LMFDB - Embedded newform 810.2.s.a.773.6

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			773.6
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.31168 + 1.81094i) q^{5} +(2.34419 + 1.64142i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.31168 + 1.81094i) q^{5} +(2.34419 + 1.64142i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.14886 - 1.91837i) q^{10} +(1.90955 - 5.24645i) q^{11} +(-0.457382 - 5.22790i) q^{13} +(-2.19221 - 1.83948i) q^{14} +(0.939693 + 0.342020i) q^{16} +(1.76190 - 0.472099i) q^{17} +(2.39674 - 1.38376i) q^{19} +(0.977290 + 2.01119i) q^{20} +(-2.35954 + 5.06006i) q^{22} +(-1.67621 - 2.39387i) q^{23} +(-1.55898 + 4.75075i) q^{25} +5.24787i q^{26} +(2.02355 + 2.02355i) q^{28} +(3.86410 - 3.24236i) q^{29} +(-0.596374 + 3.38220i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-1.79634 + 0.316743i) q^{34} +(0.102328 + 6.39820i) q^{35} +(2.87724 + 10.7380i) q^{37} +(-2.50822 + 1.16960i) q^{38} +(-0.798284 - 2.08872i) q^{40} +(0.552413 - 0.658340i) q^{41} +(-0.490236 - 1.05131i) q^{43} +(2.79158 - 4.83516i) q^{44} +(1.46119 + 2.53085i) q^{46} +(0.0739036 - 0.105545i) q^{47} +(0.406828 + 1.11775i) q^{49} +(1.96710 - 4.59679i) q^{50} +(0.457382 - 5.22790i) q^{52} +(-3.41992 + 3.41992i) q^{53} +(12.0057 - 3.42360i) q^{55} +(-1.83948 - 2.19221i) q^{56} +(-4.13198 + 2.89325i) q^{58} +(2.40477 - 0.875263i) q^{59} +(-2.46578 - 13.9841i) q^{61} +(0.888883 - 3.31736i) q^{62} +(0.866025 + 0.500000i) q^{64} +(8.86746 - 7.68564i) q^{65} +(4.46862 - 0.390954i) q^{67} +(1.81711 - 0.158976i) q^{68} +(0.455701 - 6.38277i) q^{70} +(4.00268 + 2.31095i) q^{71} +(-3.66531 + 13.6791i) q^{73} +(-1.93041 - 10.9479i) q^{74} +(2.60061 - 0.946546i) q^{76} +(13.0880 - 9.16430i) q^{77} +(-2.73501 - 3.25946i) q^{79} +(0.613202 + 2.15034i) q^{80} +(-0.607689 + 0.607689i) q^{82} +(-0.706574 + 8.07618i) q^{83} +(3.16599 + 2.57144i) q^{85} +(0.396742 + 1.09004i) q^{86} +(-3.20237 + 4.57345i) q^{88} +(6.55605 + 11.3554i) q^{89} +(7.50899 - 13.0060i) q^{91} +(-1.23505 - 2.64857i) q^{92} +(-0.0828213 + 0.0987026i) q^{94} +(5.64966 + 2.52529i) q^{95} +(-9.90462 + 4.61860i) q^{97} +(-0.307862 - 1.14896i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.31168	+	1.81094i	0.586602	+	0.809875i
$5$	1.31168	+	1.81094i	0.586602	+	0.809875i
$6$		0			0
$7$	2.34419	+	1.64142i	0.886021	+	0.620398i	0.925469	−	0.378823i	$-0.123671\pi$
$7$	2.34419	+	1.64142i	0.886021	+	0.620398i	−0.0394484	+	0.999222i	$0.512560\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	−1.14886	−	1.91837i	−0.363301	−	0.606640i
$11$	1.90955	−	5.24645i	0.575752	−	1.58186i	−0.219518	−	0.975608i	$-0.570448\pi$
$11$	1.90955	−	5.24645i	0.575752	−	1.58186i	0.795269	−	0.606256i	$-0.207329\pi$
$12$		0			0
$13$	−0.457382	−	5.22790i	−0.126855	−	1.44996i	−0.746661	−	0.665204i	$-0.768344\pi$
$13$	−0.457382	−	5.22790i	−0.126855	−	1.44996i	0.619806	−	0.784755i	$-0.287211\pi$
$14$	−2.19221	−	1.83948i	−0.585893	−	0.491623i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	1.76190	−	0.472099i	0.427323	−	0.114501i	−0.0387465	−	0.999249i	$-0.512336\pi$
$17$	1.76190	−	0.472099i	0.427323	−	0.114501i	0.466069	+	0.884748i	$0.345670\pi$
$18$		0			0
$19$	2.39674	−	1.38376i	0.549850	−	0.317456i	−0.199212	−	0.979956i	$-0.563838\pi$
$19$	2.39674	−	1.38376i	0.549850	−	0.317456i	0.749061	+	0.662501i	$0.230505\pi$
$20$	0.977290	+	2.01119i	0.218529	+	0.449717i
$21$		0			0
$22$	−2.35954	+	5.06006i	−0.503056	+	1.07881i
$23$	−1.67621	−	2.39387i	−0.349513	−	0.499156i	0.605449	−	0.795884i	$-0.292994\pi$
$23$	−1.67621	−	2.39387i	−0.349513	−	0.499156i	−0.954962	+	0.296728i	$0.904105\pi$
$24$		0			0
$25$	−1.55898	+	4.75075i	−0.311795	+	0.950149i
$26$			5.24787i			1.02919i
$27$		0			0
$28$	2.02355	+	2.02355i	0.382414	+	0.382414i
$29$	3.86410	−	3.24236i	0.717545	−	0.602092i	−0.209160	−	0.977881i	$-0.567073\pi$
$29$	3.86410	−	3.24236i	0.717545	−	0.602092i	0.926705	+	0.375790i	$0.122629\pi$
$30$		0			0
$31$	−0.596374	+	3.38220i	−0.107112	+	0.607462i	0.883244	+	0.468914i	$0.155355\pi$
$31$	−0.596374	+	3.38220i	−0.107112	+	0.607462i	−0.990356	+	0.138548i	$0.955757\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	−1.79634	+	0.316743i	−0.308069	+	0.0543209i
$35$	0.102328	+	6.39820i	0.0172966	+	1.08149i
$36$		0			0
$37$	2.87724	+	10.7380i	0.473016	+	1.76532i	0.628840	+	0.777535i	$0.283530\pi$
$37$	2.87724	+	10.7380i	0.473016	+	1.76532i	−0.155824	+	0.987785i	$0.549803\pi$
$38$	−2.50822	+	1.16960i	−0.406887	+	0.189735i
$39$		0			0
$40$	−0.798284	−	2.08872i	−0.126220	−	0.330255i
$41$	0.552413	−	0.658340i	0.0862724	−	0.102815i	−0.721181	−	0.692746i	$-0.756401\pi$
$41$	0.552413	−	0.658340i	0.0862724	−	0.102815i	0.807454	+	0.589931i	$0.200845\pi$
$42$		0			0
$43$	−0.490236	−	1.05131i	−0.0747603	−	0.160324i	0.865376	−	0.501124i	$-0.167080\pi$
$43$	−0.490236	−	1.05131i	−0.0747603	−	0.160324i	−0.940136	+	0.340800i	$0.889302\pi$
$44$	2.79158	−	4.83516i	0.420846	−	0.728927i
$45$		0			0
$46$	1.46119	+	2.53085i	0.215440	+	0.373154i
$47$	0.0739036	−	0.105545i	0.0107800	−	0.0153954i	−0.813726	−	0.581249i	$-0.802564\pi$
$47$	0.0739036	−	0.105545i	0.0107800	−	0.0153954i	0.824506	+	0.565853i	$0.191453\pi$
$48$		0			0
$49$	0.406828	+	1.11775i	0.0581183	+	0.159679i
$50$	1.96710	−	4.59679i	0.278190	−	0.650085i
$51$		0			0
$52$	0.457382	−	5.22790i	0.0634275	−	0.724980i
$53$	−3.41992	+	3.41992i	−0.469762	+	0.469762i	−0.901837	−	0.432076i	$-0.857781\pi$
$53$	−3.41992	+	3.41992i	−0.469762	+	0.469762i	0.432076	+	0.901837i	$0.357781\pi$
$54$		0			0
$55$	12.0057	−	3.42360i	1.61885	−	0.461639i
$56$	−1.83948	−	2.19221i	−0.245811	−	0.292946i
$57$		0			0
$58$	−4.13198	+	2.89325i	−0.542556	+	0.379902i
$59$	2.40477	−	0.875263i	0.313074	−	0.113950i	−0.180704	−	0.983537i	$-0.557838\pi$
$59$	2.40477	−	0.875263i	0.313074	−	0.113950i	0.493778	+	0.869588i	$0.335615\pi$
$60$		0			0
$61$	−2.46578	−	13.9841i	−0.315710	−	1.79048i	−0.568208	−	0.822885i	$-0.692363\pi$
$61$	−2.46578	−	13.9841i	−0.315710	−	1.79048i	0.252497	−	0.967598i	$-0.418748\pi$
$62$	0.888883	−	3.31736i	0.112888	−	0.421305i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	8.86746	−	7.68564i	1.09987	−	0.953286i
$66$		0			0
$67$	4.46862	−	0.390954i	0.545929	−	0.0477626i	0.189144	−	0.981949i	$-0.439429\pi$
$67$	4.46862	−	0.390954i	0.545929	−	0.0477626i	0.356785	+	0.934187i	$0.383873\pi$
$68$	1.81711	−	0.158976i	0.220357	−	0.0192787i
$69$		0			0
$70$	0.455701	−	6.38277i	0.0544667	−	0.762887i
$71$	4.00268	+	2.31095i	0.475030	+	0.274259i	0.718343	−	0.695689i	$-0.244901\pi$
$71$	4.00268	+	2.31095i	0.475030	+	0.274259i	−0.243313	+	0.969948i	$0.578234\pi$
$72$		0			0
$73$	−3.66531	+	13.6791i	−0.428992	+	1.60102i	0.326058	+	0.945350i	$0.394280\pi$
$73$	−3.66531	+	13.6791i	−0.428992	+	1.60102i	−0.755049	+	0.655668i	$0.772387\pi$
$74$	−1.93041	−	10.9479i	−0.224406	−	1.27267i
$75$		0			0
$76$	2.60061	−	0.946546i	0.298311	−	0.108576i
$77$	13.0880	−	9.16430i	1.49151	−	1.04437i
$78$		0			0
$79$	−2.73501	−	3.25946i	−0.307713	−	0.366718i	0.589920	−	0.807462i	$-0.299159\pi$
$79$	−2.73501	−	3.25946i	−0.307713	−	0.366718i	−0.897633	+	0.440744i	$0.854715\pi$
$80$	0.613202	+	2.15034i	0.0685581	+	0.240416i
$81$		0			0
$82$	−0.607689	+	0.607689i	−0.0671080	+	0.0671080i
$83$	−0.706574	+	8.07618i	−0.0775566	+	0.886476i	0.853379	+	0.521291i	$0.174550\pi$
$83$	−0.706574	+	8.07618i	−0.0775566	+	0.886476i	−0.930935	+	0.365184i	$0.881006\pi$
$84$		0			0
$85$	3.16599	+	2.57144i	0.343400	+	0.278911i
$86$	0.396742	+	1.09004i	0.0427818	+	0.117542i
$87$		0			0
$88$	−3.20237	+	4.57345i	−0.341373	+	0.487532i
