23914	+	7.23914i	−0.265578	+	0.265578i	0.561737	+	0.827316i	$0.310133\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	4.54090	+	1.21673i	0.166143	+	0.0445179i
$748$		0			0
$749$	−35.1500	+	0.600946i	−1.28435	+	0.0219581i
$750$		0			0
$751$	−3.47739	−	6.02301i	−0.126892	−	0.219783i	0.795579	−	0.605850i	$-0.207167\pi$
$751$	−3.47739	−	6.02301i	−0.126892	−	0.219783i	−0.922471	+	0.386067i	$0.873833\pi$
$752$		0			0
$753$	−0.565343	−	2.10989i	−0.0206023	−	0.0768887i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−21.5691	−	21.5691i	−0.783941	−	0.783941i	0.196552	−	0.980493i	$-0.437025\pi$
$757$	−21.5691	−	21.5691i	−0.783941	−	0.783941i	−0.980493	+	0.196552i	$0.937025\pi$
$758$		0			0
$759$	−6.21101	+	10.7578i	−0.225445	+	0.390483i
$760$		0			0
$761$	28.7783	−	16.6152i	1.04321	−	0.602299i	0.122471	−	0.992472i	$-0.460918\pi$
$761$	28.7783	−	16.6152i	1.04321	−	0.602299i	0.920741	+	0.390173i	$0.127585\pi$
$762$		0			0
$763$	9.16939	−	36.7204i	0.331954	−	1.32937i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.24176	−	1.94042i	0.261485	−	0.0700647i
$768$		0			0
$769$	11.2327			0.405061			0.202530	−	0.979276i	$-0.435083\pi$
$769$	11.2327			0.405061			0.202530	+	0.979276i	$0.435083\pi$
$770$		0			0
$771$	2.11963			0.0763366
$772$		0			0
$773$	39.3142	−	10.5342i	1.41403	−	0.378889i	0.530671	−	0.847578i	$-0.321940\pi$
$773$	39.3142	−	10.5342i	1.41403	−	0.378889i	0.883364	+	0.468688i	$0.155273\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	14.4973	−	4.15142i	0.520089	−	0.148931i
$778$		0			0
$779$	−58.1702	+	33.5846i	−2.08416	+	1.20329i
$780$		0			0
$781$	25.1826	−	43.6175i	0.901103	−	1.56076i
$782$		0			0
$783$	2.01054	+	2.01054i	0.0718508	+	0.0718508i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	13.0253	+	48.6110i	0.464301	+	1.73280i	0.659195	+	0.751972i	$0.270897\pi$
$787$	13.0253	+	48.6110i	0.464301	+	1.73280i	−0.194894	+	0.980824i	$0.562436\pi$
$788$		0			0
$789$	13.0160	+	22.5444i	0.463383	+	0.802603i
$790$		0			0
$791$	−29.8433	−	16.5564i	−1.06111	−	0.588678i
$792$		0			0
$793$	−45.5560	−	12.2067i	−1.61774	−	0.433472i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.99837	+	7.99837i	−0.283317	+	0.283317i	−0.834430	−	0.551113i	$-0.814203\pi$
$797$	−7.99837	+	7.99837i	−0.283317	+	0.283317i	0.551113	+	0.834430i	$0.314203\pi$
$798$		0			0
$799$		−	30.6103i		−	1.08292i
$800$		0			0
$801$	−15.4361	−	8.91203i	−0.545408	−	0.314891i
$802$		0			0
$803$	10.3176	−	38.5057i	0.364099	−	1.35884i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.49860	+	5.59287i	−0.0527534	+	0.196878i
$808$		0			0
$809$	−3.21773	−	1.85776i	−0.113129	−	0.0653153i	0.442368	−	0.896834i	$-0.354139\pi$
$809$	−3.21773	−	1.85776i	−0.113129	−	0.0653153i	−0.555497	+	0.831518i	$0.687472\pi$
$810$		0			0
$811$		−	38.0896i		−	1.33751i	−0.743484	−	0.668754i	$-0.766828\pi$
$811$		−	38.0896i		−	1.33751i	0.743484	−	0.668754i	$-0.233172\pi$
$812$		0			0
$813$	−4.14055	+	4.14055i	−0.145216	+	0.145216i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	20.4279	+	5.47363i	0.714681	+	0.191498i
$818$		0			0
$819$	−0.206552	−	12.0815i	−0.00721752	−	0.422160i
$820$		0			0
$821$	2.86906	+	4.96937i	0.100131	+	0.173432i	0.911739	−	0.410771i	$-0.134740\pi$
$821$	2.86906	+	4.96937i	0.100131	+	0.173432i	−0.811607	+	0.584203i	$0.801407\pi$
$822$		0			0
