LMFDB - Embedded newform 1260.2.n.a.71.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(71,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0, 0]))

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

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

chi := DirichletCharacter("1260.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.n (of order $2$, degree $1$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.5
Character	$\chi$	$=$	1260.71
Dual form			1260.2.n.a.71.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13949 - 0.837595i) q^{2} +(0.596870 + 1.90886i) q^{4} -1.00000i q^{5} -1.00000i q^{7} +(0.918725 - 2.67506i) q^{8} +(-0.837595 + 1.13949i) q^{10} +3.58982 q^{11} -2.60436 q^{13} +(-0.837595 + 1.13949i) q^{14} +(-3.28749 + 2.27868i) q^{16} -5.87840i q^{17} +2.36141i q^{19} +(1.90886 - 0.596870i) q^{20} +(-4.09056 - 3.00681i) q^{22} +0.872147 q^{23} -1.00000 q^{25} +(2.96764 + 2.18140i) q^{26} +(1.90886 - 0.596870i) q^{28} -5.80406i q^{29} +0.479206i q^{31} +(5.65467 + 0.157056i) q^{32} +(-4.92372 + 6.69837i) q^{34} -1.00000 q^{35} +1.21097 q^{37} +(1.97790 - 2.69080i) q^{38} +(-2.67506 - 0.918725i) q^{40} +3.33273i q^{41} +1.07785i q^{43} +(2.14265 + 6.85246i) q^{44} +(-0.993802 - 0.730506i) q^{46} -1.79111 q^{47} -1.00000 q^{49} +(1.13949 + 0.837595i) q^{50} +(-1.55447 - 4.97137i) q^{52} -10.2314i q^{53} -3.58982i q^{55} +(-2.67506 - 0.918725i) q^{56} +(-4.86145 + 6.61366i) q^{58} -9.15424 q^{59} +7.76517 q^{61} +(0.401381 - 0.546050i) q^{62} +(-6.31189 - 4.91529i) q^{64} +2.60436i q^{65} -11.6184i q^{67} +(11.2210 - 3.50864i) q^{68} +(1.13949 + 0.837595i) q^{70} +9.51142 q^{71} -1.40325 q^{73} +(-1.37988 - 1.01430i) q^{74} +(-4.50759 + 1.40945i) q^{76} -3.58982i q^{77} -13.2047i q^{79} +(2.27868 + 3.28749i) q^{80} +(2.79148 - 3.79761i) q^{82} -15.5080 q^{83} -5.87840 q^{85} +(0.902799 - 1.22819i) q^{86} +(3.29806 - 9.60298i) q^{88} +0.714137i q^{89} +2.60436i q^{91} +(0.520558 + 1.66481i) q^{92} +(2.04095 + 1.50023i) q^{94} +2.36141 q^{95} +2.39247 q^{97} +(1.13949 + 0.837595i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) $ 24 * q - 4 * q^4 - 4 * q^10 - 4 * q^14 + 4 * q^20 - 4 * q^22 - 24 * q^25 - 40 * q^26 + 4 * q^28 + 40 * q^32 + 8 * q^34 - 24 * q^35 + 4 * q^40 + 48 * q^44 + 36 * q^46 + 16 * q^47 - 24 * q^49 + 32 * q^52 + 4 * q^56 - 28 * q^58 - 16 * q^59 - 32 * q^61 - 56 * q^62 - 4 * q^64 + 64 * q^68 - 32 * q^74 - 72 * q^76 - 40 * q^82 - 80 * q^83 + 32 * q^85 - 80 * q^86 + 12 * q^88

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	−1.13949	−	0.837595i	−0.805740	−	0.592269i
$2$	−1.13949	−	0.837595i	−0.805740	−	0.592269i
$3$		0			0
$3$		0			0
$4$	0.596870	+	1.90886i	0.298435	+	0.954430i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	0.918725	−	2.67506i	0.324818	−	0.945776i
$9$		0			0
$10$	−0.837595	+	1.13949i	−0.264871	+	0.360338i
$11$	3.58982			1.08237			0.541186	−	0.840903i	$-0.317976\pi$
$11$	3.58982			1.08237			0.541186	+	0.840903i	$0.317976\pi$
$12$		0			0
$13$	−2.60436			−0.722321			−0.361160	−	0.932504i	$-0.617619\pi$
$13$	−2.60436			−0.722321			−0.361160	+	0.932504i	$0.617619\pi$
$14$	−0.837595	+	1.13949i	−0.223857	+	0.304541i
$15$		0			0
$16$	−3.28749	+	2.27868i	−0.821873	+	0.569670i
$17$		−	5.87840i		−	1.42572i	−0.701306	−	0.712860i	$-0.747399\pi$
$17$		−	5.87840i		−	1.42572i	0.701306	−	0.712860i	$-0.252601\pi$
$18$		0			0
$19$			2.36141i			0.541744i	0.962615	+	0.270872i	$0.0873120\pi$
$19$			2.36141i			0.541744i	−0.962615	+	0.270872i	$0.912688\pi$
$20$	1.90886	−	0.596870i	0.426834	−	0.133464i
$21$		0			0
$22$	−4.09056	−	3.00681i	−0.872110	−	0.641055i
$23$	0.872147			0.181855			0.0909276	−	0.995858i	$-0.471017\pi$
$23$	0.872147			0.181855			0.0909276	+	0.995858i	$0.471017\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	2.96764	+	2.18140i	0.582003	+	0.427808i
$27$		0			0
$28$	1.90886	−	0.596870i	0.360741	−	0.112798i
$29$		−	5.80406i		−	1.07779i	−0.842374	−	0.538894i	$-0.818843\pi$
$29$		−	5.80406i		−	1.07779i	0.842374	−	0.538894i	$-0.181157\pi$
$30$		0			0
$31$			0.479206i			0.0860679i	0.999074	+	0.0430340i	$0.0137024\pi$
$31$			0.479206i			0.0860679i	−0.999074	+	0.0430340i	$0.986298\pi$
$32$	5.65467	+	0.157056i	0.999615	+	0.0277639i
$33$		0			0
$34$	−4.92372	+	6.69837i	−0.844410	+	1.14876i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	1.21097			0.199081			0.0995407	−	0.995033i	$-0.468263\pi$
$37$	1.21097			0.199081			0.0995407	+	0.995033i	$0.468263\pi$
$38$	1.97790	−	2.69080i	0.320858	−	0.436505i
$39$		0			0
$40$	−2.67506	−	0.918725i	−0.422964	−	0.145263i
$41$			3.33273i			0.520486i	0.965543	+	0.260243i	$0.0838026\pi$
$41$			3.33273i			0.520486i	−0.965543	+	0.260243i	$0.916197\pi$
$42$		0			0
$43$			1.07785i			0.164370i	0.996617	+	0.0821850i	$0.0261898\pi$
$43$			1.07785i			0.164370i	−0.996617	+	0.0821850i	$0.973810\pi$
$44$	2.14265	+	6.85246i	0.323017	+	1.03305i
$45$		0			0
$46$	−0.993802	−	0.730506i	−0.146528	−	0.107707i
$47$	−1.79111			−0.261260			−0.130630	−	0.991431i	$-0.541700\pi$
$47$	−1.79111			−0.261260			−0.130630	+	0.991431i	$0.541700\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	1.13949	+	0.837595i	0.161148	+	0.118454i
$51$		0			0
$52$	−1.55447	−	4.97137i	−0.215566	−	0.689404i
$53$		−	10.2314i		−	1.40539i	−0.711489	−	0.702697i	$-0.751979\pi$
$53$		−	10.2314i		−	1.40539i	0.711489	−	0.702697i	$-0.248021\pi$
$54$		0			0
$55$		−	3.58982i		−	0.484051i
$56$	−2.67506	−	0.918725i	−0.357470	−	0.122770i
$57$		0			0
$58$	−4.86145	+	6.61366i	−0.638340	+	0.868416i
$59$	−9.15424			−1.19178			−0.595890	−	0.803066i	$-0.703201\pi$
$59$	−9.15424			−1.19178			−0.595890	+	0.803066i	$0.703201\pi$
$60$		0			0
$61$	7.76517			0.994228			0.497114	−	0.867685i	$-0.334393\pi$
$61$	7.76517			0.994228			0.497114	+	0.867685i	$0.334393\pi$
$62$	0.401381	−	0.546050i	0.0509754	−	0.0693484i
$63$		0			0
$64$	−6.31189	−	4.91529i	−0.788986	−	0.614411i
$65$			2.60436i			0.323032i
$66$		0			0
$67$		−	11.6184i		−	1.41942i	−0.704495	−	0.709709i	$-0.748827\pi$
$67$		−	11.6184i		−	1.41942i	0.704495	−	0.709709i	$-0.251173\pi$
$68$	11.2210	−	3.50864i	1.36075	−	0.425485i
$69$		0			0
$70$	1.13949	+	0.837595i	0.136195	+	0.100112i
$71$	9.51142			1.12880			0.564399	−	0.825502i	$-0.309108\pi$
$71$	9.51142			1.12880			0.564399	+	0.825502i	$0.309108\pi$
$72$		0			0
$73$	−1.40325			−0.164238			−0.0821192	−	0.996623i	$-0.526169\pi$
$73$	−1.40325			−0.164238			−0.0821192	+	0.996623i	$0.526169\pi$
$74$	−1.37988	−	1.01430i	−0.160408	−	0.117910i
