LMFDB - Embedded newform 810.2.s.a.773.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			773.10
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.23600 - 0.0174365i) q^{5} +(1.90858 + 1.33641i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.23600 - 0.0174365i) q^{5} +(1.90858 + 1.33641i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-2.22597 - 0.212250i) q^{10} +(0.889546 - 2.44401i) q^{11} +(0.203337 + 2.32415i) q^{13} +(1.78485 + 1.49766i) q^{14} +(0.939693 + 0.342020i) q^{16} +(5.64422 - 1.51236i) q^{17} +(2.11133 - 1.21898i) q^{19} +(-2.19900 - 0.405449i) q^{20} +(1.09917 - 2.35718i) q^{22} +(5.43990 + 7.76898i) q^{23} +(4.99939 + 0.0779761i) q^{25} +2.33303i q^{26} +(1.64752 + 1.64752i) q^{28} +(-5.39466 + 4.52666i) q^{29} +(-1.28861 + 7.30805i) q^{31} +(0.906308 + 0.422618i) q^{32} +(5.75455 - 1.01468i) q^{34} +(-4.24429 - 3.02148i) q^{35} +(-1.48751 - 5.55147i) q^{37} +(2.20954 - 1.03032i) q^{38} +(-2.15530 - 0.595562i) q^{40} +(1.75965 - 2.09706i) q^{41} +(-0.950971 - 2.03936i) q^{43} +(1.30043 - 2.25241i) q^{44} +(4.74208 + 8.21353i) q^{46} +(4.66288 - 6.65929i) q^{47} +(-0.537424 - 1.47656i) q^{49} +(4.97357 + 0.513405i) q^{50} +(-0.203337 + 2.32415i) q^{52} +(-1.68777 + 1.68777i) q^{53} +(-2.03164 + 5.44929i) q^{55} +(1.49766 + 1.78485i) q^{56} +(-5.76866 + 4.03926i) q^{58} +(5.56872 - 2.02685i) q^{59} +(-0.241191 - 1.36786i) q^{61} +(-1.92064 + 7.16793i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.414136 - 5.20035i) q^{65} +(-11.1572 + 0.976128i) q^{67} +(5.82109 - 0.509279i) q^{68} +(-3.96480 - 3.37990i) q^{70} +(1.67490 + 0.967007i) q^{71} +(-0.894627 + 3.33879i) q^{73} +(-0.998009 - 5.65999i) q^{74} +(2.29093 - 0.833829i) q^{76} +(4.96396 - 3.47580i) q^{77} +(2.76633 + 3.29678i) q^{79} +(-2.09519 - 0.781142i) q^{80} +(1.93572 - 1.93572i) q^{82} +(1.24922 - 14.2787i) q^{83} +(-12.6468 + 3.28323i) q^{85} +(-0.769610 - 2.11449i) q^{86} +(1.49179 - 2.13050i) q^{88} +(-4.56315 - 7.90360i) q^{89} +(-2.71793 + 4.70758i) q^{91} +(4.00818 + 8.59558i) q^{92} +(5.22554 - 6.22755i) q^{94} +(-4.74219 + 2.68882i) q^{95} +(6.02536 - 2.80967i) q^{97} +(-0.406688 - 1.51778i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−2.23600	−	0.0174365i	−0.999970	−	0.00779785i
$5$	−2.23600	−	0.0174365i	−0.999970	−	0.00779785i
$6$		0			0
$7$	1.90858	+	1.33641i	0.721377	+	0.505114i	0.875669	−	0.482911i	$-0.160421\pi$
$7$	1.90858	+	1.33641i	0.721377	+	0.505114i	−0.154292	+	0.988025i	$0.549310\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	−2.22597	−	0.212250i	−0.703914	−	0.0671195i
$11$	0.889546	−	2.44401i	0.268208	−	0.736896i	−0.730343	−	0.683081i	$-0.760640\pi$
$11$	0.889546	−	2.44401i	0.268208	−	0.736896i	0.998551	−	0.0538150i	$-0.0171381\pi$
$12$		0			0
$13$	0.203337	+	2.32415i	0.0563955	+	0.644604i	0.970814	+	0.239834i	$0.0770930\pi$
$13$	0.203337	+	2.32415i	0.0563955	+	0.644604i	−0.914418	+	0.404770i	$0.867351\pi$
$14$	1.78485	+	1.49766i	0.477020	+	0.400268i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	5.64422	−	1.51236i	1.36892	−	0.366802i	0.501838	−	0.864961i	$-0.332657\pi$
$17$	5.64422	−	1.51236i	1.36892	−	0.366802i	0.867085	+	0.498159i	$0.165991\pi$
$18$		0			0
$19$	2.11133	−	1.21898i	0.484372	−	0.279652i	−0.237865	−	0.971298i	$-0.576447\pi$
$19$	2.11133	−	1.21898i	0.484372	−	0.279652i	0.722237	+	0.691646i	$0.243114\pi$
$20$	−2.19900	−	0.405449i	−0.491712	−	0.0906611i
$21$		0			0
$22$	1.09917	−	2.35718i	0.234344	−	0.502552i
$23$	5.43990	+	7.76898i	1.13430	+	1.61994i	0.689443	+	0.724340i	$0.257855\pi$
$23$	5.43990	+	7.76898i	1.13430	+	1.61994i	0.444854	+	0.895603i	$0.353256\pi$
$24$		0			0
$25$	4.99939	+	0.0779761i	0.999878	+	0.0155952i
$26$			2.33303i			0.457545i
$27$		0			0
$28$	1.64752	+	1.64752i	0.311353	+	0.311353i
$29$	−5.39466	+	4.52666i	−1.00176	+	0.840580i	−0.987228	−	0.159315i	$-0.949072\pi$
$29$	−5.39466	+	4.52666i	−1.00176	+	0.840580i	−0.0145359	+	0.999894i	$0.504627\pi$
$30$		0			0
$31$	−1.28861	+	7.30805i	−0.231440	+	1.31256i	0.618541	+	0.785752i	$0.287724\pi$
$31$	−1.28861	+	7.30805i	−0.231440	+	1.31256i	−0.849982	+	0.526812i	$0.823387\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	5.75455	−	1.01468i	0.986897	−	0.174017i
$35$	−4.24429	−	3.02148i	−0.717417	−	0.510724i
$36$		0			0
$37$	−1.48751	−	5.55147i	−0.244545	−	0.912656i	−0.973611	−	0.228212i	$-0.926712\pi$
$37$	−1.48751	−	5.55147i	−0.244545	−	0.912656i	0.729066	−	0.684443i	$-0.239955\pi$
$38$	2.20954	−	1.03032i	0.358434	−	0.167141i
$39$		0			0
$40$	−2.15530	−	0.595562i	−0.340782	−	0.0941666i
$41$	1.75965	−	2.09706i	0.274810	−	0.327506i	−0.610932	−	0.791683i	$-0.709205\pi$
$41$	1.75965	−	2.09706i	0.274810	−	0.327506i	0.885743	+	0.464177i	$0.153650\pi$
$42$		0			0
$43$	−0.950971	−	2.03936i	−0.145022	−	0.311000i	0.820357	−	0.571851i	$-0.193775\pi$
$43$	−0.950971	−	2.03936i	−0.145022	−	0.311000i	−0.965379	+	0.260851i	$0.915997\pi$
$44$	1.30043	−	2.25241i	0.196047	−	0.339563i
$45$		0			0
$46$	4.74208	+	8.21353i	0.699182	+	1.21102i
$47$	4.66288	−	6.65929i	0.680152	−	0.971357i	−0.319565	−	0.947564i	$-0.603537\pi$
$47$	4.66288	−	6.65929i	0.680152	−	0.971357i	0.999717	−	0.0237928i	$-0.00757420\pi$
$48$		0			0
$49$	−0.537424	−	1.47656i	−0.0767749	−	0.210937i
$50$	4.97357	+	0.513405i	0.703369	+	0.0726064i
$51$		0			0
$52$	−0.203337	+	2.32415i	−0.0281978	+	0.322302i
$53$	−1.68777	+	1.68777i	−0.231833	+	0.231833i	−0.813457	−	0.581625i	$-0.802417\pi$
$53$	−1.68777	+	1.68777i	−0.231833	+	0.231833i	0.581625	+	0.813457i	$0.302417\pi$
$54$		0			0
$55$	−2.03164	+	5.44929i	−0.273946	+	0.734782i
$56$	1.49766	+	1.78485i	0.200134	+	0.238510i
$57$		0			0
$58$	−5.76866	+	4.03926i	−0.757462	+	0.530381i
$59$	5.56872	−	2.02685i	0.724986	−	0.263873i	0.0469450	−	0.998897i	$-0.485051\pi$
$59$	5.56872	−	2.02685i	0.724986	−	0.263873i	0.678041	+	0.735024i	$0.262829\pi$
$60$		0			0
$61$	−0.241191	−	1.36786i	−0.0308814	−	0.175137i	0.965466	−	0.260529i	$-0.0838969\pi$
$61$	−0.241191	−	1.36786i	−0.0308814	−	0.175137i	−0.996347	+	0.0853918i	$0.972786\pi$
$62$	−1.92064	+	7.16793i	−0.243922	+	0.910328i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−0.414136	−	5.20035i	−0.0513673	−	0.645024i
$66$		0			0
$67$	−11.1572	+	0.976128i	−1.36307	+	0.119253i	−0.745102	−	0.666951i	$-0.767599\pi$
$67$	−11.1572	+	0.976128i	−1.36307	+	0.119253i	−0.617967	+	0.786204i	$0.712043\pi$
$68$	5.82109	−	0.509279i	0.705911	−	0.0617592i
$69$		0			0
$70$	−3.96480	−	3.37990i	−0.473885	−	0.403975i
$71$	1.67490	+	0.967007i	0.198775	+	0.114763i	0.596084	−	0.802922i	$-0.296723\pi$
$71$	1.67490	+	0.967007i	0.198775	+	0.114763i	−0.397309	+	0.917685i	$0.630056\pi$
$72$		0			0
$73$	−0.894627	+	3.33879i	−0.104708	+	0.390776i	−0.998312	−	0.0580806i	$-0.981502\pi$
$73$	−0.894627	+	3.33879i	−0.104708	+	0.390776i	0.893604	+	0.448857i	$0.148169\pi$
$74$	−0.998009	−	5.65999i	−0.116016	−	0.657960i
$75$		0			0
$76$	2.29093	−	0.833829i	0.262787	−	0.0956467i
$77$	4.96396	−	3.47580i	0.565696	−	0.396104i
$78$		0			0
$79$	2.76633	+	3.29678i	0.311236	+	0.370917i	0.898874	−	0.438207i	$-0.144386\pi$
$79$	2.76633	+	3.29678i	0.311236	+	0.370917i	−0.587638	+	0.809124i	$0.699942\pi$
$80$	−2.09519	−	0.781142i	−0.234249	−	0.0873343i
$81$		0			0
$82$	1.93572	−	1.93572i	0.213765	−	0.213765i
$83$	1.24922	−	14.2787i	0.137120	−	1.56729i	−0.546506	−	0.837455i	$-0.684043\pi$
$83$	1.24922	−	14.2787i	0.137120	−	1.56729i	0.683626	−	0.729832i	$-0.260402\pi$
$84$		0			0
$85$	−12.6468	+	3.28323i	−1.37174	+	0.356116i
$86$	−0.769610	−	2.11449i	−0.0829892	−	0.228011i
$87$		0			0
