LMFDB - Embedded newform 91.2.q.a.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(36,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("91.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.6
Root			$-1.30089 - 0.554694i$ of defining polynomial
Character	$\chi$	$=$	91.43
Dual form			91.2.q.a.36.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82678 + 1.05469i) q^{2} +(-1.13082 + 1.95864i) q^{3} +(1.22476 + 2.12135i) q^{4} -3.60178i q^{5} +(-4.13154 + 2.38535i) q^{6} +(-0.866025 + 0.500000i) q^{7} +0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +O(q^{10})$	\(q+(1.82678 + 1.05469i) q^{2} +(-1.13082 + 1.95864i) q^{3} +(1.22476 + 2.12135i) q^{4} -3.60178i q^{5} +(-4.13154 + 2.38535i) q^{6} +(-0.866025 + 0.500000i) q^{7} +0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +(3.79878 - 6.57967i) q^{10} +(0.767631 + 0.443192i) q^{11} -5.53995 q^{12} +(-1.17349 + 3.40924i) q^{13} -2.10939 q^{14} +(7.05461 + 4.07298i) q^{15} +(1.44945 - 2.51051i) q^{16} +(-2.48008 - 4.29563i) q^{17} -4.46147i q^{18} +(2.06008 - 1.18939i) q^{19} +(7.64062 - 4.41132i) q^{20} -2.26165i q^{21} +(0.934864 + 1.61923i) q^{22} +(-1.92926 + 3.34157i) q^{23} +(-1.85721 - 1.07226i) q^{24} -7.97282 q^{25} +(-5.73942 + 4.99028i) q^{26} -2.00144 q^{27} +(-2.12135 - 1.22476i) q^{28} +(-0.640986 + 1.11022i) q^{29} +(8.59150 + 14.8809i) q^{30} +8.46921i q^{31} +(6.93800 - 4.00566i) q^{32} +(-1.73611 + 1.00234i) q^{33} -10.4629i q^{34} +(1.80089 + 3.11923i) q^{35} +(2.59043 - 4.48676i) q^{36} +(-8.34686 - 4.81906i) q^{37} +5.01776 q^{38} +(-5.35049 - 6.15370i) q^{39} +3.41525 q^{40} +(10.4652 + 6.04207i) q^{41} +(2.38535 - 4.13154i) q^{42} +(-1.82125 - 3.15450i) q^{43} +2.17122i q^{44} +(-6.59734 + 3.80898i) q^{45} +(-7.04867 + 4.06955i) q^{46} -2.98229i q^{47} +(3.27814 + 5.67790i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-14.5646 - 8.40888i) q^{50} +11.2181 q^{51} +(-8.66942 + 1.68613i) q^{52} +4.92032 q^{53} +(-3.65619 - 2.11090i) q^{54} +(1.59628 - 2.76484i) q^{55} +(-0.474106 - 0.821175i) q^{56} +5.37995i q^{57} +(-2.34189 + 1.35209i) q^{58} +(6.34577 - 3.66373i) q^{59} +19.9537i q^{60} +(0.769632 + 1.33304i) q^{61} +(-8.93242 + 15.4714i) q^{62} +(1.83169 + 1.05753i) q^{63} +11.1012 q^{64} +(12.2793 + 4.22664i) q^{65} -4.22867 q^{66} +(7.29756 + 4.21325i) q^{67} +(6.07501 - 10.5222i) q^{68} +(-4.36330 - 7.55745i) q^{69} +7.59755i q^{70} +(-5.58490 + 3.22444i) q^{71} +(1.73683 - 1.00276i) q^{72} +7.14859i q^{73} +(-10.1653 - 17.6068i) q^{74} +(9.01585 - 15.6159i) q^{75} +(5.04621 + 2.91343i) q^{76} -0.886384 q^{77} +(-3.28391 - 16.8846i) q^{78} +0.757551 q^{79} +(-9.04232 - 5.22059i) q^{80} +(5.43585 - 9.41518i) q^{81} +(12.7451 + 22.0751i) q^{82} -4.76766i q^{83} +(4.79774 - 2.76998i) q^{84} +(-15.4719 + 8.93270i) q^{85} -7.68344i q^{86} +(-1.44969 - 2.51093i) q^{87} +(-0.420240 + 0.727877i) q^{88} +(3.13400 + 1.80942i) q^{89} -16.0692 q^{90} +(-0.688351 - 3.53923i) q^{91} -9.45150 q^{92} +(-16.5882 - 9.57719i) q^{93} +(3.14541 - 5.44800i) q^{94} +(-4.28391 - 7.41995i) q^{95} +18.1188i q^{96} +(-0.401229 + 0.231650i) q^{97} +(1.82678 - 1.05469i) q^{98} -1.87475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	$ 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.82678	+	1.05469i	1.29173	+	0.745781i	0.978961	−	0.204047i	$-0.0654097\pi$
$2$	1.82678	+	1.05469i	1.29173	+	0.745781i	0.312770	+	0.949829i	$0.398743\pi$
$3$	−1.13082	+	1.95864i	−0.652882	+	1.13082i	0.329539	+	0.944142i	$0.393107\pi$
$3$	−1.13082	+	1.95864i	−0.652882	+	1.13082i	−0.982420	+	0.186682i	$0.940227\pi$
$4$	1.22476	+	2.12135i	0.612380	+	1.06067i
$5$		−	3.60178i		−	1.61076i	−0.592756	−	0.805382i	$-0.701960\pi$
$5$		−	3.60178i		−	1.61076i	0.592756	−	0.805382i	$-0.298040\pi$
$6$	−4.13154	+	2.38535i	−1.68670	+	0.973814i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$7$	−0.866025	+	0.500000i	−0.327327	+	0.188982i
$8$			0.948212i			0.335243i
$9$	−1.05753	−	1.83169i	−0.352509	−	0.610563i
$10$	3.79878	−	6.57967i	1.20128	−	2.08068i
$11$	0.767631	+	0.443192i	0.231450	+	0.133627i	0.611241	−	0.791445i	$-0.290671\pi$
$11$	0.767631	+	0.443192i	0.231450	+	0.133627i	−0.379791	+	0.925072i	$0.624004\pi$
$12$	−5.53995			−1.59925
$13$	−1.17349	+	3.40924i	−0.325467	+	0.945553i
$13$	−1.17349	+	3.40924i	−0.325467	+	0.945553i
$14$	−2.10939			−0.563758
$15$	7.05461	+	4.07298i	1.82149	+	1.05164i
$16$	1.44945	−	2.51051i	0.362362	−	0.627629i
$17$	−2.48008	−	4.29563i	−0.601508	−	1.04184i	−0.992593	−	0.121488i	$-0.961233\pi$
$17$	−2.48008	−	4.29563i	−0.601508	−	1.04184i	0.391085	−	0.920355i	$-0.372100\pi$
$18$		−	4.46147i		−	1.05158i
$19$	2.06008	−	1.18939i	0.472615	−	0.272864i	−0.244719	−	0.969594i	$-0.578696\pi$
$19$	2.06008	−	1.18939i	0.472615	−	0.272864i	0.717334	+	0.696730i	$0.245362\pi$
$20$	7.64062	−	4.41132i	1.70849	−	0.986400i
$21$		−	2.26165i		−	0.493532i
$22$	0.934864	+	1.61923i	0.199314	+	0.345222i
$23$	−1.92926	+	3.34157i	−0.402278	+	0.696765i	−0.994000	−	0.109376i	$-0.965115\pi$
$23$	−1.92926	+	3.34157i	−0.402278	+	0.696765i	0.591723	+	0.806142i	$0.298448\pi$
$24$	−1.85721	−	1.07226i	−0.379101	−	0.218874i
$25$	−7.97282			−1.59456
$26$	−5.73942	+	4.99028i	−1.12559	+	0.978674i
$27$	−2.00144			−0.385177
$28$	−2.12135	−	1.22476i	−0.400897	−	0.231458i
$29$	−0.640986	+	1.11022i	−0.119028	+	0.206163i	−0.919383	−	0.393364i	$-0.871311\pi$
$29$	−0.640986	+	1.11022i	−0.119028	+	0.206163i	0.800355	+	0.599527i	$0.204645\pi$
$30$	8.59150	+	14.8809i	1.56859	+	2.71687i
$31$			8.46921i			1.52111i	0.649271	+	0.760557i	$0.275074\pi$
$31$			8.46921i			1.52111i	−0.649271	+	0.760557i	$0.724926\pi$
$32$	6.93800	−	4.00566i	1.22648	−	0.708107i
$33$	−1.73611	+	1.00234i	−0.302218	+	0.174486i
$34$		−	10.4629i		−	1.79437i
$35$	1.80089	+	3.11923i	0.304406	+	0.527247i
$36$	2.59043	−	4.48676i	0.431739	−	0.747793i
$37$	−8.34686	−	4.81906i	−1.37222	−	0.792249i	−0.381009	−	0.924571i	$-0.624423\pi$
$37$	−8.34686	−	4.81906i	−1.37222	−	0.792249i	−0.991207	+	0.132323i	$0.957757\pi$
$38$	5.01776			0.813988
$39$	−5.35049	−	6.15370i	−0.856763	−	0.985380i
$40$	3.41525			0.539998
$41$	10.4652	+	6.04207i	1.63438	+	0.943612i	0.982719	+	0.185106i	$0.0592628\pi$
$41$	10.4652	+	6.04207i	1.63438	+	0.943612i	0.651666	+	0.758506i	$0.274071\pi$
$42$	2.38535	−	4.13154i	0.368067	−	0.637511i
$43$	−1.82125	−	3.15450i	−0.277738	−	0.481056i	0.693084	−	0.720856i	$-0.256251\pi$
$43$	−1.82125	−	3.15450i	−0.277738	−	0.481056i	−0.970822	+	0.239800i	$0.922918\pi$
$44$			2.17122i			0.327323i
$45$	−6.59734	+	3.80898i	−0.983474	+	0.567809i
$46$	−7.04867	+	4.06955i	−1.03927	+	0.600022i
$47$		−	2.98229i		−	0.435012i	−0.976059	−	0.217506i	$-0.930208\pi$
$47$		−	2.98229i		−	0.435012i	0.976059	−	0.217506i	$-0.0697922\pi$
$48$	3.27814	+	5.67790i	0.473158	+	0.819535i
$49$	0.500000	−	0.866025i	0.0714286	−	0.123718i
$50$	−14.5646	−	8.40888i	−2.05975	−	1.18920i
$51$	11.2181			1.57085
$52$	−8.66942	+	1.68613i	−1.20223	+	0.233824i
$53$	4.92032			0.675858			0.337929	−	0.941172i	$-0.390274\pi$
$53$	4.92032			0.675858			0.337929	+	0.941172i	$0.390274\pi$
$54$	−3.65619	−	2.11090i	−0.497545	−	0.287258i
$55$	1.59628	−	2.76484i	0.215242	−	0.372811i
$56$	−0.474106	−	0.821175i	−0.0633551	−	0.109734i
$57$			5.37995i			0.712592i
$58$	−2.34189	+	1.35209i	−0.307505	+	0.177538i
$59$	6.34577	−	3.66373i	0.826148	−	0.476977i	−0.0263837	−	0.999652i	$-0.508399\pi$
$59$	6.34577	−	3.66373i	0.826148	−	0.476977i	0.852532	+	0.522675i	$0.175066\pi$
$60$			19.9537i			2.57601i
$61$	0.769632	+	1.33304i	0.0985412	+	0.170678i	0.911081	−	0.412227i	$-0.135249\pi$
$61$	0.769632	+	1.33304i	0.0985412	+	0.170678i	−0.812540	+	0.582906i	$0.801916\pi$
$62$	−8.93242	+	15.4714i	−1.13442	+	1.96487i
$63$	1.83169	+	1.05753i	0.230771	+	0.133236i
$64$	11.1012			1.38765
$65$	12.2793	+	4.22664i	1.52306	+	0.524250i
$66$	−4.22867			−0.520513
$67$	7.29756	+	4.21325i	0.891539	+	0.514730i	0.874445	−	0.485124i	$-0.161225\pi$
$67$	7.29756	+	4.21325i	0.891539	+	0.514730i	0.0170931	+	0.999854i	$0.494559\pi$
$68$	6.07501	−	10.5222i	0.736703	−	1.27601i
$69$	−4.36330	−	7.55745i	−0.525279	−	0.909811i
$70$			7.59755i			0.908081i
$71$	−5.58490	+	3.22444i	−0.662805	+	0.382671i	−0.793345	−	0.608772i	$-0.791662\pi$
$71$	−5.58490	+	3.22444i	−0.662805	+	0.382671i	0.130540	+	0.991443i	$0.458329\pi$
$72$	1.73683	−	1.00276i	0.204687	−	0.118176i
$73$			7.14859i			0.836679i	0.908291	+	0.418340i	$0.137388\pi$
$73$			7.14859i			0.836679i	−0.908291	+	0.418340i	$0.862612\pi$
$74$	−10.1653	−	17.6068i	−1.18169	−	2.04675i
$75$	9.01585	−	15.6159i	1.04106	−	1.80317i
$76$	5.04621	+	2.91343i	0.578840	+	0.334193i
$77$	−0.886384			−0.101013
$78$	−3.28391	−	16.8846i	−0.371830	−	1.91180i
$79$	0.757551			0.0852311			0.0426156	−	0.999092i	$-0.486431\pi$
$79$	0.757551			0.0852311			0.0426156	+	0.999092i	$0.486431\pi$
