LMFDB - Embedded newform 720.2.cu.a.497.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(113,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 0, 10, 9]))

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

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

chi := DirichletCharacter("720.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cu (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:	$5.74922894553$
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:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			497.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	720.497
Dual form			720.2.cu.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10721 - 1.33195i) q^{3} +(0.792893 - 2.09077i) q^{5} +(1.05902 - 0.283763i) q^{7} +(-0.548188 + 2.94949i) q^{9} +(5.44949 + 3.14626i) q^{11} +(3.34607 + 0.896575i) q^{13} +(-3.66270 + 1.25882i) q^{15} +(3.14626 - 3.14626i) q^{17} -1.55051i q^{19} +(-1.55051 - 1.09638i) q^{21} +(-0.258819 + 0.965926i) q^{23} +(-3.74264 - 3.31552i) q^{25} +(4.53553 - 2.53553i) q^{27} +(-1.57313 + 2.72474i) q^{29} +(-2.22474 - 3.85337i) q^{31} +(-1.84304 - 10.7420i) q^{33} +(0.246405 - 2.43916i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-2.51059 - 5.44949i) q^{39} +(-3.39898 + 1.96240i) q^{41} +(-0.896575 - 3.34607i) q^{43} +(5.73205 + 3.48477i) q^{45} +(-2.32937 - 8.69333i) q^{47} +(-5.02118 + 2.89898i) q^{49} +(-7.67423 - 0.707107i) q^{51} +(6.61037 + 6.61037i) q^{53} +(10.8990 - 8.89898i) q^{55} +(-2.06520 + 1.71673i) q^{57} +(5.90326 + 10.2247i) q^{59} +(2.72474 - 4.71940i) q^{61} +(0.256415 + 3.27912i) q^{63} +(4.52761 - 6.28497i) q^{65} +(-0.978838 + 3.65307i) q^{67} +(1.57313 - 0.724745i) q^{69} -0.635674i q^{71} +(2.89898 - 2.89898i) q^{73} +(-0.272229 + 8.65597i) q^{75} +(6.66390 + 1.78559i) q^{77} +(-2.12132 - 1.22474i) q^{79} +(-8.39898 - 3.23375i) q^{81} +(0.531752 - 0.142483i) q^{83} +(-4.08346 - 9.07277i) q^{85} +(5.37101 - 0.921519i) q^{87} -2.36773 q^{89} +3.79796 q^{91} +(-2.66925 + 7.22973i) q^{93} +(-3.24176 - 1.22939i) q^{95} +(10.7902 - 2.89123i) q^{97} +(-12.2672 + 14.3485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 12 q^{5} + 8 q^{7} + 24 q^{11} - 16 q^{15} - 32 q^{21} + 4 q^{25} + 8 q^{27} - 8 q^{31} + 16 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} - 32 q^{51} + 48 q^{55} + 28 q^{57} + 12 q^{61} + 32 q^{63}+ \cdots + 12 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 + 12 * q^5 + 8 * q^7 + 24 * q^11 - 16 * q^15 - 32 * q^21 + 4 * q^25 + 8 * q^27 - 8 * q^31 + 16 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 - 32 * q^51 + 48 * q^55 + 28 * q^57 + 12 * q^61 + 32 * q^63 - 24 * q^65 - 4 * q^67 - 16 * q^73 - 8 * q^75 + 24 * q^77 - 28 * q^81 - 12 * q^83 - 20 * q^85 + 8 * q^87 - 48 * q^91 - 20 * q^93 + 24 * q^95 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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			0
$2$		0			0
$3$	−1.10721	−	1.33195i	−0.639246	−	0.769002i
$3$	−1.10721	−	1.33195i	−0.639246	−	0.769002i
$4$		0			0
$5$	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	$-0.516900\pi$
$7$	1.05902	−	0.283763i	0.400271	−	0.107252i	0.453338	+	0.891339i	$0.350233\pi$
$8$		0			0
$9$	−0.548188	+	2.94949i	−0.182729	+	0.983163i
$10$		0			0
$11$	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
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.691015	−	0.722840i	$-0.257164\pi$
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.237016	+	0.971506i	$0.423830\pi$
$14$		0			0
$15$	−3.66270	+	1.25882i	−0.945705	+	0.325026i
$16$		0			0
$17$	3.14626	−	3.14626i	0.763081	−	0.763081i	−0.213797	−	0.976878i	$-0.568583\pi$
$17$	3.14626	−	3.14626i	0.763081	−	0.763081i	0.976878	+	0.213797i	$0.0685831\pi$
$18$		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			0
$21$	−1.55051	−	1.09638i	−0.338349	−	0.239249i
$22$		0			0
$23$	−0.258819	+	0.965926i	−0.0539675	+	0.201409i	−0.987646	−	0.156704i	$-0.949913\pi$
$23$	−0.258819	+	0.965926i	−0.0539675	+	0.201409i	0.933678	+	0.358113i	$0.116580\pi$
$24$		0			0
$25$	−3.74264	−	3.31552i	−0.748528	−	0.663103i
$26$		0			0
$27$	4.53553	−	2.53553i	0.872864	−	0.487964i
$28$		0			0
$29$	−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	0.594098	−	0.804393i	$-0.297509\pi$
$31$	−2.22474	−	3.85337i	−0.399576	−	0.692086i	−0.993674	+	0.112307i	$0.964176\pi$
$32$		0			0
$33$	−1.84304	−	10.7420i	−0.320832	−	1.86995i
$34$		0			0
$35$	0.246405	−	2.43916i	0.0416500	−	0.412293i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$		0			0
$39$	−2.51059	−	5.44949i	−0.402016	−	0.872617i
$40$		0			0
$41$	−3.39898	+	1.96240i	−0.530831	+	0.306476i	−0.741355	−	0.671113i	$-0.765816\pi$
$41$	−3.39898	+	1.96240i	−0.530831	+	0.306476i	0.210524	+	0.977589i	$0.432483\pi$
$42$		0			0
$43$	−0.896575	−	3.34607i	−0.136726	−	0.510270i	−0.999985	−	0.00550783i	$-0.998247\pi$
$43$	−0.896575	−	3.34607i	−0.136726	−	0.510270i	0.863258	−	0.504762i	$-0.168420\pi$
$44$		0			0
$45$	5.73205	+	3.48477i	0.854484	+	0.519478i
$46$		0			0
$47$	−2.32937	−	8.69333i	−0.339774	−	1.26805i	−0.898600	−	0.438768i	$-0.855415\pi$
$47$	−2.32937	−	8.69333i	−0.339774	−	1.26805i	0.558827	−	0.829285i	$-0.311252\pi$
$48$		0			0
$49$	−5.02118	+	2.89898i	−0.717311	+	0.414140i
$50$		0			0
$51$	−7.67423	−	0.707107i	−1.07461	−	0.0990148i
$52$		0			0
$53$	6.61037	+	6.61037i	0.908004	+	0.908004i	0.996111	−	0.0881074i	$-0.0280819\pi$
$53$	6.61037	+	6.61037i	0.908004	+	0.908004i	−0.0881074	+	0.996111i	$0.528082\pi$
$54$		0			0
$55$	10.8990	−	8.89898i	1.46962	−	1.19994i
$56$		0			0
$57$	−2.06520	+	1.71673i	−0.273543	+	0.227387i
$58$		0			0
$59$	5.90326	+	10.2247i	0.768539	+	1.33115i	0.938355	+	0.345673i	$0.112349\pi$
$59$	5.90326	+	10.2247i	0.768539	+	1.33115i	−0.169816	+	0.985476i	$0.554317\pi$
$60$		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	$0.0532329\pi$
$62$		0			0
$63$	0.256415	+	3.27912i	0.0323053	+	0.413130i
$64$		0			0
$65$	4.52761	−	6.28497i	0.561580	−	0.779554i
$66$		0			0
$67$	−0.978838	+	3.65307i	−0.119584	+	0.446294i	−0.999589	−	0.0286709i	$-0.990873\pi$
$67$	−0.978838	+	3.65307i	−0.119584	+	0.446294i	0.880005	+	0.474965i	$0.157539\pi$
$68$		0			0
$69$	1.57313	−	0.724745i	0.189383	−	0.0872490i
$70$		0			0
$71$		−	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	−0.516804	−	0.856104i	$-0.672878\pi$
