LMFDB - Embedded newform 270.2.m.a.143.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(17,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("270.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.m (of order $12$, degree $4$, 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:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			143.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	270.143
Dual form			270.2.m.a.17.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(0.283763 + 1.05902i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.22474 - 0.224745i) q^{10} +(5.44949 + 3.14626i) q^{11} +(-0.896575 + 3.34607i) q^{13} +(-0.548188 - 0.949490i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.14626 + 3.14626i) q^{17} -1.55051i q^{19} +(-2.09077 + 0.792893i) q^{20} +(-6.07812 - 1.62863i) q^{22} +(-0.965926 - 0.258819i) q^{23} +(4.74264 + 1.58346i) q^{25} -3.46410i q^{26} +(0.775255 + 0.775255i) q^{28} +(-1.57313 + 2.72474i) q^{29} +(2.22474 + 3.85337i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-3.85337 - 2.22474i) q^{34} +(-0.246405 - 2.43916i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(0.401302 + 1.49768i) q^{38} +(1.81431 - 1.30701i) q^{40} +(3.39898 - 1.96240i) q^{41} +(-3.34607 + 0.896575i) q^{43} +6.29253 q^{44} +1.00000 q^{46} +(-8.69333 + 2.32937i) q^{47} +(5.02118 - 2.89898i) q^{49} +(-4.99087 - 0.302023i) q^{50} +(0.896575 + 3.34607i) q^{52} +(6.61037 - 6.61037i) q^{53} +(-10.8990 - 8.89898i) q^{55} +(-0.949490 - 0.548188i) q^{56} +(0.814313 - 3.03906i) q^{58} +(-5.90326 - 10.2247i) q^{59} +(2.72474 - 4.71940i) q^{61} +(-3.14626 - 3.14626i) q^{62} -1.00000i q^{64} +(3.17914 - 7.06350i) q^{65} +(-3.65307 - 0.978838i) q^{67} +(4.29788 + 1.15161i) q^{68} +(0.869309 + 2.29227i) q^{70} -0.635674i q^{71} +(2.89898 + 2.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(-0.775255 - 1.34278i) q^{76} +(-1.78559 + 6.66390i) q^{77} +(-2.12132 - 1.22474i) q^{79} +(-1.41421 + 1.73205i) q^{80} +(-2.77526 + 2.77526i) q^{82} +(0.142483 + 0.531752i) q^{83} +(-5.81552 - 8.07277i) q^{85} +(3.00000 - 1.73205i) q^{86} +(-6.07812 + 1.62863i) q^{88} -2.36773 q^{89} -3.79796 q^{91} +(-0.965926 + 0.258819i) q^{92} +(7.79423 - 4.50000i) q^{94} +(-0.556198 + 3.42214i) q^{95} +(-2.89123 - 10.7902i) q^{97} +(-4.09978 + 4.09978i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100}) $ 8 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 + 24 * q^11 + 4 * q^16 - 8 * q^22 + 4 * q^25 + 16 * q^28 + 8 * q^31 - 24 * q^37 - 12 * q^38 + 4 * q^40 - 12 * q^41 + 8 * q^46 - 24 * q^50 - 48 * q^55 + 12 * q^56 - 4 * q^58 + 12 * q^61 + 24 * q^65 + 4 * q^67 + 12 * q^68 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 24 * q^77 - 32 * q^82 - 12 * q^83 - 20 * q^85 + 24 * q^86 - 8 * q^88 + 48 * q^91 + 24 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$6$		0			0
$7$	0.283763	+	1.05902i	0.107252	+	0.400271i	0.998591	−	0.0530669i	$-0.0168997\pi$
$7$	0.283763	+	1.05902i	0.107252	+	0.400271i	−0.891339	+	0.453338i	$0.850233\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	2.22474	−	0.224745i	0.703526	−	0.0710706i
$11$	5.44949	+	3.14626i	1.64308	+	0.948634i	0.979729	+	0.200329i	$0.0642011\pi$
$11$	5.44949	+	3.14626i	1.64308	+	0.948634i	0.663354	+	0.748305i	$0.269132\pi$
$12$		0			0
$13$	−0.896575	+	3.34607i	−0.248665	+	0.928032i	0.722840	+	0.691015i	$0.242836\pi$
$13$	−0.896575	+	3.34607i	−0.248665	+	0.928032i	−0.971506	+	0.237016i	$0.923830\pi$
$14$	−0.548188	−	0.949490i	−0.146509	−	0.253762i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.14626	+	3.14626i	0.763081	+	0.763081i	0.976878	−	0.213797i	$-0.0685831\pi$
$17$	3.14626	+	3.14626i	0.763081	+	0.763081i	−0.213797	+	0.976878i	$0.568583\pi$
$18$		0			0
$19$		−	1.55051i		−	0.355711i	−0.984057	−	0.177856i	$-0.943084\pi$
$19$		−	1.55051i		−	0.355711i	0.984057	−	0.177856i	$-0.0569160\pi$
$20$	−2.09077	+	0.792893i	−0.467510	+	0.177296i
$21$		0			0
$22$	−6.07812	−	1.62863i	−1.29586	−	0.347224i
$23$	−0.965926	−	0.258819i	−0.201409	−	0.0539675i	0.156704	−	0.987646i	$-0.449913\pi$
$23$	−0.965926	−	0.258819i	−0.201409	−	0.0539675i	−0.358113	+	0.933678i	$0.616580\pi$
$24$		0			0
$25$	4.74264	+	1.58346i	0.948528	+	0.316693i
$26$		−	3.46410i		−	0.679366i
$27$		0			0
$28$	0.775255	+	0.775255i	0.146509	+	0.146509i
$29$	−1.57313	+	2.72474i	−0.292123	+	0.505972i	−0.974312	−	0.225204i	$-0.927695\pi$
$29$	−1.57313	+	2.72474i	−0.292123	+	0.505972i	0.682188	+	0.731177i	$0.261028\pi$
$30$		0			0
$31$	2.22474	+	3.85337i	0.399576	+	0.692086i	0.993674	−	0.112307i	$-0.0358240\pi$
$31$	2.22474	+	3.85337i	0.399576	+	0.692086i	−0.594098	+	0.804393i	$0.702491\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$		0			0
$34$	−3.85337	−	2.22474i	−0.660848	−	0.381541i
$35$	−0.246405	−	2.43916i	−0.0416500	−	0.412293i
$36$		0			0
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	−0.909312	−	0.416115i	$-0.863391\pi$
$37$	−3.00000	+	3.00000i	−0.493197	+	0.493197i	0.416115	+	0.909312i	$0.363391\pi$
$38$	0.401302	+	1.49768i	0.0650997	+	0.242955i
$39$		0			0
$40$	1.81431	−	1.30701i	0.286868	−	0.206656i
$41$	3.39898	−	1.96240i	0.530831	−	0.306476i	−0.210524	−	0.977589i	$-0.567517\pi$
$41$	3.39898	−	1.96240i	0.530831	−	0.306476i	0.741355	+	0.671113i	$0.234184\pi$
$42$		0			0
$43$	−3.34607	+	0.896575i	−0.510270	+	0.136726i	−0.504762	−	0.863258i	$-0.668420\pi$
$43$	−3.34607	+	0.896575i	−0.510270	+	0.136726i	−0.00550783	+	0.999985i	$0.501753\pi$
$44$	6.29253			0.948634
$45$		0			0
$46$	1.00000			0.147442
$47$	−8.69333	+	2.32937i	−1.26805	+	0.339774i	−0.829285	−	0.558827i	$-0.811252\pi$
$47$	−8.69333	+	2.32937i	−1.26805	+	0.339774i	−0.438768	+	0.898600i	$0.644585\pi$
$48$		0			0
$49$	5.02118	−	2.89898i	0.717311	−	0.414140i
$50$	−4.99087	−	0.302023i	−0.705816	−	0.0427126i
$51$		0			0
$52$	0.896575	+	3.34607i	0.124333	+	0.464016i
$53$	6.61037	−	6.61037i	0.908004	−	0.908004i	−0.0881074	−	0.996111i	$-0.528082\pi$
$53$	6.61037	−	6.61037i	0.908004	−	0.908004i	0.996111	+	0.0881074i	$0.0280819\pi$
$54$		0			0
$55$	−10.8990	−	8.89898i	−1.46962	−	1.19994i
$56$	−0.949490	−	0.548188i	−0.126881	−	0.0732547i
$57$		0			0
$58$	0.814313	−	3.03906i	0.106925	−	0.399048i
$59$	−5.90326	−	10.2247i	−0.768539	−	1.33115i	−0.938355	−	0.345673i	$-0.887651\pi$
$59$	−5.90326	−	10.2247i	−0.768539	−	1.33115i	0.169816	−	0.985476i	$-0.445683\pi$
$60$		0			0
$61$	2.72474	−	4.71940i	0.348868	−	0.604257i	−0.637181	−	0.770714i	$-0.719900\pi$
$61$	2.72474	−	4.71940i	0.348868	−	0.604257i	0.986049	+	0.166458i	$0.0532329\pi$
$62$	−3.14626	−	3.14626i	−0.399576	−	0.399576i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	3.17914	−	7.06350i	0.394323	−	0.876120i
$66$		0			0
$67$	−3.65307	−	0.978838i	−0.446294	−	0.119584i	0.0286709	−	0.999589i	$-0.490873\pi$
$67$	−3.65307	−	0.978838i	−0.446294	−	0.119584i	−0.474965	+	0.880005i	$0.657539\pi$
$68$	4.29788	+	1.15161i	0.521194	+	0.139654i
$69$		0			0
$70$	0.869309	+	2.29227i	0.103902	+	0.273979i
$71$		−	0.635674i		−	0.0754407i	−0.999288	−	0.0377203i	$-0.987990\pi$
$71$		−	0.635674i		−	0.0754407i	0.999288	−	0.0377203i	$-0.0120096\pi$
$72$		0			0
$73$	2.89898	+	2.89898i	0.339300	+	0.339300i	0.856104	−	0.516804i	$-0.172878\pi$
$73$	2.89898	+	2.89898i	0.339300	+	0.339300i	−0.516804	+	0.856104i	$0.672878\pi$
$74$	2.12132	−	3.67423i	0.246598	−	0.427121i
$75$		0			0
$76$	−0.775255	−	1.34278i	−0.0889279	−	0.154028i
$77$	−1.78559	+	6.66390i	−0.203487	+	0.759422i
$78$		0			0
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	0.375897	−	0.926662i	$-0.377335\pi$
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	−0.614564	+	0.788867i	$0.710668\pi$
