LMFDB - Embedded newform 2100.2.ce.d.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2100.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	2100.157
Dual form			2100.2.ce.d.1993.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.48947	−	0.895840i	0.940932	−	0.338596i
$7$	2.48947	−	0.895840i	0.940932	−	0.338596i
$8$		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	$-0.123662\pi$
$13$	1.97110	+	1.97110i	0.546684	+	0.546684i	−0.378796	+	0.925480i	$0.623662\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.980291	+	3.65850i	0.237756	+	0.887316i	0.976887	+	0.213755i	$0.0685694\pi$
$17$	0.980291	+	3.65850i	0.237756	+	0.887316i	−0.739132	+	0.673561i	$0.764764\pi$
$18$		0			0
$19$	0.643613	+	1.11477i	0.147655	+	0.255746i	0.930360	−	0.366647i	$-0.119494\pi$
$19$	0.643613	+	1.11477i	0.147655	+	0.255746i	−0.782705	+	0.622392i	$0.786161\pi$
$20$		0			0
$21$	2.17278	−	1.50964i	0.474140	−	0.329430i
$22$		0			0
$23$	−0.503908	−	0.135022i	−0.105072	−	0.0281540i	0.205900	−	0.978573i	$-0.433988\pi$
$23$	−0.503908	−	0.135022i	−0.105072	−	0.0281540i	−0.310972	+	0.950419i	$0.600655\pi$
$24$		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	$-0.807158\pi$
$29$		−	6.13312i		−	1.13889i	0.822029	−	0.569446i	$-0.192842\pi$
$30$		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
$33$	−0.373213	+	1.39285i	−0.0649681	+	0.242464i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.09471	+	4.08552i	−0.179970	+	0.671656i	0.815682	+	0.578500i	$0.196362\pi$
$37$	−1.09471	+	4.08552i	−0.179970	+	0.671656i	−0.995652	+	0.0931551i	$0.970305\pi$
$38$		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	−0.602819	−	0.797878i	$-0.705956\pi$
$43$	1.27909	−	1.27909i	0.195060	−	0.195060i	0.797878	+	0.602819i	$0.205956\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.78570	−	0.746427i	−0.406336	−	0.108878i	0.0498609	−	0.998756i	$-0.484122\pi$
$47$	−2.78570	−	0.746427i	−0.406336	−	0.108878i	−0.456197	+	0.889879i	$0.650789\pi$
$48$		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
$53$	−1.56289	−	5.83279i	−0.214680	−	0.801196i	−0.986279	−	0.165087i	$-0.947210\pi$
$53$	−1.56289	−	5.83279i	−0.214680	−	0.801196i	0.771599	−	0.636109i	$-0.219457\pi$
$54$		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	−0.727458	−	0.686153i	$-0.759298\pi$
$59$	1.77048	−	3.06656i	0.230497	−	0.399232i	0.957954	+	0.286920i	$0.0926315\pi$
$60$		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
$63$	1.70803	−	2.02056i	0.215191	−	0.254566i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.17694	+	0.583310i	−0.265956	+	0.0712626i	−0.389332	−	0.921097i	$-0.627294\pi$
$67$	−2.17694	+	0.583310i	−0.265956	+	0.0712626i	0.123377	+	0.992360i	$0.460628\pi$
$68$		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
$73$	3.43678	−	0.920882i	0.402244	−	0.107781i	−0.0520242	−	0.998646i	$-0.516567\pi$
$73$	3.43678	−	0.920882i	0.402244	−	0.107781i	0.454269	+	0.890865i	$0.349901\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−0.676169	+	3.75474i	−0.0770566	+	0.427892i
$78$		0			0
$79$	8.09350	−	4.67278i	0.910590	−	0.525729i	0.0299690	−	0.999551i	$-0.490459\pi$
$79$	8.09350	−	4.67278i	0.910590	−	0.525729i	0.880621	+	0.473821i	$0.157126\pi$
$80$		0			0
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$		0			0
$83$	−12.2773	−	12.2773i	−1.34760	−	1.34760i	−0.888257	−	0.459347i	$-0.848083\pi$
$83$	−12.2773	−	12.2773i	−1.34760	−	1.34760i	−0.459347	−	0.888257i	$-0.651917\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.58737	−	5.92414i	−0.170184	−	0.635135i
$88$		0			0
$89$	−3.94736	−	6.83702i	−0.418419	−	0.724723i	0.577362	−	0.816489i	$-0.304082\pi$
$89$	−3.94736	−	6.83702i	−0.418419	−	0.724723i	−0.995781	+	0.0917656i	$0.970749\pi$
$90$		0			0
$91$	6.67278	+	3.14120i	0.699498	+	0.329288i
$92$		0			0
$93$	8.51364	+	2.28122i	0.882824	+	0.236552i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	9.35470	−	9.35470i	0.949826	−	0.949826i	−0.0489744	−	0.998800i	$-0.515595\pi$
$97$	9.35470	−	9.35470i	0.949826	−	0.949826i	0.998800	+	0.0489744i	$0.0155953\pi$
$98$		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
$103$	−0.632032	+	2.35878i	−0.0622760	+	0.232417i	−0.990048	−	0.140731i	$-0.955055\pi$
$103$	−0.632032	+	2.35878i	−0.0622760	+	0.232417i	0.927772	+	0.373148i	$0.121722\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.82475	+	10.5421i	−0.273079	+	1.01914i	0.684039	+	0.729445i	$0.260222\pi$