$73$	2.89898	−	2.89898i	0.339300	−	0.339300i	0.856104	+	0.516804i	$0.172878\pi$
$74$		0			0
$75$	−0.272229	+	8.65597i	−0.0314343	+	0.999506i
$76$		0			0
$77$	6.66390	+	1.78559i	0.759422	+	0.203487i
$78$		0			0
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	0.375897	−	0.926662i	$-0.377335\pi$
$79$	−2.12132	−	1.22474i	−0.238667	−	0.137795i	−0.614564	+	0.788867i	$0.710668\pi$
$80$		0			0
$81$	−8.39898	−	3.23375i	−0.933220	−	0.359306i
$82$		0			0
$83$	0.531752	−	0.142483i	0.0583674	−	0.0156395i	−0.229517	−	0.973305i	$-0.573715\pi$
$83$	0.531752	−	0.142483i	0.0583674	−	0.0156395i	0.287885	+	0.957665i	$0.407048\pi$
$84$		0			0
$85$	−4.08346	−	9.07277i	−0.442914	−	0.984080i
$86$		0			0
$87$	5.37101	−	0.921519i	0.575833	−	0.0987973i
$88$		0			0
$89$	−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			0
$93$	−2.66925	+	7.22973i	−0.276788	+	0.749688i
$94$		0			0
$95$	−3.24176	−	1.22939i	−0.332598	−	0.126133i
$96$		0			0
$97$	10.7902	−	2.89123i	1.09558	−	0.293560i	0.334616	−	0.942355i	$-0.391393\pi$
$97$	10.7902	−	2.89123i	1.09558	−	0.293560i	0.760963	+	0.648795i	$0.224727\pi$
$98$		0			0
$99$	−12.2672	+	14.3485i	−1.23290	+	1.44208i
$100$		0			0
$101$	1.10102	+	0.635674i	0.109556	+	0.0632520i	0.553777	−	0.832665i	$-0.313186\pi$
$101$	1.10102	+	0.635674i	0.109556	+	0.0632520i	−0.444221	+	0.895917i	$0.646519\pi$
$102$		0			0
$103$	3.96008	+	1.06110i	0.390198	+	0.104553i	0.448584	−	0.893741i	$-0.351929\pi$
$103$	3.96008	+	1.06110i	0.390198	+	0.104553i	−0.0583855	+	0.998294i	$0.518595\pi$
$104$		0			0
$105$	−3.52166	+	2.37245i	−0.343679	+	0.231528i
$106$		0			0
$107$	−3.71051	+	3.71051i	−0.358708	+	0.358708i	−0.863337	−	0.504628i	$-0.831630\pi$
$107$	−3.71051	+	3.71051i	−0.358708	+	0.358708i	0.504628	+	0.863337i	$0.331630\pi$
$108$		0			0
$109$		−	20.3485i		−	1.94903i	−0.224323	−	0.974515i	$-0.572017\pi$
$109$		−	20.3485i		−	1.94903i	0.224323	−	0.974515i	$-0.427983\pi$
$110$		0			0
$111$	−0.674235	+	7.31747i	−0.0639955	+	0.694544i
$112$		0			0
$113$	−3.57117	+	13.3278i	−0.335948	+	1.25377i	0.566890	+	0.823793i	$0.308146\pi$
$113$	−3.57117	+	13.3278i	−0.335948	+	1.25377i	−0.902838	+	0.429981i	$0.858520\pi$
$114$		0			0
$115$	1.81431	+	1.30701i	0.169186	+	0.121879i
$116$		0			0
$117$	−4.47871	+	9.37769i	−0.414057	+	0.866968i
$118$		0			0
$119$	2.43916	−	4.22474i	0.223597	−	0.387282i
$120$		0			0
$121$	14.2980	+	24.7648i	1.29981	+	2.25134i
$122$		0			0
$123$	6.37720	+	2.35449i	0.575012	+	0.212297i
$124$		0			0
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$		0			0
$127$	−14.1237	−	14.1237i	−1.25328	−	1.25328i	−0.954242	−	0.299036i	$-0.903335\pi$
$127$	−14.1237	−	14.1237i	−1.25328	−	1.25328i	−0.299036	−	0.954242i	$-0.596665\pi$
$128$		0			0
$129$	−3.46410	+	4.89898i	−0.304997	+	0.431331i
$130$		0			0
$131$	−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
$133$	−0.439978	−	1.64202i	−0.0381509	−	0.142381i
$134$		0			0
$135$	−1.70502	−	11.4932i	−0.146745	−	0.989174i
$136$		0			0
$137$	−0.569930	−	2.12701i	−0.0486924	−	0.181723i	0.937297	−	0.348533i	$-0.113320\pi$
$137$	−0.569930	−	2.12701i	−0.0486924	−	0.181723i	−0.985989	+	0.166810i	$0.946653\pi$
$138$		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	$0.517578\pi$
$140$		0			0
$141$	−9.00000	+	12.7279i	−0.757937	+	1.07188i
$142$		0			0
$143$	15.4135	+	15.4135i	1.28894	+	1.28894i
$144$		0			0
$145$	4.44949	+	5.44949i	0.369510	+	0.452555i
$146$		0			0
$147$	9.42078	+	3.47820i	0.777013	+	0.286877i
$148$		0			0
$149$	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	$0.508272\pi$
$151$	−10.7980	+	18.7026i	−0.878725	+	1.52200i	−0.852741	+	0.522335i	$0.825061\pi$
$152$		0			0
$153$	7.55513	+	11.0046i	0.610796	+	0.889671i
$154$		0			0
$155$	−9.82050	+	1.59612i	−0.788801	+	0.128203i
$156$		0			0
$157$	1.59165	−	5.94012i	0.127028	−	0.474073i	−0.872876	−	0.487942i	$-0.837748\pi$
$157$	1.59165	−	5.94012i	0.127028	−	0.474073i	0.999904	+	0.0138684i	$0.00441459\pi$
$158$		0			0
$159$	1.48565	−	16.1237i	0.117819	−	1.27869i
$160$		0			0
$161$			1.09638i			0.0864066i
$162$		0			0
$163$	0.449490	−	0.449490i	0.0352068	−	0.0352068i	−0.689284	−	0.724491i	$-0.742075\pi$
$163$	0.449490	−	0.449490i	0.0352068	−	0.0352068i	0.724491	+	0.689284i	$0.242075\pi$
$164$		0			0
$165$	−23.9204	−	4.66390i	−1.86220	−	0.363084i
$166$		0			0
$167$	10.4300	+	2.79472i	0.807100	+	0.216262i	0.638699	−	0.769457i	$-0.279473\pi$
$167$	10.4300	+	2.79472i	0.807100	+	0.216262i	0.168401	+	0.985719i	$0.446140\pi$
$168$		0			0
$169$	−0.866025	−	0.500000i	−0.0666173	−	0.0384615i
$170$		0			0
$171$	4.57321	+	0.849971i	0.349722	+	0.0649989i
$172$		0			0
$173$	2.99536	−	0.802603i	0.227733	−	0.0610208i	−0.143148	−	0.989701i	$-0.545723\pi$
$173$	2.99536	−	0.802603i	0.227733	−	0.0610208i	0.370881	+	0.928680i	$0.379056\pi$
$174$		0			0
$175$	−4.90435	−	2.44917i	−0.370734	−	0.185140i
$176$		0			0
$177$	7.08274	−	19.1838i	0.532371	−	1.44194i
$178$		0			0
$179$	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			0
$183$	−9.30286	+	1.59612i	−0.687687	+	0.117988i
$184$		0			0
$185$	−8.65099	+	3.89363i	−0.636033	+	0.286265i
$186$		0			0
$187$	27.0445	−	7.24656i	1.97769	−	0.529921i
$188$		0			0
$189$	4.08372	−	3.97219i	0.297047	−	0.288935i
$190$		0			0
$191$	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
$193$	−16.7303	−	4.48288i	−1.20428	−	0.322685i	−0.399762	−	0.916619i	$-0.630907\pi$
$193$	−16.7303	−	4.48288i	−1.20428	−	0.322685i	−0.804513	+	0.593934i	$0.797574\pi$
$194$		0			0
$195$	−13.3843	+	0.928203i	−0.958467	+	0.0664700i
$196$		0			0
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	−0.415829	−	0.909443i	$-0.636508\pi$
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	0.909443	+	0.415829i	$0.136508\pi$
$198$		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			0
$201$	5.94949	−	2.74094i	0.419645	−	0.193331i
$202$		0			0
$203$	−0.892794	+	3.33195i	−0.0626618	+	0.233857i
$204$		0			0
$205$	1.40790	+	8.66246i	0.0983322	+	0.605012i
$206$		0			0
$207$	−2.70711	−	1.29289i	−0.188157	−	0.0898623i
$208$		0			0
$209$	4.87832	−	8.44949i	0.337440	−	0.584463i
$210$		0			0
$211$	9.44949	+	16.3670i	0.650530	+	1.12675i	0.982995	+	0.183635i	$0.0587864\pi$
$211$	9.44949	+	16.3670i	0.650530	+	1.12675i	−0.332465	+	0.943116i	$0.607880\pi$
$212$		0			0
$213$	−0.846687	+	0.703823i	−0.0580141	+	0.0482251i
$214$		0			0
