LMFDB - Embedded newform 864.2.bi.a.767.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(95,864)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: 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:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			767.3
Character	$\chi$	$=$	864.767
Dual form			864.2.bi.a.383.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70869 - 0.283541i) q^{3} +(-1.19113 + 3.27259i) q^{5} +(-0.573300 - 0.101088i) q^{7} +(2.83921 + 0.968964i) q^{9} +O(q^{10})$	\(q+(-1.70869 - 0.283541i) q^{3} +(-1.19113 + 3.27259i) q^{5} +(-0.573300 - 0.101088i) q^{7} +(2.83921 + 0.968964i) q^{9} +(1.42849 - 0.519927i) q^{11} +(-4.76553 + 3.99876i) q^{13} +(2.96317 - 5.25409i) q^{15} +(0.858874 - 0.495871i) q^{17} +(3.76282 + 2.17246i) q^{19} +(0.950926 + 0.335282i) q^{21} +(-0.715065 - 4.05534i) q^{23} +(-5.46085 - 4.58220i) q^{25} +(-4.57657 - 2.46069i) q^{27} +(0.165623 - 0.197381i) q^{29} +(-9.95515 + 1.75536i) q^{31} +(-2.58825 + 0.483357i) q^{33} +(1.01369 - 1.75577i) q^{35} +(-5.32749 - 9.22749i) q^{37} +(9.27661 - 5.48139i) q^{39} +(4.47348 + 5.33129i) q^{41} +(0.0229902 + 0.0631651i) q^{43} +(-6.55288 + 8.13741i) q^{45} +(1.42549 - 8.08438i) q^{47} +(-6.25939 - 2.27823i) q^{49} +(-1.60814 + 0.603762i) q^{51} -1.96751i q^{53} +5.29415i q^{55} +(-5.81349 - 4.77897i) q^{57} +(-11.1376 - 4.05376i) q^{59} +(-1.98322 + 11.2474i) q^{61} +(-1.52977 - 0.842517i) q^{63} +(-7.40995 - 20.3587i) q^{65} +(-4.37173 - 5.21003i) q^{67} +(0.0719681 + 7.13204i) q^{69} +(-1.76215 - 3.05214i) q^{71} +(-0.283777 + 0.491516i) q^{73} +(8.03163 + 9.37790i) q^{75} +(-0.871510 + 0.153671i) q^{77} +(-8.27612 + 9.86310i) q^{79} +(7.12222 + 5.50218i) q^{81} +(1.23417 + 1.03559i) q^{83} +(0.599756 + 3.40139i) q^{85} +(-0.338962 + 0.290302i) q^{87} +(4.61926 + 2.66693i) q^{89} +(3.13631 - 1.81075i) q^{91} +(17.5079 - 0.176669i) q^{93} +(-11.5916 + 9.72648i) q^{95} +(8.38829 - 3.05309i) q^{97} +(4.55956 - 0.0920288i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * 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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$	$-1$

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	0.323173	+	0.946340i	$0.395251\pi$
$5$	−1.19113	+	3.27259i	−0.532688	+	1.46355i	−0.855860	+	0.517207i	$0.826972\pi$
$6$		0			0
$7$	−0.573300	−	0.101088i	−0.216687	−	0.0382077i	0.0642507	−	0.997934i	$-0.479534\pi$
$7$	−0.573300	−	0.101088i	−0.216687	−	0.0382077i	−0.280938	+	0.959726i	$0.590645\pi$
$8$		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	$-0.537509\pi$
$11$	1.42849	−	0.519927i	0.430705	−	0.156764i	0.548270	+	0.836301i	$0.315287\pi$
$12$		0			0
$13$	−4.76553	+	3.99876i	−1.32172	+	1.10906i	−0.335784	+	0.941939i	$0.609001\pi$
$13$	−4.76553	+	3.99876i	−1.32172	+	1.10906i	−0.985937	+	0.167117i	$0.946554\pi$
$14$		0			0
$15$	2.96317	−	5.25409i	0.765088	−	1.35660i
$16$		0			0
$17$	0.858874	−	0.495871i	0.208308	−	0.120266i	−0.392217	−	0.919873i	$-0.628292\pi$
$17$	0.858874	−	0.495871i	0.208308	−	0.120266i	0.600525	+	0.799606i	$0.294958\pi$
$18$		0			0
$19$	3.76282	+	2.17246i	0.863249	+	0.498397i	0.865099	−	0.501601i	$-0.167255\pi$
$19$	3.76282	+	2.17246i	0.863249	+	0.498397i	−0.00184984	+	0.999998i	$0.500589\pi$
$20$		0			0
$21$	0.950926	+	0.335282i	0.207509	+	0.0731645i
$22$		0			0
$23$	−0.715065	−	4.05534i	−0.149101	−	0.845596i	−0.963982	−	0.265967i	$-0.914309\pi$
$23$	−0.715065	−	4.05534i	−0.149101	−	0.845596i	0.814881	−	0.579629i	$-0.196802\pi$
$24$		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	−0.750448	−	0.660930i	$-0.770162\pi$
$29$	0.165623	−	0.197381i	0.0307553	−	0.0366528i	0.781203	+	0.624277i	$0.214606\pi$
$30$		0			0
$31$	−9.95515	+	1.75536i	−1.78800	+	0.315272i	−0.966831	−	0.255416i	$-0.917787\pi$
$31$	−9.95515	+	1.75536i	−1.78800	+	0.315272i	−0.821167	+	0.570689i	$0.806676\pi$
$32$		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	−0.855871	−	0.517189i	$-0.826978\pi$
$37$	−5.32749	−	9.22749i	−0.875835	−	1.51699i	−0.0199635	−	0.999801i	$-0.506355\pi$
$38$		0			0
$39$	9.27661	−	5.48139i	1.48545	−	0.877726i
$40$		0			0
$41$	4.47348	+	5.33129i	0.698641	+	0.832608i	0.992372	−	0.123280i	$-0.0393414\pi$
