LMFDB - Embedded newform 1260.2.n.a.71.7

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			71.7
Character	$\chi$	$=$	1260.71
Dual form			1260.2.n.a.71.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.862943 - 1.12041i) q^{2} +(-0.510659 + 1.93371i) q^{4} +1.00000i q^{5} +1.00000i q^{7} +(2.60722 - 1.09653i) q^{8} +(1.12041 - 0.862943i) q^{10} -4.23748 q^{11} -1.31554 q^{13} +(1.12041 - 0.862943i) q^{14} +(-3.47845 - 1.97493i) q^{16} -3.77232i q^{17} +4.64697i q^{19} +(-1.93371 - 0.510659i) q^{20} +(3.65670 + 4.74773i) q^{22} -1.08635 q^{23} -1.00000 q^{25} +(1.13523 + 1.47395i) q^{26} +(-1.93371 - 0.510659i) q^{28} -7.76079i q^{29} +2.35940i q^{31} +(0.788967 + 5.60157i) q^{32} +(-4.22657 + 3.25530i) q^{34} -1.00000 q^{35} +2.46382 q^{37} +(5.20654 - 4.01007i) q^{38} +(1.09653 + 2.60722i) q^{40} -11.6084i q^{41} -11.9776i q^{43} +(2.16391 - 8.19404i) q^{44} +(0.937460 + 1.21716i) q^{46} +1.69888 q^{47} -1.00000 q^{49} +(0.862943 + 1.12041i) q^{50} +(0.671791 - 2.54387i) q^{52} -2.07653i q^{53} -4.23748i q^{55} +(1.09653 + 2.60722i) q^{56} +(-8.69530 + 6.69712i) q^{58} -1.79326 q^{59} -11.7790 q^{61} +(2.64351 - 2.03603i) q^{62} +(5.59524 - 5.71780i) q^{64} -1.31554i q^{65} +5.42889i q^{67} +(7.29458 + 1.92637i) q^{68} +(0.862943 + 1.12041i) q^{70} -3.12413 q^{71} -1.47020 q^{73} +(-2.12614 - 2.76050i) q^{74} +(-8.98589 - 2.37302i) q^{76} -4.23748i q^{77} -14.4467i q^{79} +(1.97493 - 3.47845i) q^{80} +(-13.0062 + 10.0174i) q^{82} -3.23955 q^{83} +3.77232 q^{85} +(-13.4199 + 10.3360i) q^{86} +(-11.0481 + 4.64652i) q^{88} -18.6736i q^{89} -1.31554i q^{91} +(0.554755 - 2.10069i) q^{92} +(-1.46603 - 1.90345i) q^{94} -4.64697 q^{95} +7.79292 q^{97} +(0.862943 + 1.12041i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.862943	−	1.12041i	−0.610193	−	0.792253i
$2$	−0.862943	−	1.12041i	−0.610193	−	0.792253i
$3$		0			0
$3$		0			0
$4$	−0.510659	+	1.93371i	−0.255329	+	0.966854i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.60722	−	1.09653i	0.921793	−	0.387682i
$9$		0			0
$10$	1.12041	−	0.862943i	0.354306	−	0.272887i
$11$	−4.23748			−1.27765			−0.638824	−	0.769353i	$-0.720579\pi$
$11$	−4.23748			−1.27765			−0.638824	+	0.769353i	$0.720579\pi$
$12$		0			0
$13$	−1.31554			−0.364864			−0.182432	−	0.983218i	$-0.558397\pi$
$13$	−1.31554			−0.364864			−0.182432	+	0.983218i	$0.558397\pi$
$14$	1.12041	−	0.862943i	0.299443	−	0.230631i
$15$		0			0
$16$	−3.47845	−	1.97493i	−0.869614	−	0.493733i
$17$		−	3.77232i		−	0.914923i	−0.889229	−	0.457462i	$-0.848759\pi$
$17$		−	3.77232i		−	0.914923i	0.889229	−	0.457462i	$-0.151241\pi$
$18$		0			0
$19$			4.64697i			1.06609i	0.846087	+	0.533044i	$0.178952\pi$
$19$			4.64697i			1.06609i	−0.846087	+	0.533044i	$0.821048\pi$
$20$	−1.93371	−	0.510659i	−0.432390	−	0.114187i
$21$		0			0
$22$	3.65670	+	4.74773i	0.779611	+	1.01222i
$23$	−1.08635			−0.226520			−0.113260	−	0.993565i	$-0.536129\pi$
$23$	−1.08635			−0.226520			−0.113260	+	0.993565i	$0.536129\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	1.13523	+	1.47395i	0.222638	+	0.289065i
$27$		0			0
$28$	−1.93371	−	0.510659i	−0.365437	−	0.0965055i
$29$		−	7.76079i		−	1.44114i	−0.693381	−	0.720571i	$-0.743880\pi$
$29$		−	7.76079i		−	1.44114i	0.693381	−	0.720571i	$-0.256120\pi$
$30$		0			0
$31$			2.35940i			0.423762i	0.977296	+	0.211881i	$0.0679588\pi$
$31$			2.35940i			0.423762i	−0.977296	+	0.211881i	$0.932041\pi$
$32$	0.788967	+	5.60157i	0.139471	+	0.990226i
$33$		0			0
$34$	−4.22657	+	3.25530i	−0.724851	+	0.558280i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	2.46382			0.405050			0.202525	−	0.979277i	$-0.435085\pi$
$37$	2.46382			0.405050			0.202525	+	0.979277i	$0.435085\pi$
$38$	5.20654	−	4.01007i	0.844612	−	0.650519i
$39$		0			0
$40$	1.09653	+	2.60722i	0.173377	+	0.412238i
$41$		−	11.6084i		−	1.81292i	−0.422288	−	0.906462i	$-0.638773\pi$
$41$		−	11.6084i		−	1.81292i	0.422288	−	0.906462i	$-0.361227\pi$
$42$		0			0
$43$		−	11.9776i		−	1.82657i	−0.407319	−	0.913286i	$-0.633536\pi$
$43$		−	11.9776i		−	1.82657i	0.407319	−	0.913286i	$-0.366464\pi$
$44$	2.16391	−	8.19404i	0.326221	−	1.23530i
$45$		0			0
$46$	0.937460	+	1.21716i	0.138221	+	0.179461i
$47$	1.69888			0.247806			0.123903	−	0.992294i	$-0.460459\pi$
$47$	1.69888			0.247806			0.123903	+	0.992294i	$0.460459\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$	0.862943	+	1.12041i	0.122039	+	0.158451i
$51$		0			0
$52$	0.671791	−	2.54387i	0.0931606	−	0.352771i
$53$		−	2.07653i		−	0.285233i	−0.989778	−	0.142616i	$-0.954448\pi$
$53$		−	2.07653i		−	0.285233i	0.989778	−	0.142616i	$-0.0455515\pi$
$54$		0			0
$55$		−	4.23748i		−	0.571381i
$56$	1.09653	+	2.60722i	0.146530	+	0.348405i
$57$		0			0
$58$	−8.69530	+	6.69712i	−1.14175	+	0.879375i
$59$	−1.79326			−0.233462			−0.116731	−	0.993164i	$-0.537242\pi$
$59$	−1.79326			−0.233462			−0.116731	+	0.993164i	$0.537242\pi$
$60$		0			0
$61$	−11.7790			−1.50815			−0.754075	−	0.656788i	$-0.771915\pi$
$61$	−11.7790			−1.50815			−0.754075	+	0.656788i	$0.771915\pi$
$62$	2.64351	−	2.03603i	0.335726	−	0.258576i
$63$		0			0
$64$	5.59524	−	5.71780i	0.699405	−	0.714725i
$65$		−	1.31554i		−	0.163172i
$66$		0			0
$67$			5.42889i			0.663245i	0.943412	+	0.331622i	$0.107596\pi$
$67$			5.42889i			0.663245i	−0.943412	+	0.331622i	$0.892404\pi$
$68$	7.29458	+	1.92637i	0.884597	+	0.233607i
$69$		0			0
$70$	0.862943	+	1.12041i	0.103141	+	0.133915i
$71$	−3.12413			−0.370766			−0.185383	−	0.982666i	$-0.559353\pi$
$71$	−3.12413			−0.370766			−0.185383	+	0.982666i	$0.559353\pi$
$72$		0			0
$73$	−1.47020			−0.172074			−0.0860368	−	0.996292i	$-0.527420\pi$
$73$	−1.47020			−0.172074			−0.0860368	+	0.996292i	$0.527420\pi$
$74$	−2.12614	−	2.76050i	−0.247159	−	0.320902i
$75$		0			0
$76$	−8.98589	−	2.37302i	−1.03075	−	0.272204i
$77$		−	4.23748i		−	0.482905i
$78$		0			0
$79$		−	14.4467i		−	1.62539i	−0.582692	−	0.812693i	$-0.698001\pi$
$79$		−	14.4467i		−	1.62539i	0.582692	−	0.812693i	$-0.301999\pi$
$80$	1.97493	−	3.47845i	0.220804	−	0.388903i
$81$		0			0
$82$	−13.0062	+	10.0174i	−1.43629	+	1.10623i
$83$	−3.23955			−0.355587			−0.177793	−	0.984068i	$-0.556896\pi$
$83$	−3.23955			−0.355587			−0.177793	+	0.984068i	$0.556896\pi$
$84$		0			0
$85$	3.77232			0.409166
$86$	−13.4199	+	10.3360i	−1.44711	+	1.11456i
$87$		0			0
$88$	−11.0481	+	4.64652i	−1.17773	+	0.495321i
$89$		−	18.6736i		−	1.97940i	−0.143167	−	0.989699i	$-0.545728\pi$