$823$	7.85133	+	29.3016i	0.273680	+	1.02139i	0.956721	+	0.291008i	$0.0939907\pi$
$823$	7.85133	+	29.3016i	0.273680	+	1.02139i	−0.683040	+	0.730381i	$0.739343\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−23.4343	−	23.4343i	−0.814892	−	0.814892i	0.170471	−	0.985363i	$-0.445471\pi$
$827$	−23.4343	−	23.4343i	−0.814892	−	0.814892i	−0.985363	+	0.170471i	$0.945471\pi$
$828$		0			0
$829$	−11.0697	+	19.1733i	−0.384466	+	0.665915i	−0.991695	−	0.128612i	$-0.958948\pi$
$829$	−11.0697	+	19.1733i	−0.384466	+	0.665915i	0.607229	+	0.794527i	$0.292281\pi$
$830$		0			0
$831$	6.79385	−	3.92243i	0.235676	−	0.136068i
$832$		0			0
$833$	18.2491	+	17.0420i	0.632294	+	0.590472i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.49829	+	0.401465i	−0.0517885	+	0.0138767i
$838$		0			0
$839$	−2.41782			−0.0834725			−0.0417362	−	0.999129i	$-0.513289\pi$
$839$	−2.41782			−0.0834725			−0.0417362	+	0.999129i	$0.513289\pi$
$840$		0			0
$841$	20.9155			0.721223
$842$		0			0
$843$	−0.302664	+	0.0810985i	−0.0104243	+	0.00279318i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	13.6245	−	14.0985i	0.468143	−	0.484429i
$848$		0			0
$849$	5.83539	−	3.36906i	0.200270	−	0.115626i
$850$		0			0
$851$	−8.25057	+	14.2904i	−0.282826	+	0.489869i
$852$		0			0
$853$	−18.6647	−	18.6647i	−0.639069	−	0.639069i	0.311257	−	0.950326i	$-0.399250\pi$
$853$	−18.6647	−	18.6647i	−0.639069	−	0.639069i	−0.950326	+	0.311257i	$0.899250\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−0.791896	−	2.95540i	−0.0270507	−	0.100954i	0.951081	−	0.308943i	$-0.0999751\pi$
$857$	−0.791896	−	2.95540i	−0.0270507	−	0.100954i	−0.978131	+	0.207988i	$0.933308\pi$
$858$		0			0
$859$	16.9260	+	29.3166i	0.577506	+	1.00027i	0.995764	+	0.0919421i	$0.0293075\pi$
$859$	16.9260	+	29.3166i	0.577506	+	1.00027i	−0.418258	+	0.908328i	$0.637359\pi$
$860$		0			0
$861$	24.3052	−	14.5922i	0.828318	−	0.497300i
$862$		0			0
$863$	7.39110	+	1.98044i	0.251596	+	0.0674150i	0.382413	−	0.923992i	$-0.375093\pi$
$863$	7.39110	+	1.98044i	0.251596	+	0.0674150i	−0.130817	+	0.991407i	$0.541760\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.02380	−	3.02380i	0.102694	−	0.102694i
$868$		0			0
$869$		−	33.1403i		−	1.12421i
$870$		0			0
$871$	18.3011	+	10.5661i	0.620108	+	0.358020i
$872$		0			0
$873$	0.0368147	−	0.137394i	0.00124599	−	0.00465009i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.6059	+	54.5098i	−0.493205	+	1.84067i	0.0466538	+	0.998911i	$0.485144\pi$
$877$	−14.6059	+	54.5098i	−0.493205	+	1.84067i	−0.539859	+	0.841755i	$0.681522\pi$
$878$		0			0
$879$	−10.6637	−	6.15667i	−0.359677	−	0.207659i
$880$		0			0
$881$			13.5446i			0.456328i	0.973623	+	0.228164i	$0.0732723\pi$
$881$			13.5446i			0.456328i	−0.973623	+	0.228164i	$0.926728\pi$
$882$		0			0
$883$	−34.7205	+	34.7205i	−1.16844	+	1.16844i	−0.185864	+	0.982576i	$0.559508\pi$
$883$	−34.7205	+	34.7205i	−1.16844	+	1.16844i	−0.982576	+	0.185864i	$0.940492\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−21.3222	−	5.71328i	−0.715931	−	0.191833i	−0.117575	−	0.993064i	$-0.537512\pi$
$887$	−21.3222	−	5.71328i	−0.715931	−	0.191833i	−0.598355	+	0.801231i	$0.704179\pi$
$888$		0			0
$889$	19.2777	−	34.7485i	0.646552	−	1.16543i
$890$		0			0
$891$	−2.14536	−	3.71588i	−0.0718724	−	0.124487i
$892$		0			0
$893$	−13.9231	−	51.9618i	−0.465920	−	1.73884i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	9.34931	+	9.34931i	0.312164	+	0.312164i
