LMFDB - Embedded newform 810.2.s.a.773.15

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			773.15
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.30964 - 1.81241i) q^{5} +(-3.63487 - 2.54517i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.30964 - 1.81241i) q^{5} +(-3.63487 - 2.54517i) q^{7} +(0.965926 + 0.258819i) q^{8} +(1.46262 - 1.69137i) q^{10} +(-1.06118 + 2.91557i) q^{11} +(-0.443416 - 5.06827i) q^{13} +(-3.39922 - 2.85228i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.90525 - 0.778460i) q^{17} +(4.83096 - 2.78915i) q^{19} +(1.60447 - 1.55746i) q^{20} +(-1.31125 + 2.81199i) q^{22} +(-3.26865 - 4.66812i) q^{23} +(-1.56967 - 4.74722i) q^{25} -5.08763i q^{26} +(-3.13769 - 3.13769i) q^{28} +(0.945635 - 0.793482i) q^{29} +(-0.863767 + 4.89867i) q^{31} +(0.906308 + 0.422618i) q^{32} +(2.96205 - 0.522288i) q^{34} +(-9.37328 + 3.25463i) q^{35} +(-0.154906 - 0.578116i) q^{37} +(5.05567 - 2.35750i) q^{38} +(1.73410 - 1.41169i) q^{40} +(-0.230916 + 0.275195i) q^{41} +(0.843535 + 1.80897i) q^{43} +(-1.55134 + 2.68701i) q^{44} +(-2.84936 - 4.93524i) q^{46} +(-4.62779 + 6.60916i) q^{47} +(4.34030 + 11.9249i) q^{49} +(-1.14995 - 4.86597i) q^{50} +(0.443416 - 5.06827i) q^{52} +(5.61053 - 5.61053i) q^{53} +(3.89445 + 5.74166i) q^{55} +(-2.85228 - 3.39922i) q^{56} +(1.01119 - 0.708045i) q^{58} +(4.22275 - 1.53695i) q^{59} +(0.293531 + 1.66470i) q^{61} +(-1.28743 + 4.80474i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-9.76650 - 5.83397i) q^{65} +(8.65868 - 0.757536i) q^{67} +(2.99629 - 0.262142i) q^{68} +(-9.62127 + 2.42531i) q^{70} +(-4.54040 - 2.62140i) q^{71} +(0.146181 - 0.545555i) q^{73} +(-0.103930 - 0.589417i) q^{74} +(5.24190 - 1.90789i) q^{76} +(11.2779 - 7.89686i) q^{77} +(4.05065 + 4.82738i) q^{79} +(1.85054 - 1.25519i) q^{80} +(-0.254023 + 0.254023i) q^{82} +(-1.20341 + 13.7551i) q^{83} +(2.39395 - 6.28502i) q^{85} +(0.682663 + 1.87560i) q^{86} +(-1.77963 + 2.54157i) q^{88} +(6.98069 + 12.0909i) q^{89} +(-11.2878 + 19.5511i) q^{91} +(-2.40838 - 5.16480i) q^{92} +(-5.18620 + 6.18068i) q^{94} +(1.27173 - 12.4085i) q^{95} +(13.7632 - 6.41791i) q^{97} +(3.28446 + 12.2578i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.30964	−	1.81241i	0.585690	−	0.810535i
$5$	1.30964	−	1.81241i	0.585690	−	0.810535i
$6$		0			0
$7$	−3.63487	−	2.54517i	−1.37385	−	0.961983i	−0.999396	−	0.0347383i	$-0.988940\pi$
$7$	−3.63487	−	2.54517i	−1.37385	−	0.961983i	−0.374457	−	0.927244i	$-0.622171\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$		0			0
$10$	1.46262	−	1.69137i	0.462522	−	0.534859i
$11$	−1.06118	+	2.91557i	−0.319959	+	0.879079i	0.670579	+	0.741838i	$0.266046\pi$
$11$	−1.06118	+	2.91557i	−0.319959	+	0.879079i	−0.990538	+	0.137241i	$0.956177\pi$
$12$		0			0
$13$	−0.443416	−	5.06827i	−0.122981	−	1.40568i	−0.767477	−	0.641077i	$-0.778488\pi$
$13$	−0.443416	−	5.06827i	−0.122981	−	1.40568i	0.644495	−	0.764608i	$-0.277067\pi$
$14$	−3.39922	−	2.85228i	−0.908479	−	0.762304i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	2.90525	−	0.778460i	0.704627	−	0.188804i	0.111325	−	0.993784i	$-0.464491\pi$
$17$	2.90525	−	0.778460i	0.704627	−	0.188804i	0.593302	+	0.804980i	$0.297824\pi$
$18$		0			0
$19$	4.83096	−	2.78915i	1.10830	−	0.639876i	0.169910	−	0.985460i	$-0.445652\pi$
$19$	4.83096	−	2.78915i	1.10830	−	0.639876i	0.938388	+	0.345584i	$0.112319\pi$
$20$	1.60447	−	1.55746i	0.358770	−	0.348259i
$21$		0			0
$22$	−1.31125	+	2.81199i	−0.279560	+	0.599519i
$23$	−3.26865	−	4.66812i	−0.681561	−	0.973370i	−0.999679	−	0.0253193i	$-0.991940\pi$
$23$	−3.26865	−	4.66812i	−0.681561	−	0.973370i	0.318118	−	0.948051i	$-0.396949\pi$
$24$		0			0
$25$	−1.56967	−	4.74722i	−0.313934	−	0.949445i
$26$		−	5.08763i		−	0.997766i
$27$		0			0
$28$	−3.13769	−	3.13769i	−0.592968	−	0.592968i
$29$	0.945635	−	0.793482i	0.175600	−	0.147346i	−0.550752	−	0.834669i	$-0.685659\pi$
$29$	0.945635	−	0.793482i	0.175600	−	0.147346i	0.726352	+	0.687323i	$0.241214\pi$
$30$		0			0
$31$	−0.863767	+	4.89867i	−0.155137	+	0.879827i	0.803523	+	0.595274i	$0.202956\pi$
$31$	−0.863767	+	4.89867i	−0.155137	+	0.879827i	−0.958660	+	0.284553i	$0.908155\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$		0			0
$34$	2.96205	−	0.522288i	0.507987	−	0.0895717i
$35$	−9.37328	+	3.25463i	−1.58437	+	0.550133i
$36$		0			0
$37$	−0.154906	−	0.578116i	−0.0254663	−	0.0950417i	0.952023	−	0.306026i	$-0.0989996\pi$
$37$	−0.154906	−	0.578116i	−0.0254663	−	0.0950417i	−0.977489	+	0.210985i	$0.932333\pi$
$38$	5.05567	−	2.35750i	0.820137	−	0.382436i
$39$		0			0
$40$	1.73410	−	1.41169i	0.274186	−	0.223208i
$41$	−0.230916	+	0.275195i	−0.0360631	+	0.0429783i	−0.783775	−	0.621045i	$-0.786708\pi$
$41$	−0.230916	+	0.275195i	−0.0360631	+	0.0429783i	0.747711	+	0.664024i	$0.231153\pi$
$42$		0			0
$43$	0.843535	+	1.80897i	0.128638	+	0.275865i	0.960069	−	0.279763i	$-0.0902558\pi$
$43$	0.843535	+	1.80897i	0.128638	+	0.275865i	−0.831431	+	0.555628i	$0.812478\pi$
$44$	−1.55134	+	2.68701i	−0.233874	+	0.405082i
$45$		0			0
$46$	−2.84936	−	4.93524i	−0.420115	−	0.727661i
$47$	−4.62779	+	6.60916i	−0.675032	+	0.964046i	0.324801	+	0.945782i	$0.394703\pi$
$47$	−4.62779	+	6.60916i	−0.675032	+	0.964046i	−0.999833	+	0.0182633i	$0.994186\pi$
$48$		0			0
$49$	4.34030	+	11.9249i	0.620043	+	1.70355i
$50$	−1.14995	−	4.86597i	−0.162627	−	0.688151i
$51$		0			0
$52$	0.443416	−	5.06827i	0.0614907	−	0.702842i
$53$	5.61053	−	5.61053i	0.770665	−	0.770665i	−0.207557	−	0.978223i	$-0.566551\pi$
$53$	5.61053	−	5.61053i	0.770665	−	0.770665i	0.978223	+	0.207557i	$0.0665514\pi$
$54$		0			0
$55$	3.89445	+	5.74166i	0.525128	+	0.774205i
$56$	−2.85228	−	3.39922i	−0.381152	−	0.454239i
$57$		0			0
$58$	1.01119	−	0.708045i	0.132776	−	0.0929709i
$59$	4.22275	−	1.53695i	0.549755	−	0.200094i	−0.0521828	−	0.998638i	$-0.516618\pi$
$59$	4.22275	−	1.53695i	0.549755	−	0.200094i	0.601938	+	0.798543i	$0.294396\pi$
$60$		0			0
$61$	0.293531	+	1.66470i	0.0375829	+	0.213143i	0.997816	−	0.0660570i	$-0.0210419\pi$
$61$	0.293531	+	1.66470i	0.0375829	+	0.213143i	−0.960233	+	0.279200i	$0.909931\pi$
$62$	−1.28743	+	4.80474i	−0.163503	+	0.610203i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−9.76650	−	5.83397i	−1.21139	−	0.723615i
$66$		0			0
$67$	8.65868	−	0.757536i	1.05783	−	0.0925478i	0.455056	−	0.890463i	$-0.349619\pi$
$67$	8.65868	−	0.757536i	1.05783	−	0.0925478i	0.602770	+	0.797915i	$0.294064\pi$
$68$	2.99629	−	0.262142i	0.363354	−	0.0317894i
$69$		0			0
$70$	−9.62127	+	2.42531i	−1.14996	+	0.289880i
$71$	−4.54040	−	2.62140i	−0.538847	−	0.311103i	0.205765	−	0.978601i	$-0.434032\pi$
$71$	−4.54040	−	2.62140i	−0.538847	−	0.311103i	−0.744611	+	0.667498i	$0.767365\pi$
$72$		0			0
$73$	0.146181	−	0.545555i	0.0171092	−	0.0638524i	−0.956843	−	0.290604i	$-0.906144\pi$
$73$	0.146181	−	0.545555i	0.0171092	−	0.0638524i	0.973953	+	0.226751i	$0.0728105\pi$
$74$	−0.103930	−	0.589417i	−0.0120816	−	0.0685184i
$75$		0			0
$76$	5.24190	−	1.90789i	0.601287	−	0.218850i
$77$	11.2779	−	7.89686i	1.28523	−	0.899931i
$78$		0			0
$79$	4.05065	+	4.82738i	0.455734	+	0.543122i	0.944162	−	0.329482i	$-0.106874\pi$
$79$	4.05065	+	4.82738i	0.455734	+	0.543122i	−0.488428	+	0.872604i	$0.662430\pi$
$80$	1.85054	−	1.25519i	0.206897	−	0.140334i
$81$		0			0
$82$	−0.254023	+	0.254023i	−0.0280521	+	0.0280521i
$83$	−1.20341	+	13.7551i	−0.132092	+	1.50982i	0.583968	+	0.811777i	$0.301500\pi$
$83$	−1.20341	+	13.7551i	−0.132092	+	1.50982i	−0.716059	+	0.698039i	$0.754056\pi$
$84$		0			0
$85$	2.39395	−	6.28502i	0.259661	−	0.681706i
$86$	0.682663	+	1.87560i	0.0736135	+	0.202251i
$87$		0			0
