LMFDB - Embedded newform 300.2.e.c.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(251,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("300.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.e (of order $2$, degree $1$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 60)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.1
Root			$-1.17915 + 0.780776i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.c.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.17915 - 0.780776i) q^{2} +(1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} +3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 - 2.56155i) q^{9} +O(q^{10})$	\(q+(-1.17915 - 0.780776i) q^{2} +(1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} +3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 - 2.56155i) q^{9} +1.32431 q^{11} +(2.74070 + 2.11862i) q^{12} +5.12311 q^{13} +(2.35829 - 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} -2.00000i q^{17} +(-3.84130 + 1.80122i) q^{18} +1.32431i q^{19} +(2.56155 + 4.56155i) q^{21} +(-1.56155 - 1.03399i) q^{22} -0.371834 q^{23} +(-1.57752 - 4.63804i) q^{24} +(-6.04090 - 4.00000i) q^{26} +(0.185917 - 5.19283i) q^{27} +(-5.56155 + 2.35829i) q^{28} +3.12311i q^{29} -4.71659i q^{31} +(5.52390 - 1.21922i) q^{32} +(2.00000 - 1.12311i) q^{33} +(-1.56155 + 2.35829i) q^{34} +(5.93581 + 0.875288i) q^{36} -5.12311 q^{37} +(1.03399 - 1.56155i) q^{38} +(7.73704 - 4.34475i) q^{39} -1.12311i q^{41} +(0.541105 - 7.37874i) q^{42} -7.73704i q^{43} +(1.03399 + 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} -3.02045 q^{47} +(-1.76115 + 6.70062i) q^{48} -2.12311 q^{49} +(-1.69614 - 3.02045i) q^{51} +(4.00000 + 9.43318i) q^{52} +12.2462i q^{53} +(-4.27366 + 5.97795i) q^{54} +(8.39919 + 1.56155i) q^{56} +(1.12311 + 2.00000i) q^{57} +(2.43845 - 3.68260i) q^{58} -14.1498 q^{59} +3.12311 q^{61} +(-3.68260 + 5.56155i) q^{62} +(7.73704 + 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} +(-3.23519 - 0.237246i) q^{66} +4.34475i q^{67} +(3.68260 - 1.56155i) q^{68} +(-0.561553 + 0.315342i) q^{69} +3.39228 q^{71} +(-6.31579 - 5.66664i) q^{72} -8.24621 q^{73} +(6.04090 + 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} +4.00000i q^{77} +(-12.5154 - 0.917790i) q^{78} +8.10887i q^{79} +(-4.12311 - 8.00000i) q^{81} +(-0.876894 + 1.32431i) q^{82} -15.1022 q^{83} +(-6.39919 + 8.27814i) q^{84} +(-6.04090 + 9.12311i) q^{86} +(2.64861 + 4.71659i) q^{87} +(0.684658 - 3.68260i) q^{88} +10.2462i q^{89} +15.4741i q^{91} +(-0.290319 - 0.684658i) q^{92} +(-4.00000 - 7.12311i) q^{93} +(3.56155 + 2.35829i) q^{94} +(7.30834 - 6.52596i) q^{96} +6.00000 q^{97} +(2.50345 + 1.65767i) q^{98} +(2.06798 - 3.39228i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 14 q^{16} - 16 q^{18} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 28 q^{28} + 16 q^{33} + 4 q^{34} + 18 q^{36} - 8 q^{37} + 12 q^{42} + 20 q^{46} + 36 q^{48} + 16 q^{49} + 32 q^{52} - 10 q^{54} - 24 q^{57} + 36 q^{58} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 24 q^{72} - 36 q^{76} - 40 q^{78} - 40 q^{82} + 16 q^{84} - 44 q^{88} - 32 q^{93} + 12 q^{94} + 42 q^{96} + 48 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 14 * q^16 - 16 * q^18 + 4 * q^21 + 4 * q^22 - 2 * q^24 - 28 * q^28 + 16 * q^33 + 4 * q^34 + 18 * q^36 - 8 * q^37 + 12 * q^42 + 20 * q^46 + 36 * q^48 + 16 * q^49 + 32 * q^52 - 10 * q^54 - 24 * q^57 + 36 * q^58 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 24 * q^72 - 36 * q^76 - 40 * q^78 - 40 * q^82 + 16 * q^84 - 44 * q^88 - 32 * q^93 + 12 * q^94 + 42 * q^96 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.17915	−	0.780776i	−0.833783	−	0.552092i
$2$	−1.17915	−	0.780776i	−0.833783	−	0.552092i
$3$	1.51022	−	0.848071i	0.871928	−	0.489634i
$3$	1.51022	−	0.848071i	0.871928	−	0.489634i
$4$	0.780776	+	1.84130i	0.390388	+	0.920650i
$5$		0			0
$5$		0			0
$6$	−2.44293	−	0.179147i	−0.997322	−	0.0731366i
$7$			3.02045i			1.14162i	0.821081	+	0.570811i	$0.193371\pi$
$7$			3.02045i			1.14162i	−0.821081	+	0.570811i	$0.806629\pi$
$8$	0.516994	−	2.78078i	0.182785	−	0.983153i
$9$	1.56155	−	2.56155i	0.520518	−	0.853851i
$10$		0			0
$11$	1.32431			0.399294			0.199647	−	0.979868i	$-0.436021\pi$
$11$	1.32431			0.399294			0.199647	+	0.979868i	$0.436021\pi$
$12$	2.74070	+	2.11862i	0.791172	+	0.611594i
$13$	5.12311			1.42089			0.710447	−	0.703751i	$-0.248493\pi$
$13$	5.12311			1.42089			0.710447	+	0.703751i	$0.248493\pi$
$14$	2.35829	−	3.56155i	0.630281	−	0.951865i
$15$		0			0
$16$	−2.78078	+	2.87529i	−0.695194	+	0.718822i
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$	−3.84130	+	1.80122i	−0.905403	+	0.424553i
$19$			1.32431i			0.303817i	0.988395	+	0.151908i	$0.0485419\pi$
$19$			1.32431i			0.303817i	−0.988395	+	0.151908i	$0.951458\pi$
$20$		0			0
$21$	2.56155	+	4.56155i	0.558977	+	0.995412i
$22$	−1.56155	−	1.03399i	−0.332924	−	0.220447i
$23$	−0.371834			−0.0775328			−0.0387664	−	0.999248i	$-0.512343\pi$
$23$	−0.371834			−0.0775328			−0.0387664	+	0.999248i	$0.512343\pi$
$24$	−1.57752	−	4.63804i	−0.322010	−	0.946736i
$25$		0			0
$26$	−6.04090	−	4.00000i	−1.18472	−	0.784465i
$27$	0.185917	−	5.19283i	0.0357798	−	0.999360i
$28$	−5.56155	+	2.35829i	−1.05103	+	0.445676i
$29$			3.12311i			0.579946i	0.957035	+	0.289973i	$0.0936464\pi$
$29$			3.12311i			0.579946i	−0.957035	+	0.289973i	$0.906354\pi$
$30$		0			0
$31$		−	4.71659i		−	0.847124i	−0.905867	−	0.423562i	$-0.860780\pi$
$31$		−	4.71659i		−	0.847124i	0.905867	−	0.423562i	$-0.139220\pi$
$32$	5.52390	−	1.21922i	0.976497	−	0.215530i
$33$	2.00000	−	1.12311i	0.348155	−	0.195508i
$34$	−1.56155	+	2.35829i	−0.267804	+	0.404444i
$35$		0			0
$36$	5.93581	+	0.875288i	0.989302	+	0.145881i
$37$	−5.12311			−0.842233			−0.421117	−	0.907006i	$-0.638362\pi$
$37$	−5.12311			−0.842233			−0.421117	+	0.907006i	$0.638362\pi$
$38$	1.03399	−	1.56155i	0.167735	−	0.253317i
$39$	7.73704	−	4.34475i	1.23892	−	0.695718i
$40$		0			0
$41$		−	1.12311i		−	0.175400i	−0.996147	−	0.0876998i	$-0.972048\pi$
$41$		−	1.12311i		−	0.175400i	0.996147	−	0.0876998i	$-0.0279516\pi$
$42$	0.541105	−	7.37874i	0.0834943	−	1.13856i
$43$		−	7.73704i		−	1.17989i	−0.807445	−	0.589944i	$-0.799150\pi$
$43$		−	7.73704i		−	1.17989i	0.807445	−	0.589944i	$-0.200850\pi$
$44$	1.03399	+	2.43845i	0.155879	+	0.367610i
$45$		0			0
$46$	0.438447	+	0.290319i	0.0646455	+	0.0428052i
$47$	−3.02045			−0.440578			−0.220289	−	0.975435i	$-0.570700\pi$
$47$	−3.02045			−0.440578			−0.220289	+	0.975435i	$0.570700\pi$
$48$	−1.76115	+	6.70062i	−0.254200	+	0.967152i
$49$	−2.12311			−0.303301
$50$		0			0
$51$	−1.69614	−	3.02045i	−0.237507	−	0.422947i
$52$	4.00000	+	9.43318i	0.554700	+	1.30815i
$53$			12.2462i			1.68215i	0.540921	+	0.841073i	$0.318076\pi$
$53$			12.2462i			1.68215i	−0.540921	+	0.841073i	$0.681924\pi$
$54$	−4.27366	+	5.97795i	−0.581571	+	0.813495i
$55$		0			0
$56$	8.39919	+	1.56155i	1.12239	+	0.208671i
$57$	1.12311	+	2.00000i	0.148759	+	0.264906i
$58$	2.43845	−	3.68260i	0.320184	−	0.483549i
$59$	−14.1498			−1.84214			−0.921071	−	0.389394i	$-0.872685\pi$
$59$	−14.1498			−1.84214			−0.921071	+	0.389394i	$0.872685\pi$
$60$		0			0
$61$	3.12311			0.399873			0.199936	−	0.979809i	$-0.435926\pi$
$61$	3.12311			0.399873			0.199936	+	0.979809i	$0.435926\pi$
$62$	−3.68260	+	5.56155i	−0.467691	+	0.706318i
$63$	7.73704	+	4.71659i	0.974775	+	0.594234i
$64$	−7.46543	−	2.87529i	−0.933179	−	0.359411i
$65$		0			0
$66$	−3.23519	−	0.237246i	−0.398224	−	0.0292030i
$67$			4.34475i			0.530796i	0.964139	+	0.265398i	$0.0855034\pi$
$67$			4.34475i			0.530796i	−0.964139	+	0.265398i	$0.914497\pi$
