LMFDB - Embedded newform 2100.2.ce.d.493.6

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			493.6
Character	$\chi$	$=$	2100.493
Dual form			2100.2.ce.d.1657.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{3} +(-0.895840 - 2.48947i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{3} +(-0.895840 - 2.48947i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-0.720993 + 1.24880i) q^{11} +(-1.97110 + 1.97110i) q^{13} +(3.65850 - 0.980291i) q^{17} +(-0.643613 - 1.11477i) q^{19} +(2.17278 - 1.50964i) q^{21} +(0.135022 - 0.503908i) q^{23} +(-0.707107 - 0.707107i) q^{27} +6.13312i q^{29} +(7.63312 + 4.40699i) q^{31} +(-1.39285 - 0.373213i) q^{33} +(4.08552 + 1.09471i) q^{37} +(-2.41409 - 1.39378i) q^{39} +9.57951i q^{41} +(1.27909 + 1.27909i) q^{43} +(-0.746427 + 2.78570i) q^{47} +(-5.39494 + 4.46034i) q^{49} +(1.89378 + 3.28012i) q^{51} +(5.83279 - 1.56289i) q^{53} +(0.910206 - 0.910206i) q^{57} +(-1.77048 + 3.06656i) q^{59} +(-1.71119 + 0.987954i) q^{61} +(2.02056 + 1.70803i) q^{63} +(0.583310 + 2.17694i) q^{67} +0.521684 q^{69} +9.24915 q^{71} +(0.920882 + 3.43678i) q^{73} +(3.75474 + 0.676169i) q^{77} +(-8.09350 + 4.67278i) q^{79} +(0.500000 - 0.866025i) q^{81} +(12.2773 - 12.2773i) q^{83} +(-5.92414 + 1.58737i) q^{87} +(3.94736 + 6.83702i) q^{89} +(6.67278 + 3.14120i) q^{91} +(-2.28122 + 8.51364i) q^{93} +(-9.35470 - 9.35470i) q^{97} -1.44199i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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
$3$	0.258819	+	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
$7$	−0.895840	−	2.48947i	−0.338596	−	0.940932i
$7$	−0.895840	−	2.48947i	−0.338596	−	0.940932i
$8$		0			0
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$		0			0
$11$	−0.720993	+	1.24880i	−0.217387	+	0.376526i	−0.954008	−	0.299780i	$-0.903087\pi$
$11$	−0.720993	+	1.24880i	−0.217387	+	0.376526i	0.736621	+	0.676306i	$0.236420\pi$
$12$		0			0
$13$	−1.97110	+	1.97110i	−0.546684	+	0.546684i	−0.925480	−	0.378796i	$-0.876338\pi$
$13$	−1.97110	+	1.97110i	−0.546684	+	0.546684i	0.378796	+	0.925480i	$0.376338\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.65850	−	0.980291i	0.887316	−	0.237756i	0.213755	−	0.976887i	$-0.431431\pi$
$17$	3.65850	−	0.980291i	0.887316	−	0.237756i	0.673561	+	0.739132i	$0.264764\pi$
$18$		0			0
$19$	−0.643613	−	1.11477i	−0.147655	−	0.255746i	0.782705	−	0.622392i	$-0.213839\pi$
$19$	−0.643613	−	1.11477i	−0.147655	−	0.255746i	−0.930360	+	0.366647i	$0.880506\pi$
$20$		0			0
$21$	2.17278	−	1.50964i	0.474140	−	0.329430i
$22$		0			0
$23$	0.135022	−	0.503908i	0.0281540	−	0.105072i	−0.950419	−	0.310972i	$-0.899345\pi$
$23$	0.135022	−	0.503908i	0.0281540	−	0.105072i	0.978573	+	0.205900i	$0.0660121\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			6.13312i			1.13889i	0.822029	+	0.569446i	$0.192842\pi$
$29$			6.13312i			1.13889i	−0.822029	+	0.569446i	$0.807158\pi$
$30$		0			0
$31$	7.63312	+	4.40699i	1.37095	+	0.791518i	0.991048	−	0.133509i	$-0.0426244\pi$
$31$	7.63312	+	4.40699i	1.37095	+	0.791518i	0.379902	+	0.925027i	$0.375958\pi$
$32$		0			0
$33$	−1.39285	−	0.373213i	−0.242464	−	0.0649681i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.08552	+	1.09471i	0.671656	+	0.179970i	0.578500	−	0.815682i	$-0.303638\pi$
$37$	4.08552	+	1.09471i	0.671656	+	0.179970i	0.0931551	+	0.995652i	$0.470305\pi$
$38$		0			0
$39$	−2.41409	−	1.39378i	−0.386564	−	0.223183i
$40$		0			0
$41$			9.57951i			1.49607i	0.663660	+	0.748034i	$0.269002\pi$
$41$			9.57951i			1.49607i	−0.663660	+	0.748034i	$0.730998\pi$
$42$		0			0
$43$	1.27909	+	1.27909i	0.195060	+	0.195060i	0.797878	−	0.602819i	$-0.205956\pi$
$43$	1.27909	+	1.27909i	0.195060	+	0.195060i	−0.602819	+	0.797878i	$0.705956\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.746427	+	2.78570i	−0.108878	+	0.406336i	−0.998756	−	0.0498609i	$-0.984122\pi$
$47$	−0.746427	+	2.78570i	−0.108878	+	0.406336i	0.889879	+	0.456197i	$0.150789\pi$
$48$		0			0
$49$	−5.39494	+	4.46034i	−0.770706	+	0.637191i
$50$		0			0
$51$	1.89378	+	3.28012i	0.265182	+	0.459308i
$52$		0			0
$53$	5.83279	−	1.56289i	0.801196	−	0.214680i	0.165087	−	0.986279i	$-0.447210\pi$
$53$	5.83279	−	1.56289i	0.801196	−	0.214680i	0.636109	+	0.771599i	$0.280543\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.910206	−	0.910206i	0.120560	−	0.120560i
$58$		0			0
$59$	−1.77048	+	3.06656i	−0.230497	+	0.399232i	−0.957954	−	0.286920i	$-0.907368\pi$
$59$	−1.77048	+	3.06656i	−0.230497	+	0.399232i	0.727458	+	0.686153i	$0.240702\pi$
$60$		0			0
$61$	−1.71119	+	0.987954i	−0.219095	+	0.126495i	−0.605531	−	0.795822i	$-0.707039\pi$
$61$	−1.71119	+	0.987954i	−0.219095	+	0.126495i	0.386436	+	0.922316i	$0.373706\pi$
$62$		0			0
$63$	2.02056	+	1.70803i	0.254566	+	0.215191i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	0.583310	+	2.17694i	0.0712626	+	0.265956i	0.992360	−	0.123377i	$-0.0393724\pi$
$67$	0.583310	+	2.17694i	0.0712626	+	0.265956i	−0.921097	+	0.389332i	$0.872706\pi$
$68$		0			0
$69$	0.521684			0.0628034
$70$		0			0
$71$	9.24915			1.09767			0.548836	−	0.835930i	$-0.315071\pi$
$71$	9.24915			1.09767			0.548836	+	0.835930i	$0.315071\pi$
$72$		0			0
$73$	0.920882	+	3.43678i	0.107781	+	0.402244i	0.998646	−	0.0520242i	$-0.0165673\pi$
$73$	0.920882	+	3.43678i	0.107781	+	0.402244i	−0.890865	+	0.454269i	$0.849901\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.75474	+	0.676169i	0.427892	+	0.0770566i
$78$		0			0
$79$	−8.09350	+	4.67278i	−0.910590	+	0.525729i	−0.880621	−	0.473821i	$-0.842874\pi$
$79$	−8.09350	+	4.67278i	−0.910590	+	0.525729i	−0.0299690	+	0.999551i	$0.509541\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	12.2773	−	12.2773i	1.34760	−	1.34760i	0.459347	−	0.888257i	$-0.348083\pi$
$83$	12.2773	−	12.2773i	1.34760	−	1.34760i	0.888257	−	0.459347i	$-0.151917\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.92414	+	1.58737i	−0.635135	+	0.170184i
$88$		0			0
$89$	3.94736	+	6.83702i	0.418419	+	0.724723i	0.995781	−	0.0917656i	$-0.0292511\pi$
$89$	3.94736	+	6.83702i	0.418419	+	0.724723i	−0.577362	+	0.816489i	$0.695918\pi$
$90$		0			0
$91$	6.67278	+	3.14120i	0.699498	+	0.329288i
$92$		0			0
