LMFDB - Embedded newform 360.2.w.e.163.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(163,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("360.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.w (of order $4$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			163.12
Character	$\chi$	$=$	360.163
Dual form			360.2.w.e.307.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40998 + 0.109339i) q^{2} +(1.97609 + 0.308331i) q^{4} +(-0.0696909 + 2.23498i) q^{5} +(1.21782 + 1.21782i) q^{7} +(2.75254 + 0.650804i) q^{8} +O(q^{10})$	\(q+(1.40998 + 0.109339i) q^{2} +(1.97609 + 0.308331i) q^{4} +(-0.0696909 + 2.23498i) q^{5} +(1.21782 + 1.21782i) q^{7} +(2.75254 + 0.650804i) q^{8} +(-0.342633 + 3.14366i) q^{10} -5.23822 q^{11} +(0.361752 - 0.361752i) q^{13} +(1.58395 + 1.85026i) q^{14} +(3.80986 + 1.21858i) q^{16} +(1.66215 - 1.66215i) q^{17} -3.72919i q^{19} +(-0.826829 + 4.39504i) q^{20} +(-7.38579 - 0.572740i) q^{22} +(3.17802 - 3.17802i) q^{23} +(-4.99029 - 0.311516i) q^{25} +(0.549617 - 0.470510i) q^{26} +(2.03103 + 2.78202i) q^{28} +6.70849 q^{29} +2.74770i q^{31} +(5.23860 + 2.13474i) q^{32} +(2.52533 - 2.16186i) q^{34} +(-2.80668 + 2.63694i) q^{35} +(-4.13265 - 4.13265i) q^{37} +(0.407745 - 5.25809i) q^{38} +(-1.64636 + 6.10651i) q^{40} +7.40796 q^{41} +(-5.67877 - 5.67877i) q^{43} +(-10.3512 - 1.61511i) q^{44} +(4.82843 - 4.13347i) q^{46} +(-7.31149 - 7.31149i) q^{47} -4.03382i q^{49} +(-7.00215 - 0.984863i) q^{50} +(0.826395 - 0.603316i) q^{52} +(-10.0364 + 10.0364i) q^{53} +(0.365056 - 11.7073i) q^{55} +(2.55953 + 4.14466i) q^{56} +(9.45884 + 0.733498i) q^{58} -11.3219i q^{59} +13.3665i q^{61} +(-0.300430 + 3.87421i) q^{62} +(7.15291 + 3.58272i) q^{64} +(0.783299 + 0.833721i) q^{65} +(-5.40796 + 5.40796i) q^{67} +(3.79705 - 2.77206i) q^{68} +(-4.24568 + 3.41115i) q^{70} +2.63276i q^{71} +(2.67877 + 2.67877i) q^{73} +(-5.37509 - 6.27881i) q^{74} +(1.14983 - 7.36922i) q^{76} +(-6.37922 - 6.37922i) q^{77} -5.91346 q^{79} +(-2.98901 + 8.43005i) q^{80} +(10.4451 + 0.809977i) q^{82} +(0.742352 + 0.742352i) q^{83} +(3.59903 + 3.83071i) q^{85} +(-7.38605 - 8.62787i) q^{86} +(-14.4184 - 3.40905i) q^{88} +1.75111i q^{89} +0.881100 q^{91} +(7.25994 - 5.30017i) q^{92} +(-9.50962 - 11.1085i) q^{94} +(8.33468 + 0.259891i) q^{95} +(6.64801 - 6.64801i) q^{97} +(0.441053 - 5.68761i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	1.40998	+	0.109339i	0.997007	+	0.0773141i
$2$	1.40998	+	0.109339i	0.997007	+	0.0773141i
$3$		0			0
$3$		0			0
$4$	1.97609	+	0.308331i	0.988045	+	0.154165i
$5$	−0.0696909	+	2.23498i	−0.0311667	+	0.999514i
$5$	−0.0696909	+	2.23498i	−0.0311667	+	0.999514i
$6$		0			0
$7$	1.21782	+	1.21782i	0.460293	+	0.460293i	0.898752	−	0.438458i	$-0.144475\pi$
$7$	1.21782	+	1.21782i	0.460293	+	0.460293i	−0.438458	+	0.898752i	$0.644475\pi$
$8$	2.75254	+	0.650804i	0.973168	+	0.230094i
$9$		0			0
$10$	−0.342633	+	3.14366i	−0.108350	+	0.994113i
$11$	−5.23822			−1.57938			−0.789692	−	0.613504i	$-0.789759\pi$
$11$	−5.23822			−1.57938			−0.789692	+	0.613504i	$0.789759\pi$
$12$		0			0
$13$	0.361752	−	0.361752i	0.100332	−	0.100332i	−0.655159	−	0.755491i	$-0.727398\pi$
$13$	0.361752	−	0.361752i	0.100332	−	0.100332i	0.755491	+	0.655159i	$0.227398\pi$
$14$	1.58395	+	1.85026i	0.423328	+	0.494503i
$15$		0			0
$16$	3.80986	+	1.21858i	0.952466	+	0.304645i
$17$	1.66215	−	1.66215i	0.403130	−	0.403130i	−0.476204	−	0.879335i	$-0.657988\pi$
$17$	1.66215	−	1.66215i	0.403130	−	0.403130i	0.879335	+	0.476204i	$0.157988\pi$
$18$		0			0
$19$		−	3.72919i		−	0.855535i	−0.903889	−	0.427768i	$-0.859300\pi$
$19$		−	3.72919i		−	0.855535i	0.903889	−	0.427768i	$-0.140700\pi$
$20$	−0.826829	+	4.39504i	−0.184885	+	0.982760i
$21$		0			0
$22$	−7.38579	−	0.572740i	−1.57466	−	0.122109i
$23$	3.17802	−	3.17802i	0.662663	−	0.662663i	−0.293344	−	0.956007i	$-0.594768\pi$
$23$	3.17802	−	3.17802i	0.662663	−	0.662663i	0.956007	+	0.293344i	$0.0947681\pi$
$24$		0			0
$25$	−4.99029	−	0.311516i	−0.998057	−	0.0623031i
$26$	0.549617	−	0.470510i	0.107789	−	0.0922747i
$27$		0			0
$28$	2.03103	+	2.78202i	0.383829	+	0.525752i
$29$	6.70849			1.24574			0.622868	−	0.782327i	$-0.285967\pi$
$29$	6.70849			1.24574			0.622868	+	0.782327i	$0.285967\pi$
$30$		0			0
$31$			2.74770i			0.493502i	0.969079	+	0.246751i	$0.0793630\pi$
$31$			2.74770i			0.493502i	−0.969079	+	0.246751i	$0.920637\pi$
$32$	5.23860	+	2.13474i	0.926062	+	0.377372i
$33$		0			0
$34$	2.52533	−	2.16186i	0.433091	−	0.370756i
$35$	−2.80668	+	2.63694i	−0.474415	+	0.445724i
$36$		0			0
$37$	−4.13265	−	4.13265i	−0.679403	−	0.679403i	0.280462	−	0.959865i	$-0.409512\pi$
$37$	−4.13265	−	4.13265i	−0.679403	−	0.679403i	−0.959865	+	0.280462i	$0.909512\pi$
$38$	0.407745	−	5.25809i	0.0661450	−	0.852975i
$39$		0			0
$40$	−1.64636	+	6.10651i	−0.260313	+	0.965524i
$41$	7.40796			1.15693			0.578465	−	0.815707i	$-0.303652\pi$
$41$	7.40796			1.15693			0.578465	+	0.815707i	$0.303652\pi$
$42$		0			0
$43$	−5.67877	−	5.67877i	−0.866004	−	0.866004i	0.126023	−	0.992027i	$-0.459779\pi$
$43$	−5.67877	−	5.67877i	−0.866004	−	0.866004i	−0.992027	+	0.126023i	$0.959779\pi$
$44$	−10.3512	−	1.61511i	−1.56050	−	0.243486i
$45$		0			0
$46$	4.82843	−	4.13347i	0.711913	−	0.609446i
$47$	−7.31149	−	7.31149i	−1.06649	−	1.06649i	−0.997626	−	0.0688638i	$-0.978063\pi$
$47$	−7.31149	−	7.31149i	−1.06649	−	1.06649i	−0.0688638	−	0.997626i	$-0.521937\pi$
$48$		0			0
$49$		−	4.03382i		−	0.576260i
$50$	−7.00215	−	0.984863i	−0.990253	−	0.139281i
$51$		0			0
$52$	0.826395	−	0.603316i	0.114600	−	0.0836649i
$53$	−10.0364	+	10.0364i	−1.37860	+	1.37860i	−0.531610	+	0.846989i	$0.678413\pi$
$53$	−10.0364	+	10.0364i	−1.37860	+	1.37860i	−0.846989	+	0.531610i	$0.821587\pi$
$54$		0			0
$55$	0.365056	−	11.7073i	0.0492242	−	1.57862i
$56$	2.55953	+	4.14466i	0.342032	+	0.553853i
$57$		0			0
$58$	9.45884	+	0.733498i	1.24201	+	0.0963129i
$59$		−	11.3219i		−	1.47398i	−0.675901	−	0.736992i	$-0.736245\pi$
$59$		−	11.3219i		−	1.47398i	0.675901	−	0.736992i	$-0.263755\pi$
$60$		0			0
$61$			13.3665i			1.71140i	0.517471	+	0.855701i	$0.326873\pi$
$61$			13.3665i			1.71140i	−0.517471	+	0.855701i	$0.673127\pi$
$62$	−0.300430	+	3.87421i	−0.0381547	+	0.492025i
$63$		0			0
$64$	7.15291	+	3.58272i	0.894114	+	0.447840i
$65$	0.783299	+	0.833721i	0.0971563	+	0.103410i
$66$		0			0
$67$	−5.40796	+	5.40796i	−0.660688	+	0.660688i	−0.955542	−	0.294854i	$-0.904729\pi$
$67$	−5.40796	+	5.40796i	−0.660688	+	0.660688i	0.294854	+	0.955542i	$0.404729\pi$
$68$	3.79705	−	2.77206i	0.460459	−	0.336162i
$69$		0			0
$70$	−4.24568	+	3.41115i	−0.507456	+	0.407711i
$71$			2.63276i			0.312451i	0.987721	+	0.156225i	$0.0499326\pi$
$71$			2.63276i			0.312451i	−0.987721	+	0.156225i	$0.950067\pi$
$72$		0			0
$73$	2.67877	+	2.67877i	0.313526	+	0.313526i	0.846274	−	0.532748i	$-0.178841\pi$
$73$	2.67877	+	2.67877i	0.313526	+	0.313526i	−0.532748	+	0.846274i	$0.678841\pi$
$74$	−5.37509	−	6.27881i	−0.624842	−	0.729897i
$75$		0			0
$76$	1.14983	−	7.36922i	0.131894	−	0.845308i
$77$	−6.37922	−	6.37922i	−0.726979	−	0.726979i
$78$		0			0
$79$	−5.91346			−0.665316			−0.332658	−	0.943048i	$-0.607945\pi$
$79$	−5.91346			−0.665316			−0.332658	+	0.943048i	$0.607945\pi$
$80$	−2.98901	+	8.43005i	−0.334182	+	0.942509i
$81$		0			0
$82$	10.4451	+	0.809977i	1.15347	+	0.0894470i
$83$	0.742352	+	0.742352i	0.0814837	+	0.0814837i	0.746674	−	0.665190i	$-0.231650\pi$
$83$	0.742352	+	0.742352i	0.0814837	+	0.0814837i	−0.665190	+	0.746674i	$0.731650\pi$
