LMFDB - Embedded newform 201.3.h.a.172.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,3,Mod(97,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("201.97");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	201.h (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:	$5.47685331364$
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			172.7
Character	$\chi$	$=$	201.172
Dual form			201.3.h.a.97.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.658194 + 0.380008i) q^{2} +1.73205i q^{3} +(-1.71119 - 2.96386i) q^{4} -4.20783i q^{5} +(-0.658194 + 1.14002i) q^{6} +(-7.58591 + 4.37973i) q^{7} -5.64113i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.658194 + 0.380008i) q^{2} +1.73205i q^{3} +(-1.71119 - 2.96386i) q^{4} -4.20783i q^{5} +(-0.658194 + 1.14002i) q^{6} +(-7.58591 + 4.37973i) q^{7} -5.64113i q^{8} -3.00000 q^{9} +(1.59901 - 2.76957i) q^{10} +(-10.7663 + 6.21591i) q^{11} +(5.13356 - 2.96386i) q^{12} +(-15.3902 - 8.88555i) q^{13} -6.65733 q^{14} +7.28818 q^{15} +(-4.70108 + 8.14250i) q^{16} +(1.47585 - 2.55625i) q^{17} +(-1.97458 - 1.14002i) q^{18} +(3.76267 - 6.51714i) q^{19} +(-12.4714 + 7.20039i) q^{20} +(-7.58591 - 13.1392i) q^{21} -9.44838 q^{22} +(3.18431 - 5.51539i) q^{23} +9.77072 q^{24} +7.29414 q^{25} +(-6.75317 - 11.6968i) q^{26} -5.19615i q^{27} +(25.9618 + 14.9891i) q^{28} +(-14.0457 - 24.3279i) q^{29} +(4.79703 + 2.76957i) q^{30} +(36.3473 - 20.9851i) q^{31} +(-25.7299 + 14.8551i) q^{32} +(-10.7663 - 18.6477i) q^{33} +(1.94280 - 1.12167i) q^{34} +(18.4292 + 31.9202i) q^{35} +(5.13356 + 8.89159i) q^{36} +(18.0019 - 31.1803i) q^{37} +(4.95313 - 2.85969i) q^{38} +(15.3902 - 26.6567i) q^{39} -23.7369 q^{40} +(-61.7872 + 35.6729i) q^{41} -11.5308i q^{42} +24.6048i q^{43} +(36.8462 + 21.2732i) q^{44} +12.6235i q^{45} +(4.19178 - 2.42013i) q^{46} +(12.1592 + 21.0603i) q^{47} +(-14.1032 - 8.14250i) q^{48} +(13.8640 - 24.0132i) q^{49} +(4.80095 + 2.77183i) q^{50} +(4.42756 + 2.55625i) q^{51} +60.8194i q^{52} +45.4198i q^{53} +(1.97458 - 3.42007i) q^{54} +(26.1555 + 45.3027i) q^{55} +(24.7066 + 42.7931i) q^{56} +(11.2880 + 6.51714i) q^{57} -21.3499i q^{58} -15.3914 q^{59} +(-12.4714 - 21.6012i) q^{60} +(-64.1168 - 37.0179i) q^{61} +31.8981 q^{62} +(22.7577 - 13.1392i) q^{63} +15.0283 q^{64} +(-37.3889 + 64.7595i) q^{65} -16.3651i q^{66} +(-66.6532 - 6.80782i) q^{67} -10.1019 q^{68} +(9.55293 + 5.51539i) q^{69} +28.0129i q^{70} +(23.3415 + 40.4287i) q^{71} +16.9234i q^{72} +(65.0140 - 112.607i) q^{73} +(23.6975 - 13.6818i) q^{74} +12.6338i q^{75} -25.7545 q^{76} +(54.4479 - 94.3066i) q^{77} +(20.2595 - 11.6968i) q^{78} +(96.8536 - 55.9185i) q^{79} +(34.2623 + 19.7813i) q^{80} +9.00000 q^{81} -54.2239 q^{82} +(29.2863 - 50.7254i) q^{83} +(-25.9618 + 44.9672i) q^{84} +(-10.7563 - 6.21015i) q^{85} +(-9.35002 + 16.1947i) q^{86} +(42.1371 - 24.3279i) q^{87} +(35.0647 + 60.7339i) q^{88} -81.1599 q^{89} +(-4.79703 + 8.30871i) q^{90} +155.665 q^{91} -21.7958 q^{92} +(36.3473 + 62.9554i) q^{93} +18.4823i q^{94} +(-27.4230 - 15.8327i) q^{95} +(-25.7299 - 44.5654i) q^{96} +(17.9019 + 10.3357i) q^{97} +(18.2504 - 10.5369i) q^{98} +(32.2988 - 18.6477i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	$ 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) $ 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.658194	+	0.380008i	0.329097	+	0.190004i	0.655440	−	0.755247i	$-0.272483\pi$
$2$	0.658194	+	0.380008i	0.329097	+	0.190004i	−0.326343	+	0.945251i	$0.605817\pi$
$3$			1.73205i			0.577350i
$3$			1.73205i			0.577350i
$4$	−1.71119	−	2.96386i	−0.427797	−	0.740966i
$5$		−	4.20783i		−	0.841567i	−0.907161	−	0.420783i	$-0.861755\pi$
