LMFDB - Embedded newform 4020.2.q.m.841.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, degree $2$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.4
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(-1.09486 + 1.89635i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(-1.09486 + 1.89635i) q^{7} +1.00000 q^{9} +(2.56534 - 4.44330i) q^{11} +(3.21617 + 5.57057i) q^{13} +1.00000 q^{15} +(0.653954 + 1.13268i) q^{17} +(-2.76451 - 4.78828i) q^{19} +(-1.09486 + 1.89635i) q^{21} +(-1.52897 - 2.64825i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.69002 - 6.39130i) q^{29} +(1.00060 - 1.73309i) q^{31} +(2.56534 - 4.44330i) q^{33} +(-1.09486 + 1.89635i) q^{35} +(1.40879 + 2.44010i) q^{37} +(3.21617 + 5.57057i) q^{39} +(1.19738 - 2.07392i) q^{41} +9.64370 q^{43} +1.00000 q^{45} +(1.71064 - 2.96291i) q^{47} +(1.10258 + 1.90972i) q^{49} +(0.653954 + 1.13268i) q^{51} -6.09552 q^{53} +(2.56534 - 4.44330i) q^{55} +(-2.76451 - 4.78828i) q^{57} -5.99534 q^{59} +(6.06494 + 10.5048i) q^{61} +(-1.09486 + 1.89635i) q^{63} +(3.21617 + 5.57057i) q^{65} +(-7.43204 + 3.42998i) q^{67} +(-1.52897 - 2.64825i) q^{69} +(7.59393 - 13.1531i) q^{71} +(6.15933 + 10.6683i) q^{73} +1.00000 q^{75} +(5.61736 + 9.72956i) q^{77} +(4.94026 - 8.55679i) q^{79} +1.00000 q^{81} +(6.69164 + 11.5903i) q^{83} +(0.653954 + 1.13268i) q^{85} +(3.69002 - 6.39130i) q^{87} -5.88126 q^{89} -14.0850 q^{91} +(1.00060 - 1.73309i) q^{93} +(-2.76451 - 4.78828i) q^{95} +(7.09796 + 12.2940i) q^{97} +(2.56534 - 4.44330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−1.09486	+	1.89635i	−0.413817	+	0.716752i	−0.995303	−	0.0968041i	$-0.969138\pi$
$7$	−1.09486	+	1.89635i	−0.413817	+	0.716752i	0.581487	+	0.813556i	$0.302471\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.56534	−	4.44330i	0.773480	−	1.33971i	−0.162165	−	0.986764i	$-0.551848\pi$
$11$	2.56534	−	4.44330i	0.773480	−	1.33971i	0.935645	−	0.352943i	$-0.114819\pi$
$12$		0			0
$13$	3.21617	+	5.57057i	0.892005	+	1.54500i	0.837468	+	0.546487i	$0.184035\pi$
$13$	3.21617	+	5.57057i	0.892005	+	1.54500i	0.0545377	+	0.998512i	$0.482631\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.653954	+	1.13268i	0.158607	+	0.274716i	0.934367	−	0.356313i	$-0.115966\pi$
$17$	0.653954	+	1.13268i	0.158607	+	0.274716i	−0.775759	+	0.631029i	$0.782633\pi$
$18$		0			0
$19$	−2.76451	−	4.78828i	−0.634223	−	1.09851i	−0.986679	−	0.162678i	$-0.947987\pi$
$19$	−2.76451	−	4.78828i	−0.634223	−	1.09851i	0.352456	−	0.935828i	$-0.385347\pi$
$20$		0			0
$21$	−1.09486	+	1.89635i	−0.238917	+	0.413817i
$22$		0			0
$23$	−1.52897	−	2.64825i	−0.318811	−	0.552197i	0.661429	−	0.750008i	$-0.269950\pi$
$23$	−1.52897	−	2.64825i	−0.318811	−	0.552197i	−0.980240	+	0.197810i	$0.936617\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.69002	−	6.39130i	0.685220	−	1.18684i	−0.288148	−	0.957586i	$-0.593039\pi$
$29$	3.69002	−	6.39130i	0.685220	−	1.18684i	0.973368	−	0.229250i	$-0.0736272\pi$
$30$		0			0
$31$	1.00060	−	1.73309i	0.179713	−	0.311272i	−0.762069	−	0.647496i	$-0.775816\pi$
$31$	1.00060	−	1.73309i	0.179713	−	0.311272i	0.941782	+	0.336223i	$0.109150\pi$
$32$		0			0
$33$	2.56534	−	4.44330i	0.446569	−	0.773480i
$34$		0			0
$35$	−1.09486	+	1.89635i	−0.185065	+	0.320541i
$36$		0			0
$37$	1.40879	+	2.44010i	0.231604	+	0.401150i	0.958280	−	0.285830i	$-0.0922692\pi$
$37$	1.40879	+	2.44010i	0.231604	+	0.401150i	−0.726676	+	0.686980i	$0.758936\pi$
$38$		0			0
$39$	3.21617	+	5.57057i	0.515000	+	0.892005i
$40$		0			0
$41$	1.19738	−	2.07392i	0.186999	−	0.323891i	−0.757249	−	0.653126i	$-0.773457\pi$
$41$	1.19738	−	2.07392i	0.186999	−	0.323891i	0.944248	+	0.329234i	$0.106791\pi$
$42$		0			0
$43$	9.64370			1.47065			0.735325	−	0.677714i	$-0.237029\pi$
$43$	9.64370			1.47065			0.735325	+	0.677714i	$0.237029\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	1.71064	−	2.96291i	0.249522	−	0.432185i	−0.713871	−	0.700277i	$-0.753060\pi$
$47$	1.71064	−	2.96291i	0.249522	−	0.432185i	0.963393	+	0.268092i	$0.0863931\pi$
$48$		0			0
$49$	1.10258	+	1.90972i	0.157511	+	0.272817i
$50$		0			0
$51$	0.653954	+	1.13268i	0.0915719	+	0.158607i
$52$		0			0
$53$	−6.09552			−0.837284			−0.418642	−	0.908151i	$-0.637494\pi$
$53$	−6.09552			−0.837284			−0.418642	+	0.908151i	$0.637494\pi$
$54$		0			0
$55$	2.56534	−	4.44330i	0.345911	−	0.599135i
$56$		0			0
$57$	−2.76451	−	4.78828i	−0.366169	−	0.634223i
$58$		0			0
$59$	−5.99534			−0.780527			−0.390264	−	0.920703i	$-0.627616\pi$
$59$	−5.99534			−0.780527			−0.390264	+	0.920703i	$0.627616\pi$
$60$		0			0
$61$	6.06494	+	10.5048i	0.776536	+	1.34500i	0.933927	+	0.357464i	$0.116358\pi$
$61$	6.06494	+	10.5048i	0.776536	+	1.34500i	−0.157391	+	0.987536i	$0.550308\pi$
$62$		0			0
$63$	−1.09486	+	1.89635i	−0.137939	+	0.238917i
$64$		0			0
$65$	3.21617	+	5.57057i	0.398917	+	0.690944i
$66$		0			0
$67$	−7.43204	+	3.42998i	−0.907968	+	0.419039i
$67$	−7.43204	+	3.42998i	−0.907968	+	0.419039i
$68$		0			0
$69$	−1.52897	−	2.64825i	−0.184066	−	0.318811i
$70$		0			0
$71$	7.59393	−	13.1531i	0.901234	−	1.56098i	0.0753390	−	0.997158i	$-0.475996\pi$
$71$	7.59393	−	13.1531i	0.901234	−	1.56098i	0.825895	−	0.563824i	$-0.190671\pi$
$72$		0			0
$73$	6.15933	+	10.6683i	0.720895	+	1.24863i	0.960642	+	0.277791i	$0.0896022\pi$
$73$	6.15933	+	10.6683i	0.720895	+	1.24863i	−0.239747	+	0.970835i	$0.577064\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	5.61736	+	9.72956i	0.640158	+	1.10879i
$78$		0			0
$79$	4.94026	−	8.55679i	0.555823	−	0.962714i	−0.442016	−	0.897007i	$-0.645737\pi$
$79$	4.94026	−	8.55679i	0.555823	−	0.962714i	0.997839	−	0.0657065i	$-0.0209301\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	6.69164	+	11.5903i	0.734503	+	1.27220i	0.954941	+	0.296795i	$0.0959179\pi$
$83$	6.69164	+	11.5903i	0.734503	+	1.27220i	−0.220438	+	0.975401i	$0.570749\pi$
$84$		0			0
$85$	0.653954	+	1.13268i	0.0709313	+	0.122857i
$86$		0			0
$87$	3.69002	−	6.39130i	0.395612	−	0.685220i
$88$		0			0
$89$	−5.88126			−0.623412			−0.311706	−	0.950179i	$-0.600900\pi$
$89$	−5.88126			−0.623412			−0.311706	+	0.950179i	$0.600900\pi$
$90$		0			0