$107$	−2.82475	+	10.5421i	−0.273079	+	1.01914i	−0.957118	+	0.289698i	$0.906445\pi$
$108$		0			0
$109$	−3.86386	−	2.23080i	−0.370090	−	0.213672i	0.303408	−	0.952861i	$-0.401876\pi$
$109$	−3.86386	−	2.23080i	−0.370090	−	0.213672i	−0.673498	+	0.739189i	$0.735209\pi$
$110$		0			0
$111$			4.22964i			0.401460i
$112$		0			0
$113$	−13.0939	+	13.0939i	−1.23177	+	1.23177i	−0.268489	+	0.963283i	$0.586524\pi$
$113$	−13.0939	+	13.0939i	−1.23177	+	1.23177i	−0.963283	+	0.268489i	$0.913476\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	2.69257	+	0.721472i	0.248928	+	0.0667001i
$118$		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
$123$	2.47936	+	9.25310i	0.223556	+	0.834324i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−8.94210	−	8.94210i	−0.793483	−	0.793483i	0.188576	−	0.982059i	$-0.439613\pi$
$127$	−8.94210	−	8.94210i	−0.793483	−	0.793483i	−0.982059	+	0.188576i	$0.939613\pi$
$128$		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
$133$	2.60091	+	2.19861i	0.225528	+	0.190644i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.70149	+	0.991812i	−0.316240	+	0.0847362i	−0.413448	−	0.910528i	$-0.635676\pi$
$137$	−3.70149	+	0.991812i	−0.316240	+	0.0847362i	0.0972077	+	0.995264i	$0.469009\pi$
$138$		0			0
$139$	2.33059			0.197678			0.0988392	−	0.995103i	$-0.468487\pi$
$139$	2.33059			0.197678			0.0988392	+	0.995103i	$0.468487\pi$
$140$		0			0
$141$	−2.88397			−0.242874
$142$		0			0
$143$	−3.88265	+	1.04035i	−0.324683	+	0.0869986i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	4.05669	−	5.70467i	0.334590	−	0.470513i
$148$		0			0
$149$	14.2540	−	8.22954i	1.16773	−	0.674190i	0.214587	−	0.976705i	$-0.431159\pi$
$149$	14.2540	−	8.22954i	1.16773	−	0.674190i	0.953145	+	0.302515i	$0.0978261\pi$
$150$		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
$157$	−1.44294	−	5.38514i	−0.115159	−	0.429781i	0.884139	−	0.467223i	$-0.154746\pi$
$157$	−1.44294	−	5.38514i	−0.115159	−	0.429781i	−0.999299	+	0.0374423i	$0.988079\pi$
$158$		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
$163$	10.0382	+	2.68973i	0.786252	+	0.210676i	0.629539	−	0.776969i	$-0.283244\pi$
$163$	10.0382	+	2.68973i	0.786252	+	0.210676i	0.156713	+	0.987644i	$0.449910\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.450665	−	0.450665i	0.0348735	−	0.0348735i	−0.689455	−	0.724329i	$-0.742150\pi$
$167$	0.450665	−	0.450665i	0.0348735	−	0.0348735i	0.724329	+	0.689455i	$0.242150\pi$
$168$		0			0
$169$		−	5.22954i		−	0.402272i
$170$		0			0
$171$	1.11477	+	0.643613i	0.0852486	+	0.0492183i
$172$		0			0
$173$	−0.0600611	+	0.224151i	−0.00456636	+	0.0170419i	−0.968171	−	0.250288i	$-0.919475\pi$
$173$	−0.0600611	+	0.224151i	−0.00456636	+	0.0170419i	0.963605	+	0.267330i	$0.0861414\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	0.916468	−	3.42031i	0.0688860	−	0.257086i
$178$		0			0
$179$	5.19615	+	3.00000i	0.388379	+	0.224231i	0.681457	−	0.731858i	$-0.261346\pi$
$179$	5.19615	+	3.00000i	0.388379	+	0.224231i	−0.293079	+	0.956088i	$0.594680\pi$
$180$		0			0
$181$			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
$187$	−5.27550	−	1.41357i	−0.385783	−	0.103370i
$188$		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
$193$	2.92765	+	10.9261i	0.210737	+	0.786480i	0.987624	+	0.156840i	$0.0501308\pi$
$193$	2.92765	+	10.9261i	0.210737	+	0.786480i	−0.776887	+	0.629640i	$0.783203\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−15.5194	−	15.5194i	−1.10571	−	1.10571i	−0.993708	−	0.112003i	$-0.964274\pi$
$197$	−15.5194	−	15.5194i	−1.10571	−	1.10571i	−0.112003	−	0.993708i	$-0.535726\pi$
$198$		0			0
$199$	−6.18411	+	10.7112i	−0.438380	+	0.759296i	−0.997565	−	0.0697470i	$-0.977781\pi$
$199$	−6.18411	+	10.7112i	−0.438380	+	0.759296i	0.559185	+	0.829043i	$0.311114\pi$
$200$		0			0
$201$	−1.95179	+	1.12687i	−0.137669	+	0.0794831i
$202$		0			0
$203$	−5.49430	−	15.2682i	−0.385624	−	1.07162i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−0.503908	+	0.135022i	−0.0350241	+	0.00938467i
$208$		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
$213$	8.93400	−	2.39386i	0.612147	−	0.164024i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	22.9504	+	4.13301i	1.55797	+	0.280567i
$218$		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	$-0.204375\pi$
