LMFDB - Embedded newform 464.2.bl.c.15.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [464,2,Mod(15,464)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("464.15"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(464, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 0, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 464 = 2^{4} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	464.bl (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.70505865379$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			15.10
Character	$\chi$	$=$	464.15
Dual form			464.2.bl.c.31.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36944 + 2.17945i) q^{3} +(1.55895 + 1.24322i) q^{5} +(-3.46859 - 0.791684i) q^{7} +(-1.57297 + 3.26632i) q^{9} +(0.640096 - 1.82929i) q^{11} +(2.94479 + 6.11492i) q^{13} +(-0.574651 + 5.10017i) q^{15} +(1.39955 + 1.39955i) q^{17} +(2.55350 + 1.60447i) q^{19} +(-3.02459 - 8.64377i) q^{21} +(-6.77410 + 5.40217i) q^{23} +(-0.227874 - 0.998382i) q^{25} +(-1.59948 + 0.180218i) q^{27} +(-2.07755 - 4.96828i) q^{29} +(-0.921536 - 8.17886i) q^{31} +(4.86341 - 1.11004i) q^{33} +(-4.42314 - 5.54644i) q^{35} +(-2.22728 + 0.779360i) q^{37} +(-9.29443 + 14.7920i) q^{39} +(6.38938 - 6.38938i) q^{41} +(3.40107 + 0.383208i) q^{43} +(-6.51296 + 3.13648i) q^{45} +(3.79439 + 1.32771i) q^{47} +(5.09760 + 2.45487i) q^{49} +(-1.13365 + 4.96683i) q^{51} +(0.859764 - 1.07811i) q^{53} +(3.27210 - 2.05599i) q^{55} +7.76242i q^{57} +1.49329i q^{59} +(7.30678 - 4.59116i) q^{61} +(8.04190 - 10.0842i) q^{63} +(-3.01142 + 13.1939i) q^{65} +(-0.261074 - 0.125727i) q^{67} +(-21.0504 - 7.36586i) q^{69} +(6.08147 - 2.92868i) q^{71} +(-4.67861 - 0.527152i) q^{73} +(1.86386 - 1.86386i) q^{75} +(-3.66845 + 5.83831i) q^{77} +(9.84233 - 3.44398i) q^{79} +(4.19792 + 5.26403i) q^{81} +(5.59550 - 1.27714i) q^{83} +(0.441879 + 3.92178i) q^{85} +(7.98301 - 11.3317i) q^{87} +(12.9234 - 1.45612i) q^{89} +(-5.37320 - 23.5415i) q^{91} +(16.5634 - 13.2089i) q^{93} +(1.98607 + 5.67586i) q^{95} +(-10.2431 - 6.43615i) q^{97} +(4.96818 + 4.96818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 4 q^{17} - 40 q^{21} - 28 q^{25} - 52 q^{29} - 84 q^{33} - 8 q^{37} + 4 q^{41} + 40 q^{45} - 28 q^{49} - 48 q^{53} - 4 q^{61} - 40 q^{65} + 24 q^{69} + 76 q^{73} + 156 q^{77} + 116 q^{81} + 152 q^{85}+ \cdots + 64 q^{97}+O(q^{100}) $ 120 * q + 4 * q^17 - 40 * q^21 - 28 * q^25 - 52 * q^29 - 84 * q^33 - 8 * q^37 + 4 * q^41 + 40 * q^45 - 28 * q^49 - 48 * q^53 - 4 * q^61 - 40 * q^65 + 24 * q^69 + 76 * q^73 + 156 * q^77 + 116 * q^81 + 152 * q^85 + 104 * q^89 + 112 * q^93 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/464\mathbb{Z}\right)^\times$.

$n$	$117$	$175$	$321$
$\chi(n)$	$1$	$-1$	$e\left(\frac{27}{28}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.36944	+	2.17945i	0.790644	+	1.25830i	0.961988	+	0.273092i	$0.0880463\pi$
$3$	1.36944	+	2.17945i	0.790644	+	1.25830i	−0.171344	+	0.985211i	$0.554811\pi$
$4$		0			0
$5$	1.55895	+	1.24322i	0.697185	+	0.555987i	0.906678	−	0.421824i	$-0.138610\pi$
$5$	1.55895	+	1.24322i	0.697185	+	0.555987i	−0.209493	+	0.977810i	$0.567181\pi$
$6$		0			0
$7$	−3.46859	−	0.791684i	−1.31101	−	0.299228i	−0.490787	−	0.871279i	$-0.663291\pi$
$7$	−3.46859	−	0.791684i	−1.31101	−	0.299228i	−0.820218	+	0.572051i	$0.806148\pi$
$8$		0			0
$9$	−1.57297	+	3.26632i	−0.524325	+	1.08877i
$10$		0			0
$11$	0.640096	−	1.82929i	0.192996	−	0.551551i	−0.806200	−	0.591643i	$-0.798479\pi$
$11$	0.640096	−	1.82929i	0.192996	−	0.551551i	0.999196	+	0.0400920i	$0.0127651\pi$
$12$		0			0
$13$	2.94479	+	6.11492i	0.816738	+	1.69597i	0.712776	+	0.701392i	$0.247438\pi$
$13$	2.94479	+	6.11492i	0.816738	+	1.69597i	0.103962	+	0.994581i	$0.466848\pi$
$14$		0			0
$15$	−0.574651	+	5.10017i	−0.148374	+	1.31686i
$16$		0			0
$17$	1.39955	+	1.39955i	0.339440	+	0.339440i	0.856157	−	0.516716i	$-0.172846\pi$
$17$	1.39955	+	1.39955i	0.339440	+	0.339440i	−0.516716	+	0.856157i	$0.672846\pi$
$18$		0			0
$19$	2.55350	+	1.60447i	0.585812	+	0.368090i	0.792091	−	0.610403i	$-0.208993\pi$
$19$	2.55350	+	1.60447i	0.585812	+	0.368090i	−0.206279	+	0.978493i	$0.566135\pi$
$20$		0			0
$21$	−3.02459	−	8.64377i	−0.660019	−	1.88623i
$22$		0			0
$23$	−6.77410	+	5.40217i	−1.41250	+	1.12643i	−0.438800	+	0.898585i	$0.644597\pi$
$23$	−6.77410	+	5.40217i	−1.41250	+	1.12643i	−0.973697	+	0.227845i	$0.926832\pi$
$24$		0			0
$25$	−0.227874	−	0.998382i	−0.0455748	−	0.199676i
$26$		0			0
$27$	−1.59948	+	0.180218i	−0.307820	+	0.0346830i
$28$		0			0
$29$	−2.07755	−	4.96828i	−0.385792	−	0.922586i
$29$	−2.07755	−	4.96828i	−0.385792	−	0.922586i
$30$		0			0
$31$	−0.921536	−	8.17886i	−0.165513	−	1.46897i	−0.752083	−	0.659068i	$-0.770951\pi$
$31$	−0.921536	−	8.17886i	−0.165513	−	1.46897i	0.586571	−	0.809898i	$-0.300478\pi$
$32$		0			0
$33$	4.86341	−	1.11004i	0.846610	−	0.193233i
$34$		0			0
$35$	−4.42314	−	5.54644i	−0.747647	−	0.937519i
$36$		0			0
$37$	−2.22728	+	0.779360i	−0.366163	+	0.128126i	−0.507088	−	0.861894i	$-0.669278\pi$
$37$	−2.22728	+	0.779360i	−0.366163	+	0.128126i	0.140925	+	0.990020i	$0.454992\pi$
$38$		0			0
$39$	−9.29443	+	14.7920i	−1.48830	+	2.36862i
$40$		0			0
$41$	6.38938	−	6.38938i	0.997854	−	0.997854i	−0.00214390	−	0.999998i	$-0.500682\pi$
$41$	6.38938	−	6.38938i	0.997854	−	0.997854i	0.999998	+	0.00214390i	$0.000682425\pi$
$42$		0			0
$43$	3.40107	+	0.383208i	0.518658	+	0.0584387i	0.367414	−	0.930058i	$-0.380243\pi$
$43$	3.40107	+	0.383208i	0.518658	+	0.0584387i	0.151244	+	0.988496i	$0.451672\pi$
$44$		0			0
$45$	−6.51296	+	3.13648i	−0.970894	+	0.467558i
$46$		0			0
$47$	3.79439	+	1.32771i	0.553468	+	0.193667i	0.592499	−	0.805571i	$-0.298141\pi$
$47$	3.79439	+	1.32771i	0.553468	+	0.193667i	−0.0390309	+	0.999238i	$0.512427\pi$
$48$		0			0
$49$	5.09760	+	2.45487i	0.728229	+	0.350696i
$50$		0			0
$51$	−1.13365	+	4.96683i	−0.158742	+	0.695495i
$52$		0			0
$53$	0.859764	−	1.07811i	0.118098	−	0.148090i	−0.719268	−	0.694732i	$-0.755523\pi$
$53$	0.859764	−	1.07811i	0.118098	−	0.148090i	0.837366	+	0.546642i	$0.184094\pi$
$54$		0			0
$55$	3.27210	−	2.05599i	0.441209	−	0.277230i
$56$		0			0
$57$			7.76242i			1.02816i
$58$		0			0
$59$			1.49329i			0.194410i	0.995264	+	0.0972050i	$0.0309902\pi$
$59$			1.49329i			0.194410i	−0.995264	+	0.0972050i	$0.969010\pi$
$60$		0			0
$61$	7.30678	−	4.59116i	0.935538	−	0.587837i	0.0242939	−	0.999705i	$-0.492266\pi$
$61$	7.30678	−	4.59116i	0.935538	−	0.587837i	0.911244	+	0.411868i	$0.135123\pi$
$62$		0			0
$63$	8.04190	−	10.0842i	1.01318	−	1.27049i
$64$		0			0
$65$	−3.01142	+	13.1939i	−0.373521	+	1.63650i
$66$		0			0
$67$	−0.261074	−	0.125727i	−0.0318953	−	0.0153600i	0.417868	−	0.908508i	$-0.362777\pi$
$67$	−0.261074	−	0.125727i	−0.0318953	−	0.0153600i	−0.449763	+	0.893148i	$0.648492\pi$
$68$		0			0
$69$	−21.0504	−	7.36586i	−2.53417	−	0.886746i
$70$		0			0
