LMFDB - Embedded newform 864.2.w.b.107.8

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			107.8
Character	$\chi$	$=$	864.107
Dual form			864.2.w.b.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984674 - 1.01509i) q^{2} +(-0.0608353 + 1.99907i) q^{4} +(2.42976 + 1.00644i) q^{5} +(3.62344 - 3.62344i) q^{7} +(2.08915 - 1.90668i) q^{8} +O(q^{10})$	\(q+(-0.984674 - 1.01509i) q^{2} +(-0.0608353 + 1.99907i) q^{4} +(2.42976 + 1.00644i) q^{5} +(3.62344 - 3.62344i) q^{7} +(2.08915 - 1.90668i) q^{8} +(-1.37089 - 3.45745i) q^{10} +(4.24551 + 1.75855i) q^{11} +(-1.88221 - 4.54406i) q^{13} +(-7.24605 - 0.110229i) q^{14} +(-3.99260 - 0.243229i) q^{16} +3.54583 q^{17} +(-0.517405 + 0.214316i) q^{19} +(-2.15976 + 4.79604i) q^{20} +(-2.39535 - 6.04120i) q^{22} +(-5.87371 + 5.87371i) q^{23} +(1.35528 + 1.35528i) q^{25} +(-2.75929 + 6.38504i) q^{26} +(7.02310 + 7.46397i) q^{28} +(-1.00791 - 2.43331i) q^{29} -0.930936i q^{31} +(3.68451 + 4.29237i) q^{32} +(-3.49149 - 3.59936i) q^{34} +(12.4509 - 5.15732i) q^{35} +(-2.79010 + 6.73589i) q^{37} +(0.727027 + 0.314184i) q^{38} +(6.99510 - 2.53017i) q^{40} +(-2.27293 - 2.27293i) q^{41} +(0.00236237 - 0.00570327i) q^{43} +(-3.77375 + 8.38012i) q^{44} +(11.7461 + 0.178685i) q^{46} -2.24248i q^{47} -19.2587i q^{49} +(0.0412291 - 2.71024i) q^{50} +(9.19842 - 3.48624i) q^{52} +(-1.37174 + 3.31167i) q^{53} +(8.54570 + 8.54570i) q^{55} +(0.661172 - 14.4787i) q^{56} +(-1.47758 + 3.41914i) q^{58} +(-2.72735 + 6.58441i) q^{59} +(5.70350 - 2.36247i) q^{61} +(-0.944988 + 0.916668i) q^{62} +(0.729123 - 7.96670i) q^{64} -12.9353i q^{65} +(4.56978 + 11.0324i) q^{67} +(-0.215712 + 7.08838i) q^{68} +(-17.4952 - 7.56054i) q^{70} +(-5.19995 - 5.19995i) q^{71} +(6.57149 - 6.57149i) q^{73} +(9.58491 - 3.80044i) q^{74} +(-0.396958 - 1.04737i) q^{76} +(21.7554 - 9.01137i) q^{77} -11.0397 q^{79} +(-9.45626 - 4.60929i) q^{80} +(-0.0691452 + 4.54534i) q^{82} +(0.666441 + 1.60893i) q^{83} +(8.61552 + 3.56867i) q^{85} +(-0.00811553 + 0.00321783i) q^{86} +(12.2225 - 4.42097i) q^{88} +(-3.83042 + 3.83042i) q^{89} +(-23.2852 - 9.64506i) q^{91} +(-11.3847 - 12.0993i) q^{92} +(-2.27633 + 2.20811i) q^{94} -1.47287 q^{95} +0.599606 q^{97} +(-19.5494 + 18.9635i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) $ 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	−0.984674	−	1.01509i	−0.696269	−	0.717780i
$2$	−0.984674	−	1.01509i	−0.696269	−	0.717780i
$3$		0			0
$3$		0			0
$4$	−0.0608353	+	1.99907i	−0.0304176	+	0.999537i
$5$	2.42976	+	1.00644i	1.08662	+	0.450093i	0.852827	−	0.522193i	$-0.174886\pi$
$5$	2.42976	+	1.00644i	1.08662	+	0.450093i	0.233794	+	0.972286i	$0.424886\pi$
$6$		0			0
$7$	3.62344	−	3.62344i	1.36953	−	1.36953i	0.508429	−	0.861104i	$-0.330226\pi$
$7$	3.62344	−	3.62344i	1.36953	−	1.36953i	0.861104	−	0.508429i	$-0.169774\pi$
$8$	2.08915	−	1.90668i	0.738627	−	0.674114i
$9$		0			0
$10$	−1.37089	−	3.45745i	−0.433513	−	1.09334i
$11$	4.24551	+	1.75855i	1.28007	+	0.530223i	0.916011	−	0.401153i	$-0.131390\pi$
$11$	4.24551	+	1.75855i	1.28007	+	0.530223i	0.364059	+	0.931376i	$0.381390\pi$
$12$		0			0
$13$	−1.88221	−	4.54406i	−0.522032	−	1.26030i	−0.936639	−	0.350295i	$-0.886081\pi$
$13$	−1.88221	−	4.54406i	−0.522032	−	1.26030i	0.414608	−	0.910000i	$-0.363919\pi$
$14$	−7.24605	−	0.110229i	−1.93659	−	0.0294600i
$15$		0			0
$16$	−3.99260	−	0.243229i	−0.998150	−	0.0608071i
$17$	3.54583			0.859991			0.429995	−	0.902831i	$-0.358515\pi$
$17$	3.54583			0.859991			0.429995	+	0.902831i	$0.358515\pi$
$18$		0			0
$19$	−0.517405	+	0.214316i	−0.118701	+	0.0491675i	−0.441243	−	0.897387i	$-0.645462\pi$
$19$	−0.517405	+	0.214316i	−0.118701	+	0.0491675i	0.322543	+	0.946555i	$0.395462\pi$
$20$	−2.15976	+	4.79604i	−0.482938	+	1.07243i
$21$		0			0
$22$	−2.39535	−	6.04120i	−0.510691	−	1.28799i
$23$	−5.87371	+	5.87371i	−1.22475	+	1.22475i	−0.258830	+	0.965923i	$0.583337\pi$
$23$	−5.87371	+	5.87371i	−1.22475	+	1.22475i	−0.965923	+	0.258830i	$0.916663\pi$
$24$		0			0
$25$	1.35528	+	1.35528i	0.271055	+	0.271055i
$26$	−2.75929	+	6.38504i	−0.541141	+	1.25221i
$27$		0			0
$28$	7.02310	+	7.46397i	1.32724	+	1.41056i
$29$	−1.00791	−	2.43331i	−0.187164	−	0.451854i	0.802247	−	0.596992i	$-0.203637\pi$
$29$	−1.00791	−	2.43331i	−0.187164	−	0.451854i	−0.989411	+	0.145138i	$0.953637\pi$
$30$		0			0
$31$		−	0.930936i		−	0.167201i	−0.996499	−	0.0836005i	$-0.973358\pi$
$31$		−	0.930936i		−	0.167201i	0.996499	−	0.0836005i	$-0.0266420\pi$
$32$	3.68451	+	4.29237i	0.651335	+	0.758790i
$33$		0			0
$34$	−3.49149	−	3.59936i	−0.598785	−	0.617285i
$35$	12.4509	−	5.15732i	2.10458	−	0.871746i
$36$		0			0
$37$	−2.79010	+	6.73589i	−0.458689	+	1.10737i	0.510239	+	0.860033i	$0.329557\pi$
$37$	−2.79010	+	6.73589i	−0.458689	+	1.10737i	−0.968928	+	0.247341i	$0.920443\pi$
$38$	0.727027	+	0.314184i	0.117939	+	0.0509673i
$39$		0			0
$40$	6.99510	−	2.53017i	1.10602	−	0.400056i
$41$	−2.27293	−	2.27293i	−0.354972	−	0.354972i	0.506984	−	0.861956i	$-0.330760\pi$
$41$	−2.27293	−	2.27293i	−0.354972	−	0.354972i	−0.861956	+	0.506984i	$0.830760\pi$
$42$		0			0
$43$	0.00236237	−	0.00570327i	0.000360258	−	0.000869740i	−0.923699	−	0.383118i	$-0.874850\pi$
$43$	0.00236237	−	0.00570327i	0.000360258	−	0.000869740i	0.924060	+	0.382249i	$0.124850\pi$
$44$	−3.77375	+	8.38012i	−0.568914	+	1.26335i
$45$		0			0
$46$	11.7461	+	0.178685i	1.73186	+	0.0263457i
$47$		−	2.24248i		−	0.327099i	−0.986535	−	0.163550i	$-0.947706\pi$
$47$		−	2.24248i		−	0.327099i	0.986535	−	0.163550i	$-0.0522944\pi$
$48$		0			0
$49$		−	19.2587i		−	2.75124i
$50$	0.0412291	−	2.71024i	0.00583068	−	0.383286i
$51$		0			0
$52$	9.19842	−	3.48624i	1.27559	−	0.483455i
$53$	−1.37174	+	3.31167i	−0.188423	+	0.454893i	−0.989656	−	0.143459i	$-0.954177\pi$
$53$	−1.37174	+	3.31167i	−0.188423	+	0.454893i	0.801233	+	0.598352i	$0.204177\pi$
$54$		0			0
$55$	8.54570	+	8.54570i	1.15230	+	1.15230i
$56$	0.661172	−	14.4787i	0.0883529	−	1.93480i
$57$		0			0
$58$	−1.47758	+	3.41914i	−0.194015	+	0.448955i
$59$	−2.72735	+	6.58441i	−0.355071	+	0.857217i	0.640907	+	0.767618i	$0.278558\pi$
$59$	−2.72735	+	6.58441i	−0.355071	+	0.857217i	−0.995978	+	0.0895983i	$0.971442\pi$
$60$		0			0
$61$	5.70350	−	2.36247i	0.730259	−	0.302483i	0.0136003	−	0.999908i	$-0.495671\pi$
$61$	5.70350	−	2.36247i	0.730259	−	0.302483i	0.716658	+	0.697424i	$0.245671\pi$
$62$	−0.944988	+	0.916668i	−0.120014	+	0.116417i
$63$		0			0
$64$	0.729123	−	7.96670i	0.0911404	−	0.995838i
$65$		−	12.9353i		−	1.60443i
$66$		0			0
$67$	4.56978	+	11.0324i	0.558288	+	1.34783i	0.911121	+	0.412140i	$0.135218\pi$
$67$	4.56978	+	11.0324i	0.558288	+	1.34783i	−0.352833	+	0.935686i	$0.614782\pi$
$68$	−0.215712	+	7.08838i	−0.0261589	+	0.859593i
$69$		0			0
$70$	−17.4952	−	7.56054i	−2.09108	−	0.903657i
$71$	−5.19995	−	5.19995i	−0.617120	−	0.617120i	0.327671	−	0.944792i	$-0.393736\pi$
$71$	−5.19995	−	5.19995i	−0.617120	−	0.617120i	−0.944792	+	0.327671i	$0.893736\pi$
$72$		0			0
$73$	6.57149	−	6.57149i	0.769135	−	0.769135i	−0.208819	−	0.977954i	$-0.566962\pi$
$73$	6.57149	−	6.57149i	0.769135	−	0.769135i	0.977954	+	0.208819i	$0.0669620\pi$
$74$	9.58491	−	3.80044i	1.11422	−	0.441793i
$75$		0			0
$76$	−0.396958	−	1.04737i	−0.0455342	−	0.120142i
$77$	21.7554	−	9.01137i	2.47926	−	1.02694i
$78$		0			0
$79$	−11.0397			−1.24206			−0.621032	−	0.783785i	$-0.713286\pi$
$79$	−11.0397			−1.24206			−0.621032	+	0.783785i	$0.713286\pi$
$80$	−9.45626	−	4.60929i	−1.05724	−	0.515335i
$81$		0			0