$215$	−7.70674	−	0.778539i	−0.525595	−	0.0530959i
$216$		0			0
$217$	−3.44949	−	3.44949i	−0.234167	−	0.234167i
$218$		0			0
$219$	−7.07107	−	0.651531i	−0.477818	−	0.0440264i
$220$		0			0
$221$	13.3485	−	7.70674i	0.897915	−	0.518412i
$222$		0			0
$223$	−2.15087	−	8.02714i	−0.144033	−	0.537537i	−0.999797	−	0.0201706i	$-0.993579\pi$
$223$	−2.15087	−	8.02714i	−0.144033	−	0.537537i	0.855764	−	0.517367i	$-0.173088\pi$
$224$		0			0
$225$	11.8307	−	9.22135i	0.788717	−	0.614757i
$226$		0			0
$227$	3.90843	+	14.5865i	0.259412	+	0.968138i	0.965583	+	0.260096i	$0.0837543\pi$
$227$	3.90843	+	14.5865i	0.259412	+	0.968138i	−0.706171	+	0.708041i	$0.749579\pi$
$228$		0			0
$229$	−14.1582	+	8.17423i	−0.935600	+	0.540169i	−0.888578	−	0.458725i	$-0.848306\pi$
$229$	−14.1582	+	8.17423i	−0.935600	+	0.540169i	−0.0470214	+	0.998894i	$0.514973\pi$
$230$		0			0
$231$	−5.00000	−	10.8530i	−0.328976	−	0.714075i
$232$		0			0
$233$	10.9959	+	10.9959i	0.720363	+	0.720363i	0.968679	−	0.248316i	$-0.0798770\pi$
$233$	10.9959	+	10.9959i	0.720363	+	0.720363i	−0.248316	+	0.968679i	$0.579877\pi$
$234$		0			0
$235$	−20.0227	−	2.02270i	−1.30614	−	0.131947i
$236$		0			0
$237$	0.717439	+	4.18154i	0.0466027	+	0.271620i
$238$		0			0
$239$	−8.48528	−	14.6969i	−0.548867	−	0.950666i	−0.998353	−	0.0573782i	$-0.981726\pi$
$239$	−8.48528	−	14.6969i	−0.548867	−	0.950666i	0.449485	−	0.893288i	$-0.351607\pi$
$240$		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	$0.957053\pi$
$242$		0			0
$243$	4.99221	+	14.7675i	0.320250	+	0.947333i
$244$		0			0
$245$	2.07984	+	12.7967i	0.132876	+	0.817552i
$246$		0			0
$247$	1.39015	−	5.18811i	0.0884531	−	0.330111i
$248$		0			0
$249$	−0.778539	−	0.550510i	−0.0493379	−	0.0348872i
$250$		0			0
$251$		−	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
$254$		0			0
$255$	−7.56325	+	15.4844i	−0.473629	+	0.969671i
$256$		0			0
$257$	−25.1579	−	6.74105i	−1.56931	−	0.420495i	−0.633713	−	0.773568i	$-0.718470\pi$
$257$	−25.1579	−	6.74105i	−1.56931	−	0.420495i	−0.935596	+	0.353073i	$0.885137\pi$
$258$		0			0
$259$	−4.02834	−	2.32577i	−0.250309	−	0.144516i
$260$		0			0
$261$	−7.17423	−	6.13361i	−0.444074	−	0.379661i
$262$		0			0
$263$	−12.2643	+	3.28621i	−0.756249	+	0.202636i	−0.616288	−	0.787521i	$-0.711364\pi$
$263$	−12.2643	+	3.28621i	−0.756249	+	0.202636i	−0.139961	+	0.990157i	$0.544698\pi$
$264$		0			0
$265$	19.0621	−	8.57944i	1.17097	−	0.527031i
$266$		0			0
$267$	2.62156	+	3.15369i	0.160437	+	0.193003i
$268$		0			0
$269$	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	$-0.337966\pi$
$271$	16.0454			0.974689			0.487345	+	0.873210i	$0.337966\pi$
$272$		0			0
$273$	−4.20512	−	5.05870i	−0.254506	−	0.306166i
$274$		0			0
$275$	−9.96399	−	29.8432i	−0.600851	−	1.79961i
$276$		0			0
$277$	13.7983	−	3.69723i	0.829057	−	0.222145i	0.180754	−	0.983528i	$-0.442146\pi$
$277$	13.7983	−	3.69723i	0.829057	−	0.222145i	0.648302	+	0.761383i	$0.275479\pi$
$278$		0			0
$279$	12.5851	−	4.44949i	0.753448	−	0.266384i
$280$		0			0
$281$	−0.151531	−	0.0874863i	−0.00903957	−	0.00521900i	0.495473	−	0.868623i	$-0.334995\pi$
$281$	−0.151531	−	0.0874863i	−0.00903957	−	0.00521900i	−0.504513	+	0.863404i	$0.668328\pi$
$282$		0			0
$283$	6.66112	+	1.78484i	0.395962	+	0.106098i	0.451305	−	0.892370i	$-0.350959\pi$
$283$	6.66112	+	1.78484i	0.395962	+	0.106098i	−0.0553430	+	0.998467i	$0.517625\pi$
$284$		0			0
$285$	1.95181	+	5.67905i	0.115615	+	0.336398i
$286$		0			0
$287$	−3.04272	+	3.04272i	−0.179606	+	0.179606i
$288$		0			0
$289$		−	2.79796i		−	0.164586i
$290$		0			0
$291$	−15.7980	−	11.1708i	−0.926093	−	0.654846i
$292$		0			0
$293$	5.70577	−	21.2942i	0.333335	−	1.24402i	−0.572329	−	0.820024i	$-0.693960\pi$
$293$	5.70577	−	21.2942i	0.333335	−	1.24402i	0.905663	−	0.423998i	$-0.139374\pi$
$294$		0			0
$295$	26.0582	−	4.23523i	1.51717	−	0.246585i
$296$		0			0
$297$	32.6938	+	0.452623i	1.89709	+	0.0262638i
$298$		0			0
$299$	−1.73205	+	3.00000i	−0.100167	+	0.173494i
$300$		0			0
$301$	−1.89898	−	3.28913i	−0.109455	−	0.189582i
$302$		0			0
$303$	−0.372369	−	2.17033i	−0.0213921	−	0.124682i
$304$		0			0
$305$	−7.70674	−	9.43879i	−0.441287	−	0.540464i
$306$		0			0
$307$	−0.674235	−	0.674235i	−0.0384806	−	0.0384806i	0.687605	−	0.726085i	$-0.258662\pi$
$307$	−0.674235	−	0.674235i	−0.0384806	−	0.0384806i	−0.726085	+	0.687605i	$0.758662\pi$
$308$		0			0
$309$	−2.97129	−	6.44949i	−0.169031	−	0.366899i
$310$		0			0
$311$	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
$313$	1.29958	+	4.85009i	0.0734564	+	0.274143i	0.992879	−	0.119128i	$-0.0380100\pi$
$313$	1.29958	+	4.85009i	0.0734564	+	0.274143i	−0.919422	+	0.393271i	$0.871343\pi$
$314$		0			0
$315$	7.05919	+	2.06389i	0.397741	+	0.116287i
$316$		0			0
$317$	0.284965	+	1.06350i	0.0160052	+	0.0597323i	0.973467	−	0.228829i	$-0.0734897\pi$
$317$	0.284965	+	1.06350i	0.0160052	+	0.0597323i	−0.957461	+	0.288561i	$0.906823\pi$
$318$		0			0
$319$	−17.1455	+	9.89898i	−0.959966	+	0.554236i
$320$		0			0
$321$	9.05051	+	0.833917i	0.505150	+	0.0465447i
$322$		0			0
$323$	−4.87832	−	4.87832i	−0.271437	−	0.271437i
$324$		0			0
$325$	−9.55051	−	14.4495i	−0.529767	−	0.801513i
$326$		0			0
$327$	−27.1032	+	22.5300i	−1.49881	+	1.24591i
$328$		0			0
$329$	−4.93369	−	8.54541i	−0.272003	−	0.471124i
$330$		0			0
$331$	−2.22474	+	3.85337i	−0.122283	+	0.211800i	−0.920668	−	0.390347i	$-0.872355\pi$
$331$	−2.22474	+	3.85337i	−0.122283	+	0.211800i	0.798385	+	0.602148i	$0.205688\pi$
$332$		0			0
$333$	10.4930	−	7.20390i	0.575015	−	0.394772i
$334$		0			0
$335$	6.86162	+	4.94302i	0.374890	+	0.270066i
$336$		0			0
$337$	−7.97861	+	29.7766i	−0.434622	+	1.62203i	0.307346	+	0.951598i	$0.400559\pi$
$337$	−7.97861	+	29.7766i	−0.434622	+	1.62203i	−0.741968	+	0.670435i	$0.766108\pi$
$338$		0			0
$339$	21.7060	−	10.0000i	1.17891	−	0.543125i
$340$		0			0
$341$		−	27.9985i		−	1.51621i
$342$		0			0
$343$	−9.92168	+	9.92168i	−0.535721	+	0.535721i
$344$		0			0
$345$	−0.267949	−	3.86370i	−0.0144259	−	0.208015i
$346$		0			0
$347$	4.05886	+	1.08757i	0.217891	+	0.0583837i	0.366113	−	0.930570i	$-0.380688\pi$
$347$	4.05886	+	1.08757i	0.217891	+	0.0583837i	−0.148222	+	0.988954i	$0.547355\pi$
$348$		0			0
$349$	13.0297	+	7.52270i	0.697464	+	0.402681i	0.806402	−	0.591367i	$-0.201412\pi$
$349$	13.0297	+	7.52270i	0.697464	+	0.402681i	−0.108938	+	0.994049i	$0.534745\pi$
$350$		0			0
