LMFDB - Embedded newform 810.2.s.a.737.14

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			737.14
Character	$\chi$	$=$	810.737
Dual form			810.2.s.a.233.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.573576 + 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(1.11362 - 1.93904i) q^{5} +(-1.91731 - 0.894058i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(2.22711 - 0.199964i) q^{10} +(2.96988 - 3.53937i) q^{11} +(-5.51327 - 3.86043i) q^{13} +(-0.367357 - 2.08338i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(-0.632172 - 0.169390i) q^{17} +(0.874579 + 0.504939i) q^{19} +(1.44122 + 1.70965i) q^{20} +(4.60274 + 0.402687i) q^{22} +(-1.78543 - 3.82887i) q^{23} +(-2.51972 - 4.31868i) q^{25} -6.73046i q^{26} +(1.49590 - 1.49590i) q^{28} +(-0.766601 + 4.34761i) q^{29} +(3.38938 + 1.23364i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(-0.223843 - 0.615004i) q^{34} +(-3.86876 + 2.72210i) q^{35} +(1.42322 - 5.31153i) q^{37} +(0.0880166 + 1.00603i) q^{38} +(-0.573811 + 2.16119i) q^{40} +(10.6740 - 1.88211i) q^{41} +(-2.82504 + 0.247159i) q^{43} +(2.31016 + 4.00131i) q^{44} +(2.11235 - 3.65869i) q^{46} +(-0.796430 + 1.70795i) q^{47} +(-1.62276 - 1.93393i) q^{49} +(2.09241 - 4.54113i) q^{50} +(5.51327 - 3.86043i) q^{52} +(5.85254 + 5.85254i) q^{53} +(-3.55565 - 9.70021i) q^{55} +(2.08338 + 0.367357i) q^{56} +(-4.00106 + 1.86572i) q^{58} +(1.33785 - 1.12259i) q^{59} +(-6.87841 + 2.50354i) q^{61} +(0.933536 + 3.48401i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-13.6252 + 6.39138i) q^{65} +(7.93436 - 11.3314i) q^{67} +(0.375390 - 0.536113i) q^{68} +(-4.44885 - 1.60777i) q^{70} +(-2.31694 + 1.33769i) q^{71} +(3.73141 + 13.9258i) q^{73} +(5.16727 - 1.88073i) q^{74} +(-0.773611 + 0.649137i) q^{76} +(-8.85861 + 4.13084i) q^{77} +(2.93933 + 0.518284i) q^{79} +(-2.09947 + 0.769569i) q^{80} +(7.66408 + 7.66408i) q^{82} +(12.5459 - 8.78472i) q^{83} +(-1.03245 + 1.03717i) q^{85} +(-1.82284 - 2.17237i) q^{86} +(-1.95263 + 4.18743i) q^{88} +(-6.23342 + 10.7966i) q^{89} +(7.11922 + 12.3308i) q^{91} +(4.20862 - 0.368207i) q^{92} +(-1.85588 + 0.327242i) q^{94} +(1.95304 - 1.13353i) q^{95} +(0.979769 + 11.1988i) q^{97} +(0.653406 - 2.43854i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	0.573576	+	0.819152i	0.405580	+	0.579228i
$2$	0.573576	+	0.819152i	0.405580	+	0.579228i
$3$		0			0
$3$		0			0
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	1.11362	−	1.93904i	0.498024	−	0.867163i
$5$	1.11362	−	1.93904i	0.498024	−	0.867163i
$6$		0			0
$7$	−1.91731	−	0.894058i	−0.724677	−	0.337922i	0.0250353	−	0.999687i	$-0.492030\pi$
$7$	−1.91731	−	0.894058i	−0.724677	−	0.337922i	−0.749712	+	0.661764i	$0.769808\pi$
$8$	−0.965926	+	0.258819i	−0.341506	+	0.0915064i
$9$		0			0
$10$	2.22711	−	0.199964i	0.704274	−	0.0632342i
$11$	2.96988	−	3.53937i	0.895454	−	1.06716i	−0.101924	−	0.994792i	$-0.532500\pi$
$11$	2.96988	−	3.53937i	0.895454	−	1.06716i	0.997378	−	0.0723682i	$-0.0230557\pi$
$12$		0			0
$13$	−5.51327	−	3.86043i	−1.52911	−	1.07069i	−0.970453	−	0.241289i	$-0.922430\pi$
$13$	−5.51327	−	3.86043i	−1.52911	−	1.07069i	−0.558652	−	0.829402i	$-0.688681\pi$
$14$	−0.367357	−	2.08338i	−0.0981802	−	0.556807i
$15$		0			0
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−0.632172	−	0.169390i	−0.153324	−	0.0410831i	0.181340	−	0.983420i	$-0.441956\pi$
$17$	−0.632172	−	0.169390i	−0.153324	−	0.0410831i	−0.334665	+	0.942337i	$0.608623\pi$
$18$		0			0
$19$	0.874579	+	0.504939i	0.200642	+	0.115841i	0.596955	−	0.802275i	$-0.296377\pi$
$19$	0.874579	+	0.504939i	0.200642	+	0.115841i	−0.396313	+	0.918116i	$0.629710\pi$
$20$	1.44122	+	1.70965i	0.322266	+	0.382289i
$21$		0			0
$22$	4.60274	+	0.402687i	0.981307	+	0.0858533i
$23$	−1.78543	−	3.82887i	−0.372289	−	0.798376i	−0.999805	−	0.0197718i	$-0.993706\pi$
$23$	−1.78543	−	3.82887i	−0.372289	−	0.798376i	0.627516	−	0.778604i	$-0.284072\pi$
$24$		0			0
$25$	−2.51972	−	4.31868i	−0.503944	−	0.863737i
$26$		−	6.73046i		−	1.31995i
$27$		0			0
$28$	1.49590	−	1.49590i	0.282699	−	0.282699i
$29$	−0.766601	+	4.34761i	−0.142354	+	0.807331i	0.827099	+	0.562056i	$0.189989\pi$
$29$	−0.766601	+	4.34761i	−0.142354	+	0.807331i	−0.969454	+	0.245275i	$0.921122\pi$
$30$		0			0
$31$	3.38938	+	1.23364i	0.608751	+	0.221567i	0.627957	−	0.778248i	$-0.283891\pi$
$31$	3.38938	+	1.23364i	0.608751	+	0.221567i	−0.0192054	+	0.999816i	$0.506114\pi$
$32$	0.0871557	−	0.996195i	0.0154071	−	0.176104i
$33$		0			0
$34$	−0.223843	−	0.615004i	−0.0383888	−	0.105472i
$35$	−3.86876	+	2.72210i	−0.653940	+	0.460119i
$36$		0			0
$37$	1.42322	−	5.31153i	0.233976	−	0.873210i	−0.744632	−	0.667475i	$-0.767375\pi$
$37$	1.42322	−	5.31153i	0.233976	−	0.873210i	0.978608	−	0.205734i	$-0.0659583\pi$
$38$	0.0880166	+	1.00603i	0.0142782	+	0.163200i
$39$		0			0
$40$	−0.573811	+	2.16119i	−0.0907275	+	0.341714i
$41$	10.6740	−	1.88211i	1.66700	−	0.293936i	0.741010	−	0.671495i	$-0.234347\pi$
$41$	10.6740	−	1.88211i	1.66700	−	0.293936i	0.925986	+	0.377558i	$0.123236\pi$
$42$		0			0
$43$	−2.82504	+	0.247159i	−0.430815	+	0.0376914i	−0.300501	−	0.953781i	$-0.597154\pi$
$43$	−2.82504	+	0.247159i	−0.430815	+	0.0376914i	−0.130313	+	0.991473i	$0.541598\pi$
$44$	2.31016	+	4.00131i	0.348270	+	0.603221i
$45$		0			0
$46$	2.11235	−	3.65869i	0.311449	−	0.539445i
$47$	−0.796430	+	1.70795i	−0.116171	+	0.249130i	−0.955792	−	0.294043i	$-0.904999\pi$
$47$	−0.796430	+	1.70795i	−0.116171	+	0.249130i	0.839621	+	0.543172i	$0.182777\pi$
$48$		0			0
$49$	−1.62276	−	1.93393i	−0.231823	−	0.276276i
$50$	2.09241	−	4.54113i	0.295911	−	0.642212i
$51$		0			0
$52$	5.51327	−	3.86043i	0.764553	−	0.535346i
$53$	5.85254	+	5.85254i	0.803908	+	0.803908i	0.983704	−	0.179796i	$-0.0575437\pi$
$53$	5.85254	+	5.85254i	0.803908	+	0.803908i	−0.179796	+	0.983704i	$0.557544\pi$
$54$		0			0
$55$	−3.55565	−	9.70021i	−0.479444	−	1.30798i
$56$	2.08338	+	0.367357i	0.278404	+	0.0490901i
$57$		0			0
$58$	−4.00106	+	1.86572i	−0.525365	+	0.244982i
$59$	1.33785	−	1.12259i	0.174173	−	0.146148i	−0.551534	−	0.834152i	$-0.685957\pi$
$59$	1.33785	−	1.12259i	0.174173	−	0.146148i	0.725707	+	0.688004i	$0.241513\pi$
$60$		0			0
$61$	−6.87841	+	2.50354i	−0.880690	+	0.320545i	−0.742488	−	0.669859i	$-0.766354\pi$
$61$	−6.87841	+	2.50354i	−0.880690	+	0.320545i	−0.138202	+	0.990404i	$0.544132\pi$
$62$	0.933536	+	3.48401i	0.118559	+	0.442469i
$63$		0			0
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	−13.6252	+	6.39138i	−1.69000	+	0.792754i
$66$		0			0
$67$	7.93436	−	11.3314i	0.969337	−	1.38436i	0.0466048	−	0.998913i	$-0.485160\pi$
$67$	7.93436	−	11.3314i	0.969337	−	1.38436i	0.922732	−	0.385443i	$-0.125951\pi$
$68$	0.375390	−	0.536113i	0.0455228	−	0.0650132i
$69$		0			0
$70$	−4.44885	−	1.60777i	−0.531739	−	0.192165i
$71$	−2.31694	+	1.33769i	−0.274970	+	0.158754i	−0.631144	−	0.775665i	$-0.717414\pi$
$71$	−2.31694	+	1.33769i	−0.274970	+	0.158754i	0.356174	+	0.934420i	$0.384081\pi$
$72$		0			0
$73$	3.73141	+	13.9258i	0.436728	+	1.62989i	0.736896	+	0.676006i	$0.236291\pi$
$73$	3.73141	+	13.9258i	0.436728	+	1.62989i	−0.300167	+	0.953887i	$0.597043\pi$
$74$	5.16727	−	1.88073i	0.600683	−	0.218631i
$75$		0			0
$76$	−0.773611	+	0.649137i	−0.0887392	+	0.0744611i
$77$	−8.85861	+	4.13084i	−1.00953	+	0.470752i
$78$		0			0
$79$	2.93933	+	0.518284i	0.330701	+	0.0583115i	0.336534	−	0.941671i	$-0.390745\pi$
$79$	2.93933	+	0.518284i	0.330701	+	0.0583115i	−0.00583253	+	0.999983i	$0.501857\pi$
$80$	−2.09947	+	0.769569i	−0.234728	+	0.0860404i
$81$		0			0
$82$	7.66408	+	7.66408i	0.846356	+	0.846356i
$83$	12.5459	−	8.78472i	1.37709	−	0.964248i	0.377825	−	0.925877i	$-0.376672\pi$