$223$	3.01669	+	3.01669i	0.202013	+	0.202013i	−0.598849	+	0.800862i	$0.704375\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.51443	+	24.3122i	0.432378	+	1.61366i	0.747264	+	0.664527i	$0.231367\pi$
$227$	6.51443	+	24.3122i	0.432378	+	1.61366i	−0.314886	+	0.949129i	$0.601966\pi$
$228$		0			0
$229$	−11.4120	−	19.7662i	−0.754129	−	1.30619i	−0.945806	−	0.324732i	$-0.894726\pi$
$229$	−11.4120	−	19.7662i	−0.754129	−	1.30619i	0.191677	−	0.981458i	$-0.438608\pi$
$230$		0			0
$231$	0.318668	+	3.80180i	0.0209668	+	0.250140i
$232$		0			0
$233$	−25.3468	−	6.79166i	−1.66052	−	0.444936i	−0.697993	−	0.716105i	$-0.745923\pi$
$233$	−25.3468	−	6.79166i	−1.66052	−	0.444936i	−0.962532	+	0.271169i	$0.912590\pi$
$234$		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	$0.262813\pi$
$239$			22.7253i			1.46998i	−0.678078	+	0.734990i	$0.737187\pi$
$240$		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
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.928697	+	3.46595i	−0.0590916	+	0.220533i
$248$		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
$257$	−8.18979	−	2.19445i	−0.510865	−	0.136886i	−0.00582706	−	0.999983i	$-0.501855\pi$
$257$	−8.18979	−	2.19445i	−0.510865	−	0.136886i	−0.505038	+	0.863097i	$0.668521\pi$
$258$		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
$263$	−2.53904	−	9.47582i	−0.156564	−	0.584304i	−0.998966	−	0.0454554i	$-0.985526\pi$
$263$	−2.53904	−	9.47582i	−0.156564	−	0.584304i	0.842403	−	0.538849i	$-0.181141\pi$
$264$		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	−0.881491	−	0.472201i	$-0.843460\pi$
$269$	−0.521684	+	0.903584i	−0.0318077	+	0.0550925i	0.849683	+	0.527293i	$0.176793\pi$
$270$		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
$273$	7.25842	+	1.30713i	0.439299	+	0.0791109i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−16.6104	+	4.45076i	−0.998025	+	0.267420i	−0.720618	−	0.693332i	$-0.756142\pi$
$277$	−16.6104	+	4.45076i	−0.998025	+	0.267420i	−0.277407	+	0.960752i	$0.589475\pi$
$278$		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
$283$	4.10437	−	1.09976i	0.243979	−	0.0653740i	−0.134757	−	0.990879i	$-0.543025\pi$
$283$	4.10437	−	1.09976i	0.243979	−	0.0653740i	0.378736	+	0.925505i	$0.376359\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.58172	+	23.8479i	0.506563	+	1.40770i
$288$		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	−0.955591	−	0.294696i	$-0.904782\pi$
$293$	−21.4015	−	21.4015i	−1.25029	−	1.25029i	−0.294696	−	0.955591i	$-0.595218\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.373213	+	1.39285i	0.0216560	+	0.0808214i
$298$		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
$303$	13.4585	+	3.60619i	0.773171	+	0.207170i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	21.6337	−	21.6337i	1.23470	−	1.23470i	0.272565	−	0.962137i	$-0.412128\pi$
$307$	21.6337	−	21.6337i	1.23470	−	1.23470i	0.962137	−	0.272565i	$-0.0878720\pi$
$308$		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
$313$	−0.114394	+	0.426925i	−0.00646594	+	0.0241312i	−0.969083	−	0.246733i	$-0.920643\pi$
$313$	−0.114394	+	0.426925i	−0.00646594	+	0.0241312i	0.962617	+	0.270864i	$0.0873095\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.34741	+	27.4209i	−0.412672	+	1.54011i	0.376782	+	0.926302i	$0.377031\pi$
$317$	−7.34741	+	27.4209i	−0.412672	+	1.54011i	−0.789454	+	0.613810i	$0.789636\pi$
$318$		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
$327$	−4.30957	−	1.15475i	−0.238320	−	0.0638576i
$328$		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
$333$	1.09471	+	4.08552i	0.0599899	+	0.223885i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−11.2829	−	11.2829i	−0.614618	−	0.614618i	0.329528	−	0.944146i	$-0.393111\pi$
$337$	−11.2829	−	11.2829i	−0.614618	−	0.614618i	−0.944146	+	0.329528i	$0.893111\pi$
$338$		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
$343$	9.43480	−	15.9369i	0.509431	−	0.860511i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−16.4906	+	4.41863i	−0.885260	+	0.237205i	−0.672675	−	0.739938i	$-0.734855\pi$
$347$	−16.4906	+	4.41863i	−0.885260	+	0.237205i	−0.212585	+	0.977143i	$0.568188\pi$
$348$		0			0
$349$	−13.1205			−0.702323			−0.351161	−	0.936315i	$-0.614213\pi$
$349$	−13.1205			−0.702323			−0.351161	+	0.936315i	$0.614213\pi$
$350$		0			0
$351$	2.78755			0.148789
$352$		0			0
$353$	−12.7211	+	3.40860i	−0.677075	+	0.181422i	−0.580940	−	0.813947i	$-0.697315\pi$