$89$		−	18.6736i		−	1.97940i	0.143167	−	0.989699i	$-0.454272\pi$
$90$		0			0
$91$		−	1.31554i		−	0.137906i
$92$	0.554755	−	2.10069i	0.0578372	−	0.219012i
$93$		0			0
$94$	−1.46603	−	1.90345i	−0.151210	−	0.196325i
$95$	−4.64697			−0.476769
$96$		0			0
$97$	7.79292			0.791251			0.395626	−	0.918412i	$-0.370528\pi$
$97$	7.79292			0.791251			0.395626	+	0.918412i	$0.370528\pi$
$98$	0.862943	+	1.12041i	0.0871704	+	0.113179i
$99$		0			0
$100$	0.510659	−	1.93371i	0.0510659	−	0.193371i
$101$			11.5811i			1.15236i	0.817323	+	0.576179i	$0.195457\pi$
$101$			11.5811i			1.15236i	−0.817323	+	0.576179i	$0.804543\pi$
$102$		0			0
$103$			4.48639i			0.442057i	0.975267	+	0.221029i	$0.0709414\pi$
$103$			4.48639i			0.442057i	−0.975267	+	0.221029i	$0.929059\pi$
$104$	−3.42990	+	1.44253i	−0.336330	+	0.141451i
$105$		0			0
$106$	−2.32657	+	1.79192i	−0.225977	+	0.174047i
$107$	−17.8681			−1.72738			−0.863688	−	0.504027i	$-0.831851\pi$
$107$	−17.8681			−1.72738			−0.863688	+	0.504027i	$0.831851\pi$
$108$		0			0
$109$	−1.38174			−0.132347			−0.0661735	−	0.997808i	$-0.521079\pi$
$109$	−1.38174			−0.132347			−0.0661735	+	0.997808i	$0.521079\pi$
$110$	−4.74773	+	3.65670i	−0.452678	+	0.348653i
$111$		0			0
$112$	1.97493	−	3.47845i	0.186613	−	0.328683i
$113$			18.8688i			1.77503i	0.460780	+	0.887514i	$0.347570\pi$
$113$			18.8688i			1.77503i	−0.460780	+	0.887514i	$0.652430\pi$
$114$		0			0
$115$		−	1.08635i		−	0.101303i
$116$	15.0071	+	3.96312i	1.39337	+	0.367966i
$117$		0			0
$118$	1.54748	+	2.00919i	0.142457	+	0.184961i
$119$	3.77232			0.345808
$120$		0			0
$121$	6.95621			0.632382
$122$	10.1646	+	13.1974i	0.920263	+	1.19484i
$123$		0			0
$124$	−4.56240	−	1.20485i	−0.409716	−	0.108199i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$		−	4.86559i		−	0.431751i	−0.976421	−	0.215876i	$-0.930739\pi$
$127$		−	4.86559i		−	0.431751i	0.976421	−	0.215876i	$-0.0692606\pi$
$128$	−11.2347	−	1.33486i	−0.993015	−	0.117986i
$129$		0			0
$130$	−1.47395	+	1.13523i	−0.129274	+	0.0995666i
$131$	−10.0799			−0.880689			−0.440345	−	0.897829i	$-0.645144\pi$
$131$	−10.0799			−0.880689			−0.440345	+	0.897829i	$0.645144\pi$
$132$		0			0
$133$	−4.64697			−0.402943
$134$	6.08261	−	4.68482i	0.525458	−	0.404707i
$135$		0			0
$136$	−4.13647	−	9.83530i	−0.354699	−	0.843370i
$137$			7.30663i			0.624247i	0.950042	+	0.312124i	$0.101040\pi$
$137$			7.30663i			0.624247i	−0.950042	+	0.312124i	$0.898960\pi$
$138$		0			0
$139$		−	7.32996i		−	0.621719i	−0.950456	−	0.310859i	$-0.899383\pi$
$139$		−	7.32996i		−	0.621719i	0.950456	−	0.310859i	$-0.100617\pi$
$140$	0.510659	−	1.93371i	0.0431586	−	0.163428i
$141$		0			0
$142$	2.69594	+	3.50032i	0.226239	+	0.293740i
$143$	5.57456			0.466168
$144$		0			0
$145$	7.76079			0.644498
$146$	1.26870	+	1.64723i	0.104998	+	0.136326i
$147$		0			0
$148$	−1.25817	+	4.76431i	−0.103421	+	0.391624i
$149$		−	8.80287i		−	0.721159i	−0.932728	−	0.360580i	$-0.882579\pi$
$149$		−	8.80287i		−	0.721159i	0.932728	−	0.360580i	$-0.117421\pi$
$150$		0			0
$151$			5.98779i			0.487279i	0.969866	+	0.243640i	$0.0783414\pi$
$151$			5.98779i			0.487279i	−0.969866	+	0.243640i	$0.921659\pi$
$152$	5.09554	+	12.1157i	0.413303	+	0.982713i
$153$		0			0
$154$	−4.74773	+	3.65670i	−0.382583	+	0.294665i
$155$	−2.35940			−0.189512
$156$		0			0
$157$	9.56287			0.763200			0.381600	−	0.924327i	$-0.375373\pi$
$157$	9.56287			0.763200			0.381600	+	0.924327i	$0.375373\pi$
$158$	−16.1864	+	12.4667i	−1.28772	+	0.991799i
$159$		0			0
$160$	−5.60157	+	0.788967i	−0.442843	+	0.0623733i
$161$		−	1.08635i		−	0.0856165i
$162$		0			0
$163$			7.69971i			0.603088i	0.953452	+	0.301544i	$0.0975020\pi$
$163$			7.69971i			0.603088i	−0.953452	+	0.301544i	$0.902498\pi$
$164$	22.4472	+	5.92792i	1.75283	+	0.462893i
$165$		0			0
$166$	2.79555	+	3.62964i	0.216976	+	0.281715i
$167$	6.34861			0.491270			0.245635	−	0.969362i	$-0.421003\pi$
$167$	6.34861			0.491270			0.245635	+	0.969362i	$0.421003\pi$
$168$		0			0
$169$	−11.2694			−0.866874
$170$	−3.25530	−	4.22657i	−0.249670	−	0.324163i
$171$		0			0
$172$	23.1612	+	6.11649i	1.76603	+	0.466378i
$173$			5.13430i			0.390353i	0.980768	+	0.195177i	$0.0625280\pi$
$173$			5.13430i			0.390353i	−0.980768	+	0.195177i	$0.937472\pi$
$174$		0			0
$175$		−	1.00000i		−	0.0755929i
$176$	14.7399	+	8.36872i	1.11106	+	0.630816i
$177$		0			0
$178$	−20.9222	+	16.1142i	−1.56818	+	1.20781i
$179$	−12.5019			−0.934435			−0.467217	−	0.884142i	$-0.654743\pi$
$179$	−12.5019			−0.934435			−0.467217	+	0.884142i	$0.654743\pi$
$180$		0			0
$181$	−9.87390			−0.733921			−0.366961	−	0.930236i	$-0.619602\pi$
$181$	−9.87390			−0.733921			−0.366961	+	0.930236i	$0.619602\pi$
$182$	−1.47395	+	1.13523i	−0.109256	+	0.0841491i
$183$		0			0
$184$	−2.83236	+	1.19122i	−0.208805	+	0.0878177i
$185$			2.46382i			0.181144i
$186$		0			0
$187$			15.9851i			1.16895i
$188$	−0.867546	+	3.28513i	−0.0632723	+	0.239593i
$189$		0			0
$190$	4.01007	+	5.20654i	0.290921	+	0.377722i
$191$	−15.2297			−1.10198			−0.550991	−	0.834511i	$-0.685750\pi$
$191$	−15.2297			−1.10198			−0.550991	+	0.834511i	$0.685750\pi$
$192$		0			0
$193$	3.63859			0.261912			0.130956	−	0.991388i	$-0.458195\pi$
$193$	3.63859			0.261912			0.130956	+	0.991388i	$0.458195\pi$
$194$	−6.72484	−	8.73130i	−0.482816	−	0.626871i
$195$		0			0
$196$	0.510659	−	1.93371i	0.0364756	−	0.138122i
$197$			15.4630i			1.10169i	0.834607	+	0.550846i	$0.185695\pi$
$197$			15.4630i			1.10169i	−0.834607	+	0.550846i	$0.814305\pi$
$198$		0			0
$199$		−	14.0154i		−	0.993527i	−0.867886	−	0.496764i	$-0.834522\pi$
$199$		−	14.0154i		−	0.993527i	0.867886	−	0.496764i	$-0.165478\pi$
$200$	−2.60722	+	1.09653i	−0.184359	+	0.0775364i
$201$		0			0
$202$	12.9756	−	9.99380i	0.912960	−	0.703161i
$203$	7.76079			0.544701
$204$		0			0
$205$	11.6084			0.810764
$206$	5.02662	−	3.87150i	0.350221	−	0.269740i
$207$		0			0
$208$	4.57604	+	2.59809i	0.317291	+	0.180145i
$209$		−	19.6914i		−	1.36208i
$210$		0			0
$211$		−	19.7206i		−	1.35763i	−0.734311	−	0.678813i	$-0.762495\pi$
$211$		−	19.7206i		−	1.35763i	0.734311	−	0.678813i	$-0.237505\pi$
$212$	4.01540	+	1.06040i	0.275779	+	0.0728283i
$213$		0			0
$214$	15.4192	+	20.0197i	1.05403	+	1.36852i
$215$	11.9776			0.816868
$216$		0			0
$217$	−2.35940			−0.160167
$218$	1.19237	+	1.54813i	0.0807572	+	0.104852i
$219$		0			0
$220$	8.19404	+	2.16391i	0.552442	+	0.145890i