$68$	3.68260	−	1.56155i	0.446581	−	0.189366i
$69$	−0.561553	+	0.315342i	−0.0676030	+	0.0379627i
$70$		0			0
$71$	3.39228			0.402590			0.201295	−	0.979531i	$-0.435485\pi$
$71$	3.39228			0.402590			0.201295	+	0.979531i	$0.435485\pi$
$72$	−6.31579	−	5.66664i	−0.744323	−	0.667819i
$73$	−8.24621			−0.965146			−0.482573	−	0.875856i	$-0.660298\pi$
$73$	−8.24621			−0.965146			−0.482573	+	0.875856i	$0.660298\pi$
$74$	6.04090	+	4.00000i	0.702240	+	0.464991i
$75$		0			0
$76$	−2.43845	+	1.03399i	−0.279709	+	0.118607i
$77$			4.00000i			0.455842i
$78$	−12.5154	−	0.917790i	−1.41709	−	0.103919i
$79$			8.10887i			0.912319i	0.889898	+	0.456160i	$0.150775\pi$
$79$			8.10887i			0.912319i	−0.889898	+	0.456160i	$0.849225\pi$
$80$		0			0
$81$	−4.12311	−	8.00000i	−0.458123	−	0.888889i
$82$	−0.876894	+	1.32431i	−0.0968368	+	0.146245i
$83$	−15.1022			−1.65769			−0.828843	−	0.559481i	$-0.811000\pi$
$83$	−15.1022			−1.65769			−0.828843	+	0.559481i	$0.811000\pi$
$84$	−6.39919	+	8.27814i	−0.698209	+	0.903219i
$85$		0			0
$86$	−6.04090	+	9.12311i	−0.651407	+	0.983770i
$87$	2.64861	+	4.71659i	0.283961	+	0.505671i
$88$	0.684658	−	3.68260i	0.0729848	−	0.392567i
$89$			10.2462i			1.08610i	0.839702	+	0.543048i	$0.182730\pi$
$89$			10.2462i			1.08610i	−0.839702	+	0.543048i	$0.817270\pi$
$90$		0			0
$91$			15.4741i			1.62212i
$92$	−0.290319	−	0.684658i	−0.0302679	−	0.0713806i
$93$	−4.00000	−	7.12311i	−0.414781	−	0.738632i
$94$	3.56155	+	2.35829i	0.367346	+	0.243240i
$95$		0			0
$96$	7.30834	−	6.52596i	0.745904	−	0.666053i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	2.50345	+	1.65767i	0.252887	+	0.167450i
$99$	2.06798	−	3.39228i	0.207839	−	0.340937i
$100$		0			0
$101$		−	0.876894i		−	0.0872543i	−0.999048	−	0.0436271i	$-0.986109\pi$
$101$		−	0.876894i		−	0.0872543i	0.999048	−	0.0436271i	$-0.0138914\pi$
$102$	−0.358294	+	4.88586i	−0.0354764	+	0.483772i
$103$			9.80501i			0.966117i	0.875588	+	0.483058i	$0.160474\pi$
$103$			9.80501i			0.966117i	−0.875588	+	0.483058i	$0.839526\pi$
$104$	2.64861	−	14.2462i	0.259718	−	1.39696i
$105$		0			0
$106$	9.56155	−	14.4401i	0.928700	−	1.40255i
$107$	3.02045			0.291998			0.145999	−	0.989285i	$-0.453360\pi$
$107$	3.02045			0.291998			0.145999	+	0.989285i	$0.453360\pi$
$108$	9.70671	−	3.71211i	0.934029	−	0.357198i
$109$	−0.876894			−0.0839912			−0.0419956	−	0.999118i	$-0.513372\pi$
$109$	−0.876894			−0.0839912			−0.0419956	+	0.999118i	$0.513372\pi$
$110$		0			0
$111$	−7.73704	+	4.34475i	−0.734367	+	0.412386i
$112$	−8.68466	−	8.39919i	−0.820623	−	0.793649i
$113$		−	14.0000i		−	1.31701i	−0.752577	−	0.658505i	$-0.771189\pi$
$113$		−	14.0000i		−	1.31701i	0.752577	−	0.658505i	$-0.228811\pi$
$114$	0.237246	−	3.23519i	0.0222201	−	0.303003i
$115$		0			0
$116$	−5.75058	+	2.43845i	−0.533928	+	0.226404i
$117$	8.00000	−	13.1231i	0.739600	−	1.21323i
$118$	16.6847	+	11.0478i	1.53595	+	1.01703i
$119$	6.04090			0.553768
$120$		0			0
$121$	−9.24621			−0.840565
$122$	−3.68260	−	2.43845i	−0.333407	−	0.220767i
$123$	−0.952473	−	1.69614i	−0.0858816	−	0.152936i
$124$	8.68466	−	3.68260i	0.779905	−	0.330707i
$125$		0			0
$126$	−5.44050	−	11.6024i	−0.484679	−	1.03363i
$127$		−	15.1022i		−	1.34011i	−0.742313	−	0.670054i	$-0.766271\pi$
$127$		−	15.1022i		−	1.34011i	0.742313	−	0.670054i	$-0.233729\pi$
$128$	6.55789	+	9.21922i	0.579641	+	0.814872i
$129$	−6.56155	−	11.6847i	−0.577713	−	1.02878i
$130$		0			0
$131$	5.46026			0.477065			0.238532	−	0.971135i	$-0.423334\pi$
$131$	5.46026			0.477065			0.238532	+	0.971135i	$0.423334\pi$
$132$	3.62953	+	2.80571i	0.315910	+	0.244205i
$133$	−4.00000			−0.346844
$134$	3.39228	−	5.12311i	0.293049	−	0.442569i
$135$		0			0
$136$	−5.56155	−	1.03399i	−0.476899	−	0.0886637i
$137$			8.24621i			0.704521i	0.935902	+	0.352261i	$0.114587\pi$
$137$			8.24621i			0.704521i	−0.935902	+	0.352261i	$0.885413\pi$
$138$	0.908365	+	0.0666131i	0.0773251	+	0.00567048i
$139$		−	17.5420i		−	1.48790i	−0.668237	−	0.743949i	$-0.732951\pi$
$139$		−	17.5420i		−	1.48790i	0.668237	−	0.743949i	$-0.267049\pi$
$140$		0			0
$141$	−4.56155	+	2.56155i	−0.384152	+	0.215722i
$142$	−4.00000	−	2.64861i	−0.335673	−	0.222267i
$143$	6.78456			0.567354
$144$	3.02287	+	11.6130i	0.251906	+	0.967752i
$145$		0			0
$146$	9.72350	+	6.43845i	0.804722	+	0.532850i
$147$	−3.20636	+	1.80054i	−0.264457	+	0.148506i
$148$	−4.00000	−	9.43318i	−0.328798	−	0.775402i
$149$		−	14.0000i		−	1.14692i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$		0			0
$151$		−	7.36520i		−	0.599372i	−0.954038	−	0.299686i	$-0.903118\pi$
$151$		−	7.36520i		−	0.599372i	0.954038	−	0.299686i	$-0.0968819\pi$
$152$	3.68260	+	0.684658i	0.298698	+	0.0555331i
$153$	−5.12311	−	3.12311i	−0.414179	−	0.252488i
$154$	3.12311	−	4.71659i	0.251667	−	0.380074i
$155$		0			0
$156$	14.0409	+	10.8539i	1.12417	+	0.869010i
$157$	3.36932			0.268901			0.134450	−	0.990920i	$-0.457073\pi$
$157$	3.36932			0.268901			0.134450	+	0.990920i	$0.457073\pi$
$158$	6.33122	−	9.56155i	0.503684	−	0.760676i
$159$	10.3857	+	18.4945i	0.823636	+	1.46671i
$160$		0			0
$161$		−	1.12311i		−	0.0885131i
$162$	−1.38446	+	12.6524i	−0.108774	+	0.994067i
$163$			15.6829i			1.22838i	0.789159	+	0.614189i	$0.210517\pi$
$163$			15.6829i			1.22838i	−0.789159	+	0.614189i	$0.789483\pi$
$164$	2.06798	−	0.876894i	0.161482	−	0.0684739i
$165$		0			0
$166$	17.8078	+	11.7915i	1.38215	+	0.915196i
$167$	9.06134			0.701188			0.350594	−	0.936528i	$-0.385980\pi$
$167$	9.06134			0.701188			0.350594	+	0.936528i	$0.385980\pi$
$168$	14.0090	−	4.76481i	1.08082	−	0.367613i
$169$	13.2462			1.01894
$170$		0			0
$171$	3.39228	+	2.06798i	0.259414	+	0.158142i
$172$	14.2462	−	6.04090i	1.08626	−	0.460614i
$173$		−	2.00000i		−	0.152057i	−0.997106	−	0.0760286i	$-0.975776\pi$
$173$		−	2.00000i		−	0.152057i	0.997106	−	0.0760286i	$-0.0242240\pi$
$174$	0.559496	−	7.62953i	0.0424153	−	0.578393i
$175$		0			0
$176$	−3.68260	+	3.80776i	−0.277587	+	0.287021i
$177$	−21.3693	+	12.0000i	−1.60622	+	0.901975i
$178$	8.00000	−	12.0818i	0.599625	−	0.905569i
$179$	−10.0138			−0.748468			−0.374234	−	0.927334i	$-0.622094\pi$
$179$	−10.0138			−0.748468			−0.374234	+	0.927334i	$0.622094\pi$
$180$		0			0
$181$	−12.2462			−0.910254			−0.455127	−	0.890427i	$-0.650406\pi$
$181$	−12.2462			−0.910254			−0.455127	+	0.890427i	$0.650406\pi$
$182$	12.0818	−	18.2462i	0.895562	−	1.35250i
$183$	4.71659	−	2.64861i	0.348660	−	0.195791i
$184$	−0.192236	+	1.03399i	−0.0141718	+	0.0762266i
$185$		0			0
$186$	−0.844964	+	11.5223i	−0.0619558	+	0.844856i
$187$		−	2.64861i		−	0.193686i
$188$	−2.35829	−	5.56155i	−0.171996	−	0.405618i
$189$	15.6847	+	0.561553i	1.14089	+	0.0408470i
$190$		0			0
$191$	−24.9073			−1.80223			−0.901113	−	0.433585i	$-0.857248\pi$
$191$	−24.9073			−1.80223			−0.901113	+	0.433585i	$0.857248\pi$
$192$	−13.7129	+	1.98889i	−0.989645	+	0.143535i
$193$	0.246211			0.0177227			0.00886134	−	0.999961i	$-0.497179\pi$
$193$	0.246211			0.0177227			0.00886134	+	0.999961i	$0.497179\pi$
$194$	−7.07488	−	4.68466i	−0.507947	−	0.336339i
$195$		0			0
$196$	−1.65767	−	3.90928i	−0.118405	−	0.279234i
$197$		−	4.24621i		−	0.302530i	−0.988493	−	0.151265i	$-0.951665\pi$
$197$		−	4.24621i		−	0.302530i	0.988493	−	0.151265i	$-0.0483347\pi$
$198$	−5.08706	+	2.38537i	−0.361522	+	0.169521i
$199$			5.46026i			0.387067i	0.981094	+	0.193534i	$0.0619949\pi$
$199$			5.46026i			0.387067i	−0.981094	+	0.193534i	$0.938005\pi$
$200$		0			0
$201$	3.68466	+	6.56155i	0.259896	+	0.462816i
$202$	−0.684658	+	1.03399i	−0.0481724	+	0.0727511i
$203$	−9.43318			−0.662079
$204$	4.23725	−	5.48140i	0.296667	−	0.383775i
$205$		0			0
$206$	7.65552	−	11.5616i	0.533385	−	0.805532i
