LMFDB - Embedded newform 171.3.n.a.11.33

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,3,Mod(11,171)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("171.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 4])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.33
Character	$\chi$	$=$	171.11
Dual form			171.3.n.a.140.33

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.68675 - 1.55120i) q^{2} +(-1.64208 - 2.51069i) q^{3} +(2.81242 - 4.87126i) q^{4} -4.30248i q^{5} +(-8.30645 - 4.19840i) q^{6} +(0.122000 - 0.211310i) q^{7} -5.04093i q^{8} +(-3.60712 + 8.24553i) q^{9} +(-6.67400 - 11.5597i) q^{10} +(1.58563 + 0.915463i) q^{11} +(-16.8485 + 0.937899i) q^{12} +(3.60116 - 6.23738i) q^{13} -0.756984i q^{14} +(-10.8022 + 7.06504i) q^{15} +(3.43023 + 5.94133i) q^{16} +(-4.73531 - 2.73393i) q^{17} +(3.09900 + 27.7490i) q^{18} +(-1.81089 - 18.9135i) q^{19} +(-20.9585 - 12.1004i) q^{20} +(-0.730868 + 0.0406851i) q^{21} +5.68026 q^{22} +(25.8905 + 14.9479i) q^{23} +(-12.6562 + 8.27762i) q^{24} +6.48865 q^{25} -22.3444i q^{26} +(26.6251 - 4.48349i) q^{27} +(-0.686231 - 1.18859i) q^{28} -6.18964i q^{29} +(-18.0636 + 35.7383i) q^{30} +(-12.5185 - 21.6826i) q^{31} +(35.8946 + 20.7238i) q^{32} +(-0.305293 - 5.48429i) q^{33} -16.9635 q^{34} +(-0.909158 - 0.524902i) q^{35} +(30.0214 + 40.7611i) q^{36} +25.8584 q^{37} +(-34.2040 - 48.0068i) q^{38} +(-21.5735 + 1.20093i) q^{39} -21.6885 q^{40} +58.1814i q^{41} +(-1.90055 + 1.24303i) q^{42} +(-8.06787 - 13.9740i) q^{43} +(8.91893 - 5.14934i) q^{44} +(35.4762 + 15.5196i) q^{45} +92.7484 q^{46} +31.5027i q^{47} +(9.28412 - 18.3684i) q^{48} +(24.4702 + 42.3837i) q^{49} +(17.4334 - 10.0652i) q^{50} +(0.911724 + 16.3782i) q^{51} +(-20.2560 - 35.0844i) q^{52} +(-55.2531 + 31.9004i) q^{53} +(64.5804 - 53.3469i) q^{54} +(3.93876 - 6.82214i) q^{55} +(-1.06520 - 0.614992i) q^{56} +(-44.5123 + 35.6042i) q^{57} +(-9.60136 - 16.6300i) q^{58} -22.6336i q^{59} +(4.03530 + 72.4902i) q^{60} +1.38933 q^{61} +(-67.2681 - 38.8372i) q^{62} +(1.30229 + 1.76817i) q^{63} +101.145 q^{64} +(-26.8362 - 15.4939i) q^{65} +(-9.32746 - 14.2614i) q^{66} +(9.07092 - 15.7113i) q^{67} +(-26.6354 + 15.3780i) q^{68} +(-4.98488 - 89.5486i) q^{69} -3.25691 q^{70} +(-94.7332 - 54.6943i) q^{71} +(41.5651 + 18.1832i) q^{72} +(5.53115 - 9.58024i) q^{73} +(69.4752 - 40.1115i) q^{74} +(-10.6549 - 16.2910i) q^{75} +(-97.2257 - 44.3715i) q^{76} +(0.386893 - 0.223373i) q^{77} +(-56.0999 + 36.6914i) q^{78} +(59.3754 + 102.841i) q^{79} +(25.5625 - 14.7585i) q^{80} +(-54.9774 - 59.4852i) q^{81} +(90.2508 + 156.319i) q^{82} +(-62.7808 - 36.2465i) q^{83} +(-1.85732 + 3.67467i) q^{84} +(-11.7627 + 20.3736i) q^{85} +(-43.3528 - 25.0297i) q^{86} +(-15.5403 + 10.1639i) q^{87} +(4.61478 - 7.99304i) q^{88} +(-37.8306 + 21.8415i) q^{89} +(119.390 - 13.3334i) q^{90} +(-0.878681 - 1.52192i) q^{91} +(145.630 - 84.0795i) q^{92} +(-33.8819 + 67.0347i) q^{93} +(48.8668 + 84.6398i) q^{94} +(-81.3750 + 7.79134i) q^{95} +(-6.91105 - 124.150i) q^{96} +(91.2223 + 158.002i) q^{97} +(131.491 + 75.9163i) q^{98} +(-13.2680 + 9.77216i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 3 q^{2} + q^{3} + 73 q^{4} - 13 q^{6} - q^{7} + 5 q^{9} + 6 q^{10} - 24 q^{11} + 15 q^{12} - 4 q^{13} + 49 q^{15} - 131 q^{16} + 135 q^{17} + 30 q^{18} + 4 q^{19} + 69 q^{20} - 13 q^{21} + 6 q^{22}+ \cdots - 340 q^{99}+O(q^{100}) $ 76 * q - 3 * q^2 + q^3 + 73 * q^4 - 13 * q^6 - q^7 + 5 * q^9 + 6 * q^10 - 24 * q^11 + 15 * q^12 - 4 * q^13 + 49 * q^15 - 131 * q^16 + 135 * q^17 + 30 * q^18 + 4 * q^19 + 69 * q^20 - 13 * q^21 + 6 * q^22 - 75 * q^23 - 6 * q^24 - 302 * q^25 - 59 * q^27 + 14 * q^28 + 265 * q^30 + 14 * q^31 + 45 * q^32 - 59 * q^33 + 66 * q^34 + 75 * q^35 - 127 * q^36 + 14 * q^37 - 147 * q^38 - 78 * q^39 - 24 * q^40 + 55 * q^42 + 29 * q^43 - 183 * q^44 + 145 * q^45 - 84 * q^46 - 246 * q^48 - 171 * q^49 - 363 * q^50 - 10 * q^51 + 101 * q^52 - 36 * q^53 + 245 * q^54 - 27 * q^55 + 300 * q^56 - 141 * q^57 + 6 * q^58 + 404 * q^60 - 16 * q^61 - 120 * q^62 + 402 * q^63 - 680 * q^64 - 6 * q^65 - 245 * q^66 + 8 * q^67 + 666 * q^68 + 81 * q^69 + 84 * q^70 - 135 * q^71 - 381 * q^72 + 65 * q^73 + 102 * q^74 - 139 * q^75 + 163 * q^76 - 366 * q^77 + 824 * q^78 - 16 * q^79 + 66 * q^80 + 305 * q^81 - 42 * q^82 - 177 * q^83 + 546 * q^84 + 51 * q^85 - 345 * q^86 - 375 * q^87 + 162 * q^88 - 216 * q^89 + 118 * q^90 + 265 * q^91 - 1347 * q^92 - 6 * q^93 + 6 * q^94 + 432 * q^95 + 511 * q^96 - 127 * q^97 - 882 * q^98 - 340 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.68675	−	1.55120i	1.34338	−	0.775599i	0.356075	−	0.934457i	$-0.384115\pi$
$2$	2.68675	−	1.55120i	1.34338	−	0.775599i	0.987301	+	0.158859i	$0.0507815\pi$
$3$	−1.64208	−	2.51069i	−0.547361	−	0.836896i
$3$	−1.64208	−	2.51069i	−0.547361	−	0.836896i
$4$	2.81242	−	4.87126i	0.703106	−	1.21782i
$5$		−	4.30248i		−	0.860496i	−0.902711	−	0.430248i	$-0.858426\pi$
$5$		−	4.30248i		−	0.860496i	0.902711	−	0.430248i	$-0.141574\pi$
$6$	−8.30645	−	4.19840i	−1.38441	−	0.699734i
$7$	0.122000	−	0.211310i	0.0174286	−	0.0301872i	−0.857180	−	0.515018i	$-0.827785\pi$
$7$	0.122000	−	0.211310i	0.0174286	−	0.0301872i	0.874608	+	0.484830i	$0.161119\pi$
$8$		−	5.04093i		−	0.630116i
$9$	−3.60712	+	8.24553i	−0.400791	+	0.916170i
$10$	−6.67400	−	11.5597i	−0.667400	−	1.15597i
$11$	1.58563	+	0.915463i	0.144148	+	0.0832239i	0.570339	−	0.821409i	$-0.306812\pi$
$11$	1.58563	+	0.915463i	0.144148	+	0.0832239i	−0.426191	+	0.904633i	$0.640145\pi$
$12$	−16.8485	+	0.937899i	−1.40404	+	0.0781583i
$13$	3.60116	−	6.23738i	0.277012	−	0.479799i	−0.693629	−	0.720333i	$-0.743989\pi$
$13$	3.60116	−	6.23738i	0.277012	−	0.479799i	0.970641	+	0.240534i	$0.0773225\pi$
$14$		−	0.756984i		−	0.0540703i
$15$	−10.8022	+	7.06504i	−0.720146	+	0.471003i
$16$	3.43023	+	5.94133i	0.214389	+	0.371333i
$17$	−4.73531	−	2.73393i	−0.278548	−	0.160820i	0.354218	−	0.935163i	$-0.384747\pi$
$17$	−4.73531	−	2.73393i	−0.278548	−	0.160820i	−0.632766	+	0.774343i	$0.718080\pi$
$18$	3.09900	+	27.7490i	0.172167	+	1.54161i
$19$	−1.81089	−	18.9135i	−0.0953102	−	0.995448i
$19$	−1.81089	−	18.9135i	−0.0953102	−	0.995448i
$20$	−20.9585	−	12.1004i	−1.04793	−	0.605020i
$21$	−0.730868	+	0.0406851i	−0.0348032	+	0.00193738i
$22$	5.68026			0.258193
$23$	25.8905	+	14.9479i	1.12567	+	0.649907i	0.942843	−	0.333237i	$-0.108141\pi$
$23$	25.8905	+	14.9479i	1.12567	+	0.649907i	0.182830	+	0.983145i	$0.441474\pi$
$24$	−12.6562	+	8.27762i	−0.527341	+	0.344901i
$25$	6.48865			0.259546
$26$		−	22.3444i		−	0.859400i
$27$	26.6251	−	4.48349i	0.986116	−	0.166055i
$28$	−0.686231	−	1.18859i	−0.0245083	−	0.0424495i
$29$		−	6.18964i		−	0.213436i	−0.994289	−	0.106718i	$-0.965966\pi$
$29$		−	6.18964i		−	0.213436i	0.994289	−	0.106718i	$-0.0340342\pi$
$30$	−18.0636	+	35.7383i	−0.602118	+	1.19128i
$31$	−12.5185	−	21.6826i	−0.403822	−	0.699440i	0.590362	−	0.807139i	$-0.298985\pi$
$31$	−12.5185	−	21.6826i	−0.403822	−	0.699440i	−0.994184	+	0.107699i	$0.965652\pi$
$32$	35.8946	+	20.7238i	1.12171	+	0.647618i
$33$	−0.305293	−	5.48429i	−0.00925129	−	0.166191i
$34$	−16.9635			−0.498926
$35$	−0.909158	−	0.524902i	−0.0259759	−	0.0149972i
$36$	30.0214	+	40.7611i	0.833927	+	1.13225i
$37$	25.8584			0.698876			0.349438	−	0.936959i	$-0.386372\pi$
$37$	25.8584			0.698876			0.349438	+	0.936959i	$0.386372\pi$
$38$	−34.2040	−	48.0068i	−0.900105	−	1.26334i
$39$	−21.5735	+	1.20093i	−0.553168	+	0.0307930i
$40$	−21.6885			−0.542212
$41$			58.1814i			1.41906i	0.704676	+	0.709529i	$0.251092\pi$
$41$			58.1814i			1.41906i	−0.704676	+	0.709529i	$0.748908\pi$
$42$	−1.90055	+	1.24303i	−0.0452512	+	0.0295960i
$43$	−8.06787	−	13.9740i	−0.187625	−	0.324976i	0.756833	−	0.653608i	$-0.226746\pi$
$43$	−8.06787	−	13.9740i	−0.187625	−	0.324976i	−0.944458	+	0.328632i	$0.893412\pi$
$44$	8.91893	−	5.14934i	0.202703	−	0.117031i
$45$	35.4762	+	15.5196i	0.788361	+	0.344879i
$46$	92.7484			2.01627
$47$			31.5027i			0.670269i	0.942170	+	0.335135i	$0.108782\pi$
$47$			31.5027i			0.670269i	−0.942170	+	0.335135i	$0.891218\pi$
$48$	9.28412	−	18.3684i	0.193419	−	0.382675i
$49$	24.4702	+	42.3837i	0.499392	+	0.864973i
$50$	17.4334	−	10.0652i	0.348668	−	0.201303i
$51$	0.911724	+	16.3782i	0.0178769	+	0.321142i
$52$	−20.2560	−	35.0844i	−0.389538	−	0.674699i
$53$	−55.2531	+	31.9004i	−1.04251	+	0.601894i	−0.920543	−	0.390640i	$-0.872254\pi$
$53$	−55.2531	+	31.9004i	−1.04251	+	0.601894i	−0.121967	+	0.992534i	$0.538920\pi$
$54$	64.5804	−	53.3469i	1.19593	−	0.987905i
$55$	3.93876	−	6.82214i	0.0716139	−	0.124039i
$56$	−1.06520	−	0.614992i	−0.0190214	−	0.0109820i
$57$	−44.5123	+	35.6042i	−0.780917	+	0.624634i
$58$	−9.60136	−	16.6300i	−0.165541	−	0.286725i
$59$		−	22.6336i		−	0.383620i	−0.981432	−	0.191810i	$-0.938564\pi$
$59$		−	22.6336i		−	0.383620i	0.981432	−	0.191810i	$-0.0614357\pi$
$60$	4.03530	+	72.4902i	0.0672549	+	1.20817i
$61$	1.38933			0.0227759			0.0113880	−	0.999935i	$-0.496375\pi$
$61$	1.38933			0.0227759			0.0113880	+	0.999935i	$0.496375\pi$
$62$	−67.2681	−	38.8372i	−1.08497	−	0.626407i
$63$	1.30229	+	1.76817i	0.0206713	+	0.0280663i
