LMFDB - Embedded newform 260.2.p.c.103.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(103,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("260.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.p (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.3317760000.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 7x^{4} + 16 $ x^8 - 7*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			103.4
Root			$1.40294 + 0.178197i$ of defining polynomial
Character	$\chi$	$=$	260.103
Dual form			260.2.p.c.207.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40294 + 0.178197i) q^{2} +(1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(2.44949 - 2.44949i) q^{7} +(2.62769 + 1.04655i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(1.40294 + 0.178197i) q^{2} +(1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(2.44949 - 2.44949i) q^{7} +(2.62769 + 1.04655i) q^{8} +3.00000i q^{9} +(-1.93649 - 2.50000i) q^{10} +2.44949 q^{11} +(-3.58114 - 0.418861i) q^{13} +(3.87298 - 3.00000i) q^{14} +(3.50000 + 1.93649i) q^{16} +(-1.00000 + 1.00000i) q^{17} +(-0.534591 + 4.20883i) q^{18} -2.44949i q^{19} +(-2.27129 - 3.85243i) q^{20} +(3.43649 + 0.436492i) q^{22} +(-3.87298 + 3.87298i) q^{23} +5.00000i q^{25} +(-4.94949 - 1.22579i) q^{26} +(5.96816 - 3.51867i) q^{28} +2.00000i q^{29} -9.79796 q^{31} +(4.56522 + 3.34047i) q^{32} +(-1.58114 + 1.22474i) q^{34} -7.74597 q^{35} +(-1.50000 + 5.80948i) q^{36} +(-6.32456 - 6.32456i) q^{37} +(0.436492 - 3.43649i) q^{38} +(-2.50000 - 5.80948i) q^{40} +6.32456i q^{41} +(7.74597 - 7.74597i) q^{43} +(4.74342 + 1.22474i) q^{44} +(4.74342 - 4.74342i) q^{45} +(-6.12372 + 4.74342i) q^{46} +(2.44949 - 2.44949i) q^{47} -5.00000i q^{49} +(-0.890985 + 7.01471i) q^{50} +(-6.72541 - 2.60169i) q^{52} +(2.00000 + 2.00000i) q^{53} +(-3.87298 - 3.87298i) q^{55} +(9.00000 - 3.87298i) q^{56} +(-0.356394 + 2.80588i) q^{58} +7.34847i q^{59} -6.00000 q^{61} +(-13.7460 - 1.74597i) q^{62} +(7.34847 + 7.34847i) q^{63} +(5.80948 + 5.50000i) q^{64} +(5.00000 + 6.32456i) q^{65} +(2.44949 - 2.44949i) q^{67} +(-2.43649 + 1.43649i) q^{68} +(-10.8671 - 1.38031i) q^{70} -4.89898 q^{71} +(-3.13964 + 7.88306i) q^{72} +(-3.16228 + 3.16228i) q^{73} +(-7.74597 - 10.0000i) q^{74} +(1.22474 - 4.74342i) q^{76} +(6.00000 - 6.00000i) q^{77} +7.74597 q^{79} +(-2.47212 - 8.59585i) q^{80} -9.00000 q^{81} +(-1.12702 + 8.87298i) q^{82} +(-4.89898 - 4.89898i) q^{83} +3.16228 q^{85} +(12.2474 - 9.48683i) q^{86} +(6.43649 + 2.56351i) q^{88} +12.6491 q^{89} +(7.50000 - 5.80948i) q^{90} +(-9.79796 + 7.74597i) q^{91} +(-9.43649 + 5.56351i) q^{92} +(3.87298 - 3.00000i) q^{94} +(-3.87298 + 3.87298i) q^{95} +(3.16228 + 3.16228i) q^{97} +(0.890985 - 7.01471i) q^{98} +7.34847i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 16 q^{13} + 28 q^{16} - 8 q^{17} + 12 q^{22} - 20 q^{26} - 12 q^{36} - 12 q^{38} - 20 q^{40} + 8 q^{52} + 16 q^{53} + 72 q^{56} - 48 q^{61} - 48 q^{62} + 40 q^{65} - 4 q^{68} + 48 q^{77} - 72 q^{81} - 40 q^{82} + 36 q^{88} + 60 q^{90} - 60 q^{92}+O(q^{100}) $ 8 * q - 16 * q^13 + 28 * q^16 - 8 * q^17 + 12 * q^22 - 20 * q^26 - 12 * q^36 - 12 * q^38 - 20 * q^40 + 8 * q^52 + 16 * q^53 + 72 * q^56 - 48 * q^61 - 48 * q^62 + 40 * q^65 - 4 * q^68 + 48 * q^77 - 72 * q^81 - 40 * q^82 + 36 * q^88 + 60 * q^90 - 60 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.40294	+	0.178197i	0.992030	+	0.126004i
$2$	1.40294	+	0.178197i	0.992030	+	0.126004i
$3$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$3$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$4$	1.93649	+	0.500000i	0.968246	+	0.250000i
$5$	−1.58114	−	1.58114i	−0.707107	−	0.707107i
$5$	−1.58114	−	1.58114i	−0.707107	−	0.707107i
$6$		0			0
$7$	2.44949	−	2.44949i	0.925820	−	0.925820i	−0.0716124	−	0.997433i	$-0.522814\pi$
$7$	2.44949	−	2.44949i	0.925820	−	0.925820i	0.997433	+	0.0716124i	$0.0228145\pi$
$8$	2.62769	+	1.04655i	0.929028	+	0.370011i
$9$			3.00000i			1.00000i
$10$	−1.93649	−	2.50000i	−0.612372	−	0.790569i
$11$	2.44949			0.738549			0.369274	−	0.929320i	$-0.379606\pi$
$11$	2.44949			0.738549			0.369274	+	0.929320i	$0.379606\pi$
$12$		0			0
$13$	−3.58114	−	0.418861i	−0.993229	−	0.116171i
$13$	−3.58114	−	0.418861i	−0.993229	−	0.116171i
$14$	3.87298	−	3.00000i	1.03510	−	0.801784i
$15$		0			0
$16$	3.50000	+	1.93649i	0.875000	+	0.484123i
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	−0.817898	−	0.575363i	$-0.804861\pi$
$17$	−1.00000	+	1.00000i	−0.242536	+	0.242536i	0.575363	+	0.817898i	$0.304861\pi$
$18$	−0.534591	+	4.20883i	−0.126004	+	0.992030i
$19$		−	2.44949i		−	0.561951i	−0.959715	−	0.280976i	$-0.909342\pi$
$19$		−	2.44949i		−	0.561951i	0.959715	−	0.280976i	$-0.0906580\pi$
$20$	−2.27129	−	3.85243i	−0.507877	−	0.861430i
$21$		0			0
$22$	3.43649	+	0.436492i	0.732662	+	0.0930603i
$23$	−3.87298	+	3.87298i	−0.807573	+	0.807573i	−0.984266	−	0.176693i	$-0.943460\pi$
$23$	−3.87298	+	3.87298i	−0.807573	+	0.807573i	0.176693	+	0.984266i	$0.443460\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$	−4.94949	−	1.22579i	−0.970675	−	0.240396i
$27$		0			0
$28$	5.96816	−	3.51867i	1.12788	−	0.664966i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$		0			0
$31$	−9.79796			−1.75977			−0.879883	−	0.475191i	$-0.842379\pi$
$31$	−9.79796			−1.75977			−0.879883	+	0.475191i	$0.842379\pi$
$32$	4.56522	+	3.34047i	0.807024	+	0.590518i
$33$		0			0
$34$	−1.58114	+	1.22474i	−0.271163	+	0.210042i
$35$	−7.74597			−1.30931
$36$	−1.50000	+	5.80948i	−0.250000	+	0.968246i
$37$	−6.32456	−	6.32456i	−1.03975	−	1.03975i	−0.999177	−	0.0405740i	$-0.987081\pi$
$37$	−6.32456	−	6.32456i	−1.03975	−	1.03975i	−0.0405740	−	0.999177i	$-0.512919\pi$
$38$	0.436492	−	3.43649i	0.0708083	−	0.557473i
$39$		0			0
$40$	−2.50000	−	5.80948i	−0.395285	−	0.918559i
$41$			6.32456i			0.987730i	0.869539	+	0.493865i	$0.164416\pi$
$41$			6.32456i			0.987730i	−0.869539	+	0.493865i	$0.835584\pi$
$42$		0			0
$43$	7.74597	−	7.74597i	1.18125	−	1.18125i	0.201828	−	0.979421i	$-0.435312\pi$
$43$	7.74597	−	7.74597i	1.18125	−	1.18125i	0.979421	−	0.201828i	$-0.0646881\pi$
$44$	4.74342	+	1.22474i	0.715097	+	0.184637i
$45$	4.74342	−	4.74342i	0.707107	−	0.707107i
$46$	−6.12372	+	4.74342i	−0.902894	+	0.699379i
$47$	2.44949	−	2.44949i	0.357295	−	0.357295i	−0.505520	−	0.862815i	$-0.668699\pi$
$47$	2.44949	−	2.44949i	0.357295	−	0.357295i	0.862815	+	0.505520i	$0.168699\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	−0.890985	+	7.01471i	−0.126004	+	0.992030i
$51$		0			0
$52$	−6.72541	−	2.60169i	−0.932647	−	0.360790i
$53$	2.00000	+	2.00000i	0.274721	+	0.274721i	0.830997	−	0.556276i	$-0.187770\pi$
$53$	2.00000	+	2.00000i	0.274721	+	0.274721i	−0.556276	+	0.830997i	$0.687770\pi$
$54$		0			0
$55$	−3.87298	−	3.87298i	−0.522233	−	0.522233i
$56$	9.00000	−	3.87298i	1.20268	−	0.517549i
$57$		0			0
$58$	−0.356394	+	2.80588i	−0.0467968	+	0.368431i
$59$			7.34847i			0.956689i	0.878172	+	0.478345i	$0.158763\pi$
$59$			7.34847i			0.956689i	−0.878172	+	0.478345i	$0.841237\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	−13.7460	−	1.74597i	−1.74574	−	0.221738i
$63$	7.34847	+	7.34847i	0.925820	+	0.925820i
$64$	5.80948	+	5.50000i	0.726184	+	0.687500i
$65$	5.00000	+	6.32456i	0.620174	+	0.784465i
$66$		0			0
$67$	2.44949	−	2.44949i	0.299253	−	0.299253i	−0.541468	−	0.840721i	$-0.682131\pi$
$67$	2.44949	−	2.44949i	0.299253	−	0.299253i	0.840721	+	0.541468i	$0.182131\pi$
$68$	−2.43649	+	1.43649i	−0.295468	+	0.174200i
$69$		0			0
$70$	−10.8671	−	1.38031i	−1.29887	−	0.164978i
