LMFDB - Embedded newform 51.2.e.a.13.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [51,2,Mod(4,51)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(51, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("51.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 51 = 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	51.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.407237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.836829184.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 14x^{6} + 61x^{4} + 84x^{2} + 4 $ x^8 + 14x^6 + 61x^4 + 84*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.4
Root			$2.63640i$ of defining polynomial
Character	$\chi$	$=$	51.13
Dual form			51.2.e.a.4.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.63640i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.95063 q^{4} +(1.57133 + 1.57133i) q^{5} +(1.86422 - 1.86422i) q^{6} +(1.63640 - 1.63640i) q^{7} -7.77906i q^{8} +1.00000i q^{9} +(-4.14265 + 4.14265i) q^{10} +(1.37930 - 1.37930i) q^{11} +(3.50062 + 3.50062i) q^{12} -1.32218 q^{13} +(4.31423 + 4.31423i) q^{14} -2.22219i q^{15} +10.6075 q^{16} +(-3.88555 + 1.37930i) q^{17} -2.63640 q^{18} -5.95063i q^{19} +(-7.77906 - 7.77906i) q^{20} -2.31423 q^{21} +(3.63640 + 3.63640i) q^{22} +(-3.37930 + 3.37930i) q^{23} +(-5.50062 + 5.50062i) q^{24} -0.0618655i q^{25} -3.48580i q^{26} +(0.707107 - 0.707107i) q^{27} +(-8.10124 + 8.10124i) q^{28} +(-0.122204 - 0.122204i) q^{29} +5.85860 q^{30} +(0.314226 + 0.314226i) q^{31} +12.4075i q^{32} -1.95063 q^{33} +(-3.63640 - 10.2439i) q^{34} +5.14265 q^{35} -4.95063i q^{36} +(3.75861 + 3.75861i) q^{37} +15.6883 q^{38} +(0.934922 + 0.934922i) q^{39} +(12.2234 - 12.2234i) q^{40} +(-2.84414 + 2.84414i) q^{41} -6.10124i q^{42} +8.33468i q^{43} +(-6.82843 + 6.82843i) q^{44} +(-1.57133 + 1.57133i) q^{45} +(-8.90921 - 8.90921i) q^{46} -2.38404 q^{47} +(-7.50062 - 7.50062i) q^{48} +1.64436i q^{49} +0.163102 q^{50} +(3.72282 + 1.77219i) q^{51} +6.54562 q^{52} +0.727190i q^{53} +(1.86422 + 1.86422i) q^{54} +4.33468 q^{55} +(-12.7297 - 12.7297i) q^{56} +(-4.20773 + 4.20773i) q^{57} +(0.322179 - 0.322179i) q^{58} -11.7870i q^{59} +11.0012i q^{60} +(6.14265 - 6.14265i) q^{61} +(-0.828427 + 0.828427i) q^{62} +(1.63640 + 1.63640i) q^{63} -11.4963 q^{64} +(-2.07757 - 2.07757i) q^{65} -5.14265i q^{66} -14.1866 q^{67} +(19.2359 - 6.82843i) q^{68} +4.77906 q^{69} +13.5581i q^{70} +(4.31423 + 4.31423i) q^{71} +7.77906 q^{72} +(7.46483 + 7.46483i) q^{73} +(-9.90921 + 9.90921i) q^{74} +(-0.0437455 + 0.0437455i) q^{75} +29.4594i q^{76} -4.51420i q^{77} +(-2.46483 + 2.46483i) q^{78} +(0.493752 - 0.493752i) q^{79} +(16.6678 + 16.6678i) q^{80} -1.00000 q^{81} +(-7.49830 - 7.49830i) q^{82} -8.52971i q^{83} +11.4569 q^{84} +(-8.27281 - 3.93813i) q^{85} -21.9736 q^{86} +0.172822i q^{87} +(-10.7297 - 10.7297i) q^{88} -5.40297 q^{89} +(-4.14265 - 4.14265i) q^{90} +(-2.16362 + 2.16362i) q^{91} +(16.7297 - 16.7297i) q^{92} -0.444383i q^{93} -6.28531i q^{94} +(9.35038 - 9.35038i) q^{95} +(8.77343 - 8.77343i) q^{96} +(3.33468 + 3.33468i) q^{97} -4.33519 q^{98} +(1.37930 + 1.37930i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{13} + 24 q^{14} + 12 q^{16} - 4 q^{17} - 4 q^{18} - 12 q^{20} - 8 q^{21} + 12 q^{22} - 16 q^{23} - 16 q^{24} - 8 q^{28} + 4 q^{29} + 24 q^{30} - 8 q^{31}+ \cdots - 76 q^{98}+O(q^{100}) $ 8 * q - 12 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^13 + 24 * q^14 + 12 * q^16 - 4 * q^17 - 4 * q^18 - 12 * q^20 - 8 * q^21 + 12 * q^22 - 16 * q^23 - 16 * q^24 - 8 * q^28 + 4 * q^29 + 24 * q^30 - 8 * q^31 + 12 * q^33 - 12 * q^34 + 8 * q^35 + 8 * q^37 + 24 * q^38 + 8 * q^39 + 36 * q^40 + 28 * q^41 - 32 * q^44 + 4 * q^45 - 20 * q^46 - 8 * q^47 - 32 * q^48 - 60 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^54 - 4 * q^55 - 24 * q^56 - 4 * q^58 + 16 * q^61 + 16 * q^62 - 4 * q^63 + 4 * q^64 + 16 * q^65 + 8 * q^67 + 60 * q^68 - 12 * q^69 + 24 * q^71 + 12 * q^72 + 20 * q^73 - 28 * q^74 - 16 * q^75 + 20 * q^78 + 20 * q^79 + 60 * q^80 - 8 * q^81 - 40 * q^82 + 48 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^88 - 8 * q^89 - 36 * q^91 + 56 * q^92 + 8 * q^95 + 8 * q^96 - 12 * q^97 - 76 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/51\mathbb{Z}\right)^\times$.

$n$	$35$	$37$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			2.63640i			1.86422i	0.362176	+	0.932110i	$0.382034\pi$
$2$			2.63640i			1.86422i	−0.362176	+	0.932110i	$0.617966\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−4.95063			−2.47532
$5$	1.57133	+	1.57133i	0.702719	+	0.702719i	0.964993	−	0.262275i	$-0.0844726\pi$
$5$	1.57133	+	1.57133i	0.702719	+	0.702719i	−0.262275	+	0.964993i	$0.584473\pi$
$6$	1.86422	−	1.86422i	0.761065	−	0.761065i
$7$	1.63640	−	1.63640i	0.618503	−	0.618503i	−0.326644	−	0.945147i	$-0.605918\pi$
$7$	1.63640	−	1.63640i	0.618503	−	0.618503i	0.945147	+	0.326644i	$0.105918\pi$
$8$		−	7.77906i		−	2.75031i
$9$			1.00000i			0.333333i
$10$	−4.14265	+	4.14265i	−1.31002	+	1.31002i
$11$	1.37930	−	1.37930i	0.415876	−	0.415876i	−0.467904	−	0.883780i	$-0.654991\pi$
$11$	1.37930	−	1.37930i	0.415876	−	0.415876i	0.883780	+	0.467904i	$0.154991\pi$
$12$	3.50062	+	3.50062i	1.01054	+	1.01054i
$13$	−1.32218			−0.366706			−0.183353	−	0.983047i	$-0.558695\pi$
$13$	−1.32218			−0.366706			−0.183353	+	0.983047i	$0.558695\pi$
$14$	4.31423	+	4.31423i	1.15303	+	1.15303i
$15$		−	2.22219i		−	0.573767i
$16$	10.6075			2.65187
$17$	−3.88555	+	1.37930i	−0.942385	+	0.334530i
$17$	−3.88555	+	1.37930i	−0.942385	+	0.334530i
$18$	−2.63640			−0.621407
$19$		−	5.95063i		−	1.36517i	−0.730807	−	0.682584i	$-0.760856\pi$
$19$		−	5.95063i		−	1.36517i	0.730807	−	0.682584i	$-0.239144\pi$
$20$	−7.77906	−	7.77906i	−1.73945	−	1.73945i
$21$	−2.31423			−0.505006
$22$	3.63640	+	3.63640i	0.775284	+	0.775284i
$23$	−3.37930	+	3.37930i	−0.704634	+	0.704634i	−0.965402	−	0.260768i	$-0.916024\pi$
$23$	−3.37930	+	3.37930i	−0.704634	+	0.704634i	0.260768	+	0.965402i	$0.416024\pi$
$24$	−5.50062	+	5.50062i	−1.12281	+	1.12281i
$25$		−	0.0618655i		−	0.0123731i
$26$		−	3.48580i		−	0.683621i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	−8.10124	+	8.10124i	−1.53099	+	1.53099i
$29$	−0.122204	−	0.122204i	−0.0226927	−	0.0226927i	0.695669	−	0.718362i	$-0.255108\pi$
$29$	−0.122204	−	0.122204i	−0.0226927	−	0.0226927i	−0.718362	+	0.695669i	$0.755108\pi$
$30$	5.85860			1.06963
$31$	0.314226	+	0.314226i	0.0564367	+	0.0564367i	0.734762	−	0.678325i	$-0.237294\pi$
$31$	0.314226	+	0.314226i	0.0564367	+	0.0564367i	−0.678325	+	0.734762i	$0.737294\pi$
$32$			12.4075i			2.19336i
$33$	−1.95063			−0.339561
$34$	−3.63640	−	10.2439i	−0.623638	−	1.75681i
$35$	5.14265			0.869267
$36$		−	4.95063i		−	0.825105i
$37$	3.75861	+	3.75861i	0.617911	+	0.617911i	0.944995	−	0.327084i	$-0.106066\pi$
$37$	3.75861	+	3.75861i	0.617911	+	0.617911i	−0.327084	+	0.944995i	$0.606066\pi$
$38$	15.6883			2.54497
$39$	0.934922	+	0.934922i	0.149707	+	0.149707i
$40$	12.2234	−	12.2234i	1.93270	−	1.93270i
$41$	−2.84414	+	2.84414i	−0.444179	+	0.444179i	−0.893414	−	0.449234i	$-0.851697\pi$
$41$	−2.84414	+	2.84414i	−0.444179	+	0.444179i	0.449234	+	0.893414i	$0.351697\pi$
$42$		−	6.10124i		−	0.941441i
$43$			8.33468i			1.27103i	0.772090	+	0.635513i	$0.219211\pi$
$43$			8.33468i			1.27103i	−0.772090	+	0.635513i	$0.780789\pi$
$44$	−6.82843	+	6.82843i	−1.02942	+	1.02942i
$45$	−1.57133	+	1.57133i	−0.234240	+	0.234240i
$46$	−8.90921	−	8.90921i	−1.31359	−	1.31359i
$47$	−2.38404			−0.347749			−0.173874	−	0.984768i	$-0.555629\pi$
$47$	−2.38404			−0.347749			−0.173874	+	0.984768i	$0.555629\pi$
$48$	−7.50062	−	7.50062i	−1.08262	−	1.08262i
$49$			1.64436i			0.234908i
$50$	0.163102			0.0230662
$51$	3.72282	+	1.77219i	0.521299	+	0.248156i
$52$	6.54562			0.907714
$53$			0.727190i			0.0998872i	0.998752	+	0.0499436i	$0.0159042\pi$
$53$			0.727190i			0.0998872i	−0.998752	+	0.0499436i	$0.984096\pi$
$54$	1.86422	+	1.86422i	0.253688	+	0.253688i
$55$	4.33468			0.584488
$56$	−12.7297	−	12.7297i	−1.70108	−	1.70108i
$57$	−4.20773	+	4.20773i	−0.557328	+	0.557328i
$58$	0.322179	−	0.322179i	0.0423042	−	0.0423042i
$59$		−	11.7870i		−	1.53454i	−0.641325	−	0.767269i	$-0.721615\pi$
$59$		−	11.7870i		−	1.53454i	0.641325	−	0.767269i	$-0.278385\pi$
$60$			11.0012i			1.42026i
$61$	6.14265	−	6.14265i	0.786486	−	0.786486i	−0.194430	−	0.980916i	$-0.562286\pi$
