LMFDB - Embedded newform 864.2.v.a.109.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(109,864)]

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([0, 7, 0]))

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

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

chi := DirichletCharacter("864.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.v (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			109.4
Character	$\chi$	$=$	864.109
Dual form			864.2.v.a.325.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33208 - 0.474937i) q^{2} +(1.54887 + 1.26531i) q^{4} +(-0.0485815 + 0.0201231i) q^{5} +(2.80669 - 2.80669i) q^{7} +(-1.46228 - 2.42110i) q^{8} +O(q^{10})$	\(q+(-1.33208 - 0.474937i) q^{2} +(1.54887 + 1.26531i) q^{4} +(-0.0485815 + 0.0201231i) q^{5} +(2.80669 - 2.80669i) q^{7} +(-1.46228 - 2.42110i) q^{8} +(0.0742716 - 0.00373246i) q^{10} +(2.28951 + 5.52736i) q^{11} +(4.71917 + 1.95474i) q^{13} +(-5.07173 + 2.40573i) q^{14} +(0.798000 + 3.91959i) q^{16} +4.18126i q^{17} +(-4.12114 - 1.70703i) q^{19} +(-0.100708 - 0.0303024i) q^{20} +(-0.424660 - 8.45025i) q^{22} +(-1.99266 - 1.99266i) q^{23} +(-3.53358 + 3.53358i) q^{25} +(-5.35792 - 4.84518i) q^{26} +(7.89851 - 0.795876i) q^{28} +(2.50335 - 6.04362i) q^{29} +2.26107 q^{31} +(0.798558 - 5.60021i) q^{32} +(1.98583 - 5.56977i) q^{34} +(-0.0798738 + 0.192832i) q^{35} +(1.89554 - 0.785157i) q^{37} +(4.67895 + 4.23118i) q^{38} +(0.119760 + 0.0881953i) q^{40} +(-3.69237 - 3.69237i) q^{41} +(4.03236 + 9.73497i) q^{43} +(-3.44765 + 11.4581i) q^{44} +(1.70799 + 3.60077i) q^{46} +2.45724i q^{47} -8.75498i q^{49} +(6.38523 - 3.02878i) q^{50} +(4.83603 + 8.99883i) q^{52} +(3.57639 + 8.63418i) q^{53} +(-0.222456 - 0.222456i) q^{55} +(-10.8994 - 2.69112i) q^{56} +(-6.20499 + 6.86165i) q^{58} +(12.7174 - 5.26771i) q^{59} +(-3.98195 + 9.61329i) q^{61} +(-3.01193 - 1.07387i) q^{62} +(-3.72349 + 7.08065i) q^{64} -0.268600 q^{65} +(4.48885 - 10.8370i) q^{67} +(-5.29057 + 6.47623i) q^{68} +(0.197981 - 0.218933i) q^{70} +(3.80026 - 3.80026i) q^{71} +(7.28971 + 7.28971i) q^{73} +(-2.89791 + 0.145632i) q^{74} +(-4.22319 - 7.85847i) q^{76} +(21.9395 + 9.08764i) q^{77} -1.36436i q^{79} +(-0.117642 - 0.174361i) q^{80} +(3.16489 + 6.67217i) q^{82} +(-2.99666 - 1.24126i) q^{83} +(-0.0841399 - 0.203132i) q^{85} +(-0.747925 - 14.8829i) q^{86} +(10.0344 - 13.6257i) q^{88} +(-1.78145 + 1.78145i) q^{89} +(18.7316 - 7.75887i) q^{91} +(-0.565047 - 5.60770i) q^{92} +(1.16703 - 3.27324i) q^{94} +0.234562 q^{95} -6.21324 q^{97} +(-4.15806 + 11.6623i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) $ 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

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 $

$2$	−1.33208	−	0.474937i	−0.941922	−	0.335831i
$2$	−1.33208	−	0.474937i	−0.941922	−	0.335831i
$3$		0			0
$3$		0			0
$4$	1.54887	+	1.26531i	0.774435	+	0.632653i
$5$	−0.0485815	+	0.0201231i	−0.0217263	+	0.00899933i	−0.393520	−	0.919316i	$-0.628743\pi$
$5$	−0.0485815	+	0.0201231i	−0.0217263	+	0.00899933i	0.371794	+	0.928315i	$0.378743\pi$
$6$		0			0
$7$	2.80669	−	2.80669i	1.06083	−	1.06083i	0.0628018	−	0.998026i	$-0.479996\pi$
$7$	2.80669	−	2.80669i	1.06083	−	1.06083i	0.998026	−	0.0628018i	$-0.0200036\pi$
$8$	−1.46228	−	2.42110i	−0.516993	−	0.855989i
$9$		0			0
$10$	0.0742716	−	0.00373246i	0.0234868	−	0.00118031i
$11$	2.28951	+	5.52736i	0.690313	+	1.66656i	0.744150	+	0.668012i	$0.232855\pi$
$11$	2.28951	+	5.52736i	0.690313	+	1.66656i	−0.0538375	+	0.998550i	$0.517145\pi$
$12$		0			0
$13$	4.71917	+	1.95474i	1.30886	+	0.542148i	0.924552	−	0.381056i	$-0.124440\pi$
$13$	4.71917	+	1.95474i	1.30886	+	0.542148i	0.384309	+	0.923204i	$0.374440\pi$
$14$	−5.07173	+	2.40573i	−1.35548	+	0.642959i
$15$		0			0
$16$	0.798000	+	3.91959i	0.199500	+	0.979898i
$17$			4.18126i			1.01410i	0.861916	+	0.507052i	$0.169265\pi$
$17$			4.18126i			1.01410i	−0.861916	+	0.507052i	$0.830735\pi$
$18$		0			0
$19$	−4.12114	−	1.70703i	−0.945454	−	0.391620i	−0.143933	−	0.989587i	$-0.545975\pi$
$19$	−4.12114	−	1.70703i	−0.945454	−	0.391620i	−0.801520	+	0.597968i	$0.795975\pi$
$20$	−0.100708	−	0.0303024i	−0.0225191	−	0.00677582i
$21$		0			0
$22$	−0.424660	−	8.45025i	−0.0905379	−	1.80160i
$23$	−1.99266	−	1.99266i	−0.415498	−	0.415498i	0.468151	−	0.883649i	$-0.344920\pi$
$23$	−1.99266	−	1.99266i	−0.415498	−	0.415498i	−0.883649	+	0.468151i	$0.844920\pi$
$24$		0			0
$25$	−3.53358	+	3.53358i	−0.706716	+	0.706716i
$26$	−5.35792	−	4.84518i	−1.05078	−	0.950217i
$27$		0			0
$28$	7.89851	−	0.795876i	1.49268	−	0.150406i
$29$	2.50335	−	6.04362i	0.464860	−	1.12227i	−0.501518	−	0.865147i	$-0.667225\pi$
$29$	2.50335	−	6.04362i	0.464860	−	1.12227i	0.966378	−	0.257125i	$-0.0827751\pi$
$30$		0			0
$31$	2.26107			0.406101			0.203050	−	0.979168i	$-0.434914\pi$
$31$	2.26107			0.406101			0.203050	+	0.979168i	$0.434914\pi$
$32$	0.798558	−	5.60021i	0.141167	−	0.989986i
$33$		0			0
$34$	1.98583	−	5.56977i	0.340567	−	0.955207i
$35$	−0.0798738	+	0.192832i	−0.0135011	+	0.0325946i
$36$		0			0
$37$	1.89554	−	0.785157i	0.311624	−	0.129079i	−0.221390	−	0.975185i	$-0.571059\pi$
$37$	1.89554	−	0.785157i	0.311624	−	0.129079i	0.533014	+	0.846106i	$0.321059\pi$
$38$	4.67895	+	4.23118i	0.759026	+	0.686388i
$39$		0			0
$40$	0.119760	+	0.0881953i	0.0189357	+	0.0139449i
$41$	−3.69237	−	3.69237i	−0.576651	−	0.576651i	0.357328	−	0.933979i	$-0.383688\pi$
$41$	−3.69237	−	3.69237i	−0.576651	−	0.576651i	−0.933979	+	0.357328i	$0.883688\pi$
$42$		0			0
$43$	4.03236	+	9.73497i	0.614929	+	1.48457i	0.857525	+	0.514442i	$0.172001\pi$
$43$	4.03236	+	9.73497i	0.614929	+	1.48457i	−0.242597	+	0.970127i	$0.577999\pi$
$44$	−3.44765	+	11.4581i	−0.519753	+	1.72737i
$45$		0			0
$46$	1.70799	+	3.60077i	0.251830	+	0.530904i
$47$			2.45724i			0.358426i	0.983810	+	0.179213i	$0.0573551\pi$
$47$			2.45724i			0.358426i	−0.983810	+	0.179213i	$0.942645\pi$
$48$		0			0
$49$		−	8.75498i		−	1.25071i
$50$	6.38523	−	3.02878i	0.903008	−	0.428334i
$51$		0			0
$52$	4.83603	+	8.99883i	0.670637	+	1.24791i
$53$	3.57639	+	8.63418i	0.491256	+	1.18600i	0.954082	+	0.299547i	$0.0968354\pi$
$53$	3.57639	+	8.63418i	0.491256	+	1.18600i	−0.462826	+	0.886449i	$0.653165\pi$
$54$		0			0
$55$	−0.222456	−	0.222456i	−0.0299959	−	0.0299959i
$56$	−10.8994	−	2.69112i	−1.45650	−	0.359616i
$57$		0			0
$58$	−6.20499	+	6.86165i	−0.814756	+	0.900978i
$59$	12.7174	−	5.26771i	1.65566	−	0.685798i	0.657929	−	0.753080i	$-0.271433\pi$
$59$	12.7174	−	5.26771i	1.65566	−	0.685798i	0.997734	+	0.0672821i	$0.0214327\pi$
$60$		0			0
$61$	−3.98195	+	9.61329i	−0.509837	+	1.23086i	0.434140	+	0.900845i	$0.357052\pi$
$61$	−3.98195	+	9.61329i	−0.509837	+	1.23086i	−0.943977	+	0.330010i	$0.892948\pi$
$62$	−3.01193	−	1.07387i	−0.382515	−	0.136381i
$63$		0			0
$64$	−3.72349	+	7.08065i	−0.465436	+	0.885082i
$65$	−0.268600			−0.0333157
$66$		0			0
$67$	4.48885	−	10.8370i	0.548400	−	1.32395i	−0.370268	−	0.928925i	$-0.620734\pi$
$67$	4.48885	−	10.8370i	0.548400	−	1.32395i	0.918668	−	0.395030i	$-0.129266\pi$
$68$	−5.29057	+	6.47623i	−0.641576	+	0.785358i
$69$		0			0
$70$	0.197981	−	0.218933i	0.0236633	−	0.0261675i
$71$	3.80026	−	3.80026i	0.451008	−	0.451008i	−0.444681	−	0.895689i	$-0.646683\pi$
$71$	3.80026	−	3.80026i	0.451008	−	0.451008i	0.895689	+	0.444681i	$0.146683\pi$
$72$		0			0
$73$	7.28971	+	7.28971i	0.853196	+	0.853196i	0.990525	−	0.137330i	$-0.0438520\pi$
$73$	7.28971	+	7.28971i	0.853196	+	0.853196i	−0.137330	+	0.990525i	$0.543852\pi$
$74$	−2.89791	+	0.145632i	−0.336875	+	0.0169293i
$75$		0			0
