LMFDB - Embedded newform 864.2.bi.a.383.34

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(95,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.95"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 17])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bi (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			383.34
Character	$\chi$	$=$	864.383
Dual form			864.2.bi.a.767.34

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70869 - 0.283541i) q^{3} +(-1.19113 - 3.27259i) q^{5} +(0.573300 - 0.101088i) q^{7} +(2.83921 - 0.968964i) q^{9} +(-1.42849 - 0.519927i) q^{11} +(-4.76553 - 3.99876i) q^{13} +(-2.96317 - 5.25409i) q^{15} +(0.858874 + 0.495871i) q^{17} +(-3.76282 + 2.17246i) q^{19} +(0.950926 - 0.335282i) q^{21} +(0.715065 - 4.05534i) q^{23} +(-5.46085 + 4.58220i) q^{25} +(4.57657 - 2.46069i) q^{27} +(0.165623 + 0.197381i) q^{29} +(9.95515 + 1.75536i) q^{31} +(-2.58825 - 0.483357i) q^{33} +(-1.01369 - 1.75577i) q^{35} +(-5.32749 + 9.22749i) q^{37} +(-9.27661 - 5.48139i) q^{39} +(4.47348 - 5.33129i) q^{41} +(-0.0229902 + 0.0631651i) q^{43} +(-6.55288 - 8.13741i) q^{45} +(-1.42549 - 8.08438i) q^{47} +(-6.25939 + 2.27823i) q^{49} +(1.60814 + 0.603762i) q^{51} +1.96751i q^{53} +5.29415i q^{55} +(-5.81349 + 4.77897i) q^{57} +(11.1376 - 4.05376i) q^{59} +(-1.98322 - 11.2474i) q^{61} +(1.52977 - 0.842517i) q^{63} +(-7.40995 + 20.3587i) q^{65} +(4.37173 - 5.21003i) q^{67} +(0.0719681 - 7.13204i) q^{69} +(1.76215 - 3.05214i) q^{71} +(-0.283777 - 0.491516i) q^{73} +(-8.03163 + 9.37790i) q^{75} +(-0.871510 - 0.153671i) q^{77} +(8.27612 + 9.86310i) q^{79} +(7.12222 - 5.50218i) q^{81} +(-1.23417 + 1.03559i) q^{83} +(0.599756 - 3.40139i) q^{85} +(0.338962 + 0.290302i) q^{87} +(4.61926 - 2.66693i) q^{89} +(-3.13631 - 1.81075i) q^{91} +(17.5079 + 0.176669i) q^{93} +(11.5916 + 9.72648i) q^{95} +(8.38829 + 3.05309i) q^{97} +(-4.55956 - 0.0920288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) $ 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70869	−	0.283541i	0.986510	−	0.163702i
$3$	1.70869	−	0.283541i	0.986510	−	0.163702i
$4$		0			0
$5$	−1.19113	−	3.27259i	−0.532688	−	1.46355i	−0.855860	−	0.517207i	$-0.826972\pi$
$5$	−1.19113	−	3.27259i	−0.532688	−	1.46355i	0.323173	−	0.946340i	$-0.395251\pi$
$6$		0			0
$7$	0.573300	−	0.101088i	0.216687	−	0.0382077i	−0.0642507	−	0.997934i	$-0.520466\pi$
$7$	0.573300	−	0.101088i	0.216687	−	0.0382077i	0.280938	+	0.959726i	$0.409355\pi$
$8$		0			0
$9$	2.83921	−	0.968964i	0.946403	−	0.322988i
$10$		0			0
$11$	−1.42849	−	0.519927i	−0.430705	−	0.156764i	0.117565	−	0.993065i	$-0.462491\pi$
$11$	−1.42849	−	0.519927i	−0.430705	−	0.156764i	−0.548270	+	0.836301i	$0.684713\pi$
$12$		0			0
$13$	−4.76553	−	3.99876i	−1.32172	−	1.10906i	−0.985937	−	0.167117i	$-0.946554\pi$
$13$	−4.76553	−	3.99876i	−1.32172	−	1.10906i	−0.335784	−	0.941939i	$-0.609001\pi$
$14$		0			0
$15$	−2.96317	−	5.25409i	−0.765088	−	1.35660i
$16$		0			0
$17$	0.858874	+	0.495871i	0.208308	+	0.120266i	0.600525	−	0.799606i	$-0.294958\pi$
$17$	0.858874	+	0.495871i	0.208308	+	0.120266i	−0.392217	+	0.919873i	$0.628292\pi$
$18$		0			0
$19$	−3.76282	+	2.17246i	−0.863249	+	0.498397i	−0.865099	−	0.501601i	$-0.832745\pi$
$19$	−3.76282	+	2.17246i	−0.863249	+	0.498397i	0.00184984	+	0.999998i	$0.499411\pi$
$20$		0			0
$21$	0.950926	−	0.335282i	0.207509	−	0.0731645i
$22$		0			0
$23$	0.715065	−	4.05534i	0.149101	−	0.845596i	−0.814881	−	0.579629i	$-0.803198\pi$
$23$	0.715065	−	4.05534i	0.149101	−	0.845596i	0.963982	−	0.265967i	$-0.0856913\pi$
$24$		0			0
$25$	−5.46085	+	4.58220i	−1.09217	+	0.916439i
$26$		0			0
$27$	4.57657	−	2.46069i	0.880762	−	0.473559i
$28$		0			0
$29$	0.165623	+	0.197381i	0.0307553	+	0.0366528i	0.781203	−	0.624277i	$-0.214606\pi$
$29$	0.165623	+	0.197381i	0.0307553	+	0.0366528i	−0.750448	+	0.660930i	$0.770162\pi$
$30$		0			0
$31$	9.95515	+	1.75536i	1.78800	+	0.315272i	0.966831	−	0.255416i	$-0.0822125\pi$
$31$	9.95515	+	1.75536i	1.78800	+	0.315272i	0.821167	+	0.570689i	$0.193324\pi$
$32$		0			0
$33$	−2.58825	−	0.483357i	−0.450557	−	0.0841416i
$34$		0			0
$35$	−1.01369	−	1.75577i	−0.171345	−	0.296779i
$36$		0			0
$37$	−5.32749	+	9.22749i	−0.875835	+	1.51699i	−0.0199635	+	0.999801i	$0.506355\pi$
$37$	−5.32749	+	9.22749i	−0.875835	+	1.51699i	−0.855871	+	0.517189i	$0.826978\pi$
$38$		0			0
$39$	−9.27661	−	5.48139i	−1.48545	−	0.877726i
$40$		0			0
$41$	4.47348	−	5.33129i	0.698641	−	0.832608i	−0.293731	−	0.955888i	$-0.594897\pi$
$41$	4.47348	−	5.33129i	0.698641	−	0.832608i	0.992372	+	0.123280i	$0.0393414\pi$
$42$		0			0
$43$	−0.0229902	+	0.0631651i	−0.00350597	+	0.00963258i	−0.941433	−	0.337199i	$-0.890520\pi$
$43$	−0.0229902	+	0.0631651i	−0.00350597	+	0.00963258i	0.937927	+	0.346832i	$0.112743\pi$
$44$		0			0
$45$	−6.55288	−	8.13741i	−0.976845	−	1.21305i
$46$		0			0
$47$	−1.42549	−	8.08438i	−0.207930	−	1.17923i	−0.892762	−	0.450528i	$-0.851236\pi$
$47$	−1.42549	−	8.08438i	−0.207930	−	1.17923i	0.684833	−	0.728700i	$-0.259875\pi$
$48$		0			0
$49$	−6.25939	+	2.27823i	−0.894199	+	0.325462i
$50$		0			0
$51$	1.60814	+	0.603762i	0.225185	+	0.0845436i
$52$		0			0
$53$			1.96751i			0.270258i	0.990828	+	0.135129i	$0.0431449\pi$
$53$			1.96751i			0.270258i	−0.990828	+	0.135129i	$0.956855\pi$
$54$		0			0
$55$			5.29415i			0.713863i
$56$		0			0
$57$	−5.81349	+	4.77897i	−0.770015	+	0.632990i
$58$		0			0
$59$	11.1376	−	4.05376i	1.44999	−	0.527754i	0.507404	−	0.861708i	$-0.330605\pi$
$59$	11.1376	−	4.05376i	1.44999	−	0.527754i	0.942589	+	0.333954i	$0.108383\pi$
$60$		0			0
$61$	−1.98322	−	11.2474i	−0.253925	−	1.44008i	−0.798816	−	0.601575i	$-0.794540\pi$
$61$	−1.98322	−	11.2474i	−0.253925	−	1.44008i	0.544891	−	0.838507i	$-0.316571\pi$
$62$		0			0
$63$	1.52977	−	0.842517i	0.192733	−	0.106147i
$64$		0			0
$65$	−7.40995	+	20.3587i	−0.919091	+	2.52518i
$66$		0			0
$67$	4.37173	−	5.21003i	0.534092	−	0.636506i	−0.429760	−	0.902943i	$-0.641402\pi$
$67$	4.37173	−	5.21003i	0.534092	−	0.636506i	0.963852	+	0.266437i	$0.0858463\pi$
$68$		0			0
$69$	0.0719681	−	7.13204i	0.00866394	−	0.858597i
$70$		0			0
$71$	1.76215	−	3.05214i	0.209129	−	0.362222i	−0.742311	−	0.670055i	$-0.766270\pi$
$71$	1.76215	−	3.05214i	0.209129	−	0.362222i	0.951440	+	0.307833i	$0.0996038\pi$
$72$		0			0
$73$	−0.283777	−	0.491516i	−0.0332136	−	0.0575276i	0.848941	−	0.528488i	$-0.177241\pi$
$73$	−0.283777	−	0.491516i	−0.0332136	−	0.0575276i	−0.882154	+	0.470960i	$0.843907\pi$
$74$		0			0
$75$	−8.03163	+	9.37790i	−0.927413	+	1.08287i
$76$		0			0
$77$	−0.871510	−	0.153671i	−0.0993177	−	0.0175124i
$78$		0			0
$79$	8.27612	+	9.86310i	0.931137	+	1.10969i	0.993748	+	0.111647i	$0.0356127\pi$
$79$	8.27612	+	9.86310i	0.931137	+	1.10969i	−0.0626113	+	0.998038i	$0.519943\pi$
$80$		0			0
