LMFDB - Embedded newform 864.2.w.a.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.a.323.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01437 + 0.985425i) q^{2} +(0.0578733 - 1.99916i) q^{4} +(-2.90620 - 1.20379i) q^{5} +(-0.0493336 + 0.0493336i) q^{7} +(1.91132 + 2.08491i) q^{8} +O(q^{10})$	\(q+(-1.01437 + 0.985425i) q^{2} +(0.0578733 - 1.99916i) q^{4} +(-2.90620 - 1.20379i) q^{5} +(-0.0493336 + 0.0493336i) q^{7} +(1.91132 + 2.08491i) q^{8} +(4.13418 - 1.64276i) q^{10} +(-2.53818 - 1.05135i) q^{11} +(-0.00592464 - 0.0143033i) q^{13} +(0.00142770 - 0.0986568i) q^{14} +(-3.99330 - 0.231396i) q^{16} +1.63036 q^{17} +(4.47806 - 1.85487i) q^{19} +(-2.57475 + 5.74029i) q^{20} +(3.61066 - 1.43473i) q^{22} +(-3.47977 + 3.47977i) q^{23} +(3.46134 + 3.46134i) q^{25} +(0.0201046 + 0.00867052i) q^{26} +(0.0957707 + 0.101481i) q^{28} +(-0.401813 - 0.970063i) q^{29} -0.670530i q^{31} +(4.27869 - 3.70038i) q^{32} +(-1.65378 + 1.60660i) q^{34} +(0.202760 - 0.0839859i) q^{35} +(-4.32803 + 10.4488i) q^{37} +(-2.71455 + 6.29432i) q^{38} +(-3.04489 - 8.35998i) q^{40} +(4.41014 + 4.41014i) q^{41} +(-1.26503 + 3.05405i) q^{43} +(-2.24871 + 5.01338i) q^{44} +(0.100704 - 6.95881i) q^{46} +12.5224i q^{47} +6.99513i q^{49} +(-6.92195 - 0.100170i) q^{50} +(-0.0289376 + 0.0110165i) q^{52} +(0.892308 - 2.15422i) q^{53} +(6.11084 + 6.11084i) q^{55} +(-0.197148 - 0.00856380i) q^{56} +(1.36351 + 0.588041i) q^{58} +(-2.71745 + 6.56050i) q^{59} +(5.93208 - 2.45715i) q^{61} +(0.660758 + 0.680162i) q^{62} +(-0.693704 + 7.96987i) q^{64} +0.0487003i q^{65} +(-1.94383 - 4.69282i) q^{67} +(0.0943542 - 3.25935i) q^{68} +(-0.122911 + 0.284997i) q^{70} +(7.05785 + 7.05785i) q^{71} +(-7.73891 + 7.73891i) q^{73} +(-5.90629 - 14.8638i) q^{74} +(-3.44903 - 9.05972i) q^{76} +(0.177084 - 0.0733506i) q^{77} -6.61627 q^{79} +(11.3268 + 5.47956i) q^{80} +(-8.81935 - 0.127628i) q^{82} +(-3.14910 - 7.60259i) q^{83} +(-4.73814 - 1.96260i) q^{85} +(-1.72634 - 4.34451i) q^{86} +(-2.65931 - 7.30134i) q^{88} +(9.71773 - 9.71773i) q^{89} +(0.000997919 + 0.000413351i) q^{91} +(6.75524 + 7.15802i) q^{92} +(-12.3398 - 12.7022i) q^{94} -15.2470 q^{95} +15.8065 q^{97} +(-6.89318 - 7.09562i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.01437	+	0.985425i	−0.717264	+	0.696801i
$2$	−1.01437	+	0.985425i	−0.717264	+	0.696801i
$3$		0			0
$3$		0			0
$4$	0.0578733	−	1.99916i	0.0289367	−	0.999581i
$5$	−2.90620	−	1.20379i	−1.29969	−	0.538349i	−0.377831	−	0.925875i	$-0.623330\pi$
$5$	−2.90620	−	1.20379i	−1.29969	−	0.538349i	−0.921859	+	0.387525i	$0.873330\pi$
$6$		0			0
$7$	−0.0493336	+	0.0493336i	−0.0186463	+	0.0186463i	−0.716368	−	0.697722i	$-0.754197\pi$
$7$	−0.0493336	+	0.0493336i	−0.0186463	+	0.0186463i	0.697722	+	0.716368i	$0.254197\pi$
$8$	1.91132	+	2.08491i	0.675754	+	0.737127i
$9$		0			0
$10$	4.13418	−	1.64276i	1.30734	−	0.519487i
$11$	−2.53818	−	1.05135i	−0.765289	−	0.316993i	−0.0343267	−	0.999411i	$-0.510929\pi$
$11$	−2.53818	−	1.05135i	−0.765289	−	0.316993i	−0.730963	+	0.682417i	$0.760929\pi$
$12$		0			0
$13$	−0.00592464	−	0.0143033i	−0.00164320	−	0.00396703i	0.923056	−	0.384666i	$-0.125683\pi$
$13$	−0.00592464	−	0.0143033i	−0.00164320	−	0.00396703i	−0.924699	+	0.380699i	$0.875683\pi$
$14$	0.00142770	−	0.0986568i	0.000381568	−	0.0263671i
$15$		0			0
$16$	−3.99330	−	0.231396i	−0.998325	−	0.0578491i
$17$	1.63036			0.395420			0.197710	−	0.980261i	$-0.436650\pi$
$17$	1.63036			0.395420			0.197710	+	0.980261i	$0.436650\pi$
$18$		0			0
$19$	4.47806	−	1.85487i	1.02734	−	0.425537i	0.195587	−	0.980686i	$-0.437339\pi$
$19$	4.47806	−	1.85487i	1.02734	−	0.425537i	0.831751	+	0.555149i	$0.187339\pi$
$20$	−2.57475	+	5.74029i	−0.575733	+	1.28357i
$21$		0			0
$22$	3.61066	−	1.43473i	0.769796	−	0.305886i
$23$	−3.47977	+	3.47977i	−0.725583	+	0.725583i	−0.969736	−	0.244154i	$-0.921490\pi$
$23$	−3.47977	+	3.47977i	−0.725583	+	0.725583i	0.244154	+	0.969736i	$0.421490\pi$
$24$		0			0
$25$	3.46134	+	3.46134i	0.692268	+	0.692268i
$26$	0.0201046	+	0.00867052i	0.00394284	+	0.00170043i
$27$		0			0
$28$	0.0957707	+	0.101481i	0.0180990	+	0.0191781i
$29$	−0.401813	−	0.970063i	−0.0746148	−	0.180136i	0.882171	−	0.470929i	$-0.156081\pi$
$29$	−0.401813	−	0.970063i	−0.0746148	−	0.180136i	−0.956786	+	0.290792i	$0.906081\pi$
$30$		0			0
$31$		−	0.670530i		−	0.120431i	−0.998185	−	0.0602154i	$-0.980821\pi$
$31$		−	0.670530i		−	0.120431i	0.998185	−	0.0602154i	$-0.0191788\pi$
$32$	4.27869	−	3.70038i	0.756373	−	0.654141i
$33$		0			0
$34$	−1.65378	+	1.60660i	−0.283621	+	0.275529i
$35$	0.202760	−	0.0839859i	0.0342727	−	0.0141962i
$36$		0			0
$37$	−4.32803	+	10.4488i	−0.711523	+	1.71777i	−0.0153629	+	0.999882i	$0.504890\pi$
$37$	−4.32803	+	10.4488i	−0.711523	+	1.71777i	−0.696160	+	0.717887i	$0.745110\pi$
$38$	−2.71455	+	6.29432i	−0.440358	+	1.02107i
$39$		0			0
$40$	−3.04489	−	8.35998i	−0.481439	−	1.32183i
$41$	4.41014	+	4.41014i	0.688748	+	0.688748i	0.961955	−	0.273207i	$-0.0880845\pi$
$41$	4.41014	+	4.41014i	0.688748	+	0.688748i	−0.273207	+	0.961955i	$0.588084\pi$
$42$		0			0
$43$	−1.26503	+	3.05405i	−0.192915	+	0.465738i	−0.990508	−	0.137459i	$-0.956107\pi$
$43$	−1.26503	+	3.05405i	−0.192915	+	0.465738i	0.797592	+	0.603197i	$0.206107\pi$
$44$	−2.24871	+	5.01338i	−0.339005	+	0.755796i
$45$		0			0
$46$	0.100704	−	6.95881i	0.0148479	−	1.02602i
$47$			12.5224i			1.82657i	0.407318	+	0.913287i	$0.366464\pi$
$47$			12.5224i			1.82657i	−0.407318	+	0.913287i	$0.633536\pi$
$48$		0			0
$49$			6.99513i			0.999305i
$50$	−6.92195	−	0.100170i	−0.978912	−	0.0141662i
$51$		0			0
$52$	−0.0289376	+	0.0110165i	−0.00401292	+	0.00152772i
$53$	0.892308	−	2.15422i	0.122568	−	0.295905i	−0.850672	−	0.525697i	$-0.823805\pi$
$53$	0.892308	−	2.15422i	0.122568	−	0.295905i	0.973240	+	0.229792i	$0.0738046\pi$
$54$		0			0
$55$	6.11084	+	6.11084i	0.823986	+	0.823986i
$56$	−0.197148	−	0.00856380i	−0.0263451	−	0.00114439i
$57$		0			0
$58$	1.36351	+	0.588041i	0.179038	+	0.0772136i
$59$	−2.71745	+	6.56050i	−0.353782	+	0.854105i	0.642365	+	0.766399i	$0.277953\pi$
$59$	−2.71745	+	6.56050i	−0.353782	+	0.854105i	−0.996146	+	0.0877057i	$0.972047\pi$
$60$		0			0
$61$	5.93208	−	2.45715i	0.759525	−	0.314605i	0.0309035	−	0.999522i	$-0.490162\pi$
$61$	5.93208	−	2.45715i	0.759525	−	0.314605i	0.728621	+	0.684917i	$0.240162\pi$
$62$	0.660758	+	0.680162i	0.0839163	+	0.0863807i
$63$		0			0
$64$	−0.693704	+	7.96987i	−0.0867131	+	0.996233i
$65$			0.0487003i			0.00604053i
$66$		0			0
$67$	−1.94383	−	4.69282i	−0.237477	−	0.573319i	0.759544	−	0.650456i	$-0.225422\pi$
$67$	−1.94383	−	4.69282i	−0.237477	−	0.573319i	−0.997021	+	0.0771369i	$0.975422\pi$
$68$	0.0943542	−	3.25935i	0.0114421	−	0.395254i
$69$		0			0
$70$	−0.122911	+	0.284997i	−0.0146906	+	0.0340637i
$71$	7.05785	+	7.05785i	0.837613	+	0.837613i	0.988544	−	0.150932i	$-0.0482273\pi$
$71$	7.05785	+	7.05785i	0.837613	+	0.837613i	−0.150932	+	0.988544i	$0.548227\pi$
$72$		0			0
$73$	−7.73891	+	7.73891i	−0.905771	+	0.905771i	−0.995928	−	0.0901565i	$-0.971263\pi$
$73$	−7.73891	+	7.73891i	−0.905771	+	0.905771i	0.0901565	+	0.995928i	$0.471263\pi$
$74$	−5.90629	−	14.8638i	−0.686593	−	1.72788i
$75$		0			0
$76$	−3.44903	−	9.05972i	−0.395631	−	1.03922i
$77$	0.177084	−	0.0733506i	0.0201806	−	0.00835908i
$78$		0			0
$79$	−6.61627			−0.744389			−0.372194	−	0.928155i	$-0.621394\pi$
$79$	−6.61627			−0.744389			−0.372194	+	0.928155i	$0.621394\pi$