$71$	−4.89898			−0.581402			−0.290701	−	0.956814i	$-0.593888\pi$
$71$	−4.89898			−0.581402			−0.290701	+	0.956814i	$0.593888\pi$
$72$	−3.13964	+	7.88306i	−0.370011	+	0.929028i
$73$	−3.16228	+	3.16228i	−0.370117	+	0.370117i	−0.867520	−	0.497403i	$-0.834287\pi$
$73$	−3.16228	+	3.16228i	−0.370117	+	0.370117i	0.497403	+	0.867520i	$0.334287\pi$
$74$	−7.74597	−	10.0000i	−0.900450	−	1.16248i
$75$		0			0
$76$	1.22474	−	4.74342i	0.140488	−	0.544107i
$77$	6.00000	−	6.00000i	0.683763	−	0.683763i
$78$		0			0
$79$	7.74597			0.871489			0.435745	−	0.900070i	$-0.356485\pi$
$79$	7.74597			0.871489			0.435745	+	0.900070i	$0.356485\pi$
$80$	−2.47212	−	8.59585i	−0.276392	−	0.961045i
$81$	−9.00000			−1.00000
$82$	−1.12702	+	8.87298i	−0.124458	+	0.979857i
$83$	−4.89898	−	4.89898i	−0.537733	−	0.537733i	0.385130	−	0.922862i	$-0.374157\pi$
$83$	−4.89898	−	4.89898i	−0.537733	−	0.537733i	−0.922862	+	0.385130i	$0.874157\pi$
$84$		0			0
$85$	3.16228			0.342997
$86$	12.2474	−	9.48683i	1.32068	−	1.02299i
$87$		0			0
$88$	6.43649	+	2.56351i	0.686132	+	0.273271i
$89$	12.6491			1.34080			0.670402	−	0.741999i	$-0.266122\pi$
$89$	12.6491			1.34080			0.670402	+	0.741999i	$0.266122\pi$
$90$	7.50000	−	5.80948i	0.790569	−	0.612372i
$91$	−9.79796	+	7.74597i	−1.02711	+	0.811998i
$92$	−9.43649	+	5.56351i	−0.983822	+	0.580036i
$93$		0			0
$94$	3.87298	−	3.00000i	0.399468	−	0.309426i
$95$	−3.87298	+	3.87298i	−0.397360	+	0.397360i
$96$		0			0
$97$	3.16228	+	3.16228i	0.321081	+	0.321081i	0.849182	−	0.528101i	$-0.177096\pi$
$97$	3.16228	+	3.16228i	0.321081	+	0.321081i	−0.528101	+	0.849182i	$0.677096\pi$
$98$	0.890985	−	7.01471i	0.0900031	−	0.708593i
$99$			7.34847i			0.738549i
$100$	−2.50000	+	9.68246i	−0.250000	+	0.968246i
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$		0			0
$103$	11.6190	−	11.6190i	1.14485	−	1.14485i	0.157298	−	0.987551i	$-0.449722\pi$
$103$	11.6190	−	11.6190i	1.14485	−	1.14485i	0.987551	−	0.157298i	$-0.0502783\pi$
$104$	−8.97175	−	4.84847i	−0.879753	−	0.475432i
$105$		0			0
$106$	2.44949	+	3.16228i	0.237915	+	0.307148i
$107$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$107$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$108$		0			0
$109$	3.16228			0.302891			0.151446	−	0.988466i	$-0.451607\pi$
$109$	3.16228			0.302891			0.151446	+	0.988466i	$0.451607\pi$
$110$	−4.74342	−	6.12372i	−0.452267	−	0.583874i
$111$		0			0
$112$	13.3166	−	3.82980i	1.25830	−	0.361882i
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	0.143065	−	0.989713i	$-0.454304\pi$
$113$	−9.00000	−	9.00000i	−0.846649	−	0.846649i	−0.989713	+	0.143065i	$0.954304\pi$
$114$		0			0
$115$	12.2474			1.14208
$116$	−1.00000	+	3.87298i	−0.0928477	+	0.359597i
$117$	1.25658	−	10.7434i	0.116171	−	0.993229i
$118$	−1.30948	+	10.3095i	−0.120547	+	0.949064i
$119$			4.89898i			0.449089i
$120$		0			0
$121$	−5.00000			−0.454545
$122$	−8.41765	−	1.06918i	−0.762098	−	0.0967992i
$123$		0			0
$124$	−18.9737	−	4.89898i	−1.70389	−	0.439941i
$125$	7.90569	−	7.90569i	0.707107	−	0.707107i
$126$	9.00000	+	11.6190i	0.801784	+	1.03510i
$127$	11.6190	+	11.6190i	1.03102	+	1.03102i	0.999503	+	0.0315117i	$0.0100322\pi$
$127$	11.6190	+	11.6190i	1.03102	+	1.03102i	0.0315117	+	0.999503i	$0.489968\pi$
$128$	7.17027	+	8.75141i	0.633769	+	0.773523i
$129$		0			0
$130$	5.88769	+	9.76397i	0.516385	+	0.856357i
$131$			7.74597i			0.676768i	0.941008	+	0.338384i	$0.109880\pi$
$131$			7.74597i			0.676768i	−0.941008	+	0.338384i	$0.890120\pi$
$132$		0			0
$133$	−6.00000	−	6.00000i	−0.520266	−	0.520266i
$134$	3.87298	−	3.00000i	0.334575	−	0.259161i
$135$		0			0
$136$	−3.67423	+	1.58114i	−0.315063	+	0.135582i
$137$	−3.16228	−	3.16228i	−0.270172	−	0.270172i	0.558998	−	0.829169i	$-0.311186\pi$
$137$	−3.16228	−	3.16228i	−0.270172	−	0.270172i	−0.829169	+	0.558998i	$0.811186\pi$
$138$		0			0
$139$	−7.74597			−0.657004			−0.328502	−	0.944503i	$-0.606544\pi$
$139$	−7.74597			−0.657004			−0.328502	+	0.944503i	$0.606544\pi$
$140$	−15.0000	−	3.87298i	−1.26773	−	0.327327i
$141$		0			0
$142$	−6.87298	−	0.872983i	−0.576768	−	0.0732591i
$143$	−8.77196	−	1.02600i	−0.733548	−	0.0857981i
$144$	−5.80948	+	10.5000i	−0.484123	+	0.875000i
$145$	3.16228	−	3.16228i	0.262613	−	0.262613i
$146$	−5.00000	+	3.87298i	−0.413803	+	0.320530i
$147$		0			0
$148$	−9.08517	−	15.4097i	−0.746796	−	1.26667i
$149$	−15.8114			−1.29532			−0.647660	−	0.761930i	$-0.724252\pi$
$149$	−15.8114			−1.29532			−0.647660	+	0.761930i	$0.724252\pi$
$150$		0			0
$151$	14.6969			1.19602			0.598010	−	0.801489i	$-0.295958\pi$
$151$	14.6969			1.19602			0.598010	+	0.801489i	$0.295958\pi$
$152$	2.56351	−	6.43649i	0.207928	−	0.522068i
$153$	−3.00000	−	3.00000i	−0.242536	−	0.242536i
$154$	9.48683	−	7.34847i	0.764471	−	0.592157i
$155$	15.4919	+	15.4919i	1.24434	+	1.24434i
$156$		0			0
$157$	14.0000	−	14.0000i	1.11732	−	1.11732i	0.125189	−	0.992133i	$-0.460046\pi$
$157$	14.0000	−	14.0000i	1.11732	−	1.11732i	0.992133	−	0.125189i	$-0.0399536\pi$
$158$	10.8671	+	1.38031i	0.864543	+	0.109811i
$159$		0			0
$160$	−1.93649	−	12.5000i	−0.153093	−	0.988212i
$161$			18.9737i			1.49533i
$162$	−12.6265	−	1.60377i	−0.992030	−	0.126004i
$163$	−14.6969	−	14.6969i	−1.15115	−	1.15115i	−0.986322	−	0.164831i	$-0.947292\pi$
$163$	−14.6969	−	14.6969i	−1.15115	−	1.15115i	−0.164831	−	0.986322i	$-0.552708\pi$
$164$	−3.16228	+	12.2474i	−0.246932	+	0.956365i
$165$		0			0
$166$	−6.00000	−	7.74597i	−0.465690	−	0.601204i
$167$	7.34847	−	7.34847i	0.568642	−	0.568642i	−0.363106	−	0.931748i	$-0.618284\pi$
$167$	7.34847	−	7.34847i	0.568642	−	0.568642i	0.931748	+	0.363106i	$0.118284\pi$
$168$		0			0
$169$	12.6491	+	3.00000i	0.973009	+	0.230769i
$170$	4.43649	+	0.563508i	0.340263	+	0.0432191i
$171$	7.34847			0.561951
$172$	18.8730	−	11.1270i	1.43905	−	0.848427i
$173$	12.0000	+	12.0000i	0.912343	+	0.912343i	0.996456	−	0.0841131i	$-0.0268057\pi$
$173$	12.0000	+	12.0000i	0.912343	+	0.912343i	−0.0841131	+	0.996456i	$0.526806\pi$
$174$		0			0
$175$	12.2474	+	12.2474i	0.925820	+	0.925820i
$176$	8.57321	+	4.74342i	0.646230	+	0.357548i
$177$		0			0
$178$	17.7460	+	2.25403i	1.33012	+	0.168947i
$179$	7.74597			0.578961			0.289480	−	0.957184i	$-0.406518\pi$
$179$	7.74597			0.578961			0.289480	+	0.957184i	$0.406518\pi$
$180$	11.5573	−	6.81388i	0.861430	−	0.507877i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	−15.1263	+	9.12117i	−1.12123	+	0.676106i
$183$		0			0
$184$	−14.2302	+	6.12372i	−1.04907	+	0.451447i
$185$			20.0000i			1.47043i
$186$		0			0
$187$	−2.44949	+	2.44949i	−0.179124	+	0.179124i
$188$	5.96816	−	3.51867i	0.435273	−	0.256626i
$189$		0			0
$190$	−6.12372	+	4.74342i	−0.444262	+	0.344124i
$191$		−	23.2379i		−	1.68144i	−0.541474	−	0.840718i	$-0.682133\pi$
$191$		−	23.2379i		−	1.68144i	0.541474	−	0.840718i	$-0.317867\pi$
$192$		0			0
$193$	3.16228	−	3.16228i	0.227626	−	0.227626i	−0.584074	−	0.811700i	$-0.698542\pi$
$193$	3.16228	−	3.16228i	0.227626	−	0.227626i	0.811700	+	0.584074i	$0.198542\pi$
$194$	3.87298	+	5.00000i	0.278064	+	0.358979i
$195$		0			0
$196$	2.50000	−	9.68246i	0.178571	−	0.691604i
$197$	−6.32456	−	6.32456i	−0.450606	−	0.450606i	0.444950	−	0.895556i	$-0.353222\pi$
$197$	−6.32456	−	6.32456i	−0.450606	−	0.450606i	−0.895556	+	0.444950i	$0.853222\pi$
$198$	−1.30948	+	10.3095i	−0.0930603	+	0.732662i
$199$	−15.4919			−1.09819			−0.549097	−	0.835759i	$-0.685028\pi$
$199$	−15.4919			−1.09819			−0.549097	+	0.835759i	$0.685028\pi$
$200$	−5.23274	+	13.1384i	−0.370011	+	0.929028i
$201$		0			0