$93$	−2.28122	+	8.51364i	−0.236552	+	0.882824i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.35470	−	9.35470i	−0.949826	−	0.949826i	0.0489744	−	0.998800i	$-0.484405\pi$
$97$	−9.35470	−	9.35470i	−0.949826	−	0.949826i	−0.998800	+	0.0489744i	$0.984405\pi$
$98$		0			0
$99$		−	1.44199i		−	0.144925i
$100$		0			0
$101$	12.0666	+	6.96663i	1.20067	+	0.693206i	0.960704	−	0.277576i	$-0.0895310\pi$
$101$	12.0666	+	6.96663i	1.20067	+	0.693206i	0.239964	+	0.970782i	$0.422864\pi$
$102$		0			0
$103$	−2.35878	−	0.632032i	−0.232417	−	0.0622760i	0.140731	−	0.990048i	$-0.455055\pi$
$103$	−2.35878	−	0.632032i	−0.232417	−	0.0622760i	−0.373148	+	0.927772i	$0.621722\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	10.5421	+	2.82475i	1.01914	+	0.273079i	0.729445	−	0.684039i	$-0.239778\pi$
$107$	10.5421	+	2.82475i	1.01914	+	0.273079i	0.289698	+	0.957118i	$0.406445\pi$
$108$		0			0
$109$	3.86386	+	2.23080i	0.370090	+	0.213672i	0.673498	−	0.739189i	$-0.264791\pi$
$109$	3.86386	+	2.23080i	0.370090	+	0.213672i	−0.303408	+	0.952861i	$0.598124\pi$
$110$		0			0
$111$			4.22964i			0.401460i
$112$		0			0
$113$	−13.0939	−	13.0939i	−1.23177	−	1.23177i	−0.963283	−	0.268489i	$-0.913476\pi$
$113$	−13.0939	−	13.0939i	−1.23177	−	1.23177i	−0.268489	−	0.963283i	$-0.586524\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.721472	−	2.69257i	0.0667001	−	0.248928i
$118$		0			0
$119$	−5.71784	−	8.22954i	−0.524153	−	0.754401i
$120$		0			0
$121$	4.46034	+	7.72553i	0.405485	+	0.702321i
$122$		0			0
$123$	−9.25310	+	2.47936i	−0.834324	+	0.223556i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.94210	+	8.94210i	−0.793483	+	0.793483i	−0.982059	−	0.188576i	$-0.939613\pi$
$127$	−8.94210	+	8.94210i	−0.793483	+	0.793483i	0.188576	+	0.982059i	$0.439613\pi$
$128$		0			0
$129$	−0.904455	+	1.56656i	−0.0796328	+	0.137928i
$130$		0			0
$131$	6.13312	−	3.54096i	0.535853	−	0.309375i	−0.207543	−	0.978226i	$-0.566547\pi$
$131$	6.13312	−	3.54096i	0.535853	−	0.309375i	0.743397	+	0.668851i	$0.233213\pi$
$132$		0			0
$133$	−2.19861	+	2.60091i	−0.190644	+	0.225528i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.991812	+	3.70149i	0.0847362	+	0.316240i	0.995264	−	0.0972077i	$-0.0309911\pi$
$137$	0.991812	+	3.70149i	0.0847362	+	0.316240i	−0.910528	+	0.413448i	$0.864324\pi$
$138$		0			0
$139$	−2.33059			−0.197678			−0.0988392	−	0.995103i	$-0.531513\pi$
$139$	−2.33059			−0.197678			−0.0988392	+	0.995103i	$0.531513\pi$
$140$		0			0
$141$	−2.88397			−0.242874
$142$		0			0
$143$	−1.04035	−	3.88265i	−0.0869986	−	0.324683i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.70467	−	4.05669i	−0.470513	−	0.334590i
$148$		0			0
$149$	−14.2540	+	8.22954i	−1.16773	+	0.674190i	−0.953145	−	0.302515i	$-0.902174\pi$
$149$	−14.2540	+	8.22954i	−1.16773	+	0.674190i	−0.214587	+	0.976705i	$0.568841\pi$
$150$		0			0
$151$	−2.05676	+	3.56240i	−0.167376	+	0.289904i	−0.937497	−	0.347994i	$-0.886863\pi$
$151$	−2.05676	+	3.56240i	−0.167376	+	0.289904i	0.770120	+	0.637899i	$0.220196\pi$
$152$		0			0
$153$	−2.67821	+	2.67821i	−0.216520	+	0.216520i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−5.38514	+	1.44294i	−0.429781	+	0.115159i	−0.467223	−	0.884139i	$-0.654746\pi$
$157$	−5.38514	+	1.44294i	−0.429781	+	0.115159i	0.0374423	+	0.999299i	$0.488079\pi$
$158$		0			0
$159$	3.01928	+	5.22954i	0.239444	+	0.414729i
$160$		0			0
$161$	−1.37542	+	0.115288i	−0.108399	+	0.00908600i
$162$		0			0
$163$	−2.68973	+	10.0382i	−0.210676	+	0.786252i	0.776969	+	0.629539i	$0.216756\pi$
$163$	−2.68973	+	10.0382i	−0.210676	+	0.786252i	−0.987644	+	0.156713i	$0.949910\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−0.450665	−	0.450665i	−0.0348735	−	0.0348735i	0.689455	−	0.724329i	$-0.257850\pi$
$167$	−0.450665	−	0.450665i	−0.0348735	−	0.0348735i	−0.724329	+	0.689455i	$0.757850\pi$
$168$		0			0
$169$			5.22954i			0.402272i
$170$		0			0
$171$	1.11477	+	0.643613i	0.0852486	+	0.0492183i
$172$		0			0
$173$	−0.224151	−	0.0600611i	−0.0170419	−	0.00456636i	0.250288	−	0.968171i	$-0.419475\pi$
$173$	−0.224151	−	0.0600611i	−0.0170419	−	0.00456636i	−0.267330	+	0.963605i	$0.586141\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.42031	−	0.916468i	−0.257086	−	0.0688860i
$178$		0			0
$179$	−5.19615	−	3.00000i	−0.388379	−	0.224231i	0.293079	−	0.956088i	$-0.405320\pi$
$179$	−5.19615	−	3.00000i	−0.388379	−	0.224231i	−0.681457	+	0.731858i	$0.738654\pi$
$180$		0			0
$181$			6.68435i			0.496844i	0.968652	+	0.248422i	$0.0799119\pi$
$181$			6.68435i			0.496844i	−0.968652	+	0.248422i	$0.920088\pi$
$182$		0			0
$183$	−1.39718	−	1.39718i	−0.103282	−	0.103282i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.41357	+	5.27550i	−0.103370	+	0.385783i
$188$		0			0
$189$	−1.12687	+	2.39378i	−0.0819676	+	0.174122i
$190$		0			0
$191$	0.787555	+	1.36408i	0.0569854	+	0.0987017i	0.893111	−	0.449837i	$-0.148518\pi$
$191$	0.787555	+	1.36408i	0.0569854	+	0.0987017i	−0.836125	+	0.548538i	$0.815184\pi$
$192$		0			0
$193$	−10.9261	+	2.92765i	−0.786480	+	0.210737i	−0.629640	−	0.776887i	$-0.716797\pi$
$193$	−10.9261	+	2.92765i	−0.786480	+	0.210737i	−0.156840	+	0.987624i	$0.550131\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.5194	+	15.5194i	−1.10571	+	1.10571i	−0.112003	+	0.993708i	$0.535726\pi$
$197$	−15.5194	+	15.5194i	−1.10571	+	1.10571i	−0.993708	+	0.112003i	$0.964274\pi$
$198$		0			0
$199$	6.18411	−	10.7112i	0.438380	−	0.759296i	−0.559185	−	0.829043i	$-0.688886\pi$
$199$	6.18411	−	10.7112i	0.438380	−	0.759296i	0.997565	+	0.0697470i	$0.0222192\pi$
$200$		0			0
$201$	−1.95179	+	1.12687i	−0.137669	+	0.0794831i
$202$		0			0
$203$	15.2682	−	5.49430i	1.07162	−	0.385624i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	0.135022	+	0.503908i	0.00938467	+	0.0350241i
$208$		0			0
$209$	1.85616			0.128393
$210$		0			0
$211$	19.6886			1.35542			0.677710	−	0.735329i	$-0.262972\pi$
$211$	19.6886			1.35542			0.677710	+	0.735329i	$0.262972\pi$
$212$		0			0
$213$	2.39386	+	8.93400i	0.164024	+	0.612147i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	4.13301	−	22.9504i	0.280567	−	1.55797i
$218$		0			0
$219$	−3.08133	+	1.77901i	−0.208217	+	0.120214i
$220$		0			0
$221$	−5.27901	+	9.14351i	−0.355104	+	0.615059i
$222$		0			0