$80$	−1.41421	+	1.73205i	−0.158114	+	0.193649i
$81$		0			0
$82$	−2.77526	+	2.77526i	−0.306476	+	0.306476i
$83$	0.142483	+	0.531752i	0.0156395	+	0.0583674i	0.973305	−	0.229517i	$-0.0737147\pi$
$83$	0.142483	+	0.531752i	0.0156395	+	0.0583674i	−0.957665	+	0.287885i	$0.907048\pi$
$84$		0			0
$85$	−5.81552	−	8.07277i	−0.630781	−	0.875615i
$86$	3.00000	−	1.73205i	0.323498	−	0.186772i
$87$		0			0
$88$	−6.07812	+	1.62863i	−0.647929	+	0.173612i
$89$	−2.36773			−0.250978			−0.125489	−	0.992095i	$-0.540050\pi$
$89$	−2.36773			−0.250978			−0.125489	+	0.992095i	$0.540050\pi$
$90$		0			0
$91$	−3.79796			−0.398134
$92$	−0.965926	+	0.258819i	−0.100705	+	0.0269838i
$93$		0			0
$94$	7.79423	−	4.50000i	0.803913	−	0.464140i
$95$	−0.556198	+	3.42214i	−0.0570647	+	0.351104i
$96$		0			0
$97$	−2.89123	−	10.7902i	−0.293560	−	1.09558i	−0.942355	−	0.334616i	$-0.891393\pi$
$97$	−2.89123	−	10.7902i	−0.293560	−	1.09558i	0.648795	−	0.760963i	$-0.275273\pi$
$98$	−4.09978	+	4.09978i	−0.414140	+	0.414140i
$99$		0			0
$100$	4.89898	−	1.00000i	0.489898	−	0.100000i
$101$	−1.10102	−	0.635674i	−0.109556	−	0.0632520i	0.444221	−	0.895917i	$-0.353481\pi$
$101$	−1.10102	−	0.635674i	−0.109556	−	0.0632520i	−0.553777	+	0.832665i	$0.686814\pi$
$102$		0			0
$103$	1.06110	−	3.96008i	0.104553	−	0.390198i	−0.893741	−	0.448584i	$-0.851929\pi$
$103$	1.06110	−	3.96008i	0.104553	−	0.390198i	0.998294	+	0.0583855i	$0.0185953\pi$
$104$	−1.73205	−	3.00000i	−0.169842	−	0.294174i
$105$		0			0
$106$	−4.67423	+	8.09601i	−0.454002	+	0.786354i
$107$	3.71051	+	3.71051i	0.358708	+	0.358708i	0.863337	−	0.504628i	$-0.168370\pi$
$107$	3.71051	+	3.71051i	0.358708	+	0.358708i	−0.504628	+	0.863337i	$0.668370\pi$
$108$		0			0
$109$			20.3485i			1.94903i	0.224323	+	0.974515i	$0.427983\pi$
$109$			20.3485i			1.94903i	−0.224323	+	0.974515i	$0.572017\pi$
$110$	12.8308	+	5.77489i	1.22337	+	0.550614i
$111$		0			0
$112$	1.05902	+	0.283763i	0.100068	+	0.0268131i
$113$	13.3278	+	3.57117i	1.25377	+	0.335948i	0.823793	−	0.566890i	$-0.191854\pi$
$113$	13.3278	+	3.57117i	1.25377	+	0.335948i	0.429981	+	0.902838i	$0.358520\pi$
$114$		0			0
$115$	2.03906	+	0.917738i	0.190143	+	0.0855795i
$116$			3.14626i			0.292123i
$117$		0			0
$118$	8.34847	+	8.34847i	0.768539	+	0.768539i
$119$	−2.43916	+	4.22474i	−0.223597	+	0.387282i
$120$		0			0
$121$	14.2980	+	24.7648i	1.29981	+	2.25134i
$122$	−1.41043	+	5.26380i	−0.127694	+	0.476562i
$123$		0			0
$124$	3.85337	+	2.22474i	0.346043	+	0.199788i
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$		0			0
$127$	14.1237	−	14.1237i	1.25328	−	1.25328i	0.299036	−	0.954242i	$-0.403335\pi$
$127$	14.1237	−	14.1237i	1.25328	−	1.25328i	0.954242	−	0.299036i	$-0.0966651\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$		0			0
$130$	−1.24264	+	7.64564i	−0.108987	+	0.670567i
$131$	−9.12372	+	5.26758i	−0.797143	+	0.460231i	−0.842471	−	0.538741i	$-0.818900\pi$
$131$	−9.12372	+	5.26758i	−0.797143	+	0.460231i	0.0453278	+	0.998972i	$0.485567\pi$
$132$		0			0
$133$	1.64202	−	0.439978i	0.142381	−	0.0381509i
$134$	3.78194			0.326710
$135$		0			0
$136$	−4.44949			−0.381541
$137$	2.12701	−	0.569930i	0.181723	−	0.0486924i	−0.166810	−	0.985989i	$-0.553347\pi$
$137$	2.12701	−	0.569930i	0.181723	−	0.0486924i	0.348533	+	0.937297i	$0.386680\pi$
$138$		0			0
$139$	−11.1708	+	6.44949i	−0.947499	+	0.547039i	−0.892303	−	0.451437i	$-0.850912\pi$
$139$	−11.1708	+	6.44949i	−0.947499	+	0.547039i	−0.0551956	+	0.998476i	$0.517578\pi$
$140$	−1.43297	−	1.98917i	−0.121108	−	0.168116i
$141$		0			0
$142$	0.164525	+	0.614014i	0.0138066	+	0.0515269i
$143$	−15.4135	+	15.4135i	−1.28894	+	1.28894i
$144$		0			0
$145$	4.44949	−	5.44949i	0.369510	−	0.452555i
$146$	−3.55051	−	2.04989i	−0.293842	−	0.169650i
$147$		0			0
$148$	−1.09808	+	4.09808i	−0.0902613	+	0.336860i
$149$	6.45145	+	11.1742i	0.528523	+	0.915429i	0.999447	+	0.0332550i	$0.0105874\pi$
$149$	6.45145	+	11.1742i	0.528523	+	0.915429i	−0.470924	+	0.882174i	$0.656079\pi$
$150$		0			0
$151$	10.7980	−	18.7026i	0.878725	−	1.52200i	0.0259849	−	0.999662i	$-0.491728\pi$
$151$	10.7980	−	18.7026i	0.878725	−	1.52200i	0.852741	−	0.522335i	$-0.174939\pi$
$152$	1.09638	+	1.09638i	0.0889279	+	0.0889279i
$153$		0			0
$154$		−	6.89898i		−	0.555936i
$155$	−3.52797	−	9.30286i	−0.283373	−	0.747224i
$156$		0			0
$157$	−5.94012	−	1.59165i	−0.474073	−	0.127028i	0.0138684	−	0.999904i	$-0.495585\pi$
$157$	−5.94012	−	1.59165i	−0.474073	−	0.127028i	−0.487942	+	0.872876i	$0.662252\pi$
$158$	2.36603	+	0.633975i	0.188231	+	0.0504363i
$159$		0			0
$160$	0.917738	−	2.03906i	0.0725535	−	0.161202i
$161$		−	1.09638i		−	0.0864066i
$162$		0			0
$163$	−0.449490	−	0.449490i	−0.0352068	−	0.0352068i	0.689284	−	0.724491i	$-0.257925\pi$
$163$	−0.449490	−	0.449490i	−0.0352068	−	0.0352068i	−0.724491	+	0.689284i	$0.757925\pi$
$164$	1.96240	−	3.39898i	0.153238	−	0.265416i
$165$		0			0
$166$	−0.275255	−	0.476756i	−0.0213639	−	0.0370034i
$167$	2.79472	−	10.4300i	0.216262	−	0.807100i	−0.769457	−	0.638699i	$-0.779473\pi$
$167$	2.79472	−	10.4300i	0.216262	−	0.807100i	0.985719	−	0.168401i	$-0.0538603\pi$
$168$		0			0
$169$	0.866025	+	0.500000i	0.0666173	+	0.0384615i
$170$	7.70674	+	6.29253i	0.591080	+	0.482615i
$171$		0			0
$172$	−2.44949	+	2.44949i	−0.186772	+	0.186772i
$173$	−0.802603	−	2.99536i	−0.0610208	−	0.227733i	0.928680	−	0.370881i	$-0.120944\pi$
$173$	−0.802603	−	2.99536i	−0.0610208	−	0.227733i	−0.989701	+	0.143148i	$0.954277\pi$
$174$		0			0
$175$	−0.331131	+	5.47187i	−0.0250312	+	0.413635i
$176$	5.44949	−	3.14626i	0.410771	−	0.237159i
$177$		0			0
$178$	2.28705	−	0.612812i	0.171421	−	0.0459322i
$179$	−17.6062			−1.31595			−0.657976	−	0.753039i	$-0.728587\pi$
$179$	−17.6062			−1.31595			−0.657976	+	0.753039i	$0.728587\pi$
$180$		0			0
$181$	−10.5505			−0.784213			−0.392107	−	0.919920i	$-0.628254\pi$
$181$	−10.5505			−0.784213			−0.392107	+	0.919920i	$0.628254\pi$
$182$	3.66855	−	0.982984i	0.271931	−	0.0728636i
$183$		0			0
$184$	0.866025	−	0.500000i	0.0638442	−	0.0368605i
$185$	7.69748	−	5.54516i	0.565930	−	0.407688i
$186$		0			0
$187$	7.24656	+	27.0445i	0.529921	+	1.97769i
$188$	−6.36396	+	6.36396i	−0.464140	+	0.464140i
$189$		0			0
$190$	−0.348469	−	3.44949i	−0.0252806	−	0.250252i
$191$	2.87628	+	1.66062i	0.208120	+	0.120158i	0.600437	−	0.799672i	$-0.294993\pi$
$191$	2.87628	+	1.66062i	0.208120	+	0.120158i	−0.392317	+	0.919830i	$0.628327\pi$
$192$		0			0
$193$	4.48288	−	16.7303i	0.322685	−	1.20428i	−0.593934	−	0.804513i	$-0.702426\pi$
$193$	4.48288	−	16.7303i	0.322685	−	1.20428i	0.916619	−	0.399762i	$-0.130907\pi$
$194$	5.58542	+	9.67423i	0.401010	+	0.694570i
$195$		0			0
$196$	2.89898	−	5.02118i	0.207070	−	0.358656i
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	0.909443	−	0.415829i	$-0.136508\pi$
$197$	6.92820	+	6.92820i	0.493614	+	0.493614i	−0.415829	+	0.909443i	$0.636508\pi$
$198$		0			0
$199$		−	3.55051i		−	0.251689i	−0.992050	−	0.125844i	$-0.959836\pi$
$199$		−	3.55051i		−	0.251689i	0.992050	−	0.125844i	$-0.0401640\pi$
$200$	−4.47323	+	2.23388i	−0.316305	+	0.157959i
$201$		0			0
$202$	1.22803	+	0.329049i	0.0864038	+	0.0231518i
$203$	−3.33195	−	0.892794i	−0.233857	−	0.0626618i
$204$		0			0
$205$	−8.20586	+	3.11195i	−0.573122	+	0.217348i
$206$			4.09978i			0.285645i
$207$		0			0
$208$	2.44949	+	2.44949i	0.169842	+	0.169842i
$209$	4.87832	−	8.44949i	0.337440	−	0.584463i
$210$		0			0
$211$	−9.44949	−	16.3670i	−0.650530	−	1.12675i	−0.982995	−	0.183635i	$-0.941214\pi$
$211$	−9.44949	−	16.3670i	−0.650530	−	1.12675i	0.332465	−	0.943116i	$-0.392120\pi$
$212$	2.41956	−	9.02993i	0.166176	−	0.620178i
