LMFDB - Embedded newform 260.2.p.c.103.3

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			103.3
Root			$0.178197 + 1.40294i$ of defining polynomial
Character	$\chi$	$=$	260.103
Dual form			260.2.p.c.207.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.178197 + 1.40294i) q^{2} +(-1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(-2.44949 + 2.44949i) q^{7} +(-1.04655 - 2.62769i) q^{8} +3.00000i q^{9} +O(q^{10})$	\(q+(0.178197 + 1.40294i) q^{2} +(-1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(-2.44949 + 2.44949i) q^{7} +(-1.04655 - 2.62769i) q^{8} +3.00000i q^{9} +(1.93649 - 2.50000i) q^{10} -2.44949 q^{11} +(-3.58114 - 0.418861i) q^{13} +(-3.87298 - 3.00000i) q^{14} +(3.50000 - 1.93649i) q^{16} +(-1.00000 + 1.00000i) q^{17} +(-4.20883 + 0.534591i) q^{18} +2.44949i q^{19} +(3.85243 + 2.27129i) q^{20} +(-0.436492 - 3.43649i) q^{22} +(3.87298 - 3.87298i) q^{23} +5.00000i q^{25} +(-0.0505103 - 5.09877i) q^{26} +(3.51867 - 5.96816i) q^{28} +2.00000i q^{29} +9.79796 q^{31} +(3.34047 + 4.56522i) q^{32} +(-1.58114 - 1.22474i) q^{34} +7.74597 q^{35} +(-1.50000 - 5.80948i) q^{36} +(-6.32456 - 6.32456i) q^{37} +(-3.43649 + 0.436492i) q^{38} +(-2.50000 + 5.80948i) q^{40} +6.32456i q^{41} +(-7.74597 + 7.74597i) q^{43} +(4.74342 - 1.22474i) q^{44} +(4.74342 - 4.74342i) q^{45} +(6.12372 + 4.74342i) q^{46} +(-2.44949 + 2.44949i) q^{47} -5.00000i q^{49} +(-7.01471 + 0.890985i) q^{50} +(7.14428 - 0.979448i) q^{52} +(2.00000 + 2.00000i) q^{53} +(3.87298 + 3.87298i) q^{55} +(9.00000 + 3.87298i) q^{56} +(-2.80588 + 0.356394i) q^{58} -7.34847i q^{59} -6.00000 q^{61} +(1.74597 + 13.7460i) q^{62} +(-7.34847 - 7.34847i) q^{63} +(-5.80948 + 5.50000i) q^{64} +(5.00000 + 6.32456i) q^{65} +(-2.44949 + 2.44949i) q^{67} +(1.43649 - 2.43649i) q^{68} +(1.38031 + 10.8671i) q^{70} +4.89898 q^{71} +(7.88306 - 3.13964i) q^{72} +(-3.16228 + 3.16228i) q^{73} +(7.74597 - 10.0000i) q^{74} +(-1.22474 - 4.74342i) q^{76} +(6.00000 - 6.00000i) q^{77} -7.74597 q^{79} +(-8.59585 - 2.47212i) q^{80} -9.00000 q^{81} +(-8.87298 + 1.12702i) q^{82} +(4.89898 + 4.89898i) q^{83} +3.16228 q^{85} +(-12.2474 - 9.48683i) q^{86} +(2.56351 + 6.43649i) q^{88} +12.6491 q^{89} +(7.50000 + 5.80948i) q^{90} +(9.79796 - 7.74597i) q^{91} +(-5.56351 + 9.43649i) q^{92} +(-3.87298 - 3.00000i) q^{94} +(3.87298 - 3.87298i) q^{95} +(3.16228 + 3.16228i) q^{97} +(7.01471 - 0.890985i) q^{98} -7.34847i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.178197	+	1.40294i	0.126004	+	0.992030i
$2$	0.178197	+	1.40294i	0.126004	+	0.992030i
$3$		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	−0.997433	−	0.0716124i	$-0.977186\pi$
$7$	−2.44949	+	2.44949i	−0.925820	+	0.925820i	0.0716124	+	0.997433i	$0.477186\pi$
$8$	−1.04655	−	2.62769i	−0.370011	−	0.929028i
$9$			3.00000i			1.00000i
$10$	1.93649	−	2.50000i	0.612372	−	0.790569i
$11$	−2.44949			−0.738549			−0.369274	−	0.929320i	$-0.620394\pi$
$11$	−2.44949			−0.738549			−0.369274	+	0.929320i	$0.620394\pi$
$12$		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	$0.304861\pi$
$18$	−4.20883	+	0.534591i	−0.992030	+	0.126004i
$19$			2.44949i			0.561951i	0.959715	+	0.280976i	$0.0906580\pi$
$19$			2.44949i			0.561951i	−0.959715	+	0.280976i	$0.909342\pi$
$20$	3.85243	+	2.27129i	0.861430	+	0.507877i
$21$		0			0
$22$	−0.436492	−	3.43649i	−0.0930603	−	0.732662i
$23$	3.87298	−	3.87298i	0.807573	−	0.807573i	−0.176693	−	0.984266i	$-0.556540\pi$
$23$	3.87298	−	3.87298i	0.807573	−	0.807573i	0.984266	+	0.176693i	$0.0565400\pi$
$24$		0			0
$25$			5.00000i			1.00000i
$26$	−0.0505103	−	5.09877i	−0.00990588	−	0.999951i
$27$		0			0
$28$	3.51867	−	5.96816i	0.664966	−	1.12788i
$29$			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	$-0.157621\pi$
$31$	9.79796			1.75977			0.879883	+	0.475191i	$0.157621\pi$
$32$	3.34047	+	4.56522i	0.590518	+	0.807024i
$33$		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	$-0.512919\pi$
$38$	−3.43649	+	0.436492i	−0.557473	+	0.0708083i
$39$		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	$0.564688\pi$
$43$	−7.74597	+	7.74597i	−1.18125	+	1.18125i	−0.979421	+	0.201828i	$0.935312\pi$
$44$	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	−0.862815	−	0.505520i	$-0.831301\pi$
$47$	−2.44949	+	2.44949i	−0.357295	+	0.357295i	0.505520	+	0.862815i	$0.331301\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	−7.01471	+	0.890985i	−0.992030	+	0.126004i
$51$		0			0
$52$	7.14428	−	0.979448i	0.990733	−	0.135825i
$53$	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
$58$	−2.80588	+	0.356394i	−0.368431	+	0.0467968i
$59$		−	7.34847i		−	0.956689i	−0.878172	−	0.478345i	$-0.841237\pi$
$59$		−	7.34847i		−	0.956689i	0.878172	−	0.478345i	$-0.158763\pi$
$60$		0			0
