LMFDB - Embedded newform 1134.2.k.b.971.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(647,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1134.647"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,-4,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			971.8
Root			$1.71298 + 0.256290i$ of defining polynomial
Character	$\chi$	$=$	1134.971
Dual form			1134.2.k.b.647.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.80966 - 3.13442i) q^{5} +(2.14611 - 1.54733i) q^{7} +1.00000i q^{8} +(3.13442 - 1.80966i) q^{10} +(-1.73534 + 1.00190i) q^{11} -3.40874i q^{13} +(2.63225 - 0.266972i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.08709 + 5.34700i) q^{17} +(0.877353 + 0.506540i) q^{19} +3.61932 q^{20} -2.00379 q^{22} +(-2.62232 - 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} +(1.70437 - 2.95206i) q^{26} +(2.41308 + 1.08492i) q^{28} -5.82616i q^{29} +(-0.787812 + 0.454844i) q^{31} +(-0.866025 + 0.500000i) q^{32} +6.17418i q^{34} +(-0.966257 - 9.52693i) q^{35} +(3.66825 - 6.35359i) q^{37} +(0.506540 + 0.877353i) q^{38} +(3.13442 + 1.80966i) q^{40} -5.70089 q^{41} +4.79899 q^{43} +(-1.73534 - 1.00190i) q^{44} +(-1.51400 - 2.62232i) q^{46} +(-1.11511 + 1.93143i) q^{47} +(2.21155 - 6.64146i) q^{49} -8.09945i q^{50} +(2.95206 - 1.70437i) q^{52} +(-7.58088 + 4.37683i) q^{53} +7.25237i q^{55} +(1.54733 + 2.14611i) q^{56} +(2.91308 - 5.04560i) q^{58} +(4.49313 + 7.78233i) q^{59} +(12.7410 + 7.35603i) q^{61} -0.909687 q^{62} -1.00000 q^{64} +(-10.6844 - 6.16866i) q^{65} +(4.15821 + 7.20222i) q^{67} +(-3.08709 + 5.34700i) q^{68} +(3.92666 - 8.73370i) q^{70} -0.466287i q^{71} +(-3.65022 + 2.10746i) q^{73} +(6.35359 - 3.66825i) q^{74} +1.01308i q^{76} +(-2.17395 + 4.83532i) q^{77} +(-1.91267 + 3.31284i) q^{79} +(1.80966 + 3.13442i) q^{80} +(-4.93712 - 2.85045i) q^{82} -8.00963 q^{83} +22.3463 q^{85} +(4.15605 + 2.39949i) q^{86} +(-1.00190 - 1.73534i) q^{88} +(2.39324 - 4.14521i) q^{89} +(-5.27445 - 7.31553i) q^{91} -3.02799i q^{92} +(-1.93143 + 1.11511i) q^{94} +(3.17542 - 1.83333i) q^{95} -11.7589i q^{97} +(5.23599 - 4.64590i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 4 q^{7} + 12 q^{11} - 8 q^{16} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 12 q^{41} + 4 q^{43} + 12 q^{44} + 6 q^{46} - 18 q^{47} - 2 q^{49}+ \cdots + 24 q^{98}+O(q^{100}) $ 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^11 - 8 * q^16 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 12 * q^41 + 4 * q^43 + 12 * q^44 + 6 * q^46 - 18 * q^47 - 2 * q^49 + 6 * q^52 + 36 * q^53 + 6 * q^56 + 6 * q^58 + 30 * q^59 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^70 + 18 * q^74 - 24 * q^77 - 16 * q^79 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 + 66 * q^95 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.80966	−	3.13442i	0.809304	−	1.40175i	−0.104043	−	0.994573i	$-0.533178\pi$
$5$	1.80966	−	3.13442i	0.809304	−	1.40175i	0.913347	−	0.407182i	$-0.133489\pi$
$6$		0			0
$7$	2.14611	−	1.54733i	0.811152	−	0.584835i
$7$	2.14611	−	1.54733i	0.811152	−	0.584835i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	3.13442	−	1.80966i	0.991190	−	0.572264i
$11$	−1.73534	+	1.00190i	−0.523224	+	0.302083i	−0.738253	−	0.674524i	$-0.764349\pi$
$11$	−1.73534	+	1.00190i	−0.523224	+	0.302083i	0.215029	+	0.976608i	$0.431015\pi$
$12$		0			0
$13$		−	3.40874i		−	0.945415i	−0.881219	−	0.472708i	$-0.843277\pi$
$13$		−	3.40874i		−	0.945415i	0.881219	−	0.472708i	$-0.156723\pi$
$14$	2.63225	−	0.266972i	0.703498	−	0.0713513i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.08709	+	5.34700i	0.748730	+	1.29684i	0.948432	+	0.316981i	$0.102669\pi$
$17$	3.08709	+	5.34700i	0.748730	+	1.29684i	−0.199702	+	0.979857i	$0.563998\pi$
$18$		0			0
$19$	0.877353	+	0.506540i	0.201279	+	0.116208i	0.597252	−	0.802054i	$-0.296259\pi$
$19$	0.877353	+	0.506540i	0.201279	+	0.116208i	−0.395973	+	0.918262i	$0.629593\pi$
$20$	3.61932			0.809304
$21$		0			0
$22$	−2.00379			−0.427210
$23$	−2.62232	−	1.51400i	−0.546791	−	0.315690i	0.201035	−	0.979584i	$-0.435569\pi$
$23$	−2.62232	−	1.51400i	−0.546791	−	0.315690i	−0.747827	+	0.663894i	$0.768903\pi$
$24$		0			0
$25$	−4.04972	−	7.01433i	−0.809945	−	1.40287i
$26$	1.70437	−	2.95206i	0.334255	−	0.578946i
$27$		0			0
$28$	2.41308	+	1.08492i	0.456029	+	0.205030i
$29$		−	5.82616i		−	1.08189i	−0.841058	−	0.540945i	$-0.818067\pi$
$29$		−	5.82616i		−	1.08189i	0.841058	−	0.540945i	$-0.181933\pi$
$30$		0			0
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	−0.569076	−	0.822285i	$-0.692699\pi$
$31$	−0.787812	+	0.454844i	−0.141495	+	0.0816923i	0.427581	+	0.903977i	$0.359366\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$			6.17418i			1.05886i
$35$	−0.966257	−	9.52693i	−0.163327	−	1.61035i
$36$		0			0
$37$	3.66825	−	6.35359i	0.603056	−	1.04452i	−0.389299	−	0.921111i	$-0.627283\pi$
$37$	3.66825	−	6.35359i	0.603056	−	1.04452i	0.992355	−	0.123413i	$-0.0393839\pi$
$38$	0.506540	+	0.877353i	0.0821717	+	0.142325i
$39$		0			0
$40$	3.13442	+	1.80966i	0.495595	+	0.286132i
$41$	−5.70089			−0.890330			−0.445165	−	0.895449i	$-0.646855\pi$
$41$	−5.70089			−0.890330			−0.445165	+	0.895449i	$0.646855\pi$
$42$		0			0
$43$	4.79899			0.731839			0.365919	−	0.930647i	$-0.380755\pi$
$43$	4.79899			0.731839			0.365919	+	0.930647i	$0.380755\pi$
$44$	−1.73534	−	1.00190i	−0.261612	−	0.151042i
$45$		0			0
$46$	−1.51400	−	2.62232i	−0.223227	−	0.386640i
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	−0.935820	−	0.352478i	$-0.885339\pi$
$47$	−1.11511	+	1.93143i	−0.162655	+	0.281727i	0.773165	+	0.634205i	$0.218673\pi$
$48$		0			0
$49$	2.21155	−	6.64146i	0.315936	−	0.948781i
$50$		−	8.09945i		−	1.14543i
$51$		0			0
$52$	2.95206	−	1.70437i	0.409377	−	0.236354i
$53$	−7.58088	+	4.37683i	−1.04131	+	0.601203i	−0.920205	−	0.391436i	$-0.871978\pi$
$53$	−7.58088	+	4.37683i	−1.04131	+	0.601203i	−0.121109	+	0.992639i	$0.538645\pi$
$54$		0			0
$55$			7.25237i			0.977909i
$56$	1.54733	+	2.14611i	0.206770	+	0.286786i
$57$		0			0
$58$	2.91308	−	5.04560i	0.382506	−	0.662520i
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	0.994881	+	0.101054i	$0.0322216\pi$
$59$	4.49313	+	7.78233i	0.584956	+	1.01317i	−0.409925	+	0.912119i	$0.634445\pi$
$60$		0			0
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.983686	+	0.179892i	$0.0575747\pi$
$61$	12.7410	+	7.35603i	1.63132	+	0.941843i	0.647634	+	0.761952i	$0.275759\pi$
$62$	−0.909687			−0.115530
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−10.6844	−	6.16866i	−1.32524	−	0.765128i
$66$		0			0
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	0.999957	+	0.00926908i	$0.00295048\pi$
$67$	4.15821	+	7.20222i	0.508006	+	0.879892i	−0.491951	+	0.870623i	$0.663716\pi$
$68$	−3.08709	+	5.34700i	−0.374365	+	0.648419i
$69$		0			0
$70$	3.92666	−	8.73370i	0.469326	−	1.04388i
$71$		−	0.466287i		−	0.0553381i	−0.999617	−	0.0276691i	$-0.991192\pi$
$71$		−	0.466287i		−	0.0553381i	0.999617	−	0.0276691i	$-0.00880846\pi$
$72$		0			0
$73$	−3.65022	+	2.10746i	−0.427226	+	0.246659i	−0.698164	−	0.715938i	$-0.746000\pi$
$73$	−3.65022	+	2.10746i	−0.427226	+	0.246659i	0.270938	+	0.962597i	$0.412666\pi$
$74$	6.35359	−	3.66825i	0.738590	−	0.426425i
$75$		0			0
$76$			1.01308i			0.116208i
$77$	−2.17395	+	4.83532i	−0.247745	+	0.551035i
$78$		0			0
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	−0.953332	−	0.301924i	$-0.902371\pi$
$79$	−1.91267	+	3.31284i	−0.215192	+	0.372723i	0.738140	+	0.674648i	$0.235704\pi$