$84$		0			0
$85$	3.59903	+	3.83071i	0.390370	+	0.415499i
$86$	−7.38605	−	8.62787i	−0.796458	−	0.930367i
$87$		0			0
$88$	−14.4184	−	3.40905i	−1.53701	−	0.363406i
$89$			1.75111i			0.185617i	0.995684	+	0.0928086i	$0.0295845\pi$
$89$			1.75111i			0.185617i	−0.995684	+	0.0928086i	$0.970416\pi$
$90$		0			0
$91$	0.881100			0.0923643
$92$	7.25994	−	5.30017i	0.756901	−	0.552581i
$93$		0			0
$94$	−9.50962	−	11.1085i	−0.980843	−	1.14575i
$95$	8.33468	+	0.259891i	0.855120	+	0.0266642i
$96$		0			0
$97$	6.64801	−	6.64801i	0.675004	−	0.675004i	−0.283862	−	0.958865i	$-0.591616\pi$
$97$	6.64801	−	6.64801i	0.675004	−	0.675004i	0.958865	+	0.283862i	$0.0916156\pi$
$98$	0.441053	−	5.68761i	0.0445531	−	0.574536i
$99$		0			0
$100$	−9.76521	−	2.15424i	−0.976521	−	0.215424i
$101$			7.63230i			0.759442i	0.925101	+	0.379721i	$0.123980\pi$
$101$			7.63230i			0.759442i	−0.925101	+	0.379721i	$0.876020\pi$
$102$		0			0
$103$	1.72700	−	1.72700i	0.170166	−	0.170166i	−0.616886	−	0.787052i	$-0.711606\pi$
$103$	1.72700	−	1.72700i	0.170166	−	0.170166i	0.787052	+	0.616886i	$0.211606\pi$
$104$	1.23117	−	0.760307i	0.120726	−	0.0745542i
$105$		0			0
$106$	−15.2484	+	13.0537i	−1.48106	+	1.26789i
$107$	−2.79277	+	2.79277i	−0.269988	+	0.269988i	−0.829095	−	0.559108i	$-0.811144\pi$
$107$	−2.79277	+	2.79277i	−0.269988	+	0.269988i	0.559108	+	0.829095i	$0.311144\pi$
$108$		0			0
$109$	0.115468			0.0110598			0.00552990	−	0.999985i	$-0.498240\pi$
$109$	0.115468			0.0110598			0.00552990	+	0.999985i	$0.498240\pi$
$110$	1.79479	−	16.4672i	0.171126	−	1.57008i
$111$		0			0
$112$	3.15572	+	6.12375i	0.298188	+	0.578640i
$113$	−1.61173	−	1.61173i	−0.151618	−	0.151618i	0.627222	−	0.778840i	$-0.284192\pi$
$113$	−1.61173	−	1.61173i	−0.151618	−	0.151618i	−0.778840	+	0.627222i	$0.784192\pi$
$114$		0			0
$115$	6.88134	+	7.32430i	0.641688	+	0.682994i
$116$	13.2566	+	2.06843i	1.23084	+	0.192049i
$117$		0			0
$118$	1.23792	−	15.9636i	0.113960	−	1.46957i
$119$	4.04840			0.371116
$120$		0			0
$121$	16.4390			1.49445
$122$	−1.46147	+	18.8465i	−0.132315	+	1.70628i
$123$		0			0
$124$	−0.847202	+	5.42971i	−0.0760810	+	0.487602i
$125$	1.04401	−	11.1315i	0.0933790	−	0.995631i
$126$		0			0
$127$	2.39052	+	2.39052i	0.212124	+	0.212124i	0.805169	−	0.593045i	$-0.202074\pi$
$127$	2.39052	+	2.39052i	0.212124	+	0.212124i	−0.593045	+	0.805169i	$0.702074\pi$
$128$	9.69373	+	5.83366i	0.856813	+	0.515627i
$129$		0			0
$130$	1.01328	+	1.26118i	0.0888704	+	0.110612i
$131$	5.62120			0.491127			0.245563	−	0.969381i	$-0.421027\pi$
$131$	5.62120			0.491127			0.245563	+	0.969381i	$0.421027\pi$
$132$		0			0
$133$	4.54149	−	4.54149i	0.393797	−	0.393797i
$134$	−8.21642	+	7.03382i	−0.709791	+	0.607630i
$135$		0			0
$136$	5.65685	−	3.49339i	0.485071	−	0.299556i
$137$	−11.4027	+	11.4027i	−0.974196	+	0.974196i	−0.999675	−	0.0254796i	$-0.991889\pi$
$137$	−11.4027	+	11.4027i	−0.974196	+	0.974196i	0.0254796	+	0.999675i	$0.491889\pi$
$138$		0			0
$139$			3.80050i			0.322354i	0.986926	+	0.161177i	$0.0515290\pi$
$139$			3.80050i			0.322354i	−0.986926	+	0.161177i	$0.948471\pi$
$140$	−6.35930	+	4.34544i	−0.537459	+	0.367257i
$141$		0			0
$142$	−0.287862	+	3.71214i	−0.0241569	+	0.311516i
$143$	−1.89494	+	1.89494i	−0.158463	+	0.158463i
$144$		0			0
$145$	−0.467521	+	14.9934i	−0.0388255	+	1.24513i
$146$	3.48412	+	4.06991i	0.288348	+	0.336828i
$147$		0			0
$148$	−6.89226	−	9.44071i	−0.566540	−	0.776021i
$149$	10.0554			0.823771			0.411886	−	0.911236i	$-0.364870\pi$
$149$	10.0554			0.823771			0.411886	+	0.911236i	$0.364870\pi$
$150$		0			0
$151$			3.24792i			0.264312i	0.991229	+	0.132156i	$0.0421900\pi$
$151$			3.24792i			0.264312i	−0.991229	+	0.132156i	$0.957810\pi$
$152$	2.42697	−	10.2647i	0.196853	−	0.832580i
$153$		0			0
$154$	−8.29708	−	9.69207i	−0.668597	−	0.781009i
$155$	−6.14107	−	0.191490i	−0.493262	−	0.0153808i
$156$		0			0
$157$	−4.18316	−	4.18316i	−0.333852	−	0.333852i	0.520195	−	0.854047i	$-0.325859\pi$
$157$	−4.18316	−	4.18316i	−0.333852	−	0.333852i	−0.854047	+	0.520195i	$0.825859\pi$
$158$	−8.33786	−	0.646570i	−0.663325	−	0.0514383i
$159$		0			0
$160$	−5.13618	+	11.5594i	−0.406051	+	0.913850i
$161$	7.74052			0.610039
$162$		0			0
$163$	3.02793	+	3.02793i	0.237166	+	0.237166i	0.815675	−	0.578510i	$-0.196366\pi$
$163$	3.02793	+	3.02793i	0.237166	+	0.237166i	−0.578510	+	0.815675i	$0.696366\pi$
$164$	14.6388	+	2.28410i	1.14310	+	0.178359i
$165$		0			0
$166$	0.965534	+	1.12787i	0.0749400	+	0.0875397i
$167$	−5.13436	−	5.13436i	−0.397309	−	0.397309i	0.479974	−	0.877283i	$-0.340646\pi$
$167$	−5.13436	−	5.13436i	−0.397309	−	0.397309i	−0.877283	+	0.479974i	$0.840646\pi$
$168$		0			0
$169$			12.7383i			0.979867i
$170$	4.65572	+	5.79474i	0.357078	+	0.444436i
$171$		0			0
$172$	−9.47082	−	12.9727i	−0.722143	−	0.989159i
$173$	0.375176	−	0.375176i	0.0285241	−	0.0285241i	−0.692701	−	0.721225i	$-0.743579\pi$
$173$	0.375176	−	0.375176i	0.0285241	−	0.0285241i	0.721225	+	0.692701i	$0.243579\pi$
$174$		0			0
$175$	−5.69791	−	6.45665i	−0.430721	−	0.488077i
$176$	−19.9569	−	6.38319i	−1.50431	−	0.481151i
$177$		0			0
$178$	−0.191464	+	2.46903i	−0.0143508	+	0.185062i
$179$			8.03565i			0.600613i	0.953843	+	0.300306i	$0.0970890\pi$
$179$			8.03565i			0.600613i	−0.953843	+	0.300306i	$0.902911\pi$
$180$		0			0
$181$		−	21.3530i		−	1.58716i	−0.608469	−	0.793578i	$-0.708216\pi$
$181$		−	21.3530i		−	1.58716i	0.608469	−	0.793578i	$-0.291784\pi$
$182$	1.24233	+	0.0963383i	0.0920879	+	0.00714107i
$183$		0			0
$184$	10.8159	−	6.67935i	0.797357	−	0.492408i
$185$	9.52440	−	8.94838i	0.700248	−	0.657898i
$186$		0			0
$187$	−8.70670	+	8.70670i	−0.636697	+	0.636697i
$188$	−12.1938	−	16.7025i	−0.889324	−	1.21816i
$189$		0			0
$190$	11.7233	+	1.27774i	0.850499	+	0.0926973i
$191$			19.5320i			1.41329i	0.707570	+	0.706643i	$0.249791\pi$
$191$			19.5320i			1.41329i	−0.707570	+	0.706643i	$0.750209\pi$
$192$		0			0
$193$	−2.96924	−	2.96924i	−0.213731	−	0.213731i	0.592119	−	0.805850i	$-0.298291\pi$
$193$	−2.96924	−	2.96924i	−0.213731	−	0.213731i	−0.805850	+	0.592119i	$0.798291\pi$
$194$	10.1005	−	8.64669i	0.725170	−	0.620796i
$195$		0			0
$196$	1.24375	−	7.97120i	0.0888394	−	0.569371i
$197$	1.63229	+	1.63229i	0.116296	+	0.116296i	0.762860	−	0.646564i	$-0.223795\pi$
$197$	1.63229	+	1.63229i	0.116296	+	0.116296i	−0.646564	+	0.762860i	$0.723795\pi$
$198$		0			0
$199$	21.2220			1.50438			0.752192	−	0.658944i	$-0.228996\pi$
$199$	21.2220			1.50438			0.752192	+	0.658944i	$0.228996\pi$
$200$	−13.5332	−	4.10515i	−0.956942	−	0.290278i
$201$		0			0
$202$	−0.834506	+	10.7614i	−0.0587156	+	0.757169i
$203$	8.16974	+	8.16974i	0.573403	+	0.573403i
$204$		0			0
$205$	−0.516268	+	16.5567i	−0.0360577	+	1.15637i
$206$	2.62386	−	2.24621i	0.182813	−	0.156501i
$207$		0			0
$208$	1.81905	−	0.937404i	0.126129	−	0.0649972i
$209$			19.5343i			1.35122i
$210$		0			0
$211$	1.45735			0.100328			0.0501642	−	0.998741i	$-0.484026\pi$
$211$	1.45735			0.100328			0.0501642	+	0.998741i	$0.484026\pi$
$212$	−22.9273	+	16.7382i	−1.57465	+	1.14959i
$213$		0			0
$214$	−4.24311	+	3.63240i	−0.290053	+	0.248306i
$215$	13.0877	−	12.2962i	0.892574	−	0.838593i
$216$		0			0
$217$	−3.34621	+	3.34621i	−0.227156	+	0.227156i
$218$	0.162807	+	0.0126251i	0.0110267	+	0.000855078i
$219$		0			0
$220$	4.33111	−	23.0222i	0.292004	−	1.55215i
$221$		−	1.20257i		−	0.0808938i
$222$		0			0
$223$	−13.1842	+	13.1842i	−0.882880	+	0.882880i	−0.993826	−	0.110946i	$-0.964612\pi$