$80$	−9.04232	−	5.22059i	−1.01096	−	0.583679i
$81$	5.43585	−	9.41518i	0.603984	−	1.04613i
$82$	12.7451	+	22.0751i	1.40746	+	2.43779i
$83$		−	4.76766i		−	0.523319i	−0.965160	−	0.261659i	$-0.915730\pi$
$83$		−	4.76766i		−	0.523319i	0.965160	−	0.261659i	$-0.0842697\pi$
$84$	4.79774	−	2.76998i	0.523476	−	0.302229i
$85$	−15.4719	+	8.93270i	−1.67816	+	0.968888i
$86$		−	7.68344i		−	0.828527i
$87$	−1.44969	−	2.51093i	−0.155423	−	0.269200i
$88$	−0.420240	+	0.727877i	−0.0447977	+	0.0775919i
$89$	3.13400	+	1.80942i	0.332204	+	0.191798i	0.656819	−	0.754048i	$-0.271902\pi$
$89$	3.13400	+	1.80942i	0.332204	+	0.191798i	−0.324615	+	0.945846i	$0.605235\pi$
$90$	−16.0692			−1.69385
$91$	−0.688351	−	3.53923i	−0.0721588	−	0.371012i
$92$	−9.45150			−0.985387
$93$	−16.5882	−	9.57719i	−1.72011	−	0.993108i
$94$	3.14541	−	5.44800i	0.324424	−	0.561919i
$95$	−4.28391	−	7.41995i	−0.439520	−	0.761271i
$96$			18.1188i			1.84924i
$97$	−0.401229	+	0.231650i	−0.0407386	+	0.0235205i	−0.520231	−	0.854026i	$-0.674154\pi$
$97$	−0.401229	+	0.231650i	−0.0407386	+	0.0235205i	0.479492	+	0.877546i	$0.340821\pi$
$98$	1.82678	−	1.05469i	0.184533	−	0.106540i
$99$		−	1.87475i		−	0.188419i
$100$	−9.76479	−	16.9131i	−0.976479	−	1.69131i
$101$	2.91152	−	5.04289i	0.289707	−	0.501787i	−0.684033	−	0.729451i	$-0.739776\pi$
$101$	2.91152	−	5.04289i	0.289707	−	0.501787i	0.973740	+	0.227664i	$0.0731089\pi$
$102$	20.4931	+	11.8317i	2.02912	+	1.17151i
$103$	−8.23888			−0.811801			−0.405901	−	0.913917i	$-0.633042\pi$
$103$	−8.23888			−0.811801			−0.405901	+	0.913917i	$0.633042\pi$
$104$	−3.23268	−	1.11271i	−0.316991	−	0.109111i
$105$	−8.14596			−0.794964
$106$	8.98837	+	5.18944i	0.873027	+	0.504043i
$107$	1.91630	−	3.31913i	0.185256	−	0.320872i	−0.758407	−	0.651781i	$-0.774022\pi$
$107$	1.91630	−	3.31913i	0.185256	−	0.320872i	0.943663	+	0.330909i	$0.107355\pi$
$108$	−2.45128	−	4.24574i	−0.235875	−	0.408547i
$109$		−	10.4180i		−	0.997867i	−0.866640	−	0.498934i	$-0.833725\pi$
$109$		−	10.4180i		−	0.997867i	0.866640	−	0.498934i	$-0.166275\pi$
$110$	5.83212	−	3.36718i	0.556071	−	0.321048i
$111$	18.8777	−	10.8990i	1.79179	−	1.03449i
$112$			2.89889i			0.273920i
$113$	2.45505	+	4.25228i	0.230952	+	0.400021i	0.958089	−	0.286472i	$-0.0924826\pi$
$113$	2.45505	+	4.25228i	0.230952	+	0.400021i	−0.727136	+	0.686493i	$0.759149\pi$
$114$	−5.67421	+	9.82801i	−0.531438	+	0.920478i
$115$	12.0356	+	6.94875i	1.12233	+	0.647975i
$116$	−3.14022			−0.291562
$117$	7.48567	−	1.45590i	0.692050	−	0.134598i
$118$	15.4565			1.42288
$119$	4.29563	+	2.48008i	0.393779	+	0.227349i
$120$	−3.86205	+	6.68926i	−0.352555	+	0.610643i
$121$	−5.10716	−	8.84586i	−0.464287	−	0.804169i
$122$			3.24690i			0.293961i
$123$	−23.6685	+	13.6650i	−2.13412	+	1.23213i
$124$	−17.9661	+	10.3727i	−1.61341	+	0.931500i
$125$			10.7074i			0.957702i
$126$	2.23073	+	3.86375i	0.198730	+	0.344210i
$127$	−6.15508	+	10.6609i	−0.546175	+	0.946003i	0.452357	+	0.891837i	$0.350583\pi$
$127$	−6.15508	+	10.6609i	−0.546175	+	0.946003i	−0.998532	+	0.0541658i	$0.982750\pi$
$128$	6.40347	+	3.69704i	0.565992	+	0.326776i
$129$	8.23805			0.725320
$130$	17.9739	+	20.6721i	1.57641	+	1.81306i
$131$	−8.20265			−0.716669			−0.358335	−	0.933593i	$-0.616655\pi$
$131$	−8.20265			−0.716669			−0.358335	+	0.933593i	$0.616655\pi$
$132$	−4.25264	−	2.45526i	−0.370145	−	0.213703i
$133$	−1.18939	+	2.06008i	−0.103133	+	0.178632i
$134$	8.88737	+	15.3934i	0.767752	+	1.32979i
$135$			7.20874i			0.620429i
$136$	4.07316	−	2.35164i	0.349271	−	0.201652i
$137$	6.45670	−	3.72778i	0.551633	−	0.318485i	−0.198147	−	0.980172i	$-0.563492\pi$
$137$	6.45670	−	3.72778i	0.551633	−	0.318485i	0.749780	+	0.661687i	$0.230159\pi$
$138$		−	18.4078i		−	1.56697i
$139$	−8.34028	−	14.4458i	−0.707413	−	1.22528i	−0.965813	−	0.259238i	$-0.916529\pi$
$139$	−8.34028	−	14.4458i	−0.707413	−	1.22528i	0.258400	−	0.966038i	$-0.416805\pi$
$140$	−4.41132	+	7.64062i	−0.372824	+	0.645750i
$141$	5.84125	+	3.37245i	0.491922	+	0.284011i
$142$	−13.6032			−1.14156
$143$	−2.41175	+	2.09696i	−0.201681	+	0.175357i
$144$	−6.13131			−0.510943
$145$	3.99877	+	2.30869i	0.332080	+	0.191726i
$146$	−7.53958	+	13.0589i	−0.623980	+	1.08076i
$147$	1.13082	+	1.95864i	0.0932688	+	0.161546i
$148$		−	23.6088i		−	1.94063i
$149$	−2.18380	+	1.26082i	−0.178904	+	0.103290i	−0.586777	−	0.809748i	$-0.699604\pi$
$149$	−2.18380	+	1.26082i	−0.178904	+	0.103290i	0.407874	+	0.913038i	$0.366270\pi$
$150$	32.9400	−	19.0179i	2.68954	−	1.55281i
$151$			15.8972i			1.29370i	0.762618	+	0.646849i	$0.223914\pi$
$151$			15.8972i			1.29370i	−0.762618	+	0.646849i	$0.776086\pi$
$152$	1.12779	+	1.95339i	0.0914760	+	0.158441i
$153$	−5.24550	+	9.08548i	−0.424074	+	0.734517i
$154$	−1.61923	−	0.934864i	−0.130481	−	0.0753335i
$155$	30.5042			2.45016
$156$	6.50106	−	18.8870i	0.520502	−	1.51217i
$157$	12.9831			1.03616			0.518082	−	0.855331i	$-0.326646\pi$
$157$	12.9831			1.03616			0.518082	+	0.855331i	$0.326646\pi$
$158$	1.38388	+	0.798985i	0.110096	+	0.0635638i
$159$	−5.56402	+	9.63717i	−0.441256	+	0.764277i
$160$	−14.4275	−	24.9892i	−1.14059	−	1.97557i
$161$		−	3.85851i		−	0.304093i
$162$	19.8603	−	11.4663i	1.56037	−	0.900880i
$163$	−2.00873	+	1.15974i	−0.157336	+	0.0908378i	−0.576601	−	0.817026i	$-0.695621\pi$
$163$	−2.00873	+	1.15974i	−0.157336	+	0.0908378i	0.419265	+	0.907864i	$0.362288\pi$
$164$			29.6003i			2.31140i
$165$	3.61023	+	6.25309i	0.281056	+	0.486803i
$166$	5.02843	−	8.70949i	0.390282	−	0.675987i
$167$	−11.9441	−	6.89591i	−0.924260	−	0.533622i	−0.0392682	−	0.999229i	$-0.512503\pi$
$167$	−11.9441	−	6.89591i	−0.924260	−	0.533622i	−0.884992	+	0.465607i	$0.845836\pi$
$168$	2.14452			0.165453
$169$	−10.2459	−	8.00140i	−0.788143	−	0.615493i
$170$	−37.6851			−2.89031
$171$	−4.35718	−	2.51562i	−0.333202	−	0.192374i
$172$	4.46118	−	7.72700i	0.340162	−	0.589178i
$173$	−1.84216	−	3.19071i	−0.140057	−	0.242585i	0.787461	−	0.616364i	$-0.211395\pi$
$173$	−1.84216	−	3.19071i	−0.140057	−	0.242585i	−0.927518	+	0.373779i	$0.878062\pi$
$174$		−	6.11590i		−	0.463645i
$175$	6.90466	−	3.98641i	0.521943	−	0.301344i
$176$	2.22528	−	1.28477i	0.167737	−	0.0968429i
$177$			16.5721i			1.24564i
$178$	3.81677	+	6.61083i	0.286079	+	0.495503i
$179$	−2.94638	+	5.10328i	−0.220223	+	0.381437i	−0.954876	−	0.297006i	$-0.904012\pi$
$179$	−2.94638	+	5.10328i	−0.220223	+	0.381437i	0.734653	+	0.678443i	$0.237345\pi$
$180$	−16.1603	−	9.33017i	−1.20452	−	0.695430i
$181$	−2.11543			−0.157239			−0.0786193	−	0.996905i	$-0.525051\pi$
$181$	−2.11543			−0.157239			−0.0786193	+	0.996905i	$0.525051\pi$
$182$	2.47534	−	7.19141i	0.183484	−	0.533063i
$183$	−3.48127			−0.257343
$184$	−3.16851	−	1.82934i	−0.233586	−	0.134861i
$185$	−17.3572	+	30.0635i	−1.27613	+	2.21032i
$186$	−20.2020	−	34.9909i	−1.48128	−	2.56566i
$187$		−	4.39661i		−	0.321512i
$188$	6.32647	−	3.65259i	0.461406	−	0.266393i
$189$	1.73330	−	1.00072i	0.126079	−	0.0727916i
$190$		−	18.0729i		−	1.31114i
$191$	5.68333	+	9.84381i	0.411231	+	0.712273i	0.995025	−	0.0996290i	$-0.0317656\pi$
$191$	5.68333	+	9.84381i	0.411231	+	0.712273i	−0.583794	+	0.811902i	$0.698432\pi$
$192$	−12.5535	+	21.7433i	−0.905970	+	1.56919i
$193$	12.2017	+	7.04468i	0.878301	+	0.507087i	0.870098	−	0.492879i	$-0.164055\pi$
$193$	12.2017	+	7.04468i	0.878301	+	0.507087i	0.00820314	+	0.999966i	$0.497389\pi$
$194$	−0.977279			−0.0701645
$195$	−22.1643	+	19.2713i	−1.58722	+	1.38004i
$196$	2.44952			0.174966
$197$	−19.8815	−	11.4786i	−1.41650	−	0.817814i	−0.420507	−	0.907289i	$-0.638148\pi$
$197$	−19.8815	−	11.4786i	−1.41650	−	0.817814i	−0.995989	+	0.0894753i	$0.971481\pi$
$198$	1.97729	−	3.42476i	0.140520	−	0.243387i
$199$	−1.57492	−	2.72785i	−0.111643	−	0.193372i	0.804790	−	0.593560i	$-0.202278\pi$
$199$	−1.57492	−	2.72785i	−0.111643	−	0.193372i	−0.916433	+	0.400188i	$0.868945\pi$
$200$		−	7.55992i		−	0.534567i
$201$	−16.5045	+	9.52888i	−1.16414	+	0.672116i
$202$	10.6374	−	6.14152i	0.748446	−	0.432116i
$203$		−	1.28197i		−	0.0899768i
$204$	13.7395	+	23.7976i	0.961959	+	1.66616i
$205$	21.7622	−	37.6932i	1.51994	−	2.63261i
$206$	−15.0507	−	8.68950i	−1.04863	−	0.605426i
$207$	8.16096			0.567226
$208$	6.85804	+	7.88757i	0.475520	+	0.546905i
$209$	2.10851			0.145849
$210$	−14.8809	−	8.59150i	−1.02688	−	0.592870i
$211$	7.43191	−	12.8725i	0.511634	−	0.886176i	−0.488275	−	0.872690i	$-0.662374\pi$
$211$	7.43191	−	12.8725i	0.511634	−	0.886176i	0.999909	−	0.0134864i	$-0.00429298\pi$
$212$	6.02621	+	10.4377i	0.413882	+	0.716865i
$213$		−	14.5851i		−	0.999355i
$214$	7.00133	−	4.04222i	0.478601	−	0.276321i
$215$	−11.3618	+	6.55974i	−0.774868	+	0.447370i
$216$		−	1.89779i		−	0.129128i
$217$	−4.23460	−	7.33455i	−0.287464	−	0.497902i
$218$	10.9878	−	19.0315i	0.744191	−	1.28898i
$219$	−14.0016	−	8.08380i	−0.946137	−	0.546253i