$353$	−12.7211	+	3.40860i	−0.677075	+	0.181422i	−0.0961351	+	0.995368i	$0.530648\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	7.65297	+	6.46924i	0.405038	+	0.342388i
$358$		0			0
$359$	−12.8042	+	7.39252i	−0.675781	+	0.390162i	−0.798263	−	0.602308i	$-0.794248\pi$
$359$	−12.8042	+	7.39252i	−0.675781	+	0.390162i	0.122483	+	0.992471i	$0.460914\pi$
$360$		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
$367$	3.35957	+	12.5381i	0.175368	+	0.654483i	0.996489	+	0.0837281i	$0.0266827\pi$
$367$	3.35957	+	12.5381i	0.175368	+	0.654483i	−0.821120	+	0.570755i	$0.806651\pi$
$368$		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
$373$	32.7370	+	8.77184i	1.69506	+	0.454189i	0.971687	−	0.236273i	$-0.0759258\pi$
$373$	32.7370	+	8.77184i	1.69506	+	0.454189i	0.723369	+	0.690461i	$0.242593\pi$
$374$		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	$0.0970757\pi$
$379$			11.6911i			0.600533i	−0.953855	+	0.300267i	$0.902924\pi$
$380$		0			0
$381$	−10.9518	−	6.32302i	−0.561077	−	0.323938i
$382$		0			0
$383$	0.746427	−	2.78570i	0.0381406	−	0.142343i	−0.944230	−	0.329287i	$-0.893192\pi$
$383$	0.746427	−	2.78570i	0.0381406	−	0.142343i	0.982371	+	0.186944i	$0.0598583\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	0.468180	−	1.74727i	0.0237989	−	0.0888189i
$388$		0			0
$389$	−2.61288	−	1.50855i	−0.132478	−	0.0764864i	0.432296	−	0.901732i	$-0.357704\pi$
$389$	−2.61288	−	1.50855i	−0.132478	−	0.0764864i	−0.564774	+	0.825245i	$0.691037\pi$
$390$		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
$397$	16.8065	+	4.50329i	0.843494	+	0.226014i	0.654592	−	0.755982i	$-0.272840\pi$
$397$	16.8065	+	4.50329i	0.843494	+	0.226014i	0.188902	+	0.981996i	$0.439507\pi$
$398$		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
$403$	6.35904	+	23.7322i	0.316766	+	1.18219i
$404$		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	−0.835193	−	0.549957i	$-0.814644\pi$
$409$	1.18674	−	2.05550i	0.0586806	−	0.101638i	0.893873	+	0.448320i	$0.147977\pi$
$410$		0			0
$411$	−3.31867	+	1.91603i	−0.163698	+	0.0945110i
$412$		0			0
$413$	1.66041	−	9.22019i	0.0817035	−	0.453696i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.25118	−	0.603202i	0.110241	−	0.0295389i
$418$		0			0
$419$	−27.4646			−1.34173			−0.670867	−	0.741578i	$-0.734078\pi$
$419$	−27.4646			−1.34173			−0.670867	+	0.741578i	$0.734078\pi$
$420$		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
$423$	−2.78570	+	0.746427i	−0.135445	+	0.0362925i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−3.37490	+	3.99243i	−0.163323	+	0.193207i
$428$		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	$-0.407053\pi$
$433$	−13.9376	−	13.9376i	−0.669799	−	0.669799i	−0.957669	+	0.287871i	$0.907053\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.173804	−	0.648644i	−0.00831415	−	0.0310288i
$438$		0			0
$439$	17.3287	+	30.0141i	0.827052	+	1.43250i	0.900341	+	0.435186i	$0.143317\pi$
$439$	17.3287	+	30.0141i	0.827052	+	1.43250i	−0.0732882	+	0.997311i	$0.523349\pi$
$440$		0			0
$441$	2.44199	−	6.56024i	0.116285	−	0.312392i
$442$		0			0
$443$	20.6960	+	5.54547i	0.983295	+	0.263473i	0.714432	−	0.699705i	$-0.246685\pi$
$443$	20.6960	+	5.54547i	0.983295	+	0.263473i	0.268863	+	0.963178i	$0.413352\pi$
$444$		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	$-0.908350\pi$
$449$		−	12.0342i		−	0.567928i	0.958835	−	0.283964i	$-0.0916497\pi$
$450$		0			0
$451$	−11.9629	−	6.90676i	−0.563309	−	0.325227i
$452$		0			0
$453$	−1.06465	+	3.97335i	−0.0500219	+	0.186684i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−5.06619	+	18.9073i	−0.236986	+	0.884445i	0.740257	+	0.672324i	$0.234704\pi$
$457$	−5.06619	+	18.9073i	−0.236986	+	0.884445i	−0.977243	+	0.212121i	$0.931963\pi$
$458$		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	−0.430846	+	0.902425i	$0.641785\pi$
$463$	−28.6886	+	28.6886i	−1.33327	+	1.33327i	−0.902425	+	0.430846i	$0.858215\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.5840	+	2.83598i	0.489770	+	0.131234i	0.495248	−	0.868751i	$-0.335077\pi$
$467$	10.5840	+	2.83598i	0.489770	+	0.131234i	−0.00547816	+	0.999985i	$0.501744\pi$
$468$		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
$473$	0.675109	+	2.51954i	0.0310416	+	0.115849i
$474$		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	−0.895505	−	0.445051i	$-0.853185\pi$
$479$	−1.36408	+	2.36266i	−0.0623266	+	0.107953i	0.833178	+	0.553004i	$0.186519\pi$
$480$		0			0