$223$	−3.01669	+	3.01669i	−0.202013	+	0.202013i	−0.800862	−	0.598849i	$-0.795625\pi$
$223$	−3.01669	+	3.01669i	−0.202013	+	0.202013i	0.598849	+	0.800862i	$0.295625\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	24.3122	−	6.51443i	1.61366	−	0.432378i	0.664527	−	0.747264i	$-0.268633\pi$
$227$	24.3122	−	6.51443i	1.61366	−	0.432378i	0.949129	+	0.314886i	$0.101966\pi$
$228$		0			0
$229$	11.4120	+	19.7662i	0.754129	+	1.30619i	0.945806	+	0.324732i	$0.105274\pi$
$229$	11.4120	+	19.7662i	0.754129	+	1.30619i	−0.191677	+	0.981458i	$0.561392\pi$
$230$		0			0
$231$	0.318668	+	3.80180i	0.0209668	+	0.250140i
$232$		0			0
$233$	6.79166	−	25.3468i	0.444936	−	1.66052i	−0.271169	−	0.962532i	$-0.587410\pi$
$233$	6.79166	−	25.3468i	0.444936	−	1.66052i	0.716105	−	0.697993i	$-0.245923\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.60832	−	6.60832i	−0.429256	−	0.429256i
$238$		0			0
$239$		−	22.7253i		−	1.46998i	−0.678078	−	0.734990i	$-0.737187\pi$
$239$		−	22.7253i		−	1.46998i	0.678078	−	0.734990i	$-0.262813\pi$
$240$		0			0
$241$	−19.2070	−	11.0892i	−1.23723	−	0.714315i	−0.268703	−	0.963223i	$-0.586595\pi$
$241$	−19.2070	−	11.0892i	−1.23723	−	0.714315i	−0.968527	+	0.248908i	$0.919928\pi$
$242$		0			0
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.46595	+	0.928697i	0.220533	+	0.0590916i
$248$		0			0
$249$	15.0365	+	8.68133i	0.952900	+	0.550157i
$250$		0			0
$251$		−	28.0971i		−	1.77347i	−0.462275	−	0.886737i	$-0.652967\pi$
$251$		−	28.0971i		−	1.77347i	0.462275	−	0.886737i	$-0.347033\pi$
$252$		0			0
$253$	0.531929	+	0.531929i	0.0334421	+	0.0334421i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.19445	+	8.18979i	−0.136886	+	0.510865i	0.863097	+	0.505038i	$0.168521\pi$
$257$	−2.19445	+	8.18979i	−0.136886	+	0.510865i	−0.999983	+	0.00582706i	$0.998145\pi$
$258$		0			0
$259$	−0.934720	−	11.1515i	−0.0580807	−	0.692919i
$260$		0			0
$261$	−3.06656	−	5.31144i	−0.189815	−	0.328770i
$262$		0			0
$263$	9.47582	−	2.53904i	0.584304	−	0.156564i	0.0454554	−	0.998966i	$-0.485526\pi$
$263$	9.47582	−	2.53904i	0.584304	−	0.156564i	0.538849	+	0.842403i	$0.318859\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5.58241	+	5.58241i	−0.341638	+	0.341638i
$268$		0			0
$269$	0.521684	−	0.903584i	0.0318077	−	0.0550925i	−0.849683	−	0.527293i	$-0.823207\pi$
$269$	0.521684	−	0.903584i	0.0318077	−	0.0550925i	0.881491	+	0.472201i	$0.156540\pi$
$270$		0			0
$271$	−11.6148	+	6.70579i	−0.705547	+	0.407348i	−0.809410	−	0.587244i	$-0.800213\pi$
$271$	−11.6148	+	6.70579i	−0.705547	+	0.407348i	0.103863	+	0.994592i	$0.466880\pi$
$272$		0			0
$273$	−1.30713	+	7.25842i	−0.0791109	+	0.439299i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	4.45076	+	16.6104i	0.267420	+	0.998025i	0.960752	+	0.277407i	$0.0894751\pi$
$277$	4.45076	+	16.6104i	0.267420	+	0.998025i	−0.693332	+	0.720618i	$0.743858\pi$
$278$		0			0
$279$	−8.81397			−0.527679
$280$		0			0
$281$	−18.2662			−1.08967			−0.544836	−	0.838542i	$-0.683408\pi$
$281$	−18.2662			−1.08967			−0.544836	+	0.838542i	$0.683408\pi$
$282$		0			0
$283$	1.09976	+	4.10437i	0.0653740	+	0.243979i	0.990879	−	0.134757i	$-0.0430254\pi$
$283$	1.09976	+	4.10437i	0.0653740	+	0.243979i	−0.925505	+	0.378736i	$0.876359\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	23.8479	−	8.58172i	1.40770	−	0.506563i
$288$		0			0
$289$	−2.29880	+	1.32722i	−0.135224	+	0.0780715i
$290$		0			0
$291$	6.61477	−	11.4571i	0.387765	−	0.671628i
$292$		0			0
$293$	21.4015	−	21.4015i	1.25029	−	1.25029i	0.294696	−	0.955591i	$-0.404782\pi$
$293$	21.4015	−	21.4015i	1.25029	−	1.25029i	0.955591	−	0.294696i	$-0.0952184\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.39285	−	0.373213i	0.0808214	−	0.0216560i
$298$		0			0
$299$	0.727112	+	1.25939i	0.0420500	+	0.0728327i
$300$		0			0
$301$	2.03840	−	4.33013i	0.117492	−	0.249584i
$302$		0			0
$303$	−3.60619	+	13.4585i	−0.207170	+	0.773171i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−21.6337	−	21.6337i	−1.23470	−	1.23470i	−0.962137	−	0.272565i	$-0.912128\pi$
$307$	−21.6337	−	21.6337i	−1.23470	−	1.23470i	−0.272565	−	0.962137i	$-0.587872\pi$
$308$		0			0
$309$		−	2.44199i		−	0.138920i
$310$		0			0
$311$	11.1630	+	6.44495i	0.632994	+	0.365459i	0.781911	−	0.623390i	$-0.214245\pi$
$311$	11.1630	+	6.44495i	0.632994	+	0.365459i	−0.148916	+	0.988850i	$0.547579\pi$
$312$		0			0
$313$	−0.426925	−	0.114394i	−0.0241312	−	0.00646594i	0.246733	−	0.969083i	$-0.420643\pi$
$313$	−0.426925	−	0.114394i	−0.0241312	−	0.00646594i	−0.270864	+	0.962617i	$0.587310\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	27.4209	+	7.34741i	1.54011	+	0.412672i	0.926302	−	0.376782i	$-0.122969\pi$
$317$	27.4209	+	7.34741i	1.54011	+	0.412672i	0.613810	+	0.789454i	$0.289636\pi$
$318$		0			0
$319$	−7.65902	−	4.42194i	−0.428823	−	0.247581i
$320$		0			0
$321$			10.9140i			0.609159i
$322$		0			0
$323$	−3.44745	−	3.44745i	−0.191821	−	0.191821i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−1.15475	+	4.30957i	−0.0638576	+	0.238320i
$328$		0			0
$329$	7.60361	−	0.637336i	0.419200	−	0.0351375i
$330$		0			0
$331$	−13.4207	−	23.2453i	−0.737667	−	1.27768i	−0.953543	−	0.301256i	$-0.902594\pi$
$331$	−13.4207	−	23.2453i	−0.737667	−	1.27768i	0.215876	−	0.976421i	$-0.430739\pi$
$332$		0			0
$333$	−4.08552	+	1.09471i	−0.223885	+	0.0599899i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.2829	+	11.2829i	−0.614618	+	0.614618i	−0.944146	−	0.329528i	$-0.893111\pi$
$337$	−11.2829	+	11.2829i	−0.614618	+	0.614618i	0.329528	+	0.944146i	$0.393111\pi$
$338$		0			0
$339$	9.25880	−	16.0367i	0.502869	−	0.870994i
$340$		0			0
$341$	−11.0069	+	6.35481i	−0.596054	+	0.344132i
$342$		0			0
$343$	15.9369	+	9.43480i	0.860511	+	0.509431i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.41863	+	16.4906i	0.237205	+	0.885260i	0.977143	+	0.212585i	$0.0681882\pi$
$347$	4.41863	+	16.4906i	0.237205	+	0.885260i	−0.739938	+	0.672675i	$0.765145\pi$
$348$		0			0
$349$	13.1205			0.702323			0.351161	−	0.936315i	$-0.385787\pi$
$349$	13.1205			0.702323			0.351161	+	0.936315i	$0.385787\pi$
$350$		0			0
$351$	2.78755			0.148789
$352$		0			0
$353$	−3.40860	−	12.7211i	−0.181422	−	0.677075i	−0.995368	−	0.0961351i	$-0.969352\pi$