$80$	1.80966	+	3.13442i	0.202326	+	0.350439i
$81$		0			0
$82$	−4.93712	−	2.85045i	−0.545213	−	0.314779i
$83$	−8.00963			−0.879171			−0.439585	−	0.898201i	$-0.644875\pi$
$83$	−8.00963			−0.879171			−0.439585	+	0.898201i	$0.644875\pi$
$84$		0			0
$85$	22.3463			2.42380
$86$	4.15605	+	2.39949i	0.448158	+	0.258744i
$87$		0			0
$88$	−1.00190	−	1.73534i	−0.106803	−	0.184988i
$89$	2.39324	−	4.14521i	0.253683	−	0.439391i	−0.710854	−	0.703339i	$-0.751691\pi$
$89$	2.39324	−	4.14521i	0.253683	−	0.439391i	0.964537	+	0.263948i	$0.0850248\pi$
$90$		0			0
$91$	−5.27445	−	7.31553i	−0.552912	−	0.766876i
$92$		−	3.02799i		−	0.315690i
$93$		0			0
$94$	−1.93143	+	1.11511i	−0.199211	+	0.115015i
$95$	3.17542	−	1.83333i	0.325791	−	0.188096i
$96$		0			0
$97$		−	11.7589i		−	1.19393i	−0.802266	−	0.596967i	$-0.796372\pi$
$97$		−	11.7589i		−	1.19393i	0.802266	−	0.596967i	$-0.203628\pi$
$98$	5.23599	−	4.64590i	0.528915	−	0.469307i
$99$		0			0
$100$	4.04972	−	7.01433i	0.404972	−	0.701433i
$101$	6.44610	+	11.1650i	0.641411	+	1.11096i	0.985118	+	0.171879i	$0.0549840\pi$
$101$	6.44610	+	11.1650i	0.641411	+	1.11096i	−0.343707	+	0.939077i	$0.611683\pi$
$102$		0			0
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.0350515	−	0.999386i	$-0.511160\pi$
$103$	−9.31740	−	5.37940i	−0.918070	−	0.530048i	−0.883019	+	0.469337i	$0.844493\pi$
$104$	3.40874			0.334255
$105$		0			0
$106$	−8.75365			−0.850230
$107$	2.28602	+	1.31983i	0.220998	+	0.127593i	0.606412	−	0.795151i	$-0.292608\pi$
$107$	2.28602	+	1.31983i	0.220998	+	0.127593i	−0.385414	+	0.922744i	$0.625942\pi$
$108$		0			0
$109$	4.51768	+	7.82484i	0.432715	+	0.749484i	0.997106	−	0.0760233i	$-0.0242224\pi$
$109$	4.51768	+	7.82484i	0.432715	+	0.749484i	−0.564391	+	0.825507i	$0.690889\pi$
$110$	−3.62618	+	6.28073i	−0.345743	+	0.598844i
$111$		0			0
$112$	0.266972	+	2.63225i	0.0252265	+	0.248724i
$113$		−	1.69061i		−	0.159039i	−0.996833	−	0.0795197i	$-0.974661\pi$
$113$		−	1.69061i		−	0.159039i	0.996833	−	0.0795197i	$-0.0253387\pi$
$114$		0			0
$115$	−9.49100	+	5.47963i	−0.885041	+	0.510978i
$116$	5.04560	−	2.91308i	0.468472	−	0.270473i
$117$		0			0
$118$			8.98627i			0.827253i
$119$	14.8988	+	6.69849i	1.36577	+	0.614049i
$120$		0			0
$121$	−3.49240	+	6.04902i	−0.317491	+	0.549911i
$122$	7.35603	+	12.7410i	0.665984	+	1.15352i
$123$		0			0
$124$	−0.787812	−	0.454844i	−0.0707476	−	0.0408462i
$125$	−11.2179			−1.00336
$126$		0			0
$127$	17.9292			1.59096			0.795478	−	0.605983i	$-0.207220\pi$
$127$	17.9292			1.59096			0.795478	+	0.605983i	$0.207220\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−6.16866	−	10.6844i	−0.541027	−	0.937087i
$131$	−8.66567	+	15.0094i	−0.757123	+	1.31138i	0.187188	+	0.982324i	$0.440062\pi$
$131$	−8.66567	+	15.0094i	−0.757123	+	1.31138i	−0.944312	+	0.329052i	$0.893271\pi$
$132$		0			0
$133$	2.66668	−	0.270464i	0.231230	−	0.0234522i
$134$			8.31641i			0.718429i
$135$		0			0
$136$	−5.34700	+	3.08709i	−0.458501	+	0.264716i
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	−0.499976	−	0.866039i	$-0.666658\pi$
$137$	0.000558693	0	0.000322562i	4.77324e−5	0	2.75583e-5i	0.500024	+	0.866012i	$0.333325\pi$
$138$		0			0
$139$			10.0837i			0.855288i	0.903947	+	0.427644i	$0.140656\pi$
$139$			10.0837i			0.855288i	−0.903947	+	0.427644i	$0.859344\pi$
$140$	7.76744	−	5.60027i	0.656468	−	0.473309i
$141$		0			0
$142$	0.233144	−	0.403817i	0.0195650	−	0.0338875i
$143$	3.41521	+	5.91532i	0.285594	+	0.494664i
$144$		0			0
$145$	−18.2616	−	10.5434i	−1.51655	−	0.875578i
$146$	−4.21492			−0.348829
$147$		0			0
$148$	7.33650			0.603056
$149$	−9.74064	−	5.62376i	−0.797984	−	0.460716i	0.0447816	−	0.998997i	$-0.485741\pi$
$149$	−9.74064	−	5.62376i	−0.797984	−	0.460716i	−0.842766	+	0.538280i	$0.819074\pi$
$150$		0			0
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	0.945982	−	0.324220i	$-0.105102\pi$
$151$	2.36189	+	4.09092i	0.192208	+	0.332914i	−0.753774	+	0.657134i	$0.771768\pi$
$152$	−0.506540	+	0.877353i	−0.0410858	+	0.0711627i
$153$		0			0
$154$	−4.30036	+	3.10053i	−0.346533	+	0.249848i
$155$			3.29245i			0.264456i
$156$		0			0
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	−0.602318	−	0.798256i	$-0.705756\pi$
$157$	−2.65845	+	1.53486i	−0.212168	+	0.122495i	0.390151	+	0.920751i	$0.372423\pi$
$158$	−3.31284	+	1.91267i	−0.263555	+	0.152164i
$159$		0			0
$160$			3.61932i			0.286132i
$161$	−7.97043	+	0.808390i	−0.628158	+	0.0637101i
$162$		0			0
$163$	−1.43687	+	2.48873i	−0.112544	+	0.194932i	−0.916795	−	0.399357i	$-0.869233\pi$
$163$	−1.43687	+	2.48873i	−0.112544	+	0.194932i	0.804251	+	0.594289i	$0.202567\pi$
$164$	−2.85045	−	4.93712i	−0.222582	−	0.385524i
$165$		0			0
$166$	−6.93654	−	4.00481i	−0.538380	−	0.310834i
$167$	1.46103			0.113058			0.0565291	−	0.998401i	$-0.481997\pi$
$167$	1.46103			0.113058			0.0565291	+	0.998401i	$0.481997\pi$
$168$		0			0
$169$	1.38047			0.106190
$170$	19.3525	+	11.1732i	1.48427	+	0.856942i
$171$		0			0
$172$	2.39949	+	4.15605i	0.182960	+	0.316896i
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	−0.918472	−	0.395486i	$-0.870576\pi$
$173$	−1.53541	+	2.65940i	−0.116735	+	0.202191i	0.801737	+	0.597677i	$0.203909\pi$
$174$		0			0
$175$	−19.5446	−	8.78724i	−1.47743	−	0.664253i
$176$		−	2.00379i		−	0.151042i
$177$		0			0
$178$	4.14521	−	2.39324i	0.310696	−	0.179381i
$179$	−16.7310	+	9.65966i	−1.25054	+	0.721997i	−0.971216	−	0.238201i	$-0.923442\pi$
$179$	−16.7310	+	9.65966i	−1.25054	+	0.721997i	−0.279320	+	0.960198i	$0.590109\pi$
$180$		0			0
$181$		−	7.89318i		−	0.586695i	−0.956006	−	0.293348i	$-0.905231\pi$
$181$		−	7.89318i		−	0.586695i	0.956006	−	0.293348i	$-0.0947693\pi$
$182$	−0.910040	−	8.97266i	−0.0674566	−	0.665098i
$183$		0			0
$184$	1.51400	−	2.62232i	0.111613	−	0.193320i
$185$	−13.2765	−	22.9957i	−0.976111	−	1.69067i
$186$		0			0
$187$	−10.7143	−	6.18590i	−0.783506	−	0.452358i
$188$	−2.23022			−0.162655
$189$		0			0
$190$	3.66666			0.266007
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	0.0214259	−	0.999770i	$-0.493179\pi$
$191$	−11.5218	−	6.65211i	−0.833688	−	0.481330i	−0.855114	+	0.518441i	$0.826513\pi$
$192$		0			0
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	0.724112	−	0.689682i	$-0.242250\pi$
$193$	−3.26786	−	5.66011i	−0.235226	−	0.407423i	−0.959338	+	0.282259i	$0.908916\pi$
$194$	5.87944	−	10.1835i	0.422119	−	0.731132i
$195$		0			0
$196$	6.85745	−	1.40547i	0.489818	−	0.100391i
$197$			4.44250i			0.316515i	0.987398	+	0.158258i	$0.0505876\pi$
$197$			4.44250i			0.316515i	−0.987398	+	0.158258i	$0.949412\pi$
$198$		0			0
$199$	9.96868	−	5.75542i	0.706661	−	0.407991i	−0.103163	−	0.994665i	$-0.532896\pi$
$199$	9.96868	−	5.75542i	0.706661	−	0.407991i	0.809823	+	0.586674i	$0.199563\pi$
$200$	7.01433	−	4.04972i	0.495988	−	0.286359i
$201$		0			0
$202$			12.8922i			0.907092i
$203$	−9.01498	−	12.5036i	−0.632728	−	0.877578i
$204$		0			0
$205$	−10.3167	+	17.8690i	−0.720547	+	1.24802i
$206$	−5.37940	−	9.31740i	−0.374801	−	0.649174i
$207$		0			0
$208$	2.95206	+	1.70437i	0.204688	+	0.118177i
$209$	−2.03000			−0.140418
$210$		0			0
$211$	−22.6011			−1.55592			−0.777961	−	0.628313i	$-0.783746\pi$
$211$	−22.6011			−1.55592			−0.777961	+	0.628313i	$0.783746\pi$
$212$	−7.58088	−	4.37683i	−0.520657	−	0.300602i
$213$		0			0
$214$	1.31983	+	2.28602i	0.0902219	+	0.156269i
$215$	8.68453	−	15.0420i	0.592280	−	1.02586i
$216$		0			0
$217$	−0.986937	+	2.19515i	−0.0669976	+	0.149016i
$218$			9.03535i			0.611951i
$219$		0			0