$83$	12.5459	−	8.78472i	1.37709	−	0.964248i	0.999264	−	0.0383709i	$-0.0122168\pi$
$84$		0			0
$85$	−1.03245	+	1.03717i	−0.111985	+	0.112497i
$86$	−1.82284	−	2.17237i	−0.196562	−	0.234253i
$87$		0			0
$88$	−1.95263	+	4.18743i	−0.208151	+	0.446382i
$89$	−6.23342	+	10.7966i	−0.660741	+	1.14444i	0.319680	+	0.947526i	$0.396425\pi$
$89$	−6.23342	+	10.7966i	−0.660741	+	1.14444i	−0.980421	+	0.196912i	$0.936909\pi$
$90$		0			0
$91$	7.11922	+	12.3308i	0.746297	+	1.29262i
$92$	4.20862	−	0.368207i	0.438779	−	0.0383882i
$93$		0			0
$94$	−1.85588	+	0.327242i	−0.191420	+	0.0337525i
$95$	1.95304	−	1.13353i	0.200378	−	0.116298i
$96$		0			0
$97$	0.979769	+	11.1988i	0.0994804	+	1.13707i	0.867771	+	0.496965i	$0.165552\pi$
$97$	0.979769	+	11.1988i	0.0994804	+	1.13707i	−0.768290	+	0.640102i	$0.778892\pi$
$98$	0.653406	−	2.43854i	0.0660039	−	0.246330i
$99$		0			0
$100$	4.92003	−	0.890683i	0.492003	−	0.0890683i
$101$	−0.969956	−	2.66493i	−0.0965142	−	0.265171i	0.882035	−	0.471184i	$-0.156173\pi$
$101$	−0.969956	−	2.66493i	−0.0965142	−	0.265171i	−0.978549	+	0.206013i	$0.933951\pi$
$102$		0			0
$103$	1.07479	−	12.2849i	0.105902	−	1.21047i	−0.738310	−	0.674461i	$-0.764376\pi$
$103$	1.07479	−	12.2849i	0.105902	−	1.21047i	0.844213	−	0.536008i	$-0.180068\pi$
$104$	6.32456	+	2.30195i	0.620174	+	0.225725i
$105$		0			0
$106$	−1.43724	+	8.15100i	−0.139597	+	0.791695i
$107$	2.84254	−	2.84254i	0.274798	−	0.274798i	−0.556230	−	0.831028i	$-0.687753\pi$
$107$	2.84254	−	2.84254i	0.274798	−	0.274798i	0.831028	+	0.556230i	$0.187753\pi$
$108$		0			0
$109$			1.29371i			0.123915i	0.998079	+	0.0619575i	$0.0197343\pi$
$109$			1.29371i			0.123915i	−0.998079	+	0.0619575i	$0.980266\pi$
$110$	5.90651	−	8.47643i	0.563164	−	0.808196i
$111$		0			0
$112$	0.894058	+	1.91731i	0.0844806	+	0.181169i
$113$	6.79204	+	0.594226i	0.638941	+	0.0559001i	0.402023	−	0.915629i	$-0.368307\pi$
$113$	6.79204	+	0.594226i	0.638941	+	0.0559001i	0.236918	+	0.971530i	$0.423863\pi$
$114$		0			0
$115$	−9.41261	−	0.801878i	−0.877731	−	0.0747755i
$116$	−3.82322	−	2.20734i	−0.354977	−	0.204946i
$117$		0			0
$118$	1.68693	+	0.452011i	0.155294	+	0.0416110i
$119$	1.06063	+	0.889973i	0.0972277	+	0.0815837i
$120$		0			0
$121$	−1.79680	−	10.1902i	−0.163345	−	0.926378i
$122$	−5.99607	−	4.19849i	−0.542859	−	0.380114i
$123$		0			0
$124$	−2.31848	+	2.76305i	−0.208205	+	0.248129i
$125$	−11.1801	+	0.0764662i	−0.999977	+	0.00683934i
$126$		0			0
$127$	−14.0309	+	3.75956i	−1.24504	+	0.333607i	−0.820418	−	0.571764i	$-0.806259\pi$
$127$	−14.0309	+	3.75956i	−1.24504	+	0.333607i	−0.424621	+	0.905371i	$0.639593\pi$
$128$	0.906308	+	0.422618i	0.0801070	+	0.0373545i
$129$		0			0
$130$	−13.0506	−	7.49515i	−1.14461	−	0.657368i
$131$	4.29864	−	11.8104i	0.375574	−	1.03188i	−0.597596	−	0.801797i	$-0.703877\pi$
$131$	4.29864	−	11.8104i	0.375574	−	1.03188i	0.973171	−	0.230085i	$-0.0739003\pi$
$132$		0			0
$133$	−1.22540	−	1.75005i	−0.106256	−	0.151749i
$134$	13.8331			1.19500
$135$		0			0
$136$	0.654473			0.0561206
$137$	−3.26497	−	4.66286i	−0.278945	−	0.398375i	0.655093	−	0.755548i	$-0.272630\pi$
$137$	−3.26497	−	4.66286i	−0.278945	−	0.398375i	−0.934038	+	0.357173i	$0.883741\pi$
$138$		0			0
$139$	−3.55554	+	9.76877i	−0.301577	+	0.828576i	0.692649	+	0.721274i	$0.256443\pi$
$139$	−3.55554	+	9.76877i	−0.301577	+	0.828576i	−0.994226	+	0.107302i	$0.965779\pi$
$140$	−1.23474	−	4.56646i	−0.104355	−	0.385936i
$141$		0			0
$142$	−2.42471	−	1.13066i	−0.203477	−	0.0948831i
$143$	−30.0373	+	8.04846i	−2.51184	+	0.673046i
$144$		0			0
$145$	7.57647	+	6.32804i	0.629192	+	0.525515i
$146$	−9.26711	+	11.0441i	−0.766951	+	0.914017i
$147$		0			0
$148$	4.50443	+	3.15404i	0.370262	+	0.259260i
$149$	1.07764	+	6.11157i	0.0882833	+	0.500680i	0.996600	+	0.0823958i	$0.0262572\pi$
$149$	1.07764	+	6.11157i	0.0882833	+	0.500680i	−0.908316	+	0.418284i	$0.862632\pi$
$150$		0			0
$151$	10.7455	+	9.01658i	0.874459	+	0.733759i	0.965032	−	0.262131i	$-0.0844253\pi$
$151$	10.7455	+	9.01658i	0.874459	+	0.733759i	−0.0905728	+	0.995890i	$0.528870\pi$
$152$	−0.975466	−	0.261375i	−0.0791208	−	0.0212003i
$153$		0			0
$154$	−8.46487	−	4.88720i	−0.682119	−	0.393821i
$155$	6.16654	−	5.19834i	0.495308	−	0.417541i
$156$		0			0
$157$	−24.8472	−	2.17385i	−1.98302	−	0.173492i	−0.983072	−	0.183219i	$-0.941348\pi$
$157$	−24.8472	−	2.17385i	−1.98302	−	0.173492i	−0.999953	+	0.00972700i	$0.996904\pi$
$158$	1.26138	+	2.70504i	0.100350	+	0.215201i
$159$		0			0
$160$	−1.83460	−	1.27838i	−0.145038	−	0.101065i
$161$			8.93744i			0.704369i
$162$		0			0
$163$	1.83309	−	1.83309i	0.143579	−	0.143579i	−0.631664	−	0.775242i	$-0.717628\pi$
$163$	1.83309	−	1.83309i	0.143579	−	0.143579i	0.775242	+	0.631664i	$0.217628\pi$
$164$	−1.88211	+	10.6740i	−0.146968	+	0.833498i
$165$		0			0
$166$	14.3920	+	5.23827i	1.11704	+	0.406569i
$167$	−0.954902	+	10.9146i	−0.0738925	+	0.844596i	0.865311	+	0.501235i	$0.167121\pi$
$167$	−0.954902	+	10.9146i	−0.0738925	+	0.844596i	−0.939204	+	0.343361i	$0.888435\pi$
$168$		0			0
$169$	11.0469	+	30.3512i	0.849764	+	2.33471i
$170$	−1.44179	−	0.250838i	−0.110580	−	0.0192384i
$171$		0			0
$172$	0.733967	−	2.73920i	0.0559645	−	0.208862i
$173$	1.50412	+	17.1922i	0.114356	+	1.30710i	0.809028	+	0.587770i	$0.199994\pi$
$173$	1.50412	+	17.1922i	0.114356	+	1.30710i	−0.694672	+	0.719327i	$0.744451\pi$
$174$		0			0
$175$	0.969936	+	10.5330i	0.0733203	+	0.796224i
$176$	−4.55013	+	0.802310i	−0.342979	+	0.0604764i
$177$		0			0
$178$	−12.4194	+	1.08656i	−0.930874	+	0.0814409i
$179$	−10.7340	−	18.5919i	−0.802299	−	1.38962i	−0.918100	−	0.396349i	$-0.870277\pi$
$179$	−10.7340	−	18.5919i	−0.802299	−	1.38962i	0.115801	−	0.993272i	$-0.463056\pi$
$180$		0			0
$181$	5.54152	−	9.59819i	0.411898	−	0.713428i	−0.583200	−	0.812329i	$-0.698199\pi$
$181$	5.54152	−	9.59819i	0.411898	−	0.713428i	0.995097	+	0.0989012i	$0.0315328\pi$
$182$	−6.01742	+	12.9044i	−0.446041	+	0.956538i
$183$		0			0
$184$	2.71558	+	3.23630i	0.200195	+	0.238584i
$185$	−8.71432	−	8.67468i	−0.640690	−	0.637775i
$186$		0			0
$187$	−2.47701	+	1.73442i	−0.181137	+	0.126834i
$188$	−1.33255	−	1.33255i	−0.0971863	−	0.0971863i
$189$		0			0
$190$	2.04875	+	0.949669i	0.148632	+	0.0688962i
$191$	−12.0892	−	2.13165i	−0.874743	−	0.154241i	−0.281788	−	0.959477i	$-0.590928\pi$
$191$	−12.0892	−	2.13165i	−0.874743	−	0.154241i	−0.592955	+	0.805236i	$0.702039\pi$
$192$		0			0
$193$	−3.84281	+	1.79193i	−0.276611	+	0.128986i	−0.555974	−	0.831200i	$-0.687655\pi$
$193$	−3.84281	+	1.79193i	−0.276611	+	0.128986i	0.279363	+	0.960186i	$0.409877\pi$
$194$	−8.61155	+	7.22595i	−0.618273	+	0.518793i
$195$		0			0
$196$	2.37232	−	0.863452i	0.169451	−	0.0616752i
$197$	−3.37219	−	12.5852i	−0.240259	−	0.896658i	−0.975707	−	0.219078i	$-0.929695\pi$
$197$	−3.37219	−	12.5852i	−0.240259	−	0.896658i	0.735449	−	0.677580i	$-0.236971\pi$
$198$		0			0
$199$	6.62281	−	3.82368i	0.469478	−	0.271053i	−0.246543	−	0.969132i	$-0.579295\pi$
$199$	6.62281	−	3.82368i	0.469478	−	0.271053i	0.716021	+	0.698078i	$0.245961\pi$
$200$	3.55162	+	3.51938i	0.251137	+	0.248858i
$201$		0			0
$202$	1.62664	−	2.32308i	0.114450	−	0.163452i
$203$	5.35683	−	7.65035i	0.375976	−	0.536949i
$204$		0			0
$205$	8.23724	−	22.7932i	0.575314	−	1.59194i
$206$	10.6797	−	6.16592i	0.744090	−	0.429600i
$207$		0			0
$208$	1.74197	+	6.50112i	0.120784	+	0.450772i
$209$	4.38456	−	1.59585i	0.303287	−	0.110387i
$210$		0			0
$211$	8.98764	−	7.54152i	0.618734	−	0.519180i	−0.278671	−	0.960387i	$-0.589894\pi$
$211$	8.98764	−	7.54152i	0.618734	−	0.519180i	0.897405	+	0.441207i	$0.145449\pi$
$212$	−7.50127	+	3.49790i	−0.515190	+	0.240237i
$213$		0			0