$353$	−3.40860	−	12.7211i	−0.181422	−	0.677075i	0.813947	−	0.580940i	$-0.197315\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	6.46924	−	7.65297i	0.342388	−	0.405038i
$358$		0			0
$359$	12.8042	−	7.39252i	0.675781	−	0.390162i	−0.122483	−	0.992471i	$-0.539086\pi$
$359$	12.8042	−	7.39252i	0.675781	−	0.390162i	0.798263	+	0.602308i	$0.205752\pi$
$360$		0			0
$361$	8.67153	−	15.0195i	0.456396	−	0.790501i
$362$		0			0
$363$	−6.30787	+	6.30787i	−0.331077	+	0.331077i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	12.5381	−	3.35957i	0.654483	−	0.175368i	0.0837281	−	0.996489i	$-0.473317\pi$
$367$	12.5381	−	3.35957i	0.654483	−	0.175368i	0.570755	+	0.821120i	$0.306651\pi$
$368$		0			0
$369$	−4.78976	−	8.29610i	−0.249345	−	0.431878i
$370$		0			0
$371$	−9.11603	−	13.1205i	−0.473281	−	0.681181i
$372$		0			0
$373$	−8.77184	+	32.7370i	−0.454189	+	1.69506i	0.236273	+	0.971687i	$0.424074\pi$
$373$	−8.77184	+	32.7370i	−0.454189	+	1.69506i	−0.690461	+	0.723369i	$0.742593\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−12.0890	−	12.0890i	−0.622615	−	0.622615i
$378$		0			0
$379$		−	11.6911i		−	0.600533i	−0.953855	−	0.300267i	$-0.902924\pi$
$379$		−	11.6911i		−	0.600533i	0.953855	−	0.300267i	$-0.0970757\pi$
$380$		0			0
$381$	−10.9518	−	6.32302i	−0.561077	−	0.323938i
$382$		0			0
$383$	2.78570	+	0.746427i	0.142343	+	0.0381406i	0.329287	−	0.944230i	$-0.393192\pi$
$383$	2.78570	+	0.746427i	0.142343	+	0.0381406i	−0.186944	+	0.982371i	$0.559858\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.74727	−	0.468180i	−0.0888189	−	0.0237989i
$388$		0			0
$389$	2.61288	+	1.50855i	0.132478	+	0.0764864i	0.564774	−	0.825245i	$-0.308963\pi$
$389$	2.61288	+	1.50855i	0.132478	+	0.0764864i	−0.432296	+	0.901732i	$0.642296\pi$
$390$		0			0
$391$		−	1.97591i		−	0.0999259i
$392$		0			0
$393$	5.00767	+	5.00767i	0.252604	+	0.252604i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.50329	−	16.8065i	0.226014	−	0.843494i	−0.755982	−	0.654592i	$-0.772840\pi$
$397$	4.50329	−	16.8065i	0.226014	−	0.843494i	0.981996	−	0.188902i	$-0.0604929\pi$
$398$		0			0
$399$	−3.08133	−	1.45053i	−0.154259	−	0.0726175i
$400$		0			0
$401$	−15.0171	−	26.0104i	−0.749918	−	1.29890i	−0.947862	−	0.318683i	$-0.896760\pi$
$401$	−15.0171	−	26.0104i	−0.749918	−	1.29890i	0.197944	−	0.980213i	$-0.436574\pi$
$402$		0			0
$403$	−23.7322	+	6.35904i	−1.18219	+	0.316766i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−4.31270	+	4.31270i	−0.213773	+	0.213773i
$408$		0			0
$409$	−1.18674	+	2.05550i	−0.0586806	+	0.101638i	−0.893873	−	0.448320i	$-0.852023\pi$
$409$	−1.18674	+	2.05550i	−0.0586806	+	0.101638i	0.835193	+	0.549957i	$0.185356\pi$
$410$		0			0
$411$	−3.31867	+	1.91603i	−0.163698	+	0.0945110i
$412$		0			0
$413$	9.22019	+	1.66041i	0.453696	+	0.0817035i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.603202	−	2.25118i	−0.0295389	−	0.110241i
$418$		0			0
$419$	27.4646			1.34173			0.670867	−	0.741578i	$-0.265922\pi$
$419$	27.4646			1.34173			0.670867	+	0.741578i	$0.265922\pi$
$420$		0			0
$421$	−31.6118			−1.54067			−0.770333	−	0.637642i	$-0.779910\pi$
$421$	−31.6118			−1.54067			−0.770333	+	0.637642i	$0.779910\pi$
$422$		0			0
$423$	−0.746427	−	2.78570i	−0.0362925	−	0.135445i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	3.99243	+	3.37490i	0.193207	+	0.163323i
$428$		0			0
$429$	3.48109	−	2.00981i	0.168068	−	0.0970344i
$430$		0			0
$431$	−12.9036	+	22.3497i	−0.621544	+	1.07655i	0.367655	+	0.929962i	$0.380161\pi$
$431$	−12.9036	+	22.3497i	−0.621544	+	1.07655i	−0.989198	+	0.146583i	$0.953172\pi$
$432$		0			0
$433$	13.9376	−	13.9376i	0.669799	−	0.669799i	−0.287871	−	0.957669i	$-0.592947\pi$
$433$	13.9376	−	13.9376i	0.669799	−	0.669799i	0.957669	+	0.287871i	$0.0929473\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.648644	+	0.173804i	−0.0310288	+	0.00831415i
$438$		0			0
$439$	−17.3287	−	30.0141i	−0.827052	−	1.43250i	−0.900341	−	0.435186i	$-0.856683\pi$
$439$	−17.3287	−	30.0141i	−0.827052	−	1.43250i	0.0732882	−	0.997311i	$-0.476651\pi$
$440$		0			0
$441$	2.44199	−	6.56024i	0.116285	−	0.312392i
$442$		0			0
$443$	−5.54547	+	20.6960i	−0.263473	+	0.983295i	0.699705	+	0.714432i	$0.253315\pi$
$443$	−5.54547	+	20.6960i	−0.263473	+	0.983295i	−0.963178	+	0.268863i	$0.913352\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−11.6383	−	11.6383i	−0.550474	−	0.550474i
$448$		0			0
$449$			12.0342i			0.567928i	0.958835	+	0.283964i	$0.0916497\pi$
$449$			12.0342i			0.567928i	−0.958835	+	0.283964i	$0.908350\pi$
$450$		0			0
$451$	−11.9629	−	6.90676i	−0.563309	−	0.325227i
$452$		0			0
$453$	−3.97335	−	1.06465i	−0.186684	−	0.0500219i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	18.9073	+	5.06619i	0.884445	+	0.236986i	0.672324	−	0.740257i	$-0.265296\pi$
$457$	18.9073	+	5.06619i	0.884445	+	0.236986i	0.212121	+	0.977243i	$0.431963\pi$
$458$		0			0
$459$	−3.28012	−	1.89378i	−0.153103	−	0.0883940i
$460$		0			0
$461$		−	18.9284i		−	0.881586i	−0.897609	−	0.440793i	$-0.854697\pi$
$461$		−	18.9284i		−	0.881586i	0.897609	−	0.440793i	$-0.145303\pi$
$462$		0			0
$463$	−28.6886	−	28.6886i	−1.33327	−	1.33327i	−0.902425	−	0.430846i	$-0.858215\pi$
$463$	−28.6886	−	28.6886i	−1.33327	−	1.33327i	−0.430846	−	0.902425i	$-0.641785\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.83598	−	10.5840i	0.131234	−	0.489770i	−0.868751	−	0.495248i	$-0.835077\pi$
$467$	2.83598	−	10.5840i	0.131234	−	0.489770i	0.999985	+	0.00547816i	$0.00174376\pi$
$468$		0			0
$469$	4.89688	−	3.40232i	0.226117	−	0.157105i
$470$		0			0
$471$	−2.78755	−	4.82819i	−0.128444	−	0.222471i
$472$		0			0
$473$	−2.51954	+	0.675109i	−0.115849	+	0.0310416i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−4.26990	+	4.26990i	−0.195505	+	0.195505i
$478$		0			0
$479$	1.36408	−	2.36266i	0.0623266	−	0.107953i	−0.833178	−	0.553004i	$-0.813481\pi$
$479$	1.36408	−	2.36266i	0.0623266	−	0.107953i	0.895505	+	0.445051i	$0.146815\pi$
$480$		0			0
$481$	−10.2108	+	5.89518i	−0.465570	+	0.268797i
$482$		0			0
$483$	−0.467346	−	1.29872i	−0.0212650	−	0.0590937i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−7.77124	−	29.0027i	−0.352148	−	1.31424i	−0.884035	−	0.467420i	$-0.845183\pi$
$487$	−7.77124	−	29.0027i	−0.352148	−	1.31424i	0.531887	−	0.846816i	$-0.321483\pi$
