LMFDB - Embedded newform 810.2.s.a.773.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			773.2
Character	$\chi$	$=$	810.773
Dual form			810.2.s.a.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.02590 + 0.946439i) q^{5} +(-2.76499 - 1.93607i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.02590 + 0.946439i) q^{5} +(-2.76499 - 1.93607i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.10067 - 0.766269i) q^{10} +(-0.0536510 + 0.147405i) q^{11} +(0.614250 + 7.02091i) q^{13} +(2.58573 + 2.16968i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.66312 - 0.713580i) q^{17} +(4.34868 - 2.51071i) q^{19} +(-2.15947 + 0.580268i) q^{20} +(0.0662941 - 0.142168i) q^{22} +(-4.32004 - 6.16966i) q^{23} +(3.20851 - 3.83477i) q^{25} -7.04772i q^{26} +(-2.38679 - 2.38679i) q^{28} +(0.210083 - 0.176281i) q^{29} +(1.75712 - 9.96511i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-2.71517 + 0.478758i) q^{34} +(7.43394 + 1.30537i) q^{35} +(0.581708 + 2.17096i) q^{37} +(-4.55096 + 2.12215i) q^{38} +(2.20182 - 0.389850i) q^{40} +(4.27452 - 5.09418i) q^{41} +(1.49392 + 3.20373i) q^{43} +(-0.0784326 + 0.135849i) q^{44} +(3.76588 + 6.52270i) q^{46} +(1.25741 - 1.79577i) q^{47} +(1.50267 + 4.12855i) q^{49} +(-3.53052 + 3.54054i) q^{50} +(-0.614250 + 7.02091i) q^{52} +(4.14082 - 4.14082i) q^{53} +(-0.0308185 - 0.349405i) q^{55} +(2.16968 + 2.58573i) q^{56} +(-0.224648 + 0.157300i) q^{58} +(8.92905 - 3.24991i) q^{59} +(1.06847 + 6.05962i) q^{61} +(-2.61895 + 9.77405i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-7.88927 - 13.6423i) q^{65} +(-5.61930 + 0.491625i) q^{67} +(2.74657 - 0.240294i) q^{68} +(-7.29189 - 1.94832i) q^{70} +(6.34096 + 3.66095i) q^{71} +(3.43691 - 12.8267i) q^{73} +(-0.390282 - 2.21340i) q^{74} +(4.71859 - 1.71743i) q^{76} +(0.433730 - 0.303701i) q^{77} +(-4.50205 - 5.36533i) q^{79} +(-2.22742 + 0.196465i) q^{80} +(-4.70224 + 4.70224i) q^{82} +(-0.118923 + 1.35929i) q^{83} +(-4.71983 + 3.96611i) q^{85} +(-1.20902 - 3.32174i) q^{86} +(0.0899741 - 0.128496i) q^{88} +(2.96196 + 5.13026i) q^{89} +(11.8945 - 20.6019i) q^{91} +(-3.18306 - 6.82610i) q^{92} +(-1.40914 + 1.67935i) q^{94} +(-6.43374 + 9.20220i) q^{95} +(-2.50284 + 1.16709i) q^{97} +(-1.13712 - 4.24380i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q+O(q^{10}) $ 216 * q	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$		0			0
$3$		0			0
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−2.02590	+	0.946439i	−0.906008	+	0.423260i
$5$	−2.02590	+	0.946439i	−0.906008	+	0.423260i
$6$		0			0
$7$	−2.76499	−	1.93607i	−1.04507	−	0.731764i	−0.0808093	−	0.996730i	$-0.525750\pi$
$7$	−2.76499	−	1.93607i	−1.04507	−	0.731764i	−0.964258	+	0.264966i	$0.914639\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$		0			0
$10$	2.10067	−	0.766269i	0.664291	−	0.242316i
$11$	−0.0536510	+	0.147405i	−0.0161764	+	0.0444443i	−0.947518	−	0.319702i	$-0.896417\pi$
$11$	−0.0536510	+	0.147405i	−0.0161764	+	0.0444443i	0.931342	+	0.364147i	$0.118639\pi$
$12$		0			0
$13$	0.614250	+	7.02091i	0.170362	+	1.94725i	0.296035	+	0.955177i	$0.404335\pi$
$13$	0.614250	+	7.02091i	0.170362	+	1.94725i	−0.125673	+	0.992072i	$0.540109\pi$
$14$	2.58573	+	2.16968i	0.691065	+	0.579872i
$15$		0			0
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	2.66312	−	0.713580i	0.645900	−	0.173068i	0.0790258	−	0.996873i	$-0.474819\pi$
$17$	2.66312	−	0.713580i	0.645900	−	0.173068i	0.566875	+	0.823804i	$0.308152\pi$
$18$		0			0
$19$	4.34868	−	2.51071i	0.997656	−	0.575997i	0.0901018	−	0.995933i	$-0.471281\pi$
$19$	4.34868	−	2.51071i	0.997656	−	0.575997i	0.907554	+	0.419936i	$0.137947\pi$
$20$	−2.15947	+	0.580268i	−0.482871	+	0.129752i
$21$		0			0
$22$	0.0662941	−	0.142168i	0.0141339	−	0.0303103i
$23$	−4.32004	−	6.16966i	−0.900792	−	1.28646i	−0.957607	−	0.288079i	$-0.906983\pi$
$23$	−4.32004	−	6.16966i	−0.900792	−	1.28646i	0.0568151	−	0.998385i	$-0.481905\pi$
$24$		0			0
$25$	3.20851	−	3.83477i	0.641701	−	0.766955i
$26$		−	7.04772i		−	1.38217i
$27$		0			0
$28$	−2.38679	−	2.38679i	−0.451060	−	0.451060i
$29$	0.210083	−	0.176281i	0.0390115	−	0.0327345i	−0.623073	−	0.782163i	$-0.714116\pi$
$29$	0.210083	−	0.176281i	0.0390115	−	0.0327345i	0.662085	+	0.749429i	$0.269672\pi$
$30$		0			0
$31$	1.75712	−	9.96511i	0.315588	−	1.78979i	−0.253317	−	0.967383i	$-0.581521\pi$
$31$	1.75712	−	9.96511i	0.315588	−	1.78979i	0.568904	−	0.822404i	$-0.307367\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$		0			0
$34$	−2.71517	+	0.478758i	−0.465649	+	0.0821064i
$35$	7.43394	+	1.30537i	1.25657	+	0.220648i
$36$		0			0
$37$	0.581708	+	2.17096i	0.0956322	+	0.356904i	0.997115	−	0.0759117i	$-0.0241867\pi$
$37$	0.581708	+	2.17096i	0.0956322	+	0.356904i	−0.901482	+	0.432816i	$0.857520\pi$
$38$	−4.55096	+	2.12215i	−0.738262	+	0.344257i
$39$		0			0
$40$	2.20182	−	0.389850i	0.348139	−	0.0616407i
$41$	4.27452	−	5.09418i	0.667568	−	0.795577i	−0.320883	−	0.947119i	$-0.603980\pi$
$41$	4.27452	−	5.09418i	0.667568	−	0.795577i	0.988451	+	0.151542i	$0.0484240\pi$
$42$		0			0
$43$	1.49392	+	3.20373i	0.227821	+	0.488564i	0.986676	−	0.162695i	$-0.0520187\pi$
$43$	1.49392	+	3.20373i	0.227821	+	0.488564i	−0.758855	+	0.651260i	$0.774241\pi$
$44$	−0.0784326	+	0.135849i	−0.0118242	+	0.0204800i
$45$		0			0
$46$	3.76588	+	6.52270i	0.555249	+	0.961720i
$47$	1.25741	−	1.79577i	0.183413	−	0.261940i	−0.716908	−	0.697168i	$-0.754443\pi$
$47$	1.25741	−	1.79577i	0.183413	−	0.261940i	0.900321	+	0.435228i	$0.143332\pi$
$48$		0			0
$49$	1.50267	+	4.12855i	0.214667	+	0.589792i
$50$	−3.53052	+	3.54054i	−0.499291	+	0.500708i
$51$		0			0
$52$	−0.614250	+	7.02091i	−0.0851811	+	0.973624i
$53$	4.14082	−	4.14082i	0.568786	−	0.568786i	−0.363002	−	0.931788i	$-0.618248\pi$
$53$	4.14082	−	4.14082i	0.568786	−	0.568786i	0.931788	+	0.363002i	$0.118248\pi$
$54$		0			0
$55$	−0.0308185	−	0.349405i	−0.00415556	−	0.0471137i
$56$	2.16968	+	2.58573i	0.289936	+	0.345532i
$57$		0			0
$58$	−0.224648	+	0.157300i	−0.0294977	+	0.0206545i
$59$	8.92905	−	3.24991i	1.16246	−	0.423102i	0.312486	−	0.949922i	$-0.398838\pi$
$59$	8.92905	−	3.24991i	1.16246	−	0.423102i	0.849977	+	0.526820i	$0.176616\pi$
$60$		0			0
$61$	1.06847	+	6.05962i	0.136804	+	0.775855i	0.973586	+	0.228319i	$0.0733229\pi$
$61$	1.06847	+	6.05962i	0.136804	+	0.775855i	−0.836782	+	0.547536i	$0.815566\pi$
$62$	−2.61895	+	9.77405i	−0.332607	+	1.24131i
$63$		0			0
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−7.88927	−	13.6423i	−0.978543	−	1.69212i
$66$		0			0
$67$	−5.61930	+	0.491625i	−0.686506	+	0.0600615i	−0.425072	−	0.905160i	$-0.639751\pi$
$67$	−5.61930	+	0.491625i	−0.686506	+	0.0600615i	−0.261435	+	0.965221i	$0.584196\pi$
$68$	2.74657	−	0.240294i	0.333070	−	0.0291399i
$69$		0			0
$70$	−7.29189	−	1.94832i	−0.871547	−	0.232868i
$71$	6.34096	+	3.66095i	0.752533	+	0.434475i	0.826608	−	0.562778i	$-0.190267\pi$
$71$	6.34096	+	3.66095i	0.752533	+	0.434475i	−0.0740754	+	0.997253i	$0.523601\pi$
$72$		0			0
$73$	3.43691	−	12.8267i	0.402260	−	1.50125i	−0.406795	−	0.913520i	$-0.633354\pi$
$73$	3.43691	−	12.8267i	0.402260	−	1.50125i	0.809054	−	0.587734i	$-0.199980\pi$
$74$	−0.390282	−	2.21340i	−0.0453694	−	0.257303i
$75$		0			0
$76$	4.71859	−	1.71743i	0.541260	−	0.197002i
$77$	0.433730	−	0.303701i	0.0494281	−	0.0346100i
$78$		0			0
$79$	−4.50205	−	5.36533i	−0.506520	−	0.603647i	0.450819	−	0.892615i	$-0.351132\pi$
$79$	−4.50205	−	5.36533i	−0.506520	−	0.603647i	−0.957339	+	0.288969i	$0.906688\pi$
$80$	−2.22742	+	0.196465i	−0.249033	+	0.0219654i
$81$		0			0
$82$	−4.70224	+	4.70224i	−0.519276	+	0.519276i
$83$	−0.118923	+	1.35929i	−0.0130535	+	0.149202i	−0.999924	−	0.0123101i	$-0.996081\pi$
