LMFDB - Embedded newform 63.3.n.b.32.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [63,3,Mod(2,63)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(63, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("63.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	63.n (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:	$1.71662566547$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			32.8
Character	$\chi$	$=$	63.32
Dual form			63.3.n.b.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11318 + 0.642694i) q^{2} +(2.34935 + 1.86563i) q^{3} +(-1.17389 - 2.03324i) q^{4} +7.87519i q^{5} +(1.41622 + 3.58669i) q^{6} +(0.417718 - 6.98753i) q^{7} -8.15936i q^{8} +(2.03887 + 8.76601i) q^{9} +O(q^{10})$	\(q+(1.11318 + 0.642694i) q^{2} +(2.34935 + 1.86563i) q^{3} +(-1.17389 - 2.03324i) q^{4} +7.87519i q^{5} +(1.41622 + 3.58669i) q^{6} +(0.417718 - 6.98753i) q^{7} -8.15936i q^{8} +(2.03887 + 8.76601i) q^{9} +(-5.06133 + 8.76649i) q^{10} -12.3390i q^{11} +(1.03539 - 6.96682i) q^{12} +(-3.39438 + 5.87923i) q^{13} +(4.95583 - 7.50990i) q^{14} +(-14.6922 + 18.5016i) q^{15} +(0.548409 - 0.949873i) q^{16} +(6.19653 + 3.57757i) q^{17} +(-3.36423 + 11.0685i) q^{18} +(-15.4920 - 26.8330i) q^{19} +(16.0121 - 9.24460i) q^{20} +(14.0175 - 15.6368i) q^{21} +(7.93022 - 13.7356i) q^{22} +2.16554i q^{23} +(15.2223 - 19.1692i) q^{24} -37.0186 q^{25} +(-7.55709 + 4.36309i) q^{26} +(-11.5641 + 24.3982i) q^{27} +(-14.6976 + 7.35326i) q^{28} +(-8.97062 + 5.17919i) q^{29} +(-28.2458 + 11.1530i) q^{30} +(10.0973 + 17.4891i) q^{31} +(-27.0439 + 15.6138i) q^{32} +(23.0200 - 28.9887i) q^{33} +(4.59856 + 7.96495i) q^{34} +(55.0281 + 3.28961i) q^{35} +(15.4300 - 14.4358i) q^{36} +(2.46193 + 4.26419i) q^{37} -39.8265i q^{38} +(-18.9430 + 7.47972i) q^{39} +64.2565 q^{40} +(28.0117 + 16.1725i) q^{41} +(25.6536 - 8.39762i) q^{42} +(25.5114 + 44.1870i) q^{43} +(-25.0882 + 14.4847i) q^{44} +(-69.0340 + 16.0565i) q^{45} +(-1.39178 + 2.41063i) q^{46} +(18.5364 + 10.7020i) q^{47} +(3.06051 - 1.20845i) q^{48} +(-48.6510 - 5.83763i) q^{49} +(-41.2083 - 23.7916i) q^{50} +(7.88340 + 19.9654i) q^{51} +15.9385 q^{52} +(51.0920 + 29.4980i) q^{53} +(-28.5535 + 19.7274i) q^{54} +97.1723 q^{55} +(-57.0137 - 3.40831i) q^{56} +(13.6642 - 91.9424i) q^{57} -13.3145 q^{58} +(-89.6310 + 51.7485i) q^{59} +(54.8650 + 8.15385i) q^{60} +(-4.46912 + 7.74075i) q^{61} +25.9579i q^{62} +(62.1044 - 10.5849i) q^{63} -44.5268 q^{64} +(-46.3001 - 26.7314i) q^{65} +(44.2563 - 17.4748i) q^{66} +(-45.3494 - 78.5475i) q^{67} -16.7987i q^{68} +(-4.04009 + 5.08760i) q^{69} +(59.1418 + 39.0281i) q^{70} -2.12523i q^{71} +(71.5250 - 16.6359i) q^{72} +(35.2282 - 61.0170i) q^{73} +6.32907i q^{74} +(-86.9695 - 69.0629i) q^{75} +(-36.3719 + 62.9979i) q^{76} +(-86.2194 - 5.15424i) q^{77} +(-25.8941 - 3.84830i) q^{78} +(72.3404 - 125.297i) q^{79} +(7.48043 + 4.31883i) q^{80} +(-72.6860 + 35.7456i) q^{81} +(20.7880 + 36.0058i) q^{82} +(-13.6055 + 7.85511i) q^{83} +(-48.2483 - 10.1449i) q^{84} +(-28.1740 + 48.7989i) q^{85} +65.5840i q^{86} +(-30.7375 - 4.56811i) q^{87} -100.679 q^{88} +(4.08134 - 2.35636i) q^{89} +(-87.1666 - 26.4940i) q^{90} +(39.6634 + 26.1742i) q^{91} +(4.40305 - 2.54210i) q^{92} +(-8.90596 + 59.9257i) q^{93} +(13.7562 + 23.8264i) q^{94} +(211.315 - 122.003i) q^{95} +(-92.6650 - 13.7716i) q^{96} +(-47.0097 - 81.4233i) q^{97} +(-50.4055 - 37.7660i) q^{98} +(108.164 - 25.1577i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) $ 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.11318	+	0.642694i	0.556589	+	0.321347i	0.751775	−	0.659419i	$-0.229198\pi$
$2$	1.11318	+	0.642694i	0.556589	+	0.321347i	−0.195186	+	0.980766i	$0.562531\pi$
$3$	2.34935	+	1.86563i	0.783116	+	0.621876i
$3$	2.34935	+	1.86563i	0.783116	+	0.621876i
$4$	−1.17389	−	2.03324i	−0.293472	−	0.508309i
$5$			7.87519i			1.57504i	0.616291	+	0.787519i	$0.288635\pi$
$5$			7.87519i			1.57504i	−0.616291	+	0.787519i	$0.711365\pi$
$6$	1.41622	+	3.58669i	0.236036	+	0.597781i
$7$	0.417718	−	6.98753i	0.0596740	−	0.998218i
$7$	0.417718	−	6.98753i	0.0596740	−	0.998218i
$8$		−	8.15936i		−	1.01992i
$9$	2.03887	+	8.76601i	0.226541	+	0.974002i
$10$	−5.06133	+	8.76649i	−0.506133	+	0.876649i
$11$		−	12.3390i		−	1.12173i	−0.827907	−	0.560866i	$-0.810468\pi$
$11$		−	12.3390i		−	1.12173i	0.827907	−	0.560866i	$-0.189532\pi$
$12$	1.03539	−	6.96682i	0.0862821	−	0.580568i
$13$	−3.39438	+	5.87923i	−0.261106	+	0.452249i	−0.966536	−	0.256531i	$-0.917421\pi$
$13$	−3.39438	+	5.87923i	−0.261106	+	0.452249i	0.705430	+	0.708779i	$0.250754\pi$
$14$	4.95583	−	7.50990i	0.353988	−	0.536421i
$15$	−14.6922	+	18.5016i	−0.979478	+	1.23344i
$16$	0.548409	−	0.949873i	0.0342756	−	0.0593671i
$17$	6.19653	+	3.57757i	0.364502	+	0.210445i	0.671054	−	0.741409i	$-0.265842\pi$
$17$	6.19653	+	3.57757i	0.364502	+	0.210445i	−0.306552	+	0.951854i	$0.599175\pi$
$18$	−3.36423	+	11.0685i	−0.186902	+	0.614917i
$19$	−15.4920	−	26.8330i	−0.815370	−	1.41226i	−0.909062	−	0.416662i	$-0.863200\pi$
$19$	−15.4920	−	26.8330i	−0.815370	−	1.41226i	0.0936913	−	0.995601i	$-0.470133\pi$
$20$	16.0121	−	9.24460i	0.800606	−	0.462230i
$21$	14.0175	−	15.6368i	0.667499	−	0.744611i
$22$	7.93022	−	13.7356i	0.360465	−	0.624343i
$23$			2.16554i			0.0941538i	0.998891	+	0.0470769i	$0.0149906\pi$
$23$			2.16554i			0.0941538i	−0.998891	+	0.0470769i	$0.985009\pi$
$24$	15.2223	−	19.1692i	0.634263	−	0.798715i
$25$	−37.0186			−1.48074
$26$	−7.55709	+	4.36309i	−0.290657	+	0.167811i
$27$	−11.5641	+	24.3982i	−0.428300	+	0.903637i
$28$	−14.6976	+	7.35326i	−0.524916	+	0.262617i
$29$	−8.97062	+	5.17919i	−0.309332	+	0.178593i	−0.646627	−	0.762806i	$-0.723821\pi$
$29$	−8.97062	+	5.17919i	−0.309332	+	0.178593i	0.337296	+	0.941399i	$0.390488\pi$
$30$	−28.2458	+	11.1530i	−0.941528	+	0.371766i
$31$	10.0973	+	17.4891i	0.325720	+	0.564163i	0.981658	−	0.190651i	$-0.0610600\pi$
$31$	10.0973	+	17.4891i	0.325720	+	0.564163i	−0.655938	+	0.754815i	$0.727727\pi$
$32$	−27.0439	+	15.6138i	−0.845121	+	0.487931i
$33$	23.0200	−	28.9887i	0.697577	−	0.878446i
$34$	4.59856	+	7.96495i	0.135252	+	0.234263i
$35$	55.0281	+	3.28961i	1.57223	+	0.0939888i
$36$	15.4300	−	14.4358i	0.428610	−	0.400996i
$37$	2.46193	+	4.26419i	0.0665387	+	0.115248i	0.897376	−	0.441268i	$-0.145471\pi$
$37$	2.46193	+	4.26419i	0.0665387	+	0.115248i	−0.830837	+	0.556516i	$0.812138\pi$
$38$		−	39.8265i		−	1.04807i
$39$	−18.9430	+	7.47972i	−0.485719	+	0.191788i
$40$	64.2565			1.60641
$41$	28.0117	+	16.1725i	0.683211	+	0.394452i	0.801064	−	0.598579i	$-0.204268\pi$
$41$	28.0117	+	16.1725i	0.683211	+	0.394452i	−0.117853	+	0.993031i	$0.537601\pi$
$42$	25.6536	−	8.39762i	0.610801	−	0.199943i
$43$	25.5114	+	44.1870i	0.593288	+	1.02761i	0.993786	+	0.111308i	$0.0355039\pi$
$43$	25.5114	+	44.1870i	0.593288	+	1.02761i	−0.400498	+	0.916298i	$0.631163\pi$
$44$	−25.0882	+	14.4847i	−0.570186	+	0.329197i
$45$	−69.0340	+	16.0565i	−1.53409	+	0.356811i
$46$	−1.39178	+	2.41063i	−0.0302560	+	0.0524050i
$47$	18.5364	+	10.7020i	0.394391	+	0.227702i	0.684061	−	0.729425i	$-0.260212\pi$
$47$	18.5364	+	10.7020i	0.394391	+	0.227702i	−0.289670	+	0.957127i	$0.593546\pi$
$48$	3.06051	−	1.20845i	0.0637607	−	0.0251761i
$49$	−48.6510	−	5.83763i	−0.992878	−	0.119135i
$50$	−41.2083	−	23.7916i	−0.824166	−	0.475832i
$51$	7.88340	+	19.9654i	0.154576	+	0.391478i
$52$	15.9385			0.306510
$53$	51.0920	+	29.4980i	0.964000	+	0.556566i	0.897402	−	0.441214i	$-0.145452\pi$
$53$	51.0920	+	29.4980i	0.964000	+	0.556566i	0.0665983	+	0.997780i	$0.478785\pi$
$54$	−28.5535	+	19.7274i	−0.528768	+	0.365322i
$55$	97.1723			1.76677
$56$	−57.0137	−	3.40831i	−1.01810	−	0.0608627i
$57$	13.6642	−	91.9424i	0.239722	−	1.61302i
$58$	−13.3145			−0.229561
$59$	−89.6310	+	51.7485i	−1.51917	+	0.877093i	−0.519425	+	0.854516i	$0.673854\pi$
$59$	−89.6310	+	51.7485i	−1.51917	+	0.877093i	−0.999745	+	0.0225767i	$0.992813\pi$
$60$	54.8650	+	8.15385i	0.914417	+	0.135898i
$61$	−4.46912	+	7.74075i	−0.0732643	+	0.126898i	−0.900330	−	0.435208i	$-0.856675\pi$
$61$	−4.46912	+	7.74075i	−0.0732643	+	0.126898i	0.827066	+	0.562105i	$0.190008\pi$
$62$			25.9579i			0.418676i
$63$	62.1044	−	10.5849i	0.985784	−	0.168015i
$64$	−44.5268			−0.695732
$65$	−46.3001	−	26.7314i	−0.712309	−	0.411252i
$66$	44.2563	−	17.4748i	0.670550	−	0.264769i
$67$	−45.3494	−	78.5475i	−0.676857	−	1.17235i	−0.975922	−	0.218118i	$-0.930008\pi$
$67$	−45.3494	−	78.5475i	−0.676857	−	1.17235i	0.299066	−	0.954232i	$-0.403325\pi$
$68$		−	16.7987i		−	0.247039i
$69$	−4.04009	+	5.08760i	−0.0585520	+	0.0737334i
$70$	59.1418	+	39.0281i	0.844884	+	0.557545i
$71$		−	2.12523i		−	0.0299328i	−0.999888	−	0.0149664i	$-0.995236\pi$
$71$		−	2.12523i		−	0.0299328i	0.999888	−	0.0149664i	$-0.00476412\pi$
$72$	71.5250	−	16.6359i	0.993403	−	0.231054i
$73$	35.2282	−	61.0170i	0.482577	−	0.835849i	−0.517222	−	0.855851i	$-0.673034\pi$
$73$	35.2282	−	61.0170i	0.482577	−	0.835849i	0.999800	+	0.0200023i	$0.00636734\pi$
$74$			6.32907i			0.0855280i
$75$	−86.9695	−	69.0629i	−1.15959	−	0.920838i
$76$	−36.3719	+	62.9979i	−0.478577	+	0.828920i
$77$	−86.2194	−	5.15424i	−1.11973	−	0.0669382i
$78$	−25.8941	−	3.84830i	−0.331976	−	0.0493372i
