LMFDB - Embedded newform 864.2.w.a.323.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			323.7
Character	$\chi$	$=$	864.323
Dual form			864.2.w.a.107.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07850 + 0.914792i) q^{2} +(0.326309 - 1.97320i) q^{4} +(1.10881 - 0.459283i) q^{5} +(2.29035 + 2.29035i) q^{7} +(1.45315 + 2.42660i) q^{8} +O(q^{10})$	\(q+(-1.07850 + 0.914792i) q^{2} +(0.326309 - 1.97320i) q^{4} +(1.10881 - 0.459283i) q^{5} +(2.29035 + 2.29035i) q^{7} +(1.45315 + 2.42660i) q^{8} +(-0.775695 + 1.50966i) q^{10} +(-4.23612 + 1.75466i) q^{11} +(-0.644097 + 1.55499i) q^{13} +(-4.56533 - 0.374940i) q^{14} +(-3.78704 - 1.28775i) q^{16} -5.75819 q^{17} +(4.00625 + 1.65944i) q^{19} +(-0.544443 - 2.33777i) q^{20} +(2.96349 - 5.76757i) q^{22} +(4.82067 + 4.82067i) q^{23} +(-2.51702 + 2.51702i) q^{25} +(-0.727835 - 2.26626i) q^{26} +(5.26669 - 3.77196i) q^{28} +(-1.52718 + 3.68694i) q^{29} -10.9561i q^{31} +(5.26234 - 2.07553i) q^{32} +(6.21019 - 5.26755i) q^{34} +(3.59147 + 1.48764i) q^{35} +(1.67353 + 4.04025i) q^{37} +(-5.83877 + 1.87518i) q^{38} +(2.72575 + 2.02322i) q^{40} +(-2.75672 + 2.75672i) q^{41} +(3.26736 + 7.88810i) q^{43} +(2.08001 + 8.93129i) q^{44} +(-9.60899 - 0.789163i) q^{46} -3.05588i q^{47} +3.49141i q^{49} +(0.412047 - 5.01715i) q^{50} +(2.85813 + 1.77834i) q^{52} +(3.81361 + 9.20688i) q^{53} +(-3.89116 + 3.89116i) q^{55} +(-2.22954 + 8.88597i) q^{56} +(-1.72573 - 5.37340i) q^{58} +(-2.49029 - 6.01210i) q^{59} +(4.36611 + 1.80850i) q^{61} +(10.0225 + 11.8161i) q^{62} +(-3.77673 + 7.05240i) q^{64} +2.02000i q^{65} +(-4.89651 + 11.8212i) q^{67} +(-1.87895 + 11.3621i) q^{68} +(-5.23427 + 1.68104i) q^{70} +(0.814206 - 0.814206i) q^{71} +(-6.13068 - 6.13068i) q^{73} +(-5.50089 - 2.82647i) q^{74} +(4.58169 - 7.36364i) q^{76} +(-13.7210 - 5.68342i) q^{77} -7.99746 q^{79} +(-4.79054 + 0.311461i) q^{80} +(0.451287 - 5.49495i) q^{82} +(4.51997 - 10.9122i) q^{83} +(-6.38472 + 2.64464i) q^{85} +(-10.7398 - 5.51834i) q^{86} +(-10.4136 - 7.72958i) q^{88} +(6.05533 + 6.05533i) q^{89} +(-5.03667 + 2.08626i) q^{91} +(11.0852 - 7.93912i) q^{92} +(2.79550 + 3.29576i) q^{94} +5.20430 q^{95} +11.5086 q^{97} +(-3.19392 - 3.76548i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.07850	+	0.914792i	−0.762612	+	0.646856i
$2$	−1.07850	+	0.914792i	−0.762612	+	0.646856i
$3$		0			0
$3$		0			0
$4$	0.326309	−	1.97320i	0.163155	−	0.986601i
$5$	1.10881	−	0.459283i	0.495873	−	0.205397i	−0.120709	−	0.992688i	$-0.538517\pi$
$5$	1.10881	−	0.459283i	0.495873	−	0.205397i	0.616582	+	0.787291i	$0.288517\pi$
$6$		0			0
$7$	2.29035	+	2.29035i	0.865671	+	0.865671i	0.991990	−	0.126319i	$-0.0403161\pi$
$7$	2.29035	+	2.29035i	0.865671	+	0.865671i	−0.126319	+	0.991990i	$0.540316\pi$
$8$	1.45315	+	2.42660i	0.513765	+	0.857931i
$9$		0			0
$10$	−0.775695	+	1.50966i	−0.245296	+	0.477397i
$11$	−4.23612	+	1.75466i	−1.27724	+	0.529050i	−0.915158	−	0.403096i	$-0.867934\pi$
$11$	−4.23612	+	1.75466i	−1.27724	+	0.529050i	−0.362082	+	0.932146i	$0.617934\pi$
$12$		0			0
$13$	−0.644097	+	1.55499i	−0.178640	+	0.431276i	−0.987682	−	0.156476i	$-0.949987\pi$
$13$	−0.644097	+	1.55499i	−0.178640	+	0.431276i	0.809041	+	0.587752i	$0.199987\pi$
$14$	−4.56533	−	0.374940i	−1.22014	−	0.100207i
$15$		0			0
$16$	−3.78704	−	1.28775i	−0.946761	−	0.321937i
$17$	−5.75819			−1.39657			−0.698284	−	0.715821i	$-0.746053\pi$
$17$	−5.75819			−1.39657			−0.698284	+	0.715821i	$0.746053\pi$
$18$		0			0
$19$	4.00625	+	1.65944i	0.919096	+	0.380702i	0.791531	−	0.611128i	$-0.209284\pi$
$19$	4.00625	+	1.65944i	0.919096	+	0.380702i	0.127564	+	0.991830i	$0.459284\pi$
$20$	−0.544443	−	2.33777i	−0.121741	−	0.522740i
$21$		0			0
$22$	2.96349	−	5.76757i	0.631819	−	1.22965i
$23$	4.82067	+	4.82067i	1.00518	+	1.00518i	0.999987	+	0.00519281i	$0.00165293\pi$
$23$	4.82067	+	4.82067i	1.00518	+	1.00518i	0.00519281	+	0.999987i	$0.498347\pi$
$24$		0			0
$25$	−2.51702	+	2.51702i	−0.503405	+	0.503405i
$26$	−0.727835	−	2.26626i	−0.142740	−	0.444451i
$27$		0			0
$28$	5.26669	−	3.77196i	0.995310	−	0.712833i
$29$	−1.52718	+	3.68694i	−0.283590	+	0.684647i	−0.999914	−	0.0131208i	$-0.995823\pi$
$29$	−1.52718	+	3.68694i	−0.283590	+	0.684647i	0.716324	+	0.697768i	$0.245823\pi$
$30$		0			0
$31$		−	10.9561i		−	1.96777i	−0.178802	−	0.983885i	$-0.557222\pi$
$31$		−	10.9561i		−	1.96777i	0.178802	−	0.983885i	$-0.442778\pi$
$32$	5.26234	−	2.07553i	0.930258	−	0.366905i
$33$		0			0
$34$	6.21019	−	5.26755i	1.06504	−	0.903378i
$35$	3.59147	+	1.48764i	0.607070	+	0.251457i
$36$		0			0
$37$	1.67353	+	4.04025i	0.275126	+	0.664213i	0.999688	−	0.0249970i	$-0.00795762\pi$
$37$	1.67353	+	4.04025i	0.275126	+	0.664213i	−0.724561	+	0.689210i	$0.757958\pi$
$38$	−5.83877	+	1.87518i	−0.947173	+	0.304195i
$39$		0			0
$40$	2.72575	+	2.02322i	0.430979	+	0.319899i
$41$	−2.75672	+	2.75672i	−0.430528	+	0.430528i	−0.888808	−	0.458280i	$-0.848466\pi$
$41$	−2.75672	+	2.75672i	−0.430528	+	0.430528i	0.458280	+	0.888808i	$0.348466\pi$
$42$		0			0
$43$	3.26736	+	7.88810i	0.498268	+	1.20292i	0.950416	+	0.310982i	$0.100658\pi$
$43$	3.26736	+	7.88810i	0.498268	+	1.20292i	−0.452148	+	0.891943i	$0.649342\pi$
$44$	2.08001	+	8.93129i	0.313573	+	1.34644i
$45$		0			0
$46$	−9.60899	−	0.789163i	−1.41677	−	0.116356i
$47$		−	3.05588i		−	0.445746i	−0.974847	−	0.222873i	$-0.928456\pi$
$47$		−	3.05588i		−	0.445746i	0.974847	−	0.222873i	$-0.0715436\pi$
$48$		0			0
$49$			3.49141i			0.498773i
$50$	0.412047	−	5.01715i	0.0582722	−	0.709533i
$51$		0			0
$52$	2.85813	+	1.77834i	0.396351	+	0.246611i
$53$	3.81361	+	9.20688i	0.523840	+	1.26466i	0.935501	+	0.353325i	$0.114949\pi$
$53$	3.81361	+	9.20688i	0.523840	+	1.26466i	−0.411661	+	0.911337i	$0.635051\pi$
$54$		0			0
$55$	−3.89116	+	3.89116i	−0.524683	+	0.524683i
$56$	−2.22954	+	8.88597i	−0.297935	+	1.18744i
$57$		0			0
$58$	−1.72573	−	5.37340i	−0.226599	−	0.705562i
$59$	−2.49029	−	6.01210i	−0.324208	−	0.782708i	−0.999000	−	0.0447004i	$-0.985767\pi$
$59$	−2.49029	−	6.01210i	−0.324208	−	0.782708i	0.674792	−	0.738008i	$-0.264233\pi$
$60$		0			0
$61$	4.36611	+	1.80850i	0.559023	+	0.231555i	0.644261	−	0.764806i	$-0.277165\pi$
$61$	4.36611	+	1.80850i	0.559023	+	0.231555i	−0.0852381	+	0.996361i	$0.527165\pi$
$62$	10.0225	+	11.8161i	1.27286	+	1.50065i
$63$		0			0
$64$	−3.77673	+	7.05240i	−0.472092	+	0.881549i
$65$			2.02000i			0.250550i
$66$		0			0
$67$	−4.89651	+	11.8212i	−0.598204	+	1.44419i	0.277207	+	0.960810i	$0.410591\pi$
$67$	−4.89651	+	11.8212i	−0.598204	+	1.44419i	−0.875410	+	0.483381i	$0.839409\pi$
$68$	−1.87895	+	11.3621i	−0.227857	+	1.37785i
$69$		0			0
$70$	−5.23427	+	1.68104i	−0.625615	+	0.200923i
$71$	0.814206	−	0.814206i	0.0966285	−	0.0966285i	−0.657140	−	0.753769i	$-0.728234\pi$
$71$	0.814206	−	0.814206i	0.0966285	−	0.0966285i	0.753769	+	0.657140i	$0.228234\pi$
$72$		0			0
$73$	−6.13068	−	6.13068i	−0.717541	−	0.717541i	0.250560	−	0.968101i	$-0.419385\pi$
$73$	−6.13068	−	6.13068i	−0.717541	−	0.717541i	−0.968101	+	0.250560i	$0.919385\pi$
$74$	−5.50089	−	2.82647i	−0.639465	−	0.328570i
$75$		0			0
$76$	4.58169	−	7.36364i	0.525555	−	0.844667i
$77$	−13.7210	−	5.68342i	−1.56365	−	0.647686i
$78$		0			0
$79$	−7.99746			−0.899785			−0.449892	−	0.893083i	$-0.648538\pi$
$79$	−7.99746			−0.899785			−0.449892	+	0.893083i	$0.648538\pi$
$80$	−4.79054	+	0.311461i	−0.535598	+	0.0348223i