$76$	−4.22319	−	7.85847i	−0.484433	−	0.901428i
$77$	21.9395	+	9.08764i	2.50024	+	1.03563i
$78$		0			0
$79$		−	1.36436i		−	0.153503i	−0.997050	−	0.0767515i	$-0.975545\pi$
$79$		−	1.36436i		−	0.153503i	0.997050	−	0.0767515i	$-0.0244548\pi$
$80$	−0.117642	−	0.174361i	−0.0131528	−	0.0194942i
$81$		0			0
$82$	3.16489	+	6.67217i	0.349503	+	0.736818i
$83$	−2.99666	−	1.24126i	−0.328926	−	0.136246i	0.212108	−	0.977246i	$-0.431967\pi$
$83$	−2.99666	−	1.24126i	−0.328926	−	0.136246i	−0.541034	+	0.841001i	$0.681967\pi$
$84$		0			0
$85$	−0.0841399	−	0.203132i	−0.00912626	−	0.0220327i
$86$	−0.747925	−	14.8829i	−0.0806509	−	1.60486i
$87$		0			0
$88$	10.0344	−	13.6257i	1.06967	−	1.45250i
$89$	−1.78145	+	1.78145i	−0.188833	+	0.188833i	−0.795192	−	0.606358i	$-0.792630\pi$
$89$	−1.78145	+	1.78145i	−0.188833	+	0.188833i	0.606358	+	0.795192i	$0.292630\pi$
$90$		0			0
$91$	18.7316	−	7.75887i	1.96360	−	0.813351i
$92$	−0.565047	−	5.60770i	−0.0589102	−	0.584643i
$93$		0			0
$94$	1.16703	−	3.27324i	0.120370	−	0.337609i
$95$	0.234562			0.0240655
$96$		0			0
$97$	−6.21324			−0.630859			−0.315430	−	0.948949i	$-0.602149\pi$
$97$	−6.21324			−0.630859			−0.315430	+	0.948949i	$0.602149\pi$
$98$	−4.15806	+	11.6623i	−0.420027	+	1.17807i
$99$		0			0
$100$	−9.94412	+	1.00200i	−0.994412	+	0.100200i
$101$	9.24401	−	3.82899i	0.919813	−	0.380999i	0.128008	−	0.991773i	$-0.459142\pi$
$101$	9.24401	−	3.82899i	0.919813	−	0.380999i	0.791805	+	0.610774i	$0.209142\pi$
$102$		0			0
$103$	7.67286	−	7.67286i	0.756030	−	0.756030i	−0.219568	−	0.975597i	$-0.570465\pi$
$103$	7.67286	−	7.67286i	0.756030	−	0.756030i	0.975597	+	0.219568i	$0.0704647\pi$
$104$	−2.16810	−	14.2840i	−0.212600	−	1.40066i
$105$		0			0
$106$	−0.663353	−	13.2000i	−0.0644305	−	1.28209i
$107$	−2.32541	−	5.61404i	−0.224806	−	0.542729i	0.770725	−	0.637168i	$-0.219894\pi$
$107$	−2.32541	−	5.61404i	−0.224806	−	0.542729i	−0.995531	+	0.0944388i	$0.969894\pi$
$108$		0			0
$109$	−17.3932	−	7.20452i	−1.66597	−	0.690068i	−0.667461	−	0.744645i	$-0.732619\pi$
$109$	−17.3932	−	7.20452i	−1.66597	−	0.690068i	−0.998510	+	0.0545770i	$0.982619\pi$
$110$	0.190676	+	0.401981i	0.0181803	+	0.0383274i
$111$		0			0
$112$	13.2408	+	8.76133i	1.25114	+	0.827868i
$113$			2.85891i			0.268944i	0.990917	+	0.134472i	$0.0429338\pi$
$113$			2.85891i			0.268944i	−0.990917	+	0.134472i	$0.957066\pi$
$114$		0			0
$115$	0.136905	+	0.0567079i	0.0127664	+	0.00528804i
$116$	11.5244	−	6.19328i	1.07001	−	0.575032i
$117$		0			0
$118$	−19.4424	+	0.977061i	−1.78982	+	0.0899457i
$119$	11.7355	+	11.7355i	1.07579	+	1.07579i
$120$		0			0
$121$	−17.5317	+	17.5317i	−1.59379	+	1.59379i
$122$	9.86998	−	10.9145i	0.893586	−	0.988151i
$123$		0			0
$124$	3.50211	+	2.86095i	0.314499	+	0.256921i
$125$	0.201176	−	0.485681i	0.0179937	−	0.0434406i
$126$		0			0
$127$	7.92497			0.703227			0.351613	−	0.936145i	$-0.385633\pi$
$127$	7.92497			0.703227			0.351613	+	0.936145i	$0.385633\pi$
$128$	8.32284	−	7.66357i	0.735642	−	0.677371i
$129$		0			0
$130$	0.357796	+	0.127568i	0.0313808	+	0.0111884i
$131$	4.50028	−	10.8646i	0.393191	−	0.949247i	−0.596050	−	0.802948i	$-0.703264\pi$
$131$	4.50028	−	10.8646i	0.393191	−	0.949247i	0.989240	−	0.146299i	$-0.0467362\pi$
$132$		0			0
$133$	−16.3578	+	6.77564i	−1.41840	+	0.587522i
$134$	−11.1264	+	12.3039i	−0.961175	+	1.06289i
$135$		0			0
$136$	10.1233	−	6.11416i	0.868062	−	0.524285i
$137$	−0.629832	−	0.629832i	−0.0538101	−	0.0538101i	0.679690	−	0.733500i	$-0.262114\pi$
$137$	−0.629832	−	0.629832i	−0.0538101	−	0.0538101i	−0.733500	+	0.679690i	$0.762114\pi$
$138$		0			0
$139$	−3.28703	−	7.93560i	−0.278803	−	0.673089i	0.721000	−	0.692935i	$-0.243683\pi$
$139$	−3.28703	−	7.93560i	−0.278803	−	0.673089i	−0.999803	+	0.0198456i	$0.993683\pi$
$140$	−0.367706	+	0.197608i	−0.0310768	+	0.0167009i
$141$		0			0
$142$	−6.86714	+	3.25737i	−0.576277	+	0.273352i
$143$			30.5599i			2.55555i
$144$		0			0
$145$			0.343983i			0.0285663i
$146$	−6.24832	−	13.1726i	−0.517115	−	1.09017i
$147$		0			0
$148$	3.92941	+	1.18233i	0.322995	+	0.0971868i
$149$	−1.00854	−	2.43484i	−0.0826232	−	0.199470i	0.877169	−	0.480182i	$-0.159429\pi$
$149$	−1.00854	−	2.43484i	−0.0826232	−	0.199470i	−0.959792	+	0.280712i	$0.909429\pi$
$150$		0			0
$151$	−9.67691	−	9.67691i	−0.787495	−	0.787495i	0.193588	−	0.981083i	$-0.437988\pi$
$151$	−9.67691	−	9.67691i	−0.787495	−	0.787495i	−0.981083	+	0.193588i	$0.937988\pi$
$152$	1.89335	+	12.4739i	0.153571	+	1.01176i
$153$		0			0
$154$	−24.9091	−	22.5253i	−2.00723	−	1.81514i
$155$	−0.109846	+	0.0454998i	−0.00882307	+	0.00365464i
$156$		0			0
$157$	−0.0532439	+	0.128542i	−0.00424932	+	0.0102588i	−0.925990	−	0.377548i	$-0.876767\pi$
$157$	−0.0532439	+	0.128542i	−0.00424932	+	0.0102588i	0.921741	+	0.387807i	$0.126767\pi$
$158$	−0.647987	+	1.81744i	−0.0515511	+	0.144588i
$159$		0			0
$160$	0.0738984	+	0.288136i	0.00584218	+	0.0227791i
$161$	−11.1855			−0.881544
$162$		0			0
$163$	6.78948	−	16.3912i	0.531793	−	1.28386i	−0.398542	−	0.917150i	$-0.630484\pi$
$163$	6.78948	−	16.3912i	0.531793	−	1.28386i	0.930335	−	0.366711i	$-0.119516\pi$
$164$	−1.04702	−	10.3910i	−0.0817588	−	0.811399i
$165$		0			0
$166$	3.40227	+	3.07668i	0.264067	+	0.238796i
$167$	−12.9956	+	12.9956i	−1.00563	+	1.00563i	−0.00564470	+	0.999984i	$0.501797\pi$
$167$	−12.9956	+	12.9956i	−1.00563	+	1.00563i	−0.999984	+	0.00564470i	$0.998203\pi$
$168$		0			0
$169$	9.25712	+	9.25712i	0.712086	+	0.712086i
$170$	0.0156064	+	0.310549i	0.00119695	+	0.0238180i
$171$		0			0
$172$	−6.07212	+	20.1804i	−0.462995	+	1.53874i
$173$	−9.99157	−	4.13865i	−0.759645	−	0.314655i	−0.0309751	−	0.999520i	$-0.509861\pi$
$173$	−9.99157	−	4.13865i	−0.759645	−	0.314655i	−0.728670	+	0.684865i	$0.759861\pi$
$174$		0			0
$175$			19.8353i			1.49941i
$176$	−19.8380	+	13.3848i	−1.49534	+	1.00891i
$177$		0			0
$178$	3.21911	−	1.52696i	0.241282	−	0.114450i
$179$	15.3225	+	6.34679i	1.14526	+	0.474382i	0.872941	−	0.487826i	$-0.162210\pi$
$179$	15.3225	+	6.34679i	1.14526	+	0.474382i	0.272318	+	0.962207i	$0.412210\pi$
$180$		0			0
$181$	2.98250	+	7.20039i	0.221687	+	0.535201i	0.995119	−	0.0986787i	$-0.0314616\pi$
$181$	2.98250	+	7.20039i	0.221687	+	0.535201i	−0.773432	+	0.633879i	$0.781462\pi$
$182$	−28.6369	+	1.43912i	−2.12271	+	0.106675i
$183$		0			0
$184$	−1.91061	+	7.73826i	−0.140852	+	0.570472i
$185$	−0.0762883	+	0.0762883i	−0.00560882	+	0.00560882i
$186$		0			0
$187$	−23.1113	+	9.57302i	−1.69007	+	0.700049i
$188$	−3.10917	+	3.80595i	−0.226759	+	0.277578i
$189$		0			0
$190$	−0.312455	−	0.111402i	−0.0226679	−	0.00808195i
$191$	4.44009			0.321273			0.160637	−	0.987014i	$-0.448645\pi$
$191$	4.44009			0.321273			0.160637	+	0.987014i	$0.448645\pi$
$192$		0			0
$193$	−15.4177			−1.10979			−0.554895	−	0.831920i	$-0.687242\pi$
$193$	−15.4177			−1.10979			−0.554895	+	0.831920i	$0.687242\pi$
$194$	8.27653	+	2.95090i	0.594220	+	0.211862i
$195$		0			0
$196$	11.0777	−	13.5603i	0.791267	−	0.968595i
$197$	2.42754	−	1.00552i	0.172955	−	0.0716403i	−0.294526	−	0.955644i	$-0.595162\pi$
$197$	2.42754	−	1.00552i	0.172955	−	0.0716403i	0.467481	+	0.884003i	$0.345162\pi$
$198$		0			0
$199$	−0.410226	+	0.410226i	−0.0290801	+	0.0290801i	−0.721497	−	0.692417i	$-0.756546\pi$
$199$	−0.410226	+	0.410226i	−0.0290801	+	0.0290801i	0.692417	+	0.721497i	$0.256546\pi$
$200$	13.7222	+	3.38809i	0.970309	+	0.239574i
$201$		0			0
$202$	−14.1323	+	0.710205i	−0.994343	+	0.0499699i
$203$	−9.93643	−	23.9887i	−0.697401	−	1.68367i
$204$		0			0
$205$	0.253683	+	0.105079i	0.0177180	+	0.00733903i
$206$	−13.8650	+	6.57674i	−0.966019	+	0.458223i