$71$	6.08147	−	2.92868i	0.721737	−	0.347570i	−0.0366912	−	0.999327i	$-0.511682\pi$
$71$	6.08147	−	2.92868i	0.721737	−	0.347570i	0.758428	+	0.651756i	$0.225967\pi$
$72$		0			0
$73$	−4.67861	−	0.527152i	−0.547589	−	0.0616985i	−0.166164	−	0.986098i	$-0.553138\pi$
$73$	−4.67861	−	0.527152i	−0.547589	−	0.0616985i	−0.381425	+	0.924400i	$0.624567\pi$
$74$		0			0
$75$	1.86386	−	1.86386i	0.215220	−	0.215220i
$76$		0			0
$77$	−3.66845	+	5.83831i	−0.418059	+	0.665337i
$78$		0			0
$79$	9.84233	−	3.44398i	1.10735	−	0.387478i	0.286187	−	0.958174i	$-0.407612\pi$
$79$	9.84233	−	3.44398i	1.10735	−	0.387478i	0.821162	+	0.570696i	$0.193326\pi$
$80$		0			0
$81$	4.19792	+	5.26403i	0.466436	+	0.584892i
$82$		0			0
$83$	5.59550	−	1.27714i	0.614186	−	0.140184i	0.0958997	−	0.995391i	$-0.469427\pi$
$83$	5.59550	−	1.27714i	0.614186	−	0.140184i	0.518287	+	0.855207i	$0.326570\pi$
$84$		0			0
$85$	0.441879	+	3.92178i	0.0479285	+	0.425377i
$86$		0			0
$87$	7.98301	−	11.3317i	0.855868	−	1.21488i
$88$		0			0
$89$	12.9234	−	1.45612i	1.36988	−	0.154348i	0.603820	−	0.797121i	$-0.293644\pi$
$89$	12.9234	−	1.45612i	1.36988	−	0.154348i	0.766057	+	0.642772i	$0.222216\pi$
$90$		0			0
$91$	−5.37320	−	23.5415i	−0.563264	−	2.46782i
$92$		0			0
$93$	16.5634	−	13.2089i	1.71754	−	1.36969i
$94$		0			0
$95$	1.98607	+	5.67586i	0.203766	+	0.582331i
$96$		0			0
$97$	−10.2431	−	6.43615i	−1.04003	−	0.653492i	−0.100138	−	0.994974i	$-0.531928\pi$
$97$	−10.2431	−	6.43615i	−1.04003	−	0.653492i	−0.939888	+	0.341482i	$0.889071\pi$
$98$		0			0
$99$	4.96818	+	4.96818i	0.499321	+	0.499321i
$100$		0			0
$101$	−1.86097	+	16.5166i	−0.185174	+	1.64346i	0.466181	+	0.884689i	$0.345629\pi$
$101$	−1.86097	+	16.5166i	−0.185174	+	1.64346i	−0.651355	+	0.758773i	$0.725799\pi$
$102$		0			0
$103$	−1.16337	−	2.41576i	−0.114630	−	0.238032i	0.835758	−	0.549097i	$-0.185028\pi$
$103$	−1.16337	−	2.41576i	−0.114630	−	0.238032i	−0.950388	+	0.311066i	$0.899314\pi$
$104$		0			0
$105$	6.03095	−	17.2355i	0.588561	−	1.68201i
$106$		0			0
$107$	−0.457304	+	0.949602i	−0.0442093	+	0.0918015i	−0.921904	−	0.387420i	$-0.873366\pi$
$107$	−0.457304	+	0.949602i	−0.0442093	+	0.0918015i	0.877694	+	0.479221i	$0.159081\pi$
$108$		0			0
$109$	−14.9248	−	3.40650i	−1.42954	−	0.326283i	−0.563441	−	0.826156i	$-0.690523\pi$
$109$	−14.9248	−	3.40650i	−1.42954	−	0.326283i	−0.866099	+	0.499873i	$0.833380\pi$
$110$		0			0
$111$	−4.74869	−	3.78696i	−0.450726	−	0.359442i
$112$		0			0
$113$	0.632855	+	1.00718i	0.0595340	+	0.0947478i	0.875165	−	0.483825i	$-0.160753\pi$
$113$	0.632855	+	1.00718i	0.0595340	+	0.0947478i	−0.815631	+	0.578573i	$0.803610\pi$
$114$		0			0
$115$	−17.2766			−1.61105
$116$		0			0
$117$	−24.6053			−2.27476
$118$		0			0
$119$	−3.74646	−	5.96246i	−0.343438	−	0.546578i
$120$		0			0
$121$	5.66357	+	4.51655i	0.514870	+	0.410595i
$122$		0			0
$123$	22.6752	+	5.17546i	2.04455	+	0.466655i
$124$		0			0
$125$	5.21174	−	10.8223i	0.466152	−	0.967975i
$126$		0			0
$127$	−0.429269	+	1.22678i	−0.0380914	+	0.108859i	−0.961358	−	0.275300i	$-0.911223\pi$
$127$	−0.429269	+	1.22678i	−0.0380914	+	0.108859i	0.923267	+	0.384159i	$0.125509\pi$
$128$		0			0
$129$	3.82236	+	7.93722i	0.336540	+	0.698833i
$130$		0			0
$131$	−1.36028	+	12.0728i	−0.118848	+	1.05481i	0.782781	+	0.622298i	$0.213801\pi$
$131$	−1.36028	+	12.0728i	−0.118848	+	1.05481i	−0.901629	+	0.432510i	$0.857628\pi$
$132$		0			0
$133$	−7.58681	−	7.58681i	−0.657860	−	0.657860i
$134$		0			0
$135$	−2.71757	−	1.70756i	−0.233891	−	0.146963i
$136$		0			0
$137$	−5.82492	−	16.6467i	−0.497656	−	1.42222i	−0.869504	−	0.493926i	$-0.835561\pi$
$137$	−5.82492	−	16.6467i	−0.497656	−	1.42222i	0.371847	−	0.928294i	$-0.378724\pi$
$138$		0			0
$139$	−8.73850	+	6.96872i	−0.741190	+	0.591079i	−0.919590	−	0.392879i	$-0.871479\pi$
$139$	−8.73850	+	6.96872i	−0.741190	+	0.591079i	0.178400	+	0.983958i	$0.442908\pi$
$140$		0			0
$141$	2.30249	+	10.0879i	0.193905	+	0.849552i
$142$		0			0
$143$	13.0709	−	1.47274i	1.09304	−	0.123156i
$144$		0			0
$145$	2.93787	−	10.3282i	0.243977	−	0.857709i
$146$		0			0
$147$	1.63057	+	14.4717i	0.134487	+	1.19361i
$148$		0			0
$149$	−0.591395	+	0.134982i	−0.0484490	+	0.0110582i	−0.246677	−	0.969098i	$-0.579339\pi$
$149$	−0.591395	+	0.134982i	−0.0484490	+	0.0110582i	0.198228	+	0.980156i	$0.436481\pi$
$150$		0			0
$151$	−8.47637	−	10.6290i	−0.689797	−	0.864978i	0.306418	−	0.951897i	$-0.400869\pi$
$151$	−8.47637	−	10.6290i	−0.689797	−	0.864978i	−0.996215	+	0.0869189i	$0.972298\pi$
$152$		0			0
$153$	−6.77282	+	2.36991i	−0.547550	+	0.191596i
$154$		0			0
$155$	8.73152	−	13.8961i	0.701332	−	1.11616i
$156$		0			0
$157$	−1.94679	+	1.94679i	−0.155371	+	0.155371i	−0.780512	−	0.625141i	$-0.785041\pi$
$157$	−1.94679	+	1.94679i	−0.155371	+	0.155371i	0.625141	+	0.780512i	$0.285041\pi$
$158$		0			0
$159$	3.52707	+	0.397406i	0.279715	+	0.0315163i
$160$		0			0
$161$	27.7734	−	13.3750i	2.18885	−	1.05410i
$162$		0			0
$163$	−14.4879	−	5.06954i	−1.13478	−	0.397077i	−0.303445	−	0.952849i	$-0.598137\pi$
$163$	−14.4879	−	5.06954i	−1.13478	−	0.397077i	−0.831335	+	0.555772i	$0.812423\pi$
$164$		0			0
$165$	8.96185	+	4.31580i	0.697679	+	0.335985i
$166$		0			0
$167$	−2.90516	+	12.7284i	−0.224808	+	0.984949i	0.728995	+	0.684519i	$0.239988\pi$
$167$	−2.90516	+	12.7284i	−0.224808	+	0.984949i	−0.953804	+	0.300431i	$0.902870\pi$
$168$		0			0
$169$	−20.6151	+	25.8505i	−1.58578	+	1.98850i
$170$		0			0
$171$	−9.25729	+	5.81674i	−0.707922	+	0.444817i
$172$		0			0
$173$		−	15.8612i		−	1.20591i	−0.797776	−	0.602953i	$-0.793991\pi$
$173$		−	15.8612i		−	1.20591i	0.797776	−	0.602953i	$-0.206009\pi$
$174$		0			0
$175$			3.64339i			0.275414i
$176$		0			0
$177$	−3.25455	+	2.04497i	−0.244627	+	0.153709i
$178$		0			0
$179$	9.96537	−	12.4962i	0.744847	−	0.934008i	−0.254607	−	0.967044i	$-0.581946\pi$
$179$	9.96537	−	12.4962i	0.744847	−	0.934008i	0.999454	+	0.0330363i	$0.0105177\pi$
$180$		0			0
$181$	4.87120	−	21.3421i	0.362074	−	1.58635i	−0.385849	−	0.922562i	$-0.626092\pi$
$181$	4.87120	−	21.3421i	0.362074	−	1.58635i	0.747923	−	0.663786i	$-0.231051\pi$
$182$		0			0
$183$	20.0123	+	9.63744i	1.47935	+	0.712420i
$184$		0			0
$185$	−4.44115	−	1.55402i	−0.326520	−	0.114254i
$186$		0			0
$187$	3.45602	−	1.66433i	0.252729	−	0.121708i
$188$		0			0
$189$	5.69063	+	0.641179i	0.413932	+	0.0466389i
$190$		0			0
$191$	−16.7253	+	16.7253i	−1.21020	+	1.21020i	−0.239237	+	0.970961i	$0.576897\pi$
$191$	−16.7253	+	16.7253i	−1.21020	+	1.21020i	−0.970961	+	0.239237i	$0.923103\pi$
$192$		0			0
$193$	−10.4411	+	16.6170i	−0.751569	+	1.19612i	0.223606	+	0.974680i	$0.428217\pi$
$193$	−10.4411	+	16.6170i	−0.751569	+	1.19612i	−0.975175	+	0.221436i	$0.928926\pi$
$194$		0			0
$195$	−32.8794	+	11.5050i	−2.35454	+	0.823889i
$196$		0			0
$197$	3.96532	+	4.97235i	0.282517	+	0.354265i	0.902760	−	0.430145i	$-0.141537\pi$
$197$	3.96532	+	4.97235i	0.282517	+	0.354265i	−0.620243	+	0.784410i	$0.712966\pi$