$81$		0			0
$82$	0.451287	−	5.49495i	0.0498363	−	0.606816i
$83$	4.51997	−	10.9122i	0.496131	−	1.19777i	−0.455420	−	0.890277i	$-0.650511\pi$
$83$	4.51997	−	10.9122i	0.496131	−	1.19777i	0.951551	−	0.307490i	$-0.0994891\pi$
$84$		0			0
$85$	−6.38472	+	2.64464i	−0.692520	+	0.286851i
$86$	−10.7398	−	5.51834i	−1.15810	−	0.595058i
$87$		0			0
$88$	−10.4136	−	7.72958i	−1.11009	−	0.823976i
$89$	6.05533	+	6.05533i	0.641864	+	0.641864i	0.951013	−	0.309150i	$-0.100044\pi$
$89$	6.05533	+	6.05533i	0.641864	+	0.641864i	−0.309150	+	0.951013i	$0.600044\pi$
$90$		0			0
$91$	−5.03667	+	2.08626i	−0.527987	+	0.218699i
$92$	11.0852	−	7.93912i	1.15571	−	0.827711i
$93$		0			0
$94$	2.79550	+	3.29576i	0.288334	+	0.339932i
$95$	5.20430			0.533950
$96$		0			0
$97$	11.5086			1.16852			0.584262	−	0.811565i	$-0.301384\pi$
$97$	11.5086			1.16852			0.584262	+	0.811565i	$0.301384\pi$
$98$	−3.19392	−	3.76548i	−0.322634	−	0.380371i
$99$		0			0
$100$	4.14526	+	5.78792i	0.414526	+	0.578792i
$101$	0.407683	−	0.168868i	0.0405660	−	0.0168030i	−0.362308	−	0.932058i	$-0.618011\pi$
$101$	0.407683	−	0.168868i	0.0405660	−	0.0168030i	0.402874	+	0.915255i	$0.368011\pi$
$102$		0			0
$103$	−1.14131	−	1.14131i	−0.112456	−	0.112456i	0.648639	−	0.761096i	$-0.275338\pi$
$103$	−1.14131	−	1.14131i	−0.112456	−	0.112456i	−0.761096	+	0.648639i	$0.775338\pi$
$104$	−4.70929	+	0.696661i	−0.461784	+	0.0683132i
$105$		0			0
$106$	−12.5354	−	6.44092i	−1.21754	−	0.625598i
$107$	8.61819	−	3.56977i	0.833152	−	0.345103i	0.0750020	−	0.997183i	$-0.476104\pi$
$107$	8.61819	−	3.56977i	0.833152	−	0.345103i	0.758150	+	0.652081i	$0.226104\pi$
$108$		0			0
$109$	−3.95363	+	9.54490i	−0.378689	+	0.914236i	0.613523	+	0.789677i	$0.289752\pi$
$109$	−3.95363	+	9.54490i	−0.378689	+	0.914236i	−0.992212	+	0.124559i	$0.960248\pi$
$110$	0.636998	−	7.75620i	0.0607353	−	0.739524i
$111$		0			0
$112$	−5.72427	−	11.6231i	−0.540892	−	1.09828i
$113$	−9.49602			−0.893310			−0.446655	−	0.894706i	$-0.647385\pi$
$113$	−9.49602			−0.893310			−0.446655	+	0.894706i	$0.647385\pi$
$114$		0			0
$115$	7.55924	+	3.13114i	0.704903	+	0.291980i
$116$	6.77674	+	4.21652i	0.629204	+	0.391494i
$117$		0			0
$118$	8.18559	+	4.20592i	0.753545	+	0.387187i
$119$	−13.1883	−	13.1883i	−1.20897	−	1.20897i
$120$		0			0
$121$	7.08774	−	7.08774i	0.644340	−	0.644340i
$122$	−6.36324	+	2.04362i	−0.576100	+	0.185021i
$123$		0			0
$124$	−21.6185	−	3.57507i	−1.94140	−	0.321051i
$125$	−3.93128	+	9.49095i	−0.351624	+	0.848896i
$126$		0			0
$127$			17.3638i			1.54079i	0.637568	+	0.770394i	$0.279941\pi$
$127$			17.3638i			1.54079i	−0.637568	+	0.770394i	$0.720059\pi$
$128$	−2.37828	−	11.0609i	−0.210213	−	0.977656i
$129$		0			0
$130$	−1.84788	−	2.17857i	−0.162070	−	0.191073i
$131$	12.9137	+	5.34903i	1.12827	+	0.467347i	0.867194	−	0.497970i	$-0.165921\pi$
$131$	12.9137	+	5.34903i	1.12827	+	0.467347i	0.261081	+	0.965317i	$0.415921\pi$
$132$		0			0
$133$	5.37500	+	12.9764i	0.466072	+	1.12520i
$134$	−5.53309	−	17.2284i	−0.477986	−	1.48831i
$135$		0			0
$136$	−8.36750	−	13.9728i	−0.717507	−	1.19816i
$137$	−1.43528	+	1.43528i	−0.122624	+	0.122624i	−0.765756	−	0.643132i	$-0.777635\pi$
$137$	−1.43528	+	1.43528i	−0.122624	+	0.122624i	0.643132	+	0.765756i	$0.277635\pi$
$138$		0			0
$139$	1.00602	+	2.42876i	0.0853298	+	0.206004i	0.960785	−	0.277295i	$-0.0894381\pi$
$139$	1.00602	+	2.42876i	0.0853298	+	0.206004i	−0.875455	+	0.483300i	$0.839438\pi$
$140$	4.10734	−	6.60127i	0.347133	−	0.557909i
$141$		0			0
$142$	−0.133289	+	1.62295i	−0.0111853	+	0.136195i
$143$		−	7.71729i		−	0.645352i
$144$		0			0
$145$			4.78951i			0.397747i
$146$	12.2202	+	1.00362i	1.01135	+	0.0830599i
$147$		0			0
$148$	8.51832	−	1.98383i	0.700201	−	0.163070i
$149$	−2.21125	−	5.33842i	−0.181152	−	0.437341i	0.807052	−	0.590480i	$-0.201062\pi$
$149$	−2.21125	−	5.33842i	−0.181152	−	0.437341i	−0.988205	+	0.153140i	$0.951062\pi$
$150$		0			0
$151$	7.88070	−	7.88070i	0.641322	−	0.641322i	−0.309558	−	0.950880i	$-0.600181\pi$
$151$	7.88070	−	7.88070i	0.641322	−	0.641322i	0.950880	+	0.309558i	$0.100181\pi$
$152$	1.79487	+	12.1329i	0.145583	+	0.984112i
$153$		0			0
$154$	19.9972	−	6.42231i	1.61142	−	0.517525i
$155$	−5.03194	−	12.1482i	−0.404175	−	0.975765i
$156$		0			0
$157$	−12.8602	−	5.32685i	−1.02635	−	0.425129i	−0.194957	−	0.980812i	$-0.562457\pi$
$157$	−12.8602	−	5.32685i	−1.02635	−	0.425129i	−0.831394	+	0.555683i	$0.812457\pi$
$158$	8.62523	−	7.31602i	0.686187	−	0.582031i
$159$		0			0
$160$	4.88166	−	4.71826i	0.385929	−	0.373011i
$161$			22.0821i			1.74031i
$162$		0			0
$163$	2.99107	−	7.22108i	0.234278	−	0.565598i	−0.762394	−	0.647114i	$-0.775976\pi$
$163$	2.99107	−	7.22108i	0.234278	−	0.565598i	0.996672	+	0.0815153i	$0.0259759\pi$
$164$	4.54003	+	6.33912i	0.354517	+	0.495002i
$165$		0			0
$166$	5.10760	+	15.9036i	0.396427	+	1.23436i
$167$	10.0758	−	10.0758i	0.779690	−	0.779690i	−0.200088	−	0.979778i	$-0.564123\pi$
$167$	10.0758	−	10.0758i	0.779690	−	0.779690i	0.979778	+	0.200088i	$0.0641227\pi$
$168$		0			0
$169$	7.18926	+	7.18926i	0.553020	+	0.553020i
$170$	4.46661	−	8.69293i	0.342573	−	0.666717i
$171$		0			0
$172$	16.6310	−	3.87320i	1.26810	−	0.295328i
$173$	7.96435	+	3.29894i	0.605518	+	0.250814i	0.664311	−	0.747456i	$-0.268725\pi$
$173$	7.96435	+	3.29894i	0.605518	+	0.250814i	−0.0587927	+	0.998270i	$0.518725\pi$
$174$		0			0
$175$	−11.5297			−0.871566
$176$	18.3019	−	1.18992i	1.37956	−	0.0896932i
$177$		0			0
$178$	−12.0700	−	0.991282i	−0.904687	−	0.0742997i
$179$	2.93955	−	7.09670i	0.219712	−	0.530432i	−0.775138	−	0.631793i	$-0.782319\pi$
$179$	2.93955	−	7.09670i	0.219712	−	0.530432i	0.994850	+	0.101360i	$0.0323195\pi$
$180$		0			0
$181$	−8.77358	+	3.63414i	−0.652135	+	0.270123i	−0.684125	−	0.729365i	$-0.739816\pi$
$181$	−8.77358	+	3.63414i	−0.652135	+	0.270123i	0.0319896	+	0.999488i	$0.489816\pi$
$182$	3.52354	−	6.85754i	0.261182	−	0.508314i
$183$		0			0
$184$	−4.69268	+	18.7030i	−0.345949	+	1.37880i
$185$	3.71123	+	3.71123i	0.272855	+	0.272855i
$186$		0			0
$187$	24.3924	−	10.1037i	1.78375	−	0.738854i
$188$	−6.02987	−	0.997164i	−0.439774	−	0.0727256i
$189$		0			0
$190$	−5.61282	+	4.76086i	−0.407197	+	0.345389i
$191$	11.3188			0.819002			0.409501	−	0.912310i	$-0.365703\pi$
$191$	11.3188			0.819002			0.409501	+	0.912310i	$0.365703\pi$
$192$		0			0
$193$	−1.00738			−0.0725131			−0.0362565	−	0.999343i	$-0.511543\pi$
$193$	−1.00738			−0.0725131			−0.0362565	+	0.999343i	$0.511543\pi$
$194$	−12.4120	+	10.5280i	−0.891131	+	0.755867i
$195$		0			0
$196$	6.88926	+	1.13928i	0.492090	+	0.0813772i
$197$	4.85159	−	2.00959i	0.345661	−	0.143178i	−0.203097	−	0.979159i	$-0.565101\pi$
$197$	4.85159	−	2.00959i	0.345661	−	0.143178i	0.548758	+	0.835981i	$0.315101\pi$
$198$		0			0
$199$	−11.9610	−	11.9610i	−0.847891	−	0.847891i	0.141979	−	0.989870i	$-0.454653\pi$
$199$	−11.9610	−	11.9610i	−0.847891	−	0.847891i	−0.989870	+	0.141979i	$0.954653\pi$
$200$	−9.76540	−	2.45020i	−0.690518	−	0.173255i
$201$		0			0
$202$	−0.285206	+	0.555069i	−0.0200670	+	0.0390545i
$203$	−11.9422	+	4.94660i	−0.838175	+	0.347184i
$204$		0			0
$205$	−1.79056	+	4.32279i	−0.125058	+	0.301917i
$206$	2.27496	+	0.186837i	0.158504	+	0.0130175i
$207$		0			0
$208$	4.44166	−	5.05937i	0.307973	−	0.350804i
$209$	−19.8827			−1.37532
$210$		0			0
$211$	9.78520	+	4.05316i	0.673641	+	0.279031i	0.693166	−	0.720778i	$-0.256215\pi$
