LMFDB - Embedded newform 2100.2.ce.d.1657.4

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			1657.4
Character	$\chi$	$=$	2100.1657
Dual form			2100.2.ce.d.493.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{3} +(2.54352 + 0.728357i) q^{7} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{3} +(2.54352 + 0.728357i) q^{7} +(-0.866025 - 0.500000i) q^{9} +(2.14536 + 3.71588i) q^{11} +(3.22938 + 3.22938i) q^{13} +(-3.44549 - 0.923215i) q^{17} +(3.13437 - 5.42888i) q^{19} +(1.36185 - 2.26834i) q^{21} +(0.749302 + 2.79643i) q^{23} +(-0.707107 + 0.707107i) q^{27} +2.84333i q^{29} +(-1.34333 + 0.775572i) q^{31} +(4.14453 - 1.11052i) q^{33} +(-5.50550 + 1.47519i) q^{37} +(3.95516 - 2.28351i) q^{39} +10.7150i q^{41} +(-2.38553 + 2.38553i) q^{43} +(2.22104 + 8.28905i) q^{47} +(5.93899 + 3.70518i) q^{49} +(-1.78351 + 3.08914i) q^{51} +(-8.76419 - 2.34836i) q^{53} +(-4.43266 - 4.43266i) q^{57} +(0.820799 + 1.42166i) q^{59} +(8.94331 + 5.16342i) q^{61} +(-1.83858 - 1.90254i) q^{63} +(1.19759 - 4.46947i) q^{67} +2.89508 q^{69} +11.7381 q^{71} +(2.40462 - 8.97416i) q^{73} +(2.75029 + 11.0140i) q^{77} +(-6.68892 - 3.86185i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-3.32417 - 3.32417i) q^{83} +(2.74645 + 0.735908i) q^{87} +(8.91203 - 15.4361i) q^{89} +(5.86185 + 10.5661i) q^{91} +(0.401465 + 1.49829i) q^{93} +(-0.100580 + 0.100580i) q^{97} -4.29073i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.54352	+	0.728357i	0.961360	+	0.275293i
$7$	2.54352	+	0.728357i	0.961360	+	0.275293i
$8$		0			0
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$		0			0
$11$	2.14536	+	3.71588i	0.646852	+	1.12038i	0.983870	+	0.178882i	$0.0572481\pi$
$11$	2.14536	+	3.71588i	0.646852	+	1.12038i	−0.337019	+	0.941498i	$0.609419\pi$
$12$		0			0
$13$	3.22938	+	3.22938i	0.895668	+	0.895668i	0.995049	−	0.0993812i	$-0.0316863\pi$
$13$	3.22938	+	3.22938i	0.895668	+	0.895668i	−0.0993812	+	0.995049i	$0.531686\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.44549	−	0.923215i	−0.835653	−	0.223913i	−0.184475	−	0.982837i	$-0.559058\pi$
$17$	−3.44549	−	0.923215i	−0.835653	−	0.223913i	−0.651178	+	0.758925i	$0.725725\pi$
$18$		0			0
$19$	3.13437	−	5.42888i	0.719073	−	1.24547i	−0.242295	−	0.970203i	$-0.577900\pi$
$19$	3.13437	−	5.42888i	0.719073	−	1.24547i	0.961368	−	0.275268i	$-0.0887665\pi$
$20$		0			0
$21$	1.36185	−	2.26834i	0.297180	−	0.494992i
$22$		0			0
$23$	0.749302	+	2.79643i	0.156240	+	0.583097i	0.998996	+	0.0448005i	$0.0142652\pi$
$23$	0.749302	+	2.79643i	0.156240	+	0.583097i	−0.842756	+	0.538296i	$0.819068\pi$
$24$		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	−0.615760	−	0.787934i	$-0.711151\pi$
$31$	−1.34333	+	0.775572i	−0.241269	+	0.139297i	0.374491	+	0.927231i	$0.377818\pi$
$32$		0			0
$33$	4.14453	−	1.11052i	0.721469	−	0.193317i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−5.50550	+	1.47519i	−0.905098	+	0.242520i	−0.681204	−	0.732093i	$-0.738544\pi$
$37$	−5.50550	+	1.47519i	−0.905098	+	0.242520i	−0.223894	+	0.974614i	$0.571877\pi$
$38$		0			0
$39$	3.95516	−	2.28351i	0.633333	−	0.365655i
$40$		0			0
$41$			10.7150i			1.67339i	0.547665	+	0.836697i	$0.315517\pi$
$41$			10.7150i			1.67339i	−0.547665	+	0.836697i	$0.684483\pi$
$42$		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
$47$	2.22104	+	8.28905i	0.323973	+	1.20908i	0.915341	+	0.402681i	$0.131921\pi$
$47$	2.22104	+	8.28905i	0.323973	+	1.20908i	−0.591368	+	0.806402i	$0.701412\pi$
$48$		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
$53$	−8.76419	−	2.34836i	−1.20385	−	0.322572i	−0.399506	−	0.916730i	$-0.630818\pi$
$53$	−8.76419	−	2.34836i	−1.20385	−	0.322572i	−0.804348	+	0.594159i	$0.797485\pi$
$54$		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	$-0.132587\pi$
$59$	0.820799	+	1.42166i	0.106859	+	0.185085i	−0.807637	+	0.589680i	$0.799254\pi$
$60$		0			0
$61$	8.94331	+	5.16342i	1.14507	+	0.661108i	0.947682	−	0.319216i	$-0.103420\pi$
$61$	8.94331	+	5.16342i	1.14507	+	0.661108i	0.197391	+	0.980325i	$0.436753\pi$
$62$		0			0
$63$	−1.83858	−	1.90254i	−0.231639	−	0.239697i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	1.19759	−	4.46947i	0.146309	−	0.546032i	−0.853385	−	0.521282i	$-0.825454\pi$
$67$	1.19759	−	4.46947i	0.146309	−	0.546032i	0.999694	−	0.0247507i	$-0.00787921\pi$
$68$		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
$73$	2.40462	−	8.97416i	0.281439	−	1.05035i	−0.669963	−	0.742394i	$-0.733690\pi$
$73$	2.40462	−	8.97416i	0.281439	−	1.05035i	0.951402	−	0.307951i	$-0.0996433\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.75029	+	11.0140i	0.313425	+	1.25516i
$78$		0			0
$79$	−6.68892	−	3.86185i	−0.752562	−	0.434492i	0.0740567	−	0.997254i	$-0.476405\pi$
$79$	−6.68892	−	3.86185i	−0.752562	−	0.434492i	−0.826619	+	0.562762i	$0.809739\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	−3.32417	−	3.32417i	−0.364875	−	0.364875i	0.500729	−	0.865604i	$-0.333065\pi$