$207$		0			0
$208$	−3.89590	+	20.0571i	−0.270132	+	1.39071i
$209$		−	26.6873i		−	1.84600i
$210$		0			0
$211$	7.05228	+	2.92115i	0.485499	+	0.201100i	0.611987	−	0.790868i	$-0.290370\pi$
$211$	7.05228	+	2.92115i	0.485499	+	0.201100i	−0.126488	+	0.991968i	$0.540370\pi$
$212$	−5.38551	+	17.8985i	−0.369878	+	1.22927i
$213$		0			0
$214$	0.431319	+	8.58276i	0.0294844	+	0.586706i
$215$	−0.391796	−	0.391796i	−0.0267203	−	0.0267203i
$216$		0			0
$217$	6.34612	−	6.34612i	0.430803	−	0.430803i
$218$	19.7475	+	17.8577i	1.33747	+	1.20947i
$219$		0			0
$220$	−0.0630804	−	0.626029i	−0.00425288	−	0.0422069i
$221$	−8.17328	+	19.7320i	−0.549794	+	1.32732i
$222$		0			0
$223$	−1.74336			−0.116744			−0.0583719	−	0.998295i	$-0.518591\pi$
$223$	−1.74336			−0.116744			−0.0583719	+	0.998295i	$0.518591\pi$
$224$	−13.4767	−	17.9593i	−0.900451	−	1.19996i
$225$		0			0
$226$	1.35780	−	3.80830i	0.0903197	−	0.253324i
$227$	5.12115	−	12.3635i	0.339903	−	0.820597i	−0.657822	−	0.753174i	$-0.728522\pi$
$227$	5.12115	−	12.3635i	0.339903	−	0.820597i	0.997724	−	0.0674239i	$-0.0214780\pi$
$228$		0			0
$229$	−6.88194	+	2.85059i	−0.454772	+	0.188373i	−0.598298	−	0.801274i	$-0.704156\pi$
$229$	−6.88194	+	2.85059i	−0.454772	+	0.188373i	0.143526	+	0.989647i	$0.454156\pi$
$230$	−0.155436	−	0.140561i	−0.0102491	−	0.00926829i
$231$		0			0
$232$	−18.2928	+	2.77658i	−1.20098	+	0.182292i
$233$	−9.40289	−	9.40289i	−0.616004	−	0.616004i	0.328500	−	0.944504i	$-0.393457\pi$
$233$	−9.40289	−	9.40289i	−0.616004	−	0.616004i	−0.944504	+	0.328500i	$0.893457\pi$
$234$		0			0
$235$	−0.0494474	−	0.119377i	−0.00322559	−	0.00778727i
$236$	26.3629	+	7.93238i	1.71608	+	0.516354i
$237$		0			0
$238$	−10.0590	−	21.2062i	−0.652027	−	1.37459i
$239$		−	21.0800i		−	1.36355i	−0.731561	−	0.681776i	$-0.761208\pi$
$239$		−	21.0800i		−	1.36355i	0.731561	−	0.681776i	$-0.238792\pi$
$240$		0			0
$241$		−	3.42263i		−	0.220471i	−0.993906	−	0.110235i	$-0.964840\pi$
$241$		−	3.42263i		−	0.220471i	0.993906	−	0.110235i	$-0.0351605\pi$
$242$	31.6801	−	15.0272i	2.03647	−	0.965983i
$243$		0			0
$244$	−18.3313	+	9.85135i	−1.17354	+	0.630668i
$245$	0.176178	+	0.425330i	0.0112556	+	0.0271733i
$246$		0			0
$247$	−16.1115	−	16.1115i	−1.02515	−	1.02515i
$248$	−3.30632	−	5.47429i	−0.209951	−	0.347618i
$249$		0			0
$250$	−0.498649	+	0.551420i	−0.0315374	+	0.0348748i
$251$	−12.1915	+	5.04988i	−0.769520	+	0.318745i	−0.732678	−	0.680576i	$-0.761730\pi$
$251$	−12.1915	+	5.04988i	−0.769520	+	0.318745i	−0.0368417	+	0.999321i	$0.511730\pi$
$252$		0			0
$253$	6.45194	−	15.5764i	0.405630	−	0.979277i
$254$	−10.5567	−	3.76386i	−0.662385	−	0.236165i
$255$		0			0
$256$	−14.7264	+	6.25567i	−0.920400	+	0.390979i
$257$	5.55370			0.346430			0.173215	−	0.984884i	$-0.444584\pi$
$257$	5.55370			0.346430			0.173215	+	0.984884i	$0.444584\pi$
$258$		0			0
$259$	3.11649	−	7.52387i	0.193649	−	0.467511i
$260$	−0.416026	−	0.339861i	−0.0258008	−	0.0210773i
$261$		0			0
$262$	−11.1547	+	12.3352i	−0.689142	+	0.762071i
$263$	−18.0322	+	18.0322i	−1.11191	+	1.11191i	−0.119022	+	0.992892i	$0.537976\pi$
$263$	−18.0322	+	18.0322i	−1.11191	+	1.11191i	−0.992892	+	0.119022i	$0.962024\pi$
$264$		0			0
$265$	−0.347493	−	0.347493i	−0.0213463	−	0.0213463i
$266$	25.0079	−	1.25675i	1.53334	−	0.0770564i
$267$		0			0
$268$	20.6648	−	11.1054i	1.26230	−	0.678370i
$269$	−2.75859	−	1.14264i	−0.168194	−	0.0696683i	0.296998	−	0.954878i	$-0.404015\pi$
$269$	−2.75859	−	1.14264i	−0.168194	−	0.0696683i	−0.465192	+	0.885210i	$0.654015\pi$
$270$		0			0
$271$		−	16.2421i		−	0.986636i	−0.869849	−	0.493318i	$-0.835784\pi$
$271$		−	16.2421i		−	0.986636i	0.869849	−	0.493318i	$-0.164216\pi$
$272$	−16.3888	+	3.33664i	−0.993718	+	0.202314i
$273$		0			0
$274$	0.539856	+	1.13812i	0.0326139	+	0.0687561i
$275$	−27.6215	−	11.4412i	−1.66564	−	0.689931i
$276$		0			0
$277$	−0.361093	−	0.871755i	−0.0216960	−	0.0523787i	0.912660	−	0.408719i	$-0.134024\pi$
$277$	−0.361093	−	0.871755i	−0.0216960	−	0.0523787i	−0.934356	+	0.356340i	$0.884024\pi$
$278$	0.609682	+	12.1320i	0.0365663	+	0.727628i
$279$		0			0
$280$	0.583665	−	0.0885918i	0.0348806	−	0.00529438i
$281$	−14.5533	+	14.5533i	−0.868179	+	0.868179i	−0.992271	−	0.124092i	$-0.960398\pi$
$281$	−14.5533	+	14.5533i	−0.868179	+	0.868179i	0.124092	+	0.992271i	$0.460398\pi$
$282$		0			0
$283$	−26.6401	+	11.0347i	−1.58359	+	0.655945i	−0.988977	−	0.148066i	$-0.952695\pi$
$283$	−26.6401	+	11.0347i	−1.58359	+	0.655945i	−0.594614	+	0.804011i	$0.702695\pi$
$284$	10.6946	−	1.07762i	0.634609	−	0.0639449i
$285$		0			0
$286$	14.5140	−	40.7083i	0.858233	−	2.40713i
$287$	−20.7266			−1.22345
$288$		0			0
$289$	−0.482909			−0.0284064
$290$	0.163370	−	0.458213i	0.00959343	−	0.0269072i
$291$		0			0
$292$	2.06710	+	20.5145i	0.120968	+	1.20052i
$293$	8.14677	−	3.37450i	0.475939	−	0.197140i	−0.131801	−	0.991276i	$-0.542076\pi$
$293$	8.14677	−	3.37450i	0.475939	−	0.197140i	0.607741	+	0.794136i	$0.292076\pi$
$294$		0			0
$295$	−0.511827	+	0.511827i	−0.0297997	+	0.0297997i
$296$	−4.67275	−	3.44117i	−0.271598	−	0.200014i
$297$		0			0
$298$	0.187066	+	3.72240i	0.0108364	+	0.215633i
$299$	−5.50855	−	13.2988i	−0.318568	−	0.769091i
$300$		0			0
$301$	38.6406	+	16.0054i	2.22721	+	0.922539i
$302$	8.29449	+	17.4863i	0.477294	+	1.00622i
$303$		0			0
$304$	3.40220	−	17.5154i	0.195129	−	1.00458i
$305$		−	0.547157i		−	0.0313301i
$306$		0			0
$307$	18.5753	+	7.69414i	1.06015	+	0.439128i	0.843504	−	0.537123i	$-0.180489\pi$
$307$	18.5753	+	7.69414i	1.06015	+	0.439128i	0.216645	+	0.976251i	$0.430489\pi$
$308$	22.4828	+	41.8358i	1.28108	+	2.38381i
$309$		0			0
$310$	0.167934	−	0.00843936i	0.00953799	−	0.000479323i
$311$	2.59213	+	2.59213i	0.146986	+	0.146986i	0.776770	−	0.629784i	$-0.216857\pi$
$311$	2.59213	+	2.59213i	0.146986	+	0.146986i	−0.629784	+	0.776770i	$0.716857\pi$
$312$		0			0
$313$	−9.51094	+	9.51094i	−0.537590	+	0.537590i	−0.922820	−	0.385230i	$-0.874122\pi$
$313$	−9.51094	+	9.51094i	−0.537590	+	0.537590i	0.385230	+	0.922820i	$0.374122\pi$
$314$	0.131974	−	0.145941i	0.00744774	−	0.00823591i
$315$		0			0
$316$	1.72634	−	2.11322i	0.0971142	−	0.118878i
$317$	−8.88248	+	21.4442i	−0.498890	+	1.20443i	0.451193	+	0.892427i	$0.350999\pi$
$317$	−8.88248	+	21.4442i	−0.498890	+	1.20443i	−0.950082	+	0.312000i	$0.899001\pi$
$318$		0			0
$319$	39.1367			2.19123
$320$	0.0384077	−	0.418917i	0.00214706	−	0.0234182i
$321$		0			0
$322$	14.9000	+	5.31242i	0.830346	+	0.296050i
$323$	7.13753	−	17.2315i	0.397143	−	0.958788i
$324$		0			0
$325$	−23.5828	+	9.76831i	−1.30814	+	0.541848i
$326$	−16.8289	+	18.6099i	−0.932068	+	1.03071i
$327$		0			0
$328$	−3.54034	+	14.3389i	−0.195482	+	0.791732i
$329$	6.89671	+	6.89671i	0.380228	+	0.380228i
$330$		0			0
$331$	−3.19371	−	7.71029i	−0.175542	−	0.423796i	0.811480	−	0.584380i	$-0.198662\pi$
$331$	−3.19371	−	7.71029i	−0.175542	−	0.423796i	−0.987022	+	0.160584i	$0.948662\pi$
$332$	−3.07087	−	5.71424i	−0.168536	−	0.313610i
$333$		0			0
$334$	23.4832	−	11.1391i	1.28495	−	0.609503i
$335$			0.616809i			0.0336999i
$336$		0			0
$337$		−	15.1011i		−	0.822608i	−0.911498	−	0.411304i	$-0.865073\pi$
$337$		−	15.1011i		−	0.822608i	0.911498	−	0.411304i	$-0.134927\pi$
$338$	−7.93467	−	16.7278i	−0.431589	−	0.909870i
$339$		0			0
$340$	0.126702	−	0.421088i	0.00687138	−	0.0228367i
$341$	5.17675	+	12.4978i	0.280336	+	0.676792i
$342$		0			0
$343$	−4.92568	−	4.92568i	−0.265962	−	0.265962i
$344$	17.6729	−	23.9980i	0.952861	−	1.29388i
$345$		0			0
$346$	11.3440	+	10.2584i	0.609856	+	0.551493i
$347$	−3.62863	+	1.50303i	−0.194795	+	0.0806867i	−0.477948	−	0.878388i	$-0.658619\pi$
