LMFDB - Embedded newform 300.2.e.c.251.8

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			251.8
Root			$1.17915 - 0.780776i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.c.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17915 + 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})$	\(q+(1.17915 + 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} -1.32431 q^{11} +(0.382406 - 3.44293i) q^{12} +5.12311 q^{13} +(-2.35829 + 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} +2.00000i q^{17} +(-0.158699 + 4.23967i) q^{18} +1.32431i q^{19} +(2.56155 - 4.56155i) q^{21} +(-1.56155 - 1.03399i) q^{22} +0.371834 q^{23} +(3.13907 - 3.76115i) 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} +(-3.49737 + 4.87529i) q^{36} -5.12311 q^{37} +(-1.03399 + 1.56155i) q^{38} +(-7.73704 - 4.34475i) q^{39} +1.12311i q^{41} +(6.58200 - 3.37874i) q^{42} -7.73704i q^{43} +(-1.03399 - 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} +3.02045 q^{47} +(6.63804 - 1.98403i) q^{48} -2.12311 q^{49} +(1.69614 - 3.02045i) q^{51} +(4.00000 + 9.43318i) q^{52} -12.2462i q^{53} +(3.83521 - 6.26827i) 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} +(1.48140 + 2.88586i) q^{66} +4.34475i q^{67} +(-3.68260 + 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} -3.39228 q^{71} +(-7.93042 + 3.01802i) q^{72} -8.24621 q^{73} +(-6.04090 - 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} -4.00000i q^{77} +(-5.73082 - 11.1640i) q^{78} +8.10887i q^{79} +(-4.12311 + 8.00000i) q^{81} +(-0.876894 + 1.32431i) q^{82} +15.1022 q^{83} +(10.3992 + 1.15504i) 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} +(9.37632 + 2.84336i) 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
$6$	−1.11862	−	2.17915i	−0.456676	−	0.889633i
$7$			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	$-0.563979\pi$
$11$	−1.32431			−0.399294			−0.199647	+	0.979868i	$0.563979\pi$
$12$	0.382406	−	3.44293i	0.110391	−	0.993888i
$13$	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	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	−0.158699	+	4.23967i	−0.0374058	+	0.999300i
$19$			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	$-0.487657\pi$
$23$	0.371834			0.0775328			0.0387664	+	0.999248i	$0.487657\pi$
$24$	3.13907	−	3.76115i	0.640760	−	0.767741i
$25$		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	$-0.906354\pi$
$29$		−	3.12311i		−	0.579946i	0.957035	−	0.289973i	$-0.0936464\pi$
$30$		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
$36$	−3.49737	+	4.87529i	−0.582894	+	0.812548i
$37$	−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	$0.0279516\pi$
$41$			1.12311i			0.175400i	−0.996147	+	0.0876998i	$0.972048\pi$
$42$	6.58200	−	3.37874i	1.01562	−	0.521351i
$43$		−	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	$-0.429300\pi$
$47$	3.02045			0.440578			0.220289	+	0.975435i	$0.429300\pi$
$48$	6.63804	−	1.98403i	0.958119	−	0.286371i
$49$	−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	$-0.681924\pi$
$53$		−	12.2462i		−	1.68215i	0.540921	−	0.841073i	$-0.318076\pi$
$54$	3.83521	−	6.26827i	0.521906	−	0.853003i
$55$		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	$-0.127315\pi$
$59$	14.1498			1.84214			0.921071	+	0.389394i	$0.127315\pi$
$60$		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
$66$	1.48140	+	2.88586i	0.182348	+	0.355225i
$67$			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	$-0.564515\pi$
$71$	−3.39228			−0.402590			−0.201295	+	0.979531i	$0.564515\pi$
$72$	−7.93042	+	3.01802i	−0.934609	+	0.355677i
$73$	−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
$78$	−5.73082	−	11.1640i	−0.648888	−	1.26407i
$79$			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	$-0.189000\pi$
$83$	15.1022			1.65769			0.828843	+	0.559481i	$0.189000\pi$