$89$	6.55605	+	11.3554i	0.694940	+	1.20367i	0.970201	+	0.242302i	$0.0779025\pi$
$89$	6.55605	+	11.3554i	0.694940	+	1.20367i	−0.275261	+	0.961370i	$0.588764\pi$
$90$		0			0
$91$	7.50899	−	13.0060i	0.787156	−	1.36339i
$92$	−1.23505	−	2.64857i	−0.128763	−	0.276133i
$93$		0			0
$94$	−0.0828213	+	0.0987026i	−0.00854237	+	0.0101804i
$95$	5.64966	+	2.52529i	0.579643	+	0.259089i
$96$		0			0
$97$	−9.90462	+	4.61860i	−1.00566	+	0.468948i	−0.854439	−	0.519552i	$-0.826099\pi$
$97$	−9.90462	+	4.61860i	−1.00566	+	0.468948i	−0.151223	+	0.988500i	$0.548321\pi$
$98$	−0.307862	−	1.14896i	−0.0310987	−	0.116062i
$99$		0			0
$100$	−2.36025	+	4.40786i	−0.236025	+	0.440786i
$101$	−15.5949	+	2.74980i	−1.55175	+	0.273616i	−0.882821	−	0.469709i	$-0.844359\pi$
$101$	−15.5949	+	2.74980i	−1.55175	+	0.273616i	−0.668930	+	0.743325i	$0.733248\pi$
$102$		0			0
$103$	3.13813	+	1.46333i	0.309209	+	0.144186i	0.571028	−	0.820930i	$-0.306545\pi$
$103$	3.13813	+	1.46333i	0.309209	+	0.144186i	−0.261819	+	0.965117i	$0.584322\pi$
$104$	−0.911283	+	5.16815i	−0.0893587	+	0.506778i
$105$		0			0
$106$	3.70497	−	3.10884i	0.359858	−	0.301957i
$107$	3.97773	+	3.97773i	0.384542	+	0.384542i	0.872735	−	0.488194i	$-0.162344\pi$
$107$	3.97773	+	3.97773i	0.384542	+	0.384542i	−0.488194	+	0.872735i	$0.662344\pi$
$108$		0			0
$109$		−	13.7476i		−	1.31678i	−0.752678	−	0.658389i	$-0.771238\pi$
$109$		−	13.7476i		−	1.31678i	0.752678	−	0.658389i	$-0.228762\pi$
$110$	−12.2584	+	2.36421i	−1.16879	+	0.225418i
$111$		0			0
$112$	1.64142	+	2.34419i	0.155100	+	0.221505i
$113$	−2.64402	+	5.67012i	−0.248728	+	0.533400i	−0.990543	−	0.137206i	$-0.956188\pi$
$113$	−2.64402	+	5.67012i	−0.248728	+	0.533400i	0.741814	+	0.670606i	$0.233966\pi$
$114$		0			0
$115$	2.13649	−	6.17550i	0.199229	−	0.575868i
$116$	4.36842	−	2.52211i	0.405598	−	0.234172i
$117$		0			0
$118$	−2.47190	+	0.662343i	−0.227557	+	0.0609736i
$119$	4.90513	+	1.78532i	0.449653	+	0.163660i
$120$		0			0
$121$	−15.4524	−	12.9661i	−1.40476	−	1.17873i
$122$	1.23760	+	14.1458i	0.112047	+	1.28070i
$123$		0			0
$124$	−1.17463	+	3.22726i	−0.105485	+	0.289817i
$125$	−10.6482	+	3.40826i	−0.952402	+	0.304844i
$126$		0			0
$127$	16.8895	+	4.52552i	1.49870	+	0.401575i	0.912664	−	0.408711i	$-0.134022\pi$
$127$	16.8895	+	4.52552i	1.49870	+	0.401575i	0.586035	+	0.810286i	$0.300688\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	−9.50356	+	6.88354i	−0.833517	+	0.603727i
$131$	21.1703	+	3.73290i	1.84966	+	0.326145i	0.984504	−	0.175362i	$-0.0561097\pi$
$131$	21.1703	+	3.73290i	1.84966	+	0.326145i	0.865154	+	0.501507i	$0.167221\pi$
$132$		0			0
$133$	7.88974	+	0.690263i	0.684127	+	0.0598534i
$134$	−4.48569			−0.387505
$135$		0			0
$136$	−1.82405			−0.156411
$137$	−7.93466	−	0.694193i	−0.677904	−	0.0593089i	−0.256996	−	0.966412i	$-0.582733\pi$
$137$	−7.93466	−	0.694193i	−0.677904	−	0.0593089i	−0.420908	+	0.907104i	$0.638288\pi$
$138$		0			0
$139$	1.99233	+	0.351301i	0.168987	+	0.0297970i	0.257501	−	0.966278i	$-0.417101\pi$
$139$	1.99233	+	0.351301i	0.168987	+	0.0297970i	−0.0885143	+	0.996075i	$0.528212\pi$
$140$	−1.01026	+	6.31877i	−0.0853827	+	0.534033i
$141$		0			0
$142$	−3.78603	−	2.65101i	−0.317717	−	0.222468i
$143$	−28.3013	−	7.58332i	−2.36668	−	0.634149i
$144$		0			0
$145$	10.9402	+	2.74468i	0.908532	+	0.227933i
$146$	4.84357	−	13.3076i	0.400857	−	1.10134i
$147$		0			0
$148$	0.968894	+	11.0745i	0.0796426	+	0.910319i
$149$	−14.2510	−	11.9580i	−1.16749	−	0.979640i	−0.167509	−	0.985871i	$-0.553572\pi$
$149$	−14.2510	−	11.9580i	−1.16749	−	0.979640i	−0.999981	+	0.00623066i	$0.998017\pi$
$150$		0			0
$151$	4.87226	+	1.77336i	0.396499	+	0.144314i	0.532571	−	0.846385i	$-0.321226\pi$
$151$	4.87226	+	1.77336i	0.396499	+	0.144314i	−0.136072	+	0.990699i	$0.543448\pi$
$152$	−2.67321	+	0.716286i	−0.216826	+	0.0580984i
$153$		0			0
$154$	−13.8369	+	7.98874i	−1.11501	+	0.643751i
$155$	−6.90721	+	3.35638i	−0.554800	+	0.269591i
$156$		0			0
$157$	2.38506	−	5.11479i	0.190349	−	0.408204i	−0.787852	−	0.615864i	$-0.788807\pi$
$157$	2.38506	−	5.11479i	0.190349	−	0.408204i	0.978201	+	0.207660i	$0.0665847\pi$
$158$	2.44053	+	3.48543i	0.194158	+	0.277286i
$159$		0			0
$160$	−0.423454	−	2.19561i	−0.0334770	−	0.173578i
$161$		−	8.36304i		−	0.659100i
$162$		0			0
$163$	−11.5617	−	11.5617i	−0.905580	−	0.905580i	0.0903321	−	0.995912i	$-0.471207\pi$
$163$	−11.5617	−	11.5617i	−0.905580	−	0.905580i	−0.995912	+	0.0903321i	$0.971207\pi$
$164$	0.658340	−	0.552413i	0.0514077	−	0.0431362i
$165$		0			0
$166$	1.40777	−	7.98386i	0.109264	−	0.619668i
$167$	−16.4886	−	7.68875i	−1.27592	−	0.594974i	−0.337783	−	0.941224i	$-0.609677\pi$
$167$	−16.4886	−	7.68875i	−1.27592	−	0.594974i	−0.938142	+	0.346251i	$0.887455\pi$
$168$		0			0
$169$	−14.3193	+	2.52487i	−1.10148	+	0.194221i
$170$	−2.92983	−	2.83759i	−0.224707	−	0.217633i
$171$		0			0
$172$	−0.300229	−	1.12047i	−0.0228923	−	0.0854351i
$173$	11.8056	−	5.50506i	0.897566	−	0.418542i	0.0816155	−	0.996664i	$-0.473992\pi$
$173$	11.8056	−	5.50506i	0.897566	−	0.418542i	0.815950	+	0.578122i	$0.196214\pi$
$174$		0			0
$175$	−11.4525	+	8.57772i	−0.865728	+	0.648415i
$176$	3.58878	−	4.27695i	0.270515	−	0.322387i
$177$		0			0
$178$	−5.54141	−	11.8836i	−0.415347	−	0.890714i
$179$	−11.1624	+	19.3338i	−0.834315	+	1.44508i	0.0602712	+	0.998182i	$0.480803\pi$
$179$	−11.1624	+	19.3338i	−0.834315	+	1.44508i	−0.894587	+	0.446895i	$0.852530\pi$
$180$		0			0
$181$	−1.40233	−	2.42891i	−0.104235	−	0.180540i	0.809191	−	0.587546i	$-0.199906\pi$
$181$	−1.40233	−	2.42891i	−0.104235	−	0.180540i	−0.913425	+	0.407006i	$0.866573\pi$
$182$	−8.61396	+	12.3020i	−0.638509	+	0.911886i
$183$		0			0
$184$	0.999511	+	2.74613i	0.0736850	+	0.202448i
$185$	−15.6718	+	19.2954i	−1.15222	+	1.41862i
$186$		0			0
$187$	0.887590	−	10.1452i	0.0649070	−	0.741890i
$188$	0.0911086	−	0.0911086i	0.00664478	−	0.00664478i
$189$		0			0
$190$	−5.40807	−	3.00808i	−0.392342	−	0.218229i
$191$	9.29799	+	11.0809i	0.672779	+	0.801787i	0.989159	−	0.146846i	$-0.0469120\pi$
$191$	9.29799	+	11.0809i	0.672779	+	0.801787i	−0.316380	+	0.948632i	$0.602468\pi$
$192$		0			0
$193$	−20.8006	+	14.5648i	−1.49726	+	1.04839i	−0.515807	+	0.856705i	$0.672508\pi$
$193$	−20.8006	+	14.5648i	−1.49726	+	1.04839i	−0.981456	+	0.191689i	$0.938603\pi$
$194$	10.2695	−	3.73778i	0.737304	−	0.268357i
$195$		0			0
$196$	0.206552	+	1.17142i	0.0147537	+	0.0836725i
$197$	−5.51448	+	20.5803i	−0.392890	+	1.46629i	0.432453	+	0.901656i	$0.357648\pi$
$197$	−5.51448	+	20.5803i	−0.392890	+	1.46629i	−0.825344	+	0.564631i	$0.809019\pi$
$198$		0			0
$199$	6.03981	+	3.48709i	0.428151	+	0.247193i	0.698559	−	0.715553i	$-0.253825\pi$
$199$	6.03981	+	3.48709i	0.428151	+	0.247193i	−0.270408	+	0.962746i	$0.587158\pi$
$200$	2.73544	−	4.18538i	0.193425	−	0.295951i
$201$		0			0
$202$	15.7752	−	1.38015i	1.10994	−	0.0971073i
$203$	14.3803	−	1.25811i	1.00930	−	0.0883020i
$204$		0			0
$205$	1.91680	+	0.136851i	0.133875	+	0.00955809i
$206$	−2.99865	−	1.73127i	−0.208926	−	0.120623i
$207$		0			0
$208$	1.35825	−	5.06906i	0.0941776	−	0.351476i
$209$	−2.68312	−	15.2167i	−0.185595	−	1.05256i
$210$		0			0
$211$	−4.89499	+	1.78163i	−0.336985	+	0.122653i	−0.504970	−	0.863137i	$-0.668496\pi$
$211$	−4.89499	+	1.78163i	−0.336985	+	0.122653i	0.167985	+	0.985790i	$0.446274\pi$
$212$	−3.96182	+	2.77410i	−0.272099	+	0.190526i
$213$		0			0
$214$	−3.61591	−	4.30928i	−0.247179	−	0.294576i
$215$	1.26083	−	2.26678i	0.0859878	−	0.154593i
$216$		0			0
$217$	−6.94963	+	6.94963i	−0.471772	+	0.471772i
$218$	−1.19818	+	13.6952i	−0.0811509	+	0.927559i
$219$		0			0
$220$	12.4178	−	1.28682i	0.837209	−	0.0867574i