$41$	4.47348	+	5.33129i	0.698641	+	0.832608i	−0.293731	+	0.955888i	$0.594897\pi$
$42$		0			0
$43$	0.0229902	+	0.0631651i	0.00350597	+	0.00963258i	0.941433	−	0.337199i	$-0.109480\pi$
$43$	0.0229902	+	0.0631651i	0.00350597	+	0.00963258i	−0.937927	+	0.346832i	$0.887257\pi$
$44$		0			0
$45$	−6.55288	+	8.13741i	−0.976845	+	1.21305i
$46$		0			0
$47$	1.42549	−	8.08438i	0.207930	−	1.17923i	−0.684833	−	0.728700i	$-0.740125\pi$
$47$	1.42549	−	8.08438i	0.207930	−	1.17923i	0.892762	−	0.450528i	$-0.148764\pi$
$48$		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	$-0.956855\pi$
$53$		−	1.96751i		−	0.270258i	0.990828	−	0.135129i	$-0.0431449\pi$
$54$		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	$-0.669395\pi$
$59$	−11.1376	−	4.05376i	−1.44999	−	0.527754i	−0.942589	+	0.333954i	$0.891617\pi$
$60$		0			0
$61$	−1.98322	+	11.2474i	−0.253925	+	1.44008i	0.544891	+	0.838507i	$0.316571\pi$
$61$	−1.98322	+	11.2474i	−0.253925	+	1.44008i	−0.798816	+	0.601575i	$0.794540\pi$
$62$		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	$-0.358598\pi$
$67$	−4.37173	−	5.21003i	−0.534092	−	0.636506i	−0.963852	+	0.266437i	$0.914154\pi$
$68$		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	$-0.233730\pi$
$71$	−1.76215	−	3.05214i	−0.209129	−	0.362222i	−0.951440	+	0.307833i	$0.900396\pi$
$72$		0			0
$73$	−0.283777	+	0.491516i	−0.0332136	+	0.0575276i	−0.882154	−	0.470960i	$-0.843907\pi$
$73$	−0.283777	+	0.491516i	−0.0332136	+	0.0575276i	0.848941	+	0.528488i	$0.177241\pi$
$74$		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	0.0626113	+	0.998038i	$0.480057\pi$
$79$	−8.27612	+	9.86310i	−0.931137	+	1.10969i	−0.993748	+	0.111647i	$0.964387\pi$
$80$		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	$-0.249596\pi$
$83$	1.23417	+	1.03559i	0.135468	+	0.113671i	−0.572536	+	0.819879i	$0.694040\pi$
$84$		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	0.724426	−	0.689353i	$-0.242105\pi$
$89$	4.61926	+	2.66693i	0.489641	+	0.282694i	−0.234785	+	0.972047i	$0.575438\pi$
$90$		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	0.120968	−	0.992656i	$-0.461400\pi$
$97$	8.38829	−	3.05309i	0.851702	−	0.309994i	0.730734	+	0.682662i	$0.239178\pi$
$98$		0			0
$99$	4.55956	−	0.0920288i	0.458253	−	0.00924924i
$100$		0			0
$101$	7.95496	+	1.40267i	0.791548	+	0.139571i	0.554782	−	0.831996i	$-0.312802\pi$
$101$	7.95496	+	1.40267i	0.791548	+	0.139571i	0.236766	+	0.971567i	$0.423913\pi$
$102$		0			0
$103$	1.22482	−	3.36517i	0.120685	−	0.331580i	−0.864609	−	0.502445i	$-0.832434\pi$
$103$	1.22482	−	3.36517i	0.120685	−	0.331580i	0.985294	+	0.170865i	$0.0546562\pi$
$104$		0			0
$105$	−2.22991	+	2.71263i	−0.217617	+	0.264725i
$106$		0			0
$107$	−14.1997			−1.37274			−0.686370	−	0.727253i	$-0.740797\pi$
$107$	−14.1997			−1.37274			−0.686370	+	0.727253i	$0.740797\pi$
$108$		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	−0.318988	−	0.947759i	$-0.603343\pi$
$113$	5.68265	−	15.6130i	0.534579	−	1.46874i	0.853566	−	0.520984i	$-0.174435\pi$
$114$		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	$-0.214095\pi$
$127$	7.14207	+	4.12348i	0.633757	+	0.365900i	−0.148449	+	0.988920i	$0.547428\pi$
$128$		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	$-0.0441217\pi$
$131$	0.142753	+	0.809591i	0.0124724	+	0.0707343i	−0.977936	+	0.208903i	$0.933011\pi$
$132$		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	−0.890628	−	0.454733i	$-0.849735\pi$
$137$	−3.37267	+	4.01940i	−0.288147	+	0.343400i	0.602481	+	0.798133i	$0.294179\pi$
$138$		0			0
$139$	5.17764	−	0.912958i	0.439162	−	0.0774361i	0.0503043	−	0.998734i	$-0.483981\pi$
$139$	5.17764	−	0.912958i	0.439162	−	0.0774361i	0.388858	+	0.921298i	$0.372870\pi$
$140$		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	0.845355	−	0.534205i	$-0.179389\pi$
$149$	2.10528	+	2.50897i	0.172471	+	0.205543i	−0.672884	+	0.739748i	$0.734945\pi$
$150$		0			0
$151$	−2.90758	−	7.98851i	−0.236615	−	0.650095i	−0.999991	−	0.00414108i	$-0.998682\pi$
$151$	−2.90758	−	7.98851i	−0.236615	−	0.650095i	0.763376	−	0.645954i	$-0.223540\pi$
$152$		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	0.211429	−	0.977393i	$-0.432188\pi$