$81$	7.12222	−	5.50218i	0.791358	−	0.611354i
$82$		0			0
$83$	−1.23417	+	1.03559i	−0.135468	+	0.113671i	−0.708004	−	0.706209i	$-0.750404\pi$
$83$	−1.23417	+	1.03559i	−0.135468	+	0.113671i	0.572536	+	0.819879i	$0.305960\pi$
$84$		0			0
$85$	0.599756	−	3.40139i	0.0650527	−	0.368932i
$86$		0			0
$87$	0.338962	+	0.290302i	0.0363406	+	0.0311236i
$88$		0			0
$89$	4.61926	−	2.66693i	0.489641	−	0.282694i	−0.234785	−	0.972047i	$-0.575438\pi$
$89$	4.61926	−	2.66693i	0.489641	−	0.282694i	0.724426	+	0.689353i	$0.242105\pi$
$90$		0			0
$91$	−3.13631	−	1.81075i	−0.328774	−	0.189818i
$92$		0			0
$93$	17.5079	+	0.176669i	1.81549	+	0.0183197i
$94$		0			0
$95$	11.5916	+	9.72648i	1.18927	+	0.997916i
$96$		0			0
$97$	8.38829	+	3.05309i	0.851702	+	0.309994i	0.730734	−	0.682662i	$-0.239178\pi$
$97$	8.38829	+	3.05309i	0.851702	+	0.309994i	0.120968	+	0.992656i	$0.461400\pi$
$98$		0			0
$99$	−4.55956	−	0.0920288i	−0.458253	−	0.00924924i
$100$		0			0
$101$	7.95496	−	1.40267i	0.791548	−	0.139571i	0.236766	−	0.971567i	$-0.423913\pi$
$101$	7.95496	−	1.40267i	0.791548	−	0.139571i	0.554782	+	0.831996i	$0.312802\pi$
$102$		0			0
$103$	−1.22482	−	3.36517i	−0.120685	−	0.331580i	0.864609	−	0.502445i	$-0.167566\pi$
$103$	−1.22482	−	3.36517i	−0.120685	−	0.331580i	−0.985294	+	0.170865i	$0.945344\pi$
$104$		0			0
$105$	−2.22991	−	2.71263i	−0.217617	−	0.264725i
$106$		0			0
$107$	14.1997			1.37274			0.686370	−	0.727253i	$-0.259203\pi$
$107$	14.1997			1.37274			0.686370	+	0.727253i	$0.259203\pi$
$108$		0			0
$109$	4.82293			0.461953			0.230976	−	0.972959i	$-0.425808\pi$
$109$	4.82293			0.461953			0.230976	+	0.972959i	$0.425808\pi$
$110$		0			0
$111$	−6.48664	+	17.2774i	−0.615685	+	1.63990i
$112$		0			0
$113$	5.68265	+	15.6130i	0.534579	+	1.46874i	0.853566	+	0.520984i	$0.174435\pi$
$113$	5.68265	+	15.6130i	0.534579	+	1.46874i	−0.318988	+	0.947759i	$0.603343\pi$
$114$		0			0
$115$	−14.1232	+	2.49030i	−1.31699	+	0.232222i
$116$		0			0
$117$	−17.4050	−	6.73568i	−1.60909	−	0.622714i
$118$		0			0
$119$	0.542519	+	0.197461i	0.0497326	+	0.0181012i
$120$		0			0
$121$	−6.65624	−	5.58525i	−0.605113	−	0.507750i
$122$		0			0
$123$	6.13214	−	10.3779i	0.552916	−	0.935745i
$124$		0			0
$125$	6.42003	+	3.70660i	0.574225	+	0.331529i
$126$		0			0
$127$	−7.14207	+	4.12348i	−0.633757	+	0.365900i	−0.782205	−	0.623021i	$-0.785905\pi$
$127$	−7.14207	+	4.12348i	−0.633757	+	0.365900i	0.148449	+	0.988920i	$0.452572\pi$
$128$		0			0
$129$	−0.0213731	+	0.114448i	−0.00188180	+	0.0100766i
$130$		0			0
$131$	−0.142753	+	0.809591i	−0.0124724	+	0.0707343i	−0.990409	−	0.138169i	$-0.955878\pi$
$131$	−0.142753	+	0.809591i	−0.0124724	+	0.0707343i	0.977936	+	0.208903i	$0.0669894\pi$
$132$		0			0
$133$	−1.93761	+	1.62585i	−0.168012	+	0.140979i
$134$		0			0
$135$	−13.5041	−	12.0463i	−1.16225	−	1.03678i
$136$		0			0
$137$	−3.37267	−	4.01940i	−0.288147	−	0.343400i	0.602481	−	0.798133i	$-0.294179\pi$
$137$	−3.37267	−	4.01940i	−0.288147	−	0.343400i	−0.890628	+	0.454733i	$0.849735\pi$
$138$		0			0
$139$	−5.17764	−	0.912958i	−0.439162	−	0.0774361i	−0.0503043	−	0.998734i	$-0.516019\pi$
$139$	−5.17764	−	0.912958i	−0.439162	−	0.0774361i	−0.388858	+	0.921298i	$0.627130\pi$
$140$		0			0
$141$	−4.72797	−	13.4095i	−0.398167	−	1.12928i
$142$		0			0
$143$	4.72844	+	8.18990i	0.395412	+	0.684874i
$144$		0			0
$145$	0.448671	−	0.777121i	0.0372601	−	0.0645364i
$146$		0			0
$147$	−10.0494	+	5.66758i	−0.828857	+	0.467454i
$148$		0			0
$149$	2.10528	−	2.50897i	0.172471	−	0.205543i	−0.672884	−	0.739748i	$-0.734945\pi$
$149$	2.10528	−	2.50897i	0.172471	−	0.205543i	0.845355	+	0.534205i	$0.179389\pi$
$150$		0			0
$151$	2.90758	−	7.98851i	0.236615	−	0.650095i	−0.763376	−	0.645954i	$-0.776460\pi$
$151$	2.90758	−	7.98851i	0.236615	−	0.650095i	0.999991	−	0.00414108i	$-0.00131815\pi$
$152$		0			0
$153$	2.91900	+	0.575664i	0.235987	+	0.0465397i
$154$		0			0
$155$	−6.11325	−	34.6700i	−0.491028	−	2.78476i
$156$		0			0
$157$	−3.19343	+	1.16231i	−0.254863	+	0.0927626i	−0.466292	−	0.884631i	$-0.654410\pi$
$157$	−3.19343	+	1.16231i	−0.254863	+	0.0927626i	0.211429	+	0.977393i	$0.432188\pi$
$158$		0			0
$159$	0.557869	+	3.36185i	0.0442419	+	0.266612i
$160$		0			0
$161$		−	2.39721i		−	0.188926i
$162$		0			0
$163$			11.4921i			0.900129i	0.892996	+	0.450064i	$0.148599\pi$
$163$			11.4921i			0.900129i	−0.892996	+	0.450064i	$0.851401\pi$
$164$		0			0
$165$	1.50111	+	9.04604i	0.116861	+	0.704233i
$166$		0			0
$167$	−15.4019	+	5.60583i	−1.19183	+	0.433792i	−0.860367	−	0.509675i	$-0.829766\pi$
$167$	−15.4019	+	5.60583i	−1.19183	+	0.433792i	−0.331467	+	0.943467i	$0.607543\pi$
$168$		0			0
$169$	4.46282	+	25.3099i	0.343294	+	1.94692i
$170$		0			0
$171$	−8.57838	+	9.81411i	−0.656005	+	0.750504i
$172$		0			0
$173$	−6.32756	+	17.3848i	−0.481075	+	1.32174i	0.427498	+	0.904016i	$0.359395\pi$
$173$	−6.32756	+	17.3848i	−0.481075	+	1.32174i	−0.908573	+	0.417727i	$0.862827\pi$
$174$		0			0
$175$	−2.66750	+	3.17900i	−0.201644	+	0.240310i
$176$		0			0
$177$	17.8813	−	10.0846i	1.34404	−	0.758002i
$178$		0			0
$179$	8.34873	−	14.4604i	0.624013	−	1.08082i	−0.364718	−	0.931118i	$-0.618834\pi$
$179$	8.34873	−	14.4604i	0.624013	−	1.08082i	0.988731	−	0.149704i	$-0.0478322\pi$
$180$		0			0
$181$	6.23773	+	10.8041i	0.463647	+	0.803060i	0.999139	−	0.0414800i	$-0.0132073\pi$
$181$	6.23773	+	10.8041i	0.463647	+	0.803060i	−0.535492	+	0.844540i	$0.679874\pi$
$182$		0			0
$183$	−6.57779	−	18.6559i	−0.486245	−	1.37909i
$184$		0			0
$185$	36.5435	+	6.44361i	2.68673	+	0.473743i
$186$		0			0
$187$	−0.969074	−	1.15490i	−0.0708657	−	0.0844544i
$188$		0			0
$189$	2.37500	−	1.87335i	0.172756	−	0.136266i
$190$		0			0
$191$	−19.4764	+	16.3427i	−1.40927	+	1.18251i	−0.452460	+	0.891785i	$0.649453\pi$
$191$	−19.4764	+	16.3427i	−1.40927	+	1.18251i	−0.956805	+	0.290729i	$0.906102\pi$
$192$		0			0
$193$	2.98850	−	16.9486i	0.215117	−	1.21999i	−0.665587	−	0.746320i	$-0.731819\pi$
$193$	2.98850	−	16.9486i	0.215117	−	1.21999i	0.880704	−	0.473667i	$-0.157070\pi$
$194$		0			0
$195$	−6.88876	+	36.8876i	−0.493314	+	2.64157i
$196$		0			0
$197$	3.76094	−	2.17138i	0.267956	−	0.154704i	−0.360002	−	0.932951i	$-0.617224\pi$
$197$	3.76094	−	2.17138i	0.267956	−	0.154704i	0.627958	+	0.778247i	$0.283891\pi$
$198$		0			0
$199$	23.0361	+	13.2999i	1.63299	+	0.942806i	0.983165	+	0.182721i	$0.0584904\pi$
$199$	23.0361	+	13.2999i	1.63299	+	0.942806i	0.649823	+	0.760086i	$0.274843\pi$
$200$		0			0
$201$	5.99266	−	10.1419i	0.422690	−	0.715352i
$202$		0			0
$203$	0.114904	+	0.0964161i	0.00806470	+	0.00676708i
$204$		0			0
$205$	−22.7756	−	8.28965i	−1.59072	−	0.578974i
$206$		0			0
$207$	−1.89925	−	12.2068i	−0.132007	−	0.848433i
$208$		0			0
$209$	6.50466	−	1.14695i	0.449936	−	0.0793359i
$210$		0			0
