LMFDB - Embedded newform 864.2.w.a.107.1

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			107.1
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41174 - 0.0836695i) q^{2} +(1.98600 + 0.236238i) q^{4} +(-0.833551 - 0.345268i) q^{5} +(-3.45115 + 3.45115i) q^{7} +(-2.78394 - 0.499674i) q^{8} +O(q^{10})$	\(q+(-1.41174 - 0.0836695i) q^{2} +(1.98600 + 0.236238i) q^{4} +(-0.833551 - 0.345268i) q^{5} +(-3.45115 + 3.45115i) q^{7} +(-2.78394 - 0.499674i) q^{8} +(1.14787 + 0.557170i) q^{10} +(0.588006 + 0.243560i) q^{11} +(1.02064 + 2.46404i) q^{13} +(5.16086 - 4.58335i) q^{14} +(3.88838 + 0.938339i) q^{16} -5.73510 q^{17} +(2.86396 - 1.18629i) q^{19} +(-1.57387 - 0.882619i) q^{20} +(-0.809731 - 0.393041i) q^{22} +(5.85623 - 5.85623i) q^{23} +(-2.95994 - 2.95994i) q^{25} +(-1.23471 - 3.56397i) q^{26} +(-7.66927 + 6.03868i) q^{28} +(-3.20100 - 7.72790i) q^{29} -3.21839i q^{31} +(-5.41086 - 1.65003i) q^{32} +(8.09645 + 0.479853i) q^{34} +(4.06828 - 1.68514i) q^{35} +(-0.0195107 + 0.0471029i) q^{37} +(-4.14242 + 1.43511i) q^{38} +(2.14804 + 1.37771i) q^{40} +(-1.77713 - 1.77713i) q^{41} +(2.15632 - 5.20583i) q^{43} +(1.11024 + 0.622620i) q^{44} +(-8.75744 + 7.77746i) q^{46} +8.62135i q^{47} -16.8208i q^{49} +(3.93099 + 4.42631i) q^{50} +(1.44489 + 5.13470i) q^{52} +(-5.21909 + 12.6000i) q^{53} +(-0.406040 - 0.406040i) q^{55} +(11.3322 - 7.88334i) q^{56} +(3.87238 + 11.1776i) q^{58} +(1.75051 - 4.22611i) q^{59} +(-7.88921 + 3.26782i) q^{61} +(-0.269281 + 4.54352i) q^{62} +(7.50065 + 2.78213i) q^{64} -2.40630i q^{65} +(-3.22264 - 7.78013i) q^{67} +(-11.3899 - 1.35485i) q^{68} +(-5.88433 + 2.03858i) q^{70} +(-3.71004 - 3.71004i) q^{71} +(4.02759 - 4.02759i) q^{73} +(0.0314850 - 0.0648645i) q^{74} +(5.96807 - 1.67940i) q^{76} +(-2.86986 + 1.18873i) q^{77} -7.33423 q^{79} +(-2.91719 - 2.12469i) q^{80} +(2.36015 + 2.65753i) q^{82} +(-1.32482 - 3.19840i) q^{83} +(4.78050 + 1.98015i) q^{85} +(-3.47973 + 7.16883i) q^{86} +(-1.51527 - 0.971868i) q^{88} +(6.20384 - 6.20384i) q^{89} +(-12.0261 - 4.98139i) q^{91} +(13.0139 - 10.2470i) q^{92} +(0.721344 - 12.1711i) q^{94} -2.79685 q^{95} -1.19109 q^{97} +(-1.40739 + 23.7466i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.41174	−	0.0836695i	−0.998248	−	0.0591633i
$2$	−1.41174	−	0.0836695i	−0.998248	−	0.0591633i
$3$		0			0
$3$		0			0
$4$	1.98600	+	0.236238i	0.992999	+	0.118119i
$5$	−0.833551	−	0.345268i	−0.372775	−	0.154409i	0.188427	−	0.982087i	$-0.439661\pi$
$5$	−0.833551	−	0.345268i	−0.372775	−	0.154409i	−0.561202	+	0.827679i	$0.689661\pi$
$6$		0			0
$7$	−3.45115	+	3.45115i	−1.30441	+	1.30441i	−0.379024	+	0.925387i	$0.623740\pi$
$7$	−3.45115	+	3.45115i	−1.30441	+	1.30441i	−0.925387	+	0.379024i	$0.876260\pi$
$8$	−2.78394	−	0.499674i	−0.984272	−	0.176661i
$9$		0			0
$10$	1.14787	+	0.557170i	0.362987	+	0.176193i
$11$	0.588006	+	0.243560i	0.177291	+	0.0734361i	0.469563	−	0.882899i	$-0.344411\pi$
$11$	0.588006	+	0.243560i	0.177291	+	0.0734361i	−0.292273	+	0.956335i	$0.594411\pi$
$12$		0			0
$13$	1.02064	+	2.46404i	0.283074	+	0.683402i	0.999904	−	0.0138461i	$-0.00440748\pi$
$13$	1.02064	+	2.46404i	0.283074	+	0.683402i	−0.716830	+	0.697248i	$0.754407\pi$
$14$	5.16086	−	4.58335i	1.37930	−	1.22495i
$15$		0			0
$16$	3.88838	+	0.938339i	0.972096	+	0.234585i
$17$	−5.73510			−1.39097			−0.695483	−	0.718542i	$-0.744810\pi$
$17$	−5.73510			−1.39097			−0.695483	+	0.718542i	$0.744810\pi$
$18$		0			0
$19$	2.86396	−	1.18629i	0.657038	−	0.272154i	−0.0291535	−	0.999575i	$-0.509281\pi$
$19$	2.86396	−	1.18629i	0.657038	−	0.272154i	0.686192	+	0.727421i	$0.259281\pi$
$20$	−1.57387	−	0.882619i	−0.351927	−	0.197360i
$21$		0			0
$22$	−0.809731	−	0.393041i	−0.172635	−	0.0837966i
$23$	5.85623	−	5.85623i	1.22111	−	1.22111i	0.253869	−	0.967239i	$-0.418297\pi$
$23$	5.85623	−	5.85623i	1.22111	−	1.22111i	0.967239	−	0.253869i	$-0.0817032\pi$
$24$		0			0
$25$	−2.95994	−	2.95994i	−0.591987	−	0.591987i
$26$	−1.23471	−	3.56397i	−0.242146	−	0.698953i
$27$		0			0
$28$	−7.66927	+	6.03868i	−1.44935	+	1.14120i
$29$	−3.20100	−	7.72790i	−0.594411	−	1.43504i	−0.879203	−	0.476447i	$-0.841925\pi$
$29$	−3.20100	−	7.72790i	−0.594411	−	1.43504i	0.284792	−	0.958589i	$-0.408075\pi$
$30$		0			0
$31$		−	3.21839i		−	0.578040i	−0.957323	−	0.289020i	$-0.906671\pi$
$31$		−	3.21839i		−	0.578040i	0.957323	−	0.289020i	$-0.0933295\pi$
$32$	−5.41086	−	1.65003i	−0.956514	−	0.291686i
$33$		0			0
$34$	8.09645	+	0.479853i	1.38853	+	0.0822941i
$35$	4.06828	−	1.68514i	0.687664	−	0.284840i
$36$		0			0
$37$	−0.0195107	+	0.0471029i	−0.00320753	+	0.00774367i	−0.925475	−	0.378808i	$-0.876334\pi$
$37$	−0.0195107	+	0.0471029i	−0.00320753	+	0.00774367i	0.922268	+	0.386552i	$0.126334\pi$
$38$	−4.14242	+	1.43511i	−0.671989	+	0.232805i
$39$		0			0
$40$	2.14804	+	1.37771i	0.339634	+	0.217835i
$41$	−1.77713	−	1.77713i	−0.277541	−	0.277541i	0.554585	−	0.832127i	$-0.312877\pi$
$41$	−1.77713	−	1.77713i	−0.277541	−	0.277541i	−0.832127	+	0.554585i	$0.812877\pi$
$42$		0			0
$43$	2.15632	−	5.20583i	0.328836	−	0.793881i	−0.669843	−	0.742503i	$-0.733639\pi$
$43$	2.15632	−	5.20583i	0.328836	−	0.793881i	0.998679	−	0.0513782i	$-0.0163614\pi$
$44$	1.11024	+	0.622620i	0.167375	+	0.0938635i
$45$		0			0
$46$	−8.75744	+	7.77746i	−1.29121	+	1.14672i
$47$			8.62135i			1.25755i	0.777586	+	0.628777i	$0.216444\pi$
$47$			8.62135i			1.25755i	−0.777586	+	0.628777i	$0.783556\pi$
$48$		0			0
$49$		−	16.8208i		−	2.40297i
$50$	3.93099	+	4.42631i	0.555926	+	0.625974i
$51$		0			0
$52$	1.44489	+	5.13470i	0.200370	+	0.712055i
$53$	−5.21909	+	12.6000i	−0.716897	+	1.73074i	−0.0348952	+	0.999391i	$0.511110\pi$
$53$	−5.21909	+	12.6000i	−0.716897	+	1.73074i	−0.682002	+	0.731351i	$0.738890\pi$
$54$		0			0
$55$	−0.406040	−	0.406040i	−0.0547504	−	0.0547504i
$56$	11.3322	−	7.88334i	1.51433	−	1.05346i
$57$		0			0
$58$	3.87238	+	11.1776i	0.508469	+	1.46769i
$59$	1.75051	−	4.22611i	0.227897	−	0.550192i	−0.768024	−	0.640421i	$-0.778760\pi$
$59$	1.75051	−	4.22611i	0.227897	−	0.550192i	0.995921	+	0.0902289i	$0.0287599\pi$
$60$		0			0
$61$	−7.88921	+	3.26782i	−1.01011	+	0.418401i	−0.825495	−	0.564410i	$-0.809104\pi$
$61$	−7.88921	+	3.26782i	−1.01011	+	0.418401i	−0.184615	+	0.982811i	$0.559104\pi$
$62$	−0.269281	+	4.54352i	−0.0341987	+	0.577028i
$63$		0			0
$64$	7.50065	+	2.78213i	0.937581	+	0.347766i
$65$		−	2.40630i		−	0.298465i
$66$		0			0
$67$	−3.22264	−	7.78013i	−0.393708	−	0.950495i	−0.989125	−	0.147078i	$-0.953013\pi$
$67$	−3.22264	−	7.78013i	−0.393708	−	0.950495i	0.595417	−	0.803417i	$-0.296987\pi$
$68$	−11.3899	−	1.35485i	−1.38123	−	0.164300i
$69$		0			0
$70$	−5.88433	+	2.03858i	−0.703312	+	0.243656i
$71$	−3.71004	−	3.71004i	−0.440301	−	0.440301i	0.451812	−	0.892113i	$-0.350778\pi$
$71$	−3.71004	−	3.71004i	−0.440301	−	0.440301i	−0.892113	+	0.451812i	$0.850778\pi$
$72$		0			0
$73$	4.02759	−	4.02759i	0.471394	−	0.471394i	−0.430972	−	0.902365i	$-0.641829\pi$
$73$	4.02759	−	4.02759i	0.471394	−	0.471394i	0.902365	+	0.430972i	$0.141829\pi$
$74$	0.0314850	−	0.0648645i	0.00366006	−	0.00754034i
$75$		0			0
$76$	5.96807	−	1.67940i	0.684585	−	0.192640i
$77$	−2.86986	+	1.18873i	−0.327051	+	0.135469i
$78$		0			0
$79$	−7.33423			−0.825166			−0.412583	−	0.910920i	$-0.635373\pi$
$79$	−7.33423			−0.825166			−0.412583	+	0.910920i	$0.635373\pi$
$80$	−2.91719	−	2.12469i	−0.326151	−	0.237547i
$81$		0			0
$82$	2.36015	+	2.65753i	0.260635	+	0.293475i