$207$	−0.580639	+	0.952473i	−0.0403572	+	0.0662014i
$208$	−14.2462	+	14.7304i	−0.987797	+	1.02137i
$209$			1.75379i			0.121312i
$210$		0			0
$211$		−	16.7984i		−	1.15645i	−0.815878	−	0.578224i	$-0.803746\pi$
$211$		−	16.7984i		−	1.15645i	0.815878	−	0.578224i	$-0.196254\pi$
$212$	−22.5490	+	9.56155i	−1.54867	+	0.656690i
$213$	5.12311	−	2.87689i	0.351029	−	0.197122i
$214$	−3.56155	−	2.35829i	−0.243463	−	0.161210i
$215$		0			0
$216$	−14.3440	−	3.20165i	−0.975983	−	0.217845i
$217$	14.2462			0.967096
$218$	1.03399	+	0.684658i	0.0700305	+	0.0463709i
$219$	−12.4536	+	6.99337i	−0.841538	+	0.472568i
$220$		0			0
$221$		−	10.2462i		−	0.689235i
$222$	12.5154	+	0.917790i	0.839978	+	0.0615980i
$223$		−	8.31768i		−	0.556993i	−0.960437	−	0.278496i	$-0.910164\pi$
$223$		−	8.31768i		−	0.556993i	0.960437	−	0.278496i	$-0.0898360\pi$
$224$	3.68260	+	16.6847i	0.246054	+	1.11479i
$225$		0			0
$226$	−10.9309	+	16.5081i	−0.727111	+	1.09810i
$227$	−21.8868			−1.45268			−0.726339	−	0.687337i	$-0.758780\pi$
$227$	−21.8868			−1.45268			−0.726339	+	0.687337i	$0.758780\pi$
$228$	−2.80571	+	3.62953i	−0.185812	+	0.240371i
$229$	−16.2462			−1.07358			−0.536790	−	0.843716i	$-0.680363\pi$
$229$	−16.2462			−1.07358			−0.536790	+	0.843716i	$0.680363\pi$
$230$		0			0
$231$	3.39228	+	6.04090i	0.223196	+	0.397462i
$232$	8.68466	+	1.61463i	0.570176	+	0.106005i
$233$			10.0000i			0.655122i	0.944830	+	0.327561i	$0.106227\pi$
$233$			10.0000i			0.655122i	−0.944830	+	0.327561i	$0.893773\pi$
$234$	−19.6794	+	9.22786i	−1.28648	+	0.603244i
$235$		0			0
$236$	−11.0478	−	26.0540i	−0.719151	−	1.69597i
$237$	6.87689	+	12.2462i	0.446702	+	0.795477i
$238$	−7.12311	−	4.71659i	−0.461722	−	0.305731i
$239$	17.3790			1.12416			0.562078	−	0.827084i	$-0.310002\pi$
$239$	17.3790			1.12416			0.562078	+	0.827084i	$0.310002\pi$
$240$		0			0
$241$	13.3693			0.861193			0.430597	−	0.902544i	$-0.358303\pi$
$241$	13.3693			0.861193			0.430597	+	0.902544i	$0.358303\pi$
$242$	10.9026	+	7.21922i	0.700849	+	0.464069i
$243$	−13.0114	−	8.58511i	−0.834680	−	0.550735i
$244$	2.43845	+	5.75058i	0.156106	+	0.368143i
$245$		0			0
$246$	−0.201201	+	2.74367i	−0.0128281	+	0.174930i
$247$			6.78456i			0.431691i
$248$	−13.1158	−	2.43845i	−0.832853	−	0.154842i
$249$	−22.8078	+	12.8078i	−1.44538	+	0.811659i
$250$		0			0
$251$	18.7033			1.18054			0.590272	−	0.807205i	$-0.299021\pi$
$251$	18.7033			1.18054			0.590272	+	0.807205i	$0.299021\pi$
$252$	−2.64376	+	17.9288i	−0.166541	+	1.12941i
$253$	−0.492423			−0.0309583
$254$	−11.7915	+	17.8078i	−0.739863	+	1.11736i
$255$		0			0
$256$	−0.534565	−	15.9911i	−0.0334103	−	0.999442i
$257$		−	30.4924i		−	1.90207i	−0.309091	−	0.951033i	$-0.600025\pi$
$257$		−	30.4924i		−	1.90207i	0.309091	−	0.951033i	$-0.399975\pi$
$258$	−1.38607	+	18.9010i	−0.0862929	+	1.17673i
$259$		−	15.4741i		−	0.961512i
$260$		0			0
$261$	8.00000	+	4.87689i	0.495188	+	0.301872i
$262$	−6.43845	−	4.26324i	−0.397769	−	0.263384i
$263$	23.7917			1.46706			0.733531	−	0.679656i	$-0.237871\pi$
$263$	23.7917			1.46706			0.733531	+	0.679656i	$0.237871\pi$
$264$	−2.08912	−	6.14219i	−0.128576	−	0.378026i
$265$		0			0
$266$	4.71659	+	3.12311i	0.289193	+	0.191490i
$267$	8.68951	+	15.4741i	0.531789	+	0.946998i
$268$	−8.00000	+	3.39228i	−0.488678	+	0.207217i
$269$			14.0000i			0.853595i	0.904347	+	0.426798i	$0.140358\pi$
$269$			14.0000i			0.853595i	−0.904347	+	0.426798i	$0.859642\pi$
$270$		0			0
$271$			15.3110i			0.930080i	0.885290	+	0.465040i	$0.153960\pi$
$271$			15.3110i			0.930080i	−0.885290	+	0.465040i	$0.846040\pi$
$272$	5.75058	+	5.56155i	0.348680	+	0.337219i
$273$	13.1231	+	23.3693i	0.794246	+	1.41438i
$274$	6.43845	−	9.72350i	0.388961	−	0.587418i
$275$		0			0
$276$	−1.01909	−	0.787776i	−0.0613418	−	0.0474186i
$277$	−23.3693			−1.40413			−0.702063	−	0.712115i	$-0.747738\pi$
$277$	−23.3693			−1.40413			−0.702063	+	0.712115i	$0.747738\pi$
$278$	−13.6964	+	20.6847i	−0.821457	+	1.24058i
$279$	−12.0818	−	7.36520i	−0.723318	−	0.440943i
$280$		0			0
$281$			13.6155i			0.812234i	0.913821	+	0.406117i	$0.133118\pi$
$281$			13.6155i			0.812234i	−0.913821	+	0.406117i	$0.866882\pi$
$282$	7.37874	+	0.541105i	0.439398	+	0.0322223i
$283$		−	23.2111i		−	1.37976i	−0.723925	−	0.689879i	$-0.757664\pi$
$283$		−	23.2111i		−	1.37976i	0.723925	−	0.689879i	$-0.242336\pi$
$284$	2.64861	+	6.24621i	0.157166	+	0.370644i
$285$		0			0
$286$	−8.00000	−	5.29723i	−0.473050	−	0.313232i
$287$	3.39228			0.200240
$288$	5.50276	−	16.0536i	0.324253	−	0.945970i
$289$	13.0000			0.764706
$290$		0			0
$291$	9.06134	−	5.08842i	0.531185	−	0.298289i
$292$	−6.43845	−	15.1838i	−0.376782	−	0.888562i
$293$		−	2.49242i		−	0.145609i	−0.997346	−	0.0728044i	$-0.976805\pi$
$293$		−	2.49242i		−	0.145609i	0.997346	−	0.0728044i	$-0.0231949\pi$
$294$	5.18660	+	0.380349i	0.302489	+	0.0221824i
$295$		0			0
$296$	−2.64861	+	14.2462i	−0.153948	+	0.828044i
$297$	0.246211	−	6.87689i	0.0142866	−	0.399038i
$298$	−10.9309	+	16.5081i	−0.633208	+	0.956286i
$299$	−1.90495			−0.110166
$300$		0			0
$301$	23.3693			1.34699
$302$	−5.75058	+	8.68466i	−0.330908	+	0.499746i
$303$	−0.743668	−	1.32431i	−0.0427226	−	0.0760794i
$304$	−3.80776	−	3.68260i	−0.218390	−	0.211212i
$305$		0			0
$306$	3.60245	+	7.68260i	0.205938	+	0.439185i
$307$		−	11.1293i		−	0.635184i	−0.948227	−	0.317592i	$-0.897126\pi$
$307$		−	11.1293i		−	0.635184i	0.948227	−	0.317592i	$-0.102874\pi$
$308$	−7.36520	+	3.12311i	−0.419671	+	0.177955i
$309$	8.31534	+	14.8078i	0.473043	+	0.842384i
$310$		0			0
$311$	20.7713			1.17783			0.588916	−	0.808194i	$-0.299555\pi$
$311$	20.7713			1.17783			0.588916	+	0.808194i	$0.299555\pi$
$312$	−8.08179	−	23.7612i	−0.457541	−	1.34521i
$313$	22.4924			1.27135			0.635673	−	0.771958i	$-0.280722\pi$
$313$	22.4924			1.27135			0.635673	+	0.771958i	$0.280722\pi$
$314$	−3.97292	−	2.63068i	−0.224205	−	0.148458i
$315$		0			0
$316$	−14.9309	+	6.33122i	−0.839927	+	0.356159i
$317$			16.7386i			0.940135i	0.882630	+	0.470068i	$0.155770\pi$
$317$			16.7386i			0.940135i	−0.882630	+	0.470068i	$0.844230\pi$
$318$	2.19387	−	29.9166i	0.123026	−	1.67764i
$319$			4.13595i			0.231569i
$320$		0			0
$321$	4.56155	−	2.56155i	0.254601	−	0.142972i
$322$	−0.876894	+	1.32431i	−0.0488674	+	0.0738007i
$323$	2.64861			0.147373
$324$	11.5112	−	13.8381i	0.639510	−	0.768783i
$325$		0			0
$326$	12.2448	−	18.4924i	0.678178	−	1.02420i
$327$	−1.32431	+	0.743668i	−0.0732343	+	0.0411249i
$328$	−3.12311	−	0.580639i	−0.172445	−	0.0320604i
$329$		−	9.12311i		−	0.502973i
$330$		0			0
$331$		−	3.22925i		−	0.177496i	−0.996054	−	0.0887479i	$-0.971713\pi$
$331$		−	3.22925i		−	0.177496i	0.996054	−	0.0887479i	$-0.0282865\pi$
$332$	−11.7915	−	27.8078i	−0.647141	−	1.52615i
$333$	−8.00000	+	13.1231i	−0.438397	+	0.719142i
$334$	−10.6847	−	7.07488i	−0.584638	−	0.387120i
$335$		0			0
$336$	−20.2389	−	5.31946i	−1.10412	−	0.290200i
$337$	1.50758			0.0821230			0.0410615	−	0.999157i	$-0.486926\pi$
$337$	1.50758			0.0821230			0.0410615	+	0.999157i	$0.486926\pi$
$338$	−15.6192	−	10.3423i	−0.849574	−	0.562549i
$339$	−11.8730	−	21.1431i	−0.644852	−	1.14834i
$340$		0			0
$341$		−	6.24621i		−	0.338251i
$342$	−2.38537	−	5.08706i	−0.128986	−	0.275077i
$343$			14.7304i			0.795367i
$344$	−21.5150	−	4.00000i	−1.16001	−	0.215666i
$345$		0			0
$346$	−1.56155	+	2.35829i	−0.0839496	+	0.126783i
$347$	22.6305			1.21487			0.607434	−	0.794370i	$-0.292199\pi$
$347$	22.6305			1.21487			0.607434	+	0.794370i	$0.292199\pi$
$348$	−6.61668	+	8.55950i	−0.354691	+	0.458837i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	0.952473	−	26.6034i	0.0508392	−	1.41998i
$352$	7.31534	−	1.61463i	0.389909	−	0.0860599i