$481$	−10.2108	+	5.89518i	−0.465570	+	0.268797i
$482$		0			0
$483$	−1.29872	+	0.467346i	−0.0590937	+	0.0212650i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	29.0027	−	7.77124i	1.31424	−	0.352148i	0.467420	−	0.884035i	$-0.345183\pi$
$487$	29.0027	−	7.77124i	1.31424	−	0.352148i	0.846816	+	0.531887i	$0.178517\pi$
$488$		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
$493$	22.4380	−	6.01225i	1.01056	−	0.270778i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	23.0255	−	8.28577i	1.03284	−	0.371667i
$498$		0			0
$499$	−18.0491	+	10.4207i	−0.807991	+	0.466494i	−0.846258	−	0.532774i	$-0.821150\pi$
$499$	−18.0491	+	10.4207i	−0.807991	+	0.466494i	0.0382670	+	0.999268i	$0.487816\pi$
$500$		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	$-0.381438\pi$
$503$	−12.7279	−	12.7279i	−0.567510	−	0.567510i	−0.931430	+	0.363920i	$0.881438\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.35350	−	5.05135i	−0.0601112	−	0.224338i
$508$		0			0
$509$	−14.2540	−	24.6886i	−0.631797	−	1.09430i	−0.987184	−	0.159585i	$-0.948984\pi$
$509$	−14.2540	−	24.6886i	−0.631797	−	1.09430i	0.355388	−	0.934719i	$-0.384349\pi$
$510$		0			0
$511$	7.73080	−	5.37131i	0.341990	−	0.237613i
$512$		0			0
$513$	1.24336	+	0.333158i	0.0548959	+	0.0147093i
$514$		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
$523$	−0.0249544	+	0.0931310i	−0.00109118	+	0.00407233i	−0.966469	−	0.256782i	$-0.917338\pi$
$523$	−0.0249544	+	0.0931310i	−0.00109118	+	0.00407233i	0.965378	+	0.260855i	$0.0840043\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.64026	+	32.2459i	−0.376376	+	1.40465i
$528$		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
$537$	5.79555	+	1.55291i	0.250097	+	0.0670132i
$538$		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
$543$	1.73004	+	6.45658i	0.0742430	+	0.277078i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−32.0608	−	32.0608i	−1.37082	−	1.37082i	−0.859231	−	0.511588i	$-0.829057\pi$
$547$	−32.0608	−	32.0608i	−1.37082	−	1.37082i	−0.511588	−	0.859231i	$-0.670943\pi$
$548$		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
$553$	15.9625	−	18.8833i	0.678793	−	0.802997i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−35.7732	+	9.58541i	−1.51576	+	0.406147i	−0.918344	−	0.395784i	$-0.870473\pi$
$557$	−35.7732	+	9.58541i	−1.51576	+	0.406147i	−0.597417	+	0.801931i	$0.703806\pi$
$558$		0			0
$559$	5.04243			0.213272
$560$		0			0
$561$	−5.46160			−0.230589
$562$		0			0
$563$	−11.3670	+	3.04577i	−0.479060	+	0.128364i	−0.490265	−	0.871573i	$-0.663100\pi$
$563$	−11.3670	+	3.04577i	−0.479060	+	0.128364i	0.0112048	+	0.999937i	$0.496433\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.468915	−	2.60387i	0.0196926	−	0.109352i
$568$		0			0
$569$	−18.4319	+	10.6417i	−0.772706	+	0.446122i	−0.833839	−	0.552008i	$-0.813862\pi$
$569$	−18.4319	+	10.6417i	−0.772706	+	0.446122i	0.0611330	+	0.998130i	$0.480529\pi$
$570$		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
$577$	0.432623	+	1.61457i	0.0180103	+	0.0672154i	0.974346	−	0.225055i	$-0.0722561\pi$
$577$	0.432623	+	1.61457i	0.0180103	+	0.0672154i	−0.956336	+	0.292270i	$0.905589\pi$
$578$		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
$583$	8.41080	+	2.25367i	0.348340	+	0.0933374i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.8129	−	19.8129i	0.817764	−	0.817764i	−0.168019	−	0.985784i	$-0.553737\pi$
$587$	19.8129	−	19.8129i	0.817764	−	0.817764i	0.985784	+	0.168019i	$0.0537372\pi$
$588$		0			0
$589$			11.3456i			0.467486i
$590$		0			0
$591$	−19.0073	−	10.9739i	−0.781855	−	0.451404i
$592$		0			0
$593$	0.581472	−	2.17008i	0.0238782	−	0.0891146i	−0.952958	−	0.303101i	$-0.901978\pi$
$593$	0.581472	−	2.17008i	0.0238782	−	0.0891146i	0.976837	+	0.213986i	$0.0686448\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−3.20113	+	11.9468i	−0.131013	+	0.488949i
$598$		0			0
$599$	28.7089	+	16.5751i	1.17302	+	0.677241i	0.954388	−	0.298568i	$-0.0965090\pi$
$599$	28.7089	+	16.5751i	1.17302	+	0.677241i	0.218627	+	0.975809i	$0.429842\pi$
$600$		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
$607$	−38.1665	−	10.2267i	−1.54913	−	0.415088i	−0.619928	−	0.784659i	$-0.712838\pi$
$607$	−38.1665	−	10.2267i	−1.54913	−	0.415088i	−0.929203	+	0.369570i	$0.879505\pi$
$608$		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
$613$	−5.30411	−	19.7952i	−0.214231	−	0.799521i	−0.986436	−	0.164147i	$-0.947513\pi$