$220$	−6.28073	+	3.62618i	−0.423447	+	0.244477i
$221$	18.2265	−	10.5231i	1.22605	−	0.707860i
$222$		0			0
$223$			18.8209i			1.26034i	0.776457	+	0.630170i	$0.217015\pi$
$223$			18.8209i			1.26034i	−0.776457	+	0.630170i	$0.782985\pi$
$224$	−1.08492	+	2.41308i	−0.0724892	+	0.161231i
$225$		0			0
$226$	0.845306	−	1.46411i	0.0562289	−	0.0973914i
$227$	7.30665	+	12.6555i	0.484960	+	0.839975i	0.999851	−	0.0172809i	$-0.00550095\pi$
$227$	7.30665	+	12.6555i	0.484960	+	0.839975i	−0.514891	+	0.857256i	$0.672168\pi$
$228$		0			0
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	0.430374	−	0.902651i	$-0.358382\pi$
$229$	−2.06044	−	1.18959i	−0.136158	−	0.0786106i	−0.566531	+	0.824040i	$0.691715\pi$
$230$	−10.9593			−0.722633
$231$		0			0
$232$	5.82616			0.382506
$233$	−9.03470	−	5.21619i	−0.591883	−	0.341724i	0.173959	−	0.984753i	$-0.444344\pi$
$233$	−9.03470	−	5.21619i	−0.591883	−	0.341724i	−0.765842	+	0.643029i	$0.777677\pi$
$234$		0			0
$235$	4.03593	+	6.99044i	0.263275	+	0.456006i
$236$	−4.49313	+	7.78233i	−0.292478	+	0.506587i
$237$		0			0
$238$	9.55349	+	13.2505i	0.619261	+	0.858899i
$239$			23.7835i			1.53843i	0.638992	+	0.769213i	$0.279352\pi$
$239$			23.7835i			1.53843i	−0.638992	+	0.769213i	$0.720648\pi$
$240$		0			0
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.606348	+	0.795200i	$0.707366\pi$
$241$	−24.8105	+	14.3243i	−1.59818	+	0.922712i	−0.991837	+	0.127513i	$0.959301\pi$
$242$	−6.04902	+	3.49240i	−0.388846	+	0.224500i
$243$		0			0
$244$			14.7121i			0.941843i
$245$	−16.8150	−	18.9507i	−1.07427	−	1.21072i
$246$		0			0
$247$	1.72667	−	2.99067i	0.109865	−	0.190292i
$248$	−0.454844	−	0.787812i	−0.0288826	−	0.0500261i
$249$		0			0
$250$	−9.71496	−	5.60894i	−0.614428	−	0.354740i
$251$	11.0301			0.696216			0.348108	−	0.937454i	$-0.386824\pi$
$251$	11.0301			0.696216			0.348108	+	0.937454i	$0.386824\pi$
$252$		0			0
$253$	6.06748			0.381459
$254$	15.5271	+	8.96458i	0.974257	+	0.562488i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.54890	−	13.0751i	0.470888	−	0.815601i	−0.528558	−	0.848897i	$-0.677267\pi$
$257$	7.54890	−	13.0751i	0.470888	−	0.815601i	0.999446	+	0.0332960i	$0.0106004\pi$
$258$		0			0
$259$	−1.95864	−	19.3115i	−0.121704	−	1.19996i
$260$		−	12.3373i		−	0.765128i
$261$		0			0
$262$	−15.0094	+	8.66567i	−0.927283	+	0.535367i
$263$	17.0075	−	9.81926i	1.04873	−	0.605482i	0.126433	−	0.991975i	$-0.459647\pi$
$263$	17.0075	−	9.81926i	1.04873	−	0.605482i	0.922292	+	0.386493i	$0.126314\pi$
$264$		0			0
$265$			31.6822i			1.94622i
$266$	2.44464	+	1.09911i	0.149891	+	0.0673908i
$267$		0			0
$268$	−4.15821	+	7.20222i	−0.254003	+	0.439946i
$269$	−0.245503	−	0.425223i	−0.0149686	−	0.0259263i	0.858444	−	0.512907i	$-0.171431\pi$
$269$	−0.245503	−	0.425223i	−0.0149686	−	0.0259263i	−0.873413	+	0.486981i	$0.838098\pi$
$270$		0			0
$271$	−12.1927	−	7.03945i	−0.740653	−	0.427616i	0.0816537	−	0.996661i	$-0.473980\pi$
$271$	−12.1927	−	7.03945i	−0.740653	−	0.427616i	−0.822307	+	0.569045i	$0.807313\pi$
$272$	−6.17418			−0.374365
$273$		0			0
$274$	0.000645123	0		3.89733e−5	0
$275$	14.0553	+	8.11481i	0.847565	+	0.489342i
$276$		0			0
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.794913	−	0.606723i	$-0.792484\pi$
$277$	−15.3600	−	26.6043i	−0.922894	−	1.59850i	−0.127981	−	0.991777i	$-0.540850\pi$
$278$	−5.04185	+	8.73273i	−0.302390	+	0.523755i
$279$		0			0
$280$	9.52693	−	0.966257i	0.569343	−	0.0577449i
$281$		−	7.92455i		−	0.472739i	−0.971663	−	0.236369i	$-0.924042\pi$
$281$		−	7.92455i		−	0.472739i	0.971663	−	0.236369i	$-0.0759576\pi$
$282$		0			0
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	−0.173383	−	0.984855i	$-0.555470\pi$
$283$	9.97303	−	5.75793i	0.592835	−	0.342273i	0.766218	+	0.642581i	$0.222136\pi$
$284$	0.403817	−	0.233144i	0.0239621	−	0.0138345i
$285$		0			0
$286$			6.83042i			0.403891i
$287$	−12.2347	+	8.82115i	−0.722193	+	0.520696i
$288$		0			0
$289$	−10.5603	+	18.2909i	−0.621192	+	1.07594i
$290$	−10.5434	−	18.2616i	−0.619127	−	1.07236i
$291$		0			0
$292$	−3.65022	−	2.10746i	−0.213613	−	0.123330i
$293$	−5.01875			−0.293198			−0.146599	−	0.989196i	$-0.546833\pi$
$293$	−5.01875			−0.293198			−0.146599	+	0.989196i	$0.546833\pi$
$294$		0			0
$295$	32.5241			1.89363
$296$	6.35359	+	3.66825i	0.369295	+	0.213213i
$297$		0			0
$298$	−5.62376	−	9.74064i	−0.325776	−	0.564260i
$299$	−5.16083	+	8.93882i	−0.298458	+	0.516945i
$300$		0			0
$301$	10.2991	−	7.42561i	0.593633	−	0.428005i
$302$			4.72379i			0.271824i
$303$		0			0
$304$	−0.877353	+	0.506540i	−0.0503197	+	0.0290521i
$305$	46.1138	−	26.6238i	2.64047	−	1.52447i
$306$		0			0
$307$			17.5309i			1.00054i	0.865869	+	0.500271i	$0.166766\pi$
$307$			17.5309i			1.00054i	−0.865869	+	0.500271i	$0.833234\pi$
$308$	−5.27448	+	0.534957i	−0.300542	+	0.0304820i
$309$		0			0
$310$	−1.64622	+	2.85134i	−0.0934992	+	0.161945i
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	0.999938	−	0.0110959i	$-0.00353200\pi$
$311$	8.64759	+	14.9781i	0.490360	+	0.849328i	−0.509579	+	0.860424i	$0.670199\pi$
$312$		0			0
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	0.263419	−	0.964681i	$-0.415150\pi$
$313$	−7.78988	−	4.49749i	−0.440310	−	0.254213i	−0.703729	+	0.710468i	$0.748483\pi$
$314$	−3.06972			−0.173234
$315$		0			0
$316$	−3.82533			−0.215192
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	0.654457	−	0.756099i	$-0.272897\pi$
$317$	5.82002	+	3.36019i	0.326885	+	0.188727i	−0.327572	+	0.944826i	$0.606230\pi$
$318$		0			0
$319$	5.83721	+	10.1103i	0.326821	+	0.566071i
$320$	−1.80966	+	3.13442i	−0.101163	+	0.175219i
$321$		0			0
$322$	−7.30679	−	3.28513i	−0.407191	−	0.183073i
$323$			6.25494i			0.348034i
$324$		0			0
$325$	−23.9100	+	13.8045i	−1.32629	+	0.765734i
$326$	−2.48873	+	1.43687i	−0.137838	+	0.0795807i
$327$		0			0
$328$		−	5.70089i		−	0.314779i
$329$	0.595406	+	5.87048i	0.0328258	+	0.323650i
$330$		0			0
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	−0.483858	−	0.875146i	$-0.660765\pi$
$331$	9.38725	−	16.2592i	0.515970	−	0.893686i	0.999828	−	0.0185396i	$-0.00590167\pi$
$332$	−4.00481	−	6.93654i	−0.219793	−	0.380692i
$333$		0			0
$334$	1.26529	+	0.730517i	0.0692338	+	0.0399721i
$335$	30.0997			1.64452
$336$		0			0
$337$	−4.84575			−0.263965			−0.131982	−	0.991252i	$-0.542134\pi$
$337$	−4.84575			−0.263965			−0.131982	+	0.991252i	$0.542134\pi$
$338$	1.19552	+	0.690233i	0.0650276	+	0.0375437i
$339$		0			0
$340$	11.1732	+	19.3525i	0.605949	+	1.04954i
$341$	0.911413	−	1.57861i	0.0493558	−	0.0854868i
$342$		0			0
$343$	−5.53030	−	17.6753i	−0.298608	−	0.954376i
$344$			4.79899i			0.258744i
$345$		0			0
$346$	−2.65940	+	1.53541i	−0.142970	+	0.0825440i
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	−0.0354887	−	0.999370i	$-0.511299\pi$
$347$	15.1305	−	8.73559i	0.812247	−	0.468951i	0.847736	+	0.530419i	$0.177965\pi$
$348$		0			0
$349$			23.8258i			1.27537i	0.770299	+	0.637683i	$0.220107\pi$
$349$			23.8258i			1.27537i	−0.770299	+	0.637683i	$0.779893\pi$
$350$	−12.5325	−	17.3823i	−0.669890	−	0.929122i
$351$		0			0
$352$	1.00190	−	1.73534i	0.0534013	−	0.0924938i
$353$	−5.02061	−	8.69596i	−0.267220	−	0.462839i	0.700923	−	0.713237i	$-0.252772\pi$
$353$	−5.02061	−	8.69596i	−0.267220	−	0.462839i	−0.968143	+	0.250398i	$0.919438\pi$
$354$		0			0
$355$	−1.46154	−	0.843820i	−0.0775705	−	0.0447853i
$356$	4.78647			0.253683
$357$		0			0
$358$	−19.3193			−1.02106
$359$	10.5353	+	6.08254i	0.556030	+	0.321024i	0.751550	−	0.659676i	$-0.229306\pi$