$82$	−0.0691452	+	4.54534i	−0.00763581	+	0.501948i
$83$	0.666441	+	1.60893i	0.0731514	+	0.176603i	0.956226	−	0.292630i	$-0.0945304\pi$
$83$	0.666441	+	1.60893i	0.0731514	+	0.176603i	−0.883074	+	0.469233i	$0.844530\pi$
$84$		0			0
$85$	8.61552	+	3.56867i	0.934484	+	0.387076i
$86$	−0.00811553	+	0.00321783i	−0.000875120	+	0.000346987i
$87$		0			0
$88$	12.2225	−	4.42097i	1.30293	−	0.471277i
$89$	−3.83042	+	3.83042i	−0.406023	+	0.406023i	−0.880349	−	0.474326i	$-0.842692\pi$
$89$	−3.83042	+	3.83042i	−0.406023	+	0.406023i	0.474326	+	0.880349i	$0.342692\pi$
$90$		0			0
$91$	−23.2852	−	9.64506i	−2.44096	−	1.01108i
$92$	−11.3847	−	12.0993i	−1.18693	−	1.26144i
$93$		0			0
$94$	−2.27633	+	2.20811i	−0.234785	+	0.227749i
$95$	−1.47287			−0.151113
$96$		0			0
$97$	0.599606			0.0608807			0.0304404	−	0.999537i	$-0.490309\pi$
$97$	0.599606			0.0608807			0.0304404	+	0.999537i	$0.490309\pi$
$98$	−19.5494	+	18.9635i	−1.97479	+	1.91561i
$99$		0			0
$100$	−2.79175	+	2.62685i	−0.279175	+	0.262685i
$101$	2.10347	+	0.871284i	0.209303	+	0.0866960i	0.484872	−	0.874585i	$-0.338866\pi$
$101$	2.10347	+	0.871284i	0.209303	+	0.0866960i	−0.275569	+	0.961281i	$0.588866\pi$
$102$		0			0
$103$	−5.57623	+	5.57623i	−0.549443	+	0.549443i	−0.926280	−	0.376837i	$-0.877012\pi$
$103$	−5.57623	+	5.57623i	−0.549443	+	0.549443i	0.376837	+	0.926280i	$0.377012\pi$
$104$	−12.5963	−	5.90446i	−1.23517	−	0.578980i
$105$		0			0
$106$	4.71237	−	1.86847i	0.457706	−	0.181482i
$107$	4.69696	+	1.94555i	0.454072	+	0.188083i	0.597985	−	0.801507i	$-0.295968\pi$
$107$	4.69696	+	1.94555i	0.454072	+	0.188083i	−0.143912	+	0.989590i	$0.545968\pi$
$108$		0			0
$109$	−4.33339	−	10.4617i	−0.415063	−	1.00205i	−0.983758	−	0.179502i	$-0.942551\pi$
$109$	−4.33339	−	10.4617i	−0.415063	−	1.00205i	0.568695	−	0.822549i	$-0.307449\pi$
$110$	0.259970	−	17.0894i	0.0247872	−	1.62941i
$111$		0			0
$112$	−15.3483	+	13.5856i	−1.45028	+	1.28372i
$113$	0.284232			0.0267383			0.0133692	−	0.999911i	$-0.495744\pi$
$113$	0.284232			0.0267383			0.0133692	+	0.999911i	$0.495744\pi$
$114$		0			0
$115$	−20.1832	+	8.36017i	−1.88210	+	0.779590i
$116$	4.92568	−	1.86685i	0.457338	−	0.173333i
$117$		0			0
$118$	9.36935	−	3.71497i	0.862518	−	0.341991i
$119$	12.8481	−	12.8481i	1.17779	−	1.17779i
$120$		0			0
$121$	7.15371	+	7.15371i	0.650338	+	0.650338i
$122$	−8.01422	−	3.46334i	−0.725573	−	0.313556i
$123$		0			0
$124$	1.86101	+	0.0566338i	0.167124	+	0.00508586i
$125$	−3.10320	−	7.49180i	−0.277559	−	0.670087i
$126$		0			0
$127$			21.5961i			1.91634i	0.286192	+	0.958172i	$0.407611\pi$
$127$			21.5961i			1.91634i	−0.286192	+	0.958172i	$0.592389\pi$
$128$	−8.80491	+	7.10448i	−0.778251	+	0.627953i
$129$		0			0
$130$	−13.1306	+	12.7371i	−1.15163	+	1.11711i
$131$	13.1723	−	5.45616i	1.15087	−	0.476707i	0.276047	−	0.961144i	$-0.410975\pi$
$131$	13.1723	−	5.45616i	1.15087	−	0.476707i	0.874826	+	0.484437i	$0.160975\pi$
$132$		0			0
$133$	−1.09823	+	2.65135i	−0.0952283	+	0.229901i
$134$	6.69922	−	15.5021i	0.578724	−	1.33918i
$135$		0			0
$136$	7.40779	−	6.76078i	0.635213	−	0.579732i
$137$	7.03982	+	7.03982i	0.601452	+	0.601452i	0.940698	−	0.339246i	$-0.110172\pi$
$137$	7.03982	+	7.03982i	0.601452	+	0.601452i	−0.339246	+	0.940698i	$0.610172\pi$
$138$		0			0
$139$	3.95991	−	9.56006i	0.335875	−	0.810874i	−0.662228	−	0.749303i	$-0.730389\pi$
$139$	3.95991	−	9.56006i	0.335875	−	0.810874i	0.998103	−	0.0615713i	$-0.0196112\pi$
$140$	9.55242	+	25.2040i	0.807326	+	2.13012i
$141$		0			0
$142$	−0.158188	+	10.3987i	−0.0132749	+	0.872639i
$143$		−	22.6018i		−	1.89006i
$144$		0			0
$145$		−	6.92675i		−	0.575235i
$146$	−13.1415	−	0.199913i	−1.08760	−	0.0165449i
$147$		0			0
$148$	−13.2958	−	5.98740i	−1.09291	−	0.492161i
$149$	−2.85007	+	6.88067i	−0.233487	+	0.563687i	−0.996583	−	0.0825982i	$-0.973678\pi$
$149$	−2.85007	+	6.88067i	−0.233487	+	0.563687i	0.763096	+	0.646285i	$0.223678\pi$
$150$		0			0
$151$	−8.40588	−	8.40588i	−0.684061	−	0.684061i	0.276852	−	0.960913i	$-0.410709\pi$
$151$	−8.40588	−	8.40588i	−0.684061	−	0.684061i	−0.960913	+	0.276852i	$0.910709\pi$
$152$	−0.672306	+	1.43427i	−0.0545312	+	0.116334i
$153$		0			0
$154$	−30.5694	−	13.2105i	−2.46335	−	1.06453i
$155$	0.936931	−	2.26195i	0.0752561	−	0.181684i
$156$		0			0
$157$	17.5537	−	7.27096i	1.40093	−	0.580286i	0.450941	−	0.892554i	$-0.351089\pi$
$157$	17.5537	−	7.27096i	1.40093	−	0.580286i	0.949994	+	0.312268i	$0.101089\pi$
$158$	10.8705	+	11.2063i	0.864811	+	0.891529i
$159$		0			0
$160$	4.63246	+	14.1377i	0.366228	+	1.11768i
$161$			42.5661i			3.35468i
$162$		0			0
$163$	5.95715	+	14.3818i	0.466600	+	1.12647i	0.965638	+	0.259892i	$0.0836871\pi$
$163$	5.95715	+	14.3818i	0.466600	+	1.12647i	−0.499037	+	0.866581i	$0.666313\pi$
$164$	4.68203	−	4.40548i	0.365605	−	0.344010i
$165$		0			0
$166$	0.976990	−	2.26077i	0.0758292	−	0.175470i
$167$	14.5230	+	14.5230i	1.12383	+	1.12383i	0.991161	+	0.132664i	$0.0423532\pi$
$167$	14.5230	+	14.5230i	1.12383	+	1.12383i	0.132664	+	0.991161i	$0.457647\pi$
$168$		0			0
$169$	−7.91338	+	7.91338i	−0.608721	+	0.608721i
$170$	−4.86094	−	12.2595i	−0.372817	−	0.940264i
$171$		0			0
$172$	0.0112575	+	0.00506952i	0.000858380	+	0.000386547i
$173$	0.911927	−	0.377733i	0.0693325	−	0.0287185i	−0.347748	−	0.937588i	$-0.613053\pi$
$173$	0.911927	−	0.377733i	0.0693325	−	0.0287185i	0.417080	+	0.908870i	$0.363053\pi$
$174$		0			0
$175$	9.82154			0.742439
$176$	−16.5229	−	8.05381i	−1.24546	−	0.607079i
$177$		0			0
$178$	7.65994	+	0.116526i	0.574137	+	0.00873397i
$179$	2.96764	+	7.16451i	0.221812	+	0.535501i	0.995136	−	0.0985099i	$-0.0314076\pi$
$179$	2.96764	+	7.16451i	0.221812	+	0.535501i	−0.773324	+	0.634010i	$0.781408\pi$
$180$		0			0
$181$	13.4980	+	5.59107i	1.00330	+	0.415581i	0.823007	−	0.568032i	$-0.192295\pi$
$181$	13.4980	+	5.59107i	1.00330	+	0.415581i	0.180294	+	0.983613i	$0.442295\pi$
$182$	13.1377	+	33.1340i	0.973832	+	2.45605i
$183$		0			0
$184$	−1.07178	+	23.4704i	−0.0790126	+	1.73026i
$185$	−13.5585	+	13.5585i	−0.996843	+	0.996843i
$186$		0			0
$187$	15.0539	+	6.23552i	1.10085	+	0.455986i
$188$	4.48288	+	0.136422i	0.326948	+	0.00994958i
$189$		0			0
$190$	1.45029	+	1.49510i	0.105215	+	0.108466i
$191$	−21.7325			−1.57251			−0.786255	−	0.617903i	$-0.787983\pi$
$191$	−21.7325			−1.57251			−0.786255	+	0.617903i	$0.787983\pi$
$192$		0			0
$193$	−1.36568			−0.0983039			−0.0491520	−	0.998791i	$-0.515652\pi$
$193$	−1.36568			−0.0983039			−0.0491520	+	0.998791i	$0.515652\pi$
$194$	−0.590416	−	0.608657i	−0.0423894	−	0.0436990i
$195$		0			0
$196$	38.4996	+	1.17161i	2.74997	+	0.0836863i
$197$	6.49787	+	2.69150i	0.462954	+	0.191762i	0.601954	−	0.798531i	$-0.294389\pi$
$197$	6.49787	+	2.69150i	0.462954	+	0.191762i	−0.139000	+	0.990292i	$0.544389\pi$
$198$		0			0
$199$	−17.8690	+	17.8690i	−1.26670	+	1.26670i	−0.318922	+	0.947781i	$0.603321\pi$
$199$	−17.8690	+	17.8690i	−1.26670	+	1.26670i	−0.947781	+	0.318922i	$0.896679\pi$
$200$	5.41546	+	0.247298i	0.382931	+	0.0174866i
$201$		0			0
$202$	−1.18679	−	2.99315i	−0.0835023	−	0.210597i
$203$	−12.4691	−	5.16485i	−0.875156	−	0.362501i
$204$		0			0
$205$	−3.23511	−	7.81024i	−0.225950	−	0.545491i
$206$	11.1512	+	0.169636i	0.776939	+	0.0118191i
$207$		0			0
$208$	6.40967	+	18.6004i	0.444431	+	1.28971i
$209$	−2.57354			−0.178015
$210$		0			0
$211$	8.25020	−	3.41734i	0.567967	−	0.235260i	−0.0801729	−	0.996781i	$-0.525547\pi$
$211$	8.25020	−	3.41734i	0.567967	−	0.235260i	0.648140	+	0.761521i	$0.275547\pi$
$212$	−6.53682	−	2.94367i	−0.448951	−	0.202172i
