LMFDB - Embedded newform 810.2.s.a.773.8

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			773.8
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.00125 - 0.997503i) q^{5} +(2.07619 + 1.45376i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.00125 - 0.997503i) q^{5} +(2.07619 + 1.45376i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.08057 + 0.819287i) q^{10} +(1.56319 - 4.29482i) q^{11} +(0.388268 + 4.43792i) q^{13} +(-1.94158 - 1.62918i) q^{14} +(0.939693 + 0.342020i) q^{16} +(3.33214 - 0.892843i) q^{17} +(0.649453 - 0.374962i) q^{19} +(2.14406 - 0.634835i) q^{20} +(-1.93156 + 4.14224i) q^{22} +(0.184128 + 0.262962i) q^{23} +(3.00998 - 3.99250i) q^{25} -4.45487i q^{26} +(1.79220 + 1.79220i) q^{28} +(-7.59485 + 6.37284i) q^{29} +(0.402651 - 2.28354i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-3.39727 + 0.599031i) q^{34} +(5.60510 + 0.838335i) q^{35} +(-2.33615 - 8.71863i) q^{37} +(-0.679661 + 0.316931i) q^{38} +(-2.19123 + 0.445553i) q^{40} +(-5.59486 + 6.66770i) q^{41} +(5.41671 + 11.6162i) q^{43} +(2.28523 - 3.95813i) q^{44} +(-0.160508 - 0.278009i) q^{46} +(2.83852 - 4.05383i) q^{47} +(-0.197010 - 0.541282i) q^{49} +(-3.34649 + 3.71497i) q^{50} +(-0.388268 + 4.43792i) q^{52} +(6.98671 - 6.98671i) q^{53} +(-1.15577 - 10.1543i) q^{55} +(-1.62918 - 1.94158i) q^{56} +(8.12138 - 5.68665i) q^{58} +(4.25217 - 1.54766i) q^{59} +(-0.193936 - 1.09986i) q^{61} +(-0.600142 + 2.23976i) q^{62} +(0.866025 + 0.500000i) q^{64} +(5.20385 + 8.49407i) q^{65} +(8.09502 - 0.708223i) q^{67} +(3.43655 - 0.300659i) q^{68} +(-5.51070 - 1.32366i) q^{70} +(-1.12339 - 0.648590i) q^{71} +(0.981783 - 3.66406i) q^{73} +(1.56738 + 8.88907i) q^{74} +(0.704697 - 0.256489i) q^{76} +(9.48911 - 6.64435i) q^{77} +(3.09680 + 3.69062i) q^{79} +(2.22172 - 0.252879i) q^{80} +(6.15470 - 6.15470i) q^{82} +(-0.504523 + 5.76673i) q^{83} +(5.77781 - 5.11061i) q^{85} +(-4.38368 - 12.0441i) q^{86} +(-2.62150 + 3.74389i) q^{88} +(-3.81802 - 6.61301i) q^{89} +(-5.64556 + 9.77840i) q^{91} +(0.135668 + 0.290940i) q^{92} +(-3.18104 + 3.79101i) q^{94} +(0.925690 - 1.39822i) q^{95} +(2.43551 - 1.13570i) q^{97} +(0.149085 + 0.556392i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.00125	−	0.997503i	0.894985	−	0.446097i
$5$	2.00125	−	0.997503i	0.894985	−	0.446097i
$6$		0			0
$7$	2.07619	+	1.45376i	0.784725	+	0.549470i	0.895861	−	0.444335i	$-0.146560\pi$
$7$	2.07619	+	1.45376i	0.784725	+	0.549470i	−0.111136	+	0.993805i	$0.535449\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	−2.08057	+	0.819287i	−0.657934	+	0.259081i
$11$	1.56319	−	4.29482i	0.471318	−	1.29494i	−0.445375	−	0.895344i	$-0.646929\pi$
$11$	1.56319	−	4.29482i	0.471318	−	1.29494i	0.916693	−	0.399592i	$-0.130848\pi$
$12$		0			0
$13$	0.388268	+	4.43792i	0.107686	+	1.23086i	0.837202	+	0.546894i	$0.184190\pi$
$13$	0.388268	+	4.43792i	0.107686	+	1.23086i	−0.729516	+	0.683964i	$0.760255\pi$
$14$	−1.94158	−	1.62918i	−0.518910	−	0.435417i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	3.33214	−	0.892843i	0.808162	−	0.216546i	0.168997	−	0.985617i	$-0.445947\pi$
$17$	3.33214	−	0.892843i	0.808162	−	0.216546i	0.639164	+	0.769070i	$0.279280\pi$
$18$		0			0
$19$	0.649453	−	0.374962i	0.148995	−	0.0860221i	−0.423649	−	0.905826i	$-0.639251\pi$
$19$	0.649453	−	0.374962i	0.148995	−	0.0860221i	0.572644	+	0.819804i	$0.305918\pi$
$20$	2.14406	−	0.634835i	0.479426	−	0.141954i
$21$		0			0
$22$	−1.93156	+	4.14224i	−0.411809	+	0.883127i
$23$	0.184128	+	0.262962i	0.0383933	+	0.0548313i	0.837890	−	0.545839i	$-0.183789\pi$
$23$	0.184128	+	0.262962i	0.0383933	+	0.0548313i	−0.799496	+	0.600671i	$0.794900\pi$
$24$		0			0
$25$	3.00998	−	3.99250i	0.601995	−	0.798499i
$26$		−	4.45487i		−	0.873672i
$27$		0			0
$28$	1.79220	+	1.79220i	0.338694	+	0.338694i
$29$	−7.59485	+	6.37284i	−1.41033	+	1.18341i	−0.454040	+	0.890982i	$0.650018\pi$
$29$	−7.59485	+	6.37284i	−1.41033	+	1.18341i	−0.956289	+	0.292424i	$0.905538\pi$
$30$		0			0
$31$	0.402651	−	2.28354i	0.0723182	−	0.410137i	−0.927061	−	0.374910i	$-0.877674\pi$
$31$	0.402651	−	2.28354i	0.0723182	−	0.410137i	0.999379	−	0.0352266i	$-0.0112153\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	−3.39727	+	0.599031i	−0.582627	+	0.102733i
$35$	5.60510	+	0.838335i	0.947434	+	0.141704i
$36$		0			0
$37$	−2.33615	−	8.71863i	−0.384061	−	1.43333i	−0.839642	−	0.543140i	$-0.817235\pi$
$37$	−2.33615	−	8.71863i	−0.384061	−	1.43333i	0.455581	−	0.890194i	$-0.349432\pi$
$38$	−0.679661	+	0.316931i	−0.110256	+	0.0514130i
$39$		0			0
$40$	−2.19123	+	0.445553i	−0.346464	+	0.0704481i
$41$	−5.59486	+	6.66770i	−0.873771	+	1.04132i	0.125020	+	0.992154i	$0.460101\pi$
$41$	−5.59486	+	6.66770i	−0.873771	+	1.04132i	−0.998791	+	0.0491653i	$0.984344\pi$
$42$		0			0
$43$	5.41671	+	11.6162i	0.826041	+	1.77145i	0.605073	+	0.796170i	$0.293144\pi$
$43$	5.41671	+	11.6162i	0.826041	+	1.77145i	0.220968	+	0.975281i	$0.429078\pi$
$44$	2.28523	−	3.95813i	0.344511	−	0.596710i
$45$		0			0
$46$	−0.160508	−	0.278009i	−0.0236657	−	0.0409902i
$47$	2.83852	−	4.05383i	0.414041	−	0.591312i	−0.556915	−	0.830569i	$-0.688015\pi$
$47$	2.83852	−	4.05383i	0.414041	−	0.591312i	0.970956	+	0.239257i	$0.0769040\pi$
$48$		0			0
$49$	−0.197010	−	0.541282i	−0.0281443	−	0.0773259i
$50$	−3.34649	+	3.71497i	−0.473266	+	0.525376i
$51$		0			0
$52$	−0.388268	+	4.43792i	−0.0538430	+	0.615429i
$53$	6.98671	−	6.98671i	0.959699	−	0.959699i	−0.0395200	−	0.999219i	$-0.512583\pi$
$53$	6.98671	−	6.98671i	0.959699	−	0.959699i	0.999219	+	0.0395200i	$0.0125829\pi$
$54$		0			0
$55$	−1.15577	−	10.1543i	−0.155844	−	1.36920i
$56$	−1.62918	−	1.94158i	−0.217709	−	0.259455i
$57$		0			0
$58$	8.12138	−	5.68665i	1.06639	−	0.746694i
$59$	4.25217	−	1.54766i	0.553586	−	0.201489i	−0.0500531	−	0.998747i	$-0.515939\pi$
$59$	4.25217	−	1.54766i	0.553586	−	0.201489i	0.603639	+	0.797258i	$0.293717\pi$
$60$		0			0
$61$	−0.193936	−	1.09986i	−0.0248309	−	0.140823i	0.969872	−	0.243615i	$-0.0783334\pi$
$61$	−0.193936	−	1.09986i	−0.0248309	−	0.140823i	−0.994703	+	0.102792i	$0.967222\pi$
$62$	−0.600142	+	2.23976i	−0.0762182	+	0.284450i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	5.20385	+	8.49407i	0.645459	+	1.05356i
$66$		0			0
$67$	8.09502	−	0.708223i	0.988965	−	0.0865232i	0.418821	−	0.908069i	$-0.362443\pi$
$67$	8.09502	−	0.708223i	0.988965	−	0.0865232i	0.570143	+	0.821545i	$0.306888\pi$
$68$	3.43655	−	0.300659i	0.416743	−	0.0364603i
$69$		0			0
$70$	−5.51070	−	1.32366i	−0.658655	−	0.158208i
$71$	−1.12339	−	0.648590i	−0.133322	−	0.0769735i	0.431856	−	0.901943i	$-0.357859\pi$
$71$	−1.12339	−	0.648590i	−0.133322	−	0.0769735i	−0.565178	+	0.824969i	$0.691192\pi$
$72$		0			0
$73$	0.981783	−	3.66406i	0.114909	−	0.428846i	−0.884371	−	0.466785i	$-0.845412\pi$
$73$	0.981783	−	3.66406i	0.114909	−	0.428846i	0.999280	+	0.0379383i	$0.0120790\pi$
$74$	1.56738	+	8.88907i	0.182204	+	1.03333i
$75$		0			0
$76$	0.704697	−	0.256489i	0.0808343	−	0.0294213i
$77$	9.48911	−	6.64435i	1.08138	−	0.757194i
$78$		0			0
$79$	3.09680	+	3.69062i	0.348417	+	0.415228i	0.911583	−	0.411117i	$-0.134861\pi$
$79$	3.09680	+	3.69062i	0.348417	+	0.415228i	−0.563166	+	0.826344i	$0.690417\pi$
$80$	2.22172	−	0.252879i	0.248396	−	0.0282727i
$81$		0			0
$82$	6.15470	−	6.15470i	0.679673	−	0.679673i
$83$	−0.504523	+	5.76673i	−0.0553786	+	0.632980i	0.916894	+	0.399131i	$0.130688\pi$
$83$	−0.504523	+	5.76673i	−0.0553786	+	0.632980i	−0.972273	+	0.233850i	$0.924868\pi$
$84$		0			0
$85$	5.77781	−	5.11061i	0.626692	−	0.554324i
$86$	−4.38368	−	12.0441i	−0.472705	−	1.29875i
$87$		0			0
$88$	−2.62150	+	3.74389i	−0.279453	+	0.399100i