$211$	9.11279	+	25.0372i	0.627350	+	1.72363i	0.688237	+	0.725486i	$0.258385\pi$
$211$	9.11279	+	25.0372i	0.627350	+	1.72363i	−0.0608870	+	0.998145i	$0.519393\pi$
$212$		0			0
$213$	2.14556	−	5.71479i	0.147011	−	0.391571i
$214$		0			0
$215$	0.234098			0.0159653
$216$		0			0
$217$	5.88473			0.399482
$218$		0			0
$219$	−0.624251	−	0.759384i	−0.0421830	−	0.0513144i
$220$		0			0
$221$	−2.11012	−	5.79752i	−0.141942	−	0.389983i
$222$		0			0
$223$	0.777443	−	0.137084i	0.0520614	−	0.00917983i	−0.147557	−	0.989054i	$-0.547141\pi$
$223$	0.777443	−	0.137084i	0.0520614	−	0.00917983i	0.199618	+	0.979874i	$0.436030\pi$
$224$		0			0
$225$	−11.0645	+	18.3012i	−0.737634	+	1.22008i
$226$		0			0
$227$	19.3407	+	7.03943i	1.28369	+	0.467223i	0.891649	−	0.452727i	$-0.149549\pi$
$227$	19.3407	+	7.03943i	1.28369	+	0.467223i	0.392036	+	0.919950i	$0.371771\pi$
$228$		0			0
$229$	8.12307	+	6.81607i	0.536788	+	0.450418i	0.870438	−	0.492279i	$-0.163836\pi$
$229$	8.12307	+	6.81607i	0.536788	+	0.450418i	−0.333650	+	0.942697i	$0.608280\pi$
$230$		0			0
$231$	−1.53271	−	0.0154663i	−0.100845	−	0.00101761i
$232$		0			0
$233$	−20.4551	−	11.8098i	−1.34006	−	0.773683i	−0.353242	−	0.935532i	$-0.614921\pi$
$233$	−20.4551	−	11.8098i	−1.34006	−	0.773683i	−0.986816	+	0.161849i	$0.948254\pi$
$234$		0			0
$235$	−24.7589	+	14.2946i	−1.61509	+	0.932475i
$236$		0			0
$237$	16.9379	+	14.5063i	1.10023	+	0.942286i
$238$		0			0
$239$	−3.29941	+	18.7119i	−0.213421	+	1.21037i	0.670204	+	0.742177i	$0.266207\pi$
$239$	−3.29941	+	18.7119i	−0.213421	+	1.21037i	−0.883625	+	0.468195i	$0.844904\pi$
$240$		0			0
$241$	−15.7064	+	13.1792i	−1.01174	+	0.848947i	−0.988567	−	0.150784i	$-0.951820\pi$
$241$	−15.7064	+	13.1792i	−1.01174	+	0.848947i	−0.0231694	+	0.999732i	$0.507376\pi$
$242$		0			0
$243$	10.6095	−	11.4209i	0.680602	−	0.732653i
$244$		0			0
$245$	14.9115	+	17.7708i	0.952658	+	1.13533i
$246$		0			0
$247$	26.6190	+	4.69364i	1.69373	+	0.298649i
$248$		0			0
$249$	−1.81517	+	2.11943i	−0.115032	+	0.134314i
$250$		0			0
$251$	−8.18279	−	14.1730i	−0.516493	−	0.894592i	−0.999817	−	0.0191506i	$-0.993904\pi$
$251$	−8.18279	−	14.1730i	−0.516493	−	0.894592i	0.483323	−	0.875442i	$-0.339430\pi$
$252$		0			0
$253$	−3.12994	+	5.42121i	−0.196778	+	0.340829i
$254$		0			0
$255$	0.0603628	−	5.98196i	0.00378006	−	0.374605i
$256$		0			0
$257$	7.22455	−	8.60988i	0.450655	−	0.537070i	−0.492108	−	0.870534i	$-0.663773\pi$
$257$	7.22455	−	8.60988i	0.450655	−	0.537070i	0.942763	+	0.333465i	$0.108218\pi$
$258$		0			0
$259$	−2.12146	+	5.82866i	−0.131821	+	0.362176i
$260$		0			0
$261$	0.661492	+	0.399924i	0.0409453	+	0.0247547i
$262$		0			0
$263$	3.55437	+	20.1578i	0.219172	+	1.24298i	0.873519	+	0.486790i	$0.161832\pi$
$263$	3.55437	+	20.1578i	0.219172	+	1.24298i	−0.654347	+	0.756194i	$0.727056\pi$
$264$		0			0
$265$	6.43885	−	2.34355i	0.395536	−	0.143963i
$266$		0			0
$267$	7.13668	−	5.86670i	0.436758	−	0.359036i
$268$		0			0
$269$		−	15.6928i		−	0.956805i	−0.878141	−	0.478403i	$-0.841216\pi$
$269$		−	15.6928i		−	0.956805i	0.878141	−	0.478403i	$-0.158784\pi$
$270$		0			0
$271$		−	5.04698i		−	0.306582i	−0.988181	−	0.153291i	$-0.951013\pi$
$271$		−	5.04698i		−	0.306582i	0.988181	−	0.153291i	$-0.0489873\pi$
$272$		0			0
$273$	−5.87238	−	2.20473i	−0.355413	−	0.133436i
$274$		0			0
$275$	10.1832	−	3.70637i	0.614067	−	0.223502i
$276$		0			0
$277$	0.685177	+	3.88583i	0.0411683	+	0.233477i	0.998448	−	0.0556853i	$-0.0177344\pi$
$277$	0.685177	+	3.88583i	0.0411683	+	0.233477i	−0.957280	+	0.289162i	$0.906623\pi$
$278$		0			0
$279$	29.9656	−	4.66234i	1.79400	−	0.279127i
$280$		0			0
$281$	5.27584	−	14.4953i	0.314730	−	0.864714i	−0.676955	−	0.736025i	$-0.736701\pi$
$281$	5.27584	−	14.4953i	0.314730	−	0.864714i	0.991685	−	0.128690i	$-0.0410771\pi$
$282$		0			0
$283$	2.71786	−	3.23902i	0.161560	−	0.192540i	−0.679191	−	0.733961i	$-0.737669\pi$
$283$	2.71786	−	3.23902i	0.161560	−	0.192540i	0.840751	+	0.541422i	$0.182114\pi$
$284$		0			0
$285$	22.5642	+	13.3328i	1.33659	+	0.789767i
$286$		0			0
$287$	2.02572	−	3.50864i	0.119574	−	0.207109i
$288$		0			0
$289$	−8.00822	−	13.8707i	−0.471072	−	0.815921i
$290$		0			0
$291$	15.1986	+	2.83834i	0.890959	+	0.166387i
$292$		0			0
$293$	−19.6225	−	3.45998i	−1.14636	−	0.202134i	−0.431973	−	0.901886i	$-0.642183\pi$
$293$	−19.6225	−	3.45998i	−1.14636	−	0.202134i	−0.714385	+	0.699752i	$0.753294\pi$
$294$		0			0
$295$	−26.5326	−	31.6203i	−1.54479	−	1.84101i
$296$		0			0
$297$	−7.81695	+	1.13557i	−0.453586	+	0.0658927i
$298$		0			0
$299$	−19.6240	+	16.4665i	−1.13488	+	0.952281i
$300$		0			0
$301$	−0.00679503	+	0.0385365i	−0.000391659	+	0.00222121i
$302$		0			0
$303$	13.1948	−	4.65228i	0.758022	−	0.267267i
$304$		0			0
$305$	−34.4459	+	19.8873i	−1.97236	+	1.13875i
$306$		0			0
$307$	24.7252	+	14.2751i	1.41114	+	0.814725i	0.995496	−	0.0948008i	$-0.0302214\pi$
$307$	24.7252	+	14.2751i	1.41114	+	0.814725i	0.415648	+	0.909525i	$0.363555\pi$
$308$		0			0
$309$	−3.04699	−	5.40272i	−0.173337	−	0.307350i
$310$		0			0
$311$	2.70082	+	2.26626i	0.153149	+	0.128508i	0.716143	−	0.697954i	$-0.245906\pi$
$311$	2.70082	+	2.26626i	0.153149	+	0.128508i	−0.562993	+	0.826461i	$0.690350\pi$
$312$		0			0
$313$	−22.6114	−	8.22989i	−1.27807	−	0.465181i	−0.388279	−	0.921542i	$-0.626930\pi$
$313$	−22.6114	−	8.22989i	−1.27807	−	0.465181i	−0.889795	+	0.456361i	$0.849153\pi$
$314$		0			0
$315$	−4.57936	−	4.00276i	−0.258018	−	0.225530i
$316$		0			0
$317$	20.8619	−	3.67851i	1.17172	−	0.206606i	0.446281	−	0.894893i	$-0.352748\pi$
$317$	20.8619	−	3.67851i	1.17172	−	0.206606i	0.725438	+	0.688287i	$0.241637\pi$
$318$		0			0
$319$	−0.133966	−	0.368068i	−0.00750065	−	0.0206079i
$320$		0			0
$321$	24.2629	−	4.02620i	1.35422	−	0.224721i
$322$		0			0
$323$	−4.30905			−0.239762
$324$		0			0
$325$	44.3469			2.45993
$326$		0			0
$327$	8.24087	−	1.36750i	0.455721	−	0.0756228i
$328$		0			0
$329$	−1.63447	−	4.49067i	−0.0901113	−	0.247579i
$330$		0			0
$331$	9.24695	−	1.63049i	0.508259	−	0.0896197i	0.0863623	−	0.996264i	$-0.472476\pi$
$331$	9.24695	−	1.63049i	0.508259	−	0.0896197i	0.421896	+	0.906644i	$0.361365\pi$
$332$		0			0
$333$	−6.18477	+	31.3609i	−0.338923	+	1.71857i
$334$		0			0
$335$	−22.2576	−	8.10110i	−1.21606	−	0.442610i
$336$		0			0
$337$	−1.24722	−	1.04654i	−0.0679404	−	0.0570087i	0.608185	−	0.793795i	$-0.291898\pi$
$337$	−1.24722	−	1.04654i	−0.0679404	−	0.0570087i	−0.676125	+	0.736786i	$0.736342\pi$
$338$		0			0
$339$	14.1368	+	25.0664i	0.767804	+	1.36142i
$340$		0			0
$341$	−13.3081	−	7.68346i	−0.720676	−	0.416083i
$342$		0			0
$343$	−6.88726	+	3.97636i	−0.371877	+	0.214703i
$344$		0			0
$345$	−23.4260	+	8.25964i	−1.26121	+	0.444684i
$346$		0			0
$347$	−3.34153	+	18.9508i	−0.179383	+	1.01733i	0.753580	+	0.657356i	$0.228325\pi$