$88$	−1.77963	+	2.54157i	−0.189709	+	0.270933i
$89$	6.98069	+	12.0909i	0.739952	+	1.28163i	0.952516	+	0.304487i	$0.0984851\pi$
$89$	6.98069	+	12.0909i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$90$		0			0
$91$	−11.2878	+	19.5511i	−1.18329	+	2.04951i
$92$	−2.40838	−	5.16480i	−0.251091	−	0.538467i
$93$		0			0
$94$	−5.18620	+	6.18068i	−0.534916	+	0.637488i
$95$	1.27173	−	12.4085i	0.130477	−	1.27308i
$96$		0			0
$97$	13.7632	−	6.41791i	1.39745	−	0.651640i	0.429562	−	0.903037i	$-0.358668\pi$
$97$	13.7632	−	6.41791i	1.39745	−	0.651640i	0.967884	+	0.251398i	$0.0808902\pi$
$98$	3.28446	+	12.2578i	0.331781	+	1.23822i
$99$		0			0
$100$	−0.721477	−	4.94767i	−0.0721477	−	0.494767i
$101$	−12.9642	+	2.28593i	−1.28998	+	0.227459i	−0.776214	−	0.630469i	$-0.782862\pi$
$101$	−12.9642	+	2.28593i	−1.28998	+	0.227459i	−0.513770	+	0.857928i	$0.671751\pi$
$102$		0			0
$103$	10.4924	+	4.89268i	1.03385	+	0.482090i	0.864059	−	0.503391i	$-0.167914\pi$
$103$	10.4924	+	4.89268i	1.03385	+	0.482090i	0.169787	+	0.985481i	$0.445692\pi$
$104$	0.883457	−	5.01034i	0.0866301	−	0.491304i
$105$		0			0
$106$	6.07817	−	5.10019i	0.590364	−	0.495374i
$107$	−0.623217	−	0.623217i	−0.0602487	−	0.0602487i	0.676340	−	0.736589i	$-0.263565\pi$
$107$	−0.623217	−	0.623217i	−0.0602487	−	0.0602487i	−0.736589	+	0.676340i	$0.763565\pi$
$108$		0			0
$109$		−	19.3629i		−	1.85463i	−0.374277	−	0.927317i	$-0.622109\pi$
$109$		−	19.3629i		−	1.85463i	0.374277	−	0.927317i	$-0.377891\pi$
$110$	3.37921	+	6.05924i	0.322195	+	0.577725i
$111$		0			0
$112$	−2.54517	−	3.63487i	−0.240496	−	0.343463i
$113$	−5.50579	+	11.8072i	−0.517941	+	1.11073i	0.457245	+	0.889341i	$0.348836\pi$
$113$	−5.50579	+	11.8072i	−0.517941	+	1.11073i	−0.975186	+	0.221387i	$0.928942\pi$
$114$		0			0
$115$	−12.7413	−	0.189427i	−1.18813	−	0.0176641i
$116$	1.06906	−	0.617220i	0.0992593	−	0.0573074i
$117$		0			0
$118$	4.34063	−	1.16307i	0.399588	−	0.107069i
$119$	−12.5415	−	4.56475i	−1.14968	−	0.418450i
$120$		0			0
$121$	1.05202	+	0.882752i	0.0956384	+	0.0802501i
$122$	0.147326	+	1.68395i	0.0133383	+	0.152457i
$123$		0			0
$124$	−1.70129	+	4.67425i	−0.152780	+	0.419760i
$125$	−10.6596	−	3.37228i	−0.953426	−	0.301626i
$126$		0			0
$127$	−10.4924	−	2.81142i	−0.931047	−	0.249473i	−0.238746	−	0.971082i	$-0.576736\pi$
$127$	−10.4924	−	2.81142i	−0.931047	−	0.249473i	−0.692301	+	0.721609i	$0.743403\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$		0			0
$130$	−9.22088	−	6.66298i	−0.808724	−	0.584382i
$131$	−2.41953	−	0.426628i	−0.211395	−	0.0372747i	0.0669475	−	0.997756i	$-0.478674\pi$
$131$	−2.41953	−	0.426628i	−0.211395	−	0.0372747i	−0.278343	+	0.960482i	$0.589785\pi$
$132$		0			0
$133$	−24.6588	−	2.15736i	−2.13819	−	0.187067i
$134$	8.69175			0.750853
$135$		0			0
$136$	3.00774			0.257912
$137$	6.93208	+	0.606478i	0.592247	+	0.0518149i	0.379340	−	0.925257i	$-0.376151\pi$
$137$	6.93208	+	0.606478i	0.592247	+	0.0518149i	0.212907	+	0.977072i	$0.431707\pi$
$138$		0			0
$139$	15.1508	+	2.67150i	1.28508	+	0.226594i	0.774134	−	0.633022i	$-0.218186\pi$
$139$	15.1508	+	2.67150i	1.28508	+	0.226594i	0.510942	+	0.859615i	$0.329297\pi$
$140$	−9.79604	+	1.57753i	−0.827916	+	0.133326i
$141$		0			0
$142$	−4.29465	−	3.00715i	−0.360399	−	0.252354i
$143$	15.2475	+	4.08554i	1.27506	+	0.341650i
$144$		0			0
$145$	−0.199672	−	2.75306i	−0.0165818	−	0.228629i
$146$	0.193173	−	0.530738i	0.0159871	−	0.0439242i
$147$		0			0
$148$	−0.0521636	−	0.596232i	−0.00428782	−	0.0490100i
$149$	11.7199	+	9.83419i	0.960134	+	0.805648i	0.980975	−	0.194134i	$-0.0621898\pi$
$149$	11.7199	+	9.83419i	0.960134	+	0.805648i	−0.0208405	+	0.999783i	$0.506634\pi$
$150$		0			0
$151$	−15.0661	−	5.48361i	−1.22606	−	0.446250i	−0.353815	−	0.935316i	$-0.615116\pi$
$151$	−15.0661	−	5.48361i	−1.22606	−	0.446250i	−0.872247	+	0.489066i	$0.837338\pi$
$152$	5.38823	−	1.44377i	0.437043	−	0.117105i
$153$		0			0
$154$	11.9232	−	6.88388i	0.960801	−	0.554719i
$155$	7.74717	+	7.98101i	0.622268	+	0.641050i
$156$		0			0
$157$	−9.62532	+	20.6416i	−0.768184	+	1.64738i	−0.00602994	+	0.999982i	$0.501919\pi$
$157$	−9.62532	+	20.6416i	−0.768184	+	1.64738i	−0.762155	+	0.647395i	$0.775858\pi$
$158$	3.61450	+	5.16205i	0.287554	+	0.410670i
$159$		0			0
$160$	1.95290	−	1.08912i	0.154390	−	0.0861028i
$161$			25.2873i			1.99292i
$162$		0			0
$163$	11.0646	+	11.0646i	0.866643	+	0.866643i	0.992099	−	0.125456i	$-0.0400393\pi$
$163$	11.0646	+	11.0646i	0.866643	+	0.866643i	−0.125456	+	0.992099i	$0.540039\pi$
$164$	−0.275195	+	0.230916i	−0.0214892	+	0.0180315i
$165$		0			0
$166$	−2.39767	+	13.5979i	−0.186095	+	1.05540i
$167$	−0.927334	−	0.432423i	−0.0717593	−	0.0334619i	0.386407	−	0.922328i	$-0.373716\pi$
$167$	−0.927334	−	0.432423i	−0.0717593	−	0.0334619i	−0.458167	+	0.888866i	$0.651494\pi$
$168$		0			0
$169$	−12.6882	+	2.23728i	−0.976017	+	0.172098i
$170$	2.93262	−	6.05246i	0.224922	−	0.464202i
$171$		0			0
$172$	0.516596	+	1.92796i	0.0393901	+	0.147006i
$173$	0.915017	−	0.426680i	0.0695675	−	0.0324398i	−0.387523	−	0.921860i	$-0.626669\pi$
$173$	0.915017	−	0.426680i	0.0695675	−	0.0324398i	0.457091	+	0.889420i	$0.348892\pi$
$174$		0			0
$175$	−6.37692	+	21.2506i	−0.482050	+	1.60640i
$176$	−1.99437	+	2.37680i	−0.150331	+	0.179158i
$177$		0			0
$178$	5.90034	+	12.6533i	0.442249	+	0.948406i
$179$	4.56812	−	7.91221i	0.341437	−	0.591387i	−0.643263	−	0.765646i	$-0.722420\pi$
$179$	4.56812	−	7.91221i	0.341437	−	0.591387i	0.984700	+	0.174259i	$0.0557530\pi$
$180$		0			0
$181$	0.245003	+	0.424357i	0.0182109	+	0.0315422i	0.874987	−	0.484146i	$-0.160870\pi$
$181$	0.245003	+	0.424357i	0.0182109	+	0.0315422i	−0.856776	+	0.515688i	$0.827536\pi$
$182$	−12.9489	+	18.4929i	−0.959834	+	1.37078i
$183$		0			0
$184$	−1.94908	−	5.35505i	−0.143688	−	0.394779i
$185$	−1.25066	−	0.476373i	−0.0919500	−	0.0350236i
$186$		0			0
$187$	−0.813344	+	9.29657i	−0.0594776	+	0.679833i
$188$	−5.70515	+	5.70515i	−0.416091	+	0.416091i
$189$		0			0
$190$	2.34837	−	12.2504i	0.170368	−	0.888739i
$191$	4.31791	+	5.14588i	0.312433	+	0.372343i	0.899294	−	0.437345i	$-0.144081\pi$
$191$	4.31791	+	5.14588i	0.312433	+	0.372343i	−0.586861	+	0.809688i	$0.699637\pi$
$192$		0			0
$193$	−6.71078	+	4.69894i	−0.483053	+	0.338237i	−0.789604	−	0.613617i	$-0.789714\pi$
$193$	−6.71078	+	4.69894i	−0.483053	+	0.338237i	0.306551	+	0.951854i	$0.400825\pi$
$194$	14.2702	−	5.19394i	1.02454	−	0.372903i
$195$		0			0
$196$	2.20363	+	12.4974i	0.157402	+	0.892671i
$197$	5.02384	−	18.7492i	0.357934	−	1.33583i	−0.518818	−	0.854885i	$-0.673628\pi$
$197$	5.02384	−	18.7492i	0.357934	−	1.33583i	0.876752	−	0.480943i	$-0.159706\pi$
$198$		0			0
$199$	−16.5891	−	9.57774i	−1.17597	−	0.678948i	−0.220893	−	0.975298i	$-0.570897\pi$
$199$	−16.5891	−	9.57774i	−1.17597	−	0.678948i	−0.955079	+	0.296350i	$0.904230\pi$
$200$	−0.287513	−	4.99173i	−0.0203303	−	0.352968i
$201$		0			0
$202$	−13.1141	+	1.14733i	−0.922703	+	0.0807261i
$203$	−5.45681	+	0.477409i	−0.382993	+	0.0335076i
$204$		0			0
$205$	0.196349	+	0.778923i	0.0137136	+	0.0544024i
$206$	10.0260	+	5.78854i	0.698547	+	0.403306i
$207$		0			0
$208$	1.31678	−	4.91427i	0.0913019	−	0.340743i
$209$	3.00546	+	17.0448i	0.207892	+	1.17901i
$210$		0			0
$211$	14.6011	−	5.31436i	1.00518	−	0.365856i	0.213600	−	0.976921i	$-0.431481\pi$
$211$	14.6011	−	5.31436i	1.00518	−	0.365856i	0.791580	+	0.611065i	$0.209259\pi$
$212$	6.49955	−	4.55103i	0.446391	−	0.312566i
$213$		0			0
$214$	−0.566528	−	0.675162i	−0.0387271	−	0.0461531i
$215$	4.38332	+	0.840268i	0.298940	+	0.0573058i
$216$		0			0
$217$	15.6076	−	15.6076i	1.05951	−	1.05951i