$89$	−3.81802	−	6.61301i	−0.404709	−	0.700977i	0.589578	−	0.807711i	$-0.299294\pi$
$89$	−3.81802	−	6.61301i	−0.404709	−	0.700977i	−0.994288	+	0.106734i	$0.965961\pi$
$90$		0			0
$91$	−5.64556	+	9.77840i	−0.591816	+	1.02506i
$92$	0.135668	+	0.290940i	0.0141443	+	0.0303326i
$93$		0			0
$94$	−3.18104	+	3.79101i	−0.328099	+	0.391013i
$95$	0.925690	−	1.39822i	0.0949738	−	0.143454i
$96$		0			0
$97$	2.43551	−	1.13570i	0.247289	−	0.115313i	−0.295022	−	0.955490i	$-0.595327\pi$
$97$	2.43551	−	1.13570i	0.247289	−	0.115313i	0.542311	+	0.840178i	$0.317549\pi$
$98$	0.149085	+	0.556392i	0.0150598	+	0.0562041i
$99$		0			0
$100$	3.65754	−	3.40917i	0.365754	−	0.340917i
$101$	1.53538	−	0.270729i	0.152776	−	0.0269386i	−0.0967369	−	0.995310i	$-0.530841\pi$
$101$	1.53538	−	0.270729i	0.152776	−	0.0269386i	0.249513	+	0.968371i	$0.419729\pi$
$102$		0			0
$103$	10.9377	+	5.10035i	1.07773	+	0.502552i	0.878667	−	0.477435i	$-0.158434\pi$
$103$	10.9377	+	5.10035i	1.07773	+	0.502552i	0.199059	+	0.979987i	$0.436211\pi$
$104$	0.773580	−	4.38719i	0.0758558	−	0.430200i
$105$		0			0
$106$	−7.56906	+	6.35119i	−0.735172	+	0.616882i
$107$	3.78696	+	3.78696i	0.366100	+	0.366100i	0.866053	−	0.499953i	$-0.166649\pi$
$107$	3.78696	+	3.78696i	0.366100	+	0.366100i	−0.499953	+	0.866053i	$0.666649\pi$
$108$		0			0
$109$		−	9.66329i		−	0.925575i	−0.886469	−	0.462787i	$-0.846849\pi$
$109$		−	9.66329i		−	0.925575i	0.886469	−	0.462787i	$-0.153151\pi$
$110$	0.266370	+	10.2164i	0.0253974	+	0.974092i
$111$		0			0
$112$	1.45376	+	2.07619i	0.137368	+	0.196181i
$113$	−7.78498	+	16.6949i	−0.732349	+	1.57053i	0.0863237	+	0.996267i	$0.472488\pi$
$113$	−7.78498	+	16.6949i	−0.732349	+	1.57053i	−0.818673	+	0.574260i	$0.805290\pi$
$114$		0			0
$115$	0.630790	+	0.342583i	0.0588215	+	0.0319461i
$116$	−8.58610	+	4.95719i	−0.797199	+	0.460263i
$117$		0			0
$118$	−4.37088	+	1.17117i	−0.402372	+	0.107815i
$119$	8.21612	+	2.99042i	0.753171	+	0.274132i
$120$		0			0
$121$	−7.57543	−	6.35654i	−0.688675	−	0.577867i
$122$	0.0973382	+	1.11258i	0.00881259	+	0.100728i
$123$		0			0
$124$	0.793067	−	2.17893i	0.0712195	−	0.195674i
$125$	2.04118	−	10.9924i	0.182569	−	0.983193i
$126$		0			0
$127$	−11.8164	−	3.16620i	−1.04854	−	0.280955i	−0.306891	−	0.951745i	$-0.599289\pi$
$127$	−11.8164	−	3.16620i	−1.04854	−	0.280955i	−0.741648	+	0.670789i	$0.765955\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	−4.44375	−	8.91530i	−0.389742	−	0.781923i
$131$	−1.98802	−	0.350541i	−0.173694	−	0.0306269i	0.0861246	−	0.996284i	$-0.472552\pi$
$131$	−1.98802	−	0.350541i	−0.173694	−	0.0306269i	−0.259819	+	0.965657i	$0.583663\pi$
$132$		0			0
$133$	1.89349	+	0.165659i	0.164186	+	0.0143645i
$134$	−8.12595			−0.701975
$135$		0			0
$136$	−3.44968			−0.295808
$137$	−14.1913	−	1.24158i	−1.21244	−	0.106075i	−0.537061	−	0.843544i	$-0.680465\pi$
$137$	−14.1913	−	1.24158i	−1.21244	−	0.106075i	−0.675381	+	0.737469i	$0.736021\pi$
$138$		0			0
$139$	6.92908	+	1.22178i	0.587717	+	0.103630i	0.459596	−	0.888128i	$-0.347994\pi$
$139$	6.92908	+	1.22178i	0.587717	+	0.103630i	0.128121	+	0.991759i	$0.459105\pi$
$140$	5.37437	+	1.79891i	0.454217	+	0.152036i
$141$		0			0
$142$	1.06259	+	0.744032i	0.0891704	+	0.0624378i
$143$	19.6670	+	5.26975i	1.64464	+	0.440679i
$144$		0			0
$145$	−8.84225	+	20.3295i	−0.734309	+	1.68827i
$146$	−1.29739	+	3.56455i	−0.107373	+	0.295004i
$147$		0			0
$148$	−0.786685	−	8.99185i	−0.0646651	−	0.739125i
$149$	−14.8012	−	12.4197i	−1.21256	−	1.01746i	−0.999180	−	0.0404895i	$-0.987108\pi$
$149$	−14.8012	−	12.4197i	−1.21256	−	1.01746i	−0.213380	−	0.976969i	$-0.568447\pi$
$150$		0			0
$151$	−10.5388	−	3.83583i	−0.857639	−	0.312155i	−0.124488	−	0.992221i	$-0.539729\pi$
$151$	−10.5388	−	3.83583i	−0.857639	−	0.312155i	−0.733151	+	0.680066i	$0.761951\pi$
$152$	−0.724370	+	0.194094i	−0.0587542	+	0.0157431i
$153$		0			0
$154$	−10.0321	+	5.79203i	−0.808409	+	0.466735i
$155$	−1.47204	−	4.97158i	−0.118237	−	0.399327i
$156$		0			0
$157$	−4.64747	+	9.96653i	−0.370909	+	0.795416i	0.628930	+	0.777462i	$0.283493\pi$
$157$	−4.64747	+	9.96653i	−0.370909	+	0.795416i	−0.999839	+	0.0179543i	$0.994285\pi$
$158$	−2.76336	−	3.94648i	−0.219841	−	0.313965i
$159$		0			0
$160$	−2.23531	+	0.0582809i	−0.176717	+	0.00460751i
$161$			0.813636i			0.0641235i
$162$		0			0
$163$	−3.58900	−	3.58900i	−0.281112	−	0.281112i	0.552440	−	0.833553i	$-0.313697\pi$
$163$	−3.58900	−	3.58900i	−0.281112	−	0.281112i	−0.833553	+	0.552440i	$0.813697\pi$
$164$	−6.66770	+	5.59486i	−0.520660	+	0.436885i
$165$		0			0
$166$	1.00521	−	5.70081i	0.0780192	−	0.442469i
$167$	−4.91942	−	2.29396i	−0.380676	−	0.177512i	0.222855	−	0.974852i	$-0.428462\pi$
$167$	−4.91942	−	2.29396i	−0.380676	−	0.177512i	−0.603531	+	0.797339i	$0.706240\pi$
$168$		0			0
$169$	−6.74187	+	1.18877i	−0.518606	+	0.0914442i
$170$	−6.20125	+	4.58760i	−0.475614	+	0.351853i
$171$		0			0
$172$	3.31729	+	12.3803i	0.252941	+	0.943990i
$173$	−10.8667	+	5.06724i	−0.826183	+	0.385255i	−0.789257	−	0.614063i	$-0.789534\pi$
$173$	−10.8667	+	5.06724i	−0.826183	+	0.385255i	−0.0369256	+	0.999318i	$0.511756\pi$
$174$		0			0
$175$	12.0534	−	3.91338i	0.911153	−	0.295824i
$176$	2.93783	−	3.50117i	0.221447	−	0.263910i
$177$		0			0
$178$	3.22713	+	6.92060i	0.241884	+	0.518721i
$179$	−2.39468	+	4.14771i	−0.178987	+	0.310014i	−0.941534	−	0.336919i	$-0.890615\pi$
$179$	−2.39468	+	4.14771i	−0.178987	+	0.310014i	0.762547	+	0.646933i	$0.223949\pi$
$180$		0			0
$181$	−6.09608	−	10.5587i	−0.453118	−	0.784824i	0.545459	−	0.838137i	$-0.316355\pi$
$181$	−6.09608	−	10.5587i	−0.453118	−	0.784824i	−0.998578	+	0.0533131i	$0.983022\pi$
$182$	6.47632	−	9.24915i	0.480057	−	0.685593i
$183$		0			0
$184$	−0.109794	−	0.301657i	−0.00809414	−	0.0222385i
$185$	−13.3721	−	15.1178i	−0.983135	−	1.11148i
$186$		0			0
$187$	1.37415	−	15.7066i	0.100488	−	1.14858i
$188$	3.49934	−	3.49934i	0.255216	−	0.255216i
$189$		0			0
$190$	−1.04403	+	1.31222i	−0.0757419	+	0.0951985i
$191$	−5.72675	−	6.82488i	−0.414373	−	0.493831i	0.517973	−	0.855397i	$-0.326687\pi$
$191$	−5.72675	−	6.82488i	−0.414373	−	0.493831i	−0.932346	+	0.361566i	$0.882242\pi$
$192$		0			0
$193$	−20.0646	+	14.0494i	−1.44428	+	1.01130i	−0.451384	+	0.892330i	$0.649069\pi$
$193$	−20.0646	+	14.0494i	−1.44428	+	1.01130i	−0.992898	+	0.118967i	$0.962042\pi$
$194$	−2.52523	+	0.919107i	−0.181301	+	0.0659881i
$195$		0			0
$196$	−0.100025	−	0.567269i	−0.00714463	−	0.0405192i
$197$	1.40759	−	5.25319i	0.100287	−	0.374274i	−0.897481	−	0.441052i	$-0.854605\pi$
$197$	1.40759	−	5.25319i	0.100287	−	0.374274i	0.997768	+	0.0667780i	$0.0212719\pi$
$198$		0			0
$199$	8.30072	+	4.79242i	0.588423	+	0.339726i	0.764474	−	0.644655i	$-0.222999\pi$
$199$	8.30072	+	4.79242i	0.588423	+	0.339726i	−0.176051	+	0.984381i	$0.556332\pi$
$200$	−3.94075	+	3.07742i	−0.278653	+	0.217606i
$201$		0			0
$202$	−1.55313	+	0.135882i	−0.109278	+	0.00956060i
$203$	−25.0329	+	2.19010i	−1.75697	+	0.153715i
$204$		0			0
$205$	−4.54566	+	18.9246i	−0.317482	+	1.32175i
$206$	−10.4516	−	6.03422i	−0.728196	−	0.420424i
$207$		0			0
$208$	−1.15301	+	4.30308i	−0.0799465	+	0.298365i
$209$	−0.595177	−	3.37542i	−0.0411692	−	0.233482i
$210$		0			0
$211$	−2.60204	+	0.947064i	−0.179132	+	0.0651986i	−0.430029	−	0.902815i	$-0.641497\pi$
$211$	−2.60204	+	0.947064i	−0.179132	+	0.0651986i	0.250897	+	0.968014i	$0.419274\pi$
$212$	8.09380	−	5.66734i	0.555884	−	0.389234i
$213$		0			0
$214$	−3.44250	−	4.10261i	−0.235324	−	0.280449i
$215$	22.4274	+	17.8437i	1.52953	+	1.21693i
$216$		0			0
$217$	4.15571	−	4.15571i	0.282108	−	0.282108i
$218$	−0.842211	+	9.62651i	−0.0570417	+	0.651990i