$221$	−3.27395	−	8.99509i	−0.220229	−	0.605075i
$222$		0			0
$223$	0.813307	−	1.16152i	0.0544630	−	0.0777813i	−0.790997	−	0.611820i	$-0.790438\pi$
$223$	0.813307	−	1.16152i	0.0544630	−	0.0777813i	0.845460	+	0.534039i	$0.179326\pi$
$224$	−1.43086	−	2.47833i	−0.0956036	−	0.165590i
$225$		0			0
$226$	3.12814	−	5.41810i	0.208081	−	0.360407i
$227$	1.76081	+	3.77607i	0.116869	+	0.250627i	0.956037	−	0.293246i	$-0.0947353\pi$
$227$	1.76081	+	3.77607i	0.116869	+	0.250627i	−0.839168	+	0.543872i	$0.816958\pi$
$228$		0			0
$229$	−4.75264	+	5.66397i	−0.314063	+	0.374286i	−0.899865	−	0.436168i	$-0.856335\pi$
$229$	−4.75264	+	5.66397i	−0.314063	+	0.374286i	0.585802	+	0.810454i	$0.300780\pi$
$230$	−2.66660	+	5.96579i	−0.175830	+	0.393373i
$231$		0			0
$232$	−4.57162	+	2.13178i	−0.300141	+	0.139958i
$233$	−4.06634	−	15.1758i	−0.266395	−	0.994200i	−0.961391	−	0.275186i	$-0.911261\pi$
$233$	−4.06634	−	15.1758i	−0.266395	−	0.994200i	0.694996	−	0.719014i	$-0.255406\pi$
$234$		0			0
$235$	0.288074	−	0.00460725i	0.0187919	−	0.000300544i
$236$	2.52022	−	0.444383i	0.164052	−	0.0289269i
$237$		0			0
$238$	−4.73086	−	2.20604i	−0.306656	−	0.142996i
$239$	1.83464	−	10.4048i	0.118673	−	0.673029i	−0.866193	−	0.499710i	$-0.833440\pi$
$239$	1.83464	−	10.4048i	0.118673	−	0.673029i	0.984866	−	0.173318i	$-0.0554490\pi$
$240$		0			0
$241$	−3.74440	+	3.14193i	−0.241198	+	0.202389i	−0.755371	−	0.655297i	$-0.772543\pi$
$241$	−3.74440	+	3.14193i	−0.241198	+	0.202389i	0.514173	+	0.857687i	$0.328099\pi$
$242$	14.2635	+	14.2635i	0.916893	+	0.916893i
$243$		0			0
$244$		−	14.1998i		−	0.909052i
$245$	−1.49055	+	2.20288i	−0.0952276	+	0.140737i
$246$		0			0
$247$	−8.33038	−	11.8970i	−0.530049	−	0.756989i
$248$	1.45143	−	3.11261i	0.0921660	−	0.197651i
$249$		0			0
$250$	10.9047	−	2.46725i	0.689674	−	0.156042i
$251$	−1.46778	+	0.847424i	−0.0926456	+	0.0534890i	−0.545607	−	0.838041i	$-0.683701\pi$
$251$	−1.46778	+	0.847424i	−0.0926456	+	0.0534890i	0.452961	+	0.891530i	$0.350368\pi$
$252$		0			0
$253$	−15.7601	+	4.22291i	−0.990831	+	0.265492i
$254$	−16.4308	−	5.98032i	−1.03096	−	0.375238i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−1.23091	−	14.0693i	−0.0767818	−	0.877620i	−0.932734	−	0.360565i	$-0.882584\pi$
$257$	−1.23091	−	14.0693i	−0.0767818	−	0.877620i	0.855952	−	0.517055i	$-0.172972\pi$
$258$		0			0
$259$	−10.8808	+	29.8947i	−0.676099	+	1.85757i
$260$	10.0673	−	6.02906i	0.624350	−	0.373906i
$261$		0			0
$262$	−20.7644	−	5.56380i	−1.28283	−	0.343733i
$263$	−8.24305	−	5.77184i	−0.508288	−	0.355907i	0.291129	−	0.956684i	$-0.405969\pi$
$263$	−8.24305	−	5.77184i	−0.508288	−	0.355907i	−0.799417	+	0.600777i	$0.794858\pi$
$264$		0			0
$265$	−10.6791	−	1.70740i	−0.656012	−	0.104885i
$266$	−7.79956	−	1.37527i	−0.478221	−	0.0843233i
$267$		0			0
$268$	4.46862	+	0.390954i	0.272965	+	0.0238813i
$269$	9.54948			0.582242			0.291121	−	0.956686i	$-0.405972\pi$
$269$	9.54948			0.582242			0.291121	+	0.956686i	$0.405972\pi$
$270$		0			0
$271$	0.509576			0.0309545			0.0154773	−	0.999880i	$-0.495073\pi$
$271$	0.509576			0.0309545			0.0154773	+	0.999880i	$0.495073\pi$
$272$	1.81711	+	0.158976i	0.110178	+	0.00963936i
$273$		0			0
$274$	7.84396	+	1.38310i	0.473871	+	0.0835563i
$275$	21.9476	+	17.2509i	1.32349	+	1.04027i
$276$		0			0
$277$	−3.37551	−	2.36355i	−0.202814	−	0.142012i	0.467757	−	0.883857i	$-0.345062\pi$
$277$	−3.37551	−	2.36355i	−0.202814	−	0.142012i	−0.670572	+	0.741845i	$0.733951\pi$
$278$	−1.95413	−	0.523608i	−0.117201	−	0.0314039i
$279$		0			0
$280$	1.55713	−	6.20667i	0.0930566	−	0.370920i
$281$	1.68906	−	4.64065i	0.100761	−	0.276838i	−0.879062	−	0.476708i	$-0.841830\pi$
$281$	1.68906	−	4.64065i	0.100761	−	0.276838i	0.979822	+	0.199870i	$0.0640521\pi$
$282$		0			0
$283$	1.38979	+	15.8854i	0.0826145	+	0.944288i	0.918510	+	0.395399i	$0.129394\pi$
$283$	1.38979	+	15.8854i	0.0826145	+	0.944288i	−0.835895	+	0.548889i	$0.815051\pi$
$284$	3.54057	+	2.97089i	0.210094	+	0.176290i
$285$		0			0
$286$	27.5327	+	10.0211i	1.62804	+	0.592559i
$287$	2.37557	−	0.636533i	0.140226	−	0.0375733i
$288$		0			0
$289$	−11.8410	+	6.83642i	−0.696531	+	0.402143i
$290$	−10.6593	−	3.68774i	−0.625938	−	0.216551i
$291$		0			0
$292$	−5.98497	+	12.8348i	−0.350244	+	0.751101i
$293$	−11.3575	−	16.2202i	−0.663512	−	0.947594i	−0.999983	−	0.00589986i	$-0.998122\pi$
$293$	−11.3575	−	16.2202i	−0.663512	−	0.947594i	0.336470	−	0.941694i	$-0.390767\pi$
$294$		0			0
$295$	4.73933	+	3.20681i	0.275935	+	0.186708i
$296$		−	11.1168i		−	0.646152i
$297$		0			0
$298$	13.1546	+	13.1546i	0.762025	+	0.762025i
$299$	−11.7483	+	9.85795i	−0.679419	+	0.570100i
$300$		0			0
$301$	0.576442	−	3.26916i	0.0332256	−	0.188432i
$302$	−4.69916	−	2.19126i	−0.270406	−	0.126093i
$303$		0			0
$304$	2.72547	−	0.480574i	0.156316	−	0.0275628i
$305$	22.0900	−	22.8081i	1.26487	−	1.30599i
$306$		0			0
$307$	−1.71821	−	6.41244i	−0.0980634	−	0.365978i	0.899403	−	0.437121i	$-0.144002\pi$
$307$	−1.71821	−	6.41244i	−0.0980634	−	0.365978i	−0.997466	+	0.0711435i	$0.977335\pi$
$308$	14.4805	−	6.75237i	0.825104	−	0.384752i
$309$		0			0
$310$	7.17345	−	2.74161i	0.407425	−	0.155713i
$311$	10.8249	−	12.9007i	0.613826	−	0.731529i	−0.366170	−	0.930548i	$-0.619331\pi$
$311$	10.8249	−	12.9007i	0.613826	−	0.731529i	0.979996	+	0.199019i	$0.0637755\pi$
$312$		0			0
$313$	−8.74255	−	18.7485i	−0.494158	−	1.05973i	−0.982361	−	0.186995i	$-0.940125\pi$
$313$	−8.74255	−	18.7485i	−0.494158	−	1.05973i	0.488203	−	0.872730i	$-0.337653\pi$
$314$	−2.82177	+	4.88745i	−0.159242	+	0.275815i
$315$		0			0
$316$	−2.12746	−	3.68487i	−0.119679	−	0.207290i
$317$	3.22616	−	4.60743i	0.181199	−	0.258779i	−0.718269	−	0.695766i	$-0.755065\pi$
$317$	3.22616	−	4.60743i	0.181199	−	0.258779i	0.899468	+	0.436986i	$0.143954\pi$
$318$		0			0
$319$	−9.63220	−	26.4643i	−0.539300	−	1.48171i
$320$	0.230483	+	2.22416i	0.0128844	+	0.124334i
$321$		0			0
$322$	−0.728887	+	8.33122i	−0.0406193	+	0.464281i
$323$	3.56953	−	3.56953i	0.198614	−	0.198614i
$324$		0			0
$325$	25.5495	+	5.97727i	1.41723	+	0.331559i
$326$	10.5100	+	12.5253i	0.582095	+	0.693714i
$327$		0			0
$328$	−0.703981	+	0.492933i	−0.0388708	+	0.0272176i
$329$	0.346488	−	0.126111i	0.0191025	−	0.00695275i
$330$		0			0
$331$	3.05304	+	17.3146i	0.167810	+	0.951699i	0.946119	+	0.323818i	$0.104966\pi$
$331$	3.05304	+	17.3146i	0.167810	+	0.951699i	−0.778309	+	0.627881i	$0.783922\pi$
$332$	−2.09825	+	7.83079i	−0.115157	+	0.429770i
$333$		0			0
$334$	15.7557	+	9.09657i	0.862115	+	0.497742i
$335$	6.56941	+	7.57958i	0.358925	+	0.414117i
$336$		0			0
$337$	11.4389	−	1.00078i	0.623117	−	0.0545157i	0.228775	−	0.973479i	$-0.426528\pi$
$337$	11.4389	−	1.00078i	0.623117	−	0.0545157i	0.394342	+	0.918964i	$0.370972\pi$
$338$	14.4848	−	1.26726i	0.787871	−	0.0689298i
$339$		0			0
$340$	2.67136	+	3.08214i	0.144875	+	0.167152i
$341$	16.6058	+	9.58734i	0.899252	+	0.519184i
$342$		0			0
$343$	4.30367	−	16.0615i	0.232376	−	0.867241i
$344$	0.201431	+	1.14237i	0.0108605	+	0.0615927i
$345$		0			0
$346$	−12.2405	+	4.45518i	−0.658054	+	0.239512i
$347$	−5.16640	+	3.61756i	−0.277347	+	0.194201i	−0.703971	−	0.710228i	$-0.748592\pi$
$347$	−5.16640	+	3.61756i	−0.277347	+	0.194201i	0.426624	+	0.904429i	$0.359703\pi$
$348$		0			0
$349$	7.64152	+	9.10681i	0.409041	+	0.487477i	0.930755	−	0.365644i	$-0.119151\pi$
$349$	7.64152	+	9.10681i	0.409041	+	0.487477i	−0.521713	+	0.853121i	$0.674707\pi$
$350$	12.1565	−	7.54693i	0.649794	−	0.403400i
$351$		0			0
$352$	−3.94789	+	3.94789i	−0.210423	+	0.210423i
$353$	−2.06736	+	23.6300i	−0.110034	+	1.25770i	0.717609	+	0.696446i	$0.245236\pi$