$88$	1.49179	−	2.13050i	0.159025	−	0.227112i
$89$	−4.56315	−	7.90360i	−0.483693	−	0.837780i	0.516132	−	0.856509i	$-0.327371\pi$
$89$	−4.56315	−	7.90360i	−0.483693	−	0.837780i	−0.999825	+	0.0187289i	$0.994038\pi$
$90$		0			0
$91$	−2.71793	+	4.70758i	−0.284916	+	0.493489i
$92$	4.00818	+	8.59558i	0.417882	+	0.896151i
$93$		0			0
$94$	5.22554	−	6.22755i	0.538973	−	0.642323i
$95$	−4.74219	+	2.68882i	−0.486538	+	0.275867i
$96$		0			0
$97$	6.02536	−	2.80967i	0.611783	−	0.285279i	−0.0919280	−	0.995766i	$-0.529303\pi$
$97$	6.02536	−	2.80967i	0.611783	−	0.285279i	0.703711	+	0.710487i	$0.251525\pi$
$98$	−0.406688	−	1.51778i	−0.0410817	−	0.153319i
$99$		0			0
$100$	4.90990	+	0.944927i	0.490990	+	0.0944927i
$101$	−15.6496	+	2.75945i	−1.55719	+	0.274575i	−0.884925	−	0.465733i	$-0.845791\pi$
$101$	−15.6496	+	2.75945i	−1.55719	+	0.274575i	−0.672268	+	0.740308i	$0.734680\pi$
$102$		0			0
$103$	−16.7144	−	7.79404i	−1.64692	−	0.767969i	−0.999985	−	0.00541966i	$-0.998275\pi$
$103$	−16.7144	−	7.79404i	−1.64692	−	0.767969i	−0.646930	−	0.762550i	$-0.723947\pi$
$104$	−0.405127	+	2.29759i	−0.0397259	+	0.225297i
$105$		0			0
$106$	−1.82844	+	1.53425i	−0.177594	+	0.149019i
$107$	−4.15283	−	4.15283i	−0.401469	−	0.401469i	0.477281	−	0.878751i	$-0.341622\pi$
$107$	−4.15283	−	4.15283i	−0.401469	−	0.401469i	−0.878751	+	0.477281i	$0.841622\pi$
$108$		0			0
$109$			5.17673i			0.495841i	0.968780	+	0.247920i	$0.0797471\pi$
$109$			5.17673i			0.495841i	−0.968780	+	0.247920i	$0.920253\pi$
$110$	−2.49885	+	5.25148i	−0.238256	+	0.500709i
$111$		0			0
$112$	1.33641	+	1.90858i	0.126278	+	0.180344i
$113$	−4.33970	+	9.30652i	−0.408245	+	0.875484i	0.589462	+	0.807796i	$0.299340\pi$
$113$	−4.33970	+	9.30652i	−0.408245	+	0.875484i	−0.997707	+	0.0676877i	$0.978438\pi$
$114$		0			0
$115$	−12.0281	−	17.4663i	−1.12163	−	1.62874i
$116$	−6.09875	+	3.52112i	−0.566255	+	0.326927i
$117$		0			0
$118$	5.72418	−	1.53379i	0.526954	−	0.141197i
$119$	12.7936	+	4.65649i	1.17279	+	0.426860i
$120$		0			0
$121$	3.24461	+	2.72255i	0.294964	+	0.247505i
$122$	−0.121056	−	1.38368i	−0.0109599	−	0.125272i
$123$		0			0
$124$	−2.53806	+	6.97326i	−0.227924	+	0.626217i
$125$	−11.1773	−	0.261526i	−0.999726	−	0.0233916i
$126$		0			0
$127$	−0.342785	−	0.0918491i	−0.0304173	−	0.00815029i	0.243578	−	0.969881i	$-0.421679\pi$
$127$	−0.342785	−	0.0918491i	−0.0304173	−	0.00815029i	−0.273996	+	0.961731i	$0.588345\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	0.0406799	−	5.21666i	0.00356787	−	0.457531i
$131$	−9.70889	−	1.71194i	−0.848270	−	0.149573i	−0.267416	−	0.963581i	$-0.586170\pi$
$131$	−9.70889	−	1.71194i	−0.848270	−	0.149573i	−0.580853	+	0.814008i	$0.697281\pi$
$132$		0			0
$133$	5.65870	+	0.495072i	0.490671	+	0.0429282i
$134$	−11.1998			−0.967517
$135$		0			0
$136$	5.84332			0.501061
$137$	−18.2078	−	1.59298i	−1.55560	−	0.136097i	−0.723343	−	0.690489i	$-0.757396\pi$
$137$	−18.2078	−	1.59298i	−1.55560	−	0.136097i	−0.832256	+	0.554391i	$0.812951\pi$
$138$		0			0
$139$	9.69094	+	1.70877i	0.821974	+	0.144936i	0.568791	−	0.822482i	$-0.307411\pi$
$139$	9.69094	+	1.70877i	0.821974	+	0.144936i	0.253183	+	0.967418i	$0.418522\pi$
$140$	−3.65514	−	3.71259i	−0.308916	−	0.313771i
$141$		0			0
$142$	1.58425	+	1.10930i	0.132947	+	0.0930908i
$143$	5.86112	+	1.57048i	0.490132	+	0.131330i
$144$		0			0
$145$	12.1414	−	10.0275i	1.00829	−	0.832742i
$146$	−1.18222	+	3.24812i	−0.0978410	+	0.268816i
$147$		0			0
$148$	−0.500911	−	5.72543i	−0.0411746	−	0.470628i
$149$	17.2507	+	14.4750i	1.41323	+	1.18584i	0.954852	+	0.297083i	$0.0960137\pi$
$149$	17.2507	+	14.4750i	1.41323	+	1.18584i	0.458377	+	0.888758i	$0.348431\pi$
$150$		0			0
$151$	−5.95925	−	2.16899i	−0.484957	−	0.176510i	0.0879591	−	0.996124i	$-0.471966\pi$
$151$	−5.95925	−	2.16899i	−0.484957	−	0.176510i	−0.572916	+	0.819614i	$0.694188\pi$
$152$	2.35488	−	0.630989i	0.191006	−	0.0511799i
$153$		0			0
$154$	5.24801	−	3.02994i	0.422896	−	0.244159i
$155$	3.00875	−	16.3183i	0.241669	−	1.31072i
$156$		0			0
$157$	−1.24291	+	2.66544i	−0.0991953	+	0.212725i	−0.949643	−	0.313335i	$-0.898554\pi$
$157$	−1.24291	+	2.66544i	−0.0991953	+	0.212725i	0.850447	+	0.526060i	$0.176331\pi$
$158$	2.46847	+	3.52534i	0.196381	+	0.280461i
$159$		0			0
$160$	−2.01914	−	0.960777i	−0.159627	−	0.0759561i
$161$			22.0977i			1.74154i
$162$		0			0
$163$	2.31630	+	2.31630i	0.181427	+	0.181427i	0.791977	−	0.610551i	$-0.209052\pi$
$163$	2.31630	+	2.31630i	0.181427	+	0.181427i	−0.610551	+	0.791977i	$0.709052\pi$
$164$	2.09706	−	1.75965i	0.163753	−	0.137405i
$165$		0			0
$166$	2.48894	−	14.1155i	0.193179	−	1.09557i
$167$	−10.4347	−	4.86577i	−0.807460	−	0.376525i	−0.0253607	−	0.999678i	$-0.508073\pi$
$167$	−10.4347	−	4.86577i	−0.807460	−	0.376525i	−0.782100	+	0.623153i	$0.785851\pi$
$168$		0			0
$169$	7.44216	−	1.31225i	0.572474	−	0.100943i
$170$	−12.8849	+	2.16849i	−0.988224	+	0.166316i
$171$		0			0
$172$	−0.582392	−	2.17352i	−0.0444070	−	0.165729i
$173$	20.9796	−	9.78294i	1.59505	−	0.743783i	0.596768	−	0.802414i	$-0.296451\pi$
$173$	20.9796	−	9.78294i	1.59505	−	0.743783i	0.998280	+	0.0586307i	$0.0186734\pi$
$174$		0			0
$175$	9.43756	+	6.83004i	0.713412	+	0.516302i
$176$	1.67180	−	1.99237i	0.126017	−	0.150181i
$177$		0			0
$178$	−3.85694	−	8.27123i	−0.289090	−	0.619955i
$179$	−5.15883	+	8.93536i	−0.385589	+	0.667860i	−0.991851	−	0.127405i	$-0.959335\pi$
$179$	−5.15883	+	8.93536i	−0.385589	+	0.667860i	0.606262	+	0.795265i	$0.292668\pi$
$180$		0			0
$181$	−0.902701	−	1.56352i	−0.0670972	−	0.116216i	0.830525	−	0.556981i	$-0.188040\pi$
$181$	−0.902701	−	1.56352i	−0.0670972	−	0.116216i	−0.897622	+	0.440765i	$0.854707\pi$
$182$	−3.11788	+	4.45279i	−0.231112	+	0.330063i
$183$		0			0
$184$	3.24378	+	8.91220i	0.239134	+	0.657016i
$185$	3.22928	+	12.4390i	0.237421	+	0.914535i
$186$		0			0
$187$	1.32456	−	15.1398i	0.0968616	−	1.10713i
$188$	5.74842	−	5.74842i	0.419246	−	0.419246i
$189$		0			0
$190$	−4.95849	+	2.26528i	−0.359726	+	0.164340i
$191$	−3.11725	−	3.71500i	−0.225556	−	0.268808i	0.641383	−	0.767221i	$-0.278361\pi$
$191$	−3.11725	−	3.71500i	−0.225556	−	0.268808i	−0.866940	+	0.498413i	$0.833916\pi$
$192$		0			0
$193$	10.7848	−	7.55159i	0.776306	−	0.543575i	−0.116943	−	0.993139i	$-0.537309\pi$
$193$	10.7848	−	7.55159i	0.776306	−	0.543575i	0.893248	+	0.449564i	$0.148420\pi$
$194$	6.24731	−	2.27383i	0.448531	−	0.163252i
$195$		0			0
$196$	−0.272857	−	1.54745i	−0.0194898	−	0.110532i
$197$	4.18205	−	15.6076i	0.297958	−	1.11200i	−0.640881	−	0.767640i	$-0.721431\pi$
$197$	4.18205	−	15.6076i	0.297958	−	1.11200i	0.938839	−	0.344356i	$-0.111903\pi$
$198$		0			0
$199$	−22.6166	−	13.0577i	−1.60325	−	0.925636i	−0.990832	−	0.135101i	$-0.956864\pi$
$199$	−22.6166	−	13.0577i	−1.60325	−	0.925636i	−0.612417	−	0.790535i	$-0.709803\pi$
$200$	4.80886	+	1.36926i	0.340038	+	0.0968211i
$201$		0			0
$202$	−15.8305	+	1.38499i	−1.11383	+	0.0974478i
$203$	−16.3456	+	1.43006i	−1.14724	+	0.100370i
$204$		0			0
$205$	−3.97113	+	4.65835i	−0.277356	+	0.325353i
$206$	−15.9715	−	9.22113i	−1.11278	−	0.642467i
$207$		0			0
$208$	−0.603833	+	2.25353i	−0.0418683	+	0.156255i
$209$	−1.10106	−	6.24444i	−0.0761621	−	0.431937i
$210$		0			0
$211$	−17.2848	+	6.29115i	−1.18993	+	0.433101i	−0.859701	−	0.510798i	$-0.829350\pi$
$211$	−17.2848	+	6.29115i	−1.18993	+	0.433101i	−0.330234	+	0.943899i	$0.607128\pi$
$212$	−1.95520	+	1.36905i	−0.134284	+	0.0940266i
$213$		0			0
$214$	−3.77509	−	4.49897i	−0.258060	−	0.307543i
$215$	2.09081	+	4.57660i	0.142592	+	0.312122i
$216$		0			0
$217$	−12.2259	+	12.2259i	−0.829950	+	0.829950i
$218$	−0.451182	+	5.15703i	−0.0305579	+	0.349278i