$202$	19.6412	+	2.49476i	1.38195	+	0.175531i
$203$	4.89898	+	4.89898i	0.343841	+	0.343841i
$204$		0			0
$205$	10.0000	−	10.0000i	0.698430	−	0.698430i
$206$	18.3712	−	14.2302i	1.27998	−	0.991468i
$207$	−11.6190	−	11.6190i	−0.807573	−	0.807573i
$208$	−11.7229	−	8.40086i	−0.812834	−	0.582495i
$209$		−	6.00000i		−	0.415029i
$210$		0			0
$211$		−	23.2379i		−	1.59976i	−0.600158	−	0.799882i	$-0.704896\pi$
$211$		−	23.2379i		−	1.59976i	0.600158	−	0.799882i	$-0.295104\pi$
$212$	2.87298	+	4.87298i	0.197317	+	0.334678i
$213$		0			0
$214$		0			0
$215$	−24.4949			−1.67054
$216$		0			0
$217$	−24.0000	+	24.0000i	−1.62923	+	1.62923i
$218$	4.43649	+	0.563508i	0.300477	+	0.0381656i
$219$		0			0
$220$	−5.56351	−	9.43649i	−0.375092	−	0.636208i
$221$	4.00000	−	3.16228i	0.269069	−	0.212718i
$222$		0			0
$223$	−2.44949	−	2.44949i	−0.164030	−	0.164030i	0.620319	−	0.784349i	$-0.287003\pi$
$223$	−2.44949	−	2.44949i	−0.164030	−	0.164030i	−0.784349	+	0.620319i	$0.787003\pi$
$224$	19.3649	−	3.00000i	1.29387	−	0.200446i
$225$	−15.0000			−1.00000
$226$	−11.0227	−	14.2302i	−0.733219	−	0.946582i
$227$	−9.79796	+	9.79796i	−0.650313	+	0.650313i	−0.953068	−	0.302755i	$-0.902094\pi$
$227$	−9.79796	+	9.79796i	−0.650313	+	0.650313i	0.302755	+	0.953068i	$0.402094\pi$
$228$		0			0
$229$	−9.48683			−0.626908			−0.313454	−	0.949603i	$-0.601486\pi$
$229$	−9.48683			−0.626908			−0.313454	+	0.949603i	$0.601486\pi$
$230$	17.1825	+	2.18246i	1.13298	+	0.143907i
$231$		0			0
$232$	−2.09310	+	5.25537i	−0.137418	+	0.345032i
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$	3.67736	−	14.8485i	0.240396	−	0.970675i
$235$	−7.74597			−0.505291
$236$	−3.67423	+	14.2302i	−0.239172	+	0.926310i
$237$		0			0
$238$	−0.872983	+	6.87298i	−0.0565871	+	0.445509i
$239$		−	4.89898i		−	0.316889i	−0.987368	−	0.158444i	$-0.949352\pi$
$239$		−	4.89898i		−	0.316889i	0.987368	−	0.158444i	$-0.0506478\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−7.01471	−	0.890985i	−0.450923	−	0.0572747i
$243$		0			0
$244$	−11.6190	−	3.00000i	−0.743827	−	0.192055i
$245$	−7.90569	+	7.90569i	−0.505076	+	0.505076i
$246$		0			0
$247$	−1.02600	+	8.77196i	−0.0652826	+	0.558147i
$248$	−25.7460	−	10.2540i	−1.63487	−	0.651132i
$249$		0			0
$250$	12.5000	−	9.68246i	0.790569	−	0.612372i
$251$		−	7.74597i		−	0.488921i	−0.969659	−	0.244461i	$-0.921389\pi$
$251$		−	7.74597i		−	0.488921i	0.969659	−	0.244461i	$-0.0786109\pi$
$252$	10.5560	+	17.9045i	0.664966	+	1.12788i
$253$	−9.48683	+	9.48683i	−0.596432	+	0.596432i
$254$	14.2302	+	18.3712i	0.892885	+	1.15271i
$255$		0			0
$256$	8.50000	+	13.5554i	0.531250	+	0.847215i
$257$	9.00000	−	9.00000i	0.561405	−	0.561405i	−0.368302	−	0.929706i	$-0.620061\pi$
$257$	9.00000	−	9.00000i	0.561405	−	0.561405i	0.929706	+	0.368302i	$0.120061\pi$
$258$		0			0
$259$	−30.9839			−1.92524
$260$	6.52018	+	14.7474i	0.404364	+	0.914598i
$261$	−6.00000			−0.371391
$262$	−1.38031	+	10.8671i	−0.0852757	+	0.671374i
$263$	−19.3649	+	19.3649i	−1.19409	+	1.19409i	−0.218184	+	0.975908i	$0.570013\pi$
$263$	−19.3649	+	19.3649i	−1.19409	+	1.19409i	−0.975908	+	0.218184i	$0.929987\pi$
$264$		0			0
$265$		−	6.32456i		−	0.388514i
$266$	−7.34847	−	9.48683i	−0.450564	−	0.581675i
$267$		0			0
$268$	5.96816	−	3.51867i	0.364563	−	0.214937i
$269$			22.0000i			1.34136i	0.741745	+	0.670682i	$0.233998\pi$
$269$			22.0000i			1.34136i	−0.741745	+	0.670682i	$0.766002\pi$
$270$		0			0
$271$	−9.79796			−0.595184			−0.297592	−	0.954693i	$-0.596183\pi$
$271$	−9.79796			−0.595184			−0.297592	+	0.954693i	$0.596183\pi$
$272$	−5.43649	+	1.56351i	−0.329636	+	0.0948016i
$273$		0			0
$274$	−3.87298	−	5.00000i	−0.233975	−	0.302061i
$275$			12.2474i			0.738549i
$276$		0			0
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	−0.905347	−	0.424673i	$-0.860389\pi$
$277$	−8.00000	+	8.00000i	−0.480673	+	0.480673i	0.424673	+	0.905347i	$0.360389\pi$
$278$	−10.8671	−	1.38031i	−0.651768	−	0.0827854i
$279$		−	29.3939i		−	1.75977i
$280$	−20.3540	−	8.10653i	−1.21638	−	0.484458i
$281$			6.32456i			0.377291i	0.982045	+	0.188646i	$0.0604098\pi$
$281$			6.32456i			0.377291i	−0.982045	+	0.188646i	$0.939590\pi$
$282$		0			0
$283$	−7.74597	+	7.74597i	−0.460450	+	0.460450i	−0.898803	−	0.438353i	$-0.855562\pi$
$283$	−7.74597	+	7.74597i	−0.460450	+	0.460450i	0.438353	+	0.898803i	$0.355562\pi$
$284$	−9.48683	−	2.44949i	−0.562940	−	0.145350i
$285$		0			0
$286$	−12.1237	−	3.00255i	−0.716891	−	0.177545i
$287$	15.4919	+	15.4919i	0.914460	+	0.914460i
$288$	−10.0214	+	13.6957i	−0.590518	+	0.807024i
$289$			15.0000i			0.882353i
$290$	5.00000	−	3.87298i	0.293610	−	0.227429i
$291$		0			0
$292$	−7.70486	+	4.54259i	−0.450893	+	0.265835i
$293$	−12.6491	+	12.6491i	−0.738969	+	0.738969i	−0.972379	−	0.233410i	$-0.925012\pi$
$293$	−12.6491	+	12.6491i	−0.738969	+	0.738969i	0.233410	+	0.972379i	$0.425012\pi$
$294$		0			0
$295$	11.6190	−	11.6190i	0.676481	−	0.676481i
$296$	−10.0000	−	23.2379i	−0.581238	−	1.35068i
$297$		0			0
$298$	−22.1825	−	2.81754i	−1.28500	−	0.163216i
$299$	15.4919	−	12.2474i	0.895922	−	0.708288i
$300$		0			0
$301$		−	37.9473i		−	2.18725i
$302$	20.6190	+	2.61895i	1.18649	+	0.150704i
$303$		0			0
$304$	4.74342	−	8.57321i	0.272054	−	0.491708i
$305$	9.48683	+	9.48683i	0.543214	+	0.543214i
$306$	−3.67423	−	4.74342i	−0.210042	−	0.271163i
$307$	19.5959	−	19.5959i	1.11840	−	1.11840i	0.126421	−	0.991977i	$-0.459651\pi$
$307$	19.5959	−	19.5959i	1.11840	−	1.11840i	0.991977	−	0.126421i	$-0.0403492\pi$
$308$	14.6190	−	8.61895i	0.832992	−	0.491110i
$309$		0			0
$310$	18.9737	+	24.4949i	1.07763	+	1.39122i
$311$			23.2379i			1.31770i	0.752274	+	0.658850i	$0.228957\pi$
$311$			23.2379i			1.31770i	−0.752274	+	0.658850i	$0.771043\pi$
$312$		0			0
$313$	7.00000	+	7.00000i	0.395663	+	0.395663i	0.876700	−	0.481037i	$-0.159740\pi$
$313$	7.00000	+	7.00000i	0.395663	+	0.395663i	−0.481037	+	0.876700i	$0.659740\pi$
$314$	22.1359	−	17.1464i	1.24920	−	0.967629i
$315$		−	23.2379i		−	1.30931i
$316$	15.0000	+	3.87298i	0.843816	+	0.217872i
$317$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$317$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$318$		0			0
$319$			4.89898i			0.274290i
$320$	−0.489323	−	17.8819i	−0.0273540	−	0.999626i
$321$		0			0
$322$	−3.38105	+	26.6190i	−0.188419	+	1.48342i
$323$	2.44949	+	2.44949i	0.136293	+	0.136293i
$324$	−17.4284	−	4.50000i	−0.968246	−	0.250000i
$325$	2.09431	−	17.9057i	0.116171	−	0.993229i
$326$	−18.0000	−	23.2379i	−0.996928	−	1.28703i
$327$		0			0
$328$	−6.61895	+	16.6190i	−0.365470	+	0.917628i
$329$		−	12.0000i		−	0.661581i
$330$		0			0
$331$	7.34847			0.403908			0.201954	−	0.979395i	$-0.435271\pi$
$331$	7.34847			0.403908			0.201954	+	0.979395i	$0.435271\pi$
$332$	−7.03734	−	11.9363i	−0.386224	−	0.655091i
$333$	18.9737	−	18.9737i	1.03975	−	1.03975i
$334$	11.6190	−	9.00000i	0.635761	−	0.492458i
$335$	−7.74597			−0.423207
$336$		0			0
$337$	−1.00000	+	1.00000i	−0.0544735	+	0.0544735i	−0.733819	−	0.679345i	$-0.762264\pi$
$337$	−1.00000	+	1.00000i	−0.0544735	+	0.0544735i	0.679345	+	0.733819i	$0.262264\pi$
$338$	17.2114	+	6.46286i	0.936175	+	0.351533i
$339$		0			0
$340$	6.12372	+	1.58114i	0.332106	+	0.0857493i
$341$	−24.0000			−1.29967
$342$	10.3095	+	1.30948i	0.557473	+	0.0708083i
$343$	4.89898	+	4.89898i	0.264520	+	0.264520i
$344$	28.4605	−	12.2474i	1.53449	−	0.660338i
$345$		0			0
$346$	14.6969	+	18.9737i	0.790112	+	1.02003i
$347$	−15.4919	−	15.4919i	−0.831651	−	0.831651i	0.156092	−	0.987743i	$-0.450110\pi$
$347$	−15.4919	−	15.4919i	−0.831651	−	0.831651i	−0.987743	+	0.156092i	$0.950110\pi$