$347$	−3.62863	+	1.50303i	−0.194795	+	0.0806867i	0.283153	+	0.959075i	$0.408619\pi$
$348$		0			0
$349$	2.26230	−	5.46167i	0.121098	−	0.292357i	−0.851693	−	0.524041i	$-0.824424\pi$
$349$	2.26230	−	5.46167i	0.121098	−	0.292357i	0.972791	+	0.231685i	$0.0744237\pi$
$350$	9.42051	−	26.4222i	0.503547	−	1.41233i
$351$		0			0
$352$	32.7827	−	8.40779i	1.74732	−	0.448137i
$353$	−34.3406			−1.82777			−0.913884	−	0.405976i	$-0.866932\pi$
$353$	−34.3406			−1.82777			−0.913884	+	0.405976i	$0.866932\pi$
$354$		0			0
$355$	−0.108149	+	0.261096i	−0.00573997	+	0.0138575i
$356$	−5.01331	+	0.505155i	−0.265705	+	0.0267732i
$357$		0			0
$358$	−17.3965	−	15.7317i	−0.919433	−	0.831444i
$359$	−1.72212	+	1.72212i	−0.0908902	+	0.0908902i	−0.751090	−	0.660200i	$-0.770472\pi$
$359$	−1.72212	+	1.72212i	−0.0908902	+	0.0908902i	0.660200	+	0.751090i	$0.270472\pi$
$360$		0			0
$361$	0.634789	+	0.634789i	0.0334099	+	0.0334099i
$362$	−0.553197	−	11.0080i	−0.0290754	−	0.578567i
$363$		0			0
$364$	38.8301	+	11.6837i	2.03525	+	0.612392i
$365$	−0.500837	−	0.207453i	−0.0262150	−	0.0108586i
$366$		0			0
$367$			20.8557i			1.08866i	0.838872	+	0.544329i	$0.183216\pi$
$367$			20.8557i			1.08866i	−0.838872	+	0.544329i	$0.816784\pi$
$368$	6.22027	−	9.40055i	0.324254	−	0.490038i
$369$		0			0
$370$	0.137854	−	0.0653899i	0.00716669	−	0.00339946i
$371$	34.2713	+	14.1956i	1.77927	+	0.737000i
$372$		0			0
$373$	2.52776	+	6.10255i	0.130882	+	0.315978i	0.975712	−	0.219057i	$-0.0702982\pi$
$373$	2.52776	+	6.10255i	0.130882	+	0.315978i	−0.844830	+	0.535036i	$0.820298\pi$
$374$	35.3327	−	1.77561i	1.82701	−	0.0918148i
$375$		0			0
$376$	5.94924	−	3.59317i	0.306809	−	0.185304i
$377$	23.6274	−	23.6274i	1.21687	−	1.21687i
$378$		0			0
$379$	−12.1682	+	5.04024i	−0.625039	+	0.258900i	−0.672644	−	0.739967i	$-0.734841\pi$
$379$	−12.1682	+	5.04024i	−0.625039	+	0.258900i	0.0476045	+	0.998866i	$0.484841\pi$
$380$	0.363306	+	0.296793i	0.0186372	+	0.0152251i
$381$		0			0
$382$	−5.91455	−	2.10876i	−0.302615	−	0.107894i
$383$	10.5665			0.539923			0.269961	−	0.962871i	$-0.412989\pi$
$383$	10.5665			0.539923			0.269961	+	0.962871i	$0.412989\pi$
$384$		0			0
$385$	−1.24873			−0.0636410
$386$	20.5376	+	7.32243i	1.04534	+	0.372702i
$387$		0			0
$388$	−9.62351	−	7.86165i	−0.488560	−	0.399115i
$389$	14.8004	−	6.13051i	0.750409	−	0.310829i	0.0255003	−	0.999675i	$-0.491882\pi$
$389$	14.8004	−	6.13051i	0.750409	−	0.310829i	0.724908	+	0.688845i	$0.241882\pi$
$390$		0			0
$391$	8.33182	−	8.33182i	0.421358	−	0.421358i
$392$	−21.1967	+	12.8022i	−1.07060	+	0.646609i
$393$		0			0
$394$	−3.71123	+	0.186505i	−0.186969	+	0.00939597i
$395$	0.0274553	+	0.0662829i	0.00138142	+	0.00333505i
$396$		0			0
$397$	31.4137	+	13.0120i	1.57661	+	0.653053i	0.987872	−	0.155271i	$-0.0496251\pi$
$397$	31.4137	+	13.0120i	1.57661	+	0.653053i	0.588738	+	0.808324i	$0.299625\pi$
$398$	0.741285	−	0.351622i	0.0371572	−	0.0176252i
$399$		0			0
$400$	−16.6700	−	11.0304i	−0.833499	−	0.551519i
$401$			0.410506i			0.0204997i	0.999947	+	0.0102498i	$0.00326269\pi$
$401$			0.410506i			0.0204997i	−0.999947	+	0.0102498i	$0.996737\pi$
$402$		0			0
$403$	10.6704	+	4.41982i	0.531529	+	0.220167i
$404$	19.1626	+	5.76589i	0.953376	+	0.286864i
$405$		0			0
$406$	1.84302	+	36.6740i	0.0914675	+	1.82010i
$407$	8.67970	+	8.67970i	0.430237	+	0.430237i
$408$		0			0
$409$	12.2157	−	12.2157i	0.604027	−	0.604027i	−0.337352	−	0.941379i	$-0.609531\pi$
$409$	12.2157	−	12.2157i	0.604027	−	0.604027i	0.941379	+	0.337352i	$0.109531\pi$
$410$	−0.288020	−	0.260457i	−0.0142243	−	0.0128630i
$411$		0			0
$412$	21.5928	−	2.17575i	1.06380	−	0.107191i
$413$	20.9089	−	50.4785i	1.02886	−	2.48389i
$414$		0			0
$415$	0.170560			0.00837247
$416$	14.7155	−	24.8673i	0.721486	−	1.21922i
$417$		0			0
$418$	−12.6748	+	35.5496i	−0.619943	+	1.73879i
$419$	−2.05388	+	4.95851i	−0.100339	+	0.242239i	−0.966075	−	0.258261i	$-0.916850\pi$
$419$	−2.05388	+	4.95851i	−0.100339	+	0.242239i	0.865737	+	0.500500i	$0.166850\pi$
$420$		0			0
$421$	−26.5615	+	11.0021i	−1.29453	+	0.536212i	−0.920332	−	0.391137i	$-0.872082\pi$
$421$	−26.5615	+	11.0021i	−1.29453	+	0.536212i	−0.374197	+	0.927349i	$0.622082\pi$
$422$	−8.00684	−	7.24059i	−0.389767	−	0.352466i
$423$		0			0
$424$	15.6746	−	21.2844i	0.761224	−	1.03366i
$425$	−14.7748	−	14.7748i	−0.716683	−	0.716683i
$426$		0			0
$427$	15.8054	+	38.1576i	0.764876	+	1.84657i
$428$	3.50172	−	11.6378i	0.169262	−	0.562533i
$429$		0			0
$430$	0.335825	+	0.707981i	0.0161949	+	0.0341419i
$431$			6.38142i			0.307382i	0.988119	+	0.153691i	$0.0491161\pi$
$431$			6.38142i			0.307382i	−0.988119	+	0.153691i	$0.950884\pi$
$432$		0			0
$433$			9.48039i			0.455599i	0.973708	+	0.227799i	$0.0731530\pi$
$433$			9.48039i			0.455599i	−0.973708	+	0.227799i	$0.926847\pi$
$434$	−11.4675	+	5.43953i	−0.550460	+	0.261106i
$435$		0			0
$436$	−17.8240	−	33.1666i	−0.853613	−	1.58839i
$437$	4.81049	+	11.6136i	0.230117	+	0.555552i
$438$		0			0
$439$	−0.0508675	−	0.0508675i	−0.00242777	−	0.00242777i	0.705892	−	0.708320i	$-0.250546\pi$
$439$	−0.0508675	−	0.0508675i	−0.00242777	−	0.00242777i	−0.708320	+	0.705892i	$0.750546\pi$
$440$	−0.213296	+	0.863880i	−0.0101685	+	0.0411838i
$441$		0			0
$442$	20.2589	−	22.4029i	0.963619	−	1.06560i
$443$	7.02822	−	2.91118i	0.333921	−	0.138315i	−0.209422	−	0.977825i	$-0.567158\pi$
$443$	7.02822	−	2.91118i	0.333921	−	0.138315i	0.543343	+	0.839511i	$0.317158\pi$
$444$		0			0
$445$	0.0506972	−	0.122394i	0.00240328	−	0.00580202i
$446$	2.32229	+	0.827983i	0.109963	+	0.0392061i
$447$		0			0
$448$	9.42252	+	30.3238i	0.445172	+	1.43267i
$449$	−38.5353			−1.81859			−0.909296	−	0.416150i	$-0.863379\pi$
$449$	−38.5353			−1.81859			−0.909296	+	0.416150i	$0.863379\pi$
$450$		0			0
$451$	11.9553	−	28.8628i	0.562955	−	1.35909i
$452$	−3.61740	+	4.42809i	−0.170148	+	0.208280i
$453$		0			0
$454$	−12.6937	+	14.0370i	−0.595744	+	0.658789i
$455$	−0.753875	+	0.753875i	−0.0353422	+	0.0353422i
$456$		0			0
$457$	−5.04973	−	5.04973i	−0.236216	−	0.236216i	0.579065	−	0.815281i	$-0.303418\pi$
$457$	−5.04973	−	5.04973i	−0.236216	−	0.236216i	−0.815281	+	0.579065i	$0.803418\pi$
$458$	10.5211	−	0.528731i	0.491621	−	0.0247060i
$459$		0			0
$460$	0.140295	+	0.261060i	0.00654130	+	0.0121720i
$461$	16.6478	+	6.89576i	0.775368	+	0.321168i	0.735044	−	0.678019i	$-0.237161\pi$
$461$	16.6478	+	6.89576i	0.775368	+	0.321168i	0.0403231	+	0.999187i	$0.487161\pi$
$462$		0			0
$463$		−	39.1312i		−	1.81858i	−0.416160	−	0.909291i	$-0.636624\pi$
$463$		−	39.1312i		−	1.81858i	0.416160	−	0.909291i	$-0.363376\pi$
$464$	25.6862	+	4.98930i	1.19245	+	0.231622i
$465$		0			0
$466$	8.05962	+	16.9912i	0.373355	+	0.787101i
$467$	−34.7355	−	14.3879i	−1.60737	−	0.665794i	−0.614935	−	0.788578i	$-0.710818\pi$
$467$	−34.7355	−	14.3879i	−1.60737	−	0.665794i	−0.992433	+	0.122784i	$0.960818\pi$
$468$		0			0
$469$	−17.8174	−	43.0149i	−0.822730	−	1.98625i
$470$	0.00917155	+	0.182503i	0.000423052	+	0.00841826i
$471$		0			0
$472$	−31.3500	−	23.0873i	−1.44300	−	1.06268i
$473$	−44.5766	+	44.5766i	−2.04963	+	2.04963i
$474$		0			0
$475$	20.5943	−	8.53043i	0.944931	−	0.391403i
$476$	3.32776	+	33.0257i	0.152528	+	1.51373i
$477$		0			0
$478$	−10.0117	+	28.0802i	−0.457923	+	1.28436i
$479$	−21.8802			−0.999732			−0.499866	−	0.866103i	$-0.666617\pi$
$479$	−21.8802			−0.999732			−0.499866	+	0.866103i	$0.666617\pi$
$480$		0			0
$481$	10.4801			0.477853
$482$	−1.62553	+	4.55921i	−0.0740409	+	0.207666i
$483$		0			0
$484$	−49.3373	+	4.97136i	−2.24260	+	0.225971i