$61$	6.14265	−	6.14265i	0.786486	−	0.786486i	0.980916	+	0.194430i	$0.0622858\pi$
$62$	−0.828427	+	0.828427i	−0.105210	+	0.105210i
$63$	1.63640	+	1.63640i	0.206168	+	0.206168i
$64$	−11.4963			−1.43703
$65$	−2.07757	−	2.07757i	−0.257691	−	0.257691i
$66$		−	5.14265i		−	0.633017i
$67$	−14.1866			−1.73317			−0.866583	−	0.499034i	$-0.833688\pi$
$67$	−14.1866			−1.73317			−0.866583	+	0.499034i	$0.833688\pi$
$68$	19.2359	−	6.82843i	2.33270	−	0.828068i
$69$	4.77906			0.575331
$70$			13.5581i			1.62050i
$71$	4.31423	+	4.31423i	0.512004	+	0.512004i	0.915140	−	0.403136i	$-0.132080\pi$
$71$	4.31423	+	4.31423i	0.512004	+	0.512004i	−0.403136	+	0.915140i	$0.632080\pi$
$72$	7.77906			0.916771
$73$	7.46483	+	7.46483i	0.873693	+	0.873693i	0.992873	−	0.119180i	$-0.0380266\pi$
$73$	7.46483	+	7.46483i	0.873693	+	0.873693i	−0.119180	+	0.992873i	$0.538027\pi$
$74$	−9.90921	+	9.90921i	−1.15192	+	1.15192i
$75$	−0.0437455	+	0.0437455i	−0.00505130	+	0.00505130i
$76$			29.4594i			3.37922i
$77$		−	4.51420i		−	0.514441i
$78$	−2.46483	+	2.46483i	−0.279087	+	0.279087i
$79$	0.493752	−	0.493752i	0.0555514	−	0.0555514i	−0.678785	−	0.734337i	$-0.737493\pi$
$79$	0.493752	−	0.493752i	0.0555514	−	0.0555514i	0.734337	+	0.678785i	$0.237493\pi$
$80$	16.6678	+	16.6678i	1.86352	+	1.86352i
$81$	−1.00000			−0.111111
$82$	−7.49830	−	7.49830i	−0.828048	−	0.828048i
$83$		−	8.52971i		−	0.936258i	−0.883660	−	0.468129i	$-0.844928\pi$
$83$		−	8.52971i		−	0.936258i	0.883660	−	0.468129i	$-0.155072\pi$
$84$	11.4569			1.25005
$85$	−8.27281	−	3.93813i	−0.897312	−	0.427151i
$86$	−21.9736			−2.36947
$87$			0.172822i			0.0185285i
$88$	−10.7297	−	10.7297i	−1.14379	−	1.14379i
$89$	−5.40297			−0.572713			−0.286357	−	0.958123i	$-0.592444\pi$
$89$	−5.40297			−0.572713			−0.286357	+	0.958123i	$0.592444\pi$
$90$	−4.14265	−	4.14265i	−0.436674	−	0.436674i
$91$	−2.16362	+	2.16362i	−0.226809	+	0.226809i
$92$	16.7297	−	16.7297i	1.74419	−	1.74419i
$93$		−	0.444383i		−	0.0460803i
$94$		−	6.28531i		−	0.648280i
$95$	9.35038	−	9.35038i	0.959329	−	0.959329i
$96$	8.77343	−	8.77343i	0.895435	−	0.895435i
$97$	3.33468	+	3.33468i	0.338585	+	0.338585i	0.855835	−	0.517250i	$-0.173044\pi$
$97$	3.33468	+	3.33468i	0.338585	+	0.338585i	−0.517250	+	0.855835i	$0.673044\pi$
$98$	−4.33519			−0.437921
$99$	1.37930	+	1.37930i	0.138625	+	0.138625i
$100$			0.306273i			0.0306273i
$101$	−7.11123			−0.707594			−0.353797	−	0.935322i	$-0.615110\pi$
$101$	−7.11123			−0.707594			−0.353797	+	0.935322i	$0.615110\pi$
$102$	−4.67220	+	9.81485i	−0.462616	+	0.971815i
$103$	−9.22344			−0.908813			−0.454406	−	0.890795i	$-0.650149\pi$
$103$	−9.22344			−0.908813			−0.454406	+	0.890795i	$0.650149\pi$
$104$			10.2853i			1.00856i
$105$	−3.63640	−	3.63640i	−0.354877	−	0.354877i
$106$	−1.91717			−0.186212
$107$	3.66461	+	3.66461i	0.354271	+	0.354271i	0.861696	−	0.507425i	$-0.169402\pi$
$107$	3.66461	+	3.66461i	0.354271	+	0.354271i	−0.507425	+	0.861696i	$0.669402\pi$
$108$	−3.50062	+	3.50062i	−0.336848	+	0.336848i
$109$	14.1247	−	14.1247i	1.35290	−	1.35290i	0.470503	−	0.882399i	$-0.344073\pi$
$109$	14.1247	−	14.1247i	1.35290	−	1.35290i	0.882399	−	0.470503i	$-0.155927\pi$
$110$			11.4280i			1.08961i
$111$		−	5.31548i		−	0.504523i
$112$	17.3581	−	17.3581i	1.64019	−	1.64019i
$113$	−12.3299	+	12.3299i	−1.15990	+	1.15990i	−0.175407	+	0.984496i	$0.556124\pi$
$113$	−12.3299	+	12.3299i	−1.15990	+	1.15990i	−0.984496	+	0.175407i	$0.943876\pi$
$114$	−11.0933	−	11.0933i	−1.03898	−	1.03898i
$115$	−10.6200			−0.990318
$116$	0.604986	+	0.604986i	0.0561716	+	0.0561716i
$117$		−	1.32218i		−	0.122235i
$118$	31.0753			2.86072
$119$	−4.10124	+	8.61544i	−0.375960	+	0.789776i
$120$	−17.2866			−1.57804
$121$			7.19504i			0.654094i
$122$	16.1945	+	16.1945i	1.46618	+	1.46618i
$123$	4.02222			0.362671
$124$	−1.55562	−	1.55562i	−0.139699	−	0.139699i
$125$	7.95384	−	7.95384i	0.711413	−	0.711413i
$126$	−4.31423	+	4.31423i	−0.384342	+	0.384342i
$127$		−	9.85189i		−	0.874214i	−0.899409	−	0.437107i	$-0.856003\pi$
$127$		−	9.85189i		−	0.874214i	0.899409	−	0.437107i	$-0.143997\pi$
$128$		−	5.49375i		−	0.485584i
$129$	5.89351	−	5.89351i	0.518894	−	0.518894i
$130$	5.47733	−	5.47733i	0.480393	−	0.480393i
$131$	5.37930	+	5.37930i	0.469992	+	0.469992i	0.901912	−	0.431920i	$-0.142164\pi$
$131$	5.37930	+	5.37930i	0.469992	+	0.469992i	−0.431920	+	0.901912i	$0.642164\pi$
$132$	9.65685			0.840521
$133$	−9.73764	−	9.73764i	−0.844361	−	0.844361i
$134$		−	37.4015i		−	3.23100i
$135$	2.22219			0.191256
$136$	10.7297	+	30.2259i	0.920063	+	2.59185i
$137$	22.0723			1.88577			0.942883	−	0.333125i	$-0.108103\pi$
$137$	22.0723			1.88577			0.942883	+	0.333125i	$0.108103\pi$
$138$			12.5995i			1.07254i
$139$	2.53465	+	2.53465i	0.214986	+	0.214986i	0.806382	−	0.591395i	$-0.201423\pi$
$139$	2.53465	+	2.53465i	0.214986	+	0.214986i	−0.591395	+	0.806382i	$0.701423\pi$
$140$	−25.4594			−2.15171
$141$	1.68577	+	1.68577i	0.141968	+	0.141968i
$142$	−11.3740	+	11.3740i	−0.954489	+	0.954489i
$143$	−1.82369	+	1.82369i	−0.152504	+	0.152504i
$144$			10.6075i			0.883957i
$145$		−	0.384044i		−	0.0318931i
$146$	−19.6803	+	19.6803i	−1.62875	+	1.62875i
$147$	1.16274	−	1.16274i	0.0959009	−	0.0959009i
$148$	−18.6075	−	18.6075i	−1.52953	−	1.52953i
$149$	11.7711			0.964327			0.482163	−	0.876081i	$-0.339851\pi$
$149$	11.7711			0.964327			0.482163	+	0.876081i	$0.339851\pi$
$150$	−0.115331	−	0.115331i	−0.00941673	−	0.00941673i
$151$			16.1037i			1.31050i	0.755411	+	0.655252i	$0.227437\pi$
$151$			16.1037i			1.31050i	−0.755411	+	0.655252i	$0.772563\pi$
$152$	−46.2903			−3.75464
$153$	−1.37930	−	3.88555i	−0.111510	−	0.314128i
$154$	11.9013			0.959031
$155$			0.987504i			0.0793182i
$156$	−4.62845	−	4.62845i	−0.370573	−	0.370573i
$157$	6.45535			0.515193			0.257597	−	0.966253i	$-0.417069\pi$
$157$	6.45535			0.515193			0.257597	+	0.966253i	$0.417069\pi$
$158$	1.30173	+	1.30173i	0.103560	+	0.103560i
$159$	0.514201	−	0.514201i	0.0407788	−	0.0407788i
$160$	−19.4963	+	19.4963i	−1.54131	+	1.54131i
$161$			11.0598i			0.871636i
$162$		−	2.63640i		−	0.207136i
$163$	−11.8314	+	11.8314i	−0.926710	+	0.926710i	−0.997492	−	0.0707816i	$-0.977451\pi$
$163$	−11.8314	+	11.8314i	−0.926710	+	0.926710i	0.0707816	+	0.997492i	$0.477451\pi$
$164$	14.0803	−	14.0803i	1.09948	−	1.09948i
$165$	−3.06508	−	3.06508i	−0.238616	−	0.238616i
$166$	22.4878			1.74539
$167$	1.13490	+	1.13490i	0.0878209	+	0.0878209i	0.749653	−	0.661832i	$-0.230221\pi$
$167$	1.13490	+	1.13490i	0.0878209	+	0.0878209i	−0.661832	+	0.749653i	$0.730221\pi$
$168$			18.0025i			1.38892i
$169$	−11.2518			−0.865526
$170$	10.3825	−	21.8105i	0.796303	−	1.67279i
$171$	5.95063			0.455056
$172$		−	41.2619i		−	3.14619i
$173$	−12.1169	−	12.1169i	−0.921234	−	0.921234i	0.0758824	−	0.997117i	$-0.475823\pi$
$173$	−12.1169	−	12.1169i	−0.921234	−	0.921234i	−0.997117	+	0.0758824i	$0.975823\pi$
$174$	−0.455630			−0.0345412
$175$	−0.101237	−	0.101237i	−0.00765280	−	0.00765280i
$176$	14.6310	−	14.6310i	1.10285	−	1.10285i
$177$	−8.33468	+	8.33468i	−0.626473	+	0.626473i
$178$		−	14.2444i		−	1.06766i
$179$			11.0753i			0.827809i	0.910320	+	0.413905i	$0.135835\pi$
$179$			11.0753i			0.827809i	−0.910320	+	0.413905i	$0.864165\pi$
$180$	7.77906	−	7.77906i	0.579817	−	0.579817i
$181$	13.9297	−	13.9297i	1.03538	−	1.03538i	0.0360332	−	0.999351i	$-0.488528\pi$
$181$	13.9297	−	13.9297i	1.03538	−	1.03538i	0.999351	−	0.0360332i	$-0.0114722\pi$
$182$	−5.70418	−	5.70418i	−0.422822	−	0.422822i
$183$	−8.68702			−0.642163
$184$	26.2878	+	26.2878i	1.93796	+	1.93796i
$185$			11.8120i			0.868436i
$186$	1.17157			0.0859039
$187$	−3.45688	+	7.26184i	−0.252792	+	0.531038i
$188$	11.8025			0.860788
$189$		−	2.31423i		−	0.168335i
$190$	24.6514	+	24.6514i	1.78840	+	1.78840i
$191$	−1.60953			−0.116461			−0.0582307	−	0.998303i	$-0.518546\pi$
$191$	−1.60953			−0.116461			−0.0582307	+	0.998303i	$0.518546\pi$
$192$	8.12908	+	8.12908i	0.586666	+	0.586666i
$193$	3.16362	−	3.16362i	0.227722	−	0.227722i	−0.584018	−	0.811741i	$-0.698520\pi$
$193$	3.16362	−	3.16362i	0.227722	−	0.227722i	0.811741	+	0.584018i	$0.198520\pi$
$194$	−8.79155	+	8.79155i	−0.631197	+	0.631197i
$195$			2.93813i			0.210404i
$196$		−	8.14061i		−	0.581472i
$197$	5.22818	−	5.22818i	0.372492	−	0.372492i	−0.495892	−	0.868384i	$-0.665159\pi$
$197$	5.22818	−	5.22818i	0.372492	−	0.372492i	0.868384	+	0.495892i	$0.165159\pi$