$353$	−2.06736	+	23.6300i	−0.110034	+	1.25770i	−0.827644	+	0.561254i	$0.810319\pi$
$354$		0			0
$355$	1.06527	+	10.2798i	0.0565384	+	0.545596i
$356$	4.48460	+	12.3213i	0.237684	+	0.653030i
$357$		0			0
$358$	12.8050	−	18.2874i	0.676763	−	0.966518i
$359$	−5.53155	−	9.58093i	−0.291944	−	0.505662i	0.682325	−	0.731049i	$-0.260969\pi$
$359$	−5.53155	−	9.58093i	−0.291944	−	0.505662i	−0.974269	+	0.225387i	$0.927635\pi$
$360$		0			0
$361$	−5.67043	+	9.82147i	−0.298444	+	0.516920i
$362$	1.18530	+	2.54189i	0.0622982	+	0.133599i
$363$		0			0
$364$	9.65337	−	11.5044i	0.505974	−	0.602997i
$365$	−29.5797	+	11.3050i	−1.54827	+	0.591731i
$366$		0			0
$367$	23.8648	−	11.1283i	1.24573	−	0.580895i	0.315870	−	0.948802i	$-0.397704\pi$
$367$	23.8648	−	11.1283i	1.24573	−	0.580895i	0.929862	+	0.367908i	$0.119926\pi$
$368$	−0.756367	−	2.82280i	−0.0394283	−	0.147149i
$369$		0			0
$370$	17.2939	−	17.8561i	0.899067	−	0.928293i
$371$	−13.6305	+	2.40342i	−0.707658	+	0.124779i
$372$		0			0
$373$	14.9723	+	6.98172i	0.775238	+	0.361500i	0.769635	−	0.638485i	$-0.220438\pi$
$373$	14.9723	+	6.98172i	0.775238	+	0.361500i	0.00560388	+	0.999984i	$0.498216\pi$
$374$	−1.76842	+	10.0292i	−0.0914431	+	0.518599i
$375$		0			0
$376$	−0.0987026	+	0.0828213i	−0.00509020	+	0.00427118i
$377$	−18.7181	−	18.7181i	−0.964032	−	0.964032i
$378$		0			0
$379$			10.8529i			0.557478i	0.960367	+	0.278739i	$0.0899164\pi$
$379$			10.8529i			0.557478i	−0.960367	+	0.278739i	$0.910084\pi$
$380$	5.12531	+	3.46798i	0.262923	+	0.177903i
$381$		0			0
$382$	−8.29685	−	11.8491i	−0.424504	−	0.606254i
$383$	−0.477942	+	1.02495i	−0.0244217	+	0.0523725i	−0.918140	−	0.396256i	$-0.870309\pi$
$383$	−0.477942	+	1.02495i	−0.0244217	+	0.0523725i	0.893719	+	0.448628i	$0.148087\pi$
$384$		0			0
$385$	33.7632	+	11.6808i	1.72073	+	0.595311i
$386$	21.9909	−	12.6964i	1.11931	−	0.646232i
$387$		0			0
$388$	−10.5562	+	2.82851i	−0.535907	+	0.143596i
$389$	4.82910	+	1.75765i	0.244845	+	0.0891164i	0.461528	−	0.887126i	$-0.347301\pi$
$389$	4.82910	+	1.75765i	0.244845	+	0.0891164i	−0.216683	+	0.976242i	$0.569524\pi$
$390$		0			0
$391$	−4.08344	−	3.42642i	−0.206509	−	0.173281i
$392$	−0.103671	−	1.18496i	−0.00523616	−	0.0598495i
$393$		0			0
$394$	7.28719	−	20.0214i	0.367123	−	1.00866i
$395$	2.31521	−	9.22831i	0.116491	−	0.464327i
$396$		0			0
$397$	17.4019	+	4.66281i	0.873374	+	0.234020i	0.667546	−	0.744568i	$-0.267345\pi$
$397$	17.4019	+	4.66281i	0.873374	+	0.234020i	0.205828	+	0.978588i	$0.434011\pi$
$398$	−5.71291	−	4.00022i	−0.286362	−	0.200513i
$399$		0			0
$400$	−3.08981	+	3.93104i	−0.154491	+	0.196552i
$401$	−16.6355	−	2.93328i	−0.830736	−	0.146481i	−0.257921	−	0.966166i	$-0.583038\pi$
$401$	−16.6355	−	2.93328i	−0.830736	−	0.146481i	−0.572815	+	0.819685i	$0.694149\pi$
$402$		0			0
$403$	17.9546	+	1.57082i	0.894383	+	0.0782483i
$404$	−15.8355			−0.787845
$405$		0			0
$406$	−14.4352			−0.716406
$407$	61.8307	+	5.40949i	3.06484	+	0.268138i
$408$		0			0
$409$	24.3191	+	4.28812i	1.20250	+	0.212034i	0.738780	−	0.673946i	$-0.235402\pi$
$409$	24.3191	+	4.28812i	1.20250	+	0.212034i	0.463723	+	0.885980i	$0.346513\pi$
$410$	−1.89758	−	0.303390i	−0.0937148	−	0.0149834i
$411$		0			0
$412$	2.83635	+	1.98603i	0.139737	+	0.0978447i
$413$	7.07390	+	1.89545i	0.348084	+	0.0932688i
$414$		0			0
$415$	−15.5522	+	9.31382i	−0.763429	+	0.457198i
$416$	−1.79488	+	4.93139i	−0.0880011	+	0.241781i
$417$		0			0
$418$	1.34668	+	15.3927i	0.0658685	+	0.752880i
$419$	−7.41890	−	6.22519i	−0.362437	−	0.304121i	0.443324	−	0.896361i	$-0.353799\pi$
$419$	−7.41890	−	6.22519i	−0.362437	−	0.304121i	−0.805761	+	0.592241i	$0.798243\pi$
$420$		0			0
$421$	−26.1943	−	9.53394i	−1.27663	−	0.464656i	−0.387315	−	0.921948i	$-0.626597\pi$
$421$	−26.1943	−	9.53394i	−1.27663	−	0.464656i	−0.889317	+	0.457292i	$0.848820\pi$
$422$	5.03164	−	1.34822i	0.244937	−	0.0656306i
$423$		0			0
$424$	4.18853	−	2.41825i	0.203413	−	0.117440i
$425$	−0.503934	+	9.10631i	−0.0244444	+	0.441721i
$426$		0			0
$427$	17.1736	−	36.8288i	0.831087	−	1.78227i
$428$	3.22657	+	4.60803i	0.155962	+	0.222737i
$429$		0			0
$430$	−1.45359	+	2.14826i	−0.0700985	+	0.103598i
$431$			24.7655i			1.19291i	0.802646	+	0.596455i	$0.203425\pi$
$431$			24.7655i			1.19291i	−0.802646	+	0.596455i	$0.796575\pi$
$432$		0			0
$433$	−22.8149	−	22.8149i	−1.09641	−	1.09641i	−0.994827	−	0.101585i	$-0.967609\pi$
$433$	−22.8149	−	22.8149i	−1.09641	−	1.09641i	−0.101585	−	0.994827i	$-0.532391\pi$
$434$	7.52889	−	6.31748i	0.361398	−	0.303249i
$435$		0			0
$436$	2.38724	−	13.5387i	0.114328	−	0.648386i
$437$	−7.32996	−	3.41802i	−0.350640	−	0.163506i
$438$		0			0
$439$	−37.9671	+	6.69462i	−1.81207	+	0.319517i	−0.974086	−	0.226180i	$-0.927376\pi$
$439$	−37.9671	+	6.69462i	−1.81207	+	0.319517i	−0.837983	+	0.545696i	$0.816265\pi$
$440$	−12.4827	+	0.199640i	−0.595090	+	0.00951744i
$441$		0			0
$442$	2.47751	+	9.24620i	0.117843	+	0.439797i
$443$	−15.7754	+	7.35621i	−0.749514	+	0.349504i	−0.759553	−	0.650446i	$-0.774582\pi$
$443$	−15.7754	+	7.35621i	−0.749514	+	0.349504i	0.0100391	+	0.999950i	$0.496804\pi$
$444$		0			0
$445$	−11.9645	+	26.7673i	−0.567170	+	1.26889i
$446$	−0.911445	+	1.08622i	−0.0431582	+	0.0514339i
$447$		0			0
$448$	1.20942	+	2.59361i	0.0571397	+	0.122536i
$449$	1.02423	−	1.77401i	0.0483362	−	0.0837207i	−0.840845	−	0.541276i	$-0.817941\pi$
$449$	1.02423	−	1.77401i	0.0483362	−	0.0837207i	0.889181	+	0.457555i	$0.151275\pi$
$450$		0			0
$451$	−2.39909	−	4.15534i	−0.112969	−	0.195667i
$452$	−3.58846	+	5.12485i	−0.168787	+	0.241053i
$453$		0			0
$454$	−1.42501	−	3.91517i	−0.0668788	−	0.183748i
$455$	33.4024	−	3.46138i	1.56593	−	0.162272i
$456$		0			0
$457$	−1.08303	+	12.3790i	−0.0506618	+	0.579067i	0.927861	+	0.372927i	$0.121646\pi$
$457$	−1.08303	+	12.3790i	−0.0506618	+	0.579067i	−0.978522	+	0.206140i	$0.933910\pi$
$458$	5.22820	−	5.22820i	0.244298	−	0.244298i
$459$		0			0
$460$	3.17640	−	5.71068i	0.148100	−	0.266262i
$461$	−2.66240	−	3.17293i	−0.124001	−	0.147778i	0.700472	−	0.713680i	$-0.252973\pi$
$461$	−2.66240	−	3.17293i	−0.124001	−	0.147778i	−0.824473	+	0.565901i	$0.808528\pi$
$462$		0			0
$463$	18.9766	−	13.2875i	0.881916	−	0.617525i	−0.0424213	−	0.999100i	$-0.513507\pi$
$463$	18.9766	−	13.2875i	0.881916	−	0.617525i	0.924338	+	0.381575i	$0.124618\pi$
$464$	4.74002	−	1.72522i	0.220050	−	0.0800916i
$465$		0			0
$466$	2.72821	+	15.4725i	0.126382	+	0.716748i
$467$	2.71786	−	10.1432i	0.125767	−	0.469371i	−0.874098	−	0.485749i	$-0.838547\pi$
$467$	2.71786	−	10.1432i	0.125767	−	0.469371i	0.999866	+	0.0163783i	$0.00521360\pi$
$468$		0			0
$469$	11.1170	+	6.41842i	0.513336	+	0.296375i
$470$	−0.287379	−	0.0205176i	−0.0132558	−	0.000946406i
$471$		0			0
$472$	−2.54936	+	0.223040i	−0.117344	+	0.0102663i
$473$	−6.45180	+	0.564460i	−0.296654	+	0.0259539i
$474$		0			0
$475$	2.83742	+	13.5435i	0.130190	+	0.621420i
$476$	4.52059	+	2.60997i	0.207201	+	0.119628i
$477$		0			0
$478$	−2.73450	+	10.2053i	−0.125073	+	0.466778i
$479$	−5.13909	−	29.1452i	−0.234811	−	1.33168i	−0.843011	−	0.537896i	$-0.819219\pi$
$479$	−5.13909	−	29.1452i	−0.234811	−	1.33168i	0.608200	−	0.793784i	$-0.291892\pi$
$480$		0			0
$481$	54.8213	−	19.9533i	2.49964	−	0.909793i
$482$	4.00399	−	2.80362i	0.182377	−	0.127702i
$483$		0			0
$484$	−12.9661	−	15.4524i	−0.589367	−	0.702381i
$485$	−21.3557	−	11.8785i	−0.969712	−	0.539374i
$486$		0			0
$487$	−16.8081	+	16.8081i	−0.761649	+	0.761649i	−0.976620	−	0.214971i	$-0.931034\pi$
$487$	−16.8081	+	16.8081i	−0.761649	+	0.761649i	0.214971	+	0.976620i	$0.431034\pi$
$488$	−1.23760	+	14.1458i	−0.0560234	+	0.640351i