$485$	0.301849	−	0.125030i	0.0137062	−	0.00567731i
$486$		0			0
$487$	−26.5283	+	26.5283i	−1.20211	+	1.20211i	−0.228588	+	0.973523i	$0.573411\pi$
$487$	−26.5283	+	26.5283i	−1.20211	+	1.20211i	−0.973523	+	0.228588i	$0.926589\pi$
$488$	29.0975	−	4.41658i	1.31718	−	0.199929i
$489$		0			0
$490$	−0.0326776	−	0.650247i	−0.00147622	−	0.0293751i
$491$	4.60332	+	11.1134i	0.207745	+	0.501540i	0.993067	−	0.117547i	$-0.0375029\pi$
$491$	4.60332	+	11.1134i	0.207745	+	0.501540i	−0.785323	+	0.619087i	$0.787503\pi$
$492$		0			0
$493$	25.2699	+	10.4671i	1.13810	+	0.471416i
$494$	13.8099	+	29.1138i	0.621336	+	1.30989i
$495$		0			0
$496$	1.80434	+	8.86248i	0.0810171	+	0.397937i
$497$		−	21.3323i		−	0.956884i
$498$		0			0
$499$	0.520275	+	0.215505i	0.0232907	+	0.00964733i	0.394298	−	0.918982i	$-0.370988\pi$
$499$	0.520275	+	0.215505i	0.0232907	+	0.00964733i	−0.371008	+	0.928630i	$0.620988\pi$
$500$	0.926130	−	0.497708i	0.0414178	−	0.0222582i
$501$		0			0
$502$	18.6384	−	0.936656i	0.831872	−	0.0418050i
$503$	−13.2340	−	13.2340i	−0.590074	−	0.590074i	0.347577	−	0.937651i	$-0.387004\pi$
$503$	−13.2340	−	13.2340i	−0.590074	−	0.590074i	−0.937651	+	0.347577i	$0.887004\pi$
$504$		0			0
$505$	−0.372036	+	0.372036i	−0.0165554	+	0.0165554i
$506$	−15.9923	+	17.6847i	−0.710943	+	0.786180i
$507$		0			0
$508$	12.2747	+	10.0275i	0.544604	+	0.444899i
$509$	7.62872	−	18.4174i	0.338137	−	0.816335i	−0.659757	−	0.751479i	$-0.729341\pi$
$509$	7.62872	−	18.4174i	0.338137	−	0.816335i	0.997895	−	0.0648568i	$-0.0206591\pi$
$510$		0			0
$511$	40.9198			1.81019
$512$	22.5878	−	1.33894i	0.998248	−	0.0591733i
$513$		0			0
$514$	−7.39797	−	2.63766i	−0.326311	−	0.116342i
$515$	−0.218357	+	0.527161i	−0.00962197	+	0.0232295i
$516$		0			0
$517$	−13.5821	+	5.62588i	−0.597339	+	0.247426i
$518$	−7.72477	+	8.54226i	−0.339407	+	0.375325i
$519$		0			0
$520$	0.392767	+	0.650308i	0.0172240	+	0.0285179i
$521$	−22.8313	−	22.8313i	−1.00026	−	1.00026i	−1.00000		0.000258583i	$-0.999918\pi$
$521$	−22.8313	−	22.8313i	−1.00026	−	1.00026i	−0.000258583	−	1.00000i	$-0.500082\pi$
$522$		0			0
$523$	−3.86514	−	9.33126i	−0.169011	−	0.408028i	0.816567	−	0.577250i	$-0.195874\pi$
$523$	−3.86514	−	9.33126i	−0.169011	−	0.408028i	−0.985578	+	0.169223i	$0.945874\pi$
$524$	20.7174	−	11.1337i	0.905045	−	0.486377i
$525$		0			0
$526$	32.5845	−	15.4562i	1.42075	−	0.673921i
$527$			9.45413i			0.411828i
$528$		0			0
$529$		−	15.0586i		−	0.654723i
$530$	0.297851	+	0.627926i	0.0129378	+	0.0272754i
$531$		0			0
$532$	−33.9094	−	10.2031i	−1.47016	−	0.442360i
$533$	−10.2073	−	24.6425i	−0.442126	−	1.06739i
$534$		0			0
$535$	0.225944	+	0.225944i	0.00976840	+	0.00976840i
$536$	−32.8015	+	4.97880i	−1.41681	+	0.215051i
$537$		0			0
$538$	3.13197	+	2.83225i	0.135029	+	0.122107i
$539$	48.3919	−	20.0446i	2.08439	−	0.863382i
$540$		0			0
$541$	11.7220	−	28.2994i	0.503968	−	1.21669i	−0.443338	−	0.896355i	$-0.646206\pi$
$541$	11.7220	−	28.2994i	0.503968	−	1.21669i	0.947306	−	0.320331i	$-0.103794\pi$
$542$	−7.71396	+	21.6357i	−0.331343	+	0.929334i
$543$		0			0
$544$	23.4159	+	3.33898i	1.00395	+	0.143157i
$545$	0.989967			0.0424055
$546$		0			0
$547$	−0.0200433	+	0.0483889i	−0.000856990	+	0.00206896i	−0.924307	−	0.381649i	$-0.875356\pi$
$547$	−0.0200433	+	0.0483889i	−0.000856990	+	0.00206896i	0.923450	+	0.383718i	$0.125356\pi$
$548$	−0.178598	−	1.77246i	−0.00762931	−	0.0757156i
$549$		0			0
$550$	31.3602	+	28.3591i	1.33720	+	1.20923i
$551$	−20.6333	+	20.6333i	−0.879008	+	0.879008i
$552$		0			0
$553$	−3.82934	−	3.82934i	−0.162840	−	0.162840i
$554$	0.0669758	+	1.33274i	0.00284553	+	0.0566228i
$555$		0			0
$556$	4.94978	−	16.4503i	0.209917	−	0.697649i
$557$	19.3191	+	8.00225i	0.818578	+	0.339066i	0.752371	−	0.658740i	$-0.228910\pi$
$557$	19.3191	+	8.00225i	0.818578	+	0.339066i	0.0662072	+	0.997806i	$0.478910\pi$
$558$		0			0
$559$			53.8231i			2.27648i
$560$	−0.819563	−	0.159192i	−0.0346329	−	0.00672711i
$561$		0			0
$562$	26.2981	−	12.4743i	1.10932	−	0.526196i
$563$	−15.7975	−	6.54353i	−0.665784	−	0.275777i	0.0240861	−	0.999710i	$-0.492332\pi$
$563$	−15.7975	−	6.54353i	−0.665784	−	0.275777i	−0.689870	+	0.723933i	$0.742332\pi$
$564$		0			0
$565$	−0.0575302	−	0.138890i	−0.00242032	−	0.00584316i
$566$	40.7276	−	2.04673i	1.71191	−	0.0860304i
$567$		0			0
$568$	−14.7579	−	3.64379i	−0.619227	−	0.152890i
$569$	10.0008	−	10.0008i	0.419254	−	0.419254i	−0.465693	−	0.884946i	$-0.654195\pi$
$569$	10.0008	−	10.0008i	0.419254	−	0.419254i	0.884946	+	0.465693i	$0.154195\pi$
$570$		0			0
$571$	−18.5723	+	7.69288i	−0.777225	+	0.321937i	−0.735795	−	0.677204i	$-0.763191\pi$
$571$	−18.5723	+	7.69288i	−0.777225	+	0.321937i	−0.0414300	+	0.999141i	$0.513191\pi$
$572$	−38.6677	+	47.3334i	−1.61678	+	1.97911i
$573$		0			0
$574$	27.6095	+	9.84384i	1.15240	+	0.410874i
$575$	14.0824			0.587278
$576$		0			0
$577$	37.9925			1.58165			0.790825	−	0.612043i	$-0.209652\pi$
$577$	37.9925			1.58165			0.790825	+	0.612043i	$0.209652\pi$
$578$	0.643273	+	0.229351i	0.0267566	+	0.00953975i
$579$		0			0
$580$	−0.435244	+	0.532786i	−0.0180725	+	0.0221227i
$581$	−11.8945	+	4.92687i	−0.493467	+	0.204401i
$582$		0			0
$583$	−39.5360	+	39.5360i	−1.63742	+	1.63742i
$584$	6.98956	−	28.3087i	0.289230	−	1.17142i
$585$		0			0
$586$	−12.4548	+	0.625906i	−0.514504	+	0.0258559i
$587$	−2.13226	−	5.14773i	−0.0880078	−	0.212470i	0.873747	−	0.486380i	$-0.161683\pi$
$587$	−2.13226	−	5.14773i	−0.0880078	−	0.212470i	−0.961755	+	0.273910i	$0.911683\pi$
$588$		0			0
$589$	−9.31819	−	3.85972i	−0.383949	−	0.159037i
$590$	0.924880	−	0.438709i	0.0380767	−	0.0180614i
$591$		0			0
$592$	4.59013	+	6.80318i	0.188653	+	0.279609i
$593$			34.9255i			1.43422i	0.696961	+	0.717109i	$0.254535\pi$
$593$			34.9255i			1.43422i	−0.696961	+	0.717109i	$0.745465\pi$
$594$		0			0
$595$	−0.806282	−	0.333973i	−0.0330543	−	0.0136915i
$596$	1.51872	−	5.04737i	0.0622091	−	0.206749i
$597$		0			0
$598$	1.02173	+	20.3313i	0.0417817	+	0.831409i
$599$	−21.2589	−	21.2589i	−0.868616	−	0.868616i	0.123704	−	0.992319i	$-0.460523\pi$
$599$	−21.2589	−	21.2589i	−0.868616	−	0.868616i	−0.992319	+	0.123704i	$0.960523\pi$
$600$		0			0
$601$	−17.7928	+	17.7928i	−0.725782	+	0.725782i	−0.969777	−	0.243995i	$-0.921542\pi$
$601$	−17.7928	+	17.7928i	−0.725782	+	0.725782i	0.243995	+	0.969777i	$0.421542\pi$
$602$	−43.8707	−	39.6723i	−1.78804	−	1.61692i
$603$		0			0
$604$	−2.74402	−	27.2325i	−0.111653	−	1.10808i
$605$	0.498924	−	1.20451i	0.0202841	−	0.0489703i
$606$		0			0
$607$	−11.2946			−0.458433			−0.229216	−	0.973376i	$-0.573616\pi$
$607$	−11.2946			−0.458433			−0.229216	+	0.973376i	$0.573616\pi$
$608$	−12.8507	+	21.7161i	−0.521164	+	0.880702i
$609$		0			0
$610$	−0.259865	+	0.728857i	−0.0105216	+	0.0295106i
$611$	−4.80328	+	11.5961i	−0.194320	+	0.469130i
$612$		0			0
$613$	−8.81953	+	3.65317i	−0.356218	+	0.147550i	−0.553614	−	0.832774i	$-0.686752\pi$
$613$	−8.81953	+	3.65317i	−0.356218	+	0.147550i	0.197396	+	0.980324i	$0.436752\pi$
$614$	−21.0896	−	19.0713i	−0.851105	−	0.769655i
$615$		0			0
$616$	−10.0795	−	66.4065i	−0.406116	−	2.67559i
$617$	3.75533	+	3.75533i	0.151184	+	0.151184i	0.778647	−	0.627463i	$-0.215907\pi$
$617$	3.75533	+	3.75533i	0.151184	+	0.151184i	−0.627463	+	0.778647i	$0.715907\pi$
$618$		0			0
$619$	0.888196	+	2.14430i	0.0356996	+	0.0861865i	0.940724	−	0.339174i	$-0.110147\pi$
$619$	0.888196	+	2.14430i	0.0356996	+	0.0861865i	−0.905024	+	0.425360i	$0.860147\pi$
$620$	−0.227709	−	0.0685159i	−0.00914501	−	0.00275167i
$621$		0			0
$622$	−2.22182	−	4.68401i	−0.0890869	−	0.187812i
$623$			9.99994i			0.400639i
