LMFDB - Embedded newform 810.2.s.a.557.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.10
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.10295 - 0.759988i) q^{5} +(-0.894058 - 1.91731i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.28673 - 1.82875i) q^{10} +(2.96988 + 3.53937i) q^{11} +(3.86043 + 5.51327i) q^{13} +(0.367357 - 2.08338i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.169390 - 0.632172i) q^{17} +(-0.874579 + 0.504939i) q^{19} +(-0.00509778 - 2.23606i) q^{20} +(0.402687 + 4.60274i) q^{22} +(3.82887 + 1.78543i) q^{23} +(3.84484 + 3.19644i) q^{25} +6.73046i q^{26} +(1.49590 - 1.49590i) q^{28} +(0.766601 + 4.34761i) q^{29} +(3.38938 - 1.23364i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(0.223843 - 0.615004i) q^{34} +(0.423028 + 4.71150i) q^{35} +(-5.31153 + 1.42322i) q^{37} +(-1.00603 - 0.0880166i) q^{38} +(1.27838 - 1.83460i) q^{40} +(10.6740 + 1.88211i) q^{41} +(-0.247159 + 2.82504i) q^{43} +(-2.31016 + 4.00131i) q^{44} +(2.11235 + 3.65869i) q^{46} +(1.70795 - 0.796430i) q^{47} +(1.62276 - 1.93393i) q^{49} +(1.31610 + 4.82368i) q^{50} +(-3.86043 + 5.51327i) q^{52} +(-5.85254 - 5.85254i) q^{53} +(-3.55565 - 9.70021i) q^{55} +(2.08338 - 0.367357i) q^{56} +(-1.86572 + 4.00106i) q^{58} +(-1.33785 - 1.12259i) q^{59} +(-6.87841 - 2.50354i) q^{61} +(3.48401 + 0.933536i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.92830 - 14.5280i) q^{65} +(-11.3314 + 7.93436i) q^{67} +(0.536113 - 0.375390i) q^{68} +(-2.35588 + 4.10207i) q^{70} +(-2.31694 - 1.33769i) q^{71} +(-13.9258 - 3.73141i) q^{73} +(-5.16727 - 1.88073i) q^{74} +(-0.773611 - 0.649137i) q^{76} +(4.13084 - 8.85861i) q^{77} +(-2.93933 + 0.518284i) q^{79} +(2.09947 - 0.769569i) q^{80} +(7.66408 + 7.66408i) q^{82} +(8.78472 - 12.5459i) q^{83} +(-0.124224 + 1.45816i) q^{85} +(-1.82284 + 2.17237i) q^{86} +(-4.18743 + 1.95263i) q^{88} +(6.23342 + 10.7966i) q^{89} +(7.11922 - 12.3308i) q^{91} +(-0.368207 + 4.20862i) q^{92} +(1.85588 + 0.327242i) q^{94} +(2.22295 - 0.397193i) q^{95} +(11.1988 + 0.979769i) q^{97} +(2.43854 - 0.653406i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−2.10295	−	0.759988i	−0.940470	−	0.339877i
$5$	−2.10295	−	0.759988i	−0.940470	−	0.339877i
$6$		0			0
$7$	−0.894058	−	1.91731i	−0.337922	−	0.724677i	0.661764	−	0.749712i	$-0.269808\pi$
$7$	−0.894058	−	1.91731i	−0.337922	−	0.724677i	−0.999687	+	0.0250353i	$0.992030\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−1.28673	−	1.82875i	−0.406899	−	0.578302i
$11$	2.96988	+	3.53937i	0.895454	+	1.06716i	0.997378	+	0.0723682i	$0.0230557\pi$
$11$	2.96988	+	3.53937i	0.895454	+	1.06716i	−0.101924	+	0.994792i	$0.532500\pi$
$12$		0			0
$13$	3.86043	+	5.51327i	1.07069	+	1.52911i	0.829402	+	0.558652i	$0.188681\pi$
$13$	3.86043	+	5.51327i	1.07069	+	1.52911i	0.241289	+	0.970453i	$0.422430\pi$
$14$	0.367357	−	2.08338i	0.0981802	−	0.556807i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.169390	−	0.632172i	−0.0410831	−	0.153324i	0.942337	−	0.334665i	$-0.108623\pi$
$17$	−0.169390	−	0.632172i	−0.0410831	−	0.153324i	−0.983420	+	0.181340i	$0.941956\pi$
$18$		0			0
$19$	−0.874579	+	0.504939i	−0.200642	+	0.115841i	−0.596955	−	0.802275i	$-0.703623\pi$
$19$	−0.874579	+	0.504939i	−0.200642	+	0.115841i	0.396313	+	0.918116i	$0.370290\pi$
$20$	−0.00509778	−	2.23606i	−0.00113990	−	0.499999i
$21$		0			0
$22$	0.402687	+	4.60274i	0.0858533	+	0.981307i
$23$	3.82887	+	1.78543i	0.798376	+	0.372289i	0.778604	−	0.627516i	$-0.215928\pi$
$23$	3.82887	+	1.78543i	0.798376	+	0.372289i	0.0197718	+	0.999805i	$0.493706\pi$
$24$		0			0
$25$	3.84484	+	3.19644i	0.768967	+	0.639288i
$26$			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	0.969454	+	0.245275i	$0.0788783\pi$
$29$	0.766601	+	4.34761i	0.142354	+	0.807331i	−0.827099	+	0.562056i	$0.810011\pi$
$30$		0			0
$31$	3.38938	−	1.23364i	0.608751	−	0.221567i	−0.0192054	−	0.999816i	$-0.506114\pi$
$31$	3.38938	−	1.23364i	0.608751	−	0.221567i	0.627957	+	0.778248i	$0.283891\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$		0			0
$34$	0.223843	−	0.615004i	0.0383888	−	0.105472i
$35$	0.423028	+	4.71150i	0.0715048	+	0.796389i
$36$		0			0
$37$	−5.31153	+	1.42322i	−0.873210	+	0.233976i	−0.667475	−	0.744632i	$-0.732625\pi$
$37$	−5.31153	+	1.42322i	−0.873210	+	0.233976i	−0.205734	+	0.978608i	$0.565958\pi$
$38$	−1.00603	−	0.0880166i	−0.163200	−	0.0142782i
$39$		0			0
$40$	1.27838	−	1.83460i	0.202129	−	0.290076i
$41$	10.6740	+	1.88211i	1.66700	+	0.293936i	0.925986	−	0.377558i	$-0.123236\pi$
$41$	10.6740	+	1.88211i	1.66700	+	0.293936i	0.741010	+	0.671495i	$0.234347\pi$
$42$		0			0
$43$	−0.247159	+	2.82504i	−0.0376914	+	0.430815i	0.953781	+	0.300501i	$0.0971539\pi$
$43$	−0.247159	+	2.82504i	−0.0376914	+	0.430815i	−0.991473	+	0.130313i	$0.958402\pi$
$44$	−2.31016	+	4.00131i	−0.348270	+	0.603221i
$45$		0			0
$46$	2.11235	+	3.65869i	0.311449	+	0.539445i
$47$	1.70795	−	0.796430i	0.249130	−	0.116171i	−0.294043	−	0.955792i	$-0.595001\pi$
$47$	1.70795	−	0.796430i	0.249130	−	0.116171i	0.543172	+	0.839621i	$0.317223\pi$
$48$		0			0
$49$	1.62276	−	1.93393i	0.231823	−	0.276276i
$50$	1.31610	+	4.82368i	0.186125	+	0.682171i
$51$		0			0
$52$	−3.86043	+	5.51327i	−0.535346	+	0.764553i
$53$	−5.85254	−	5.85254i	−0.803908	−	0.803908i	0.179796	−	0.983704i	$-0.442456\pi$
$53$	−5.85254	−	5.85254i	−0.803908	−	0.803908i	−0.983704	+	0.179796i	$0.942456\pi$
$54$		0			0
$55$	−3.55565	−	9.70021i	−0.479444	−	1.30798i
$56$	2.08338	−	0.367357i	0.278404	−	0.0490901i
$57$		0			0
$58$	−1.86572	+	4.00106i	−0.244982	+	0.525365i
$59$	−1.33785	−	1.12259i	−0.174173	−	0.146148i	0.551534	−	0.834152i	$-0.314043\pi$
$59$	−1.33785	−	1.12259i	−0.174173	−	0.146148i	−0.725707	+	0.688004i	$0.758487\pi$
$60$		0			0
$61$	−6.87841	−	2.50354i	−0.880690	−	0.320545i	−0.138202	−	0.990404i	$-0.544132\pi$
$61$	−6.87841	−	2.50354i	−0.880690	−	0.320545i	−0.742488	+	0.669859i	$0.766354\pi$
$62$	3.48401	+	0.933536i	0.442469	+	0.118559i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−3.92830	−	14.5280i	−0.487245	−	1.80198i
$66$		0			0
$67$	−11.3314	+	7.93436i	−1.38436	+	0.969337i	−0.385443	+	0.922732i	$0.625951\pi$
$67$	−11.3314	+	7.93436i	−1.38436	+	0.969337i	−0.998913	+	0.0466048i	$0.985160\pi$
$68$	0.536113	−	0.375390i	0.0650132	−	0.0455228i
$69$		0			0
$70$	−2.35588	+	4.10207i	−0.281582	+	0.490291i
$71$	−2.31694	−	1.33769i	−0.274970	−	0.158754i	0.356174	−	0.934420i	$-0.384081\pi$
$71$	−2.31694	−	1.33769i	−0.274970	−	0.158754i	−0.631144	+	0.775665i	$0.717414\pi$
$72$		0			0
$73$	−13.9258	−	3.73141i	−1.62989	−	0.436728i	−0.676006	−	0.736896i	$-0.736291\pi$
$73$	−13.9258	−	3.73141i	−1.62989	−	0.436728i	−0.953887	+	0.300167i	$0.902957\pi$
$74$	−5.16727	−	1.88073i	−0.600683	−	0.218631i
$75$		0			0
$76$	−0.773611	−	0.649137i	−0.0887392	−	0.0744611i
$77$	4.13084	−	8.85861i	0.470752	−	1.00953i
$78$		0			0
$79$	−2.93933	+	0.518284i	−0.330701	+	0.0583115i	−0.336534	−	0.941671i	$-0.609255\pi$
$79$	−2.93933	+	0.518284i	−0.330701	+	0.0583115i	0.00583253	+	0.999983i	$0.498143\pi$
$80$	2.09947	−	0.769569i	0.234728	−	0.0860404i
$81$		0			0
$82$	7.66408	+	7.66408i	0.846356	+	0.846356i
$83$	8.78472	−	12.5459i	0.964248	−	1.37709i	0.0383709	−	0.999264i	$-0.487783\pi$