$348$		0			0
$349$	−3.16228			−0.169273			−0.0846364	−	0.996412i	$-0.526973\pi$
$349$	−3.16228			−0.169273			−0.0846364	+	0.996412i	$0.526973\pi$
$350$	15.0000	+	19.3649i	0.801784	+	1.03510i
$351$		0			0
$352$	11.1825	+	8.18246i	0.596027	+	0.436126i
$353$	−9.48683	+	9.48683i	−0.504933	+	0.504933i	−0.912967	−	0.408034i	$-0.866215\pi$
$353$	−9.48683	+	9.48683i	−0.504933	+	0.504933i	0.408034	+	0.912967i	$0.366215\pi$
$354$		0			0
$355$	7.74597	+	7.74597i	0.411113	+	0.411113i
$356$	24.4949	+	6.32456i	1.29823	+	0.335201i
$357$		0			0
$358$	10.8671	+	1.38031i	0.574346	+	0.0729515i
$359$			19.5959i			1.03423i	0.855915	+	0.517116i	$0.172995\pi$
$359$			19.5959i			1.03423i	−0.855915	+	0.517116i	$0.827005\pi$
$360$	17.4284	−	7.50000i	0.918559	−	0.395285i
$361$	13.0000			0.684211
$362$	−8.41765	−	1.06918i	−0.442422	−	0.0561950i
$363$		0			0
$364$	−22.8466	+	10.1010i	−1.19749	+	0.529437i
$365$	10.0000			0.523424
$366$		0			0
$367$	−3.87298	−	3.87298i	−0.202168	−	0.202168i	0.598760	−	0.800928i	$-0.295660\pi$
$367$	−3.87298	−	3.87298i	−0.202168	−	0.202168i	−0.800928	+	0.598760i	$0.795660\pi$
$368$	−21.0554	+	6.05544i	−1.09759	+	0.315662i
$369$	−18.9737			−0.987730
$370$	−3.56394	+	28.0588i	−0.185280	+	1.45871i
$371$	9.79796			0.508685
$372$		0			0
$373$	2.00000	+	2.00000i	0.103556	+	0.103556i	0.756987	−	0.653430i	$-0.226671\pi$
$373$	2.00000	+	2.00000i	0.103556	+	0.103556i	−0.653430	+	0.756987i	$0.726671\pi$
$374$	−3.87298	+	3.00000i	−0.200267	+	0.155126i
$375$		0			0
$376$	9.00000	−	3.87298i	0.464140	−	0.199734i
$377$	0.837722	−	7.16228i	0.0431449	−	0.368876i
$378$		0			0
$379$		−	17.1464i		−	0.880753i	−0.897813	−	0.440376i	$-0.854845\pi$
$379$		−	17.1464i		−	0.880753i	0.897813	−	0.440376i	$-0.145155\pi$
$380$	−9.43649	+	5.56351i	−0.484082	+	0.285402i
$381$		0			0
$382$	4.14092	−	32.6014i	0.211868	−	1.66803i
$383$	−2.44949	−	2.44949i	−0.125163	−	0.125163i	0.641750	−	0.766914i	$-0.278208\pi$
$383$	−2.44949	−	2.44949i	−0.125163	−	0.125163i	−0.766914	+	0.641750i	$0.778208\pi$
$384$		0			0
$385$	−18.9737			−0.966988
$386$	5.00000	−	3.87298i	0.254493	−	0.197130i
$387$	23.2379	+	23.2379i	1.18125	+	1.18125i
$388$	4.54259	+	7.70486i	0.230615	+	0.391155i
$389$		−	14.0000i		−	0.709828i	−0.934899	−	0.354914i	$-0.884510\pi$
$389$		−	14.0000i		−	0.709828i	0.934899	−	0.354914i	$-0.115490\pi$
$390$		0			0
$391$		−	7.74597i		−	0.391730i
$392$	5.23274	−	13.1384i	0.264293	−	0.663591i
$393$		0			0
$394$	−7.74597	−	10.0000i	−0.390236	−	0.503793i
$395$	−12.2474	−	12.2474i	−0.616236	−	0.616236i
$396$	−3.67423	+	14.2302i	−0.184637	+	0.715097i
$397$	15.8114	+	15.8114i	0.793551	+	0.793551i	0.982070	−	0.188519i	$-0.0603686\pi$
$397$	15.8114	+	15.8114i	0.793551	+	0.793551i	−0.188519	+	0.982070i	$0.560369\pi$
$398$	−21.7343	−	2.76062i	−1.08944	−	0.138377i
$399$		0			0
$400$	−9.68246	+	17.5000i	−0.484123	+	0.875000i
$401$			12.6491i			0.631666i	0.948815	+	0.315833i	$0.102284\pi$
$401$			12.6491i			0.631666i	−0.948815	+	0.315833i	$0.897716\pi$
$402$		0			0
$403$	35.0879	+	4.10398i	1.74785	+	0.204434i
$404$	27.1109	+	7.00000i	1.34882	+	0.348263i
$405$	14.2302	+	14.2302i	0.707107	+	0.707107i
$406$	6.00000	+	7.74597i	0.297775	+	0.384426i
$407$	−15.4919	−	15.4919i	−0.767907	−	0.767907i
$408$		0			0
$409$	25.2982			1.25092			0.625458	−	0.780258i	$-0.284912\pi$
$409$	25.2982			1.25092			0.625458	+	0.780258i	$0.284912\pi$
$410$	15.8114	−	12.2474i	0.780869	−	0.604858i
$411$		0			0
$412$	28.3095	−	16.6905i	1.39471	−	0.822283i
$413$	18.0000	+	18.0000i	0.885722	+	0.885722i
$414$	−14.2302	−	18.3712i	−0.699379	−	0.902894i
$415$			15.4919i			0.760469i
$416$	−14.9495	−	13.8749i	−0.732959	−	0.680273i
$417$		0			0
$418$	1.06918	−	8.41765i	0.0522954	−	0.411721i
$419$	23.2379			1.13525			0.567623	−	0.823289i	$-0.307863\pi$
$419$	23.2379			1.13525			0.567623	+	0.823289i	$0.307863\pi$
$420$		0			0
$421$		−	9.48683i		−	0.462360i	−0.972911	−	0.231180i	$-0.925741\pi$
$421$		−	9.48683i		−	0.462360i	0.972911	−	0.231180i	$-0.0742586\pi$
$422$	4.14092	−	32.6014i	0.201577	−	1.58701i
$423$	7.34847	+	7.34847i	0.357295	+	0.357295i
$424$	3.16228	+	7.34847i	0.153574	+	0.356873i
$425$	−5.00000	−	5.00000i	−0.242536	−	0.242536i
$426$		0			0
$427$	−14.6969	+	14.6969i	−0.711235	+	0.711235i
$428$		0			0
$429$		0			0
$430$	−34.3649	−	4.36492i	−1.65722	−	0.210495i
$431$	19.5959			0.943902			0.471951	−	0.881625i	$-0.343550\pi$
$431$	19.5959			0.943902			0.471951	+	0.881625i	$0.343550\pi$
$432$		0			0
$433$	−19.0000	−	19.0000i	−0.913082	−	0.913082i	0.0834318	−	0.996513i	$-0.473412\pi$
$433$	−19.0000	−	19.0000i	−0.913082	−	0.913082i	−0.996513	+	0.0834318i	$0.973412\pi$
$434$	−37.9473	+	29.3939i	−1.82153	+	1.41095i
$435$		0			0
$436$	6.12372	+	1.58114i	0.293273	+	0.0757228i
$437$	9.48683	+	9.48683i	0.453817	+	0.453817i
$438$		0			0
$439$	23.2379			1.10908			0.554542	−	0.832156i	$-0.312893\pi$
$439$	23.2379			1.10908			0.554542	+	0.832156i	$0.312893\pi$
$440$	−6.12372	−	14.2302i	−0.291937	−	0.678401i
$441$	15.0000			0.714286
$442$	6.17528	−	3.72370i	0.293728	−	0.177119i
$443$	−23.2379	+	23.2379i	−1.10407	+	1.10407i	−0.110151	+	0.993915i	$0.535133\pi$
$443$	−23.2379	+	23.2379i	−1.10407	+	1.10407i	−0.993915	+	0.110151i	$0.964867\pi$
$444$		0			0
$445$	−20.0000	−	20.0000i	−0.948091	−	0.948091i
$446$	−3.00000	−	3.87298i	−0.142054	−	0.183391i
$447$		0			0
$448$	27.7024	−	0.758056i	1.30882	−	0.0358148i
$449$	−6.32456			−0.298474			−0.149237	−	0.988801i	$-0.547682\pi$
$449$	−6.32456			−0.298474			−0.149237	+	0.988801i	$0.547682\pi$
$450$	−21.0441	−	2.67295i	−0.992030	−	0.126004i
$451$			15.4919i			0.729487i
$452$	−12.9284	−	21.9284i	−0.608102	−	1.03143i
$453$		0			0
$454$	−15.4919	+	12.0000i	−0.727072	+	0.563188i
$455$	27.7394	+	3.24448i	1.30044	+	0.152104i
$456$		0			0
$457$	22.1359	+	22.1359i	1.03548	+	1.03548i	0.999347	+	0.0361286i	$0.0115026\pi$
$457$	22.1359	+	22.1359i	1.03548	+	1.03548i	0.0361286	+	0.999347i	$0.488497\pi$
$458$	−13.3095	−	1.69052i	−0.621911	−	0.0789930i
$459$		0			0
$460$	23.7171	+	6.12372i	1.10581	+	0.285520i
$461$		−	34.7851i		−	1.62010i	−0.586360	−	0.810051i	$-0.699440\pi$
$461$		−	34.7851i		−	1.62010i	0.586360	−	0.810051i	$-0.300560\pi$
$462$		0			0
$463$	−17.1464	−	17.1464i	−0.796862	−	0.796862i	0.185737	−	0.982599i	$-0.440533\pi$
$463$	−17.1464	−	17.1464i	−0.796862	−	0.796862i	−0.982599	+	0.185737i	$0.940533\pi$
$464$	−3.87298	+	7.00000i	−0.179799	+	0.324967i
$465$		0			0
$466$	1.22474	+	1.58114i	0.0567352	+	0.0732448i
$467$	−7.74597	−	7.74597i	−0.358441	−	0.358441i	0.504797	−	0.863238i	$-0.331567\pi$
$467$	−7.74597	−	7.74597i	−0.358441	−	0.358441i	−0.863238	+	0.504797i	$0.831567\pi$
$468$	7.80507	−	20.1762i	0.360790	−	0.932647i
$469$		−	12.0000i		−	0.554109i
$470$	−10.8671	−	1.38031i	−0.501264	−	0.0636689i
$471$		0			0
$472$	−7.69052	+	19.3095i	−0.353985	+	0.888791i
$473$	18.9737	−	18.9737i	0.872410	−	0.872410i
$474$		0			0
$475$	12.2474			0.561951
$476$	−2.44949	+	9.48683i	−0.112272	+	0.434828i
$477$	−6.00000	+	6.00000i	−0.274721	+	0.274721i
$478$	0.872983	−	6.87298i	0.0399293	−	0.314363i
$479$		−	4.89898i		−	0.223840i	−0.993717	−	0.111920i	$-0.964300\pi$
$479$		−	4.89898i		−	0.223840i	0.993717	−	0.111920i	$-0.0357001\pi$
$480$		0			0
$481$	20.0000	+	25.2982i	0.911922	+	1.15350i
$482$		0			0
$483$		0			0
$484$	−9.68246	−	2.50000i	−0.440112	−	0.113636i
$485$		−	10.0000i		−	0.454077i
$486$		0			0
$487$	−22.0454	+	22.0454i	−0.998973	+	0.998973i	−0.999999	−	0.00102669i	$-0.999673\pi$