$80$	11.3268	+	5.47956i	1.26637	+	0.612634i
$81$		0			0
$82$	−8.81935	−	0.127628i	−0.973935	−	0.0140942i
$83$	−3.14910	−	7.60259i	−0.345658	−	0.834493i	−0.997122	−	0.0758129i	$-0.975845\pi$
$83$	−3.14910	−	7.60259i	−0.345658	−	0.834493i	0.651464	−	0.758680i	$-0.274155\pi$
$84$		0			0
$85$	−4.73814	−	1.96260i	−0.513923	−	0.212874i
$86$	−1.72634	−	4.34451i	−0.186156	−	0.468481i
$87$		0			0
$88$	−2.65931	−	7.30134i	−0.283483	−	0.778325i
$89$	9.71773	−	9.71773i	1.03008	−	1.03008i	0.0305444	−	0.999533i	$-0.490276\pi$
$89$	9.71773	−	9.71773i	1.03008	−	1.03008i	0.999533	−	0.0305444i	$-0.00972411\pi$
$90$		0			0
$91$	0.000997919	0	0.000413351i	0.000104610	0	4.33310e-5i
$92$	6.75524	+	7.15802i	0.704283	+	0.746275i
$93$		0			0
$94$	−12.3398	−	12.7022i	−1.27276	−	1.31014i
$95$	−15.2470			−1.56431
$96$		0			0
$97$	15.8065			1.60490			0.802452	−	0.596717i	$-0.203528\pi$
$97$	15.8065			1.60490			0.802452	+	0.596717i	$0.203528\pi$
$98$	−6.89318	−	7.09562i	−0.696316	−	0.716766i
$99$		0			0
$100$	7.12010	−	6.71946i	0.712010	−	0.671946i
$101$	−5.84043	−	2.41919i	−0.581145	−	0.240718i	0.0726909	−	0.997355i	$-0.476841\pi$
$101$	−5.84043	−	2.41919i	−0.581145	−	0.240718i	−0.653836	+	0.756636i	$0.726841\pi$
$102$		0			0
$103$	−13.5607	+	13.5607i	−1.33617	+	1.33617i	−0.436443	+	0.899732i	$0.643762\pi$
$103$	−13.5607	+	13.5607i	−1.33617	+	1.33617i	−0.899732	+	0.436443i	$0.856238\pi$
$104$	0.0184973	−	0.0396906i	0.00181381	−	0.00389199i
$105$		0			0
$106$	1.21770	+	3.06447i	0.118273	+	0.297648i
$107$	9.88145	+	4.09303i	0.955276	+	0.395688i	0.805211	−	0.592988i	$-0.202052\pi$
$107$	9.88145	+	4.09303i	0.955276	+	0.395688i	0.150064	+	0.988676i	$0.452052\pi$
$108$		0			0
$109$	−5.19017	−	12.5302i	−0.497128	−	1.20017i	−0.951024	−	0.309118i	$-0.899966\pi$
$109$	−5.19017	−	12.5302i	−0.497128	−	1.20017i	0.453896	−	0.891055i	$-0.350034\pi$
$110$	−12.2204	−	0.176846i	−1.16517	−	0.0168616i
$111$		0			0
$112$	0.208419	−	0.185588i	0.0196938	−	0.0175364i
$113$	7.60880			0.715776			0.357888	−	0.933765i	$-0.383497\pi$
$113$	7.60880			0.715776			0.357888	+	0.933765i	$0.383497\pi$
$114$		0			0
$115$	14.3018	−	5.92400i	1.33365	−	0.552416i
$116$	−1.96257	+	0.747149i	−0.182220	+	0.0693710i
$117$		0			0
$118$	−3.70840	−	9.33259i	−0.341386	−	0.859135i
$119$	−0.0804314	+	0.0804314i	−0.00737313	+	0.00737313i
$120$		0			0
$121$	−2.44116	−	2.44116i	−0.221924	−	0.221924i
$122$	−3.59596	+	8.33806i	−0.325563	+	0.754893i
$123$		0			0
$124$	−1.34050	−	0.0388058i	−0.120380	−	0.00348486i
$125$	0.126312	+	0.304944i	0.0112977	+	0.0272750i
$126$		0			0
$127$			12.3585i			1.09664i	0.836270	+	0.548319i	$0.184732\pi$
$127$			12.3585i			1.09664i	−0.836270	+	0.548319i	$0.815268\pi$
$128$	−7.15004	−	8.76795i	−0.631980	−	0.774985i
$129$		0			0
$130$	−0.0479905	−	0.0493999i	−0.00420905	−	0.00433266i
$131$	−7.29335	+	3.02101i	−0.637223	+	0.263947i	−0.677819	−	0.735229i	$-0.737075\pi$
$131$	−7.29335	+	3.02101i	−0.637223	+	0.263947i	0.0405954	+	0.999176i	$0.487075\pi$
$132$		0			0
$133$	−0.129411	+	0.312426i	−0.0112214	+	0.0270908i
$134$	6.59618	+	2.84473i	0.569823	+	0.245747i
$135$		0			0
$136$	3.11614	+	3.39915i	0.267207	+	0.291475i
$137$	−12.1212	−	12.1212i	−1.03558	−	1.03558i	−0.999343	−	0.0362394i	$-0.988462\pi$
$137$	−12.1212	−	12.1212i	−1.03558	−	1.03558i	−0.0362394	−	0.999343i	$-0.511538\pi$
$138$		0			0
$139$	−6.30795	+	15.2287i	−0.535033	+	1.29168i	0.393121	+	0.919487i	$0.371395\pi$
$139$	−6.30795	+	15.2287i	−0.535033	+	1.29168i	−0.928154	+	0.372197i	$0.878605\pi$
$140$	−0.156167	−	0.410211i	−0.0131985	−	0.0346691i
$141$		0			0
$142$	−14.1142	−	0.204252i	−1.18444	−	0.0171404i
$143$			0.0425333i			0.00355681i
$144$		0			0
$145$			3.30289i			0.274290i
$146$	0.223962	−	15.4762i	0.0185352	−	1.28082i
$147$		0			0
$148$	20.6383	+	9.25713i	1.69646	+	0.760932i
$149$	3.16320	−	7.63664i	0.259139	−	0.625618i	−0.739743	−	0.672890i	$-0.765053\pi$
$149$	3.16320	−	7.63664i	0.259139	−	0.625618i	0.998882	+	0.0472720i	$0.0150528\pi$
$150$		0			0
$151$	10.0365	+	10.0365i	0.816759	+	0.816759i	0.985637	−	0.168878i	$-0.0540144\pi$
$151$	10.0365	+	10.0365i	0.816759	+	0.816759i	−0.168878	+	0.985637i	$0.554014\pi$
$152$	12.4263	+	5.79110i	1.00790	+	0.469720i
$153$		0			0
$154$	−0.107346	+	0.248907i	−0.00865021	+	0.0200575i
$155$	−0.807175	+	1.94869i	−0.0648338	+	0.156523i
$156$		0			0
$157$	−15.6293	+	6.47385i	−1.24735	+	0.516670i	−0.906005	−	0.423268i	$-0.860883\pi$
$157$	−15.6293	+	6.47385i	−1.24735	+	0.516670i	−0.341346	+	0.939938i	$0.610883\pi$
$158$	6.71131	−	6.51984i	0.533923	−	0.518691i
$159$		0			0
$160$	−16.8892	+	5.60340i	−1.33521	+	0.442988i
$161$		−	0.343339i		−	0.0270589i
$162$		0			0
$163$	0.733211	+	1.77013i	0.0574295	+	0.138647i	0.949990	−	0.312281i	$-0.101093\pi$
$163$	0.733211	+	1.77013i	0.0574295	+	0.138647i	−0.892560	+	0.450928i	$0.851093\pi$
$164$	9.07181	−	8.56135i	0.708390	−	0.668529i
$165$		0			0
$166$	10.6861	+	4.60860i	0.829404	+	0.357697i
$167$	−4.36254	−	4.36254i	−0.337584	−	0.337584i	0.517873	−	0.855457i	$-0.326724\pi$
$167$	−4.36254	−	4.36254i	−0.337584	−	0.337584i	−0.855457	+	0.517873i	$0.826724\pi$
$168$		0			0
$169$	9.19222	−	9.19222i	0.707094	−	0.707094i
$170$	6.74020	−	2.67829i	0.516950	−	0.205415i
$171$		0			0
$172$	6.03233	+	2.70575i	0.459961	+	0.206311i
$173$	22.1954	−	9.19362i	1.68748	−	0.698978i	0.687843	−	0.725859i	$-0.258558\pi$
$173$	22.1954	−	9.19362i	1.68748	−	0.698978i	0.999639	+	0.0268814i	$0.00855765\pi$
$174$		0			0
$175$	−0.341520			−0.0258165
$176$	9.89243	+	4.78567i	0.745670	+	0.360734i
$177$		0			0
$178$	−0.281228	+	19.4334i	−0.0210789	+	1.45660i
$179$	2.13973	+	5.16577i	0.159931	+	0.386108i	0.983450	−	0.181181i	$-0.0579921\pi$
$179$	2.13973	+	5.16577i	0.159931	+	0.386108i	−0.823518	+	0.567289i	$0.807992\pi$
$180$		0			0
$181$	1.20375	+	0.498609i	0.0894740	+	0.0370613i	0.426972	−	0.904265i	$-0.359580\pi$
$181$	1.20375	+	0.498609i	0.0894740	+	0.0370613i	−0.337498	+	0.941326i	$0.609580\pi$
$182$	−0.00141958		0.000564085i	−0.000105226		4.18128e-5i
$183$		0			0
$184$	−13.9060	−	0.604052i	−1.02516	−	0.0445313i
$185$	25.1562	−	25.1562i	1.84952	−	1.84952i
$186$		0			0
$187$	−4.13814	−	1.71407i	−0.302611	−	0.125345i
$188$	25.0342	+	0.724710i	1.82581	+	0.0528549i
$189$		0			0
$190$	15.4660	−	15.0248i	1.12202	−	1.09001i
$191$	−9.88718			−0.715411			−0.357706	−	0.933834i	$-0.616441\pi$
$191$	−9.88718			−0.715411			−0.357706	+	0.933834i	$0.616441\pi$
$192$		0			0
$193$	27.3260			1.96697			0.983483	−	0.181001i	$-0.0579338\pi$
$193$	27.3260			1.96697			0.983483	+	0.181001i	$0.0579338\pi$
$194$	−16.0335	+	15.5761i	−1.15114	+	1.11830i
$195$		0			0
$196$	13.9844	+	0.404832i	0.998886	+	0.0289165i
$197$	−7.80681	−	3.23369i	−0.556212	−	0.230391i	0.0868275	−	0.996223i	$-0.472327\pi$
$197$	−7.80681	−	3.23369i	−0.556212	−	0.230391i	−0.643040	+	0.765833i	$0.722327\pi$
$198$		0			0
$199$	−8.96286	+	8.96286i	−0.635360	+	0.635360i	−0.949407	−	0.314047i	$-0.898315\pi$
$199$	−8.96286	+	8.96286i	−0.635360	+	0.635360i	0.314047	+	0.949407i	$0.398315\pi$
$200$	−0.600852	+	13.8323i	−0.0424867	+	0.978092i
$201$		0			0
$202$	8.30826	−	3.30137i	0.584567	−	0.232284i
$203$	0.0676795	+	0.0280338i	0.00475017	+	0.00196759i
$204$		0			0
$205$	−7.50786	−	18.1256i	−0.524372	−	1.26595i
$206$	0.392442	−	27.1185i	0.0273427	−	1.88944i
$207$		0			0
$208$	0.0203491	+	0.0584885i	0.00141096	+	0.00405545i
$209$	−13.3162			−0.921103
$210$		0			0