$489$		0			0
$490$	1.67687	−	2.06458i	0.0757532	−	0.0932684i
$491$	0.884081	+	2.42899i	0.0398980	+	0.109619i	0.958042	−	0.286628i	$-0.0925345\pi$
$491$	0.884081	+	2.42899i	0.0398980	+	0.109619i	−0.918144	+	0.396247i	$0.870312\pi$
$492$		0			0
$493$	5.27742	−	7.53694i	0.237683	−	0.339447i
$494$	7.26178	+	12.5778i	0.326723	+	0.565901i
$495$		0			0
$496$	−1.71719	+	2.97426i	−0.0771041	+	0.133548i
$497$	5.58980	+	11.9874i	0.250737	+	0.537707i
$498$		0			0
$499$	22.9688	−	27.3731i	1.02822	−	1.22539i	0.0542986	−	0.998525i	$-0.482708\pi$
$499$	22.9688	−	27.3731i	1.02822	−	1.22539i	0.973926	−	0.226866i	$-0.0728478\pi$
$500$	−11.0782	+	1.50745i	−0.495434	+	0.0674151i
$501$		0			0
$502$	1.53605	−	0.716274i	0.0685575	−	0.0319689i
$503$	−8.13026	−	30.3426i	−0.362511	−	1.35291i	−0.870764	−	0.491701i	$-0.836375\pi$
$503$	−8.13026	−	30.3426i	−0.362511	−	1.35291i	0.508254	−	0.861207i	$-0.330291\pi$
$504$		0			0
$505$	−25.4353	−	24.6345i	−1.13186	−	1.09622i
$506$	16.0682	−	2.83326i	0.714319	−	0.125954i
$507$		0			0
$508$	15.8470	+	7.38960i	0.703099	+	0.327860i
$509$	−3.07523	+	17.4405i	−0.136307	+	0.773037i	0.837633	+	0.546233i	$0.183939\pi$
$509$	−3.07523	+	17.4405i	−0.136307	+	0.773037i	−0.973940	+	0.226804i	$0.927172\pi$
$510$		0			0
$511$	−31.0453	+	26.0501i	−1.37336	+	1.15239i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$			14.1231i			0.622942i
$515$	1.46622	+	7.60237i	0.0646096	+	0.335001i
$516$		0			0
$517$	−0.412616	−	0.589276i	−0.0181468	−	0.0259163i
$518$	13.4449	−	28.8326i	0.590734	−	1.26683i
$519$		0			0
$520$	−10.5545	+	5.12869i	−0.462845	+	0.224908i
$521$	13.1465	−	7.59012i	0.575958	−	0.332529i	−0.183568	−	0.983007i	$-0.558765\pi$
$521$	13.1465	−	7.59012i	0.575958	−	0.332529i	0.759525	+	0.650478i	$0.225431\pi$
$522$		0			0
$523$	5.84084	−	1.56505i	0.255402	−	0.0684348i	−0.128846	−	0.991665i	$-0.541127\pi$
$523$	5.84084	−	1.56505i	0.255402	−	0.0684348i	0.384248	+	0.923230i	$0.374461\pi$
$524$	20.2005	+	7.35237i	0.882461	+	0.321190i
$525$		0			0
$526$	7.70863	+	6.46831i	0.336112	+	0.282032i
$527$	0.545985	+	6.24064i	0.0237835	+	0.271846i
$528$		0			0
$529$	4.94552	−	13.5877i	0.215022	−	0.590769i
$530$	10.4896	+	2.63165i	0.455641	+	0.114312i
$531$		0			0
$532$	7.65001	+	2.04981i	0.331670	+	0.0888707i
$533$	−3.69440	−	2.58685i	−0.160022	−	0.112049i
$534$		0			0
$535$	−1.98589	+	12.4209i	−0.0858577	+	0.537004i
$536$	−4.41754	−	0.778932i	−0.190809	−	0.0336447i
$537$		0			0
$538$	−9.51314	−	0.832292i	−0.410141	−	0.0358827i
$539$	6.64109			0.286052
$540$		0			0
$541$	−13.1395			−0.564913			−0.282456	−	0.959280i	$-0.591149\pi$
$541$	−13.1395			−0.564913			−0.282456	+	0.959280i	$0.591149\pi$
$542$	−0.507637	−	0.0444125i	−0.0218049	−	0.00190768i
$543$		0			0
$544$	−1.79634	−	0.316743i	−0.0770173	−	0.0135802i
$545$	24.8959	−	18.0324i	1.06642	−	0.772424i
$546$		0			0
$547$	11.5585	+	8.09337i	0.494207	+	0.346047i	0.793961	−	0.607969i	$-0.208016\pi$
$547$	11.5585	+	8.09337i	0.494207	+	0.346047i	−0.299754	+	0.954017i	$0.596904\pi$
$548$	−7.69357	−	2.06149i	−0.328653	−	0.0880623i
$549$		0			0
$550$	−20.3606	−	19.0981i	−0.868178	−	0.814346i
$551$	4.77459	−	13.1181i	0.203404	−	0.558849i
$552$		0			0
$553$	−1.06125	−	12.1301i	−0.0451288	−	0.515825i
$554$	3.15666	+	2.64876i	0.134114	+	0.112535i
$555$		0			0
$556$	1.90106	+	0.691929i	0.0806228	+	0.0293443i
$557$	−19.0486	+	5.10405i	−0.807114	+	0.216266i	−0.638705	−	0.769452i	$-0.720530\pi$
$557$	−19.0486	+	5.10405i	−0.807114	+	0.216266i	−0.168409	+	0.985717i	$0.553863\pi$
$558$		0			0
$559$	−5.27194	+	3.04376i	−0.222980	+	0.128737i
$560$	−2.09216	+	6.04734i	−0.0884097	+	0.255547i
$561$		0			0
$562$	−2.08709	+	4.47578i	−0.0880386	+	0.188799i
$563$	−6.42514	−	9.17604i	−0.270787	−	0.386724i	0.660610	−	0.750730i	$-0.270298\pi$
$563$	−6.42514	−	9.17604i	−0.270787	−	0.386724i	−0.931397	+	0.364005i	$0.881409\pi$
$564$		0			0
$565$	−13.7363	+	2.64925i	−0.577892	+	0.111455i
$566$		−	15.9461i		−	0.670263i
$567$		0			0
$568$	−3.26817	−	3.26817i	−0.137129	−	0.137129i
$569$	17.8600	−	14.9863i	0.748731	−	0.628260i	−0.186436	−	0.982467i	$-0.559694\pi$
$569$	17.8600	−	14.9863i	0.748731	−	0.628260i	0.935167	+	0.354207i	$0.115249\pi$
$570$		0			0
$571$	−4.96561	+	28.1614i	−0.207804	+	1.17852i	0.685161	+	0.728391i	$0.259732\pi$
$571$	−4.96561	+	28.1614i	−0.207804	+	1.17852i	−0.892966	+	0.450125i	$0.851379\pi$
$572$	−26.5545	−	12.3826i	−1.11030	−	0.517742i
$573$		0			0
$574$	−2.42201	+	0.427066i	−0.101093	+	0.0178254i
$575$	13.9858	−	4.23124i	0.583250	−	0.176455i
$576$		0			0
$577$	0.709795	+	2.64899i	0.0295491	+	0.110279i	0.979125	−	0.203258i	$-0.0651529\pi$
$577$	0.709795	+	2.64899i	0.0295491	+	0.110279i	−0.949576	+	0.313536i	$0.898486\pi$
$578$	12.3918	−	5.77839i	0.515431	−	0.240350i
$579$		0			0
$580$	10.2974	+	4.60273i	0.427575	+	0.191118i
$581$	−14.9127	+	17.7723i	−0.618685	+	0.737320i
$582$		0			0
$583$	11.4119	+	24.4729i	0.472633	+	1.01357i
$584$	7.08083	−	12.2644i	0.293007	−	0.507502i
$585$		0			0
$586$	9.90060	+	17.1483i	0.408990	+	0.708392i
$587$	9.89672	−	14.1340i	0.408481	−	0.583372i	−0.561220	−	0.827667i	$-0.689668\pi$
$587$	9.89672	−	14.1340i	0.408481	−	0.583372i	0.969701	+	0.244295i	$0.0785565\pi$
$588$		0			0
$589$	3.25080	+	8.93150i	0.133947	+	0.368016i
$590$	−4.44181	−	3.60767i	−0.182866	−	0.148525i
$591$		0			0
$592$	−0.968894	+	11.0745i	−0.0398213	+	0.455160i
$593$	−8.51667	+	8.51667i	−0.349738	+	0.349738i	−0.860012	−	0.510274i	$-0.829544\pi$
$593$	−8.51667	+	8.51667i	−0.349738	+	0.349738i	0.510274	+	0.860012i	$0.329544\pi$
$594$		0			0
$595$	3.20087	+	11.2247i	0.131223	+	0.460166i
$596$	−11.9580	−	14.2510i	−0.489820	−	0.583745i
$597$		0			0
$598$	12.5627	−	8.79651i	0.513728	−	0.359716i
$599$	−21.4880	+	7.82099i	−0.877976	+	0.319557i	−0.741393	−	0.671071i	$-0.765834\pi$
$599$	−21.4880	+	7.82099i	−0.877976	+	0.319557i	−0.136583	+	0.990629i	$0.543612\pi$
$600$		0			0
$601$	2.84165	+	16.1158i	0.115913	+	0.657377i	0.986294	+	0.164998i	$0.0527617\pi$
$601$	2.84165	+	16.1158i	0.115913	+	0.657377i	−0.870381	+	0.492380i	$0.836127\pi$
$602$	−0.859175	+	3.20648i	−0.0350174	+	0.130687i
$603$		0			0
$604$	4.49030	+	2.59248i	0.182708	+	0.105486i
$605$	3.21213	−	44.9906i	0.130592	−	1.82913i
$606$		0			0
$607$	−33.1972	+	2.90438i	−1.34743	+	0.117885i	−0.737918	−	0.674890i	$-0.764191\pi$
$607$	−33.1972	+	2.90438i	−1.34743	+	0.117885i	−0.609514	+	0.792775i	$0.708635\pi$
$608$	−2.75698	+	0.241205i	−0.111810	+	0.00978215i
$609$		0			0
$610$	−23.9938	+	20.7960i	−0.971481	+	0.842007i
$611$	−0.585583	−	0.338087i	−0.0236902	−	0.0136775i
$612$		0			0
$613$	−1.64755	+	6.14875i	−0.0665440	+	0.248346i	−0.991183	−	0.132499i	$-0.957700\pi$
$613$	−1.64755	+	6.14875i	−0.0665440	+	0.248346i	0.924639	+	0.380844i	$0.124367\pi$
$614$	1.15279	+	6.53779i	0.0465228	+	0.263844i
$615$		0			0
$616$	−15.0139	+	5.46462i	−0.604928	+	0.220176i
$617$	−17.6245	+	12.3408i	−0.709536	+	0.496822i	−0.871761	−	0.489932i	$-0.837022\pi$
$617$	−17.6245	+	12.3408i	−0.709536	+	0.496822i	0.162225	+	0.986754i	$0.448133\pi$
$618$		0			0
$619$	−5.99389	−	7.14324i	−0.240915	−	0.287111i	0.632016	−	0.774955i	$-0.282228\pi$
$619$	−5.99389	−	7.14324i	−0.240915	−	0.287111i	−0.872931	+	0.487845i	$0.837783\pi$
$620$	−7.38510	+	2.10597i	−0.296593	+	0.0845777i
$621$		0			0
$622$	−11.9081	+	11.9081i	−0.477472	+	0.477472i
$623$	−3.27037	+	37.3805i	−0.131025	+	1.49762i
$624$		0			0
$625$	−20.1392	−	14.8126i	−0.805567	−	0.592504i
$626$	7.07525	+	19.4391i	0.282784	+	0.776942i
$627$		0			0
$628$	3.23700	−	4.62292i	0.129170	−	0.184475i
$629$	10.1388	+	17.5609i	0.404261	+	0.700200i