$487$	−22.0454	+	22.0454i	−0.998973	+	0.998973i	0.00102669	+	0.999999i	$0.499673\pi$
$488$	−15.7661	−	6.27929i	−0.713699	−	0.284250i
$489$		0			0
$490$	−12.5000	+	9.68246i	−0.564692	+	0.437409i
$491$		−	7.74597i		−	0.349571i	−0.984607	−	0.174785i	$-0.944077\pi$
$491$		−	7.74597i		−	0.349571i	0.984607	−	0.174785i	$-0.0559231\pi$
$492$		0			0
$493$	−2.00000	−	2.00000i	−0.0900755	−	0.0900755i
$494$	−3.00255	+	12.1237i	−0.135091	+	0.545472i
$495$	11.6190	−	11.6190i	0.522233	−	0.522233i
$496$	−34.2929	−	18.9737i	−1.53979	−	0.851943i
$497$	−12.0000	+	12.0000i	−0.538274	+	0.538274i
$498$		0			0
$499$			31.8434i			1.42550i	0.701416	+	0.712752i	$0.252552\pi$
$499$			31.8434i			1.42550i	−0.701416	+	0.712752i	$0.747448\pi$
$500$	19.2622	−	11.3565i	0.861430	−	0.507877i
$501$		0			0
$502$	1.38031	−	10.8671i	0.0616062	−	0.485024i
$503$	19.3649	−	19.3649i	0.863439	−	0.863439i	−0.128297	−	0.991736i	$-0.540951\pi$
$503$	19.3649	−	19.3649i	0.863439	−	0.863439i	0.991736	+	0.128297i	$0.0409510\pi$
$504$	11.6190	+	27.0000i	0.517549	+	1.20268i
$505$	−22.1359	−	22.1359i	−0.985037	−	0.985037i
$506$	−15.0000	+	11.6190i	−0.666831	+	0.516525i
$507$		0			0
$508$	16.6905	+	28.3095i	0.740522	+	1.25603i
$509$	−3.16228			−0.140165			−0.0700827	−	0.997541i	$-0.522326\pi$
$509$	−3.16228			−0.140165			−0.0700827	+	0.997541i	$0.522326\pi$
$510$		0			0
$511$			15.4919i			0.685323i
$512$	9.50947	+	20.5322i	0.420263	+	0.907402i
$513$		0			0
$514$	14.2302	−	11.0227i	0.627669	−	0.486191i
$515$	−36.7423			−1.61906
$516$		0			0
$517$	6.00000	−	6.00000i	0.263880	−	0.263880i
$518$	−43.4686	−	5.52123i	−1.90990	−	0.242589i
$519$		0			0
$520$	6.51948	+	21.8517i	0.285898	+	0.958260i
$521$	32.0000			1.40195			0.700973	−	0.713188i	$-0.252749\pi$
$521$	32.0000			1.40195			0.700973	+	0.713188i	$0.252749\pi$
$522$	−8.41765	−	1.06918i	−0.368431	−	0.0467968i
$523$	−7.74597	+	7.74597i	−0.338707	+	0.338707i	−0.855881	−	0.517173i	$-0.826984\pi$
$523$	−7.74597	+	7.74597i	−0.338707	+	0.338707i	0.517173	+	0.855881i	$0.326984\pi$
$524$	−3.87298	+	15.0000i	−0.169192	+	0.655278i
$525$		0			0
$526$	−30.6186	+	23.7171i	−1.33504	+	1.03411i
$527$	9.79796	−	9.79796i	0.426806	−	0.426806i
$528$		0			0
$529$		−	7.00000i		−	0.304348i
$530$	1.12702	−	8.87298i	0.0489545	−	0.385418i
$531$	−22.0454			−0.956689
$532$	−8.61895	−	14.6190i	−0.373679	−	0.633812i
$533$	2.64911	−	22.6491i	0.114746	−	0.981042i
$534$		0			0
$535$		0			0
$536$	9.00000	−	3.87298i	0.388741	−	0.167287i
$537$		0			0
$538$	−3.92033	+	30.8647i	−0.169018	+	1.33067i
$539$		−	12.2474i		−	0.527535i
$540$		0			0
$541$			3.16228i			0.135957i	0.997687	+	0.0679785i	$0.0216549\pi$
$541$			3.16228i			0.135957i	−0.997687	+	0.0679785i	$0.978345\pi$
$542$	−13.7460	−	1.74597i	−0.590440	−	0.0749957i
$543$		0			0
$544$	−7.90569	+	1.22474i	−0.338954	+	0.0525105i
$545$	−5.00000	−	5.00000i	−0.214176	−	0.214176i
$546$		0			0
$547$	7.74597	+	7.74597i	0.331194	+	0.331194i	0.853040	−	0.521846i	$-0.174756\pi$
$547$	7.74597	+	7.74597i	0.331194	+	0.331194i	−0.521846	+	0.853040i	$0.674756\pi$
$548$	−4.54259	−	7.70486i	−0.194050	−	0.329135i
$549$		−	18.0000i		−	0.768221i
$550$	−2.18246	+	17.1825i	−0.0930603	+	0.732662i
$551$	4.89898			0.208704
$552$		0			0
$553$	18.9737	−	18.9737i	0.806842	−	0.806842i
$554$	−12.6491	+	9.79796i	−0.537409	+	0.416275i
$555$		0			0
$556$	−15.0000	−	3.87298i	−0.636142	−	0.164251i
$557$	9.48683	+	9.48683i	0.401970	+	0.401970i	0.878927	−	0.476957i	$-0.158260\pi$
$557$	9.48683	+	9.48683i	0.401970	+	0.401970i	−0.476957	+	0.878927i	$0.658260\pi$
$558$	5.23790	−	41.2379i	0.221738	−	1.74574i
$559$	−30.9839	+	24.4949i	−1.31048	+	1.03602i
$560$	−27.1109	−	15.0000i	−1.14564	−	0.633866i
$561$		0			0
$562$	−1.12702	+	8.87298i	−0.0475403	+	0.374284i
$563$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$563$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$564$		0			0
$565$			28.4605i			1.19734i
$566$	−12.2474	+	9.48683i	−0.514799	+	0.398761i
$567$	−22.0454	+	22.0454i	−0.925820	+	0.925820i
$568$	−12.8730	−	5.12702i	−0.540138	−	0.215125i
$569$		−	28.0000i		−	1.17382i	−0.809652	−	0.586911i	$-0.800344\pi$
$569$		−	28.0000i		−	1.17382i	0.809652	−	0.586911i	$-0.199656\pi$
$570$		0			0
$571$			7.74597i			0.324159i	0.986778	+	0.162079i	$0.0518200\pi$
$571$			7.74597i			0.324159i	−0.986778	+	0.162079i	$0.948180\pi$
$572$	−16.4738	−	6.37281i	−0.688806	−	0.266461i
$573$		0			0
$574$	18.9737	+	24.4949i	0.791946	+	1.02240i
$575$	−19.3649	−	19.3649i	−0.807573	−	0.807573i
$576$	−16.5000	+	17.4284i	−0.687500	+	0.726184i
$577$	3.16228	+	3.16228i	0.131647	+	0.131647i	0.769860	−	0.638213i	$-0.220326\pi$
$577$	3.16228	+	3.16228i	0.131647	+	0.131647i	−0.638213	+	0.769860i	$0.720326\pi$
$578$	−2.67295	+	21.0441i	−0.111180	+	0.875320i
$579$		0			0
$580$	7.70486	−	4.54259i	0.319927	−	0.188621i
$581$	−24.0000			−0.995688
$582$		0			0
$583$	4.89898	+	4.89898i	0.202895	+	0.202895i
$584$	−11.6190	+	5.00000i	−0.480796	+	0.206901i
$585$	−18.9737	+	15.0000i	−0.784465	+	0.620174i
$586$	−20.0000	+	15.4919i	−0.826192	+	0.639966i
$587$	−22.0454	+	22.0454i	−0.909911	+	0.909911i	−0.996265	−	0.0863532i	$-0.972479\pi$
$587$	−22.0454	+	22.0454i	−0.909911	+	0.909911i	0.0863532	+	0.996265i	$0.472479\pi$
$588$		0			0
$589$			24.0000i			0.988903i
$590$	18.3712	−	14.2302i	0.756329	−	0.585850i
$591$		0			0
$592$	−9.88849	−	34.3834i	−0.406415	−	1.41315i
$593$	−3.16228	+	3.16228i	−0.129859	+	0.129859i	−0.769049	−	0.639190i	$-0.779270\pi$
$593$	−3.16228	+	3.16228i	−0.129859	+	0.129859i	0.639190	+	0.769049i	$0.279270\pi$
$594$		0			0
$595$	7.74597	−	7.74597i	0.317554	−	0.317554i
$596$	−30.6186	−	7.90569i	−1.25419	−	0.323830i
$597$		0			0
$598$	23.9167	−	14.4218i	0.978028	−	0.589753i
$599$	15.4919			0.632983			0.316492	−	0.948595i	$-0.397495\pi$
$599$	15.4919			0.632983			0.316492	+	0.948595i	$0.397495\pi$
$600$		0			0
$601$	24.0000			0.978980			0.489490	−	0.872009i	$-0.337183\pi$
$601$	24.0000			0.978980			0.489490	+	0.872009i	$0.337183\pi$
$602$	6.76210	−	53.2379i	0.275603	−	2.16981i
$603$	7.34847	+	7.34847i	0.299253	+	0.299253i
$604$	28.4605	+	7.34847i	1.15804	+	0.299005i
$605$	7.90569	+	7.90569i	0.321412	+	0.321412i
$606$		0			0
$607$	−19.3649	−	19.3649i	−0.785998	−	0.785998i	0.194838	−	0.980835i	$-0.437582\pi$
$607$	−19.3649	−	19.3649i	−0.785998	−	0.785998i	−0.980835	+	0.194838i	$0.937582\pi$
$608$	8.18246	−	11.1825i	0.331843	−	0.453509i
$609$		0			0
$610$	11.6190	+	15.0000i	0.470438	+	0.607332i
$611$	−9.79796	+	7.74597i	−0.396383	+	0.313368i
$612$	−4.30948	−	7.30948i	−0.174200	−	0.295468i
$613$	−12.6491	+	12.6491i	−0.510893	+	0.510893i	−0.914800	−	0.403907i	$-0.867652\pi$
$613$	−12.6491	+	12.6491i	−0.510893	+	0.510893i	0.403907	+	0.914800i	$0.367652\pi$
$614$	30.9839	−	24.0000i	1.25041	−	0.968561i
$615$		0			0
$616$	22.0454	−	9.48683i	0.888235	−	0.382235i
$617$	−9.48683	−	9.48683i	−0.381926	−	0.381926i	0.489870	−	0.871796i	$-0.337044\pi$
$617$	−9.48683	−	9.48683i	−0.381926	−	0.381926i	−0.871796	+	0.489870i	$0.837044\pi$
$618$		0			0
$619$		−	2.44949i		−	0.0984533i	−0.998788	−	0.0492267i	$-0.984324\pi$
$619$		−	2.44949i		−	0.0984533i	0.998788	−	0.0492267i	$-0.0156757\pi$
$620$	22.2540	+	37.7460i	0.893743	+	1.51591i
$621$		0			0
$622$	−4.14092	+	32.6014i	−0.166036	+	1.30720i
$623$	30.9839	−	30.9839i	1.24134	−	1.24134i
$624$		0			0
$625$	−25.0000			−1.00000
$626$	8.57321	+	11.0680i	0.342655	+	0.442365i
$627$		0			0
$628$	34.1109	−	20.1109i	1.36117	−	0.802512i
$629$	12.6491			0.504353
