LMFDB - Embedded newform 360.2.bi.b.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19594 - 1.25289i) q^{3} +(-2.14796 - 0.621508i) q^{5} +(-1.98012 + 1.14322i) q^{7} +(-0.139458 + 2.99676i) q^{9} +O(q^{10})$	\(q+(-1.19594 - 1.25289i) q^{3} +(-2.14796 - 0.621508i) q^{5} +(-1.98012 + 1.14322i) q^{7} +(-0.139458 + 2.99676i) q^{9} +(0.864628 + 1.49758i) q^{11} +(5.20118 + 3.00291i) q^{13} +(1.79015 + 3.43444i) q^{15} +4.65465i q^{17} -0.888934 q^{19} +(3.80044 + 1.11364i) q^{21} +(-5.17546 - 2.98806i) q^{23} +(4.22745 + 2.66995i) q^{25} +(3.92138 - 3.40922i) q^{27} +(-2.34652 - 4.06430i) q^{29} +(-2.98190 + 5.16479i) q^{31} +(0.842257 - 2.87430i) q^{33} +(4.96374 - 1.22493i) q^{35} +8.68683i q^{37} +(-2.45800 - 10.1078i) q^{39} +(-3.15468 + 5.46406i) q^{41} +(-1.46119 + 0.843618i) q^{43} +(2.16206 - 6.35024i) q^{45} +(-10.8177 + 6.24559i) q^{47} +(-0.886081 + 1.53474i) q^{49} +(5.83175 - 5.56667i) q^{51} -2.66110i q^{53} +(-0.926427 - 3.75411i) q^{55} +(1.06311 + 1.11374i) q^{57} +(1.62355 - 2.81207i) q^{59} +(-6.08732 - 10.5436i) q^{61} +(-3.14982 - 6.09337i) q^{63} +(-9.30560 - 9.68270i) q^{65} +(10.8344 + 6.25524i) q^{67} +(2.44584 + 10.0578i) q^{69} +7.25413 q^{71} +1.69305i q^{73} +(-1.71063 - 8.48963i) q^{75} +(-3.42413 - 1.97693i) q^{77} +(-1.99175 - 3.44982i) q^{79} +(-8.96110 - 0.835841i) q^{81} +(3.63578 - 2.09912i) q^{83} +(2.89290 - 9.99799i) q^{85} +(-2.28581 + 7.80059i) q^{87} +2.60891 q^{89} -13.7320 q^{91} +(10.0371 - 2.44080i) q^{93} +(1.90939 + 0.552480i) q^{95} +(3.46355 - 1.99968i) q^{97} +(-4.60846 + 2.38223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 4 * q^9	$ 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) $ 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.19594	−	1.25289i	−0.690476	−	0.723355i
$3$	−1.19594	−	1.25289i	−0.690476	−	0.723355i
$4$		0			0
$5$	−2.14796	−	0.621508i	−0.960596	−	0.277947i
$5$	−2.14796	−	0.621508i	−0.960596	−	0.277947i
$6$		0			0
$7$	−1.98012	+	1.14322i	−0.748415	+	0.432098i	−0.825121	−	0.564956i	$-0.808893\pi$
$7$	−1.98012	+	1.14322i	−0.748415	+	0.432098i	0.0767057	+	0.997054i	$0.475560\pi$
$8$		0			0
$9$	−0.139458	+	2.99676i	−0.0464858	+	0.998919i
$10$		0			0
$11$	0.864628	+	1.49758i	0.260695	+	0.451537i	0.966427	−	0.256942i	$-0.0827149\pi$
$11$	0.864628	+	1.49758i	0.260695	+	0.451537i	−0.705732	+	0.708479i	$0.749382\pi$
$12$		0			0
$13$	5.20118	+	3.00291i	1.44255	+	0.832856i	0.998019	−	0.0629081i	$-0.0200375\pi$
$13$	5.20118	+	3.00291i	1.44255	+	0.832856i	0.444530	+	0.895764i	$0.353371\pi$
$14$		0			0
$15$	1.79015	+	3.43444i	0.462214	+	0.886768i
$16$		0			0
$17$			4.65465i			1.12892i	0.825461	+	0.564459i	$0.190915\pi$
$17$			4.65465i			1.12892i	−0.825461	+	0.564459i	$0.809085\pi$
$18$		0			0
$19$	−0.888934			−0.203936			−0.101968	−	0.994788i	$-0.532514\pi$
$19$	−0.888934			−0.203936			−0.101968	+	0.994788i	$0.532514\pi$
$20$		0			0
$21$	3.80044	+	1.11364i	0.829323	+	0.243017i
$22$		0			0
$23$	−5.17546	−	2.98806i	−1.07916	−	0.623053i	−0.148489	−	0.988914i	$-0.547441\pi$
$23$	−5.17546	−	2.98806i	−1.07916	−	0.623053i	−0.930669	+	0.365861i	$0.880774\pi$
$24$		0			0
$25$	4.22745	+	2.66995i	0.845491	+	0.533990i
$26$		0			0
$27$	3.92138	−	3.40922i	0.754671	−	0.656104i
$28$		0			0
$29$	−2.34652	−	4.06430i	−0.435738	−	0.754721i	0.561617	−	0.827397i	$-0.310179\pi$
$29$	−2.34652	−	4.06430i	−0.435738	−	0.754721i	−0.997356	+	0.0726761i	$0.976846\pi$
$30$		0			0
$31$	−2.98190	+	5.16479i	−0.535564	+	0.927625i	0.463572	+	0.886059i	$0.346568\pi$
$31$	−2.98190	+	5.16479i	−0.535564	+	0.927625i	−0.999136	+	0.0415650i	$0.986766\pi$
$32$		0			0
$33$	0.842257	−	2.87430i	0.146618	−	0.500351i
$34$		0			0
$35$	4.96374	−	1.22493i	0.839025	−	0.207052i
$36$		0			0
$37$			8.68683i			1.42811i	0.700091	+	0.714053i	$0.253143\pi$
$37$			8.68683i			1.42811i	−0.700091	+	0.714053i	$0.746857\pi$
$38$		0			0
$39$	−2.45800	−	10.1078i	−0.393595	−	1.61854i
$40$		0			0
$41$	−3.15468	+	5.46406i	−0.492678	+	0.853343i	−0.999964	−	0.00843414i	$-0.997315\pi$
$41$	−3.15468	+	5.46406i	−0.492678	+	0.853343i	0.507286	+	0.861778i	$0.330649\pi$
$42$		0			0
$43$	−1.46119	+	0.843618i	−0.222829	+	0.128651i	−0.607260	−	0.794503i	$-0.707731\pi$
$43$	−1.46119	+	0.843618i	−0.222829	+	0.128651i	0.384430	+	0.923154i	$0.374398\pi$
$44$		0			0
$45$	2.16206	−	6.35024i	0.322301	−	0.946637i
$46$		0			0
$47$	−10.8177	+	6.24559i	−1.57792	+	0.911014i	−0.582773	+	0.812635i	$0.698032\pi$
$47$	−10.8177	+	6.24559i	−1.57792	+	0.911014i	−0.995149	+	0.0983785i	$0.968634\pi$
$48$		0			0
$49$	−0.886081	+	1.53474i	−0.126583	+	0.219248i
$50$		0			0
$51$	5.83175	−	5.56667i	0.816608	−	0.779490i
$52$		0			0
$53$		−	2.66110i		−	0.365530i	−0.983157	−	0.182765i	$-0.941495\pi$
$53$		−	2.66110i		−	0.365530i	0.983157	−	0.182765i	$-0.0585047\pi$
$54$		0			0
$55$	−0.926427	−	3.75411i	−0.124919	−	0.506204i
$56$		0			0
$57$	1.06311	+	1.11374i	0.140813	+	0.147518i
$58$		0			0
$59$	1.62355	−	2.81207i	0.211368	−	0.366100i	−0.740775	−	0.671753i	$-0.765541\pi$
$59$	1.62355	−	2.81207i	0.211368	−	0.366100i	0.952143	+	0.305653i	$0.0988748\pi$
$60$		0			0
$61$	−6.08732	−	10.5436i	−0.779402	−	1.34996i	−0.932287	−	0.361720i	$-0.882190\pi$
$61$	−6.08732	−	10.5436i	−0.779402	−	1.34996i	0.152885	−	0.988244i	$-0.451144\pi$
$62$		0			0
$63$	−3.14982	−	6.09337i	−0.396840	−	0.767693i
$64$		0			0
$65$	−9.30560	−	9.68270i	−1.15422	−	1.20099i
$66$		0			0
$67$	10.8344	+	6.25524i	1.32363	+	0.764199i	0.984306	−	0.176470i	$-0.0564679\pi$
$67$	10.8344	+	6.25524i	1.32363	+	0.764199i	0.339325	+	0.940669i	$0.389801\pi$
$68$		0			0
$69$	2.44584	+	10.0578i	0.294445	+	1.21082i
$70$		0			0
$71$	7.25413			0.860906			0.430453	−	0.902613i	$-0.358354\pi$
$71$	7.25413			0.860906			0.430453	+	0.902613i	$0.358354\pi$
$72$		0			0
$73$			1.69305i			0.198156i	0.995080	+	0.0990781i	$0.0315894\pi$
$73$			1.69305i			0.198156i	−0.995080	+	0.0990781i	$0.968411\pi$
$74$		0			0
$75$	−1.71063	−	8.48963i	−0.197527	−	0.980297i
$76$		0			0
$77$	−3.42413	−	1.97693i	−0.390216	−	0.225292i
$78$		0			0
$79$	−1.99175	−	3.44982i	−0.224090	−	0.388135i	0.731956	−	0.681352i	$-0.238608\pi$
$79$	−1.99175	−	3.44982i	−0.224090	−	0.388135i	−0.956046	+	0.293217i	$0.905274\pi$
$80$		0			0
$81$	−8.96110	−	0.835841i	−0.995678	−	0.0928712i
$82$		0			0
$83$	3.63578	−	2.09912i	0.399079	−	0.230408i	−0.287007	−	0.957928i	$-0.592660\pi$
$83$	3.63578	−	2.09912i	0.399079	−	0.230408i	0.686087	+	0.727520i	$0.259327\pi$
$84$		0			0
$85$	2.89290	−	9.99799i	0.313779	−	1.08443i
$86$		0			0
$87$	−2.28581	+	7.80059i	−0.245065	+	0.836311i
$88$		0			0