$353$			20.2462i			1.07760i	0.842435	+	0.538799i	$0.181122\pi$
$353$			20.2462i			1.07760i	−0.842435	+	0.538799i	$0.818878\pi$
$354$	34.5669	+	2.53489i	1.83721	+	0.134728i
$355$		0			0
$356$	−18.8664	+	8.00000i	−0.999915	+	0.423999i
$357$	9.12311	−	5.12311i	0.482846	−	0.271144i
$358$	11.8078	+	7.81855i	0.624060	+	0.413223i
$359$	21.5150			1.13552			0.567758	−	0.823195i	$-0.307811\pi$
$359$	21.5150			1.13552			0.567758	+	0.823195i	$0.307811\pi$
$360$		0			0
$361$	17.2462			0.907695
$362$	14.4401	+	9.56155i	0.758954	+	0.502544i
$363$	−13.9638	+	7.84144i	−0.732912	+	0.411569i
$364$	−28.4924	+	12.0818i	−1.49341	+	0.633258i
$365$		0			0
$366$	−7.62953	−	0.559496i	−0.398802	−	0.0292453i
$367$			10.9663i			0.572436i	0.958165	+	0.286218i	$0.0923981\pi$
$367$			10.9663i			0.572436i	−0.958165	+	0.286218i	$0.907602\pi$
$368$	1.03399	−	1.06913i	0.0539003	−	0.0557323i
$369$	−2.87689	−	1.75379i	−0.149765	−	0.0912986i
$370$		0			0
$371$	−36.9890			−1.92038
$372$	9.99267	−	12.9268i	0.518096	−	0.670221i
$373$	9.12311			0.472377			0.236188	−	0.971707i	$-0.424102\pi$
$373$	9.12311			0.472377			0.236188	+	0.971707i	$0.424102\pi$
$374$	−2.06798	+	3.12311i	−0.106932	+	0.161492i
$375$		0			0
$376$	−1.56155	+	8.39919i	−0.0805309	+	0.433155i
$377$			16.0000i			0.824042i
$378$	−18.0561	−	12.9084i	−0.928704	−	0.663935i
$379$			18.7033i			0.960725i	0.877070	+	0.480363i	$0.159495\pi$
$379$			18.7033i			0.960725i	−0.877070	+	0.480363i	$0.840505\pi$
$380$		0			0
$381$	−12.8078	−	22.8078i	−0.656162	−	1.16848i
$382$	29.3693	+	19.4470i	1.50266	+	0.994995i
$383$	15.1022			0.771688			0.385844	−	0.922564i	$-0.373910\pi$
$383$	15.1022			0.771688			0.385844	+	0.922564i	$0.373910\pi$
$384$	17.7224	+	8.36154i	0.904394	+	0.426698i
$385$		0			0
$386$	−0.290319	−	0.192236i	−0.0147769	−	0.00978455i
$387$	−19.8188	−	12.0818i	−1.00745	−	0.614152i
$388$	4.68466	+	11.0478i	0.237827	+	0.560867i
$389$		−	20.7386i		−	1.05149i	−0.850642	−	0.525745i	$-0.823787\pi$
$389$		−	20.7386i		−	1.05149i	0.850642	−	0.525745i	$-0.176213\pi$
$390$		0			0
$391$			0.743668i			0.0376089i
$392$	−1.09763	+	5.90388i	−0.0554388	+	0.298191i
$393$	8.24621	−	4.63068i	0.415966	−	0.233587i
$394$	−3.31534	+	5.00691i	−0.167024	+	0.252244i
$395$		0			0
$396$	7.86084	+	1.15915i	0.395022	+	0.0582495i
$397$	−14.8769			−0.746650			−0.373325	−	0.927701i	$-0.621782\pi$
$397$	−14.8769			−0.746650			−0.373325	+	0.927701i	$0.621782\pi$
$398$	4.26324	−	6.43845i	0.213697	−	0.322730i
$399$	−6.04090	+	3.39228i	−0.302423	+	0.169827i
$400$		0			0
$401$			24.0000i			1.19850i	0.800561	+	0.599251i	$0.204535\pi$
$401$			24.0000i			1.19850i	−0.800561	+	0.599251i	$0.795465\pi$
$402$	0.778351	−	10.6139i	0.0388206	−	0.529375i
$403$		−	24.1636i		−	1.20367i
$404$	1.61463	−	0.684658i	0.0803307	−	0.0340630i
$405$		0			0
$406$	11.1231	+	7.36520i	0.552030	+	0.365529i
$407$	−6.78456			−0.336298
$408$	−9.27608	+	3.15504i	−0.459235	+	0.156198i
$409$	25.3693			1.25443			0.627216	−	0.778845i	$-0.284194\pi$
$409$	25.3693			1.25443			0.627216	+	0.778845i	$0.284194\pi$
$410$		0			0
$411$	6.99337	+	12.4536i	0.344957	+	0.614292i
$412$	−18.0540	+	7.65552i	−0.889456	+	0.377161i
$413$		−	42.7386i		−	2.10303i
$414$	1.42833	−	0.669757i	0.0701984	−	0.0329167i
$415$		0			0
$416$	28.2995	−	6.24621i	1.38750	−	0.306246i
$417$	−14.8769	−	26.4924i	−0.728525	−	1.29734i
$418$	1.36932	−	2.06798i	0.0669755	−	0.101148i
$419$	7.36520			0.359814			0.179907	−	0.983684i	$-0.442420\pi$
$419$	7.36520			0.359814			0.179907	+	0.983684i	$0.442420\pi$
$420$		0			0
$421$	−25.3693			−1.23642			−0.618212	−	0.786011i	$-0.712143\pi$
$421$	−25.3693			−1.23642			−0.618212	+	0.786011i	$0.712143\pi$
$422$	−13.1158	+	19.8078i	−0.638466	+	0.964227i
$423$	−4.71659	+	7.73704i	−0.229328	+	0.376188i
$424$	34.0540	+	6.33122i	1.65381	+	0.307471i
$425$		0			0
$426$	−8.28711	−	0.607718i	−0.401512	−	0.0294440i
$427$			9.43318i			0.456503i
$428$	2.35829	+	5.56155i	0.113992	+	0.268828i
$429$	10.2462	−	5.75379i	0.494692	−	0.277796i
$430$		0			0
$431$	−16.6354			−0.801297			−0.400648	−	0.916232i	$-0.631215\pi$
$431$	−16.6354			−0.801297			−0.400648	+	0.916232i	$0.631215\pi$
$432$	14.4139	+	14.9747i	0.693488	+	0.720468i
$433$	−18.0000			−0.865025			−0.432512	−	0.901628i	$-0.642373\pi$
$433$	−18.0000			−0.865025			−0.432512	+	0.901628i	$0.642373\pi$
$434$	−16.7984	−	11.1231i	−0.806348	−	0.533926i
$435$		0			0
$436$	−0.684658	−	1.61463i	−0.0327892	−	0.0773266i
$437$		−	0.492423i		−	0.0235558i
$438$	20.1449	+	1.47729i	0.962561	+	0.0705875i
$439$			9.27015i			0.442440i	0.975224	+	0.221220i	$0.0710039\pi$
$439$			9.27015i			0.442440i	−0.975224	+	0.221220i	$0.928996\pi$
$440$		0			0
$441$	−3.31534	+	5.43845i	−0.157873	+	0.258974i
$442$	−8.00000	+	12.0818i	−0.380521	+	0.574672i
$443$	16.5896			0.788195			0.394097	−	0.919069i	$-0.371057\pi$
$443$	16.5896			0.788195			0.394097	+	0.919069i	$0.371057\pi$
$444$	−14.0409	−	10.8539i	−0.666351	−	0.515105i
$445$		0			0
$446$	−6.49424	+	9.80776i	−0.307511	+	0.464411i
$447$	−11.8730	−	21.1431i	−0.561573	−	1.00004i
$448$	8.68466	−	22.5490i	0.410312	−	1.06534i
$449$		−	27.3693i		−	1.29164i	−0.763491	−	0.645819i	$-0.776516\pi$
$449$		−	27.3693i		−	1.29164i	0.763491	−	0.645819i	$-0.223484\pi$
$450$		0			0
$451$		−	1.48734i		−	0.0700359i
$452$	25.7782	−	10.9309i	1.21250	−	0.514145i
$453$	−6.24621	−	11.1231i	−0.293473	−	0.522609i
$454$	25.8078	+	17.0887i	1.21122	+	0.802012i
$455$		0			0
$456$	6.14219	−	2.08912i	0.287634	−	0.0978319i
$457$	10.0000			0.467780			0.233890	−	0.972263i	$-0.424854\pi$
$457$	10.0000			0.467780			0.233890	+	0.972263i	$0.424854\pi$
$458$	19.1567	+	12.6847i	0.895133	+	0.592715i
$459$	−10.3857	−	0.371834i	−0.484761	−	0.0173557i
$460$		0			0
$461$			41.8617i			1.94970i	0.222872	+	0.974848i	$0.428457\pi$
$461$			41.8617i			1.94970i	−0.222872	+	0.974848i	$0.571543\pi$
$462$	0.716589	−	9.77172i	0.0333387	−	0.454622i
$463$		−	3.02045i		−	0.140372i	−0.997534	−	0.0701861i	$-0.977641\pi$
$463$		−	3.02045i		−	0.140372i	0.997534	−	0.0701861i	$-0.0223593\pi$
$464$	−8.97983	−	8.68466i	−0.416878	−	0.403175i
$465$		0			0
$466$	7.80776	−	11.7915i	0.361688	−	0.546229i
$467$	−2.27678			−0.105357			−0.0526784	−	0.998612i	$-0.516776\pi$
$467$	−2.27678			−0.105357			−0.0526784	+	0.998612i	$0.516776\pi$
$468$	30.4098	+	4.48419i	1.40569	+	0.207282i
$469$	−13.1231			−0.605969
$470$		0			0
$471$	5.08842	−	2.85742i	0.234462	−	0.131663i
$472$	−7.31534	+	39.3473i	−0.336716	+	1.81111i
$473$		−	10.2462i		−	0.471121i
$474$	1.45268	−	19.8094i	0.0667239	−	0.909876i
$475$		0			0
$476$	4.71659	+	11.1231i	0.216184	+	0.509827i
$477$	31.3693	+	19.1231i	1.43630	+	0.875587i
$478$	−20.4924	−	13.5691i	−0.937302	−	0.620637i
$479$	25.6509			1.17202			0.586010	−	0.810304i	$-0.300698\pi$
$479$	25.6509			1.17202			0.586010	+	0.810304i	$0.300698\pi$
$480$		0			0
$481$	−26.2462			−1.19672
$482$	−15.7644	−	10.4384i	−0.718048	−	0.475458i
$483$	−0.952473	−	1.69614i	−0.0433390	−	0.0771771i
$484$	−7.21922	−	17.0251i	−0.328147	−	0.773866i
$485$		0			0
$486$	8.63928	+	20.2821i	0.391886	+	0.920014i
$487$			25.2791i			1.14550i	0.819728	+	0.572752i	$0.194124\pi$
$487$			25.2791i			1.14550i	−0.819728	+	0.572752i	$0.805876\pi$
$488$	1.61463	−	8.68466i	0.0730907	−	0.393136i
$489$	13.3002	+	23.6847i	0.601455	+	1.07106i
$490$		0			0
$491$	26.9752			1.21737			0.608687	−	0.793410i	$-0.291696\pi$
$491$	26.9752			1.21737			0.608687	+	0.793410i	$0.291696\pi$
$492$	2.37944	−	3.07810i	0.107273	−	0.138771i
$493$	6.24621			0.281315
$494$	5.29723	−	8.00000i	0.238334	−	0.359937i
$495$		0			0
$496$	13.5616	+	13.1158i	0.608932	+	0.588916i
$497$			10.2462i			0.459605i