$359$	10.5353	+	6.08254i	0.556030	+	0.321024i	−0.195521	+	0.980700i	$0.562640\pi$
$360$		0			0
$361$	−8.98683	−	15.5657i	−0.472991	−	0.819245i
$362$	3.94659	−	6.83569i	0.207428	−	0.359276i
$363$		0			0
$364$	3.69821	−	8.22557i	0.193839	−	0.431137i
$365$			15.2551i			0.798489i
$366$		0			0
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	−0.579813	−	0.814749i	$-0.696874\pi$
$367$	−3.14420	+	1.81531i	−0.164126	+	0.0947582i	0.415687	+	0.909508i	$0.363541\pi$
$368$	2.62232	−	1.51400i	0.136698	−	0.0789225i
$369$		0			0
$370$		−	26.5531i		−	1.38043i
$371$	−9.49700	+	21.1233i	−0.493060	+	1.09666i
$372$		0			0
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	−0.928321	−	0.371779i	$-0.878748\pi$
$373$	−2.74616	+	4.75648i	−0.142191	+	0.246281i	0.786131	+	0.618060i	$0.212081\pi$
$374$	−6.18590	−	10.7143i	−0.319865	−	0.554023i
$375$		0			0
$376$	−1.93143	−	1.11511i	−0.0996057	−	0.0575074i
$377$	−19.8599			−1.02284
$378$		0			0
$379$	−15.5960			−0.801112			−0.400556	−	0.916272i	$-0.631183\pi$
$379$	−15.5960			−0.801112			−0.400556	+	0.916272i	$0.631183\pi$
$380$	3.17542	+	1.83333i	0.162896	+	0.0940478i
$381$		0			0
$382$	−6.65211	−	11.5218i	−0.340352	−	0.589506i
$383$	−4.71534	+	8.16720i	−0.240942	+	0.417324i	−0.960983	−	0.276607i	$-0.910790\pi$
$383$	−4.71534	+	8.16720i	−0.240942	+	0.417324i	0.720041	+	0.693932i	$0.244123\pi$
$384$		0			0
$385$	11.2218	+	15.5644i	0.571915	+	0.793233i
$386$		−	6.53573i		−	0.332660i
$387$		0			0
$388$	10.1835	−	5.87944i	0.516989	−	0.298483i
$389$	5.56142	−	3.21089i	0.281975	−	0.162798i	−0.352342	−	0.935871i	$-0.614615\pi$
$389$	5.56142	−	3.21089i	0.281975	−	0.162798i	0.634317	+	0.773073i	$0.281281\pi$
$390$		0			0
$391$		−	18.6954i		−	0.945466i
$392$	6.64146	+	2.21155i	0.335445	+	0.111700i
$393$		0			0
$394$	−2.22125	+	3.84732i	−0.111905	+	0.193825i
$395$	6.92255	+	11.9902i	0.348311	+	0.603293i
$396$		0			0
$397$	5.99750	+	3.46266i	0.301006	+	0.173786i	0.642895	−	0.765955i	$-0.277733\pi$
$397$	5.99750	+	3.46266i	0.301006	+	0.173786i	−0.341889	+	0.939740i	$0.611067\pi$
$398$	11.5108			0.576986
$399$		0			0
$400$	8.09945			0.404972
$401$	−9.16848	−	5.29343i	−0.457852	−	0.264341i	0.253289	−	0.967391i	$-0.418488\pi$
$401$	−9.16848	−	5.29343i	−0.457852	−	0.264341i	−0.711141	+	0.703050i	$0.751821\pi$
$402$		0			0
$403$	1.55045	+	2.68545i	0.0772332	+	0.133772i
$404$	−6.44610	+	11.1650i	−0.320705	+	0.555478i
$405$		0			0
$406$	−1.55542	−	15.3359i	−0.0771943	−	0.761107i
$407$			14.7008i			0.728693i
$408$		0			0
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	−0.678741	−	0.734378i	$-0.737474\pi$
$409$	−7.72792	+	4.46172i	−0.382121	+	0.220618i	0.296620	+	0.954996i	$0.404141\pi$
$410$	−17.8690	+	10.3167i	−0.882486	+	0.509504i
$411$		0			0
$412$		−	10.7588i		−	0.530048i
$413$	21.6846	+	9.74937i	1.06703	+	0.479735i
$414$		0			0
$415$	−14.4947	+	25.1055i	−0.711516	+	1.23238i
$416$	1.70437	+	2.95206i	0.0835637	+	0.144737i
$417$		0			0
$418$	−1.75804	−	1.01500i	−0.0859883	−	0.0496454i
$419$	34.3848			1.67981			0.839903	−	0.542737i	$-0.182612\pi$
$419$	34.3848			1.67981			0.839903	+	0.542737i	$0.182612\pi$
$420$		0			0
$421$	35.5680			1.73348			0.866739	−	0.498762i	$-0.166212\pi$
$421$	35.5680			1.73348			0.866739	+	0.498762i	$0.166212\pi$
$422$	−19.5731	−	11.3005i	−0.952803	−	0.550101i
$423$		0			0
$424$	−4.37683	−	7.58088i	−0.212557	−	0.368160i
$425$	25.0037	−	43.3077i	1.21286	−	2.10073i
$426$		0			0
$427$	38.7258	−	3.92771i	1.87407	−	0.190075i
$428$			2.63967i			0.127593i
$429$		0			0
$430$	15.0420	−	8.68453i	0.725392	−	0.418805i
$431$	26.7338	−	15.4348i	1.28772	−	0.743466i	0.309474	−	0.950908i	$-0.399847\pi$
$431$	26.7338	−	15.4348i	1.28772	−	0.743466i	0.978247	+	0.207442i	$0.0665138\pi$
$432$		0			0
$433$			23.2463i			1.11715i	0.829455	+	0.558574i	$0.188651\pi$
$433$			23.2463i			1.11715i	−0.829455	+	0.558574i	$0.811349\pi$
$434$	−1.95229	+	1.40758i	−0.0937127	+	0.0675662i
$435$		0			0
$436$	−4.51768	+	7.82484i	−0.216357	+	0.374742i
$437$	−1.53380	−	2.65662i	−0.0733716	−	0.127083i
$438$		0			0
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.0367744	−	0.999324i	$-0.511708\pi$
$439$	−19.2887	−	11.1364i	−0.920601	−	0.531509i	−0.883827	+	0.467814i	$0.845042\pi$
$440$	−7.25237			−0.345743
$441$		0			0
$442$	21.0462			1.00107
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	0.0820566	−	0.996628i	$-0.473851\pi$
$443$	−15.5756	−	8.99259i	−0.740020	−	0.427251i	−0.822077	+	0.569377i	$0.807185\pi$
$444$		0			0
$445$	−8.66188	−	15.0028i	−0.410612	−	0.711202i
$446$	−9.41045	+	16.2994i	−0.445598	+	0.771798i
$447$		0			0
$448$	−2.14611	+	1.54733i	−0.101394	+	0.0731044i
$449$		−	9.44363i		−	0.445673i	−0.974856	−	0.222836i	$-0.928468\pi$
$449$		−	9.44363i		−	0.445673i	0.974856	−	0.222836i	$-0.0715315\pi$
$450$		0			0
$451$	9.89297	−	5.71171i	0.465842	−	0.268954i
$452$	1.46411	−	0.845306i	0.0688661	−	0.0397599i
$453$		0			0
$454$			14.6133i			0.685837i
$455$	−32.4749	+	3.29372i	−1.52245	+	0.154412i
$456$		0			0
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	−0.843649	−	0.536896i	$-0.819597\pi$
$457$	0.922251	−	1.59739i	0.0431411	−	0.0747225i	0.886790	+	0.462173i	$0.152930\pi$
$458$	−1.18959	−	2.06044i	−0.0555861	−	0.0962779i
$459$		0			0
$460$	−9.49100	−	5.47963i	−0.442520	−	0.255489i
$461$	−36.3739			−1.69410			−0.847050	−	0.531513i	$-0.821624\pi$
$461$	−36.3739			−1.69410			−0.847050	+	0.531513i	$0.821624\pi$
$462$		0			0
$463$	31.9660			1.48559			0.742794	−	0.669520i	$-0.233500\pi$
$463$	31.9660			1.48559			0.742794	+	0.669520i	$0.233500\pi$
$464$	5.04560	+	2.91308i	0.234236	+	0.135236i
$465$		0			0
$466$	−5.21619	−	9.03470i	−0.241635	−	0.418525i
$467$	−12.2206	+	21.1666i	−0.565500	+	0.979475i	0.431503	+	0.902112i	$0.357983\pi$
$467$	−12.2206	+	21.1666i	−0.565500	+	0.979475i	−0.997003	+	0.0773632i	$0.975350\pi$
$468$		0			0
$469$	20.0682	+	9.02263i	0.926662	+	0.416627i
$470$			8.07186i			0.372327i
$471$		0			0
$472$	−7.78233	+	4.49313i	−0.358211	+	0.206813i
$473$	−8.32786	+	4.80809i	−0.382916	+	0.221076i
$474$		0			0
$475$		−	8.20539i		−	0.376489i
$476$	1.64833	+	16.2520i	0.0755513	+	0.744908i
$477$		0			0
$478$	−11.8917	+	20.5971i	−0.543916	+	0.942090i
$479$	−5.48032	−	9.49220i	−0.250402	−	0.433710i	0.713234	−	0.700926i	$-0.247230\pi$
$479$	−5.48032	−	9.49220i	−0.250402	−	0.433710i	−0.963637	+	0.267216i	$0.913896\pi$
$480$		0			0
$481$	−21.6578	−	12.5041i	−0.987509	−	0.570139i
$482$	−28.6487			−1.30491
$483$		0			0
$484$	−6.98481			−0.317491
$485$	−36.8573	−	21.2796i	−1.67360	−	0.966255i
$486$		0			0
$487$	−16.8087	−	29.1136i	−0.761677	−	1.31926i	−0.941986	−	0.335653i	$-0.891043\pi$
$487$	−16.8087	−	29.1136i	−0.761677	−	1.31926i	0.180309	−	0.983610i	$-0.442290\pi$
$488$	−7.35603	+	12.7410i	−0.332992	+	0.576759i
$489$		0			0
$490$	−5.08685	−	24.8193i	−0.229801	−	1.12122i
$491$		−	22.7353i		−	1.02603i	−0.858380	−	0.513015i	$-0.828529\pi$
$491$		−	22.7353i		−	1.02603i	0.858380	−	0.513015i	$-0.171471\pi$
$492$		0			0
$493$	31.1525	−	17.9859i	1.40304	−	0.810043i
$494$	2.99067	−	1.72667i	0.134557	−	0.0776863i
$495$		0			0
$496$		−	0.909687i		−	0.0408462i
$497$	−0.721500	−	1.00070i	−0.0323637	−	0.0448876i
$498$		0			0
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	−0.997456	−	0.0712820i	$-0.977291\pi$
$499$	−9.76175	+	16.9079i	−0.436996	+	0.756899i	0.560460	+	0.828181i	$0.310624\pi$
$500$	−5.60894	−	9.71496i	−0.250839	−	0.434466i
$501$		0			0
$502$	9.55238	+	5.51507i	0.426343	+	0.246149i