$157$	−3.19343	−	1.16231i	−0.254863	−	0.0927626i	−0.466292	+	0.884631i	$0.654410\pi$
$158$		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	$-0.170234\pi$
$167$	15.4019	+	5.60583i	1.19183	+	0.433792i	0.331467	+	0.943467i	$0.392457\pi$
$168$		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	−0.908573	−	0.417727i	$-0.862827\pi$
$173$	−6.32756	−	17.3848i	−0.481075	−	1.32174i	0.427498	−	0.904016i	$-0.359395\pi$
$174$		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	−0.988731	−	0.149704i	$-0.952168\pi$
$179$	−8.34873	−	14.4604i	−0.624013	−	1.08082i	0.364718	−	0.931118i	$-0.381166\pi$
$180$		0			0
$181$	6.23773	−	10.8041i	0.463647	−	0.803060i	−0.535492	−	0.844540i	$-0.679874\pi$
$181$	6.23773	−	10.8041i	0.463647	−	0.803060i	0.999139	+	0.0414800i	$0.0132073\pi$
$182$		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	0.956805	+	0.290729i	$0.0938978\pi$
$191$	19.4764	+	16.3427i	1.40927	+	1.18251i	0.452460	+	0.891785i	$0.350547\pi$
$192$		0			0
$193$	2.98850	+	16.9486i	0.215117	+	1.21999i	0.880704	+	0.473667i	$0.157070\pi$
$193$	2.98850	+	16.9486i	0.215117	+	1.21999i	−0.665587	+	0.746320i	$0.731819\pi$
$194$		0			0
$195$	6.88876	+	36.8876i	0.493314	+	2.64157i
$196$		0			0
$197$	3.76094	+	2.17138i	0.267956	+	0.154704i	0.627958	−	0.778247i	$-0.283891\pi$
$197$	3.76094	+	2.17138i	0.267956	+	0.154704i	−0.360002	+	0.932951i	$0.617224\pi$
$198$		0			0
$199$	−23.0361	+	13.2999i	−1.63299	+	0.942806i	−0.649823	+	0.760086i	$0.725157\pi$
$199$	−23.0361	+	13.2999i	−1.63299	+	0.942806i	−0.983165	+	0.182721i	$0.941510\pi$
$200$		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	0.0608870	+	0.998145i	$0.480607\pi$
$211$	−9.11279	+	25.0372i	−0.627350	+	1.72363i	−0.688237	+	0.725486i	$0.741615\pi$
$212$		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	$-0.452859\pi$
$223$	−0.777443	−	0.137084i	−0.0520614	−	0.00917983i	−0.199618	+	0.979874i	$0.563970\pi$
$224$		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	$-0.850451\pi$
$227$	−19.3407	+	7.03943i	−1.28369	+	0.467223i	−0.392036	+	0.919950i	$0.628229\pi$
$228$		0			0
$229$	8.12307	−	6.81607i	0.536788	−	0.450418i	−0.333650	−	0.942697i	$-0.608280\pi$
$229$	8.12307	−	6.81607i	0.536788	−	0.450418i	0.870438	+	0.492279i	$0.163836\pi$
$230$		0			0
$231$	1.53271	−	0.0154663i	0.100845	−	0.00101761i
$232$		0			0
$233$	−20.4551	+	11.8098i	−1.34006	+	0.773683i	−0.986816	−	0.161849i	$-0.948254\pi$
$233$	−20.4551	+	11.8098i	−1.34006	+	0.773683i	−0.353242	+	0.935532i	$0.614921\pi$
$234$		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	0.883625	+	0.468195i	$0.155096\pi$
$239$	3.29941	+	18.7119i	0.213421	+	1.21037i	−0.670204	+	0.742177i	$0.733793\pi$
$240$		0			0
$241$	−15.7064	−	13.1792i	−1.01174	−	0.848947i	−0.0231694	−	0.999732i	$-0.507376\pi$
$241$	−15.7064	−	13.1792i	−1.01174	−	0.848947i	−0.988567	+	0.150784i	$0.951820\pi$
$242$		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	−0.483323	−	0.875442i	$-0.660570\pi$
$251$	8.18279	−	14.1730i	0.516493	−	0.894592i	0.999817	−	0.0191506i	$-0.00609618\pi$
$252$		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	0.942763	−	0.333465i	$-0.108218\pi$
$257$	7.22455	+	8.60988i	0.450655	+	0.537070i	−0.492108	+	0.870534i	$0.663773\pi$
$258$		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	0.654347	+	0.756194i	$0.272944\pi$
$263$	−3.55437	+	20.1578i	−0.219172	+	1.24298i	−0.873519	+	0.486790i	$0.838168\pi$
$264$		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	$0.158784\pi$
$269$			15.6928i			0.956805i	−0.878141	+	0.478403i	$0.841216\pi$
$270$		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	−0.957280	−	0.289162i	$-0.906623\pi$
$277$	0.685177	−	3.88583i	0.0411683	−	0.233477i	0.998448	+	0.0556853i	$0.0177344\pi$
$278$		0			0
$279$	−29.9656	−	4.66234i	−1.79400	−	0.279127i
$280$		0			0
$281$	5.27584	+	14.4953i	0.314730	+	0.864714i	0.991685	+	0.128690i	$0.0410771\pi$
$281$	5.27584	+	14.4953i	0.314730	+	0.864714i	−0.676955	+	0.736025i	$0.736701\pi$
$282$		0			0
$283$	−2.71786	−	3.23902i	−0.161560	−	0.192540i	0.679191	−	0.733961i	$-0.262331\pi$
$283$	−2.71786	−	3.23902i	−0.161560	−	0.192540i	−0.840751	+	0.541422i	$0.817886\pi$