$64$	101.145			1.58039
$65$	−26.8362	−	15.4939i	−0.412865	−	0.238368i
$66$	−9.32746	−	14.2614i	−0.141325	−	0.216081i
$67$	9.07092	−	15.7113i	0.135387	−	0.234497i	−0.790358	−	0.612645i	$-0.790106\pi$
$67$	9.07092	−	15.7113i	0.135387	−	0.234497i	0.925745	+	0.378148i	$0.123439\pi$
$68$	−26.6354	+	15.3780i	−0.391697	+	0.226147i
$69$	−4.98488	−	89.5486i	−0.0722446	−	1.29781i
$70$	−3.25691			−0.0465273
$71$	−94.7332	−	54.6943i	−1.33427	−	0.770342i	−0.348320	−	0.937376i	$-0.613248\pi$
$71$	−94.7332	−	54.6943i	−1.33427	−	0.770342i	−0.985951	+	0.167034i	$0.946581\pi$
$72$	41.5651	+	18.1832i	0.577293	+	0.252545i
$73$	5.53115	−	9.58024i	0.0757692	−	0.131236i	−0.825651	−	0.564181i	$-0.809192\pi$
$73$	5.53115	−	9.58024i	0.0757692	−	0.131236i	0.901421	+	0.432945i	$0.142525\pi$
$74$	69.4752	−	40.1115i	0.938854	−	0.542048i
$75$	−10.6549	−	16.2910i	−0.142065	−	0.217213i
$76$	−97.2257	−	44.3715i	−1.27928	−	0.583835i
$77$	0.386893	−	0.223373i	0.00502459	−	0.00290095i
$78$	−56.0999	+	36.6914i	−0.719229	+	0.470403i
$79$	59.3754	+	102.841i	0.751587	+	1.30179i	0.947053	+	0.321077i	$0.104045\pi$
$79$	59.3754	+	102.841i	0.751587	+	1.30179i	−0.195466	+	0.980711i	$0.562622\pi$
$80$	25.5625	−	14.7585i	0.319531	−	0.184481i
$81$	−54.9774	−	59.4852i	−0.678733	−	0.734385i
$82$	90.2508	+	156.319i	1.10062	+	1.90633i
$83$	−62.7808	−	36.2465i	−0.756395	−	0.436705i	0.0716052	−	0.997433i	$-0.477188\pi$
$83$	−62.7808	−	36.2465i	−0.756395	−	0.436705i	−0.828000	+	0.560728i	$0.810521\pi$
$84$	−1.85732	+	3.67467i	−0.0221110	+	0.0437461i
$85$	−11.7627	+	20.3736i	−0.138385	+	0.239689i
$86$	−43.3528	−	25.0297i	−0.504102	−	0.291043i
$87$	−15.5403	+	10.1639i	−0.178624	+	0.116827i
$88$	4.61478	−	7.99304i	0.0524407	−	0.0908300i
$89$	−37.8306	+	21.8415i	−0.425063	+	0.245410i	−0.697241	−	0.716837i	$-0.745589\pi$
$89$	−37.8306	+	21.8415i	−0.425063	+	0.245410i	0.272178	+	0.962247i	$0.412256\pi$
$90$	119.390	−	13.3334i	1.32655	−	0.148149i
$91$	−0.878681	−	1.52192i	−0.00965584	−	0.0167244i
$92$	145.630	−	84.0795i	1.58293	−	0.913908i
$93$	−33.8819	+	67.0347i	−0.364322	+	0.720803i
$94$	48.8668	+	84.6398i	0.519860	+	0.900424i
$95$	−81.3750	+	7.79134i	−0.856579	+	0.0820141i
$96$	−6.91105	−	124.150i	−0.0719901	−	1.29323i
$97$	91.2223	+	158.002i	0.940436	+	1.62888i	0.764642	+	0.644455i	$0.222916\pi$
$97$	91.2223	+	158.002i	0.940436	+	1.62888i	0.175794	+	0.984427i	$0.443751\pi$
$98$	131.491	+	75.9163i	1.34174	+	0.774656i
$99$	−13.2680	+	9.77216i	−0.134020	+	0.0987087i
$100$	18.2488	−	31.6079i	0.182488	−	0.316079i
$101$			63.5855i			0.629560i	0.949165	+	0.314780i	$0.101931\pi$
$101$			63.5855i			0.629560i	−0.949165	+	0.314780i	$0.898069\pi$
$102$	27.8555	+	42.5900i	0.273093	+	0.417549i
$103$	−34.0216	−	58.9272i	−0.330307	−	0.572108i	0.652265	−	0.757991i	$-0.273819\pi$
$103$	−34.0216	−	58.9272i	−0.330307	−	0.572108i	−0.982572	+	0.185883i	$0.940486\pi$
$104$	−31.4422	−	18.1532i	−0.302329	−	0.174550i
$105$	0.175047	+	3.14455i	0.00166711	+	0.0299481i
$106$	−98.9676	+	171.417i	−0.933656	+	1.61714i
$107$			53.8099i			0.502897i	0.967871	+	0.251448i	$0.0809068\pi$
$107$			53.8099i			0.502897i	−0.967871	+	0.251448i	$0.919093\pi$
$108$	53.0409	−	142.308i	0.491120	−	1.31766i
$109$	1.25329	−	2.17076i	0.0114980	−	0.0199152i	−0.860219	−	0.509925i	$-0.829673\pi$
$109$	1.25329	−	2.17076i	0.0114980	−	0.0199152i	0.871717	+	0.490009i	$0.163007\pi$
$110$		−	24.4392i		−	0.222175i
$111$	−42.4617	−	64.9225i	−0.382538	−	0.584887i
$112$	1.67395			0.0149460
$113$	−179.813	+	103.815i	−1.59127	+	0.918718i	−0.598176	+	0.801365i	$0.704108\pi$
$113$	−179.813	+	103.815i	−1.59127	+	0.918718i	−0.993090	+	0.117353i	$0.962559\pi$
$114$	−64.3644	+	164.707i	−0.564600	+	1.44480i
$115$	64.3129	−	111.393i	0.559243	−	0.968637i
$116$	−30.1514	−	17.4079i	−0.259926	−	0.150068i
$117$	38.4407	+	52.1924i	0.328553	+	0.446089i
$118$	−35.1091	−	60.8108i	−0.297535	−	0.515346i
$119$	−1.15542	+	0.667079i	−0.00970937	+	0.00560571i
$120$	35.6143	+	54.4531i	0.296786	+	0.453775i
$121$	−58.8239	−	101.886i	−0.486148	−	0.842032i
$122$	3.73279	−	2.15513i	0.0305966	−	0.0176650i
$123$	146.075	−	95.5387i	1.18760	−	0.776738i
$124$	−140.829			−1.13572
$125$		−	135.479i		−	1.08383i
$126$	6.24173	+	2.73053i	0.0495375	+	0.0216709i
$127$	−74.4050	−	128.873i	−0.585866	−	1.01475i	−0.994767	−	0.102171i	$-0.967421\pi$
$127$	−74.4050	−	128.873i	−0.585866	−	1.01475i	0.408900	−	0.912579i	$-0.365912\pi$
$128$	128.173	−	74.0004i	1.00135	−	0.578128i
$129$	−21.8362	+	43.2024i	−0.169273	+	0.334902i
$130$	−96.1364			−0.739511
$131$		−	53.0116i		−	0.404669i	−0.979316	−	0.202335i	$-0.935147\pi$
$131$		−	53.0116i		−	0.404669i	0.979316	−	0.202335i	$-0.0648528\pi$
$132$	−27.5740	−	13.9370i	−0.208894	−	0.105583i
$133$	−4.21754	−	1.92479i	−0.0317108	−	0.0144721i
$134$		−	56.2831i		−	0.420023i
$135$	−19.2902	−	114.554i	−0.142890	−	0.848550i
$136$	−13.7816	+	23.8704i	−0.101335	+	0.175517i
$137$			218.542i			1.59520i	0.603189	+	0.797598i	$0.293896\pi$
$137$			218.542i			1.59520i	−0.603189	+	0.797598i	$0.706104\pi$
$138$	−152.301	−	232.862i	−1.10363	−	1.68741i
$139$	−20.2874	+	35.1388i	−0.145953	+	0.252797i	−0.929728	−	0.368247i	$-0.879958\pi$
$139$	−20.2874	+	35.1388i	−0.145953	+	0.252797i	0.783775	+	0.621045i	$0.213291\pi$
$140$	−5.11388	+	2.95250i	−0.0365277	+	0.0210893i
$141$	79.0934	−	51.7300i	0.560946	−	0.366880i
$142$	−339.366			−2.38990
$143$	11.4202	−	6.59345i	0.0798615	−	0.0461081i
$144$	−61.3627	+	6.85296i	−0.426130	+	0.0475900i
$145$	−26.6308			−0.183661
$146$		−	34.3196i		−	0.235066i
$147$	66.2301	−	131.035i	0.450545	−	0.891393i
$148$	72.7249	−	125.963i	0.491384	−	0.851103i
$149$			45.8506i			0.307722i	0.988093	+	0.153861i	$0.0491708\pi$
$149$			45.8506i			0.307722i	−0.988093	+	0.153861i	$0.950829\pi$
$150$	−53.8976	−	27.2420i	−0.359317	−	0.181613i
$151$	89.9816	−	155.853i	0.595904	−	1.03214i	−0.397514	−	0.917596i	$-0.630127\pi$
$151$	89.9816	−	155.853i	0.595904	−	1.03214i	0.993419	−	0.114541i	$-0.0365396\pi$
$152$	−95.3416	+	9.12858i	−0.627247	+	0.0600565i
$153$	39.6236	−	29.1835i	0.258977	−	0.190742i
$154$	0.692991	−	1.20030i	0.00449994	−	0.00779413i
$155$	−93.2891	+	53.8605i	−0.601865	+	0.347487i
$156$	−54.8239	+	108.468i	−0.351435	+	0.695307i
$157$	143.764			0.915695			0.457848	−	0.889031i	$-0.348621\pi$
$157$	143.764			0.915695			0.457848	+	0.889031i	$0.348621\pi$
$158$	319.054	+	184.206i	2.01933	+	1.16586i
$159$	170.822	+	86.3402i	1.07435	+	0.543020i
$160$	89.1637	−	154.436i	0.557273	−	0.965225i
$161$	6.31727	−	3.64728i	0.0392377	−	0.0226539i
$162$	−239.984	−	74.5412i	−1.48138	−	0.460131i
$163$	−305.866			−1.87648			−0.938240	−	0.345984i	$-0.887545\pi$
$163$	−305.866			−1.87648			−0.938240	+	0.345984i	$0.887545\pi$
$164$	283.417	+	163.631i	1.72815	+	0.997748i
$165$	−23.5961	+	1.31352i	−0.143006	+	0.00796070i
$166$	−224.902			−1.35483
$167$	59.8260	+	34.5405i	0.358239	+	0.206830i	0.668308	−	0.743885i	$-0.267019\pi$
$167$	59.8260	+	34.5405i	0.358239	+	0.206830i	−0.310069	+	0.950714i	$0.600352\pi$
$168$	0.205090	+	3.68425i	0.00122078	+	0.0219301i
$169$	58.5634	+	101.435i	0.346529	+	0.600205i
$170$			72.9851i			0.429324i
$171$	162.484	+	53.2915i	0.950198	+	0.311646i
$172$	−90.7612			−0.527681
$173$	208.100	−	120.147i	1.20289	−	0.694490i	0.241695	−	0.970352i	$-0.422297\pi$
$173$	208.100	−	120.147i	1.20289	−	0.694490i	0.961197	+	0.275862i	$0.0889632\pi$
$174$	−25.9866	+	51.4139i	−0.149348	+	0.295482i
$175$	0.791614	−	1.37112i	0.00452351	−	0.00783495i
$176$			12.5610i			0.0713693i
$177$	−56.8258	+	37.1662i	−0.321050	+	0.209979i
$178$	−67.7610	+	117.365i	−0.380680	+	0.659356i
$179$		−	114.747i		−	0.641042i	−0.947241	−	0.320521i	$-0.896142\pi$
$179$		−	114.747i		−	0.641042i	0.947241	−	0.320521i	$-0.103858\pi$
$180$	175.374	−	129.166i	0.974301	−	0.717591i
$181$	−155.928	−	270.076i	−0.861483	−	1.49213i	−0.870497	−	0.492173i	$-0.836203\pi$
$181$	−155.928	−	270.076i	−0.861483	−	1.49213i	0.00901439	−	0.999959i	$-0.497131\pi$
$182$	−4.72160	−	2.72602i	−0.0259428	−	0.0149781i
$183$	−2.28140	−	3.48818i	−0.0124667	−	0.0190611i
$184$	75.3511	−	130.512i	0.409517	−	0.709304i
$185$		−	111.255i		−	0.601381i
$186$	12.9516	+	232.663i	0.0696323	+	1.25088i
$187$	−5.00563	−	8.67001i	−0.0267681	−	0.0463637i
$188$	153.458	+	88.5989i	0.816265	+	0.471271i
$189$	2.30086	−	6.17315i	0.0121739	−	0.0326622i
$190$	−206.549	+	147.162i	−1.08710	+	0.774537i
$191$	37.6935	+	21.7623i	0.197348	+	0.113939i	0.595418	−	0.803416i	$-0.296987\pi$
$191$	37.6935	+	21.7623i	0.197348	+	0.113939i	−0.398070	+	0.917355i	$0.630320\pi$
$192$	−166.088	−	253.943i	−0.865043	−	1.32262i
$193$	54.0007			0.279797			0.139898	−	0.990166i	$-0.455322\pi$
$193$	54.0007			0.279797			0.139898	+	0.990166i	$0.455322\pi$
$194$	490.183	+	283.007i	2.52672	+	1.45880i
$195$	5.16697	+	92.8197i	0.0264973	+	0.475999i
$196$	275.283			1.40450
$197$			350.299i			1.77817i	0.457743	+	0.889085i	$0.348658\pi$
$197$			350.299i			1.77817i	−0.457743	+	0.889085i	$0.651342\pi$
$198$	−20.4894	+	46.8367i	−0.103482	+	0.236549i
$199$	29.9017	+	51.7913i	0.150260	+	0.260258i	0.931323	−	0.364194i	$-0.118656\pi$