$498$	36.8937	+	2.70552i	1.65325	+	0.121237i
$499$			32.2725i			1.44471i	0.691521	+	0.722357i	$0.256941\pi$
$499$			32.2725i			1.44471i	−0.691521	+	0.722357i	$0.743059\pi$
$500$		0			0
$501$	13.6847	−	7.68466i	0.611385	−	0.343325i
$502$	−22.0540	−	14.6031i	−0.984317	−	0.651769i
$503$	−14.3586			−0.640217			−0.320109	−	0.947381i	$-0.603719\pi$
$503$	−14.3586			−0.640217			−0.320109	+	0.947381i	$0.603719\pi$
$504$	17.1158	−	19.0765i	0.762397	−	0.849736i
$505$		0			0
$506$	0.580639	+	0.384472i	0.0258125	+	0.0170919i
$507$	20.0047	−	11.2337i	0.888442	−	0.498907i
$508$	27.8078	−	11.7915i	1.23377	−	0.523162i
$509$			11.1231i			0.493023i	0.969140	+	0.246511i	$0.0792843\pi$
$509$			11.1231i			0.493023i	−0.969140	+	0.246511i	$0.920716\pi$
$510$		0			0
$511$		−	24.9073i		−	1.10183i
$512$	−11.8551	+	19.2732i	−0.523927	+	0.851763i
$513$	6.87689	+	0.246211i	0.303622	+	0.0108705i
$514$	−23.8078	+	35.9551i	−1.05012	+	1.58591i
$515$		0			0
$516$	16.3919	−	21.2049i	0.721612	−	0.933494i
$517$	−4.00000			−0.175920
$518$	−12.0818	+	18.2462i	−0.530843	+	0.801692i
$519$	−1.69614	−	3.02045i	−0.0744523	−	0.132583i
$520$		0			0
$521$		−	38.2462i		−	1.67560i	−0.545980	−	0.837798i	$-0.683842\pi$
$521$		−	38.2462i		−	1.67560i	0.545980	−	0.837798i	$-0.316158\pi$
$522$	−5.62541	−	11.9968i	−0.246218	−	0.525085i
$523$			35.2929i			1.54325i	0.636077	+	0.771625i	$0.280556\pi$
$523$			35.2929i			1.54325i	−0.636077	+	0.771625i	$0.719444\pi$
$524$	4.26324	+	10.0540i	0.186241	+	0.439210i
$525$		0			0
$526$	−28.0540	−	18.5760i	−1.22321	−	0.809954i
$527$	−9.43318			−0.410916
$528$	−2.33230	+	8.87368i	−0.101500	+	0.386177i
$529$	−22.8617			−0.993989
$530$		0			0
$531$	−22.0956	+	36.2454i	−0.958868	+	1.57292i
$532$	−3.12311	−	7.36520i	−0.135404	−	0.319322i
$533$		−	5.75379i		−	0.249224i
$534$	1.83558	−	25.0308i	0.0794333	−	1.08319i
$535$		0			0
$536$	12.0818	+	2.24621i	0.521854	+	0.0970215i
$537$	−15.1231	+	8.49242i	−0.652610	+	0.366475i
$538$	10.9309	−	16.5081i	0.471263	−	0.711713i
$539$	−2.81164			−0.121106
$540$		0			0
$541$	−26.9848			−1.16017			−0.580085	−	0.814556i	$-0.696980\pi$
$541$	−26.9848			−1.16017			−0.580085	+	0.814556i	$0.696980\pi$
$542$	11.9545	−	18.0540i	0.513490	−	0.775485i
$543$	−18.4945	+	10.3857i	−0.793676	+	0.445691i
$544$	−2.43845	−	11.0478i	−0.104548	−	0.473671i
$545$		0			0
$546$	2.77214	−	37.8021i	0.118637	−	1.61778i
$547$		−	5.83209i		−	0.249362i	−0.992197	−	0.124681i	$-0.960209\pi$
$547$		−	5.83209i		−	0.249362i	0.992197	−	0.124681i	$-0.0397908\pi$
$548$	−15.1838	+	6.43845i	−0.648618	+	0.275037i
$549$	4.87689	−	8.00000i	0.208141	−	0.341432i
$550$		0			0
$551$	−4.13595			−0.176197
$552$	0.586575	+	1.72458i	0.0249663	+	0.0734031i
$553$	−24.4924			−1.04152
$554$	27.5559	+	18.2462i	1.17074	+	0.775207i
$555$		0			0
$556$	32.3002	−	13.6964i	1.36983	−	0.580858i
$557$		−	36.2462i		−	1.53580i	−0.640569	−	0.767901i	$-0.721301\pi$
$557$		−	36.2462i		−	1.53580i	0.640569	−	0.767901i	$-0.278699\pi$
$558$	8.49563	+	18.1178i	0.359649	+	0.766989i
$559$		−	39.6377i		−	1.67649i
$560$		0			0
$561$	−2.24621	−	4.00000i	−0.0948351	−	0.168880i
$562$	10.6307	−	16.0547i	0.448428	−	0.677227i
$563$	7.90007			0.332948			0.166474	−	0.986046i	$-0.446762\pi$
$563$	7.90007			0.332948			0.166474	+	0.986046i	$0.446762\pi$
$564$	−8.27814	−	6.39919i	−0.348573	−	0.269455i
$565$		0			0
$566$	−18.1227	+	27.3693i	−0.761753	+	1.15042i
$567$	24.1636	−	12.4536i	1.01478	−	0.523003i
$568$	1.75379	−	9.43318i	0.0735873	−	0.395807i
$569$		−	13.1231i		−	0.550149i	−0.961423	−	0.275075i	$-0.911297\pi$
$569$		−	13.1231i		−	0.550149i	0.961423	−	0.275075i	$-0.0887026\pi$
$570$		0			0
$571$			33.0161i			1.38168i	0.723007	+	0.690841i	$0.242759\pi$
$571$			33.0161i			1.38168i	−0.723007	+	0.690841i	$0.757241\pi$
$572$	5.29723	+	12.4924i	0.221488	+	0.522334i
$573$	−37.6155	+	21.1231i	−1.57141	+	0.882430i
$574$	−4.00000	−	2.64861i	−0.166957	−	0.110551i
$575$		0			0
$576$	−19.0229	+	14.6332i	−0.792620	+	0.609716i
$577$	32.2462			1.34243			0.671214	−	0.741264i	$-0.265773\pi$
$577$	32.2462			1.34243			0.671214	+	0.741264i	$0.265773\pi$
$578$	−15.3289	−	10.1501i	−0.637599	−	0.422188i
$579$	0.371834	−	0.208805i	0.0154529	−	0.00867762i
$580$		0			0
$581$		−	45.6155i		−	1.89245i
$582$	−14.6576	−	1.07488i	−0.607576	−	0.0445554i
$583$			16.2177i			0.671670i
$584$	−4.26324	+	22.9309i	−0.176414	+	0.948886i
$585$		0			0
$586$	−1.94602	+	2.93893i	−0.0803895	+	0.121406i
$587$	−1.85917			−0.0767362			−0.0383681	−	0.999264i	$-0.512216\pi$
$587$	−1.85917			−0.0767362			−0.0383681	+	0.999264i	$0.512216\pi$
$588$	−5.81880	−	4.49806i	−0.239963	−	0.185497i
$589$	6.24621			0.257371
$590$		0			0
$591$	−3.60109	−	6.41273i	−0.148129	−	0.263784i
$592$	14.2462	−	14.7304i	0.585516	−	0.605416i
$593$		−	8.24621i		−	0.338631i	−0.985562	−	0.169316i	$-0.945844\pi$
$593$		−	8.24621i		−	0.338631i	0.985562	−	0.169316i	$-0.0541557\pi$
$594$	−5.65964	+	7.91664i	−0.232218	+	0.324823i
$595$		0			0
$596$	25.7782	−	10.9309i	1.05592	−	0.447746i
$597$	4.63068	+	8.24621i	0.189521	+	0.337495i
$598$	2.24621	+	1.48734i	0.0918544	+	0.0608217i
$599$	−44.1912			−1.80560			−0.902802	−	0.430056i	$-0.858494\pi$
$599$	−44.1912			−1.80560			−0.902802	+	0.430056i	$0.858494\pi$
$600$		0			0
$601$	23.1231			0.943211			0.471606	−	0.881810i	$-0.343675\pi$
$601$	23.1231			0.943211			0.471606	+	0.881810i	$0.343675\pi$
$602$	−27.5559	−	18.2462i	−1.12309	−	0.743660i
$603$	11.1293	+	6.78456i	0.453221	+	0.276289i
$604$	13.5616	−	5.75058i	0.551812	−	0.233988i
$605$		0			0
$606$	−0.157093	+	2.14219i	−0.00638148	+	0.0870206i
$607$		−	4.50778i		−	0.182965i	−0.995807	−	0.0914827i	$-0.970839\pi$
$607$		−	4.50778i		−	0.182965i	0.995807	−	0.0914827i	$-0.0291606\pi$
$608$	1.61463	+	7.31534i	0.0654817	+	0.296676i
$609$	−14.2462	+	8.00000i	−0.577286	+	0.324176i
$610$		0			0
$611$	−15.4741			−0.626014
$612$	1.75058	−	11.8716i	0.0707629	−	0.479882i
$613$	−9.12311			−0.368479			−0.184239	−	0.982881i	$-0.558982\pi$
$613$	−9.12311			−0.368479			−0.184239	+	0.982881i	$0.558982\pi$
$614$	−8.68951	+	13.1231i	−0.350680	+	0.529605i
$615$		0			0
$616$	11.1231	+	2.06798i	0.448163	+	0.0833211i
$617$			14.0000i			0.563619i	0.959470	+	0.281809i	$0.0909346\pi$
$617$			14.0000i			0.563619i	−0.959470	+	0.281809i	$0.909065\pi$
$618$	1.75654	−	23.9530i	0.0706584	−	0.963529i
$619$		−	28.1365i		−	1.13090i	−0.824782	−	0.565451i	$-0.808702\pi$
$619$		−	28.1365i		−	1.13090i	0.824782	−	0.565451i	$-0.191298\pi$
$620$		0			0
$621$	−0.0691303	+	1.93087i	−0.00277410	+	0.0774831i
$622$	−24.4924	−	16.2177i	−0.982057	−	0.650272i
$623$	−30.9481			−1.23991
$624$	−9.02255	+	34.3280i	−0.361191	+	1.37422i
$625$		0			0
$626$	−26.5219	−	17.5616i	−1.06003	−	0.701901i
$627$	1.48734	+	2.64861i	0.0593985	+	0.105775i
$628$	2.63068	+	6.20393i	0.104976	+	0.247564i
$629$			10.2462i			0.408543i
$630$		0			0
$631$			39.8007i			1.58444i	0.610235	+	0.792220i	$0.291075\pi$
$631$			39.8007i			1.58444i	−0.610235	+	0.792220i	$0.708925\pi$
$632$	22.5490	+	4.19224i	0.896949	+	0.166758i
$633$	−14.2462	−	25.3693i	−0.566236	−	1.00834i
$634$	13.0691	−	19.7373i	0.519041	−	0.783869i
$635$		0			0
$636$	−25.9451	+	33.5632i	−1.02879	+	1.33087i
$637$	−10.8769			−0.430958
$638$	3.22925	−	4.87689i	0.127847	−	0.193078i
$639$	5.29723	−	8.68951i	0.209555	−	0.343752i
$640$		0			0
$641$		−	6.38447i		−	0.252171i	−0.992019	−	0.126086i	$-0.959759\pi$
$641$		−	6.38447i		−	0.252171i	0.992019	−	0.126086i	$-0.0402414\pi$
$642$	−7.37874	−	0.541105i	−0.291216	−	0.0213557i
$643$		−	3.60109i		−	0.142013i	−0.997476	−	0.0710065i	$-0.977379\pi$
$643$		−	3.60109i		−	0.142013i	0.997476	−	0.0710065i	$-0.0226211\pi$