$214$	3.95888	+	0.698058i	0.270624	+	0.0477182i
$215$	−2.66676	+	5.75309i	−0.181872	+	0.392358i
$216$		0			0
$217$	−5.39557	−	5.39557i	−0.366275	−	0.366275i
$218$	−1.05975	+	0.742042i	−0.0717750	+	0.0502574i
$219$		0			0
$220$	10.3313	−	0.0235534i	0.696538	−	0.00158797i
$221$	2.83142	+	3.37435i	0.190462	+	0.226983i
$222$		0			0
$223$	5.23170	−	11.2194i	0.350340	−	0.751308i	−0.649619	−	0.760260i	$-0.725072\pi$
$223$	5.23170	−	11.2194i	0.350340	−	0.751308i	0.999960	+	0.00895195i	$0.00284953\pi$
$224$	−1.05776	+	1.83210i	−0.0706746	+	0.122412i
$225$		0			0
$226$	3.40899	+	5.90455i	0.226763	+	0.392765i
$227$	17.2666	−	1.51063i	1.14603	−	0.100264i	0.501718	−	0.865031i	$-0.332701\pi$
$227$	17.2666	−	1.51063i	1.14603	−	0.100264i	0.644307	+	0.764767i	$0.277146\pi$
$228$		0			0
$229$	1.83558	−	0.323662i	0.121298	−	0.0213882i	−0.112669	−	0.993633i	$-0.535940\pi$
$229$	1.83558	−	0.323662i	0.121298	−	0.0213882i	0.233968	+	0.972244i	$0.424829\pi$
$230$	−4.74199	−	8.17030i	−0.312678	−	0.538734i
$231$		0			0
$232$	−0.384765	−	4.39788i	−0.0252610	−	0.288735i
$233$	−2.30909	+	8.61765i	−0.151274	+	0.564561i	0.848122	+	0.529801i	$0.177733\pi$
$233$	−2.30909	+	8.61765i	−0.151274	+	0.564561i	−0.999396	+	0.0347602i	$0.988933\pi$
$234$		0			0
$235$	2.42486	+	3.44631i	0.158180	+	0.224812i
$236$	0.597317	+	1.64111i	0.0388820	+	0.106827i
$237$		0			0
$238$	−0.120672	+	1.37928i	−0.00782198	+	0.0894057i
$239$	−1.54448	−	0.562146i	−0.0999043	−	0.0363622i	0.291584	−	0.956545i	$-0.405818\pi$
$239$	−1.54448	−	0.562146i	−0.0999043	−	0.0363622i	−0.391489	+	0.920183i	$0.628040\pi$
$240$		0			0
$241$	−2.73836	+	15.5300i	−0.176393	+	1.00038i	0.760130	+	0.649771i	$0.225135\pi$
$241$	−2.73836	+	15.5300i	−0.176393	+	1.00038i	−0.936523	+	0.350606i	$0.885976\pi$
$242$	7.31669	−	7.31669i	0.470335	−	0.470335i
$243$		0			0
$244$		−	7.31985i		−	0.468605i
$245$	−5.55709	+	0.992933i	−0.355029	+	0.0634362i
$246$		0			0
$247$	−2.87251	−	6.16012i	−0.182773	−	0.391959i
$248$	−3.59318	−	0.314363i	−0.228167	−	0.0199621i
$249$		0			0
$250$	−6.47527	−	9.11432i	−0.409532	−	0.576441i
$251$	21.4009	+	12.3558i	1.35081	+	0.779891i	0.988363	−	0.152113i	$-0.0486076\pi$
$251$	21.4009	+	12.3558i	1.35081	+	0.779891i	0.362448	+	0.932004i	$0.381941\pi$
$252$		0			0
$253$	−18.8543	−	5.05201i	−1.18536	−	0.317617i
$254$	−11.1274	−	9.33703i	−0.698197	−	0.585857i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−10.3797	−	7.26793i	−0.647467	−	0.453361i	0.203150	−	0.979148i	$-0.434882\pi$
$257$	−10.3797	−	7.26793i	−0.647467	−	0.453361i	−0.850616	+	0.525787i	$0.823771\pi$
$258$		0			0
$259$	−7.47757	+	8.91143i	−0.464634	+	0.553729i
$260$	−1.34585	−	14.9895i	−0.0834661	−	0.929607i
$261$		0			0
$262$	12.1401	−	3.25294i	0.750020	−	0.200967i
$263$	12.3615	+	5.76426i	0.762243	+	0.355440i	0.764556	−	0.644558i	$-0.222958\pi$
$263$	12.3615	+	5.76426i	0.762243	+	0.355440i	−0.00231293	+	0.999997i	$0.500736\pi$
$264$		0			0
$265$	17.8658	−	4.83080i	1.09749	−	0.296754i
$266$	0.730698	−	2.00758i	0.0448020	−	0.123092i
$267$		0			0
$268$	7.93436	+	11.3314i	0.484668	+	0.692178i
$269$	27.6798			1.68767			0.843834	−	0.536604i	$-0.180293\pi$
$269$	27.6798			1.68767			0.843834	+	0.536604i	$0.180293\pi$
$270$		0			0
$271$	4.32582			0.262775			0.131388	−	0.991331i	$-0.458057\pi$
$271$	4.32582			0.262775			0.131388	+	0.991331i	$0.458057\pi$
$272$	0.375390	+	0.536113i	0.0227614	+	0.0325066i
$273$		0			0
$274$	1.94688	−	5.34902i	0.117616	−	0.323146i
$275$	−22.7687	−	3.90778i	−1.37300	−	0.235648i
$276$		0			0
$277$	0.0874915	+	0.0407980i	0.00525685	+	0.00245131i	0.425245	−	0.905078i	$-0.360188\pi$
$277$	0.0874915	+	0.0407980i	0.00525685	+	0.00245131i	−0.419988	+	0.907530i	$0.637966\pi$
$278$	−10.0415	+	2.69061i	−0.602248	+	0.161372i
$279$		0			0
$280$	3.03241	−	3.63066i	0.181221	−	0.216973i
$281$	10.5947	−	12.6263i	0.632026	−	0.753220i	−0.351062	−	0.936352i	$-0.614179\pi$
$281$	10.5947	−	12.6263i	0.632026	−	0.753220i	0.983088	+	0.183133i	$0.0586238\pi$
$282$		0			0
$283$	−11.9515	−	8.36856i	−0.710446	−	0.497460i	0.161617	−	0.986854i	$-0.448329\pi$
$283$	−11.9515	−	8.36856i	−0.710446	−	0.497460i	−0.872063	+	0.489394i	$0.837218\pi$
$284$	−0.464574	−	2.63473i	−0.0275674	−	0.156342i
$285$		0			0
$286$	−23.8216	−	19.9887i	−1.40860	−	1.18196i
$287$	−22.1481	−	5.93456i	−1.30736	−	0.350306i
$288$		0			0
$289$	−14.3515	−	8.28583i	−0.844205	−	0.487402i
$290$	−0.837938	+	9.83589i	−0.0492054	+	0.577584i
$291$		0			0
$292$	−14.3622	−	1.25653i	−0.840484	−	0.0735328i
$293$	8.28275	+	17.7624i	0.483883	+	1.03769i	0.985039	+	0.172334i	$0.0551307\pi$
$293$	8.28275	+	17.7624i	0.483883	+	1.03769i	−0.501155	+	0.865357i	$0.667092\pi$
$294$		0			0
$295$	−0.686888	−	3.84427i	−0.0399922	−	0.223822i
$296$			5.49890i			0.319617i
$297$		0			0
$298$	−4.38820	+	4.38820i	−0.254202	+	0.254202i
$299$	−4.93754	+	28.0022i	−0.285545	+	1.61941i
$300$		0			0
$301$	5.63746	+	2.05187i	0.324938	+	0.118268i
$302$	−1.22256	+	13.9739i	−0.0703504	+	0.804109i
$303$		0			0
$304$	−0.345398	−	0.948974i	−0.0198100	−	0.0544274i
$305$	−2.80546	+	16.1255i	−0.160640	+	0.923341i
$306$		0			0
$307$	−5.21294	+	19.4549i	−0.297518	+	1.11035i	0.641679	+	0.766973i	$0.278238\pi$
$307$	−5.21294	+	19.4549i	−0.297518	+	1.11035i	−0.939197	+	0.343379i	$0.888428\pi$
$308$	−0.851894	−	9.73720i	−0.0485412	−	0.554828i
$309$		0			0
$310$	7.79521	+	2.06968i	0.442738	+	0.117550i
$311$	−3.15134	+	0.555667i	−0.178696	+	0.0315090i	−0.262280	−	0.964992i	$-0.584474\pi$
$311$	−3.15134	+	0.555667i	−0.178696	+	0.0315090i	0.0835839	+	0.996501i	$0.473363\pi$
$312$		0			0
$313$	22.0147	−	1.92604i	1.24434	−	0.108866i	0.554104	−	0.832447i	$-0.313061\pi$
$313$	22.0147	−	1.92604i	1.24434	−	0.108866i	0.690239	+	0.723581i	$0.257505\pi$
$314$	−12.4711	−	21.6005i	−0.703783	−	1.21899i
$315$		0			0
$316$	−1.49234	+	2.58481i	−0.0839506	+	0.145407i
$317$	2.72788	−	5.84995i	0.153213	−	0.328566i	−0.814688	−	0.579900i	$-0.803092\pi$
$317$	2.72788	−	5.84995i	0.153213	−	0.328566i	0.967900	+	0.251334i	$0.0808693\pi$
$318$		0			0
$319$	13.1111	+	15.6252i	0.734080	+	0.874842i
$320$	−0.00509778	−	2.23606i	−0.000284974	−	0.125000i
$321$		0			0
$322$	−7.32112	+	5.12630i	−0.407990	+	0.285678i
$323$	−0.467353	−	0.467353i	−0.0260042	−	0.0260042i
$324$		0			0
$325$	−2.78010	+	33.5373i	−0.154212	+	1.86031i
$326$	2.55300	+	0.450162i	0.141397	+	0.0249322i
$327$		0			0
$328$	−9.82315	+	4.58061i	−0.542392	+	0.252922i
$329$	3.05401	−	2.56262i	0.168373	−	0.141282i
$330$		0			0
$331$	24.1172	−	8.77794i	1.32560	−	0.482479i	0.420352	−	0.907361i	$-0.361907\pi$
$331$	24.1172	−	8.77794i	1.32560	−	0.482479i	0.905249	+	0.424882i	$0.139684\pi$
$332$	3.96399	+	14.7938i	0.217552	+	0.811916i
$333$		0			0
$334$	−9.48841	+	5.47814i	−0.519183	+	0.299750i
$335$	−13.1362	−	28.0039i	−0.717709	−	1.53002i
$336$		0			0
$337$	13.0089	−	18.5786i	0.708639	−	1.01204i	−0.289849	−	0.957072i	$-0.593605\pi$
$337$	13.0089	−	18.5786i	0.708639	−	1.01204i	0.998488	−	0.0549686i	$-0.0175059\pi$
$338$	−18.5260	+	26.4579i	−1.00768	+	1.43912i
$339$		0			0
$340$	−0.621501	−	1.32492i	−0.0337056	−	0.0718538i
$341$	14.4324	−	8.33253i	0.781557	−	0.451232i
$342$		0			0
$343$	5.21506	+	19.4629i	0.281587	+	1.05090i
$344$	2.66481	−	0.969911i	0.143677	−	0.0522941i
$345$		0			0
$346$	−13.2203	+	11.0931i	−0.710726	+	0.596370i
$347$	11.6045	−	5.41129i	0.622965	−	0.290493i	−0.0853924	−	0.996347i	$-0.527214\pi$
$347$	11.6045	−	5.41129i	0.622965	−	0.290493i	0.708357	+	0.705854i	$0.249437\pi$
$348$		0			0
$349$	−0.968550	−	0.170782i	−0.0518453	−	0.00914173i	0.147665	−	0.989037i	$-0.452824\pi$