$218$	1.68759	−	19.2893i	0.114298	−	1.30643i
$219$		0			0
$220$	2.83826	+	6.33070i	0.191355	+	0.426815i
$221$	−5.23368	−	14.3794i	−0.352055	−	0.967265i
$222$		0			0
$223$	3.02226	−	4.31623i	0.202385	−	0.289036i	−0.705110	−	0.709098i	$-0.749103\pi$
$223$	3.02226	−	4.31623i	0.202385	−	0.289036i	0.907496	+	0.420061i	$0.137991\pi$
$224$	−2.21868	−	3.84287i	−0.148242	−	0.256762i
$225$		0			0
$226$	−6.51390	+	11.2824i	−0.433298	+	0.750495i
$227$	−12.4885	−	26.7817i	−0.828891	−	1.77756i	−0.591821	−	0.806070i	$-0.701591\pi$
$227$	−12.4885	−	26.7817i	−0.828891	−	1.77756i	−0.237070	−	0.971493i	$-0.576187\pi$
$228$		0			0
$229$	6.53349	−	7.78631i	0.431745	−	0.514534i	−0.505680	−	0.862721i	$-0.668758\pi$
$229$	6.53349	−	7.78631i	0.431745	−	0.514534i	0.937425	+	0.348187i	$0.113203\pi$
$230$	−12.6763	−	1.29919i	−0.835852	−	0.0856658i
$231$		0			0
$232$	1.11878	−	0.521697i	0.0734516	−	0.0342511i
$233$	−1.64017	−	6.12119i	−0.107451	−	0.401012i	0.891161	−	0.453688i	$-0.149892\pi$
$233$	−1.64017	−	6.12119i	−0.107451	−	0.401012i	−0.998612	+	0.0526753i	$0.983225\pi$
$234$		0			0
$235$	5.91778	+	17.0431i	0.386033	+	1.11177i
$236$	4.42548	−	0.780332i	0.288074	−	0.0507953i
$237$		0			0
$238$	−12.0960	−	5.64045i	−0.784066	−	0.365616i
$239$	−2.96781	+	16.8313i	−0.191972	+	1.08873i	0.724694	+	0.689071i	$0.241981\pi$
$239$	−2.96781	+	16.8313i	−0.191972	+	1.08873i	−0.916666	+	0.399655i	$0.869130\pi$
$240$		0			0
$241$	−0.980613	+	0.822832i	−0.0631668	+	0.0530032i	−0.673824	−	0.738891i	$-0.735350\pi$
$241$	−0.980613	+	0.822832i	−0.0631668	+	0.0530032i	0.610658	+	0.791895i	$0.290905\pi$
$242$	0.971082	+	0.971082i	0.0624235	+	0.0624235i
$243$		0			0
$244$			1.69038i			0.108216i
$245$	27.2970	+	7.75092i	1.74394	+	0.495188i
$246$		0			0
$247$	−16.2783	−	23.2478i	−1.03576	−	1.47922i
$248$	−2.10220	+	4.50819i	−0.133490	+	0.286270i
$249$		0			0
$250$	−10.3252	−	4.28850i	−0.653020	−	0.271228i
$251$	−5.83227	+	3.36726i	−0.368129	+	0.212540i	−0.672641	−	0.739969i	$-0.734840\pi$
$251$	−5.83227	+	3.36726i	−0.368129	+	0.212540i	0.304511	+	0.952509i	$0.401507\pi$
$252$		0			0
$253$	17.0789	−	4.57627i	1.07374	−	0.287708i
$254$	−10.2074	−	3.71519i	−0.640470	−	0.233112i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.171851	+	1.96427i	0.0107198	+	0.122528i	0.999669	−	0.0257269i	$-0.00819004\pi$
$257$	0.171851	+	1.96427i	0.0107198	+	0.122528i	−0.988949	+	0.148255i	$0.952634\pi$
$258$		0			0
$259$	−0.908339	+	2.49564i	−0.0564414	+	0.155072i
$260$	−8.60507	−	7.44127i	−0.533664	−	0.461488i
$261$		0			0
$262$	−2.37314	−	0.635881i	−0.146613	−	0.0392848i
$263$	0.156523	+	0.109599i	0.00965163	+	0.00675815i	0.578392	−	0.815759i	$-0.303680\pi$
$263$	0.156523	+	0.109599i	0.00965163	+	0.00675815i	−0.568741	+	0.822517i	$0.692569\pi$
$264$		0			0
$265$	−2.82080	−	17.5164i	−0.173280	−	1.07602i
$266$	−24.3769	−	4.29831i	−1.49465	−	0.263546i
$267$		0			0
$268$	8.65868	+	0.757536i	0.528913	+	0.0462739i
$269$	−7.89719			−0.481500			−0.240750	−	0.970587i	$-0.577393\pi$
$269$	−7.89719			−0.481500			−0.240750	+	0.970587i	$0.577393\pi$
$270$		0			0
$271$	1.68579			0.102404			0.0512022	−	0.998688i	$-0.483695\pi$
$271$	1.68579			0.102404			0.0512022	+	0.998688i	$0.483695\pi$
$272$	2.99629	+	0.262142i	0.181677	+	0.0158947i
$273$		0			0
$274$	6.85284	+	1.20834i	0.413995	+	0.0729985i
$275$	15.5066	+	0.461179i	0.935083	+	0.0278101i
$276$		0			0
$277$	21.9259	+	15.3527i	1.31740	+	0.922453i	0.999669	−	0.0257282i	$-0.00819046\pi$
$277$	21.9259	+	15.3527i	1.31740	+	0.922453i	0.317730	+	0.948181i	$0.397079\pi$
$278$	14.8603	+	3.98181i	0.891264	+	0.238813i
$279$		0			0
$280$	−9.89625	+	0.717747i	−0.591414	+	0.0428936i
$281$	1.59078	−	4.37064i	0.0948981	−	0.260730i	−0.883157	−	0.469078i	$-0.844586\pi$
$281$	1.59078	−	4.37064i	0.0948981	−	0.260730i	0.978055	+	0.208348i	$0.0668085\pi$
$282$		0			0
$283$	−2.80478	−	32.0588i	−0.166727	−	1.90570i	−0.374027	−	0.927418i	$-0.622023\pi$
$283$	−2.80478	−	32.0588i	−0.166727	−	1.90570i	0.207301	−	0.978277i	$-0.433532\pi$
$284$	−4.01622	−	3.37001i	−0.238319	−	0.199973i
$285$		0			0
$286$	14.8334	+	5.39890i	0.877115	+	0.319244i
$287$	1.53977	−	0.412580i	0.0908898	−	0.0243538i
$288$		0			0
$289$	−6.88794	+	3.97675i	−0.405173	+	0.233927i
$290$	0.0410330	−	2.75999i	0.00240954	−	0.162072i
$291$		0			0
$292$	0.238695	−	0.511883i	0.0139686	−	0.0299557i
$293$	1.28660	+	1.83746i	0.0751642	+	0.107346i	0.854974	−	0.518671i	$-0.173573\pi$
$293$	1.28660	+	1.83746i	0.0751642	+	0.107346i	−0.779810	+	0.626017i	$0.784684\pi$
$294$		0			0
$295$	2.74470	−	9.66622i	0.159802	−	0.562789i
$296$		−	0.598510i		−	0.0347877i
$297$		0			0
$298$	10.8182	+	10.8182i	0.626683	+	0.626683i
$299$	−22.2099	+	18.6363i	−1.28443	+	1.07777i
$300$		0			0
$301$	1.53798	−	8.72231i	0.0886476	−	0.502745i
$302$	−14.5308	−	6.77584i	−0.836156	−	0.389906i
$303$		0			0
$304$	5.49356	−	0.968663i	0.315077	−	0.0555567i
$305$	3.40154	+	1.64816i	0.194772	+	0.0943735i
$306$		0			0
$307$	2.15073	+	8.02664i	0.122749	+	0.458104i	0.999749	−	0.0223847i	$-0.00712586\pi$
$307$	2.15073	+	8.02664i	0.122749	+	0.458104i	−0.877001	+	0.480489i	$0.840459\pi$
$308$	12.4778	−	5.81851i	0.710990	−	0.331540i
$309$		0			0
$310$	7.02210	+	8.62585i	0.398829	+	0.489915i
$311$	1.22596	−	1.46104i	0.0695177	−	0.0828479i	−0.730165	−	0.683271i	$-0.760557\pi$
$311$	1.22596	−	1.46104i	0.0695177	−	0.0828479i	0.799682	+	0.600423i	$0.205001\pi$
$312$		0			0
$313$	−3.35295	−	7.19043i	−0.189520	−	0.406427i	0.788472	−	0.615071i	$-0.210873\pi$
$313$	−3.35295	−	7.19043i	−0.189520	−	0.406427i	−0.977992	+	0.208644i	$0.933095\pi$
$314$	−11.3877	+	19.7241i	−0.642647	+	1.11310i
$315$		0			0
$316$	3.15085	+	5.45743i	0.177249	+	0.307004i
$317$	9.55065	−	13.6397i	0.536418	−	0.766084i	−0.455869	−	0.890047i	$-0.650671\pi$
$317$	9.55065	−	13.6397i	0.536418	−	0.766084i	0.992287	+	0.123963i	$0.0395604\pi$
$318$		0			0
$319$	1.30997	+	3.59910i	0.0733440	+	0.201511i
$320$	2.04039	−	0.914773i	0.114061	−	0.0511374i
$321$		0			0
$322$	−2.20393	+	25.1911i	−0.122820	+	1.40384i
$323$	11.8639	−	11.8639i	0.660126	−	0.660126i
$324$		0			0
$325$	−23.3642	+	10.0605i	−1.29601	+	0.558057i
$326$	10.0581	+	11.9868i	0.557068	+	0.663887i
$327$		0			0
$328$	−0.294274	+	0.206053i	−0.0162486	+	0.0113774i
$329$	33.6428	−	12.2450i	1.85479	−	0.675088i
$330$		0			0
$331$	1.08932	+	6.17783i	0.0598744	+	0.339564i	0.999999	−	0.00126593i	$-0.000402958\pi$
$331$	1.08932	+	6.17783i	0.0598744	+	0.339564i	−0.940125	+	0.340830i	$0.889292\pi$
$332$	−3.57368	+	13.3371i	−0.196131	+	0.731971i
$333$		0			0
$334$	−0.886117	−	0.511600i	−0.0484862	−	0.0279935i
$335$	9.96681	−	16.6852i	0.544545	−	0.911609i
$336$		0			0
$337$	−10.2705	+	0.898553i	−0.559470	+	0.0489473i	−0.363384	−	0.931639i	$-0.618379\pi$
$337$	−10.2705	+	0.898553i	−0.559470	+	0.0489473i	−0.196086	+	0.980587i	$0.562823\pi$
$338$	−12.8349	+	1.12291i	−0.698128	+	0.0610783i
$339$		0			0
$340$	3.44897	−	5.77383i	0.187046	−	0.313130i
$341$	−13.3658	−	7.71676i	−0.723799	−	0.417886i
$342$		0			0
$343$	6.53503	−	24.3891i	0.352859	−	1.31689i
$344$	0.346597	+	1.96565i	0.0186873	+	0.105981i
$345$		0			0
$346$	0.948723	−	0.345307i	0.0510037	−	0.0185638i
$347$	−10.5911	+	7.41594i	−0.568558	+	0.398108i	−0.822208	−	0.569188i	$-0.807258\pi$
$347$	−10.5911	+	7.41594i	−0.568558	+	0.398108i	0.253650	+	0.967296i	$0.418369\pi$
$348$		0			0
$349$	2.40775	+	2.86944i	0.128884	+	0.153598i	0.826627	−	0.562750i	$-0.190257\pi$
$349$	2.40775	+	2.86944i	0.128884	+	0.153598i	−0.697743	+	0.716348i	$0.745812\pi$
$350$	−8.20477	+	20.6140i	−0.438563	+	1.10186i
$351$		0			0