$613$	−5.30411	−	19.7952i	−0.214231	−	0.799521i	0.772205	−	0.635374i	$-0.219154\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−23.5210	−	23.5210i	−0.946918	−	0.946918i	0.0517425	−	0.998660i	$-0.483522\pi$
$617$	−23.5210	−	23.5210i	−0.946918	−	0.946918i	−0.998660	+	0.0517425i	$0.983522\pi$
$618$		0			0
$619$	−16.9289	+	29.3217i	−0.680431	+	1.17854i	0.294419	+	0.955676i	$0.404874\pi$
$619$	−16.9289	+	29.3217i	−0.680431	+	1.17854i	−0.974850	+	0.222864i	$0.928459\pi$
$620$		0			0
$621$	−0.451792	+	0.260842i	−0.0181298	+	0.0104672i
$622$		0			0
$623$	−15.9517	−	13.4844i	−0.639092	−	0.540240i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−1.79291	+	0.480410i	−0.0716021	+	0.0191857i
$628$		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
$633$	19.0177	−	5.09579i	0.755888	−	0.202539i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	19.4257	+	1.84219i	0.769675	+	0.0729902i
$638$		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	$-0.472147\pi$
$643$	−23.0444	−	23.0444i	−0.908782	−	0.908782i	−0.996174	+	0.0873921i	$0.972147\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.01721	+	14.9924i	0.157933	+	0.589413i	0.998836	+	0.0482282i	$0.0153575\pi$
$647$	4.01721	+	14.9924i	0.157933	+	0.589413i	−0.840904	+	0.541185i	$0.817976\pi$
$648$		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
$653$	−4.14693	−	1.11117i	−0.162282	−	0.0434833i	0.176763	−	0.984253i	$-0.443437\pi$
$653$	−4.14693	−	1.11117i	−0.162282	−	0.0434833i	−0.339045	+	0.940770i	$0.610104\pi$
$654$		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	$-0.855885\pi$
$659$		−	22.4591i		−	0.874882i	0.899247	−	0.437441i	$-0.144115\pi$
$660$		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
$663$	−2.73262	+	10.1983i	−0.106126	+	0.396068i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.828106	+	3.09053i	−0.0320644	+	0.119666i
$668$		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	−0.898384	−	0.439211i	$-0.855258\pi$
$673$	−11.9120	+	11.9120i	−0.459173	+	0.459173i	0.439211	+	0.898384i	$0.355258\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−44.5176	−	11.9284i	−1.71095	−	0.458448i	−0.735293	−	0.677750i	$-0.762955\pi$
$677$	−44.5176	−	11.9284i	−1.71095	−	0.458448i	−0.975657	+	0.219302i	$0.929622\pi$
$678$		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
$683$	5.95053	+	22.2077i	0.227691	+	0.849754i	0.981309	+	0.192441i	$0.0616403\pi$
$683$	5.95053	+	22.2077i	0.227691	+	0.849754i	−0.753618	+	0.657313i	$0.771693\pi$
$684$		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
$693$	1.29179	+	3.58978i	0.0490710	+	0.136365i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−35.0466	+	9.39071i	−1.32749	+	0.355699i
$698$		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
$703$	−5.25899	+	1.40914i	−0.198346	+	0.0531468i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	36.2804	+	6.53352i	1.36446	+	0.245718i
$708$		0			0
$709$	9.58768	−	5.53545i	0.360073	−	0.207888i	−0.309040	−	0.951049i	$-0.600008\pi$
$709$	9.58768	−	5.53545i	0.360073	−	0.207888i	0.669113	+	0.743161i	$0.266674\pi$
$710$		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
$717$	5.88175	+	21.9510i	0.219658	+	0.819774i
$718$		0			0
$719$	22.4694	+	38.9182i	0.837968	+	1.45140i	0.891591	+	0.452841i	$0.149590\pi$
$719$	22.4694	+	38.9182i	0.837968	+	1.45140i	−0.0536236	+	0.998561i	$0.517077\pi$
$720$		0			0
$721$	0.539661	+	6.43831i	0.0200980	+	0.239775i
$722$		0			0
$723$	−21.4226	−	5.74017i	−0.796715	−	0.213479i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	25.9289	−	25.9289i	0.961650	−	0.961650i	−0.0376415	−	0.999291i	$-0.511984\pi$
$727$	25.9289	−	25.9289i	0.961650	−	0.961650i	0.999291	+	0.0376415i	$0.0119845\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	5.93344	+	3.42567i	0.219456	+	0.126703i
$732$		0			0
$733$	−8.49489	+	31.7034i	−0.313766	+	1.17099i	0.611367	+	0.791347i	$0.290620\pi$
$733$	−8.49489	+	31.7034i	−0.313766	+	1.17099i	−0.925133	+	0.379643i	$0.876047\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.841124	−	3.13912i	0.0309832	−	0.115631i
$738$		0			0
$739$	−21.7785	−	12.5738i	−0.801137	−	0.462537i	0.0427317	−	0.999087i	$-0.486394\pi$
$739$	−21.7785	−	12.5738i	−0.801137	−	0.462537i	−0.843869	+	0.536550i	$0.819727\pi$
$740$		0			0
$741$			3.58821i			0.131816i
$742$		0			0
$743$	20.3996	−	20.3996i	0.748388	−	0.748388i	−0.225788	−	0.974176i	$-0.572496\pi$