$83$	−3.32417	−	3.32417i	−0.364875	−	0.364875i	−0.865604	+	0.500729i	$0.833065\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	2.74645	+	0.735908i	0.294450	+	0.0788976i
$88$		0			0
$89$	8.91203	−	15.4361i	0.944674	−	1.63622i	0.188270	−	0.982117i	$-0.439712\pi$
$89$	8.91203	−	15.4361i	0.944674	−	1.63622i	0.756403	−	0.654105i	$-0.226955\pi$
$90$		0			0
$91$	5.86185	+	10.5661i	0.614489	+	1.10763i
$92$		0			0
$93$	0.401465	+	1.49829i	0.0416300	+	0.155365i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.100580	+	0.100580i	−0.0102123	+	0.0102123i	−0.712194	−	0.701982i	$-0.752299\pi$
$97$	−0.100580	+	0.100580i	−0.0102123	+	0.0102123i	0.701982	+	0.712194i	$0.252299\pi$
$98$		0			0
$99$		−	4.29073i		−	0.431235i
$100$		0			0
$101$	7.57834	−	4.37535i	0.754073	−	0.435364i	−0.0730910	−	0.997325i	$-0.523286\pi$
$101$	7.57834	−	4.37535i	0.754073	−	0.435364i	0.827164	+	0.561961i	$0.189953\pi$
$102$		0			0
$103$	3.17860	−	0.851703i	0.313197	−	0.0839208i	−0.0987966	−	0.995108i	$-0.531499\pi$
$103$	3.17860	−	0.851703i	0.313197	−	0.0839208i	0.411993	+	0.911187i	$0.364833\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.8346	−	3.43903i	1.24077	−	0.332463i	0.422006	−	0.906593i	$-0.361326\pi$
$107$	12.8346	−	3.43903i	1.24077	−	0.332463i	0.818764	+	0.574130i	$0.194659\pi$
$108$		0			0
$109$	12.3886	−	7.15258i	1.18662	−	0.685093i	0.229080	−	0.973408i	$-0.426428\pi$
$109$	12.3886	−	7.15258i	1.18662	−	0.685093i	0.957536	+	0.288315i	$0.0930949\pi$
$110$		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
$117$	−1.18203	−	4.41141i	−0.109279	−	0.407835i
$118$		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
$123$	10.3499	+	2.77323i	0.933215	+	0.250054i
$124$		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	0.370619	−	0.928785i	$-0.379146\pi$
$131$	−2.84333	−	1.64160i	−0.248423	−	0.143427i	−0.619042	+	0.785358i	$0.712479\pi$
$132$		0			0
$133$	11.9265	−	11.5255i	1.03416	−	0.999390i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.28878	−	16.0060i	0.366415	−	1.36748i	−0.499077	−	0.866558i	$-0.666327\pi$
$137$	4.28878	−	16.0060i	0.366415	−	1.36748i	0.865492	−	0.500923i	$-0.167006\pi$
$138$		0			0
$139$	0.478566			0.0405914			0.0202957	−	0.999794i	$-0.493539\pi$
$139$	0.478566			0.0405914			0.0202957	+	0.999794i	$0.493539\pi$
$140$		0			0
$141$	8.58146			0.722689
$142$		0			0
$143$	−5.07179	+	18.9282i	−0.424124	+	1.58285i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	5.11605	−	4.77766i	0.421965	−	0.394054i
$148$		0			0
$149$	8.41389	+	4.85776i	0.689292	+	0.397963i	0.803347	−	0.595511i	$-0.203051\pi$
$149$	8.41389	+	4.85776i	0.689292	+	0.397963i	−0.114055	+	0.993474i	$0.536384\pi$
$150$		0			0
$151$	10.2196	+	17.7009i	0.831660	+	1.44048i	0.896721	+	0.442596i	$0.145942\pi$
$151$	10.2196	+	17.7009i	0.831660	+	1.44048i	−0.0650611	+	0.997881i	$0.520724\pi$
$152$		0			0
$153$	2.52227	+	2.52227i	0.203914	+	0.203914i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.82282	+	2.36407i	0.704138	+	0.188673i	0.593083	−	0.805141i	$-0.297910\pi$
$157$	8.82282	+	2.36407i	0.704138	+	0.188673i	0.111055	+	0.993814i	$0.464577\pi$
$158$		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
$163$	−2.68973	−	10.0382i	−0.210676	−	0.786252i	−0.987644	−	0.156713i	$-0.949910\pi$
$163$	−2.68973	−	10.0382i	−0.210676	−	0.786252i	0.776969	−	0.629539i	$-0.216756\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−16.0521	+	16.0521i	−1.24215	+	1.24215i	−0.283040	+	0.959108i	$0.591343\pi$
$167$	−16.0521	+	16.0521i	−1.24215	+	1.24215i	−0.959108	+	0.283040i	$0.908657\pi$
$168$		0			0
$169$			7.85776i			0.604443i
$170$		0			0
$171$	−5.42888	+	3.13437i	−0.415157	+	0.239691i
$172$		0			0
$173$	−22.3737	+	5.99500i	−1.70104	+	0.455792i	−0.973201	−	0.229958i	$-0.926141\pi$
$173$	−22.3737	+	5.99500i	−1.70104	+	0.455792i	−0.727837	+	0.685750i	$0.759474\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.58566	−	0.424877i	0.119186	−	0.0319357i
$178$		0			0
$179$	−5.19615	+	3.00000i	−0.388379	+	0.224231i	−0.681457	−	0.731858i	$-0.738654\pi$
$179$	−5.19615	+	3.00000i	−0.388379	+	0.224231i	0.293079	+	0.956088i	$0.405320\pi$
$180$		0			0
$181$		−	18.9871i		−	1.41130i	−0.708561	−	0.705650i	$-0.750655\pi$
$181$		−	18.9871i		−	1.41130i	0.708561	−	0.705650i	$-0.249345\pi$
$182$		0			0
$183$	7.30218	−	7.30218i	0.539793	−	0.539793i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.96127	−	14.7836i	−0.289677	−	1.08109i
$188$		0			0
$189$	−2.31357	+	1.28351i	−0.168287	+	0.0933620i
$190$		0			0
$191$	−6.56703	+	11.3744i	−0.475174	+	0.823025i	−0.999596	−	0.0284336i	$-0.990948\pi$
$191$	−6.56703	+	11.3744i	−0.475174	+	0.823025i	0.524422	+	0.851458i	$0.324281\pi$
$192$		0			0
$193$	8.67682	+	2.32495i	0.624571	+	0.167353i	0.557205	−	0.830375i	$-0.311874\pi$