$630$		0			0
$631$	23.4299	−	40.5818i	0.932731	−	1.61554i	0.154100	−	0.988055i	$-0.450752\pi$
$631$	23.4299	−	40.5818i	0.932731	−	1.61554i	0.778631	−	0.627482i	$-0.215915\pi$
$632$	1.79821	+	3.85627i	0.0715289	+	0.153394i
$633$		0			0
$634$	−3.61545	+	4.30872i	−0.143588	+	0.171121i
$635$	13.9582	+	36.5218i	0.553914	+	1.44932i
$636$		0			0
$637$	5.65742	−	2.63810i	0.224155	−	0.104525i
$638$	7.28904	+	27.2031i	0.288576	+	1.07698i
$639$		0			0
$640$	−0.0357575	−	2.23578i	−0.00141344	−	0.0883770i
$641$	−43.1919	+	7.61590i	−1.70598	+	0.300810i	−0.939777	−	0.341790i	$-0.888967\pi$
$641$	−43.1919	+	7.61590i	−1.70598	+	0.300810i	−0.766202	+	0.642600i	$0.777856\pi$
$642$		0			0
$643$	18.2910	+	8.52925i	0.721328	+	0.336361i	0.748377	−	0.663273i	$-0.230833\pi$
$643$	18.2910	+	8.52925i	0.721328	+	0.336361i	−0.0270494	+	0.999634i	$0.508611\pi$
$644$	1.45223	−	8.23599i	0.0572258	−	0.324544i
$645$		0			0
$646$	−3.86706	+	3.24485i	−0.152147	+	0.127667i
$647$	−17.1064	−	17.1064i	−0.672521	−	0.672521i	0.285775	−	0.958297i	$-0.407749\pi$
$647$	−17.1064	−	17.1064i	−0.672521	−	0.672521i	−0.958297	+	0.285775i	$0.907749\pi$
$648$		0			0
$649$		−	14.2878i		−	0.560847i
$650$	−24.9313	−	8.18131i	−0.977886	−	0.320897i
$651$		0			0
$652$	−9.37836	−	13.3937i	−0.367285	−	0.524537i
$653$	5.13258	−	11.0069i	0.200854	−	0.430732i	−0.779921	−	0.625879i	$-0.784741\pi$
$653$	5.13258	−	11.0069i	0.200854	−	0.430732i	0.980774	+	0.195147i	$0.0625183\pi$
$654$		0			0
$655$	21.0087	+	43.2344i	0.820877	+	1.68931i
$656$	0.744264	−	0.429701i	0.0290586	−	0.0167770i
$657$		0			0
$658$	−0.356161	+	0.0954331i	−0.0138846	+	0.00372037i
$659$	37.9015	+	13.7950i	1.47643	+	0.537378i	0.949839	−	0.312739i	$-0.101247\pi$
$659$	37.9015	+	13.7950i	1.47643	+	0.537378i	0.526594	+	0.850117i	$0.323469\pi$
$660$		0			0
$661$	−8.10770	−	6.80317i	−0.315353	−	0.264613i	0.471347	−	0.881948i	$-0.343768\pi$
$661$	−8.10770	−	6.80317i	−0.315353	−	0.264613i	−0.786700	+	0.617335i	$0.788212\pi$
$662$	−1.53235	−	17.5148i	−0.0595565	−	0.680734i
$663$		0			0
$664$	2.77277	−	7.61811i	0.107604	−	0.295640i
$665$	9.09881	+	15.1932i	0.352837	+	0.589168i
$666$		0			0
$667$	−14.2388	−	3.81528i	−0.551329	−	0.147728i
$668$	−14.9029	−	10.4352i	−0.576612	−	0.403748i
$669$		0			0
$670$	−5.88380	−	8.12330i	−0.227311	−	0.313830i
$671$	−78.0755	−	13.7668i	−3.01407	−	0.531462i
$672$		0			0
$673$	−15.8202	−	1.38409i	−0.609826	−	0.0533528i	−0.221940	−	0.975060i	$-0.571239\pi$
$673$	−15.8202	−	1.38409i	−0.609826	−	0.0533528i	−0.387886	+	0.921707i	$0.626794\pi$
$674$	−11.4826			−0.442294
$675$		0			0
$676$	−14.5402			−0.559237
$677$	−11.5595	−	1.01133i	−0.444269	−	0.0388685i	−0.137173	−	0.990547i	$-0.543802\pi$
$677$	−11.5595	−	1.01133i	−0.444269	−	0.0388685i	−0.307096	+	0.951679i	$0.599357\pi$
$678$		0			0
$679$	−30.7994	−	5.43076i	−1.18197	−	0.208413i
$680$	−2.39257	−	3.30324i	−0.0917510	−	0.126673i
$681$		0			0
$682$	−15.7070	−	10.9981i	−0.601451	−	0.421141i
$683$	27.0012	+	7.23496i	1.03317	+	0.276838i	0.735282	−	0.677762i	$-0.237050\pi$
$683$	27.0012	+	7.23496i	1.03317	+	0.276838i	0.297892	+	0.954600i	$0.403717\pi$
$684$		0			0
$685$	−9.15062	−	15.2797i	−0.349627	−	0.583808i
$686$	−5.68715	+	15.6253i	−0.217136	+	0.596577i
$687$		0			0
$688$	−0.101100	−	1.15558i	−0.00385442	−	0.0440562i
$689$	19.4432	+	16.3148i	0.740727	+	0.621544i
$690$		0			0
$691$	17.0495	+	6.20552i	0.648595	+	0.236069i	0.645305	−	0.763925i	$-0.276730\pi$
$691$	17.0495	+	6.20552i	0.648595	+	0.236069i	0.00329034	+	0.999995i	$0.498953\pi$
$692$	12.5822	−	3.37140i	0.478304	−	0.128161i
$693$		0			0
$694$	5.46204	−	3.15351i	0.207336	−	0.119706i
$695$	1.97712	+	4.06878i	0.0749964	+	0.154338i
$696$		0			0
$697$	0.662492	−	1.42072i	0.0250937	−	0.0538136i
$698$	−6.81873	−	9.73816i	−0.258093	−	0.368595i
$699$		0			0
$700$	−12.7680	+	6.45870i	−0.482586	+	0.244116i
$701$			16.6910i			0.630411i	0.949023	+	0.315206i	$0.102073\pi$
$701$			16.6910i			0.630411i	−0.949023	+	0.315206i	$0.897927\pi$
$702$		0			0
$703$	21.7548	+	21.7548i	0.820499	+	0.820499i
$704$	4.27695	−	3.58878i	0.161193	−	0.135257i
$705$		0			0
$706$	4.11899	−	23.3599i	0.155020	−	0.879163i
$707$	−41.0710	−	19.1517i	−1.54463	−	0.720275i
$708$		0			0
$709$	−24.9783	+	4.40435i	−0.938081	+	0.165409i	−0.621728	−	0.783233i	$-0.713569\pi$
$709$	−24.9783	+	4.40435i	−0.938081	+	0.165409i	−0.316352	+	0.948642i	$0.602458\pi$
$710$	−0.165267	−	10.3335i	−0.00620237	−	0.387811i
$711$		0			0
$712$	−3.39366	−	12.6653i	−0.127183	−	0.474653i
$713$	9.09620	−	4.24163i	0.340655	−	0.158850i
$714$		0			0
$715$	−23.3895	−	61.1988i	−0.874716	−	2.28871i
$716$	−14.3501	+	17.1018i	−0.536288	+	0.639123i
$717$		0			0
$718$	4.67547	+	10.0266i	0.174487	+	0.374189i
$719$	−3.32620	+	5.76114i	−0.124046	+	0.214854i	−0.921360	−	0.388711i	$-0.872920\pi$
$719$	−3.32620	+	5.76114i	−0.124046	+	0.214854i	0.797314	+	0.603565i	$0.206254\pi$
$720$		0			0
$721$	4.95442	+	8.58131i	0.184512	+	0.319585i
$722$	6.50485	−	9.28989i	0.242085	−	0.345734i
$723$		0			0
$724$	−0.959253	−	2.63553i	−0.0356504	−	0.0979486i
$725$	9.37960	+	23.4121i	0.348350	+	0.869504i
$726$		0			0
$727$	2.05205	−	23.4550i	0.0761062	−	0.869898i	−0.858174	−	0.513359i	$-0.828401\pi$
$727$	2.05205	−	23.4550i	0.0761062	−	0.869898i	0.934280	−	0.356539i	$-0.116043\pi$
$728$	−10.6193	+	10.6193i	−0.393578	+	0.393578i
$729$		0			0
$730$	30.4524	−	8.68395i	1.12710	−	0.321408i
$731$	−1.36007	−	1.62087i	−0.0503040	−	0.0599499i
$732$		0			0
$733$	7.04551	−	4.93332i	0.260232	−	0.182216i	−0.436178	−	0.899860i	$-0.643668\pi$
$733$	7.04551	−	4.93332i	0.260232	−	0.182216i	0.696410	+	0.717644i	$0.254779\pi$
$734$	−24.7439	+	9.00604i	−0.913314	+	0.332419i
$735$		0			0
$736$	0.507465	+	2.87798i	0.0187054	+	0.106084i
$737$	6.48195	−	24.1910i	0.238766	−	0.891085i
$738$		0			0
$739$	29.8191	+	17.2160i	1.09691	+	0.633303i	0.935408	−	0.353570i	$-0.115032\pi$
$739$	29.8191	+	17.2160i	1.09691	+	0.633303i	0.161504	+	0.986872i	$0.448366\pi$
$740$	−18.7844	+	16.2809i	−0.690526	+	0.598496i
$741$		0			0
$742$	13.7881	−	1.20630i	0.506176	−	0.0442846i
$743$	6.41979	−	0.561659i	0.235519	−	0.0206053i	0.0312150	−	0.999513i	$-0.490062\pi$
$743$	6.41979	−	0.561659i	0.235519	−	0.0206053i	0.204304	+	0.978907i	$0.434507\pi$
$744$		0			0
$745$	2.96240	−	41.4928i	0.108534	−	1.52018i
$746$	−14.3069	−	8.26007i	−0.523812	−	0.302423i
$747$		0			0
$748$	2.63580	−	9.83694i	0.0963744	−	0.359674i
$749$	2.79543	+	15.8537i	0.102143	+	0.579281i
$750$		0			0
$751$	−29.6954	+	10.8082i	−1.08360	+	0.394398i	−0.821246	−	0.570574i	$-0.806721\pi$
$751$	−29.6954	+	10.8082i	−1.08360	+	0.394398i	−0.262353	+	0.964972i	$0.584499\pi$
$752$	0.105545	−	0.0739036i	0.00384884	−	0.00269499i
$753$		0			0
$754$	17.0155	+	20.2783i	0.619668	+	0.738492i
$755$	3.17942	+	11.1494i	0.115711	+	0.405769i
$756$		0			0
$757$	−29.3556	+	29.3556i	−1.06695	+	1.06695i	−0.0693558	+	0.997592i	$0.522094\pi$
$757$	−29.3556	+	29.3556i	−1.06695	+	1.06695i	−0.997592	+	0.0693558i	$0.977906\pi$
$758$	0.945896	−	10.8116i	0.0343565	−	0.392696i
$759$		0			0
$760$	−4.80356	−	3.90148i	−0.174243	−	0.141522i
$761$	13.1733	+	36.1935i	0.477533	+	1.31201i	0.911581	+	0.411122i	$0.134863\pi$
$761$	13.1733	+	36.1935i	0.477533	+	1.31201i	−0.434047	+	0.900890i	$0.642915\pi$
$762$		0			0
$763$	22.5655	−	32.2269i	0.816926	−	1.16669i
$764$	7.23255	+	12.5272i	0.261665	+	0.453216i
$765$		0			0
$766$	0.565454	−	0.979395i	0.0204307	−	0.0353870i
$767$	−5.67569	−	12.1715i	−0.204937	−	0.439489i
$768$		0			0
$769$	−7.70368	+	9.18089i	−0.277802	+	0.331071i	−0.886846	−	0.462065i	$-0.847109\pi$