$75$		0			0
$76$	−4.50759	+	1.40945i	−0.517057	+	0.161675i
$77$		−	3.58982i		−	0.409098i
$78$		0			0
$79$		−	13.2047i		−	1.48564i	−0.669489	−	0.742822i	$-0.733487\pi$
$79$		−	13.2047i		−	1.48564i	0.669489	−	0.742822i	$-0.266513\pi$
$80$	2.27868	+	3.28749i	0.254764	+	0.367553i
$81$		0			0
$82$	2.79148	−	3.79761i	0.308267	−	0.419376i
$83$	−15.5080			−1.70222			−0.851111	−	0.524985i	$-0.824071\pi$
$83$	−15.5080			−1.70222			−0.851111	+	0.524985i	$0.824071\pi$
$84$		0			0
$85$	−5.87840			−0.637602
$86$	0.902799	−	1.22819i	0.0973513	−	0.132440i
$87$		0			0
$88$	3.29806	−	9.60298i	0.351574	−	1.02368i
$89$			0.714137i			0.0756984i	0.999283	+	0.0378492i	$0.0120506\pi$
$89$			0.714137i			0.0756984i	−0.999283	+	0.0378492i	$0.987949\pi$
$90$		0			0
$91$			2.60436i			0.273012i
$92$	0.520558	+	1.66481i	0.0542719	+	0.173568i
$93$		0			0
$94$	2.04095	+	1.50023i	0.210508	+	0.154736i
$95$	2.36141			0.242275
$96$		0			0
$97$	2.39247			0.242918			0.121459	−	0.992596i	$-0.461243\pi$
$97$	2.39247			0.242918			0.121459	+	0.992596i	$0.461243\pi$
$98$	1.13949	+	0.837595i	0.115106	+	0.0846099i
$99$		0			0
$100$	−0.596870	−	1.90886i	−0.0596870	−	0.190886i
$101$		−	17.3805i		−	1.72943i	−0.502267	−	0.864713i	$-0.667501\pi$
$101$		−	17.3805i		−	1.72943i	0.502267	−	0.864713i	$-0.332499\pi$
$102$		0			0
$103$			1.99963i			0.197030i	0.995136	+	0.0985149i	$0.0314092\pi$
$103$			1.99963i			0.197030i	−0.995136	+	0.0985149i	$0.968591\pi$
$104$	−2.39269	+	6.96683i	−0.234623	+	0.683154i
$105$		0			0
$106$	−8.56979	+	11.6586i	−0.832372	+	1.13238i
$107$	6.34669			0.613558			0.306779	−	0.951781i	$-0.400749\pi$
$107$	6.34669			0.613558			0.306779	+	0.951781i	$0.400749\pi$
$108$		0			0
$109$	−4.55888			−0.436662			−0.218331	−	0.975875i	$-0.570061\pi$
$109$	−4.55888			−0.436662			−0.218331	+	0.975875i	$0.570061\pi$
$110$	−3.00681	+	4.09056i	−0.286688	+	0.390019i
$111$		0			0
$112$	2.27868	+	3.28749i	0.215315	+	0.310639i
$113$		−	9.72497i		−	0.914848i	−0.889249	−	0.457424i	$-0.848772\pi$
$113$		−	9.72497i		−	0.914848i	0.889249	−	0.457424i	$-0.151228\pi$
$114$		0			0
$115$		−	0.872147i		−	0.0813281i
$116$	11.0791	−	3.46427i	1.02867	−	0.321649i
$117$		0			0
$118$	10.4312	+	7.66755i	0.960266	+	0.705855i
$119$	−5.87840			−0.538872
$120$		0			0
$121$	1.88680			0.171527
$122$	−8.84832	−	6.50407i	−0.801090	−	0.588850i
$123$		0			0
$124$	−0.914737	+	0.286023i	−0.0821458	+	0.0256857i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	7.17430i		−	0.636616i	−0.947987	−	0.318308i	$-0.896885\pi$
$127$		−	7.17430i		−	0.636616i	0.947987	−	0.318308i	$-0.103115\pi$
$128$	3.07530	+	10.8877i	0.271821	+	0.962348i
$129$		0			0
$130$	2.18140	−	2.96764i	0.191322	−	0.260280i
$131$	−11.3808			−0.994343			−0.497171	−	0.867652i	$-0.665628\pi$
$131$	−11.3808			−0.994343			−0.497171	+	0.867652i	$0.665628\pi$
$132$		0			0
$133$	2.36141			0.204760
$134$	−9.73154	+	13.2391i	−0.840677	+	1.14368i
$135$		0			0
$136$	−15.7251	−	5.40063i	−1.34841	−	0.463100i
$137$		−	8.84221i		−	0.755441i	−0.925920	−	0.377721i	$-0.876708\pi$
$137$		−	8.84221i		−	0.755441i	0.925920	−	0.377721i	$-0.123292\pi$
$138$		0			0
$139$			6.51008i			0.552178i	0.961132	+	0.276089i	$0.0890384\pi$
$139$			6.51008i			0.552178i	−0.961132	+	0.276089i	$0.910962\pi$
$140$	−0.596870	−	1.90886i	−0.0504447	−	0.161328i
$141$		0			0
$142$	−10.8382	−	7.96672i	−0.909518	−	0.668552i
$143$	−9.34920			−0.781819
$144$		0			0
$145$	−5.80406			−0.482001
$146$	1.59899	+	1.17536i	0.132333	+	0.0972733i
$147$		0			0
$148$	0.722788	+	2.31156i	0.0594128	+	0.190009i
$149$			22.9084i			1.87673i	0.345647	+	0.938365i	$0.387660\pi$
$149$			22.9084i			1.87673i	−0.345647	+	0.938365i	$0.612340\pi$
$150$		0			0
$151$		−	15.3898i		−	1.25241i	−0.779660	−	0.626203i	$-0.784608\pi$
$151$		−	15.3898i		−	1.25241i	0.779660	−	0.626203i	$-0.215392\pi$
$152$	6.31690	+	2.16948i	0.512368	+	0.175968i
$153$		0			0
$154$	−3.00681	+	4.09056i	−0.242296	+	0.329627i
$155$	0.479206			0.0384908
$156$		0			0
$157$	1.98895			0.158735			0.0793677	−	0.996845i	$-0.474710\pi$
$157$	1.98895			0.158735			0.0793677	+	0.996845i	$0.474710\pi$
$158$	−11.0602	+	15.0466i	−0.879901	+	1.19704i
$159$		0			0
$160$	0.157056	−	5.65467i	0.0124164	−	0.447041i
$161$		−	0.872147i		−	0.0687348i
$162$		0			0
$163$			18.4312i			1.44364i	0.692079	+	0.721821i	$0.256695\pi$
$163$			18.4312i			1.44364i	−0.692079	+	0.721821i	$0.743305\pi$
$164$	−6.36172	+	1.98921i	−0.496767	+	0.155331i
$165$		0			0
$166$	17.6712	+	12.9894i	1.37155	+	1.00817i
$167$	−8.43531			−0.652744			−0.326372	−	0.945241i	$-0.605826\pi$
$167$	−8.43531			−0.652744			−0.326372	+	0.945241i	$0.605826\pi$
$168$		0			0
$169$	−6.21729			−0.478253
$170$	6.69837	+	4.92372i	0.513741	+	0.377632i
$171$		0			0
$172$	−2.05746	+	0.643334i	−0.156880	+	0.0490537i
$173$		−	20.6332i		−	1.56871i	−0.620312	−	0.784355i	$-0.712994\pi$
$173$		−	20.6332i		−	1.56871i	0.620312	−	0.784355i	$-0.287006\pi$
$174$		0			0
$175$			1.00000i			0.0755929i
$176$	−11.8015	+	8.18005i	−0.889572	+	0.616595i
$177$		0			0
$178$	0.598158	−	0.813751i	0.0448338	−	0.0609932i
$179$	−10.4672			−0.782354			−0.391177	−	0.920315i	$-0.627932\pi$
$179$	−10.4672			−0.782354			−0.391177	+	0.920315i	$0.627932\pi$
$180$		0			0
$181$	2.32299			0.172667			0.0863333	−	0.996266i	$-0.472485\pi$
$181$	2.32299			0.172667			0.0863333	+	0.996266i	$0.472485\pi$
$182$	2.18140	−	2.96764i	0.161696	−	0.219976i
$183$		0			0
$184$	0.801264	−	2.33305i	0.0590699	−	0.171994i
$185$		−	1.21097i		−	0.0890319i
$186$		0			0
$187$		−	21.1024i		−	1.54316i
$188$	−1.06906	−	3.41898i	−0.0779692	−	0.249355i
$189$		0			0
$190$	−2.69080	−	1.97790i	−0.195211	−	0.143492i
$191$	−19.2308			−1.39149			−0.695745	−	0.718289i	$-0.744925\pi$
$191$	−19.2308			−1.39149			−0.695745	+	0.718289i	$0.744925\pi$
$192$		0			0
$193$	26.8100			1.92983			0.964913	−	0.262571i	$-0.0845703\pi$
$193$	26.8100			1.92983			0.964913	+	0.262571i	$0.0845703\pi$
$194$	−2.72619	−	2.00392i	−0.195729	−	0.143873i
$195$		0			0
$196$	−0.596870	−	1.90886i	−0.0426335	−	0.136347i
$197$		−	9.19939i		−	0.655430i	−0.944777	−	0.327715i	$-0.893721\pi$
$197$		−	9.19939i		−	0.655430i	0.944777	−	0.327715i	$-0.106279\pi$
$198$		0			0
$199$			14.1951i			1.00626i	0.864209	+	0.503132i	$0.167819\pi$
$199$			14.1951i			1.00626i	−0.864209	+	0.503132i	$0.832181\pi$
$200$	−0.918725	+	2.67506i	−0.0649637	+	0.189155i
$201$		0			0
$202$	−14.5578	+	19.8049i	−1.02429	+	1.39347i
$203$	−5.80406			−0.407365
$204$		0			0
