LMFDB - Embedded newform 931.2.i.e.411.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [931,2,Mod(411,931)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(931, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("931.411"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			411.1
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	931.411
Dual form			931.2.i.e.521.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.18890i q^{2} +(0.500000 - 0.866025i) q^{3} -2.79129 q^{4} +2.64575i q^{5} +(-1.89564 - 1.09445i) q^{6} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +5.79129 q^{10} +(-1.39564 + 2.41733i) q^{12} +(-2.29129 + 3.96863i) q^{13} +(2.29129 + 1.32288i) q^{15} -1.79129 q^{16} +(5.29129 + 3.05493i) q^{17} +(3.79129 - 2.18890i) q^{18} +(-0.500000 + 4.33013i) q^{19} -7.38505i q^{20} +(2.29129 + 3.96863i) q^{23} +(1.50000 + 0.866025i) q^{24} -2.00000 q^{25} +(8.68693 + 5.01540i) q^{26} +5.00000 q^{27} +(-6.08258 - 3.51178i) q^{29} +(2.89564 - 5.01540i) q^{30} +7.38505i q^{32} +(6.68693 - 11.5821i) q^{34} +(-2.79129 - 4.83465i) q^{36} +(9.47822 + 1.09445i) q^{38} +(2.29129 + 3.96863i) q^{39} -4.58258 q^{40} +(-0.708712 - 1.22753i) q^{41} +(-0.708712 - 1.22753i) q^{43} +(-4.58258 + 2.64575i) q^{45} +(8.68693 - 5.01540i) q^{46} +(3.08258 - 1.77973i) q^{47} +(-0.895644 + 1.55130i) q^{48} +4.37780i q^{50} +(5.29129 - 3.05493i) q^{51} +(6.39564 - 11.0776i) q^{52} -10.4877i q^{53} -10.9445i q^{54} +(3.50000 + 2.59808i) q^{57} +(-7.68693 + 13.3142i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-6.39564 - 3.69253i) q^{60} +(12.8739 - 7.43273i) q^{61} +12.5826 q^{64} +(-10.5000 - 6.06218i) q^{65} +11.4014i q^{67} +(-14.7695 - 8.52718i) q^{68} +4.58258 q^{69} +(-3.70871 + 2.14123i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-3.87386 - 2.23658i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(1.39564 - 12.0866i) q^{76} +(8.68693 - 5.01540i) q^{78} -1.00905i q^{79} -4.73930i q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.68693 + 1.55130i) q^{82} +7.11890i q^{83} +(-8.08258 + 13.9994i) q^{85} +(-2.68693 + 1.55130i) q^{86} +(-6.08258 + 3.51178i) q^{87} +(-0.708712 - 1.22753i) q^{89} +(5.79129 + 10.0308i) q^{90} +(-6.39564 - 11.0776i) q^{92} +(-3.89564 - 6.74745i) q^{94} +(-11.4564 - 1.32288i) q^{95} +(6.39564 + 3.69253i) q^{96} +(-7.87386 - 13.6379i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{9} + 14 q^{10} - q^{12} + 2 q^{16} + 12 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{24} - 8 q^{25} + 21 q^{26} + 20 q^{27} - 6 q^{29} + 7 q^{30} + 13 q^{34} - 2 q^{36}+ \cdots - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^9 + 14 * q^10 - q^12 + 2 * q^16 + 12 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^24 - 8 * q^25 + 21 * q^26 + 20 * q^27 - 6 * q^29 + 7 * q^30 + 13 * q^34 - 2 * q^36 + 15 * q^38 - 12 * q^41 - 12 * q^43 + 21 * q^46 - 6 * q^47 + q^48 + 12 * q^51 + 21 * q^52 + 14 * q^57 - 17 * q^58 - 6 * q^59 - 21 * q^60 + 24 * q^61 + 32 * q^64 - 42 * q^65 - 27 * q^68 - 24 * q^71 - 12 * q^72 + 12 * q^73 - 4 * q^75 + q^76 + 21 * q^78 - 2 * q^81 + 3 * q^82 - 14 * q^85 + 3 * q^86 - 6 * q^87 - 12 * q^89 + 14 * q^90 - 21 * q^92 - 11 * q^94 + 21 * q^96 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	2.18890i		−	1.54779i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$		−	2.18890i		−	1.54779i	0.633316	−	0.773893i	$-0.281693\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	−2.79129			−1.39564
$5$			2.64575i			1.18322i	0.806226	+	0.591608i	$0.201507\pi$
$5$			2.64575i			1.18322i	−0.806226	+	0.591608i	$0.798493\pi$
$6$	−1.89564	−	1.09445i	−0.773893	−	0.446808i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	5.79129			1.83137
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.39564	+	2.41733i	−0.402888	+	0.697822i
$13$	−2.29129	+	3.96863i	−0.635489	+	1.10070i	0.350922	+	0.936405i	$0.385868\pi$
$13$	−2.29129	+	3.96863i	−0.635489	+	1.10070i	−0.986411	+	0.164295i	$0.947465\pi$
$14$		0			0
$15$	2.29129	+	1.32288i	0.591608	+	0.341565i
$16$	−1.79129			−0.447822
$17$	5.29129	+	3.05493i	1.28333	+	0.740928i	0.977455	−	0.211144i	$-0.0677191\pi$
$17$	5.29129	+	3.05493i	1.28333	+	0.740928i	0.305871	+	0.952073i	$0.401052\pi$
$18$	3.79129	−	2.18890i	0.893615	−	0.515929i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$19$	−0.500000	+	4.33013i	−0.114708	+	0.993399i
$20$		−	7.38505i		−	1.65135i
$21$		0			0
$22$		0			0
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	0.999675	−	0.0254855i	$-0.00811315\pi$
$23$	2.29129	+	3.96863i	0.477767	+	0.827516i	−0.521909	+	0.853001i	$0.674780\pi$
$24$	1.50000	+	0.866025i	0.306186	+	0.176777i
$25$	−2.00000			−0.400000
$26$	8.68693	+	5.01540i	1.70365	+	0.983601i
$27$	5.00000			0.962250
$28$		0			0
$29$	−6.08258	−	3.51178i	−1.12951	−	0.652121i	−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−6.08258	−	3.51178i	−1.12951	−	0.652121i	−0.943811	+	0.330487i	$0.892787\pi$
$30$	2.89564	−	5.01540i	0.528670	−	0.915683i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$			7.38505i			1.30551i
$33$		0			0
$34$	6.68693	−	11.5821i	1.14680	−	1.98631i
$35$		0			0
$36$	−2.79129	−	4.83465i	−0.465215	−	0.805775i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$	9.47822	+	1.09445i	1.53757	+	0.177543i
$39$	2.29129	+	3.96863i	0.366900	+	0.635489i
$40$	−4.58258			−0.724569
$41$	−0.708712	−	1.22753i	−0.110682	−	0.191707i	0.805363	−	0.592782i	$-0.201970\pi$
$41$	−0.708712	−	1.22753i	−0.110682	−	0.191707i	−0.916046	+	0.401074i	$0.868637\pi$
$42$		0			0
$43$	−0.708712	−	1.22753i	−0.108078	−	0.187196i	0.806914	−	0.590669i	$-0.201136\pi$
$43$	−0.708712	−	1.22753i	−0.108078	−	0.187196i	−0.914991	+	0.403473i	$0.867803\pi$
$44$		0			0
$45$	−4.58258	+	2.64575i	−0.683130	+	0.394405i
$46$	8.68693	−	5.01540i	1.28082	−	0.739481i
$47$	3.08258	−	1.77973i	0.449640	−	0.259600i	−0.258038	−	0.966135i	$-0.583076\pi$
$47$	3.08258	−	1.77973i	0.449640	−	0.259600i	0.707678	+	0.706535i	$0.249743\pi$
$48$	−0.895644	+	1.55130i	−0.129275	+	0.223911i
$49$		0			0
$50$			4.37780i			0.619115i
$51$	5.29129	−	3.05493i	0.740928	−	0.427775i
$52$	6.39564	−	11.0776i	0.886916	−	1.53618i
$53$		−	10.4877i		−	1.44059i	−0.693668	−	0.720295i	$-0.744006\pi$
$53$		−	10.4877i		−	1.44059i	0.693668	−	0.720295i	$-0.255994\pi$
$54$		−	10.9445i		−	1.48936i
$55$		0			0
$56$		0			0
$57$	3.50000	+	2.59808i	0.463586	+	0.344124i
$58$	−7.68693	+	13.3142i	−1.00934	+	1.74823i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$	−6.39564	−	3.69253i	−0.825674	−	0.476703i
$61$	12.8739	−	7.43273i	1.64833	−	0.951663i	0.670593	−	0.741825i	$-0.266040\pi$
$61$	12.8739	−	7.43273i	1.64833	−	0.951663i	0.977736	−	0.209838i	$-0.0672937\pi$
$62$		0			0
$63$		0			0
$64$	12.5826			1.57282
$65$	−10.5000	−	6.06218i	−1.30236	−	0.751921i
$66$		0			0
$67$			11.4014i			1.39290i	0.717607	+	0.696449i	$0.245238\pi$
$67$			11.4014i			1.39290i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−14.7695	−	8.52718i	−1.79107	−	1.03407i
$69$	4.58258			0.551677
$70$		0			0
$71$	−3.70871	+	2.14123i	−0.440143	+	0.254117i	−0.703658	−	0.710538i	$-0.748451\pi$
$71$	−3.70871	+	2.14123i	−0.440143	+	0.254117i	0.263515	+	0.964655i	$0.415118\pi$
$72$	−3.00000	+	1.73205i	−0.353553	+	0.204124i
$73$	−3.87386	−	2.23658i	−0.453401	−	0.261771i	0.255864	−	0.966713i	$-0.417640\pi$
$73$	−3.87386	−	2.23658i	−0.453401	−	0.261771i	−0.709266	+	0.704941i	$0.750973\pi$