$630$	4.14092	−	32.6014i	0.164978	−	1.29887i
$631$	44.0908			1.75523			0.877614	−	0.479368i	$-0.159134\pi$
$631$	44.0908			1.75523			0.877614	+	0.479368i	$0.159134\pi$
$632$	20.3540	+	8.10653i	0.809638	+	0.322460i
$633$		0			0
$634$		0			0
$635$		−	36.7423i		−	1.45808i
$636$		0			0
$637$	−2.09431	+	17.9057i	−0.0829794	+	0.709449i
$638$	−0.872983	+	6.87298i	−0.0345617	+	0.272104i
$639$		−	14.6969i		−	0.581402i
$640$	2.50000	−	25.1744i	0.0988212	−	0.995105i
$641$	4.00000			0.157991			0.0789953	−	0.996875i	$-0.474829\pi$
$641$	4.00000			0.157991			0.0789953	+	0.996875i	$0.474829\pi$
$642$		0			0
$643$	−2.44949	−	2.44949i	−0.0965984	−	0.0965984i	0.657156	−	0.753755i	$-0.271759\pi$
$643$	−2.44949	−	2.44949i	−0.0965984	−	0.0965984i	−0.753755	+	0.657156i	$0.771759\pi$
$644$	−9.48683	+	36.7423i	−0.373834	+	1.44785i
$645$		0			0
$646$	3.00000	+	3.87298i	0.118033	+	0.152380i
$647$	−19.3649	−	19.3649i	−0.761313	−	0.761313i	0.215246	−	0.976560i	$-0.430945\pi$
$647$	−19.3649	−	19.3649i	−0.761313	−	0.761313i	−0.976560	+	0.215246i	$0.930945\pi$
$648$	−23.6492	−	9.41893i	−0.929028	−	0.370011i
$649$			18.0000i			0.706562i
$650$	6.12893	−	24.7474i	0.240396	−	0.970675i
$651$		0			0
$652$	−21.1120	−	35.8090i	−0.826811	−	1.40239i
$653$	32.0000	+	32.0000i	1.25226	+	1.25226i	0.954706	+	0.297551i	$0.0961698\pi$
$653$	32.0000	+	32.0000i	1.25226	+	1.25226i	0.297551	+	0.954706i	$0.403830\pi$
$654$		0			0
$655$	12.2474	−	12.2474i	0.478547	−	0.478547i
$656$	−12.2474	+	22.1359i	−0.478183	+	0.864263i
$657$	−9.48683	−	9.48683i	−0.370117	−	0.370117i
$658$	2.13836	−	16.8353i	0.0833621	−	0.656308i
$659$	−7.74597			−0.301740			−0.150870	−	0.988554i	$-0.548207\pi$
$659$	−7.74597			−0.301740			−0.150870	+	0.988554i	$0.548207\pi$
$660$		0			0
$661$			34.7851i			1.35298i	0.736451	+	0.676491i	$0.236500\pi$
$661$			34.7851i			1.35298i	−0.736451	+	0.676491i	$0.763500\pi$
$662$	10.3095	+	1.30948i	0.400689	+	0.0508942i
$663$		0			0
$664$	−7.74597	−	18.0000i	−0.300602	−	0.698535i
$665$			18.9737i			0.735767i
$666$	30.0000	−	23.2379i	1.16248	−	0.900450i
$667$	−7.74597	−	7.74597i	−0.299925	−	0.299925i
$668$	17.9045	−	10.5560i	0.692745	−	0.408424i
$669$		0			0
$670$	−10.8671	−	1.38031i	−0.419834	−	0.0533259i
$671$	−14.6969			−0.567369
$672$		0			0
$673$	−13.0000	−	13.0000i	−0.501113	−	0.501113i	0.410671	−	0.911784i	$-0.365295\pi$
$673$	−13.0000	−	13.0000i	−0.501113	−	0.501113i	−0.911784	+	0.410671i	$0.865295\pi$
$674$	−1.58114	+	1.22474i	−0.0609032	+	0.0471754i
$675$		0			0
$676$	22.9949	+	12.1340i	0.884419	+	0.466693i
$677$	−8.00000	+	8.00000i	−0.307465	+	0.307465i	−0.843925	−	0.536460i	$-0.819761\pi$
$677$	−8.00000	+	8.00000i	−0.307465	+	0.307465i	0.536460	+	0.843925i	$0.319761\pi$
$678$		0			0
$679$	15.4919			0.594526
$680$	8.30948	+	3.30948i	0.318654	+	0.126913i
$681$		0			0
$682$	−33.6706	−	4.27673i	−1.28931	−	0.163764i
$683$	19.5959	+	19.5959i	0.749817	+	0.749817i	0.974445	−	0.224628i	$-0.0721166\pi$
$683$	19.5959	+	19.5959i	0.749817	+	0.749817i	−0.224628	+	0.974445i	$0.572117\pi$
$684$	14.2302	+	3.67423i	0.544107	+	0.140488i
$685$			10.0000i			0.382080i
$686$	6.00000	+	7.74597i	0.229081	+	0.295742i
$687$		0			0
$688$	42.1109	−	12.1109i	1.60546	−	0.461723i
$689$	−6.32456	−	8.00000i	−0.240946	−	0.304776i
$690$		0			0
$691$	−22.0454			−0.838647			−0.419323	−	0.907837i	$-0.637733\pi$
$691$	−22.0454			−0.838647			−0.419323	+	0.907837i	$0.637733\pi$
$692$	17.2379	+	29.2379i	0.655287	+	1.11146i
$693$	18.0000	+	18.0000i	0.683763	+	0.683763i
$694$	−18.9737	−	24.4949i	−0.720231	−	0.929814i
$695$	12.2474	+	12.2474i	0.464572	+	0.464572i
$696$		0			0
$697$	−6.32456	−	6.32456i	−0.239560	−	0.239560i
$698$	−4.43649	−	0.563508i	−0.167924	−	0.0213291i
$699$		0			0
$700$	17.5934	+	29.8408i	0.664966	+	1.12788i
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$		0			0
$703$	−15.4919	+	15.4919i	−0.584289	+	0.584289i
$704$	14.2302	+	13.4722i	0.536323	+	0.507752i
$705$		0			0
$706$	−15.0000	+	11.6190i	−0.564532	+	0.437285i
$707$	34.2929	−	34.2929i	1.28972	−	1.28972i
$708$		0			0
$709$	−28.4605			−1.06886			−0.534428	−	0.845214i	$-0.679473\pi$
$709$	−28.4605			−1.06886			−0.534428	+	0.845214i	$0.679473\pi$
$710$	9.48683	+	12.2474i	0.356034	+	0.459639i
$711$			23.2379i			0.871489i
$712$	33.2379	+	13.2379i	1.24564	+	0.496111i
$713$	37.9473	−	37.9473i	1.42114	−	1.42114i
$714$		0			0
$715$	12.2474	+	15.4919i	0.458029	+	0.579365i
$716$	15.0000	+	3.87298i	0.560576	+	0.144740i
$717$		0			0
$718$	−3.49193	+	27.4919i	−0.130318	+	1.02599i
$719$	7.74597			0.288876			0.144438	−	0.989514i	$-0.453863\pi$
$719$	7.74597			0.288876			0.144438	+	0.989514i	$0.453863\pi$
$720$	25.7875	−	7.41637i	0.961045	−	0.276392i
$721$		−	56.9210i		−	2.11985i
$722$	18.2382	+	2.31656i	0.678757	+	0.0862135i
$723$		0			0
$724$	−11.6190	−	3.00000i	−0.431815	−	0.111494i
$725$	−10.0000			−0.371391
$726$		0			0
$727$	−3.87298	−	3.87298i	−0.143641	−	0.143641i	0.631629	−	0.775270i	$-0.282386\pi$
$727$	−3.87298	−	3.87298i	−0.143641	−	0.143641i	−0.775270	+	0.631629i	$0.782386\pi$
$728$	−33.8525	+	10.0999i	−1.25466	+	0.374329i
$729$		−	27.0000i		−	1.00000i
$730$	14.0294	+	1.78197i	0.519252	+	0.0659537i
$731$			15.4919i			0.572990i
$732$		0			0
$733$	−3.16228	+	3.16228i	−0.116801	+	0.116801i	−0.763092	−	0.646290i	$-0.776320\pi$
$733$	−3.16228	+	3.16228i	−0.116801	+	0.116801i	0.646290	+	0.763092i	$0.276320\pi$
$734$	−4.74342	−	6.12372i	−0.175083	−	0.226031i
$735$		0			0
$736$	−30.6186	+	4.74342i	−1.12862	+	0.174845i
$737$	6.00000	−	6.00000i	0.221013	−	0.221013i
$738$	−26.6190	−	3.38105i	−0.979857	−	0.124458i
$739$			7.34847i			0.270318i	0.990824	+	0.135159i	$0.0431545\pi$
$739$			7.34847i			0.270318i	−0.990824	+	0.135159i	$0.956846\pi$
$740$	−10.0000	+	38.7298i	−0.367607	+	1.42374i
$741$		0			0
$742$	13.7460	+	1.74597i	0.504630	+	0.0640965i
$743$	−17.1464	−	17.1464i	−0.629041	−	0.629041i	0.318785	−	0.947827i	$-0.396725\pi$
$743$	−17.1464	−	17.1464i	−0.629041	−	0.629041i	−0.947827	+	0.318785i	$0.896725\pi$
$744$		0			0
$745$	25.0000	+	25.0000i	0.915929	+	0.915929i
$746$	2.44949	+	3.16228i	0.0896822	+	0.115779i
$747$	14.6969	−	14.6969i	0.537733	−	0.537733i
$748$	−5.96816	+	3.51867i	−0.218218	+	0.128655i
$749$		0			0
$750$		0			0
$751$			46.4758i			1.69593i	0.530055	+	0.847963i	$0.322171\pi$
$751$			46.4758i			1.69593i	−0.530055	+	0.847963i	$0.677829\pi$
$752$	13.3166	−	3.82980i	0.485608	−	0.139658i
$753$		0			0
$754$	2.45157	−	9.89898i	0.0892810	−	0.360500i
$755$	−23.2379	−	23.2379i	−0.845714	−	0.845714i
$756$		0			0
$757$	−16.0000	+	16.0000i	−0.581530	+	0.581530i	−0.935324	−	0.353794i	$-0.884892\pi$
$757$	−16.0000	+	16.0000i	−0.581530	+	0.581530i	0.353794	+	0.935324i	$0.384892\pi$
$758$	3.05544	−	24.0554i	0.110979	−	0.873733i
$759$		0			0
$760$	−14.2302	+	6.12372i	−0.516185	+	0.222131i
$761$		−	44.2719i		−	1.60485i	−0.596750	−	0.802427i	$-0.703542\pi$
$761$		−	44.2719i		−	1.60485i	0.596750	−	0.802427i	$-0.296458\pi$
$762$		0			0
$763$	7.74597	−	7.74597i	0.280423	−	0.280423i
$764$	11.6190	−	45.0000i	0.420359	−	1.62804i
$765$			9.48683i			0.342997i
$766$	−3.00000	−	3.87298i	−0.108394	−	0.139937i
$767$	3.07799	−	26.3159i	0.111140	−	0.950212i
$768$		0			0
$769$	−44.2719			−1.59649			−0.798243	−	0.602336i	$-0.794237\pi$
$769$	−44.2719			−1.59649			−0.798243	+	0.602336i	$0.794237\pi$
$770$	−26.6190	−	3.38105i	−0.959280	−	0.121845i
$771$		0			0
$772$	7.70486	−	4.54259i	0.277304	−	0.163491i
$773$	−28.4605	+	28.4605i	−1.02365	+	1.02365i	−0.0239396	+	0.999713i	$0.507621\pi$