$89$	2.60891			0.276544			0.138272	−	0.990394i	$-0.455845\pi$
$89$	2.60891			0.276544			0.138272	+	0.990394i	$0.455845\pi$
$90$		0			0
$91$	−13.7320			−1.43950
$92$		0			0
$93$	10.0371	−	2.44080i	1.04080	−	0.253099i
$94$		0			0
$95$	1.90939	+	0.552480i	0.195900	+	0.0566833i
$96$		0			0
$97$	3.46355	−	1.99968i	0.351670	−	0.203037i	−0.313751	−	0.949505i	$-0.601586\pi$
$97$	3.46355	−	1.99968i	0.351670	−	0.203037i	0.665420	+	0.746469i	$0.268252\pi$
$98$		0			0
$99$	−4.60846	+	2.38223i	−0.463168	+	0.239423i
$100$		0			0
$101$	−3.10733	−	5.38206i	−0.309191	−	0.535535i	0.668995	−	0.743267i	$-0.266725\pi$
$101$	−3.10733	−	5.38206i	−0.309191	−	0.535535i	−0.978186	+	0.207733i	$0.933392\pi$
$102$		0			0
$103$	−0.00503185	−	0.00290514i	−0.000495803	−	0.000286252i	0.499752	−	0.866168i	$-0.333424\pi$
$103$	−0.00503185	−	0.00290514i	−0.000495803	−	0.000286252i	−0.500248	+	0.865882i	$0.666758\pi$
$104$		0			0
$105$	−7.47104	−	4.75406i	−0.729099	−	0.463949i
$106$		0			0
$107$			4.54091i			0.438986i	0.975614	+	0.219493i	$0.0704403\pi$
$107$			4.54091i			0.438986i	−0.975614	+	0.219493i	$0.929560\pi$
$108$		0			0
$109$	15.5326			1.48776			0.743878	−	0.668315i	$-0.232984\pi$
$109$	15.5326			1.48776			0.743878	+	0.668315i	$0.232984\pi$
$110$		0			0
$111$	10.8836	−	10.3889i	1.03303	−	0.986073i
$112$		0			0
$113$	−1.45560	−	0.840393i	−0.136932	−	0.0790575i	0.429969	−	0.902844i	$-0.358524\pi$
$113$	−1.45560	−	0.840393i	−0.136932	−	0.0790575i	−0.566901	+	0.823786i	$0.691858\pi$
$114$		0			0
$115$	9.25958	+	9.63481i	0.863461	+	0.898451i
$116$		0			0
$117$	−9.72432	+	15.1679i	−0.899014	+	1.40227i
$118$		0			0
$119$	−5.32130	−	9.21676i	−0.487803	−	0.844899i
$120$		0			0
$121$	4.00484	−	6.93658i	0.364076	−	0.630598i
$122$		0			0
$123$	10.6187	−	2.58223i	0.957453	−	0.232832i
$124$		0			0
$125$	−7.42100	−	8.36234i	−0.663755	−	0.747950i
$126$		0			0
$127$			10.5663i			0.937612i	0.883301	+	0.468806i	$0.155316\pi$
$127$			10.5663i			0.937612i	−0.883301	+	0.468806i	$0.844684\pi$
$128$		0			0
$129$	2.80445	+	0.821791i	0.246918	+	0.0723547i
$130$		0			0
$131$	−10.0803	+	17.4596i	−0.880718	+	1.52545i	−0.0301741	+	0.999545i	$0.509606\pi$
$131$	−10.0803	+	17.4596i	−0.880718	+	1.52545i	−0.850544	+	0.525904i	$0.823727\pi$
$132$		0			0
$133$	1.76020	−	1.01625i	0.152628	−	0.0881201i
$134$		0			0
$135$	−10.5418	+	4.88568i	−0.907296	+	0.420492i
$136$		0			0
$137$	13.3242	−	7.69273i	1.13836	−	0.657234i	0.192338	−	0.981329i	$-0.438393\pi$
$137$	13.3242	−	7.69273i	1.13836	−	0.657234i	0.946025	+	0.324095i	$0.105060\pi$
$138$		0			0
$139$	−3.49575	+	6.05482i	−0.296506	+	0.513564i	−0.975334	−	0.220734i	$-0.929155\pi$
$139$	−3.49575	+	6.05482i	−0.296506	+	0.513564i	0.678828	+	0.734297i	$0.262488\pi$
$140$		0			0
$141$	20.7623	+	6.08400i	1.74850	+	0.512365i
$142$		0			0
$143$			10.3856i			0.868486i
$144$		0			0
$145$	2.51424	+	10.1883i	0.208796	+	0.846095i
$146$		0			0
$147$	2.98255	−	0.725293i	0.245997	−	0.0598211i
$148$		0			0
$149$	−7.84354	+	13.5854i	−0.642568	+	1.11296i	0.342290	+	0.939594i	$0.388798\pi$
$149$	−7.84354	+	13.5854i	−0.642568	+	1.11296i	−0.984858	+	0.173366i	$0.944536\pi$
$150$		0			0
$151$	−2.79420	−	4.83970i	−0.227389	−	0.393849i	0.729644	−	0.683827i	$-0.239686\pi$
$151$	−2.79420	−	4.83970i	−0.227389	−	0.393849i	−0.957034	+	0.289977i	$0.906352\pi$
$152$		0			0
$153$	−13.9488	−	0.649125i	−1.12770	−	0.0524787i
$154$		0			0
$155$	9.61495	−	9.24049i	0.772292	−	0.742214i
$156$		0			0
$157$	−18.9780	−	10.9569i	−1.51461	−	0.874458i	−0.999853	−	0.0171197i	$-0.994550\pi$
$157$	−18.9780	−	10.9569i	−1.51461	−	0.874458i	−0.514753	−	0.857339i	$-0.672116\pi$
$158$		0			0
$159$	−3.33406	+	3.18251i	−0.264408	+	0.252390i
$160$		0			0
$161$	13.6641			1.07688
$162$		0			0
$163$		−	22.8885i		−	1.79277i	−0.443280	−	0.896383i	$-0.646185\pi$
$163$		−	22.8885i		−	1.79277i	0.443280	−	0.896383i	$-0.353815\pi$
$164$		0			0
$165$	−3.59553	+	5.65040i	−0.279912	+	0.439883i
$166$		0			0
$167$	3.64205	+	2.10274i	0.281830	+	0.162715i	0.634252	−	0.773127i	$-0.281308\pi$
$167$	3.64205	+	2.10274i	0.281830	+	0.162715i	−0.352421	+	0.935841i	$0.614642\pi$
$168$		0			0
$169$	11.5349	+	19.9790i	0.887298	+	1.53685i
$170$		0			0
$171$	0.123969	−	2.66392i	0.00948011	−	0.203715i
$172$		0			0
$173$	−7.10273	+	4.10077i	−0.540011	+	0.311775i	−0.745083	−	0.666971i	$-0.767590\pi$
$173$	−7.10273	+	4.10077i	−0.540011	+	0.311775i	0.205072	+	0.978747i	$0.434257\pi$
$174$		0			0
$175$	−11.4232	−	0.453897i	−0.863514	−	0.0343114i
$176$		0			0
$177$	−5.46488	+	1.32894i	−0.410765	+	0.0998892i
$178$		0			0
$179$	22.4354			1.67690			0.838449	−	0.544980i	$-0.183463\pi$
$179$	22.4354			1.67690			0.838449	+	0.544980i	$0.183463\pi$
$180$		0			0
$181$	−20.3832			−1.51507			−0.757537	−	0.652792i	$-0.773597\pi$
$181$	−20.3832			−1.51507			−0.757537	+	0.652792i	$0.773597\pi$
$182$		0			0
$183$	−5.92982	+	20.2362i	−0.438345	+	1.49590i
$184$		0			0
$185$	5.39894	−	18.6590i	0.396938	−	1.37183i
$186$		0			0
$187$	−6.97070	+	4.02454i	−0.509748	+	0.294303i
$188$		0			0
$189$	−3.86732	+	11.2337i	−0.281306	+	0.817130i
$190$		0			0
$191$	13.0270	+	22.5634i	0.942598	+	1.63263i	0.760491	+	0.649348i	$0.224958\pi$
$191$	13.0270	+	22.5634i	0.942598	+	1.63263i	0.182107	+	0.983279i	$0.441708\pi$
$192$		0			0
$193$	−10.9966	−	6.34891i	−0.791555	−	0.457004i	0.0489549	−	0.998801i	$-0.484411\pi$
$193$	−10.9966	−	6.34891i	−0.791555	−	0.457004i	−0.840510	+	0.541797i	$0.817744\pi$
$194$		0			0
$195$	−1.00240	+	23.2388i	−0.0717835	+	1.66416i
$196$		0			0
$197$			6.79988i			0.484471i	0.970217	+	0.242236i	$0.0778807\pi$
$197$			6.79988i			0.484471i	−0.970217	+	0.242236i	$0.922119\pi$
$198$		0			0
$199$	4.13197			0.292907			0.146454	−	0.989218i	$-0.453214\pi$
$199$	4.13197			0.292907			0.146454	+	0.989218i	$0.453214\pi$
$200$		0			0
$201$	−5.12016	−	21.0552i	−0.361148	−	1.48512i
$202$		0			0
$203$	9.29280	+	5.36520i	0.652227	+	0.376563i
$204$		0			0
$205$	10.1721	−	9.77592i	0.710449	−	0.682780i
$206$		0			0
$207$	9.67623	−	15.0929i	0.672545	−	1.04903i
$208$		0			0
$209$	−0.768597	−	1.33125i	−0.0531650	−	0.0920845i
$210$		0			0
$211$	−1.22846	+	2.12776i	−0.0845710	+	0.146481i	−0.905208	−	0.424968i	$-0.860285\pi$
$211$	−1.22846	+	2.12776i	−0.0845710	+	0.146481i	0.820637	+	0.571449i	$0.193619\pi$
$212$		0			0
$213$	−8.67549	−	9.08861i	−0.594435	−	0.622741i
$214$		0			0
$215$	3.66289	−	0.903916i	0.249807	−	0.0616465i
$216$		0			0
$217$		−	13.6359i		−	0.925664i
$218$		0			0
$219$	2.12120	−	2.02478i	0.143337	−	0.136822i
$220$		0			0
$221$	−13.9775	+	24.2097i	−0.940226	+	1.62852i
$222$		0			0