$219$		0			0
$220$	−2.94703	+	5.01371i	−0.198689	+	0.338024i
$221$	4.66264	+	12.8105i	0.313643	+	0.861728i
$222$		0			0
$223$	6.02848	−	8.60957i	0.403697	−	0.576539i	−0.564905	−	0.825156i	$-0.691087\pi$
$223$	6.02848	−	8.60957i	0.403697	−	0.576539i	0.968602	+	0.248617i	$0.0799760\pi$
$224$	1.16498	+	2.01780i	0.0778382	+	0.134820i
$225$		0			0
$226$	−5.13431	+	8.89288i	−0.341529	+	0.591546i
$227$	1.49345	+	3.20272i	0.0991239	+	0.212572i	0.949616	−	0.313416i	$-0.101473\pi$
$227$	1.49345	+	3.20272i	0.0991239	+	0.212572i	−0.850492	+	0.525988i	$0.823696\pi$
$228$		0			0
$229$	1.16443	−	1.38771i	0.0769474	−	0.0917023i	−0.726197	−	0.687486i	$-0.758714\pi$
$229$	1.16443	−	1.38771i	0.0769474	−	0.0917023i	0.803145	+	0.595784i	$0.203159\pi$
$230$	−10.4601	−	18.4481i	−0.689718	−	1.21643i
$231$		0			0
$232$	−6.38243	+	2.97618i	−0.419027	+	0.195396i
$233$	4.50398	+	16.8091i	0.295066	+	1.10120i	0.941165	+	0.337947i	$0.109733\pi$
$233$	4.50398	+	16.8091i	0.295066	+	1.10120i	−0.646099	+	0.763253i	$0.723601\pi$
$234$		0			0
$235$	−10.5423	+	14.8089i	−0.687705	+	0.966024i
$236$	5.83608	−	1.02906i	0.379896	−	0.0669860i
$237$		0			0
$238$	12.3391	+	5.75381i	0.799824	+	0.372964i
$239$	0.850472	−	4.82327i	0.0550125	−	0.311991i	−0.944868	−	0.327451i	$-0.893810\pi$
$239$	0.850472	−	4.82327i	0.0550125	−	0.311991i	0.999880	+	0.0154602i	$0.00492133\pi$
$240$		0			0
$241$	8.81184	−	7.39401i	0.567620	−	0.476290i	−0.313235	−	0.949676i	$-0.601413\pi$
$241$	8.81184	−	7.39401i	0.567620	−	0.476290i	0.880855	+	0.473386i	$0.156968\pi$
$242$	2.99498	+	2.99498i	0.192524	+	0.192524i
$243$		0			0
$244$		−	1.38897i		−	0.0889194i
$245$	1.17593	+	3.31096i	0.0751277	+	0.211530i
$246$		0			0
$247$	3.26240	+	4.65919i	0.207581	+	0.296457i
$248$	−3.13616	+	6.72552i	−0.199146	+	0.427071i
$249$		0			0
$250$	−11.1120	−	1.23470i	−0.702782	−	0.0780890i
$251$	−8.05152	+	4.64855i	−0.508207	+	0.293414i	−0.732096	−	0.681201i	$-0.761458\pi$
$251$	−8.05152	+	4.64855i	−0.508207	+	0.293414i	0.223889	+	0.974615i	$0.428125\pi$
$252$		0			0
$253$	23.8265	−	6.38428i	1.49796	−	0.401376i
$254$	−0.333476	−	0.121375i	−0.0209241	−	0.00761576i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.261012	−	2.98339i	−0.0162815	−	0.186098i	−0.999980	−	0.00627451i	$-0.998003\pi$
$257$	−0.261012	−	2.98339i	−0.0162815	−	0.186098i	0.983699	−	0.179824i	$-0.0575528\pi$
$258$		0			0
$259$	4.57997	−	12.5834i	0.284586	−	0.781893i
$260$	0.495187	−	5.19326i	0.0307102	−	0.322072i
$261$		0			0
$262$	−9.52274	−	2.55161i	−0.588317	−	0.157639i
$263$	−22.1295	−	15.4953i	−1.36457	−	0.955479i	−0.999702	−	0.0244179i	$-0.992227\pi$
$263$	−22.1295	−	15.4953i	−1.36457	−	0.955479i	−0.364863	−	0.931061i	$-0.618884\pi$
$264$		0			0
$265$	3.80328	−	3.74442i	0.233633	−	0.230018i
$266$	5.59402	+	0.986376i	0.342991	+	0.0604786i
$267$		0			0
$268$	−11.1572	−	0.976128i	−0.681534	−	0.0596265i
$269$	13.3975			0.816857			0.408429	−	0.912790i	$-0.366077\pi$
$269$	13.3975			0.816857			0.408429	+	0.912790i	$0.366077\pi$
$270$		0			0
$271$	−8.70603			−0.528853			−0.264427	−	0.964406i	$-0.585183\pi$
$271$	−8.70603			−0.528853			−0.264427	+	0.964406i	$0.585183\pi$
$272$	5.82109	+	0.509279i	0.352955	+	0.0308796i
$273$		0			0
$274$	−17.9997	−	3.17383i	−1.08740	−	0.191738i
$275$	4.63776	−	12.1492i	0.279668	−	0.732624i
$276$		0			0
$277$	13.4158	+	9.39385i	0.806078	+	0.564422i	0.902385	−	0.430930i	$-0.141814\pi$
$277$	13.4158	+	9.39385i	0.806078	+	0.564422i	−0.0963075	+	0.995352i	$0.530703\pi$
$278$	9.50513	+	2.54689i	0.570080	+	0.152752i
$279$		0			0
$280$	−3.31766	−	4.01703i	−0.198268	−	0.240064i
$281$	−4.12738	+	11.3399i	−0.246219	+	0.676481i	0.753598	+	0.657336i	$0.228317\pi$
$281$	−4.12738	+	11.3399i	−0.246219	+	0.676481i	−0.999817	+	0.0191452i	$0.993906\pi$
$282$		0			0
$283$	−1.44977	−	16.5709i	−0.0861797	−	0.985039i	−0.909016	−	0.416761i	$-0.863165\pi$
$283$	−1.44977	−	16.5709i	−0.0861797	−	0.985039i	0.822837	−	0.568278i	$-0.192390\pi$
$284$	1.48154	+	1.24316i	0.0879132	+	0.0737680i
$285$		0			0
$286$	5.70194	+	2.07534i	0.337163	+	0.122717i
$287$	6.16096	−	1.65082i	0.363670	−	0.0974451i
$288$		0			0
$289$	14.8475	−	8.57222i	0.873383	−	0.504248i
$290$	12.9692	−	8.93120i	0.761575	−	0.524458i
$291$		0			0
$292$	−1.46081	+	3.13272i	−0.0854875	+	0.183329i
$293$	−9.73015	−	13.8961i	−0.568441	−	0.811818i	0.427290	−	0.904114i	$-0.359468\pi$
$293$	−9.73015	−	13.8961i	−0.568441	−	0.811818i	−0.995732	+	0.0922963i	$0.970579\pi$
$294$		0			0
$295$	−12.4870	+	4.43494i	−0.727021	+	0.258212i
$296$		−	5.74730i		−	0.334055i
$297$		0			0
$298$	15.9234	+	15.9234i	0.922420	+	0.922420i
$299$	−16.9502	+	14.2229i	−0.980253	+	0.822530i
$300$		0			0
$301$	0.910409	−	5.16318i	0.0524751	−	0.297601i
$302$	−5.74753	−	2.68012i	−0.330733	−	0.154223i
$303$		0			0
$304$	2.40091	−	0.423346i	0.137702	−	0.0242806i
$305$	0.515453	+	3.06275i	0.0295147	+	0.175372i
$306$		0			0
$307$	−1.24708	−	4.65417i	−0.0711747	−	0.265627i	0.921164	−	0.389174i	$-0.127240\pi$
$307$	−1.24708	−	4.65417i	−0.0711747	−	0.265627i	−0.992339	+	0.123547i	$0.960573\pi$
$308$	5.49211	−	2.56101i	0.312942	−	0.145927i
$309$		0			0
$310$	4.41954	−	15.9940i	0.251013	−	0.908398i
$311$	−3.33552	+	3.97511i	−0.189140	+	0.225408i	−0.852278	−	0.523089i	$-0.824780\pi$
$311$	−3.33552	+	3.97511i	−0.189140	+	0.225408i	0.663138	+	0.748497i	$0.269224\pi$
$312$		0			0
$313$	11.2831	+	24.1966i	0.637757	+	1.36767i	0.913657	+	0.406487i	$0.133246\pi$
$313$	11.2831	+	24.1966i	0.637757	+	1.36767i	−0.275900	+	0.961186i	$0.588976\pi$
$314$	−1.47049	+	2.54697i	−0.0829846	+	0.143734i
$315$		0			0
$316$	2.15182	+	3.72707i	0.121049	+	0.209664i
$317$	−0.851720	+	1.21638i	−0.0478373	+	0.0683188i	−0.842358	−	0.538918i	$-0.818833\pi$
$317$	−0.851720	+	1.21638i	−0.0478373	+	0.0683188i	0.794521	+	0.607237i	$0.207722\pi$
$318$		0			0
$319$	6.26439	+	17.2113i	0.350738	+	0.963646i
$320$	−1.92771	−	1.13310i	−0.107763	−	0.0633422i
$321$		0			0
$322$	−1.92594	+	22.0136i	−0.107328	+	1.22677i
$323$	10.0733	−	10.0733i	0.560491	−	0.560491i
$324$		0			0
$325$	0.835333	+	11.6352i	0.0463359	+	0.645405i
$326$	2.10561	+	2.50936i	0.116619	+	0.138981i
$327$		0			0
$328$	2.24245	−	1.57018i	0.123818	−	0.0866986i
$329$	17.7990	−	6.47831i	0.981292	−	0.357161i
$330$		0			0
$331$	4.04851	+	22.9602i	0.222526	+	1.26201i	0.867358	+	0.497685i	$0.165816\pi$
$331$	4.04851	+	22.9602i	0.222526	+	1.26201i	−0.644832	+	0.764325i	$0.723073\pi$
$332$	3.70971	−	13.8448i	0.203597	−	0.759833i
$333$		0			0
$334$	−9.97090	−	5.75670i	−0.545583	−	0.314993i
$335$	24.9645	−	1.98808i	1.36396	−	0.108620i
$336$		0			0
$337$	14.5683	−	1.27456i	0.793585	−	0.0694297i	0.316849	−	0.948476i	$-0.397375\pi$
$337$	14.5683	−	1.27456i	0.793585	−	0.0694297i	0.476736	+	0.879046i	$0.341820\pi$
$338$	7.52821	−	0.658633i	0.409481	−	0.0358249i
$339$		0			0
$340$	−13.0248	+	1.03725i	−0.706371	+	0.0562527i
$341$	16.7146	+	9.65021i	0.905149	+	0.522588i
$342$		0			0
$343$	5.16882	−	19.2903i	0.279090	−	1.04158i
$344$	−0.390741	−	2.21600i	−0.0210674	−	0.119479i
$345$		0			0
$346$	21.7524	−	7.91722i	1.16942	−	0.425632i
$347$	0.126122	−	0.0883116i	0.00677058	−	0.00474081i	−0.570186	−	0.821515i	$-0.693129\pi$
$347$	0.126122	−	0.0883116i	0.00677058	−	0.00474081i	0.576957	+	0.816775i	$0.304240\pi$
$348$		0			0
$349$	1.50732	+	1.79635i	0.0806848	+	0.0961564i	0.804877	−	0.593442i	$-0.202231\pi$
$349$	1.50732	+	1.79635i	0.0806848	+	0.0961564i	−0.724192	+	0.689599i	$0.757787\pi$
$350$	8.80637	+	7.62659i	0.470720	+	0.407658i
$351$		0			0
$352$	1.83908	−	1.83908i	0.0980235	−	0.0980235i