$349$	−0.968550	−	0.170782i	−0.0518453	−	0.00914173i	−0.199511	+	0.979896i	$0.563935\pi$
$350$	−8.07183	+	6.83603i	−0.431458	+	0.365401i
$351$		0			0
$352$	−3.26706	−	3.26706i	−0.174135	−	0.174135i
$353$	3.79326	−	2.65607i	0.201895	−	0.141368i	−0.468257	−	0.883592i	$-0.655118\pi$
$353$	3.79326	−	2.65607i	0.201895	−	0.141368i	0.670152	+	0.742224i	$0.266229\pi$
$354$		0			0
$355$	0.0136385	+	5.98230i	0.000723855	+	0.317508i
$356$	−8.01353	−	9.55016i	−0.424716	−	0.506157i
$357$		0			0
$358$	9.07279	−	19.4567i	0.479512	−	1.02832i
$359$	12.5665	−	21.7659i	0.663237	−	1.14876i	−0.316523	−	0.948585i	$-0.602516\pi$
$359$	12.5665	−	21.7659i	0.663237	−	1.14876i	0.979760	−	0.200175i	$-0.0641512\pi$
$360$		0			0
$361$	−8.99007	−	15.5713i	−0.473162	−	0.819540i
$362$	11.0409	−	0.965950i	0.580295	−	0.0507692i
$363$		0			0
$364$	−14.0221	+	2.47248i	−0.734959	+	0.129593i
$365$	31.1580	+	8.27267i	1.63088	+	0.433012i
$366$		0			0
$367$	−0.0874539	−	0.999602i	−0.00456505	−	0.0521788i	0.993570	−	0.113215i	$-0.0361150\pi$
$367$	−0.0874539	−	0.999602i	−0.00456505	−	0.0521788i	−0.998136	+	0.0610364i	$0.980559\pi$
$368$	−1.09343	+	4.08074i	−0.0569991	+	0.212723i
$369$		0			0
$370$	2.10755	−	12.1139i	0.109566	−	0.629774i
$371$	−5.98865	−	16.4537i	−0.310915	−	0.854232i
$372$		0			0
$373$	−0.227555	+	2.60097i	−0.0117824	+	0.134673i	−0.999808	−	0.0196199i	$-0.993754\pi$
$373$	−0.227555	+	2.60097i	−0.0117824	+	0.134673i	0.988025	+	0.154293i	$0.0493099\pi$
$374$	−2.84151	−	1.03423i	−0.146931	−	0.0534786i
$375$		0			0
$376$	0.327242	−	1.85588i	0.0168762	−	0.0957099i
$377$	21.0101	−	21.0101i	1.08208	−	1.08208i
$378$		0			0
$379$		−	18.4301i		−	0.946693i	−0.880876	−	0.473346i	$-0.843046\pi$
$379$		−	18.4301i		−	0.946693i	0.880876	−	0.473346i	$-0.156954\pi$
$380$	0.397193	+	2.22295i	0.0203756	+	0.114035i
$381$		0			0
$382$	−5.18793	−	11.1255i	−0.265437	−	0.569232i
$383$	23.5070	+	2.05660i	1.20115	+	0.105087i	0.670113	−	0.742259i	$-0.266246\pi$
$383$	23.5070	+	2.05660i	1.20115	+	0.105087i	0.531040	+	0.847347i	$0.321801\pi$
$384$		0			0
$385$	−1.85525	+	21.7773i	−0.0945523	+	1.10987i
$386$	−3.67201	−	2.12003i	−0.186900	−	0.107907i
$387$		0			0
$388$	−10.8585	−	2.90954i	−0.551259	−	0.147709i
$389$	22.3201	+	18.7287i	1.13167	+	0.949585i	0.999135	−	0.0415928i	$-0.0132432\pi$
$389$	22.3201	+	18.7287i	1.13167	+	0.949585i	0.132537	+	0.991178i	$0.457688\pi$
$390$		0			0
$391$	0.480128	+	2.72294i	0.0242811	+	0.137705i
$392$	2.06800	+	1.44803i	0.104450	+	0.0731366i
$393$		0			0
$394$	8.37498	−	9.98091i	0.421925	−	0.502831i
$395$	4.27826	−	5.12231i	0.215263	−	0.257731i
$396$		0			0
$397$	−20.1971	+	5.41180i	−1.01366	+	0.271610i	−0.727160	−	0.686469i	$-0.759160\pi$
$397$	−20.1971	+	5.41180i	−1.01366	+	0.271610i	−0.286504	+	0.958079i	$0.592493\pi$
$398$	6.93086	+	3.23191i	0.347413	+	0.162001i
$399$		0			0
$400$	−0.845780	+	4.92795i	−0.0422890	+	0.246397i
$401$	0.181796	−	0.499479i	0.00907844	−	0.0249428i	−0.935071	−	0.354461i	$-0.884664\pi$
$401$	0.181796	−	0.499479i	0.00907844	−	0.0249428i	0.944149	+	0.329519i	$0.106886\pi$
$402$		0			0
$403$	−13.9242	−	19.8859i	−0.693615	−	0.990585i
$404$	2.83596			0.141094
$405$		0			0
$406$	9.33935			0.463504
$407$	−14.5727	−	20.8119i	−0.722340	−	1.03161i
$408$		0			0
$409$	9.48042	−	26.0472i	0.468777	−	1.28795i	−0.449948	−	0.893055i	$-0.648558\pi$
$409$	9.48042	−	26.0472i	0.468777	−	1.28795i	0.918725	−	0.394898i	$-0.129220\pi$
$410$	23.3958	−	6.32608i	1.15543	−	0.312423i
$411$		0			0
$412$	11.1764	+	5.21166i	0.550624	+	0.256760i
$413$	−3.56873	+	0.956240i	−0.175606	+	0.0470535i
$414$		0			0
$415$	−3.06259	−	34.1097i	−0.150336	−	1.67438i
$416$	−4.32626	+	5.15583i	−0.212112	+	0.252785i
$417$		0			0
$418$	3.82213	+	2.67628i	0.186946	+	0.130901i
$419$	2.25043	+	12.7628i	0.109941	+	0.623504i	0.989131	+	0.147034i	$0.0469728\pi$
$419$	2.25043	+	12.7628i	0.109941	+	0.623504i	−0.879191	+	0.476470i	$0.841916\pi$
$420$		0			0
$421$	6.51042	+	5.46289i	0.317299	+	0.266245i	0.787501	−	0.616314i	$-0.211375\pi$
$421$	6.51042	+	5.46289i	0.317299	+	0.266245i	−0.470202	+	0.882559i	$0.655819\pi$
$422$	11.3328	+	3.03660i	0.551670	+	0.147819i
$423$		0			0
$424$	−7.16787	−	4.13837i	−0.348102	−	0.200977i
$425$	0.861354	+	3.15697i	0.0417818	+	0.153135i
$426$		0			0
$427$	15.4264	+	1.34963i	0.746535	+	0.0653133i
$428$	1.69891	+	3.64332i	0.0821197	+	0.176106i
$429$		0			0
$430$	−6.24225	+	1.11536i	−0.301028	+	0.0537873i
$431$			3.57420i			0.172163i	0.996288	+	0.0860815i	$0.0274345\pi$
$431$			3.57420i			0.172163i	−0.996288	+	0.0860815i	$0.972565\pi$
$432$		0			0
$433$	−28.5111	+	28.5111i	−1.37016	+	1.37016i	−0.509958	+	0.860199i	$0.670339\pi$
$433$	−28.5111	+	28.5111i	−1.37016	+	1.37016i	−0.860199	+	0.509958i	$0.829661\pi$
$434$	1.32502	−	7.51457i	0.0636031	−	0.360711i
$435$		0			0
$436$	−1.21569	−	0.442475i	−0.0582210	−	0.0211907i
$437$	0.371843	−	4.25019i	0.0177877	−	0.203314i
$438$		0			0
$439$	1.17519	+	3.22882i	0.0560890	+	0.154103i	0.964573	−	0.263817i	$-0.0849814\pi$
$439$	1.17519	+	3.22882i	0.0560890	+	0.154103i	−0.908484	+	0.417920i	$0.862759\pi$
$440$	5.94510	+	8.44941i	0.283421	+	0.402810i
$441$		0			0
$442$	−1.14007	+	4.25481i	−0.0542277	+	0.202381i
$443$	−1.73656	−	19.8490i	−0.0825065	−	0.943053i	−0.918788	−	0.394752i	$-0.870830\pi$
$443$	−1.73656	−	19.8490i	−0.0825065	−	0.943053i	0.836281	−	0.548301i	$-0.184725\pi$
$444$		0			0
$445$	13.9934	+	24.1101i	0.663349	+	1.14293i
$446$	12.1912	−	2.14964i	0.577269	−	0.101788i
$447$		0			0
$448$	−2.10747	+	0.184380i	−0.0995687	+	0.00871113i
$449$	−7.37572	−	12.7751i	−0.348082	−	0.602896i	0.637827	−	0.770180i	$-0.279834\pi$
$449$	−7.37572	−	12.7751i	−0.348082	−	0.602896i	−0.985909	+	0.167284i	$0.946500\pi$
$450$		0			0
$451$	25.0390	−	43.3688i	1.17904	−	2.04216i
$452$	−2.88140	+	6.17919i	−0.135530	+	0.290645i
$453$		0			0
$454$	11.1412	+	13.2775i	0.522880	+	0.623145i
$455$	31.8380	−	0.0725844i	1.49259	−	0.00340281i
$456$		0			0
$457$	12.1045	−	8.47568i	0.566226	−	0.396476i	−0.255117	−	0.966910i	$-0.582114\pi$
$457$	12.1045	−	8.47568i	0.566226	−	0.396476i	0.821343	+	0.570434i	$0.193225\pi$
$458$	1.31797	+	1.31797i	0.0615848	+	0.0615848i
$459$		0			0
$460$	3.97282	−	8.57070i	0.185234	−	0.399611i
$461$	16.1281	+	2.84382i	0.751162	+	0.132450i	0.536105	−	0.844151i	$-0.319895\pi$
$461$	16.1281	+	2.84382i	0.751162	+	0.132450i	0.215057	+	0.976601i	$0.431006\pi$
$462$		0			0
$463$	−4.09851	+	1.91117i	−0.190474	+	0.0888194i	−0.515515	−	0.856880i	$-0.672399\pi$
$463$	−4.09851	+	1.91117i	−0.190474	+	0.0888194i	0.325042	+	0.945700i	$0.394622\pi$
$464$	3.38184	−	2.83770i	0.156998	−	0.131737i
$465$		0			0
$466$	−8.38361	+	3.05138i	−0.388363	+	0.141353i
$467$	7.24056	+	27.0221i	0.335053	+	1.25044i	0.903812	+	0.427931i	$0.140757\pi$
$467$	7.24056	+	27.0221i	0.335053	+	1.25044i	−0.568758	+	0.822505i	$0.692576\pi$
$468$		0			0
$469$	−25.3436	+	14.6322i	−1.17026	+	0.675650i
$470$	−1.43221	+	3.96305i	−0.0660628	+	0.182802i
$471$		0			0
$472$	−1.00171	+	1.43060i	−0.0461077	+	0.0658486i
$473$	−7.51525	+	10.7329i	−0.345552	+	0.493499i
$474$		0			0
$475$	−0.0230231	−	5.04933i	−0.00105637	−	0.231679i
$476$	−1.19906	+	0.692276i	−0.0549587	+	0.0317304i
$477$		0			0
$478$	−0.425396	−	1.58760i	−0.0194572	−	0.0726151i
$479$	−18.7815	+	6.83589i	−0.858146	+	0.312340i	−0.733357	−	0.679844i	$-0.762048\pi$
$479$	−18.7815	+	6.83589i	−0.858146	+	0.312340i	−0.124789	+	0.992183i	$0.539825\pi$
$480$		0			0
$481$	−28.3514	+	23.7896i	−1.29271	+	1.08471i
$482$	−14.2921	+	6.66452i	−0.650988	+	0.303561i
$483$		0			0
$484$	10.1902	+	1.79680i	0.463189	+	0.0816727i
$485$	22.8060	+	10.5714i	1.03557	+	0.480021i
$486$		0			0