$488$		0			0
$489$	−10.3923			−0.469956
$490$		0			0
$491$	−0.498306			−0.0224882			−0.0112441	−	0.999937i	$-0.503579\pi$
$491$	−0.498306			−0.0224882			−0.0112441	+	0.999937i	$0.503579\pi$
$492$		0			0
$493$	6.01225	+	22.4380i	0.270778	+	1.01056i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.28577	−	23.0255i	−0.371667	−	1.03284i
$498$		0			0
$499$	18.0491	−	10.4207i	0.807991	−	0.466494i	−0.0382670	−	0.999268i	$-0.512184\pi$
$499$	18.0491	−	10.4207i	0.807991	−	0.466494i	0.846258	+	0.532774i	$0.178850\pi$
$500$		0			0
$501$	0.318668	−	0.551950i	0.0142370	−	0.0246593i
$502$		0			0
$503$	12.7279	−	12.7279i	0.567510	−	0.567510i	−0.363920	−	0.931430i	$-0.618562\pi$
$503$	12.7279	−	12.7279i	0.567510	−	0.567510i	0.931430	+	0.363920i	$0.118562\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−5.05135	+	1.35350i	−0.224338	+	0.0601112i
$508$		0			0
$509$	14.2540	+	24.6886i	0.631797	+	1.09430i	0.987184	+	0.159585i	$0.0510155\pi$
$509$	14.2540	+	24.6886i	0.631797	+	1.09430i	−0.355388	+	0.934719i	$0.615651\pi$
$510$		0			0
$511$	7.73080	−	5.37131i	0.341990	−	0.237613i
$512$		0			0
$513$	−0.333158	+	1.24336i	−0.0147093	+	0.0548959i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−2.94061	−	2.94061i	−0.129328	−	0.129328i
$518$		0			0
$519$		−	0.232058i		−	0.0101862i
$520$		0			0
$521$	0.504213	+	0.291107i	0.0220900	+	0.0127536i	0.511004	−	0.859578i	$-0.329274\pi$
$521$	0.504213	+	0.291107i	0.0220900	+	0.0127536i	−0.488914	+	0.872332i	$0.662607\pi$
$522$		0			0
$523$	−0.0931310	−	0.0249544i	−0.00407233	−	0.00109118i	0.256782	−	0.966469i	$-0.417338\pi$
$523$	−0.0931310	−	0.0249544i	−0.00407233	−	0.00109118i	−0.260855	+	0.965378i	$0.584004\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	32.2459	+	8.64026i	1.40465	+	0.376376i
$528$		0			0
$529$	19.6829	+	11.3639i	0.855778	+	0.494084i
$530$		0			0
$531$		−	3.54096i		−	0.153665i
$532$		0			0
$533$	−18.8822	−	18.8822i	−0.817877	−	0.817877i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.55291	−	5.79555i	0.0670132	−	0.250097i
$538$		0			0
$539$	−1.68034	−	9.95305i	−0.0723774	−	0.428708i
$540$		0			0
$541$	−5.51709	−	9.55589i	−0.237198	−	0.410840i	0.722711	−	0.691150i	$-0.242896\pi$
$541$	−5.51709	−	9.55589i	−0.237198	−	0.410840i	−0.959909	+	0.280311i	$0.909562\pi$
$542$		0			0
$543$	−6.45658	+	1.73004i	−0.277078	+	0.0742430i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−32.0608	+	32.0608i	−1.37082	+	1.37082i	−0.511588	+	0.859231i	$0.670943\pi$
$547$	−32.0608	+	32.0608i	−1.37082	+	1.37082i	−0.859231	+	0.511588i	$0.829057\pi$
$548$		0			0
$549$	0.987954	−	1.71119i	0.0421648	−	0.0730316i
$550$		0			0
$551$	6.83702	−	3.94736i	0.291267	−	0.168163i
$552$		0			0
$553$	18.8833	+	15.9625i	0.802997	+	0.678793i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.58541	+	35.7732i	0.406147	+	1.51576i	0.801931	+	0.597417i	$0.203806\pi$
$557$	9.58541	+	35.7732i	0.406147	+	1.51576i	−0.395784	+	0.918344i	$0.629527\pi$
$558$		0			0
$559$	−5.04243			−0.213272
$560$		0			0
$561$	−5.46160			−0.230589
$562$		0			0
$563$	−3.04577	−	11.3670i	−0.128364	−	0.479060i	0.871573	−	0.490265i	$-0.163100\pi$
$563$	−3.04577	−	11.3670i	−0.128364	−	0.479060i	−0.999937	+	0.0112048i	$0.996433\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−2.60387	−	0.468915i	−0.109352	−	0.0196926i
$568$		0			0
$569$	18.4319	−	10.6417i	0.772706	−	0.446122i	−0.0611330	−	0.998130i	$-0.519471\pi$
$569$	18.4319	−	10.6417i	0.772706	−	0.446122i	0.833839	+	0.552008i	$0.186138\pi$
$570$		0			0
$571$	16.6899	−	28.9077i	0.698450	−	1.20975i	−0.270554	−	0.962705i	$-0.587207\pi$
$571$	16.6899	−	28.9077i	0.698450	−	1.20975i	0.969004	−	0.247046i	$-0.0794597\pi$
$572$		0			0
$573$	−1.11377	+	1.11377i	−0.0465284	+	0.0465284i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	1.61457	−	0.432623i	0.0672154	−	0.0180103i	−0.225055	−	0.974346i	$-0.572256\pi$
$577$	1.61457	−	0.432623i	0.0672154	−	0.0180103i	0.292270	+	0.956336i	$0.405589\pi$
$578$		0			0
$579$	−5.65578	−	9.79610i	−0.235046	−	0.407112i
$580$		0			0
$581$	−41.5623	−	19.5654i	−1.72430	−	0.811710i
$582$		0			0
$583$	−2.25367	+	8.41080i	−0.0933374	+	0.348340i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.8129	−	19.8129i	−0.817764	−	0.817764i	0.168019	−	0.985784i	$-0.446263\pi$
$587$	−19.8129	−	19.8129i	−0.817764	−	0.817764i	−0.985784	+	0.168019i	$0.946263\pi$
$588$		0			0
$589$		−	11.3456i		−	0.467486i
$590$		0			0
$591$	−19.0073	−	10.9739i	−0.781855	−	0.451404i
$592$		0			0
$593$	2.17008	+	0.581472i	0.0891146	+	0.0238782i	0.303101	−	0.952958i	$-0.401978\pi$
$593$	2.17008	+	0.581472i	0.0891146	+	0.0238782i	−0.213986	+	0.976837i	$0.568645\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	11.9468	+	3.20113i	0.488949	+	0.131013i
$598$		0			0
$599$	−28.7089	−	16.5751i	−1.17302	−	0.677241i	−0.218627	−	0.975809i	$-0.570158\pi$
$599$	−28.7089	−	16.5751i	−1.17302	−	0.677241i	−0.954388	+	0.298568i	$0.903491\pi$
$600$		0			0
$601$			13.9465i			0.568891i	0.958692	+	0.284446i	$0.0918096\pi$
$601$			13.9465i			0.568891i	−0.958692	+	0.284446i	$0.908190\pi$
$602$		0			0
$603$	−1.59363	−	1.59363i	−0.0648977	−	0.0648977i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−10.2267	+	38.1665i	−0.415088	+	1.54913i	0.369570	+	0.929203i	$0.379505\pi$
$607$	−10.2267	+	38.1665i	−0.415088	+	1.54913i	−0.784659	+	0.619928i	$0.787162\pi$
$608$		0			0
$609$	9.25880	+	13.3260i	0.375185	+	0.539995i
$610$		0			0
$611$	−4.01961	−	6.96217i	−0.162616	−	0.281659i
$612$		0			0
$613$	19.7952	−	5.30411i	0.799521	−	0.214231i	0.164147	−	0.986436i	$-0.447513\pi$
$613$	19.7952	−	5.30411i	0.799521	−	0.214231i	0.635374	+	0.772205i	$0.280846\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.5210	+	23.5210i	−0.946918	+	0.946918i	−0.998660	−	0.0517425i	$-0.983522\pi$
$617$	−23.5210	+	23.5210i	−0.946918	+	0.946918i	0.0517425	+	0.998660i	$0.483522\pi$
$618$		0			0
$619$	16.9289	−	29.3217i	0.680431	−	1.17854i	−0.294419	−	0.955676i	$-0.595126\pi$
$619$	16.9289	−	29.3217i	0.680431	−	1.17854i	0.974850	−	0.222864i	$-0.0715406\pi$
$620$		0			0
$621$	−0.451792	+	0.260842i	−0.0181298	+	0.0104672i
$622$		0			0