$284$		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	−0.714385	−	0.699752i	$-0.753294\pi$
$293$	−19.6225	+	3.45998i	−1.14636	+	0.202134i	−0.431973	+	0.901886i	$0.642183\pi$
$294$		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	$-0.969779\pi$
$307$	−24.7252	+	14.2751i	−1.41114	+	0.814725i	−0.415648	+	0.909525i	$0.636445\pi$
$308$		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	$-0.754094\pi$
$311$	−2.70082	+	2.26626i	−0.153149	+	0.128508i	0.562993	+	0.826461i	$0.309650\pi$
$312$		0			0
$313$	−22.6114	+	8.22989i	−1.27807	+	0.465181i	−0.889795	−	0.456361i	$-0.849153\pi$
$313$	−22.6114	+	8.22989i	−1.27807	+	0.465181i	−0.388279	+	0.921542i	$0.626930\pi$
$314$		0			0
$315$	4.57936	−	4.00276i	0.258018	−	0.225530i
$316$		0			0
$317$	20.8619	+	3.67851i	1.17172	+	0.206606i	0.725438	−	0.688287i	$-0.241637\pi$
$317$	20.8619	+	3.67851i	1.17172	+	0.206606i	0.446281	+	0.894893i	$0.352748\pi$
$318$		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	$-0.527524\pi$
$331$	−9.24695	−	1.63049i	−0.508259	−	0.0896197i	−0.421896	+	0.906644i	$0.638635\pi$
$332$		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	−0.676125	−	0.736786i	$-0.736342\pi$
$337$	−1.24722	+	1.04654i	−0.0679404	+	0.0570087i	0.608185	+	0.793795i	$0.291898\pi$
$338$		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	0.932963	+	0.359974i	$0.117214\pi$
$347$	3.34153	+	18.9508i	0.179383	+	1.01733i	−0.753580	+	0.657356i	$0.771675\pi$
$348$		0			0
$349$	−16.1769	−	13.5741i	−0.865932	−	0.726603i	0.0973055	−	0.995255i	$-0.468978\pi$
$349$	−16.1769	−	13.5741i	−0.865932	−	0.726603i	−0.963237	+	0.268651i	$0.913422\pi$
$350$		0			0
$351$	31.6495	−	6.57413i	1.68933	−	0.350901i
$352$		0			0
$353$	−21.6145	+	25.7592i	−1.15043	+	1.37102i	−0.233311	+	0.972402i	$0.574956\pi$
$353$	−21.6145	+	25.7592i	−1.15043	+	1.37102i	−0.917115	+	0.398623i	$0.869488\pi$
$354$		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	0.137663	−	0.990479i	$-0.456041\pi$
$359$	17.5568	−	30.4092i	0.926612	−	1.60494i	0.788948	−	0.614459i	$-0.210626\pi$
$360$		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	$-0.110561\pi$
$367$	0.0226511	+	0.0622335i	0.00118238	+	0.00324856i	−0.939100	+	0.343644i	$0.888339\pi$
$368$		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	0.340350	−	0.940299i	$-0.389454\pi$
$373$	−0.0644945	−	0.0234741i	−0.00333940	−	0.00121544i	−0.343689	+	0.939083i	$0.611677\pi$
$374$		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	$-0.335954\pi$
$383$	6.08836	+	2.21598i	0.311101	+	0.113231i	−0.181751	+	0.983345i	$0.558177\pi$
$384$		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	−0.866872	−	0.498531i	$-0.833873\pi$
$389$	−10.3203	−	28.3548i	−0.523259	−	1.43764i	0.343612	−	0.939112i	$-0.388349\pi$
$390$		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	−0.897091	−	0.441847i	$-0.854324\pi$
$397$	−1.31295	+	2.27409i	−0.0658950	+	0.114133i	0.831196	+	0.555980i	$0.187657\pi$
$398$		0			0
$399$	2.84977	+	3.32745i	0.142667	+	0.166581i
$400$		0			0
$401$	11.8095	−	2.08234i	0.589740	−	0.103987i	0.129189	−	0.991620i	$-0.458763\pi$
$401$	11.8095	−	2.08234i	0.589740	−	0.103987i	0.460552	+	0.887633i	$0.347652\pi$
$402$		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	0.927830	+	0.373003i	$0.121672\pi$
$409$	3.71166	+	21.0498i	0.183530	+	1.04085i	−0.744300	+	0.667845i	$0.767217\pi$
$410$		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	$-0.678714\pi$
$419$	4.27322	−	3.58565i	0.208760	−	0.175171i	0.741173	+	0.671314i	$0.234270\pi$
$420$		0			0
$421$	−4.29843	+	1.56450i	−0.209493	+	0.0762492i	−0.444635	−	0.895712i	$-0.646667\pi$
$421$	−4.29843	+	1.56450i	−0.209493	+	0.0762492i	0.235142	+	0.971961i	$0.424444\pi$
$422$		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	$-0.674959\pi$
$431$	−21.6902			−1.04478			−0.522390	+	0.852707i	$0.674959\pi$
$432$		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	$-0.497090\pi$
$439$	−6.79424	−	1.19801i	−0.324272	−	0.0571778i	−0.333414	+	0.942780i	$0.608201\pi$
$440$		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	$-0.667853\pi$