$221$			4.96263i			0.333823i
$222$		0			0
$223$		−	28.8639i		−	1.93287i	−0.256906	−	0.966436i	$-0.582703\pi$
$223$		−	28.8639i		−	1.93287i	0.256906	−	0.966436i	$-0.417297\pi$
$224$	−5.60157	+	0.788967i	−0.374270	+	0.0527150i
$225$		0			0
$226$	21.1409	−	16.2827i	1.40627	−	1.08311i
$227$	−14.6043			−0.969323			−0.484662	−	0.874702i	$-0.661057\pi$
$227$	−14.6043			−0.969323			−0.484662	+	0.874702i	$0.661057\pi$
$228$		0			0
$229$	30.1559			1.99276			0.996378	−	0.0850370i	$-0.0271008\pi$
$229$	30.1559			1.99276			0.996378	+	0.0850370i	$0.0271008\pi$
$230$	−1.21716	+	0.937460i	−0.0802575	+	0.0618143i
$231$		0			0
$232$	−8.50994	−	20.2341i	−0.558705	−	1.32844i
$233$		−	12.3687i		−	0.810298i	−0.914251	−	0.405149i	$-0.867220\pi$
$233$		−	12.3687i		−	0.810298i	0.914251	−	0.405149i	$-0.132780\pi$
$234$		0			0
$235$			1.69888i			0.110822i
$236$	0.915742	−	3.46763i	0.0596097	−	0.225724i
$237$		0			0
$238$	−3.25530	−	4.22657i	−0.211010	−	0.273968i
$239$	−18.9704			−1.22709			−0.613547	−	0.789658i	$-0.710258\pi$
$239$	−18.9704			−1.22709			−0.613547	+	0.789658i	$0.710258\pi$
$240$		0			0
$241$	−17.2866			−1.11353			−0.556764	−	0.830671i	$-0.687957\pi$
$241$	−17.2866			−1.11353			−0.556764	+	0.830671i	$0.687957\pi$
$242$	−6.00281	−	7.79384i	−0.385875	−	0.501007i
$243$		0			0
$244$	6.01507	−	22.7772i	0.385075	−	1.45816i
$245$		−	1.00000i		−	0.0638877i
$246$		0			0
$247$		−	6.11326i		−	0.388978i
$248$	2.58716	+	6.15150i	0.164285	+	0.390620i
$249$		0			0
$250$	−1.12041	+	0.862943i	−0.0708613	+	0.0545773i
$251$	8.58477			0.541866			0.270933	−	0.962598i	$-0.412668\pi$
$251$	8.58477			0.541866			0.270933	+	0.962598i	$0.412668\pi$
$252$		0			0
$253$	4.60339			0.289413
$254$	−5.45148	+	4.19873i	−0.342056	+	0.263452i
$255$		0			0
$256$	8.19930	+	13.7394i	0.512456	+	0.858713i
$257$			11.8992i			0.742250i	0.928583	+	0.371125i	$0.121028\pi$
$257$			11.8992i			0.742250i	−0.928583	+	0.371125i	$0.878972\pi$
$258$		0			0
$259$			2.46382i			0.153095i
$260$	2.54387	+	0.671791i	0.157764	+	0.0416627i
$261$		0			0
$262$	8.69842	+	11.2937i	0.537390	+	0.697729i
$263$	14.5407			0.896620			0.448310	−	0.893878i	$-0.352026\pi$
$263$	14.5407			0.896620			0.448310	+	0.893878i	$0.352026\pi$
$264$		0			0
$265$	2.07653			0.127560
$266$	4.01007	+	5.20654i	0.245873	+	0.319233i
$267$		0			0
$268$	−10.4979	−	2.77231i	−0.641261	−	0.169346i
$269$			1.70559i			0.103991i	0.998647	+	0.0519957i	$0.0165582\pi$
$269$			1.70559i			0.103991i	−0.998647	+	0.0519957i	$0.983442\pi$
$270$		0			0
$271$			20.1881i			1.22634i	0.789952	+	0.613169i	$0.210106\pi$
$271$			20.1881i			1.22634i	−0.789952	+	0.613169i	$0.789894\pi$
$272$	−7.45008	+	13.1219i	−0.451727	+	0.795630i
$273$		0			0
$274$	8.18645	−	6.30520i	0.494562	−	0.380911i
$275$	4.23748			0.255529
$276$		0			0
$277$	7.46554			0.448561			0.224280	−	0.974525i	$-0.427997\pi$
$277$	7.46554			0.448561			0.224280	+	0.974525i	$0.427997\pi$
$278$	−8.21259	+	6.32533i	−0.492559	+	0.379368i
$279$		0			0
$280$	−2.60722	+	1.09653i	−0.155811	+	0.0655302i
$281$		−	3.18026i		−	0.189718i	−0.995491	−	0.0948592i	$-0.969760\pi$
$281$		−	3.18026i		−	0.189718i	0.995491	−	0.0948592i	$-0.0302401\pi$
$282$		0			0
$283$		−	11.8824i		−	0.706333i	−0.935561	−	0.353166i	$-0.885105\pi$
$283$		−	11.8824i		−	0.706333i	0.935561	−	0.353166i	$-0.114895\pi$
$284$	1.59536	−	6.04115i	0.0946674	−	0.358476i
$285$		0			0
$286$	−4.81053	−	6.24582i	−0.284452	−	0.369323i
$287$	11.6084			0.685221
$288$		0			0
$289$	2.76956			0.162916
$290$	−6.69712	−	8.69530i	−0.393268	−	0.510606i
$291$		0			0
$292$	0.750769	−	2.84293i	0.0439354	−	0.166370i
$293$			16.1811i			0.945311i	0.881247	+	0.472656i	$0.156704\pi$
$293$			16.1811i			0.945311i	−0.881247	+	0.472656i	$0.843296\pi$
$294$		0			0
$295$		−	1.79326i		−	0.104407i
$296$	6.42374	−	2.70166i	0.373372	−	0.157031i
$297$		0			0
$298$	−9.86286	+	7.59637i	−0.571340	+	0.440046i
$299$	1.42914			0.0826491
$300$		0			0
$301$	11.9776			0.690379
$302$	6.70880	−	5.16712i	0.386048	−	0.297334i
$303$		0			0
$304$	9.17745	−	16.1643i	0.526363	−	0.927085i
$305$		−	11.7790i		−	0.674466i
$306$		0			0
$307$			18.9644i			1.08236i	0.840908	+	0.541178i	$0.182022\pi$
$307$			18.9644i			1.08236i	−0.840908	+	0.541178i	$0.817978\pi$
$308$	8.19404	+	2.16391i	0.466899	+	0.123300i
$309$		0			0
$310$	2.03603	+	2.64351i	0.115639	+	0.150141i
$311$	28.6640			1.62539			0.812693	−	0.582692i	$-0.198001\pi$
$311$	28.6640			1.62539			0.812693	+	0.582692i	$0.198001\pi$
$312$		0			0
$313$	29.0626			1.64271			0.821356	−	0.570415i	$-0.193218\pi$
$313$	29.0626			1.64271			0.821356	+	0.570415i	$0.193218\pi$
$314$	−8.25221	−	10.7144i	−0.465699	−	0.604648i
$315$		0			0
$316$	27.9358	+	7.37736i	1.57151	+	0.415009i
$317$		−	27.0582i		−	1.51974i	−0.650076	−	0.759870i	$-0.725263\pi$
$317$		−	27.0582i		−	1.51974i	0.650076	−	0.759870i	$-0.274737\pi$
$318$		0			0
$319$			32.8862i			1.84127i
$320$	5.71780	+	5.59524i	0.319635	+	0.312784i
$321$		0			0
$322$	−1.21716	+	0.937460i	−0.0678299	+	0.0522426i
$323$	17.5299			0.975389
$324$		0			0
$325$	1.31554			0.0729729
$326$	8.62687	−	6.64441i	0.477798	−	0.368000i
$327$		0			0
$328$	−12.7289	−	30.2656i	−0.702838	−	1.67114i
$329$			1.69888i			0.0936620i
$330$		0			0
$331$			28.4611i			1.56436i	0.623050	+	0.782182i	$0.285893\pi$
$331$			28.4611i			1.56436i	−0.623050	+	0.782182i	$0.714107\pi$
$332$	1.65430	−	6.26434i	0.0907918	−	0.343800i
$333$		0			0
$334$	−5.47849	−	7.11308i	−0.299770	−	0.389210i
$335$	−5.42889			−0.296612
$336$		0			0
$337$	−29.6313			−1.61412			−0.807061	−	0.590468i	$-0.798943\pi$
$337$	−29.6313			−1.61412			−0.807061	+	0.590468i	$0.798943\pi$
$338$	9.72482	+	12.6264i	0.528960	+	0.686783i
$339$		0			0
$340$	−1.92637	+	7.29458i	−0.104472	+	0.395604i
$341$		−	9.99792i		−	0.541418i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$	−13.1338	−	31.2284i	−0.708129	−	1.68372i
$345$		0			0
$346$	5.75254	−	4.43061i	0.309259	−	0.238191i
$347$	−9.51489			−0.510786			−0.255393	−	0.966837i	$-0.582205\pi$
$347$	−9.51489			−0.510786			−0.255393	+	0.966837i	$0.582205\pi$
$348$		0			0
$349$	20.3042			1.08686			0.543430	−	0.839454i	$-0.317125\pi$
$349$	20.3042			1.08686			0.543430	+	0.839454i	$0.317125\pi$
$350$	−1.12041	+	0.862943i	−0.0598887	+	0.0461262i
$351$		0			0
$352$	−3.34323	−	23.7365i	−0.178195	−	1.26516i
$353$			29.9901i			1.59621i	0.602517	+	0.798106i	$0.294164\pi$