$91$	−14.0850			−1.47651
$92$		0			0
$93$	1.00060	−	1.73309i	0.103757	−	0.179713i
$94$		0			0
$95$	−2.76451	−	4.78828i	−0.283633	−	0.491267i
$96$		0			0
$97$	7.09796	+	12.2940i	0.720688	+	1.24827i	0.960724	+	0.277505i	$0.0895075\pi$
$97$	7.09796	+	12.2940i	0.720688	+	1.24827i	−0.240036	+	0.970764i	$0.577159\pi$
$98$		0			0
$99$	2.56534	−	4.44330i	0.257827	−	0.446569i
$100$		0			0
$101$	8.95422	−	15.5092i	0.890978	−	1.54322i	0.0522739	−	0.998633i	$-0.483353\pi$
$101$	8.95422	−	15.5092i	0.890978	−	1.54322i	0.838704	−	0.544587i	$-0.183314\pi$
$102$		0			0
$103$	−2.17465	+	3.76661i	−0.214275	+	0.371135i	−0.953048	−	0.302819i	$-0.902072\pi$
$103$	−2.17465	+	3.76661i	−0.214275	+	0.371135i	0.738773	+	0.673954i	$0.235405\pi$
$104$		0			0
$105$	−1.09486	+	1.89635i	−0.106847	+	0.185065i
$106$		0			0
$107$	−16.3415			−1.57980			−0.789898	−	0.613238i	$-0.789867\pi$
$107$	−16.3415			−1.57980			−0.789898	+	0.613238i	$0.789867\pi$
$108$		0			0
$109$	−11.4267			−1.09448			−0.547240	−	0.836976i	$-0.684321\pi$
$109$	−11.4267			−1.09448			−0.547240	+	0.836976i	$0.684321\pi$
$110$		0			0
$111$	1.40879	+	2.44010i	0.133717	+	0.231604i
$112$		0			0
$113$	−6.89488	+	11.9423i	−0.648616	+	1.12344i	0.334838	+	0.942276i	$0.391319\pi$
$113$	−6.89488	+	11.9423i	−0.648616	+	1.12344i	−0.983454	+	0.181160i	$0.942015\pi$
$114$		0			0
$115$	−1.52897	−	2.64825i	−0.142577	−	0.246950i
$116$		0			0
$117$	3.21617	+	5.57057i	0.297335	+	0.515000i
$118$		0			0
$119$	−2.86394			−0.262537
$120$		0			0
$121$	−7.66197	−	13.2709i	−0.696542	−	1.20645i
$122$		0			0
$123$	1.19738	−	2.07392i	0.107964	−	0.186999i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.98026	+	8.62607i	−0.441927	+	0.765440i	−0.997832	−	0.0658058i	$-0.979038\pi$
$127$	−4.98026	+	8.62607i	−0.441927	+	0.765440i	0.555906	+	0.831245i	$0.312372\pi$
$128$		0			0
$129$	9.64370			0.849081
$130$		0			0
$131$	4.69171			0.409917			0.204958	−	0.978771i	$-0.434294\pi$
$131$	4.69171			0.409917			0.204958	+	0.978771i	$0.434294\pi$
$132$		0			0
$133$	12.1070			1.04981
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	10.6501			0.909899			0.454949	−	0.890517i	$-0.349657\pi$
$137$	10.6501			0.909899			0.454949	+	0.890517i	$0.349657\pi$
$138$		0			0
$139$	21.2588			1.80315			0.901576	−	0.432621i	$-0.142411\pi$
$139$	21.2588			1.80315			0.901576	+	0.432621i	$0.142411\pi$
$140$		0			0
$141$	1.71064	−	2.96291i	0.144062	−	0.249522i
$142$		0			0
$143$	33.0023			2.75979
$144$		0			0
$145$	3.69002	−	6.39130i	0.306440	−	0.530769i
$146$		0			0
$147$	1.10258	+	1.90972i	0.0909391	+	0.157511i
$148$		0			0
$149$	16.8858			1.38334			0.691670	−	0.722214i	$-0.256875\pi$
$149$	16.8858			1.38334			0.691670	+	0.722214i	$0.256875\pi$
$150$		0			0
$151$	3.19850	+	5.53996i	0.260290	+	0.450835i	0.966319	−	0.257348i	$-0.0828485\pi$
$151$	3.19850	+	5.53996i	0.260290	+	0.450835i	−0.706029	+	0.708183i	$0.749515\pi$
$152$		0			0
$153$	0.653954	+	1.13268i	0.0528691	+	0.0915719i
$154$		0			0
$155$	1.00060	−	1.73309i	0.0803701	−	0.139205i
$156$		0			0
$157$	−11.8207	−	20.4740i	−0.943392	−	1.63400i	−0.758939	−	0.651161i	$-0.774282\pi$
$157$	−11.8207	−	20.4740i	−0.943392	−	1.63400i	−0.184453	−	0.982841i	$-0.559051\pi$
$158$		0			0
$159$	−6.09552			−0.483406
$160$		0			0
$161$	6.69599			0.527718
$162$		0			0
$163$	9.34983	−	16.1944i	0.732335	−	1.26844i	−0.223547	−	0.974693i	$-0.571764\pi$
$163$	9.34983	−	16.1944i	0.732335	−	1.26844i	0.955883	−	0.293749i	$-0.0949030\pi$
$164$		0			0
$165$	2.56534	−	4.44330i	0.199712	−	0.345911i
$166$		0			0
$167$	−0.867052	+	1.50178i	−0.0670945	+	0.116211i	−0.897621	−	0.440768i	$-0.854706\pi$
$167$	−0.867052	+	1.50178i	−0.0670945	+	0.116211i	0.830527	+	0.556979i	$0.188040\pi$
$168$		0			0
$169$	−14.1875	+	24.5735i	−1.09135	+	1.89027i
$170$		0			0
$171$	−2.76451	−	4.78828i	−0.211408	−	0.366169i
$172$		0			0
$173$	−2.87760	−	4.98415i	−0.218780	−	0.378938i	0.735655	−	0.677356i	$-0.236874\pi$
$173$	−2.87760	−	4.98415i	−0.218780	−	0.378938i	−0.954435	+	0.298418i	$0.903541\pi$
$174$		0			0
$175$	−1.09486	+	1.89635i	−0.0827634	+	0.143350i
$176$		0			0
$177$	−5.99534			−0.450638
$178$		0			0
$179$	−3.48707			−0.260636			−0.130318	−	0.991472i	$-0.541600\pi$
$179$	−3.48707			−0.260636			−0.130318	+	0.991472i	$0.541600\pi$
$180$		0			0
$181$	4.44487	−	7.69874i	0.330384	−	0.572243i	−0.652203	−	0.758045i	$-0.726155\pi$
$181$	4.44487	−	7.69874i	0.330384	−	0.572243i	0.982587	+	0.185802i	$0.0594883\pi$
$182$		0			0
$183$	6.06494	+	10.5048i	0.448333	+	0.776536i
$184$		0			0
$185$	1.40879	+	2.44010i	0.103577	+	0.179400i
$186$		0			0
$187$	6.71047			0.490718
$188$		0			0
$189$	−1.09486	+	1.89635i	−0.0796391	+	0.137939i
$190$		0			0
$191$	8.80189	+	15.2453i	0.636883	+	1.10311i	0.986113	+	0.166076i	$0.0531097\pi$
$191$	8.80189	+	15.2453i	0.636883	+	1.10311i	−0.349230	+	0.937037i	$0.613557\pi$
$192$		0			0
$193$	−2.90313			−0.208972			−0.104486	−	0.994526i	$-0.533320\pi$
$193$	−2.90313			−0.208972			−0.104486	+	0.994526i	$0.533320\pi$
$194$		0			0
$195$	3.21617	+	5.57057i	0.230315	+	0.398917i
$196$		0			0
$197$	10.2625	−	17.7752i	0.731175	−	1.26643i	−0.225206	−	0.974311i	$-0.572306\pi$
$197$	10.2625	−	17.7752i	0.731175	−	1.26643i	0.956381	−	0.292121i	$-0.0943610\pi$
$198$		0			0
$199$	−2.49651	−	4.32408i	−0.176973	−	0.306526i	0.763869	−	0.645371i	$-0.223297\pi$
$199$	−2.49651	−	4.32408i	−0.176973	−	0.306526i	−0.940842	+	0.338845i	$0.889964\pi$
$200$		0			0
$201$	−7.43204	+	3.42998i	−0.524216	+	0.241932i
$202$		0			0
$203$	8.08009	+	13.9951i	0.567111	+	0.982265i
$204$		0			0
$205$	1.19738	−	2.07392i	0.0836284	−	0.144849i
$206$		0			0
$207$	−1.52897	−	2.64825i	−0.106270	−	0.184066i
$208$		0			0
$209$	−28.3677			−1.96223
$210$		0			0
$211$	10.4849	+	18.1604i	0.721810	+	1.25021i	0.960273	+	0.279061i	$0.0900231\pi$
$211$	10.4849	+	18.1604i	0.721810	+	1.25021i	−0.238463	+	0.971152i	$0.576644\pi$
$212$		0			0
$213$	7.59393	−	13.1531i	0.520327	−	0.901234i
$214$		0			0
$215$	9.64370			0.657695
$216$		0			0
$217$	2.19103	+	3.79497i	0.148737	+	0.257619i
$218$		0			0
$219$	6.15933	+	10.6683i	0.416209	+	0.720895i
$220$		0			0