$83$	−0.118923	+	1.35929i	−0.0130535	+	0.149202i	0.986871	+	0.161512i	$0.0516370\pi$
$84$		0			0
$85$	−4.71983	+	3.96611i	−0.511938	+	0.430186i
$86$	−1.20902	−	3.32174i	−0.130372	−	0.358193i
$87$		0			0
$88$	0.0899741	−	0.128496i	0.00959128	−	0.0136978i
$89$	2.96196	+	5.13026i	0.313967	+	0.543806i	0.979217	−	0.202814i	$-0.0650086\pi$
$89$	2.96196	+	5.13026i	0.313967	+	0.543806i	−0.665251	+	0.746620i	$0.731675\pi$
$90$		0			0
$91$	11.8945	−	20.6019i	1.24689	−	2.15967i
$92$	−3.18306	−	6.82610i	−0.331857	−	0.711670i
$93$		0			0
$94$	−1.40914	+	1.67935i	−0.145342	+	0.173212i
$95$	−6.43374	+	9.20220i	−0.660087	+	0.944126i
$96$		0			0
$97$	−2.50284	+	1.16709i	−0.254125	+	0.118500i	−0.545507	−	0.838106i	$-0.683663\pi$
$97$	−2.50284	+	1.16709i	−0.254125	+	0.118500i	0.291382	+	0.956607i	$0.405885\pi$
$98$	−1.13712	−	4.24380i	−0.114867	−	0.428689i
$99$		0			0
$100$	3.82566	−	3.21936i	0.382566	−	0.321936i
$101$	−2.36001	+	0.416133i	−0.234829	+	0.0414068i	−0.289824	−	0.957080i	$-0.593597\pi$
$101$	−2.36001	+	0.416133i	−0.234829	+	0.0414068i	0.0549949	+	0.998487i	$0.482486\pi$
$102$		0			0
$103$	−9.34600	−	4.35811i	−0.920889	−	0.429417i	−0.0964301	−	0.995340i	$-0.530742\pi$
$103$	−9.34600	−	4.35811i	−0.920889	−	0.429417i	−0.824459	+	0.565922i	$0.808520\pi$
$104$	1.22382	−	6.94065i	0.120006	−	0.680587i
$105$		0			0
$106$	−4.48596	+	3.76417i	−0.435715	+	0.365608i
$107$	6.46061	+	6.46061i	0.624571	+	0.624571i	0.946697	−	0.322126i	$-0.104397\pi$
$107$	6.46061	+	6.46061i	0.624571	+	0.624571i	−0.322126	+	0.946697i	$0.604397\pi$
$108$		0			0
$109$		−	6.23309i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$109$		−	6.23309i		−	0.597022i	0.954406	−	0.298511i	$-0.0964899\pi$
$110$	0.000248601		0.350761i	2.37032e−5		0.0334438i
$111$		0			0
$112$	−1.93607	−	2.76499i	−0.182941	−	0.261267i
$113$	2.95310	−	6.33293i	0.277804	−	0.595752i	−0.717056	−	0.697016i	$-0.754511\pi$
$113$	2.95310	−	6.33293i	0.277804	−	0.595752i	0.994860	+	0.101263i	$0.0322885\pi$
$114$		0			0
$115$	14.5912	+	8.41043i	1.36063	+	0.784277i
$116$	0.237502	−	0.137122i	0.0220515	−	0.0127315i
$117$		0			0
$118$	−9.17832	+	2.45932i	−0.844933	+	0.226399i
$119$	−8.74502	−	3.18293i	−0.801655	−	0.291778i
$120$		0			0
$121$	8.40764	+	7.05485i	0.764331	+	0.641350i
$122$	−0.536278	−	6.12968i	−0.0485523	−	0.554955i
$123$		0			0
$124$	3.46085	−	9.50860i	0.310793	−	0.853898i
$125$	−2.87072	+	10.8055i	−0.256765	+	0.966474i
$126$		0			0
$127$	8.32416	+	2.23045i	0.738650	+	0.197921i	0.608478	−	0.793571i	$-0.291780\pi$
$127$	8.32416	+	2.23045i	0.738650	+	0.197921i	0.130172	+	0.991491i	$0.458447\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$		0			0
$130$	6.67024	+	14.2780i	0.585019	+	1.25226i
$131$	−5.40876	−	0.953710i	−0.472565	−	0.0833260i	−0.0677067	−	0.997705i	$-0.521568\pi$
$131$	−5.40876	−	0.953710i	−0.472565	−	0.0833260i	−0.404859	+	0.914379i	$0.632679\pi$
$132$		0			0
$133$	−16.8849	−	1.47724i	−1.46411	−	0.128093i
$134$	5.64076			0.487287
$135$		0			0
$136$	−2.75706			−0.236416
$137$	15.3849	+	1.34600i	1.31442	+	0.114997i	0.722707	−	0.691154i	$-0.242898\pi$
$137$	15.3849	+	1.34600i	1.31442	+	0.114997i	0.591710	+	0.806151i	$0.298453\pi$
$138$		0			0
$139$	12.2294	+	2.15638i	1.03729	+	0.182902i	0.666259	−	0.745720i	$-0.267894\pi$
$139$	12.2294	+	2.15638i	1.03729	+	0.182902i	0.371028	+	0.928622i	$0.379005\pi$
$140$	7.09433	+	2.57643i	0.599580	+	0.217748i
$141$		0			0
$142$	−5.99775	−	4.19967i	−0.503320	−	0.352429i
$143$	−1.06787	−	0.286135i	−0.0892999	−	0.0239278i
$144$		0			0
$145$	−0.258768	+	0.555957i	−0.0214895	+	0.0461698i
$146$	−4.54175	+	12.4784i	−0.375878	+	1.03272i
$147$		0			0
$148$	0.195887	+	2.23899i	0.0161018	+	0.184044i
$149$	−5.77544	−	4.84617i	−0.473143	−	0.397014i	0.374797	−	0.927107i	$-0.377712\pi$
$149$	−5.77544	−	4.84617i	−0.473143	−	0.397014i	−0.847939	+	0.530093i	$0.822157\pi$
$150$		0			0
$151$	7.50644	+	2.73212i	0.610865	+	0.222337i	0.628882	−	0.777501i	$-0.283513\pi$
$151$	7.50644	+	2.73212i	0.610865	+	0.222337i	−0.0180166	+	0.999838i	$0.505735\pi$
$152$	−4.85032	+	1.29964i	−0.393413	+	0.105415i
$153$		0			0
$154$	−0.458549	+	0.264743i	−0.0369509	+	0.0213336i
$155$	5.87164	+	21.8513i	0.471621	+	1.75514i
$156$		0			0
$157$	4.08417	−	8.75854i	0.325952	−	0.699007i	−0.673230	−	0.739433i	$-0.735094\pi$
$157$	4.08417	−	8.75854i	0.325952	−	0.699007i	0.999183	+	0.0404258i	$0.0128714\pi$
$158$	4.01729	+	5.73729i	0.319599	+	0.456434i
$159$		0			0
$160$	2.23607	−	0.00158481i	0.176777	−	0.000125290i
$161$			25.4229i			2.00361i
$162$		0			0
$163$	−10.1046	−	10.1046i	−0.791450	−	0.791450i	0.190280	−	0.981730i	$-0.439060\pi$
$163$	−10.1046	−	10.1046i	−0.791450	−	0.791450i	−0.981730	+	0.190280i	$0.939060\pi$
$164$	5.09418	−	4.27452i	0.397788	−	0.333784i
$165$		0			0
$166$	0.236940	−	1.34376i	0.0183901	−	0.104296i
$167$	−6.46401	−	3.01422i	−0.500200	−	0.233247i	0.156108	−	0.987740i	$-0.450105\pi$
$167$	−6.46401	−	3.01422i	−0.500200	−	0.233247i	−0.656308	+	0.754493i	$0.727883\pi$
$168$		0			0
$169$	−36.1133	+	6.36775i	−2.77795	+	0.489827i
$170$	5.04754	−	3.53966i	0.387129	−	0.271480i
$171$		0			0
$172$	0.914906	+	3.41448i	0.0697609	+	0.260351i
$173$	−19.2728	+	8.98704i	−1.46528	+	0.683272i	−0.981420	−	0.191872i	$-0.938544\pi$
$173$	−19.2728	+	8.98704i	−1.46528	+	0.683272i	−0.483862	+	0.875144i	$0.660766\pi$
$174$		0			0
$175$	−16.2959	+	4.39123i	−1.23185	+	0.331946i
$176$	−0.100831	+	0.120166i	−0.00760042	+	0.00905783i
$177$		0			0
$178$	−2.50355	−	5.36889i	−0.187649	−	0.402415i
$179$	−5.20501	+	9.01535i	−0.389041	+	0.673839i	−0.992321	−	0.123691i	$-0.960527\pi$
$179$	−5.20501	+	9.01535i	−0.389041	+	0.673839i	0.603280	+	0.797530i	$0.293860\pi$
$180$		0			0
$181$	−0.473902	−	0.820822i	−0.0352248	−	0.0610112i	0.847876	−	0.530195i	$-0.177881\pi$
$181$	−0.473902	−	0.820822i	−0.0352248	−	0.0610112i	−0.883100	+	0.469184i	$0.844548\pi$
$182$	−13.6449	+	19.4869i	−1.01142	+	1.44446i
$183$		0			0
$184$	2.57602	+	7.07755i	0.189906	+	0.521764i
$185$	−3.23316	−	3.84759i	−0.237707	−	0.282881i
$186$		0			0
$187$	−0.0376937	+	0.430841i	−0.00275644	+	0.0315062i
$188$	1.55014	−	1.55014i	0.113056	−	0.113056i
$189$		0			0
$190$	7.21128	−	8.60645i	0.523161	−	0.624377i
$191$	1.20750	+	1.43904i	0.0873714	+	0.104125i	0.807959	−	0.589239i	$-0.200572\pi$
$191$	1.20750	+	1.43904i	0.0873714	+	0.104125i	−0.720588	+	0.693364i	$0.756128\pi$
$192$		0			0
$193$	−6.75391	+	4.72914i	−0.486157	+	0.340411i	−0.790820	−	0.612049i	$-0.790345\pi$
$193$	−6.75391	+	4.72914i	−0.486157	+	0.340411i	0.304662	+	0.952460i	$0.401456\pi$
$194$	2.59504	−	0.944516i	0.186313	−	0.0678123i
$195$		0			0
$196$	0.762924	+	4.32676i	0.0544946	+	0.309054i
$197$	2.78731	−	10.4024i	0.198588	−	0.741139i	−0.792721	−	0.609584i	$-0.791336\pi$
$197$	2.78731	−	10.4024i	0.198588	−	0.741139i	0.991309	−	0.131555i	$-0.0419969\pi$
$198$		0			0
$199$	0.415328	+	0.239790i	0.0294419	+	0.0169983i	0.514649	−	0.857401i	$-0.327922\pi$
$199$	0.415328	+	0.239790i	0.0294419	+	0.0169983i	−0.485207	+	0.874399i	$0.661256\pi$
$200$	−4.09169	+	2.87369i	−0.289326	+	0.203200i
$201$		0			0
$202$	2.38729	−	0.208861i	0.167969	−	0.0146954i
$203$	−0.922169	+	0.0806793i	−0.0647236	+	0.00566258i
$204$		0			0
$205$	−3.83841	+	14.3658i	−0.268086	+	1.00335i
$206$	8.93060	+	5.15608i	0.622224	+	0.359241i
$207$		0			0
$208$	−1.82409	+	6.80758i	−0.126478	+	0.472021i
$209$	0.136780	+	0.775720i	0.00946129	+	0.0536576i
$210$		0			0
$211$	−10.9492	+	3.98519i	−0.753775	+	0.274352i	−0.690193	−	0.723625i	$-0.742474\pi$
$211$	−10.9492	+	3.98519i	−0.753775	+	0.274352i	−0.0635814	+	0.997977i	$0.520252\pi$
$212$	4.79696	−	3.35887i	0.329457	−	0.230688i