$211$	9.44697	−	3.91306i	0.650356	−	0.269386i	−0.0330177	−	0.999455i	$-0.510512\pi$
$211$	9.44697	−	3.91306i	0.650356	−	0.269386i	0.683374	+	0.730068i	$0.260512\pi$
$212$	−4.25500	−	1.90854i	−0.292234	−	0.131079i
$213$		0			0
$214$	−14.0568	+	5.58560i	−0.960901	+	0.381824i
$215$	7.35284	−	7.35284i	0.501460	−	0.501460i
$216$		0			0
$217$	0.0330796	+	0.0330796i	0.00224559	+	0.00224559i
$218$	17.6123	+	7.59565i	1.19285	+	0.514442i
$219$		0			0
$220$	12.5702	−	11.8629i	0.847484	−	0.799797i
$221$	−0.00965929	−	0.0233196i	−0.000649754	−	0.00156864i
$222$		0			0
$223$		−	10.6349i		−	0.712167i	−0.934454	−	0.356083i	$-0.884112\pi$
$223$		−	10.6349i		−	0.712167i	0.934454	−	0.356083i	$-0.115888\pi$
$224$	−0.0285300	+	0.393636i	−0.00190624	+	0.0263009i
$225$		0			0
$226$	−7.71810	+	7.49790i	−0.513400	+	0.498753i
$227$	−0.241509	+	0.100036i	−0.0160295	+	0.00663964i	−0.390684	−	0.920525i	$-0.627761\pi$
$227$	−0.241509	+	0.100036i	−0.0160295	+	0.00663964i	0.374654	+	0.927165i	$0.377761\pi$
$228$		0			0
$229$	2.53073	−	6.10971i	0.167235	−	0.403741i	−0.817938	−	0.575307i	$-0.804883\pi$
$229$	2.53073	−	6.10971i	0.167235	−	0.403741i	0.985173	+	0.171566i	$0.0548826\pi$
$230$	−8.66958	+	20.1024i	−0.571655	+	1.32552i
$231$		0			0
$232$	1.25450	−	2.69185i	0.0823620	−	0.176728i
$233$	−1.24913	−	1.24913i	−0.0818331	−	0.0818331i	0.665005	−	0.746839i	$-0.268429\pi$
$233$	−1.24913	−	1.24913i	−0.0818331	−	0.0818331i	−0.746839	+	0.665005i	$0.768429\pi$
$234$		0			0
$235$	15.0742	−	36.3924i	0.983334	−	2.37398i
$236$	12.9582	+	5.81230i	0.843510	+	0.378349i
$237$		0			0
$238$	0.00232766	−	0.160846i	0.000150880	−	0.0104261i
$239$		−	13.3415i		−	0.862993i	−0.902115	−	0.431496i	$-0.857986\pi$
$239$		−	13.3415i		−	0.862993i	0.902115	−	0.431496i	$-0.142014\pi$
$240$		0			0
$241$		−	1.90093i		−	0.122449i	−0.998124	−	0.0612247i	$-0.980499\pi$
$241$		−	1.90093i		−	0.122449i	0.998124	−	0.0612247i	$-0.0195006\pi$
$242$	4.88181	+	0.0706464i	0.313815	+	0.00454132i
$243$		0			0
$244$	−4.56893	−	12.0014i	−0.292496	−	0.768310i
$245$	8.42064	−	20.3292i	0.537975	−	1.29879i
$246$		0			0
$247$	−0.0530618	−	0.0530618i	−0.00337624	−	0.00337624i
$248$	1.39800	−	1.28160i	0.0887728	−	0.0813816i
$249$		0			0
$250$	−0.428626	−	0.184854i	−0.0271087	−	0.0116912i
$251$	−9.57699	+	23.1209i	−0.604494	+	1.45938i	0.264417	+	0.964409i	$0.414821\pi$
$251$	−9.57699	+	23.1209i	−0.604494	+	1.45938i	−0.868911	+	0.494969i	$0.835179\pi$
$252$		0			0
$253$	12.4907	−	5.17383i	0.785285	−	0.325276i
$254$	−12.1784	−	12.5360i	−0.764138	−	0.786579i
$255$		0			0
$256$	15.8929	+	1.84807i	0.993307	+	0.115504i
$257$			6.81632i			0.425191i	0.977140	+	0.212595i	$0.0681916\pi$
$257$			6.81632i			0.425191i	−0.977140	+	0.212595i	$0.931808\pi$
$258$		0			0
$259$	−0.301959	−	0.728992i	−0.0187628	−	0.0452974i
$260$	0.0973598	+	0.00281845i	0.00603800	+	0.000174793i
$261$		0			0
$262$	4.42115	−	10.2515i	0.273139	−	0.633337i
$263$	13.8187	+	13.8187i	0.852097	+	0.852097i	0.990391	−	0.138294i	$-0.0441619\pi$
$263$	13.8187	+	13.8187i	0.852097	+	0.852097i	−0.138294	+	0.990391i	$0.544162\pi$
$264$		0			0
$265$	−5.18644	+	5.18644i	−0.318601	+	0.318601i
$266$	−0.176603	−	0.444440i	−0.0108282	−	0.0272503i
$267$		0			0
$268$	−9.49420	+	3.61444i	−0.579951	+	0.220787i
$269$	1.72264	−	0.713543i	0.105031	−	0.0435055i	−0.329549	−	0.944138i	$-0.606897\pi$
$269$	1.72264	−	0.713543i	0.105031	−	0.0435055i	0.434580	+	0.900633i	$0.356897\pi$
$270$		0			0
$271$	−29.7737			−1.80862			−0.904311	−	0.426874i	$-0.859615\pi$
$271$	−29.7737			−1.80862			−0.904311	+	0.426874i	$0.859615\pi$
$272$	−6.51051	−	0.377259i	−0.394758	−	0.0228747i
$273$		0			0
$274$	24.2398	+	0.350783i	1.46438	+	0.0211916i
$275$	−5.14642	−	12.4246i	−0.310341	−	0.749229i
$276$		0			0
$277$	−19.8700	−	8.23044i	−1.19387	−	0.494519i	−0.304859	−	0.952397i	$-0.598609\pi$
$277$	−19.8700	−	8.23044i	−1.19387	−	0.494519i	−0.889015	+	0.457878i	$0.848609\pi$
$278$	−8.60822	−	21.6635i	−0.516287	−	1.29929i
$279$		0			0
$280$	0.562643	+	0.262212i	0.0336243	+	0.0156702i
$281$	−13.9303	+	13.9303i	−0.831009	+	0.831009i	−0.987655	−	0.156646i	$-0.949932\pi$
$281$	−13.9303	+	13.9303i	−0.831009	+	0.831009i	0.156646	+	0.987655i	$0.449932\pi$
$282$		0			0
$283$	6.50707	+	2.69532i	0.386805	+	0.160220i	0.567607	−	0.823300i	$-0.307869\pi$
$283$	6.50707	+	2.69532i	0.386805	+	0.160220i	−0.180802	+	0.983520i	$0.557869\pi$
$284$	14.5182	−	13.7013i	0.861500	−	0.813024i
$285$		0			0
$286$	−0.0419134	−	0.0431443i	−0.00247839	−	0.00255117i
$287$	−0.435136			−0.0256852
$288$		0			0
$289$	−14.3419			−0.843643
$290$	−3.25475	−	3.35034i	−0.191126	−	0.196738i
$291$		0			0
$292$	15.0235	+	15.9192i	0.879182	+	0.931602i
$293$	13.2633	+	5.49383i	0.774849	+	0.320953i	0.734835	−	0.678246i	$-0.237260\pi$
$293$	13.2633	+	5.49383i	0.774849	+	0.320953i	0.0400140	+	0.999199i	$0.487260\pi$
$294$		0			0
$295$	15.7949	−	15.7949i	0.919613	−	0.919613i
$296$	−30.0570	+	10.9474i	−1.74703	+	0.636306i
$297$		0			0
$298$	4.31670	+	10.8634i	0.250060	+	0.629302i
$299$	0.0703888	+	0.0291560i	0.00407069	+	0.00168613i
$300$		0			0
$301$	−0.0882588	−	0.213076i	−0.00508715	−	0.0122815i
$302$	−20.0709	−	0.290453i	−1.15495	−	0.0167137i
$303$		0			0
$304$	−18.3115	+	6.37086i	−1.05023	+	0.365394i
$305$	−20.1977			−1.15651
$306$		0			0
$307$	2.00290	−	0.829629i	0.114312	−	0.0473494i	−0.324795	−	0.945785i	$-0.605295\pi$
$307$	2.00290	−	0.829629i	0.114312	−	0.0473494i	0.439106	+	0.898435i	$0.355295\pi$
$308$	−0.136391	−	0.358265i	−0.00777162	−	0.0204140i
$309$		0			0
$310$	−1.10152	−	2.77210i	−0.0625622	−	0.157444i
$311$	8.02393	−	8.02393i	0.454995	−	0.454995i	−0.442013	−	0.897009i	$-0.645736\pi$
$311$	8.02393	−	8.02393i	0.454995	−	0.454995i	0.897009	+	0.442013i	$0.145736\pi$
$312$		0			0
$313$	16.0292	+	16.0292i	0.906026	+	0.906026i	0.995949	−	0.0899223i	$-0.0286619\pi$
$313$	16.0292	+	16.0292i	0.906026	+	0.906026i	−0.0899223	+	0.995949i	$0.528662\pi$
$314$	9.47428	−	21.9683i	0.534665	−	1.23974i
$315$		0			0
$316$	−0.382905	+	13.2270i	−0.0215401	+	0.744077i
$317$	12.5989	+	30.4165i	0.707626	+	1.70836i	0.705850	+	0.708362i	$0.250565\pi$
$317$	12.5989	+	30.4165i	0.707626	+	1.70836i	0.00177621	+	0.999998i	$0.499435\pi$
$318$		0			0
$319$			2.88464i			0.161509i
$320$	11.6101	−	22.3269i	0.649022	−	1.24811i
$321$		0			0
$322$	0.338335	+	0.348271i	0.0188547	+	0.0194084i
$323$	7.30085	−	3.02411i	0.406230	−	0.168266i
$324$		0			0
$325$	0.0290015	−	0.0700159i	0.00160872	−	0.00388378i
$326$	−2.48807	−	1.07303i	−0.137802	−	0.0594297i
$327$		0			0
$328$	−0.765554	+	17.6239i	−0.0422707	+	0.973119i
$329$	−0.617772	−	0.617772i	−0.0340589	−	0.0340589i
$330$		0			0
$331$	12.4405	−	30.0339i	0.683789	−	1.65081i	−0.0731438	−	0.997321i	$-0.523303\pi$
$331$	12.4405	−	30.0339i	0.683789	−	1.65081i	0.756933	−	0.653492i	$-0.226697\pi$
$332$	−15.3811	+	5.85557i	−0.844145	+	0.321366i
$333$		0			0
$334$	8.72417	+	0.126251i	0.477366	+	0.00690813i
$335$			15.9782i			0.872982i
$336$		0			0
$337$			25.2978i			1.37806i	0.724734	+	0.689028i	$0.241962\pi$
$337$			25.2978i			1.37806i	−0.724734	+	0.689028i	$0.758038\pi$
$338$	−0.266020	+	18.3825i	−0.0144696	+	0.999877i
$339$		0			0
$340$	−4.19777	+	9.35873i	−0.227656	+	0.507548i
$341$	−0.704960	+	1.70192i	−0.0381757	+	0.0921644i
$342$		0			0
$343$	−0.690430	−	0.690430i	−0.0372797	−	0.0372797i
$344$	−8.78530	+	3.19980i	−0.473671	+	0.172522i
$345$		0			0
$346$	−13.4546	+	31.1976i	−0.723322	+	1.67719i