$205$	3.33273			0.232768
$206$	1.67488	−	2.27856i	0.116695	−	0.158755i
$207$		0			0
$208$	8.56183	−	5.93451i	0.593656	−	0.411485i
$209$			8.47702i			0.586368i
$210$		0			0
$211$			16.1624i			1.11267i	0.830959	+	0.556334i	$0.187793\pi$
$211$			16.1624i			1.11267i	−0.830959	+	0.556334i	$0.812207\pi$
$212$	19.5304	−	6.10683i	1.34135	−	0.419419i
$213$		0			0
$214$	−7.23199	−	5.31596i	−0.494368	−	0.363391i
$215$	1.07785			0.0735085
$216$		0			0
$217$	0.479206			0.0325306
$218$	5.19480	+	3.81850i	0.351836	+	0.258621i
$219$		0			0
$220$	6.85246	−	2.14265i	0.461993	−	0.144458i
$221$			15.3095i			1.02983i
$222$		0			0
$223$		−	1.03839i		−	0.0695357i	−0.999395	−	0.0347679i	$-0.988931\pi$
$223$		−	1.03839i		−	0.0695357i	0.999395	−	0.0347679i	$-0.0110692\pi$
$224$	0.157056	−	5.65467i	0.0104938	−	0.377819i
$225$		0			0
$226$	−8.14558	+	11.0815i	−0.541836	+	0.737130i
$227$	15.8964			1.05508			0.527539	−	0.849531i	$-0.323115\pi$
$227$	15.8964			1.05508			0.527539	+	0.849531i	$0.323115\pi$
$228$		0			0
$229$	24.2848			1.60479			0.802393	−	0.596796i	$-0.203560\pi$
$229$	24.2848			1.60479			0.802393	+	0.596796i	$0.203560\pi$
$230$	−0.730506	+	0.993802i	−0.0481681	+	0.0655294i
$231$		0			0
$232$	−15.5262	−	5.33234i	−1.01935	−	0.350085i
$233$		−	3.33491i		−	0.218477i	−0.994016	−	0.109239i	$-0.965159\pi$
$233$		−	3.33491i		−	0.218477i	0.994016	−	0.109239i	$-0.0348413\pi$
$234$		0			0
$235$			1.79111i			0.116839i
$236$	−5.46389	−	17.4742i	−0.355669	−	1.13747i
$237$		0			0
$238$	6.69837	+	4.92372i	0.434191	+	0.319157i
$239$	3.31866			0.214667			0.107333	−	0.994223i	$-0.465769\pi$
$239$	3.31866			0.214667			0.107333	+	0.994223i	$0.465769\pi$
$240$		0			0
$241$	30.0266			1.93418			0.967092	−	0.254429i	$-0.0818874\pi$
$241$	30.0266			1.93418			0.967092	+	0.254429i	$0.0818874\pi$
$242$	−2.14999	−	1.58037i	−0.138207	−	0.101590i
$243$		0			0
$244$	4.63479	+	14.8226i	0.296712	+	0.948921i
$245$			1.00000i			0.0638877i
$246$		0			0
$247$		−	6.14996i		−	0.391313i
$248$	1.28190	+	0.440259i	0.0814010	+	0.0279565i
$249$		0			0
$250$	0.837595	−	1.13949i	0.0529742	−	0.0720676i
$251$	22.9155			1.44641			0.723206	−	0.690632i	$-0.242668\pi$
$251$	22.9155			1.44641			0.723206	+	0.690632i	$0.242668\pi$
$252$		0			0
$253$	3.13085			0.196835
$254$	−6.00916	+	8.17503i	−0.377048	+	0.512947i
$255$		0			0
$256$	5.61523	−	14.9823i	0.350952	−	0.936394i
$257$			28.2082i			1.75958i	0.475361	+	0.879791i	$0.342317\pi$
$257$			28.2082i			1.75958i	−0.475361	+	0.879791i	$0.657683\pi$
$258$		0			0
$259$		−	1.21097i		−	0.0752457i
$260$	−4.97137	+	1.55447i	−0.308311	+	0.0964039i
$261$		0			0
$262$	12.9683	+	9.53248i	0.801182	+	0.588918i
$263$	19.5448			1.20518			0.602591	−	0.798050i	$-0.294135\pi$
$263$	19.5448			1.20518			0.602591	+	0.798050i	$0.294135\pi$
$264$		0			0
$265$	−10.2314			−0.628511
$266$	−2.69080	−	1.97790i	−0.164983	−	0.121273i
$267$		0			0
$268$	22.1780	−	6.93469i	1.35473	−	0.423603i
$269$			23.4068i			1.42714i	0.700584	+	0.713569i	$0.252923\pi$
$269$			23.4068i			1.42714i	−0.700584	+	0.713569i	$0.747077\pi$
$270$		0			0
$271$		−	32.2986i		−	1.96200i	−0.194014	−	0.980999i	$-0.562151\pi$
$271$		−	32.2986i		−	1.96200i	0.194014	−	0.980999i	$-0.437849\pi$
$272$	13.3950	+	19.3252i	0.812191	+	1.17176i
$273$		0			0
$274$	−7.40619	+	10.0756i	−0.447425	+	0.608690i
$275$	−3.58982			−0.216474
$276$		0			0
$277$	13.0963			0.786882			0.393441	−	0.919350i	$-0.371285\pi$
$277$	13.0963			0.786882			0.393441	+	0.919350i	$0.371285\pi$
$278$	5.45281	−	7.41816i	0.327038	−	0.444912i
$279$		0			0
$280$	−0.918725	+	2.67506i	−0.0549043	+	0.159865i
$281$			5.09428i			0.303899i	0.988388	+	0.151950i	$0.0485552\pi$
$281$			5.09428i			0.303899i	−0.988388	+	0.151950i	$0.951445\pi$
$282$		0			0
$283$			25.6782i			1.52641i	0.646156	+	0.763205i	$0.276376\pi$
$283$			25.6782i			1.52641i	−0.646156	+	0.763205i	$0.723624\pi$
$284$	5.67708	+	18.1560i	0.336873	+	1.07736i
$285$		0			0
$286$	10.6533	+	7.83084i	0.629943	+	0.463047i
$287$	3.33273			0.196725
$288$		0			0
$289$	−17.5556			−1.03268
$290$	6.61366	+	4.86145i	0.388368	+	0.285474i
$291$		0			0
$292$	−0.837559	−	2.67861i	−0.0490144	−	0.156754i
$293$		−	12.5836i		−	0.735140i	−0.929996	−	0.367570i	$-0.880190\pi$
$293$		−	12.5836i		−	0.735140i	0.929996	−	0.367570i	$-0.119810\pi$
$294$		0			0
$295$			9.15424i			0.532981i
$296$	1.11254	−	3.23940i	0.0646653	−	0.188287i
$297$		0			0
$298$	19.1880	−	26.1039i	1.11153	−	1.51216i
$299$	−2.27139			−0.131358
$300$		0			0
$301$	1.07785			0.0621260
$302$	−12.8904	+	17.5365i	−0.741761	+	1.00911i
$303$		0			0
$304$	−5.38089	−	7.76311i	−0.308615	−	0.445245i
$305$		−	7.76517i		−	0.444632i
$306$		0			0
$307$			28.5693i			1.63054i	0.579082	+	0.815269i	$0.303411\pi$
$307$			28.5693i			1.63054i	−0.579082	+	0.815269i	$0.696589\pi$
$308$	6.85246	−	2.14265i	0.390455	−	0.122089i
$309$		0			0
$310$	−0.546050	−	0.401381i	−0.0310136	−	0.0227969i
$311$	−0.482828			−0.0273786			−0.0136893	−	0.999906i	$-0.504358\pi$
$311$	−0.482828			−0.0273786			−0.0136893	+	0.999906i	$0.504358\pi$
$312$		0			0
$313$	−13.7234			−0.775693			−0.387847	−	0.921724i	$-0.626781\pi$
$313$	−13.7234			−0.775693			−0.387847	+	0.921724i	$0.626781\pi$
$314$	−2.26638	−	1.66593i	−0.127899	−	0.0940140i
$315$		0			0
$316$	25.2059	−	7.88148i	1.41794	−	0.443368i
$317$			19.3004i			1.08402i	0.840372	+	0.542010i	$0.182336\pi$
$317$			19.3004i			1.08402i	−0.840372	+	0.542010i	$0.817664\pi$
$318$		0			0
$319$		−	20.8355i		−	1.16657i
$320$	−4.91529	+	6.31189i	−0.274773	+	0.352845i
$321$		0			0
$322$	−0.730506	+	0.993802i	−0.0407095	+	0.0553824i
$323$	13.8813			0.772375
$324$		0			0
$325$	2.60436			0.144464
$326$	15.4379	−	21.0021i	0.855025	−	1.16320i
$327$		0			0
$328$	8.91526	+	3.06187i	0.492263	+	0.169063i
$329$			1.79111i			0.0987471i
$330$		0			0
$331$		−	10.4267i		−	0.573103i	−0.958065	−	0.286551i	$-0.907491\pi$
$331$		−	10.4267i		−	0.573103i	0.958065	−	0.286551i	$-0.0925089\pi$
$332$	−9.25624	−	29.6026i	−0.508002	−	1.62465i
$333$		0			0
$334$	9.61194	+	7.06537i	0.525942	+	0.386600i
$335$	−11.6184			−0.634783
$336$		0			0
$337$	23.6446			1.28800			0.644000	−	0.765025i	$-0.277273\pi$
$337$	23.6446			1.28800			0.644000	+	0.765025i	$0.277273\pi$
$338$	7.08453	+	5.20757i	0.385348	+	0.283254i
$339$		0			0
$340$	−3.50864	−	11.2210i	−0.190283	−	0.608546i
$341$			1.72026i			0.0931575i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	2.88330	+	0.990245i	0.155457	+	0.0533904i
$345$		0			0