$213$		0			0
$214$	−4.54442	−	2.62372i	−0.310650	−	0.179354i
$215$	7.70674	−	0.778539i	0.525595	−	0.0530959i
$216$		0			0
$217$	−3.44949	+	3.44949i	−0.234167	+	0.234167i
$218$	−5.26657	−	19.6551i	−0.356697	−	1.33121i
$219$		0			0
$220$	−13.8883	−	2.25725i	−0.936348	−	0.152184i
$221$	−13.3485	+	7.70674i	−0.897915	+	0.518412i
$222$		0			0
$223$	−8.02714	+	2.15087i	−0.537537	+	0.144033i	−0.517367	−	0.855764i	$-0.673088\pi$
$223$	−8.02714	+	2.15087i	−0.537537	+	0.144033i	−0.0201706	+	0.999797i	$0.506421\pi$
$224$	−1.09638			−0.0732547
$225$		0			0
$226$	−13.7980			−0.917827
$227$	14.5865	−	3.90843i	0.968138	−	0.259412i	0.260096	−	0.965583i	$-0.416246\pi$
$227$	14.5865	−	3.90843i	0.968138	−	0.259412i	0.708041	+	0.706171i	$0.249579\pi$
$228$		0			0
$229$	14.1582	−	8.17423i	0.935600	−	0.540169i	0.0470214	−	0.998894i	$-0.485027\pi$
$229$	14.1582	−	8.17423i	0.935600	−	0.540169i	0.888578	+	0.458725i	$0.151694\pi$
$230$	−2.20711	−	0.358719i	−0.145532	−	0.0236533i
$231$		0			0
$232$	−0.814313	−	3.03906i	−0.0534623	−	0.199524i
$233$	10.9959	−	10.9959i	0.720363	−	0.720363i	−0.248316	−	0.968679i	$-0.579877\pi$
$233$	10.9959	−	10.9959i	0.720363	−	0.720363i	0.968679	+	0.248316i	$0.0798770\pi$
$234$		0			0
$235$	20.0227	−	2.02270i	1.30614	−	0.131947i
$236$	−10.2247	−	5.90326i	−0.665574	−	0.384269i
$237$		0			0
$238$	1.26260	−	4.71209i	0.0818423	−	0.305439i
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	0.998353	+	0.0573782i	$0.0182741\pi$
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	−0.449485	+	0.893288i	$0.648393\pi$
$240$		0			0
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$	−20.2204	−	20.2204i	−1.29981	−	1.29981i
$243$		0			0
$244$		−	5.44949i		−	0.348868i
$245$	−12.1222	+	4.59716i	−0.774459	+	0.293702i
$246$		0			0
$247$	5.18811	+	1.39015i	0.330111	+	0.0884531i
$248$	−4.29788	−	1.15161i	−0.272915	−	0.0731275i
$249$		0			0
$250$	10.9070	+	2.45692i	0.689822	+	0.155389i
$251$		−	11.1708i		−	0.705097i	−0.935793	−	0.352549i	$-0.885315\pi$
$251$		−	11.1708i		−	0.705097i	0.935793	−	0.352549i	$-0.114685\pi$
$252$		0			0
$253$	−4.44949	−	4.44949i	−0.279737	−	0.279737i
$254$	−9.98698	+	17.2980i	−0.626639	+	1.08537i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.74105	−	25.1579i	0.420495	−	1.56931i	−0.353073	−	0.935596i	$-0.614863\pi$
$257$	6.74105	−	25.1579i	0.420495	−	1.56931i	0.773568	−	0.633713i	$-0.218470\pi$
$258$		0			0
$259$	−4.02834	−	2.32577i	−0.250309	−	0.144516i
$260$	−0.778539	−	7.70674i	−0.0482829	−	0.477952i
$261$		0			0
$262$	7.44949	−	7.44949i	0.460231	−	0.460231i
$263$	−3.28621	−	12.2643i	−0.202636	−	0.756249i	−0.990157	−	0.139961i	$-0.955302\pi$
$263$	−3.28621	−	12.2643i	−0.202636	−	0.756249i	0.787521	−	0.616288i	$-0.211364\pi$
$264$		0			0
$265$	−16.9611	+	12.2185i	−1.04191	+	0.750578i
$266$	−1.47219	+	0.849971i	−0.0902660	+	0.0521151i
$267$		0			0
$268$	−3.65307	+	0.978838i	−0.223147	+	0.0597920i
$269$	4.70334			0.286768			0.143384	−	0.989667i	$-0.454202\pi$
$269$	4.70334			0.286768			0.143384	+	0.989667i	$0.454202\pi$
$270$		0			0
$271$	−16.0454			−0.974689			−0.487345	−	0.873210i	$-0.662034\pi$
$271$	−16.0454			−0.974689			−0.487345	+	0.873210i	$0.662034\pi$
$272$	4.29788	−	1.15161i	0.260597	−	0.0698268i
$273$		0			0
$274$	−1.90702	+	1.10102i	−0.115208	+	0.0665151i
$275$	20.8630	+	23.5507i	1.25808	+	1.42016i
$276$		0			0
$277$	−3.69723	−	13.7983i	−0.222145	−	0.829057i	−0.983528	−	0.180754i	$-0.942146\pi$
$277$	−3.69723	−	13.7983i	−0.222145	−	0.829057i	0.761383	−	0.648302i	$-0.224521\pi$
$278$	9.12096	−	9.12096i	0.547039	−	0.547039i
$279$		0			0
$280$	1.89898	+	1.55051i	0.113486	+	0.0926607i
$281$	0.151531	+	0.0874863i	0.00903957	+	0.00521900i	0.504513	−	0.863404i	$-0.331672\pi$
$281$	0.151531	+	0.0874863i	0.00903957	+	0.00521900i	−0.495473	+	0.868623i	$0.665005\pi$
$282$		0			0
$283$	1.78484	−	6.66112i	0.106098	−	0.395962i	−0.892370	−	0.451305i	$-0.850959\pi$
$283$	1.78484	−	6.66112i	0.106098	−	0.395962i	0.998467	+	0.0553430i	$0.0176252\pi$
$284$	−0.317837	−	0.550510i	−0.0188602	−	0.0326668i
$285$		0			0
$286$	10.8990	−	18.8776i	0.644470	−	1.11626i
$287$	3.04272	+	3.04272i	0.179606	+	0.179606i
$288$		0			0
$289$			2.79796i			0.164586i
$290$	−2.88745	+	6.41542i	−0.169557	+	0.376726i
$291$		0			0
$292$	3.96008	+	1.06110i	0.231746	+	0.0620962i
$293$	−21.2942	−	5.70577i	−1.24402	−	0.333335i	−0.423998	−	0.905663i	$-0.639374\pi$
$293$	−21.2942	−	5.70577i	−1.24402	−	0.333335i	−0.820024	+	0.572329i	$0.806040\pi$
$294$		0			0
$295$	9.36131	+	24.6847i	0.545036	+	1.43720i
$296$		−	4.24264i		−	0.246598i
$297$		0			0
$298$	−9.12372	−	9.12372i	−0.528523	−	0.528523i
$299$	1.73205	−	3.00000i	0.100167	−	0.173494i
$300$		0			0
$301$	−1.89898	−	3.28913i	−0.109455	−	0.189582i
$302$	−5.58943	+	20.8601i	−0.321636	+	1.20036i
$303$		0			0
$304$	−1.34278	−	0.775255i	−0.0770138	−	0.0444639i
$305$	−7.70674	+	9.43879i	−0.441287	+	0.540464i
$306$		0			0
$307$	0.674235	−	0.674235i	0.0384806	−	0.0384806i	−0.687605	−	0.726085i	$-0.741338\pi$
$307$	0.674235	−	0.674235i	0.0384806	−	0.0384806i	0.726085	+	0.687605i	$0.241338\pi$
$308$	1.78559	+	6.66390i	0.101743	+	0.379711i
$309$		0			0
$310$	5.81552	+	8.07277i	0.330299	+	0.458502i
$311$	17.8207	−	10.2888i	1.01052	−	0.583422i	0.0991741	−	0.995070i	$-0.468380\pi$
$311$	17.8207	−	10.2888i	1.01052	−	0.583422i	0.911343	+	0.411648i	$0.135047\pi$
$312$		0			0
$313$	−4.85009	+	1.29958i	−0.274143	+	0.0734564i	−0.393271	−	0.919422i	$-0.628657\pi$
$313$	−4.85009	+	1.29958i	−0.274143	+	0.0734564i	0.119128	+	0.992879i	$0.461990\pi$
$314$	6.14966			0.347046
$315$		0			0
$316$	−2.44949			−0.137795
$317$	−1.06350	+	0.284965i	−0.0597323	+	0.0160052i	−0.288561	−	0.957461i	$-0.593177\pi$
$317$	−1.06350	+	0.284965i	−0.0597323	+	0.0160052i	0.228829	+	0.973467i	$0.426510\pi$
$318$		0			0
$319$	−17.1455	+	9.89898i	−0.959966	+	0.554236i
$320$	−0.358719	+	2.20711i	−0.0200530	+	0.123381i
$321$		0			0
$322$	0.283763	+	1.05902i	0.0158135	+	0.0590168i
$323$	4.87832	−	4.87832i	0.271437	−	0.271437i
$324$		0			0
$325$	−9.55051	+	14.4495i	−0.529767	+	0.801513i
$326$	0.550510	+	0.317837i	0.0304899	+	0.0176034i
$327$		0			0
$328$	−1.01581	+	3.79107i	−0.0560889	+	0.209327i
$329$	−4.93369	−	8.54541i	−0.272003	−	0.471124i
$330$		0			0
$331$	2.22474	−	3.85337i	0.122283	−	0.211800i	−0.798385	−	0.602148i	$-0.794312\pi$
$331$	2.22474	−	3.85337i	0.122283	−	0.211800i	0.920668	+	0.390347i	$0.127645\pi$
$332$	0.389270	+	0.389270i	0.0213639	+	0.0213639i
$333$		0			0
$334$			10.7980i			0.590838i
$335$	7.71159	+	3.47083i	0.421329	+	0.189632i
$336$		0			0
$337$	29.7766	+	7.97861i	1.62203	+	0.434622i	0.951598	−	0.307346i	$-0.0994408\pi$
$337$	29.7766	+	7.97861i	1.62203	+	0.434622i	0.670435	+	0.741968i	$0.266108\pi$
$338$	−0.965926	−	0.258819i	−0.0525394	−	0.0140779i
$339$		0			0
$340$	−9.07277	−	4.08346i	−0.492040	−	0.221457i
$341$			27.9985i			1.51621i
$342$		0			0
$343$	9.92168	+	9.92168i	0.535721	+	0.535721i
$344$	1.73205	−	3.00000i	0.0933859	−	0.161749i
$345$		0			0
$346$	1.55051	+	2.68556i	0.0833559	+	0.144377i
$347$	1.08757	−	4.05886i	0.0583837	−	0.217891i	−0.930570	−	0.366113i	$-0.880688\pi$
$347$	1.08757	−	4.05886i	0.0583837	−	0.217891i	0.988954	+	0.148222i	$0.0473550\pi$
$348$		0			0
$349$	−13.0297	−	7.52270i	−0.697464	−	0.402681i	0.108938	−	0.994049i	$-0.465255\pi$
$349$	−13.0297	−	7.52270i	−0.697464	−	0.402681i	−0.806402	+	0.591367i	$0.798588\pi$
$350$	−1.09638	−	5.37113i	−0.0586038	−	0.287099i
$351$		0			0
$352$	−4.44949	+	4.44949i	−0.237159	+	0.237159i
$353$	8.87564	+	33.1244i	0.472403	+	1.76303i	0.631097	+	0.775704i	$0.282605\pi$