$347$	−12.3947	+	29.9234i	−0.665381	+	1.60637i	0.123869	+	0.992299i	$0.460470\pi$
$347$	−12.3947	+	29.9234i	−0.665381	+	1.60637i	−0.789250	+	0.614072i	$0.789530\pi$
$348$		0			0
$349$	−14.9803	+	6.20503i	−0.801876	+	0.332148i	−0.745708	−	0.666273i	$-0.767888\pi$
$349$	−14.9803	+	6.20503i	−0.801876	+	0.332148i	−0.0561684	+	0.998421i	$0.517888\pi$
$350$	0.346426	−	0.336543i	0.0185173	−	0.0179890i
$351$		0			0
$352$	−14.7505	+	4.89383i	−0.786202	+	0.260842i
$353$			0.897574i			0.0477730i	0.999715	+	0.0238865i	$0.00760404\pi$
$353$			0.897574i			0.0477730i	−0.999715	+	0.0238865i	$0.992396\pi$
$354$		0			0
$355$	−12.0154	−	29.0076i	−0.637709	−	1.53956i
$356$	−18.8649	−	19.9897i	−0.999839	−	1.05945i
$357$		0			0
$358$	−7.26096	−	3.13143i	−0.383754	−	0.165501i
$359$	−3.72247	−	3.72247i	−0.196464	−	0.196464i	0.602018	−	0.798482i	$-0.294363\pi$
$359$	−3.72247	−	3.72247i	−0.196464	−	0.196464i	−0.798482	+	0.602018i	$0.794363\pi$
$360$		0			0
$361$	3.17746	−	3.17746i	0.167235	−	0.167235i
$362$	−1.71238	+	0.680434i	−0.0900009	+	0.0357628i
$363$		0			0
$364$	0.000884109	−	0.00197108i	4.63399e−5	−	0.000103313i
$365$	31.8068	−	13.1748i	1.66484	−	0.689600i
$366$		0			0
$367$	−0.691313			−0.0360863			−0.0180431	−	0.999837i	$-0.505744\pi$
$367$	−0.691313			−0.0360863			−0.0180431	+	0.999837i	$0.505744\pi$
$368$	14.7010	−	13.0906i	0.766342	−	0.682393i
$369$		0			0
$370$	−0.728012	+	50.3071i	−0.0378475	+	2.61534i
$371$	0.0622547	+	0.150296i	0.00323210	+	0.00780299i
$372$		0			0
$373$	−15.1129	−	6.25998i	−0.782517	−	0.324129i	−0.0445864	−	0.999006i	$-0.514197\pi$
$373$	−15.1129	−	6.25998i	−0.782517	−	0.324129i	−0.737931	+	0.674876i	$0.764197\pi$
$374$	5.88668	−	2.33913i	0.304393	−	0.120954i
$375$		0			0
$376$	−26.1080	+	23.9342i	−1.34642	+	1.23431i
$377$	−0.0114945	+	0.0114945i	−0.000591999	+	0.000591999i
$378$		0			0
$379$	−24.5636	−	10.1746i	−1.26174	−	0.522632i	−0.351300	−	0.936263i	$-0.614260\pi$
$379$	−24.5636	−	10.1746i	−1.26174	−	0.522632i	−0.910445	+	0.413631i	$0.864260\pi$
$380$	−0.882394	+	30.4812i	−0.0452659	+	1.56365i
$381$		0			0
$382$	10.0292	−	9.74308i	0.513139	−	0.498499i
$383$	−19.4811			−0.995435			−0.497718	−	0.867339i	$-0.665828\pi$
$383$	−19.4811			−0.995435			−0.497718	+	0.867339i	$0.665828\pi$
$384$		0			0
$385$	−0.602939			−0.0307286
$386$	−27.7185	+	26.9277i	−1.41083	+	1.37058i
$387$		0			0
$388$	0.914773	−	31.5997i	0.0464406	−	1.60423i
$389$	−18.9184	−	7.83624i	−0.959199	−	0.397313i	−0.152518	−	0.988301i	$-0.548738\pi$
$389$	−18.9184	−	7.83624i	−0.959199	−	0.397313i	−0.806681	+	0.590987i	$0.798738\pi$
$390$		0			0
$391$	−5.67327	+	5.67327i	−0.286910	+	0.286910i
$392$	−14.5842	+	13.3699i	−0.736615	+	0.675284i
$393$		0			0
$394$	11.1055	−	4.41289i	0.559488	−	0.222318i
$395$	19.2282	+	7.96457i	0.967474	+	0.400741i
$396$		0			0
$397$	−1.11369	−	2.68868i	−0.0558944	−	0.134941i	0.893465	−	0.449132i	$-0.148267\pi$
$397$	−1.11369	−	2.68868i	−0.0558944	−	0.134941i	−0.949360	+	0.314191i	$0.898267\pi$
$398$	0.259382	−	17.9238i	0.0130017	−	0.898441i
$399$		0			0
$400$	−13.0212	−	14.6231i	−0.651061	−	0.731155i
$401$	−5.30588			−0.264963			−0.132481	−	0.991185i	$-0.542295\pi$
$401$	−5.30588			−0.264963			−0.132481	+	0.991185i	$0.542295\pi$
$402$		0			0
$403$	−0.00959082	+	0.00397265i	−0.000477753	+	0.000197892i
$404$	−5.17435	+	11.5360i	−0.257434	+	0.573936i
$405$		0			0
$406$	−0.0962769	+	0.0382566i	−0.00477814	+	0.00189865i
$407$	21.9706	−	21.9706i	1.08904	−	1.08904i
$408$		0			0
$409$	−5.41490	−	5.41490i	−0.267750	−	0.267750i	0.560443	−	0.828193i	$-0.310631\pi$
$409$	−5.41490	−	5.41490i	−0.267750	−	0.267750i	−0.828193	+	0.560443i	$0.810631\pi$
$410$	25.4771	+	10.9875i	1.25823	+	0.542635i
$411$		0			0
$412$	26.3252	+	27.8948i	1.29695	+	1.37428i
$413$	−0.189592	−	0.457715i	−0.00932919	−	0.0225227i
$414$		0			0
$415$			25.8854i			1.27067i
$416$	−0.0782775	−	0.0392762i	−0.00383787	−	0.00192567i
$417$		0			0
$418$	13.5075	−	13.1222i	0.660675	−	0.641826i
$419$	−32.4439	+	13.4387i	−1.58499	+	0.656523i	−0.989194	−	0.146614i	$-0.953162\pi$
$419$	−32.4439	+	13.4387i	−1.58499	+	0.656523i	−0.595794	+	0.803138i	$0.703162\pi$
$420$		0			0
$421$	4.27023	−	10.3092i	0.208118	−	0.502442i	−0.785009	−	0.619485i	$-0.787342\pi$
$421$	4.27023	−	10.3092i	0.208118	−	0.502442i	0.993127	+	0.117043i	$0.0373415\pi$
$422$	−5.72665	+	13.2786i	−0.278769	+	0.646390i
$423$		0			0
$424$	6.19685	−	2.25703i	0.300945	−	0.109611i
$425$	5.64322	+	5.64322i	0.273736	+	0.273736i
$426$		0			0
$427$	−0.171431	+	0.413870i	−0.00829611	+	0.0200286i
$428$	8.75450	−	19.5177i	0.423165	−	0.943426i
$429$		0			0
$430$	−0.212789	+	14.7041i	−0.0102616	+	0.709097i
$431$			2.93438i			0.141344i	0.997500	+	0.0706720i	$0.0225144\pi$
$431$			2.93438i			0.141344i	−0.997500	+	0.0706720i	$0.977486\pi$
$432$		0			0
$433$		−	16.8489i		−	0.809704i	−0.914382	−	0.404852i	$-0.867323\pi$
$433$		−	16.8489i		−	0.809704i	0.914382	−	0.404852i	$-0.132677\pi$
$434$	−0.0661524		0.000957315i	−0.00317541		4.59526e-5i
$435$		0			0
$436$	−25.3502	+	9.65082i	−1.21406	+	0.462191i
$437$	−9.12810	+	22.0372i	−0.436656	+	1.05418i
$438$		0			0
$439$	−18.8645	−	18.8645i	−0.900353	−	0.900353i	0.0951132	−	0.995466i	$-0.469679\pi$
$439$	−18.8645	−	18.8645i	−0.900353	−	0.900353i	−0.995466	+	0.0951132i	$0.969679\pi$
$440$	−1.06078	+	24.4203i	−0.0505707	+	1.16419i
$441$		0			0
$442$	0.0327777	+	0.0141361i	0.00155908	+	0.000672384i
$443$	−7.59703	+	18.3408i	−0.360946	+	0.871400i	0.634217	+	0.773155i	$0.281323\pi$
$443$	−7.59703	+	18.3408i	−0.360946	+	0.871400i	−0.995162	+	0.0982445i	$0.968677\pi$
$444$		0			0
$445$	−39.9397	+	16.5436i	−1.89332	+	0.784240i
$446$	10.4799	+	10.7877i	0.496238	+	0.510812i
$447$		0			0
$448$	−0.358959	−	0.427405i	−0.0169592	−	0.0201930i
$449$			25.3542i			1.19654i	0.801296	+	0.598269i	$0.204144\pi$
$449$			25.3542i			1.19654i	−0.801296	+	0.598269i	$0.795856\pi$
$450$		0			0
$451$	−6.55713	−	15.8303i	−0.308763	−	0.745420i
$452$	0.440346	−	15.2112i	0.0207122	−	0.715476i
$453$		0			0
$454$	0.146400	−	0.339462i	0.00687089	−	0.0159318i
$455$	−0.00240256	−	0.00240256i	−0.000112634	−	0.000112634i
$456$		0			0
$457$	18.6763	−	18.6763i	0.873641	−	0.873641i	−0.119226	−	0.992867i	$-0.538041\pi$
$457$	18.6763	−	18.6763i	0.873641	−	0.873641i	0.992867	+	0.119226i	$0.0380414\pi$
$458$	3.45359	+	8.69132i	0.161376	+	0.406119i
$459$		0			0
$460$	−11.0153	−	28.9345i	−0.513593	−	1.34908i
$461$	−20.2480	+	8.38699i	−0.943043	+	0.390621i	−0.800612	−	0.599184i	$-0.795492\pi$
$461$	−20.2480	+	8.38699i	−0.943043	+	0.390621i	−0.142431	+	0.989805i	$0.545492\pi$
$462$		0			0
$463$	17.0048			0.790280			0.395140	−	0.918621i	$-0.370696\pi$
$463$	17.0048			0.790280			0.395140	+	0.918621i	$0.370696\pi$
$464$	1.38009	+	3.96673i	0.0640692	+	0.184151i
$465$		0			0
$466$	2.49800	+	0.0361494i	0.115717	+	0.00167459i
$467$	−9.56899	−	23.1016i	−0.442800	−	1.06901i	−0.974962	−	0.222371i	$-0.928620\pi$
$467$	−9.56899	−	23.1016i	−0.442800	−	1.06901i	0.532162	−	0.846642i	$-0.321380\pi$
$468$		0			0
$469$	0.327409	+	0.135617i	0.0151184	+	0.00626223i
$470$	20.5712	+	51.7697i	0.948880	+	2.38796i
$471$		0			0
$472$	−18.8720	+	6.87359i	−0.868653	+	0.316383i
$473$	6.42174	−	6.42174i	0.295272	−	0.295272i
$474$		0			0
$475$	21.9204	+	9.07974i	1.00578	+	0.416607i
$476$	0.156141	+	0.165450i	0.00715669	+	0.00758340i
$477$		0			0
$478$	13.1471	+	13.5332i	0.601334	+	0.618994i