$211$	9.78520	+	4.05316i	0.673641	+	0.279031i	−0.0195249	+	0.999809i	$0.506215\pi$
$212$	19.4114	−	4.52074i	1.33318	−	0.310485i
$213$		0			0
$214$	−6.02909	+	11.7338i	−0.412140	+	0.802109i
$215$	7.24574	+	7.24574i	0.494155	+	0.494155i
$216$		0			0
$217$	25.0933	−	25.0933i	1.70344	−	1.70344i
$218$	−4.46763	−	13.9109i	−0.302586	−	0.942164i
$219$		0			0
$220$	6.40831	+	8.94775i	0.432048	+	0.603257i
$221$	3.70884	−	8.95392i	0.249483	−	0.602306i
$222$		0			0
$223$		−	11.6867i		−	0.782596i	−0.920264	−	0.391298i	$-0.872026\pi$
$223$		−	11.6867i		−	0.782596i	0.920264	−	0.391298i	$-0.127974\pi$
$224$	16.8063	+	7.29891i	1.12292	+	0.487679i
$225$		0			0
$226$	10.2414	−	8.68688i	0.681249	−	0.577843i
$227$	27.4221	+	11.3586i	1.82007	+	0.753897i	0.976038	+	0.217600i	$0.0698227\pi$
$227$	27.4221	+	11.3586i	1.82007	+	0.753897i	0.844029	+	0.536297i	$0.180177\pi$
$228$		0			0
$229$	−4.97093	−	12.0009i	−0.328488	−	0.793040i	−0.998705	−	0.0508750i	$-0.983799\pi$
$229$	−4.97093	−	12.0009i	−0.328488	−	0.793040i	0.670217	−	0.742165i	$-0.266201\pi$
$230$	−11.0170	+	3.53821i	−0.726437	+	0.233303i
$231$		0			0
$232$	−11.1659	+	1.65181i	−0.733079	+	0.108447i
$233$	15.1524	−	15.1524i	0.992666	−	0.992666i	−0.00730690	−	0.999973i	$-0.502326\pi$
$233$	15.1524	−	15.1524i	0.992666	−	0.992666i	0.999973	+	0.00730690i	$0.00232588\pi$
$234$		0			0
$235$	−1.40351	−	3.38838i	−0.0915552	−	0.221034i
$236$	−12.6757	+	2.95204i	−0.825117	+	0.192162i
$237$		0			0
$238$	26.2881	+	2.15898i	1.70400	+	0.139946i
$239$			23.6477i			1.52964i	0.644241	+	0.764822i	$0.277173\pi$
$239$			23.6477i			1.52964i	−0.644241	+	0.764822i	$0.722827\pi$
$240$		0			0
$241$		−	15.2836i		−	0.984506i	−0.870452	−	0.492253i	$-0.836174\pi$
$241$		−	15.2836i		−	0.984506i	0.870452	−	0.492253i	$-0.163826\pi$
$242$	−1.16029	+	14.1279i	−0.0745863	+	0.908177i
$243$		0			0
$244$	4.99324	−	8.02508i	0.319659	−	0.513753i
$245$	1.60354	+	3.87130i	0.102447	+	0.247328i
$246$		0			0
$247$	−5.16082	+	5.16082i	−0.328375	+	0.328375i
$248$	26.5860	−	15.9208i	1.68821	−	1.01097i
$249$		0			0
$250$	−4.44238	−	13.8323i	−0.280961	−	0.874829i
$251$	−4.23813	−	10.2317i	−0.267508	−	0.645822i	0.731857	−	0.681459i	$-0.238654\pi$
$251$	−4.23813	−	10.2317i	−0.267508	−	0.645822i	−0.999365	+	0.0356366i	$0.988654\pi$
$252$		0			0
$253$	−28.8796	−	11.9623i	−1.81564	−	0.752065i
$254$	−15.8843	−	18.7268i	−0.996668	−	1.17502i
$255$		0			0
$256$	12.6834	+	9.75352i	0.792713	+	0.609595i
$257$		−	24.2953i		−	1.51550i	−0.652544	−	0.757751i	$-0.726298\pi$
$257$		−	24.2953i		−	1.51550i	0.652544	−	0.757751i	$-0.273702\pi$
$258$		0			0
$259$	−5.42063	+	13.0866i	−0.336822	+	0.813159i
$260$	3.98587	+	0.659146i	0.247193	+	0.0408785i
$261$		0			0
$262$	−18.8206	+	6.04444i	−1.16274	+	0.373427i
$263$	17.0847	−	17.0847i	1.05349	−	1.05349i	0.0550047	−	0.998486i	$-0.482483\pi$
$263$	17.0847	−	17.0847i	1.05349	−	1.05349i	0.998486	−	0.0550047i	$-0.0175174\pi$
$264$		0			0
$265$	8.45712	+	8.45712i	0.519517	+	0.519517i
$266$	−17.6676	−	9.07800i	−1.08327	−	0.556608i
$267$		0			0
$268$	21.7279	+	13.5192i	1.32724	+	0.825814i
$269$	−27.5091	−	11.3947i	−1.67726	−	0.694745i	−0.678072	−	0.734995i	$-0.737184\pi$
$269$	−27.5091	−	11.3947i	−1.67726	−	0.694745i	−0.999190	+	0.0402507i	$0.987184\pi$
$270$		0			0
$271$	−1.03250			−0.0627197			−0.0313598	−	0.999508i	$-0.509984\pi$
$271$	−1.03250			−0.0627197			−0.0313598	+	0.999508i	$0.509984\pi$
$272$	21.8065	+	7.41510i	1.32222	+	0.449607i
$273$		0			0
$274$	0.234960	−	2.86092i	0.0141945	−	0.172835i
$275$	6.24590	−	15.0789i	0.376642	−	0.909294i
$276$		0			0
$277$	6.98129	−	2.89174i	0.419465	−	0.173748i	−0.162960	−	0.986633i	$-0.552104\pi$
$277$	6.98129	−	2.89174i	0.419465	−	0.173748i	0.582425	+	0.812885i	$0.302104\pi$
$278$	−3.30680	−	1.69910i	−0.198329	−	0.101905i
$279$		0			0
$280$	1.60904	+	10.8768i	0.0961586	+	0.650014i
$281$	−5.66031	−	5.66031i	−0.337666	−	0.337666i	0.517822	−	0.855488i	$-0.326743\pi$
$281$	−5.66031	−	5.66031i	−0.337666	−	0.337666i	−0.855488	+	0.517822i	$0.826743\pi$
$282$		0			0
$283$	−8.97137	+	3.71606i	−0.533292	+	0.220897i	−0.633045	−	0.774115i	$-0.718195\pi$
$283$	−8.97137	+	3.71606i	−0.533292	+	0.220897i	0.0997521	+	0.995012i	$0.468195\pi$
$284$	−1.34091	−	1.87228i	−0.0795683	−	0.111099i
$285$		0			0
$286$	7.05972	+	8.32307i	0.417450	+	0.492154i
$287$	−12.6277			−0.745391
$288$		0			0
$289$	16.1568			0.950401
$290$	−4.38141	−	5.16547i	−0.257285	−	0.303327i
$291$		0			0
$292$	−14.0976	+	10.0966i	−0.824997	+	0.590856i
$293$	−12.4522	+	5.15788i	−0.727467	+	0.301327i	−0.715510	−	0.698602i	$-0.753806\pi$
$293$	−12.4522	+	5.15788i	−0.727467	+	0.301327i	−0.0119561	+	0.999929i	$0.503806\pi$
$294$		0			0
$295$	−5.52250	−	5.52250i	−0.321533	−	0.321533i
$296$	−7.37218	+	9.93205i	−0.428499	+	0.577289i
$297$		0			0
$298$	7.26837	+	3.73464i	0.421045	+	0.216342i
$299$	−10.6011	+	4.39110i	−0.613075	+	0.253944i
$300$		0			0
$301$	−10.5831	+	25.5499i	−0.610001	+	1.47267i
$302$	−1.29010	+	15.7085i	−0.0742370	+	0.903923i
$303$		0			0
$304$	−13.0349	−	11.4434i	−0.747602	−	0.656325i
$305$	5.67178			0.324765
$306$		0			0
$307$	−15.2016	−	6.29670i	−0.867600	−	0.359372i	−0.0959250	−	0.995389i	$-0.530581\pi$
$307$	−15.2016	−	6.29670i	−0.867600	−	0.359372i	−0.771675	+	0.636017i	$0.780581\pi$
$308$	−15.6918	+	25.2197i	−0.894125	+	1.43703i
$309$		0			0
$310$	16.5400	+	8.49858i	0.939408	+	0.482687i
$311$	−14.4880	−	14.4880i	−0.821542	−	0.821542i	0.164787	−	0.986329i	$-0.447306\pi$
$311$	−14.4880	−	14.4880i	−0.821542	−	0.821542i	−0.986329	+	0.164787i	$0.947306\pi$
$312$		0			0
$313$	7.88864	−	7.88864i	0.445893	−	0.445893i	−0.448094	−	0.893986i	$-0.647897\pi$
$313$	7.88864	−	7.88864i	0.445893	−	0.445893i	0.893986	+	0.448094i	$0.147897\pi$
$314$	18.7426	−	6.01938i	1.05771	−	0.339693i
$315$		0			0
$316$	−2.60965	+	15.7806i	−0.146804	+	0.887728i
$317$	2.14940	−	5.18912i	0.120722	−	0.291450i	−0.851953	−	0.523618i	$-0.824582\pi$
$317$	2.14940	−	5.18912i	0.120722	−	0.291450i	0.972676	+	0.232168i	$0.0745819\pi$
$318$		0			0
$319$		−	18.2980i		−	1.02449i
$320$	−0.948623	+	9.55433i	−0.0530297	+	0.534103i
$321$		0			0
$322$	−20.2005	−	23.8154i	−1.12573	−	1.32718i
$323$	−23.0687	−	9.55539i	−1.28358	−	0.531676i
$324$		0			0
$325$	−2.29273	−	5.53515i	−0.127178	−	0.307035i
$326$	3.37993	+	10.5241i	0.187197	+	0.582877i
$327$		0			0
$328$	−10.6954	−	2.68353i	−0.590554	−	0.148173i
$329$	6.99905	−	6.99905i	0.385870	−	0.385870i
$330$		0			0
$331$	4.79808	+	11.5836i	0.263726	+	0.636692i	0.999163	−	0.0409015i	$-0.0130230\pi$
$331$	4.79808	+	11.5836i	0.263726	+	0.636692i	−0.735437	+	0.677593i	$0.763023\pi$
$332$	−20.0570	−	12.4796i	−1.10077	−	0.684905i
$333$		0			0
$334$	−1.64945	+	20.0840i	−0.0902540	+	1.09895i
$335$			15.3563i			0.839005i
$336$		0			0
$337$		−	34.5409i		−	1.88156i	−0.339011	−	0.940782i	$-0.610093\pi$
$337$		−	34.5409i		−	1.88156i	0.339011	−	0.940782i	$-0.389907\pi$
$338$	−14.3303	−	1.17691i	−0.779464	−	0.0640155i
$339$		0			0
$340$	3.13501	+	13.4613i	0.170020	+	0.730042i
$341$	19.2242	+	46.4113i	1.04105	+	2.51331i
$342$		0			0
$343$	8.03590	−	8.03590i	0.433898	−	0.433898i
$344$	−14.3933	+	19.3911i	−0.776034	+	1.04550i
$345$		0			0
$346$	−11.6074	+	3.72783i	−0.624016	+	0.200409i
$347$	13.4976	+	32.5861i	0.724590	+	1.74932i	0.659830	+	0.751415i	$0.270628\pi$
$347$	13.4976	+	32.5861i	0.724590	+	1.74932i	0.0647598	+	0.997901i	$0.479372\pi$