$623$	13.4844	−	15.9517i	0.540240	−	0.639092i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	0.480410	+	1.79291i	0.0191857	+	0.0716021i
$628$		0			0
$629$	16.0200			0.638759
$630$		0			0
$631$	−20.4933			−0.815824			−0.407912	−	0.913021i	$-0.633743\pi$
$631$	−20.4933			−0.815824			−0.407912	+	0.913021i	$0.633743\pi$
$632$		0			0
$633$	5.09579	+	19.0177i	0.202539	+	0.755888i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.84219	−	19.4257i	0.0729902	−	0.769675i
$638$		0			0
$639$	−8.01000	+	4.62458i	−0.316871	+	0.182945i
$640$		0			0
$641$	−10.4915	+	18.1717i	−0.414387	+	0.717740i	−0.995364	−	0.0961802i	$-0.969337\pi$
$641$	−10.4915	+	18.1717i	−0.414387	+	0.717740i	0.580976	+	0.813920i	$0.302671\pi$
$642$		0			0
$643$	23.0444	−	23.0444i	0.908782	−	0.908782i	−0.0873921	−	0.996174i	$-0.527853\pi$
$643$	23.0444	−	23.0444i	0.908782	−	0.908782i	0.996174	+	0.0873921i	$0.0278533\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.9924	−	4.01721i	0.589413	−	0.157933i	0.0482282	−	0.998836i	$-0.484643\pi$
$647$	14.9924	−	4.01721i	0.589413	−	0.157933i	0.541185	+	0.840904i	$0.317976\pi$
$648$		0			0
$649$	−2.55301	−	4.42194i	−0.100214	−	0.173576i
$650$		0			0
$651$	23.2381	−	1.94782i	0.910772	−	0.0763412i
$652$		0			0
$653$	1.11117	−	4.14693i	0.0434833	−	0.162282i	−0.940770	−	0.339045i	$-0.889896\pi$
$653$	1.11117	−	4.14693i	0.0434833	−	0.162282i	0.984253	+	0.176763i	$0.0565627\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−2.51590	−	2.51590i	−0.0981545	−	0.0981545i
$658$		0			0
$659$			22.4591i			0.874882i	0.899247	+	0.437441i	$0.144115\pi$
$659$			22.4591i			0.874882i	−0.899247	+	0.437441i	$0.855885\pi$
$660$		0			0
$661$	−2.52257	−	1.45640i	−0.0981165	−	0.0566476i	0.450139	−	0.892959i	$-0.351374\pi$
$661$	−2.52257	−	1.45640i	−0.0981165	−	0.0566476i	−0.548255	+	0.836311i	$0.684708\pi$
$662$		0			0
$663$	−10.1983	−	2.73262i	−0.396068	−	0.106126i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.09053	+	0.828106i	0.119666	+	0.0320644i
$668$		0			0
$669$	−3.69468	−	2.13312i	−0.142845	−	0.0824713i
$670$		0			0
$671$		−	2.84923i		−	0.109993i
$672$		0			0
$673$	−11.9120	−	11.9120i	−0.459173	−	0.459173i	0.439211	−	0.898384i	$-0.355258\pi$
$673$	−11.9120	−	11.9120i	−0.459173	−	0.459173i	−0.898384	+	0.439211i	$0.855258\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.9284	+	44.5176i	−0.458448	+	1.71095i	0.219302	+	0.975657i	$0.429622\pi$
$677$	−11.9284	+	44.5176i	−0.458448	+	1.71095i	−0.677750	+	0.735293i	$0.737045\pi$
$678$		0			0
$679$	−14.9079	+	31.6686i	−0.572114	+	1.21533i
$680$		0			0
$681$	12.5849	+	21.7977i	0.482255	+	0.835290i
$682$		0			0
$683$	−22.2077	+	5.95053i	−0.849754	+	0.227691i	−0.657313	−	0.753618i	$-0.728307\pi$
$683$	−22.2077	+	5.95053i	−0.849754	+	0.227691i	−0.192441	+	0.981309i	$0.561640\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−16.1391	+	16.1391i	−0.615744	+	0.615744i
$688$		0			0
$689$	−8.41640	+	14.5776i	−0.320639	+	0.555363i
$690$		0			0
$691$	13.4182	−	7.74698i	0.510451	−	0.294709i	−0.222568	−	0.974917i	$-0.571444\pi$
$691$	13.4182	−	7.74698i	0.510451	−	0.294709i	0.733019	+	0.680208i	$0.238111\pi$
$692$		0			0
$693$	−3.58978	+	1.29179i	−0.136365	+	0.0490710i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	9.39071	+	35.0466i	0.355699	+	1.32749i
$698$		0			0
$699$	26.2409			0.992524
$700$		0			0
$701$	22.8585			0.863352			0.431676	−	0.902029i	$-0.357922\pi$
$701$	22.8585			0.863352			0.431676	+	0.902029i	$0.357922\pi$
$702$		0			0
$703$	−1.40914	−	5.25899i	−0.0531468	−	0.198346i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.53352	−	36.2804i	0.245718	−	1.36446i
$708$		0			0
$709$	−9.58768	+	5.53545i	−0.360073	+	0.207888i	−0.669113	−	0.743161i	$-0.733326\pi$
$709$	−9.58768	+	5.53545i	−0.360073	+	0.207888i	0.309040	+	0.951049i	$0.399992\pi$
$710$		0			0
$711$	4.67278	−	8.09350i	0.175243	−	0.303530i
$712$		0			0
$713$	3.25136	−	3.25136i	0.121764	−	0.121764i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	21.9510	−	5.88175i	0.819774	−	0.219658i
$718$		0			0
$719$	−22.4694	−	38.9182i	−0.837968	−	1.45140i	−0.891591	−	0.452841i	$-0.850410\pi$
$719$	−22.4694	−	38.9182i	−0.837968	−	1.45140i	0.0536236	−	0.998561i	$-0.482923\pi$
$720$		0			0
$721$	0.539661	+	6.43831i	0.0200980	+	0.239775i
$722$		0			0
$723$	5.74017	−	21.4226i	0.213479	−	0.796715i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−25.9289	−	25.9289i	−0.961650	−	0.961650i	0.0376415	−	0.999291i	$-0.488016\pi$
$727$	−25.9289	−	25.9289i	−0.961650	−	0.961650i	−0.999291	+	0.0376415i	$0.988016\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	5.93344	+	3.42567i	0.219456	+	0.126703i
$732$		0			0
$733$	−31.7034	−	8.49489i	−1.17099	−	0.313766i	−0.379643	−	0.925133i	$-0.623953\pi$
$733$	−31.7034	−	8.49489i	−1.17099	−	0.313766i	−0.791347	+	0.611367i	$0.790620\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.13912	−	0.841124i	−0.115631	−	0.0309832i
$738$		0			0
$739$	21.7785	+	12.5738i	0.801137	+	0.462537i	0.843869	−	0.536550i	$-0.180273\pi$
$739$	21.7785	+	12.5738i	0.801137	+	0.462537i	−0.0427317	+	0.999087i	$0.513606\pi$
$740$		0			0
$741$			3.58821i			0.131816i
$742$		0			0
$743$	20.3996	+	20.3996i	0.748388	+	0.748388i	0.974176	−	0.225788i	$-0.0724957\pi$
$743$	20.3996	+	20.3996i	0.748388	+	0.748388i	−0.225788	+	0.974176i	$0.572496\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−4.49379	+	16.7710i	−0.164419	+	0.613620i
$748$		0			0
$749$	−2.41191	−	28.7748i	−0.0881293	−	1.05141i
$750$		0			0
$751$	20.2082	+	35.0017i	0.737409	+	1.27723i	0.953658	+	0.300892i	$0.0972842\pi$
$751$	20.2082	+	35.0017i	0.737409	+	1.27723i	−0.216249	+	0.976338i	$0.569382\pi$
$752$		0			0
$753$	27.1397	−	7.27207i	0.989026	−	0.265009i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	17.8174	−	17.8174i	0.647584	−	0.647584i	−0.304825	−	0.952408i	$-0.598598\pi$
$757$	17.8174	−	17.8174i	0.647584	−	0.647584i	0.952408	+	0.304825i	$0.0985979\pi$
$758$		0			0
$759$	−0.376131	+	0.651477i	−0.0136527	+	0.0236471i
$760$		0			0
$761$	29.9104	−	17.2688i	1.08425	−	0.625993i	0.152212	−	0.988348i	$-0.451360\pi$
$761$	29.9104	−	17.2688i	1.08425	−	0.625993i	0.932040	+	0.362354i	$0.118027\pi$
$762$		0			0