$223$	−14.3020	+	8.25727i	−0.957733	+	0.552947i	−0.895475	−	0.445113i	$-0.853164\pi$
$223$	−14.3020	+	8.25727i	−0.957733	+	0.552947i	−0.0622584	+	0.998060i	$0.519830\pi$
$224$		0			0
$225$	−8.59074	+	12.2963i	−0.572716	+	0.819754i
$226$		0			0
$227$	2.88936	−	1.66817i	0.191773	−	0.110720i	−0.401039	−	0.916061i	$-0.631351\pi$
$227$	2.88936	−	1.66817i	0.191773	−	0.110720i	0.592813	+	0.805341i	$0.298018\pi$
$228$		0			0
$229$	4.22081	−	7.31066i	0.278919	−	0.483102i	−0.692197	−	0.721708i	$-0.743357\pi$
$229$	4.22081	−	7.31066i	0.278919	−	0.483102i	0.971116	+	0.238606i	$0.0766905\pi$
$230$		0			0
$231$	1.61819	+	6.65434i	0.106469	+	0.437823i
$232$		0			0
$233$		−	5.85320i		−	0.383456i	−0.981448	−	0.191728i	$-0.938591\pi$
$233$		−	5.85320i		−	0.383456i	0.981448	−	0.191728i	$-0.0614091\pi$
$234$		0			0
$235$	27.1176	−	6.69200i	1.76896	−	0.436538i
$236$		0			0
$237$	−1.94022	+	6.62122i	−0.126031	+	0.430095i
$238$		0			0
$239$	−1.54025	+	2.66779i	−0.0996304	+	0.172565i	−0.911532	−	0.411230i	$-0.865099\pi$
$239$	−1.54025	+	2.66779i	−0.0996304	+	0.172565i	0.811901	+	0.583795i	$0.198433\pi$
$240$		0			0
$241$	1.14795	+	1.98831i	0.0739459	+	0.128078i	0.900627	−	0.434592i	$-0.143107\pi$
$241$	1.14795	+	1.98831i	0.0739459	+	0.128078i	−0.826681	+	0.562670i	$0.809774\pi$
$242$		0			0
$243$	9.66972	+	12.2269i	0.620313	+	0.784354i
$244$		0			0
$245$	2.85712	−	2.74585i	0.182535	−	0.175426i
$246$		0			0
$247$	−4.62351	−	2.66939i	−0.294187	−	0.169849i
$248$		0			0
$249$	−6.97814	−	2.04481i	−0.442222	−	0.129585i
$250$		0			0
$251$	−2.66918			−0.168477			−0.0842387	−	0.996446i	$-0.526846\pi$
$251$	−2.66918			−0.168477			−0.0842387	+	0.996446i	$0.526846\pi$
$252$		0			0
$253$		−	10.3342i		−	0.649707i
$254$		0			0
$255$	−15.9861	+	8.33251i	−1.00109	+	0.521802i
$256$		0			0
$257$	18.9713	+	10.9531i	1.18340	+	0.683236i	0.956798	−	0.290752i	$-0.0939056\pi$
$257$	18.9713	+	10.9531i	1.18340	+	0.683236i	0.226600	+	0.973988i	$0.427239\pi$
$258$		0			0
$259$	−9.93099	−	17.2010i	−0.617082	−	1.06882i
$260$		0			0
$261$	12.5070	−	6.46516i	0.774161	−	0.400184i
$262$		0			0
$263$	21.3919	−	12.3506i	1.31908	−	0.761570i	0.335498	−	0.942041i	$-0.391095\pi$
$263$	21.3919	−	12.3506i	1.31908	−	0.761570i	0.983580	+	0.180470i	$0.0577620\pi$
$264$		0			0
$265$	−1.65389	+	5.71593i	−0.101598	+	0.351127i
$266$		0			0
$267$	−3.12010	−	3.26867i	−0.190947	−	0.200039i
$268$		0			0
$269$	−3.77073			−0.229905			−0.114953	−	0.993371i	$-0.536672\pi$
$269$	−3.77073			−0.229905			−0.114953	+	0.993371i	$0.536672\pi$
$270$		0			0
$271$	−4.44729			−0.270154			−0.135077	−	0.990835i	$-0.543128\pi$
$271$	−4.44729			−0.270154			−0.135077	+	0.990835i	$0.543128\pi$
$272$		0			0
$273$	16.4226	+	17.2046i	0.993941	+	1.04127i
$274$		0			0
$275$	−0.343285	+	8.63946i	−0.0207009	+	0.520979i
$276$		0			0
$277$	7.73881	−	4.46801i	0.464980	−	0.268456i	−0.249156	−	0.968463i	$-0.580153\pi$
$277$	7.73881	−	4.46801i	0.464980	−	0.268456i	0.714136	+	0.700007i	$0.246820\pi$
$278$		0			0
$279$	−15.0618	−	9.65629i	−0.901726	−	0.578107i
$280$		0			0
$281$	4.53764	+	7.85942i	0.270693	+	0.468854i	0.969039	−	0.246906i	$-0.0794139\pi$
$281$	4.53764	+	7.85942i	0.270693	+	0.468854i	−0.698347	+	0.715760i	$0.746081\pi$
$282$		0			0
$283$	18.4847	+	10.6722i	1.09880	+	0.634394i	0.935906	−	0.352249i	$-0.114583\pi$
$283$	18.4847	+	10.6722i	1.09880	+	0.634394i	0.162896	+	0.986643i	$0.447916\pi$
$284$		0			0
$285$	−1.59132	−	3.05299i	−0.0942619	−	0.180844i
$286$		0			0
$287$		−	14.4260i		−	0.851540i
$288$		0			0
$289$	−4.66573			−0.274455
$290$		0			0
$291$	−6.64757	−	1.94794i	−0.389687	−	0.114190i
$292$		0			0
$293$	5.36286	+	3.09625i	0.313301	+	0.180885i	0.648403	−	0.761297i	$-0.275437\pi$
$293$	5.36286	+	3.09625i	0.313301	+	0.180885i	−0.335101	+	0.942182i	$0.608771\pi$
$294$		0			0
$295$	−5.23504	+	5.03116i	−0.304796	+	0.292926i
$296$		0			0
$297$	8.49611	+	2.92488i	0.492994	+	0.169719i
$298$		0			0
$299$	−17.9457	−	31.0829i	−1.03783	−	1.79757i
$300$		0			0
$301$	1.92889	−	3.34093i	0.111179	−	0.192568i
$302$		0			0
$303$	−3.02693	+	10.3298i	−0.173893	+	0.593429i
$304$		0			0
$305$	6.52241	+	26.4304i	0.373472	+	1.51340i
$306$		0			0
$307$		−	14.8211i		−	0.845887i	−0.906156	−	0.422944i	$-0.860997\pi$
$307$		−	14.8211i		−	0.845887i	0.906156	−	0.422944i	$-0.139003\pi$
$308$		0			0
$309$	0.00237797	+	0.00977871i	0.000135278	+	0.000556291i
$310$		0			0
$311$	1.96694	−	3.40683i	0.111535	−	0.193184i	−0.804854	−	0.593472i	$-0.797757\pi$
$311$	1.96694	−	3.40683i	0.111535	−	0.193184i	0.916389	+	0.400288i	$0.131090\pi$
$312$		0			0
$313$	−15.0551	+	8.69208i	−0.850966	+	0.491305i	−0.860977	−	0.508645i	$-0.830147\pi$
$313$	−15.0551	+	8.69208i	−0.850966	+	0.491305i	0.0100110	+	0.999950i	$0.496813\pi$
$314$		0			0
$315$	2.97860	+	15.0460i	0.167825	+	0.847743i
$316$		0			0
$317$	22.0187	−	12.7125i	1.23669	−	0.714006i	0.268277	−	0.963342i	$-0.413546\pi$
$317$	22.0187	−	12.7125i	1.23669	−	0.714006i	0.968417	+	0.249336i	$0.0802125\pi$
$318$		0			0
$319$	4.05774	−	7.02821i	0.227190	−	0.393504i
$320$		0			0
$321$	5.68925	−	5.43065i	0.317543	−	0.303109i
$322$		0			0
$323$		−	4.13767i		−	0.230226i
$324$		0			0
$325$	13.9702	+	26.5815i	0.774925	+	1.47448i
$326$		0			0
$327$	−18.5761	−	19.4606i	−1.02726	−	1.07618i
$328$		0			0
$329$	14.2802	−	24.7341i	0.787294	−	1.36363i
$330$		0			0
$331$	−7.50445	−	12.9981i	−0.412482	−	0.714439i	0.582679	−	0.812703i	$-0.302005\pi$
$331$	−7.50445	−	12.9981i	−0.412482	−	0.714439i	−0.995160	+	0.0982634i	$0.968671\pi$
$332$		0			0
$333$	−26.0323	−	1.21144i	−1.42656	−	0.0663867i
$334$		0			0
$335$	−19.3841	−	20.1697i	−1.05907	−	1.10199i
$336$		0			0
$337$	−17.8677	−	10.3159i	−0.973317	−	0.561945i	−0.0730711	−	0.997327i	$-0.523280\pi$
$337$	−17.8677	−	10.3159i	−0.973317	−	0.561945i	−0.900246	+	0.435382i	$0.856613\pi$
$338$		0			0
$339$	0.687895	+	2.82877i	0.0373613	+	0.153637i
$340$		0			0
$341$	−10.3129			−0.558476
$342$		0			0
$343$		−	20.0571i		−	1.08298i
$344$		0			0
$345$	0.997445	−	23.1239i	0.0537006	−	1.24495i
$346$		0			0
$347$	−30.2610	−	17.4712i	−1.62450	−	0.937904i	−0.985696	−	0.168532i	$-0.946097\pi$
$347$	−30.2610	−	17.4712i	−1.62450	−	0.937904i	−0.638801	−	0.769372i	$-0.720569\pi$
$348$		0			0
$349$	−7.96471	−	13.7953i	−0.426341	−	0.738445i	0.570203	−	0.821504i	$-0.306864\pi$
$349$	−7.96471	−	13.7953i	−0.426341	−	0.738445i	−0.996545	+	0.0830588i	$0.973531\pi$
$350$		0			0
$351$	30.6334	−	5.95641i	1.63509	−	0.317930i
$352$		0			0
$353$	−1.48879	+	0.859556i	−0.0792405	+	0.0457495i	−0.539097	−	0.842244i	$-0.681234\pi$
$353$	−1.48879	+	0.859556i	−0.0792405	+	0.0457495i	0.459856	+	0.887993i	$0.347901\pi$