$346$	−17.2822	+	23.5112i	−0.929098	+	1.26397i
$347$	27.7318			1.48872			0.744359	−	0.667779i	$-0.232755\pi$
$347$	27.7318			1.48872			0.744359	+	0.667779i	$0.232755\pi$
$348$		0			0
$349$	−22.4719			−1.20289			−0.601447	−	0.798913i	$-0.705409\pi$
$349$	−22.4719			−1.20289			−0.601447	+	0.798913i	$0.705409\pi$
$350$	0.837595	−	1.13949i	0.0447713	−	0.0609082i
$351$		0			0
$352$	20.2993	+	0.563804i	1.08195	+	0.0300508i
$353$		−	33.2233i		−	1.76830i	−0.467206	−	0.884148i	$-0.654739\pi$
$353$		−	33.2233i		−	1.76830i	0.467206	−	0.884148i	$-0.345261\pi$
$354$		0			0
$355$		−	9.51142i		−	0.504814i
$356$	−1.36319	+	0.426247i	−0.0722488	+	0.0225910i
$357$		0			0
$358$	11.9272	+	8.76726i	0.630374	+	0.463364i
$359$	5.18864			0.273846			0.136923	−	0.990582i	$-0.456279\pi$
$359$	5.18864			0.273846			0.136923	+	0.990582i	$0.456279\pi$
$360$		0			0
$361$	13.4238			0.706514
$362$	−2.64702	−	1.94573i	−0.139124	−	0.102265i
$363$		0			0
$364$	−4.97137	+	1.55447i	−0.260570	+	0.0814761i
$365$			1.40325i			0.0734496i
$366$		0			0
$367$			16.3430i			0.853095i	0.904465	+	0.426548i	$0.140270\pi$
$367$			16.3430i			0.853095i	−0.904465	+	0.426548i	$0.859730\pi$
$368$	−2.86718	+	1.98734i	−0.149462	+	0.103598i
$369$		0			0
$370$	−1.01430	+	1.37988i	−0.0527309	+	0.0717366i
$371$	−10.2314			−0.531189
$372$		0			0
$373$	−34.5059			−1.78665			−0.893325	−	0.449412i	$-0.851634\pi$
$373$	−34.5059			−1.78665			−0.893325	+	0.449412i	$0.851634\pi$
$374$	−17.6753	+	24.0459i	−0.913965	+	1.24339i
$375$		0			0
$376$	−1.64554	+	4.79133i	−0.0848622	+	0.247094i
$377$			15.1159i			0.778508i
$378$		0			0
$379$			29.8103i			1.53125i	0.643287	+	0.765625i	$0.277570\pi$
$379$			29.8103i			1.53125i	−0.643287	+	0.765625i	$0.722430\pi$
$380$	1.40945	+	4.50759i	0.0723033	+	0.231235i
$381$		0			0
$382$	21.9132	+	16.1076i	1.12118	+	0.824136i
$383$	6.66634			0.340634			0.170317	−	0.985389i	$-0.445521\pi$
$383$	6.66634			0.340634			0.170317	+	0.985389i	$0.445521\pi$
$384$		0			0
$385$	−3.58982			−0.182954
$386$	−30.5497	−	22.4559i	−1.55494	−	1.14298i
$387$		0			0
$388$	1.42799	+	4.56689i	0.0724953	+	0.231849i
$389$			15.4102i			0.781330i	0.920533	+	0.390665i	$0.127755\pi$
$389$			15.4102i			0.781330i	−0.920533	+	0.390665i	$0.872245\pi$
$390$		0			0
$391$		−	5.12683i		−	0.259275i
$392$	−0.918725	+	2.67506i	−0.0464026	+	0.135111i
$393$		0			0
$394$	−7.70537	+	10.4826i	−0.388191	+	0.528106i
$395$	−13.2047			−0.664400
$396$		0			0
$397$	−8.50360			−0.426783			−0.213392	−	0.976967i	$-0.568451\pi$
$397$	−8.50360			−0.426783			−0.213392	+	0.976967i	$0.568451\pi$
$398$	11.8898	−	16.1752i	0.595980	−	0.810788i
$399$		0			0
$400$	3.28749	−	2.27868i	0.164375	−	0.113934i
$401$			4.78726i			0.239064i	0.992830	+	0.119532i	$0.0381395\pi$
$401$			4.78726i			0.239064i	−0.992830	+	0.119532i	$0.961861\pi$
$402$		0			0
$403$		−	1.24803i		−	0.0621686i
$404$	33.1770	−	10.3739i	1.65062	−	0.516121i
$405$		0			0
$406$	6.61366	+	4.86145i	0.328231	+	0.241270i
$407$	4.34715			0.215480
$408$		0			0
$409$	22.4758			1.11136			0.555680	−	0.831397i	$-0.312458\pi$
$409$	22.4758			1.11136			0.555680	+	0.831397i	$0.312458\pi$
$410$	−3.79761	−	2.79148i	−0.187551	−	0.137861i
$411$		0			0
$412$	−3.81702	+	1.19352i	−0.188051	+	0.0588006i
$413$			9.15424i			0.450451i
$414$		0			0
$415$			15.5080i			0.761257i
$416$	−14.7268	−	0.409032i	−0.722042	−	0.0200544i
$417$		0			0
$418$	7.10031	−	9.65947i	0.347288	−	0.472460i
$419$	−23.8180			−1.16358			−0.581792	−	0.813337i	$-0.697648\pi$
$419$	−23.8180			−1.16358			−0.581792	+	0.813337i	$0.697648\pi$
$420$		0			0
$421$	30.4389			1.48350			0.741752	−	0.670675i	$-0.233995\pi$
$421$	30.4389			1.48350			0.741752	+	0.670675i	$0.233995\pi$
$422$	13.5376	−	18.4169i	0.658999	−	0.896522i
$423$		0			0
$424$	−27.3697	−	9.39987i	−1.32919	−	0.456498i
$425$			5.87840i			0.285144i
$426$		0			0
$427$		−	7.76517i		−	0.375783i
$428$	3.78815	+	12.1149i	0.183107	+	0.585598i
$429$		0			0
$430$	−1.22819	−	0.902799i	−0.0592288	−	0.0435368i
$431$	30.5890			1.47342			0.736710	−	0.676209i	$-0.236378\pi$
$431$	30.5890			1.47342			0.736710	+	0.676209i	$0.236378\pi$
$432$		0			0
$433$	−18.8112			−0.904009			−0.452005	−	0.892016i	$-0.649291\pi$
$433$	−18.8112			−0.904009			−0.452005	+	0.892016i	$0.649291\pi$
$434$	−0.546050	−	0.401381i	−0.0262112	−	0.0192669i
$435$		0			0
$436$	−2.72106	−	8.70227i	−0.130315	−	0.416763i
$437$			2.05949i			0.0985189i
$438$		0			0
$439$		−	12.5370i		−	0.598359i	−0.954197	−	0.299180i	$-0.903287\pi$
$439$		−	12.5370i		−	0.598359i	0.954197	−	0.299180i	$-0.0967130\pi$
$440$	−9.60298	−	3.29806i	−0.457804	−	0.157229i
$441$		0			0
$442$	12.8231	−	17.4450i	0.609935	−	0.829774i
$443$	12.4287			0.590506			0.295253	−	0.955419i	$-0.404596\pi$
$443$	12.4287			0.590506			0.295253	+	0.955419i	$0.404596\pi$
$444$		0			0
$445$	0.714137			0.0338533
$446$	−0.869750	+	1.18323i	−0.0411839	+	0.0560277i
$447$		0			0
$448$	−4.91529	+	6.31189i	−0.232226	+	0.298209i
$449$		−	19.0317i		−	0.898163i	−0.893491	−	0.449081i	$-0.851751\pi$
$449$		−	19.0317i		−	0.898163i	0.893491	−	0.449081i	$-0.148249\pi$
$450$		0			0
$451$			11.9639i			0.563359i
$452$	18.5636	−	5.80454i	0.873158	−	0.273022i
$453$		0			0
$454$	−18.1137	−	13.3147i	−0.850119	−	0.624890i
$455$	2.60436			0.122094
$456$		0			0
$457$	−8.37088			−0.391573			−0.195787	−	0.980647i	$-0.562726\pi$
$457$	−8.37088			−0.391573			−0.195787	+	0.980647i	$0.562726\pi$
$458$	−27.6723	−	20.3408i	−1.29304	−	0.950465i
$459$		0			0
$460$	1.66481	−	0.520558i	0.0776220	−	0.0242711i
$461$			14.0183i			0.652898i	0.945215	+	0.326449i	$0.105852\pi$
$461$			14.0183i			0.652898i	−0.945215	+	0.326449i	$0.894148\pi$
$462$		0			0
$463$			37.2795i			1.73252i	0.499590	+	0.866262i	$0.333484\pi$
$463$			37.2795i			1.73252i	−0.499590	+	0.866262i	$0.666516\pi$
$464$	13.2256	+	19.0808i	0.613983	+	0.885805i
$465$		0			0
$466$	−2.79330	+	3.80009i	−0.129397	+	0.176036i
$467$	−26.1681			−1.21092			−0.605459	−	0.795877i	$-0.707010\pi$
$467$	−26.1681			−1.21092			−0.605459	+	0.795877i	$0.707010\pi$
$468$		0			0
$469$	−11.6184			−0.536489
$470$	1.50023	−	2.04095i	0.0692002	−	0.0941420i
$471$		0			0
$472$	−8.41023	+	24.4881i	−0.387112	+	1.12716i
$473$			3.86927i			0.177909i
$474$		0			0
$475$		−	2.36141i		−	0.108349i
$476$	−3.50864	−	11.2210i	−0.160818	−	0.514315i
$477$		0			0
$478$	−3.78158	−	2.77970i	−0.172965	−	0.127140i
$479$	34.7589			1.58818			0.794088	−	0.607803i	$-0.207949\pi$
$479$	34.7589			1.58818			0.794088	+	0.607803i	$0.207949\pi$
$480$		0			0