$193$	8.67682	+	2.32495i	0.624571	+	0.167353i	0.0673662	+	0.997728i	$0.478540\pi$
$194$		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	$-0.165928\pi$
$199$	0.0327307	+	0.0566912i	0.00232021	+	0.00401873i	−0.864863	+	0.502008i	$0.832595\pi$
$200$		0			0
$201$	−4.00721	−	2.31357i	−0.282647	−	0.163186i
$202$		0			0
$203$	−2.07096	+	7.23207i	−0.145353	+	0.507592i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.749302	−	2.79643i	0.0520801	−	0.194366i
$208$		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
$213$	3.03805	−	11.3382i	0.208164	−	0.776878i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.98168	+	0.994260i	−0.270294	+	0.0674947i
$218$		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	0.952529	−	0.304447i	$-0.0984717\pi$
$223$	9.67793	+	9.67793i	0.648082	+	0.648082i	−0.304447	+	0.952529i	$0.598472\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.9418	+	2.93184i	0.726232	+	0.194593i	0.602951	−	0.797779i	$-0.293992\pi$
$227$	10.9418	+	2.93184i	0.726232	+	0.194593i	0.123281	+	0.992372i	$0.460658\pi$
$228$		0			0
$229$	1.04693	−	1.81334i	0.0691833	−	0.119829i	−0.829359	−	0.558716i	$-0.811294\pi$
$229$	1.04693	−	1.81334i	0.0691833	−	0.119829i	0.898542	+	0.438888i	$0.144627\pi$
$230$		0			0
$231$	11.3505	+	0.194056i	0.746811	+	0.0127680i
$232$		0			0
$233$	−6.39622	−	23.8710i	−0.419030	−	1.56384i	−0.776623	−	0.629965i	$-0.783069\pi$
$233$	−6.39622	−	23.8710i	−0.419030	−	1.56384i	0.357593	−	0.933878i	$-0.383598\pi$
$234$		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	0.450166	−	0.892945i	$-0.351365\pi$
$241$	22.4877	−	12.9833i	1.44856	−	0.836328i	0.998396	+	0.0566174i	$0.0180315\pi$
$242$		0			0
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	27.6539	−	7.40985i	1.75958	−	0.471478i
$248$		0			0
$249$	−4.07126	+	2.35054i	−0.258006	+	0.148960i
$250$		0			0
$251$			2.18432i			0.137873i	0.997621	+	0.0689365i	$0.0219606\pi$
$251$			2.18432i			0.137873i	−0.997621	+	0.0689365i	$0.978039\pi$
$252$		0			0
$253$	−8.78369	+	8.78369i	−0.552226	+	0.552226i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.548601	+	2.04741i	0.0342208	+	0.127714i	0.980923	−	0.194396i	$-0.0622747\pi$
$257$	0.548601	+	2.04741i	0.0342208	+	0.127714i	−0.946702	+	0.322110i	$0.895608\pi$
$258$		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
$263$	−25.1450	−	6.73759i	−1.55051	−	0.415458i	−0.620865	−	0.783917i	$-0.713219\pi$
$263$	−25.1450	−	6.73759i	−1.55051	−	0.415458i	−0.929644	+	0.368460i	$0.879885\pi$
$264$		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	$-0.110184\pi$
$269$	2.89508	+	5.01443i	0.176516	+	0.305735i	−0.764169	+	0.645016i	$0.776851\pi$
$270$		0			0
$271$	−5.07112	−	2.92781i	−0.308049	−	0.177852i	0.338004	−	0.941145i	$-0.390248\pi$
$271$	−5.07112	−	2.92781i	−0.308049	−	0.177852i	−0.646053	+	0.763293i	$0.723581\pi$
$272$		0			0
$273$	11.7233	−	2.92740i	0.709524	−	0.177174i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.03040	+	7.57756i	−0.121995	+	0.455291i	−0.999715	−	0.0238829i	$-0.992397\pi$
$277$	−2.03040	+	7.57756i	−0.121995	+	0.455291i	0.877720	+	0.479174i	$0.159064\pi$
$278$		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
$283$	1.74396	−	6.50853i	0.103667	−	0.386892i	−0.894523	−	0.447022i	$-0.852485\pi$
$283$	1.74396	−	6.50853i	0.103667	−	0.386892i	0.998191	+	0.0601295i	$0.0191514\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.80431	+	27.2537i	−0.460674	+	1.60874i
$288$		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	0.914115	−	0.405455i	$-0.132887\pi$
$293$	8.70685	+	8.70685i	0.508659	+	0.508659i	−0.405455	+	0.914115i	$0.632887\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4.14453	−	1.11052i	−0.240490	−	0.0644391i
$298$		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
$303$	−2.26485	−	8.45253i	−0.130112	−	0.485585i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−22.2469	+	22.2469i	−1.26970	+	1.26970i	−0.323451	+	0.946245i	$0.604843\pi$
$307$	−22.2469	+	22.2469i	−1.26970	+	1.26970i	−0.946245	+	0.323451i	$0.895157\pi$
$308$		0			0
$309$		−	3.29073i		−	0.187203i
$310$		0			0
$311$	2.56391	−	1.48027i	0.145386	−	0.0839385i	−0.425543	−	0.904938i	$-0.639917\pi$
$311$	2.56391	−	1.48027i	0.145386	−	0.0839385i	0.570928	+	0.821000i	$0.306583\pi$
$312$		0			0
$313$	5.11045	−	1.36934i	0.288860	−	0.0773998i	−0.111479	−	0.993767i	$-0.535559\pi$
$313$	5.11045	−	1.36934i	0.288860	−	0.0773998i	0.400339	+	0.916367i	$0.368892\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	19.7015	−	5.27900i	1.10655	−	0.296498i	0.341119	−	0.940020i	$-0.389194\pi$
$317$	19.7015	−	5.27900i	1.10655	−	0.296498i	0.765428	+	0.643522i	$0.222527\pi$
$318$		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
$327$	−3.70245	−	13.8177i	−0.204746	−	0.764122i
$328$		0			0
$329$	−0.388112	+	22.7011i	−0.0213973	+	1.25155i
$330$		0			0
$331$	2.91036	−	5.04089i	0.159968	−	0.277072i	−0.774889	−	0.632097i	$-0.782194\pi$