$198$	−3.63640	+	3.63640i	−0.258428	+	0.258428i
$199$	5.08874	+	5.08874i	0.360731	+	0.360731i	0.864082	−	0.503351i	$-0.167900\pi$
$199$	5.08874	+	5.08874i	0.360731	+	0.360731i	−0.503351	+	0.864082i	$0.667900\pi$
$200$	−0.481255			−0.0340299
$201$	10.0314	+	10.0314i	0.707562	+	0.707562i
$202$		−	18.7481i		−	1.31911i
$203$	−0.399950			−0.0280710
$204$	−18.4303	−	8.77343i	−1.29038	−	0.614263i
$205$	−8.93813			−0.624266
$206$		−	24.3167i		−	1.69423i
$207$	−3.37930	−	3.37930i	−0.234878	−	0.234878i
$208$	−14.0250			−0.972458
$209$	−8.20773	−	8.20773i	−0.567741	−	0.567741i
$210$	9.58704	−	9.58704i	0.661568	−	0.661568i
$211$	−9.48830	+	9.48830i	−0.653201	+	0.653201i	−0.953763	−	0.300561i	$-0.902826\pi$
$211$	−9.48830	+	9.48830i	−0.653201	+	0.653201i	0.300561	+	0.953763i	$0.402826\pi$
$212$		−	3.60005i		−	0.247252i
$213$		−	6.10124i		−	0.418050i
$214$	−9.66140	+	9.66140i	−0.660440	+	0.660440i
$215$	−13.0965	+	13.0965i	−0.893174	+	0.893174i
$216$	−5.50062	−	5.50062i	−0.374270	−	0.374270i
$217$	1.02840			0.0698125
$218$	37.2384	+	37.2384i	2.52211	+	2.52211i
$219$		−	10.5569i		−	0.713367i
$220$	−21.4594			−1.44679
$221$	5.13740	−	1.82369i	0.345579	−	0.122674i
$222$	14.0137			0.940541
$223$		−	21.2643i		−	1.42397i	−0.702197	−	0.711983i	$-0.747797\pi$
$223$		−	21.2643i		−	1.42397i	0.702197	−	0.711983i	$-0.252203\pi$
$224$	20.3037	+	20.3037i	1.35660	+	1.35660i
$225$	0.0618655			0.00412437
$226$	−32.5067	−	32.5067i	−2.16231	−	2.16231i
$227$	3.50304	−	3.50304i	0.232505	−	0.232505i	−0.581233	−	0.813737i	$-0.697429\pi$
$227$	3.50304	−	3.50304i	0.232505	−	0.232505i	0.813737	+	0.581233i	$0.197429\pi$
$228$	20.8309	−	20.8309i	1.37956	−	1.37956i
$229$			1.83842i			0.121487i	0.998153	+	0.0607433i	$0.0193471\pi$
$229$			1.83842i			0.121487i	−0.998153	+	0.0607433i	$0.980653\pi$
$230$		−	27.9986i		−	1.84617i
$231$	−3.19202	+	3.19202i	−0.210020	+	0.210020i
$232$	−0.950631	+	0.950631i	−0.0624120	+	0.0624120i
$233$	−1.05713	−	1.05713i	−0.0692546	−	0.0692546i	0.671631	−	0.740886i	$-0.265594\pi$
$233$	−1.05713	−	1.05713i	−0.0692546	−	0.0692546i	−0.740886	+	0.671631i	$0.765594\pi$
$234$	3.48580			0.227874
$235$	−3.74611	−	3.74611i	−0.244369	−	0.244369i
$236$			58.3531i			3.79847i
$237$	−0.698270			−0.0453575
$238$	−22.7138	−	10.8125i	−1.47232	−	0.700872i
$239$	−10.0250			−0.648463			−0.324231	−	0.945978i	$-0.605106\pi$
$239$	−10.0250			−0.648463			−0.324231	+	0.945978i	$0.605106\pi$
$240$		−	23.5719i		−	1.52156i
$241$	−8.14265	−	8.14265i	−0.524514	−	0.524514i	0.394417	−	0.918932i	$-0.370947\pi$
$241$	−8.14265	−	8.14265i	−0.524514	−	0.524514i	−0.918932	+	0.394417i	$0.870947\pi$
$242$	−18.9690			−1.21938
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−30.4100	+	30.4100i	−1.94680	+	1.94680i
$245$	−2.58382	+	2.58382i	−0.165074	+	0.165074i
$246$			10.6042i			0.676099i
$247$			7.86780i			0.500616i
$248$	2.44438	−	2.44438i	0.155218	−	0.155218i
$249$	−6.03142	+	6.03142i	−0.382226	+	0.382226i
$250$	20.9696	+	20.9696i	1.32623	+	1.32623i
$251$	0.940179			0.0593436			0.0296718	−	0.999560i	$-0.490554\pi$
$251$	0.940179			0.0593436			0.0296718	+	0.999560i	$0.490554\pi$
$252$	−8.10124	−	8.10124i	−0.510330	−	0.510330i
$253$			9.32218i			0.586080i
$254$	25.9736			1.62973
$255$	3.06508	+	8.63444i	0.191943	+	0.540710i
$256$	−8.50875			−0.531797
$257$		−	2.15515i		−	0.134435i	−0.997738	−	0.0672173i	$-0.978588\pi$
$257$		−	2.15515i		−	0.134435i	0.997738	−	0.0672173i	$-0.0214121\pi$
$258$	15.5377	+	15.5377i	0.967333	+	0.967333i
$259$	12.3012			0.764360
$260$	10.2853	+	10.2853i	0.637868	+	0.637868i
$261$	0.122204	−	0.122204i	0.00756423	−	0.00756423i
$262$	−14.1820	+	14.1820i	−0.876168	+	0.876168i
$263$		−	13.1427i		−	0.810411i	−0.914226	−	0.405205i	$-0.867200\pi$
$263$		−	13.1427i		−	0.810411i	0.914226	−	0.405205i	$-0.132800\pi$
$264$			15.1741i			0.933900i
$265$	−1.14265	+	1.14265i	−0.0701926	+	0.0701926i
$266$	25.6724	−	25.6724i	1.57407	−	1.57407i
$267$	3.82047	+	3.82047i	0.233809	+	0.233809i
$268$	70.2325			4.29013
$269$	−10.7299	−	10.7299i	−0.654213	−	0.654213i	0.299792	−	0.954005i	$-0.403083\pi$
$269$	−10.7299	−	10.7299i	−0.654213	−	0.654213i	−0.954005	+	0.299792i	$0.903083\pi$
$270$			5.85860i			0.356543i
$271$	11.8360			0.718985			0.359493	−	0.933148i	$-0.382950\pi$
$271$	11.8360			0.718985			0.359493	+	0.933148i	$0.382950\pi$
$272$	−41.2159	+	14.6310i	−2.49908	+	0.887132i
$273$	3.05982			0.185189
$274$			58.1916i			3.51548i
$275$	−0.0853313	−	0.0853313i	−0.00514567	−	0.00514567i
$276$	−23.6594			−1.42413
$277$	19.0229	+	19.0229i	1.14298	+	1.14298i	0.987903	+	0.155076i	$0.0495621\pi$
$277$	19.0229	+	19.0229i	1.14298	+	1.14298i	0.155076	+	0.987903i	$0.450438\pi$
$278$	−6.68236	+	6.68236i	−0.400782	+	0.400782i
$279$	−0.314226	+	0.314226i	−0.0188122	+	0.0188122i
$280$		−	40.0050i		−	2.39076i
$281$		−	22.2339i		−	1.32636i	−0.748459	−	0.663181i	$-0.769206\pi$
$281$		−	22.2339i		−	1.32636i	0.748459	−	0.663181i	$-0.230794\pi$
$282$	−4.44438	+	4.44438i	−0.264659	+	0.264659i
$283$	16.9406	−	16.9406i	1.00702	−	1.00702i	0.00704092	−	0.999975i	$-0.497759\pi$
$283$	16.9406	−	16.9406i	1.00702	−	1.00702i	0.999975	−	0.00704092i	$-0.00224121\pi$
$284$	−21.3581	−	21.3581i	−1.26737	−	1.26737i
$285$	−13.2234			−0.783289
$286$	−4.80798	−	4.80798i	−0.284302	−	0.284302i
$287$			9.30832i			0.549453i
$288$	−12.4075			−0.731120
$289$	13.1950	−	10.7187i	0.776179	−	0.630513i
$290$	1.01250			0.0594558
$291$		−	4.71594i		−	0.276453i
$292$	−36.9556	−	36.9556i	−2.16266	−	2.16266i
$293$	−7.44387			−0.434875			−0.217438	−	0.976074i	$-0.569770\pi$
$293$	−7.44387			−0.434875			−0.217438	+	0.976074i	$0.569770\pi$
$294$	3.06544	+	3.06544i	0.178780	+	0.178780i
$295$	18.5212	−	18.5212i	1.07835	−	1.07835i
$296$	29.2384	−	29.2384i	1.69945	−	1.69945i
$297$		−	1.95063i		−	0.113187i
$298$			31.0334i			1.79772i
$299$	4.46804	−	4.46804i	0.258394	−	0.258394i
$300$	0.216568	−	0.216568i	0.0125036	−	0.0125036i
$301$	13.6389	+	13.6389i	0.786133	+	0.786133i
$302$	−42.4560			−2.44307
$303$	5.02840	+	5.02840i	0.288874	+	0.288874i
$304$		−	63.1212i		−	3.62025i
$305$	19.3042			1.10536
$306$	10.2439	−	3.63640i	0.585604	−	0.207879i
$307$	−14.2184			−0.811486			−0.405743	−	0.913987i	$-0.632987\pi$
$307$	−14.2184			−0.811486			−0.405743	+	0.913987i	$0.632987\pi$
$308$			22.3481i			1.27340i
$309$	6.52196	+	6.52196i	0.371021	+	0.371021i
$310$	−2.60346			−0.147867
$311$	−7.32672	−	7.32672i	−0.415460	−	0.415460i	0.468175	−	0.883636i	$-0.344912\pi$
$311$	−7.32672	−	7.32672i	−0.415460	−	0.415460i	−0.883636	+	0.468175i	$0.844912\pi$
$312$	7.27281	−	7.27281i	0.411742	−	0.411742i
$313$	−12.3222	+	12.3222i	−0.696491	+	0.696491i	−0.963652	−	0.267161i	$-0.913914\pi$
$313$	−12.3222	+	12.3222i	−0.696491	+	0.696491i	0.267161	+	0.963652i	$0.413914\pi$
$314$			17.0189i			0.960433i
$315$			5.14265i			0.289756i
$316$	−2.44438	+	2.44438i	−0.137507	+	0.137507i
$317$	10.0235	−	10.0235i	0.562974	−	0.562974i	−0.367177	−	0.930151i	$-0.619676\pi$
$317$	10.0235	−	10.0235i	0.562974	−	0.562974i	0.930151	+	0.367177i	$0.119676\pi$
$318$	1.35564	+	1.35564i	0.0760206	+	0.0760206i
$319$	−0.337113			−0.0188747
$320$	−18.0644	−	18.0644i	−1.00983	−	1.00983i
$321$		−	5.18254i		−	0.289261i
$322$	−29.1582			−1.62492
$323$	8.20773	+	23.1215i	0.456690	+	1.28651i
$324$	4.95063			0.275035
$325$			0.0817972i			0.00453730i
$326$	−31.1925	−	31.1925i	−1.72759	−	1.72759i
$327$	−19.9753			−1.10464
$328$	22.1247	+	22.1247i	1.22163	+	1.22163i
$329$	−3.90126	+	3.90126i	−0.215084	+	0.215084i
$330$	8.08079	−	8.08079i	0.444833	−	0.444833i
$331$			10.8485i			0.596287i	0.954521	+	0.298143i	$0.0963673\pi$
$331$			10.8485i			0.596287i	−0.954521	+	0.298143i	$0.903633\pi$
$332$			42.2275i			2.31753i
$333$	−3.75861	+	3.75861i	−0.205970	+	0.205970i
$334$	−2.99205	+	2.99205i	−0.163718	+	0.163718i
$335$	−22.2917	−	22.2917i	−1.21793	−	1.21793i
$336$	−24.5481			−1.33921
$337$	−6.94216	−	6.94216i	−0.378164	−	0.378164i	0.492276	−	0.870439i	$-0.336165\pi$
$337$	−6.94216	−	6.94216i	−0.378164	−	0.378164i	−0.870439	+	0.492276i	$0.836165\pi$
$338$		−	29.6644i		−	1.61353i
$339$	17.4372			0.947057
$340$	40.9556	+	19.4963i	2.22113	+	1.05733i
$341$	0.866827			0.0469413
$342$			15.6883i			0.848325i
$343$	14.1457	+	14.1457i	0.763794	+	0.763794i
$344$	64.8359			3.49572
$345$	7.50946	+	7.50946i	0.404296	+	0.404296i
$346$	31.9452	−	31.9452i	1.71738	−	1.71738i