$79$	72.3404	−	125.297i	0.915701	−	1.58604i	0.109829	−	0.993950i	$-0.464970\pi$
$79$	72.3404	−	125.297i	0.915701	−	1.58604i	0.805872	−	0.592090i	$-0.201697\pi$
$80$	7.48043	+	4.31883i	0.0935054	+	0.0539853i
$81$	−72.6860	+	35.7456i	−0.897358	+	0.441303i
$82$	20.7880	+	36.0058i	0.253512	+	0.439096i
$83$	−13.6055	+	7.85511i	−0.163921	+	0.0946399i	−0.579716	−	0.814818i	$-0.696837\pi$
$83$	−13.6055	+	7.85511i	−0.163921	+	0.0946399i	0.415795	+	0.909458i	$0.363503\pi$
$84$	−48.2483	−	10.1449i	−0.574385	−	0.120773i
$85$	−28.1740	+	48.7989i	−0.331459	+	0.574104i
$86$			65.5840i			0.762605i
$87$	−30.7375	−	4.56811i	−0.353305	−	0.0525070i
$88$	−100.679			−1.14408
$89$	4.08134	−	2.35636i	0.0458578	−	0.0264760i	−0.476896	−	0.878960i	$-0.658238\pi$
$89$	4.08134	−	2.35636i	0.0458578	−	0.0264760i	0.522754	+	0.852484i	$0.324905\pi$
$90$	−87.1666	−	26.4940i	−0.968517	−	0.294378i
$91$	39.6634	+	26.1742i	0.435862	+	0.287628i
$92$	4.40305	−	2.54210i	0.0478592	−	0.0276315i
$93$	−8.90596	+	59.9257i	−0.0957630	+	0.644363i
$94$	13.7562	+	23.8264i	0.146343	+	0.253473i
$95$	211.315	−	122.003i	2.22437	−	1.28424i
$96$	−92.6650	−	13.7716i	−0.965260	−	0.143454i
$97$	−47.0097	−	81.4233i	−0.484637	−	0.839415i	0.515208	−	0.857065i	$-0.327715\pi$
$97$	−47.0097	−	81.4233i	−0.484637	−	0.839415i	−0.999844	+	0.0176503i	$0.994381\pi$
$98$	−50.4055	−	37.7660i	−0.514341	−	0.385368i
$99$	108.164	−	25.1577i	1.09257	−	0.254118i
$100$	43.4557	+	75.2675i	0.434557	+	0.752675i
$101$		−	6.75096i		−	0.0668412i	−0.999441	−	0.0334206i	$-0.989360\pi$
$101$		−	6.75096i		−	0.0668412i	0.999441	−	0.0334206i	$-0.0106401\pi$
$102$	−4.05599	+	27.2916i	−0.0397646	+	0.267565i
$103$	71.5356			0.694520			0.347260	−	0.937769i	$-0.387112\pi$
$103$	71.5356			0.694520			0.347260	+	0.937769i	$0.387112\pi$
$104$	47.9708	+	27.6959i	0.461257	+	0.266307i
$105$	123.143	+	110.390i	1.17279	+	1.05134i
$106$	37.9163	+	65.6730i	0.357701	+	0.619557i
$107$	14.2600	−	8.23301i	0.133271	−	0.0769440i	−0.431882	−	0.901930i	$-0.642150\pi$
$107$	14.2600	−	8.23301i	0.133271	−	0.0769440i	0.565153	+	0.824986i	$0.308817\pi$
$108$	63.1823	−	5.12825i	0.585021	−	0.0474838i
$109$	−38.5448	+	66.7615i	−0.353622	+	0.612491i	−0.986881	−	0.161449i	$-0.948383\pi$
$109$	−38.5448	+	66.7615i	−0.353622	+	0.612491i	0.633259	+	0.773940i	$0.281717\pi$
$110$	108.170	+	62.4520i	0.983364	+	0.567746i
$111$	−2.17146	+	14.6111i	−0.0195627	+	0.131632i
$112$	−6.40818	−	4.22880i	−0.0572159	−	0.0377572i
$113$	5.45295	+	3.14826i	0.0482562	+	0.0278607i	0.523934	−	0.851759i	$-0.324464\pi$
$113$	5.45295	+	3.14826i	0.0482562	+	0.0278607i	−0.475678	+	0.879620i	$0.657797\pi$
$114$	74.3015	−	93.5664i	0.651767	−	0.820758i
$115$	−17.0540			−0.148296
$116$	21.0610	+	12.1596i	0.181561	+	0.104824i
$117$	−58.4581	−	17.7682i	−0.499642	−	0.151865i
$118$	−133.034			−1.12740
$119$	27.5868	−	41.8040i	0.231822	−	0.351294i
$120$	150.961	+	119.879i	1.25801	+	0.998988i
$121$	−31.2519			−0.258280
$122$	−9.94986	+	5.74456i	−0.0815563	+	0.0470865i
$123$	35.6372	+	90.2542i	0.289733	+	0.733774i
$124$	23.7063	−	41.0605i	0.191180	−	0.331133i
$125$		−	94.6486i		−	0.757189i
$126$	75.9362	+	28.1312i	0.602668	+	0.223263i
$127$	−143.267			−1.12808			−0.564042	−	0.825746i	$-0.690754\pi$
$127$	−143.267			−1.12808			−0.564042	+	0.825746i	$0.690754\pi$
$128$	58.6092	+	33.8381i	0.457885	+	0.264360i
$129$	−22.5014	+	151.405i	−0.174429	+	1.17369i
$130$	−34.3602	−	59.5135i	−0.264309	−	0.457796i
$131$			178.447i			1.36219i	0.732194	+	0.681096i	$0.238496\pi$
$131$			178.447i			1.36219i	−0.732194	+	0.681096i	$0.761504\pi$
$132$	−85.9639	−	12.7757i	−0.651241	−	0.0967853i
$133$	−193.968	+	97.0424i	−1.45840	+	0.729642i
$134$		−	116.583i		−	0.870023i
$135$	−192.140	−	91.0694i	−1.42326	−	0.674588i
$136$	29.1907	−	50.5597i	0.214637	−	0.371763i
$137$		−	72.3511i		−	0.528110i	−0.964508	−	0.264055i	$-0.914940\pi$
$137$		−	72.3511i		−	0.528110i	0.964508	−	0.264055i	$-0.0850600\pi$
$138$	−7.76711	+	3.06687i	−0.0562834	+	0.0222237i
$139$	96.9860	−	167.985i	0.697741	−	1.20852i	−0.271506	−	0.962437i	$-0.587522\pi$
$139$	96.9860	−	167.985i	0.697741	−	1.20852i	0.969248	−	0.246087i	$-0.0791448\pi$
$140$	−57.9083	−	115.747i	−0.413631	−	0.826762i
$141$	23.5825	+	59.7247i	0.167252	+	0.423579i
$142$	1.36587	−	2.36576i	0.00961880	−	0.0166602i
$143$	72.5441	+	41.8834i	0.507301	+	0.292891i
$144$	9.44474	+	2.87070i	0.0655885	+	0.0199354i
$145$	−40.7871	−	70.6453i	−0.281290	−	0.487209i
$146$	78.4304	−	45.2818i	0.537195	−	0.310150i
$147$	−103.407	−	104.479i	−0.703451	−	0.710743i
$148$	5.78007	−	10.0114i	0.0390545	−	0.0676444i
$149$		−	65.1571i		−	0.437296i	−0.975804	−	0.218648i	$-0.929835\pi$
$149$		−	65.1571i		−	0.437296i	0.975804	−	0.218648i	$-0.0701646\pi$
$150$	−52.4263	−	132.774i	−0.349509	−	0.885160i
$151$	163.634			1.08367			0.541834	−	0.840486i	$-0.317730\pi$
$151$	163.634			1.08367			0.541834	+	0.840486i	$0.317730\pi$
$152$	−218.940	+	126.405i	−1.44039	+	0.831612i
$153$	−18.7271	+	61.6131i	−0.122399	+	0.402700i
$154$	−92.6649	−	61.1502i	−0.601720	−	0.397079i
$155$	−137.730	+	79.5183i	−0.888579	+	0.513021i
$156$	37.4451	+	29.7353i	0.240032	+	0.190611i
$157$	85.5689	+	148.210i	0.545025	+	0.944010i	0.998605	+	0.0527952i	$0.0168130\pi$
$157$	85.5689	+	148.210i	0.545025	+	0.944010i	−0.453581	+	0.891215i	$0.649854\pi$
$158$	161.055	−	92.9854i	1.01934	−	0.588515i
$159$	65.0007	+	164.620i	0.408809	+	1.03534i
$160$	−122.962	−	212.976i	−0.768510	−	1.33110i
$161$	15.1317	+	0.904584i	0.0939860	+	0.00561854i
$162$	−103.886	−	6.92366i	−0.641271	−	0.0427386i
$163$	−33.3826	−	57.8203i	−0.204801	−	0.354726i	0.745268	−	0.666765i	$-0.232321\pi$
$163$	−33.3826	−	57.8203i	−0.204801	−	0.354726i	−0.950069	+	0.312039i	$0.898988\pi$
$164$		−	75.9391i		−	0.463043i
$165$	228.291	+	181.287i	1.38358	+	1.09871i
$166$	−20.1937			−0.121649
$167$	12.2509	+	7.07305i	0.0733586	+	0.0423536i	0.536231	−	0.844072i	$-0.319848\pi$
$167$	12.2509	+	7.07305i	0.0733586	+	0.0423536i	−0.462872	+	0.886425i	$0.653181\pi$
$168$	−127.586	−	114.374i	−0.759443	−	0.680795i
$169$	61.4564	+	106.446i	0.363647	+	0.629856i
$170$	−62.7254	+	36.2145i	−0.368973	+	0.213027i
$171$	203.632	−	190.512i	1.19083	−	1.11411i
$172$	59.8951	−	103.741i	0.348227	−	0.603147i
$173$	42.3431	+	24.4468i	0.244758	+	0.141311i	0.617362	−	0.786679i	$-0.288202\pi$
$173$	42.3431	+	24.4468i	0.244758	+	0.141311i	−0.372604	+	0.927991i	$0.621535\pi$
$174$	−31.2805	−	24.8399i	−0.179773	−	0.142758i
$175$	−15.4633	+	258.668i	−0.0883619	+	1.47810i
$176$	−11.7205	−	6.76685i	−0.0665939	−	0.0384480i
$177$	−307.118	−	45.6428i	−1.73513	−	0.257869i
$178$	6.05768			0.0340319
$179$	−163.746	−	94.5386i	−0.914780	−	0.528149i	−0.0328141	−	0.999461i	$-0.510447\pi$
$179$	−163.746	−	94.5386i	−0.914780	−	0.528149i	−0.881966	+	0.471313i	$0.843780\pi$
$180$	113.685	+	121.514i	0.631583	+	0.675077i
$181$	130.455			0.720743			0.360372	−	0.932809i	$-0.382650\pi$
$181$	130.455			0.720743			0.360372	+	0.932809i	$0.382650\pi$
$182$	27.3305	+	54.6279i	0.150167	+	0.300153i
$183$	−24.9409	+	9.84800i	−0.136289	+	0.0538142i
$184$	17.6694			0.0960293
$185$	−33.5813	+	19.3882i	−0.181521	+	0.104801i
$186$	−48.4278	+	60.9842i	−0.260365	+	0.327872i
$187$	44.1438	−	76.4593i	0.236063	−	0.408873i
$188$		−	50.2518i		−	0.267297i
$189$	165.652	+	90.9960i	0.876468	+	0.481460i
$190$	313.641			1.65074
$191$	98.5384	+	56.8911i	0.515908	+	0.297859i	0.735259	−	0.677787i	$-0.237061\pi$
$191$	98.5384	+	56.8911i	0.515908	+	0.297859i	−0.219351	+	0.975646i	$0.570394\pi$
$192$	−104.609	−	83.0704i	−0.544839	−	0.432659i
$193$	−131.368	−	227.536i	−0.680663	−	1.17894i	−0.974779	−	0.223173i	$-0.928359\pi$
$193$	−131.368	−	227.536i	−0.680663	−	1.17894i	0.294116	−	0.955770i	$-0.404975\pi$
$194$		−	120.851i		−	0.622946i
$195$	−58.9042	−	149.180i	−0.302073	−	0.765025i
$196$	45.2416	+	105.772i	0.230825	+	0.539652i
$197$		−	184.907i		−	0.938615i	−0.883035	−	0.469307i	$-0.844504\pi$
$197$		−	184.907i		−	0.938615i	0.883035	−	0.469307i	$-0.155496\pi$
$198$	136.575	+	41.5114i	0.689772	+	0.209654i
$199$	−122.873	+	212.822i	−0.617452	+	1.06946i	0.372497	+	0.928033i	$0.378502\pi$
$199$	−122.873	+	212.822i	−0.617452	+	1.06946i	−0.989949	+	0.141425i	$0.954832\pi$
$200$			302.048i			1.51024i
$201$	39.9987	−	269.140i	0.198999	−	1.33901i
$202$	4.33880	−	7.51502i	0.0214792	−	0.0372031i
$203$	32.4425	+	64.8458i	0.159815	+	0.319438i
$204$	31.3401	−	39.4660i	0.153628	−	0.193461i
$205$	−127.362	+	220.597i	−0.621277	+	1.07608i
$206$	79.6318	+	45.9755i	0.386562	+	0.223182i
$207$	−18.9831	+	4.41525i	−0.0917060	+	0.0213297i
$208$	3.72302	+	6.44845i	0.0178991	+	0.0310022i
$209$	−331.093	+	191.157i	−1.58418	+	0.914626i
$210$	66.1329	+	202.027i	0.314918	+	0.962035i
$211$	−23.1354	+	40.0718i	−0.109647	+	0.189914i	−0.915627	−	0.402029i	$-0.868305\pi$
$211$	−23.1354	+	40.0718i	−0.109647	+	0.189914i	0.805981	+	0.591942i	$0.201639\pi$
$212$		−	138.509i		−	0.653347i
$213$	3.96488	−	4.99290i	0.0186145	−	0.0234408i
$214$	21.1652			0.0989029
$215$	−347.981	+	200.907i	−1.61852	+	0.934451i
$216$	199.074	+	94.3555i	0.921637	+	0.436831i
$217$	126.423	−	63.2498i	0.582595	−	0.291474i
$218$	−85.8144	+	49.5450i	−0.393644	+	0.227270i