$353$	−2.71224	+	31.0010i	−0.144358	+	1.65002i	0.486180	+	0.873859i	$0.338390\pi$
$353$	−2.71224	+	31.0010i	−0.144358	+	1.65002i	−0.630538	+	0.776158i	$0.717166\pi$
$354$		0			0
$355$	−3.72823	−	2.19143i	−0.197874	−	0.116309i
$356$	−3.12138	−	8.57591i	−0.165433	−	0.454522i
$357$		0			0
$358$	−5.91797	+	8.45174i	−0.312774	+	0.446688i
$359$	13.0429	+	22.5909i	0.688375	+	1.19230i	0.972363	+	0.233473i	$0.0750091\pi$
$359$	13.0429	+	22.5909i	0.688375	+	1.19230i	−0.283988	+	0.958828i	$0.591658\pi$
$360$		0			0
$361$	−6.52819	+	11.3072i	−0.343589	+	0.595114i
$362$	−0.762995	−	1.63625i	−0.0401022	−	0.0859993i
$363$		0			0
$364$	−3.49410	+	4.16410i	−0.183140	+	0.218258i
$365$	2.05860	−	7.44994i	0.107752	−	0.389948i
$366$		0			0
$367$	32.3795	−	15.0988i	1.69020	−	0.788151i	0.692420	−	0.721494i	$-0.256544\pi$
$367$	32.3795	−	15.0988i	1.69020	−	0.788151i	0.997776	−	0.0666572i	$-0.0212334\pi$
$368$	2.45468	+	9.16100i	0.127959	+	0.477550i
$369$		0			0
$370$	2.13286	+	12.6731i	0.110882	+	0.658845i
$371$	−5.47679	+	0.965705i	−0.284341	+	0.0501369i
$372$		0			0
$373$	−33.1439	−	15.4553i	−1.71613	−	0.800244i	−0.994111	−	0.108369i	$-0.965437\pi$
$373$	−33.1439	−	15.4553i	−1.71613	−	0.800244i	−0.722018	−	0.691874i	$-0.756785\pi$
$374$	2.63905	−	14.9668i	0.136462	−	0.773913i
$375$		0			0
$376$	6.22755	−	5.22554i	0.321161	−	0.269486i
$377$	−11.6176	−	11.6176i	−0.598336	−	0.598336i
$378$		0			0
$379$		−	4.00379i		−	0.205661i	−0.994699	−	0.102830i	$-0.967210\pi$
$379$		−	4.00379i		−	0.205661i	0.994699	−	0.102830i	$-0.0327899\pi$
$380$	−5.13705	+	1.82450i	−0.263525	+	0.0935947i
$381$		0			0
$382$	−2.78161	−	3.97255i	−0.142319	−	0.203253i
$383$	−10.3993	+	22.3014i	−0.531379	+	1.13955i	0.439117	+	0.898430i	$0.355291\pi$
$383$	−10.3993	+	22.3014i	−0.531379	+	1.13955i	−0.970496	+	0.241116i	$0.922486\pi$
$384$		0			0
$385$	−11.1600	+	7.68534i	−0.568767	+	0.391681i
$386$	11.4019	−	6.58289i	0.580342	−	0.335061i
$387$		0			0
$388$	6.42171	−	1.72069i	0.326013	−	0.0873550i
$389$	9.40124	+	3.42177i	0.476662	+	0.173491i	0.569168	−	0.822221i	$-0.307266\pi$
$389$	9.40124	+	3.42177i	0.476662	+	0.173491i	−0.0925060	+	0.995712i	$0.529488\pi$
$390$		0			0
$391$	42.4535	+	35.6227i	2.14696	+	1.80152i
$392$	−0.136950	−	1.56534i	−0.00691701	−	0.0790618i
$393$		0			0
$394$	5.52642	−	15.1837i	0.278417	−	0.764945i
$395$	−6.12803	−	7.41984i	−0.308335	−	0.373333i
$396$		0			0
$397$	−4.92936	−	1.32082i	−0.247397	−	0.0662899i	0.132989	−	0.991117i	$-0.457542\pi$
$397$	−4.92936	−	1.32082i	−0.247397	−	0.0662899i	−0.380387	+	0.924828i	$0.624209\pi$
$398$	−21.3925	−	14.9792i	−1.07231	−	0.750838i
$399$		0			0
$400$	4.67122	+	1.78317i	0.233561	+	0.0891583i
$401$	−18.8980	−	3.33223i	−0.943721	−	0.166403i	−0.319443	−	0.947606i	$-0.603496\pi$
$401$	−18.8980	−	3.33223i	−0.943721	−	0.166403i	−0.624278	+	0.781202i	$0.714607\pi$
$402$		0			0
$403$	−17.2470	−	1.50892i	−0.859136	−	0.0751647i
$404$	−15.8910			−0.790608
$405$		0			0
$406$	−16.4081			−0.814318
$407$	−14.8910	−	1.30280i	−0.738121	−	0.0645773i
$408$		0			0
$409$	16.9845	+	2.99483i	0.839831	+	0.148085i	0.576987	−	0.816753i	$-0.304228\pi$
$409$	16.9845	+	2.99483i	0.839831	+	0.148085i	0.262844	+	0.964838i	$0.415339\pi$
$410$	−4.36202	+	4.29452i	−0.215425	+	0.212091i
$411$		0			0
$412$	−15.1070	−	10.5780i	−0.744269	−	0.521143i
$413$	13.3371	+	3.57366i	0.656274	+	0.175848i
$414$		0			0
$415$	−3.04223	+	31.9053i	−0.149337	+	1.56617i
$416$	−0.797944	+	2.19233i	−0.0391224	+	0.107488i
$417$		0			0
$418$	−0.552634	−	6.31664i	−0.0270302	−	0.308957i
$419$	−20.3550	−	17.0799i	−0.994406	−	0.834406i	−0.00820633	−	0.999966i	$-0.502612\pi$
$419$	−20.3550	−	17.0799i	−0.994406	−	0.834406i	−0.986200	+	0.165561i	$0.947057\pi$
$420$		0			0
$421$	−10.7086	−	3.89762i	−0.521906	−	0.189958i	0.0676147	−	0.997712i	$-0.478461\pi$
$421$	−10.7086	−	3.89762i	−0.521906	−	0.189958i	−0.589521	+	0.807753i	$0.700683\pi$
$422$	−17.7673	+	4.76074i	−0.864900	+	0.231749i
$423$		0			0
$424$	−2.06708	+	1.19343i	−0.100386	+	0.0579582i
$425$	28.3356	−	7.12078i	1.37448	−	0.345409i
$426$		0			0
$427$	1.36769	−	2.93301i	0.0661870	−	0.141938i
$428$	−3.36861	−	4.81087i	−0.162828	−	0.232542i
$429$		0			0
$430$	1.68398	+	4.74141i	0.0812087	+	0.228651i
$431$		−	11.7891i		−	0.567859i	−0.958845	−	0.283930i	$-0.908362\pi$
$431$		−	11.7891i		−	0.567859i	0.958845	−	0.283930i	$-0.0916382\pi$
$432$		0			0
$433$	−17.0811	−	17.0811i	−0.820865	−	0.820865i	0.165367	−	0.986232i	$-0.447119\pi$
$433$	−17.0811	−	17.0811i	−0.820865	−	0.820865i	−0.986232	+	0.165367i	$0.947119\pi$
$434$	−13.2450	+	11.1138i	−0.635779	+	0.533482i
$435$		0			0
$436$	−0.898930	+	5.09808i	−0.0430509	+	0.244154i
$437$	20.9556	+	9.77176i	1.00244	+	0.467447i
$438$		0			0
$439$	−7.07448	+	1.24742i	−0.337646	+	0.0595362i	−0.339901	−	0.940461i	$-0.610393\pi$
$439$	−7.07448	+	1.24742i	−0.337646	+	0.0595362i	0.00225447	+	0.999997i	$0.499282\pi$
$440$	−3.37279	+	4.73778i	−0.160792	+	0.225865i
$441$		0			0
$442$	3.52839	+	13.1681i	0.167828	+	0.626344i
$443$	13.3658	−	6.23255i	0.635026	−	0.296118i	−0.0783212	−	0.996928i	$-0.524956\pi$
$443$	13.3658	−	6.23255i	0.635026	−	0.296118i	0.713347	+	0.700811i	$0.247178\pi$
$444$		0			0
$445$	10.0654	+	17.7520i	0.477145	+	0.841526i
$446$	6.75592	−	8.05139i	0.319902	−	0.381244i
$447$		0			0
$448$	0.984680	+	2.11165i	0.0465218	+	0.0997663i
$449$	10.3081	−	17.8542i	0.486470	−	0.842591i	−0.513409	−	0.858144i	$-0.671618\pi$
$449$	10.3081	−	17.8542i	0.486470	−	0.842591i	0.999879	+	0.0155530i	$0.00495088\pi$
$450$		0			0
$451$	−3.55995	−	6.16602i	−0.167632	−	0.290347i
$452$	−5.88983	+	8.41156i	−0.277035	+	0.395646i
$453$		0			0
$454$	1.20863	+	3.32069i	0.0567240	+	0.155848i
$455$	6.15936	−	10.4788i	0.288755	−	0.491252i
$456$		0			0
$457$	−0.145192	+	1.65956i	−0.00679181	+	0.0776308i	−0.998834	−	0.0482742i	$-0.984628\pi$
$457$	−0.145192	+	1.65956i	−0.00679181	+	0.0776308i	0.992042	+	0.125905i	$0.0401834\pi$
$458$	1.28094	−	1.28094i	0.0598544	−	0.0598544i
$459$		0			0
$460$	−8.81242	−	19.2896i	−0.410881	−	0.899382i
$461$	16.0429	+	19.1192i	0.747193	+	0.890470i	0.996966	−	0.0778342i	$-0.0248005\pi$
$461$	16.0429	+	19.1192i	0.747193	+	0.890470i	−0.249773	+	0.968304i	$0.580356\pi$
$462$		0			0
$463$	20.5533	−	14.3916i	0.955195	−	0.668834i	0.0115983	−	0.999933i	$-0.496308\pi$
$463$	20.5533	−	14.3916i	0.955195	−	0.668834i	0.943596	+	0.331098i	$0.107419\pi$
$464$	−6.61753	+	2.40859i	−0.307211	+	0.111816i
$465$		0			0
$466$	3.02184	+	17.1377i	0.139984	+	0.793888i
$467$	6.08974	−	22.7272i	0.281800	−	1.05169i	−0.669347	−	0.742950i	$-0.733426\pi$
$467$	6.08974	−	22.7272i	0.281800	−	1.05169i	0.951146	−	0.308740i	$-0.0999073\pi$
$468$		0			0
$469$	−22.5990	−	13.0475i	−1.04352	−	0.602478i
$470$	−11.7929	+	13.8337i	−0.543965	+	0.638100i
$471$		0			0
$472$	5.90356	−	0.516495i	0.271733	−	0.0237736i
$473$	−5.83016	+	0.510073i	−0.268071	+	0.0234532i
$474$		0			0
$475$	10.6504	−	5.92951i	0.488674	−	0.272064i
$476$	11.7906	+	6.80733i	0.540423	+	0.312014i
$477$		0			0
$478$	1.26761	−	4.73079i	0.0579792	−	0.216381i
$479$	−0.472206	−	2.67801i	−0.0215756	−	0.122362i	0.972118	−	0.234494i	$-0.0753432\pi$
$479$	−0.472206	−	2.67801i	−0.0215756	−	0.122362i	−0.993693	+	0.112132i	$0.964232\pi$
$480$		0			0
$481$	12.6000	−	4.58602i	0.574510	−	0.209105i
$482$	9.42273	−	6.59787i	0.429194	−	0.300525i
$483$		0			0
$484$	2.72255	+	3.24461i	0.123752	+	0.147482i
$485$	−13.5217	+	6.17736i	−0.613988	+	0.280500i
$486$		0			0
$487$	30.9015	−	30.9015i	1.40028	−	1.40028i	0.601130	−	0.799152i	$-0.294718\pi$