$353$	8.87564	+	33.1244i	0.472403	+	1.76303i	−0.158694	+	0.987328i	$0.550728\pi$
$354$		0			0
$355$	−0.228029	+	1.40300i	−0.0121025	+	0.0744636i
$356$	−2.05051	+	1.18386i	−0.108677	+	0.0627446i
$357$		0			0
$358$	17.0063	−	4.55683i	0.898812	−	0.240836i
$359$	17.4634			0.921682			0.460841	−	0.887483i	$-0.347548\pi$
$359$	17.4634			0.921682			0.460841	+	0.887483i	$0.347548\pi$
$360$		0			0
$361$	16.5959			0.873469
$362$	10.1910	−	2.73067i	0.535628	−	0.143521i
$363$		0			0
$364$	−3.28913	+	1.89898i	−0.172397	+	0.0995336i
$365$	−5.35844	−	7.43828i	−0.280473	−	0.389337i
$366$		0			0
$367$	2.52520	+	9.42418i	0.131814	+	0.491938i	0.999991	−	0.00431778i	$-0.00137440\pi$
$367$	2.52520	+	9.42418i	0.131814	+	0.491938i	−0.868176	+	0.496256i	$0.834708\pi$
$368$	−0.707107	+	0.707107i	−0.0368605	+	0.0368605i
$369$		0			0
$370$	−6.00000	+	7.34847i	−0.311925	+	0.382029i
$371$	8.87628	+	5.12472i	0.460833	+	0.266062i
$372$		0			0
$373$	5.25190	−	19.6004i	0.271933	−	1.01487i	−0.685935	−	0.727662i	$-0.740607\pi$
$373$	5.25190	−	19.6004i	0.271933	−	1.01487i	0.957869	−	0.287206i	$-0.0927266\pi$
$374$	−13.9993	−	24.2474i	−0.723885	−	1.25381i
$375$		0			0
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$	−7.70674	−	7.70674i	−0.396917	−	0.396917i
$378$		0			0
$379$			6.65153i			0.341666i	0.985300	+	0.170833i	$0.0546459\pi$
$379$			6.65153i			0.341666i	−0.985300	+	0.170833i	$0.945354\pi$
$380$	1.22939	+	3.24176i	0.0630663	+	0.166299i
$381$		0			0
$382$	−3.20807	−	0.859599i	−0.164139	−	0.0439809i
$383$	−26.8508	−	7.19464i	−1.37201	−	0.367629i	−0.503798	−	0.863822i	$-0.668064\pi$
$383$	−26.8508	−	7.19464i	−1.37201	−	0.367629i	−0.868212	+	0.496193i	$0.834731\pi$
$384$		0			0
$385$	6.33145	−	14.0674i	0.322681	−	0.716942i
$386$			17.3205i			0.881591i
$387$		0			0
$388$	−7.89898	−	7.89898i	−0.401010	−	0.401010i
$389$	−2.81237	+	4.87117i	−0.142593	+	0.246978i	−0.928472	−	0.371402i	$-0.878877\pi$
$389$	−2.81237	+	4.87117i	−0.142593	+	0.246978i	0.785879	+	0.618380i	$0.212211\pi$
$390$		0			0
$391$	−2.22474	−	3.85337i	−0.112510	−	0.194873i
$392$	−1.50062	+	5.60040i	−0.0757929	+	0.282863i
$393$		0			0
$394$	−8.48528	−	4.89898i	−0.427482	−	0.246807i
$395$	4.24264	+	3.46410i	0.213470	+	0.174298i
$396$		0			0
$397$	15.4495	−	15.4495i	0.775388	−	0.775388i	−0.203655	−	0.979043i	$-0.565282\pi$
$397$	15.4495	−	15.4495i	0.775388	−	0.775388i	0.979043	+	0.203655i	$0.0652821\pi$
$398$	0.918940	+	3.42953i	0.0460623	+	0.171907i
$399$		0			0
$400$	3.74264	−	3.31552i	0.187132	−	0.165776i
$401$	−22.3485	+	12.9029i	−1.11603	+	0.644340i	−0.940384	−	0.340114i	$-0.889534\pi$
$401$	−22.3485	+	12.9029i	−1.11603	+	0.644340i	−0.175645	+	0.984454i	$0.556201\pi$
$402$		0			0
$403$	−14.8883	+	3.98930i	−0.741638	+	0.198721i
$404$	−1.27135			−0.0632520
$405$		0			0
$406$	3.44949			0.171195
$407$	−25.7873	+	6.90968i	−1.27823	+	0.342500i
$408$		0			0
$409$	16.5420	−	9.55051i	0.817948	−	0.472242i	−0.0317605	−	0.999496i	$-0.510111\pi$
$409$	16.5420	−	9.55051i	0.817948	−	0.472242i	0.849708	+	0.527253i	$0.176778\pi$
$410$	7.12082	−	5.12975i	0.351672	−	0.253340i
$411$		0			0
$412$	−1.06110	−	3.96008i	−0.0522767	−	0.195099i
$413$	9.15306	−	9.15306i	0.450393	−	0.450393i
$414$		0			0
$415$	−0.123724	−	1.22474i	−0.00607339	−	0.0601204i
$416$	−3.00000	−	1.73205i	−0.147087	−	0.0849208i
$417$		0			0
$418$	−2.52520	+	9.42418i	−0.123512	+	0.460952i
$419$	−5.97469	−	10.3485i	−0.291883	−	0.505556i	0.682372	−	0.731005i	$-0.260948\pi$
$419$	−5.97469	−	10.3485i	−0.291883	−	0.505556i	−0.974255	+	0.225449i	$0.927615\pi$
$420$		0			0
$421$	7.44949	−	12.9029i	0.363066	−	0.628849i	−0.625398	−	0.780306i	$-0.715063\pi$
$421$	7.44949	−	12.9029i	0.363066	−	0.628849i	0.988464	+	0.151457i	$0.0483966\pi$
$422$	13.3636	+	13.3636i	0.650530	+	0.650530i
$423$		0			0
$424$			9.34847i			0.454002i
$425$	9.93960	+	19.9036i	0.482142	+	0.965466i
$426$		0			0
$427$	5.77111	+	1.54636i	0.279284	+	0.0748338i
$428$	5.06865	+	1.35814i	0.245002	+	0.0656482i
$429$		0			0
$430$	−7.24264	+	2.74666i	−0.349271	+	0.132456i
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$		0			0
$433$	8.55051	+	8.55051i	0.410911	+	0.410911i	0.882056	−	0.471145i	$-0.156159\pi$
$433$	8.55051	+	8.55051i	0.410911	+	0.410911i	−0.471145	+	0.882056i	$0.656159\pi$
$434$	2.43916	−	4.22474i	0.117083	−	0.202794i
$435$		0			0
$436$	10.1742	+	17.6223i	0.487257	+	0.843955i
$437$	−0.401302	+	1.49768i	−0.0191969	+	0.0716436i
$438$		0			0
$439$	8.83523	+	5.10102i	0.421682	+	0.243458i	0.695797	−	0.718239i	$-0.255051\pi$
$439$	8.83523	+	5.10102i	0.421682	+	0.243458i	−0.274114	+	0.961697i	$0.588385\pi$
$440$	13.9993	−	1.41421i	0.667389	−	0.0674200i
$441$		0			0
$442$	10.8990	−	10.8990i	0.518412	−	0.518412i
$443$	−0.142483	−	0.531752i	−0.00676955	−	0.0252643i	0.962458	−	0.271429i	$-0.0874962\pi$
$443$	−0.142483	−	0.531752i	−0.00676955	−	0.0252643i	−0.969228	+	0.246165i	$0.920830\pi$
$444$		0			0
$445$	5.22582	+	0.849349i	0.247728	+	0.0402630i
$446$	7.19694	−	4.15515i	0.340785	−	0.196752i
$447$		0			0
$448$	1.05902	−	0.283763i	0.0500339	−	0.0134065i
$449$	−21.7060			−1.02437			−0.512185	−	0.858875i	$-0.671164\pi$
$449$	−21.7060			−1.02437			−0.512185	+	0.858875i	$0.671164\pi$
$450$		0			0
$451$	24.6969			1.16293
$452$	13.3278	−	3.57117i	0.626887	−	0.167974i
$453$		0			0
$454$	−13.0779	+	7.55051i	−0.613775	+	0.354363i
$455$	8.38250	+	1.36240i	0.392978	+	0.0638704i
$456$		0			0
$457$	1.59165	+	5.94012i	0.0744543	+	0.277867i	0.993109	−	0.117194i	$-0.0373900\pi$
$457$	1.59165	+	5.94012i	0.0744543	+	0.277867i	−0.918655	+	0.395061i	$0.870723\pi$
$458$	−11.5601	+	11.5601i	−0.540169	+	0.540169i
$459$		0			0
$460$	2.22474	−	0.224745i	0.103729	−	0.0104788i
$461$	−16.3763	−	9.45485i	−0.762719	−	0.440356i	0.0675520	−	0.997716i	$-0.478481\pi$
$461$	−16.3763	−	9.45485i	−0.762719	−	0.440356i	−0.830271	+	0.557360i	$0.811814\pi$
$462$		0			0
$463$	−8.54613	+	31.8946i	−0.397172	+	1.48227i	0.420876	+	0.907118i	$0.361723\pi$
$463$	−8.54613	+	31.8946i	−0.397172	+	1.48227i	−0.818048	+	0.575150i	$0.804944\pi$
$464$	1.57313	+	2.72474i	0.0730308	+	0.126493i
$465$		0			0
$466$	−7.77526	+	13.4671i	−0.360182	+	0.623853i
$467$	−2.82843	−	2.82843i	−0.130884	−	0.130884i	0.638630	−	0.769514i	$-0.279501\pi$
$467$	−2.82843	−	2.82843i	−0.130884	−	0.130884i	−0.769514	+	0.638630i	$0.779501\pi$
$468$		0			0
$469$		−	4.14643i		−	0.191464i
$470$	−18.8169	+	7.13604i	−0.867960	+	0.329161i
$471$		0			0
$472$	11.4042	+	3.05575i	0.524922	+	0.140652i
$473$	−21.0552	−	5.64173i	−0.968120	−	0.259407i
$474$		0			0
$475$	2.45518	−	7.35351i	0.112651	−	0.337402i
$476$			4.87832i			0.223597i
$477$		0			0
$478$	−12.0000	−	12.0000i	−0.548867	−	0.548867i
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	−0.773879	−	0.633333i	$-0.781686\pi$
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	0.935422	+	0.353533i	$0.115020\pi$
$480$		0			0
$481$	−7.34847	−	12.7279i	−0.335061	−	0.580343i
$482$	4.91756	−	18.3526i	0.223989	−	0.835938i
$483$		0			0
$484$	24.7648	+	14.2980i	1.12567	+	0.649907i
$485$	2.51059	+	24.8523i	0.114000	+	1.12848i
$486$		0			0
$487$	−12.0000	+	12.0000i	−0.543772	+	0.543772i	−0.924632	−	0.380861i	$-0.875628\pi$
$487$	−12.0000	+	12.0000i	−0.543772	+	0.543772i	0.380861	+	0.924632i	$0.375628\pi$
$488$	1.41043	+	5.26380i	0.0638472	+	0.238281i
$489$		0			0
$490$	10.5193	−	7.57797i	0.475214	−	0.342338i
$491$	−0.247449	+	0.142865i	−0.0111672	+	0.00644739i	−0.505573	−	0.862784i	$-0.668719\pi$
$491$	−0.247449	+	0.142865i	−0.0111672	+	0.00644739i	0.494406	+	0.869231i	$0.335386\pi$
$492$		0			0
$493$	−13.5223	+	3.62328i	−0.609012	+	0.163184i