$84$	10.3992	+	1.15504i	1.13464	+	0.126025i
$85$		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	$-0.817270\pi$
$89$		−	10.2462i		−	1.08610i	0.839702	−	0.543048i	$-0.182730\pi$
$90$		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
$96$	9.37632	+	2.84336i	0.956966	+	0.290199i
$97$	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	$0.0138914\pi$
$101$			0.876894i			0.0872543i	−0.999048	+	0.0436271i	$0.986109\pi$
$102$	4.35829	−	2.23725i	0.431535	−	0.221520i
$103$			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	$-0.546640\pi$
$107$	−3.02045			−0.291998			−0.145999	+	0.989285i	$0.546640\pi$
$108$	9.41639	−	4.39676i	0.906093	−	0.423079i
$109$	−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	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	2.88586	−	1.48140i	0.270286	−	0.138746i
$115$		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
$126$	−12.8057	−	0.479343i	−1.14082	−	0.0427033i
$127$		−	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	$-0.576666\pi$
$131$	−5.46026			−0.477065			−0.238532	+	0.971135i	$0.576666\pi$
$132$	−0.506422	+	4.55950i	−0.0440784	+	0.396853i
$133$	−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	$-0.885413\pi$
$137$		−	8.24621i		−	0.704521i	0.935902	−	0.352261i	$-0.114587\pi$
$138$	−0.415942	−	0.810281i	−0.0354074	−	0.0689757i
$139$		−	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
$144$	−11.7075	−	2.63319i	−0.975628	−	0.219433i
$145$		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	$0.194400\pi$
$149$			14.0000i			1.14692i	−0.819232	+	0.573462i	$0.805600\pi$
$150$		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
$156$	1.95910	−	17.6385i	0.156854	−	1.41221i
$157$	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
$162$	−11.1080	+	6.21395i	−0.872724	+	0.488214i
$163$			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	$-0.614020\pi$
$167$	−9.06134			−0.701188			−0.350594	+	0.936528i	$0.614020\pi$
$168$	11.3604	+	9.48140i	0.876470	+	0.731506i
$169$	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	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	−6.80571	+	3.49358i	−0.515939	+	0.264847i
$175$		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	$-0.377906\pi$
$179$	10.0138			0.748468			0.374234	+	0.927334i	$0.377906\pi$
$180$		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
$186$	−10.2781	+	5.27608i	−0.753630	+	0.386861i
$187$		−	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	$-0.142752\pi$
$191$	24.9073			1.80223			0.901113	+	0.433585i	$0.142752\pi$
$192$	8.83603	+	10.6735i	0.637686	+	0.770297i
$193$	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	$0.0483347\pi$
$197$			4.24621i			0.302530i	−0.988493	+	0.151265i	$0.951665\pi$
$198$	0.210167	−	5.61463i	0.0149359	−	0.399014i
$199$			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
$204$	6.88586	+	0.764811i	0.482107	+	0.0535475i
$205$		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
$216$	14.5362	+	2.16766i	0.989063	+	0.147491i
$217$	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
$222$	5.73082	+	11.1640i	0.384628	+	0.749279i
$223$		−	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	$-0.241220\pi$
$227$	21.8868			1.45268			0.726339	+	0.687337i	$0.241220\pi$
$228$	4.55950	+	0.506422i	0.301960	+	0.0335386i
$229$	−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	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$	−0.813033	+	21.7203i	−0.0531497	+	1.41990i
$235$		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	$-0.689998\pi$
$239$	−17.3790			−1.12416			−0.562078	+	0.827084i	$0.689998\pi$
$240$		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
$246$	2.44741	−	1.25633i	0.156041	−	0.0801008i
$247$			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	$-0.700979\pi$
$251$	−18.7033			−1.18054			−0.590272	+	0.807205i	$0.700979\pi$