$743$	20.3996	−	20.3996i	0.748388	−	0.748388i	0.974176	+	0.225788i	$0.0724957\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−16.7710	−	4.49379i	−0.613620	−	0.164419i
$748$		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
$753$	−7.27207	−	27.1397i	−0.265009	−	0.989026i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	17.8174	+	17.8174i	0.647584	+	0.647584i	0.952408	−	0.304825i	$-0.0985979\pi$
$757$	17.8174	+	17.8174i	0.647584	+	0.647584i	−0.304825	+	0.952408i	$0.598598\pi$
$758$		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
$763$	−11.6174	−	2.09211i	−0.420578	−	0.0757395i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.53429	−	2.55470i	0.344263	−	0.0922450i
$768$		0			0
$769$	29.1538			1.05131			0.525656	−	0.850697i	$-0.323820\pi$
$769$	29.1538			1.05131			0.525656	+	0.850697i	$0.323820\pi$
$770$		0			0
$771$	−8.47869			−0.305353
$772$		0			0
$773$	18.0023	−	4.82370i	0.647497	−	0.173496i	0.0799002	−	0.996803i	$-0.474540\pi$
$773$	18.0023	−	4.82370i	0.647497	−	0.173496i	0.567597	+	0.823307i	$0.307873\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	3.78909	+	10.5296i	0.135933	+	0.377746i
$778$		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
$787$	1.15540	+	4.31201i	0.0411855	+	0.153706i	0.983456	−	0.181145i	$-0.0579804\pi$
$787$	1.15540	+	4.31201i	0.0411855	+	0.153706i	−0.942271	+	0.334852i	$0.891314\pi$
$788$		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
$793$	−5.32027	−	1.42556i	−0.188928	−	0.0506232i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.5240	−	21.5240i	0.762418	−	0.762418i	−0.214341	−	0.976759i	$-0.568760\pi$
$797$	21.5240	−	21.5240i	0.762418	−	0.762418i	0.976759	+	0.214341i	$0.0687605\pi$
$798$		0			0
$799$		−	10.9232i		−	0.386435i
$800$		0			0
$801$	−6.83702	−	3.94736i	−0.241574	−	0.139473i
$802$		0			0
$803$	−1.32790	+	4.95578i	−0.0468605	+	0.174886i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.270044	+	1.00782i	−0.00950599	+	0.0354768i
$808$		0			0
$809$	19.4501	+	11.2295i	0.683830	+	0.394810i	0.801297	−	0.598267i	$-0.204144\pi$
$809$	19.4501	+	11.2295i	0.683830	+	0.394810i	−0.117466	+	0.993077i	$0.537477\pi$
$810$		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
$817$	2.24913	+	0.602654i	0.0786872	+	0.0210842i
$818$		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
$823$	8.80397	+	32.8568i	0.306887	+	1.14532i	0.931309	+	0.364230i	$0.118668\pi$
$823$	8.80397	+	32.8568i	0.306887	+	1.14532i	−0.624422	+	0.781087i	$0.714665\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.41936	−	5.41936i	−0.188450	−	0.188450i	0.606576	−	0.795026i	$-0.292543\pi$
$827$	−5.41936	−	5.41936i	−0.188450	−	0.188450i	−0.795026	+	0.606576i	$0.792543\pi$
$828$		0			0
$829$	12.5670	−	21.7667i	0.436470	−	0.755988i	−0.560944	−	0.827853i	$-0.689562\pi$
$829$	12.5670	−	21.7667i	0.436470	−	0.755988i	0.997414	+	0.0718654i	$0.0228952\pi$
$830$		0			0
$831$	−14.8925	+	8.59820i	−0.516616	+	0.298268i
$832$		0			0
$833$	21.6067	+	15.3649i	0.748629	+	0.532364i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	8.51364	−	2.28122i	0.294275	−	0.0788506i
$838$		0			0
$839$	18.7482			0.647259			0.323629	−	0.946184i	$-0.395097\pi$
$839$	18.7482			0.647259			0.323629	+	0.946184i	$0.395097\pi$
$840$		0			0
$841$	−8.61521			−0.297076
$842$		0			0
$843$	−17.6438	+	4.72765i	−0.607686	+	0.162829i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	18.0247	+	15.2367i	0.619337	+	0.523541i
$848$		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	$-0.328028\pi$
$853$	−10.0238	−	10.0238i	−0.343207	−	0.343207i	−0.857572	+	0.514365i	$0.828028\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.9885	−	44.7417i	−0.409520	−	1.52835i	−0.795565	−	0.605869i	$-0.792826\pi$
$857$	−11.9885	−	44.7417i	−0.409520	−	1.52835i	0.386045	−	0.922480i	$-0.373841\pi$
$858$		0			0
$859$	−9.95564	−	17.2437i	−0.339682	−	0.588347i	0.644691	−	0.764444i	$-0.276986\pi$
$859$	−9.95564	−	17.2437i	−0.339682	−	0.588347i	−0.984373	+	0.176097i	$0.943653\pi$
$860$		0			0
$861$	14.4616	+	20.8142i	0.492850	+	0.709347i
$862$		0			0
$863$	47.4388	+	12.7112i	1.61484	+	0.432694i	0.949479	−	0.313831i	$-0.101612\pi$
$863$	47.4388	+	12.7112i	1.61484	+	0.432694i	0.665358	+	0.746525i	$0.268279\pi$
$864$		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