$354$		0			0
$355$	−15.5816	−	4.50850i	−0.826983	−	0.239286i
$356$		0			0
$357$	−5.18362	+	17.6897i	−0.274346	+	0.936237i
$358$		0			0
$359$	−34.6658			−1.82959			−0.914797	−	0.403915i	$-0.867649\pi$
$359$	−34.6658			−1.82959			−0.914797	+	0.403915i	$0.867649\pi$
$360$		0			0
$361$	−18.2098			−0.958410
$362$		0			0
$363$	−13.4803	+	3.27812i	−0.707533	+	0.172057i
$364$		0			0
$365$	1.05224	−	3.63659i	0.0550769	−	0.190348i
$366$		0			0
$367$	22.4914	−	12.9854i	1.17404	−	0.677834i	0.219414	−	0.975632i	$-0.429586\pi$
$367$	22.4914	−	12.9854i	1.17404	−	0.677834i	0.954629	+	0.297798i	$0.0962522\pi$
$368$		0			0
$369$	−15.9345	−	10.2158i	−0.829518	−	0.531814i
$370$		0			0
$371$	3.04223	+	5.26929i	0.157945	+	0.273568i
$372$		0			0
$373$	25.0807	+	14.4803i	1.29863	+	0.749763i	0.980167	−	0.198172i	$-0.0635006\pi$
$373$	25.0807	+	14.4803i	1.29863	+	0.749763i	0.318461	+	0.947936i	$0.396834\pi$
$374$		0			0
$375$	−1.60200	+	19.2985i	−0.0827272	+	0.996572i
$376$		0			0
$377$		−	28.1855i		−	1.45163i
$378$		0			0
$379$	22.8816			1.17535			0.587674	−	0.809098i	$-0.300044\pi$
$379$	22.8816			1.17535			0.587674	+	0.809098i	$0.300044\pi$
$380$		0			0
$381$	13.2385	−	12.6367i	0.678226	−	0.647398i
$382$		0			0
$383$	0.0595976	+	0.0344087i	0.00304529	+	0.00175820i	0.501522	−	0.865145i	$-0.332774\pi$
$383$	0.0595976	+	0.0344087i	0.00304529	+	0.00175820i	−0.498477	+	0.866903i	$0.666107\pi$
$384$		0			0
$385$	6.12623	+	6.37448i	0.312221	+	0.324874i
$386$		0			0
$387$	−2.32434	−	4.49648i	−0.118153	−	0.228569i
$388$		0			0
$389$	9.31848	+	16.1401i	0.472466	+	0.818334i	0.999504	−	0.0315074i	$-0.0100308\pi$
$389$	9.31848	+	16.1401i	0.472466	+	0.818334i	−0.527038	+	0.849842i	$0.676697\pi$
$390$		0			0
$391$	13.9083	−	24.0900i	0.703375	−	1.21828i
$392$		0			0
$393$	33.9303	−	8.25111i	1.71156	−	0.416213i
$394$		0			0
$395$	2.13411	+	8.64796i	0.107379	+	0.435126i
$396$		0			0
$397$		−	18.8002i		−	0.943554i	−0.881718	−	0.471777i	$-0.843613\pi$
$397$		−	18.8002i		−	0.943554i	0.881718	−	0.471777i	$-0.156387\pi$
$398$		0			0
$399$	−3.37834	−	0.989956i	−0.169128	−	0.0495598i
$400$		0			0
$401$	1.19535	−	2.07041i	0.0596930	−	0.103391i	−0.834635	−	0.550804i	$-0.814321\pi$
$401$	1.19535	−	2.07041i	0.0596930	−	0.103391i	0.894328	+	0.447413i	$0.147654\pi$
$402$		0			0
$403$	−31.0188	+	17.9087i	−1.54516	+	0.892096i
$404$		0			0
$405$	18.7286	+	7.36475i	0.930632	+	0.365957i
$406$		0			0
$407$	−13.0092	+	7.51088i	−0.644843	+	0.372300i
$408$		0			0
$409$	−9.65718	+	16.7267i	−0.477517	+	0.827083i	−0.999668	−	0.0257696i	$-0.991796\pi$
$409$	−9.65718	+	16.7267i	−0.477517	+	0.827083i	0.522151	+	0.852853i	$0.325130\pi$
$410$		0			0
$411$	−25.5731	−	7.49369i	−1.26143	−	0.369636i
$412$		0			0
$413$			7.42432i			0.365327i
$414$		0			0
$415$	−9.11414	+	2.24916i	−0.447395	+	0.110407i
$416$		0			0
$417$	11.7667	−	2.86141i	0.576219	−	0.140124i
$418$		0			0
$419$	−3.52444	+	6.10450i	−0.172180	+	0.298224i	−0.939182	−	0.343421i	$-0.888414\pi$
$419$	−3.52444	+	6.10450i	−0.172180	+	0.298224i	0.767002	+	0.641645i	$0.221748\pi$
$420$		0			0
$421$	−7.07655	−	12.2569i	−0.344890	−	0.597367i	0.640444	−	0.768005i	$-0.278750\pi$
$421$	−7.07655	−	12.2569i	−0.344890	−	0.597367i	−0.985334	+	0.170638i	$0.945417\pi$
$422$		0			0
$423$	−17.2079	−	33.2890i	−0.836678	−	1.61857i
$424$		0			0
$425$	−12.4277	+	19.6773i	−0.602830	+	0.954489i
$426$		0			0
$427$	24.1073	+	13.9183i	1.16663	+	0.673556i
$428$		0			0
$429$	13.0120	−	12.4205i	0.628224	−	0.599669i
$430$		0			0
$431$	0.388711			0.0187236			0.00936178	−	0.999956i	$-0.497020\pi$
$431$	0.388711			0.0187236			0.00936178	+	0.999956i	$0.497020\pi$
$432$		0			0
$433$			29.2319i			1.40479i	0.711786	+	0.702397i	$0.247887\pi$
$433$			29.2319i			1.40479i	−0.711786	+	0.702397i	$0.752113\pi$
$434$		0			0
$435$	9.75796	−	15.3347i	0.467858	−	0.735242i
$436$		0			0
$437$	4.60065	+	2.65619i	0.220079	+	0.127063i
$438$		0			0
$439$	19.5275	+	33.8226i	0.931995	+	1.61426i	0.779907	+	0.625895i	$0.215266\pi$
$439$	19.5275	+	33.8226i	0.931995	+	1.61426i	0.152088	+	0.988367i	$0.451400\pi$
$440$		0			0
$441$	−4.47567	−	2.86940i	−0.213127	−	0.136638i
$442$		0			0
$443$	−17.3321	+	10.0067i	−0.823472	+	0.475432i	−0.851612	−	0.524172i	$-0.824375\pi$
$443$	−17.3321	+	10.0067i	−0.823472	+	0.475432i	0.0281404	+	0.999604i	$0.491041\pi$
$444$		0			0
$445$	−5.60383	−	1.62146i	−0.265647	−	0.0768645i
$446$		0			0
$447$	26.4014	−	6.42025i	1.24874	−	0.303667i
$448$		0			0
$449$	23.4031			1.10446			0.552230	−	0.833692i	$-0.313777\pi$
$449$	23.4031			1.10446			0.552230	+	0.833692i	$0.313777\pi$
$450$		0			0
$451$	−10.9105			−0.513755
$452$		0			0
$453$	−2.72191	+	9.28881i	−0.127886	+	0.436427i
$454$		0			0
$455$	29.4957	+	8.53453i	1.38278	+	0.400105i
$456$		0			0
$457$	16.3691	−	9.45069i	0.765713	−	0.442084i	−0.0656303	−	0.997844i	$-0.520906\pi$
$457$	16.3691	−	9.45069i	0.765713	−	0.442084i	0.831343	+	0.555760i	$0.187572\pi$
$458$		0			0
$459$	15.8687	+	18.2527i	0.740687	+	0.851961i
$460$		0			0
$461$	9.29895	+	16.1063i	0.433095	+	0.750143i	0.997138	−	0.0756026i	$-0.0240880\pi$
$461$	9.29895	+	16.1063i	0.433095	+	0.750143i	−0.564043	+	0.825746i	$0.690755\pi$
$462$		0			0
$463$	21.7115	+	12.5352i	1.00902	+	0.582558i	0.910905	−	0.412617i	$-0.135385\pi$
$463$	21.7115	+	12.5352i	1.00902	+	0.582558i	0.0981153	+	0.995175i	$0.468719\pi$
$464$		0			0
$465$	−23.0762	−	0.995389i	−1.07013	−	0.0461601i
$466$		0			0
$467$			4.90450i			0.226953i	0.993541	+	0.113476i	$0.0361987\pi$
$467$			4.90450i			0.226953i	−0.993541	+	0.113476i	$0.963801\pi$
$468$		0			0
$469$	−28.6045			−1.32083
$470$		0			0
$471$	8.96868	+	36.8811i	0.413255	+	1.69939i
$472$		0			0
$473$	−2.52677	−	1.45883i	−0.116181	−	0.0670771i
$474$		0			0
$475$	−3.75793	−	2.37341i	−0.172426	−	0.108899i
$476$		0			0
$477$	7.97466	+	0.371110i	0.365135	+	0.0169920i
$478$		0			0
$479$	10.5302	+	18.2388i	0.481136	+	0.833353i	0.999766	−	0.0216466i	$-0.00689087\pi$
$479$	10.5302	+	18.2388i	0.481136	+	0.833353i	−0.518629	+	0.854999i	$0.673558\pi$
$480$		0			0
$481$	−26.0857	+	45.1818i	−1.18941	+	2.06011i
$482$		0			0
$483$	−16.3414	−	17.1195i	−0.743559	−	0.778966i
$484$		0			0
$485$	−8.68237	+	2.14261i	−0.394246	+	0.0972907i
$486$		0			0
$487$			31.2503i			1.41609i	0.706170	+	0.708043i	$0.250422\pi$
$487$			31.2503i			1.41609i	−0.706170	+	0.708043i	$0.749578\pi$
$488$		0			0
$489$	−28.6767	+	27.3733i	−1.29681	+	1.23786i
$490$		0			0
$491$	7.95579	−	13.7798i	0.359040	−	0.621876i	−0.628761	−	0.777599i	$-0.716437\pi$
$491$	7.95579	−	13.7798i	0.359040	−	0.621876i	0.987801	+	0.155723i	$0.0497708\pi$