$503$	13.6867			0.610262			0.305131	−	0.952310i	$-0.401300\pi$
$503$	13.6867			0.610262			0.305131	+	0.952310i	$0.401300\pi$
$504$		0			0
$505$	46.6609			2.07638
$506$	5.25459	+	3.03374i	0.233595	+	0.134866i
$507$		0			0
$508$	8.96458	+	15.5271i	0.397739	+	0.688904i
$509$	1.14583	−	1.98464i	0.0507881	−	0.0879675i	−0.839514	−	0.543338i	$-0.817160\pi$
$509$	1.14583	−	1.98464i	0.0507881	−	0.0879675i	0.890302	+	0.455371i	$0.150493\pi$
$510$		0			0
$511$	−4.57284	+	10.1709i	−0.202291	+	0.449935i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	13.0751	−	7.54890i	0.576717	−	0.332968i
$515$	−33.7226	+	19.4698i	−1.48600	+	0.857940i
$516$		0			0
$517$		−	4.46890i		−	0.196542i
$518$	7.95950	−	17.7035i	0.349720	−	0.777849i
$519$		0			0
$520$	6.16866	−	10.6844i	0.270514	−	0.468543i
$521$	−8.54102	−	14.7935i	−0.374189	−	0.648114i	0.616017	−	0.787733i	$-0.288745\pi$
$521$	−8.54102	−	14.7935i	−0.374189	−	0.648114i	−0.990205	+	0.139619i	$0.955412\pi$
$522$		0			0
$523$	35.7462	+	20.6381i	1.56307	+	0.902440i	0.996944	+	0.0781229i	$0.0248927\pi$
$523$	35.7462	+	20.6381i	1.56307	+	0.902440i	0.566128	+	0.824317i	$0.308441\pi$
$524$	−17.3313			−0.757123
$525$		0			0
$526$	19.6385			0.856280
$527$	−4.86410	−	2.80829i	−0.211883	−	0.122331i
$528$		0			0
$529$	−6.91563	−	11.9782i	−0.300679	−	0.520792i
$530$	−15.8411	+	27.4376i	−0.688094	+	1.19181i
$531$		0			0
$532$	1.56757	+	2.17418i	0.0679627	+	0.0942626i
$533$			19.4329i			0.841731i
$534$		0			0
$535$	8.27382	−	4.77689i	0.357708	−	0.206523i
$536$	−7.20222	+	4.15821i	−0.311089	+	0.179607i
$537$		0			0
$538$		−	0.491005i		−	0.0211687i
$539$	2.81628	+	13.7409i	0.121306	+	0.591864i
$540$		0			0
$541$	22.7197	−	39.3516i	0.976795	−	1.69186i	0.302915	−	0.953018i	$-0.402040\pi$
$541$	22.7197	−	39.3516i	0.976795	−	1.69186i	0.673880	−	0.738841i	$-0.264627\pi$
$542$	−7.03945	−	12.1927i	−0.302370	−	0.523721i
$543$		0			0
$544$	−5.34700	−	3.08709i	−0.229251	−	0.132358i
$545$	32.7018			1.40079
$546$		0			0
$547$	−30.2191			−1.29207			−0.646037	−	0.763306i	$-0.723575\pi$
$547$	−30.2191			−1.29207			−0.646037	+	0.763306i	$0.723575\pi$
$548$	0.000558693	0	0.000322562i	2.38662e−5	0	1.37791e-5i
$549$		0			0
$550$	8.11481	+	14.0553i	0.346017	+	0.599319i
$551$	2.95118	−	5.11160i	0.125725	−	0.217761i
$552$		0			0
$553$	1.02126	+	10.0692i	0.0434283	+	0.428187i
$554$		−	30.7200i		−	1.30517i
$555$		0			0
$556$	−8.73273	+	5.04185i	−0.370350	+	0.213822i
$557$	−22.0154	+	12.7106i	−0.932822	+	0.538565i	−0.887703	−	0.460417i	$-0.847700\pi$
$557$	−22.0154	+	12.7106i	−0.932822	+	0.538565i	−0.0451189	+	0.998982i	$0.514367\pi$
$558$		0			0
$559$		−	16.3585i		−	0.691892i
$560$	8.73370	+	3.92666i	0.369066	+	0.165932i
$561$		0			0
$562$	3.96227	−	6.86286i	0.167138	−	0.289492i
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	0.894839	−	0.446390i	$-0.147290\pi$
$563$	1.44346	+	2.50015i	0.0608346	+	0.105369i	−0.834004	+	0.551758i	$0.813957\pi$
$564$		0			0
$565$	−5.29909	−	3.05943i	−0.222934	−	0.128711i
$566$	11.5159			0.484048
$567$		0			0
$568$	0.466287			0.0195650
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.987445	+	0.157963i	$0.0504927\pi$
$569$	38.5945	+	22.2826i	1.61797	+	0.934134i	0.630523	+	0.776171i	$0.282841\pi$
$570$		0			0
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	0.926216	−	0.376992i	$-0.123042\pi$
$571$	3.26470	+	5.65462i	0.136623	+	0.236638i	−0.789593	+	0.613631i	$0.789708\pi$
$572$	−3.41521	+	5.91532i	−0.142797	+	0.247332i
$573$		0			0
$574$	−15.0062	+	1.52198i	−0.626345	+	0.0635262i
$575$			24.5251i			1.02277i
$576$		0			0
$577$	1.17720	−	0.679658i	0.0490076	−	0.0282945i	−0.475296	−	0.879826i	$-0.657659\pi$
$577$	1.17720	−	0.679658i	0.0490076	−	0.0282945i	0.524304	+	0.851531i	$0.324326\pi$
$578$	−18.2909	+	10.5603i	−0.760802	+	0.439249i
$579$		0			0
$580$		−	21.0867i		−	0.875578i
$581$	−17.1895	+	12.3935i	−0.713141	+	0.514170i
$582$		0			0
$583$	8.77026	−	15.1905i	0.363227	−	0.629128i
$584$	−2.10746	−	3.65022i	−0.0872072	−	0.151047i
$585$		0			0
$586$	−4.34636	−	2.50937i	−0.179547	−	0.103661i
$587$	44.4051			1.83279			0.916397	−	0.400270i	$-0.131084\pi$
$587$	44.4051			1.83279			0.916397	+	0.400270i	$0.131084\pi$
$588$		0			0
$589$	−0.921586			−0.0379733
$590$	28.1667	+	16.2621i	1.15961	+	0.669499i
$591$		0			0
$592$	3.66825	+	6.35359i	0.150764	+	0.261131i
$593$	−7.17564	+	12.4286i	−0.294668	+	0.510380i	−0.974908	−	0.222610i	$-0.928542\pi$
$593$	−7.17564	+	12.4286i	−0.294668	+	0.510380i	0.680240	+	0.732990i	$0.261876\pi$
$594$		0			0
$595$	47.9576	−	34.5771i	1.96607	−	1.41752i
$596$		−	11.2475i		−	0.460716i
$597$		0			0
$598$	−8.93882	+	5.16083i	−0.365535	+	0.211042i
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	−0.436746	−	0.899585i	$-0.643869\pi$
$599$	3.03349	−	1.75139i	0.123945	−	0.0715597i	0.560691	+	0.828025i	$0.310536\pi$
$600$		0			0
$601$			17.5337i			0.715214i	0.933872	+	0.357607i	$0.116407\pi$
$601$			17.5337i			0.715214i	−0.933872	+	0.357607i	$0.883593\pi$
$602$	12.6321	−	1.28120i	0.514847	−	0.0522177i
$603$		0			0
$604$	−2.36189	+	4.09092i	−0.0961041	+	0.166457i
$605$	12.6401	+	21.8933i	0.513894	+	0.890090i
$606$		0			0
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	0.498465	−	0.866910i	$-0.333897\pi$
$607$	−0.0755923	−	0.0436432i	−0.00306820	−	0.00177142i	−0.501533	+	0.865138i	$0.667231\pi$
$608$	−1.01308			−0.0410858
$609$		0			0
$610$	53.2476			2.15593
$611$	6.58373	+	3.80112i	0.266349	+	0.153777i
$612$		0			0
$613$	12.5352	+	21.7116i	0.506292	+	0.876924i	0.999973	+	0.00728071i	$0.00231754\pi$
$613$	12.5352	+	21.7116i	0.506292	+	0.876924i	−0.493681	+	0.869643i	$0.664349\pi$
$614$	−8.76545	+	15.1822i	−0.353745	+	0.612704i
$615$		0			0
$616$	−4.83532	−	2.17395i	−0.194820	−	0.0875911i
$617$		−	12.2820i		−	0.494455i	−0.968957	−	0.247228i	$-0.920480\pi$
$617$		−	12.2820i		−	0.494455i	0.968957	−	0.247228i	$-0.0795196\pi$
$618$		0			0
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	−0.103028	−	0.994678i	$-0.532853\pi$
$619$	17.5869	−	10.1538i	0.706875	−	0.408115i	0.809903	+	0.586564i	$0.199520\pi$
$620$	−2.85134	+	1.64622i	−0.114513	+	0.0661139i
$621$		0			0
$622$			17.2952i			0.693474i
$623$	−1.27786	−	12.5992i	−0.0511962	−	0.504776i
$624$		0			0
$625$	−0.0518970	+	0.0898882i	−0.00207588	+	0.00359553i
$626$	−4.49749	−	7.78988i	−0.179756	−	0.311346i
$627$		0			0
$628$	−2.65845	−	1.53486i	−0.106084	−	0.0612475i
$629$	45.2969			1.80610
$630$		0			0
$631$	−45.9665			−1.82990			−0.914950	−	0.403568i	$-0.867770\pi$
$631$	−45.9665			−1.82990			−0.914950	+	0.403568i	$0.867770\pi$
$632$	−3.31284	−	1.91267i	−0.131778	−	0.0760818i
$633$		0			0
$634$	3.36019	+	5.82002i	0.133450	+	0.231143i
$635$	32.4456	−	56.1975i	1.28757	−	2.23013i
$636$		0			0
$637$	−22.6390	−	7.53861i	−0.896992	−	0.298690i
$638$			11.6744i			0.462195i
$639$		0			0
$640$	−3.13442	+	1.80966i	−0.123899	+	0.0715330i
$641$	−27.4104	+	15.8254i	−1.08265	+	0.625067i	−0.931609	−	0.363461i	$-0.881595\pi$
$641$	−27.4104	+	15.8254i	−1.08265	+	0.625067i	−0.151038	+	0.988528i	$0.548262\pi$
$642$		0			0
$643$			11.5592i			0.455851i	0.973679	+	0.227925i	$0.0731942\pi$
$643$			11.5592i			0.455851i	−0.973679	+	0.227925i	$0.926806\pi$
$644$	−4.68530	−	6.49840i	−0.184627	−	0.256073i
$645$		0			0
$646$	−3.12747	+	5.41694i	−0.123049	+	0.213127i
$647$	13.0365	+	22.5799i	0.512519	+	0.887708i	0.999895	+	0.0145160i	$0.00462076\pi$
$647$	13.0365	+	22.5799i	0.512519	+	0.887708i	−0.487376	+	0.873192i	$0.662046\pi$
$648$		0			0