$213$		0			0
$214$	−2.65006	−	6.68359i	−0.181155	−	0.456881i
$215$	0.0114800	−	0.0114800i	0.000782929	−	0.000782929i
$216$		0			0
$217$	−3.37319	−	3.37319i	−0.228987	−	0.228987i
$218$	−6.35267	+	14.7002i	−0.430257	+	0.995621i
$219$		0			0
$220$	−17.6034	+	16.5636i	−1.18682	+	1.11672i
$221$	−6.67401	−	16.1125i	−0.448942	−	1.08384i
$222$		0			0
$223$		−	10.3687i		−	0.694342i	−0.937802	−	0.347171i	$-0.887142\pi$
$223$		−	10.3687i		−	0.694342i	0.937802	−	0.347171i	$-0.112858\pi$
$224$	28.9038	+	2.20255i	1.93121	+	0.147164i
$225$		0			0
$226$	−0.279876	−	0.288523i	−0.0186171	−	0.0191922i
$227$	−18.0003	+	7.45597i	−1.19472	+	0.494870i	−0.889290	−	0.457344i	$-0.848801\pi$
$227$	−18.0003	+	7.45597i	−1.19472	+	0.494870i	−0.305432	+	0.952214i	$0.598801\pi$
$228$		0			0
$229$	8.78395	−	21.2063i	0.580459	−	1.40135i	−0.311938	−	0.950103i	$-0.600978\pi$
$229$	8.78395	−	21.2063i	0.580459	−	1.40135i	0.892397	−	0.451251i	$-0.149022\pi$
$230$	28.3603	+	12.2559i	1.87002	+	0.808127i
$231$		0			0
$232$	−6.74522	−	3.16179i	−0.442845	−	0.207582i
$233$	−7.59606	−	7.59606i	−0.497634	−	0.497634i	0.413067	−	0.910701i	$-0.364458\pi$
$233$	−7.59606	−	7.59606i	−0.497634	−	0.497634i	−0.910701	+	0.413067i	$0.864458\pi$
$234$		0			0
$235$	2.25692	−	5.44868i	0.147225	−	0.355433i
$236$	−12.9968	−	5.85274i	−0.846020	−	0.380981i
$237$		0			0
$238$	−25.6933	−	0.390855i	−1.66545	−	0.0253354i
$239$		−	8.73486i		−	0.565011i	−0.959266	−	0.282505i	$-0.908834\pi$
$239$		−	8.73486i		−	0.565011i	0.959266	−	0.282505i	$-0.0911655\pi$
$240$		0			0
$241$			0.920267i			0.0592796i	0.999561	+	0.0296398i	$0.00943603\pi$
$241$			0.920267i			0.0592796i	−0.999561	+	0.0296398i	$0.990564\pi$
$242$	0.217624	−	14.3058i	0.0139894	−	0.919610i
$243$		0			0
$244$	4.37578	+	11.5454i	0.280130	+	0.739122i
$245$	19.3827	−	46.7940i	1.23832	−	2.98956i
$246$		0			0
$247$	1.94773	+	1.94773i	0.123931	+	0.123931i
$248$	−1.77500	−	1.94487i	−0.112713	−	0.123499i
$249$		0			0
$250$	−4.54924	+	10.5270i	−0.287719	+	0.665787i
$251$	−5.26796	+	12.7180i	−0.332511	+	0.802752i	0.665881	+	0.746058i	$0.268056\pi$
$251$	−5.26796	+	12.7180i	−0.332511	+	0.802752i	−0.998392	+	0.0566938i	$0.981944\pi$
$252$		0			0
$253$	−35.2661	+	14.6077i	−2.21716	+	0.918378i
$254$	21.9221	−	21.2651i	1.37551	−	1.33429i
$255$		0			0
$256$	15.8817	+	1.94223i	0.992605	+	0.121389i
$257$			19.7731i			1.23341i	0.787194	+	0.616705i	$0.211533\pi$
$257$			19.7731i			1.23341i	−0.787194	+	0.616705i	$0.788467\pi$
$258$		0			0
$259$	14.2974	+	34.5169i	0.888395	+	2.14478i
$260$	25.8586	+	0.786923i	1.60368	+	0.0488029i
$261$		0			0
$262$	−18.5090	−	7.99864i	−1.14349	−	0.494158i
$263$	−10.4818	−	10.4818i	−0.646333	−	0.646333i	0.305772	−	0.952105i	$-0.401086\pi$
$263$	−10.4818	−	10.4818i	−0.646333	−	0.646333i	−0.952105	+	0.305772i	$0.901086\pi$
$264$		0			0
$265$	−6.66599	+	6.66599i	−0.409488	+	0.409488i
$266$	3.77277	−	1.49591i	0.231323	−	0.0917203i
$267$		0			0
$268$	−22.3327	+	8.46417i	−1.36418	+	0.517032i
$269$	−16.6876	+	6.91223i	−1.01746	+	0.421446i	−0.828171	−	0.560475i	$-0.810619\pi$
$269$	−16.6876	+	6.91223i	−1.01746	+	0.421446i	−0.189290	+	0.981921i	$0.560619\pi$
$270$		0			0
$271$	15.9734			0.970316			0.485158	−	0.874426i	$-0.338762\pi$
$271$	15.9734			0.970316			0.485158	+	0.874426i	$0.338762\pi$
$272$	−14.1571	−	0.862448i	−0.858399	−	0.0522936i
$273$		0			0
$274$	0.214159	−	14.0780i	0.0129378	−	0.850483i
$275$	3.37052	+	8.13717i	0.203250	+	0.490690i
$276$		0			0
$277$	−22.6982	−	9.40189i	−1.36380	−	0.564905i	−0.423701	−	0.905802i	$-0.639269\pi$
$277$	−22.6982	−	9.40189i	−1.36380	−	0.564905i	−0.940101	+	0.340897i	$0.889269\pi$
$278$	−13.6036	+	5.39386i	−0.815889	+	0.323502i
$279$		0			0
$280$	16.1784	−	34.5143i	0.966845	−	2.06262i
$281$	−8.85531	+	8.85531i	−0.528264	+	0.528264i	−0.920054	−	0.391791i	$-0.871856\pi$
$281$	−8.85531	+	8.85531i	−0.528264	+	0.528264i	0.391791	+	0.920054i	$0.371856\pi$
$282$		0			0
$283$	−1.27657	−	0.528771i	−0.0758840	−	0.0314322i	0.344419	−	0.938816i	$-0.388076\pi$
$283$	−1.27657	−	0.528771i	−0.0758840	−	0.0314322i	−0.420303	+	0.907384i	$0.638076\pi$
$284$	10.7114	−	10.0787i	0.635606	−	0.598063i
$285$		0			0
$286$	−22.9430	+	22.2554i	−1.35665	+	1.31599i
$287$	−16.4717			−0.972292
$288$		0			0
$289$	−4.42707			−0.260416
$290$	−7.03131	+	6.82059i	−0.412893	+	0.400519i
$291$		0			0
$292$	12.7371	+	13.5367i	0.745384	+	0.792175i
$293$	−19.9613	−	8.26824i	−1.16615	−	0.483036i	−0.286233	−	0.958160i	$-0.592403\pi$
$293$	−19.9613	−	8.26824i	−1.16615	−	0.483036i	−0.879919	+	0.475125i	$0.842403\pi$
$294$		0			0
$295$	−13.2536	+	13.2536i	−0.771655	+	0.771655i
$296$	7.01427	+	19.3921i	0.407696	+	1.12715i
$297$		0			0
$298$	9.79092	−	3.88213i	0.567173	−	0.224886i
$299$	37.7461	+	15.6349i	2.18291	+	0.904191i
$300$		0			0
$301$	−0.0121056	−	0.0292254i	−0.000697753	−	0.00168452i
$302$	−0.255717	+	16.8098i	−0.0147148	+	0.967297i
$303$		0			0
$304$	2.11792	−	0.729831i	0.121471	−	0.0418587i
$305$	16.2358			0.929660
$306$		0			0
$307$	2.88746	−	1.19603i	0.164796	−	0.0682609i	−0.298760	−	0.954328i	$-0.596573\pi$
$307$	2.88746	−	1.19603i	0.164796	−	0.0682609i	0.463557	+	0.886067i	$0.346573\pi$
$308$	16.6909	+	44.0388i	0.951053	+	2.50935i
$309$		0			0
$310$	−3.21867	+	1.27621i	−0.182808	+	0.0724839i
$311$	−13.2531	+	13.2531i	−0.751515	+	0.751515i	−0.974762	−	0.223247i	$-0.928335\pi$
$311$	−13.2531	+	13.2531i	−0.751515	+	0.751515i	0.223247	+	0.974762i	$0.428335\pi$
$312$		0			0
$313$	4.76348	+	4.76348i	0.269248	+	0.269248i	0.828797	−	0.559549i	$-0.189026\pi$
$313$	4.76348	+	4.76348i	0.269248	+	0.269248i	−0.559549	+	0.828797i	$0.689026\pi$
$314$	−24.6653	−	10.6591i	−1.39195	−	0.601528i
$315$		0			0
$316$	0.671604	−	22.0692i	0.0377807	−	1.24149i
$317$	−7.86514	−	18.9881i	−0.441750	−	1.06648i	−0.975334	−	0.220733i	$-0.929155\pi$
$317$	−7.86514	−	18.9881i	−0.441750	−	1.06648i	0.533584	−	0.845747i	$-0.320845\pi$
$318$		0			0
$319$		−	12.1031i		−	0.677643i
$320$	9.78960	−	18.6234i	0.547255	−	1.04108i
$321$		0			0
$322$	43.2086	−	41.9137i	2.40792	−	2.33576i
$323$	−1.83463	+	0.759930i	−0.102082	+	0.0422836i
$324$		0			0
$325$	3.60754	−	8.70938i	0.200110	−	0.483109i
$326$	8.73308	−	20.2085i	0.483681	−	1.11925i
$327$		0			0
$328$	−9.08226	−	0.414743i	−0.501484	−	0.0229004i
$329$	−8.12549	−	8.12549i	−0.447973	−	0.447973i
$330$		0			0
$331$	−5.90561	+	14.2574i	−0.324602	+	0.783658i	0.674373	+	0.738391i	$0.264414\pi$
$331$	−5.90561	+	14.2574i	−0.324602	+	0.783658i	−0.998975	+	0.0452672i	$0.985586\pi$
$332$	−3.25692	+	1.23439i	−0.178746	+	0.0677457i
$333$		0			0
$334$	0.441807	−	29.0427i	0.0241746	−	1.58915i
$335$			31.4054i			1.71586i
$336$		0			0
$337$			6.73776i			0.367029i	0.983017	+	0.183514i	$0.0587474\pi$
$337$			6.73776i			0.367029i	−0.983017	+	0.183514i	$0.941253\pi$
$338$	15.8249	+	0.240734i	0.860763	+	0.0130942i
$339$		0			0
$340$	−7.65816	+	17.0060i	−0.415322	+	0.922278i
$341$	1.63710	−	3.95230i	0.0886538	−	0.214029i
$342$		0			0
$343$	−44.4187	−	44.4187i	−2.39838	−	2.39838i
$344$	−0.00593897	−	0.0164193i	−0.000320208	−	0.000885269i
$345$		0			0
$346$	−1.28139	−	0.553749i	−0.0688877	−	0.0297697i
$347$	1.06956	−	2.58214i	0.0574168	−	0.138616i	−0.892568	−	0.450913i	$-0.851098\pi$
$347$	1.06956	−	2.58214i	0.0574168	−	0.138616i	0.949985	+	0.312297i	$0.101098\pi$
$348$		0			0
$349$	−3.96489	+	1.64231i	−0.212235	+	0.0879108i	−0.486268	−	0.873810i	$-0.661642\pi$