$347$	18.4180	−	18.4180i	0.988728	−	0.988728i	−0.0112092	−	0.999937i	$-0.503568\pi$
$347$	18.4180	−	18.4180i	0.988728	−	0.988728i	0.999937	+	0.0112092i	$0.00356806\pi$
$348$		−	0.855580i		−	0.0458639i
$349$		−	18.6609i		−	0.998894i	−0.866344	−	0.499447i	$-0.833537\pi$
$349$		−	18.6609i		−	0.998894i	0.866344	−	0.499447i	$-0.166463\pi$
$350$	0.266902	−	0.266902i	0.0142665	−	0.0142665i
$351$	−0.934922	+	0.934922i	−0.0499024	+	0.0499024i
$352$	17.1137	+	17.1137i	0.912165	+	0.912165i
$353$	−11.8339			−0.629857			−0.314929	−	0.949115i	$-0.601981\pi$
$353$	−11.8339			−0.629857			−0.314929	+	0.949115i	$0.601981\pi$
$354$	−21.9736	−	21.9736i	−1.16788	−	1.16788i
$355$			13.5581i			0.719590i
$356$	26.7481			1.41765
$357$	8.99205	−	3.19202i	0.475910	−	0.168940i
$358$	−29.1991			−1.54322
$359$			14.1392i			0.746241i	0.927783	+	0.373120i	$0.121712\pi$
$359$			14.1392i			0.746241i	−0.927783	+	0.373120i	$0.878288\pi$
$360$	12.2234	+	12.2234i	0.644232	+	0.644232i
$361$	−16.4100			−0.863685
$362$	36.7242	+	36.7242i	1.93018	+	1.93018i
$363$	5.08766	−	5.08766i	0.267033	−	0.267033i
$364$	10.7113	−	10.7113i	0.561424	−	0.561424i
$365$			23.4594i			1.22792i
$366$		−	22.9025i		−	1.19713i
$367$	2.63300	−	2.63300i	0.137441	−	0.137441i	−0.635039	−	0.772480i	$-0.719016\pi$
$367$	2.63300	−	2.63300i	0.137441	−	0.137441i	0.772480	+	0.635039i	$0.219016\pi$
$368$	−35.8459	+	35.8459i	−1.86860	+	1.86860i
$369$	−2.84414	−	2.84414i	−0.148060	−	0.148060i
$370$	−31.1412			−1.61896
$371$	1.18998	+	1.18998i	0.0617806	+	0.0617806i
$372$			2.19998i			0.114063i
$373$	1.53618			0.0795403			0.0397701	−	0.999209i	$-0.487337\pi$
$373$	1.53618			0.0795403			0.0397701	+	0.999209i	$0.487337\pi$
$374$	−19.1452	−	9.11373i	−0.989972	−	0.471260i
$375$	−11.2484			−0.580867
$376$			18.5456i			0.956417i
$377$	0.161575	+	0.161575i	0.00832156	+	0.00832156i
$378$	6.10124			0.313814
$379$	−25.5627	−	25.5627i	−1.31307	−	1.31307i	−0.919144	−	0.393922i	$-0.871118\pi$
$379$	−25.5627	−	25.5627i	−1.31307	−	1.31307i	−0.393922	−	0.919144i	$-0.628882\pi$
$380$	−46.2903	+	46.2903i	−2.37464	+	2.37464i
$381$	−6.96634	+	6.96634i	−0.356896	+	0.356896i
$382$		−	4.24337i		−	0.217110i
$383$		−	16.3492i		−	0.835404i	−0.908584	−	0.417702i	$-0.862836\pi$
$383$		−	16.3492i		−	0.835404i	0.908584	−	0.417702i	$-0.137164\pi$
$384$	−3.88467	+	3.88467i	−0.198239	+	0.198239i
$385$	7.09328	−	7.09328i	0.361507	−	0.361507i
$386$	8.34058	+	8.34058i	0.424525	+	0.424525i
$387$	−8.33468			−0.423675
$388$	−16.5087	−	16.5087i	−0.838105	−	0.838105i
$389$			16.4533i			0.834216i	0.908857	+	0.417108i	$0.136956\pi$
$389$			16.4533i			0.834216i	−0.908857	+	0.417108i	$0.863044\pi$
$390$	−7.74611			−0.392240
$391$	8.46938	−	17.7916i	0.428315	−	0.899758i
$392$	12.7916			0.646071
$393$		−	7.60749i		−	0.383747i
$394$	13.7836	+	13.7836i	0.694408	+	0.694408i
$395$	1.55169			0.0780740
$396$	−6.82843	−	6.82843i	−0.343141	−	0.343141i
$397$	−25.7816	+	25.7816i	−1.29394	+	1.29394i	−0.361610	+	0.932330i	$0.617773\pi$
$397$	−25.7816	+	25.7816i	−1.29394	+	1.29394i	−0.932330	+	0.361610i	$0.882227\pi$
$398$	−13.4160	+	13.4160i	−0.672482	+	0.672482i
$399$			13.7711i			0.689418i
$400$		−	0.656237i		−	0.0328119i
$401$	−6.84414	+	6.84414i	−0.341780	+	0.341780i	−0.857036	−	0.515256i	$-0.827697\pi$
$401$	−6.84414	+	6.84414i	−0.341780	+	0.341780i	0.515256	+	0.857036i	$0.327697\pi$
$402$	−26.4469	+	26.4469i	−1.31905	+	1.31905i
$403$	−0.415463	−	0.415463i	−0.0206957	−	0.0206957i
$404$	35.2051			1.75152
$405$	−1.57133	−	1.57133i	−0.0780798	−	0.0780798i
$406$		−	1.05443i		−	0.0523305i
$407$	10.3685			0.513949
$408$	13.7859	−	28.9600i	0.682505	−	1.43373i
$409$	−2.52228			−0.124719			−0.0623593	−	0.998054i	$-0.519862\pi$
$409$	−2.52228			−0.124719			−0.0623593	+	0.998054i	$0.519862\pi$
$410$		−	23.5645i		−	1.16377i
$411$	−15.6075	−	15.6075i	−0.769860	−	0.769860i
$412$	45.6619			2.24960
$413$	−19.2883	−	19.2883i	−0.949116	−	0.949116i
$414$	8.90921	−	8.90921i	0.437864	−	0.437864i
$415$	13.4030	−	13.4030i	0.657926	−	0.657926i
$416$		−	16.4049i		−	0.804319i
$417$		−	3.58454i		−	0.175536i
$418$	21.6389	−	21.6389i	1.05839	−	1.05839i
$419$	−18.6154	+	18.6154i	−0.909424	+	0.909424i	−0.996226	−	0.0868019i	$-0.972335\pi$
$419$	−18.6154	+	18.6154i	−0.909424	+	0.909424i	0.0868019	+	0.996226i	$0.472335\pi$
$420$	18.0025	+	18.0025i	0.878432	+	0.878432i
$421$	6.61089			0.322195			0.161098	−	0.986938i	$-0.448497\pi$
$421$	6.61089			0.322195			0.161098	+	0.986938i	$0.448497\pi$
$422$	−25.0150	−	25.0150i	−1.21771	−	1.21771i
$423$		−	2.38404i		−	0.115916i
$424$	5.65685			0.274721
$425$	0.0853313	+	0.240382i	0.00413918	+	0.0116602i
$426$	16.0853			0.779337
$427$		−	20.1037i		−	0.972888i
$428$	−18.1421	−	18.1421i	−0.876933	−	0.876933i
$429$	2.57908			0.124519
$430$	−34.5277	−	34.5277i	−1.66507	−	1.66507i
$431$	19.8882	−	19.8882i	0.957983	−	0.957983i	−0.0411690	−	0.999152i	$-0.513108\pi$
$431$	19.8882	−	19.8882i	0.957983	−	0.957983i	0.999152	+	0.0411690i	$0.0131082\pi$
$432$	7.50062	−	7.50062i	0.360874	−	0.360874i
$433$			17.1497i			0.824162i	0.911147	+	0.412081i	$0.135198\pi$
$433$			17.1497i			0.824162i	−0.911147	+	0.412081i	$0.864802\pi$
$434$			2.71128i			0.130146i
$435$	−0.271560	+	0.271560i	−0.0130203	+	0.0130203i
$436$	−69.9262	+	69.9262i	−3.34886	+	3.34886i
$437$	20.1090	+	20.1090i	0.961944	+	0.961944i
$438$	27.8322			1.32987
$439$	5.81593	+	5.81593i	0.277579	+	0.277579i	0.832142	−	0.554563i	$-0.187114\pi$
$439$	5.81593	+	5.81593i	0.277579	+	0.277579i	−0.554563	+	0.832142i	$0.687114\pi$
$440$		−	33.7197i		−	1.60752i
$441$	−1.64436			−0.0783028
$442$	4.80798	+	13.5443i	0.228692	+	0.644235i
$443$	−18.4658			−0.877339			−0.438669	−	0.898649i	$-0.644550\pi$
$443$	−18.4658			−0.877339			−0.438669	+	0.898649i	$0.644550\pi$
$444$			26.3150i			1.24885i
$445$	−8.48983	−	8.48983i	−0.402456	−	0.402456i
$446$	56.0614			2.65458
$447$	−8.32343	−	8.32343i	−0.393685	−	0.393685i
$448$	−18.8125	+	18.8125i	−0.888808	+	0.888808i
$449$	−21.8673	+	21.8673i	−1.03198	+	1.03198i	−0.0325094	+	0.999471i	$0.510350\pi$
$449$	−21.8673	+	21.8673i	−1.03198	+	1.03198i	−0.999471	+	0.0325094i	$0.989650\pi$
$450$			0.163102i			0.00768873i
$451$			7.84586i			0.369447i
$452$	61.0410	−	61.0410i	2.87113	−	2.87113i
$453$	11.3871	−	11.3871i	0.535011	−	0.535011i
$454$	9.23542	+	9.23542i	0.433440	+	0.433440i
$455$	−6.79951			−0.318766
$456$	32.7322	+	32.7322i	1.53283	+	1.53283i
$457$			15.5337i			0.726638i	0.931665	+	0.363319i	$0.118356\pi$
$457$			15.5337i			0.726638i	−0.931665	+	0.363319i	$0.881644\pi$
$458$	−4.84683			−0.226478
$459$	−1.77219	+	3.72282i	−0.0827185	+	0.173766i
$460$	52.5756			2.45135
$461$			38.9032i			1.81190i	0.423380	+	0.905952i	$0.360844\pi$
$461$			38.9032i			1.81190i	−0.423380	+	0.905952i	$0.639156\pi$
$462$	−8.41546	−	8.41546i	−0.391523	−	0.391523i
$463$	22.7572			1.05762			0.528808	−	0.848742i	$-0.322639\pi$
$463$	22.7572			1.05762			0.528808	+	0.848742i	$0.322639\pi$
$464$	−1.29628	−	1.29628i	−0.0601781	−	0.0601781i
$465$	0.698270	−	0.698270i	0.0323815	−	0.0323815i
$466$	2.78701	−	2.78701i	0.129106	−	0.129106i
$467$		−	12.5551i		−	0.580981i	−0.956878	−	0.290490i	$-0.906182\pi$
$467$		−	12.5551i		−	0.580981i	0.956878	−	0.290490i	$-0.0938184\pi$
$468$			6.54562i			0.302571i
$469$	−23.2150	+	23.2150i	−1.07197	+	1.07197i
$470$	9.87627	−	9.87627i	0.455558	−	0.455558i
$471$	−4.56462	−	4.56462i	−0.210327	−	0.210327i
$472$	−91.6918			−4.22046
$473$	11.4961	+	11.4961i	0.528589	+	0.528589i
$474$		−	1.84092i		−	0.0845564i
$475$	−0.368139			−0.0168914
$476$	20.3037	−	42.6519i	0.930619	−	1.95494i
$477$	−0.727190			−0.0332957
$478$		−	26.4299i		−	1.20888i
$479$	26.3340	+	26.3340i	1.20323	+	1.20323i	0.973179	+	0.230051i	$0.0738892\pi$
$479$	26.3340	+	26.3340i	1.20323	+	1.20323i	0.230051	+	0.973179i	$0.426111\pi$
$480$	27.5719			1.25848
$481$	−4.96955	−	4.96955i	−0.226592	−	0.226592i
$482$	21.4673	−	21.4673i	0.977810	−	0.977810i
$483$	7.82047	−	7.82047i	0.355844	−	0.355844i
$484$		−	35.6200i		−	1.61909i
$485$			10.4797i			0.475860i
$486$	−1.86422	+	1.86422i	−0.0845627	+	0.0845627i
$487$	−1.16310	+	1.16310i	−0.0527052	+	0.0527052i	−0.732968	−	0.680263i	$-0.761866\pi$
$487$	−1.16310	+	1.16310i	−0.0527052	+	0.0527052i	0.680263	+	0.732968i	$0.261866\pi$
$488$	−47.7841	−	47.7841i	−2.16308	−	2.16308i
$489$	16.7322			0.756656
$490$	−6.81200	−	6.81200i	−0.307735	−	0.307735i