$348$		0			0
$349$	19.4574	+	8.05954i	1.04153	+	0.431417i	0.836862	−	0.547414i	$-0.184388\pi$
$349$	19.4574	+	8.05954i	1.04153	+	0.431417i	0.204671	+	0.978831i	$0.434388\pi$
$350$	12.4348	−	10.5473i	0.664667	−	0.563778i
$351$		0			0
$352$	−18.6501	+	18.0258i	−0.994052	+	0.960779i
$353$			28.8838i			1.53733i	0.639653	+	0.768664i	$0.279078\pi$
$353$			28.8838i			1.53733i	−0.639653	+	0.768664i	$0.720922\pi$
$354$		0			0
$355$	0.528846	−	1.27675i	0.0280682	−	0.0677627i
$356$	13.9243	−	9.97248i	0.737986	−	0.528540i
$357$		0			0
$358$	3.32171	+	10.3428i	0.175558	+	0.546636i
$359$	21.9015	−	21.9015i	1.15592	−	1.15592i	0.170574	−	0.985345i	$-0.445438\pi$
$359$	21.9015	−	21.9015i	1.15592	−	1.15592i	0.985345	−	0.170574i	$-0.0545623\pi$
$360$		0			0
$361$	−0.138774	−	0.138774i	−0.00730389	−	0.00730389i
$362$	6.13780	−	11.9454i	0.322595	−	0.627837i
$363$		0			0
$364$	2.47309	+	10.6191i	0.129625	+	0.556594i
$365$	−9.61344	−	3.98202i	−0.503191	−	0.208428i
$366$		0			0
$367$	4.27993			0.223411			0.111705	−	0.993741i	$-0.464369\pi$
$367$	4.27993			0.223411			0.111705	+	0.993741i	$0.464369\pi$
$368$	−12.0483	−	24.4639i	−0.628060	−	1.27527i
$369$		0			0
$370$	−7.39756	−	0.607544i	−0.384581	−	0.0315847i
$371$	−12.3525	+	29.8215i	−0.641308	+	1.54825i
$372$		0			0
$373$	−1.63995	+	0.679288i	−0.0849132	+	0.0351722i	−0.424736	−	0.905317i	$-0.639633\pi$
$373$	−1.63995	+	0.679288i	−0.0849132	+	0.0351722i	0.339823	+	0.940490i	$0.389633\pi$
$374$	−17.0644	+	33.2108i	−0.882378	+	1.71729i
$375$		0			0
$376$	7.41539	−	4.44065i	0.382420	−	0.229009i
$377$	−4.74949	−	4.74949i	−0.244611	−	0.244611i
$378$		0			0
$379$	24.5928	−	10.1867i	1.26325	−	0.523254i	0.352342	−	0.935871i	$-0.385385\pi$
$379$	24.5928	−	10.1867i	1.26325	−	0.523254i	0.910904	+	0.412618i	$0.135385\pi$
$380$	1.69821	−	10.2691i	0.0871165	−	0.526795i
$381$		0			0
$382$	−12.2073	+	10.3544i	−0.624581	+	0.529777i
$383$	−8.94049			−0.456838			−0.228419	−	0.973563i	$-0.573356\pi$
$383$	−8.94049			−0.456838			−0.228419	+	0.973563i	$0.573356\pi$
$384$		0			0
$385$	−17.8242			−0.908406
$386$	1.08646	−	0.921547i	0.0552994	−	0.0469055i
$387$		0			0
$388$	3.75537	−	22.7088i	0.190650	−	1.15287i
$389$	−26.3896	+	10.9309i	−1.33801	+	0.554221i	−0.932929	−	0.360061i	$-0.882756\pi$
$389$	−26.3896	+	10.9309i	−1.33801	+	0.554221i	−0.405079	+	0.914282i	$0.632756\pi$
$390$		0			0
$391$	−27.7584	−	27.7584i	−1.40380	−	1.40380i
$392$	−8.47225	+	5.07353i	−0.427913	+	0.256252i
$393$		0			0
$394$	−3.39406	+	6.60553i	−0.170990	+	0.332782i
$395$	−8.86763	+	3.67309i	−0.446179	+	0.184813i
$396$		0			0
$397$	−5.22517	+	12.6147i	−0.262244	+	0.633113i	−0.999077	−	0.0429622i	$-0.986320\pi$
$397$	−5.22517	+	12.6147i	−0.262244	+	0.633113i	0.736833	+	0.676075i	$0.236320\pi$
$398$	23.8417	+	1.95806i	1.19507	+	0.0981486i
$399$		0			0
$400$	12.7734	−	6.29079i	0.638669	−	0.314539i
$401$	5.30249			0.264794			0.132397	−	0.991197i	$-0.457733\pi$
$401$	5.30249			0.264794			0.132397	+	0.991197i	$0.457733\pi$
$402$		0			0
$403$	17.0366	+	7.05678i	0.848652	+	0.351523i
$404$	−0.200180	−	0.859544i	−0.00995931	−	0.0427639i
$405$		0			0
$406$	8.35446	−	16.2595i	0.414625	−	0.806945i
$407$	−14.1785	−	14.1785i	−0.702804	−	0.702804i
$408$		0			0
$409$	−22.2095	+	22.2095i	−1.09819	+	1.09819i	−0.103568	+	0.994622i	$0.533026\pi$
$409$	−22.2095	+	22.2095i	−1.09819	+	1.09819i	−0.994622	+	0.103568i	$0.966974\pi$
$410$	−2.02334	−	6.30010i	−0.0999259	−	0.311140i
$411$		0			0
$412$	−2.62445	+	1.87961i	−0.129297	+	0.0926018i
$413$	8.06617	−	19.4735i	0.396910	−	0.958226i
$414$		0			0
$415$		−	14.1754i		−	0.695844i
$416$	−0.162034	+	9.51971i	−0.00794438	+	0.466742i
$417$		0			0
$418$	21.4434	−	18.1885i	1.04883	−	0.889631i
$419$	19.3284	+	8.00610i	0.944256	+	0.391124i	0.801069	−	0.598572i	$-0.204265\pi$
$419$	19.3284	+	8.00610i	0.944256	+	0.391124i	0.143187	+	0.989696i	$0.454265\pi$
$420$		0			0
$421$	−8.19769	−	19.7910i	−0.399531	−	0.964554i	−0.987777	−	0.155872i	$-0.950181\pi$
$421$	−8.19769	−	19.7910i	−0.399531	−	0.964554i	0.588246	−	0.808682i	$-0.299819\pi$
$422$	−14.2611	+	4.58011i	−0.694220	+	0.222956i
$423$		0			0
$424$	−16.7996	+	22.6330i	−0.815862	+	1.09916i
$425$	14.4935	−	14.4935i	0.703039	−	0.703039i
$426$		0			0
$427$	5.85782	+	14.1420i	0.283480	+	0.684380i
$428$	−4.23168	−	18.1703i	−0.204546	−	0.878293i
$429$		0			0
$430$	−14.4428	−	1.18616i	−0.696496	−	0.0572015i
$431$			4.03116i			0.194174i	0.995276	+	0.0970871i	$0.0309526\pi$
$431$			4.03116i			0.194174i	−0.995276	+	0.0970871i	$0.969047\pi$
$432$		0			0
$433$		−	19.5320i		−	0.938650i	−0.883025	−	0.469325i	$-0.844497\pi$
$433$		−	19.5320i		−	0.938650i	0.883025	−	0.469325i	$-0.155503\pi$
$434$	−4.10787	+	50.0181i	−0.197184	+	2.40095i
$435$		0			0
$436$	17.5439	+	10.9159i	0.840201	+	0.522776i
$437$	11.3132	+	27.3124i	0.541182	+	1.30653i
$438$		0			0
$439$	−2.79500	+	2.79500i	−0.133398	+	0.133398i	−0.770653	−	0.637255i	$-0.780070\pi$
$439$	−2.79500	+	2.79500i	−0.133398	+	0.133398i	0.637255	+	0.770653i	$0.280070\pi$
$440$	−15.0967	−	3.78784i	−0.719706	−	0.180578i
$441$		0			0
$442$	4.19101	+	13.0496i	0.199346	+	0.620706i
$443$	−7.32465	−	17.6833i	−0.348005	−	0.840157i	−0.996855	−	0.0792418i	$-0.974750\pi$
$443$	−7.32465	−	17.6833i	−0.348005	−	0.840157i	0.648851	−	0.760916i	$-0.275250\pi$
$444$		0			0
$445$	9.49530	+	3.93308i	0.450120	+	0.186446i
$446$	10.6909	+	12.6040i	0.506227	+	0.596817i
$447$		0			0
$448$	−24.8025	+	7.50241i	−1.17181	+	0.354456i
$449$			32.9730i			1.55609i	0.628208	+	0.778045i	$0.283789\pi$
$449$			32.9730i			1.55609i	−0.628208	+	0.778045i	$0.716211\pi$
$450$		0			0
$451$	6.84071	−	16.5149i	0.322117	−	0.777658i
$452$	−3.09864	+	18.7375i	−0.145748	+	0.881340i
$453$		0			0
$454$	−39.9654	+	12.8353i	−1.87567	+	0.602391i
$455$	−4.62651	+	4.62651i	−0.216894	+	0.216894i
$456$		0			0
$457$	−16.3157	−	16.3157i	−0.763214	−	0.763214i	0.213688	−	0.976902i	$-0.431452\pi$
$457$	−16.3157	−	16.3157i	−0.763214	−	0.763214i	−0.976902	+	0.213688i	$0.931452\pi$
$458$	16.3394	+	8.39554i	0.763492	+	0.392298i
$459$		0			0
$460$	8.64502	−	13.8942i	0.403076	−	0.647819i
$461$	12.1576	+	5.03583i	0.566234	+	0.234542i	0.647389	−	0.762160i	$-0.275861\pi$
$461$	12.1576	+	5.03583i	0.566234	+	0.234542i	−0.0811549	+	0.996702i	$0.525861\pi$
$462$		0			0
$463$	−7.60945			−0.353641			−0.176821	−	0.984243i	$-0.556581\pi$
$463$	−7.60945			−0.353641			−0.176821	+	0.984243i	$0.556581\pi$
$464$	10.5313	−	11.9960i	0.488905	−	0.556899i
$465$		0			0
$466$	−2.48051	+	30.2031i	−0.114907	+	1.39913i
$467$	1.94882	−	4.70488i	0.0901809	−	0.217716i	−0.872353	−	0.488876i	$-0.837407\pi$
$467$	1.94882	−	4.70488i	0.0901809	−	0.217716i	0.962534	+	0.271160i	$0.0874072\pi$
$468$		0			0
$469$	−38.2894	+	15.8600i	−1.76804	+	0.732347i
$470$	4.61335	+	2.37043i	0.212798	+	0.109340i
$471$		0			0
$472$	10.9702	−	14.7794i	0.504943	−	0.680276i
$473$	−27.6819	−	27.6819i	−1.27281	−	1.27281i
$474$		0			0
$475$	−14.2607	+	5.90696i	−0.654324	+	0.271030i
$476$	−30.3266	+	21.7197i	−1.39002	+	0.995520i
$477$		0			0
$478$	−21.6328	−	25.5040i	−0.989460	−	1.16653i
$479$	8.04063			0.367386			0.183693	−	0.982984i	$-0.441195\pi$
$479$	8.04063			0.367386			0.183693	+	0.982984i	$0.441195\pi$
$480$		0			0
$481$	−7.36045			−0.335608
$482$	13.9814	+	16.4834i	0.636833	+	0.750796i
$483$		0			0