$61$	−6.00000			−0.768221			−0.384111	−	0.923287i	$-0.625492\pi$
$61$	−6.00000			−0.768221			−0.384111	+	0.923287i	$0.625492\pi$
$62$	1.74597	+	13.7460i	0.221738	+	1.74574i
$63$	−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	−0.840721	−	0.541468i	$-0.817869\pi$
$67$	−2.44949	+	2.44949i	−0.299253	+	0.299253i	0.541468	+	0.840721i	$0.317869\pi$
$68$	1.43649	−	2.43649i	0.174200	−	0.295468i
$69$		0			0
$70$	1.38031	+	10.8671i	0.164978	+	1.29887i
$71$	4.89898			0.581402			0.290701	−	0.956814i	$-0.406112\pi$
$71$	4.89898			0.581402			0.290701	+	0.956814i	$0.406112\pi$
$72$	7.88306	−	3.13964i	0.929028	−	0.370011i
$73$	−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	$-0.643515\pi$
$79$	−7.74597			−0.871489			−0.435745	+	0.900070i	$0.643515\pi$
$80$	−8.59585	−	2.47212i	−0.961045	−	0.276392i
$81$	−9.00000			−1.00000
$82$	−8.87298	+	1.12702i	−0.979857	+	0.124458i
$83$	4.89898	+	4.89898i	0.537733	+	0.537733i	0.922862	−	0.385130i	$-0.125843\pi$
$83$	4.89898	+	4.89898i	0.537733	+	0.537733i	−0.385130	+	0.922862i	$0.625843\pi$
$84$		0			0
$85$	3.16228			0.342997
$86$	−12.2474	−	9.48683i	−1.32068	−	1.02299i
$87$		0			0
$88$	2.56351	+	6.43649i	0.273271	+	0.686132i
$89$	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
$92$	−5.56351	+	9.43649i	−0.580036	+	0.983822i
$93$		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	$0.677096\pi$
$98$	7.01471	−	0.890985i	0.708593	−	0.0900031i
$99$		−	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	$0.550278\pi$
$103$	−11.6190	+	11.6190i	−1.14485	+	1.14485i	−0.987551	+	0.157298i	$0.949722\pi$
$104$	2.64720	+	9.84847i	0.259579	+	0.965722i
$105$		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
$112$	−3.82980	+	13.3166i	−0.361882	+	1.25830i
$113$	−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
$118$	10.3095	−	1.30948i	0.949064	−	0.120547i
$119$		−	4.89898i		−	0.449089i
$120$		0			0
$121$	−5.00000			−0.454545
$122$	−1.06918	−	8.41765i	−0.0967992	−	0.762098i
$123$		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	$-0.989968\pi$
$127$	−11.6190	−	11.6190i	−1.03102	−	1.03102i	−0.0315117	−	0.999503i	$-0.510032\pi$
$128$	−8.75141	−	7.17027i	−0.773523	−	0.633769i
$129$		0			0
$130$	−7.98200	+	8.14173i	−0.700068	+	0.714077i
$131$		−	7.74597i		−	0.676768i	−0.941008	−	0.338384i	$-0.890120\pi$
$131$		−	7.74597i		−	0.676768i	0.941008	−	0.338384i	$-0.109880\pi$
$132$		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	$-0.393456\pi$
$139$	7.74597			0.657004			0.328502	+	0.944503i	$0.393456\pi$
$140$	−15.0000	+	3.87298i	−1.26773	+	0.327327i
$141$		0			0
$142$	0.872983	+	6.87298i	0.0732591	+	0.576768i
$143$	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
$148$	15.4097	+	9.08517i	1.26667	+	0.746796i
$149$	−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	$-0.704042\pi$
$151$	−14.6969			−1.19602			−0.598010	+	0.801489i	$0.704042\pi$
$152$	6.43649	−	2.56351i	0.522068	−	0.207928i
$153$	−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	$-0.0399536\pi$
$158$	−1.38031	−	10.8671i	−0.109811	−	0.864543i
$159$		0			0
$160$	1.93649	−	12.5000i	0.153093	−	0.988212i
$161$			18.9737i			1.49533i
$162$	−1.60377	−	12.6265i	−0.126004	−	0.992030i
$163$	14.6969	+	14.6969i	1.15115	+	1.15115i	0.986322	+	0.164831i	$0.0527080\pi$
$163$	14.6969	+	14.6969i	1.15115	+	1.15115i	0.164831	+	0.986322i	$0.447292\pi$
$164$	−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	−0.931748	−	0.363106i	$-0.881716\pi$
$167$	−7.34847	+	7.34847i	−0.568642	+	0.568642i	0.363106	+	0.931748i	$0.381716\pi$
$168$		0			0
$169$	12.6491	+	3.00000i	0.973009	+	0.230769i
$170$	0.563508	+	4.43649i	0.0432191	+	0.340263i
$171$	−7.34847			−0.561951
$172$	11.1270	−	18.8730i	0.848427	−	1.43905i
$173$	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
$178$	2.25403	+	17.7460i	0.168947	+	1.33012i
$179$	−7.74597			−0.578961			−0.289480	−	0.957184i	$-0.593482\pi$
$179$	−7.74597			−0.578961			−0.289480	+	0.957184i	$0.593482\pi$
$180$	−6.81388	+	11.5573i	−0.507877	+	0.861430i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$	12.6131	+	12.3657i	0.934946	+	0.916604i
$183$		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
$188$	3.51867	−	5.96816i	0.256626	−	0.435273i
$189$		0			0
$190$	6.12372	+	4.74342i	0.444262	+	0.344124i
$191$			23.2379i			1.68144i	0.541474	+	0.840718i	$0.317867\pi$
$191$			23.2379i			1.68144i	−0.541474	+	0.840718i	$0.682133\pi$
$192$		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	$0.853222\pi$
$198$	10.3095	−	1.30948i	0.732662	−	0.0930603i
$199$	15.4919			1.09819			0.549097	−	0.835759i	$-0.314972\pi$
$199$	15.4919			1.09819			0.549097	+	0.835759i	$0.314972\pi$
$200$	13.1384	−	5.23274i	0.929028	−	0.370011i
$201$		0			0
$202$	2.49476	+	19.6412i	0.175531	+	1.38195i