$349$	−3.96489	+	1.64231i	−0.212235	+	0.0879108i	0.274033	+	0.961720i	$0.411642\pi$
$350$	−9.67101	−	9.96979i	−0.516937	−	0.532908i
$351$		0			0
$352$	8.09428	+	24.7027i	0.431427	+	1.31666i
$353$		−	3.24910i		−	0.172932i	−0.996255	−	0.0864662i	$-0.972443\pi$
$353$		−	3.24910i		−	0.172932i	0.996255	−	0.0864662i	$-0.0275575\pi$
$354$		0			0
$355$	−7.40119	−	17.8681i	−0.392814	−	0.948338i
$356$	−7.42426	−	7.89031i	−0.393485	−	0.418186i
$357$		0			0
$358$	4.35050	−	10.0671i	0.229931	−	0.532065i
$359$	−8.60795	−	8.60795i	−0.454310	−	0.454310i	0.442472	−	0.896782i	$-0.354102\pi$
$359$	−8.60795	−	8.60795i	−0.454310	−	0.454310i	−0.896782	+	0.442472i	$0.854102\pi$
$360$		0			0
$361$	−13.2133	+	13.2133i	−0.695434	+	0.695434i
$362$	−7.61569	−	19.2072i	−0.400272	−	1.00951i
$363$		0			0
$364$	20.6978	−	45.9622i	1.08486	−	2.40907i
$365$	22.5810	−	9.35334i	1.18194	−	0.489576i
$366$		0			0
$367$	30.1399			1.57329			0.786645	−	0.617405i	$-0.211816\pi$
$367$	30.1399			1.57329			0.786645	+	0.617405i	$0.211816\pi$
$368$	24.8800	−	22.0227i	1.29696	−	1.14801i
$369$		0			0
$370$	27.1139	+	0.412466i	1.40959	+	0.0214431i
$371$	7.02923	+	16.9701i	0.364940	+	0.881042i
$372$		0			0
$373$	23.0811	+	9.56050i	1.19509	+	0.495024i	0.889410	−	0.457110i	$-0.151115\pi$
$373$	23.0811	+	9.56050i	1.19509	+	0.495024i	0.305683	+	0.952133i	$0.401115\pi$
$374$	−8.49351	−	21.4211i	−0.439189	−	1.10766i
$375$		0			0
$376$	−4.27569	−	4.68488i	−0.220502	−	0.241604i
$377$	−9.16000	+	9.16000i	−0.471764	+	0.471764i
$378$		0			0
$379$	1.00638	+	0.416857i	0.0516944	+	0.0214125i	0.408381	−	0.912812i	$-0.366094\pi$
$379$	1.00638	+	0.416857i	0.0516944	+	0.0214125i	−0.356686	+	0.934224i	$0.616094\pi$
$380$	0.0896023	−	2.94437i	0.00459650	−	0.151043i
$381$		0			0
$382$	21.3994	+	22.0606i	1.09489	+	1.12872i
$383$	6.80552			0.347746			0.173873	−	0.984768i	$-0.444372\pi$
$383$	6.80552			0.347746			0.173873	+	0.984768i	$0.444372\pi$
$384$		0			0
$385$	61.9297			3.15623
$386$	1.34475	+	1.38630i	0.0684460	+	0.0705606i
$387$		0			0
$388$	−0.0364772	+	1.19866i	−0.00185185	+	0.0608526i
$389$	13.0369	+	5.40005i	0.660996	+	0.273793i	0.687858	−	0.725846i	$-0.258551\pi$
$389$	13.0369	+	5.40005i	0.660996	+	0.273793i	−0.0268617	+	0.999639i	$0.508551\pi$
$390$		0			0
$391$	−20.8272	+	20.8272i	−1.05328	+	1.05328i
$392$	−36.7202	−	40.2344i	−1.85465	−	2.03214i
$393$		0			0
$394$	−3.66615	−	9.24621i	−0.184698	−	0.465817i
$395$	−26.8238	−	11.1108i	−1.34965	−	0.559045i
$396$		0			0
$397$	−8.78592	−	21.2111i	−0.440953	−	1.06455i	−0.975615	−	0.219488i	$-0.929561\pi$
$397$	−8.78592	−	21.2111i	−0.440953	−	1.06455i	0.534663	−	0.845066i	$-0.320439\pi$
$398$	35.7340	+	0.543597i	1.79118	+	0.0272481i
$399$		0			0
$400$	−5.08143	−	5.74072i	−0.254072	−	0.287036i
$401$	−33.3357			−1.66471			−0.832353	−	0.554246i	$-0.813007\pi$
$401$	−33.3357			−1.66471			−0.832353	+	0.554246i	$0.813007\pi$
$402$		0			0
$403$	−4.23023	+	1.75222i	−0.210723	+	0.0872842i
$404$	−1.86973	+	4.15198i	−0.0930224	+	0.206569i
$405$		0			0
$406$	7.03513	+	17.7430i	0.349148	+	0.880568i
$407$	−23.6908	+	23.6908i	−1.17431	+	1.17431i
$408$		0			0
$409$	−20.0203	−	20.0203i	−0.989938	−	0.989938i	0.0100116	−	0.999950i	$-0.496813\pi$
$409$	−20.0203	−	20.0203i	−0.989938	−	0.989938i	−0.999950	+	0.0100116i	$0.996813\pi$
$410$	−4.74261	+	10.9745i	−0.234221	+	0.541991i
$411$		0			0
$412$	−10.8081	−	11.4865i	−0.532476	−	0.565901i
$413$	13.9758	+	33.7406i	0.687705	+	1.66027i
$414$		0			0
$415$			4.58005i			0.224826i
$416$	12.5698	−	24.8218i	0.616283	−	1.21699i
$417$		0			0
$418$	2.53409	+	2.61238i	0.123947	+	0.127776i
$419$	16.5834	−	6.86908i	0.810153	−	0.335576i	0.0611381	−	0.998129i	$-0.480527\pi$
$419$	16.5834	−	6.86908i	0.810153	−	0.335576i	0.749015	+	0.662553i	$0.230527\pi$
$420$		0			0
$421$	2.56349	−	6.18882i	0.124937	−	0.301625i	−0.849019	−	0.528363i	$-0.822806\pi$
$421$	2.56349	−	6.18882i	0.124937	−	0.301625i	0.973956	+	0.226738i	$0.0728061\pi$
$422$	−11.5927	−	5.00976i	−0.564323	−	0.243871i
$423$		0			0
$424$	3.44853	+	9.53406i	0.167475	+	0.463015i
$425$	4.80558	+	4.80558i	0.233105	+	0.233105i
$426$		0			0
$427$	12.1060	−	29.2266i	0.585853	−	1.41437i
$428$	−4.17503	+	9.27122i	−0.201808	+	0.448141i
$429$		0			0
$430$	−0.0229573		0.000349235i	−0.00110710		1.68416e-5i
$431$		−	17.2594i		−	0.831356i	−0.909512	−	0.415678i	$-0.863544\pi$
$431$		−	17.2594i		−	0.831356i	0.909512	−	0.415678i	$-0.136456\pi$
$432$		0			0
$433$			2.97628i			0.143031i	0.997439	+	0.0715154i	$0.0227835\pi$
$433$			2.97628i			0.143031i	−0.997439	+	0.0715154i	$0.977217\pi$
$434$	−0.102617	+	6.74561i	−0.00492575	+	0.323800i
$435$		0			0
$436$	21.1774	−	8.02632i	1.01421	−	0.384391i
$437$	1.78026	−	4.29792i	0.0851612	−	0.205597i
$438$		0			0
$439$	3.82630	+	3.82630i	0.182619	+	0.182619i	0.792496	−	0.609877i	$-0.208781\pi$
$439$	3.82630	+	3.82630i	0.182619	+	0.182619i	−0.609877	+	0.792496i	$0.708781\pi$
$440$	34.1472	+	1.55934i	1.62791	+	0.0743386i
$441$		0			0
$442$	−9.78398	+	22.6403i	−0.465376	+	1.07689i
$443$	−5.25721	+	12.6920i	−0.249778	+	0.603017i	−0.998185	−	0.0602228i	$-0.980819\pi$
$443$	−5.25721	+	12.6920i	−0.249778	+	0.603017i	0.748407	+	0.663239i	$0.230819\pi$
$444$		0			0
$445$	−13.1621	+	5.45191i	−0.623942	+	0.258445i
$446$	−10.5253	+	10.2098i	−0.498385	+	0.483449i
$447$		0			0
$448$	−26.2250	−	31.5088i	−1.23901	−	1.48865i
$449$		−	24.4313i		−	1.15299i	−0.817102	−	0.576493i	$-0.804421\pi$
$449$		−	24.4313i		−	1.15299i	0.817102	−	0.576493i	$-0.195579\pi$
$450$		0			0
$451$	−5.65270	−	13.6468i	−0.266175	−	0.642604i
$452$	−0.0172913	+	0.568201i	−0.000813316	+	0.0267259i
$453$		0			0
$454$	25.2929	+	10.9303i	1.18706	+	0.512985i
$455$	−46.8704	−	46.8704i	−2.19732	−	2.19732i
$456$		0			0
$457$	−2.69456	+	2.69456i	−0.126046	+	0.126046i	−0.767316	−	0.641270i	$-0.778408\pi$
$457$	−2.69456	+	2.69456i	−0.126046	+	0.126046i	0.641270	+	0.767316i	$0.278408\pi$
$458$	−30.1757	+	11.9648i	−1.41002	+	0.559077i
$459$		0			0
$460$	−15.4847	−	40.8564i	−0.721980	−	1.90494i
$461$	−35.2621	+	14.6060i	−1.64232	+	0.680270i	−0.996529	−	0.0832459i	$-0.973471\pi$
$461$	−35.2621	+	14.6060i	−1.64232	+	0.680270i	−0.645789	+	0.763516i	$0.723471\pi$
$462$		0			0
$463$	31.4237			1.46038			0.730191	−	0.683243i	$-0.239431\pi$
$463$	31.4237			1.46038			0.730191	+	0.683243i	$0.239431\pi$
$464$	3.43232	+	9.96037i	0.159342	+	0.462399i
$465$		0			0
$466$	−0.231081	+	15.1904i	−0.0107046	+	0.703680i
$467$	4.57049	+	11.0341i	0.211497	+	0.510599i	0.993654	−	0.112483i	$-0.0358804\pi$
$467$	4.57049	+	11.0341i	0.211497	+	0.510599i	−0.782157	+	0.623082i	$0.785880\pi$
$468$		0			0
$469$	56.5337	+	23.4170i	2.61049	+	1.08130i
$470$	−7.75326	+	3.07419i	−0.357631	+	0.141802i
$471$		0			0
$472$	6.85652	+	18.9560i	0.315597	+	0.872522i
$473$	0.0200590	−	0.0200590i	0.000922312	−	0.000922312i
$474$		0			0
$475$	−0.991685	−	0.410769i	−0.0455016	−	0.0188474i
$476$	24.9027	+	26.4660i	1.14142	+	1.21307i
$477$		0			0
$478$	−8.86671	+	8.60098i	−0.405554	+	0.393400i
$479$	−17.3035			−0.790616			−0.395308	−	0.918549i	$-0.629362\pi$
$479$	−17.3035			−0.790616			−0.395308	+	0.918549i	$0.629362\pi$
$480$		0			0
$481$	35.8599			1.63507
$482$	0.934159	−	0.906163i	0.0425498	−	0.0412746i
$483$		0			0
$484$	−14.7360	+	13.8656i	−0.669818	+	0.630255i
$485$	1.45690	+	0.603467i	0.0661543	+	0.0274020i
$486$		0			0
$487$	8.91636	−	8.91636i	0.404039	−	0.404039i	−0.475615	−	0.879654i	$-0.657774\pi$
$487$	8.91636	−	8.91636i	0.404039	−	0.404039i	0.879654	+	0.475615i	$0.157774\pi$