$351$	17.4495	−	4.41761i	0.931385	−	0.235795i
$352$		0			0
$353$	−33.1244	+	8.87564i	−1.76303	+	0.472403i	−0.987328	−	0.158694i	$-0.949272\pi$
$353$	−33.1244	+	8.87564i	−1.76303	+	0.472403i	−0.775704	+	0.631097i	$0.782605\pi$
$354$		0			0
$355$	−1.32905	−	0.504022i	−0.0705386	−	0.0267507i
$356$		0			0
$357$	−8.32780	+	1.42883i	−0.440754	+	0.0756215i
$358$		0			0
$359$	−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
$362$		0			0
$363$	17.1547	−	46.4639i	0.900388	−	2.43872i
$364$		0			0
$365$	−3.76252	−	8.35968i	−0.196939	−	0.437566i
$366$		0			0
$367$	9.42418	−	2.52520i	0.491938	−	0.131814i	−0.00431778	−	0.999991i	$-0.501374\pi$
$367$	9.42418	−	2.52520i	0.491938	−	0.131814i	0.496256	+	0.868176i	$0.334708\pi$
$368$		0			0
$369$	−3.92480	−	11.1010i	−0.204317	−	0.577896i
$370$		0			0
$371$	8.87628	+	5.12472i	0.460833	+	0.266062i
$372$		0			0
$373$	−19.6004	−	5.25190i	−1.01487	−	0.271933i	−0.287206	−	0.957869i	$-0.592727\pi$
$373$	−19.6004	−	5.25190i	−1.01487	−	0.271933i	−0.727662	+	0.685935i	$0.759393\pi$
$374$		0			0
$375$	17.8818	+	7.43243i	0.923412	+	0.383809i
$376$		0			0
$377$	−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	$0.945354\pi$
$380$		0			0
$381$	−3.17423	+	34.4500i	−0.162621	+	1.76493i
$382$		0			0
$383$	−7.19464	+	26.8508i	−0.367629	+	1.37201i	0.496193	+	0.868212i	$0.334731\pi$
$383$	−7.19464	+	26.8508i	−0.367629	+	1.37201i	−0.863822	+	0.503798i	$0.831936\pi$
$384$		0			0
$385$	9.01702	−	12.5169i	0.459550	−	0.637921i
$386$		0			0
$387$	10.3607	−	0.810167i	0.526663	−	0.0411831i
$388$		0			0
$389$	−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
$392$		0			0
$393$	17.1180	+	6.32005i	0.863489	+	0.318804i
$394$		0			0
$395$	−4.24264	+	3.46410i	−0.213470	+	0.174298i
$396$		0			0
$397$	15.4495	+	15.4495i	0.775388	+	0.775388i	0.979043	−	0.203655i	$-0.0652821\pi$
$397$	15.4495	+	15.4495i	0.775388	+	0.775388i	−0.203655	+	0.979043i	$0.565282\pi$
$398$		0			0
$399$	−1.69994	+	2.40408i	−0.0851036	+	0.120355i
$400$		0			0
$401$	22.3485	−	12.9029i	1.11603	−	0.644340i	0.175645	−	0.984454i	$-0.443799\pi$
$401$	22.3485	−	12.9029i	1.11603	−	0.644340i	0.940384	+	0.340114i	$0.110466\pi$
$402$		0			0
$403$	−3.98930	−	14.8883i	−0.198721	−	0.741638i
$404$		0			0
$405$	−13.4205	+	14.9963i	−0.666871	+	0.745173i
$406$		0			0
$407$	−6.90968	−	25.7873i	−0.342500	−	1.27823i
$408$		0			0
$409$	−16.5420	+	9.55051i	−0.817948	+	0.472242i	−0.849708	−	0.527253i	$-0.823222\pi$
$409$	−16.5420	+	9.55051i	−0.817948	+	0.472242i	0.0317605	+	0.999496i	$0.489889\pi$
$410$		0			0
$411$	−2.20204	+	3.11416i	−0.108619	+	0.153610i
$412$		0			0
$413$	9.15306	+	9.15306i	0.450393	+	0.450393i
$414$		0			0
$415$	0.123724	−	1.22474i	0.00607339	−	0.0601204i
$416$		0			0
$417$	20.9588	+	7.73810i	1.02636	+	0.378937i
$418$		0			0
$419$	5.97469	+	10.3485i	0.291883	+	0.505556i	0.974255	−	0.225449i	$-0.0723850\pi$
$419$	5.97469	+	10.3485i	0.291883	+	0.505556i	−0.682372	+	0.731005i	$0.739052\pi$
$420$		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	$0.0483966\pi$
$422$		0			0
$423$	26.9178	−	2.10488i	1.30879	−	0.102343i
$424$		0			0
$425$	−22.2068	+	1.34385i	−1.07719	+	0.0651863i
$426$		0			0
$427$	1.54636	−	5.77111i	0.0748338	−	0.279284i
$428$		0			0
$429$	3.46410	−	37.5959i	0.167248	−	1.81515i
$430$		0			0
$431$		−	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	−0.471145	−	0.882056i	$-0.656159\pi$
$433$	8.55051	−	8.55051i	0.410911	−	0.410911i	0.882056	+	0.471145i	$0.156159\pi$
$434$		0			0
$435$	2.33195	−	11.9602i	0.111809	−	0.573448i
$436$		0			0
$437$	1.49768	+	0.401302i	0.0716436	+	0.0191969i
$438$		0			0
$439$	8.83523	+	5.10102i	0.421682	+	0.243458i	0.695797	−	0.718239i	$-0.255051\pi$
$439$	8.83523	+	5.10102i	0.421682	+	0.243458i	−0.274114	+	0.961697i	$0.588385\pi$
$440$		0			0
$441$	−5.79796	−	16.3991i	−0.276093	−	0.780910i
$442$		0			0
$443$	−0.531752	+	0.142483i	−0.0252643	+	0.00676955i	−0.271429	−	0.962458i	$-0.587496\pi$
$443$	−0.531752	+	0.142483i	−0.0252643	+	0.00676955i	0.246165	+	0.969228i	$0.420830\pi$
$444$		0			0
$445$	−1.87735	+	4.95037i	−0.0889951	+	0.234670i
$446$		0			0
$447$	7.74045	−	20.9652i	0.366111	−	0.991620i
$448$		0			0
$449$	−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
$452$		0			0
$453$	36.8665	−	6.32530i	1.73214	−	0.297188i
$454$		0			0
$455$	3.01138	−	7.94066i	0.141175	−	0.372264i
$456$		0			0
$457$	−5.94012	+	1.59165i	−0.277867	+	0.0744543i	−0.395061	−	0.918655i	$-0.629277\pi$
$457$	−5.94012	+	1.59165i	−0.277867	+	0.0744543i	0.117194	+	0.993109i	$0.462610\pi$
$458$		0			0
$459$	6.29253	−	22.2474i	0.293710	−	1.03842i
$460$		0			0
$461$	16.3763	+	9.45485i	0.762719	+	0.440356i	0.830271	−	0.557360i	$-0.188186\pi$
$461$	16.3763	+	9.45485i	0.762719	+	0.440356i	−0.0675520	+	0.997716i	$0.521519\pi$
$462$		0			0
$463$	−31.8946	−	8.54613i	−1.48227	−	0.397172i	−0.575150	−	0.818048i	$-0.695056\pi$
$463$	−31.8946	−	8.54613i	−1.48227	−	0.397172i	−0.907118	+	0.420876i	$0.861723\pi$
$464$		0			0
$465$	12.9993	+	11.3132i	0.602827	+	0.524637i
$466$		0			0
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	−0.638630	−	0.769514i	$-0.720499\pi$
$467$	2.82843	−	2.82843i	0.130884	−	0.130884i	0.769514	+	0.638630i	$0.220499\pi$
$468$		0			0
$469$			4.14643i			0.191464i
$470$		0			0
$471$	−9.67423	+	4.45694i	−0.445765	+	0.205365i
$472$		0			0
$473$	5.64173	−	21.0552i	0.259407	−	0.968120i
$474$		0			0
$475$	−5.14074	+	5.80300i	−0.235873	+	0.266260i
$476$		0			0
$477$	−23.1209	+	15.8735i	−1.05863	+	0.726797i
$478$		0			0
$479$	−3.53553	+	6.12372i	−0.161543	+	0.279800i	−0.935422	−	0.353533i	$-0.884980\pi$
$479$	−3.53553	+	6.12372i	−0.161543	+	0.279800i	0.773879	+	0.633333i	$0.218314\pi$
$480$		0			0
$481$	−7.34847	−	12.7279i	−0.335061	−	0.580343i
$482$		0			0
$483$	1.46032	−	1.21391i	0.0664469	−	0.0552350i
$484$		0			0
$485$	2.51059	−	24.8523i	0.114000	−	1.12848i
$486$		0			0
$487$	12.0000	+	12.0000i	0.543772	+	0.543772i	0.924632	−	0.380861i	$-0.124372\pi$
$487$	12.0000	+	12.0000i	0.543772	+	0.543772i	−0.380861	+	0.924632i	$0.624372\pi$
$488$		0			0
$489$	−1.09638	−	0.101021i	−0.0495799	−	0.00456831i
$490$		0			0
$491$	−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
$493$	3.62328	+	13.5223i	0.163184	+	0.609012i
$494$		0			0
$495$	20.2728	+	37.0247i	0.911193	+	1.66414i
$496$		0			0
$497$	−0.180381	−	0.673191i	−0.00809119	−	0.0301967i