$487$	30.9015	−	30.9015i	1.40028	−	1.40028i	0.799152	−	0.601130i	$-0.205282\pi$
$488$	0.121056	−	1.38368i	0.00547996	−	0.0626362i
$489$		0			0
$490$	0.882891	+	3.40085i	0.0398849	+	0.153635i
$491$	−3.26728	−	8.97679i	−0.147450	−	0.405117i	0.843876	−	0.536538i	$-0.180268\pi$
$491$	−3.26728	−	8.97679i	−0.147450	−	0.405117i	−0.991327	+	0.131421i	$0.958046\pi$
$492$		0			0
$493$	−23.6027	+	33.7081i	−1.06301	+	1.51814i
$494$	2.84391	+	4.92580i	0.127954	+	0.221622i
$495$		0			0
$496$	−3.71039	+	6.42659i	−0.166602	+	0.288562i
$497$	1.90438	+	4.08397i	0.0854233	+	0.183191i
$498$		0			0
$499$	−15.7768	+	18.8020i	−0.706265	+	0.841694i	−0.993220	−	0.116250i	$-0.962913\pi$
$499$	−15.7768	+	18.8020i	−0.706265	+	0.841694i	0.286955	+	0.957944i	$0.407357\pi$
$500$	−10.9621	−	2.19847i	−0.490238	−	0.0983185i
$501$		0			0
$502$	−8.42603	+	3.92912i	−0.376072	+	0.175365i
$503$	−6.84739	−	25.5548i	−0.305310	−	1.13943i	−0.932678	−	0.360709i	$-0.882535\pi$
$503$	−6.84739	−	25.5548i	−0.305310	−	1.13943i	0.627368	−	0.778723i	$-0.284132\pi$
$504$		0			0
$505$	35.0406	−	5.89725i	1.55929	−	0.262424i
$506$	24.2922	−	4.28338i	1.07992	−	0.190419i
$507$		0			0
$508$	−0.321628	−	0.149978i	−0.0142699	−	0.00665418i
$509$	−3.62824	+	20.5768i	−0.160819	+	0.912050i	0.792452	+	0.609934i	$0.208804\pi$
$509$	−3.62824	+	20.5768i	−0.160819	+	0.912050i	−0.953271	+	0.302116i	$0.902307\pi$
$510$		0			0
$511$	−6.16945	+	5.17679i	−0.272921	+	0.229008i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$		−	2.99478i		−	0.132094i
$515$	37.2374	+	17.7189i	1.64088	+	0.780788i
$516$		0			0
$517$	−12.1275	−	17.3199i	−0.533367	−	0.761727i
$518$	5.65926	−	12.1363i	0.248653	−	0.533239i
$519$		0			0
$520$	0.945925	−	5.13034i	0.0414816	−	0.224980i
$521$	−2.43098	+	1.40352i	−0.106503	+	0.0614895i	−0.552305	−	0.833642i	$-0.686252\pi$
$521$	−2.43098	+	1.40352i	−0.106503	+	0.0614895i	0.445802	+	0.895131i	$0.352918\pi$
$522$		0			0
$523$	15.4185	−	4.13136i	0.674202	−	0.180652i	0.0945552	−	0.995520i	$-0.469857\pi$
$523$	15.4185	−	4.13136i	0.674202	−	0.180652i	0.579647	+	0.814868i	$0.303190\pi$
$524$	−9.26411	−	3.37186i	−0.404705	−	0.147300i
$525$		0			0
$526$	−20.6948	−	17.3650i	−0.902337	−	0.757151i
$527$	3.77925	+	43.1970i	0.164627	+	1.88169i
$528$		0			0
$529$	−22.8981	+	62.9119i	−0.995568	+	2.73530i
$530$	4.11515	−	3.39869i	0.178751	−	0.147630i
$531$		0			0
$532$	5.48676	+	1.47017i	0.237881	+	0.0637401i
$533$	5.23170	+	3.66327i	0.226610	+	0.158674i
$534$		0			0
$535$	9.21332	+	9.35814i	0.398327	+	0.404588i
$536$	−11.0297	−	1.94483i	−0.476409	−	0.0840038i
$537$		0			0
$538$	13.3465	+	1.16767i	0.575407	+	0.0503416i
$539$	−4.08679			−0.176030
$540$		0			0
$541$	−1.18698			−0.0510321			−0.0255160	−	0.999674i	$-0.508123\pi$
$541$	−1.18698			−0.0510321			−0.0255160	+	0.999674i	$0.508123\pi$
$542$	−8.67290	−	0.758780i	−0.372533	−	0.0325924i
$543$		0			0
$544$	5.75455	+	1.01468i	0.246724	+	0.0435042i
$545$	0.0902641	−	11.5752i	0.00386649	−	0.495826i
$546$		0			0
$547$	2.17525	+	1.52312i	0.0930069	+	0.0651241i	0.619155	−	0.785269i	$-0.287475\pi$
$547$	2.17525	+	1.52312i	0.0930069	+	0.0651241i	−0.526148	+	0.850393i	$0.676364\pi$
$548$	−17.6546	−	4.73053i	−0.754167	−	0.202078i
$549$		0			0
$550$	5.67899	−	11.6987i	0.242153	−	0.498836i
$551$	−5.87202	+	16.1332i	−0.250156	+	0.687299i
$552$		0			0
$553$	0.873936	+	9.98913i	0.0371635	+	0.424781i
$554$	12.5460	+	10.5274i	0.533030	+	0.447265i
$555$		0			0
$556$	9.24698	+	3.36563i	0.392159	+	0.142734i
$557$	16.9645	−	4.54561i	0.718807	−	0.192604i	0.119168	−	0.992874i	$-0.461977\pi$
$557$	16.9645	−	4.54561i	0.718807	−	0.192604i	0.599639	+	0.800270i	$0.295311\pi$
$558$		0			0
$559$	4.54643	−	2.62488i	0.192293	−	0.111021i
$560$	−2.95492	−	4.29090i	−0.124868	−	0.181324i
$561$		0			0
$562$	−5.10001	+	10.9370i	−0.215131	+	0.461350i
$563$	−11.3353	−	16.1885i	−0.477726	−	0.682263i	0.505878	−	0.862605i	$-0.331168\pi$
$563$	−11.3353	−	16.1885i	−0.477726	−	0.682263i	−0.983604	+	0.180342i	$0.942280\pi$
$564$		0			0
$565$	9.86585	−	20.7337i	0.415059	−	0.872274i
$566$		−	16.6342i		−	0.699188i
$567$		0			0
$568$	1.36755	+	1.36755i	0.0573813	+	0.0573813i
$569$	−30.8786	+	25.9102i	−1.29450	+	1.08621i	−0.303431	+	0.952853i	$0.598132\pi$
$569$	−30.8786	+	25.9102i	−1.29450	+	1.08621i	−0.991068	+	0.133360i	$0.957423\pi$
$570$		0			0
$571$	3.94448	−	22.3703i	0.165071	−	0.936166i	−0.783919	−	0.620862i	$-0.786783\pi$
$571$	3.94448	−	22.3703i	0.165071	−	0.936166i	0.948991	−	0.315304i	$-0.102106\pi$
$572$	5.49937	+	2.56440i	0.229940	+	0.107223i
$573$		0			0
$574$	6.28140	−	1.10758i	0.262180	−	0.0462295i
$575$	26.5904	+	39.2643i	1.10890	+	1.63744i
$576$		0			0
$577$	6.78696	+	25.3293i	0.282545	+	1.05447i	0.950615	+	0.310373i	$0.100454\pi$
$577$	6.78696	+	25.3293i	0.282545	+	1.05447i	−0.668070	+	0.744098i	$0.732879\pi$
$578$	15.5381	−	7.24555i	0.646301	−	0.301375i
$579$		0			0
$580$	13.6982	−	7.76687i	0.568787	−	0.322502i
$581$	21.4663	−	25.5826i	0.890574	−	1.06134i
$582$		0			0
$583$	2.62357	+	5.62626i	0.108657	+	0.233016i
$584$	−1.72829	+	2.99348i	−0.0715170	+	0.123871i
$585$		0			0
$586$	−8.48200	−	14.6912i	−0.350388	−	0.606890i
$587$	−0.622873	+	0.889555i	−0.0257087	+	0.0367158i	−0.831801	−	0.555074i	$-0.812690\pi$
$587$	−0.622873	+	0.889555i	−0.0257087	+	0.0367158i	0.806092	+	0.591790i	$0.201579\pi$
$588$		0			0
$589$	6.18767	+	17.0005i	0.254958	+	0.700492i
$590$	−12.8260	+	3.32975i	−0.528039	+	0.137083i
$591$		0			0
$592$	0.500911	−	5.72543i	0.0205873	−	0.235314i
$593$	28.4601	−	28.4601i	1.16872	−	1.16872i	0.186205	−	0.982511i	$-0.440381\pi$
$593$	28.4601	−	28.4601i	1.16872	−	1.16872i	0.982511	−	0.186205i	$-0.0596189\pi$
$594$		0			0
$595$	−28.5253	−	10.6350i	−1.16942	−	0.435992i
$596$	14.4750	+	17.2507i	0.592920	+	0.706615i
$597$		0			0
$598$	−18.1253	+	12.6914i	−0.741197	+	0.518992i
$599$	17.8300	−	6.48958i	0.728513	−	0.265157i	0.0489777	−	0.998800i	$-0.484404\pi$
$599$	17.8300	−	6.48958i	0.728513	−	0.265157i	0.679535	+	0.733643i	$0.262181\pi$
$600$		0			0
$601$	−5.76224	−	32.6793i	−0.235047	−	1.33302i	−0.842515	−	0.538672i	$-0.818926\pi$
$601$	−5.76224	−	32.6793i	−0.235047	−	1.33302i	0.607469	−	0.794344i	$-0.292185\pi$
$602$	1.35695	−	5.06419i	0.0553050	−	0.206401i
$603$		0			0
$604$	−5.49207	−	3.17085i	−0.223469	−	0.129020i
$605$	−7.20747	−	6.14420i	−0.293026	−	0.249797i
$606$		0			0
$607$	−39.6382	+	3.46789i	−1.60886	+	0.140757i	−0.855842	−	0.517238i	$-0.826960\pi$
$607$	−39.6382	+	3.46789i	−1.60886	+	0.140757i	−0.753022	+	0.657995i	$0.771405\pi$
$608$	2.42868	−	0.212482i	0.0984958	−	0.00861727i
$609$		0			0
$610$	0.246555	+	3.09602i	0.00998273	+	0.125354i
$611$	16.4253	+	9.48318i	0.664498	+	0.383648i
$612$		0			0
$613$	−1.61805	+	6.03866i	−0.0653526	+	0.243899i	−0.990873	−	0.134799i	$-0.956961\pi$
$613$	−1.61805	+	6.03866i	−0.0653526	+	0.243899i	0.925520	+	0.378698i	$0.123628\pi$
$614$	−0.836698	−	4.74515i	−0.0337664	−	0.191499i
$615$		0			0
$616$	5.69442	−	2.07260i	0.229435	−	0.0835074i
$617$	13.7417	−	9.62201i	0.553218	−	0.387367i	−0.263277	−	0.964720i	$-0.584803\pi$
$617$	13.7417	−	9.62201i	0.553218	−	0.387367i	0.816495	+	0.577353i	$0.195914\pi$
$618$		0			0
$619$	5.45396	+	6.49978i	0.219213	+	0.261248i	0.864432	−	0.502750i	$-0.167678\pi$
$619$	5.45396	+	6.49978i	0.219213	+	0.261248i	−0.645219	+	0.763998i	$0.723234\pi$
$620$	5.79669	−	15.5479i	0.232801	−	0.624421i
$621$		0			0
$622$	−3.66928	+	3.66928i	−0.147125	+	0.147125i
$623$	1.85326	−	21.1829i	0.0742495	−	0.848675i
$624$		0			0
$625$	24.9878	+	0.779666i	0.999514	+	0.0311866i
$626$	9.13126	+	25.0879i	0.364958	+	1.00271i