$199$	29.9017	+	51.7913i	0.150260	+	0.260258i	−0.781063	+	0.624452i	$0.785322\pi$
$200$		−	32.7088i		−	0.163544i
$201$	−54.3414	+	3.02501i	−0.270355	+	0.0150498i
$202$	98.6337	+	170.839i	0.488285	+	0.845735i
$203$	−1.30793	−	0.755136i	−0.00644302	−	0.00371988i
$204$	82.3469	+	41.6213i	0.403661	+	0.204026i
$205$	250.324			1.22109
$206$	−182.815	−	105.548i	−0.887453	−	0.512371i
$207$	−216.643	+	159.562i	−1.04658	+	0.770830i
$208$	49.4112			0.237554
$209$	14.4432	−	31.6476i	0.0691063	−	0.151424i
$210$	5.34812	+	8.17709i	0.0254672	+	0.0389385i
$211$	321.050			1.52156			0.760781	−	0.649008i	$-0.224816\pi$
$211$	321.050			1.52156			0.760781	+	0.649008i	$0.224816\pi$
$212$			358.870i			1.69278i
$213$	18.2397	+	327.658i	0.0856323	+	1.53830i
$214$	83.4698	+	144.574i	0.390046	+	0.675579i
$215$	−60.1227	+	34.7119i	−0.279641	+	0.161451i
$216$	−22.6010	−	134.215i	−0.104634	−	0.621367i
$217$	−6.10901			−0.0281521
$218$		−	7.77638i		−	0.0356715i
$219$	−33.1356	+	1.84455i	−0.151304	+	0.00842261i
$220$	−22.1550	−	38.3735i	−0.100704	−	0.174425i
$221$	−34.1052	+	19.6906i	−0.154322	+	0.0890979i
$222$	−214.792	−	108.564i	−0.967530	−	0.489028i
$223$	−181.033	−	313.558i	−0.811806	−	1.40609i	−0.911599	−	0.411081i	$-0.865151\pi$
$223$	−181.033	−	313.558i	−0.811806	−	1.40609i	0.0997930	−	0.995008i	$-0.468182\pi$
$224$	8.75829	−	5.05660i	0.0390995	−	0.0225741i
$225$	−23.4053	+	53.5023i	−0.104024	+	0.237788i
$226$	−322.075	+	557.851i	−1.42511	+	2.46837i
$227$	137.742	+	79.5252i	0.606792	+	0.350331i	0.771709	−	0.635976i	$-0.219402\pi$
$227$	137.742	+	79.5252i	0.606792	+	0.350331i	−0.164917	+	0.986307i	$0.552736\pi$
$228$	48.2498	+	316.965i	0.211622	+	1.39020i
$229$	127.999	+	221.700i	0.558946	+	0.968124i	0.997585	+	0.0694600i	$0.0221276\pi$
$229$	127.999	+	221.700i	0.558946	+	0.968124i	−0.438638	+	0.898664i	$0.644539\pi$
$230$		−	399.048i		−	1.73499i
$231$	−1.19613	−	0.604571i	−0.00517806	−	0.00261719i
$232$	−31.2015			−0.134489
$233$	184.915	+	106.761i	0.793626	+	0.458200i	0.841237	−	0.540666i	$-0.181828\pi$
$233$	184.915	+	106.761i	0.793626	+	0.458200i	−0.0476116	+	0.998866i	$0.515161\pi$
$234$	184.241	+	80.5989i	0.787356	+	0.344440i
$235$	135.540			0.576764
$236$	−110.254	−	63.6552i	−0.467178	−	0.269725i
$237$	160.703	−	317.947i	0.678071	−	1.34155i
$238$	−2.06954	+	3.58455i	−0.00869556	+	0.0150612i
$239$	331.738	−	191.529i	1.38802	−	0.801376i	0.394931	−	0.918711i	$-0.370768\pi$
$239$	331.738	−	191.529i	1.38802	−	0.801376i	0.993092	+	0.117335i	$0.0374351\pi$
$240$	−79.0298	−	39.9447i	−0.329291	−	0.166436i
$241$	158.704			0.658522			0.329261	−	0.944239i	$-0.393200\pi$
$241$	158.704			0.658522			0.329261	+	0.944239i	$0.393200\pi$
$242$	−316.090	−	182.495i	−1.30616	−	0.754111i
$243$	−59.0713	+	235.711i	−0.243092	+	0.970003i
$244$	3.90739	−	6.76780i	0.0160139	−	0.0277369i
$245$	182.355	−	105.283i	0.744306	−	0.429725i
$246$	244.269	−	483.280i	0.992963	−	1.96455i
$247$	−124.492	−	56.8152i	−0.504017	−	0.230021i
$248$	−109.300	+	63.1047i	−0.440728	+	0.254454i
$249$	12.0876	+	217.143i	0.0485447	+	0.872059i
$250$	−210.155	−	363.999i	−0.840621	−	1.45600i
$251$	53.4985	−	30.8874i	0.213141	−	0.123057i	−0.389629	−	0.920972i	$-0.627397\pi$
$251$	53.4985	−	30.8874i	0.213141	−	0.123057i	0.602771	+	0.797915i	$0.294063\pi$
$252$	12.2758	−	1.37096i	0.0487137	−	0.00544032i
$253$	27.3685	+	47.4035i	0.108176	+	0.187366i
$254$	−399.816	−	230.834i	−1.57408	−	0.908794i
$255$	70.4671	−	3.92268i	0.276342	−	0.0153830i
$256$	27.2889	−	47.2657i	0.106597	−	0.184632i
$257$	−348.573	−	201.249i	−1.35632	−	0.783069i	−0.367190	−	0.930146i	$-0.619680\pi$
$257$	−348.573	−	201.249i	−1.35632	−	0.783069i	−0.989125	+	0.147077i	$0.953014\pi$
$258$	8.34702	+	149.946i	0.0323528	+	0.581187i
$259$	3.15473	−	5.46415i	0.0121804	−	0.0210971i
$260$	−150.950	+	87.1509i	−0.580576	+	0.335196i
$261$	51.0369	+	22.3268i	0.195544	+	0.0855432i
$262$	−82.2315	−	142.429i	−0.313861	−	0.543623i
$263$	−4.24555	+	2.45117i	−0.0161428	+	0.00932004i	−0.508050	−	0.861328i	$-0.669633\pi$
$263$	−4.24555	+	2.45117i	−0.0161428	+	0.00932004i	0.491907	+	0.870648i	$0.336300\pi$
$264$	−27.6459	+	1.53896i	−0.104719	+	0.00582938i
$265$	137.251	+	237.725i	0.517928	+	0.897077i
$266$	−14.3172	+	1.37082i	−0.0538241	+	0.00515345i
$267$	116.958	+	59.1153i	0.438046	+	0.221406i
$268$	−51.0226	−	88.3737i	−0.190383	−	0.329753i
$269$	−169.855	−	98.0660i	−0.631432	−	0.364558i	0.149874	−	0.988705i	$-0.452113\pi$
$269$	−169.855	−	98.0660i	−0.631432	−	0.364558i	−0.781307	+	0.624148i	$0.785446\pi$
$270$	−229.524	−	277.856i	−0.850089	−	1.02910i
$271$	−141.237	+	244.629i	−0.521169	+	0.902691i	0.478528	+	0.878072i	$0.341171\pi$
$271$	−141.237	+	244.629i	−0.521169	+	0.902691i	−0.999697	+	0.0246188i	$0.992163\pi$
$272$		−	37.5121i		−	0.137912i
$273$	−2.37820	+	4.70522i	−0.00871136	+	0.0172352i
$274$	339.002	+	587.168i	1.23723	+	2.14295i
$275$	10.2886	+	5.94012i	0.0374130	+	0.0216004i
$276$	−450.234	−	227.566i	−1.63128	−	0.824514i
$277$	−23.6491	+	40.9615i	−0.0853759	+	0.147875i	−0.905551	−	0.424237i	$-0.860542\pi$
$277$	−23.6491	+	40.9615i	−0.0853759	+	0.147875i	0.820175	+	0.572112i	$0.193876\pi$
$278$			125.879i			0.452803i
$279$	223.940	−	25.0096i	0.802653	−	0.0896400i
$280$	−2.64599	+	4.58300i	−0.00944998	+	0.0163678i
$281$		−	501.792i		−	1.78574i	−0.450317	−	0.892869i	$-0.648689\pi$
$281$		−	501.792i		−	1.78574i	0.450317	−	0.892869i	$-0.351311\pi$
$282$	132.261	−	261.675i	0.469010	−	0.927926i
$283$	−350.417			−1.23822			−0.619111	−	0.785303i	$-0.712507\pi$
$283$	−350.417			−1.23822			−0.619111	+	0.785303i	$0.712507\pi$
$284$	−532.860	+	307.647i	−1.87627	+	1.08326i
$285$	153.186	+	191.513i	0.537496	+	0.671977i
$286$	20.4555	−	35.4299i	0.0715227	−	0.123881i
$287$	12.2943	+	7.09812i	0.0428373	+	0.0247321i
$288$	−300.355	+	221.217i	−1.04290	+	0.768115i
$289$	−129.551	−	224.389i	−0.448274	−	0.776433i
$290$	−71.5504	+	41.3097i	−0.246726	+	0.142447i
$291$	246.898	−	488.483i	0.848447	−	1.67863i
$292$	−31.1119	−	53.8874i	−0.106548	−	0.184546i
$293$	−432.408	+	249.651i	−1.47580	+	0.852051i	−0.999627	−	0.0273032i	$-0.991308\pi$
$293$	−432.408	+	249.651i	−1.47580	+	0.852051i	−0.476168	+	0.879354i	$0.657975\pi$
$294$	−25.3169	−	454.794i	−0.0861119	−	1.54692i
$295$	−97.3805			−0.330103
$296$		−	130.350i		−	0.440373i
$297$	46.3221	+	17.2652i	0.155967	+	0.0581319i
$298$	71.1233	+	123.189i	0.238669	+	0.413386i
$299$	186.471	−	107.659i	0.623650	−	0.360064i
$300$	−109.324	+	6.08570i	−0.364413	+	0.0202857i
$301$	−3.93712			−0.0130801
$302$		−	558.317i		−	1.84873i
$303$	159.643	−	104.413i	0.526876	−	0.344597i
$304$	106.160	−	75.6368i	0.349209	−	0.248805i
$305$		−	5.97757i		−	0.0195986i
$306$	61.1893	−	139.873i	0.199965	−	0.457101i
$307$	287.121	−	497.309i	0.935249	−	1.61990i	0.161059	−	0.986945i	$-0.448509\pi$
$307$	287.121	−	497.309i	0.935249	−	1.61990i	0.774190	−	0.632953i	$-0.218158\pi$
$308$		−	2.51288i		−	0.00815870i
$309$	−92.0814	+	182.181i	−0.297998	+	0.589583i
$310$	−167.096	+	289.420i	−0.539021	+	0.933612i
$311$	−47.8179	+	27.6077i	−0.153755	+	0.0887707i	−0.574904	−	0.818221i	$-0.694960\pi$
$311$	−47.8179	+	27.6077i	−0.153755	+	0.0887707i	0.421148	+	0.906992i	$0.361627\pi$
$312$	6.05379	+	108.751i	0.0194032	+	0.348560i
$313$	−175.033			−0.559211			−0.279605	−	0.960115i	$-0.590204\pi$
$313$	−175.033			−0.559211			−0.279605	+	0.960115i	$0.590204\pi$
$314$	386.259	−	223.007i	1.23012	−	0.710212i
$315$	7.60754	−	5.60310i	0.0241509	−	0.0177876i
$316$	667.955			2.11378
$317$		−	21.0506i		−	0.0664058i	−0.999449	−	0.0332029i	$-0.989429\pi$
$317$		−	21.0506i		−	0.0664058i	0.999449	−	0.0332029i	$-0.0105708\pi$
$318$	592.887	−	33.0041i	1.86443	−	0.103787i
$319$	5.66639	−	9.81448i	0.0177630	−	0.0307664i
$320$		−	435.174i		−	1.35992i
$321$	135.100	−	88.3604i	0.420872	−	0.275266i
$322$	11.3153	−	19.5987i	0.0351407	−	0.0608654i
$323$	−43.1331	+	94.5122i	−0.133539	+	0.292607i
$324$	−444.388	+	100.512i	−1.37157	+	0.310221i
$325$	23.3666	−	40.4722i	0.0718973	−	0.124530i
$326$	−821.787	+	474.459i	−2.52082	+	1.45540i
$327$	−7.50810	+	0.417951i	−0.0229605	+	0.00127814i
$328$	293.288			0.894171
$329$	6.65683	+	3.84332i	0.0202335	+	0.0116818i
$330$	−61.3592	+	40.1312i	−0.185937	+	0.121610i
$331$	218.982	−	379.288i	0.661578	−	1.14589i	−0.318623	−	0.947881i	$-0.603220\pi$
$331$	218.982	−	379.288i	0.661578	−	1.14589i	0.980201	−	0.198005i	$-0.0634462\pi$
$332$	−353.132	+	203.881i	−1.06365	+	0.614100i
$333$	−93.2744	+	213.216i	−0.280103	+	0.640289i
$334$	214.317			0.641667
$335$	−67.5976	−	39.0275i	−0.201784	−	0.116500i
$336$	−2.74877	−	4.20277i	−0.00818086	−	0.0125083i
$337$	−587.488			−1.74329			−0.871644	−	0.490139i	$-0.836946\pi$
$337$	−587.488			−1.74329			−0.871644	+	0.490139i	$0.836946\pi$
$338$	314.690	+	181.687i	0.931037	+	0.537534i
$339$	555.916	+	280.982i	1.63987	+	0.828854i
$340$	66.1634	+	114.598i	0.194598	+	0.337054i
$341$		−	45.8408i		−	0.134430i
$342$	519.220	−	108.864i	1.51819	−	0.318314i
$343$	23.8975			0.0696719
$344$	−70.4417	+	40.6695i	−0.204772	+	0.118225i