$479$	−8.28759			−0.378670			−0.189335	−	0.981913i	$-0.560633\pi$
$479$	−8.28759			−0.378670			−0.189335	+	0.981913i	$0.560633\pi$
$480$		0			0
$481$	0.175094			0.00798362
$482$	1.87322	+	1.92823i	0.0853229	+	0.0878286i
$483$		0			0
$484$	−5.02156	+	4.73900i	−0.228253	+	0.215409i
$485$	−45.9367	−	19.0276i	−2.08588	−	0.863999i
$486$		0			0
$487$	−14.4003	+	14.4003i	−0.652542	+	0.652542i	−0.953604	−	0.301062i	$-0.902659\pi$
$487$	−14.4003	+	14.4003i	−0.652542	+	0.652542i	0.301062	+	0.953604i	$0.402659\pi$
$488$	16.4610	+	7.67145i	0.745156	+	0.347270i
$489$		0			0
$490$	11.4913	+	28.9192i	0.519125	+	1.30643i
$491$	8.88362	+	3.67972i	0.400912	+	0.166063i	0.574023	−	0.818839i	$-0.305382\pi$
$491$	8.88362	+	3.67972i	0.400912	+	0.166063i	−0.173111	+	0.984902i	$0.555382\pi$
$492$		0			0
$493$	−0.655099	−	1.58155i	−0.0295042	−	0.0712294i
$494$	0.106113	+	0.00153559i	0.00477423	+	6.90896e-5i
$495$		0			0
$496$	−0.155158	+	2.67763i	−0.00696681	+	0.120229i
$497$	−0.696378			−0.0312368
$498$		0			0
$499$	−4.85505	+	2.01103i	−0.217342	+	0.0900259i	−0.488698	−	0.872453i	$-0.662528\pi$
$499$	−4.85505	+	2.01103i	−0.217342	+	0.0900259i	0.271356	+	0.962479i	$0.412528\pi$
$500$	0.616943	−	0.234870i	0.0275905	−	0.0105037i
$501$		0			0
$502$	−13.0694	−	32.8904i	−0.583314	−	1.46797i
$503$	10.2193	−	10.2193i	0.455657	−	0.455657i	−0.441570	−	0.897227i	$-0.645578\pi$
$503$	10.2193	−	10.2193i	0.455657	−	0.455657i	0.897227	+	0.441570i	$0.145578\pi$
$504$		0			0
$505$	14.0613	+	14.0613i	0.625718	+	0.625718i
$506$	−7.57174	+	17.5568i	−0.336605	+	0.780496i
$507$		0			0
$508$	24.7066	+	0.715226i	1.09618	+	0.0317330i
$509$	14.0877	+	34.0107i	0.624427	+	1.50750i	0.846456	+	0.532459i	$0.178732\pi$
$509$	14.0877	+	34.0107i	0.624427	+	1.50750i	−0.222029	+	0.975040i	$0.571268\pi$
$510$		0			0
$511$		−	0.763576i		−	0.0337786i
$512$	−17.9424	+	13.7867i	−0.792947	+	0.609290i
$513$		0			0
$514$	−6.71698	−	6.91424i	−0.296273	−	0.304974i
$515$	55.7342	−	23.0859i	2.45594	−	1.01728i
$516$		0			0
$517$	13.1653	−	31.7840i	0.579011	−	1.39786i
$518$	1.02466	+	0.441907i	0.0450211	+	0.0194163i
$519$		0			0
$520$	−0.101536	+	0.0930819i	−0.00445264	+	0.00408191i
$521$	−23.5270	−	23.5270i	−1.03074	−	1.03074i	−0.999512	−	0.0312256i	$-0.990059\pi$
$521$	−23.5270	−	23.5270i	−1.03074	−	1.03074i	−0.0312256	−	0.999512i	$-0.509941\pi$
$522$		0			0
$523$	6.32107	−	15.2604i	0.276401	−	0.667292i	−0.723329	−	0.690503i	$-0.757389\pi$
$523$	6.32107	−	15.2604i	0.276401	−	0.667292i	0.999731	+	0.0232115i	$0.00738911\pi$
$524$	5.61739	+	14.7554i	0.245397	+	0.644594i
$525$		0			0
$526$	−27.6345	−	0.399909i	−1.20492	−	0.0174368i
$527$		−	1.09320i		−	0.0476207i
$528$		0			0
$529$		−	1.21762i		−	0.0529401i
$530$	0.150094	−	10.3718i	0.00651967	−	0.450522i
$531$		0			0
$532$	0.617102	+	0.276795i	0.0267547	+	0.0120006i
$533$	0.0369513	−	0.0892082i	0.00160054	−	0.00386404i
$534$		0			0
$535$	−23.7903	−	23.7903i	−1.02854	−	1.02854i
$536$	6.06883	−	13.0222i	0.262133	−	0.562473i
$537$		0			0
$538$	−1.04425	+	2.42133i	−0.0450207	+	0.104391i
$539$	7.35432	−	17.7549i	0.316773	−	0.764757i
$540$		0			0
$541$	25.1815	−	10.4305i	1.08264	−	0.448443i	0.231204	−	0.972905i	$-0.425733\pi$
$541$	25.1815	−	10.4305i	1.08264	−	0.448443i	0.851434	+	0.524462i	$0.175733\pi$
$542$	30.2014	−	29.3397i	1.29726	−	1.26025i
$543$		0			0
$544$	6.97580	−	6.03295i	0.299085	−	0.258660i
$545$			42.6630i			1.82748i
$546$		0			0
$547$	8.65940	+	20.9056i	0.370249	+	0.893861i	0.993708	+	0.112004i	$0.0357270\pi$
$547$	8.65940	+	20.9056i	0.370249	+	0.893861i	−0.623459	+	0.781856i	$0.714273\pi$
$548$	−24.9337	+	23.5307i	−1.06512	+	1.00518i
$549$		0			0
$550$	17.4638	+	7.53163i	0.744660	+	0.321150i
$551$	−3.59869	−	3.59869i	−0.153309	−	0.153309i
$552$		0			0
$553$	0.326404	−	0.326404i	0.0138801	−	0.0138801i
$554$	28.2659	−	11.2318i	1.20090	−	0.477192i
$555$		0			0
$556$	30.0796	+	13.4919i	1.27566	+	0.572186i
$557$	−0.192990	+	0.0799389i	−0.00817723	+	0.00338712i	−0.386768	−	0.922177i	$-0.626409\pi$
$557$	−0.192990	+	0.0799389i	−0.00817723	+	0.00338712i	0.378591	+	0.925564i	$0.376409\pi$
$558$		0			0
$559$	0.0511780			0.00216460
$560$	−0.829116	+	0.288463i	−0.0350365	+	0.0121898i
$561$		0			0
$562$	0.403137	−	27.8576i	0.0170053	−	1.17510i
$563$	−14.9181	−	36.0154i	−0.628722	−	1.51787i	−0.841212	−	0.540706i	$-0.818157\pi$
$563$	−14.9181	−	36.0154i	−0.628722	−	1.51787i	0.212490	−	0.977163i	$-0.431843\pi$
$564$		0			0
$565$	−22.1127	−	9.15936i	−0.930286	−	0.385337i
$566$	−9.25657	+	3.67820i	−0.389083	+	0.154606i
$567$		0			0
$568$	−1.22517	+	28.2048i	−0.0514070	+	1.18345i
$569$	29.2833	−	29.2833i	1.22762	−	1.22762i	0.262760	−	0.964861i	$-0.415367\pi$
$569$	29.2833	−	29.2833i	1.22762	−	1.22762i	0.964861	−	0.262760i	$-0.0846326\pi$
$570$		0			0
$571$	29.3768	+	12.1683i	1.22938	+	0.509226i	0.900380	−	0.435104i	$-0.143288\pi$
$571$	29.3768	+	12.1683i	1.22938	+	0.509226i	0.329000	+	0.944330i	$0.393288\pi$
$572$	0.0850309	+	0.00246154i	0.00355532	+	0.000102922i
$573$		0			0
$574$	0.441387	−	0.428794i	0.0184231	−	0.0178975i
$575$	−24.0893			−1.00459
$576$		0			0
$577$	−21.1600			−0.880902			−0.440451	−	0.897777i	$-0.645181\pi$
$577$	−21.1600			−0.880902			−0.440451	+	0.897777i	$0.645181\pi$
$578$	14.5480	−	14.1329i	0.605115	−	0.587851i
$579$		0			0
$580$	6.60301	+	0.191149i	0.274175	+	0.00793703i
$581$	0.530419	+	0.219707i	0.0220055	+	0.00911497i
$582$		0			0
$583$	−4.52967	+	4.52967i	−0.187600	+	0.187600i
$584$	−30.9265	−	1.34339i	−1.27975	−	0.0555901i
$585$		0			0
$586$	−18.8676	+	7.49722i	−0.779412	+	0.309707i
$587$	−7.83466	−	3.24522i	−0.323371	−	0.133945i	0.215092	−	0.976594i	$-0.430995\pi$
$587$	−7.83466	−	3.24522i	−0.323371	−	0.133945i	−0.538463	+	0.842649i	$0.680995\pi$
$588$		0			0
$589$	−1.24375	−	3.00268i	−0.0512478	−	0.123723i
$590$	−0.457099	+	31.5865i	−0.0188185	+	1.30039i
$591$		0			0
$592$	19.7009	−	40.7236i	0.809703	−	1.67373i
$593$	−31.7225			−1.30269			−0.651343	−	0.758783i	$-0.725794\pi$
$593$	−31.7225			−1.30269			−0.651343	+	0.758783i	$0.725794\pi$
$594$		0			0
$595$	0.330571	−	0.136927i	0.0135521	−	0.00561347i
$596$	−15.0838	−	6.76571i	−0.617857	−	0.277134i
$597$		0			0
$598$	−0.100131	+	0.0397881i	−0.00409466	+	0.00162706i
$599$	−18.9888	+	18.9888i	−0.775863	+	0.775863i	−0.979124	−	0.203262i	$-0.934846\pi$
$599$	−18.9888	+	18.9888i	−0.775863	+	0.775863i	0.203262	+	0.979124i	$0.434846\pi$
$600$		0			0
$601$	20.3137	+	20.3137i	0.828613	+	0.828613i	0.987325	−	0.158712i	$-0.0507340\pi$
$601$	20.3137	+	20.3137i	0.828613	+	0.828613i	−0.158712	+	0.987325i	$0.550734\pi$
$602$	0.299497	+	0.129164i	0.0122066	+	0.00526433i
$603$		0			0
$604$	20.6454	−	19.4838i	0.840051	−	0.792783i
$605$	4.15586	+	10.0331i	0.168960	+	0.407905i
$606$		0			0
$607$			0.546071i			0.0221643i	0.999939	+	0.0110822i	$0.00352763\pi$
$607$			0.546071i			0.0221643i	−0.999939	+	0.0110822i	$0.996472\pi$
$608$	12.2965	−	24.5070i	0.498689	−	0.993889i
$609$		0			0
$610$	20.4878	−	19.9033i	0.829527	−	0.805860i
$611$	0.179112	−	0.0741904i	0.00724608	−	0.00300142i
$612$		0			0
$613$	7.19350	−	17.3666i	0.290543	−	0.701432i	−0.709452	−	0.704754i	$-0.751057\pi$
$613$	7.19350	−	17.3666i	0.290543	−	0.701432i	0.999994	+	0.00332204i	$0.00105744\pi$
$614$	−1.21414	+	2.81526i	−0.0489985	+	0.113615i
$615$		0			0
$616$	0.491394	+	0.229008i	0.0197988	+	0.00922699i
$617$	15.7906	+	15.7906i	0.635706	+	0.635706i	0.949493	−	0.313787i	$-0.101598\pi$