$83$	8.78472	−	12.5459i	0.964248	−	1.37709i	0.925877	−	0.377825i	$-0.123328\pi$
$84$		0			0
$85$	−0.124224	+	1.45816i	−0.0134740	+	0.158160i
$86$	−1.82284	+	2.17237i	−0.196562	+	0.234253i
$87$		0			0
$88$	−4.18743	+	1.95263i	−0.446382	+	0.208151i
$89$	6.23342	+	10.7966i	0.660741	+	1.14444i	0.980421	+	0.196912i	$0.0630913\pi$
$89$	6.23342	+	10.7966i	0.660741	+	1.14444i	−0.319680	+	0.947526i	$0.603575\pi$
$90$		0			0
$91$	7.11922	−	12.3308i	0.746297	−	1.29262i
$92$	−0.368207	+	4.20862i	−0.0383882	+	0.438779i
$93$		0			0
$94$	1.85588	+	0.327242i	0.191420	+	0.0337525i
$95$	2.22295	−	0.397193i	0.228070	−	0.0407512i
$96$		0			0
$97$	11.1988	+	0.979769i	1.13707	+	0.0994804i	0.640102	−	0.768290i	$-0.278892\pi$
$97$	11.1988	+	0.979769i	1.13707	+	0.0994804i	0.496965	+	0.867771i	$0.334448\pi$
$98$	2.43854	−	0.653406i	0.246330	−	0.0660039i
$99$		0			0
$100$	−1.68866	+	4.70621i	−0.168866	+	0.470621i
$101$	−0.969956	+	2.66493i	−0.0965142	+	0.265171i	−0.978549	−	0.206013i	$-0.933951\pi$
$101$	−0.969956	+	2.66493i	−0.0965142	+	0.265171i	0.882035	+	0.471184i	$0.156173\pi$
$102$		0			0
$103$	12.2849	−	1.07479i	1.21047	−	0.105902i	0.536008	−	0.844213i	$-0.319932\pi$
$103$	12.2849	−	1.07479i	1.21047	−	0.105902i	0.674461	+	0.738310i	$0.264376\pi$
$104$	−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	−0.831028	−	0.556230i	$-0.812247\pi$
$107$	−2.84254	+	2.84254i	−0.274798	+	0.274798i	0.556230	+	0.831028i	$0.312247\pi$
$108$		0			0
$109$			1.29371i			0.123915i	0.998079	+	0.0619575i	$0.0197343\pi$
$109$			1.29371i			0.123915i	−0.998079	+	0.0619575i	$0.980266\pi$
$110$	2.65119	−	9.98539i	0.252781	−	0.952069i
$111$		0			0
$112$	1.91731	+	0.894058i	0.181169	+	0.0844806i
$113$	−0.594226	−	6.79204i	−0.0559001	−	0.638941i	−0.971530	−	0.236918i	$-0.923863\pi$
$113$	−0.594226	−	6.79204i	−0.0559001	−	0.638941i	0.915629	−	0.402023i	$-0.131693\pi$
$114$		0			0
$115$	−6.69504	−	6.66458i	−0.624316	−	0.621476i
$116$	−3.82322	+	2.20734i	−0.354977	+	0.204946i
$117$		0			0
$118$	−0.452011	−	1.68693i	−0.0416110	−	0.155294i
$119$	−1.06063	+	0.889973i	−0.0972277	+	0.0815837i
$120$		0			0
$121$	−1.79680	+	10.1902i	−0.163345	+	0.926378i
$122$	−4.19849	−	5.99607i	−0.380114	−	0.542859i
$123$		0			0
$124$	2.31848	+	2.76305i	0.208205	+	0.248129i
$125$	−5.65626	−	9.64400i	−0.505911	−	0.862585i
$126$		0			0
$127$	3.75956	−	14.0309i	0.333607	−	1.24504i	−0.571764	−	0.820418i	$-0.693741\pi$
$127$	3.75956	−	14.0309i	0.333607	−	1.24504i	0.905371	−	0.424621i	$-0.139593\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$		0			0
$130$	5.11507	−	14.1538i	0.448621	−	1.24137i
$131$	4.29864	+	11.8104i	0.375574	+	1.03188i	0.973171	+	0.230085i	$0.0739003\pi$
$131$	4.29864	+	11.8104i	0.375574	+	1.03188i	−0.597596	+	0.801797i	$0.703877\pi$
$132$		0			0
$133$	1.75005	+	1.22540i	0.151749	+	0.106256i
$134$	−13.8331			−1.19500
$135$		0			0
$136$	0.654473			0.0561206
$137$	−4.66286	−	3.26497i	−0.398375	−	0.278945i	0.357173	−	0.934038i	$-0.383741\pi$
$137$	−4.66286	−	3.26497i	−0.398375	−	0.278945i	−0.755548	+	0.655093i	$0.772630\pi$
$138$		0			0
$139$	3.55554	+	9.76877i	0.301577	+	0.828576i	0.994226	+	0.107302i	$0.0342211\pi$
$139$	3.55554	+	9.76877i	0.301577	+	0.828576i	−0.692649	+	0.721274i	$0.743557\pi$
$140$	−4.28268	+	2.00894i	−0.361952	+	0.169787i
$141$		0			0
$142$	−1.13066	−	2.42471i	−0.0948831	−	0.203477i
$143$	−8.04846	+	30.0373i	−0.673046	+	2.51184i
$144$		0			0
$145$	1.69200	−	9.72543i	0.140513	−	0.807653i
$146$	−9.26711	−	11.0441i	−0.766951	−	0.914017i
$147$		0			0
$148$	−3.15404	−	4.50443i	−0.259260	−	0.370262i
$149$	−1.07764	+	6.11157i	−0.0882833	+	0.500680i	0.908316	+	0.418284i	$0.137368\pi$
$149$	−1.07764	+	6.11157i	−0.0882833	+	0.500680i	−0.996600	+	0.0823958i	$0.973743\pi$
$150$		0			0
$151$	10.7455	−	9.01658i	0.874459	−	0.733759i	−0.0905728	−	0.995890i	$-0.528870\pi$
$151$	10.7455	−	9.01658i	0.874459	−	0.733759i	0.965032	+	0.262131i	$0.0844253\pi$
$152$	−0.261375	−	0.975466i	−0.0212003	−	0.0791208i
$153$		0			0
$154$	8.46487	−	4.88720i	0.682119	−	0.393821i
$155$	−8.06527	+	0.0183872i	−0.647818	+	0.00147690i
$156$		0			0
$157$	−2.17385	−	24.8472i	−0.173492	−	1.98302i	−0.183219	−	0.983072i	$-0.558652\pi$
$157$	−2.17385	−	24.8472i	−0.173492	−	1.98302i	0.00972700	−	0.999953i	$-0.496904\pi$
$158$	−2.70504	−	1.26138i	−0.215201	−	0.100350i
$159$		0			0
$160$	2.16119	+	0.573811i	0.170857	+	0.0453638i
$161$		−	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
$167$	10.9146	−	0.954902i	0.844596	−	0.0738925i	0.343361	−	0.939204i	$-0.388435\pi$
$167$	10.9146	−	0.954902i	0.844596	−	0.0738925i	0.501235	+	0.865311i	$0.332879\pi$
$168$		0			0
$169$	−11.0469	+	30.3512i	−0.849764	+	2.33471i
$170$	−0.938127	+	1.12321i	−0.0719510	+	0.0861460i
$171$		0			0
$172$	−2.73920	+	0.733967i	−0.208862	+	0.0559645i
$173$	−17.1922	−	1.50412i	−1.30710	−	0.114356i	−0.587770	−	0.809028i	$-0.699994\pi$
$173$	−17.1922	−	1.50412i	−1.30710	−	0.114356i	−0.719327	+	0.694672i	$0.755549\pi$
$174$		0			0
$175$	2.69107	−	10.2296i	0.203426	−	0.773282i
$176$	−4.55013	−	0.802310i	−0.342979	−	0.0604764i
$177$		0			0
$178$	−1.08656	+	12.4194i	−0.0814409	+	0.930874i
$179$	10.7340	−	18.5919i	0.802299	−	1.38962i	−0.115801	−	0.993272i	$-0.536944\pi$
$179$	10.7340	−	18.5919i	0.802299	−	1.38962i	0.918100	−	0.396349i	$-0.129723\pi$
$180$		0			0
$181$	5.54152	+	9.59819i	0.411898	+	0.713428i	0.995097	−	0.0989012i	$-0.0315328\pi$
$181$	5.54152	+	9.59819i	0.411898	+	0.713428i	−0.583200	+	0.812329i	$0.698199\pi$
$182$	12.9044	−	6.01742i	0.956538	−	0.446041i
$183$		0			0
$184$	−2.71558	+	3.23630i	−0.200195	+	0.238584i
$185$	12.2515	+	1.04373i	0.900750	+	0.0767366i
$186$		0			0
$187$	1.73442	−	2.47701i	0.126834	−	0.181137i
$188$	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	−0.592955	−	0.805236i	$-0.702039\pi$
$191$	−12.0892	+	2.13165i	−0.874743	+	0.154241i	−0.281788	+	0.959477i	$0.590928\pi$
$192$		0			0
$193$	−1.79193	+	3.84281i	−0.128986	+	0.276611i	−0.960186	−	0.279363i	$-0.909877\pi$
$193$	−1.79193	+	3.84281i	−0.128986	+	0.276611i	0.831200	+	0.555974i	$0.187655\pi$
$194$	8.61155	+	7.22595i	0.618273	+	0.518793i
$195$		0			0
$196$	2.37232	+	0.863452i	0.169451	+	0.0616752i
$197$	−12.5852	−	3.37219i	−0.896658	−	0.240259i	−0.219078	−	0.975707i	$-0.570305\pi$
$197$	−12.5852	−	3.37219i	−0.896658	−	0.240259i	−0.677580	+	0.735449i	$0.736971\pi$
$198$		0			0
$199$	−6.62281	−	3.82368i	−0.469478	−	0.271053i	0.246543	−	0.969132i	$-0.420705\pi$
$199$	−6.62281	−	3.82368i	−0.469478	−	0.271053i	−0.716021	+	0.698078i	$0.754039\pi$
$200$	−4.08264	+	2.88653i	−0.288686	+	0.204108i
$201$		0			0
$202$	−2.32308	+	1.62664i	−0.163452	+	0.114450i
$203$	7.65035	−	5.35683i	0.536949	−	0.375976i
$204$		0			0
$205$	−21.0165	−	12.0701i	−1.46786	−	0.843012i
$206$	10.6797	+	6.16592i	0.744090	+	0.429600i
$207$		0			0
$208$	−6.50112	−	1.74197i	−0.450772	−	0.120784i
$209$	−4.38456	−	1.59585i	−0.303287	−	0.110387i
$210$		0			0
$211$	8.98764	+	7.54152i	0.618734	+	0.519180i	0.897405	−	0.441207i	$-0.145449\pi$
$211$	8.98764	+	7.54152i	0.618734	+	0.519180i	−0.278671	+	0.960387i	$0.589894\pi$
$212$	3.49790	−	7.50127i	0.240237	−	0.515190i