$352$	−2.19393	+	2.19393i	−0.116937	+	0.116937i
$353$	2.49499	−	28.5179i	0.132795	−	1.51785i	−0.578919	−	0.815385i	$-0.696525\pi$
$353$	2.49499	−	28.5179i	0.132795	−	1.51785i	0.711714	−	0.702470i	$-0.247919\pi$
$354$		0			0
$355$	−10.6974	+	4.79597i	−0.567757	+	0.254544i
$356$	4.77507	+	13.1194i	0.253078	+	0.695327i
$357$		0			0
$358$	5.24033	−	7.48397i	0.276960	−	0.395540i
$359$	−9.70513	−	16.8098i	−0.512217	−	0.887186i	−0.999900	−	0.0141649i	$-0.995491\pi$
$359$	−9.70513	−	16.8098i	−0.512217	−	0.887186i	0.487683	−	0.873021i	$-0.337842\pi$
$360$		0			0
$361$	6.05877	−	10.4941i	0.318883	−	0.552321i
$362$	0.207085	+	0.444096i	0.0108842	+	0.0233411i
$363$		0			0
$364$	−14.5113	+	17.2940i	−0.760601	+	0.906449i
$365$	−0.797325	−	0.979422i	−0.0417339	−	0.0512653i
$366$		0			0
$367$	−14.6723	+	6.84182i	−0.765890	+	0.357140i	−0.765984	−	0.642860i	$-0.777748\pi$
$367$	−14.6723	+	6.84182i	−0.765890	+	0.357140i	9.42303e−5		1.00000i	$0.499970\pi$
$368$	−1.47494	−	5.50454i	−0.0768865	−	0.286944i
$369$		0			0
$370$	−1.20438	−	0.583562i	−0.0626126	−	0.0303379i
$371$	−34.6733	+	6.11384i	−1.80015	+	0.317415i
$372$		0			0
$373$	−2.93247	−	1.36743i	−0.151837	−	0.0708030i	0.345214	−	0.938524i	$-0.387806\pi$
$373$	−2.93247	−	1.36743i	−0.151837	−	0.0708030i	−0.497052	+	0.867721i	$0.665584\pi$
$374$	−1.62050	+	9.19031i	−0.0837940	+	0.475219i
$375$		0			0
$376$	−6.18068	+	5.18620i	−0.318744	+	0.267458i
$377$	−4.44089	−	4.44089i	−0.228718	−	0.228718i
$378$		0			0
$379$			34.2390i			1.75874i	0.476139	+	0.879370i	$0.342036\pi$
$379$			34.2390i			1.75874i	−0.476139	+	0.879370i	$0.657964\pi$
$380$	3.40712	−	11.9991i	0.174782	−	0.615543i
$381$		0			0
$382$	3.85298	+	5.50263i	0.197136	+	0.281539i
$383$	−9.49994	+	20.3727i	−0.485424	+	1.04100i	0.499228	+	0.866471i	$0.333617\pi$
$383$	−9.49994	+	20.3727i	−0.485424	+	1.04100i	−0.984653	+	0.174526i	$0.944161\pi$
$384$		0			0
$385$	0.457643	−	30.7822i	0.0233237	−	1.56881i
$386$	−7.09478	+	4.09618i	−0.361115	+	0.208490i
$387$		0			0
$388$	14.6686	−	3.93044i	0.744686	−	0.199538i
$389$	−1.45361	−	0.529072i	−0.0737011	−	0.0268250i	0.304906	−	0.952382i	$-0.401375\pi$
$389$	−1.45361	−	0.529072i	−0.0737011	−	0.0268250i	−0.378608	+	0.925557i	$0.623597\pi$
$390$		0			0
$391$	−13.1302	−	11.0176i	−0.664023	−	0.557182i
$392$	1.10602	+	12.6419i	0.0558626	+	0.638512i
$393$		0			0
$394$	6.63883	−	18.2400i	0.334459	−	0.918920i
$395$	14.0541	−	1.01930i	0.707139	−	0.0512868i
$396$		0			0
$397$	−8.93003	−	2.39279i	−0.448185	−	0.120091i	0.0276648	−	0.999617i	$-0.491193\pi$
$397$	−8.93003	−	2.39279i	−0.448185	−	0.120091i	−0.475850	+	0.879526i	$0.657860\pi$
$398$	−15.6912	−	10.9871i	−0.786531	−	0.550735i
$399$		0			0
$400$	0.148638	−	4.99779i	0.00743192	−	0.249890i
$401$	8.77551	+	1.54736i	0.438228	+	0.0772714i	0.388410	−	0.921487i	$-0.373025\pi$
$401$	8.77551	+	1.54736i	0.438228	+	0.0772714i	0.0498185	+	0.998758i	$0.484136\pi$
$402$		0			0
$403$	25.2108	+	2.20566i	1.25584	+	0.109872i
$404$	−13.1642			−0.654942
$405$		0			0
$406$	−5.47766			−0.271851
$407$	1.84992	+	0.161847i	0.0916973	+	0.00802248i
$408$		0			0
$409$	10.9136	+	1.92436i	0.539642	+	0.0951534i	0.436824	−	0.899547i	$-0.356103\pi$
$409$	10.9136	+	1.92436i	0.539642	+	0.0951534i	0.102817	+	0.994700i	$0.467214\pi$
$410$	0.127715	+	0.793072i	0.00630737	+	0.0391670i
$411$		0			0
$412$	9.48338	+	6.64034i	0.467213	+	0.327146i
$413$	−19.2610	−	5.16096i	−0.947770	−	0.253954i
$414$		0			0
$415$	23.3538	+	20.1953i	1.14639	+	0.991350i
$416$	1.74007	−	4.78081i	0.0853140	−	0.234398i
$417$		0			0
$418$	1.50847	+	17.2419i	0.0737817	+	0.843329i
$419$	16.3946	+	13.7567i	0.800930	+	0.672060i	0.948425	−	0.317002i	$-0.102676\pi$
$419$	16.3946	+	13.7567i	0.800930	+	0.672060i	−0.147494	+	0.989063i	$0.547121\pi$
$420$		0			0
$421$	−5.73607	−	2.08776i	−0.279559	−	0.101751i	0.198436	−	0.980114i	$-0.436414\pi$
$421$	−5.73607	−	2.08776i	−0.279559	−	0.101751i	−0.477995	+	0.878363i	$0.658636\pi$
$422$	15.0087	−	4.02157i	0.730612	−	0.195767i
$423$		0			0
$424$	6.87147	−	3.96724i	0.333708	−	0.192666i
$425$	−8.25582	−	12.5700i	−0.400466	−	0.609733i
$426$		0			0
$427$	3.16999	−	6.79806i	0.153406	−	0.328981i
$428$	−0.505528	−	0.721969i	−0.0244356	−	0.0348977i
$429$		0			0
$430$	4.29341	+	1.21910i	0.207047	+	0.0587903i
$431$		−	6.37864i		−	0.307248i	−0.988129	−	0.153624i	$-0.950905\pi$
$431$		−	6.37864i		−	0.307248i	0.988129	−	0.153624i	$-0.0490945\pi$
$432$		0			0
$433$	−1.29802	−	1.29802i	−0.0623789	−	0.0623789i	0.675229	−	0.737608i	$-0.264045\pi$
$433$	−1.29802	−	1.29802i	−0.0623789	−	0.0623789i	−0.737608	+	0.675229i	$0.764045\pi$
$434$	16.9085	−	14.1879i	0.811634	−	0.681042i
$435$		0			0
$436$	3.36234	−	19.0688i	0.161027	−	0.913229i
$437$	−28.8108	−	13.4347i	−1.37821	−	0.642670i
$438$		0			0
$439$	36.5242	−	6.44020i	1.74320	−	0.307374i	0.790768	−	0.612116i	$-0.209681\pi$
$439$	36.5242	−	6.44020i	1.74320	−	0.307374i	0.952435	+	0.304742i	$0.0985701\pi$
$440$	2.27570	+	6.55398i	0.108490	+	0.312449i
$441$		0			0
$442$	−3.96052	−	14.7808i	−0.188383	−	0.703053i
$443$	−8.63573	+	4.02691i	−0.410296	+	0.191324i	−0.616797	−	0.787122i	$-0.711570\pi$
$443$	−8.63573	+	4.02691i	−0.410296	+	0.191324i	0.206501	+	0.978446i	$0.433792\pi$
$444$		0			0
$445$	31.0559	+	3.18289i	1.47219	+	0.150884i
$446$	3.38694	−	4.03640i	0.160376	−	0.191129i
$447$		0			0
$448$	−1.87531	−	4.02162i	−0.0886001	−	0.190004i
$449$	10.1214	−	17.5309i	0.477661	−	0.827333i	−0.522011	−	0.852939i	$-0.674818\pi$
$449$	10.1214	−	17.5309i	0.477661	−	0.827333i	0.999672	+	0.0256059i	$0.00815150\pi$
$450$		0			0
$451$	−0.557308	−	0.965287i	−0.0262426	−	0.0454536i
$452$	−7.47244	+	10.6718i	−0.351474	+	0.501957i
$453$		0			0
$454$	−10.1068	−	27.7682i	−0.474336	−	1.30323i
$455$	20.6516	+	46.0631i	0.968162	+	2.15947i
$456$		0			0
$457$	2.16049	−	24.6946i	0.101064	−	1.15516i	−0.761135	−	0.648593i	$-0.775358\pi$
$457$	2.16049	−	24.6946i	0.101064	−	1.15516i	0.862199	−	0.506570i	$-0.169087\pi$
$458$	7.18725	−	7.18725i	0.335838	−	0.335838i
$459$		0			0
$460$	−12.5149	−	2.39906i	−0.583508	−	0.111857i
$461$	22.7869	+	27.1564i	1.06129	+	1.26480i	0.962960	+	0.269644i	$0.0869060\pi$
$461$	22.7869	+	27.1564i	1.06129	+	1.26480i	0.0983312	+	0.995154i	$0.468650\pi$
$462$		0			0
$463$	20.2735	−	14.1957i	0.942190	−	0.659729i	0.00186244	−	0.999998i	$-0.499407\pi$
$463$	20.2735	−	14.1957i	0.942190	−	0.659729i	0.940328	+	0.340269i	$0.110518\pi$
$464$	1.15999	−	0.422203i	0.0538514	−	0.0196003i
$465$		0			0
$466$	−1.10043	−	6.24085i	−0.0509764	−	0.289102i
$467$	9.86375	−	36.8120i	0.456440	−	1.70346i	−0.227380	−	0.973806i	$-0.573016\pi$
$467$	9.86375	−	36.8120i	0.456440	−	1.70346i	0.683820	−	0.729651i	$-0.260317\pi$
$468$		0			0
$469$	−33.4013	−	19.2842i	−1.54233	−	0.890463i
$470$	4.40985	+	17.4940i	0.203411	+	0.806939i
$471$		0			0
$472$	4.47665	−	0.391656i	0.206055	−	0.0180274i
$473$	−6.16932	+	0.539746i	−0.283666	+	0.0248175i
$474$		0			0
$475$	−20.8238	−	18.5556i	−0.955459	−	0.851389i
$476$	−11.5583	−	6.67322i	−0.529776	−	0.305866i
$477$		0			0
$478$	−4.42346	+	16.5086i	−0.202324	+	0.755085i
$479$	3.17088	+	17.9830i	0.144881	+	0.821663i	0.967462	+	0.253015i	$0.0814221\pi$
$479$	3.17088	+	17.9830i	0.144881	+	0.821663i	−0.822581	+	0.568648i	$0.807467\pi$
$480$		0			0
$481$	−2.86136	+	1.04145i	−0.130467	+	0.0474860i
$482$	−1.04860	+	0.734235i	−0.0477622	+	0.0334435i
$483$		0			0
$484$	0.882752	+	1.05202i	0.0401251	+	0.0478192i
$485$	6.39305	−	33.3498i	0.290293	−	1.51434i
$486$		0			0
$487$	14.7251	−	14.7251i	0.667257	−	0.667257i	−0.289823	−	0.957080i	$-0.593597\pi$