$74$		0			0
$75$	−1.00000	+	1.73205i	−0.115470	+	0.200000i
$76$	1.39564	−	12.0866i	0.160091	−	1.38643i
$77$		0			0
$78$	8.68693	−	5.01540i	0.983601	−	0.567882i
$79$		−	1.00905i		−	0.113527i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$		−	1.00905i		−	0.113527i	0.998388	−	0.0567635i	$-0.0180781\pi$
$80$		−	4.73930i		−	0.529870i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.68693	+	1.55130i	−0.296722	+	0.171313i
$83$			7.11890i			0.781401i	0.920518	+	0.390701i	$0.127767\pi$
$83$			7.11890i			0.781401i	−0.920518	+	0.390701i	$0.872233\pi$
$84$		0			0
$85$	−8.08258	+	13.9994i	−0.876678	+	1.51845i
$86$	−2.68693	+	1.55130i	−0.289739	+	0.167281i
$87$	−6.08258	+	3.51178i	−0.652121	+	0.376502i
$88$		0			0
$89$	−0.708712	−	1.22753i	−0.0751233	−	0.130117i	0.826017	−	0.563646i	$-0.190602\pi$
$89$	−0.708712	−	1.22753i	−0.0751233	−	0.130117i	−0.901140	+	0.433528i	$0.857268\pi$
$90$	5.79129	+	10.0308i	0.610455	+	1.05734i
$91$		0			0
$92$	−6.39564	−	11.0776i	−0.666792	−	1.15492i
$93$		0			0
$94$	−3.89564	−	6.74745i	−0.401805	−	0.695947i
$95$	−11.4564	−	1.32288i	−1.17541	−	0.135724i
$96$	6.39564	+	3.69253i	0.652753	+	0.376867i
$97$	−7.87386	−	13.6379i	−0.799470	−	1.38472i	−0.919962	−	0.392008i	$-0.871781\pi$
$97$	−7.87386	−	13.6379i	−0.799470	−	1.38472i	0.120492	−	0.992714i	$-0.461553\pi$
$98$		0			0
$99$		0			0
$100$	5.58258			0.558258
$101$			11.2107i			1.11550i	0.830008	+	0.557751i	$0.188336\pi$
$101$			11.2107i			1.11550i	−0.830008	+	0.557751i	$0.811664\pi$
$102$	−6.68693	−	11.5821i	−0.662105	−	1.14680i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−6.87386	−	3.96863i	−0.674038	−	0.389156i
$105$		0			0
$106$	−22.9564			−2.22973
$107$	1.41742	+	0.818350i	0.137028	+	0.0791129i	0.566947	−	0.823755i	$-0.308125\pi$
$107$	1.41742	+	0.818350i	0.137028	+	0.0791129i	−0.429919	+	0.902867i	$0.641458\pi$
$108$	−13.9564			−1.34296
$109$	−12.2477	−	7.07123i	−1.17312	−	0.677301i	−0.218707	−	0.975791i	$-0.570184\pi$
$109$	−12.2477	−	7.07123i	−1.17312	−	0.677301i	−0.954413	+	0.298490i	$0.903517\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	10.5830i		−	0.995565i	−0.867302	−	0.497783i	$-0.834148\pi$
$113$		−	10.5830i		−	0.995565i	0.867302	−	0.497783i	$-0.165852\pi$
$114$	5.68693	−	7.66115i	0.532630	−	0.717533i
$115$	−10.5000	+	6.06218i	−0.979130	+	0.565301i
$116$	16.9782	+	9.80238i	1.57639	+	0.910128i
$117$	−9.16515			−0.847319
$118$	5.68693	+	3.28335i	0.523525	+	0.302257i
$119$		0			0
$120$	−2.29129	+	3.96863i	−0.209165	+	0.362284i
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−16.2695	−	28.1796i	−1.47297	−	2.55126i
$123$	−1.41742			−0.127805
$124$		0			0
$125$			7.93725i			0.709930i
$126$		0			0
$127$	12.8739	+	7.43273i	1.14237	+	0.659548i	0.947017	−	0.321185i	$-0.104081\pi$
$127$	12.8739	+	7.43273i	1.14237	+	0.659548i	0.195354	+	0.980733i	$0.437414\pi$
$128$		−	12.7719i		−	1.12889i
$129$	−1.41742			−0.124797
$130$	−13.2695	+	22.9835i	−1.16381	+	2.01578i
$131$			19.2433i			1.68129i	0.541585	+	0.840646i	$0.317824\pi$
$131$			19.2433i			1.68129i	−0.541585	+	0.840646i	$0.682176\pi$
$132$		0			0
$133$		0			0
$134$	24.9564			2.15591
$135$			13.2288i			1.13855i
$136$	−5.29129	+	9.16478i	−0.453724	+	0.785873i
$137$	21.3303			1.82237			0.911185	−	0.411997i	$-0.135168\pi$
$137$	21.3303			1.82237			0.911185	+	0.411997i	$0.135168\pi$
$138$		−	10.0308i		−	0.853879i
$139$	−1.50000	−	0.866025i	−0.127228	−	0.0734553i	0.435035	−	0.900414i	$-0.356736\pi$
$139$	−1.50000	−	0.866025i	−0.127228	−	0.0734553i	−0.562263	+	0.826958i	$0.690069\pi$
$140$		0			0
$141$		−	3.55945i		−	0.299760i
$142$	4.68693	+	8.11800i	0.393319	+	0.681248i
$143$		0			0
$144$	−1.79129	−	3.10260i	−0.149274	−	0.258550i
$145$	9.29129	−	16.0930i	0.771599	−	1.33645i
$146$	−4.89564	+	8.47950i	−0.405166	+	0.701769i
$147$		0			0
$148$		0			0
$149$	−12.1652			−0.996608			−0.498304	−	0.867002i	$-0.666044\pi$
$149$	−12.1652			−0.996608			−0.498304	+	0.867002i	$0.666044\pi$
$150$	3.79129	+	2.18890i	0.309557	+	0.178723i
$151$	19.7477	−	11.4014i	1.60705	−	0.927829i	0.617021	−	0.786947i	$-0.288339\pi$
$151$	19.7477	−	11.4014i	1.60705	−	0.927829i	0.990026	−	0.140882i	$-0.0449939\pi$
$152$	−7.50000	−	0.866025i	−0.608330	−	0.0702439i
$153$			12.2197i			0.987905i
$154$		0			0
$155$		0			0
$156$	−6.39564	−	11.0776i	−0.512061	−	0.886916i
$157$	6.87386	+	3.96863i	0.548594	+	0.316731i	0.748555	−	0.663073i	$-0.230748\pi$
$157$	6.87386	+	3.96863i	0.548594	+	0.316731i	−0.199961	+	0.979804i	$0.564081\pi$
$158$	−2.20871			−0.175716
$159$	−9.08258	−	5.24383i	−0.720295	−	0.415863i
$160$	−19.5390			−1.54469
$161$		0			0
$162$	1.89564	+	1.09445i	0.148936	+	0.0859882i
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	−0.529454	−	0.848339i	$-0.677603\pi$
$163$	6.00000	−	10.3923i	0.469956	−	0.813988i	0.999410	+	0.0343508i	$0.0109363\pi$
$164$	1.97822	+	3.42638i	0.154473	+	0.267555i
$165$		0			0
$166$	15.5826			1.20944
$167$	−2.91742	+	5.05313i	−0.225757	+	0.391023i	−0.956546	−	0.291580i	$-0.905819\pi$
$167$	−2.91742	+	5.05313i	−0.225757	+	0.391023i	0.730789	+	0.682603i	$0.239152\pi$
$168$		0			0
$169$	−4.00000	−	6.92820i	−0.307692	−	0.532939i
$170$	30.6434	+	17.6920i	2.35024	+	1.35691i
$171$	−8.00000	+	3.46410i	−0.611775	+	0.264906i
$172$	1.97822	+	3.42638i	0.150838	+	0.261259i
$173$	−7.41742			−0.563936			−0.281968	−	0.959424i	$-0.590987\pi$
$173$	−7.41742			−0.563936			−0.281968	+	0.959424i	$0.590987\pi$
$174$	7.68693	+	13.3142i	0.582745	+	1.00934i
$175$		0			0
$176$		0			0
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$	−2.68693	+	1.55130i	−0.201394	+	0.116275i
$179$	10.5826	−	6.10985i	0.790979	−	0.456672i	−0.0493282	−	0.998783i	$-0.515708\pi$
$179$	10.5826	−	6.10985i	0.790979	−	0.456672i	0.840307	+	0.542111i	$0.182375\pi$
$180$	12.7913	−	7.38505i	0.953406	−	0.550449i
$181$	4.87386	−	8.44178i	0.362271	−	0.627473i	−0.626063	−	0.779773i	$-0.715335\pi$
$181$	4.87386	−	8.44178i	0.362271	−	0.627473i	0.988334	+	0.152300i	$0.0486680\pi$
$182$		0			0
$183$		−	14.8655i		−	1.09889i
$184$	−6.87386	+	3.96863i	−0.506748	+	0.292571i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−8.60436	+	4.96773i	−0.627537	+	0.362309i
$189$		0			0
$190$	−2.89564	+	25.0770i	−0.210072	+	1.81928i
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	−0.997225	−	0.0744412i	$-0.976283\pi$
$191$	−6.00000	+	10.3923i	−0.434145	+	0.751961i	0.563081	+	0.826402i	$0.309616\pi$
$192$	6.29129	−	10.8968i	0.454035	−	0.786411i
$193$	−1.50000	−	0.866025i	−0.107972	−	0.0623379i	0.445041	−	0.895510i	$-0.353189\pi$
$193$	−1.50000	−	0.866025i	−0.107972	−	0.0623379i	−0.553014	+	0.833172i	$0.686522\pi$
$194$	−29.8521	+	17.2351i	−2.14325	+	1.23741i
$195$	−10.5000	+	6.06218i	−0.751921	+	0.434122i
$196$		0			0
$197$	−12.3303			−0.878498			−0.439249	−	0.898365i	$-0.644755\pi$
$197$	−12.3303			−0.878498			−0.439249	+	0.898365i	$0.644755\pi$
$198$		0			0
$199$		−	10.6784i		−	0.756969i	−0.925608	−	0.378484i	$-0.876445\pi$
$199$		−	10.6784i		−	0.756969i	0.925608	−	0.378484i	$-0.123555\pi$
$200$		−	3.46410i		−	0.244949i
$201$	9.87386	+	5.70068i	0.696449	+	0.402095i
$202$	24.5390			1.72656
$203$		0			0
$204$	−14.7695	+	8.52718i	−1.03407	+	0.597022i
$205$	3.24773	−	1.87508i	0.226831	−	0.130961i
$206$	15.1652	+	8.75560i	1.05661	+	0.610032i
$207$	−4.58258	+	7.93725i	−0.318511	+	0.551677i
$208$	4.10436	−	7.10895i	0.284586	−	0.492917i