$331$	2.91036	−	5.04089i	0.159968	−	0.277072i	0.934857	+	0.355025i	$0.115528\pi$
$332$		0			0
$333$	5.50550	+	1.47519i	0.301699	+	0.0808401i
$334$		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
$343$	12.4073	+	13.7499i	0.669929	+	0.742425i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.54368	+	31.8854i	−0.458649	+	1.71170i	0.218485	+	0.975840i	$0.429889\pi$
$347$	−8.54368	+	31.8854i	−0.458649	+	1.71170i	−0.677134	+	0.735860i	$0.736778\pi$
$348$		0			0
$349$	−12.3566			−0.661431			−0.330716	−	0.943730i	$-0.607290\pi$
$349$	−12.3566			−0.661431			−0.330716	+	0.943730i	$0.607290\pi$
$350$		0			0
$351$	−4.56703			−0.243770
$352$		0			0
$353$	0.173986	−	0.649324i	0.00926034	−	0.0345600i	−0.961141	−	0.276058i	$-0.910972\pi$
$353$	0.173986	−	0.649324i	0.00926034	−	0.0345600i	0.970401	+	0.241498i	$0.0776386\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−6.78640	+	6.55825i	−0.359174	+	0.347099i
$358$		0			0
$359$	−24.7577	−	14.2939i	−1.30666	−	0.754401i	−0.325123	−	0.945672i	$-0.605406\pi$
$359$	−24.7577	−	14.2939i	−1.30666	−	0.754401i	−0.981537	+	0.191271i	$0.938739\pi$
$360$		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
$367$	−2.50744	−	0.671865i	−0.130887	−	0.0350711i	0.192781	−	0.981242i	$-0.438249\pi$
$367$	−2.50744	−	0.671865i	−0.130887	−	0.0350711i	−0.323668	+	0.946171i	$0.604916\pi$
$368$		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
$373$	−1.33806	−	4.99370i	−0.0692820	−	0.258564i	0.922594	−	0.385772i	$-0.126065\pi$
$373$	−1.33806	−	4.99370i	−0.0692820	−	0.258564i	−0.991876	+	0.127208i	$0.959398\pi$
$374$		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
$383$	−8.28905	+	2.22104i	−0.423551	+	0.113490i	−0.464297	−	0.885679i	$-0.653693\pi$
$383$	−8.28905	+	2.22104i	−0.423551	+	0.113490i	0.0407465	+	0.999170i	$0.487026\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	3.25869	−	0.873164i	0.165649	−	0.0443854i
$388$		0			0
$389$	−15.0903	+	8.71239i	−0.765109	+	0.441736i	−0.831127	−	0.556083i	$-0.812304\pi$
$389$	−15.0903	+	8.71239i	−0.765109	+	0.441736i	0.0660180	+	0.997818i	$0.478971\pi$
$390$		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
$397$	−2.46654	−	9.20526i	−0.123792	−	0.461999i	0.876002	−	0.482308i	$-0.160202\pi$
$397$	−2.46654	−	9.20526i	−0.123792	−	0.461999i	−0.999794	+	0.0203095i	$0.993535\pi$
$398$		0			0
$399$	−8.04601	−	14.5031i	−0.402804	−	0.726064i
$400$		0			0
$401$	5.42479	−	9.39601i	0.270901	−	0.469214i	−0.698192	−	0.715911i	$-0.746012\pi$
$401$	5.42479	−	9.39601i	0.270901	−	0.469214i	0.969093	+	0.246696i	$0.0793451\pi$
$402$		0			0
$403$	−6.84273	−	1.83350i	−0.340861	−	0.0913334i
$404$		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	0.915673	+	0.401923i	$0.131658\pi$
$409$	16.2986	+	28.2299i	0.805912	+	1.39588i	−0.109761	+	0.993958i	$0.535009\pi$
$410$		0			0
$411$	−14.3505	−	8.28529i	−0.707860	−	0.408683i
$412$		0			0
$413$	1.05224	+	4.21387i	0.0517773	+	0.207351i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.123862	−	0.462259i	0.00606555	−	0.0226369i
$418$		0			0
$419$	−22.6179			−1.10496			−0.552479	−	0.833527i	$-0.686318\pi$
$419$	−22.6179			−1.10496			−0.552479	+	0.833527i	$0.686318\pi$
$420$		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
$423$	2.22104	−	8.28905i	0.107991	−	0.403028i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	18.9867	+	19.6472i	0.918830	+	0.950794i
$428$		0			0
$429$	16.9705	+	9.79794i	0.819345	+	0.473049i
$430$		0			0
$431$	−17.0144	−	29.4699i	−0.819556	−	1.41951i	−0.906010	−	0.423257i	$-0.860887\pi$
$431$	−17.0144	−	29.4699i	−0.819556	−	1.41951i	0.0864534	−	0.996256i	$-0.472447\pi$
$432$		0			0
$433$	22.6580	+	22.6580i	1.08888	+	1.08888i	0.995645	+	0.0932307i	$0.0297194\pi$
$433$	22.6580	+	22.6580i	1.08888	+	1.08888i	0.0932307	+	0.995645i	$0.470281\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	17.5301	+	4.69717i	0.838578	+	0.224696i
$438$		0			0
$439$	1.99698	−	3.45887i	0.0953106	−	0.165083i	−0.814428	−	0.580265i	$-0.802949\pi$
$439$	1.99698	−	3.45887i	0.0953106	−	0.165083i	0.909738	+	0.415182i	$0.136282\pi$
$440$		0			0
$441$	−3.29073	−	6.17828i	−0.156701	−	0.294204i
$442$		0			0
$443$	3.50559	+	13.0831i	0.166556	+	0.621595i	0.997837	+	0.0657421i	$0.0209415\pi$
$443$	3.50559	+	13.0831i	0.166556	+	0.621595i	−0.831281	+	0.555853i	$0.812392\pi$
$444$		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
$453$	19.7428	−	5.29006i	0.927596	−	0.248549i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	21.1998	−	5.68047i	0.991685	−	0.265721i	0.273727	−	0.961808i	$-0.411744\pi$
$457$	21.1998	−	5.68047i	0.991685	−	0.265721i	0.717958	+	0.696086i	$0.245077\pi$
$458$		0			0
$459$	3.08914	−	1.78351i	0.144189	−	0.0832473i
$460$		0			0
$461$		−	6.11282i		−	0.284702i	−0.989816	−	0.142351i	$-0.954534\pi$
$461$		−	6.11282i		−	0.284702i	0.989816	−	0.142351i	$-0.0454662\pi$