$213$		0			0
$214$	−5.87295	−	6.99910i	−0.401466	−	0.478449i
$215$	−6.05867	−	5.07652i	−0.413198	−	0.346215i
$216$		0			0
$217$	−24.1515	+	24.1515i	−1.63951	+	1.63951i
$218$	−0.543250	+	6.20937i	−0.0367935	+	0.420552i
$219$		0			0
$220$	0.0303232	−	0.349448i	0.00204439	−	0.0235598i
$221$	6.64579	+	18.2592i	0.447044	+	1.22824i
$222$		0			0
$223$	8.17360	−	11.6731i	0.547345	−	0.781689i	−0.446224	−	0.894921i	$-0.647232\pi$
$223$	8.17360	−	11.6731i	0.547345	−	0.781689i	0.993569	+	0.113232i	$0.0361204\pi$
$224$	1.68771	+	2.92321i	0.112765	+	0.195315i
$225$		0			0
$226$	−3.49381	+	6.05146i	−0.232405	+	0.402537i
$227$	−1.26293	−	2.70835i	−0.0838233	−	0.179760i	0.859928	−	0.510415i	$-0.170508\pi$
$227$	−1.26293	−	2.70835i	−0.0838233	−	0.179760i	−0.943752	+	0.330655i	$0.892730\pi$
$228$		0			0
$229$	8.45187	−	10.0725i	0.558515	−	0.665612i	−0.410716	−	0.911763i	$-0.634721\pi$
$229$	8.45187	−	10.0725i	0.558515	−	0.665612i	0.969232	+	0.246151i	$0.0791658\pi$
$230$	−13.8026	−	9.65013i	−0.910118	−	0.636311i
$231$		0			0
$232$	−0.248550	+	0.115901i	−0.0163181	+	0.00760925i
$233$	−2.54408	−	9.49465i	−0.166668	−	0.622015i	−0.997822	−	0.0659714i	$-0.978985\pi$
$233$	−2.54408	−	9.49465i	−0.166668	−	0.622015i	0.831153	−	0.556044i	$-0.187681\pi$
$234$		0			0
$235$	−0.847799	+	4.82812i	−0.0553043	+	0.314952i
$236$	9.35774	−	1.65002i	0.609137	−	0.107407i
$237$		0			0
$238$	8.43433	+	3.93299i	0.546716	+	0.254938i
$239$	1.34900	−	7.65056i	0.0872595	−	0.494873i	−0.909587	−	0.415514i	$-0.863602\pi$
$239$	1.34900	−	7.65056i	0.0872595	−	0.494873i	0.996846	−	0.0793589i	$-0.0252873\pi$
$240$		0			0
$241$	10.5110	−	8.81980i	0.677075	−	0.568133i	−0.238075	−	0.971247i	$-0.576516\pi$
$241$	10.5110	−	8.81980i	0.677075	−	0.568133i	0.915150	+	0.403114i	$0.132072\pi$
$242$	−7.76078	−	7.76078i	−0.498882	−	0.498882i
$243$		0			0
$244$			6.15310i			0.393912i
$245$	−6.95167	−	6.94182i	−0.444126	−	0.443496i
$246$		0			0
$247$	20.2986	+	28.9895i	1.29157	+	1.84456i
$248$	−4.27641	+	9.17078i	−0.271552	+	0.582345i
$249$		0			0
$250$	3.80155	−	10.5142i	0.240431	−	0.664976i
$251$	16.4462	−	9.49521i	1.03807	−	0.599333i	0.118787	−	0.992920i	$-0.462099\pi$
$251$	16.4462	−	9.49521i	1.03807	−	0.599333i	0.919287	+	0.393587i	$0.128766\pi$
$252$		0			0
$253$	1.14121	−	0.305787i	0.0717475	−	0.0192247i
$254$	−8.09809	−	2.94746i	−0.508119	−	0.184940i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.998091	+	11.4082i	0.0622592	+	0.711626i	0.961614	+	0.274406i	$0.0884813\pi$
$257$	0.998091	+	11.4082i	0.0622592	+	0.711626i	−0.899355	+	0.437220i	$0.855963\pi$
$258$		0			0
$259$	2.59471	−	7.12891i	0.161228	−	0.442969i
$260$	−5.40045	−	14.8050i	−0.334922	−	0.918165i
$261$		0			0
$262$	5.30506	+	1.42149i	0.327747	+	0.0878196i
$263$	6.53529	+	4.57606i	0.402983	+	0.282172i	0.757445	−	0.652899i	$-0.226447\pi$
$263$	6.53529	+	4.57606i	0.402983	+	0.282172i	−0.354462	+	0.935070i	$0.615336\pi$
$264$		0			0
$265$	−4.46984	+	12.3079i	−0.274580	+	0.756069i
$266$	16.6919	+	2.94324i	1.02345	+	0.180462i
$267$		0			0
$268$	−5.61930	−	0.491625i	−0.343253	−	0.0300308i
$269$	−23.8729			−1.45556			−0.727780	−	0.685811i	$-0.759448\pi$
$269$	−23.8729			−1.45556			−0.727780	+	0.685811i	$0.759448\pi$
$270$		0			0
$271$	−13.7477			−0.835112			−0.417556	−	0.908651i	$-0.637113\pi$
$271$	−13.7477			−0.835112			−0.417556	+	0.908651i	$0.637113\pi$
$272$	2.74657	+	0.240294i	0.166535	+	0.0145699i
$273$		0			0
$274$	−15.2090	−	2.68176i	−0.918809	−	0.162011i
$275$	0.393125	+	0.678689i	0.0237063	+	0.0409265i
$276$		0			0
$277$	17.3388	+	12.1407i	1.04179	+	0.729467i	0.963566	−	0.267469i	$-0.0861874\pi$
$277$	17.3388	+	12.1407i	1.04179	+	0.729467i	0.0782202	+	0.996936i	$0.475076\pi$
$278$	−11.9950	−	3.21404i	−0.719410	−	0.192765i
$279$		0			0
$280$	−6.84278	−	3.18494i	−0.408935	−	0.190337i
$281$	8.31974	−	22.8583i	0.496314	−	1.36361i	−0.398498	−	0.917169i	$-0.630468\pi$
$281$	8.31974	−	22.8583i	0.496314	−	1.36361i	0.894812	−	0.446443i	$-0.147309\pi$
$282$		0			0
$283$	0.696445	+	7.96040i	0.0413993	+	0.473197i	0.988390	+	0.151936i	$0.0485509\pi$
$283$	0.696445	+	7.96040i	0.0413993	+	0.473197i	−0.946991	+	0.321260i	$0.895894\pi$
$284$	5.60890	+	4.70643i	0.332827	+	0.279275i
$285$		0			0
$286$	1.03887	+	0.378118i	0.0614297	+	0.0223586i
$287$	−21.6817	+	5.80958i	−1.27983	+	0.342929i
$288$		0			0
$289$	−8.13944	+	4.69931i	−0.478791	+	0.276430i
$290$	0.306238	−	0.531289i	0.0179829	−	0.0311984i
$291$		0			0
$292$	5.61203	−	12.0350i	0.328419	−	0.704297i
$293$	−7.63355	−	10.9018i	−0.445957	−	0.636892i	0.531741	−	0.846907i	$-0.321538\pi$
$293$	−7.63355	−	10.9018i	−0.445957	−	0.636892i	−0.977698	+	0.210014i	$0.932649\pi$
$294$		0			0
$295$	−15.0135	+	15.0348i	−0.874119	+	0.875358i
$296$		−	2.24755i		−	0.130636i
$297$		0			0
$298$	5.33109	+	5.33109i	0.308822	+	0.308822i
$299$	40.6630	−	34.1203i	2.35160	−	1.97323i
$300$		0			0
$301$	2.07195	−	11.7506i	0.119425	−	0.677294i
$302$	−7.23975	−	3.37595i	−0.416601	−	0.194264i
$303$		0			0
$304$	4.94514	−	0.871961i	0.283623	−	0.0500104i
$305$	−7.89968	−	11.2649i	−0.452334	−	0.645027i
$306$		0			0
$307$	−2.83155	−	10.5675i	−0.161605	−	0.603118i	−0.998449	−	0.0556765i	$-0.982268\pi$
$307$	−2.83155	−	10.5675i	−0.161605	−	0.603118i	0.836844	−	0.547442i	$-0.184398\pi$
$308$	0.479878	−	0.223771i	0.0273436	−	0.0127505i
$309$		0			0
$310$	−3.94483	−	22.2799i	−0.224051	−	1.26541i
$311$	2.19146	−	2.61168i	0.124266	−	0.148095i	−0.700324	−	0.713825i	$-0.746961\pi$
$311$	2.19146	−	2.61168i	0.124266	−	0.148095i	0.824590	+	0.565730i	$0.191406\pi$
$312$		0			0
$313$	−3.50123	−	7.50842i	−0.197901	−	0.424401i	0.782165	−	0.623071i	$-0.214115\pi$
$313$	−3.50123	−	7.50842i	−0.197901	−	0.424401i	−0.980066	+	0.198671i	$0.936338\pi$
$314$	−4.83199	+	8.36925i	−0.272685	+	0.472304i
$315$		0			0
$316$	−3.50197	−	6.06559i	−0.197001	−	0.341216i
$317$	−17.8751	+	25.5282i	−1.00396	+	1.43381i	−0.105675	+	0.994401i	$0.533700\pi$
$317$	−17.8751	+	25.5282i	−1.00396	+	1.43381i	−0.898288	+	0.439407i	$0.855189\pi$
$318$		0			0
$319$	0.0147135	+	0.0404250i	0.000823797	+	0.00226336i
$320$	−2.22770	−	0.193307i	−0.124532	−	0.0108062i
$321$		0			0
$322$	2.21575	−	25.3262i	0.123479	−	1.41137i
$323$	9.78944	−	9.78944i	0.544699	−	0.544699i
$324$		0			0
$325$	28.8944	+	20.1711i	1.60277	+	1.11889i
$326$	9.18543	+	10.9468i	0.508734	+	0.606286i
$327$		0			0
$328$	−5.44734	+	3.81427i	−0.300779	+	0.210608i
$329$	−6.95347	+	2.53086i	−0.383357	+	0.139531i
$330$		0			0
$331$	−1.55033	−	8.79236i	−0.0852138	−	0.483272i	−0.997310	−	0.0732958i	$-0.976648\pi$
$331$	−1.55033	−	8.79236i	−0.0852138	−	0.483272i	0.912096	−	0.409976i	$-0.134463\pi$
$332$	−0.353155	+	1.31799i	−0.0193819	+	0.0723342i
$333$		0			0
$334$	6.17670	+	3.56612i	0.337974	+	0.195129i
$335$	10.9188	−	6.31430i	0.596558	−	0.344987i
$336$		0			0
$337$	8.64895	−	0.756685i	0.471138	−	0.0412193i	0.150885	−	0.988551i	$-0.451788\pi$
$337$	8.64895	−	0.756685i	0.471138	−	0.0412193i	0.320253	+	0.947332i	$0.396232\pi$
$338$	36.5309	−	3.19604i	1.98702	−	0.173842i
$339$		0			0
$340$	−5.33684	+	3.08627i	−0.289431	+	0.167376i
$341$	1.37464	+	0.793647i	0.0744407	+	0.0429784i
$342$		0			0
$343$	−2.27710	+	8.49824i	−0.122952	+	0.458862i
$344$	−0.613833	−	3.48122i	−0.0330957	−	0.187695i
$345$		0			0
$346$	19.9827	−	7.27311i	1.07428	−	0.391005i
$347$	14.8942	−	10.4291i	0.799565	−	0.559862i	−0.100846	−	0.994902i	$-0.532155\pi$
$347$	14.8942	−	10.4291i	0.799565	−	0.559862i	0.900411	+	0.435041i	$0.143266\pi$
$348$		0			0
$349$	5.55475	+	6.61989i	0.297339	+	0.354355i	0.893943	−	0.448181i	$-0.147928\pi$