$649$	−15.5942	−	9.00332i	−0.612126	−	0.353411i
$650$	−27.6089			−1.08291
$651$		0			0
$652$	−2.87373			−0.112544
$653$	16.3952	+	9.46576i	0.641593	+	0.370424i	0.785228	−	0.619207i	$-0.212546\pi$
$653$	16.3952	+	9.46576i	0.641593	+	0.370424i	−0.143635	+	0.989631i	$0.545879\pi$
$654$		0			0
$655$	31.3638	+	54.3237i	1.22549	+	2.12260i
$656$	2.85045	−	4.93712i	0.111291	−	0.192762i
$657$		0			0
$658$	−2.41961	+	5.38169i	−0.0943260	+	0.209800i
$659$		−	26.9632i		−	1.05034i	−0.850998	−	0.525168i	$-0.824002\pi$
$659$		−	26.9632i		−	1.05034i	0.850998	−	0.525168i	$-0.175998\pi$
$660$		0			0
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.866733	−	0.498772i	$-0.833785\pi$
$661$	−22.3201	+	12.8865i	−0.868151	+	0.501227i	−0.00141768	+	0.999999i	$0.500451\pi$
$662$	16.2592	−	9.38725i	0.631931	−	0.364846i
$663$		0			0
$664$		−	8.00963i		−	0.310834i
$665$	3.97803	−	8.84793i	0.154261	−	0.343108i
$666$		0			0
$667$	−8.82079	+	15.2780i	−0.341542	+	0.591568i
$668$	0.730517	+	1.26529i	0.0282646	+	0.0489557i
$669$		0			0
$670$	26.0671	+	15.0499i	1.00706	+	0.581427i
$671$	−29.4800			−1.13806
$672$		0			0
$673$	25.9216			0.999203			0.499601	−	0.866255i	$-0.333480\pi$
$673$	25.9216			0.999203			0.499601	+	0.866255i	$0.333480\pi$
$674$	−4.19654	−	2.42287i	−0.161645	−	0.0933256i
$675$		0			0
$676$	0.690233	+	1.19552i	0.0265474	+	0.0459815i
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	−0.712161	−	0.702016i	$-0.752283\pi$
$677$	6.55382	−	11.3515i	0.251884	−	0.436275i	0.964044	+	0.265741i	$0.0856166\pi$
$678$		0			0
$679$	−18.1949	−	25.2358i	−0.698254	−	0.968462i
$680$			22.3463i			0.856942i
$681$		0			0
$682$	1.57861	−	0.911413i	0.0604483	−	0.0348998i
$683$	−25.6910	+	14.8327i	−0.983038	+	0.567557i	−0.903186	−	0.429249i	$-0.858778\pi$
$683$	−25.6910	+	14.8327i	−0.983038	+	0.567557i	−0.0798523	+	0.996807i	$0.525445\pi$
$684$		0			0
$685$		−	0.00233490i		−	8.92121e-5i
$686$	4.04826	−	18.0724i	0.154563	−	0.690007i
$687$		0			0
$688$	−2.39949	+	4.15605i	−0.0914799	+	0.158448i
$689$	14.9195	+	25.8413i	0.568387	+	0.984475i
$690$		0			0
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.997369	−	0.0724857i	$-0.976907\pi$
$691$	−40.9767	−	23.6579i	−1.55883	−	0.899990i	−0.561459	−	0.827504i	$-0.689760\pi$
$692$	−3.07081			−0.116735
$693$		0			0
$694$	17.4712			0.663197
$695$	31.6065	+	18.2480i	1.19890	+	0.692187i
$696$		0			0
$697$	−17.5992	−	30.4827i	−0.666616	−	1.15461i
$698$	−11.9129	+	20.6338i	−0.450910	+	0.780999i
$699$		0			0
$700$	−2.16233	−	21.3197i	−0.0817283	−	0.805811i
$701$		−	13.7742i		−	0.520244i	−0.965576	−	0.260122i	$-0.916237\pi$
$701$		−	13.7742i		−	0.520244i	0.965576	−	0.260122i	$-0.0837627\pi$
$702$		0			0
$703$	6.43670	−	3.71623i	0.242765	−	0.140160i
$704$	1.73534	−	1.00190i	0.0654030	−	0.0377604i
$705$		0			0
$706$		−	10.0412i		−	0.377907i
$707$	31.1099	+	13.9870i	1.17001	+	0.526035i
$708$		0			0
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	−0.0767981	−	0.997047i	$-0.524470\pi$
$709$	21.9691	−	38.0517i	0.825069	−	1.42906i	0.901867	−	0.432014i	$-0.142197\pi$
$710$	−0.843820	−	1.46154i	−0.0316680	−	0.0548506i
$711$		0			0
$712$	4.14521	+	2.39324i	0.155348	+	0.0896903i
$713$	2.75453			0.103158
$714$		0			0
$715$	24.7215			0.924530
$716$	−16.7310	−	9.65966i	−0.625268	−	0.360998i
$717$		0			0
$718$	6.08254	+	10.5353i	0.226998	+	0.393173i
$719$	14.7930	−	25.6223i	0.551687	−	0.955549i	−0.446466	−	0.894800i	$-0.647318\pi$
$719$	14.7930	−	25.6223i	0.551687	−	0.955549i	0.998153	−	0.0607489i	$-0.0193489\pi$
$720$		0			0
$721$	−28.3198	+	2.87230i	−1.05469	+	0.106970i
$722$		−	17.9737i		−	0.668911i
$723$		0			0
$724$	6.83569	−	3.94659i	0.254046	−	0.146674i
$725$	−40.8666	+	23.5943i	−1.51775	+	0.876271i
$726$		0			0
$727$			11.6907i			0.433584i	0.976218	+	0.216792i	$0.0695593\pi$
$727$			11.6907i			0.433584i	−0.976218	+	0.216792i	$0.930441\pi$
$728$	7.31553	−	5.27445i	0.271132	−	0.195484i
$729$		0			0
$730$	−7.62756	+	13.2113i	−0.282308	+	0.488973i
$731$	14.8149	+	25.6602i	0.547949	+	0.949076i
$732$		0			0
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.924858	−	0.380312i	$-0.124183\pi$
$733$	28.6423	+	16.5366i	1.05793	+	0.610795i	0.133070	+	0.991107i	$0.457517\pi$
$734$	−3.63061			−0.134008
$735$		0			0
$736$	3.02799			0.111613
$737$	−14.4318	−	8.33219i	−0.531601	−	0.306920i
$738$		0			0
$739$	−21.7528	−	37.6770i	−0.800190	−	1.38597i	−0.919491	−	0.393111i	$-0.871399\pi$
$739$	−21.7528	−	37.6770i	−0.800190	−	1.38597i	0.119301	−	0.992858i	$-0.461935\pi$
$740$	13.2765	−	22.9957i	0.488056	−	0.845337i
$741$		0			0
$742$	−18.7863	+	13.5448i	−0.689666	+	0.497244i
$743$			20.8084i			0.763386i	0.924289	+	0.381693i	$0.124659\pi$
$743$			20.8084i			0.763386i	−0.924289	+	0.381693i	$0.875341\pi$
$744$		0			0
$745$	−35.2544	+	20.3542i	−1.29162	+	0.745719i
$746$	−4.75648	+	2.74616i	−0.174147	+	0.100544i
$747$		0			0
$748$		−	12.3718i		−	0.452358i
$749$	6.94825	−	0.704717i	0.253884	−	0.0257498i
$750$		0			0
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	−0.229788	−	0.973241i	$-0.573803\pi$
$751$	19.9492	−	34.5531i	0.727957	−	1.26086i	0.957745	−	0.287618i	$-0.0928634\pi$
$752$	−1.11511	−	1.93143i	−0.0406638	−	0.0704318i
$753$		0			0
$754$	−17.1992	−	9.92994i	−0.626357	−	0.361627i
$755$	17.0969			0.622219
$756$		0			0
$757$	7.45545			0.270973			0.135486	−	0.990779i	$-0.456740\pi$
$757$	7.45545			0.270973			0.135486	+	0.990779i	$0.456740\pi$
$758$	−13.5065	−	7.79800i	−0.490579	−	0.283236i
$759$		0			0
$760$	1.83333	+	3.17542i	0.0665018	+	0.115185i
$761$	4.32462	−	7.49046i	0.156767	−	0.271529i	−0.776934	−	0.629582i	$-0.783226\pi$
$761$	4.32462	−	7.49046i	0.156767	−	0.271529i	0.933701	+	0.358053i	$0.116559\pi$
$762$		0			0
$763$	21.8030	+	9.80262i	0.789322	+	0.354879i
$764$		−	13.3042i		−	0.481330i
$765$		0			0
$766$	−8.16720	+	4.71534i	−0.295093	+	0.170372i
$767$	26.5280	−	15.3159i	0.957870	−	0.553026i
$768$		0			0
$769$		−	23.6503i		−	0.852853i	−0.904522	−	0.426426i	$-0.859772\pi$
$769$		−	23.6503i		−	0.852853i	0.904522	−	0.426426i	$-0.140228\pi$
$770$	1.93618	+	19.0900i	0.0697751	+	0.687957i
$771$		0			0
$772$	3.26786	−	5.66011i	0.117613	−	0.203712i
$773$	−23.2849	−	40.3307i	−0.837501	−	1.45059i	−0.891978	−	0.452079i	$-0.850683\pi$
$773$	−23.2849	−	40.3307i	−0.837501	−	1.45059i	0.0544774	−	0.998515i	$-0.482651\pi$
$774$		0			0
$775$	6.38084	+	3.68398i	0.229207	+	0.132333i
$776$	11.7589			0.422119
$777$		0			0
$778$	6.42177			0.230232
$779$	−5.00170	−	2.88773i	−0.179204	−	0.103464i
$780$		0			0
$781$	0.467172	+	0.809166i	0.0167167	+	0.0289542i
$782$	9.34769	−	16.1907i	0.334273	−	0.578977i
$783$		0			0
$784$	4.64590	+	5.23599i	0.165925	+	0.187000i
$785$			11.1103i			0.396543i
$786$		0			0
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	−0.0728341	−	0.997344i	$-0.523204\pi$
$787$	21.1657	−	12.2200i	0.754474	−	0.435596i	0.827308	+	0.561748i	$0.189871\pi$
$788$	−3.84732	+	2.22125i	−0.137055	+	0.0791288i
$789$		0			0
$790$			13.8451i			0.492586i
$791$	−2.61593	−	3.62823i	−0.0930118	−	0.129005i
$792$		0			0
$793$	25.0748	−	43.4309i	0.890433	−	1.54228i
$794$	3.46266	+	5.99750i	0.122885	+	0.212843i
$795$		0			0
$796$	9.96868	+	5.75542i	0.353330	+	0.203995i
$797$	−49.8404			−1.76544			−0.882719	−	0.469901i	$-0.844289\pi$
$797$	−49.8404			−1.76544			−0.882719	+	0.469901i	$0.844289\pi$
$798$		0			0
$799$	−13.7698			−0.487139
$800$	7.01433	+	4.04972i	0.247994	+	0.143179i
$801$		0			0
$802$	−5.29343	−	9.16848i	−0.186917	−	0.323750i