$627$		0			0
$628$	−1.68688	+	2.40911i	−0.0673138	+	0.0961340i
$629$	−16.7917	−	29.0840i	−0.669528	−	1.15966i
$630$		0			0
$631$	−2.79090	+	4.83399i	−0.111104	+	0.192438i	−0.916216	−	0.400685i	$-0.868772\pi$
$631$	−2.79090	+	4.83399i	−0.111104	+	0.192438i	0.805112	+	0.593123i	$0.202105\pi$
$632$	1.81880	+	3.90043i	0.0723479	+	0.155151i
$633$		0			0
$634$	−0.954493	+	1.13752i	−0.0379078	+	0.0451767i
$635$	0.764866	+	0.211351i	0.0303528	+	0.00838723i
$636$		0			0
$637$	3.32248	−	1.54930i	0.131641	−	0.0613853i
$638$	4.74049	+	17.6917i	0.187678	+	0.700423i
$639$		0			0
$640$	−1.82162	−	1.29680i	−0.0720060	−	0.0512605i
$641$	16.7576	−	2.95482i	0.661885	−	0.116708i	0.167393	−	0.985890i	$-0.446465\pi$
$641$	16.7576	−	2.95482i	0.661885	−	0.116708i	0.494492	+	0.869182i	$0.335354\pi$
$642$		0			0
$643$	21.9000	+	10.2121i	0.863651	+	0.402727i	0.803388	−	0.595455i	$-0.203028\pi$
$643$	21.9000	+	10.2121i	0.863651	+	0.402727i	0.0602627	+	0.998183i	$0.480806\pi$
$644$	−3.83722	+	21.7619i	−0.151208	+	0.857541i
$645$		0			0
$646$	10.9129	−	9.15699i	0.429361	−	0.360277i
$647$	−1.71297	−	1.71297i	−0.0673437	−	0.0673437i	0.672633	−	0.739976i	$-0.265163\pi$
$647$	−1.71297	−	1.71297i	−0.0673437	−	0.0673437i	−0.739976	+	0.672633i	$0.765163\pi$
$648$		0			0
$649$		−	15.4130i		−	0.605012i
$650$	−0.181921	+	11.6637i	−0.00713551	+	0.457489i
$651$		0			0
$652$	1.87889	+	2.68333i	0.0735830	+	0.105087i
$653$	−16.0419	+	34.4019i	−0.627767	+	1.34625i	0.292990	+	0.956115i	$0.405350\pi$
$653$	−16.0419	+	34.4019i	−0.627767	+	1.34625i	−0.920757	+	0.390136i	$0.872428\pi$
$654$		0			0
$655$	21.6792	+	3.99719i	0.847077	+	0.156183i
$656$	2.37076	−	1.36876i	0.0925628	−	0.0534412i
$657$		0			0
$658$	18.2959	−	4.90237i	0.713249	−	0.191114i
$659$	−14.3066	−	5.20716i	−0.557305	−	0.202842i	0.0479843	−	0.998848i	$-0.484720\pi$
$659$	−14.3066	−	5.20716i	−0.557305	−	0.202842i	−0.605289	+	0.796006i	$0.706942\pi$
$660$		0			0
$661$	−24.5359	−	20.5880i	−0.954334	−	0.800781i	0.0256880	−	0.999670i	$-0.491822\pi$
$661$	−24.5359	−	20.5880i	−0.954334	−	0.800781i	−0.980022	+	0.198889i	$0.936267\pi$
$662$	2.03199	+	23.2257i	0.0789754	+	0.902693i
$663$		0			0
$664$	4.90225	−	13.4688i	0.190244	−	0.522691i
$665$	−12.6442	−	1.20565i	−0.490322	−	0.0467531i
$666$		0			0
$667$	−64.5139	−	17.2864i	−2.49799	−	0.669334i
$668$	−9.43123	−	6.60382i	−0.364905	−	0.255509i
$669$		0			0
$670$	25.0428	+	0.195286i	0.967487	+	0.00754455i
$671$	−3.55762	−	0.627304i	−0.137340	−	0.0242168i
$672$		0			0
$673$	−33.2529	−	2.90925i	−1.28181	−	0.112143i	−0.574179	−	0.818730i	$-0.694679\pi$
$673$	−33.2529	−	2.90925i	−1.28181	−	0.112143i	−0.707627	+	0.706586i	$0.750234\pi$
$674$	14.6239			0.563293
$675$		0			0
$676$	7.55697			0.290653
$677$	−28.9414	−	2.53204i	−1.11231	−	0.0973142i	−0.483844	−	0.875154i	$-0.660760\pi$
$677$	−28.9414	−	2.53204i	−1.11231	−	0.0973142i	−0.628462	+	0.777840i	$0.716315\pi$
$678$		0			0
$679$	15.2548	+	2.68983i	0.585424	+	0.103226i
$680$	−13.0657	−	0.101887i	−0.501046	−	0.00390720i
$681$		0			0
$682$	15.8100	+	11.0703i	0.605395	+	0.423902i
$683$	21.9721	+	5.88741i	0.840739	+	0.225275i	0.653393	−	0.757019i	$-0.273345\pi$
$683$	21.9721	+	5.88741i	0.840739	+	0.225275i	0.187346	+	0.982294i	$0.440011\pi$
$684$		0			0
$685$	40.6849	+	3.87938i	1.55449	+	0.148223i
$686$	6.83041	−	18.7664i	0.260786	−	0.716504i
$687$		0			0
$688$	−0.196117	−	2.24163i	−0.00747689	−	0.0854613i
$689$	−4.26581	−	3.57944i	−0.162515	−	0.136366i
$690$		0			0
$691$	−17.4980	−	6.36876i	−0.665656	−	0.242279i	−0.0129799	−	0.999916i	$-0.504132\pi$
$691$	−17.4980	−	6.36876i	−0.665656	−	0.242279i	−0.652677	+	0.757637i	$0.726354\pi$
$692$	22.3596	−	5.99125i	0.849986	−	0.227753i
$693$		0			0
$694$	0.133339	−	0.0769833i	0.00506148	−	0.00292224i
$695$	−21.6391	−	3.98979i	−0.820819	−	0.151341i
$696$		0			0
$697$	6.76030	−	14.4975i	0.256065	−	0.549132i
$698$	1.34502	+	1.92088i	0.0509097	+	0.0727066i
$699$		0			0
$700$	8.10816	+	8.36509i	0.306459	+	0.316171i
$701$		−	6.96946i		−	0.263233i	−0.991301	−	0.131616i	$-0.957983\pi$
$701$		−	6.96946i		−	0.263233i	0.991301	−	0.131616i	$-0.0420167\pi$
$702$		0			0
$703$	−9.90774	−	9.90774i	−0.373677	−	0.373677i
$704$	1.99237	−	1.67180i	0.0750904	−	0.0630083i
$705$		0			0
$706$	−5.40383	+	30.6466i	−0.203376	+	1.15340i
$707$	−33.5563	−	15.6476i	−1.26202	−	0.588488i
$708$		0			0
$709$	27.8311	−	4.90737i	1.04522	−	0.184300i	0.375429	−	0.926851i	$-0.377496\pi$
$709$	27.8311	−	4.90737i	1.04522	−	0.184300i	0.669789	+	0.742551i	$0.266384\pi$
$710$	−3.52304	−	2.50803i	−0.132217	−	0.0941246i
$711$		0			0
$712$	−2.36206	−	8.81532i	−0.0885219	−	0.330368i
$713$	−63.7859	+	29.7439i	−2.38880	+	1.11392i
$714$		0			0
$715$	−13.0781	−	3.61380i	−0.489093	−	0.135148i
$716$	−6.63207	+	7.90379i	−0.247852	+	0.295378i
$717$		0			0
$718$	11.0243	+	23.6417i	0.411423	+	0.882299i
$719$	−2.02321	+	3.50430i	−0.0754530	+	0.130688i	−0.901283	−	0.433230i	$-0.857374\pi$
$719$	−2.02321	+	3.50430i	−0.0754530	+	0.130688i	0.825830	+	0.563919i	$0.190707\pi$
$720$		0			0
$721$	−21.4848	−	37.2127i	−0.800135	−	1.38588i
$722$	−7.48884	+	10.6952i	−0.278706	+	0.398033i
$723$		0			0
$724$	−0.617484	−	1.69652i	−0.0229486	−	0.0630507i
$725$	−27.3230	+	22.2099i	−1.01475	+	0.824855i
$726$		0			0
$727$	−2.52428	+	28.8526i	−0.0936202	+	1.07008i	0.793508	+	0.608560i	$0.208253\pi$
$727$	−2.52428	+	28.8526i	−0.0936202	+	1.07008i	−0.887128	+	0.461524i	$0.847303\pi$
$728$	−3.84373	+	3.84373i	−0.142458	+	0.142458i
$729$		0			0
$730$	2.70007	−	7.24217i	0.0999342	−	0.268045i
$731$	−8.45175	−	10.0724i	−0.312599	−	0.372541i
$732$		0			0
$733$	−22.8787	+	16.0199i	−0.845045	+	0.591707i	−0.913909	−	0.405919i	$-0.866951\pi$
$733$	−22.8787	+	16.0199i	−0.845045	+	0.591707i	0.0688642	+	0.997626i	$0.478062\pi$
$734$	33.5722	−	12.2193i	1.23917	−	0.451022i
$735$		0			0
$736$	1.64691	+	9.34008i	0.0607059	+	0.344280i
$737$	−7.53917	+	28.1366i	−0.277709	+	1.03642i
$738$		0			0
$739$	−42.4394	−	24.5024i	−1.56116	−	0.901336i	−0.997140	−	0.0755754i	$-0.975921\pi$
$739$	−42.4394	−	24.5024i	−1.56116	−	0.901336i	−0.564020	−	0.825761i	$-0.690746\pi$
$740$	1.02020	+	12.8108i	0.0375035	+	0.470934i
$741$		0			0
$742$	−5.54011	+	0.484697i	−0.203384	+	0.0177938i
$743$	−29.5223	+	2.58287i	−1.08307	+	0.0947563i	−0.614688	−	0.788770i	$-0.710718\pi$
$743$	−29.5223	+	2.58287i	−1.08307	+	0.0947563i	−0.468381	+	0.883527i	$0.655163\pi$
$744$		0			0
$745$	−38.3201	−	32.6669i	−1.40394	−	1.19682i
$746$	−31.6708	−	18.2851i	−1.15955	−	0.669467i
$747$		0			0
$748$	3.93344	−	14.6798i	0.143821	−	0.536747i
$749$	−2.37616	−	13.4759i	−0.0868232	−	0.492399i
$750$		0			0
$751$	−1.70556	+	0.620772i	−0.0622367	+	0.0226523i	−0.372951	−	0.927851i	$-0.621654\pi$
$751$	−1.70556	+	0.620772i	−0.0622367	+	0.0226523i	0.310714	+	0.950503i	$0.399432\pi$
$752$	6.65929	−	4.66288i	0.242839	−	0.170038i
$753$		0			0
$754$	−10.5608	−	12.5859i	−0.384603	−	0.458352i
$755$	13.2871	+	4.95377i	0.483565	+	0.180286i
$756$		0			0
$757$	38.6401	−	38.6401i	1.40440	−	1.40440i	0.619029	−	0.785368i	$-0.287526\pi$
$757$	38.6401	−	38.6401i	1.40440	−	1.40440i	0.785368	−	0.619029i	$-0.212474\pi$
$758$	0.348953	−	3.98855i	0.0126745	−	0.144871i
$759$		0			0
$760$	−5.27652	+	1.36983i	−0.191399	+	0.0496889i
$761$	−16.9535	−	46.5792i	−0.614562	−	1.68850i	−0.719916	−	0.694062i	$-0.755820\pi$
$761$	−16.9535	−	46.5792i	−0.614562	−	1.68850i	0.105353	−	0.994435i	$-0.466403\pi$
$762$		0			0
$763$	−6.91821	+	9.88023i	−0.250456	+	0.357688i
$764$	−2.42479	−	4.19986i	−0.0877259	−	0.151946i
$765$		0			0