$462$		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
$467$	−2.65012	−	9.89037i	−0.122633	−	0.457672i	0.877112	−	0.480287i	$-0.159467\pi$
$467$	−2.65012	−	9.89037i	−0.122633	−	0.457672i	−0.999744	+	0.0226152i	$0.992801\pi$
$468$		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
$473$	−13.9822	−	3.74651i	−0.642901	−	0.172265i
$474$		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	−0.999737	−	0.0229118i	$-0.992706\pi$
$479$	−11.3744	−	19.7011i	−0.519711	−	0.900166i	0.480027	−	0.877254i	$-0.340627\pi$
$480$		0			0
$481$	−22.5433	−	13.0154i	−1.02789	−	0.593450i
$482$		0			0
$483$	7.36370	+	2.10865i	0.335060	+	0.0959470i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	9.94217	−	37.1047i	0.450523	−	1.68137i	−0.250405	−	0.968141i	$-0.580564\pi$
$487$	9.94217	−	37.1047i	0.450523	−	1.68137i	0.700927	−	0.713233i	$-0.252770\pi$
$488$		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
$493$	2.62501	−	9.79665i	0.118224	−	0.441219i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	29.8562	+	8.54954i	1.33923	+	0.383499i
$498$		0			0
$499$	−10.2370	−	5.91036i	−0.458273	−	0.264584i	0.253045	−	0.967455i	$-0.418568\pi$
$499$	−10.2370	−	5.91036i	−0.458273	−	0.264584i	−0.711318	+	0.702871i	$0.751901\pi$
$500$		0			0
$501$	11.3505	+	19.6597i	0.507105	+	0.878331i
$502$		0			0
$503$	12.7279	+	12.7279i	0.567510	+	0.567510i	0.931430	−	0.363920i	$-0.118562\pi$
$503$	12.7279	+	12.7279i	0.567510	+	0.567510i	−0.363920	+	0.931430i	$0.618562\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	7.59001	+	2.03374i	0.337084	+	0.0903215i
$508$		0			0
$509$	−8.41389	+	14.5733i	−0.372939	+	0.645949i	−0.990016	−	0.140953i	$-0.954983\pi$
$509$	−8.41389	+	14.5733i	−0.372939	+	0.645949i	0.617077	+	0.786903i	$0.288317\pi$
$510$		0			0
$511$	12.6526	−	21.0745i	0.559717	−	0.932282i
$512$		0			0
$513$	1.62247	+	6.05513i	0.0716337	+	0.267340i
$514$		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	0.389592	−	0.920988i	$-0.372616\pi$
$521$	31.5444	−	18.2122i	1.38199	−	0.797890i	0.992395	+	0.123098i	$0.0392829\pi$
$522$		0			0
$523$	3.87764	−	1.03901i	0.169557	−	0.0454328i	−0.173042	−	0.984915i	$-0.555359\pi$
$523$	3.87764	−	1.03901i	0.169557	−	0.0454328i	0.342599	+	0.939482i	$0.388693\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.34444	−	1.43204i	0.232808	−	0.0623806i
$528$		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
$537$	1.55291	+	5.79555i	0.0670132	+	0.250097i
$538$		0			0
$539$	−1.02670	+	30.0176i	−0.0442230	+	1.29295i
$540$		0			0
$541$	14.9248	−	25.8505i	0.641667	−	1.11140i	−0.343394	−	0.939191i	$-0.611577\pi$
$541$	14.9248	−	25.8505i	0.641667	−	1.11140i	0.985061	−	0.172208i	$-0.0550901\pi$
$542$		0			0
$543$	−18.3401	−	4.91422i	−0.787050	−	0.210889i
$544$		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
$553$	−14.2006	−	14.6946i	−0.603871	−	0.624879i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.67716	−	24.9195i	0.282920	−	1.05587i	−0.667426	−	0.744677i	$-0.732604\pi$
$557$	6.67716	−	24.9195i	0.282920	−	1.05587i	0.950346	−	0.311196i	$-0.100730\pi$
$558$		0			0
$559$	−15.4075			−0.651670
$560$		0			0
$561$	−15.3052			−0.646184
$562$		0			0
$563$	2.88918	−	10.7826i	0.121764	−	0.454430i	−0.877939	−	0.478772i	$-0.841082\pi$
$563$	2.88918	−	10.7826i	0.121764	−	0.454430i	0.999704	+	0.0243413i	$0.00774885\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.640985	+	2.56693i	0.0269188	+	0.107801i
$568$		0			0
$569$	−14.8189	−	8.55572i	−0.621243	−	0.358675i	0.156110	−	0.987740i	$-0.450105\pi$
$569$	−14.8189	−	8.55572i	−0.621243	−	0.358675i	−0.777353	+	0.629065i	$0.783438\pi$
$570$		0			0
$571$	−4.56294	−	7.90324i	−0.190953	−	0.330740i	0.754613	−	0.656170i	$-0.227824\pi$
$571$	−4.56294	−	7.90324i	−0.190953	−	0.330740i	−0.945566	+	0.325429i	$0.894491\pi$
$572$		0			0
$573$	9.28718	+	9.28718i	0.387978	+	0.387978i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−16.5642	−	4.43836i	−0.689575	−	0.184771i	−0.103019	−	0.994679i	$-0.532850\pi$
$577$	−16.5642	−	4.43836i	−0.689575	−	0.184771i	−0.586557	+	0.809908i	$0.699517\pi$
$578$		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
$583$	−10.0762	−	37.6048i	−0.417312	−	1.55743i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−30.8269	+	30.8269i	−1.27236	+	1.27236i	−0.327520	+	0.944844i	$0.606213\pi$
$587$	−30.8269	+	30.8269i	−1.27236	+	1.27236i	−0.944844	+	0.327520i	$0.893787\pi$
$588$		0			0
$589$			9.72370i			0.400658i
$590$		0			0
$591$	9.22273	−	5.32475i	0.379373	−	0.219031i
$592$		0			0
$593$	−30.2166	+	8.09652i	−1.24085	+	0.332484i	−0.818794	−	0.574087i	$-0.805357\pi$
$593$	−30.2166	+	8.09652i	−1.24085	+	0.332484i	−0.422053	+	0.906571i	$0.638691\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.0632308	−	0.0169426i	0.00258786	−	0.000693416i
$598$		0			0
$599$	−3.23190	+	1.86594i	−0.132052	+	0.0762403i	−0.564571	−	0.825385i	$-0.690958\pi$