$898$		0			0
$899$	2.20521	−	3.81953i	0.0735477	−	0.127388i
$900$		0			0
$901$	28.0289	−	16.1825i	0.933777	−	0.539116i
$902$		0			0
$903$	−8.65992	−	2.16246i	−0.288184	−	0.0719621i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.98469	−	0.531796i	0.0659005	−	0.0176580i	−0.225718	−	0.974193i	$-0.572473\pi$
$907$	1.98469	−	0.531796i	0.0659005	−	0.0176580i	0.291619	+	0.956535i	$0.405806\pi$
$908$		0			0
$909$	8.75071			0.290243
$910$		0			0
$911$	37.1855			1.23201			0.616006	−	0.787742i	$-0.288750\pi$
$911$	37.1855			1.23201			0.616006	+	0.787742i	$0.288750\pi$
$912$		0			0
$913$	19.4838	−	5.22066i	0.644819	−	0.172779i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.24639	−	6.03640i	−0.206274	−	0.199339i
$918$		0			0
$919$	2.39087	−	1.38037i	0.0788676	−	0.0455342i	−0.460048	−	0.887894i	$-0.652168\pi$
$919$	2.39087	−	1.38037i	0.0788676	−	0.0455342i	0.538915	+	0.842360i	$0.318834\pi$
$920$		0			0
$921$	15.7309	−	27.2467i	0.518351	−	0.897811i
$922$		0			0
$923$	−37.9069	−	37.9069i	−1.24772	−	1.24772i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.851703	−	3.17860i	−0.0279736	−	0.104399i
$928$		0			0
$929$	−18.2568	−	31.6216i	−0.598985	−	1.03747i	−0.992971	−	0.118356i	$-0.962238\pi$
$929$	−18.2568	−	31.6216i	−0.598985	−	1.03747i	0.393987	−	0.919116i	$-0.371096\pi$
$930$		0			0
$931$	38.7299	+	20.6287i	1.26932	+	0.676078i
$932$		0			0
$933$	2.85967	+	0.766245i	0.0936212	+	0.0250857i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	40.5719	−	40.5719i	1.32543	−	1.32543i	0.416112	−	0.909313i	$-0.363392\pi$
$937$	40.5719	−	40.5719i	1.32543	−	1.32543i	0.909313	−	0.416112i	$-0.136608\pi$
$938$		0			0
$939$		−	5.29073i		−	0.172656i
$940$		0			0
$941$	28.8917	+	16.6806i	0.941842	+	0.543773i	0.890537	−	0.454910i	$-0.150329\pi$
$941$	28.8917	+	16.6806i	0.941842	+	0.543773i	0.0513045	+	0.998683i	$0.483662\pi$
$942$		0			0
$943$	−8.02874	+	29.9637i	−0.261452	+	0.975751i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	13.3408	−	49.7887i	0.433519	−	1.61792i	−0.311066	−	0.950388i	$-0.600686\pi$
$947$	13.3408	−	49.7887i	0.433519	−	1.61792i	0.744585	−	0.667527i	$-0.232647\pi$
$948$		0			0
$949$	−36.7464	−	21.2155i	−1.19284	−	0.688685i
$950$		0			0
$951$			20.3965i			0.661402i
$952$		0			0
$953$	17.3822	−	17.3822i	0.563066	−	0.563066i	−0.367111	−	0.930177i	$-0.619653\pi$
$953$	17.3822	−	17.3822i	0.563066	−	0.563066i	0.930177	+	0.367111i	$0.119653\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	11.7843	+	3.15758i	0.380931	+	0.102070i
$958$		0			0
$959$	−22.5666	−	37.5877i	−0.728715	−	1.21377i
$960$		0			0
$961$	−14.2970	−	24.7631i	−0.461193	−	0.798809i
$962$		0			0
$963$	3.43903	+	12.8346i	0.110821	+	0.413590i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	7.77615	+	7.77615i	0.250064	+	0.250064i	0.820997	−	0.570933i	$-0.193418\pi$
$967$	7.77615	+	7.77615i	0.250064	+	0.250064i	−0.570933	+	0.820997i	$0.693418\pi$
$968$		0			0
$969$	−11.1804	+	19.3650i	−0.359165	+	0.622093i
$970$		0			0
$971$	21.9856	−	12.6934i	0.705551	−	0.407350i	−0.103861	−	0.994592i	$-0.533120\pi$
$971$	21.9856	−	12.6934i	0.705551	−	0.407350i	0.809411	+	0.587242i	$0.199786\pi$
$972$		0			0
$973$	−0.348567	−	1.21724i	−0.0111745	−	0.0390230i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−48.0179	+	12.8663i	−1.53623	+	0.411631i	−0.925045	−	0.379859i	$-0.875973\pi$