$487$	14.7251	−	14.7251i	0.667257	−	0.667257i	0.957080	+	0.289823i	$0.0935966\pi$
$488$	−0.147326	+	1.68395i	−0.00666915	+	0.0762287i
$489$		0			0
$490$	26.5176	+	10.1005i	1.19794	+	0.456295i
$491$	−4.42963	−	12.1703i	−0.199907	−	0.549239i	0.798716	−	0.601708i	$-0.205513\pi$
$491$	−4.42963	−	12.1703i	−0.199907	−	0.549239i	−0.998623	+	0.0524694i	$0.983291\pi$
$492$		0			0
$493$	2.12962	−	3.04141i	0.0959131	−	0.136978i
$494$	−14.1902	−	24.5781i	−0.638447	−	1.10582i
$495$		0			0
$496$	−2.48712	+	4.30782i	−0.111675	+	0.193427i
$497$	9.83189	+	21.0845i	0.441020	+	0.945771i
$498$		0			0
$499$	−8.70391	+	10.3729i	−0.389640	+	0.464355i	−0.924832	−	0.380375i	$-0.875795\pi$
$499$	−8.70391	+	10.3729i	−0.389640	+	0.464355i	0.535192	+	0.844731i	$0.320239\pi$
$500$	−9.91210	−	5.17207i	−0.443282	−	0.231302i
$501$		0			0
$502$	−6.10355	+	2.84613i	−0.272415	+	0.127029i
$503$	6.38589	+	23.8324i	0.284733	+	1.06264i	0.949035	+	0.315172i	$0.102062\pi$
$503$	6.38589	+	23.8324i	0.284733	+	1.06264i	−0.664302	+	0.747464i	$0.731271\pi$
$504$		0			0
$505$	−12.8354	+	26.4902i	−0.571167	+	1.17880i
$506$	17.4127	−	3.07034i	0.774091	−	0.136493i
$507$		0			0
$508$	−9.84477	−	4.59069i	−0.436791	−	0.203679i
$509$	3.22302	−	18.2786i	0.142858	−	0.810187i	−0.826205	−	0.563370i	$-0.809504\pi$
$509$	3.22302	−	18.2786i	0.142858	−	0.810187i	0.969062	−	0.246816i	$-0.0793844\pi$
$510$		0			0
$511$	−1.91988	+	1.61097i	−0.0849304	+	0.0712651i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			1.97177i			0.0869711i
$515$	22.6088	−	12.6089i	0.996264	−	0.555613i
$516$		0			0
$517$	−14.3586	−	20.5062i	−0.631490	−	0.901861i
$518$	−1.12239	+	2.40698i	−0.0493151	+	0.105756i
$519$		0			0
$520$	−7.92378	−	8.16294i	−0.347481	−	0.357969i
$521$	−31.0099	+	17.9036i	−1.35857	+	0.784371i	−0.989431	−	0.145004i	$-0.953681\pi$
$521$	−31.0099	+	17.9036i	−1.35857	+	0.784371i	−0.369139	+	0.929374i	$0.620347\pi$
$522$		0			0
$523$	−3.95334	+	1.05929i	−0.172867	+	0.0463197i	−0.344214	−	0.938891i	$-0.611855\pi$
$523$	−3.95334	+	1.05929i	−0.172867	+	0.0463197i	0.171347	+	0.985211i	$0.445188\pi$
$524$	−2.30869	−	0.840294i	−0.100855	−	0.0367084i
$525$		0			0
$526$	0.146375	+	0.122824i	0.00638227	+	0.00535536i
$527$	1.30396	+	14.9043i	0.0568012	+	0.649240i
$528$		0			0
$529$	−3.24079	+	8.90400i	−0.140904	+	0.387131i
$530$	−1.28341	−	17.6956i	−0.0557478	−	0.768647i
$531$		0			0
$532$	−23.9095	−	6.40654i	−1.03661	−	0.277759i
$533$	1.49716	+	1.04832i	0.0648490	+	0.0454078i
$534$		0			0
$535$	−1.94572	+	0.313334i	−0.0841207	+	0.0135466i
$536$	8.55971	+	1.50931i	0.369723	+	0.0651922i
$537$		0			0
$538$	−7.86713	−	0.688285i	−0.339176	−	0.0296741i
$539$	−39.3737			−1.69595
$540$		0			0
$541$	−0.366352			−0.0157507			−0.00787535	−	0.999969i	$-0.502507\pi$
$541$	−0.366352			−0.0157507			−0.00787535	+	0.999969i	$0.502507\pi$
$542$	1.67938	+	0.146926i	0.0721353	+	0.00631102i
$543$		0			0
$544$	2.96205	+	0.522288i	0.126997	+	0.0223929i
$545$	−35.0936	−	25.3585i	−1.50325	−	1.08624i
$546$		0			0
$547$	12.3209	+	8.62717i	0.526802	+	0.368871i	0.806516	−	0.591213i	$-0.201351\pi$
$547$	12.3209	+	8.62717i	0.526802	+	0.368871i	−0.279713	+	0.960084i	$0.590239\pi$
$548$	6.72145	+	1.80101i	0.287126	+	0.0769352i
$549$		0			0
$550$	15.4074	+	1.81091i	0.656973	+	0.0772176i
$551$	2.35518	−	6.47080i	0.100334	−	0.275666i
$552$		0			0
$553$	−2.43713	−	27.8565i	−0.103637	−	1.18458i
$554$	20.5044	+	17.2052i	0.871148	+	0.730980i
$555$		0			0
$556$	14.4567	+	5.26183i	0.613103	+	0.223151i
$557$	6.83257	−	1.83078i	0.289505	−	0.0775727i	−0.111144	−	0.993804i	$-0.535451\pi$
$557$	6.83257	−	1.83078i	0.289505	−	0.0775727i	0.400649	+	0.916232i	$0.368785\pi$
$558$		0			0
$559$	8.79429	−	5.07739i	0.371959	−	0.214751i
$560$	−9.92115	−	0.147499i	−0.419245	−	0.00623297i
$561$		0			0
$562$	1.96565	−	4.21536i	0.0829161	−	0.177814i
$563$	−15.6316	−	22.3243i	−0.658795	−	0.940857i	−1.00000		0.000868128i	$-0.999724\pi$
$563$	−15.6316	−	22.3243i	−0.658795	−	0.940857i	0.341204	−	0.939989i	$-0.389165\pi$
$564$		0			0
$565$	14.1889	+	25.4420i	0.596931	+	1.07035i
$566$		−	32.1812i		−	1.35268i
$567$		0			0
$568$	−3.70722	−	3.70722i	−0.155552	−	0.155552i
$569$	32.3161	−	27.1164i	1.35476	−	1.13678i	0.377199	−	0.926132i	$-0.376887\pi$
$569$	32.3161	−	27.1164i	1.35476	−	1.13678i	0.977562	−	0.210647i	$-0.0675570\pi$
$570$		0			0
$571$	−5.32517	+	30.2005i	−0.222851	+	1.26385i	0.643899	+	0.765111i	$0.277316\pi$
$571$	−5.32517	+	30.2005i	−0.222851	+	1.26385i	−0.866750	+	0.498742i	$0.833795\pi$
$572$	14.3064	+	6.67117i	0.598179	+	0.278936i
$573$		0			0
$574$	1.56987	−	0.276810i	0.0655251	−	0.0115538i
$575$	−17.0299	+	22.8444i	−0.710196	+	0.952679i
$576$		0			0
$577$	2.76612	+	10.3233i	0.115155	+	0.429765i	0.999298	−	0.0374510i	$-0.0119238\pi$
$577$	2.76612	+	10.3233i	0.115155	+	0.429765i	−0.884143	+	0.467216i	$0.845257\pi$
$578$	−7.20832	+	3.36130i	−0.299827	+	0.139811i
$579$		0			0
$580$	0.281425	−	2.74591i	0.0116856	−	0.114018i
$581$	39.3832	−	46.9351i	1.63389	−	1.94720i
$582$		0			0
$583$	10.4041	+	22.3117i	0.430895	+	0.924057i
$584$	0.282400	−	0.489131i	0.0116858	−	0.0202404i
$585$		0			0
$586$	1.12156	+	1.94260i	0.0463313	+	0.0802482i
$587$	−26.7496	+	38.2024i	−1.10407	+	1.57678i	−0.329662	+	0.944099i	$0.606935\pi$
$587$	−26.7496	+	38.2024i	−1.10407	+	1.57678i	−0.774412	+	0.632682i	$0.781954\pi$
$588$		0			0
$589$	9.49032	+	26.0744i	0.391042	+	1.07438i
$590$	3.57672	−	9.39022i	0.147251	−	0.386589i
$591$		0			0
$592$	0.0521636	−	0.596232i	0.00214391	−	0.0245050i
$593$	7.24736	−	7.24736i	0.297613	−	0.297613i	−0.542465	−	0.840078i	$-0.682509\pi$
$593$	7.24736	−	7.24736i	0.297613	−	0.297613i	0.840078	+	0.542465i	$0.182509\pi$
$594$		0			0
$595$	−24.6981	+	16.7522i	−1.01253	+	0.686775i
$596$	9.83419	+	11.7199i	0.402824	+	0.480067i
$597$		0			0
$598$	−23.7497	+	16.6297i	−0.971196	+	0.680039i
$599$	−21.6974	+	7.89721i	−0.886532	+	0.322671i	−0.744843	−	0.667240i	$-0.767476\pi$
$599$	−21.6974	+	7.89721i	−0.886532	+	0.322671i	−0.141689	+	0.989911i	$0.545253\pi$
$600$		0			0
$601$	−1.22918	−	6.97100i	−0.0501391	−	0.284353i	0.949421	−	0.314006i	$-0.101671\pi$
$601$	−1.22918	−	6.97100i	−0.0501391	−	0.284353i	−0.999560	+	0.0296525i	$0.990560\pi$
$602$	2.29232	−	8.55507i	0.0934282	−	0.348679i
$603$		0			0
$604$	−13.8850	−	8.01650i	−0.564972	−	0.326187i
$605$	2.97768	−	0.750608i	0.121060	−	0.0305166i
$606$		0			0
$607$	36.7043	−	3.21121i	1.48978	−	0.130339i	0.687020	−	0.726638i	$-0.258918\pi$
$607$	36.7043	−	3.21121i	1.48978	−	0.130339i	0.802762	+	0.596299i	$0.203363\pi$
$608$	5.55708	−	0.486182i	0.225369	−	0.0197173i
$609$		0			0
$610$	3.24495	+	1.93835i	0.131384	+	0.0784817i
$611$	35.5490	+	20.5243i	1.43816	+	0.830322i
$612$		0			0
$613$	−11.0838	+	41.3653i	−0.447671	+	1.67073i	0.261117	+	0.965307i	$0.415909\pi$
$613$	−11.0838	+	41.3653i	−0.447671	+	1.67073i	−0.708787	+	0.705422i	$0.750757\pi$
$614$	1.44298	+	8.18354i	0.0582339	+	0.330261i
$615$		0			0
$616$	12.9375	−	4.70885i	0.521265	−	0.189725i
$617$	2.39325	−	1.67577i	0.0963488	−	0.0674641i	−0.524409	−	0.851466i	$-0.675714\pi$
$617$	2.39325	−	1.67577i	0.0963488	−	0.0674641i	0.620758	+	0.784002i	$0.286825\pi$
$618$		0			0
$619$	−21.4009	−	25.5046i	−0.860175	−	1.02512i	−0.999392	−	0.0348549i	$-0.988903\pi$
$619$	−21.4009	−	25.5046i	−0.860175	−	1.02512i	0.139217	−	0.990262i	$-0.455541\pi$
$620$	6.24359	+	9.20504i	0.250749	+	0.369683i
$621$		0			0
$622$	1.34863	−	1.34863i	0.0540752	−	0.0540752i
$623$	5.39945	−	61.7160i	0.216324	−	2.47260i
$624$		0			0
$625$	−20.0723	+	14.9032i	−0.802891	+	0.596126i
$626$	−2.71351	−	7.45529i	−0.108453	−	0.297973i