$345$	−385.281	+	21.4474i	−1.11676	+	0.0621662i
$346$	372.743	−	645.609i	1.07729	−	1.86592i
$347$			293.706i			0.846415i	0.906033	+	0.423207i	$0.139096\pi$
$347$			293.706i			0.846415i	−0.906033	+	0.423207i	$0.860904\pi$
$348$	5.80526	+	104.286i	0.0166818	+	0.299672i
$349$	60.3052	−	104.452i	0.172794	−	0.299289i	−0.766601	−	0.642123i	$-0.778054\pi$
$349$	60.3052	−	104.452i	0.172794	−	0.299289i	0.939396	+	0.342835i	$0.111387\pi$
$350$		−	4.91180i		−	0.0140337i
$351$	67.9160	−	182.217i	0.193493	−	0.519137i
$352$	37.9437	+	65.7205i	0.107795	+	0.186706i
$353$	302.080	+	174.406i	0.855750	+	0.494068i	0.862587	−	0.505909i	$-0.168843\pi$
$353$	302.080	+	174.406i	0.855750	+	0.494068i	−0.00683651	+	0.999977i	$0.502176\pi$
$354$	−95.0248	+	188.004i	−0.268432	+	0.531086i
$355$	−235.321	+	407.588i	−0.662876	+	1.14814i
$356$			245.710i			0.690198i
$357$	3.57212	+	1.80549i	0.0100059	+	0.00505739i
$358$	−177.995	−	308.296i	−0.497192	−	0.861161i
$359$	−277.550	−	160.244i	−0.773121	−	0.446362i	0.0608659	−	0.998146i	$-0.480614\pi$
$359$	−277.550	−	160.244i	−0.773121	−	0.446362i	−0.833987	+	0.551784i	$0.813947\pi$
$360$	78.2330	−	178.833i	0.217314	−	0.496758i
$361$	−354.441	+	68.5007i	−0.981832	+	0.189753i
$362$	−837.882	−	483.751i	−2.31459	−	1.33633i
$363$	−159.210	+	314.994i	−0.438595	+	0.867751i
$364$	−9.88490			−0.0271563
$365$	−41.2188	−	23.7977i	−0.112928	−	0.0651991i
$366$	−11.5404	−	5.83297i	−0.0315312	−	0.0159371i
$367$	29.7717			0.0811219			0.0405609	−	0.999177i	$-0.487086\pi$
$367$	29.7717			0.0811219			0.0405609	+	0.999177i	$0.487086\pi$
$368$			205.099i			0.557333i
$369$	−479.736	−	209.867i	−1.30010	−	0.568746i
$370$	−172.579	−	298.916i	−0.466430	−	0.807880i
$371$			15.5674i			0.0419606i
$372$	231.253	+	353.578i	0.621648	+	0.950478i
$373$	−6.86222	−	11.8857i	−0.0183974	−	0.0318652i	0.856680	−	0.515848i	$-0.172523\pi$
$373$	−6.86222	−	11.8857i	−0.0183974	−	0.0318652i	−0.875078	+	0.483983i	$0.839190\pi$
$374$	−26.8978	−	15.5294i	−0.0719192	−	0.0415226i
$375$	−340.147	+	222.468i	−0.907057	+	0.593249i
$376$	158.803			0.422347
$377$	−38.6072	−	22.2899i	−0.102406	−	0.0591243i
$378$	−3.39393	−	20.1548i	−0.00897865	−	0.0533196i
$379$	343.933			0.907476			0.453738	−	0.891135i	$-0.350090\pi$
$379$	343.933			0.907476			0.453738	+	0.891135i	$0.350090\pi$
$380$	−190.907	+	418.312i	−0.502388	+	1.10082i
$381$	−201.381	+	398.429i	−0.528560	+	1.04574i
$382$	135.031			0.353483
$383$			462.846i			1.20848i	0.796804	+	0.604238i	$0.206522\pi$
$383$			462.846i			1.20848i	−0.796804	+	0.604238i	$0.793478\pi$
$384$	−396.262	−	200.286i	−1.03193	−	0.521579i
$385$	−0.961058	−	1.66460i	−0.00249625	−	0.00432364i
$386$	145.087	−	83.7658i	0.375872	−	0.217010i
$387$	144.324	−	16.1181i	0.372931	−	0.0416488i
$388$	1026.22			2.64490
$389$			111.592i			0.286868i	0.989660	+	0.143434i	$0.0458145\pi$
$389$			111.592i			0.286868i	−0.989660	+	0.143434i	$0.954185\pi$
$390$	157.864	+	241.369i	0.404780	+	0.618894i
$391$	−81.7330	−	141.566i	−0.209036	−	0.362061i
$392$	213.653	−	123.353i	0.545033	−	0.314675i
$393$	−133.096	+	87.0496i	−0.338666	+	0.221500i
$394$	543.383	+	941.168i	1.37915	+	2.38875i
$395$	442.472	−	255.462i	1.12018	−	0.646738i
$396$	10.2874	+	92.1155i	0.0259783	+	0.232615i
$397$	−300.313	+	520.157i	−0.756455	+	1.31022i	0.188193	+	0.982132i	$0.439737\pi$
$397$	−300.313	+	520.157i	−0.756455	+	1.31022i	−0.944648	+	0.328086i	$0.893596\pi$
$398$	160.677	+	92.7669i	0.403711	+	0.233083i
$399$	2.09302	+	13.7496i	0.00524567	+	0.0344601i
$400$	22.2576	+	38.5512i	0.0556439	+	0.0963781i
$401$		−	464.842i		−	1.15921i	−0.814899	−	0.579603i	$-0.803208\pi$
$401$		−	464.842i		−	1.15921i	0.814899	−	0.579603i	$-0.196792\pi$
$402$	−141.309	+	92.4217i	−0.351516	+	0.229905i
$403$	−180.324			−0.447454
$404$	309.742	+	178.829i	0.766687	+	0.442647i
$405$	−255.934	+	236.539i	−0.631936	+	0.584047i
$406$	−4.68546			−0.0115405
$407$	41.0019	+	23.6724i	0.100742	+	0.0581633i
$408$	82.5615	−	4.59593i	0.202357	−	0.0112645i
$409$	157.989	−	273.645i	0.386281	−	0.669058i	−0.605665	−	0.795719i	$-0.707093\pi$
$409$	157.989	−	273.645i	0.386281	−	0.669058i	0.991946	+	0.126662i	$0.0404263\pi$
$410$	672.559	−	388.302i	1.64039	−	0.947079i
$411$	548.691	−	358.864i	1.33501	−	0.873149i
$412$	−382.733			−0.928963
$413$	−4.78270	−	2.76129i	−0.0115804	−	0.00668594i
$414$	−334.554	+	764.759i	−0.808102	+	1.84724i
$415$	−155.950	+	270.113i	−0.375783	+	0.650875i
$416$	258.524	−	149.259i	0.621453	−	0.358796i
$417$	121.536	−	6.76554i	0.291454	−	0.0162243i
$418$	−10.2863	−	107.434i	−0.0246085	−	0.257018i
$419$	−191.611	+	110.627i	−0.457306	+	0.264026i	−0.710911	−	0.703282i	$-0.751717\pi$
$419$	−191.611	+	110.627i	−0.457306	+	0.264026i	0.253605	+	0.967308i	$0.418384\pi$
$420$	15.8102	+	7.99110i	0.0376434	+	0.0190264i
$421$	127.617	+	221.039i	0.303128	+	0.525033i	0.976843	−	0.213959i	$-0.0686358\pi$
$421$	127.617	+	221.039i	0.303128	+	0.525033i	−0.673715	+	0.738991i	$0.735302\pi$
$422$	862.581	−	498.011i	2.04403	−	1.18012i
$423$	−259.756	−	113.634i	−0.614080	−	0.268638i
$424$	160.807	+	278.527i	0.379263	+	0.656902i
$425$	−30.7258	−	17.7395i	−0.0722959	−	0.0417401i
$426$	557.268	+	852.043i	1.30814	+	2.00010i
$427$	0.169498	−	0.293580i	0.000396952	−	0.000687540i
$428$	262.122	+	151.336i	0.612435	+	0.353590i
$429$	−35.3070	−	17.8456i	−0.0823008	−	0.0415980i
$430$	−107.690	+	186.524i	−0.250442	+	0.433778i
$431$	−515.063	+	297.372i	−1.19504	+	0.689957i	−0.959446	−	0.281894i	$-0.909037\pi$
$431$	−515.063	+	297.372i	−1.19504	+	0.689957i	−0.235595	+	0.971851i	$0.575704\pi$
$432$	117.968	+	142.809i	0.273075	+	0.330577i
$433$	−213.469	−	369.739i	−0.493000	−	0.853902i	0.506967	−	0.861965i	$-0.330767\pi$
$433$	−213.469	−	369.739i	−0.493000	−	0.853902i	−0.999967	+	0.00806366i	$0.997433\pi$
$434$	−16.4134	+	9.47628i	−0.0378189	+	0.0218347i
$435$	43.7301	+	66.8617i	0.100529	+	0.153705i
$436$	−7.04955	−	12.2102i	−0.0161687	−	0.0280050i
$437$	235.832	−	516.749i	0.539661	−	1.18249i
$438$	−86.1659	+	56.3557i	−0.196726	+	0.128666i
$439$	−133.387	−	231.033i	−0.303843	−	0.526272i	0.673160	−	0.739497i	$-0.264937\pi$
$439$	−133.387	−	231.033i	−0.303843	−	0.526272i	−0.977003	+	0.213225i	$0.931603\pi$
$440$	−34.3899	−	19.8550i	−0.0781589	−	0.0451250i
$441$	−437.743	+	48.8869i	−0.992614	+	0.110855i
$442$	−61.0881	+	105.808i	−0.138208	+	0.239384i
$443$		−	362.026i		−	0.817214i	−0.912710	−	0.408607i	$-0.866015\pi$
$443$		−	362.026i		−	0.817214i	0.912710	−	0.408607i	$-0.133985\pi$
$444$	−435.675	+	24.2526i	−0.981250	+	0.0546230i
$445$	93.9727	+	162.766i	0.211175	+	0.365765i
$446$	−972.780	−	561.635i	−2.18112	−	1.25927i
$447$	115.117	−	75.2905i	0.257531	−	0.168435i
$448$	12.3397	−	21.3729i	0.0275439	−	0.0477074i
$449$		−	482.220i		−	1.07399i	−0.843587	−	0.536993i	$-0.819560\pi$
$449$		−	482.220i		−	1.07399i	0.843587	−	0.536993i	$-0.180440\pi$
$450$	20.1083	+	180.054i	0.0446852	+	0.400119i
$451$	−53.2629	+	92.2541i	−0.118100	+	0.204554i
$452$			1167.89i			2.58383i
$453$	−539.055	+	30.0074i	−1.18997	+	0.0662416i
$454$	493.437			1.08687
$455$	−6.54804	+	3.78051i	−0.0143913	+	0.00830882i
$456$	179.478	+	224.383i	0.393592	+	0.492068i
$457$	−118.786	+	205.744i	−0.259926	+	0.450205i	−0.966222	−	0.257712i	$-0.917032\pi$
$457$	−118.786	+	205.744i	−0.259926	+	0.450205i	0.706296	+	0.707917i	$0.250365\pi$
$458$	687.802	+	397.103i	1.50175	+	0.867036i
$459$	−138.336	−	51.5606i	−0.301386	−	0.112333i
$460$	−361.751	−	626.570i	−0.786414	−	1.36211i
$461$	−126.969	+	73.3054i	−0.275420	+	0.159014i	−0.631348	−	0.775499i	$-0.717498\pi$
$461$	−126.969	+	73.3054i	−0.275420	+	0.159014i	0.355928	+	0.934513i	$0.384165\pi$
$462$	−4.15152	+	0.231102i	−0.00898597	+	0.000500220i
$463$	−252.501	−	437.345i	−0.545359	−	0.944590i	−0.998584	−	0.0531940i	$-0.983060\pi$
$463$	−252.501	−	437.345i	−0.545359	−	0.944590i	0.453225	−	0.891396i	$-0.350274\pi$
$464$	36.7747	−	21.2319i	0.0792559	−	0.0457584i
$465$	288.416	+	145.776i	0.620248	+	0.313498i
$466$	662.427			1.42152
$467$		−	793.589i		−	1.69934i	−0.527319	−	0.849668i	$-0.676803\pi$
$467$		−	793.589i		−	1.69934i	0.527319	−	0.849668i	$-0.323197\pi$
$468$	362.355	−	40.4676i	0.774262	−	0.0864693i
$469$	−2.21330	−	3.83355i	−0.00471920	−	0.00817389i
$470$	364.161	−	210.249i	0.774812	−	0.447338i
$471$	−236.073	−	360.947i	−0.501216	−	0.766342i
$472$	−114.094			−0.241725
$473$		−	29.5434i		−	0.0624596i
$474$	−61.4298	−	1103.53i	−0.129599	−	2.32812i
$475$	−11.7503	−	122.723i	−0.0247374	−	0.258364i
$476$			7.50444i			0.0157656i
$477$	−63.7310	−	570.659i	−0.133608	−	1.19635i
$478$	594.198	−	1029.18i	1.24309	−	2.15310i
$479$			774.322i			1.61654i	0.588812	+	0.808270i	$0.299596\pi$
$479$			774.322i			1.61654i	−0.588812	+	0.808270i	$0.700404\pi$
$480$	−534.155	+	29.7347i	−1.11282	+	0.0619473i
$481$	93.1202	−	161.289i	0.193597	−	0.335320i
$482$	426.398	−	246.181i	0.884642	−	0.510749i
$483$	−19.5307	−	9.87156i	−0.0404362	−	0.0204380i
$484$	−661.751			−1.36725
$485$	679.799	−	392.482i	1.40165	−	0.809241i
$486$	206.924	+	724.928i	0.425769	+	1.49162i
$487$	368.935			0.757567			0.378783	−	0.925485i	$-0.376343\pi$