$221$	−4.20646	+	7.28580i	−0.282957	+	0.490096i
$222$		0			0
$223$	15.0267			1.00626			0.503131	−	0.864210i	$-0.332182\pi$
$223$	15.0267			1.00626			0.503131	+	0.864210i	$0.332182\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−1.70708	+	2.95674i	−0.113303	+	0.196246i	−0.917100	−	0.398657i	$-0.869476\pi$
$227$	−1.70708	+	2.95674i	−0.113303	+	0.196246i	0.803797	+	0.594903i	$0.202810\pi$
$228$		0			0
$229$	−7.38564	−	12.7923i	−0.488057	−	0.845339i	0.511849	−	0.859075i	$-0.328961\pi$
$229$	−7.38564	−	12.7923i	−0.488057	−	0.845339i	−0.999906	+	0.0137365i	$0.995627\pi$
$230$		0			0
$231$	5.61736	+	9.72956i	0.369595	+	0.640158i
$232$		0			0
$233$	−7.28641	+	12.6204i	−0.477349	+	0.826792i	−0.999663	−	0.0259607i	$-0.991736\pi$
$233$	−7.28641	+	12.6204i	−0.477349	+	0.826792i	0.522314	+	0.852753i	$0.325069\pi$
$234$		0			0
$235$	1.71064	−	2.96291i	0.111590	−	0.193279i
$236$		0			0
$237$	4.94026	−	8.55679i	0.320905	−	0.555823i
$238$		0			0
$239$	−7.82106	+	13.5465i	−0.505902	+	0.876249i	0.494074	+	0.869420i	$0.335507\pi$
$239$	−7.82106	+	13.5465i	−0.505902	+	0.876249i	−0.999977	+	0.00682886i	$0.997826\pi$
$240$		0			0
$241$	−27.5691			−1.77588			−0.887942	−	0.459955i	$-0.847866\pi$
$241$	−27.5691			−1.77588			−0.887942	+	0.459955i	$0.847866\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	1.10258	+	1.90972i	0.0704411	+	0.122008i
$246$		0			0
$247$	17.7823	−	30.7998i	1.13146	−	1.95975i
$248$		0			0
$249$	6.69164	+	11.5903i	0.424065	+	0.734503i
$250$		0			0
$251$	−1.92360	−	3.33177i	−0.121416	−	0.210300i	0.798910	−	0.601451i	$-0.205410\pi$
$251$	−1.92360	−	3.33177i	−0.121416	−	0.210300i	−0.920326	+	0.391151i	$0.872077\pi$
$252$		0			0
$253$	−15.6893			−0.986376
$254$		0			0
$255$	0.653954	+	1.13268i	0.0409522	+	0.0709313i
$256$		0			0
$257$	−7.46624	+	12.9319i	−0.465731	+	0.806670i	−0.999234	−	0.0391282i	$-0.987542\pi$
$257$	−7.46624	+	12.9319i	−0.465731	+	0.806670i	0.533503	+	0.845798i	$0.320875\pi$
$258$		0			0
$259$	−6.16971			−0.383367
$260$		0			0
$261$	3.69002	−	6.39130i	0.228407	−	0.395612i
$262$		0			0
$263$	−11.8497			−0.730683			−0.365342	−	0.930874i	$-0.619048\pi$
$263$	−11.8497			−0.730683			−0.365342	+	0.930874i	$0.619048\pi$
$264$		0			0
$265$	−6.09552			−0.374445
$266$		0			0
$267$	−5.88126			−0.359927
$268$		0			0
$269$	20.3661			1.24174			0.620871	−	0.783913i	$-0.286779\pi$
$269$	20.3661			1.24174			0.620871	+	0.783913i	$0.286779\pi$
$270$		0			0
$271$	12.0754			0.733531			0.366765	−	0.930313i	$-0.380465\pi$
$271$	12.0754			0.733531			0.366765	+	0.930313i	$0.380465\pi$
$272$		0			0
$273$	−14.0850			−0.852462
$274$		0			0
$275$	2.56534	−	4.44330i	0.154696	−	0.267941i
$276$		0			0
$277$	−15.4329			−0.927272			−0.463636	−	0.886026i	$-0.653455\pi$
$277$	−15.4329			−0.927272			−0.463636	+	0.886026i	$0.653455\pi$
$278$		0			0
$279$	1.00060	−	1.73309i	0.0599044	−	0.103757i
$280$		0			0
$281$	−0.837123	−	1.44994i	−0.0499386	−	0.0864962i	0.839976	−	0.542624i	$-0.182569\pi$
$281$	−0.837123	−	1.44994i	−0.0499386	−	0.0864962i	−0.889914	+	0.456128i	$0.849236\pi$
$282$		0			0
$283$	−6.71825			−0.399358			−0.199679	−	0.979861i	$-0.563990\pi$
$283$	−6.71825			−0.399358			−0.199679	+	0.979861i	$0.563990\pi$
$284$		0			0
$285$	−2.76451	−	4.78828i	−0.163756	−	0.283633i
$286$		0			0
$287$	2.62191	+	4.54128i	0.154766	+	0.268063i
$288$		0			0
$289$	7.64469	−	13.2410i	0.449688	−	0.778882i
$290$		0			0
$291$	7.09796	+	12.2940i	0.416090	+	0.720688i
$292$		0			0
$293$	24.8308			1.45063			0.725315	−	0.688418i	$-0.241694\pi$
$293$	24.8308			1.45063			0.725315	+	0.688418i	$0.241694\pi$
$294$		0			0
$295$	−5.99534			−0.349062
$296$		0			0
$297$	2.56534	−	4.44330i	0.148856	−	0.257827i
$298$		0			0
$299$	9.83483	−	17.0344i	0.568763	−	0.985126i
$300$		0			0
$301$	−10.5585	+	18.2878i	−0.608580	+	1.05409i
$302$		0			0
$303$	8.95422	−	15.5092i	0.514407	−	0.890978i
$304$		0			0
$305$	6.06494	+	10.5048i	0.347278	+	0.601502i
$306$		0			0
$307$	−4.87572	−	8.44500i	−0.278272	−	0.481982i	0.692683	−	0.721242i	$-0.256428\pi$
$307$	−4.87572	−	8.44500i	−0.278272	−	0.481982i	−0.970955	+	0.239260i	$0.923095\pi$
$308$		0			0
$309$	−2.17465	+	3.76661i	−0.123712	+	0.214275i
$310$		0			0
$311$	−2.57755			−0.146159			−0.0730797	−	0.997326i	$-0.523283\pi$
$311$	−2.57755			−0.146159			−0.0730797	+	0.997326i	$0.523283\pi$
$312$		0			0
$313$	−2.12885			−0.120329			−0.0601647	−	0.998188i	$-0.519163\pi$
$313$	−2.12885			−0.120329			−0.0601647	+	0.998188i	$0.519163\pi$
$314$		0			0
$315$	−1.09486	+	1.89635i	−0.0616882	+	0.106847i
$316$		0			0
$317$	−12.0111	−	20.8038i	−0.674608	−	1.16846i	−0.976583	−	0.215140i	$-0.930979\pi$
$317$	−12.0111	−	20.8038i	−0.674608	−	1.16846i	0.301975	−	0.953316i	$-0.402354\pi$
$318$		0			0
$319$	−18.9323	−	32.7918i	−1.06001	−	1.83599i
$320$		0			0
$321$	−16.3415			−0.912096
$322$		0			0
$323$	3.61573	−	6.26263i	0.201185	−	0.348462i
$324$		0			0
$325$	3.21617	+	5.57057i	0.178401	+	0.309000i
$326$		0			0
$327$	−11.4267			−0.631898
$328$		0			0
$329$	3.74581	+	6.48793i	0.206513	+	0.357691i
$330$		0			0
$331$	−1.23470	+	2.13857i	−0.0678654	+	0.117546i	−0.897961	−	0.440074i	$-0.854952\pi$
$331$	−1.23470	+	2.13857i	−0.0678654	+	0.117546i	0.830096	+	0.557620i	$0.188286\pi$
$332$		0			0
$333$	1.40879	+	2.44010i	0.0772014	+	0.133717i
$334$		0			0
$335$	−7.43204	+	3.42998i	−0.406056	+	0.187400i
$336$		0			0
$337$	−1.16405	−	2.01620i	−0.0634101	−	0.109829i	0.832578	−	0.553909i	$-0.186864\pi$
$337$	−1.16405	−	2.01620i	−0.0634101	−	0.109829i	−0.895988	+	0.444079i	$0.853531\pi$
$338$		0			0
$339$	−6.89488	+	11.9423i	−0.374479	+	0.648616i
$340$		0			0
$341$	−5.13376	−	8.89194i	−0.278009	−	0.481525i
$342$		0			0
$343$	−20.1567			−1.08836
$344$		0			0
$345$	−1.52897	−	2.64825i	−0.0823167	−	0.142577i
$346$		0			0
$347$	−13.8506	+	23.9900i	−0.743541	+	1.28785i	0.207332	+	0.978271i	$0.433522\pi$
$347$	−13.8506	+	23.9900i	−0.743541	+	1.28785i	−0.950873	+	0.309580i	$0.899812\pi$
$348$		0			0
$349$	−25.4323			−1.36136			−0.680680	−	0.732581i	$-0.738316\pi$
$349$	−25.4323			−1.36136			−0.680680	+	0.732581i	$0.738316\pi$
$350$		0			0