$492$		0			0
$493$	18.9179	−	10.9222i	0.852018	−	0.491913i
$494$		0			0
$495$	11.3794	−	2.25274i	0.511464	−	0.101253i
$496$		0			0
$497$	−14.3640	+	8.29308i	−0.644315	+	0.371996i
$498$		0			0
$499$	12.0304	−	20.8373i	0.538556	−	0.932806i	−0.460426	−	0.887698i	$-0.652303\pi$
$499$	12.0304	−	20.8373i	0.538556	−	0.932806i	0.998982	−	0.0451079i	$-0.0143632\pi$
$500$		0			0
$501$	−1.72118	−	7.07783i	−0.0768964	−	0.316214i
$502$		0			0
$503$		−	5.52657i		−	0.246417i	−0.992381	−	0.123209i	$-0.960682\pi$
$503$		−	5.52657i		−	0.246417i	0.992381	−	0.123209i	$-0.0393185\pi$
$504$		0			0
$505$	3.32943	+	13.4917i	0.148158	+	0.600371i
$506$		0			0
$507$	11.2364	−	38.3456i	0.499027	−	1.70299i
$508$		0			0
$509$	4.57604	−	7.92593i	0.202829	−	0.351311i	−0.746610	−	0.665262i	$-0.768320\pi$
$509$	4.57604	−	7.92593i	0.202829	−	0.351311i	0.949439	+	0.313952i	$0.101653\pi$
$510$		0			0
$511$	−1.93553	−	3.35244i	−0.0856228	−	0.148303i
$512$		0			0
$513$	−3.48585	+	3.03057i	−0.153904	+	0.133803i
$514$		0			0
$515$	0.00900263	+	0.00936745i	0.000396703	+	0.000412779i
$516$		0			0
$517$	−18.7065	−	10.8002i	−0.822713	−	0.474994i
$518$		0			0
$519$	13.6322	+	3.99466i	0.598389	+	0.175346i
$520$		0			0
$521$	28.6259			1.25412			0.627061	−	0.778970i	$-0.284258\pi$
$521$	28.6259			1.25412			0.627061	+	0.778970i	$0.284258\pi$
$522$		0			0
$523$		−	8.60074i		−	0.376084i	−0.982161	−	0.188042i	$-0.939786\pi$
$523$		−	8.60074i		−	0.376084i	0.982161	−	0.188042i	$-0.0602141\pi$
$524$		0			0
$525$	13.0928	+	14.8548i	0.571416	+	0.648319i
$526$		0			0
$527$	−24.0403	−	13.8797i	−1.04721	−	0.604608i
$528$		0			0
$529$	6.35695	+	11.0106i	0.276389	+	0.478720i
$530$		0			0
$531$	8.20067	+	5.25755i	0.355879	+	0.228158i
$532$		0			0
$533$	−32.8161	+	18.9464i	−1.42142	+	0.820660i
$534$		0			0
$535$	2.82221	−	9.75369i	0.122015	−	0.421689i
$536$		0			0
$537$	−26.8313	−	28.1090i	−1.15786	−	1.21299i
$538$		0			0
$539$	−3.06452			−0.131998
$540$		0			0
$541$	14.2900			0.614377			0.307188	−	0.951649i	$-0.400612\pi$
$541$	14.2900			0.614377			0.307188	+	0.951649i	$0.400612\pi$
$542$		0			0
$543$	24.3771	+	25.5379i	1.04612	+	1.09594i
$544$		0			0
$545$	−33.3634	−	9.65366i	−1.42913	−	0.413517i
$546$		0			0
$547$	−14.4638	+	8.35071i	−0.618429	+	0.357050i	−0.776257	−	0.630416i	$-0.782884\pi$
$547$	−14.4638	+	8.35071i	−0.618429	+	0.357050i	0.157828	+	0.987467i	$0.449551\pi$
$548$		0			0
$549$	32.4454	−	16.7718i	1.38474	−	0.715805i
$550$		0			0
$551$	2.08591	+	3.61289i	0.0888626	+	0.153914i
$552$		0			0
$553$	7.88783	+	4.55404i	0.335425	+	0.193657i
$554$		0			0
$555$	−29.8344	+	15.5507i	−1.26640	+	0.660091i
$556$		0			0
$557$		−	5.13418i		−	0.217542i	−0.994067	−	0.108771i	$-0.965308\pi$
$557$		−	5.13418i		−	0.217542i	0.994067	−	0.108771i	$-0.0346915\pi$
$558$		0			0
$559$	−10.1332			−0.428590
$560$		0			0
$561$	13.3788	+	3.92041i	0.564855	+	0.165520i
$562$		0			0
$563$	1.22820	+	0.709103i	0.0517625	+	0.0298851i	0.525658	−	0.850696i	$-0.323819\pi$
$563$	1.22820	+	0.709103i	0.0517625	+	0.0298851i	−0.473895	+	0.880581i	$0.657153\pi$
$564$		0			0
$565$	2.60426	+	2.70980i	0.109562	+	0.114002i
$566$		0			0
$567$	18.6996	−	8.58948i	0.785310	−	0.360724i
$568$		0			0
$569$	4.08734	+	7.07948i	0.171350	+	0.296787i	0.938892	−	0.344211i	$-0.111854\pi$
$569$	4.08734	+	7.07948i	0.171350	+	0.296787i	−0.767542	+	0.640999i	$0.778520\pi$
$570$		0			0
$571$	−13.0685	+	22.6352i	−0.546898	+	0.947255i	0.451587	+	0.892227i	$0.350858\pi$
$571$	−13.0685	+	22.6352i	−0.546898	+	0.947255i	−0.998485	+	0.0550277i	$0.982475\pi$
$572$		0			0
$573$	12.6899	−	43.3057i	0.530128	−	1.80912i
$574$		0			0
$575$	−13.9011	−	26.4501i	−0.579715	−	1.10305i
$576$		0			0
$577$			15.8687i			0.660622i	0.943872	+	0.330311i	$0.107154\pi$
$577$			15.8687i			0.660622i	−0.943872	+	0.330311i	$0.892846\pi$
$578$		0			0
$579$	5.19683	+	21.3705i	0.215973	+	0.888126i
$580$		0			0
$581$	−4.79953	+	8.31303i	−0.199118	+	0.344882i
$582$		0			0
$583$	3.98520	−	2.30086i	0.165050	−	0.0952918i
$584$		0			0
$585$	30.3144	−	26.5363i	1.25335	−	1.09714i
$586$		0			0
$587$	−15.5489	+	8.97715i	−0.641771	+	0.370527i	−0.785296	−	0.619120i	$-0.787489\pi$
$587$	−15.5489	+	8.97715i	−0.641771	+	0.370527i	0.143526	+	0.989647i	$0.454156\pi$
$588$		0			0
$589$	2.65071	−	4.59116i	0.109221	−	0.189176i
$590$		0			0
$591$	8.51949	−	8.13225i	0.350445	−	0.334516i
$592$		0			0
$593$			0.875924i			0.0359699i	0.999838	+	0.0179849i	$0.00572510\pi$
$593$			0.875924i			0.0359699i	−0.999838	+	0.0179849i	$0.994275\pi$
$594$		0			0
$595$	5.70164	+	23.1045i	0.233744	+	0.947190i
$596$		0			0
$597$	−4.94158	−	5.17689i	−0.202246	−	0.211876i
$598$		0			0
$599$	8.16182	−	14.1367i	0.333483	−	0.577609i	−0.649709	−	0.760183i	$-0.725109\pi$
$599$	8.16182	−	14.1367i	0.333483	−	0.577609i	0.983192	+	0.182573i	$0.0584427\pi$
$600$		0			0
$601$	7.79862	+	13.5076i	0.318112	+	0.550987i	0.980094	−	0.198533i	$-0.0636178\pi$
$601$	7.79862	+	13.5076i	0.318112	+	0.550987i	−0.661982	+	0.749520i	$0.730284\pi$
$602$		0			0
$603$	−20.2564	+	31.5957i	−0.824903	+	1.28668i
$604$		0			0
$605$	−12.9134	+	12.4105i	−0.525003	+	0.504557i
$606$		0			0
$607$	11.2066	+	6.47016i	0.454864	+	0.262616i	0.709882	−	0.704321i	$-0.248748\pi$
$607$	11.2066	+	6.47016i	0.454864	+	0.262616i	−0.255018	+	0.966936i	$0.582082\pi$
$608$		0			0
$609$	−4.39163	−	18.0593i	−0.177958	−	0.731799i
$610$		0			0
$611$	−75.0197			−3.03497
$612$		0			0
$613$		−	1.16228i		−	0.0469439i	−0.999724	−	0.0234719i	$-0.992528\pi$
$613$		−	1.16228i		−	0.0469439i	0.999724	−	0.0234719i	$-0.00747204\pi$
$614$		0			0
$615$	−24.4133	−	1.05307i	−0.984441	−	0.0424637i
$616$		0			0
$617$	15.9879	+	9.23060i	0.643647	+	0.371610i	0.786018	−	0.618203i	$-0.212139\pi$
$617$	15.9879	+	9.23060i	0.643647	+	0.371610i	−0.142371	+	0.989813i	$0.545473\pi$
$618$		0			0
$619$	18.0563	+	31.2744i	0.725742	+	1.25702i	0.958668	+	0.284528i	$0.0918369\pi$
$619$	18.0563	+	31.2744i	0.725742	+	1.25702i	−0.232925	+	0.972495i	$0.574830\pi$
$620$		0			0
$621$	−30.4819	+	5.92696i	−1.22320	+	0.237841i
$622$		0			0
$623$	−5.16595	+	2.98256i	−0.206970	+	0.119494i
$624$		0			0
$625$	10.7427	+	22.5742i	0.429710	+	0.902967i
$626$		0			0
$627$	−0.748711	+	2.55506i	−0.0299006	+	0.102039i
$628$		0			0
$629$	−40.4341			−1.61221
$630$		0			0
$631$	40.6445			1.61803			0.809017	−	0.587786i	$-0.200000\pi$
$631$	40.6445			1.61803			0.809017	+	0.587786i	$0.200000\pi$
$632$		0			0
$633$	4.13502	−	1.00555i	0.164352	−	0.0399669i
$634$		0			0
$635$	6.56707	−	22.6961i	0.260606	−	0.900666i
$636$		0			0
$637$	−9.21734	+	5.32164i	−0.365204	+	0.210851i