$219$	196.598	−	77.6275i	0.897708	−	0.354463i
$220$	−114.069	−	197.574i	−0.518498	−	0.898064i
$221$	−42.0667	+	24.2872i	−0.190347	+	0.109897i
$222$	−11.8077	+	14.8692i	−0.0531878	+	0.0669784i
$223$	55.8857	+	96.7968i	0.250608	+	0.434066i	0.963693	−	0.267011i	$-0.0860360\pi$
$223$	55.8857	+	96.7968i	0.250608	+	0.434066i	−0.713085	+	0.701078i	$0.752703\pi$
$224$	97.8051	+	195.492i	0.436630	+	0.872732i
$225$	−75.4762	−	324.505i	−0.335450	−	1.44225i
$226$	4.04674	+	7.00915i	0.0179059	+	0.0310139i
$227$			256.634i			1.13055i	0.824904	+	0.565273i	$0.191229\pi$
$227$			256.634i			1.13055i	−0.824904	+	0.565273i	$0.808771\pi$
$228$	−202.981	+	80.1477i	−0.890267	+	0.351525i
$229$	154.248			0.673573			0.336787	−	0.941581i	$-0.390660\pi$
$229$	154.248			0.673573			0.336787	+	0.941581i	$0.390660\pi$
$230$	−18.9842	−	10.9605i	−0.0825398	−	0.0476544i
$231$	−192.943	−	172.962i	−0.835253	−	0.748754i
$232$	42.2588	+	73.1945i	0.182150	+	0.315493i
$233$	319.392	−	184.401i	1.37078	−	0.791422i	0.379756	−	0.925087i	$-0.376008\pi$
$233$	319.392	−	184.401i	1.37078	−	0.791422i	0.991027	+	0.133665i	$0.0426746\pi$
$234$	−53.6549	−	57.3498i	−0.229294	−	0.245085i
$235$	−84.2802	+	145.978i	−0.358639	+	0.621181i
$236$	210.434	+	121.494i	0.891669	+	0.514805i
$237$	403.711	−	159.407i	1.70342	−	0.672602i
$238$	57.5762	−	28.8055i	0.241917	−	0.121031i
$239$	172.453	+	99.5658i	0.721561	+	0.416593i	0.815327	−	0.579001i	$-0.196557\pi$
$239$	172.453	+	99.5658i	0.721561	+	0.416593i	−0.0937659	+	0.995594i	$0.529891\pi$
$240$	9.51681	+	24.1021i	0.0396534	+	0.100425i
$241$	195.137			0.809698			0.404849	−	0.914384i	$-0.367324\pi$
$241$	195.137			0.809698			0.404849	+	0.914384i	$0.367324\pi$
$242$	−34.7890	−	20.0854i	−0.143756	−	0.0829976i
$243$	−237.453	−	51.6262i	−0.977171	−	0.212453i
$244$	20.9850			0.0860042
$245$	45.9724	−	383.136i	0.187643	−	1.56382i
$246$	−18.3353	+	123.373i	−0.0745336	+	0.501516i
$247$	210.343			0.851592
$248$	142.700	−	82.3876i	0.575401	−	0.332208i
$249$	−46.6186	−	6.92831i	−0.187223	−	0.0278245i
$250$	60.8301	−	105.361i	0.243320	−	0.421443i
$251$			194.630i			0.775417i	0.921782	+	0.387709i	$0.126733\pi$
$251$			194.630i			0.775417i	−0.921782	+	0.387709i	$0.873267\pi$
$252$	−94.4254	−	113.847i	−0.374704	−	0.451775i
$253$	26.7207			0.105615
$254$	−159.481	−	92.0766i	−0.627879	−	0.362506i
$255$	−157.231	+	62.0833i	−0.616592	+	0.243464i
$256$	132.549	+	229.581i	0.517768	+	0.896801i
$257$		−	401.148i		−	1.56089i	−0.625226	−	0.780444i	$-0.714993\pi$
$257$		−	401.148i		−	1.56089i	0.625226	−	0.780444i	$-0.285007\pi$
$258$	−122.355	+	154.080i	−0.474246	+	0.597208i
$259$	30.8245	−	15.4216i	0.119014	−	0.0595428i
$260$			125.519i			0.482764i
$261$	−63.6908	−	68.0768i	−0.244026	−	0.260831i
$262$	−114.687	+	198.643i	−0.437736	+	0.758181i
$263$		−	292.298i		−	1.11140i	−0.831383	−	0.555699i	$-0.812451\pi$
$263$		−	292.298i		−	1.11140i	0.831383	−	0.555699i	$-0.187549\pi$
$264$	−236.529	−	187.829i	−0.895944	−	0.711473i
$265$	−232.302	+	402.359i	−0.876612	+	1.51834i
$266$	−278.289	−	16.6363i	−1.04620	−	0.0625424i
$267$	13.9846	+	2.07834i	0.0523767	+	0.00778405i
$268$	−106.470	+	184.412i	−0.397277	+	0.688105i
$269$	−285.220	−	164.672i	−1.06030	−	0.612162i	−0.134782	−	0.990875i	$-0.543033\pi$
$269$	−285.220	−	164.672i	−1.06030	−	0.612162i	−0.925514	+	0.378713i	$0.876367\pi$
$270$	−155.357	−	224.864i	−0.575395	−	0.832829i
$271$	25.4109	+	44.0130i	0.0937673	+	0.162410i	0.909093	−	0.416592i	$-0.136776\pi$
$271$	25.4109	+	44.0130i	0.0937673	+	0.162410i	−0.815326	+	0.579002i	$0.803442\pi$
$272$	6.79647	−	3.92395i	0.0249870	−	0.0144263i
$273$	44.3519	+	135.489i	0.162461	+	0.496298i
$274$	46.4996	−	80.5396i	0.169706	−	0.293940i
$275$			456.774i			1.66100i
$276$	15.0869	+	2.24217i	0.0546627	+	0.00812379i
$277$	−13.2632			−0.0478814			−0.0239407	−	0.999713i	$-0.507621\pi$
$277$	−13.2632			−0.0478814			−0.0239407	+	0.999713i	$0.507621\pi$
$278$	215.926	−	124.665i	0.776710	−	0.448434i
$279$	−132.722	+	124.171i	−0.475707	+	0.445058i
$280$	26.8411	−	448.994i	0.0958610	−	1.60355i
$281$	−375.796	+	216.966i	−1.33735	+	0.772120i	−0.986414	−	0.164279i	$-0.947470\pi$
$281$	−375.796	+	216.966i	−1.33735	+	0.772120i	−0.350937	+	0.936399i	$0.614137\pi$
$282$	−12.1331	+	81.6405i	−0.0430253	+	0.289505i
$283$	−192.732	−	333.822i	−0.681033	−	1.17958i	−0.974666	−	0.223666i	$-0.928198\pi$
$283$	−192.732	−	333.822i	−0.681033	−	1.17958i	0.293633	−	0.955918i	$-0.405136\pi$
$284$	−4.32109	+	2.49478i	−0.0152151	+	0.00878444i
$285$	724.064	+	107.608i	2.54057	+	0.377572i
$286$	53.8363	+	93.2473i	0.188239	+	0.326039i
$287$	124.707	−	188.977i	0.434519	−	0.658455i
$288$	−192.010	−	205.233i	−0.666701	−	0.712613i
$289$	−118.902	−	205.944i	−0.411426	−	0.712610i
$290$		−	104.854i		−	0.361567i
$291$	41.4632	−	278.994i	0.142485	−	0.958743i
$292$	−165.416			−0.566493
$293$	167.296	+	96.5885i	0.570977	+	0.329653i	0.757539	−	0.652790i	$-0.226401\pi$
$293$	167.296	+	96.5885i	0.570977	+	0.329653i	−0.186563	+	0.982443i	$0.559735\pi$
$294$	−47.9626	−	182.763i	−0.163138	−	0.621644i
$295$	−407.529	−	705.861i	−1.38145	−	2.39275i
$296$	34.7931	−	20.0878i	0.117544	−	0.0678641i
$297$	301.050	+	142.690i	1.01364	+	0.480437i
$298$	41.8761	−	72.5315i	0.140524	−	0.243394i
$299$	−12.7317	−	7.35065i	−0.0425809	−	0.0245841i
$300$	−38.3285	+	257.902i	−0.127762	+	0.859673i
$301$	319.415	−	159.804i	1.06118	−	0.530910i
$302$	182.154	+	105.166i	0.603158	+	0.348233i
$303$	12.5948	−	15.8603i	0.0415669	−	0.0523444i
$304$	−33.9839			−0.111789
$305$	−60.9599	−	35.1952i	−0.199868	−	0.115394i
$306$	−60.4449	+	56.5506i	−0.197532	+	0.184806i
$307$	16.4744			0.0536625			0.0268313	−	0.999640i	$-0.491458\pi$
$307$	16.4744			0.0536625			0.0268313	+	0.999640i	$0.491458\pi$
$308$	90.7322	+	181.355i	0.294585	+	0.588814i
$309$	168.062	+	133.459i	0.543890	+	0.431905i
$310$	−204.424			−0.659431
$311$	−420.238	+	242.625i	−1.35125	+	0.780143i	−0.988424	−	0.151714i	$-0.951521\pi$
$311$	−420.238	+	242.625i	−1.35125	+	0.780143i	−0.362824	+	0.931858i	$0.618187\pi$
$312$	61.0297	+	154.563i	0.195608	+	0.495394i
$313$	−205.370	+	355.711i	−0.656134	+	1.13646i	0.325475	+	0.945551i	$0.394476\pi$
$313$	−205.370	+	355.711i	−0.656134	+	1.13646i	−0.981608	+	0.190906i	$0.938857\pi$
$314$			219.978i			0.700568i
$315$	83.3585	+	489.084i	0.264630	+	1.55265i
$316$	−339.678			−1.07493
$317$	113.285	+	65.4049i	0.357365	+	0.206325i	0.667924	−	0.744229i	$-0.267183\pi$
$317$	113.285	+	65.4049i	0.357365	+	0.206325i	−0.310559	+	0.950554i	$0.600516\pi$
$318$	−33.4427	+	225.027i	−0.105166	+	0.707631i
$319$	63.9062	+	110.689i	0.200333	+	0.346987i
$320$		−	350.657i		−	1.09580i
$321$	48.8614	+	7.26162i	0.152216	+	0.0226219i
$322$	16.2630	+	10.7320i	0.0505061	+	0.0333293i
$323$		−	221.695i		−	0.686363i
$324$	158.004	+	105.826i	0.487668	+	0.326625i
$325$	125.655	−	217.641i	0.386631	−	0.669664i
$326$		−	85.8191i		−	0.263249i
$327$	−215.107	+	84.9358i	−0.657820	+	0.259743i
$328$	131.958	−	228.557i	0.402309	−	0.696820i
$329$	82.5234	−	125.053i	0.250831	−	0.380100i
$330$	137.617	+	348.526i	0.417021	+	1.05614i
$331$	120.470	−	208.660i	0.363957	−	0.630393i	−0.624651	−	0.780904i	$-0.714759\pi$
$331$	120.470	−	208.660i	0.363957	−	0.630393i	0.988608	+	0.150512i	$0.0480921\pi$
$332$	31.9426	+	18.4421i	0.0962126	+	0.0555484i
$333$	−32.3604	+	30.2755i	−0.0971784	+	0.0909173i
$334$	9.09161	+	15.7471i	0.0272204	+	0.0471471i
$335$	618.576	−	357.135i	1.84650	−	1.06607i
$336$	−7.16568	−	21.8902i	−0.0213264	−	0.0651494i
$337$	−149.637	+	259.179i	−0.444026	+	0.769076i	−0.997984	−	0.0634687i	$-0.979784\pi$
$337$	−149.637	+	259.179i	−0.444026	+	0.769076i	0.553957	+	0.832545i	$0.313117\pi$
$338$			157.991i			0.467428i
$339$	6.93739	+	17.5695i	0.0204643	+	0.0518275i
$340$	132.293			0.389096
$341$	215.798	−	124.591i	0.632840	−	0.365370i
$342$	349.120	−	81.2012i	1.02082	−	0.237430i
$343$	−61.1130	+	337.512i	−0.178172	+	0.983999i
$344$	360.538	−	208.157i	1.04807	−	0.605106i
$345$	−40.0658	−	31.8164i	−0.116133	−	0.0922215i
$346$	31.4236	+	54.4273i	0.0908198	+	0.157304i
$347$	−527.606	+	304.613i	−1.52048	+	0.877848i	−0.520770	+	0.853697i	$0.674355\pi$
$347$	−527.606	+	304.613i	−1.52048	+	0.877848i	−0.999708	+	0.0241511i	$0.992312\pi$
$348$	26.7944	+	67.8591i	0.0769955	+	0.194997i
$349$	66.8442	+	115.778i	0.191531	+	0.331741i	0.945758	−	0.324873i	$-0.105322\pi$
$349$	66.8442	+	115.778i	0.191531	+	0.331741i	−0.754227	+	0.656614i	$0.771988\pi$
$350$	−183.458	+	278.006i	−0.524166	+	0.794302i
$351$	−104.190	−	150.805i	−0.296837	−	0.429643i
$352$	192.659	+	333.696i	0.547327	+	0.947999i
$353$		−	603.362i		−	1.70924i	−0.519252	−	0.854621i	$-0.673790\pi$
$353$		−	603.362i		−	1.70924i	0.519252	−	0.854621i	$-0.326210\pi$
$354$	−312.543	−	248.191i	−0.882888	−	0.701105i
$355$	16.7366			0.0471452
$356$	−9.58209	−	5.53222i	−0.0269160	−	0.0155399i
$357$	142.802	−	46.7456i	0.400004	−	0.130940i
$358$	−121.519	−	210.477i	−0.339438	−	0.587924i
$359$	−166.585	+	96.1780i	−0.464026	+	0.267905i	−0.713736	−	0.700415i	$-0.752998\pi$
$359$	−166.585	+	96.1780i	−0.464026	+	0.267905i	0.249710	+	0.968321i	$0.419665\pi$
$360$	131.011	+	563.273i	0.363919	+	1.56465i