$494$	−5.37113			−0.241658
$495$		0			0
$496$	4.44949			0.199788
$497$	0.673191	−	0.180381i	0.0301967	−	0.00809119i
$498$		0			0
$499$	7.70674	−	4.44949i	0.345001	−	0.199187i	−0.317480	−	0.948265i	$-0.602837\pi$
$499$	7.70674	−	4.44949i	0.345001	−	0.199187i	0.662481	+	0.749078i	$0.269503\pi$
$500$	−11.1713	+	0.449747i	−0.499595	+	0.0201133i
$501$		0			0
$502$	2.89123	+	10.7902i	0.129042	+	0.481590i
$503$	16.7563	−	16.7563i	0.747125	−	0.747125i	−0.226813	−	0.973938i	$-0.572831\pi$
$503$	16.7563	−	16.7563i	0.747125	−	0.747125i	0.973938	+	0.226813i	$0.0728307\pi$
$504$		0			0
$505$	2.20204	+	1.79796i	0.0979895	+	0.0800081i
$506$	5.44949	+	3.14626i	0.242259	+	0.139869i
$507$		0			0
$508$	5.16964	−	19.2934i	0.229366	−	0.856005i
$509$	19.8150	+	34.3207i	0.878286	+	1.52124i	0.853220	+	0.521551i	$0.174646\pi$
$509$	19.8150	+	34.3207i	0.878286	+	1.52124i	0.0250662	+	0.999686i	$0.492020\pi$
$510$		0			0
$511$	−2.24745	+	3.89270i	−0.0994213	+	0.172203i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			26.0454i			1.14881i
$515$	−3.76252	+	8.35968i	−0.165796	+	0.368372i
$516$		0			0
$517$	−54.7030	−	14.6576i	−2.40584	−	0.644642i
$518$	4.49303	+	1.20390i	0.197413	+	0.0528965i
$519$		0			0
$520$	2.74666	+	7.24264i	0.120449	+	0.317611i
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$		0			0
$523$	1.77526	+	1.77526i	0.0776265	+	0.0776265i	0.744854	−	0.667228i	$-0.232519\pi$
$523$	1.77526	+	1.77526i	0.0776265	+	0.0776265i	−0.667228	+	0.744854i	$0.732519\pi$
$524$	−5.26758	+	9.12372i	−0.230116	+	0.398572i
$525$		0			0
$526$	6.34847	+	10.9959i	0.276806	+	0.479443i
$527$	−5.12409	+	19.1234i	−0.223209	+	0.833027i
$528$		0			0
$529$	−19.0526	−	11.0000i	−0.828372	−	0.478261i
$530$	13.2207	−	16.1920i	0.574272	−	0.703337i
$531$		0			0
$532$	1.20204	−	1.20204i	0.0521151	−	0.0521151i
$533$	3.51888	+	13.1326i	0.152420	+	0.568838i
$534$		0			0
$535$	−6.85845	−	9.52052i	−0.296517	−	0.411608i
$536$	3.27526	−	1.89097i	0.141469	−	0.0816774i
$537$		0			0
$538$	−4.54308	+	1.21731i	−0.195866	+	0.0524822i
$539$	36.4838			1.57147
$540$		0			0
$541$	−25.9444			−1.11544			−0.557718	−	0.830030i	$-0.688323\pi$
$541$	−25.9444			−1.11544			−0.557718	+	0.830030i	$0.688323\pi$
$542$	15.4987	−	4.15286i	0.665725	−	0.178380i
$543$		0			0
$544$	−3.85337	+	2.22474i	−0.165212	+	0.0953851i
$545$	7.29939	−	44.9112i	0.312672	−	1.92379i
$546$		0			0
$547$	−5.53567	−	20.6594i	−0.236688	−	0.883332i	−0.977381	−	0.211488i	$-0.932169\pi$
$547$	−5.53567	−	20.6594i	−0.236688	−	0.883332i	0.740693	−	0.671844i	$-0.234498\pi$
$548$	1.55708	−	1.55708i	0.0665151	−	0.0665151i
$549$		0			0
$550$	−26.2474	−	17.3485i	−1.11919	−	0.739741i
$551$	4.22474	+	2.43916i	0.179980	+	0.103912i
$552$		0			0
$553$	0.695075	−	2.59405i	0.0295576	−	0.110310i
$554$	7.14250	+	12.3712i	0.303456	+	0.525601i
$555$		0			0
$556$	−6.44949	+	11.1708i	−0.273519	+	0.473749i
$557$	−16.3670	−	16.3670i	−0.693492	−	0.693492i	0.269507	−	0.962999i	$-0.413139\pi$
$557$	−16.3670	−	16.3670i	−0.693492	−	0.693492i	−0.962999	+	0.269507i	$0.913139\pi$
$558$		0			0
$559$		−	12.0000i		−	0.507546i
$560$	−2.23557	−	1.00619i	−0.0944703	−	0.0425191i
$561$		0			0
$562$	−0.169011	−	0.0452863i	−0.00712928	−	0.00191029i
$563$	33.1781	+	8.89004i	1.39829	+	0.374670i	0.877730	−	0.479155i	$-0.159057\pi$
$563$	33.1781	+	8.89004i	1.39829	+	0.374670i	0.520559	+	0.853826i	$0.325724\pi$
$564$		0			0
$565$	−28.1348	−	12.6629i	−1.18364	−	0.532732i
$566$			6.89610i			0.289864i
$567$		0			0
$568$	0.449490	+	0.449490i	0.0188602	+	0.0188602i
$569$	13.0458	−	22.5959i	0.546907	−	0.947270i	−0.451578	−	0.892232i	$-0.649139\pi$
$569$	13.0458	−	22.5959i	0.546907	−	0.947270i	0.998484	−	0.0550383i	$-0.0175281\pi$
$570$		0			0
$571$	−13.5505	−	23.4702i	−0.567071	−	0.982196i	−0.996854	−	0.0792637i	$-0.974743\pi$
$571$	−13.5505	−	23.4702i	−0.567071	−	0.982196i	0.429782	−	0.902932i	$-0.358590\pi$
$572$	−5.64173	+	21.0552i	−0.235892	+	0.880363i
$573$		0			0
$574$	−3.72656	−	2.15153i	−0.155544	−	0.0898032i
$575$	−4.17121	−	2.75699i	−0.173951	−	0.114975i
$576$		0			0
$577$	−17.0000	+	17.0000i	−0.707719	+	0.707719i	−0.966055	−	0.258336i	$-0.916826\pi$
$577$	−17.0000	+	17.0000i	−0.707719	+	0.707719i	0.258336	+	0.966055i	$0.416826\pi$
$578$	−0.724165	−	2.70262i	−0.0301213	−	0.112414i
$579$		0			0
$580$	1.12863	−	6.94414i	0.0468637	−	0.288340i
$581$	−0.522704	+	0.301783i	−0.0216854	+	0.0125201i
$582$		0			0
$583$	56.8211	−	15.2252i	2.35329	−	0.630562i
$584$	−4.09978			−0.169650
$585$		0			0
$586$	22.0454			0.910687
$587$	−29.9876	+	8.03514i	−1.23772	+	0.331646i	−0.817581	−	0.575814i	$-0.804685\pi$
$587$	−29.9876	+	8.03514i	−1.23772	+	0.331646i	−0.420138	+	0.907460i	$0.638019\pi$
$588$		0			0
$589$	5.97469	−	3.44949i	0.246183	−	0.142134i
$590$	−15.4312	−	21.4207i	−0.635293	−	0.881877i
$591$		0			0
$592$	1.09808	+	4.09808i	0.0451307	+	0.168430i
$593$	−10.0745	+	10.0745i	−0.413709	+	0.413709i	−0.883028	−	0.469320i	$-0.844499\pi$
$593$	−10.0745	+	10.0745i	−0.413709	+	0.413709i	0.469320	+	0.883028i	$0.344499\pi$
$594$		0			0
$595$	6.89898	−	8.44949i	0.282831	−	0.346395i
$596$	11.1742	+	6.45145i	0.457714	+	0.264262i
$597$		0			0
$598$	−0.896575	+	3.34607i	−0.0366637	+	0.136831i
$599$	−16.8991	−	29.2702i	−0.690480	−	1.19595i	−0.971681	−	0.236297i	$-0.924066\pi$
$599$	−16.8991	−	29.2702i	−0.690480	−	1.19595i	0.281201	−	0.959649i	$-0.409267\pi$
$600$		0			0
$601$	−17.3485	+	30.0484i	−0.707659	+	1.22570i	0.258065	+	0.966128i	$0.416915\pi$
$601$	−17.3485	+	30.0484i	−0.707659	+	1.22570i	−0.965723	+	0.259573i	$0.916418\pi$
$602$	2.68556	+	2.68556i	0.109455	+	0.109455i
$603$		0			0
$604$		−	21.5959i		−	0.878725i
$605$	−22.6735	−	59.7875i	−0.921809	−	2.43071i
$606$		0			0
$607$	−21.4114	−	5.73717i	−0.869062	−	0.232864i	−0.203380	−	0.979100i	$-0.565193\pi$
$607$	−21.4114	−	5.73717i	−0.869062	−	0.232864i	−0.665682	+	0.746235i	$0.731859\pi$
$608$	1.49768	+	0.401302i	0.0607389	+	0.0162749i
$609$		0			0
$610$	5.00120	−	11.1118i	0.202493	−	0.449905i
$611$		−	31.1769i		−	1.26128i
$612$		0			0
$613$	−12.7980	−	12.7980i	−0.516905	−	0.516905i	0.399729	−	0.916633i	$-0.369104\pi$
$613$	−12.7980	−	12.7980i	−0.516905	−	0.516905i	−0.916633	+	0.399729i	$0.869104\pi$
$614$	−0.476756	+	0.825765i	−0.0192403	+	0.0333252i
$615$		0			0
$616$	−3.44949	−	5.97469i	−0.138984	−	0.240727i
$617$	−1.83788	+	6.85906i	−0.0739902	+	0.276135i	−0.993002	−	0.118094i	$-0.962322\pi$
$617$	−1.83788	+	6.85906i	−0.0739902	+	0.276135i	0.919012	+	0.394229i	$0.128988\pi$
$618$		0			0
$619$	21.4275	+	12.3712i	0.861244	+	0.497239i	0.864429	−	0.502756i	$-0.167680\pi$
$619$	21.4275	+	12.3712i	0.861244	+	0.497239i	−0.00318471	+	0.999995i	$0.501014\pi$
$620$	−7.70674	−	6.29253i	−0.309510	−	0.252714i
$621$		0			0
$622$	−14.5505	+	14.5505i	−0.583422	+	0.583422i
$623$	−0.671873	−	2.50746i	−0.0269180	−	0.100459i
$624$		0			0
$625$	19.9853	+	15.0196i	0.799411	+	0.600784i
$626$	4.34847	−	2.51059i	0.173800	−	0.100343i
$627$		0			0
$628$	−5.94012	+	1.59165i	−0.237037	+	0.0635138i
$629$	−18.8776			−0.752699
$630$		0			0
$631$	−12.8990			−0.513500			−0.256750	−	0.966478i	$-0.582652\pi$
$631$	−12.8990			−0.513500			−0.256750	+	0.966478i	$0.582652\pi$
$632$	2.36603	−	0.633975i	0.0941154	−	0.0252182i
$633$		0			0
$634$	0.953512	−	0.550510i	0.0378688	−	0.0218636i
$635$	−36.2390	+	26.1061i	−1.43810	+	1.03599i
$636$		0			0
$637$	5.19831	+	19.4003i	0.205964	+	0.768670i
$638$	13.9993	−	13.9993i	0.554236	−	0.554236i
$639$		0			0
$640$	−0.224745	−	2.22474i	−0.00888382	−	0.0879408i
$641$	7.74745	+	4.47299i	0.306006	+	0.176673i	0.645138	−	0.764066i	$-0.276800\pi$