$347$	−3.34153	+	18.9508i	−0.179383	+	1.01733i	−0.932963	+	0.359974i	$0.882786\pi$
$348$		0			0
$349$	−16.1769	+	13.5741i	−0.865932	+	0.726603i	−0.963237	−	0.268651i	$-0.913422\pi$
$349$	−16.1769	+	13.5741i	−0.865932	+	0.726603i	0.0973055	+	0.995255i	$0.468978\pi$
$350$		0			0
$351$	−31.6495	−	6.57413i	−1.68933	−	0.350901i
$352$		0			0
$353$	−21.6145	−	25.7592i	−1.15043	−	1.37102i	−0.917115	−	0.398623i	$-0.869488\pi$
$353$	−21.6145	−	25.7592i	−1.15043	−	1.37102i	−0.233311	−	0.972402i	$-0.574956\pi$
$354$		0			0
$355$	−12.0873	−	2.13133i	−0.641530	−	0.113119i
$356$		0			0
$357$	0.982982	+	0.183572i	0.0520249	+	0.00971566i
$358$		0			0
$359$	−17.5568	−	30.4092i	−0.926612	−	1.60494i	−0.788948	−	0.614459i	$-0.789374\pi$
$359$	−17.5568	−	30.4092i	−0.926612	−	1.60494i	−0.137663	−	0.990479i	$-0.543959\pi$
$360$		0			0
$361$	−0.0608111	+	0.105328i	−0.00320058	+	0.00554357i
$362$		0			0
$363$	−12.9571	−	7.65611i	−0.680069	−	0.401842i
$364$		0			0
$365$	−1.27052	+	1.51414i	−0.0665019	+	0.0792539i
$366$		0			0
$367$	−0.0226511	+	0.0622335i	−0.00118238	+	0.00324856i	−0.940282	−	0.340395i	$-0.889439\pi$
$367$	−0.0226511	+	0.0622335i	−0.00118238	+	0.00324856i	0.939100	+	0.343644i	$0.111661\pi$
$368$		0			0
$369$	7.53533	−	19.4713i	0.392274	−	1.01364i
$370$		0			0
$371$	0.198892	+	1.12797i	0.0103260	+	0.0585614i
$372$		0			0
$373$	−0.0644945	+	0.0234741i	−0.00333940	+	0.00121544i	−0.343689	−	0.939083i	$-0.611677\pi$
$373$	−0.0644945	+	0.0234741i	−0.00333940	+	0.00121544i	0.340350	+	0.940299i	$0.389454\pi$
$374$		0			0
$375$	12.0208	+	4.51308i	0.620750	+	0.233054i
$376$		0			0
$377$		−	1.60291i		−	0.0825541i
$378$		0			0
$379$		−	27.8705i		−	1.43161i	−0.698299	−	0.715806i	$-0.746059\pi$
$379$		−	27.8705i		−	1.43161i	0.698299	−	0.715806i	$-0.253941\pi$
$380$		0			0
$381$	−11.0344	+	9.07079i	−0.565308	+	0.464711i
$382$		0			0
$383$	−6.08836	+	2.21598i	−0.311101	+	0.113231i	−0.492852	−	0.870113i	$-0.664046\pi$
$383$	−6.08836	+	2.21598i	−0.311101	+	0.113231i	0.181751	+	0.983345i	$0.441823\pi$
$384$		0			0
$385$	0.535176	+	3.03514i	0.0272751	+	0.154685i
$386$		0			0
$387$	−0.00406934	+	0.201616i	−0.000206856	+	0.0102487i
$388$		0			0
$389$	−10.3203	+	28.3548i	−0.523259	+	1.43764i	0.343612	+	0.939112i	$0.388349\pi$
$389$	−10.3203	+	28.3548i	−0.523259	+	1.43764i	−0.866872	+	0.498531i	$0.833873\pi$
$390$		0			0
$391$	2.62508	−	3.12844i	0.132756	−	0.158212i
$392$		0			0
$393$	−0.0143674	+	1.42381i	−0.000724741	+	0.0718218i
$394$		0			0
$395$	22.4200	−	38.8326i	1.12807	−	1.95388i
$396$		0			0
$397$	−1.31295	−	2.27409i	−0.0658950	−	0.114133i	0.831196	−	0.555980i	$-0.187657\pi$
$397$	−1.31295	−	2.27409i	−0.0658950	−	0.114133i	−0.897091	+	0.441847i	$0.854324\pi$
$398$		0			0
$399$	−2.84977	+	3.32745i	−0.142667	+	0.166581i
$400$		0			0
$401$	11.8095	+	2.08234i	0.589740	+	0.103987i	0.460552	−	0.887633i	$-0.347652\pi$
$401$	11.8095	+	2.08234i	0.589740	+	0.103987i	0.129189	+	0.991620i	$0.458763\pi$
$402$		0			0
$403$	−40.4223	−	48.1735i	−2.01358	−	2.39969i
$404$		0			0
$405$	−26.4898	−	16.7543i	−1.31629	−	0.832529i
$406$		0			0
$407$	12.4079	−	10.4114i	0.615036	−	0.516076i
$408$		0			0
$409$	3.71166	−	21.0498i	0.183530	−	1.04085i	−0.744300	−	0.667845i	$-0.767217\pi$
$409$	3.71166	−	21.0498i	0.183530	−	1.04085i	0.927830	−	0.373003i	$-0.121672\pi$
$410$		0			0
$411$	−6.90250	−	5.91159i	−0.340475	−	0.291597i
$412$		0			0
$413$	5.97540	−	3.44990i	0.294030	−	0.169758i
$414$		0			0
$415$	4.85911	+	2.80541i	0.238524	+	0.137712i
$416$		0			0
$417$	−9.10582	−	0.0918851i	−0.445914	−	0.00449963i
$418$		0			0
$419$	−4.27322	−	3.58565i	−0.208760	−	0.175171i	0.532412	−	0.846485i	$-0.321286\pi$
$419$	−4.27322	−	3.58565i	−0.208760	−	0.175171i	−0.741173	+	0.671314i	$0.765730\pi$
$420$		0			0
$421$	−4.29843	−	1.56450i	−0.209493	−	0.0762492i	0.235142	−	0.971961i	$-0.424444\pi$
$421$	−4.29843	−	1.56450i	−0.209493	−	0.0762492i	−0.444635	+	0.895712i	$0.646667\pi$
$422$		0			0
$423$	−11.8808	−	21.5720i	−0.577662	−	1.04887i
$424$		0			0
$425$	−6.96236	+	1.22765i	−0.337724	+	0.0595498i
$426$		0			0
$427$	−2.27396	−	6.24765i	−0.110045	−	0.302345i
$428$		0			0
$429$	10.4016	+	12.6533i	0.502193	+	0.610905i
$430$		0			0
$431$	21.6902			1.04478			0.522390	−	0.852707i	$-0.325041\pi$
$431$	21.6902			1.04478			0.522390	+	0.852707i	$0.325041\pi$
$432$		0			0
$433$	14.4385			0.693870			0.346935	−	0.937889i	$-0.387222\pi$
$433$	14.4385			0.693870			0.346935	+	0.937889i	$0.387222\pi$
$434$		0			0
$435$	0.546292	−	1.45507i	0.0261927	−	0.0697653i
$436$		0			0
$437$	6.11941	+	16.8129i	0.292731	+	0.804272i
$438$		0			0
$439$	6.79424	−	1.19801i	0.324272	−	0.0571778i	−0.00914283	−	0.999958i	$-0.502910\pi$
$439$	6.79424	−	1.19801i	0.324272	−	0.0571778i	0.333414	+	0.942780i	$0.391799\pi$
$440$		0			0
$441$	−15.5642	+	12.5335i	−0.741153	+	0.596834i
$442$		0			0
$443$	7.01410	+	2.55292i	0.333250	+	0.121293i	0.503225	−	0.864155i	$-0.332147\pi$
$443$	7.01410	+	2.55292i	0.333250	+	0.121293i	−0.169975	+	0.985448i	$0.554369\pi$
$444$		0			0
$445$	−14.2299	−	11.9403i	−0.674562	−	0.566025i
$446$		0			0
$447$	2.88586	−	4.88397i	0.136496	−	0.231004i
$448$		0			0
$449$	−21.1658	−	12.2201i	−0.998877	−	0.576702i	−0.0909615	−	0.995854i	$-0.528994\pi$
$449$	−21.1658	−	12.2201i	−0.998877	−	0.576702i	−0.907916	+	0.419152i	$0.862327\pi$
$450$		0			0
$451$	−9.16220	+	5.28980i	−0.431431	+	0.249087i
$452$		0			0
$453$	2.70307	−	14.4743i	0.127001	−	0.680060i
$454$		0			0
$455$	−2.19010	+	12.4207i	−0.102673	+	0.582290i
$456$		0			0
$457$	0.996769	−	0.836388i	0.0466269	−	0.0391246i	−0.619176	−	0.785252i	$-0.712533\pi$
$457$	0.996769	−	0.836388i	0.0466269	−	0.0391246i	0.665803	+	0.746127i	$0.268089\pi$
$458$		0			0
$459$	5.15088	+	0.155972i	0.240423	+	0.00728015i
$460$		0			0
$461$	−9.12564	−	10.8755i	−0.425023	−	0.506523i	0.510456	−	0.859904i	$-0.329477\pi$
$461$	−9.12564	−	10.8755i	−0.425023	−	0.506523i	−0.935480	+	0.353381i	$0.885032\pi$
$462$		0			0
$463$	33.2154	+	5.85677i	1.54365	+	0.272187i	0.879677	−	0.475571i	$-0.157758\pi$
$463$	33.2154	+	5.85677i	1.54365	+	0.272187i	0.663972	+	0.747758i	$0.268870\pi$
$464$		0			0
$465$	−20.2760	−	57.5067i	−0.940276	−	2.66681i
$466$		0			0
$467$	13.0487	+	22.6011i	0.603824	+	1.04585i	0.992236	+	0.124368i	$0.0396902\pi$
$467$	13.0487	+	22.6011i	0.603824	+	1.04585i	−0.388413	+	0.921486i	$0.626976\pi$
$468$		0			0
$469$	1.97964	−	3.42884i	0.0914113	−	0.158329i
$470$		0			0
$471$	−5.12699	+	2.89149i	−0.236239	+	0.133233i
$472$		0			0
$473$	0.0656824	−	0.0782773i	0.00302008	−	0.00359919i
$474$		0			0
$475$	10.5935	−	29.1054i	0.486064	−	1.33545i
$476$		0			0
$477$	1.90645	+	5.58617i	0.0872901	+	0.255773i
$478$		0			0
$479$	−1.39041	−	7.88541i	−0.0635295	−	0.360293i	−0.999956	−	0.00942856i	$-0.996999\pi$