$353$			29.9901i			1.59621i	−0.602517	+	0.798106i	$0.705836\pi$
$354$		0			0
$355$		−	3.12413i		−	0.165812i
$356$	36.1093	+	9.53584i	1.91379	+	0.505398i
$357$		0			0
$358$	10.7884	+	14.0073i	0.570185	+	0.740309i
$359$	−3.99394			−0.210792			−0.105396	−	0.994430i	$-0.533611\pi$
$359$	−3.99394			−0.210792			−0.105396	+	0.994430i	$0.533611\pi$
$360$		0			0
$361$	−2.59434			−0.136544
$362$	8.52062	+	11.0629i	0.447834	+	0.581451i
$363$		0			0
$364$	2.54387	+	0.671791i	0.133335	+	0.0352114i
$365$		−	1.47020i		−	0.0769536i
$366$		0			0
$367$		−	25.7643i		−	1.34489i	−0.740149	−	0.672443i	$-0.765245\pi$
$367$		−	25.7643i		−	1.34489i	0.740149	−	0.672443i	$-0.234755\pi$
$368$	3.77883	+	2.14547i	0.196985	+	0.111840i
$369$		0			0
$370$	2.76050	−	2.12614i	0.143512	−	0.110533i
$371$	2.07653			0.107808
$372$		0			0
$373$	−1.61689			−0.0837194			−0.0418597	−	0.999123i	$-0.513328\pi$
$373$	−1.61689			−0.0837194			−0.0418597	+	0.999123i	$0.513328\pi$
$374$	17.9100	−	13.7943i	0.926103	−	0.713284i
$375$		0			0
$376$	4.42935	−	1.86287i	0.228426	−	0.0960701i
$377$			10.2096i			0.525821i
$378$		0			0
$379$			8.07523i			0.414797i	0.978257	+	0.207398i	$0.0664996\pi$
$379$			8.07523i			0.414797i	−0.978257	+	0.207398i	$0.933500\pi$
$380$	2.37302	−	8.98589i	0.121733	−	0.460966i
$381$		0			0
$382$	13.1424	+	17.0636i	0.672422	+	0.873049i
$383$	21.3124			1.08901			0.544507	−	0.838756i	$-0.316717\pi$
$383$	21.3124			1.08901			0.544507	+	0.838756i	$0.316717\pi$
$384$		0			0
$385$	4.23748			0.215962
$386$	−3.13990	−	4.07673i	−0.159817	−	0.207500i
$387$		0			0
$388$	−3.97952	+	15.0692i	−0.202030	+	0.765024i
$389$			9.64962i			0.489255i	0.969617	+	0.244628i	$0.0786657\pi$
$389$			9.64962i			0.489255i	−0.969617	+	0.244628i	$0.921334\pi$
$390$		0			0
$391$			4.09807i			0.207248i
$392$	−2.60722	+	1.09653i	−0.131685	+	0.0553831i
$393$		0			0
$394$	17.3250	−	13.3437i	0.872819	−	0.672245i
$395$	14.4467			0.726895
$396$		0			0
$397$	−20.8203			−1.04494			−0.522471	−	0.852657i	$-0.674990\pi$
$397$	−20.8203			−1.04494			−0.522471	+	0.852657i	$0.674990\pi$
$398$	−15.7031	+	12.0945i	−0.787125	+	0.606243i
$399$		0			0
$400$	3.47845	+	1.97493i	0.173923	+	0.0987465i
$401$			26.6966i			1.33316i	0.745432	+	0.666582i	$0.232243\pi$
$401$			26.6966i			1.33316i	−0.745432	+	0.666582i	$0.767757\pi$
$402$		0			0
$403$		−	3.10388i		−	0.154615i
$404$	−22.3944	−	5.91397i	−1.11416	−	0.294231i
$405$		0			0
$406$	−6.69712	−	8.69530i	−0.332372	−	0.431541i
$407$	−10.4404			−0.517511
$408$		0			0
$409$	11.6715			0.577117			0.288559	−	0.957462i	$-0.406824\pi$
$409$	11.6715			0.577117			0.288559	+	0.957462i	$0.406824\pi$
$410$	−10.0174	−	13.0062i	−0.494722	−	0.642330i
$411$		0			0
$412$	−8.67537	−	2.29101i	−0.427405	−	0.112870i
$413$		−	1.79326i		−	0.0882403i
$414$		0			0
$415$		−	3.23955i		−	0.159023i
$416$	−1.03791	−	7.36907i	−0.0508880	−	0.361298i
$417$		0			0
$418$	−22.0626	+	16.9926i	−1.07912	+	0.831134i
$419$	15.8171			0.772717			0.386359	−	0.922349i	$-0.373733\pi$
$419$	15.8171			0.772717			0.386359	+	0.922349i	$0.373733\pi$
$420$		0			0
$421$	−24.0192			−1.17062			−0.585312	−	0.810808i	$-0.699028\pi$
$421$	−24.0192			−1.17062			−0.585312	+	0.810808i	$0.699028\pi$
$422$	−22.0953	+	17.0178i	−1.07558	+	0.828413i
$423$		0			0
$424$	−2.27697	−	5.41397i	−0.110580	−	0.262926i
$425$			3.77232i			0.182985i
$426$		0			0
$427$		−	11.7790i		−	0.570027i
$428$	9.12451	−	34.5517i	0.441050	−	1.67012i
$429$		0			0
$430$	−10.3360	−	13.4199i	−0.498447	−	0.647166i
$431$	−24.5202			−1.18109			−0.590547	−	0.807003i	$-0.701088\pi$
$431$	−24.5202			−1.18109			−0.590547	+	0.807003i	$0.701088\pi$
$432$		0			0
$433$	3.69889			0.177757			0.0888786	−	0.996042i	$-0.471672\pi$
$433$	3.69889			0.177757			0.0888786	+	0.996042i	$0.471672\pi$
$434$	2.03603	+	2.64351i	0.0977326	+	0.126893i
$435$		0			0
$436$	0.705600	−	2.67189i	0.0337921	−	0.127960i
$437$		−	5.04825i		−	0.241490i
$438$		0			0
$439$		−	21.0026i		−	1.00240i	−0.865332	−	0.501199i	$-0.832892\pi$
$439$		−	21.0026i		−	1.00240i	0.865332	−	0.501199i	$-0.167108\pi$
$440$	−4.64652	−	11.0481i	−0.221514	−	0.526695i
$441$		0			0
$442$	5.56021	−	4.28247i	0.264472	−	0.203696i
$443$	26.7907			1.27287			0.636433	−	0.771332i	$-0.280409\pi$
$443$	26.7907			1.27287			0.636433	+	0.771332i	$0.280409\pi$
$444$		0			0
$445$	18.6736			0.885213
$446$	−32.3396	+	24.9079i	−1.53132	+	1.17943i
$447$		0			0
$448$	5.71780	+	5.59524i	0.270141	+	0.264350i
$449$		−	0.544339i		−	0.0256889i	−0.999918	−	0.0128445i	$-0.995911\pi$
$449$		−	0.544339i		−	0.0256889i	0.999918	−	0.0128445i	$-0.00408863\pi$
$450$		0			0
$451$			49.1902i			2.31628i
$452$	−36.4868	−	9.63553i	−1.71619	−	0.453217i
$453$		0			0
$454$	12.6027	+	16.3629i	0.591474	+	0.767949i
$455$	1.31554			0.0616733
$456$		0			0
$457$	13.5598			0.634302			0.317151	−	0.948375i	$-0.397274\pi$
$457$	13.5598			0.634302			0.317151	+	0.948375i	$0.397274\pi$
$458$	−26.0228	−	33.7871i	−1.21597	−	1.57877i
$459$		0			0
$460$	2.10069	+	0.554755i	0.0979451	+	0.0258656i
$461$		−	35.9347i		−	1.67365i	−0.547474	−	0.836823i	$-0.684411\pi$
$461$		−	35.9347i		−	1.67365i	0.547474	−	0.836823i	$-0.315589\pi$
$462$		0			0
$463$		−	38.9453i		−	1.80994i	−0.425475	−	0.904970i	$-0.639893\pi$
$463$		−	38.9453i		−	1.80994i	0.425475	−	0.904970i	$-0.360107\pi$
$464$	−15.3270	+	26.9956i	−0.711539	+	1.25324i
$465$		0			0
$466$	−13.8580	+	10.6735i	−0.641961	+	0.494438i
$467$	−9.09883			−0.421044			−0.210522	−	0.977589i	$-0.567516\pi$
$467$	−9.09883			−0.421044			−0.210522	+	0.977589i	$0.567516\pi$
$468$		0			0
$469$	−5.42889			−0.250683
$470$	1.90345	−	1.46603i	0.0877994	−	0.0676230i
$471$		0			0
$472$	−4.67542	+	1.96636i	−0.215204	+	0.0905090i
$473$			50.7549i			2.33371i
$474$		0			0
$475$		−	4.64697i		−	0.213218i
$476$	−1.92637	+	7.29458i	−0.0882951	+	0.334346i
$477$		0			0
$478$	16.3704	+	21.2547i	0.748764	+	0.972168i
$479$	22.3339			1.02046			0.510231	−	0.860038i	$-0.329560\pi$
$479$	22.3339			1.02046			0.510231	+	0.860038i	$0.329560\pi$
$480$		0			0
$481$	−3.24125			−0.147788
$482$	14.9173	+	19.3682i	0.679466	+	0.882195i
$483$		0			0
$484$	−3.55225	+	13.4513i	−0.161466	+	0.611422i
$485$			7.79292i			0.353858i
$486$		0			0
$487$			11.7332i			0.531681i	0.964017	+	0.265840i	$0.0856494\pi$
$487$			11.7332i			0.531681i	−0.964017	+	0.265840i	$0.914351\pi$