$484$	−11.6727	−	16.2983i	−0.530579	−	0.740833i
$485$	12.7608	−	5.28571i	0.579440	−	0.240012i
$486$		0			0
$487$	13.0819	+	13.0819i	0.592796	+	0.592796i	0.938386	−	0.345590i	$-0.112321\pi$
$487$	13.0819	+	13.0819i	0.592796	+	0.592796i	−0.345590	+	0.938386i	$0.612321\pi$
$488$	1.95609	+	13.2228i	0.0885481	+	0.598568i
$489$		0			0
$490$	−5.27085	−	2.70827i	−0.238113	−	0.122347i
$491$	−1.59917	+	0.662398i	−0.0721696	+	0.0298936i	−0.418476	−	0.908228i	$-0.637436\pi$
$491$	−1.59917	+	0.662398i	−0.0721696	+	0.0298936i	0.346307	+	0.938121i	$0.387436\pi$
$492$		0			0
$493$	8.79380	−	21.2301i	0.396053	−	0.956156i
$494$	0.844847	−	10.2870i	0.0380115	−	0.462834i
$495$		0			0
$496$	−14.1087	+	41.4912i	−0.633498	+	1.86301i
$497$	3.72963			0.167297
$498$		0			0
$499$	13.5962	+	5.63174i	0.608651	+	0.252111i	0.665652	−	0.746263i	$-0.268154\pi$
$499$	13.5962	+	5.63174i	0.608651	+	0.252111i	−0.0570007	+	0.998374i	$0.518154\pi$
$500$	17.4447	+	10.8542i	0.780152	+	0.485414i
$501$		0			0
$502$	13.9307	+	7.15790i	0.621759	+	0.319472i
$503$	−25.4762	−	25.4762i	−1.13593	−	1.13593i	−0.989173	−	0.146752i	$-0.953118\pi$
$503$	−25.4762	−	25.4762i	−1.13593	−	1.13593i	−0.146752	−	0.989173i	$-0.546882\pi$
$504$		0			0
$505$	0.374484	−	0.374484i	0.0166643	−	0.0166643i
$506$	42.0896	−	13.5175i	1.87111	−	0.600927i
$507$		0			0
$508$	34.2623	+	5.66597i	1.52014	+	0.251387i
$509$	5.65965	−	13.6636i	0.250860	−	0.605629i	−0.747414	−	0.664358i	$-0.768705\pi$
$509$	5.65965	−	13.6636i	0.250860	−	0.605629i	0.998274	+	0.0587294i	$0.0187049\pi$
$510$		0			0
$511$		−	28.0828i		−	1.24231i
$512$	−22.6015	+	1.08355i	−0.998853	+	0.0478868i
$513$		0			0
$514$	22.2252	+	26.2024i	0.980311	+	1.15574i
$515$	−1.78967	−	0.741307i	−0.0788624	−	0.0326659i
$516$		0			0
$517$	5.36204	+	12.9451i	0.235822	+	0.569325i
$518$	−6.12535	−	19.0726i	−0.269133	−	0.838000i
$519$		0			0
$520$	−4.90173	+	2.93536i	−0.214955	+	0.128724i
$521$	−6.11420	+	6.11420i	−0.267868	+	0.267868i	−0.828241	−	0.560373i	$-0.810658\pi$
$521$	−6.11420	+	6.11420i	−0.267868	+	0.267868i	0.560373	+	0.828241i	$0.310658\pi$
$522$		0			0
$523$	−3.45240	−	8.33482i	−0.150963	−	0.364456i	0.830248	−	0.557394i	$-0.188199\pi$
$523$	−3.45240	−	8.33482i	−0.150963	−	0.364456i	−0.981211	+	0.192937i	$0.938199\pi$
$524$	14.7686	−	23.7359i	0.645168	−	1.03691i
$525$		0			0
$526$	−2.79684	+	34.0548i	−0.121948	+	1.48486i
$527$			63.0872i			2.74812i
$528$		0			0
$529$			23.4777i			1.02077i
$530$	−16.8575	−	1.38446i	−0.732242	−	0.0601373i
$531$		0			0
$532$	27.3590	−	6.37164i	1.18616	−	0.276246i
$533$	−2.51107	−	6.06227i	−0.108767	−	0.262586i
$534$		0			0
$535$	7.91637	−	7.91637i	0.342254	−	0.342254i
$536$	−35.8006	+	5.29611i	−1.54635	+	0.228757i
$537$		0			0
$538$	40.0923	−	12.8761i	1.72850	−	0.555126i
$539$	−6.12624	−	14.7901i	−0.263876	−	0.637053i
$540$		0			0
$541$	8.67432	+	3.59302i	0.372938	+	0.154476i	0.561277	−	0.827628i	$-0.310310\pi$
$541$	8.67432	+	3.59302i	0.372938	+	0.154476i	−0.188339	+	0.982104i	$0.560310\pi$
$542$	1.11354	−	0.944520i	0.0478308	−	0.0405706i
$543$		0			0
$544$	−30.3016	+	11.9513i	−1.29917	+	0.512408i
$545$			12.3993i			0.531127i
$546$		0			0
$547$	−8.99937	+	21.7264i	−0.384785	+	0.928954i	0.606240	+	0.795282i	$0.292677\pi$
$547$	−8.99937	+	21.7264i	−0.384785	+	0.928954i	−0.991026	+	0.133673i	$0.957323\pi$
$548$	2.36374	+	3.30043i	0.100974	+	0.140988i
$549$		0			0
$550$	7.05792	+	21.9763i	0.300951	+	0.937072i
$551$	−12.2365	+	12.2365i	−0.521293	+	0.521293i
$552$		0			0
$553$	−18.3170	−	18.3170i	−0.778918	−	0.778918i
$554$	−4.88395	+	9.50517i	−0.207499	+	0.403836i
$555$		0			0
$556$	5.12070	−	1.19256i	0.217166	−	0.0505759i
$557$	−12.0218	−	4.97960i	−0.509380	−	0.210992i	0.113165	−	0.993576i	$-0.463901\pi$
$557$	−12.0218	−	4.97960i	−0.509380	−	0.210992i	−0.622545	+	0.782584i	$0.713901\pi$
$558$		0			0
$559$	−14.3704			−0.607803
$560$	−11.6854	−	10.2587i	−0.493797	−	0.433507i
$561$		0			0
$562$	11.2826	+	0.926616i	0.475929	+	0.0390869i
$563$	−3.87198	+	9.34780i	−0.163185	+	0.393963i	−0.984228	−	0.176903i	$-0.943392\pi$
$563$	−3.87198	+	9.34780i	−0.163185	+	0.393963i	0.821044	+	0.570865i	$0.193392\pi$
$564$		0			0
$565$	−10.5292	+	4.36135i	−0.442969	+	0.183484i
$566$	6.27616	−	12.2147i	0.263807	−	0.513422i
$567$		0			0
$568$	3.15891	+	0.792589i	0.132545	+	0.0332563i
$569$	27.9604	+	27.9604i	1.17216	+	1.17216i	0.981693	+	0.190469i	$0.0610008\pi$
$569$	27.9604	+	27.9604i	1.17216	+	1.17216i	0.190469	+	0.981693i	$0.438999\pi$
$570$		0			0
$571$	−1.06863	+	0.442642i	−0.0447209	+	0.0185240i	−0.404932	−	0.914347i	$-0.632705\pi$
$571$	−1.06863	+	0.442642i	−0.0447209	+	0.0185240i	0.360211	+	0.932871i	$0.382705\pi$
$572$	−15.2278	−	2.51822i	−0.636705	−	0.105292i
$573$		0			0
$574$	13.6190	−	11.5518i	0.568445	−	0.482161i
$575$	−24.2675			−1.01202
$576$		0			0
$577$	39.9542			1.66332			0.831658	−	0.555288i	$-0.187392\pi$
$577$	39.9542			1.66332			0.831658	+	0.555288i	$0.187392\pi$
$578$	−17.4251	+	14.7801i	−0.724787	+	0.614772i
$579$		0			0
$580$	9.45066	+	1.56286i	0.392417	+	0.0648943i
$581$	35.3450	−	14.6404i	1.46636	−	0.607386i
$582$		0			0
$583$	−32.3099	−	32.3099i	−1.33814	−	1.33814i
$584$	5.96790	−	23.7854i	0.246954	−	0.984248i
$585$		0			0
$586$	8.71129	−	16.9540i	0.359860	−	0.700361i
$587$	−6.65416	+	2.75624i	−0.274646	+	0.113762i	−0.515756	−	0.856736i	$-0.672489\pi$
$587$	−6.65416	+	2.75624i	−0.274646	+	0.113762i	0.241109	+	0.970498i	$0.422489\pi$
$588$		0			0
$589$	18.1810	−	43.8927i	0.749134	−	1.80857i
$590$	11.0079	+	0.904056i	0.453190	+	0.0372194i
$591$		0			0
$592$	−1.13490	−	17.4557i	−0.0466439	−	0.717425i
$593$	−30.4542			−1.25060			−0.625302	−	0.780383i	$-0.715024\pi$
$593$	−30.4542			−1.25060			−0.625302	+	0.780383i	$0.715024\pi$
$594$		0			0
$595$	−20.6804	−	8.56610i	−0.847814	−	0.351176i
$596$	−11.2553	+	2.62126i	−0.461036	+	0.107371i
$597$		0			0
$598$	7.41626	−	14.4336i	0.303273	−	0.590232i
$599$	27.7991	+	27.7991i	1.13584	+	1.13584i	0.989188	+	0.146654i	$0.0468502\pi$
$599$	27.7991	+	27.7991i	1.13584	+	1.13584i	0.146654	+	0.989188i	$0.453150\pi$
$600$		0			0
$601$	10.9042	−	10.9042i	0.444792	−	0.444792i	−0.448827	−	0.893619i	$-0.648158\pi$
$601$	10.9042	−	10.9042i	0.444792	−	0.444792i	0.893619	+	0.448827i	$0.148158\pi$
$602$	−11.9590	−	37.2369i	−0.487413	−	1.51766i
$603$		0			0
$604$	−12.9787	−	18.1217i	−0.528094	−	0.737363i
$605$	4.60365	−	11.1142i	0.187165	−	0.451857i
$606$		0			0
$607$			12.2609i			0.497654i	0.968548	+	0.248827i	$0.0800451\pi$
$607$			12.2609i			0.497654i	−0.968548	+	0.248827i	$0.919955\pi$
$608$	24.5264	+	0.417462i	0.994678	+	0.0169303i
$609$		0			0
$610$	−6.11700	+	5.18850i	−0.247670	+	0.210076i
$611$	4.75186	+	1.96829i	0.192240	+	0.0796283i
$612$		0			0
$613$	12.0970	+	29.2047i	0.488593	+	1.17957i	0.955428	+	0.295224i	$0.0953942\pi$
$613$	12.0970	+	29.2047i	0.488593	+	1.17957i	−0.466835	+	0.884344i	$0.654606\pi$
$614$	22.1550	−	7.11532i	0.894104	−	0.287151i
$615$		0			0
$616$	−6.14724	−	41.5542i	−0.247679	−	1.67426i
$617$	20.3519	−	20.3519i	0.819336	−	0.819336i	−0.166676	−	0.986012i	$-0.553303\pi$
$617$	20.3519	−	20.3519i	0.819336	−	0.819336i	0.986012	+	0.166676i	$0.0533033\pi$
$618$		0			0
$619$	17.1759	+	41.4663i	0.690358	+	1.66667i	0.744059	+	0.668114i	$0.232898\pi$
$619$	17.1759	+	41.4663i	0.690358	+	1.66667i	−0.0537006	+	0.998557i	$0.517102\pi$