$213$		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
$218$	−0.742042	+	1.05975i	−0.0502574	+	0.0717750i
$219$		0			0
$220$	7.89911	−	6.65889i	0.532558	−	0.448942i
$221$	2.83142	−	3.37435i	0.190462	−	0.226983i
$222$		0			0
$223$	11.2194	−	5.23170i	0.751308	−	0.350340i	−0.00895195	−	0.999960i	$-0.502850\pi$
$223$	11.2194	−	5.23170i	0.751308	−	0.350340i	0.760260	+	0.649619i	$0.225072\pi$
$224$	1.05776	+	1.83210i	0.0706746	+	0.122412i
$225$		0			0
$226$	3.40899	−	5.90455i	0.226763	−	0.392765i
$227$	−1.51063	+	17.2666i	−0.100264	+	1.14603i	0.764767	+	0.644307i	$0.222854\pi$
$227$	−1.51063	+	17.2666i	−0.100264	+	1.14603i	−0.865031	+	0.501718i	$0.832701\pi$
$228$		0			0
$229$	−1.83558	−	0.323662i	−0.121298	−	0.0213882i	0.112669	−	0.993633i	$-0.464060\pi$
$229$	−1.83558	−	0.323662i	−0.121298	−	0.0213882i	−0.233968	+	0.972244i	$0.575171\pi$
$230$	−1.66161	−	9.29943i	−0.109563	−	0.613186i
$231$		0			0
$232$	−4.39788	−	0.384765i	−0.288735	−	0.0252610i
$233$	−8.61765	+	2.30909i	−0.564561	+	0.151274i	−0.529801	−	0.848122i	$-0.677733\pi$
$233$	−8.61765	+	2.30909i	−0.564561	+	0.151274i	−0.0347602	+	0.999396i	$0.511067\pi$
$234$		0			0
$235$	−4.19702	+	0.376835i	−0.273783	+	0.0245820i
$236$	0.597317	−	1.64111i	0.0388820	−	0.106827i
$237$		0			0
$238$	−1.37928	+	0.120672i	−0.0894057	+	0.00782198i
$239$	1.54448	−	0.562146i	0.0999043	−	0.0363622i	−0.291584	−	0.956545i	$-0.594182\pi$
$239$	1.54448	−	0.562146i	0.0999043	−	0.0363622i	0.391489	+	0.920183i	$0.371960\pi$
$240$		0			0
$241$	−2.73836	−	15.5300i	−0.176393	−	1.00038i	−0.936523	−	0.350606i	$-0.885976\pi$
$241$	−2.73836	−	15.5300i	−0.176393	−	1.00038i	0.760130	−	0.649771i	$-0.225135\pi$
$242$	−7.31669	+	7.31669i	−0.470335	+	0.470335i
$243$		0			0
$244$		−	7.31985i		−	0.468605i
$245$	−4.88235	+	2.83369i	−0.311922	+	0.181038i
$246$		0			0
$247$	−6.16012	−	2.87251i	−0.391959	−	0.182773i
$248$	0.314363	+	3.59318i	0.0199621	+	0.228167i
$249$		0			0
$250$	0.898233	−	11.1442i	0.0568092	−	0.704821i
$251$	21.4009	−	12.3558i	1.35081	−	0.779891i	0.362448	−	0.932004i	$-0.381941\pi$
$251$	21.4009	−	12.3558i	1.35081	−	0.779891i	0.988363	+	0.152113i	$0.0486076\pi$
$252$		0			0
$253$	5.05201	+	18.8543i	0.317617	+	1.18536i
$254$	11.1274	−	9.33703i	0.698197	−	0.585857i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−7.26793	−	10.3797i	−0.453361	−	0.647467i	0.525787	−	0.850616i	$-0.323771\pi$
$257$	−7.26793	−	10.3797i	−0.453361	−	0.647467i	−0.979148	+	0.203150i	$0.934882\pi$
$258$		0			0
$259$	7.47757	+	8.91143i	0.464634	+	0.553729i
$260$	12.3083	−	8.66027i	0.763330	−	0.537087i
$261$		0			0
$262$	−3.25294	+	12.1401i	−0.200967	+	0.750020i
$263$	−5.76426	−	12.3615i	−0.355440	−	0.762243i	0.644558	−	0.764556i	$-0.277042\pi$
$263$	−5.76426	−	12.3615i	−0.355440	−	0.762243i	−0.999997	+	0.00231293i	$0.999264\pi$
$264$		0			0
$265$	7.85977	+	16.7555i	0.482822	+	1.02928i
$266$	0.730698	+	2.00758i	0.0448020	+	0.123092i
$267$		0			0
$268$	−11.3314	−	7.93436i	−0.692178	−	0.484668i
$269$	−27.6798			−1.68767			−0.843834	−	0.536604i	$-0.819707\pi$
$269$	−27.6798			−1.68767			−0.843834	+	0.536604i	$0.819707\pi$
$270$		0			0
$271$	4.32582			0.262775			0.131388	−	0.991331i	$-0.458057\pi$
$271$	4.32582			0.262775			0.131388	+	0.991331i	$0.458057\pi$
$272$	0.536113	+	0.375390i	0.0325066	+	0.0227614i
$273$		0			0
$274$	−1.94688	−	5.34902i	−0.117616	−	0.323146i
$275$	0.105334	+	23.1014i	0.00635186	+	1.39306i
$276$		0			0
$277$	0.0407980	+	0.0874915i	0.00245131	+	0.00525685i	0.907530	−	0.419988i	$-0.137966\pi$
$277$	0.0407980	+	0.0874915i	0.00245131	+	0.00525685i	−0.905078	+	0.425245i	$0.860188\pi$
$278$	−2.69061	+	10.0415i	−0.161372	+	0.602248i
$279$		0			0
$280$	−4.66045	−	0.810812i	−0.278515	−	0.0484553i
$281$	10.5947	+	12.6263i	0.632026	+	0.753220i	0.983088	−	0.183133i	$-0.0586238\pi$
$281$	10.5947	+	12.6263i	0.632026	+	0.753220i	−0.351062	+	0.936352i	$0.614179\pi$
$282$		0			0
$283$	8.36856	+	11.9515i	0.497460	+	0.710446i	0.986854	−	0.161617i	$-0.0516709\pi$
$283$	8.36856	+	11.9515i	0.497460	+	0.710446i	−0.489394	+	0.872063i	$0.662782\pi$
$284$	0.464574	−	2.63473i	0.0275674	−	0.156342i
$285$		0			0
$286$	−23.8216	+	19.9887i	−1.40860	+	1.18196i
$287$	−5.93456	−	22.1481i	−0.350306	−	1.30736i
$288$		0			0
$289$	14.3515	−	8.28583i	0.844205	−	0.487402i
$290$	6.96429	−	6.99612i	0.408957	−	0.410826i
$291$		0			0
$292$	−1.25653	−	14.3622i	−0.0735328	−	0.840484i
$293$	−17.7624	−	8.28275i	−1.03769	−	0.483883i	−0.172334	−	0.985039i	$-0.555131\pi$
$293$	−17.7624	−	8.28275i	−1.03769	−	0.483883i	−0.865357	+	0.501155i	$0.832908\pi$
$294$		0			0
$295$	1.96028	+	3.37750i	0.114132	+	0.196646i
$296$		−	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
$302$	13.9739	−	1.22256i	0.804109	−	0.0703504i
$303$		0			0
$304$	0.345398	−	0.948974i	0.0198100	−	0.0544274i
$305$	12.5623	+	10.4923i	0.719317	+	0.600789i
$306$		0			0
$307$	19.4549	−	5.21294i	1.11035	−	0.297518i	0.343379	−	0.939197i	$-0.388428\pi$
$307$	19.4549	−	5.21294i	1.11035	−	0.297518i	0.766973	+	0.641679i	$0.221762\pi$
$308$	9.73720	+	0.851894i	0.554828	+	0.0485412i
$309$		0			0
$310$	−6.61723	−	4.61099i	−0.375833	−	0.261886i
$311$	−3.15134	−	0.555667i	−0.178696	−	0.0315090i	0.0835839	−	0.996501i	$-0.473363\pi$
$311$	−3.15134	−	0.555667i	−0.178696	−	0.0315090i	−0.262280	+	0.964992i	$0.584474\pi$
$312$		0			0
$313$	1.92604	−	22.0147i	0.108866	−	1.24434i	−0.723581	−	0.690239i	$-0.757505\pi$
$313$	1.92604	−	22.0147i	0.108866	−	1.24434i	0.832447	−	0.554104i	$-0.186939\pi$
$314$	12.4711	−	21.6005i	0.703783	−	1.21899i
$315$		0			0
$316$	−1.49234	−	2.58481i	−0.0839506	−	0.145407i
$317$	−5.84995	+	2.72788i	−0.328566	+	0.153213i	−0.579900	−	0.814688i	$-0.696908\pi$
$317$	−5.84995	+	2.72788i	−0.328566	+	0.153213i	0.251334	+	0.967900i	$0.419131\pi$
$318$		0			0
$319$	−13.1111	+	15.6252i	−0.734080	+	0.874842i
$320$	1.44122	+	1.70965i	0.0805665	+	0.0955721i
$321$		0			0
$322$	5.12630	−	7.32112i	0.285678	−	0.407990i
$323$	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
$328$	−4.58061	+	9.82315i	−0.252922	+	0.542392i
$329$	−3.05401	−	2.56262i	−0.168373	−	0.141282i
$330$		0			0
$331$	24.1172	+	8.77794i	1.32560	+	0.482479i	0.905249	−	0.424882i	$-0.139684\pi$
$331$	24.1172	+	8.77794i	1.32560	+	0.482479i	0.420352	+	0.907361i	$0.361907\pi$
$332$	14.7938	+	3.96399i	0.811916	+	0.217552i
$333$		0			0
$334$	9.48841	+	5.47814i	0.519183	+	0.299750i
$335$	29.8595	−	8.07384i	1.63140	−	0.441121i
$336$		0			0
$337$	−18.5786	+	13.0089i	−1.01204	+	0.708639i	−0.957072	−	0.289849i	$-0.906395\pi$
$337$	−18.5786	+	13.0089i	−1.01204	+	0.708639i	−0.0549686	+	0.998488i	$0.517506\pi$
$338$	−26.4579	+	18.5260i	−1.43912	+	1.00768i
$339$		0			0
$340$	−1.41271	+	0.381989i	−0.0766151	+	0.0207163i
$341$	14.4324	+	8.33253i	0.781557	+	0.451232i
$342$		0			0
$343$	−19.4629	−	5.21506i	−1.05090	−	0.281587i
$344$	−2.66481	−	0.969911i	−0.143677	−	0.0522941i
$345$		0			0
$346$	−13.2203	−	11.0931i	−0.710726	−	0.596370i
$347$	−5.41129	+	11.6045i	−0.290493	+	0.622965i	−0.996347	−	0.0853924i	$-0.972786\pi$
$347$	−5.41129	+	11.6045i	−0.290493	+	0.622965i	0.705854	+	0.708357i	$0.250563\pi$
$348$		0			0