$769$	−7.70368	+	9.18089i	−0.277802	+	0.331071i	0.609044	+	0.793136i	$0.291553\pi$
$770$	−32.6167	−	14.5790i	−1.17542	−	0.525392i
$771$		0			0
$772$	−23.0138	+	10.7315i	−0.828284	+	0.386235i
$773$	4.87067	+	18.1776i	0.175186	+	0.653802i	0.996520	+	0.0833549i	$0.0265635\pi$
$773$	4.87067	+	18.1776i	0.175186	+	0.653802i	−0.821334	+	0.570447i	$0.806770\pi$
$774$		0			0
$775$	−15.1383	−	8.10600i	−0.543782	−	0.291176i
$776$	10.7625	−	1.89772i	0.386351	−	0.0681242i
$777$		0			0
$778$	−4.65754	−	2.17185i	−0.166981	−	0.0778644i
$779$	0.413006	−	2.34227i	0.0147975	−	0.0839207i
$780$		0			0
$781$	19.7676	−	16.5870i	0.707340	−	0.593528i
$782$	3.76927	+	3.76927i	0.134789	+	0.134789i
$783$		0			0
$784$			1.18949i			0.0424817i
$785$	12.3910	−	2.38978i	0.442254	−	0.0852949i
$786$		0			0
$787$	29.3155	+	41.8668i	1.04498	+	1.49239i	0.860430	+	0.509568i	$0.170195\pi$
$787$	29.3155	+	41.8668i	1.04498	+	1.49239i	0.184553	+	0.982823i	$0.440916\pi$
$788$	−9.00444	+	19.3101i	−0.320770	+	0.687893i
$789$		0			0
$790$	−3.11070	+	8.99141i	−0.110674	+	0.319900i
$791$	−15.5051	+	8.95189i	−0.551299	+	0.318293i
$792$		0			0
$793$	−71.9798	+	19.2869i	−2.55608	+	0.684899i
$794$	−16.9293	−	6.16174i	−0.600797	−	0.218672i
$795$		0			0
$796$	5.34253	+	4.48291i	0.189361	+	0.158893i
$797$	−0.703754	−	8.04394i	−0.0249282	−	0.284931i	−0.998419	−	0.0562057i	$-0.982100\pi$
$797$	−0.703754	−	8.04394i	−0.0249282	−	0.284931i	0.973491	−	0.228725i	$-0.0734558\pi$
$798$		0			0
$799$	0.0803827	−	0.220850i	0.00284374	−	0.00781310i
$800$	3.42067	−	3.64679i	0.120939	−	0.128933i
$801$		0			0
$802$	16.3165	+	4.37200i	0.576157	+	0.154381i
$803$	64.7677	+	45.3508i	2.28560	+	1.60040i
$804$		0			0
$805$	15.1449	−	10.9697i	0.533789	−	0.386630i
$806$	−17.7494	−	3.12969i	−0.625195	−	0.110239i
$807$		0			0
$808$	15.7752	+	1.38015i	0.554971	+	0.0485536i
$809$	16.1277			0.567020			0.283510	−	0.958969i	$-0.408501\pi$
$809$	16.1277			0.567020			0.283510	+	0.958969i	$0.408501\pi$
$810$		0			0
$811$	26.3024			0.923603			0.461801	−	0.886983i	$-0.347203\pi$
$811$	26.3024			0.923603			0.461801	+	0.886983i	$0.347203\pi$
$812$	14.3803	+	1.25811i	0.504648	+	0.0441510i
$813$		0			0
$814$	−61.1240	−	10.7778i	−2.14239	−	0.377762i
$815$	5.77220	−	36.1027i	0.202191	−	1.26462i
$816$		0			0
$817$	−2.62973	−	1.84136i	−0.0920027	−	0.0644210i
$818$	−23.8529	−	6.39135i	−0.833995	−	0.223468i
$819$		0			0
$820$	1.86392	+	0.467621i	0.0650908	+	0.0163300i
$821$	−7.03161	+	19.3192i	−0.245405	+	0.674244i	0.754436	+	0.656374i	$0.227911\pi$
$821$	−7.03161	+	19.3192i	−0.245405	+	0.674244i	−0.999840	+	0.0178700i	$0.994312\pi$
$822$		0			0
$823$	−0.973719	−	11.1297i	−0.0339417	−	0.387956i	−0.994098	−	0.108490i	$-0.965398\pi$
$823$	−0.973719	−	11.1297i	−0.0339417	−	0.387956i	0.960156	−	0.279465i	$-0.0901572\pi$
$824$	−2.65246	−	2.22568i	−0.0924028	−	0.0775351i
$825$		0			0
$826$	−6.88178	−	2.50476i	−0.239448	−	0.0871519i
$827$	−5.39379	+	1.44526i	−0.187561	+	0.0502567i	−0.351377	−	0.936234i	$-0.614286\pi$
$827$	−5.39379	+	1.44526i	−0.187561	+	0.0502567i	0.163816	+	0.986491i	$0.447620\pi$
$828$		0			0
$829$	−12.3780	+	7.14645i	−0.429906	+	0.248207i	−0.699307	−	0.714822i	$-0.746508\pi$
$829$	−12.3780	+	7.14645i	−0.429906	+	0.248207i	0.269400	+	0.963028i	$0.413175\pi$
$830$	16.3048	−	7.92291i	0.565948	−	0.275008i
$831$		0			0
$832$	2.21785	−	4.75619i	0.0768900	−	0.164891i
$833$	1.24448	+	1.77730i	0.0431186	+	0.0615798i
$834$		0			0
$835$	−7.70395	−	39.9450i	−0.266606	−	1.38235i
$836$		−	15.4515i		−	0.534400i
$837$		0			0
$838$	6.84810	+	6.84810i	0.236564	+	0.236564i
$839$	−39.1140	+	32.8205i	−1.35036	+	1.13309i	−0.371534	+	0.928419i	$0.621168\pi$
$839$	−39.1140	+	32.8205i	−1.35036	+	1.13309i	−0.978831	+	0.204671i	$0.934388\pi$
$840$		0			0
$841$	−0.617466	+	3.50182i	−0.0212919	+	0.120752i
$842$	25.2637	+	11.7806i	0.870644	+	0.405988i
$843$		0			0
$844$	−5.13000	+	0.904558i	−0.176582	+	0.0311362i
$845$	−23.3547	−	22.6194i	−0.803427	−	0.778132i
$846$		0			0
$847$	−14.9405	−	55.7588i	−0.513362	−	1.91589i
$848$	−4.38335	+	2.04399i	−0.150525	+	0.0701909i
$849$		0			0
$850$	1.29568	−	9.02774i	0.0444416	−	0.309649i
$851$	20.8826	−	24.8869i	0.715845	−	0.853111i
$852$		0			0
$853$	−16.1800	−	34.6982i	−0.553994	−	1.18804i	−0.961491	−	0.274837i	$-0.911376\pi$
$853$	−16.1800	−	34.6982i	−0.553994	−	1.18804i	0.407497	−	0.913207i	$-0.366402\pi$
$854$	−20.3180	+	35.1919i	−0.695269	+	1.20424i
$855$		0			0
$856$	−2.81268	−	4.87171i	−0.0961355	−	0.166511i
$857$	8.10463	−	11.5746i	0.276849	−	0.395381i	−0.656515	−	0.754313i	$-0.727970\pi$
$857$	8.10463	−	11.5746i	0.276849	−	0.395381i	0.933364	+	0.358932i	$0.116859\pi$
$858$		0			0
$859$	4.19609	+	11.5287i	0.143169	+	0.393353i	0.990464	−	0.137769i	$-0.0439931\pi$
$859$	4.19609	+	11.5287i	0.143169	+	0.393353i	−0.847296	+	0.531121i	$0.821771\pi$
$860$	1.63530	−	2.01340i	0.0557631	−	0.0686563i
$861$		0			0
$862$	2.15845	−	24.6712i	0.0735172	−	0.840305i
$863$	11.5506	−	11.5506i	0.393187	−	0.393187i	−0.482635	−	0.875822i	$-0.660320\pi$
$863$	11.5506	−	11.5506i	0.393187	−	0.393187i	0.875822	+	0.482635i	$0.160320\pi$
$864$		0			0
$865$	25.4546	+	14.1584i	0.865481	+	0.481399i
$866$	20.7396	+	24.7165i	0.704760	+	0.839900i
$867$		0			0
$868$	−8.05084	+	5.63726i	−0.273263	+	0.191341i
$869$	−22.3233	+	8.12500i	−0.757265	+	0.275622i
$870$		0			0
$871$	−4.08774	−	23.1827i	−0.138508	−	0.785516i
$872$	−3.55813	+	13.2791i	−0.120493	+	0.449688i
$873$		0			0
$874$	7.00417	+	4.04386i	0.236920	+	0.136786i
$875$	−30.5558	−	9.48851i	−1.03297	−	0.320770i
$876$		0			0
$877$	44.5980	−	3.90182i	1.50597	−	0.131755i	0.695920	−	0.718119i	$-0.254997\pi$
$877$	44.5980	−	3.90182i	1.50597	−	0.131755i	0.810048	+	0.586364i	$0.199441\pi$
$878$	38.4061	−	3.36009i	1.29614	−	0.113398i
$879$		0			0
$880$	12.4526	+	0.889061i	0.419778	+	0.0299702i
$881$	14.1208	+	8.15265i	0.475742	+	0.274670i	0.718640	−	0.695382i	$-0.244765\pi$
$881$	14.1208	+	8.15265i	0.475742	+	0.274670i	−0.242898	+	0.970052i	$0.578098\pi$
$882$		0			0
$883$	15.1025	−	56.3634i	0.508241	−	1.89678i	0.0709036	−	0.997483i	$-0.477412\pi$
$883$	15.1025	−	56.3634i	0.508241	−	1.89678i	0.437337	−	0.899298i	$-0.355922\pi$
$884$	−1.66223	−	9.42695i	−0.0559067	−	0.317063i
$885$		0			0
$886$	16.3565	−	5.95330i	0.549509	−	0.200005i
$887$	22.7541	−	15.9326i	0.764008	−	0.534964i	−0.125385	−	0.992108i	$-0.540017\pi$
$887$	22.7541	−	15.9326i	0.764008	−	0.534964i	0.889393	+	0.457144i	$0.151128\pi$
$888$		0			0
$889$	32.1639	+	38.3314i	1.07874	+	1.28559i
$890$	14.2519	−	25.6227i	0.477724	−	0.858874i
$891$		0			0
$892$	1.00265	−	1.00265i	0.0335711	−	0.0335711i
$893$	0.0310785	−	0.355229i	0.00104000	−	0.0118873i
$894$		0			0
$895$	−49.6538	+	5.14547i	−1.65974	+	0.171994i
$896$	−0.978769	−	2.68914i	−0.0326984	−	0.0898380i
$897$		0			0
$898$	−1.17494	+	1.67799i	−0.0392084	+	0.0559953i
$899$	8.66188	+	15.0028i	0.288890	+	0.500372i
$900$		0			0
$901$	−4.41100	+	7.64008i	−0.146952	+	0.254528i
$902$	2.02780	+	4.34862i	0.0675182	+	0.144793i
$903$		0			0
$904$	4.02146	−	4.79259i	0.133752	−	0.159399i
$905$	2.55919	−	5.72550i	0.0850704	−	0.190322i
$906$		0			0
$907$	−23.4690	+	10.9438i	−0.779274	+	0.363381i	−0.771206	−	0.636586i	$-0.780346\pi$
$907$	−23.4690	+	10.9438i	−0.779274	+	0.363381i	−0.00806823	+	0.999967i	$0.502568\pi$
$908$	1.07835	+	4.02447i	0.0357864	+	0.133557i
$909$		0			0
$910$	−33.5769	+	0.537005i	−1.11306	+	0.0178015i
$911$	−21.3358	+	3.76207i	−0.706886	+	0.124643i	−0.515522	−	0.856876i	$-0.672402\pi$
$911$	−21.3358	+	3.76207i	−0.706886	+	0.124643i	−0.191364	+	0.981519i	$0.561291\pi$
$912$		0			0