$487$	−7.00609	−	7.00609i	−0.317476	−	0.317476i	0.530321	−	0.847797i	$-0.322071\pi$
$487$	−7.00609	−	7.00609i	−0.317476	−	0.317476i	−0.847797	+	0.530321i	$0.822071\pi$
$488$	5.99607	−	4.19849i	0.271429	−	0.190057i
$489$		0			0
$490$	−4.00078	−	3.98258i	−0.180737	−	0.179915i
$491$	−0.404039	−	0.481514i	−0.0182340	−	0.0217304i	0.756850	−	0.653588i	$-0.226737\pi$
$491$	−0.404039	−	0.481514i	−0.0182340	−	0.0217304i	−0.775084	+	0.631858i	$0.782293\pi$
$492$		0			0
$493$	1.22107	−	2.61858i	0.0549940	−	0.117935i
$494$	3.39847	−	5.88632i	0.152904	−	0.264838i
$495$		0			0
$496$	−1.80345	−	3.12367i	−0.0809775	−	0.140257i
$497$	5.63828	−	0.493285i	0.252911	−	0.0221269i
$498$		0			0
$499$	4.16362	−	0.734159i	0.186389	−	0.0328655i	−0.0796743	−	0.996821i	$-0.525388\pi$
$499$	4.16362	−	0.734159i	0.186389	−	0.0328655i	0.266064	+	0.963955i	$0.414277\pi$
$500$	3.75196	−	10.5320i	0.167793	−	0.471005i
$501$		0			0
$502$	2.15376	+	24.6176i	0.0961269	+	1.09874i
$503$	10.7059	−	39.9551i	0.477354	−	1.78151i	−0.134910	−	0.990858i	$-0.543074\pi$
$503$	10.7059	−	39.9551i	0.477354	−	1.78151i	0.612264	−	0.790653i	$-0.290259\pi$
$504$		0			0
$505$	−6.24756	−	1.08693i	−0.278013	−	0.0483679i
$506$	−6.67604	−	18.3423i	−0.296786	−	0.815414i
$507$		0			0
$508$	1.26601	−	14.4706i	0.0561701	−	0.642027i
$509$	−17.2829	−	6.29047i	−0.766052	−	0.278820i	−0.0707079	−	0.997497i	$-0.522526\pi$
$509$	−17.2829	−	6.29047i	−0.766052	−	0.278820i	−0.695344	+	0.718677i	$0.744748\pi$
$510$		0			0
$511$	5.29620	−	30.0363i	0.234290	−	1.32873i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	12.6712i		−	0.558905i
$515$	−22.6240	−	15.7647i	−0.996932	−	0.694678i
$516$		0			0
$517$	3.67976	+	7.89127i	0.161836	+	0.347058i
$518$	−11.5888	−	1.01389i	−0.509181	−	0.0445476i
$519$		0			0
$520$	11.5067	−	9.70006i	0.504602	−	0.425376i
$521$	14.7763	+	8.53111i	0.647362	+	0.373755i	0.787445	−	0.616385i	$-0.211403\pi$
$521$	14.7763	+	8.53111i	0.647362	+	0.373755i	−0.140083	+	0.990140i	$0.544737\pi$
$522$		0			0
$523$	37.4455	+	10.0335i	1.63738	+	0.438734i	0.956041	−	0.293234i	$-0.0947316\pi$
$523$	37.4455	+	10.0335i	1.63738	+	0.438734i	0.681338	+	0.731969i	$0.261398\pi$
$524$	9.62795	+	8.07881i	0.420599	+	0.352924i
$525$		0			0
$526$	2.36846	+	13.4322i	0.103270	+	0.585671i
$527$	−1.93371	−	1.35400i	−0.0842337	−	0.0589811i
$528$		0			0
$529$	3.31161	−	3.94662i	0.143983	−	0.171592i
$530$	14.2045	+	11.8639i	0.617006	+	0.515337i
$531$		0			0
$532$	2.06362	−	0.552946i	0.0894693	−	0.0239732i
$533$	−66.1143	−	30.8296i	−2.86373	−	1.33538i
$534$		0			0
$535$	−2.34628	−	8.67728i	−0.101439	−	0.375151i
$536$	−4.73121	+	12.9989i	−0.204357	+	0.561467i
$537$		0			0
$538$	15.8765	+	22.6740i	0.684484	+	0.977545i
$539$	−11.6643			−0.502417
$540$		0			0
$541$	22.2305			0.955763			0.477881	−	0.878424i	$-0.341405\pi$
$541$	22.2305			0.955763			0.477881	+	0.878424i	$0.341405\pi$
$542$	2.48119	+	3.54351i	0.106576	+	0.152207i
$543$		0			0
$544$	−0.223843	+	0.615004i	−0.00959719	+	0.0263681i
$545$	2.50855	+	1.44070i	0.107455	+	0.0617127i
$546$		0			0
$547$	−6.88060	−	3.20848i	−0.294193	−	0.137185i	0.269918	−	0.962883i	$-0.413003\pi$
$547$	−6.88060	−	3.20848i	−0.294193	−	0.137185i	−0.564111	+	0.825699i	$0.690781\pi$
$548$	5.49834	−	1.47328i	0.234878	−	0.0629353i
$549$		0			0
$550$	−9.85852	−	20.8924i	−0.420369	−	0.890856i
$551$	−2.86573	+	3.41524i	−0.122084	+	0.145494i
$552$		0			0
$553$	−5.17225	−	3.62165i	−0.219947	−	0.154008i
$554$	0.0167633	+	0.0950696i	0.000712206	+	0.00403912i
$555$		0			0
$556$	−7.96357	−	6.68223i	−0.337731	−	0.283390i
$557$	1.84723	+	0.494965i	0.0782698	+	0.0209723i	0.297741	−	0.954647i	$-0.403767\pi$
$557$	1.84723	+	0.494965i	0.0782698	+	0.0209723i	−0.219472	+	0.975619i	$0.570433\pi$
$558$		0			0
$559$	16.5293	+	9.54322i	0.699117	+	0.403635i
$560$	4.71338	+	0.401542i	0.199177	+	0.0169682i
$561$		0			0
$562$	16.4197	+	1.43654i	0.692623	+	0.0605967i
$563$	13.4584	+	28.8616i	0.567203	+	1.21637i	0.955542	+	0.294854i	$0.0952709\pi$
$563$	13.4584	+	28.8616i	0.567203	+	1.21637i	−0.388340	+	0.921516i	$0.626951\pi$
$564$		0			0
$565$	8.71595	−	12.5083i	0.366683	−	0.526227i
$566$		−	14.5901i		−	0.613270i
$567$		0			0
$568$	1.89178	−	1.89178i	0.0793771	−	0.0793771i
$569$	−1.34776	+	7.64350i	−0.0565009	+	0.320432i	−0.999938	−	0.0111186i	$-0.996461\pi$
$569$	−1.34776	+	7.64350i	−0.0565009	+	0.320432i	0.943437	+	0.331551i	$0.107572\pi$
$570$		0			0
$571$	−11.3216	−	4.12074i	−0.473796	−	0.172447i	0.0940754	−	0.995565i	$-0.470011\pi$
$571$	−11.3216	−	4.12074i	−0.473796	−	0.172447i	−0.567871	+	0.823118i	$0.692233\pi$
$572$	2.71027	−	30.9785i	0.113322	−	1.29528i
$573$		0			0
$574$	−7.84231	−	21.5466i	−0.327332	−	0.899337i
$575$	−12.0369	+	17.3584i	−0.501974	+	0.723896i
$576$		0			0
$577$	2.33656	−	8.72015i	0.0972721	−	0.363024i	−0.900082	−	0.435720i	$-0.856494\pi$
$577$	2.33656	−	8.72015i	0.0972721	−	0.363024i	0.997354	+	0.0726960i	$0.0231603\pi$
$578$	−1.44432	−	16.5086i	−0.0600756	−	0.686667i
$579$		0			0
$580$	−8.53771	+	4.95524i	−0.354509	+	0.205755i
$581$	−31.9084	+	5.62632i	−1.32378	+	0.233419i
$582$		0			0
$583$	38.0957	−	3.33294i	1.57776	−	0.138036i
$584$	−7.20853	−	12.4855i	−0.298291	−	0.516655i
$585$		0			0
$586$	−9.79932	+	16.9729i	−0.404806	+	0.701145i
$587$	0.650726	−	1.39549i	0.0268583	−	0.0575979i	−0.892421	−	0.451204i	$-0.850995\pi$
$587$	0.650726	−	1.39549i	0.0268583	−	0.0575979i	0.919279	+	0.393606i	$0.128773\pi$
$588$		0			0
$589$	2.34138	+	2.79034i	0.0964747	+	0.114974i
$590$	2.75506	−	2.76765i	0.113424	−	0.113942i
$591$		0			0
$592$	−4.50443	+	3.15404i	−0.185131	+	0.129630i
$593$	3.61163	+	3.61163i	0.148312	+	0.148312i	0.777363	−	0.629052i	$-0.216557\pi$
$593$	3.61163	+	3.61163i	0.148312	+	0.148312i	−0.629052	+	0.777363i	$0.716557\pi$
$594$		0			0
$595$	2.90682	−	1.06551i	0.119168	−	0.0436816i
$596$	−6.11157	−	1.07764i	−0.250340	−	0.0441417i
$597$		0			0
$598$	−25.7701	+	12.0168i	−1.05382	+	0.491403i
$599$	−9.40405	+	7.89093i	−0.384239	+	0.322415i	−0.814364	−	0.580355i	$-0.802914\pi$
$599$	−9.40405	+	7.89093i	−0.384239	+	0.322415i	0.430125	+	0.902769i	$0.358469\pi$
$600$		0			0
$601$	−1.70889	+	0.621984i	−0.0697070	+	0.0253713i	−0.376638	−	0.926360i	$-0.622920\pi$
$601$	−1.70889	+	0.621984i	−0.0697070	+	0.0253713i	0.306931	+	0.951732i	$0.400698\pi$
$602$	1.55272	+	5.79484i	0.0632843	+	0.236180i
$603$		0			0
$604$	−12.1480	+	7.01365i	−0.494295	+	0.285381i
$605$	−21.7600	−	7.86387i	−0.884671	−	0.319712i
$606$		0			0
$607$	8.41715	−	12.0209i	0.341641	−	0.487915i	−0.611161	−	0.791507i	$-0.709297\pi$
$607$	8.41715	−	12.0209i	0.341641	−	0.487915i	0.952802	+	0.303592i	$0.0981860\pi$
$608$	0.579242	−	0.827243i	0.0234914	−	0.0335491i
$609$		0			0
$610$	−14.8184	+	6.95108i	−0.599977	+	0.281441i
$611$	10.9844	−	6.34182i	0.444379	−	0.256563i
$612$		0			0
$613$	1.31473	+	4.90665i	0.0531016	+	0.198178i	0.987381	−	0.158365i	$-0.0506222\pi$
$613$	1.31473	+	4.90665i	0.0531016	+	0.198178i	−0.934279	+	0.356543i	$0.883955\pi$
$614$	−18.9266	+	6.88871i	−0.763815	+	0.278006i
$615$		0			0
$616$	7.48762	−	6.28286i	0.301685	−	0.253144i
$617$	−18.5840	+	8.66586i	−0.748164	+	0.348875i	−0.759021	−	0.651067i	$-0.774322\pi$
$617$	−18.5840	+	8.66586i	−0.748164	+	0.348875i	0.0108568	+	0.999941i	$0.496544\pi$
$618$		0			0
$619$	−42.8351	−	7.55298i	−1.72169	−	0.303580i	−0.776501	−	0.630116i	$-0.783007\pi$
$619$	−42.8351	−	7.55298i	−1.72169	−	0.303580i	−0.945185	+	0.326536i	$0.894119\pi$
$620$	2.77576	+	7.57259i	0.111477	+	0.304122i
$621$		0			0
$622$	−2.26271	−	2.26271i	−0.0907265	−	0.0907265i
$623$	21.6042	−	15.1274i	0.865555	−	0.606068i
$624$		0			0
