LMFDB - Embedded newform 270.2.m.a.233.1

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			233.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	270.233
Dual form			270.2.m.a.197.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(-0.792893 - 2.09077i) q^{5} +(-1.05902 - 0.283763i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.22474 - 0.224745i) q^{10} +(5.44949 - 3.14626i) q^{11} +(3.34607 - 0.896575i) q^{13} +(0.548188 - 0.949490i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.14626 - 3.14626i) q^{17} -1.55051i q^{19} +(-0.358719 + 2.20711i) q^{20} +(1.62863 + 6.07812i) q^{22} +(-0.258819 - 0.965926i) q^{23} +(-3.74264 + 3.31552i) q^{25} +3.46410i q^{26} +(0.775255 + 0.775255i) q^{28} +(1.57313 + 2.72474i) q^{29} +(2.22474 - 3.85337i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(3.85337 - 2.22474i) q^{34} +(0.246405 + 2.43916i) q^{35} +(-3.00000 + 3.00000i) q^{37} +(1.49768 + 0.401302i) q^{38} +(-2.03906 - 0.917738i) q^{40} +(3.39898 + 1.96240i) q^{41} +(0.896575 - 3.34607i) q^{43} -6.29253 q^{44} +1.00000 q^{46} +(-2.32937 + 8.69333i) q^{47} +(-5.02118 - 2.89898i) q^{49} +(-2.23388 - 4.47323i) q^{50} +(-3.34607 - 0.896575i) q^{52} +(-6.61037 + 6.61037i) q^{53} +(-10.8990 - 8.89898i) q^{55} +(-0.949490 + 0.548188i) q^{56} +(-3.03906 + 0.814313i) q^{58} +(5.90326 - 10.2247i) q^{59} +(2.72474 + 4.71940i) q^{61} +(3.14626 + 3.14626i) q^{62} -1.00000i q^{64} +(-4.52761 - 6.28497i) q^{65} +(0.978838 + 3.65307i) q^{67} +(1.15161 + 4.29788i) q^{68} +(-2.41982 - 0.393292i) q^{70} +0.635674i q^{71} +(2.89898 + 2.89898i) q^{73} +(-2.12132 - 3.67423i) q^{74} +(-0.775255 + 1.34278i) q^{76} +(-6.66390 + 1.78559i) q^{77} +(2.12132 - 1.22474i) q^{79} +(1.41421 - 1.73205i) q^{80} +(-2.77526 + 2.77526i) q^{82} +(0.531752 + 0.142483i) q^{83} +(-4.08346 + 9.07277i) q^{85} +(3.00000 + 1.73205i) q^{86} +(1.62863 - 6.07812i) q^{88} +2.36773 q^{89} -3.79796 q^{91} +(-0.258819 + 0.965926i) q^{92} +(-7.79423 - 4.50000i) q^{94} +(-3.24176 + 1.22939i) q^{95} +(10.7902 + 2.89123i) q^{97} +(4.09978 - 4.09978i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 12 q^{5} - 8 q^{7} + 8 q^{10} + 24 q^{11} + 4 q^{16} - 8 q^{22} + 4 q^{25} + 16 q^{28} + 8 q^{31} - 24 q^{37} - 12 q^{38} + 4 q^{40} - 12 q^{41} + 8 q^{46} - 24 q^{50} - 48 q^{55} + 12 q^{56} - 4 q^{58}+ \cdots + 12 q^{97}+O(q^{100})$ 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$ .

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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

)

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$5$	−0.792893	−	2.09077i	−0.354593	−	0.935021i
$6$		0			0
$7$	−1.05902	−	0.283763i	−0.400271	−	0.107252i	0.0530669	−	0.998591i	$-0.483100\pi$
$7$	−1.05902	−	0.283763i	−0.400271	−	0.107252i	−0.453338	+	0.891339i	$0.649767\pi$
$8$	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	0.663354	−	0.748305i	$-0.269132\pi$
$11$	5.44949	−	3.14626i	1.64308	−	0.948634i	0.979729	−	0.200329i	$-0.0642011\pi$
$12$		0			0
$13$	3.34607	−	0.896575i	0.928032	−	0.248665i	0.237016	−	0.971506i	$-0.423830\pi$
$13$	3.34607	−	0.896575i	0.928032	−	0.248665i	0.691015	+	0.722840i	$0.257164\pi$
$14$	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	0.213797	−	0.976878i	$-0.431417\pi$
$17$	−3.14626	−	3.14626i	−0.763081	−	0.763081i	−0.976878	+	0.213797i	$0.931417\pi$
$18$		0			0
$19$		−	1.55051i		−	0.355711i	−0.984057	−	0.177856i	$-0.943084\pi$
$19$		−	1.55051i		−	0.355711i	0.984057	−	0.177856i	$-0.0569160\pi$
$20$	−0.358719	+	2.20711i	−0.0802121	+	0.493524i
$21$		0			0
$22$	1.62863	+	6.07812i	0.347224	+	1.29586i
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	0.933678	−	0.358113i	$-0.116580\pi$
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	−0.987646	+	0.156704i	$0.949913\pi$
$24$		0			0
$25$	−3.74264	+	3.31552i	−0.748528	+	0.663103i
$26$			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	$-0.0723049\pi$
$29$	1.57313	+	2.72474i	0.292123	+	0.505972i	−0.682188	+	0.731177i	$0.738972\pi$
$30$		0			0
$31$	2.22474	−	3.85337i	0.399576	−	0.692086i	−0.594098	−	0.804393i	$-0.702491\pi$
$31$	2.22474	−	3.85337i	0.399576	−	0.692086i	0.993674	+	0.112307i	$0.0358240\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		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	$0.363391\pi$
$38$	1.49768	+	0.401302i	0.242955	+	0.0650997i
$39$		0			0
$40$	−2.03906	−	0.917738i	−0.322403	−	0.145107i
$41$	3.39898	+	1.96240i	0.530831	+	0.306476i	0.741355	−	0.671113i	$-0.234184\pi$
$41$	3.39898	+	1.96240i	0.530831	+	0.306476i	−0.210524	+	0.977589i	$0.567517\pi$
$42$		0			0
$43$	0.896575	−	3.34607i	0.136726	−	0.510270i	−0.863258	−	0.504762i	$-0.831580\pi$
$43$	0.896575	−	3.34607i	0.136726	−	0.510270i	0.999985	−	0.00550783i	$-0.00175320\pi$
$44$	−6.29253			−0.948634
$45$		0			0
$46$	1.00000			0.147442
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	0.558827	+	0.829285i	$0.311252\pi$
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	−0.898600	+	0.438768i	$0.855415\pi$
$48$		0			0
$49$	−5.02118	−	2.89898i	−0.717311	−	0.414140i
$50$	−2.23388	−	4.47323i	−0.315918	−	0.632611i
$51$		0			0
$52$	−3.34607	−	0.896575i	−0.464016	−	0.124333i
$53$	−6.61037	+	6.61037i	−0.908004	+	0.908004i	−0.996111	−	0.0881074i	$-0.971918\pi$
$53$	−6.61037	+	6.61037i	−0.908004	+	0.908004i	0.0881074	+	0.996111i	$0.471918\pi$
$54$		0			0
$55$	−10.8990	−	8.89898i	−1.46962	−	1.19994i
$56$	−0.949490	+	0.548188i	−0.126881	+	0.0732547i
$57$		0			0
$58$	−3.03906	+	0.814313i	−0.399048	+	0.106925i
$59$	5.90326	−	10.2247i	0.768539	−	1.33115i	−0.169816	−	0.985476i	$-0.554317\pi$
$59$	5.90326	−	10.2247i	0.768539	−	1.33115i	0.938355	−	0.345673i	$-0.112349\pi$
$60$		0			0
$61$	2.72474	+	4.71940i	0.348868	+	0.604257i	0.986049	−	0.166458i	$-0.0532329\pi$
$61$	2.72474	+	4.71940i	0.348868	+	0.604257i	−0.637181	+	0.770714i	$0.719900\pi$
$62$	3.14626	+	3.14626i	0.399576	+	0.399576i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−4.52761	−	6.28497i	−0.561580	−	0.779554i