$83$	−1.32482	−	3.19840i	−0.145418	−	0.351070i	0.834342	−	0.551248i	$-0.185848\pi$
$83$	−1.32482	−	3.19840i	−0.145418	−	0.351070i	−0.979760	+	0.200178i	$0.935848\pi$
$84$		0			0
$85$	4.78050	+	1.98015i	0.518518	+	0.214777i
$86$	−3.47973	+	7.16883i	−0.375229	+	0.773035i
$87$		0			0
$88$	−1.51527	−	0.971868i	−0.161529	−	0.103602i
$89$	6.20384	−	6.20384i	0.657606	−	0.657606i	−0.297207	−	0.954813i	$-0.596055\pi$
$89$	6.20384	−	6.20384i	0.657606	−	0.657606i	0.954813	+	0.297207i	$0.0960552\pi$
$90$		0			0
$91$	−12.0261	−	4.98139i	−1.26068	−	0.522192i
$92$	13.0139	−	10.2470i	1.35680	−	1.06832i
$93$		0			0
$94$	0.721344	−	12.1711i	0.0744010	−	1.25535i
$95$	−2.79685			−0.286951
$96$		0			0
$97$	−1.19109			−0.120937			−0.0604685	−	0.998170i	$-0.519259\pi$
$97$	−1.19109			−0.120937			−0.0604685	+	0.998170i	$0.519259\pi$
$98$	−1.40739	+	23.7466i	−0.142168	+	2.39876i
$99$		0			0
$100$	−5.17918	−	6.57768i	−0.517918	−	0.657768i
$101$	2.88218	+	1.19384i	0.286788	+	0.118791i	0.521440	−	0.853288i	$-0.325395\pi$
$101$	2.88218	+	1.19384i	0.286788	+	0.118791i	−0.234652	+	0.972079i	$0.575395\pi$
$102$		0			0
$103$	13.0488	−	13.0488i	1.28574	−	1.28574i	0.348386	−	0.937351i	$-0.386730\pi$
$103$	13.0488	−	13.0488i	1.28574	−	1.28574i	0.937351	−	0.348386i	$-0.113270\pi$
$104$	−1.61018	−	7.36973i	−0.157891	−	0.722662i
$105$		0			0
$106$	8.42221	−	17.3512i	0.818037	−	1.68530i
$107$	−10.0756	−	4.17343i	−0.974041	−	0.403461i	−0.161826	−	0.986819i	$-0.551738\pi$
$107$	−10.0756	−	4.17343i	−0.974041	−	0.403461i	−0.812215	+	0.583358i	$0.801738\pi$
$108$		0			0
$109$	−3.36541	−	8.12483i	−0.322348	−	0.778217i	−0.999117	−	0.0420214i	$-0.986620\pi$
$109$	−3.36541	−	8.12483i	−0.322348	−	0.778217i	0.676769	−	0.736196i	$-0.263380\pi$
$110$	0.539248	+	0.607194i	0.0514153	+	0.0578937i
$111$		0			0
$112$	−16.6577	+	10.1810i	−1.57401	+	0.962017i
$113$	−12.3567			−1.16242			−0.581211	−	0.813753i	$-0.697421\pi$
$113$	−12.3567			−1.16242			−0.581211	+	0.813753i	$0.697421\pi$
$114$		0			0
$115$	−6.90343	+	2.85950i	−0.643748	+	0.266649i
$116$	−4.53156	−	16.1038i	−0.420745	−	1.49520i
$117$		0			0
$118$	−2.82486	+	5.81968i	−0.260049	+	0.535745i
$119$	19.7927	−	19.7927i	1.81439	−	1.81439i
$120$		0			0
$121$	−7.49174	−	7.49174i	−0.681068	−	0.681068i
$122$	11.4109	−	3.95321i	1.03309	−	0.357907i
$123$		0			0
$124$	0.760308	−	6.39172i	0.0682777	−	0.573994i
$125$	3.17163	+	7.65699i	0.283679	+	0.684862i
$126$		0			0
$127$			6.82730i			0.605825i	0.953018	+	0.302912i	$0.0979590\pi$
$127$			6.82730i			0.605825i	−0.953018	+	0.302912i	$0.902041\pi$
$128$	−10.3562	−	4.55520i	−0.915364	−	0.402627i
$129$		0			0
$130$	−0.201334	+	3.39706i	−0.0176581	+	0.297942i
$131$	3.95798	−	1.63945i	0.345810	−	0.143239i	−0.203017	−	0.979175i	$-0.565075\pi$
$131$	3.95798	−	1.63945i	0.345810	−	0.143239i	0.548827	+	0.835936i	$0.315075\pi$
$132$		0			0
$133$	−5.78989	+	13.9780i	−0.502047	+	1.21205i
$134$	3.89855	+	11.2531i	0.336784	+	0.972123i
$135$		0			0
$136$	15.9662	+	2.86568i	1.36909	+	0.245730i
$137$	2.08105	+	2.08105i	0.177796	+	0.177796i	0.790394	−	0.612599i	$-0.209876\pi$
$137$	2.08105	+	2.08105i	0.177796	+	0.177796i	−0.612599	+	0.790394i	$0.709876\pi$
$138$		0			0
$139$	−4.29535	+	10.3699i	−0.364327	+	0.879564i	0.630330	+	0.776328i	$0.282920\pi$
$139$	−4.29535	+	10.3699i	−0.364327	+	0.879564i	−0.994657	+	0.103236i	$0.967080\pi$
$140$	8.47769	−	2.38559i	0.716495	−	0.201619i
$141$		0			0
$142$	4.92718	+	5.54802i	0.413480	+	0.465579i
$143$			1.69746i			0.141949i
$144$		0			0
$145$			7.54681i			0.626728i
$146$	−6.02288	+	5.34891i	−0.498457	+	0.442679i
$147$		0			0
$148$	−0.0498757	+	0.0889372i	−0.00409976	+	0.00731059i
$149$	−2.57254	+	6.21066i	−0.210751	+	0.508797i	−0.993539	−	0.113491i	$-0.963797\pi$
$149$	−2.57254	+	6.21066i	−0.210751	+	0.508797i	0.782788	+	0.622288i	$0.213797\pi$
$150$		0			0
$151$	9.39527	+	9.39527i	0.764576	+	0.764576i	0.977146	−	0.212570i	$-0.0681832\pi$
$151$	9.39527	+	9.39527i	0.764576	+	0.764576i	−0.212570	+	0.977146i	$0.568183\pi$
$152$	−8.56586	+	1.87152i	−0.694783	+	0.151800i
$153$		0			0
$154$	4.15094	−	1.43806i	0.334492	−	0.115882i
$155$	−1.11121	+	2.68269i	−0.0892544	+	0.215479i
$156$		0			0
$157$	0.0824980	−	0.0341718i	0.00658406	−	0.00272721i	−0.379389	−	0.925237i	$-0.623866\pi$
$157$	0.0824980	−	0.0341718i	0.00658406	−	0.00272721i	0.385973	+	0.922510i	$0.373866\pi$
$158$	10.3540	+	0.613652i	0.823720	+	0.0488195i
$159$		0			0
$160$	3.94053	+	3.24358i	0.311526	+	0.256427i
$161$			40.4214i			3.18565i
$162$		0			0
$163$	−6.03334	−	14.5658i	−0.472567	−	1.14088i	−0.963025	−	0.269413i	$-0.913170\pi$
$163$	−6.03334	−	14.5658i	−0.472567	−	1.14088i	0.490457	−	0.871465i	$-0.336830\pi$
$164$	−3.10955	−	3.94921i	−0.242815	−	0.308381i
$165$		0			0
$166$	1.60269	+	4.62615i	0.124393	+	0.359059i
$167$	13.2769	+	13.2769i	1.02740	+	1.02740i	0.999614	+	0.0277834i	$0.00884486\pi$
$167$	13.2769	+	13.2769i	1.02740	+	1.02740i	0.0277834	+	0.999614i	$0.491155\pi$
$168$		0			0
$169$	4.16259	−	4.16259i	0.320199	−	0.320199i
$170$	−6.58313	−	3.19543i	−0.504903	−	0.245078i
$171$		0			0
$172$	5.51227	−	9.82936i	0.420307	−	0.749481i
$173$	0.478594	−	0.198240i	0.0363869	−	0.0150719i	−0.364416	−	0.931236i	$-0.618731\pi$
$173$	0.478594	−	0.198240i	0.0363869	−	0.0150719i	0.400803	+	0.916164i	$0.368731\pi$
$174$		0			0
$175$	20.4303			1.54439
$176$	2.05785	+	1.49880i	0.155116	+	0.112977i
$177$		0			0
$178$	−9.27726	+	8.23912i	−0.695360	+	0.617548i
$179$	4.86942	+	11.7558i	0.363958	+	0.878672i	0.994713	+	0.102690i	$0.0327450\pi$
$179$	4.86942	+	11.7558i	0.363958	+	0.878672i	−0.630756	+	0.775981i	$0.717255\pi$
$180$		0			0
$181$	−14.2927	−	5.92024i	−1.06237	−	0.440048i	−0.218077	−	0.975932i	$-0.569978\pi$
$181$	−14.2927	−	5.92024i	−1.06237	−	0.440048i	−0.844292	+	0.535884i	$0.819978\pi$
$182$	16.5610	+	8.03863i	1.22758	+	0.595863i
$183$		0			0
$184$	−19.2296	+	13.3772i	−1.41762	+	0.986179i
$185$	0.0325263	−	0.0325263i	0.00239138	−	0.00239138i
$186$		0			0
$187$	−3.37228	−	1.39684i	−0.246605	−	0.102147i
$188$	−2.03670	+	17.1220i	−0.148541	+	1.24875i
$189$		0			0
$190$	3.94841	+	0.234011i	0.286448	+	0.0169769i
$191$	0.439679			0.0318141			0.0159070	−	0.999873i	$-0.494936\pi$
$191$	0.439679			0.0318141			0.0159070	+	0.999873i	$0.494936\pi$
$192$		0			0
$193$	10.6670			0.767826			0.383913	−	0.923369i	$-0.374576\pi$
$193$	10.6670			0.767826			0.383913	+	0.923369i	$0.374576\pi$
$194$	1.68151	+	0.0996579i	0.120725	+	0.00715502i
$195$		0			0
$196$	3.97372	−	33.4061i	0.283837	−	2.38615i
$197$	−19.3795	−	8.02724i	−1.38073	−	0.571917i	−0.436053	−	0.899921i	$-0.643624\pi$
$197$	−19.3795	−	8.02724i	−1.38073	−	0.571917i	−0.944676	+	0.328004i	$0.893624\pi$
$198$		0			0
$199$	6.04325	−	6.04325i	0.428394	−	0.428394i	−0.459687	−	0.888081i	$-0.652038\pi$
$199$	6.04325	−	6.04325i	0.428394	−	0.428394i	0.888081	+	0.459687i	$0.152038\pi$
$200$	6.76128	+	9.71929i	0.478095	+	0.687258i
$201$		0			0
$202$	−3.96899	−	1.92653i	−0.279257	−	0.135551i
$203$	37.7173	+	15.6230i	2.64723	+	1.09652i
$204$		0			0
$205$	0.867743	+	2.09492i	0.0606058	+	0.146315i
$206$	−19.5133	+	17.3297i	−1.35955	+	1.20742i
$207$		0			0
$208$	1.65653	+	10.5388i	0.114860	+	0.730737i
$209$	1.97296			0.136473
$210$		0			0
$211$	−11.1986	+	4.63862i	−0.770945	+	0.319336i	−0.733255	−	0.679954i	$-0.762000\pi$
$211$	−11.1986	+	4.63862i	−0.770945	+	0.319336i	−0.0376897	+	0.999289i	$0.512000\pi$