$625$	−12.3020	+	21.7637i	−0.492082	+	0.870549i
$626$	14.2048	+	16.9286i	0.567739	+	0.676605i
$627$		0			0
$628$	10.5410	−	22.6053i	0.420632	−	0.902048i
$629$	−1.79944	+	3.11672i	−0.0717484	+	0.124272i
$630$		0			0
$631$	−13.9920	−	24.2349i	−0.557013	−	0.964775i	−0.997744	−	0.0671358i	$-0.978614\pi$
$631$	−13.9920	−	24.2349i	−0.557013	−	0.964775i	0.440731	−	0.897639i	$-0.354719\pi$
$632$	−2.97332	+	0.260132i	−0.118272	+	0.0103475i
$633$		0			0
$634$	6.35665	−	1.12085i	0.252455	−	0.0445146i
$635$	−8.33509	+	31.3931i	−0.330768	+	1.24580i
$636$		0			0
$637$	1.48091	+	16.9268i	0.0586756	+	0.670665i
$638$	−5.27919	+	19.7022i	−0.209005	+	0.780018i
$639$		0			0
$640$	1.82875	−	1.28673i	0.0722877	−	0.0508624i
$641$	1.93139	+	5.30644i	0.0762852	+	0.209592i	0.971973	−	0.235091i	$-0.0755387\pi$
$641$	1.93139	+	5.30644i	0.0762852	+	0.209592i	−0.895688	+	0.444683i	$0.853316\pi$
$642$		0			0
$643$	−1.75397	+	20.0479i	−0.0691697	+	0.790614i	0.879820	+	0.475307i	$0.157663\pi$
$643$	−1.75397	+	20.0479i	−0.0691697	+	0.790614i	−0.948990	+	0.315307i	$0.897893\pi$
$644$	−8.39845	−	3.05678i	−0.330945	−	0.120454i
$645$		0			0
$646$	0.114771	−	0.650896i	0.00451559	−	0.0256092i
$647$	−6.94763	+	6.94763i	−0.273139	+	0.273139i	−0.830363	−	0.557223i	$-0.811867\pi$
$647$	−6.94763	+	6.94763i	−0.273139	+	0.273139i	0.557223	+	0.830363i	$0.311867\pi$
$648$		0			0
$649$		−	8.06910i		−	0.316740i
$650$	−29.0667	+	16.9589i	−1.14009	+	0.665181i
$651$		0			0
$652$	1.09559	+	2.34950i	0.0429065	+	0.0920134i
$653$	−7.13226	−	0.623992i	−0.279107	−	0.0244187i	−0.0532571	−	0.998581i	$-0.516960\pi$
$653$	−7.13226	−	0.623992i	−0.279107	−	0.0244187i	−0.225850	+	0.974162i	$0.572516\pi$
$654$		0			0
$655$	−18.1138	−	21.4875i	−0.707765	−	0.839586i
$656$	−9.38654	−	5.41932i	−0.366483	−	0.211589i
$657$		0			0
$658$	3.85088	+	1.03184i	0.150123	+	0.0402254i
$659$	−14.1465	−	11.8703i	−0.551070	−	0.462403i	0.324233	−	0.945977i	$-0.394894\pi$
$659$	−14.1465	−	11.8703i	−0.551070	−	0.462403i	−0.875303	+	0.483575i	$0.839338\pi$
$660$		0			0
$661$	−0.176638	−	1.00176i	−0.00687041	−	0.0389640i	0.981180	−	0.193096i	$-0.0618529\pi$
$661$	−0.176638	−	1.00176i	−0.00687041	−	0.0389640i	−0.988050	+	0.154132i	$0.950742\pi$
$662$	21.0235	+	14.7208i	0.817102	+	0.572141i
$663$		0			0
$664$	−9.84473	+	11.7325i	−0.382050	+	0.455309i
$665$	−4.75803	+	0.427207i	−0.184509	+	0.0165664i
$666$		0			0
$667$	18.0152	−	4.82715i	0.697550	−	0.186908i
$668$	−9.92976	−	4.63032i	−0.384194	−	0.179153i
$669$		0			0
$670$	15.4048	−	26.8229i	0.595140	−	1.03626i
$671$	−11.5671	+	31.7805i	−0.446544	+	1.22687i
$672$		0			0
$673$	−11.9783	−	17.1068i	−0.461731	−	0.659421i	0.519002	−	0.854773i	$-0.326304\pi$
$673$	−11.9783	−	17.1068i	−0.461731	−	0.659421i	−0.980733	+	0.195353i	$0.937415\pi$
$674$	22.6803			0.873612
$675$		0			0
$676$	−32.2991			−1.24227
$677$	12.6980	+	18.1346i	0.488023	+	0.696970i	0.985341	−	0.170599i	$-0.0545703\pi$
$677$	12.6980	+	18.1346i	0.488023	+	0.696970i	−0.497317	+	0.867569i	$0.665681\pi$
$678$		0			0
$679$	8.13386	−	22.3476i	0.312149	−	0.857622i
$680$	0.728832	−	1.26905i	0.0279494	−	0.0486657i
$681$		0			0
$682$	15.1037	+	7.04296i	0.578350	+	0.269689i
$683$	−28.2845	+	7.57881i	−1.08228	+	0.289995i	−0.755528	−	0.655116i	$-0.772620\pi$
$683$	−28.2845	+	7.57881i	−1.08228	+	0.289995i	−0.326748	+	0.945111i	$0.605953\pi$
$684$		0			0
$685$	−12.6774	+	1.13826i	−0.484378	+	0.0434905i
$686$	−12.9518	+	15.4354i	−0.494502	+	0.589325i
$687$		0			0
$688$	2.32298	+	1.62657i	0.0885627	+	0.0620122i
$689$	−9.67329	−	54.8600i	−0.368523	−	2.09000i
$690$		0			0
$691$	18.9434	+	15.8954i	0.720640	+	0.604689i	0.927562	−	0.373669i	$-0.121900\pi$
$691$	18.9434	+	15.8954i	0.720640	+	0.604689i	−0.206922	+	0.978357i	$0.566345\pi$
$692$	−16.6698	−	4.46666i	−0.633690	−	0.169797i
$693$		0			0
$694$	11.0888	+	6.40210i	0.420924	+	0.243020i
$695$	14.9825	+	17.7730i	0.568318	+	0.674168i
$696$		0			0
$697$	−7.06661	−	0.618248i	−0.267667	−	0.0234178i
$698$	−0.415642	−	0.891346i	−0.0157323	−	0.0337379i
$699$		0			0
$700$	−10.2296	−	2.69107i	−0.386641	−	0.101713i
$701$			34.8732i			1.31714i	0.752519	+	0.658571i	$0.228839\pi$
$701$			34.8732i			1.31714i	−0.752519	+	0.658571i	$0.771161\pi$
$702$		0			0
$703$	3.92671	−	3.92671i	0.148099	−	0.148099i
$704$	0.802310	−	4.55013i	0.0302382	−	0.171489i
$705$		0			0
$706$	4.35145	+	1.58380i	0.163769	+	0.0596071i
$707$	−0.522894	+	5.97671i	−0.0196655	+	0.224777i
$708$		0			0
$709$	−10.6201	−	29.1786i	−0.398848	−	1.09583i	−0.962846	−	0.270050i	$-0.912960\pi$
$709$	−10.6201	−	29.1786i	−0.398848	−	1.09583i	0.563998	−	0.825776i	$-0.309262\pi$
$710$	−4.89259	+	3.44248i	−0.183616	+	0.129194i
$711$		0			0
$712$	3.22666	−	12.0420i	0.120924	−	0.451295i
$713$	−1.32809	−	15.1801i	−0.0497372	−	0.568499i
$714$		0			0
$715$	−17.8437	+	67.2062i	−0.667318	+	2.51337i
$716$	21.1419	−	3.72789i	0.790110	−	0.139318i
$717$		0			0
$718$	25.0375	−	2.19049i	0.934389	−	0.0817485i
$719$	12.1648	+	21.0700i	0.453670	+	0.785779i	0.998611	−	0.0526953i	$-0.0167812\pi$
$719$	12.1648	+	21.0700i	0.453670	+	0.785779i	−0.544941	+	0.838475i	$0.683448\pi$
$720$		0			0
$721$	−13.0441	+	22.5931i	−0.485790	+	0.841412i
$722$	7.59874	−	16.2955i	0.282796	−	0.606458i
$723$		0			0
$724$	7.12404	+	8.49010i	0.264763	+	0.315532i
$725$	20.7076	−	7.64404i	0.769060	−	0.283893i
$726$		0			0
$727$	−29.1241	+	20.3929i	−1.08015	+	0.756332i	−0.971331	−	0.237729i	$-0.923597\pi$
$727$	−29.1241	+	20.3929i	−1.08015	+	0.756332i	−0.108823	+	0.994061i	$0.534708\pi$
$728$	−10.0681	−	10.0681i	−0.373148	−	0.373148i
$729$		0			0
$730$	11.0949	+	30.2682i	0.410641	+	1.12027i
$731$	1.82778	+	0.322287i	0.0676028	+	0.0119202i
$732$		0			0
$733$	−5.53133	+	2.57930i	−0.204304	+	0.0952687i	−0.522077	−	0.852898i	$-0.674843\pi$
$733$	−5.53133	+	2.57930i	−0.204304	+	0.0952687i	0.317773	+	0.948167i	$0.397065\pi$
$734$	0.768665	−	0.644986i	0.0283719	−	0.0238069i
$735$		0			0
$736$	−3.96992	+	1.44493i	−0.146333	+	0.0532609i
$737$	−16.5420	−	61.7357i	−0.609334	−	2.27406i
$738$		0			0
$739$	−1.19508	+	0.689982i	−0.0439618	+	0.0253814i	−0.521820	−	0.853056i	$-0.674747\pi$
$739$	−1.19508	+	0.689982i	−0.0439618	+	0.0253814i	0.477858	+	0.878437i	$0.341413\pi$
$740$	11.1320	−	5.22187i	0.409221	−	0.191960i
$741$		0			0
$742$	10.0431	−	14.3430i	0.368694	−	0.526550i
$743$	−0.816455	+	1.16602i	−0.0299528	+	0.0427771i	−0.833849	−	0.551992i	$-0.813868\pi$
$743$	−0.816455	+	1.16602i	−0.0299528	+	0.0427771i	0.803896	+	0.594769i	$0.202757\pi$
$744$		0			0
$745$	13.0506	+	4.71638i	0.478138	+	0.172795i
$746$	−2.26111	+	1.30545i	−0.0827851	+	0.0477960i
$747$		0			0
$748$	−0.782636	−	2.92084i	−0.0286160	−	0.106796i
$749$	−7.99143	+	2.90864i	−0.292001	+	0.106280i
$750$		0			0
$751$	−30.1408	+	25.2911i	−1.09985	+	0.922886i	−0.997415	−	0.0718539i	$-0.977108\pi$
$751$	−30.1408	+	25.2911i	−1.09985	+	0.922886i	−0.102437	+	0.994739i	$0.532664\pi$
$752$	1.70795	−	0.796430i	0.0622825	−	0.0290428i
$753$		0			0
$754$	29.2614	+	5.15958i	1.06564	+	0.187901i
$755$	29.4499	−	10.7950i	1.07179	−	0.392869i
$756$		0			0
$757$	0.921486	+	0.921486i	0.0334920	+	0.0334920i	0.723654	−	0.690162i	$-0.242461\pi$
$757$	0.921486	+	0.921486i	0.0334920	+	0.0334920i	−0.690162	+	0.723654i	$0.742461\pi$
$758$	15.0971	−	10.5711i	0.548351	−	0.383959i
$759$		0			0
$760$	−1.59311	+	1.60039i	−0.0577882	+	0.0580523i
$761$	−11.2508	−	13.4081i	−0.407840	−	0.486044i	0.522554	−	0.852606i	$-0.324979\pi$
$761$	−11.2508	−	13.4081i	−0.407840	−	0.486044i	−0.930394	+	0.366562i	$0.880535\pi$
$762$		0			0
$763$	1.15665	−	2.48045i	0.0418736	−	0.0897983i
$764$	6.13784	−	10.6311i	0.222059	−	0.384618i