$66$		0			0
$67$	0.978838	+	3.65307i	0.119584	+	0.446294i	0.999589	−	0.0286709i	$-0.00912748\pi$
$67$	0.978838	+	3.65307i	0.119584	+	0.446294i	−0.880005	+	0.474965i	$0.842461\pi$
$68$	1.15161	+	4.29788i	0.139654	+	0.521194i
$69$		0			0
$70$	−2.41982	−	0.393292i	−0.289224	−	0.0470073i
$71$			0.635674i			0.0754407i	0.999288	+	0.0377203i	$0.0120096\pi$
$71$			0.635674i			0.0754407i	−0.999288	+	0.0377203i	$0.987990\pi$
$72$		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
$77$	−6.66390	+	1.78559i	−0.759422	+	0.203487i
$78$		0			0
$79$	2.12132	−	1.22474i	0.238667	−	0.137795i	−0.375897	−	0.926662i	$-0.622665\pi$
$79$	2.12132	−	1.22474i	0.238667	−	0.137795i	0.614564	+	0.788867i	$0.289332\pi$
$80$	1.41421	−	1.73205i	0.158114	−	0.193649i
$81$		0			0
$82$	−2.77526	+	2.77526i	−0.306476	+	0.306476i
$83$	0.531752	+	0.142483i	0.0583674	+	0.0156395i	0.287885	−	0.957665i	$-0.407048\pi$
$83$	0.531752	+	0.142483i	0.0583674	+	0.0156395i	−0.229517	+	0.973305i	$0.573715\pi$
$84$		0			0
$85$	−4.08346	+	9.07277i	−0.442914	+	0.984080i
$86$	3.00000	+	1.73205i	0.323498	+	0.186772i
$87$		0			0
$88$	1.62863	−	6.07812i	0.173612	−	0.647929i
$89$	2.36773			0.250978			0.125489	−	0.992095i	$-0.459950\pi$
$89$	2.36773			0.250978			0.125489	+	0.992095i	$0.459950\pi$
$90$		0			0
$91$	−3.79796			−0.398134
$92$	−0.258819	+	0.965926i	−0.0269838	+	0.100705i
$93$		0			0
$94$	−7.79423	−	4.50000i	−0.803913	−	0.464140i
$95$	−3.24176	+	1.22939i	−0.332598	+	0.126133i
$96$		0			0
$97$	10.7902	+	2.89123i	1.09558	+	0.293560i	0.760963	−	0.648795i	$-0.224727\pi$
$97$	10.7902	+	2.89123i	1.09558	+	0.293560i	0.334616	+	0.942355i	$0.391393\pi$
$98$	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	−0.553777	−	0.832665i	$-0.686814\pi$
$101$	−1.10102	+	0.635674i	−0.109556	+	0.0632520i	0.444221	+	0.895917i	$0.353481\pi$
$102$		0			0
$103$	−3.96008	+	1.06110i	−0.390198	+	0.104553i	−0.448584	−	0.893741i	$-0.648071\pi$
$103$	−3.96008	+	1.06110i	−0.390198	+	0.104553i	0.0583855	+	0.998294i	$0.481405\pi$
$104$	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	0.504628	−	0.863337i	$-0.331630\pi$
$107$	−3.71051	−	3.71051i	−0.358708	−	0.358708i	−0.863337	+	0.504628i	$0.831630\pi$
$108$		0			0
$109$			20.3485i			1.94903i	0.224323	+	0.974515i	$0.427983\pi$
$109$			20.3485i			1.94903i	−0.224323	+	0.974515i	$0.572017\pi$
$110$	11.4166	−	8.22438i	1.08853	−	0.784164i
$111$		0			0
$112$	−0.283763	−	1.05902i	−0.0268131	−	0.100068i
$113$	3.57117	+	13.3278i	0.335948	+	1.25377i	0.902838	+	0.429981i	$0.141480\pi$
$113$	3.57117	+	13.3278i	0.335948	+	1.25377i	−0.566890	+	0.823793i	$0.691854\pi$
$114$		0			0
$115$	−1.81431	+	1.30701i	−0.169186	+	0.121879i
$116$		−	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
$122$	−5.26380	+	1.41043i	−0.476562	+	0.127694i
$123$		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	$-0.0966651\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	7.24264	−	2.74666i	0.635222	−	0.240898i
$131$	−9.12372	−	5.26758i	−0.797143	−	0.460231i	0.0453278	−	0.998972i	$-0.485567\pi$
$131$	−9.12372	−	5.26758i	−0.797143	−	0.460231i	−0.842471	+	0.538741i	$0.818900\pi$
$132$		0			0
$133$	−0.439978	+	1.64202i	−0.0381509	+	0.142381i
$134$	−3.78194			−0.326710
$135$		0			0
$136$	−4.44949			−0.381541
$137$	0.569930	−	2.12701i	0.0486924	−	0.181723i	−0.937297	−	0.348533i	$-0.886680\pi$
$137$	0.569930	−	2.12701i	0.0486924	−	0.181723i	0.985989	+	0.166810i	$0.0533467\pi$
$138$		0			0
$139$	11.1708	+	6.44949i	0.947499	+	0.547039i	0.892303	−	0.451437i	$-0.149088\pi$
$139$	11.1708	+	6.44949i	0.947499	+	0.547039i	0.0551956	+	0.998476i	$0.482422\pi$
$140$	1.00619	−	2.23557i	0.0850382	−	0.188941i
$141$		0			0
$142$	−0.614014	−	0.164525i	−0.0515269	−	0.0138066i
$143$	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
$148$	4.09808	−	1.09808i	0.336860	−	0.0902613i
$149$	−6.45145	+	11.1742i	−0.528523	+	0.915429i	0.470924	+	0.882174i	$0.343921\pi$
$149$	−6.45145	+	11.1742i	−0.528523	+	0.915429i	−0.999447	+	0.0332550i	$0.989413\pi$
$150$		0			0
$151$	10.7980	+	18.7026i	0.878725	+	1.52200i	0.852741	+	0.522335i	$0.174939\pi$
$151$	10.7980	+	18.7026i	0.878725	+	1.52200i	0.0259849	+	0.999662i	$0.491728\pi$
$152$	−1.09638	−	1.09638i	−0.0889279	−	0.0889279i
$153$		0			0
$154$		−	6.89898i		−	0.555936i
$155$	−9.82050	−	1.59612i	−0.788801	−	0.128203i
$156$		0			0
$157$	1.59165	+	5.94012i	0.127028	+	0.474073i	0.999904	−	0.0138684i	$-0.00441459\pi$
$157$	1.59165	+	5.94012i	0.127028	+	0.474073i	−0.872876	+	0.487942i	$0.837748\pi$
$158$	0.633975	+	2.36603i	0.0504363	+	0.188231i
$159$		0			0
$160$	1.30701	+	1.81431i	0.103328	+	0.143434i
$161$			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
$167$	10.4300	−	2.79472i	0.807100	−	0.216262i	0.168401	−	0.985719i	$-0.446140\pi$
$167$	10.4300	−	2.79472i	0.807100	−	0.216262i	0.638699	+	0.769457i	$0.279473\pi$
$168$		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
$173$	−2.99536	−	0.802603i	−0.227733	−	0.0610208i	0.143148	−	0.989701i	$-0.454277\pi$
$173$	−2.99536	−	0.802603i	−0.227733	−	0.0610208i	−0.370881	+	0.928680i	$0.620944\pi$
$174$		0			0
$175$	4.90435	−	2.44917i	0.370734	−	0.185140i
$176$	5.44949	+	3.14626i	0.410771	+	0.237159i
$177$		0			0
$178$	−0.612812	+	2.28705i	−0.0459322	+	0.171421i
$179$	17.6062			1.31595			0.657976	−	0.753039i	$-0.271413\pi$
$179$	17.6062			1.31595			0.657976	+	0.753039i	$0.271413\pi$
$180$		0			0
$181$	−10.5505			−0.784213			−0.392107	−	0.919920i	$-0.628254\pi$
$181$	−10.5505			−0.784213			−0.392107	+	0.919920i	$0.628254\pi$
$182$	0.982984	−	3.66855i	0.0728636	−	0.271931i
$183$		0			0
$184$	−0.866025	−	0.500000i	−0.0638442	−	0.0368605i
$185$	8.65099	+	3.89363i	0.636033	+	0.286265i
$186$		0			0
$187$	−27.0445	−	7.24656i	−1.97769	−	0.529921i
$188$	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	−0.392317	−	0.919830i	$-0.628327\pi$
$191$	2.87628	−	1.66062i	0.208120	−	0.120158i	0.600437	+	0.799672i	$0.294993\pi$
$192$		0			0
$193$	−16.7303	+	4.48288i	−1.20428	+	0.322685i	−0.804513	−	0.593934i	$-0.797574\pi$