$443$	−7.01410	+	2.55292i	−0.333250	+	0.121293i	0.169975	+	0.985448i	$0.445631\pi$
$444$		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	−0.907916	−	0.419152i	$-0.862327\pi$
$449$	−21.1658	+	12.2201i	−0.998877	+	0.576702i	−0.0909615	+	0.995854i	$0.528994\pi$
$450$		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	0.665803	−	0.746127i	$-0.268089\pi$
$457$	0.996769	+	0.836388i	0.0466269	+	0.0391246i	−0.619176	+	0.785252i	$0.712533\pi$
$458$		0			0
$459$	−5.15088	+	0.155972i	−0.240423	+	0.00728015i
$460$		0			0
$461$	−9.12564	+	10.8755i	−0.425023	+	0.506523i	−0.935480	−	0.353381i	$-0.885032\pi$
$461$	−9.12564	+	10.8755i	−0.425023	+	0.506523i	0.510456	+	0.859904i	$0.329477\pi$
$462$		0			0
$463$	−33.2154	+	5.85677i	−1.54365	+	0.272187i	−0.879677	−	0.475571i	$-0.842242\pi$
$463$	−33.2154	+	5.85677i	−1.54365	+	0.272187i	−0.663972	+	0.747758i	$0.731130\pi$
$464$		0			0
$465$	−20.2760	+	57.5067i	−0.940276	+	2.66681i
$466$		0			0
$467$	−13.0487	+	22.6011i	−0.603824	+	1.04585i	0.388413	+	0.921486i	$0.373024\pi$
$467$	−13.0487	+	22.6011i	−0.603824	+	1.04585i	−0.992236	+	0.124368i	$0.960310\pi$
$468$		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	−0.936426	−	0.350865i	$-0.885888\pi$
$479$	1.39041	−	7.88541i	0.0635295	−	0.360293i	0.999956	−	0.00942856i	$-0.00300125\pi$
$480$		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	$-0.0877340\pi$
$491$	33.7796	+	12.2948i	1.52445	+	0.554855i	0.562197	+	0.827003i	$0.309956\pi$
$492$		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	−0.995359	−	0.0962330i	$-0.969321\pi$
$499$	−20.4907	−	24.4198i	−0.917288	−	1.09318i	0.0780713	−	0.996948i	$-0.475124\pi$
$500$		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	$-0.0995039\pi$
$503$	4.69716	+	8.13572i	0.209436	+	0.362754i	−0.742101	+	0.670288i	$0.766171\pi$
$504$		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	0.379950	−	0.925007i	$-0.375941\pi$
$509$	23.7648	−	4.19038i	1.05336	−	0.185735i	0.673407	+	0.739272i	$0.264830\pi$
$510$		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	0.617865	−	0.786284i	$-0.287998\pi$
$521$	5.61174	+	3.23994i	0.245855	+	0.141944i	−0.372010	+	0.928229i	$0.621331\pi$
$522$		0			0
$523$	16.0544	−	9.26903i	0.702011	−	0.405306i	−0.106085	−	0.994357i	$-0.533832\pi$
$523$	16.0544	−	9.26903i	0.702011	−	0.405306i	0.808096	+	0.589051i	$0.200498\pi$
$524$		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	$-0.340125\pi$
$547$	14.8282	+	2.61461i	0.634007	+	0.111792i	0.152597	+	0.988288i	$0.451236\pi$
$548$		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	−0.872148	−	0.489243i	$-0.837273\pi$
$557$	−20.8755	+	12.0525i	−0.884524	+	0.510680i	−0.0123769	+	0.999923i	$0.503940\pi$
$558$		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	$-0.107039\pi$
$563$	−1.32702	−	7.52589i	−0.0559271	−	0.317179i	−0.999918	+	0.0127925i	$0.995928\pi$
$564$		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	−0.502841	−	0.864379i	$-0.667712\pi$
$569$	10.3936	−	12.3866i	0.435724	−	0.519275i	0.938565	+	0.345104i	$0.112156\pi$
$570$		0			0
$571$	34.7174	−	6.12161i	1.45288	−	0.256181i	0.609193	−	0.793022i	$-0.291493\pi$
$571$	34.7174	−	6.12161i	1.45288	−	0.256181i	0.843684	+	0.536840i	$0.180382\pi$
$572$		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	0.751219	−	0.660053i	$-0.229466\pi$
$577$	−4.70841	−	8.15521i	−0.196014	−	0.339506i	−0.947232	+	0.320548i	$0.896133\pi$
$578$		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	$-0.916537\pi$
$587$	0.736783	−	4.17851i	0.0304103	−	0.172465i	0.996230	+	0.0867485i	$0.0276477\pi$
$588$		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	$-0.878676\pi$
$593$		−	18.1170i		−	0.743976i	0.928238	−	0.371988i	$-0.121324\pi$
$594$		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	$-0.503435\pi$
$599$	−16.1974	−	5.89539i	−0.661810	−	0.240879i	−0.651017	+	0.759063i	$0.725658\pi$
$600$		0			0
$601$	1.91764	−	10.8755i	0.0782221	−	0.443619i	−0.920392	−	0.390996i	$-0.872131\pi$
$601$	1.91764	−	10.8755i	0.0782221	−	0.443619i	0.998614	−	0.0526234i	$-0.0167583\pi$
$602$		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	0.990618	+	0.136663i	$0.0436379\pi$