$620$	−25.6127	+	5.96496i	−1.02863	+	0.239559i
$621$		0			0
$622$	28.8789	+	2.37175i	1.15794	+	0.0950986i
$623$			27.7377i			1.11129i
$624$		0			0
$625$		−	5.46885i		−	0.218754i
$626$	−1.29140	+	15.7243i	−0.0516148	+	0.628471i
$627$		0			0
$628$	−14.7073	+	23.6375i	−0.586886	+	0.943237i
$629$	−9.63649	−	23.2646i	−0.384232	−	0.927619i
$630$		0			0
$631$	−12.5561	+	12.5561i	−0.499851	+	0.499851i	−0.911392	−	0.411540i	$-0.864991\pi$
$631$	−12.5561	+	12.5561i	−0.499851	+	0.499851i	0.411540	+	0.911392i	$0.364991\pi$
$632$	−11.6215	−	19.4066i	−0.462278	−	0.771953i
$633$		0			0
$634$	2.42884	+	7.56270i	0.0964617	+	0.300353i
$635$	7.97489	+	19.2531i	0.316474	+	0.764036i
$636$		0			0
$637$	−5.42910	−	2.24881i	−0.215109	−	0.0891010i
$638$	16.7389	+	19.7343i	0.662699	+	0.781290i
$639$		0			0
$640$	−7.71714	−	11.1721i	−0.305047	−	0.441616i
$641$			23.6971i			0.935980i	0.883734	+	0.467990i	$0.155022\pi$
$641$			23.6971i			0.935980i	−0.883734	+	0.467990i	$0.844978\pi$
$642$		0			0
$643$	14.2539	−	34.4119i	0.562118	−	1.35707i	−0.345952	−	0.938252i	$-0.612444\pi$
$643$	14.2539	−	34.4119i	0.562118	−	1.35707i	0.908069	−	0.418820i	$-0.137556\pi$
$644$	43.5723	+	7.20558i	1.71699	+	0.283940i
$645$		0			0
$646$	33.6207	−	10.7977i	1.32279	−	0.424828i
$647$	−9.10926	+	9.10926i	−0.358122	+	0.358122i	−0.863120	−	0.504998i	$-0.831493\pi$
$647$	−9.10926	+	9.10926i	−0.358122	+	0.358122i	0.504998	+	0.863120i	$0.331493\pi$
$648$		0			0
$649$	21.0984	+	21.0984i	0.828183	+	0.828183i
$650$	7.53621	+	3.87226i	0.295595	+	0.151883i
$651$		0			0
$652$	−13.2726	−	8.25828i	−0.519796	−	0.323419i
$653$	−45.0078	−	18.6428i	−1.76129	−	0.729551i	−0.996341	−	0.0854621i	$-0.972763\pi$
$653$	−45.0078	−	18.6428i	−1.76129	−	0.729551i	−0.764951	−	0.644089i	$-0.777237\pi$
$654$		0			0
$655$	16.7755			0.655473
$656$	13.9898	−	6.88987i	0.546210	−	0.269004i
$657$		0			0
$658$	−1.14577	+	13.9511i	−0.0446668	+	0.543871i
$659$	7.19109	−	17.3608i	0.280125	−	0.676281i	−0.719713	−	0.694271i	$-0.755727\pi$
$659$	7.19109	−	17.3608i	0.280125	−	0.676281i	0.999838	+	0.0179900i	$0.00572670\pi$
$660$		0			0
$661$	33.0166	−	13.6759i	1.28420	−	0.531931i	0.366945	−	0.930243i	$-0.380404\pi$
$661$	33.0166	−	13.6759i	1.28420	−	0.531931i	0.917250	+	0.398312i	$0.130404\pi$
$662$	−15.7713	−	8.10362i	−0.612969	−	0.314956i
$663$		0			0
$664$	33.0476	−	4.88884i	1.28250	−	0.189724i
$665$	11.9197	+	11.9197i	0.462225	+	0.462225i
$666$		0			0
$667$	−25.1355	+	10.4115i	−0.973252	+	0.403134i
$668$	−16.5938	−	23.1695i	−0.642033	−	0.896453i
$669$		0			0
$670$	−14.0478	−	16.5617i	−0.542715	−	0.639836i
$671$	−21.6687			−0.836510
$672$		0			0
$673$	24.2342			0.934159			0.467080	−	0.884215i	$-0.345306\pi$
$673$	24.2342			0.934159			0.467080	+	0.884215i	$0.345306\pi$
$674$	31.5978	+	37.2523i	1.21710	+	1.43490i
$675$		0			0
$676$	16.5318	−	11.8399i	0.635838	−	0.455382i
$677$	13.5836	−	5.62649i	0.522058	−	0.216244i	−0.106062	−	0.994359i	$-0.533824\pi$
$677$	13.5836	−	5.62649i	0.522058	−	0.216244i	0.628121	+	0.778116i	$0.283824\pi$
$678$		0			0
$679$	26.3588	+	26.3588i	1.01156	+	1.01156i
$680$	−15.6954	−	11.6501i	−0.601891	−	0.446761i
$681$		0			0
$682$	−63.1900	−	32.4683i	−2.41967	−	1.24328i
$683$	−36.2049	+	14.9966i	−1.38534	+	0.573828i	−0.945905	−	0.324445i	$-0.894822\pi$
$683$	−36.2049	+	14.9966i	−1.38534	+	0.573828i	−0.439438	+	0.898273i	$0.644822\pi$
$684$		0			0
$685$	−0.932246	+	2.25064i	−0.0356193	+	0.0859926i
$686$	−1.31551	+	16.0179i	−0.0502263	+	0.611565i
$687$		0			0
$688$	−2.21575	−	34.0801i	−0.0844745	−	1.29929i
$689$	−16.7729			−0.638997
$690$		0			0
$691$	27.6470	+	11.4518i	1.05174	+	0.435645i	0.840513	−	0.541792i	$-0.182254\pi$
$691$	27.6470	+	11.4518i	1.05174	+	0.435645i	0.211228	+	0.977437i	$0.432254\pi$
$692$	9.10832	−	14.6388i	0.346246	−	0.556483i
$693$		0			0
$694$	−44.3667	−	22.7965i	−1.68414	−	0.865344i
$695$	2.23097	+	2.23097i	0.0846256	+	0.0846256i
$696$		0			0
$697$	15.8738	−	15.8738i	0.601261	−	0.601261i
$698$	−28.3576	+	9.10734i	−1.07335	+	0.344718i
$699$		0			0
$700$	−3.76226	+	22.7505i	−0.142200	+	0.859887i
$701$	12.3452	−	29.8040i	0.466272	−	1.12568i	−0.499506	−	0.866310i	$-0.666485\pi$
$701$	12.3452	−	29.8040i	0.466272	−	1.12568i	0.965778	−	0.259369i	$-0.0835147\pi$
$702$		0			0
$703$			18.9634i			0.715217i
$704$	3.62416	−	36.5017i	0.136590	−	1.37571i
$705$		0			0
$706$	−26.4227	−	31.1510i	−0.994430	−	1.17239i
$707$	1.32050	+	0.546971i	0.0496627	+	0.0205710i
$708$		0			0
$709$	6.65689	+	16.0712i	0.250005	+	0.603565i	0.998204	−	0.0599095i	$-0.0190812\pi$
$709$	6.65689	+	16.0712i	0.250005	+	0.603565i	−0.748199	+	0.663474i	$0.769081\pi$
$710$	0.597600	+	1.86075i	0.0224275	+	0.0698328i
$711$		0			0
$712$	−5.89456	+	23.4931i	−0.220908	+	0.880442i
$713$	52.8157	−	52.8157i	1.97796	−	1.97796i
$714$		0			0
$715$	−3.54442	−	8.55698i	−0.132554	−	0.320013i
$716$	−13.0440	−	8.11604i	−0.487478	−	0.303311i
$717$		0			0
$718$	−3.58537	+	43.6561i	−0.133805	+	1.62923i
$719$			9.06929i			0.338228i	0.985597	+	0.169114i	$0.0540905\pi$
$719$			9.06929i			0.338228i	−0.985597	+	0.169114i	$0.945909\pi$
$720$		0			0
$721$		−	5.22799i		−	0.194701i
$722$	0.276616	+	0.0227178i	0.0102946	+	0.000845470i
$723$		0			0
$724$	4.30798	+	18.4979i	0.160105	+	0.687469i
$725$	−5.43616	−	13.1241i	−0.201894	−	0.487415i
$726$		0			0
$727$	4.93965	−	4.93965i	0.183201	−	0.183201i	−0.609548	−	0.792749i	$-0.708649\pi$
$727$	4.93965	−	4.93965i	0.183201	−	0.183201i	0.792749	+	0.609548i	$0.208649\pi$
$728$	−12.3815	−	9.19033i	−0.458890	−	0.340616i
$729$		0			0
$730$	14.0108	−	4.49971i	0.518562	−	0.166542i
$731$	−18.8141	−	45.4212i	−0.695864	−	1.67997i
$732$		0			0
$733$	18.9279	+	7.84021i	0.699119	+	0.289585i	0.703794	−	0.710404i	$-0.251488\pi$
$733$	18.9279	+	7.84021i	0.699119	+	0.289585i	−0.00467439	+	0.999989i	$0.501488\pi$
$734$	−4.61589	+	3.91525i	−0.170376	+	0.144515i
$735$		0			0
$736$	35.3734	+	15.3626i	1.30388	+	0.566271i
$737$		−	58.6678i		−	2.16106i
$738$		0			0
$739$	−8.94853	+	21.6037i	−0.329177	+	0.794704i	0.669477	+	0.742833i	$0.266518\pi$
$739$	−8.94853	+	21.6037i	−0.329177	+	0.794704i	−0.998654	+	0.0518708i	$0.983482\pi$
$740$	8.53402	−	6.11200i	0.313717	−	0.224682i
$741$		0			0
$742$	−13.9584	−	43.4623i	−0.512429	−	1.59555i
$743$	34.2959	−	34.2959i	1.25819	−	1.25819i	0.306239	−	0.951955i	$-0.400929\pi$
$743$	34.2959	−	34.2959i	1.25819	−	1.25819i	0.951955	−	0.306239i	$-0.0990708\pi$
$744$		0			0
$745$	−4.90369	−	4.90369i	−0.179657	−	0.179657i
$746$	1.14727	−	2.23282i	0.0420045	−	0.0817494i
$747$		0			0
$748$	−11.9771	−	51.4281i	−0.437926	−	1.88040i
$749$	27.9147	+	11.5626i	1.01998	+	0.422490i
$750$		0			0
$751$	−8.46502			−0.308893			−0.154446	−	0.988001i	$-0.549359\pi$
$751$	−8.46502			−0.308893			−0.154446	+	0.988001i	$0.549359\pi$
$752$	−3.93521	+	11.5728i	−0.143502	+	0.422015i
$753$		0			0
$754$	9.46711	+	0.777511i	0.344772	+	0.0283153i
$755$	5.11870	−	12.3576i	0.186289	−	0.449740i
$756$		0			0
$757$	−38.2928	+	15.8614i	−1.39178	+	0.576493i	−0.947604	−	0.319449i	$-0.896502\pi$
$757$	−38.2928	+	15.8614i	−1.39178	+	0.576493i	−0.444173	+	0.895941i	$0.646502\pi$
$758$	−17.2045	+	33.4836i	−0.624897	+	1.21618i
$759$		0			0
$760$	7.56261	+	12.6287i	0.274325	+	0.458092i
$761$	0.833887	+	0.833887i	0.0302284	+	0.0302284i	0.722059	−	0.691831i	$-0.243196\pi$