$220$	7.82024			0.527241
$221$	17.5552	−	3.41433i	1.18089	−	0.229673i
$222$	45.9805			3.08601
$223$	3.79396	+	2.19044i	0.254062	+	0.146683i	0.621623	−	0.783317i	$-0.286474\pi$
$223$	3.79396	+	2.19044i	0.254062	+	0.146683i	−0.367561	+	0.930000i	$0.619807\pi$
$224$	−4.00566	+	6.93800i	−0.267639	+	0.463565i
$225$	8.43147	+	14.6037i	0.562098	+	0.973582i
$226$			10.3573i			0.688959i
$227$	11.7488	−	6.78316i	0.779793	−	0.450214i	−0.0565636	−	0.998399i	$-0.518014\pi$
$227$	11.7488	−	6.78316i	0.779793	−	0.450214i	0.836357	+	0.548185i	$0.184681\pi$
$228$	−11.4127	+	6.58915i	−0.755827	+	0.436377i
$229$		−	16.5180i		−	1.09154i	−0.837935	−	0.545770i	$-0.816237\pi$
$229$		−	16.5180i		−	1.09154i	0.837935	−	0.545770i	$-0.183763\pi$
$230$	14.6576	+	25.3877i	0.966495	+	1.67402i
$231$	1.00234	−	1.73611i	0.0659494	−	0.114228i
$232$	−1.05272	−	0.607791i	−0.0691147	−	0.0399034i
$233$	16.5026			1.08112			0.540561	−	0.841305i	$-0.318212\pi$
$233$	16.5026			1.08112			0.540561	+	0.841305i	$0.318212\pi$
$234$	15.2102	+	5.23548i	0.994324	+	0.342254i
$235$	−10.7416			−0.700702
$236$	15.5441	+	8.97438i	1.01183	+	0.584182i
$237$	−0.856657	+	1.48377i	−0.0556458	+	0.0963814i
$238$	5.23145	+	9.06114i	0.339105	+	0.587347i
$239$			30.4210i			1.96777i	0.178796	+	0.983886i	$0.442780\pi$
$239$			30.4210i			1.96777i	−0.178796	+	0.983886i	$0.557220\pi$
$240$	20.4506	−	11.8071i	1.32008	−	0.762147i
$241$	−25.5602	+	14.7572i	−1.64648	+	0.950593i	−0.668018	+	0.744145i	$0.732857\pi$
$241$	−25.5602	+	14.7572i	−1.64648	+	0.950593i	−0.978458	+	0.206448i	$0.933810\pi$
$242$		−	21.5460i		−	1.38503i
$243$	9.29184	+	16.0939i	0.596072	+	1.03243i
$244$	−1.88523	+	3.26531i	−0.120689	+	0.209040i
$245$	−3.11923	−	1.80089i	−0.199280	−	0.115055i
$246$	−57.6497			−3.67561
$247$	1.63743	+	8.41904i	0.104187	+	0.535691i
$248$	−8.03060			−0.509944
$249$	9.33816	+	5.39139i	0.591782	+	0.341665i
$250$	−11.2931	+	19.5602i	−0.714236	+	1.23709i
$251$	−6.49134	−	11.2433i	−0.409730	−	0.709673i	0.585130	−	0.810940i	$-0.301044\pi$
$251$	−6.49134	−	11.2433i	−0.409730	−	0.709673i	−0.994859	+	0.101267i	$0.967710\pi$
$252$			5.18087i			0.326364i
$253$	−2.96191	+	1.71006i	−0.186214	+	0.107511i
$254$	−22.4880	+	12.9835i	−1.41102	+	0.814654i
$255$		−	40.4053i		−	2.53028i
$256$	−3.30268	−	5.72042i	−0.206418	−	0.357526i
$257$	−2.29261	+	3.97091i	−0.143009	+	0.247698i	−0.928628	−	0.371011i	$-0.879011\pi$
$257$	−2.29261	+	3.97091i	−0.143009	+	0.247698i	0.785620	+	0.618710i	$0.212344\pi$
$258$	15.0491	+	8.68862i	0.936918	+	0.540930i
$259$	9.63812			0.598884
$260$	6.07307	+	31.2253i	0.376636	+	1.93651i
$261$	2.71144			0.167834
$262$	−14.9845	−	8.65129i	−0.925744	−	0.534479i
$263$	1.33250	−	2.30795i	0.0821652	−	0.142314i	−0.822015	−	0.569466i	$-0.807150\pi$
$263$	1.33250	−	2.30795i	0.0821652	−	0.142314i	0.904180	+	0.427152i	$0.140483\pi$
$264$	−0.950435	−	1.64620i	−0.0584952	−	0.101317i
$265$		−	17.7219i		−	1.08865i
$266$	−4.34551	+	2.50888i	−0.266440	+	0.153829i
$267$	−7.08801	+	4.09227i	−0.433779	+	0.250443i
$268$			20.6409i			1.26084i
$269$	−5.96282	−	10.3279i	−0.363559	−	0.629703i	0.624984	−	0.780637i	$-0.285105\pi$
$269$	−5.96282	−	10.3279i	−0.363559	−	0.629703i	−0.988544	+	0.150934i	$0.951772\pi$
$270$	−7.60301	+	13.1688i	−0.462705	+	0.801428i
$271$	−11.2828	−	6.51416i	−0.685384	−	0.395707i	0.116496	−	0.993191i	$-0.462834\pi$
$271$	−11.2828	−	6.51416i	−0.685384	−	0.395707i	−0.801881	+	0.597484i	$0.796167\pi$
$272$	−14.3790			−0.871853
$273$	7.71051	+	2.65402i	0.466661	+	0.160628i
$274$	15.7267			0.950082
$275$	−6.12018	−	3.53349i	−0.369061	−	0.213077i
$276$	10.6880	−	18.5121i	0.643341	−	1.11430i
$277$	10.6824	+	18.5025i	0.641846	+	1.11171i	0.985020	+	0.172438i	$0.0551646\pi$
$277$	10.6824	+	18.5025i	0.641846	+	1.11171i	−0.343174	+	0.939272i	$0.611502\pi$
$278$		−	35.1858i		−	2.11030i
$279$	15.5130	−	8.95641i	0.928737	−	0.536206i
$280$	−2.95769	+	1.70762i	−0.176756	+	0.102050i
$281$		−	17.2678i		−	1.03011i	−0.857158	−	0.515054i	$-0.827772\pi$
$281$		−	17.2678i		−	1.03011i	0.857158	−	0.515054i	$-0.172228\pi$
$282$	7.11380	+	12.3215i	0.423621	+	0.733733i
$283$	−10.6201	+	18.3946i	−0.631299	+	1.09344i	0.355987	+	0.934491i	$0.384145\pi$
$283$	−10.6201	+	18.3946i	−0.631299	+	1.09344i	−0.987286	+	0.158952i	$0.949189\pi$
$284$	−13.6803	−	7.89833i	−0.811777	−	0.468680i
$285$	19.3774			1.14782
$286$	−6.61741	+	1.28703i	−0.391295	+	0.0761037i
$287$	−12.0841			−0.713304
$288$	−14.6742	−	8.47218i	−0.864688	−	0.499228i
$289$	−3.80160	+	6.58457i	−0.223624	+	0.387327i
$290$	4.86993	+	8.43496i	0.285972	+	0.495318i
$291$		−	1.04782i		−	0.0614243i
$292$	−15.1646	+	8.75531i	−0.887443	+	0.512366i
$293$	−0.363782	+	0.210030i	−0.0212524	+	0.0122701i	−0.510589	−	0.859825i	$-0.670572\pi$
$293$	−0.363782	+	0.210030i	−0.0212524	+	0.0122701i	0.489336	+	0.872095i	$0.337239\pi$
$294$			4.77070i			0.278233i
$295$	−13.1959	−	22.8561i	−0.768298	−	1.33073i
$296$	4.56949	−	7.91459i	0.265596	−	0.460026i
$297$	−1.53637	−	0.887022i	−0.0891490	−	0.0514702i
$298$	−5.31910			−0.308127
$299$	−9.12826	−	10.4986i	−0.527901	−	0.607149i
$300$	44.1690			2.55010
$301$	3.15450	+	1.82125i	0.181822	+	0.104975i
$302$	−16.7667	+	29.0408i	−0.964817	+	1.67111i
$303$	6.58482	+	11.4053i	0.378288	+	0.655215i
$304$		−	6.89581i		−	0.395502i
$305$	4.80132	−	2.77204i	0.274923	−	0.158727i
$306$	−19.1648	+	11.0648i	−1.09558	+	0.632533i
$307$			14.0807i			0.803628i	0.915721	+	0.401814i	$0.131620\pi$
$307$			14.0807i			0.803628i	−0.915721	+	0.401814i	$0.868380\pi$
$308$	−1.08561	−	1.88033i	−0.0618583	−	0.107142i
$309$	9.31673	−	16.1370i	0.530010	−	0.918004i
$310$	55.7246	+	32.1726i	3.16495	+	1.82728i
$311$	−10.3848			−0.588867			−0.294434	−	0.955672i	$-0.595131\pi$
$311$	−10.3848			−0.588867			−0.294434	+	0.955672i	$0.595131\pi$
$312$	5.83501	−	5.07339i	0.330342	−	0.287224i
$313$	6.84759			0.387048			0.193524	−	0.981096i	$-0.438008\pi$
$313$	6.84759			0.387048			0.193524	+	0.981096i	$0.438008\pi$
$314$	23.7173	+	13.6932i	1.33845	+	0.772752i
$315$	3.80898	−	6.59734i	0.214612	−	0.371718i
$316$	0.927818	+	1.60703i	0.0521938	+	0.0904024i
$317$		−	0.701249i		−	0.0393861i	−0.999806	−	0.0196930i	$-0.993731\pi$
$317$		−	0.701249i		−	0.0393861i	0.999806	−	0.0196930i	$-0.00626889\pi$
$318$	−20.3285	+	11.7367i	−1.13997	+	0.658160i
$319$	−0.984082	+	0.568160i	−0.0550980	+	0.0318109i
$320$		−	39.9840i		−	2.23518i
$321$	4.33400	+	7.50670i	0.241900	+	0.418983i
$322$	4.06955	−	7.04867i	0.226787	−	0.392807i
$323$	−10.2183	−	5.89956i	−0.568563	−	0.328260i
$324$	26.6305			1.47947
$325$	9.35600	−	27.1813i	0.518977	−	1.50774i
$326$	−4.89268			−0.270980
$327$	20.4052	+	11.7810i	1.12841	+	0.651489i
$328$	−5.72916	+	9.92319i	−0.316340	+	0.547917i
$329$	1.49115	+	2.58274i	0.0822095	+	0.142391i
$330$			15.2307i			0.838424i
$331$	3.63613	−	2.09932i	0.199860	−	0.115389i	−0.396730	−	0.917935i	$-0.629855\pi$
$331$	3.63613	−	2.09932i	0.199860	−	0.115389i	0.596590	+	0.802546i	$0.296522\pi$
$332$	10.1139	−	5.83924i	0.555070	−	0.320470i
$333$			20.3851i			1.11710i
$334$	−14.5462	−	25.1947i	−0.795930	−	1.37859i
$335$	15.1752	−	26.2842i	0.829109	−	1.43606i
$336$	−5.67790	−	3.27814i	−0.309755	−	0.178837i
$337$	−20.4278			−1.11278			−0.556388	−	0.830923i	$-0.687813\pi$
$337$	−20.4278			−1.11278			−0.556388	+	0.830923i	$0.687813\pi$
$338$	−10.2779	−	25.4231i	−0.559046	−	1.38283i
$339$	−11.1049			−0.603138
$340$	−37.8987	−	21.8808i	−2.05535	−	1.18665i
$341$	−3.75349	+	6.50123i	−0.203263	+	0.352061i
$342$	−5.30642	−	9.19098i	−0.286938	−	0.496991i
$343$			1.00000i			0.0539949i
$344$	2.99113	−	1.72693i	0.161271	−	0.0931098i
$345$	−27.2203	+	15.7156i	−1.46549	+	0.846102i
$346$		−	7.77165i		−	0.417807i
$347$	−3.98500	−	6.90222i	−0.213926	−	0.370531i	0.739014	−	0.673690i	$-0.235292\pi$
$347$	−3.98500	−	6.90222i	−0.213926	−	0.370531i	−0.952940	+	0.303160i	$0.901959\pi$
$348$	3.55103	−	6.15057i	0.190355	−	0.329705i
$349$	18.7038	+	10.7986i	1.00119	+	0.578037i	0.908600	−	0.417668i	$-0.137152\pi$
$349$	18.7038	+	10.7986i	1.00119	+	0.578037i	0.0925892	+	0.995704i	$0.470486\pi$
$350$	16.8178			0.898947
$351$	2.34866	−	6.82338i	0.125362	−	0.364205i
$352$	7.10110			0.378490
$353$	18.7214	+	10.8088i	0.996439	+	0.575295i	0.907193	−	0.420715i	$-0.138221\pi$
$353$	18.7214	+	10.8088i	0.996439	+	0.575295i	0.0892465	+	0.996010i	$0.471554\pi$
$354$	−17.4785	+	30.2737i	−0.928974	+	1.60903i
$355$	11.6137	+	20.1156i	0.616393	+	1.06762i
$356$			8.86441i			0.469813i
$357$	−9.71520	+	5.60907i	−0.514183	+	0.296863i
$358$	−10.7648	+	6.21507i	−0.568938	+	0.328476i
$359$		−	13.6834i		−	0.722180i	−0.932531	−	0.361090i	$-0.882405\pi$
$359$		−	13.6834i		−	0.722180i	0.932531	−	0.361090i	$-0.117595\pi$
$360$	−3.61172	−	6.25568i	−0.190354	−	0.329703i
$361$	−6.67071	+	11.5540i	−0.351090	+	0.608106i