$223$	−13.1842	+	13.1842i	−0.882880	+	0.882880i	0.110946	+	0.993826i	$0.464612\pi$
$224$	3.77994	+	8.97940i	0.252558	+	0.599962i
$225$		0			0
$226$	−2.09628	−	2.44873i	−0.139442	−	0.162887i
$227$	−2.96252	+	2.96252i	−0.196629	+	0.196629i	−0.798553	−	0.601924i	$-0.794401\pi$
$227$	−2.96252	+	2.96252i	−0.196629	+	0.196629i	0.601924	+	0.798553i	$0.294401\pi$
$228$		0			0
$229$	23.7000			1.56614			0.783071	−	0.621932i	$-0.213652\pi$
$229$	23.7000			1.56614			0.783071	+	0.621932i	$0.213652\pi$
$230$	8.90172	+	11.0795i	0.586962	+	0.730561i
$231$		0			0
$232$	18.4654	+	4.36591i	1.21231	+	0.286636i
$233$	−5.41326	−	5.41326i	−0.354634	−	0.354634i	0.507196	−	0.861831i	$-0.330682\pi$
$233$	−5.41326	−	5.41326i	−0.354634	−	0.354634i	−0.861831	+	0.507196i	$0.830682\pi$
$234$		0			0
$235$	16.8506	−	15.8315i	1.09921	−	1.03273i
$236$	3.49089	−	22.3731i	0.227237	−	1.45636i
$237$		0			0
$238$	5.70816	+	0.442647i	0.370005	+	0.0286925i
$239$	−18.4415			−1.19288			−0.596440	−	0.802658i	$-0.703419\pi$
$239$	−18.4415			−1.19288			−0.596440	+	0.802658i	$0.703419\pi$
$240$		0			0
$241$	−20.2046			−1.30149			−0.650746	−	0.759295i	$-0.725544\pi$
$241$	−20.2046			−1.30149			−0.650746	+	0.759295i	$0.725544\pi$
$242$	23.1786	+	1.79741i	1.48998	+	0.115542i
$243$		0			0
$244$	−4.12130	+	26.4134i	−0.263839	+	1.69094i
$245$	9.01552	+	0.281121i	0.575980	+	0.0179601i
$246$		0			0
$247$	−1.34904	−	1.34904i	−0.0858376	−	0.0858376i
$248$	−1.78822	+	7.56315i	−0.113552	+	0.480261i
$249$		0			0
$250$	2.68914	−	15.5810i	0.170076	−	0.985431i
$251$	6.11932			0.386248			0.193124	−	0.981174i	$-0.438138\pi$
$251$	6.11932			0.386248			0.193124	+	0.981174i	$0.438138\pi$
$252$		0			0
$253$	−16.6472	+	16.6472i	−1.04660	+	1.04660i
$254$	3.10920	+	3.63196i	0.195089	+	0.227889i
$255$		0			0
$256$	13.0301	+	9.28524i	0.814383	+	0.580328i
$257$	16.2658	−	16.2658i	1.01463	−	1.01463i	0.0147384	−	0.999891i	$-0.495308\pi$
$257$	16.2658	−	16.2658i	1.01463	−	1.01463i	0.999891	−	0.0147384i	$-0.00469154\pi$
$258$		0			0
$259$		−	10.0657i		−	0.625449i
$260$	1.29081	+	1.88902i	0.0800525	+	0.117152i
$261$		0			0
$262$	7.92578	+	0.614615i	0.489657	+	0.0379710i
$263$	−0.0331870	+	0.0331870i	−0.00204640	+	0.00204640i	−0.708129	−	0.706083i	$-0.750461\pi$
$263$	−0.0331870	+	0.0331870i	−0.00204640	+	0.00204640i	0.706083	+	0.708129i	$0.250461\pi$
$264$		0			0
$265$	−21.7316	−	23.1305i	−1.33496	−	1.42090i
$266$	6.89997	−	5.90685i	0.423064	−	0.362172i
$267$		0			0
$268$	−12.3541	+	9.01918i	−0.754645	+	0.550934i
$269$	4.14553			0.252757			0.126379	−	0.991982i	$-0.459665\pi$
$269$	4.14553			0.252757			0.126379	+	0.991982i	$0.459665\pi$
$270$		0			0
$271$			20.1717i			1.22534i	0.790337	+	0.612672i	$0.209905\pi$
$271$			20.1717i			1.22534i	−0.790337	+	0.612672i	$0.790095\pi$
$272$	8.35802	−	4.30710i	0.506779	−	0.261156i
$273$		0			0
$274$	−17.3243	+	14.8308i	−1.04660	+	0.895961i
$275$	26.1402	+	1.63179i	1.57631	+	0.0984005i
$276$		0			0
$277$	−20.8477	−	20.8477i	−1.25262	−	1.25262i	−0.954543	−	0.298072i	$-0.903656\pi$
$277$	−20.8477	−	20.8477i	−1.25262	−	1.25262i	−0.298072	−	0.954543i	$-0.596344\pi$
$278$	−0.415542	+	5.35863i	−0.0249225	+	0.321389i
$279$		0			0
$280$	−9.44161	+	5.43167i	−0.564244	+	0.324604i
$281$	−15.3919			−0.918206			−0.459103	−	0.888383i	$-0.651829\pi$
$281$	−15.3919			−0.918206			−0.459103	+	0.888383i	$0.651829\pi$
$282$		0			0
$283$	15.8844	+	15.8844i	0.944230	+	0.944230i	0.998525	−	0.0542951i	$-0.0172912\pi$
$283$	15.8844	+	15.8844i	0.944230	+	0.944230i	−0.0542951	+	0.998525i	$0.517291\pi$
$284$	−0.811761	+	5.20257i	−0.0481691	+	0.308716i
$285$		0			0
$286$	−2.87902	+	2.46464i	−0.170240	+	0.145737i
$287$	9.02157	+	9.02157i	0.532527	+	0.532527i
$288$		0			0
$289$			11.4745i			0.674972i
$290$	−2.29855	+	21.0892i	−0.134975	+	1.23840i
$291$		0			0
$292$	4.46754	+	6.11944i	0.261443	+	0.358113i
$293$	−1.84536	+	1.84536i	−0.107807	+	0.107807i	−0.758953	−	0.651146i	$-0.774289\pi$
$293$	−1.84536	+	1.84536i	−0.107807	+	0.107807i	0.651146	+	0.758953i	$0.274289\pi$
$294$		0			0
$295$	25.3042	+	0.789032i	1.47327	+	0.0459392i
$296$	−8.68572	−	14.0648i	−0.504847	−	0.817500i
$297$		0			0
$298$	14.1779	+	1.09945i	0.821305	+	0.0636892i
$299$		−	2.29931i		−	0.132973i
$300$		0			0
$301$		−	13.8315i		−	0.797232i
$302$	−0.355124	+	4.57951i	−0.0204351	+	0.263521i
$303$		0			0
$304$	4.54432	−	14.2077i	0.260634	−	0.814868i
$305$	−29.8738	−	0.931521i	−1.71057	−	0.0533388i
$306$		0			0
$307$	9.31156	−	9.31156i	0.531439	−	0.531439i	−0.389562	−	0.921000i	$-0.627374\pi$
$307$	9.31156	−	9.31156i	0.531439	−	0.531439i	0.921000	+	0.389562i	$0.127374\pi$
$308$	−10.6390	−	14.5728i	−0.606213	−	0.830363i
$309$		0			0
$310$	−8.63785	−	0.941453i	−0.490597	−	0.0534710i
$311$			5.01005i			0.284094i	0.989860	+	0.142047i	$0.0453684\pi$
$311$			5.01005i			0.284094i	−0.989860	+	0.142047i	$0.954632\pi$
$312$		0			0
$313$	−8.46971	−	8.46971i	−0.478737	−	0.478737i	0.425991	−	0.904727i	$-0.359926\pi$
$313$	−8.46971	−	8.46971i	−0.478737	−	0.478737i	−0.904727	+	0.425991i	$0.859926\pi$
$314$	−5.44079	−	6.35555i	−0.307041	−	0.358664i
$315$		0			0
$316$	−11.6855	−	1.82330i	−0.657362	−	0.102569i
$317$	−10.6205	−	10.6205i	−0.596505	−	0.596505i	0.342875	−	0.939381i	$-0.388599\pi$
$317$	−10.6205	−	10.6205i	−0.596505	−	0.596505i	−0.939381	+	0.342875i	$0.888599\pi$
$318$		0			0
$319$	−35.1406			−1.96749
$320$	−8.50581	+	15.7369i	−0.475489	+	0.879722i
$321$		0			0
$322$	10.9140	+	0.846338i	0.608213	+	0.0471646i
$323$	−6.19847	−	6.19847i	−0.344892	−	0.344892i
$324$		0			0
$325$	−1.91794	+	1.69256i	−0.106388	+	0.0938861i
$326$	3.93825	+	4.60039i	0.218119	+	0.254792i
$327$		0			0
$328$	20.3907	+	4.82113i	1.12589	+	0.266202i
$329$		−	17.8082i		−	0.981796i
$330$		0			0
$331$	−7.08673			−0.389522			−0.194761	−	0.980851i	$-0.562393\pi$
$331$	−7.08673			−0.389522			−0.194761	+	0.980851i	$0.562393\pi$
$332$	1.23806	+	1.69584i	0.0679476	+	0.0930715i
$333$		0			0
$334$	−6.67797	−	7.80074i	−0.365402	−	0.426837i
$335$	−11.7098	−	12.4636i	−0.639775	−	0.680958i
$336$		0			0
$337$	5.44648	−	5.44648i	0.296689	−	0.296689i	−0.543027	−	0.839715i	$-0.682722\pi$
$337$	5.44648	−	5.44648i	0.296689	−	0.296689i	0.839715	+	0.543027i	$0.182722\pi$
$338$	−1.39279	+	17.9607i	−0.0757576	+	0.976934i
$339$		0			0
$340$	5.93089	+	8.67952i	0.321648	+	0.470713i
$341$		−	14.3931i		−	0.779429i
$342$		0			0
$343$	13.4372	−	13.4372i	0.725542	−	0.725542i
$344$	−11.9353	−	19.3268i	−0.643506	−	1.04203i
$345$		0			0
$346$	0.570012	−	0.487970i	0.0306440	−	0.0262334i
$347$	2.15272	−	2.15272i	0.115564	−	0.115564i	−0.646960	−	0.762524i	$-0.723960\pi$
$347$	2.15272	−	2.15272i	0.115564	−	0.115564i	0.762524	+	0.646960i	$0.223960\pi$
$348$		0			0
$349$	21.4726			1.14940			0.574702	−	0.818363i	$-0.305118\pi$
$349$	21.4726			1.14940			0.574702	+	0.818363i	$0.305118\pi$
$350$	−7.32798	−	9.72675i	−0.391697	−	0.519917i
$351$		0			0
$352$	−27.4409	−	11.1822i	−1.46261	−	0.596015i
$353$	−16.3162	−	16.3162i	−0.868422	−	0.868422i	0.123875	−	0.992298i	$-0.460468\pi$
$353$	−16.3162	−	16.3162i	−0.868422	−	0.868422i	−0.992298	+	0.123875i	$0.960468\pi$
$354$		0			0
$355$	−5.88417	−	0.183479i	−0.312299	−	0.00973807i
$356$	−0.539921	+	3.46035i	−0.0286157	+	0.183398i
$357$		0			0
$358$	−0.878608	+	11.3301i	−0.0464359	+	0.598815i
$359$	−16.2275			−0.856454			−0.428227	−	0.903671i	$-0.640862\pi$
$359$	−16.2275			−0.856454			−0.428227	+	0.903671i	$0.640862\pi$