$209$		0			0
$210$		0			0
$211$	15.8739	−	9.16478i	1.09280	−	0.630929i	0.158481	−	0.987362i	$-0.449340\pi$
$211$	15.8739	−	9.16478i	1.09280	−	0.630929i	0.934321	+	0.356433i	$0.116007\pi$
$212$			29.2741i			2.01055i
$213$			4.28245i			0.293429i
$214$	1.79129	−	3.10260i	0.122450	−	0.212089i
$215$	3.24773	−	1.87508i	0.221493	−	0.127879i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−15.4782	+	26.8091i	−1.04832	+	1.81574i
$219$	−3.87386	+	2.23658i	−0.261771	+	0.151134i
$220$		0			0
$221$	−24.2477	+	13.9994i	−1.63108	+	0.941704i
$222$		0			0
$223$	−3.08258	−	5.33918i	−0.206425	−	0.357538i	0.744161	−	0.668000i	$-0.232849\pi$
$223$	−3.08258	−	5.33918i	−0.206425	−	0.357538i	−0.950586	+	0.310462i	$0.899516\pi$
$224$		0			0
$225$	−2.00000	−	3.46410i	−0.133333	−	0.230940i
$226$	−23.1652			−1.54092
$227$	9.16515	+	15.8745i	0.608312	+	1.05363i	0.991519	+	0.129965i	$0.0414866\pi$
$227$	9.16515	+	15.8745i	0.608312	+	1.05363i	−0.383206	+	0.923663i	$0.625180\pi$
$228$	−9.76951	−	7.25198i	−0.647001	−	0.480274i
$229$	−6.00000	−	3.46410i	−0.396491	−	0.228914i	0.288478	−	0.957487i	$-0.406851\pi$
$229$	−6.00000	−	3.46410i	−0.396491	−	0.228914i	−0.684969	+	0.728572i	$0.740184\pi$
$230$	13.2695	+	22.9835i	0.874965	+	1.51548i
$231$		0			0
$232$	6.08258	−	10.5353i	0.399341	−	0.691678i
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$			20.0616i			1.31147i
$235$	4.70871	+	8.15573i	0.307163	+	0.532021i
$236$	4.18693	−	7.25198i	0.272546	−	0.472064i
$237$	−0.873864	−	0.504525i	−0.0567635	−	0.0327724i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	−4.10436	−	2.36965i	−0.264935	−	0.152960i
$241$	11.7477			0.756738			0.378369	−	0.925655i	$-0.376485\pi$
$241$	11.7477			0.756738			0.378369	+	0.925655i	$0.376485\pi$
$242$	−20.8521	−	12.0390i	−1.34042	−	0.773893i
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	−35.9347	+	20.7469i	−2.30048	+	1.32818i
$245$		0			0
$246$			3.10260i			0.197815i
$247$	−16.0390	−	11.9059i	−1.02054	−	0.757553i
$248$		0			0
$249$	6.16515	+	3.55945i	0.390701	+	0.225571i
$250$	17.3739			1.09882
$251$	7.66515	+	4.42548i	0.483820	+	0.279334i	0.722007	−	0.691886i	$-0.243220\pi$
$251$	7.66515	+	4.42548i	0.483820	+	0.279334i	−0.238187	+	0.971219i	$0.576553\pi$
$252$		0			0
$253$		0			0
$254$	16.2695	−	28.1796i	1.02084	−	1.76815i
$255$	8.08258	+	13.9994i	0.506151	+	0.876678i
$256$	−2.79129			−0.174455
$257$	−9.87386	−	17.1020i	−0.615915	−	1.06680i	−0.990223	−	0.139491i	$-0.955453\pi$
$257$	−9.87386	−	17.1020i	−0.615915	−	1.06680i	0.374309	−	0.927304i	$-0.377880\pi$
$258$			3.10260i			0.193160i
$259$		0			0
$260$	29.3085	+	16.9213i	1.81764	+	1.04941i
$261$		−	14.0471i		−	0.869494i
$262$	42.1216			2.60228
$263$	3.70871	−	6.42368i	0.228689	−	0.396101i	−0.728731	−	0.684800i	$-0.759889\pi$
$263$	3.70871	−	6.42368i	0.228689	−	0.396101i	0.957420	+	0.288699i	$0.0932228\pi$
$264$		0			0
$265$	27.7477			1.70453
$266$		0			0
$267$	−1.41742			−0.0867450
$268$		−	31.8245i		−	1.94399i
$269$	−8.29129	+	14.3609i	−0.505529	+	0.875601i	0.494451	+	0.869206i	$0.335369\pi$
$269$	−8.29129	+	14.3609i	−0.505529	+	0.875601i	−0.999980	+	0.00639585i	$0.997964\pi$
$270$	28.9564			1.76223
$271$			14.1425i			0.859093i	0.903045	+	0.429547i	$0.141327\pi$
$271$			14.1425i			0.859093i	−0.903045	+	0.429547i	$0.858673\pi$
$272$	−9.47822	−	5.47225i	−0.574701	−	0.331804i
$273$		0			0
$274$		−	46.6899i		−	2.82064i
$275$		0			0
$276$	−12.7913			−0.769945
$277$	−12.1652	−	21.0707i	−0.730933	−	1.26601i	−0.956485	−	0.291782i	$-0.905752\pi$
$277$	−12.1652	−	21.0707i	−0.730933	−	1.26601i	0.225552	−	0.974231i	$-0.427582\pi$
$278$	−1.89564	+	3.28335i	−0.113693	+	0.196922i
$279$		0			0
$280$		0			0
$281$	13.8303	+	7.98493i	0.825047	+	0.476341i	0.852154	−	0.523292i	$-0.175296\pi$
$281$	13.8303	+	7.98493i	0.825047	+	0.476341i	−0.0271070	+	0.999633i	$0.508629\pi$
$282$	−7.79129			−0.463964
$283$	−13.5000	−	7.79423i	−0.802492	−	0.463319i	0.0418500	−	0.999124i	$-0.486675\pi$
$283$	−13.5000	−	7.79423i	−0.802492	−	0.463319i	−0.844342	+	0.535805i	$0.820008\pi$
$284$	10.3521	−	5.97678i	0.614283	−	0.354657i
$285$	−6.87386	+	9.26013i	−0.407173	+	0.548523i
$286$		0			0
$287$		0			0
$288$	−12.7913	+	7.38505i	−0.753734	+	0.435168i
$289$	10.1652	+	17.6066i	0.597950	+	1.03568i
$290$	−35.2259	−	20.3377i	−2.06854	−	1.19427i
$291$	−15.7477			−0.923148
$292$	10.8131	+	6.24293i	0.632787	+	0.365340i
$293$	−9.16515			−0.535434			−0.267717	−	0.963498i	$-0.586269\pi$
$293$	−9.16515			−0.535434			−0.267717	+	0.963498i	$0.586269\pi$
$294$		0			0
$295$	−6.87386	−	3.96863i	−0.400212	−	0.231062i
$296$		0			0
$297$		0			0
$298$			26.6283i			1.54254i
$299$	−21.0000			−1.21446
$300$	2.79129	−	4.83465i	0.161155	−	0.279129i
$301$		0			0
$302$	−24.9564	−	43.2258i	−1.43608	−	2.48737i
$303$	9.70871	+	5.60533i	0.557751	+	0.322018i
$304$	0.895644	−	7.75650i	0.0513687	−	0.444866i
$305$	19.6652	+	34.0610i	1.12602	+	1.95033i
$306$	26.7477			1.52907
$307$	−16.6652	−	28.8649i	−0.951130	−	1.64741i	−0.742985	−	0.669308i	$-0.766591\pi$
$307$	−16.6652	−	28.8649i	−0.951130	−	1.64741i	−0.208146	−	0.978098i	$-0.566743\pi$
$308$		0			0
$309$	4.00000	+	6.92820i	0.227552	+	0.394132i
$310$		0			0
$311$	24.1652	−	13.9518i	1.37028	−	0.791132i	0.379317	−	0.925267i	$-0.376159\pi$
$311$	24.1652	−	13.9518i	1.37028	−	0.791132i	0.990963	+	0.134135i	$0.0428257\pi$
$312$	−6.87386	+	3.96863i	−0.389156	+	0.224679i
$313$	−9.87386	+	5.70068i	−0.558104	+	0.322221i	−0.752384	−	0.658725i	$-0.771096\pi$
$313$	−9.87386	+	5.70068i	−0.558104	+	0.322221i	0.194280	+	0.980946i	$0.437763\pi$
$314$	8.68693	−	15.0462i	0.490232	−	0.849107i
$315$		0			0
$316$			2.81655i			0.158443i
$317$	−5.91742	+	3.41643i	−0.332356	+	0.191886i	−0.656886	−	0.753989i	$-0.728127\pi$
$317$	−5.91742	+	3.41643i	−0.332356	+	0.191886i	0.324531	+	0.945875i	$0.394794\pi$
$318$	−11.4782	+	19.8809i	−0.643667	+	1.11486i
$319$		0			0
$320$			33.2904i			1.86099i
$321$	1.41742	−	0.818350i	0.0791129	−	0.0456759i
$322$		0			0
$323$	−15.8739	+	21.3845i	−0.883245	+	1.18986i
$324$	1.39564	−	2.41733i	0.0775358	−	0.134296i
$325$	4.58258	−	7.93725i	0.254196	−	0.440280i
$326$	−22.7477	−	13.1334i	−1.25988	−	0.727392i
$327$	−12.2477	+	7.07123i	−0.677301	+	0.391040i
$328$	2.12614	−	1.22753i	0.117396	−	0.0677788i
$329$		0			0
$330$		0			0
$331$	19.7477	+	11.4014i	1.08543	+	0.626675i	0.932357	−	0.361539i	$-0.117749\pi$
$331$	19.7477	+	11.4014i	1.08543	+	0.626675i	0.153076	+	0.988214i	$0.451082\pi$
$332$		−	19.8709i		−	1.09056i
$333$		0			0
$334$	11.0608	+	6.38595i	0.605220	+	0.349424i
$335$	−30.1652			−1.64810
$336$		0			0
$337$	1.50000	−	0.866025i	0.0817102	−	0.0471754i	−0.458588	−	0.888649i	$-0.651645\pi$
$337$	1.50000	−	0.866025i	0.0817102	−	0.0471754i	0.540298	+	0.841473i	$0.318311\pi$
$338$	−15.1652	+	8.75560i	−0.824875	+	0.476242i
$339$	−9.16515	−	5.29150i	−0.497783	−	0.287395i
$340$	22.5608	−	39.0764i	1.22353	−	2.11922i
$341$		0			0
$342$	7.58258	+	17.5112i	0.410019	+	0.946898i
$343$		0			0
$344$	2.12614	−	1.22753i	0.114634	−	0.0661837i
$345$			12.1244i			0.652753i
$346$			16.2360i			0.872853i
$347$	−0.708712	+	1.22753i	−0.0380457	+	0.0658970i	−0.884421	−	0.466689i	$-0.845447\pi$
$347$	−0.708712	+	1.22753i	−0.0380457	+	0.0658970i	0.846376	+	0.532587i	$0.178780\pi$
$348$	16.9782	−	9.80238i	0.910128	−	0.525463i
$349$			6.92820i			0.370858i	0.982658	+	0.185429i	$0.0593675\pi$