$349$	0.968550	−	0.170782i	0.0518453	−	0.00914173i	−0.147665	−	0.989037i	$-0.547176\pi$
$349$	0.968550	−	0.170782i	0.0518453	−	0.00914173i	0.199511	+	0.979896i	$0.436065\pi$
$350$	8.07183	−	6.83603i	0.431458	−	0.365401i
$351$		0			0
$352$	−3.26706	−	3.26706i	−0.174135	−	0.174135i
$353$	2.65607	−	3.79326i	0.141368	−	0.201895i	−0.742224	−	0.670152i	$-0.766229\pi$
$353$	2.65607	−	3.79326i	0.141368	−	0.201895i	0.883592	+	0.468257i	$0.155118\pi$
$354$		0			0
$355$	3.85580	+	4.57394i	0.204645	+	0.242760i
$356$	−8.01353	+	9.55016i	−0.424716	+	0.506157i
$357$		0			0
$358$	19.4567	−	9.07279i	1.02832	−	0.479512i
$359$	−12.5665	−	21.7659i	−0.663237	−	1.14876i	−0.979760	−	0.200175i	$-0.935849\pi$
$359$	−12.5665	−	21.7659i	−0.663237	−	1.14876i	0.316523	−	0.948585i	$-0.397484\pi$
$360$		0			0
$361$	−8.99007	+	15.5713i	−0.473162	+	0.819540i
$362$	−0.965950	+	11.0409i	−0.0507692	+	0.580295i
$363$		0			0
$364$	14.0221	+	2.47248i	0.734959	+	0.129593i
$365$	26.4495	+	18.4304i	1.38443	+	0.964693i
$366$		0			0
$367$	−0.999602	−	0.0874539i	−0.0521788	−	0.00456505i	0.0610364	−	0.998136i	$-0.480559\pi$
$367$	−0.999602	−	0.0874539i	−0.0521788	−	0.00456505i	−0.113215	+	0.993570i	$0.536115\pi$
$368$	−4.08074	+	1.09343i	−0.212723	+	0.0569991i
$369$		0			0
$370$	9.43721	+	7.88216i	0.490617	+	0.409774i
$371$	−5.98865	+	16.4537i	−0.310915	+	0.854232i
$372$		0			0
$373$	−2.60097	+	0.227555i	−0.134673	+	0.0117824i	−0.154293	−	0.988025i	$-0.549310\pi$
$373$	−2.60097	+	0.227555i	−0.134673	+	0.0117824i	0.0196199	+	0.999808i	$0.493754\pi$
$374$	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	$-0.156954\pi$
$380$	1.13353	+	1.95304i	0.0581490	+	0.100189i
$381$		0			0
$382$	−11.1255	−	5.18793i	−0.569232	−	0.265437i
$383$	−2.05660	−	23.5070i	−0.105087	−	1.20115i	−0.847347	−	0.531040i	$-0.821801\pi$
$383$	−2.05660	−	23.5070i	−0.105087	−	1.20115i	0.742259	−	0.670113i	$-0.233754\pi$
$384$		0			0
$385$	−15.4194	+	15.4899i	−0.785845	+	0.789436i
$386$	−3.67201	+	2.12003i	−0.186900	+	0.107907i
$387$		0			0
$388$	2.90954	+	10.8585i	0.147709	+	0.551259i
$389$	−22.3201	+	18.7287i	−1.13167	+	0.949585i	−0.999135	−	0.0415928i	$-0.986757\pi$
$389$	−22.3201	+	18.7287i	−1.13167	+	0.949585i	−0.132537	+	0.991178i	$0.542312\pi$
$390$		0			0
$391$	0.480128	−	2.72294i	0.0242811	−	0.137705i
$392$	1.44803	+	2.06800i	0.0731366	+	0.104450i
$393$		0			0
$394$	−8.37498	−	9.98091i	−0.421925	−	0.502831i
$395$	6.57518	+	1.14393i	0.330833	+	0.0575574i
$396$		0			0
$397$	5.41180	−	20.1971i	0.271610	−	1.01366i	−0.686469	−	0.727160i	$-0.740840\pi$
$397$	5.41180	−	20.1971i	0.271610	−	1.01366i	0.958079	−	0.286504i	$-0.0924933\pi$
$398$	−3.23191	−	6.93086i	−0.162001	−	0.347413i
$399$		0			0
$400$	−4.99995	+	0.0227979i	−0.249997	+	0.00113990i
$401$	0.181796	+	0.499479i	0.00907844	+	0.0249428i	0.944149	−	0.329519i	$-0.106886\pi$
$401$	0.181796	+	0.499479i	0.00907844	+	0.0249428i	−0.935071	+	0.354461i	$0.884664\pi$
$402$		0			0
$403$	19.8859	+	13.9242i	0.990585	+	0.693615i
$404$	−2.83596			−0.141094
$405$		0			0
$406$	9.33935			0.463504
$407$	−20.8119	−	14.5727i	−1.03161	−	0.722340i
$408$		0			0
$409$	−9.48042	−	26.0472i	−0.468777	−	1.28795i	−0.918725	−	0.394898i	$-0.870780\pi$
$409$	−9.48042	−	26.0472i	−0.468777	−	1.28795i	0.449948	−	0.893055i	$-0.351442\pi$
$410$	−10.2926	−	21.9418i	−0.508315	−	1.08363i
$411$		0			0
$412$	5.21166	+	11.1764i	0.256760	+	0.550624i
$413$	−0.956240	+	3.56873i	−0.0470535	+	0.175606i
$414$		0			0
$415$	−28.0086	+	19.7071i	−1.37489	+	0.967385i
$416$	−4.32626	−	5.15583i	−0.212112	−	0.252785i
$417$		0			0
$418$	−2.67628	−	3.82213i	−0.130901	−	0.186946i
$419$	−2.25043	+	12.7628i	−0.109941	+	0.623504i	0.879191	+	0.476470i	$0.158084\pi$
$419$	−2.25043	+	12.7628i	−0.109941	+	0.623504i	−0.989131	+	0.147034i	$0.953027\pi$
$420$		0			0
$421$	6.51042	−	5.46289i	0.317299	−	0.266245i	−0.470202	−	0.882559i	$-0.655819\pi$
$421$	6.51042	−	5.46289i	0.317299	−	0.266245i	0.787501	+	0.616314i	$0.211375\pi$
$422$	3.03660	+	11.3328i	0.147819	+	0.551670i
$423$		0			0
$424$	7.16787	−	4.13837i	0.348102	−	0.200977i
$425$	1.36942	−	2.97205i	0.0664268	−	0.144165i
$426$		0			0
$427$	1.34963	+	15.4264i	0.0653133	+	0.746535i
$428$	−3.64332	−	1.69891i	−0.176106	−	0.0821197i
$429$		0			0
$430$	5.48432	−	3.18307i	0.264477	−	0.153501i
$431$		−	3.57420i		−	0.172163i	−0.996288	−	0.0860815i	$-0.972565\pi$
$431$		−	3.57420i		−	0.172163i	0.996288	−	0.0860815i	$-0.0274345\pi$
$432$		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
$437$	−4.25019	+	0.371843i	−0.203314	+	0.0177877i
$438$		0			0
$439$	−1.17519	+	3.22882i	−0.0560890	+	0.154103i	−0.964573	−	0.263817i	$-0.915019\pi$
$439$	−1.17519	+	3.22882i	−0.0560890	+	0.154103i	0.908484	+	0.417920i	$0.137241\pi$
$440$	10.2900	−	0.923898i	0.490554	−	0.0440451i
$441$		0			0
$442$	4.25481	−	1.14007i	0.202381	−	0.0542277i
$443$	19.8490	+	1.73656i	0.943053	+	0.0825065i	0.548301	−	0.836281i	$-0.315275\pi$
$443$	19.8490	+	1.73656i	0.943053	+	0.0825065i	0.394752	+	0.918788i	$0.370830\pi$
$444$		0			0
$445$	−4.90332	−	27.4421i	−0.232439	−	1.30088i
$446$	12.1912	+	2.14964i	0.577269	+	0.101788i
$447$		0			0
$448$	−0.184380	+	2.10747i	−0.00871113	+	0.0995687i
$449$	7.37572	−	12.7751i	0.348082	−	0.602896i	−0.637827	−	0.770180i	$-0.720166\pi$
$449$	7.37572	−	12.7751i	0.348082	−	0.602896i	0.985909	+	0.167284i	$0.0534998\pi$
$450$		0			0
$451$	25.0390	+	43.3688i	1.17904	+	2.04216i
$452$	6.17919	−	2.88140i	0.290645	−	0.135530i
$453$		0			0
$454$	−11.1412	+	13.2775i	−0.522880	+	0.623145i
$455$	−24.3427	+	20.5207i	−1.14120	+	0.962025i
$456$		0			0
$457$	−8.47568	+	12.1045i	−0.396476	+	0.566226i	−0.966910	−	0.255117i	$-0.917886\pi$
$457$	−8.47568	+	12.1045i	−0.396476	+	0.566226i	0.570434	+	0.821343i	$0.306775\pi$
$458$	−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	0.215057	−	0.976601i	$-0.431006\pi$
$461$	16.1281	−	2.84382i	0.751162	−	0.132450i	0.536105	+	0.844151i	$0.319895\pi$
$462$		0			0
$463$	−1.91117	+	4.09851i	−0.0888194	+	0.190474i	−0.945700	−	0.325042i	$-0.894622\pi$
$463$	−1.91117	+	4.09851i	−0.0888194	+	0.190474i	0.856880	+	0.515515i	$0.172399\pi$
$464$	−3.38184	−	2.83770i	−0.156998	−	0.131737i
$465$		0			0
$466$	−8.38361	−	3.05138i	−0.388363	−	0.141353i
$467$	27.0221	+	7.24056i	1.25044	+	0.335053i	0.822505	−	0.568758i	$-0.192576\pi$
$467$	27.0221	+	7.24056i	1.25044	+	0.335053i	0.427931	+	0.903812i	$0.359243\pi$
$468$		0			0
$469$	25.3436	+	14.6322i	1.17026	+	0.675650i
$470$	−3.65414	−	2.09862i	−0.168553	−	0.0968023i
$471$		0			0
$472$	1.43060	−	1.00171i	0.0658486	−	0.0461077i
$473$	−10.7329	+	7.51525i	−0.493499	+	0.345552i
$474$		0			0
$475$	−4.97662	−	0.854134i	−0.228343	−	0.0391904i
$476$	−1.19906	−	0.692276i	−0.0549587	−	0.0317304i
$477$		0			0
$478$	1.58760	+	0.425396i	0.0726151	+	0.0194572i
$479$	18.7815	+	6.83589i	0.858146	+	0.312340i	0.733357	−	0.679844i	$-0.237952\pi$
$479$	18.7815	+	6.83589i	0.858146	+	0.312340i	0.124789	+	0.992183i	$0.460175\pi$
$480$		0			0
$481$	−28.3514	−	23.7896i	−1.29271	−	1.08471i
$482$	6.66452	−	14.2921i	0.303561	−	0.650988i
$483$		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	$0.822071\pi$
$488$	4.19849	−	5.99607i	0.190057	−	0.271429i
$489$		0			0
$490$	−5.62473	−	0.479181i	−0.254099	−	0.0216472i