$193$	−16.7303	+	4.48288i	−1.20428	+	0.322685i	−0.399762	+	0.916619i	$0.630907\pi$
$194$	−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	0.415829	−	0.909443i	$-0.363492\pi$
$197$	−6.92820	−	6.92820i	−0.493614	−	0.493614i	−0.909443	+	0.415829i	$0.863492\pi$
$198$		0			0
$199$		−	3.55051i		−	0.251689i	−0.992050	−	0.125844i	$-0.959836\pi$
$199$		−	3.55051i		−	0.251689i	0.992050	−	0.125844i	$-0.0401640\pi$
$200$	−0.302023	+	4.99087i	−0.0213563	+	0.352908i
$201$		0			0
$202$	−0.329049	−	1.22803i	−0.0231518	−	0.0864038i
$203$	−0.892794	−	3.33195i	−0.0626618	−	0.233857i
$204$		0			0
$205$	1.40790	−	8.66246i	0.0983322	−	0.605012i
$206$		−	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	0.332465	+	0.943116i	$0.392120\pi$
$211$	−9.44949	+	16.3670i	−0.650530	+	1.12675i	−0.982995	+	0.183635i	$0.941214\pi$
$212$	9.02993	−	2.41956i	0.620178	−	0.166176i
$213$		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
$218$	−19.6551	−	5.26657i	−1.33121	−	0.356697i
$219$		0			0
$220$	4.98930	+	13.1562i	0.336379	+	0.886993i
$221$	−13.3485	−	7.70674i	−0.897915	−	0.518412i
$222$		0			0
$223$	2.15087	−	8.02714i	0.144033	−	0.537537i	−0.855764	−	0.517367i	$-0.826912\pi$
$223$	2.15087	−	8.02714i	0.144033	−	0.537537i	0.999797	−	0.0201706i	$-0.00642094\pi$
$224$	1.09638			0.0732547
$225$		0			0
$226$	−13.7980			−0.917827
$227$	3.90843	−	14.5865i	0.259412	−	0.968138i	−0.706171	−	0.708041i	$-0.749579\pi$
$227$	3.90843	−	14.5865i	0.259412	−	0.968138i	0.965583	−	0.260096i	$-0.0837543\pi$
$228$		0			0
$229$	−14.1582	−	8.17423i	−0.935600	−	0.540169i	−0.0470214	−	0.998894i	$-0.514973\pi$
$229$	−14.1582	−	8.17423i	−0.935600	−	0.540169i	−0.888578	+	0.458725i	$0.848306\pi$
$230$	−0.792893	−	2.09077i	−0.0522818	−	0.137861i
$231$		0			0
$232$	3.03906	+	0.814313i	0.199524	+	0.0534623i
$233$	−10.9959	+	10.9959i	−0.720363	+	0.720363i	−0.968679	−	0.248316i	$-0.920123\pi$
$233$	−10.9959	+	10.9959i	−0.720363	+	0.720363i	0.248316	+	0.968679i	$0.420123\pi$
$234$		0			0
$235$	20.0227	−	2.02270i	1.30614	−	0.131947i
$236$	−10.2247	+	5.90326i	−0.665574	+	0.384269i
$237$		0			0
$238$	−4.71209	+	1.26260i	−0.305439	+	0.0818423i
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	0.449485	+	0.893288i	$0.351607\pi$
$239$	−8.48528	+	14.6969i	−0.548867	+	0.950666i	−0.998353	+	0.0573782i	$0.981726\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$	20.2204	+	20.2204i	1.29981	+	1.29981i
$243$		0			0
$244$		−	5.44949i		−	0.348868i
$245$	−2.07984	+	12.7967i	−0.132876	+	0.817552i
$246$		0			0
$247$	−1.39015	−	5.18811i	−0.0884531	−	0.330111i
$248$	−1.15161	−	4.29788i	−0.0731275	−	0.272915i
$249$		0			0
$250$	−7.58128	+	8.21731i	−0.479482	+	0.519709i
$251$			11.1708i			0.705097i	0.935793	+	0.352549i	$0.114685\pi$
$251$			11.1708i			0.705097i	−0.935793	+	0.352549i	$0.885315\pi$
$252$		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
$257$	25.1579	−	6.74105i	1.56931	−	0.420495i	0.633713	−	0.773568i	$-0.281530\pi$
$257$	25.1579	−	6.74105i	1.56931	−	0.420495i	0.935596	+	0.353073i	$0.114863\pi$
$258$		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
$263$	−12.2643	−	3.28621i	−0.756249	−	0.202636i	−0.139961	−	0.990157i	$-0.544698\pi$
$263$	−12.2643	−	3.28621i	−0.756249	−	0.202636i	−0.616288	+	0.787521i	$0.711364\pi$
$264$		0			0
$265$	19.0621	+	8.57944i	1.17097	+	0.527031i
$266$	−1.47219	−	0.849971i	−0.0902660	−	0.0521151i
$267$		0			0
$268$	0.978838	−	3.65307i	0.0597920	−	0.223147i
$269$	−4.70334			−0.286768			−0.143384	−	0.989667i	$-0.545798\pi$
$269$	−4.70334			−0.286768			−0.143384	+	0.989667i	$0.545798\pi$
$270$		0			0
$271$	−16.0454			−0.974689			−0.487345	−	0.873210i	$-0.662034\pi$
$271$	−16.0454			−0.974689			−0.487345	+	0.873210i	$0.662034\pi$
$272$	1.15161	−	4.29788i	0.0698268	−	0.260597i
$273$		0			0
$274$	1.90702	+	1.10102i	0.115208	+	0.0665151i
$275$	−9.96399	+	29.8432i	−0.600851	+	1.79961i
$276$		0			0
$277$	13.7983	+	3.69723i	0.829057	+	0.222145i	0.648302	−	0.761383i	$-0.275479\pi$
$277$	13.7983	+	3.69723i	0.829057	+	0.222145i	0.180754	+	0.983528i	$0.442146\pi$
$278$	−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	−0.495473	−	0.868623i	$-0.665005\pi$
$281$	0.151531	−	0.0874863i	0.00903957	−	0.00521900i	0.504513	+	0.863404i	$0.331672\pi$
$282$		0			0
$283$	−6.66112	+	1.78484i	−0.395962	+	0.106098i	−0.451305	−	0.892370i	$-0.649041\pi$
$283$	−6.66112	+	1.78484i	−0.395962	+	0.106098i	0.0553430	+	0.998467i	$0.482375\pi$
$284$	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
$290$	4.11219	+	5.70831i	0.241476	+	0.335203i
$291$		0			0
$292$	−1.06110	−	3.96008i	−0.0620962	−	0.231746i
$293$	−5.70577	−	21.2942i	−0.333335	−	1.24402i	−0.905663	−	0.423998i	$-0.860626\pi$
$293$	−5.70577	−	21.2942i	−0.333335	−	1.24402i	0.572329	−	0.820024i	$-0.306040\pi$
$294$		0			0
$295$	−26.0582	−	4.23523i	−1.51717	−	0.246585i
$296$			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
$302$	−20.8601	+	5.58943i	−1.20036	+	0.321636i
$303$		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	$0.241338\pi$
$308$	6.66390	+	1.78559i	0.379711	+	0.101743i
$309$		0			0
$310$	4.08346	−	9.07277i	0.231925	−	0.515299i
$311$	17.8207	+	10.2888i	1.01052	+	0.583422i	0.911343	−	0.411648i	$-0.135047\pi$
$311$	17.8207	+	10.2888i	1.01052	+	0.583422i	0.0991741	+	0.995070i	$0.468380\pi$
$312$		0			0
$313$	1.29958	−	4.85009i	0.0734564	−	0.274143i	−0.919422	−	0.393271i	$-0.871343\pi$
$313$	1.29958	−	4.85009i	0.0734564	−	0.274143i	0.992879	+	0.119128i	$0.0380100\pi$
$314$	−6.14966			−0.347046
$315$		0			0
$316$	−2.44949			−0.137795
$317$	−0.284965	+	1.06350i	−0.0160052	+	0.0597323i	−0.973467	−	0.228829i	$-0.926510\pi$
$317$	−0.284965	+	1.06350i	−0.0160052	+	0.0597323i	0.957461	+	0.288561i	$0.0931770\pi$
$318$		0			0
$319$	17.1455	+	9.89898i	0.959966	+	0.554236i
$320$	−2.09077	+	0.792893i	−0.116878	+	0.0443241i
$321$		0			0
$322$	−1.05902	−	0.283763i	−0.0590168	−	0.0158135i
$323$	−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