$803$	4.22291	−	7.31430i	0.149023	−	0.258116i
$804$		0			0
$805$	−11.8899	+	26.4456i	−0.419064	+	0.932084i
$806$			3.10089i			0.109224i
$807$		0			0
$808$	−11.1650	+	6.44610i	−0.392782	+	0.226773i
$809$	10.6735	−	6.16237i	0.375262	−	0.216657i	−0.300493	−	0.953784i	$-0.597151\pi$
$809$	10.6735	−	6.16237i	0.375262	−	0.216657i	0.675755	+	0.737127i	$0.263818\pi$
$810$		0			0
$811$			24.8017i			0.870906i	0.900212	+	0.435453i	$0.143412\pi$
$811$			24.8017i			0.870906i	−0.900212	+	0.435453i	$0.856588\pi$
$812$	6.32091	−	14.0590i	0.221820	−	0.493374i
$813$		0			0
$814$	−7.35042	+	12.7313i	−0.257632	+	0.446232i
$815$	5.20047	+	9.00748i	0.182165	+	0.315518i
$816$		0			0
$817$	4.21041	+	2.43088i	0.147304	+	0.0850457i
$818$	−8.92343			−0.312000
$819$		0			0
$820$	−20.6333			−0.720547
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.159639	−	0.987175i	$-0.551033\pi$
$821$	−31.3573	−	18.1041i	−1.09438	−	0.631839i	−0.934738	+	0.355336i	$0.884366\pi$
$822$		0			0
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	0.983016	−	0.183519i	$-0.0587489\pi$
$823$	9.54093	+	16.5254i	0.332576	+	0.576038i	−0.650440	+	0.759557i	$0.725416\pi$
$824$	5.37940	−	9.31740i	0.187400	−	0.324587i
$825$		0			0
$826$	13.9047	+	19.2855i	0.483807	+	0.671028i
$827$		−	31.9013i		−	1.10932i	−0.832079	−	0.554658i	$-0.812849\pi$
$827$		−	31.9013i		−	1.10932i	0.832079	−	0.554658i	$-0.187151\pi$
$828$		0			0
$829$	13.0645	−	7.54278i	0.453748	−	0.261971i	−0.255664	−	0.966766i	$-0.582294\pi$
$829$	13.0645	−	7.54278i	0.453748	−	0.261971i	0.709412	+	0.704794i	$0.248961\pi$
$830$	−25.1055	+	14.4947i	−0.871425	+	0.503118i
$831$		0			0
$832$			3.40874i			0.118177i
$833$	42.3392	−	8.67765i	1.46696	−	0.300663i
$834$		0			0
$835$	2.64397	−	4.57950i	0.0914985	−	0.158480i
$836$	−1.01500	−	1.75804i	−0.0351046	−	0.0608029i
$837$		0			0
$838$	29.7781	+	17.1924i	1.02867	+	0.593901i
$839$	−16.3972			−0.566094			−0.283047	−	0.959106i	$-0.591345\pi$
$839$	−16.3972			−0.566094			−0.283047	+	0.959106i	$0.591345\pi$
$840$		0			0
$841$	−4.94412			−0.170487
$842$	30.8028	+	17.7840i	1.06153	+	0.612877i
$843$		0			0
$844$	−11.3005	−	19.5731i	−0.388980	−	0.673734i
$845$	2.49817	−	4.32696i	0.0859397	−	0.148852i
$846$		0			0
$847$	1.86475	+	18.3857i	0.0640735	+	0.631741i
$848$		−	8.75365i		−	0.300602i
$849$		0			0
$850$	43.3077	−	25.0037i	1.48544	−	0.857621i
$851$	−19.2386	+	11.1074i	−0.659492	+	0.380758i
$852$		0			0
$853$			19.1606i			0.656046i	0.944670	+	0.328023i	$0.106382\pi$
$853$			19.1606i			0.656046i	−0.944670	+	0.328023i	$0.893618\pi$
$854$	35.5014	+	15.9614i	1.21483	+	0.546188i
$855$		0			0
$856$	−1.31983	+	2.28602i	−0.0451110	+	0.0781345i
$857$	−8.05723	−	13.9555i	−0.275230	−	0.476712i	0.694963	−	0.719045i	$-0.255421\pi$
$857$	−8.05723	−	13.9555i	−0.275230	−	0.476712i	−0.970193	+	0.242333i	$0.922087\pi$
$858$		0			0
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	0.310384	−	0.950611i	$-0.399542\pi$
$859$	−10.4830	−	6.05238i	−0.357677	−	0.206505i	−0.668061	+	0.744106i	$0.732876\pi$
$860$	17.3691			0.592280
$861$		0			0
$862$	30.8695			1.05142
$863$	−32.2728	−	18.6327i	−1.09858	−	0.634265i	−0.162732	−	0.986670i	$-0.552031\pi$
$863$	−32.2728	−	18.6327i	−1.09858	−	0.634265i	−0.935848	+	0.352405i	$0.885364\pi$
$864$		0			0
$865$	5.55712	+	9.62522i	0.188948	+	0.327267i
$866$	−11.6232	+	20.1319i	−0.394971	+	0.684110i
$867$		0			0
$868$	−2.39452	+	0.242861i	−0.0812754	+	0.00824325i
$869$		−	7.66518i		−	0.260024i
$870$		0			0
$871$	24.5505	−	14.1743i	0.831863	−	0.480276i
$872$	−7.82484	+	4.51768i	−0.264983	+	0.152988i
$873$		0			0
$874$		−	3.06760i		−	0.103763i
$875$	−24.0748	+	17.3577i	−0.813875	+	0.586798i
$876$		0			0
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	−0.772343	−	0.635206i	$-0.780915\pi$
$877$	4.85474	−	8.40866i	0.163933	−	0.283940i	0.936276	+	0.351266i	$0.114249\pi$
$878$	−11.1364	−	19.2887i	−0.375834	−	0.650963i
$879$		0			0
$880$	−6.28073	−	3.62618i	−0.211723	−	0.122239i
$881$	2.63241			0.0886881			0.0443440	−	0.999016i	$-0.485880\pi$
$881$	2.63241			0.0886881			0.0443440	+	0.999016i	$0.485880\pi$
$882$		0			0
$883$	−36.3181			−1.22220			−0.611101	−	0.791553i	$-0.709273\pi$
$883$	−36.3181			−1.22220			−0.611101	+	0.791553i	$0.709273\pi$
$884$	18.2265	+	10.5231i	0.613025	+	0.353930i
$885$		0			0
$886$	−8.99259	−	15.5756i	−0.302112	−	0.523273i
$887$	8.18209	−	14.1718i	0.274728	−	0.475842i	−0.695339	−	0.718682i	$-0.744746\pi$
$887$	8.18209	−	14.1718i	0.274728	−	0.475842i	0.970066	+	0.242840i	$0.0780790\pi$
$888$		0			0
$889$	38.4779	−	27.7423i	1.29051	−	0.930447i
$890$		−	17.3238i		−	0.580694i
$891$		0			0
$892$	−16.2994	+	9.41045i	−0.545744	+	0.315085i
$893$	−1.95669	+	1.12969i	−0.0654781	+	0.0378038i
$894$		0			0
$895$			69.9227i			2.33726i
$896$	−2.63225	+	0.266972i	−0.0879372	+	0.00891892i
$897$		0			0
$898$	4.72182	−	8.17843i	0.157569	−	0.272918i
$899$	2.64999	+	4.58992i	0.0883822	+	0.153082i
$900$		0			0
$901$	−46.8058	−	27.0233i	−1.55933	−	0.900277i
$902$	11.4234			0.380358
$903$		0			0
$904$	1.69061			0.0562289
$905$	−24.7405	−	14.2839i	−0.822403	−	0.474814i
$906$		0			0
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	0.761974	−	0.647607i	$-0.224230\pi$
$907$	−5.41666	−	9.38192i	−0.179857	−	0.311522i	−0.941831	+	0.336086i	$0.890897\pi$
$908$	−7.30665	+	12.6555i	−0.242480	+	0.419987i
$909$		0			0
$910$	−29.7709	−	13.3850i	−0.986897	−	0.443708i
$911$		−	42.5521i		−	1.40981i	−0.709300	−	0.704907i	$-0.750989\pi$
$911$		−	42.5521i		−	1.40981i	0.709300	−	0.704907i	$-0.249011\pi$
$912$		0			0
$913$	13.8994	−	8.02482i	0.460003	−	0.265583i
$914$	1.59739	−	0.922251i	0.0528368	−	0.0305053i
$915$		0			0
$916$		−	2.37919i		−	0.0786106i
$917$	4.62699	+	45.6204i	0.152797	+	1.50652i
$918$		0			0
$919$	−12.9697	+	22.4641i	−0.427829	+	0.741022i	−0.996680	−	0.0814187i	$-0.974055\pi$
$919$	−12.9697	+	22.4641i	−0.427829	+	0.741022i	0.568851	+	0.822441i	$0.307388\pi$
$920$	−5.47963	−	9.49100i	−0.180658	−	0.312909i
$921$		0			0
$922$	−31.5007	−	18.1869i	−1.03742	−	0.598955i
$923$	−1.58945			−0.0523175
$924$		0			0
$925$	−59.4216			−1.95377
$926$	27.6834	+	15.9830i	0.909733	+	0.525234i
$927$		0			0
$928$	2.91308	+	5.04560i	0.0956265	+	0.165630i
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	−0.168760	−	0.985657i	$-0.553976\pi$
$929$	23.4456	−	40.6089i	0.769224	−	1.33234i	0.937984	−	0.346678i	$-0.112690\pi$
$930$		0			0
$931$	5.30448	−	4.70667i	0.173847	−	0.154255i
$932$		−	10.4324i		−	0.341724i
$933$		0			0
$934$	−21.1666	+	12.2206i	−0.692593	+	0.399869i
$935$	−38.7784	+	22.3887i	−1.26819	+	0.732189i
$936$		0			0
$937$			0.209357i			0.00683939i	0.999994	+	0.00341969i	$0.00108852\pi$
$937$			0.209357i			0.00683939i	−0.999994	+	0.00341969i	$0.998911\pi$
$938$	12.8682	+	17.8479i	0.420162	+	0.582755i
$939$		0			0
$940$	−4.03593	+	6.99044i	−0.131638	+	0.228003i
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	0.859622	−	0.510930i	$-0.170699\pi$
$941$	−0.388565	−	0.673014i	−0.0126669	−	0.0219396i	−0.872289	+	0.488990i	$0.837365\pi$
$942$		0			0
$943$	14.9496	+	8.63113i	0.486825	+	0.281068i
$944$	−8.98627			−0.292478
$945$		0			0
$946$	−9.61619			−0.312649
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.406791	−	0.913521i	$-0.633352\pi$
$947$	−43.1233	−	24.8972i	−1.40132	−	0.809052i	−0.994528	+	0.104470i	$0.966686\pi$
$948$		0			0
$949$	7.18378	+	12.4427i	0.233196	+	0.403906i
$950$	4.10269	−	7.10607i	0.133109	−	0.230552i
$951$		0			0