$641$	7.74745	+	4.47299i	0.306006	+	0.176673i	−0.339132	+	0.940739i	$0.610133\pi$
$642$		0			0
$643$	−8.22539	+	30.6976i	−0.324378	+	1.21059i	0.590558	+	0.806995i	$0.298908\pi$
$643$	−8.22539	+	30.6976i	−0.324378	+	1.21059i	−0.914936	+	0.403599i	$0.867759\pi$
$644$	−0.548188	−	0.949490i	−0.0216016	−	0.0374151i
$645$		0			0
$646$	−3.44949	+	5.97469i	−0.135718	+	0.235071i
$647$	24.9558	+	24.9558i	0.981114	+	0.981114i	0.999825	−	0.0187105i	$-0.00595608\pi$
$647$	24.9558	+	24.9558i	0.981114	+	0.981114i	−0.0187105	+	0.999825i	$0.505956\pi$
$648$		0			0
$649$		−	74.2929i		−	2.91625i
$650$	5.48528	−	16.4290i	0.215150	−	0.644398i
$651$		0			0
$652$	−0.614014	−	0.164525i	−0.0240467	−	0.00644328i
$653$	20.8162	+	5.57768i	0.814601	+	0.218272i	0.641985	−	0.766718i	$-0.278111\pi$
$653$	20.8162	+	5.57768i	0.814601	+	0.218272i	0.172616	+	0.984989i	$0.444778\pi$
$654$		0			0
$655$	22.0266	−	8.35326i	0.860651	−	0.326389i
$656$		−	3.92480i		−	0.153238i
$657$		0			0
$658$	6.97730	+	6.97730i	0.272003	+	0.272003i
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	−0.954917	−	0.296872i	$-0.904056\pi$
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	0.734557	+	0.678546i	$0.237390\pi$
$660$		0			0
$661$	15.3485	+	26.5843i	0.596986	+	1.03401i	0.993263	+	0.115880i	$0.0369687\pi$
$661$	15.3485	+	26.5843i	0.596986	+	1.03401i	−0.396277	+	0.918131i	$0.629698\pi$
$662$	−1.15161	+	4.29788i	−0.0447587	+	0.167042i
$663$		0			0
$664$	−0.476756	−	0.275255i	−0.0185017	−	0.0106820i
$665$	−3.78194	+	0.382053i	−0.146657	+	0.0148154i
$666$		0			0
$667$	2.22474	−	2.22474i	0.0861425	−	0.0861425i
$668$	−2.79472	−	10.4300i	−0.108131	−	0.403550i
$669$		0			0
$670$	−8.34714	−	1.35666i	−0.322478	−	0.0524122i
$671$	29.6969	−	17.1455i	1.14644	−	0.661896i
$672$		0			0
$673$	15.7783	−	4.22778i	0.608208	−	0.162969i	0.0584468	−	0.998291i	$-0.481385\pi$
$673$	15.7783	−	4.22778i	0.608208	−	0.162969i	0.549762	+	0.835322i	$0.314719\pi$
$674$	−30.8270			−1.18741
$675$		0			0
$676$	1.00000			0.0384615
$677$	−6.18587	+	1.65750i	−0.237742	+	0.0637028i	−0.375723	−	0.926732i	$-0.622606\pi$
$677$	−6.18587	+	1.65750i	−0.237742	+	0.0637028i	0.137981	+	0.990435i	$0.455939\pi$
$678$		0			0
$679$	10.6066	−	6.12372i	0.407044	−	0.235007i
$680$	9.82050	+	1.59612i	0.376599	+	0.0612084i
$681$		0			0
$682$	−7.24656	−	27.0445i	−0.277485	−	1.03559i
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	−0.920632	−	0.390431i	$-0.872326\pi$
$683$	−13.8564	+	13.8564i	−0.530201	+	0.530201i	0.390431	+	0.920632i	$0.372326\pi$
$684$		0			0
$685$	−4.89898	+	0.494897i	−0.187180	+	0.0189091i
$686$	−12.1515	−	7.01569i	−0.463948	−	0.267860i
$687$		0			0
$688$	−0.896575	+	3.34607i	−0.0341816	+	0.127568i
$689$	16.1920	+	28.0454i	0.616867	+	1.06844i
$690$		0			0
$691$	−16.4722	+	28.5307i	−0.626632	+	1.08536i	0.361591	+	0.932337i	$0.382234\pi$
$691$	−16.4722	+	28.5307i	−0.626632	+	1.08536i	−0.988223	+	0.153021i	$0.951100\pi$
$692$	−2.19275	−	2.19275i	−0.0833559	−	0.0833559i
$693$		0			0
$694$			4.20204i			0.159507i
$695$	26.9688	−	10.2275i	1.02299	−	0.387952i
$696$		0			0
$697$	16.8683	+	4.51985i	0.638933	+	0.171202i
$698$	14.5327	+	3.89404i	0.550073	+	0.147392i
$699$		0			0
$700$	2.44917	+	4.90435i	0.0925698	+	0.185367i
$701$			23.9309i			0.903857i	0.892054	+	0.451928i	$0.149264\pi$
$701$			23.9309i			0.903857i	−0.892054	+	0.451928i	$0.850736\pi$
$702$		0			0
$703$	4.65153	+	4.65153i	0.175436	+	0.175436i
$704$	3.14626	−	5.44949i	0.118579	−	0.205385i
$705$		0			0
$706$	−17.1464	−	29.6985i	−0.645314	−	1.11772i
$707$	0.360762	−	1.34638i	0.0135678	−	0.0506359i
$708$		0			0
$709$	38.4069	+	22.1742i	1.44240	+	0.832771i	0.998010	−	0.0630617i	$-0.0200865\pi$
$709$	38.4069	+	22.1742i	1.44240	+	0.832771i	0.444392	+	0.895833i	$0.353420\pi$
$710$	−0.142865	−	1.41421i	−0.00536161	−	0.0530745i
$711$		0			0
$712$	1.67423	−	1.67423i	0.0627446	−	0.0627446i
$713$	−1.15161	−	4.29788i	−0.0431282	−	0.160957i
$714$		0			0
$715$	39.5483	−	28.4901i	1.47902	−	1.06547i
$716$	−15.2474	+	8.80312i	−0.569824	+	0.328988i
$717$		0			0
$718$	−16.8683	+	4.51985i	−0.629520	+	0.168679i
$719$	−32.5269			−1.21305			−0.606525	−	0.795065i	$-0.707437\pi$
$719$	−32.5269			−1.21305			−0.606525	+	0.795065i	$0.707437\pi$
$720$		0			0
$721$	4.49490			0.167399
$722$	−16.0304	+	4.29534i	−0.596591	+	0.159856i
$723$		0			0
$724$	−9.13701	+	5.27526i	−0.339574	+	0.196053i
$725$	−11.7753	+	10.4315i	−0.437325	+	0.387416i
$726$		0			0
$727$	−8.11447	−	30.2836i	−0.300949	−	1.12316i	−0.936377	−	0.350996i	$-0.885843\pi$
$727$	−8.11447	−	30.2836i	−0.300949	−	1.12316i	0.635428	−	0.772160i	$-0.280824\pi$
$728$	2.68556	−	2.68556i	0.0995336	−	0.0995336i
$729$		0			0
$730$	7.10102	+	5.79796i	0.262821	+	0.214592i
$731$	−13.3485	−	7.70674i	−0.493711	−	0.285044i
$732$		0			0
$733$	−3.71385	+	13.8603i	−0.137174	+	0.511941i	0.862805	+	0.505536i	$0.168705\pi$
$733$	−3.71385	+	13.8603i	−0.137174	+	0.511941i	−0.999979	+	0.00640470i	$0.997961\pi$
$734$	−4.87832	−	8.44949i	−0.180062	−	0.311876i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	−16.8277	−	16.8277i	−0.619856	−	0.619856i
$738$		0			0
$739$			24.9444i			0.917594i	0.888541	+	0.458797i	$0.151720\pi$
$739$			24.9444i			0.917594i	−0.888541	+	0.458797i	$0.848280\pi$
$740$	3.89363	−	8.65099i	0.143133	−	0.318017i
$741$		0			0
$742$	−9.90020	−	2.65275i	−0.363448	−	0.0973855i
$743$	−0.0975783	−	0.0261460i	−0.00357980	−	0.000959205i	0.257029	−	0.966404i	$-0.417257\pi$
$743$	−0.0975783	−	0.0261460i	−0.00357980	−	0.000959205i	−0.260609	+	0.965445i	$0.583923\pi$
$744$		0			0
$745$	−10.2306	−	26.9770i	−0.374821	−	0.988360i
$746$			20.2918i			0.742936i
$747$		0			0
$748$	19.7980	+	19.7980i	0.723885	+	0.723885i
$749$	−2.87659	+	4.98240i	−0.105108	+	0.182053i
$750$		0			0
$751$	4.34847	+	7.53177i	0.158678	+	0.274838i	0.934392	−	0.356246i	$-0.115944\pi$
$751$	4.34847	+	7.53177i	0.158678	+	0.274838i	−0.775714	+	0.631084i	$0.782610\pi$
$752$	−2.32937	+	8.69333i	−0.0849434	+	0.317013i
$753$		0			0
$754$	9.43879	+	5.44949i	0.343741	+	0.198459i
$755$	−30.5412	+	37.4052i	−1.11151	+	1.36132i
$756$		0			0
$757$	−22.0454	+	22.0454i	−0.801254	+	0.801254i	−0.983292	−	0.182038i	$-0.941731\pi$
$757$	−22.0454	+	22.0454i	−0.801254	+	0.801254i	0.182038	+	0.983292i	$0.441731\pi$
$758$	−1.72154	−	6.42489i	−0.0625293	−	0.233362i
$759$		0			0
$760$	−2.02653	−	2.81311i	−0.0735099	−	0.102042i
$761$	15.3990	−	8.89060i	0.558213	−	0.322284i	−0.194215	−	0.980959i	$-0.562216\pi$
$761$	15.3990	−	8.89060i	0.558213	−	0.322284i	0.752428	+	0.658675i	$0.228883\pi$
$762$		0			0
$763$	−21.5494	+	5.77414i	−0.780141	+	0.209038i
$764$	3.32124			0.120158
$765$		0			0
$766$	27.7980			1.00438
$767$	39.5054	−	10.5854i	1.42646	−	0.382218i
$768$		0			0
$769$	−17.0580	+	9.84847i	−0.615129	+	0.355145i	−0.774970	−	0.631998i	$-0.782235\pi$
$769$	−17.0580	+	9.84847i	−0.615129	+	0.355145i	0.159841	+	0.987143i	$0.448902\pi$
$770$	−2.47480	+	15.2268i	−0.0891855	+	0.548735i
$771$		0			0
$772$	−4.48288	−	16.7303i	−0.161342	−	0.602138i
$773$	−3.11416	+	3.11416i	−0.112008	+	0.112008i	−0.760890	−	0.648881i	$-0.775237\pi$
$773$	−3.11416	+	3.11416i	−0.112008	+	0.112008i	0.648881	+	0.760890i	$0.275237\pi$
$774$		0			0
$775$	4.44949	+	21.7980i	0.159830	+	0.783006i
$776$	9.67423	+	5.58542i	0.347285	+	0.200505i
$777$		0			0
$778$	1.45579	−	5.43309i	0.0521927	−	0.194786i
$779$	−3.04272	−	5.27015i	−0.109017	−	0.188823i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	3.14626	+	3.14626i	0.112510	+	0.112510i
$783$		0			0
$784$		−	5.79796i		−	0.207070i
$785$	12.5395	+	5.64378i	0.447555	+	0.201435i
$786$		0			0