$360$		0			0
$361$	5.09312			0.268059
$362$	2.33471	−	30.1073i	0.122710	−	1.58241i
$363$		0			0
$364$	1.74113	+	0.271670i	0.0912601	+	0.0142394i
$365$	−6.17369	+	5.80032i	−0.323146	+	0.303602i
$366$		0			0
$367$	−2.14505	−	2.14505i	−0.111971	−	0.111971i	0.648902	−	0.760872i	$-0.275229\pi$
$367$	−2.14505	−	2.14505i	−0.111971	−	0.111971i	−0.760872	+	0.648902i	$0.775229\pi$
$368$	15.9805	−	8.23516i	0.833041	−	0.429287i
$369$		0			0
$370$	14.4076	−	11.5757i	0.749016	−	0.601790i
$371$	−24.4450			−1.26912
$372$		0			0
$373$	−5.83818	+	5.83818i	−0.302289	+	0.302289i	−0.841909	−	0.539620i	$-0.818568\pi$
$373$	−5.83818	+	5.83818i	−0.302289	+	0.302289i	0.539620	+	0.841909i	$0.318568\pi$
$374$	−13.2283	+	11.3243i	−0.684017	+	0.585565i
$375$		0			0
$376$	−15.3668	−	24.8835i	−0.792482	−	1.28327i
$377$	2.42681	−	2.42681i	0.124987	−	0.124987i
$378$		0			0
$379$		−	33.6252i		−	1.72721i	−0.504170	−	0.863604i	$-0.668202\pi$
$379$		−	33.6252i		−	1.72721i	0.504170	−	0.863604i	$-0.331798\pi$
$380$	16.3899	+	3.08341i	0.840786	+	0.158175i
$381$		0			0
$382$	−2.13560	+	27.5397i	−0.109267	+	1.40906i
$383$	−17.0709	+	17.0709i	−0.872281	+	0.872281i	−0.992721	−	0.120439i	$-0.961570\pi$
$383$	−17.0709	+	17.0709i	−0.872281	+	0.872281i	0.120439	+	0.992721i	$0.461570\pi$
$384$		0			0
$385$	14.7020	−	13.8129i	0.749284	−	0.703968i
$386$	−3.86192	−	4.51123i	−0.196567	−	0.229616i
$387$		0			0
$388$	15.1869	−	11.0873i	0.770996	−	0.562872i
$389$	−16.7710			−0.850323			−0.425161	−	0.905118i	$-0.639783\pi$
$389$	−16.7710			−0.850323			−0.425161	+	0.905118i	$0.639783\pi$
$390$		0			0
$391$		−	10.5647i		−	0.534279i
$392$	2.62523	−	11.1032i	0.132594	−	0.560798i
$393$		0			0
$394$	2.12303	+	2.47998i	0.106957	+	0.124939i
$395$	0.412114	−	13.2165i	0.0207357	−	0.664993i
$396$		0			0
$397$	−2.59093	−	2.59093i	−0.130035	−	0.130035i	0.639094	−	0.769129i	$-0.279310\pi$
$397$	−2.59093	−	2.59093i	−0.130035	−	0.130035i	−0.769129	+	0.639094i	$0.779310\pi$
$398$	29.9225	+	2.32038i	1.49988	+	0.116310i
$399$		0			0
$400$	−18.6327	−	7.26789i	−0.931635	−	0.363395i
$401$	−14.1336			−0.705800			−0.352900	−	0.935661i	$-0.614804\pi$
$401$	−14.1336			−0.705800			−0.352900	+	0.935661i	$0.614804\pi$
$402$		0			0
$403$	0.993989	+	0.993989i	0.0495141	+	0.0495141i
$404$	−2.35327	+	15.0821i	−0.117080	+	0.750363i
$405$		0			0
$406$	10.6259	+	12.4124i	0.527355	+	0.616019i
$407$	21.6477	+	21.6477i	1.07304	+	1.07304i
$408$		0			0
$409$			3.28815i			0.162588i	0.996690	+	0.0812942i	$0.0259053\pi$
$409$			3.28815i			0.162588i	−0.996690	+	0.0812942i	$0.974095\pi$
$410$	−2.53821	+	23.2881i	−0.125353	+	1.15012i
$411$		0			0
$412$	3.94519	−	2.88022i	0.194366	−	0.141898i
$413$	13.7880	−	13.7880i	0.678465	−	0.678465i
$414$		0			0
$415$	−1.71088	+	1.60741i	−0.0839837	+	0.0789045i
$416$	2.66732	−	1.12283i	0.130776	−	0.0550512i
$417$		0			0
$418$	−2.13586	+	27.5430i	−0.104468	+	1.34717i
$419$		−	20.8299i		−	1.01761i	−0.860883	−	0.508804i	$-0.830088\pi$
$419$		−	20.8299i		−	1.01761i	0.860883	−	0.508804i	$-0.169912\pi$
$420$		0			0
$421$		−	0.378145i		−	0.0184297i	−0.999958	−	0.00921484i	$-0.997067\pi$
$421$		−	0.378145i		−	0.0184297i	0.999958	−	0.00921484i	$-0.00293322\pi$
$422$	2.05484	+	0.159345i	0.100028	+	0.00775680i
$423$		0			0
$424$	−34.1571	+	21.0937i	−1.65882	+	1.02440i
$425$	−8.81238	+	7.77681i	−0.427463	+	0.377231i
$426$		0			0
$427$	−16.2780	+	16.2780i	−0.787746	+	0.787746i
$428$	−6.37987	+	4.65767i	−0.308383	+	0.225137i
$429$		0			0
$430$	19.7979	−	15.9064i	0.954738	−	0.767074i
$431$			12.2457i			0.589854i	0.955520	+	0.294927i	$0.0952953\pi$
$431$			12.2457i			0.589854i	−0.955520	+	0.294927i	$0.904705\pi$
$432$		0			0
$433$	−1.66686	−	1.66686i	−0.0801044	−	0.0801044i	0.665919	−	0.746024i	$-0.268039\pi$
$433$	−1.66686	−	1.66686i	−0.0801044	−	0.0801044i	−0.746024	+	0.665919i	$0.768039\pi$
$434$	−5.08396	+	4.35222i	−0.244038	+	0.208913i
$435$		0			0
$436$	0.228174	+	0.0356022i	0.0109276	+	0.00170504i
$437$	−11.8514	−	11.8514i	−0.566932	−	0.566932i
$438$		0			0
$439$	−37.0618			−1.76886			−0.884432	−	0.466669i	$-0.845454\pi$
$439$	−37.0618			−1.76886			−0.884432	+	0.466669i	$0.845454\pi$
$440$	8.62400	−	31.9873i	0.411133	−	1.52493i
$441$		0			0
$442$	0.131488	−	1.69560i	0.00625423	−	0.0806516i
$443$	21.0995	+	21.0995i	1.00247	+	1.00247i	0.999997	+	0.00246927i	$0.000785994\pi$
$443$	21.0995	+	21.0995i	1.00247	+	1.00247i	0.00246927	+	0.999997i	$0.499214\pi$
$444$		0			0
$445$	−3.91370	−	0.122036i	−0.185527	−	0.00578508i
$446$	−20.0310	+	17.1479i	−0.948497	+	0.811979i
$447$		0			0
$448$	4.34785	+	13.0741i	0.205417	+	0.617692i
$449$			17.8253i			0.841230i	0.907239	+	0.420615i	$0.138186\pi$
$449$			17.8253i			0.841230i	−0.907239	+	0.420615i	$0.861814\pi$
$450$		0			0
$451$	−38.8045			−1.82723
$452$	−2.68797	−	3.68186i	−0.126432	−	0.173180i
$453$		0			0
$454$	−4.50101	+	3.85317i	−0.211243	+	0.180838i
$455$	−0.0614046	+	1.96924i	−0.00287869	+	0.0923195i
$456$		0			0
$457$	17.4395	−	17.4395i	0.815787	−	0.815787i	−0.169707	−	0.985494i	$-0.554282\pi$
$457$	17.4395	−	17.4395i	0.815787	−	0.815787i	0.985494	+	0.169707i	$0.0542823\pi$
$458$	33.4166	+	2.59133i	1.56145	+	0.121085i
$459$		0			0
$460$	11.3398	+	16.5952i	0.528723	+	0.773755i
$461$		−	14.8981i		−	0.693872i	−0.937889	−	0.346936i	$-0.887222\pi$
$461$		−	14.8981i		−	0.693872i	0.937889	−	0.346936i	$-0.112778\pi$
$462$		0			0
$463$	−7.47612	+	7.47612i	−0.347445	+	0.347445i	−0.859157	−	0.511712i	$-0.829011\pi$
$463$	−7.47612	+	7.47612i	−0.347445	+	0.347445i	0.511712	+	0.859157i	$0.329011\pi$
$464$	25.5584	+	8.17483i	1.18652	+	0.379507i
$465$		0			0
$466$	−7.04071	−	8.22446i	−0.326155	−	0.380991i
$467$	13.2540	−	13.2540i	0.613321	−	0.613321i	−0.330489	−	0.943810i	$-0.607214\pi$
$467$	13.2540	−	13.2540i	0.613321	−	0.613321i	0.943810	+	0.330489i	$0.107214\pi$
$468$		0			0
$469$	−13.1719			−0.608220
$470$	25.4900	−	20.4797i	1.17577	−	0.944657i
$471$		0			0
$472$	7.36833	−	31.1639i	0.339155	−	1.43443i
$473$	29.7467	+	29.7467i	1.36775	+	1.36775i
$474$		0			0
$475$	−1.16170	+	18.6097i	−0.0533025	+	0.853873i
$476$	8.00000	+	1.24825i	0.366679	+	0.0572133i
$477$		0			0
$478$	−26.0021	−	2.01637i	−1.18931	−	0.0922265i
$479$	15.9629			0.729363			0.364682	−	0.931132i	$-0.381178\pi$
$479$	15.9629			0.729363			0.364682	+	0.931132i	$0.381178\pi$
$480$		0			0
$481$	−2.98999			−0.136332
$482$	−28.4881	−	2.20914i	−1.29760	−	0.100624i
$483$		0			0
$484$	32.4849	+	5.06864i	1.47658	+	0.230393i
$485$	14.3949	+	15.3215i	0.653638	+	0.695713i
$486$		0			0
$487$	27.8490	+	27.8490i	1.26196	+	1.26196i	0.950142	+	0.311818i	$0.100938\pi$
$487$	27.8490	+	27.8490i	1.26196	+	1.26196i	0.311818	+	0.950142i	$0.399062\pi$
$488$	−8.69895	+	36.7917i	−0.393783	+	1.66548i
$489$		0			0
$490$	12.6810	+	1.38212i	0.572868	+	0.0624378i
$491$	23.2165			1.04775			0.523874	−	0.851796i	$-0.324486\pi$
$491$	23.2165			1.04775			0.523874	+	0.851796i	$0.324486\pi$
$492$		0			0
$493$	11.1505	−	11.1505i	0.502193	−	0.502193i
$494$	−1.75462	−	2.04963i	−0.0789442	−	0.0922172i
$495$		0			0
$496$	−3.34829	+	10.4684i	−0.150343	+	0.470044i
$497$	−3.20623	+	3.20623i	−0.143819	+	0.143819i
$498$		0			0
$499$			5.26255i			0.235584i	0.993038	+	0.117792i	$0.0375816\pi$
$499$			5.26255i			0.235584i	−0.993038	+	0.117792i	$0.962418\pi$
$500$	5.49524	−	21.6749i	0.245755	−	0.969332i
$501$		0			0
$502$	8.62812	+	0.669078i	0.385092	+	0.0298624i
$503$	14.3869	−	14.3869i	0.641479	−	0.641479i	−0.309440	−	0.950919i	$-0.600142\pi$