$766$	−12.3034	+	21.3101i	−0.444540	+	0.769966i
$767$	5.84303	+	12.5304i	0.210980	+	0.452448i
$768$		0			0
$769$	−14.2537	+	16.9869i	−0.514003	+	0.612564i	−0.959152	−	0.282892i	$-0.908706\pi$
$769$	−14.2537	+	16.9869i	−0.514003	+	0.612564i	0.445149	+	0.895456i	$0.353151\pi$
$770$	−11.7874	+	6.68343i	−0.424787	+	0.240854i
$771$		0			0
$772$	11.9323	−	5.56410i	0.429451	−	0.200256i
$773$	−7.92351	−	29.5709i	−0.284989	−	1.06359i	−0.948847	−	0.315735i	$-0.897749\pi$
$773$	−7.92351	−	29.5709i	−0.284989	−	1.06359i	0.663859	−	0.747858i	$-0.268918\pi$
$774$		0			0
$775$	−7.01210	+	36.4353i	−0.251882	+	1.30880i
$776$	6.54725	−	1.15446i	0.235032	−	0.0414426i
$777$		0			0
$778$	9.06724	+	4.22812i	0.325076	+	0.151585i
$779$	1.15892	−	6.57256i	0.0415226	−	0.235486i
$780$		0			0
$781$	3.85328	−	3.23328i	0.137881	−	0.115696i
$782$	39.1872	+	39.1872i	1.40133	+	1.40133i
$783$		0			0
$784$		−	1.57132i		−	0.0561187i
$785$	2.82563	−	5.93824i	0.100851	−	0.211945i
$786$		0			0
$787$	0.104995	+	0.149948i	0.00374267	+	0.00534508i	0.821019	−	0.570901i	$-0.193406\pi$
$787$	0.104995	+	0.149948i	0.00374267	+	0.00534508i	−0.817276	+	0.576246i	$0.804517\pi$
$788$	6.82874	−	14.6443i	0.243264	−	0.521681i
$789$		0			0
$790$	−5.45803	−	7.92570i	−0.194188	−	0.281984i
$791$	−20.7200	+	11.9627i	−0.736718	+	0.425344i
$792$		0			0
$793$	3.13008	−	0.838703i	0.111152	−	0.0297832i
$794$	−4.79548	−	1.74541i	−0.170185	−	0.0619424i
$795$		0			0
$796$	−20.0056	−	16.7867i	−0.709078	−	0.594987i
$797$	3.68558	+	42.1264i	0.130550	+	1.49219i	0.725384	+	0.688345i	$0.241662\pi$
$797$	3.68558	+	42.1264i	0.130550	+	1.49219i	−0.594834	+	0.803849i	$0.702782\pi$
$798$		0			0
$799$	16.2471	−	44.6384i	0.574780	−	1.57919i
$800$	4.49803	+	2.18350i	0.159030	+	0.0771985i
$801$		0			0
$802$	−18.5357	−	4.96662i	−0.654517	−	0.175377i
$803$	7.36422	+	5.15648i	0.259878	+	0.181968i
$804$		0			0
$805$	0.385306	−	49.4104i	0.0135803	−	1.74149i
$806$	−17.0499	−	3.00636i	−0.600557	−	0.105894i
$807$		0			0
$808$	−15.8305	−	1.38499i	−0.556917	−	0.0487239i
$809$	−31.0110			−1.09029			−0.545145	−	0.838342i	$-0.683525\pi$
$809$	−31.0110			−1.09029			−0.545145	+	0.838342i	$0.683525\pi$
$810$		0			0
$811$	32.3108			1.13458			0.567292	−	0.823516i	$-0.307991\pi$
$811$	32.3108			1.13458			0.567292	+	0.823516i	$0.307991\pi$
$812$	−16.3456	−	1.43006i	−0.573619	−	0.0501852i
$813$		0			0
$814$	−14.7208	−	2.59568i	−0.515965	−	0.0909785i
$815$	−5.13886	−	5.21964i	−0.180006	−	0.182836i
$816$		0			0
$817$	−4.49375	−	3.14656i	−0.157216	−	0.110084i
$818$	16.6589	+	4.46373i	0.582464	+	0.156071i
$819$		0			0
$820$	−4.71972	+	3.89800i	−0.164820	+	0.136124i
$821$	4.98240	−	13.6890i	0.173887	−	0.477750i	−0.821880	−	0.569660i	$-0.807075\pi$
$821$	4.98240	−	13.6890i	0.173887	−	0.477750i	0.995767	+	0.0919097i	$0.0292971\pi$
$822$		0			0
$823$	−0.474895	−	5.42808i	−0.0165538	−	0.189211i	−0.999969	−	0.00784357i	$-0.997503\pi$
$823$	−0.474895	−	5.42808i	−0.0165538	−	0.189211i	0.983415	−	0.181367i	$-0.0580523\pi$
$824$	−14.1276	−	11.8545i	−0.492158	−	0.412970i
$825$		0			0
$826$	12.9749	+	4.72246i	0.451453	+	0.164315i
$827$	−23.4166	+	6.27446i	−0.814275	+	0.218184i	−0.641842	−	0.766837i	$-0.721829\pi$
$827$	−23.4166	+	6.27446i	−0.814275	+	0.218184i	−0.172433	+	0.985021i	$0.555163\pi$
$828$		0			0
$829$	−3.21221	+	1.85457i	−0.111565	+	0.0644119i	−0.554744	−	0.832021i	$-0.687184\pi$
$829$	−3.21221	+	1.85457i	−0.111565	+	0.0644119i	0.443179	+	0.896433i	$0.353850\pi$
$830$	−5.81138	+	31.5188i	−0.201716	+	1.09403i
$831$		0			0
$832$	−0.985981	+	2.11444i	−0.0341828	+	0.0733052i
$833$	−5.26644	−	7.52125i	−0.182471	−	0.260596i
$834$		0			0
$835$	23.2471	+	11.0618i	0.804500	+	0.382810i
$836$		−	6.34077i		−	0.219300i
$837$		0			0
$838$	−18.7889	−	18.7889i	−0.649052	−	0.649052i
$839$	−19.3948	+	16.2742i	−0.669583	+	0.561847i	−0.912942	−	0.408090i	$-0.866195\pi$
$839$	−19.3948	+	16.2742i	−0.669583	+	0.561847i	0.243359	+	0.969936i	$0.421751\pi$
$840$		0			0
$841$	3.57594	−	20.2802i	0.123308	−	0.699316i
$842$	−10.3282	−	4.81610i	−0.355932	−	0.165974i
$843$		0			0
$844$	−18.1147	+	3.19410i	−0.623532	+	0.109946i
$845$	−16.6636	+	2.80443i	−0.573244	+	0.0964754i
$846$		0			0
$847$	2.55418	+	9.53233i	0.0877627	+	0.327535i
$848$	−2.16323	+	1.00873i	−0.0742857	+	0.0346400i
$849$		0			0
$850$	28.8484	−	4.62408i	0.989491	−	0.158605i
$851$	35.0373	−	41.7558i	1.20106	−	1.43137i
$852$		0			0
$853$	15.3939	+	33.0123i	0.527077	+	1.13032i	0.972049	+	0.234776i	$0.0754358\pi$
$853$	15.3939	+	33.0123i	0.527077	+	1.13032i	−0.444972	+	0.895544i	$0.646786\pi$
$854$	1.61811	−	2.80265i	0.0553706	−	0.0959047i
$855$		0			0
$856$	−2.93649	−	5.08616i	−0.100367	−	0.173841i
$857$	6.27591	−	8.96293i	0.214381	−	0.306168i	−0.697530	−	0.716555i	$-0.745718\pi$
$857$	6.27591	−	8.96293i	0.214381	−	0.306168i	0.911911	+	0.410387i	$0.134607\pi$
$858$		0			0
$859$	−5.17282	−	14.2122i	−0.176494	−	0.484914i	0.819628	−	0.572896i	$-0.194180\pi$
$859$	−5.17282	−	14.2122i	−0.176494	−	0.484914i	−0.996122	+	0.0879824i	$0.971958\pi$
$860$	1.26433	+	4.87014i	0.0431133	+	0.166070i
$861$		0			0
$862$	1.02748	−	11.7442i	0.0349963	−	0.400009i
$863$	−15.8714	+	15.8714i	−0.540270	+	0.540270i	−0.923608	−	0.383338i	$-0.874774\pi$
$863$	−15.8714	+	15.8714i	−0.540270	+	0.540270i	0.383338	+	0.923608i	$0.374774\pi$
$864$		0			0
$865$	−47.0809	+	21.5088i	−1.60080	+	0.731322i
$866$	−15.5274	−	18.5048i	−0.527642	−	0.628819i
$867$		0			0
$868$	−14.1632	+	9.91718i	−0.480730	+	0.336611i
$869$	10.5181	−	3.82829i	0.356803	−	0.129866i
$870$		0			0
$871$	−4.53734	−	25.7326i	−0.153742	−	0.871914i
$872$	−1.33984	+	5.00034i	−0.0453726	+	0.169333i
$873$		0			0
$874$	20.0242	+	11.5610i	0.677329	+	0.391056i
$875$	−20.9833	−	15.4365i	−0.709364	−	0.521850i
$876$		0			0
$877$	6.62667	−	0.579758i	0.223767	−	0.0195771i	0.0252790	−	0.999680i	$-0.491953\pi$
$877$	6.62667	−	0.579758i	0.223767	−	0.0195771i	0.198488	+	0.980103i	$0.436397\pi$
$878$	−7.15627	+	0.626093i	−0.241513	+	0.0211296i
$879$		0			0
$880$	−3.77288	+	4.42580i	−0.127184	+	0.149194i
$881$	−35.7082	−	20.6162i	−1.20304	−	0.694576i	−0.241811	−	0.970323i	$-0.577741\pi$
$881$	−35.7082	−	20.6162i	−1.20304	−	0.694576i	−0.961230	+	0.275747i	$0.911075\pi$
$882$		0			0
$883$	−7.82768	+	29.2133i	−0.263422	+	0.983106i	0.699787	+	0.714352i	$0.253278\pi$
$883$	−7.82768	+	29.2133i	−0.263422	+	0.983106i	−0.963209	+	0.268754i	$0.913388\pi$
$884$	2.36729	+	13.4255i	0.0796204	+	0.451550i
$885$		0			0
$886$	13.8581	−	5.04394i	0.465572	−	0.169454i
$887$	13.2971	−	9.31072i	0.446472	−	0.312623i	−0.328630	−	0.944459i	$-0.606587\pi$
$887$	13.2971	−	9.31072i	0.446472	−	0.312623i	0.775103	+	0.631835i	$0.217698\pi$
$888$		0			0
$889$	−0.531487	−	0.633402i	−0.0178255	−	0.0212436i
$890$	8.47989	+	18.5617i	0.284247	+	0.622190i
$891$		0			0
$892$	7.43193	−	7.43193i	0.248840	−	0.248840i
$893$	1.72737	−	19.7439i	0.0578041	−	0.660704i
$894$		0			0
$895$	11.6909	−	19.8895i	0.390785	−	0.664833i
$896$	0.796891	+	2.18944i	0.0266222	+	0.0731440i
$897$		0			0
$898$	11.8250	−	16.8878i	0.394605	−	0.563554i
$899$	−26.1294	−	45.2575i	−0.871466	−	1.50942i
$900$		0			0
$901$	−6.97361	+	12.0786i	−0.232325	+	0.402398i
$902$	−3.00900	−	6.45283i	−0.100189	−	0.214856i
$903$		0			0
$904$	−6.60054	+	7.86621i	−0.219531	+	0.261626i
$905$	1.99118	+	3.51178i	0.0661889	+	0.116735i
$906$		0			0
$907$	−22.5078	+	10.4956i	−0.747360	+	0.348500i	−0.758704	−	0.651436i	$-0.774167\pi$
$907$	−22.5078	+	10.4956i	−0.747360	+	0.348500i	0.0113436	+	0.999936i	$0.496389\pi$
$908$	0.914617	+	3.41340i	0.0303526	+	0.113278i