$481$	−3.15379			−0.143801
$482$	−34.2150	−	25.1501i	−1.55845	−	1.14556i
$483$		0			0
$484$	1.12617	+	3.60164i	0.0511897	+	0.163711i
$485$		−	2.39247i		−	0.108636i
$486$		0			0
$487$		−	8.68409i		−	0.393514i	−0.980452	−	0.196757i	$-0.936959\pi$
$487$		−	8.68409i		−	0.393514i	0.980452	−	0.196757i	$-0.0630409\pi$
$488$	7.13406	−	20.7723i	0.322944	−	0.940317i
$489$		0			0
$490$	0.837595	−	1.13949i	0.0378387	−	0.0514769i
$491$	16.8740			0.761513			0.380756	−	0.924675i	$-0.375664\pi$
$491$	16.8740			0.761513			0.380756	+	0.924675i	$0.375664\pi$
$492$		0			0
$493$	−34.1186			−1.53662
$494$	−5.15118	+	7.00781i	−0.231762	+	0.315296i
$495$		0			0
$496$	−1.09196	−	1.57539i	−0.0490303	−	0.0707369i
$497$		−	9.51142i		−	0.426646i
$498$		0			0
$499$		−	11.4898i		−	0.514356i	−0.966364	−	0.257178i	$-0.917207\pi$
$499$		−	11.4898i		−	0.514356i	0.966364	−	0.257178i	$-0.0827926\pi$
$500$	−1.90886	+	0.596870i	−0.0853668	+	0.0266928i
$501$		0			0
$502$	−26.1119	−	19.1939i	−1.16543	−	0.856665i
$503$	−37.9135			−1.69048			−0.845240	−	0.534387i	$-0.820542\pi$
$503$	−37.9135			−1.69048			−0.845240	+	0.534387i	$0.820542\pi$
$504$		0			0
$505$	−17.3805			−0.773422
$506$	−3.56757	−	2.62238i	−0.158598	−	0.116579i
$507$		0			0
$508$	13.6947	−	4.28212i	0.607606	−	0.189988i
$509$			29.2840i			1.29799i	0.760792	+	0.648996i	$0.224811\pi$
$509$			29.2840i			1.29799i	−0.760792	+	0.648996i	$0.775189\pi$
$510$		0			0
$511$			1.40325i			0.0620763i
$512$	−18.9476	+	12.3689i	−0.837373	+	0.546632i
$513$		0			0
$514$	23.6271	−	32.1430i	1.04215	−	1.41777i
$515$	1.99963			0.0881144
$516$		0			0
$517$	−6.42976			−0.282781
$518$	−1.01430	+	1.37988i	−0.0445657	+	0.0606285i
$519$		0			0
$520$	6.96683	+	2.39269i	0.305516	+	0.104927i
$521$		−	5.66968i		−	0.248393i	−0.992258	−	0.124196i	$-0.960365\pi$
$521$		−	5.66968i		−	0.248393i	0.992258	−	0.124196i	$-0.0396353\pi$
$522$		0			0
$523$			21.6997i			0.948863i	0.880292	+	0.474432i	$0.157346\pi$
$523$			21.6997i			0.948863i	−0.880292	+	0.474432i	$0.842654\pi$
$524$	−6.79284	−	21.7243i	−0.296746	−	0.949031i
$525$		0			0
$526$	−22.2710	−	16.3706i	−0.971064	−	0.713792i
$527$	2.81696			0.122709
$528$		0			0
$529$	−22.2394			−0.966929
$530$	11.6586	+	8.56979i	0.506417	+	0.372248i
$531$		0			0
$532$	1.40945	+	4.50759i	0.0611075	+	0.195429i
$533$		−	8.67965i		−	0.375957i
$534$		0			0
$535$		−	6.34669i		−	0.274391i
$536$	−31.0800	−	10.6741i	−1.34245	−	0.461053i
$537$		0			0
$538$	19.6054	−	26.6718i	0.845250	−	1.14990i
$539$	−3.58982			−0.154624
$540$		0			0
$541$	15.0023			0.645001			0.322501	−	0.946569i	$-0.395477\pi$
$541$	15.0023			0.645001			0.322501	+	0.946569i	$0.395477\pi$
$542$	−27.0531	+	36.8038i	−1.16203	+	1.58086i
$543$		0			0
$544$	0.923239	−	33.2404i	0.0395836	−	1.42517i
$545$			4.55888i			0.195281i
$546$		0			0
$547$			36.1766i			1.54680i	0.633917	+	0.773401i	$0.281446\pi$
$547$			36.1766i			1.54680i	−0.633917	+	0.773401i	$0.718554\pi$
$548$	16.8785	−	5.27765i	0.721016	−	0.225450i
$549$		0			0
$550$	4.09056	+	3.00681i	0.174422	+	0.128211i
$551$	13.7057			0.583884
$552$		0			0
$553$	−13.2047			−0.561521
$554$	−14.9231	−	10.9694i	−0.634023	−	0.466046i
$555$		0			0
$556$	−12.4268	+	3.88567i	−0.527015	+	0.164789i
$557$		−	20.7444i		−	0.878970i	−0.898250	−	0.439485i	$-0.855161\pi$
$557$		−	20.7444i		−	0.878970i	0.898250	−	0.439485i	$-0.144839\pi$
$558$		0			0
$559$		−	2.80710i		−	0.118728i
$560$	3.28749	−	2.27868i	0.138922	−	0.0962918i
$561$		0			0
$562$	4.26695	−	5.80488i	0.179990	−	0.244864i
$563$	−24.8774			−1.04846			−0.524230	−	0.851577i	$-0.675647\pi$
$563$	−24.8774			−1.04846			−0.524230	+	0.851577i	$0.675647\pi$
$564$		0			0
$565$	−9.72497			−0.409132
$566$	21.5079	−	29.2600i	0.904046	−	1.22989i
$567$		0			0
$568$	8.73838	−	25.4436i	0.366654	−	1.06759i
$569$			7.89228i			0.330861i	0.986221	+	0.165431i	$0.0529014\pi$
$569$			7.89228i			0.330861i	−0.986221	+	0.165431i	$0.947099\pi$
$570$		0			0
$571$			6.33939i			0.265295i	0.991163	+	0.132648i	$0.0423478\pi$
$571$			6.33939i			0.265295i	−0.991163	+	0.132648i	$0.957652\pi$
$572$	−5.58025	−	17.8463i	−0.233322	−	0.746192i
$573$		0			0
$574$	−3.79761	−	2.79148i	−0.158509	−	0.116514i
$575$	−0.872147			−0.0363710
$576$		0			0
$577$	−21.9071			−0.912006			−0.456003	−	0.889978i	$-0.650719\pi$
$577$	−21.9071			−0.912006			−0.456003	+	0.889978i	$0.650719\pi$
$578$	20.0044	+	14.7044i	0.832072	+	0.611624i
$579$		0			0
$580$	−3.46427	−	11.0791i	−0.143846	−	0.460036i
$581$			15.5080i			0.643380i
$582$		0			0
$583$		−	36.7290i		−	1.52116i
$584$	−1.28920	+	3.75379i	−0.0533476	+	0.155333i
$585$		0			0
$586$	−10.5399	+	14.3388i	−0.435401	+	0.592332i
$587$	−22.1877			−0.915784			−0.457892	−	0.889008i	$-0.651395\pi$
$587$	−22.1877			−0.915784			−0.457892	+	0.889008i	$0.651395\pi$
$588$		0			0
$589$	−1.13160			−0.0466268
$590$	7.66755	−	10.4312i	0.315668	−	0.429444i
$591$		0			0
$592$	−3.98104	+	2.75940i	−0.163620	+	0.113411i
$593$			3.01170i			0.123676i	0.998086	+	0.0618378i	$0.0196962\pi$
$593$			3.01170i			0.123676i	−0.998086	+	0.0618378i	$0.980304\pi$
$594$		0			0
$595$			5.87840i			0.240991i
$596$	−43.7289	+	13.6733i	−1.79121	+	0.560081i
$597$		0			0
$598$	2.58822	+	1.90250i	0.105840	+	0.0777992i
$599$	35.9136			1.46739			0.733696	−	0.679478i	$-0.237794\pi$
$599$	35.9136			1.46739			0.733696	+	0.679478i	$0.237794\pi$
$600$		0			0
$601$	−13.0045			−0.530465			−0.265232	−	0.964184i	$-0.585449\pi$
$601$	−13.0045			−0.530465			−0.265232	+	0.964184i	$0.585449\pi$
$602$	−1.22819	−	0.902799i	−0.0500575	−	0.0367953i
$603$		0			0
$604$	29.3770	−	9.18571i	1.19533	−	0.373761i
$605$		−	1.88680i		−	0.0767094i
$606$		0			0
$607$		−	1.24671i		−	0.0506022i	−0.999680	−	0.0253011i	$-0.991946\pi$
$607$		−	1.24671i		−	0.0506022i	0.999680	−	0.0253011i	$-0.00805446\pi$
$608$	−0.370874	+	13.3530i	−0.0150409	+	0.541535i
$609$		0			0
$610$	−6.50407	+	8.84832i	−0.263342	+	0.358258i
$611$	4.66470			0.188714
$612$		0			0
$613$	−38.4840			−1.55436			−0.777178	−	0.629281i	$-0.783350\pi$
$613$	−38.4840			−1.55436			−0.777178	+	0.629281i	$0.783350\pi$
$614$	23.9295	−	32.5544i	0.965717	−	1.31379i
$615$		0			0
$616$	−9.60298	−	3.29806i	−0.386915	−	0.132883i
$617$			23.6915i			0.953784i	0.878962	+	0.476892i	$0.158237\pi$
$617$			23.6915i			0.953784i	−0.878962	+	0.476892i	$0.841763\pi$
$618$		0			0
$619$		−	24.6978i		−	0.992687i	−0.868126	−	0.496343i	$-0.834676\pi$
$619$		−	24.6978i		−	0.992687i	0.868126	−	0.496343i	$-0.165324\pi$
$620$	0.286023	+	0.914737i	0.0114870	+	0.0367367i