$328$	3.79107	−	1.01581i	0.209327	−	0.0560889i
$329$	4.93369	−	8.54541i	0.272003	−	0.471124i
$330$		0			0
$331$	2.22474	+	3.85337i	0.122283	+	0.211800i	0.920668	−	0.390347i	$-0.127645\pi$
$331$	2.22474	+	3.85337i	0.122283	+	0.211800i	−0.798385	+	0.602148i	$0.794312\pi$
$332$	−0.389270	−	0.389270i	−0.0213639	−	0.0213639i
$333$		0			0
$334$			10.7980i			0.590838i
$335$	6.86162	−	4.94302i	0.374890	−	0.270066i
$336$		0			0
$337$	−7.97861	−	29.7766i	−0.434622	−	1.62203i	−0.741968	−	0.670435i	$-0.766108\pi$
$337$	−7.97861	−	29.7766i	−0.434622	−	1.62203i	0.307346	−	0.951598i	$-0.400559\pi$
$338$	−0.258819	−	0.965926i	−0.0140779	−	0.0525394i
$339$		0			0
$340$	8.07277	−	5.81552i	0.437807	−	0.315391i
$341$		−	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
$347$	4.05886	−	1.08757i	0.217891	−	0.0583837i	−0.148222	−	0.988954i	$-0.547355\pi$
$347$	4.05886	−	1.08757i	0.217891	−	0.0583837i	0.366113	+	0.930570i	$0.380688\pi$
$348$		0			0
$349$	13.0297	−	7.52270i	0.697464	−	0.402681i	−0.108938	−	0.994049i	$-0.534745\pi$
$349$	13.0297	−	7.52270i	0.697464	−	0.402681i	0.806402	+	0.591367i	$0.201412\pi$
$350$	1.09638	+	5.37113i	0.0586038	+	0.287099i
$351$		0			0
$352$	−4.44949	+	4.44949i	−0.237159	+	0.237159i
$353$	33.1244	+	8.87564i	1.76303	+	0.472403i	0.987328	−	0.158694i	$-0.0507284\pi$
$353$	33.1244	+	8.87564i	1.76303	+	0.472403i	0.775704	+	0.631097i	$0.217395\pi$
$354$		0			0
$355$	1.32905	−	0.504022i	0.0705386	−	0.0267507i
$356$	−2.05051	−	1.18386i	−0.108677	−	0.0627446i
$357$		0			0
$358$	−4.55683	+	17.0063i	−0.240836	+	0.898812i
$359$	−17.4634			−0.921682			−0.460841	−	0.887483i	$-0.652452\pi$
$359$	−17.4634			−0.921682			−0.460841	+	0.887483i	$0.652452\pi$
$360$		0			0
$361$	16.5959			0.873469
$362$	2.73067	−	10.1910i	0.143521	−	0.535628i
$363$		0			0
$364$	3.28913	+	1.89898i	0.172397	+	0.0995336i
$365$	3.76252	−	8.35968i	0.196939	−	0.437566i
$366$		0			0
$367$	−9.42418	−	2.52520i	−0.491938	−	0.131814i	0.00431778	−	0.999991i	$-0.498626\pi$
$367$	−9.42418	−	2.52520i	−0.491938	−	0.131814i	−0.496256	+	0.868176i	$0.665292\pi$
$368$	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
$373$	−19.6004	+	5.25190i	−1.01487	+	0.271933i	−0.727662	−	0.685935i	$-0.759393\pi$
$373$	−19.6004	+	5.25190i	−1.01487	+	0.271933i	−0.287206	+	0.957869i	$0.592727\pi$
$374$	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	$0.945354\pi$
$380$	3.42214	+	0.556198i	0.175552	+	0.0285324i
$381$		0			0
$382$	0.859599	+	3.20807i	0.0439809	+	0.164139i
$383$	−7.19464	−	26.8508i	−0.367629	−	1.37201i	−0.863822	−	0.503798i	$-0.831936\pi$
$383$	−7.19464	−	26.8508i	−0.367629	−	1.37201i	0.496193	−	0.868212i	$-0.334731\pi$
$384$		0			0
$385$	9.01702	+	12.5169i	0.459550	+	0.637921i
$386$		−	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	$-0.121123\pi$
$389$	2.81237	+	4.87117i	0.142593	+	0.246978i	−0.785879	+	0.618380i	$0.787789\pi$
$390$		0			0
$391$	−2.22474	+	3.85337i	−0.112510	+	0.194873i
$392$	−5.60040	+	1.50062i	−0.282863	+	0.0757929i
$393$		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	$0.0652821\pi$
$398$	3.42953	+	0.918940i	0.171907	+	0.0460623i
$399$		0			0
$400$	−4.74264	−	1.58346i	−0.237132	−	0.0791732i
$401$	−22.3485	−	12.9029i	−1.11603	−	0.644340i	−0.175645	−	0.984454i	$-0.556201\pi$
$401$	−22.3485	−	12.9029i	−1.11603	−	0.644340i	−0.940384	+	0.340114i	$0.889534\pi$
$402$		0			0
$403$	3.98930	−	14.8883i	0.198721	−	0.741638i
$404$	1.27135			0.0632520
$405$		0			0
$406$	3.44949			0.171195
$407$	−6.90968	+	25.7873i	−0.342500	+	1.27823i
$408$		0			0
$409$	−16.5420	−	9.55051i	−0.817948	−	0.472242i	0.0317605	−	0.999496i	$-0.489889\pi$
$409$	−16.5420	−	9.55051i	−0.817948	−	0.472242i	−0.849708	+	0.527253i	$0.823222\pi$
$410$	8.00290	+	3.60194i	0.395235	+	0.177887i
$411$		0			0
$412$	3.96008	+	1.06110i	0.195099	+	0.0522767i
$413$	−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
$418$	9.42418	−	2.52520i	0.460952	−	0.123512i
$419$	5.97469	−	10.3485i	0.291883	−	0.505556i	−0.682372	−	0.731005i	$-0.739052\pi$
$419$	5.97469	−	10.3485i	0.291883	−	0.505556i	0.974255	+	0.225449i	$0.0723850\pi$
$420$		0			0
$421$	7.44949	+	12.9029i	0.363066	+	0.628849i	0.988464	−	0.151457i	$-0.0483966\pi$
$421$	7.44949	+	12.9029i	0.363066	+	0.628849i	−0.625398	+	0.780306i	$0.715063\pi$
$422$	−13.3636	−	13.3636i	−0.650530	−	0.650530i
$423$		0			0
$424$			9.34847i			0.454002i
$425$	22.2068	+	1.34385i	1.07719	+	0.0651863i
$426$		0			0
$427$	−1.54636	−	5.77111i	−0.0748338	−	0.279284i
$428$	1.35814	+	5.06865i	0.0656482	+	0.245002i
$429$		0			0
$430$	1.24264	−	7.64564i	0.0599255	−	0.368706i
$431$			15.5563i			0.749323i	0.927162	+	0.374661i	$0.122241\pi$
$431$			15.5563i			0.749323i	−0.927162	+	0.374661i	$0.877759\pi$
$432$		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
$437$	−1.49768	+	0.401302i	−0.0716436	+	0.0191969i
$438$		0			0
$439$	−8.83523	+	5.10102i	−0.421682	+	0.243458i	−0.695797	−	0.718239i	$-0.744949\pi$
$439$	−8.83523	+	5.10102i	−0.421682	+	0.243458i	0.274114	+	0.961697i	$0.411615\pi$
$440$	−13.9993	+	1.41421i	−0.667389	+	0.0674200i
$441$		0			0
$442$	10.8990	−	10.8990i	0.518412	−	0.518412i
$443$	−0.531752	−	0.142483i	−0.0252643	−	0.00676955i	0.246165	−	0.969228i	$-0.420830\pi$
$443$	−0.531752	−	0.142483i	−0.0252643	−	0.00676955i	−0.271429	+	0.962458i	$0.587496\pi$
$444$		0			0
$445$	−1.87735	−	4.95037i	−0.0889951	−	0.234670i
$446$	7.19694	+	4.15515i	0.340785	+	0.196752i
$447$		0			0
$448$	−0.283763	+	1.05902i	−0.0134065	+	0.0500339i
$449$	21.7060			1.02437			0.512185	−	0.858875i	$-0.328836\pi$
$449$	21.7060			1.02437			0.512185	+	0.858875i	$0.328836\pi$
$450$		0			0
$451$	24.6969			1.16293
$452$	3.57117	−	13.3278i	0.167974	−	0.626887i
$453$		0			0
$454$	13.0779	+	7.55051i	0.613775	+	0.354363i
$455$	3.01138	+	7.94066i	0.141175	+	0.372264i
$456$		0			0
$457$	−5.94012	−	1.59165i	−0.277867	−	0.0744543i	0.117194	−	0.993109i	$-0.462610\pi$
$457$	−5.94012	−	1.59165i	−0.277867	−	0.0744543i	−0.395061	+	0.918655i	$0.629277\pi$