$479$	−1.39041	−	7.88541i	−0.0635295	−	0.360293i	0.936426	−	0.350865i	$-0.114112\pi$
$480$		0			0
$481$	62.2868	−	22.6706i	2.84004	−	1.03369i
$482$		0			0
$483$	−0.679706	−	4.09607i	−0.0309277	−	0.186378i
$484$		0			0
$485$		−	31.0881i		−	1.41164i
$486$		0			0
$487$		−	1.43126i		−	0.0648566i	−0.999474	−	0.0324283i	$-0.989676\pi$
$487$		−	1.43126i		−	0.0648566i	0.999474	−	0.0324283i	$-0.0103241\pi$
$488$		0			0
$489$	3.25847	+	19.6363i	0.147353	+	0.887986i
$490$		0			0
$491$	−33.7796	+	12.2948i	−1.52445	+	0.554855i	−0.962255	−	0.272148i	$-0.912266\pi$
$491$	−33.7796	+	12.2948i	−1.52445	+	0.554855i	−0.562197	+	0.827003i	$0.690044\pi$
$492$		0			0
$493$	0.0443732	+	0.251653i	0.00199847	+	0.0113339i
$494$		0			0
$495$	5.12984	+	15.0312i	0.230569	+	0.675602i
$496$		0			0
$497$	0.701707	−	1.92792i	0.0314758	−	0.0864792i
$498$		0			0
$499$	20.4907	−	24.4198i	0.917288	−	1.09318i	−0.0780713	−	0.996948i	$-0.524876\pi$
$499$	20.4907	−	24.4198i	0.917288	−	1.09318i	0.995359	−	0.0962330i	$-0.0306794\pi$
$500$		0			0
$501$	−24.7275	+	13.9457i	−1.10474	+	0.623046i
$502$		0			0
$503$	−4.69716	+	8.13572i	−0.209436	+	0.362754i	−0.951537	−	0.307534i	$-0.900496\pi$
$503$	−4.69716	+	8.13572i	−0.209436	+	0.362754i	0.742101	+	0.670288i	$0.233829\pi$
$504$		0			0
$505$	−14.0657	−	24.3626i	−0.625917	−	1.08412i
$506$		0			0
$507$	14.8020	+	41.9813i	0.657378	+	1.86446i
$508$		0			0
$509$	23.7648	+	4.19038i	1.05336	+	0.185735i	0.673407	−	0.739272i	$-0.264830\pi$
$509$	23.7648	+	4.19038i	1.05336	+	0.185735i	0.379950	+	0.925007i	$0.375941\pi$
$510$		0			0
$511$	−0.212376	−	0.253100i	−0.00939495	−	0.0111965i
$512$		0			0
$513$	−11.8751	+	19.2015i	−0.524297	+	0.847769i
$514$		0			0
$515$	−9.55390	+	8.01667i	−0.420995	+	0.353257i
$516$		0			0
$517$	−2.16699	+	12.2896i	−0.0953039	+	0.540495i
$518$		0			0
$519$	−5.88250	+	31.4993i	−0.258213	+	1.38267i
$520$		0			0
$521$	5.61174	−	3.23994i	0.245855	−	0.141944i	−0.372010	−	0.928229i	$-0.621331\pi$
$521$	5.61174	−	3.23994i	0.245855	−	0.141944i	0.617865	+	0.786284i	$0.287998\pi$
$522$		0			0
$523$	−16.0544	−	9.26903i	−0.702011	−	0.405306i	0.106085	−	0.994357i	$-0.466168\pi$
$523$	−16.0544	−	9.26903i	−0.702011	−	0.405306i	−0.808096	+	0.589051i	$0.799502\pi$
$524$		0			0
$525$	−3.65654	+	6.18825i	−0.159584	+	0.270077i
$526$		0			0
$527$	7.67979	+	6.44411i	0.334537	+	0.280710i
$528$		0			0
$529$	5.67849	+	2.06680i	0.246891	+	0.0898609i
$530$		0			0
$531$	27.6941	−	22.3014i	1.20182	−	0.967799i
$532$		0			0
$533$	−42.6371	+	7.51807i	−1.84682	+	0.325644i
$534$		0			0
$535$	−16.9137	−	46.4699i	−0.731241	−	2.00907i
$536$		0			0
$537$	10.1652	−	27.0755i	0.438662	−	1.16839i
$538$		0			0
$539$	10.1260			0.436157
$540$		0			0
$541$	41.5057			1.78447			0.892235	−	0.451570i	$-0.149136\pi$
$541$	41.5057			1.78447			0.892235	+	0.451570i	$0.149136\pi$
$542$		0			0
$543$	13.7217	+	16.6921i	0.588855	+	0.716326i
$544$		0			0
$545$	−5.74472	−	15.7835i	−0.246077	−	0.676090i
$546$		0			0
$547$	−14.8282	+	2.61461i	−0.634007	+	0.111792i	−0.481409	−	0.876496i	$-0.659875\pi$
$547$	−14.8282	+	2.61461i	−0.634007	+	0.111792i	−0.152597	+	0.988288i	$0.548764\pi$
$548$		0			0
$549$	−16.5291	−	30.0121i	−0.705445	−	1.28088i
$550$		0			0
$551$	−1.05201	−	0.382901i	−0.0448172	−	0.0163121i
$552$		0			0
$553$	5.74174	+	4.81789i	0.244164	+	0.204878i
$554$		0			0
$555$	64.2684	+	0.648520i	2.72804	+	0.0275281i
$556$		0			0
$557$	−20.8755	−	12.0525i	−0.884524	−	0.510680i	−0.0123769	−	0.999923i	$-0.503940\pi$
$557$	−20.8755	−	12.0525i	−0.884524	−	0.510680i	−0.872148	+	0.489243i	$0.837273\pi$
$558$		0			0
$559$	0.362142	−	0.209083i	0.0153170	−	0.00884327i
$560$		0			0
$561$	−1.98330	−	1.69858i	−0.0837351	−	0.0717142i
$562$		0			0
$563$	1.32702	−	7.52589i	0.0559271	−	0.317179i	−0.943991	−	0.329971i	$-0.892961\pi$
$563$	1.32702	−	7.52589i	0.0559271	−	0.317179i	0.999918	+	0.0127925i	$0.00407210\pi$
$564$		0			0
$565$	44.3261	−	37.1940i	1.86481	−	1.56476i
$566$		0			0
$567$	3.52696	−	3.87437i	0.148118	−	0.162708i
$568$		0			0
$569$	10.3936	+	12.3866i	0.435724	+	0.519275i	0.938565	−	0.345104i	$-0.112156\pi$
$569$	10.3936	+	12.3866i	0.435724	+	0.519275i	−0.502841	+	0.864379i	$0.667712\pi$
$570$		0			0
$571$	−34.7174	−	6.12161i	−1.45288	−	0.256181i	−0.609193	−	0.793022i	$-0.708507\pi$
$571$	−34.7174	−	6.12161i	−1.45288	−	0.256181i	−0.843684	+	0.536840i	$0.819618\pi$
$572$		0			0
$573$	−28.6453	+	33.4468i	−1.19667	+	1.39726i
$574$		0			0
$575$	14.6775	+	25.4221i	0.612093	+	1.06018i
$576$		0			0
$577$	−4.70841	+	8.15521i	−0.196014	+	0.339506i	−0.947232	−	0.320548i	$-0.896133\pi$
$577$	−4.70841	+	8.15521i	−0.196014	+	0.339506i	0.751219	+	0.660053i	$0.229466\pi$
$578$		0			0
$579$	0.300779	−	29.8072i	0.0124999	−	1.23874i
$580$		0			0
$581$	−0.602862	+	0.718463i	−0.0250109	+	0.0298069i
$582$		0			0
$583$	1.02296	−	2.81056i	0.0423667	−	0.116402i
$584$		0			0
$585$	−1.31159	+	64.9825i	−0.0542274	+	2.68669i
$586$		0			0
$587$	−0.736783	−	4.17851i	−0.0304103	−	0.172465i	0.965820	−	0.259214i	$-0.0834635\pi$
$587$	−0.736783	−	4.17851i	−0.0304103	−	0.172465i	−0.996230	+	0.0867485i	$0.972352\pi$
$588$		0			0
$589$	−41.2729	+	15.0221i	−1.70062	+	0.618974i
$590$		0			0
$591$	5.81059	−	4.77659i	0.239016	−	0.196483i
$592$		0			0
$593$			18.1170i			0.743976i	0.928238	+	0.371988i	$0.121324\pi$
$593$			18.1170i			0.743976i	−0.928238	+	0.371988i	$0.878676\pi$
$594$		0			0
$595$		−	2.01064i		−	0.0824283i
$596$		0			0
$597$	43.1326	+	16.1937i	1.76530	+	0.662763i
$598$		0			0
$599$	16.1974	−	5.89539i	0.661810	−	0.240879i	0.0107921	−	0.999942i	$-0.496565\pi$
$599$	16.1974	−	5.89539i	0.661810	−	0.240879i	0.651017	+	0.759063i	$0.274342\pi$
$600$		0			0
$601$	1.91764	+	10.8755i	0.0782221	+	0.443619i	0.998614	+	0.0526234i	$0.0167583\pi$
$601$	1.91764	+	10.8755i	0.0782221	+	0.443619i	−0.920392	+	0.390996i	$0.872131\pi$
$602$		0			0
$603$	7.36394	−	19.0284i	0.299883	−	0.774897i
$604$		0			0
$605$	−10.3498	+	28.4359i	−0.420780	+	1.15608i
$606$		0			0
$607$	−23.4840	+	27.9871i	−0.953186	+	1.13596i	0.0374318	+	0.999299i	$0.488082\pi$
$607$	−23.4840	+	27.9871i	−0.953186	+	1.13596i	−0.990618	+	0.136663i	$0.956362\pi$
$608$		0			0
$609$	0.223673	+	0.132165i	0.00906369	+	0.00535559i
$610$		0			0
$611$	−25.5342	+	44.2266i	−1.03300	+	1.78922i
$612$		0			0
$613$	−1.03350	−	1.79008i	−0.0417427	−	0.0723005i	0.844399	−	0.535714i	$-0.179958\pi$
$613$	−1.03350	−	1.79008i	−0.0417427	−	0.0723005i	−0.886142	+	0.463414i	$0.846624\pi$
$614$		0			0
$615$	−41.2668	−	7.70658i	−1.66404	−	0.310759i
$616$		0			0
$617$	−22.6757	−	3.99834i	−0.912891	−	0.160967i	−0.302575	−	0.953126i	$-0.597846\pi$
$617$	−22.6757	−	3.99834i	−0.912891	−	0.160967i	−0.610316	+	0.792158i	$0.708957\pi$
$618$		0			0
$619$	15.5198	+	18.4958i	0.623794	+	0.743409i	0.981718	−	0.190342i	$-0.0609596\pi$