$491$	−0.404039	+	0.481514i	−0.0182340	+	0.0217304i	−0.775084	−	0.631858i	$-0.782293\pi$
$491$	−0.404039	+	0.481514i	−0.0182340	+	0.0217304i	0.756850	+	0.653588i	$0.226737\pi$
$492$		0			0
$493$	2.61858	−	1.22107i	0.117935	−	0.0549940i
$494$	−3.39847	−	5.88632i	−0.152904	−	0.264838i
$495$		0			0
$496$	−1.80345	+	3.12367i	−0.0809775	+	0.140257i
$497$	−0.493285	+	5.63828i	−0.0221269	+	0.252911i
$498$		0			0
$499$	−4.16362	−	0.734159i	−0.186389	−	0.0328655i	0.0796743	−	0.996821i	$-0.474612\pi$
$499$	−4.16362	−	0.734159i	−0.186389	−	0.0328655i	−0.266064	+	0.963955i	$0.585723\pi$
$500$	7.12784	−	8.61359i	0.318767	−	0.385211i
$501$		0			0
$502$	24.6176	+	2.15376i	1.09874	+	0.0961269i
$503$	39.9551	−	10.7059i	1.78151	−	0.477354i	0.790653	−	0.612264i	$-0.209741\pi$
$503$	39.9551	−	10.7059i	1.78151	−	0.477354i	0.990858	+	0.134910i	$0.0430745\pi$
$504$		0			0
$505$	4.06509	−	4.86708i	0.180894	−	0.216582i
$506$	−6.67604	+	18.3423i	−0.296786	+	0.815414i
$507$		0			0
$508$	14.4706	−	1.26601i	0.642027	−	0.0561701i
$509$	17.2829	−	6.29047i	0.766052	−	0.278820i	0.0707079	−	0.997497i	$-0.477474\pi$
$509$	17.2829	−	6.29047i	0.766052	−	0.278820i	0.695344	+	0.718677i	$0.255252\pi$
$510$		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
$515$	−26.6515	−	7.07615i	−1.17440	−	0.311813i
$516$		0			0
$517$	7.89127	+	3.67976i	0.347058	+	0.161836i
$518$	1.01389	+	11.5888i	0.0445476	+	0.509181i
$519$		0			0
$520$	15.0497	−	0.0343104i	0.659974	−	0.00150461i
$521$	14.7763	−	8.53111i	0.647362	−	0.373755i	−0.140083	−	0.990140i	$-0.544737\pi$
$521$	14.7763	−	8.53111i	0.647362	−	0.373755i	0.787445	+	0.616385i	$0.211403\pi$
$522$		0			0
$523$	−10.0335	−	37.4455i	−0.438734	−	1.63738i	−0.731969	−	0.681338i	$-0.761398\pi$
$523$	−10.0335	−	37.4455i	−0.438734	−	1.63738i	0.293234	−	0.956041i	$-0.405268\pi$
$524$	−9.62795	+	8.07881i	−0.420599	+	0.352924i
$525$		0			0
$526$	2.36846	−	13.4322i	0.103270	−	0.585671i
$527$	−1.35400	−	1.93371i	−0.0589811	−	0.0842337i
$528$		0			0
$529$	−3.31161	−	3.94662i	−0.143983	−	0.171592i
$530$	−3.17221	+	18.2335i	−0.137792	+	0.792011i
$531$		0			0
$532$	−0.552946	+	2.06362i	−0.0239732	+	0.0894693i
$533$	30.8296	+	66.1143i	1.33538	+	2.86373i
$534$		0			0
$535$	8.13802	−	3.81743i	0.351837	−	0.165042i
$536$	−4.73121	−	12.9989i	−0.204357	−	0.561467i
$537$		0			0
$538$	−22.6740	−	15.8765i	−0.977545	−	0.684484i
$539$	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	$0.341405\pi$
$542$	3.54351	+	2.48119i	0.152207	+	0.106576i
$543$		0			0
$544$	0.223843	+	0.615004i	0.00959719	+	0.0263681i
$545$	0.983205	−	2.72061i	0.0421159	−	0.116538i
$546$		0			0
$547$	−3.20848	−	6.88060i	−0.137185	−	0.294193i	0.825699	−	0.564111i	$-0.190781\pi$
$547$	−3.20848	−	6.88060i	−0.137185	−	0.294193i	−0.962883	+	0.269918i	$0.913003\pi$
$548$	1.47328	−	5.49834i	0.0629353	−	0.234878i
$549$		0			0
$550$	−13.1641	+	18.9839i	−0.561320	+	0.809478i
$551$	−2.86573	−	3.41524i	−0.122084	−	0.145494i
$552$		0			0
$553$	3.62165	+	5.17225i	0.154008	+	0.219947i
$554$	−0.0167633	+	0.0950696i	−0.000712206	+	0.00403912i
$555$		0			0
$556$	−7.96357	+	6.68223i	−0.337731	+	0.283390i
$557$	0.494965	+	1.84723i	0.0209723	+	0.0782698i	0.975619	−	0.219472i	$-0.0704333\pi$
$557$	0.494965	+	1.84723i	0.0209723	+	0.0782698i	−0.954647	+	0.297741i	$0.903767\pi$
$558$		0			0
$559$	−16.5293	+	9.54322i	−0.699117	+	0.403635i
$560$	−3.35255	−	3.33730i	−0.141671	−	0.141027i
$561$		0			0
$562$	1.43654	+	16.4197i	0.0605967	+	0.692623i
$563$	−28.8616	−	13.4584i	−1.21637	−	0.567203i	−0.294854	−	0.955542i	$-0.595271\pi$
$563$	−28.8616	−	13.4584i	−1.21637	−	0.567203i	−0.921516	+	0.388340i	$0.873049\pi$
$564$		0			0
$565$	−3.91224	+	14.7350i	−0.164589	+	0.619904i
$566$			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	$-0.00353923\pi$
$569$	1.34776	+	7.64350i	0.0565009	+	0.320432i	−0.943437	+	0.331551i	$0.892428\pi$
$570$		0			0
$571$	−11.3216	+	4.12074i	−0.473796	+	0.172447i	−0.567871	−	0.823118i	$-0.692233\pi$
$571$	−11.3216	+	4.12074i	−0.473796	+	0.172447i	0.0940754	+	0.995565i	$0.470011\pi$
$572$	−30.9785	+	2.71027i	−1.29528	+	0.113322i
$573$		0			0
$574$	7.84231	−	21.5466i	0.327332	−	0.899337i
$575$	9.01437	+	19.1035i	0.375925	+	0.796670i
$576$		0			0
$577$	−8.72015	+	2.33656i	−0.363024	+	0.0972721i	−0.435720	−	0.900082i	$-0.643506\pi$
$577$	−8.72015	+	2.33656i	−0.363024	+	0.0972721i	0.0726960	+	0.997354i	$0.476840\pi$
$578$	16.5086	+	1.44432i	0.686667	+	0.0600756i
$579$		0			0
$580$	9.71762	−	1.73633i	0.403502	−	0.0720972i
$581$	−31.9084	−	5.62632i	−1.32378	−	0.233419i
$582$		0			0
$583$	3.33294	−	38.0957i	0.138036	−	1.57776i
$584$	7.20853	−	12.4855i	0.298291	−	0.516655i
$585$		0			0
$586$	−9.79932	−	16.9729i	−0.404806	−	0.701145i
$587$	−1.39549	+	0.650726i	−0.0575979	+	0.0268583i	−0.451204	−	0.892421i	$-0.649005\pi$
$587$	−1.39549	+	0.650726i	−0.0575979	+	0.0268583i	0.393606	+	0.919279i	$0.371227\pi$
$588$		0			0
$589$	−2.34138	+	2.79034i	−0.0964747	+	0.114974i
$590$	−0.331486	+	3.89106i	−0.0136471	+	0.160192i
$591$		0			0
$592$	3.15404	−	4.50443i	0.129630	−	0.185131i
$593$	−3.61163	−	3.61163i	−0.148312	−	0.148312i	0.629052	−	0.777363i	$-0.283443\pi$
$593$	−3.61163	−	3.61163i	−0.148312	−	0.148312i	−0.777363	+	0.629052i	$0.783443\pi$
$594$		0			0
$595$	2.90682	−	1.06551i	0.119168	−	0.0436816i
$596$	−6.11157	+	1.07764i	−0.250340	+	0.0441417i
$597$		0			0
$598$	−12.0168	+	25.7701i	−0.491403	+	1.05382i
$599$	9.40405	+	7.89093i	0.384239	+	0.322415i	0.814364	−	0.580355i	$-0.197086\pi$
$599$	9.40405	+	7.89093i	0.384239	+	0.322415i	−0.430125	+	0.902769i	$0.641531\pi$
$600$		0			0
$601$	−1.70889	−	0.621984i	−0.0697070	−	0.0253713i	0.306931	−	0.951732i	$-0.400698\pi$
$601$	−1.70889	−	0.621984i	−0.0697070	−	0.0253713i	−0.376638	+	0.926360i	$0.622920\pi$
$602$	5.79484	+	1.55272i	0.236180	+	0.0632843i
$603$		0			0
$604$	12.1480	+	7.01365i	0.494295	+	0.285381i
$605$	11.5230	−	20.0639i	0.468476	−	0.815713i
$606$		0			0
$607$	−12.0209	+	8.41715i	−0.487915	+	0.341641i	−0.791507	−	0.611161i	$-0.790703\pi$
$607$	−12.0209	+	8.41715i	−0.487915	+	0.341641i	0.303592	+	0.952802i	$0.401814\pi$
$608$	0.827243	−	0.579242i	0.0335491	−	0.0234914i
$609$		0			0
$610$	4.27230	+	15.8003i	0.172980	+	0.639734i
$611$	10.9844	+	6.34182i	0.444379	+	0.256563i
$612$		0			0
$613$	−4.90665	−	1.31473i	−0.198178	−	0.0531016i	0.158365	−	0.987381i	$-0.449378\pi$
$613$	−4.90665	−	1.31473i	−0.198178	−	0.0531016i	−0.356543	+	0.934279i	$0.616045\pi$
$614$	18.9266	+	6.88871i	0.763815	+	0.278006i
$615$		0			0
$616$	7.48762	+	6.28286i	0.301685	+	0.253144i
$617$	8.66586	−	18.5840i	0.348875	−	0.748164i	−0.651067	−	0.759021i	$-0.725678\pi$
$617$	8.66586	−	18.5840i	0.348875	−	0.748164i	0.999941	+	0.0108568i	$0.00345589\pi$
$618$		0			0
$619$	42.8351	−	7.55298i	1.72169	−	0.303580i	0.776501	−	0.630116i	$-0.216993\pi$
$619$	42.8351	−	7.55298i	1.72169	−	0.303580i	0.945185	+	0.326536i	$0.105881\pi$
$620$	−2.77576	−	7.57259i	−0.111477	−	0.304122i
$621$		0			0
$622$	−2.26271	−	2.26271i	−0.0907265	−	0.0907265i
$623$	15.1274	−	21.6042i	0.606068	−	0.865555i
$624$		0			0
$625$	4.56554	+	24.5796i	0.182621	+	0.983183i
$626$	14.2048	−	16.9286i	0.567739	−	0.676605i