$198$		0			0
$199$	−7.97710	+	1.82072i	−0.565482	+	0.129068i	−0.495699	−	0.868495i	$-0.665088\pi$
$199$	−7.97710	+	1.82072i	−0.565482	+	0.129068i	−0.0697833	+	0.997562i	$0.522231\pi$
$200$		0			0
$201$	−0.0835100	−	0.741172i	−0.00589034	−	0.0522782i
$202$		0			0
$203$	3.27289	+	18.8777i	0.229712	+	1.32495i
$204$		0			0
$205$	17.9042	−	2.01732i	1.25048	−	0.140896i
$206$		0			0
$207$	−6.98969	−	30.6238i	−0.485817	−	2.12850i
$208$		0			0
$209$	4.56952	−	3.64407i	0.316080	−	0.252066i
$210$		0			0
$211$	−7.64295	−	21.8423i	−0.526162	−	1.50368i	−0.833737	−	0.552161i	$-0.813803\pi$
$211$	−7.64295	−	21.8423i	−0.526162	−	1.50368i	0.307575	−	0.951524i	$-0.400482\pi$
$212$		0			0
$213$	14.7111	+	9.24358i	1.00799	+	0.633360i
$214$		0			0
$215$	4.82569	+	4.82569i	0.329110	+	0.329110i
$216$		0			0
$217$	−3.27864	+	29.0987i	−0.222568	+	1.97535i
$218$		0			0
$219$	−5.25815	−	10.9187i	−0.355313	−	0.737815i
$220$		0			0
$221$	−4.43675	+	12.6795i	−0.298448	+	0.852915i
$222$		0			0
$223$	11.3190	−	23.5042i	0.757979	−	1.57396i	−0.0596545	−	0.998219i	$-0.519000\pi$
$223$	11.3190	−	23.5042i	0.757979	−	1.57396i	0.817633	−	0.575740i	$-0.195286\pi$
$224$		0			0
$225$	3.61947	+	0.826121i	0.241298	+	0.0550747i
$226$		0			0
$227$	11.6554	+	9.29487i	0.773596	+	0.616922i	0.928639	−	0.370986i	$-0.120980\pi$
$227$	11.6554	+	9.29487i	0.773596	+	0.616922i	−0.155043	+	0.987908i	$0.549551\pi$
$228$		0			0
$229$	−8.48169	−	13.4985i	−0.560486	−	0.892008i	0.439495	−	0.898245i	$-0.355158\pi$
$229$	−8.48169	−	13.4985i	−0.560486	−	0.892008i	−0.999981	+	0.00623691i	$0.998015\pi$
$230$		0			0
$231$	−17.7480			−1.16773
$232$		0			0
$233$	−22.3647			−1.46516			−0.732579	−	0.680682i	$-0.761684\pi$
$233$	−22.3647			−1.46516			−0.732579	+	0.680682i	$0.761684\pi$
$234$		0			0
$235$	4.26463	+	6.78712i	0.278194	+	0.442743i
$236$		0			0
$237$	20.9844	+	16.7345i	1.36308	+	1.08702i
$238$		0			0
$239$	25.0994	+	5.72878i	1.62355	+	0.370564i	0.935006	−	0.354632i	$-0.115394\pi$
$239$	25.0994	+	5.72878i	1.62355	+	0.370564i	0.688542	+	0.725197i	$0.258251\pi$
$240$		0			0
$241$	−6.42874	+	13.3494i	−0.414112	+	0.859912i	0.584704	+	0.811247i	$0.301211\pi$
$241$	−6.42874	+	13.3494i	−0.414112	+	0.859912i	−0.998815	+	0.0486646i	$0.984503\pi$
$242$		0			0
$243$	−7.31872	+	20.9157i	−0.469496	+	1.34174i
$244$		0			0
$245$	4.89496	+	10.1645i	0.312728	+	0.649386i
$246$		0			0
$247$	−2.29168	+	20.3392i	−0.145816	+	1.29416i
$248$		0			0
$249$	10.4461	+	10.4461i	0.661997	+	0.661997i
$250$		0			0
$251$	4.88700	+	3.07071i	0.308465	+	0.193821i	0.677364	−	0.735648i	$-0.263122\pi$
$251$	4.88700	+	3.07071i	0.308465	+	0.193821i	−0.368899	+	0.929469i	$0.620265\pi$
$252$		0			0
$253$	5.54605	+	15.8497i	0.348677	+	0.996462i
$254$		0			0
$255$	−7.94218	+	6.33368i	−0.497359	+	0.396630i
$256$		0			0
$257$	0.833135	+	3.65020i	0.0519696	+	0.227693i	0.994243	−	0.107152i	$-0.0341731\pi$
$257$	0.833135	+	3.65020i	0.0519696	+	0.227693i	−0.942273	+	0.334845i	$0.891316\pi$
$258$		0			0
$259$	8.34254	−	0.939979i	0.518380	−	0.0584075i
$260$		0			0
$261$	19.4959	+	1.02902i	1.20677	+	0.0636950i
$262$		0			0
$263$	1.70747	+	15.1542i	0.105287	+	0.934449i	0.929664	+	0.368408i	$0.120097\pi$
$263$	1.70747	+	15.1542i	0.105287	+	0.934449i	−0.824377	+	0.566041i	$0.808474\pi$
$264$		0			0
$265$	2.68066	−	0.611844i	0.164672	−	0.0375853i
$266$		0			0
$267$	20.8713	+	26.1718i	1.27730	+	1.60169i
$268$		0			0
$269$	−3.56649	+	1.24797i	−0.217453	+	0.0760900i	−0.436807	−	0.899555i	$-0.643891\pi$
$269$	−3.56649	+	1.24797i	−0.217453	+	0.0760900i	0.219354	+	0.975645i	$0.429605\pi$
$270$		0			0
$271$	−7.42925	+	11.8236i	−0.451295	+	0.718231i	−0.992444	−	0.122695i	$-0.960846\pi$
$271$	−7.42925	+	11.8236i	−0.451295	+	0.718231i	0.541150	+	0.840926i	$0.317989\pi$
$272$		0			0
$273$	43.9492	−	43.9492i	2.65993	−	2.65993i
$274$		0			0
$275$	−1.97219	−	0.222212i	−0.118928	−	0.0133999i
$276$		0			0
$277$	−15.8898	+	7.65213i	−0.954727	+	0.459772i	−0.845341	−	0.534227i	$-0.820603\pi$
$277$	−15.8898	+	7.65213i	−0.954727	+	0.459772i	−0.109386	+	0.993999i	$0.534888\pi$
$278$		0			0
$279$	28.1643	+	9.85511i	1.68615	+	0.590010i
$280$		0			0
$281$	−14.5745	−	7.01872i	−0.869443	−	0.418702i	−0.0546857	−	0.998504i	$-0.517416\pi$
$281$	−14.5745	−	7.01872i	−0.869443	−	0.418702i	−0.814758	+	0.579802i	$0.803130\pi$
$282$		0			0
$283$	0.889996	−	3.89933i	0.0529048	−	0.231791i	−0.941562	−	0.336839i	$-0.890642\pi$
$283$	0.889996	−	3.89933i	0.0529048	−	0.231791i	0.994467	+	0.105048i	$0.0334995\pi$
$284$		0			0
$285$	−9.65043	+	12.1013i	−0.571642	+	0.716817i
$286$		0			0
$287$	−27.2205	+	17.1038i	−1.60678	+	1.00961i
$288$		0			0
$289$		−	13.0825i		−	0.769561i
$290$		0			0
$291$		−	31.1381i		−	1.82535i
$292$		0			0
$293$	−9.57646	+	6.01729i	−0.559463	+	0.351534i	−0.781891	−	0.623415i	$-0.785745\pi$
$293$	−9.57646	+	6.01729i	−0.559463	+	0.351534i	0.222428	+	0.974949i	$0.428602\pi$
$294$		0			0
$295$	−1.85650	+	2.32797i	−0.108089	+	0.135540i
$296$		0			0
$297$	−0.694150	+	3.04127i	−0.0402787	+	0.176472i
$298$		0			0
$299$	−52.9821	−	25.5148i	−3.06403	−	1.47556i
$300$		0			0
$301$	−11.4935	−	4.02177i	−0.662477	−	0.231811i
$302$		0			0
$303$	−38.5455	+	18.5625i	−2.21438	+	1.06639i
$304$		0			0
$305$	17.0988	+	1.92657i	0.979073	+	0.110315i
$306$		0			0
$307$	13.7560	−	13.7560i	0.785096	−	0.785096i	−0.195590	−	0.980686i	$-0.562662\pi$
$307$	13.7560	−	13.7560i	0.785096	−	0.785096i	0.980686	+	0.195590i	$0.0626620\pi$
$308$		0			0
$309$	3.67186	−	5.84373i	0.208885	−	0.332438i
$310$		0			0
$311$	−11.4157	+	3.99454i	−0.647327	+	0.226510i	−0.633918	−	0.773400i	$-0.718554\pi$
$311$	−11.4157	+	3.99454i	−0.647327	+	0.226510i	−0.0134095	+	0.999910i	$0.504269\pi$
$312$		0			0
$313$	−16.8081	−	21.0766i	−0.950047	−	1.19132i	−0.981431	−	0.191814i	$-0.938563\pi$
$313$	−16.8081	−	21.0766i	−0.950047	−	1.19132i	0.0313841	−	0.999507i	$-0.490009\pi$
$314$		0			0
$315$	25.0739	−	5.72296i	1.41275	−	0.322452i
$316$		0			0
$317$	1.32619	+	11.7703i	0.0744863	+	0.661084i	0.974370	+	0.224953i	$0.0722229\pi$
$317$	1.32619	+	11.7703i	0.0744863	+	0.661084i	−0.899883	+	0.436131i	$0.856349\pi$
$318$		0			0
$319$	−10.4182	+	0.620274i	−0.583310	+	0.0347287i
$320$		0			0
$321$	−2.69585	+	0.303750i	−0.150468	+	0.0169537i
$322$		0			0
$323$	1.32821	+	5.81927i	0.0739036	+	0.323793i
$324$		0			0
$325$	5.43398	−	4.33346i	0.301423	−	0.240377i
$326$		0			0
$327$	−13.0143	−	37.1928i	−0.719695	−	2.05677i
$328$		0			0
$329$	−12.1101	−	7.60925i	−0.667649	−	0.419512i
$330$		0			0
$331$	−1.89043	−	1.89043i	−0.103907	−	0.103907i	0.653242	−	0.757149i	$-0.273408\pi$
$331$	−1.89043	−	1.89043i	−0.103907	−	0.103907i	−0.757149	+	0.653242i	$0.773408\pi$
$332$		0			0
$333$	0.957824	−	8.50092i	0.0524884	−	0.465848i
$334$		0			0
$335$	−0.250696	−	0.520576i	−0.0136970	−	0.0284421i
$336$		0			0
$337$	0.0622566	−	0.177919i	0.00339133	−	0.00969187i	−0.942175	−	0.335121i	$-0.891223\pi$