$503$	14.3869	−	14.3869i	0.641479	−	0.641479i	0.950919	+	0.309440i	$0.100142\pi$
$504$		0			0
$505$	−17.0580	−	0.531902i	−0.759073	−	0.0236693i
$506$	−25.2924	+	21.6520i	−1.12438	+	0.962549i
$507$		0			0
$508$	3.98680	+	5.46094i	0.176886	+	0.242290i
$509$	11.1825			0.495655			0.247828	−	0.968804i	$-0.420283\pi$
$509$	11.1825			0.495655			0.247828	+	0.968804i	$0.420283\pi$
$510$		0			0
$511$			6.52453i			0.288628i
$512$	17.3570	+	14.5167i	0.767078	+	0.641554i
$513$		0			0
$514$	24.7129	−	21.1559i	1.09004	−	0.933148i
$515$	3.73945	+	3.98017i	0.164780	+	0.175387i
$516$		0			0
$517$	38.2992	+	38.2992i	1.68440	+	1.68440i
$518$	1.10057	−	14.1924i	0.0483561	−	0.623577i
$519$		0			0
$520$	1.61347	+	2.80462i	0.0707554	+	0.122991i
$521$	−4.32197			−0.189349			−0.0946745	−	0.995508i	$-0.530181\pi$
$521$	−4.32197			−0.189349			−0.0946745	+	0.995508i	$0.530181\pi$
$522$		0			0
$523$	0.519319	+	0.519319i	0.0227082	+	0.0227082i	0.718370	−	0.695661i	$-0.244889\pi$
$523$	0.519319	+	0.519319i	0.0227082	+	0.0227082i	−0.695661	+	0.718370i	$0.744889\pi$
$524$	11.1080	+	1.73319i	0.485255	+	0.0757147i
$525$		0			0
$526$	−0.0504217	+	0.0431644i	−0.00219849	+	0.00188206i
$527$	4.56709	+	4.56709i	0.198946	+	0.198946i
$528$		0			0
$529$			2.80038i			0.121755i
$530$	−28.1121	−	34.9897i	−1.22111	−	1.51985i
$531$		0			0
$532$	10.3747	−	7.57411i	0.449799	−	0.328379i
$533$	2.67985	−	2.67985i	0.116077	−	0.116077i
$534$		0			0
$535$	−6.04717	−	6.43643i	−0.261442	−	0.278271i
$536$	−18.4051	+	11.3661i	−0.794981	+	0.490940i
$537$		0			0
$538$	5.84511	+	0.453266i	0.252001	+	0.0195417i
$539$			21.1301i			0.910136i
$540$		0			0
$541$		−	10.4911i		−	0.451046i	−0.974238	−	0.225523i	$-0.927591\pi$
$541$		−	10.4911i		−	0.451046i	0.974238	−	0.225523i	$-0.0724090\pi$
$542$	−2.20555	+	28.4417i	−0.0947364	+	1.22168i
$543$		0			0
$544$	12.2556	−	5.15907i	0.525453	−	0.221193i
$545$	−0.00804704	+	0.258068i	−0.000344697	+	0.0110544i
$546$		0			0
$547$	22.3537	−	22.3537i	0.955774	−	0.955774i	−0.0432882	−	0.999063i	$-0.513783\pi$
$547$	22.3537	−	22.3537i	0.955774	−	0.955774i	0.999063	+	0.0432882i	$0.0137834\pi$
$548$	−26.0485	+	19.0169i	−1.11274	+	0.812362i
$549$		0			0
$550$	36.6788	+	5.15893i	1.56399	+	0.219977i
$551$		−	25.0173i		−	1.06577i
$552$		0			0
$553$	−7.20154	−	7.20154i	−0.306240	−	0.306240i
$554$	−27.1154	−	31.6743i	−1.15202	−	1.34571i
$555$		0			0
$556$	−1.17181	+	7.51013i	−0.0496959	+	0.318500i
$557$	6.93719	+	6.93719i	0.293938	+	0.293938i	0.838634	−	0.544696i	$-0.183355\pi$
$557$	6.93719	+	6.93719i	0.293938	+	0.293938i	−0.544696	+	0.838634i	$0.683355\pi$
$558$		0			0
$559$	−4.10862			−0.173776
$560$	−13.9064	+	6.62621i	−0.587652	+	0.280009i
$561$		0			0
$562$	−21.7023	−	1.68293i	−0.915458	−	0.0709903i
$563$	−19.6100	−	19.6100i	−0.826461	−	0.826461i	0.160564	−	0.987025i	$-0.448669\pi$
$563$	−19.6100	−	19.6100i	−0.826461	−	0.826461i	−0.987025	+	0.160564i	$0.948669\pi$
$564$		0			0
$565$	3.71450	−	3.48986i	0.156270	−	0.146819i
$566$	20.6599	+	24.1335i	0.868401	+	1.01441i
$567$		0			0
$568$	−1.71341	+	7.24676i	−0.0718930	+	0.304067i
$569$		−	37.8398i		−	1.58633i	−0.609009	−	0.793163i	$-0.708433\pi$
$569$		−	37.8398i		−	1.58633i	0.609009	−	0.793163i	$-0.291567\pi$
$570$		0			0
$571$	−2.23967			−0.0937273			−0.0468637	−	0.998901i	$-0.514923\pi$
$571$	−2.23967			−0.0937273			−0.0468637	+	0.998901i	$0.514923\pi$
$572$	−4.32884	+	3.16030i	−0.180998	+	0.132139i
$573$		0			0
$574$	11.7338	+	13.7067i	0.489761	+	0.572105i
$575$	−16.8492	+	14.8692i	−0.702662	+	0.620090i
$576$		0			0
$577$	−23.0369	+	23.0369i	−0.959038	+	0.959038i	−0.999193	−	0.0401552i	$-0.987215\pi$
$577$	−23.0369	+	23.0369i	−0.959038	+	0.959038i	0.0401552	+	0.999193i	$0.487215\pi$
$578$	−1.25461	+	16.1789i	−0.0521849	+	0.672952i
$579$		0			0
$580$	−5.54678	+	29.4841i	−0.230317	+	1.22426i
$581$			1.80810i			0.0750128i
$582$		0			0
$583$	52.5726	−	52.5726i	2.17734	−	2.17734i
$584$	5.63006	+	9.11677i	0.232974	+	0.377254i
$585$		0			0
$586$	−2.80369	+	2.40015i	−0.115820	+	0.0991495i
$587$	−23.2134	+	23.2134i	−0.958118	+	0.958118i	−0.999158	−	0.0410396i	$-0.986933\pi$
$587$	−23.2134	+	23.2134i	−0.958118	+	0.958118i	0.0410396	+	0.999158i	$0.486933\pi$
$588$		0			0
$589$	10.2467			0.422209
$590$	35.5922	+	3.87925i	1.46531	+	0.159706i
$591$		0			0
$592$	−10.7089	−	20.7808i	−0.440132	−	0.854085i
$593$	12.1755	+	12.1755i	0.499988	+	0.499988i	0.911434	−	0.411446i	$-0.134976\pi$
$593$	12.1755	+	12.1755i	0.499988	+	0.499988i	−0.411446	+	0.911434i	$0.634976\pi$
$594$		0			0
$595$	−0.282137	+	9.04810i	−0.0115665	+	0.370936i
$596$	19.8704	+	3.10039i	0.813923	+	0.126997i
$597$		0			0
$598$	0.251404	−	3.24199i	0.0102807	−	0.132575i
$599$	42.9318			1.75415			0.877073	−	0.480357i	$-0.159493\pi$
$599$	42.9318			1.75415			0.877073	+	0.480357i	$0.159493\pi$
$600$		0			0
$601$	24.0032			0.979112			0.489556	−	0.871972i	$-0.337159\pi$
$601$	24.0032			0.979112			0.489556	+	0.871972i	$0.337159\pi$
$602$	1.51231	−	19.5021i	0.0616373	−	0.794846i
$603$		0			0
$604$	−1.00144	+	6.41819i	−0.0407478	+	0.261153i
$605$	−1.14565	+	36.7408i	−0.0465771	+	1.49372i
$606$		0			0
$607$	−3.98935	−	3.98935i	−0.161923	−	0.161923i	0.621495	−	0.783418i	$-0.286525\pi$
$607$	−3.98935	−	3.98935i	−0.161923	−	0.161923i	−0.783418	+	0.621495i	$0.786525\pi$
$608$	7.96085	−	19.5357i	0.322855	−	0.792279i
$609$		0			0
$610$	−42.0196	−	4.57979i	−1.70133	−	0.185430i
$611$	−5.28990			−0.214006
$612$		0			0
$613$	−31.8671	+	31.8671i	−1.28710	+	1.28710i	−0.350563	+	0.936539i	$0.614010\pi$
$613$	−31.8671	+	31.8671i	−1.28710	+	1.28710i	−0.936539	+	0.350563i	$0.885990\pi$
$614$	14.1472	−	12.1110i	0.570936	−	0.488760i
$615$		0			0
$616$	−13.4074	−	21.7106i	−0.540200	−	0.874747i
$617$	−6.45265	+	6.45265i	−0.259774	+	0.259774i	−0.824962	−	0.565188i	$-0.808804\pi$
$617$	−6.45265	+	6.45265i	−0.259774	+	0.259774i	0.565188	+	0.824962i	$0.308804\pi$
$618$		0			0
$619$			27.4744i			1.10429i	0.833749	+	0.552144i	$0.186190\pi$
$619$			27.4744i			1.10429i	−0.833749	+	0.552144i	$0.813810\pi$
$620$	−12.0763	−	2.27188i	−0.484994	−	0.0912410i
$621$		0			0
$622$	−0.547792	+	7.06407i	−0.0219645	+	0.283244i
$623$	−2.13254	+	2.13254i	−0.0854383	+	0.0854383i
$624$		0			0
$625$	24.8059	+	3.10911i	0.992237	+	0.124364i
$626$	−11.0161	−	12.8682i	−0.440290	−	0.514317i
$627$		0			0
$628$	−6.97650	−	9.55609i	−0.278393	−	0.381330i
$629$	−13.7381			−0.547776
$630$		0			0
$631$		−	13.1266i		−	0.522560i	−0.965263	−	0.261280i	$-0.915855\pi$
$631$		−	13.1266i		−	0.522560i	0.965263	−	0.261280i	$-0.0841447\pi$
$632$	−16.2770	−	3.84850i	−0.647465	−	0.153085i
$633$		0			0
$634$	−13.8134	−	16.1359i	−0.548602	−	0.640838i
$635$	−5.50935	+	5.17616i	−0.218632	+	0.205410i
$636$		0			0
$637$	−1.45925	−	1.45925i	−0.0578174	−	0.0578174i
$638$	−49.5475	−	3.84222i	−1.96160	−	0.152115i
$639$		0			0
$640$	−13.7137	+	21.2588i	−0.542081	+	0.840326i
$641$	44.4068			1.75396			0.876982	−	0.480524i	$-0.159553\pi$
$641$	44.4068			1.75396			0.876982	+	0.480524i	$0.159553\pi$
$642$		0			0
$643$	18.2206	+	18.2206i	0.718551	+	0.718551i	0.968308	−	0.249758i	$-0.0803510\pi$
$643$	18.2206	+	18.2206i	0.718551	+	0.718551i	−0.249758	+	0.968308i	$0.580351\pi$
$644$	15.2960	+	2.38664i	0.602746	+	0.0940468i
$645$		0			0
$646$	−8.06199	−	9.41745i	−0.317195	−	0.370525i
$647$	−18.3745	−	18.3745i	−0.722375	−	0.722375i	0.246713	−	0.969088i	$-0.420649\pi$