$351$	3.21617	+	5.57057i	0.171667	+	0.297335i
$352$		0			0
$353$	−8.32428	−	14.4181i	−0.443057	−	0.767397i	0.554858	−	0.831945i	$-0.312773\pi$
$353$	−8.32428	−	14.4181i	−0.443057	−	0.767397i	−0.997915	+	0.0645483i	$0.979439\pi$
$354$		0			0
$355$	7.59393	−	13.1531i	0.403044	−	0.698093i
$356$		0			0
$357$	−2.86394			−0.151576
$358$		0			0
$359$	11.0289			0.582085			0.291043	−	0.956710i	$-0.405998\pi$
$359$	11.0289			0.582085			0.291043	+	0.956710i	$0.405998\pi$
$360$		0			0
$361$	−5.78507	+	10.0200i	−0.304478	+	0.527371i
$362$		0			0
$363$	−7.66197	−	13.2709i	−0.402149	−	0.696542i
$364$		0			0
$365$	6.15933	+	10.6683i	0.322394	+	0.558403i
$366$		0			0
$367$	2.56468	−	4.44215i	0.133875	−	0.231878i	−0.791292	−	0.611438i	$-0.790591\pi$
$367$	2.56468	−	4.44215i	0.133875	−	0.231878i	0.925167	+	0.379560i	$0.123925\pi$
$368$		0			0
$369$	1.19738	−	2.07392i	0.0623329	−	0.107964i
$370$		0			0
$371$	6.67372	−	11.5592i	0.346482	−	0.600125i
$372$		0			0
$373$	−0.633359	+	1.09701i	−0.0327941	+	0.0568010i	−0.881957	−	0.471331i	$-0.843774\pi$
$373$	−0.633359	+	1.09701i	−0.0327941	+	0.0568010i	0.849163	+	0.528132i	$0.177107\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	47.4710			2.44488
$378$		0			0
$379$	−9.97798	−	17.2824i	−0.512535	−	0.887736i	−0.999894	−	0.0145347i	$-0.995373\pi$
$379$	−9.97798	−	17.2824i	−0.512535	−	0.887736i	0.487360	−	0.873201i	$-0.337960\pi$
$380$		0			0
$381$	−4.98026	+	8.62607i	−0.255147	+	0.441927i
$382$		0			0
$383$	5.84522	+	10.1242i	0.298677	+	0.517324i	0.975834	−	0.218515i	$-0.0701214\pi$
$383$	5.84522	+	10.1242i	0.298677	+	0.517324i	−0.677157	+	0.735839i	$0.736788\pi$
$384$		0			0
$385$	5.61736	+	9.72956i	0.286287	+	0.495864i
$386$		0			0
$387$	9.64370			0.490217
$388$		0			0
$389$	7.84799	+	13.5931i	0.397909	+	0.689198i	0.993468	−	0.114113i	$-0.0364027\pi$
$389$	7.84799	+	13.5931i	0.397909	+	0.689198i	−0.595559	+	0.803312i	$0.703069\pi$
$390$		0			0
$391$	1.99975	−	3.46366i	0.101132	−	0.175165i
$392$		0			0
$393$	4.69171			0.236666
$394$		0			0
$395$	4.94026	−	8.55679i	0.248572	−	0.430539i
$396$		0			0
$397$	−32.6028			−1.63629			−0.818144	−	0.575013i	$-0.804997\pi$
$397$	−32.6028			−1.63629			−0.818144	+	0.575013i	$0.804997\pi$
$398$		0			0
$399$	12.1070			0.606107
$400$		0			0
$401$	−12.0617			−0.602334			−0.301167	−	0.953571i	$-0.597376\pi$
$401$	−12.0617			−0.602334			−0.301167	+	0.953571i	$0.597376\pi$
$402$		0			0
$403$	12.8724			0.641220
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	14.4562			0.716565
$408$		0			0
$409$	7.02900	−	12.1746i	0.347562	−	0.601995i	−0.638254	−	0.769826i	$-0.720343\pi$
$409$	7.02900	−	12.1746i	0.347562	−	0.601995i	0.985816	+	0.167831i	$0.0536763\pi$
$410$		0			0
$411$	10.6501			0.525330
$412$		0			0
$413$	6.56404	−	11.3693i	0.322995	−	0.559444i
$414$		0			0
$415$	6.69164	+	11.5903i	0.328480	+	0.568943i
$416$		0			0
$417$	21.2588			1.04105
$418$		0			0
$419$	−10.3224	−	17.8789i	−0.504281	−	0.873440i	−0.999988	−	0.00494998i	$-0.998424\pi$
$419$	−10.3224	−	17.8789i	−0.504281	−	0.873440i	0.495707	−	0.868490i	$-0.334909\pi$
$420$		0			0
$421$	15.1937	+	26.3163i	0.740498	+	1.28258i	0.952269	+	0.305261i	$0.0987436\pi$
$421$	15.1937	+	26.3163i	0.740498	+	1.28258i	−0.211771	+	0.977319i	$0.567923\pi$
$422$		0			0
$423$	1.71064	−	2.96291i	0.0831741	−	0.144062i
$424$		0			0
$425$	0.653954	+	1.13268i	0.0317214	+	0.0549431i
$426$		0			0
$427$	−26.5610			−1.28538
$428$		0			0
$429$	33.0023			1.59337
$430$		0			0
$431$	−11.4033	+	19.7512i	−0.549280	+	0.951380i	0.449044	+	0.893509i	$0.351765\pi$
$431$	−11.4033	+	19.7512i	−0.549280	+	0.951380i	−0.998324	+	0.0578709i	$0.981569\pi$
$432$		0			0
$433$	9.30756	−	16.1212i	0.447293	−	0.774734i	−0.550916	−	0.834561i	$-0.685721\pi$
$433$	9.30756	−	16.1212i	0.447293	−	0.774734i	0.998209	+	0.0598268i	$0.0190548\pi$
$434$		0			0
$435$	3.69002	−	6.39130i	0.176923	−	0.306440i
$436$		0			0
$437$	−8.45369	+	14.6422i	−0.404395	+	0.700432i
$438$		0			0
$439$	2.03543	+	3.52548i	0.0971460	+	0.168262i	0.910502	−	0.413504i	$-0.135695\pi$
$439$	2.03543	+	3.52548i	0.0971460	+	0.168262i	−0.813356	+	0.581766i	$0.802362\pi$
$440$		0			0
$441$	1.10258	+	1.90972i	0.0525037	+	0.0909391i
$442$		0			0
$443$	3.55314	−	6.15422i	0.168815	−	0.292396i	−0.769189	−	0.639022i	$-0.779339\pi$
$443$	3.55314	−	6.15422i	0.168815	−	0.292396i	0.938003	+	0.346626i	$0.112673\pi$
$444$		0			0
$445$	−5.88126			−0.278799
$446$		0			0
$447$	16.8858			0.798672
$448$		0			0
$449$	−12.9189	+	22.3761i	−0.609679	+	1.05599i	0.381615	+	0.924322i	$0.375368\pi$
$449$	−12.9189	+	22.3761i	−0.609679	+	1.05599i	−0.991293	+	0.131673i	$0.957965\pi$
$450$		0			0
$451$	−6.14336	−	10.6406i	−0.289280	−	0.501047i
$452$		0			0
$453$	3.19850	+	5.53996i	0.150278	+	0.260290i
$454$		0			0
$455$	−14.0850			−0.660314
$456$		0			0
$457$	−16.3814	+	28.3735i	−0.766292	+	1.32726i	0.173270	+	0.984874i	$0.444567\pi$
$457$	−16.3814	+	28.3735i	−0.766292	+	1.32726i	−0.939561	+	0.342381i	$0.888767\pi$
$458$		0			0
$459$	0.653954	+	1.13268i	0.0305240	+	0.0528691i
$460$		0			0
$461$	21.3170			0.992830			0.496415	−	0.868085i	$-0.334649\pi$
$461$	21.3170			0.992830			0.496415	+	0.868085i	$0.334649\pi$
$462$		0			0
$463$	−2.59481	−	4.49434i	−0.120591	−	0.208870i	0.799410	−	0.600786i	$-0.205146\pi$
$463$	−2.59481	−	4.49434i	−0.120591	−	0.208870i	−0.920001	+	0.391916i	$0.871812\pi$
$464$		0			0
$465$	1.00060	−	1.73309i	0.0464017	−	0.0803701i
$466$		0			0
$467$	−4.84248	−	8.38742i	−0.224083	−	0.388124i	0.731961	−	0.681347i	$-0.238605\pi$
$467$	−4.84248	−	8.38742i	−0.224083	−	0.388124i	−0.956044	+	0.293223i	$0.905272\pi$
$468$		0			0
$469$	1.63259	−	17.8491i	0.0753859	−	0.824193i
$470$		0			0
$471$	−11.8207	−	20.4740i	−0.544668	−	0.943392i
$472$		0			0
$473$	24.7394	−	42.8499i	1.13752	−	1.97024i
$474$		0			0
$475$	−2.76451	−	4.78828i	−0.126845	−	0.219701i
$476$		0			0
$477$	−6.09552			−0.279095
$478$		0			0
$479$	−12.9993	−	22.5155i	−0.593954	−	1.02876i	−0.993694	−	0.112129i	$-0.964233\pi$
$479$	−12.9993	−	22.5155i	−0.593954	−	1.02876i	0.399740	−	0.916629i	$-0.369100\pi$
$480$		0			0
$481$	−9.06184	+	15.6956i	−0.413184	+	0.715656i