$212$	−13.3417	+	23.7906i	−0.916312	+	1.63395i
$213$		0			0
$214$	13.8748	+	6.73480i	0.948465	+	0.460382i
$215$	−3.59481	+	3.59481i	−0.245164	+	0.245164i
$216$		0			0
$217$	11.1071	+	11.1071i	0.754002	+	0.754002i
$218$	4.07128	+	11.7517i	0.275742	+	0.795925i
$219$		0			0
$220$	−0.710472	−	0.902316i	−0.0479000	−	0.0608342i
$221$	−5.85347	−	14.1315i	−0.393747	−	0.950590i
$222$		0			0
$223$			9.60333i			0.643087i	0.946895	+	0.321543i	$0.104202\pi$
$223$			9.60333i			0.643087i	−0.946895	+	0.321543i	$0.895798\pi$
$224$	24.3682	−	12.9792i	1.62817	−	0.867209i
$225$		0			0
$226$	17.4444	+	1.03388i	1.16039	+	0.0687727i
$227$	6.66899	−	2.76239i	0.442636	−	0.183346i	−0.150223	−	0.988652i	$-0.547999\pi$
$227$	6.66899	−	2.76239i	0.442636	−	0.183346i	0.592859	+	0.805306i	$0.297999\pi$
$228$		0			0
$229$	−4.33945	+	10.4764i	−0.286759	+	0.692298i	−0.999963	−	0.00865930i	$-0.997244\pi$
$229$	−4.33945	+	10.4764i	−0.286759	+	0.692298i	0.713203	+	0.700957i	$0.247244\pi$
$230$	9.98508	−	3.45925i	0.658397	−	0.228096i
$231$		0			0
$232$	5.04997	+	23.1135i	0.331547	+	1.51747i
$233$	−15.0108	−	15.0108i	−0.983393	−	0.983393i	0.0164715	−	0.999864i	$-0.494757\pi$
$233$	−15.0108	−	15.0108i	−0.983393	−	0.983393i	−0.999864	+	0.0164715i	$0.994757\pi$
$234$		0			0
$235$	2.97668	−	7.18634i	0.194177	−	0.468785i
$236$	4.47488	−	7.97950i	0.291290	−	0.519421i
$237$		0			0
$238$	−29.5981	+	26.2860i	−1.91856	+	1.70387i
$239$			15.2045i			0.983499i	0.870737	+	0.491749i	$0.163642\pi$
$239$			15.2045i			0.983499i	−0.870737	+	0.491749i	$0.836358\pi$
$240$		0			0
$241$			0.135183i			0.00870787i	0.999991	+	0.00435394i	$0.00138591\pi$
$241$			0.135183i			0.00870787i	−0.999991	+	0.00435394i	$0.998614\pi$
$242$	9.94954	+	11.2032i	0.639581	+	0.720169i
$243$		0			0
$244$	−16.4399	+	4.62615i	−1.05246	+	0.296159i
$245$	−5.80769	+	14.0210i	−0.371040	+	0.895770i
$246$		0			0
$247$	5.84615	+	5.84615i	0.371981	+	0.371981i
$248$	−1.60815	+	8.95981i	−0.102117	+	0.568949i
$249$		0			0
$250$	−3.83685	−	11.0750i	−0.242663	−	0.700445i
$251$	7.63290	−	18.4275i	0.481784	−	1.16313i	−0.476976	−	0.878916i	$-0.658267\pi$
$251$	7.63290	−	18.4275i	0.481784	−	1.16313i	0.958761	−	0.284214i	$-0.0917328\pi$
$252$		0			0
$253$	4.86984	−	2.01715i	0.306164	−	0.126817i
$254$	0.571237	−	9.63835i	0.0358426	−	0.604764i
$255$		0			0
$256$	14.2390	+	7.29724i	0.889940	+	0.456078i
$257$		−	5.03984i		−	0.314377i	−0.987569	−	0.157188i	$-0.949757\pi$
$257$		−	5.03984i		−	0.314377i	0.987569	−	0.157188i	$-0.0502430\pi$
$258$		0			0
$259$	−0.0952249	−	0.229893i	−0.00591699	−	0.0142849i
$260$	0.568460	−	4.77891i	0.0352544	−	0.296375i
$261$		0			0
$262$	−5.72479	+	1.98331i	−0.353679	+	0.122529i
$263$	−14.2240	−	14.2240i	−0.877091	−	0.877091i	0.116141	−	0.993233i	$-0.462947\pi$
$263$	−14.2240	−	14.2240i	−0.877091	−	0.877091i	−0.993233	+	0.116141i	$0.962947\pi$
$264$		0			0
$265$	8.70075	−	8.70075i	0.534483	−	0.534483i
$266$	9.34332	−	19.2488i	0.572876	−	1.18022i
$267$		0			0
$268$	−4.56219	−	16.2126i	−0.278680	−	0.990345i
$269$	26.3106	−	10.8982i	1.60419	−	0.664476i	0.612187	−	0.790713i	$-0.290290\pi$
$269$	26.3106	−	10.8982i	1.60419	−	0.664476i	0.992000	+	0.126237i	$0.0402901\pi$
$270$		0			0
$271$	24.3810			1.48104			0.740521	−	0.672033i	$-0.234579\pi$
$271$	24.3810			1.48104			0.740521	+	0.672033i	$0.234579\pi$
$272$	−22.3003	−	5.38147i	−1.35215	−	0.326299i
$273$		0			0
$274$	−2.76377	−	3.11201i	−0.166965	−	0.188003i
$275$	−1.01954	−	2.46138i	−0.0614805	−	0.148427i
$276$		0			0
$277$	1.12617	+	0.466476i	0.0676651	+	0.0280278i	0.416259	−	0.909246i	$-0.363341\pi$
$277$	1.12617	+	0.466476i	0.0676651	+	0.0280278i	−0.348594	+	0.937274i	$0.613341\pi$
$278$	6.93155	−	14.2802i	0.415727	−	0.856468i
$279$		0			0
$280$	−12.1679	+	2.65851i	−0.727169	+	0.158876i
$281$	−17.5287	+	17.5287i	−1.04568	+	1.04568i	−0.0467705	+	0.998906i	$0.514893\pi$
$281$	−17.5287	+	17.5287i	−1.04568	+	1.04568i	−0.998906	+	0.0467705i	$0.985107\pi$
$282$		0			0
$283$	−10.1310	−	4.19638i	−0.602223	−	0.249449i	0.0606765	−	0.998157i	$-0.480674\pi$
$283$	−10.1310	−	4.19638i	−0.602223	−	0.249449i	−0.662899	+	0.748709i	$0.730674\pi$
$284$	−6.49168	−	8.24459i	−0.385210	−	0.489226i
$285$		0			0
$286$	0.142026	−	2.39636i	0.00839815	−	0.141700i
$287$	12.2663			0.724055
$288$		0			0
$289$	15.8914			0.934788
$290$	0.631438	−	10.6541i	0.0370793	−	0.625630i
$291$		0			0
$292$	8.95026	−	7.04732i	0.523774	−	0.412413i
$293$	−21.7206	−	8.99697i	−1.26893	−	0.525609i	−0.356292	−	0.934375i	$-0.615959\pi$
$293$	−21.7206	−	8.99697i	−1.26893	−	0.525609i	−0.912639	+	0.408766i	$0.865959\pi$
$294$		0			0
$295$	−2.91828	+	2.91828i	−0.169909	+	0.169909i
$296$	0.0778526	−	0.121383i	0.00452509	−	0.00705523i
$297$		0			0
$298$	4.15139	−	8.55257i	0.240484	−	0.495437i
$299$	20.4071	+	8.45289i	1.18017	+	0.488843i
$300$		0			0
$301$	10.5243	+	25.4079i	0.606609	+	1.46448i
$302$	−12.4775	−	14.0497i	−0.718002	−	0.808472i
$303$		0			0
$304$	12.2493	−	1.92539i	0.702547	−	0.110429i
$305$	7.70433			0.441149
$306$		0			0
$307$	−19.3644	+	8.02101i	−1.10519	+	0.457783i	−0.859277	−	0.511510i	$-0.829086\pi$
$307$	−19.3644	+	8.02101i	−1.10519	+	0.457783i	−0.245909	+	0.969293i	$0.579086\pi$
$308$	−5.98036	+	1.68285i	−0.340762	+	0.0958894i
$309$		0			0
$310$	1.79319	−	3.69428i	0.101847	−	0.209821i
$311$	4.53457	−	4.53457i	0.257132	−	0.257132i	−0.566755	−	0.823887i	$-0.691801\pi$
$311$	4.53457	−	4.53457i	0.257132	−	0.257132i	0.823887	+	0.566755i	$0.191801\pi$
$312$		0			0
$313$	2.69020	+	2.69020i	0.152059	+	0.152059i	0.779037	−	0.626978i	$-0.215708\pi$
$313$	2.69020	+	2.69020i	0.152059	+	0.152059i	−0.626978	+	0.779037i	$0.715708\pi$
$314$	−0.119325	+	0.0413390i	−0.00673387	+	0.00233289i
$315$		0			0
$316$	−14.5658	−	1.73263i	−0.819389	−	0.0974680i
$317$	10.0583	+	24.2828i	0.564929	+	1.36386i	0.905783	+	0.423743i	$0.139284\pi$
$317$	10.0583	+	24.2828i	0.564929	+	1.36386i	−0.340854	+	0.940116i	$0.610716\pi$
$318$		0			0
$319$		−	5.32369i		−	0.298070i
$320$	−5.29160	−	4.90878i	−0.295809	−	0.274409i
$321$		0			0
$322$	3.38204	−	57.0643i	0.188474	−	3.18007i
$323$	−16.4251	+	6.80351i	−0.913918	+	0.378557i
$324$		0			0
$325$	4.27238	−	10.3144i	0.236989	−	0.572142i
$326$	7.29877	+	21.0678i	0.404241	+	1.16684i
$327$		0			0
$328$	4.05944	+	5.83541i	0.224145	+	0.322207i
$329$	−29.7536	−	29.7536i	−1.64037	−	1.64037i
$330$		0			0
$331$	−11.5046	+	27.7745i	−0.632349	+	1.52662i	0.204313	+	0.978906i	$0.434504\pi$
$331$	−11.5046	+	27.7745i	−0.632349	+	1.52662i	−0.836662	+	0.547719i	$0.815496\pi$
$332$	−1.87551	−	6.66499i	−0.102932	−	0.365789i
$333$		0			0
$334$	−17.6326	−	19.8544i	−0.964813	−	1.08638i
$335$			7.59781i			0.415113i
$336$		0			0
$337$		−	1.63569i		−	0.0891019i	−0.999007	−	0.0445510i	$-0.985814\pi$
$337$		−	1.63569i		−	0.0891019i	0.999007	−	0.0445510i	$-0.0141857\pi$
$338$	−6.22476	+	5.52820i	−0.338582	+	0.300694i
$339$		0			0
$340$	9.02628	+	5.06191i	0.489519	+	0.274521i
$341$	0.783872	−	1.89243i	0.0424491	−	0.102481i
$342$		0			0
$343$	33.8931	+	33.8931i	1.83005	+	1.83005i
$344$	−8.60429	+	13.4153i	−0.463912	+	0.723302i
$345$		0			0
$346$	−0.692236	+	0.239819i	−0.0372148	+	0.0128928i
$347$	−5.02771	+	12.1380i	−0.269901	+	0.651600i	−0.999478	−	0.0322991i	$-0.989717\pi$
$347$	−5.02771	+	12.1380i	−0.269901	+	0.651600i	0.729577	+	0.683899i	$0.239717\pi$
$348$		0			0