$765$		0			0
$766$	11.7984	+	20.4354i	0.426294	+	0.738363i
$767$	−11.7096	+	1.02446i	−0.422809	+	0.0369910i
$768$		0			0
$769$	−11.7918	+	2.07921i	−0.425223	+	0.0749783i	−0.382165	−	0.924094i	$-0.624821\pi$
$769$	−11.7918	+	2.07921i	−0.425223	+	0.0749783i	−0.0430584	+	0.999073i	$0.513710\pi$
$770$	−18.9031	+	10.9712i	−0.681219	+	0.395375i
$771$		0			0
$772$	−0.369546	−	4.22393i	−0.0133003	−	0.152023i
$773$	5.47920	−	20.4487i	0.197073	−	0.735487i	−0.794647	−	0.607071i	$-0.792344\pi$
$773$	5.47920	−	20.4487i	0.197073	−	0.735487i	0.991720	−	0.128416i	$-0.0409892\pi$
$774$		0			0
$775$	−3.21261	−	17.7461i	−0.115400	−	0.637458i
$776$	−3.84485	−	10.5636i	−0.138022	−	0.379212i
$777$		0			0
$778$	−2.53944	+	29.0259i	−0.0910432	+	1.04063i
$779$	10.2856	+	3.74365i	0.368520	+	0.134130i
$780$		0			0
$781$	−2.14648	+	12.1733i	−0.0768071	+	0.435595i
$782$	−1.95511	+	1.95511i	−0.0699148	+	0.0699148i
$783$		0			0
$784$			2.52457i			0.0901631i
$785$	−31.8855	+	45.7588i	−1.13804	+	1.63320i
$786$		0			0
$787$	16.1184	+	34.5659i	0.574557	+	1.23214i	0.951997	+	0.306108i	$0.0990268\pi$
$787$	16.1184	+	34.5659i	0.574557	+	1.23214i	−0.377439	+	0.926034i	$0.623195\pi$
$788$	12.9796	+	1.13557i	0.462378	+	0.0404528i
$789$		0			0
$790$	6.64986	+	0.566514i	0.236591	+	0.0201557i
$791$	−12.4912	−	7.21180i	−0.444136	−	0.256422i
$792$		0			0
$793$	47.5873	+	12.7510i	1.68987	+	0.452800i
$794$	−16.0177	−	13.4404i	−0.568446	−	0.476983i
$795$		0			0
$796$	1.32795	+	7.53118i	0.0470679	+	0.266936i
$797$	−22.4618	−	15.7279i	−0.795636	−	0.557111i	0.103577	−	0.994621i	$-0.466971\pi$
$797$	−22.4618	−	15.7279i	−0.795636	−	0.557111i	−0.899213	+	0.437511i	$0.855860\pi$
$798$		0			0
$799$	0.792790	−	0.944811i	0.0280469	−	0.0334250i
$800$	−4.52186	+	2.13373i	−0.159872	+	0.0754388i
$801$		0			0
$802$	0.513423	−	0.137571i	0.0181296	−	0.00485781i
$803$	60.3705	+	28.1512i	2.13043	+	0.993435i
$804$		0			0
$805$	17.3300	+	9.95288i	0.610803	+	0.350793i
$806$	8.30293	−	22.8121i	0.292458	−	0.803522i
$807$		0			0
$808$	1.62664	+	2.32308i	0.0572250	+	0.0817258i
$809$	25.0745			0.881574			0.440787	−	0.897612i	$-0.354699\pi$
$809$	25.0745			0.881574			0.440787	+	0.897612i	$0.354699\pi$
$810$		0			0
$811$	−30.7391			−1.07939			−0.539697	−	0.841859i	$-0.681461\pi$
$811$	−30.7391			−1.07939			−0.539697	+	0.841859i	$0.681461\pi$
$812$	5.35683	+	7.65035i	0.187988	+	0.268475i
$813$		0			0
$814$	8.68959	−	23.8745i	0.304570	−	0.836799i
$815$	−1.51307	−	5.59579i	−0.0530005	−	0.196012i
$816$		0			0
$817$	−2.59552	−	1.21031i	−0.0908058	−	0.0423434i
$818$	26.7744	−	7.17418i	0.936145	−	0.250839i
$819$		0			0
$820$	18.6013	+	15.5362i	0.649585	+	0.542547i
$821$	−31.7068	+	37.7867i	−1.10657	+	1.31876i	−0.163365	+	0.986566i	$0.552235\pi$
$821$	−31.7068	+	37.7867i	−1.10657	+	1.31876i	−0.943210	+	0.332198i	$0.892210\pi$
$822$		0			0
$823$	25.8690	+	18.1137i	0.901738	+	0.631404i	0.929745	−	0.368204i	$-0.120027\pi$
$823$	25.8690	+	18.1137i	0.901738	+	0.631404i	−0.0280071	+	0.999608i	$0.508916\pi$
$824$	2.14140	+	12.1445i	0.0745993	+	0.423074i
$825$		0			0
$826$	−2.83025	−	2.37486i	−0.0984769	−	0.0826319i
$827$	13.2486	+	3.54994i	0.460697	+	0.123443i	0.481700	−	0.876336i	$-0.340019\pi$
$827$	13.2486	+	3.54994i	0.460697	+	0.123443i	−0.0210031	+	0.999779i	$0.506686\pi$
$828$		0			0
$829$	−27.7273	−	16.0084i	−0.963010	−	0.555994i	−0.0659121	−	0.997825i	$-0.520996\pi$
$829$	−27.7273	−	16.0084i	−0.963010	−	0.555994i	−0.897098	+	0.441831i	$0.854329\pi$
$830$	26.1844	−	22.0732i	0.908874	−	0.766174i
$831$		0			0
$832$	−6.70485	−	0.586598i	−0.232449	−	0.0203366i
$833$	0.698275	+	1.49746i	0.0241938	+	0.0518838i
$834$		0			0
$835$	20.1004	+	14.0062i	0.695602	+	0.484706i
$836$			4.66596i			0.161375i
$837$		0			0
$838$	−9.16389	+	9.16389i	−0.316561	+	0.316561i
$839$	1.56707	−	8.88729i	0.0541013	−	0.306823i	−0.945735	−	0.324940i	$-0.894656\pi$
$839$	1.56707	−	8.88729i	0.0541013	−	0.306823i	0.999836	+	0.0181166i	$0.00576700\pi$
$840$		0			0
$841$	8.93705	+	3.25282i	0.308174	+	0.112166i
$842$	−0.740715	+	8.46641i	−0.0255267	+	0.291772i
$843$		0			0
$844$	4.01276	+	11.0250i	0.138125	+	0.379495i
$845$	71.1541	+	12.3792i	2.44778	+	0.425857i
$846$		0			0
$847$	−5.66557	+	21.1442i	−0.194671	+	0.726523i
$848$	−0.721365	−	8.24524i	−0.0247718	−	0.283143i
$849$		0			0
$850$	−2.09198	+	2.51634i	−0.0717545	+	0.0863098i
$851$	−22.8782	+	4.03405i	−0.784256	+	0.138285i
$852$		0			0
$853$	−24.0520	+	2.10428i	−0.823526	+	0.0720492i	−0.491125	−	0.871089i	$-0.663414\pi$
$853$	−24.0520	+	2.10428i	−0.823526	+	0.0720492i	−0.332401	+	0.943138i	$0.607859\pi$
$854$	7.74265	+	13.4107i	0.264948	+	0.458904i
$855$		0			0
$856$	−2.00998	+	3.48138i	−0.0686996	+	0.118991i
$857$	−14.0140	+	30.0532i	−0.478710	+	1.02660i	0.507584	+	0.861602i	$0.330539\pi$
$857$	−14.0140	+	30.0532i	−0.478710	+	1.02660i	−0.986294	+	0.164996i	$0.947239\pi$
$858$		0			0
$859$	30.6829	+	36.5664i	1.04689	+	1.24763i	0.968054	+	0.250742i	$0.0806746\pi$
$859$	30.6829	+	36.5664i	1.04689	+	1.24763i	0.0788321	+	0.996888i	$0.474881\pi$
$860$	−4.49405	−	4.47361i	−0.153246	−	0.152549i
$861$		0			0
$862$	−2.92781	+	2.05007i	−0.0997216	+	0.0698258i
$863$	−22.5058	−	22.5058i	−0.766105	−	0.766105i	0.211313	−	0.977418i	$-0.432226\pi$
$863$	−22.5058	−	22.5058i	−0.766105	−	0.766105i	−0.977418	+	0.211313i	$0.932226\pi$
$864$		0			0
$865$	35.0112	+	16.2289i	1.19042	+	0.551800i
$866$	−39.7083	−	7.00164i	−1.34934	−	0.237925i
$867$		0			0
$868$	6.91558	−	3.22479i	0.234730	−	0.109456i
$869$	10.5639	−	8.86415i	0.358355	−	0.300696i
$870$		0			0
$871$	−87.4885	+	31.8432i	−2.96444	+	1.07897i
$872$	−0.334837	−	1.24963i	−0.0113390	−	0.0423178i
$873$		0			0
$874$	3.69483	−	2.13321i	0.124980	−	0.0721570i
$875$	21.5041	+	9.84903i	0.726971	+	0.332958i
$876$		0			0
$877$	−18.1168	+	25.8734i	−0.611760	+	0.873684i	−0.998830	−	0.0483666i	$-0.984598\pi$
$877$	−18.1168	+	25.8734i	−0.611760	+	0.873684i	0.387070	+	0.922051i	$0.373487\pi$
$878$	−1.97083	+	2.81464i	−0.0665123	+	0.0949895i
$879$		0			0
$880$	−3.51139	+	9.71632i	−0.118369	+	0.327537i
$881$	−33.8539	+	19.5455i	−1.14057	+	0.658506i	−0.946571	−	0.322497i	$-0.895478\pi$
$881$	−33.8539	+	19.5455i	−1.14057	+	0.658506i	−0.193995	+	0.981003i	$0.562145\pi$
$882$		0			0
$883$	−1.02361	−	3.82015i	−0.0344471	−	0.128558i	0.946561	−	0.322524i	$-0.104531\pi$
$883$	−1.02361	−	3.82015i	−0.0344471	−	0.128558i	−0.981008	+	0.193966i	$0.937865\pi$
$884$	−4.13926	+	1.50657i	−0.139218	+	0.0506713i
$885$		0			0
$886$	15.2633	−	12.8074i	0.512780	−	0.430273i
$887$	−30.9397	+	14.4274i	−1.03885	+	0.484426i	−0.865749	−	0.500478i	$-0.833158\pi$
$887$	−30.9397	+	14.4274i	−1.03885	+	0.484426i	−0.173105	+	0.984903i	$0.555380\pi$
$888$		0			0
$889$	30.2629	+	5.33616i	1.01498	+	0.178969i
$890$	−11.7236	+	25.2917i	−0.392975	+	0.847779i
$891$		0			0
$892$	8.75345	+	8.75345i	0.293087	+	0.293087i
$893$	−1.55895	+	1.09159i	−0.0521683	+	0.0365286i
$894$		0			0
$895$	−48.0039	+	0.109439i	−1.60459	+	0.00365815i
$896$	−1.35983	−	1.62058i	−0.0454288	−	0.0541399i
$897$		0			0
$898$	6.23423	−	13.3694i	0.208039	−	0.446141i
$899$	−7.96167	+	13.7900i	−0.265537	+	0.459923i
$900$		0			0
$901$	−2.70845	−	4.69118i	−0.0902316	−	0.156286i
$902$	49.8874	−	4.36458i	1.66107	−	0.145325i
$903$		0			0
$904$	−6.71440	+	1.18393i	−0.223318	+	0.0393769i
$905$	−12.4401	−	21.4339i	−0.413523	−	0.712487i
$906$		0			0
$907$	−1.25434	−	14.3371i	−0.0416495	−	0.476056i	−0.988165	−	0.153397i	$-0.950979\pi$
$907$	−1.25434	−	14.3371i	−0.0416495	−	0.476056i	0.946515	−	0.322659i	$-0.104577\pi$
$908$	−4.48600	+	16.7420i	−0.148873	+	0.555602i
$909$		0			0