$458$	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	−0.830271	−	0.557360i	$-0.811814\pi$
$461$	−16.3763	+	9.45485i	−0.762719	+	0.440356i	0.0675520	+	0.997716i	$0.478481\pi$
$462$		0			0
$463$	31.8946	−	8.54613i	1.48227	−	0.397172i	0.575150	−	0.818048i	$-0.304944\pi$
$463$	31.8946	−	8.54613i	1.48227	−	0.397172i	0.907118	+	0.420876i	$0.138277\pi$
$464$	−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	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$		0			0
$469$		−	4.14643i		−	0.191464i
$470$	−3.22848	+	19.8640i	−0.148918	+	0.916256i
$471$		0			0
$472$	−3.05575	−	11.4042i	−0.140652	−	0.524922i
$473$	−5.64173	−	21.0552i	−0.259407	−	0.968120i
$474$		0			0
$475$	5.14074	+	5.80300i	0.235873	+	0.266260i
$476$		−	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	$-0.218314\pi$
$479$	−3.53553	−	6.12372i	−0.161543	−	0.279800i	−0.935422	+	0.353533i	$0.884980\pi$
$480$		0			0
$481$	−7.34847	+	12.7279i	−0.335061	+	0.580343i
$482$	18.3526	−	4.91756i	0.835938	−	0.223989i
$483$		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	$0.375628\pi$
$488$	5.26380	+	1.41043i	0.238281	+	0.0638472i
$489$		0			0
$490$	−11.8224	−	5.32101i	−0.534080	−	0.240379i
$491$	−0.247449	−	0.142865i	−0.0111672	−	0.00644739i	0.494406	−	0.869231i	$-0.335386\pi$
$491$	−0.247449	−	0.142865i	−0.0111672	−	0.00644739i	−0.505573	+	0.862784i	$0.668719\pi$
$492$		0			0
$493$	3.62328	−	13.5223i	0.163184	−	0.609012i
$494$	5.37113			0.241658
$495$		0			0
$496$	4.44949			0.199788
$497$	0.180381	−	0.673191i	0.00809119	−	0.0301967i
$498$		0			0
$499$	−7.70674	−	4.44949i	−0.345001	−	0.199187i	0.317480	−	0.948265i	$-0.397163\pi$
$499$	−7.70674	−	4.44949i	−0.345001	−	0.199187i	−0.662481	+	0.749078i	$0.730497\pi$
$500$	−5.97514	−	9.44975i	−0.267216	−	0.422606i
$501$		0			0
$502$	−10.7902	−	2.89123i	−0.481590	−	0.129042i
$503$	−16.7563	+	16.7563i	−0.747125	+	0.747125i	−0.973938	−	0.226813i	$-0.927169\pi$
$503$	−16.7563	+	16.7563i	−0.747125	+	0.747125i	0.226813	+	0.973938i	$0.427169\pi$
$504$		0			0
$505$	2.20204	+	1.79796i	0.0979895	+	0.0800081i
$506$	5.44949	−	3.14626i	0.242259	−	0.139869i
$507$		0			0
$508$	−19.2934	+	5.16964i	−0.856005	+	0.229366i
$509$	−19.8150	+	34.3207i	−0.878286	+	1.52124i	−0.0250662	+	0.999686i	$0.507980\pi$
$509$	−19.8150	+	34.3207i	−0.878286	+	1.52124i	−0.853220	+	0.521551i	$0.825354\pi$
$510$		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
$515$	5.35844	+	7.43828i	0.236121	+	0.327770i
$516$		0			0
$517$	14.6576	+	54.7030i	0.644642	+	2.40584i
$518$	1.20390	+	4.49303i	0.0528965	+	0.197413i
$519$		0			0
$520$	−7.64564	−	1.24264i	−0.335284	−	0.0544934i
$521$			29.4449i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$521$			29.4449i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$522$		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
$527$	−19.1234	+	5.12409i	−0.833027	+	0.223209i
$528$		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
$533$	13.1326	+	3.51888i	0.568838	+	0.152420i
$534$		0			0
$535$	−4.81578	+	10.6999i	−0.208204	+	0.462595i
$536$	3.27526	+	1.89097i	0.141469	+	0.0816774i
$537$		0			0
$538$	1.21731	−	4.54308i	0.0524822	−	0.195866i
$539$	−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	$0.688323\pi$
$542$	4.15286	−	15.4987i	0.178380	−	0.665725i
$543$		0			0
$544$	3.85337	+	2.22474i	0.165212	+	0.0953851i
$545$	42.5440	−	16.1342i	1.82238	−	0.691112i
$546$		0			0
$547$	20.6594	+	5.53567i	0.883332	+	0.236688i	0.671844	−	0.740693i	$-0.265502\pi$
$547$	20.6594	+	5.53567i	0.883332	+	0.236688i	0.211488	+	0.977381i	$0.432169\pi$
$548$	−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
$553$	−2.59405	+	0.695075i	−0.110310	+	0.0295576i
$554$	−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	0.962999	−	0.269507i	$-0.0868606\pi$
$557$	16.3670	+	16.3670i	0.693492	+	0.693492i	−0.269507	+	0.962999i	$0.586861\pi$
$558$		0			0
$559$		−	12.0000i		−	0.507546i
$560$	−1.98917	+	1.43297i	−0.0840578	+	0.0605541i
$561$		0			0
$562$	0.0452863	+	0.169011i	0.00191029	+	0.00712928i
$563$	8.89004	+	33.1781i	0.374670	+	1.39829i	0.853826	+	0.520559i	$0.174276\pi$
$563$	8.89004	+	33.1781i	0.374670	+	1.39829i	−0.479155	+	0.877730i	$0.659057\pi$
$564$		0			0
$565$	25.0338	−	18.0340i	1.05318	−	0.758697i
$566$		−	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	−0.998484	−	0.0550383i	$-0.982472\pi$
$569$	−13.0458	−	22.5959i	−0.546907	−	0.947270i	0.451578	−	0.892232i	$-0.350861\pi$
$570$		0			0
$571$	−13.5505	+	23.4702i	−0.567071	+	0.982196i	0.429782	+	0.902932i	$0.358590\pi$
$571$	−13.5505	+	23.4702i	−0.567071	+	0.982196i	−0.996854	+	0.0792637i	$0.974743\pi$
$572$	−21.0552	+	5.64173i	−0.880363	+	0.235892i
$573$		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	$0.416826\pi$
$578$	−2.70262	−	0.724165i	−0.112414	−	0.0301213i
$579$		0			0
$580$	−6.57812	+	2.49465i	−0.273141	+	0.103585i
$581$	−0.522704	−	0.301783i	−0.0216854	−	0.0125201i
$582$		0			0
$583$	−15.2252	+	56.8211i	−0.630562	+	2.35329i
$584$	4.09978			0.169650
$585$		0			0
$586$	22.0454			0.910687
$587$	−8.03514	+	29.9876i	−0.331646	+	1.23772i	0.575814	+	0.817581i	$0.304685\pi$
$587$	−8.03514	+	29.9876i	−0.331646	+	1.23772i	−0.907460	+	0.420138i	$0.861981\pi$
$588$		0			0
$589$	−5.97469	−	3.44949i	−0.246183	−	0.142134i
$590$	10.8353	−	24.0742i	0.446082	−	0.991118i
$591$		0			0
$592$	−4.09808	−	1.09808i	−0.168430	−	0.0451307i
$593$	10.0745	−	10.0745i	0.413709	−	0.413709i	−0.469320	−	0.883028i	$-0.655501\pi$
$593$	10.0745	−	10.0745i	0.413709	−	0.413709i	0.883028	+	0.469320i	$0.155501\pi$
$594$		0			0
$595$	6.89898	−	8.44949i	0.282831	−	0.346395i
$596$	11.1742	−	6.45145i	0.457714	−	0.264262i
$597$		0			0
$598$	3.34607	−	0.896575i	0.136831	−	0.0366637i
$599$	16.8991	−	29.2702i	0.690480	−	1.19595i	−0.281201	−	0.959649i	$-0.590733\pi$
$599$	16.8991	−	29.2702i	0.690480	−	1.19595i	0.971681	−	0.236297i	$-0.0759339\pi$
$600$		0			0
$601$	−17.3485	−	30.0484i	−0.707659	−	1.22570i	−0.965723	−	0.259573i	$-0.916418\pi$
$601$	−17.3485	−	30.0484i	−0.707659	−	1.22570i	0.258065	−	0.966128i	$-0.416915\pi$