$491$		−	4.30121i		−	0.194111i	−0.995279	−	0.0970555i	$-0.969058\pi$
$491$		−	4.30121i		−	0.194111i	0.995279	−	0.0970555i	$-0.0309424\pi$
$492$	−19.9125			−0.897725
$493$	0.643386	+	0.306273i	0.0289766	+	0.0137939i
$494$	−20.7427			−0.933258
$495$			4.33468i			0.194829i
$496$	3.33315	+	3.33315i	0.149663	+	0.149663i
$497$	14.1196			0.633352
$498$	−15.9013	−	15.9013i	−0.712553	−	0.712553i
$499$	1.05732	−	1.05732i	0.0473322	−	0.0473322i	−0.683045	−	0.730377i	$-0.739345\pi$
$499$	1.05732	−	1.05732i	0.0473322	−	0.0473322i	0.730377	+	0.683045i	$0.239345\pi$
$500$	−39.3765	+	39.3765i	−1.76097	+	1.76097i
$501$		−	1.60499i		−	0.0717055i
$502$			2.47869i			0.110629i
$503$	1.19274	−	1.19274i	0.0531815	−	0.0531815i	−0.680016	−	0.733197i	$-0.738027\pi$
$503$	1.19274	−	1.19274i	0.0531815	−	0.0531815i	0.733197	+	0.680016i	$0.238027\pi$
$504$	12.7297	−	12.7297i	0.567025	−	0.567025i
$505$	−11.1741	−	11.1741i	−0.497240	−	0.497240i
$506$	−24.5770			−1.09258
$507$	7.95625	+	7.95625i	0.353350	+	0.353350i
$508$			48.7731i			2.16396i
$509$	−6.91070			−0.306312			−0.153156	−	0.988202i	$-0.548944\pi$
$509$	−6.91070			−0.306312			−0.153156	+	0.988202i	$0.548944\pi$
$510$	−22.7639	+	8.08079i	−1.00800	+	0.357823i
$511$	24.4310			1.08076
$512$		−	33.4200i		−	1.47697i
$513$	−4.20773	−	4.20773i	−0.185776	−	0.185776i
$514$	5.68185			0.250616
$515$	−14.4930	−	14.4930i	−0.638640	−	0.638640i
$516$	−29.1766	+	29.1766i	−1.28443	+	1.28443i
$517$	−3.28832	+	3.28832i	−0.144620	+	0.144620i
$518$			32.4310i			1.42494i
$519$			17.1359i			0.752185i
$520$	−16.1616	+	16.1616i	−0.708732	+	0.708732i
$521$	9.47259	−	9.47259i	0.415002	−	0.415002i	−0.468475	−	0.883477i	$-0.655196\pi$
$521$	9.47259	−	9.47259i	0.415002	−	0.415002i	0.883477	+	0.468475i	$0.155196\pi$
$522$	0.322179	+	0.322179i	0.0141014	+	0.0141014i
$523$	4.40904			0.192794			0.0963969	−	0.995343i	$-0.469268\pi$
$523$	4.40904			0.192794			0.0963969	+	0.995343i	$0.469268\pi$
$524$	−26.6310	−	26.6310i	−1.16338	−	1.16338i
$525$			0.143171i			0.00624848i
$526$	34.6494			1.51078
$527$	−1.65436	−	0.787529i	−0.0720648	−	0.0343053i
$528$	−20.6913			−0.900473
$529$			0.160604i			0.00698276i
$530$	−3.01250	−	3.01250i	−0.130854	−	0.130854i
$531$	11.7870			0.511513
$532$	48.2075	+	48.2075i	2.09006	+	2.09006i
$533$	3.76046	−	3.76046i	0.162883	−	0.162883i
$534$	−10.0723	+	10.0723i	−0.435872	+	0.435872i
$535$			11.5166i			0.497906i
$536$			110.358i			4.76675i
$537$	7.83144	−	7.83144i	0.337952	−	0.337952i
$538$	28.2883	−	28.2883i	1.21960	−	1.21960i
$539$	2.26807	+	2.26807i	0.0976927	+	0.0976927i
$540$	−11.0012			−0.473418
$541$	−16.3451	−	16.3451i	−0.702732	−	0.702732i	0.262264	−	0.964996i	$-0.415531\pi$
$541$	−16.3451	−	16.3451i	−0.702732	−	0.702732i	−0.964996	+	0.262264i	$0.915531\pi$
$542$			31.2045i			1.34035i
$543$	−19.6995			−0.845387
$544$	−17.1137	−	48.2100i	−0.733745	−	2.06699i
$545$	44.3890			1.90142
$546$			8.06693i			0.345233i
$547$	−6.70674	−	6.70674i	−0.286760	−	0.286760i	0.549038	−	0.835797i	$-0.314994\pi$
$547$	−6.70674	−	6.70674i	−0.286760	−	0.286760i	−0.835797	+	0.549038i	$0.814994\pi$
$548$	−109.272			−4.66786
$549$	6.14265	+	6.14265i	0.262162	+	0.262162i
$550$	0.224968	−	0.224968i	0.00959267	−	0.00959267i
$551$	−0.727190	+	0.727190i	−0.0309793	+	0.0309793i
$552$		−	37.1766i		−	1.58234i
$553$		−	1.61596i		−	0.0687174i
$554$	−50.1522	+	50.1522i	−2.13076	+	2.13076i
$555$	8.35235	−	8.35235i	0.354537	−	0.354537i
$556$	−12.5481	−	12.5481i	−0.532159	−	0.532159i
$557$	38.1670			1.61719			0.808593	−	0.588368i	$-0.200229\pi$
$557$	38.1670			1.61719			0.808593	+	0.588368i	$0.200229\pi$
$558$	−0.828427	−	0.828427i	−0.0350701	−	0.0350701i
$559$		−	11.0199i		−	0.466093i
$560$	54.5506			2.30518
$561$	7.57928	−	2.69051i	0.319997	−	0.113594i
$562$	58.6175			2.47263
$563$			13.8184i			0.582377i	0.956666	+	0.291189i	$0.0940507\pi$
$563$			13.8184i			0.582377i	−0.956666	+	0.291189i	$0.905949\pi$
$564$	−8.34564	−	8.34564i	−0.351415	−	0.351415i
$565$	−38.7487			−1.63017
$566$	44.6624	+	44.6624i	1.87730	+	1.87730i
$567$	−1.63640	+	1.63640i	−0.0687225	+	0.0687225i
$568$	33.5606	−	33.5606i	1.40817	−	1.40817i
$569$		−	12.9516i		−	0.542959i	−0.962444	−	0.271480i	$-0.912487\pi$
$569$		−	12.9516i		−	0.542959i	0.962444	−	0.271480i	$-0.0875130\pi$
$570$		−	34.8623i		−	1.46022i
$571$	4.60596	−	4.60596i	0.192753	−	0.192753i	−0.604131	−	0.796885i	$-0.706480\pi$
$571$	4.60596	−	4.60596i	0.192753	−	0.192753i	0.796885	+	0.604131i	$0.206480\pi$
$572$	9.02840	−	9.02840i	0.377496	−	0.377496i
$573$	1.13811	+	1.13811i	0.0475452	+	0.0475452i
$574$	−24.5405			−1.02430
$575$	0.209062	+	0.209062i	0.00871850	+	0.00871850i
$576$		−	11.4963i		−	0.479010i
$577$	15.6703			0.652364			0.326182	−	0.945307i	$-0.394238\pi$
$577$	15.6703			0.652364			0.326182	+	0.945307i	$0.394238\pi$
$578$	28.2589	+	34.7875i	1.17541	+	1.44697i
$579$	−4.47403			−0.185935
$580$			1.90126i			0.0789456i
$581$	−13.9581	−	13.9581i	−0.579078	−	0.579078i
$582$	12.4331			0.515370
$583$	1.00302	+	1.00302i	0.0415407	+	0.0415407i
$584$	58.0694	−	58.0694i	2.40293	−	2.40293i
$585$	2.07757	−	2.07757i	0.0858971	−	0.0858971i
$586$		−	19.6250i		−	0.810703i
$587$		−	14.9766i		−	0.618150i	−0.951038	−	0.309075i	$-0.899981\pi$
$587$		−	14.9766i		−	0.618150i	0.951038	−	0.309075i	$-0.100019\pi$
$588$	−5.75628	+	5.75628i	−0.237385	+	0.237385i
$589$	1.86984	−	1.86984i	0.0770456	−	0.0770456i
$590$	48.8295	+	48.8295i	2.01028	+	2.01028i
$591$	−7.39376			−0.304139
$592$	39.8694	+	39.8694i	1.63862	+	1.63862i
$593$		−	46.3701i		−	1.90419i	−0.305801	−	0.952096i	$-0.598924\pi$
$593$		−	46.3701i		−	1.90419i	0.305801	−	0.952096i	$-0.401076\pi$
$594$	5.14265			0.211006
$595$	−19.9820	+	7.09328i	−0.819184	+	0.290796i
$596$	−58.2744			−2.38701
$597$		−	7.19657i		−	0.294536i
$598$	11.7796	+	11.7796i	0.481703	+	0.481703i
$599$	−28.7068			−1.17293			−0.586464	−	0.809975i	$-0.699480\pi$
$599$	−28.7068			−1.17293			−0.586464	+	0.809975i	$0.699480\pi$
$600$	0.340299	+	0.340299i	0.0138926	+	0.0138926i
$601$	−14.6998	+	14.6998i	−0.599617	+	0.599617i	−0.940211	−	0.340593i	$-0.889372\pi$
$601$	−14.6998	+	14.6998i	−0.599617	+	0.599617i	0.340593	+	0.940211i	$0.389372\pi$
$602$	−35.9577	+	35.9577i	−1.46553	+	1.46553i
$603$		−	14.1866i		−	0.577722i
$604$		−	79.7237i		−	3.24391i
$605$	−11.3058	+	11.3058i	−0.459644	+	0.459644i
$606$	−13.2569	+	13.2569i	−0.538525	+	0.538525i
$607$	−12.1665	−	12.1665i	−0.493823	−	0.493823i	0.415685	−	0.909509i	$-0.363542\pi$
$607$	−12.1665	−	12.1665i	−0.493823	−	0.493823i	−0.909509	+	0.415685i	$0.863542\pi$
$608$	73.8325			2.99430
$609$	0.282807	+	0.282807i	0.0114599	+	0.0114599i
$610$			50.8938i			2.06063i
$611$	3.15213			0.127522
$612$	6.82843	+	19.2359i	0.276023	+	0.777567i
$613$	−42.7657			−1.72729			−0.863644	−	0.504102i	$-0.831824\pi$
$613$	−42.7657			−1.72729			−0.863644	+	0.504102i	$0.831824\pi$
$614$		−	37.4854i		−	1.51279i
$615$	6.32022	+	6.32022i	0.254856	+	0.254856i
$616$	−35.1162			−1.41487
$617$	−27.0678	−	27.0678i	−1.08971	−	1.08971i	−0.995558	−	0.0941495i	$-0.969987\pi$
$617$	−27.0678	−	27.0678i	−1.08971	−	1.08971i	−0.0941495	−	0.995558i	$-0.530013\pi$
$618$	−17.1945	+	17.1945i	−0.691665	+	0.691665i
$619$	6.55659	−	6.55659i	0.263532	−	0.263532i	−0.562956	−	0.826487i	$-0.690336\pi$
$619$	6.55659	−	6.55659i	0.263532	−	0.263532i	0.826487	+	0.562956i	$0.190336\pi$
$620$		−	4.88877i		−	0.196338i
$621$			4.77906i			0.191777i
$622$	19.3162	−	19.3162i	0.774509	−	0.774509i
$623$	−8.84144	+	8.84144i	−0.354225	+	0.354225i
$624$	9.91717	+	9.91717i	0.397004	+	0.397004i
$625$	24.6868			0.987474
$626$	−32.4863	−	32.4863i	−1.29841	−	1.29841i
$627$			11.6075i			0.463558i
$628$	−31.9581			−1.27527
$629$	−19.7885	−	9.42001i	−0.789021	−	0.375600i
$630$	−13.5581			−0.540168
$631$			33.8478i			1.34746i	0.738978	+	0.673730i	$0.235309\pi$
$631$			33.8478i			1.34746i	−0.738978	+	0.673730i	$0.764691\pi$
$632$	−3.84092	−	3.84092i	−0.152784	−	0.152784i
$633$	13.4185			0.533337
$634$	26.4259	+	26.4259i	1.04951	+	1.04951i
$635$	15.4805	−	15.4805i	0.614327	−	0.614327i
$636$	−2.54562	+	2.54562i	−0.100940	+	0.100940i
$637$		−	2.17414i		−	0.0861424i
$638$		−	0.888765i		−	0.0351866i
$639$	−4.31423	+	4.31423i	−0.170668	+	0.170668i
$640$	8.63248	−	8.63248i	0.341229	−	0.341229i
$641$	7.54594	+	7.54594i	0.298047	+	0.298047i	0.840248	−	0.542202i	$-0.182409\pi$
$641$	7.54594	+	7.54594i	0.298047	+	0.298047i	−0.542202	+	0.840248i	$0.682409\pi$