$624$		0			0
$625$		−	24.9585i		−	0.998341i
$626$	17.1864	−	8.15223i	0.686907	−	0.325829i
$627$		0			0
$628$	−0.245113	+	0.131725i	−0.00978107	+	0.00525641i
$629$	3.28294	+	7.92573i	0.130900	+	0.316019i
$630$		0			0
$631$	−6.14991	−	6.14991i	−0.244824	−	0.244824i	0.574018	−	0.818842i	$-0.305384\pi$
$631$	−6.14991	−	6.14991i	−0.244824	−	0.244824i	−0.818842	+	0.574018i	$0.805384\pi$
$632$	−3.30327	+	1.99508i	−0.131397	+	0.0793600i
$633$		0			0
$634$	22.0168	−	24.3468i	0.874399	−	0.966933i
$635$	−0.385007	+	0.159475i	−0.0152785	+	0.00632857i
$636$		0			0
$637$	17.1137	−	41.3162i	0.678071	−	1.63701i
$638$	−52.1332	−	18.5875i	−2.06397	−	0.735884i
$639$		0			0
$640$	−0.250121	+	0.539789i	−0.00988691	+	0.0213371i
$641$	−6.14567			−0.242739			−0.121370	−	0.992607i	$-0.538729\pi$
$641$	−6.14567			−0.242739			−0.121370	+	0.992607i	$0.538729\pi$
$642$		0			0
$643$	−10.3818	+	25.0640i	−0.409420	+	0.988426i	0.575871	+	0.817540i	$0.304663\pi$
$643$	−10.3818	+	25.0640i	−0.409420	+	0.988426i	−0.985291	+	0.170886i	$0.945337\pi$
$644$	−17.3250	−	14.1531i	−0.682699	−	0.557712i
$645$		0			0
$646$	−17.6916	+	19.5639i	−0.696069	+	0.769731i
$647$	26.5716	−	26.5716i	1.04464	−	1.04464i	0.0456809	−	0.998956i	$-0.485454\pi$
$647$	26.5716	−	26.5716i	1.04464	−	1.04464i	0.998956	−	0.0456809i	$-0.0145457\pi$
$648$		0			0
$649$	58.2331	+	58.2331i	2.28585	+	2.28585i
$650$	36.0535	−	1.81184i	1.41413	−	0.0710660i
$651$		0			0
$652$	31.2560	−	16.7972i	1.22408	−	0.657827i
$653$	26.1042	+	10.8127i	1.02154	+	0.423135i	0.829651	−	0.558282i	$-0.188539\pi$
$653$	26.1042	+	10.8127i	1.02154	+	0.423135i	0.191887	+	0.981417i	$0.438539\pi$
$654$		0			0
$655$			0.618380i			0.0241621i
$656$	11.5261	−	17.4191i	0.450017	−	0.680101i
$657$		0			0
$658$	−5.91147	−	12.4625i	−0.230453	−	0.485838i
$659$	19.2460	+	7.97197i	0.749719	+	0.310544i	0.724627	−	0.689141i	$-0.242012\pi$
$659$	19.2460	+	7.97197i	0.749719	+	0.310544i	0.0250923	+	0.999685i	$0.492012\pi$
$660$		0			0
$661$	−1.70210	−	4.10923i	−0.0662040	−	0.159831i	0.887315	−	0.461164i	$-0.152568\pi$
$661$	−1.70210	−	4.10923i	−0.0662040	−	0.159831i	−0.953519	+	0.301334i	$0.902568\pi$
$662$	0.592372	+	11.7875i	0.0230232	+	0.458135i
$663$		0			0
$664$	1.37674	+	9.07029i	0.0534278	+	0.351995i
$665$	0.658342	−	0.658342i	0.0255294	−	0.0255294i
$666$		0			0
$667$	−17.0312	+	7.05455i	−0.659450	+	0.273153i
$668$	−36.5719	+	3.68508i	−1.41501	+	0.142580i
$669$		0			0
$670$	0.292945	−	0.821639i	0.0113175	−	0.0317427i
$671$	−62.2528			−2.40324
$672$		0			0
$673$	−0.0647898			−0.00249746			−0.00124873	−	0.999999i	$-0.500397\pi$
$673$	−0.0647898			−0.00249746			−0.00124873	+	0.999999i	$0.500397\pi$
$674$	−7.17206	+	20.1158i	−0.276257	+	0.774833i
$675$		0			0
$676$	2.62499	+	26.0512i	0.100961	+	1.00197i
$677$	16.9643	−	7.02684i	0.651991	−	0.270064i	−0.0320730	−	0.999486i	$-0.510211\pi$
$677$	16.9643	−	7.02684i	0.651991	−	0.270064i	0.684064	+	0.729422i	$0.260211\pi$
$678$		0			0
$679$	−17.4386	+	17.4386i	−0.669233	+	0.669233i
$680$	−0.368767	+	0.500747i	−0.0141416	+	0.0192028i
$681$		0			0
$682$	−0.960188	−	19.1066i	−0.0367675	−	0.731631i
$683$	4.02367	+	9.71400i	0.153961	+	0.371696i	0.981975	−	0.189013i	$-0.0605288\pi$
$683$	4.02367	+	9.71400i	0.153961	+	0.371696i	−0.828013	+	0.560709i	$0.810529\pi$
$684$		0			0
$685$	0.0432723	+	0.0179240i	0.00165335	+	0.000684841i
$686$	4.22201	+	8.90078i	0.161197	+	0.339833i
$687$		0			0
$688$	−34.9393	+	23.5737i	−1.33205	+	0.898738i
$689$			47.7371i			1.81864i
$690$		0			0
$691$	−14.5726	−	6.03615i	−0.554366	−	0.229626i	0.0878712	−	0.996132i	$-0.471994\pi$
$691$	−14.5726	−	6.03615i	−0.554366	−	0.229626i	−0.642237	+	0.766506i	$0.721994\pi$
$692$	−10.2390	−	19.0526i	−0.389228	−	0.724272i
$693$		0			0
$694$	5.54746	−	0.278783i	0.210579	−	0.0105825i
$695$	0.319378	+	0.319378i	0.0121147	+	0.0121147i
$696$		0			0
$697$	15.4387	−	15.4387i	0.584784	−	0.584784i
$698$	−5.60751	+	6.20093i	−0.212247	+	0.234709i
$699$		0			0
$700$	−25.0977	+	30.7223i	−0.948605	+	1.16119i
$701$	−12.5789	+	30.3681i	−0.475098	+	1.14699i	0.486784	+	0.873522i	$0.338170\pi$
$701$	−12.5789	+	30.3681i	−0.475098	+	1.14699i	−0.961882	+	0.273465i	$0.911830\pi$
$702$		0			0
$703$	−9.15206			−0.345176
$704$	−47.6623	−	4.36984i	−1.79634	−	0.164694i
$705$		0			0
$706$	45.7444	+	16.3096i	1.72161	+	0.613821i
$707$	15.1982	−	36.6918i	0.571589	−	1.37994i
$708$		0			0
$709$	35.1691	−	14.5675i	1.32080	−	0.547094i	0.392785	−	0.919630i	$-0.371512\pi$
$709$	35.1691	−	14.5675i	1.32080	−	0.547094i	0.928018	+	0.372536i	$0.121512\pi$
$710$	0.268067	−	0.296436i	0.0100604	−	0.0111250i
$711$		0			0
$712$	6.91805	+	1.70810i	0.259265	+	0.0640137i
$713$	−4.50555	−	4.50555i	−0.168734	−	0.168734i
$714$		0			0
$715$	−0.614961	−	1.48465i	−0.0229982	−	0.0555227i
$716$	15.7020	+	29.2180i	0.586810	+	1.09193i
$717$		0			0
$718$	3.11190	−	1.47610i	0.116135	−	0.0550877i
$719$			33.7186i			1.25749i	0.777611	+	0.628745i	$0.216431\pi$
$719$			33.7186i			1.25749i	−0.777611	+	0.628745i	$0.783569\pi$
$720$		0			0
$721$		−	43.0706i		−	1.60403i
$722$	−0.544105	−	1.14707i	−0.0202495	−	0.0426897i
$723$		0			0
$724$	−4.49119	+	14.9262i	−0.166914	+	0.554729i
$725$	12.5098	+	30.2014i	0.464603	+	1.12165i
$726$		0			0
$727$	−15.6905	−	15.6905i	−0.581929	−	0.581929i	0.353504	−	0.935433i	$-0.384990\pi$
$727$	−15.6905	−	15.6905i	−0.581929	−	0.581929i	−0.935433	+	0.353504i	$0.884990\pi$
$728$	−46.1758	−	34.0054i	−1.71139	−	1.26033i
$729$		0			0
$730$	0.568627	+	0.514210i	0.0210458	+	0.0190318i
$731$	−40.7044	+	16.8603i	−1.50551	+	0.623601i
$732$		0			0
$733$	3.19679	−	7.71774i	0.118076	−	0.285061i	−0.853781	−	0.520633i	$-0.825696\pi$
$733$	3.19679	−	7.71774i	0.118076	−	0.285061i	0.971857	+	0.235571i	$0.0756962\pi$
$734$	9.90514	−	27.7814i	0.365605	−	1.02543i
$735$		0			0
$736$	−12.7506	+	9.56805i	−0.469992	+	0.352683i
$737$	70.1775			2.58502
$738$		0			0
$739$	16.6857	−	40.2830i	0.613795	−	1.48183i	−0.245005	−	0.969522i	$-0.578790\pi$
$739$	16.6857	−	40.2830i	0.613795	−	1.48183i	0.858800	−	0.512311i	$-0.171210\pi$
$740$	−0.214689	+	0.0216326i	−0.00789211	+	0.000795231i
$741$		0			0
$742$	−38.9100	−	35.1864i	−1.42843	−	1.29173i
$743$	36.2830	−	36.2830i	1.33109	−	1.33109i	0.426703	−	0.904392i	$-0.359675\pi$
$743$	36.2830	−	36.2830i	1.33109	−	1.33109i	0.904392	−	0.426703i	$-0.140325\pi$
$744$		0			0
$745$	0.0979933	+	0.0979933i	0.00359020	+	0.00359020i
$746$	−0.468851	−	9.32961i	−0.0171659	−	0.341581i
$747$		0			0
$748$	−47.9092	−	14.4155i	−1.75174	−	0.527084i
$749$	−22.2835	−	9.23014i	−0.814223	−	0.337262i
$750$		0			0
$751$		−	28.9288i		−	1.05563i	−0.849360	−	0.527813i	$-0.823012\pi$
$751$		−	28.9288i		−	1.05563i	0.849360	−	0.527813i	$-0.176988\pi$
$752$	−9.63139	+	1.96088i	−0.351221	+	0.0715059i
$753$		0			0
$754$	−42.6952	+	20.2521i	−1.55487	+	0.737537i
$755$	0.664848	+	0.275389i	0.0241963	+	0.0100224i
$756$		0			0
$757$	−18.5678	−	44.8267i	−0.674859	−	1.62925i	−0.773246	−	0.634107i	$-0.781368\pi$
$757$	−18.5678	−	44.8267i	−0.674859	−	1.62925i	0.0983861	−	0.995148i	$-0.468632\pi$
$758$	18.6028	−	0.934869i	0.675685	−	0.0339560i
$759$		0			0
$760$	−0.342995	−	0.567899i	−0.0124417	−	0.0205998i
$761$	21.7042	−	21.7042i	0.786777	−	0.786777i	−0.194187	−	0.980964i	$-0.562207\pi$
$761$	21.7042	−	21.7042i	0.786777	−	0.786777i	0.980964	+	0.194187i	$0.0622070\pi$
$762$		0			0
$763$	−69.0382	+	28.5966i	−2.49935	+	1.03527i
$764$	6.87712	+	5.61807i	0.248805	+	0.203255i
$765$		0			0
$766$	−14.0754	−	5.01841i	−0.508565	−	0.181323i
$767$	70.3125			2.53884