$761$	0.833887	+	0.833887i	0.0302284	+	0.0302284i	−0.691831	+	0.722059i	$0.743196\pi$
$762$		0			0
$763$	−30.9164	+	12.8060i	−1.11925	+	0.463608i
$764$	3.69344	−	22.3343i	0.133624	−	0.808028i
$765$		0			0
$766$	9.64229	−	8.17870i	0.348390	−	0.295508i
$767$	10.9527			0.395480
$768$		0			0
$769$	−32.1393			−1.15897			−0.579486	−	0.814982i	$-0.696747\pi$
$769$	−32.1393			−1.15897			−0.579486	+	0.814982i	$0.696747\pi$
$770$	19.2234	−	16.3055i	0.692762	−	0.587608i
$771$		0			0
$772$	−0.328719	+	1.98777i	−0.0118309	+	0.0715415i
$773$	28.3337	−	11.7362i	1.01909	−	0.422122i	0.190329	−	0.981720i	$-0.439045\pi$
$773$	28.3337	−	11.7362i	1.01909	−	0.422122i	0.828764	+	0.559598i	$0.189045\pi$
$774$		0			0
$775$	27.5767	+	27.5767i	0.990585	+	0.990585i
$776$	16.7237	+	27.9268i	0.600347	+	1.00251i
$777$		0			0
$778$	18.4616	−	35.9300i	0.661880	−	1.28815i
$779$	−15.6187	+	6.46949i	−0.559599	+	0.231794i
$780$		0			0
$781$	−2.02042	+	4.87773i	−0.0722964	+	0.174539i
$782$	55.3304	+	4.54415i	1.97861	+	0.162499i
$783$		0			0
$784$	4.49606	−	13.2221i	0.160574	−	0.472219i
$785$	−16.7059			−0.596261
$786$		0			0
$787$	17.1011	+	7.08351i	0.609588	+	0.252500i	0.666052	−	0.745905i	$-0.267983\pi$
$787$	17.1011	+	7.08351i	0.609588	+	0.252500i	−0.0564642	+	0.998405i	$0.517983\pi$
$788$	−2.38221	−	10.2289i	−0.0848628	−	0.364390i
$789$		0			0
$790$	6.20359	−	12.0735i	0.220714	−	0.429555i
$791$	−21.7492	−	21.7492i	−0.773313	−	0.773313i
$792$		0			0
$793$	−5.62439	+	5.62439i	−0.199728	+	0.199728i
$794$	−5.90449	−	18.3848i	−0.209542	−	0.652454i
$795$		0			0
$796$	−27.5044	+	19.6984i	−0.974867	+	0.698192i
$797$	8.89124	−	21.4654i	0.314944	−	0.760342i	−0.684563	−	0.728953i	$-0.740007\pi$
$797$	8.89124	−	21.4654i	0.314944	−	0.760342i	0.999507	−	0.0313886i	$-0.00999293\pi$
$798$		0			0
$799$			17.5964i			0.622515i
$800$	−8.02127	+	18.4696i	−0.283595	+	0.652998i
$801$		0			0
$802$	−5.71872	+	4.85068i	−0.201935	+	0.171284i
$803$	36.7275	+	15.2130i	1.29609	+	0.536857i
$804$		0			0
$805$	10.1419	+	24.4847i	0.357455	+	0.862973i
$806$	−24.8294	+	7.97422i	−0.874577	+	0.280880i
$807$		0			0
$808$	1.00220	+	0.743893i	0.0352572	+	0.0261701i
$809$	19.3208	−	19.3208i	0.679283	−	0.679283i	−0.280555	−	0.959838i	$-0.590519\pi$
$809$	19.3208	−	19.3208i	0.679283	−	0.679283i	0.959838	+	0.280555i	$0.0905186\pi$
$810$		0			0
$811$	−4.77409	−	11.5257i	−0.167641	−	0.404721i	0.817625	−	0.575751i	$-0.195290\pi$
$811$	−4.77409	−	11.5257i	−0.167641	−	0.404721i	−0.985266	+	0.171030i	$0.945290\pi$
$812$	5.86381	+	25.1784i	0.205779	+	0.883589i
$813$		0			0
$814$	28.2619	+	2.32108i	0.990580	+	0.0813539i
$815$		−	9.38052i		−	0.328585i
$816$		0			0
$817$			37.0237i			1.29529i
$818$	3.63579	−	44.2700i	0.127122	−	1.54786i
$819$		0			0
$820$	7.94546	+	4.94370i	0.277467	+	0.172641i
$821$	9.80936	+	23.6819i	0.342349	+	0.826504i	0.997477	+	0.0709861i	$0.0226146\pi$
$821$	9.80936	+	23.6819i	0.342349	+	0.826504i	−0.655128	+	0.755518i	$0.727385\pi$
$822$		0			0
$823$	−13.2750	+	13.2750i	−0.462739	+	0.462739i	−0.899552	−	0.436813i	$-0.856107\pi$
$823$	−13.2750	+	13.2750i	−0.462739	+	0.462739i	0.436813	+	0.899552i	$0.356107\pi$
$824$	1.11101	−	4.42798i	0.0387038	−	0.154256i
$825$		0			0
$826$	9.11483	+	28.3809i	0.317146	+	0.987498i
$827$	6.87946	+	16.6085i	0.239222	+	0.577533i	0.997203	−	0.0747437i	$-0.0238139\pi$
$827$	6.87946	+	16.6085i	0.239222	+	0.577533i	−0.757981	+	0.652277i	$0.773814\pi$
$828$		0			0
$829$	−16.3836	−	6.78632i	−0.569027	−	0.235699i	0.0795718	−	0.996829i	$-0.474645\pi$
$829$	−16.3836	−	6.78632i	−0.569027	−	0.235699i	−0.648599	+	0.761130i	$0.724645\pi$
$830$	12.9676	+	15.2882i	0.450111	+	0.530659i
$831$		0			0
$832$	−8.53380	−	10.4152i	−0.295856	−	0.361082i
$833$		−	20.1042i		−	0.696570i
$834$		0			0
$835$	6.54448	−	15.7998i	0.226481	−	0.546774i
$836$	−6.48791	+	39.2326i	−0.224389	+	1.35689i
$837$		0			0
$838$	−28.1696	+	9.04696i	−0.973102	+	0.312522i
$839$	−38.9846	+	38.9846i	−1.34590	+	1.34590i	−0.455830	+	0.890067i	$0.650657\pi$
$839$	−38.9846	+	38.9846i	−1.34590	+	1.34590i	−0.890067	+	0.455830i	$0.849343\pi$
$840$		0			0
$841$	9.24486	+	9.24486i	0.318788	+	0.318788i
$842$	26.9458	+	13.8453i	0.928615	+	0.477141i
$843$		0			0
$844$	11.1907	−	17.9856i	0.385200	−	0.619089i
$845$	11.2734	+	4.66960i	0.387817	+	0.160639i
$846$		0			0
$847$	32.4668			1.11557
$848$	−2.58619	−	39.7778i	−0.0888100	−	1.36598i
$849$		0			0
$850$	−2.37265	+	28.8898i	−0.0813811	+	0.990910i
$851$	−11.4092	+	27.5442i	−0.391102	+	0.944205i
$852$		0			0
$853$	16.8941	−	6.99775i	0.578442	−	0.239598i	−0.0742276	−	0.997241i	$-0.523649\pi$
$853$	16.8941	−	6.99775i	0.578442	−	0.239598i	0.652669	+	0.757643i	$0.273649\pi$
$854$	−19.2546	−	9.89343i	−0.658881	−	0.338546i
$855$		0			0
$856$	21.1859	+	15.7255i	0.724118	+	0.537485i
$857$	−17.0344	−	17.0344i	−0.581884	−	0.581884i	0.353537	−	0.935421i	$-0.384979\pi$
$857$	−17.0344	−	17.0344i	−0.581884	−	0.581884i	−0.935421	+	0.353537i	$0.884979\pi$
$858$		0			0
$859$	−2.63796	+	1.09268i	−0.0900062	+	0.0372818i	−0.427232	−	0.904142i	$-0.640511\pi$
$859$	−2.63796	+	1.09268i	−0.0900062	+	0.0372818i	0.337226	+	0.941424i	$0.390511\pi$
$860$	16.6616	−	11.9329i	0.568157	−	0.406910i
$861$		0			0
$862$	−3.68768	−	4.34760i	−0.125603	−	0.148080i
$863$	21.2829			0.724480			0.362240	−	0.932085i	$-0.382012\pi$
$863$	21.2829			0.724480			0.362240	+	0.932085i	$0.382012\pi$
$864$		0			0
$865$	10.3461			0.351777
$866$	17.8678	+	21.0652i	0.607171	+	0.715826i
$867$		0			0
$868$	−41.3259	−	57.7022i	−1.40269	−	1.95854i
$869$	33.8782	−	14.0328i	1.14924	−	0.476031i
$870$		0			0
$871$	−15.2280	−	15.2280i	−0.515982	−	0.515982i
$872$	−28.9068	+	4.27628i	−0.978908	+	0.144813i
$873$		0			0
$874$	−37.1864	−	19.1071i	−1.25785	−	0.646308i
$875$	−30.7416	+	12.7336i	−1.03926	+	0.430474i
$876$		0			0
$877$	−14.6254	+	35.3090i	−0.493866	+	1.19230i	0.458871	+	0.888503i	$0.348254\pi$
$877$	−14.6254	+	35.3090i	−0.493866	+	1.19230i	−0.952737	+	0.303796i	$0.901746\pi$
$878$	0.457552	−	5.57124i	0.0154416	−	0.188020i
$879$		0			0
$880$	19.7468	−	9.72515i	0.665665	−	0.327835i
$881$	11.3793			0.383379			0.191690	−	0.981456i	$-0.438603\pi$
$881$	11.3793			0.383379			0.191690	+	0.981456i	$0.438603\pi$
$882$		0			0
$883$	21.1622	+	8.76567i	0.712165	+	0.294988i	0.709200	−	0.705007i	$-0.249056\pi$
$883$	21.1622	+	8.76567i	0.712165	+	0.294988i	0.00296458	+	0.999996i	$0.499056\pi$
$884$	−16.4577	−	10.2400i	−0.553531	−	0.344409i
$885$		0			0
$886$	24.0761	+	12.3708i	0.808853	+	0.415605i
$887$	10.7830	+	10.7830i	0.362058	+	0.362058i	0.864570	−	0.502512i	$-0.167591\pi$
$887$	10.7830	+	10.7830i	0.362058	+	0.362058i	−0.502512	+	0.864570i	$0.667591\pi$
$888$		0			0
$889$	−39.7692	+	39.7692i	−1.33382	+	1.33382i
$890$	−13.8386	+	4.44441i	−0.463871	+	0.148977i
$891$		0			0
$892$	−23.0601	−	3.81346i	−0.772110	−	0.127684i
$893$	5.07106	−	12.2426i	0.169697	−	0.409684i
$894$		0			0
$895$		−	9.21895i		−	0.308156i
$896$	19.8863	−	30.7805i	0.664353	−	1.02830i
$897$		0			0
$898$	−30.1634	−	35.5612i	−1.00657	−	1.18669i
$899$	40.3944	+	16.7319i	1.34723	+	0.558040i
$900$		0			0
$901$	−21.9595	−	53.0150i	−0.731578	−	1.76619i
$902$	7.73006	+	24.0691i	0.257383	+	0.801415i
$903$		0			0
$904$	−13.7991	−	23.0430i	−0.458951	−	0.766399i
$905$	−8.05911	+	8.05911i	−0.267894	+	0.267894i
$906$		0			0
$907$	−19.8154	−	47.8385i	−0.657959	−	1.58845i	−0.800952	−	0.598729i	$-0.795673\pi$