$627$		0			0
$628$	22.6053	−	10.5410i	0.902048	−	0.420632i
$629$	1.79944	+	3.11672i	0.0717484	+	0.124272i
$630$		0			0
$631$	−13.9920	+	24.2349i	−0.557013	+	0.964775i	0.440731	+	0.897639i	$0.354719\pi$
$631$	−13.9920	+	24.2349i	−0.557013	+	0.964775i	−0.997744	+	0.0671358i	$0.978614\pi$
$632$	0.260132	−	2.97332i	0.0103475	−	0.118272i
$633$		0			0
$634$	−6.35665	−	1.12085i	−0.252455	−	0.0445146i
$635$	−18.5695	+	26.6491i	−0.736908	+	1.05754i
$636$		0			0
$637$	16.9268	+	1.48091i	0.670665	+	0.0586756i
$638$	−19.7022	+	5.27919i	−0.780018	+	0.209005i
$639$		0			0
$640$	0.199964	+	2.22711i	0.00790427	+	0.0880342i
$641$	1.93139	−	5.30644i	0.0762852	−	0.209592i	−0.895688	−	0.444683i	$-0.853316\pi$
$641$	1.93139	−	5.30644i	0.0762852	−	0.209592i	0.971973	+	0.235091i	$0.0755387\pi$
$642$		0			0
$643$	−20.0479	+	1.75397i	−0.790614	+	0.0691697i	−0.475307	−	0.879820i	$-0.657663\pi$
$643$	−20.0479	+	1.75397i	−0.790614	+	0.0691697i	−0.315307	+	0.948990i	$0.602107\pi$
$644$	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	−0.557223	−	0.830363i	$-0.688133\pi$
$647$	6.94763	−	6.94763i	0.273139	−	0.273139i	0.830363	+	0.557223i	$0.188133\pi$
$648$		0			0
$649$		−	8.06910i		−	0.316740i
$650$	−21.5135	+	25.8775i	−0.843829	+	1.01500i
$651$		0			0
$652$	2.34950	+	1.09559i	0.0920134	+	0.0429065i
$653$	0.623992	+	7.13226i	0.0244187	+	0.279107i	0.998581	+	0.0532571i	$0.0169603\pi$
$653$	0.623992	+	7.13226i	0.0244187	+	0.279107i	−0.974162	+	0.225850i	$0.927484\pi$
$654$		0			0
$655$	−0.0640709	−	28.1037i	−0.00250346	−	1.09810i
$656$	−9.38654	+	5.41932i	−0.366483	+	0.211589i
$657$		0			0
$658$	−1.03184	−	3.85088i	−0.0402254	−	0.150123i
$659$	14.1465	−	11.8703i	0.551070	−	0.462403i	−0.324233	−	0.945977i	$-0.605106\pi$
$659$	14.1465	−	11.8703i	0.551070	−	0.462403i	0.875303	+	0.483575i	$0.160662\pi$
$660$		0			0
$661$	−0.176638	+	1.00176i	−0.00687041	+	0.0389640i	−0.988050	−	0.154132i	$-0.950742\pi$
$661$	−0.176638	+	1.00176i	−0.00687041	+	0.0389640i	0.981180	+	0.193096i	$0.0618529\pi$
$662$	14.7208	+	21.0235i	0.572141	+	0.817102i
$663$		0			0
$664$	9.84473	+	11.7325i	0.382050	+	0.455309i
$665$	−2.74899	−	3.90698i	−0.106601	−	0.151506i
$666$		0			0
$667$	−4.82715	+	18.0152i	−0.186908	+	0.697550i
$668$	4.63032	+	9.92976i	0.179153	+	0.384194i
$669$		0			0
$670$	29.0905	+	10.5130i	1.12386	+	0.406153i
$671$	−11.5671	−	31.7805i	−0.446544	−	1.22687i
$672$		0			0
$673$	17.1068	+	11.9783i	0.659421	+	0.461731i	0.854773	−	0.519002i	$-0.173696\pi$
$673$	17.1068	+	11.9783i	0.659421	+	0.461731i	−0.195353	+	0.980733i	$0.562585\pi$
$674$	−22.6803			−0.873612
$675$		0			0
$676$	−32.2991			−1.24227
$677$	18.1346	+	12.6980i	0.696970	+	0.488023i	0.867569	−	0.497317i	$-0.165681\pi$
$677$	18.1346	+	12.6980i	0.696970	+	0.488023i	−0.170599	+	0.985341i	$0.554570\pi$
$678$		0			0
$679$	−8.13386	−	22.3476i	−0.312149	−	0.857622i
$680$	−1.37633	−	0.497392i	−0.0527797	−	0.0190741i
$681$		0			0
$682$	7.04296	+	15.1037i	0.269689	+	0.578350i
$683$	−7.57881	+	28.2845i	−0.289995	+	1.08228i	0.655116	+	0.755528i	$0.272620\pi$
$683$	−7.57881	+	28.2845i	−0.289995	+	1.08228i	−0.945111	+	0.326748i	$0.894047\pi$
$684$		0			0
$685$	7.32445	+	10.4098i	0.279853	+	0.397738i
$686$	−12.9518	−	15.4354i	−0.494502	−	0.589325i
$687$		0			0
$688$	−1.62657	−	2.32298i	−0.0620122	−	0.0885627i
$689$	9.67329	−	54.8600i	0.368523	−	2.09000i
$690$		0			0
$691$	18.9434	−	15.8954i	0.720640	−	0.604689i	−0.206922	−	0.978357i	$-0.566345\pi$
$691$	18.9434	−	15.8954i	0.720640	−	0.604689i	0.927562	+	0.373669i	$0.121900\pi$
$692$	−4.46666	−	16.6698i	−0.169797	−	0.633690i
$693$		0			0
$694$	−11.0888	+	6.40210i	−0.420924	+	0.243020i
$695$	−0.0529950	−	23.2454i	−0.00201022	−	0.881750i
$696$		0			0
$697$	−0.618248	−	7.06661i	−0.0234178	−	0.267667i
$698$	0.891346	+	0.415642i	0.0337379	+	0.0157323i
$699$		0			0
$700$	10.5330	−	0.969936i	0.398112	−	0.0366601i
$701$		−	34.8732i		−	1.31714i	−0.752519	−	0.658571i	$-0.771161\pi$
$701$		−	34.8732i		−	1.31714i	0.752519	−	0.658571i	$-0.228839\pi$
$702$		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
$707$	5.97671	−	0.522894i	0.224777	−	0.0196655i
$708$		0			0
$709$	10.6201	−	29.1786i	0.398848	−	1.09583i	−0.563998	−	0.825776i	$-0.690738\pi$
$709$	10.6201	−	29.1786i	0.398848	−	1.09583i	0.962846	−	0.270050i	$-0.0870402\pi$
$710$	0.534979	+	5.95835i	0.0200774	+	0.223613i
$711$		0			0
$712$	−12.0420	+	3.22666i	−0.451295	+	0.120924i
$713$	15.1801	+	1.32809i	0.568499	+	0.0497372i
$714$		0			0
$715$	39.7535	−	57.0503i	1.48670	−	2.13356i
$716$	21.1419	+	3.72789i	0.790110	+	0.139318i
$717$		0			0
$718$	2.19049	−	25.0375i	0.0817485	−	0.934389i
$719$	−12.1648	+	21.0700i	−0.453670	+	0.785779i	−0.998611	−	0.0526953i	$-0.983219\pi$
$719$	−12.1648	+	21.0700i	−0.453670	+	0.785779i	0.544941	+	0.838475i	$0.316552\pi$
$720$		0			0
$721$	−13.0441	−	22.5931i	−0.485790	−	0.841412i
$722$	−16.2955	+	7.59874i	−0.606458	+	0.282796i
$723$		0			0
$724$	−7.12404	+	8.49010i	−0.264763	+	0.315532i
$725$	−10.9494	+	19.1662i	−0.406651	+	0.711816i
$726$		0			0
$727$	20.3929	−	29.1241i	0.756332	−	1.08015i	−0.237729	−	0.971331i	$-0.576403\pi$
$727$	20.3929	−	29.1241i	0.756332	−	1.08015i	0.994061	−	0.108823i	$-0.0347081\pi$
$728$	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
$733$	−2.57930	+	5.53133i	−0.0952687	+	0.204304i	−0.948167	−	0.317773i	$-0.897065\pi$
$733$	−2.57930	+	5.53133i	−0.0952687	+	0.204304i	0.852898	+	0.522077i	$0.174843\pi$
$734$	−0.768665	−	0.644986i	−0.0283719	−	0.0238069i
$735$		0			0
$736$	−3.96992	−	1.44493i	−0.146333	−	0.0532609i
$737$	−61.7357	−	16.5420i	−2.27406	−	0.609334i
$738$		0			0
$739$	1.19508	+	0.689982i	0.0439618	+	0.0253814i	0.521820	−	0.853056i	$-0.325253\pi$
$739$	1.19508	+	0.689982i	0.0439618	+	0.0253814i	−0.477858	+	0.878437i	$0.658587\pi$
$740$	3.20948	+	11.8696i	0.117983	+	0.436337i
$741$		0			0
$742$	−14.3430	+	10.0431i	−0.526550	+	0.368694i
$743$	−1.16602	+	0.816455i	−0.0427771	+	0.0299528i	−0.594769	−	0.803896i	$-0.702757\pi$
$743$	−1.16602	+	0.816455i	−0.0427771	+	0.0299528i	0.551992	+	0.833849i	$0.313868\pi$
$744$		0			0
$745$	6.91094	−	12.0334i	0.253197	−	0.440869i
$746$	−2.26111	−	1.30545i	−0.0827851	−	0.0477960i
$747$		0			0
$748$	2.92084	+	0.782636i	0.106796	+	0.0286160i
$749$	7.99143	+	2.90864i	0.292001	+	0.106280i
$750$		0			0
$751$	−30.1408	−	25.2911i	−1.09985	−	0.922886i	−0.102437	−	0.994739i	$-0.532664\pi$
$751$	−30.1408	−	25.2911i	−1.09985	−	0.922886i	−0.997415	+	0.0718539i	$0.977108\pi$
$752$	−0.796430	+	1.70795i	−0.0290428	+	0.0622825i
$753$		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	$0.742461\pi$
$758$	10.5711	−	15.0971i	0.383959	−	0.548351i
$759$		0			0
$760$	−0.191682	+	2.25000i	−0.00695304	+	0.0816162i
$761$	−11.2508	+	13.4081i	−0.407840	+	0.486044i	−0.930394	−	0.366562i	$-0.880535\pi$
$761$	−11.2508	+	13.4081i	−0.407840	+	0.486044i	0.522554	+	0.852606i	$0.324979\pi$
$762$		0			0
$763$	2.48045	−	1.15665i	0.0897983	−	0.0418736i
$764$	−6.13784	−	10.6311i	−0.222059	−	0.384618i
$765$		0			0
$766$	11.7984	−	20.4354i	0.426294	−	0.738363i
$767$	1.02446	−	11.7096i	0.0369910	−	0.422809i
$768$		0			0