$952$	−6.69849	+	14.8988i	−0.217099	+	0.482873i
$953$		−	41.4104i		−	1.34141i	−0.741722	−	0.670707i	$-0.765991\pi$
$953$		−	41.4104i		−	1.34141i	0.741722	−	0.670707i	$-0.234009\pi$
$954$		0			0
$955$	−41.7010	+	24.0761i	−1.34941	+	0.779084i
$956$	−20.5971	+	11.8917i	−0.666158	+	0.384607i
$957$		0			0
$958$		−	10.9606i		−	0.354122i
$959$	0.000699906	−	0.00155673i	2.26012e−5	−	5.02695e-5i
$960$		0			0
$961$	−15.0862	+	26.1301i	−0.486653	+	0.842907i
$962$	−12.5041	−	21.6578i	−0.403149	−	0.698274i
$963$		0			0
$964$	−24.8105	−	14.3243i	−0.799092	−	0.461356i
$965$	−23.6549			−0.761477
$966$		0			0
$967$	−45.6056			−1.46658			−0.733289	−	0.679917i	$-0.762016\pi$
$967$	−45.6056			−1.46658			−0.733289	+	0.679917i	$0.762016\pi$
$968$	−6.04902	−	3.49240i	−0.194423	−	0.112250i
$969$		0			0
$970$	−21.2796	−	36.8573i	−0.683245	−	1.18342i
$971$	4.36733	−	7.56444i	0.140154	−	0.242754i	−0.787400	−	0.616442i	$-0.788573\pi$
$971$	4.36733	−	7.56444i	0.140154	−	0.242754i	0.927555	+	0.373688i	$0.121907\pi$
$972$		0			0
$973$	15.6028	+	21.6407i	0.500202	+	0.693768i
$974$		−	33.6175i		−	1.07717i
$975$		0			0
$976$	−12.7410	+	7.35603i	−0.407830	+	0.235461i
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	−0.279140	−	0.960250i	$-0.590049\pi$
$977$	12.9058	−	7.45114i	0.412892	−	0.238383i	0.692031	+	0.721867i	$0.256716\pi$
$978$		0			0
$979$			9.59111i			0.306533i
$980$	8.00430	−	24.0376i	0.255688	−	0.767852i
$981$		0			0
$982$	11.3676	−	19.6893i	0.362756	−	0.628312i
$983$	1.53458	+	2.65798i	0.0489456	+	0.0847763i	0.889460	−	0.457013i	$-0.151081\pi$
$983$	1.53458	+	2.65798i	0.0489456	+	0.0847763i	−0.840515	+	0.541789i	$0.817747\pi$
$984$		0			0
$985$	13.9247	+	8.03941i	0.443677	+	0.256157i
$986$	35.9718			1.14557
$987$		0			0
$988$	3.45333			0.109865
$989$	−12.5845	−	7.26565i	−0.400163	−	0.231034i
$990$		0			0
$991$	27.9075	+	48.3372i	0.886510	+	1.53548i	0.843973	+	0.536386i	$0.180211\pi$
$991$	27.9075	+	48.3372i	0.886510	+	1.53548i	0.0425375	+	0.999095i	$0.486456\pi$
$992$	0.454844	−	0.787812i	0.0144413	−	0.0250131i
$993$		0			0
$994$	−0.124486	−	1.22738i	−0.00394845	−	0.0389302i
$995$		−	41.6614i		−	1.32075i
$996$		0			0
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	−0.581664	−	0.813429i	$-0.697598\pi$
$997$	−5.30607	+	3.06346i	−0.168045	+	0.0970208i	0.413619	+	0.910450i	$0.364265\pi$
$998$	−16.9079	+	9.76175i	−0.535209	+	0.309003i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.k.b.971.8		16
3.2	odd	2		1134.2.k.a.971.1		16
7.3	odd	6		1134.2.k.a.647.1		16
9.2	odd	6		126.2.l.a.5.5	✓	16
9.4	even	3		126.2.t.a.47.2	yes	16
9.5	odd	6		378.2.t.a.89.8		16
9.7	even	3		378.2.l.a.341.4		16
21.17	even	6	inner	1134.2.k.b.647.8		16
36.7	odd	6		3024.2.ca.c.2609.7		16
36.11	even	6		1008.2.ca.c.257.8		16
36.23	even	6		3024.2.df.c.1601.7		16
36.31	odd	6		1008.2.df.c.929.5		16
63.2	odd	6		882.2.m.b.293.7		16
63.4	even	3		882.2.l.b.227.4		16
63.5	even	6		2646.2.m.b.1763.4		16
63.11	odd	6		882.2.t.a.815.3		16
63.13	odd	6		882.2.t.a.803.3		16
63.16	even	3		2646.2.m.b.881.4		16
63.20	even	6		882.2.l.b.509.8		16
63.23	odd	6		2646.2.m.a.1763.1		16
63.25	even	3		2646.2.t.b.2285.5		16
63.31	odd	6		126.2.l.a.101.1	yes	16
63.32	odd	6		2646.2.l.a.521.5		16
63.34	odd	6		2646.2.l.a.1097.1		16
63.38	even	6		126.2.t.a.59.2	yes	16
63.40	odd	6		882.2.m.b.587.7		16
63.41	even	6		2646.2.t.b.1979.5		16
63.47	even	6		882.2.m.a.293.6		16
63.52	odd	6		378.2.t.a.17.8		16
63.58	even	3		882.2.m.a.587.6		16
63.59	even	6		378.2.l.a.143.8		16
63.61	odd	6		2646.2.m.a.881.1		16
252.31	even	6		1008.2.ca.c.353.8		16
252.59	odd	6		3024.2.ca.c.2033.7		16
252.115	even	6		3024.2.df.c.17.7		16
252.227	odd	6		1008.2.df.c.689.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.5	✓	16	9.2	odd	6
126.2.l.a.101.1	yes	16	63.31	odd	6
126.2.t.a.47.2	yes	16	9.4	even	3
126.2.t.a.59.2	yes	16	63.38	even	6
378.2.l.a.143.8		16	63.59	even	6
378.2.l.a.341.4		16	9.7	even	3
378.2.t.a.17.8		16	63.52	odd	6
378.2.t.a.89.8		16	9.5	odd	6
882.2.l.b.227.4		16	63.4	even	3
882.2.l.b.509.8		16	63.20	even	6
882.2.m.a.293.6		16	63.47	even	6
882.2.m.a.587.6		16	63.58	even	3
882.2.m.b.293.7		16	63.2	odd	6
882.2.m.b.587.7		16	63.40	odd	6
882.2.t.a.803.3		16	63.13	odd	6
882.2.t.a.815.3		16	63.11	odd	6
1008.2.ca.c.257.8		16	36.11	even	6
1008.2.ca.c.353.8		16	252.31	even	6
1008.2.df.c.689.5		16	252.227	odd	6
1008.2.df.c.929.5		16	36.31	odd	6
1134.2.k.a.647.1		16	7.3	odd	6
1134.2.k.a.971.1		16	3.2	odd	2
1134.2.k.b.647.8		16	21.17	even	6	inner
1134.2.k.b.971.8		16	1.1	even	1	trivial
2646.2.l.a.521.5		16	63.32	odd	6
2646.2.l.a.1097.1		16	63.34	odd	6
2646.2.m.a.881.1		16	63.61	odd	6
2646.2.m.a.1763.1		16	63.23	odd	6
2646.2.m.b.881.4		16	63.16	even	3
2646.2.m.b.1763.4		16	63.5	even	6
2646.2.t.b.1979.5		16	63.41	even	6
2646.2.t.b.2285.5		16	63.25	even	3
3024.2.ca.c.2033.7		16	252.59	odd	6
3024.2.ca.c.2609.7		16	36.7	odd	6
3024.2.df.c.17.7		16	252.115	even	6
3024.2.df.c.1601.7		16	36.23	even	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.80966 - 3.13442i) q^{5} +(2.14611 - 1.54733i) q^{7} +1.00000i q^{8} +(3.13442 - 1.80966i) q^{10} +(-1.73534 + 1.00190i) q^{11} -3.40874i q^{13} +(2.63225 - 0.266972i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.08709 + 5.34700i) q^{17} +(0.877353 + 0.506540i) q^{19} +3.61932 q^{20} -2.00379 q^{22} +(-2.62232 - 1.51400i) q^{23} +(-4.04972 - 7.01433i) q^{25} +(1.70437 - 2.95206i) q^{26} +(2.41308 + 1.08492i) q^{28} -5.82616i q^{29} +(-0.787812 + 0.454844i) q^{31} +(-0.866025 + 0.500000i) q^{32} +6.17418i q^{34} +(-0.966257 - 9.52693i) q^{35} +(3.66825 - 6.35359i) q^{37} +(0.506540 + 0.877353i) q^{38} +(3.13442 + 1.80966i) q^{40} -5.70089 q^{41} +4.79899 q^{43} +(-1.73534 - 1.00190i) q^{44} +(-1.51400 - 2.62232i) q^{46} +(-1.11511 + 1.93143i) q^{47} +(2.21155 - 6.64146i) q^{49} -8.09945i q^{50} +(2.95206 - 1.70437i) q^{52} +(-7.58088 + 4.37683i) q^{53} +7.25237i q^{55} +(1.54733 + 2.14611i) q^{56} +(2.91308 - 5.04560i) q^{58} +(4.49313 + 7.78233i) q^{59} +(12.7410 + 7.35603i) q^{61} -0.909687 q^{62} -1.00000 q^{64} +(-10.6844 - 6.16866i) q^{65} +(4.15821 + 7.20222i) q^{67} +(-3.08709 + 5.34700i) q^{68} +(3.92666 - 8.73370i) q^{70} -0.466287i q^{71} +(-3.65022 + 2.10746i) q^{73} +(6.35359 - 3.66825i) q^{74} +1.01308i q^{76} +(-2.17395 + 4.83532i) q^{77} +(-1.91267 + 3.31284i) q^{79} +(1.80966 + 3.13442i) q^{80} +(-4.93712 - 2.85045i) q^{82} -8.00963 q^{83} +22.3463 q^{85} +(4.15605 + 2.39949i) q^{86} +(-1.00190 - 1.73534i) q^{88} +(2.39324 - 4.14521i) q^{89} +(-5.27445 - 7.31553i) q^{91} -3.02799i q^{92} +(-1.93143 + 1.11511i) q^{94} +(3.17542 - 1.83333i) q^{95} -11.7589i q^{97} +(5.23599 - 4.64590i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 4 q^{7} + 12 q^{11} - 8 q^{16} + 18 q^{17} - 6 q^{23} - 8 q^{25} - 12 q^{26} - 2 q^{28} - 6 q^{31} - 30 q^{35} - 2 q^{37} - 12 q^{41} + 4 q^{43} + 12 q^{44} + 6 q^{46} - 18 q^{47} - 2 q^{49}+ \cdots + 24 q^{98}+O(q^{100}) \) 16 * q + 8 * q^4 - 4 * q^7 + 12 * q^11 - 8 * q^16 + 18 * q^17 - 6 * q^23 - 8 * q^25 - 12 * q^26 - 2 * q^28 - 6 * q^31 - 30 * q^35 - 2 * q^37 - 12 * q^41 + 4 * q^43 + 12 * q^44 + 6 * q^46 - 18 * q^47 - 2 * q^49 + 6 * q^52 + 36 * q^53 + 6 * q^56 + 6 * q^58 + 30 * q^59 + 60 * q^61 - 36 * q^62 - 16 * q^64 - 42 * q^65 + 14 * q^67 - 18 * q^68 + 18 * q^70 + 18 * q^74 - 24 * q^77 - 16 * q^79 + 24 * q^85 + 24 * q^86 + 24 * q^89 - 12 * q^91 + 66 * q^95 + 24 * q^98

Introduction

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