$488$	7.41101	−	15.8103i	0.335481	−	0.715700i
$489$		0			0
$490$	−66.5860	+	26.4015i	−3.00805	+	1.19270i
$491$	30.7004	+	12.7165i	1.38549	+	0.573889i	0.945944	−	0.324331i	$-0.105139\pi$
$491$	30.7004	+	12.7165i	1.38549	+	0.573889i	0.439547	+	0.898220i	$0.355139\pi$
$492$		0			0
$493$	−3.57388	−	8.62810i	−0.160959	−	0.388590i
$494$	0.0592523	−	3.89501i	0.00266589	−	0.175245i
$495$		0			0
$496$	−0.226430	+	3.71685i	−0.0101670	+	0.166892i
$497$	−37.6834			−1.69033
$498$		0			0
$499$	−0.00262933	+	0.00108911i	−0.000117705	+	4.87551e-5i	−0.382742	−	0.923855i	$-0.625020\pi$
$499$	−0.00262933	+	0.00108911i	−0.000117705	+	4.87551e-5i	0.382625	+	0.923904i	$0.375020\pi$
$500$	15.1654	−	5.74777i	0.678219	−	0.257048i
$501$		0			0
$502$	18.0972	−	7.17558i	0.807717	−	0.320262i
$503$	26.2731	−	26.2731i	1.17146	−	1.17146i	0.189600	−	0.981861i	$-0.439281\pi$
$503$	26.2731	−	26.2731i	1.17146	−	1.17146i	0.981861	−	0.189600i	$-0.0607192\pi$
$504$		0			0
$505$	4.23402	+	4.23402i	0.188411	+	0.188411i
$506$	49.5538	+	21.4146i	2.20294	+	0.951996i
$507$		0			0
$508$	−43.1722	−	1.31381i	−1.91546	−	0.0582907i
$509$	−0.312495	−	0.754430i	−0.0138511	−	0.0334395i	0.916803	−	0.399341i	$-0.130761\pi$
$509$	−0.312495	−	0.754430i	−0.0138511	−	0.0334395i	−0.930654	+	0.365901i	$0.880761\pi$
$510$		0			0
$511$		−	47.6229i		−	2.10671i
$512$	−13.6667	−	18.0339i	−0.603990	−	0.796992i
$513$		0			0
$514$	20.0715	−	19.4700i	0.885318	−	0.858786i
$515$	−19.1610	+	7.93676i	−0.844337	+	0.349736i
$516$		0			0
$517$	3.94351	−	9.52047i	0.173435	−	0.418710i
$518$	20.9597	−	48.5011i	0.920916	−	2.13101i
$519$		0			0
$520$	−24.6635	−	27.0238i	−1.08157	−	1.18507i
$521$	−0.996712	−	0.996712i	−0.0436667	−	0.0436667i	0.684936	−	0.728603i	$-0.259830\pi$
$521$	−0.996712	−	0.996712i	−0.0436667	−	0.0436667i	−0.728603	+	0.684936i	$0.759830\pi$
$522$		0			0
$523$	−6.30996	+	15.2336i	−0.275915	+	0.666118i	−0.999715	−	0.0238924i	$-0.992394\pi$
$523$	−6.30996	+	15.2336i	−0.275915	+	0.666118i	0.723799	+	0.690010i	$0.242394\pi$
$524$	10.1059	+	26.6644i	0.441480	+	1.16484i
$525$		0			0
$526$	−0.318868	+	20.9611i	−0.0139033	+	0.913948i
$527$		−	3.30094i		−	0.143791i
$528$		0			0
$529$		−	46.0009i		−	2.00004i
$530$	13.3304	+	0.202787i	0.579037	+	0.00880851i
$531$		0			0
$532$	−5.23344	−	2.35673i	−0.226898	−	0.102177i
$533$	−6.05020	+	14.6065i	−0.262063	+	0.632677i
$534$		0			0
$535$	9.45442	+	9.45442i	0.408750	+	0.408750i
$536$	30.5823	+	14.3353i	1.32095	+	0.619191i
$537$		0			0
$538$	23.4484	+	10.1332i	1.01093	+	0.436873i
$539$	33.8674	−	81.7630i	1.45877	−	3.52178i
$540$		0			0
$541$	13.5104	−	5.59617i	0.580855	−	0.240598i	−0.0728555	−	0.997343i	$-0.523211\pi$
$541$	13.5104	−	5.59617i	0.580855	−	0.240598i	0.653711	+	0.756744i	$0.273211\pi$
$542$	−15.7286	−	16.2145i	−0.675601	−	0.696474i
$543$		0			0
$544$	13.0646	+	15.2200i	0.560142	+	0.652553i
$545$		−	29.7807i		−	1.27567i
$546$		0			0
$547$	−6.71660	−	16.2153i	−0.287181	−	0.693317i	0.712786	−	0.701381i	$-0.247433\pi$
$547$	−6.71660	−	16.2153i	−0.287181	−	0.693317i	−0.999967	+	0.00806456i	$0.997433\pi$
$548$	−14.5014	+	13.6448i	−0.619469	+	0.582879i
$549$		0			0
$550$	4.94113	−	11.4339i	0.210690	−	0.487541i
$551$	1.04299	+	1.04299i	0.0444331	+	0.0444331i
$552$		0			0
$553$	−40.0018	+	40.0018i	−1.70105	+	1.70105i
$554$	12.8065	+	32.2986i	0.544095	+	1.37224i
$555$		0			0
$556$	18.8704	+	8.49774i	0.800282	+	0.360384i
$557$	22.0212	−	9.12148i	0.933068	−	0.386489i	0.136226	−	0.990678i	$-0.456503\pi$
$557$	22.0212	−	9.12148i	0.933068	−	0.386489i	0.796842	+	0.604188i	$0.206503\pi$
$558$		0			0
$559$	−0.0303625			−0.00128420
$560$	−50.9657	+	17.5627i	−2.15370	+	0.742160i
$561$		0			0
$562$	17.7086	+	0.269389i	0.746991	+	0.0113635i
$563$	−1.78540	−	4.31033i	−0.0752455	−	0.181659i	0.881781	−	0.471659i	$-0.156345\pi$
$563$	−1.78540	−	4.31033i	−0.0752455	−	0.181659i	−0.957027	+	0.290000i	$0.906345\pi$
$564$		0			0
$565$	0.690616	+	0.286062i	0.0290544	+	0.0120347i
$566$	0.720248	+	1.81650i	0.0302743	+	0.0763533i
$567$		0			0
$568$	−20.7781	−	0.948838i	−0.871831	−	0.0398124i
$569$	15.7638	−	15.7638i	0.660855	−	0.660855i	−0.294727	−	0.955582i	$-0.595229\pi$
$569$	15.7638	−	15.7638i	0.660855	−	0.660855i	0.955582	+	0.294727i	$0.0952286\pi$
$570$		0			0
$571$	−20.8628	−	8.64167i	−0.873082	−	0.361643i	−0.0992723	−	0.995060i	$-0.531651\pi$
$571$	−20.8628	−	8.64167i	−0.873082	−	0.361643i	−0.773810	+	0.633418i	$0.781651\pi$
$572$	45.1827	+	1.37499i	1.88919	+	0.0574912i
$573$		0			0
$574$	16.2192	+	16.7203i	0.676977	+	0.697892i
$575$	−15.9210			−0.663952
$576$		0			0
$577$	−27.3649			−1.13922			−0.569608	−	0.821916i	$-0.692905\pi$
$577$	−27.3649			−1.13922			−0.569608	+	0.821916i	$0.692905\pi$
$578$	4.35922	+	4.49390i	0.181320	+	0.186921i
$579$		0			0
$580$	13.8471	+	0.421391i	0.574969	+	0.0174973i
$581$	8.24468	+	3.41506i	0.342047	+	0.141681i
$582$		0			0
$583$	−11.6475	+	11.6475i	−0.482389	+	0.482389i
$584$	1.19911	−	26.2586i	0.0496193	−	1.08659i
$585$		0			0
$586$	11.2623	+	28.4041i	0.465242	+	1.17336i
$587$	1.21100	+	0.501612i	0.0499833	+	0.0207038i	0.407535	−	0.913190i	$-0.366388\pi$
$587$	1.21100	+	0.501612i	0.0499833	+	0.0207038i	−0.357552	+	0.933893i	$0.616388\pi$
$588$		0			0
$589$	0.199515	+	0.481671i	0.00822086	+	0.0198469i
$590$	26.5042	+	0.403190i	1.09116	+	0.0165991i
$591$		0			0
$592$	12.7781	−	26.2151i	0.525177	−	1.07743i
$593$	−42.5626			−1.74784			−0.873919	−	0.486072i	$-0.838429\pi$
$593$	−42.5626			−1.74784			−0.873919	+	0.486072i	$0.838429\pi$
$594$		0			0
$595$	44.1487	−	18.2870i	1.80992	−	0.749694i
$596$	−13.5816	−	6.11609i	−0.556324	−	0.250525i
$597$		0			0
$598$	−21.2966	−	53.7111i	−0.870883	−	2.19641i
$599$	−25.7280	+	25.7280i	−1.05122	+	1.05122i	−0.0526040	+	0.998615i	$0.516752\pi$
$599$	−25.7280	+	25.7280i	−1.05122	+	1.05122i	−0.998615	+	0.0526040i	$0.983248\pi$
$600$		0			0
$601$	0.0304140	+	0.0304140i	0.00124061	+	0.00124061i	0.707727	−	0.706486i	$-0.249721\pi$
$601$	0.0304140	+	0.0304140i	0.00124061	+	0.00124061i	−0.706486	+	0.707727i	$0.749721\pi$
$602$	−0.0177465	+	0.0410658i	−0.000723295	+	0.00167372i
$603$		0			0
$604$	17.3154	−	16.2926i	0.704552	−	0.662937i
$605$	10.1820	+	24.5816i	0.413958	+	0.999383i
$606$		0			0
$607$			16.2841i			0.660950i	0.943815	+	0.330475i	$0.107209\pi$
$607$			16.2841i			0.660950i	−0.943815	+	0.330475i	$0.892791\pi$
$608$	−2.82631	−	1.43124i	−0.114622	−	0.0580446i
$609$		0			0
$610$	−15.9870	−	16.4809i	−0.647294	−	0.667292i
$611$	−10.1900	+	4.22082i	−0.412242	+	0.170756i
$612$		0			0
$613$	−2.14878	+	5.18760i	−0.0867882	+	0.209525i	−0.961315	−	0.275453i	$-0.911172\pi$
$613$	−2.14878	+	5.18760i	−0.0867882	+	0.209525i	0.874526	+	0.484978i	$0.161172\pi$
$614$	−4.05729	−	1.75335i	−0.163739	−	0.0707596i
$615$		0			0
$616$	28.2685	−	60.3068i	1.13897	−	2.42983i
$617$	29.6588	+	29.6588i	1.19402	+	1.19402i	0.975929	+	0.218089i	$0.0699825\pi$
$617$	29.6588	+	29.6588i	1.19402	+	1.19402i	0.218089	+	0.975929i	$0.430018\pi$
$618$		0			0
$619$	3.93318	−	9.49553i	0.158088	−	0.381658i	−0.824913	−	0.565260i	$-0.808776\pi$
$619$	3.93318	−	9.49553i	0.158088	−	0.381658i	0.983001	+	0.183602i	$0.0587759\pi$
$620$	4.46481	+	2.01060i	0.179311	+	0.0807477i
$621$		0			0
$622$	26.5032	+	0.403175i	1.06268	+	0.0161659i
$623$			27.7586i			1.11212i
$624$		0			0
$625$		−	30.9097i		−	1.23639i
$626$	0.144911	−	9.52586i	0.00579180	−	0.380730i
$627$		0			0
$628$	13.4673	+	35.5334i	0.537405	+	1.41794i