$252$	−14.7256	−	10.5636i	−0.927623	−	0.665445i
$253$	−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	$0.399975\pi$
$257$			30.4924i			1.90207i	−0.309091	+	0.951033i	$0.600025\pi$
$258$	−16.8601	+	8.65483i	−1.04967	+	0.538826i
$259$		−	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	$-0.762129\pi$
$263$	−23.7917			−1.46706			−0.733531	+	0.679656i	$0.762129\pi$
$264$	−4.15709	+	4.98091i	−0.255851	+	0.306554i
$265$		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	$-0.859642\pi$
$269$		−	14.0000i		−	0.853595i	0.904347	−	0.426798i	$-0.140358\pi$
$270$		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
$276$	0.142191	−	1.28020i	0.00855892	−	0.0770589i
$277$	−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	$-0.866882\pi$
$281$		−	13.6155i		−	0.812234i	0.913821	−	0.406117i	$-0.133118\pi$
$282$	−3.37874	−	6.58200i	−0.201201	−	0.391952i
$283$		−	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
$288$	−11.7490	−	12.2459i	−0.692315	−	0.721596i
$289$	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	$0.0231949\pi$
$293$			2.49242i			0.145609i	−0.997346	+	0.0728044i	$0.976805\pi$
$294$	2.37495	+	4.62656i	0.138510	+	0.269826i
$295$		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
$306$	−8.47934	−	0.317399i	−0.484732	−	0.0181445i
$307$		−	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	$-0.700445\pi$
$311$	−20.7713			−1.17783			−0.588916	+	0.808194i	$0.700445\pi$
$312$	16.0818	−	19.2688i	0.910452	−	1.09088i
$313$	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	$-0.844230\pi$
$317$		−	16.7386i		−	0.940135i	0.882630	−	0.470068i	$-0.155770\pi$
$318$	−26.6863	+	13.6989i	−1.49649	+	0.768196i
$319$			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
$324$	−17.9496	−	1.34567i	−0.997202	−	0.0747592i
$325$		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
$336$	5.99267	+	20.0499i	0.326927	+	1.09381i
$337$	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
$342$	−5.61463	−	0.210167i	−0.303604	−	0.0113645i
$343$			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	$-0.707801\pi$
$347$	−22.6305			−1.21487			−0.607434	+	0.794370i	$0.707801\pi$
$348$	−10.7526	−	1.19429i	−0.576402	−	0.0640208i
$349$	−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	$-0.818878\pi$
$353$		−	20.2462i		−	1.07760i	0.842435	−	0.538799i	$-0.181122\pi$
$354$	−15.8283	−	30.8344i	−0.841262	−	1.63883i
$355$		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	$-0.692189\pi$
$359$	−21.5150			−1.13552			−0.567758	+	0.823195i	$0.692189\pi$
$360$		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
$366$	−3.49358	−	6.80571i	−0.182612	−	0.355740i
$367$			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
$372$	−16.2389	−	1.80365i	−0.841947	−	0.0935149i
$373$	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
$378$	18.9330	+	11.5841i	0.973807	+	0.595820i
$379$			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	$-0.626090\pi$
$383$	−15.1022			−0.771688			−0.385844	+	0.922564i	$0.626090\pi$
$384$	2.08533	+	19.4846i	0.106417	+	0.994322i
$385$		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	$0.176213\pi$
$389$			20.7386i			1.05149i	−0.850642	+	0.525745i	$0.823787\pi$
$390$		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
$396$	4.63159	−	6.45638i	0.232746	−	0.324445i
$397$	−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	$-0.795465\pi$
$401$		−	24.0000i		−	1.19850i	0.800561	−	0.599251i	$-0.204535\pi$
$402$	9.46786	−	4.86014i	0.472214	−	0.242402i
$403$		−	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
$408$	7.52230	+	6.27814i	0.372409	+	0.310814i
$409$	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
$414$	−0.0590098	+	1.57645i	−0.00290017	+	0.0774785i
$415$		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	$-0.557580\pi$