$599$	−3.23190	+	1.86594i	−0.132052	+	0.0762403i	0.432519	+	0.901625i	$0.357625\pi$
$600$		0			0
$601$		−	12.0089i		−	0.489854i	−0.969542	−	0.244927i	$-0.921236\pi$
$601$		−	12.0089i		−	0.489854i	0.969542	−	0.244927i	$-0.0787639\pi$
$602$		0			0
$603$	−3.27188	+	3.27188i	−0.133241	+	0.133241i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.09786	+	11.5614i	0.125738	+	0.469261i	0.999865	−	0.0164366i	$-0.00523216\pi$
$607$	3.09786	+	11.5614i	0.125738	+	0.469261i	−0.874127	+	0.485698i	$0.838565\pi$
$608$		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
$613$	2.48478	+	0.665794i	0.100359	+	0.0268912i	0.308649	−	0.951176i	$-0.400123\pi$
$613$	2.48478	+	0.665794i	0.100359	+	0.0268912i	−0.208290	+	0.978067i	$0.566790\pi$
$614$		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	$-0.311324\pi$
$619$	−10.9215	−	18.9166i	−0.438972	−	0.760323i	−0.997611	+	0.0690889i	$0.977991\pi$
$620$		0			0
$621$	−2.50721	−	1.44754i	−0.100611	−	0.0580878i
$622$		0			0
$623$	33.9109	−	32.7709i	1.35861	−	1.31294i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.96157	−	25.9809i	0.278018	−	1.03758i
$628$		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
$633$	−5.06594	+	18.9063i	−0.201353	+	0.751459i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	7.21383	+	31.1447i	0.285822	+	1.23400i
$638$		0			0
$639$	−10.1655	−	5.86906i	−0.402142	−	0.232177i
$640$		0			0
$641$	−20.7124	−	35.8749i	−0.818090	−	1.41697i	−0.907087	−	0.420942i	$-0.861700\pi$
$641$	−20.7124	−	35.8749i	−0.818090	−	1.41697i	0.0889971	−	0.996032i	$-0.471634\pi$
$642$		0			0
$643$	−27.2798	−	27.2798i	−1.07581	−	1.07581i	−0.996880	−	0.0789320i	$-0.974849\pi$
$643$	−27.2798	−	27.2798i	−1.07581	−	1.07581i	−0.0789320	−	0.996880i	$-0.525151\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	25.2296	+	6.76026i	0.991879	+	0.265773i	0.718040	−	0.696002i	$-0.245040\pi$
$647$	25.2296	+	6.76026i	0.991879	+	0.265773i	0.273839	+	0.961775i	$0.411706\pi$
$648$		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
$653$	−3.63993	−	13.5844i	−0.142441	−	0.531599i	−0.999856	−	0.0169724i	$-0.994597\pi$
$653$	−3.63993	−	13.5844i	−0.142441	−	0.531599i	0.857414	−	0.514626i	$-0.172069\pi$
$654$		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	−0.962937	−	0.269727i	$-0.913067\pi$
$661$	−31.1300	+	17.9729i	−1.21082	+	0.699065i	−0.247878	+	0.968791i	$0.579733\pi$
$662$		0			0
$663$	−15.7356	+	4.21635i	−0.611121	+	0.163750i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.95119	+	2.13051i	−0.307871	+	0.0824938i
$668$		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
$677$	5.20311	+	19.4183i	0.199972	+	0.746305i	0.990924	+	0.134426i	$0.0429191\pi$
$677$	5.20311	+	19.4183i	0.199972	+	0.746305i	−0.790952	+	0.611878i	$0.790414\pi$
$678$		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
$683$	4.69375	+	1.25769i	0.179601	+	0.0481241i	0.347499	−	0.937680i	$-0.387031\pi$
$683$	4.69375	+	1.25769i	0.179601	+	0.0481241i	−0.167897	+	0.985804i	$0.553698\pi$
$684$		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	−0.481238	−	0.876590i	$-0.659813\pi$
$691$	−38.9310	−	22.4768i	−1.48101	−	0.855059i	−0.999768	+	0.0215304i	$0.993146\pi$
$692$		0			0
$693$	3.12518	−	10.9136i	0.118716	−	0.414572i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.89221	−	36.9182i	0.374694	−	1.39838i
$698$		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
$703$	−9.24759	+	34.5125i	−0.348779	+	1.30166i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	22.4625	−	5.60907i	0.844788	−	0.210951i
$708$		0			0
$709$	30.0324	+	17.3392i	1.12789	+	0.651189i	0.943404	−	0.331646i	$-0.107604\pi$
$709$	30.0324	+	17.3392i	1.12789	+	0.651189i	0.184488	+	0.982835i	$0.440937\pi$
$710$		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
$717$	−20.6729	−	5.53929i	−0.772044	−	0.206869i
$718$		0			0
$719$	7.75441	−	13.4310i	0.289191	−	0.500893i	−0.684426	−	0.729082i	$-0.739947\pi$
$719$	7.75441	−	13.4310i	0.289191	−	0.500893i	0.973617	+	0.228189i	$0.0732805\pi$
$720$		0			0
$721$	8.70518	+	0.148829i	0.324198	+	0.00554269i
$722$		0			0
$723$	−6.72065	−	25.0818i	−0.249944	−	0.932802i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	12.8475	−	12.8475i	0.476489	−	0.476489i	−0.427518	−	0.904007i	$-0.640612\pi$
$727$	12.8475	−	12.8475i	0.476489	−	0.476489i	0.904007	+	0.427518i	$0.140612\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	10.4217	−	6.01695i	0.385459	−	0.222545i
$732$		0			0
$733$	14.8913	−	3.99011i	0.550023	−	0.147378i	0.0269041	−	0.999638i	$-0.491435\pi$
$733$	14.8913	−	3.99011i	0.550023	−	0.147378i	0.523119	+	0.852260i	$0.324768\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	19.1773	−	5.13854i	0.706404	−	0.189280i
$738$		0			0
$739$	−34.8911	+	20.1444i	−1.28349	+	0.741024i	−0.977485	−	0.211006i	$-0.932326\pi$