$349$	−29.6535	+	12.2829i	−1.58732	+	0.657488i	−0.989551	−	0.144184i	$-0.953944\pi$
$349$	−29.6535	+	12.2829i	−1.58732	+	0.657488i	−0.597764	+	0.801672i	$0.703944\pi$
$350$	−28.8423	−	1.70940i	−1.54168	−	0.0913711i
$351$		0			0
$352$	−2.77974	−	2.28810i	−0.148161	−	0.121956i
$353$			3.02795i			0.161161i	0.996748	+	0.0805807i	$0.0256775\pi$
$353$			3.02795i			0.161161i	−0.996748	+	0.0805807i	$0.974323\pi$
$354$		0			0
$355$	1.81155	+	4.37347i	0.0961470	+	0.232119i
$356$	13.7864	−	10.8552i	0.730678	−	0.575326i
$357$		0			0
$358$	−5.89074	−	17.0035i	−0.311335	−	0.898665i
$359$	−3.56488	−	3.56488i	−0.188147	−	0.188147i	0.606748	−	0.794895i	$-0.292474\pi$
$359$	−3.56488	−	3.56488i	−0.188147	−	0.188147i	−0.794895	+	0.606748i	$0.792474\pi$
$360$		0			0
$361$	−6.64004	+	6.64004i	−0.349476	+	0.349476i
$362$	19.6822	+	9.55368i	1.03447	+	0.502130i
$363$		0			0
$364$	−22.7071	−	12.7341i	−1.19018	−	0.667447i
$365$	−4.74780	+	1.96660i	−0.248511	+	0.102937i
$366$		0			0
$367$	3.01328			0.157292			0.0786460	−	0.996903i	$-0.474940\pi$
$367$	3.01328			0.157292			0.0786460	+	0.996903i	$0.474940\pi$
$368$	28.2664	−	17.2761i	1.47349	−	0.900580i
$369$		0			0
$370$	−0.0486400	+	0.0431971i	−0.00252867	+	0.00224571i
$371$	−25.4726	−	61.4962i	−1.32247	−	3.19273i
$372$		0			0
$373$	0.479700	+	0.198698i	0.0248379	+	0.0102882i	0.395068	−	0.918652i	$-0.370721\pi$
$373$	0.479700	+	0.198698i	0.0248379	+	0.0102882i	−0.370230	+	0.928940i	$0.620721\pi$
$374$	4.64389	+	2.25413i	0.240130	+	0.116558i
$375$		0			0
$376$	4.30787	−	24.0013i	0.222161	−	1.23777i
$377$	15.7748	−	15.7748i	0.812444	−	0.812444i
$378$		0			0
$379$	−1.25025	−	0.517871i	−0.0642211	−	0.0266012i	0.350342	−	0.936622i	$-0.386065\pi$
$379$	−1.25025	−	0.517871i	−0.0642211	−	0.0266012i	−0.414563	+	0.910021i	$0.636065\pi$
$380$	−5.55454	−	0.660723i	−0.284942	−	0.0338944i
$381$		0			0
$382$	−0.620711	−	0.0367878i	−0.0317584	−	0.00188223i
$383$	−3.69633			−0.188874			−0.0944368	−	0.995531i	$-0.530105\pi$
$383$	−3.69633			−0.188874			−0.0944368	+	0.995531i	$0.530105\pi$
$384$		0			0
$385$	2.80260			0.142834
$386$	−15.0590	−	0.892500i	−0.766481	−	0.0454271i
$387$		0			0
$388$	−2.36550	−	0.281381i	−0.120090	−	0.0142850i
$389$	−23.5984	−	9.77479i	−1.19649	−	0.495602i	−0.306626	−	0.951830i	$-0.599200\pi$
$389$	−23.5984	−	9.77479i	−1.19649	−	0.495602i	−0.889863	+	0.456228i	$0.849200\pi$
$390$		0			0
$391$	−33.5861	+	33.5861i	−1.69852	+	1.69852i
$392$	−8.40492	+	46.8282i	−0.424513	+	2.36518i
$393$		0			0
$394$	26.6871	+	12.9538i	1.34447	+	0.652604i
$395$	6.11346	+	2.53228i	0.307601	+	0.127413i
$396$		0			0
$397$	−1.83523	−	4.43063i	−0.0921075	−	0.222367i	0.871111	−	0.491086i	$-0.163400\pi$
$397$	−1.83523	−	4.43063i	−0.0921075	−	0.222367i	−0.963219	+	0.268719i	$0.913400\pi$
$398$	−9.03711	+	8.02584i	−0.452989	+	0.402299i
$399$		0			0
$400$	−8.73194	−	14.2868i	−0.436597	−	0.714339i
$401$	22.4463			1.12092			0.560458	−	0.828183i	$-0.310625\pi$
$401$	22.4463			1.12092			0.560458	+	0.828183i	$0.310625\pi$
$402$		0			0
$403$	7.93025	−	3.28482i	0.395034	−	0.163628i
$404$	5.44197	+	3.05184i	0.270748	+	0.151835i
$405$		0			0
$406$	−51.9397	−	25.2113i	−2.57772	−	1.25122i
$407$	−0.0229448	+	0.0229448i	−0.00113733	+	0.00113733i
$408$		0			0
$409$	−5.09707	−	5.09707i	−0.252034	−	0.252034i	0.569770	−	0.821804i	$-0.307032\pi$
$409$	−5.09707	−	5.09707i	−0.252034	−	0.252034i	−0.821804	+	0.569770i	$0.807032\pi$
$410$	−1.04974	−	3.03007i	−0.0518431	−	0.149645i
$411$		0			0
$412$	28.9975	−	22.8323i	1.42861	−	1.12487i
$413$	8.54364	+	20.6262i	0.420405	+	1.01495i
$414$		0			0
$415$			3.12345i			0.153324i
$416$	−1.45681	−	15.0167i	−0.0714258	−	0.736253i
$417$		0			0
$418$	−2.78530	−	0.165077i	−0.136234	−	0.00807416i
$419$	−32.8525	+	13.6079i	−1.60495	+	0.664791i	−0.992105	−	0.125413i	$-0.959974\pi$
$419$	−32.8525	+	13.6079i	−1.60495	+	0.664791i	−0.612843	+	0.790205i	$0.709974\pi$
$420$		0			0
$421$	−11.8756	+	28.6702i	−0.578780	+	1.39730i	0.315128	+	0.949049i	$0.397953\pi$
$421$	−11.8756	+	28.6702i	−0.578780	+	1.39730i	−0.893908	+	0.448250i	$0.852047\pi$
$422$	16.1976	−	5.61153i	0.788487	−	0.273165i
$423$		0			0
$424$	20.8255	−	32.4698i	1.01138	−	1.57687i
$425$	16.9755	+	16.9755i	0.823435	+	0.823435i
$426$		0			0
$427$	15.9491	−	38.5045i	0.771831	−	1.86337i
$428$	−19.0241	−	10.6687i	−0.919566	−	0.515690i
$429$		0			0
$430$	5.37570	−	4.77415i	0.259239	−	0.230230i
$431$		−	37.7545i		−	1.81857i	−0.416176	−	0.909284i	$-0.636630\pi$
$431$		−	37.7545i		−	1.81857i	0.416176	−	0.909284i	$-0.363370\pi$
$432$		0			0
$433$		−	24.4795i		−	1.17641i	−0.808712	−	0.588205i	$-0.799835\pi$
$433$		−	24.4795i		−	1.17641i	0.808712	−	0.588205i	$-0.200165\pi$
$434$	−14.7510	−	16.6097i	−0.708072	−	0.797290i
$435$		0			0
$436$	−4.76431	−	16.9309i	−0.228169	−	0.810845i
$437$	9.82482	−	23.7192i	0.469985	−	1.13464i
$438$		0			0
$439$	−24.7303	−	24.7303i	−1.18031	−	1.18031i	−0.979664	−	0.200647i	$-0.935696\pi$
$439$	−24.7303	−	24.7303i	−1.18031	−	1.18031i	−0.200647	−	0.979664i	$-0.564304\pi$
$440$	0.927503	+	1.33328i	0.0442170	+	0.0635615i
$441$		0			0
$442$	7.08118	+	20.4398i	0.336817	+	0.972220i
$443$	−11.9139	+	28.7626i	−0.566044	+	1.36655i	0.338820	+	0.940851i	$0.389972\pi$
$443$	−11.9139	+	28.7626i	−0.566044	+	1.36655i	−0.904864	+	0.425701i	$0.860028\pi$
$444$		0			0
$445$	−7.31321	+	3.02923i	−0.346679	+	0.143599i
$446$	0.803506	−	13.5574i	0.0380471	−	0.641960i
$447$		0			0
$448$	−35.4874	+	16.2843i	−1.67662	+	0.769362i
$449$			16.3125i			0.769836i	0.922951	+	0.384918i	$0.125770\pi$
$449$			16.3125i			0.769836i	−0.922951	+	0.384918i	$0.874230\pi$
$450$		0			0
$451$	−0.612126	−	1.47780i	−0.0288239	−	0.0695870i
$452$	−24.5404	−	2.91913i	−1.15428	−	0.137304i
$453$		0			0
$454$	−9.64598	+	3.34177i	−0.452708	+	0.156837i
$455$	8.30449	+	8.30449i	0.389320	+	0.389320i
$456$		0			0
$457$	8.68958	−	8.68958i	0.406481	−	0.406481i	−0.474028	−	0.880510i	$-0.657201\pi$
$457$	8.68958	−	8.68958i	0.406481	−	0.406481i	0.880510	+	0.474028i	$0.157201\pi$
$458$	7.00272	−	14.4268i	0.327215	−	0.674120i
$459$		0			0
$460$	−14.3857	+	4.04810i	−0.670738	+	0.188744i
$461$	26.3401	−	10.9104i	1.22678	−	0.508149i	0.327221	−	0.944948i	$-0.393888\pi$
$461$	26.3401	−	10.9104i	1.22678	−	0.508149i	0.899559	+	0.436799i	$0.143888\pi$
$462$		0			0
$463$	−11.8225			−0.549439			−0.274720	−	0.961524i	$-0.588585\pi$
$463$	−11.8225			−0.549439			−0.274720	+	0.961524i	$0.588585\pi$
$464$	−5.19533	−	33.0527i	−0.241187	−	1.53443i
$465$		0			0
$466$	19.9354	+	22.4473i	0.923490	+	1.03985i
$467$	−13.3871	−	32.3194i	−0.619483	−	1.49556i	−0.852305	−	0.523044i	$-0.824796\pi$
$467$	−13.3871	−	32.3194i	−0.619483	−	1.49556i	0.232823	−	0.972519i	$-0.425204\pi$
$468$		0			0
$469$	37.9722	+	15.7286i	1.75339	+	0.726279i
$470$	−4.80356	+	9.89616i	−0.221572	+	0.456476i
$471$		0			0
$472$	−6.98499	+	10.8905i	−0.321510	+	0.501278i
$473$	2.53586	−	2.53586i	0.116599	−	0.116599i
$474$		0			0
$475$	−11.9885	−	4.96580i	−0.550070	−	0.227846i
$476$	43.9840	−	34.6324i	2.01600	−	1.58738i
$477$		0			0
$478$	1.27215	−	21.4648i	0.0581870	−	0.981776i
$479$	−25.0496			−1.14455			−0.572273	−	0.820063i	$-0.693938\pi$
$479$	−25.0496			−1.14455			−0.572273	+	0.820063i	$0.693938\pi$
$480$		0			0
$481$	−0.135977			−0.00620001
$482$	0.0113107	−	0.190842i	0.000515186	−	0.00869262i
$483$		0			0
$484$	−13.1088	−	16.6484i	−0.595853	−	0.756747i