$362$	−3.86443	−	2.23113i	−0.203110	−	0.117266i
$363$	23.1012			1.21250
$364$	6.66487	−	5.79494i	0.349334	−	0.303737i
$365$	25.7477			1.34769
$366$	−6.35953	−	3.67168i	−0.332418	−	0.191922i
$367$	5.70638	−	9.88374i	0.297871	−	0.515927i	−0.677778	−	0.735267i	$-0.737057\pi$
$367$	5.70638	−	9.88374i	0.297871	−	0.515927i	0.975649	+	0.219339i	$0.0703902\pi$
$368$	5.59271	+	9.68685i	0.291540	+	0.504962i
$369$		−	25.5586i		−	1.33053i
$370$	−63.4157	+	36.6131i	−3.29683	+	1.90342i
$371$	−4.26112	+	2.46016i	−0.221227	+	0.127725i
$372$		−	46.9190i		−	2.43264i
$373$	15.6404	+	27.0900i	0.809830	+	1.40267i	0.912981	+	0.408002i	$0.133774\pi$
$373$	15.6404	+	27.0900i	0.809830	+	1.40267i	−0.103151	+	0.994666i	$0.532892\pi$
$374$	4.63708	−	8.03166i	0.239778	−	0.415307i
$375$	−20.9721	−	12.1082i	−1.08299	−	0.625266i
$376$	2.82784			0.145835
$377$	−3.03282	−	3.48811i	−0.156198	−	0.179647i
$378$	4.22181			0.217146
$379$	23.7421	+	13.7075i	1.21955	+	0.704108i	0.964822	−	0.262904i	$-0.0846803\pi$
$379$	23.7421	+	13.7075i	1.21955	+	0.704108i	0.254729	+	0.967012i	$0.418014\pi$
$380$	10.4935	−	18.1753i	0.538307	−	0.932374i
$381$	−13.9206	−	24.1112i	−0.713175	−	1.23526i
$382$			23.9767i			1.22675i
$383$	13.9436	−	8.05032i	0.712483	−	0.411352i	−0.0994967	−	0.995038i	$-0.531723\pi$
$383$	13.9436	−	8.05032i	0.712483	−	0.411352i	0.811980	+	0.583686i	$0.198390\pi$
$384$	−14.4824	+	8.36142i	−0.739052	+	0.426692i
$385$			3.19256i			0.162708i
$386$	14.8600	+	25.7382i	0.756353	+	1.31004i
$387$	−3.85204	+	6.67193i	−0.195810	+	0.339153i
$388$	−0.982819	−	0.567431i	−0.0498951	−	0.0288069i
$389$	−21.1380			−1.07174			−0.535870	−	0.844301i	$-0.680016\pi$
$389$	−21.1380			−1.07174			−0.535870	+	0.844301i	$0.680016\pi$
$390$	−60.8146	+	11.8279i	−3.07947	+	0.598930i
$391$	19.1388			0.967893
$392$	0.821175	+	0.474106i	0.0414756	+	0.0239460i
$393$	9.27576	−	16.0661i	0.467900	−	0.810427i
$394$	−24.2128	−	41.9377i	−1.21982	−	2.11279i
$395$		−	2.72853i		−	0.137287i
$396$	3.97699	−	2.29612i	0.199851	−	0.115384i
$397$	11.3436	−	6.54921i	0.569317	−	0.328695i	−0.187560	−	0.982253i	$-0.560058\pi$
$397$	11.3436	−	6.54921i	0.569317	−	0.328695i	0.756876	+	0.653558i	$0.226724\pi$
$398$		−	6.64426i		−	0.333046i
$399$	−2.68998	−	4.65918i	−0.134667	−	0.233251i
$400$	−11.5562	+	20.0159i	−0.577808	+	1.00079i
$401$	16.8396	+	9.72236i	0.840930	+	0.485511i	0.857580	−	0.514350i	$-0.171967\pi$
$401$	16.8396	+	9.72236i	0.840930	+	0.485511i	−0.0166501	+	0.999861i	$0.505300\pi$
$402$	−40.2002			−2.00501
$403$	−28.8736	−	9.93851i	−1.43830	−	0.495072i
$404$	14.2636			0.709642
$405$	−33.9114	−	19.5788i	−1.68507	−	0.972876i
$406$	1.35209	−	2.34189i	0.0671031	−	0.116226i
$407$	−4.27154	−	7.39853i	−0.211732	−	0.366731i
$408$			10.6372i			0.526618i
$409$	20.8330	−	12.0279i	1.03013	−	0.594743i	0.113105	−	0.993583i	$-0.463921\pi$
$409$	20.8330	−	12.0279i	1.03013	−	0.594743i	0.917020	+	0.398840i	$0.130587\pi$
$410$	79.5096	−	45.9049i	3.92670	−	2.26708i
$411$			16.8618i			0.831733i
$412$	−10.0907	−	17.4775i	−0.497131	−	0.861056i
$413$	−3.66373	+	6.34577i	−0.180280	+	0.312255i
$414$	14.9083	+	8.60732i	0.732703	+	0.423026i
$415$	−17.1721			−0.842944
$416$	5.51460	+	28.3539i	0.270375	+	1.39016i
$417$	37.7256			1.84743
$418$	3.85179	+	2.22383i	0.188397	+	0.108771i
$419$	−19.5119	+	33.7956i	−0.953218	+	1.65102i	−0.214825	+	0.976653i	$0.568918\pi$
$419$	−19.5119	+	33.7956i	−0.953218	+	1.65102i	−0.738394	+	0.674370i	$0.764415\pi$
$420$	−9.97684	−	17.2804i	−0.486820	−	0.843197i
$421$			22.0284i			1.07360i	0.843710	+	0.536799i	$0.180367\pi$
$421$			22.0284i			1.07360i	−0.843710	+	0.536799i	$0.819633\pi$
$422$	27.1530	−	15.6768i	1.32179	−	0.763134i
$423$	−5.46263	+	3.15385i	−0.265602	+	0.153346i
$424$			4.66551i			0.226577i
$425$	19.7732	+	34.2482i	0.959142	+	1.66128i
$426$	15.3828	−	26.6438i	0.745301	−	1.29090i
$427$	−1.33304	−	0.769632i	−0.0645104	−	0.0372451i
$428$	9.38803			0.453787
$429$	−1.37993	−	7.09506i	−0.0666237	−	0.342553i
$430$	−27.6741			−1.33456
$431$	−31.0727	−	17.9398i	−1.49672	−	0.864131i	−0.496726	−	0.867907i	$-0.665465\pi$
$431$	−31.0727	−	17.9398i	−1.49672	−	0.864131i	−0.999993	+	0.00377645i	$0.998798\pi$
$432$	−2.90098	+	5.02464i	−0.139573	+	0.241748i
$433$	6.10678	+	10.5773i	0.293473	+	0.508310i	0.974629	−	0.223828i	$-0.0718555\pi$
$433$	6.10678	+	10.5773i	0.293473	+	0.508310i	−0.681155	+	0.732139i	$0.738522\pi$
$434$		−	17.8648i		−	0.857540i
$435$	−9.04381	+	5.22145i	−0.433618	+	0.250349i
$436$	22.1003	−	12.7596i	1.05841	−	0.611074i
$437$			9.17853i			0.439069i
$438$	−17.0519	−	29.5347i	−0.814770	−	1.41122i
$439$	−7.87765	+	13.6445i	−0.375980	+	0.651216i	−0.990473	−	0.137706i	$-0.956027\pi$
$439$	−7.87765	+	13.6445i	−0.375980	+	0.651216i	0.614493	+	0.788922i	$0.289361\pi$
$440$	2.62165	+	1.51361i	0.124982	+	0.0721586i
$441$	−2.11505			−0.100717
$442$	35.6706	+	12.2781i	1.69668	+	0.584009i
$443$	−15.0706			−0.716028			−0.358014	−	0.933716i	$-0.616546\pi$
$443$	−15.0706			−0.716028			−0.358014	+	0.933716i	$0.616546\pi$
$444$	46.2412	+	26.6974i	2.19451	+	1.26700i
$445$	6.51712	−	11.2880i	0.308941	−	0.535102i
$446$	4.62050	+	8.00293i	0.218787	+	0.378950i
$447$		−	5.70305i		−	0.269745i
$448$	−9.61391	+	5.55059i	−0.454215	+	0.262241i
$449$	26.6585	−	15.3913i	1.25809	−	0.726360i	0.285388	−	0.958412i	$-0.407877\pi$
$449$	26.6585	−	15.3913i	1.25809	−	0.726360i	0.972703	+	0.232052i	$0.0745441\pi$
$450$			35.5705i			1.67681i
$451$	5.35559	+	9.27616i	0.252185	+	0.436797i
$452$	−6.01371	+	10.4160i	−0.282861	+	0.489929i
$453$	−31.1370	−	17.9770i	−1.46295	−	0.844632i
$454$	28.6166			1.34304
$455$	−12.7475	+	2.47929i	−0.597614	+	0.116231i
$456$	−5.10133			−0.238892
$457$	−6.71687	−	3.87799i	−0.314202	−	0.181405i	0.334603	−	0.942359i	$-0.391398\pi$
$457$	−6.71687	−	3.87799i	−0.314202	−	0.181405i	−0.648805	+	0.760955i	$0.724731\pi$
$458$	17.4214	−	30.1748i	0.814050	−	1.40998i
$459$	4.96373	+	8.59743i	0.231687	+	0.401294i
$460$			34.0422i			1.58723i
$461$	1.27498	−	0.736110i	0.0593817	−	0.0342840i	−0.470015	−	0.882658i	$-0.655752\pi$
$461$	1.27498	−	0.736110i	0.0593817	−	0.0342840i	0.529397	+	0.848374i	$0.322418\pi$
$462$	3.66213	−	2.11433i	0.170378	−	0.0983677i
$463$			14.0366i			0.652335i	0.945312	+	0.326168i	$0.105757\pi$
$463$			14.0366i			0.652335i	−0.945312	+	0.326168i	$0.894243\pi$
$464$	1.85815	+	3.21841i	0.0862625	+	0.149411i
$465$	−34.4949	+	59.7469i	−1.59966	+	2.77070i
$466$	30.1467	+	17.4052i	1.39652	+	0.806281i
$467$	−31.3806			−1.45212			−0.726060	−	0.687631i	$-0.758651\pi$
$467$	−31.3806			−1.45212			−0.726060	+	0.687631i	$0.758651\pi$
$468$	12.2566	+	14.0966i	0.566562	+	0.651614i
$469$	−8.42649			−0.389099
$470$	−19.6225	−	11.3291i	−0.905119	−	0.522571i
$471$	−14.6816	+	25.4293i	−0.676492	+	1.17172i
$472$	3.47399	+	6.01713i	0.159903	+	0.276961i
$473$		−	3.22865i		−	0.148454i
$474$	−3.12985	+	1.80702i	−0.143759	+	0.0829993i
$475$	−16.4246	+	9.48277i	−0.753614	+	0.435099i
$476$			12.1500i			0.556895i
$477$	−5.20337	−	9.01251i	−0.238246	−	0.412654i
$478$	−32.0849	+	55.5726i	−1.46753	+	2.54183i
$479$	35.6760	+	20.5975i	1.63008	+	0.941125i	0.984068	+	0.177795i	$0.0568964\pi$
$479$	35.6760	+	20.5975i	1.63008	+	0.941125i	0.646009	+	0.763330i	$0.276437\pi$
$480$	65.2598			2.97869
$481$	26.2243	−	22.8014i	1.19572	−	1.03965i
$482$	−62.2572			−2.83574
$483$	7.55745	+	4.36330i	0.343876	+	0.198537i
$484$	12.5101	−	21.6681i	0.568641	−	0.984914i
$485$	0.834351	+	1.44514i	0.0378859	+	0.0656204i
$486$			39.2002i			1.77816i
$487$	24.5314	−	14.1632i	1.11163	−	0.641798i	0.172376	−	0.985031i	$-0.444856\pi$
$487$	24.5314	−	14.1632i	1.11163	−	0.641798i	0.939250	+	0.343234i	$0.111522\pi$
$488$	−1.26400	+	0.729774i	−0.0572188	+	0.0330353i
$489$		−	5.24584i		−	0.237225i
$490$	−3.79878	−	6.57967i	−0.171611	−	0.297239i
$491$	17.3931	−	30.1258i	0.784941	−	1.35956i	−0.144094	−	0.989564i	$-0.546027\pi$
$491$	17.3931	−	30.1258i	0.784941	−	1.35956i	0.929034	−	0.369993i	$-0.120640\pi$
$492$	−57.9765	−	33.4728i	−2.61378	−	1.50907i
$493$	6.35879			0.286386
$494$	−5.88828	+	17.1068i	−0.264926	+	0.769670i
$495$	−6.75244			−0.303499
$496$	21.2621	+	12.2757i	0.954695	+	0.551194i
$497$	3.22444	−	5.58490i	0.144636	−	0.250517i
$498$	11.3725	+	19.6978i	0.509615	+	0.882680i
$499$			0.0694885i			0.00311073i	0.999999	+	0.00155537i	$0.000495089\pi$
$499$			0.0694885i			0.00311073i	−0.999999	+	0.00155537i	$0.999505\pi$
$500$	−22.7142	+	13.1140i	−1.01581	+	0.586477i
$501$	27.0133	−	15.5961i	1.20686	−	0.696783i
$502$		−	27.3855i		−	1.22228i
$503$	−12.8686	−	22.2891i	−0.573782	−	0.993820i	−0.996173	−	0.0874060i	$-0.972142\pi$
$503$	−12.8686	−	22.2891i	−0.573782	−	0.993820i	0.422391	−	0.906414i	$-0.361191\pi$
$504$	−1.00276	+	1.73683i	−0.0446664	+	0.0773646i
$505$	−18.1634	−	10.4866i	−0.808260	−	0.466649i