$607$	23.4840	+	27.9871i	0.953186	+	1.13596i	−0.0374318	+	0.999299i	$0.511918\pi$
$608$		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	−0.886142	−	0.463414i	$-0.846624\pi$
$613$	−1.03350	+	1.79008i	−0.0417427	+	0.0723005i	0.844399	+	0.535714i	$0.179958\pi$
$614$		0			0
$615$	41.2668	−	7.70658i	1.66404	−	0.310759i
$616$		0			0
$617$	−22.6757	+	3.99834i	−0.912891	+	0.160967i	−0.610316	−	0.792158i	$-0.708957\pi$
$617$	−22.6757	+	3.99834i	−0.912891	+	0.160967i	−0.302575	+	0.953126i	$0.597846\pi$
$618$		0			0
$619$	−15.5198	+	18.4958i	−0.623794	+	0.743409i	−0.981718	−	0.190342i	$-0.939040\pi$
$619$	−15.5198	+	18.4958i	−0.623794	+	0.743409i	0.357923	+	0.933751i	$0.383485\pi$
$620$		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	$-0.712601\pi$
$631$	−6.25684	+	3.61239i	−0.249081	+	0.143807i	0.370263	+	0.928927i	$0.379268\pi$
$632$		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	−0.00833877	−	0.999965i	$-0.502654\pi$
$641$	−9.06847	−	1.59902i	−0.358183	−	0.0631573i	−0.349844	+	0.936808i	$0.613765\pi$
$642$		0			0
$643$	0.106356	−	0.292210i	0.00419425	−	0.0115236i	−0.937578	−	0.347776i	$-0.886937\pi$
$643$	0.106356	−	0.292210i	0.00419425	−	0.0115236i	0.941772	+	0.336252i	$0.109159\pi$
$644$		0			0
$645$	0.399999	+	0.0663762i	0.0157500	+	0.00261356i
$646$		0			0
$647$	13.6389			0.536200			0.268100	−	0.963391i	$-0.413604\pi$
$647$	13.6389			0.536200			0.268100	+	0.963391i	$0.413604\pi$
$648$		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	0.477859	+	0.878437i	$0.341413\pi$
$653$	−11.5721	+	31.7940i	−0.452851	+	1.24420i	−0.930709	+	0.365760i	$0.880809\pi$
$654$		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	$-0.328205\pi$
$659$	37.4531	−	13.6318i	1.45897	−	0.531020i	0.945080	+	0.326838i	$0.105983\pi$
$660$		0			0
$661$	−28.9434	+	24.2864i	−1.12577	+	0.944632i	−0.998881	−	0.0472854i	$-0.984943\pi$
$661$	−28.9434	+	24.2864i	−1.12577	+	0.944632i	−0.126887	+	0.991917i	$0.540499\pi$
$662$		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	0.464060	−	0.885804i	$-0.346392\pi$
$673$	−8.50135	−	7.13348i	−0.327703	−	0.274975i	−0.791763	+	0.610828i	$0.790837\pi$
$674$		0			0
$675$	13.7166	+	34.4082i	0.527953	+	1.32437i
$676$		0			0
$677$	8.86465	−	10.5645i	0.340696	−	0.406026i	−0.568306	−	0.822817i	$-0.692401\pi$
$677$	8.86465	−	10.5645i	0.340696	−	0.406026i	0.909002	+	0.416791i	$0.136845\pi$
$678$		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	$-0.731432\pi$
$683$	8.22428	−	14.2449i	0.314693	−	0.545065i	0.979372	+	0.202064i	$0.0647650\pi$
$684$		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	$-0.0276329\pi$
$691$	4.66180	+	12.8082i	0.177343	+	0.487247i	−0.818891	+	0.573949i	$0.805411\pi$
$692$		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	$0.190518\pi$
$701$			29.8352i			1.12686i	−0.826164	+	0.563429i	$0.809482\pi$
$702$		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	−0.912640	−	0.408765i	$-0.865960\pi$
$709$	2.25709	−	12.8006i	0.0847670	−	0.480737i	0.997407	−	0.0719723i	$-0.0229293\pi$
$710$		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	$-0.233193\pi$
$719$	−5.56340	−	9.63609i	−0.207480	−	0.359365i	−0.950920	+	0.309437i	$0.899859\pi$
$720$		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	$-0.918419\pi$
$727$	−14.8219	+	17.6641i	−0.549714	+	0.655123i	0.417622	+	0.908621i	$0.362864\pi$
$728$		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	0.958553	+	0.284915i	$0.0919653\pi$
$733$	4.20335	+	23.8384i	0.155254	+	0.880492i	−0.803298	+	0.595577i	$0.796924\pi$
$734$		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	$-0.649851\pi$
$739$	2.48625	−	1.43543i	0.0914580	−	0.0528033i	0.545031	+	0.838416i	$0.316518\pi$
$740$		0			0
$741$	46.8143	−	0.472394i	1.71977	−	0.0173538i
$742$		0			0
$743$	37.1866	−	31.2033i	1.36424	−	1.14474i	0.389599	−	0.920985i	$-0.372614\pi$
$743$	37.1866	−	31.2033i	1.36424	−	1.14474i	0.974646	−	0.223752i	$-0.0718307\pi$
$744$		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	0.476235	+	0.879318i	$0.342001\pi$
$751$	−12.4360	+	34.1677i	−0.453797	+	1.24680i	−0.930032	+	0.367479i	$0.880221\pi$
$752$		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	−0.950129	−	0.311857i	$-0.899049\pi$