$619$	15.5198	+	18.4958i	0.623794	+	0.743409i	−0.357923	+	0.933751i	$0.616515\pi$
$620$		0			0
$621$	−6.70636	−	20.3191i	−0.269117	−	0.815377i
$622$		0			0
$623$	2.37863	−	1.99590i	0.0952977	−	0.0799642i
$624$		0			0
$625$	−1.70623	+	9.67651i	−0.0682492	+	0.387060i
$626$		0			0
$627$	10.7892	−	3.80410i	0.430879	−	0.151921i
$628$		0			0
$629$	−9.15129	+	5.28350i	−0.364886	+	0.210667i
$630$		0			0
$631$	6.25684	+	3.61239i	0.249081	+	0.143807i	0.619343	−	0.785120i	$-0.287399\pi$
$631$	6.25684	+	3.61239i	0.249081	+	0.143807i	−0.370263	+	0.928927i	$0.620732\pi$
$632$		0			0
$633$	22.6699	+	40.1968i	0.901049	+	1.59768i
$634$		0			0
$635$	22.0016	+	18.4615i	0.873105	+	0.732622i
$636$		0			0
$637$	38.9395	+	14.1728i	1.54284	+	0.561547i
$638$		0			0
$639$	2.04571	−	10.3731i	0.0809270	−	0.410354i
$640$		0			0
$641$	−9.06847	+	1.59902i	−0.358183	+	0.0631573i	−0.349844	−	0.936808i	$-0.613765\pi$
$641$	−9.06847	+	1.59902i	−0.358183	+	0.0631573i	−0.00833877	+	0.999965i	$0.502654\pi$
$642$		0			0
$643$	−0.106356	−	0.292210i	−0.00419425	−	0.0115236i	0.937578	−	0.347776i	$-0.113063\pi$
$643$	−0.106356	−	0.292210i	−0.00419425	−	0.0115236i	−0.941772	+	0.336252i	$0.890841\pi$
$644$		0			0
$645$	0.399999	−	0.0663762i	0.0157500	−	0.00261356i
$646$		0			0
$647$	−13.6389			−0.536200			−0.268100	−	0.963391i	$-0.586396\pi$
$647$	−13.6389			−0.536200			−0.268100	+	0.963391i	$0.586396\pi$
$648$		0			0
$649$	−18.0176			−0.707252
$650$		0			0
$651$	10.0552	−	1.66856i	0.394092	−	0.0653961i
$652$		0			0
$653$	−11.5721	−	31.7940i	−0.452851	−	1.24420i	−0.930709	−	0.365760i	$-0.880809\pi$
$653$	−11.5721	−	31.7940i	−0.452851	−	1.24420i	0.477859	−	0.878437i	$-0.341413\pi$
$654$		0			0
$655$	2.81950	−	0.497153i	0.110167	−	0.0194254i
$656$		0			0
$657$	−1.28196	−	1.12055i	−0.0500142	−	0.0437167i
$658$		0			0
$659$	−37.4531	−	13.6318i	−1.45897	−	0.531020i	−0.513886	−	0.857858i	$-0.671795\pi$
$659$	−37.4531	−	13.6318i	−1.45897	−	0.531020i	−0.945080	+	0.326838i	$0.894017\pi$
$660$		0			0
$661$	−28.9434	−	24.2864i	−1.12577	−	0.944632i	−0.126887	−	0.991917i	$-0.540499\pi$
$661$	−28.9434	−	24.2864i	−1.12577	−	0.944632i	−0.998881	+	0.0472854i	$0.984943\pi$
$662$		0			0
$663$	−5.24937	−	9.30783i	−0.203869	−	0.361486i
$664$		0			0
$665$	7.62867	+	4.40442i	0.295827	+	0.170796i
$666$		0			0
$667$	0.918878	−	0.530515i	0.0355791	−	0.0205416i
$668$		0			0
$669$	1.28954	−	0.454670i	0.0498563	−	0.0175786i
$670$		0			0
$671$	−3.01482	+	17.0979i	−0.116386	+	0.660057i
$672$		0			0
$673$	−8.50135	+	7.13348i	−0.327703	+	0.274975i	−0.791763	−	0.610828i	$-0.790837\pi$
$673$	−8.50135	+	7.13348i	−0.327703	+	0.274975i	0.464060	+	0.885804i	$0.346392\pi$
$674$		0			0
$675$	−13.7166	+	34.4082i	−0.527953	+	1.32437i
$676$		0			0
$677$	8.86465	+	10.5645i	0.340696	+	0.406026i	0.909002	−	0.416791i	$-0.136845\pi$
$677$	8.86465	+	10.5645i	0.340696	+	0.406026i	−0.568306	+	0.822817i	$0.692401\pi$
$678$		0			0
$679$	5.11764	+	0.902377i	0.196397	+	0.0346301i
$680$		0			0
$681$	35.0431	+	6.54430i	1.34285	+	0.250778i
$682$		0			0
$683$	−8.22428	−	14.2449i	−0.314693	−	0.545065i	0.664679	−	0.747129i	$-0.268568\pi$
$683$	−8.22428	−	14.2449i	−0.314693	−	0.545065i	−0.979372	+	0.202064i	$0.935235\pi$
$684$		0			0
$685$	−9.13656	+	15.8250i	−0.349090	+	0.604642i
$686$		0			0
$687$	15.8124	+	9.34329i	0.603281	+	0.356469i
$688$		0			0
$689$	7.86759	−	9.37623i	0.299731	−	0.357206i
$690$		0			0
$691$	−4.66180	+	12.8082i	−0.177343	+	0.487247i	−0.996234	−	0.0867022i	$-0.972367\pi$
$691$	−4.66180	+	12.8082i	−0.177343	+	0.487247i	0.818891	+	0.573949i	$0.194589\pi$
$692$		0			0
$693$	−2.62330	+	0.408158i	−0.0996509	+	0.0155046i
$694$		0			0
$695$	3.17948	+	18.0318i	0.120605	+	0.683983i
$696$		0			0
$697$	6.48579	−	2.36064i	0.245667	−	0.0894154i
$698$		0			0
$699$	−38.2999	−	14.3793i	−1.44863	−	0.543875i
$700$		0			0
$701$		−	29.8352i		−	1.12686i	−0.826164	−	0.563429i	$-0.809482\pi$
$701$		−	29.8352i		−	1.12686i	0.826164	−	0.563429i	$-0.190518\pi$
$702$		0			0
$703$		−	46.2951i		−	1.74605i
$704$		0			0
$705$	−38.2521	+	31.4451i	−1.44066	+	1.18429i
$706$		0			0
$707$	4.41878	−	1.60830i	0.166185	−	0.0604865i
$708$		0			0
$709$	2.25709	+	12.8006i	0.0847670	+	0.480737i	0.997407	+	0.0719723i	$0.0229293\pi$
$709$	2.25709	+	12.8006i	0.0847670	+	0.480737i	−0.912640	+	0.408765i	$0.865960\pi$
$710$		0			0
$711$	33.0546	+	19.9841i	1.23965	+	0.749464i
$712$		0			0
$713$	14.2372	−	39.1163i	0.533186	−	1.46492i
$714$		0			0
$715$	21.1700	−	25.2295i	0.791714	−	0.943528i
$716$		0			0
$717$	−0.332071	+	32.9083i	−0.0124014	+	1.22898i
$718$		0			0
$719$	5.56340	−	9.63609i	0.207480	−	0.359365i	−0.743440	−	0.668802i	$-0.766807\pi$
$719$	5.56340	−	9.63609i	0.207480	−	0.359365i	0.950920	+	0.309437i	$0.100141\pi$
$720$		0			0
$721$	−1.04237	−	1.80543i	−0.0388198	−	0.0672379i
$722$		0			0
$723$	−23.1004	+	26.9725i	−0.859113	+	1.00312i
$724$		0			0
$725$	−1.80888	−	0.318954i	−0.0671801	−	0.0118457i
$726$		0			0
$727$	14.8219	+	17.6641i	0.549714	+	0.655123i	0.967336	−	0.253497i	$-0.0815809\pi$
$727$	14.8219	+	17.6641i	0.549714	+	0.655123i	−0.417622	+	0.908621i	$0.637136\pi$
$728$		0			0
$729$	14.8901	−	22.5230i	0.551484	−	0.834186i
$730$		0			0
$731$	−0.0510674	+	0.0428507i	−0.00188880	+	0.00158489i
$732$		0			0
$733$	4.20335	−	23.8384i	0.155254	−	0.880492i	−0.803298	−	0.595577i	$-0.796924\pi$
$733$	4.20335	−	23.8384i	0.155254	−	0.880492i	0.958553	−	0.284915i	$-0.0919653\pi$
$734$		0			0
$735$	30.5177	+	26.1367i	1.12566	+	0.964065i
$736$		0			0
$737$	−8.95380	+	5.16948i	−0.329817	+	0.190420i
$738$		0			0
$739$	−2.48625	−	1.43543i	−0.0914580	−	0.0528033i	0.453573	−	0.891219i	$-0.350149\pi$
$739$	−2.48625	−	1.43543i	−0.0914580	−	0.0528033i	−0.545031	+	0.838416i	$0.683482\pi$
$740$		0			0
$741$	46.8143	+	0.472394i	1.71977	+	0.0173538i
$742$		0			0
$743$	−37.1866	−	31.2033i	−1.36424	−	1.14474i	−0.974646	−	0.223752i	$-0.928169\pi$
$743$	−37.1866	−	31.2033i	−1.36424	−	1.14474i	−0.389599	−	0.920985i	$-0.627386\pi$
$744$		0			0
$745$	−10.7185	−	3.90121i	−0.392695	−	0.142929i
$746$		0			0
$747$	−2.50061	+	4.13612i	−0.0914926	+	0.151333i
$748$		0			0
$749$	8.14070	−	1.43542i	0.297455	−	0.0524493i
$750$		0			0
$751$	12.4360	+	34.1677i	0.453797	+	1.24680i	0.930032	+	0.367479i	$0.119779\pi$
$751$	12.4360	+	34.1677i	0.453797	+	1.24680i	−0.476235	+	0.879318i	$0.657999\pi$
$752$		0			0
$753$	−18.0004	−	21.8971i	−0.655972	−	0.797973i
$754$		0			0
$755$	−29.6064			−1.07749
$756$		0			0
$757$	34.7205			1.26194			0.630969	−	0.775808i	$-0.282658\pi$
$757$	34.7205			1.26194			0.630969	+	0.775808i	$0.282658\pi$
$758$		0			0
$759$	−3.81095	+	10.1506i	−0.138329	+	0.368444i
$760$		0			0
$761$	−0.602221	−	1.65459i	−0.0218305	−	0.0599788i	0.928299	−	0.371835i	$-0.121271\pi$