$349$			6.92820i			0.370858i	−0.982658	+	0.185429i	$0.940632\pi$
$350$		0			0
$351$	−11.4564	+	19.8431i	−0.611499	+	1.05915i
$352$		0			0
$353$	−24.3303	+	14.0471i	−1.29497	+	0.747652i	−0.979531	−	0.201293i	$-0.935486\pi$
$353$	−24.3303	+	14.0471i	−1.29497	+	0.747652i	−0.315440	+	0.948945i	$0.602152\pi$
$354$	5.68693	−	3.28335i	0.302257	−	0.174508i
$355$	−5.66515	−	9.81233i	−0.300675	−	0.520784i
$356$	1.97822	+	3.42638i	0.104845	+	0.181598i
$357$		0			0
$358$	−13.3739	−	23.1642i	−0.706831	−	1.22427i
$359$	−19.4174			−1.02481			−0.512406	−	0.858743i	$-0.671246\pi$
$359$	−19.4174			−1.02481			−0.512406	+	0.858743i	$0.671246\pi$
$360$	−4.58258	−	7.93725i	−0.241523	−	0.418330i
$361$	−18.5000	−	4.33013i	−0.973684	−	0.227901i
$362$	−18.4782	−	10.6684i	−0.971194	−	0.560719i
$363$	−5.50000	−	9.52628i	−0.288675	−	0.500000i
$364$		0			0
$365$	5.91742	−	10.2493i	0.309732	−	0.536472i
$366$	−32.5390			−1.70084
$367$		−	31.4630i		−	1.64235i	−0.570674	−	0.821177i	$-0.693318\pi$
$367$		−	31.4630i		−	1.64235i	0.570674	−	0.821177i	$-0.306682\pi$
$368$	−4.10436	−	7.10895i	−0.213954	−	0.370580i
$369$	1.41742	−	2.45505i	0.0737882	−	0.127805i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	12.0000	+	6.92820i	0.621336	+	0.358729i	0.777389	−	0.629020i	$-0.216544\pi$
$373$	12.0000	+	6.92820i	0.621336	+	0.358729i	−0.156053	+	0.987749i	$0.549877\pi$
$374$		0			0
$375$	6.87386	+	3.96863i	0.354965	+	0.204939i
$376$	3.08258	+	5.33918i	0.158972	+	0.275347i
$377$	27.8739	−	16.0930i	1.43558	−	0.828831i
$378$		0			0
$379$			4.91010i			0.252215i	0.992017	+	0.126107i	$0.0402484\pi$
$379$			4.91010i			0.252215i	−0.992017	+	0.126107i	$0.959752\pi$
$380$	31.9782	+	3.69253i	1.64045	+	0.189423i
$381$	12.8739	−	7.43273i	0.659548	−	0.380790i
$382$	22.7477	+	13.1334i	1.16387	+	0.671964i
$383$	−36.1652			−1.84795			−0.923976	−	0.382449i	$-0.875081\pi$
$383$	−36.1652			−1.84795			−0.923976	+	0.382449i	$0.875081\pi$
$384$	−11.0608	−	6.38595i	−0.564444	−	0.325882i
$385$		0			0
$386$	−1.89564	+	3.28335i	−0.0964857	+	0.167118i
$387$	1.41742	−	2.45505i	0.0720517	−	0.124797i
$388$	21.9782	+	38.0674i	1.11578	+	1.93258i
$389$	−12.1652			−0.616798			−0.308399	−	0.951257i	$-0.599793\pi$
$389$	−12.1652			−0.616798			−0.308399	+	0.951257i	$0.599793\pi$
$390$	13.2695	+	22.9835i	0.671928	+	1.16381i
$391$			27.9989i			1.41596i
$392$		0			0
$393$	16.6652	+	9.62163i	0.840646	+	0.485347i
$394$			26.9898i			1.35973i
$395$	2.66970			0.134327
$396$		0			0
$397$		−	21.7937i		−	1.09379i	−0.837200	−	0.546896i	$-0.815809\pi$
$397$		−	21.7937i		−	1.09379i	0.837200	−	0.546896i	$-0.184191\pi$
$398$	−23.3739			−1.17163
$399$		0			0
$400$	3.58258			0.179129
$401$		−	15.3978i		−	0.768927i	−0.923140	−	0.384464i	$-0.874386\pi$
$401$		−	15.3978i		−	0.768927i	0.923140	−	0.384464i	$-0.125614\pi$
$402$	12.4782	−	21.6129i	0.622357	−	1.07795i
$403$		0			0
$404$		−	31.2922i		−	1.55684i
$405$	−2.29129	−	1.32288i	−0.113855	−	0.0657342i
$406$		0			0
$407$		0			0
$408$	5.29129	+	9.16478i	0.261958	+	0.453724i
$409$	13.4174			0.663449			0.331724	−	0.943376i	$-0.392370\pi$
$409$	13.4174			0.663449			0.331724	+	0.943376i	$0.392370\pi$
$410$	−4.10436	−	7.10895i	−0.202700	−	0.351086i
$411$	10.6652	−	18.4726i	0.526073	−	0.911185i
$412$	11.1652	−	19.3386i	0.550068	−	0.952745i
$413$		0			0
$414$	17.3739	+	10.0308i	0.853879	+	0.492987i
$415$	−18.8348			−0.924566
$416$	−29.3085	−	16.9213i	−1.43697	−	0.829634i
$417$	−1.50000	+	0.866025i	−0.0734553	+	0.0424094i
$418$		0			0
$419$		−	27.9035i		−	1.36318i	−0.731736	−	0.681588i	$-0.761290\pi$
$419$		−	27.9035i		−	1.36318i	0.731736	−	0.681588i	$-0.238710\pi$
$420$		0			0
$421$	6.24773	−	3.60713i	0.304496	−	0.175801i	−0.339965	−	0.940438i	$-0.610415\pi$
$421$	6.24773	−	3.60713i	0.304496	−	0.175801i	0.644461	+	0.764637i	$0.277082\pi$
$422$	−20.0608	−	34.7463i	−0.976544	−	1.69142i
$423$	6.16515	+	3.55945i	0.299760	+	0.173066i
$424$	18.1652			0.882178
$425$	−10.5826	−	6.10985i	−0.513330	−	0.296371i
$426$	9.37386			0.454165
$427$		0			0
$428$	−3.95644	−	2.28425i	−0.191242	−	0.110413i
$429$		0			0
$430$	−4.10436	−	7.10895i	−0.197930	−	0.342824i
$431$		−	7.55585i		−	0.363953i	−0.983303	−	0.181976i	$-0.941751\pi$
$431$		−	7.55585i		−	0.363953i	0.983303	−	0.181976i	$-0.0582494\pi$
$432$	−8.95644			−0.430917
$433$	0.126136	−	0.218475i	0.00606173	−	0.0104992i	−0.862979	−	0.505240i	$-0.831404\pi$
$433$	0.126136	−	0.218475i	0.00606173	−	0.0104992i	0.869040	+	0.494741i	$0.164737\pi$
$434$		0			0
$435$	−9.29129	−	16.0930i	−0.445483	−	0.771599i
$436$	34.1869	+	19.7378i	1.63726	+	0.945271i
$437$	−18.3303	+	7.93725i	−0.876857	+	0.379690i
$438$	4.89564	+	8.47950i	0.233923	+	0.405166i
$439$	−0.165151			−0.00788225			−0.00394112	−	0.999992i	$-0.501255\pi$
$439$	−0.165151			−0.00788225			−0.00394112	+	0.999992i	$0.501255\pi$
$440$		0			0
$441$		0			0
$442$	30.6434	+	53.0759i	1.45756	+	2.52456i
$443$	−5.29129	−	9.16478i	−0.251397	−	0.435432i	0.712514	−	0.701658i	$-0.247557\pi$
$443$	−5.29129	−	9.16478i	−0.251397	−	0.435432i	−0.963911	+	0.266226i	$0.914223\pi$
$444$		0			0
$445$	3.24773	−	1.87508i	0.153957	−	0.0888871i
$446$	−11.6869	+	6.74745i	−0.553392	+	0.319501i
$447$	−6.08258	+	10.5353i	−0.287696	+	0.498304i
$448$		0			0
$449$		−	3.27340i		−	0.154481i	−0.997012	−	0.0772407i	$-0.975389\pi$
$449$		−	3.27340i		−	0.154481i	0.997012	−	0.0772407i	$-0.0246110\pi$
$450$	−7.58258	+	4.37780i	−0.357446	+	0.206372i
$451$		0			0
$452$			29.5402i			1.38945i
$453$		−	22.8027i		−	1.07136i
$454$	34.7477	−	20.0616i	1.63079	−	0.941538i
$455$		0			0
$456$	−4.50000	+	6.06218i	−0.210732	+	0.283887i
$457$	−6.16515	+	10.6784i	−0.288394	+	0.499512i	−0.973426	−	0.229000i	$-0.926454\pi$
$457$	−6.16515	+	10.6784i	−0.288394	+	0.499512i	0.685033	+	0.728512i	$0.259788\pi$
$458$	−7.58258	+	13.1334i	−0.354310	+	0.613684i
$459$	26.4564	+	15.2746i	1.23488	+	0.712959i
$460$	29.3085	−	16.9213i	1.36652	−	0.788959i
$461$	29.4564	−	17.0067i	1.37192	−	0.792080i	0.380753	−	0.924677i	$-0.375665\pi$
$461$	29.4564	−	17.0067i	1.37192	−	0.792080i	0.991170	+	0.132597i	$0.0423315\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	10.8956	+	6.29060i	0.505818	+	0.292034i
$465$		0			0
$466$		−	6.56670i		−	0.304197i
$467$	5.83485	+	3.36875i	0.270005	+	0.155887i	0.628890	−	0.777495i	$-0.283510\pi$
$467$	5.83485	+	3.36875i	0.270005	+	0.155887i	−0.358885	+	0.933382i	$0.616843\pi$
$468$	25.5826			1.18255
$469$		0			0
$470$	17.8521	−	10.3069i	0.823455	−	0.475422i
$471$	6.87386	−	3.96863i	0.316731	−	0.182865i
$472$	−4.50000	−	2.59808i	−0.207129	−	0.119586i
$473$		0			0
$474$	−1.10436	+	1.91280i	−0.0507248	+	0.0878579i
$475$	1.00000	−	8.66025i	0.0458831	−	0.397360i
$476$		0			0
$477$	18.1652	−	10.4877i	0.831725	−	0.480197i
$478$		−	26.2668i		−	1.20142i
$479$			31.2723i			1.42887i	0.699704	+	0.714433i	$0.253315\pi$
$479$			31.2723i			1.42887i	−0.699704	+	0.714433i	$0.746685\pi$
$480$	−9.76951	+	16.9213i	−0.445915	+	0.772347i
$481$		0			0
$482$		−	25.7146i		−	1.17127i
$483$		0			0
$484$	−15.3521	+	26.5906i	−0.697822	+	1.20866i
$485$	36.0826	−	20.8323i	1.63843	−	0.945945i
$486$	30.3303	−	17.5112i	1.37581	−	0.794325i
$487$	31.7477	−	18.3296i	1.43863	−	0.830592i	0.440872	−	0.897570i	$-0.354669\pi$
$487$	31.7477	−	18.3296i	1.43863	−	0.830592i	0.997754	+	0.0669782i	$0.0213358\pi$
$488$	12.8739	+	22.2982i	0.582772	+	1.00939i
$489$	−6.00000	−	10.3923i	−0.271329	−	0.469956i
$490$		0			0