$761$	−0.602221	+	1.65459i	−0.0218305	+	0.0599788i	0.928299	+	0.371835i	$0.121271\pi$
$762$		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	0.0464302	−	0.998922i	$-0.485215\pi$
$769$	28.7912	−	24.1587i	1.03824	−	0.871185i	0.991808	+	0.127736i	$0.0407710\pi$
$770$		0			0
$771$	−9.90323	−	16.7600i	−0.356656	−	0.603598i
$772$		0			0
$773$	6.18041	−	3.56826i	0.222294	−	0.128341i	−0.384718	−	0.923034i	$-0.625701\pi$
$773$	6.18041	−	3.56826i	0.222294	−	0.128341i	0.607012	+	0.794693i	$0.292368\pi$
$774$		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	$-0.821891\pi$
$787$	−41.0237	+	7.23358i	−1.46234	+	0.257849i	−0.614841	+	0.788651i	$0.710780\pi$
$788$		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	0.887910	−	0.460017i	$-0.152157\pi$
$797$	7.92442	+	9.44395i	0.280697	+	0.334522i	−0.607213	+	0.794539i	$0.707712\pi$
$798$		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	$-0.869612\pi$
$809$		−	22.6558i		−	0.796534i	0.917270	−	0.398267i	$-0.130388\pi$
$810$		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	0.999706	−	0.0242532i	$-0.00772079\pi$
$821$	6.25489	+	17.1852i	0.218297	+	0.599766i	−0.781409	+	0.624020i	$0.785499\pi$
$822$		0			0
$823$	−17.9729	−	21.4193i	−0.626497	−	0.746631i	0.355676	−	0.934609i	$-0.384251\pi$
$823$	−17.9729	−	21.4193i	−0.626497	−	0.746631i	−0.982173	+	0.187979i	$0.939806\pi$
$824$		0			0
$825$	16.3489	+	9.22035i	0.569196	+	0.321011i
$826$		0			0
$827$	18.5651	+	32.1557i	0.645573	+	1.11816i	0.984169	+	0.177233i	$0.0567147\pi$
$827$	18.5651	+	32.1557i	0.645573	+	1.11816i	−0.338596	+	0.940932i	$0.609952\pi$
$828$		0			0
$829$	10.0595	−	17.4236i	0.349382	−	0.605147i	−0.636758	−	0.771064i	$-0.719725\pi$
$829$	10.0595	−	17.4236i	0.349382	−	0.605147i	0.986140	+	0.165917i	$0.0530584\pi$
$830$		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	$-0.408474\pi$
$839$	−17.7136	−	14.8634i	−0.611540	−	0.513143i	−0.895131	+	0.445802i	$0.852918\pi$
$840$		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	−0.617241	−	0.786774i	$-0.711750\pi$
$853$	−17.0665	+	6.21171i	−0.584347	+	0.212685i	0.0328941	+	0.999459i	$0.489528\pi$
$854$		0			0
$855$	−42.3355	+	16.3837i	−1.44784	+	0.560311i
$856$		0			0
$857$	−22.6751	−	3.99823i	−0.774566	−	0.136577i	−0.227626	−	0.973749i	$-0.573096\pi$
$857$	−22.6751	−	3.99823i	−0.774566	−	0.136577i	−0.546940	+	0.837172i	$0.684207\pi$
$858$		0			0
$859$	−11.9011	+	32.6979i	−0.406059	+	1.11564i	0.553185	+	0.833058i	$0.313412\pi$
$859$	−11.9011	+	32.6979i	−0.406059	+	1.11564i	−0.959244	+	0.282579i	$0.908810\pi$
$860$		0			0
$861$	2.46647	+	6.56954i	0.0840570	+	0.223889i
$862$		0			0
$863$	16.2935			0.554638			0.277319	−	0.960778i	$-0.410554\pi$
$863$	16.2935			0.554638			0.277319	+	0.960778i	$0.410554\pi$
$864$		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	−0.777571	−	0.628795i	$-0.783549\pi$
$877$	−8.68742	+	7.28961i	−0.293353	+	0.246153i	0.484218	+	0.874947i	$0.339104\pi$
$878$		0			0
$879$	34.5097	−	0.348231i	1.16398	−	0.0117455i
$880$		0			0
$881$	45.1724	−	26.0803i	1.52190	−	0.878668i	0.522232	−	0.852803i	$-0.325099\pi$
$881$	45.1724	−	26.0803i	1.52190	−	0.878668i	0.999665	−	0.0258648i	$-0.00823393\pi$
$882$		0			0
$883$	37.5310	+	21.6685i	1.26302	+	0.729205i	0.973658	−	0.228015i	$-0.0732236\pi$
$883$	37.5310	+	21.6685i	1.26302	+	0.729205i	0.289362	+	0.957220i	$0.406557\pi$
$884$		0			0
$885$	−54.3015	+	46.5061i	−1.82532	+	1.56328i
$886$		0			0
$887$	−1.93441	−	10.9706i	−0.0649510	−	0.368355i	−0.999908	−	0.0135933i	$-0.995673\pi$
$887$	−1.93441	−	10.9706i	−0.0649510	−	0.368355i	0.934957	−	0.354762i	$-0.115438\pi$
$888$		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	$-0.156216\pi$
$907$	−2.90941	−	7.99354i	−0.0966054	−	0.265421i	−0.978577	+	0.205882i	$0.933994\pi$
$908$		0			0
$909$	21.2267	+	11.6906i	0.704044	+	0.387751i
$910$		0			0
$911$	−7.22116	+	40.9532i	−0.239248	+	1.35684i	0.594233	+	0.804293i	$0.297456\pi$
$911$	−7.22116	+	40.9532i	−0.239248	+	1.35684i	−0.833481	+	0.552548i	$0.813656\pi$
$912$		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	0.999283	−	0.0378565i	$-0.0120530\pi$
$929$	6.38406	+	17.5401i	0.209454	+	0.575471i	−0.789829	+	0.613327i	$0.789831\pi$