$647$	−18.3745	−	18.3745i	−0.722375	−	0.722375i	−0.969088	+	0.246713i	$0.920649\pi$
$648$		0			0
$649$			59.3065i			2.32799i
$650$	−2.88932	+	2.17677i	−0.113328	+	0.0853798i
$651$		0			0
$652$	5.04985	+	6.91706i	0.197768	+	0.270893i
$653$	−1.11550	+	1.11550i	−0.0436531	+	0.0436531i	−0.728596	−	0.684943i	$-0.759827\pi$
$653$	−1.11550	+	1.11550i	−0.0436531	+	0.0436531i	0.684943	+	0.728596i	$0.259827\pi$
$654$		0			0
$655$	−0.391747	+	12.5633i	−0.0153068	+	0.490888i
$656$	28.2233	+	9.02719i	1.10194	+	0.352453i
$657$		0			0
$658$	1.94712	−	25.1092i	0.0759067	−	0.978857i
$659$			25.3850i			0.988860i	0.869217	+	0.494430i	$0.164623\pi$
$659$			25.3850i			0.988860i	−0.869217	+	0.494430i	$0.835377\pi$
$660$		0			0
$661$			7.30922i			0.284296i	0.989845	+	0.142148i	$0.0454008\pi$
$661$			7.30922i			0.284296i	−0.989845	+	0.142148i	$0.954599\pi$
$662$	−9.99216	−	0.774854i	−0.388356	−	0.0301156i
$663$		0			0
$664$	1.56023	+	2.52648i	0.0605485	+	0.0980463i
$665$	9.83365	+	10.4666i	0.381332	+	0.405879i
$666$		0			0
$667$	21.3197	−	21.3197i	0.825503	−	0.825503i
$668$	−8.56288	−	11.7290i	−0.331308	−	0.453811i
$669$		0			0
$670$	−15.1479	−	18.8537i	−0.585213	−	0.728384i
$671$		−	70.0165i		−	2.70296i
$672$		0			0
$673$	10.1902	+	10.1902i	0.392804	+	0.392804i	0.875686	−	0.482882i	$-0.160410\pi$
$673$	10.1902	+	10.1902i	0.392804	+	0.392804i	−0.482882	+	0.875686i	$0.660410\pi$
$674$	8.27494	−	7.08392i	0.318739	−	0.272862i
$675$		0			0
$676$	−3.92760	+	25.1720i	−0.151062	+	0.968153i
$677$	14.0161	+	14.0161i	0.538683	+	0.538683i	0.923142	−	0.384459i	$-0.125612\pi$
$677$	14.0161	+	14.0161i	0.538683	+	0.538683i	−0.384459	+	0.923142i	$0.625612\pi$
$678$		0			0
$679$	16.1922			0.621399
$680$	7.41343	+	12.8864i	0.284292	+	0.494172i
$681$		0			0
$682$	1.57372	−	20.2940i	0.0602609	−	0.777096i
$683$	−19.0880	−	19.0880i	−0.730381	−	0.730381i	0.240314	−	0.970695i	$-0.422749\pi$
$683$	−19.0880	−	19.0880i	−0.730381	−	0.730381i	−0.970695	+	0.240314i	$0.922749\pi$
$684$		0			0
$685$	−24.6901	−	26.2794i	−0.943360	−	1.00408i
$686$	20.4154	−	17.4770i	0.779465	−	0.667276i
$687$		0			0
$688$	−14.7153	−	28.5554i	−0.561016	−	1.08866i
$689$			7.26135i			0.276635i
$690$		0			0
$691$	9.95032			0.378528			0.189264	−	0.981926i	$-0.439390\pi$
$691$	9.95032			0.378528			0.189264	+	0.981926i	$0.439390\pi$
$692$	0.857060	−	0.625703i	0.0325805	−	0.0237857i
$693$		0			0
$694$	3.27067	−	2.79992i	0.124153	−	0.106284i
$695$	−8.49405	−	0.264860i	−0.322198	−	0.0100467i
$696$		0			0
$697$	12.3131	−	12.3131i	0.466393	−	0.466393i
$698$	30.2760	+	2.34779i	1.14596	+	0.0888651i
$699$		0			0
$700$	−9.26879	−	14.5158i	−0.350327	−	0.548644i
$701$			45.3620i			1.71330i	0.515899	+	0.856649i	$0.327458\pi$
$701$			45.3620i			1.71330i	−0.515899	+	0.856649i	$0.672542\pi$
$702$		0			0
$703$	−15.4114	+	15.4114i	−0.581253	+	0.581253i
$704$	−37.4685	−	18.7671i	−1.41215	−	0.707311i
$705$		0			0
$706$	−21.2215	−	24.7895i	−0.798682	−	0.932964i
$707$	−9.29478	+	9.29478i	−0.349566	+	0.349566i
$708$		0			0
$709$	−23.5307			−0.883713			−0.441856	−	0.897086i	$-0.645680\pi$
$709$	−23.5307			−0.883713			−0.441856	+	0.897086i	$0.645680\pi$
$710$	−8.27650	−	0.902069i	−0.310611	−	0.0338541i
$711$		0			0
$712$	−1.13963	+	4.81999i	−0.0427094	+	0.180637i
$713$	8.73226	+	8.73226i	0.327026	+	0.327026i
$714$		0			0
$715$	−4.10309	−	4.36721i	−0.153447	−	0.163325i
$716$	−2.47764	+	15.8792i	−0.0925937	+	0.593433i
$717$		0			0
$718$	−22.8804	−	1.77429i	−0.853890	−	0.0662160i
$719$	−28.7704			−1.07296			−0.536478	−	0.843914i	$-0.680246\pi$
$719$	−28.7704			−1.07296			−0.536478	+	0.843914i	$0.680246\pi$
$720$		0			0
$721$	4.20635			0.156653
$722$	7.18121	+	0.556876i	0.267257	+	0.0207248i
$723$		0			0
$724$	6.58379	−	42.1955i	0.244685	−	1.56818i
$725$	−33.4773	−	2.08980i	−1.24332	−	0.0776132i
$726$		0			0
$727$	−16.9689	−	16.9689i	−0.629342	−	0.629342i	0.318561	−	0.947902i	$-0.396801\pi$
$727$	−16.9689	−	16.9689i	−0.629342	−	0.629342i	−0.947902	+	0.318561i	$0.896801\pi$
$728$	2.42526	+	0.573423i	0.0898861	+	0.0212525i
$729$		0			0
$730$	−9.33898	+	7.50331i	−0.345651	+	0.277710i
$731$	−18.8779			−0.698225
$732$		0			0
$733$	15.4998	−	15.4998i	0.572499	−	0.572499i	−0.360327	−	0.932826i	$-0.617335\pi$
$733$	15.4998	−	15.4998i	0.572499	−	0.572499i	0.932826	+	0.360327i	$0.117335\pi$
$734$	−2.78994	−	3.25901i	−0.102979	−	0.120292i
$735$		0			0
$736$	23.4326	−	9.86412i	0.863737	−	0.363596i
$737$	28.3281	−	28.3281i	1.04348	−	1.04348i
$738$		0			0
$739$		−	9.34289i		−	0.343684i	−0.985125	−	0.171842i	$-0.945028\pi$
$739$		−	9.34289i		−	0.343684i	0.985125	−	0.171842i	$-0.0549718\pi$
$740$	21.5801	−	14.7461i	0.793301	−	0.542079i
$741$		0			0
$742$	−34.4669	−	2.67278i	−1.26532	−	0.0981209i
$743$	−6.89738	+	6.89738i	−0.253040	+	0.253040i	−0.822216	−	0.569176i	$-0.807262\pi$
$743$	−6.89738	+	6.89738i	−0.253040	+	0.253040i	0.569176	+	0.822216i	$0.307262\pi$
$744$		0			0
$745$	−0.700770	+	22.4737i	−0.0256742	+	0.823371i
$746$	−8.87005	+	7.59338i	−0.324756	+	0.278013i
$747$		0			0
$748$	−19.8898	+	14.5207i	−0.727242	+	0.530929i
$749$	−6.80220			−0.248547
$750$		0			0
$751$			23.0607i			0.841499i	0.907177	+	0.420749i	$0.138233\pi$
$751$			23.0607i			0.841499i	−0.907177	+	0.420749i	$0.861767\pi$
$752$	−18.9461	−	36.7654i	−0.690895	−	1.34070i
$753$		0			0
$754$	3.68710	−	3.15641i	0.134276	−	0.114950i
$755$	−7.25905	−	0.226351i	−0.264184	−	0.00823775i
$756$		0			0
$757$	−4.92349	−	4.92349i	−0.178947	−	0.178947i	0.611950	−	0.790897i	$-0.290386\pi$
$757$	−4.92349	−	4.92349i	−0.178947	−	0.178947i	−0.790897	+	0.611950i	$0.790386\pi$
$758$	3.67653	−	47.4108i	0.133538	−	1.72204i
$759$		0			0
$760$	22.7724	+	6.13960i	0.826040	+	0.222707i
$761$	−22.4172			−0.812621			−0.406311	−	0.913735i	$-0.633185\pi$
$761$	−22.4172			−0.812621			−0.406311	+	0.913735i	$0.633185\pi$
$762$		0			0
$763$	0.140619	+	0.140619i	0.00509075	+	0.00509075i
$764$	−6.02232	+	38.5970i	−0.217880	+	1.39639i
$765$		0			0
$766$	−25.9361	+	22.2031i	−0.937110	+	0.802231i
$767$	−4.09572	−	4.09572i	−0.147888	−	0.147888i
$768$		0			0
$769$		−	50.3148i		−	1.81440i	−0.420701	−	0.907199i	$-0.638216\pi$
$769$		−	50.3148i		−	1.81440i	0.420701	−	0.907199i	$-0.361784\pi$
$770$	22.2398	−	17.8684i	0.801468	−	0.643931i
$771$		0			0
$772$	−4.95198	−	6.78300i	−0.178226	−	0.244126i
$773$	12.8067	−	12.8067i	0.460625	−	0.460625i	−0.438235	−	0.898860i	$-0.644396\pi$
$773$	12.8067	−	12.8067i	0.460625	−	0.460625i	0.898860	+	0.438235i	$0.144396\pi$
$774$		0			0
$775$	0.855953	−	13.7118i	0.0307467	−	0.492543i
$776$	22.6255	−	13.9723i	0.812206	−	0.501578i
$777$		0			0
$778$	−23.6468	−	1.83372i	−0.847778	−	0.0657420i
$779$		−	27.6257i		−	0.989794i
$780$		0			0
$781$		−	13.7910i		−	0.493480i
$782$	1.15513	−	14.8960i	0.0413073	−	0.532680i
$783$		0			0
$784$	4.91553	−	15.3683i	0.175555	−	0.548868i
$785$	9.64081	−	9.05775i	0.344095	−	0.323285i
$786$		0			0
$787$	−28.1921	+	28.1921i	−1.00494	+	1.00494i	−0.00495215	+	0.999988i	$0.501576\pi$
$787$	−28.1921	+	28.1921i	−1.00494	+	1.00494i	−0.999988	+	0.00495215i	$0.998424\pi$
$788$	2.72227	+	3.72885i	0.0969770	+	0.132835i
$789$		0			0
$790$	2.02614	−	18.5899i	0.0720870	−	0.661399i
$791$		−	3.92559i		−	0.139578i
$792$		0			0
$793$	4.83535	+	4.83535i	0.171708	+	0.171708i
$794$	−3.36988	−	3.93646i	−0.119592	−	0.139700i
$795$		0			0
$796$	41.9365	+	6.54338i	1.48640	+	0.231924i
$797$	15.1514	+	15.1514i	0.536689	+	0.536689i	0.922555	−	0.385866i	$-0.126097\pi$