$491$	11.2913	+	19.5571i	0.509569	+	0.882599i	0.999939	+	0.0110844i	$0.00352836\pi$
$491$	11.2913	+	19.5571i	0.509569	+	0.882599i	−0.490370	+	0.871514i	$0.663138\pi$
$492$	3.95644			0.178370
$493$	−21.4564	−	37.1636i	−0.966349	−	1.67377i
$494$	−26.0608	+	35.1078i	−1.17253	+	1.57958i
$495$		0			0
$496$		0			0
$497$		0			0
$498$	7.79129	−	13.4949i	0.349136	−	0.604721i
$499$	27.7477			1.24216			0.621079	−	0.783748i	$-0.286694\pi$
$499$	27.7477			1.24216			0.621079	+	0.783748i	$0.286694\pi$
$500$		−	22.1552i		−	0.990809i
$501$	2.91742	+	5.05313i	0.130341	+	0.225757i
$502$	9.68693	−	16.7783i	0.432349	−	0.748850i
$503$	−11.9174	−	6.88053i	−0.531372	−	0.306788i	0.210203	−	0.977658i	$-0.432587\pi$
$503$	−11.9174	−	6.88053i	−0.531372	−	0.306788i	−0.741575	+	0.670870i	$0.765921\pi$
$504$		0			0
$505$	−29.6606			−1.31988
$506$		0			0
$507$	−8.00000			−0.355292
$508$	−35.9347	−	20.7469i	−1.59434	−	0.920494i
$509$	−2.29129	−	3.96863i	−0.101560	−	0.175906i	0.810768	−	0.585368i	$-0.199050\pi$
$509$	−2.29129	−	3.96863i	−0.101560	−	0.175906i	−0.912327	+	0.409462i	$0.865717\pi$
$510$	30.6434	−	17.6920i	1.35691	−	0.783413i
$511$		0			0
$512$		−	19.4340i		−	0.858868i
$513$	−2.50000	+	21.6506i	−0.110378	+	0.955899i
$514$	−37.4347	+	21.6129i	−1.65117	+	0.953305i
$515$	−18.3303	−	10.5830i	−0.807730	−	0.466343i
$516$	3.95644			0.174173
$517$		0			0
$518$		0			0
$519$	−3.70871	+	6.42368i	−0.162794	+	0.281968i
$520$	10.5000	−	18.1865i	0.460455	−	0.797532i
$521$	−10.5826	−	18.3296i	−0.463631	−	0.803033i	0.535508	−	0.844530i	$-0.320120\pi$
$521$	−10.5826	−	18.3296i	−0.463631	−	0.803033i	−0.999139	+	0.0414979i	$0.986787\pi$
$522$	−30.7477			−1.34579
$523$	13.5000	+	23.3827i	0.590314	+	1.02245i	0.994190	+	0.107640i	$0.0343293\pi$
$523$	13.5000	+	23.3827i	0.590314	+	1.02245i	−0.403876	+	0.914814i	$0.632337\pi$
$524$		−	53.7135i		−	2.34648i
$525$		0			0
$526$	−14.0608	−	8.11800i	−0.613080	−	0.353962i
$527$		0			0
$528$		0			0
$529$	1.00000	−	1.73205i	0.0434783	−	0.0753066i
$530$		−	60.7370i		−	2.63825i
$531$	−6.00000			−0.260378
$532$		0			0
$533$	6.49545			0.281349
$534$			3.10260i			0.134263i
$535$	−2.16515	+	3.75015i	−0.0936077	+	0.162133i
$536$	−19.7477			−0.852972
$537$		−	12.2197i		−	0.527319i
$538$	31.4347	+	18.1488i	1.35524	+	0.782451i
$539$		0			0
$540$		−	36.9253i		−	1.58901i
$541$	−14.2477	−	24.6778i	−0.612558	−	1.06098i	−0.990808	−	0.135278i	$-0.956807\pi$
$541$	−14.2477	−	24.6778i	−0.612558	−	1.06098i	0.378250	−	0.925703i	$-0.376526\pi$
$542$	30.9564			1.32969
$543$	−4.87386	−	8.44178i	−0.209158	−	0.362271i
$544$	−22.5608	+	39.0764i	−0.967286	+	1.67539i
$545$	18.7087	−	32.4044i	0.801393	−	1.38805i
$546$		0			0
$547$	−27.8739	−	16.0930i	−1.19180	−	0.688086i	−0.233086	−	0.972456i	$-0.574882\pi$
$547$	−27.8739	−	16.0930i	−1.19180	−	0.688086i	−0.958715	+	0.284370i	$0.908216\pi$
$548$	−59.5390			−2.54338
$549$	25.7477	+	14.8655i	1.09889	+	0.634442i
$550$		0			0
$551$	18.2477	−	24.5824i	0.777379	−	1.04725i
$552$			7.93725i			0.337832i
$553$		0			0
$554$	−46.1216	+	26.6283i	−1.95952	+	1.13133i
$555$		0			0
$556$	4.18693	+	2.41733i	0.177565	+	0.102517i
$557$	−0.165151			−0.00699769			−0.00349884	−	0.999994i	$-0.501114\pi$
$557$	−0.165151			−0.00699769			−0.00349884	+	0.999994i	$0.501114\pi$
$558$		0			0
$559$	6.49545			0.274728
$560$		0			0
$561$		0			0
$562$	17.4782	−	30.2732i	0.737274	−	1.27700i
$563$	−9.16515	−	15.8745i	−0.386265	−	0.669031i	0.605679	−	0.795709i	$-0.292902\pi$
$563$	−9.16515	−	15.8745i	−0.386265	−	0.669031i	−0.991944	+	0.126679i	$0.959568\pi$
$564$			9.93545i			0.418358i
$565$	28.0000			1.17797
$566$	−17.0608	+	29.5502i	−0.717119	+	1.24209i
$567$		0			0
$568$	−3.70871	−	6.42368i	−0.155614	−	0.269532i
$569$	2.83485	+	1.63670i	0.118843	+	0.0686141i	0.558243	−	0.829677i	$-0.311476\pi$
$569$	2.83485	+	1.63670i	0.118843	+	0.0686141i	−0.439400	+	0.898291i	$0.644809\pi$
$570$	20.2695	+	15.0462i	0.848996	+	0.630216i
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$		0			0
$573$	6.00000	+	10.3923i	0.250654	+	0.434145i
$574$		0			0
$575$	−4.58258	−	7.93725i	−0.191107	−	0.331006i
$576$	12.5826	+	21.7937i	0.524274	+	0.908069i
$577$	12.0000	−	6.92820i	0.499567	−	0.288425i	−0.228968	−	0.973434i	$-0.573535\pi$
$577$	12.0000	−	6.92820i	0.499567	−	0.288425i	0.728535	+	0.685009i	$0.240202\pi$
$578$	38.5390	−	22.2505i	1.60301	−	0.925499i
$579$	−1.50000	+	0.866025i	−0.0623379	+	0.0359908i
$580$	−25.9347	+	44.9201i	−1.07688	+	1.86521i
$581$		0			0
$582$			34.4702i			1.42884i
$583$		0			0
$584$	3.87386	−	6.70973i	0.160302	−	0.277651i
$585$		−	24.2487i		−	1.00256i
$586$			20.0616i			0.828737i
$587$	−19.6652	+	11.3537i	−0.811668	+	0.468617i	−0.847535	−	0.530740i	$-0.821914\pi$
$587$	−19.6652	+	11.3537i	−0.811668	+	0.468617i	0.0358670	+	0.999357i	$0.488581\pi$
$588$		0			0
$589$		0			0
$590$	−8.68693	+	15.0462i	−0.357635	+	0.619443i
$591$	−6.16515	+	10.6784i	−0.253600	+	0.439249i
$592$		0			0
$593$	17.2913	−	9.98313i	0.710068	−	0.409958i	−0.101018	−	0.994885i	$-0.532210\pi$
$593$	17.2913	−	9.98313i	0.710068	−	0.409958i	0.811086	+	0.584927i	$0.198877\pi$
$594$		0			0
$595$		0			0
$596$	33.9564			1.39091
$597$	−9.24773	−	5.33918i	−0.378484	−	0.218518i
$598$			45.9669i			1.87973i
$599$		−	25.4485i		−	1.03980i	−0.854228	−	0.519898i	$-0.825970\pi$
$599$		−	25.4485i		−	1.03980i	0.854228	−	0.519898i	$-0.174030\pi$
$600$	−3.00000	−	1.73205i	−0.122474	−	0.0707107i
$601$	−7.49545			−0.305746			−0.152873	−	0.988246i	$-0.548853\pi$
$601$	−7.49545			−0.305746			−0.152873	+	0.988246i	$0.548853\pi$
$602$		0			0
$603$	−19.7477	+	11.4014i	−0.804190	+	0.464299i
$604$	−55.1216	+	31.8245i	−2.24287	+	1.29492i
$605$	25.2042	+	14.5516i	1.02470	+	0.591608i
$606$	12.2695	−	21.2514i	0.498415	−	0.863280i
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	−0.773358	−	0.633970i	$-0.781424\pi$
$607$	4.00000	−	6.92820i	0.162355	−	0.281207i	0.935713	+	0.352763i	$0.114758\pi$
$608$	−31.9782	−	3.69253i	−1.29689	−	0.149752i
$609$		0			0
$610$	74.5562	−	43.0451i	3.01869	−	1.74284i
$611$			16.3115i			0.659891i
$612$		−	34.1087i		−	1.37876i
$613$	−12.2477	+	21.2137i	−0.494681	+	0.856813i	−0.999981	−	0.00613096i	$-0.998048\pi$
$613$	−12.2477	+	21.2137i	−0.494681	+	0.856813i	0.505300	+	0.862944i	$0.331382\pi$
$614$	−63.1824	+	36.4784i	−2.54983	+	1.47215i
$615$		−	3.75015i		−	0.151221i
$616$		0			0
$617$	−4.33485	+	7.50818i	−0.174514	+	0.302268i	−0.939993	−	0.341193i	$-0.889169\pi$
$617$	−4.33485	+	7.50818i	−0.174514	+	0.302268i	0.765479	+	0.643461i	$0.222502\pi$
$618$	15.1652	−	8.75560i	0.610032	−	0.352202i
$619$	24.4955	−	14.1425i	0.984555	−	0.568433i	0.0809131	−	0.996721i	$-0.474216\pi$
$619$	24.4955	−	14.1425i	0.984555	−	0.568433i	0.903642	+	0.428288i	$0.140883\pi$
$620$		0			0
$621$	11.4564	+	19.8431i	0.459731	+	0.796278i
$622$	−30.5390	−	52.8951i	−1.22450	−	2.12090i
$623$		0			0
$624$	−4.10436	−	7.10895i	−0.164306	−	0.284586i
$625$	−31.0000			−1.24000
$626$	12.4782	+	21.6129i	0.498730	+	0.863826i
$627$		0			0
$628$	−19.1869	−	11.0776i	−0.765642	−	0.442044i
$629$		0			0
$630$		0			0
$631$	20.2913	−	35.1455i	0.807783	−	1.39912i	−0.106612	−	0.994301i	$-0.534000\pi$
$631$	20.2913	−	35.1455i	0.807783	−	1.39912i	0.914396	−	0.404821i	$-0.132666\pi$
$632$	1.74773			0.0695209
$633$		−	18.3296i		−	0.728535i
$634$	7.47822	+	12.9527i	0.296998	+	0.514416i
$635$	−19.6652	+	34.0610i	−0.780388	+	1.35167i