$739$	−34.8911	+	20.1444i	−1.28349	+	0.741024i	−0.306006	+	0.952030i	$0.598993\pi$
$740$		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
$747$	1.21673	+	4.54090i	0.0445179	+	0.166143i
$748$		0			0
$749$	35.1500	+	0.600946i	1.28435	+	0.0219581i
$750$		0			0
$751$	−3.47739	+	6.02301i	−0.126892	+	0.219783i	−0.922471	−	0.386067i	$-0.873833\pi$
$751$	−3.47739	+	6.02301i	−0.126892	+	0.219783i	0.795579	+	0.605850i	$0.207167\pi$
$752$		0			0
$753$	2.10989	+	0.565343i	0.0768887	+	0.0206023i
$754$		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	0.920741	−	0.390173i	$-0.127585\pi$
$761$	28.7783	+	16.6152i	1.04321	+	0.602299i	0.122471	+	0.992472i	$0.460918\pi$
$762$		0			0
$763$	36.7204	−	9.16939i	1.32937	−	0.331954i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−1.94042	+	7.24176i	−0.0700647	+	0.261485i
$768$		0			0
$769$	−11.2327			−0.405061			−0.202530	−	0.979276i	$-0.564917\pi$
$769$	−11.2327			−0.405061			−0.202530	+	0.979276i	$0.564917\pi$
$770$		0			0
$771$	2.11963			0.0763366
$772$		0			0
$773$	10.5342	−	39.3142i	0.378889	−	1.41403i	−0.468688	−	0.883364i	$-0.655273\pi$
$773$	10.5342	−	39.3142i	0.378889	−	1.41403i	0.847578	−	0.530671i	$-0.178060\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−4.15142	+	14.4973i	−0.148931	+	0.520089i
$778$		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
$787$	48.6110	+	13.0253i	1.73280	+	0.464301i	0.980824	−	0.194894i	$-0.0624364\pi$
$787$	48.6110	+	13.0253i	1.73280	+	0.464301i	0.751972	+	0.659195i	$0.229103\pi$
$788$		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
$793$	12.2067	+	45.5560i	0.433472	+	1.61774i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.99837	−	7.99837i	0.283317	−	0.283317i	−0.551113	−	0.834430i	$-0.685797\pi$
$797$	7.99837	−	7.99837i	0.283317	−	0.283317i	0.834430	+	0.551113i	$0.185797\pi$
$798$		0			0
$799$		−	30.6103i		−	1.08292i
$800$		0			0
$801$	−15.4361	+	8.91203i	−0.545408	+	0.314891i
$802$		0			0
$803$	38.5057	−	10.3176i	1.35884	−	0.364099i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	5.59287	−	1.49860i	0.196878	−	0.0527534i
$808$		0			0
$809$	3.21773	−	1.85776i	0.113129	−	0.0653153i	−0.442368	−	0.896834i	$-0.645861\pi$
$809$	3.21773	−	1.85776i	0.113129	−	0.0653153i	0.555497	+	0.831518i	$0.312528\pi$
$810$		0			0
$811$			38.0896i			1.33751i	0.743484	+	0.668754i	$0.233172\pi$
$811$			38.0896i			1.33751i	−0.743484	+	0.668754i	$0.766828\pi$
$812$		0			0
$813$	−4.14055	+	4.14055i	−0.145216	+	0.145216i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	5.47363	+	20.4279i	0.191498	+	0.714681i
$818$		0			0
$819$	0.206552	−	12.0815i	0.00721752	−	0.422160i
$820$		0			0
$821$	2.86906	−	4.96937i	0.100131	−	0.173432i	−0.811607	−	0.584203i	$-0.801407\pi$
$821$	2.86906	−	4.96937i	0.100131	−	0.173432i	0.911739	+	0.410771i	$0.134740\pi$
$822$		0			0
$823$	−29.3016	−	7.85133i	−1.02139	−	0.273680i	−0.291008	−	0.956721i	$-0.593991\pi$
$823$	−29.3016	−	7.85133i	−1.02139	−	0.273680i	−0.730381	+	0.683040i	$0.760657\pi$
$824$		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	$-0.0410522\pi$
$829$	11.0697	+	19.1733i	0.384466	+	0.665915i	−0.607229	+	0.794527i	$0.707719\pi$
$830$		0			0
$831$	6.79385	+	3.92243i	0.235676	+	0.136068i
$832$		0			0
$833$	−17.0420	−	18.2491i	−0.590472	−	0.632294i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	0.401465	−	1.49829i	0.0138767	−	0.0517885i
$838$		0			0
$839$	2.41782			0.0834725			0.0417362	−	0.999129i	$-0.486711\pi$
$839$	2.41782			0.0834725			0.0417362	+	0.999129i	$0.486711\pi$
$840$		0			0
$841$	20.9155			0.721223
$842$		0			0
$843$	−0.0810985	+	0.302664i	−0.00279318	+	0.0104243i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.0985	+	13.6245i	−0.484429	+	0.468143i
$848$		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	0.950326	−	0.311257i	$-0.100750\pi$
$853$	18.6647	+	18.6647i	0.639069	+	0.639069i	−0.311257	+	0.950326i	$0.600750\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−2.95540	−	0.791896i	−0.100954	−	0.0270507i	0.207988	−	0.978131i	$-0.433308\pi$
$857$	−2.95540	−	0.791896i	−0.100954	−	0.0270507i	−0.308943	+	0.951081i	$0.599975\pi$
$858$		0			0
$859$	−16.9260	+	29.3166i	−0.577506	+	1.00027i	0.418258	+	0.908328i	$0.362641\pi$
$859$	−16.9260	+	29.3166i	−0.577506	+	1.00027i	−0.995764	+	0.0919421i	$0.970693\pi$
$860$		0			0
$861$	24.3052	+	14.5922i	0.828318	+	0.497300i
$862$		0			0
$863$	−1.98044	−	7.39110i	−0.0674150	−	0.251596i	0.923992	−	0.382413i	$-0.124907\pi$
$863$	−1.98044	−	7.39110i	−0.0674150	−	0.251596i	−0.991407	+	0.130817i	$0.958240\pi$
$864$		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
$873$	0.137394	−	0.0368147i	0.00465009	−	0.00124599i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	54.5098	−	14.6059i	1.84067	−	0.493205i	0.841755	−	0.539859i	$-0.181522\pi$
$877$	54.5098	−	14.6059i	1.84067	−	0.493205i	0.998911	+	0.0466538i	$0.0148558\pi$
$878$		0			0