$485$	0.992835	+	0.411246i	0.0450823	+	0.0186737i
$486$		0			0
$487$	28.8971	−	28.8971i	1.30945	−	1.30945i	0.387643	−	0.921810i	$-0.373289\pi$
$487$	28.8971	−	28.8971i	1.30945	−	1.30945i	0.921810	−	0.387643i	$-0.126711\pi$
$488$	23.5959	−	5.15538i	1.06814	−	0.233373i
$489$		0			0
$490$	9.37206	−	19.3080i	0.423387	−	0.872248i
$491$	25.7140	+	10.6511i	1.16046	+	0.480677i	0.878027	−	0.478611i	$-0.158859\pi$
$491$	25.7140	+	10.6511i	1.16046	+	0.480677i	0.282430	+	0.959288i	$0.408859\pi$
$492$		0			0
$493$	18.3581	+	44.3203i	0.826806	+	1.99609i
$494$	−7.76407	−	8.74236i	−0.349322	−	0.393337i
$495$		0			0
$496$	3.01994	−	12.5143i	0.135599	−	0.561910i
$497$	25.6078			1.14867
$498$		0			0
$499$	29.4590	−	12.2023i	1.31876	−	0.546250i	0.391335	−	0.920248i	$-0.372013\pi$
$499$	29.4590	−	12.2023i	1.31876	−	0.546250i	0.927430	+	0.373998i	$0.122013\pi$
$500$	4.48997	+	15.9560i	0.200798	+	0.713575i
$501$		0			0
$502$	−12.3175	+	25.3761i	−0.549755	+	1.13259i
$503$	−8.37801	+	8.37801i	−0.373557	+	0.373557i	−0.868771	−	0.495214i	$-0.835090\pi$
$503$	−8.37801	+	8.37801i	−0.373557	+	0.373557i	0.495214	+	0.868771i	$0.335090\pi$
$504$		0			0
$505$	−1.99025	−	1.99025i	−0.0885650	−	0.0885650i
$506$	−7.04371	+	2.44023i	−0.313131	+	0.108482i
$507$		0			0
$508$	−1.61287	+	13.5590i	−0.0715596	+	0.601584i
$509$	−4.19708	−	10.1326i	−0.186032	−	0.449122i	0.803157	−	0.595768i	$-0.203152\pi$
$509$	−4.19708	−	10.1326i	−0.186032	−	0.449122i	−0.989189	+	0.146646i	$0.953152\pi$
$510$		0			0
$511$			27.7996i			1.22978i
$512$	−19.4912	−	11.4932i	−0.861398	−	0.507930i
$513$		0			0
$514$	−0.421681	+	7.11493i	−0.0185995	+	0.313826i
$515$	−15.3822	+	6.37151i	−0.677820	+	0.280762i
$516$		0			0
$517$	−2.09982	+	5.06941i	−0.0923499	+	0.222952i
$518$	0.115197	+	0.332516i	0.00506148	+	0.0146099i
$519$		0			0
$520$	−1.20237	+	6.69899i	−0.0527272	+	0.293770i
$521$	−10.6298	−	10.6298i	−0.465702	−	0.465702i	0.434817	−	0.900519i	$-0.356813\pi$
$521$	−10.6298	−	10.6298i	−0.465702	−	0.465702i	−0.900519	+	0.434817i	$0.856813\pi$
$522$		0			0
$523$	−9.12300	+	22.0249i	−0.398921	+	0.963081i	0.589001	+	0.808132i	$0.299521\pi$
$523$	−9.12300	+	22.0249i	−0.398921	+	0.963081i	−0.987923	+	0.154949i	$0.950479\pi$
$524$	8.24784	−	2.32092i	0.360309	−	0.101390i
$525$		0			0
$526$	18.8905	+	21.2707i	0.823663	+	0.927447i
$527$			18.4578i			0.804035i
$528$		0			0
$529$		−	45.5908i		−	1.98221i
$530$	−13.0112	+	11.5552i	−0.565168	+	0.501925i
$531$		0			0
$532$	−14.8009	+	26.3925i	−0.641698	+	1.14426i
$533$	2.56512	−	6.19274i	0.111107	−	0.268237i
$534$		0			0
$535$	6.95754	+	6.95754i	0.300801	+	0.300801i
$536$	5.08410	+	23.2697i	0.219600	+	1.00510i
$537$		0			0
$538$	−38.0555	+	13.1840i	−1.64069	+	0.568403i
$539$	4.09688	−	9.89075i	0.176465	−	0.426025i
$540$		0			0
$541$	−10.8444	+	4.49190i	−0.466238	+	0.193122i	−0.603420	−	0.797424i	$-0.706196\pi$
$541$	−10.8444	+	4.49190i	−0.466238	+	0.193122i	0.137182	+	0.990546i	$0.456196\pi$
$542$	−34.4196	−	2.03995i	−1.47845	−	0.0876233i
$543$		0			0
$544$	31.0318	+	9.46307i	1.33048	+	0.405726i
$545$			7.93443i			0.339874i
$546$		0			0
$547$	5.18305	+	12.5130i	0.221611	+	0.535016i	0.995109	−	0.0987824i	$-0.0314948\pi$
$547$	5.18305	+	12.5130i	0.221611	+	0.535016i	−0.773498	+	0.633799i	$0.781495\pi$
$548$	3.64133	+	4.62458i	0.155550	+	0.197552i
$549$		0			0
$550$	1.23338	+	3.56013i	0.0525914	+	0.151804i
$551$	−18.3351	−	18.3351i	−0.781102	−	0.781102i
$552$		0			0
$553$	25.3115	−	25.3115i	1.07635	−	1.07635i
$554$	−1.55083	−	0.752767i	−0.0658884	−	0.0319820i
$555$		0			0
$556$	−10.9803	+	19.5799i	−0.465670	+	0.830372i
$557$	21.1742	−	8.77062i	0.897178	−	0.371623i	0.114044	−	0.993476i	$-0.463620\pi$
$557$	21.1742	−	8.77062i	0.897178	−	0.371623i	0.783134	+	0.621852i	$0.213620\pi$
$558$		0			0
$559$	15.0282			0.635625
$560$	17.4002	−	2.73503i	0.735295	−	0.115576i
$561$		0			0
$562$	26.2126	−	23.2793i	1.10571	−	0.981979i
$563$	−0.103899	−	0.250835i	−0.00437882	−	0.0105714i	0.921675	−	0.387963i	$-0.126821\pi$
$563$	−0.103899	−	0.250835i	−0.00437882	−	0.0105714i	−0.926054	+	0.377391i	$0.876821\pi$
$564$		0			0
$565$	10.3000	+	4.26638i	0.433322	+	0.179488i
$566$	13.9511	+	6.77183i	0.586410	+	0.284641i
$567$		0			0
$568$	8.47472	+	12.1823i	0.355591	+	0.511160i
$569$	−6.63868	+	6.63868i	−0.278308	+	0.278308i	−0.832433	−	0.554125i	$-0.813053\pi$
$569$	−6.63868	+	6.63868i	−0.278308	+	0.278308i	0.554125	+	0.832433i	$0.313053\pi$
$570$		0			0
$571$	32.5158	+	13.4685i	1.36074	+	0.563639i	0.939263	−	0.343198i	$-0.111510\pi$
$571$	32.5158	+	13.4685i	1.36074	+	0.563639i	0.421482	+	0.906837i	$0.361510\pi$
$572$	−0.401005	+	3.37115i	−0.0167669	+	0.140955i
$573$		0			0
$574$	−17.3168	−	1.02631i	−0.722787	−	0.0428375i
$575$	−34.6681			−1.44576
$576$		0			0
$577$	−42.7843			−1.78113			−0.890566	−	0.454854i	$-0.849692\pi$
$577$	−42.7843			−1.78113			−0.890566	+	0.454854i	$0.849692\pi$
$578$	−22.4345	−	1.32963i	−0.933151	−	0.0553051i
$579$		0			0
$580$	−1.78285	+	14.9880i	−0.0740287	+	0.622341i
$581$	15.6103	+	6.46600i	0.647624	+	0.268255i
$582$		0			0
$583$	−6.13771	+	6.13771i	−0.254198	+	0.254198i
$584$	−13.2251	+	9.20009i	−0.547257	+	0.380702i
$585$		0			0
$586$	29.9110	+	14.5187i	1.23561	+	0.599762i
$587$	−0.435632	−	0.180445i	−0.0179804	−	0.00744775i	0.373675	−	0.927560i	$-0.378098\pi$
$587$	−0.435632	−	0.180445i	−0.0179804	−	0.00744775i	−0.391656	+	0.920112i	$0.628098\pi$
$588$		0			0
$589$	−3.81795	−	9.21735i	−0.157316	−	0.379794i
$590$	4.36401	−	3.87567i	0.179664	−	0.159559i
$591$		0			0
$592$	−0.120063	+	0.164847i	−0.00493458	+	0.00677515i
$593$	40.4300			1.66026			0.830130	−	0.557570i	$-0.188266\pi$
$593$	40.4300			1.66026			0.830130	+	0.557570i	$0.188266\pi$
$594$		0			0
$595$	−23.3320	+	9.66443i	−0.956518	+	0.396203i
$596$	−6.57626	+	11.7266i	−0.269374	+	0.480342i
$597$		0			0
$598$	−28.1022	−	13.6407i	−1.14918	−	0.557810i
$599$	9.57920	−	9.57920i	0.391396	−	0.391396i	−0.483789	−	0.875185i	$-0.660740\pi$
$599$	9.57920	−	9.57920i	0.391396	−	0.391396i	0.875185	+	0.483789i	$0.160740\pi$
$600$		0			0
$601$	−8.08181	−	8.08181i	−0.329664	−	0.329664i	0.522795	−	0.852459i	$-0.324889\pi$
$601$	−8.08181	−	8.08181i	−0.329664	−	0.329664i	−0.852459	+	0.522795i	$0.824889\pi$
$602$	−12.7316	−	36.7497i	−0.518903	−	1.49781i
$603$		0			0
$604$	16.4395	+	20.8785i	0.668913	+	0.849535i
$605$	3.65809	+	8.83141i	0.148723	+	0.359048i
$606$		0			0
$607$			11.8167i			0.479627i	0.970819	+	0.239813i	$0.0770863\pi$
$607$			11.8167i			0.479627i	−0.970819	+	0.239813i	$0.922914\pi$
$608$	−17.4539	+	1.69325i	−0.707850	+	0.0686703i
$609$		0			0
$610$	−10.8765	−	0.644618i	−0.440376	−	0.0260998i
$611$	−21.2434	+	8.79930i	−0.859415	+	0.355981i
$612$		0			0
$613$	−6.80285	+	16.4235i	−0.274764	+	0.663340i	−0.999675	−	0.0255033i	$-0.991881\pi$
$613$	−6.80285	+	16.4235i	−0.274764	+	0.663340i	0.724910	+	0.688843i	$0.241881\pi$
$614$	28.0086	−	9.70334i	1.13033	−	0.391595i
$615$		0			0
$616$	8.58349	−	1.87537i	0.345839	−	0.0755609i
$617$	−19.3722	−	19.3722i	−0.779894	−	0.779894i	0.199919	−	0.979812i	$-0.435932\pi$
$617$	−19.3722	−	19.3722i	−0.779894	−	0.779894i	−0.979812	+	0.199919i	$0.935932\pi$
$618$		0			0
$619$	14.0130	−	33.8305i	0.563231	−	1.35976i	−0.343937	−	0.938993i	$-0.611761\pi$
$619$	14.0130	−	33.8305i	0.563231	−	1.35976i	0.907168	−	0.420768i	$-0.138239\pi$
$620$	−2.84061	+	5.06532i	−0.114082	+	0.203428i