$629$	−9.89322	+	23.8844i	−0.394469	+	0.952332i
$630$		0			0
$631$	4.27328	+	4.27328i	0.170117	+	0.170117i	0.787031	−	0.616914i	$-0.211617\pi$
$631$	4.27328	+	4.27328i	0.170117	+	0.170117i	−0.616914	+	0.787031i	$0.711617\pi$
$632$	−23.0636	+	21.0492i	−0.917422	+	0.837293i
$633$		0			0
$634$	−11.5302	+	26.6810i	−0.457921	+	1.05964i
$635$	−21.7352	+	52.4733i	−0.862534	+	2.08234i
$636$		0			0
$637$	−87.5127	+	36.2489i	−3.46738	+	1.43623i
$638$	−12.2858	+	11.9176i	−0.486399	+	0.471822i
$639$		0			0
$640$	−28.5440	+	8.40056i	−1.12830	+	0.332061i
$641$			16.0610i			0.634373i	0.948363	+	0.317186i	$0.102738\pi$
$641$			16.0610i			0.634373i	−0.948363	+	0.317186i	$0.897262\pi$
$642$		0			0
$643$	1.36036	+	3.28421i	0.0536475	+	0.129517i	0.948431	−	0.316984i	$-0.102670\pi$
$643$	1.36036	+	3.28421i	0.0536475	+	0.129517i	−0.894783	+	0.446500i	$0.852670\pi$
$644$	−85.0928	−	2.58952i	−3.35313	−	0.102041i
$645$		0			0
$646$	2.57791	+	1.11404i	0.101427	+	0.0438314i
$647$	8.12861	+	8.12861i	0.319569	+	0.319569i	0.848601	−	0.529033i	$-0.177445\pi$
$647$	8.12861	+	8.12861i	0.319569	+	0.319569i	−0.529033	+	0.848601i	$0.677445\pi$
$648$		0			0
$649$	−23.1580	+	23.1580i	−0.909031	+	0.909031i
$650$	−12.3931	+	4.91390i	−0.486097	+	0.192739i
$651$		0			0
$652$	−29.1128	+	11.0339i	−1.14014	+	0.432120i
$653$	12.9100	−	5.34749i	0.505207	−	0.209263i	−0.115498	−	0.993308i	$-0.536846\pi$
$653$	12.9100	−	5.34749i	0.505207	−	0.209263i	0.620705	+	0.784044i	$0.286846\pi$
$654$		0			0
$655$	37.4969			1.46513
$656$	8.52206	+	9.62774i	0.332730	+	0.375900i
$657$		0			0
$658$	−0.247187	+	16.2491i	−0.00963635	+	0.633456i
$659$	5.52315	+	13.3341i	0.215152	+	0.519422i	0.994201	−	0.107541i	$-0.0342977\pi$
$659$	5.52315	+	13.3341i	0.215152	+	0.519422i	−0.779049	+	0.626963i	$0.784298\pi$
$660$		0			0
$661$	32.3769	+	13.4110i	1.25932	+	0.521626i	0.909699	−	0.415267i	$-0.136312\pi$
$661$	32.3769	+	13.4110i	1.25932	+	0.521626i	0.349616	+	0.936893i	$0.386312\pi$
$662$	20.2877	−	8.04414i	0.788505	−	0.312644i
$663$		0			0
$664$	4.46002	+	2.09061i	0.173082	+	0.0811315i
$665$	−5.33685	+	5.33685i	−0.206954	+	0.206954i
$666$		0			0
$667$	20.2127	+	8.37237i	0.782639	+	0.324180i
$668$	−29.9161	+	28.1491i	−1.15749	+	1.08912i
$669$		0			0
$670$	31.8794	−	30.9240i	1.23161	−	1.19470i
$671$	28.3688			1.09517
$672$		0			0
$673$	−6.00391			−0.231434			−0.115717	−	0.993282i	$-0.536917\pi$
$673$	−6.00391			−0.231434			−0.115717	+	0.993282i	$0.536917\pi$
$674$	6.83946	−	6.63449i	0.263446	−	0.255551i
$675$		0			0
$676$	−15.3380	−	16.3008i	−0.589924	−	0.626956i
$677$	−2.27105	−	0.940701i	−0.0872836	−	0.0361541i	0.338614	−	0.940925i	$-0.390042\pi$
$677$	−2.27105	−	0.940701i	−0.0872836	−	0.0361541i	−0.425898	+	0.904771i	$0.640042\pi$
$678$		0			0
$679$	2.17264	−	2.17264i	0.0833782	−	0.0833782i
$680$	24.8035	−	8.97157i	0.951169	−	0.344044i
$681$		0			0
$682$	−5.62397	+	2.22992i	−0.215353	+	0.0853880i
$683$	43.2822	+	17.9281i	1.65615	+	0.685998i	0.997774	−	0.0666932i	$-0.0212449\pi$
$683$	43.2822	+	17.9281i	1.65615	+	0.685998i	0.658373	+	0.752692i	$0.271245\pi$
$684$		0			0
$685$	10.0199	+	24.1902i	0.382841	+	0.924260i
$686$	−1.35127	+	88.8271i	−0.0515916	+	3.39143i
$687$		0			0
$688$	−0.0108192	+	0.0221963i	−0.000412478	+	0.000846225i
$689$	17.6303			0.671662
$690$		0			0
$691$	−9.81989	+	4.06753i	−0.373566	+	0.154736i	−0.561564	−	0.827433i	$-0.689800\pi$
$691$	−9.81989	+	4.06753i	−0.373566	+	0.154736i	0.187998	+	0.982169i	$0.439800\pi$
$692$	0.699638	+	1.84599i	0.0265963	+	0.0701740i
$693$		0			0
$694$	−3.67428	+	1.45686i	−0.139474	+	0.0553017i
$695$	19.2432	−	19.2432i	0.729938	−	0.729938i
$696$		0			0
$697$	−8.05943	−	8.05943i	−0.305273	−	0.305273i
$698$	5.57122	+	2.40760i	0.210874	+	0.0911289i
$699$		0			0
$700$	−0.597496	+	19.6340i	−0.0225832	+	0.742095i
$701$	0.0525846	+	0.126950i	0.00198609	+	0.00479485i	0.924869	−	0.380285i	$-0.124174\pi$
$701$	0.0525846	+	0.126950i	0.00198609	+	0.00479485i	−0.922883	+	0.385080i	$0.874174\pi$
$702$		0			0
$703$		−	4.08315i		−	0.153999i
$704$	17.1053	−	32.5406i	0.644682	−	1.22642i
$705$		0			0
$706$	−3.29815	+	3.19931i	−0.124127	+	0.120408i
$707$	10.7788	−	4.46474i	0.405380	−	0.167914i
$708$		0			0
$709$	−19.9935	+	48.2685i	−0.750870	+	1.81276i	−0.196471	+	0.980510i	$0.562948\pi$
$709$	−19.9935	+	48.2685i	−0.750870	+	1.81276i	−0.554399	+	0.832251i	$0.687052\pi$
$710$	−10.8500	+	25.1071i	−0.407194	+	0.942253i
$711$		0			0
$712$	−0.698938	+	15.3057i	−0.0261938	+	0.573606i
$713$	5.46805	+	5.46805i	0.204780	+	0.204780i
$714$		0			0
$715$	22.7474	−	54.9170i	0.850703	−	2.05378i
$716$	−14.5029	+	5.49667i	−0.542000	+	0.205420i
$717$		0			0
$718$	−0.261864	+	17.2139i	−0.00977268	+	0.642418i
$719$		−	9.06963i		−	0.338240i	−0.985595	−	0.169120i	$-0.945907\pi$
$719$		−	9.06963i		−	0.338240i	0.985595	−	0.169120i	$-0.0540926\pi$
$720$		0			0
$721$			40.4103i			1.50496i
$722$	26.4234	+	0.401963i	0.983379	+	0.0149595i
$723$		0			0
$724$	−11.9981	+	26.6434i	−0.445907	+	0.990196i
$725$	1.93181	−	4.66380i	0.0717456	−	0.173209i
$726$		0			0
$727$	−4.73147	−	4.73147i	−0.175481	−	0.175481i	0.613902	−	0.789382i	$-0.289599\pi$
$727$	−4.73147	−	4.73147i	−0.175481	−	0.175481i	−0.789382	+	0.613902i	$0.789599\pi$
$728$	−67.0365	+	24.2475i	−2.48454	+	0.898674i
$729$		0			0
$730$	−31.7294	−	13.7118i	−1.17436	−	0.507498i
$731$	0.00837657	−	0.0202228i	0.000309819	−	0.000747969i
$732$		0			0
$733$	−20.3121	+	8.41354i	−0.750244	+	0.310761i	−0.724841	−	0.688916i	$-0.758087\pi$
$733$	−20.3121	+	8.41354i	−0.750244	+	0.310761i	−0.0254028	+	0.999677i	$0.508087\pi$
$734$	−29.6780	−	30.5949i	−1.09543	−	1.12928i
$735$		0			0
$736$	−46.8538	−	3.57039i	−1.72706	−	0.131606i
$737$			54.8745i			2.02133i
$738$		0			0
$739$	8.18448	+	19.7591i	0.301071	+	0.726850i	0.999933	+	0.0115930i	$0.00369025\pi$
$739$	8.18448	+	19.7591i	0.301071	+	0.726850i	−0.698862	+	0.715257i	$0.746310\pi$
$740$	−26.2797	−	27.9294i	−0.966061	−	1.02670i
$741$		0			0
$742$	10.3047	−	23.8453i	0.378298	−	0.875389i
$743$	−4.33638	−	4.33638i	−0.159086	−	0.159086i	0.623075	−	0.782162i	$-0.285883\pi$
$743$	−4.33638	−	4.33638i	−0.159086	−	0.159086i	−0.782162	+	0.623075i	$0.785883\pi$
$744$		0			0
$745$	−13.8500	+	13.8500i	−0.507423	+	0.507423i
$746$	−13.0225	−	32.8435i	−0.476788	−	1.20248i
$747$		0			0
$748$	−13.3811	+	29.7145i	−0.489261	+	1.08647i
$749$	24.0688	−	9.96960i	0.879453	−	0.364281i
$750$		0			0
$751$	−6.66286			−0.243131			−0.121566	−	0.992583i	$-0.538791\pi$
$751$	−6.66286			−0.243131			−0.121566	+	0.992583i	$0.538791\pi$
$752$	−0.545435	+	8.95331i	−0.0198900	+	0.326494i
$753$		0			0
$754$	18.3179	+	0.278658i	0.667098	+	0.0101481i
$755$	−11.9643	−	28.8843i	−0.435424	−	1.05121i
$756$		0			0
$757$	−2.93718	−	1.21662i	−0.106754	−	0.0442188i	0.328667	−	0.944446i	$-0.393400\pi$
$757$	−2.93718	−	1.21662i	−0.106754	−	0.0442188i	−0.435421	+	0.900227i	$0.643400\pi$
$758$	−0.567809	−	1.43204i	−0.0206237	−	0.0520141i
$759$		0			0
$760$	−3.07704	+	2.80829i	−0.111616	+	0.101867i
$761$	27.1040	−	27.1040i	0.982521	−	0.982521i	−0.0173290	−	0.999850i	$-0.505516\pi$
$761$	27.1040	−	27.1040i	0.982521	−	0.982521i	0.999850	+	0.0173290i	$0.00551626\pi$
$762$		0			0
$763$	−53.6092	−	22.2057i	−1.94078	−	0.803899i
$764$	1.32210	−	43.4449i	0.0478320	−	1.57178i
$765$		0			0
$766$	−6.70122	−	6.90825i	−0.242125	−	0.249605i
$767$	35.0534			1.26570
$768$		0			0
$769$	−32.6675			−1.17802			−0.589011	−	0.808125i	$-0.700482\pi$