$361$	−299.506	+	518.760i	−0.829658	+	1.43701i
$362$	145.219	+	83.8423i	0.401158	+	0.231609i
$363$	−73.4217	−	58.3045i	−0.202264	−	0.160618i
$364$	6.65780	−	111.371i	0.0182907	−	0.305963i
$365$	480.520	+	277.428i	1.31649	+	0.760078i
$366$	−34.0929	−	5.06677i	−0.0931500	−	0.0138436i
$367$	186.792			0.508971			0.254485	−	0.967077i	$-0.418094\pi$
$367$	186.792			0.508971			0.254485	+	0.967077i	$0.418094\pi$
$368$	2.05699	+	1.18760i	0.00558964	+	0.00322718i
$369$	−84.6565	+	278.524i	−0.229421	+	0.754809i
$370$	−49.8426			−0.134710
$371$	227.460	−	344.685i	0.613100	−	0.929070i
$372$	132.298	−	52.2383i	0.355639	−	0.140425i
$373$	−361.251			−0.968500			−0.484250	−	0.874930i	$-0.660908\pi$
$373$	−361.251			−0.968500			−0.484250	+	0.874930i	$0.660908\pi$
$374$	98.2798	−	56.7419i	0.262780	−	0.151716i
$375$	176.579	−	222.363i	0.470877	−	0.592967i
$376$	87.3213	−	151.245i	0.232238	−	0.402247i
$377$		−	70.3205i		−	0.186526i
$378$	125.918	+	207.759i	0.333117	+	0.549626i
$379$	384.791			1.01528			0.507640	−	0.861569i	$-0.330518\pi$
$379$	384.791			1.01528			0.507640	+	0.861569i	$0.330518\pi$
$380$	−496.121	−	286.435i	−1.30558	−	0.753777i
$381$	−336.583	−	267.282i	−0.883421	−	0.701528i
$382$	73.1272	+	126.660i	0.191432	+	0.331571i
$383$		−	422.377i		−	1.10281i	−0.834237	−	0.551406i	$-0.814091\pi$
$383$		−	422.377i		−	1.10281i	0.834237	−	0.551406i	$-0.185909\pi$
$384$	74.5643	+	188.840i	0.194178	+	0.491772i
$385$	40.5906	−	678.994i	0.105430	−	1.76362i
$386$		−	337.717i		−	0.874916i
$387$	−335.330	+	313.725i	−0.866485	+	0.810659i
$388$	−110.368	+	191.164i	−0.284455	+	0.492690i
$389$			719.166i			1.84876i	0.381478	+	0.924378i	$0.375415\pi$
$389$			719.166i			1.84876i	−0.381478	+	0.924378i	$0.624585\pi$
$390$	30.3061	−	203.921i	0.0777079	−	0.522875i
$391$	−7.74736	+	13.4188i	−0.0198142	+	0.0343192i
$392$	−47.6313	+	396.961i	−0.121508	+	1.01266i
$393$	−332.916	+	419.234i	−0.847114	+	1.06675i
$394$	118.839	−	205.835i	0.301621	−	0.522423i
$395$	986.739	+	569.694i	2.49807	+	1.44226i
$396$	−178.124	−	190.391i	−0.449809	−	0.480785i
$397$	−77.9179	−	134.958i	−0.196267	−	0.339944i	0.751048	−	0.660247i	$-0.229548\pi$
$397$	−77.9179	−	134.958i	−0.196267	−	0.339944i	−0.947315	+	0.320303i	$0.896215\pi$
$398$	−273.559	+	157.939i	−0.687334	+	0.396832i
$399$	−636.742	−	133.885i	−1.59584	−	0.335551i
$400$	−20.3013	+	35.1630i	−0.0507534	+	0.0879074i
$401$		−	131.150i		−	0.327057i	−0.986539	−	0.163528i	$-0.947712\pi$
$401$		−	131.150i		−	0.327057i	0.986539	−	0.163528i	$-0.0522875\pi$
$402$	217.501	−	273.894i	0.541046	−	0.681329i
$403$	−137.096			−0.340190
$404$	−13.7263	+	7.92488i	−0.0339760	+	0.0196160i
$405$	−281.503	−	572.416i	−0.695069	−	1.41337i
$406$	−5.56172	+	93.0356i	−0.0136988	+	0.229152i
$407$	52.6160	−	30.3779i	0.129278	−	0.0746385i
$408$	162.905	−	64.3235i	0.399276	−	0.157656i
$409$	−106.085	−	183.745i	−0.259377	−	0.449254i	0.706698	−	0.707515i	$-0.250184\pi$
$409$	−106.085	−	183.745i	−0.259377	−	0.449254i	−0.966075	+	0.258261i	$0.916850\pi$
$410$	−283.553	+	163.709i	−0.691592	+	0.399291i
$411$	134.980	−	169.978i	0.328419	−	0.413571i
$412$	−83.9748	−	145.449i	−0.203822	−	0.353031i
$413$	324.153	+	647.915i	0.784875	+	1.56880i
$414$	−23.9693	−	7.28538i	−0.0578968	−	0.0175975i
$415$	−61.8605	−	107.145i	−0.149061	−	0.258182i
$416$		−	211.996i		−	0.509607i
$417$	541.251	−	213.715i	1.29796	−	0.512506i
$418$	−491.421			−1.17565
$419$	−641.691	−	370.481i	−1.53148	−	0.884202i	−0.999294	−	0.0375766i	$-0.988036\pi$
$419$	−641.691	−	370.481i	−1.53148	−	0.884202i	−0.532189	−	0.846625i	$-0.678631\pi$
$420$	79.8934	−	379.965i	0.190222	−	0.904678i
$421$	281.034	+	486.765i	0.667539	+	1.15621i	0.978590	+	0.205819i	$0.0659857\pi$
$421$	281.034	+	486.765i	0.667539	+	1.15621i	−0.311051	+	0.950393i	$0.600681\pi$
$422$	−51.5077	+	29.7380i	−0.122056	+	0.0704692i
$423$	−56.0204	+	184.310i	−0.132436	+	0.435722i
$424$	240.685	−	416.878i	0.567652	−	0.983203i
$425$	−229.387	−	132.437i	−0.539734	−	0.311615i
$426$	7.62252	−	3.00978i	0.0178932	−	0.00706521i
$427$	52.2219	+	34.4616i	0.122299	+	0.0807063i
$428$	−33.4793	−	19.3293i	−0.0782227	−	0.0451619i
$429$	92.2926	+	233.739i	0.215134	+	0.544846i
$430$	−516.487			−1.20113
$431$	−290.022	−	167.444i	−0.672904	−	0.388501i	0.124272	−	0.992248i	$-0.460340\pi$
$431$	−290.022	−	167.444i	−0.672904	−	0.388501i	−0.797176	+	0.603747i	$0.793674\pi$
$432$	16.8333	+	24.3646i	0.0389660	+	0.0563996i
$433$	108.934			0.251579			0.125789	−	0.992057i	$-0.459854\pi$
$433$	108.934			0.251579			0.125789	+	0.992057i	$0.459854\pi$
$434$	181.382	+	10.8431i	0.417930	+	0.0249841i
$435$	35.9747	−	242.064i	0.0827005	−	0.556469i
$436$	180.989			0.415113
$437$	58.1079	−	33.5486i	0.132970	−	0.0767702i
$438$	268.739	+	39.9392i	0.613560	+	0.0911853i
$439$	−291.989	+	505.739i	−0.665122	+	1.15202i	0.314130	+	0.949380i	$0.398287\pi$
$439$	−291.989	+	505.739i	−0.665122	+	1.15202i	−0.979252	+	0.202645i	$0.935046\pi$
$440$		−	792.863i		−	1.80196i
$441$	−48.0205	−	438.378i	−0.108890	−	0.994054i
$442$	−62.4370			−0.141260
$443$	−496.904	−	286.888i	−1.12168	−	0.647602i	−0.179851	−	0.983694i	$-0.557561\pi$
$443$	−496.904	−	286.888i	−1.12168	−	0.647602i	−0.941829	+	0.336092i	$0.890895\pi$
$444$	32.2569	−	12.7368i	0.0726507	−	0.0286864i
$445$	18.5568	+	32.1413i	0.0417007	+	0.0722277i
$446$			143.669i			0.322129i
$447$	121.559	−	153.077i	0.271944	−	0.342453i
$448$	−18.5997	+	311.132i	−0.0415171	+	0.694492i
$449$			274.994i			0.612459i	0.951958	+	0.306229i	$0.0990675\pi$
$449$			274.994i			0.612459i	−0.951958	+	0.306229i	$0.900933\pi$
$450$	124.539	−	409.740i	0.276754	−	0.910534i
$451$	199.554	−	345.637i	0.442469	−	0.766379i
$452$		−	14.7828i		−	0.0327054i
$453$	384.433	+	305.280i	0.848637	+	0.673907i
$454$	−164.937	+	285.679i	−0.363297	+	0.629249i
$455$	−206.126	+	312.357i	−0.453025	+	0.686498i
$456$	−750.191	−	111.491i	−1.64516	−	0.244497i
$457$	37.2674	−	64.5490i	0.0815479	−	0.141245i	−0.822367	−	0.568957i	$-0.807347\pi$
$457$	37.2674	−	64.5490i	0.0815479	−	0.141245i	0.903915	+	0.427712i	$0.140680\pi$
$458$	171.706	+	99.1344i	0.374903	+	0.216451i
$459$	−158.943	+	109.813i	−0.346282	+	0.239244i
$460$	20.0195	+	34.6748i	0.0435207	+	0.0753801i
$461$	−602.709	+	347.974i	−1.30740	+	0.754825i	−0.981661	−	0.190636i	$-0.938945\pi$
$461$	−602.709	+	347.974i	−1.30740	+	0.754825i	−0.325735	+	0.945461i	$0.605612\pi$
$462$	−103.619	−	316.541i	−0.224283	−	0.685154i
$463$	336.870	−	583.475i	0.727580	−	1.26021i	−0.230323	−	0.973114i	$-0.573978\pi$
$463$	336.870	−	583.475i	0.727580	−	1.26021i	0.957903	−	0.287092i	$-0.0926884\pi$
$464$			11.3613i			0.0244855i
$465$	−471.926	−	70.1361i	−1.01490	−	0.150830i
$466$	474.054			1.01728
$467$	−280.524	+	161.960i	−0.600693	+	0.346810i	−0.769314	−	0.638871i	$-0.779402\pi$
$467$	−280.524	+	161.960i	−0.600693	+	0.346810i	0.168621	+	0.985681i	$0.446069\pi$
$468$	32.4966	+	139.717i	0.0694371	+	0.298541i
$469$	−567.796	+	284.069i	−1.21065	+	0.605692i
$470$	−187.638	+	108.333i	−0.399229	+	0.230495i
$471$	−75.4728	+	507.836i	−0.160240	+	1.07821i
$472$	422.234	+	731.331i	0.894564	+	1.54943i
$473$	545.226	−	314.786i	1.15270	−	0.665510i
$474$	551.852	+	82.0143i	1.16424	+	0.173026i
$475$	573.493	+	993.319i	1.20735	+	2.09120i
$476$	−117.381	−	7.01711i	−0.246599	−	0.0147418i
$477$	−154.410	+	508.016i	−0.323710	+	1.06502i
$478$	127.981	+	221.669i	0.267742	+	0.463743i
$479$			28.7437i			0.0600077i	0.999550	+	0.0300038i	$0.00955196\pi$
$479$			28.7437i			0.0600077i	−0.999550	+	0.0300038i	$0.990448\pi$
$480$	108.454	−	729.754i	0.225945	−	1.52032i
$481$	−33.4269			−0.0694946
$482$	217.222	+	125.413i	0.450669	+	0.260194i
$483$	33.8621	+	30.3554i	0.0701079	+	0.0628476i
$484$	36.6863	+	63.5426i	0.0757982	+	0.131286i
$485$	641.224	−	370.211i	1.32211	−	0.763321i
$486$	−231.147	−	210.078i	−0.475612	−	0.432260i
$487$	438.026	−	758.683i	0.899437	−	1.55787i	0.0712210	−	0.997461i	$-0.477310\pi$
$487$	438.026	−	758.683i	0.899437	−	1.55787i	0.828216	−	0.560409i	$-0.189356\pi$
$488$	63.1595	+	36.4652i	0.129425	+	0.0747237i
$489$	29.4439	−	198.120i	0.0602124	−	0.405152i
$490$	297.415	−	396.952i	0.606969	−	0.810107i
$491$	−52.5833	−	30.3590i	−0.107094	−	0.0618310i	0.445496	−	0.895284i	$-0.353027\pi$
$491$	−52.5833	−	30.3590i	−0.107094	−	0.0618310i	−0.552591	+	0.833453i	$0.686361\pi$
$492$	141.674	−	178.407i	0.287955	−	0.362617i
$493$	−74.1156			−0.150336
$494$	234.150	+	135.186i	0.473987	+	0.273656i
$495$	198.122	+	851.813i	0.400246	+	1.72084i
$496$	22.1499			0.0446570
$497$	−14.8501	−	0.887745i	−0.0298794	−	0.00178621i
$498$	−47.4421	−	37.6740i	−0.0952652	−	0.0756505i
$499$	699.521			1.40185			0.700923	−	0.713237i	$-0.252772\pi$
$499$	699.521			1.40185			0.700923	+	0.713237i	$0.252772\pi$
$500$	−192.443	+	111.107i	−0.384886	+	0.222214i
$501$	15.5859	+	39.4726i	0.0311096	+	0.0787877i
$502$	−125.087	+	216.658i	−0.249178	+	0.431589i
$503$			136.689i			0.271747i	0.990726	+	0.135873i	$0.0433840\pi$
$503$			136.689i			0.271747i	−0.990726	+	0.135873i	$0.956616\pi$
$504$	−86.3664	−	506.732i	−0.171362	−	1.00542i
$505$	53.1651			0.105277
$506$	29.7449	+	17.1732i	0.0587843	+	0.0339391i
$507$	−54.2053	+	364.733i	−0.106914	+	0.719394i