$627$		0			0
$628$	−13.0635	+	18.6566i	−0.521289	+	0.744478i
$629$	−0.900081	−	1.55899i	−0.0358886	−	0.0621608i
$630$		0			0
$631$	0.339476	−	0.587990i	0.0135143	−	0.0234075i	−0.859189	−	0.511658i	$-0.829031\pi$
$631$	0.339476	−	0.587990i	0.0135143	−	0.0234075i	0.872703	+	0.488251i	$0.162365\pi$
$632$	2.66321	+	5.71127i	0.105937	+	0.227182i
$633$		0			0
$634$	10.7031	−	12.7554i	0.425074	−	0.506583i
$635$	−18.8367	+	15.3345i	−0.747512	+	0.608532i
$636$		0			0
$637$	58.5139	−	27.2855i	2.31841	−	1.08109i
$638$	0.991298	+	3.69958i	0.0392459	+	0.146468i
$639$		0			0
$640$	2.11235	−	0.733460i	0.0834981	−	0.0289926i
$641$	0.101929	−	0.0179728i	0.00402596	−	0.000709885i	−0.171635	−	0.985161i	$-0.554905\pi$
$641$	0.101929	−	0.0179728i	0.00402596	−	0.000709885i	0.175661	+	0.984451i	$0.443794\pi$
$642$		0			0
$643$	−23.7203	−	11.0609i	−0.935436	−	0.436201i	−0.105726	−	0.994395i	$-0.533717\pi$
$643$	−23.7203	−	11.0609i	−0.935436	−	0.436201i	−0.829710	+	0.558194i	$0.811494\pi$
$644$	−4.39109	+	24.9031i	−0.173033	+	0.981321i
$645$		0			0
$646$	12.8528	−	10.7848i	0.505686	−	0.424321i
$647$	−3.62858	−	3.62858i	−0.142654	−	0.142654i	0.632173	−	0.774827i	$-0.282163\pi$
$647$	−3.62858	−	3.62858i	−0.142654	−	0.142654i	−0.774827	+	0.632173i	$0.782163\pi$
$648$		0			0
$649$			13.9427i			0.547300i
$650$	−24.1521	+	7.98590i	−0.947324	+	0.313233i
$651$		0			0
$652$	8.97513	+	12.8178i	0.351493	+	0.501984i
$653$	−7.31060	+	15.6776i	−0.286086	+	0.613513i	−0.995858	−	0.0909179i	$-0.971020\pi$
$653$	−7.31060	+	15.6776i	−0.286086	+	0.613513i	0.709773	+	0.704431i	$0.248798\pi$
$654$		0			0
$655$	−3.94194	+	3.82645i	−0.154025	+	0.149512i
$656$	−0.311113	+	0.179621i	−0.0121469	+	0.00701302i
$657$		0			0
$658$	34.5820	−	9.26623i	1.34815	−	0.361235i
$659$	0.834066	+	0.303575i	0.0324906	+	0.0118256i	0.358214	−	0.933639i	$-0.383386\pi$
$659$	0.834066	+	0.303575i	0.0324906	+	0.0118256i	−0.325724	+	0.945465i	$0.605608\pi$
$660$		0			0
$661$	20.3875	+	17.1071i	0.792980	+	0.665389i	0.946481	−	0.322759i	$-0.104610\pi$
$661$	20.3875	+	17.1071i	0.792980	+	0.665389i	−0.153501	+	0.988148i	$0.549055\pi$
$662$	0.546740	+	6.24926i	0.0212496	+	0.242885i
$663$		0			0
$664$	−4.72249	+	12.9749i	−0.183268	+	0.503525i
$665$	−36.2042	+	41.8665i	−1.40394	+	1.62351i
$666$		0			0
$667$	−6.79503	−	1.82072i	−0.263104	−	0.0704986i
$668$	−0.838157	−	0.586884i	−0.0324292	−	0.0227072i
$669$		0			0
$670$	11.3831	−	15.7530i	0.439767	−	0.608593i
$671$	−5.16505	−	0.910737i	−0.199394	−	0.0351586i
$672$		0			0
$673$	−11.6515	−	1.01938i	−0.449133	−	0.0392940i	−0.139654	−	0.990200i	$-0.544599\pi$
$673$	−11.6515	−	1.01938i	−0.449133	−	0.0392940i	−0.309479	+	0.950906i	$0.600155\pi$
$674$	−10.3097			−0.397116
$675$		0			0
$676$	−12.8840			−0.495537
$677$	8.80303	+	0.770165i	0.338328	+	0.0295999i	0.255054	−	0.966927i	$-0.417907\pi$
$677$	8.80303	+	0.770165i	0.338328	+	0.0295999i	0.0832740	+	0.996527i	$0.473462\pi$
$678$		0			0
$679$	−66.3623	−	11.7015i	−2.54675	−	0.449061i
$680$	3.93906	−	5.45126i	0.151056	−	0.209046i
$681$		0			0
$682$	−12.6424	−	8.85230i	−0.484102	−	0.338972i
$683$	−9.23383	−	2.47420i	−0.353323	−	0.0946725i	0.0777922	−	0.996970i	$-0.475213\pi$
$683$	−9.23383	−	2.47420i	−0.353323	−	0.0946725i	−0.431115	+	0.902297i	$0.641880\pi$
$684$		0			0
$685$	10.1777	−	11.7695i	0.388871	−	0.449690i
$686$	8.63581	−	23.7267i	0.329717	−	0.905890i
$687$		0			0
$688$	0.173961	+	1.98838i	0.00663219	+	0.0758062i
$689$	−30.9235	−	25.9479i	−1.17809	−	0.988535i
$690$		0			0
$691$	−22.9766	−	8.36278i	−0.874069	−	0.318135i	−0.134255	−	0.990947i	$-0.542864\pi$
$691$	−22.9766	−	8.36278i	−0.874069	−	0.318135i	−0.739814	+	0.672811i	$0.765087\pi$
$692$	0.975208	−	0.261306i	0.0370719	−	0.00993337i
$693$		0			0
$694$	−11.1971	+	6.46464i	−0.425036	+	0.245395i
$695$	24.6840	−	23.9608i	0.936318	−	0.908886i
$696$		0			0
$697$	−0.456642	+	0.979272i	−0.0172965	+	0.0370926i
$698$	2.14850	+	3.06837i	0.0813218	+	0.116140i
$699$		0			0
$700$	−9.97017	+	19.8205i	−0.376837	+	0.749143i
$701$			21.3548i			0.806559i	0.915077	+	0.403280i	$0.132130\pi$
$701$			21.3548i			0.806559i	−0.915077	+	0.403280i	$0.867870\pi$
$702$		0			0
$703$	−2.36080	−	2.36080i	−0.0890392	−	0.0890392i
$704$	−2.37680	+	1.99437i	−0.0895789	+	0.0751657i
$705$		0			0
$706$	4.97100	−	28.1919i	0.187086	−	1.06102i
$707$	52.9412	+	24.6869i	1.99106	+	0.928447i
$708$		0			0
$709$	31.1737	−	5.49676i	1.17075	−	0.206435i	0.445735	−	0.895165i	$-0.352942\pi$
$709$	31.1737	−	5.49676i	1.17075	−	0.206435i	0.725018	+	0.688730i	$0.241831\pi$
$710$	−11.0747	+	3.84539i	−0.415624	+	0.144315i
$711$		0			0
$712$	3.61347	+	13.4857i	0.135421	+	0.505397i
$713$	25.6909	−	11.9799i	0.962133	−	0.448650i
$714$		0			0
$715$	27.3734	−	22.2841i	1.02371	−	0.833377i
$716$	5.87266	−	6.99876i	0.219472	−	0.261556i
$717$		0			0
$718$	−8.20313	−	17.5917i	−0.306138	−	0.656515i
$719$	4.10372	−	7.10784i	0.153043	−	0.265078i	−0.779302	−	0.626649i	$-0.784426\pi$
$719$	4.10372	−	7.10784i	0.153043	−	0.265078i	0.932345	+	0.361571i	$0.117759\pi$
$720$		0			0
$721$	−25.6858	−	44.4892i	−0.956590	−	1.65686i
$722$	6.95034	−	9.92611i	0.258665	−	0.369412i
$723$		0			0
$724$	0.167592	+	0.460454i	0.00622850	+	0.0171127i
$725$	−5.25117	−	3.24364i	−0.195024	−	0.120466i
$726$		0			0
$727$	−0.514111	+	5.87631i	−0.0190673	+	0.217940i	0.980683	+	0.195603i	$0.0626664\pi$
$727$	−0.514111	+	5.87631i	−0.0190673	+	0.217940i	−0.999750	+	0.0223375i	$0.992889\pi$
$728$	−15.9634	+	15.9634i	−0.591643	+	0.591643i
$729$		0			0
$730$	−0.708929	−	1.04519i	−0.0262386	−	0.0386841i
$731$	3.85889	+	4.59885i	0.142726	+	0.170095i
$732$		0			0
$733$	−33.2312	+	23.2687i	−1.22742	+	0.859449i	−0.993614	−	0.112834i	$-0.964007\pi$
$733$	−33.2312	+	23.2687i	−1.22742	+	0.859449i	−0.233807	+	0.972283i	$0.575118\pi$
$734$	−15.2128	+	5.53701i	−0.561515	+	0.204375i
$735$		0			0
$736$	−0.989573	−	5.61215i	−0.0364761	−	0.206866i
$737$	−6.97978	+	26.0489i	−0.257104	+	0.959524i
$738$		0			0
$739$	−5.31652	−	3.06949i	−0.195571	−	0.112913i	0.399017	−	0.916944i	$-0.369352\pi$
$739$	−5.31652	−	3.06949i	−0.195571	−	0.112913i	−0.594588	+	0.804031i	$0.702685\pi$
$740$	−1.14893	−	0.686310i	−0.0422357	−	0.0252292i
$741$		0			0
$742$	−35.0742	+	3.06860i	−1.28762	+	0.112652i
$743$	−7.74465	+	0.677569i	−0.284124	+	0.0248576i	−0.228327	−	0.973585i	$-0.573325\pi$
$743$	−7.74465	+	0.677569i	−0.284124	+	0.0248576i	−0.0557968	+	0.998442i	$0.517770\pi$
$744$		0			0
$745$	33.1725	−	8.36206i	1.21535	−	0.306362i
$746$	−2.80213	−	1.61781i	−0.102593	−	0.0592322i
$747$		0			0
$748$	−2.41532	+	9.01410i	−0.0883129	+	0.329588i
$749$	0.679124	+	3.85151i	0.0248147	+	0.140731i
$750$		0			0
$751$	−9.55059	+	3.47613i	−0.348506	+	0.126846i	−0.510341	−	0.859972i	$-0.670481\pi$
$751$	−9.55059	+	3.47613i	−0.348506	+	0.126846i	0.161835	+	0.986818i	$0.448259\pi$
$752$	−6.60916	+	4.62779i	−0.241011	+	0.168758i
$753$		0			0
$754$	−4.03694	−	4.81104i	−0.147017	−	0.175208i
$755$	−29.6698	+	20.1244i	−1.07979	+	0.732402i
$756$		0			0
$757$	−29.0503	+	29.0503i	−1.05585	+	1.05585i	−0.0575070	+	0.998345i	$0.518315\pi$
$757$	−29.0503	+	29.0503i	−1.05585	+	1.05585i	−0.998345	+	0.0575070i	$0.981685\pi$
$758$	−2.98413	+	34.1087i	−0.108388	+	1.23888i
$759$		0			0
$760$	4.43995	−	11.6565i	0.161054	−	0.422827i
$761$	12.8115	+	35.1993i	0.464416	+	1.27597i	0.922133	+	0.386874i	$0.126445\pi$
$761$	12.8115	+	35.1993i	0.464416	+	1.27597i	−0.457717	+	0.889098i	$0.651333\pi$
$762$		0			0
$763$	−49.2819	+	70.3819i	−1.78413	+	2.54800i
$764$	3.35873	+	5.81750i	0.121515	+	0.210470i
$765$		0			0