$636$	25.3521	+	14.6370i	1.00528	+	0.580396i
$637$		0			0
$638$		0			0
$639$	−7.41742	−	4.28245i	−0.293429	−	0.169411i
$640$	33.7913			1.33572
$641$	35.1606	+	20.3000i	1.38876	+	0.801801i	0.993176	−	0.116628i	$-0.0372086\pi$
$641$	35.1606	+	20.3000i	1.38876	+	0.801801i	0.395585	+	0.918429i	$0.370542\pi$
$642$	−1.79129	−	3.10260i	−0.0706965	−	0.122450i
$643$	−4.50000	+	2.59808i	−0.177463	+	0.102458i	−0.586100	−	0.810239i	$-0.699337\pi$
$643$	−4.50000	+	2.59808i	−0.177463	+	0.102458i	0.408637	+	0.912697i	$0.366004\pi$
$644$		0			0
$645$		−	3.75015i		−	0.147662i
$646$	46.8085	+	34.7463i	1.84166	+	1.36708i
$647$	17.8348	−	10.2970i	0.701160	−	0.404815i	−0.106619	−	0.994300i	$-0.534003\pi$
$647$	17.8348	−	10.2970i	0.701160	−	0.404815i	0.807779	+	0.589485i	$0.200669\pi$
$648$	−1.50000	−	0.866025i	−0.0589256	−	0.0340207i
$649$		0			0
$650$	−17.3739	−	10.0308i	−0.681459	−	0.393441i
$651$		0			0
$652$	−16.7477	+	29.0079i	−0.655892	+	1.13604i
$653$	−0.165151	+	0.286051i	−0.00646287	+	0.0111940i	−0.869239	−	0.494393i	$-0.835391\pi$
$653$	−0.165151	+	0.286051i	−0.00646287	+	0.0111940i	0.862776	+	0.505587i	$0.168724\pi$
$654$	15.4782	+	26.8091i	0.605246	+	1.04832i
$655$	−50.9129			−1.98933
$656$	1.26951	+	2.19885i	0.0495659	+	0.0858507i
$657$		−	8.94630i		−	0.349029i
$658$		0			0
$659$	32.4564	+	18.7387i	1.26432	+	0.729957i	0.973908	−	0.226943i	$-0.0728732\pi$
$659$	32.4564	+	18.7387i	1.26432	+	0.729957i	0.290415	+	0.956901i	$0.406207\pi$
$660$		0			0
$661$	−25.7477			−1.00147			−0.500735	−	0.865600i	$-0.666937\pi$
$661$	−25.7477			−1.00147			−0.500735	+	0.865600i	$0.666937\pi$
$662$	24.9564	−	43.2258i	0.969960	−	1.68002i
$663$			27.9989i			1.08739i
$664$	−12.3303			−0.478509
$665$		0			0
$666$		0			0
$667$		−	32.1860i		−	1.24625i
$668$	8.14337	−	14.1047i	0.315076	−	0.545728i
$669$	−6.16515			−0.238359
$670$			66.0285i			2.55090i
$671$		0			0
$672$		0			0
$673$		0			0		1.00000			$0$
$673$		0			0		−1.00000			$\pi$
$674$	−1.89564	−	3.28335i	−0.0730175	−	0.126470i
$675$	−10.0000			−0.384900
$676$	11.1652	+	19.3386i	0.429429	+	0.743793i
$677$	−7.74773	+	13.4195i	−0.297769	+	0.515752i	−0.975625	−	0.219443i	$-0.929576\pi$
$677$	−7.74773	+	13.4195i	−0.297769	+	0.515752i	0.677856	+	0.735195i	$0.262909\pi$
$678$	−11.5826	+	20.0616i	−0.444826	+	0.770461i
$679$		0			0
$680$	−24.2477	−	13.9994i	−0.929858	−	0.536854i
$681$	18.3303			0.702419
$682$		0			0
$683$	−19.4174	+	11.2107i	−0.742987	+	0.428964i	−0.823154	−	0.567818i	$-0.807788\pi$
$683$	−19.4174	+	11.2107i	−0.742987	+	0.428964i	0.0801673	+	0.996781i	$0.474455\pi$
$684$	22.3303	−	9.66930i	0.853820	−	0.369715i
$685$			56.4347i			2.15626i
$686$		0			0
$687$	−6.00000	+	3.46410i	−0.228914	+	0.132164i
$688$	1.26951	+	2.19885i	0.0483995	+	0.0838304i
$689$	41.6216	+	24.0302i	1.58566	+	0.915479i
$690$	26.5390			1.01032
$691$	18.4955	+	10.6784i	0.703600	+	0.406224i	0.808687	−	0.588239i	$-0.200179\pi$
$691$	18.4955	+	10.6784i	0.703600	+	0.406224i	−0.105087	+	0.994463i	$0.533512\pi$
$692$	20.7042			0.787054
$693$		0			0
$694$	2.68693	+	1.55130i	0.101995	+	0.0588866i
$695$	2.29129	−	3.96863i	0.0869135	−	0.150539i
$696$	−6.08258	−	10.5353i	−0.230559	−	0.399341i
$697$		−	8.66025i		−	0.328031i
$698$	15.1652			0.574009
$699$	1.50000	−	2.59808i	0.0567352	−	0.0982683i
$700$		0			0
$701$	−21.0826	−	36.5161i	−0.796278	−	1.37919i	−0.922025	−	0.387131i	$-0.873466\pi$
$701$	−21.0826	−	36.5161i	−0.796278	−	1.37919i	0.125747	−	0.992062i	$-0.459867\pi$
$702$	43.4347	+	25.0770i	1.63934	+	0.946471i
$703$		0			0
$704$		0			0
$705$	9.41742			0.354681
$706$	30.7477	+	53.2566i	1.15721	+	2.00434i
$707$		0			0
$708$	−4.18693	−	7.25198i	−0.157355	−	0.272546i
$709$	−15.0826	−	26.1238i	−0.566438	−	0.981099i	−0.996914	−	0.0784975i	$-0.974988\pi$
$709$	−15.0826	−	26.1238i	−0.566438	−	0.981099i	0.430476	−	0.902602i	$-0.358346\pi$
$710$	−21.4782	+	12.4005i	−0.806063	+	0.465381i
$711$	1.74773	−	1.00905i	0.0655449	−	0.0378424i
$712$	2.12614	−	1.22753i	0.0796803	−	0.0460035i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−29.5390	+	17.0544i	−1.10392	+	0.637351i
$717$	6.00000	−	10.3923i	0.224074	−	0.388108i
$718$			42.5028i			1.58619i
$719$			20.6893i			0.771579i	0.922587	+	0.385790i	$0.126071\pi$
$719$			20.6893i			0.771579i	−0.922587	+	0.385790i	$0.873929\pi$
$720$	8.20871	−	4.73930i	0.305921	−	0.176623i
$721$		0			0
$722$	−9.47822	+	40.4947i	−0.352743	+	1.50706i
$723$	5.87386	−	10.1738i	0.218451	−	0.378369i
$724$	−13.6044	+	23.5634i	−0.505602	+	0.875728i
$725$	12.1652	+	7.02355i	0.451802	+	0.260848i
$726$	−20.8521	+	12.0390i	−0.773893	+	0.446808i
$727$	−9.24773	+	5.33918i	−0.342979	+	0.198019i	−0.661589	−	0.749867i	$-0.730117\pi$
$727$	−9.24773	+	5.33918i	−0.342979	+	0.198019i	0.318609	+	0.947886i	$0.396784\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−22.4347	−	12.9527i	−0.830344	−	0.479399i
$731$		−	8.66025i		−	0.320311i
$732$			41.4938i			1.53365i
$733$	−18.0000	−	10.3923i	−0.664845	−	0.383849i	0.129275	−	0.991609i	$-0.458735\pi$
$733$	−18.0000	−	10.3923i	−0.664845	−	0.383849i	−0.794121	+	0.607760i	$0.792068\pi$
$734$	−68.8693			−2.54201
$735$		0			0
$736$	−29.3085	+	16.9213i	−1.08033	+	0.623727i
$737$		0			0
$738$	−5.37386	−	3.10260i	−0.197815	−	0.114208i
$739$	2.12614	−	3.68258i	0.0782112	−	0.135466i	−0.824267	−	0.566201i	$-0.808412\pi$
$739$	2.12614	−	3.68258i	0.0782112	−	0.135466i	0.902478	+	0.430736i	$0.141746\pi$
$740$		0			0
$741$	−18.3303	+	7.93725i	−0.673380	+	0.291582i
$742$		0			0
$743$	−10.0390	+	5.79603i	−0.368296	+	0.212636i	−0.672714	−	0.739903i	$-0.734871\pi$
$743$	−10.0390	+	5.79603i	−0.368296	+	0.212636i	0.304418	+	0.952539i	$0.401538\pi$
$744$		0			0
$745$		−	32.1860i		−	1.17920i
$746$	15.1652	−	26.2668i	0.555236	−	0.961696i
$747$	−12.3303	+	7.11890i	−0.451142	+	0.260467i
$748$		0			0
$749$		0			0
$750$	8.68693	−	15.0462i	0.317202	−	0.549410i
$751$	−18.8739	+	10.8968i	−0.688717	+	0.397631i	−0.803131	−	0.595802i	$-0.796834\pi$
$751$	−18.8739	+	10.8968i	−0.688717	+	0.397631i	0.114414	+	0.993433i	$0.463501\pi$
$752$	−5.52178	+	3.18800i	−0.201359	+	0.116254i
$753$	7.66515	−	4.42548i	0.279334	−	0.161273i
$754$	−35.2259	−	61.0131i	−1.28285	−	2.22197i
$755$	30.1652	+	52.2476i	1.09782	+	1.90148i
$756$		0			0
$757$	7.24773	+	12.5534i	0.263423	+	0.456262i	0.967149	−	0.254209i	$-0.0818151\pi$
$757$	7.24773	+	12.5534i	0.263423	+	0.456262i	−0.703726	+	0.710471i	$0.748482\pi$
$758$	10.7477			0.390375
$759$		0			0
$760$	2.29129	−	19.8431i	0.0831137	−	0.719786i
$761$	24.3303	+	14.0471i	0.881973	+	0.509207i	0.871308	−	0.490736i	$-0.163272\pi$
$761$	24.3303	+	14.0471i	0.881973	+	0.509207i	0.0106644	+	0.999943i	$0.496605\pi$
$762$	−16.2695	−	28.1796i	−0.589382	−	1.02084i
$763$		0			0
$764$	16.7477	−	29.0079i	0.605912	−	1.04947i
$765$	−32.3303			−1.16890
$766$			79.1619i			2.86024i
$767$	−6.87386	−	11.9059i	−0.248201	−	0.429896i
$768$	−1.39564	+	2.41733i	−0.0503610	+	0.0872277i
$769$	31.3693	+	18.1111i	1.13121	+	0.653102i	0.944238	−	0.329264i	$-0.106800\pi$
$769$	31.3693	+	18.1111i	1.13121	+	0.653102i	0.186968	+	0.982366i	$0.440134\pi$
$770$		0			0
$771$	−19.7477			−0.711197
$772$	4.18693	+	2.41733i	0.150691	+	0.0870015i
$773$	−1.08712			−0.0391010			−0.0195505	−	0.999809i	$-0.506224\pi$
$773$	−1.08712			−0.0391010			−0.0195505	+	0.999809i	$0.506224\pi$
$774$	−5.37386	−	3.10260i	−0.193160	−	0.111521i
$775$		0			0