$797$	15.1514	+	15.1514i	0.536689	+	0.536689i	−0.385866	+	0.922555i	$0.626097\pi$
$798$		0			0
$799$	−24.3055			−0.859868
$800$	−25.4771	−	12.2849i	−0.900751	−	0.434335i
$801$		0			0
$802$	−19.9281	−	1.54535i	−0.703687	−	0.0545683i
$803$	−14.0320	−	14.0320i	−0.495178	−	0.495178i
$804$		0			0
$805$	−0.539444	+	17.2999i	−0.0190129	+	0.609742i
$806$	1.29282	+	1.51019i	0.0455378	+	0.0531940i
$807$		0			0
$808$	−4.96713	+	21.0082i	−0.174743	+	0.739065i
$809$			25.8847i			0.910059i	0.890476	+	0.455030i	$0.150371\pi$
$809$			25.8847i			0.910059i	−0.890476	+	0.455030i	$0.849629\pi$
$810$		0			0
$811$	40.2556			1.41357			0.706783	−	0.707431i	$-0.250146\pi$
$811$	40.2556			1.41357			0.706783	+	0.707431i	$0.250146\pi$
$812$	13.6252	+	18.6631i	0.478149	+	0.654947i
$813$		0			0
$814$	28.1559	+	32.8898i	0.986865	+	1.15279i
$815$	−6.97838	+	6.55634i	−0.244442	+	0.229659i
$816$		0			0
$817$	−21.1772	+	21.1772i	−0.740897	+	0.740897i
$818$	−0.359522	+	4.63622i	−0.0125704	+	0.162102i
$819$		0			0
$820$	−6.12512	+	32.5583i	−0.213898	+	1.13698i
$821$		−	46.6073i		−	1.62661i	−0.581840	−	0.813303i	$-0.697667\pi$
$821$		−	46.6073i		−	1.62661i	0.581840	−	0.813303i	$-0.302333\pi$
$822$		0			0
$823$	−6.40117	+	6.40117i	−0.223131	+	0.223131i	−0.809815	−	0.586685i	$-0.800433\pi$
$823$	−6.40117	+	6.40117i	−0.223131	+	0.223131i	0.586685	+	0.809815i	$0.300433\pi$
$824$	5.87756	−	3.62969i	0.204755	−	0.126446i
$825$		0			0
$826$	20.9484	−	17.9333i	0.728889	−	0.623979i
$827$	−12.3618	+	12.3618i	−0.429861	+	0.429861i	−0.888581	−	0.458720i	$-0.848308\pi$
$827$	−12.3618	+	12.3618i	−0.429861	+	0.429861i	0.458720	+	0.888581i	$0.348308\pi$
$828$		0			0
$829$	5.60983			0.194838			0.0974188	−	0.995243i	$-0.468941\pi$
$829$	5.60983			0.194838			0.0974188	+	0.995243i	$0.468941\pi$
$830$	−2.58806	+	2.07935i	−0.0898328	+	0.0721752i
$831$		0			0
$832$	3.88364	−	1.29152i	0.134641	−	0.0447756i
$833$	−6.70481	−	6.70481i	−0.232308	−	0.232308i
$834$		0			0
$835$	11.8330	−	11.1174i	0.409499	−	0.384733i
$836$	−6.02304	+	38.6016i	−0.208311	+	1.33506i
$837$		0			0
$838$	2.27751	−	29.3698i	0.0786754	−	1.01456i
$839$	−3.22857			−0.111462			−0.0557312	−	0.998446i	$-0.517749\pi$
$839$	−3.22857			−0.111462			−0.0557312	+	0.998446i	$0.517749\pi$
$840$		0			0
$841$	16.0038			0.551857
$842$	0.0413459	−	0.533178i	0.00142487	−	0.0183745i
$843$		0			0
$844$	2.87986	+	0.449347i	0.0991289	+	0.0154672i
$845$	−28.4698	−	0.887741i	−0.979391	−	0.0305392i
$846$		0			0
$847$	20.0197	+	20.0197i	0.687885	+	0.687885i
$848$	−50.4672	+	26.0071i	−1.73305	+	0.893086i
$849$		0			0
$850$	−13.2756	+	10.0016i	−0.455349	+	0.343053i
$851$	−26.2673			−0.900430
$852$		0			0
$853$	23.8817	−	23.8817i	0.817692	−	0.817692i	−0.168081	−	0.985773i	$-0.553757\pi$
$853$	23.8817	−	23.8817i	0.817692	−	0.817692i	0.985773	+	0.168081i	$0.0537569\pi$
$854$	−24.7314	+	21.1718i	−0.846292	+	0.724484i
$855$		0			0
$856$	−9.50476	+	5.86966i	−0.324866	+	0.200621i
$857$	10.9520	−	10.9520i	0.374115	−	0.374115i	−0.494859	−	0.868973i	$-0.664780\pi$
$857$	10.9520	−	10.9520i	0.374115	−	0.374115i	0.868973	+	0.494859i	$0.164780\pi$
$858$		0			0
$859$		−	11.8875i		−	0.405596i	−0.979221	−	0.202798i	$-0.934997\pi$
$859$		−	11.8875i		−	0.405596i	0.979221	−	0.202798i	$-0.0650035\pi$
$860$	29.6538	−	20.2630i	1.01119	−	0.690964i
$861$		0			0
$862$	−1.33893	+	17.2662i	−0.0456040	+	0.588088i
$863$	22.9476	−	22.9476i	0.781146	−	0.781146i	−0.198878	−	0.980024i	$-0.563730\pi$
$863$	22.9476	−	22.9476i	0.781146	−	0.781146i	0.980024	+	0.198878i	$0.0637298\pi$
$864$		0			0
$865$	0.812365	+	0.864658i	0.0276212	+	0.0293992i
$866$	−2.16799	−	2.53250i	−0.0736714	−	0.0860578i
$867$		0			0
$868$	−7.64416	+	5.58068i	−0.259460	+	0.189421i
$869$	30.9760			1.05079
$870$		0			0
$871$			3.91269i			0.132576i
$872$	0.317829	+	0.0751468i	0.0107630	+	0.00254479i
$873$		0			0
$874$	−15.4145	−	18.0061i	−0.521403	−	0.609067i
$875$	14.8276	−	12.2847i	0.501264	−	0.415300i
$876$		0			0
$877$	−7.53116	−	7.53116i	−0.254309	−	0.254309i	0.568425	−	0.822735i	$-0.307553\pi$
$877$	−7.53116	−	7.53116i	−0.254309	−	0.254309i	−0.822735	+	0.568425i	$0.807553\pi$
$878$	−52.2565	−	4.05229i	−1.76357	−	0.136758i
$879$		0			0
$880$	15.6571	−	44.1585i	0.527801	−	1.48858i
$881$	30.4673			1.02647			0.513235	−	0.858248i	$-0.328447\pi$
$881$	30.4673			1.02647			0.513235	+	0.858248i	$0.328447\pi$
$882$		0			0
$883$	−39.9926	−	39.9926i	−1.34586	−	1.34586i	−0.890107	−	0.455751i	$-0.849371\pi$
$883$	−39.9926	−	39.9926i	−1.34586	−	1.34586i	−0.455751	−	0.890107i	$-0.650629\pi$
$884$	0.370790	−	2.37639i	0.0124710	−	0.0799267i
$885$		0			0
$886$	27.4429	+	32.0568i	0.921961	+	1.07697i
$887$	26.9715	+	26.9715i	0.905614	+	0.905614i	0.995915	−	0.0903006i	$-0.0287828\pi$
$887$	26.9715	+	26.9715i	0.905614	+	0.905614i	−0.0903006	+	0.995915i	$0.528783\pi$
$888$		0			0
$889$			5.82244i			0.195278i
$890$	−5.50489	−	0.599987i	−0.184524	−	0.0201116i
$891$		0			0
$892$	−30.1183	+	21.9881i	−1.00844	+	0.736216i
$893$	−27.2659	+	27.2659i	−0.912420	+	0.912420i
$894$		0			0
$895$	−17.9595	−	0.560012i	−0.600321	−	0.0187191i
$896$	4.70088	+	18.9096i	0.157045	+	0.631725i
$897$		0			0
$898$	−1.94900	+	25.1334i	−0.0650390	+	0.838712i
$899$			18.4329i			0.614773i
$900$		0			0
$901$			33.3638i			1.11151i
$902$	−54.7137	−	4.24284i	−1.82177	−	0.141271i
$903$		0			0
$904$	−3.38742	−	5.48525i	−0.112664	−	0.182437i
$905$	47.7236	+	1.48811i	1.58638	+	0.0494664i
$906$		0			0
$907$	−29.0296	+	29.0296i	−0.963913	+	0.963913i	−0.999371	−	0.0354583i	$-0.988711\pi$
$907$	−29.0296	+	29.0296i	−0.963913	+	0.963913i	0.0354583	+	0.999371i	$0.488711\pi$
$908$	−6.76763	+	4.94076i	−0.224592	+	0.163965i
$909$		0			0
$910$	−0.301894	+	2.76988i	−0.0100077	+	0.0918206i
$911$			23.8639i			0.790647i	0.918542	+	0.395323i	$0.129367\pi$
$911$			23.8639i			0.790647i	−0.918542	+	0.395323i	$0.870633\pi$
$912$		0			0
$913$	−3.88860	−	3.88860i	−0.128694	−	0.128694i
$914$	26.4962	−	22.6826i	0.876417	−	0.750273i
$915$		0			0
$916$	46.8334	+	7.30745i	1.54742	+	0.241445i
$917$	6.84562	+	6.84562i	0.226062	+	0.226062i
$918$		0			0
$919$	45.2701			1.49332			0.746661	−	0.665204i	$-0.231656\pi$
$919$	45.2701			1.49332			0.746661	+	0.665204i	$0.231656\pi$
$920$	14.1745	+	24.6388i	0.467318	+	0.812317i
$921$		0			0
$922$	1.62893	−	21.0060i	0.0536461	−	0.691795i
$923$	0.952407	+	0.952407i	0.0313488	+	0.0313488i
$924$		0			0
$925$	19.3357	+	21.9105i	0.635754	+	0.720412i
$926$	−11.3586	+	9.72375i	−0.373267	+	0.319542i
$927$		0			0
$928$	35.1431	+	14.3209i	1.15363	+	0.470106i
$929$			26.7024i			0.876077i	0.898956	+	0.438038i	$0.144327\pi$
$929$			26.7024i			0.876077i	−0.898956	+	0.438038i	$0.855673\pi$
$930$		0			0
$931$	−15.0429			−0.493011
$932$	−9.02801	−	12.3662i	−0.295722	−	0.405067i
$933$		0			0
$934$	20.1370	−	17.2387i	0.658904	−	0.564067i
$935$	−18.8525	−	20.0661i	−0.616544	−	0.656231i
$936$		0			0
$937$	14.5936	−	14.5936i	0.476752	−	0.476752i	−0.427339	−	0.904091i	$-0.640549\pi$
$937$	14.5936	−	14.5936i	0.476752	−	0.476752i	0.904091	+	0.427339i	$0.140549\pi$
$938$	−18.5721	−	1.44019i	−0.606400	−	0.0470240i
$939$		0			0
$940$	38.1796	−	26.0889i	1.24528	−	0.850926i
$941$			16.6141i			0.541603i	0.962635	+	0.270802i	$0.0872887\pi$
$941$			16.6141i			0.541603i	−0.962635	+	0.270802i	$0.912711\pi$
$942$		0			0
$943$	23.5427	−	23.5427i	0.766654	−	0.766654i
$944$	13.7966	−	43.1349i	0.449042	−	1.40392i
$945$		0			0
$946$	38.6897	+	45.1947i	1.25791	+	1.46941i