$621$		0			0
$622$	−6.78102	+	6.02221i	−0.271894	+	0.241469i
$623$			42.8207i			1.71558i
$624$		0			0
$625$			13.4524i			0.538094i
$626$	−3.57277	−	4.02295i	−0.142797	−	0.160789i
$627$		0			0
$628$	0.171914	−	0.0483759i	0.00686010	−	0.00193041i
$629$	0.111896	−	0.270140i	0.00446157	−	0.0107712i
$630$		0			0
$631$	−11.1070	−	11.1070i	−0.442163	−	0.442163i	0.450575	−	0.892738i	$-0.351219\pi$
$631$	−11.1070	−	11.1070i	−0.442163	−	0.442163i	−0.892738	+	0.450575i	$0.851219\pi$
$632$	20.4181	+	3.66473i	0.812187	+	0.145775i
$633$		0			0
$634$	−12.1679	−	35.1225i	−0.483249	−	1.39489i
$635$	2.35725	−	5.69090i	0.0935446	−	0.225837i
$636$		0			0
$637$	41.4472	−	17.1680i	1.64220	−	0.680221i
$638$	−0.445431	+	7.51565i	−0.0176348	+	0.297547i
$639$		0			0
$640$	7.05962	+	7.37265i	0.279056	+	0.291430i
$641$		−	19.0121i		−	0.750933i	−0.926836	−	0.375466i	$-0.877483\pi$
$641$		−	19.0121i		−	0.750933i	0.926836	−	0.375466i	$-0.122517\pi$
$642$		0			0
$643$	−0.331999	−	0.801516i	−0.0130928	−	0.0316087i	0.917198	−	0.398432i	$-0.130445\pi$
$643$	−0.331999	−	0.801516i	−0.0130928	−	0.0316087i	−0.930291	+	0.366823i	$0.880445\pi$
$644$	−9.54909	+	80.2768i	−0.376287	+	3.16335i
$645$		0			0
$646$	23.7572	−	8.23048i	0.934714	−	0.323824i
$647$	−7.40726	−	7.40726i	−0.291210	−	0.291210i	0.546348	−	0.837558i	$-0.316017\pi$
$647$	−7.40726	−	7.40726i	−0.291210	−	0.291210i	−0.837558	+	0.546348i	$0.816017\pi$
$648$		0			0
$649$	2.05862	−	2.05862i	0.0808080	−	0.0808080i
$650$	−6.89448	+	14.2038i	−0.270424	+	0.557119i
$651$		0			0
$652$	−8.54120	−	30.3529i	−0.334499	−	1.18871i
$653$	−4.20199	+	1.74052i	−0.164437	+	0.0681119i	−0.463383	−	0.886158i	$-0.653365\pi$
$653$	−4.20199	+	1.74052i	−0.164437	+	0.0681119i	0.298947	+	0.954270i	$0.403365\pi$
$654$		0			0
$655$	−3.86523			−0.151027
$656$	−5.24261	−	8.57772i	−0.204690	−	0.334904i
$657$		0			0
$658$	39.5147	+	44.4936i	1.54044	+	1.73454i
$659$	8.97301	+	21.6628i	0.349539	+	0.843861i	0.996674	+	0.0814864i	$0.0259667\pi$
$659$	8.97301	+	21.6628i	0.349539	+	0.843861i	−0.647136	+	0.762375i	$0.724033\pi$
$660$		0			0
$661$	−31.2193	−	12.9315i	−1.21429	−	0.502975i	−0.318700	−	0.947856i	$-0.603246\pi$
$661$	−31.2193	−	12.9315i	−1.21429	−	0.502975i	−0.895590	+	0.444880i	$0.853246\pi$
$662$	18.5653	−	38.2477i	0.721561	−	1.48654i
$663$		0			0
$664$	2.09007	+	9.56614i	0.0811103	+	0.371238i
$665$	9.65233	−	9.65233i	0.374301	−	0.374301i
$666$		0			0
$667$	−64.0022	−	26.5106i	−2.47817	−	1.02649i
$668$	23.2314	+	29.5044i	0.898850	+	1.14156i
$669$		0			0
$670$	0.635705	−	10.7261i	0.0245594	−	0.414386i
$671$	−5.43482			−0.209809
$672$		0			0
$673$	−4.66326			−0.179756			−0.0898778	−	0.995953i	$-0.528648\pi$
$673$	−4.66326			−0.179756			−0.0898778	+	0.995953i	$0.528648\pi$
$674$	−0.136858	+	2.30917i	−0.00527156	+	0.0889458i
$675$		0			0
$676$	9.25026	−	7.28354i	0.355779	−	0.280136i
$677$	−27.8340	−	11.5292i	−1.06975	−	0.443104i	−0.222846	−	0.974854i	$-0.571535\pi$
$677$	−27.8340	−	11.5292i	−1.06975	−	0.443104i	−0.846901	+	0.531750i	$0.821535\pi$
$678$		0			0
$679$	4.11063	−	4.11063i	0.157751	−	0.157751i
$680$	−12.3192	−	7.90131i	−0.472420	−	0.303001i
$681$		0			0
$682$	−1.26496	+	2.60603i	−0.0484378	+	0.0997901i
$683$	32.4842	+	13.4554i	1.24297	+	0.514856i	0.904642	−	0.426171i	$-0.140138\pi$
$683$	32.4842	+	13.4554i	1.24297	+	0.514856i	0.338330	+	0.941027i	$0.390138\pi$
$684$		0			0
$685$	−1.01614	−	2.45318i	−0.0388247	−	0.0937310i
$686$	−45.0123	−	50.6839i	−1.71858	−	1.93512i
$687$		0			0
$688$	13.2694	−	18.2189i	0.505893	−	0.694588i
$689$	−36.3737			−1.38573
$690$		0			0
$691$	15.6190	−	6.46959i	0.594173	−	0.246115i	−0.0652715	−	0.997868i	$-0.520791\pi$
$691$	15.6190	−	6.46959i	0.594173	−	0.246115i	0.659445	+	0.751753i	$0.270791\pi$
$692$	0.997320	−	0.280643i	0.0379124	−	0.0106684i
$693$		0			0
$694$	8.11337	−	16.7149i	0.307979	−	0.634490i
$695$	7.16079	−	7.16079i	0.271624	−	0.271624i
$696$		0			0
$697$	10.1920	+	10.1920i	0.386051	+	0.386051i
$698$	42.8906	−	14.8591i	1.62343	−	0.562425i
$699$		0			0
$700$	40.5746	+	4.82643i	1.53358	+	0.182422i
$701$	2.80669	+	6.77595i	0.106007	+	0.255924i	0.967979	−	0.251033i	$-0.0807702\pi$
$701$	2.80669	+	6.77595i	0.106007	+	0.255924i	−0.861971	+	0.506957i	$0.830770\pi$
$702$		0			0
$703$			0.158046i			0.00596083i
$704$	3.73281	+	3.46277i	0.140686	+	0.130508i
$705$		0			0
$706$	0.253347	−	4.27466i	0.00953483	−	0.160879i
$707$	−14.0669	+	5.82671i	−0.529041	+	0.219136i
$708$		0			0
$709$	−6.10522	+	14.7393i	−0.229286	+	0.553546i	−0.996091	−	0.0883343i	$-0.971846\pi$
$709$	−6.10522	+	14.7393i	−0.229286	+	0.553546i	0.766804	+	0.641881i	$0.221846\pi$
$710$	−2.19150	−	6.32575i	−0.0822457	−	0.237401i
$711$		0			0
$712$	−20.3710	+	14.1712i	−0.763436	+	0.531089i
$713$	−18.8476	−	18.8476i	−0.705849	−	0.705849i
$714$		0			0
$715$	0.586079	−	1.41492i	0.0219181	−	0.0529150i
$716$	6.89349	+	24.4974i	0.257622	+	0.915511i
$717$		0			0
$718$	4.73439	+	5.33094i	0.176686	+	0.198949i
$719$			25.8821i			0.965239i	0.875830	+	0.482620i	$0.160315\pi$
$719$			25.8821i			0.965239i	−0.875830	+	0.482620i	$0.839685\pi$
$720$		0			0
$721$			90.0667i			3.35426i
$722$	9.92955	−	8.81841i	0.369540	−	0.328187i
$723$		0			0
$724$	−26.9867	−	15.1341i	−1.00295	−	0.562453i
$725$	−13.3993	+	32.3489i	−0.497639	+	1.20141i
$726$		0			0
$727$	12.7455	+	12.7455i	0.472705	+	0.472705i	0.902789	−	0.430084i	$-0.141516\pi$
$727$	12.7455	+	12.7455i	0.472705	+	0.472705i	−0.430084	+	0.902789i	$0.641516\pi$
$728$	30.9910	+	19.8771i	1.14860	+	0.736693i
$729$		0			0
$730$	6.86719	−	2.37908i	0.254166	−	0.0880537i
$731$	−12.3667	+	29.8559i	−0.457400	+	1.10426i
$732$		0			0
$733$	−16.9164	+	7.00700i	−0.624822	+	0.258810i	−0.672551	−	0.740051i	$-0.734801\pi$
$733$	−16.9164	+	7.00700i	−0.624822	+	0.258810i	0.0477294	+	0.998860i	$0.484801\pi$
$734$	−4.25396	−	0.252120i	−0.157017	−	0.00930591i
$735$		0			0
$736$	−41.3502	+	22.0243i	−1.52419	+	0.811827i
$737$		−	5.35967i		−	0.197426i
$738$		0			0
$739$	3.73120	+	9.00791i	0.137254	+	0.331361i	0.977529	−	0.210799i	$-0.0676065\pi$
$739$	3.73120	+	9.00791i	0.137254	+	0.331361i	−0.840275	+	0.542160i	$0.817607\pi$
$740$	0.0722811	−	0.0569132i	0.00265711	−	0.00209217i
$741$		0			0
$742$	30.8152	+	88.9477i	1.13126	+	3.26537i
$743$	12.1162	+	12.1162i	0.444502	+	0.444502i	0.893522	−	0.449020i	$-0.148227\pi$
$743$	12.1162	+	12.1162i	0.444502	+	0.444502i	−0.449020	+	0.893522i	$0.648227\pi$
$744$		0			0
$745$	4.28869	−	4.28869i	0.157125	−	0.157125i
$746$	−0.660585	−	0.320646i	−0.0241857	−	0.0117397i
$747$		0			0
$748$	−6.36735	−	3.57079i	−0.232813	−	0.130561i
$749$	49.1753	−	20.3691i	1.79683	−	0.744271i
$750$		0			0
$751$	−26.4456			−0.965014			−0.482507	−	0.875892i	$-0.660274\pi$
$751$	−26.4456			−0.965014			−0.482507	+	0.875892i	$0.660274\pi$
$752$	−8.08975	+	33.5231i	−0.295003	+	1.22246i
$753$		0			0
$754$	−23.5897	+	20.9500i	−0.859088	+	0.762954i
$755$	−4.58755	−	11.0753i	−0.166958	−	0.403072i
$756$		0			0
$757$	−40.9342	−	16.9555i	−1.48778	−	0.616258i	−0.516946	−	0.856018i	$-0.672931\pi$
$757$	−40.9342	−	16.9555i	−1.48778	−	0.616258i	−0.970832	+	0.239760i	$0.922931\pi$
$758$	1.72169	+	0.835705i	0.0625347	+	0.0303542i
$759$		0			0
$760$	7.78626	+	1.39751i	0.282437	+	0.0506931i
$761$	37.9127	−	37.9127i	1.37434	−	1.37434i	0.520434	−	0.853902i	$-0.325770\pi$
$761$	37.9127	−	37.9127i	1.37434	−	1.37434i	0.853902	−	0.520434i	$-0.174230\pi$