$487$	368.935			0.757567			0.378783	+	0.925485i	$0.376343\pi$
$488$		−	7.00351i		−	0.0143515i
$489$	502.258	+	767.935i	1.02711	+	1.57042i
$490$	326.629	−	565.737i	0.666589	−	1.15457i
$491$			93.5098i			0.190448i	0.995456	+	0.0952238i	$0.0303567\pi$
$491$			93.5098i			0.190448i	−0.995456	+	0.0952238i	$0.969643\pi$
$492$	−54.5683	−	980.267i	−0.110911	−	1.99241i
$493$	−16.9221	+	29.3099i	−0.0343247	+	0.0594521i
$494$	−422.611	+	40.4634i	−0.855488	+	0.0819096i
$495$	42.0445	+	57.0855i	0.0849385	+	0.115324i
$496$	85.8825	−	148.753i	0.173150	−	0.299905i
$497$	−23.1149	+	13.3454i	−0.0465088	+	0.0268519i
$498$	369.308	+	564.658i	0.741582	+	1.13385i
$499$	−435.366			−0.872477			−0.436238	−	0.899831i	$-0.643690\pi$
$499$	−435.366			−0.872477			−0.436238	+	0.899831i	$0.643690\pi$
$500$	−659.956	−	381.025i	−1.31991	−	0.762051i
$501$	−11.5187	−	206.923i	−0.0229915	−	0.413020i
$502$	95.8248	−	165.973i	0.190886	−	0.330624i
$503$	44.8428	−	25.8900i	0.0891507	−	0.0514712i	−0.454762	−	0.890613i	$-0.650276\pi$
$503$	44.8428	−	25.8900i	0.0891507	−	0.0514712i	0.543913	+	0.839142i	$0.316942\pi$
$504$	8.91323	−	6.56477i	0.0176850	−	0.0130253i
$505$	273.576			0.541734
$506$	147.064	+	84.9077i	0.290641	+	0.167802i
$507$	158.505	−	313.599i	0.312633	−	0.618538i
$508$	−837.034			−1.64771
$509$	374.724	+	216.347i	0.736197	+	0.425043i	0.820685	−	0.571381i	$-0.193592\pi$
$509$	374.724	+	216.347i	0.736197	+	0.425043i	−0.0844880	+	0.996424i	$0.526925\pi$
$510$	183.243	−	119.848i	0.359300	−	0.234995i
$511$	−1.34960	−	2.33758i	−0.00264110	−	0.00457451i
$512$			422.682i			0.825550i
$513$	−133.014	−	495.456i	−0.259286	−	0.965800i
$514$	−1248.71			−2.42939
$515$	−253.533	+	146.377i	−0.492297	+	0.284228i
$516$	149.037	+	227.873i	0.288832	+	0.441614i
$517$	−28.8395	+	49.9515i	−0.0557825	+	0.0966181i
$518$		−	19.5744i		−	0.0377884i
$519$	−643.370	−	325.184i	−1.23963	−	0.626559i
$520$	−78.1036	+	135.279i	−0.150199	+	0.260153i
$521$		−	156.298i		−	0.299996i	−0.988686	−	0.149998i	$-0.952073\pi$
$521$		−	156.298i		−	0.299996i	0.988686	−	0.149998i	$-0.0479267\pi$
$522$	171.757	−	19.1817i	0.329036	−	0.0367466i
$523$	−96.3542	−	166.890i	−0.184234	−	0.319102i	0.759084	−	0.650992i	$-0.225647\pi$
$523$	−96.3542	−	166.890i	−0.184234	−	0.319102i	−0.943318	+	0.331890i	$0.892314\pi$
$524$	−258.234	−	149.091i	−0.492812	−	0.284525i
$525$	−4.74234	+	0.263991i	−0.00903304	+	0.000502840i
$526$	−7.60449	+	13.1714i	−0.0144572	+	0.0250406i
$527$			136.899i			0.259770i
$528$	31.5368	−	20.6262i	0.0597287	−	0.0390648i
$529$	182.378	+	315.887i	0.344759	+	0.597140i
$530$	737.518	+	425.806i	1.39154	+	0.803408i
$531$	186.626	+	81.6419i	0.351461	+	0.153751i
$532$	−21.2377	+	15.1314i	−0.0399204	+	0.0284426i
$533$	362.900	+	209.520i	0.680862	+	0.393096i
$534$	405.937	−	22.5972i	0.760182	−	0.0423169i
$535$	231.516			0.432741
$536$	−79.1995	−	45.7258i	−0.147760	−	0.0853094i
$537$	−288.093	+	188.424i	−0.536486	+	0.350882i
$538$	−608.479			−1.13100
$539$			89.6064i			0.166246i
$540$	−612.276	−	228.208i	−1.13384	−	0.422607i
$541$	298.072	+	516.277i	0.550966	+	0.954301i	0.998205	+	0.0598864i	$0.0190738\pi$
$541$	298.072	+	516.277i	0.550966	+	0.954301i	−0.447239	+	0.894414i	$0.647593\pi$
$542$			876.344i			1.61687i
$543$	−422.029	+	834.975i	−0.777218	+	1.53771i
$544$	−113.315	−	196.267i	−0.208299	−	0.360785i
$545$	−9.33964	−	5.39224i	−0.0171370	−	0.00989403i
$546$	0.909083	+	16.3308i	0.00166499	+	0.0299099i
$547$	−899.237			−1.64394			−0.821971	−	0.569529i	$-0.807126\pi$
$547$	−899.237			−1.64394			−0.821971	+	0.569529i	$0.807126\pi$
$548$	1064.57	+	614.633i	1.94265	+	1.12159i
$549$	−5.01148	+	11.4558i	−0.00912838	+	0.0208666i
$550$	36.8572			0.0670131
$551$	−117.068	+	11.2088i	−0.212464	+	0.0203426i
$552$	−451.408	+	25.1284i	−0.817768	+	0.0455225i
$553$	28.9752			0.0523963
$554$			146.738i			0.264870i
$555$	−279.328	+	182.691i	−0.503293	+	0.329173i
$556$	114.114	+	197.651i	0.205240	+	0.355487i
$557$	−317.565	+	183.346i	−0.570134	+	0.329167i	−0.757203	−	0.653180i	$-0.773435\pi$
$557$	−317.565	+	183.346i	−0.570134	+	0.329167i	0.187069	+	0.982347i	$0.440101\pi$
$558$	562.877	−	414.570i	1.00874	−	0.742957i
$559$	−116.215			−0.207897
$560$		−	7.20215i		−	0.0128610i
$561$	−13.5480	+	26.8045i	−0.0241498	+	0.0477798i
$562$	−778.379	−	1348.19i	−1.38502	−	2.39892i
$563$	−684.854	+	395.400i	−1.21644	+	0.702310i	−0.964154	−	0.265344i	$-0.914515\pi$
$563$	−684.854	+	395.400i	−1.21644	+	0.702310i	−0.252282	+	0.967654i	$0.581181\pi$
$564$	−29.5463	−	530.772i	−0.0523871	−	0.941084i
$565$	446.663	+	773.643i	0.790554	+	1.36928i
$566$	−941.484	+	543.566i	−1.66340	+	0.960364i
$567$	−19.2771	+	4.36009i	−0.0339983	+	0.00768975i
$568$	−275.710	+	477.543i	−0.485404	+	0.840745i
$569$	686.573	+	396.393i	1.20663	+	0.696648i	0.962022	−	0.272974i	$-0.0880072\pi$
$569$	686.573	+	396.393i	1.20663	+	0.696648i	0.244609	+	0.969622i	$0.421341\pi$
$570$	708.648	+	276.927i	1.24324	+	0.485836i
$571$	284.891	+	493.446i	0.498934	+	0.864179i	0.999999	−	0.00123074i	$-0.000391755\pi$
$571$	284.891	+	493.446i	0.498934	+	0.864179i	−0.501065	+	0.865409i	$0.667058\pi$
$572$		−	74.1744i		−	0.129675i
$573$	−7.25739	−	130.372i	−0.0126656	−	0.227526i
$574$	44.0423			0.0767288
$575$	167.994	+	96.9915i	0.292164	+	0.168681i
$576$	−364.841	+	833.992i	−0.633405	+	1.44790i
$577$	678.670			1.17620			0.588102	−	0.808786i	$-0.299875\pi$
$577$	678.670			1.17620			0.588102	+	0.808786i	$0.299875\pi$
$578$	−696.144	−	401.919i	−1.20440	−	0.695361i
$579$	−88.6737	−	135.579i	−0.153150	−	0.234161i
$580$	−74.8972	+	129.726i	−0.129133	+	0.223665i
$581$	−15.3185	+	8.84414i	−0.0263657	+	0.0152223i
$582$	−94.3785	−	1695.42i	−0.162162	−	2.91309i
$583$	−116.815			−0.200368
$584$	−48.2933	−	27.8821i	−0.0826939	−	0.0477434i
$585$	224.557	−	165.391i	0.383858	−	0.282719i
$586$	−774.516	+	1341.50i	−1.32170	+	2.28925i
$587$	−420.730	+	242.908i	−0.716746	+	0.413813i	−0.813554	−	0.581490i	$-0.802470\pi$
$587$	−420.730	+	242.908i	−0.716746	+	0.413813i	0.0968079	+	0.995303i	$0.469137\pi$
$588$	−452.037	−	691.149i	−0.768771	−	1.17542i
$589$	−387.425	+	276.033i	−0.657767	+	0.468647i
$590$	−261.637	+	151.056i	−0.443453	+	0.256028i
$591$	879.493	−	575.221i	1.48814	−	0.973301i
$592$	88.7004	+	153.634i	0.149832	+	0.259516i
$593$	54.2566	−	31.3251i	0.0914951	−	0.0528247i	−0.453554	−	0.891229i	$-0.649844\pi$
$593$	54.2566	−	31.3251i	0.0914951	−	0.0528247i	0.545049	+	0.838404i	$0.316511\pi$
$594$	151.238	−	25.4674i	0.254609	−	0.0428744i
$595$	2.87010	+	4.97115i	0.00482369	+	0.00835488i
$596$	223.350	+	128.951i	0.374749	+	0.216361i
$597$	80.9307	−	160.120i	0.135562	−	0.268207i
$598$	334.001	−	578.507i	0.558531	−	0.967403i
$599$	733.678	+	423.589i	1.22484	+	0.707160i	0.965945	−	0.258746i	$-0.0833092\pi$
$599$	733.678	+	423.589i	1.22484	+	0.707160i	0.258892	+	0.965906i	$0.416643\pi$
$600$	−82.1216	+	53.7106i	−0.136869	+	0.0895176i
$601$	−178.361	+	308.930i	−0.296774	+	0.514027i	−0.975396	−	0.220461i	$-0.929244\pi$
$601$	−178.361	+	308.930i	−0.296774	+	0.514027i	0.678622	+	0.734487i	$0.262577\pi$
$602$	−10.5781	+	6.10725i	−0.0175715	+	0.0101449i
$603$	96.8280	+	131.467i	0.160577	+	0.218022i
$604$	−506.133	−	876.648i	−0.837968	−	1.45140i
$605$	−438.362	+	253.089i	−0.724566	+	0.418328i
$606$	266.958	−	528.170i	0.440524	−	0.871567i
$607$	357.464	+	619.147i	0.588904	+	1.02001i	0.994376	+	0.105904i	$0.0337736\pi$
$607$	357.464	+	619.147i	0.588904	+	1.02001i	−0.405473	+	0.914107i	$0.632893\pi$
$608$	326.958	−	716.422i	0.537760	−	1.17833i
$609$	0.251826	+	4.52381i	0.000413507	+	0.00742826i
$610$	−9.27239	−	16.0603i	−0.0152006	−	0.0263283i
$611$	196.494	+	113.446i	0.321594	+	0.185673i
$612$	−30.7223	−	275.093i	−0.0501998	−	0.449499i
$613$	−0.225456	+	0.390501i	−0.000367791	+	0.000637032i	−0.866209	−	0.499681i	$-0.833450\pi$
$613$	−0.225456	+	0.390501i	−0.000367791	+	0.000637032i	0.865841	+	0.500318i	$0.166784\pi$
$614$		−	1781.53i		−	2.90151i
$615$	−411.054	−	628.487i	−0.668380	−	1.02193i
$616$	−1.12601	−	1.95030i	−0.00182793	−	0.00316607i
$617$	−775.122	−	447.517i	−1.25628	−	0.725311i	−0.283927	−	0.958846i	$-0.591637\pi$
$617$	−775.122	−	447.517i	−1.25628	−	0.725311i	−0.972348	+	0.233535i	$0.924971\pi$
$618$	35.1987	+	632.312i	0.0569559	+	1.02316i
$619$	93.6789	−	162.257i	0.151339	−	0.262127i	−0.780381	−	0.625304i	$-0.784975\pi$
$619$	93.6789	−	162.257i	0.151339	−	0.262127i	0.931720	+	0.363177i	$0.118308\pi$
$620$			605.914i			0.977281i
$621$	756.356	+	281.909i	1.21796	+	0.453960i
$622$	−85.6499	+	148.350i	−0.137701	+	0.238505i
$623$			10.6587i			0.0171086i
$624$	−81.1373	−	124.056i	−0.130028	−	0.198808i
$625$	−420.681			−0.673090
$626$	−470.270	+	271.511i	−0.751231	+	0.433723i
$627$	−103.174	+	15.7056i	−0.164552	+	0.0250488i
$628$	404.326	−	700.313i	0.643831	−	1.11515i
$629$	−122.448	−	70.6952i	−0.194670	−	0.112393i
$630$	11.7481	−	26.8549i	0.0186477	−	0.0426269i
$631$	63.5948	+	110.149i	0.100784	+	0.174563i	0.912008	−	0.410173i	$-0.134532\pi$
$631$	63.5948	+	110.149i	0.100784	+	0.174563i	−0.811224	+	0.584736i	$0.801198\pi$