$482$		0			0
$483$	6.69599			0.304678
$484$		0			0
$485$	7.09796	+	12.2940i	0.322302	+	0.558243i
$486$		0			0
$487$	−4.18670	−	7.25157i	−0.189717	−	0.328600i	0.755439	−	0.655219i	$-0.227424\pi$
$487$	−4.18670	−	7.25157i	−0.189717	−	0.328600i	−0.945156	+	0.326619i	$0.894090\pi$
$488$		0			0
$489$	9.34983	−	16.1944i	0.422814	−	0.732335i
$490$		0			0
$491$	12.0276			0.542796			0.271398	−	0.962467i	$-0.412514\pi$
$491$	12.0276			0.542796			0.271398	+	0.962467i	$0.412514\pi$
$492$		0			0
$493$	9.65242			0.434723
$494$		0			0
$495$	2.56534	−	4.44330i	0.115304	−	0.199712i
$496$		0			0
$497$	16.6285	+	28.8015i	0.745891	+	1.29192i
$498$		0			0
$499$	18.1760	+	31.4817i	0.813668	+	1.40931i	0.910280	+	0.413992i	$0.135866\pi$
$499$	18.1760	+	31.4817i	0.813668	+	1.40931i	−0.0966125	+	0.995322i	$0.530801\pi$
$500$		0			0
$501$	−0.867052	+	1.50178i	−0.0387370	+	0.0670945i
$502$		0			0
$503$	17.1626	−	29.7265i	0.765242	−	1.32544i	−0.174876	−	0.984590i	$-0.555953\pi$
$503$	17.1626	−	29.7265i	0.765242	−	1.32544i	0.940118	−	0.340848i	$-0.110714\pi$
$504$		0			0
$505$	8.95422	−	15.5092i	0.398458	−	0.690149i
$506$		0			0
$507$	−14.1875	+	24.5735i	−0.630090	+	1.09135i
$508$		0			0
$509$	0.296174			0.0131277			0.00656385	−	0.999978i	$-0.497911\pi$
$509$	0.296174			0.0131277			0.00656385	+	0.999978i	$0.497911\pi$
$510$		0			0
$511$	−26.9743			−1.19327
$512$		0			0
$513$	−2.76451	−	4.78828i	−0.122056	−	0.211408i
$514$		0			0
$515$	−2.17465	+	3.76661i	−0.0958266	+	0.165977i
$516$		0			0
$517$	−8.77675	−	15.2018i	−0.386001	−	0.668573i
$518$		0			0
$519$	−2.87760	−	4.98415i	−0.126313	−	0.218780i
$520$		0			0
$521$	−4.54903			−0.199297			−0.0996484	−	0.995023i	$-0.531772\pi$
$521$	−4.54903			−0.199297			−0.0996484	+	0.995023i	$0.531772\pi$
$522$		0			0
$523$	0.473267	+	0.819723i	0.0206945	+	0.0358440i	0.876187	−	0.481971i	$-0.160079\pi$
$523$	0.473267	+	0.819723i	0.0206945	+	0.0358440i	−0.855493	+	0.517815i	$0.826746\pi$
$524$		0			0
$525$	−1.09486	+	1.89635i	−0.0477835	+	0.0827634i
$526$		0			0
$527$	2.61739			0.114015
$528$		0			0
$529$	6.82453	−	11.8204i	0.296719	−	0.513932i
$530$		0			0
$531$	−5.99534			−0.260176
$532$		0			0
$533$	15.4039			0.667215
$534$		0			0
$535$	−16.3415			−0.706506
$536$		0			0
$537$	−3.48707			−0.150478
$538$		0			0
$539$	11.3140			0.487327
$540$		0			0
$541$	−9.61021			−0.413175			−0.206588	−	0.978428i	$-0.566236\pi$
$541$	−9.61021			−0.413175			−0.206588	+	0.978428i	$0.566236\pi$
$542$		0			0
$543$	4.44487	−	7.69874i	0.190748	−	0.330384i
$544$		0			0
$545$	−11.4267			−0.489466
$546$		0			0
$547$	−4.39368	+	7.61007i	−0.187860	+	0.325383i	−0.944537	−	0.328406i	$-0.893488\pi$
$547$	−4.39368	+	7.61007i	−0.187860	+	0.325383i	0.756676	+	0.653790i	$0.226822\pi$
$548$		0			0
$549$	6.06494	+	10.5048i	0.258845	+	0.448333i
$550$		0			0
$551$	−40.8045			−1.73833
$552$		0			0
$553$	10.8178	+	18.7369i	0.460018	+	0.796774i
$554$		0			0
$555$	1.40879	+	2.44010i	0.0598000	+	0.103577i
$556$		0			0
$557$	15.5966	−	27.0140i	0.660848	−	1.14462i	−0.319546	−	0.947571i	$-0.603530\pi$
$557$	15.5966	−	27.0140i	0.660848	−	1.14462i	0.980393	−	0.197051i	$-0.0631364\pi$
$558$		0			0
$559$	31.0158	+	53.7209i	1.31183	+	2.27215i
$560$		0			0
$561$	6.71047			0.283316
$562$		0			0
$563$	15.1080			0.636728			0.318364	−	0.947969i	$-0.396867\pi$
$563$	15.1080			0.636728			0.318364	+	0.947969i	$0.396867\pi$
$564$		0			0
$565$	−6.89488	+	11.9423i	−0.290070	+	0.502416i
$566$		0			0
$567$	−1.09486	+	1.89635i	−0.0459797	+	0.0796391i
$568$		0			0
$569$	−5.46892	+	9.47245i	−0.229269	+	0.397106i	−0.957592	−	0.288129i	$-0.906967\pi$
$569$	−5.46892	+	9.47245i	−0.229269	+	0.397106i	0.728323	+	0.685234i	$0.240300\pi$
$570$		0			0
$571$	−18.2021	+	31.5269i	−0.761733	+	1.31936i	0.180223	+	0.983626i	$0.442318\pi$
$571$	−18.2021	+	31.5269i	−0.761733	+	1.31936i	−0.941956	+	0.335735i	$0.891015\pi$
$572$		0			0
$573$	8.80189	+	15.2453i	0.367704	+	0.636883i
$574$		0			0
$575$	−1.52897	−	2.64825i	−0.0637623	−	0.110439i
$576$		0			0
$577$	−20.2555	+	35.0836i	−0.843249	+	1.46055i	0.0438849	+	0.999037i	$0.486027\pi$
$577$	−20.2555	+	35.0836i	−0.843249	+	1.46055i	−0.887134	+	0.461513i	$0.847307\pi$
$578$		0			0
$579$	−2.90313			−0.120650
$580$		0			0
$581$	−29.3055			−1.21580
$582$		0			0
$583$	−15.6371	+	27.0842i	−0.647622	+	1.12171i
$584$		0			0
$585$	3.21617	+	5.57057i	0.132972	+	0.230315i
$586$		0			0
$587$	−17.7514	−	30.7463i	−0.732677	−	1.26903i	−0.955735	−	0.294229i	$-0.904937\pi$
$587$	−17.7514	−	30.7463i	−0.732677	−	1.26903i	0.223058	−	0.974805i	$-0.428396\pi$
$588$		0			0
$589$	−11.0647			−0.455913
$590$		0			0
$591$	10.2625	−	17.7752i	0.422144	−	0.731175i
$592$		0			0
$593$	9.99456	+	17.3111i	0.410427	+	0.710881i	0.994936	−	0.100506i	$-0.0320462\pi$
$593$	9.99456	+	17.3111i	0.410427	+	0.710881i	−0.584509	+	0.811387i	$0.698713\pi$
$594$		0			0
$595$	−2.86394			−0.117410
$596$		0			0
$597$	−2.49651	−	4.32408i	−0.102175	−	0.176973i
$598$		0			0
$599$	−8.07834	+	13.9921i	−0.330072	+	0.571701i	−0.982526	−	0.186127i	$-0.940406\pi$
$599$	−8.07834	+	13.9921i	−0.330072	+	0.571701i	0.652454	+	0.757829i	$0.273740\pi$
$600$		0			0
$601$	−5.94057	−	10.2894i	−0.242321	−	0.419712i	0.719054	−	0.694954i	$-0.244575\pi$
$601$	−5.94057	−	10.2894i	−0.242321	−	0.419712i	−0.961375	+	0.275242i	$0.911242\pi$
$602$		0			0
$603$	−7.43204	+	3.42998i	−0.302656	+	0.139680i
$604$		0			0
$605$	−7.66197	−	13.2709i	−0.311503	−	0.539539i
$606$		0			0
$607$	−7.60851	+	13.1783i	−0.308820	+	0.534892i	−0.978104	−	0.208114i	$-0.933267\pi$
$607$	−7.60851	+	13.1783i	−0.308820	+	0.534892i	0.669285	+	0.743006i	$0.266601\pi$
$608$		0			0
$609$	8.08009	+	13.9951i	0.327422	+	0.567111i
$610$		0			0
$611$	22.0068			0.890301
$612$		0			0
$613$	−15.4993	−	26.8456i	−0.626012	−	1.08428i	−0.988344	−	0.152235i	$-0.951353\pi$
$613$	−15.4993	−	26.8456i	−0.626012	−	1.08428i	0.362333	−	0.932049i	$-0.381980\pi$
$614$		0			0
$615$	1.19738	−	2.07392i	0.0482829	−	0.0836284i
$616$		0			0
$617$	20.9244			0.842386			0.421193	−	0.906971i	$-0.361612\pi$
$617$	20.9244			0.842386			0.421193	+	0.906971i	$0.361612\pi$