$508$	168.179	+	291.295i	0.331061	+	0.573415i
$509$			172.803i			0.339495i	0.985488	+	0.169747i	$0.0542952\pi$
$509$			172.803i			0.339495i	−0.985488	+	0.169747i	$0.945705\pi$
$510$	−214.927	−	31.9417i	−0.421425	−	0.0626308i
$511$	−411.642	−	271.646i	−0.805562	−	0.531596i
$512$			70.0483i			0.136813i
$513$	833.828	−	67.6785i	1.62540	−	0.131927i
$514$	257.815	−	446.549i	0.501586	−	0.868773i
$515$			563.356i			1.09389i
$516$	334.257	−	131.983i	0.647785	−	0.255780i
$517$	132.052	−	228.721i	0.255420	−	0.442401i
$518$	44.2246	+	2.64377i	0.0853756	+	0.00510380i
$519$	53.8701	+	136.431i	0.103796	+	0.262872i
$520$	−218.111	+	377.779i	−0.419444	+	0.726498i
$521$	−481.965	−	278.263i	−0.925077	−	0.534094i	−0.0398260	−	0.999207i	$-0.512680\pi$
$521$	−481.965	−	278.263i	−0.925077	−	0.534094i	−0.885251	+	0.465113i	$0.846014\pi$
$522$	−27.1466	−	116.715i	−0.0520050	−	0.223593i
$523$	−155.825	−	269.897i	−0.297945	−	0.516055i	0.677721	−	0.735319i	$-0.262968\pi$
$523$	−155.825	−	269.897i	−0.297945	−	0.516055i	−0.975666	+	0.219264i	$0.929634\pi$
$524$	362.825	−	209.477i	0.692414	−	0.399766i
$525$	−518.907	+	578.853i	−0.988395	+	1.10258i
$526$	187.858	−	325.380i	0.357144	−	0.618592i
$527$			144.495i			0.274185i
$528$	−14.9112	−	37.7638i	−0.0282409	−	0.0715223i
$529$	524.310			0.991135
$530$	−517.187	+	298.598i	−0.975825	+	0.563393i
$531$	−636.374	−	680.198i	−1.19844	−	1.28098i
$532$	425.007	+	280.465i	0.798884	+	0.527189i
$533$	−190.164	+	109.791i	−0.356781	+	0.205988i
$534$	14.2316	+	11.3014i	0.0266509	+	0.0211636i
$535$	64.8365	+	112.300i	0.121190	+	0.209907i
$536$	−640.897	+	370.022i	−1.19570	+	0.690339i
$537$	−208.322	−	527.592i	−0.387936	−	0.982481i
$538$	−211.667	−	366.618i	−0.393433	−	0.681446i
$539$	−72.0308	+	600.307i	−0.133638	+	1.11374i
$540$	40.3859	+	497.572i	0.0747888	+	0.921430i
$541$	−205.505	−	355.946i	−0.379862	−	0.657941i	0.611180	−	0.791492i	$-0.290695\pi$
$541$	−205.505	−	355.946i	−0.379862	−	0.657941i	−0.991042	+	0.133551i	$0.957362\pi$
$542$			65.3258i			0.120527i
$543$	306.483	+	243.380i	0.564426	+	0.448213i
$544$	−223.438			−0.410731
$545$	−525.759	−	303.547i	−0.964696	−	0.556967i
$546$	−37.7066	+	179.328i	−0.0690596	+	0.328440i
$547$	205.309	+	355.605i	0.375336	+	0.650101i	0.990377	−	0.138394i	$-0.0441940\pi$
$547$	205.309	+	355.605i	0.375336	+	0.650101i	−0.615041	+	0.788495i	$0.710861\pi$
$548$	−147.107	+	84.9321i	−0.268443	+	0.154986i
$549$	−76.9675	−	23.3940i	−0.140196	−	0.0426120i
$550$	−293.566	+	508.471i	−0.533756	+	0.924492i
$551$	277.946	+	160.472i	0.504440	+	0.291238i
$552$	41.5116	+	32.9645i	0.0752021	+	0.0597183i
$553$	−845.300	−	557.819i	−1.52857	−	1.00871i
$554$	−14.7643	−	8.52415i	−0.0266503	−	0.0153865i
$555$	−115.065	−	17.1006i	−0.207325	−	0.0308119i
$556$	−455.404			−0.819071
$557$	−539.330	−	311.382i	−0.968276	−	0.559034i	−0.0695656	−	0.997577i	$-0.522161\pi$
$557$	−539.330	−	311.382i	−0.968276	−	0.559034i	−0.898710	+	0.438543i	$0.855495\pi$
$558$	−227.548	+	52.9249i	−0.407791	+	0.0948475i
$559$	−346.381			−0.619644
$560$	33.3026	−	50.4656i	0.0594690	−	0.0901172i
$561$	246.354	−	97.2736i	0.439133	−	0.173393i
$562$	−557.770			−0.992474
$563$	547.707	−	316.219i	0.972836	−	0.561667i	0.0727367	−	0.997351i	$-0.476827\pi$
$563$	547.707	−	316.219i	0.972836	−	0.561667i	0.900100	+	0.435684i	$0.143493\pi$
$564$	93.7511	−	118.059i	0.166225	−	0.209324i
$565$	−24.7932	+	42.9430i	−0.0438817	+	0.0760053i
$566$		−	495.472i		−	0.875391i
$567$	219.411	+	522.827i	0.386968	+	0.922093i
$568$	−17.3405			−0.0305290
$569$	953.554	+	550.535i	1.67584	+	0.967548i	0.964265	+	0.264939i	$0.0853519\pi$
$569$	953.554	+	550.535i	1.67584	+	0.967548i	0.711577	+	0.702608i	$0.247981\pi$
$570$	736.853	+	585.138i	1.29272	+	1.02656i
$571$	319.146	+	552.777i	0.558924	+	0.968086i	0.997587	+	0.0694335i	$0.0221192\pi$
$571$	319.146	+	552.777i	0.558924	+	0.968086i	−0.438662	+	0.898652i	$0.644548\pi$
$572$		−	196.666i		−	0.343821i
$573$	125.363	+	317.493i	0.218784	+	0.554089i
$574$	260.275	−	130.216i	0.453441	−	0.226858i
$575$		−	80.1651i		−	0.139418i
$576$	−90.7845	−	390.323i	−0.157612	−	0.677644i
$577$	12.4886	−	21.6309i	0.0216441	−	0.0374886i	−0.855000	−	0.518627i	$-0.826443\pi$
$577$	12.4886	−	21.6309i	0.0216441	−	0.0374886i	0.876645	+	0.481139i	$0.159777\pi$
$578$		−	305.670i		−	0.528841i
$579$	115.868	−	779.645i	0.200118	−	1.34654i
$580$	−95.7590	+	165.860i	−0.165102	+	0.285965i
$581$	49.2045	+	98.3497i	0.0846894	+	0.169277i
$582$	225.464	−	283.922i	0.387395	−	0.487839i
$583$	363.977	−	630.426i	0.624317	−	1.08135i
$584$	−497.859	−	287.439i	−0.852498	−	0.492190i
$585$	139.928	−	460.369i	0.239192	−	0.786955i
$586$	124.154	+	215.040i	0.211866	+	0.366963i
$587$	−192.680	+	111.244i	−0.328246	+	0.189513i	−0.655062	−	0.755575i	$-0.727358\pi$
$587$	−192.680	+	111.244i	−0.328246	+	0.189513i	0.326816	+	0.945088i	$0.394024\pi$
$588$	−91.0423	+	332.899i	−0.154834	+	0.566154i
$589$	312.856	−	541.883i	0.531165	−	0.920004i
$590$		−	1047.67i		−	1.77570i
$591$	344.968	−	434.411i	0.583702	−	0.735044i
$592$	5.40059			0.00912261
$593$	326.783	−	188.668i	0.551068	−	0.318159i	−0.198485	−	0.980104i	$-0.563602\pi$
$593$	326.783	−	188.668i	0.551068	−	0.318159i	0.749553	+	0.661945i	$0.230269\pi$
$594$	243.417	+	352.322i	0.409793	+	0.593135i
$595$	329.214	+	217.251i	0.553302	+	0.365128i
$596$	−132.480	+	76.4872i	−0.222281	+	0.128334i
$597$	−685.718	+	270.758i	−1.14861	+	0.453531i
$598$	−9.44844	−	16.3652i	−0.0158001	−	0.0273665i
$599$	729.103	−	420.948i	1.21720	−	0.702751i	0.252882	−	0.967497i	$-0.418621\pi$
$599$	729.103	−	420.948i	1.21720	−	0.702751i	0.964318	+	0.264746i	$0.0852882\pi$
$600$	−563.509	+	709.615i	−0.939181	+	1.18269i
$601$	−348.065	−	602.867i	−0.579144	−	1.00311i	−0.995578	−	0.0939405i	$-0.970054\pi$
$601$	−348.065	−	602.867i	−0.579144	−	1.00311i	0.416434	−	0.909166i	$-0.363280\pi$
$602$	458.270	+	27.3956i	0.761246	+	0.0455077i
$603$	596.086	−	557.682i	0.988535	−	0.924845i
$604$	−192.088	−	332.706i	−0.318027	−	0.550838i
$605$		−	246.115i		−	0.406801i
$606$	24.2136	−	9.56082i	0.0399564	−	0.0157769i
$607$	−757.947			−1.24868			−0.624338	−	0.781154i	$-0.714631\pi$
$607$	−757.947			−1.24868			−0.624338	+	0.781154i	$0.714631\pi$
$608$	837.930	+	483.779i	1.37817	+	0.795689i
$609$	−44.7594	+	212.871i	−0.0734966	+	0.349542i
$610$	−45.2395	−	78.3571i	−0.0741631	−	0.128454i
$611$	−125.839	+	72.6532i	−0.205956	+	0.118909i
$612$	147.257	−	34.2504i	0.240617	−	0.0559647i
$613$	−110.823	+	191.951i	−0.180788	+	0.313134i	−0.942149	−	0.335194i	$-0.891198\pi$
$613$	−110.823	+	191.951i	−0.180788	+	0.313134i	0.761361	+	0.648328i	$0.224532\pi$
$614$	18.3389	+	10.5880i	0.0298680	+	0.0172443i
$615$	−710.769	+	280.650i	−1.15572	+	0.456341i
$616$	−42.0553	+	703.494i	−0.0682716	+	1.14204i
$617$	713.225	+	411.781i	1.15596	+	0.667392i	0.950332	−	0.311239i	$-0.100744\pi$
$617$	713.225	+	411.781i	1.15596	+	0.667392i	0.205625	+	0.978631i	$0.434077\pi$
$618$	101.310	+	256.576i	0.163932	+	0.415171i
$619$	−156.620			−0.253021			−0.126510	−	0.991965i	$-0.540378\pi$
$619$	−156.620			−0.253021			−0.126510	+	0.991965i	$0.540378\pi$
$620$	323.359	+	186.691i	0.521547	+	0.301115i
$621$	−52.8352	−	25.0425i	−0.0850808	−	0.0403261i
$622$	−623.733			−1.00279
$623$	−14.7603	−	29.5028i	−0.0236923	−	0.0473560i
$624$	−3.28375	+	22.0954i	−0.00526242	+	0.0354093i
$625$	−180.089			−0.288142
$626$	−457.227	+	263.980i	−0.730394	+	0.421693i
$627$	−1134.48	−	168.603i	−1.80938	−	0.268904i
$628$	200.897	−	347.963i	0.319899	−	0.554082i
$629$			35.2309i			0.0560110i
$630$	−221.538	+	598.012i	−0.351648	+	0.949225i
$631$	−857.637			−1.35917			−0.679586	−	0.733596i	$-0.737840\pi$
$631$	−857.637			−1.35917			−0.679586	+	0.733596i	$0.737840\pi$
$632$	−1022.34	−	590.251i	−1.61763	−	0.933941i
$633$	−129.112	+	50.9804i	−0.203969	+	0.0805378i
$634$	84.0707	+	145.615i	0.132604	+	0.229676i
$635$		−	1128.25i		−	1.77677i
$636$	258.407	−	325.407i	0.406300	−	0.511646i
$637$	199.461	−	266.216i	0.313125	−	0.417921i
$638$			164.288i			0.257505i
$639$	18.6298	−	4.33306i	0.0291546	−	0.00678101i
$640$	−266.481	+	461.559i	−0.416377	+	0.721186i
$641$		−	128.273i		−	0.200115i	−0.994982	−	0.100057i	$-0.968097\pi$
$641$		−	128.273i		−	0.200115i	0.994982	−	0.100057i	$-0.0319026\pi$
$642$	49.7245	+	39.4864i	0.0774524	+	0.0615053i
$643$	27.7356	−	48.0395i	0.0431347	−	0.0747116i	−0.843652	−	0.536890i	$-0.819599\pi$
$643$	27.7356	−	48.0395i	0.0431347	−	0.0747116i	0.886787	+	0.462179i	$0.152932\pi$
$644$	−15.9238	−	31.8283i	−0.0247263	−	0.0494228i
$645$	−1192.35	−	177.203i	−1.84860	−	0.274733i
$646$	142.482	−	246.786i	0.220561	−	0.382022i
$647$	410.064	+	236.751i	0.633794	+	0.365921i	0.782220	−	0.623003i	$-0.214087\pi$
$647$	410.064	+	236.751i	0.633794	+	0.365921i	−0.148426	+	0.988923i	$0.547421\pi$
$648$	291.661	+	593.071i	0.450094	+	0.915233i
$649$	638.527	+	1105.96i	0.983862	+	1.70410i
$650$	279.753	−	161.515i	0.430389	−	0.248485i
$651$	415.012	+	87.2627i	0.637500	+	0.134044i
$652$	−78.3749	+	135.749i	−0.120207	+	0.208205i
$653$			482.186i			0.738416i	0.929347	+	0.369208i	$0.120371\pi$
$653$			482.186i			0.738416i	−0.929347	+	0.369208i	$0.879629\pi$