$947$	42.3488	−	42.3488i	1.37615	−	1.37615i	0.525128	−	0.851023i	$-0.324018\pi$
$947$	42.3488	−	42.3488i	1.37615	−	1.37615i	0.851023	−	0.525128i	$-0.175982\pi$
$948$		0			0
$949$	1.93810			0.0629135
$950$	−3.67274	+	26.1123i	−0.119159	+	0.847196i
$951$		0			0
$952$	11.1434	+	2.63471i	0.361158	+	0.0853915i
$953$	−24.6483	−	24.6483i	−0.798436	−	0.798436i	0.184413	−	0.982849i	$-0.440962\pi$
$953$	−24.6483	−	24.6483i	−0.798436	−	0.798436i	−0.982849	+	0.184413i	$0.940962\pi$
$954$		0			0
$955$	−43.6537	−	1.36120i	−1.41260	−	0.0440475i
$956$	−36.4420	−	5.68608i	−1.17862	−	0.183901i
$957$		0			0
$958$	22.5074	+	1.74536i	0.727180	+	0.0563901i
$959$	−27.7728			−0.896831
$960$		0			0
$961$	23.4501			0.756456
$962$	−4.21583	−	0.326922i	−0.135924	−	0.0105404i
$963$		0			0
$964$	−39.9261	−	6.22970i	−1.28593	−	0.200645i
$965$	6.84314	−	6.42928i	0.220288	−	0.206966i
$966$		0			0
$967$	−0.316328	−	0.316328i	−0.0101724	−	0.0101724i	0.702002	−	0.712175i	$-0.252290\pi$
$967$	−0.316328	−	0.316328i	−0.0101724	−	0.0101724i	−0.712175	+	0.702002i	$0.752290\pi$
$968$	45.2488	+	10.6985i	1.45435	+	0.343864i
$969$		0			0
$970$	18.6213	+	23.1769i	0.597893	+	0.744166i
$971$	36.8392			1.18223			0.591113	−	0.806588i	$-0.298689\pi$
$971$	36.8392			1.18223			0.591113	+	0.806588i	$0.298689\pi$
$972$		0			0
$973$	−4.62833	+	4.62833i	−0.148377	+	0.148377i
$974$	36.2216	+	42.3116i	1.16062	+	1.35575i
$975$		0			0
$976$	−16.2881	+	50.9244i	−0.521369	+	1.63005i
$977$	−18.8490	+	18.8490i	−0.603034	+	0.603034i	−0.941116	−	0.338083i	$-0.890222\pi$
$977$	−18.8490	+	18.8490i	−0.603034	+	0.603034i	0.338083	+	0.941116i	$0.390222\pi$
$978$		0			0
$979$		−	9.17269i		−	0.293161i
$980$	17.7288	+	3.33528i	0.566326	+	0.106542i
$981$		0			0
$982$	32.7349	+	2.53847i	1.04461	+	0.0810057i
$983$	28.1727	−	28.1727i	0.898568	−	0.898568i	−0.0967414	−	0.995310i	$-0.530842\pi$
$983$	28.1727	−	28.1727i	0.898568	−	0.898568i	0.995310	+	0.0967414i	$0.0308420\pi$
$984$		0			0
$985$	−3.76190	+	3.53439i	−0.119864	+	0.112615i
$986$	16.9412	−	14.5028i	0.539517	−	0.461864i
$987$		0			0
$988$	−2.24988	−	3.08179i	−0.0715783	−	0.0980446i
$989$	−36.0945			−1.14774
$990$		0			0
$991$		−	29.4982i		−	0.937043i	−0.883452	−	0.468521i	$-0.844787\pi$
$991$		−	29.4982i		−	0.937043i	0.883452	−	0.468521i	$-0.155213\pi$
$992$	−5.86563	+	14.3941i	−0.186234	+	0.457014i
$993$		0			0
$994$	−4.87129	+	4.17016i	−0.154508	+	0.132269i
$995$	−1.47898	+	47.4307i	−0.0468867	+	1.50365i
$996$		0			0
$997$	23.9484	+	23.9484i	0.758455	+	0.758455i	0.976041	−	0.217586i	$-0.0698183\pi$
$997$	23.9484	+	23.9484i	0.758455	+	0.758455i	−0.217586	+	0.976041i	$0.569818\pi$
$998$	−0.575400	+	7.42009i	−0.0182140	+	0.234879i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.w.e.163.12		24
3.2	odd	2		120.2.v.a.43.1	✓	24
4.3	odd	2		1440.2.bi.e.1423.6		24
5.2	odd	4	inner	360.2.w.e.307.7		24
8.3	odd	2	inner	360.2.w.e.163.7		24
8.5	even	2		1440.2.bi.e.1423.7		24
12.11	even	2		480.2.bh.a.463.4		24
15.2	even	4		120.2.v.a.67.6	yes	24
15.8	even	4		600.2.v.b.307.7		24
15.14	odd	2		600.2.v.b.43.12		24
20.7	even	4		1440.2.bi.e.847.7		24
24.5	odd	2		480.2.bh.a.463.3		24
24.11	even	2		120.2.v.a.43.6	yes	24
40.27	even	4	inner	360.2.w.e.307.12		24
40.37	odd	4		1440.2.bi.e.847.6		24
60.23	odd	4		2400.2.bh.b.1807.9		24
60.47	odd	4		480.2.bh.a.367.3		24
60.59	even	2		2400.2.bh.b.943.10		24
120.29	odd	2		2400.2.bh.b.943.9		24
120.53	even	4		2400.2.bh.b.1807.10		24
120.59	even	2		600.2.v.b.43.7		24
120.77	even	4		480.2.bh.a.367.4		24
120.83	odd	4		600.2.v.b.307.12		24
120.107	odd	4		120.2.v.a.67.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.1	✓	24	3.2	odd	2
120.2.v.a.43.6	yes	24	24.11	even	2
120.2.v.a.67.1	yes	24	120.107	odd	4
120.2.v.a.67.6	yes	24	15.2	even	4
360.2.w.e.163.7		24	8.3	odd	2	inner
360.2.w.e.163.12		24	1.1	even	1	trivial
360.2.w.e.307.7		24	5.2	odd	4	inner
360.2.w.e.307.12		24	40.27	even	4	inner
480.2.bh.a.367.3		24	60.47	odd	4
480.2.bh.a.367.4		24	120.77	even	4
480.2.bh.a.463.3		24	24.5	odd	2
480.2.bh.a.463.4		24	12.11	even	2
600.2.v.b.43.7		24	120.59	even	2
600.2.v.b.43.12		24	15.14	odd	2
600.2.v.b.307.7		24	15.8	even	4
600.2.v.b.307.12		24	120.83	odd	4
1440.2.bi.e.847.6		24	40.37	odd	4
1440.2.bi.e.847.7		24	20.7	even	4
1440.2.bi.e.1423.6		24	4.3	odd	2
1440.2.bi.e.1423.7		24	8.5	even	2
2400.2.bh.b.943.9		24	120.29	odd	2
2400.2.bh.b.943.10		24	60.59	even	2
2400.2.bh.b.1807.9		24	60.23	odd	4
2400.2.bh.b.1807.10		24	120.53	even	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40998 + 0.109339i) q^{2} +(1.97609 + 0.308331i) q^{4} +(-0.0696909 + 2.23498i) q^{5} +(1.21782 + 1.21782i) q^{7} +(2.75254 + 0.650804i) q^{8} +O(q^{10})\)	\(q+(1.40998 + 0.109339i) q^{2} +(1.97609 + 0.308331i) q^{4} +(-0.0696909 + 2.23498i) q^{5} +(1.21782 + 1.21782i) q^{7} +(2.75254 + 0.650804i) q^{8} +(-0.342633 + 3.14366i) q^{10} -5.23822 q^{11} +(0.361752 - 0.361752i) q^{13} +(1.58395 + 1.85026i) q^{14} +(3.80986 + 1.21858i) q^{16} +(1.66215 - 1.66215i) q^{17} -3.72919i q^{19} +(-0.826829 + 4.39504i) q^{20} +(-7.38579 - 0.572740i) q^{22} +(3.17802 - 3.17802i) q^{23} +(-4.99029 - 0.311516i) q^{25} +(0.549617 - 0.470510i) q^{26} +(2.03103 + 2.78202i) q^{28} +6.70849 q^{29} +2.74770i q^{31} +(5.23860 + 2.13474i) q^{32} +(2.52533 - 2.16186i) q^{34} +(-2.80668 + 2.63694i) q^{35} +(-4.13265 - 4.13265i) q^{37} +(0.407745 - 5.25809i) q^{38} +(-1.64636 + 6.10651i) q^{40} +7.40796 q^{41} +(-5.67877 - 5.67877i) q^{43} +(-10.3512 - 1.61511i) q^{44} +(4.82843 - 4.13347i) q^{46} +(-7.31149 - 7.31149i) q^{47} -4.03382i q^{49} +(-7.00215 - 0.984863i) q^{50} +(0.826395 - 0.603316i) q^{52} +(-10.0364 + 10.0364i) q^{53} +(0.365056 - 11.7073i) q^{55} +(2.55953 + 4.14466i) q^{56} +(9.45884 + 0.733498i) q^{58} -11.3219i q^{59} +13.3665i q^{61} +(-0.300430 + 3.87421i) q^{62} +(7.15291 + 3.58272i) q^{64} +(0.783299 + 0.833721i) q^{65} +(-5.40796 + 5.40796i) q^{67} +(3.79705 - 2.77206i) q^{68} +(-4.24568 + 3.41115i) q^{70} +2.63276i q^{71} +(2.67877 + 2.67877i) q^{73} +(-5.37509 - 6.27881i) q^{74} +(1.14983 - 7.36922i) q^{76} +(-6.37922 - 6.37922i) q^{77} -5.91346 q^{79} +(-2.98901 + 8.43005i) q^{80} +(10.4451 + 0.809977i) q^{82} +(0.742352 + 0.742352i) q^{83} +(3.59903 + 3.83071i) q^{85} +(-7.38605 - 8.62787i) q^{86} +(-14.4184 - 3.40905i) q^{88} +1.75111i q^{89} +0.881100 q^{91} +(7.25994 - 5.30017i) q^{92} +(-9.50962 - 11.1085i) q^{94} +(8.33468 + 0.259891i) q^{95} +(6.64801 - 6.64801i) q^{97} +(0.441053 - 5.68761i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 8 q^{10} - 20 q^{16} - 8 q^{17} + 20 q^{20} - 28 q^{22} - 8 q^{25} + 16 q^{26} + 4 q^{28} - 20 q^{32} + 48 q^{35} - 40 q^{38} + 8 q^{40} - 32 q^{43} + 48 q^{46} - 56 q^{50} - 48 q^{52} + 32 q^{56} - 12 q^{58} + 16 q^{62} + 8 q^{65} + 48 q^{67} - 72 q^{68} + 4 q^{70} - 40 q^{73} + 48 q^{76} - 76 q^{80} + 24 q^{82} - 80 q^{83} + 32 q^{86} + 12 q^{88} + 64 q^{91} - 16 q^{92} - 24 q^{97} + 88 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 8 * q^10 - 20 * q^16 - 8 * q^17 + 20 * q^20 - 28 * q^22 - 8 * q^25 + 16 * q^26 + 4 * q^28 - 20 * q^32 + 48 * q^35 - 40 * q^38 + 8 * q^40 - 32 * q^43 + 48 * q^46 - 56 * q^50 - 48 * q^52 + 32 * q^56 - 12 * q^58 + 16 * q^62 + 8 * q^65 + 48 * q^67 - 72 * q^68 + 4 * q^70 - 40 * q^73 + 48 * q^76 - 76 * q^80 + 24 * q^82 - 80 * q^83 + 32 * q^86 + 12 * q^88 + 64 * q^91 - 16 * q^92 - 24 * q^97 + 88 * q^98

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