$910$	18.3210	+	26.0386i	0.607335	+	0.863170i
$911$	−5.42614	−	14.9082i	−0.179776	−	0.493931i	0.816771	−	0.576962i	$-0.195762\pi$
$911$	−5.42614	−	14.9082i	−0.179776	−	0.493931i	−0.996547	+	0.0830314i	$0.973540\pi$
$912$		0			0
$913$	6.16743	−	70.4941i	0.204112	−	2.33301i
$914$	13.8857	+	5.05400i	0.459300	+	0.167171i
$915$		0			0
$916$	−0.323662	+	1.83558i	−0.0106941	+	0.0606492i
$917$	−18.8011	+	18.8011i	−0.620866	+	0.620866i
$918$		0			0
$919$		−	21.1543i		−	0.697817i	−0.937157	−	0.348909i	$-0.886552\pi$
$919$		−	21.1543i		−	0.697817i	0.937157	−	0.348909i	$-0.113448\pi$
$920$	9.29943	−	1.66161i	0.306593	−	0.0547816i
$921$		0			0
$922$	6.92119	+	14.8425i	0.227937	+	0.488813i
$923$	17.9380	+	1.56937i	0.590436	+	0.0516564i
$924$		0			0
$925$	−26.5249	+	7.23711i	−0.872134	+	0.237955i
$926$	−3.91634	−	2.26110i	−0.128699	−	0.0743044i
$927$		0			0
$928$	4.26425	+	1.14260i	0.139981	+	0.0375078i
$929$	16.0779	+	13.4909i	0.527497	+	0.442623i	0.867236	−	0.497897i	$-0.165894\pi$
$929$	16.0779	+	13.4909i	0.527497	+	0.442623i	−0.339739	+	0.940520i	$0.610339\pi$
$930$		0			0
$931$	−0.442716	−	2.51077i	−0.0145094	−	0.0822871i
$932$	−7.30819	−	5.11725i	−0.239388	−	0.167621i
$933$		0			0
$934$	−17.9822	+	21.4304i	−0.588396	+	0.701223i
$935$	0.604666	+	6.73450i	0.0197747	+	0.220242i
$936$		0			0
$937$	−20.6538	+	5.53418i	−0.674732	+	0.180794i	−0.579885	−	0.814698i	$-0.696903\pi$
$937$	−20.6538	+	5.53418i	−0.674732	+	0.180794i	−0.0948464	+	0.995492i	$0.530236\pi$
$938$	−26.5225	−	12.3676i	−0.865989	−	0.403817i
$939$		0			0
$940$	−4.06782	+	1.09991i	−0.132678	+	0.0358752i
$941$	9.45573	−	25.9794i	0.308248	−	0.846904i	−0.684751	−	0.728777i	$-0.740089\pi$
$941$	9.45573	−	25.9794i	0.308248	−	0.846904i	0.992999	−	0.118127i	$-0.0376889\pi$
$942$		0			0
$943$	−26.2640	−	37.5089i	−0.855275	−	1.22146i
$944$	−1.74644			−0.0568417
$945$		0			0
$946$	−13.1024			−0.425997
$947$	−9.89530	−	14.1320i	−0.321554	−	0.459227i	0.625536	−	0.780196i	$-0.284880\pi$
$947$	−9.89530	−	14.1320i	−0.321554	−	0.459227i	−0.947090	+	0.320969i	$0.895992\pi$
$948$		0			0
$949$	33.1874	−	91.1816i	1.07731	−	2.95988i
$950$	4.12297	−	2.91504i	0.133767	−	0.0945763i
$951$		0			0
$952$	−1.25483	−	0.585137i	−0.0406693	−	0.0189644i
$953$	−39.0858	+	10.4730i	−1.26611	+	0.339254i	−0.828540	−	0.559930i	$-0.810828\pi$
$953$	−39.0858	+	10.4730i	−1.26611	+	0.339254i	−0.437572	+	0.899183i	$0.644161\pi$
$954$		0			0
$955$	−17.5961	+	21.0675i	−0.569395	+	0.681729i
$956$	1.05649	−	1.25907i	0.0341693	−	0.0407214i
$957$		0			0
$958$	−16.3722	−	11.4640i	−0.528963	−	0.370384i
$959$	2.09111	+	11.8593i	0.0675253	+	0.382955i
$960$		0			0
$961$	−13.7813	−	11.5639i	−0.444558	−	0.373029i
$962$	−35.7490	−	9.57892i	−1.15259	−	0.308837i
$963$		0			0
$964$	−13.6569	−	7.88480i	−0.439858	−	0.253952i
$965$	−0.804796	+	9.44686i	−0.0259073	+	0.304105i
$966$		0			0
$967$	12.9935	+	1.13679i	0.417844	+	0.0365566i	0.294140	−	0.955762i	$-0.404967\pi$
$967$	12.9935	+	1.13679i	0.417844	+	0.0365566i	0.123705	+	0.992319i	$0.460522\pi$
$968$	4.37298	+	9.37789i	0.140553	+	0.301417i
$969$		0			0
$970$	4.42141	+	24.7450i	0.141963	+	0.794515i
$971$			0.324954i			0.0104283i	0.999986	+	0.00521414i	$0.00165972\pi$
$971$			0.324954i			0.0104283i	−0.999986	+	0.00521414i	$0.998340\pi$
$972$		0			0
$973$	15.5509	−	15.5509i	0.498540	−	0.498540i
$974$	1.72052	−	9.75758i	0.0551292	−	0.312653i
$975$		0			0
$976$	6.87841	+	2.50354i	0.220173	+	0.0801362i
$977$	−4.09406	+	46.7953i	−0.130980	+	1.49711i	0.591828	+	0.806065i	$0.298407\pi$
$977$	−4.09406	+	46.7953i	−0.130980	+	1.49711i	−0.722808	+	0.691049i	$0.757149\pi$
$978$		0			0
$979$	19.7006	+	54.1271i	0.629635	+	1.72991i
$980$	0.967585	−	5.56156i	0.0309084	−	0.177657i
$981$		0			0
$982$	0.162687	−	0.607154i	0.00519154	−	0.0193751i
$983$	−0.433920	−	4.95973i	−0.0138399	−	0.158191i	0.986130	−	0.165976i	$-0.0530774\pi$
$983$	−0.433920	−	4.95973i	−0.0138399	−	0.158191i	−0.999970	+	0.00778525i	$0.997522\pi$
$984$		0			0
$985$	−28.1585	−	7.47628i	−0.897203	−	0.238214i
$986$	2.84539	−	0.501720i	0.0906158	−	0.0159780i
$987$		0			0
$988$	6.77107	−	0.592392i	0.215416	−	0.0188465i
$989$	5.99026	+	10.3754i	0.190479	+	0.329920i
$990$		0			0
$991$	1.07297	−	1.85843i	0.0340839	−	0.0590350i	−0.848480	−	0.529227i	$-0.822482\pi$
$991$	1.07297	−	1.85843i	0.0340839	−	0.0590350i	0.882564	+	0.470192i	$0.155815\pi$
$992$	1.52435	−	3.26897i	0.0483980	−	0.103790i
$993$		0			0
$994$	3.63806	+	4.33567i	0.115392	+	0.137519i
$995$	−0.0389845	−	17.1000i	−0.00123589	−	0.542105i
$996$		0			0
$997$	48.9117	−	34.2483i	1.54905	−	1.08466i	0.587787	−	0.809016i	$-0.299999\pi$
$997$	48.9117	−	34.2483i	1.54905	−	1.08466i	0.961261	−	0.275640i	$-0.0888897\pi$
$998$	2.98954	+	2.98954i	0.0946323	+	0.0946323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.737.14		216
3.2	odd	2		270.2.r.a.137.5	yes	216
5.3	odd	4	inner	810.2.s.a.413.10		216
15.8	even	4		270.2.r.a.83.9	✓	216
27.13	even	9		270.2.r.a.257.9	yes	216
27.14	odd	18	inner	810.2.s.a.557.10		216
135.13	odd	36		270.2.r.a.203.5	yes	216
135.68	even	36	inner	810.2.s.a.233.14		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.9	✓	216	15.8	even	4
270.2.r.a.137.5	yes	216	3.2	odd	2
270.2.r.a.203.5	yes	216	135.13	odd	36
270.2.r.a.257.9	yes	216	27.13	even	9
810.2.s.a.233.14		216	135.68	even	36	inner
810.2.s.a.413.10		216	5.3	odd	4	inner
810.2.s.a.557.10		216	27.14	odd	18	inner
810.2.s.a.737.14		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)

\(f(q)\)	\(=\)	\(q+(0.573576 + 0.819152i) q^{2} +(-0.342020 + 0.939693i) q^{4} +(1.11362 - 1.93904i) q^{5} +(-1.91731 - 0.894058i) q^{7} +(-0.965926 + 0.258819i) q^{8} +(2.22711 - 0.199964i) q^{10} +(2.96988 - 3.53937i) q^{11} +(-5.51327 - 3.86043i) q^{13} +(-0.367357 - 2.08338i) q^{14} +(-0.766044 - 0.642788i) q^{16} +(-0.632172 - 0.169390i) q^{17} +(0.874579 + 0.504939i) q^{19} +(1.44122 + 1.70965i) q^{20} +(4.60274 + 0.402687i) q^{22} +(-1.78543 - 3.82887i) q^{23} +(-2.51972 - 4.31868i) q^{25} -6.73046i q^{26} +(1.49590 - 1.49590i) q^{28} +(-0.766601 + 4.34761i) q^{29} +(3.38938 + 1.23364i) q^{31} +(0.0871557 - 0.996195i) q^{32} +(-0.223843 - 0.615004i) q^{34} +(-3.86876 + 2.72210i) q^{35} +(1.42322 - 5.31153i) q^{37} +(0.0880166 + 1.00603i) q^{38} +(-0.573811 + 2.16119i) q^{40} +(10.6740 - 1.88211i) q^{41} +(-2.82504 + 0.247159i) q^{43} +(2.31016 + 4.00131i) q^{44} +(2.11235 - 3.65869i) q^{46} +(-0.796430 + 1.70795i) q^{47} +(-1.62276 - 1.93393i) q^{49} +(2.09241 - 4.54113i) q^{50} +(5.51327 - 3.86043i) q^{52} +(5.85254 + 5.85254i) q^{53} +(-3.55565 - 9.70021i) q^{55} +(2.08338 + 0.367357i) q^{56} +(-4.00106 + 1.86572i) q^{58} +(1.33785 - 1.12259i) q^{59} +(-6.87841 + 2.50354i) q^{61} +(0.933536 + 3.48401i) q^{62} +(0.866025 - 0.500000i) q^{64} +(-13.6252 + 6.39138i) q^{65} +(7.93436 - 11.3314i) q^{67} +(0.375390 - 0.536113i) q^{68} +(-4.44885 - 1.60777i) q^{70} +(-2.31694 + 1.33769i) q^{71} +(3.73141 + 13.9258i) q^{73} +(5.16727 - 1.88073i) q^{74} +(-0.773611 + 0.649137i) q^{76} +(-8.85861 + 4.13084i) q^{77} +(2.93933 + 0.518284i) q^{79} +(-2.09947 + 0.769569i) q^{80} +(7.66408 + 7.66408i) q^{82} +(12.5459 - 8.78472i) q^{83} +(-1.03245 + 1.03717i) q^{85} +(-1.82284 - 2.17237i) q^{86} +(-1.95263 + 4.18743i) q^{88} +(-6.23342 + 10.7966i) q^{89} +(7.11922 + 12.3308i) q^{91} +(4.20862 - 0.368207i) q^{92} +(-1.85588 + 0.327242i) q^{94} +(1.95304 - 1.13353i) q^{95} +(0.979769 + 11.1988i) q^{97} +(0.653406 - 2.43854i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 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

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