$618$		0			0
$619$	15.0689	+	26.1002i	0.605672	+	1.04905i	0.991945	+	0.126670i	$0.0404289\pi$
$619$	15.0689	+	26.1002i	0.605672	+	1.04905i	−0.386273	+	0.922384i	$0.626238\pi$
$620$		0			0
$621$	−1.52897	−	2.64825i	−0.0613553	−	0.106270i
$622$		0			0
$623$	6.43914	−	11.1529i	0.257979	−	0.446832i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−28.3677			−1.13290
$628$		0			0
$629$	−1.84257	+	3.19143i	−0.0734682	+	0.127251i
$630$		0			0
$631$	−2.87033	−	4.97155i	−0.114266	−	0.197914i	0.803220	−	0.595682i	$-0.203118\pi$
$631$	−2.87033	−	4.97155i	−0.114266	−	0.197914i	−0.917486	+	0.397768i	$0.869785\pi$
$632$		0			0
$633$	10.4849	+	18.1604i	0.416737	+	0.721810i
$634$		0			0
$635$	−4.98026	+	8.62607i	−0.197636	+	0.342315i
$636$		0			0
$637$	−7.09216	+	12.2840i	−0.281002	+	0.486709i
$638$		0			0
$639$	7.59393	−	13.1531i	0.300411	−	0.520327i
$640$		0			0
$641$	−17.6342	+	30.5434i	−0.696511	+	1.20639i	0.273158	+	0.961969i	$0.411932\pi$
$641$	−17.6342	+	30.5434i	−0.696511	+	1.20639i	−0.969669	+	0.244423i	$0.921402\pi$
$642$		0			0
$643$	−25.5756			−1.00861			−0.504303	−	0.863527i	$-0.668250\pi$
$643$	−25.5756			−1.00861			−0.504303	+	0.863527i	$0.668250\pi$
$644$		0			0
$645$	9.64370			0.379720
$646$		0			0
$647$	−20.4109	−	35.3528i	−0.802437	−	1.38986i	−0.918008	−	0.396562i	$-0.870203\pi$
$647$	−20.4109	−	35.3528i	−0.802437	−	1.38986i	0.115571	−	0.993299i	$-0.463130\pi$
$648$		0			0
$649$	−15.3801	+	26.6391i	−0.603722	+	1.04568i
$650$		0			0
$651$	2.19103	+	3.79497i	0.0858731	+	0.148737i
$652$		0			0
$653$	−8.93268	−	15.4719i	−0.349563	−	0.605461i	0.636609	−	0.771187i	$-0.280337\pi$
$653$	−8.93268	−	15.4719i	−0.349563	−	0.605461i	−0.986172	+	0.165726i	$0.947003\pi$
$654$		0			0
$655$	4.69171			0.183320
$656$		0			0
$657$	6.15933	+	10.6683i	0.240298	+	0.416209i
$658$		0			0
$659$	−14.0009	+	24.2502i	−0.545396	+	0.944654i	0.453185	+	0.891416i	$0.350288\pi$
$659$	−14.0009	+	24.2502i	−0.545396	+	0.944654i	−0.998582	+	0.0532380i	$0.983046\pi$
$660$		0			0
$661$	−4.51742			−0.175707			−0.0878536	−	0.996133i	$-0.528001\pi$
$661$	−4.51742			−0.175707			−0.0878536	+	0.996133i	$0.528001\pi$
$662$		0			0
$663$	−4.20646	+	7.28580i	−0.163365	+	0.282957i
$664$		0			0
$665$	12.1070			0.469489
$666$		0			0
$667$	−22.5677			−0.873823
$668$		0			0
$669$	15.0267			0.580965
$670$		0			0
$671$	62.2346			2.40254
$672$		0			0
$673$	5.75306			0.221764			0.110882	−	0.993834i	$-0.464632\pi$
$673$	5.75306			0.221764			0.110882	+	0.993834i	$0.464632\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	−20.8807	+	36.1665i	−0.802511	+	1.38999i	0.115447	+	0.993314i	$0.463170\pi$
$677$	−20.8807	+	36.1665i	−0.802511	+	1.38999i	−0.917959	+	0.396676i	$0.870164\pi$
$678$		0			0
$679$	−31.0850			−1.19293
$680$		0			0
$681$	−1.70708	+	2.95674i	−0.0654153	+	0.113303i
$682$		0			0
$683$	−17.0221	−	29.4831i	−0.651332	−	1.12814i	−0.982800	−	0.184673i	$-0.940877\pi$
$683$	−17.0221	−	29.4831i	−0.651332	−	1.12814i	0.331468	−	0.943466i	$-0.392456\pi$
$684$		0			0
$685$	10.6501			0.406919
$686$		0			0
$687$	−7.38564	−	12.7923i	−0.281780	−	0.488057i
$688$		0			0
$689$	−19.6042	−	33.9555i	−0.746862	−	1.29360i
$690$		0			0
$691$	23.5182	−	40.7347i	0.894674	−	1.54962i	0.0604666	−	0.998170i	$-0.480741\pi$
$691$	23.5182	−	40.7347i	0.894674	−	1.54962i	0.834207	−	0.551451i	$-0.185926\pi$
$692$		0			0
$693$	5.61736	+	9.72956i	0.213386	+	0.369595i
$694$		0			0
$695$	21.2588			0.806394
$696$		0			0
$697$	3.13212			0.118637
$698$		0			0
$699$	−7.28641	+	12.6204i	−0.275597	+	0.477349i
$700$		0			0
$701$	3.32651	−	5.76168i	0.125640	−	0.217616i	−0.796343	−	0.604846i	$-0.793235\pi$
$701$	3.32651	−	5.76168i	0.125640	−	0.217616i	0.921983	+	0.387230i	$0.126568\pi$
$702$		0			0
$703$	7.78926	−	13.4914i	0.293777	−	0.508838i
$704$		0			0
$705$	1.71064	−	2.96291i	0.0644264	−	0.111590i
$706$		0			0
$707$	19.6072	+	33.9606i	0.737404	+	1.27722i
$708$		0			0
$709$	18.2579	+	31.6236i	0.685689	+	1.18765i	0.973220	+	0.229877i	$0.0738323\pi$
$709$	18.2579	+	31.6236i	0.685689	+	1.18765i	−0.287531	+	0.957771i	$0.592834\pi$
$710$		0			0
$711$	4.94026	−	8.55679i	0.185274	−	0.320905i
$712$		0			0
$713$	−6.11953			−0.229178
$714$		0			0
$715$	33.0023			1.23422
$716$		0			0
$717$	−7.82106	+	13.5465i	−0.292083	+	0.505902i
$718$		0			0
$719$	−4.88473	−	8.46060i	−0.182170	−	0.315527i	0.760449	−	0.649397i	$-0.224979\pi$
$719$	−4.88473	−	8.46060i	−0.182170	−	0.315527i	−0.942619	+	0.333870i	$0.891645\pi$
$720$		0			0
$721$	−4.76187	−	8.24779i	−0.177341	−	0.307164i
$722$		0			0
$723$	−27.5691			−1.02531
$724$		0			0
$725$	3.69002	−	6.39130i	0.137044	−	0.237367i
$726$		0			0
$727$	−24.7491	−	42.8668i	−0.917895	−	1.58984i	−0.802607	−	0.596508i	$-0.796554\pi$
$727$	−24.7491	−	42.8668i	−0.917895	−	1.58984i	−0.115288	−	0.993332i	$-0.536779\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	6.30654	+	10.9232i	0.233256	+	0.404011i
$732$		0			0
$733$	−17.3823	+	30.1070i	−0.642030	+	1.11203i	0.342949	+	0.939354i	$0.388574\pi$
$733$	−17.3823	+	30.1070i	−0.642030	+	1.11203i	−0.984979	+	0.172675i	$0.944759\pi$
$734$		0			0
$735$	1.10258	+	1.90972i	0.0406692	+	0.0704411i
$736$		0			0
$737$	−3.82529	+	41.8219i	−0.140906	+	1.54053i
$738$		0			0
$739$	−16.8296	−	29.1497i	−0.619086	−	1.07229i	−0.989653	−	0.143482i	$-0.954170\pi$
$739$	−16.8296	−	29.1497i	−0.619086	−	1.07229i	0.370567	−	0.928806i	$-0.379163\pi$
$740$		0			0
$741$	17.7823	−	30.7998i	0.653249	−	1.13146i
$742$		0			0
$743$	20.0164	+	34.6694i	0.734330	+	1.27190i	0.955017	+	0.296552i	$0.0958367\pi$
$743$	20.0164	+	34.6694i	0.734330	+	1.27190i	−0.220687	+	0.975345i	$0.570830\pi$
$744$		0			0
$745$	16.8858			0.618648
$746$		0			0
$747$	6.69164	+	11.5903i	0.244834	+	0.424065i
$748$		0			0
$749$	17.8916	−	30.9892i	0.653746	−	1.13232i
$750$		0			0
$751$	−29.2614			−1.06776			−0.533881	−	0.845559i	$-0.679267\pi$
$751$	−29.2614			−1.06776			−0.533881	+	0.845559i	$0.679267\pi$
$752$		0			0
$753$	−1.92360	−	3.33177i	−0.0700998	−	0.121416i
$754$		0			0
$755$	3.19850	+	5.53996i	0.116405	+	0.201620i
$756$		0			0
$757$	1.71468	−	2.96992i	0.0623212	−	0.107943i	−0.833181	−	0.553000i	$-0.813483\pi$