$337$	0.0622566	−	0.177919i	0.00339133	−	0.00969187i	0.945567	+	0.325429i	$0.105509\pi$
$338$		0			0
$339$	−1.32845	+	2.75855i	−0.0721512	+	0.149824i
$340$		0			0
$341$	−15.5514	−	3.54950i	−0.842153	−	0.192216i
$342$		0			0
$343$	3.73316	+	2.97709i	0.201571	+	0.160748i
$344$		0			0
$345$	−23.6592	−	37.6534i	−1.27377	−	2.02719i
$346$		0			0
$347$	10.7333			0.576194			0.288097	−	0.957601i	$-0.406978\pi$
$347$	10.7333			0.576194			0.288097	+	0.957601i	$0.406978\pi$
$348$		0			0
$349$	28.9983			1.55225			0.776123	−	0.630582i	$-0.217184\pi$
$349$	28.9983			1.55225			0.776123	+	0.630582i	$0.217184\pi$
$350$		0			0
$351$	−5.81215	−	9.24999i	−0.310230	−	0.493728i
$352$		0			0
$353$	−6.21349	−	4.95509i	−0.330711	−	0.263733i	0.444030	−	0.896012i	$-0.353548\pi$
$353$	−6.21349	−	4.95509i	−0.330711	−	0.263733i	−0.774741	+	0.632279i	$0.782120\pi$
$354$		0			0
$355$	13.1217	+	2.99495i	0.696429	+	0.158955i
$356$		0			0
$357$	7.86432	−	16.3304i	0.416224	−	0.864298i
$358$		0			0
$359$	5.82727	−	16.6534i	0.307551	−	0.878931i	−0.681560	−	0.731762i	$-0.738698\pi$
$359$	5.82727	−	16.6534i	0.307551	−	0.878931i	0.989111	−	0.147169i	$-0.0470161\pi$
$360$		0			0
$361$	−4.29777	−	8.92440i	−0.226198	−	0.469705i
$362$		0			0
$363$	−2.08767	+	18.5286i	−0.109574	+	0.972498i
$364$		0			0
$365$	−6.63836	−	6.63836i	−0.347468	−	0.347468i
$366$		0			0
$367$	6.11542	+	3.84257i	0.319222	+	0.200581i	0.682105	−	0.731254i	$-0.261065\pi$
$367$	6.11542	+	3.84257i	0.319222	+	0.200581i	−0.362883	+	0.931835i	$0.618208\pi$
$368$		0			0
$369$	10.8194	+	30.9201i	0.563236	+	1.60963i
$370$		0			0
$371$	−3.83569	+	3.05886i	−0.199139	+	0.158808i
$372$		0			0
$373$	−1.80076	−	7.88966i	−0.0932399	−	0.408511i	0.906671	−	0.421838i	$-0.138615\pi$
$373$	−1.80076	−	7.88966i	−0.0932399	−	0.408511i	−0.999911	+	0.0133271i	$0.995758\pi$
$374$		0			0
$375$	30.7237	−	3.46173i	1.58657	−	0.178763i
$376$		0			0
$377$	24.2626	−	27.3346i	1.24959	−	1.40780i
$378$		0			0
$379$	−0.0234273	−	0.207923i	−0.00120338	−	0.0106803i	0.993096	−	0.117303i	$-0.0374249\pi$
$379$	−0.0234273	−	0.207923i	−0.00120338	−	0.0106803i	−0.994300	+	0.106623i	$0.965996\pi$
$380$		0			0
$381$	−3.26155	+	0.744428i	−0.167094	+	0.0381382i
$382$		0			0
$383$	−2.48043	−	3.11037i	−0.126744	−	0.158932i	0.714410	−	0.699727i	$-0.246695\pi$
$383$	−2.48043	−	3.11037i	−0.126744	−	0.158932i	−0.841155	+	0.540795i	$0.818124\pi$
$384$		0			0
$385$	−12.9773	+	4.54094i	−0.661383	+	0.231428i
$386$		0			0
$387$	−6.60147	+	10.5062i	−0.335572	+	0.534059i
$388$		0			0
$389$	−2.40354	+	2.40354i	−0.121864	+	0.121864i	−0.765409	−	0.643544i	$-0.777463\pi$
$389$	−2.40354	+	2.40354i	−0.121864	+	0.121864i	0.643544	+	0.765409i	$0.277463\pi$
$390$		0			0
$391$	−17.0413	−	1.92009i	−0.861814	−	0.0971031i
$392$		0			0
$393$	−28.1749	+	13.5683i	−1.42124	+	0.684431i
$394$		0			0
$395$	19.6254	+	6.86722i	0.987460	+	0.345527i
$396$		0			0
$397$	−3.31818	−	1.59795i	−0.166535	−	0.0801990i	0.348759	−	0.937212i	$-0.386603\pi$
$397$	−3.31818	−	1.59795i	−0.166535	−	0.0801990i	−0.515294	+	0.857013i	$0.672317\pi$
$398$		0			0
$399$	6.14539	−	26.9247i	0.307654	−	1.34792i
$400$		0			0
$401$	−8.10246	+	10.1602i	−0.404617	+	0.507374i	−0.941838	−	0.336068i	$-0.890903\pi$
$401$	−8.10246	+	10.1602i	−0.404617	+	0.507374i	0.537220	+	0.843442i	$0.319474\pi$
$402$		0			0
$403$	47.2993	−	29.7201i	2.35615	−	1.48046i
$404$		0			0
$405$			13.4253i			0.667110i
$406$		0			0
$407$			4.57321i			0.226685i
$408$		0			0
$409$	−15.9048	+	9.99364i	−0.786441	+	0.494154i	−0.864401	−	0.502803i	$-0.832302\pi$
$409$	−15.9048	+	9.99364i	−0.786441	+	0.494154i	0.0779601	+	0.996956i	$0.475159\pi$
$410$		0			0
$411$	28.3036	−	35.4916i	1.39612	−	1.75067i
$412$		0			0
$413$	1.18221	−	5.17962i	0.0581730	−	0.254873i
$414$		0			0
$415$	10.3109	+	4.96547i	0.506142	+	0.243745i
$416$		0			0
$417$	−27.1548	−	9.50187i	−1.32978	−	0.465308i
$418$		0			0
$419$	−9.61354	+	4.62964i	−0.469652	+	0.226173i	−0.653713	−	0.756742i	$-0.726790\pi$
$419$	−9.61354	+	4.62964i	−0.469652	+	0.226173i	0.184061	+	0.982915i	$0.441076\pi$
$420$		0			0
$421$	10.7804	+	1.21466i	0.525405	+	0.0591990i	0.370684	−	0.928759i	$-0.379123\pi$
$421$	10.7804	+	1.21466i	0.525405	+	0.0591990i	0.154722	+	0.987958i	$0.450552\pi$
$422$		0			0
$423$	−10.3052	+	10.3052i	−0.501056	+	0.501056i
$424$		0			0
$425$	1.07836	−	1.71620i	0.0523083	−	0.0832481i
$426$		0			0
$427$	−28.9790	+	10.1402i	−1.40239	+	0.490718i
$428$		0			0
$429$	21.1095	+	26.4705i	1.01918	+	1.27801i
$430$		0			0
$431$	8.70553	−	1.98698i	0.419331	−	0.0957095i	−0.00764900	−	0.999971i	$-0.502435\pi$
$431$	8.70553	−	1.98698i	0.419331	−	0.0957095i	0.426980	+	0.904261i	$0.359578\pi$
$432$		0			0
$433$	2.15772	+	19.1503i	0.103694	+	0.920306i	0.932598	+	0.360916i	$0.117536\pi$
$433$	2.15772	+	19.1503i	0.103694	+	0.920306i	−0.828905	+	0.559390i	$0.811035\pi$
$434$		0			0
$435$	26.5329	−	7.74086i	1.27216	−	0.371146i
$436$		0			0
$437$	−25.9652	+	2.92558i	−1.24209	+	0.139949i
$438$		0			0
$439$	0.739971	+	3.24202i	0.0353169	+	0.154733i	0.989512	−	0.144452i	$-0.0461421\pi$
$439$	0.739971	+	3.24202i	0.0353169	+	0.154733i	−0.954195	+	0.299186i	$0.903285\pi$
$440$		0			0
$441$	−16.0368	+	12.7889i	−0.763657	+	0.608996i
$442$		0			0
$443$	0.844672	+	2.41393i	0.0401316	+	0.114689i	0.962206	−	0.272324i	$-0.0877923\pi$
$443$	0.844672	+	2.41393i	0.0401316	+	0.114689i	−0.922074	+	0.387014i	$0.873507\pi$
$444$		0			0
$445$	21.9573	+	13.7967i	1.04087	+	0.654024i
$446$		0			0
$447$	−1.10406	−	1.10406i	−0.0522204	−	0.0522204i
$448$		0			0
$449$	−1.77657	+	15.7675i	−0.0838416	+	0.744115i	0.879511	+	0.475878i	$0.157870\pi$
$449$	−1.77657	+	15.7675i	−0.0838416	+	0.744115i	−0.963353	+	0.268237i	$0.913559\pi$
$450$		0			0
$451$	−7.59821	−	15.7778i	−0.357786	−	0.742950i
$452$		0			0
$453$	11.5575	−	33.0296i	0.543021	−	1.55186i
$454$		0			0
$455$	20.8908	−	43.3802i	0.979376	−	2.03370i
$456$		0			0
$457$	14.3026	+	3.26447i	0.669047	+	0.152706i	0.543535	−	0.839386i	$-0.317085\pi$
$457$	14.3026	+	3.26447i	0.669047	+	0.152706i	0.125512	+	0.992092i	$0.459943\pi$
$458$		0			0
$459$	−2.49077	−	1.98633i	−0.116259	−	0.0927138i
$460$		0			0
$461$	13.4443	+	21.3966i	0.626166	+	0.996537i	0.997678	+	0.0681088i	$0.0216965\pi$
$461$	13.4443	+	21.3966i	0.626166	+	0.996537i	−0.371512	+	0.928428i	$0.621161\pi$
$462$		0			0
$463$	−1.15030			−0.0534589			−0.0267294	−	0.999643i	$-0.508509\pi$
$463$	−1.15030			−0.0534589			−0.0267294	+	0.999643i	$0.508509\pi$
$464$		0			0
$465$	42.2431			1.95898
$466$		0			0
$467$	−10.0605	−	16.0112i	−0.465544	−	0.740908i	0.528612	−	0.848863i	$-0.322713\pi$
$467$	−10.0605	−	16.0112i	−0.465544	−	0.740908i	−0.994156	+	0.107955i	$0.965570\pi$
$468$		0			0
$469$	0.806025	+	0.642783i	0.0372188	+	0.0296810i
$470$		0			0
$471$	−6.90893	−	1.57692i	−0.318347	−	0.0726605i
$472$		0			0
$473$	2.87801	−	5.97625i	0.132331	−	0.274788i