$203$	−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
$208$	−13.3451	+	5.46883i	−0.925317	+	0.379195i
$209$		−	6.00000i		−	0.415029i
$210$		0			0
$211$			23.2379i			1.59976i	0.600158	+	0.799882i	$0.295104\pi$
$211$			23.2379i			1.59976i	−0.600158	+	0.799882i	$0.704896\pi$
$212$	−4.87298	−	2.87298i	−0.334678	−	0.197317i
$213$		0			0
$214$		0			0
$215$	24.4949			1.67054
$216$		0			0
$217$	−24.0000	+	24.0000i	−1.62923	+	1.62923i
$218$	0.563508	+	4.43649i	0.0381656	+	0.300477i
$219$		0			0
$220$	−9.43649	−	5.56351i	−0.636208	−	0.375092i
$221$	4.00000	−	3.16228i	0.269069	−	0.212718i
$222$		0			0
$223$	2.44949	+	2.44949i	0.164030	+	0.164030i	0.784349	−	0.620319i	$-0.212997\pi$
$223$	2.44949	+	2.44949i	0.164030	+	0.164030i	−0.620319	+	0.784349i	$0.712997\pi$
$224$	−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	−0.302755	−	0.953068i	$-0.597906\pi$
$227$	9.79796	−	9.79796i	0.650313	−	0.650313i	0.953068	+	0.302755i	$0.0979064\pi$
$228$		0			0
$229$	−9.48683			−0.626908			−0.313454	−	0.949603i	$-0.601486\pi$
$229$	−9.48683			−0.626908			−0.313454	+	0.949603i	$0.601486\pi$
$230$	−2.18246	−	17.1825i	−0.143907	−	1.13298i
$231$		0			0
$232$	5.25537	−	2.09310i	0.345032	−	0.137418i
$233$	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	$0.735249\pi$
$234$	15.2963	−	0.151531i	0.999951	−	0.00990588i
$235$	7.74597			0.505291
$236$	3.67423	+	14.2302i	0.239172	+	0.926310i
$237$		0			0
$238$	6.87298	−	0.872983i	0.445509	−	0.0565871i
$239$			4.89898i			0.316889i	0.987368	+	0.158444i	$0.0506478\pi$
$239$			4.89898i			0.316889i	−0.987368	+	0.158444i	$0.949352\pi$
$240$		0			0
$241$		0			0		1.00000			$0$
$241$		0			0		−1.00000			$\pi$
$242$	−0.890985	−	7.01471i	−0.0572747	−	0.450923i
$243$		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
$248$	−10.2540	−	25.7460i	−0.651132	−	1.63487i
$249$		0			0
$250$	12.5000	+	9.68246i	0.790569	+	0.612372i
$251$			7.74597i			0.488921i	0.969659	+	0.244461i	$0.0786109\pi$
$251$			7.74597i			0.488921i	−0.969659	+	0.244461i	$0.921389\pi$
$252$	17.9045	+	10.5560i	1.12788	+	0.664966i
$253$	−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
$260$	−12.8447	−	9.74745i	−0.796597	−	0.604511i
$261$	−6.00000			−0.371391
$262$	10.8671	−	1.38031i	0.671374	−	0.0852757i
$263$	19.3649	−	19.3649i	1.19409	−	1.19409i	0.218184	−	0.975908i	$-0.429987\pi$
$263$	19.3649	−	19.3649i	1.19409	−	1.19409i	0.975908	−	0.218184i	$-0.0700134\pi$
$264$		0			0
$265$		−	6.32456i		−	0.388514i
$266$	7.34847	−	9.48683i	0.450564	−	0.581675i
$267$		0			0
$268$	3.51867	−	5.96816i	0.214937	−	0.364563i
$269$			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	$-0.403817\pi$
$271$	9.79796			0.595184			0.297592	+	0.954693i	$0.403817\pi$
$272$	−1.56351	+	5.43649i	−0.0948016	+	0.329636i
$273$		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	$0.360389\pi$
$278$	1.38031	+	10.8671i	0.0827854	+	0.651768i
$279$			29.3939i			1.75977i
$280$	−8.10653	−	20.3540i	−0.484458	−	1.21638i
$281$			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	−0.438353	−	0.898803i	$-0.644438\pi$
$283$	7.74597	−	7.74597i	0.460450	−	0.460450i	0.898803	+	0.438353i	$0.144438\pi$
$284$	−9.48683	+	2.44949i	−0.562940	+	0.145350i
$285$		0			0
$286$	0.123724	+	12.4894i	0.00731597	+	0.738513i
$287$	−15.4919	−	15.4919i	−0.914460	−	0.914460i
$288$	−13.6957	+	10.0214i	−0.807024	+	0.590518i
$289$			15.0000i			0.882353i
$290$	5.00000	+	3.87298i	0.293610	+	0.227429i
$291$		0			0
$292$	4.54259	−	7.70486i	0.265835	−	0.450893i
$293$	−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
$298$	−2.81754	−	22.1825i	−0.163216	−	1.28500i
$299$	−15.4919	+	12.2474i	−0.895922	+	0.708288i
$300$		0			0
$301$		−	37.9473i		−	2.18725i
$302$	−2.61895	−	20.6190i	−0.150704	−	1.18649i
$303$		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	$0.540349\pi$
$307$	−19.5959	+	19.5959i	−1.11840	+	1.11840i	−0.991977	+	0.126421i	$0.959651\pi$
$308$	−8.61895	+	14.6190i	−0.491110	+	0.832992i
$309$		0			0
$310$	18.9737	−	24.4949i	1.07763	−	1.39122i
$311$		−	23.2379i		−	1.31770i	−0.752274	−	0.658850i	$-0.771043\pi$
$311$		−	23.2379i		−	1.31770i	0.752274	−	0.658850i	$-0.228957\pi$
$312$		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
$320$	17.8819	+	0.489323i	0.999626	+	0.0273540i
$321$		0			0
$322$	−26.6190	+	3.38105i	−1.48342	+	0.188419i
$323$	−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
$328$	16.6190	−	6.61895i	0.917628	−	0.365470i
$329$		−	12.0000i		−	0.661581i
$330$		0			0
$331$	−7.34847			−0.403908			−0.201954	−	0.979395i	$-0.564729\pi$
$331$	−7.34847			−0.403908			−0.201954	+	0.979395i	$0.564729\pi$
$332$	−11.9363	−	7.03734i	−0.655091	−	0.386224i
$333$	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	$0.262264\pi$