$787$	−3.96008	−	1.06110i	−0.141162	−	0.0378241i	0.187546	−	0.982256i	$-0.439947\pi$
$787$	−3.96008	−	1.06110i	−0.141162	−	0.0378241i	−0.328708	+	0.944432i	$0.606613\pi$
$788$	9.46410	+	2.53590i	0.337145	+	0.0903376i
$789$		0			0
$790$	−4.99465	−	2.24799i	−0.177702	−	0.0799799i
$791$			15.1278i			0.537881i
$792$		0			0
$793$	13.3485	+	13.3485i	0.474018	+	0.474018i
$794$	−10.9244	+	18.9217i	−0.387694	+	0.671505i
$795$		0			0
$796$	−1.77526	−	3.07483i	−0.0629222	−	0.108985i
$797$	5.22867	−	19.5137i	0.185209	−	0.691210i	−0.809377	−	0.587290i	$-0.800195\pi$
$797$	5.22867	−	19.5137i	0.185209	−	0.691210i	0.994586	−	0.103920i	$-0.0331385\pi$
$798$		0			0
$799$	−34.6803	−	20.0227i	−1.22690	−	0.708352i
$800$	−2.75699	+	4.17121i	−0.0974745	+	0.147474i
$801$		0			0
$802$	18.2474	−	18.2474i	0.644340	−	0.644340i
$803$	6.67700	+	24.9189i	0.235626	+	0.879369i
$804$		0			0
$805$	−0.393292	+	2.41982i	−0.0138617	+	0.0852874i
$806$	13.3485	−	7.70674i	0.470180	−	0.271458i
$807$		0			0
$808$	1.22803	−	0.329049i	0.0432019	−	0.0115759i
$809$	54.0901			1.90171			0.950853	−	0.309644i	$-0.100210\pi$
$809$	54.0901			1.90171			0.950853	+	0.309644i	$0.100210\pi$
$810$		0			0
$811$	43.6413			1.53245			0.766227	−	0.642570i	$-0.222132\pi$
$811$	43.6413			1.53245			0.766227	+	0.642570i	$0.222132\pi$
$812$	−3.33195	+	0.892794i	−0.116929	+	0.0313309i
$813$		0			0
$814$	23.1202	−	13.3485i	0.810364	−	0.467864i
$815$	0.830831	+	1.15331i	0.0291027	+	0.0403988i
$816$		0			0
$817$	1.39015	+	5.18811i	0.0486352	+	0.181509i
$818$	−13.5065	+	13.5065i	−0.472242	+	0.472242i
$819$		0			0
$820$	−5.55051	+	6.79796i	−0.193832	+	0.237395i
$821$	22.3207	+	12.8868i	0.778997	+	0.449754i	0.836075	−	0.548616i	$-0.184845\pi$
$821$	22.3207	+	12.8868i	0.778997	+	0.449754i	−0.0570780	+	0.998370i	$0.518178\pi$
$822$		0			0
$823$	−12.5807	+	46.9519i	−0.438536	+	1.63664i	0.293923	+	0.955829i	$0.405039\pi$
$823$	−12.5807	+	46.9519i	−0.438536	+	1.63664i	−0.732459	+	0.680811i	$0.761627\pi$
$824$	2.04989	+	3.55051i	0.0714112	+	0.123688i
$825$		0			0
$826$	−6.47219	+	11.2102i	−0.225196	+	0.390052i
$827$	27.3235	+	27.3235i	0.950133	+	0.950133i	0.998814	−	0.0486816i	$-0.0155020\pi$
$827$	27.3235	+	27.3235i	0.950133	+	0.950133i	−0.0486816	+	0.998814i	$0.515502\pi$
$828$		0			0
$829$			15.4495i			0.536583i	0.963338	+	0.268291i	$0.0864590\pi$
$829$			15.4495i			0.536583i	−0.963338	+	0.268291i	$0.913541\pi$
$830$	0.436496	+	1.15099i	0.0151510	+	0.0399515i
$831$		0			0
$832$	3.34607	+	0.896575i	0.116004	+	0.0310832i
$833$	24.9189	+	6.67700i	0.863389	+	0.231344i
$834$		0			0
$835$	−9.90969	+	22.0177i	−0.342939	+	0.761953i
$836$		−	9.75663i		−	0.337440i
$837$		0			0
$838$	8.44949	+	8.44949i	0.291883	+	0.291883i
$839$	10.1459	−	17.5732i	0.350275	−	0.606695i	−0.636022	−	0.771671i	$-0.719421\pi$
$839$	10.1459	−	17.5732i	0.350275	−	0.606695i	0.986298	+	0.164976i	$0.0527547\pi$
$840$		0			0
$841$	9.55051	+	16.5420i	0.329328	+	0.570413i
$842$	−3.85614	+	14.3913i	−0.132891	+	0.495957i
$843$		0			0
$844$	−16.3670	−	9.44949i	−0.563375	−	0.325265i
$845$	−1.73205	−	1.41421i	−0.0595844	−	0.0486504i
$846$		0			0
$847$	−22.1691	+	22.1691i	−0.761740	+	0.761740i
$848$	−2.41956	−	9.02993i	−0.0830881	−	0.310089i
$849$		0			0
$850$	−14.7524	−	16.6528i	−0.506001	−	0.571188i
$851$	3.67423	−	2.12132i	0.125951	−	0.0727179i
$852$		0			0
$853$	35.8547	−	9.60723i	1.22764	−	0.328945i	0.413980	−	0.910286i	$-0.364138\pi$
$853$	35.8547	−	9.60723i	1.22764	−	0.328945i	0.813660	+	0.581340i	$0.197472\pi$
$854$	−5.97469			−0.204450
$855$		0			0
$856$	−5.24745			−0.179354
$857$	−3.66855	+	0.982984i	−0.125315	+	0.0335781i	−0.320932	−	0.947102i	$-0.603996\pi$
$857$	−3.66855	+	0.982984i	−0.125315	+	0.0335781i	0.195616	+	0.980680i	$0.437329\pi$
$858$		0			0
$859$	−2.16064	+	1.24745i	−0.0737202	+	0.0425624i	−0.536407	−	0.843959i	$-0.680219\pi$
$859$	−2.16064	+	1.24745i	−0.0737202	+	0.0425624i	0.462687	+	0.886522i	$0.346885\pi$
$860$	6.28497	−	4.52761i	0.214316	−	0.154390i
$861$		0			0
$862$	4.02628	+	15.0263i	0.137136	+	0.511797i
$863$	−27.7842	+	27.7842i	−0.945787	+	0.945787i	−0.998604	−	0.0528175i	$-0.983180\pi$
$863$	−27.7842	+	27.7842i	−0.945787	+	0.945787i	0.0528175	+	0.998604i	$0.483180\pi$
$864$		0			0
$865$	0.696938	+	6.89898i	0.0236966	+	0.234572i
$866$	−10.4722	−	6.04612i	−0.355860	−	0.205456i
$867$		0			0
$868$	−1.26260	+	4.71209i	−0.0428555	+	0.159939i
$869$	−7.70674	−	13.3485i	−0.261433	−	0.452816i
$870$		0			0
$871$	6.55051	−	11.3458i	0.221956	−	0.384438i
$872$	−14.3885	−	14.3885i	−0.487257	−	0.487257i
$873$		0			0
$874$		−	1.55051i		−	0.0524468i
$875$	2.69371	−	11.9582i	0.0910640	−	0.404262i
$876$		0			0
$877$	−7.85813	−	2.10558i	−0.265350	−	0.0711004i	0.123691	−	0.992321i	$-0.460527\pi$
$877$	−7.85813	−	2.10558i	−0.265350	−	0.0711004i	−0.389041	+	0.921220i	$0.627194\pi$
$878$	−9.85441	−	2.64048i	−0.332570	−	0.0891120i
$879$		0			0
$880$	−13.1562	+	4.98930i	−0.443496	+	0.168189i
$881$			58.3006i			1.96420i	0.188368	+	0.982098i	$0.439680\pi$
$881$			58.3006i			1.96420i	−0.188368	+	0.982098i	$0.560320\pi$
$882$		0			0
$883$	−40.2702	−	40.2702i	−1.35520	−	1.35520i	−0.879736	−	0.475463i	$-0.842281\pi$
$883$	−40.2702	−	40.2702i	−1.35520	−	1.35520i	−0.475463	−	0.879736i	$-0.657719\pi$
$884$	−7.70674	+	13.3485i	−0.259206	+	0.448958i
$885$		0			0
$886$	0.275255	+	0.476756i	0.00924738	+	0.0160169i
$887$	−7.19464	+	26.8508i	−0.241572	+	0.901561i	0.733503	+	0.679686i	$0.237884\pi$
$887$	−7.19464	+	26.8508i	−0.241572	+	0.901561i	−0.975075	+	0.221874i	$0.928783\pi$
$888$		0			0
$889$	18.9651	+	10.9495i	0.636068	+	0.367234i
$890$	−5.26758	+	0.532134i	−0.176570	+	0.0178372i
$891$		0			0
$892$	−5.87628	+	5.87628i	−0.196752	+	0.196752i
$893$	3.61171	+	13.4791i	0.120861	+	0.451061i
$894$		0			0
$895$	38.8588	+	6.31570i	1.29891	+	0.211111i
$896$	−0.949490	+	0.548188i	−0.0317202	+	0.0183137i
$897$		0			0
$898$	20.9664	−	5.61793i	0.699658	−	0.187473i
$899$	−13.9993			−0.466902
$900$		0			0
$901$	41.5959			1.38576
$902$	−23.8554	+	6.39204i	−0.794298	+	0.212832i
$903$		0			0
$904$	−11.9494	+	6.89898i	−0.397431	+	0.229457i
$905$	23.2861	+	3.78467i	0.774056	+	0.125807i
$906$		0			0
$907$	1.71089	+	6.38512i	0.0568091	+	0.212015i	0.988496	−	0.151248i	$-0.0483293\pi$
$907$	1.71089	+	6.38512i	0.0568091	+	0.212015i	−0.931687	+	0.363263i	$0.881663\pi$
$908$	10.6780	−	10.6780i	0.354363	−	0.354363i
$909$		0			0
$910$	−8.44949	+	0.853572i	−0.280098	+	0.0282956i
$911$	−6.12372	−	3.53553i	−0.202888	−	0.117137i	0.395114	−	0.918632i	$-0.370705\pi$
$911$	−6.12372	−	3.53553i	−0.202888	−	0.117137i	−0.598002	+	0.801495i	$0.704038\pi$
$912$		0			0
$913$	−0.896575	+	3.34607i	−0.0296723	+	0.110739i
$914$	−3.07483	−	5.32577i	−0.101706	−	0.176161i
$915$		0			0
$916$	8.17423	−	14.1582i	0.270084	−	0.467800i
$917$	−8.16744	−	8.16744i	−0.269713	−	0.269713i
$918$		0			0
$919$		−	27.3485i		−	0.902143i	−0.892488	−	0.451071i	$-0.851042\pi$
$919$		−	27.3485i		−	0.902143i	0.892488	−	0.451071i	$-0.148958\pi$
$920$	−2.09077	+	0.792893i	−0.0689307	+	0.0261409i
$921$		0			0
$922$	18.2654	+	4.89419i	0.601538	+	0.161182i
$923$	2.12701	+	0.569930i	0.0700113	+	0.0187595i
$924$		0			0
$925$	−18.9783	+	9.47753i	−0.624003	+	0.311619i
$926$		−	33.0197i		−	1.08510i
$927$		0			0
$928$	−2.22474	−	2.22474i	−0.0730308	−	0.0730308i
$929$	23.9309	−	41.4495i	0.785147	−	1.35991i	−0.143765	−	0.989612i	$-0.545921\pi$
$929$	23.9309	−	41.4495i	0.785147	−	1.35991i	0.928912	−	0.370302i	$-0.120746\pi$
$930$		0			0
$931$	−4.49490	−	7.78539i	−0.147314	−	0.255156i
$932$	4.02477	−	15.0206i	0.131836	−	0.492017i
$933$		0			0
$934$	3.46410	+	2.00000i	0.113349	+	0.0654420i