$488$	−30.7106	+	12.9161i	−1.39020	+	0.584683i
$489$		0			0
$490$	−1.12041	+	0.862943i	−0.0506152	+	0.0389838i
$491$	−40.4564			−1.82577			−0.912887	−	0.408213i	$-0.866152\pi$
$491$	−40.4564			−1.82577			−0.912887	+	0.408213i	$0.866152\pi$
$492$		0			0
$493$	−29.2762			−1.31853
$494$	−6.84939	+	5.27540i	−0.308169	+	0.237351i
$495$		0			0
$496$	4.65966	−	8.20708i	0.209225	−	0.368509i
$497$		−	3.12413i		−	0.140136i
$498$		0			0
$499$			26.0278i			1.16516i	0.812772	+	0.582582i	$0.197957\pi$
$499$			26.0278i			1.16516i	−0.812772	+	0.582582i	$0.802043\pi$
$500$	1.93371	+	0.510659i	0.0864781	+	0.0228374i
$501$		0			0
$502$	−7.40817	−	9.61851i	−0.330643	−	0.429295i
$503$	9.18153			0.409384			0.204692	−	0.978826i	$-0.434381\pi$
$503$	9.18153			0.409384			0.204692	+	0.978826i	$0.434381\pi$
$504$		0			0
$505$	−11.5811			−0.515351
$506$	−3.97246	−	5.15771i	−0.176598	−	0.229288i
$507$		0			0
$508$	9.40863	+	2.48466i	0.417441	+	0.110239i
$509$			12.0124i			0.532441i	0.963912	+	0.266220i	$0.0857749\pi$
$509$			12.0124i			0.532441i	−0.963912	+	0.266220i	$0.914225\pi$
$510$		0			0
$511$		−	1.47020i		−	0.0650377i
$512$	8.31832	−	21.0429i	0.367621	−	0.929976i
$513$		0			0
$514$	13.3320	−	10.2683i	0.588049	−	0.452915i
$515$	−4.48639			−0.197694
$516$		0			0
$517$	−7.19894			−0.316609
$518$	2.76050	−	2.12614i	0.121290	−	0.0934172i
$519$		0			0
$520$	−1.44253	−	3.42990i	−0.0632590	−	0.150411i
$521$		−	6.93500i		−	0.303828i	−0.988394	−	0.151914i	$-0.951456\pi$
$521$		−	6.93500i		−	0.303828i	0.988394	−	0.151914i	$-0.0485437\pi$
$522$		0			0
$523$			14.5179i			0.634823i	0.948288	+	0.317412i	$0.102814\pi$
$523$			14.5179i			0.634823i	−0.948288	+	0.317412i	$0.897186\pi$
$524$	5.14742	−	19.4917i	0.224866	−	0.851498i
$525$		0			0
$526$	−12.5478	−	16.2917i	−0.547111	−	0.710350i
$527$	8.90044			0.387709
$528$		0			0
$529$	−21.8198			−0.948689
$530$	−1.79192	−	2.32657i	−0.0778362	−	0.101060i
$531$		0			0
$532$	2.37302	−	8.98589i	0.102883	−	0.389588i
$533$			15.2712i			0.661471i
$534$		0			0
$535$		−	17.8681i		−	0.772506i
$536$	5.95294	+	14.1543i	0.257128	+	0.611374i
$537$		0			0
$538$	1.91097	−	1.47182i	0.0823876	−	0.0634549i
$539$	4.23748			0.182521
$540$		0			0
$541$	−25.8429			−1.11107			−0.555536	−	0.831493i	$-0.687487\pi$
$541$	−25.8429			−1.11107			−0.555536	+	0.831493i	$0.687487\pi$
$542$	22.6190	−	17.4212i	0.971570	−	0.748303i
$543$		0			0
$544$	21.1309	−	2.97624i	0.905981	−	0.127605i
$545$		−	1.38174i		−	0.0591874i
$546$		0			0
$547$			20.6299i			0.882071i	0.897490	+	0.441036i	$0.145389\pi$
$547$			20.6299i			0.882071i	−0.897490	+	0.441036i	$0.854611\pi$
$548$	−14.1289	−	3.73119i	−0.603556	−	0.159389i
$549$		0			0
$550$	−3.65670	−	4.74773i	−0.155922	−	0.202444i
$551$	36.0642			1.53638
$552$		0			0
$553$	14.4467			0.614338
$554$	−6.44233	−	8.36450i	−0.273708	−	0.355373i
$555$		0			0
$556$	14.1740	+	3.74311i	0.601111	+	0.158743i
$557$		−	14.1785i		−	0.600762i	−0.953819	−	0.300381i	$-0.902886\pi$
$557$		−	14.1785i		−	0.600762i	0.953819	−	0.300381i	$-0.0971139\pi$
$558$		0			0
$559$			15.7570i			0.666451i
$560$	3.47845	+	1.97493i	0.146992	+	0.0834561i
$561$		0			0
$562$	−3.56321	+	2.74438i	−0.150305	+	0.115765i
$563$	−35.4562			−1.49430			−0.747151	−	0.664655i	$-0.768579\pi$
$563$	−35.4562			−1.49430			−0.747151	+	0.664655i	$0.768579\pi$
$564$		0			0
$565$	−18.8688			−0.793817
$566$	−13.3132	+	10.2538i	−0.559594	+	0.430999i
$567$		0			0
$568$	−8.14531	+	3.42570i	−0.341769	+	0.143739i
$569$		−	0.442179i		−	0.0185371i	−0.999957	−	0.00926854i	$-0.997050\pi$
$569$		−	0.442179i		−	0.0185371i	0.999957	−	0.00926854i	$-0.00295031\pi$
$570$		0			0
$571$			38.8059i			1.62398i	0.583673	+	0.811989i	$0.301615\pi$
$571$			38.8059i			1.62398i	−0.583673	+	0.811989i	$0.698385\pi$
$572$	−2.84670	+	10.7796i	−0.119026	+	0.450716i
$573$		0			0
$574$	−10.0174	−	13.0062i	−0.418117	−	0.542868i
$575$	1.08635			0.0453040
$576$		0			0
$577$	−40.8359			−1.70002			−0.850009	−	0.526767i	$-0.823404\pi$
$577$	−40.8359			−1.70002			−0.850009	+	0.526767i	$0.823404\pi$
$578$	−2.38998	−	3.10306i	−0.0994099	−	0.129070i
$579$		0			0
$580$	−3.96312	+	15.0071i	−0.164559	+	0.623136i
$581$		−	3.23955i		−	0.134399i
$582$		0			0
$583$			8.79923i			0.364427i
$584$	−3.83313	+	1.61211i	−0.158616	+	0.0667098i
$585$		0			0
$586$	18.1296	−	13.9634i	0.748925	−	0.576822i
$587$	42.5975			1.75819			0.879093	−	0.476651i	$-0.158149\pi$
$587$	42.5975			1.75819			0.879093	+	0.476651i	$0.158149\pi$
$588$		0			0
$589$	−10.9641			−0.451767
$590$	−2.00919	+	1.54748i	−0.0827171	+	0.0637086i
$591$		0			0
$592$	−8.57030	−	4.86588i	−0.352237	−	0.199986i
$593$		−	18.4177i		−	0.756326i	−0.925739	−	0.378163i	$-0.876556\pi$
$593$		−	18.4177i		−	0.756326i	0.925739	−	0.378163i	$-0.123444\pi$
$594$		0			0
$595$			3.77232i			0.154650i
$596$	17.0222	+	4.49526i	0.697256	+	0.184133i
$597$		0			0
$598$	−1.23326	−	1.60123i	−0.0504319	−	0.0654790i
$599$	2.39564			0.0978832			0.0489416	−	0.998802i	$-0.484415\pi$
$599$	2.39564			0.0978832			0.0489416	+	0.998802i	$0.484415\pi$
$600$		0			0
$601$	−7.59185			−0.309678			−0.154839	−	0.987940i	$-0.549486\pi$
$601$	−7.59185			−0.309678			−0.154839	+	0.987940i	$0.549486\pi$
$602$	−10.3360	−	13.4199i	−0.421265	−	0.546955i
$603$		0			0
$604$	−11.5786	−	3.05772i	−0.471128	−	0.124417i
$605$			6.95621i			0.282810i
$606$		0			0
$607$			32.4082i			1.31541i	0.753276	+	0.657705i	$0.228473\pi$
$607$			32.4082i			1.31541i	−0.753276	+	0.657705i	$0.771527\pi$
$608$	−26.0303	+	3.66630i	−1.05567	+	0.148688i
$609$		0			0
$610$	−13.1974	+	10.1646i	−0.534347	+	0.411554i
$611$	−2.23493			−0.0904157
$612$		0			0
$613$	−4.29133			−0.173325			−0.0866625	−	0.996238i	$-0.527620\pi$
$613$	−4.29133			−0.173325			−0.0866625	+	0.996238i	$0.527620\pi$
$614$	21.2480	−	16.3652i	0.857500	−	0.660446i
$615$		0			0
$616$	−4.64652	−	11.0481i	−0.187214	−	0.445139i
$617$			31.9496i			1.28624i	0.765764	+	0.643121i	$0.222361\pi$
$617$			31.9496i			1.28624i	−0.765764	+	0.643121i	$0.777639\pi$
$618$		0			0
$619$		−	44.0560i		−	1.77076i	−0.464866	−	0.885381i	$-0.653898\pi$
$619$		−	44.0560i		−	1.77076i	0.464866	−	0.885381i	$-0.346102\pi$
$620$	1.20485	−	4.56240i	0.0483880	−	0.183230i
$621$		0			0
$622$	−24.7354	−	32.1156i	−0.991799	−	1.28772i
$623$	18.6736			0.748142
$624$		0			0
$625$	1.00000			0.0400000
$626$	−25.0793	−	32.5621i	−1.00237	−	1.30144i
$627$		0			0