$776$	23.6216	−	13.6379i	0.847966	−	0.489573i
$777$		0			0
$778$			26.6283i			0.954671i
$779$	5.66970	−	2.45505i	0.203138	−	0.0879613i
$780$	29.3085	−	16.9213i	1.04941	−	0.605879i
$781$		0			0
$782$	61.2867			2.19161
$783$	−30.4129	−	17.5589i	−1.08687	−	0.627503i
$784$		0			0
$785$	−10.5000	+	18.1865i	−0.374761	+	0.649105i
$786$	21.0608	−	36.4784i	0.751214	−	1.30114i
$787$	−2.83485	−	4.91010i	−0.101051	−	0.175026i	0.811067	−	0.584954i	$-0.198887\pi$
$787$	−2.83485	−	4.91010i	−0.101051	−	0.175026i	−0.912118	+	0.409927i	$0.865554\pi$
$788$	34.4174			1.22607
$789$	−3.70871	−	6.42368i	−0.132034	−	0.228689i
$790$		−	5.84370i		−	0.207910i
$791$		0			0
$792$		0			0
$793$			68.1221i			2.41909i
$794$	−47.7042			−1.69296
$795$	13.8739	−	24.0302i	0.492055	−	0.852265i
$796$			29.8064i			1.05646i
$797$	2.83485			0.100415			0.0502077	−	0.998739i	$-0.484012\pi$
$797$	2.83485			0.100415			0.0502077	+	0.998739i	$0.484012\pi$
$798$		0			0
$799$	21.7477			0.769379
$800$		−	14.7701i		−	0.522202i
$801$	1.41742	−	2.45505i	0.0500822	−	0.0867450i
$802$	−33.7042			−1.19014
$803$		0			0
$804$	−27.5608	−	15.9122i	−0.971994	−	0.561181i
$805$		0			0
$806$		0			0
$807$	8.29129	+	14.3609i	0.291867	+	0.505529i
$808$	−19.4174			−0.683103
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$	−2.89564	+	5.01540i	−0.101743	+	0.176223i
$811$	−14.5000	+	25.1147i	−0.509164	+	0.881898i	0.490780	+	0.871284i	$0.336712\pi$
$811$	−14.5000	+	25.1147i	−0.509164	+	0.881898i	−0.999944	+	0.0106140i	$0.996621\pi$
$812$		0			0
$813$	12.2477	+	7.07123i	0.429547	+	0.247999i
$814$		0			0
$815$	27.4955	+	15.8745i	0.963124	+	0.556060i
$816$	−9.47822	+	5.47225i	−0.331804	+	0.191567i
$817$	5.66970	−	2.45505i	0.198358	−	0.0858914i
$818$		−	29.3694i		−	1.02688i
$819$		0			0
$820$	−9.06534	+	5.23388i	−0.316575	+	0.182775i
$821$	6.08258	+	10.5353i	0.212283	+	0.367686i	0.952429	−	0.304761i	$-0.0985767\pi$
$821$	6.08258	+	10.5353i	0.212283	+	0.367686i	−0.740145	+	0.672447i	$0.765243\pi$
$822$	−40.4347	−	23.3450i	−1.41032	−	0.814249i
$823$	−40.5826			−1.41462			−0.707310	−	0.706904i	$-0.750091\pi$
$823$	−40.5826			−1.41462			−0.707310	+	0.706904i	$0.750091\pi$
$824$	−12.0000	−	6.92820i	−0.418040	−	0.241355i
$825$		0			0
$826$		0			0
$827$	−13.0390	−	7.52808i	−0.453411	−	0.261777i	0.255859	−	0.966714i	$-0.417642\pi$
$827$	−13.0390	−	7.52808i	−0.453411	−	0.261777i	−0.709270	+	0.704937i	$0.750975\pi$
$828$	12.7913	−	22.1552i	0.444528	−	0.769945i
$829$	−5.74773	−	9.95536i	−0.199627	−	0.345764i	0.748781	−	0.662818i	$-0.230640\pi$
$829$	−5.74773	−	9.95536i	−0.199627	−	0.345764i	−0.948407	+	0.317054i	$0.897306\pi$
$830$			41.2276i			1.43103i
$831$	−24.3303			−0.844009
$832$	−28.8303	+	49.9355i	−0.999511	+	1.73120i
$833$		0			0
$834$	1.89564	+	3.28335i	0.0656408	+	0.113693i
$835$	−13.3693	−	7.71878i	−0.462664	−	0.267119i
$836$		0			0
$837$		0			0
$838$	−61.0780			−2.10991
$839$	12.0826	+	20.9276i	0.417137	+	0.722502i	0.995650	−	0.0931707i	$-0.0297002\pi$
$839$	12.0826	+	20.9276i	0.417137	+	0.722502i	−0.578513	+	0.815673i	$0.696367\pi$
$840$		0			0
$841$	10.1652	+	17.6066i	0.350522	+	0.607123i
$842$	−7.89564	−	13.6757i	−0.272102	−	0.471294i
$843$	13.8303	−	7.98493i	0.476341	−	0.275016i
$844$	−44.3085	+	25.5815i	−1.52516	+	0.880553i
$845$	18.3303	−	10.5830i	0.630582	−	0.364066i
$846$	7.79129	−	13.4949i	0.267870	−	0.463964i
$847$		0			0
$848$			18.7864i			0.645128i
$849$	−13.5000	+	7.79423i	−0.463319	+	0.267497i
$850$	−13.3739	+	23.1642i	−0.458720	+	0.794526i
$851$		0			0
$852$		−	11.9536i		−	0.409522i
$853$	8.62159	−	4.97768i	0.295198	−	0.170432i	−0.345086	−	0.938571i	$-0.612150\pi$
$853$	8.62159	−	4.97768i	0.295198	−	0.170432i	0.640284	+	0.768139i	$0.278817\pi$
$854$		0			0
$855$	−9.16515	−	21.1660i	−0.313442	−	0.723862i
$856$	−1.41742	+	2.45505i	−0.0484466	+	0.0839119i
$857$	11.2913	−	19.5571i	0.385703	−	0.668057i	−0.606163	−	0.795340i	$-0.707292\pi$
$857$	11.2913	−	19.5571i	0.385703	−	0.668057i	0.991866	+	0.127283i	$0.0406256\pi$
$858$		0			0
$859$	28.9955	−	16.7405i	0.989312	−	0.571180i	0.0842435	−	0.996445i	$-0.473153\pi$
$859$	28.9955	−	16.7405i	0.989312	−	0.571180i	0.905069	+	0.425266i	$0.139819\pi$
$860$	−9.06534	+	5.23388i	−0.309126	+	0.178474i
$861$		0			0
$862$	−16.5390			−0.563321
$863$	4.91288	+	2.83645i	0.167236	+	0.0965539i	0.581282	−	0.813702i	$-0.302551\pi$
$863$	4.91288	+	2.83645i	0.167236	+	0.0965539i	−0.414046	+	0.910256i	$0.635885\pi$
$864$			36.9253i			1.25622i
$865$		−	19.6247i		−	0.667258i
$866$	−0.478220	−	0.276100i	−0.0162506	−	0.00938227i
$867$	20.3303			0.690453
$868$		0			0
$869$		0			0
$870$	−35.2259	+	20.3377i	−1.19427	+	0.689513i
$871$	−45.2477	−	26.1238i	−1.53316	−	0.885171i
$872$	12.2477	−	21.2137i	0.414760	−	0.718386i
$873$	15.7477	−	27.2759i	0.532980	−	0.923148i
$874$	17.3739	+	40.1232i	0.587680	+	1.35719i
$875$		0			0
$876$	10.8131	−	6.24293i	0.365340	−	0.210929i
$877$			41.8553i			1.41335i	0.707537	+	0.706676i	$0.249806\pi$
$877$			41.8553i			1.41335i	−0.707537	+	0.706676i	$0.750194\pi$
$878$			0.361500i			0.0122000i
$879$	−4.58258	+	7.93725i	−0.154566	+	0.267717i
$880$		0			0
$881$		−	35.0224i		−	1.17994i	−0.807427	−	0.589968i	$-0.799141\pi$
$881$		−	35.0224i		−	1.17994i	0.807427	−	0.589968i	$-0.200859\pi$
$882$		0			0
$883$	5.87386	−	10.1738i	0.197671	−	0.342377i	−0.750102	−	0.661323i	$-0.769995\pi$
$883$	5.87386	−	10.1738i	0.197671	−	0.342377i	0.947773	+	0.318946i	$0.103329\pi$
$884$	67.6824	−	39.0764i	2.27640	−	1.31428i
$885$	−6.87386	+	3.96863i	−0.231062	+	0.133404i
$886$	−20.0608	+	11.5821i	−0.673956	+	0.389108i
$887$	9.08258	+	15.7315i	0.304963	+	0.528211i	0.977253	−	0.212076i	$-0.0680226\pi$
$887$	9.08258	+	15.7315i	0.304963	+	0.528211i	−0.672290	+	0.740288i	$0.734689\pi$
$888$		0			0
$889$		0			0
$890$	−4.10436	−	7.10895i	−0.137578	−	0.238293i
$891$		0			0
$892$	8.60436	+	14.9032i	0.288095	+	0.498995i
$893$	6.16515	+	14.2378i	0.206309	+	0.476450i
$894$	23.0608	+	13.3142i	0.771268	+	0.445292i
$895$	16.1652	+	27.9989i	0.540341	+	0.935899i
$896$		0			0
$897$	−10.5000	+	18.1865i	−0.350585	+	0.607231i
$898$	−7.16515			−0.239104
$899$		0			0
$900$	5.58258	+	9.66930i	0.186086	+	0.322310i
$901$	32.0390	−	55.4932i	1.06737	−	1.84875i
$902$		0			0
$903$		0			0
$904$	18.3303			0.609657
$905$	22.3348	+	12.8950i	0.742435	+	0.428645i
$906$	−49.9129			−1.65824
$907$	41.6216	+	24.0302i	1.38202	+	0.797911i	0.992399	−	0.123063i	$-0.0392718\pi$
$907$	41.6216	+	24.0302i	1.38202	+	0.797911i	0.389623	+	0.920974i	$0.372605\pi$
$908$	−25.5826	−	44.3103i	−0.848988	−	1.47049i
$909$	−19.4174	+	11.2107i	−0.644035	+	0.371834i
$910$		0			0
$911$		−	12.2197i		−	0.404857i	−0.979297	−	0.202428i	$-0.935117\pi$
$911$		−	12.2197i		−	0.404857i	0.979297	−	0.202428i	$-0.0648834\pi$
$912$	−6.26951	−	4.65390i	−0.207604	−	0.154106i
$913$		0			0
$914$	23.3739	+	13.4949i	0.773139	+	0.446372i
$915$	39.3303			1.30022
$916$	16.7477	+	9.66930i	0.553360	+	0.319483i
$917$		0			0
$918$	33.4347	−	57.9105i	1.10351	−	1.91133i
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	−0.471684	−	0.881768i	$-0.656354\pi$
$919$	16.0000	−	27.7128i	0.527791	−	0.914161i	0.999475	−	0.0323936i	$-0.0103130\pi$
$920$	−10.5000	−	18.1865i	−0.346175	−	0.599592i
$921$	−33.3303			−1.09827
$922$	−37.2259	−	64.4772i	−1.22597	−	2.12344i
$923$		−	19.6247i		−	0.645954i
$924$		0			0
$925$		0			0
$926$			8.75560i			0.287727i