$219$		0			0
$220$	0.625059	−	10.2007i	0.0421415	−	0.687731i
$221$	5.25613	+	14.4411i	0.353565	+	0.971413i
$222$		0			0
$223$	−6.68267	+	9.54384i	−0.447505	+	0.639103i	−0.978005	−	0.208582i	$-0.933115\pi$
$223$	−6.68267	+	9.54384i	−0.447505	+	0.639103i	0.530500	+	0.847685i	$0.322004\pi$
$224$	−1.26728	−	2.19499i	−0.0846736	−	0.146659i
$225$		0			0
$226$	9.21041	−	15.9529i	0.612668	−	1.06117i
$227$	9.40564	+	20.1705i	0.624274	+	1.33876i	0.923140	+	0.384465i	$0.125614\pi$
$227$	9.40564	+	20.1705i	0.624274	+	1.33876i	−0.298866	+	0.954295i	$0.596608\pi$
$228$		0			0
$229$	−7.72135	+	9.20195i	−0.510241	+	0.608082i	−0.958245	−	0.285950i	$-0.907691\pi$
$229$	−7.72135	+	9.20195i	−0.510241	+	0.608082i	0.448003	+	0.894032i	$0.352135\pi$
$230$	−0.598532	−	0.396257i	−0.0394660	−	0.0261284i
$231$		0			0
$232$	8.98547	−	4.18999i	0.589925	−	0.275087i
$233$	3.29469	+	12.2959i	0.215842	+	0.805534i	0.985868	+	0.167522i	$0.0535765\pi$
$233$	3.29469	+	12.2959i	0.215842	+	0.805534i	−0.770026	+	0.638012i	$0.779757\pi$
$234$		0			0
$235$	1.63688	−	10.9442i	0.106778	−	0.713918i
$236$	4.45632	−	0.785770i	0.290082	−	0.0511493i
$237$		0			0
$238$	−7.92422	−	3.69513i	−0.513651	−	0.239519i
$239$	−4.41392	+	25.0326i	−0.285512	+	1.61922i	0.417937	+	0.908476i	$0.362753\pi$
$239$	−4.41392	+	25.0326i	−0.285512	+	1.61922i	−0.703449	+	0.710745i	$0.748358\pi$
$240$		0			0
$241$	−6.87860	+	5.77183i	−0.443089	+	0.371796i	−0.836864	−	0.547411i	$-0.815614\pi$
$241$	−6.87860	+	5.77183i	−0.443089	+	0.371796i	0.393775	+	0.919207i	$0.371169\pi$
$242$	6.99259	+	6.99259i	0.449501	+	0.449501i
$243$		0			0
$244$		−	1.11683i		−	0.0714977i
$245$	−0.934196	−	0.886720i	−0.0596836	−	0.0566504i
$246$		0			0
$247$	1.91621	+	2.73663i	0.121926	+	0.174128i
$248$	−0.979955	+	2.10152i	−0.0622272	+	0.133447i
$249$		0			0
$250$	−2.99147	+	10.7727i	−0.189197	+	0.681326i
$251$	3.35304	−	1.93588i	0.211642	−	0.122191i	−0.390432	−	0.920632i	$-0.627674\pi$
$251$	3.35304	−	1.93588i	0.211642	−	0.122191i	0.602074	+	0.798440i	$0.294341\pi$
$252$		0			0
$253$	1.41720	−	0.379737i	0.0890985	−	0.0238739i
$254$	11.4955	+	4.18403i	0.721293	+	0.262529i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	2.27169	+	25.9655i	0.141704	+	1.61969i	0.650988	+	0.759088i	$0.274355\pi$
$257$	2.27169	+	25.9655i	0.141704	+	1.61969i	−0.509284	+	0.860598i	$0.670090\pi$
$258$		0			0
$259$	7.82453	−	21.4977i	0.486193	−	1.33580i
$260$	3.64982	+	9.26867i	0.226352	+	0.574818i
$261$		0			0
$262$	1.94990	+	0.522475i	0.120465	+	0.0322786i
$263$	−17.5407	−	12.2821i	−1.08161	−	0.757349i	−0.109996	−	0.993932i	$-0.535084\pi$
$263$	−17.5407	−	12.2821i	−1.08161	−	0.757349i	−0.971611	+	0.236583i	$0.923973\pi$
$264$		0			0
$265$	7.01287	−	20.9514i	0.430797	−	1.28703i
$266$	−1.87185	−	0.330057i	−0.114770	−	0.0202371i
$267$		0			0
$268$	8.09502	+	0.708223i	0.494482	+	0.0432616i
$269$	−15.6036			−0.951367			−0.475684	−	0.879616i	$-0.657799\pi$
$269$	−15.6036			−0.951367			−0.475684	+	0.879616i	$0.657799\pi$
$270$		0			0
$271$	−19.8324			−1.20473			−0.602366	−	0.798220i	$-0.705775\pi$
$271$	−19.8324			−1.20473			−0.602366	+	0.798220i	$0.705775\pi$
$272$	3.43655	+	0.300659i	0.208372	+	0.0182302i
$273$		0			0
$274$	14.0291	+	2.47370i	0.847526	+	0.149442i
$275$	−12.4419	−	19.1683i	−0.750275	−	1.15589i
$276$		0			0
$277$	−10.4169	−	7.29397i	−0.625889	−	0.438252i	0.217125	−	0.976144i	$-0.430332\pi$
$277$	−10.4169	−	7.29397i	−0.625889	−	0.438252i	−0.843014	+	0.537891i	$0.819221\pi$
$278$	−6.79622	−	1.82104i	−0.407610	−	0.109219i
$279$		0			0
$280$	−5.19713	−	2.26047i	−0.310588	−	0.135089i
$281$	3.62972	−	9.97257i	0.216531	−	0.594914i	−0.783105	−	0.621889i	$-0.786365\pi$
$281$	3.62972	−	9.97257i	0.216531	−	0.594914i	0.999636	+	0.0269756i	$0.00858765\pi$
$282$		0			0
$283$	−2.48295	−	28.3802i	−0.147596	−	1.68703i	−0.603785	−	0.797147i	$-0.706342\pi$
$283$	−2.48295	−	28.3802i	−0.147596	−	1.68703i	0.456189	−	0.889883i	$-0.349214\pi$
$284$	−0.993698	−	0.833812i	−0.0589651	−	0.0494776i
$285$		0			0
$286$	−19.1329	−	6.96379i	−1.13135	−	0.411778i
$287$	−21.3092	+	5.70979i	−1.25784	+	0.337038i
$288$		0			0
$289$	−4.41647	+	2.54985i	−0.259793	+	0.149991i
$290$	10.5804	−	19.4815i	0.621304	−	1.14399i
$291$		0			0
$292$	1.60313	−	3.43791i	0.0938158	−	0.201189i
$293$	3.29390	+	4.70418i	0.192432	+	0.274821i	0.903761	−	0.428038i	$-0.140795\pi$
$293$	3.29390	+	4.70418i	0.192432	+	0.274821i	−0.711329	+	0.702859i	$0.751906\pi$
$294$		0			0
$295$	6.96585	−	7.33881i	0.405567	−	0.427282i
$296$			9.02619i			0.524637i
$297$		0			0
$298$	13.6624	+	13.6624i	0.791442	+	0.791442i
$299$	−1.09551	+	0.919243i	−0.0633551	+	0.0531612i
$300$		0			0
$301$	−5.64105	+	31.9920i	−0.325145	+	1.84399i
$302$	10.1644	+	4.73975i	0.584897	+	0.272742i
$303$		0			0
$304$	0.738530	−	0.130223i	0.0423576	−	0.00746879i
$305$	−1.48523	−	2.00765i	−0.0850440	−	0.114958i
$306$		0			0
$307$	−6.66852	−	24.8873i	−0.380593	−	1.42039i	−0.844998	−	0.534769i	$-0.820399\pi$
$307$	−6.66852	−	24.8873i	−0.380593	−	1.42039i	0.464406	−	0.885623i	$-0.346268\pi$
$308$	10.4987	−	4.89564i	0.598221	−	0.278955i
$309$		0			0
$310$	1.03314	+	5.08096i	0.0586781	+	0.288579i
$311$	19.3169	−	23.0210i	1.09536	−	1.30540i	0.146673	−	0.989185i	$-0.453144\pi$
$311$	19.3169	−	23.0210i	1.09536	−	1.30540i	0.948688	−	0.316214i	$-0.102412\pi$
$312$		0			0
$313$	4.07582	+	8.74063i	0.230379	+	0.494050i	0.987183	−	0.159592i	$-0.0510180\pi$
$313$	4.07582	+	8.74063i	0.230379	+	0.494050i	−0.756804	+	0.653642i	$0.773240\pi$
$314$	5.49843	−	9.52356i	0.310294	−	0.537445i
$315$		0			0
$316$	2.40888	+	4.17231i	0.135510	+	0.234711i
$317$	2.43438	−	3.47666i	0.136729	−	0.195269i	−0.744948	−	0.667122i	$-0.767526\pi$
$317$	2.43438	−	3.47666i	0.136729	−	0.195269i	0.881677	+	0.471853i	$0.156415\pi$
$318$		0			0
$319$	15.4980	+	42.5804i	0.867722	+	2.38405i
$320$	2.23188	+	0.136761i	0.124766	+	0.00764517i
$321$		0			0
$322$	0.0709130	−	0.810540i	0.00395183	−	0.0451696i
$323$	1.82928	−	1.82928i	0.101784	−	0.101784i
$324$		0			0
$325$	18.8871	+	11.8079i	1.04767	+	0.654983i
$326$	3.26254	+	3.88815i	0.180696	+	0.215345i
$327$		0			0
$328$	7.12995	−	4.99244i	0.393686	−	0.275662i
$329$	11.7866	−	4.28998i	0.649817	−	0.236514i
$330$		0			0
$331$	−3.07179	−	17.4210i	−0.168841	−	0.957545i	−0.945015	−	0.327026i	$-0.893953\pi$
$331$	−3.07179	−	17.4210i	−0.168841	−	0.957545i	0.776174	−	0.630519i	$-0.217158\pi$
$332$	−1.49824	+	5.59151i	−0.0822266	+	0.306874i
$333$		0			0
$334$	4.70077	+	2.71399i	0.257215	+	0.148503i
$335$	15.4937	−	9.49214i	0.846511	−	0.518611i
$336$		0			0
$337$	24.8278	−	2.17215i	1.35246	−	0.118325i	0.612229	−	0.790680i	$-0.290273\pi$
$337$	24.8278	−	2.17215i	1.35246	−	0.118325i	0.740228	+	0.672356i	$0.234717\pi$
$338$	6.81983	−	0.596657i	0.370950	−	0.0324539i
$339$		0			0
$340$	6.57748	−	4.02966i	0.356714	−	0.218539i
$341$	−9.17799	−	5.29892i	−0.497016	−	0.286952i
$342$		0			0
$343$	4.96981	−	18.5476i	0.268344	−	1.00147i
$344$	−2.22566	−	12.6223i	−0.119999	−	0.680550i
$345$		0			0
$346$	11.2670	−	4.10086i	0.605719	−	0.220464i
$347$	10.4396	−	7.30989i	0.560427	−	0.392415i	−0.258760	−	0.965942i	$-0.583314\pi$
$347$	10.4396	−	7.30989i	0.560427	−	0.392415i	0.819187	+	0.573526i	$0.194425\pi$
$348$		0			0
$349$	5.00000	+	5.95877i	0.267644	+	0.318966i	0.883081	−	0.469220i	$-0.155465\pi$
$349$	5.00000	+	5.95877i	0.267644	+	0.318966i	−0.615437	+	0.788186i	$0.711021\pi$
$350$	−12.3486	+	2.84797i	−0.660062	+	0.152230i
$351$		0			0
$352$	−3.23180	+	3.23180i	−0.172255	+	0.172255i
$353$	1.07440	−	12.2804i	0.0571845	−	0.653621i	−0.912470	−	0.409143i	$-0.865828\pi$