$873$	3.42406	−	12.7788i	0.115887	−	0.432495i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.46606	+	35.3278i	−0.319646	+	1.19294i	0.599940	+	0.800045i	$0.295191\pi$
$877$	−9.46606	+	35.3278i	−0.319646	+	1.19294i	−0.919586	+	0.392890i	$0.871475\pi$
$878$		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	−0.565288	−	0.824894i	$-0.691235\pi$
$883$	7.71427	−	7.71427i	0.259606	−	0.259606i	0.824894	+	0.565288i	$0.191235\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	34.6721	+	9.29035i	1.16417	+	0.311939i	0.788632	−	0.614866i	$-0.210790\pi$
$887$	34.6721	+	9.29035i	1.16417	+	0.311939i	0.375542	+	0.926805i	$0.377457\pi$
$888$		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
$893$	−0.960819	−	3.58583i	−0.0321526	−	0.119995i
$894$		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
$903$	0.848226	−	4.71016i	0.0282272	−	0.156744i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−17.6183	+	4.72080i	−0.585005	+	0.156752i	−0.539169	−	0.842197i	$-0.681262\pi$
$907$	−17.6183	+	4.72080i	−0.585005	+	0.156752i	−0.0458355	+	0.998949i	$0.514595\pi$
$908$		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
$913$	24.1836	−	6.47998i	0.800360	−	0.214456i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	12.0961	−	14.3094i	0.399449	−	0.472539i
$918$		0			0
$919$	20.7477	−	11.9787i	0.684404	−	0.395141i	−0.117109	−	0.993119i	$-0.537363\pi$
$919$	20.7477	−	11.9787i	0.684404	−	0.395141i	0.801512	+	0.597979i	$0.204029\pi$
$920$		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
$927$	0.632032	+	2.35878i	0.0207587	+	0.0774724i
$928$		0			0
$929$	−13.7278	−	23.7773i	−0.450396	−	0.780108i	0.548015	−	0.836469i	$-0.315384\pi$
$929$	−13.7278	−	23.7773i	−0.450396	−	0.780108i	−0.998410	+	0.0563603i	$0.982050\pi$
$930$		0			0
$931$	8.44450	+	3.14339i	0.276757	+	0.103020i
$932$		0			0
$933$	12.4507	+	3.33615i	0.407617	+	0.109221i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	19.0774	−	19.0774i	0.623231	−	0.623231i	−0.323125	−	0.946356i	$-0.604733\pi$
$937$	19.0774	−	19.0774i	0.623231	−	0.623231i	0.946356	+	0.323125i	$0.104733\pi$
$938$		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
$943$	1.29344	−	4.82720i	0.0421203	−	0.157195i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.51238	+	35.5007i	−0.309111	+	1.15362i	0.620238	+	0.784414i	$0.287036\pi$
$947$	−9.51238	+	35.5007i	−0.309111	+	1.15362i	−0.929349	+	0.369203i	$0.879631\pi$
$948$		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	−0.184902	+	0.982757i	$0.559197\pi$
$953$	−36.0464	+	36.0464i	−1.16766	+	1.16766i	−0.982757	+	0.184902i	$0.940803\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	8.54253	+	2.28896i	0.276141	+	0.0739917i
$958$		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
$963$	2.82475	+	10.5421i	0.0910262	+	0.339715i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−34.6587	−	34.6587i	−1.11455	−	1.11455i	−0.992528	−	0.122020i	$-0.961063\pi$
$967$	−34.6587	−	34.6587i	−1.11455	−	1.11455i	−0.122020	−	0.992528i	$-0.538937\pi$
$968$		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
$973$	5.80195	−	2.08784i	0.186002	−	0.0669331i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.1045	+	2.97544i	−0.355264	+	0.0951926i	−0.432037	−	0.901856i	$-0.642205\pi$
$977$	−11.1045	+	2.97544i	−0.355264	+	0.0951926i	0.0767731	+	0.997049i	$0.475538\pi$
$978$		0			0
$979$	11.3841			0.363836
$980$		0			0
$981$	−4.46160			−0.142448
$982$		0			0
$983$	24.0880	−	6.45437i	0.768289	−	0.205862i	0.146674	−	0.989185i	$-0.453143\pi$
$983$	24.0880	−	6.45437i	0.768289	−	0.205862i	0.621616	+	0.783323i	$0.286477\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−7.17956	+	2.58358i	−0.228528	+	0.0822362i
$988$		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
$997$	6.46387	+	24.1235i	0.204713	+	0.763999i	0.989537	+	0.144280i	$0.0460866\pi$
$997$	6.46387	+	24.1235i	0.204713	+	0.763999i	−0.784824	+	0.619719i	$0.787247\pi$
$998$		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.157.5	yes	24
5.2	odd	4	inner	2100.2.ce.d.493.3	yes	24
5.3	odd	4	inner	2100.2.ce.d.493.6	yes	24
5.4	even	2	inner	2100.2.ce.d.157.3	✓	24
7.5	odd	6	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.1657.3	yes	24
35.33	even	12	inner	2100.2.ce.d.1993.6	yes	24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.ce (of order \(12\), degree \(4\), minimal)

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

Related objects

Downloads

Learn more