$762$		0			0
$763$	39.6545	+	16.4254i	1.43559	+	0.594641i
$764$	0.873203	+	0.103869i	0.0315914	+	0.00375786i
$765$		0			0
$766$	5.21824	+	0.309270i	0.188543	+	0.0111744i
$767$	12.1999			0.440514
$768$		0			0
$769$	44.1163			1.59088			0.795438	−	0.606036i	$-0.207241\pi$
$769$	44.1163			1.59088			0.795438	+	0.606036i	$0.207241\pi$
$770$	−3.95654	−	0.234492i	−0.142584	−	0.00845052i
$771$		0			0
$772$	21.1846	+	2.51995i	0.762450	+	0.0906950i
$773$	21.7738	+	9.01900i	0.783149	+	0.324391i	0.738186	−	0.674598i	$-0.235683\pi$
$773$	21.7738	+	9.01900i	0.783149	+	0.324391i	0.0449634	+	0.998989i	$0.485683\pi$
$774$		0			0
$775$	−9.52624	+	9.52624i	−0.342193	+	0.342193i
$776$	3.31593	+	0.595157i	0.119035	+	0.0213649i
$777$		0			0
$778$	32.4969	+	15.7739i	1.16507	+	0.565522i
$779$	−7.19783	−	2.98144i	−0.257889	−	0.106821i
$780$		0			0
$781$	−1.27791	−	3.08514i	−0.0457272	−	0.110395i
$782$	50.2248	−	44.6045i	1.79603	−	1.59505i
$783$		0			0
$784$	15.7836	−	65.4058i	0.563701	−	2.33592i
$785$	−0.0805647			−0.00287548
$786$		0			0
$787$	−10.1048	+	4.18555i	−0.360197	+	0.149199i	−0.555441	−	0.831556i	$-0.687450\pi$
$787$	−10.1048	+	4.18555i	−0.360197	+	0.149199i	0.195243	+	0.980755i	$0.437450\pi$
$788$	−36.5912	−	20.5203i	−1.30351	−	0.731004i
$789$		0			0
$790$	−8.41872	−	4.08642i	−0.299525	−	0.145388i
$791$	42.6448	−	42.6448i	1.51628	−	1.51628i
$792$		0			0
$793$	−16.1041	−	16.1041i	−0.571873	−	0.571873i
$794$	2.22015	+	6.40844i	0.0787902	+	0.227427i
$795$		0			0
$796$	13.4295	−	10.5742i	0.475997	−	0.374794i
$797$	−9.00806	−	21.7474i	−0.319082	−	0.770331i	−0.999303	−	0.0373247i	$-0.988116\pi$
$797$	−9.00806	−	21.7474i	−0.319082	−	0.770331i	0.680222	−	0.733007i	$-0.261884\pi$
$798$		0			0
$799$		−	49.4444i		−	1.74922i
$800$	11.1318	+	20.8998i	0.393570	+	0.738919i
$801$		0			0
$802$	−31.6883	−	1.87807i	−1.11895	−	0.0663170i
$803$	3.34921	−	1.38729i	0.118191	−	0.0489563i
$804$		0			0
$805$	13.9562	−	33.6933i	0.491892	−	1.18753i
$806$	−11.4703	+	3.97378i	−0.404023	+	0.139970i
$807$		0			0
$808$	−7.42729	−	4.76372i	−0.261291	−	0.167587i
$809$	16.4641	+	16.4641i	0.578846	+	0.578846i	0.934585	−	0.355739i	$-0.115771\pi$
$809$	16.4641	+	16.4641i	0.578846	+	0.578846i	−0.355739	+	0.934585i	$0.615771\pi$
$810$		0			0
$811$	−2.95139	+	7.12528i	−0.103637	+	0.250202i	−0.967189	−	0.254058i	$-0.918235\pi$
$811$	−2.95139	+	7.12528i	−0.103637	+	0.250202i	0.863552	+	0.504260i	$0.168235\pi$
$812$	71.2157	+	39.9375i	2.49918	+	1.40153i
$813$		0			0
$814$	0.0343118	−	0.0304722i	0.00120263	−	0.00106805i
$815$			14.2244i			0.498260i
$816$		0			0
$817$		−	17.4673i		−	0.611104i
$818$	6.76925	+	7.62218i	0.236681	+	0.266503i
$819$		0			0
$820$	1.22844	+	4.36550i	0.0428989	+	0.152450i
$821$	−7.72256	+	18.6439i	−0.269519	+	0.650677i	−0.999461	−	0.0328326i	$-0.989547\pi$
$821$	−7.72256	+	18.6439i	−0.269519	+	0.650677i	0.729942	+	0.683509i	$0.239547\pi$
$822$		0			0
$823$	−23.2777	−	23.2777i	−0.811410	−	0.811410i	0.173435	−	0.984845i	$-0.444513\pi$
$823$	−23.2777	−	23.2777i	−0.811410	−	0.811410i	−0.984845	+	0.173435i	$0.944513\pi$
$824$	−42.8472	+	29.8070i	−1.49265	+	1.03837i
$825$		0			0
$826$	−10.3356	−	29.8336i	−0.359621	−	1.03804i
$827$	−5.93927	+	14.3387i	−0.206529	+	0.498605i	−0.992872	−	0.119185i	$-0.961972\pi$
$827$	−5.93927	+	14.3387i	−0.206529	+	0.498605i	0.786343	+	0.617790i	$0.211972\pi$
$828$		0			0
$829$	19.5176	−	8.08444i	0.677873	−	0.280784i	−0.0170645	−	0.999854i	$-0.505432\pi$
$829$	19.5176	−	8.08444i	0.677873	−	0.280784i	0.694937	+	0.719070i	$0.255432\pi$
$830$	0.261337	−	4.40949i	0.00907115	−	0.153056i
$831$		0			0
$832$	0.800189	+	21.3215i	0.0277415	+	0.739189i
$833$			96.4691i			3.34246i
$834$		0			0
$835$	−6.48288	−	15.6511i	−0.224349	−	0.541627i
$836$	3.91830	+	0.466089i	0.135517	+	0.0161200i
$837$		0			0
$838$	47.5176	−	16.4621i	1.64147	−	0.568673i
$839$	12.7778	+	12.7778i	0.441139	+	0.441139i	0.892395	−	0.451256i	$-0.149024\pi$
$839$	12.7778	+	12.7778i	0.441139	+	0.441139i	−0.451256	+	0.892395i	$0.649024\pi$
$840$		0			0
$841$	−28.9680	+	28.9680i	−0.998896	+	0.998896i
$842$	19.1640	−	39.4811i	0.660435	−	1.36061i
$843$		0			0
$844$	−23.3363	+	6.56675i	−0.803267	+	0.226037i
$845$	−4.90694	+	2.03252i	−0.168804	+	0.0699209i
$846$		0			0
$847$	51.7102			1.77678
$848$	−32.1169	+	44.0963i	−1.10290	+	1.51427i
$849$		0			0
$850$	−22.5447	−	25.3853i	−0.773275	−	0.870709i
$851$	0.161586	+	0.390104i	0.00553911	+	0.0133726i
$852$		0			0
$853$	−37.7373	−	15.6313i	−1.29210	−	0.535206i	−0.372490	−	0.928036i	$-0.621496\pi$
$853$	−37.7373	−	15.6313i	−1.29210	−	0.535206i	−0.919611	+	0.392831i	$0.871496\pi$
$854$	−25.7376	+	53.0238i	−0.880722	+	1.81444i
$855$		0			0
$856$	25.9644	+	16.6531i	0.887445	+	0.569191i
$857$	23.3010	−	23.3010i	0.795946	−	0.795946i	−0.186508	−	0.982453i	$-0.559717\pi$
$857$	23.3010	−	23.3010i	0.795946	−	0.795946i	0.982453	+	0.186508i	$0.0597170\pi$
$858$		0			0
$859$	6.12129	+	2.53552i	0.208856	+	0.0865109i	0.484659	−	0.874703i	$-0.338944\pi$
$859$	6.12129	+	2.53552i	0.208856	+	0.0865109i	−0.275803	+	0.961214i	$0.588944\pi$
$860$	−7.98852	+	6.29006i	−0.272406	+	0.214489i
$861$		0			0
$862$	−3.15890	+	53.2993i	−0.107592	+	1.81538i
$863$	−32.4832			−1.10574			−0.552871	−	0.833267i	$-0.686468\pi$
$863$	−32.4832			−1.10574			−0.552871	+	0.833267i	$0.686468\pi$
$864$		0			0
$865$	−0.467379			−0.0158914
$866$	−2.04819	+	34.5586i	−0.0696003	+	1.17435i
$867$		0			0
$868$	19.4348	+	24.6827i	0.659661	+	0.837786i
$869$	−4.31258	−	1.78633i	−0.146294	−	0.0605970i
$870$		0			0
$871$	15.8814	−	15.8814i	0.538122	−	0.538122i
$872$	5.30935	+	24.3006i	0.179797	+	0.822924i
$873$		0			0
$874$	−15.8546	+	32.6632i	−0.536291	+	1.10485i
$875$	−37.3711	−	15.4796i	−1.26337	−	0.523307i
$876$		0			0
$877$	−11.9266	−	28.7933i	−0.402732	−	0.972282i	−0.987000	−	0.160721i	$-0.948618\pi$
$877$	−11.9266	−	28.7933i	−0.402732	−	0.972282i	0.584267	−	0.811561i	$-0.301382\pi$
$878$	32.8434	+	36.9818i	1.10841	+	1.24807i
$879$		0			0
$880$	−1.19783	−	1.95984i	−0.0403790	−	0.0660662i
$881$	15.6103			0.525925			0.262962	−	0.964806i	$-0.415301\pi$
$881$	15.6103			0.525925			0.262962	+	0.964806i	$0.415301\pi$
$882$		0			0
$883$	−36.8077	+	15.2463i	−1.23868	+	0.513077i	−0.903301	−	0.429007i	$-0.858864\pi$
$883$	−36.8077	+	15.2463i	−1.23868	+	0.513077i	−0.335377	+	0.942084i	$0.608864\pi$
$884$	−8.28658	−	29.4480i	−0.278708	−	0.990444i
$885$		0			0
$886$	19.2258	−	39.6084i	0.645902	−	1.33067i
$887$	−7.06761	+	7.06761i	−0.237307	+	0.237307i	−0.815734	−	0.578427i	$-0.803667\pi$
$887$	−7.06761	+	7.06761i	−0.237307	+	0.237307i	0.578427	+	0.815734i	$0.303667\pi$
$888$		0			0
$889$	−23.5620	−	23.5620i	−0.790244	−	0.790244i
$890$	10.5778	−	3.66458i	0.354568	−	0.122837i
$891$		0			0
$892$	−2.26868	+	19.0722i	−0.0759609	+	0.638585i
$893$	10.2274	+	24.6912i	0.342248	+	0.826261i
$894$		0			0
$895$		−	11.4803i		−	0.383745i
$896$	51.4613	−	20.0200i	1.71920	−	0.668820i
$897$		0			0
$898$	1.36486	−	23.0290i	0.0455460	−	0.768487i
$899$	−24.8714	+	10.3021i	−0.829509	+	0.343594i
$900$		0			0
$901$	29.9320	−	72.2622i	0.997179	−	2.40740i
$902$	0.740513	+	2.13748i	0.0246564	+	0.0711704i
$903$		0			0
$904$	34.4004	+	6.17433i	1.14414	+	0.205355i
$905$	9.86964	+	9.86964i	0.328078	+	0.328078i
$906$		0			0
$907$	1.37859	−	3.32820i	0.0457752	−	0.110511i	−0.899338	−	0.437254i	$-0.855951\pi$