$763$	2.09211	−	11.6174i	0.0757395	−	0.420578i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.55470	−	9.53429i	−0.0922450	−	0.344263i
$768$		0			0
$769$	−29.1538			−1.05131			−0.525656	−	0.850697i	$-0.676180\pi$
$769$	−29.1538			−1.05131			−0.525656	+	0.850697i	$0.676180\pi$
$770$		0			0
$771$	−8.47869			−0.305353
$772$		0			0
$773$	4.82370	+	18.0023i	0.173496	+	0.647497i	0.996803	+	0.0799002i	$0.0254602\pi$
$773$	4.82370	+	18.0023i	0.173496	+	0.647497i	−0.823307	+	0.567597i	$0.807873\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	10.5296	−	3.78909i	0.377746	−	0.135933i
$778$		0			0
$779$	10.6790	−	6.16550i	0.382613	−	0.220902i
$780$		0			0
$781$	−6.66857	+	11.5503i	−0.238620	+	0.413302i
$782$		0			0
$783$	4.33677	−	4.33677i	0.154984	−	0.154984i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	4.31201	−	1.15540i	0.153706	−	0.0411855i	−0.181145	−	0.983456i	$-0.557980\pi$
$787$	4.31201	−	1.15540i	0.153706	−	0.0411855i	0.334852	+	0.942271i	$0.391314\pi$
$788$		0			0
$789$	4.90504	+	8.49579i	0.174624	+	0.302458i
$790$		0			0
$791$	−20.8669	+	44.3270i	−0.741941	+	1.57609i
$792$		0			0
$793$	1.42556	−	5.32027i	0.0506232	−	0.188928i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−21.5240	−	21.5240i	−0.762418	−	0.762418i	0.214341	−	0.976759i	$-0.431240\pi$
$797$	−21.5240	−	21.5240i	−0.762418	−	0.762418i	−0.976759	+	0.214341i	$0.931240\pi$
$798$		0			0
$799$			10.9232i			0.386435i
$800$		0			0
$801$	−6.83702	−	3.94736i	−0.241574	−	0.139473i
$802$		0			0
$803$	−4.95578	−	1.32790i	−0.174886	−	0.0468605i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.00782	+	0.270044i	0.0354768	+	0.00950599i
$808$		0			0
$809$	−19.4501	−	11.2295i	−0.683830	−	0.394810i	0.117466	−	0.993077i	$-0.462523\pi$
$809$	−19.4501	−	11.2295i	−0.683830	−	0.394810i	−0.801297	+	0.598267i	$0.795856\pi$
$810$		0			0
$811$		−	11.5465i		−	0.405453i	−0.979235	−	0.202726i	$-0.935020\pi$
$811$		−	11.5465i		−	0.405453i	0.979235	−	0.202726i	$-0.0649802\pi$
$812$		0			0
$813$	−9.48342	−	9.48342i	−0.332598	−	0.332598i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	0.602654	−	2.24913i	0.0210842	−	0.0786872i
$818$		0			0
$819$	−7.34940	+	0.616029i	−0.256809	+	0.0215258i
$820$		0			0
$821$	1.62458	+	2.81385i	0.0566981	+	0.0982040i	0.892981	−	0.450094i	$-0.148609\pi$
$821$	1.62458	+	2.81385i	0.0566981	+	0.0982040i	−0.836283	+	0.548298i	$0.815276\pi$
$822$		0			0
$823$	−32.8568	+	8.80397i	−1.14532	+	0.306887i	−0.781087	−	0.624422i	$-0.785335\pi$
$823$	−32.8568	+	8.80397i	−1.14532	+	0.306887i	−0.364230	+	0.931309i	$0.618668\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.41936	+	5.41936i	−0.188450	+	0.188450i	−0.795026	−	0.606576i	$-0.792543\pi$
$827$	−5.41936	+	5.41936i	−0.188450	+	0.188450i	0.606576	+	0.795026i	$0.292543\pi$
$828$		0			0
$829$	−12.5670	+	21.7667i	−0.436470	+	0.755988i	−0.997414	−	0.0718654i	$-0.977105\pi$
$829$	−12.5670	+	21.7667i	−0.436470	+	0.755988i	0.560944	+	0.827853i	$0.310438\pi$
$830$		0			0
$831$	−14.8925	+	8.59820i	−0.516616	+	0.298268i
$832$		0			0
$833$	−15.3649	+	21.6067i	−0.532364	+	0.748629i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.28122	−	8.51364i	−0.0788506	−	0.294275i
$838$		0			0
$839$	−18.7482			−0.647259			−0.323629	−	0.946184i	$-0.604903\pi$
$839$	−18.7482			−0.647259			−0.323629	+	0.946184i	$0.604903\pi$
$840$		0			0
$841$	−8.61521			−0.297076
$842$		0			0
$843$	−4.72765	−	17.6438i	−0.162829	−	0.607686i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	15.2367	−	18.0247i	0.523541	−	0.619337i
$848$		0			0
$849$	−3.67987	+	2.12458i	−0.126293	+	0.0729153i
$850$		0			0
$851$	1.10327	−	1.91092i	0.0378196	−	0.0655054i
$852$		0			0
$853$	10.0238	−	10.0238i	0.343207	−	0.343207i	−0.514365	−	0.857572i	$-0.671972\pi$
$853$	10.0238	−	10.0238i	0.343207	−	0.343207i	0.857572	+	0.514365i	$0.171972\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−44.7417	+	11.9885i	−1.52835	+	0.409520i	−0.922480	−	0.386045i	$-0.873841\pi$
$857$	−44.7417	+	11.9885i	−1.52835	+	0.409520i	−0.605869	+	0.795565i	$0.707174\pi$
$858$		0			0
$859$	9.95564	+	17.2437i	0.339682	+	0.588347i	0.984373	−	0.176097i	$-0.0563472\pi$
$859$	9.95564	+	17.2437i	0.339682	+	0.588347i	−0.644691	+	0.764444i	$0.723014\pi$
$860$		0			0
$861$	14.4616	+	20.8142i	0.492850	+	0.709347i
$862$		0			0
$863$	−12.7112	+	47.4388i	−0.432694	+	1.61484i	0.313831	+	0.949479i	$0.398388\pi$
$863$	−12.7112	+	47.4388i	−0.432694	+	1.61484i	−0.746525	+	0.665358i	$0.768279\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.87697	−	1.87697i	−0.0637451	−	0.0637451i
$868$		0			0
$869$		−	13.4762i		−	0.457148i
$870$		0			0
$871$	−5.44073	−	3.14120i	−0.184352	−	0.106436i
$872$		0			0
$873$	12.7788	+	3.42406i	0.432495	+	0.115887i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	35.3278	+	9.46606i	1.19294	+	0.319646i	0.800045	−	0.599940i	$-0.204809\pi$
$877$	35.3278	+	9.46606i	1.19294	+	0.319646i	0.392890	+	0.919586i	$0.371475\pi$
$878$		0			0
$879$	26.2113	+	15.1331i	0.884087	+	0.510428i
$880$		0			0
$881$		−	21.4260i		−	0.721862i	−0.932593	−	0.360931i	$-0.882459\pi$
$881$		−	21.4260i		−	0.721862i	0.932593	−	0.360931i	$-0.117541\pi$
$882$		0			0
$883$	7.71427	+	7.71427i	0.259606	+	0.259606i	0.824894	−	0.565288i	$-0.191235\pi$
$883$	7.71427	+	7.71427i	0.259606	+	0.259606i	−0.565288	+	0.824894i	$0.691235\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.29035	−	34.6721i	0.311939	−	1.16417i	−0.614866	−	0.788632i	$-0.710790\pi$
$887$	9.29035	−	34.6721i	0.311939	−	1.16417i	0.926805	−	0.375542i	$-0.122543\pi$
$888$		0			0
$889$	30.2718	+	14.2504i	1.01528	+	0.477943i
$890$		0			0
$891$	0.720993	+	1.24880i	0.0241542	+	0.0418362i
$892$		0			0
$893$	3.58583	−	0.960819i	0.119995	−	0.0321526i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1.02829	+	1.02829i	−0.0343336	+	0.0343336i
$898$		0			0
$899$	−27.0286	+	46.8149i	−0.901454	+	1.56136i
$900$		0			0
$901$	19.8072	−	11.4357i	0.659872	−	0.380978i
$902$		0			0
$903$	4.71016	+	0.848226i	0.156744	+	0.0282272i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	4.72080	+	17.6183i	0.156752	+	0.585005i	0.998949	+	0.0458355i	$0.0145950\pi$
$907$	4.72080	+	17.6183i	0.156752	+	0.585005i	−0.842197	+	0.539169i	$0.818738\pi$