$419$	−7.36520			−0.359814			−0.179907	+	0.983684i	$0.557580\pi$
$420$		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
$426$	3.79468	+	7.39228i	0.183853	+	0.358157i
$427$			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	$-0.368785\pi$
$431$	16.6354			0.801297			0.400648	+	0.916232i	$0.368785\pi$
$432$	15.4479	+	13.9055i	0.743236	+	0.669030i
$433$	−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
$438$	9.22440	+	17.9697i	0.440759	+	0.858626i
$439$			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	$-0.628943\pi$
$443$	−16.5896			−0.788195			−0.394097	+	0.919069i	$0.628943\pi$
$444$	−1.95910	+	17.6385i	−0.0929750	+	0.837086i
$445$		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	$0.223484\pi$
$449$			27.3693i			1.29164i	−0.763491	+	0.645819i	$0.776516\pi$
$450$		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
$456$	4.98091	+	4.15709i	0.233253	+	0.194674i
$457$	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	$-0.571543\pi$
$461$		−	41.8617i		−	1.94970i	0.222872	−	0.974848i	$-0.428457\pi$
$462$	−8.71659	+	4.47449i	−0.405532	+	0.208172i
$463$		−	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	$-0.483224\pi$
$467$	2.27678			0.105357			0.0526784	+	0.998612i	$0.483224\pi$
$468$	−17.9174	+	24.9766i	−0.828231	+	1.15454i
$469$	−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
$474$	17.6704	−	9.07077i	0.811629	−	0.416634i
$475$		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	$-0.699302\pi$
$479$	−25.6509			−1.17202			−0.586010	+	0.810304i	$0.699302\pi$
$480$		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
$486$	22.0454	+	0.0358705i	0.999999	+	0.00162712i
$487$			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	$-0.708304\pi$
$491$	−26.9752			−1.21737			−0.608687	+	0.793410i	$0.708304\pi$
$492$	3.86677	+	0.429482i	0.174328	+	0.0193625i
$493$	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
$498$	−16.8937	−	32.9100i	−0.757025	−	1.47473i
$499$			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	$-0.396281\pi$
$503$	14.3586			0.640217			0.320109	+	0.947381i	$0.396281\pi$
$504$	−9.11578	−	23.9534i	−0.406049	−	1.06697i
$505$		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	$-0.920716\pi$
$509$		−	11.1231i		−	0.493023i	0.969140	−	0.246511i	$-0.0792843\pi$
$510$		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
$516$	−26.6381	−	2.95869i	−1.17268	−	0.130249i
$517$	−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	$0.316158\pi$
$521$			38.2462i			1.67560i	−0.545980	+	0.837798i	$0.683842\pi$
$522$	13.2409	+	0.495635i	0.579540	+	0.0216933i
$523$			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
$528$	−8.79081	+	2.62747i	−0.382571	+	0.114346i
$529$	−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
$534$	−22.3280	+	11.4616i	−0.966227	+	0.495994i
$535$		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
$546$	33.7203	−	17.3097i	1.44309	−	0.740785i
$547$		−	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
$552$	1.16721	−	1.39852i	0.0496799	−	0.0595251i
$553$	−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	$0.278699\pi$
$557$			36.2462i			1.53580i	−0.640569	+	0.767901i	$0.721301\pi$
$558$	19.9968	+	0.748519i	0.846532	+	0.0316874i
$559$		−	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	$-0.553238\pi$
$563$	−7.90007			−0.332948			−0.166474	+	0.986046i	$0.553238\pi$
$564$	1.15504	−	10.3992i	0.0486358	−	0.437885i
$565$		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	$0.0887026\pi$
$569$			13.1231i			0.550149i	−0.961423	+	0.275075i	$0.911297\pi$
$570$		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
$576$	−4.29247	−	23.6130i	−0.178853	−	0.983876i
$577$	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
$582$	−6.71174	−	13.0749i	−0.278210	−	0.541971i