$761$	−0.602221	−	1.65459i	−0.0218305	−	0.0599788i	−0.950129	+	0.311857i	$0.899049\pi$
$762$		0			0
$763$	2.76498	−	0.487541i	0.100099	−	0.0176502i
$764$		0			0
$765$	−1.59299	−	10.2384i	−0.0575946	−	0.370170i
$766$		0			0
$767$	−69.2867	−	25.2183i	−2.50180	−	0.910579i
$768$		0			0
$769$	28.7912	+	24.1587i	1.03824	+	0.871185i	0.991808	−	0.127736i	$-0.0407710\pi$
$769$	28.7912	+	24.1587i	1.03824	+	0.871185i	0.0464302	+	0.998922i	$0.485215\pi$
$770$		0			0
$771$	9.90323	−	16.7600i	0.356656	−	0.603598i
$772$		0			0
$773$	6.18041	+	3.56826i	0.222294	+	0.128341i	0.607012	−	0.794693i	$-0.292368\pi$
$773$	6.18041	+	3.56826i	0.222294	+	0.128341i	−0.384718	+	0.923034i	$0.625701\pi$
$774$		0			0
$775$	−62.4070	+	36.0307i	−2.24172	+	1.29426i
$776$		0			0
$777$	−1.97224	+	10.5609i	−0.0707538	+	0.378869i
$778$		0			0
$779$	−5.25087	+	29.7791i	−0.188132	+	1.06695i
$780$		0			0
$781$	−4.10410	+	3.44375i	−0.146856	+	0.123227i
$782$		0			0
$783$	1.24368	+	0.495785i	0.0444454	+	0.0177179i
$784$		0			0
$785$	7.60754	+	9.06631i	0.271525	+	0.323591i
$786$		0			0
$787$	41.0237	+	7.23358i	1.46234	+	0.257849i	0.847496	−	0.530802i	$-0.178109\pi$
$787$	41.0237	+	7.23358i	1.46234	+	0.257849i	0.614841	+	0.788651i	$0.289220\pi$
$788$		0			0
$789$	11.7889	+	33.4356i	0.419695	+	1.19034i
$790$		0			0
$791$	4.83615	+	8.37645i	0.171954	+	0.297832i
$792$		0			0
$793$	−35.5245	+	61.5303i	−1.26151	+	2.18500i
$794$		0			0
$795$	10.3375	−	5.83007i	0.366633	−	0.206771i
$796$		0			0
$797$	7.92442	−	9.44395i	0.280697	−	0.334522i	−0.607213	−	0.794539i	$-0.707712\pi$
$797$	7.92442	−	9.44395i	0.280697	−	0.334522i	0.887910	+	0.460017i	$0.152157\pi$
$798$		0			0
$799$	2.78449	−	7.65033i	0.0985082	−	0.270649i
$800$		0			0
$801$	10.5309	−	12.0479i	0.372091	−	0.425691i
$802$		0			0
$803$	0.149819	+	0.849668i	0.00528701	+	0.0299841i
$804$		0			0
$805$	−7.84508	+	2.85538i	−0.276503	+	0.100639i
$806$		0			0
$807$	−4.44954	−	26.8140i	−0.156631	−	0.943898i
$808$		0			0
$809$			22.6558i			0.796534i	0.917270	+	0.398267i	$0.130388\pi$
$809$			22.6558i			0.796534i	−0.917270	+	0.398267i	$0.869612\pi$
$810$		0			0
$811$			18.3727i			0.645153i	0.946543	+	0.322577i	$0.104549\pi$
$811$			18.3727i			0.645153i	−0.946543	+	0.322577i	$0.895451\pi$
$812$		0			0
$813$	−1.43103	−	8.62371i	−0.0501883	−	0.302447i
$814$		0			0
$815$	37.6089	−	13.6885i	1.31738	−	0.479487i
$816$		0			0
$817$	−0.0507159	−	0.287624i	−0.00177432	−	0.0100627i
$818$		0			0
$819$	−10.6592	−	2.10212i	−0.372462	−	0.0734541i
$820$		0			0
$821$	6.25489	−	17.1852i	0.218297	−	0.599766i	−0.781409	−	0.624020i	$-0.785499\pi$
$821$	6.25489	−	17.1852i	0.218297	−	0.599766i	0.999706	+	0.0242532i	$0.00772079\pi$
$822$		0			0
$823$	17.9729	−	21.4193i	0.626497	−	0.746631i	−0.355676	−	0.934609i	$-0.615749\pi$
$823$	17.9729	−	21.4193i	0.626497	−	0.746631i	0.982173	+	0.187979i	$0.0601937\pi$
$824$		0			0
$825$	16.3489	−	9.22035i	0.569196	−	0.321011i
$826$		0			0
$827$	−18.5651	+	32.1557i	−0.645573	+	1.11816i	0.338596	+	0.940932i	$0.390048\pi$
$827$	−18.5651	+	32.1557i	−0.645573	+	1.11816i	−0.984169	+	0.177233i	$0.943285\pi$
$828$		0			0
$829$	10.0595	+	17.4236i	0.349382	+	0.605147i	0.986140	−	0.165917i	$-0.0530584\pi$
$829$	10.0595	+	17.4236i	0.349382	+	0.605147i	−0.636758	+	0.771064i	$0.719725\pi$
$830$		0			0
$831$	2.27254	+	6.44539i	0.0788337	+	0.223588i
$832$		0			0
$833$	−6.50574	−	1.14714i	−0.225411	−	0.0397460i
$834$		0			0
$835$	36.6912	+	43.7268i	1.26975	+	1.51323i
$836$		0			0
$837$	49.8799	−	16.4630i	1.72410	−	0.569043i
$838$		0			0
$839$	17.7136	−	14.8634i	0.611540	−	0.513143i	−0.283592	−	0.958945i	$-0.591526\pi$
$839$	17.7136	−	14.8634i	0.611540	−	0.513143i	0.895131	+	0.445802i	$0.147082\pi$
$840$		0			0
$841$	5.02427	−	28.4940i	0.173251	−	0.982553i
$842$		0			0
$843$	4.90475	−	26.2637i	0.168929	−	0.904571i
$844$		0			0
$845$	77.5133	−	44.7523i	2.66654	−	1.53953i
$846$		0			0
$847$	−4.38062	−	2.52915i	−0.150520	−	0.0869027i
$848$		0			0
$849$	3.72557	−	6.30509i	0.127861	−	0.216390i
$850$		0			0
$851$	33.6111	+	28.2030i	1.15217	+	0.966788i
$852$		0			0
$853$	−17.0665	−	6.21171i	−0.584347	−	0.212685i	0.0328941	−	0.999459i	$-0.489528\pi$
$853$	−17.0665	−	6.21171i	−0.584347	−	0.212685i	−0.617241	+	0.786774i	$0.711750\pi$
$854$		0			0
$855$	42.3355	+	16.3837i	1.44784	+	0.560311i
$856$		0			0
$857$	−22.6751	+	3.99823i	−0.774566	+	0.136577i	−0.546940	−	0.837172i	$-0.684207\pi$
$857$	−22.6751	+	3.99823i	−0.774566	+	0.136577i	−0.227626	+	0.973749i	$0.573096\pi$
$858$		0			0
$859$	11.9011	+	32.6979i	0.406059	+	1.11564i	0.959244	+	0.282579i	$0.0911900\pi$
$859$	11.9011	+	32.6979i	0.406059	+	1.11564i	−0.553185	+	0.833058i	$0.686588\pi$
$860$		0			0
$861$	2.46647	−	6.56954i	0.0840570	−	0.223889i
$862$		0			0
$863$	−16.2935			−0.554638			−0.277319	−	0.960778i	$-0.589446\pi$
$863$	−16.2935			−0.554638			−0.277319	+	0.960778i	$0.589446\pi$
$864$		0			0
$865$	64.4303			2.19070
$866$		0			0
$867$	−17.6164	−	21.4299i	−0.598285	−	0.727798i
$868$		0			0
$869$	−6.69425	−	18.3923i	−0.227087	−	0.623916i
$870$		0			0
$871$	−41.6673	+	7.34707i	−1.41184	+	0.248946i
$872$		0			0
$873$	26.7745	+	0.540407i	0.906178	+	0.0182900i
$874$		0			0
$875$	4.05529	+	1.47601i	0.137094	+	0.0498981i
$876$		0			0
$877$	−8.68742	−	7.28961i	−0.293353	−	0.246153i	0.484218	−	0.874947i	$-0.339104\pi$
$877$	−8.68742	−	7.28961i	−0.293353	−	0.246153i	−0.777571	+	0.628795i	$0.783549\pi$
$878$		0			0
$879$	−34.5097	−	0.348231i	−1.16398	−	0.0117455i
$880$		0			0
$881$	45.1724	+	26.0803i	1.52190	+	0.878668i	0.999665	+	0.0258648i	$0.00823393\pi$
$881$	45.1724	+	26.0803i	1.52190	+	0.878668i	0.522232	+	0.852803i	$0.325099\pi$
$882$		0			0
$883$	−37.5310	+	21.6685i	−1.26302	+	0.729205i	−0.973658	−	0.228015i	$-0.926776\pi$
$883$	−37.5310	+	21.6685i	−1.26302	+	0.729205i	−0.289362	+	0.957220i	$0.593443\pi$
$884$		0			0
$885$	−54.3015	−	46.5061i	−1.82532	−	1.56328i
$886$		0			0
$887$	1.93441	−	10.9706i	0.0649510	−	0.368355i	−0.934957	−	0.354762i	$-0.884562\pi$
$887$	1.93441	−	10.9706i	0.0649510	−	0.368355i	0.999908	−	0.0135933i	$-0.00432703\pi$
$888$		0			0
$889$	−3.67771	+	3.08597i	−0.123347	+	0.103500i
$890$		0			0
$891$	−13.0347	+	4.15676i	−0.436680	+	0.139257i
$892$		0			0
$893$	22.9269	+	27.3232i	0.767219	+	0.914336i
$894$		0			0
$895$	−57.2674	−	10.0978i	−1.91424	−	0.337532i
$896$		0			0
$897$	−28.8623	+	33.7002i	−0.963684	+	1.12522i
$898$		0			0
$899$	1.30232	+	2.25569i	0.0434349	+	0.0752314i
$900$		0			0
$901$	−0.975631	+	1.68984i	−0.0325030	+	0.0562968i
$902$		0			0
$903$	−0.000683890		0.0677735i	−2.27584e−5		0.00225536i
$904$		0			0
$905$	27.9274	−	33.2825i	0.928337	−	1.10635i
$906$		0			0
$907$	2.90941	−	7.99354i	0.0966054	−	0.265421i	−0.881972	−	0.471303i	$-0.843784\pi$