$498$		0			0
$499$	7.70674	−	4.44949i	0.345001	−	0.199187i	−0.317480	−	0.948265i	$-0.602837\pi$
$499$	7.70674	−	4.44949i	0.345001	−	0.199187i	0.662481	+	0.749078i	$0.269503\pi$
$500$		0			0
$501$	−7.82577	−	16.9866i	−0.349629	−	0.758906i
$502$		0			0
$503$	−16.7563	−	16.7563i	−0.747125	−	0.747125i	0.226813	−	0.973938i	$-0.427169\pi$
$503$	−16.7563	−	16.7563i	−0.747125	−	0.747125i	−0.973938	+	0.226813i	$0.927169\pi$
$504$		0			0
$505$	2.20204	−	1.79796i	0.0979895	−	0.0800081i
$506$		0			0
$507$	0.292893	+	1.70711i	0.0130078	+	0.0758153i
$508$		0			0
$509$	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			0
$513$	−3.93137	−	7.03239i	−0.173574	−	0.310488i
$514$		0			0
$515$	5.35844	−	7.43828i	0.236121	−	0.327770i
$516$		0			0
$517$	14.6576	−	54.7030i	0.644642	−	2.40584i
$518$		0			0
$519$	−4.38551	−	3.10102i	−0.192502	−	0.136120i
$520$		0			0
$521$			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	$-0.767481\pi$
$523$	−1.77526	+	1.77526i	−0.0776265	+	0.0776265i	0.667228	+	0.744854i	$0.267481\pi$
$524$		0			0
$525$	2.16795	+	9.24408i	0.0946171	+	0.403445i
$526$		0			0
$527$	−19.1234	−	5.12409i	−0.833027	−	0.223209i
$528$		0			0
$529$	19.0526	+	11.0000i	0.828372	+	0.478261i
$530$		0			0
$531$	−33.3939	+	11.8065i	−1.44917	+	0.512359i
$532$		0			0
$533$	−13.1326	+	3.51888i	−0.568838	+	0.152420i
$534$		0			0
$535$	4.81578	+	10.6999i	0.208204	+	0.462595i
$536$		0			0
$537$	−19.4937	−	23.4506i	−0.841217	−	1.01197i
$538$		0			0
$539$	−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	$0.688323\pi$
$542$		0			0
$543$	11.6816	+	14.0528i	0.501305	+	0.603062i
$544$		0			0
$545$	−42.5440	−	16.1342i	−1.82238	−	0.691112i
$546$		0			0
$547$	−20.6594	+	5.53567i	−0.883332	+	0.236688i	−0.671844	−	0.740693i	$-0.734498\pi$
$547$	−20.6594	+	5.53567i	−0.883332	+	0.236688i	−0.211488	+	0.977381i	$0.567831\pi$
$548$		0			0
$549$	12.4261	+	10.6237i	0.530335	+	0.453410i
$550$		0			0
$551$	4.22474	+	2.43916i	0.179980	+	0.103912i
$552$		0			0
$553$	−2.59405	−	0.695075i	−0.110310	−	0.0295576i
$554$		0			0
$555$	14.7646	+	7.21164i	0.626721	+	0.306117i
$556$		0			0
$557$	−16.3670	+	16.3670i	−0.693492	+	0.693492i	−0.962999	−	0.269507i	$-0.913139\pi$
$557$	−16.3670	+	16.3670i	−0.693492	+	0.693492i	0.269507	+	0.962999i	$0.413139\pi$
$558$		0			0
$559$		−	12.0000i		−	0.507546i
$560$		0			0
$561$	−39.5959	−	27.9985i	−1.67174	−	1.18210i
$562$		0			0
$563$	8.89004	−	33.1781i	0.374670	−	1.39829i	−0.479155	−	0.877730i	$-0.659057\pi$
$563$	8.89004	−	33.1781i	0.374670	−	1.39829i	0.853826	−	0.520559i	$-0.174276\pi$
$564$		0			0
$565$	25.0338	+	18.0340i	1.05318	+	0.758697i
$566$		0			0
$567$	−9.81229	−	1.04128i	−0.412077	−	0.0437297i
$568$		0			0
$569$	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	$0.0252569\pi$
$571$	13.5505	+	23.4702i	0.567071	+	0.982196i	−0.429782	+	0.902932i	$0.641410\pi$
$572$		0			0
$573$	−0.972768	−	5.66971i	−0.0406380	−	0.236855i
$574$		0			0
$575$	4.17121	−	2.75699i	0.173951	−	0.114975i
$576$		0			0
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$		0			0
$579$	12.5529	+	27.2474i	0.521683	+	1.13237i
$580$		0			0
$581$	0.522704	−	0.301783i	0.0216854	−	0.0125201i
$582$		0			0
$583$	15.2252	+	56.8211i	0.630562	+	2.35329i
$584$		0			0
$585$	16.0555	+	16.7995i	0.663812	+	0.694573i
$586$		0			0
$587$	−8.03514	−	29.9876i	−0.331646	−	1.23772i	−0.907460	−	0.420138i	$-0.861981\pi$
$587$	−8.03514	−	29.9876i	−0.331646	−	1.23772i	0.575814	−	0.817581i	$-0.304685\pi$
$588$		0			0
$589$	−5.97469	+	3.44949i	−0.246183	+	0.142134i
$590$		0			0
$591$	−16.8990	−	1.55708i	−0.695131	−	0.0640496i
$592$		0			0
$593$	−10.0745	−	10.0745i	−0.413709	−	0.413709i	0.469320	−	0.883028i	$-0.344499\pi$
$593$	−10.0745	−	10.0745i	−0.413709	−	0.413709i	−0.883028	+	0.469320i	$0.844499\pi$
$594$		0			0
$595$	−6.89898	−	8.44949i	−0.282831	−	0.346395i
$596$		0			0
$597$	−4.72911	+	3.93115i	−0.193549	+	0.160891i
$598$		0			0
$599$	16.8991	+	29.2702i	0.690480	+	1.19595i	0.971681	+	0.236297i	$0.0759339\pi$
$599$	16.8991	+	29.2702i	0.690480	+	1.19595i	−0.281201	+	0.959649i	$0.590733\pi$
$600$		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	$0.916418\pi$
$602$		0			0
$603$	−10.2381	−	4.88964i	−0.416928	−	0.199122i
$604$		0			0
$605$	63.1142	−	10.2579i	2.56596	−	0.417043i
$606$		0			0
$607$	−5.73717	+	21.4114i	−0.232864	+	0.869062i	0.746235	+	0.665682i	$0.231859\pi$
$607$	−5.73717	+	21.4114i	−0.232864	+	0.869062i	−0.979100	+	0.203380i	$0.934807\pi$
$608$		0			0
$609$	5.42650	−	2.50000i	0.219893	−	0.101305i
$610$		0			0
$611$		−	31.1769i		−	1.26128i
$612$		0			0
$613$	−12.7980	+	12.7980i	−0.516905	+	0.516905i	−0.916633	−	0.399729i	$-0.869104\pi$
$613$	−12.7980	+	12.7980i	−0.516905	+	0.516905i	0.399729	+	0.916633i	$0.369104\pi$
$614$		0			0
$615$	9.97914	−	11.4664i	0.402398	−	0.462369i
$616$		0			0
$617$	6.85906	+	1.83788i	0.276135	+	0.0739902i	0.394229	−	0.919012i	$-0.371012\pi$
$617$	6.85906	+	1.83788i	0.276135	+	0.0739902i	−0.118094	+	0.993002i	$0.537678\pi$
$618$		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	$0.501014\pi$
$620$		0			0
$621$	1.27526	+	5.03723i	0.0511742	+	0.202137i
$622$		0			0
$623$	−2.50746	+	0.671873i	−0.100459	+	0.0269180i
$624$		0			0
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$		0			0
$627$	−16.6556	+	2.85765i	−0.665161	+	0.114124i
$628$		0			0
$629$	−18.8776			−0.752699
$630$		0			0
$631$	12.8990			0.513500			0.256750	−	0.966478i	$-0.417348\pi$
$631$	12.8990			0.513500			0.256750	+	0.966478i	$0.417348\pi$
$632$		0			0
$633$	11.3375	−	30.7079i	0.450625	−	1.22053i
$634$		0			0
$635$	−40.7281	+	18.3309i	−1.61624	+	0.727438i
$636$		0			0
$637$	−19.4003	+	5.19831i	−0.768670	+	0.205964i
$638$		0			0
$639$	1.87492	+	0.348469i	0.0741705	+	0.0137852i
$640$		0			0
$641$	−7.74745	−	4.47299i	−0.306006	−	0.176673i	0.339132	−	0.940739i	$-0.389867\pi$
$641$	−7.74745	−	4.47299i	−0.306006	−	0.176673i	−0.645138	+	0.764066i	$0.723200\pi$
$642$		0			0
$643$	−30.6976	−	8.22539i	−1.21059	−	0.324378i	−0.403599	−	0.914936i	$-0.632241\pi$
$643$	−30.6976	−	8.22539i	−1.21059	−	0.324378i	−0.806995	+	0.590558i	$0.798908\pi$
$644$		0			0
$645$	7.49598	+	11.1270i	0.295154	+	0.438126i
$646$		0			0
$647$	−24.9558	+	24.9558i	−0.981114	+	0.981114i	−0.999825	−	0.0187105i	$-0.994044\pi$
$647$	−24.9558	+	24.9558i	−0.981114	+	0.981114i	0.0187105	+	0.999825i	$0.494044\pi$