$583$			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	$-0.487784\pi$
$587$	1.85917			0.0767362			0.0383681	+	0.999264i	$0.487784\pi$
$588$	−0.811887	+	7.30970i	−0.0334817	+	0.301447i
$589$	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	$0.0541557\pi$
$593$			8.24621i			0.338631i	−0.985562	+	0.169316i	$0.945844\pi$
$594$	−5.07900	+	8.30111i	−0.208394	+	0.340599i
$595$		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	$-0.141506\pi$
$599$	44.1912			1.80560			0.902802	+	0.430056i	$0.141506\pi$
$600$		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
$606$	1.91088	−	0.980914i	0.0776243	−	0.0398469i
$607$		−	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
$612$	−9.75058	−	6.99473i	−0.394144	−	0.282745i
$613$	−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	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$	21.3666	−	10.9681i	0.859489	−	0.441202i
$619$		−	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
$624$	34.0074	−	10.1644i	1.36139	−	0.406902i
$625$		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
$636$	−42.1628	−	4.68302i	−1.67187	−	0.185694i
$637$	−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	$0.0402414\pi$
$641$			6.38447i			0.252171i	−0.992019	+	0.126086i	$0.959759\pi$
$642$	3.37874	+	6.58200i	0.133348	+	0.259771i
$643$		−	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	$-0.755760\pi$
$647$	−36.6172			−1.43957			−0.719786	+	0.694197i	$0.755760\pi$
$648$	−20.1146	−	15.6014i	−0.790176	−	0.612880i
$649$	−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	$-0.723825\pi$
$653$		−	38.9848i		−	1.52559i	0.646638	−	0.762797i	$-0.276175\pi$
$654$	0.980914	+	1.91088i	0.0383568	+	0.0747214i
$655$		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	$-0.660071\pi$
$659$	−24.7442			−0.963898			−0.481949	+	0.876199i	$0.660071\pi$
$660$		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
$666$	0.813033	−	21.7203i	0.0315044	−	0.841644i
$667$		−	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
$672$	−8.58821	+	28.3207i	−0.331298	+	1.09249i
$673$	−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	$0.00922287\pi$
$677$			1.50758i			0.0579409i	−0.999580	+	0.0289705i	$0.990777\pi$
$678$	30.5081	−	15.6607i	1.17166	−	0.601446i
$679$			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	$-0.451704\pi$
$683$	7.90007			0.302288			0.151144	+	0.988512i	$0.451704\pi$
$684$	−6.45638	−	4.63159i	−0.246866	−	0.177093i
$685$		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
$696$	−11.7465	−	9.80365i	−0.445249	−	0.371606i
$697$	−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	$-0.892740\pi$
$701$		−	17.5076i		−	0.661252i	0.943762	−	0.330626i	$-0.107260\pi$
$702$	19.6482	−	32.1130i	0.741573	−	1.21203i
$703$		−	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
$708$	5.41095	−	48.7167i	0.203356	−	1.83088i
$709$	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
$714$	6.75748	+	13.1640i	0.252893	+	0.492650i
$715$		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	$-0.304190\pi$
$719$	30.9481			1.15417			0.577086	+	0.816684i	$0.304190\pi$
$720$		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
$726$	10.3430	+	20.1489i	0.383866	+	0.747794i
$727$		−	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
$732$	1.19429	−	10.7526i	0.0441423	−	0.397429i
$733$	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
$738$	−4.76160	−	0.178236i	−0.175277	−	0.00656096i
$739$			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	$-0.557563\pi$
$743$	−9.80501			−0.359711			−0.179856	+	0.983693i	$0.557563\pi$
$744$	−17.7398	−	14.8057i	−0.650372	−	0.542804i
$745$		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
$756$	13.2802	+	28.4417i	0.482996	+	1.03442i
$757$	−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	$0.191534\pi$