$474$		0			0
$475$	1.02000	−	2.91498i	0.0468006	−	0.133749i
$476$		0			0
$477$	2.16906	+	4.50410i	0.0993144	+	0.206229i
$478$		0			0
$479$	−3.94121	+	34.9792i	−0.180079	+	1.59824i	0.500613	+	0.865671i	$0.333108\pi$
$479$	−3.94121	+	34.9792i	−0.180079	+	1.59824i	−0.680691	+	0.732570i	$0.738321\pi$
$480$		0			0
$481$	−11.3246	−	11.3246i	−0.516357	−	0.516357i
$482$		0			0
$483$	67.1839	+	42.2145i	3.05698	+	1.92083i
$484$		0			0
$485$	−7.96690	−	22.7681i	−0.361758	−	1.03385i
$486$		0			0
$487$	−12.6321	+	10.0738i	−0.572416	+	0.456486i	−0.866419	−	0.499318i	$-0.833584\pi$
$487$	−12.6321	+	10.0738i	−0.572416	+	0.456486i	0.294003	+	0.955805i	$0.405012\pi$
$488$		0			0
$489$	−8.79148	−	38.5180i	−0.397565	−	1.74184i
$490$		0			0
$491$	−2.78508	+	0.313803i	−0.125689	+	0.0141617i	−0.174585	−	0.984642i	$-0.555858\pi$
$491$	−2.78508	+	0.313803i	−0.125689	+	0.0141617i	0.0488959	+	0.998804i	$0.484430\pi$
$492$		0			0
$493$	4.04570	−	9.86098i	0.182209	−	0.444116i
$494$		0			0
$495$	1.56860	+	13.9217i	0.0705034	+	0.625735i
$496$		0			0
$497$	−23.4127	+	5.34380i	−1.05020	+	0.239702i
$498$		0			0
$499$	−5.13016	−	6.43301i	−0.229657	−	0.287981i	0.653629	−	0.756815i	$-0.273246\pi$
$499$	−5.13016	−	6.43301i	−0.229657	−	0.287981i	−0.883286	+	0.468834i	$0.844674\pi$
$500$		0			0
$501$	−31.7192	+	11.0990i	−1.41711	+	0.495868i
$502$		0			0
$503$	12.5782	−	20.0181i	0.560835	−	0.892563i	−0.439148	−	0.898415i	$-0.644720\pi$
$503$	12.5782	−	20.0181i	0.560835	−	0.892563i	0.999983	+	0.00585127i	$0.00186253\pi$
$504$		0			0
$505$	−23.4350	+	23.4350i	−1.04284	+	1.04284i
$506$		0			0
$507$	−84.5708	−	9.52884i	−3.75592	−	0.423191i
$508$		0			0
$509$	24.4093	−	11.7549i	1.08192	−	0.521027i	0.193992	−	0.981003i	$-0.437856\pi$
$509$	24.4093	−	11.7549i	1.08192	−	0.521027i	0.887931	+	0.459976i	$0.152142\pi$
$510$		0			0
$511$	15.8108	+	5.53246i	0.699431	+	0.244741i
$512$		0			0
$513$	−4.37342	−	2.10613i	−0.193091	−	0.0929879i
$514$		0			0
$515$	1.18969	−	5.21239i	0.0524241	−	0.229685i
$516$		0			0
$517$	4.85754	−	6.09116i	0.213634	−	0.267889i
$518$		0			0
$519$	34.5687	−	21.7209i	1.51740	−	0.953443i
$520$		0			0
$521$			24.0335i			1.05293i	0.850197	+	0.526464i	$0.176483\pi$
$521$			24.0335i			1.05293i	−0.850197	+	0.526464i	$0.823517\pi$
$522$		0			0
$523$			10.4664i			0.457662i	0.973466	+	0.228831i	$0.0734903\pi$
$523$			10.4664i			0.457662i	−0.973466	+	0.228831i	$0.926510\pi$
$524$		0			0
$525$	−7.94056	+	4.98939i	−0.346554	+	0.217755i
$526$		0			0
$527$	10.1570	−	12.7364i	0.442444	−	0.554808i
$528$		0			0
$529$	11.5871	−	50.7663i	0.503786	−	2.20723i
$530$		0			0
$531$	−4.87756	−	2.34891i	−0.211668	−	0.101934i
$532$		0			0
$533$	57.8859	+	20.2552i	2.50732	+	0.877349i
$534$		0			0
$535$	−1.89348	+	0.911854i	−0.0818625	+	0.0394229i
$536$		0			0
$537$	40.8817	+	4.60626i	1.76417	+	0.198775i
$538$		0			0
$539$	7.75363	−	7.75363i	0.333972	−	0.333972i
$540$		0			0
$541$	9.11443	−	14.5055i	0.391860	−	0.623642i	−0.591286	−	0.806462i	$-0.701380\pi$
$541$	9.11443	−	14.5055i	0.391860	−	0.623642i	0.983146	+	0.182820i	$0.0585226\pi$
$542$		0			0
$543$	53.1848	−	18.6102i	2.28238	−	0.798639i
$544$		0			0
$545$	−19.0321	−	23.8655i	−0.815245	−	1.02229i
$546$		0			0
$547$	−15.8083	+	3.60815i	−0.675915	+	0.154273i	−0.546681	−	0.837341i	$-0.684109\pi$
$547$	−15.8083	+	3.60815i	−0.675915	+	0.154273i	−0.129234	+	0.991614i	$0.541252\pi$
$548$		0			0
$549$	3.50278	+	31.0880i	0.149495	+	1.32680i
$550$		0			0
$551$	2.66641	−	16.0198i	0.113593	−	0.682468i
$552$		0			0
$553$	−36.8656	+	4.15375i	−1.56768	+	0.176636i
$554$		0			0
$555$	−2.69496	−	11.8074i	−0.114395	−	0.501195i
$556$		0			0
$557$	−4.10992	+	3.27755i	−0.174143	+	0.138874i	−0.706683	−	0.707531i	$-0.749809\pi$
$557$	−4.10992	+	3.27755i	−0.174143	+	0.138874i	0.532540	+	0.846405i	$0.321238\pi$
$558$		0			0
$559$	7.67214	+	21.9257i	0.324497	+	0.927359i
$560$		0			0
$561$	8.36012	+	5.25301i	0.352965	+	0.221782i
$562$		0			0
$563$	6.76498	+	6.76498i	0.285110	+	0.285110i	0.835143	−	0.550033i	$-0.185385\pi$
$563$	6.76498	+	6.76498i	0.285110	+	0.285110i	−0.550033	+	0.835143i	$0.685385\pi$
$564$		0			0
$565$	−0.265562	+	2.35693i	−0.0111723	+	0.0991569i
$566$		0			0
$567$	−10.3934	−	21.5822i	−0.436483	−	0.906367i
$568$		0			0
$569$	−2.33417	+	6.67067i	−0.0978535	+	0.279649i	−0.982396	−	0.186810i	$-0.940185\pi$
$569$	−2.33417	+	6.67067i	−0.0978535	+	0.279649i	0.884543	+	0.466460i	$0.154471\pi$
$570$		0			0
$571$	−19.8226	+	41.1621i	−0.829550	+	1.72258i	−0.150340	+	0.988634i	$0.548037\pi$
$571$	−19.8226	+	41.1621i	−0.829550	+	1.72258i	−0.679210	+	0.733944i	$0.737677\pi$
$572$		0			0
$573$	−59.3560	−	13.5476i	−2.47963	−	0.565960i
$574$		0			0
$575$	6.93707	+	5.53213i	0.289296	+	0.230706i
$576$		0			0
$577$	0.557629	+	0.887462i	0.0232144	+	0.0369455i	0.858130	−	0.513433i	$-0.171626\pi$
$577$	0.557629	+	0.887462i	0.0232144	+	0.0369455i	−0.834915	+	0.550378i	$0.814484\pi$
$578$		0			0
$579$	−50.5142			−2.09930
$580$		0			0
$581$	−20.4196			−0.847149
$582$		0			0
$583$	−1.42184	−	2.26285i	−0.0588867	−	0.0937176i
$584$		0			0
$585$	−38.3586	−	30.5899i	−1.58593	−	1.26474i
$586$		0			0
$587$	−28.1947	−	6.43525i	−1.16372	−	0.265611i	−0.403314	−	0.915061i	$-0.632142\pi$
$587$	−28.1947	−	6.43525i	−1.16372	−	0.265611i	−0.760404	+	0.649450i	$0.774999\pi$
$588$		0			0
$589$	10.7696	−	22.3633i	0.443753	−	0.921462i
$590$		0			0
$591$	−5.40671	+	15.4515i	−0.222403	+	0.635590i
$592$		0			0
$593$	15.4485	+	32.0791i	0.634393	+	1.31733i	0.931936	+	0.362622i	$0.118118\pi$
$593$	15.4485	+	32.0791i	0.634393	+	1.31733i	−0.297544	+	0.954708i	$0.596167\pi$
$594$		0			0
$595$	1.57211	−	13.9529i	0.0644504	−	0.572013i
$596$		0			0
$597$	−14.8923	−	14.8923i	−0.609501	−	0.609501i
$598$		0			0
$599$	−35.4111	−	22.2503i	−1.44686	−	0.909122i	−0.999894	−	0.0145706i	$-0.995362\pi$
$599$	−35.4111	−	22.2503i	−1.44686	−	0.909122i	−0.446965	−	0.894551i	$-0.647495\pi$
$600$		0			0
$601$	−5.13240	−	14.6676i	−0.209355	−	0.598302i	0.790546	−	0.612403i	$-0.209797\pi$
$601$	−5.13240	−	14.6676i	−0.209355	−	0.598302i	−0.999901	+	0.0141010i	$0.995511\pi$
$602$		0			0
$603$	0.821326	−	0.654986i	0.0334470	−	0.0266731i
$604$		0			0
$605$	3.21416	+	14.0822i	0.130674	+	0.572522i
$606$		0			0
$607$	−10.5002	+	1.18308i	−0.426189	+	0.0480199i	−0.322454	−	0.946585i	$-0.604508\pi$
$607$	−10.5002	+	1.18308i	−0.426189	+	0.0480199i	−0.103735	+	0.994605i	$0.533079\pi$
$608$		0			0
$609$	−36.6609	+	32.9849i	−1.48557	+	1.33662i
$610$		0			0
$611$	3.05481	+	27.1122i	0.123584	+	1.09684i
$612$		0			0
$613$	−6.52626	+	1.48958i	−0.263593	+	0.0601634i	−0.352275	−	0.935897i	$-0.614592\pi$
$613$	−6.52626	+	1.48958i	−0.263593	+	0.0601634i	0.0886816	+	0.996060i	$0.471735\pi$
$614$		0			0
$615$	28.9153	+	36.2586i	1.16598	+	1.46209i
$616$		0			0
$617$	26.1172	−	9.13881i	1.05144	−	0.367915i	0.251413	−	0.967880i	$-0.419105\pi$