$349$	5.55475	+	6.61989i	0.297339	+	0.354355i	−0.596604	+	0.802536i	$0.703484\pi$
$350$	16.6166	−	2.95424i	0.888193	−	0.157911i
$351$		0			0
$352$	0.110920	−	0.110920i	0.00591208	−	0.00591208i
$353$	−1.11150	+	12.7045i	−0.0591590	+	0.676191i	0.907488	+	0.420078i	$0.137997\pi$
$353$	−1.11150	+	12.7045i	−0.0591590	+	0.676191i	−0.966647	+	0.256113i	$0.917558\pi$
$354$		0			0
$355$	−16.3110	−	1.41538i	−0.865697	−	0.0751205i
$356$	2.02610	+	5.56666i	0.107383	+	0.295032i
$357$		0			0
$358$	5.97095	−	8.52740i	0.315574	−	0.450687i
$359$	13.0182	+	22.5482i	0.687074	+	1.19005i	0.972780	+	0.231730i	$0.0744387\pi$
$359$	13.0182	+	22.5482i	0.687074	+	1.19005i	−0.285706	+	0.958317i	$0.592228\pi$
$360$		0			0
$361$	3.10735	−	5.38208i	0.163545	−	0.283267i
$362$	0.400559	+	0.859001i	0.0210529	+	0.0451481i
$363$		0			0
$364$	15.2913	−	18.2235i	0.801483	−	0.955170i
$365$	5.17689	+	29.2384i	0.270971	+	1.53041i
$366$		0			0
$367$	22.8217	−	10.6419i	1.19128	−	0.555505i	0.277114	−	0.960837i	$-0.410622\pi$
$367$	22.8217	−	10.6419i	1.19128	−	0.555505i	0.914169	+	0.405333i	$0.132844\pi$
$368$	−1.94936	−	7.27513i	−0.101618	−	0.379242i
$369$		0			0
$370$	2.88552	+	4.11474i	0.150011	+	0.213915i
$371$	−19.4662	+	3.43242i	−1.01064	+	0.178202i
$372$		0			0
$373$	−13.0243	−	6.07335i	−0.674375	−	0.314466i	0.0550932	−	0.998481i	$-0.482454\pi$
$373$	−13.0243	−	6.07335i	−0.674375	−	0.314466i	−0.729468	+	0.684015i	$0.760232\pi$
$374$	0.0751005	−	0.425916i	0.00388335	−	0.0220236i
$375$		0			0
$376$	−1.67935	+	1.40914i	−0.0866058	+	0.0726709i
$377$	1.36669	+	1.36669i	0.0703883	+	0.0703883i
$378$		0			0
$379$		−	21.2421i		−	1.09113i	−0.838067	−	0.545567i	$-0.816314\pi$
$379$		−	21.2421i		−	1.09113i	0.838067	−	0.545567i	$-0.183686\pi$
$380$	−7.93394	+	7.94519i	−0.407002	+	0.407580i
$381$		0			0
$382$	−1.07748	−	1.53880i	−0.0551287	−	0.0787320i
$383$	12.4126	−	26.6190i	0.634256	−	1.36017i	−0.281939	−	0.959432i	$-0.590977\pi$
$383$	12.4126	−	26.6190i	0.634256	−	1.36017i	0.916195	−	0.400734i	$-0.131245\pi$
$384$		0			0
$385$	−0.591257	+	1.02577i	−0.0301333	+	0.0522779i
$386$	7.14039	−	4.12250i	0.363436	−	0.209830i
$387$		0			0
$388$	−2.66748	+	0.714749i	−0.135421	+	0.0362859i
$389$	8.20972	+	2.98809i	0.416249	+	0.151502i	0.541651	−	0.840604i	$-0.317800\pi$
$389$	8.20972	+	2.98809i	0.416249	+	0.151502i	−0.125401	+	0.992106i	$0.540022\pi$
$390$		0			0
$391$	−15.9073	−	13.3478i	−0.804468	−	0.675029i
$392$	−0.382919	−	4.37679i	−0.0193403	−	0.221061i
$393$		0			0
$394$	−3.68333	+	10.1199i	−0.185563	+	0.509831i
$395$	14.1986	+	6.60868i	0.714411	+	0.332519i
$396$		0			0
$397$	−4.58547	−	1.22867i	−0.230138	−	0.0616653i	0.141907	−	0.989880i	$-0.454677\pi$
$397$	−4.58547	−	1.22867i	−0.230138	−	0.0616653i	−0.372045	+	0.928215i	$0.621343\pi$
$398$	−0.392849	−	0.275076i	−0.0196917	−	0.0137883i
$399$		0			0
$400$	4.32658	−	2.50614i	0.216329	−	0.125307i
$401$	−16.1036	−	2.83951i	−0.804178	−	0.141798i	−0.243574	−	0.969882i	$-0.578320\pi$
$401$	−16.1036	−	2.83951i	−0.804178	−	0.141798i	−0.560604	+	0.828084i	$0.689431\pi$
$402$		0			0
$403$	71.0434	+	6.21549i	3.53893	+	0.309616i
$404$	−2.39641			−0.119226
$405$		0			0
$406$	0.925691			0.0459413
$407$	−0.351220	−	0.0307278i	−0.0174093	−	0.00152312i
$408$		0			0
$409$	2.97423	+	0.524437i	0.147066	+	0.0259317i	0.246696	−	0.969093i	$-0.420655\pi$
$409$	2.97423	+	0.524437i	0.147066	+	0.0259317i	−0.0996304	+	0.995025i	$0.531766\pi$
$410$	5.07586	−	13.9766i	0.250679	−	0.690257i
$411$		0			0
$412$	−8.44723	−	5.91482i	−0.416165	−	0.291402i
$413$	−30.9807	−	8.30126i	−1.52446	−	0.408479i
$414$		0			0
$415$	−1.04556	−	2.86634i	−0.0513247	−	0.140703i
$416$	2.41046	−	6.62269i	0.118183	−	0.324704i
$417$		0			0
$418$	−0.0686514	−	0.784689i	−0.00335785	−	0.0383804i
$419$	−28.7021	−	24.0840i	−1.40219	−	1.17658i	−0.960116	−	0.279601i	$-0.909798\pi$
$419$	−28.7021	−	24.0840i	−1.40219	−	1.17658i	−0.442075	−	0.896978i	$-0.645758\pi$
$420$		0			0
$421$	9.12077	+	3.31969i	0.444519	+	0.161792i	0.554575	−	0.832134i	$-0.312881\pi$
$421$	9.12077	+	3.31969i	0.444519	+	0.161792i	−0.110056	+	0.993925i	$0.535103\pi$
$422$	11.2549	−	3.01573i	0.547879	−	0.146804i
$423$		0			0
$424$	−5.07145	+	2.92800i	−0.246291	+	0.142196i
$425$	5.80820	−	12.5020i	0.281739	−	0.606435i
$426$		0			0
$427$	8.77750	−	18.8234i	0.424773	−	0.910928i
$428$	5.24059	+	7.48433i	0.253313	+	0.361769i
$429$		0			0
$430$	5.59317	+	5.58525i	0.269727	+	0.269344i
$431$		−	1.48091i		−	0.0713331i	−0.999364	−	0.0356666i	$-0.988645\pi$
$431$		−	1.48091i		−	0.0713331i	0.999364	−	0.0356666i	$-0.0113554\pi$
$432$		0			0
$433$	−2.84796	−	2.84796i	−0.136864	−	0.136864i	0.635356	−	0.772220i	$-0.280854\pi$
$433$	−2.84796	−	2.84796i	−0.136864	−	0.136864i	−0.772220	+	0.635356i	$0.780854\pi$
$434$	26.1646	−	21.9547i	1.25594	−	1.05386i
$435$		0			0
$436$	1.08236	−	6.13840i	0.0518359	−	0.293976i
$437$	−34.2767	−	15.9835i	−1.63968	−	0.764595i
$438$		0			0
$439$	4.66120	−	0.821895i	0.222467	−	0.0392269i	−0.0613035	−	0.998119i	$-0.519526\pi$
$439$	4.66120	−	0.821895i	0.222467	−	0.0392269i	0.283770	+	0.958892i	$0.408415\pi$
$440$	−0.0606642	+	0.345475i	−0.00289205	+	0.0164699i
$441$		0			0
$442$	−5.02911	−	18.7689i	−0.239210	−	0.892746i
$443$	23.5424	−	10.9780i	1.11853	−	0.521580i	0.226709	−	0.973963i	$-0.427203\pi$
$443$	23.5424	−	10.9780i	1.11853	−	0.521580i	0.891824	+	0.452382i	$0.149426\pi$
$444$		0			0
$445$	−10.8561	−	7.59006i	−0.514628	−	0.359803i
$446$	−9.15987	+	10.9163i	−0.433733	+	0.516902i
$447$		0			0
$448$	−1.42652	−	3.05918i	−0.0673966	−	0.144532i
$449$	3.45907	−	5.99129i	0.163244	−	0.282746i	−0.772787	−	0.634666i	$-0.781138\pi$
$449$	3.45907	−	5.99129i	0.163244	−	0.282746i	0.936030	+	0.351920i	$0.114471\pi$
$450$		0			0
$451$	0.521575	+	0.903394i	0.0245600	+	0.0425391i
$452$	4.00793	−	5.72392i	0.188517	−	0.269231i
$453$		0			0
$454$	1.02207	+	2.80812i	0.0479682	+	0.131791i
$455$	−4.59860	+	52.9948i	−0.215586	+	2.48444i
$456$		0			0
$457$	1.47692	−	16.8812i	0.0690872	−	0.789671i	−0.880065	−	0.474853i	$-0.842501\pi$
$457$	1.47692	−	16.8812i	0.0690872	−	0.789671i	0.949152	−	0.314818i	$-0.101943\pi$
$458$	−9.29758	+	9.29758i	−0.434448	+	0.434448i
$459$		0			0
$460$	12.9090	+	10.8164i	0.601887	+	0.504317i
$461$	−24.9242	−	29.7035i	−1.16084	−	1.38343i	−0.909590	−	0.415507i	$-0.863604\pi$
$461$	−24.9242	−	29.7035i	−1.16084	−	1.38343i	−0.251246	−	0.967923i	$-0.580840\pi$
$462$		0			0
$463$	19.3367	−	13.5397i	0.898651	−	0.629242i	−0.0302612	−	0.999542i	$-0.509634\pi$
$463$	19.3367	−	13.5397i	0.898651	−	0.629242i	0.928912	+	0.370300i	$0.120745\pi$
$464$	0.257705	−	0.0937970i	0.0119637	−	0.00435442i
$465$		0			0
$466$	1.70689	+	9.68025i	0.0790701	+	0.448429i
$467$	−4.42576	+	16.5171i	−0.204800	+	0.764322i	0.784711	+	0.619862i	$0.212811\pi$
$467$	−4.42576	+	16.5171i	−0.204800	+	0.764322i	−0.989511	+	0.144461i	$0.953855\pi$
$468$		0			0
$469$	16.4891	+	9.51999i	0.761396	+	0.439592i
$470$	1.26537	−	4.73585i	0.0583672	−	0.218449i
$471$		0			0
$472$	−9.46594	+	0.828162i	−0.435705	+	0.0381193i
$473$	−0.552397	+	0.0483284i	−0.0253992	+	0.00222214i
$474$		0			0
$475$	4.32475	−	24.7318i	0.198433	−	1.13477i
$476$	−8.05945	−	4.65313i	−0.369404	−	0.213276i
$477$		0			0
$478$	−2.01066	+	7.50387i	−0.0919653	+	0.343219i
$479$	5.73160	+	32.5055i	0.261884	+	1.48522i	0.777765	+	0.628555i	$0.216353\pi$
$479$	5.73160	+	32.5055i	0.261884	+	1.48522i	−0.515881	+	0.856660i	$0.672535\pi$
$480$		0			0
$481$	−14.8848	+	5.41763i	−0.678689	+	0.247023i
$482$	−11.2397	+	7.87014i	−0.511955	+	0.358475i
$483$		0			0
$484$	7.05485	+	8.40764i	0.320675	+	0.382165i
$485$	3.96591	−	4.73320i	0.180083	−	0.214923i
$486$		0			0