$506$	−7.21437			−0.320718
$507$	27.2582	−	11.0198i	1.21058	−	0.489407i
$508$	−30.1540			−1.33787
$509$	−6.09682	−	3.52000i	−0.270237	−	0.156021i	0.358759	−	0.933430i	$-0.383200\pi$
$509$	−6.09682	−	3.52000i	−0.270237	−	0.156021i	−0.628995	+	0.777409i	$0.716533\pi$
$510$	42.6152	−	73.8117i	1.88703	−	3.26844i
$511$	−3.57430	−	6.19086i	−0.158118	−	0.273868i
$512$		−	28.7215i		−	1.26932i
$513$	−4.12312	+	2.38049i	−0.182040	+	0.105101i
$514$	−8.37619	+	4.83599i	−0.369458	+	0.213307i
$515$			29.6746i			1.30762i
$516$	10.0896	+	17.4758i	0.444171	+	0.769327i
$517$	1.32173	−	2.28930i	0.0581295	−	0.100683i
$518$	17.6068	+	10.1653i	0.773597	+	0.446636i
$519$	8.33263			0.365762
$520$	−4.00775	+	11.6434i	−0.175752	+	0.510597i
$521$	16.3253			0.715225			0.357613	−	0.933870i	$-0.383591\pi$
$521$	16.3253			0.715225			0.357613	+	0.933870i	$0.383591\pi$
$522$	4.95322	+	2.85974i	0.216796	+	0.125167i
$523$	3.54473	−	6.13965i	0.155000	−	0.268468i	−0.778059	−	0.628191i	$-0.783796\pi$
$523$	3.54473	−	6.13965i	0.155000	−	0.268468i	0.933059	+	0.359723i	$0.117129\pi$
$524$	−10.0463	−	17.4007i	−0.438874	−	0.760152i
$525$			18.0317i			0.786968i
$526$	4.86836	−	2.81075i	0.212271	−	0.122555i
$527$	36.3805	−	21.0043i	1.58476	−	0.914963i
$528$			5.81138i			0.252908i
$529$	4.05594	+	7.02510i	0.176345	+	0.305439i
$530$	18.6912	−	32.3741i	0.811894	−	1.40624i
$531$	−13.4216	−	7.74899i	−0.582449	−	0.336277i
$532$	−5.82686			−0.252626
$533$	−32.8796	+	28.5880i	−1.42417	+	1.23828i
$534$	−17.2644			−0.747102
$535$	−11.9548	−	6.90209i	−0.516850	−	0.298403i
$536$	−3.99505	+	6.91963i	−0.172560	+	0.298882i
$537$	−6.66368	−	11.5418i	−0.287559	−	0.498067i
$538$		−	25.1558i		−	1.08454i
$539$	0.767631	−	0.443192i	0.0330642	−	0.0190896i
$540$	−15.2922	+	8.82897i	−0.658073	+	0.379938i
$541$			25.5162i			1.09703i	0.836141	+	0.548515i	$0.184806\pi$
$541$			25.5162i			1.09703i	−0.836141	+	0.548515i	$0.815194\pi$
$542$	−13.7409	−	23.7999i	−0.590222	−	1.02229i
$543$	2.39218	−	4.14338i	0.102658	−	0.177809i
$544$	−34.4136	−	19.8687i	−1.47547	−	0.851864i
$545$	−37.5235			−1.60733
$546$	11.2863	+	12.9805i	0.483007	+	0.555516i
$547$	−13.3073			−0.568978			−0.284489	−	0.958679i	$-0.591824\pi$
$547$	−13.3073			−0.568978			−0.284489	+	0.958679i	$0.591824\pi$
$548$	15.8158	+	9.13126i	0.675618	+	0.390068i
$549$	1.62781	−	2.81945i	0.0694733	−	0.120331i
$550$	−7.45350	−	12.9098i	−0.317818	−	0.550478i
$551$			3.04952i			0.129914i
$552$	7.16607	−	4.13733i	0.305008	−	0.176096i
$553$	−0.656058	+	0.378775i	−0.0278984	+	0.0161072i
$554$			45.0669i			1.91471i
$555$	−39.2559	−	67.9932i	−1.66632	−	2.88615i
$556$	20.4297	−	35.3852i	0.866412	−	1.50067i
$557$	−14.7285	−	8.50353i	−0.624069	−	0.360306i	0.154383	−	0.988011i	$-0.450661\pi$
$557$	−14.7285	−	8.50353i	−0.624069	−	0.360306i	−0.778451	+	0.627705i	$0.783994\pi$
$558$	37.7851			1.59957
$559$	12.8916	−	2.50732i	0.545259	−	0.106048i
$560$	10.4412			0.441220
$561$	8.61140	+	4.97179i	0.363573	+	0.209909i
$562$	18.2122	−	31.5445i	0.768235	−	1.33062i
$563$	−12.4596	−	21.5807i	−0.525111	−	0.909519i	−0.999572	−	0.0292428i	$-0.990690\pi$
$563$	−12.4596	−	21.5807i	−0.525111	−	0.909519i	0.474461	−	0.880276i	$-0.342643\pi$
$564$			16.5218i			0.695691i
$565$	15.3158	−	8.84257i	0.644340	−	0.372010i
$566$	−38.8013	+	22.4019i	−1.63094	+	0.941623i
$567$			10.8717i			0.456569i
$568$	−3.05745	−	5.29566i	−0.128288	−	0.222201i
$569$	2.94065	−	5.09335i	0.123278	−	0.213524i	−0.797780	−	0.602948i	$-0.793993\pi$
$569$	2.94065	−	5.09335i	0.123278	−	0.213524i	0.921059	+	0.389424i	$0.127326\pi$
$570$	35.3983	+	20.4372i	1.48267	+	0.856022i
$571$	−8.92622			−0.373551			−0.186775	−	0.982403i	$-0.559804\pi$
$571$	−8.92622			−0.373551			−0.186775	+	0.982403i	$0.559804\pi$
$572$	−7.40220	−	2.54789i	−0.309501	−	0.106533i
$573$	−25.7074			−1.07394
$574$	−22.0751	−	12.7451i	−0.921397	−	0.531969i
$575$	15.3816	−	26.6417i	0.641457	−	1.11104i
$576$	−11.7398	−	20.3339i	−0.489158	−	0.847247i
$577$		−	36.1933i		−	1.50675i	−0.657592	−	0.753374i	$-0.728425\pi$
$577$		−	36.1933i		−	1.50675i	0.657592	−	0.753374i	$-0.271575\pi$
$578$	−13.8894	+	8.01905i	−0.577723	+	0.333549i
$579$	−27.5961	+	15.9326i	−1.14685	+	0.662136i
$580$			11.3104i			0.469638i
$581$	2.38383	+	4.12892i	0.0988980	+	0.171296i
$582$	1.10513	−	1.91414i	0.0458091	−	0.0793437i
$583$	3.77699	+	2.18065i	0.156427	+	0.0903132i
$584$	−6.77838			−0.280491
$585$	−5.24383	−	26.9617i	−0.216806	−	1.11473i
$586$	−0.886069			−0.0366032
$587$	31.6008	+	18.2447i	1.30431	+	0.753041i	0.981139	−	0.193301i	$-0.0619195\pi$
$587$	31.6008	+	18.2447i	1.30431	+	0.753041i	0.323166	+	0.946342i	$0.395253\pi$
$588$	−2.76998	+	4.79774i	−0.114232	+	0.197855i
$589$	10.0732	+	17.4472i	0.415058	+	0.718901i
$590$		−	55.6708i		−	2.29193i
$591$	44.9649	−	25.9605i	1.84961	−	1.06787i
$592$	−24.1967	+	13.9699i	−0.994476	+	0.574161i
$593$			34.9930i			1.43699i	0.695533	+	0.718495i	$0.255168\pi$
$593$			34.9930i			1.43699i	−0.695533	+	0.718495i	$0.744832\pi$
$594$	−1.87107	−	3.24079i	−0.0767711	−	0.132971i
$595$	8.93270	−	15.4719i	0.366205	−	0.634286i
$596$	−5.34926	−	3.08839i	−0.219114	−	0.126506i
$597$	7.12385			0.291560
$598$	−5.60256	−	28.8062i	−0.229106	−	1.17797i
$599$	−32.5052			−1.32812			−0.664062	−	0.747677i	$-0.731169\pi$
$599$	−32.5052			−1.32812			−0.664062	+	0.747677i	$0.731169\pi$
$600$	14.8072	+	8.54894i	0.604501	+	0.349009i
$601$	−10.0390	+	17.3881i	−0.409500	+	0.709275i	−0.994834	−	0.101518i	$-0.967630\pi$
$601$	−10.0390	+	17.3881i	−0.409500	+	0.709275i	0.585334	+	0.810792i	$0.300963\pi$
$602$	3.84172	+	6.65406i	0.156577	+	0.271199i
$603$		−	17.8225i		−	0.725788i
$604$	−33.7235	+	19.4703i	−1.37219	+	0.792235i
$605$	−31.8608	+	18.3949i	−1.29533	+	0.747858i
$606$			27.7799i			1.12848i
$607$	−4.85800	−	8.41431i	−0.197180	−	0.341526i	0.750433	−	0.660947i	$-0.229845\pi$
$607$	−4.85800	−	8.41431i	−0.197180	−	0.341526i	−0.947613	+	0.319420i	$0.896512\pi$
$608$	9.52856	−	16.5039i	0.386434	−	0.669323i
$609$	2.51093	+	1.44969i	0.101748	+	0.0587442i
$610$	11.6946			0.473502
$611$	10.1674	+	3.49968i	0.411327	+	0.141582i
$612$	−25.6979			−1.03878
$613$	−10.2898	−	5.94080i	−0.415600	−	0.239947i	0.277593	−	0.960699i	$-0.410463\pi$
$613$	−10.2898	−	5.94080i	−0.415600	−	0.239947i	−0.693193	+	0.720752i	$0.743797\pi$
$614$	−14.8508	+	25.7224i	−0.599331	+	1.03807i
$615$	49.2184	+	85.2488i	1.98468	+	3.43756i
$616$		−	0.840480i		−	0.0338639i
$617$	−17.3105	+	9.99422i	−0.696895	+	0.402352i	−0.806190	−	0.591657i	$-0.798474\pi$
$617$	−17.3105	+	9.99422i	−0.696895	+	0.402352i	0.109295	+	0.994009i	$0.465141\pi$
$618$	34.0393	−	19.6526i	1.36926	−	0.790543i
$619$			41.7176i			1.67677i	0.545078	+	0.838386i	$0.316500\pi$
$619$			41.7176i			1.67677i	−0.545078	+	0.838386i	$0.683500\pi$
$620$	37.3603	+	64.7100i	1.50043	+	2.59882i
$621$	3.86129	−	6.68794i	0.154948	−	0.268378i
$622$	−18.9708	−	10.9528i	−0.760659	−	0.439166i
$623$	−3.61884			−0.144986
$624$	−23.2042	+	4.51302i	−0.928911	+	0.180665i
$625$	−1.29828			−0.0519312
$626$	12.5091	+	7.22211i	0.499963	+	0.288654i
$627$	−2.38435	+	4.12982i	−0.0952219	+	0.164929i
$628$	15.9012	+	27.5416i	0.634526	+	1.09903i
$629$			47.8066i			1.90618i
$630$	13.9164	−	8.03461i	0.554441	−	0.320107i
$631$	15.2780	−	8.82074i	0.608206	−	0.351148i	−0.164057	−	0.986451i	$-0.552458\pi$
$631$	15.2780	−	8.82074i	0.608206	−	0.351148i	0.772263	+	0.635303i	$0.219125\pi$
$632$			0.718319i			0.0285732i
$633$	16.8084	+	29.1130i	0.668073	+	1.15714i
$634$	0.739603	−	1.28103i	0.0293734	−	0.0508762i
$635$	38.3982	+	22.1692i	1.52379	+	0.879759i
$636$	−27.2584			−1.08086
$637$	2.36575	+	2.72089i	0.0937343	+	0.107806i
$638$	−2.39694			−0.0948958
$639$	11.8124	+	6.81987i	0.467290	+	0.269790i
$640$	13.3159	−	23.0639i	0.526359	−	0.911680i
$641$	−5.46012	−	9.45721i	−0.215662	−	0.373537i	0.737815	−	0.675003i	$-0.235858\pi$
$641$	−5.46012	−	9.45721i	−0.215662	−	0.373537i	−0.953477	+	0.301465i	$0.902524\pi$
$642$			18.2842i			0.721618i
$643$	15.2725	−	8.81757i	0.602288	−	0.347731i	−0.167653	−	0.985846i	$-0.553619\pi$
$643$	15.2725	−	8.81757i	0.602288	−	0.347731i	0.769941	+	0.638115i	$0.220286\pi$
$644$	8.18524	−	4.72575i	0.322544	−	0.186221i
$645$		−	29.6716i		−	1.16832i
$646$	−12.4445	−	21.5544i	−0.489620	−	0.848048i
$647$	8.33632	−	14.4389i	0.327735	−	0.567653i	−0.654327	−	0.756211i	$-0.727048\pi$
$647$	8.33632	−	14.4389i	0.327735	−	0.567653i	0.982062	+	0.188558i	$0.0603815\pi$
$648$	8.92758	+	5.15434i	0.350708	+	0.202482i
$649$	6.49495			0.254949
$650$	45.7593	−	39.7866i	1.79483	−	1.56056i
$651$	19.1544			0.750719
$652$	−4.92042	−	2.84080i	−0.192698	−	0.111254i
$653$	3.38664	−	5.86584i	0.132530	−	0.229548i	−0.792121	−	0.610364i	$-0.791023\pi$
$653$	3.38664	−	5.86584i	0.132530	−	0.229548i	0.924651	+	0.380816i	$0.124357\pi$