$654$	−294.040	−	43.6993i	−0.449603	−	0.0668185i
$655$	−1405.30			−2.14550
$656$	30.7237	−	17.7383i	0.0468349	−	0.0270402i
$657$	606.701	+	184.405i	0.923442	+	0.280677i
$658$	172.234	−	86.1691i	0.261754	−	0.130956i
$659$	900.528	−	519.920i	1.36651	−	0.788953i	0.376027	−	0.926609i	$-0.377290\pi$
$659$	900.528	−	519.920i	1.36651	−	0.788953i	0.990480	+	0.137655i	$0.0439566\pi$
$660$	100.611	−	676.982i	0.152441	−	1.02573i
$661$	−173.864	−	301.141i	−0.263031	−	0.455584i	0.704015	−	0.710186i	$-0.251389\pi$
$661$	−173.864	−	301.141i	−0.263031	−	0.455584i	−0.967046	+	0.254602i	$0.918056\pi$
$662$	268.209	−	154.850i	0.405149	−	0.233913i
$663$	−144.140	−	21.4217i	−0.217406	−	0.0323102i
$664$	64.0926	+	111.012i	0.0965251	+	0.167186i
$665$	−764.227	−	1527.53i	−1.14921	−	2.29704i
$666$	−55.4807	+	12.9042i	−0.0833044	+	0.0193756i
$667$	−11.2157	−	19.4262i	−0.0168152	−	0.0291247i
$668$		−	33.2119i		−	0.0497184i
$669$	−49.2919	+	331.671i	−0.0736799	+	0.495772i
$670$	918.114			1.37032
$671$	95.5134	+	55.1447i	0.142345	+	0.0821829i
$672$	−134.937	+	641.746i	−0.200799	+	0.954980i
$673$	−123.764	−	214.366i	−0.183899	−	0.318523i	0.759306	−	0.650734i	$-0.225539\pi$
$673$	−123.764	−	214.366i	−0.183899	−	0.318523i	−0.943205	+	0.332211i	$0.892205\pi$
$674$	−333.145	+	192.341i	−0.494281	+	0.285373i
$675$	428.086	−	903.187i	0.634202	−	1.33805i
$676$	144.286	−	249.911i	0.213441	−	0.369690i
$677$	574.625	+	331.760i	0.848782	+	0.490045i	0.860240	−	0.509890i	$-0.170314\pi$
$677$	574.625	+	331.760i	0.848782	+	0.490045i	−0.0114577	+	0.999934i	$0.503647\pi$
$678$	−3.56927	+	24.0166i	−0.00526441	+	0.0354228i
$679$	−588.584	+	294.470i	−0.866839	+	0.433682i
$680$	398.167	+	229.882i	0.585540	+	0.338062i
$681$	−478.783	+	602.922i	−0.703059	+	0.885348i
$682$	320.296			0.469642
$683$	−54.4337	−	31.4273i	−0.0796979	−	0.0460136i	0.459621	−	0.888115i	$-0.347985\pi$
$683$	−54.4337	−	31.4273i	−0.0796979	−	0.0460136i	−0.539319	+	0.842101i	$0.681318\pi$
$684$	−626.398	−	190.392i	−0.915787	−	0.278350i
$685$	569.778			0.831793
$686$	−284.946	+	336.434i	−0.415374	+	0.490428i
$687$	362.383	+	287.770i	0.527486	+	0.418879i
$688$	55.9628			0.0813412
$689$	−346.851	+	200.255i	−0.503412	+	0.290645i
$690$	−24.1522	−	61.1674i	−0.0350032	−	0.0886484i
$691$	163.978	−	284.018i	0.237305	−	0.411024i	−0.722635	−	0.691230i	$-0.757069\pi$
$691$	163.978	−	284.018i	0.237305	−	0.411024i	0.959940	+	0.280205i	$0.0904026\pi$
$692$		−	114.791i		−	0.165884i
$693$	−130.608	−	766.309i	−0.188468	−	1.10578i
$694$	−783.092			−1.12838
$695$	1322.91	+	763.783i	1.90347	+	1.09897i
$696$	−37.2728	+	250.798i	−0.0535529	+	0.360343i
$697$	115.717	+	200.427i	0.166021	+	0.287557i
$698$			171.841i			0.246191i
$699$	1094.39	+	162.644i	1.56565	+	0.232681i
$700$	544.086	−	272.207i	0.777266	−	0.388868i
$701$		−	93.8066i		−	0.133818i	−0.997759	−	0.0669091i	$-0.978686\pi$
$701$		−	93.8066i		−	0.133818i	0.997759	−	0.0669091i	$-0.0213138\pi$
$702$	−19.0606	−	234.835i	−0.0271518	−	0.334522i
$703$	76.2807	−	132.122i	0.108507	−	0.187940i
$704$			549.418i			0.780424i
$705$	−470.343	+	185.717i	−0.667153	+	0.263428i
$706$	387.777	−	671.650i	0.549260	−	0.951345i
$707$	−47.1725	−	2.82000i	−0.0667220	−	0.00398868i
$708$	267.720	+	678.023i	0.378135	+	0.957659i
$709$	−545.930	+	945.578i	−0.770000	+	1.33368i	0.167563	+	0.985861i	$0.446410\pi$
$709$	−545.930	+	945.578i	−0.770000	+	1.33368i	−0.937562	+	0.347817i	$0.886923\pi$
$710$	18.6308	+	10.7565i	0.0262405	+	0.0151500i
$711$	1245.85	+	378.672i	1.75225	+	0.532590i
$712$	−19.2264	−	33.3011i	−0.0270034	−	0.0467712i
$713$	−37.8732	+	21.8661i	−0.0531181	+	0.0306678i
$714$	189.007	+	39.7415i	0.264715	+	0.0556604i
$715$	−329.839	+	571.298i	−0.461314	+	0.799019i
$716$			443.911i			0.619988i
$717$	219.400	+	555.648i	0.305997	+	0.774962i
$718$	−247.252			−0.344362
$719$	−158.261	+	91.3719i	−0.220112	+	0.127082i	−0.606002	−	0.795463i	$-0.707228\pi$
$719$	−158.261	+	91.3719i	−0.220112	+	0.127082i	0.385890	+	0.922545i	$0.373894\pi$
$720$	−22.6073	+	74.3791i	−0.0313990	+	0.103304i
$721$	29.8817	−	499.856i	0.0414448	−	0.693282i
$722$	−666.808	+	384.982i	−0.923557	+	0.533216i
$723$	458.445	+	364.053i	0.634087	+	0.503531i
$724$	−153.139	−	265.245i	−0.211518	−	0.366360i
$725$	332.080	−	191.726i	0.458041	−	0.264450i
$726$	−44.2595	−	112.091i	−0.0609635	−	0.154395i
$727$	−186.677	−	323.334i	−0.256777	−	0.444750i	0.708600	−	0.705611i	$-0.249327\pi$
$727$	−186.677	−	323.334i	−0.256777	−	0.444750i	−0.965377	+	0.260860i	$0.915994\pi$
$728$	213.564	−	323.628i	0.293358	−	0.444544i
$729$	−461.544	−	564.286i	−0.633119	−	0.774055i
$730$	356.603	+	617.654i	0.488497	+	0.846102i
$731$			365.075i			0.499419i
$732$	49.3011	+	39.1502i	0.0673513	+	0.0534839i
$733$	694.476			0.947443			0.473722	−	0.880675i	$-0.342910\pi$
$733$	694.476			0.947443			0.473722	+	0.880675i	$0.342910\pi$
$734$	207.933	+	120.050i	0.283288	+	0.163556i
$735$	822.794	−	814.352i	1.11945	−	1.10796i
$736$	−33.8123	−	58.5645i	−0.0459406	−	0.0795714i
$737$	−969.200	+	559.568i	−1.31506	+	0.759251i
$738$	−273.244	+	255.639i	−0.370249	+	0.346394i
$739$	143.041	−	247.755i	0.193560	−	0.335256i	−0.752867	−	0.658172i	$-0.771330\pi$
$739$	143.041	−	247.755i	0.193560	−	0.335256i	0.946428	+	0.322916i	$0.104663\pi$
$740$	78.8415	+	45.5192i	0.106543	+	0.0615124i
$741$	494.170	+	392.422i	0.666895	+	0.529584i
$742$	474.730	−	237.509i	0.639798	−	0.320092i
$743$	−700.673	−	404.534i	−0.943033	−	0.544460i	−0.0521232	−	0.998641i	$-0.516599\pi$
$743$	−700.673	−	404.534i	−0.943033	−	0.544460i	−0.890910	+	0.454180i	$0.849932\pi$
$744$	488.955	+	72.6669i	0.657198	+	0.0976706i
$745$	513.124			0.688757
$746$	−402.136	−	232.174i	−0.539057	−	0.311225i
$747$	−96.5978	−	103.250i	−0.129314	−	0.138220i
$748$	−207.280			−0.277112
$749$	−51.5717	−	103.081i	−0.0688541	−	0.137625i
$750$	339.475	−	134.043i	0.452633	−	0.178724i
$751$	−263.348			−0.350663			−0.175332	−	0.984509i	$-0.556100\pi$
$751$	−263.348			−0.350663			−0.175332	+	0.984509i	$0.556100\pi$
$752$	20.3311	−	11.7381i	0.0270360	−	0.0156092i
$753$	−363.106	+	457.253i	−0.482213	+	0.607242i
$754$	45.1945	−	78.2792i	0.0599397	−	0.103819i
$755$			1288.65i			1.70682i
$756$	−9.44141	−	443.630i	−0.0124886	−	0.586812i
$757$	946.293			1.25006			0.625028	−	0.780602i	$-0.285087\pi$
$757$	946.293			1.25006			0.625028	+	0.780602i	$0.285087\pi$
$758$	428.341	+	247.303i	0.565094	+	0.326257i
$759$	62.7761	+	49.8508i	0.0827090	+	0.0656796i
$760$	−995.463	−	1724.19i	−1.30982	−	2.26868i
$761$			646.797i			0.849930i	0.905210	+	0.424965i	$0.139714\pi$
$761$			646.797i			0.849930i	−0.905210	+	0.424965i	$0.860286\pi$
$762$	−202.897	−	513.853i	−0.266269	−	0.674347i
$763$	450.397	+	297.220i	0.590297	+	0.389541i
$764$		−	267.136i		−	0.349654i
$765$	−485.215	−	147.479i	−0.634268	−	0.192783i
$766$	271.459	−	470.181i	0.354385	−	0.613814i
$767$		−	702.616i		−	0.916057i
$768$	−116.910	+	786.652i	−0.152226	+	1.02429i
$769$	−212.086	+	367.344i	−0.275795	+	0.477691i	−0.970335	−	0.241763i	$-0.922274\pi$
$769$	−212.086	+	367.344i	−0.275795	+	0.477691i	0.694541	+	0.719454i	$0.255608\pi$
$770$	481.570	−	729.754i	0.625415	−	0.947732i
$771$	748.393	−	942.437i	0.970678	−	1.22236i
$772$	−308.423	+	534.204i	−0.399511	+	0.691974i
$773$	−359.361	−	207.477i	−0.464891	−	0.268405i	0.249208	−	0.968450i	$-0.419830\pi$
$773$	−359.361	−	207.477i	−0.464891	−	0.268405i	−0.714099	+	0.700045i	$0.753163\pi$
$774$	−574.911	+	133.717i	−0.742779	+	0.172762i
$775$	−373.788	−	647.420i	−0.482308	−	0.835381i
$776$	−664.361	+	383.569i	−0.856136	+	0.494290i
$777$	101.188	+	21.2764i	0.130230	+	0.0273828i
$778$	−462.204	+	800.560i	−0.594092	+	1.02900i
$779$		−	1002.18i		−	1.28650i
$780$	−234.171	+	294.887i	−0.300219	+	0.378060i
$781$	−26.2232			−0.0335765
$782$	−17.2484	+	9.95836i	−0.0220568	+	0.0127345i
$783$	−22.6258	−	278.759i	−0.0288963	−	0.356015i
$784$	−32.2257	+	43.0109i	−0.0411042	+	0.0548608i
$785$	−1167.18	+	673.871i	−1.48685	+	0.858434i
$786$	−640.034	+	252.720i	−0.814292	+	0.321526i
$787$	316.288	+	547.827i	0.401891	+	0.696095i	0.993954	−	0.109796i	$-0.0350198\pi$
$787$	316.288	+	547.827i	0.401891	+	0.696095i	−0.592063	+	0.805891i	$0.701686\pi$
$788$	−375.960	+	217.061i	−0.477106	+	0.275458i
$789$	545.319	−	686.709i	0.691152	−	0.870354i
$790$	732.278	+	1268.34i	0.926934	+	1.60550i
$791$	24.2764	−	36.7875i	0.0306907	−	0.0465076i
$792$	−205.271	−	882.550i	−0.259180	−	1.11433i
$793$	−30.3398	−	52.5501i	−0.0382595	−	0.0662674i
$794$		−	200.309i		−	0.252279i
$795$	−1296.41	+	511.892i	−1.63071	+	0.643890i
$796$	576.957			0.724820
$797$	−242.578	−	140.052i	−0.304364	−	0.175724i	0.340038	−	0.940412i	$-0.389560\pi$
$797$	−242.578	−	140.052i	−0.304364	−	0.175724i	−0.644401	+	0.764687i	$0.722893\pi$
$798$	−622.761	−	558.268i	−0.780402	−	0.699584i
$799$	76.5742	+	132.630i	0.0958376	+	0.165996i
$800$	1001.13	−	578.001i	1.25141	−	0.722501i
$801$	28.9772	+	30.9728i	0.0361763	+	0.0386676i
$802$	84.2891	−	145.993i	0.105099	−	0.182036i
$803$	−752.891	−	434.682i	−0.937597	−	0.541322i
$804$	−594.180	+	234.614i	−0.739030	+	0.291809i
$805$	−7.12377	+	119.165i	−0.00884941	+	0.148032i
$806$	−152.613	−	88.1110i	−0.189346	−	0.109319i