$628$	−4.88337	+	18.4918i	−0.194868	+	0.737903i
$629$		−	9.29434i		−	0.370590i
$630$		0			0
$631$		−	17.4015i		−	0.692742i	−0.938098	−	0.346371i	$-0.887414\pi$
$631$		−	17.4015i		−	0.692742i	0.938098	−	0.346371i	$-0.112586\pi$
$632$	−15.8413	−	37.6659i	−0.630133	−	1.49827i
$633$		0			0
$634$	−30.3164	+	23.3497i	−1.20402	+	0.927334i
$635$	4.86559			0.193085
$636$		0			0
$637$	1.31554			0.0521235
$638$	36.8461	−	28.3789i	1.45875	−	1.12353i
$639$		0			0
$640$	1.33486	−	11.2347i	0.0527649	−	0.444090i
$641$			10.8073i			0.426863i	0.976958	+	0.213431i	$0.0684640\pi$
$641$			10.8073i			0.426863i	−0.976958	+	0.213431i	$0.931536\pi$
$642$		0			0
$643$		−	26.2818i		−	1.03645i	−0.855244	−	0.518226i	$-0.826593\pi$
$643$		−	26.2818i		−	1.03645i	0.855244	−	0.518226i	$-0.173407\pi$
$644$	2.10069	+	0.554755i	0.0827787	+	0.0218604i
$645$		0			0
$646$	−15.1273	−	19.6407i	−0.595175	−	0.772755i
$647$	9.07329			0.356708			0.178354	−	0.983966i	$-0.442923\pi$
$647$	9.07329			0.356708			0.178354	+	0.983966i	$0.442923\pi$
$648$		0			0
$649$	7.59888			0.298282
$650$	−1.13523	−	1.47395i	−0.0445275	−	0.0578130i
$651$		0			0
$652$	−14.8890	−	3.93192i	−0.583098	−	0.153986i
$653$			35.6329i			1.39442i	0.716865	+	0.697212i	$0.245576\pi$
$653$			35.6329i			1.39442i	−0.716865	+	0.697212i	$0.754424\pi$
$654$		0			0
$655$		−	10.0799i		−	0.393856i
$656$	−22.9257	+	40.3792i	−0.895099	+	1.57654i
$657$		0			0
$658$	1.90345	−	1.46603i	0.0742040	−	0.0571519i
$659$	−34.3086			−1.33647			−0.668237	−	0.743948i	$-0.732951\pi$
$659$	−34.3086			−1.33647			−0.668237	+	0.743948i	$0.732951\pi$
$660$		0			0
$661$	−20.7598			−0.807462			−0.403731	−	0.914878i	$-0.632287\pi$
$661$	−20.7598			−0.807462			−0.403731	+	0.914878i	$0.632287\pi$
$662$	31.8883	−	24.5603i	1.23937	−	0.954564i
$663$		0			0
$664$	−8.44623	+	3.55226i	−0.327777	+	0.137855i
$665$		−	4.64697i		−	0.180202i
$666$		0			0
$667$			8.43095i			0.326448i
$668$	−3.24198	+	12.2764i	−0.125436	+	0.474987i
$669$		0			0
$670$	4.68482	+	6.08261i	0.180991	+	0.234992i
$671$	49.9134			1.92688
$672$		0			0
$673$	−13.0915			−0.504642			−0.252321	−	0.967644i	$-0.581194\pi$
$673$	−13.0915			−0.504642			−0.252321	+	0.967644i	$0.581194\pi$
$674$	25.5702	+	33.1994i	0.984926	+	1.27879i
$675$		0			0
$676$	5.75480	−	21.7917i	0.221338	−	0.838141i
$677$		−	5.34791i		−	0.205537i	−0.994705	−	0.102768i	$-0.967230\pi$
$677$		−	5.34791i		−	0.205537i	0.994705	−	0.102768i	$-0.0327701\pi$
$678$		0			0
$679$			7.79292i			0.299065i
$680$	9.83530	−	4.13647i	0.377167	−	0.158626i
$681$		0			0
$682$	−11.2018	+	8.62763i	−0.428940	+	0.330369i
$683$	−38.8206			−1.48543			−0.742715	−	0.669608i	$-0.766462\pi$
$683$	−38.8206			−1.48543			−0.742715	+	0.669608i	$0.766462\pi$
$684$		0			0
$685$	−7.30663			−0.279172
$686$	−1.12041	+	0.862943i	−0.0427776	+	0.0329473i
$687$		0			0
$688$	−23.6550	+	41.6637i	−0.901838	+	1.58841i
$689$			2.73175i			0.104071i
$690$		0			0
$691$		−	8.41840i		−	0.320251i	−0.987097	−	0.160126i	$-0.948810\pi$
$691$		−	8.41840i		−	0.320251i	0.987097	−	0.160126i	$-0.0511899\pi$
$692$	−9.92823	−	2.62187i	−0.377415	−	0.0996687i
$693$		0			0
$694$	8.21081	+	10.6606i	0.311678	+	0.404672i
$695$	7.32996			0.278041
$696$		0			0
$697$	−43.7906			−1.65869
$698$	−17.5214	−	22.7492i	−0.663194	−	0.861068i
$699$		0			0
$700$	1.93371	+	0.510659i	0.0730873	+	0.0193011i
$701$			31.6971i			1.19718i	0.801054	+	0.598592i	$0.204273\pi$
$701$			31.6971i			1.19718i	−0.801054	+	0.598592i	$0.795727\pi$
$702$		0			0
$703$			11.4493i			0.431819i
$704$	−23.7097	+	24.2290i	−0.893593	+	0.913167i
$705$		0			0
$706$	33.6013	−	25.8797i	1.26460	−	0.973997i
$707$	−11.5811			−0.435551
$708$		0			0
$709$	5.42488			0.203736			0.101868	−	0.994798i	$-0.467518\pi$
$709$	5.42488			0.203736			0.101868	+	0.994798i	$0.467518\pi$
$710$	−3.50032	+	2.69594i	−0.131365	+	0.101177i
$711$		0			0
$712$	−20.4762	−	48.6863i	−0.767377	−	1.82459i
$713$		−	2.56314i		−	0.0959905i
$714$		0			0
$715$			5.57456i			0.208477i
$716$	6.38420	−	24.1750i	0.238589	−	0.903462i
$717$		0			0
$718$	3.44654	+	4.47487i	0.128624	+	0.167001i
$719$	−34.3125			−1.27964			−0.639821	−	0.768524i	$-0.720992\pi$
$719$	−34.3125			−1.27964			−0.639821	+	0.768524i	$0.720992\pi$
$720$		0			0
$721$	−4.48639			−0.167082
$722$	2.23876	+	2.90673i	0.0833182	+	0.108177i
$723$		0			0
$724$	5.04220	−	19.0932i	0.187392	−	0.709595i
$725$			7.76079i			0.288228i
$726$		0			0
$727$			2.56269i			0.0950448i	0.998870	+	0.0475224i	$0.0151325\pi$
$727$			2.56269i			0.0950448i	−0.998870	+	0.0475224i	$0.984867\pi$
$728$	−1.44253	−	3.42990i	−0.0534636	−	0.127121i
$729$		0			0
$730$	−1.64723	+	1.26870i	−0.0609667	+	0.0469565i
$731$	−45.1835			−1.67117
$732$		0			0
$733$	0.324469			0.0119845			0.00599226	−	0.999982i	$-0.498093\pi$
$733$	0.324469			0.0119845			0.00599226	+	0.999982i	$0.498093\pi$
$734$	−28.8667	+	22.2331i	−1.06549	+	0.820640i
$735$		0			0
$736$	−0.857095	−	6.08527i	−0.0315930	−	0.224306i
$737$		−	23.0048i		−	0.847393i
$738$		0			0
$739$			33.4804i			1.23160i	0.787904	+	0.615798i	$0.211166\pi$
$739$			33.4804i			1.23160i	−0.787904	+	0.615798i	$0.788834\pi$
$740$	−4.76431	−	1.25817i	−0.175140	−	0.0462514i
$741$		0			0
$742$	−1.79192	−	2.32657i	−0.0657836	−	0.0854111i
$743$	44.7481			1.64165			0.820824	−	0.571181i	$-0.193515\pi$
$743$	44.7481			1.64165			0.820824	+	0.571181i	$0.193515\pi$
$744$		0			0
$745$	8.80287			0.322512
$746$	1.39528	+	1.81159i	0.0510850	+	0.0663269i
$747$		0			0
$748$	−30.9106	−	8.16295i	−1.13020	−	0.298467i
$749$		−	17.8681i		−	0.652887i
$750$		0			0
$751$		−	4.39318i		−	0.160309i	−0.996782	−	0.0801547i	$-0.974459\pi$
$751$		−	4.39318i		−	0.160309i	0.996782	−	0.0801547i	$-0.0255414\pi$
$752$	−5.90946	−	3.35516i	−0.215496	−	0.122350i
$753$		0			0
$754$	11.4390	−	8.81031i	0.416584	−	0.320852i
$755$	−5.98779			−0.217918
$756$		0			0
$757$	−26.5993			−0.966768			−0.483384	−	0.875408i	$-0.660592\pi$
$757$	−26.5993			−0.966768			−0.483384	+	0.875408i	$0.660592\pi$
$758$	9.04761	−	6.96846i	0.328624	−	0.253106i
$759$		0			0
$760$	−12.1157	+	5.09554i	−0.439483	+	0.184835i
$761$		−	42.2116i		−	1.53017i	−0.643930	−	0.765085i	$-0.722697\pi$
$761$		−	42.2116i		−	1.53017i	0.643930	−	0.765085i	$-0.277303\pi$
$762$		0			0
$763$		−	1.38174i		−	0.0500225i
$764$	7.77718	−	29.4498i	0.281369	−	1.06546i
$765$		0			0
$766$	−18.3914	−	23.8788i	−0.664509	−	0.862775i