$654$	24.8506	+	43.0426i	0.971737	+	1.68310i
$655$			29.5441i			1.15439i
$656$	30.3374	−	17.5153i	1.18448	−	0.683858i
$657$	13.0940	−	7.55983i	0.510846	−	0.294937i
$658$			6.29081i			0.245241i
$659$	−16.7680	−	29.0431i	−0.653190	−	1.13136i	−0.982344	−	0.187082i	$-0.940097\pi$
$659$	−16.7680	−	29.0431i	−0.653190	−	1.13136i	0.329154	−	0.944276i	$-0.393236\pi$
$660$	−8.84332	+	15.3171i	−0.344226	+	0.596216i
$661$	−21.7945	−	12.5830i	−0.847707	−	0.489424i	0.0121696	−	0.999926i	$-0.496126\pi$
$661$	−21.7945	−	12.5830i	−0.847707	−	0.489424i	−0.859876	+	0.510502i	$0.829460\pi$
$662$	8.85657			0.344221
$663$	−13.1643	+	38.2454i	−0.511261	+	1.48533i
$664$	4.52075			0.175439
$665$	7.41995	+	4.28391i	0.287733	+	0.166123i
$666$	−21.5001	+	37.2393i	−0.833112	+	1.44299i
$667$	−2.47325	−	4.28380i	−0.0957647	−	0.165869i
$668$		−	33.7833i		−	1.30712i
$669$	−8.58060	+	4.95401i	−0.331745	+	0.191533i
$670$	55.4436	−	32.0104i	2.14197	−	1.23667i
$671$			1.36438i			0.0526713i
$672$	−9.05939	−	15.6913i	−0.349473	−	0.605306i
$673$	−0.927341	+	1.60620i	−0.0357464	+	0.0619145i	−0.883345	−	0.468723i	$-0.844714\pi$
$673$	−0.927341	+	1.60620i	−0.0357464	+	0.0619145i	0.847599	+	0.530638i	$0.178048\pi$
$674$	−37.3172	−	21.5451i	−1.43741	−	0.829887i
$675$	15.9571			0.614189
$676$	4.42503	−	31.5348i	0.170194	−	1.21288i
$677$	−14.7209			−0.565770			−0.282885	−	0.959154i	$-0.591291\pi$
$677$	−14.7209			−0.565770			−0.282885	+	0.959154i	$0.591291\pi$
$678$	−20.2863	−	11.7123i	−0.779092	−	0.449809i
$679$	0.231650	−	0.401229i	0.00888990	−	0.0153978i
$680$	−8.47009	−	14.6706i	−0.324813	−	0.562593i
$681$			30.6822i			1.17575i
$682$	−13.7136	+	7.91756i	−0.525122	+	0.303179i
$683$	6.87930	−	3.97177i	0.263229	−	0.151975i	−0.362578	−	0.931954i	$-0.618103\pi$
$683$	6.87930	−	3.97177i	0.263229	−	0.151975i	0.625807	+	0.779978i	$0.284770\pi$
$684$		−	12.3241i		−	0.471224i
$685$	−13.4266	−	23.2556i	−0.513005	−	0.888551i
$686$	−1.05469	+	1.82678i	−0.0402684	+	0.0697469i
$687$	32.3529	+	18.6790i	1.23434	+	0.712647i
$688$	−10.5592			−0.402566
$689$	−5.77394	+	16.7746i	−0.219969	+	0.639060i
$690$	−66.3008			−2.52403
$691$	8.86002	+	5.11534i	0.337051	+	0.194597i	0.658967	−	0.752172i	$-0.270994\pi$
$691$	8.86002	+	5.11534i	0.337051	+	0.194597i	−0.321916	+	0.946768i	$0.604327\pi$
$692$	4.51240	−	7.81571i	0.171536	−	0.297109i
$693$	0.937375	+	1.62358i	0.0356079	+	0.0616748i
$694$		−	16.8118i		−	0.638168i
$695$	−52.0306	+	30.0399i	−1.97363	+	1.13948i
$696$	2.38089	−	1.37461i	0.0902475	−	0.0521044i
$697$		−	59.9392i		−	2.27036i
$698$	22.7785	+	39.4535i	0.862178	+	1.49334i
$699$	−18.6616	+	32.3228i	−0.705845	+	1.22256i
$700$	16.9131	+	9.76479i	0.639255	+	0.369074i
$701$	−16.5978			−0.626891			−0.313445	−	0.949606i	$-0.601483\pi$
$701$	−16.5978			−0.626891			−0.313445	+	0.949606i	$0.601483\pi$
$702$	11.4871	−	9.98773i	0.433552	−	0.376963i
$703$	−22.9269			−0.864706
$704$	8.52162	+	4.91996i	0.321171	+	0.185428i
$705$	12.1468	−	21.0389i	0.457475	−	0.792371i
$706$	22.8000	+	39.4907i	0.858088	+	1.48625i
$707$			5.82303i			0.218998i
$708$	−35.1552	+	20.2969i	−1.32121	+	0.762804i
$709$	41.4531	−	23.9329i	1.55680	−	0.898820i	0.559242	−	0.829004i	$-0.311092\pi$
$709$	41.4531	−	23.9329i	1.55680	−	0.898820i	0.997560	−	0.0698158i	$-0.0222412\pi$
$710$			48.9957i			1.83878i
$711$	−0.801130	−	1.38760i	−0.0300447	−	0.0520390i
$712$	−1.71571	+	2.97170i	−0.0642990	+	0.111369i
$713$	−28.3004	−	16.3393i	−1.05986	−	0.611910i
$714$	−23.6634			−0.885581
$715$	7.55279	+	8.68661i	0.282458	+	0.324861i
$716$	−14.4344			−0.539441
$717$	−59.5840	−	34.4008i	−2.22520	−	1.28472i
$718$	14.4318	−	24.9965i	0.538588	−	0.932862i
$719$	−19.0461	−	32.9888i	−0.710300	−	1.23028i	−0.964744	−	0.263188i	$-0.915226\pi$
$719$	−19.0461	−	32.9888i	−0.710300	−	1.23028i	0.254444	−	0.967087i	$-0.418107\pi$
$720$			22.0836i			0.823009i
$721$	7.13508	−	4.11944i	0.265724	−	0.153416i
$722$	−24.3719	+	14.0711i	−0.907028	+	0.523673i
$723$		−	66.7511i		−	2.48250i
$724$	−2.59089	−	4.48756i	−0.0962898	−	0.166779i
$725$	5.11047	−	8.85159i	0.189798	−	0.328740i
$726$	42.2009	+	24.3647i	1.56622	+	0.904259i
$727$	15.4059			0.571374			0.285687	−	0.958323i	$-0.407778\pi$
$727$	15.4059			0.571374			0.285687	+	0.958323i	$0.407778\pi$
$728$	3.35594	−	0.652702i	0.124379	−	0.0241908i
$729$	−9.41460			−0.348689
$730$	47.0354	+	27.1559i	1.74086	+	1.00508i
$731$	−9.03369	+	15.6468i	−0.334123	+	0.578718i
$732$	−4.26372	−	7.38498i	−0.157592	−	0.272957i
$733$			11.6298i			0.429557i	0.976663	+	0.214778i	$0.0689029\pi$
$733$			11.6298i			0.429557i	−0.976663	+	0.214778i	$0.931097\pi$
$734$	20.8487	−	12.0370i	0.769538	−	0.444293i
$735$	7.05461	−	4.07298i	0.260213	−	0.150234i
$736$			30.9117i			1.13942i
$737$	3.73456	+	6.46844i	0.137564	+	0.238268i
$738$	26.9565	−	46.6900i	0.992282	−	1.71868i
$739$	2.32875	+	1.34451i	0.0856645	+	0.0494584i	0.542220	−	0.840236i	$-0.317584\pi$
$739$	2.32875	+	1.34451i	0.0856645	+	0.0494584i	−0.456556	+	0.889695i	$0.650917\pi$
$740$	−85.0336			−3.12590
$741$	−18.3416	−	6.31331i	−0.673794	−	0.231925i
$742$	−10.3789			−0.381020
$743$	−2.13665	−	1.23360i	−0.0783862	−	0.0452563i	0.460295	−	0.887766i	$-0.347744\pi$
$743$	−2.13665	−	1.23360i	−0.0783862	−	0.0452563i	−0.538681	+	0.842510i	$0.681077\pi$
$744$	9.08120	−	15.7291i	0.332933	−	0.576657i
$745$	4.54118	+	7.86556i	0.166376	+	0.288172i
$746$			65.9835i			2.41583i
$747$	−8.73288	+	5.04193i	−0.319519	+	0.184475i
$748$	9.32673	−	5.38479i	0.341019	−	0.196887i
$749$			3.83260i			0.140040i
$750$	−25.5409	−	44.2382i	−0.932623	−	1.61535i
$751$	−18.9592	+	32.8383i	−0.691832	+	1.19829i	0.279405	+	0.960173i	$0.409863\pi$
$751$	−18.9592	+	32.8383i	−0.691832	+	1.19829i	−0.971237	+	0.238115i	$0.923471\pi$
$752$	−7.48709	−	4.32267i	−0.273026	−	0.157632i
$753$	29.3623			1.07002
$754$	−1.86142	−	9.57072i	−0.0677890	−	0.348545i
$755$	57.2583			2.08384
$756$	4.24574	+	2.45128i	0.154416	+	0.0891522i
$757$	−17.3225	+	30.0035i	−0.629598	+	1.09050i	0.358034	+	0.933709i	$0.383447\pi$
$757$	−17.3225	+	30.0035i	−0.629598	+	1.09050i	−0.987632	+	0.156788i	$0.949886\pi$
$758$	28.9145	+	50.0814i	1.05022	+	1.81904i
$759$		−	7.73512i		−	0.280767i
$760$	7.03569	−	4.06206i	0.255211	−	0.147346i
$761$	19.7969	−	11.4297i	0.717636	−	0.414328i	−0.0962458	−	0.995358i	$-0.530683\pi$
$761$	19.7969	−	11.4297i	0.717636	−	0.414328i	0.813882	+	0.581030i	$0.197350\pi$
$762$		−	58.7280i		−	2.12749i
$763$	5.20902	+	9.02229i	0.188579	+	0.326629i
$764$	−13.9214	+	24.1126i	−0.503659	+	0.872363i
$765$	32.7239	+	18.8931i	1.18313	+	0.683083i
$766$	33.9625			1.22712
$767$	5.04386	+	25.9336i	0.182123	+	0.936408i
$768$	14.9390			0.539065
$769$	−44.8839	−	25.9137i	−1.61855	−	0.934473i	−0.987294	−	0.158902i	$-0.949205\pi$
$769$	−44.8839	−	25.9137i	−1.61855	−	0.934473i	−0.631260	−	0.775571i	$-0.717462\pi$
$770$	−3.36718	+	5.83212i	−0.121345	+	0.210175i
$771$	−5.18507	−	8.98080i	−0.186736	−	0.323436i
$772$			34.5122i			1.24212i
$773$	−4.93605	+	2.84983i	−0.177538	+	0.102501i	−0.586135	−	0.810213i	$-0.699351\pi$
$773$	−4.93605	+	2.84983i	−0.177538	+	0.102501i	0.408598	+	0.912715i	$0.366018\pi$
$774$	−14.0737	+	8.12545i	−0.505868	+	0.292063i
$775$		−	67.5234i		−	2.42551i
$776$	−0.219653	−	0.380450i	−0.00788508	−	0.0136574i
$777$	−10.8990	+	18.8777i	−0.391000	+	0.677232i
$778$	−38.6146	−	22.2941i	−1.38440	−	0.799283i
$779$	28.7454			1.02991
$780$	−68.0269	−	23.4154i	−2.43576	−	0.838406i
$781$	−5.71619			−0.204541
$782$	34.9625	+	20.1856i	1.25026	+	0.721836i
$783$	1.28289	−	2.22204i	0.0458469	−	0.0794092i
$784$	−1.44945	−	2.51051i	−0.0517659	−	0.0896612i
$785$		−	46.7622i		−	1.66902i
$786$	33.8896	−	19.5662i	1.20880	−	0.697902i
$787$	−14.5614	+	8.40705i	−0.519059	+	0.299679i	−0.736550	−	0.676384i	$-0.763546\pi$
$787$	−14.5614	+	8.40705i	−0.519059	+	0.299679i	0.217490	+	0.976062i	$0.430213\pi$
$788$		−	56.2340i		−	2.00325i
$789$	3.01364	+	5.21977i	0.107288	+	0.185829i
$790$	2.87777	−	4.98444i	0.102386	−	0.177338i
$791$	−4.25228	−	2.45505i	−0.151194	−	0.0872917i
$792$	1.77766			0.0631664
$793$	−5.44781	+	1.05955i	−0.193457	+	0.0376258i
$794$	27.6296			0.980539
$795$	34.7109	+	20.0404i	1.23107	+	0.710759i
$796$	3.85781	−	6.68192i	0.136736	−	0.236834i
$797$	21.0651	+	36.4858i	0.746163	+	1.29239i	0.949650	+	0.313314i	$0.101439\pi$
$797$	21.0651	+	36.4858i	0.746163	+	1.29239i	−0.203487	+	0.979078i	$0.565227\pi$
$798$		−	11.3484i		−	0.401729i
$799$	−12.8108	+	7.39632i	−0.453214	+	0.261663i
$800$	−55.3154	+	31.9364i	−1.95570	+	1.12912i
$801$		−	7.65403i		−	0.270442i
$802$	20.5082	+	35.5213i	0.724171	+	1.25430i
$803$	−3.16820	+	5.48748i	−0.111803	+	0.193649i
$804$	−40.4281	−	23.3412i	−1.42579	−	0.823180i
$805$	−13.8975			−0.489823
$806$	−42.2637	−	48.6083i	−1.48868	−	1.71215i
$807$	26.9716			0.949445