$761$			31.2311i			1.13212i	−0.824362	+	0.566062i	$0.808466\pi$
$762$	−32.9100	+	16.8937i	−1.19220	+	0.611995i
$763$		−	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
$768$	−12.7542	+	24.6034i	−0.460229	+	0.887800i
$769$	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	$-0.998591\pi$
$773$		−	0.246211i		−	0.00885560i	0.999990	−	0.00442780i	$-0.00140942\pi$
$774$	32.8025	+	1.22786i	1.17906	+	0.0441346i
$775$		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
$786$	6.10797	+	11.8987i	0.217864	+	0.424413i
$787$		−	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
$792$	10.5023	−	3.99679i	0.373183	−	0.142020i
$793$	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	$0.0724384\pi$
$797$			12.7386i			0.451226i	−0.974217	+	0.225613i	$0.927562\pi$
$798$	4.47449	+	8.71659i	0.158395	+	0.308564i
$799$			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
$804$	14.9587	+	1.66146i	0.527552	+	0.0585951i
$805$		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	$0.175204\pi$
$809$			29.7538i			1.04609i	−0.852306	+	0.523044i	$0.824796\pi$
$810$		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
$816$	3.96807	+	13.2761i	0.138910	+	0.464756i
$817$	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	$-0.620766\pi$
$821$		−	53.2311i		−	1.85778i	0.370360	−	0.928888i	$-0.379234\pi$
$822$	−17.9697	+	9.22440i	−0.626766	+	0.321738i
$823$		−	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	$-0.599870\pi$
$827$	−17.7509			−0.617258			−0.308629	+	0.951183i	$0.599870\pi$
$828$	−1.30044	+	1.81280i	−0.0451934	+	0.0629991i
$829$	−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
$834$	−38.2267	+	19.6229i	−1.32368	+	0.679487i
$835$		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	$-0.401135\pi$
$839$	17.7051			0.611247			0.305624	+	0.952152i	$0.401135\pi$
$840$		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
$846$	−0.479343	+	12.8057i	−0.0164802	+	0.440269i
$847$		−	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
$852$	−1.29723	+	11.6794i	−0.0444423	+	0.400129i
$853$	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	$-0.884750\pi$
$857$		−	20.7386i		−	0.708418i	0.935166	−	0.354209i	$-0.115250\pi$
$858$	7.58937	+	14.7846i	0.259097	+	0.504737i
$859$		−	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	$-0.442539\pi$
$863$	10.5487			0.359081			0.179541	+	0.983751i	$0.442539\pi$
$864$	7.35820	+	28.4580i	0.250331	+	0.968160i
$865$		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
$876$	−3.15340	+	28.3911i	−0.106543	+	0.959247i
$877$	−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	$-0.996618\pi$
$881$		−	0.630683i		−	0.0212483i	0.999944	−	0.0106241i	$-0.00338183\pi$
$882$	0.336935	−	9.00127i	0.0113452	−	0.303089i
$883$			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	$-0.834285\pi$
$887$	−51.6737			−1.73503			−0.867516	+	0.497409i	$0.834285\pi$
$888$	−16.0818	+	19.2688i	−0.539670	+	0.646617i
$889$	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
$894$	30.5081	−	15.6607i	1.02034	−	0.523773i
$895$		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
$906$	−16.0499	+	8.23888i	−0.533221	+	0.273719i
$907$			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	$-0.423802\pi$
$911$	14.3128			0.474204			0.237102	+	0.971485i	$0.423802\pi$
$912$	2.62747	+	8.79081i	0.0870043	+	0.291093i
$913$	−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
$918$	12.5365	+	7.67042i	0.413767	+	0.253162i
$919$		−	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
$924$	−13.7717	−	1.52962i	−0.453056	−	0.0503209i
$925$		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	$0.182851\pi$
$929$			33.1231i			1.08673i	−0.839495	+	0.543367i	$0.817149\pi$
$930$		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
$936$	−40.6284	+	15.4616i	−1.32798	+	0.505380i