$621$		0			0
$622$	0.550177	+	0.404414i	0.0220601	+	0.0162155i
$623$	0.714137			0.0286113
$624$		0			0
$625$	1.00000			0.0400000
$626$	15.6377	+	11.4947i	0.625007	+	0.459419i
$627$		0			0
$628$	1.18714	+	3.79662i	0.0473721	+	0.151502i
$629$		−	7.11854i		−	0.283835i
$630$		0			0
$631$		−	25.1132i		−	0.999740i	−0.866100	−	0.499870i	$-0.833381\pi$
$631$		−	25.1132i		−	0.999740i	0.866100	−	0.499870i	$-0.166619\pi$
$632$	−35.3233	−	12.1315i	−1.40509	−	0.482565i
$633$		0			0
$634$	16.1659	−	21.9926i	0.642031	−	0.873438i
$635$	−7.17430			−0.284703
$636$		0			0
$637$	2.60436			0.103189
$638$	−17.4517	+	23.7419i	−0.690921	+	0.939949i
$639$		0			0
$640$	10.8877	−	3.07530i	0.430375	−	0.121562i
$641$			38.4579i			1.51900i	0.650510	+	0.759498i	$0.274555\pi$
$641$			38.4579i			1.51900i	−0.650510	+	0.759498i	$0.725445\pi$
$642$		0			0
$643$		−	11.6798i		−	0.460608i	−0.973119	−	0.230304i	$-0.926028\pi$
$643$		−	11.6798i		−	0.460608i	0.973119	−	0.230304i	$-0.0739720\pi$
$644$	1.66481	−	0.520558i	0.0656026	−	0.0205129i
$645$		0			0
$646$	−15.8176	−	11.6269i	−0.622334	−	0.457454i
$647$	29.1208			1.14486			0.572428	−	0.819955i	$-0.306001\pi$
$647$	29.1208			1.14486			0.572428	+	0.819955i	$0.306001\pi$
$648$		0			0
$649$	−32.8621			−1.28995
$650$	−2.96764	−	2.18140i	−0.116401	−	0.0855616i
$651$		0			0
$652$	−35.1826	+	11.0010i	−1.37786	+	0.430833i
$653$		−	9.45117i		−	0.369853i	−0.982752	−	0.184927i	$-0.940795\pi$
$653$		−	9.45117i		−	0.369853i	0.982752	−	0.184927i	$-0.0592047\pi$
$654$		0			0
$655$			11.3808i			0.444684i
$656$	−7.59424	−	10.9563i	−0.296505	−	0.427773i
$657$		0			0
$658$	1.50023	−	2.04095i	0.0584849	−	0.0795645i
$659$	10.8158			0.421325			0.210663	−	0.977559i	$-0.432438\pi$
$659$	10.8158			0.421325			0.210663	+	0.977559i	$0.432438\pi$
$660$		0			0
$661$	−30.8184			−1.19870			−0.599348	−	0.800489i	$-0.704573\pi$
$661$	−30.8184			−1.19870			−0.599348	+	0.800489i	$0.704573\pi$
$662$	−8.73335	+	11.8811i	−0.339431	+	0.461772i
$663$		0			0
$664$	−14.2476	+	41.4848i	−0.552913	+	1.60992i
$665$		−	2.36141i		−	0.0915714i
$666$		0			0
$667$		−	5.06200i		−	0.196001i
$668$	−5.03478	−	16.1018i	−0.194801	−	0.622998i
$669$		0			0
$670$	13.2391	+	9.73154i	0.511470	+	0.375962i
$671$	27.8756			1.07612
$672$		0			0
$673$	20.8541			0.803867			0.401933	−	0.915669i	$-0.368338\pi$
$673$	20.8541			0.803867			0.401933	+	0.915669i	$0.368338\pi$
$674$	−26.9427	−	19.8046i	−1.03779	−	0.762843i
$675$		0			0
$676$	−3.71091	−	11.8679i	−0.142727	−	0.456459i
$677$			24.5631i			0.944037i	0.881589	+	0.472018i	$0.156474\pi$
$677$			24.5631i			0.944037i	−0.881589	+	0.472018i	$0.843526\pi$
$678$		0			0
$679$		−	2.39247i		−	0.0918145i
$680$	−5.40063	+	15.7251i	−0.207105	+	0.603029i
$681$		0			0
$682$	1.44088	−	1.96022i	0.0551743	−	0.0750607i
$683$	−30.3548			−1.16149			−0.580747	−	0.814084i	$-0.697239\pi$
$683$	−30.3548			−1.16149			−0.580747	+	0.814084i	$0.697239\pi$
$684$		0			0
$685$	−8.84221			−0.337844
$686$	0.837595	−	1.13949i	0.0319795	−	0.0435059i
$687$		0			0
$688$	−2.45607	−	3.54341i	−0.0936367	−	0.135091i
$689$			26.6464i			1.01515i
$690$		0			0
$691$		−	22.5570i		−	0.858108i	−0.903279	−	0.429054i	$-0.858847\pi$
$691$		−	22.5570i		−	0.858108i	0.903279	−	0.429054i	$-0.141153\pi$
$692$	39.3858	−	12.3153i	1.49722	−	0.468158i
$693$		0			0
$694$	−31.6000	−	23.2280i	−1.19952	−	0.881722i
$695$	6.51008			0.246941
$696$		0			0
$697$	19.5911			0.742067
$698$	25.6065	+	18.8224i	0.969220	+	0.712437i
$699$		0			0
$700$	−1.90886	+	0.596870i	−0.0721481	+	0.0225595i
$701$		−	26.6571i		−	1.00682i	−0.864047	−	0.503412i	$-0.832078\pi$
$701$		−	26.6571i		−	1.00682i	0.864047	−	0.503412i	$-0.167922\pi$
$702$		0			0
$703$			2.85958i			0.107851i
$704$	−22.6585	−	17.6450i	−0.853976	−	0.665021i
$705$		0			0
$706$	−27.8277	+	37.8576i	−1.04731	+	1.42479i
$707$	−17.3805			−0.653661
$708$		0			0
$709$	7.09780			0.266564			0.133282	−	0.991078i	$-0.457448\pi$
$709$	7.09780			0.266564			0.133282	+	0.991078i	$0.457448\pi$
$710$	−7.96672	+	10.8382i	−0.298986	+	0.406749i
$711$		0			0
$712$	1.91036	+	0.656096i	0.0715937	+	0.0245882i
$713$			0.417938i			0.0156519i
$714$		0			0
$715$			9.34920i			0.349640i
$716$	−6.24754	−	19.9804i	−0.233482	−	0.746702i
$717$		0			0
$718$	−5.91239	−	4.34598i	−0.220649	−	0.162190i
$719$	16.0257			0.597657			0.298828	−	0.954307i	$-0.403404\pi$
$719$	16.0257			0.597657			0.298828	+	0.954307i	$0.403404\pi$
$720$		0			0
$721$	1.99963			0.0744703
$722$	−15.2962	−	11.2437i	−0.569267	−	0.418446i
$723$		0			0
$724$	1.38652	+	4.43427i	0.0515297	+	0.164798i
$725$			5.80406i			0.215557i
$726$		0			0
$727$		−	34.9152i		−	1.29493i	−0.762093	−	0.647467i	$-0.775828\pi$
$727$		−	34.9152i		−	1.29493i	0.762093	−	0.647467i	$-0.224172\pi$
$728$	6.96683	+	2.39269i	0.258208	+	0.0886792i
$729$		0			0
$730$	1.17536	−	1.59899i	0.0435019	−	0.0591813i
$731$	6.33601			0.234346
$732$		0			0
$733$	−1.81762			−0.0671355			−0.0335677	−	0.999436i	$-0.510687\pi$
$733$	−1.81762			−0.0671355			−0.0335677	+	0.999436i	$0.510687\pi$
$734$	13.6888	−	18.6226i	0.505262	−	0.687373i
$735$		0			0
$736$	4.93171	+	0.136976i	0.181785	+	0.00504901i
$737$		−	41.7081i		−	1.53634i
$738$		0			0
$739$			3.62547i			0.133365i	0.997774	+	0.0666826i	$0.0212415\pi$
$739$			3.62547i			0.133365i	−0.997774	+	0.0666826i	$0.978759\pi$
$740$	2.31156	−	0.722788i	0.0849748	−	0.0265702i
$741$		0			0
$742$	11.6586	+	8.56979i	0.428000	+	0.314607i
$743$	47.6574			1.74838			0.874191	−	0.485582i	$-0.161392\pi$
$743$	47.6574			1.74838			0.874191	+	0.485582i	$0.161392\pi$
$744$		0			0
$745$	22.9084			0.839299
$746$	39.3191	+	28.9020i	1.43958	+	1.05818i
$747$		0			0
$748$	40.2815	−	12.5954i	1.47284	−	0.460532i
$749$		−	6.34669i		−	0.231903i
$750$		0			0
$751$		−	23.8259i		−	0.869419i	−0.900571	−	0.434710i	$-0.856851\pi$
$751$		−	23.8259i		−	0.869419i	0.900571	−	0.434710i	$-0.143149\pi$
$752$	5.88826	−	4.08137i	0.214723	−	0.148832i
$753$		0			0
$754$	12.6610	−	17.2244i	0.461086	−	0.627275i
$755$	−15.3898			−0.560093
$756$		0			0
$757$	8.81992			0.320565			0.160283	−	0.987071i	$-0.448759\pi$
$757$	8.81992			0.320565			0.160283	+	0.987071i	$0.448759\pi$
$758$	24.9689	−	33.9685i	0.906912	−	1.23379i
$759$		0			0
$760$	2.16948	−	6.31690i	0.0786954	−	0.229138i
$761$		−	16.3035i		−	0.591003i	−0.955342	−	0.295502i	$-0.904513\pi$
$761$		−	16.3035i		−	0.591003i	0.955342	−	0.295502i	$-0.0954868\pi$
$762$		0			0
$763$			4.55888i			0.165043i
$764$	−11.4783	−	36.7088i	−0.415269	−	1.32808i