$353$	1.07440	−	12.2804i	0.0571845	−	0.653621i	0.969655	−	0.244478i	$-0.0786167\pi$
$354$		0			0
$355$	−2.89515	−	0.177404i	−0.153659	−	0.00941561i
$356$	−2.61168	−	7.17553i	−0.138419	−	0.380302i
$357$		0			0
$358$	2.74707	−	3.92322i	0.145187	−	0.207348i
$359$	−2.96843	−	5.14147i	−0.156668	−	0.271357i	0.776997	−	0.629504i	$-0.216742\pi$
$359$	−2.96843	−	5.14147i	−0.156668	−	0.271357i	−0.933665	+	0.358147i	$0.883409\pi$
$360$		0			0
$361$	−9.21881	+	15.9674i	−0.485200	+	0.840392i
$362$	5.15263	+	11.0499i	0.270816	+	0.580768i
$363$		0			0
$364$	−7.25780	+	8.64950i	−0.380412	+	0.453357i
$365$	−1.69012	−	8.31203i	−0.0884651	−	0.435071i
$366$		0			0
$367$	−1.99183	+	0.928803i	−0.103972	+	0.0484831i	−0.473909	−	0.880574i	$-0.657157\pi$
$367$	−1.99183	+	0.928803i	−0.103972	+	0.0484831i	0.369936	+	0.929057i	$0.379380\pi$
$368$	0.0830853	+	0.310079i	0.00433112	+	0.0161640i
$369$		0			0
$370$	12.0036	+	16.2257i	0.624037	+	0.843536i
$371$	24.6627	−	4.34871i	1.28043	−	0.225774i
$372$		0			0
$373$	−17.9096	−	8.35138i	−0.927324	−	0.432418i	−0.100537	−	0.994933i	$-0.532056\pi$
$373$	−17.9096	−	8.35138i	−0.927324	−	0.432418i	−0.826787	+	0.562515i	$0.809834\pi$
$374$	−2.73784	+	15.5271i	−0.141570	+	0.802885i
$375$		0			0
$376$	−3.79101	+	3.18104i	−0.195506	+	0.164049i
$377$	−31.2310	−	31.2310i	−1.60848	−	1.60848i
$378$		0			0
$379$			23.2798i			1.19580i	0.801570	+	0.597901i	$0.203998\pi$
$379$			23.2798i			1.19580i	−0.801570	+	0.597901i	$0.796002\pi$
$380$	1.15442	−	1.21623i	0.0592207	−	0.0623915i
$381$		0			0
$382$	5.11013	+	7.29802i	0.261457	+	0.373399i
$383$	−5.41319	+	11.6086i	−0.276601	+	0.593173i	−0.994706	−	0.102762i	$-0.967232\pi$
$383$	−5.41319	+	11.6086i	−0.276601	+	0.593173i	0.718105	+	0.695935i	$0.245010\pi$
$384$		0			0
$385$	12.3623	−	22.7624i	0.630041	−	1.16008i
$386$	21.2127	−	12.2472i	1.07970	−	0.623365i
$387$		0			0
$388$	2.59572	−	0.695522i	0.131778	−	0.0353098i
$389$	36.1051	+	13.1412i	1.83060	+	0.666284i	0.992723	+	0.120423i	$0.0384252\pi$
$389$	36.1051	+	13.1412i	1.83060	+	0.666284i	0.837876	+	0.545860i	$0.183797\pi$
$390$		0			0
$391$	0.848322	+	0.711827i	0.0429015	+	0.0359986i
$392$	0.0502034	+	0.573828i	0.00253566	+	0.0289827i
$393$		0			0
$394$	−1.86008	+	5.11052i	−0.0937094	+	0.257464i
$395$	9.87887	+	4.29678i	0.497060	+	0.216195i
$396$		0			0
$397$	9.14046	+	2.44918i	0.458746	+	0.122921i	0.480789	−	0.876836i	$-0.340350\pi$
$397$	9.14046	+	2.44918i	0.458746	+	0.122921i	−0.0220427	+	0.999757i	$0.507017\pi$
$398$	−7.85145	−	5.49764i	−0.393558	−	0.275572i
$399$		0			0
$400$	4.19397	−	2.72225i	0.209698	−	0.136112i
$401$	−12.5849	−	2.21905i	−0.628458	−	0.110814i	−0.149657	−	0.988738i	$-0.547817\pi$
$401$	−12.5849	−	2.21905i	−0.628458	−	0.110814i	−0.478800	+	0.877924i	$0.658928\pi$
$402$		0			0
$403$	10.2905	+	0.900304i	0.512607	+	0.0448473i
$404$	1.55907			0.0775665
$405$		0			0
$406$	25.1285			1.24711
$407$	−41.0968	−	3.59550i	−2.03709	−	0.178223i
$408$		0			0
$409$	−39.7891	−	7.01589i	−1.96744	−	0.346914i	−0.991873	−	0.127234i	$-0.959390\pi$
$409$	−39.7891	−	7.01589i	−1.96744	−	0.346914i	−0.975572	−	0.219680i	$-0.929499\pi$
$410$	6.17775	−	18.4564i	0.305097	−	0.911497i
$411$		0			0
$412$	9.88589	+	6.92218i	0.487043	+	0.341031i
$413$	11.0782	+	2.96841i	0.545125	+	0.146066i
$414$		0			0
$415$	4.74265	+	12.0439i	0.232807	+	0.591212i
$416$	1.52366	−	4.18621i	0.0747034	−	0.205246i
$417$		0			0
$418$	0.298725	+	3.41444i	0.0146111	+	0.167006i
$419$	17.4614	+	14.6519i	0.853047	+	0.715791i	0.960458	−	0.278424i	$-0.0898119\pi$
$419$	17.4614	+	14.6519i	0.853047	+	0.715791i	−0.107412	+	0.994215i	$0.534256\pi$
$420$		0			0
$421$	5.48882	+	1.99777i	0.267509	+	0.0973653i	0.472292	−	0.881442i	$-0.343427\pi$
$421$	5.48882	+	1.99777i	0.267509	+	0.0973653i	−0.204783	+	0.978807i	$0.565649\pi$
$422$	2.67468	−	0.716678i	0.130201	−	0.0348873i
$423$		0			0
$424$	−8.55694	+	4.94035i	−0.415562	+	0.239925i
$425$	6.46498	−	15.9910i	0.313598	−	0.775676i
$426$		0			0
$427$	1.19629	−	2.56546i	0.0578927	−	0.124151i
$428$	3.07183	+	4.38703i	0.148483	+	0.212055i
$429$		0			0
$430$	−20.7868	−	19.7304i	−1.00243	−	0.951486i
$431$		−	14.0693i		−	0.677696i	−0.940841	−	0.338848i	$-0.889963\pi$
$431$		−	14.0693i		−	0.677696i	0.940841	−	0.338848i	$-0.110037\pi$
$432$		0			0
$433$	6.46477	+	6.46477i	0.310677	+	0.310677i	0.845172	−	0.534495i	$-0.179498\pi$
$433$	6.46477	+	6.46477i	0.310677	+	0.310677i	−0.534495	+	0.845172i	$0.679498\pi$
$434$	−4.50209	+	3.77770i	−0.216107	+	0.181335i
$435$		0			0
$436$	1.67801	−	9.51648i	0.0803622	−	0.455757i
$437$	0.218183	+	0.101740i	0.0104371	+	0.00486690i
$438$		0			0
$439$	32.4688	−	5.72513i	1.54965	−	0.273246i	0.667645	−	0.744480i	$-0.267303\pi$
$439$	32.4688	−	5.72513i	1.54965	−	0.273246i	0.882008	+	0.471235i	$0.156191\pi$
$440$	−1.51173	+	10.1074i	−0.0720689	+	0.481852i
$441$		0			0
$442$	−3.97750	−	14.8442i	−0.189190	−	0.706068i
$443$	−6.36590	+	2.96847i	−0.302453	+	0.141036i	−0.567920	−	0.823084i	$-0.692252\pi$
$443$	−6.36590	+	2.96847i	−0.302453	+	0.141036i	0.265467	+	0.964120i	$0.414474\pi$
$444$		0			0
$445$	−14.2373	−	9.42577i	−0.674912	−	0.446824i
$446$	7.48904	−	8.92509i	0.354616	−	0.422615i
$447$		0			0
$448$	1.07115	+	2.29709i	0.0506071	+	0.108527i
$449$	−1.76787	+	3.06204i	−0.0834308	+	0.144506i	−0.904721	−	0.426004i	$-0.859921\pi$
$449$	−1.76787	+	3.06204i	−0.0834308	+	0.144506i	0.821291	+	0.570510i	$0.193254\pi$
$450$		0			0
$451$	19.8907	+	34.4518i	0.936619	+	1.62227i
$452$	−10.5658	+	15.0895i	−0.496971	+	0.709748i
$453$		0			0
$454$	−7.61187	−	20.9135i	−0.357243	−	0.981517i
$455$	−1.54418	+	25.2005i	−0.0723925	+	1.18142i
$456$		0			0
$457$	−1.88888	+	21.5900i	−0.0883581	+	1.00994i	0.814547	+	0.580098i	$0.196986\pi$
$457$	−1.88888	+	21.5900i	−0.0883581	+	1.00994i	−0.902905	+	0.429840i	$0.858570\pi$
$458$	8.49398	−	8.49398i	0.396897	−	0.396897i
$459$		0			0
$460$	0.561718	+	0.446914i	0.0261902	+	0.0208375i
$461$	−9.16242	−	10.9193i	−0.426736	−	0.508565i	0.509241	−	0.860624i	$-0.329926\pi$
$461$	−9.16242	−	10.9193i	−0.426736	−	0.508565i	−0.935978	+	0.352059i	$0.885482\pi$
$462$		0			0
$463$	−18.5143	+	12.9638i	−0.860432	+	0.602481i	−0.918319	−	0.395842i	$-0.870453\pi$
$463$	−18.5143	+	12.9638i	−0.860432	+	0.602481i	0.0578865	+	0.998323i	$0.481564\pi$
$464$	−9.31646	+	3.39092i	−0.432506	+	0.157419i
$465$		0			0
$466$	−2.21049	−	12.5363i	−0.102399	−	0.580733i
$467$	−5.57249	+	20.7968i	−0.257864	+	0.962361i	0.708611	+	0.705600i	$0.249322\pi$
$467$	−5.57249	+	20.7968i	−0.257864	+	0.962361i	−0.966475	+	0.256762i	$0.917344\pi$
$468$		0			0
$469$	17.8364	+	10.2978i	0.823607	+	0.475510i
$470$	−2.58450	+	10.7598i	−0.119214	+	0.496314i
$471$		0			0
$472$	−4.50785	+	0.394386i	−0.207491	+	0.0181531i
$473$	58.3567	−	5.10555i	2.68324	−	0.234754i
$474$		0			0
$475$	0.457804	−	3.72156i	0.0210055	−	0.170757i
$476$	7.57202	+	4.37171i	0.347063	+	0.200377i
$477$		0			0
$478$	6.57885	−	24.5526i	0.300910	−	1.12301i
$479$	−5.34729	−	30.3260i	−0.244324	−	1.38563i	−0.822057	−	0.569405i	$-0.807174\pi$
$479$	−5.34729	−	30.3260i	−0.244324	−	1.38563i	0.577733	−	0.816226i	$-0.303937\pi$
$480$		0			0
$481$	37.7855	−	13.7528i	1.72287	−	0.627074i
$482$	7.35547	−	5.15036i	0.335033	−	0.234592i
$483$		0			0
$484$	−6.35654	−	7.57543i	−0.288934	−	0.344338i
$485$	3.74120	−	4.70224i	0.169879	−	0.213518i
$486$		0			0
$487$	−18.5575	+	18.5575i	−0.840922	+	0.840922i	−0.988979	−	0.148057i	$-0.952698\pi$
$487$	−18.5575	+	18.5575i	−0.840922	+	0.840922i	0.148057	+	0.988979i	$0.452698\pi$
$488$	−0.0973382	+	1.11258i	−0.00440629	+	0.0503642i
$489$		0			0