$769$	11.7918	+	2.07921i	0.425223	+	0.0749783i	0.382165	−	0.924094i	$-0.375179\pi$
$769$	11.7918	+	2.07921i	0.425223	+	0.0749783i	0.0430584	+	0.999073i	$0.486290\pi$
$770$	−21.5154	+	3.84435i	−0.775363	+	0.138541i
$771$		0			0
$772$	−4.22393	−	0.369546i	−0.152023	−	0.0133003i
$773$	20.4487	−	5.47920i	0.735487	−	0.197073i	0.128416	−	0.991720i	$-0.459011\pi$
$773$	20.4487	−	5.47920i	0.735487	−	0.197073i	0.607071	+	0.794647i	$0.292344\pi$
$774$		0			0
$775$	16.9749	+	6.09084i	0.609755	+	0.218789i
$776$	−3.84485	+	10.5636i	−0.138022	+	0.379212i
$777$		0			0
$778$	−29.0259	+	2.53944i	−1.04063	+	0.0910432i
$779$	−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
$785$	−14.3121	+	53.9047i	−0.510820	+	1.92394i
$786$		0			0
$787$	34.5659	+	16.1184i	1.23214	+	0.574557i	0.926034	−	0.377439i	$-0.123195\pi$
$787$	34.5659	+	16.1184i	1.23214	+	0.574557i	0.306108	+	0.951997i	$0.400973\pi$
$788$	−1.13557	−	12.9796i	−0.0404528	−	0.462378i
$789$		0			0
$790$	4.72994	+	4.70842i	0.168284	+	0.167518i
$791$	−12.4912	+	7.21180i	−0.444136	+	0.256422i
$792$		0			0
$793$	−12.7510	−	47.5873i	−0.452800	−	1.68987i
$794$	16.0177	−	13.4404i	0.568446	−	0.476983i
$795$		0			0
$796$	1.32795	−	7.53118i	0.0470679	−	0.266936i
$797$	−15.7279	−	22.4618i	−0.557111	−	0.795636i	0.437511	−	0.899213i	$-0.355860\pi$
$797$	−15.7279	−	22.4618i	−0.557111	−	0.795636i	−0.994621	+	0.103577i	$0.966971\pi$
$798$		0			0
$799$	−0.792790	−	0.944811i	−0.0280469	−	0.0334250i
$800$	−4.10879	−	2.84918i	−0.145268	−	0.100734i
$801$		0			0
$802$	−0.137571	+	0.513423i	−0.00485781	+	0.0181296i
$803$	−28.1512	−	60.3705i	−0.993435	−	2.13043i
$804$		0			0
$805$	−6.79235	+	18.7950i	−0.239399	+	0.662438i
$806$	8.30293	+	22.8121i	0.292458	+	0.803522i
$807$		0			0
$808$	−2.32308	−	1.62664i	−0.0817258	−	0.0572250i
$809$	−25.0745			−0.881574			−0.440787	−	0.897612i	$-0.645301\pi$
$809$	−25.0745			−0.881574			−0.440787	+	0.897612i	$0.645301\pi$
$810$		0			0
$811$	−30.7391			−1.07939			−0.539697	−	0.841859i	$-0.681461\pi$
$811$	−30.7391			−1.07939			−0.539697	+	0.841859i	$0.681461\pi$
$812$	7.65035	+	5.35683i	0.268475	+	0.187988i
$813$		0			0
$814$	−8.68959	−	23.8745i	−0.304570	−	0.836799i
$815$	−5.24803	+	2.46178i	−0.183831	+	0.0862324i
$816$		0			0
$817$	−1.21031	−	2.59552i	−0.0423434	−	0.0908058i
$818$	7.17418	−	26.7744i	0.250839	−	0.936145i
$819$		0			0
$820$	4.15410	−	23.8773i	0.145068	−	0.833831i
$821$	−31.7068	−	37.7867i	−1.10657	−	1.31876i	−0.943210	−	0.332198i	$-0.892210\pi$
$821$	−31.7068	−	37.7867i	−1.10657	−	1.31876i	−0.163365	−	0.986566i	$-0.552235\pi$
$822$		0			0
$823$	−18.1137	−	25.8690i	−0.631404	−	0.901738i	0.368204	−	0.929745i	$-0.379973\pi$
$823$	−18.1137	−	25.8690i	−0.631404	−	0.901738i	−0.999608	+	0.0280071i	$0.991084\pi$
$824$	−2.14140	+	12.1445i	−0.0745993	+	0.423074i
$825$		0			0
$826$	−2.83025	+	2.37486i	−0.0984769	+	0.0826319i
$827$	3.54994	+	13.2486i	0.123443	+	0.460697i	0.999779	−	0.0210031i	$-0.00668600\pi$
$827$	3.54994	+	13.2486i	0.123443	+	0.460697i	−0.876336	+	0.481700i	$0.840019\pi$
$828$		0			0
$829$	27.7273	−	16.0084i	0.963010	−	0.555994i	0.0659121	−	0.997825i	$-0.479004\pi$
$829$	27.7273	−	16.0084i	0.963010	−	0.555994i	0.897098	+	0.441831i	$0.145671\pi$
$830$	−34.2468	+	0.0780760i	−1.18872	+	0.00271006i
$831$		0			0
$832$	−0.586598	−	6.70485i	−0.0203366	−	0.232449i
$833$	−1.49746	−	0.698275i	−0.0518838	−	0.0241938i
$834$		0			0
$835$	−23.6786	−	6.28683i	−0.819431	−	0.217565i
$836$		−	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	$-0.105344\pi$
$839$	−1.56707	−	8.88729i	−0.0541013	−	0.306823i	−0.999836	+	0.0181166i	$0.994233\pi$
$840$		0			0
$841$	8.93705	−	3.25282i	0.308174	−	0.112166i
$842$	8.46641	−	0.740715i	0.291772	−	0.0255267i
$843$		0			0
$844$	−4.01276	+	11.0250i	−0.138125	+	0.379495i
$845$	46.2977	−	55.4317i	1.59269	−	1.90691i
$846$		0			0
$847$	21.1442	−	5.66557i	0.726523	−	0.194671i
$848$	8.24524	+	0.721365i	0.283143	+	0.0247718i
$849$		0			0
$850$	2.82646	−	1.64909i	0.0969468	−	0.0565632i
$851$	−22.8782	−	4.03405i	−0.784256	−	0.138285i
$852$		0			0
$853$	−2.10428	+	24.0520i	−0.0720492	+	0.823526i	0.871089	+	0.491125i	$0.163414\pi$
$853$	−2.10428	+	24.0520i	−0.0720492	+	0.823526i	−0.943138	+	0.332401i	$0.892141\pi$
$854$	−7.74265	+	13.4107i	−0.264948	+	0.458904i
$855$		0			0
$856$	−2.00998	−	3.48138i	−0.0686996	−	0.118991i
$857$	30.0532	−	14.0140i	1.02660	−	0.478710i	0.164996	−	0.986294i	$-0.447239\pi$
$857$	30.0532	−	14.0140i	1.02660	−	0.478710i	0.861602	+	0.507584i	$0.169461\pi$
$858$		0			0
$859$	−30.6829	+	36.5664i	−1.04689	+	1.24763i	−0.0788321	+	0.996888i	$0.525119\pi$
$859$	−30.6829	+	36.5664i	−1.04689	+	1.24763i	−0.968054	+	0.250742i	$0.919325\pi$
$860$	6.31822	+	0.538261i	0.215450	+	0.0183546i
$861$		0			0
$862$	2.05007	−	2.92781i	0.0698258	−	0.0997216i
$863$	22.5058	+	22.5058i	0.766105	+	0.766105i	0.977418	−	0.211313i	$-0.0677740\pi$
$863$	22.5058	+	22.5058i	0.766105	+	0.766105i	−0.211313	+	0.977418i	$0.567774\pi$
$864$		0			0
$865$	35.0112	+	16.2289i	1.19042	+	0.551800i
$866$	−39.7083	+	7.00164i	−1.34934	+	0.237925i
$867$		0			0
$868$	3.22479	−	6.91558i	0.109456	−	0.234730i
$869$	−10.5639	−	8.86415i	−0.358355	−	0.300696i
$870$		0			0
$871$	−87.4885	−	31.8432i	−2.96444	−	1.07897i
$872$	−1.24963	−	0.334837i	−0.0423178	−	0.0113390i
$873$		0			0
$874$	−3.69483	−	2.13321i	−0.124980	−	0.0721570i
$875$	−13.4335	+	19.4671i	−0.454137	+	0.658109i
$876$		0			0
$877$	25.8734	−	18.1168i	0.873684	−	0.611760i	−0.0483666	−	0.998830i	$-0.515402\pi$
$877$	25.8734	−	18.1168i	0.873684	−	0.611760i	0.922051	+	0.387070i	$0.126513\pi$
$878$	−2.81464	+	1.97083i	−0.0949895	+	0.0665123i
$879$		0			0
$880$	8.95897	+	5.14526i	0.302007	+	0.173447i
$881$	−33.8539	−	19.5455i	−1.14057	−	0.658506i	−0.193995	−	0.981003i	$-0.562145\pi$
$881$	−33.8539	−	19.5455i	−1.14057	−	0.658506i	−0.946571	+	0.322497i	$0.895478\pi$
$882$		0			0
$883$	3.82015	+	1.02361i	0.128558	+	0.0344471i	0.322524	−	0.946561i	$-0.395469\pi$
$883$	3.82015	+	1.02361i	0.128558	+	0.0344471i	−0.193966	+	0.981008i	$0.562135\pi$
$884$	4.13926	+	1.50657i	0.139218	+	0.0506713i
$885$		0			0
$886$	15.2633	+	12.8074i	0.512780	+	0.430273i
$887$	14.4274	−	30.9397i	0.484426	−	1.03885i	−0.500478	−	0.865749i	$-0.666842\pi$
$887$	14.4274	−	30.9397i	0.484426	−	1.03885i	0.984903	−	0.173105i	$-0.0553799\pi$
$888$		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
$893$	−1.09159	+	1.55895i	−0.0365286	+	0.0521683i
$894$		0			0
$895$	−36.7028	+	30.9401i	−1.22684	+	1.03421i
$896$	−1.35983	+	1.62058i	−0.0454288	+	0.0541399i
$897$		0			0
$898$	13.3694	−	6.23423i	0.446141	−	0.208039i
$899$	7.96167	+	13.7900i	0.265537	+	0.459923i
$900$		0			0
$901$	−2.70845	+	4.69118i	−0.0902316	+	0.156286i
$902$	−4.36458	+	49.8874i	−0.145325	+	1.66107i
$903$		0			0
$904$	6.71440	+	1.18393i	0.223318	+	0.0393769i
$905$	−4.35905	−	24.3960i	−0.144900	−	0.810952i
$906$		0			0
$907$	−14.3371	−	1.25434i	−0.476056	−	0.0416495i	−0.153397	−	0.988165i	$-0.549021\pi$
$907$	−14.3371	−	1.25434i	−0.476056	−	0.0416495i	−0.322659	+	0.946515i	$0.604577\pi$
$908$	−16.7420	+	4.48600i	−0.555602	+	0.148873i
$909$		0			0
$910$	−31.7105	+	2.84717i	−1.05119	+	0.0943829i
$911$	−5.42614	+	14.9082i	−0.179776	+	0.493931i	−0.996547	−	0.0830314i	$-0.973540\pi$