$644$	2.06798	−	0.876894i	0.0814896	−	0.0345545i
$645$		0			0
$646$	−3.12311	−	2.06798i	−0.122877	−	0.0813634i
$647$	36.6172			1.43957			0.719786	−	0.694197i	$-0.244240\pi$
$647$	36.6172			1.43957			0.719786	+	0.694197i	$0.244240\pi$
$648$	−24.3778	+	7.32948i	−0.957652	+	0.287929i
$649$	−18.7386			−0.735556
$650$		0			0
$651$	21.5150	−	12.0818i	0.843238	−	0.473523i
$652$	−28.8769	+	12.2448i	−1.13091	+	0.479544i
$653$			38.9848i			1.52559i	0.646638	+	0.762797i	$0.276175\pi$
$653$			38.9848i			1.52559i	−0.646638	+	0.762797i	$0.723825\pi$
$654$	2.14219	+	0.157093i	0.0837663	+	0.00614283i
$655$		0			0
$656$	3.22925	+	3.12311i	0.126081	+	0.121937i
$657$	−12.8769	+	21.1231i	−0.502375	+	0.824091i
$658$	−7.12311	+	10.7575i	−0.277688	+	0.419370i
$659$	24.7442			0.963898			0.481949	−	0.876199i	$-0.339929\pi$
$659$	24.7442			0.963898			0.481949	+	0.876199i	$0.339929\pi$
$660$		0			0
$661$	28.1080			1.09327			0.546636	−	0.837370i	$-0.315908\pi$
$661$	28.1080			1.09327			0.546636	+	0.837370i	$0.315908\pi$
$662$	−2.52132	+	3.80776i	−0.0979940	+	0.147993i
$663$	−8.68951	−	15.4741i	−0.337473	−	0.600963i
$664$	−7.80776	+	41.9960i	−0.303000	+	1.62976i
$665$		0			0
$666$	19.6794	−	9.22786i	0.762561	−	0.357572i
$667$		−	1.16128i		−	0.0449648i
$668$	7.07488	+	16.6847i	0.273735	+	0.645549i
$669$	−7.05398	−	12.5616i	−0.272722	−	0.485658i
$670$		0			0
$671$	4.13595			0.159667
$672$	19.7113	+	22.0745i	0.760381	+	0.851541i
$673$	−22.4924			−0.867019			−0.433510	−	0.901149i	$-0.642725\pi$
$673$	−22.4924			−0.867019			−0.433510	+	0.901149i	$0.642725\pi$
$674$	−1.77766	−	1.17708i	−0.0684727	−	0.0453395i
$675$		0			0
$676$	10.3423	+	24.3903i	0.397782	+	0.938087i
$677$		−	1.50758i		−	0.0579409i	−0.999580	−	0.0289705i	$-0.990777\pi$
$677$		−	1.50758i		−	0.0579409i	0.999580	−	0.0289705i	$-0.00922287\pi$
$678$	−2.50806	+	34.2010i	−0.0963215	+	1.31348i
$679$			18.1227i			0.695485i
$680$		0			0
$681$	−33.0540	+	18.5616i	−1.26663	+	0.711280i
$682$	−4.87689	+	7.36520i	−0.186746	+	0.282028i
$683$	−7.90007			−0.302288			−0.151144	−	0.988512i	$-0.548296\pi$
$683$	−7.90007			−0.302288			−0.151144	+	0.988512i	$0.548296\pi$
$684$	−1.15915	+	7.86084i	−0.0443212	+	0.300567i
$685$		0			0
$686$	11.5012	−	17.3693i	0.439116	−	0.663164i
$687$	−24.5354	+	13.7779i	−0.936085	+	0.525661i
$688$	22.2462	+	21.5150i	0.848129	+	0.820251i
$689$			62.7386i			2.39015i
$690$		0			0
$691$		−	18.2857i		−	0.695621i	−0.937565	−	0.347811i	$-0.886925\pi$
$691$		−	18.2857i		−	0.695621i	0.937565	−	0.347811i	$-0.113075\pi$
$692$	3.68260	−	1.56155i	0.139991	−	0.0593613i
$693$	10.2462	+	6.24621i	0.389221	+	0.237274i
$694$	−26.6847	−	17.6693i	−1.01294	−	0.670719i
$695$		0			0
$696$	14.4851	−	4.92676i	0.549056	−	0.186748i
$697$	−2.24621			−0.0850813
$698$	16.5081	+	10.9309i	0.624839	+	0.413740i
$699$	8.48071	+	15.1022i	0.320770	+	0.571219i
$700$		0			0
$701$			17.5076i			0.661252i	0.943762	+	0.330626i	$0.107260\pi$
$701$			17.5076i			0.661252i	−0.943762	+	0.330626i	$0.892740\pi$
$702$	−21.8944	+	30.6256i	−0.826351	+	1.15589i
$703$		−	6.78456i		−	0.255885i
$704$	−9.88653	−	3.80776i	−0.372612	−	0.143511i
$705$		0			0
$706$	15.8078	−	23.8733i	0.594933	−	0.898482i
$707$	2.64861			0.0996114
$708$	−38.7803	−	29.9780i	−1.45745	−	1.12664i
$709$	6.49242			0.243828			0.121914	−	0.992541i	$-0.461097\pi$
$709$	6.49242			0.243828			0.121914	+	0.992541i	$0.461097\pi$
$710$		0			0
$711$	20.7713	+	12.6624i	0.778985	+	0.474878i
$712$	28.4924	+	5.29723i	1.06780	+	0.198522i
$713$			1.75379i			0.0656799i
$714$	−14.7575	−	1.08221i	−0.552285	−	0.0405007i
$715$		0			0
$716$	−7.81855	−	18.4384i	−0.292193	−	0.689077i
$717$	26.2462	−	14.7386i	0.980183	−	0.550424i
$718$	−25.3693	−	16.7984i	−0.946774	−	0.626910i
$719$	−30.9481			−1.15417			−0.577086	−	0.816684i	$-0.695810\pi$
$719$	−30.9481			−1.15417			−0.577086	+	0.816684i	$0.695810\pi$
$720$		0			0
$721$	−29.6155			−1.10294
$722$	−20.3358	−	13.4654i	−0.756821	−	0.501132i
$723$	20.1907	−	11.3381i	0.750899	−	0.421669i
$724$	−9.56155	−	22.5490i	−0.355352	−	0.838025i
$725$		0			0
$726$	22.5878	+	1.65643i	0.838314	+	0.0614760i
$727$		−	10.9663i		−	0.406717i	−0.979104	−	0.203359i	$-0.934814\pi$
$727$		−	10.9663i		−	0.406717i	0.979104	−	0.203359i	$-0.0651857\pi$
$728$	43.0299	+	8.00000i	1.59480	+	0.296500i
$729$	−26.9309	−	1.93087i	−0.997440	−	0.0715137i
$730$		0			0
$731$	−15.4741			−0.572329
$732$	8.55950	+	6.61668i	0.316368	+	0.244560i
$733$	26.8769			0.992721			0.496360	−	0.868117i	$-0.334669\pi$
$733$	26.8769			0.992721			0.496360	+	0.868117i	$0.334669\pi$
$734$	8.56222	−	12.9309i	0.316037	−	0.477287i
$735$		0			0
$736$	−2.05398	+	0.453349i	−0.0757105	+	0.0167107i
$737$			5.75379i			0.211944i
$738$	2.02297	+	4.31419i	0.0744664	+	0.158807i
$739$			26.9752i			0.992300i	0.868237	+	0.496150i	$0.165253\pi$
$739$			26.9752i			0.992300i	−0.868237	+	0.496150i	$0.834747\pi$
$740$		0			0
$741$	5.75379	+	10.2462i	0.211371	+	0.376404i
$742$	43.6155	+	28.8802i	1.60118	+	1.06022i
$743$	9.80501			0.359711			0.179856	−	0.983693i	$-0.442437\pi$
$743$	9.80501			0.359711			0.179856	+	0.983693i	$0.442437\pi$
$744$	−21.8757	+	7.44050i	−0.802004	+	0.272782i
$745$		0			0
$746$	−10.7575	−	7.12311i	−0.393860	−	0.260795i
$747$	−23.5829	+	38.6852i	−0.862855	+	1.41542i
$748$	4.87689	−	2.06798i	0.178317	−	0.0756127i
$749$			9.12311i			0.333351i
$750$		0			0
$751$		−	11.5012i		−	0.419683i	−0.977735	−	0.209842i	$-0.932705\pi$
$751$		−	11.5012i		−	0.419683i	0.977735	−	0.209842i	$-0.0672948\pi$
$752$	8.39919	−	8.68466i	0.306287	−	0.316697i
$753$	28.2462	−	15.8617i	1.02935	−	0.578034i
$754$	12.4924	−	18.8664i	0.454947	−	0.687072i
$755$		0			0
$756$	11.2122	+	29.3186i	0.407785	+	1.06631i
$757$	−10.8769			−0.395327			−0.197664	−	0.980270i	$-0.563335\pi$
$757$	−10.8769			−0.395327			−0.197664	+	0.980270i	$0.563335\pi$
$758$	14.6031	−	22.0540i	0.530409	−	0.801036i
$759$	−0.743668	+	0.417609i	−0.0269934	+	0.0151582i
$760$		0			0
$761$		−	31.2311i		−	1.13212i	−0.824362	−	0.566062i	$-0.808466\pi$
$761$		−	31.2311i		−	1.13212i	0.824362	−	0.566062i	$-0.191534\pi$
$762$	−2.70552	+	36.8937i	−0.0980108	+	1.33652i
$763$		−	2.64861i		−	0.0958863i
$764$	−19.4470	−	45.8617i	−0.703568	−	1.65922i
$765$		0			0
$766$	−17.8078	−	11.7915i	−0.643421	−	0.426043i
$767$	−72.4908			−2.61749
$768$	−14.3689	−	23.6967i	−0.518492	−	0.855083i
$769$	38.9848			1.40583			0.702915	−	0.711274i	$-0.251882\pi$
$769$	38.9848			1.40583			0.702915	+	0.711274i	$0.251882\pi$
$770$		0			0
$771$	−25.8597	−	46.0504i	−0.931315	−	1.65846i
$772$	0.192236	+	0.453349i	0.00691872	+	0.0163164i
$773$			0.246211i			0.00885560i	0.999990	+	0.00442780i	$0.00140942\pi$
$773$			0.246211i			0.00885560i	−0.999990	+	0.00442780i	$0.998591\pi$
$774$	13.9361	+	29.7203i	0.500924	+	1.06827i
$775$		0			0
$776$	3.10196	−	16.6847i	0.111354	−	0.598944i
$777$	−13.1231	−	23.3693i	−0.470789	−	0.838370i
$778$	−16.1922	+	24.4539i	−0.580520	+	0.876715i
$779$	1.48734			0.0532894
$780$		0			0
$781$	4.49242			0.160752
$782$	0.580639	−	0.876894i	0.0207636	−	0.0313577i
$783$	16.2177	+	0.580639i	0.579575	+	0.0207503i
$784$	5.90388	−	6.10454i	0.210853	−	0.218019i
$785$		0			0
$786$	−13.3390	−	0.978190i	−0.475787	−	0.0348909i
$787$		−	42.0775i		−	1.49990i	−0.661495	−	0.749950i	$-0.730078\pi$
$787$		−	42.0775i		−	1.49990i	0.661495	−	0.749950i	$-0.269922\pi$
$788$	7.81855	−	3.31534i	0.278524	−	0.118104i
$789$	35.9309	−	20.1771i	1.27917	−	0.718323i
$790$		0			0
$791$	42.2863			1.50353
$792$	−8.36405	−	7.50437i	−0.297203	−	0.266656i
$793$	16.0000			0.568177
$794$	17.5420	+	11.6155i	0.622544	+	0.412220i
$795$		0			0