$907$	2.90941	−	7.99354i	0.0966054	−	0.265421i	0.978577	+	0.205882i	$0.0660062\pi$
$908$		0			0
$909$	21.2267	−	11.6906i	0.704044	−	0.387751i
$910$		0			0
$911$	7.22116	+	40.9532i	0.239248	+	1.35684i	0.833481	+	0.552548i	$0.186344\pi$
$911$	7.22116	+	40.9532i	0.239248	+	1.35684i	−0.594233	+	0.804293i	$0.702544\pi$
$912$		0			0
$913$	2.30142	−	0.837650i	0.0761660	−	0.0277222i
$914$		0			0
$915$	−53.2183	+	43.7480i	−1.75934	+	1.44626i
$916$		0			0
$917$			0.478569i			0.0158037i
$918$		0			0
$919$			29.7513i			0.981404i	0.871328	+	0.490702i	$0.163260\pi$
$919$			29.7513i			0.981404i	−0.871328	+	0.490702i	$0.836740\pi$
$920$		0			0
$921$	46.2952	+	17.3811i	1.52548	+	0.572726i
$922$		0			0
$923$	−20.6024	+	7.49865i	−0.678135	+	0.246821i
$924$		0			0
$925$	−13.1895	−	74.8015i	−0.433669	−	2.45946i
$926$		0			0
$927$	−6.73825	−	8.36760i	−0.221313	−	0.274828i
$928$		0			0
$929$	6.38406	−	17.5401i	0.209454	−	0.575471i	−0.789829	−	0.613327i	$-0.789831\pi$
$929$	6.38406	−	17.5401i	0.209454	−	0.575471i	0.999283	+	0.0378565i	$0.0120530\pi$
$930$		0			0
$931$	18.6036	−	22.1709i	0.609707	−	0.726621i
$932$		0			0
$933$	5.25743	+	3.10653i	0.172120	+	0.101703i
$934$		0			0
$935$	−2.62522	+	4.54701i	−0.0858538	+	0.148703i
$936$		0			0
$937$	−20.1936	−	34.9764i	−0.659697	−	1.14263i	−0.980694	−	0.195549i	$-0.937351\pi$
$937$	−20.1936	−	34.9764i	−0.659697	−	1.14263i	0.320997	−	0.947080i	$-0.395982\pi$
$938$		0			0
$939$	−40.9693	−	7.65102i	−1.33698	−	0.249682i
$940$		0			0
$941$	−30.9752	−	5.46176i	−1.00976	−	0.178048i	−0.355789	−	0.934566i	$-0.615788\pi$
$941$	−30.9752	−	5.46176i	−1.00976	−	0.178048i	−0.653972	+	0.756518i	$0.726899\pi$
$942$		0			0
$943$	−18.4213	−	21.9537i	−0.599882	−	0.714911i
$944$		0			0
$945$	−8.95963	−	5.54102i	−0.291457	−	0.180249i
$946$		0			0
$947$	−32.5062	+	27.2759i	−1.05631	+	0.886348i	−0.993743	−	0.111692i	$-0.964373\pi$
$947$	−32.5062	+	27.2759i	−1.05631	+	0.886348i	−0.0625661	+	0.998041i	$0.519928\pi$
$948$		0			0
$949$	−0.613105	+	3.47709i	−0.0199022	+	0.112871i
$950$		0			0
$951$	34.6034	−	12.2006i	1.12209	−	0.395632i
$952$		0			0
$953$	−27.9512	+	16.1376i	−0.905429	+	0.522749i	−0.878957	−	0.476900i	$-0.841760\pi$
$953$	−27.9512	+	16.1376i	−0.905429	+	0.522749i	−0.0264711	+	0.999650i	$0.508427\pi$
$954$		0			0
$955$	76.6817	+	44.2722i	2.48136	+	1.43262i
$956$		0			0
$957$	−0.333268	−	0.590928i	−0.0107730	−	0.0191020i
$958$		0			0
$959$	−2.33987	−	1.96338i	−0.0755582	−	0.0634009i
$960$		0			0
$961$	66.8932	+	24.3472i	2.15785	+	0.785392i
$962$		0			0
$963$	40.3160	−	13.7590i	1.29916	−	0.443378i
$964$		0			0
$965$	−59.0255	+	10.4078i	−1.90010	+	0.335039i
$966$		0			0
$967$	−14.2016	−	39.0186i	−0.456693	−	1.25475i	−0.927932	−	0.372749i	$-0.878415\pi$
$967$	−14.2016	−	39.0186i	−0.456693	−	1.25475i	0.471239	−	0.882005i	$-0.343807\pi$
$968$		0			0
$969$	−7.36280	+	1.22179i	−0.236527	+	0.0392496i
$970$		0			0
$971$	14.5385			0.466564			0.233282	−	0.972409i	$-0.425054\pi$
$971$	14.5385			0.466564			0.233282	+	0.972409i	$0.425054\pi$
$972$		0			0
$973$	−3.06063			−0.0981193
$974$		0			0
$975$	75.7750	−	12.5742i	2.42674	−	0.402696i
$976$		0			0
$977$	11.4395	+	31.4298i	0.365982	+	1.00553i	0.976874	+	0.213814i	$0.0685886\pi$
$977$	11.4395	+	31.4298i	0.365982	+	1.00553i	−0.610892	+	0.791714i	$0.709189\pi$
$978$		0			0
$979$	−7.98517	+	1.40800i	−0.255207	+	0.0449999i
$980$		0			0
$981$	13.6933	−	4.67324i	0.437194	−	0.149205i
$982$		0			0
$983$	3.63677	+	1.32368i	0.115995	+	0.0422187i	0.399366	−	0.916792i	$-0.369230\pi$
$983$	3.63677	+	1.32368i	0.115995	+	0.0422187i	−0.283371	+	0.959010i	$0.591453\pi$
$984$		0			0
$985$	−11.5858	−	9.72164i	−0.369154	−	0.309757i
$986$		0			0
$987$	−4.06609	−	7.20971i	−0.129425	−	0.229487i
$988$		0			0
$989$	0.239716	+	0.138400i	0.00762253	+	0.00440087i
$990$		0			0
$991$	−7.46425	+	4.30949i	−0.237110	+	0.136895i	−0.613848	−	0.789425i	$-0.710379\pi$
$991$	−7.46425	+	4.30949i	−0.237110	+	0.136895i	0.376738	+	0.926320i	$0.377046\pi$
$992$		0			0
$993$	15.3378	−	5.40788i	0.486731	−	0.171614i
$994$		0			0
$995$	16.0863	−	91.2297i	0.509969	−	2.89218i
$996$		0			0
$997$	−3.42878	+	2.87709i	−0.108591	+	0.0911184i	−0.695466	−	0.718559i	$-0.744802\pi$
$997$	−3.42878	+	2.87709i	−0.108591	+	0.0911184i	0.586876	+	0.809677i	$0.300358\pi$
$998$		0			0
$999$	−1.67572	+	55.3396i	−0.0530174	+	1.75087i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bi.a.383.34	yes	216
4.3	odd	2	inner	864.2.bi.a.383.3	✓	216
27.11	odd	18	inner	864.2.bi.a.767.3	yes	216
108.11	even	18	inner	864.2.bi.a.767.34	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.3	✓	216	4.3	odd	2	inner
864.2.bi.a.383.34	yes	216	1.1	even	1	trivial
864.2.bi.a.767.3	yes	216	27.11	odd	18	inner
864.2.bi.a.767.34	yes	216	108.11	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.70869 - 0.283541i) q^{3} +(-1.19113 - 3.27259i) q^{5} +(0.573300 - 0.101088i) q^{7} +(2.83921 - 0.968964i) q^{9} +(-1.42849 - 0.519927i) q^{11} +(-4.76553 - 3.99876i) q^{13} +(-2.96317 - 5.25409i) q^{15} +(0.858874 + 0.495871i) q^{17} +(-3.76282 + 2.17246i) q^{19} +(0.950926 - 0.335282i) q^{21} +(0.715065 - 4.05534i) q^{23} +(-5.46085 + 4.58220i) q^{25} +(4.57657 - 2.46069i) q^{27} +(0.165623 + 0.197381i) q^{29} +(9.95515 + 1.75536i) q^{31} +(-2.58825 - 0.483357i) q^{33} +(-1.01369 - 1.75577i) q^{35} +(-5.32749 + 9.22749i) q^{37} +(-9.27661 - 5.48139i) q^{39} +(4.47348 - 5.33129i) q^{41} +(-0.0229902 + 0.0631651i) q^{43} +(-6.55288 - 8.13741i) q^{45} +(-1.42549 - 8.08438i) q^{47} +(-6.25939 + 2.27823i) q^{49} +(1.60814 + 0.603762i) q^{51} +1.96751i q^{53} +5.29415i q^{55} +(-5.81349 + 4.77897i) q^{57} +(11.1376 - 4.05376i) q^{59} +(-1.98322 - 11.2474i) q^{61} +(1.52977 - 0.842517i) q^{63} +(-7.40995 + 20.3587i) q^{65} +(4.37173 - 5.21003i) q^{67} +(0.0719681 - 7.13204i) q^{69} +(1.76215 - 3.05214i) q^{71} +(-0.283777 - 0.491516i) q^{73} +(-8.03163 + 9.37790i) q^{75} +(-0.871510 - 0.153671i) q^{77} +(8.27612 + 9.86310i) q^{79} +(7.12222 - 5.50218i) q^{81} +(-1.23417 + 1.03559i) q^{83} +(0.599756 - 3.40139i) q^{85} +(0.338962 + 0.290302i) q^{87} +(4.61926 - 2.66693i) q^{89} +(-3.13631 - 1.81075i) q^{91} +(17.5079 + 0.176669i) q^{93} +(11.5916 + 9.72648i) q^{95} +(8.38829 + 3.05309i) q^{97} +(-4.55956 - 0.0920288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{29} + 36 q^{33} + 36 q^{41} - 24 q^{45} + 12 q^{57} + 48 q^{65} + 48 q^{69} + 48 q^{77} + 48 q^{81} + 36 q^{89} - 144 q^{93} - 36 q^{97}+O(q^{100}) \) 216 * q - 24 * q^29 + 36 * q^33 + 36 * q^41 - 24 * q^45 + 12 * q^57 + 48 * q^65 + 48 * q^69 + 48 * q^77 + 48 * q^81 + 36 * q^89 - 144 * q^93 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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