$487$	−4.51491	+	4.51491i	−0.204590	+	0.204590i	−0.801963	−	0.597373i	$-0.796211\pi$
$487$	−4.51491	+	4.51491i	−0.204590	+	0.204590i	0.597373	+	0.801963i	$0.296211\pi$
$488$	0.536278	−	6.12968i	0.0242762	−	0.277478i
$489$		0			0
$490$	6.32019	+	7.52128i	0.285517	+	0.339777i
$491$	−0.523591	−	1.43855i	−0.0236293	−	0.0649211i	0.927317	−	0.374277i	$-0.122109\pi$
$491$	−0.523591	−	1.43855i	−0.0236293	−	0.0649211i	−0.950946	+	0.309355i	$0.899887\pi$
$492$		0			0
$493$	0.433686	−	0.619367i	0.0195322	−	0.0278949i
$494$	−17.6948	−	30.6483i	−0.796127	−	1.37893i
$495$		0			0
$496$	5.05942	−	8.76317i	0.227175	−	0.393478i
$497$	−10.4448	−	22.3990i	−0.468514	−	1.00473i
$498$		0			0
$499$	−11.0899	+	13.2165i	−0.496454	+	0.591651i	−0.954847	−	0.297099i	$-0.903981\pi$
$499$	−11.0899	+	13.2165i	−0.496454	+	0.591651i	0.458393	+	0.888750i	$0.348425\pi$
$500$	−4.70346	+	10.1429i	−0.210345	+	0.453602i
$501$		0			0
$502$	−17.2112	+	8.02570i	−0.768172	+	0.358205i
$503$	−8.52155	−	31.8029i	−0.379957	−	1.41802i	−0.845965	−	0.533239i	$-0.820975\pi$
$503$	−8.52155	−	31.8029i	−0.379957	−	1.41802i	0.466007	−	0.884781i	$-0.345692\pi$
$504$		0			0
$505$	4.38728	−	3.07664i	0.195231	−	0.136909i
$506$	−1.16352	+	0.205160i	−0.0517249	+	0.00912049i
$507$		0			0
$508$	7.81038	+	3.64204i	0.346530	+	0.161589i
$509$	−5.96465	+	33.8272i	−0.264378	+	1.49936i	0.506421	+	0.862286i	$0.330968\pi$
$509$	−5.96465	+	33.8272i	−0.264378	+	1.49936i	−0.770800	+	0.637078i	$0.780143\pi$
$510$		0			0
$511$	−34.3364	+	28.8116i	−1.51895	+	1.27455i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$		−	11.4518i		−	0.505118i
$515$	23.0587	−	0.0163428i	1.01609	−	0.000720149i
$516$		0			0
$517$	0.197244	+	0.281694i	0.00867480	+	0.0123889i
$518$	−3.20616	+	6.87564i	−0.140871	+	0.302098i
$519$		0			0
$520$	4.08957	+	15.2193i	0.179339	+	0.667411i
$521$	−16.0538	+	9.26867i	−0.703330	+	0.406068i	−0.808586	−	0.588377i	$-0.799767\pi$
$521$	−16.0538	+	9.26867i	−0.703330	+	0.406068i	0.105256	+	0.994445i	$0.466434\pi$
$522$		0			0
$523$	−31.5805	+	8.46196i	−1.38092	+	0.370016i	−0.871454	−	0.490477i	$-0.836823\pi$
$523$	−31.5805	+	8.46196i	−1.38092	+	0.370016i	−0.509463	+	0.860493i	$0.670156\pi$
$524$	−5.16098	−	1.87844i	−0.225458	−	0.0820601i
$525$		0			0
$526$	−6.11159	−	5.12823i	−0.266478	−	0.223601i
$527$	−2.43149	−	27.7921i	−0.105917	−	1.21064i
$528$		0			0
$529$	−11.5355	+	31.6935i	−0.501543	+	1.37798i
$530$	5.52553	−	11.8715i	0.240014	−	0.515665i
$531$		0			0
$532$	−16.3719	−	4.38684i	−0.709812	−	0.190194i
$533$	38.3914	+	26.8819i	1.66291	+	1.16438i
$534$		0			0
$535$	−19.2031	−	6.97395i	−0.830222	−	0.301510i
$536$	5.55506	+	0.979508i	0.239942	+	0.0423083i
$537$		0			0
$538$	23.7821	+	2.08066i	1.02532	+	0.0897038i
$539$	−0.689188			−0.0296854
$540$		0			0
$541$	45.6107			1.96096			0.980479	−	0.196626i	$-0.0629984\pi$
$541$	45.6107			1.96096			0.980479	+	0.196626i	$0.0629984\pi$
$542$	13.6954	+	1.19819i	0.588266	+	0.0514666i
$543$		0			0
$544$	−2.71517	−	0.478758i	−0.116412	−	0.0205266i
$545$	5.89924	+	12.6276i	0.252696	+	0.540907i
$546$		0			0
$547$	−5.72610	−	4.00946i	−0.244830	−	0.171432i	0.444720	−	0.895669i	$-0.353303\pi$
$547$	−5.72610	−	4.00946i	−0.244830	−	0.171432i	−0.689551	+	0.724237i	$0.742192\pi$
$548$	14.9174	+	3.99710i	0.637240	+	0.170748i
$549$		0			0
$550$	−0.332478	−	0.710370i	−0.0141769	−	0.0302903i
$551$	0.470995	−	1.29405i	0.0200650	−	0.0551283i
$552$		0			0
$553$	2.06047	+	23.5513i	0.0876203	+	1.00150i
$554$	−16.2147	−	13.6057i	−0.688895	−	0.578052i
$555$		0			0
$556$	11.6692	+	4.24724i	0.494884	+	0.180123i
$557$	44.1035	−	11.8175i	1.86872	−	0.500723i	0.868738	−	0.495271i	$-0.164931\pi$
$557$	44.1035	−	11.8175i	1.86872	−	0.500723i	0.999985	−	0.00545188i	$-0.00173540\pi$
$558$		0			0
$559$	−21.5754	+	12.4566i	−0.912544	+	0.526858i
$560$	6.53916	+	3.76921i	0.276330	+	0.159278i
$561$		0			0
$562$	−10.2803	+	22.0462i	−0.433649	+	0.929963i
$563$	16.4145	+	23.4423i	0.691787	+	0.987974i	0.999336	+	0.0364420i	$0.0116024\pi$
$563$	16.4145	+	23.4423i	0.691787	+	0.987974i	−0.307549	+	0.951532i	$0.599509\pi$
$564$		0			0
$565$	0.0110740	+	15.6248i	0.000465888	+	0.657340i
$566$		−	7.99081i		−	0.335879i
$567$		0			0
$568$	−5.17737	−	5.17737i	−0.217238	−	0.217238i
$569$	−10.7604	+	9.02905i	−0.451099	+	0.378517i	−0.839844	−	0.542828i	$-0.817353\pi$
$569$	−10.7604	+	9.02905i	−0.451099	+	0.378517i	0.388744	+	0.921346i	$0.372909\pi$
$570$		0			0
$571$	−2.43093	+	13.7865i	−0.101731	+	0.576947i	0.890744	+	0.454505i	$0.150184\pi$
$571$	−2.43093	+	13.7865i	−0.101731	+	0.576947i	−0.992476	+	0.122442i	$0.960927\pi$
$572$	−1.00196	−	0.467222i	−0.0418941	−	0.0195355i
$573$		0			0
$574$	22.1055	−	3.89779i	0.922665	−	0.162691i
$575$	−37.5201	−	3.22900i	−1.56470	−	0.134659i
$576$		0			0
$577$	7.72593	+	28.8336i	0.321635	+	1.20036i	0.917652	+	0.397386i	$0.130082\pi$
$577$	7.72593	+	28.8336i	0.321635	+	1.20036i	−0.596017	+	0.802972i	$0.703251\pi$
$578$	8.51804	−	3.97203i	0.354304	−	0.165215i
$579$		0			0
$580$	−0.351377	+	0.502577i	−0.0145902	+	0.0208684i
$581$	2.96050	−	3.52819i	0.122822	−	0.146374i
$582$		0			0
$583$	0.388219	+	0.832537i	0.0160784	+	0.0344802i
$584$	−6.63960	+	11.5001i	−0.274748	+	0.475878i
$585$		0			0
$586$	6.65434	+	11.5257i	0.274888	+	0.476121i
$587$	18.9349	−	27.0418i	0.781525	−	1.11613i	−0.208880	−	0.977941i	$-0.566982\pi$
$587$	18.9349	−	27.0418i	0.781525	−	1.11613i	0.990405	−	0.138193i	$-0.0441293\pi$
$588$		0			0
$589$	−17.3784	−	47.7467i	−0.716064	−	1.96737i
$590$	16.2667	−	13.6691i	0.669690	−	0.562746i
$591$		0			0
$592$	−0.195887	+	2.23899i	−0.00805089	+	0.0920221i
$593$	6.32665	−	6.32665i	0.259804	−	0.259804i	−0.565170	−	0.824974i	$-0.691189\pi$
$593$	6.32665	−	6.32665i	0.259804	−	0.259804i	0.824974	+	0.565170i	$0.191189\pi$
$594$		0			0
$595$	20.7289	−	1.82835i	0.849804	−	0.0749551i
$596$	−4.84617	−	5.77544i	−0.198507	−	0.236571i
$597$		0			0
$598$	−43.4821	+	30.4465i	−1.77811	+	1.24505i
$599$	−7.37153	+	2.68302i	−0.301193	+	0.109625i	−0.488196	−	0.872734i	$-0.662345\pi$
$599$	−7.37153	+	2.68302i	−0.301193	+	0.109625i	0.187003	+	0.982359i	$0.440123\pi$
$600$		0			0
$601$	−3.87288	−	21.9642i	−0.157978	−	0.895938i	−0.956012	−	0.293326i	$-0.905238\pi$
$601$	−3.87288	−	21.9642i	−0.157978	−	0.895938i	0.798034	−	0.602612i	$-0.205873\pi$
$602$	−3.08820	+	11.5253i	−0.125866	+	0.469737i
$603$		0			0
$604$	6.91797	+	3.99409i	0.281488	+	0.162517i
$605$	−23.7100	−	6.33506i	−0.963948	−	0.257557i
$606$		0			0
$607$	28.1948	−	2.46673i	1.14439	−	0.100121i	0.500852	−	0.865533i	$-0.333020\pi$
$607$	28.1948	−	2.46673i	1.14439	−	0.100121i	0.643541	+	0.765412i	$0.277465\pi$
$608$	−5.00232	+	0.437646i	−0.202871	+	0.0177489i
$609$		0			0
$610$	6.88781	+	11.9105i	0.278879	+	0.482244i
$611$	13.3803	+	7.72513i	0.541310	+	0.312525i
$612$		0			0
$613$	6.67128	−	24.8976i	0.269451	−	1.00560i	−0.690019	−	0.723791i	$-0.742398\pi$
$613$	6.67128	−	24.8976i	0.269451	−	1.00560i	0.959470	−	0.281812i	$-0.0909355\pi$
$614$	1.89976	+	10.7741i	0.0766679	+	0.434806i
$615$		0			0
$616$	−0.497555	+	0.181095i	−0.0200471	+	0.00729653i
$617$	27.4565	−	19.2253i	1.10536	−	0.773981i	0.129326	−	0.991602i	$-0.458719\pi$
$617$	27.4565	−	19.2253i	1.10536	−	0.773981i	0.976033	+	0.217622i	$0.0698299\pi$
$618$		0			0
$619$	−16.3858	−	19.5278i	−0.658601	−	0.784890i	0.328583	−	0.944475i	$-0.393429\pi$
$619$	−16.3858	−	19.5278i	−0.658601	−	0.784890i	−0.987184	+	0.159585i	$0.948984\pi$
$620$	1.98800	+	22.5389i	0.0798399	+	0.905185i
$621$		0			0
$622$	−2.41074	+	2.41074i	−0.0966620	+	0.0966620i
$623$	1.74274	−	19.9196i	0.0698215	−	0.798064i
$624$		0			0
$625$	−4.41098	−	24.6078i	−0.176439	−	0.984312i