$907$	−19.8154	−	47.8385i	−0.657959	−	1.58845i	0.142993	−	0.989724i	$-0.454327\pi$
$908$	31.3609	−	50.4029i	1.04075	−	1.67268i
$909$		0			0
$910$	0.757379	−	9.22198i	0.0251069	−	0.305706i
$911$		−	8.30716i		−	0.275229i	−0.990486	−	0.137614i	$-0.956057\pi$
$911$		−	8.30716i		−	0.275229i	0.990486	−	0.137614i	$-0.0439434\pi$
$912$		0			0
$913$			54.1563i			1.79231i
$914$	32.5218	+	2.67094i	1.07573	+	0.0883467i
$915$		0			0
$916$	−25.3022	+	5.89264i	−0.836008	+	0.194698i
$917$	17.3257	+	41.8280i	0.572146	+	1.38128i
$918$		0			0
$919$	−4.11417	+	4.11417i	−0.135714	+	0.135714i	−0.771700	−	0.635986i	$-0.780593\pi$
$919$	−4.11417	+	4.11417i	−0.135714	+	0.135714i	0.635986	+	0.771700i	$0.280593\pi$
$920$	3.38667	+	22.8932i	0.111655	+	0.754767i
$921$		0			0
$922$	−17.7186	+	5.69053i	−0.583532	+	0.187408i
$923$	0.741653	+	1.79051i	0.0244118	+	0.0589353i
$924$		0			0
$925$	−14.3817	−	5.95710i	−0.472868	−	0.195868i
$926$	8.20677	−	6.96107i	0.269691	−	0.228755i
$927$		0			0
$928$	−0.384190	+	22.5716i	−0.0126116	+	0.740950i
$929$			8.53638i			0.280069i	0.990147	+	0.140035i	$0.0447214\pi$
$929$			8.53638i			0.280069i	−0.990147	+	0.140035i	$0.955279\pi$
$930$		0			0
$931$	−5.79379	+	13.9875i	−0.189884	+	0.458420i
$932$	−24.9544	−	34.8431i	−0.817407	−	1.14132i
$933$		0			0
$934$	2.20219	+	6.85697i	0.0720578	+	0.224367i
$935$	22.4060	−	22.4060i	0.732756	−	0.732756i
$936$		0			0
$937$	33.6362	+	33.6362i	1.09885	+	1.09885i	0.994546	+	0.104302i	$0.0332609\pi$
$937$	33.6362	+	33.6362i	1.09885	+	1.09885i	0.104302	+	0.994546i	$0.466739\pi$
$938$	26.7864	−	52.1319i	0.874607	−	1.70217i
$939$		0			0
$940$	−7.14394	+	1.66375i	−0.233010	+	0.0542657i
$941$	−26.9327	−	11.1559i	−0.877979	−	0.363671i	−0.102267	−	0.994757i	$-0.532609\pi$
$941$	−26.9327	−	11.1559i	−0.877979	−	0.363671i	−0.775713	+	0.631086i	$0.782609\pi$
$942$		0			0
$943$	−26.5785			−0.865516
$944$	1.68878	+	25.9749i	0.0549651	+	0.845412i
$945$		0			0
$946$	55.1780	+	4.53163i	1.79399	+	0.147336i
$947$	−14.4578	+	34.9042i	−0.469816	+	1.13424i	0.494428	+	0.869219i	$0.335378\pi$
$947$	−14.4578	+	34.9042i	−0.469816	+	1.13424i	−0.964244	+	0.265017i	$0.914622\pi$
$948$		0			0
$949$	13.4819	−	5.58437i	0.437640	−	0.181276i
$950$	9.97643	−	19.4162i	0.323678	−	0.629944i
$951$		0			0
$952$	12.8381	−	51.1671i	0.416086	−	1.65834i
$953$	−0.567609	−	0.567609i	−0.0183867	−	0.0183867i	0.697854	−	0.716240i	$-0.254139\pi$
$953$	−0.567609	−	0.567609i	−0.0183867	−	0.0183867i	−0.716240	+	0.697854i	$0.754139\pi$
$954$		0			0
$955$	12.5504	−	5.19855i	0.406121	−	0.168221i
$956$	46.6617	+	7.71648i	1.50915	+	0.249569i
$957$		0			0
$958$	−8.67179	+	7.35551i	−0.280173	+	0.237646i
$959$	−6.57457			−0.212304
$960$		0			0
$961$	−89.0357			−2.87212
$962$	7.93822	−	6.73329i	0.255939	−	0.217090i
$963$		0			0
$964$	−30.1577	−	4.98719i	−0.971314	−	0.160627i
$965$	−1.11699	+	0.462674i	−0.0359573	+	0.0148940i
$966$		0			0
$967$	2.62874	+	2.62874i	0.0845344	+	0.0845344i	0.748110	−	0.663575i	$-0.230962\pi$
$967$	2.62874	+	2.62874i	0.0845344	+	0.0845344i	−0.663575	+	0.748110i	$0.730962\pi$
$968$	27.4986	+	6.89956i	0.883838	+	0.221760i
$969$		0			0
$970$	−8.92719	+	17.3741i	−0.286635	+	0.557850i
$971$	−10.7209	+	4.44073i	−0.344049	+	0.142510i	−0.548016	−	0.836468i	$-0.684617\pi$
$971$	−10.7209	+	4.44073i	−0.344049	+	0.142510i	0.203967	+	0.978978i	$0.434617\pi$
$972$		0			0
$973$	−3.25856	+	7.86685i	−0.104465	+	0.252200i
$974$	−26.0759	−	2.14155i	−0.835526	−	0.0686198i
$975$		0			0
$976$	−14.2058	−	12.4713i	−0.454715	−	0.399197i
$977$	−0.278119			−0.00889781			−0.00444890	−	0.999990i	$-0.501416\pi$
$977$	−0.278119			−0.00889781			−0.00444890	+	0.999990i	$0.501416\pi$
$978$		0			0
$979$	−36.2762	−	15.0261i	−1.15939	−	0.480236i
$980$	8.16210	−	1.90088i	0.260729	−	0.0607212i
$981$		0			0
$982$	1.11874	−	2.17730i	0.0357005	−	0.0694805i
$983$	−32.0355	−	32.0355i	−1.02177	−	1.02177i	−0.999758	−	0.0220153i	$-0.992992\pi$
$983$	−32.0355	−	32.0355i	−1.02177	−	1.02177i	−0.0220153	−	0.999758i	$-0.507008\pi$
$984$		0			0
$985$	4.45650	−	4.45650i	0.141996	−	0.141996i
$986$	9.93706	+	30.9411i	0.316461	+	0.985365i
$987$		0			0
$988$	8.49931	+	11.8674i	0.270399	+	0.377551i
$989$	−22.2751	+	53.7768i	−0.708307	+	1.71000i
$990$		0			0
$991$			53.8273i			1.70988i	0.518728	+	0.854939i	$0.326406\pi$
$991$			53.8273i			1.70988i	−0.518728	+	0.854939i	$0.673594\pi$
$992$	−22.7397	−	57.6546i	−0.721985	−	1.83053i
$993$		0			0
$994$	−4.02240	+	3.41184i	−0.127583	+	0.108217i
$995$	−18.7559	−	7.76893i	−0.594601	−	0.246292i
$996$		0			0
$997$	−0.181447	−	0.438051i	−0.00574648	−	0.0138732i	0.920980	−	0.389609i	$-0.127390\pi$
$997$	−0.181447	−	0.438051i	−0.00574648	−	0.0138732i	−0.926727	+	0.375736i	$0.877390\pi$
$998$	−19.8154	+	6.36391i	−0.627244	+	0.201446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.323.7	yes	128
3.2	odd	2	inner	864.2.w.a.323.26	yes	128
32.11	odd	8	inner	864.2.w.a.107.26	yes	128
96.11	even	8	inner	864.2.w.a.107.7	✓	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.7	✓	128	96.11	even	8	inner
864.2.w.a.107.26	yes	128	32.11	odd	8	inner
864.2.w.a.323.7	yes	128	1.1	even	1	trivial
864.2.w.a.323.26	yes	128	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07850 + 0.914792i) q^{2} +(0.326309 - 1.97320i) q^{4} +(1.10881 - 0.459283i) q^{5} +(2.29035 + 2.29035i) q^{7} +(1.45315 + 2.42660i) q^{8} +O(q^{10})\)	\(q+(-1.07850 + 0.914792i) q^{2} +(0.326309 - 1.97320i) q^{4} +(1.10881 - 0.459283i) q^{5} +(2.29035 + 2.29035i) q^{7} +(1.45315 + 2.42660i) q^{8} +(-0.775695 + 1.50966i) q^{10} +(-4.23612 + 1.75466i) q^{11} +(-0.644097 + 1.55499i) q^{13} +(-4.56533 - 0.374940i) q^{14} +(-3.78704 - 1.28775i) q^{16} -5.75819 q^{17} +(4.00625 + 1.65944i) q^{19} +(-0.544443 - 2.33777i) q^{20} +(2.96349 - 5.76757i) q^{22} +(4.82067 + 4.82067i) q^{23} +(-2.51702 + 2.51702i) q^{25} +(-0.727835 - 2.26626i) q^{26} +(5.26669 - 3.77196i) q^{28} +(-1.52718 + 3.68694i) q^{29} -10.9561i q^{31} +(5.26234 - 2.07553i) q^{32} +(6.21019 - 5.26755i) q^{34} +(3.59147 + 1.48764i) q^{35} +(1.67353 + 4.04025i) q^{37} +(-5.83877 + 1.87518i) q^{38} +(2.72575 + 2.02322i) q^{40} +(-2.75672 + 2.75672i) q^{41} +(3.26736 + 7.88810i) q^{43} +(2.08001 + 8.93129i) q^{44} +(-9.60899 - 0.789163i) q^{46} -3.05588i q^{47} +3.49141i q^{49} +(0.412047 - 5.01715i) q^{50} +(2.85813 + 1.77834i) q^{52} +(3.81361 + 9.20688i) q^{53} +(-3.89116 + 3.89116i) q^{55} +(-2.22954 + 8.88597i) q^{56} +(-1.72573 - 5.37340i) q^{58} +(-2.49029 - 6.01210i) q^{59} +(4.36611 + 1.80850i) q^{61} +(10.0225 + 11.8161i) q^{62} +(-3.77673 + 7.05240i) q^{64} +2.02000i q^{65} +(-4.89651 + 11.8212i) q^{67} +(-1.87895 + 11.3621i) q^{68} +(-5.23427 + 1.68104i) q^{70} +(0.814206 - 0.814206i) q^{71} +(-6.13068 - 6.13068i) q^{73} +(-5.50089 - 2.82647i) q^{74} +(4.58169 - 7.36364i) q^{76} +(-13.7210 - 5.68342i) q^{77} -7.99746 q^{79} +(-4.79054 + 0.311461i) q^{80} +(0.451287 - 5.49495i) q^{82} +(4.51997 - 10.9122i) q^{83} +(-6.38472 + 2.64464i) q^{85} +(-10.7398 - 5.51834i) q^{86} +(-10.4136 - 7.72958i) q^{88} +(6.05533 + 6.05533i) q^{89} +(-5.03667 + 2.08626i) q^{91} +(11.0852 - 7.93912i) q^{92} +(2.79550 + 3.29576i) q^{94} +5.20430 q^{95} +11.5086 q^{97} +(-3.19392 - 3.76548i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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