$757$	1.71468	−	2.96992i	0.0623212	−	0.107943i	0.895503	+	0.445056i	$0.146816\pi$
$758$		0			0
$759$	−15.6893			−0.569485
$760$		0			0
$761$	−34.8831			−1.26451			−0.632256	−	0.774759i	$-0.717871\pi$
$761$	−34.8831			−1.26451			−0.632256	+	0.774759i	$0.717871\pi$
$762$		0			0
$763$	12.5106	−	21.6690i	0.452914	−	0.784470i
$764$		0			0
$765$	0.653954	+	1.13268i	0.0236438	+	0.0409522i
$766$		0			0
$767$	−19.2820	−	33.3975i	−0.696234	−	1.20591i
$768$		0			0
$769$	2.46613	−	4.27146i	0.0889309	−	0.154033i	−0.818129	−	0.575035i	$-0.804988\pi$
$769$	2.46613	−	4.27146i	0.0889309	−	0.154033i	0.907059	+	0.421002i	$0.138322\pi$
$770$		0			0
$771$	−7.46624	+	12.9319i	−0.268890	+	0.465731i
$772$		0			0
$773$	−9.91770	+	17.1780i	−0.356715	+	0.617848i	−0.987410	−	0.158183i	$-0.949437\pi$
$773$	−9.91770	+	17.1780i	−0.356715	+	0.617848i	0.630695	+	0.776031i	$0.282770\pi$
$774$		0			0
$775$	1.00060	−	1.73309i	0.0359426	−	0.0622544i
$776$		0			0
$777$	−6.16971			−0.221337
$778$		0			0
$779$	−13.2407			−0.474396
$780$		0			0
$781$	−38.9621	−	67.4843i	−1.39417	−	2.41478i
$782$		0			0
$783$	3.69002	−	6.39130i	0.131871	−	0.228407i
$784$		0			0
$785$	−11.8207	−	20.4740i	−0.421898	−	0.730748i
$786$		0			0
$787$	−8.97185	−	15.5397i	−0.319812	−	0.553930i	0.660637	−	0.750706i	$-0.270286\pi$
$787$	−8.97185	−	15.5397i	−0.319812	−	0.553930i	−0.980449	+	0.196775i	$0.936953\pi$
$788$		0			0
$789$	−11.8497			−0.421860
$790$		0			0
$791$	−15.0978	−	26.1502i	−0.536817	−	0.929794i
$792$		0			0
$793$	−39.0118	+	67.5704i	−1.38535	+	2.39949i
$794$		0			0
$795$	−6.09552			−0.216186
$796$		0			0
$797$	−10.8259	+	18.7510i	−0.383473	+	0.664194i	−0.991556	−	0.129679i	$-0.958605\pi$
$797$	−10.8259	+	18.7510i	−0.383473	+	0.664194i	0.608083	+	0.793873i	$0.291939\pi$
$798$		0			0
$799$	4.47472			0.158304
$800$		0			0
$801$	−5.88126			−0.207804
$802$		0			0
$803$	63.2031			2.23039
$804$		0			0
$805$	6.69599			0.236003
$806$		0			0
$807$	20.3661			0.716920
$808$		0			0
$809$	−17.7650			−0.624583			−0.312291	−	0.949986i	$-0.601097\pi$
$809$	−17.7650			−0.624583			−0.312291	+	0.949986i	$0.601097\pi$
$810$		0			0
$811$	19.1863	−	33.2317i	0.673724	−	1.16692i	−0.303116	−	0.952954i	$-0.598027\pi$
$811$	19.1863	−	33.2317i	0.673724	−	1.16692i	0.976840	−	0.213970i	$-0.0686396\pi$
$812$		0			0
$813$	12.0754			0.423504
$814$		0			0
$815$	9.34983	−	16.1944i	0.327510	−	0.567265i
$816$		0			0
$817$	−26.6602	−	46.1767i	−0.932721	−	1.61552i
$818$		0			0
$819$	−14.0850			−0.492169
$820$		0			0
$821$	−27.0148	−	46.7910i	−0.942823	−	1.63302i	−0.760053	−	0.649862i	$-0.774827\pi$
$821$	−27.0148	−	46.7910i	−0.942823	−	1.63302i	−0.182770	−	0.983156i	$-0.558506\pi$
$822$		0			0
$823$	11.6125	+	20.1134i	0.404786	+	0.701109i	0.994296	−	0.106651i	$-0.0340128\pi$
$823$	11.6125	+	20.1134i	0.404786	+	0.701109i	−0.589511	+	0.807760i	$0.700680\pi$
$824$		0			0
$825$	2.56534	−	4.44330i	0.0893138	−	0.154696i
$826$		0			0
$827$	−20.9642	−	36.3111i	−0.728997	−	1.26266i	−0.957308	−	0.289072i	$-0.906653\pi$
$827$	−20.9642	−	36.3111i	−0.728997	−	1.26266i	0.228310	−	0.973588i	$-0.426680\pi$
$828$		0			0
$829$	−4.33054			−0.150406			−0.0752029	−	0.997168i	$-0.523960\pi$
$829$	−4.33054			−0.150406			−0.0752029	+	0.997168i	$0.523960\pi$
$830$		0			0
$831$	−15.4329			−0.535361
$832$		0			0
$833$	−1.44207	+	2.49774i	−0.0499648	+	0.0865415i
$834$		0			0
$835$	−0.867052	+	1.50178i	−0.0300056	+	0.0519712i
$836$		0			0
$837$	1.00060	−	1.73309i	0.0345858	−	0.0599044i
$838$		0			0
$839$	−1.82418	+	3.15958i	−0.0629778	+	0.109081i	−0.895795	−	0.444467i	$-0.853393\pi$
$839$	−1.82418	+	3.15958i	−0.0629778	+	0.109081i	0.832817	+	0.553548i	$0.186726\pi$
$840$		0			0
$841$	−12.7325	−	22.0534i	−0.439052	−	0.760461i
$842$		0			0
$843$	−0.837123	−	1.44994i	−0.0288321	−	0.0499386i
$844$		0			0
$845$	−14.1875	+	24.5735i	−0.488065	+	0.845354i
$846$		0			0
$847$	33.5550			1.15296
$848$		0			0
$849$	−6.71825			−0.230570
$850$		0			0
$851$	4.30799	−	7.46166i	0.147676	−	0.255782i
$852$		0			0
$853$	−3.74019	−	6.47820i	−0.128062	−	0.221809i	0.794864	−	0.606788i	$-0.207542\pi$
$853$	−3.74019	−	6.47820i	−0.128062	−	0.221809i	−0.922926	+	0.384978i	$0.874209\pi$
$854$		0			0
$855$	−2.76451	−	4.78828i	−0.0945444	−	0.163756i
$856$		0			0
$857$	−56.4449			−1.92812			−0.964061	−	0.265682i	$-0.914403\pi$
$857$	−56.4449			−1.92812			−0.964061	+	0.265682i	$0.914403\pi$
$858$		0			0
$859$	−20.5849	+	35.6542i	−0.702349	+	1.21650i	0.265291	+	0.964168i	$0.414532\pi$
$859$	−20.5849	+	35.6542i	−0.702349	+	1.21650i	−0.967640	+	0.252336i	$0.918801\pi$
$860$		0			0
$861$	2.62191	+	4.54128i	0.0893545	+	0.154766i
$862$		0			0
$863$	−17.3023			−0.588978			−0.294489	−	0.955655i	$-0.595150\pi$
$863$	−17.3023			−0.588978			−0.294489	+	0.955655i	$0.595150\pi$
$864$		0			0
$865$	−2.87760	−	4.98415i	−0.0978413	−	0.169466i
$866$		0			0
$867$	7.64469	−	13.2410i	0.259627	−	0.449688i
$868$		0			0
$869$	−25.3469	−	43.9022i	−0.859836	−	1.48928i
$870$		0			0
$871$	−43.0097	−	30.3693i	−1.45733	−	1.02903i
$872$		0			0
$873$	7.09796	+	12.2940i	0.240229	+	0.416090i
$874$		0			0
$875$	−1.09486	+	1.89635i	−0.0370129	+	0.0641082i
$876$		0			0
$877$	1.95341	+	3.38340i	0.0659618	+	0.114249i	0.897120	−	0.441786i	$-0.145655\pi$
$877$	1.95341	+	3.38340i	0.0659618	+	0.114249i	−0.831158	+	0.556036i	$0.812322\pi$
$878$		0			0
$879$	24.8308			0.837521
$880$		0			0
$881$	19.2478	+	33.3382i	0.648476	+	1.12319i	0.983487	+	0.180979i	$0.0579265\pi$
$881$	19.2478	+	33.3382i	0.648476	+	1.12319i	−0.335011	+	0.942214i	$0.608740\pi$
$882$		0			0
$883$	24.3758	−	42.2201i	0.820311	−	1.42082i	−0.0851400	−	0.996369i	$-0.527134\pi$
$883$	24.3758	−	42.2201i	0.820311	−	1.42082i	0.905451	−	0.424451i	$-0.139533\pi$
$884$		0			0
$885$	−5.99534			−0.201531
$886$		0			0
$887$	−1.46384	−	2.53545i	−0.0491510	−	0.0851321i	0.840403	−	0.541962i	$-0.182318\pi$
$887$	−1.46384	−	2.53545i	−0.0491510	−	0.0851321i	−0.889554	+	0.456830i	$0.848985\pi$
$888$		0			0
$889$	−10.9053	−	18.8886i	−0.365754	−	0.633504i
$890$		0			0
$891$	2.56534	−	4.44330i	0.0859422	−	0.148856i