$768$		0			0
$769$	−8.82916			−0.318388			−0.159194	−	0.987247i	$-0.550889\pi$
$769$	−8.82916			−0.318388			−0.159194	+	0.987247i	$0.550889\pi$
$770$	1.66340	+	0.593066i	0.0599448	+	0.0213726i
$771$		0			0
$772$	−23.8800	−	19.5081i	−0.859461	−	0.702113i
$773$	−45.4847	+	18.8404i	−1.63597	+	0.677642i	−0.995882	−	0.0906581i	$-0.971103\pi$
$773$	−45.4847	+	18.8404i	−1.63597	+	0.677642i	−0.640090	+	0.768300i	$0.721103\pi$
$774$		0			0
$775$	−7.98968	+	7.98968i	−0.286998	+	0.286998i
$776$	9.08549	+	15.0429i	0.326150	+	0.540009i
$777$		0			0
$778$	−22.6269	+	1.13709i	−0.811213	+	0.0407668i
$779$	8.91377	+	21.5197i	0.319369	+	0.771025i
$780$		0			0
$781$	29.7062	+	12.3047i	1.06297	+	0.440297i
$782$	−15.0557	+	7.14156i	−0.538392	+	0.255382i
$783$		0			0
$784$	34.3159	−	6.98647i	1.22557	−	0.249517i
$785$		−	0.00731620i		−	0.000261126i
$786$		0			0
$787$	−10.1939	−	4.22245i	−0.363373	−	0.150514i	0.193524	−	0.981096i	$-0.438008\pi$
$787$	−10.1939	−	4.22245i	−0.363373	−	0.150514i	−0.556897	+	0.830581i	$0.688008\pi$
$788$	5.03223	+	1.51416i	0.179266	+	0.0539397i
$789$		0			0
$790$	−0.00509243	−	0.101334i	−0.000181181	−	0.00360529i
$791$	8.02407	+	8.02407i	0.285303	+	0.285303i
$792$		0			0
$793$	−37.5830	+	37.5830i	−1.33461	+	1.33461i
$794$	−35.6657	−	32.2525i	−1.26573	−	1.14460i
$795$		0			0
$796$	−1.15445	+	0.116325i	−0.0409183	+	0.00412304i
$797$	−8.36408	+	20.1927i	−0.296271	+	0.715261i	0.703718	+	0.710480i	$0.251522\pi$
$797$	−8.36408	+	20.1927i	−0.296271	+	0.715261i	−0.999989	+	0.00478157i	$0.998478\pi$
$798$		0			0
$799$	−10.2744			−0.363481
$800$	16.9670	+	22.6105i	0.599874	+	0.799403i
$801$		0			0
$802$	0.194964	−	0.546827i	0.00688443	−	0.0193091i
$803$	−23.6030	+	56.9827i	−0.832932	+	2.01088i
$804$		0			0
$805$	0.543410	−	0.225088i	0.0191527	−	0.00793331i
$806$	−12.1147	−	10.9553i	−0.426721	−	0.385884i
$807$		0			0
$808$	−22.7877	−	16.7816i	−0.801668	−	0.590376i
$809$	−2.47723	−	2.47723i	−0.0870946	−	0.0870946i	0.662217	−	0.749312i	$-0.269616\pi$
$809$	−2.47723	−	2.47723i	−0.0870946	−	0.0870946i	−0.749312	+	0.662217i	$0.769616\pi$
$810$		0			0
$811$	5.57286	+	13.4541i	0.195689	+	0.472436i	0.991016	−	0.133745i	$-0.0427005\pi$
$811$	5.57286	+	13.4541i	0.195689	+	0.472436i	−0.795326	+	0.606182i	$0.792700\pi$
$812$	14.9628	−	49.7280i	0.525090	−	1.74511i
$813$		0			0
$814$	−7.43974	−	15.6843i	−0.260763	−	0.549736i
$815$			0.932937i			0.0326794i
$816$		0			0
$817$		−	47.0025i		−	1.64441i
$818$	−22.0739	+	10.4706i	−0.771797	+	0.366096i
$819$		0			0
$820$	0.259965	+	0.483740i	0.00907837	+	0.0168929i
$821$	−6.31465	−	15.2449i	−0.220383	−	0.532052i	0.774559	−	0.632501i	$-0.217972\pi$
$821$	−6.31465	−	15.2449i	−0.220383	−	0.532052i	−0.994942	+	0.100450i	$0.967972\pi$
$822$		0			0
$823$	−27.8179	−	27.8179i	−0.969670	−	0.969670i	0.0298834	−	0.999553i	$-0.490486\pi$
$823$	−27.8179	−	27.8179i	−0.969670	−	0.969670i	−0.999553	+	0.0298834i	$0.990486\pi$
$824$	−29.7967	−	7.35694i	−1.03802	−	0.256291i
$825$		0			0
$826$	−51.8264	+	57.3110i	−1.80327	+	1.99411i
$827$	5.66971	−	2.34847i	0.197155	−	0.0816643i	−0.281921	−	0.959438i	$-0.590972\pi$
$827$	5.66971	−	2.34847i	0.197155	−	0.0816643i	0.479076	+	0.877773i	$0.340972\pi$
$828$		0			0
$829$	−17.6862	+	42.6983i	−0.614268	+	1.48297i	0.244002	+	0.969775i	$0.421540\pi$
$829$	−17.6862	+	42.6983i	−0.614268	+	1.48297i	−0.858270	+	0.513198i	$0.828460\pi$
$830$	−0.227200	−	0.0810053i	−0.00788622	−	0.00281174i
$831$		0			0
$832$	−31.4126	+	26.1363i	−1.08904	+	0.906114i
$833$	36.6068			1.26835
$834$		0			0
$835$	0.369834	−	0.892857i	0.0127986	−	0.0308986i
$836$	33.7676	−	41.3351i	1.16788	−	1.42961i
$837$		0			0
$838$	5.09091	−	5.62966i	0.175862	−	0.194473i
$839$	−2.69906	+	2.69906i	−0.0931817	+	0.0931817i	−0.752161	−	0.658979i	$-0.770988\pi$
$839$	−2.69906	+	2.69906i	−0.0931817	+	0.0931817i	0.658979	+	0.752161i	$0.270988\pi$
$840$		0			0
$841$	−9.75247	−	9.75247i	−0.336292	−	0.336292i
$842$	40.6074	−	2.04069i	1.39942	−	0.0703268i
$843$		0			0
$844$	7.22692	+	13.4478i	0.248761	+	0.462892i
$845$	−0.636007	−	0.263443i	−0.0218793	−	0.00906270i
$846$		0			0
$847$			98.4120i			3.38148i
$848$	−30.9885	+	20.9081i	−1.06415	+	0.717986i
$849$		0			0
$850$	12.6641	+	26.6983i	0.434375	+	0.915744i
$851$	−5.34171	−	2.21261i	−0.183111	−	0.0758473i
$852$		0			0
$853$	16.0824	+	38.8264i	0.550652	+	1.32939i	0.916990	+	0.398910i	$0.130611\pi$
$853$	16.0824	+	38.8264i	0.550652	+	1.32939i	−0.366338	+	0.930482i	$0.619389\pi$
$854$	−2.93160	−	58.3355i	−0.100317	−	1.99620i
$855$		0			0
$856$	−10.1918	+	13.8393i	−0.348347	+	0.473019i
$857$	16.7194	−	16.7194i	0.571124	−	0.571124i	−0.361318	−	0.932442i	$-0.617673\pi$
$857$	16.7194	−	16.7194i	0.571124	−	0.571124i	0.932442	+	0.361318i	$0.117673\pi$
$858$		0			0
$859$	−23.7139	+	9.82264i	−0.809109	+	0.335144i	−0.748599	−	0.663024i	$-0.769273\pi$
$859$	−23.7139	+	9.82264i	−0.809109	+	0.335144i	−0.0605107	+	0.998168i	$0.519273\pi$
$860$	−0.111099	−	1.10258i	−0.00378845	−	0.0375978i
$861$		0			0
$862$	3.03077	−	8.50056i	0.103228	−	0.289530i
$863$	29.1681			0.992895			0.496447	−	0.868067i	$-0.334638\pi$
$863$	29.1681			0.992895			0.496447	+	0.868067i	$0.334638\pi$
$864$		0			0
$865$	0.568688			0.0193360
$866$	4.50258	−	12.6286i	0.153004	−	0.429138i
$867$		0			0
$868$	17.8591	−	1.79953i	0.606178	−	0.0610801i
$869$	7.54134	−	3.12372i	0.255822	−	0.105965i
$870$		0			0
$871$	42.3672	−	42.3672i	1.43556	−	1.43556i
$872$	7.99088	+	52.6459i	0.270605	+	1.78281i
$873$		0			0
$874$	−0.892255	−	17.7549i	−0.0301810	−	0.600567i
$875$	−0.798517	−	1.92779i	−0.0269948	−	0.0651712i
$876$		0			0
$877$	6.91295	+	2.86344i	0.233434	+	0.0966914i	0.496334	−	0.868132i	$-0.334679\pi$
$877$	6.91295	+	2.86344i	0.233434	+	0.0966914i	−0.262900	+	0.964823i	$0.584679\pi$
$878$	0.0436007	+	0.0919184i	0.00147145	+	0.00310209i
$879$		0			0
$880$	0.694415	−	1.04945i	0.0234087	−	0.0353771i
$881$		−	41.7577i		−	1.40685i	−0.710768	−	0.703427i	$-0.751652\pi$
$881$		−	41.7577i		−	1.40685i	0.710768	−	0.703427i	$-0.248348\pi$
$882$		0			0
$883$	14.9227	+	6.18119i	0.502189	+	0.208014i	0.619373	−	0.785097i	$-0.287387\pi$
$883$	14.9227	+	6.18119i	0.502189	+	0.208014i	−0.117184	+	0.993110i	$0.537387\pi$
$884$	−37.6264	+	20.2207i	−1.26551	+	0.680095i
$885$		0			0
$886$	−10.7448	+	0.539969i	−0.360978	+	0.0181406i
$887$	22.4394	+	22.4394i	0.753442	+	0.753442i	0.975120	−	0.221678i	$-0.0711533\pi$
$887$	22.4394	+	22.4394i	0.753442	+	0.753442i	−0.221678	+	0.975120i	$0.571153\pi$
$888$		0			0
$889$	22.2429	−	22.2429i	0.746003	−	0.746003i
$890$	−0.125662	+	0.138960i	−0.00421220	+	0.00465796i
$891$		0			0
$892$	−2.70023	−	2.20588i	−0.0904104	−	0.0738583i
$893$	4.19459	−	10.1266i	0.140367	−	0.338875i
$894$		0			0
$895$	−0.872108			−0.0291514
$896$	1.85036	−	44.8688i	0.0618161	−	1.49896i
$897$		0			0
$898$	51.3320	+	18.3018i	1.71297	+	0.610739i
$899$	5.66025	−	13.6651i	0.188780	−	0.455755i
$900$		0			0
$901$	−36.1017	+	14.9538i	−1.20272	+	0.498184i
$902$	−29.6335	+	32.7695i	−0.986686	+	1.09110i
$903$		0			0
$904$	6.92172	−	4.18053i	0.230213	−	0.139042i
$905$	−0.289788	−	0.289788i	−0.00963290	−	0.00963290i
$906$		0			0
$907$	10.9011	+	26.3176i	0.361966	+	0.873863i	0.995013	+	0.0997492i	$0.0318041\pi$
$907$	10.9011	+	26.3176i	0.361966	+	0.873863i	−0.633047	+	0.774114i	$0.718196\pi$
$908$	23.5757	−	12.6697i	0.782386	−	0.420459i
$909$		0			0
$910$	1.36226	−	0.646179i	0.0451586	−	0.0214206i
$911$		−	14.4569i		−	0.478977i	−0.970899	−	0.239489i	$-0.923020\pi$
$911$		−	14.4569i		−	0.478977i	0.970899	−	0.239489i	$-0.0769798\pi$