$977$	−48.0179	+	12.8663i	−1.53623	+	0.411631i	−0.611183	+	0.791489i	$0.709306\pi$
$978$		0			0
$979$	−76.4782			−2.44426
$980$		0			0
$981$	−14.3052			−0.456729
$982$		0			0
$983$	−11.4319	+	3.06316i	−0.364620	+	0.0976997i	−0.436477	−	0.899715i	$-0.643774\pi$
$983$	−11.4319	+	3.06316i	−0.364620	+	0.0976997i	0.0718572	+	0.997415i	$0.477107\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	6.25036	+	21.8271i	0.198951	+	0.694765i
$988$		0			0
$989$	8.45846	−	4.88349i	0.268963	−	0.155286i
$990$		0			0
$991$	11.2866	−	19.5490i	0.358532	−	0.620995i	−0.629184	−	0.777256i	$-0.716611\pi$
$991$	11.2866	−	19.5490i	0.358532	−	0.620995i	0.987716	+	0.156261i	$0.0499441\pi$
$992$		0			0
$993$	4.11587	+	4.11587i	0.130613	+	0.130613i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−4.31297	−	16.0962i	−0.136593	−	0.509773i	−0.999986	−	0.00524094i	$-0.998332\pi$
$997$	−4.31297	−	16.0962i	−0.136593	−	0.509773i	0.863393	−	0.504532i	$-0.168335\pi$
$998$		0			0
$999$	−2.84986	−	4.93609i	−0.0901654	−	0.156171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.d.157.4	yes	24
5.2	odd	4	inner	2100.2.ce.d.493.2	yes	24
5.3	odd	4	inner	2100.2.ce.d.493.4	yes	24
5.4	even	2	inner	2100.2.ce.d.157.2	✓	24
7.5	odd	6	inner	2100.2.ce.d.1657.4	yes	24
35.12	even	12	inner	2100.2.ce.d.1993.2	yes	24
35.19	odd	6	inner	2100.2.ce.d.1657.2	yes	24
35.33	even	12	inner	2100.2.ce.d.1993.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.d.157.2	✓	24	5.4	even	2	inner
2100.2.ce.d.157.4	yes	24	1.1	even	1	trivial
2100.2.ce.d.493.2	yes	24	5.2	odd	4	inner
2100.2.ce.d.493.4	yes	24	5.3	odd	4	inner
2100.2.ce.d.1657.2	yes	24	35.19	odd	6	inner
2100.2.ce.d.1657.4	yes	24	7.5	odd	6	inner
2100.2.ce.d.1993.2	yes	24	35.12	even	12	inner
2100.2.ce.d.1993.4	yes	24	35.33	even	12	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:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{3} +(0.728357 + 2.54352i) q^{7} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{3} +(0.728357 + 2.54352i) q^{7} +(0.866025 - 0.500000i) q^{9} +(2.14536 - 3.71588i) q^{11} +(-3.22938 - 3.22938i) q^{13} +(-0.923215 - 3.44549i) q^{17} +(-3.13437 - 5.42888i) q^{19} +(1.36185 + 2.26834i) q^{21} +(-2.79643 - 0.749302i) q^{23} +(0.707107 - 0.707107i) q^{27} +2.84333i q^{29} +(-1.34333 - 0.775572i) q^{31} +(1.11052 - 4.14453i) q^{33} +(1.47519 - 5.50550i) q^{37} +(-3.95516 - 2.28351i) q^{39} -10.7150i q^{41} +(-2.38553 + 2.38553i) q^{43} +(8.28905 + 2.22104i) q^{47} +(-5.93899 + 3.70518i) q^{49} +(-1.78351 - 3.08914i) q^{51} +(2.34836 + 8.76419i) q^{53} +(-4.43266 - 4.43266i) q^{57} +(-0.820799 + 1.42166i) q^{59} +(8.94331 - 5.16342i) q^{61} +(1.90254 + 1.83858i) q^{63} +(-4.46947 + 1.19759i) q^{67} -2.89508 q^{69} +11.7381 q^{71} +(8.97416 - 2.40462i) q^{73} +(11.0140 + 2.75029i) q^{77} +(6.68892 - 3.86185i) q^{79} +(0.500000 - 0.866025i) q^{81} +(3.32417 + 3.32417i) q^{83} +(0.735908 + 2.74645i) q^{87} +(-8.91203 - 15.4361i) q^{89} +(5.86185 - 10.5661i) q^{91} +(-1.49829 - 0.401465i) q^{93} +(0.100580 - 0.100580i) q^{97} -4.29073i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{11} + 8 q^{21} - 12 q^{31} - 8 q^{51} - 48 q^{61} + 64 q^{71} + 12 q^{81} + 116 q^{91}+O(q^{100}) \) 24 * q - 8 * q^11 + 8 * q^21 - 12 * q^31 - 8 * q^51 - 48 * q^61 + 64 * q^71 + 12 * q^81 + 116 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more