$338$	−1.95479	+	18.2806i	−0.106327	+	0.994331i
$339$		0			0
$340$	−6.12372	+	1.58114i	−0.332106	+	0.0857493i
$341$	−24.0000			−1.29967
$342$	−1.30948	−	10.3095i	−0.0708083	−	0.557473i
$343$	−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	0.987743	−	0.156092i	$-0.0498896\pi$
$347$	15.4919	+	15.4919i	0.831651	+	0.831651i	−0.156092	+	0.987743i	$0.549890\pi$
$348$		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
$352$	−8.18246	−	11.1825i	−0.436126	−	0.596027i
$353$	−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
$358$	−1.38031	−	10.8671i	−0.0729515	−	0.574346i
$359$		−	19.5959i		−	1.03423i	−0.855915	−	0.517116i	$-0.827005\pi$
$359$		−	19.5959i		−	1.03423i	0.855915	−	0.517116i	$-0.172995\pi$
$360$	−17.4284	−	7.50000i	−0.918559	−	0.395285i
$361$	13.0000			0.684211
$362$	−1.06918	−	8.41765i	−0.0561950	−	0.442422i
$363$		0			0
$364$	−15.1007	+	19.8990i	−0.791491	+	1.04299i
$365$	10.0000			0.523424
$366$		0			0
$367$	3.87298	+	3.87298i	0.202168	+	0.202168i	0.800928	−	0.598760i	$-0.204340\pi$
$367$	3.87298	+	3.87298i	0.202168	+	0.202168i	−0.598760	+	0.800928i	$0.704340\pi$
$368$	6.05544	−	21.0554i	0.315662	−	1.09759i
$369$	−18.9737			−0.987730
$370$	−28.0588	+	3.56394i	−1.45871	+	0.185280i
$371$	−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	$0.145155\pi$
$379$			17.1464i			0.880753i	−0.897813	+	0.440376i	$0.854845\pi$
$380$	−5.56351	+	9.43649i	−0.285402	+	0.484082i
$381$		0			0
$382$	−32.6014	+	4.14092i	−1.66803	+	0.211868i
$383$	2.44949	+	2.44949i	0.125163	+	0.125163i	0.766914	−	0.641750i	$-0.221792\pi$
$383$	2.44949	+	2.44949i	0.125163	+	0.125163i	−0.641750	+	0.766914i	$0.721792\pi$
$384$		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
$388$	−7.70486	−	4.54259i	−0.391155	−	0.230615i
$389$		−	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
$392$	−13.1384	+	5.23274i	−0.663591	+	0.264293i
$393$		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	$0.560369\pi$
$398$	2.76062	+	21.7343i	0.138377	+	1.08944i
$399$		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
$412$	16.6905	−	28.3095i	0.822283	−	1.39471i
$413$	18.0000	+	18.0000i	0.885722	+	0.885722i
$414$	−14.2302	+	18.3712i	−0.699379	+	0.902894i
$415$		−	15.4919i		−	0.760469i
$416$	−10.0505	−	17.7479i	−0.492767	−	0.870161i
$417$		0			0
$418$	8.41765	−	1.06918i	0.411721	−	0.0522954i
$419$	−23.2379			−1.13525			−0.567623	−	0.823289i	$-0.692137\pi$
$419$	−23.2379			−1.13525			−0.567623	+	0.823289i	$0.692137\pi$
$420$		0			0
$421$		−	9.48683i		−	0.462360i	−0.972911	−	0.231180i	$-0.925741\pi$
$421$		−	9.48683i		−	0.462360i	0.972911	−	0.231180i	$-0.0742586\pi$
$422$	−32.6014	+	4.14092i	−1.58701	+	0.201577i
$423$	−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
$430$	4.36492	+	34.3649i	0.210495	+	1.65722i
$431$	−19.5959			−0.943902			−0.471951	−	0.881625i	$-0.656450\pi$
$431$	−19.5959			−0.943902			−0.471951	+	0.881625i	$0.656450\pi$
$432$		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	$-0.687107\pi$
$439$	−23.2379			−1.10908			−0.554542	+	0.832156i	$0.687107\pi$
$440$	6.12372	−	14.2302i	0.291937	−	0.678401i
$441$	15.0000			0.714286
$442$	5.14928	+	5.04826i	0.244926	+	0.240121i
$443$	23.2379	−	23.2379i	1.10407	−	1.10407i	0.110151	−	0.993915i	$-0.464867\pi$
$443$	23.2379	−	23.2379i	1.10407	−	1.10407i	0.993915	−	0.110151i	$-0.0351335\pi$
$444$		0			0
$445$	−20.0000	−	20.0000i	−0.948091	−	0.948091i
$446$	−3.00000	+	3.87298i	−0.142054	+	0.183391i
$447$		0			0
$448$	0.758056	−	27.7024i	0.0358148	−	1.30882i
$449$	−6.32456			−0.298474			−0.149237	−	0.988801i	$-0.547682\pi$
$449$	−6.32456			−0.298474			−0.149237	+	0.988801i	$0.547682\pi$
$450$	−2.67295	−	21.0441i	−0.126004	−	0.992030i
$451$		−	15.4919i		−	0.729487i
$452$	21.9284	+	12.9284i	1.03143	+	0.608102i
$453$		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	$0.488497\pi$
$458$	−1.69052	−	13.3095i	−0.0789930	−	0.621911i
$459$		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	0.982599	−	0.185737i	$-0.0594674\pi$
$463$	17.1464	+	17.1464i	0.796862	+	0.796862i	−0.185737	+	0.982599i	$0.559467\pi$
$464$	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	0.863238	−	0.504797i	$-0.168433\pi$
$467$	7.74597	+	7.74597i	0.358441	+	0.358441i	−0.504797	+	0.863238i	$0.668433\pi$
$468$	2.93834	+	21.4328i	0.135825	+	0.990733i
$469$		−	12.0000i		−	0.554109i
$470$	1.38031	+	10.8671i	0.0636689	+	0.501264i
$471$		0			0
$472$	−19.3095	+	7.69052i	−0.888791	+	0.353985i
$473$	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
$478$	−6.87298	+	0.872983i	−0.314363	+	0.0399293i
$479$			4.89898i			0.223840i	0.993717	+	0.111920i	$0.0357001\pi$
$479$			4.89898i			0.223840i	−0.993717	+	0.111920i	$0.964300\pi$
$480$		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	−0.00102669	−	0.999999i	$-0.500327\pi$