$766$	−11.2394	+	19.4672i	−0.406096	+	0.703378i
$767$	−9.66213	−	20.7205i	−0.348879	−	0.748174i
$768$		0			0
$769$	1.89455	−	2.25784i	0.0683193	−	0.0814198i	−0.730802	−	0.682589i	$-0.760854\pi$
$769$	1.89455	−	2.25784i	0.0683193	−	0.0814198i	0.799122	+	0.601169i	$0.205298\pi$
$770$	3.13875	−	30.6252i	0.113113	−	1.10366i
$771$		0			0
$772$	−7.42479	+	3.46224i	−0.267224	+	0.124609i
$773$	5.09577	+	19.0177i	0.183282	+	0.684018i	0.994992	+	0.0999568i	$0.0318705\pi$
$773$	5.09577	+	19.0177i	0.183282	+	0.684018i	−0.811710	+	0.584061i	$0.801463\pi$
$774$		0			0
$775$	24.6109	−	3.58880i	0.884050	−	0.128913i
$776$	14.9554	−	2.63703i	0.536866	−	0.0946639i
$777$		0			0
$778$	−1.40197	−	0.653750i	−0.0502631	−	0.0234381i
$779$	−0.347985	+	1.97352i	−0.0124678	+	0.0707087i
$780$		0			0
$781$	12.4611	−	10.4561i	0.445893	−	0.374148i
$782$	−12.1200	−	12.1200i	−0.433410	−	0.433410i
$783$		0			0
$784$			12.6902i			0.453221i
$785$	24.8053	+	44.4781i	0.885339	+	1.58749i
$786$		0			0
$787$	−7.86375	−	11.2306i	−0.280312	−	0.400328i	0.654164	−	0.756353i	$-0.273021\pi$
$787$	−7.86375	−	11.2306i	−0.280312	−	0.400328i	−0.934476	+	0.356025i	$0.884132\pi$
$788$	8.20329	−	17.5920i	0.292230	−	0.626689i
$789$		0			0
$790$	14.0895	+	0.209470i	0.501281	+	0.00745260i
$791$	50.0641	−	28.9045i	1.78008	−	1.02773i
$792$		0			0
$793$	8.30699	−	2.22585i	0.294990	−	0.0790423i
$794$	−8.68750	−	3.16199i	−0.308308	−	0.112215i
$795$		0			0
$796$	−14.6739	−	12.3129i	−0.520104	−	0.436419i
$797$	3.93848	+	45.0171i	0.139508	+	1.59459i	0.667021	+	0.745039i	$0.267569\pi$
$797$	3.93848	+	45.0171i	0.139508	+	1.59459i	−0.527513	+	0.849547i	$0.676875\pi$
$798$		0			0
$799$	−8.29992	+	22.8038i	−0.293630	+	0.806742i
$800$	0.583659	−	4.96582i	0.0206355	−	0.175568i
$801$		0			0
$802$	8.60726	+	2.30631i	0.303933	+	0.0814385i
$803$	1.43548	+	1.00513i	0.0506570	+	0.0354704i
$804$		0			0
$805$	45.8310	+	33.1173i	1.61533	+	1.16723i
$806$	24.9226	+	4.39453i	0.877861	+	0.154791i
$807$		0			0
$808$	−13.1141	−	1.14733i	−0.461352	−	0.0403630i
$809$	25.6186			0.900702			0.450351	−	0.892852i	$-0.351299\pi$
$809$	25.6186			0.900702			0.450351	+	0.892852i	$0.351299\pi$
$810$		0			0
$811$	6.51385			0.228732			0.114366	−	0.993439i	$-0.463516\pi$
$811$	6.51385			0.228732			0.114366	+	0.993439i	$0.463516\pi$
$812$	−5.45681	−	0.477409i	−0.191497	−	0.0167538i
$813$		0			0
$814$	1.82878	+	0.322463i	0.0640986	+	0.0113023i
$815$	34.5442	−	5.56291i	1.21003	−	0.194860i
$816$		0			0
$817$	9.12057	+	6.38629i	0.319088	+	0.223428i
$818$	10.7043	+	2.86822i	0.374268	+	0.100285i
$819$		0			0
$820$	0.0581077	+	0.801185i	0.00202921	+	0.0279786i
$821$	−4.38626	+	12.0512i	−0.153082	+	0.420588i	−0.992400	−	0.123051i	$-0.960732\pi$
$821$	−4.38626	+	12.0512i	−0.153082	+	0.420588i	0.839319	+	0.543640i	$0.182954\pi$
$822$		0			0
$823$	−2.88989	−	33.0316i	−0.100735	−	1.15141i	−0.863367	−	0.504576i	$-0.831649\pi$
$823$	−2.88989	−	33.0316i	−0.100735	−	1.15141i	0.762632	−	0.646832i	$-0.223907\pi$
$824$	8.86855	+	7.44160i	0.308951	+	0.259240i
$825$		0			0
$826$	−18.7379	−	6.82002i	−0.651973	−	0.237299i
$827$	−38.6520	+	10.3568i	−1.34406	+	0.360140i	−0.857939	−	0.513751i	$-0.828256\pi$
$827$	−38.6520	+	10.3568i	−1.34406	+	0.360140i	−0.486122	+	0.873891i	$0.661589\pi$
$828$		0			0
$829$	−5.73770	+	3.31267i	−0.199279	+	0.115054i	−0.596319	−	0.802748i	$-0.703371\pi$
$829$	−5.73770	+	3.31267i	−0.199279	+	0.115054i	0.397040	+	0.917801i	$0.370037\pi$
$830$	21.5048	+	22.1539i	0.746443	+	0.768973i
$831$		0			0
$832$	2.15012	−	4.61096i	0.0745422	−	0.159856i
$833$	21.8927	+	31.2660i	0.758537	+	1.08330i
$834$		0			0
$835$	−1.99821	+	1.11439i	−0.0691507	+	0.0385651i
$836$			17.3078i			0.598602i
$837$		0			0
$838$	15.1333	+	15.1333i	0.522770	+	0.522770i
$839$	−23.7978	+	19.9687i	−0.821591	+	0.689397i	−0.953344	−	0.301886i	$-0.902384\pi$
$839$	−23.7978	+	19.9687i	−0.821591	+	0.689397i	0.131753	+	0.991283i	$0.457939\pi$
$840$		0			0
$841$	−4.77118	+	27.0587i	−0.164524	+	0.933060i
$842$	−5.53228	−	2.57975i	−0.190655	−	0.0889039i
$843$		0			0
$844$	15.3021	−	2.69817i	0.526720	−	0.0928749i
$845$	−12.5622	+	25.9263i	−0.432152	+	0.891893i
$846$		0			0
$847$	−1.57722	−	5.88626i	−0.0541939	−	0.202254i
$848$	7.19109	−	3.35326i	0.246943	−	0.115151i
$849$		0			0
$850$	−7.12886	−	13.2417i	−0.244518	−	0.454186i
$851$	−2.19238	+	2.61278i	−0.0751539	+	0.0895649i
$852$		0			0
$853$	13.3417	+	28.6114i	0.456811	+	0.979635i	0.990949	+	0.134237i	$0.0428585\pi$
$853$	13.3417	+	28.6114i	0.456811	+	0.979635i	−0.534138	+	0.845397i	$0.679364\pi$
$854$	3.75042	−	6.49591i	0.128337	−	0.222285i
$855$		0			0
$856$	−0.440681	−	0.763282i	−0.0150622	−	0.0260884i
$857$	−7.77494	+	11.1038i	−0.265587	+	0.379297i	−0.929690	−	0.368344i	$-0.879925\pi$
$857$	−7.77494	+	11.1038i	−0.265587	+	0.379297i	0.664103	+	0.747641i	$0.268814\pi$
$858$		0			0
$859$	12.4029	+	34.0766i	0.423181	+	1.16268i	0.949877	+	0.312625i	$0.101208\pi$
$859$	12.4029	+	34.0766i	0.423181	+	1.16268i	−0.526696	+	0.850054i	$0.676569\pi$
$860$	4.17082	+	1.58866i	0.142224	+	0.0541728i
$861$		0			0
$862$	0.555935	−	6.35437i	0.0189352	−	0.216431i
$863$	−4.37666	+	4.37666i	−0.148983	+	0.148983i	−0.777664	−	0.628680i	$-0.783595\pi$
$863$	−4.37666	+	4.37666i	−0.148983	+	0.148983i	0.628680	+	0.777664i	$0.283595\pi$
$864$		0			0
$865$	0.425027	−	2.21719i	0.0144514	−	0.0753866i
$866$	−1.17995	−	1.40621i	−0.0400964	−	0.0477850i
$867$		0			0
$868$	18.0807	−	12.6603i	0.613700	−	0.429717i
$869$	−18.3731	+	6.68725i	−0.623263	+	0.226849i
$870$		0			0
$871$	−7.67880	−	43.5486i	−0.260186	−	1.47559i
$872$	5.01150	−	18.7032i	0.169711	−	0.633369i
$873$		0			0
$874$	−27.5303	−	15.8946i	−0.931226	−	0.537644i
$875$	30.1634	+	39.3884i	1.01971	+	1.33157i
$876$		0			0
$877$	−37.0637	+	3.24266i	−1.25155	+	0.109497i	−0.693591	−	0.720369i	$-0.743972\pi$
$877$	−37.0637	+	3.24266i	−1.25155	+	0.109497i	−0.557962	+	0.829866i	$0.688417\pi$
$878$	36.9465	−	3.23240i	1.24688	−	0.109088i
$879$		0			0
$880$	1.69582	+	6.72738i	0.0571662	+	0.226780i
$881$	−20.4902	−	11.8301i	−0.690334	−	0.398565i	0.113403	−	0.993549i	$-0.463825\pi$
$881$	−20.4902	−	11.8301i	−0.690334	−	0.398565i	−0.803737	+	0.594985i	$0.797158\pi$
$882$		0			0
$883$	−8.22323	+	30.6895i	−0.276734	+	1.03278i	0.677937	+	0.735120i	$0.262874\pi$
$883$	−8.22323	+	30.6895i	−0.276734	+	1.03278i	−0.954671	+	0.297664i	$0.903792\pi$
$884$	−2.65721	−	15.0698i	−0.0893716	−	0.506852i
$885$		0			0
$886$	−8.95384	+	3.25893i	−0.300810	+	0.109486i
$887$	7.56247	−	5.29530i	0.253923	−	0.177799i	−0.439684	−	0.898153i	$-0.644910\pi$
$887$	7.56247	−	5.29530i	0.253923	−	0.177799i	0.693607	+	0.720354i	$0.256021\pi$
$888$		0			0
$889$	30.9829	+	36.9240i	1.03913	+	1.23839i
$890$	30.6603	+	5.87748i	1.02774	+	0.197014i
$891$		0			0
$892$	3.72585	−	3.72585i	0.124751	−	0.124751i
$893$	−3.92266	+	44.8362i	−0.131267	+	1.50039i
$894$		0			0
$895$	−8.35758	−	18.6415i	−0.279363	−	0.623116i
$896$	−1.51767	−	4.16976i	−0.0507017	−	0.139302i
$897$		0			0
$898$	11.6108	−	16.5820i	0.387459	−	0.553349i
$899$	3.07020	+	5.31774i	0.102397	+	0.177356i
$900$		0			0
$901$	11.9324	−	20.6676i	0.397527	−	0.688537i
$902$	−0.471057	−	1.01019i	−0.0156845	−	0.0336355i
$903$		0			0
$904$	−8.37411	+	9.97988i	−0.278519	+	0.331926i
$905$	1.08998	+	0.111711i	0.0362320	+	0.00371339i
$906$		0			0
$907$	−23.5402	+	10.9770i	−0.781639	+	0.364484i	−0.772125	−	0.635470i	$-0.780806\pi$
$907$	−23.5402	+	10.9770i	−0.781639	+	0.364484i	−0.00951394	+	0.999955i	$0.503028\pi$
$908$	−7.64818	−	28.5434i	−0.253814	−	0.947246i
$909$		0			0
$910$	16.5583	+	47.6878i	0.548904	+	1.58083i