$617$	26.1172	−	9.13881i	1.05144	−	0.367915i	0.800026	+	0.599965i	$0.204819\pi$
$618$		0			0
$619$	−18.6559	+	29.6906i	−0.749843	+	1.19337i	0.225837	+	0.974165i	$0.427488\pi$
$619$	−18.6559	+	29.6906i	−0.749843	+	1.19337i	−0.975679	+	0.219203i	$0.929654\pi$
$620$		0			0
$621$	9.86148	−	9.86148i	0.395727	−	0.395727i
$622$		0			0
$623$	−45.9788	−	5.18057i	−1.84210	−	0.207555i
$624$		0			0
$625$	16.9662	−	8.17047i	0.678647	−	0.326819i
$626$		0			0
$627$	14.1997	+	4.96869i	0.567082	+	0.198431i
$628$		0			0
$629$	−4.20794	−	2.02644i	−0.167782	−	0.0807993i
$630$		0			0
$631$	5.74363	−	25.1645i	0.228650	−	1.00178i	−0.722091	−	0.691798i	$-0.756819\pi$
$631$	5.74363	−	25.1645i	0.228650	−	1.00178i	0.950742	−	0.309985i	$-0.100324\pi$
$632$		0			0
$633$	37.1375	−	46.5690i	1.47608	−	1.85095i
$634$		0			0
$635$	−2.19437	+	1.37881i	−0.0870810	+	0.0547166i
$636$		0			0
$637$			38.4005i			1.52148i
$638$		0			0
$639$			24.4707i			0.968047i
$640$		0			0
$641$	2.42283	−	1.52236i	0.0956959	−	0.0601297i	−0.483334	−	0.875436i	$-0.660574\pi$
$641$	2.42283	−	1.52236i	0.0956959	−	0.0601297i	0.579030	+	0.815306i	$0.303431\pi$
$642$		0			0
$643$	10.3425	−	12.9691i	0.407869	−	0.511451i	−0.534892	−	0.844920i	$-0.679648\pi$
$643$	10.3425	−	12.9691i	0.407869	−	0.511451i	0.942761	+	0.333469i	$0.108219\pi$
$644$		0			0
$645$	−3.90886	+	17.1258i	−0.153911	+	0.674328i
$646$		0			0
$647$	38.6773	+	18.6260i	1.52056	+	0.732264i	0.993095	−	0.117313i	$-0.0374280\pi$
$647$	38.6773	+	18.6260i	1.52056	+	0.732264i	0.527466	+	0.849576i	$0.323142\pi$
$648$		0			0
$649$	2.73166	+	0.955850i	0.107227	+	0.0375204i
$650$		0			0
$651$	−67.9089	+	32.7032i	−2.66156	+	1.28174i
$652$		0			0
$653$	10.5116	+	1.18437i	0.411350	+	0.0463480i	0.315215	−	0.949020i	$-0.397923\pi$
$653$	10.5116	+	1.18437i	0.411350	+	0.0463480i	0.0961352	+	0.995368i	$0.469352\pi$
$654$		0			0
$655$	−17.1299	+	17.1299i	−0.669319	+	0.669319i
$656$		0			0
$657$	9.08118	−	14.4526i	0.354290	−	0.563850i
$658$		0			0
$659$	−22.3892	+	7.83432i	−0.872160	+	0.305182i	−0.728997	−	0.684517i	$-0.760013\pi$
$659$	−22.3892	+	7.83432i	−0.872160	+	0.305182i	−0.143163	+	0.989699i	$0.545727\pi$
$660$		0			0
$661$	26.4825	+	33.2080i	1.03005	+	1.29164i	0.955679	+	0.294410i	$0.0951230\pi$
$661$	26.4825	+	33.2080i	1.03005	+	1.29164i	0.0743694	+	0.997231i	$0.476306\pi$
$662$		0			0
$663$	−33.7101	+	7.69411i	−1.30919	+	0.298815i
$664$		0			0
$665$	−2.39538	−	21.2596i	−0.0928889	−	0.824412i
$666$		0			0
$667$	40.9130	+	22.4323i	1.58416	+	0.868583i
$668$		0			0
$669$	66.7268	−	7.51831i	2.57981	−	0.290675i
$670$		0			0
$671$	−3.72151	−	16.3050i	−0.143667	−	0.629447i
$672$		0			0
$673$	8.08596	−	6.44834i	0.311691	−	0.248565i	−0.455132	−	0.890424i	$-0.650408\pi$
$673$	8.08596	−	6.44834i	0.311691	−	0.248565i	0.766823	+	0.641859i	$0.221837\pi$
$674$		0			0
$675$	0.544407	+	1.55583i	0.0209542	+	0.0598838i
$676$		0			0
$677$	−10.4383	−	6.55879i	−0.401175	−	0.252075i	0.316300	−	0.948659i	$-0.397559\pi$
$677$	−10.4383	−	6.55879i	−0.401175	−	0.252075i	−0.717475	+	0.696584i	$0.754702\pi$
$678$		0			0
$679$	30.4336	+	30.4336i	1.16794	+	1.16794i
$680$		0			0
$681$	−4.29634	+	38.1310i	−0.164636	+	1.46118i
$682$		0			0
$683$	19.3819	+	40.2469i	0.741627	+	1.54000i	0.838619	+	0.544719i	$0.183364\pi$
$683$	19.3819	+	40.2469i	0.741627	+	1.54000i	−0.0969922	+	0.995285i	$0.530922\pi$
$684$		0			0
$685$	11.6148	−	33.1930i	0.443777	−	1.26824i
$686$		0			0
$687$	17.8042	−	36.9708i	0.679272	−	1.41052i
$688$		0			0
$689$	9.12438	+	2.08258i	0.347611	+	0.0793399i
$690$		0			0
$691$	−11.0409	−	8.80479i	−0.420014	−	0.334950i	0.390569	−	0.920574i	$-0.372278\pi$
$691$	−11.0409	−	8.80479i	−0.420014	−	0.334950i	−0.810583	+	0.585624i	$0.800850\pi$
$692$		0			0
$693$	−13.2994	−	21.1658i	−0.505201	−	0.804023i
$694$		0			0
$695$	−22.2866			−0.845379
$696$		0			0
$697$	17.8845			0.677423
$698$		0			0
$699$	−30.6270	−	48.7426i	−1.15842	−	1.84361i
$700$		0			0
$701$	−31.6858	−	25.2686i	−1.19676	−	0.954381i	−0.197093	−	0.980385i	$-0.563150\pi$
$701$	−31.6858	−	25.2686i	−1.19676	−	0.954381i	−0.999662	+	0.0260042i	$0.991722\pi$
$702$		0			0
$703$	−6.93781	−	1.58351i	−0.261665	−	0.0597232i
$704$		0			0
$705$	−8.95201	+	18.5890i	−0.337152	+	0.700104i
$706$		0			0
$707$	19.5309	−	55.8160i	0.734534	−	2.09918i
$708$		0			0
$709$	−8.41729	−	17.4787i	−0.316118	−	0.656426i	0.681001	−	0.732283i	$-0.261545\pi$
$709$	−8.41729	−	17.4787i	−0.316118	−	0.656426i	−0.997119	+	0.0758571i	$0.975831\pi$
$710$		0			0
$711$	−4.23261	+	37.5655i	−0.158735	+	1.40881i
$712$		0			0
$713$	50.4261	+	50.4261i	1.88847	+	1.88847i
$714$		0			0
$715$	22.2079	+	13.9541i	0.830527	+	0.521855i
$716$		0			0
$717$	21.8865	+	62.5481i	0.817367	+	2.33590i
$718$		0			0
$719$	−9.48290	+	7.56236i	−0.353653	+	0.282028i	−0.784160	−	0.620558i	$-0.786906\pi$
$719$	−9.48290	+	7.56236i	−0.353653	+	0.282028i	0.430508	+	0.902587i	$0.358335\pi$
$720$		0			0
$721$	2.12274	+	9.30031i	0.0790548	+	0.346362i
$722$		0			0
$723$	−37.8981	+	4.27009i	−1.40944	+	0.158806i
$724$		0			0
$725$	−4.48682	+	3.20633i	−0.166636	+	0.119080i
$726$		0			0
$727$	−3.22080	−	28.5854i	−0.119453	−	1.06017i	−0.900245	−	0.435383i	$-0.856613\pi$
$727$	−3.22080	−	28.5854i	−0.119453	−	1.06017i	0.780792	−	0.624790i	$-0.214816\pi$
$728$		0			0
$729$	−35.9148	+	8.19731i	−1.33018	+	0.303604i
$730$		0			0
$731$	4.22364	+	5.29628i	0.156217	+	0.195890i
$732$		0			0
$733$	32.8287	−	11.4873i	1.21256	−	0.424292i	0.353141	−	0.935570i	$-0.385114\pi$
$733$	32.8287	−	11.4873i	1.21256	−	0.424292i	0.859415	+	0.511279i	$0.170828\pi$
$734$		0			0
$735$	−15.4496	+	24.5879i	−0.569868	+	0.906940i
$736$		0			0
$737$	−0.397103	+	0.397103i	−0.0146275	+	0.0146275i
$738$		0			0
$739$	21.4351	+	2.41516i	0.788503	+	0.0888430i	0.497027	−	0.867735i	$-0.334425\pi$
$739$	21.4351	+	2.41516i	0.788503	+	0.0888430i	0.291476	+	0.956578i	$0.405854\pi$
$740$		0			0
$741$	−47.4666	+	22.8587i	−1.74373	+	0.839735i
$742$		0			0
$743$	30.7659	+	10.7654i	1.12869	+	0.394946i	0.829088	−	0.559119i	$-0.188860\pi$
$743$	30.7659	+	10.7654i	1.12869	+	0.394946i	0.299602	+	0.954064i	$0.403146\pi$
$744$		0			0
$745$	−1.08977	−	0.524806i	−0.0399261	−	0.0192274i
$746$		0			0
$747$	−4.63005	+	20.2856i	−0.169405	+	0.742211i
$748$		0			0
$749$	2.33799	−	2.93174i	0.0854282	−	0.107124i
$750$		0			0
$751$	3.66629	−	2.30368i	0.133785	−	0.0840626i	−0.463477	−	0.886109i	$-0.653398\pi$
$751$	3.66629	−	2.30368i	0.133785	−	0.0840626i	0.597262	+	0.802046i	$0.296255\pi$
$752$		0			0
$753$			14.8561i			0.541386i
$754$		0			0
$755$		−	27.1082i		−	0.986568i
$756$		0			0
$757$	−15.4006	+	9.67683i	−0.559744	+	0.351710i	−0.782001	−	0.623278i	$-0.785801\pi$
$757$	−15.4006	+	9.67683i	−0.559744	+	0.351710i	0.222257	+	0.974988i	$0.428658\pi$
$758$		0			0
$759$	−26.9486	+	33.7925i	−0.978172	+	1.22659i
$760$		0			0
$761$	−3.18930	+	13.9732i	−0.115612	+	0.506530i	0.883651	+	0.468146i	$0.155078\pi$