$638$		0			0
$639$	−1.01164	+	21.7388i	−0.0400200	+	0.859976i
$640$		0			0
$641$	−12.2380	−	21.1968i	−0.483371	−	0.837223i	0.516447	−	0.856319i	$-0.327254\pi$
$641$	−12.2380	−	21.1968i	−0.483371	−	0.837223i	−0.999818	+	0.0190966i	$0.993921\pi$
$642$		0			0
$643$	7.99487	+	4.61584i	0.315287	+	0.182031i	0.649290	−	0.760541i	$-0.275066\pi$
$643$	7.99487	+	4.61584i	0.315287	+	0.182031i	−0.334003	+	0.942572i	$0.608400\pi$
$644$		0			0
$645$	−5.51310	−	3.50816i	−0.217078	−	0.138134i
$646$		0			0
$647$			20.0509i			0.788282i	0.919050	+	0.394141i	$0.128958\pi$
$647$			20.0509i			0.788282i	−0.919050	+	0.394141i	$0.871042\pi$
$648$		0			0
$649$	5.61506			0.220411
$650$		0			0
$651$	−17.0842	+	16.3077i	−0.669584	+	0.639149i
$652$		0			0
$653$	−27.0382	−	15.6105i	−1.05809	−	0.610887i	−0.133185	−	0.991091i	$-0.542520\pi$
$653$	−27.0382	−	15.6105i	−1.05809	−	0.610887i	−0.924903	+	0.380204i	$0.875854\pi$
$654$		0			0
$655$	32.5033	−	31.2374i	1.27001	−	1.22055i
$656$		0			0
$657$	−5.07365	−	0.236108i	−0.197942	−	0.00921145i
$658$		0			0
$659$	21.6530	+	37.5041i	0.843480	+	1.46095i	0.886934	+	0.461895i	$0.152830\pi$
$659$	21.6530	+	37.5041i	0.843480	+	1.46095i	−0.0434542	+	0.999055i	$0.513836\pi$
$660$		0			0
$661$	17.2404	−	29.8612i	0.670573	−	1.16147i	−0.307168	−	0.951655i	$-0.599381\pi$
$661$	17.2404	−	29.8612i	0.670573	−	1.16147i	0.977742	−	0.209812i	$-0.0672852\pi$
$662$		0			0
$663$	47.0482	−	11.4411i	1.82720	−	0.444336i
$664$		0			0
$665$	−4.41244	+	1.08889i	−0.171107	+	0.0422252i
$666$		0			0
$667$			28.0462i			1.08595i
$668$		0			0
$669$	27.4498	+	8.04362i	1.06127	+	0.310984i
$670$		0			0
$671$	10.5265	−	18.2325i	0.406372	−	0.703858i
$672$		0			0
$673$	−26.2234	+	15.1401i	−1.01084	+	0.583606i	−0.911436	−	0.411441i	$-0.865026\pi$
$673$	−26.2234	+	15.1401i	−1.01084	+	0.583606i	−0.0993997	+	0.995048i	$0.531692\pi$
$674$		0			0
$675$	25.6799	−	3.94241i	0.988420	−	0.151743i
$676$		0			0
$677$	8.03094	−	4.63666i	0.308654	−	0.178201i	−0.337670	−	0.941265i	$-0.609639\pi$
$677$	8.03094	−	4.63666i	0.308654	−	0.178201i	0.646324	+	0.763063i	$0.276305\pi$
$678$		0			0
$679$	−4.57216	+	7.91921i	−0.175463	+	0.303912i
$680$		0			0
$681$	−5.54553	−	1.62501i	−0.212505	−	0.0622705i
$682$		0			0
$683$		−	18.0856i		−	0.692028i	−0.938229	−	0.346014i	$-0.887535\pi$
$683$		−	18.0856i		−	0.692028i	0.938229	−	0.346014i	$-0.112465\pi$
$684$		0			0
$685$	−33.4009	+	8.24256i	−1.27618	+	0.314932i
$686$		0			0
$687$	−14.2073	+	3.45490i	−0.542041	+	0.131813i
$688$		0			0
$689$	7.99102	−	13.8409i	0.304434	−	0.527295i
$690$		0			0
$691$	−20.7805	−	35.9928i	−0.790527	−	1.36923i	−0.925641	−	0.378402i	$-0.876474\pi$
$691$	−20.7805	−	35.9928i	−0.790527	−	1.36923i	0.135114	−	0.990830i	$-0.456860\pi$
$692$		0			0
$693$	6.40189	−	9.98560i	0.243188	−	0.379322i
$694$		0			0
$695$	11.2719	−	10.8329i	0.427566	−	0.410914i
$696$		0			0
$697$	−25.4333	−	14.6839i	−0.963354	−	0.556193i
$698$		0			0
$699$	−7.33340	+	7.00007i	−0.277375	+	0.264767i
$700$		0			0
$701$	23.4059			0.884030			0.442015	−	0.897008i	$-0.354264\pi$
$701$	23.4059			0.884030			0.442015	+	0.897008i	$0.354264\pi$
$702$		0			0
$703$		−	7.72203i		−	0.291242i
$704$		0			0
$705$	−40.8154	−	25.9721i	−1.53720	−	0.978167i
$706$		0			0
$707$	12.3058	+	7.10475i	0.462807	+	0.267201i
$708$		0			0
$709$	−4.93075	−	8.54030i	−0.185178	−	0.320738i	0.758458	−	0.651721i	$-0.225953\pi$
$709$	−4.93075	−	8.54030i	−0.185178	−	0.320738i	−0.943637	+	0.330984i	$0.892620\pi$
$710$		0			0
$711$	10.6160	−	5.48770i	0.398132	−	0.205805i
$712$		0			0
$713$	30.8654	−	17.8201i	1.15592	−	0.667369i
$714$		0			0
$715$	6.45473	−	22.3078i	0.241393	−	0.834264i
$716$		0			0
$717$	5.18449	−	1.26075i	0.193618	−	0.0470837i
$718$		0			0
$719$	7.32159			0.273049			0.136525	−	0.990637i	$-0.456407\pi$
$719$	7.32159			0.273049			0.136525	+	0.990637i	$0.456407\pi$
$720$		0			0
$721$	0.0132849			0.000494755
$722$		0			0
$723$	1.11825	−	3.81615i	0.0415881	−	0.141924i
$724$		0			0
$725$	0.931646	−	23.4467i	0.0346005	−	0.870790i
$726$		0			0
$727$	31.1998	−	18.0132i	1.15714	−	0.668073i	0.206521	−	0.978442i	$-0.433786\pi$
$727$	31.1998	−	18.0132i	1.15714	−	0.668073i	0.950616	+	0.310369i	$0.100453\pi$
$728$		0			0
$729$	3.75450	−	26.7377i	0.139056	−	0.990285i
$730$		0			0
$731$	−3.92674	−	6.80132i	−0.145236	−	0.251556i
$732$		0			0
$733$	24.8324	+	14.3370i	0.917207	+	0.529550i	0.882743	−	0.469856i	$-0.155694\pi$
$733$	24.8324	+	14.3370i	0.917207	+	0.529550i	0.0344639	+	0.999406i	$0.489028\pi$
$734$		0			0
$735$	−6.85718	−	0.295783i	−0.252931	−	0.0109101i
$736$		0			0
$737$			21.6338i			0.796892i
$738$		0			0
$739$	−34.2481			−1.25984			−0.629918	−	0.776662i	$-0.716912\pi$
$739$	−34.2481			−1.25984			−0.629918	+	0.776662i	$0.716912\pi$
$740$		0			0
$741$	2.18500	+	8.98517i	0.0802679	+	0.330078i
$742$		0			0
$743$	−0.562189	−	0.324580i	−0.0206247	−	0.0119077i	0.489652	−	0.871918i	$-0.337124\pi$
$743$	−0.562189	−	0.324580i	−0.0206247	−	0.0119077i	−0.510277	+	0.860010i	$0.670457\pi$
$744$		0			0
$745$	25.2910	−	24.3061i	0.926592	−	0.890506i
$746$		0			0
$747$	5.78352	+	11.1883i	0.211608	+	0.409359i
$748$		0			0
$749$	−5.19127	−	8.99155i	−0.189685	−	0.328544i
$750$		0			0
$751$	−6.93481	+	12.0114i	−0.253055	+	0.438304i	−0.964365	−	0.264574i	$-0.914769\pi$
$751$	−6.93481	+	12.0114i	−0.253055	+	0.438304i	0.711311	+	0.702878i	$0.248102\pi$
$752$		0			0
$753$	3.19218	+	3.34419i	0.116330	+	0.121869i
$754$		0			0
$755$	2.99392	+	12.1321i	0.108960	+	0.441532i
$756$		0			0
$757$			9.30142i			0.338066i	0.985610	+	0.169033i	$0.0540644\pi$
$757$			9.30142i			0.338066i	−0.985610	+	0.169033i	$0.945936\pi$
$758$		0			0
$759$	−12.9476	+	12.3591i	−0.469969	+	0.448607i
$760$		0			0
$761$	13.4133	−	23.2326i	0.486233	−	0.842181i	−0.513642	−	0.858005i	$-0.671704\pi$
$761$	13.4133	−	23.2326i	0.486233	−	0.842181i	0.999875	+	0.0158243i	$0.00503723\pi$
$762$		0			0
$763$	−30.7565	+	17.7573i	−1.11346	+	0.642856i
$764$		0			0
$765$	29.5581	+	10.0636i	1.06868	+	0.363851i
$766$		0			0
$767$	16.8888	−	9.75073i	0.609818	−	0.352078i
$768$		0			0
$769$	19.1864	−	33.2317i	0.691878	−	1.19837i	−0.279344	−	0.960191i	$-0.590117\pi$
$769$	19.1864	−	33.2317i	0.691878	−	1.19837i	0.971222	−	0.238176i	$-0.0765495\pi$
$770$		0			0
$771$	−8.96555	−	36.8682i	−0.322886	−	1.32778i
$772$		0			0
$773$			41.6235i			1.49709i	0.663082	+	0.748546i	$0.269248\pi$
$773$			41.6235i			1.49709i	−0.663082	+	0.748546i	$0.730752\pi$
$774$		0			0
$775$	−26.3956	+	13.8724i	−0.948157	+	0.498312i
$776$		0			0
$777$	−9.67404	+	33.0138i	−0.347054	+	1.18436i