$767$	2.35909			0.0851820
$768$		0			0
$769$	5.36652			0.193522			0.0967609	−	0.995308i	$-0.469152\pi$
$769$	5.36652			0.193522			0.0967609	+	0.995308i	$0.469152\pi$
$770$	−3.65670	−	4.74773i	−0.131778	−	0.171096i
$771$		0			0
$772$	−1.85808	+	7.03597i	−0.0668737	+	0.253230i
$773$		−	0.776297i		−	0.0279215i	−0.999903	−	0.0139607i	$-0.995556\pi$
$773$		−	0.776297i		−	0.0279215i	0.999903	−	0.0139607i	$-0.00444399\pi$
$774$		0			0
$775$		−	2.35940i		−	0.0847523i
$776$	20.3179	−	8.54517i	0.729370	−	0.306754i
$777$		0			0
$778$	10.8116	−	8.32707i	0.387614	−	0.298540i
$779$	53.9438			1.93274
$780$		0			0
$781$	13.2384			0.473708
$782$	4.59154	−	3.53640i	0.164193	−	0.126462i
$783$		0			0
$784$	3.47845	+	1.97493i	0.124231	+	0.0705332i
$785$			9.56287i			0.341314i
$786$		0			0
$787$			1.67264i			0.0596233i	0.999556	+	0.0298117i	$0.00949075\pi$
$787$			1.67264i			0.0596233i	−0.999556	+	0.0298117i	$0.990509\pi$
$788$	−29.9009	−	7.89631i	−1.06518	−	0.281294i
$789$		0			0
$790$	−12.4667	−	16.1864i	−0.443546	−	0.575885i
$791$	−18.8688			−0.670898
$792$		0			0
$793$	15.4958			0.550271
$794$	17.9667	+	23.3274i	0.637616	+	0.827858i
$795$		0			0
$796$	27.1017	+	7.15710i	0.960596	+	0.253677i
$797$		−	32.6861i		−	1.15780i	−0.815398	−	0.578900i	$-0.803482\pi$
$797$		−	32.6861i		−	1.15780i	0.815398	−	0.578900i	$-0.196518\pi$
$798$		0			0
$799$		−	6.40871i		−	0.226724i
$800$	−0.788967	−	5.60157i	−0.0278942	−	0.198045i
$801$		0			0
$802$	29.9112	−	23.0376i	1.05620	−	0.813486i
$803$	6.22992			0.219849
$804$		0			0
$805$	1.08635			0.0382889
$806$	−3.47764	+	2.67847i	−0.122495	+	0.0943453i
$807$		0			0
$808$	12.6990	+	30.1944i	0.446749	+	1.06224i
$809$		−	0.255102i		−	0.00896889i	−0.999990	−	0.00448445i	$-0.998573\pi$
$809$		−	0.255102i		−	0.00896889i	0.999990	−	0.00448445i	$-0.00142745\pi$
$810$		0			0
$811$			25.6840i			0.901886i	0.892553	+	0.450943i	$0.148912\pi$
$811$			25.6840i			0.901886i	−0.892553	+	0.450943i	$0.851088\pi$
$812$	−3.96312	+	15.0071i	−0.139078	+	0.526646i
$813$		0			0
$814$	9.00946	+	11.6976i	0.315781	+	0.410000i
$815$	−7.69971			−0.269709
$816$		0			0
$817$	55.6597			1.94729
$818$	−10.0718	−	13.0769i	−0.352153	−	0.457223i
$819$		0			0
$820$	−5.92792	+	22.4472i	−0.207012	+	0.783890i
$821$		−	37.1669i		−	1.29713i	−0.761158	−	0.648567i	$-0.775369\pi$
$821$		−	37.1669i		−	1.29713i	0.761158	−	0.648567i	$-0.224631\pi$
$822$		0			0
$823$		−	38.2124i		−	1.33200i	−0.745951	−	0.666000i	$-0.768005\pi$
$823$		−	38.2124i		−	1.33200i	0.745951	−	0.666000i	$-0.231995\pi$
$824$	4.91946	+	11.6970i	0.171378	+	0.407485i
$825$		0			0
$826$	−2.00919	+	1.54748i	−0.0699087	+	0.0538436i
$827$	14.3871			0.500289			0.250145	−	0.968208i	$-0.419522\pi$
$827$	14.3871			0.500289			0.250145	+	0.968208i	$0.419522\pi$
$828$		0			0
$829$	−13.1711			−0.457451			−0.228726	−	0.973491i	$-0.573456\pi$
$829$	−13.1711			−0.457451			−0.228726	+	0.973491i	$0.573456\pi$
$830$	−3.62964	+	2.79555i	−0.125987	+	0.0970348i
$831$		0			0
$832$	−7.36075	+	7.52198i	−0.255188	+	0.260778i
$833$			3.77232i			0.130703i
$834$		0			0
$835$			6.34861i			0.219703i
$836$	38.0775	+	10.0556i	1.31694	+	0.347780i
$837$		0			0
$838$	−13.6493	−	17.7217i	−0.471507	−	0.612188i
$839$	−15.2636			−0.526960			−0.263480	−	0.964665i	$-0.584870\pi$
$839$	−15.2636			−0.526960			−0.263480	+	0.964665i	$0.584870\pi$
$840$		0			0
$841$	−31.2298			−1.07689
$842$	20.7272	+	26.9115i	0.714306	+	0.927430i
$843$		0			0
$844$	38.1340	+	10.0705i	1.31263	+	0.346642i
$845$		−	11.2694i		−	0.387678i
$846$		0			0
$847$			6.95621i			0.239018i
$848$	−4.10100	+	7.22310i	−0.140829	+	0.248042i
$849$		0			0
$850$	4.22657	−	3.25530i	0.144970	−	0.111656i
$851$	−2.67658			−0.0917519
$852$		0			0
$853$	49.3068			1.68823			0.844117	−	0.536159i	$-0.180125\pi$
$853$	49.3068			1.68823			0.844117	+	0.536159i	$0.180125\pi$
$854$	−13.1974	+	10.1646i	−0.451606	+	0.347827i
$855$		0			0
$856$	−46.5862	+	19.5929i	−1.59228	+	0.669672i
$857$		−	50.0615i		−	1.71007i	−0.518571	−	0.855035i	$-0.673536\pi$
$857$		−	50.0615i		−	1.71007i	0.518571	−	0.855035i	$-0.326464\pi$
$858$		0			0
$859$			45.2832i			1.54504i	0.634989	+	0.772521i	$0.281004\pi$
$859$			45.2832i			1.54504i	−0.634989	+	0.772521i	$0.718996\pi$
$860$	−6.11649	+	23.1612i	−0.208570	+	0.789792i
$861$		0			0
$862$	21.1595	+	27.4728i	0.720696	+	0.935726i
$863$	37.9740			1.29265			0.646326	−	0.763062i	$-0.276305\pi$
$863$	37.9740			1.29265			0.646326	+	0.763062i	$0.276305\pi$
$864$		0			0
$865$	−5.13430			−0.174571
$866$	−3.19193	−	4.14429i	−0.108466	−	0.140829i
$867$		0			0
$868$	1.20485	−	4.56240i	0.0408953	−	0.154858i
$869$			61.2178i			2.07667i
$870$		0			0
$871$		−	7.14191i		−	0.241994i
$872$	−3.60252	+	1.51512i	−0.121997	+	0.0513086i
$873$		0			0
$874$	−5.65613	+	4.35635i	−0.191321	+	0.147356i
$875$	1.00000			0.0338062
$876$		0			0
$877$	−35.1869			−1.18818			−0.594088	−	0.804400i	$-0.702487\pi$
$877$	−35.1869			−1.18818			−0.594088	+	0.804400i	$0.702487\pi$
$878$	−23.5316	+	18.1240i	−0.794153	+	0.611656i
$879$		0			0
$880$	−8.36872	+	14.7399i	−0.282110	+	0.496881i
$881$			23.7680i			0.800766i	0.916348	+	0.400383i	$0.131123\pi$
$881$			23.7680i			0.800766i	−0.916348	+	0.400383i	$0.868877\pi$
$882$		0			0
$883$			37.0669i			1.24740i	0.781664	+	0.623700i	$0.214371\pi$
$883$			37.0669i			1.24740i	−0.781664	+	0.623700i	$0.785629\pi$
$884$	−9.59629	−	2.53421i	−0.322758	−	0.0852348i
$885$		0			0
$886$	−23.1189	−	30.0167i	−0.776694	−	1.00843i
$887$	4.93846			0.165817			0.0829086	−	0.996557i	$-0.473579\pi$
$887$	4.93846			0.165817			0.0829086	+	0.996557i	$0.473579\pi$
$888$		0			0
$889$	4.86559			0.163187
$890$	−16.1142	−	20.9222i	−0.540151	−	0.701313i
$891$		0			0
$892$	55.8145	+	14.7396i	1.86881	+	0.493519i
$893$			7.89462i			0.264184i
$894$		0			0
$895$		−	12.5019i		−	0.417892i
$896$	1.33486	−	11.2347i	0.0445945	−	0.375324i
$897$		0			0
$898$	−0.609885	+	0.469733i	−0.0203521	+	0.0156752i
$899$	18.3108			0.610701
$900$		0			0
$901$	−7.83333			−0.260966
$902$	55.1134	−	42.4483i	1.83508	−	1.41338i
$903$		0			0
$904$	20.6902	+	49.1952i	0.688146	+	1.63621i
$905$		−	9.87390i		−	0.328220i
$906$		0			0
$907$		−	14.9517i		−	0.496462i	−0.968701	−	0.248231i	$-0.920151\pi$
$907$		−	14.9517i		−	0.496462i	0.968701	−	0.248231i	$-0.0798492\pi$
$908$	7.45783	−	28.2405i	0.247497	−	0.937194i
$909$		0			0
$910$	−1.13523	−	1.47395i	−0.0376326	−	0.0488609i