$617$	15.7906	+	15.7906i	0.635706	+	0.635706i	−0.313787	+	0.949493i	$0.601598\pi$
$618$		0			0
$619$	−6.28443	+	15.1720i	−0.252593	+	0.609812i	−0.998412	−	0.0563359i	$-0.982058\pi$
$619$	−6.28443	+	15.1720i	−0.252593	+	0.609812i	0.745819	+	0.666148i	$0.232058\pi$
$620$	3.84904	+	1.72645i	0.154581	+	0.0693359i
$621$		0			0
$622$	−0.232210	+	16.0462i	−0.00931078	+	0.643393i
$623$			0.958821i			0.0384144i
$624$		0			0
$625$		−	25.5136i		−	1.02055i
$626$	−32.0551	−	0.463881i	−1.28118	−	0.0185404i
$627$		0			0
$628$	12.0378	+	31.6201i	0.480359	+	1.26178i
$629$	−7.05623	+	17.0353i	−0.281350	+	0.679240i
$630$		0			0
$631$	13.9686	+	13.9686i	0.556080	+	0.556080i	0.928189	−	0.372109i	$-0.121365\pi$
$631$	13.9686	+	13.9686i	0.556080	+	0.556080i	−0.372109	+	0.928189i	$0.621365\pi$
$632$	−12.6458	−	13.7943i	−0.503024	−	0.548709i
$633$		0			0
$634$	−42.7531	−	18.4381i	−1.69794	−	0.732272i
$635$	14.8769	−	35.9161i	0.590374	−	1.42529i
$636$		0			0
$637$	0.100054	−	0.0414436i	0.00396428	−	0.00164206i
$638$	−2.84259	−	2.92607i	−0.112539	−	0.115844i
$639$		0			0
$640$	10.2247	+	34.0885i	0.404166	+	1.34747i
$641$			17.0648i			0.674019i	0.941501	+	0.337009i	$0.109415\pi$
$641$			17.0648i			0.674019i	−0.941501	+	0.337009i	$0.890585\pi$
$642$		0			0
$643$	4.90959	+	11.8528i	0.193615	+	0.467429i	0.990637	−	0.136522i	$-0.0435924\pi$
$643$	4.90959	+	11.8528i	0.193615	+	0.467429i	−0.797022	+	0.603951i	$0.793592\pi$
$644$	−0.686391	−	0.0198702i	−0.0270476	−	0.000782994i
$645$		0			0
$646$	−4.42569	+	10.2620i	−0.174126	+	0.403753i
$647$	28.1803	+	28.1803i	1.10788	+	1.10788i	0.993429	+	0.114453i	$0.0365114\pi$
$647$	28.1803	+	28.1803i	1.10788	+	1.10788i	0.114453	+	0.993429i	$0.463489\pi$
$648$		0			0
$649$	13.7947	−	13.7947i	0.541491	−	0.541491i
$650$	0.0395773	+	0.0996005i	0.00155235	+	0.00390665i
$651$		0			0
$652$	3.58121	−	1.36336i	0.140251	−	0.0533935i
$653$	−12.4733	+	5.16661i	−0.488118	+	0.202185i	−0.613148	−	0.789968i	$-0.710097\pi$
$653$	−12.4733	+	5.16661i	−0.488118	+	0.202185i	0.125030	+	0.992153i	$0.460097\pi$
$654$		0			0
$655$	24.8326			0.970288
$656$	−16.5905	−	18.6315i	−0.647751	−	0.727438i
$657$		0			0
$658$	1.23542	+	0.0178781i	0.0481615	+	0.000696962i
$659$	0.172672	+	0.416868i	0.00672635	+	0.0162389i	0.927207	−	0.374549i	$-0.122203\pi$
$659$	0.172672	+	0.416868i	0.00672635	+	0.0162389i	−0.920481	+	0.390788i	$0.872203\pi$
$660$		0			0
$661$	−6.25429	−	2.59061i	−0.243264	−	0.100763i	0.257721	−	0.966219i	$-0.417029\pi$
$661$	−6.25429	−	2.59061i	−0.243264	−	0.100763i	−0.500984	+	0.865456i	$0.667029\pi$
$662$	16.9770	+	42.7245i	0.659831	+	1.66054i
$663$		0			0
$664$	9.83179	−	21.0966i	0.381547	−	0.818706i
$665$	0.752189	−	0.752189i	0.0291686	−	0.0291686i
$666$		0			0
$667$	4.77381	+	1.97738i	0.184843	+	0.0765644i
$668$	−8.97391	+	8.46896i	−0.347211	+	0.327674i
$669$		0			0
$670$	−15.7453	−	16.2077i	−0.608295	−	0.626159i
$671$	−17.6400			−0.680984
$672$		0			0
$673$	−3.75293			−0.144665			−0.0723323	−	0.997381i	$-0.523044\pi$
$673$	−3.75293			−0.144665			−0.0723323	+	0.997381i	$0.523044\pi$
$674$	−24.9291	−	25.6612i	−0.960231	−	0.988431i
$675$		0			0
$676$	−17.8448	−	18.9087i	−0.686337	−	0.727259i
$677$	−41.3110	−	17.1116i	−1.58771	−	0.657651i	−0.598099	−	0.801422i	$-0.704077\pi$
$677$	−41.3110	−	17.1116i	−1.58771	−	0.657651i	−0.989611	+	0.143771i	$0.954077\pi$
$678$		0			0
$679$	−0.779789	+	0.779789i	−0.0299256	+	0.0299256i
$680$	−4.96426	−	13.6298i	−0.190371	−	0.522677i
$681$		0			0
$682$	−0.962033	−	2.42106i	−0.0368381	−	0.0927071i
$683$	21.8007	+	9.03015i	0.834181	+	0.345529i	0.758557	−	0.651607i	$-0.225905\pi$
$683$	21.8007	+	9.03015i	0.834181	+	0.345529i	0.0756247	+	0.997136i	$0.475905\pi$
$684$		0			0
$685$	20.6352	+	49.8178i	0.788431	+	1.90344i
$686$	1.38071	+	0.0199808i	0.0527159	+	0.000762871i
$687$		0			0
$688$	5.75834	−	11.9030i	0.219535	−	0.453798i
$689$	−0.0360992			−0.00137527
$690$		0			0
$691$	−32.2652	+	13.3647i	−1.22743	+	0.508417i	−0.899764	−	0.436378i	$-0.856261\pi$
$691$	−32.2652	+	13.3647i	−1.22743	+	0.508417i	−0.327663	+	0.944795i	$0.606261\pi$
$692$	−17.0950	−	44.9042i	−0.649855	−	1.70700i
$693$		0			0
$694$	−16.9145	−	42.5672i	−0.642067	−	1.61583i
$695$	36.6642	−	36.6642i	1.39075	−	1.39075i
$696$		0			0
$697$	7.19011	+	7.19011i	0.272345	+	0.272345i
$698$	9.08087	−	21.0561i	0.343716	−	0.796986i
$699$		0			0
$700$	−0.0197649	+	0.682755i	−0.000747043	+	0.0258057i
$701$	1.66366	+	4.01643i	0.0628356	+	0.151699i	0.952179	−	0.305542i	$-0.0988377\pi$
$701$	1.66366	+	4.01643i	0.0628356	+	0.151699i	−0.889343	+	0.457241i	$0.848838\pi$
$702$		0			0
$703$			54.8182i			2.06751i
$704$	10.1398	−	19.4996i	0.382160	−	0.734919i
$705$		0			0
$706$	−0.884492	−	0.910468i	−0.0332883	−	0.0342659i
$707$	0.407477	−	0.168782i	0.0153247	−	0.00634771i
$708$		0			0
$709$	−9.19367	+	22.1955i	−0.345276	+	0.833569i	0.651889	+	0.758315i	$0.273977\pi$
$709$	−9.19367	+	22.1955i	−0.345276	+	0.833569i	−0.997164	+	0.0752543i	$0.976023\pi$
$710$	40.7728	+	17.5841i	1.53018	+	0.659919i
$711$		0			0
$712$	38.8343	+	1.68690i	1.45538	+	0.0632192i
$713$	2.33329	+	2.33329i	0.0873825	+	0.0873825i
$714$		0			0
$715$	0.0512010	−	0.123610i	0.00191481	−	0.00462275i
$716$	10.4511	−	3.97872i	0.390574	−	0.148692i
$717$		0			0
$718$	7.44415	+	0.107727i	0.277813	+	0.00402034i
$719$		−	12.4409i		−	0.463967i	−0.972720	−	0.231983i	$-0.925478\pi$
$719$		−	12.4409i		−	0.463967i	0.972720	−	0.231983i	$-0.0745215\pi$
$720$		0			0
$721$		−	1.33799i		−	0.0498295i
$722$	−0.0919547	+	6.35425i	−0.00342220	+	0.236481i
$723$		0			0
$724$	1.06647	−	2.37764i	0.0396349	−	0.0883641i
$725$	1.96690	−	4.74853i	0.0730490	−	0.176356i
$726$		0			0
$727$	−5.81227	−	5.81227i	−0.215565	−	0.215565i	0.591061	−	0.806627i	$-0.298709\pi$
$727$	−5.81227	−	5.81227i	−0.215565	−	0.215565i	−0.806627	+	0.591061i	$0.798709\pi$
$728$	0.00104554	+	0.00287062i	3.87504e−5	+	0.000106392i
$729$		0			0
$730$	−19.2809	+	44.7073i	−0.713618	+	1.65469i
$731$	−2.06245	+	4.97920i	−0.0762825	+	0.184162i
$732$		0			0
$733$	6.78818	−	2.81176i	0.250727	−	0.103855i	−0.253780	−	0.967262i	$-0.581674\pi$
$733$	6.78818	−	2.81176i	0.250727	−	0.103855i	0.504508	+	0.863407i	$0.331674\pi$
$734$	0.701244	−	0.681238i	0.0258834	−	0.0251449i
$735$		0			0
$736$	−2.01238	+	27.7653i	−0.0741774	+	1.02344i
$737$			13.9548i			0.514033i
$738$		0			0
$739$	−5.71001	−	13.7852i	−0.210046	−	0.507097i	0.783384	−	0.621538i	$-0.213492\pi$
$739$	−5.71001	−	13.7852i	−0.210046	−	0.507097i	−0.993430	+	0.114442i	$0.963492\pi$
$740$	−48.8354	−	51.7472i	−1.79523	−	1.90226i
$741$		0			0
$742$	−0.211255	−	0.0911078i	−0.00775540	−	0.00334467i
$743$	28.5758	+	28.5758i	1.04834	+	1.04834i	0.998771	+	0.0495724i	$0.0157859\pi$
$743$	28.5758	+	28.5758i	1.04834	+	1.04834i	0.0495724	+	0.998771i	$0.484214\pi$
$744$		0			0
$745$	−18.3858	+	18.3858i	−0.673602	+	0.673602i
$746$	21.4988	−	8.54275i	0.787125	−	0.312772i
$747$		0			0
$748$	−3.66620	+	8.17361i	−0.134050	+	0.298857i
$749$	−0.689411	+	0.285563i	−0.0251905	+	0.0104343i
$750$		0			0
$751$	26.4367			0.964689			0.482344	−	0.875982i	$-0.339785\pi$
$751$	26.4367			0.964689			0.482344	+	0.875982i	$0.339785\pi$
$752$	2.89763	−	50.0055i	0.105666	−	1.82351i
$753$		0			0
$754$	0.000332649	−	0.0229867i	1.21143e−5	−	0.000837126i
$755$	−17.0862	−	41.2498i	−0.621832	−	1.50124i
$756$		0			0
$757$	26.7671	+	11.0873i	0.972867	+	0.402975i	0.811779	−	0.583965i	$-0.198500\pi$