$765$		0			0
$766$	−7.59622	−	5.58369i	−0.274463	−	0.201747i
$767$	23.8410			0.860848
$768$		0			0
$769$	−8.98768			−0.324104			−0.162052	−	0.986782i	$-0.551811\pi$
$769$	−8.98768			−0.324104			−0.162052	+	0.986782i	$0.551811\pi$
$770$	4.09056	+	3.00681i	0.147414	+	0.108358i
$771$		0			0
$772$	16.0021	+	51.1765i	0.575927	+	1.84188i
$773$		−	25.7264i		−	0.925316i	−0.886537	−	0.462658i	$-0.846896\pi$
$773$		−	25.7264i		−	0.925316i	0.886537	−	0.462658i	$-0.153104\pi$
$774$		0			0
$775$		−	0.479206i		−	0.0172136i
$776$	2.19802	−	6.40000i	0.0789044	−	0.229747i
$777$		0			0
$778$	12.9075	−	17.5598i	0.462758	−	0.629549i
$779$	−7.86994			−0.281970
$780$		0			0
$781$	34.1443			1.22178
$782$	−4.29420	+	5.84196i	−0.153560	+	0.208908i
$783$		0			0
$784$	3.28749	−	2.27868i	0.117410	−	0.0813815i
$785$		−	1.98895i		−	0.0709886i
$786$		0			0
$787$			26.0679i			0.929220i	0.885516	+	0.464610i	$0.153805\pi$
$787$			26.0679i			0.929220i	−0.885516	+	0.464610i	$0.846195\pi$
$788$	17.5604	−	5.49084i	0.625562	−	0.195603i
$789$		0			0
$790$	15.0466	+	11.0602i	0.535334	+	0.393504i
$791$	−9.72497			−0.345780
$792$		0			0
$793$	−20.2233			−0.718151
$794$	9.68975	+	7.12257i	0.343876	+	0.252770i
$795$		0			0
$796$	−27.0965	+	8.47263i	−0.960409	+	0.300304i
$797$			20.8372i			0.738090i	0.929412	+	0.369045i	$0.120315\pi$
$797$			20.8372i			0.738090i	−0.929412	+	0.369045i	$0.879685\pi$
$798$		0			0
$799$			10.5289i			0.372484i
$800$	−5.65467	−	0.157056i	−0.199923	−	0.00555278i
$801$		0			0
$802$	4.00978	−	5.45503i	0.141590	−	0.192624i
$803$	−5.03742			−0.177767
$804$		0			0
$805$	−0.872147			−0.0307391
$806$	−1.04534	+	1.42211i	−0.0368206	+	0.0500918i
$807$		0			0
$808$	−46.4939	−	15.9679i	−1.63565	−	0.561749i
$809$		−	23.3563i		−	0.821165i	−0.911823	−	0.410582i	$-0.865325\pi$
$809$		−	23.3563i		−	0.821165i	0.911823	−	0.410582i	$-0.134675\pi$
$810$		0			0
$811$			24.0752i			0.845396i	0.906271	+	0.422698i	$0.138917\pi$
$811$			24.0752i			0.845396i	−0.906271	+	0.422698i	$0.861083\pi$
$812$	−3.46427	−	11.0791i	−0.121572	−	0.388802i
$813$		0			0
$814$	−4.95353	−	3.64115i	−0.173621	−	0.127622i
$815$	18.4312			0.645617
$816$		0			0
$817$	−2.54523			−0.0890464
$818$	−25.6110	−	18.8257i	−0.895467	−	0.658224i
$819$		0			0
$820$	1.98921	+	6.36172i	0.0694661	+	0.222161i
$821$			12.2285i			0.426778i	0.976967	+	0.213389i	$0.0684501\pi$
$821$			12.2285i			0.426778i	−0.976967	+	0.213389i	$0.931550\pi$
$822$		0			0
$823$		−	32.3094i		−	1.12623i	−0.826377	−	0.563117i	$-0.809602\pi$
$823$		−	32.3094i		−	1.12623i	0.826377	−	0.563117i	$-0.190398\pi$
$824$	5.34914	+	1.83711i	0.186346	+	0.0639989i
$825$		0			0
$826$	7.66755	−	10.4312i	0.266788	−	0.362946i
$827$	−16.7250			−0.581585			−0.290793	−	0.956786i	$-0.593919\pi$
$827$	−16.7250			−0.581585			−0.290793	+	0.956786i	$0.593919\pi$
$828$		0			0
$829$	10.0479			0.348979			0.174490	−	0.984659i	$-0.444172\pi$
$829$	10.0479			0.348979			0.174490	+	0.984659i	$0.444172\pi$
$830$	12.9894	−	17.6712i	0.450869	−	0.613376i
$831$		0			0
$832$	16.4385	+	12.8012i	0.569901	+	0.443802i
$833$			5.87840i			0.203674i
$834$		0			0
$835$			8.43531i			0.291916i
$836$	−16.1814	+	5.05968i	−0.559647	+	0.174993i
$837$		0			0
$838$	27.1403	+	19.9498i	0.937547	+	0.689155i
$839$	−4.77268			−0.164771			−0.0823856	−	0.996601i	$-0.526254\pi$
$839$	−4.77268			−0.164771			−0.0823856	+	0.996601i	$0.526254\pi$
$840$		0			0
$841$	−4.68713			−0.161625
$842$	−34.6848	−	25.4955i	−1.19532	−	0.878633i
$843$		0			0
$844$	−30.8518	+	9.64687i	−1.06196	+	0.332059i
$845$			6.21729i			0.213881i
$846$		0			0
$847$		−	1.88680i		−	0.0648313i
$848$	23.3142	+	33.6357i	0.800611	+	1.15506i
$849$		0			0
$850$	4.92372	−	6.69837i	0.168882	−	0.229752i
$851$	1.05614			0.0362040
$852$		0			0
$853$	39.4076			1.34929			0.674645	−	0.738142i	$-0.264297\pi$
$853$	39.4076			1.34929			0.674645	+	0.738142i	$0.264297\pi$
$854$	−6.50407	+	8.84832i	−0.222565	+	0.302783i
$855$		0			0
$856$	5.83087	−	16.9778i	0.199295	−	0.580289i
$857$			1.85185i			0.0632579i	0.999500	+	0.0316290i	$0.0100695\pi$
$857$			1.85185i			0.0632579i	−0.999500	+	0.0316290i	$0.989931\pi$
$858$		0			0
$859$		−	18.9182i		−	0.645480i	−0.946488	−	0.322740i	$-0.895396\pi$
$859$		−	18.9182i		−	0.645480i	0.946488	−	0.322740i	$-0.104604\pi$
$860$	0.643334	+	2.05746i	0.0219375	+	0.0701587i
$861$		0			0
$862$	−34.8558	−	25.6212i	−1.18719	−	0.872661i
$863$	−5.40450			−0.183971			−0.0919856	−	0.995760i	$-0.529321\pi$
$863$	−5.40450			−0.183971			−0.0919856	+	0.995760i	$0.529321\pi$
$864$		0			0
$865$	−20.6332			−0.701548
$866$	21.4352	+	15.7562i	0.728397	+	0.535417i
$867$		0			0
$868$	0.286023	+	0.914737i	0.00970827	+	0.0310482i
$869$		−	47.4025i		−	1.60802i
$870$		0			0
$871$			30.2586i			1.02527i
$872$	−4.18836	+	12.1953i	−0.141836	+	0.412984i
$873$		0			0
$874$	1.72502	−	2.34677i	0.0583497	−	0.0793807i
$875$	1.00000			0.0338062
$876$		0			0
$877$	40.8534			1.37952			0.689760	−	0.724038i	$-0.257716\pi$
$877$	40.8534			1.37952			0.689760	+	0.724038i	$0.257716\pi$
$878$	−10.5009	+	14.2858i	−0.354390	+	0.482122i
$879$		0			0
$880$	8.18005	+	11.8015i	0.275750	+	0.397829i
$881$			31.8457i			1.07291i	0.843929	+	0.536455i	$0.180237\pi$
$881$			31.8457i			1.07291i	−0.843929	+	0.536455i	$0.819763\pi$
$882$		0			0
$883$			48.7222i			1.63963i	0.572627	+	0.819816i	$0.305924\pi$
$883$			48.7222i			1.63963i	−0.572627	+	0.819816i	$0.694076\pi$
$884$	−29.2237	+	9.13777i	−0.982898	+	0.307336i
$885$		0			0
$886$	−14.1624	−	10.4102i	−0.475795	−	0.349738i
$887$	−30.3870			−1.02030			−0.510148	−	0.860087i	$-0.670409\pi$
$887$	−30.3870			−1.02030			−0.510148	+	0.860087i	$0.670409\pi$
$888$		0			0
$889$	−7.17430			−0.240618
$890$	−0.813751	−	0.598158i	−0.0272770	−	0.0200503i
$891$		0			0
$892$	1.98214	−	0.619783i	0.0663670	−	0.0207519i
$893$		−	4.22954i		−	0.141536i
$894$		0			0
$895$			10.4672i			0.349879i
$896$	10.8877	−	3.07530i	0.363733	−	0.102739i
$897$		0			0
$898$	−15.9409	+	21.6864i	−0.531954	+	0.723686i
$899$	2.78134			0.0927629
$900$		0			0
$901$	−60.1444			−2.00370
$902$	10.0209	−	13.6327i	0.333660	−	0.453921i
$903$		0			0
$904$	−26.0149	−	8.93457i	−0.865242	−	0.297159i
$905$		−	2.32299i		−	0.0772189i
$906$		0			0
$907$			10.9457i			0.363446i	0.983350	+	0.181723i	$0.0581674\pi$
$907$			10.9457i			0.363446i	−0.983350	+	0.181723i	$0.941833\pi$
$908$	9.48805	+	30.3439i	0.314872	+	1.00700i
$909$		0			0
$910$	−2.96764	−	2.18140i	−0.0983764	−	0.0723128i