$632$	518.415	−	299.307i	0.820277	−	0.473587i
$633$	−527.191	−	806.056i	−0.832845	−	1.27339i
$634$	−32.6537	−	56.5579i	−0.0515043	−	0.0892080i
$635$	−554.475	+	320.126i	−0.873189	+	0.504136i
$636$	901.010	−	589.294i	1.41668	−	0.926563i
$637$	352.484			0.553351
$638$		−	35.1588i		−	0.0551078i
$639$	792.697	−	583.837i	1.24053	−	0.913672i
$640$	−318.386	−	551.460i	−0.497477	−	0.861656i
$641$	326.311	−	188.396i	0.509065	−	0.293909i	−0.223384	−	0.974730i	$-0.571710\pi$
$641$	326.311	−	188.396i	0.509065	−	0.293909i	0.732449	+	0.680822i	$0.238377\pi$
$642$	225.916	−	446.969i	0.351894	−	0.696214i
$643$	506.354			0.787486			0.393743	−	0.919220i	$-0.371180\pi$
$643$	506.354			0.787486			0.393743	+	0.919220i	$0.371180\pi$
$644$		−	41.0308i		−	0.0637124i
$645$	185.877	+	93.9497i	0.288182	+	0.145658i
$646$	30.7191	+	320.839i	0.0475527	+	0.496655i
$647$			497.371i			0.768734i	0.923180	+	0.384367i	$0.125580\pi$
$647$			497.371i			0.768734i	−0.923180	+	0.384367i	$0.874420\pi$
$648$	−299.860	+	277.137i	−0.462747	+	0.427680i
$649$	20.7202	−	35.8884i	0.0319263	−	0.0552980i
$650$		−	144.985i		−	0.223054i
$651$	10.0315	+	15.3378i	0.0154094	+	0.0235604i
$652$	−860.226	+	1489.96i	−1.31937	+	2.28521i
$653$	1112.53	−	642.317i	1.70371	−	0.983640i	0.761785	−	0.647830i	$-0.224323\pi$
$653$	1112.53	−	642.317i	1.70371	−	0.983640i	0.941930	−	0.335811i	$-0.109010\pi$
$654$	−19.5241	+	12.7695i	−0.0298533	+	0.0195252i
$655$	−228.082			−0.348216
$656$	−345.675	+	199.576i	−0.526944	+	0.304231i
$657$	59.0426	+	80.1643i	0.0898669	+	0.122016i
$658$	23.8470			0.0362416
$659$		−	720.460i		−	1.09326i	−0.837374	−	0.546631i	$-0.815910\pi$
$659$		−	720.460i		−	1.09326i	0.837374	−	0.546631i	$-0.184090\pi$
$660$	−59.9637	+	118.637i	−0.0908540	+	0.179753i
$661$	−76.4214	+	132.366i	−0.115615	+	0.200251i	−0.918025	−	0.396522i	$-0.870217\pi$
$661$	−76.4214	+	132.366i	−0.115615	+	0.200251i	0.802411	+	0.596772i	$0.203550\pi$
$662$		−	1358.74i		−	2.05248i
$663$	105.441	+	53.2938i	0.159036	+	0.0803829i
$664$	−182.716	+	316.473i	−0.275174	+	0.476616i
$665$	−8.28136	+	18.1459i	−0.0124532	+	0.0272871i
$666$	80.1353	+	717.547i	0.120323	+	1.07740i
$667$	92.5220	−	160.253i	0.138714	−	0.240259i
$668$	336.512	−	194.285i	0.503761	−	0.290846i
$669$	−489.975	+	969.405i	−0.732400	+	1.44904i
$670$	−242.157			−0.361429
$671$	2.20296	+	1.27188i	0.00328311	+	0.00189550i
$672$	−27.0774	−	13.6860i	−0.0402937	−	0.0203660i
$673$	−134.985	+	233.801i	−0.200572	+	0.347402i	−0.948713	−	0.316139i	$-0.897614\pi$
$673$	−134.985	+	233.801i	−0.200572	+	0.347402i	0.748141	+	0.663540i	$0.230947\pi$
$674$	−1578.44	+	911.310i	−2.34189	+	1.35209i
$675$	172.761	−	29.0918i	0.255942	−	0.0430990i
$676$	658.820			0.974586
$677$	212.209	+	122.519i	0.313455	+	0.180973i	0.648471	−	0.761239i	$-0.275409\pi$
$677$	212.209	+	122.519i	0.313455	+	0.180973i	−0.335017	+	0.942212i	$0.608742\pi$
$678$	1929.47	−	107.407i	2.84582	−	0.158418i
$679$	44.5164			0.0655618
$680$	102.702	+	59.2949i	0.151032	+	0.0871984i
$681$	−26.5204	−	476.414i	−0.0389433	−	0.699580i
$682$	−71.1081	−	123.163i	−0.104264	−	0.180591i
$683$			298.653i			0.437266i	0.975807	+	0.218633i	$0.0701597\pi$
$683$			298.653i			0.437266i	−0.975807	+	0.218633i	$0.929840\pi$
$684$	716.571	−	641.624i	1.04762	−	0.938046i
$685$	940.272			1.37266
$686$	64.2065	−	37.0697i	0.0935955	−	0.0540374i
$687$	346.436	−	685.416i	0.504273	−	0.997694i
$688$	55.3493	−	95.8679i	0.0804496	−	0.139343i
$689$			459.513i			0.666927i
$690$	−1001.89	+	655.271i	−1.45201	+	0.949668i
$691$	−385.934	+	668.458i	−0.558516	+	0.967378i	0.439105	+	0.898436i	$0.355296\pi$
$691$	−385.934	+	668.458i	−0.558516	+	0.967378i	−0.997621	+	0.0689420i	$0.978038\pi$
$692$		−	1351.62i		−	1.95320i
$693$	0.446257	+	3.99587i	0.000643950	+	0.00576605i
$694$	455.596	+	789.115i	0.656478	+	1.13705i
$695$	151.184	+	87.2863i	0.217531	+	0.125592i
$696$	51.2355	+	78.3373i	0.0736143	+	0.112554i
$697$	159.064	−	275.507i	0.228212	−	0.395275i
$698$		−	374.181i		−	0.536076i
$699$	−35.6030	−	639.574i	−0.0509342	−	0.914984i
$700$	−4.45271	−	7.71232i	−0.00636102	−	0.0110176i
$701$	−343.160	−	198.123i	−0.489529	−	0.282630i	0.234850	−	0.972032i	$-0.424540\pi$
$701$	−343.160	−	198.123i	−0.489529	−	0.282630i	−0.724379	+	0.689402i	$0.757873\pi$
$702$	−100.181	−	594.923i	−0.142708	−	0.847469i
$703$	−46.8269	−	489.074i	−0.0666101	−	0.695695i
$704$	160.378	+	92.5944i	0.227810	+	0.131526i
$705$	−222.568	−	340.298i	−0.315699	−	0.482692i
$706$	1082.15			1.53279
$707$	13.4363	+	7.75743i	0.0190046	+	0.0109723i
$708$	21.2280	+	381.341i	0.0299831	+	0.538617i
$709$	1338.26			1.88753			0.943767	−	0.330610i	$-0.107254\pi$
$709$	1338.26			1.88753			0.943767	+	0.330610i	$0.107254\pi$
$710$			1460.12i			2.05650i
$711$	−1062.15	+	118.621i	−1.49389	+	0.166837i
$712$	110.101	+	190.701i	0.154637	+	0.267839i
$713$		−	748.498i		−	1.04979i
$714$	12.3981	−	0.690160i	0.0173642	−	0.000966611i
$715$	−28.3682	−	49.1352i	−0.0396758	−	0.0687205i
$716$	−558.961	−	322.716i	−0.780672	−	0.450721i
$717$	−1025.61	−	518.384i	−1.43042	−	0.722990i
$718$	−994.279			−1.38479
$719$	552.103	+	318.757i	0.767876	+	0.443333i	0.832116	−	0.554601i	$-0.187129\pi$
$719$	552.103	+	318.757i	0.767876	+	0.443333i	−0.0642405	+	0.997934i	$0.520462\pi$
$720$	29.4847	+	264.012i	0.0409510	+	0.366683i
$721$	−16.6025			−0.0230271
$722$	−846.038	+	733.853i	−1.17180	+	1.01642i
$723$	−260.605	−	398.456i	−0.360449	−	0.551114i
$724$	−1754.15			−2.42286
$725$		−	40.1624i		−	0.0553964i
$726$	60.8591	+	1093.28i	0.0838280	+	1.50589i
$727$	−263.615	−	456.594i	−0.362606	−	0.628052i	0.625783	−	0.779997i	$-0.284780\pi$
$727$	−263.615	−	456.594i	−0.362606	−	0.628052i	−0.988389	+	0.151945i	$0.951446\pi$
$728$	−7.67189	+	4.42937i	−0.0105383	+	0.00608430i
$729$	688.797	−	238.747i	0.944851	−	0.327500i
$730$	−147.660			−0.202273
$731$			88.2281i			0.120695i
$732$	−23.4081	+	1.30305i	−0.0319783	+	0.00178013i
$733$	−40.8186	−	70.6999i	−0.0556870	−	0.0964528i	0.836838	−	0.547451i	$-0.184402\pi$
$733$	−40.8186	−	70.6999i	−0.0556870	−	0.0964528i	−0.892525	+	0.450998i	$0.851068\pi$
$734$	79.9893	−	46.1818i	0.108977	−	0.0629180i
$735$	−563.775	−	284.954i	−0.767040	−	0.387692i
$736$	619.553	+	1073.10i	0.841784	+	1.45801i
$737$	28.7662	−	16.6082i	0.0390315	−	0.0225349i
$738$	−1614.48	+	180.304i	−2.18764	+	0.244315i
$739$	−261.428	+	452.807i	−0.353759	+	0.612729i	−0.986905	−	0.161304i	$-0.948430\pi$
$739$	−261.428	+	452.807i	−0.353759	+	0.612729i	0.633145	+	0.774033i	$0.281764\pi$
$740$	−541.954	−	312.898i	−0.732371	−	0.422835i
$741$	61.7812	+	405.856i	0.0833754	+	0.547714i
$742$	24.1481	+	41.8257i	0.0325446	+	0.0563688i
$743$			543.024i			0.730854i	0.930840	+	0.365427i	$0.119077\pi$
$743$			543.024i			0.730854i	−0.930840	+	0.365427i	$0.880923\pi$
$744$	337.917	+	170.796i	0.454189	+	0.229565i
$745$	197.271			0.264794
$746$	−36.8742	−	21.2893i	−0.0494292	−	0.0285380i
$747$	525.329	−	386.915i	0.703252	−	0.517958i
$748$	−56.3119			−0.0752832
$749$	11.3706	+	6.56481i	0.0151810	+	0.00876476i
$750$	−568.797	+	1125.35i	−0.758396	+	1.50047i
$751$	−42.7039	+	73.9653i	−0.0568627	+	0.0984891i	−0.893056	−	0.449946i	$-0.851443\pi$
$751$	−42.7039	+	73.9653i	−0.0568627	+	0.0984891i	0.836193	+	0.548436i	$0.184776\pi$
$752$	−187.168	+	108.061i	−0.248893	+	0.143699i
$753$	−165.398	−	83.5984i	−0.219652	−	0.111021i
$754$	−138.304			−0.183427
$755$	−670.553	−	387.144i	−0.888150	−	0.512774i
$756$	−23.6000	−	28.5696i	−0.0312170	−	0.0377905i
$757$	−471.884	+	817.326i	−0.623360	+	1.07969i	0.365496	+	0.930813i	$0.380900\pi$
$757$	−471.884	+	817.326i	−0.623360	+	1.07969i	−0.988856	+	0.148878i	$0.952434\pi$
$758$	924.063	−	533.508i	1.21908	−	0.703837i
$759$	74.0743	−	146.554i	0.0975946	−	0.193089i
$760$	39.2756	+	410.205i	0.0516784	+	0.539744i
$761$	−36.1731	+	20.8846i	−0.0475337	+	0.0274436i	−0.523579	−	0.851977i	$-0.675403\pi$
$761$	−36.1731	+	20.8846i	−0.0475337	+	0.0274436i	0.476045	+	0.879421i	$0.342070\pi$
$762$	76.9794	+	1382.86i	0.101023	+	1.81478i
$763$	−0.305802	−	0.529664i	−0.000400789	−	0.000694186i
$764$	212.020	−	122.410i	0.277513	−	0.160222i
$765$	−125.562	−	170.480i	−0.164133	−	0.222849i
$766$	717.966	+	1243.55i	0.937292	+	1.62344i
$767$	−141.174	−	81.5070i	−0.184060	−	0.106267i
$768$	−163.480	+	9.10041i	−0.212865	+	0.0118495i
$769$	420.985	−	729.167i	0.547444	−	0.948201i	−0.451005	−	0.892522i	$-0.648934\pi$
$769$	420.985	−	729.167i	0.547444	−	0.948201i	0.998449	−	0.0556795i	$-0.0177325\pi$
$770$	−5.16425	−	2.98158i	−0.00670682	−	0.00387218i
$771$	67.1133	+	1205.63i	0.0870471	+	1.56372i
$772$	151.873	−	263.052i	0.196727	−	0.340741i
$773$	733.888	−	423.711i	0.949403	−	0.548138i	0.0565075	−	0.998402i	$-0.482004\pi$
$773$	733.888	−	423.711i	0.949403	−	0.548138i	0.892895	+	0.450264i	$0.148670\pi$
$774$	362.762	−	267.181i	0.468684	−	0.345195i
$775$	−81.2279	−	140.691i	−0.104810	−	0.181537i
$776$	796.474	−	459.845i	1.02638	−	0.592583i
$777$	−18.8991	+	1.05205i	−0.0243232	+	0.00135399i
$778$	173.101	+	299.819i	0.222495	+	0.385372i
$779$	1100.41	−	105.360i	1.41260	−	0.135251i
$780$	466.681	+	235.879i	0.598309	+	0.302409i