$490$	0.853359	+	0.964766i	0.0385508	+	0.0435837i
$491$	7.17890	+	19.7239i	0.323979	+	0.890126i	0.989601	+	0.143837i	$0.0459440\pi$
$491$	7.17890	+	19.7239i	0.323979	+	0.890126i	−0.665622	+	0.746289i	$0.731834\pi$
$492$		0			0
$493$	−19.6171	+	28.0162i	−0.883511	+	1.26178i
$494$	−1.67041	−	2.89323i	−0.0751551	−	0.130172i
$495$		0			0
$496$	1.15939	−	2.00812i	0.0520580	−	0.0901670i
$497$	−1.38948	−	2.97974i	−0.0623265	−	0.133660i
$498$		0			0
$499$	−7.97424	+	9.50332i	−0.356976	+	0.425427i	−0.914407	−	0.404796i	$-0.867343\pi$
$499$	−7.97424	+	9.50332i	−0.356976	+	0.425427i	0.557431	+	0.830223i	$0.311787\pi$
$500$	3.91899	−	10.4710i	0.175262	−	0.468277i
$501$		0			0
$502$	−3.50900	+	1.63627i	−0.156614	+	0.0730304i
$503$	2.79824	+	10.4432i	0.124767	+	0.465638i	0.999831	−	0.0183691i	$-0.00584740\pi$
$503$	2.79824	+	10.4432i	0.124767	+	0.465638i	−0.875064	+	0.484008i	$0.839181\pi$
$504$		0			0
$505$	2.80263	−	2.07334i	0.124715	−	0.0922626i
$506$	−1.44490	+	0.254775i	−0.0642337	+	0.0113261i
$507$		0			0
$508$	−11.0871	−	5.17000i	−0.491911	−	0.229382i
$509$	7.19749	−	40.8190i	0.319023	−	1.80927i	−0.229695	−	0.973263i	$-0.573773\pi$
$509$	7.19749	−	40.8190i	0.319023	−	1.80927i	0.548718	−	0.836008i	$-0.315116\pi$
$510$		0			0
$511$	7.36504	−	6.18000i	0.325810	−	0.273387i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	26.0647i		−	1.14967i
$515$	26.9767	−	0.703359i	1.18874	−	0.0309937i
$516$		0			0
$517$	−12.9733	−	18.5278i	−0.570566	−	0.814853i
$518$	−9.66841	+	20.7340i	−0.424806	+	0.910998i
$519$		0			0
$520$	−2.82811	−	9.55150i	−0.124021	−	0.418861i
$521$	−29.6414	+	17.1135i	−1.29861	+	0.749755i	−0.980165	−	0.198185i	$-0.936495\pi$
$521$	−29.6414	+	17.1135i	−1.29861	+	0.749755i	−0.318449	+	0.947940i	$0.603162\pi$
$522$		0			0
$523$	43.1131	−	11.5521i	1.88520	−	0.505139i	0.886069	−	0.463554i	$-0.153426\pi$
$523$	43.1131	−	11.5521i	1.88520	−	0.505139i	0.999135	−	0.0415849i	$-0.0132407\pi$
$524$	−1.89695	−	0.690432i	−0.0828685	−	0.0301617i
$525$		0			0
$526$	16.4035	+	13.7642i	0.715227	+	0.600147i
$527$	−0.697161	−	7.96858i	−0.0303688	−	0.347117i
$528$		0			0
$529$	7.83122	−	21.5161i	0.340488	−	0.935482i
$530$	−8.81222	+	20.2605i	−0.382778	+	0.880058i
$531$		0			0
$532$	1.83596	+	0.491943i	0.0795989	+	0.0213285i
$533$	−31.7630	−	22.2407i	−1.37581	−	0.963352i
$534$		0			0
$535$	11.3562	+	3.80114i	0.490969	+	0.164338i
$536$	−8.00249	−	1.41106i	−0.345655	−	0.0609483i
$537$		0			0
$538$	15.5442	+	1.35994i	0.670158	+	0.0586312i
$539$	−2.63267			−0.113397
$540$		0			0
$541$	−12.0107			−0.516379			−0.258190	−	0.966094i	$-0.583126\pi$
$541$	−12.0107			−0.516379			−0.258190	+	0.966094i	$0.583126\pi$
$542$	19.7569	+	1.72851i	0.848633	+	0.0742458i
$543$		0			0
$544$	−3.39727	−	0.599031i	−0.145657	−	0.0256832i
$545$	−9.63915	−	19.3386i	−0.412896	−	0.828376i
$546$		0			0
$547$	24.4474	+	17.1182i	1.04529	+	0.731923i	0.964306	−	0.264792i	$-0.0853033\pi$
$547$	24.4474	+	17.1182i	1.04529	+	0.731923i	0.0809889	+	0.996715i	$0.474192\pi$
$548$	−13.7601	−	3.68700i	−0.587801	−	0.157501i
$549$		0			0
$550$	10.7239	+	20.1798i	0.457270	+	0.860468i
$551$	−2.54293	+	6.98663i	−0.108332	+	0.297641i
$552$		0			0
$553$	1.06425	+	12.1644i	0.0452565	+	0.517284i
$554$	9.74152	+	8.17411i	0.413878	+	0.347285i
$555$		0			0
$556$	6.61165	+	2.40644i	0.280396	+	0.102056i
$557$	36.0806	−	9.66776i	1.52878	−	0.409636i	0.606161	−	0.795342i	$-0.292709\pi$
$557$	36.0806	−	9.66776i	1.52878	−	0.409636i	0.922622	+	0.385706i	$0.126042\pi$
$558$		0			0
$559$	−49.4485	+	28.5491i	−2.09145	+	1.20750i
$560$	4.98034	+	2.70483i	0.210458	+	0.114300i
$561$		0			0
$562$	−4.48507	+	9.61827i	−0.189191	+	0.405722i
$563$	7.68669	+	10.9777i	0.323955	+	0.462656i	0.947788	−	0.318902i	$-0.103314\pi$
$563$	7.68669	+	10.9777i	0.323955	+	0.462656i	−0.623832	+	0.781558i	$0.714425\pi$
$564$		0			0
$565$	1.07358	+	41.1762i	0.0451659	+	1.73230i
$566$			28.4886i			1.19747i
$567$		0			0
$568$	0.917245	+	0.917245i	0.0384868	+	0.0384868i
$569$	−22.5000	+	18.8798i	−0.943250	+	0.791481i	−0.978148	−	0.207910i	$-0.933334\pi$
$569$	−22.5000	+	18.8798i	−0.943250	+	0.791481i	0.0348980	+	0.999391i	$0.488889\pi$
$570$		0			0
$571$	−0.486315	+	2.75803i	−0.0203517	+	0.115420i	−0.993291	−	0.115640i	$-0.963108\pi$
$571$	−0.486315	+	2.75803i	−0.0203517	+	0.115420i	0.972940	+	0.231060i	$0.0742193\pi$
$572$	18.4531	+	8.60483i	0.771564	+	0.359786i
$573$		0			0
$574$	21.7258	−	3.83084i	0.906817	−	0.159896i
$575$	1.60409	+	0.0563792i	0.0668953	+	0.00235117i
$576$		0			0
$577$	−6.06105	−	22.6201i	−0.252325	−	0.941689i	−0.969559	−	0.244857i	$-0.921259\pi$
$577$	−6.06105	−	22.6201i	−0.252325	−	0.941689i	0.717234	−	0.696832i	$-0.245408\pi$
$578$	4.62190	−	2.15523i	0.192246	−	0.0896457i
$579$		0			0
$580$	−12.2381	+	18.4852i	−0.508159	+	0.767556i
$581$	−9.43093	+	11.2393i	−0.391261	+	0.466287i
$582$		0			0
$583$	−19.0851	−	40.9282i	−0.790425	−	1.69507i
$584$	−1.89666	+	3.28511i	−0.0784843	+	0.135939i
$585$		0			0
$586$	−2.87137	−	4.97336i	−0.118615	−	0.205448i
$587$	−6.86712	+	9.80727i	−0.283436	+	0.404789i	−0.935473	−	0.353398i	$-0.885026\pi$
$587$	−6.86712	+	9.80727i	−0.283436	+	0.404789i	0.652036	+	0.758188i	$0.273915\pi$
$588$		0			0
$589$	−0.594739	−	1.63403i	−0.0245058	−	0.0673291i
$590$	−7.57896	+	6.70377i	−0.312021	+	0.275990i
$591$		0			0
$592$	0.786685	−	8.99185i	0.0323325	−	0.369563i
$593$	−28.6341	+	28.6341i	−1.17586	+	1.17586i	−0.195071	+	0.980789i	$0.562494\pi$
$593$	−28.6341	+	28.6341i	−1.17586	+	1.17586i	−0.980789	+	0.195071i	$0.937506\pi$
$594$		0			0
$595$	19.4254	−	2.21103i	0.796365	−	0.0906432i
$596$	−12.4197	−	14.8012i	−0.508729	−	0.606280i
$597$		0			0
$598$	1.17146	−	0.820265i	0.0479046	−	0.0335431i
$599$	15.7253	−	5.72356i	0.642520	−	0.233858i	−0.000151368	−	1.00000i	$-0.500048\pi$
$599$	15.7253	−	5.72356i	0.642520	−	0.233858i	0.642672	+	0.766142i	$0.277826\pi$
$600$		0			0
$601$	−2.69318	−	15.2738i	−0.109857	−	0.623030i	−0.989169	−	0.146783i	$-0.953108\pi$
$601$	−2.69318	−	15.2738i	−0.109857	−	0.623030i	0.879312	−	0.476247i	$-0.158003\pi$
$602$	8.40787	−	31.3786i	0.342679	−	1.27890i
$603$		0			0
$604$	−9.71265	−	5.60760i	−0.395202	−	0.228170i
$605$	−21.5010	−	5.16449i	−0.874139	−	0.209967i
$606$		0			0
$607$	−32.8409	+	2.87321i	−1.33297	+	0.116620i	−0.731263	−	0.682096i	$-0.761069\pi$
$607$	−32.8409	+	2.87321i	−1.33297	+	0.116620i	−0.601709	+	0.798716i	$0.705513\pi$
$608$	−0.747070	+	0.0653601i	−0.0302977	+	0.00265070i
$609$		0			0
$610$	1.30460	+	2.12945i	0.0528217	+	0.0862190i
$611$	19.0927	+	11.0232i	0.772407	+	0.445949i
$612$		0			0
$613$	1.14653	−	4.27892i	0.0463081	−	0.172824i	−0.938899	−	0.344193i	$-0.888152\pi$
$613$	1.14653	−	4.27892i	0.0463081	−	0.172824i	0.985207	+	0.171369i	$0.0548191\pi$
$614$	4.47408	+	25.3738i	0.180559	+	1.02400i
$615$		0			0
$616$	−10.8855	+	3.96198i	−0.438588	+	0.159633i
$617$	−0.172478	+	0.120770i	−0.00694369	+	0.00486202i	−0.577043	−	0.816714i	$-0.695794\pi$
$617$	−0.172478	+	0.120770i	−0.00694369	+	0.00486202i	0.570099	+	0.821576i	$0.306905\pi$
$618$		0			0
$619$	−23.0278	−	27.4434i	−0.925564	−	1.10304i	−0.994428	−	0.105418i	$-0.966382\pi$
$619$	−23.0278	−	27.4434i	−0.925564	−	1.10304i	0.0688642	−	0.997626i	$-0.478062\pi$
$620$	−0.586369	−	5.15167i	−0.0235491	−	0.206896i
$621$		0			0
$622$	−21.2498	+	21.2498i	−0.852039	+	0.852039i
$623$	1.68681	−	19.2803i	0.0675806	−	0.772450i
$624$		0			0
$625$	−6.88007	−	24.0347i	−0.275203	−	0.961386i
$626$	−3.29852	−	9.06260i	−0.131835	−	0.362214i
$627$		0			0
$628$	−6.30754	+	9.00810i	−0.251698	+	0.359462i
$629$	−15.5687	−	26.9659i	−0.620767	−	1.07520i
$630$		0			0