$908$		0			0
$909$	−13.9333			−0.462137
$910$		0			0
$911$	37.9403			1.25702			0.628509	−	0.777802i	$-0.283666\pi$
$911$	37.9403			1.25702			0.628509	+	0.777802i	$0.283666\pi$
$912$		0			0
$913$	6.47998	+	24.1836i	0.214456	+	0.800360i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.3094	−	12.0961i	−0.472539	−	0.399449i
$918$		0			0
$919$	−20.7477	+	11.9787i	−0.684404	+	0.395141i	−0.801512	−	0.597979i	$-0.795971\pi$
$919$	−20.7477	+	11.9787i	−0.684404	+	0.395141i	0.117109	+	0.993119i	$0.462637\pi$
$920$		0			0
$921$	15.2974	−	26.4958i	0.504065	−	0.873067i
$922$		0			0
$923$	−18.2310	+	18.2310i	−0.600080	+	0.600080i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	2.35878	−	0.632032i	0.0774724	−	0.0207587i
$928$		0			0
$929$	13.7278	+	23.7773i	0.450396	+	0.780108i	0.998410	−	0.0563603i	$-0.0179496\pi$
$929$	13.7278	+	23.7773i	0.450396	+	0.780108i	−0.548015	+	0.836469i	$0.684616\pi$
$930$		0			0
$931$	8.44450	+	3.14339i	0.276757	+	0.103020i
$932$		0			0
$933$	−3.33615	+	12.4507i	−0.109221	+	0.407617i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−19.0774	−	19.0774i	−0.623231	−	0.623231i	0.323125	−	0.946356i	$-0.395267\pi$
$937$	−19.0774	−	19.0774i	−0.623231	−	0.623231i	−0.946356	+	0.323125i	$0.895267\pi$
$938$		0			0
$939$		−	0.441985i		−	0.0144236i
$940$		0			0
$941$	51.3328	+	29.6370i	1.67340	+	0.966139i	0.965712	+	0.259616i	$0.0835958\pi$
$941$	51.3328	+	29.6370i	1.67340	+	0.966139i	0.707690	+	0.706523i	$0.249737\pi$
$942$		0			0
$943$	4.82720	+	1.29344i	0.157195	+	0.0421203i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	35.5007	+	9.51238i	1.15362	+	0.309111i	0.784414	−	0.620238i	$-0.212964\pi$
$947$	35.5007	+	9.51238i	1.15362	+	0.309111i	0.369203	+	0.929349i	$0.379631\pi$
$948$		0			0
$949$	−8.58938	−	4.95908i	−0.278823	−	0.160979i
$950$		0			0
$951$			28.3882i			0.920551i
$952$		0			0
$953$	−36.0464	−	36.0464i	−1.16766	−	1.16766i	−0.982757	−	0.184902i	$-0.940803\pi$
$953$	−36.0464	−	36.0464i	−1.16766	−	1.16766i	−0.184902	−	0.982757i	$-0.559197\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	2.28896	−	8.54253i	0.0739917	−	0.276141i
$958$		0			0
$959$	8.32626	−	5.78504i	0.268869	−	0.186809i
$960$		0			0
$961$	23.3431	+	40.4313i	0.753002	+	1.30424i
$962$		0			0
$963$	−10.5421	+	2.82475i	−0.339715	+	0.0910262i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−34.6587	+	34.6587i	−1.11455	+	1.11455i	−0.122020	+	0.992528i	$0.538937\pi$
$967$	−34.6587	+	34.6587i	−1.11455	+	1.11455i	−0.992528	+	0.122020i	$0.961063\pi$
$968$		0			0
$969$	2.43772	−	4.22225i	0.0783108	−	0.135638i
$970$		0			0
$971$	26.0964	−	15.0668i	0.837474	−	0.483516i	−0.0189309	−	0.999821i	$-0.506026\pi$
$971$	26.0964	−	15.0668i	0.837474	−	0.483516i	0.856405	+	0.516305i	$0.172693\pi$
$972$		0			0
$973$	2.08784	+	5.80195i	0.0669331	+	0.186002i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.97544	+	11.1045i	0.0951926	+	0.355264i	0.997049	−	0.0767731i	$-0.0244617\pi$
$977$	2.97544	+	11.1045i	0.0951926	+	0.355264i	−0.901856	+	0.432037i	$0.857795\pi$
$978$		0			0
$979$	−11.3841			−0.363836
$980$		0			0
$981$	−4.46160			−0.142448
$982$		0			0
$983$	6.45437	+	24.0880i	0.205862	+	0.768289i	0.989185	+	0.146674i	$0.0468567\pi$
$983$	6.45437	+	24.0880i	0.205862	+	0.768289i	−0.783323	+	0.621616i	$0.786477\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2.58358	+	7.17956i	0.0822362	+	0.228528i
$988$		0			0
$989$	0.817251	−	0.471840i	0.0259871	−	0.0150036i
$990$		0			0
$991$	−8.34431	+	14.4528i	−0.265066	+	0.459107i	−0.967581	−	0.252562i	$-0.918727\pi$
$991$	−8.34431	+	14.4528i	−0.265066	+	0.459107i	0.702515	+	0.711669i	$0.252060\pi$
$992$		0			0
$993$	18.9797	−	18.9797i	0.602303	−	0.602303i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	24.1235	−	6.46387i	0.763999	−	0.204713i	0.144280	−	0.989537i	$-0.453913\pi$
$997$	24.1235	−	6.46387i	0.763999	−	0.204713i	0.619719	+	0.784824i	$0.287247\pi$
$998$		0			0
$999$	−2.11482	−	3.66298i	−0.0669100	−	0.115891i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.ce.d.493.6	yes	24
5.2	odd	4	inner	2100.2.ce.d.157.5	yes	24
5.3	odd	4	inner	2100.2.ce.d.157.3	✓	24
5.4	even	2	inner	2100.2.ce.d.493.3	yes	24
7.5	odd	6	inner	2100.2.ce.d.1993.6	yes	24
35.12	even	12	inner	2100.2.ce.d.1657.6	yes	24
35.19	odd	6	inner	2100.2.ce.d.1993.3	yes	24
35.33	even	12	inner	2100.2.ce.d.1657.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.ce.d.157.3	✓	24	5.3	odd	4	inner
2100.2.ce.d.157.5	yes	24	5.2	odd	4	inner
2100.2.ce.d.493.3	yes	24	5.4	even	2	inner
2100.2.ce.d.493.6	yes	24	1.1	even	1	trivial
2100.2.ce.d.1657.3	yes	24	35.33	even	12	inner
2100.2.ce.d.1657.6	yes	24	35.12	even	12	inner
2100.2.ce.d.1993.3	yes	24	35.19	odd	6	inner
2100.2.ce.d.1993.6	yes	24	7.5	odd	6	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)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{3} +(-0.895840 - 2.48947i) q^{7} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{3} +(-0.895840 - 2.48947i) q^{7} +(-0.866025 + 0.500000i) q^{9} +(-0.720993 + 1.24880i) q^{11} +(-1.97110 + 1.97110i) q^{13} +(3.65850 - 0.980291i) q^{17} +(-0.643613 - 1.11477i) q^{19} +(2.17278 - 1.50964i) q^{21} +(0.135022 - 0.503908i) q^{23} +(-0.707107 - 0.707107i) q^{27} +6.13312i q^{29} +(7.63312 + 4.40699i) q^{31} +(-1.39285 - 0.373213i) q^{33} +(4.08552 + 1.09471i) q^{37} +(-2.41409 - 1.39378i) q^{39} +9.57951i q^{41} +(1.27909 + 1.27909i) q^{43} +(-0.746427 + 2.78570i) q^{47} +(-5.39494 + 4.46034i) q^{49} +(1.89378 + 3.28012i) q^{51} +(5.83279 - 1.56289i) q^{53} +(0.910206 - 0.910206i) q^{57} +(-1.77048 + 3.06656i) q^{59} +(-1.71119 + 0.987954i) q^{61} +(2.02056 + 1.70803i) q^{63} +(0.583310 + 2.17694i) q^{67} +0.521684 q^{69} +9.24915 q^{71} +(0.920882 + 3.43678i) q^{73} +(3.75474 + 0.676169i) q^{77} +(-8.09350 + 4.67278i) q^{79} +(0.500000 - 0.866025i) q^{81} +(12.2773 - 12.2773i) q^{83} +(-5.92414 + 1.58737i) q^{87} +(3.94736 + 6.83702i) q^{89} +(6.67278 + 3.14120i) q^{91} +(-2.28122 + 8.51364i) q^{93} +(-9.35470 - 9.35470i) q^{97} -1.44199i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 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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