$757$	26.7671	+	11.0873i	0.972867	+	0.402975i	0.161088	+	0.986940i	$0.448500\pi$
$758$	34.9427	−	13.8848i	1.26918	−	0.504320i
$759$		0			0
$760$	−29.1419	−	31.7886i	−1.05709	−	1.15309i
$761$	24.5287	−	24.5287i	0.889164	−	0.889164i	−0.105279	−	0.994443i	$-0.533574\pi$
$761$	24.5287	−	24.5287i	0.889164	−	0.889164i	0.994443	+	0.105279i	$0.0335735\pi$
$762$		0			0
$763$	0.874207	+	0.362109i	0.0316484	+	0.0131092i
$764$	−0.572204	+	19.7661i	−0.0207016	+	0.715112i
$765$		0			0
$766$	19.7609	−	19.1971i	0.713990	−	0.693620i
$767$	0.109937			0.00396960
$768$		0			0
$769$	19.7989			0.713967			0.356984	−	0.934111i	$-0.383805\pi$
$769$	19.7989			0.713967			0.356984	+	0.934111i	$0.383805\pi$
$770$	0.611601	−	0.594152i	0.0220406	−	0.0214117i
$771$		0			0
$772$	1.58144	−	54.6290i	0.0569174	−	1.96614i
$773$	20.5200	+	8.49965i	0.738052	+	0.305711i	0.719856	−	0.694123i	$-0.244208\pi$
$773$	20.5200	+	8.49965i	0.738052	+	0.305711i	0.0181959	+	0.999834i	$0.494208\pi$
$774$		0			0
$775$	2.32093	−	2.32093i	0.0833703	−	0.0833703i
$776$	30.2112	+	32.9551i	1.08452	+	1.18302i
$777$		0			0
$778$	26.9122	−	10.6938i	0.964848	−	0.383392i
$779$	27.9291	+	11.5686i	1.00066	+	0.414489i
$780$		0			0
$781$	−10.4938	−	25.3343i	−0.375498	−	0.906534i
$782$	0.164183	−	11.3454i	0.00587117	−	0.405709i
$783$		0			0
$784$	1.61865	−	27.9337i	0.0578089	−	0.997631i
$785$	53.2148			1.89932
$786$		0			0
$787$	−11.2027	+	4.64029i	−0.399331	+	0.165409i	−0.573305	−	0.819342i	$-0.694339\pi$
$787$	−11.2027	+	4.64029i	−0.399331	+	0.165409i	0.173974	+	0.984750i	$0.444339\pi$
$788$	−6.91647	+	15.4199i	−0.246389	+	0.549313i
$789$		0			0
$790$	−27.3529	+	10.8689i	−0.973172	+	0.386700i
$791$	−0.375369	+	0.375369i	−0.0133466	+	0.0133466i
$792$		0			0
$793$	−0.0702908	−	0.0702908i	−0.00249610	−	0.00249610i
$794$	3.77918	+	1.62985i	0.134118	+	0.0578412i
$795$		0			0
$796$	17.3995	+	18.4369i	0.616709	+	0.653479i
$797$	−11.7344	−	28.3294i	−0.415654	−	1.00348i	−0.983592	−	0.180406i	$-0.942259\pi$
$797$	−11.7344	−	28.3294i	−0.415654	−	1.00348i	0.567938	−	0.823071i	$-0.307741\pi$
$798$		0			0
$799$			20.4159i			0.722264i
$800$	27.6183	+	2.00172i	0.976453	+	0.0707716i
$801$		0			0
$802$	5.38210	−	5.22855i	0.190049	−	0.184626i
$803$	27.7790	−	11.5064i	0.980300	−	0.406054i
$804$		0			0
$805$	−0.413307	+	0.997810i	−0.0145671	+	0.0351682i
$806$	0.00581385	−	0.0134808i	0.000204784	−	0.000474840i
$807$		0			0
$808$	−6.11916	−	16.8006i	−0.215271	−	0.591044i
$809$	22.1946	+	22.1946i	0.780320	+	0.780320i	0.979885	−	0.199565i	$-0.0639528\pi$
$809$	22.1946	+	22.1946i	0.780320	+	0.780320i	−0.199565	+	0.979885i	$0.563953\pi$
$810$		0			0
$811$	7.28501	−	17.5876i	0.255811	−	0.617583i	−0.742842	−	0.669467i	$-0.766523\pi$
$811$	7.28501	−	17.5876i	0.255811	−	0.617583i	0.998653	+	0.0518841i	$0.0165226\pi$
$812$	0.0599609	−	0.133680i	0.00210422	−	0.00469125i
$813$		0			0
$814$	−0.635822	+	43.9366i	−0.0222856	+	1.53998i
$815$		−	6.02696i		−	0.211115i
$816$		0			0
$817$			16.0227i			0.560563i
$818$	10.8287	+	0.156706i	0.378615	+	0.00547908i
$819$		0			0
$820$	−36.6705	+	13.9605i	−1.28059	+	0.487520i
$821$	−1.66246	+	4.01352i	−0.0580201	+	0.140073i	−0.950231	−	0.311546i	$-0.899153\pi$
$821$	−1.66246	+	4.01352i	−0.0580201	+	0.140073i	0.892211	+	0.451619i	$0.149153\pi$
$822$		0			0
$823$	−11.0135	−	11.0135i	−0.383908	−	0.383908i	0.488600	−	0.872508i	$-0.337508\pi$
$823$	−11.0135	−	11.0135i	−0.383908	−	0.383908i	−0.872508	+	0.488600i	$0.837508\pi$
$824$	−54.1917	−	2.35400i	−1.88786	−	0.0820053i
$825$		0			0
$826$	0.643359	+	0.277461i	0.0223853	+	0.00965411i
$827$	6.63273	−	16.0128i	0.230643	−	0.556821i	−0.765611	−	0.643304i	$-0.777563\pi$
$827$	6.63273	−	16.0128i	0.230643	−	0.556821i	0.996253	+	0.0864837i	$0.0275630\pi$
$828$		0			0
$829$	11.9601	−	4.95405i	0.415393	−	0.172061i	−0.165191	−	0.986262i	$-0.552824\pi$
$829$	11.9601	−	4.95405i	0.415393	−	0.172061i	0.580584	+	0.814200i	$0.302824\pi$
$830$	−25.5082	−	26.2573i	−0.885402	−	0.911404i
$831$		0			0
$832$	0.118106	−	0.0372963i	0.00409458	−	0.00129302i
$833$			11.4046i			0.395145i
$834$		0			0
$835$	7.42684	+	17.9300i	0.257016	+	0.620492i
$836$	−0.770655	+	26.6213i	−0.0266537	+	0.920718i
$837$		0			0
$838$	19.6671	−	45.6028i	0.679389	−	1.57532i
$839$	−22.7966	−	22.7966i	−0.787026	−	0.787026i	0.193980	−	0.981006i	$-0.437860\pi$
$839$	−22.7966	−	22.7966i	−0.787026	−	0.787026i	−0.981006	+	0.193980i	$0.937860\pi$
$840$		0			0
$841$	19.7265	−	19.7265i	0.680225	−	0.680225i
$842$	5.82742	+	14.6653i	0.200826	+	0.505401i
$843$		0			0
$844$	−7.27612	−	19.1125i	−0.250455	−	0.657879i
$845$	−37.7798	+	15.6489i	−1.29967	+	0.538339i
$846$		0			0
$847$	0.240862			0.00827613
$848$	−4.06173	+	8.39598i	−0.139480	+	0.288319i
$849$		0			0
$850$	−11.2853	−	0.163313i	−0.387081	−	0.00560159i
$851$	−21.2988	−	51.4199i	−0.730114	−	1.76265i
$852$		0			0
$853$	12.3720	+	5.12463i	0.423608	+	0.175464i	0.584295	−	0.811541i	$-0.301371\pi$
$853$	12.3720	+	5.12463i	0.423608	+	0.175464i	−0.160687	+	0.987005i	$0.551371\pi$
$854$	−0.233945	−	0.588748i	−0.00800543	−	0.0201465i
$855$		0			0
$856$	10.3530	+	28.4250i	0.353859	+	0.971547i
$857$	−40.3165	+	40.3165i	−1.37719	+	1.37719i	−0.527846	+	0.849340i	$0.677000\pi$
$857$	−40.3165	+	40.3165i	−1.37719	+	1.37719i	−0.849340	+	0.527846i	$0.823000\pi$
$858$		0			0
$859$	−25.1076	−	10.3999i	−0.856660	−	0.354840i	−0.0892596	−	0.996008i	$-0.528450\pi$
$859$	−25.1076	−	10.3999i	−0.856660	−	0.354840i	−0.767400	+	0.641168i	$0.778450\pi$
$860$	−14.2740	−	15.1251i	−0.486739	−	0.515760i
$861$		0			0
$862$	−2.89161	−	2.97653i	−0.0984886	−	0.101381i
$863$	16.3557			0.556754			0.278377	−	0.960472i	$-0.410204\pi$
$863$	16.3557			0.556754			0.278377	+	0.960472i	$0.410204\pi$
$864$		0			0
$865$	−75.5712			−2.56950
$866$	16.6033	+	17.0909i	0.564203	+	0.580772i
$867$		0			0
$868$	0.0680460	−	0.0642172i	0.00230963	−	0.00217967i
$869$	16.7933	+	6.95600i	0.569673	+	0.235966i
$870$		0			0
$871$	−0.0556065	+	0.0556065i	−0.00188415	+	0.00188415i
$872$	16.2042	−	34.7702i	0.548744	−	1.17747i
$873$		0			0
$874$	−12.4568	−	31.3488i	−0.421357	−	1.06039i
$875$	−0.0212754	−	0.00881256i	−0.000719240	−	0.000297919i
$876$		0			0
$877$	7.17015	+	17.3103i	0.242119	+	0.584527i	0.997493	−	0.0707673i	$-0.0225448\pi$
$877$	7.17015	+	17.3103i	0.242119	+	0.584527i	−0.755374	+	0.655294i	$0.772545\pi$
$878$	37.7250	+	0.545933i	1.27316	+	0.0184243i
$879$		0			0
$880$	−22.9884	−	25.8165i	−0.774939	−	0.870273i
$881$	−29.1493			−0.982064			−0.491032	−	0.871141i	$-0.663380\pi$
$881$	−29.1493			−0.982064			−0.491032	+	0.871141i	$0.663380\pi$
$882$		0			0
$883$	29.5808	−	12.2528i	0.995474	−	0.412339i	0.175339	−	0.984508i	$-0.443898\pi$
$883$	29.5808	−	12.2528i	0.995474	−	0.412339i	0.820136	+	0.572169i	$0.193898\pi$
$884$	−0.0471786	+	0.0179609i	−0.00158679	+	0.000604090i
$885$		0			0
$886$	−10.3674	−	26.0906i	−0.348299	−	0.876531i
$887$	23.3124	−	23.3124i	0.782755	−	0.782755i	−0.197540	−	0.980295i	$-0.563295\pi$
$887$	23.3124	−	23.3124i	0.782755	−	0.782755i	0.980295	+	0.197540i	$0.0632953\pi$
$888$		0			0
$889$	−0.609687	−	0.609687i	−0.0204483	−	0.0204483i
$890$	24.2110	−	56.1388i	0.811554	−	1.88178i
$891$		0			0
$892$	−21.2609	−	0.615478i	−0.711868	−	0.0206077i
$893$	23.2274	+	56.0759i	0.777275	+	1.87651i
$894$		0			0
$895$		−	17.5885i		−	0.587920i
$896$	0.785291	+	0.0798172i	0.0262347	+	0.00266651i
$897$		0			0
$898$	−24.9846	−	25.7184i	−0.833748	−	0.858234i