$778$		0			0
$779$	2.80430	−	4.85719i	0.100475	−	0.174027i
$780$		0			0
$781$	6.27212	+	10.8636i	0.224434	+	0.388731i
$782$		0			0
$783$	−23.0577	−	7.93787i	−0.824014	−	0.283676i
$784$		0			0
$785$	33.9541	+	35.3300i	1.21187	+	1.26098i
$786$		0			0
$787$	18.1836	+	10.4983i	0.648177	+	0.374225i	0.787757	−	0.615986i	$-0.211242\pi$
$787$	18.1836	+	10.4983i	0.648177	+	0.374225i	−0.139581	+	0.990211i	$0.544575\pi$
$788$		0			0
$789$	−41.0573	−	12.0310i	−1.46168	−	0.428317i
$790$		0			0
$791$	3.84303			0.136642
$792$		0			0
$793$		−	73.1186i		−	2.59652i
$794$		0			0
$795$	9.13937	−	4.76376i	0.324140	−	0.168953i
$796$		0			0
$797$	−1.31920	−	0.761643i	−0.0467286	−	0.0269788i	0.476454	−	0.879200i	$-0.341922\pi$
$797$	−1.31920	−	0.761643i	−0.0467286	−	0.0269788i	−0.523182	+	0.852221i	$0.675255\pi$
$798$		0			0
$799$	−29.0710	−	50.3525i	−1.02846	−	1.78134i
$800$		0			0
$801$	−0.363832	+	7.81826i	−0.0128554	+	0.276245i
$802$		0			0
$803$	−2.53547	+	1.46386i	−0.0894749	+	0.0516583i
$804$		0			0
$805$	−29.3498	−	8.49233i	−1.03445	−	0.299315i
$806$		0			0
$807$	4.50956	+	4.72430i	0.158744	+	0.166303i
$808$		0			0
$809$	−35.7106			−1.25552			−0.627758	−	0.778408i	$-0.716027\pi$
$809$	−35.7106			−1.25552			−0.627758	+	0.778408i	$0.716027\pi$
$810$		0			0
$811$	30.3963			1.06736			0.533679	−	0.845687i	$-0.320809\pi$
$811$	30.3963			1.06736			0.533679	+	0.845687i	$0.320809\pi$
$812$		0			0
$813$	5.31869	+	5.57196i	0.186535	+	0.195417i
$814$		0			0
$815$	−14.2254	+	49.1636i	−0.498294	+	1.72212i
$816$		0			0
$817$	1.29890	−	0.749921i	0.0454428	−	0.0262364i
$818$		0			0
$819$	1.91503	−	41.1514i	0.0669164	−	1.43794i
$820$		0			0
$821$	−3.00587	−	5.20632i	−0.104906	−	0.181702i	0.808794	−	0.588092i	$-0.200121\pi$
$821$	−3.00587	−	5.20632i	−0.104906	−	0.181702i	−0.913700	+	0.406390i	$0.866787\pi$
$822$		0			0
$823$	−29.2509	−	16.8880i	−1.01962	−	0.588680i	−0.105629	−	0.994406i	$-0.533686\pi$
$823$	−29.2509	−	16.8880i	−1.01962	−	0.588680i	−0.913995	+	0.405726i	$0.867019\pi$
$824$		0			0
$825$	11.2348	−	9.90217i	0.391146	−	0.344749i
$826$		0			0
$827$		−	3.36732i		−	0.117093i	−0.998285	−	0.0585466i	$-0.981353\pi$
$827$		−	3.36732i		−	0.117093i	0.998285	−	0.0585466i	$-0.0186466\pi$
$828$		0			0
$829$	−6.57350			−0.228307			−0.114154	−	0.993463i	$-0.536416\pi$
$829$	−6.57350			−0.228307			−0.114154	+	0.993463i	$0.536416\pi$
$830$		0			0
$831$	−14.8531	−	4.35240i	−0.515247	−	0.150983i
$832$		0			0
$833$	−7.14366	−	4.12439i	−0.247513	−	0.142902i
$834$		0			0
$835$	−6.51610	−	6.78016i	−0.225499	−	0.234637i
$836$		0			0
$837$	5.91474	+	30.4191i	0.204443	+	1.05144i
$838$		0			0
$839$	−2.40071	−	4.15814i	−0.0828816	−	0.143555i	0.821605	−	0.570057i	$-0.193079\pi$
$839$	−2.40071	−	4.15814i	−0.0828816	−	0.143555i	−0.904487	+	0.426502i	$0.859746\pi$
$840$		0			0
$841$	3.48766	−	6.04080i	0.120264	−	0.208303i
$842$		0			0
$843$	4.42023	−	15.0845i	0.152241	−	0.519539i
$844$		0			0
$845$	−12.3593	−	50.0831i	−0.425174	−	1.72291i
$846$		0			0
$847$			18.3137i			0.629266i
$848$		0			0
$849$	−8.73559	−	35.9225i	−0.299805	−	1.23286i
$850$		0			0
$851$	25.9567	−	44.9584i	0.889786	−	1.54115i
$852$		0			0
$853$	−13.0511	+	7.53504i	−0.446860	+	0.257995i	−0.706503	−	0.707710i	$-0.749728\pi$
$853$	−13.0511	+	7.53504i	−0.446860	+	0.257995i	0.259643	+	0.965705i	$0.416395\pi$
$854$		0			0
$855$	−1.92193	+	5.64494i	−0.0657286	+	0.193053i
$856$		0			0
$857$	−27.8833	+	16.0984i	−0.952476	+	0.549912i	−0.893849	−	0.448368i	$-0.852006\pi$
$857$	−27.8833	+	16.0984i	−0.952476	+	0.549912i	−0.0586268	+	0.998280i	$0.518672\pi$
$858$		0			0
$859$	−14.4187	+	24.9740i	−0.491961	+	0.852102i	−0.999957	−	0.00925765i	$-0.997053\pi$
$859$	−14.4187	+	24.9740i	−0.491961	+	0.852102i	0.507996	+	0.861359i	$0.330386\pi$
$860$		0			0
$861$	−18.0742	+	17.2526i	−0.615966	+	0.587968i
$862$		0			0
$863$			19.7667i			0.672866i	0.941707	+	0.336433i	$0.109221\pi$
$863$			19.7667i			0.672866i	−0.941707	+	0.336433i	$0.890779\pi$
$864$		0			0
$865$	17.8050	−	4.39387i	0.605390	−	0.149396i
$866$		0			0
$867$	5.57993	+	5.84563i	0.189504	+	0.198528i
$868$		0			0
$869$	3.44425	−	5.96562i	0.116838	−	0.202370i
$870$		0			0
$871$	37.5678	+	65.0693i	1.27294	+	2.20479i
$872$		0			0
$873$	5.50954	+	10.6583i	0.186470	+	0.360728i
$874$		0			0
$875$	24.2545	+	8.07458i	0.819952	+	0.272971i
$876$		0			0
$877$	17.7188	+	10.2300i	0.598322	+	0.345441i	0.768381	−	0.639993i	$-0.221063\pi$
$877$	17.7188	+	10.2300i	0.598322	+	0.345441i	−0.170059	+	0.985434i	$0.554396\pi$
$878$		0			0
$879$	−2.53440	−	10.4220i	−0.0854832	−	0.351525i
$880$		0			0
$881$	−20.4830			−0.690090			−0.345045	−	0.938586i	$-0.612136\pi$
$881$	−20.4830			−0.690090			−0.345045	+	0.938586i	$0.612136\pi$
$882$		0			0
$883$		−	45.9847i		−	1.54751i	−0.633486	−	0.773754i	$-0.718376\pi$
$883$		−	45.9847i		−	1.54751i	0.633486	−	0.773754i	$-0.281624\pi$
$884$		0			0
$885$	12.5643	+	0.541958i	0.422344	+	0.0182177i
$886$		0			0
$887$	8.92804	+	5.15461i	0.299774	+	0.173075i	0.642341	−	0.766419i	$-0.277963\pi$
$887$	8.92804	+	5.15461i	0.299774	+	0.173075i	−0.342567	+	0.939493i	$0.611296\pi$
$888$		0			0
$889$	−12.0797	−	20.9226i	−0.405140	−	0.701723i
$890$		0			0
$891$	−6.49628	−	14.1427i	−0.217634	−	0.473797i
$892$		0			0
$893$	9.61621	−	5.55192i	0.321794	−	0.185788i
$894$		0			0
$895$	−48.1902	−	13.9438i	−1.61082	−	0.466089i
$896$		0			0
$897$	−17.4814	+	59.6572i	−0.583686	+	1.99189i
$898$		0			0
$899$	27.9884			0.933464
$900$		0			0
$901$	12.3865			0.412653
$902$		0			0
$903$	−6.49265	+	1.57887i	−0.216062	+	0.0525416i
$904$		0			0
$905$	43.7824	+	12.6684i	1.45537	+	0.421110i
$906$		0			0
$907$	−25.4011	+	14.6653i	−0.843428	+	0.486953i	−0.858428	−	0.512934i	$-0.828559\pi$
$907$	−25.4011	+	14.6653i	−0.843428	+	0.486953i	0.0149999	+	0.999887i	$0.495225\pi$
$908$		0			0
$909$	16.5621	−	8.56135i	0.549329	−	0.283962i
$910$		0			0
$911$	9.03057	+	15.6414i	0.299196	+	0.518223i	0.975952	−	0.217984i	$-0.0699482\pi$
$911$	9.03057	+	15.6414i	0.299196	+	0.518223i	−0.676756	+	0.736207i	$0.736615\pi$
$912$		0			0
$913$	6.28720	+	3.62992i	0.208076	+	0.120133i
$914$		0			0
$915$	25.3140	−	39.7811i	0.836854	−	1.31512i
$916$		0			0
$917$		−	46.0960i		−	1.52223i
$918$		0			0
$919$	6.69380			0.220808			0.110404	−	0.993887i	$-0.464786\pi$
$919$	6.69380			0.220808			0.110404	+	0.993887i	$0.464786\pi$
$920$		0			0
$921$	−18.5692	+	17.7252i	−0.611877	+	0.584065i
$922$		0			0
$923$	37.7300	+	21.7834i	1.24190	+	0.717011i
$924$		0			0
$925$	−23.1934	+	36.7232i	−0.762594	+	1.20745i
$926$		0			0
$927$	0.00940772	−	0.0146741i	0.000308990	−	0.000481960i