$642$	13.6633			0.539247
$643$	27.7990	+	27.7990i	1.09629	+	1.09629i	0.994841	+	0.101444i	$0.0323462\pi$
$643$	27.7990	+	27.7990i	1.09629	+	1.09629i	0.101444	+	0.994841i	$0.467654\pi$
$644$		−	54.7531i		−	2.15757i
$645$	18.5212			0.729273
$646$	−60.9576	+	21.6389i	−2.39835	+	0.851371i
$647$	−27.9895			−1.10038			−0.550190	−	0.835039i	$-0.685445\pi$
$647$	−27.9895			−1.10038			−0.550190	+	0.835039i	$0.685445\pi$
$648$			7.77906i			0.305590i
$649$	−16.2579	−	16.2579i	−0.638177	−	0.638177i
$650$	−0.215651			−0.00845852
$651$	−0.727190	−	0.727190i	−0.0285008	−	0.0285008i
$652$	58.5731	−	58.5731i	2.29390	−	2.29390i
$653$	28.9574	−	28.9574i	1.13319	−	1.13319i	0.143545	−	0.989644i	$-0.454150\pi$
$653$	28.9574	−	28.9574i	1.13319	−	1.13319i	0.989644	−	0.143545i	$-0.0458502\pi$
$654$		−	52.6631i		−	2.05929i
$655$			16.9053i			0.660544i
$656$	−30.1691	+	30.1691i	−1.17791	+	1.17791i
$657$	−7.46483	+	7.46483i	−0.291231	+	0.291231i
$658$	−10.2853	−	10.2853i	−0.400963	−	0.400963i
$659$	10.8164			0.421349			0.210674	−	0.977556i	$-0.432434\pi$
$659$	10.8164			0.421349			0.210674	+	0.977556i	$0.432434\pi$
$660$	15.1741	+	15.1741i	0.590650	+	0.590650i
$661$		−	20.0794i		−	0.780997i	−0.920604	−	0.390498i	$-0.872303\pi$
$661$		−	20.0794i		−	0.780997i	0.920604	−	0.390498i	$-0.127697\pi$
$662$	−28.6010			−1.11161
$663$	−4.92223	−	2.34315i	−0.191164	−	0.0910002i
$664$	−66.3531			−2.57500
$665$		−	30.6020i		−	1.18670i
$666$	−9.90921	−	9.90921i	−0.383974	−	0.383974i
$667$	0.825928			0.0319801
$668$	−5.61845	−	5.61845i	−0.217385	−	0.217385i
$669$	−15.0362	+	15.0362i	−0.581331	+	0.581331i
$670$	58.7700	−	58.7700i	2.27048	−	2.27048i
$671$		−	16.9452i		−	0.654161i
$672$		−	28.7138i		−	1.10766i
$673$	19.3820	−	19.3820i	0.747121	−	0.747121i	−0.226816	−	0.973938i	$-0.572832\pi$
$673$	19.3820	−	19.3820i	0.747121	−	0.747121i	0.973938	+	0.226816i	$0.0728317\pi$
$674$	18.3023	−	18.3023i	0.704980	−	0.704980i
$675$	−0.0437455	−	0.0437455i	−0.00168377	−	0.00168377i
$676$	55.7037			2.14245
$677$	−16.0696	−	16.0696i	−0.617606	−	0.617606i	0.327311	−	0.944917i	$-0.393858\pi$
$677$	−16.0696	−	16.0696i	−0.617606	−	0.617606i	−0.944917	+	0.327311i	$0.893858\pi$
$678$			45.9714i			1.76552i
$679$	10.9138			0.418832
$680$	−30.6350	+	64.3547i	−1.17480	+	2.46789i
$681$	−4.95404			−0.189839
$682$			2.28531i			0.0875089i
$683$	26.3090	+	26.3090i	1.00668	+	1.00668i	0.999978	+	0.00670720i	$0.00213498\pi$
$683$	26.3090	+	26.3090i	1.00668	+	1.00668i	0.00670720	+	0.999978i	$0.497865\pi$
$684$	−29.4594			−1.12641
$685$	34.6828	+	34.6828i	1.32516	+	1.32516i
$686$	−37.2937	+	37.2937i	−1.42388	+	1.42388i
$687$	1.29996	−	1.29996i	0.0495967	−	0.0495967i
$688$			88.4099i			3.37060i
$689$		−	0.961475i		−	0.0366293i
$690$	−19.7980	+	19.7980i	−0.753696	+	0.753696i
$691$	−12.7675	+	12.7675i	−0.485700	+	0.485700i	−0.906946	−	0.421246i	$-0.861593\pi$
$691$	−12.7675	+	12.7675i	−0.485700	+	0.485700i	0.421246	+	0.906946i	$0.361593\pi$
$692$	59.9865	+	59.9865i	2.28035	+	2.28035i
$693$	4.51420			0.171480
$694$	48.5572	+	48.5572i	1.84321	+	1.84321i
$695$			7.96553i			0.302150i
$696$	1.34440			0.0509592
$697$	7.12811	−	14.9740i	0.269996	−	0.567180i
$698$	49.1976			1.86216
$699$			1.49500i			0.0565461i
$700$	0.501187	+	0.501187i	0.0189431	+	0.0189431i
$701$	−9.99896			−0.377656			−0.188828	−	0.982010i	$-0.560469\pi$
$701$	−9.99896			−0.377656			−0.188828	+	0.982010i	$0.560469\pi$
$702$	−2.46483	−	2.46483i	−0.0930291	−	0.0930291i
$703$	22.3661	−	22.3661i	0.843553	−	0.843553i
$704$	−15.8568	+	15.8568i	−0.597627	+	0.597627i
$705$			5.29780i			0.199527i
$706$		−	31.1991i		−	1.17419i
$707$	−11.6369	+	11.6369i	−0.437649	+	0.437649i
$708$	41.2619	−	41.2619i	1.55072	−	1.55072i
$709$	0.773543	+	0.773543i	0.0290510	+	0.0290510i	0.721483	−	0.692432i	$-0.243461\pi$
$709$	0.773543	+	0.773543i	0.0290510	+	0.0290510i	−0.692432	+	0.721483i	$0.743461\pi$
$710$	−35.7447			−1.34147
$711$	0.493752	+	0.493752i	0.0185171	+	0.0185171i
$712$			42.0300i			1.57514i
$713$	−2.12373			−0.0795344
$714$	8.41546	+	23.7067i	0.314941	+	0.887200i
$715$	−5.73122			−0.214335
$716$		−	54.8299i		−	2.04909i
$717$	7.08874	+	7.08874i	0.264734	+	0.264734i
$718$	−37.2768			−1.39116
$719$	30.0392	+	30.0392i	1.12027	+	1.12027i	0.991700	+	0.128572i	$0.0410393\pi$
$719$	30.0392	+	30.0392i	1.12027	+	1.12027i	0.128572	+	0.991700i	$0.458961\pi$
$720$	−16.6678	+	16.6678i	−0.621173	+	0.621173i
$721$	−15.0933	+	15.0933i	−0.562103	+	0.562103i
$722$		−	43.2634i		−	1.61010i
$723$			11.5155i			0.428264i
$724$	−68.9606	+	68.9606i	−2.56290	+	2.56290i
$725$	−0.00756020	+	0.00756020i	−0.000280779	+	0.000280779i
$726$	13.4131	+	13.4131i	0.497808	+	0.497808i
$727$	−45.2169			−1.67700			−0.838501	−	0.544900i	$-0.816568\pi$
$727$	−45.2169			−1.67700			−0.838501	+	0.544900i	$0.816568\pi$
$728$	16.8309	+	16.8309i	0.623796	+	0.623796i
$729$		−	1.00000i		−	0.0370370i
$730$	−61.8484			−2.28911
$731$	−11.4961	−	32.3848i	−0.425197	−	1.19780i
$732$	43.0062			1.58956
$733$			21.5990i			0.797778i	0.916999	+	0.398889i	$0.130604\pi$
$733$			21.5990i			0.797778i	−0.916999	+	0.398889i	$0.869396\pi$
$734$	6.94164	+	6.94164i	0.256221	+	0.256221i
$735$	3.65408			0.134783
$736$	−41.9288	−	41.9288i	−1.54551	−	1.54551i
$737$	−19.5676	+	19.5676i	−0.720782	+	0.720782i
$738$	7.49830	−	7.49830i	0.276016	−	0.276016i
$739$			19.0419i			0.700467i	0.936663	+	0.350233i	$0.113898\pi$
$739$			19.0419i			0.700467i	−0.936663	+	0.350233i	$0.886102\pi$
$740$		−	58.4769i		−	2.14965i
$741$	5.56337	−	5.56337i	0.204376	−	0.204376i
$742$	−3.13726	+	3.13726i	−0.115173	+	0.115173i
$743$	−18.6918	−	18.6918i	−0.685737	−	0.685737i	0.275550	−	0.961287i	$-0.411140\pi$
$743$	−18.6918	−	18.6918i	−0.685737	−	0.685737i	−0.961287	+	0.275550i	$0.911140\pi$
$744$	−3.45688			−0.126735
$745$	18.4963	+	18.4963i	0.677650	+	0.677650i
$746$			4.04999i			0.148281i
$747$	8.52971			0.312086
$748$	17.1137	−	35.9507i	0.625740	−	1.31449i
$749$	11.9936			0.438236
$750$		−	29.6554i		−	1.08286i
$751$	−3.28582	−	3.28582i	−0.119901	−	0.119901i	0.644610	−	0.764512i	$-0.277020\pi$
$751$	−3.28582	−	3.28582i	−0.119901	−	0.119901i	−0.764512	+	0.644610i	$0.777020\pi$
$752$	−25.2887			−0.922185
$753$	−0.664807	−	0.664807i	−0.0242269	−	0.0242269i
$754$	−0.425978	+	0.425978i	−0.0155132	+	0.0155132i
$755$	−25.3042	+	25.3042i	−0.920915	+	0.920915i
$756$			11.4569i			0.416683i
$757$		−	10.4074i		−	0.378263i	−0.981952	−	0.189131i	$-0.939433\pi$
$757$		−	10.4074i		−	0.378263i	0.981952	−	0.189131i	$-0.0605672\pi$
$758$	67.3935	−	67.3935i	2.44784	−	2.44784i
$759$	6.59178	−	6.59178i	0.239266	−	0.239266i
$760$	−72.7372	−	72.7372i	−2.63846	−	2.63846i
$761$	38.6365			1.40057			0.700286	−	0.713862i	$-0.253056\pi$
$761$	38.6365			1.40057			0.700286	+	0.713862i	$0.253056\pi$
$762$	−18.3661	−	18.3661i	−0.665333	−	0.665333i
$763$		−	46.2275i		−	1.67355i
$764$	7.96819			0.288279
$765$	3.93813	−	8.27281i	0.142384	−	0.299104i
$766$	43.1031			1.55738
$767$			15.5845i			0.562725i
$768$	6.01659	+	6.01659i	0.217105	+	0.217105i
$769$	0.178098			0.00642238			0.00321119	−	0.999995i	$-0.498978\pi$
$769$	0.178098			0.00642238			0.00321119	+	0.999995i	$0.498978\pi$
$770$	18.7008	+	18.7008i	0.673929	+	0.673929i
$771$	−1.52392	+	1.52392i	−0.0548827	+	0.0548827i
$772$	−15.6619	+	15.6619i	−0.563685	+	0.563685i
$773$			4.15554i			0.149464i	0.997204	+	0.0747322i	$0.0238102\pi$
$773$			4.15554i			0.149464i	−0.997204	+	0.0747322i	$0.976190\pi$
$774$		−	21.9736i		−	0.789824i
$775$	0.0194398	−	0.0194398i	0.000698296	−	0.000698296i
$776$	25.9406	−	25.9406i	0.931214	−	0.931214i
$777$	−8.69827	−	8.69827i	−0.312049	−	0.312049i
$778$	−43.3776			−1.55516
$779$	16.9244	+	16.9244i	0.606380	+	0.606380i
$780$		−	14.5456i		−	0.520817i
$781$	11.9013			0.425861
$782$	46.9057	+	22.3287i	1.67735	+	0.798473i
$783$	−0.172822			−0.00617617
$784$			17.4425i			0.622946i
$785$	10.1435	+	10.1435i	0.362036	+	0.362036i
$786$	20.0564			0.715389
$787$	1.22941	+	1.22941i	0.0438238	+	0.0438238i	0.728679	−	0.684855i	$-0.240135\pi$
$787$	1.22941	+	1.22941i	0.0438238	+	0.0438238i	−0.684855	+	0.728679i	$0.740135\pi$
$788$	−25.8828	+	25.8828i	−0.922036	+	0.922036i
$789$	−9.29326	+	9.29326i	−0.330849	+	0.330849i
$790$			4.09088i			0.145547i
$791$			40.3535i			1.43481i
$792$	10.7297	−	10.7297i	0.381263	−	0.381263i
$793$	−8.12169	+	8.12169i	−0.288410	+	0.288410i