$899$	−0.650456	+	0.269428i	−0.0216939	+	0.00898592i
$900$		0			0
$901$	1.45478	−	3.51215i	0.0484658	−	0.117007i
$902$	22.2509	+	9.59615i	0.740874	+	0.319517i
$903$		0			0
$904$	14.5429	+	15.8637i	0.483688	+	0.527618i
$905$	−2.89811	−	2.89811i	−0.0963365	−	0.0963365i
$906$		0			0
$907$	−15.1123	+	36.4844i	−0.501797	+	1.21144i	0.446708	+	0.894680i	$0.352596\pi$
$907$	−15.1123	+	36.4844i	−0.501797	+	1.21144i	−0.948504	+	0.316764i	$0.897404\pi$
$908$	0.186012	+	0.488605i	0.00617302	+	0.0162149i
$909$		0			0
$910$	0.00480462		6.95293e-5i	0.000159271		2.30487e-6i
$911$			12.7626i			0.422844i	0.977395	+	0.211422i	$0.0678095\pi$
$911$			12.7626i			0.422844i	−0.977395	+	0.211422i	$0.932191\pi$
$912$		0			0
$913$			22.6075i			0.748199i
$914$	−0.540487	+	37.3487i	−0.0178777	+	1.23539i
$915$		0			0
$916$	−12.0679	−	5.41292i	−0.398733	−	0.178848i
$917$	0.210770	−	0.508844i	0.00696024	−	0.0168035i
$918$		0			0
$919$	22.3311	+	22.3311i	0.736635	+	0.736635i	0.971925	−	0.235290i	$-0.0756041\pi$
$919$	22.3311	+	22.3311i	0.736635	+	0.736635i	−0.235290	+	0.971925i	$0.575604\pi$
$920$	39.6863	+	18.4953i	1.30842	+	0.609772i
$921$		0			0
$922$	12.2741	−	28.4603i	0.404226	−	0.937292i
$923$	0.0591356	−	0.142766i	0.00194647	−	0.00469920i
$924$		0			0
$925$	−51.1475	+	21.1860i	−1.68172	+	0.696591i
$926$	−17.2491	+	16.7570i	−0.566840	+	0.550668i
$927$		0			0
$928$	−5.30883	−	2.66374i	−0.174271	−	0.0874414i
$929$		−	20.0439i		−	0.657617i	−0.944397	−	0.328809i	$-0.893353\pi$
$929$		−	20.0439i		−	0.657617i	0.944397	−	0.328809i	$-0.106647\pi$
$930$		0			0
$931$	12.9751	+	31.3246i	0.425241	+	1.02662i
$932$	−2.56950	+	2.42492i	−0.0841669	+	0.0794309i
$933$		0			0
$934$	32.4713	+	14.0039i	1.06249	+	0.458222i
$935$	9.96286	+	9.96286i	0.325820	+	0.325820i
$936$		0			0
$937$	−32.1758	+	32.1758i	−1.05114	+	1.05114i	−0.0525163	+	0.998620i	$0.516724\pi$
$937$	−32.1758	+	32.1758i	−1.05114	+	1.05114i	−0.998620	+	0.0525163i	$0.983276\pi$
$938$	−0.465754	+	0.185072i	−0.0152074	+	0.00604282i
$939$		0			0
$940$	−71.8819	−	32.2420i	−2.34453	−	1.05162i
$941$	32.7805	−	13.5781i	1.06861	−	0.442634i	0.222112	−	0.975021i	$-0.428705\pi$
$941$	32.7805	−	13.5781i	1.06861	−	0.442634i	0.846501	+	0.532387i	$0.178705\pi$
$942$		0			0
$943$	−30.6926			−0.999487
$944$	12.3697	−	25.5693i	0.402599	−	0.832209i
$945$		0			0
$946$	−0.185843	+	12.8421i	−0.00604228	+	0.417534i
$947$	11.4034	+	27.5302i	0.370560	+	0.894611i	0.993656	+	0.112465i	$0.0358747\pi$
$947$	11.4034	+	27.5302i	0.370560	+	0.894611i	−0.623096	+	0.782146i	$0.714125\pi$
$948$		0			0
$949$	0.156543	+	0.0648421i	0.00508159	+	0.00210486i
$950$	−31.1827	+	12.3908i	−1.01170	+	0.402010i
$951$		0			0
$952$	−0.321422	−	0.0139621i	−0.0104174	−	0.000452513i
$953$	28.4394	−	28.4394i	0.921243	−	0.921243i	−0.0758744	−	0.997117i	$-0.524175\pi$
$953$	28.4394	−	28.4394i	0.921243	−	0.921243i	0.997117	+	0.0758744i	$0.0241748\pi$
$954$		0			0
$955$	28.7341	+	11.9020i	0.929813	+	0.385141i
$956$	−26.6719	−	0.772119i	−0.862631	−	0.0249721i
$957$		0			0
$958$	8.40664	−	8.16680i	0.271606	−	0.263857i
$959$	1.19596			0.0386196
$960$		0			0
$961$	30.5504			0.985496
$962$	−0.177610	+	0.172543i	−0.00572637	+	0.00556300i
$963$		0			0
$964$	−3.80026	−	0.110013i	−0.122398	−	0.00354328i
$965$	−79.4146	−	32.8946i	−2.55645	−	1.05891i
$966$		0			0
$967$	9.70473	−	9.70473i	0.312083	−	0.312083i	−0.533633	−	0.845716i	$-0.679174\pi$
$967$	9.70473	−	9.70473i	0.312083	−	0.312083i	0.845716	+	0.533633i	$0.179174\pi$
$968$	0.423760	−	9.75544i	0.0136202	−	0.313552i
$969$		0			0
$970$	65.3469	−	25.9662i	2.09816	−	0.833726i
$971$	−16.6765	−	6.90764i	−0.535175	−	0.221677i	0.0986932	−	0.995118i	$-0.468534\pi$
$971$	−16.6765	−	6.90764i	−0.535175	−	0.221677i	−0.633868	+	0.773441i	$0.718534\pi$
$972$		0			0
$973$	−0.440094	−	1.06248i	−0.0141088	−	0.0340616i
$974$	0.416742	−	28.7977i	0.0133533	−	0.922737i
$975$		0			0
$976$	−24.2571	+	8.43947i	−0.776452	+	0.270141i
$977$	−56.0336			−1.79267			−0.896337	−	0.443374i	$-0.853781\pi$
$977$	−56.0336			−1.79267			−0.896337	+	0.443374i	$0.853781\pi$
$978$		0			0
$979$	−34.8821	+	14.4486i	−1.11484	+	0.461780i
$980$	−40.1541	−	18.0107i	−1.28268	−	0.575332i
$981$		0			0
$982$	−12.6373	+	5.02157i	−0.403273	+	0.160245i
$983$	34.5526	−	34.5526i	1.10206	−	1.10206i	0.107896	−	0.994162i	$-0.465589\pi$
$983$	34.5526	−	34.5526i	1.10206	−	1.10206i	0.994162	−	0.107896i	$-0.0344112\pi$
$984$		0			0
$985$	18.7955	+	18.7955i	0.598873	+	0.598873i
$986$	2.22301	+	0.958717i	0.0707950	+	0.0305318i
$987$		0			0
$988$	−0.109150	+	0.103008i	−0.00347253	+	0.00327713i
$989$	−6.22538	−	15.0294i	−0.197956	−	0.477907i
$990$		0			0
$991$		−	35.9914i		−	1.14331i	−0.820496	−	0.571653i	$-0.806302\pi$
$991$		−	35.9914i		−	1.14331i	0.820496	−	0.571653i	$-0.193698\pi$
$992$	−2.48122	−	2.86899i	−0.0787787	−	0.0910905i
$993$		0			0
$994$	0.706381	−	0.686228i	0.0224051	−	0.0217658i
$995$	36.8372	−	15.2585i	1.16782	−	0.483726i
$996$		0			0
$997$	−13.9742	+	33.7366i	−0.442566	+	1.06845i	0.532479	+	0.846443i	$0.321260\pi$
$997$	−13.9742	+	33.7366i	−0.442566	+	1.06845i	−0.975045	+	0.222006i	$0.928740\pi$
$998$	2.94307	−	6.82420i	0.0931613	−	0.216016i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.01437 + 0.985425i) q^{2} +(0.0578733 - 1.99916i) q^{4} +(-2.90620 - 1.20379i) q^{5} +(-0.0493336 + 0.0493336i) q^{7} +(1.91132 + 2.08491i) q^{8} +O(q^{10})\)	\(q+(-1.01437 + 0.985425i) q^{2} +(0.0578733 - 1.99916i) q^{4} +(-2.90620 - 1.20379i) q^{5} +(-0.0493336 + 0.0493336i) q^{7} +(1.91132 + 2.08491i) q^{8} +(4.13418 - 1.64276i) q^{10} +(-2.53818 - 1.05135i) q^{11} +(-0.00592464 - 0.0143033i) q^{13} +(0.00142770 - 0.0986568i) q^{14} +(-3.99330 - 0.231396i) q^{16} +1.63036 q^{17} +(4.47806 - 1.85487i) q^{19} +(-2.57475 + 5.74029i) q^{20} +(3.61066 - 1.43473i) q^{22} +(-3.47977 + 3.47977i) q^{23} +(3.46134 + 3.46134i) q^{25} +(0.0201046 + 0.00867052i) q^{26} +(0.0957707 + 0.101481i) q^{28} +(-0.401813 - 0.970063i) q^{29} -0.670530i q^{31} +(4.27869 - 3.70038i) q^{32} +(-1.65378 + 1.60660i) q^{34} +(0.202760 - 0.0839859i) q^{35} +(-4.32803 + 10.4488i) q^{37} +(-2.71455 + 6.29432i) q^{38} +(-3.04489 - 8.35998i) q^{40} +(4.41014 + 4.41014i) q^{41} +(-1.26503 + 3.05405i) q^{43} +(-2.24871 + 5.01338i) q^{44} +(0.100704 - 6.95881i) q^{46} +12.5224i q^{47} +6.99513i q^{49} +(-6.92195 - 0.100170i) q^{50} +(-0.0289376 + 0.0110165i) q^{52} +(0.892308 - 2.15422i) q^{53} +(6.11084 + 6.11084i) q^{55} +(-0.197148 - 0.00856380i) q^{56} +(1.36351 + 0.588041i) q^{58} +(-2.71745 + 6.56050i) q^{59} +(5.93208 - 2.45715i) q^{61} +(0.660758 + 0.680162i) q^{62} +(-0.693704 + 7.96987i) q^{64} +0.0487003i q^{65} +(-1.94383 - 4.69282i) q^{67} +(0.0943542 - 3.25935i) q^{68} +(-0.122911 + 0.284997i) q^{70} +(7.05785 + 7.05785i) q^{71} +(-7.73891 + 7.73891i) q^{73} +(-5.90629 - 14.8638i) q^{74} +(-3.44903 - 9.05972i) q^{76} +(0.177084 - 0.0733506i) q^{77} -6.61627 q^{79} +(11.3268 + 5.47956i) q^{80} +(-8.81935 - 0.127628i) q^{82} +(-3.14910 - 7.60259i) q^{83} +(-4.73814 - 1.96260i) q^{85} +(-1.72634 - 4.34451i) q^{86} +(-2.65931 - 7.30134i) q^{88} +(9.71773 - 9.71773i) q^{89} +(0.000997919 + 0.000413351i) q^{91} +(6.75524 + 7.15802i) q^{92} +(-12.3398 - 12.7022i) q^{94} -15.2470 q^{95} +15.8065 q^{97} +(-6.89318 - 7.09562i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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