$487$	22.0454	−	22.0454i	0.998973	−	0.998973i	0.999999	+	0.00102669i	$0.000326807\pi$
$488$	6.27929	+	15.7661i	0.284250	+	0.713699i
$489$		0			0
$490$	−12.5000	−	9.68246i	−0.564692	−	0.437409i
$491$			7.74597i			0.349571i	0.984607	+	0.174785i	$0.0559231\pi$
$491$			7.74597i			0.349571i	−0.984607	+	0.174785i	$0.944077\pi$
$492$		0			0
$493$	−2.00000	−	2.00000i	−0.0900755	−	0.0900755i
$494$	12.4894	−	0.123724i	0.561924	−	0.00556662i
$495$	−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	$-0.747448\pi$
$499$		−	31.8434i		−	1.42550i	0.701416	−	0.712752i	$-0.252552\pi$
$500$	−11.3565	+	19.2622i	−0.507877	+	0.861430i
$501$		0			0
$502$	−10.8671	+	1.38031i	−0.485024	+	0.0616062i
$503$	−19.3649	+	19.3649i	−0.863439	+	0.863439i	−0.991736	−	0.128297i	$-0.959049\pi$
$503$	−19.3649	+	19.3649i	−0.863439	+	0.863439i	0.128297	+	0.991736i	$0.459049\pi$
$504$	−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
$508$	28.3095	+	16.6905i	1.25603	+	0.740522i
$509$	−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
$512$	20.5322	+	9.50947i	0.907402	+	0.420263i
$513$		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
$518$	5.52123	+	43.4686i	0.242589	+	1.90990i
$519$		0			0
$520$	11.3862	−	19.7574i	0.499318	−	0.866419i
$521$	32.0000			1.40195			0.700973	−	0.713188i	$-0.252749\pi$
$521$	32.0000			1.40195			0.700973	+	0.713188i	$0.252749\pi$
$522$	−1.06918	−	8.41765i	−0.0467968	−	0.368431i
$523$	7.74597	−	7.74597i	0.338707	−	0.338707i	−0.517173	−	0.855881i	$-0.673016\pi$
$523$	7.74597	−	7.74597i	0.338707	−	0.338707i	0.855881	+	0.517173i	$0.173016\pi$
$524$	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
$530$	8.87298	−	1.12702i	0.385418	−	0.0489545i
$531$	22.0454			0.956689
$532$	14.6190	+	8.61895i	0.633812	+	0.373679i
$533$	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
$538$	−30.8647	+	3.92033i	−1.33067	+	0.169018i
$539$			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	$0.978345\pi$
$542$	1.74597	+	13.7460i	0.0749957	+	0.590440i
$543$		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	0.521846	−	0.853040i	$-0.325244\pi$
$547$	−7.74597	−	7.74597i	−0.331194	−	0.331194i	−0.853040	+	0.521846i	$0.825244\pi$
$548$	7.70486	+	4.54259i	0.329135	+	0.194050i
$549$		−	18.0000i		−	0.768221i
$550$	17.1825	−	2.18246i	0.732662	−	0.0930603i
$551$	−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	$0.658260\pi$
$558$	−41.2379	+	5.23790i	−1.74574	+	0.221738i
$559$	30.9839	−	24.4949i	1.31048	−	1.03602i
$560$	27.1109	−	15.0000i	1.14564	−	0.633866i
$561$		0			0
$562$	−8.87298	+	1.12702i	−0.374284	+	0.0475403i
$563$		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
$568$	−5.12702	−	12.8730i	−0.215125	−	0.540138i
$569$		−	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	$-0.948180\pi$
$571$		−	7.74597i		−	0.324159i	0.986778	−	0.162079i	$-0.0518200\pi$
$572$	−17.4998	+	2.39915i	−0.731705	+	0.100313i
$573$		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	$0.720326\pi$
$578$	−21.0441	+	2.67295i	−0.875320	+	0.111180i
$579$		0			0
$580$	−4.54259	+	7.70486i	−0.188621	+	0.319927i
$581$	−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	−0.0863532	−	0.996265i	$-0.527521\pi$
$587$	22.0454	−	22.0454i	0.909911	−	0.909911i	0.996265	+	0.0863532i	$0.0275214\pi$
$588$		0			0
$589$			24.0000i			0.988903i
$590$	−18.3712	−	14.2302i	−0.756329	−	0.585850i
$591$		0			0
$592$	−34.3834	−	9.88849i	−1.41315	−	0.406415i
$593$	−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
$598$	−19.9431	−	19.5518i	−0.815533	−	0.799534i
$599$	−15.4919			−0.632983			−0.316492	−	0.948595i	$-0.602505\pi$
$599$	−15.4919			−0.632983			−0.316492	+	0.948595i	$0.602505\pi$
$600$		0			0
$601$	24.0000			0.978980			0.489490	−	0.872009i	$-0.337183\pi$
$601$	24.0000			0.978980			0.489490	+	0.872009i	$0.337183\pi$
$602$	53.2379	−	6.76210i	2.16981	−	0.275603i
$603$	−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	0.980835	−	0.194838i	$-0.0624180\pi$
$607$	19.3649	+	19.3649i	0.785998	+	0.785998i	−0.194838	+	0.980835i	$0.562418\pi$
$608$	−11.1825	+	8.18246i	−0.453509	+	0.331843i
$609$		0			0
$610$	−11.6190	+	15.0000i	−0.470438	+	0.607332i
$611$	9.79796	−	7.74597i	0.396383	−	0.313368i
$612$	7.30948	+	4.30948i	0.295468	+	0.174200i
$613$	−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	$0.0156757\pi$
$619$			2.44949i			0.0984533i	−0.998788	+	0.0492267i	$0.984324\pi$
$620$	37.7460	+	22.2540i	1.51591	+	0.893743i
$621$		0			0
$622$	32.6014	−	4.14092i	1.30720	−	0.166036i
$623$	−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
$628$	−20.1109	+	34.1109i	−0.802512	+	1.36117i
$629$	12.6491			0.504353
$630$	−32.6014	+	4.14092i	−1.29887	+	0.164978i
$631$	−44.0908			−1.75523			−0.877614	−	0.479368i	$-0.840866\pi$