$626$	2.83351	+	7.78500i	0.113250	+	0.311151i
$627$		0			0
$628$	5.54303	−	7.91626i	0.221191	−	0.315893i
$629$	3.09831	+	5.36643i	0.123538	+	0.213974i
$630$		0			0
$631$	−5.38398	+	9.32532i	−0.214333	+	0.371235i	−0.953066	−	0.302763i	$-0.902091\pi$
$631$	−5.38398	+	9.32532i	−0.214333	+	0.371235i	0.738733	+	0.673998i	$0.235424\pi$
$632$	2.95999	+	6.34772i	0.117742	+	0.252499i
$633$		0			0
$634$	20.0320	−	23.8732i	0.795571	−	0.948125i
$635$	−18.9749	+	3.35965i	−0.752995	+	0.133324i
$636$		0			0
$637$	−28.0631	+	13.0860i	−1.11190	+	0.518488i
$638$	−0.0111342	−	0.0415535i	−0.000440808	−	0.00164512i
$639$		0			0
$640$	2.20237	+	0.386728i	0.0870564	+	0.0152868i
$641$	−34.5159	+	6.08608i	−1.36330	+	0.240386i	−0.806977	−	0.590583i	$-0.798898\pi$
$641$	−34.5159	+	6.08608i	−1.36330	+	0.240386i	−0.556319	+	0.830969i	$0.687787\pi$
$642$		0			0
$643$	12.3592	+	5.76318i	0.487398	+	0.227278i	0.650753	−	0.759290i	$-0.274454\pi$
$643$	12.3592	+	5.76318i	0.487398	+	0.227278i	−0.163354	+	0.986567i	$0.552231\pi$
$644$	−4.41465	+	25.0367i	−0.173961	+	0.986584i
$645$		0			0
$646$	−10.6054	+	8.89899i	−0.417264	+	0.350126i
$647$	−19.4755	−	19.4755i	−0.765662	−	0.765662i	0.211677	−	0.977340i	$-0.432107\pi$
$647$	−19.4755	−	19.4755i	−0.765662	−	0.765662i	−0.977340	+	0.211677i	$0.932107\pi$
$648$		0			0
$649$			1.49055i			0.0585091i
$650$	−27.0264	−	22.6127i	−1.06006	−	0.886942i
$651$		0			0
$652$	−8.19640	−	11.7057i	−0.320996	−	0.458430i
$653$	−18.3431	+	39.3369i	−0.717821	+	1.53937i	0.119604	+	0.992822i	$0.461837\pi$
$653$	−18.3431	+	39.3369i	−0.717821	+	1.53937i	−0.837426	+	0.546551i	$0.815940\pi$
$654$		0			0
$655$	11.8602	−	3.18694i	0.463417	−	0.124524i
$656$	5.75905	−	3.32499i	0.224853	−	0.129819i
$657$		0			0
$658$	7.14759	−	1.91519i	0.278642	−	0.0746619i
$659$	−7.20356	−	2.62188i	−0.280611	−	0.102134i	0.197881	−	0.980226i	$-0.436594\pi$
$659$	−7.20356	−	2.62188i	−0.280611	−	0.102134i	−0.478492	+	0.878092i	$0.658816\pi$
$660$		0			0
$661$	0.132252	+	0.110973i	0.00514401	+	0.00431634i	0.645356	−	0.763882i	$-0.276709\pi$
$661$	0.132252	+	0.110973i	0.00514401	+	0.00431634i	−0.640212	+	0.768198i	$0.721153\pi$
$662$	0.778126	+	8.89402i	0.0302427	+	0.345676i
$663$		0			0
$664$	0.466682	−	1.28220i	0.0181108	−	0.0497589i
$665$	35.6053	−	12.9878i	1.38071	−	0.503647i
$666$		0			0
$667$	−1.99516	−	0.534602i	−0.0772530	−	0.0206999i
$668$	−5.84239	−	4.09089i	−0.226049	−	0.158281i
$669$		0			0
$670$	−11.4276	+	5.33864i	−0.441486	+	0.206250i
$671$	−0.950543	−	0.167606i	−0.0366953	−	0.00647037i
$672$		0			0
$673$	37.8215	+	3.30895i	1.45791	+	0.127551i	0.788360	−	0.615214i	$-0.210930\pi$
$673$	37.8215	+	3.30895i	1.45791	+	0.127551i	0.669552	+	0.742765i	$0.266486\pi$
$674$	−8.68199			−0.334418
$675$		0			0
$676$	−36.6704			−1.41040
$677$	39.8783	+	3.48890i	1.53265	+	0.134089i	0.822012	−	0.569470i	$-0.192852\pi$
$677$	39.8783	+	3.48890i	1.53265	+	0.134089i	0.710636	+	0.703560i	$0.248407\pi$
$678$		0			0
$679$	9.17989	+	1.61866i	0.352292	+	0.0621186i
$680$	5.58552	−	2.60939i	0.214195	−	0.100066i
$681$		0			0
$682$	−1.30023	−	0.910434i	−0.0497886	−	0.0348623i
$683$	−9.73412	−	2.60825i	−0.372466	−	0.0998019i	0.0677301	−	0.997704i	$-0.478424\pi$
$683$	−9.73412	−	2.60825i	−0.372466	−	0.0998019i	−0.440196	+	0.897902i	$0.645091\pi$
$684$		0			0
$685$	−32.4420	+	11.8340i	−1.23955	+	0.452153i
$686$	3.00910	−	8.26744i	0.114888	−	0.315652i
$687$		0			0
$688$	0.308089	+	3.52147i	0.0117458	+	0.134255i
$689$	31.6158	+	26.5288i	1.20447	+	1.01067i
$690$		0			0
$691$	−10.8420	−	3.94617i	−0.412449	−	0.150119i	0.127458	−	0.991844i	$-0.459318\pi$
$691$	−10.8420	−	3.94617i	−0.412449	−	0.150119i	−0.539907	+	0.841725i	$0.681541\pi$
$692$	−20.5406	+	5.50383i	−0.780835	+	0.209224i
$693$		0			0
$694$	−15.7465	+	9.09126i	−0.597730	+	0.345100i
$695$	−26.8164	+	7.20582i	−1.01721	+	0.273332i
$696$		0			0
$697$	7.74844	−	16.6166i	0.293493	−	0.629398i
$698$	−4.95665	−	7.07883i	−0.187612	−	0.267938i
$699$		0			0
$700$	−16.8108	+	1.49477i	−0.635389	+	0.0564970i
$701$		−	9.18014i		−	0.346729i	−0.984858	−	0.173365i	$-0.944536\pi$
$701$		−	9.18014i		−	0.346729i	0.984858	−	0.173365i	$-0.0554639\pi$
$702$		0			0
$703$	7.98032	+	7.98032i	0.300984	+	0.300984i
$704$	−0.120166	+	0.100831i	−0.00452891	+	0.00380021i
$705$		0			0
$706$	2.21453	−	12.5593i	0.0833451	−	0.472674i
$707$	7.33105	+	3.41852i	0.275712	+	0.128567i
$708$		0			0
$709$	−0.207408	+	0.0365716i	−0.00778937	+	0.00137348i	−0.177542	−	0.984113i	$-0.556814\pi$
$709$	−0.207408	+	0.0365716i	−0.00778937	+	0.00137348i	0.169752	+	0.985487i	$0.445703\pi$
$710$	16.1256	+	2.83159i	0.605181	+	0.106268i
$711$		0			0
$712$	−1.53322	−	5.72206i	−0.0574599	−	0.214443i
$713$	−69.0722	+	32.2089i	−2.58677	+	1.20623i
$714$		0			0
$715$	2.43421	−	0.430995i	0.0910342	−	0.0161183i
$716$	−6.69144	+	7.97455i	−0.250071	+	0.298023i
$717$		0			0
$718$	−11.0035	−	23.5970i	−0.410645	−	0.880632i
$719$	−6.88689	+	11.9284i	−0.256838	+	0.444856i	−0.965393	−	0.260799i	$-0.916014\pi$
$719$	−6.88689	+	11.9284i	−0.256838	+	0.444856i	0.708555	+	0.705655i	$0.249347\pi$
$720$		0			0
$721$	17.4040	+	30.1446i	0.648158	+	1.12264i
$722$	−3.56460	+	5.09078i	−0.132661	+	0.189459i
$723$		0			0
$724$	−0.324168	−	0.890644i	−0.0120476	−	0.0331005i
$725$	−0.00194370	−	1.37122i	−7.21871e−5	−	0.0509258i
$726$		0			0
$727$	−2.37274	+	27.1205i	−0.0880000	+	1.00585i	0.815926	+	0.578156i	$0.196228\pi$
$727$	−2.37274	+	27.1205i	−0.0880000	+	1.00585i	−0.903926	+	0.427689i	$0.859328\pi$
$728$	−16.8214	+	16.8214i	−0.623443	+	0.623443i
$729$		0			0
$730$	−2.60889	−	29.5783i	−0.0965595	−	1.09474i
$731$	6.26461	+	7.46587i	0.231705	+	0.276135i
$732$		0			0
$733$	24.5528	−	17.1921i	0.906880	−	0.635004i	−0.0242446	−	0.999706i	$-0.507718\pi$
$733$	24.5528	−	17.1921i	0.906880	−	0.635004i	0.931124	+	0.364702i	$0.118829\pi$
$734$	−23.6624	+	8.61240i	−0.873394	+	0.317889i
$735$		0			0
$736$	1.30788	+	7.41734i	0.0482090	+	0.273407i
$737$	0.229013	−	0.854688i	0.00843581	−	0.0314829i
$738$		0			0
$739$	34.9872	+	20.1999i	1.28703	+	0.743065i	0.978123	−	0.208029i	$-0.0667048\pi$
$739$	34.9872	+	20.1999i	1.28703	+	0.743065i	0.308903	+	0.951093i	$0.400038\pi$
$740$	−2.51592	−	4.35057i	−0.0924870	−	0.159930i
$741$		0			0
$742$	19.6913	−	1.72277i	0.722891	−	0.0632447i
$743$	44.8398	−	3.92298i	1.64501	−	0.143920i	0.773335	−	0.633997i	$-0.218587\pi$
$743$	44.8398	−	3.92298i	1.64501	−	0.143920i	0.871679	+	0.490077i	$0.163031\pi$
$744$		0			0
$745$	16.2870	+	4.35173i	0.596711	+	0.159435i
$746$	12.4454	+	7.18538i	0.455660	+	0.263076i
$747$		0			0
$748$	−0.111936	+	0.417750i	−0.00409278	+	0.0152745i
$749$	−5.35534	−	30.3717i	−0.195680	−	1.10976i
$750$		0			0
$751$	−30.1604	+	10.9775i	−1.10057	+	0.400574i	−0.827526	−	0.561428i	$-0.810252\pi$
$751$	−30.1604	+	10.9775i	−1.10057	+	0.400574i	−0.273043	+	0.962002i	$0.588030\pi$
$752$	1.79577	−	1.25741i	0.0654851	−	0.0458532i
$753$		0			0
$754$	−1.24238	−	1.48061i	−0.0452447	−	0.0539206i
$755$	−17.7930	+	1.56940i	−0.647555	+	0.0571162i
$756$		0			0
$757$	−17.3572	+	17.3572i	−0.630859	+	0.630859i	−0.948284	−	0.317424i	$-0.897182\pi$
$757$	−17.3572	+	17.3572i	−0.630859	+	0.630859i	0.317424	+	0.948284i	$0.397182\pi$
$758$	−1.85137	+	21.1613i	−0.0672449	+	0.768612i
$759$		0			0
$760$	8.59622	−	7.22347i	0.311818	−	0.262023i
$761$	4.09191	+	11.2424i	0.148332	+	0.407538i	0.991499	−	0.130113i	$-0.0415340\pi$
$761$	4.09191	+	11.2424i	0.148332	+	0.407538i	−0.843167	+	0.537651i	$0.819312\pi$
$762$		0			0
$763$	−12.0677	+	17.2344i	−0.436879	+	0.623928i
$764$	0.939266	+	1.62686i	0.0339814	+	0.0588576i
$765$		0			0
$766$	−14.6854	+	25.4359i	−0.530605	+	0.919035i