$911$	−20.0427			−0.664044			−0.332022	−	0.943272i	$-0.607731\pi$
$911$	−20.0427			−0.664044			−0.332022	+	0.943272i	$0.607731\pi$
$912$		0			0
$913$	13.7275			0.454314
$914$	−11.7014	−	15.1926i	−0.387047	−	0.502528i
$915$		0			0
$916$	−15.3994	+	58.3126i	−0.508809	+	1.92670i
$917$		−	10.0799i		−	0.332869i
$918$		0			0
$919$		−	35.9364i		−	1.18543i	−0.805412	−	0.592715i	$-0.798056\pi$
$919$		−	35.9364i		−	1.18543i	0.805412	−	0.592715i	$-0.201944\pi$
$920$	−1.19122	−	2.83236i	−0.0392733	−	0.0933803i
$921$		0			0
$922$	−40.2618	+	31.0096i	−1.32595	+	1.02125i
$923$	4.10991			0.135279
$924$		0			0
$925$	−2.46382			−0.0810100
$926$	−43.6349	+	33.6076i	−1.43393	+	1.10441i
$927$		0			0
$928$	43.4726	−	6.12300i	1.42706	−	0.200997i
$929$		−	29.0377i		−	0.952696i	−0.879257	−	0.476348i	$-0.841960\pi$
$929$		−	29.0377i		−	0.952696i	0.879257	−	0.476348i	$-0.158040\pi$
$930$		0			0
$931$		−	4.64697i		−	0.152298i
$932$	23.9174	+	6.31617i	0.783440	+	0.206893i
$933$		0			0
$934$	7.85177	+	10.1945i	0.256918	+	0.333573i
$935$	−15.9851			−0.522770
$936$		0			0
$937$	7.13523			0.233098			0.116549	−	0.993185i	$-0.462817\pi$
$937$	7.13523			0.233098			0.116549	+	0.993185i	$0.462817\pi$
$938$	4.68482	+	6.08261i	0.152965	+	0.198604i
$939$		0			0
$940$	−3.28513	−	0.867546i	−0.107149	−	0.0282962i
$941$			25.8277i			0.841959i	0.907070	+	0.420979i	$0.138313\pi$
$941$			25.8277i			0.841959i	−0.907070	+	0.420979i	$0.861687\pi$
$942$		0			0
$943$			12.6108i			0.410663i
$944$	6.23776	+	3.54156i	0.203022	+	0.115268i
$945$		0			0
$946$	56.8666	−	43.7986i	1.84889	−	1.42402i
$947$	−5.91834			−0.192320			−0.0961601	−	0.995366i	$-0.530656\pi$
$947$	−5.91834			−0.192320			−0.0961601	+	0.995366i	$0.530656\pi$
$948$		0			0
$949$	1.93410			0.0627835
$950$	−5.20654	+	4.01007i	−0.168922	+	0.130104i
$951$		0			0
$952$	9.83530	−	4.13647i	0.318764	−	0.134064i
$953$		−	12.4045i		−	0.401820i	−0.979610	−	0.200910i	$-0.935610\pi$
$953$		−	12.4045i		−	0.401820i	0.979610	−	0.200910i	$-0.0643899\pi$
$954$		0			0
$955$		−	15.2297i		−	0.492821i
$956$	9.68741	−	36.6832i	0.313313	−	1.18642i
$957$		0			0
$958$	−19.2729	−	25.0232i	−0.622678	−	0.808464i
$959$	−7.30663			−0.235943
$960$		0			0
$961$	25.4332			0.820426
$962$	2.79701	+	3.63155i	0.0901794	+	0.117086i
$963$		0			0
$964$	8.82755	−	33.4272i	0.284316	−	1.07662i
$965$			3.63859i			0.117130i
$966$		0			0
$967$		−	36.7509i		−	1.18183i	−0.806734	−	0.590914i	$-0.798767\pi$
$967$		−	36.7509i		−	1.18183i	0.806734	−	0.590914i	$-0.201233\pi$
$968$	18.1364	−	7.62769i	0.582926	−	0.245163i
$969$		0			0
$970$	8.73130	−	6.72484i	0.280345	−	0.215922i
$971$	−42.4798			−1.36324			−0.681620	−	0.731706i	$-0.738724\pi$
$971$	−42.4798			−1.36324			−0.681620	+	0.731706i	$0.738724\pi$
$972$		0			0
$973$	7.32996			0.234988
$974$	13.1460	−	10.1251i	0.421226	−	0.324428i
$975$		0			0
$976$	40.9728	+	23.2628i	1.31151	+	0.744623i
$977$		−	55.9107i		−	1.78874i	−0.447326	−	0.894371i	$-0.647624\pi$
$977$		−	55.9107i		−	1.78874i	0.447326	−	0.894371i	$-0.352376\pi$
$978$		0			0
$979$			79.1289i			2.52897i
$980$	1.93371	+	0.510659i	0.0617700	+	0.0163124i
$981$		0			0
$982$	34.9116	+	45.3280i	1.11407	+	1.44647i
$983$	−30.6691			−0.978194			−0.489097	−	0.872229i	$-0.662674\pi$
$983$	−30.6691			−0.978194			−0.489097	+	0.872229i	$0.662674\pi$
$984$		0			0
$985$	−15.4630			−0.492692
$986$	25.2637	+	32.8015i	0.804560	+	1.04461i
$987$		0			0
$988$	11.8213	+	3.12179i	0.376085	+	0.0993174i
$989$			13.0119i			0.413755i
$990$		0			0
$991$			0.211793i			0.00672783i	0.999994	+	0.00336392i	$0.00107077\pi$
$991$			0.211793i			0.00672783i	−0.999994	+	0.00336392i	$0.998929\pi$
$992$	−13.2164	+	1.86149i	−0.419620	+	0.0591024i
$993$		0			0
$994$	−3.50032	+	2.69594i	−0.111023	+	0.0855102i
$995$	14.0154			0.444319
$996$		0			0
$997$	−0.290163			−0.00918954			−0.00459477	−	0.999989i	$-0.501463\pi$
$997$	−0.290163			−0.00918954			−0.00459477	+	0.999989i	$0.501463\pi$
$998$	29.1619	−	22.4605i	0.923104	−	0.710974i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.n.a.71.7	✓	24
3.2	odd	2		1260.2.n.b.71.18	yes	24
4.3	odd	2		1260.2.n.b.71.17	yes	24
12.11	even	2	inner	1260.2.n.a.71.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.n.a.71.7	✓	24	1.1	even	1	trivial
1260.2.n.a.71.8	yes	24	12.11	even	2	inner
1260.2.n.b.71.17	yes	24	4.3	odd	2
1260.2.n.b.71.18	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)

\(f(q)\)	\(=\)	\(q+(-0.862943 - 1.12041i) q^{2} +(-0.510659 + 1.93371i) q^{4} +1.00000i q^{5} +1.00000i q^{7} +(2.60722 - 1.09653i) q^{8} +(1.12041 - 0.862943i) q^{10} -4.23748 q^{11} -1.31554 q^{13} +(1.12041 - 0.862943i) q^{14} +(-3.47845 - 1.97493i) q^{16} -3.77232i q^{17} +4.64697i q^{19} +(-1.93371 - 0.510659i) q^{20} +(3.65670 + 4.74773i) q^{22} -1.08635 q^{23} -1.00000 q^{25} +(1.13523 + 1.47395i) q^{26} +(-1.93371 - 0.510659i) q^{28} -7.76079i q^{29} +2.35940i q^{31} +(0.788967 + 5.60157i) q^{32} +(-4.22657 + 3.25530i) q^{34} -1.00000 q^{35} +2.46382 q^{37} +(5.20654 - 4.01007i) q^{38} +(1.09653 + 2.60722i) q^{40} -11.6084i q^{41} -11.9776i q^{43} +(2.16391 - 8.19404i) q^{44} +(0.937460 + 1.21716i) q^{46} +1.69888 q^{47} -1.00000 q^{49} +(0.862943 + 1.12041i) q^{50} +(0.671791 - 2.54387i) q^{52} -2.07653i q^{53} -4.23748i q^{55} +(1.09653 + 2.60722i) q^{56} +(-8.69530 + 6.69712i) q^{58} -1.79326 q^{59} -11.7790 q^{61} +(2.64351 - 2.03603i) q^{62} +(5.59524 - 5.71780i) q^{64} -1.31554i q^{65} +5.42889i q^{67} +(7.29458 + 1.92637i) q^{68} +(0.862943 + 1.12041i) q^{70} -3.12413 q^{71} -1.47020 q^{73} +(-2.12614 - 2.76050i) q^{74} +(-8.98589 - 2.37302i) q^{76} -4.23748i q^{77} -14.4467i q^{79} +(1.97493 - 3.47845i) q^{80} +(-13.0062 + 10.0174i) q^{82} -3.23955 q^{83} +3.77232 q^{85} +(-13.4199 + 10.3360i) q^{86} +(-11.0481 + 4.64652i) q^{88} -18.6736i q^{89} -1.31554i q^{91} +(0.554755 - 2.10069i) q^{92} +(-1.46603 - 1.90345i) q^{94} -4.64697 q^{95} +7.79292 q^{97} +(0.862943 + 1.12041i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{4} - 4 q^{10} - 4 q^{14} + 4 q^{20} - 4 q^{22} - 24 q^{25} - 40 q^{26} + 4 q^{28} + 40 q^{32} + 8 q^{34} - 24 q^{35} + 4 q^{40} + 48 q^{44} + 36 q^{46} + 16 q^{47} - 24 q^{49} + 32 q^{52} + 4 q^{56}+ \cdots + 12 q^{88}+O(q^{100}) \) 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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