$911$	20.1917	−	3.56035i	0.668982	−	0.117960i	0.171166	−	0.985242i	$-0.445247\pi$
$911$	20.1917	−	3.56035i	0.668982	−	0.117960i	0.497816	+	0.867283i	$0.334135\pi$
$912$		0			0
$913$	−38.8269	−	18.1053i	−1.28498	−	0.599198i
$914$	4.30454	−	24.4123i	0.142382	−	0.807487i
$915$		0			0
$916$	7.78631	−	6.53349i	0.257267	−	0.215873i
$917$	7.70884	+	7.70884i	0.254568	+	0.254568i
$918$		0			0
$919$		−	28.4664i		−	0.939020i	−0.882927	−	0.469510i	$-0.844431\pi$
$919$		−	28.4664i		−	0.939020i	0.882927	−	0.469510i	$-0.155569\pi$
$920$	−12.2581	−	3.48067i	−0.404139	−	0.114754i
$921$		0			0
$922$	20.3333	+	29.0390i	0.669643	+	0.956349i
$923$	−11.2727	+	24.1743i	−0.371045	+	0.795708i
$924$		0			0
$925$	−2.50130	+	1.64282i	−0.0822421	+	0.0540157i
$926$	21.4336	−	12.3747i	0.704352	−	0.406658i
$927$		0			0
$928$	1.19238	−	0.319496i	0.0391417	−	0.0104880i
$929$	−5.40638	−	1.96776i	−0.177378	−	0.0645602i	0.251805	−	0.967778i	$-0.418976\pi$
$929$	−5.40638	−	1.96776i	−0.177378	−	0.0645602i	−0.429182	+	0.903218i	$0.641198\pi$
$930$		0			0
$931$	54.2281	+	45.5028i	1.77726	+	1.49129i
$932$	−0.552317	−	6.31301i	−0.0180917	−	0.206789i
$933$		0			0
$934$	13.0346	−	35.8122i	0.426505	−	1.17181i
$935$	15.7840	+	13.6493i	0.516193	+	0.446380i
$936$		0			0
$937$	25.1757	+	6.74581i	0.822455	+	0.220376i	0.645419	−	0.763828i	$-0.276683\pi$
$937$	25.1757	+	6.74581i	0.822455	+	0.220376i	0.177035	+	0.984204i	$0.443349\pi$
$938$	−31.5934	−	22.1220i	−1.03156	−	0.722308i
$939$		0			0
$940$	2.86837	+	17.8118i	0.0935559	+	0.580956i
$941$	−52.3223	−	9.22584i	−1.70566	−	0.300754i	−0.765994	−	0.642848i	$-0.777753\pi$
$941$	−52.3223	−	9.22584i	−1.70566	−	0.300754i	−0.939666	+	0.342094i	$0.888864\pi$
$942$		0			0
$943$	2.03943	+	0.178427i	0.0664130	+	0.00581039i
$944$	4.49375			0.146259
$945$		0			0
$946$	−6.19289			−0.201348
$947$	−51.1947	−	4.47895i	−1.66360	−	0.145546i	−0.783842	−	0.620961i	$-0.786743\pi$
$947$	−51.1947	−	4.47895i	−1.66360	−	0.145546i	−0.879762	+	0.475414i	$0.842298\pi$
$948$		0			0
$949$	−2.82984	−	0.498977i	−0.0918604	−	0.0161975i
$950$	−19.1273	−	20.2999i	−0.620571	−	0.658615i
$951$		0			0
$952$	−10.9328	−	7.65520i	−0.354333	−	0.248106i
$953$	26.0061	+	6.96831i	0.842419	+	0.225726i	0.654124	−	0.756387i	$-0.273037\pi$
$953$	26.0061	+	6.96831i	0.842419	+	0.225726i	0.188295	+	0.982113i	$0.439704\pi$
$954$		0			0
$955$	14.9814	−	1.08656i	0.484786	−	0.0351601i
$956$	−5.84544	+	16.0602i	−0.189055	+	0.519425i
$957$		0			0
$958$	1.59150	+	18.1909i	0.0514189	+	0.587721i
$959$	−23.6536	−	19.8478i	−0.763816	−	0.640918i
$960$		0			0
$961$	5.87963	+	2.14001i	0.189665	+	0.0690326i
$962$	−2.94124	+	0.788103i	−0.0948294	+	0.0254095i
$963$		0			0
$964$	−1.10860	+	0.640049i	−0.0357055	+	0.0206146i
$965$	−0.272316	+	18.3166i	−0.00876615	+	0.589633i
$966$		0			0
$967$	4.22001	−	9.04984i	0.135706	−	0.291023i	−0.826697	−	0.562647i	$-0.809783\pi$
$967$	4.22001	−	9.04984i	0.135706	−	0.291023i	0.962403	+	0.271624i	$0.0875607\pi$
$968$	0.787703	+	1.12496i	0.0253177	+	0.0361575i
$969$		0			0
$970$	9.27535	−	32.6657i	0.297814	−	1.04883i
$971$		−	8.51742i		−	0.273337i	−0.990617	−	0.136668i	$-0.956360\pi$
$971$		−	8.51742i		−	0.273337i	0.990617	−	0.136668i	$-0.0436395\pi$
$972$		0			0
$973$	−48.2719	−	48.2719i	−1.54753	−	1.54753i
$974$	15.9524	−	13.3857i	0.511148	−	0.428904i
$975$		0			0
$976$	−0.293531	+	1.66470i	−0.00939571	+	0.0532857i
$977$	−22.3736	−	10.4330i	−0.715796	−	0.333781i	0.0303720	−	0.999539i	$-0.490331\pi$
$977$	−22.3736	−	10.4330i	−0.715796	−	0.333781i	−0.746168	+	0.665757i	$0.768109\pi$
$978$		0			0
$979$	−42.6597	+	7.52206i	−1.36341	+	0.240406i
$980$	25.5364	+	12.3732i	0.815730	+	0.395249i
$981$		0			0
$982$	−3.35206	−	12.5101i	−0.106969	−	0.399213i
$983$	−38.7656	+	18.0767i	−1.23643	+	0.576557i	−0.927249	−	0.374446i	$-0.877833\pi$
$983$	−38.7656	+	18.0767i	−1.23643	+	0.576557i	−0.309182	+	0.951003i	$0.600055\pi$
$984$		0			0
$985$	−27.4019	−	33.6601i	−0.873097	−	1.07250i
$986$	2.38659	−	2.84423i	0.0760045	−	0.0905786i
$987$		0			0
$988$	−11.9941	−	25.7213i	−0.381582	−	0.818305i
$989$	5.68725	−	9.85061i	0.180844	−	0.313231i
$990$		0			0
$991$	19.3895	+	33.5836i	0.615927	+	1.06682i	0.990221	+	0.139507i	$0.0445519\pi$
$991$	19.3895	+	33.5836i	0.615927	+	1.06682i	−0.374294	+	0.927310i	$0.622115\pi$
$992$	−2.85310	+	4.07466i	−0.0905862	+	0.129370i
$993$		0			0
$994$	7.95683	+	21.8612i	0.252375	+	0.693396i
$995$	−39.0846	+	17.5229i	−1.23907	+	0.555514i
$996$		0			0
$997$	−4.17803	+	47.7552i	−0.132320	+	1.51242i	0.582338	+	0.812947i	$0.302138\pi$
$997$	−4.17803	+	47.7552i	−0.132320	+	1.51242i	−0.714658	+	0.699474i	$0.753418\pi$
$998$	−9.57484	+	9.57484i	−0.303086	+	0.303086i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.15		216
3.2	odd	2		270.2.r.a.113.7	✓	216
5.2	odd	4	inner	810.2.s.a.287.2		216
15.2	even	4		270.2.r.a.167.11	yes	216
27.11	odd	18	inner	810.2.s.a.683.2		216
27.16	even	9		270.2.r.a.173.11	yes	216
135.92	even	36	inner	810.2.s.a.197.15		216
135.97	odd	36		270.2.r.a.227.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.7	✓	216	3.2	odd	2
270.2.r.a.167.11	yes	216	15.2	even	4
270.2.r.a.173.11	yes	216	27.16	even	9
270.2.r.a.227.7	yes	216	135.97	odd	36
810.2.s.a.197.15		216	135.92	even	36	inner
810.2.s.a.287.2		216	5.2	odd	4	inner
810.2.s.a.683.2		216	27.11	odd	18	inner
810.2.s.a.773.15		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)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.30964 - 1.81241i) q^{5} +(-3.63487 - 2.54517i) q^{7} +(0.965926 + 0.258819i) q^{8} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(1.30964 - 1.81241i) q^{5} +(-3.63487 - 2.54517i) q^{7} +(0.965926 + 0.258819i) q^{8} +(1.46262 - 1.69137i) q^{10} +(-1.06118 + 2.91557i) q^{11} +(-0.443416 - 5.06827i) q^{13} +(-3.39922 - 2.85228i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.90525 - 0.778460i) q^{17} +(4.83096 - 2.78915i) q^{19} +(1.60447 - 1.55746i) q^{20} +(-1.31125 + 2.81199i) q^{22} +(-3.26865 - 4.66812i) q^{23} +(-1.56967 - 4.74722i) q^{25} -5.08763i q^{26} +(-3.13769 - 3.13769i) q^{28} +(0.945635 - 0.793482i) q^{29} +(-0.863767 + 4.89867i) q^{31} +(0.906308 + 0.422618i) q^{32} +(2.96205 - 0.522288i) q^{34} +(-9.37328 + 3.25463i) q^{35} +(-0.154906 - 0.578116i) q^{37} +(5.05567 - 2.35750i) q^{38} +(1.73410 - 1.41169i) q^{40} +(-0.230916 + 0.275195i) q^{41} +(0.843535 + 1.80897i) q^{43} +(-1.55134 + 2.68701i) q^{44} +(-2.84936 - 4.93524i) q^{46} +(-4.62779 + 6.60916i) q^{47} +(4.34030 + 11.9249i) q^{49} +(-1.14995 - 4.86597i) q^{50} +(0.443416 - 5.06827i) q^{52} +(5.61053 - 5.61053i) q^{53} +(3.89445 + 5.74166i) q^{55} +(-2.85228 - 3.39922i) q^{56} +(1.01119 - 0.708045i) q^{58} +(4.22275 - 1.53695i) q^{59} +(0.293531 + 1.66470i) q^{61} +(-1.28743 + 4.80474i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-9.76650 - 5.83397i) q^{65} +(8.65868 - 0.757536i) q^{67} +(2.99629 - 0.262142i) q^{68} +(-9.62127 + 2.42531i) q^{70} +(-4.54040 - 2.62140i) q^{71} +(0.146181 - 0.545555i) q^{73} +(-0.103930 - 0.589417i) q^{74} +(5.24190 - 1.90789i) q^{76} +(11.2779 - 7.89686i) q^{77} +(4.05065 + 4.82738i) q^{79} +(1.85054 - 1.25519i) q^{80} +(-0.254023 + 0.254023i) q^{82} +(-1.20341 + 13.7551i) q^{83} +(2.39395 - 6.28502i) q^{85} +(0.682663 + 1.87560i) q^{86} +(-1.77963 + 2.54157i) q^{88} +(6.98069 + 12.0909i) q^{89} +(-11.2878 + 19.5511i) q^{91} +(-2.40838 - 5.16480i) q^{92} +(-5.18620 + 6.18068i) q^{94} +(1.27173 - 12.4085i) q^{95} +(13.7632 - 6.41791i) q^{97} +(3.28446 + 12.2578i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more