$767$	28.3020	+	60.6937i	1.02192	+	2.19152i
$768$		0			0
$769$	3.23373	−	3.85381i	0.116611	−	0.138972i	−0.704581	−	0.709624i	$-0.748865\pi$
$769$	3.23373	−	3.85381i	0.116611	−	0.138972i	0.821192	+	0.570652i	$0.193309\pi$
$770$	0.678409	−	0.970331i	0.0244482	−	0.0349683i
$771$		0			0
$772$	−7.47251	+	3.48449i	−0.268942	+	0.125410i
$773$	−0.745136	−	2.78088i	−0.0268007	−	0.100021i	0.951230	−	0.308483i	$-0.0998212\pi$
$773$	−0.745136	−	2.78088i	−0.0268007	−	0.100021i	−0.978031	+	0.208461i	$0.933155\pi$
$774$		0			0
$775$	−32.5762	−	38.7113i	−1.17017	−	1.39055i
$776$	2.71962	−	0.479543i	0.0976288	−	0.0172146i
$777$		0			0
$778$	−7.91805	−	3.69225i	−0.283876	−	0.132373i
$779$	5.79852	−	32.8850i	0.207753	−	1.17823i
$780$		0			0
$781$	−0.879842	+	0.738275i	−0.0314832	+	0.0264175i
$782$	14.6835	+	14.6835i	0.525079	+	0.525079i
$783$		0			0
$784$			4.39351i			0.156911i
$785$	0.0153155	+	21.6093i	0.000546635	+	0.771269i
$786$		0			0
$787$	−27.4814	−	39.2475i	−0.979605	−	1.39902i	−0.916060	−	0.401042i	$-0.868648\pi$
$787$	−27.4814	−	39.2475i	−0.979605	−	1.39902i	−0.0635454	−	0.997979i	$-0.520241\pi$
$788$	4.55132	−	9.76033i	0.162134	−	0.347697i
$789$		0			0
$790$	−13.5686	−	7.82103i	−0.482750	−	0.278260i
$791$	−20.4262	+	11.7931i	−0.726274	+	0.419314i
$792$		0			0
$793$	−41.8877	+	11.2238i	−1.48748	+	0.398568i
$794$	4.46093	+	1.62365i	0.158312	+	0.0576210i
$795$		0			0
$796$	0.367380	+	0.308268i	0.0130214	+	0.0109263i
$797$	2.92961	+	33.4856i	0.103772	+	1.18612i	0.852313	+	0.523032i	$0.175199\pi$
$797$	2.92961	+	33.4856i	0.103772	+	1.18612i	−0.748541	+	0.663088i	$0.769245\pi$
$798$		0			0
$799$	2.06721	−	5.67962i	0.0731327	−	0.200930i
$800$	−4.52854	+	2.11951i	−0.160108	+	0.0749361i
$801$		0			0
$802$	15.7949	+	4.23223i	0.557737	+	0.149445i
$803$	1.70633	+	1.19478i	0.0602150	+	0.0421630i
$804$		0			0
$805$	−24.0613	−	51.5042i	−0.848048	−	1.81528i
$806$	−70.2314	−	12.3837i	−2.47379	−	0.436197i
$807$		0			0
$808$	2.38729	+	0.208861i	0.0839847	+	0.00734771i
$809$	39.5234			1.38957			0.694784	−	0.719218i	$-0.255500\pi$
$809$	39.5234			1.38957			0.694784	+	0.719218i	$0.255500\pi$
$810$		0			0
$811$	−21.1540			−0.742818			−0.371409	−	0.928469i	$-0.621125\pi$
$811$	−21.1540			−0.742818			−0.371409	+	0.928469i	$0.621125\pi$
$812$	−0.922169	−	0.0806793i	−0.0323618	−	0.00283129i
$813$		0			0
$814$	0.347205	+	0.0612217i	0.0121695	+	0.00214582i
$815$	30.0341	+	10.9074i	1.05205	+	0.382070i
$816$		0			0
$817$	14.5402	+	10.1812i	0.508699	+	0.356195i
$818$	−2.91720	−	0.781662i	−0.101998	−	0.0273302i
$819$		0			0
$820$	−6.27469	+	13.4811i	−0.219122	+	0.470779i
$821$	14.3479	−	39.4206i	0.500745	−	1.37579i	−0.389803	−	0.920898i	$-0.627457\pi$
$821$	14.3479	−	39.4206i	0.500745	−	1.37579i	0.890548	−	0.454889i	$-0.150321\pi$
$822$		0			0
$823$	4.02896	+	46.0512i	0.140441	+	1.60524i	0.660307	+	0.750996i	$0.270426\pi$
$823$	4.02896	+	46.0512i	0.140441	+	1.60524i	−0.519866	+	0.854248i	$0.674018\pi$
$824$	7.89958	+	6.62853i	0.275195	+	0.230916i
$825$		0			0
$826$	30.1393	+	10.9698i	1.04868	+	0.381689i
$827$	−47.9396	+	12.8454i	−1.66702	+	0.446677i	−0.964306	−	0.264792i	$-0.914697\pi$
$827$	−47.9396	+	12.8454i	−1.66702	+	0.446677i	−0.702717	+	0.711469i	$0.748030\pi$
$828$		0			0
$829$	−39.6831	+	22.9111i	−1.37825	+	0.795734i	−0.991949	−	0.126639i	$-0.959581\pi$
$829$	−39.6831	+	22.9111i	−1.37825	+	0.795734i	−0.386302	+	0.922372i	$0.626248\pi$
$830$	0.791767	+	2.94656i	0.0274826	+	0.102277i
$831$		0			0
$832$	−2.97850	+	6.38741i	−0.103261	+	0.221444i
$833$	6.94782	+	9.92252i	0.240728	+	0.343795i
$834$		0			0
$835$	15.9482	−	0.0113032i	0.551909	−	0.000391164i
$836$			0.787686i			0.0272427i
$837$		0			0
$838$	26.4939	+	26.4939i	0.915216	+	0.915216i
$839$	−38.0359	+	31.9159i	−1.31314	+	1.10186i	−0.325433	+	0.945565i	$0.605510\pi$
$839$	−38.0359	+	31.9159i	−1.31314	+	1.10186i	−0.987711	+	0.156293i	$0.950045\pi$
$840$		0			0
$841$	−5.02274	+	28.4854i	−0.173198	+	0.982254i
$842$	−8.79673	−	4.10198i	−0.303155	−	0.141364i
$843$		0			0
$844$	−11.4749	+	2.02333i	−0.394982	+	0.0696460i
$845$	67.1351	−	47.0795i	2.30952	−	1.61958i
$846$		0			0
$847$	−9.58838	−	35.7843i	−0.329460	−	1.22956i
$848$	5.30734	−	2.47486i	0.182255	−	0.0849869i
$849$		0			0
$850$	−6.87572	+	11.9482i	−0.235835	+	0.409819i
$851$	10.8811	−	12.9676i	0.373000	−	0.444524i
$852$		0			0
$853$	−6.54631	−	14.0386i	−0.224141	−	0.480673i	0.761790	−	0.647824i	$-0.224321\pi$
$853$	−6.54631	−	14.0386i	−0.224141	−	0.480673i	−0.985931	+	0.167152i	$0.946543\pi$
$854$	−10.3847	+	17.9868i	−0.355356	+	0.615494i
$855$		0			0
$856$	−4.56834	−	7.91260i	−0.156143	−	0.270447i
$857$	12.8243	−	18.3150i	0.438071	−	0.625630i	−0.538036	−	0.842922i	$-0.680834\pi$
$857$	12.8243	−	18.3150i	0.438071	−	0.625630i	0.976107	+	0.217292i	$0.0697224\pi$
$858$		0			0
$859$	3.57578	+	9.82439i	0.122004	+	0.335204i	0.985627	−	0.168934i	$-0.0540325\pi$
$859$	3.57578	+	9.82439i	0.122004	+	0.335204i	−0.863623	+	0.504138i	$0.831810\pi$
$860$	−5.08510	−	6.05147i	−0.173400	−	0.206353i
$861$		0			0
$862$	−0.129070	+	1.47528i	−0.00439615	+	0.0502482i
$863$	−12.2209	+	12.2209i	−0.416005	+	0.416005i	−0.883824	−	0.467819i	$-0.845040\pi$
$863$	−12.2209	+	12.2209i	−0.416005	+	0.416005i	0.467819	+	0.883824i	$0.345040\pi$
$864$		0			0
$865$	30.5389	−	36.4473i	1.03836	−	1.23925i
$866$	2.58890	+	3.08534i	0.0879746	+	0.104844i
$867$		0			0
$868$	−27.9785	+	19.5907i	−0.949651	+	0.664953i
$869$	1.03242	−	0.375769i	0.0350223	−	0.0127471i
$870$		0			0
$871$	−6.90330	−	39.1506i	−0.233909	−	1.32657i
$872$	−1.61324	+	6.02070i	−0.0546313	+	0.203887i
$873$		0			0
$874$	32.7532	+	18.9101i	1.10790	+	0.639644i
$875$	28.8577	−	24.3192i	0.975567	−	0.822139i
$876$		0			0
$877$	−33.2624	+	2.91008i	−1.12319	+	0.0982665i	−0.633582	−	0.773676i	$-0.718416\pi$
$877$	−33.2624	+	2.91008i	−1.12319	+	0.0982665i	−0.489609	+	0.871942i	$0.662860\pi$
$878$	−4.71509	+	0.412517i	−0.159127	+	0.0139218i
$879$		0			0
$880$	0.0905435	−	0.338873i	0.00305222	−	0.0114234i
$881$	−26.7397	−	15.4382i	−0.900882	−	0.520125i	−0.0233961	−	0.999726i	$-0.507448\pi$
$881$	−26.7397	−	15.4382i	−0.900882	−	0.520125i	−0.877486	+	0.479602i	$0.840781\pi$
$882$		0			0
$883$	4.35431	−	16.2505i	0.146534	−	0.546874i	−0.853148	−	0.521669i	$-0.825310\pi$
$883$	4.35431	−	16.2505i	0.146534	−	0.546874i	0.999682	−	0.0252047i	$-0.00802374\pi$
$884$	3.37416	+	19.1358i	0.113485	+	0.643607i
$885$		0			0
$886$	−24.4096	+	8.88437i	−0.820057	+	0.298476i
$887$	17.0340	−	11.9273i	0.571946	−	0.400481i	−0.251515	−	0.967853i	$-0.580929\pi$
$887$	17.0340	−	11.9273i	0.571946	−	0.400481i	0.823461	+	0.567372i	$0.192040\pi$
$888$		0			0
$889$	−18.6979	−	22.2833i	−0.627108	−	0.747358i
$890$	10.1533	+	8.50734i	0.340338	+	0.285167i
$891$		0			0
$892$	10.0764	−	10.0764i	0.337384	−	0.337384i
$893$	0.959422	−	10.9662i	0.0321058	−	0.366971i
$894$		0			0
$895$	2.01234	−	23.1904i	0.0672649	−	0.775169i
$896$	1.15446	+	3.17186i	0.0385679	+	0.105965i
$897$		0			0
$898$	−3.96808	+	5.66701i	−0.132417	+	0.189111i
$899$	−1.38752	−	2.40325i	−0.0462763	−	0.0801529i
$900$		0			0
$901$	8.07268	−	13.9823i	0.268940	−	0.465818i
$902$	−0.440854	−	0.945414i	−0.0146788	−	0.0314788i
$903$		0			0
$904$	−4.49156	+	5.35283i	−0.149387	+	0.178032i
$905$	1.73693	+	1.21438i	0.0577376	+	0.0403674i
$906$		0			0
$907$	20.7260	−	9.66469i	0.688195	−	0.320911i	−0.0468760	−	0.998901i	$-0.514927\pi$
$907$	20.7260	−	9.66469i	0.688195	−	0.320911i	0.735071	+	0.677990i	$0.237149\pi$
$908$	−0.773438	−	2.88651i	−0.0256675	−	0.0957922i
$909$		0			0
$910$	9.19991	−	52.3924i	0.304974	−	1.73679i