$807$	−362.864	−	918.985i	−0.449646	−	1.13877i
$808$	−55.0835			−0.0681726
$809$	−300.584	−	173.543i	−0.371551	−	0.214515i	0.302585	−	0.953122i	$-0.402150\pi$
$809$	−300.584	−	173.543i	−0.371551	−	0.214515i	−0.674136	+	0.738608i	$0.735484\pi$
$810$	54.5251	−	818.121i	0.0673149	−	1.01003i
$811$	101.532			0.125193			0.0625965	−	0.998039i	$-0.480062\pi$
$811$	101.532			0.125193			0.0625965	+	0.998039i	$0.480062\pi$
$812$	93.7630	−	142.085i	0.115472	−	0.174982i
$813$	−22.4128	+	150.809i	−0.0275680	+	0.185497i
$814$	78.0947			0.0959394
$815$	455.346	−	262.894i	0.558707	−	0.322569i
$816$	23.2879	+	3.46097i	0.0285391	+	0.00424138i
$817$	790.447	−	1369.09i	0.967499	−	1.67576i
$818$		−	272.721i		−	0.333400i
$819$	−148.574	+	401.056i	−0.181410	+	0.489690i
$820$	598.035			0.729311
$821$	−471.102	−	271.991i	−0.573815	−	0.331292i	0.184856	−	0.982766i	$-0.440818\pi$
$821$	−471.102	−	271.991i	−0.573815	−	0.331292i	−0.758672	+	0.651473i	$0.774151\pi$
$822$	259.501	−	102.465i	0.315694	−	0.124653i
$823$	218.442	+	378.353i	0.265422	+	0.459724i	0.967674	−	0.252204i	$-0.0811555\pi$
$823$	218.442	+	378.353i	0.265422	+	0.459724i	−0.702252	+	0.711928i	$0.747822\pi$
$824$		−	583.684i		−	0.708354i
$825$	−852.170	+	1073.12i	−1.03293	+	1.30075i
$826$	−55.5706	+	929.577i	−0.0672767	+	1.12540i
$827$		−	571.254i		−	0.690754i	−0.938464	−	0.345377i	$-0.887751\pi$
$827$		−	571.254i		−	0.690754i	0.938464	−	0.345377i	$-0.112249\pi$
$828$	31.2614	+	33.4142i	0.0377553	+	0.0403553i
$829$	−497.006	+	860.840i	−0.599525	+	1.03841i	0.393366	+	0.919382i	$0.371310\pi$
$829$	−497.006	+	860.840i	−0.599525	+	1.03841i	−0.992891	+	0.119026i	$0.962023\pi$
$830$		−	159.029i		−	0.191602i
$831$	−31.1598	−	24.7441i	−0.0374967	−	0.0297763i
$832$	151.141	−	261.784i	0.181660	−	0.314644i
$833$	−280.583	−	210.225i	−0.336834	−	0.252372i
$834$	739.862	+	109.956i	0.887125	+	0.131841i
$835$	−55.7016	+	96.4780i	−0.0667085	+	0.115542i
$836$	777.334	+	448.794i	0.929826	+	0.536835i
$837$	−543.468	+	44.1111i	−0.649305	+	0.0527014i
$838$	−476.211	−	824.822i	−0.568271	−	0.984275i
$839$	−397.098	+	229.265i	−0.473299	+	0.273259i	−0.717620	−	0.696435i	$-0.754768\pi$
$839$	−397.098	+	229.265i	−0.473299	+	0.273259i	0.244321	+	0.969695i	$0.421435\pi$
$840$	900.714	−	1004.77i	1.07228	−	1.19615i
$841$	−366.852	+	635.406i	−0.436209	+	0.755537i
$842$			722.475i			0.858047i
$843$	−1287.65	−	191.367i	−1.52746	−	0.227007i
$844$	108.634			0.128713
$845$	−838.279	+	483.981i	−0.992046	+	0.572758i
$846$	−180.816	+	169.166i	−0.213730	+	0.199960i
$847$	−13.0545	+	218.374i	−0.0154126	+	0.257820i
$848$	56.0387	−	32.3539i	0.0660833	−	0.0381532i
$849$	169.992	−	1143.83i	0.200227	−	1.34727i
$850$	−170.232	−	294.851i	−0.200273	−	0.346884i
$851$	−9.23427	+	5.33141i	−0.0108511	+	0.00626487i
$852$	−14.8061	−	2.20043i	−0.0173780	−	0.00258266i
$853$	−119.513	−	207.002i	−0.140109	−	0.242676i	0.787429	−	0.616406i	$-0.211412\pi$
$853$	−119.513	−	207.002i	−0.140109	−	0.242676i	−0.927537	+	0.373730i	$0.878079\pi$
$854$	35.9840	+	71.9245i	0.0421358	+	0.0842208i
$855$	1500.32	+	1603.64i	1.75476	+	1.87560i
$856$	−67.1760	−	116.352i	−0.0784767	−	0.135926i
$857$			1577.33i			1.84053i	0.391299	+	0.920263i	$0.372026\pi$
$857$			1577.33i			1.84053i	−0.391299	+	0.920263i	$0.627974\pi$
$858$	−47.4843	+	319.509i	−0.0553431	+	0.372388i
$859$	−929.635			−1.08223			−0.541115	−	0.840949i	$-0.681998\pi$
$859$	−929.635			−1.08223			−0.541115	+	0.840949i	$0.681998\pi$
$860$	816.983	+	471.685i	0.949980	+	0.548471i
$861$	645.540	−	211.315i	0.749756	−	0.245430i
$862$	−215.231	−	372.790i	−0.249687	−	0.432471i
$863$	−169.007	+	97.5764i	−0.195837	+	0.113066i	−0.594712	−	0.803939i	$-0.702734\pi$
$863$	−169.007	+	97.5764i	−0.195837	+	0.113066i	0.398875	+	0.917005i	$0.369401\pi$
$864$	−68.2104	−	840.381i	−0.0789472	−	0.972663i
$865$	−192.523	+	333.460i	−0.222570	+	0.385503i
$866$	121.262	+	70.0109i	0.140026	+	0.0808440i
$867$	104.873	−	705.662i	0.120961	−	0.813912i
$868$	−277.008	−	182.800i	−0.319134	−	0.210599i
$869$	−1546.05	−	892.611i	−1.77911	−	1.02717i
$870$	195.619	−	246.339i	0.224850	−	0.283149i
$871$	615.732			0.706925
$872$	544.731	+	314.500i	0.624691	+	0.360666i
$873$	617.911	−	578.100i	0.707801	−	0.662199i
$874$	86.2459			0.0986795
$875$	−661.360	−	39.5364i	−0.755839	−	0.0451845i
$876$	−388.619	−	308.604i	−0.443629	−	0.352288i
$877$	1129.67			1.28811			0.644053	−	0.764981i	$-0.277252\pi$
$877$	1129.67			1.28811			0.644053	+	0.764981i	$0.277252\pi$
$878$	−650.071	+	375.318i	−0.740399	+	0.427470i
$879$	212.839	+	539.032i	0.242137	+	0.613233i
$880$	53.2902	−	92.3013i	0.0605570	−	0.104888i
$881$			1585.64i			1.79982i	0.436075	+	0.899910i	$0.356368\pi$
$881$			1585.64i			1.79982i	−0.436075	+	0.899910i	$0.643632\pi$
$882$	228.287	−	518.855i	0.258829	−	0.588271i
$883$	1194.30			1.35255			0.676273	−	0.736651i	$-0.263594\pi$
$883$	1194.30			1.35255			0.676273	+	0.736651i	$0.263594\pi$
$884$	98.7634	+	57.0211i	0.111723	+	0.0645035i
$885$	359.446	−	2418.61i	0.406153	−	2.73289i
$886$	−368.762	−	638.715i	−0.416210	−	0.720897i
$887$			1526.52i			1.72099i	0.509457	+	0.860496i	$0.329846\pi$
$887$			1526.52i			1.72099i	−0.509457	+	0.860496i	$0.670154\pi$
$888$	119.217	+	17.7177i	0.134254	+	0.0199523i
$889$	−59.8451	+	1001.08i	−0.0673173	+	1.12607i
$890$			47.7054i			0.0536015i
$891$	441.066	+	896.876i	0.495024	+	1.00659i
$892$	131.207	−	227.258i	0.147093	−	0.254773i
$893$		−	663.182i		−	0.742645i
$894$	233.698	−	92.2765i	0.261407	−	0.103218i
$895$	744.509	−	1289.53i	0.831854	−	1.44081i
$896$	260.926	−	395.399i	0.291213	−	0.441293i
$897$	−16.1976	−	41.0218i	−0.0180576	−	0.0457323i
$898$	−176.737	+	306.117i	−0.196812	+	0.340888i
$899$	−181.158	−	104.592i	−0.201511	−	0.116342i
$900$	−571.195	+	534.394i	−0.634662	+	0.593771i
$901$	211.062	+	365.570i	0.234253	+	0.405739i
$902$	444.278	−	256.504i	0.492547	−	0.284372i
$903$	1048.55	+	220.474i	1.16119	+	0.244157i
$904$	25.6878	−	44.4926i	0.0284157	−	0.0492174i
$905$			1027.35i			1.13520i
$906$	231.741	+	586.903i	0.255785	+	0.647796i
$907$	−922.718			−1.01733			−0.508665	−	0.860965i	$-0.669861\pi$
$907$	−922.718			−1.01733			−0.508665	+	0.860965i	$0.669861\pi$
$908$	521.797	−	301.260i	0.574666	−	0.331784i
$909$	59.1790	−	13.7643i	0.0651034	−	0.0151423i
$910$	−430.205	+	215.233i	−0.472753	+	0.236519i
$911$	1137.89	−	656.958i	1.24905	−	0.721140i	0.278131	−	0.960543i	$-0.410285\pi$
$911$	1137.89	−	656.958i	1.24905	−	0.721140i	0.970920	+	0.239404i	$0.0769519\pi$
$912$	−79.8400	−	63.4013i	−0.0875439	−	0.0695190i
$913$	96.9245	+	167.878i	0.106161	+	0.183875i
$914$	82.9705	−	47.9030i	0.0907773	−	0.0524103i
$915$	−77.5548	−	196.414i	−0.0847594	−	0.214660i
$916$	−181.070	−	313.623i	−0.197675	−	0.342383i
$917$	1246.90	+	74.5406i	1.35976	+	0.0812874i
$918$	−247.508	+	20.0893i	−0.269617	+	0.0218837i
$919$	507.584	+	879.162i	0.552322	+	0.956651i	0.998106	+	0.0615100i	$0.0195916\pi$
$919$	507.584	+	879.162i	0.552322	+	0.956651i	−0.445784	+	0.895141i	$0.647075\pi$
$920$			139.150i			0.151250i
$921$	38.7041	+	30.7351i	0.0420240	+	0.0333714i
$922$	−894.564			−0.970243
$923$	12.4947	+	7.21382i	0.0135371	+	0.00781562i
$924$	−125.179	+	595.338i	−0.135475	+	0.644305i
$925$	−91.1372	−	157.854i	−0.0985267	−	0.170653i
$926$	749.992	−	433.008i	0.809926	−	0.467611i
$927$	145.852	+	627.082i	0.157337	+	0.676463i
$928$	161.734	−	280.131i	0.174282	−	0.301865i
$929$	239.568	+	138.314i	0.257877	+	0.148885i	0.623366	−	0.781930i	$-0.285765\pi$
$929$	239.568	+	138.314i	0.257877	+	0.148885i	−0.365489	+	0.930816i	$0.619098\pi$
$930$	−480.262	−	381.378i	−0.516411	−	0.410084i
$931$	597.062	+	1395.89i	0.641313	+	1.49934i
$932$	−749.863	−	432.933i	−0.804574	−	0.464521i
$933$	−1439.93	−	213.998i	−1.54334	−	0.229365i
$934$	−416.364			−0.445785
$935$	602.131	+	347.641i	0.643990	+	0.371808i
$936$	−144.977	+	476.981i	−0.154890	+	0.509595i
$937$	114.886			0.122610			0.0613051	−	0.998119i	$-0.480474\pi$
$937$	114.886			0.122610			0.0613051	+	0.998119i	$0.480474\pi$
$938$	−814.627	−	48.6989i	−0.868473	−	0.0519178i
$939$	−1146.11	+	452.545i	−1.22056	+	0.481944i
$940$	395.742			0.421003
$941$	489.279	−	282.485i	0.519957	−	0.300197i	−0.216960	−	0.976180i	$-0.569614\pi$
$941$	489.279	−	282.485i	0.519957	−	0.300197i	0.736917	+	0.675983i	$0.236281\pi$
$942$	−410.397	+	516.806i	−0.435666	+	0.548626i
$943$	−35.0222	+	60.6603i	−0.0371392	+	0.0643269i
$944$			113.517i			0.120252i
$945$	−716.610	+	1304.54i	−0.758318	+	1.38047i
$946$	809.244			0.855438
$947$	−432.763	−	249.856i	−0.456983	−	0.263839i	0.253792	−	0.967259i	$-0.418322\pi$
$947$	−432.763	−	249.856i	−0.456983	−	0.263839i	−0.710775	+	0.703420i	$0.751656\pi$
$948$	−798.023	−	633.713i	−0.841796	−	0.668474i
$949$	239.155	+	414.229i	0.252008	+	0.436490i
$950$			1474.32i			1.55192i
$951$	144.124	+	365.006i	0.151550	+	0.383813i
$952$	−341.094	−	225.090i	−0.358292	−	0.236439i
$953$			75.9158i			0.0796598i	0.999206	+	0.0398299i	$0.0126816\pi$
$953$			75.9158i			0.0796598i	−0.999206	+	0.0398299i	$0.987318\pi$
$954$	−498.384	+	466.274i	−0.522415	+	0.488757i
$955$	−448.028	+	776.008i	−0.469140	+	0.812574i
$956$		−	467.517i		−	0.489035i