$911$	18.9089			0.626480			0.313240	−	0.949674i	$-0.398586\pi$
$911$	18.9089			0.626480			0.313240	+	0.949674i	$0.398586\pi$
$912$		0			0
$913$	−55.6709			−1.84244
$914$	9.53852	+	7.01141i	0.315506	+	0.231917i
$915$		0			0
$916$	14.4949	+	46.3563i	0.478924	+	1.53166i
$917$			11.3808i			0.375826i
$918$		0			0
$919$		−	28.9497i		−	0.954961i	−0.878642	−	0.477481i	$-0.841550\pi$
$919$		−	28.9497i		−	0.954961i	0.878642	−	0.477481i	$-0.158450\pi$
$920$	−2.33305	−	0.801264i	−0.0769182	−	0.0264169i
$921$		0			0
$922$	11.7417	−	15.9737i	0.386691	−	0.526066i
$923$	−24.7712			−0.815354
$924$		0			0
$925$	−1.21097			−0.0398163
$926$	31.2251	−	42.4795i	1.02612	−	1.39596i
$927$		0			0
$928$	0.911564	−	32.8201i	0.0299236	−	1.07737i
$929$		−	20.1647i		−	0.661584i	−0.943704	−	0.330792i	$-0.892684\pi$
$929$		−	20.1647i		−	0.661584i	0.943704	−	0.330792i	$-0.107316\pi$
$930$		0			0
$931$		−	2.36141i		−	0.0773920i
$932$	6.36588	−	1.99051i	0.208521	−	0.0652012i
$933$		0			0
$934$	29.8183	+	21.9183i	0.975685	+	0.717189i
$935$	−21.1024			−0.690122
$936$		0			0
$937$	12.4656			0.407234			0.203617	−	0.979051i	$-0.434730\pi$
$937$	12.4656			0.407234			0.203617	+	0.979051i	$0.434730\pi$
$938$	13.2391	+	9.73154i	0.432271	+	0.317746i
$939$		0			0
$940$	−3.41898	+	1.06906i	−0.111515	+	0.0348689i
$941$			27.9547i			0.911299i	0.890159	+	0.455649i	$0.150593\pi$
$941$			27.9547i			0.911299i	−0.890159	+	0.455649i	$0.849407\pi$
$942$		0			0
$943$			2.90663i			0.0946530i
$944$	30.0945	−	20.8596i	0.979493	−	0.678922i
$945$		0			0
$946$	3.24088	−	4.40899i	0.105370	−	0.143349i
$947$	−23.3661			−0.759298			−0.379649	−	0.925131i	$-0.623955\pi$
$947$	−23.3661			−0.759298			−0.379649	+	0.925131i	$0.623955\pi$
$948$		0			0
$949$	3.65458			0.118633
$950$	−1.97790	+	2.69080i	−0.0641716	+	0.0873010i
$951$		0			0
$952$	−5.40063	+	15.7251i	−0.175036	+	0.509652i
$953$			2.47400i			0.0801409i	0.999197	+	0.0400704i	$0.0127582\pi$
$953$			2.47400i			0.0801409i	−0.999197	+	0.0400704i	$0.987242\pi$
$954$		0			0
$955$			19.2308i			0.622293i
$956$	1.98081	+	6.33486i	0.0640640	+	0.204884i
$957$		0			0
$958$	−39.6074	−	29.1139i	−1.27966	−	0.940627i
$959$	−8.84221			−0.285530
$960$		0			0
$961$	30.7704			0.992592
$962$	3.59371	+	2.64160i	0.115866	+	0.0851687i
$963$		0			0
$964$	17.9220	+	57.3166i	0.577227	+	1.84604i
$965$		−	26.8100i		−	0.863044i
$966$		0			0
$967$			7.25947i			0.233449i	0.993164	+	0.116724i	$0.0372394\pi$
$967$			7.25947i			0.233449i	−0.993164	+	0.116724i	$0.962761\pi$
$968$	1.73345	−	5.04731i	0.0557153	−	0.162227i
$969$		0			0
$970$	−2.00392	+	2.72619i	−0.0643420	+	0.0875327i
$971$	41.7114			1.33858			0.669291	−	0.743000i	$-0.266598\pi$
$971$	41.7114			1.33858			0.669291	+	0.743000i	$0.266598\pi$
$972$		0			0
$973$	6.51008			0.208704
$974$	−7.27375	+	9.89542i	−0.233066	+	0.317070i
$975$		0			0
$976$	−25.5279	+	17.6943i	−0.817130	+	0.566382i
$977$			32.1833i			1.02963i	0.857300	+	0.514817i	$0.172140\pi$
$977$			32.1833i			1.02963i	−0.857300	+	0.514817i	$0.827860\pi$
$978$		0			0
$979$			2.56362i			0.0819337i
$980$	−1.90886	+	0.596870i	−0.0609763	+	0.0190663i
$981$		0			0
$982$	−19.2277	−	14.1336i	−0.613582	−	0.451020i
$983$	21.4545			0.684291			0.342145	−	0.939647i	$-0.388846\pi$
$983$	21.4545			0.684291			0.342145	+	0.939647i	$0.388846\pi$
$984$		0			0
$985$	−9.19939			−0.293117
$986$	38.8777	+	28.5775i	1.23812	+	0.910095i
$987$		0			0
$988$	11.7394	−	3.67072i	0.373481	−	0.116781i
$989$			0.940041i			0.0298916i
$990$		0			0
$991$			49.4406i			1.57053i	0.619158	+	0.785266i	$0.287474\pi$
$991$			49.4406i			1.57053i	−0.619158	+	0.785266i	$0.712526\pi$
$992$	−0.0752623	+	2.70975i	−0.00238958	+	0.0860348i
$993$		0			0
$994$	−7.96672	+	10.8382i	−0.252689	+	0.343766i
$995$	14.1951			0.450015
$996$		0			0
$997$	19.2350			0.609179			0.304589	−	0.952484i	$-0.401481\pi$
$997$	19.2350			0.609179			0.304589	+	0.952484i	$0.401481\pi$
$998$	−9.62383	+	13.0925i	−0.304637	+	0.414437i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.n.a.71.5	✓	24
3.2	odd	2		1260.2.n.b.71.20	yes	24
4.3	odd	2		1260.2.n.b.71.19	yes	24
12.11	even	2	inner	1260.2.n.a.71.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.n.a.71.5	✓	24	1.1	even	1	trivial
1260.2.n.a.71.6	yes	24	12.11	even	2	inner
1260.2.n.b.71.19	yes	24	4.3	odd	2
1260.2.n.b.71.20	yes	24	3.2	odd	2

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.n (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13949 - 0.837595i) q^{2} +(0.596870 + 1.90886i) q^{4} -1.00000i q^{5} -1.00000i q^{7} +(0.918725 - 2.67506i) q^{8} +(-0.837595 + 1.13949i) q^{10} +3.58982 q^{11} -2.60436 q^{13} +(-0.837595 + 1.13949i) q^{14} +(-3.28749 + 2.27868i) q^{16} -5.87840i q^{17} +2.36141i q^{19} +(1.90886 - 0.596870i) q^{20} +(-4.09056 - 3.00681i) q^{22} +0.872147 q^{23} -1.00000 q^{25} +(2.96764 + 2.18140i) q^{26} +(1.90886 - 0.596870i) q^{28} -5.80406i q^{29} +0.479206i q^{31} +(5.65467 + 0.157056i) q^{32} +(-4.92372 + 6.69837i) q^{34} -1.00000 q^{35} +1.21097 q^{37} +(1.97790 - 2.69080i) q^{38} +(-2.67506 - 0.918725i) q^{40} +3.33273i q^{41} +1.07785i q^{43} +(2.14265 + 6.85246i) q^{44} +(-0.993802 - 0.730506i) q^{46} -1.79111 q^{47} -1.00000 q^{49} +(1.13949 + 0.837595i) q^{50} +(-1.55447 - 4.97137i) q^{52} -10.2314i q^{53} -3.58982i q^{55} +(-2.67506 - 0.918725i) q^{56} +(-4.86145 + 6.61366i) q^{58} -9.15424 q^{59} +7.76517 q^{61} +(0.401381 - 0.546050i) q^{62} +(-6.31189 - 4.91529i) q^{64} +2.60436i q^{65} -11.6184i q^{67} +(11.2210 - 3.50864i) q^{68} +(1.13949 + 0.837595i) q^{70} +9.51142 q^{71} -1.40325 q^{73} +(-1.37988 - 1.01430i) q^{74} +(-4.50759 + 1.40945i) q^{76} -3.58982i q^{77} -13.2047i q^{79} +(2.27868 + 3.28749i) q^{80} +(2.79148 - 3.79761i) q^{82} -15.5080 q^{83} -5.87840 q^{85} +(0.902799 - 1.22819i) q^{86} +(3.29806 - 9.60298i) q^{88} +0.714137i q^{89} +2.60436i q^{91} +(0.520558 + 1.66481i) q^{92} +(2.04095 + 1.50023i) q^{94} +2.36141 q^{95} +2.39247 q^{97} +(1.13949 + 0.837595i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) \) 24 * q - 4 * q^4 - 4 * q^10 - 4 * q^14 + 4 * q^20 - 4 * q^22 - 24 * q^25 - 40 * q^26 + 4 * q^28 + 40 * q^32 + 8 * q^34 - 24 * q^35 + 4 * q^40 + 48 * q^44 + 36 * q^46 + 16 * q^47 - 24 * q^49 + 32 * q^52 + 4 * q^56 - 28 * q^58 - 16 * q^59 - 32 * q^61 - 56 * q^62 - 4 * q^64 + 64 * q^68 - 32 * q^74 - 72 * q^76 - 40 * q^82 - 80 * q^83 + 32 * q^85 - 80 * q^86 + 12 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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