$631$	−44.0908			−1.75523			−0.877614	+	0.479368i	$0.840866\pi$
$632$	8.10653	+	20.3540i	0.322460	+	0.809638i
$633$		0			0
$634$		0			0
$635$			36.7423i			1.45808i
$636$		0			0
$637$	−2.09431	+	17.9057i	−0.0829794	+	0.709449i
$638$	6.87298	−	0.872983i	0.272104	−	0.0345617i
$639$			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	0.753755	−	0.657156i	$-0.228241\pi$
$643$	2.44949	+	2.44949i	0.0965984	+	0.0965984i	−0.657156	+	0.753755i	$0.728241\pi$
$644$	−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	0.976560	−	0.215246i	$-0.0690554\pi$
$647$	19.3649	+	19.3649i	0.761313	+	0.761313i	−0.215246	+	0.976560i	$0.569055\pi$
$648$	9.41893	+	23.6492i	0.370011	+	0.929028i
$649$			18.0000i			0.706562i
$650$	25.4938	−	0.252551i	0.999951	−	0.00990588i
$651$		0			0
$652$	−35.8090	−	21.1120i	−1.40239	−	0.826811i
$653$	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
$658$	16.8353	−	2.13836i	0.656308	−	0.0833621i
$659$	7.74597			0.301740			0.150870	−	0.988554i	$-0.451793\pi$
$659$	7.74597			0.301740			0.150870	+	0.988554i	$0.451793\pi$
$660$		0			0
$661$			34.7851i			1.35298i	0.736451	+	0.676491i	$0.236500\pi$
$661$			34.7851i			1.35298i	−0.736451	+	0.676491i	$0.763500\pi$
$662$	−1.30948	−	10.3095i	−0.0508942	−	0.400689i
$663$		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
$668$	10.5560	−	17.9045i	0.408424	−	0.692745i
$669$		0			0
$670$	1.38031	+	10.8671i	0.0533259	+	0.419834i
$671$	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
$676$	−25.9949	+	0.515080i	−0.999804	+	0.0198108i
$677$	−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
$680$	−3.30948	−	8.30948i	−0.126913	−	0.318654i
$681$		0			0
$682$	−4.27673	−	33.6706i	−0.163764	−	1.28931i
$683$	−19.5959	−	19.5959i	−0.749817	−	0.749817i	0.224628	−	0.974445i	$-0.427883\pi$
$683$	−19.5959	−	19.5959i	−0.749817	−	0.749817i	−0.974445	+	0.224628i	$0.927883\pi$
$684$	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
$688$	−12.1109	+	42.1109i	−0.461723	+	1.60546i
$689$	−6.32456	−	8.00000i	−0.240946	−	0.304776i
$690$		0			0
$691$	22.0454			0.838647			0.419323	−	0.907837i	$-0.362267\pi$
$691$	22.0454			0.838647			0.419323	+	0.907837i	$0.362267\pi$
$692$	−29.2379	−	17.2379i	−1.11146	−	0.655287i
$693$	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
$698$	−0.563508	−	4.43649i	−0.0213291	−	0.167924i
$699$		0			0
$700$	29.8408	+	17.5934i	1.12788	+	0.664966i
$701$	−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
$712$	−13.2379	−	33.2379i	−0.496111	−	1.24564i
$713$	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
$718$	27.4919	−	3.49193i	1.02599	−	0.130318i
$719$	−7.74597			−0.288876			−0.144438	−	0.989514i	$-0.546137\pi$
$719$	−7.74597			−0.288876			−0.144438	+	0.989514i	$0.546137\pi$
$720$	7.41637	−	25.7875i	0.276392	−	0.961045i
$721$		−	56.9210i		−	2.11985i
$722$	2.31656	+	18.2382i	0.0862135	+	0.678757i
$723$		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	0.775270	−	0.631629i	$-0.217614\pi$
$727$	3.87298	+	3.87298i	0.143641	+	0.143641i	−0.631629	+	0.775270i	$0.717614\pi$
$728$	−30.6080	−	17.6394i	−1.13441	−	0.653761i
$729$		−	27.0000i		−	1.00000i
$730$	1.78197	+	14.0294i	0.0659537	+	0.519252i
$731$		−	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
$738$	−3.38105	−	26.6190i	−0.124458	−	0.979857i
$739$		−	7.34847i		−	0.270318i	−0.990824	−	0.135159i	$-0.956846\pi$
$739$		−	7.34847i		−	0.270318i	0.990824	−	0.135159i	$-0.0431545\pi$
$740$	−10.0000	−	38.7298i	−0.367607	−	1.42374i
$741$		0			0
$742$	−1.74597	−	13.7460i	−0.0640965	−	0.504630i
$743$	17.1464	+	17.1464i	0.629041	+	0.629041i	0.947827	−	0.318785i	$-0.103275\pi$
$743$	17.1464	+	17.1464i	0.629041	+	0.629041i	−0.318785	+	0.947827i	$0.603275\pi$
$744$		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
$748$	−3.51867	+	5.96816i	−0.128655	+	0.218218i
$749$		0			0
$750$		0			0
$751$		−	46.4758i		−	1.69593i	−0.530055	−	0.847963i	$-0.677829\pi$
$751$		−	46.4758i		−	1.69593i	0.530055	−	0.847963i	$-0.322171\pi$
$752$	−3.82980	+	13.3166i	−0.139658	+	0.485608i
$753$		0			0
$754$	10.1975	−	0.101021i	0.371372	−	0.00367895i
$755$	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	$0.384892\pi$
$758$	−24.0554	+	3.05544i	−0.873733	+	0.110979i
$759$		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	$0.794237\pi$
$770$	−3.38105	−	26.6190i	−0.121845	−	0.959280i
$771$		0			0
$772$	−4.54259	+	7.70486i	−0.163491	+	0.277304i
$773$	−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
$778$	19.6412	−	2.49476i	0.704171	−	0.0894414i
$779$	−15.4919			−0.555056
$780$		0			0
$781$	−12.0000			−0.429394
$782$	−10.8671	+	1.38031i	−0.388608	+	0.0493597i
$783$		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	−0.510574	−	0.859834i	$-0.670567\pi$