$909$		0			0
$910$	7.04921	−	9.90207i	0.233679	−	0.328250i
$911$	−3.09910	+	0.546454i	−0.102678	+	0.0181048i	−0.224751	−	0.974416i	$-0.572157\pi$
$911$	−3.09910	+	0.546454i	−0.102678	+	0.0181048i	0.122073	+	0.992521i	$0.461046\pi$
$912$		0			0
$913$	−33.7859	−	15.7546i	−1.11815	−	0.521402i
$914$	−0.289280	+	1.64059i	−0.00956852	+	0.0542658i
$915$		0			0
$916$	1.38771	−	1.16443i	0.0458512	−	0.0384737i
$917$	−16.2424	−	16.2424i	−0.536371	−	0.536371i
$918$		0			0
$919$			50.8427i			1.67715i	0.544789	+	0.838573i	$0.316610\pi$
$919$			50.8427i			1.67715i	−0.544789	+	0.838573i	$0.683390\pi$
$920$	−7.09769	−	19.9842i	−0.234004	−	0.658861i
$921$		0			0
$922$	14.3155	+	20.4447i	0.471457	+	0.673310i
$923$	−1.90690	+	4.08936i	−0.0627664	+	0.134603i
$924$		0			0
$925$	−7.00377	−	27.8700i	−0.230283	−	0.916359i
$926$	21.7294	−	12.5455i	0.714074	−	0.412271i
$927$		0			0
$928$	−6.80227	+	1.82266i	−0.223296	+	0.0598319i
$929$	33.5667	+	12.2173i	1.10129	+	0.400836i	0.827791	−	0.561037i	$-0.189597\pi$
$929$	33.5667	+	12.2173i	1.10129	+	0.400836i	0.273497	+	0.961873i	$0.411820\pi$
$930$		0			0
$931$	−2.93457	−	2.46240i	−0.0961767	−	0.0807019i
$932$	1.51669	+	17.3358i	0.0496808	+	0.567854i
$933$		0			0
$934$	8.04737	−	22.1100i	0.263318	−	0.723460i
$935$	−3.22571	+	33.8296i	−0.105492	+	1.10634i
$936$		0			0
$937$	48.2320	+	12.9237i	1.57567	+	0.422200i	0.937582	−	0.347764i	$-0.113059\pi$
$937$	48.2320	+	12.9237i	1.57567	+	0.422200i	0.638088	+	0.769963i	$0.279726\pi$
$938$	−21.3758	−	14.9675i	−0.697945	−	0.488706i
$939$		0			0
$940$	−12.9537	+	12.7532i	−0.422503	+	0.415964i
$941$	23.3202	+	4.11198i	0.760217	+	0.134047i	0.540301	−	0.841472i	$-0.318311\pi$
$941$	23.3202	+	4.11198i	0.760217	+	0.134047i	0.219916	+	0.975519i	$0.429422\pi$
$942$		0			0
$943$	25.8643	+	2.26284i	0.842258	+	0.0736881i
$944$	5.92611			0.192878
$945$		0			0
$946$	−5.85243			−0.190279
$947$	42.0838	+	3.68185i	1.36754	+	0.119644i	0.747153	−	0.664652i	$-0.231420\pi$
$947$	42.0838	+	3.68185i	1.36754	+	0.119644i	0.620386	+	0.784297i	$0.286976\pi$
$948$		0			0
$949$	−7.94178	−	1.40035i	−0.257801	−	0.0454573i
$950$	11.1267	−	4.97870i	0.360997	−	0.161530i
$951$		0			0
$952$	11.1525	+	7.80905i	0.361454	+	0.253093i
$953$	7.21290	+	1.93269i	0.233649	+	0.0626060i	0.373744	−	0.927532i	$-0.378074\pi$
$953$	7.21290	+	1.93269i	0.233649	+	0.0626060i	−0.140095	+	0.990138i	$0.544741\pi$
$954$		0			0
$955$	6.90540	+	8.36109i	0.223453	+	0.270558i
$956$	1.67510	−	4.60231i	0.0541767	−	0.148849i
$957$		0			0
$958$	−0.237005	−	2.70898i	−0.00765728	−	0.0875231i
$959$	−32.6223	−	27.3734i	−1.05343	−	0.883932i
$960$		0			0
$961$	−22.6166	−	8.23176i	−0.729567	−	0.265541i
$962$	12.9517	−	3.47041i	0.417581	−	0.111891i
$963$		0			0
$964$	9.96192	−	5.75152i	0.320852	−	0.185244i
$965$	−24.2464	+	16.6973i	−0.780521	+	0.537505i
$966$		0			0
$967$	−4.87887	+	10.4628i	−0.156894	+	0.336460i	−0.969004	−	0.247044i	$-0.920541\pi$
$967$	−4.87887	+	10.4628i	−0.156894	+	0.336460i	0.812110	+	0.583504i	$0.198319\pi$
$968$	2.42940	+	3.46955i	0.0780840	+	0.111516i
$969$		0			0
$970$	−14.0086	+	4.97536i	−0.449790	+	0.159749i
$971$			19.7342i			0.633299i	0.948543	+	0.316650i	$0.102558\pi$
$971$			19.7342i			0.633299i	−0.948543	+	0.316650i	$0.897442\pi$
$972$		0			0
$973$	16.2124	+	16.2124i	0.519744	+	0.519744i
$974$	33.4772	−	28.0907i	1.07268	−	0.900083i
$975$		0			0
$976$	0.241191	−	1.36786i	0.00772034	−	0.0437842i
$977$	11.7586	+	5.48311i	0.376190	+	0.175420i	0.601511	−	0.798864i	$-0.294566\pi$
$977$	11.7586	+	5.48311i	0.376190	+	0.175420i	−0.225322	+	0.974284i	$0.572343\pi$
$978$		0			0
$979$	−23.3756	+	4.12175i	−0.747087	+	0.131732i
$980$	0.583127	+	3.46486i	0.0186273	+	0.110681i
$981$		0			0
$982$	−2.47247	−	9.22739i	−0.0788998	−	0.294458i
$983$	7.20494	−	3.35972i	0.229802	−	0.107158i	−0.304307	−	0.952574i	$-0.598425\pi$
$983$	7.20494	−	3.35972i	0.229802	−	0.107158i	0.534109	+	0.845416i	$0.320647\pi$
$984$		0			0
$985$	−9.62320	+	34.8257i	−0.306621	+	1.10964i
$986$	−26.4507	+	31.5228i	−0.842363	+	1.00389i
$987$		0			0
$988$	2.40378	+	5.15491i	0.0764743	+	0.164000i
$989$	10.6706	−	18.4820i	0.339305	−	0.587694i
$990$		0			0
$991$	−12.4295	−	21.5285i	−0.394835	−	0.683874i	0.598245	−	0.801313i	$-0.295865\pi$
$991$	−12.4295	−	21.5285i	−0.394835	−	0.683874i	−0.993080	+	0.117439i	$0.962532\pi$
$992$	−4.25639	+	6.07875i	−0.135140	+	0.193001i
$993$		0			0
$994$	1.54120	+	4.23440i	0.0488838	+	0.134307i
$995$	50.3430	+	29.5914i	1.59598	+	0.938110i
$996$		0			0
$997$	−1.20248	+	13.7444i	−0.0380828	+	0.435289i	0.953088	+	0.302695i	$0.0978862\pi$
$997$	−1.20248	+	13.7444i	−0.0380828	+	0.435289i	−0.991170	+	0.132594i	$0.957669\pi$
$998$	−17.3554	+	17.3554i	−0.549377	+	0.549377i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.10		216
3.2	odd	2		270.2.r.a.113.8	✓	216
5.2	odd	4	inner	810.2.s.a.287.8		216
15.2	even	4		270.2.r.a.167.12	yes	216
27.11	odd	18	inner	810.2.s.a.683.8		216
27.16	even	9		270.2.r.a.173.12	yes	216
135.92	even	36	inner	810.2.s.a.197.10		216
135.97	odd	36		270.2.r.a.227.8	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.8	✓	216	3.2	odd	2
270.2.r.a.167.12	yes	216	15.2	even	4
270.2.r.a.173.12	yes	216	27.16	even	9
270.2.r.a.227.8	yes	216	135.97	odd	36
810.2.s.a.197.10		216	135.92	even	36	inner
810.2.s.a.287.8		216	5.2	odd	4	inner
810.2.s.a.683.8		216	27.11	odd	18	inner
810.2.s.a.773.10		216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.23600 - 0.0174365i) q^{5} +(1.90858 + 1.33641i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.23600 - 0.0174365i) q^{5} +(1.90858 + 1.33641i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-2.22597 - 0.212250i) q^{10} +(0.889546 - 2.44401i) q^{11} +(0.203337 + 2.32415i) q^{13} +(1.78485 + 1.49766i) q^{14} +(0.939693 + 0.342020i) q^{16} +(5.64422 - 1.51236i) q^{17} +(2.11133 - 1.21898i) q^{19} +(-2.19900 - 0.405449i) q^{20} +(1.09917 - 2.35718i) q^{22} +(5.43990 + 7.76898i) q^{23} +(4.99939 + 0.0779761i) q^{25} +2.33303i q^{26} +(1.64752 + 1.64752i) q^{28} +(-5.39466 + 4.52666i) q^{29} +(-1.28861 + 7.30805i) q^{31} +(0.906308 + 0.422618i) q^{32} +(5.75455 - 1.01468i) q^{34} +(-4.24429 - 3.02148i) q^{35} +(-1.48751 - 5.55147i) q^{37} +(2.20954 - 1.03032i) q^{38} +(-2.15530 - 0.595562i) q^{40} +(1.75965 - 2.09706i) q^{41} +(-0.950971 - 2.03936i) q^{43} +(1.30043 - 2.25241i) q^{44} +(4.74208 + 8.21353i) q^{46} +(4.66288 - 6.65929i) q^{47} +(-0.537424 - 1.47656i) q^{49} +(4.97357 + 0.513405i) q^{50} +(-0.203337 + 2.32415i) q^{52} +(-1.68777 + 1.68777i) q^{53} +(-2.03164 + 5.44929i) q^{55} +(1.49766 + 1.78485i) q^{56} +(-5.76866 + 4.03926i) q^{58} +(5.56872 - 2.02685i) q^{59} +(-0.241191 - 1.36786i) q^{61} +(-1.92064 + 7.16793i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-0.414136 - 5.20035i) q^{65} +(-11.1572 + 0.976128i) q^{67} +(5.82109 - 0.509279i) q^{68} +(-3.96480 - 3.37990i) q^{70} +(1.67490 + 0.967007i) q^{71} +(-0.894627 + 3.33879i) q^{73} +(-0.998009 - 5.65999i) q^{74} +(2.29093 - 0.833829i) q^{76} +(4.96396 - 3.47580i) q^{77} +(2.76633 + 3.29678i) q^{79} +(-2.09519 - 0.781142i) q^{80} +(1.93572 - 1.93572i) q^{82} +(1.24922 - 14.2787i) q^{83} +(-12.6468 + 3.28323i) q^{85} +(-0.769610 - 2.11449i) q^{86} +(1.49179 - 2.13050i) q^{88} +(-4.56315 - 7.90360i) q^{89} +(-2.71793 + 4.70758i) q^{91} +(4.00818 + 8.59558i) q^{92} +(5.22554 - 6.22755i) q^{94} +(-4.74219 + 2.68882i) q^{95} +(6.02536 - 2.80967i) q^{97} +(-0.406688 - 1.51778i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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