$808$	4.78173	+	2.76073i	0.168221	+	0.0971223i
$809$	15.0843	−	26.1268i	0.530336	−	0.918569i	−0.469037	−	0.883178i	$-0.655399\pi$
$809$	15.0843	−	26.1268i	0.530336	−	0.918569i	0.999374	−	0.0353910i	$-0.0112677\pi$
$810$	−41.2992	−	71.5323i	−1.45111	−	2.51339i
$811$		−	23.7929i		−	0.835480i	−0.908567	−	0.417740i	$-0.862822\pi$
$811$		−	23.7929i		−	0.835480i	0.908567	−	0.417740i	$-0.137178\pi$
$812$	2.71951	−	1.57011i	0.0954360	−	0.0551000i
$813$	25.5178	−	14.7327i	0.894950	−	0.516699i
$814$		−	18.0207i		−	0.631624i
$815$	4.17712	+	7.23499i	0.146318	+	0.253431i
$816$	16.2601	−	28.1633i	0.569217	−	0.985913i
$817$	−7.50384	−	4.33234i	−0.262526	−	0.151569i
$818$	50.7432			1.77419
$819$	−5.75483	+	5.00368i	−0.201090	+	0.174843i
$820$	106.614			3.72312
$821$	−31.0771	−	17.9424i	−1.08460	−	0.626193i	−0.152465	−	0.988309i	$-0.548721\pi$
$821$	−31.0771	−	17.9424i	−1.08460	−	0.626193i	−0.932133	+	0.362116i	$0.882054\pi$
$822$	−17.7841	+	30.8029i	−0.620291	+	1.07438i
$823$	−6.11728	−	10.5954i	−0.213235	−	0.369334i	0.739490	−	0.673167i	$-0.235067\pi$
$823$	−6.11728	−	10.5954i	−0.213235	−	0.369334i	−0.952725	+	0.303833i	$0.901733\pi$
$824$		−	7.81220i		−	0.272151i
$825$	13.8417	−	7.99151i	0.481906	−	0.278229i
$826$	−13.3857	+	7.72823i	−0.465748	+	0.268900i
$827$			27.3474i			0.950962i	0.879726	+	0.475481i	$0.157726\pi$
$827$			27.3474i			0.950962i	−0.879726	+	0.475481i	$0.842274\pi$
$828$	9.99521	+	17.3122i	0.347358	+	0.601641i
$829$	11.7869	−	20.4155i	0.409376	−	0.709060i	−0.585444	−	0.810713i	$-0.699080\pi$
$829$	11.7869	−	20.4155i	0.409376	−	0.709060i	0.994820	+	0.101653i	$0.0324132\pi$
$830$	−31.3697	−	18.1113i	−1.08886	−	0.628652i
$831$	−48.3199			−1.67620
$832$	−13.0271	+	37.8466i	−0.451634	+	1.31210i
$833$	−4.96016			−0.171859
$834$	68.9165	+	39.7889i	2.38638	+	1.37778i
$835$	−24.8376	+	43.0199i	−0.859539	+	1.48877i
$836$	2.58242	+	4.47288i	0.0893148	+	0.154698i
$837$		−	16.9506i		−	0.585898i
$838$	−71.2880	+	41.1582i	−2.46260	+	1.42179i
$839$	9.16975	−	5.29416i	0.316575	−	0.182775i	−0.333290	−	0.942824i	$-0.608159\pi$
$839$	9.16975	−	5.29416i	0.316575	−	0.182775i	0.649865	+	0.760050i	$0.274825\pi$
$840$		−	7.72409i		−	0.266507i
$841$	13.6783	+	23.6915i	0.471665	+	0.816947i
$842$	−23.2332	+	40.2411i	−0.800669	+	1.38680i
$843$	33.8214	+	19.5268i	1.16487	+	0.672538i
$844$	36.4092			1.25326
$845$	−28.8193	+	36.9033i	−0.991414	+	1.26951i
$846$	−13.3054			−0.457449
$847$	8.84586	+	5.10716i	0.303947	+	0.175484i
$848$	7.13174	−	12.3525i	0.244905	−	0.424188i
$849$	−24.0189	−	41.6020i	−0.824328	−	1.42778i
$850$			83.4188i			2.86124i
$851$	32.2065	−	18.5944i	1.10402	−	0.637408i
$852$	30.9401	−	17.8633i	1.05999	−	0.611985i
$853$			21.3925i			0.732464i	0.930524	+	0.366232i	$0.119352\pi$
$853$			21.3925i			0.732464i	−0.930524	+	0.366232i	$0.880648\pi$
$854$	−1.62345	−	2.81190i	−0.0555534	−	0.0962213i
$855$	−9.06070	+	15.6936i	−0.309870	+	0.536710i
$856$	3.14724	+	1.81706i	0.107570	+	0.0621058i
$857$	−7.22129			−0.246675			−0.123337	−	0.992365i	$-0.539360\pi$
$857$	−7.22129			−0.246675			−0.123337	+	0.992365i	$0.539360\pi$
$858$	4.96229	−	14.4166i	0.169410	−	0.492173i
$859$	57.1073			1.94848			0.974238	−	0.225524i	$-0.0724095\pi$
$859$	57.1073			1.94848			0.974238	+	0.225524i	$0.0724095\pi$
$860$	−27.8309	−	16.0682i	−0.949027	−	0.547921i
$861$	13.6650	−	23.6685i	0.465703	−	0.806621i
$862$	−37.8421	−	65.5444i	−1.28891	−	2.23245i
$863$		−	51.3361i		−	1.74750i	−0.486374	−	0.873751i	$-0.661681\pi$
$863$		−	51.3361i		−	1.74750i	0.486374	−	0.873751i	$-0.338319\pi$
$864$	−13.8860	+	8.01707i	−0.472411	+	0.272746i
$865$	−11.4922	+	6.63505i	−0.390748	+	0.225598i
$866$			25.7631i			0.875467i
$867$	−8.59788	−	14.8920i	−0.291999	−	0.505758i
$868$	10.3727	−	17.9661i	0.352074	−	0.609810i
$869$	0.581520	+	0.335741i	0.0197267	+	0.0113892i
$870$	−22.0281			−0.746823
$871$	−22.9276	+	19.9349i	−0.776871	+	0.675470i
$872$	9.87851			0.334528
$873$	0.848621	+	0.489952i	0.0287215	+	0.0165824i
$874$	−9.68055	+	16.7672i	−0.327449	+	0.567159i
$875$	−5.35371	−	9.27291i	−0.180989	−	0.313481i
$876$		−	39.6029i		−	1.33806i
$877$	−18.5570	+	10.7139i	−0.626624	+	0.361781i	−0.779443	−	0.626473i	$-0.784498\pi$
$877$	−18.5570	+	10.7139i	−0.626624	+	0.361781i	0.152820	+	0.988254i	$0.451165\pi$
$878$	−28.7815	+	16.6170i	−0.971330	+	0.560798i
$879$		−	0.950027i		−	0.0320436i
$880$	−4.62745	−	8.01497i	−0.155991	−	0.270185i
$881$	14.5309	−	25.1683i	0.489560	−	0.847943i	−0.510368	−	0.859956i	$-0.670491\pi$
$881$	14.5309	−	25.1683i	0.489560	−	0.847943i	0.999928	+	0.0120134i	$0.00382406\pi$
$882$	−3.86375	−	2.23073i	−0.130099	−	0.0751127i
$883$	4.83594			0.162742			0.0813711	−	0.996684i	$-0.474070\pi$
$883$	4.83594			0.162742			0.0813711	+	0.996684i	$0.474070\pi$
$884$	28.7438	+	33.0589i	0.966760	+	1.11189i
$885$	59.6892			2.00643
$886$	−27.5308	−	15.8949i	−0.924916	−	0.534000i
$887$	12.4949	−	21.6418i	0.419538	−	0.726660i	−0.576355	−	0.817199i	$-0.695526\pi$
$887$	12.4949	−	21.6418i	0.419538	−	0.726660i	0.995893	+	0.0905387i	$0.0288589\pi$
$888$	10.3346	+	17.9000i	0.346806	+	0.600685i
$889$		−	12.3102i		−	0.412869i
$890$	23.8108	−	13.7471i	0.798138	−	0.460805i
$891$	8.34546	−	4.81826i	0.279584	−	0.161418i
$892$			10.7311i			0.359303i
$893$	−3.54710	−	6.14376i	−0.118699	−	0.205593i
$894$	6.01497	−	10.4182i	0.201171	−	0.348438i
$895$	18.3809	+	10.6122i	0.614406	+	0.354727i
$896$	−7.39409			−0.247019
$897$	30.8855	−	6.00696i	1.03124	−	0.200567i
$898$	64.9324			2.16682
$899$	−9.40269	−	5.42865i	−0.313597	−	0.181055i
$900$	−20.6530	+	35.7721i	−0.688435	+	1.19240i
$901$	−12.2028	−	21.1359i	−0.406534	−	0.704138i
$902$			22.5940i			0.752300i
$903$	−7.13436	+	4.11902i	−0.237417	+	0.137073i
$904$	−4.03206	+	2.32791i	−0.134104	+	0.0774252i
$905$			7.61931i			0.253274i
$906$	−37.9204	−	65.6801i	−1.25982	−	2.18208i
$907$	7.52060	−	13.0261i	0.249717	−	0.432523i	−0.713730	−	0.700421i	$-0.752996\pi$
$907$	7.52060	−	13.0261i	0.249717	−	0.432523i	0.963447	+	0.267898i	$0.0863290\pi$
$908$	28.7789	+	16.6155i	0.955060	+	0.551404i
$909$	−12.3160			−0.408497
$910$	−25.9019	−	8.91563i	−0.858639	−	0.295550i
$911$	−9.22150			−0.305522			−0.152761	−	0.988263i	$-0.548816\pi$
$911$	−9.22150			−0.305522			−0.152761	+	0.988263i	$0.548816\pi$
$912$	13.5065	+	7.79795i	0.447243	+	0.258216i
$913$	2.11299	−	3.65981i	0.0699298	−	0.121122i
$914$	−8.18018	−	14.1685i	−0.270576	−	0.468652i
$915$			12.5388i			0.414519i
$916$	35.0404	−	20.2306i	1.15777	−	0.668437i
$917$	7.10371	−	4.10133i	0.234585	−	0.135438i
$918$			20.9409i			0.691151i
$919$	22.5402	+	39.0407i	0.743531	+	1.28783i	0.950878	+	0.309567i	$0.100184\pi$
$919$	22.5402	+	39.0407i	0.743531	+	1.28783i	−0.207346	+	0.978268i	$0.566483\pi$
$920$	−6.58889	+	11.4123i	−0.217229	+	0.376252i
$921$	−27.5791	−	15.9228i	−0.908762	−	0.524674i
$922$	3.10548			0.102274
$923$	−4.43910	−	22.8241i	−0.146115	−	0.751265i
$924$	4.91053			0.161544
$925$	66.5480	+	38.4215i	2.18808	+	1.26329i
$926$	−14.8043	+	25.6418i	−0.486499	+	0.842642i
$927$	8.71284	+	15.0911i	0.286167	+	0.495656i
$928$			10.2703i			0.337139i
$929$	−40.6313	+	23.4585i	−1.33307	+	0.769647i	−0.985769	−	0.168107i	$-0.946235\pi$
$929$	−40.6313	+	23.4585i	−1.33307	+	0.769647i	−0.347300	+	0.937754i	$0.612901\pi$
$930$	−126.030	+	72.7632i	−4.13267	+	2.38600i
$931$		−	2.37878i		−	0.0779612i
$932$	20.2117	+	35.0078i	0.662058	+	1.14672i
$933$	11.7434	−	20.3401i	0.384461	−	0.665906i
$934$	−57.3256	−	33.0969i	−1.87575	−	1.08296i
$935$	−15.8356			−0.517880
$936$	1.38050	+	7.09800i	0.0451231	+	0.232005i
$937$	−28.3912			−0.927501			−0.463750	−	0.885966i	$-0.653497\pi$
$937$	−28.3912			−0.927501			−0.463750	+	0.885966i	$0.653497\pi$
$938$	−15.3934	−	8.88737i	−0.502612	−	0.290183i
$939$	−7.74342	+	13.4120i	−0.252697	+	0.437684i
$940$	−13.1558	−	22.7866i	−0.429096	−	0.743216i
$941$		−	17.8718i		−	0.582603i	−0.956631	−	0.291302i	$-0.905912\pi$
$941$		−	17.8718i		−	0.582603i	0.956631	−	0.291302i	$-0.0940883\pi$
$942$	−53.6402	+	30.9692i	−1.74769	+	1.00903i
$943$	−40.3800	+	23.3134i	−1.31495	+	0.759188i
$944$		−	21.2415i		−	0.691353i
$945$	−3.60437	−	6.24295i	−0.117250	−	0.203083i
$946$	3.40524	−	5.89805i	0.110714	−	0.191762i
$947$	8.24659	+	4.76117i	0.267978	+	0.154717i	0.627969	−	0.778239i	$-0.283887\pi$
$947$	8.24659	+	4.76117i	0.267978	+	0.154717i	−0.359990	+	0.932956i	$0.617220\pi$
$948$	−4.19680			−0.136306
$949$	−24.3713	−	8.38878i	−0.791125	−	0.272311i
$950$	−40.0057			−1.29796
$951$	1.37350	+	0.792989i	0.0445387	+	0.0257144i
$952$	−2.35164	+	4.07316i	−0.0762171	+	0.132012i
$953$	−6.70900	−	11.6203i	−0.217326	−	0.376419i	0.736664	−	0.676259i	$-0.236400\pi$
$953$	−6.70900	−	11.6203i	−0.217326	−	0.376419i	−0.953990	+	0.299840i	$0.903067\pi$
$954$		−	21.9519i		−	0.710718i
$955$	35.4552	−	20.4701i	1.14730	−	0.662397i