$892$		0			0
$893$	−18.9163			−0.633011
$894$		0			0
$895$	−3.48707			−0.116560
$896$		0			0
$897$	9.83483	−	17.0344i	0.328375	−	0.568763i
$898$		0			0
$899$	−7.38447	−	12.7903i	−0.246286	−	0.426580i
$900$		0			0
$901$	−3.98619	−	6.90428i	−0.132799	−	0.230015i
$902$		0			0
$903$	−10.5585	+	18.2878i	−0.351364	+	0.608580i
$904$		0			0
$905$	4.44487	−	7.69874i	0.147752	−	0.255915i
$906$		0			0
$907$	−12.5020	+	21.6541i	−0.415122	+	0.719013i	−0.995441	−	0.0953763i	$-0.969595\pi$
$907$	−12.5020	+	21.6541i	−0.415122	+	0.719013i	0.580319	+	0.814389i	$0.302928\pi$
$908$		0			0
$909$	8.95422	−	15.5092i	0.296993	−	0.514407i
$910$		0			0
$911$	−41.0407			−1.35974			−0.679870	−	0.733332i	$-0.737964\pi$
$911$	−41.0407			−1.35974			−0.679870	+	0.733332i	$0.737964\pi$
$912$		0			0
$913$	68.6654			2.27249
$914$		0			0
$915$	6.06494	+	10.5048i	0.200501	+	0.347278i
$916$		0			0
$917$	−5.13675	+	8.89711i	−0.169630	+	0.293809i
$918$		0			0
$919$	−9.76458	−	16.9127i	−0.322104	−	0.557900i	0.658818	−	0.752302i	$-0.271057\pi$
$919$	−9.76458	−	16.9127i	−0.322104	−	0.557900i	−0.980922	+	0.194402i	$0.937723\pi$
$920$		0			0
$921$	−4.87572	−	8.44500i	−0.160661	−	0.278272i
$922$		0			0
$923$	97.6935			3.21562
$924$		0			0
$925$	1.40879	+	2.44010i	0.0463208	+	0.0802301i
$926$		0			0
$927$	−2.17465	+	3.76661i	−0.0714250	+	0.123712i
$928$		0			0
$929$	42.6080			1.39792			0.698962	−	0.715159i	$-0.253646\pi$
$929$	42.6080			1.39792			0.698962	+	0.715159i	$0.253646\pi$
$930$		0			0
$931$	6.09618	−	10.5589i	0.199794	−	0.346054i
$932$		0			0
$933$	−2.57755			−0.0843852
$934$		0			0
$935$	6.71047			0.219456
$936$		0			0
$937$	26.8048			0.875675			0.437838	−	0.899054i	$-0.355744\pi$
$937$	26.8048			0.875675			0.437838	+	0.899054i	$0.355744\pi$
$938$		0			0
$939$	−2.12885			−0.0694722
$940$		0			0
$941$	16.0030			0.521682			0.260841	−	0.965382i	$-0.416000\pi$
$941$	16.0030			0.521682			0.260841	+	0.965382i	$0.416000\pi$
$942$		0			0
$943$	−7.32298			−0.238469
$944$		0			0
$945$	−1.09486	+	1.89635i	−0.0356157	+	0.0616882i
$946$		0			0
$947$	−55.5867			−1.80633			−0.903163	−	0.429297i	$-0.858761\pi$
$947$	−55.5867			−1.80633			−0.903163	+	0.429297i	$0.858761\pi$
$948$		0			0
$949$	−39.6189	+	68.6220i	−1.28608	+	2.22756i
$950$		0			0
$951$	−12.0111	−	20.8038i	−0.389485	−	0.674608i
$952$		0			0
$953$	10.3582			0.335534			0.167767	−	0.985827i	$-0.446344\pi$
$953$	10.3582			0.335534			0.167767	+	0.985827i	$0.446344\pi$
$954$		0			0
$955$	8.80189	+	15.2453i	0.284823	+	0.493327i
$956$		0			0
$957$	−18.9323	−	32.7918i	−0.611996	−	1.06001i
$958$		0			0
$959$	−11.6603	+	20.1963i	−0.376532	+	0.652172i
$960$		0			0
$961$	13.4976	+	23.3785i	0.435406	+	0.754146i
$962$		0			0
$963$	−16.3415			−0.526599
$964$		0			0
$965$	−2.90313			−0.0934551
$966$		0			0
$967$	11.7759	−	20.3965i	0.378687	−	0.655906i	−0.612184	−	0.790715i	$-0.709709\pi$
$967$	11.7759	−	20.3965i	0.378687	−	0.655906i	0.990872	+	0.134809i	$0.0430422\pi$
$968$		0			0
$969$	3.61573	−	6.26263i	0.116154	−	0.201185i
$970$		0			0
$971$	−2.29652	+	3.97770i	−0.0736990	+	0.127650i	−0.900520	−	0.434815i	$-0.856814\pi$
$971$	−2.29652	+	3.97770i	−0.0736990	+	0.127650i	0.826821	+	0.562465i	$0.190147\pi$
$972$		0			0
$973$	−23.2754	+	40.3142i	−0.746175	+	1.29241i
$974$		0			0
$975$	3.21617	+	5.57057i	0.103000	+	0.178401i
$976$		0			0
$977$	16.1599	+	27.9898i	0.517001	+	0.895472i	0.999805	+	0.0197434i	$0.00628492\pi$
$977$	16.1599	+	27.9898i	0.517001	+	0.895472i	−0.482804	+	0.875728i	$0.660382\pi$
$978$		0			0
$979$	−15.0875	+	26.1322i	−0.482197	+	0.835190i
$980$		0			0
$981$	−11.4267			−0.364826
$982$		0			0
$983$	37.3018			1.18974			0.594872	−	0.803820i	$-0.297203\pi$
$983$	37.3018			1.18974			0.594872	+	0.803820i	$0.297203\pi$
$984$		0			0
$985$	10.2625	−	17.7752i	0.326991	−	0.566366i
$986$		0			0
$987$	3.74581	+	6.48793i	0.119230	+	0.206513i
$988$		0			0
$989$	−14.7449	−	25.5389i	−0.468860	−	0.812089i
$990$		0			0
$991$	−60.3838			−1.91815			−0.959077	−	0.283146i	$-0.908622\pi$
$991$	−60.3838			−1.91815			−0.959077	+	0.283146i	$0.908622\pi$
$992$		0			0
$993$	−1.23470	+	2.13857i	−0.0391821	+	0.0678654i
$994$		0			0
$995$	−2.49651	−	4.32408i	−0.0791446	−	0.137083i
$996$		0			0
$997$	−35.4117			−1.12150			−0.560750	−	0.827985i	$-0.689487\pi$
$997$	−35.4117			−1.12150			−0.560750	+	0.827985i	$0.689487\pi$
$998$		0			0
$999$	1.40879	+	2.44010i	0.0445723	+	0.0772014i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.4	✓	24
67.29	even	3	inner	4020.2.q.m.3781.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.4	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.4	yes	24	67.29	even	3	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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-1.09486 + 1.89635i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(-1.09486 + 1.89635i) q^{7} +1.00000 q^{9} +(2.56534 - 4.44330i) q^{11} +(3.21617 + 5.57057i) q^{13} +1.00000 q^{15} +(0.653954 + 1.13268i) q^{17} +(-2.76451 - 4.78828i) q^{19} +(-1.09486 + 1.89635i) q^{21} +(-1.52897 - 2.64825i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.69002 - 6.39130i) q^{29} +(1.00060 - 1.73309i) q^{31} +(2.56534 - 4.44330i) q^{33} +(-1.09486 + 1.89635i) q^{35} +(1.40879 + 2.44010i) q^{37} +(3.21617 + 5.57057i) q^{39} +(1.19738 - 2.07392i) q^{41} +9.64370 q^{43} +1.00000 q^{45} +(1.71064 - 2.96291i) q^{47} +(1.10258 + 1.90972i) q^{49} +(0.653954 + 1.13268i) q^{51} -6.09552 q^{53} +(2.56534 - 4.44330i) q^{55} +(-2.76451 - 4.78828i) q^{57} -5.99534 q^{59} +(6.06494 + 10.5048i) q^{61} +(-1.09486 + 1.89635i) q^{63} +(3.21617 + 5.57057i) q^{65} +(-7.43204 + 3.42998i) q^{67} +(-1.52897 - 2.64825i) q^{69} +(7.59393 - 13.1531i) q^{71} +(6.15933 + 10.6683i) q^{73} +1.00000 q^{75} +(5.61736 + 9.72956i) q^{77} +(4.94026 - 8.55679i) q^{79} +1.00000 q^{81} +(6.69164 + 11.5903i) q^{83} +(0.653954 + 1.13268i) q^{85} +(3.69002 - 6.39130i) q^{87} -5.88126 q^{89} -14.0850 q^{91} +(1.00060 - 1.73309i) q^{93} +(-2.76451 - 4.78828i) q^{95} +(7.09796 + 12.2940i) q^{97} +(2.56534 - 4.44330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more