$928$		0			0
$929$	−9.17475	−	15.8911i	−0.301014	−	0.521371i	0.675352	−	0.737495i	$-0.263992\pi$
$929$	−9.17475	−	15.8911i	−0.301014	−	0.521371i	−0.976366	+	0.216124i	$0.930658\pi$
$930$		0			0
$931$	0.787668	−	1.36428i	0.0258148	−	0.0447125i
$932$		0			0
$933$	−6.62072	+	1.61002i	−0.216753	+	0.0527096i
$934$		0			0
$935$	17.4741	−	4.31219i	0.571463	−	0.141024i
$936$		0			0
$937$		−	5.15287i		−	0.168337i	−0.996452	−	0.0841684i	$-0.973177\pi$
$937$		−	5.15287i		−	0.168337i	0.996452	−	0.0841684i	$-0.0268234\pi$
$938$		0			0
$939$	28.8952	+	8.46718i	0.942959	+	0.276316i
$940$		0			0
$941$	−12.2567	+	21.2293i	−0.399557	+	0.692054i	−0.993671	−	0.112327i	$-0.964170\pi$
$941$	−12.2567	+	21.2293i	−0.399557	+	0.692054i	0.594114	+	0.804381i	$0.297503\pi$
$942$		0			0
$943$	32.6539	−	18.8527i	1.06336	−	0.613929i
$944$		0			0
$945$	15.2887	−	21.7259i	0.497340	−	0.706744i
$946$		0			0
$947$	−45.6887	+	26.3784i	−1.48468	+	0.857183i	−0.999848	−	0.0174217i	$-0.994454\pi$
$947$	−45.6887	+	26.3784i	−1.48468	+	0.857183i	−0.484836	+	0.874605i	$0.661121\pi$
$948$		0			0
$949$	−5.08406	+	8.80585i	−0.165036	+	0.285850i
$950$		0			0
$951$	−42.2604	−	12.3836i	−1.37039	−	0.401565i
$952$		0			0
$953$		−	43.2040i		−	1.39952i	−0.714380	−	0.699758i	$-0.753291\pi$
$953$		−	43.2040i		−	1.39952i	0.714380	−	0.699758i	$-0.246709\pi$
$954$		0			0
$955$	−13.9581	−	56.5615i	−0.451672	−	1.83029i
$956$		0			0
$957$	−13.6584	+	3.32142i	−0.441512	+	0.107366i
$958$		0			0
$959$	−17.5890	+	30.4651i	−0.567979	+	0.983768i
$960$		0			0
$961$	−2.28340	−	3.95497i	−0.0736582	−	0.127580i
$962$		0			0
$963$	−13.6080	−	0.633264i	−0.438512	−	0.0204066i
$964$		0			0
$965$	19.6744	+	20.4717i	0.633342	+	0.659007i
$966$		0			0
$967$	−21.2701	−	12.2803i	−0.683999	−	0.394907i	0.117361	−	0.993089i	$-0.462557\pi$
$967$	−21.2701	−	12.2803i	−0.683999	−	0.394907i	−0.801360	+	0.598182i	$0.795890\pi$
$968$		0			0
$969$	−5.18404	+	4.94841i	−0.166535	+	0.158966i
$970$		0			0
$971$	−28.9959			−0.930524			−0.465262	−	0.885173i	$-0.654040\pi$
$971$	−28.9959			−0.930524			−0.465262	+	0.885173i	$0.654040\pi$
$972$		0			0
$973$		−	15.9857i		−	0.512478i
$974$		0			0
$975$	16.5962	−	49.2930i	0.531505	−	1.57864i
$976$		0			0
$977$	33.8566	+	19.5471i	1.08317	+	0.625368i	0.931750	−	0.363101i	$-0.118282\pi$
$977$	33.8566	+	19.5471i	1.08317	+	0.625368i	0.151420	+	0.988469i	$0.451615\pi$
$978$		0			0
$979$	2.25573	+	3.90705i	0.0720936	+	0.124870i
$980$		0			0
$981$	−2.16614	+	46.5475i	−0.0691596	+	1.48615i
$982$		0			0
$983$	3.60163	−	2.07940i	0.114874	−	0.0663227i	−0.441462	−	0.897280i	$-0.645540\pi$
$983$	3.60163	−	2.07940i	0.114874	−	0.0663227i	0.556336	+	0.830957i	$0.312207\pi$
$984$		0			0
$985$	4.22618	−	14.6059i	0.134657	−	0.465382i
$986$		0			0
$987$	−48.0673	+	11.6889i	−1.53000	+	0.372063i
$988$		0			0
$989$	10.0831			0.320624
$990$		0			0
$991$	−9.79485			−0.311144			−0.155572	−	0.987825i	$-0.549722\pi$
$991$	−9.79485			−0.311144			−0.155572	+	0.987825i	$0.549722\pi$
$992$		0			0
$993$	−7.31028	+	24.9471i	−0.231985	+	0.791674i
$994$		0			0
$995$	−8.87530	−	2.56805i	−0.281366	−	0.0814128i
$996$		0			0
$997$	−4.98551	+	2.87839i	−0.157893	+	0.0911594i	−0.576865	−	0.816840i	$-0.695724\pi$
$997$	−4.98551	+	2.87839i	−0.157893	+	0.0911594i	0.418972	+	0.907999i	$0.362391\pi$
$998$		0			0
$999$	29.6153	+	34.0644i	0.936986	+	1.07775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.49.5	✓	32
3.2	odd	2		1080.2.bi.b.1009.14		32
4.3	odd	2		720.2.by.f.49.12		32
5.4	even	2	inner	360.2.bi.b.49.12	yes	32
9.2	odd	6		1080.2.bi.b.289.2		32
9.4	even	3		3240.2.f.k.649.8		16
9.5	odd	6		3240.2.f.i.649.9		16
9.7	even	3	inner	360.2.bi.b.169.12	yes	32
12.11	even	2		2160.2.by.f.1009.14		32
15.14	odd	2		1080.2.bi.b.1009.2		32
20.19	odd	2		720.2.by.f.49.5		32
36.7	odd	6		720.2.by.f.529.5		32
36.11	even	6		2160.2.by.f.289.2		32
45.4	even	6		3240.2.f.k.649.7		16
45.14	odd	6		3240.2.f.i.649.10		16
45.29	odd	6		1080.2.bi.b.289.14		32
45.34	even	6	inner	360.2.bi.b.169.5	yes	32
60.59	even	2		2160.2.by.f.1009.2		32
180.79	odd	6		720.2.by.f.529.12		32
180.119	even	6		2160.2.by.f.289.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.5	✓	32	1.1	even	1	trivial
360.2.bi.b.49.12	yes	32	5.4	even	2	inner
360.2.bi.b.169.5	yes	32	45.34	even	6	inner
360.2.bi.b.169.12	yes	32	9.7	even	3	inner
720.2.by.f.49.5		32	20.19	odd	2
720.2.by.f.49.12		32	4.3	odd	2
720.2.by.f.529.5		32	36.7	odd	6
720.2.by.f.529.12		32	180.79	odd	6
1080.2.bi.b.289.2		32	9.2	odd	6
1080.2.bi.b.289.14		32	45.29	odd	6
1080.2.bi.b.1009.2		32	15.14	odd	2
1080.2.bi.b.1009.14		32	3.2	odd	2
2160.2.by.f.289.2		32	36.11	even	6
2160.2.by.f.289.14		32	180.119	even	6
2160.2.by.f.1009.2		32	60.59	even	2
2160.2.by.f.1009.14		32	12.11	even	2
3240.2.f.i.649.9		16	9.5	odd	6
3240.2.f.i.649.10		16	45.14	odd	6
3240.2.f.k.649.7		16	45.4	even	6
3240.2.f.k.649.8		16	9.4	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19594 - 1.25289i) q^{3} +(-2.14796 - 0.621508i) q^{5} +(-1.98012 + 1.14322i) q^{7} +(-0.139458 + 2.99676i) q^{9} +O(q^{10})\)	\(q+(-1.19594 - 1.25289i) q^{3} +(-2.14796 - 0.621508i) q^{5} +(-1.98012 + 1.14322i) q^{7} +(-0.139458 + 2.99676i) q^{9} +(0.864628 + 1.49758i) q^{11} +(5.20118 + 3.00291i) q^{13} +(1.79015 + 3.43444i) q^{15} +4.65465i q^{17} -0.888934 q^{19} +(3.80044 + 1.11364i) q^{21} +(-5.17546 - 2.98806i) q^{23} +(4.22745 + 2.66995i) q^{25} +(3.92138 - 3.40922i) q^{27} +(-2.34652 - 4.06430i) q^{29} +(-2.98190 + 5.16479i) q^{31} +(0.842257 - 2.87430i) q^{33} +(4.96374 - 1.22493i) q^{35} +8.68683i q^{37} +(-2.45800 - 10.1078i) q^{39} +(-3.15468 + 5.46406i) q^{41} +(-1.46119 + 0.843618i) q^{43} +(2.16206 - 6.35024i) q^{45} +(-10.8177 + 6.24559i) q^{47} +(-0.886081 + 1.53474i) q^{49} +(5.83175 - 5.56667i) q^{51} -2.66110i q^{53} +(-0.926427 - 3.75411i) q^{55} +(1.06311 + 1.11374i) q^{57} +(1.62355 - 2.81207i) q^{59} +(-6.08732 - 10.5436i) q^{61} +(-3.14982 - 6.09337i) q^{63} +(-9.30560 - 9.68270i) q^{65} +(10.8344 + 6.25524i) q^{67} +(2.44584 + 10.0578i) q^{69} +7.25413 q^{71} +1.69305i q^{73} +(-1.71063 - 8.48963i) q^{75} +(-3.42413 - 1.97693i) q^{77} +(-1.99175 - 3.44982i) q^{79} +(-8.96110 - 0.835841i) q^{81} +(3.63578 - 2.09912i) q^{83} +(2.89290 - 9.99799i) q^{85} +(-2.28581 + 7.80059i) q^{87} +2.60891 q^{89} -13.7320 q^{91} +(10.0371 - 2.44080i) q^{93} +(1.90939 + 0.552480i) q^{95} +(3.46355 - 1.99968i) q^{97} +(-4.60846 + 2.38223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 4 * q^9	\( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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