$761$	−3.18930	+	13.9732i	−0.115612	+	0.506530i	−0.999263	+	0.0383834i	$0.987779\pi$
$762$		0			0
$763$	49.0713	+	23.6315i	1.77650	+	0.855518i
$764$		0			0
$765$	−13.5048	−	4.72555i	−0.488269	−	0.170853i
$766$		0			0
$767$	−9.13136	+	4.39743i	−0.329714	+	0.158782i
$768$		0			0
$769$	12.6937	+	1.43024i	0.457746	+	0.0515756i	0.337827	−	0.941208i	$-0.390308\pi$
$769$	12.6937	+	1.43024i	0.457746	+	0.0515756i	0.119919	+	0.992784i	$0.461737\pi$
$770$		0			0
$771$	−6.81450	+	6.81450i	−0.245418	+	0.245418i
$772$		0			0
$773$	22.5207	−	35.8415i	0.810014	−	1.28913i	−0.144063	−	0.989569i	$-0.546017\pi$
$773$	22.5207	−	35.8415i	0.810014	−	1.28913i	0.954077	−	0.299561i	$-0.0968404\pi$
$774$		0			0
$775$	−7.95563	+	2.78379i	−0.285775	+	0.0999969i
$776$		0			0
$777$	13.4732	+	16.8949i	0.483349	+	0.606100i
$778$		0			0
$779$	26.5668	−	6.06370i	0.951855	−	0.217255i
$780$		0			0
$781$	−1.46468	−	12.9994i	−0.0524104	−	0.465155i
$782$		0			0
$783$	4.21838	+	7.57225i	0.150753	+	0.270610i
$784$		0			0
$785$	−5.45525	+	0.614659i	−0.194706	+	0.0219381i
$786$		0			0
$787$	−2.11042	−	9.24636i	−0.0752284	−	0.329597i	0.923284	−	0.384117i	$-0.125494\pi$
$787$	−2.11042	−	9.24636i	−0.0752284	−	0.329597i	−0.998513	+	0.0545202i	$0.982637\pi$
$788$		0			0
$789$	−30.6895	+	24.4741i	−1.09258	+	0.871300i
$790$		0			0
$791$	−1.39775	−	3.99453i	−0.0496981	−	0.142029i
$792$		0			0
$793$	49.5915	+	31.1604i	1.76105	+	1.10654i
$794$		0			0
$795$	5.00448	+	5.00448i	0.177491	+	0.177491i
$796$		0			0
$797$	5.30503	−	47.0835i	0.187914	−	1.66778i	−0.446497	−	0.894785i	$-0.647329\pi$
$797$	5.30503	−	47.0835i	0.187914	−	1.66778i	0.634411	−	0.772996i	$-0.281243\pi$
$798$		0			0
$799$	3.45223	+	7.16862i	0.122131	+	0.253608i
$800$		0			0
$801$	−15.5720	+	44.5023i	−0.550211	+	1.57241i
$802$		0			0
$803$	−3.95907	+	8.22109i	−0.139713	+	0.290116i
$804$		0			0
$805$	59.9256	+	13.6776i	2.11210	+	0.482073i
$806$		0			0
$807$	−7.60396	−	6.06395i	−0.267672	−	0.213461i
$808$		0			0
$809$	6.90821	+	10.9944i	0.242880	+	0.386541i	0.945811	−	0.324716i	$-0.105269\pi$
$809$	6.90821	+	10.9944i	0.242880	+	0.386541i	−0.702932	+	0.711257i	$0.748126\pi$
$810$		0			0
$811$	13.0844			0.459456			0.229728	−	0.973255i	$-0.426216\pi$
$811$	13.0844			0.459456			0.229728	+	0.973255i	$0.426216\pi$
$812$		0			0
$813$	−35.9427			−1.26057
$814$		0			0
$815$	−16.2834	−	25.9149i	−0.570383	−	0.907759i
$816$		0			0
$817$	8.06977	+	6.43543i	0.282325	+	0.225147i
$818$		0			0
$819$	85.3459	+	19.4797i	2.98223	+	0.680674i
$820$		0			0
$821$	−17.0075	+	35.3164i	−0.593565	+	1.23255i	0.360447	+	0.932780i	$0.382624\pi$
$821$	−17.0075	+	35.3164i	−0.593565	+	1.23255i	−0.954012	+	0.299770i	$0.903090\pi$
$822$		0			0
$823$	−1.60541	+	4.58801i	−0.0559612	+	0.159928i	−0.968471	−	0.249128i	$-0.919856\pi$
$823$	−1.60541	+	4.58801i	−0.0559612	+	0.159928i	0.912509	+	0.409056i	$0.134142\pi$
$824$		0			0
$825$	−2.21649	−	4.60259i	−0.0771682	−	0.160242i
$826$		0			0
$827$	3.98337	−	35.3534i	0.138515	−	1.22936i	−0.711533	−	0.702653i	$-0.751999\pi$
$827$	3.98337	−	35.3534i	0.138515	−	1.22936i	0.850048	−	0.526705i	$-0.176573\pi$
$828$		0			0
$829$	8.08293	+	8.08293i	0.280732	+	0.280732i	0.833401	−	0.552669i	$-0.186391\pi$
$829$	8.08293	+	8.08293i	0.280732	+	0.280732i	−0.552669	+	0.833401i	$0.686391\pi$
$830$		0			0
$831$	−38.4375	−	24.1519i	−1.33338	−	0.837819i
$832$		0			0
$833$	3.69862	+	10.5701i	0.128150	+	0.366231i
$834$		0			0
$835$	−20.3532	+	16.2311i	−0.704352	+	0.561702i
$836$		0			0
$837$	2.94796	+	12.9158i	0.101896	+	0.446437i
$838$		0			0
$839$	5.82134	−	0.655908i	0.200975	−	0.0226445i	−0.0109030	−	0.999941i	$-0.503471\pi$
$839$	5.82134	−	0.655908i	0.200975	−	0.0226445i	0.211878	+	0.977296i	$0.432042\pi$
$840$		0			0
$841$	−20.3675	+	20.6437i	−0.702329	+	0.711853i
$842$		0			0
$843$	−4.66196	−	41.3761i	−0.160567	−	1.42507i
$844$		0			0
$845$	−64.2759	+	14.6706i	−2.21116	+	0.504683i
$846$		0			0
$847$	−16.0690	−	20.1498i	−0.552136	−	0.692356i
$848$		0			0
$849$	9.71716	−	3.40018i	0.333492	−	0.116694i
$850$		0			0
$851$	10.8776	−	17.3116i	0.372879	−	0.593434i
$852$		0			0
$853$	−11.7703	+	11.7703i	−0.403007	+	0.403007i	−0.879291	−	0.476284i	$-0.841983\pi$
$853$	−11.7703	+	11.7703i	−0.403007	+	0.403007i	0.476284	+	0.879291i	$0.341983\pi$
$854$		0			0
$855$	−21.6632	−	2.44086i	−0.740865	−	0.0834755i
$856$		0			0
$857$	−1.68201	+	0.810012i	−0.0574563	+	0.0276695i	−0.462391	−	0.886676i	$-0.653008\pi$
$857$	−1.68201	+	0.810012i	−0.0574563	+	0.0276695i	0.404935	+	0.914345i	$0.367294\pi$
$858$		0			0
$859$	0.559837	+	0.195896i	0.0191014	+	0.00668387i	0.339813	−	0.940493i	$-0.389636\pi$
$859$	0.559837	+	0.195896i	0.0191014	+	0.00668387i	−0.320711	+	0.947177i	$0.603922\pi$
$860$		0			0
$861$	−74.5536	−	35.9031i	−2.54078	−	1.22358i
$862$		0			0
$863$	8.26596	−	36.2155i	0.281376	−	1.23279i	−0.614653	−	0.788797i	$-0.710704\pi$
$863$	8.26596	−	36.2155i	0.281376	−	1.23279i	0.896030	−	0.443994i	$-0.146439\pi$
$864$		0			0
$865$	19.7191	−	24.7269i	0.670468	−	0.840740i
$866$		0			0
$867$	28.5127	−	17.9157i	0.968341	−	0.608449i
$868$		0			0
$869$		−	20.2089i		−	0.685541i
$870$		0			0
$871$		−	1.96669i		−	0.0666386i
$872$		0			0
$873$	37.1346	−	23.3332i	1.25681	−	0.789709i
$874$		0			0
$875$	−26.6452	+	33.4121i	−0.900773	+	1.12953i
$876$		0			0
$877$	−0.669295	+	2.93237i	−0.0226005	+	0.0990193i	−0.984970	−	0.172724i	$-0.944743\pi$
$877$	−0.669295	+	2.93237i	−0.0226005	+	0.0990193i	0.962370	+	0.271743i	$0.0876002\pi$
$878$		0			0
$879$	−26.2287	−	12.6311i	−0.884672	−	0.426036i
$880$		0			0
$881$	30.7861	+	10.7725i	1.03721	+	0.362935i	0.794564	−	0.607180i	$-0.207699\pi$
$881$	30.7861	+	10.7725i	1.03721	+	0.362935i	0.242645	+	0.970115i	$0.421985\pi$
$882$		0			0
$883$	−18.6301	+	8.97179i	−0.626953	+	0.301925i	−0.720251	−	0.693714i	$-0.755973\pi$
$883$	−18.6301	+	8.97179i	−0.626953	+	0.301925i	0.0932979	+	0.995638i	$0.470259\pi$
$884$		0			0
$885$	−7.61604	−	0.858122i	−0.256010	−	0.0288454i
$886$		0			0
$887$	−2.73746	+	2.73746i	−0.0919148	+	0.0919148i	−0.751569	−	0.659654i	$-0.770703\pi$
$887$	−2.73746	+	2.73746i	−0.0919148	+	0.0919148i	0.659654	+	0.751569i	$0.270703\pi$
$888$		0			0
$889$	2.46018	−	3.91535i	0.0825118	−	0.131317i
$890$		0			0
$891$	12.3165	−	4.30973i	0.412618	−	0.144381i
$892$		0			0
$893$	7.55868	+	9.47828i	0.252942	+	0.317179i
$894$		0			0
$895$	31.0711	−	7.09178i	1.03859	−	0.237052i
$896$		0			0
$897$	−16.9474	−	150.413i	−0.565858	−	5.02213i
$898$		0			0
$899$	−38.7203	+	21.5705i	−1.29139	+	0.719415i
$900$		0			0
$901$	2.71215	−	0.305585i	0.0903547	−	0.0101805i
$902$		0			0
$903$	−6.97446	−	30.5571i	−0.232095	−	1.01688i
$904$		0			0
$905$	34.1270	−	27.2154i	1.13442	−	0.904670i
$906$		0			0
$907$	−13.2052	−	37.7382i	−0.438471	−	1.25308i	−0.925185	−	0.379516i	$-0.876091\pi$
$907$	−13.2052	−	37.7382i	−0.438471	−	1.25308i	0.486715	−	0.873561i	$-0.338195\pi$
$908$		0			0