$937$	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	$-0.995450\pi$
$941$		−	0.876894i		−	0.0285859i	0.999898	−	0.0142930i	$-0.00454975\pi$
$942$	−3.76900	−	7.34224i	−0.122800	−	0.239223i
$943$			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	$-0.323036\pi$
$947$	32.4813			1.05550			0.527750	+	0.849400i	$0.323036\pi$
$948$	27.9183	+	3.10088i	0.906743	+	0.100712i
$949$	−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	$-0.881308\pi$
$953$		−	22.4924i		−	0.728601i	0.931281	−	0.364301i	$-0.118692\pi$
$954$	51.9199	+	1.94347i	1.68097	+	0.0629220i
$955$		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
$966$	2.44741	−	1.25633i	0.0787442	−	0.0404218i
$967$		−	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	$-0.820059\pi$
$971$	−52.6261			−1.68885			−0.844427	+	0.535671i	$0.820059\pi$
$972$	25.9667	+	17.2548i	0.832884	+	0.553448i
$973$	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	$0.169595\pi$
$977$			31.7538i			1.01589i	−0.861388	+	0.507947i	$0.830405\pi$
$978$	34.1753	−	17.5432i	1.09281	−	0.560971i
$979$			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	$-0.279740\pi$
$983$	40.0095			1.27610			0.638052	+	0.769993i	$0.279740\pi$
$984$	4.22417	+	3.52551i	0.134662	+	0.112389i
$985$		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
$996$	5.77518	−	51.9960i	0.182994	−	1.64755i
$997$	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.251.8		8
3.2	odd	2	inner	300.2.e.c.251.1		8
4.3	odd	2	inner	300.2.e.c.251.2		8
5.2	odd	4		300.2.h.b.299.3		8
5.3	odd	4		300.2.h.a.299.6		8
5.4	even	2		60.2.e.a.11.1	✓	8
12.11	even	2	inner	300.2.e.c.251.7		8
15.2	even	4		300.2.h.a.299.5		8
15.8	even	4		300.2.h.b.299.4		8
15.14	odd	2		60.2.e.a.11.8	yes	8
20.3	even	4		300.2.h.a.299.7		8
20.7	even	4		300.2.h.b.299.2		8
20.19	odd	2		60.2.e.a.11.7	yes	8
40.19	odd	2		960.2.h.g.191.8		8
40.29	even	2		960.2.h.g.191.1		8
60.23	odd	4		300.2.h.b.299.1		8
60.47	odd	4		300.2.h.a.299.8		8
60.59	even	2		60.2.e.a.11.2	yes	8
120.29	odd	2		960.2.h.g.191.7		8
120.59	even	2		960.2.h.g.191.2		8

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

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

\(f(q)\)	\(=\)	\(q+(1.17915 + 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} +O(q^{10})\)	\(q+(1.17915 + 0.780776i) q^{2} +(-1.51022 - 0.848071i) q^{3} +(0.780776 + 1.84130i) q^{4} +(-1.11862 - 2.17915i) q^{6} +3.02045i q^{7} +(-0.516994 + 2.78078i) q^{8} +(1.56155 + 2.56155i) q^{9} -1.32431 q^{11} +(0.382406 - 3.44293i) q^{12} +5.12311 q^{13} +(-2.35829 + 3.56155i) q^{14} +(-2.78078 + 2.87529i) q^{16} +2.00000i q^{17} +(-0.158699 + 4.23967i) q^{18} +1.32431i q^{19} +(2.56155 - 4.56155i) q^{21} +(-1.56155 - 1.03399i) q^{22} +0.371834 q^{23} +(3.13907 - 3.76115i) 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} +(-3.49737 + 4.87529i) q^{36} -5.12311 q^{37} +(-1.03399 + 1.56155i) q^{38} +(-7.73704 - 4.34475i) q^{39} +1.12311i q^{41} +(6.58200 - 3.37874i) q^{42} -7.73704i q^{43} +(-1.03399 - 2.43845i) q^{44} +(0.438447 + 0.290319i) q^{46} +3.02045 q^{47} +(6.63804 - 1.98403i) q^{48} -2.12311 q^{49} +(1.69614 - 3.02045i) q^{51} +(4.00000 + 9.43318i) q^{52} -12.2462i q^{53} +(3.83521 - 6.26827i) 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} +(1.48140 + 2.88586i) q^{66} +4.34475i q^{67} +(-3.68260 + 1.56155i) q^{68} +(-0.561553 - 0.315342i) q^{69} -3.39228 q^{71} +(-7.93042 + 3.01802i) q^{72} -8.24621 q^{73} +(-6.04090 - 4.00000i) q^{74} +(-2.43845 + 1.03399i) q^{76} -4.00000i q^{77} +(-5.73082 - 11.1640i) q^{78} +8.10887i q^{79} +(-4.12311 + 8.00000i) q^{81} +(-0.876894 + 1.32431i) q^{82} +15.1022 q^{83} +(10.3992 + 1.15504i) 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} +(9.37632 + 2.84336i) 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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