$907$	1.37859	−	3.32820i	0.0457752	−	0.110511i	0.945113	+	0.326743i	$0.105951\pi$
$908$	13.8972	−	3.91062i	0.461194	−	0.129779i
$909$		0			0
$910$	−11.0289	−	12.4186i	−0.365605	−	0.411672i
$911$			44.8720i			1.48668i	0.668916	+	0.743338i	$0.266759\pi$
$911$			44.8720i			1.48668i	−0.668916	+	0.743338i	$0.733241\pi$
$912$		0			0
$913$		−	2.20335i		−	0.0729203i
$914$	−12.9944	+	11.5403i	−0.429818	+	0.381721i
$915$		0			0
$916$	−11.0931	+	19.7809i	−0.366525	+	0.653580i
$917$	−8.00158	+	19.3175i	−0.264236	+	0.637921i
$918$		0			0
$919$	−3.53947	−	3.53947i	−0.116756	−	0.116756i	0.646315	−	0.763071i	$-0.276309\pi$
$919$	−3.53947	−	3.53947i	−0.116756	−	0.116756i	−0.763071	+	0.646315i	$0.776309\pi$
$920$	20.6476	−	4.51120i	0.680730	−	0.148730i
$921$		0			0
$922$	−38.0981	+	13.1988i	−1.25469	+	0.434679i
$923$	5.35508	−	12.9283i	0.176265	−	0.425540i
$924$		0			0
$925$	0.197172	−	0.0816713i	0.00648297	−	0.00268534i
$926$	16.6903	+	0.989185i	0.548477	+	0.0325066i
$927$		0			0
$928$	4.56894	+	47.0964i	0.149983	+	1.54601i
$929$		−	12.1913i		−	0.399984i	−0.979798	−	0.199992i	$-0.935908\pi$
$929$		−	12.1913i		−	0.399984i	0.979798	−	0.199992i	$-0.0640916\pi$
$930$		0			0
$931$	−19.9544	−	48.1742i	−0.653979	−	1.57885i
$932$	−26.2654	−	33.3576i	−0.860351	−	1.09267i
$933$		0			0
$934$	16.1950	+	46.7466i	0.529915	+	1.52959i
$935$	2.32868	+	2.32868i	0.0761559	+	0.0761559i
$936$		0			0
$937$	−11.3070	+	11.3070i	−0.369383	+	0.369383i	−0.867252	−	0.497869i	$-0.834116\pi$
$937$	−11.3070	+	11.3070i	−0.369383	+	0.369383i	0.497869	+	0.867252i	$0.334116\pi$
$938$	−52.2907	−	25.3817i	−1.70735	−	0.828743i
$939$		0			0
$940$	7.60937	−	13.5689i	0.248190	−	0.442567i
$941$	27.0067	−	11.1865i	0.880393	−	0.364671i	0.103744	−	0.994604i	$-0.466918\pi$
$941$	27.0067	−	11.1865i	0.880393	−	0.364671i	0.776649	+	0.629933i	$0.216918\pi$
$942$		0			0
$943$	−20.8146			−0.677816
$944$	10.7722	−	14.7901i	0.350604	−	0.481378i
$945$		0			0
$946$	−3.79214	+	3.36780i	−0.123293	+	0.109496i
$947$	9.49553	+	22.9242i	0.308563	+	0.744938i	0.999752	+	0.0222635i	$0.00708728\pi$
$947$	9.49553	+	22.9242i	0.308563	+	0.744938i	−0.691189	+	0.722674i	$0.742913\pi$
$948$		0			0
$949$	14.0349	+	5.81343i	0.455591	+	0.188712i
$950$	16.5091	+	8.01347i	0.535626	+	0.259991i
$951$		0			0
$952$	−64.9915	+	45.2118i	−2.10639	+	1.46532i
$953$	4.87562	−	4.87562i	0.157937	−	0.157937i	−0.623715	−	0.781652i	$-0.714377\pi$
$953$	4.87562	−	4.87562i	0.157937	−	0.157937i	0.781652	+	0.623715i	$0.214377\pi$
$954$		0			0
$955$	−0.366495	−	0.151807i	−0.0118595	−	0.00491237i
$956$	−3.59189	+	30.1962i	−0.116170	+	0.976614i
$957$		0			0
$958$	35.3635	+	2.09589i	1.14254	+	0.0677151i
$959$	−14.3640			−0.463837
$960$		0			0
$961$	20.6420			0.665869
$962$	0.191964	+	0.0113771i	0.00618915	+	0.000366813i
$963$		0			0
$964$	−0.0319353	+	0.268472i	−0.00102857	+	0.00864691i
$965$	−8.89147	−	3.68297i	−0.286226	−	0.118559i
$966$		0			0
$967$	6.83543	−	6.83543i	0.219813	−	0.219813i	−0.588607	−	0.808419i	$-0.700323\pi$
$967$	6.83543	−	6.83543i	0.219813	−	0.219813i	0.808419	+	0.588607i	$0.200323\pi$
$968$	17.1131	+	24.6000i	0.550037	+	0.790674i
$969$		0			0
$970$	−1.36721	−	0.663640i	−0.0438985	−	0.0213082i
$971$	−24.1721	−	10.0124i	−0.775719	−	0.321313i	−0.0405323	−	0.999178i	$-0.512905\pi$
$971$	−24.1721	−	10.0124i	−0.775719	−	0.321313i	−0.735186	+	0.677865i	$0.762905\pi$
$972$		0			0
$973$	−20.9642	−	50.6119i	−0.672080	−	1.62254i
$974$	−43.2129	+	38.3773i	−1.38463	+	1.22969i
$975$		0			0
$976$	−33.7426	+	5.30378i	−1.08007	+	0.169770i
$977$	13.8469			0.443001			0.221500	−	0.975160i	$-0.428905\pi$
$977$	13.8469			0.443001			0.221500	+	0.975160i	$0.428905\pi$
$978$		0			0
$979$	5.15891	−	2.13689i	0.164879	−	0.0682953i
$980$	−14.8464	+	26.4737i	−0.474250	+	0.845672i
$981$		0			0
$982$	−35.4102	−	17.1880i	−1.12999	−	0.548492i
$983$	−11.5899	+	11.5899i	−0.369660	+	0.369660i	−0.867353	−	0.497693i	$-0.834181\pi$
$983$	−11.5899	+	11.5899i	−0.369660	+	0.369660i	0.497693	+	0.867353i	$0.334181\pi$
$984$		0			0
$985$	13.3822	+	13.3822i	0.426393	+	0.426393i
$986$	−22.2085	−	64.1046i	−0.707263	−	2.04151i
$987$		0			0
$988$	10.2294	+	12.9915i	0.325439	+	0.413315i
$989$	−17.8586	−	43.1144i	−0.567870	−	1.37096i
$990$		0			0
$991$		−	3.50092i		−	0.111210i	−0.998453	−	0.0556051i	$-0.982291\pi$
$991$		−	3.50092i		−	0.111210i	0.998453	−	0.0556051i	$-0.0177088\pi$
$992$	−5.31043	+	17.4143i	−0.168606	+	0.552904i
$993$		0			0
$994$	−36.1514	−	2.14259i	−1.14665	−	0.0679588i
$995$	−7.12390	+	2.95081i	−0.225843	+	0.0935471i
$996$		0			0
$997$	22.2934	−	53.8211i	0.706040	−	1.70453i	−0.00362468	−	0.999993i	$-0.501154\pi$
$997$	22.2934	−	53.8211i	0.706040	−	1.70453i	0.709665	−	0.704539i	$-0.248846\pi$
$998$	−42.6093	+	14.7616i	−1.34877	+	0.467271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.1	✓	128
3.2	odd	2	inner	864.2.w.a.107.32	yes	128
32.3	odd	8	inner	864.2.w.a.323.32	yes	128
96.35	even	8	inner	864.2.w.a.323.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.1	✓	128	1.1	even	1	trivial
864.2.w.a.107.32	yes	128	3.2	odd	2	inner
864.2.w.a.323.1	yes	128	96.35	even	8	inner
864.2.w.a.323.32	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)

\(f(q)\)	\(=\)	\(q+(-1.41174 - 0.0836695i) q^{2} +(1.98600 + 0.236238i) q^{4} +(-0.833551 - 0.345268i) q^{5} +(-3.45115 + 3.45115i) q^{7} +(-2.78394 - 0.499674i) q^{8} +O(q^{10})\)	\(q+(-1.41174 - 0.0836695i) q^{2} +(1.98600 + 0.236238i) q^{4} +(-0.833551 - 0.345268i) q^{5} +(-3.45115 + 3.45115i) q^{7} +(-2.78394 - 0.499674i) q^{8} +(1.14787 + 0.557170i) q^{10} +(0.588006 + 0.243560i) q^{11} +(1.02064 + 2.46404i) q^{13} +(5.16086 - 4.58335i) q^{14} +(3.88838 + 0.938339i) q^{16} -5.73510 q^{17} +(2.86396 - 1.18629i) q^{19} +(-1.57387 - 0.882619i) q^{20} +(-0.809731 - 0.393041i) q^{22} +(5.85623 - 5.85623i) q^{23} +(-2.95994 - 2.95994i) q^{25} +(-1.23471 - 3.56397i) q^{26} +(-7.66927 + 6.03868i) q^{28} +(-3.20100 - 7.72790i) q^{29} -3.21839i q^{31} +(-5.41086 - 1.65003i) q^{32} +(8.09645 + 0.479853i) q^{34} +(4.06828 - 1.68514i) q^{35} +(-0.0195107 + 0.0471029i) q^{37} +(-4.14242 + 1.43511i) q^{38} +(2.14804 + 1.37771i) q^{40} +(-1.77713 - 1.77713i) q^{41} +(2.15632 - 5.20583i) q^{43} +(1.11024 + 0.622620i) q^{44} +(-8.75744 + 7.77746i) q^{46} +8.62135i q^{47} -16.8208i q^{49} +(3.93099 + 4.42631i) q^{50} +(1.44489 + 5.13470i) q^{52} +(-5.21909 + 12.6000i) q^{53} +(-0.406040 - 0.406040i) q^{55} +(11.3322 - 7.88334i) q^{56} +(3.87238 + 11.1776i) q^{58} +(1.75051 - 4.22611i) q^{59} +(-7.88921 + 3.26782i) q^{61} +(-0.269281 + 4.54352i) q^{62} +(7.50065 + 2.78213i) q^{64} -2.40630i q^{65} +(-3.22264 - 7.78013i) q^{67} +(-11.3899 - 1.35485i) q^{68} +(-5.88433 + 2.03858i) q^{70} +(-3.71004 - 3.71004i) q^{71} +(4.02759 - 4.02759i) q^{73} +(0.0314850 - 0.0648645i) q^{74} +(5.96807 - 1.67940i) q^{76} +(-2.86986 + 1.18873i) q^{77} -7.33423 q^{79} +(-2.91719 - 2.12469i) q^{80} +(2.36015 + 2.65753i) q^{82} +(-1.32482 - 3.19840i) q^{83} +(4.78050 + 1.98015i) q^{85} +(-3.47973 + 7.16883i) q^{86} +(-1.51527 - 0.971868i) q^{88} +(6.20384 - 6.20384i) q^{89} +(-12.0261 - 4.98139i) q^{91} +(13.0139 - 10.2470i) q^{92} +(0.721344 - 12.1711i) q^{94} -2.79685 q^{95} -1.19109 q^{97} +(-1.40739 + 23.7466i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 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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