$773$	−28.4605	+	28.4605i	−1.02365	+	1.02365i	−0.999713	+	0.0239396i	$0.992379\pi$
$774$	28.4605	+	36.7423i	1.02299	+	1.32068i
$775$		−	48.9898i		−	1.75977i
$776$	5.00000	+	11.6190i	0.179490	+	0.417096i
$777$		0			0
$778$	2.49476	−	19.6412i	0.0894414	−	0.704171i
$779$	15.4919			0.555056
$780$		0			0
$781$	−12.0000			−0.429394
$782$	1.38031	−	10.8671i	0.0493597	−	0.388608i
$783$		0			0
$784$	9.68246	−	17.5000i	0.345802	−	0.625000i
$785$	−44.2719			−1.58013
$786$		0			0
$787$	−9.79796	+	9.79796i	−0.349260	+	0.349260i	−0.859834	−	0.510574i	$-0.829433\pi$
$787$	−9.79796	+	9.79796i	−0.349260	+	0.349260i	0.510574	+	0.859834i	$0.329433\pi$
$788$	−9.08517	−	15.4097i	−0.323646	−	0.548949i
$789$		0			0
$790$	−15.0000	−	19.3649i	−0.533676	−	0.688973i
$791$	−44.0908			−1.56769
$792$	−7.69052	+	19.3095i	−0.273271	+	0.686132i
$793$	21.4868	+	2.51317i	0.763020	+	0.0892452i
$794$	19.3649	+	25.0000i	0.687235	+	0.887217i
$795$		0			0
$796$	−30.0000	−	7.74597i	−1.06332	−	0.274549i
$797$	−6.00000	+	6.00000i	−0.212531	+	0.212531i	−0.805342	−	0.592811i	$-0.798018\pi$
$797$	−6.00000	+	6.00000i	−0.212531	+	0.212531i	0.592811	+	0.805342i	$0.298018\pi$
$798$		0			0
$799$			4.89898i			0.173313i
$800$	−16.7024	+	22.8261i	−0.590518	+	0.807024i
$801$			37.9473i			1.34080i
$802$	−2.25403	+	17.7460i	−0.0795927	+	0.626632i
$803$	−7.74597	+	7.74597i	−0.273349	+	0.273349i
$804$		0			0
$805$	30.0000	−	30.0000i	1.05736	−	1.05736i
$806$	48.4949	+	12.0102i	1.70816	+	0.423041i
$807$		0			0
$808$	36.7876	+	14.6517i	1.29418	+	0.515444i
$809$		−	4.00000i		−	0.140633i	−0.997525	−	0.0703163i	$-0.977599\pi$
$809$		−	4.00000i		−	0.140633i	0.997525	−	0.0703163i	$-0.0224008\pi$
$810$	17.4284	+	22.5000i	0.612372	+	0.790569i
$811$	26.9444			0.946145			0.473073	−	0.881023i	$-0.343145\pi$
$811$	26.9444			0.946145			0.473073	+	0.881023i	$0.343145\pi$
$812$	7.03734	+	11.9363i	0.246962	+	0.418883i
$813$		0			0
$814$	−18.9737	−	24.4949i	−0.665027	−	0.858546i
$815$			46.4758i			1.62798i
$816$		0			0
$817$	−18.9737	−	18.9737i	−0.663805	−	0.663805i
$818$	35.4919	+	4.50807i	1.24095	+	0.157621i
$819$	−23.2379	−	29.3939i	−0.811998	−	1.02711i
$820$	24.3649	−	14.3649i	0.850860	−	0.501645i
$821$		−	15.8114i		−	0.551821i	−0.961183	−	0.275911i	$-0.911021\pi$
$821$		−	15.8114i		−	0.551821i	0.961183	−	0.275911i	$-0.0889794\pi$
$822$		0			0
$823$	−11.6190	+	11.6190i	−0.405011	+	0.405011i	−0.879995	−	0.474984i	$-0.842454\pi$
$823$	−11.6190	+	11.6190i	−0.405011	+	0.405011i	0.474984	+	0.879995i	$0.342454\pi$
$824$	42.6907	−	18.3712i	1.48720	−	0.639990i
$825$		0			0
$826$	22.0454	+	28.4605i	0.767058	+	0.990267i
$827$	2.44949	−	2.44949i	0.0851771	−	0.0851771i	−0.663235	−	0.748412i	$-0.730817\pi$
$827$	2.44949	−	2.44949i	0.0851771	−	0.0851771i	0.748412	+	0.663235i	$0.230817\pi$
$828$	−16.6905	−	28.3095i	−0.580036	−	0.983822i
$829$			42.0000i			1.45872i	0.684130	+	0.729360i	$0.260182\pi$
$829$			42.0000i			1.45872i	−0.684130	+	0.729360i	$0.739818\pi$
$830$	−2.76062	+	21.7343i	−0.0958224	+	0.754408i
$831$		0			0
$832$	−18.5008	−	22.1296i	−0.641400	−	0.767207i
$833$	5.00000	+	5.00000i	0.173240	+	0.173240i
$834$		0			0
$835$	−23.2379			−0.804181
$836$	3.00000	−	11.6190i	0.103757	−	0.401850i
$837$		0			0
$838$	32.6014	+	4.14092i	1.12620	+	0.143046i
$839$			9.79796i			0.338263i	0.985593	+	0.169132i	$0.0540963\pi$
$839$			9.79796i			0.338263i	−0.985593	+	0.169132i	$0.945904\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	1.69052	−	13.3095i	0.0582593	−	0.458675i
$843$		0			0
$844$	11.6190	−	45.0000i	0.399941	−	1.54896i
$845$	−15.2566	−	24.7434i	−0.524842	−	0.851199i
$846$	9.00000	+	11.6190i	0.309426	+	0.399468i
$847$	−12.2474	+	12.2474i	−0.420827	+	0.420827i
$848$	3.12702	+	10.8730i	0.107382	+	0.373380i
$849$		0			0
$850$	−6.12372	−	7.90569i	−0.210042	−	0.271163i
$851$	48.9898			1.67935
$852$		0			0
$853$	−22.1359	+	22.1359i	−0.757920	+	0.757920i	−0.975944	−	0.218023i	$-0.930039\pi$
$853$	−22.1359	+	22.1359i	−0.757920	+	0.757920i	0.218023	+	0.975944i	$0.430039\pi$
$854$	−23.2379	+	18.0000i	−0.795185	+	0.615947i
$855$	−11.6190	−	11.6190i	−0.397360	−	0.397360i
$856$		0			0
$857$	−23.0000	+	23.0000i	−0.785665	+	0.785665i	−0.980780	−	0.195115i	$-0.937492\pi$
$857$	−23.0000	+	23.0000i	−0.785665	+	0.785665i	0.195115	+	0.980780i	$0.437492\pi$
$858$		0			0
$859$	38.7298			1.32144			0.660722	−	0.750630i	$-0.270250\pi$
$859$	38.7298			1.32144			0.660722	+	0.750630i	$0.270250\pi$
$860$	−47.4342	−	12.2474i	−1.61749	−	0.417635i
$861$		0			0
$862$	27.4919	+	3.49193i	0.936379	+	0.118936i
$863$	31.8434	+	31.8434i	1.08396	+	1.08396i	0.996136	+	0.0878249i	$0.0279916\pi$
$863$	31.8434	+	31.8434i	1.08396	+	1.08396i	0.0878249	+	0.996136i	$0.472008\pi$
$864$		0			0
$865$		−	37.9473i		−	1.29025i
$866$	−23.2702	−	30.0416i	−0.790752	−	1.02086i
$867$		0			0
$868$	−58.4758	+	34.4758i	−1.98480	+	1.17018i
$869$	18.9737			0.643638
$870$		0			0
$871$	−9.79796	+	7.74597i	−0.331991	+	0.262462i
$872$	8.30948	+	3.30948i	0.281394	+	0.112073i
$873$	−9.48683	+	9.48683i	−0.321081	+	0.321081i
$874$	11.6190	+	15.0000i	0.393017	+	0.507383i
$875$		−	38.7298i		−	1.30931i
$876$		0			0
$877$	25.2982	+	25.2982i	0.854260	+	0.854260i	0.990655	−	0.136394i	$-0.0435514\pi$
$877$	25.2982	+	25.2982i	0.854260	+	0.854260i	−0.136394	+	0.990655i	$0.543551\pi$
$878$	32.6014	+	4.14092i	1.10024	+	0.139749i
$879$		0			0
$880$	−6.05544	−	21.0554i	−0.204129	−	0.709779i
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$	21.0441	+	2.67295i	0.708593	+	0.0900031i
$883$	15.4919	−	15.4919i	0.521345	−	0.521345i	−0.396632	−	0.917978i	$-0.629821\pi$
$883$	15.4919	−	15.4919i	0.521345	−	0.521345i	0.917978	+	0.396632i	$0.129821\pi$
$884$	9.32711	−	4.12372i	0.313705	−	0.138696i
$885$		0			0
$886$	−36.7423	+	28.4605i	−1.23438	+	0.956149i
$887$	27.1109	+	27.1109i	0.910294	+	0.910294i	0.996295	−	0.0860007i	$-0.0274087\pi$
$887$	27.1109	+	27.1109i	0.910294	+	0.910294i	−0.0860007	+	0.996295i	$0.527409\pi$
$888$		0			0
$889$	56.9210			1.90907
$890$	−24.4949	−	31.6228i	−0.821071	−	1.06000i
$891$	−22.0454			−0.738549
$892$	−3.51867	−	5.96816i	−0.117814	−	0.199829i
$893$	−6.00000	−	6.00000i	−0.200782	−	0.200782i
$894$		0			0
$895$	−12.2474	−	12.2474i	−0.409387	−	0.409387i
$896$	39.0000	+	3.87298i	1.30290	+	0.129387i
$897$		0			0
$898$	−8.87298	−	1.12702i	−0.296095	−	0.0376090i
$899$		−	19.5959i		−	0.653560i
$900$	−29.0474	−	7.50000i	−0.968246	−	0.250000i
$901$	−4.00000			−0.133259
$902$	−2.76062	+	21.7343i	−0.0919184	+	0.723672i
$903$		0			0
$904$	−14.2302	−	33.0681i	−0.473291	−	1.09983i
$905$	9.48683	+	9.48683i	0.315353	+	0.315353i
$906$		0			0
$907$	−30.9839	−	30.9839i	−1.02880	−	1.02880i	−0.999573	−	0.0292297i	$-0.990695\pi$
$907$	−30.9839	−	30.9839i	−1.02880	−	1.02880i	−0.0292297	−	0.999573i	$-0.509305\pi$
$908$	−23.8726	+	14.0747i	−0.792242	+	0.467085i
$909$			42.0000i			1.39305i
$910$	38.3386	+	9.49490i	1.27091	+	0.314753i
$911$		−	38.7298i		−	1.28318i	−0.767049	−	0.641588i	$-0.778276\pi$
$911$		−	38.7298i		−	1.28318i	0.767049	−	0.641588i	$-0.221724\pi$
$912$		0			0
$913$	−12.0000	−	12.0000i	−0.397142	−	0.397142i
$914$	27.1109	+	35.0000i	0.896748	+	1.15770i
$915$		0			0
$916$	−18.3712	−	4.74342i	−0.607001	−	0.156727i
$917$	18.9737	+	18.9737i	0.626566	+	0.626566i
$918$		0			0
$919$	−46.4758			−1.53310			−0.766548	−	0.642188i	$-0.778027\pi$
$919$	−46.4758			−1.53310			−0.766548	+	0.642188i	$0.778027\pi$
$920$	32.1825	+	12.8175i	1.06102	+	0.422582i
$921$		0			0
$922$	6.19859	−	48.8014i	0.204140	−	1.60719i