$957$	−56.3661	+	379.272i	−0.0588987	+	0.396313i
$958$	−18.4734	+	31.9968i	−0.0192833	+	0.0333996i
$959$	−505.555	−	30.2223i	−0.527169	−	0.0315144i
$960$	654.195	−	823.816i	0.681454	−	0.858141i
$961$	276.588	−	479.065i	0.287813	−	0.498507i
$962$	−37.2101	−	21.4833i	−0.0386799	−	0.0223319i
$963$	101.245	+	108.217i	0.105135	+	0.112375i
$964$	−229.069	−	396.760i	−0.237624	−	0.411577i
$965$	1791.89	−	1034.55i	1.85688	−	1.07207i
$966$	18.1854	+	55.5539i	0.0188254	+	0.0575092i
$967$	−427.761	+	740.905i	−0.442359	+	0.766189i	−0.997864	−	0.0653246i	$-0.979192\pi$
$967$	−427.761	+	740.905i	−0.442359	+	0.766189i	0.555505	+	0.831513i	$0.312525\pi$
$968$			254.996i			0.263425i
$969$	413.601	−	520.840i	0.426833	−	0.537502i
$970$	951.728			0.981163
$971$	361.225	−	208.553i	0.372013	−	0.214782i	−0.302324	−	0.953205i	$-0.597763\pi$
$971$	361.225	−	208.553i	0.372013	−	0.214782i	0.674338	+	0.738423i	$0.264429\pi$
$972$	173.775	+	543.401i	0.178781	+	0.559054i
$973$	−1133.28	−	747.863i	−1.16473	−	0.768615i
$974$	975.201	−	563.033i	1.00123	−	0.578062i
$975$	701.244	−	276.889i	0.719225	−	0.283989i
$976$	4.90182	+	8.49020i	0.00502236	+	0.00869898i
$977$	1130.11	−	652.468i	1.15671	−	0.667828i	0.206198	−	0.978510i	$-0.433891\pi$
$977$	1130.11	−	652.468i	1.15671	−	0.667828i	0.950514	+	0.310683i	$0.100558\pi$
$978$	160.106	−	201.619i	0.163708	−	0.206154i
$979$	−29.0753	−	50.3598i	−0.0296989	−	0.0514401i
$980$	−832.972	+	356.286i	−0.849972	+	0.363558i
$981$	−663.820	−	201.766i	−0.676677	−	0.205674i
$982$	−39.0231	−	67.5900i	−0.0397384	−	0.0688289i
$983$		−	850.301i		−	0.865006i	−0.901632	−	0.432503i	$-0.857630\pi$
$983$		−	850.301i		−	0.865006i	0.901632	−	0.432503i	$-0.142370\pi$
$984$	736.416	−	290.777i	0.748391	−	0.295505i
$985$	1456.18			1.47835
$986$	−82.5039	−	47.6336i	−0.0836753	−	0.0483100i
$987$	427.179	−	139.835i	0.432805	−	0.141677i
$988$	−246.920	−	427.678i	−0.249919	−	0.432872i
$989$	−95.6887	+	55.2459i	−0.0967530	+	0.0558603i
$990$	−326.910	+	1075.55i	−0.330212	+	1.08642i
$991$	−68.1967	+	118.120i	−0.0688161	+	0.119193i	−0.898380	−	0.439218i	$-0.855255\pi$
$991$	−68.1967	+	118.120i	−0.0688161	+	0.119193i	0.829564	+	0.558411i	$0.188589\pi$
$992$	−546.141	−	315.315i	−0.550546	−	0.317858i
$993$	672.307	−	265.463i	0.677047	−	0.267334i
$994$	−15.9602	−	10.5323i	−0.0160566	−	0.0105958i
$995$	−1676.01	−	967.647i	−1.68444	−	0.972510i
$996$	40.6383	+	102.920i	0.0408015	+	0.103333i
$997$	−664.806			−0.666806			−0.333403	−	0.942784i	$-0.608197\pi$
$997$	−664.806			−0.666806			−0.333403	+	0.942784i	$0.608197\pi$
$998$	778.692	+	449.578i	0.780252	+	0.450479i
$999$	−132.509	+	10.7552i	−0.132641	+	0.0107660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.3.n.b.32.8	yes	22
3.2	odd	2		189.3.n.b.179.4		22
7.2	even	3		63.3.j.b.23.4	yes	22
7.3	odd	6		441.3.r.f.50.4		22
7.4	even	3		441.3.r.g.50.4		22
7.5	odd	6		441.3.j.f.275.4		22
7.6	odd	2		441.3.n.f.410.8		22
9.2	odd	6		63.3.j.b.11.8	✓	22
9.7	even	3		189.3.j.b.116.4		22
21.2	odd	6		189.3.j.b.44.8		22
63.2	odd	6	inner	63.3.n.b.2.8	yes	22
63.11	odd	6		441.3.r.g.344.4		22
63.16	even	3		189.3.n.b.170.4		22
63.20	even	6		441.3.j.f.263.8		22
63.38	even	6		441.3.r.f.344.4		22
63.47	even	6		441.3.n.f.128.8		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.3.j.b.11.8	✓	22	9.2	odd	6
63.3.j.b.23.4	yes	22	7.2	even	3
63.3.n.b.2.8	yes	22	63.2	odd	6	inner
63.3.n.b.32.8	yes	22	1.1	even	1	trivial
189.3.j.b.44.8		22	21.2	odd	6
189.3.j.b.116.4		22	9.7	even	3
189.3.n.b.170.4		22	63.16	even	3
189.3.n.b.179.4		22	3.2	odd	2
441.3.j.f.263.8		22	63.20	even	6
441.3.j.f.275.4		22	7.5	odd	6
441.3.n.f.128.8		22	63.47	even	6
441.3.n.f.410.8		22	7.6	odd	2
441.3.r.f.50.4		22	7.3	odd	6
441.3.r.f.344.4		22	63.38	even	6
441.3.r.g.50.4		22	7.4	even	3
441.3.r.g.344.4		22	63.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11318 + 0.642694i) q^{2} +(2.34935 + 1.86563i) q^{3} +(-1.17389 - 2.03324i) q^{4} +7.87519i q^{5} +(1.41622 + 3.58669i) q^{6} +(0.417718 - 6.98753i) q^{7} -8.15936i q^{8} +(2.03887 + 8.76601i) q^{9} +O(q^{10})\)	\(q+(1.11318 + 0.642694i) q^{2} +(2.34935 + 1.86563i) q^{3} +(-1.17389 - 2.03324i) q^{4} +7.87519i q^{5} +(1.41622 + 3.58669i) q^{6} +(0.417718 - 6.98753i) q^{7} -8.15936i q^{8} +(2.03887 + 8.76601i) q^{9} +(-5.06133 + 8.76649i) q^{10} -12.3390i q^{11} +(1.03539 - 6.96682i) q^{12} +(-3.39438 + 5.87923i) q^{13} +(4.95583 - 7.50990i) q^{14} +(-14.6922 + 18.5016i) q^{15} +(0.548409 - 0.949873i) q^{16} +(6.19653 + 3.57757i) q^{17} +(-3.36423 + 11.0685i) q^{18} +(-15.4920 - 26.8330i) q^{19} +(16.0121 - 9.24460i) q^{20} +(14.0175 - 15.6368i) q^{21} +(7.93022 - 13.7356i) q^{22} +2.16554i q^{23} +(15.2223 - 19.1692i) q^{24} -37.0186 q^{25} +(-7.55709 + 4.36309i) q^{26} +(-11.5641 + 24.3982i) q^{27} +(-14.6976 + 7.35326i) q^{28} +(-8.97062 + 5.17919i) q^{29} +(-28.2458 + 11.1530i) q^{30} +(10.0973 + 17.4891i) q^{31} +(-27.0439 + 15.6138i) q^{32} +(23.0200 - 28.9887i) q^{33} +(4.59856 + 7.96495i) q^{34} +(55.0281 + 3.28961i) q^{35} +(15.4300 - 14.4358i) q^{36} +(2.46193 + 4.26419i) q^{37} -39.8265i q^{38} +(-18.9430 + 7.47972i) q^{39} +64.2565 q^{40} +(28.0117 + 16.1725i) q^{41} +(25.6536 - 8.39762i) q^{42} +(25.5114 + 44.1870i) q^{43} +(-25.0882 + 14.4847i) q^{44} +(-69.0340 + 16.0565i) q^{45} +(-1.39178 + 2.41063i) q^{46} +(18.5364 + 10.7020i) q^{47} +(3.06051 - 1.20845i) q^{48} +(-48.6510 - 5.83763i) q^{49} +(-41.2083 - 23.7916i) q^{50} +(7.88340 + 19.9654i) q^{51} +15.9385 q^{52} +(51.0920 + 29.4980i) q^{53} +(-28.5535 + 19.7274i) q^{54} +97.1723 q^{55} +(-57.0137 - 3.40831i) q^{56} +(13.6642 - 91.9424i) q^{57} -13.3145 q^{58} +(-89.6310 + 51.7485i) q^{59} +(54.8650 + 8.15385i) q^{60} +(-4.46912 + 7.74075i) q^{61} +25.9579i q^{62} +(62.1044 - 10.5849i) q^{63} -44.5268 q^{64} +(-46.3001 - 26.7314i) q^{65} +(44.2563 - 17.4748i) q^{66} +(-45.3494 - 78.5475i) q^{67} -16.7987i q^{68} +(-4.04009 + 5.08760i) q^{69} +(59.1418 + 39.0281i) q^{70} -2.12523i q^{71} +(71.5250 - 16.6359i) q^{72} +(35.2282 - 61.0170i) q^{73} +6.32907i q^{74} +(-86.9695 - 69.0629i) q^{75} +(-36.3719 + 62.9979i) q^{76} +(-86.2194 - 5.15424i) q^{77} +(-25.8941 - 3.84830i) q^{78} +(72.3404 - 125.297i) q^{79} +(7.48043 + 4.31883i) q^{80} +(-72.6860 + 35.7456i) q^{81} +(20.7880 + 36.0058i) q^{82} +(-13.6055 + 7.85511i) q^{83} +(-48.2483 - 10.1449i) q^{84} +(-28.1740 + 48.7989i) q^{85} +65.5840i q^{86} +(-30.7375 - 4.56811i) q^{87} -100.679 q^{88} +(4.08134 - 2.35636i) q^{89} +(-87.1666 - 26.4940i) q^{90} +(39.6634 + 26.1742i) q^{91} +(4.40305 - 2.54210i) q^{92} +(-8.90596 + 59.9257i) q^{93} +(13.7562 + 23.8264i) q^{94} +(211.315 - 122.003i) q^{95} +(-92.6650 - 13.7716i) q^{96} +(-47.0097 - 81.4233i) q^{97} +(-50.4055 - 37.7660i) q^{98} +(108.164 - 25.1577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9}+O(q^{10}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9	\( 22 q - 6 q^{2} + 8 q^{3} + 12 q^{4} - 8 q^{6} + 3 q^{7} + 20 q^{9} + 25 q^{10} - 20 q^{12} - 18 q^{13} - 90 q^{14} + 53 q^{15} + 12 q^{16} + 6 q^{17} - 56 q^{18} + 3 q^{19} - 39 q^{20} - 2 q^{21} - 59 q^{22} + 15 q^{24} - 114 q^{25} - 3 q^{26} - 97 q^{27} + 34 q^{28} - 63 q^{29} - 20 q^{30} - 29 q^{31} + 246 q^{32} + 77 q^{33} - 99 q^{34} - 27 q^{35} + 76 q^{36} - 20 q^{37} + 200 q^{39} + 210 q^{40} - 51 q^{41} + 80 q^{42} + 65 q^{43} + 54 q^{44} + 71 q^{45} + 75 q^{46} + 261 q^{47} - 113 q^{48} - 131 q^{49} + 63 q^{50} - 78 q^{51} + 92 q^{52} - 63 q^{53} - 485 q^{54} - 100 q^{55} + 153 q^{56} + 224 q^{57} - 80 q^{58} - 102 q^{59} + 103 q^{60} + 78 q^{61} + 421 q^{63} + 106 q^{64} - 225 q^{65} - 401 q^{66} - 132 q^{67} - 297 q^{69} + 179 q^{70} - 66 q^{72} + q^{73} - 245 q^{75} + 233 q^{76} - 447 q^{77} - 440 q^{78} + 140 q^{79} + 96 q^{80} + 104 q^{81} - 157 q^{82} + 255 q^{83} - 316 q^{84} + 102 q^{85} - 136 q^{87} - 816 q^{88} - 720 q^{89} + 418 q^{90} - 70 q^{91} - 1239 q^{92} + 210 q^{93} + 261 q^{94} + 642 q^{95} + 539 q^{96} + 178 q^{97} + 483 q^{98} - 103 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 + 8 * q^3 + 12 * q^4 - 8 * q^6 + 3 * q^7 + 20 * q^9 + 25 * q^10 - 20 * q^12 - 18 * q^13 - 90 * q^14 + 53 * q^15 + 12 * q^16 + 6 * q^17 - 56 * q^18 + 3 * q^19 - 39 * q^20 - 2 * q^21 - 59 * q^22 + 15 * q^24 - 114 * q^25 - 3 * q^26 - 97 * q^27 + 34 * q^28 - 63 * q^29 - 20 * q^30 - 29 * q^31 + 246 * q^32 + 77 * q^33 - 99 * q^34 - 27 * q^35 + 76 * q^36 - 20 * q^37 + 200 * q^39 + 210 * q^40 - 51 * q^41 + 80 * q^42 + 65 * q^43 + 54 * q^44 + 71 * q^45 + 75 * q^46 + 261 * q^47 - 113 * q^48 - 131 * q^49 + 63 * q^50 - 78 * q^51 + 92 * q^52 - 63 * q^53 - 485 * q^54 - 100 * q^55 + 153 * q^56 + 224 * q^57 - 80 * q^58 - 102 * q^59 + 103 * q^60 + 78 * q^61 + 421 * q^63 + 106 * q^64 - 225 * q^65 - 401 * q^66 - 132 * q^67 - 297 * q^69 + 179 * q^70 - 66 * q^72 + q^73 - 245 * q^75 + 233 * q^76 - 447 * q^77 - 440 * q^78 + 140 * q^79 + 96 * q^80 + 104 * q^81 - 157 * q^82 + 255 * q^83 - 316 * q^84 + 102 * q^85 - 136 * q^87 - 816 * q^88 - 720 * q^89 + 418 * q^90 - 70 * q^91 - 1239 * q^92 + 210 * q^93 + 261 * q^94 + 642 * q^95 + 539 * q^96 + 178 * q^97 + 483 * q^98 - 103 * q^99

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