$879$	10.6637	−	6.15667i	0.359677	−	0.207659i
$880$		0			0
$881$		−	13.5446i		−	0.456328i	−0.973623	−	0.228164i	$-0.926728\pi$
$881$		−	13.5446i		−	0.456328i	0.973623	−	0.228164i	$-0.0732723\pi$
$882$		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
$887$	−5.71328	−	21.3222i	−0.191833	−	0.715931i	−0.993064	−	0.117575i	$-0.962488\pi$
$887$	−5.71328	−	21.3222i	−0.191833	−	0.715931i	0.801231	−	0.598355i	$-0.204179\pi$
$888$		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
$893$	51.9618	+	13.9231i	1.73884	+	0.465920i
$894$		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
$903$	2.16246	+	8.65992i	0.0719621	+	0.288184i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.531796	+	1.98469i	−0.0176580	+	0.0659005i	−0.974193	−	0.225718i	$-0.927527\pi$
$907$	−0.531796	+	1.98469i	−0.0176580	+	0.0659005i	0.956535	+	0.291619i	$0.0941938\pi$
$908$		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
$913$	5.22066	−	19.4838i	0.172779	−	0.644819i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.03640	−	6.24639i	−0.199339	−	0.206274i
$918$		0			0
$919$	−2.39087	−	1.38037i	−0.0788676	−	0.0455342i	0.460048	−	0.887894i	$-0.347832\pi$
$919$	−2.39087	−	1.38037i	−0.0788676	−	0.0455342i	−0.538915	+	0.842360i	$0.681166\pi$
$920$		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
$927$	−3.17860	−	0.851703i	−0.104399	−	0.0279736i
$928$		0			0
$929$	18.2568	−	31.6216i	0.598985	−	1.03747i	−0.393987	−	0.919116i	$-0.628904\pi$
$929$	18.2568	−	31.6216i	0.598985	−	1.03747i	0.992971	−	0.118356i	$-0.0377623\pi$
$930$		0			0
$931$	38.7299	−	20.6287i	1.26932	−	0.676078i
$932$		0			0
$933$	−0.766245	−	2.85967i	−0.0250857	−	0.0936212i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−40.5719	+	40.5719i	−1.32543	+	1.32543i	−0.416112	+	0.909313i	$0.636608\pi$
$937$	−40.5719	+	40.5719i	−1.32543	+	1.32543i	−0.909313	+	0.416112i	$0.863392\pi$
$938$		0			0
$939$		−	5.29073i		−	0.172656i
$940$		0			0
$941$	28.8917	−	16.6806i	0.941842	−	0.543773i	0.0513045	−	0.998683i	$-0.483662\pi$
$941$	28.8917	−	16.6806i	0.941842	−	0.543773i	0.890537	+	0.454910i	$0.150329\pi$
$942$		0			0
$943$	−29.9637	+	8.02874i	−0.975751	+	0.261452i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−49.7887	+	13.3408i	−1.61792	+	0.433519i	−0.950388	−	0.311066i	$-0.899314\pi$
$947$	−49.7887	+	13.3408i	−1.61792	+	0.433519i	−0.667527	+	0.744585i	$0.732647\pi$
$948$		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
$957$	3.15758	+	11.7843i	0.102070	+	0.380931i
$958$		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
$963$	−12.8346	−	3.43903i	−0.413590	−	0.110821i
$964$		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	0.809411	−	0.587242i	$-0.199786\pi$
$971$	21.9856	+	12.6934i	0.705551	+	0.407350i	−0.103861	+	0.994592i	$0.533120\pi$
$972$		0			0
$973$	1.21724	+	0.348567i	0.0390230	+	0.0111745i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	12.8663	−	48.0179i	0.411631	−	1.53623i	−0.379859	−	0.925045i	$-0.624027\pi$
$977$	12.8663	−	48.0179i	0.411631	−	1.53623i	0.791489	−	0.611183i	$-0.209306\pi$
$978$		0			0
$979$	76.4782			2.44426
$980$		0			0
$981$	−14.3052			−0.456729
$982$		0			0
$983$	−3.06316	+	11.4319i	−0.0976997	+	0.364620i	−0.997415	−	0.0718572i	$-0.977107\pi$
$983$	−3.06316	+	11.4319i	−0.0976997	+	0.364620i	0.899715	+	0.436477i	$0.143774\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	21.8271	+	6.25036i	0.694765	+	0.198951i
$988$		0			0
$989$	−8.45846	−	4.88349i	−0.268963	−	0.155286i
$990$		0			0
$991$	11.2866	+	19.5490i	0.358532	+	0.620995i	0.987716	−	0.156261i	$-0.0499441\pi$
$991$	11.2866	+	19.5490i	0.358532	+	0.620995i	−0.629184	+	0.777256i	$0.716611\pi$
$992$		0			0
$993$	−4.11587	−	4.11587i	−0.130613	−	0.130613i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−16.0962	−	4.31297i	−0.509773	−	0.136593i	−0.00524094	−	0.999986i	$-0.501668\pi$
$997$	−16.0962	−	4.31297i	−0.509773	−	0.136593i	−0.504532	+	0.863393i	$0.668335\pi$
$998$		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.1657.4	yes	24
5.2	odd	4	inner	2100.2.ce.d.1993.2	yes	24
5.3	odd	4	inner	2100.2.ce.d.1993.4	yes	24
5.4	even	2	inner	2100.2.ce.d.1657.2	yes	24
7.3	odd	6	inner	2100.2.ce.d.157.4	yes	24
35.3	even	12	inner	2100.2.ce.d.493.4	yes	24
35.17	even	12	inner	2100.2.ce.d.493.2	yes	24
35.24	odd	6	inner	2100.2.ce.d.157.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.d.157.2	✓	24	35.24	odd	6	inner
2100.2.ce.d.157.4	yes	24	7.3	odd	6	inner
2100.2.ce.d.493.2	yes	24	35.17	even	12	inner
2100.2.ce.d.493.4	yes	24	35.3	even	12	inner
2100.2.ce.d.1657.2	yes	24	5.4	even	2	inner
2100.2.ce.d.1657.4	yes	24	1.1	even	1	trivial
2100.2.ce.d.1993.2	yes	24	5.2	odd	4	inner
2100.2.ce.d.1993.4	yes	24	5.3	odd	4	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)

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

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