$769$	−32.6675			−1.17802			−0.589011	+	0.808125i	$0.700482\pi$
$770$	−60.9806	−	62.8646i	−2.19759	−	2.26548i
$771$		0			0
$772$	0.0830817	−	2.73010i	0.00299017	−	0.0982585i
$773$	−9.57099	−	3.96444i	−0.344245	−	0.142591i	0.203861	−	0.979000i	$-0.434651\pi$
$773$	−9.57099	−	3.96444i	−0.344245	−	0.142591i	−0.548106	+	0.836409i	$0.684651\pi$
$774$		0			0
$775$	1.26168	−	1.26168i	0.0453207	−	0.0453207i
$776$	1.25267	−	1.14326i	0.0449682	−	0.0410406i
$777$		0			0
$778$	−7.35551	−	18.5510i	−0.263708	−	0.665084i
$779$	1.66315	+	0.688900i	0.0595886	+	0.0246824i
$780$		0			0
$781$	−12.9321	−	31.2208i	−0.462746	−	1.11717i
$782$	41.6496	+	0.633587i	1.48939	+	0.0226570i
$783$		0			0
$784$	−4.68426	+	76.8922i	−0.167295	+	2.74615i
$785$	49.9690			1.78347
$786$		0			0
$787$	−17.1046	+	7.08495i	−0.609713	+	0.252551i	−0.666106	−	0.745857i	$-0.732040\pi$
$787$	−17.1046	+	7.08495i	−0.609713	+	0.252551i	0.0563928	+	0.998409i	$0.482040\pi$
$788$	−5.77582	+	12.8260i	−0.205755	+	0.456907i
$789$		0			0
$790$	15.1342	+	38.1692i	0.538451	+	1.35800i
$791$	1.02990	−	1.02990i	0.0366190	−	0.0366190i
$792$		0			0
$793$	−21.4704	−	21.4704i	−0.762436	−	0.762436i
$794$	−12.8800	+	29.8045i	−0.457094	+	1.05772i
$795$		0			0
$796$	−34.6345	−	36.8086i	−1.22759	−	1.30465i
$797$	−4.10595	−	9.91264i	−0.145440	−	0.351124i	0.834325	−	0.551272i	$-0.185858\pi$
$797$	−4.10595	−	9.91264i	−0.145440	−	0.351124i	−0.979766	+	0.200149i	$0.935858\pi$
$798$		0			0
$799$		−	7.95145i		−	0.281302i
$800$	−0.823819	+	10.8109i	−0.0291264	+	0.382222i
$801$		0			0
$802$	32.8248	+	33.8389i	1.15908	+	1.19489i
$803$	39.4557	−	16.3431i	1.39236	−	0.576734i
$804$		0			0
$805$	−42.8402	+	103.425i	−1.50992	+	3.64527i
$806$	5.94406	+	2.56872i	0.209371	+	0.0904793i
$807$		0			0
$808$	6.05572	−	2.19040i	0.213040	−	0.0770578i
$809$	31.6777	+	31.6777i	1.11373	+	1.11373i	0.992642	+	0.121086i	$0.0386376\pi$
$809$	31.6777	+	31.6777i	1.11373	+	1.11373i	0.121086	+	0.992642i	$0.461362\pi$
$810$		0			0
$811$	11.6854	−	28.2111i	0.410330	−	0.990625i	−0.574719	−	0.818351i	$-0.694889\pi$
$811$	11.6854	−	28.2111i	0.410330	−	0.990625i	0.985049	−	0.172274i	$-0.0551114\pi$
$812$	11.0835	−	24.6124i	0.388954	−	0.863724i
$813$		0			0
$814$	47.3761	+	0.720702i	1.66053	+	0.0252606i
$815$			40.9399i			1.43406i
$816$		0			0
$817$			0.00345720i			0.000120952i
$818$	−0.609040	+	40.0359i	−0.0212946	+	1.39982i
$819$		0			0
$820$	15.8101	−	5.99208i	0.552111	−	0.209253i
$821$	18.9200	−	45.6770i	0.660313	−	1.59414i	−0.137000	−	0.990571i	$-0.543746\pi$
$821$	18.9200	−	45.6770i	0.660313	−	1.59414i	0.797313	−	0.603566i	$-0.206254\pi$
$822$		0			0
$823$	−13.7446	−	13.7446i	−0.479108	−	0.479108i	0.425739	−	0.904846i	$-0.360014\pi$
$823$	−13.7446	−	13.7446i	−0.479108	−	0.479108i	−0.904846	+	0.425739i	$0.860014\pi$
$824$	−1.01750	+	22.2817i	−0.0354463	+	0.776220i
$825$		0			0
$826$	20.4883	−	47.4103i	0.712879	−	1.64962i
$827$	6.54367	−	15.7978i	0.227546	−	0.549344i	−0.768332	−	0.640052i	$-0.778913\pi$
$827$	6.54367	−	15.7978i	0.227546	−	0.549344i	0.995878	+	0.0907077i	$0.0289129\pi$
$828$		0			0
$829$	46.5090	−	19.2646i	1.61532	−	0.669089i	0.621848	−	0.783138i	$-0.286382\pi$
$829$	46.5090	−	19.2646i	1.61532	−	0.669089i	0.993475	+	0.114049i	$0.0363820\pi$
$830$	4.64918	−	4.50985i	0.161375	−	0.156539i
$831$		0			0
$832$	−37.5736	+	11.6818i	−1.30263	+	0.404995i
$833$		−	68.2881i		−	2.36604i
$834$		0			0
$835$	20.6709	+	49.9040i	0.715346	+	1.72700i
$836$	0.156562	−	5.14469i	0.00541480	−	0.177933i
$837$		0			0
$838$	−23.3020	−	10.0699i	−0.804955	−	0.347861i
$839$	−15.0204	−	15.0204i	−0.518561	−	0.518561i	0.398575	−	0.917136i	$-0.369505\pi$
$839$	−15.0204	−	15.0204i	−0.518561	−	0.518561i	−0.917136	+	0.398575i	$0.869505\pi$
$840$		0			0
$841$	15.6010	−	15.6010i	0.537965	−	0.537965i
$842$	−8.80645	+	3.49178i	−0.303490	+	0.120335i
$843$		0			0
$844$	6.32962	+	16.7007i	0.217875	+	0.574860i
$845$	−27.1919	+	11.2633i	−0.935431	+	0.387468i
$846$		0			0
$847$	51.8422			1.78132
$848$	6.28229	−	12.8885i	0.215735	−	0.442594i
$849$		0			0
$850$	0.146191	−	9.61006i	0.00501433	−	0.329622i
$851$	−23.1765	−	55.9529i	−0.794479	−	1.91804i
$852$		0			0
$853$	−18.0633	−	7.48206i	−0.618476	−	0.256181i	0.0513720	−	0.998680i	$-0.483641\pi$
$853$	−18.0633	−	7.48206i	−0.618476	−	0.256181i	−0.669848	+	0.742499i	$0.733641\pi$
$854$	−41.5883	+	16.4899i	−1.42312	+	0.564272i
$855$		0			0
$856$	13.5222	−	4.89107i	0.462180	−	0.167173i
$857$	−12.6566	+	12.6566i	−0.432341	+	0.432341i	−0.889424	−	0.457083i	$-0.848894\pi$
$857$	−12.6566	+	12.6566i	−0.432341	+	0.432341i	0.457083	+	0.889424i	$0.348894\pi$
$858$		0			0
$859$	8.83448	+	3.65936i	0.301429	+	0.124856i	0.528271	−	0.849076i	$-0.322840\pi$
$859$	8.83448	+	3.65936i	0.301429	+	0.124856i	−0.226843	+	0.973931i	$0.572840\pi$
$860$	0.0222510	+	0.0236477i	0.000758752	+	0.000806381i
$861$		0			0
$862$	−17.5199	+	16.9949i	−0.596731	+	0.578848i
$863$	17.1720			0.584540			0.292270	−	0.956336i	$-0.405589\pi$
$863$	17.1720			0.584540			0.292270	+	0.956336i	$0.405589\pi$
$864$		0			0
$865$	2.59593			0.0882642
$866$	3.02120	−	2.93066i	0.102665	−	0.0995879i
$867$		0			0
$868$	6.94848	−	6.53806i	0.235847	−	0.221916i
$869$	−46.8692	−	19.4139i	−1.58993	−	0.658570i
$870$		0			0
$871$	41.5307	−	41.5307i	1.40722	−	1.40722i
$872$	−29.0003	−	13.5937i	−0.982073	−	0.460342i
$873$		0			0
$874$	−6.11577	+	2.42492i	−0.206869	+	0.0820241i
$875$	−38.3904	−	15.9018i	−1.29783	−	0.537580i
$876$		0			0
$877$	12.0208	+	29.0209i	0.405915	+	0.979966i	0.986201	+	0.165553i	$0.0529408\pi$
$877$	12.0208	+	29.0209i	0.405915	+	0.979966i	−0.580286	+	0.814413i	$0.697059\pi$
$878$	0.116400	−	7.65171i	0.00392833	−	0.258233i
$879$		0			0
$880$	−32.0410	−	36.1981i	−1.08010	−	1.22024i
$881$	−14.2736			−0.480888			−0.240444	−	0.970663i	$-0.577293\pi$
$881$	−14.2736			−0.480888			−0.240444	+	0.970663i	$0.577293\pi$
$882$		0			0
$883$	−33.8267	+	14.0115i	−1.13836	+	0.471524i	−0.870614	−	0.491966i	$-0.836278\pi$
$883$	−33.8267	+	14.0115i	−1.13836	+	0.471524i	−0.267745	+	0.963490i	$0.586278\pi$
$884$	32.6161	−	12.3616i	1.09700	−	0.415767i
$885$		0			0
$886$	18.0603	−	7.16094i	0.606746	−	0.240577i
$887$	35.5343	−	35.5343i	1.19312	−	1.19312i	0.216939	−	0.976185i	$-0.430393\pi$
$887$	35.5343	−	35.5343i	1.19312	−	1.19312i	0.976185	−	0.216939i	$-0.0696073\pi$
$888$		0			0
$889$	78.2523	+	78.2523i	2.62450	+	2.62450i
$890$	18.4945	+	7.99240i	0.619939	+	0.267906i
$891$		0			0
$892$	20.7279	+	0.630785i	0.694021	+	0.0211202i
$893$	0.480600	+	1.16027i	0.0160827	+	0.0388270i
$894$		0			0
$895$			20.3948i			0.681722i
$896$	−6.16143	+	57.6468i	−0.205839	+	1.92584i
$897$		0			0
$898$	−24.8001	+	24.0569i	−0.827590	+	0.802789i
$899$	−2.26525	+	0.938299i	−0.0755504	+	0.0312940i
$900$		0			0
$901$	−4.86396	+	11.7426i	−0.162042	+	0.391204i
$902$	−8.28675	+	19.1757i	−0.275919	+	0.638481i
$903$		0			0
$904$	0.593804	−	0.541940i	0.0197496	−	0.0180247i
$905$	27.1699	+	27.1699i	0.903158	+	0.903158i
$906$		0			0
$907$	6.37563	−	15.3921i	0.211699	−	0.511088i	−0.781985	−	0.623297i	$-0.785793\pi$
$907$	6.37563	−	15.3921i	0.211699	−	0.511088i	0.993685	+	0.112209i	$0.0357927\pi$
$908$	−13.8100	−	36.4375i	−0.458300	−	1.20922i
$909$		0			0
$910$	−1.42585	+	93.7299i	−0.0472665	+	3.10711i
$911$		−	32.3451i		−	1.07164i	−0.844332	−	0.535820i	$-0.820003\pi$
$911$		−	32.3451i		−	1.07164i	0.844332	−	0.535820i	$-0.179997\pi$
$912$		0			0
$913$			8.00271i			0.264851i
$914$	5.38849	+	0.0819715i	0.178235	+	0.00271138i