$956$	−64.5335	+	37.2584i	−2.08716	+	1.20502i
$957$		−	2.56996i		−	0.0830749i
$958$	43.4482	+	75.2545i	1.40375	+	2.43136i
$959$	−3.72778	+	6.45670i	−0.120376	+	0.208498i
$960$	78.3145	+	45.2149i	2.52759	+	1.45931i
$961$	−40.7275			−1.31379
$962$	71.9545	−	13.9946i	2.31991	−	0.451202i
$963$	−8.10615			−0.261217
$964$	−62.6102	−	36.1480i	−2.01654	−	1.16425i
$965$	25.3734	−	43.9480i	0.816798	−	1.41474i
$966$	9.20389	+	15.9416i	0.296130	+	0.512913i
$967$			12.9316i			0.415851i	0.978145	+	0.207926i	$0.0666712\pi$
$967$			12.9316i			0.415851i	−0.978145	+	0.207926i	$0.933329\pi$
$968$	8.38775	−	4.84267i	0.269593	−	0.155649i
$969$	23.1103	−	13.3427i	0.742409	−	0.428630i
$970$			3.51994i			0.113019i
$971$	−23.7607	−	41.1547i	−0.762516	−	1.32072i	−0.941550	−	0.336874i	$-0.890630\pi$
$971$	−23.7607	−	41.1547i	−0.762516	−	1.32072i	0.179034	−	0.983843i	$-0.442703\pi$
$972$	−22.7605	+	39.4224i	−0.730044	+	1.26447i
$973$	14.4458	+	8.34028i	0.463111	+	0.267377i
$974$	59.7515			1.91456
$975$	42.6584	+	49.0623i	1.36616	+	1.57125i
$976$	4.46216			0.142830
$977$	31.6049	+	18.2471i	1.01113	+	0.583776i	0.911522	−	0.411251i	$-0.134908\pi$
$977$	31.6049	+	18.2471i	1.01113	+	0.583776i	0.0996074	+	0.995027i	$0.468241\pi$
$978$	5.53276	−	9.58302i	0.176918	−	0.306431i
$979$	1.60384	+	2.77793i	0.0512589	+	0.0887831i
$980$		−	8.82263i		−	0.281829i
$981$	−19.0826	+	11.0174i	−0.609261	+	0.351757i
$982$	63.5470	−	36.6889i	2.02787	−	1.17079i
$983$		−	44.1843i		−	1.40926i	−0.709576	−	0.704629i	$-0.751113\pi$
$983$		−	44.1843i		−	1.40926i	0.709576	−	0.704629i	$-0.248887\pi$
$984$	−12.9573	−	22.4428i	−0.413065	−	0.715449i
$985$	−41.3433	+	71.6087i	−1.31731	+	2.28164i
$986$	11.6161	+	6.70658i	0.369933	+	0.213581i
$987$	−6.74490			−0.214692
$988$	−15.8542	+	13.7849i	−0.504391	+	0.438555i
$989$	14.0546			0.446911
$990$	−12.3352	−	7.12176i	−0.392040	−	0.226344i
$991$	25.3549	−	43.9159i	0.805424	−	1.39504i	−0.110581	−	0.993867i	$-0.535271\pi$
$991$	25.3549	−	43.9159i	0.805424	−	1.39504i	0.916005	−	0.401168i	$-0.131396\pi$
$992$	33.9247	+	58.7594i	1.07711	+	1.86561i
$993$			9.49586i			0.301342i
$994$	11.7807	−	6.80160i	0.373662	−	0.215734i
$995$	−9.82511	+	5.67253i	−0.311477	+	0.179831i
$996$			26.4126i			0.836916i
$997$	25.1384	+	43.5410i	0.796141	+	1.37896i	0.922112	+	0.386923i	$0.126462\pi$
$997$	25.1384	+	43.5410i	0.796141	+	1.37896i	−0.125971	+	0.992034i	$0.540205\pi$
$998$	−0.0732891	+	0.126940i	−0.00231993	+	0.00401823i
$999$	16.7057	+	9.64505i	0.528546	+	0.305156i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.2.q.a.43.6	yes	12
3.2	odd	2		819.2.ct.a.316.1		12
4.3	odd	2		1456.2.cc.c.225.5		12
7.2	even	3		637.2.k.h.459.1		12
7.3	odd	6		637.2.u.i.30.1		12
7.4	even	3		637.2.u.h.30.1		12
7.5	odd	6		637.2.k.g.459.1		12
7.6	odd	2		637.2.q.h.589.6		12
13.4	even	6		1183.2.c.i.337.11		12
13.6	odd	12		1183.2.a.m.1.2		6
13.7	odd	12		1183.2.a.p.1.5		6
13.9	even	3		1183.2.c.i.337.2		12
13.10	even	6	inner	91.2.q.a.36.6	✓	12
39.23	odd	6		819.2.ct.a.127.1		12
52.23	odd	6		1456.2.cc.c.673.5		12
91.6	even	12		8281.2.a.by.1.2		6
91.10	odd	6		637.2.k.g.569.6		12
91.20	even	12		8281.2.a.ch.1.5		6
91.23	even	6		637.2.u.h.361.1		12
91.62	odd	6		637.2.q.h.491.6		12
91.75	odd	6		637.2.u.i.361.1		12
91.88	even	6		637.2.k.h.569.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	13.10	even	6	inner
91.2.q.a.43.6	yes	12	1.1	even	1	trivial
637.2.k.g.459.1		12	7.5	odd	6
637.2.k.g.569.6		12	91.10	odd	6
637.2.k.h.459.1		12	7.2	even	3
637.2.k.h.569.6		12	91.88	even	6
637.2.q.h.491.6		12	91.62	odd	6
637.2.q.h.589.6		12	7.6	odd	2
637.2.u.h.30.1		12	7.4	even	3
637.2.u.h.361.1		12	91.23	even	6
637.2.u.i.30.1		12	7.3	odd	6
637.2.u.i.361.1		12	91.75	odd	6
819.2.ct.a.127.1		12	39.23	odd	6
819.2.ct.a.316.1		12	3.2	odd	2
1183.2.a.m.1.2		6	13.6	odd	12
1183.2.a.p.1.5		6	13.7	odd	12
1183.2.c.i.337.2		12	13.9	even	3
1183.2.c.i.337.11		12	13.4	even	6
1456.2.cc.c.225.5		12	4.3	odd	2
1456.2.cc.c.673.5		12	52.23	odd	6
8281.2.a.by.1.2		6	91.6	even	12
8281.2.a.ch.1.5		6	91.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82678 + 1.05469i) q^{2} +(-1.13082 + 1.95864i) q^{3} +(1.22476 + 2.12135i) q^{4} -3.60178i q^{5} +(-4.13154 + 2.38535i) q^{6} +(-0.866025 + 0.500000i) q^{7} +0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +O(q^{10})\)	\(q+(1.82678 + 1.05469i) q^{2} +(-1.13082 + 1.95864i) q^{3} +(1.22476 + 2.12135i) q^{4} -3.60178i q^{5} +(-4.13154 + 2.38535i) q^{6} +(-0.866025 + 0.500000i) q^{7} +0.948212i q^{8} +(-1.05753 - 1.83169i) q^{9} +(3.79878 - 6.57967i) q^{10} +(0.767631 + 0.443192i) q^{11} -5.53995 q^{12} +(-1.17349 + 3.40924i) q^{13} -2.10939 q^{14} +(7.05461 + 4.07298i) q^{15} +(1.44945 - 2.51051i) q^{16} +(-2.48008 - 4.29563i) q^{17} -4.46147i q^{18} +(2.06008 - 1.18939i) q^{19} +(7.64062 - 4.41132i) q^{20} -2.26165i q^{21} +(0.934864 + 1.61923i) q^{22} +(-1.92926 + 3.34157i) q^{23} +(-1.85721 - 1.07226i) q^{24} -7.97282 q^{25} +(-5.73942 + 4.99028i) q^{26} -2.00144 q^{27} +(-2.12135 - 1.22476i) q^{28} +(-0.640986 + 1.11022i) q^{29} +(8.59150 + 14.8809i) q^{30} +8.46921i q^{31} +(6.93800 - 4.00566i) q^{32} +(-1.73611 + 1.00234i) q^{33} -10.4629i q^{34} +(1.80089 + 3.11923i) q^{35} +(2.59043 - 4.48676i) q^{36} +(-8.34686 - 4.81906i) q^{37} +5.01776 q^{38} +(-5.35049 - 6.15370i) q^{39} +3.41525 q^{40} +(10.4652 + 6.04207i) q^{41} +(2.38535 - 4.13154i) q^{42} +(-1.82125 - 3.15450i) q^{43} +2.17122i q^{44} +(-6.59734 + 3.80898i) q^{45} +(-7.04867 + 4.06955i) q^{46} -2.98229i q^{47} +(3.27814 + 5.67790i) q^{48} +(0.500000 - 0.866025i) q^{49} +(-14.5646 - 8.40888i) q^{50} +11.2181 q^{51} +(-8.66942 + 1.68613i) q^{52} +4.92032 q^{53} +(-3.65619 - 2.11090i) q^{54} +(1.59628 - 2.76484i) q^{55} +(-0.474106 - 0.821175i) q^{56} +5.37995i q^{57} +(-2.34189 + 1.35209i) q^{58} +(6.34577 - 3.66373i) q^{59} +19.9537i q^{60} +(0.769632 + 1.33304i) q^{61} +(-8.93242 + 15.4714i) q^{62} +(1.83169 + 1.05753i) q^{63} +11.1012 q^{64} +(12.2793 + 4.22664i) q^{65} -4.22867 q^{66} +(7.29756 + 4.21325i) q^{67} +(6.07501 - 10.5222i) q^{68} +(-4.36330 - 7.55745i) q^{69} +7.59755i q^{70} +(-5.58490 + 3.22444i) q^{71} +(1.73683 - 1.00276i) q^{72} +7.14859i q^{73} +(-10.1653 - 17.6068i) q^{74} +(9.01585 - 15.6159i) q^{75} +(5.04621 + 2.91343i) q^{76} -0.886384 q^{77} +(-3.28391 - 16.8846i) q^{78} +0.757551 q^{79} +(-9.04232 - 5.22059i) q^{80} +(5.43585 - 9.41518i) q^{81} +(12.7451 + 22.0751i) q^{82} -4.76766i q^{83} +(4.79774 - 2.76998i) q^{84} +(-15.4719 + 8.93270i) q^{85} -7.68344i q^{86} +(-1.44969 - 2.51093i) q^{87} +(-0.420240 + 0.727877i) q^{88} +(3.13400 + 1.80942i) q^{89} -16.0692 q^{90} +(-0.688351 - 3.53923i) q^{91} -9.45150 q^{92} +(-16.5882 - 9.57719i) q^{93} +(3.14541 - 5.44800i) q^{94} +(-4.28391 - 7.41995i) q^{95} +18.1188i q^{96} +(-0.401229 + 0.231650i) q^{97} +(1.82678 - 1.05469i) q^{98} -1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9	\( 12 q + 4 q^{4} - 18 q^{6} - 4 q^{9} + 12 q^{10} + 6 q^{11} - 4 q^{12} + 4 q^{13} - 8 q^{14} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 12 q^{24} - 20 q^{25} - 42 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} - 30 q^{33} + 6 q^{35} - 10 q^{36} - 42 q^{37} + 4 q^{38} - 4 q^{39} + 92 q^{40} + 30 q^{41} + 4 q^{42} + 2 q^{43} + 12 q^{46} - 2 q^{48} + 6 q^{49} - 18 q^{50} + 52 q^{51} + 2 q^{52} - 44 q^{53} + 12 q^{54} - 6 q^{55} - 12 q^{56} - 12 q^{58} + 18 q^{59} + 14 q^{61} - 4 q^{62} + 12 q^{63} - 52 q^{64} + 60 q^{65} - 52 q^{66} - 24 q^{67} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} + 46 q^{75} - 18 q^{76} + 8 q^{77} - 10 q^{78} - 56 q^{79} - 72 q^{80} + 2 q^{81} + 14 q^{82} + 18 q^{84} - 48 q^{85} - 2 q^{87} - 14 q^{88} - 12 q^{89} + 24 q^{90} + 14 q^{91} + 24 q^{92} - 18 q^{93} + 4 q^{94} - 22 q^{95} + 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 - 18 * q^6 - 4 * q^9 + 12 * q^10 + 6 * q^11 - 4 * q^12 + 4 * q^13 - 8 * q^14 + 6 * q^15 - 8 * q^16 - 4 * q^17 - 12 * q^20 + 6 * q^22 - 12 * q^23 + 12 * q^24 - 20 * q^25 - 42 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 + 36 * q^32 - 30 * q^33 + 6 * q^35 - 10 * q^36 - 42 * q^37 + 4 * q^38 - 4 * q^39 + 92 * q^40 + 30 * q^41 + 4 * q^42 + 2 * q^43 + 12 * q^46 - 2 * q^48 + 6 * q^49 - 18 * q^50 + 52 * q^51 + 2 * q^52 - 44 * q^53 + 12 * q^54 - 6 * q^55 - 12 * q^56 - 12 * q^58 + 18 * q^59 + 14 * q^61 - 4 * q^62 + 12 * q^63 - 52 * q^64 + 60 * q^65 - 52 * q^66 - 24 * q^67 - 8 * q^68 + 4 * q^69 - 24 * q^71 + 60 * q^72 + 6 * q^74 + 46 * q^75 - 18 * q^76 + 8 * q^77 - 10 * q^78 - 56 * q^79 - 72 * q^80 + 2 * q^81 + 14 * q^82 + 18 * q^84 - 48 * q^85 - 2 * q^87 - 14 * q^88 - 12 * q^89 + 24 * q^90 + 14 * q^91 + 24 * q^92 - 18 * q^93 + 4 * q^94 - 22 * q^95 + 6 * q^97

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