$602$	−2.68556	−	2.68556i	−0.109455	−	0.109455i
$603$		0			0
$604$		−	21.5959i		−	0.878725i
$605$	−63.1142	−	10.2579i	−2.56596	−	0.417043i
$606$		0			0
$607$	5.73717	+	21.4114i	0.232864	+	0.869062i	0.979100	+	0.203380i	$0.0651926\pi$
$607$	5.73717	+	21.4114i	0.232864	+	0.869062i	−0.746235	+	0.665682i	$0.768141\pi$
$608$	0.401302	+	1.49768i	0.0162749	+	0.0607389i
$609$		0			0
$610$	7.12252	+	9.88708i	0.288383	+	0.400316i
$611$			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
$617$	−6.85906	+	1.83788i	−0.276135	+	0.0739902i	−0.394229	−	0.919012i	$-0.628988\pi$
$617$	−6.85906	+	1.83788i	−0.276135	+	0.0739902i	0.118094	+	0.993002i	$0.462322\pi$
$618$		0			0
$619$	−21.4275	+	12.3712i	−0.861244	+	0.497239i	−0.864429	−	0.502756i	$-0.832320\pi$
$619$	−21.4275	+	12.3712i	−0.861244	+	0.497239i	0.00318471	+	0.999995i	$0.498986\pi$
$620$	7.70674	+	6.29253i	0.309510	+	0.252714i
$621$		0			0
$622$	−14.5505	+	14.5505i	−0.583422	+	0.583422i
$623$	−2.50746	−	0.671873i	−0.100459	−	0.0269180i
$624$		0			0
$625$	3.01472	−	24.8176i	0.120589	−	0.992703i
$626$	4.34847	+	2.51059i	0.173800	+	0.100343i
$627$		0			0
$628$	1.59165	−	5.94012i	0.0635138	−	0.237037i
$629$	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	$0.582652\pi$
$632$	0.633975	−	2.36603i	0.0252182	−	0.0941154i
$633$		0			0
$634$	−0.953512	−	0.550510i	−0.0378688	−	0.0218636i
$635$	−40.7281	−	18.3309i	−1.61624	−	0.727438i
$636$		0			0
$637$	−19.4003	−	5.19831i	−0.768670	−	0.205964i
$638$	−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	−0.339132	−	0.940739i	$-0.610133\pi$
$641$	7.74745	−	4.47299i	0.306006	−	0.176673i	0.645138	+	0.764066i	$0.276800\pi$
$642$		0			0
$643$	30.6976	−	8.22539i	1.21059	−	0.324378i	0.403599	−	0.914936i	$-0.367759\pi$
$643$	30.6976	−	8.22539i	1.21059	−	0.324378i	0.806995	+	0.590558i	$0.201092\pi$
$644$	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	0.0187105	−	0.999825i	$-0.494044\pi$
$647$	−24.9558	−	24.9558i	−0.981114	−	0.981114i	−0.999825	+	0.0187105i	$0.994044\pi$
$648$		0			0
$649$		−	74.2929i		−	2.91625i
$650$	−11.4853	−	12.9649i	−0.450490	−	0.508525i
$651$		0			0
$652$	0.164525	+	0.614014i	0.00644328	+	0.0240467i
$653$	5.57768	+	20.8162i	0.218272	+	0.814601i	0.984989	+	0.172616i	$0.0552220\pi$
$653$	5.57768	+	20.8162i	0.218272	+	0.814601i	−0.766718	+	0.641985i	$0.778111\pi$
$654$		0			0
$655$	−3.77917	+	23.2522i	−0.147664	+	0.908540i
$656$			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	$-0.0959435\pi$
$659$	5.65685	+	9.79796i	0.220360	+	0.381674i	−0.734557	+	0.678546i	$0.762610\pi$
$660$		0			0
$661$	15.3485	−	26.5843i	0.596986	−	1.03401i	−0.396277	−	0.918131i	$-0.629698\pi$
$661$	15.3485	−	26.5843i	0.596986	−	1.03401i	0.993263	−	0.115880i	$-0.0369687\pi$
$662$	−4.29788	+	1.15161i	−0.167042	+	0.0447587i
$663$		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
$668$	−10.4300	−	2.79472i	−0.403550	−	0.108131i
$669$		0			0
$670$	2.99867	+	7.90717i	0.115849	+	0.305480i
$671$	29.6969	+	17.1455i	1.14644	+	0.661896i
$672$		0			0
$673$	−4.22778	+	15.7783i	−0.162969	+	0.608208i	0.835322	+	0.549762i	$0.185281\pi$
$673$	−4.22778	+	15.7783i	−0.162969	+	0.608208i	−0.998291	+	0.0584468i	$0.981385\pi$
$674$	30.8270			1.18741
$675$		0			0
$676$	1.00000			0.0384615
$677$	−1.65750	+	6.18587i	−0.0637028	+	0.237742i	−0.990435	−	0.137981i	$-0.955939\pi$
$677$	−1.65750	+	6.18587i	−0.0637028	+	0.237742i	0.926732	+	0.375723i	$0.122606\pi$
$678$		0			0
$679$	−10.6066	−	6.12372i	−0.407044	−	0.235007i
$680$	3.52797	+	9.30286i	0.135291	+	0.356748i
$681$		0			0
$682$	27.0445	+	7.24656i	1.03559	+	0.277485i
$683$	13.8564	−	13.8564i	0.530201	−	0.530201i	−0.390431	−	0.920632i	$-0.627674\pi$
$683$	13.8564	−	13.8564i	0.530201	−	0.530201i	0.920632	+	0.390431i	$0.127674\pi$
$684$		0			0
$685$	−4.89898	+	0.494897i	−0.187180	+	0.0189091i
$686$	−12.1515	+	7.01569i	−0.463948	+	0.267860i
$687$		0			0
$688$	3.34607	−	0.896575i	0.127568	−	0.0341816i
$689$	−16.1920	+	28.0454i	−0.616867	+	1.06844i
$690$		0			0
$691$	−16.4722	−	28.5307i	−0.626632	−	1.08536i	−0.988223	−	0.153021i	$-0.951100\pi$
$691$	−16.4722	−	28.5307i	−0.626632	−	1.08536i	0.361591	−	0.932337i	$-0.382234\pi$
$692$	2.19275	+	2.19275i	0.0833559	+	0.0833559i
$693$		0			0
$694$			4.20204i			0.159507i
$695$	4.62712	−	28.4694i	0.175516	−	1.07991i
$696$		0			0
$697$	−4.51985	−	16.8683i	−0.171202	−	0.638933i
$698$	3.89404	+	14.5327i	0.147392	+	0.550073i
$699$		0			0
$700$	−5.47187	−	0.331131i	−0.206817	−	0.0125156i
$701$		−	23.9309i		−	0.903857i	−0.892054	−	0.451928i	$-0.850736\pi$
$701$		−	23.9309i		−	0.903857i	0.892054	−	0.451928i	$-0.149264\pi$
$702$		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
$707$	1.34638	−	0.360762i	0.0506359	−	0.0135678i
$708$		0			0
$709$	−38.4069	+	22.1742i	−1.44240	+	0.832771i	−0.998010	−	0.0630617i	$-0.979914\pi$
$709$	−38.4069	+	22.1742i	−1.44240	+	0.832771i	−0.444392	+	0.895833i	$0.646580\pi$
$710$	0.142865	+	1.41421i	0.00536161	+	0.0530745i
$711$		0			0
$712$	1.67423	−	1.67423i	0.0627446	−	0.0627446i
$713$	−4.29788	−	1.15161i	−0.160957	−	0.0431282i
$714$		0			0
$715$	−44.4473	−	20.0048i	−1.66223	−	0.748137i
$716$	−15.2474	−	8.80312i	−0.569824	−	0.328988i
$717$		0			0
$718$	4.51985	−	16.8683i	0.168679	−	0.629520i
$719$	32.5269			1.21305			0.606525	−	0.795065i	$-0.292563\pi$
$719$	32.5269			1.21305			0.606525	+	0.795065i	$0.292563\pi$
$720$		0			0
$721$	4.49490			0.167399
$722$	−4.29534	+	16.0304i	−0.159856	+	0.596591i
$723$		0			0
$724$	9.13701	+	5.27526i	0.339574	+	0.196053i
$725$	−14.9216	−	4.98200i	−0.554174	−	0.185027i
$726$		0			0
$727$	30.2836	+	8.11447i	1.12316	+	0.300949i	0.772160	−	0.635428i	$-0.219176\pi$
$727$	30.2836	+	8.11447i	1.12316	+	0.300949i	0.350996	+	0.936377i	$0.385843\pi$
$728$	−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
$733$	13.8603	−	3.71385i	0.511941	−	0.137174i	0.00640470	−	0.999979i	$-0.497961\pi$
$733$	13.8603	−	3.71385i	0.511941	−	0.137174i	0.505536	+	0.862805i	$0.331295\pi$