$911$	9.67975	−	1.70680i	0.320705	−	0.0565489i	−0.0109786	−	0.999940i	$-0.503495\pi$
$911$	9.67975	−	1.70680i	0.320705	−	0.0565489i	0.331683	+	0.943391i	$0.392384\pi$
$912$		0			0
$913$	−0.193986	−	0.0904573i	−0.00642001	−	0.00299370i
$914$	−2.94259	+	16.6883i	−0.0973323	+	0.551999i
$915$		0			0
$916$	10.0725	−	8.45187i	0.332806	−	0.279258i
$917$	13.1087	+	13.1087i	0.432888	+	0.432888i
$918$		0			0
$919$			4.32140i			0.142550i	0.997457	+	0.0712749i	$0.0227067\pi$
$919$			4.32140i			0.142550i	−0.997457	+	0.0712749i	$0.977293\pi$
$920$	−11.9172	−	11.9003i	−0.392899	−	0.392342i
$921$		0			0
$922$	22.2405	+	31.7628i	0.732453	+	1.04605i
$923$	−21.8083	+	46.7680i	−0.717828	+	1.53939i
$924$		0			0
$925$	10.1916	+	4.73483i	0.335097	+	0.155680i
$926$	−20.4431	+	11.8029i	−0.671803	+	0.387866i
$927$		0			0
$928$	−0.264900	+	0.0709796i	−0.00869575	+	0.00233002i
$929$	29.4359	+	10.7138i	0.965761	+	0.351508i	0.776289	−	0.630378i	$-0.217100\pi$
$929$	29.4359	+	10.7138i	0.965761	+	0.351508i	0.189473	+	0.981886i	$0.439322\pi$
$930$		0			0
$931$	16.9002	+	14.1810i	0.553882	+	0.464762i
$932$	−0.856705	−	9.79218i	−0.0280623	−	0.320753i
$933$		0			0
$934$	5.84848	−	16.0686i	0.191368	−	0.525779i
$935$	−0.331401	−	0.908513i	−0.0108380	−	0.0297116i
$936$		0			0
$937$	25.3282	+	6.78666i	0.827435	+	0.221711i	0.647595	−	0.761985i	$-0.275775\pi$
$937$	25.3282	+	6.78666i	0.827435	+	0.221711i	0.179841	+	0.983696i	$0.442442\pi$
$938$	−15.5966	−	10.9209i	−0.509248	−	0.356579i
$939$		0			0
$940$	−1.67331	+	4.60755i	−0.0545774	+	0.150282i
$941$	−22.1394	−	3.90377i	−0.721722	−	0.127259i	−0.199291	−	0.979940i	$-0.563864\pi$
$941$	−22.1394	−	3.90377i	−0.721722	−	0.127259i	−0.522432	+	0.852681i	$0.674975\pi$
$942$		0			0
$943$	−49.8955	−	4.36529i	−1.62482	−	0.142153i
$944$	9.50209			0.309267
$945$		0			0
$946$	0.554507			0.0180286
$947$	36.2086	+	3.16785i	1.17662	+	0.102941i	0.658646	−	0.752453i	$-0.271130\pi$
$947$	36.2086	+	3.16785i	1.17662	+	0.102941i	0.517977	+	0.855394i	$0.326685\pi$
$948$		0			0
$949$	92.1663	+	16.2514i	2.99184	+	0.527543i
$950$	−6.46382	+	24.2608i	−0.209714	+	0.787124i
$951$		0			0
$952$	7.62324	+	5.33785i	0.247071	+	0.173001i
$953$	7.20699	+	1.93111i	0.233457	+	0.0625547i	0.373651	−	0.927569i	$-0.378106\pi$
$953$	7.20699	+	1.93111i	0.233457	+	0.0625547i	−0.140194	+	0.990124i	$0.544773\pi$
$954$		0			0
$955$	−3.80822	−	1.77252i	−0.123231	−	0.0573574i
$956$	2.65701	−	7.30007i	0.0859338	−	0.236101i
$957$		0			0
$958$	−2.87675	−	32.8814i	−0.0929435	−	1.06235i
$959$	−39.9330	−	33.5078i	−1.28950	−	1.08202i
$960$		0			0
$961$	−67.0855	−	24.4171i	−2.16405	−	0.787650i
$962$	15.3003	−	4.09972i	0.493303	−	0.132180i
$963$		0			0
$964$	11.8829	−	6.86058i	0.382722	−	0.220965i
$965$	9.20688	−	15.9729i	0.296380	−	0.514186i
$966$		0			0
$967$	−22.8262	+	48.9510i	−0.734042	+	1.57416i	0.0823126	+	0.996607i	$0.473769\pi$
$967$	−22.8262	+	48.9510i	−0.734042	+	1.57416i	−0.816354	+	0.577551i	$0.804008\pi$
$968$	−6.29523	−	8.99052i	−0.202336	−	0.288966i
$969$		0			0
$970$	−4.36334	+	4.36953i	−0.140099	+	0.140297i
$971$			31.5940i			1.01390i	0.861975	+	0.506951i	$0.169227\pi$
$971$			31.5940i			1.01390i	−0.861975	+	0.506951i	$0.830773\pi$
$972$		0			0
$973$	−29.6393	−	29.6393i	−0.950194	−	0.950194i
$974$	4.89123	−	4.10423i	0.156725	−	0.131508i
$975$		0			0
$976$	−1.06847	+	6.05962i	−0.0342010	+	0.193964i
$977$	10.5588	+	4.92366i	0.337807	+	0.157522i	0.584118	−	0.811669i	$-0.301441\pi$
$977$	10.5588	+	4.92366i	0.337807	+	0.157522i	−0.246311	+	0.969191i	$0.579218\pi$
$978$		0			0
$979$	−0.915138	+	0.161363i	−0.0292479	+	0.00515720i
$980$	−5.64062	−	8.04350i	−0.180183	−	0.256940i
$981$		0			0
$982$	0.396220	+	1.47871i	0.0126439	+	0.0471877i
$983$	−24.5995	+	11.4709i	−0.784601	+	0.365865i	−0.773275	−	0.634070i	$-0.781383\pi$
$983$	−24.5995	+	11.4709i	−0.784601	+	0.365865i	−0.0113256	+	0.999936i	$0.503605\pi$
$984$		0			0
$985$	4.19842	+	23.7122i	0.133773	+	0.755532i
$986$	−0.486017	+	0.579212i	−0.0154779	+	0.0184459i
$987$		0			0
$988$	14.9563	+	32.0739i	0.475823	+	1.02041i
$989$	13.3121	−	23.0573i	0.423301	−	0.733178i
$990$		0			0
$991$	21.5210	+	37.2754i	0.683636	+	1.18409i	0.973863	+	0.227135i	$0.0729358\pi$
$991$	21.5210	+	37.2754i	0.683636	+	1.18409i	−0.290227	+	0.956958i	$0.593731\pi$
$992$	−5.80393	+	8.28887i	−0.184275	+	0.263172i
$993$		0			0
$994$	8.45288	+	23.2241i	0.268109	+	0.736623i
$995$	−1.06836	−	0.0927063i	−0.0338693	−	0.00293899i
$996$		0			0
$997$	5.39187	−	61.6293i	0.170762	−	1.95182i	−0.114626	−	0.993409i	$-0.536567\pi$
$997$	5.39187	−	61.6293i	0.170762	−	1.95182i	0.285388	−	0.958412i	$-0.407878\pi$
$998$	12.1996	−	12.1996i	0.386173	−	0.386173i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.773.2		216
3.2	odd	2		270.2.r.a.113.14	✓	216
5.2	odd	4	inner	810.2.s.a.287.18		216
15.2	even	4		270.2.r.a.167.1	yes	216
27.11	odd	18	inner	810.2.s.a.683.18		216
27.16	even	9		270.2.r.a.173.1	yes	216
135.92	even	36	inner	810.2.s.a.197.2		216
135.97	odd	36		270.2.r.a.227.14	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.14	✓	216	3.2	odd	2
270.2.r.a.167.1	yes	216	15.2	even	4
270.2.r.a.173.1	yes	216	27.16	even	9
270.2.r.a.227.14	yes	216	135.97	odd	36
810.2.s.a.197.2		216	135.92	even	36	inner
810.2.s.a.287.18		216	5.2	odd	4	inner
810.2.s.a.683.18		216	27.11	odd	18	inner
810.2.s.a.773.2		216	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.02590 + 0.946439i) q^{5} +(-2.76499 - 1.93607i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(0.984808 + 0.173648i) q^{4} +(-2.02590 + 0.946439i) q^{5} +(-2.76499 - 1.93607i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(2.10067 - 0.766269i) q^{10} +(-0.0536510 + 0.147405i) q^{11} +(0.614250 + 7.02091i) q^{13} +(2.58573 + 2.16968i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.66312 - 0.713580i) q^{17} +(4.34868 - 2.51071i) q^{19} +(-2.15947 + 0.580268i) q^{20} +(0.0662941 - 0.142168i) q^{22} +(-4.32004 - 6.16966i) q^{23} +(3.20851 - 3.83477i) q^{25} -7.04772i q^{26} +(-2.38679 - 2.38679i) q^{28} +(0.210083 - 0.176281i) q^{29} +(1.75712 - 9.96511i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(-2.71517 + 0.478758i) q^{34} +(7.43394 + 1.30537i) q^{35} +(0.581708 + 2.17096i) q^{37} +(-4.55096 + 2.12215i) q^{38} +(2.20182 - 0.389850i) q^{40} +(4.27452 - 5.09418i) q^{41} +(1.49392 + 3.20373i) q^{43} +(-0.0784326 + 0.135849i) q^{44} +(3.76588 + 6.52270i) q^{46} +(1.25741 - 1.79577i) q^{47} +(1.50267 + 4.12855i) q^{49} +(-3.53052 + 3.54054i) q^{50} +(-0.614250 + 7.02091i) q^{52} +(4.14082 - 4.14082i) q^{53} +(-0.0308185 - 0.349405i) q^{55} +(2.16968 + 2.58573i) q^{56} +(-0.224648 + 0.157300i) q^{58} +(8.92905 - 3.24991i) q^{59} +(1.06847 + 6.05962i) q^{61} +(-2.61895 + 9.77405i) q^{62} +(0.866025 + 0.500000i) q^{64} +(-7.88927 - 13.6423i) q^{65} +(-5.61930 + 0.491625i) q^{67} +(2.74657 - 0.240294i) q^{68} +(-7.29189 - 1.94832i) q^{70} +(6.34096 + 3.66095i) q^{71} +(3.43691 - 12.8267i) q^{73} +(-0.390282 - 2.21340i) q^{74} +(4.71859 - 1.71743i) q^{76} +(0.433730 - 0.303701i) q^{77} +(-4.50205 - 5.36533i) q^{79} +(-2.22742 + 0.196465i) q^{80} +(-4.70224 + 4.70224i) q^{82} +(-0.118923 + 1.35929i) q^{83} +(-4.71983 + 3.96611i) q^{85} +(-1.20902 - 3.32174i) q^{86} +(0.0899741 - 0.128496i) q^{88} +(2.96196 + 5.13026i) q^{89} +(11.8945 - 20.6019i) q^{91} +(-3.18306 - 6.82610i) q^{92} +(-1.40914 + 1.67935i) q^{94} +(-6.43374 + 9.20220i) q^{95} +(-2.50284 + 1.16709i) q^{97} +(-1.13712 - 4.24380i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q+O(q^{10}) \) 216 * q	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86} + 48 q^{92} + 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more