$935$	−6.29253	−	62.2896i	−0.205788	−	2.03709i
$936$		0			0
$937$	−12.8990	+	12.8990i	−0.421391	+	0.421391i	−0.885683	−	0.464291i	$-0.846309\pi$
$937$	−12.8990	+	12.8990i	−0.421391	+	0.421391i	0.464291	+	0.885683i	$0.346309\pi$
$938$	1.07317	+	4.00514i	0.0350404	+	0.130773i
$939$		0			0
$940$	16.3288	−	11.7631i	0.532587	−	0.383669i
$941$	−5.47730	+	3.16232i	−0.178555	+	0.103089i	−0.586613	−	0.809867i	$-0.699539\pi$
$941$	−5.47730	+	3.16232i	−0.178555	+	0.103089i	0.408059	+	0.912956i	$0.366206\pi$
$942$		0			0
$943$	−3.79107	+	1.01581i	−0.123454	+	0.0330795i
$944$	−11.8065			−0.384269
$945$		0			0
$946$	21.7980			0.708713
$947$	−39.6468	+	10.6233i	−1.28835	+	0.345212i	−0.837033	−	0.547152i	$-0.815712\pi$
$947$	−39.6468	+	10.6233i	−1.28835	+	0.345212i	−0.451316	+	0.892364i	$0.649045\pi$
$948$		0			0
$949$	−12.2993	+	7.10102i	−0.399253	+	0.230509i
$950$	−0.468290	+	7.73839i	−0.0151933	+	0.251067i
$951$		0			0
$952$	−1.26260	−	4.71209i	−0.0409211	−	0.152720i
$953$	19.6561	−	19.6561i	0.636724	−	0.636724i	−0.313022	−	0.949746i	$-0.601341\pi$
$953$	19.6561	−	19.6561i	0.636724	−	0.636724i	0.949746	+	0.313022i	$0.101341\pi$
$954$		0			0
$955$	−5.75255	−	4.69694i	−0.186148	−	0.151989i
$956$	14.6969	+	8.48528i	0.475333	+	0.274434i
$957$		0			0
$958$	−1.83013	+	6.83013i	−0.0591287	+	0.220671i
$959$	1.20713	+	2.09082i	0.0389804	+	0.0675159i
$960$		0			0
$961$	5.60102	−	9.70125i	0.180678	−	0.312944i
$962$	10.3923	+	10.3923i	0.335061	+	0.335061i
$963$		0			0
$964$			19.0000i			0.611949i
$965$	−15.8957	+	35.3175i	−0.511700	+	1.13691i
$966$		0			0
$967$	48.7319	+	13.0577i	1.56711	+	0.419907i	0.934907	−	0.354894i	$-0.115483\pi$
$967$	48.7319	+	13.0577i	1.56711	+	0.419907i	0.632206	+	0.774800i	$0.282150\pi$
$968$	−27.6215	−	7.40117i	−0.887790	−	0.237883i
$969$		0			0
$970$	−8.85729	−	23.3557i	−0.284390	−	0.749905i
$971$		−	49.2117i		−	1.57928i	−0.613570	−	0.789640i	$-0.710267\pi$
$971$		−	49.2117i		−	1.57928i	0.613570	−	0.789640i	$-0.289733\pi$
$972$		0			0
$973$	−10.0000	−	10.0000i	−0.320585	−	0.320585i
$974$	8.48528	−	14.6969i	0.271886	−	0.470920i
$975$		0			0
$976$	−2.72474	−	4.71940i	−0.0872170	−	0.151064i
$977$	−10.9985	+	41.0469i	−0.351873	+	1.31321i	0.532502	+	0.846429i	$0.321252\pi$
$977$	−10.9985	+	41.0469i	−0.351873	+	1.31321i	−0.884374	+	0.466778i	$0.845415\pi$
$978$		0			0
$979$	−12.9029	−	7.44949i	−0.412378	−	0.238087i
$980$	−8.19955	+	10.0424i	−0.261925	+	0.320791i
$981$		0			0
$982$	0.202041	−	0.202041i	0.00644739	−	0.00644739i
$983$	−12.1122	−	45.2034i	−0.386319	−	1.44176i	−0.836077	−	0.548612i	$-0.815156\pi$
$983$	−12.1122	−	45.2034i	−0.386319	−	1.44176i	0.449757	−	0.893151i	$-0.351510\pi$
$984$		0			0
$985$	−12.8060	−	17.7766i	−0.408033	−	0.566408i
$986$	12.1237	−	6.99964i	0.386098	−	0.222914i
$987$		0			0
$988$	5.18811	−	1.39015i	0.165056	−	0.0442265i
$989$	3.46410			0.110152
$990$		0			0
$991$	−56.7423			−1.80248			−0.901240	−	0.433320i	$-0.857342\pi$
$991$	−56.7423			−1.80248			−0.901240	+	0.433320i	$0.857342\pi$
$992$	−4.29788	+	1.15161i	−0.136458	+	0.0365637i
$993$		0			0
$994$	−0.603566	+	0.348469i	−0.0191440	+	0.0110528i
$995$	−1.27364	+	7.83636i	−0.0403770	+	0.248429i
$996$		0			0
$997$	−10.7053	−	39.9528i	−0.339041	−	1.26532i	−0.899422	−	0.437082i	$-0.856012\pi$
$997$	−10.7053	−	39.9528i	−0.339041	−	1.26532i	0.560381	−	0.828235i	$-0.310655\pi$
$998$	−6.29253	+	6.29253i	−0.199187	+	0.199187i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.m.a.143.1		8
3.2	odd	2		90.2.l.a.83.2	yes	8
5.2	odd	4	inner	270.2.m.a.197.1		8
5.3	odd	4		1350.2.q.g.1007.2		8
5.4	even	2		1350.2.q.g.143.2		8
9.2	odd	6		810.2.f.b.323.2		8
9.4	even	3		90.2.l.a.23.2	✓	8
9.5	odd	6	inner	270.2.m.a.233.1		8
9.7	even	3		810.2.f.b.323.3		8
12.11	even	2		720.2.cu.a.353.2		8
15.2	even	4		90.2.l.a.47.2	yes	8
15.8	even	4		450.2.p.a.407.1		8
15.14	odd	2		450.2.p.a.443.1		8
36.31	odd	6		720.2.cu.a.113.2		8
45.2	even	12		810.2.f.b.647.4		8
45.4	even	6		450.2.p.a.293.1		8
45.7	odd	12		810.2.f.b.647.1		8
45.13	odd	12		450.2.p.a.257.1		8
45.14	odd	6		1350.2.q.g.1043.2		8
45.22	odd	12		90.2.l.a.77.2	yes	8
45.23	even	12		1350.2.q.g.557.2		8
45.32	even	12	inner	270.2.m.a.17.1		8
60.47	odd	4		720.2.cu.a.497.2		8
180.67	even	12		720.2.cu.a.257.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.2	✓	8	9.4	even	3
90.2.l.a.47.2	yes	8	15.2	even	4
90.2.l.a.77.2	yes	8	45.22	odd	12
90.2.l.a.83.2	yes	8	3.2	odd	2
270.2.m.a.17.1		8	45.32	even	12	inner
270.2.m.a.143.1		8	1.1	even	1	trivial
270.2.m.a.197.1		8	5.2	odd	4	inner
270.2.m.a.233.1		8	9.5	odd	6	inner
450.2.p.a.257.1		8	45.13	odd	12
450.2.p.a.293.1		8	45.4	even	6
450.2.p.a.407.1		8	15.8	even	4
450.2.p.a.443.1		8	15.14	odd	2
720.2.cu.a.113.2		8	36.31	odd	6
720.2.cu.a.257.2		8	180.67	even	12
720.2.cu.a.353.2		8	12.11	even	2
720.2.cu.a.497.2		8	60.47	odd	4
810.2.f.b.323.2		8	9.2	odd	6
810.2.f.b.323.3		8	9.7	even	3
810.2.f.b.647.1		8	45.7	odd	12
810.2.f.b.647.4		8	45.2	even	12
1350.2.q.g.143.2		8	5.4	even	2
1350.2.q.g.557.2		8	45.23	even	12
1350.2.q.g.1007.2		8	5.3	odd	4
1350.2.q.g.1043.2		8	45.14	odd	6

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.866025 - 0.500000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +(0.283763 + 1.05902i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.22474 - 0.224745i) q^{10} +(5.44949 + 3.14626i) q^{11} +(-0.896575 + 3.34607i) q^{13} +(-0.548188 - 0.949490i) q^{14} +(0.500000 - 0.866025i) q^{16} +(3.14626 + 3.14626i) q^{17} -1.55051i q^{19} +(-2.09077 + 0.792893i) q^{20} +(-6.07812 - 1.62863i) q^{22} +(-0.965926 - 0.258819i) q^{23} +(4.74264 + 1.58346i) q^{25} -3.46410i q^{26} +(0.775255 + 0.775255i) q^{28} +(-1.57313 + 2.72474i) q^{29} +(2.22474 + 3.85337i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-3.85337 - 2.22474i) q^{34} +(-0.246405 - 2.43916i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(0.401302 + 1.49768i) q^{38} +(1.81431 - 1.30701i) q^{40} +(3.39898 - 1.96240i) q^{41} +(-3.34607 + 0.896575i) q^{43} +6.29253 q^{44} +1.00000 q^{46} +(-8.69333 + 2.32937i) q^{47} +(5.02118 - 2.89898i) q^{49} +(-4.99087 - 0.302023i) q^{50} +(0.896575 + 3.34607i) q^{52} +(6.61037 - 6.61037i) q^{53} +(-10.8990 - 8.89898i) q^{55} +(-0.949490 - 0.548188i) q^{56} +(0.814313 - 3.03906i) q^{58} +(-5.90326 - 10.2247i) q^{59} +(2.72474 - 4.71940i) q^{61} +(-3.14626 - 3.14626i) q^{62} -1.00000i q^{64} +(3.17914 - 7.06350i) q^{65} +(-3.65307 - 0.978838i) q^{67} +(4.29788 + 1.15161i) q^{68} +(0.869309 + 2.29227i) q^{70} -0.635674i q^{71} +(2.89898 + 2.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(-0.775255 - 1.34278i) q^{76} +(-1.78559 + 6.66390i) q^{77} +(-2.12132 - 1.22474i) q^{79} +(-1.41421 + 1.73205i) q^{80} +(-2.77526 + 2.77526i) q^{82} +(0.142483 + 0.531752i) q^{83} +(-5.81552 - 8.07277i) q^{85} +(3.00000 - 1.73205i) q^{86} +(-6.07812 + 1.62863i) q^{88} -2.36773 q^{89} -3.79796 q^{91} +(-0.965926 + 0.258819i) q^{92} +(7.79423 - 4.50000i) q^{94} +(-0.556198 + 3.42214i) q^{95} +(-2.89123 - 10.7902i) q^{97} +(-4.09978 + 4.09978i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100}) \) 8 * q - 12 * q^5 - 8 * q^7 + 8 * q^10 + 24 * q^11 + 4 * q^16 - 8 * q^22 + 4 * q^25 + 16 * q^28 + 8 * q^31 - 24 * q^37 - 12 * q^38 + 4 * q^40 - 12 * q^41 + 8 * q^46 - 24 * q^50 - 48 * q^55 + 12 * q^56 - 4 * q^58 + 12 * q^61 + 24 * q^65 + 4 * q^67 + 12 * q^68 - 16 * q^70 - 16 * q^73 - 16 * q^76 - 24 * q^77 - 32 * q^82 - 12 * q^83 - 20 * q^85 + 24 * q^86 - 8 * q^88 + 48 * q^91 + 24 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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