$912$		0			0
$913$		−	19.4055i		−	0.642228i
$914$	4.32834	+	9.12493i	0.143169	+	0.301826i
$915$		0			0
$916$	−14.2661	−	4.29256i	−0.471366	−	0.141830i
$917$	−17.8627	−	43.1245i	−0.589880	−	1.42410i
$918$		0			0
$919$	−42.2518	−	42.2518i	−1.39376	−	1.39376i	−0.816706	−	0.577054i	$-0.804202\pi$
$919$	−42.2518	−	42.2518i	−1.39376	−	1.39376i	−0.577054	−	0.816706i	$-0.695798\pi$
$920$	−0.0628974	−	0.414384i	−0.00207367	−	0.0136618i
$921$		0			0
$922$	−18.9012	−	17.0924i	−0.622478	−	0.562907i
$923$	25.3626	−	10.5055i	0.834820	−	0.345794i
$924$		0			0
$925$	−3.92362	+	9.47245i	−0.129008	+	0.311452i
$926$	−18.5849	+	52.1259i	−0.610736	+	1.71296i
$927$		0			0
$928$	−31.8464	−	18.8455i	−1.04541	−	0.618632i
$929$	23.4486			0.769323			0.384661	−	0.923058i	$-0.374318\pi$
$929$	23.4486			0.769323			0.384661	+	0.923058i	$0.374318\pi$
$930$		0			0
$931$	−14.9450	+	36.0805i	−0.489803	+	1.18249i
$932$	−2.66632	−	26.4614i	−0.0873383	−	0.866772i
$933$		0			0
$934$	39.4371	+	35.6630i	1.29042	+	1.16693i
$935$	0.930144	−	0.930144i	0.0304190	−	0.0304190i
$936$		0			0
$937$	−8.97642	−	8.97642i	−0.293247	−	0.293247i	0.545115	−	0.838361i	$-0.316486\pi$
$937$	−8.97642	−	8.97642i	−0.293247	−	0.293247i	−0.838361	+	0.545115i	$0.816486\pi$
$938$	3.30478	+	65.7614i	0.107905	+	2.14719i
$939$		0			0
$940$	0.0744603	−	0.247465i	0.00242863	−	0.00807142i
$941$	−19.3743	−	8.02509i	−0.631583	−	0.261610i	0.0438424	−	0.999038i	$-0.486040\pi$
$941$	−19.3743	−	8.02509i	−0.631583	−	0.261610i	−0.675426	+	0.737428i	$0.736040\pi$
$942$		0			0
$943$			14.7153i			0.479195i
$944$	30.7958	+	45.6433i	1.00232	+	1.48556i
$945$		0			0
$946$	80.5506	−	38.2085i	2.61893	−	1.24227i
$947$	29.9128	+	12.3903i	0.972037	+	0.402631i	0.811470	−	0.584394i	$-0.198668\pi$
$947$	29.9128	+	12.3903i	0.972037	+	0.402631i	0.160567	+	0.987025i	$0.448668\pi$
$948$		0			0
$949$	20.1518	+	48.6508i	0.654156	+	1.57927i
$950$	−31.4846	+	1.58223i	−1.02150	+	0.0513344i
$951$		0			0
$952$	11.2523	−	45.5733i	0.364688	−	1.47704i
$953$	−24.5427	+	24.5427i	−0.795017	+	0.795017i	−0.982305	−	0.187288i	$-0.940030\pi$
$953$	−24.5427	+	24.5427i	−0.795017	+	0.795017i	0.187288	+	0.982305i	$0.440030\pi$
$954$		0			0
$955$	−0.215706	+	0.0893484i	−0.00698009	+	0.00289125i
$956$	26.6727	−	32.6502i	0.862656	−	1.05598i
$957$		0			0
$958$	29.1462	+	10.3917i	0.941670	+	0.335741i
$959$	−3.53548			−0.114167
$960$		0			0
$961$	−25.8875			−0.835082
$962$	−13.9604	−	4.97740i	−0.450100	−	0.160478i
$963$		0			0
$964$	4.33067	−	5.30121i	0.139482	−	0.170740i
$965$	0.749016	−	0.310252i	0.0241117	−	0.00998738i
$966$		0			0
$967$	38.6683	−	38.6683i	1.24349	−	1.24349i	0.284944	−	0.958544i	$-0.408025\pi$
$967$	38.6683	−	38.6683i	1.24349	−	1.24349i	0.958544	−	0.284944i	$-0.0919750\pi$
$968$	68.0823	+	16.8098i	2.18825	+	0.540289i
$969$		0			0
$970$	−0.461468	+	0.0231907i	−0.0148168	+	0.000744607i
$971$	1.70288	+	4.11111i	0.0546479	+	0.131932i	0.948845	−	0.315741i	$-0.102253\pi$
$971$	1.70288	+	4.11111i	0.0546479	+	0.131932i	−0.894198	+	0.447673i	$0.852253\pi$
$972$		0			0
$973$	−31.4984	−	13.0471i	−1.00979	−	0.418270i
$974$	47.9370	−	22.7385i	1.53600	−	0.728589i
$975$		0			0
$976$	−40.8578	−	7.93623i	−1.30782	−	0.254033i
$977$		−	40.3295i		−	1.29025i	−0.764075	−	0.645127i	$-0.776805\pi$
$977$		−	40.3295i		−	1.29025i	0.764075	−	0.645127i	$-0.223195\pi$
$978$		0			0
$979$	−13.9254	−	5.76807i	−0.445056	−	0.184348i
$980$	−0.265297	+	0.881700i	−0.00847459	+	0.0281649i
$981$		0			0
$982$	−0.853828	−	16.9902i	−0.0272467	−	0.542179i
$983$	36.4908	+	36.4908i	1.16388	+	1.16388i	0.983620	+	0.180256i	$0.0576928\pi$
$983$	36.4908	+	36.4908i	1.16388	+	1.16388i	0.180256	+	0.983620i	$0.442307\pi$
$984$		0			0
$985$	−0.0976993	+	0.0976993i	−0.00311296	+	0.00311296i
$986$	−28.6903	−	25.9447i	−0.913686	−	0.826247i
$987$		0			0
$988$	−4.56865	−	45.3407i	−0.145348	−	1.44248i
$989$	11.3634	−	27.4336i	0.361334	−	0.872337i
$990$		0			0
$991$	−24.6898			−0.784296			−0.392148	−	0.919902i	$-0.628268\pi$
$991$	−24.6898			−0.784296			−0.392148	+	0.919902i	$0.628268\pi$
$992$	1.80560	−	12.6625i	0.0573278	−	0.402034i
$993$		0			0
$994$	−10.1315	+	28.4163i	−0.321351	+	0.901311i
$995$	0.0116744	−	0.0281844i	0.000370102	−	0.000893506i
$996$		0			0
$997$	38.4126	−	15.9110i	1.21654	−	0.503907i	0.320231	−	0.947339i	$-0.396239\pi$
$997$	38.4126	−	15.9110i	1.21654	−	0.503907i	0.896308	+	0.443432i	$0.146239\pi$
$998$	−0.590696	−	0.534167i	−0.0186982	−	0.0169088i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.v.a.109.4	✓	128
3.2	odd	2	inner	864.2.v.a.109.29	yes	128
32.5	even	8	inner	864.2.v.a.325.4	yes	128
96.5	odd	8	inner	864.2.v.a.325.29	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.v.a.109.4	✓	128	1.1	even	1	trivial
864.2.v.a.109.29	yes	128	3.2	odd	2	inner
864.2.v.a.325.4	yes	128	32.5	even	8	inner
864.2.v.a.325.29	yes	128	96.5	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.v (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33208 - 0.474937i) q^{2} +(1.54887 + 1.26531i) q^{4} +(-0.0485815 + 0.0201231i) q^{5} +(2.80669 - 2.80669i) q^{7} +(-1.46228 - 2.42110i) q^{8} +O(q^{10})\)	\(q+(-1.33208 - 0.474937i) q^{2} +(1.54887 + 1.26531i) q^{4} +(-0.0485815 + 0.0201231i) q^{5} +(2.80669 - 2.80669i) q^{7} +(-1.46228 - 2.42110i) q^{8} +(0.0742716 - 0.00373246i) q^{10} +(2.28951 + 5.52736i) q^{11} +(4.71917 + 1.95474i) q^{13} +(-5.07173 + 2.40573i) q^{14} +(0.798000 + 3.91959i) q^{16} +4.18126i q^{17} +(-4.12114 - 1.70703i) q^{19} +(-0.100708 - 0.0303024i) q^{20} +(-0.424660 - 8.45025i) q^{22} +(-1.99266 - 1.99266i) q^{23} +(-3.53358 + 3.53358i) q^{25} +(-5.35792 - 4.84518i) q^{26} +(7.89851 - 0.795876i) q^{28} +(2.50335 - 6.04362i) q^{29} +2.26107 q^{31} +(0.798558 - 5.60021i) q^{32} +(1.98583 - 5.56977i) q^{34} +(-0.0798738 + 0.192832i) q^{35} +(1.89554 - 0.785157i) q^{37} +(4.67895 + 4.23118i) q^{38} +(0.119760 + 0.0881953i) q^{40} +(-3.69237 - 3.69237i) q^{41} +(4.03236 + 9.73497i) q^{43} +(-3.44765 + 11.4581i) q^{44} +(1.70799 + 3.60077i) q^{46} +2.45724i q^{47} -8.75498i q^{49} +(6.38523 - 3.02878i) q^{50} +(4.83603 + 8.99883i) q^{52} +(3.57639 + 8.63418i) q^{53} +(-0.222456 - 0.222456i) q^{55} +(-10.8994 - 2.69112i) q^{56} +(-6.20499 + 6.86165i) q^{58} +(12.7174 - 5.26771i) q^{59} +(-3.98195 + 9.61329i) q^{61} +(-3.01193 - 1.07387i) q^{62} +(-3.72349 + 7.08065i) q^{64} -0.268600 q^{65} +(4.48885 - 10.8370i) q^{67} +(-5.29057 + 6.47623i) q^{68} +(0.197981 - 0.218933i) q^{70} +(3.80026 - 3.80026i) q^{71} +(7.28971 + 7.28971i) q^{73} +(-2.89791 + 0.145632i) q^{74} +(-4.22319 - 7.85847i) q^{76} +(21.9395 + 9.08764i) q^{77} -1.36436i q^{79} +(-0.117642 - 0.174361i) q^{80} +(3.16489 + 6.67217i) q^{82} +(-2.99666 - 1.24126i) q^{83} +(-0.0841399 - 0.203132i) q^{85} +(-0.747925 - 14.8829i) q^{86} +(10.0344 - 13.6257i) q^{88} +(-1.78145 + 1.78145i) q^{89} +(18.7316 - 7.75887i) q^{91} +(-0.565047 - 5.60770i) q^{92} +(1.16703 - 3.27324i) q^{94} +0.234562 q^{95} -6.21324 q^{97} +(-4.15806 + 11.6623i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 8 q^{10} - 32 q^{16} + 32 q^{22} + 64 q^{40} + 64 q^{46} + 88 q^{52} - 64 q^{55} + 64 q^{58} - 32 q^{61} - 96 q^{64} + 64 q^{67} + 48 q^{70} + 32 q^{76} + 40 q^{82} + 40 q^{88} - 48 q^{91} + 24 q^{94}+O(q^{100}) \) 128 * q - 8 * q^10 - 32 * q^16 + 32 * q^22 + 64 * q^40 + 64 * q^46 + 88 * q^52 - 64 * q^55 + 64 * q^58 - 32 * q^61 - 96 * q^64 + 64 * q^67 + 48 * q^70 + 32 * q^76 + 40 * q^82 + 40 * q^88 - 48 * q^91 + 24 * q^94

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