$923$	17.5439	+	2.05199i	0.577465	+	0.0675421i
$924$		0			0
$925$	31.6228	−	31.6228i	1.03975	−	1.03975i
$926$	−21.0000	−	27.1109i	−0.690103	−	0.890919i
$927$	34.8569	+	34.8569i	1.14485	+	1.14485i
$928$	−6.68095	+	9.13044i	−0.219313	+	0.299721i
$929$	−44.2719			−1.45251			−0.726257	−	0.687424i	$-0.758742\pi$
$929$	−44.2719			−1.45251			−0.726257	+	0.687424i	$0.758742\pi$
$930$		0			0
$931$	−12.2474			−0.401394
$932$	1.43649	+	2.43649i	0.0470538	+	0.0798099i
$933$		0			0
$934$	−9.48683	−	12.2474i	−0.310419	−	0.400749i
$935$	7.74597			0.253320
$936$	14.5454	−	26.9153i	0.475432	−	0.879753i
$937$	−11.0000	+	11.0000i	−0.359354	+	0.359354i	−0.863575	−	0.504221i	$-0.831780\pi$
$937$	−11.0000	+	11.0000i	−0.359354	+	0.359354i	0.504221	+	0.863575i	$0.331780\pi$
$938$	2.13836	−	16.8353i	0.0698201	−	0.549692i
$939$		0			0
$940$	−15.0000	−	3.87298i	−0.489246	−	0.126323i
$941$			22.1359i			0.721611i	0.932641	+	0.360806i	$0.117498\pi$
$941$			22.1359i			0.721611i	−0.932641	+	0.360806i	$0.882502\pi$
$942$		0			0
$943$	−24.4949	−	24.4949i	−0.797664	−	0.797664i
$944$	−14.2302	+	25.7196i	−0.463155	+	0.837103i
$945$		0			0
$946$	30.0000	−	23.2379i	0.975384	−	0.755529i
$947$	2.44949	−	2.44949i	0.0795977	−	0.0795977i	−0.666187	−	0.745785i	$-0.732075\pi$
$947$	2.44949	−	2.44949i	0.0795977	−	0.0795977i	0.745785	+	0.666187i	$0.232075\pi$
$948$		0			0
$949$	12.6491	−	10.0000i	0.410608	−	0.324614i
$950$	17.1825	+	2.18246i	0.557473	+	0.0708083i
$951$		0			0
$952$	−5.12702	+	12.8730i	−0.166168	+	0.417216i
$953$	−33.0000	−	33.0000i	−1.06897	−	1.06897i	−0.997438	−	0.0715369i	$-0.977210\pi$
$953$	−33.0000	−	33.0000i	−1.06897	−	1.06897i	−0.0715369	−	0.997438i	$-0.522790\pi$
$954$	−9.48683	+	7.34847i	−0.307148	+	0.237915i
$955$	−36.7423	+	36.7423i	−1.18895	+	1.18895i
$956$	2.44949	−	9.48683i	0.0792222	−	0.306826i
$957$		0			0
$958$	0.872983	−	6.87298i	0.0282048	−	0.222056i
$959$	−15.4919			−0.500261
$960$		0			0
$961$	65.0000			2.09677
$962$	23.5508	+	39.0559i	0.759307	+	1.25921i
$963$		0			0
$964$		0			0
$965$	−10.0000			−0.321911
$966$		0			0
$967$	2.44949	−	2.44949i	0.0787703	−	0.0787703i	−0.666624	−	0.745394i	$-0.732261\pi$
$967$	2.44949	−	2.44949i	0.0787703	−	0.0787703i	0.745394	+	0.666624i	$0.232261\pi$
$968$	−13.1384	−	5.23274i	−0.422285	−	0.168187i
$969$		0			0
$970$	1.78197	−	14.0294i	0.0572156	−	0.450457i
$971$		−	7.74597i		−	0.248580i	−0.992246	−	0.124290i	$-0.960335\pi$
$971$		−	7.74597i		−	0.248580i	0.992246	−	0.124290i	$-0.0396653\pi$
$972$		0			0
$973$	−18.9737	+	18.9737i	−0.608268	+	0.608268i
$974$	−34.8569	+	27.0000i	−1.11689	+	0.865136i
$975$		0			0
$976$	−21.0000	−	11.6190i	−0.672194	−	0.371914i
$977$	−9.48683	−	9.48683i	−0.303511	−	0.303511i	0.538875	−	0.842386i	$-0.318849\pi$
$977$	−9.48683	−	9.48683i	−0.303511	−	0.303511i	−0.842386	+	0.538875i	$0.818849\pi$
$978$		0			0
$979$	30.9839			0.990249
$980$	−19.2622	+	11.3565i	−0.615307	+	0.362769i
$981$			9.48683i			0.302891i
$982$	1.38031	−	10.8671i	0.0440474	−	0.346784i
$983$	7.34847	+	7.34847i	0.234380	+	0.234380i	0.814518	−	0.580138i	$-0.197001\pi$
$983$	7.34847	+	7.34847i	0.234380	+	0.234380i	−0.580138	+	0.814518i	$0.697001\pi$
$984$		0			0
$985$			20.0000i			0.637253i
$986$	−2.44949	−	3.16228i	−0.0780076	−	0.100707i
$987$		0			0
$988$	−6.37281	+	16.4738i	−0.202746	+	0.524103i
$989$			60.0000i			1.90789i
$990$	18.3712	−	14.2302i	0.583874	−	0.452267i
$991$		−	46.4758i		−	1.47635i	−0.674608	−	0.738176i	$-0.735687\pi$
$991$		−	46.4758i		−	1.47635i	0.674608	−	0.738176i	$-0.264313\pi$
$992$	−44.7298	−	32.7298i	−1.42017	−	1.03917i
$993$		0			0
$994$	−18.9737	+	14.6969i	−0.601808	+	0.466159i
$995$	24.4949	+	24.4949i	0.776540	+	0.776540i
$996$		0			0
$997$	44.0000	−	44.0000i	1.39349	−	1.39349i	0.576150	−	0.817344i	$-0.304554\pi$
$997$	44.0000	−	44.0000i	1.39349	−	1.39349i	0.817344	−	0.576150i	$-0.195446\pi$
$998$	−5.67439	+	44.6744i	−0.179620	+	1.41414i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.p.c.103.4	yes	8
4.3	odd	2	inner	260.2.p.c.103.3	yes	8
5.2	odd	4	inner	260.2.p.c.207.2	yes	8
13.12	even	2	inner	260.2.p.c.103.1	✓	8
20.7	even	4	inner	260.2.p.c.207.1	yes	8
52.51	odd	2	inner	260.2.p.c.103.2	yes	8
65.12	odd	4	inner	260.2.p.c.207.3	yes	8
260.207	even	4	inner	260.2.p.c.207.4	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.p.c.103.1	✓	8	13.12	even	2	inner
260.2.p.c.103.2	yes	8	52.51	odd	2	inner
260.2.p.c.103.3	yes	8	4.3	odd	2	inner
260.2.p.c.103.4	yes	8	1.1	even	1	trivial
260.2.p.c.207.1	yes	8	20.7	even	4	inner
260.2.p.c.207.2	yes	8	5.2	odd	4	inner
260.2.p.c.207.3	yes	8	65.12	odd	4	inner
260.2.p.c.207.4	yes	8	260.207	even	4	inner

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40294 + 0.178197i) q^{2} +(1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(2.44949 - 2.44949i) q^{7} +(2.62769 + 1.04655i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(1.40294 + 0.178197i) q^{2} +(1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(2.44949 - 2.44949i) q^{7} +(2.62769 + 1.04655i) q^{8} +3.00000i q^{9} +(-1.93649 - 2.50000i) q^{10} +2.44949 q^{11} +(-3.58114 - 0.418861i) q^{13} +(3.87298 - 3.00000i) q^{14} +(3.50000 + 1.93649i) q^{16} +(-1.00000 + 1.00000i) q^{17} +(-0.534591 + 4.20883i) q^{18} -2.44949i q^{19} +(-2.27129 - 3.85243i) q^{20} +(3.43649 + 0.436492i) q^{22} +(-3.87298 + 3.87298i) q^{23} +5.00000i q^{25} +(-4.94949 - 1.22579i) q^{26} +(5.96816 - 3.51867i) q^{28} +2.00000i q^{29} -9.79796 q^{31} +(4.56522 + 3.34047i) q^{32} +(-1.58114 + 1.22474i) q^{34} -7.74597 q^{35} +(-1.50000 + 5.80948i) q^{36} +(-6.32456 - 6.32456i) q^{37} +(0.436492 - 3.43649i) q^{38} +(-2.50000 - 5.80948i) q^{40} +6.32456i q^{41} +(7.74597 - 7.74597i) q^{43} +(4.74342 + 1.22474i) q^{44} +(4.74342 - 4.74342i) q^{45} +(-6.12372 + 4.74342i) q^{46} +(2.44949 - 2.44949i) q^{47} -5.00000i q^{49} +(-0.890985 + 7.01471i) q^{50} +(-6.72541 - 2.60169i) q^{52} +(2.00000 + 2.00000i) q^{53} +(-3.87298 - 3.87298i) q^{55} +(9.00000 - 3.87298i) q^{56} +(-0.356394 + 2.80588i) q^{58} +7.34847i q^{59} -6.00000 q^{61} +(-13.7460 - 1.74597i) q^{62} +(7.34847 + 7.34847i) q^{63} +(5.80948 + 5.50000i) q^{64} +(5.00000 + 6.32456i) q^{65} +(2.44949 - 2.44949i) q^{67} +(-2.43649 + 1.43649i) q^{68} +(-10.8671 - 1.38031i) q^{70} -4.89898 q^{71} +(-3.13964 + 7.88306i) q^{72} +(-3.16228 + 3.16228i) q^{73} +(-7.74597 - 10.0000i) q^{74} +(1.22474 - 4.74342i) q^{76} +(6.00000 - 6.00000i) q^{77} +7.74597 q^{79} +(-2.47212 - 8.59585i) q^{80} -9.00000 q^{81} +(-1.12702 + 8.87298i) q^{82} +(-4.89898 - 4.89898i) q^{83} +3.16228 q^{85} +(12.2474 - 9.48683i) q^{86} +(6.43649 + 2.56351i) q^{88} +12.6491 q^{89} +(7.50000 - 5.80948i) q^{90} +(-9.79796 + 7.74597i) q^{91} +(-9.43649 + 5.56351i) q^{92} +(3.87298 - 3.00000i) q^{94} +(-3.87298 + 3.87298i) q^{95} +(3.16228 + 3.16228i) q^{97} +(0.890985 - 7.01471i) q^{98} +7.34847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 16 q^{13} + 28 q^{16} - 8 q^{17} + 12 q^{22} - 20 q^{26} - 12 q^{36} - 12 q^{38} - 20 q^{40} + 8 q^{52} + 16 q^{53} + 72 q^{56} - 48 q^{61} - 48 q^{62} + 40 q^{65} - 4 q^{68} + 48 q^{77} - 72 q^{81} - 40 q^{82} + 36 q^{88} + 60 q^{90} - 60 q^{92}+O(q^{100}) \) 8 * q - 16 * q^13 + 28 * q^16 - 8 * q^17 + 12 * q^22 - 20 * q^26 - 12 * q^36 - 12 * q^38 - 20 * q^40 + 8 * q^52 + 16 * q^53 + 72 * q^56 - 48 * q^61 - 48 * q^62 + 40 * q^65 - 4 * q^68 + 48 * q^77 - 72 * q^81 - 40 * q^82 + 36 * q^88 + 60 * q^90 - 60 * q^92

Introduction

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