$796$	−10.0540	+	4.26324i	−0.356354	+	0.151107i
$797$		−	12.7386i		−	0.451226i	−0.974217	−	0.225613i	$-0.927562\pi$
$797$		−	12.7386i		−	0.451226i	0.974217	−	0.225613i	$-0.0724384\pi$
$798$	9.77172	+	0.716589i	0.345915	+	0.0253670i
$799$			6.04090i			0.213712i
$800$		0			0
$801$	26.2462	+	16.0000i	0.927364	+	0.565332i
$802$	18.7386	−	28.2995i	0.661684	−	0.999291i
$803$	−10.9205			−0.385377
$804$	−9.20490	+	11.9077i	−0.324632	+	0.419951i
$805$		0			0
$806$	−18.8664	+	28.4924i	−0.664539	+	1.00360i
$807$	11.8730	+	21.1431i	0.417949	+	0.744274i
$808$	−2.43845	−	0.453349i	−0.0857843	−	0.0159488i
$809$		−	29.7538i		−	1.04609i	−0.852306	−	0.523044i	$-0.824796\pi$
$809$		−	29.7538i		−	1.04609i	0.852306	−	0.523044i	$-0.175204\pi$
$810$		0			0
$811$		−	46.2592i		−	1.62438i	−0.583393	−	0.812190i	$-0.698275\pi$
$811$		−	46.2592i		−	1.62438i	0.583393	−	0.812190i	$-0.301725\pi$
$812$	−7.36520	−	17.3693i	−0.258468	−	0.609544i
$813$	12.9848	+	23.1231i	0.455398	+	0.810963i
$814$	8.00000	+	5.29723i	0.280400	+	0.185668i
$815$		0			0
$816$	13.4012	+	3.52230i	0.469137	+	0.123305i
$817$	10.2462			0.358470
$818$	−29.9142	−	19.8078i	−1.04592	−	0.692562i
$819$	39.6377	+	24.1636i	1.38505	+	0.844344i
$820$		0			0
$821$			53.2311i			1.85778i	0.370360	+	0.928888i	$0.379234\pi$
$821$			53.2311i			1.85778i	−0.370360	+	0.928888i	$0.620766\pi$
$822$	1.47729	−	20.1449i	0.0515263	−	0.702635i
$823$		−	48.2814i		−	1.68298i	−0.540270	−	0.841492i	$-0.681678\pi$
$823$		−	48.2814i		−	1.68298i	0.540270	−	0.841492i	$-0.318322\pi$
$824$	27.2655	+	5.06913i	0.949840	+	0.176592i
$825$		0			0
$826$	−33.3693	+	50.3951i	−1.16107	+	1.75347i
$827$	17.7509			0.617258			0.308629	−	0.951183i	$-0.400130\pi$
$827$	17.7509			0.617258			0.308629	+	0.951183i	$0.400130\pi$
$828$	−2.20714	−	0.325462i	−0.0767033	−	0.0113106i
$829$	−8.87689			−0.308307			−0.154154	−	0.988047i	$-0.549265\pi$
$829$	−8.87689			−0.308307			−0.154154	+	0.988047i	$0.549265\pi$
$830$		0			0
$831$	−35.2929	+	19.8188i	−1.22430	+	0.687508i
$832$	−38.2462	−	14.7304i	−1.32595	−	0.510685i
$833$			4.24621i			0.147122i
$834$	−3.14261	+	42.8540i	−0.108820	+	1.48391i
$835$		0			0
$836$	−3.22925	+	1.36932i	−0.111686	+	0.0473588i
$837$	−24.4924	−	0.876894i	−0.846582	−	0.0303099i
$838$	−8.68466	−	5.75058i	−0.300007	−	0.198650i
$839$	−17.7051			−0.611247			−0.305624	−	0.952152i	$-0.598865\pi$
$839$	−17.7051			−0.611247			−0.305624	+	0.952152i	$0.598865\pi$
$840$		0			0
$841$	19.2462			0.663662
$842$	29.9142	+	19.8078i	1.03091	+	0.682621i
$843$	11.5469	+	20.5625i	0.397697	+	0.708210i
$844$	30.9309	−	13.1158i	1.06468	−	0.451464i
$845$		0			0
$846$	11.6024	−	5.44050i	0.398900	−	0.187048i
$847$		−	27.9277i		−	0.959607i
$848$	−35.2114	−	34.0540i	−1.20916	−	1.16942i
$849$	−19.6847	−	35.0540i	−0.675576	−	1.20305i
$850$		0			0
$851$	1.90495			0.0653007
$852$	9.29723	+	7.18697i	0.318518	+	0.246221i
$853$	7.86174			0.269181			0.134590	−	0.990901i	$-0.457028\pi$
$853$	7.86174			0.269181			0.134590	+	0.990901i	$0.457028\pi$
$854$	7.36520	−	11.1231i	0.252032	−	0.380625i
$855$		0			0
$856$	1.56155	−	8.39919i	0.0533728	−	0.287078i
$857$			20.7386i			0.708418i	0.935166	+	0.354209i	$0.115250\pi$
$857$			20.7386i			0.708418i	−0.935166	+	0.354209i	$0.884750\pi$
$858$	−16.5742	−	1.21544i	−0.565834	−	0.0414943i
$859$		−	33.4337i		−	1.14074i	−0.821386	−	0.570372i	$-0.806799\pi$
$859$		−	33.4337i		−	1.14074i	0.821386	−	0.570372i	$-0.193201\pi$
$860$		0			0
$861$	5.12311	−	2.87689i	0.174595	−	0.0980443i
$862$	19.6155	+	12.9885i	0.668108	+	0.442390i
$863$	−10.5487			−0.359081			−0.179541	−	0.983751i	$-0.557461\pi$
$863$	−10.5487			−0.359081			−0.179541	+	0.983751i	$0.557461\pi$
$864$	−5.30423	−	28.9113i	−0.180453	−	0.983584i
$865$		0			0
$866$	21.2247	+	14.0540i	0.721243	+	0.477574i
$867$	19.6329	−	11.0249i	0.666769	−	0.374426i
$868$	11.1231	+	26.2316i	0.377543	+	0.890357i
$869$			10.7386i			0.364283i
$870$		0			0
$871$			22.2586i			0.754205i
$872$	−0.453349	+	2.43845i	−0.0153523	+	0.0825762i
$873$	9.36932	−	15.3693i	0.317103	−	0.520173i
$874$	−0.384472	+	0.580639i	−0.0130050	+	0.0196404i
$875$		0			0
$876$	−22.6004	−	17.4706i	−0.763596	−	0.590277i
$877$	−37.6155			−1.27019			−0.635093	−	0.772436i	$-0.719038\pi$
$877$	−37.6155			−1.27019			−0.635093	+	0.772436i	$0.719038\pi$
$878$	7.23791	−	10.9309i	0.244268	−	0.368899i
$879$	−2.11375	−	3.76412i	−0.0712950	−	0.126960i
$880$		0			0
$881$			0.630683i			0.0212483i	0.999944	+	0.0106241i	$0.00338183\pi$
$881$			0.630683i			0.0212483i	−0.999944	+	0.0106241i	$0.996618\pi$
$882$	8.15549	−	3.82419i	0.274610	−	0.128767i
$883$			22.4674i			0.756090i	0.925787	+	0.378045i	$0.123403\pi$
$883$			22.4674i			0.756090i	−0.925787	+	0.378045i	$0.876597\pi$
$884$	18.8664	−	8.00000i	0.634544	−	0.269069i
$885$		0			0
$886$	−19.5616	−	12.9527i	−0.657183	−	0.435156i
$887$	51.6737			1.73503			0.867516	−	0.497409i	$-0.165715\pi$
$887$	51.6737			1.73503			0.867516	+	0.497409i	$0.165715\pi$
$888$	8.08179	+	23.7612i	0.271207	+	0.797373i
$889$	45.6155			1.52990
$890$		0			0
$891$	−5.46026	−	10.5945i	−0.182925	−	0.354928i
$892$	15.3153	−	6.49424i	0.512796	−	0.217443i
$893$		−	4.00000i		−	0.133855i
$894$	−2.50806	+	34.2010i	−0.0838821	+	1.14385i
$895$		0			0
$896$	−27.8462	+	19.8078i	−0.930276	+	0.661731i
$897$	−2.87689	+	1.61553i	−0.0960567	+	0.0539409i
$898$	−21.3693	+	32.2725i	−0.713103	+	1.07695i
$899$	14.7304			0.491287
$900$		0			0
$901$	24.4924			0.815961
$902$	−1.16128	+	1.75379i	−0.0386663	+	0.0583948i
$903$	35.2929	−	19.8188i	1.17447	−	0.659529i
$904$	−38.9309	−	7.23791i	−1.29482	−	0.240729i
$905$		0			0
$906$	−1.31946	+	17.9927i	−0.0438360	+	0.597767i
$907$			46.2134i			1.53449i	0.641353	+	0.767246i	$0.278373\pi$
$907$			46.2134i			1.53449i	−0.641353	+	0.767246i	$0.721627\pi$
$908$	−17.0887	−	40.3002i	−0.567108	−	1.33741i
$909$	−2.24621	−	1.36932i	−0.0745021	−	0.0454174i
$910$		0			0
$911$	−14.3128			−0.474204			−0.237102	−	0.971485i	$-0.576198\pi$
$911$	−14.3128			−0.474204			−0.237102	+	0.971485i	$0.576198\pi$
$912$	−8.87368	−	2.33230i	−0.293837	−	0.0772302i
$913$	−20.0000			−0.661903
$914$	−11.7915	−	7.80776i	−0.390027	−	0.258258i
$915$		0			0
$916$	−12.6847	−	29.9142i	−0.419113	−	0.988392i
$917$			16.4924i			0.544628i
$918$	11.9559	+	8.54732i	0.394603	+	0.282104i
$919$		−	49.9775i		−	1.64861i	−0.566148	−	0.824303i	$-0.691567\pi$
$919$		−	49.9775i		−	1.64861i	0.566148	−	0.824303i	$-0.308433\pi$
$920$		0			0
$921$	−9.43845	−	16.8078i	−0.311007	−	0.553835i
$922$	32.6847	−	49.3612i	1.07641	−	1.62562i
$923$	17.3790			0.572037
$924$	−8.47449	+	10.9628i	−0.278790	+	0.360650i
$925$		0			0
$926$	−2.35829	+	3.56155i	−0.0774984	+	0.117040i
$927$	25.1161	+	15.3110i	0.824920	+	0.502881i
$928$	3.80776	+	17.2517i	0.124996	+	0.566316i
$929$		−	33.1231i		−	1.08673i	−0.839495	−	0.543367i	$-0.817149\pi$
$929$		−	33.1231i		−	1.08673i	0.839495	−	0.543367i	$-0.182851\pi$
$930$		0			0
$931$		−	2.81164i		−	0.0921479i
$932$	−18.4130	+	7.80776i	−0.603138	+	0.255752i
$933$	31.3693	−	17.6155i	1.02699	−	0.576707i
$934$	2.68466	+	1.77766i	0.0878447	+	0.0581667i
$935$		0			0
$936$	−32.3565	−	29.0308i	−1.05760	−	0.948901i
$937$	22.4924			0.734795			0.367398	−	0.930064i	$-0.380249\pi$
$937$	22.4924			0.734795			0.367398	+	0.930064i	$0.380249\pi$
$938$	15.4741	+	10.2462i	0.505246	+	0.334551i
$939$	33.9686	−	19.0752i	1.10852	−	0.622494i
$940$		0			0
$941$			0.876894i			0.0285859i	0.999898	+	0.0142930i	$0.00454975\pi$
$941$			0.876894i			0.0285859i	−0.999898	+	0.0142930i	$0.995450\pi$
$942$	−8.23100	−	0.603604i	−0.268181	−	0.0196665i
$943$			0.417609i			0.0135992i
$944$	39.3473	−	40.6847i	1.28065	−	1.32417i