$787$	9.79796	−	9.79796i	0.349260	−	0.349260i	0.859834	+	0.510574i	$0.170567\pi$
$788$	15.4097	+	9.08517i	0.548949	+	0.323646i
$789$		0			0
$790$	−15.0000	+	19.3649i	−0.533676	+	0.688973i
$791$	44.0908			1.56769
$792$	−19.3095	+	7.69052i	−0.686132	+	0.273271i
$793$	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
$800$	−22.8261	+	16.7024i	−0.807024	+	0.590518i
$801$			37.9473i			1.34080i
$802$	−17.7460	+	2.25403i	−0.626632	+	0.0795927i
$803$	7.74597	−	7.74597i	0.273349	−	0.273349i
$804$		0			0
$805$	30.0000	−	30.0000i	1.05736	−	1.05736i
$806$	−0.494897	−	49.9575i	−0.0174320	−	1.75968i
$807$		0			0
$808$	−14.6517	−	36.7876i	−0.515444	−	1.29418i
$809$		−	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	$-0.656855\pi$
$811$	−26.9444			−0.946145			−0.473073	+	0.881023i	$0.656855\pi$
$812$	11.9363	+	7.03734i	0.418883	+	0.246962i
$813$		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
$818$	4.50807	+	35.4919i	0.157621	+	1.24095i
$819$	23.2379	+	29.3939i	0.811998	+	1.02711i
$820$	−14.3649	+	24.3649i	−0.501645	+	0.850860i
$821$		−	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	−0.474984	−	0.879995i	$-0.657546\pi$
$823$	11.6190	−	11.6190i	0.405011	−	0.405011i	0.879995	+	0.474984i	$0.157546\pi$
$824$	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	−0.748412	−	0.663235i	$-0.769183\pi$
$827$	−2.44949	+	2.44949i	−0.0851771	+	0.0851771i	0.663235	+	0.748412i	$0.269183\pi$
$828$	−28.3095	−	16.6905i	−0.983822	−	0.580036i
$829$			42.0000i			1.45872i	0.684130	+	0.729360i	$0.260182\pi$
$829$			42.0000i			1.45872i	−0.684130	+	0.729360i	$0.739818\pi$
$830$	21.7343	−	2.76062i	0.754408	−	0.0958224i
$831$		0			0
$832$	23.1083	−	17.2629i	0.801135	−	0.598483i
$833$	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
$838$	−4.14092	−	32.6014i	−0.143046	−	1.12620i
$839$		−	9.79796i		−	0.338263i	−0.985593	−	0.169132i	$-0.945904\pi$
$839$		−	9.79796i		−	0.338263i	0.985593	−	0.169132i	$-0.0540963\pi$
$840$		0			0
$841$	25.0000			0.862069
$842$	13.3095	−	1.69052i	0.458675	−	0.0582593i
$843$		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
$848$	10.8730	+	3.12702i	0.373380	+	0.107382i
$849$		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	$-0.729750\pi$
$859$	−38.7298			−1.32144			−0.660722	+	0.750630i	$0.729750\pi$
$860$	−47.4342	+	12.2474i	−1.61749	+	0.417635i
$861$		0			0
$862$	−3.49193	−	27.4919i	−0.118936	−	0.936379i
$863$	−31.8434	−	31.8434i	−1.08396	−	1.08396i	−0.996136	−	0.0878249i	$-0.972008\pi$
$863$	−31.8434	−	31.8434i	−1.08396	−	1.08396i	−0.0878249	−	0.996136i	$-0.527992\pi$
$864$		0			0
$865$		−	37.9473i		−	1.29025i
$866$	23.2702	−	30.0416i	0.790752	−	1.02086i
$867$		0			0
$868$	34.4758	−	58.4758i	1.17018	−	1.98480i
$869$	18.9737			0.643638
$870$		0			0
$871$	9.79796	−	7.74597i	0.331991	−	0.262462i
$872$	−3.30948	−	8.30948i	−0.112073	−	0.281394i
$873$	−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	$0.543551\pi$
$878$	−4.14092	−	32.6014i	−0.139749	−	1.10024i
$879$		0			0
$880$	21.0554	+	6.05544i	0.709779	+	0.204129i
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$	2.67295	+	21.0441i	0.0900031	+	0.708593i
$883$	−15.4919	+	15.4919i	−0.521345	+	0.521345i	−0.917978	−	0.396632i	$-0.870179\pi$
$883$	−15.4919	+	15.4919i	−0.521345	+	0.521345i	0.396632	+	0.917978i	$0.370179\pi$
$884$	−6.16483	+	8.12372i	−0.207346	+	0.273230i
$885$		0			0
$886$	36.7423	+	28.4605i	1.23438	+	0.956149i
$887$	−27.1109	−	27.1109i	−0.910294	−	0.910294i	0.0860007	−	0.996295i	$-0.472591\pi$
$887$	−27.1109	−	27.1109i	−0.910294	−	0.910294i	−0.996295	+	0.0860007i	$0.972591\pi$
$888$		0			0
$889$	56.9210			1.90907
$890$	24.4949	−	31.6228i	0.821071	−	1.06000i
$891$	22.0454			0.738549
$892$	−5.96816	−	3.51867i	−0.199829	−	0.117814i
$893$	−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
$898$	−1.12702	−	8.87298i	−0.0376090	−	0.296095i
$899$			19.5959i			0.653560i
$900$	29.0474	−	7.50000i	0.968246	−	0.250000i
$901$	−4.00000			−0.133259
$902$	21.7343	−	2.76062i	0.723672	−	0.0919184i
$903$		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	$0.00930542\pi$
$907$	30.9839	+	30.9839i	1.02880	+	1.02880i	0.0292297	+	0.999573i	$0.490695\pi$
$908$	−14.0747	+	23.8726i	−0.467085	+	0.792242i
$909$			42.0000i			1.39305i
$910$	−0.391251	−	39.4949i	−0.0129698	−	1.30924i
$911$			38.7298i			1.28318i	0.767049	+	0.641588i	$0.221724\pi$
$911$			38.7298i			1.28318i	−0.767049	+	0.641588i	$0.778276\pi$
$912$		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	$-0.221973\pi$
$919$	46.4758			1.53310			0.766548	+	0.642188i	$0.221973\pi$
$920$	12.8175	+	32.1825i	0.422582	+	1.06102i
$921$		0			0
$922$	48.8014	−	6.19859i	1.60719	−	0.204140i
$923$	−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