$794$	−67.9706	−	67.9706i	−2.41219	−	2.41219i
$795$	1.61596			0.0573120
$796$	−25.1925	−	25.1925i	−0.892924	−	0.892924i
$797$			22.2085i			0.786666i	0.919396	+	0.393333i	$0.128678\pi$
$797$			22.2085i			0.786666i	−0.919396	+	0.393333i	$0.871322\pi$
$798$	−36.3062			−1.28523
$799$	9.26333	−	3.28832i	0.327713	−	0.116333i
$800$	0.767597			0.0271386
$801$		−	5.40297i		−	0.190904i
$802$	−18.0439	−	18.0439i	−0.637153	−	0.637153i
$803$	20.5926			0.726695
$804$	−49.6619	−	49.6619i	−1.75144	−	1.75144i
$805$	−17.3786	+	17.3786i	−0.612515	+	0.612515i
$806$	1.09533	−	1.09533i	0.0385813	−	0.0385813i
$807$			15.1743i			0.534162i
$808$			55.3187i			1.94611i
$809$	−2.28300	+	2.28300i	−0.0802661	+	0.0802661i	−0.746100	−	0.665834i	$-0.768076\pi$
$809$	−2.28300	+	2.28300i	−0.0802661	+	0.0802661i	0.665834	+	0.746100i	$0.268076\pi$
$810$	4.14265	−	4.14265i	0.145558	−	0.145558i
$811$	−17.8304	−	17.8304i	−0.626110	−	0.626110i	0.320977	−	0.947087i	$-0.395989\pi$
$811$	−17.8304	−	17.8304i	−0.626110	−	0.626110i	−0.947087	+	0.320977i	$0.895989\pi$
$812$	1.98000			0.0694846
$813$	−8.36931	−	8.36931i	−0.293524	−	0.293524i
$814$			27.3356i			0.958114i
$815$	−37.1821			−1.30243
$816$	39.4897	+	18.7984i	1.38242	+	0.658077i
$817$	49.5966			1.73516
$818$		−	6.64975i		−	0.232503i
$819$	−2.16362	−	2.16362i	−0.0756030	−	0.0756030i
$820$	44.2494			1.54526
$821$	24.3444	+	24.3444i	0.849626	+	0.849626i	0.990086	−	0.140460i	$-0.0448583\pi$
$821$	24.3444	+	24.3444i	0.849626	+	0.849626i	−0.140460	+	0.990086i	$0.544858\pi$
$822$	41.1477	−	41.1477i	1.43519	−	1.43519i
$823$	12.5861	−	12.5861i	0.438723	−	0.438723i	−0.452859	−	0.891582i	$-0.649596\pi$
$823$	12.5861	−	12.5861i	0.438723	−	0.438723i	0.891582	+	0.452859i	$0.149596\pi$
$824$			71.7497i			2.49952i
$825$			0.120677i			0.00420143i
$826$	50.8518	−	50.8518i	1.76936	−	1.76936i
$827$	−1.37930	+	1.37930i	−0.0479631	+	0.0479631i	−0.730682	−	0.682718i	$-0.760798\pi$
$827$	−1.37930	+	1.37930i	−0.0479631	+	0.0479631i	0.682718	+	0.730682i	$0.260798\pi$
$828$	16.7297	+	16.7297i	0.581397	+	0.581397i
$829$	−0.904671			−0.0314205			−0.0157103	−	0.999877i	$-0.505001\pi$
$829$	−0.904671			−0.0314205			−0.0157103	+	0.999877i	$0.505001\pi$
$830$	35.3356	+	35.3356i	1.22652	+	1.22652i
$831$		−	26.9025i		−	0.933238i
$832$	15.2001			0.526969
$833$	−2.26807	−	6.38924i	−0.0785840	−	0.221374i
$834$	9.45029			0.327237
$835$			3.56659i			0.123427i
$836$	40.6335	+	40.6335i	1.40534	+	1.40534i
$837$	0.444383			0.0153601
$838$	−49.0778	−	49.0778i	−1.69537	−	1.69537i
$839$	−17.1659	+	17.1659i	−0.592633	+	0.592633i	−0.938342	−	0.345708i	$-0.887639\pi$
$839$	−17.1659	+	17.1659i	−0.592633	+	0.592633i	0.345708	+	0.938342i	$0.387639\pi$
$840$	−28.2878	+	28.2878i	−0.976022	+	0.976022i
$841$		−	28.9701i		−	0.998970i
$842$			17.4290i			0.600643i
$843$	−15.7217	+	15.7217i	−0.541485	+	0.541485i
$844$	46.9731	−	46.9731i	1.61688	−	1.61688i
$845$	−17.6803	−	17.6803i	−0.608222	−	0.608222i
$846$	6.28531			0.216093
$847$	11.7740	+	11.7740i	0.404559	+	0.404559i
$848$			7.71366i			0.264888i
$849$	−23.9577			−0.822225
$850$	−0.633743	+	0.224968i	−0.0217372	+	0.00771634i
$851$	−25.4030			−0.870802
$852$			30.2050i			1.03481i
$853$	26.9482	+	26.9482i	0.922689	+	0.922689i	0.997219	−	0.0745302i	$-0.0237457\pi$
$853$	26.9482	+	26.9482i	0.922689	+	0.922689i	−0.0745302	+	0.997219i	$0.523746\pi$
$854$	53.0016			1.81368
$855$	9.35038	+	9.35038i	0.319776	+	0.319776i
$856$	28.5072	−	28.5072i	0.974357	−	0.974357i
$857$	4.80850	−	4.80850i	0.164255	−	0.164255i	−0.620194	−	0.784449i	$-0.712946\pi$
$857$	4.80850	−	4.80850i	0.164255	−	0.164255i	0.784449	+	0.620194i	$0.212946\pi$
$858$			6.79951i			0.232131i
$859$			22.3072i			0.761113i	0.924758	+	0.380557i	$0.124268\pi$
$859$			22.3072i			0.761113i	−0.924758	+	0.380557i	$0.875732\pi$
$860$	64.8359	−	64.8359i	2.21089	−	2.21089i
$861$	6.58197	−	6.58197i	0.224313	−	0.224313i
$862$	52.4335	+	52.4335i	1.78589	+	1.78589i
$863$	−0.400593			−0.0136363			−0.00681816	−	0.999977i	$-0.502170\pi$
$863$	−0.400593			−0.0136363			−0.00681816	+	0.999977i	$0.502170\pi$
$864$	8.77343	+	8.77343i	0.298478	+	0.298478i
$865$		−	38.0794i		−	1.29474i
$866$	−45.2135			−1.53642
$867$	−16.9096	−	1.75102i	−0.574279	−	0.0594678i
$868$	−5.09124			−0.172808
$869$		−	1.36207i		−	0.0462050i
$870$	−0.715943	−	0.715943i	−0.0242727	−	0.0242727i
$871$	18.7572			0.635563
$872$	−109.877	−	109.877i	−3.72090	−	3.72090i
$873$	−3.33468	+	3.33468i	−0.112862	+	0.112862i
$874$	−53.0154	+	53.0154i	−1.79327	+	1.79327i
$875$		−	26.0314i		−	0.880023i
$876$			52.2632i			1.76581i
$877$	−0.149079	+	0.149079i	−0.00503404	+	0.00503404i	−0.709619	−	0.704585i	$-0.751133\pi$
$877$	−0.149079	+	0.149079i	−0.00503404	+	0.00503404i	0.704585	+	0.709619i	$0.251133\pi$
$878$	−15.3331	+	15.3331i	−0.517469	+	0.517469i
$879$	5.26361	+	5.26361i	0.177537	+	0.177537i
$880$	45.9800			1.54999
$881$	−36.6255	−	36.6255i	−1.23394	−	1.23394i	−0.962436	−	0.271508i	$-0.912478\pi$
$881$	−36.6255	−	36.6255i	−1.23394	−	1.23394i	−0.271508	−	0.962436i	$-0.587522\pi$
$882$		−	4.33519i		−	0.145974i
$883$	−23.5757			−0.793385			−0.396692	−	0.917952i	$-0.629842\pi$
$883$	−23.5757			−0.793385			−0.396692	+	0.917952i	$0.629842\pi$
$884$	−25.4334	+	9.02840i	−0.855416	+	0.303658i
$885$	−26.1930			−0.880468
$886$		−	48.6834i		−	1.63555i
$887$	−11.5500	−	11.5500i	−0.387810	−	0.387810i	0.486096	−	0.873906i	$-0.338421\pi$
$887$	−11.5500	−	11.5500i	−0.387810	−	0.387810i	−0.873906	+	0.486096i	$0.838421\pi$
$888$	−41.3494			−1.38759
$889$	−16.1217	−	16.1217i	−0.540704	−	0.540704i
$890$	22.3826	−	22.3826i	0.750267	−	0.750267i
$891$	−1.37930	+	1.37930i	−0.0462084	+	0.0462084i
$892$			105.272i			3.52476i
$893$			14.1866i			0.474735i
$894$	21.9439	−	21.9439i	0.733915	−	0.733915i
$895$	−17.4030	+	17.4030i	−0.581717	+	0.581717i
$896$	−8.99000	−	8.99000i	−0.300335	−	0.300335i
$897$	−6.31877			−0.210978
$898$	−57.6510	−	57.6510i	−1.92384	−	1.92384i
$899$		−	0.0767993i		−	0.00256140i
$900$	−0.306273			−0.0102091
$901$	−1.00302	−	2.82554i	−0.0334153	−	0.0941322i
$902$	−20.6849			−0.688731
$903$		−	19.2883i		−	0.641875i
$904$	95.9153	+	95.9153i	3.19009	+	3.19009i
$905$	43.7761			1.45517
$906$	30.0209	+	30.0209i	0.997378	+	0.997378i
$907$	−21.7666	+	21.7666i	−0.722747	+	0.722747i	−0.969164	−	0.246417i	$-0.920747\pi$
$907$	−21.7666	+	21.7666i	−0.722747	+	0.722747i	0.246417	+	0.969164i	$0.420747\pi$
$908$	−17.3422	+	17.3422i	−0.575522	+	0.575522i
$909$		−	7.11123i		−	0.235865i
$910$		−	17.9263i		−	0.594250i
$911$	5.08757	−	5.08757i	0.168559	−	0.168559i	−0.617787	−	0.786346i	$-0.711971\pi$
$911$	5.08757	−	5.08757i	0.168559	−	0.168559i	0.786346	+	0.617787i	$0.211971\pi$
$912$	−44.6335	+	44.6335i	−1.47796	+	1.47796i
$913$	−11.7651	−	11.7651i	−0.389367	−	0.389367i
$914$	−40.9532			−1.35461
$915$	−13.6502	−	13.6502i	−0.451260	−	0.451260i
$916$		−	9.10136i		−	0.300717i
$917$	17.6054			0.581383
$918$	−9.81485	−	4.67220i	−0.323938	−	0.154205i
$919$	11.6873			0.385527			0.192764	−	0.981245i	$-0.438255\pi$
$919$	11.6873			0.385527			0.192764	+	0.981245i	$0.438255\pi$
$920$			82.6135i			2.72368i
$921$	10.0539	+	10.0539i	0.331288	+	0.331288i
$922$	−102.565			−3.37779
$923$	−5.70418	−	5.70418i	−0.187755	−	0.187755i
$924$	15.8025	−	15.8025i	0.519865	−	0.519865i
$925$	0.232528	−	0.232528i	0.00764548	−	0.00764548i
$926$			59.9971i			1.97163i
$927$		−	9.22344i		−	0.302938i
$928$	1.51625	−	1.51625i	0.0497732	−	0.0497732i
$929$	−10.0287	+	10.0287i	−0.329032	+	0.329032i	−0.852218	−	0.523186i	$-0.824743\pi$
$929$	−10.0287	+	10.0287i	−0.329032	+	0.329032i	0.523186	+	0.852218i	$0.324743\pi$
$930$	1.84092	+	1.84092i	0.0603663	+	0.0603663i
$931$	9.78497			0.320689
$932$	5.23344	+	5.23344i	0.171427	+	0.171427i
$933$			10.3616i			0.339222i
$934$	33.1003			1.08308
$935$	−16.8426	+	5.97884i	−0.550812	+	0.195529i
$936$	−10.2853			−0.336186
$937$		−	25.4693i		−	0.832044i	−0.909355	−	0.416022i	$-0.863424\pi$
$937$		−	25.4693i		−	0.832044i	0.909355	−	0.416022i	$-0.136576\pi$
$938$	−61.2041	−	61.2041i	−1.99838	−	1.99838i
$939$	17.4262			0.568682
$940$	18.5456	+	18.5456i	0.604891	+	0.604891i
$941$	−41.4250	+	41.4250i	−1.35042	+	1.35042i	−0.465223	+	0.885193i	$0.654026\pi$
$941$	−41.4250	+	41.4250i	−1.35042	+	1.35042i	−0.885193	+	0.465223i	$0.845974\pi$
$942$	12.0342	−	12.0342i	0.392095	−	0.392095i
$943$		−	19.2224i		−	0.625968i