$631$	15.8828	−	27.5099i	0.632286	−	1.09515i	−0.354797	−	0.934943i	$-0.615450\pi$
$631$	15.8828	−	27.5099i	0.632286	−	1.09515i	0.987083	−	0.160208i	$-0.0512165\pi$
$632$	−2.03608	−	4.36638i	−0.0809908	−	0.173685i
$633$		0			0
$634$	−2.72813	+	3.25126i	−0.108348	+	0.129124i
$635$	−26.8059	+	5.45057i	−1.06376	+	0.216299i
$636$		0			0
$637$	2.32567	−	1.08448i	0.0921464	−	0.0429686i
$638$	−11.7279	−	43.7691i	−0.464312	−	1.73284i
$639$		0			0
$640$	−2.21147	−	0.330762i	−0.0874160	−	0.0130745i
$641$	−6.36472	+	1.12227i	−0.251391	+	0.0443271i	−0.297924	−	0.954590i	$-0.596294\pi$
$641$	−6.36472	+	1.12227i	−0.251391	+	0.0443271i	0.0465322	+	0.998917i	$0.485183\pi$
$642$		0			0
$643$	−20.8874	−	9.73996i	−0.823719	−	0.384106i	−0.0354000	−	0.999373i	$-0.511271\pi$
$643$	−20.8874	−	9.73996i	−0.823719	−	0.384106i	−0.788319	+	0.615267i	$0.789048\pi$
$644$	−0.141286	+	0.801275i	−0.00556746	+	0.0315746i
$645$		0			0
$646$	−1.98175	+	1.66289i	−0.0779711	+	0.0654255i
$647$	−3.13288	−	3.13288i	−0.123166	−	0.123166i	0.642837	−	0.766003i	$-0.277757\pi$
$647$	−3.13288	−	3.13288i	−0.123166	−	0.123166i	−0.766003	+	0.642837i	$0.777757\pi$
$648$		0			0
$649$		−	20.6816i		−	0.811824i
$650$	−17.7861	−	13.4091i	−0.697627	−	0.525947i
$651$		0			0
$652$	−2.91125	−	4.15770i	−0.114013	−	0.162828i
$653$	4.93031	−	10.5731i	0.192938	−	0.413757i	−0.785911	−	0.618339i	$-0.787806\pi$
$653$	4.93031	−	10.5731i	0.192938	−	0.413757i	0.978849	+	0.204582i	$0.0655836\pi$
$654$		0			0
$655$	−4.32818	+	1.28153i	−0.169116	+	0.0500737i
$656$	−7.53794	+	4.35203i	−0.294307	+	0.169918i
$657$		0			0
$658$	−12.1157	+	3.24638i	−0.472318	+	0.126557i
$659$	−3.83555	−	1.39602i	−0.149412	−	0.0543814i	0.266232	−	0.963909i	$-0.414221\pi$
$659$	−3.83555	−	1.39602i	−0.149412	−	0.0543814i	−0.415643	+	0.909528i	$0.636444\pi$
$660$		0			0
$661$	1.20787	+	1.01352i	0.0469805	+	0.0394213i	0.665976	−	0.745974i	$-0.268015\pi$
$661$	1.20787	+	1.01352i	0.0469805	+	0.0394213i	−0.618995	+	0.785395i	$0.712460\pi$
$662$	1.54176	+	17.6224i	0.0599223	+	0.684915i
$663$		0			0
$664$	1.97987	−	5.43965i	0.0768339	−	0.211099i
$665$	3.95459	−	1.55724i	0.153352	−	0.0603871i
$666$		0			0
$667$	−3.07423	−	0.823738i	−0.119035	−	0.0318953i
$668$	−4.44634	−	3.11336i	−0.172034	−	0.120460i
$669$		0			0
$670$	−16.2620	+	8.10565i	−0.628257	+	0.313149i
$671$	−5.02687	−	0.886373i	−0.194060	−	0.0342181i
$672$		0			0
$673$	−5.21091	−	0.455896i	−0.200866	−	0.0175735i	−0.0137213	−	0.999906i	$-0.504368\pi$
$673$	−5.21091	−	0.455896i	−0.200866	−	0.0175735i	−0.187145	+	0.982332i	$0.559923\pi$
$674$	−24.9227			−0.959985
$675$		0			0
$676$	−6.84588			−0.263303
$677$	−14.9725	−	1.30993i	−0.575441	−	0.0503445i	−0.204279	−	0.978913i	$-0.565485\pi$
$677$	−14.9725	−	1.30993i	−0.575441	−	0.0503445i	−0.371162	+	0.928568i	$0.621041\pi$
$678$		0			0
$679$	6.70761	+	1.18273i	0.257415	+	0.0453891i
$680$	−6.90366	+	3.44107i	−0.264743	+	0.131959i
$681$		0			0
$682$	8.68124	+	6.07867i	0.332422	+	0.232764i
$683$	−1.46274	−	0.391940i	−0.0559701	−	0.0149972i	0.230725	−	0.973019i	$-0.425890\pi$
$683$	−1.46274	−	0.391940i	−0.0559701	−	0.0149972i	−0.286695	+	0.958022i	$0.592557\pi$
$684$		0			0
$685$	−29.6387	+	11.6711i	−1.13244	+	0.445931i
$686$	−6.56742	+	18.0438i	−0.250745	+	0.688917i
$687$		0			0
$688$	1.11708	+	12.7683i	0.0425882	+	0.486786i
$689$	33.7192	+	28.2937i	1.28460	+	1.07791i
$690$		0			0
$691$	35.7765	+	13.0216i	1.36100	+	0.495364i	0.916364	−	0.400346i	$-0.131110\pi$
$691$	35.7765	+	13.0216i	1.36100	+	0.495364i	0.444638	+	0.895710i	$0.353332\pi$
$692$	−11.5816	+	3.10327i	−0.440265	+	0.117969i
$693$		0			0
$694$	−11.0370	+	6.37220i	−0.418958	+	0.241885i
$695$	15.0855	−	4.46668i	0.572227	−	0.169431i
$696$		0			0
$697$	−12.6896	+	27.2130i	−0.480654	+	1.03077i
$698$	−4.46163	−	6.37187i	−0.168875	−	0.241179i
$699$		0			0
$700$	12.5499	−	1.76087i	0.474340	−	0.0665548i
$701$			25.4564i			0.961477i	0.876864	+	0.480738i	$0.159631\pi$
$701$			25.4564i			0.961477i	−0.876864	+	0.480738i	$0.840369\pi$
$702$		0			0
$703$	−4.78637	−	4.78637i	−0.180521	−	0.180521i
$704$	3.50117	−	2.93783i	0.131955	−	0.110724i
$705$		0			0
$706$	−2.14062	+	12.1401i	−0.0805633	+	0.456897i
$707$	3.58132	+	1.67000i	0.134689	+	0.0628066i
$708$		0			0
$709$	9.51739	−	1.67817i	0.357433	−	0.0630251i	0.00795163	−	0.999968i	$-0.497469\pi$
$709$	9.51739	−	1.67817i	0.357433	−	0.0630251i	0.349481	+	0.936943i	$0.386358\pi$
$710$	2.86868	+	0.429058i	0.107659	+	0.0161023i
$711$		0			0
$712$	1.97635	+	7.37585i	0.0740670	+	0.276422i
$713$	0.674624	−	0.314582i	0.0252649	−	0.0117812i
$714$		0			0
$715$	44.6151	−	9.07179i	1.66851	−	0.339266i
$716$	−3.07854	+	3.66886i	−0.115051	+	0.137112i
$717$		0			0
$718$	2.50903	+	5.38062i	0.0936360	+	0.200803i
$719$	−6.12455	+	10.6080i	−0.228407	+	0.395613i	−0.957336	−	0.288976i	$-0.906685\pi$
$719$	−6.12455	+	10.6080i	−0.228407	+	0.395613i	0.728929	+	0.684589i	$0.240018\pi$
$720$		0			0
$721$	15.2941	+	26.4901i	0.569581	+	0.986544i
$722$	10.5754	−	15.1032i	0.393575	−	0.562083i
$723$		0			0
$724$	−4.16997	−	11.4569i	−0.154976	−	0.425792i
$725$	2.58320	+	49.5045i	0.0959378	+	1.83855i
$726$		0			0
$727$	1.21031	−	13.8339i	0.0448880	−	0.513073i	−0.940153	−	0.340753i	$-0.889318\pi$
$727$	1.21031	−	13.8339i	0.0448880	−	0.513073i	0.985041	−	0.172320i	$-0.0551263\pi$
$728$	7.98403	−	7.98403i	0.295908	−	0.295908i
$729$		0			0
$730$	0.959251	+	8.42770i	0.0355035	+	0.311923i
$731$	28.4207	+	33.8704i	1.05118	+	1.25274i
$732$		0			0
$733$	−22.7839	+	15.9535i	−0.841543	+	0.589255i	−0.912894	−	0.408196i	$-0.866158\pi$
$733$	−22.7839	+	15.9535i	−0.841543	+	0.589255i	0.0713511	+	0.997451i	$0.477269\pi$
$734$	2.06520	−	0.751670i	0.0762278	−	0.0277446i
$735$		0			0
$736$	−0.0557440	−	0.316140i	−0.00205475	−	0.0116531i
$737$	9.61234	−	35.8737i	0.354075	−	1.32143i
$738$		0			0
$739$	−15.5183	−	8.95947i	−0.570848	−	0.329579i	0.186640	−	0.982428i	$-0.440240\pi$
$739$	−15.5183	−	8.95947i	−0.570848	−	0.329579i	−0.757488	+	0.652849i	$0.773574\pi$
$740$	−10.5437	−	17.2102i	−0.387596	−	0.632659i
$741$		0			0
$742$	−24.9479	+	2.18266i	−0.915867	+	0.0801279i
$743$	−22.7045	+	1.98639i	−0.832949	+	0.0728736i	−0.495648	−	0.868523i	$-0.665069\pi$
$743$	−22.7045	+	1.98639i	−0.832949	+	0.0728736i	−0.337301	+	0.941397i	$0.609514\pi$
$744$		0			0
$745$	−42.0095	−	10.0906i	−1.53911	−	0.369691i
$746$	17.1136	+	9.88053i	0.626573	+	0.361752i
$747$		0			0
$748$	4.08070	−	15.2294i	0.149205	−	0.556841i
$749$	2.35710	+	13.3678i	0.0861267	+	0.488449i
$750$		0			0
$751$	−47.7320	+	17.3730i	−1.74176	+	0.633950i	−0.999352	−	0.0359930i	$-0.988541\pi$
$751$	−47.7320	+	17.3730i	−1.74176	+	0.633950i	−0.742412	+	0.669943i	$0.766318\pi$
$752$	4.05383	−	2.83852i	0.147828	−	0.103510i
$753$		0			0
$754$	28.3902	+	33.8341i	1.03391	+	1.23216i
$755$	−24.9171	+	2.83609i	−0.906825	+	0.103216i
$756$		0			0
$757$	0.751133	−	0.751133i	0.0273004	−	0.0273004i	−0.693325	−	0.720625i	$-0.743855\pi$
$757$	0.751133	−	0.751133i	0.0273004	−	0.0273004i	0.720625	+	0.693325i	$0.243855\pi$
$758$	2.02897	−	23.1912i	0.0736954	−	0.842342i
$759$		0			0
$760$	−1.25603	+	1.11099i	−0.0455611	+	0.0402999i
$761$	3.39595	+	9.33028i	0.123103	+	0.338223i	0.985902	−	0.167325i	$-0.0535128\pi$
$761$	3.39595	+	9.33028i	0.123103	+	0.338223i	−0.862799	+	0.505547i	$0.831291\pi$
$762$		0			0
$763$	14.0481	−	20.0628i	0.508576	−	0.726322i
$764$	−4.45462	−	7.71563i	−0.161163	−	0.279142i
$765$		0			0
$766$	6.40435	−	11.0927i	0.231399	−	0.400794i
$767$	8.51939	+	18.2699i	0.307617	+	0.659688i
$768$		0			0
$769$	12.7295	−	15.1704i	0.459038	−	0.547060i	−0.486027	−	0.873944i	$-0.661554\pi$