$734$	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	$0.848280\pi$
$740$	−5.54516	−	7.69748i	−0.203844	−	0.282965i
$741$		0			0
$742$	2.65275	+	9.90020i	0.0973855	+	0.363448i
$743$	−0.0261460	−	0.0975783i	−0.000959205	−	0.00357980i	0.965445	−	0.260609i	$-0.0839232\pi$
$743$	−0.0261460	−	0.0975783i	−0.000959205	−	0.00357980i	−0.966404	+	0.257029i	$0.917257\pi$
$744$		0			0
$745$	28.4781	+	4.62852i	1.04336	+	0.169576i
$746$		−	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	−0.775714	−	0.631084i	$-0.782610\pi$
$751$	4.34847	−	7.53177i	0.158678	−	0.274838i	0.934392	+	0.356246i	$0.115944\pi$
$752$	−8.69333	+	2.32937i	−0.317013	+	0.0849434i
$753$		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	$0.441731\pi$
$758$	−6.42489	−	1.72154i	−0.233362	−	0.0625293i
$759$		0			0
$760$	−1.42296	+	3.16158i	−0.0516162	+	0.114683i
$761$	15.3990	+	8.89060i	0.558213	+	0.322284i	0.752428	−	0.658675i	$-0.228883\pi$
$761$	15.3990	+	8.89060i	0.558213	+	0.322284i	−0.194215	+	0.980959i	$0.562216\pi$
$762$		0			0
$763$	5.77414	−	21.5494i	0.209038	−	0.780141i
$764$	−3.32124			−0.120158
$765$		0			0
$766$	27.7980			1.00438
$767$	10.5854	−	39.5054i	0.382218	−	1.42646i
$768$		0			0
$769$	17.0580	+	9.84847i	0.615129	+	0.355145i	0.774970	−	0.631998i	$-0.217765\pi$
$769$	17.0580	+	9.84847i	0.615129	+	0.355145i	−0.159841	+	0.987143i	$0.551098\pi$
$770$	−14.4242	+	5.47015i	−0.519811	+	0.197131i
$771$		0			0
$772$	16.7303	+	4.48288i	0.602138	+	0.161342i
$773$	3.11416	−	3.11416i	0.112008	−	0.112008i	−0.648881	−	0.760890i	$-0.724763\pi$
$773$	3.11416	−	3.11416i	0.112008	−	0.112008i	0.760890	+	0.648881i	$0.224763\pi$
$774$		0			0
$775$	4.44949	+	21.7980i	0.159830	+	0.783006i
$776$	9.67423	−	5.58542i	0.347285	−	0.200505i
$777$		0			0
$778$	−5.43309	+	1.45579i	−0.194786	+	0.0521927i
$779$	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
$785$	11.1574	−	8.03766i	0.398225	−	0.286876i
$786$		0			0
$787$	1.06110	+	3.96008i	0.0378241	+	0.141162i	0.982256	−	0.187546i	$-0.0600535\pi$
$787$	1.06110	+	3.96008i	0.0378241	+	0.141162i	−0.944432	+	0.328708i	$0.893387\pi$
$788$	2.53590	+	9.46410i	0.0903376	+	0.337145i
$789$		0			0
$790$	4.44414	−	3.20150i	0.158115	−	0.113904i
$791$		−	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
$797$	19.5137	−	5.22867i	0.691210	−	0.185209i	0.103920	−	0.994586i	$-0.466861\pi$
$797$	19.5137	−	5.22867i	0.691210	−	0.185209i	0.587290	+	0.809377i	$0.300195\pi$
$798$		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
$803$	24.9189	+	6.67700i	0.879369	+	0.235626i
$804$		0			0
$805$	2.29227	−	0.869309i	0.0807919	−	0.0306391i
$806$	13.3485	+	7.70674i	0.470180	+	0.271458i
$807$		0			0
$808$	−0.329049	+	1.22803i	−0.0115759	+	0.0432019i
$809$	−54.0901			−1.90171			−0.950853	−	0.309644i	$-0.899790\pi$
$809$	−54.0901			−1.90171			−0.950853	+	0.309644i	$0.899790\pi$
$810$		0			0
$811$	43.6413			1.53245			0.766227	−	0.642570i	$-0.222132\pi$
$811$	43.6413			1.53245			0.766227	+	0.642570i	$0.222132\pi$
$812$	−0.892794	+	3.33195i	−0.0313309	+	0.116929i
$813$		0			0
$814$	−23.1202	−	13.3485i	−0.810364	−	0.467864i
$815$	−0.583382	+	1.29618i	−0.0204350	+	0.0454031i
$816$		0			0
$817$	−5.18811	−	1.39015i	−0.181509	−	0.0486352i
$818$	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	−0.0570780	−	0.998370i	$-0.518178\pi$
$821$	22.3207	−	12.8868i	0.778997	−	0.449754i	0.836075	+	0.548616i	$0.184845\pi$
$822$		0			0
$823$	46.9519	−	12.5807i	1.63664	−	0.438536i	0.680811	−	0.732459i	$-0.261627\pi$
$823$	46.9519	−	12.5807i	1.63664	−	0.438536i	0.955829	+	0.293923i	$0.0949608\pi$
$824$	−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	0.0486816	−	0.998814i	$-0.484498\pi$
$827$	−27.3235	−	27.3235i	−0.950133	−	0.950133i	−0.998814	+	0.0486816i	$0.984498\pi$
$828$		0			0
$829$			15.4495i			0.536583i	0.963338	+	0.268291i	$0.0864590\pi$
$829$			15.4495i			0.536583i	−0.963338	+	0.268291i	$0.913541\pi$
$830$	1.21503	+	0.197479i	0.0421745	+	0.00685459i
$831$		0			0
$832$	−0.896575	−	3.34607i	−0.0310832	−	0.116004i
$833$	6.67700	+	24.9189i	0.231344	+	0.863389i
$834$		0			0
$835$	−14.1130	−	19.5909i	−0.488401	−	0.677970i
$836$			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	$-0.280579\pi$
$839$	−10.1459	−	17.5732i	−0.350275	−	0.606695i	−0.986298	+	0.164976i	$0.947245\pi$
$840$		0			0
$841$	9.55051	−	16.5420i	0.329328	−	0.570413i
$842$	−14.3913	+	3.85614i	−0.495957	+	0.132891i
$843$		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
$848$	−9.02993	−	2.41956i	−0.310089	−	0.0830881i
$849$		0			0
$850$	−7.04561	+	21.1023i	−0.241662	+	0.723804i
$851$	3.67423	+	2.12132i	0.125951	+	0.0727179i
$852$		0			0
$853$	−9.60723	+	35.8547i	−0.328945	+	1.22764i	0.581340	+	0.813660i	$0.302528\pi$
$853$	−9.60723	+	35.8547i	−0.328945	+	1.22764i	−0.910286	+	0.413980i	$0.864138\pi$
$854$	5.97469			0.204450
$855$		0			0
$856$	−5.24745			−0.179354
$857$	−0.982984	+	3.66855i	−0.0335781	+	0.125315i	−0.980680	−	0.195616i	$-0.937329\pi$
$857$	−0.982984	+	3.66855i	−0.0335781	+	0.125315i	0.947102	+	0.320932i	$0.103996\pi$
$858$		0			0
$859$	2.16064	+	1.24745i	0.0737202	+	0.0425624i	0.536407	−	0.843959i	$-0.319781\pi$
$859$	2.16064	+	1.24745i	0.0737202	+	0.0425624i	−0.462687	+	0.886522i	$0.653115\pi$
$860$	7.06350	+	3.17914i	0.240863	+	0.108408i
$861$		0			0
$862$	−15.0263	−	4.02628i	−0.511797	−	0.137136i
$863$	27.7842	−	27.7842i	0.945787	−	0.945787i	−0.0528175	−	0.998604i	$-0.516820\pi$
$863$	27.7842	−	27.7842i	0.945787	−	0.945787i	0.998604	+	0.0528175i	$0.0168202\pi$
$864$		0			0
$865$	0.696938	+	6.89898i	0.0236966	+	0.234572i
$866$	−10.4722	+	6.04612i	−0.355860	+	0.205456i
$867$		0			0
$868$	4.71209	−	1.26260i	0.159939	−	0.0428555i
$869$	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
$875$	−9.00927	−	8.31193i	−0.304569	−	0.280995i
$876$		0			0
$877$	2.10558	+	7.85813i	0.0711004	+	0.265350i	0.992321	−	0.123691i	$-0.0394731\pi$
$877$	2.10558	+	7.85813i	0.0711004	+	0.265350i	−0.921220	+	0.389041i	$0.872806\pi$
$878$	−2.64048	−	9.85441i	−0.0891120	−	0.332570i