$927$	−16.0000			−0.525509
$928$	25.9347	−	44.9201i	0.851347	−	1.47458i
$929$			7.74655i			0.254156i	0.991893	+	0.127078i	$0.0405599\pi$
$929$			7.74655i			0.254156i	−0.991893	+	0.127078i	$0.959440\pi$
$930$		0			0
$931$		0			0
$932$	−8.37386			−0.274295
$933$		−	27.9035i		−	0.913520i
$934$	7.37386	−	12.7719i	0.241280	−	0.417910i
$935$		0			0
$936$		−	15.8745i		−	0.518875i
$937$	15.8739	+	9.16478i	0.518577	+	0.299400i	0.736352	−	0.676599i	$-0.236547\pi$
$937$	15.8739	+	9.16478i	0.518577	+	0.299400i	−0.217776	+	0.975999i	$0.569880\pi$
$938$		0			0
$939$			11.4014i			0.372069i
$940$	−13.1434	−	22.7650i	−0.428689	−	0.742512i
$941$	−44.0780			−1.43690			−0.718451	−	0.695577i	$-0.755149\pi$
$941$	−44.0780			−1.43690			−0.718451	+	0.695577i	$0.755149\pi$
$942$	−8.68693	−	15.0462i	−0.283036	−	0.490232i
$943$	3.24773	−	5.62523i	0.105761	−	0.183183i
$944$	2.68693	−	4.65390i	0.0874522	−	0.151472i
$945$		0			0
$946$		0			0
$947$	44.4083			1.44308			0.721538	−	0.692374i	$-0.243435\pi$
$947$	44.4083			1.44308			0.721538	+	0.692374i	$0.243435\pi$
$948$	2.43920	+	1.40828i	0.0792217	+	0.0457387i
$949$	17.7523	−	10.2493i	0.576263	−	0.332706i
$950$	−18.9564	−	2.18890i	−0.615028	−	0.0710173i
$951$			6.83285i			0.221570i
$952$		0			0
$953$	−10.8303	+	6.25288i	−0.350828	+	0.202551i	−0.665050	−	0.746799i	$-0.731590\pi$
$953$	−10.8303	+	6.25288i	−0.350828	+	0.202551i	0.314222	+	0.949350i	$0.398256\pi$
$954$	−22.9564	−	39.7617i	−0.743242	−	1.28733i
$955$	−27.4955	−	15.8745i	−0.889732	−	0.513687i
$956$	−33.4955			−1.08332
$957$		0			0
$958$	68.4519			2.21158
$959$		0			0
$960$	28.8303	+	16.6452i	0.930494	+	0.537221i
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$			3.27340i			0.105484i
$964$	−32.7913			−1.05614
$965$	2.29129	−	3.96863i	0.0737592	−	0.127755i
$966$		0			0
$967$	−2.29129	−	3.96863i	−0.0736828	−	0.127622i	0.826830	−	0.562452i	$-0.190142\pi$
$967$	−2.29129	−	3.96863i	−0.0736828	−	0.127622i	−0.900513	+	0.434830i	$0.856809\pi$
$968$	16.5000	+	9.52628i	0.530330	+	0.306186i
$969$	10.5826	+	24.4394i	0.339961	+	0.785107i
$970$	−45.5998	−	78.9812i	−1.46412	−	2.53593i
$971$	−2.66970			−0.0856747			−0.0428373	−	0.999082i	$-0.513640\pi$
$971$	−2.66970			−0.0856747			−0.0428373	+	0.999082i	$0.513640\pi$
$972$	−22.3303	−	38.6772i	−0.716245	−	1.24057i
$973$		0			0
$974$	−40.1216	−	69.4926i	−1.28558	−	2.22669i
$975$	−4.58258	−	7.93725i	−0.146760	−	0.254196i
$976$	−23.0608	+	13.3142i	−0.738158	+	0.426176i
$977$	5.66970	−	3.27340i	0.181390	−	0.104725i	−0.406556	−	0.913626i	$-0.633270\pi$
$977$	5.66970	−	3.27340i	0.181390	−	0.104725i	0.587945	+	0.808901i	$0.299937\pi$
$978$	−22.7477	+	13.1334i	−0.727392	+	0.419960i
$979$		0			0
$980$		0			0
$981$		−	28.2849i		−	0.903068i
$982$	42.8085	−	24.7155i	1.36607	−	0.788704i
$983$	21.2477	−	36.8021i	0.677697	−	1.17381i	−0.297975	−	0.954574i	$-0.596311\pi$
$983$	21.2477	−	36.8021i	0.677697	−	1.17381i	0.975673	−	0.219233i	$-0.0703553\pi$
$984$		−	2.45505i		−	0.0782642i
$985$		−	32.6229i		−	1.03945i
$986$	−81.3475	+	46.9660i	−2.59063	+	1.49570i
$987$		0			0
$988$	44.7695	+	33.2327i	1.42431	+	1.05727i
$989$	3.24773	−	5.62523i	0.103272	−	0.178872i
$990$		0			0
$991$	0.873864	+	0.504525i	0.0277592	+	0.0160268i	0.513815	−	0.857901i	$-0.328232\pi$
$991$	0.873864	+	0.504525i	0.0277592	+	0.0160268i	−0.486056	+	0.873928i	$0.661565\pi$
$992$		0			0
$993$	19.7477	−	11.4014i	0.626675	−	0.361811i
$994$		0			0
$995$	28.2523			0.895657
$996$	−17.2087	−	9.93545i	−0.545279	−	0.314817i
$997$			32.7581i			1.03746i	0.854939	+	0.518729i	$0.173595\pi$
$997$			32.7581i			1.03746i	−0.854939	+	0.518729i	$0.826405\pi$
$998$		−	60.7370i		−	1.92260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.i.e.411.1		4
7.2	even	3		133.2.p.b.69.1	yes	4
7.3	odd	6		931.2.s.e.31.2		4
7.4	even	3		931.2.s.d.31.2		4
7.5	odd	6		133.2.p.a.69.1	yes	4
7.6	odd	2		931.2.i.c.411.1		4
19.8	odd	6		931.2.s.e.901.2		4
133.27	even	6		931.2.s.d.901.2		4
133.46	odd	6		931.2.i.c.521.2		4
133.65	odd	6		133.2.p.a.27.1	✓	4
133.103	even	6		133.2.p.b.27.1	yes	4
133.122	even	6	inner	931.2.i.e.521.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.p.a.27.1	✓	4	133.65	odd	6
133.2.p.a.69.1	yes	4	7.5	odd	6
133.2.p.b.27.1	yes	4	133.103	even	6
133.2.p.b.69.1	yes	4	7.2	even	3
931.2.i.c.411.1		4	7.6	odd	2
931.2.i.c.521.2		4	133.46	odd	6
931.2.i.e.411.1		4	1.1	even	1	trivial
931.2.i.e.521.2		4	133.122	even	6	inner
931.2.s.d.31.2		4	7.4	even	3
931.2.s.d.901.2		4	133.27	even	6
931.2.s.e.31.2		4	7.3	odd	6
931.2.s.e.901.2		4	19.8	odd	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.18890i q^{2} +(0.500000 - 0.866025i) q^{3} -2.79129 q^{4} +2.64575i q^{5} +(-1.89564 - 1.09445i) q^{6} +1.73205i q^{8} +(1.00000 + 1.73205i) q^{9} +5.79129 q^{10} +(-1.39564 + 2.41733i) q^{12} +(-2.29129 + 3.96863i) q^{13} +(2.29129 + 1.32288i) q^{15} -1.79129 q^{16} +(5.29129 + 3.05493i) q^{17} +(3.79129 - 2.18890i) q^{18} +(-0.500000 + 4.33013i) q^{19} -7.38505i q^{20} +(2.29129 + 3.96863i) q^{23} +(1.50000 + 0.866025i) q^{24} -2.00000 q^{25} +(8.68693 + 5.01540i) q^{26} +5.00000 q^{27} +(-6.08258 - 3.51178i) q^{29} +(2.89564 - 5.01540i) q^{30} +7.38505i q^{32} +(6.68693 - 11.5821i) q^{34} +(-2.79129 - 4.83465i) q^{36} +(9.47822 + 1.09445i) q^{38} +(2.29129 + 3.96863i) q^{39} -4.58258 q^{40} +(-0.708712 - 1.22753i) q^{41} +(-0.708712 - 1.22753i) q^{43} +(-4.58258 + 2.64575i) q^{45} +(8.68693 - 5.01540i) q^{46} +(3.08258 - 1.77973i) q^{47} +(-0.895644 + 1.55130i) q^{48} +4.37780i q^{50} +(5.29129 - 3.05493i) q^{51} +(6.39564 - 11.0776i) q^{52} -10.4877i q^{53} -10.9445i q^{54} +(3.50000 + 2.59808i) q^{57} +(-7.68693 + 13.3142i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(-6.39564 - 3.69253i) q^{60} +(12.8739 - 7.43273i) q^{61} +12.5826 q^{64} +(-10.5000 - 6.06218i) q^{65} +11.4014i q^{67} +(-14.7695 - 8.52718i) q^{68} +4.58258 q^{69} +(-3.70871 + 2.14123i) q^{71} +(-3.00000 + 1.73205i) q^{72} +(-3.87386 - 2.23658i) q^{73} +(-1.00000 + 1.73205i) q^{75} +(1.39564 - 12.0866i) q^{76} +(8.68693 - 5.01540i) q^{78} -1.00905i q^{79} -4.73930i q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.68693 + 1.55130i) q^{82} +7.11890i q^{83} +(-8.08258 + 13.9994i) q^{85} +(-2.68693 + 1.55130i) q^{86} +(-6.08258 + 3.51178i) q^{87} +(-0.708712 - 1.22753i) q^{89} +(5.79129 + 10.0308i) q^{90} +(-6.39564 - 11.0776i) q^{92} +(-3.89564 - 6.74745i) q^{94} +(-11.4564 - 1.32288i) q^{95} +(6.39564 + 3.69253i) q^{96} +(-7.87386 - 13.6379i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} - 3 q^{6} + 4 q^{9} + 14 q^{10} - q^{12} + 2 q^{16} + 12 q^{17} + 6 q^{18} - 2 q^{19} + 6 q^{24} - 8 q^{25} + 21 q^{26} + 20 q^{27} - 6 q^{29} + 7 q^{30} + 13 q^{34} - 2 q^{36}+ \cdots - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 - 3 * q^6 + 4 * q^9 + 14 * q^10 - q^12 + 2 * q^16 + 12 * q^17 + 6 * q^18 - 2 * q^19 + 6 * q^24 - 8 * q^25 + 21 * q^26 + 20 * q^27 - 6 * q^29 + 7 * q^30 + 13 * q^34 - 2 * q^36 + 15 * q^38 - 12 * q^41 - 12 * q^43 + 21 * q^46 - 6 * q^47 + q^48 + 12 * q^51 + 21 * q^52 + 14 * q^57 - 17 * q^58 - 6 * q^59 - 21 * q^60 + 24 * q^61 + 32 * q^64 - 42 * q^65 - 27 * q^68 - 24 * q^71 - 12 * q^72 + 12 * q^73 - 4 * q^75 + q^76 + 21 * q^78 - 2 * q^81 + 3 * q^82 - 14 * q^85 + 3 * q^86 - 6 * q^87 - 12 * q^89 + 14 * q^90 - 21 * q^92 - 11 * q^94 + 21 * q^96 - 4 * q^97

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