$769$	12.7295	−	15.1704i	0.459038	−	0.547060i	0.945064	+	0.326884i	$0.105999\pi$
$770$	−14.2991	+	21.5983i	−0.515305	+	0.778350i
$771$		0			0
$772$	−22.1994	+	10.3518i	−0.798975	+	0.372568i
$773$	1.85379	+	6.91845i	0.0666763	+	0.248839i	0.991217	−	0.132243i	$-0.0422180\pi$
$773$	1.85379	+	6.91845i	0.0666763	+	0.248839i	−0.924541	+	0.381083i	$0.875551\pi$
$774$		0			0
$775$	−7.90508	−	8.48100i	−0.283959	−	0.304646i
$776$	−2.64646	+	0.466643i	−0.0950025	+	0.0167515i
$777$		0			0
$778$	−34.8223	−	16.2379i	−1.24844	−	0.582158i
$779$	−1.13347	+	6.42821i	−0.0406107	+	0.230315i
$780$		0			0
$781$	−4.54165	+	3.81090i	−0.162513	+	0.136365i
$782$	−0.783054	−	0.783054i	−0.0280020	−	0.0280020i
$783$		0			0
$784$		−	0.576020i		−	0.0205721i
$785$	0.640906	+	24.5814i	0.0228749	+	0.877346i
$786$		0			0
$787$	18.7231	+	26.7393i	0.667406	+	0.953155i	0.999949	+	0.0100667i	$0.00320438\pi$
$787$	18.7231	+	26.7393i	0.667406	+	0.953155i	−0.332543	+	0.943088i	$0.607907\pi$
$788$	2.29841	−	4.92896i	0.0818775	−	0.175587i
$789$		0			0
$790$	−9.46679	−	5.14143i	−0.336813	−	0.182924i
$791$	−40.4335	+	23.3443i	−1.43765	+	0.830028i
$792$		0			0
$793$	4.80581	−	1.28771i	0.170659	−	0.0457280i
$794$	−8.89221	−	3.23650i	−0.315573	−	0.114859i
$795$		0			0
$796$	7.34242	+	6.16102i	0.260245	+	0.218372i
$797$	0.119877	+	1.37020i	0.00424625	+	0.0485348i	0.998022	−	0.0628625i	$-0.0200229\pi$
$797$	0.119877	+	1.37020i	0.00424625	+	0.0485348i	−0.993776	+	0.111397i	$0.964467\pi$
$798$		0			0
$799$	5.83891	−	16.0423i	0.206566	−	0.567535i
$800$	−4.41527	+	2.34636i	−0.156103	+	0.0829564i
$801$		0			0
$802$	12.3436	+	3.30745i	0.435866	+	0.116790i
$803$	−14.2018	−	9.94419i	−0.501170	−	0.350923i
$804$		0			0
$805$	0.811604	+	1.62829i	0.0286053	+	0.0573895i
$806$	−10.1729	−	1.79376i	−0.358325	−	0.0631824i
$807$		0			0
$808$	−1.55313	−	0.135882i	−0.0546391	−	0.00478030i
$809$	27.7857			0.976894			0.488447	−	0.872594i	$-0.337564\pi$
$809$	27.7857			0.976894			0.488447	+	0.872594i	$0.337564\pi$
$810$		0			0
$811$	10.3689			0.364103			0.182051	−	0.983289i	$-0.441726\pi$
$811$	10.3689			0.364103			0.182051	+	0.983289i	$0.441726\pi$
$812$	−25.0329	−	2.19010i	−0.878483	−	0.0768573i
$813$		0			0
$814$	40.6270	+	7.16364i	1.42398	+	0.251086i
$815$	−10.7625	−	3.60244i	−0.376995	−	0.126188i
$816$		0			0
$817$	7.87352	+	5.51310i	0.275460	+	0.192879i
$818$	39.0262	+	10.4570i	1.36452	+	0.365622i
$819$		0			0
$820$	−7.76282	+	17.8477i	−0.271089	+	0.623270i
$821$	−2.76752	+	7.60370i	−0.0965872	+	0.265371i	−0.978571	−	0.205908i	$-0.933985\pi$
$821$	−2.76752	+	7.60370i	−0.0965872	+	0.265371i	0.881984	+	0.471279i	$0.156207\pi$
$822$		0			0
$823$	−0.918373	−	10.4971i	−0.0320125	−	0.365904i	−0.995257	−	0.0972788i	$-0.968986\pi$
$823$	−0.918373	−	10.4971i	−0.0320125	−	0.365904i	0.963245	−	0.268626i	$-0.0865694\pi$
$824$	−9.24497	−	7.75745i	−0.322064	−	0.270244i
$825$		0			0
$826$	−10.7774	−	3.92264i	−0.374993	−	0.136486i
$827$	11.1947	−	2.99962i	0.389280	−	0.104307i	−0.0588702	−	0.998266i	$-0.518750\pi$
$827$	11.1947	−	2.99962i	0.389280	−	0.104307i	0.448150	+	0.893959i	$0.352083\pi$
$828$		0			0
$829$	38.9153	−	22.4678i	1.35158	−	0.780337i	0.363113	−	0.931745i	$-0.381714\pi$
$829$	38.9153	−	22.4678i	1.35158	−	0.780337i	0.988471	+	0.151408i	$0.0483806\pi$
$830$	−3.67491	−	12.4114i	−0.127558	−	0.430807i
$831$		0			0
$832$	−1.88271	+	4.03748i	−0.0652712	+	0.139975i
$833$	−1.13974	−	1.62772i	−0.0394898	−	0.0563973i
$834$		0			0
$835$	−12.1332	+	0.316347i	−0.419887	+	0.0109477i
$836$		−	3.42749i		−	0.118542i
$837$		0			0
$838$	−16.1180	−	16.1180i	−0.556787	−	0.556787i
$839$	27.5846	−	23.1462i	0.952324	−	0.799095i	−0.0273630	−	0.999626i	$-0.508711\pi$
$839$	27.5846	−	23.1462i	0.952324	−	0.799095i	0.979687	+	0.200530i	$0.0642666\pi$
$840$		0			0
$841$	12.0329	−	68.2420i	0.414928	−	2.35317i
$842$	−5.29382	−	2.46855i	−0.182437	−	0.0850718i
$843$		0			0
$844$	−2.72696	+	0.480837i	−0.0938659	+	0.0165511i
$845$	−12.3063	+	9.10407i	−0.423351	+	0.313189i
$846$		0			0
$847$	−6.48711	−	24.2102i	−0.222900	−	0.831874i
$848$	8.95496	−	4.17577i	0.307515	−	0.143396i
$849$		0			0
$850$	−7.83408	+	15.3667i	−0.268707	+	0.527072i
$851$	1.86252	−	2.21966i	0.0638462	−	0.0760890i
$852$		0			0
$853$	8.48642	+	18.1992i	0.290569	+	0.623128i	0.996356	−	0.0852968i	$-0.0271839\pi$
$853$	8.48642	+	18.1992i	0.290569	+	0.623128i	−0.705786	+	0.708425i	$0.749406\pi$
$854$	−1.41534	+	2.45143i	−0.0484318	+	0.0838863i
$855$		0			0
$856$	−2.67779	−	4.63807i	−0.0915249	−	0.158526i
$857$	−6.52736	+	9.32203i	−0.222970	+	0.318435i	−0.915015	−	0.403420i	$-0.867821\pi$
$857$	−6.52736	+	9.32203i	−0.222970	+	0.318435i	0.692045	+	0.721855i	$0.256710\pi$
$858$		0			0
$859$	−1.42217	−	3.90737i	−0.0485236	−	0.133318i	0.913064	−	0.407817i	$-0.133710\pi$
$859$	−1.42217	−	3.90737i	−0.0485236	−	0.133318i	−0.961587	+	0.274500i	$0.911488\pi$
$860$	18.9881	+	21.4670i	0.647489	+	0.732020i
$861$		0			0
$862$	−1.22622	+	14.0158i	−0.0417653	+	0.477380i
$863$	27.4819	−	27.4819i	0.935494	−	0.935494i	−0.0625484	−	0.998042i	$-0.519923\pi$
$863$	27.4819	−	27.4819i	0.935494	−	0.935494i	0.998042	+	0.0625484i	$0.0199228\pi$
$864$		0			0
$865$	−16.6924	+	20.9804i	−0.567560	+	0.713355i
$866$	−5.87673	−	7.00362i	−0.199699	−	0.237993i
$867$		0			0
$868$	4.81421	−	3.37094i	0.163405	−	0.114417i
$869$	20.6914	−	7.53107i	0.701909	−	0.255474i
$870$		0			0
$871$	6.28607	+	35.6501i	0.212995	+	1.20796i
$872$	−2.50104	+	9.33402i	−0.0846960	+	0.316090i
$873$		0			0
$874$	−0.208485	−	0.120369i	−0.00705212	−	0.00407154i
$875$	20.2183	−	19.8550i	0.683502	−	0.671220i
$876$		0			0
$877$	−8.64931	+	0.756716i	−0.292066	+	0.0255525i	−0.232247	−	0.972657i	$-0.574608\pi$
$877$	−8.64931	+	0.756716i	−0.292066	+	0.0255525i	−0.0598190	+	0.998209i	$0.519052\pi$
$878$	−32.8443	+	2.87350i	−1.10844	+	0.0969759i
$879$		0			0
$880$	2.38690	−	9.93719i	0.0804623	−	0.334983i
$881$	−17.0919	−	9.86804i	−0.575842	−	0.332463i	0.183637	−	0.982994i	$-0.441213\pi$
$881$	−17.0919	−	9.86804i	−0.575842	−	0.332463i	−0.759479	+	0.650531i	$0.774546\pi$
$882$		0			0
$883$	4.58725	−	17.1198i	0.154373	−	0.576128i	−0.844785	−	0.535106i	$-0.820272\pi$
$883$	4.58725	−	17.1198i	0.154373	−	0.576128i	0.999158	−	0.0410227i	$-0.0130616\pi$
$884$	2.66860	+	15.1344i	0.0897549	+	0.509025i
$885$		0			0
$886$	6.60039	−	2.40235i	0.221745	−	0.0807084i
$887$	−6.07170	+	4.25145i	−0.203868	+	0.142750i	−0.671052	−	0.741410i	$-0.734157\pi$
$887$	−6.07170	+	4.25145i	−0.203868	+	0.142750i	0.467184	+	0.884160i	$0.345268\pi$
$888$		0			0
$889$	−19.9302	−	23.7519i	−0.668438	−	0.796614i
$890$	13.3616	+	10.6308i	0.447882	+	0.356344i
$891$		0			0
$892$	−8.23842	+	8.23842i	−0.275843	+	0.275843i
$893$	0.323455	−	3.69711i	0.0108240	−	0.123719i
$894$		0			0
$895$	−0.654997	+	10.6893i	−0.0218942	+	0.357304i
$896$	−0.866870	−	2.38170i	−0.0289601	−	0.0795672i
$897$		0			0
$898$	2.02801	−	2.89630i	0.0676757	−	0.0966509i
$899$	11.4946	+	19.9092i	0.383366	+	0.664009i
$900$		0			0
$901$	17.0426	−	29.5187i	0.567773	−	0.983411i
$902$	−16.8124	−	36.0543i	−0.559791	−	1.20048i
$903$		0			0
$904$	11.8407	−	14.1112i	0.393815	−	0.469331i
$905$	−22.7321	−	15.0498i	−0.755641	−	0.500271i
$906$		0			0
$907$	−9.04352	+	4.21706i	−0.300285	+	0.140025i	−0.566921	−	0.823772i	$-0.691866\pi$
$907$	−9.04352	+	4.21706i	−0.300285	+	0.140025i	0.266636	+	0.963797i	$0.414088\pi$
$908$	5.76018	+	21.4973i	0.191158	+	0.713413i
$909$		0			0
$910$	3.73467	−	24.9700i	0.123803	−	0.827747i
$911$	53.2557	−	9.39041i	1.76444	−	0.311118i	0.805051	−	0.593206i	$-0.202138\pi$