$781$	−100.141	−	173.450i	−0.128222	−	0.222087i
$782$	−439.192	−	253.568i	−0.561627	−	0.324256i
$783$	−27.7512	−	164.800i	−0.0354422	−	0.210473i
$784$	−167.877	+	290.772i	−0.214129	+	0.370882i
$785$		−	618.543i		−	0.787952i
$786$	−222.564	+	440.338i	−0.283161	+	0.560227i
$787$	352.339	+	610.268i	0.447698	+	0.775436i	0.998236	−	0.0593743i	$-0.0189106\pi$
$787$	352.339	+	610.268i	0.447698	+	0.775436i	−0.550538	+	0.834810i	$0.685577\pi$
$788$	1706.40	+	985.191i	2.16548	+	1.25024i
$789$	13.1257	+	6.63423i	0.0166358	+	0.00840840i
$790$	792.543	−	1372.72i	1.00322	−	1.73763i
$791$			50.6618i			0.0640477i
$792$	49.2607	+	66.8831i	0.0621979	+	0.0844484i
$793$	5.00320	−	8.66579i	0.00630920	−	0.0109279i
$794$			1863.38i			2.34682i
$795$	371.477	−	734.959i	0.467267	−	0.924477i
$796$	336.385			0.422595
$797$	423.299	−	244.392i	0.531115	−	0.306639i	−0.210355	−	0.977625i	$-0.567462\pi$
$797$	423.299	−	244.392i	0.531115	−	0.306639i	0.741470	+	0.670986i	$0.234129\pi$
$798$	26.9518	+	33.6951i	0.0337741	+	0.0422244i
$799$	86.1262	−	149.175i	0.107792	−	0.186702i
$800$	232.908	+	134.469i	0.291135	+	0.168087i
$801$	−43.6352	−	390.718i	−0.0544760	−	0.487788i
$802$	−721.061	−	1248.91i	−0.899079	−	1.55725i
$803$	17.5407	−	10.1271i	0.0218440	−	0.0126116i
$804$	−138.095	+	273.219i	−0.171761	+	0.339824i
$805$	−15.6923	−	27.1799i	−0.0194936	−	0.0337639i
$806$	−484.485	+	279.718i	−0.601099	+	0.347044i
$807$	32.7035	+	587.486i	0.0405247	+	0.727988i
$808$	320.530			0.396695
$809$		−	515.502i		−	0.637209i	−0.947888	−	0.318604i	$-0.896786\pi$
$809$		−	515.502i		−	0.637209i	0.947888	−	0.318604i	$-0.103214\pi$
$810$	−320.712	+	1032.53i	−0.395941	+	1.27472i
$811$	−173.236	−	300.054i	−0.213608	−	0.369980i	0.739233	−	0.673450i	$-0.235188\pi$
$811$	−173.236	−	300.054i	−0.213608	−	0.369980i	−0.952841	+	0.303470i	$0.901855\pi$
$812$	−7.35693	+	4.24753i	−0.00906026	+	0.00523094i
$813$	846.111	−	47.1002i	1.04073	−	0.0579339i
$814$	146.883			0.180445
$815$			1315.98i			1.61470i
$816$	−94.1812	+	61.5980i	−0.115418	+	0.0754878i
$817$	−249.687	+	177.897i	−0.305614	+	0.217744i
$818$		−	980.287i		−	1.19839i
$819$	15.7185	−	1.75544i	0.0191924	−	0.00214340i
$820$	704.018	−	1219.40i	0.858559	−	1.48707i
$821$			828.656i			1.00933i	0.863317	+	0.504663i	$0.168383\pi$
$821$			828.656i			1.00933i	−0.863317	+	0.504663i	$0.831617\pi$
$822$	917.527	−	1815.31i	1.11621	−	2.20840i
$823$	630.309	−	1091.73i	0.765868	−	1.32652i	−0.173919	−	0.984760i	$-0.555643\pi$
$823$	630.309	−	1091.73i	0.765868	−	1.32652i	0.939787	−	0.341762i	$-0.111024\pi$
$824$	−297.047	+	171.500i	−0.360494	+	0.208132i
$825$	−1.98094	−	35.5856i	−0.00240113	−	0.0431341i
$826$	−17.1332			−0.0207424
$827$	637.979	−	368.337i	0.771438	−	0.445390i	−0.0619494	−	0.998079i	$-0.519732\pi$
$827$	637.979	−	368.337i	0.771438	−	0.445390i	0.833387	+	0.552689i	$0.186398\pi$
$828$	167.975	+	1504.08i	0.202869	+	1.81652i
$829$	−230.711			−0.278301			−0.139150	−	0.990271i	$-0.544437\pi$
$829$	−230.711			−0.278301			−0.139150	+	0.990271i	$0.544437\pi$
$830$			967.636i			1.16583i
$831$	141.675	−	7.88661i	0.170488	−	0.00949051i
$832$	364.238	−	630.879i	0.437786	−	0.758268i
$833$		−	267.600i		−	0.321248i
$834$	316.043	−	206.704i	0.378949	−	0.247847i
$835$	148.610	−	257.400i	0.177976	−	0.308264i
$836$	−113.543	−	159.363i	−0.135817	−	0.190626i
$837$	−430.520	−	521.177i	−0.514361	−	0.622672i
$838$	−343.208	+	594.454i	−0.409556	+	0.709372i
$839$	−893.964	+	516.130i	−1.06551	+	0.615173i	−0.926952	−	0.375181i	$-0.877581\pi$
$839$	−893.964	+	516.130i	−1.06551	+	0.615173i	−0.138560	+	0.990354i	$0.544247\pi$
$840$	15.8514	−	0.882397i	0.0188707	−	0.00105047i
$841$	802.688			0.954445
$842$	685.749	+	395.917i	0.814429	+	0.470211i
$843$	−1259.84	+	823.985i	−1.49448	+	0.977444i
$844$	902.928	−	1563.92i	1.06982	−	1.85298i
$845$	436.421	−	251.968i	0.516475	−	0.298187i
$846$	−874.169	+	97.6268i	−1.03330	+	0.115398i
$847$	−28.7060			−0.0338914
$848$	−379.062	−	218.851i	−0.447007	−	0.258079i
$849$	575.414	+	879.788i	0.677755	+	1.03626i
$850$	−110.070			−0.129494
$851$	669.487	+	386.528i	0.786706	+	0.454205i
$852$	1647.41	+	832.664i	1.93358	+	0.977305i
$853$	−592.173	−	1025.67i	−0.694224	−	1.20243i	−0.970442	−	0.241336i	$-0.922414\pi$
$853$	−592.173	−	1025.67i	−0.694224	−	1.20243i	0.276217	−	0.961095i	$-0.410919\pi$
$854$		−	1.05170i		−	0.00123150i
$855$	229.286	−	699.084i	0.268170	−	0.817642i
$856$	271.252			0.316883
$857$	−1184.65	+	683.958i	−1.38232	+	0.798084i	−0.992434	−	0.122778i	$-0.960820\pi$
$857$	−1184.65	+	683.958i	−1.38232	+	0.798084i	−0.389888	+	0.920862i	$0.627486\pi$
$858$	−122.543	+	6.82158i	−0.142824	+	0.00795056i
$859$	−679.709	+	1177.29i	−0.791279	+	1.37054i	0.133896	+	0.990995i	$0.457251\pi$
$859$	−679.709	+	1177.29i	−0.791279	+	1.37054i	−0.925175	+	0.379541i	$0.876082\pi$
$860$			390.498i			0.454068i
$861$	−2.36711	−	42.5229i	−0.00274926	−	0.0493878i
$862$	−922.564	+	1597.93i	−1.07026	+	1.85374i
$863$		−	493.046i		−	0.571317i	−0.958332	−	0.285658i	$-0.907788\pi$
$863$		−	493.046i		−	0.571317i	0.958332	−	0.285658i	$-0.0922122\pi$
$864$	1048.61	+	390.840i	1.21367	+	0.452361i
$865$	−516.930	−	895.348i	−0.597606	−	1.03508i
$866$	−1147.08	−	662.266i	−1.32457	−	0.764741i
$867$	−350.638	+	693.729i	−0.404426	+	0.800149i
$868$	−17.1811	+	29.7586i	−0.0197939	+	0.0342841i
$869$			217.424i			0.250200i
$870$	221.208	+	111.807i	0.254262	+	0.128514i
$871$	−65.3316	−	113.158i	−0.0750076	−	0.129917i
$872$	−10.9426	−	6.31773i	−0.0125489	−	0.00724510i
$873$	−1631.86	+	182.245i	−1.86925	+	0.208757i
$874$	−167.957	−	1754.20i	−0.192171	−	2.00709i
$875$	−28.6281	−	16.5285i	−0.0327179	−	0.0188897i
$876$	−84.2061	+	166.600i	−0.0961257	+	0.190183i
$877$	1337.86			1.52550			0.762748	−	0.646696i	$-0.223850\pi$
$877$	1337.86			1.52550			0.762748	+	0.646696i	$0.223850\pi$
$878$	−716.756	−	413.819i	−0.816351	−	0.471320i
$879$	1336.85	+	675.694i	1.52087	+	0.768708i
$880$	54.0435			0.0614131
$881$		−	789.581i		−	0.896233i	−0.893975	−	0.448116i	$-0.852095\pi$
$881$		−	789.581i		−	0.896233i	0.893975	−	0.448116i	$-0.147905\pi$
$882$	−1100.27	+	810.372i	−1.24748	+	0.918790i
$883$	406.118	+	703.417i	0.459930	+	0.796622i	0.998957	−	0.0456667i	$-0.0145412\pi$
$883$	406.118	+	703.417i	0.459930	+	0.796622i	−0.539027	+	0.842289i	$0.681208\pi$
$884$			221.514i			0.250581i
$885$	159.907	+	244.492i	0.180686	+	0.276262i
$886$	−561.574	−	972.674i	−0.633830	−	1.09783i
$887$	−147.041	−	84.8941i	−0.165773	−	0.0957093i	0.414818	−	0.909904i	$-0.363845\pi$
$887$	−147.041	−	84.8941i	−0.165773	−	0.0957093i	−0.580591	+	0.814195i	$0.697179\pi$
$888$	−327.269	+	214.046i	−0.368547	+	0.241043i
$889$	−36.3096			−0.0408432
$890$	504.963	+	291.540i	0.567374	+	0.327573i
$891$	−32.7172	−	144.651i	−0.0367197	−	0.162347i
$892$	−2036.56			−2.28314
$893$	595.826	−	57.0480i	0.667218	−	0.0638835i
$894$	192.499	−	380.855i	0.215323	−	0.426013i
$895$	−493.695			−0.551615
$896$		−	36.1122i		−	0.0403038i
$897$	−576.500	−	291.386i	−0.642698	−	0.324845i
$898$	−748.018	−	1295.61i	−0.832982	−	1.44277i
$899$	−134.208	+	77.4849i	−0.149286	+	0.0861901i
$900$	194.798	+	264.485i	0.216442	+	0.293872i
$901$	348.854			0.387185
$902$			330.485i			0.366391i
$903$	6.46508	+	9.88488i	0.00715956	+	0.0109467i
$904$	523.324	+	906.424i	0.578899	+	1.00268i
$905$	−1162.00	+	670.879i	−1.28397	+	0.741303i
$906$	−1401.76	+	916.803i	−1.54720	+	1.01192i
$907$	−336.788	−	583.333i	−0.371320	−	0.643146i	0.618449	−	0.785825i	$-0.287762\pi$
$907$	−336.788	−	583.333i	−0.371320	−	0.643146i	−0.989769	+	0.142680i	$0.954428\pi$
$908$	774.777	−	447.317i	0.853278	−	0.492640i
$909$	−524.296	−	229.360i	−0.576783	−	0.252322i
$910$	−11.7286	+	20.3146i	−0.0128886	+	0.0223237i
$911$	918.101	+	530.066i	1.00779	+	0.581851i	0.910545	−	0.413409i	$-0.135662\pi$
$911$	918.101	+	530.066i	1.00779	+	0.581851i	0.0972495	+	0.995260i	$0.468996\pi$
$912$	−364.224	−	142.332i	−0.399368	−	0.156066i
$913$	−66.3647	−	114.947i	−0.0726886	−	0.125900i
$914$			737.043i			0.806393i
$915$	−15.0078	+	9.81568i	−0.0164020	+	0.0107275i
$916$	1439.95			1.57199
$917$	−11.2019	−	6.46742i	−0.0122158	−	0.00705280i
$918$	−451.655	+	76.0557i	−0.491999	+	0.0828493i
$919$	−402.026			−0.437461			−0.218730	−	0.975785i	$-0.570191\pi$
$919$	−402.026			−0.437461			−0.218730	+	0.975785i	$0.570191\pi$
$920$	−561.525	−	324.197i	−0.610353	−	0.352388i
$921$	−1720.06	+	95.7504i	−1.86761	+	0.103964i
$922$	−227.422	+	393.907i	−0.246662	+	0.427231i
$923$	−682.298	+	393.925i	−0.739218	+	0.426788i
$924$	−6.30906	+	4.12636i	−0.00682798	+	0.00446575i
$925$	167.786			0.181391
$926$	−1356.82	−	783.359i	−1.46525	−	0.845960i
$927$	608.605	−	67.9688i	0.656532	−	0.0733213i
$928$	128.273	−	222.175i	0.138225	−	0.239413i
$929$	1376.78	−	794.887i	1.48201	−	0.855637i	0.482215	−	0.876053i	$-0.339832\pi$
$929$	1376.78	−	794.887i	1.48201	−	0.855637i	0.999792	+	0.0204157i	$0.00649896\pi$
$930$	1001.03	−	55.7240i	1.07638	−	0.0599183i
$931$	757.311	−	539.570i	0.813438	−	0.579560i
$932$	1040.12	−	600.512i	1.11601	−	0.644327i