$909$	−51.0211	−	32.0587i	−1.69226	−	1.06332i
$910$		0			0
$911$	27.5161	+	27.5161i	0.911649	+	0.911649i	0.996402	−	0.0847531i	$-0.0270101\pi$
$911$	27.5161	+	27.5161i	0.911649	+	0.911649i	−0.0847531	+	0.996402i	$0.527010\pi$
$912$		0			0
$913$	1.24541	−	11.0533i	0.0412169	−	0.365810i
$914$		0			0
$915$	19.2168	+	39.9041i	0.635289	+	1.31919i
$916$		0			0
$917$	14.2761	−	40.7988i	0.471439	−	1.34730i
$918$		0			0
$919$	11.7957	−	24.4940i	0.389103	−	0.807981i	−0.610766	−	0.791811i	$-0.709138\pi$
$919$	11.7957	−	24.4940i	0.389103	−	0.807981i	0.999869	−	0.0161700i	$-0.00514731\pi$
$920$		0			0
$921$	48.8184	+	11.1425i	1.60862	+	0.367157i
$922$		0			0
$923$	35.8173	+	28.5633i	1.17894	+	0.940173i
$924$		0			0
$925$	1.28564	+	2.04608i	0.0422715	+	0.0672748i
$926$		0			0
$927$	9.72059			0.319266
$928$		0			0
$929$	−20.6867			−0.678707			−0.339354	−	0.940659i	$-0.610208\pi$
$929$	−20.6867			−0.678707			−0.339354	+	0.940659i	$0.610208\pi$
$930$		0			0
$931$	9.07793	+	14.4474i	0.297517	+	0.473496i
$932$		0			0
$933$	−24.3390	−	19.4097i	−0.796823	−	0.635445i
$934$		0			0
$935$	7.45692	+	1.70199i	0.243867	+	0.0556611i
$936$		0			0
$937$	−2.43514	+	5.05661i	−0.0795524	+	0.165192i	−0.936951	−	0.349461i	$-0.886365\pi$
$937$	−2.43514	+	5.05661i	−0.0795524	+	0.165192i	0.857399	+	0.514653i	$0.172079\pi$
$938$		0			0
$939$	22.9178	−	65.4953i	0.747894	−	2.13736i
$940$		0			0
$941$	14.2254	+	29.5393i	0.463734	+	0.962953i	0.993395	+	0.114744i	$0.0366048\pi$
$941$	14.2254	+	29.5393i	0.463734	+	0.962953i	−0.529661	+	0.848209i	$0.677681\pi$
$942$		0			0
$943$	−8.76582	+	77.7988i	−0.285454	+	2.53348i
$944$		0			0
$945$	8.07429	+	8.07429i	0.262657	+	0.262657i
$946$		0			0
$947$	−47.1964	−	29.6554i	−1.53368	−	0.963673i	−0.992430	−	0.122808i	$-0.960810\pi$
$947$	−47.1964	−	29.6554i	−1.53368	−	0.963673i	−0.541246	−	0.840864i	$-0.682047\pi$
$948$		0			0
$949$	−10.5540	−	30.1617i	−0.342598	−	0.979089i
$950$		0			0
$951$	−23.8365	+	19.0090i	−0.772952	+	0.616409i
$952$		0			0
$953$	−5.65872	−	24.7925i	−0.183304	−	0.803107i	−0.980043	−	0.198784i	$-0.936301\pi$
$953$	−5.65872	−	24.7925i	−0.183304	−	0.803107i	0.796739	−	0.604323i	$-0.206556\pi$
$954$		0			0
$955$	−46.8672	+	5.28066i	−1.51659	+	0.170878i
$956$		0			0
$957$	−15.6190	−	21.8566i	−0.504890	−	0.706523i
$958$		0			0
$959$	7.02538	+	62.3520i	0.226861	+	2.01345i
$960$		0			0
$961$	−35.8217	+	8.17607i	−1.15554	+	0.263744i
$962$		0			0
$963$	−2.38237	−	2.98740i	−0.0767709	−	0.0962676i
$964$		0			0
$965$	−36.9359	+	12.9244i	−1.18901	+	0.416052i
$966$		0			0
$967$	8.13225	−	12.9424i	0.261516	−	0.416200i	−0.689996	−	0.723813i	$-0.742388\pi$
$967$	8.13225	−	12.9424i	0.261516	−	0.416200i	0.951511	+	0.307614i	$0.0995305\pi$
$968$		0			0
$969$	−10.8639	+	10.8639i	−0.348998	+	0.348998i
$970$		0			0
$971$	54.0050	+	6.08491i	1.73310	+	0.195274i	0.921352	−	0.388729i	$-0.127086\pi$
$971$	54.0050	+	6.08491i	1.73310	+	0.195274i	0.811752	+	0.584003i	$0.198514\pi$
$972$		0			0
$973$	35.8273	−	17.2535i	1.14857	−	0.553123i
$974$		0			0
$975$	16.8860	+	5.90868i	0.540786	+	0.189229i
$976$		0			0
$977$	−18.5350	−	8.92599i	−0.592987	−	0.285568i	0.113223	−	0.993570i	$-0.463883\pi$
$977$	−18.5350	−	8.92599i	−0.592987	−	0.285568i	−0.706211	+	0.708002i	$0.749597\pi$
$978$		0			0
$979$	5.60855	−	24.5727i	0.179250	−	0.785346i
$980$		0			0
$981$	34.6031	−	43.3909i	1.10479	−	1.38536i
$982$		0			0
$983$	20.1986	−	12.6916i	0.644235	−	0.404799i	−0.169912	−	0.985459i	$-0.554348\pi$
$983$	20.1986	−	12.6916i	0.644235	−	0.404799i	0.814146	+	0.580660i	$0.197205\pi$
$984$		0			0
$985$			12.6814i			0.404064i
$986$		0			0
$987$		−	36.8136i		−	1.17179i
$988$		0			0
$989$	−25.1093	+	15.7772i	−0.798430	+	0.501687i
$990$		0			0
$991$	−6.97839	+	8.75062i	−0.221676	+	0.277973i	−0.880216	−	0.474573i	$-0.842603\pi$
$991$	−6.97839	+	8.75062i	−0.221676	+	0.277973i	0.658541	+	0.752545i	$0.271174\pi$
$992$		0			0
$993$	1.53126	−	6.70891i	0.0485932	−	0.212901i
$994$		0			0
$995$	−14.6995	−	7.07891i	−0.466005	−	0.224416i
$996$		0			0
$997$	31.5573	+	11.0424i	0.999429	+	0.349715i	0.779909	−	0.625893i	$-0.215265\pi$
$997$	31.5573	+	11.0424i	0.999429	+	0.349715i	0.219520	+	0.975608i	$0.429551\pi$
$998$		0			0
$999$	3.42204	−	1.64797i	0.108269	−	0.0521394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	464.2.bl.c.15.10	yes	120
4.3	odd	2	inner	464.2.bl.c.15.1	✓	120
29.2	odd	28	inner	464.2.bl.c.31.1	yes	120
116.31	even	28	inner	464.2.bl.c.31.10	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
464.2.bl.c.15.1	✓	120	4.3	odd	2	inner
464.2.bl.c.15.10	yes	120	1.1	even	1	trivial
464.2.bl.c.31.1	yes	120	29.2	odd	28	inner
464.2.bl.c.31.10	yes	120	116.31	even	28	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 464 = 2^{4} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	464.bl (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36944 + 2.17945i) q^{3} +(1.55895 + 1.24322i) q^{5} +(-3.46859 - 0.791684i) q^{7} +(-1.57297 + 3.26632i) q^{9} +(0.640096 - 1.82929i) q^{11} +(2.94479 + 6.11492i) q^{13} +(-0.574651 + 5.10017i) q^{15} +(1.39955 + 1.39955i) q^{17} +(2.55350 + 1.60447i) q^{19} +(-3.02459 - 8.64377i) q^{21} +(-6.77410 + 5.40217i) q^{23} +(-0.227874 - 0.998382i) q^{25} +(-1.59948 + 0.180218i) q^{27} +(-2.07755 - 4.96828i) q^{29} +(-0.921536 - 8.17886i) q^{31} +(4.86341 - 1.11004i) q^{33} +(-4.42314 - 5.54644i) q^{35} +(-2.22728 + 0.779360i) q^{37} +(-9.29443 + 14.7920i) q^{39} +(6.38938 - 6.38938i) q^{41} +(3.40107 + 0.383208i) q^{43} +(-6.51296 + 3.13648i) q^{45} +(3.79439 + 1.32771i) q^{47} +(5.09760 + 2.45487i) q^{49} +(-1.13365 + 4.96683i) q^{51} +(0.859764 - 1.07811i) q^{53} +(3.27210 - 2.05599i) q^{55} +7.76242i q^{57} +1.49329i q^{59} +(7.30678 - 4.59116i) q^{61} +(8.04190 - 10.0842i) q^{63} +(-3.01142 + 13.1939i) q^{65} +(-0.261074 - 0.125727i) q^{67} +(-21.0504 - 7.36586i) q^{69} +(6.08147 - 2.92868i) q^{71} +(-4.67861 - 0.527152i) q^{73} +(1.86386 - 1.86386i) q^{75} +(-3.66845 + 5.83831i) q^{77} +(9.84233 - 3.44398i) q^{79} +(4.19792 + 5.26403i) q^{81} +(5.59550 - 1.27714i) q^{83} +(0.441879 + 3.92178i) q^{85} +(7.98301 - 11.3317i) q^{87} +(12.9234 - 1.45612i) q^{89} +(-5.37320 - 23.5415i) q^{91} +(16.5634 - 13.2089i) q^{93} +(1.98607 + 5.67586i) q^{95} +(-10.2431 - 6.43615i) q^{97} +(4.96818 + 4.96818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 4 q^{17} - 40 q^{21} - 28 q^{25} - 52 q^{29} - 84 q^{33} - 8 q^{37} + 4 q^{41} + 40 q^{45} - 28 q^{49} - 48 q^{53} - 4 q^{61} - 40 q^{65} + 24 q^{69} + 76 q^{73} + 156 q^{77} + 116 q^{81} + 152 q^{85}+ \cdots + 64 q^{97}+O(q^{100}) \) 120 * q + 4 * q^17 - 40 * q^21 - 28 * q^25 - 52 * q^29 - 84 * q^33 - 8 * q^37 + 4 * q^41 + 40 * q^45 - 28 * q^49 - 48 * q^53 - 4 * q^61 - 40 * q^65 + 24 * q^69 + 76 * q^73 + 156 * q^77 + 116 * q^81 + 152 * q^85 + 104 * q^89 + 112 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more