$911$	53.2557	−	9.39041i	1.76444	−	0.311118i	0.959389	+	0.282088i	$0.0910270\pi$
$912$		0			0
$913$	23.9784	+	11.1813i	0.793569	+	0.370047i
$914$	3.76339	−	21.3432i	0.124482	−	0.705971i
$915$		0			0
$916$	−9.20195	+	7.72135i	−0.304041	+	0.255121i
$917$	−3.61790	−	3.61790i	−0.119473	−	0.119473i
$918$		0			0
$919$		−	20.6866i		−	0.682387i	−0.939993	−	0.341193i	$-0.889169\pi$
$919$		−	20.6866i		−	0.682387i	0.939993	−	0.341193i	$-0.110831\pi$
$920$	−0.520629	−	0.494171i	−0.0171646	−	0.0162923i
$921$		0			0
$922$	8.17587	+	11.6764i	0.269258	+	0.384540i
$923$	2.44222	−	5.23735i	0.0803865	−	0.172389i
$924$		0			0
$925$	−41.8409	−	16.9158i	−1.37572	−	0.556189i
$926$	19.5737	−	11.3009i	0.643232	−	0.371370i
$927$		0			0
$928$	9.57655	−	2.56603i	0.314366	−	0.0842340i
$929$	11.4589	+	4.17069i	0.375953	+	0.136836i	0.523084	−	0.852281i	$-0.324781\pi$
$929$	11.4589	+	4.17069i	0.375953	+	0.136836i	−0.147130	+	0.989117i	$0.547004\pi$
$930$		0			0
$931$	−0.330909	−	0.277665i	−0.0108451	−	0.00910011i
$932$	1.10947	+	12.6813i	0.0363418	+	0.415389i
$933$		0			0
$934$	7.36384	−	20.2320i	0.240952	−	0.662011i
$935$	−12.9174	−	32.8035i	−0.422443	−	1.07279i
$936$		0			0
$937$	47.4270	+	12.7080i	1.54937	+	0.415153i	0.929280	−	0.369376i	$-0.120429\pi$
$937$	47.4270	+	12.7080i	1.54937	+	0.415153i	0.620092	+	0.784529i	$0.287095\pi$
$938$	−16.8710	−	11.8132i	−0.550857	−	0.385714i
$939$		0			0
$940$	3.51244	−	10.4936i	0.114563	−	0.342265i
$941$	10.6194	+	1.87249i	0.346183	+	0.0610414i	0.344036	−	0.938956i	$-0.388206\pi$
$941$	10.6194	+	1.87249i	0.346183	+	0.0610414i	0.00214645	+	0.999998i	$0.499317\pi$
$942$		0			0
$943$	−2.78352	−	0.243526i	−0.0906438	−	0.00793031i
$944$	4.52507			0.147278
$945$		0			0
$946$	−58.5796			−1.90459
$947$	20.1801	+	1.76553i	0.655766	+	0.0573721i	0.410183	−	0.912003i	$-0.365465\pi$
$947$	20.1801	+	1.76553i	0.655766	+	0.0573721i	0.245584	+	0.969375i	$0.421020\pi$
$948$		0			0
$949$	16.6420	+	2.93444i	0.540223	+	0.0952558i
$950$	−0.780418	+	3.66750i	−0.0253201	+	0.118989i
$951$		0			0
$952$	−7.16218	−	5.01502i	−0.232128	−	0.162538i
$953$	9.71258	+	2.60248i	0.314621	+	0.0843025i	0.412674	−	0.910879i	$-0.364595\pi$
$953$	9.71258	+	2.60248i	0.314621	+	0.0843025i	−0.0980530	+	0.995181i	$0.531261\pi$
$954$		0			0
$955$	−18.2685	−	7.94581i	−0.591154	−	0.257120i
$956$	−8.69372	+	23.8858i	−0.281175	+	0.772522i
$957$		0			0
$958$	2.68386	+	30.6767i	0.0867116	+	0.991118i
$959$	−27.6588	−	23.2085i	−0.893149	−	0.749441i
$960$		0			0
$961$	24.0780	+	8.76368i	0.776710	+	0.282699i
$962$	−38.8404	+	10.4073i	−1.25226	+	0.335543i
$963$		0			0
$964$	−7.77636	+	4.48969i	−0.250460	+	0.144603i
$965$	−26.1399	+	48.1308i	−0.841474	+	1.54938i
$966$		0			0
$967$	10.1913	−	21.8553i	0.327731	−	0.702820i	−0.671542	−	0.740967i	$-0.734368\pi$
$967$	10.1913	−	21.8553i	0.327731	−	0.702820i	0.999272	+	0.0381464i	$0.0121453\pi$
$968$	5.67211	+	8.10061i	0.182308	+	0.260363i
$969$		0			0
$970$	−4.13679	+	4.35828i	−0.132824	+	0.139936i
$971$			17.4735i			0.560751i	0.959890	+	0.280375i	$0.0904590\pi$
$971$			17.4735i			0.560751i	−0.959890	+	0.280375i	$0.909541\pi$
$972$		0			0
$973$	12.6099	+	12.6099i	0.404254	+	0.404254i
$974$	20.1043	−	16.8695i	0.644183	−	0.540534i
$975$		0			0
$976$	0.193936	−	1.09986i	0.00620773	−	0.0352058i
$977$	−8.96432	−	4.18013i	−0.286794	−	0.133734i	0.273898	−	0.961759i	$-0.411687\pi$
$977$	−8.96432	−	4.18013i	−0.286794	−	0.133734i	−0.560692	+	0.828025i	$0.689465\pi$
$978$		0			0
$979$	−34.3699	+	6.06035i	−1.09847	+	0.193690i
$980$	−0.766026	−	1.03547i	−0.0244698	−	0.0330769i
$981$		0			0
$982$	−5.43253	−	20.2745i	−0.173359	−	0.646985i
$983$	−43.6314	+	20.3457i	−1.39163	+	0.648926i	−0.966608	−	0.256258i	$-0.917510\pi$
$983$	−43.6314	+	20.3457i	−1.39163	+	0.648926i	−0.425019	+	0.905185i	$0.639732\pi$
$984$		0			0
$985$	−2.42314	−	11.9170i	−0.0772077	−	0.379707i
$986$	21.9842	−	26.1998i	0.700121	−	0.834372i
$987$		0			0
$988$	1.41189	+	3.02780i	0.0449181	+	0.0963273i
$989$	−2.05724	+	3.56325i	−0.0654165	+	0.113305i
$990$		0			0
$991$	31.0478	+	53.7764i	0.986267	+	1.70826i	0.636164	+	0.771554i	$0.280520\pi$
$991$	31.0478	+	53.7764i	0.986267	+	1.70826i	0.350103	+	0.936711i	$0.386147\pi$
$992$	−1.32999	+	1.89943i	−0.0422273	+	0.0603069i
$993$		0			0
$994$	1.12449	+	3.08950i	0.0356666	+	0.0979931i
$995$	21.3922	+	1.31083i	0.678180	+	0.0415562i
$996$		0			0
$997$	−0.291531	+	3.33222i	−0.00923288	+	0.105532i	−0.999413	−	0.0342672i	$-0.989090\pi$
$997$	−0.291531	+	3.33222i	−0.00923288	+	0.105532i	0.990180	+	0.139800i	$0.0446458\pi$
$998$	8.77216	−	8.77216i	0.277678	−	0.277678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.8		216
3.2	odd	2		270.2.r.a.113.10	✓	216
5.2	odd	4	inner	810.2.s.a.287.11		216
15.2	even	4		270.2.r.a.167.6	yes	216
27.11	odd	18	inner	810.2.s.a.683.11		216
27.16	even	9		270.2.r.a.173.6	yes	216
135.92	even	36	inner	810.2.s.a.197.8		216
135.97	odd	36		270.2.r.a.227.10	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.10	✓	216	3.2	odd	2
270.2.r.a.167.6	yes	216	15.2	even	4
270.2.r.a.173.6	yes	216	27.16	even	9
270.2.r.a.227.10	yes	216	135.97	odd	36
810.2.s.a.197.8		216	135.92	even	36	inner
810.2.s.a.287.11		216	5.2	odd	4	inner
810.2.s.a.683.11		216	27.11	odd	18	inner
810.2.s.a.773.8		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)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.00125 - 0.997503i) q^{5} +(2.07619 + 1.45376i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(2.00125 - 0.997503i) q^{5} +(2.07619 + 1.45376i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-2.08057 + 0.819287i) q^{10} +(1.56319 - 4.29482i) q^{11} +(0.388268 + 4.43792i) q^{13} +(-1.94158 - 1.62918i) q^{14} +(0.939693 + 0.342020i) q^{16} +(3.33214 - 0.892843i) q^{17} +(0.649453 - 0.374962i) q^{19} +(2.14406 - 0.634835i) q^{20} +(-1.93156 + 4.14224i) q^{22} +(0.184128 + 0.262962i) q^{23} +(3.00998 - 3.99250i) q^{25} -4.45487i q^{26} +(1.79220 + 1.79220i) q^{28} +(-7.59485 + 6.37284i) q^{29} +(0.402651 - 2.28354i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-3.39727 + 0.599031i) q^{34} +(5.60510 + 0.838335i) q^{35} +(-2.33615 - 8.71863i) q^{37} +(-0.679661 + 0.316931i) q^{38} +(-2.19123 + 0.445553i) q^{40} +(-5.59486 + 6.66770i) q^{41} +(5.41671 + 11.6162i) q^{43} +(2.28523 - 3.95813i) q^{44} +(-0.160508 - 0.278009i) q^{46} +(2.83852 - 4.05383i) q^{47} +(-0.197010 - 0.541282i) q^{49} +(-3.34649 + 3.71497i) q^{50} +(-0.388268 + 4.43792i) q^{52} +(6.98671 - 6.98671i) q^{53} +(-1.15577 - 10.1543i) q^{55} +(-1.62918 - 1.94158i) q^{56} +(8.12138 - 5.68665i) q^{58} +(4.25217 - 1.54766i) q^{59} +(-0.193936 - 1.09986i) q^{61} +(-0.600142 + 2.23976i) q^{62} +(0.866025 + 0.500000i) q^{64} +(5.20385 + 8.49407i) q^{65} +(8.09502 - 0.708223i) q^{67} +(3.43655 - 0.300659i) q^{68} +(-5.51070 - 1.32366i) q^{70} +(-1.12339 - 0.648590i) q^{71} +(0.981783 - 3.66406i) q^{73} +(1.56738 + 8.88907i) q^{74} +(0.704697 - 0.256489i) q^{76} +(9.48911 - 6.64435i) q^{77} +(3.09680 + 3.69062i) q^{79} +(2.22172 - 0.252879i) q^{80} +(6.15470 - 6.15470i) q^{82} +(-0.504523 + 5.76673i) q^{83} +(5.77781 - 5.11061i) q^{85} +(-4.38368 - 12.0441i) q^{86} +(-2.62150 + 3.74389i) q^{88} +(-3.81802 - 6.61301i) q^{89} +(-5.64556 + 9.77840i) q^{91} +(0.135668 + 0.290940i) q^{92} +(-3.18104 + 3.79101i) q^{94} +(0.925690 - 1.39822i) q^{95} +(2.43551 - 1.13570i) q^{97} +(0.149085 + 0.556392i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 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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Database

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