$911$	−5.42614	+	14.9082i	−0.179776	+	0.493931i	0.816771	+	0.576962i	$0.195762\pi$
$912$		0			0
$913$	70.4941	−	6.16743i	2.33301	−	0.204112i
$914$	−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	$-0.113448\pi$
$920$	8.17030	−	4.74199i	0.269367	−	0.156339i
$921$		0			0
$922$	14.8425	+	6.92119i	0.488813	+	0.227937i
$923$	−1.56937	−	17.9380i	−0.0516564	−	0.590436i
$924$		0			0
$925$	−24.9712	−	11.5059i	−0.821048	−	0.378313i
$926$	−3.91634	+	2.26110i	−0.128699	+	0.0743044i
$927$		0			0
$928$	−1.14260	−	4.26425i	−0.0375078	−	0.139981i
$929$	−16.0779	+	13.4909i	−0.527497	+	0.442623i	−0.867236	−	0.497897i	$-0.834106\pi$
$929$	−16.0779	+	13.4909i	−0.527497	+	0.442623i	0.339739	+	0.940520i	$0.389661\pi$
$930$		0			0
$931$	−0.442716	+	2.51077i	−0.0145094	+	0.0822871i
$932$	−5.11725	−	7.30819i	−0.167621	−	0.239388i
$933$		0			0
$934$	17.9822	+	21.4304i	0.588396	+	0.701223i
$935$	−5.52991	+	3.89091i	−0.180848	+	0.127246i
$936$		0			0
$937$	5.53418	−	20.6538i	0.180794	−	0.674732i	−0.814698	−	0.579885i	$-0.803097\pi$
$937$	5.53418	−	20.6538i	0.180794	−	0.674732i	0.995492	−	0.0948464i	$-0.0302360\pi$
$938$	12.3676	+	26.5225i	0.403817	+	0.865989i
$939$		0			0
$940$	−1.78957	−	3.81502i	−0.0583694	−	0.124432i
$941$	9.45573	+	25.9794i	0.308248	+	0.846904i	0.992999	+	0.118127i	$0.0376889\pi$
$941$	9.45573	+	25.9794i	0.308248	+	0.846904i	−0.684751	+	0.728777i	$0.740089\pi$
$942$		0			0
$943$	37.5089	+	26.2640i	1.22146	+	0.855275i
$944$	1.74644			0.0568417
$945$		0			0
$946$	−13.1024			−0.425997
$947$	−14.1320	−	9.89530i	−0.459227	−	0.321554i	0.320969	−	0.947090i	$-0.395992\pi$
$947$	−14.1320	−	9.89530i	−0.459227	−	0.321554i	−0.780196	+	0.625536i	$0.784880\pi$
$948$		0			0
$949$	−33.1874	−	91.1816i	−1.07731	−	2.95988i
$950$	−3.58670	−	3.55414i	−0.116368	−	0.115311i
$951$		0			0
$952$	−0.585137	−	1.25483i	−0.0189644	−	0.0406693i
$953$	−10.4730	+	39.0858i	−0.339254	+	1.26611i	0.559930	+	0.828540i	$0.310828\pi$
$953$	−10.4730	+	39.0858i	−0.339254	+	1.26611i	−0.899183	+	0.437572i	$0.855839\pi$
$954$		0			0
$955$	27.0430	+	4.70487i	0.875092	+	0.152246i
$956$	1.05649	+	1.25907i	0.0341693	+	0.0407214i
$957$		0			0
$958$	11.4640	+	16.3722i	0.370384	+	0.528963i
$959$	−2.09111	+	11.8593i	−0.0675253	+	0.382955i
$960$		0			0
$961$	−13.7813	+	11.5639i	−0.444558	+	0.373029i
$962$	−9.57892	−	35.7490i	−0.308837	−	1.15259i
$963$		0			0
$964$	13.6569	−	7.88480i	0.439858	−	0.253952i
$965$	6.68884	−	6.71940i	0.215321	−	0.216305i
$966$		0			0
$967$	1.13679	+	12.9935i	0.0365566	+	0.417844i	0.992319	+	0.123705i	$0.0394775\pi$
$967$	1.13679	+	12.9935i	0.0365566	+	0.417844i	−0.955762	+	0.294140i	$0.904967\pi$
$968$	−9.37789	−	4.37298i	−0.301417	−	0.140553i
$969$		0			0
$970$	−12.6181	−	21.7405i	−0.405142	−	0.698046i
$971$		−	0.324954i		−	0.0104283i	−0.999986	−	0.00521414i	$-0.998340\pi$
$971$		−	0.324954i		−	0.0104283i	0.999986	−	0.00521414i	$-0.00165972\pi$
$972$		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
$977$	46.7953	−	4.09406i	1.49711	−	0.130980i	0.691049	−	0.722808i	$-0.257149\pi$
$977$	46.7953	−	4.09406i	1.49711	−	0.130980i	0.806065	+	0.591828i	$0.201593\pi$
$978$		0			0
$979$	−19.7006	+	54.1271i	−0.629635	+	1.72991i
$980$	−4.33266	−	3.61873i	−0.138402	−	0.115596i
$981$		0			0
$982$	−0.607154	+	0.162687i	−0.0193751	+	0.00519154i
$983$	4.95973	+	0.433920i	0.158191	+	0.0138399i	0.165976	−	0.986130i	$-0.446923\pi$
$983$	4.95973	+	0.433920i	0.158191	+	0.0138399i	−0.00778525	+	0.999970i	$0.502478\pi$
$984$		0			0
$985$	23.9033	+	16.6562i	0.761621	+	0.530710i
$986$	2.84539	+	0.501720i	0.0906158	+	0.0159780i
$987$		0			0
$988$	0.592392	−	6.77107i	0.0188465	−	0.215416i
$989$	−5.99026	+	10.3754i	−0.190479	+	0.329920i
$990$		0			0
$991$	1.07297	+	1.85843i	0.0340839	+	0.0590350i	0.882564	−	0.470192i	$-0.155815\pi$
$991$	1.07297	+	1.85843i	0.0340839	+	0.0590350i	−0.848480	+	0.529227i	$0.822482\pi$
$992$	−3.26897	+	1.52435i	−0.103790	+	0.0483980i
$993$		0			0
$994$	−3.63806	+	4.33567i	−0.115392	+	0.137519i
$995$	11.0215	+	13.0743i	0.349405	+	0.414482i
$996$		0			0
$997$	−34.2483	+	48.9117i	−1.08466	+	1.54905i	−0.275640	+	0.961261i	$0.588890\pi$
$997$	−34.2483	+	48.9117i	−1.08466	+	1.54905i	−0.809016	+	0.587787i	$0.799999\pi$
$998$	−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.557.10		216
3.2	odd	2		270.2.r.a.257.9	yes	216
5.3	odd	4	inner	810.2.s.a.233.14		216
15.8	even	4		270.2.r.a.203.5	yes	216
27.2	odd	18	inner	810.2.s.a.737.14		216
27.25	even	9		270.2.r.a.137.5	yes	216
135.83	even	36	inner	810.2.s.a.413.10		216
135.133	odd	36		270.2.r.a.83.9	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.9	✓	216	135.133	odd	36
270.2.r.a.137.5	yes	216	27.25	even	9
270.2.r.a.203.5	yes	216	15.8	even	4
270.2.r.a.257.9	yes	216	3.2	odd	2
810.2.s.a.233.14		216	5.3	odd	4	inner
810.2.s.a.413.10		216	135.83	even	36	inner
810.2.s.a.557.10		216	1.1	even	1	trivial
810.2.s.a.737.14		216	27.2	odd	18	inner

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)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-2.10295 - 0.759988i) q^{5} +(-0.894058 - 1.91731i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-1.28673 - 1.82875i) q^{10} +(2.96988 + 3.53937i) q^{11} +(3.86043 + 5.51327i) q^{13} +(0.367357 - 2.08338i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.169390 - 0.632172i) q^{17} +(-0.874579 + 0.504939i) q^{19} +(-0.00509778 - 2.23606i) q^{20} +(0.402687 + 4.60274i) q^{22} +(3.82887 + 1.78543i) q^{23} +(3.84484 + 3.19644i) q^{25} +6.73046i q^{26} +(1.49590 - 1.49590i) q^{28} +(0.766601 + 4.34761i) q^{29} +(3.38938 - 1.23364i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(0.223843 - 0.615004i) q^{34} +(0.423028 + 4.71150i) q^{35} +(-5.31153 + 1.42322i) q^{37} +(-1.00603 - 0.0880166i) q^{38} +(1.27838 - 1.83460i) q^{40} +(10.6740 + 1.88211i) q^{41} +(-0.247159 + 2.82504i) q^{43} +(-2.31016 + 4.00131i) q^{44} +(2.11235 + 3.65869i) q^{46} +(1.70795 - 0.796430i) q^{47} +(1.62276 - 1.93393i) q^{49} +(1.31610 + 4.82368i) q^{50} +(-3.86043 + 5.51327i) q^{52} +(-5.85254 - 5.85254i) q^{53} +(-3.55565 - 9.70021i) q^{55} +(2.08338 - 0.367357i) q^{56} +(-1.86572 + 4.00106i) q^{58} +(-1.33785 - 1.12259i) q^{59} +(-6.87841 - 2.50354i) q^{61} +(3.48401 + 0.933536i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-3.92830 - 14.5280i) q^{65} +(-11.3314 + 7.93436i) q^{67} +(0.536113 - 0.375390i) q^{68} +(-2.35588 + 4.10207i) q^{70} +(-2.31694 - 1.33769i) q^{71} +(-13.9258 - 3.73141i) q^{73} +(-5.16727 - 1.88073i) q^{74} +(-0.773611 - 0.649137i) q^{76} +(4.13084 - 8.85861i) q^{77} +(-2.93933 + 0.518284i) q^{79} +(2.09947 - 0.769569i) q^{80} +(7.66408 + 7.66408i) q^{82} +(8.78472 - 12.5459i) q^{83} +(-0.124224 + 1.45816i) q^{85} +(-1.82284 + 2.17237i) q^{86} +(-4.18743 + 1.95263i) q^{88} +(6.23342 + 10.7966i) q^{89} +(7.11922 - 12.3308i) q^{91} +(-0.368207 + 4.20862i) q^{92} +(1.85588 + 0.327242i) q^{94} +(2.22295 - 0.397193i) q^{95} +(11.1988 + 0.979769i) q^{97} +(2.43854 - 0.653406i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 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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