$933$	147.835	+	74.7218i	0.158452	+	0.0800876i
$934$	−1231.01	−	2132.18i	−1.31800	−	2.28285i
$935$	−37.3026	+	21.5366i	−0.0398958	+	0.0230338i
$936$	263.098	−	193.777i	0.281088	−	0.207026i
$937$	53.1253	+	92.0157i	0.0566972	+	0.0982025i	0.892981	−	0.450094i	$-0.148610\pi$
$937$	53.1253	+	92.0157i	0.0566972	+	0.0982025i	−0.836284	+	0.548297i	$0.815276\pi$
$938$	−11.8932	−	6.86654i	−0.0126793	−	0.00732040i
$939$	287.419	+	439.454i	0.306091	+	0.468002i
$940$	381.195	−	660.249i	0.405527	−	0.702393i
$941$	−1226.80	−	708.294i	−1.30372	−	0.752703i	−0.322680	−	0.946508i	$-0.604584\pi$
$941$	−1226.80	−	708.294i	−1.30372	−	0.752703i	−0.981040	+	0.193805i	$0.937917\pi$
$942$	−1194.17	−	603.580i	−1.26770	−	0.640743i
$943$	−869.688	+	1506.34i	−0.922256	+	1.59739i
$944$	134.474	−	77.6384i	0.142451	−	0.0822440i
$945$	−26.5599	−	9.89940i	−0.0281057	−	0.0104756i
$946$	−45.8276	−	79.3757i	−0.0484435	−	0.0839067i
$947$	−719.112	+	415.180i	−0.759358	+	0.438416i	−0.829065	−	0.559152i	$-0.811127\pi$
$947$	−719.112	+	415.180i	−0.759358	+	0.438416i	0.0697072	+	0.997567i	$0.477793\pi$
$948$	−1096.84	−	1677.03i	−1.15700	−	1.76902i
$949$	−39.8371	−	68.9998i	−0.0419780	−	0.0727079i
$950$	−221.938	−	311.500i	−0.233619	−	0.327894i
$951$	−52.8516	+	34.5669i	−0.0555748	+	0.0363480i
$952$	3.36270	+	5.82436i	0.00353225	+	0.00611803i
$953$	−909.963	−	525.367i	−0.954840	−	0.551277i	−0.0602589	−	0.998183i	$-0.519193\pi$
$953$	−909.963	−	525.367i	−0.954840	−	0.551277i	−0.894581	+	0.446906i	$0.852526\pi$
$954$	−1056.43	−	1434.36i	−1.10737	−	1.50352i
$955$	93.6320	−	162.175i	0.0980440	−	0.169817i
$956$		−	2154.64i		−	2.25381i
$957$	−33.9458	+	1.88965i	−0.0354711	+	0.00197456i
$958$	1201.13	+	2080.41i	1.25379	+	2.17162i
$959$	46.1801	+	26.6621i	0.0481544	+	0.0278020i
$960$	−1092.59	+	714.592i	−1.13811	+	0.744367i
$961$	167.076	−	289.384i	0.173856	−	0.301128i
$962$		−	577.791i		−	0.600615i
$963$	−443.691	−	194.099i	−0.460738	−	0.201556i
$964$	446.342	−	773.088i	0.463011	−	0.801958i
$965$		−	232.337i		−	0.240764i
$966$	−67.7868	+	3.77347i	−0.0701727	+	0.00390629i
$967$	−1389.61			−1.43704			−0.718518	−	0.695508i	$-0.755179\pi$
$967$	−1389.61			−1.43704			−0.718518	+	0.695508i	$0.755179\pi$
$968$	−513.599	+	296.527i	−0.530578	+	0.306329i
$969$	308.119	−	46.9032i	0.317976	−	0.0484037i
$970$	1217.63	−	2109.00i	1.25529	−	2.17423i
$971$	−350.798	−	202.533i	−0.361275	−	0.208582i	0.308365	−	0.951268i	$-0.400218\pi$
$971$	−350.798	−	202.533i	−0.361275	−	0.208582i	−0.669640	+	0.742686i	$0.733552\pi$
$972$	982.076	+	950.671i	1.01037	+	0.978056i
$973$	4.95013	+	8.57387i	0.00508749	+	0.00881179i
$974$	991.237	−	572.291i	1.01770	−	0.587568i
$975$	−139.983	+	7.79240i	−0.143572	+	0.00799221i
$976$	4.76573	+	8.25448i	0.00488292	+	0.00845746i
$977$	720.527	−	415.996i	0.737489	−	0.425790i	−0.0836664	−	0.996494i	$-0.526663\pi$
$977$	720.527	−	415.996i	0.737489	−	0.425790i	0.821156	+	0.570704i	$0.193330\pi$
$978$	2540.66	+	1284.15i	2.59781	+	1.31304i
$979$	−79.9804			−0.0816960
$980$		−	1184.40i		−	1.20857i
$981$	13.3783	+	18.1642i	0.0136374	+	0.0185160i
$982$	145.052	+	251.238i	0.147711	+	0.255843i
$983$	676.360	−	390.497i	0.688057	−	0.397250i	−0.114827	−	0.993386i	$-0.536631\pi$
$983$	676.360	−	390.497i	0.688057	−	0.397250i	0.802884	+	0.596136i	$0.203298\pi$
$984$	−481.604	−	736.355i	−0.489434	−	0.748328i
$985$	1507.16			1.53011
$986$			104.998i			0.106489i
$987$	−1.28169	−	23.0243i	−0.00129857	−	0.0233275i
$988$	−626.887	+	446.645i	−0.634501	+	0.452070i
$989$		−	482.390i		−	0.487755i
$990$	201.514	+	88.1551i	0.203550	+	0.0890456i
$991$	−452.505	+	783.761i	−0.456614	+	0.790879i	−0.998779	−	0.0493930i	$-0.984271\pi$
$991$	−452.505	+	783.761i	−0.456614	+	0.790879i	0.542165	+	0.840272i	$0.317605\pi$
$992$		−	1037.72i		−	1.04609i
$993$	−1311.86	+	73.0271i	−1.32111	+	0.0735419i
$994$	−41.4027	+	71.7115i	−0.0416526	+	0.0721444i
$995$	222.831	−	128.652i	0.223951	−	0.129298i
$996$	1091.75	+	551.816i	1.09614	+	0.554032i
$997$	−210.568			−0.211202			−0.105601	−	0.994409i	$-0.533677\pi$
$997$	−210.568			−0.211202			−0.105601	+	0.994409i	$0.533677\pi$
$998$	−1169.72	+	675.338i	−1.17206	+	0.676692i
$999$	688.484	−	115.936i	0.689174	−	0.116052i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.n.a.11.33	yes	76
3.2	odd	2		513.3.n.a.467.6		76
9.4	even	3		513.3.j.a.125.33		76
9.5	odd	6		171.3.j.a.68.6	✓	76
19.7	even	3		171.3.j.a.83.33	yes	76
57.26	odd	6		513.3.j.a.197.6		76
171.121	even	3		513.3.n.a.368.6		76
171.140	odd	6	inner	171.3.n.a.140.33	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.j.a.68.6	✓	76	9.5	odd	6
171.3.j.a.83.33	yes	76	19.7	even	3
171.3.n.a.11.33	yes	76	1.1	even	1	trivial
171.3.n.a.140.33	yes	76	171.140	odd	6	inner
513.3.j.a.125.33		76	9.4	even	3
513.3.j.a.197.6		76	57.26	odd	6
513.3.n.a.368.6		76	171.121	even	3
513.3.n.a.467.6		76	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.68675 - 1.55120i) q^{2} +(-1.64208 - 2.51069i) q^{3} +(2.81242 - 4.87126i) q^{4} -4.30248i q^{5} +(-8.30645 - 4.19840i) q^{6} +(0.122000 - 0.211310i) q^{7} -5.04093i q^{8} +(-3.60712 + 8.24553i) q^{9} +(-6.67400 - 11.5597i) q^{10} +(1.58563 + 0.915463i) q^{11} +(-16.8485 + 0.937899i) q^{12} +(3.60116 - 6.23738i) q^{13} -0.756984i q^{14} +(-10.8022 + 7.06504i) q^{15} +(3.43023 + 5.94133i) q^{16} +(-4.73531 - 2.73393i) q^{17} +(3.09900 + 27.7490i) q^{18} +(-1.81089 - 18.9135i) q^{19} +(-20.9585 - 12.1004i) q^{20} +(-0.730868 + 0.0406851i) q^{21} +5.68026 q^{22} +(25.8905 + 14.9479i) q^{23} +(-12.6562 + 8.27762i) q^{24} +6.48865 q^{25} -22.3444i q^{26} +(26.6251 - 4.48349i) q^{27} +(-0.686231 - 1.18859i) q^{28} -6.18964i q^{29} +(-18.0636 + 35.7383i) q^{30} +(-12.5185 - 21.6826i) q^{31} +(35.8946 + 20.7238i) q^{32} +(-0.305293 - 5.48429i) q^{33} -16.9635 q^{34} +(-0.909158 - 0.524902i) q^{35} +(30.0214 + 40.7611i) q^{36} +25.8584 q^{37} +(-34.2040 - 48.0068i) q^{38} +(-21.5735 + 1.20093i) q^{39} -21.6885 q^{40} +58.1814i q^{41} +(-1.90055 + 1.24303i) q^{42} +(-8.06787 - 13.9740i) q^{43} +(8.91893 - 5.14934i) q^{44} +(35.4762 + 15.5196i) q^{45} +92.7484 q^{46} +31.5027i q^{47} +(9.28412 - 18.3684i) q^{48} +(24.4702 + 42.3837i) q^{49} +(17.4334 - 10.0652i) q^{50} +(0.911724 + 16.3782i) q^{51} +(-20.2560 - 35.0844i) q^{52} +(-55.2531 + 31.9004i) q^{53} +(64.5804 - 53.3469i) q^{54} +(3.93876 - 6.82214i) q^{55} +(-1.06520 - 0.614992i) q^{56} +(-44.5123 + 35.6042i) q^{57} +(-9.60136 - 16.6300i) q^{58} -22.6336i q^{59} +(4.03530 + 72.4902i) q^{60} +1.38933 q^{61} +(-67.2681 - 38.8372i) q^{62} +(1.30229 + 1.76817i) q^{63} +101.145 q^{64} +(-26.8362 - 15.4939i) q^{65} +(-9.32746 - 14.2614i) q^{66} +(9.07092 - 15.7113i) q^{67} +(-26.6354 + 15.3780i) q^{68} +(-4.98488 - 89.5486i) q^{69} -3.25691 q^{70} +(-94.7332 - 54.6943i) q^{71} +(41.5651 + 18.1832i) q^{72} +(5.53115 - 9.58024i) q^{73} +(69.4752 - 40.1115i) q^{74} +(-10.6549 - 16.2910i) q^{75} +(-97.2257 - 44.3715i) q^{76} +(0.386893 - 0.223373i) q^{77} +(-56.0999 + 36.6914i) q^{78} +(59.3754 + 102.841i) q^{79} +(25.5625 - 14.7585i) q^{80} +(-54.9774 - 59.4852i) q^{81} +(90.2508 + 156.319i) q^{82} +(-62.7808 - 36.2465i) q^{83} +(-1.85732 + 3.67467i) q^{84} +(-11.7627 + 20.3736i) q^{85} +(-43.3528 - 25.0297i) q^{86} +(-15.5403 + 10.1639i) q^{87} +(4.61478 - 7.99304i) q^{88} +(-37.8306 + 21.8415i) q^{89} +(119.390 - 13.3334i) q^{90} +(-0.878681 - 1.52192i) q^{91} +(145.630 - 84.0795i) q^{92} +(-33.8819 + 67.0347i) q^{93} +(48.8668 + 84.6398i) q^{94} +(-81.3750 + 7.79134i) q^{95} +(-6.91105 - 124.150i) q^{96} +(91.2223 + 158.002i) q^{97} +(131.491 + 75.9163i) q^{98} +(-13.2680 + 9.77216i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 3 q^{2} + q^{3} + 73 q^{4} - 13 q^{6} - q^{7} + 5 q^{9} + 6 q^{10} - 24 q^{11} + 15 q^{12} - 4 q^{13} + 49 q^{15} - 131 q^{16} + 135 q^{17} + 30 q^{18} + 4 q^{19} + 69 q^{20} - 13 q^{21} + 6 q^{22}+ \cdots - 340 q^{99}+O(q^{100}) \) 76 * q - 3 * q^2 + q^3 + 73 * q^4 - 13 * q^6 - q^7 + 5 * q^9 + 6 * q^10 - 24 * q^11 + 15 * q^12 - 4 * q^13 + 49 * q^15 - 131 * q^16 + 135 * q^17 + 30 * q^18 + 4 * q^19 + 69 * q^20 - 13 * q^21 + 6 * q^22 - 75 * q^23 - 6 * q^24 - 302 * q^25 - 59 * q^27 + 14 * q^28 + 265 * q^30 + 14 * q^31 + 45 * q^32 - 59 * q^33 + 66 * q^34 + 75 * q^35 - 127 * q^36 + 14 * q^37 - 147 * q^38 - 78 * q^39 - 24 * q^40 + 55 * q^42 + 29 * q^43 - 183 * q^44 + 145 * q^45 - 84 * q^46 - 246 * q^48 - 171 * q^49 - 363 * q^50 - 10 * q^51 + 101 * q^52 - 36 * q^53 + 245 * q^54 - 27 * q^55 + 300 * q^56 - 141 * q^57 + 6 * q^58 + 404 * q^60 - 16 * q^61 - 120 * q^62 + 402 * q^63 - 680 * q^64 - 6 * q^65 - 245 * q^66 + 8 * q^67 + 666 * q^68 + 81 * q^69 + 84 * q^70 - 135 * q^71 - 381 * q^72 + 65 * q^73 + 102 * q^74 - 139 * q^75 + 163 * q^76 - 366 * q^77 + 824 * q^78 - 16 * q^79 + 66 * q^80 + 305 * q^81 - 42 * q^82 - 177 * q^83 + 546 * q^84 + 51 * q^85 - 345 * q^86 - 375 * q^87 + 162 * q^88 - 216 * q^89 + 118 * q^90 + 265 * q^91 - 1347 * q^92 - 6 * q^93 + 6 * q^94 + 432 * q^95 + 511 * q^96 - 127 * q^97 - 882 * q^98 - 340 * q^99

Introduction

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