$913$	41.0220	+	19.1289i	1.35763	+	0.633074i
$914$	2.15781	−	12.2376i	0.0713740	−	0.404782i
$915$		0			0
$916$	−5.66397	+	4.75264i	−0.187143	+	0.157032i
$917$	43.5000	+	43.5000i	1.43650	+	1.43650i
$918$		0			0
$919$		−	16.8649i		−	0.556321i	−0.960535	−	0.278161i	$-0.910275\pi$
$919$		−	16.8649i		−	0.556321i	0.960535	−	0.278161i	$-0.0897248\pi$
$920$	−3.66203	+	5.41211i	−0.120734	+	0.178432i
$921$		0			0
$922$	2.37573	+	3.39290i	0.0782406	+	0.111739i
$923$	10.2506	−	21.9826i	0.337404	−	0.723566i
$924$		0			0
$925$	−55.4992	−	3.07127i	−1.82480	−	0.100983i
$926$	−20.0625	+	11.5831i	−0.659293	+	0.380643i
$927$		0			0
$928$	−4.87234	+	1.30554i	−0.159942	+	0.0428565i
$929$	17.5792	+	6.39829i	0.576753	+	0.209921i	0.613893	−	0.789389i	$-0.289602\pi$
$929$	17.5792	+	6.39829i	0.576753	+	0.209921i	−0.0371399	+	0.999310i	$0.511825\pi$
$930$		0			0
$931$	2.52176	+	2.11601i	0.0826473	+	0.0693493i
$932$	−1.36932	−	15.6514i	−0.0448535	−	0.512677i
$933$		0			0
$934$	−3.59155	+	9.86771i	−0.117519	+	0.322881i
$935$	19.5365	−	11.6999i	0.638913	−	0.382628i
$936$		0			0
$937$	25.8098	+	6.91572i	0.843170	+	0.225927i	0.654451	−	0.756105i	$-0.272900\pi$
$937$	25.8098	+	6.91572i	0.843170	+	0.225927i	0.188719	+	0.982031i	$0.439567\pi$
$938$	−10.5153	−	7.36290i	−0.343337	−	0.240407i
$939$		0			0
$940$	0.284498	+	0.0454863i	0.00927929	+	0.00148360i
$941$	39.0693	+	6.88897i	1.27362	+	0.224574i	0.769270	−	0.638924i	$-0.220620\pi$
$941$	39.0693	+	6.88897i	1.27362	+	0.224574i	0.504352	+	0.863498i	$0.331731\pi$
$942$		0			0
$943$	−2.50194	−	0.218891i	−0.0814743	−	0.00712808i
$944$	2.55910			0.0832915
$945$		0			0
$946$	6.47645			0.210567
$947$	−31.7992	−	2.78207i	−1.03333	−	0.0904051i	−0.442150	−	0.896941i	$-0.645784\pi$
$947$	−31.7992	−	2.78207i	−1.03333	−	0.0904051i	−0.591185	+	0.806536i	$0.701340\pi$
$948$		0			0
$949$	73.1895	+	12.9053i	2.37583	+	0.418923i
$950$	−1.64623	−	13.7393i	−0.0534106	−	0.445762i
$951$		0			0
$952$	−4.27592	−	2.99403i	−0.138583	−	0.0970371i
$953$	−11.1200	−	2.97959i	−0.360212	−	0.0965185i	0.0741740	−	0.997245i	$-0.476368\pi$
$953$	−11.1200	−	2.97959i	−0.360212	−	0.0965185i	−0.434386	+	0.900727i	$0.643035\pi$
$954$		0			0
$955$	−7.87081	+	31.3727i	−0.254693	+	1.01520i
$956$	3.61354	−	9.92811i	0.116870	−	0.321098i
$957$		0			0
$958$	2.57936	+	29.4822i	0.0833354	+	0.952528i
$959$	−17.4609	−	14.6514i	−0.563841	−	0.473119i
$960$		0			0
$961$	18.0468	+	6.56851i	0.582156	+	0.211887i
$962$	−56.3518	+	15.0994i	−1.81685	+	0.486824i
$963$		0			0
$964$	−4.23311	+	2.44398i	−0.136339	+	0.0787155i
$965$	−53.6597	−	18.5643i	−1.72737	−	0.597605i
$966$		0			0
$967$	5.55165	−	11.9056i	0.178529	−	0.382857i	−0.796596	−	0.604512i	$-0.793368\pi$
$967$	5.55165	−	11.9056i	0.178529	−	0.382857i	0.975125	+	0.221655i	$0.0711459\pi$
$968$	11.5700	+	16.5236i	0.371873	+	0.531090i
$969$		0			0
$970$	20.2392	+	13.6946i	0.649840	+	0.439706i
$971$		−	36.4290i		−	1.16906i	−0.811372	−	0.584530i	$-0.801279\pi$
$971$		−	36.4290i		−	1.16906i	0.811372	−	0.584530i	$-0.198721\pi$
$972$		0			0
$973$	4.09377	+	4.09377i	0.131240	+	0.131240i
$974$	18.2091	−	15.2792i	0.583457	−	0.489578i
$975$		0			0
$976$	2.46578	−	13.9841i	0.0789276	−	0.447621i
$977$	46.5478	+	21.7056i	1.48919	+	0.694423i	0.985534	−	0.169479i	$-0.0542083\pi$
$977$	46.5478	+	21.7056i	1.48919	+	0.694423i	0.503661	+	0.863901i	$0.331986\pi$
$978$		0			0
$979$	72.0948	−	12.7123i	2.30416	−	0.406285i
$980$	−1.85043	+	1.91058i	−0.0591097	+	0.0610312i
$981$		0			0
$982$	−0.669016	−	2.49680i	−0.0213492	−	0.0796762i
$983$	−15.1599	+	7.06918i	−0.483526	+	0.225472i	−0.649067	−	0.760731i	$-0.724841\pi$
$983$	−15.1599	+	7.06918i	−0.483526	+	0.225472i	0.165541	+	0.986203i	$0.447063\pi$
$984$		0			0
$985$	−44.5029	+	17.0085i	−1.41798	+	0.541935i
$986$	−5.91423	+	7.04830i	−0.188347	+	0.224464i
$987$		0			0
$988$	−6.13793	−	13.1628i	−0.195273	−	0.418765i
$989$	−1.69497	+	2.93578i	−0.0538970	+	0.0933524i
$990$		0			0
$991$	17.8367	+	30.8941i	0.566603	+	0.981385i	0.996899	+	0.0786969i	$0.0250759\pi$
$991$	17.8367	+	30.8941i	0.566603	+	0.981385i	−0.430296	+	0.902688i	$0.641591\pi$
$992$	1.96988	−	2.81328i	0.0625437	−	0.0893217i
$993$		0			0
$994$	−4.52376	−	12.4289i	−0.143485	−	0.394222i
$995$	1.60743	+	15.5117i	0.0509589	+	0.491753i
$996$		0			0
$997$	1.26033	−	14.4056i	0.0399150	−	0.456231i	−0.949768	−	0.312955i	$-0.898681\pi$
$997$	1.26033	−	14.4056i	0.0399150	−	0.456231i	0.989683	−	0.143275i	$-0.0457635\pi$
$998$	−25.2671	+	25.2671i	−0.799817	+	0.799817i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.6		216
3.2	odd	2		270.2.r.a.113.16	✓	216
5.2	odd	4	inner	810.2.s.a.287.15		216
15.2	even	4		270.2.r.a.167.4	yes	216
27.11	odd	18	inner	810.2.s.a.683.15		216
27.16	even	9		270.2.r.a.173.4	yes	216
135.92	even	36	inner	810.2.s.a.197.6		216
135.97	odd	36		270.2.r.a.227.16	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.16	✓	216	3.2	odd	2
270.2.r.a.167.4	yes	216	15.2	even	4
270.2.r.a.173.4	yes	216	27.16	even	9
270.2.r.a.227.16	yes	216	135.97	odd	36
810.2.s.a.197.6		216	135.92	even	36	inner
810.2.s.a.287.15		216	5.2	odd	4	inner
810.2.s.a.683.15		216	27.11	odd	18	inner
810.2.s.a.773.6		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)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.31168 + 1.81094i) q^{5} +(2.34419 + 1.64142i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.31168 + 1.81094i) q^{5} +(2.34419 + 1.64142i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-1.14886 - 1.91837i) q^{10} +(1.90955 - 5.24645i) q^{11} +(-0.457382 - 5.22790i) q^{13} +(-2.19221 - 1.83948i) q^{14} +(0.939693 + 0.342020i) q^{16} +(1.76190 - 0.472099i) q^{17} +(2.39674 - 1.38376i) q^{19} +(0.977290 + 2.01119i) q^{20} +(-2.35954 + 5.06006i) q^{22} +(-1.67621 - 2.39387i) q^{23} +(-1.55898 + 4.75075i) q^{25} +5.24787i q^{26} +(2.02355 + 2.02355i) q^{28} +(3.86410 - 3.24236i) q^{29} +(-0.596374 + 3.38220i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-1.79634 + 0.316743i) q^{34} +(0.102328 + 6.39820i) q^{35} +(2.87724 + 10.7380i) q^{37} +(-2.50822 + 1.16960i) q^{38} +(-0.798284 - 2.08872i) q^{40} +(0.552413 - 0.658340i) q^{41} +(-0.490236 - 1.05131i) q^{43} +(2.79158 - 4.83516i) q^{44} +(1.46119 + 2.53085i) q^{46} +(0.0739036 - 0.105545i) q^{47} +(0.406828 + 1.11775i) q^{49} +(1.96710 - 4.59679i) q^{50} +(0.457382 - 5.22790i) q^{52} +(-3.41992 + 3.41992i) q^{53} +(12.0057 - 3.42360i) q^{55} +(-1.83948 - 2.19221i) q^{56} +(-4.13198 + 2.89325i) q^{58} +(2.40477 - 0.875263i) q^{59} +(-2.46578 - 13.9841i) q^{61} +(0.888883 - 3.31736i) q^{62} +(0.866025 + 0.500000i) q^{64} +(8.86746 - 7.68564i) q^{65} +(4.46862 - 0.390954i) q^{67} +(1.81711 - 0.158976i) q^{68} +(0.455701 - 6.38277i) q^{70} +(4.00268 + 2.31095i) q^{71} +(-3.66531 + 13.6791i) q^{73} +(-1.93041 - 10.9479i) q^{74} +(2.60061 - 0.946546i) q^{76} +(13.0880 - 9.16430i) q^{77} +(-2.73501 - 3.25946i) q^{79} +(0.613202 + 2.15034i) q^{80} +(-0.607689 + 0.607689i) q^{82} +(-0.706574 + 8.07618i) q^{83} +(3.16599 + 2.57144i) q^{85} +(0.396742 + 1.09004i) q^{86} +(-3.20237 + 4.57345i) q^{88} +(6.55605 + 11.3554i) q^{89} +(7.50899 - 13.0060i) q^{91} +(-1.23505 - 2.64857i) q^{92} +(-0.0828213 + 0.0987026i) q^{94} +(5.64966 + 2.52529i) q^{95} +(-9.90462 + 4.61860i) q^{97} +(-0.307862 - 1.14896i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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

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Representations

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Database

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