$930$		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	0.320997	+	0.947080i	$0.395982\pi$
$937$	−20.1936	+	34.9764i	−0.659697	+	1.14263i	−0.980694	+	0.195549i	$0.937351\pi$
$938$		0			0
$939$	40.9693	−	7.65102i	1.33698	−	0.249682i
$940$		0			0
$941$	−30.9752	+	5.46176i	−1.00976	+	0.178048i	−0.653972	−	0.756518i	$-0.726899\pi$
$941$	−30.9752	+	5.46176i	−1.00976	+	0.178048i	−0.355789	+	0.934566i	$0.615788\pi$
$942$		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	$-0.0356271\pi$
$947$	32.5062	+	27.2759i	1.05631	+	0.886348i	0.0625661	+	0.998041i	$0.480072\pi$
$948$		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	−0.0264711	−	0.999650i	$-0.508427\pi$
$953$	−27.9512	−	16.1376i	−0.905429	−	0.522749i	−0.878957	+	0.476900i	$0.841760\pi$
$954$		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	−0.471239	−	0.882005i	$-0.656193\pi$
$967$	14.2016	−	39.0186i	0.456693	−	1.25475i	0.927932	−	0.372749i	$-0.121585\pi$
$968$		0			0
$969$	−7.36280	−	1.22179i	−0.236527	−	0.0392496i
$970$		0			0
$971$	−14.5385			−0.466564			−0.233282	−	0.972409i	$-0.574946\pi$
$971$	−14.5385			−0.466564			−0.233282	+	0.972409i	$0.574946\pi$
$972$		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	−0.610892	−	0.791714i	$-0.709189\pi$
$977$	11.4395	−	31.4298i	0.365982	−	1.00553i	0.976874	−	0.213814i	$-0.0685886\pi$
$978$		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	$-0.630770\pi$
$983$	−3.63677	+	1.32368i	−0.115995	+	0.0422187i	0.283371	+	0.959010i	$0.408547\pi$
$984$		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	$-0.289621\pi$
$991$	7.46425	+	4.30949i	0.237110	+	0.136895i	−0.376738	+	0.926320i	$0.622954\pi$
$992$		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	0.586876	−	0.809677i	$-0.300358\pi$
$997$	−3.42878	−	2.87709i	−0.108591	−	0.0911184i	−0.695466	+	0.718559i	$0.744802\pi$
$998$		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.767.3	yes	216
4.3	odd	2	inner	864.2.bi.a.767.34	yes	216
27.5	odd	18	inner	864.2.bi.a.383.34	yes	216
108.59	even	18	inner	864.2.bi.a.383.3	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.bi.a.383.3	✓	216	108.59	even	18	inner
864.2.bi.a.383.34	yes	216	27.5	odd	18	inner
864.2.bi.a.767.3	yes	216	1.1	even	1	trivial
864.2.bi.a.767.34	yes	216	4.3	odd	2	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.bi (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.70869 - 0.283541i) q^{3} +(-1.19113 + 3.27259i) q^{5} +(-0.573300 - 0.101088i) q^{7} +(2.83921 + 0.968964i) q^{9} +O(q^{10})\)	\(q+(-1.70869 - 0.283541i) q^{3} +(-1.19113 + 3.27259i) q^{5} +(-0.573300 - 0.101088i) q^{7} +(2.83921 + 0.968964i) q^{9} +(1.42849 - 0.519927i) q^{11} +(-4.76553 + 3.99876i) q^{13} +(2.96317 - 5.25409i) q^{15} +(0.858874 - 0.495871i) q^{17} +(3.76282 + 2.17246i) q^{19} +(0.950926 + 0.335282i) q^{21} +(-0.715065 - 4.05534i) q^{23} +(-5.46085 - 4.58220i) q^{25} +(-4.57657 - 2.46069i) q^{27} +(0.165623 - 0.197381i) q^{29} +(-9.95515 + 1.75536i) q^{31} +(-2.58825 + 0.483357i) q^{33} +(1.01369 - 1.75577i) q^{35} +(-5.32749 - 9.22749i) q^{37} +(9.27661 - 5.48139i) q^{39} +(4.47348 + 5.33129i) q^{41} +(0.0229902 + 0.0631651i) q^{43} +(-6.55288 + 8.13741i) q^{45} +(1.42549 - 8.08438i) q^{47} +(-6.25939 - 2.27823i) q^{49} +(-1.60814 + 0.603762i) q^{51} -1.96751i q^{53} +5.29415i q^{55} +(-5.81349 - 4.77897i) q^{57} +(-11.1376 - 4.05376i) q^{59} +(-1.98322 + 11.2474i) q^{61} +(-1.52977 - 0.842517i) q^{63} +(-7.40995 - 20.3587i) q^{65} +(-4.37173 - 5.21003i) q^{67} +(0.0719681 + 7.13204i) q^{69} +(-1.76215 - 3.05214i) q^{71} +(-0.283777 + 0.491516i) q^{73} +(8.03163 + 9.37790i) q^{75} +(-0.871510 + 0.153671i) q^{77} +(-8.27612 + 9.86310i) q^{79} +(7.12222 + 5.50218i) q^{81} +(1.23417 + 1.03559i) q^{83} +(0.599756 + 3.40139i) q^{85} +(-0.338962 + 0.290302i) q^{87} +(4.61926 + 2.66693i) q^{89} +(3.13631 - 1.81075i) q^{91} +(17.5079 - 0.176669i) q^{93} +(-11.5916 + 9.72648i) q^{95} +(8.38829 - 3.05309i) q^{97} +(4.55956 - 0.0920288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * 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

Related objects

Downloads

Learn more