$879$		0			0
$880$	2.25725	−	13.8883i	0.0760920	−	0.468174i
$881$		−	58.3006i		−	1.96420i	−0.188368	−	0.982098i	$-0.560320\pi$
$881$		−	58.3006i		−	1.96420i	0.188368	−	0.982098i	$-0.439680\pi$
$882$		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
$887$	−26.8508	+	7.19464i	−0.901561	+	0.241572i	−0.679686	−	0.733503i	$-0.737884\pi$
$887$	−26.8508	+	7.19464i	−0.901561	+	0.241572i	−0.221874	+	0.975075i	$0.571217\pi$
$888$		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
$893$	13.4791	+	3.61171i	0.451061	+	0.120861i
$894$		0			0
$895$	−13.9599	−	36.8106i	−0.466627	−	1.23044i
$896$	−0.949490	−	0.548188i	−0.0317202	−	0.0183137i
$897$		0			0
$898$	−5.61793	+	20.9664i	−0.187473	+	0.699658i
$899$	13.9993			0.466902
$900$		0			0
$901$	41.5959			1.38576
$902$	−6.39204	+	23.8554i	−0.212832	+	0.794298i
$903$		0			0
$904$	11.9494	+	6.89898i	0.397431	+	0.229457i
$905$	8.36543	+	22.0587i	0.278076	+	0.733256i
$906$		0			0
$907$	−6.38512	−	1.71089i	−0.212015	−	0.0568091i	0.151248	−	0.988496i	$-0.451671\pi$
$907$	−6.38512	−	1.71089i	−0.212015	−	0.0568091i	−0.363263	+	0.931687i	$0.618337\pi$
$908$	−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	−0.598002	−	0.801495i	$-0.704038\pi$
$911$	−6.12372	+	3.53553i	−0.202888	+	0.117137i	0.395114	+	0.918632i	$0.370705\pi$
$912$		0			0
$913$	3.34607	−	0.896575i	0.110739	−	0.0296723i
$914$	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	$-0.148958\pi$
$920$	−0.358719	+	2.20711i	−0.0118266	+	0.0727662i
$921$		0			0
$922$	−4.89419	−	18.2654i	−0.161182	−	0.601538i
$923$	0.569930	+	2.12701i	0.0187595	+	0.0700113i
$924$		0			0
$925$	1.28138	−	21.1745i	0.0421314	−	0.696212i
$926$			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	−0.928912	−	0.370302i	$-0.879254\pi$
$929$	−23.9309	−	41.4495i	−0.785147	−	1.35991i	0.143765	−	0.989612i	$-0.454079\pi$
$930$		0			0
$931$	−4.49490	+	7.78539i	−0.147314	+	0.255156i
$932$	15.0206	−	4.02477i	0.492017	−	0.131836i
$933$		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	$0.346309\pi$
$938$	4.00514	+	1.07317i	0.130773	+	0.0350404i
$939$		0			0
$940$	−18.3515	−	8.25964i	−0.598561	−	0.269400i
$941$	−5.47730	−	3.16232i	−0.178555	−	0.103089i	0.408059	−	0.912956i	$-0.366206\pi$
$941$	−5.47730	−	3.16232i	−0.178555	−	0.103089i	−0.586613	+	0.809867i	$0.699539\pi$
$942$		0			0
$943$	1.01581	−	3.79107i	0.0330795	−	0.123454i
$944$	11.8065			0.384269
$945$		0			0
$946$	21.7980			0.708713
$947$	−10.6233	+	39.6468i	−0.345212	+	1.28835i	0.547152	+	0.837033i	$0.315712\pi$
$947$	−10.6233	+	39.6468i	−0.345212	+	1.28835i	−0.892364	+	0.451316i	$0.850955\pi$
$948$		0			0
$949$	12.2993	+	7.10102i	0.399253	+	0.230509i
$950$	−6.93579	+	3.46365i	−0.225027	+	0.112376i
$951$		0			0
$952$	4.71209	+	1.26260i	0.152720	+	0.0409211i
$953$	−19.6561	+	19.6561i	−0.636724	+	0.636724i	−0.949746	−	0.313022i	$-0.898659\pi$
$953$	−19.6561	+	19.6561i	−0.636724	+	0.636724i	0.313022	+	0.949746i	$0.398659\pi$
$954$		0			0
$955$	−5.75255	−	4.69694i	−0.186148	−	0.151989i
$956$	14.6969	−	8.48528i	0.475333	−	0.274434i
$957$		0			0
$958$	6.83013	−	1.83013i	0.220671	−	0.0591287i
$959$	−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
$965$	22.6380	+	31.4248i	0.728744	+	1.01160i
$966$		0			0
$967$	−13.0577	−	48.7319i	−0.419907	−	1.56711i	−0.774800	−	0.632206i	$-0.782150\pi$
$967$	−13.0577	−	48.7319i	−0.419907	−	1.56711i	0.354894	−	0.934907i	$-0.384517\pi$
$968$	−7.40117	−	27.6215i	−0.237883	−	0.887790i
$969$		0			0
$970$	24.6552	+	4.00720i	0.791632	+	0.128663i
$971$			49.2117i			1.57928i	0.613570	+	0.789640i	$0.289733\pi$
$971$			49.2117i			1.57928i	−0.613570	+	0.789640i	$0.710267\pi$
$972$		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
$977$	−41.0469	+	10.9985i	−1.31321	+	0.351873i	−0.846429	−	0.532502i	$-0.821252\pi$
$977$	−41.0469	+	10.9985i	−1.31321	+	0.351873i	−0.466778	+	0.884374i	$0.654585\pi$
$978$		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
$983$	−45.2034	−	12.1122i	−1.44176	−	0.386319i	−0.548612	−	0.836077i	$-0.684844\pi$
$983$	−45.2034	−	12.1122i	−1.44176	−	0.386319i	−0.893151	+	0.449757i	$0.851510\pi$
$984$		0			0
$985$	−8.99196	+	19.9786i	−0.286508	+	0.636571i
$986$	12.1237	+	6.99964i	0.386098	+	0.222914i
$987$		0			0
$988$	−1.39015	+	5.18811i	−0.0442265	+	0.165056i
$989$	−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	$0.857342\pi$
$992$	−1.15161	+	4.29788i	−0.0365637	+	0.136458i
$993$		0			0
$994$	0.603566	+	0.348469i	0.0191440	+	0.0110528i
$995$	−7.42330	+	2.81518i	−0.235334	+	0.0892471i
$996$		0			0
$997$	39.9528	+	10.7053i	1.26532	+	0.339041i	0.828235	−	0.560381i	$-0.189345\pi$
$997$	39.9528	+	10.7053i	1.26532	+	0.339041i	0.437082	+	0.899422i	$0.356012\pi$
$998$	6.29253	−	6.29253i	0.199187	−	0.199187i
$999$		0			0

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instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.2	✓	8	3.2	odd	2
90.2.l.a.47.2	yes	8	45.7	odd	12
90.2.l.a.77.2	yes	8	15.2	even	4
90.2.l.a.83.2	yes	8	9.7	even	3
270.2.m.a.17.1		8	5.2	odd	4	inner
270.2.m.a.143.1		8	9.2	odd	6	inner
270.2.m.a.197.1		8	45.2	even	12	inner
270.2.m.a.233.1		8	1.1	even	1	trivial
450.2.p.a.257.1		8	15.8	even	4
450.2.p.a.293.1		8	15.14	odd	2
450.2.p.a.407.1		8	45.43	odd	12
450.2.p.a.443.1		8	45.34	even	6
720.2.cu.a.113.2		8	12.11	even	2
720.2.cu.a.257.2		8	60.47	odd	4
720.2.cu.a.353.2		8	36.7	odd	6
720.2.cu.a.497.2		8	180.7	even	12
810.2.f.b.323.2		8	9.4	even	3
810.2.f.b.323.3		8	9.5	odd	6
810.2.f.b.647.1		8	45.32	even	12
810.2.f.b.647.4		8	45.22	odd	12
1350.2.q.g.143.2		8	45.29	odd	6
1350.2.q.g.557.2		8	5.3	odd	4
1350.2.q.g.1007.2		8	45.38	even	12
1350.2.q.g.1043.2		8	5.4	even	2

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Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

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$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	270.2.m.a.233.1

Level	$270$
Weight	$2$
Character	270.233
Analytic conductor	$2.156$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$