$648$		0			0
$649$			74.2929i			2.91625i
$650$		0			0
$651$	−0.775255	+	8.41385i	−0.0303846	+	0.329765i
$652$		0			0
$653$	−5.57768	+	20.8162i	−0.218272	+	0.814601i	0.766718	+	0.641985i	$0.221889\pi$
$653$	−5.57768	+	20.8162i	−0.218272	+	0.814601i	−0.984989	+	0.172616i	$0.944778\pi$
$654$		0			0
$655$	3.77917	+	23.2522i	0.147664	+	0.908540i
$656$		0			0
$657$	6.96132	+	10.1397i	0.271587	+	0.395587i
$658$		0			0
$659$	5.65685	−	9.79796i	0.220360	−	0.381674i	−0.734557	−	0.678546i	$-0.762610\pi$
$659$	5.65685	−	9.79796i	0.220360	−	0.381674i	0.954917	+	0.296872i	$0.0959435\pi$
$660$		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	$0.629698\pi$
$662$		0			0
$663$	−25.0445	−	9.24656i	−0.972648	−	0.359106i
$664$		0			0
$665$	−3.78194	−	0.382053i	−0.146657	−	0.0148154i
$666$		0			0
$667$	−2.22474	−	2.22474i	−0.0861425	−	0.0861425i
$668$		0			0
$669$	−8.31031	+	11.7526i	−0.321295	+	0.454380i
$670$		0			0
$671$	29.6969	−	17.1455i	1.14644	−	0.661896i
$672$		0			0
$673$	−4.22778	−	15.7783i	−0.162969	−	0.608208i	−0.998291	−	0.0584468i	$-0.981385\pi$
$673$	−4.22778	−	15.7783i	−0.162969	−	0.608208i	0.835322	−	0.549762i	$-0.185281\pi$
$674$		0			0
$675$	−25.3815	−	5.54804i	−0.976933	−	0.213544i
$676$		0			0
$677$	1.65750	+	6.18587i	0.0637028	+	0.237742i	0.990435	−	0.137981i	$-0.0440612\pi$
$677$	1.65750	+	6.18587i	0.0637028	+	0.237742i	−0.926732	+	0.375723i	$0.877394\pi$
$678$		0			0
$679$	10.6066	−	6.12372i	0.407044	−	0.235007i
$680$		0			0
$681$	15.1010	−	21.3561i	0.578672	−	0.818366i
$682$		0			0
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	0.920632	−	0.390431i	$-0.127674\pi$
$683$	13.8564	+	13.8564i	0.530201	+	0.530201i	−0.390431	+	0.920632i	$0.627674\pi$
$684$		0			0
$685$	−4.89898	−	0.494897i	−0.187180	−	0.0189091i
$686$		0			0
$687$	26.5637	+	9.80745i	1.01347	+	0.374178i
$688$		0			0
$689$	16.1920	+	28.0454i	0.616867	+	1.06844i
$690$		0			0
$691$	16.4722	−	28.5307i	0.626632	−	1.08536i	−0.361591	−	0.932337i	$-0.617766\pi$
$691$	16.4722	−	28.5307i	0.626632	−	1.08536i	0.988223	−	0.153021i	$-0.0489003\pi$
$692$		0			0
$693$	−8.91964	+	18.6763i	−0.338829	+	0.709453i
$694$		0			0
$695$	4.62712	+	28.4694i	0.175516	+	1.07991i
$696$		0			0
$697$	−4.51985	+	16.8683i	−0.171202	+	0.638933i
$698$		0			0
$699$	2.47127	−	26.8207i	0.0934719	−	1.01445i
$700$		0			0
$701$		−	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
$704$		0			0
$705$	19.4751	+	28.9088i	0.733476	+	1.08877i
$706$		0			0
$707$	1.34638	+	0.360762i	0.0506359	+	0.0135678i
$708$		0			0
$709$	−38.4069	−	22.1742i	−1.44240	−	0.832771i	−0.444392	−	0.895833i	$-0.646580\pi$
$709$	−38.4069	−	22.1742i	−1.44240	−	0.832771i	−0.998010	+	0.0630617i	$0.979914\pi$
$710$		0			0
$711$	4.77526	−	5.58542i	0.179086	−	0.209470i
$712$		0			0
$713$	4.29788	−	1.15161i	0.160957	−	0.0431282i
$714$		0			0
$715$	44.4473	−	20.0048i	1.66223	−	0.748137i
$716$		0			0
$717$	−10.1806	+	27.5745i	−0.380203	+	1.02979i
$718$		0			0
$719$	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
$722$		0			0
$723$	32.4350	−	5.56497i	1.20627	−	0.206964i
$724$		0			0
$725$	14.9216	−	4.98200i	0.554174	−	0.185027i
$726$		0			0
$727$	−30.2836	+	8.11447i	−1.12316	+	0.300949i	−0.772160	−	0.635428i	$-0.780824\pi$
$727$	−30.2836	+	8.11447i	−1.12316	+	0.300949i	−0.350996	+	0.936377i	$0.614157\pi$
$728$		0			0
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$		0			0
$731$	−13.3485	−	7.70674i	−0.493711	−	0.285044i
$732$		0			0
$733$	13.8603	+	3.71385i	0.511941	+	0.137174i	0.505536	−	0.862805i	$-0.331295\pi$
$733$	13.8603	+	3.71385i	0.511941	+	0.137174i	0.00640470	+	0.999979i	$0.497961\pi$
$734$		0			0
$735$	14.7418	−	16.9389i	0.543759	−	0.624799i
$736$		0			0
$737$	−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	$0.848280\pi$
$740$		0			0
$741$	−8.44949	+	3.89270i	−0.310400	+	0.143002i
$742$		0			0
$743$	−0.0261460	+	0.0975783i	−0.000959205	+	0.00357980i	−0.966404	−	0.257029i	$-0.917257\pi$
$743$	−0.0261460	+	0.0975783i	−0.000959205	+	0.00357980i	0.965445	+	0.260609i	$0.0839232\pi$
$744$		0			0
$745$	28.4781	−	4.62852i	1.04336	−	0.169576i
$746$		0			0
$747$	0.128751	+	1.64650i	0.00471074	+	0.0602425i
$748$		0			0
$749$	−2.87659	+	4.98240i	−0.105108	+	0.182053i
$750$		0			0
$751$	−4.34847	−	7.53177i	−0.158678	−	0.274838i	0.775714	−	0.631084i	$-0.217390\pi$
$751$	−4.34847	−	7.53177i	−0.158678	−	0.274838i	−0.934392	+	0.356246i	$0.884056\pi$
$752$		0			0
$753$	−14.8790	+	12.3684i	−0.542222	+	0.450731i
$754$		0			0
$755$	30.5412	+	37.4052i	1.11151	+	1.36132i
$756$		0			0
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	0.182038	−	0.983292i	$-0.441731\pi$
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	−0.983292	+	0.182038i	$0.941731\pi$
$758$		0			0
$759$	10.8530	+	1.00000i	0.393939	+	0.0362977i
$760$		0			0
$761$	−15.3990	+	8.89060i	−0.558213	+	0.322284i	−0.752428	−	0.658675i	$-0.771117\pi$
$761$	−15.3990	+	8.89060i	−0.558213	+	0.322284i	0.194215	+	0.980959i	$0.437784\pi$
$762$		0			0
$763$	−5.77414	−	21.5494i	−0.209038	−	0.780141i
$764$		0			0
$765$	28.9985	−	7.07055i	1.04844	−	0.255636i
$766$		0			0
$767$	10.5854	+	39.5054i	0.382218	+	1.42646i
$768$		0			0
$769$	17.0580	−	9.84847i	0.615129	−	0.355145i	−0.159841	−	0.987143i	$-0.551098\pi$
$769$	17.0580	−	9.84847i	0.615129	−	0.355145i	0.774970	+	0.631998i	$0.217765\pi$
$770$		0			0
$771$	18.8763	+	40.9729i	0.679812	+	1.47560i
$772$		0			0
$773$	−3.11416	−	3.11416i	−0.112008	−	0.112008i	0.648881	−	0.760890i	$-0.275237\pi$
$773$	−3.11416	−	3.11416i	−0.112008	−	0.112008i	−0.760890	+	0.648881i	$0.775237\pi$
$774$		0			0
$775$	−4.44949	+	21.7980i	−0.159830	+	0.783006i
$776$		0			0
$777$	1.36240	+	7.94066i	0.0488759	+	0.284870i
$778$		0			0
$779$	3.04272	+	5.27015i	0.109017	+	0.188823i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$	−0.226311	+	16.3469i	−0.00808771	+	0.584191i
$784$		0			0
$785$	−11.1574	−	8.03766i	−0.398225	−	0.286876i
$786$		0			0
$787$	−1.06110	+	3.96008i	−0.0378241	+	0.141162i	−0.982256	−	0.187546i	$-0.939947\pi$
$787$	−1.06110	+	3.96008i	−0.0378241	+	0.141162i	0.944432	+	0.328708i	$0.106613\pi$
$788$		0			0
$789$	17.9562	+	12.6969i	0.639257	+	0.452023i
$790$		0			0
$791$			15.1278i			0.537881i
$792$		0			0
$793$	13.3485	−	13.3485i	0.474018	−	0.474018i
$794$		0			0