$928$	−9.13044	+	6.68095i	−0.299721	+	0.219313i
$929$	−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
$932$	−2.43649	−	1.43649i	−0.0798099	−	0.0470538i
$933$		0			0
$934$	−9.48683	+	12.2474i	−0.310419	+	0.400749i
$935$	−7.74597			−0.253320
$936$	−29.5454	+	7.94159i	−0.965722	+	0.259579i
$937$	−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	$0.331780\pi$
$938$	16.8353	−	2.13836i	0.549692	−	0.0698201i
$939$		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	−0.745785	−	0.666187i	$-0.767925\pi$
$947$	−2.44949	+	2.44949i	−0.0795977	+	0.0795977i	0.666187	+	0.745785i	$0.267925\pi$
$948$		0			0
$949$	12.6491	−	10.0000i	0.410608	−	0.324614i
$950$	−2.18246	−	17.1825i	−0.0708083	−	0.557473i
$951$		0			0
$952$	−12.8730	+	5.12702i	−0.417216	+	0.166168i
$953$	−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
$958$	−6.87298	+	0.872983i	−0.222056	+	0.0282048i
$959$	15.4919			0.500261
$960$		0			0
$961$	65.0000			2.09677
$962$	−31.9280	+	32.5669i	−1.02940	+	1.05000i
$963$		0			0
$964$		0			0
$965$	−10.0000			−0.321911
$966$		0			0
$967$	−2.44949	+	2.44949i	−0.0787703	+	0.0787703i	−0.745394	−	0.666624i	$-0.767739\pi$
$967$	−2.44949	+	2.44949i	−0.0787703	+	0.0787703i	0.666624	+	0.745394i	$0.267739\pi$
$968$	5.23274	+	13.1384i	0.168187	+	0.422285i
$969$		0			0
$970$	14.0294	−	1.78197i	0.450457	−	0.0572156i
$971$			7.74597i			0.248580i	0.992246	+	0.124290i	$0.0396653\pi$
$971$			7.74597i			0.248580i	−0.992246	+	0.124290i	$0.960335\pi$
$972$		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
$980$	11.3565	−	19.2622i	0.362769	−	0.615307i
$981$			9.48683i			0.302891i
$982$	−10.8671	+	1.38031i	−0.346784	+	0.0440474i
$983$	−7.34847	−	7.34847i	−0.234380	−	0.234380i	0.580138	−	0.814518i	$-0.302999\pi$
$983$	−7.34847	−	7.34847i	−0.234380	−	0.234380i	−0.814518	+	0.580138i	$0.802999\pi$
$984$		0			0
$985$			20.0000i			0.637253i
$986$	2.44949	−	3.16228i	0.0780076	−	0.100707i
$987$		0			0
$988$	2.39915	+	17.4998i	0.0763271	+	0.556744i
$989$			60.0000i			1.90789i
$990$	−18.3712	−	14.2302i	−0.583874	−	0.452267i
$991$			46.4758i			1.47635i	0.674608	+	0.738176i	$0.264313\pi$
$991$			46.4758i			1.47635i	−0.674608	+	0.738176i	$0.735687\pi$
$992$	32.7298	+	44.7298i	1.03917	+	1.42017i
$993$		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	$-0.195446\pi$
$998$	44.6744	−	5.67439i	1.41414	−	0.179620i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.178197 + 1.40294i) q^{2} +(-1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(-2.44949 + 2.44949i) q^{7} +(-1.04655 - 2.62769i) q^{8} +3.00000i q^{9} +O(q^{10})\)	\(q+(0.178197 + 1.40294i) q^{2} +(-1.93649 + 0.500000i) q^{4} +(-1.58114 - 1.58114i) q^{5} +(-2.44949 + 2.44949i) q^{7} +(-1.04655 - 2.62769i) q^{8} +3.00000i q^{9} +(1.93649 - 2.50000i) q^{10} -2.44949 q^{11} +(-3.58114 - 0.418861i) q^{13} +(-3.87298 - 3.00000i) q^{14} +(3.50000 - 1.93649i) q^{16} +(-1.00000 + 1.00000i) q^{17} +(-4.20883 + 0.534591i) q^{18} +2.44949i q^{19} +(3.85243 + 2.27129i) q^{20} +(-0.436492 - 3.43649i) q^{22} +(3.87298 - 3.87298i) q^{23} +5.00000i q^{25} +(-0.0505103 - 5.09877i) q^{26} +(3.51867 - 5.96816i) q^{28} +2.00000i q^{29} +9.79796 q^{31} +(3.34047 + 4.56522i) q^{32} +(-1.58114 - 1.22474i) q^{34} +7.74597 q^{35} +(-1.50000 - 5.80948i) q^{36} +(-6.32456 - 6.32456i) q^{37} +(-3.43649 + 0.436492i) q^{38} +(-2.50000 + 5.80948i) q^{40} +6.32456i q^{41} +(-7.74597 + 7.74597i) q^{43} +(4.74342 - 1.22474i) q^{44} +(4.74342 - 4.74342i) q^{45} +(6.12372 + 4.74342i) q^{46} +(-2.44949 + 2.44949i) q^{47} -5.00000i q^{49} +(-7.01471 + 0.890985i) q^{50} +(7.14428 - 0.979448i) q^{52} +(2.00000 + 2.00000i) q^{53} +(3.87298 + 3.87298i) q^{55} +(9.00000 + 3.87298i) q^{56} +(-2.80588 + 0.356394i) q^{58} -7.34847i q^{59} -6.00000 q^{61} +(1.74597 + 13.7460i) q^{62} +(-7.34847 - 7.34847i) q^{63} +(-5.80948 + 5.50000i) q^{64} +(5.00000 + 6.32456i) q^{65} +(-2.44949 + 2.44949i) q^{67} +(1.43649 - 2.43649i) q^{68} +(1.38031 + 10.8671i) q^{70} +4.89898 q^{71} +(7.88306 - 3.13964i) q^{72} +(-3.16228 + 3.16228i) q^{73} +(7.74597 - 10.0000i) q^{74} +(-1.22474 - 4.74342i) q^{76} +(6.00000 - 6.00000i) q^{77} -7.74597 q^{79} +(-8.59585 - 2.47212i) q^{80} -9.00000 q^{81} +(-8.87298 + 1.12702i) q^{82} +(4.89898 + 4.89898i) q^{83} +3.16228 q^{85} +(-12.2474 - 9.48683i) q^{86} +(2.56351 + 6.43649i) q^{88} +12.6491 q^{89} +(7.50000 + 5.80948i) q^{90} +(9.79796 - 7.74597i) q^{91} +(-5.56351 + 9.43649i) q^{92} +(-3.87298 - 3.00000i) q^{94} +(3.87298 - 3.87298i) q^{95} +(3.16228 + 3.16228i) q^{97} +(7.01471 - 0.890985i) q^{98} -7.34847i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 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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