$945$		0			0
$946$	−8.00000	+	12.0818i	−0.260102	+	0.392813i
$947$	−32.4813			−1.05550			−0.527750	−	0.849400i	$-0.676964\pi$
$947$	−32.4813			−1.05550			−0.527750	+	0.849400i	$0.676964\pi$
$948$	−17.1796	+	22.2240i	−0.557969	+	0.721801i
$949$	−42.2462			−1.37137
$950$		0			0
$951$	14.1955	+	25.2791i	0.460322	+	0.819731i
$952$	3.12311	−	16.7984i	0.101220	−	0.544439i
$953$			22.4924i			0.728601i	0.931281	+	0.364301i	$0.118692\pi$
$953$			22.4924i			0.728601i	−0.931281	+	0.364301i	$0.881308\pi$
$954$	−22.0582	−	47.0414i	−0.714160	−	1.52302i
$955$		0			0
$956$	13.5691	+	32.0000i	0.438857	+	1.03495i
$957$	3.50758	+	6.24621i	0.113384	+	0.201911i
$958$	−30.2462	−	20.0276i	−0.977211	−	0.647063i
$959$	−24.9073			−0.804297
$960$		0			0
$961$	8.75379			0.282380
$962$	30.9481	+	20.4924i	0.997808	+	0.660702i
$963$	4.71659	−	7.73704i	0.151990	−	0.249323i
$964$	10.4384	+	24.6169i	0.336200	+	0.792858i
$965$		0			0
$966$	−0.201201	+	2.74367i	−0.00647354	+	0.0882761i
$967$		−	26.4404i		−	0.850265i	−0.905131	−	0.425132i	$-0.860228\pi$
$967$		−	26.4404i		−	0.850265i	0.905131	−	0.425132i	$-0.139772\pi$
$968$	−4.78023	+	25.7116i	−0.153643	+	0.826404i
$969$	4.00000	−	2.24621i	0.128499	−	0.0721587i
$970$		0			0
$971$	52.6261			1.68885			0.844427	−	0.535671i	$-0.179941\pi$
$971$	52.6261			1.68885			0.844427	+	0.535671i	$0.179941\pi$
$972$	5.64879	−	30.6609i	0.181185	−	0.983449i
$973$	52.9848			1.69862
$974$	19.7373	−	29.8078i	0.632424	−	0.955102i
$975$		0			0
$976$	−8.68466	+	8.97983i	−0.277989	+	0.287437i
$977$		−	31.7538i		−	1.01589i	−0.861388	−	0.507947i	$-0.830405\pi$
$977$		−	31.7538i		−	1.01589i	0.861388	−	0.507947i	$-0.169595\pi$
$978$	2.80954	−	38.3122i	0.0898393	−	1.22509i
$979$			13.5691i			0.433671i
$980$		0			0
$981$	−1.36932	+	2.24621i	−0.0437189	+	0.0717160i
$982$	−31.8078	−	21.0616i	−1.01503	−	0.672103i
$983$	−40.0095			−1.27610			−0.638052	−	0.769993i	$-0.720260\pi$
$983$	−40.0095			−1.27610			−0.638052	+	0.769993i	$0.720260\pi$
$984$	−5.20901	+	1.77172i	−0.166057	+	0.0564804i
$985$		0			0
$986$	−7.36520	−	4.87689i	−0.234556	−	0.155312i
$987$	−7.73704	−	13.7779i	−0.246273	−	0.438556i
$988$	−12.4924	+	5.29723i	−0.397437	+	0.168527i
$989$			2.87689i			0.0914799i
$990$		0			0
$991$		−	33.0161i		−	1.04879i	−0.851475	−	0.524396i	$-0.824291\pi$
$991$		−	33.0161i		−	1.04879i	0.851475	−	0.524396i	$-0.175709\pi$
$992$	−5.75058	−	26.0540i	−0.182581	−	0.827215i
$993$	−2.73863	−	4.87689i	−0.0869079	−	0.154764i
$994$	8.00000	−	12.0818i	0.253745	−	0.383211i
$995$		0			0
$996$	−41.3907	−	31.9960i	−1.31151	−	1.01383i
$997$	33.6155			1.06461			0.532307	−	0.846551i	$-0.321325\pi$
$997$	33.6155			1.06461			0.532307	+	0.846551i	$0.321325\pi$
$998$	25.1976	−	38.0540i	0.797615	−	1.20458i
$999$	−0.952473	+	26.6034i	−0.0301349	+	0.841694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.e.c.251.1		8
3.2	odd	2	inner	300.2.e.c.251.8		8
4.3	odd	2	inner	300.2.e.c.251.7		8
5.2	odd	4		300.2.h.a.299.5		8
5.3	odd	4		300.2.h.b.299.4		8
5.4	even	2		60.2.e.a.11.8	yes	8
12.11	even	2	inner	300.2.e.c.251.2		8
15.2	even	4		300.2.h.b.299.3		8
15.8	even	4		300.2.h.a.299.6		8
15.14	odd	2		60.2.e.a.11.1	✓	8
20.3	even	4		300.2.h.b.299.1		8
20.7	even	4		300.2.h.a.299.8		8
20.19	odd	2		60.2.e.a.11.2	yes	8
40.19	odd	2		960.2.h.g.191.2		8
40.29	even	2		960.2.h.g.191.7		8
60.23	odd	4		300.2.h.a.299.7		8
60.47	odd	4		300.2.h.b.299.2		8
60.59	even	2		60.2.e.a.11.7	yes	8
120.29	odd	2		960.2.h.g.191.1		8
120.59	even	2		960.2.h.g.191.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.2.e.a.11.1	✓	8	15.14	odd	2
60.2.e.a.11.2	yes	8	20.19	odd	2
60.2.e.a.11.7	yes	8	60.59	even	2
60.2.e.a.11.8	yes	8	5.4	even	2
300.2.e.c.251.1		8	1.1	even	1	trivial
300.2.e.c.251.2		8	12.11	even	2	inner
300.2.e.c.251.7		8	4.3	odd	2	inner
300.2.e.c.251.8		8	3.2	odd	2	inner
300.2.h.a.299.5		8	5.2	odd	4
300.2.h.a.299.6		8	15.8	even	4
300.2.h.a.299.7		8	60.23	odd	4
300.2.h.a.299.8		8	20.7	even	4
300.2.h.b.299.1		8	20.3	even	4
300.2.h.b.299.2		8	60.47	odd	4
300.2.h.b.299.3		8	15.2	even	4
300.2.h.b.299.4		8	5.3	odd	4
960.2.h.g.191.1		8	120.29	odd	2
960.2.h.g.191.2		8	40.19	odd	2
960.2.h.g.191.7		8	40.29	even	2
960.2.h.g.191.8		8	120.59	even	2

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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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17915 - 0.780776i) q^{2} +(1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} +3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 - 2.56155i) q^{9} +O(q^{10})\)	\(q+(-1.17915 - 0.780776i) q^{2} +(1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-2.44293 - 0.179147i) q^{6} +3.02045i q^{7} +(0.516994 - 2.78078i) q^{8} +(1.56155 - 2.56155i) q^{9} +1.32431 q^{11} +(2.74070 + 2.11862i) q^{12} +5.12311 q^{13} +(2.35829 - 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} -2.00000i q^{17} +(-3.84130 + 1.80122i) q^{18} +1.32431i q^{19} +(2.56155 + 4.56155i) q^{21} +(-1.56155 - 1.03399i) q^{22} -0.371834 q^{23} +(-1.57752 - 4.63804i) q^{24} +(-6.04090 - 4.00000i) q^{26} +(0.185917 - 5.19283i) q^{27} +(-5.56155 + 2.35829i) q^{28} +3.12311i q^{29} -4.71659i q^{31} +(5.52390 - 1.21922i) q^{32} +(2.00000 - 1.12311i) q^{33} +(-1.56155 + 2.35829i) q^{34} +(5.93581 + 0.875288i) q^{36} -5.12311 q^{37} +(1.03399 - 1.56155i) q^{38} +(7.73704 - 4.34475i) q^{39} -1.12311i q^{41} +(0.541105 - 7.37874i) q^{42} -7.73704i q^{43} +(1.03399 + 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} -3.02045 q^{47} +(-1.76115 + 6.70062i) q^{48} -2.12311 q^{49} +(-1.69614 - 3.02045i) q^{51} +(4.00000 + 9.43318i) q^{52} +12.2462i q^{53} +(-4.27366 + 5.97795i) q^{54} +(8.39919 + 1.56155i) q^{56} +(1.12311 + 2.00000i) q^{57} +(2.43845 - 3.68260i) q^{58} -14.1498 q^{59} +3.12311 q^{61} +(-3.68260 + 5.56155i) q^{62} +(7.73704 + 4.71659i) q^{63} +(-7.46543 - 2.87529i) q^{64} +(-3.23519 - 0.237246i) q^{66} +4.34475i q^{67} +(3.68260 - 1.56155i) q^{68} +(-0.561553 + 0.315342i) q^{69} +3.39228 q^{71} +(-6.31579 - 5.66664i) q^{72} -8.24621 q^{73} +(6.04090 + 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} +4.00000i q^{77} +(-12.5154 - 0.917790i) q^{78} +8.10887i q^{79} +(-4.12311 - 8.00000i) q^{81} +(-0.876894 + 1.32431i) q^{82} -15.1022 q^{83} +(-6.39919 + 8.27814i) q^{84} +(-6.04090 + 9.12311i) q^{86} +(2.64861 + 4.71659i) q^{87} +(0.684658 - 3.68260i) q^{88} +10.2462i q^{89} +15.4741i q^{91} +(-0.290319 - 0.684658i) q^{92} +(-4.00000 - 7.12311i) q^{93} +(3.56155 + 2.35829i) q^{94} +(7.30834 - 6.52596i) q^{96} +6.00000 q^{97} +(2.50345 + 1.65767i) q^{98} +(2.06798 - 3.39228i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{4} - 6 q^{6} - 4 q^{9} - 4 q^{12} + 8 q^{13} - 14 q^{16} - 16 q^{18} + 4 q^{21} + 4 q^{22} - 2 q^{24} - 28 q^{28} + 16 q^{33} + 4 q^{34} + 18 q^{36} - 8 q^{37} + 12 q^{42} + 20 q^{46} + 36 q^{48} + 16 q^{49} + 32 q^{52} - 10 q^{54} - 24 q^{57} + 36 q^{58} - 8 q^{61} - 2 q^{64} - 40 q^{66} + 12 q^{69} - 24 q^{72} - 36 q^{76} - 40 q^{78} - 40 q^{82} + 16 q^{84} - 44 q^{88} - 32 q^{93} + 12 q^{94} + 42 q^{96} + 48 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 6 * q^6 - 4 * q^9 - 4 * q^12 + 8 * q^13 - 14 * q^16 - 16 * q^18 + 4 * q^21 + 4 * q^22 - 2 * q^24 - 28 * q^28 + 16 * q^33 + 4 * q^34 + 18 * q^36 - 8 * q^37 + 12 * q^42 + 20 * q^46 + 36 * q^48 + 16 * q^49 + 32 * q^52 - 10 * q^54 - 24 * q^57 + 36 * q^58 - 8 * q^61 - 2 * q^64 - 40 * q^66 + 12 * q^69 - 24 * q^72 - 36 * q^76 - 40 * q^78 - 40 * q^82 + 16 * q^84 - 44 * q^88 - 32 * q^93 + 12 * q^94 + 42 * q^96 + 48 * q^97

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