$795$	−32.5330	−	15.8905i	−1.15383	−	0.563579i
$796$		0			0
$797$	−19.5137	−	5.22867i	−0.691210	−	0.185209i	−0.103920	−	0.994586i	$-0.533139\pi$
$797$	−19.5137	−	5.22867i	−0.691210	−	0.185209i	−0.587290	+	0.809377i	$0.699805\pi$
$798$		0			0
$799$	−34.6803	−	20.0227i	−1.22690	−	0.708352i
$800$		0			0
$801$	1.29796	−	6.98358i	0.0458611	−	0.246753i
$802$		0			0
$803$	24.9189	−	6.67700i	0.879369	−	0.235626i
$804$		0			0
$805$	2.29227	+	0.869309i	0.0807919	+	0.0306391i
$806$		0			0
$807$	−5.20757	−	6.26462i	−0.183315	−	0.220525i
$808$		0			0
$809$	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	$-0.777868\pi$
$811$	−43.6413			−1.53245			−0.766227	+	0.642570i	$0.777868\pi$
$812$		0			0
$813$	−17.7656	−	21.3717i	−0.623066	−	0.749538i
$814$		0			0
$815$	−0.583382	−	1.29618i	−0.0204350	−	0.0454031i
$816$		0			0
$817$	−5.18811	+	1.39015i	−0.181509	+	0.0486352i
$818$		0			0
$819$	−2.08200	+	11.2020i	−0.0727508	+	0.391431i
$820$		0			0
$821$	−22.3207	−	12.8868i	−0.778997	−	0.449754i	0.0570780	−	0.998370i	$-0.481822\pi$
$821$	−22.3207	−	12.8868i	−0.778997	−	0.449754i	−0.836075	+	0.548616i	$0.815155\pi$
$822$		0			0
$823$	−46.9519	−	12.5807i	−1.63664	−	0.438536i	−0.680811	−	0.732459i	$-0.738373\pi$
$823$	−46.9519	−	12.5807i	−1.63664	−	0.438536i	−0.955829	+	0.293923i	$0.905039\pi$
$824$		0			0
$825$	−28.7175	+	46.3141i	−0.999815	+	1.61245i
$826$		0			0
$827$	−27.3235	+	27.3235i	−0.950133	+	0.950133i	−0.998814	−	0.0486816i	$-0.984498\pi$
$827$	−27.3235	+	27.3235i	−0.950133	+	0.950133i	0.0486816	+	0.998814i	$0.484498\pi$
$828$		0			0
$829$		−	15.4495i		−	0.536583i	−0.963338	−	0.268291i	$-0.913541\pi$
$829$		−	15.4495i		−	0.536583i	0.963338	−	0.268291i	$-0.0864590\pi$
$830$		0			0
$831$	−20.2020	−	14.2850i	−0.700801	−	0.495541i
$832$		0			0
$833$	−6.67700	+	24.9189i	−0.231344	+	0.863389i
$834$		0			0
$835$	14.1130	−	19.5909i	0.488401	−	0.677970i
$836$		0			0
$837$	−19.8608	−	11.8362i	−0.686488	−	0.409118i
$838$		0			0
$839$	−10.1459	+	17.5732i	−0.350275	+	0.606695i	−0.986298	−	0.164976i	$-0.947245\pi$
$839$	−10.1459	+	17.5732i	−0.350275	+	0.606695i	0.636022	+	0.771671i	$0.280579\pi$
$840$		0			0
$841$	9.55051	+	16.5420i	0.329328	+	0.570413i
$842$		0			0
$843$	0.0512483	+	0.298697i	0.00176509	+	0.0102877i
$844$		0			0
$845$	−1.73205	+	1.41421i	−0.0595844	+	0.0486504i
$846$		0			0
$847$	22.1691	+	22.1691i	0.761740	+	0.761740i
$848$		0			0
$849$	−4.99791	−	10.8485i	−0.171528	−	0.372319i
$850$		0			0
$851$	3.67423	−	2.12132i	0.125951	−	0.0727179i
$852$		0			0
$853$	−9.60723	−	35.8547i	−0.328945	−	1.22764i	−0.910286	−	0.413980i	$-0.864138\pi$
$853$	−9.60723	−	35.8547i	−0.328945	−	1.22764i	0.581340	−	0.813660i	$-0.302528\pi$
$854$		0			0
$855$	5.40317	−	8.88760i	0.184784	−	0.303950i
$856$		0			0
$857$	0.982984	+	3.66855i	0.0335781	+	0.125315i	0.980680	−	0.195616i	$-0.0626707\pi$
$857$	0.982984	+	3.66855i	0.0335781	+	0.125315i	−0.947102	+	0.320932i	$0.896004\pi$
$858$		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	$0.346885\pi$
$860$		0			0
$861$	7.42168	+	0.683837i	0.252930	+	0.0233051i
$862$		0			0
$863$	27.7842	+	27.7842i	0.945787	+	0.945787i	0.998604	−	0.0528175i	$-0.0168202\pi$
$863$	27.7842	+	27.7842i	0.945787	+	0.945787i	−0.0528175	+	0.998604i	$0.516820\pi$
$864$		0			0
$865$	0.696938	−	6.89898i	0.0236966	−	0.234572i
$866$		0			0
$867$	−3.72674	+	3.09792i	−0.126567	+	0.105211i
$868$		0			0
$869$	−7.70674	−	13.3485i	−0.261433	−	0.452816i
$870$		0			0
$871$	−6.55051	+	11.3458i	−0.221956	+	0.384438i
$872$		0			0
$873$	2.61258	+	33.4105i	0.0884225	+	1.13078i
$874$		0			0
$875$	−9.00927	+	8.31193i	−0.304569	+	0.280995i
$876$		0			0
$877$	2.10558	−	7.85813i	0.0711004	−	0.265350i	−0.921220	−	0.389041i	$-0.872806\pi$
$877$	2.10558	−	7.85813i	0.0711004	−	0.265350i	0.992321	+	0.123691i	$0.0394731\pi$
$878$		0			0
$879$	−34.6803	+	15.9773i	−1.16974	+	0.538901i
$880$		0			0
$881$		−	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	0.475463	−	0.879736i	$-0.342281\pi$
$883$	40.2702	−	40.2702i	1.35520	−	1.35520i	0.879736	−	0.475463i	$-0.157719\pi$
$884$		0			0
$885$	−34.4930	−	30.0190i	−1.15947	−	1.00908i
$886$		0			0
$887$	−26.8508	−	7.19464i	−0.901561	−	0.241572i	−0.221874	−	0.975075i	$-0.571217\pi$
$887$	−26.8508	−	7.19464i	−0.901561	−	0.241572i	−0.679686	+	0.733503i	$0.737884\pi$
$888$		0			0
$889$	−18.9651	−	10.9495i	−0.636068	−	0.367234i
$890$		0			0
$891$	−35.5959	−	44.0477i	−1.19251	−	1.47565i
$892$		0			0
$893$	−13.4791	+	3.61171i	−0.451061	+	0.120861i
$894$		0			0
$895$	13.9599	−	36.8106i	0.466627	−	1.23044i
$896$		0			0
$897$	5.91359	−	1.01461i	0.197449	−	0.0338769i
$898$		0			0
$899$	13.9993			0.466902
$900$		0			0
$901$	41.5959			1.38576
$902$		0			0
$903$	−2.27840	+	6.17109i	−0.0758203	+	0.205361i
$904$		0			0
$905$	−8.36543	+	22.0587i	−0.278076	+	0.733256i
$906$		0			0
$907$	6.38512	−	1.71089i	0.212015	−	0.0568091i	−0.151248	−	0.988496i	$-0.548329\pi$
$907$	6.38512	−	1.71089i	0.212015	−	0.0568091i	0.363263	+	0.931687i	$0.381663\pi$
$908$		0			0
$909$	−2.47848	+	2.89898i	−0.0822061	+	0.0961531i
$910$		0			0
$911$	−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
$913$	3.34607	+	0.896575i	0.110739	+	0.0296723i
$914$		0			0
$915$	−4.03906	+	20.7157i	−0.133527	+	0.684840i
$916$		0			0
$917$	−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			0
$921$	−0.151531	+	1.64456i	−0.00499311	+	0.0541902i
$922$		0			0
$923$	0.569930	−	2.12701i	0.0187595	−	0.0700113i
$924$		0			0
$925$	1.28138	+	21.1745i	0.0421314	+	0.696212i
$926$		0			0
$927$	−5.30057	+	11.0985i	−0.174094	+	0.364524i
$928$		0			0
$929$	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
$932$		0			0
$933$	−33.4353	−	12.3445i	−1.09462	−	0.404140i
$934$		0			0
$935$	6.29253	−	62.2896i	0.205788	−	2.03709i
$936$		0			0
$937$	−12.8990	−	12.8990i	−0.421391	−	0.421391i	0.464291	−	0.885683i	$-0.346309\pi$
$937$	−12.8990	−	12.8990i	−0.421391	−	0.421391i	−0.885683	+	0.464291i	$0.846309\pi$
$938$		0			0
$939$	5.02118	−	7.10102i	0.163860	−	0.231733i
$940$		0			0
$941$	5.47730	−	3.16232i	0.178555	−	0.103089i	−0.408059	−	0.912956i	$-0.633794\pi$
$941$	5.47730	−	3.16232i	0.178555	−	0.103089i	0.586613	+	0.809867i	$0.300461\pi$
$942$		0			0
$943$	−1.01581	−	3.79107i	−0.0330795	−	0.123454i
$944$		0			0
$945$	−5.06699	−	11.6877i	−0.164829	−	0.380199i
$946$		0			0