$915$		0			0
$916$	41.8586	+	18.8499i	1.38305	+	0.622817i
$917$	27.9592	−	67.4994i	0.923292	−	2.22903i
$918$		0			0
$919$	21.7353	+	21.7353i	0.716980	+	0.716980i	0.967986	−	0.251005i	$-0.0807612\pi$
$919$	21.7353	+	21.7353i	0.716980	+	0.716980i	−0.251005	+	0.967986i	$0.580761\pi$
$920$	−26.2257	+	55.9487i	−0.864635	+	1.84457i
$921$		0			0
$922$	49.5481	+	21.4122i	1.63178	+	0.705172i
$923$	−13.8415	+	33.4163i	−0.455598	+	1.09991i
$924$		0			0
$925$	−12.9104	+	5.34764i	−0.424490	+	0.175829i
$926$	−30.9421	−	31.8980i	−1.01682	−	1.04823i
$927$		0			0
$928$	6.73100	−	13.2918i	0.220956	−	0.436326i
$929$			36.6928i			1.20385i	0.798552	+	0.601926i	$0.205600\pi$
$929$			36.6928i			1.20385i	−0.798552	+	0.601926i	$0.794400\pi$
$930$		0			0
$931$	4.12745	+	9.96455i	0.135272	+	0.326575i
$932$	15.6472	−	14.7230i	0.512541	−	0.482267i
$933$		0			0
$934$	6.70025	−	15.5045i	0.219239	−	0.507322i
$935$	30.3016	+	30.3016i	0.990969	+	0.990969i
$936$		0			0
$937$	−12.0338	+	12.0338i	−0.393128	+	0.393128i	−0.875801	−	0.482673i	$-0.839666\pi$
$937$	−12.0338	+	12.0338i	−0.393128	+	0.393128i	0.482673	+	0.875801i	$0.339666\pi$
$938$	−31.8968	−	80.4453i	−1.04147	−	2.62663i
$939$		0			0
$940$	10.7550	+	4.84322i	0.350790	+	0.157968i
$941$	−6.21416	+	2.57399i	−0.202576	+	0.0839096i	−0.481665	−	0.876356i	$-0.659968\pi$
$941$	−6.21416	+	2.57399i	−0.202576	+	0.0839096i	0.279089	+	0.960265i	$0.409968\pi$
$942$		0			0
$943$	26.7011			0.869506
$944$	12.4907	−	25.6255i	0.406539	−	0.834040i
$945$		0			0
$946$	−0.0401133		0.000610217i	−0.00130420		1.98399e-5i
$947$	−0.861475	−	2.07979i	−0.0279942	−	0.0675839i	0.909264	−	0.416219i	$-0.136645\pi$
$947$	−0.861475	−	2.07979i	−0.0279942	−	0.0675839i	−0.937258	+	0.348635i	$0.886645\pi$
$948$		0			0
$949$	−42.2302	−	17.4923i	−1.37085	−	0.567825i
$950$	0.559516	+	1.41113i	0.0181531	+	0.0457831i
$951$		0			0
$952$	2.34441	−	51.3390i	0.0759826	−	1.66391i
$953$	−21.8229	+	21.8229i	−0.706913	+	0.706913i	−0.965885	−	0.258972i	$-0.916616\pi$
$953$	−21.8229	+	21.8229i	−0.706913	+	0.706913i	0.258972	+	0.965885i	$0.416616\pi$
$954$		0			0
$955$	−52.8048	−	21.8725i	−1.70872	−	0.707776i
$956$	17.4616	+	0.531388i	0.564749	+	0.0171863i
$957$		0			0
$958$	17.0383	+	17.5647i	0.550481	+	0.567488i
$959$	51.0168			1.64742
$960$		0			0
$961$	30.1334			0.972044
$962$	−35.3103	−	36.4012i	−1.13845	−	1.17362i
$963$		0			0
$964$	−1.83968	−	0.0559847i	−0.0592522	−	0.00180315i
$965$	−3.31828	−	1.37448i	−0.106819	−	0.0442459i
$966$		0			0
$967$	−6.41320	+	6.41320i	−0.206235	+	0.206235i	−0.802665	−	0.596430i	$-0.796585\pi$
$967$	−6.41320	+	6.41320i	−0.206235	+	0.206235i	0.596430	+	0.802665i	$0.296585\pi$
$968$	28.5851	+	1.30534i	0.918759	+	0.0419553i
$969$		0			0
$970$	−0.821993	−	2.07311i	−0.0263926	−	0.0665634i
$971$	−22.7672	−	9.43048i	−0.730634	−	0.302639i	−0.0138215	−	0.999904i	$-0.504400\pi$
$971$	−22.7672	−	9.43048i	−0.730634	−	0.302639i	−0.716813	+	0.697266i	$0.754400\pi$
$972$		0			0
$973$	−20.2918	−	48.9889i	−0.650527	−	1.57051i
$974$	−17.8307	−	0.271246i	−0.571331	−	0.00869128i
$975$		0			0
$976$	−23.3464	+	8.04513i	−0.747300	+	0.257518i
$977$	27.0926			0.866770			0.433385	−	0.901209i	$-0.357319\pi$
$977$	27.0926			0.866770			0.433385	+	0.901209i	$0.357319\pi$
$978$		0			0
$979$	−22.9981	+	9.52610i	−0.735021	+	0.304456i
$980$	92.3655	+	41.5942i	2.95051	+	1.32868i
$981$		0			0
$982$	−17.3214	−	43.6855i	−0.552748	−	1.39406i
$983$	−11.9199	+	11.9199i	−0.380187	+	0.380187i	−0.871169	−	0.490983i	$-0.836638\pi$
$983$	−11.9199	+	11.9199i	−0.380187	+	0.380187i	0.490983	+	0.871169i	$0.336638\pi$
$984$		0			0
$985$	13.0794	+	13.0794i	0.416745	+	0.416745i
$986$	−5.23924	+	12.1237i	−0.166851	+	0.386097i
$987$		0			0
$988$	−4.01215	+	3.77517i	−0.127644	+	0.120104i
$989$	0.0196235	+	0.0473752i	0.000623990	+	0.00150644i
$990$		0			0
$991$		−	31.9068i		−	1.01355i	−0.862077	−	0.506777i	$-0.830837\pi$
$991$		−	31.9068i		−	1.01355i	0.862077	−	0.506777i	$-0.169163\pi$
$992$	3.99592	−	3.43004i	0.126871	−	0.108904i
$993$		0			0
$994$	37.1059	+	38.2523i	1.17693	+	1.21329i
$995$	−61.4016	+	25.4334i	−1.94656	+	0.806292i
$996$		0			0
$997$	18.8069	−	45.4039i	0.595621	−	1.43796i	−0.282383	−	0.959302i	$-0.591125\pi$
$997$	18.8069	−	45.4039i	0.595621	−	1.43796i	0.878004	−	0.478654i	$-0.158875\pi$
$998$	0.00369458	+	0.00159661i	0.000116950	+	5.05398e-5i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.b.107.8	✓	128
3.2	odd	2	inner	864.2.w.b.107.25	yes	128
32.3	odd	8	inner	864.2.w.b.323.25	yes	128
96.35	even	8	inner	864.2.w.b.323.8	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.b.107.8	✓	128	1.1	even	1	trivial
864.2.w.b.107.25	yes	128	3.2	odd	2	inner
864.2.w.b.323.8	yes	128	96.35	even	8	inner
864.2.w.b.323.25	yes	128	32.3	odd	8	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)

\(f(q)\)	\(=\)	\(q+(-0.984674 - 1.01509i) q^{2} +(-0.0608353 + 1.99907i) q^{4} +(2.42976 + 1.00644i) q^{5} +(3.62344 - 3.62344i) q^{7} +(2.08915 - 1.90668i) q^{8} +O(q^{10})\)	\(q+(-0.984674 - 1.01509i) q^{2} +(-0.0608353 + 1.99907i) q^{4} +(2.42976 + 1.00644i) q^{5} +(3.62344 - 3.62344i) q^{7} +(2.08915 - 1.90668i) q^{8} +(-1.37089 - 3.45745i) q^{10} +(4.24551 + 1.75855i) q^{11} +(-1.88221 - 4.54406i) q^{13} +(-7.24605 - 0.110229i) q^{14} +(-3.99260 - 0.243229i) q^{16} +3.54583 q^{17} +(-0.517405 + 0.214316i) q^{19} +(-2.15976 + 4.79604i) q^{20} +(-2.39535 - 6.04120i) q^{22} +(-5.87371 + 5.87371i) q^{23} +(1.35528 + 1.35528i) q^{25} +(-2.75929 + 6.38504i) q^{26} +(7.02310 + 7.46397i) q^{28} +(-1.00791 - 2.43331i) q^{29} -0.930936i q^{31} +(3.68451 + 4.29237i) q^{32} +(-3.49149 - 3.59936i) q^{34} +(12.4509 - 5.15732i) q^{35} +(-2.79010 + 6.73589i) q^{37} +(0.727027 + 0.314184i) q^{38} +(6.99510 - 2.53017i) q^{40} +(-2.27293 - 2.27293i) q^{41} +(0.00236237 - 0.00570327i) q^{43} +(-3.77375 + 8.38012i) q^{44} +(11.7461 + 0.178685i) q^{46} -2.24248i q^{47} -19.2587i q^{49} +(0.0412291 - 2.71024i) q^{50} +(9.19842 - 3.48624i) q^{52} +(-1.37174 + 3.31167i) q^{53} +(8.54570 + 8.54570i) q^{55} +(0.661172 - 14.4787i) q^{56} +(-1.47758 + 3.41914i) q^{58} +(-2.72735 + 6.58441i) q^{59} +(5.70350 - 2.36247i) q^{61} +(-0.944988 + 0.916668i) q^{62} +(0.729123 - 7.96670i) q^{64} -12.9353i q^{65} +(4.56978 + 11.0324i) q^{67} +(-0.215712 + 7.08838i) q^{68} +(-17.4952 - 7.56054i) q^{70} +(-5.19995 - 5.19995i) q^{71} +(6.57149 - 6.57149i) q^{73} +(9.58491 - 3.80044i) q^{74} +(-0.396958 - 1.04737i) q^{76} +(21.7554 - 9.01137i) q^{77} -11.0397 q^{79} +(-9.45626 - 4.60929i) q^{80} +(-0.0691452 + 4.54534i) q^{82} +(0.666441 + 1.60893i) q^{83} +(8.61552 + 3.56867i) q^{85} +(-0.00811553 + 0.00321783i) q^{86} +(12.2225 - 4.42097i) q^{88} +(-3.83042 + 3.83042i) q^{89} +(-23.2852 - 9.64506i) q^{91} +(-11.3847 - 12.0993i) q^{92} +(-2.27633 + 2.20811i) q^{94} -1.47287 q^{95} +0.599606 q^{97} +(-19.5494 + 18.9635i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q + 8 q^{10} + 32 q^{16} - 32 q^{22} + 64 q^{40} + 64 q^{46} + 40 q^{52} + 64 q^{55} + 64 q^{58} + 32 q^{61} + 96 q^{64} - 64 q^{67} - 48 q^{70} - 32 q^{76} - 32 q^{79} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 72 q^{94}+O(q^{100}) \) 128 * q + 8 * q^10 + 32 * q^16 - 32 * q^22 + 64 * q^40 + 64 * q^46 + 40 * q^52 + 64 * q^55 + 64 * q^58 + 32 * q^61 + 96 * q^64 - 64 * q^67 - 48 * q^70 - 32 * q^76 - 32 * q^79 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 72 * q^94

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