$944$		−	125.031i		−	4.06940i
$945$	3.63640	−	3.63640i	0.118292	−	0.118292i
$946$	−30.3083	+	30.3083i	−0.985406	+	0.985406i
$947$	13.4664	+	13.4664i	0.437598	+	0.437598i	0.891203	−	0.453605i	$-0.149862\pi$
$947$	13.4664	+	13.4664i	0.437598	+	0.437598i	−0.453605	+	0.891203i	$0.649862\pi$
$948$	3.45688			0.112274
$949$	−9.86984	−	9.86984i	−0.320389	−	0.320389i
$950$		−	0.970563i		−	0.0314892i
$951$	−14.1753			−0.459666
$952$	67.0200	+	31.9038i	2.17213	+	1.03401i
$953$	19.8922			0.644371			0.322185	−	0.946677i	$-0.395583\pi$
$953$	19.8922			0.644371			0.322185	+	0.946677i	$0.395583\pi$
$954$		−	1.91717i		−	0.0620706i
$955$	−2.52910	−	2.52910i	−0.0818397	−	0.0818397i
$956$	49.6300			1.60515
$957$	0.238375	+	0.238375i	0.00770556	+	0.00770556i
$958$	−69.4270	+	69.4270i	−2.24308	+	2.24308i
$959$	36.1192	−	36.1192i	1.16635	−	1.16635i
$960$			25.5469i			0.824522i
$961$		−	30.8025i		−	0.993630i
$962$	13.1018	−	13.1018i	0.422418	−	0.422418i
$963$	−3.66461	+	3.66461i	−0.118090	+	0.118090i
$964$	40.3113	+	40.3113i	1.29834	+	1.29834i
$965$	9.94216			0.320049
$966$	20.6179	+	20.6179i	0.663371	+	0.663371i
$967$		−	53.0310i		−	1.70536i	−0.522433	−	0.852680i	$-0.674975\pi$
$967$		−	53.0310i		−	1.70536i	0.522433	−	0.852680i	$-0.325025\pi$
$968$	55.9706			1.79896
$969$	10.5456	−	22.1531i	0.338774	−	0.711660i
$970$	−27.6288			−0.887108
$971$		−	3.02535i		−	0.0970880i	−0.998821	−	0.0485440i	$-0.984542\pi$
$971$		−	3.02535i		−	0.0970880i	0.998821	−	0.0485440i	$-0.0154581\pi$
$972$	−3.50062	−	3.50062i	−0.112283	−	0.112283i
$973$	8.29543			0.265939
$974$	−3.06641	−	3.06641i	−0.0982541	−	0.0982541i
$975$	0.0578394	−	0.0578394i	0.00185234	−	0.00185234i
$976$	65.1581	−	65.1581i	2.08566	−	2.08566i
$977$			11.2664i			0.360444i	0.983626	+	0.180222i	$0.0576815\pi$
$977$			11.2664i			0.360444i	−0.983626	+	0.180222i	$0.942318\pi$
$978$			44.1128i			1.41057i
$979$	−7.45234	+	7.45234i	−0.238178	+	0.238178i
$980$	12.7916	−	12.7916i	0.408611	−	0.408611i
$981$	14.1247	+	14.1247i	0.450967	+	0.450967i
$982$	11.3397			0.361866
$983$	34.1943	+	34.1943i	1.09063	+	1.09063i	0.995461	+	0.0951684i	$0.0303390\pi$
$983$	34.1943	+	34.1943i	1.09063	+	1.09063i	0.0951684	+	0.995461i	$0.469661\pi$
$984$		−	31.2891i		−	0.997459i
$985$	16.4304			0.523515
$986$	−0.807460	+	1.69623i	−0.0257148	+	0.0540188i
$987$	5.51722			0.175615
$988$		−	38.9506i		−	1.23918i
$989$	−28.1654	−	28.1654i	−0.895608	−	0.895608i
$990$	−11.4280			−0.363204
$991$	16.9991	+	16.9991i	0.539994	+	0.539994i	0.923527	−	0.383533i	$-0.125293\pi$
$991$	16.9991	+	16.9991i	0.539994	+	0.539994i	−0.383533	+	0.923527i	$0.625293\pi$
$992$	−3.89876	+	3.89876i	−0.123786	+	0.123786i
$993$	7.67104	−	7.67104i	0.243433	−	0.243433i
$994$			37.2251i			1.18071i
$995$			15.9921i			0.506985i
$996$	29.8593	−	29.8593i	0.946129	−	0.946129i
$997$	−18.6250	+	18.6250i	−0.589861	+	0.589861i	−0.937594	−	0.347733i	$-0.886952\pi$
$997$	−18.6250	+	18.6250i	−0.589861	+	0.589861i	0.347733	+	0.937594i	$0.386952\pi$
$998$	2.78753	+	2.78753i	0.0882377	+	0.0882377i
$999$	5.31548			0.168174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	51.2.e.a.13.4	yes	8
3.2	odd	2		153.2.f.b.64.1		8
4.3	odd	2		816.2.bd.e.625.4		8
12.11	even	2		2448.2.be.x.1441.1		8
17.2	even	8		867.2.a.k.1.1		4
17.3	odd	16		867.2.h.k.712.3		16
17.4	even	4	inner	51.2.e.a.4.1	✓	8
17.5	odd	16		867.2.h.i.733.2		16
17.6	odd	16		867.2.h.i.757.1		16
17.7	odd	16		867.2.h.k.688.3		16
17.8	even	8		867.2.d.f.577.8		8
17.9	even	8		867.2.d.f.577.7		8
17.10	odd	16		867.2.h.k.688.4		16
17.11	odd	16		867.2.h.i.757.2		16
17.12	odd	16		867.2.h.i.733.1		16
17.13	even	4		867.2.e.g.616.1		8
17.14	odd	16		867.2.h.k.712.4		16
17.15	even	8		867.2.a.l.1.1		4
17.16	even	2		867.2.e.g.829.4		8
51.2	odd	8		2601.2.a.bf.1.4		4
51.32	odd	8		2601.2.a.be.1.4		4
51.38	odd	4		153.2.f.b.55.4		8
68.55	odd	4		816.2.bd.e.769.4		8
204.191	even	4		2448.2.be.x.1585.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.1	✓	8	17.4	even	4	inner
51.2.e.a.13.4	yes	8	1.1	even	1	trivial
153.2.f.b.55.4		8	51.38	odd	4
153.2.f.b.64.1		8	3.2	odd	2
816.2.bd.e.625.4		8	4.3	odd	2
816.2.bd.e.769.4		8	68.55	odd	4
867.2.a.k.1.1		4	17.2	even	8
867.2.a.l.1.1		4	17.15	even	8
867.2.d.f.577.7		8	17.9	even	8
867.2.d.f.577.8		8	17.8	even	8
867.2.e.g.616.1		8	17.13	even	4
867.2.e.g.829.4		8	17.16	even	2
867.2.h.i.733.1		16	17.12	odd	16
867.2.h.i.733.2		16	17.5	odd	16
867.2.h.i.757.1		16	17.6	odd	16
867.2.h.i.757.2		16	17.11	odd	16
867.2.h.k.688.3		16	17.7	odd	16
867.2.h.k.688.4		16	17.10	odd	16
867.2.h.k.712.3		16	17.3	odd	16
867.2.h.k.712.4		16	17.14	odd	16
2448.2.be.x.1441.1		8	12.11	even	2
2448.2.be.x.1585.1		8	204.191	even	4
2601.2.a.be.1.4		4	51.32	odd	8
2601.2.a.bf.1.4		4	51.2	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 51 = 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	51.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.63640i q^{2} +(-0.707107 - 0.707107i) q^{3} -4.95063 q^{4} +(1.57133 + 1.57133i) q^{5} +(1.86422 - 1.86422i) q^{6} +(1.63640 - 1.63640i) q^{7} -7.77906i q^{8} +1.00000i q^{9} +(-4.14265 + 4.14265i) q^{10} +(1.37930 - 1.37930i) q^{11} +(3.50062 + 3.50062i) q^{12} -1.32218 q^{13} +(4.31423 + 4.31423i) q^{14} -2.22219i q^{15} +10.6075 q^{16} +(-3.88555 + 1.37930i) q^{17} -2.63640 q^{18} -5.95063i q^{19} +(-7.77906 - 7.77906i) q^{20} -2.31423 q^{21} +(3.63640 + 3.63640i) q^{22} +(-3.37930 + 3.37930i) q^{23} +(-5.50062 + 5.50062i) q^{24} -0.0618655i q^{25} -3.48580i q^{26} +(0.707107 - 0.707107i) q^{27} +(-8.10124 + 8.10124i) q^{28} +(-0.122204 - 0.122204i) q^{29} +5.85860 q^{30} +(0.314226 + 0.314226i) q^{31} +12.4075i q^{32} -1.95063 q^{33} +(-3.63640 - 10.2439i) q^{34} +5.14265 q^{35} -4.95063i q^{36} +(3.75861 + 3.75861i) q^{37} +15.6883 q^{38} +(0.934922 + 0.934922i) q^{39} +(12.2234 - 12.2234i) q^{40} +(-2.84414 + 2.84414i) q^{41} -6.10124i q^{42} +8.33468i q^{43} +(-6.82843 + 6.82843i) q^{44} +(-1.57133 + 1.57133i) q^{45} +(-8.90921 - 8.90921i) q^{46} -2.38404 q^{47} +(-7.50062 - 7.50062i) q^{48} +1.64436i q^{49} +0.163102 q^{50} +(3.72282 + 1.77219i) q^{51} +6.54562 q^{52} +0.727190i q^{53} +(1.86422 + 1.86422i) q^{54} +4.33468 q^{55} +(-12.7297 - 12.7297i) q^{56} +(-4.20773 + 4.20773i) q^{57} +(0.322179 - 0.322179i) q^{58} -11.7870i q^{59} +11.0012i q^{60} +(6.14265 - 6.14265i) q^{61} +(-0.828427 + 0.828427i) q^{62} +(1.63640 + 1.63640i) q^{63} -11.4963 q^{64} +(-2.07757 - 2.07757i) q^{65} -5.14265i q^{66} -14.1866 q^{67} +(19.2359 - 6.82843i) q^{68} +4.77906 q^{69} +13.5581i q^{70} +(4.31423 + 4.31423i) q^{71} +7.77906 q^{72} +(7.46483 + 7.46483i) q^{73} +(-9.90921 + 9.90921i) q^{74} +(-0.0437455 + 0.0437455i) q^{75} +29.4594i q^{76} -4.51420i q^{77} +(-2.46483 + 2.46483i) q^{78} +(0.493752 - 0.493752i) q^{79} +(16.6678 + 16.6678i) q^{80} -1.00000 q^{81} +(-7.49830 - 7.49830i) q^{82} -8.52971i q^{83} +11.4569 q^{84} +(-8.27281 - 3.93813i) q^{85} -21.9736 q^{86} +0.172822i q^{87} +(-10.7297 - 10.7297i) q^{88} -5.40297 q^{89} +(-4.14265 - 4.14265i) q^{90} +(-2.16362 + 2.16362i) q^{91} +(16.7297 - 16.7297i) q^{92} -0.444383i q^{93} -6.28531i q^{94} +(9.35038 - 9.35038i) q^{95} +(8.77343 - 8.77343i) q^{96} +(3.33468 + 3.33468i) q^{97} -4.33519 q^{98} +(1.37930 + 1.37930i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{7} - 4 q^{13} + 24 q^{14} + 12 q^{16} - 4 q^{17} - 4 q^{18} - 12 q^{20} - 8 q^{21} + 12 q^{22} - 16 q^{23} - 16 q^{24} - 8 q^{28} + 4 q^{29} + 24 q^{30} - 8 q^{31}+ \cdots - 76 q^{98}+O(q^{100}) \) 8 * q - 12 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^7 - 4 * q^13 + 24 * q^14 + 12 * q^16 - 4 * q^17 - 4 * q^18 - 12 * q^20 - 8 * q^21 + 12 * q^22 - 16 * q^23 - 16 * q^24 - 8 * q^28 + 4 * q^29 + 24 * q^30 - 8 * q^31 + 12 * q^33 - 12 * q^34 + 8 * q^35 + 8 * q^37 + 24 * q^38 + 8 * q^39 + 36 * q^40 + 28 * q^41 - 32 * q^44 + 4 * q^45 - 20 * q^46 - 8 * q^47 - 32 * q^48 - 60 * q^50 - 4 * q^51 - 16 * q^52 + 4 * q^54 - 4 * q^55 - 24 * q^56 - 4 * q^58 + 16 * q^61 + 16 * q^62 - 4 * q^63 + 4 * q^64 + 16 * q^65 + 8 * q^67 + 60 * q^68 - 12 * q^69 + 24 * q^71 + 12 * q^72 + 20 * q^73 - 28 * q^74 - 16 * q^75 + 20 * q^78 + 20 * q^79 + 60 * q^80 - 8 * q^81 - 40 * q^82 + 48 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^88 - 8 * q^89 - 36 * q^91 + 56 * q^92 + 8 * q^95 + 8 * q^96 - 12 * q^97 - 76 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more