$947$	−10.6233	−	39.6468i	−0.345212	−	1.28835i	−0.892364	−	0.451316i	$-0.850955\pi$
$947$	−10.6233	−	39.6468i	−0.345212	−	1.28835i	0.547152	−	0.837033i	$-0.315712\pi$
$948$		0			0
$949$	12.2993	−	7.10102i	0.399253	−	0.230509i
$950$		0			0
$951$	1.10102	−	1.55708i	0.0357030	−	0.0504917i
$952$		0			0
$953$	19.6561	+	19.6561i	0.636724	+	0.636724i	0.949746	−	0.313022i	$-0.101341\pi$
$953$	19.6561	+	19.6561i	0.636724	+	0.636724i	−0.313022	+	0.949746i	$0.601341\pi$
$954$		0			0
$955$	5.75255	−	4.69694i	0.186148	−	0.151989i
$956$		0			0
$957$	32.1686	+	11.8768i	1.03986	+	0.383923i
$958$		0			0
$959$	−1.20713	−	2.09082i	−0.0389804	−	0.0675159i
$960$		0			0
$961$	5.60102	−	9.70125i	0.180678	−	0.312944i
$962$		0			0
$963$	−8.91005	−	12.9782i	−0.287122	−	0.418215i
$964$		0			0
$965$	−22.6380	+	31.4248i	−0.728744	+	1.01160i
$966$		0			0
$967$	13.0577	−	48.7319i	0.419907	−	1.56711i	−0.354894	−	0.934907i	$-0.615483\pi$
$967$	13.0577	−	48.7319i	0.419907	−	1.56711i	0.774800	−	0.632206i	$-0.217850\pi$
$968$		0			0
$969$	−1.09638	+	11.8990i	−0.0352207	+	0.382250i
$970$		0			0
$971$		−	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
$974$		0			0
$975$	−8.67163	+	28.7194i	−0.277714	+	0.919756i
$976$		0			0
$977$	41.0469	+	10.9985i	1.31321	+	0.351873i	0.846429	−	0.532502i	$-0.178748\pi$
$977$	41.0469	+	10.9985i	1.31321	+	0.351873i	0.466778	+	0.884374i	$0.345415\pi$
$978$		0			0
$979$	−12.9029	−	7.44949i	−0.412378	−	0.238087i
$980$		0			0
$981$	60.0176	+	11.1548i	1.91621	+	0.356145i
$982$		0			0
$983$	−45.2034	+	12.1122i	−1.44176	+	0.386319i	−0.893151	−	0.449757i	$-0.851510\pi$
$983$	−45.2034	+	12.1122i	−1.44176	+	0.386319i	−0.548612	+	0.836077i	$0.684844\pi$
$984$		0			0
$985$	−8.99196	−	19.9786i	−0.286508	−	0.636571i
$986$		0			0
$987$	−5.91945	+	16.0330i	−0.188418	+	0.510335i
$988$		0			0
$989$	3.46410			0.110152
$990$		0			0
$991$	56.7423			1.80248			0.901240	−	0.433320i	$-0.142658\pi$
$991$	56.7423			1.80248			0.901240	+	0.433320i	$0.142658\pi$
$992$		0			0
$993$	7.59575	−	1.30323i	0.241044	−	0.0413566i
$994$		0			0
$995$	−7.42330	−	2.81518i	−0.235334	−	0.0892471i
$996$		0			0
$997$	39.9528	−	10.7053i	1.26532	−	0.339041i	0.437082	−	0.899422i	$-0.356012\pi$
$997$	39.9528	−	10.7053i	1.26532	−	0.339041i	0.828235	+	0.560381i	$0.189345\pi$
$998$		0			0
$999$	−21.2132	−	6.00000i	−0.671156	−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cu.a.497.2		8
4.3	odd	2		90.2.l.a.47.2	yes	8
5.3	odd	4	inner	720.2.cu.a.353.2		8
9.5	odd	6	inner	720.2.cu.a.257.2		8
12.11	even	2		270.2.m.a.197.1		8
20.3	even	4		90.2.l.a.83.2	yes	8
20.7	even	4		450.2.p.a.443.1		8
20.19	odd	2		450.2.p.a.407.1		8
36.7	odd	6		810.2.f.b.647.4		8
36.11	even	6		810.2.f.b.647.1		8
36.23	even	6		90.2.l.a.77.2	yes	8
36.31	odd	6		270.2.m.a.17.1		8
45.23	even	12	inner	720.2.cu.a.113.2		8
60.23	odd	4		270.2.m.a.143.1		8
60.47	odd	4		1350.2.q.g.143.2		8
60.59	even	2		1350.2.q.g.1007.2		8
180.23	odd	12		90.2.l.a.23.2	✓	8
180.43	even	12		810.2.f.b.323.2		8
180.59	even	6		450.2.p.a.257.1		8
180.67	even	12		1350.2.q.g.1043.2		8
180.83	odd	12		810.2.f.b.323.3		8
180.103	even	12		270.2.m.a.233.1		8
180.139	odd	6		1350.2.q.g.557.2		8
180.167	odd	12		450.2.p.a.293.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.2	✓	8	180.23	odd	12
90.2.l.a.47.2	yes	8	4.3	odd	2
90.2.l.a.77.2	yes	8	36.23	even	6
90.2.l.a.83.2	yes	8	20.3	even	4
270.2.m.a.17.1		8	36.31	odd	6
270.2.m.a.143.1		8	60.23	odd	4
270.2.m.a.197.1		8	12.11	even	2
270.2.m.a.233.1		8	180.103	even	12
450.2.p.a.257.1		8	180.59	even	6
450.2.p.a.293.1		8	180.167	odd	12
450.2.p.a.407.1		8	20.19	odd	2
450.2.p.a.443.1		8	20.7	even	4
720.2.cu.a.113.2		8	45.23	even	12	inner
720.2.cu.a.257.2		8	9.5	odd	6	inner
720.2.cu.a.353.2		8	5.3	odd	4	inner
720.2.cu.a.497.2		8	1.1	even	1	trivial
810.2.f.b.323.2		8	180.43	even	12
810.2.f.b.323.3		8	180.83	odd	12
810.2.f.b.647.1		8	36.11	even	6
810.2.f.b.647.4		8	36.7	odd	6
1350.2.q.g.143.2		8	60.47	odd	4
1350.2.q.g.557.2		8	180.139	odd	6
1350.2.q.g.1007.2		8	60.59	even	2
1350.2.q.g.1043.2		8	180.67	even	12

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cu (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10721 - 1.33195i) q^{3} +(0.792893 - 2.09077i) q^{5} +(1.05902 - 0.283763i) q^{7} +(-0.548188 + 2.94949i) q^{9} +(5.44949 + 3.14626i) q^{11} +(3.34607 + 0.896575i) q^{13} +(-3.66270 + 1.25882i) q^{15} +(3.14626 - 3.14626i) q^{17} -1.55051i q^{19} +(-1.55051 - 1.09638i) q^{21} +(-0.258819 + 0.965926i) q^{23} +(-3.74264 - 3.31552i) q^{25} +(4.53553 - 2.53553i) q^{27} +(-1.57313 + 2.72474i) q^{29} +(-2.22474 - 3.85337i) q^{31} +(-1.84304 - 10.7420i) q^{33} +(0.246405 - 2.43916i) q^{35} +(-3.00000 - 3.00000i) q^{37} +(-2.51059 - 5.44949i) q^{39} +(-3.39898 + 1.96240i) q^{41} +(-0.896575 - 3.34607i) q^{43} +(5.73205 + 3.48477i) q^{45} +(-2.32937 - 8.69333i) q^{47} +(-5.02118 + 2.89898i) q^{49} +(-7.67423 - 0.707107i) q^{51} +(6.61037 + 6.61037i) q^{53} +(10.8990 - 8.89898i) q^{55} +(-2.06520 + 1.71673i) q^{57} +(5.90326 + 10.2247i) q^{59} +(2.72474 - 4.71940i) q^{61} +(0.256415 + 3.27912i) q^{63} +(4.52761 - 6.28497i) q^{65} +(-0.978838 + 3.65307i) q^{67} +(1.57313 - 0.724745i) q^{69} -0.635674i q^{71} +(2.89898 - 2.89898i) q^{73} +(-0.272229 + 8.65597i) q^{75} +(6.66390 + 1.78559i) q^{77} +(-2.12132 - 1.22474i) q^{79} +(-8.39898 - 3.23375i) q^{81} +(0.531752 - 0.142483i) q^{83} +(-4.08346 - 9.07277i) q^{85} +(5.37101 - 0.921519i) q^{87} -2.36773 q^{89} +3.79796 q^{91} +(-2.66925 + 7.22973i) q^{93} +(-3.24176 - 1.22939i) q^{95} +(10.7902 - 2.89123i) q^{97} +(-12.2672 + 14.3485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 12 q^{5} + 8 q^{7} + 24 q^{11} - 16 q^{15} - 32 q^{21} + 4 q^{25} + 8 q^{27} - 8 q^{31} + 16 q^{33} - 24 q^{37} + 12 q^{41} + 32 q^{45} - 32 q^{51} + 48 q^{55} + 28 q^{57} + 12 q^{61} + 32 q^{63}+ \cdots + 12 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 + 12 * q^5 + 8 * q^7 + 24 * q^11 - 16 * q^15 - 32 * q^21 + 4 * q^25 + 8 * q^27 - 8 * q^31 + 16 * q^33 - 24 * q^37 + 12 * q^41 + 32 * q^45 - 32 * q^51 + 48 * q^55 + 28 * q^57 + 12 * q^61 + 32 * q^63 - 24 * q^65 - 4 * q^67 - 16 * q^73 - 8 * q^75 + 24 * q^77 - 28 * q^81 - 12 * q^83 - 20 * q^85 + 8 * q^87 - 48 * q^91 - 20 * q^93 + 24 * q^95 + 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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