$5$		−	4.20783i		−	0.841567i	0.907161	−	0.420783i	$-0.138245\pi$
$6$	−0.658194	+	1.14002i	−0.109699	+	0.190004i
$7$	−7.58591	+	4.37973i	−1.08370	+	0.625675i	−0.931892	−	0.362735i	$-0.881843\pi$
$7$	−7.58591	+	4.37973i	−1.08370	+	0.625675i	−0.151809	+	0.988410i	$0.548510\pi$
$8$		−	5.64113i		−	0.705141i
$9$	−3.00000			−0.333333
$10$	1.59901	−	2.76957i	0.159901	−	0.276957i
$11$	−10.7663	+	6.21591i	−0.978752	+	0.565082i	−0.901893	−	0.431960i	$-0.857822\pi$
$11$	−10.7663	+	6.21591i	−0.978752	+	0.565082i	−0.0768586	+	0.997042i	$0.524489\pi$
$12$	5.13356	−	2.96386i	0.427797	−	0.246989i
$13$	−15.3902	−	8.88555i	−1.18386	−	0.683504i	−0.226958	−	0.973904i	$-0.572878\pi$
$13$	−15.3902	−	8.88555i	−1.18386	−	0.683504i	−0.956905	+	0.290400i	$0.906211\pi$
$14$	−6.65733			−0.475523
$15$	7.28818			0.485879
$16$	−4.70108	+	8.14250i	−0.293817	+	0.508906i
$17$	1.47585	−	2.55625i	0.0868150	−	0.150368i	−0.819348	−	0.573296i	$-0.805664\pi$
$17$	1.47585	−	2.55625i	0.0868150	−	0.150368i	0.906163	+	0.422928i	$0.138998\pi$
$18$	−1.97458	−	1.14002i	−0.109699	−	0.0633347i
$19$	3.76267	−	6.51714i	0.198035	−	0.343007i	−0.749856	−	0.661601i	$-0.769877\pi$
$19$	3.76267	−	6.51714i	0.198035	−	0.343007i	0.947891	+	0.318594i	$0.103211\pi$
$20$	−12.4714	+	7.20039i	−0.623572	+	0.360020i
$21$	−7.58591	−	13.1392i	−0.361234	−	0.625675i
$22$	−9.44838			−0.429472
$23$	3.18431	−	5.51539i	0.138448	−	0.239799i	−0.788461	−	0.615085i	$-0.789122\pi$
$23$	3.18431	−	5.51539i	0.138448	−	0.239799i	0.926909	+	0.375285i	$0.122455\pi$
$24$	9.77072			0.407113
$25$	7.29414			0.291766
$26$	−6.75317	−	11.6968i	−0.259737	−	0.449878i
$27$		−	5.19615i		−	0.192450i
$28$	25.9618	+	14.9891i	0.927208	+	0.535324i
$29$	−14.0457	−	24.3279i	−0.484335	−	0.838892i	0.515503	−	0.856887i	$-0.327605\pi$
$29$	−14.0457	−	24.3279i	−0.484335	−	0.838892i	−0.999838	+	0.0179954i	$0.994272\pi$
$30$	4.79703	+	2.76957i	0.159901	+	0.0923190i
$31$	36.3473	−	20.9851i	1.17249	−	0.676940i	0.218228	−	0.975898i	$-0.429973\pi$
$31$	36.3473	−	20.9851i	1.17249	−	0.676940i	0.954266	+	0.298958i	$0.0966392\pi$
$32$	−25.7299	+	14.8551i	−0.804058	+	0.464223i
$33$	−10.7663	−	18.6477i	−0.326251	−	0.565082i
$34$	1.94280	−	1.12167i	0.0571410	−	0.0329904i
$35$	18.4292	+	31.9202i	0.526547	+	0.912007i
$36$	5.13356	+	8.89159i	0.142599	+	0.246989i
$37$	18.0019	−	31.1803i	0.486539	−	0.842710i	−0.513341	−	0.858184i	$-0.671593\pi$
$37$	18.0019	−	31.1803i	0.486539	−	0.842710i	0.999880	+	0.0154744i	$0.00492586\pi$
$38$	4.95313	−	2.85969i	0.130346	−	0.0752550i
$39$	15.3902	−	26.6567i	0.394621	−	0.683504i
$40$	−23.7369			−0.593423
$41$	−61.7872	+	35.6729i	−1.50700	+	0.870070i	−0.507038	+	0.861924i	$0.669260\pi$
$41$	−61.7872	+	35.6729i	−1.50700	+	0.870070i	−0.999967	+	0.00814575i	$0.997407\pi$
$42$		−	11.5308i		−	0.274544i
$43$			24.6048i			0.572204i	0.958199	+	0.286102i	$0.0923597\pi$
$43$			24.6048i			0.572204i	−0.958199	+	0.286102i	$0.907640\pi$
$44$	36.8462	+	21.2732i	0.837414	+	0.483481i
$45$			12.6235i			0.280522i
$46$	4.19178	−	2.42013i	0.0911257	−	0.0526115i
$47$	12.1592	+	21.0603i	0.258705	+	0.448091i	0.965895	−	0.258933i	$-0.0833708\pi$
$47$	12.1592	+	21.0603i	0.258705	+	0.448091i	−0.707190	+	0.707024i	$0.750037\pi$
$48$	−14.1032	−	8.14250i	−0.293817	−	0.169635i
$49$	13.8640	−	24.0132i	0.282939	−	0.490064i
$50$	4.80095	+	2.77183i	0.0960191	+	0.0554367i
$51$	4.42756	+	2.55625i	0.0868150	+	0.0501226i
$52$			60.8194i			1.16960i
$53$			45.4198i			0.856978i	0.903547	+	0.428489i	$0.140954\pi$
$53$			45.4198i			0.856978i	−0.903547	+	0.428489i	$0.859046\pi$
$54$	1.97458	−	3.42007i	0.0365663	−	0.0633347i
$55$	26.1555	+	45.3027i	0.475555	+	0.823685i
$56$	24.7066	+	42.7931i	0.441189	+	0.764162i
$57$	11.2880	+	6.51714i	0.198035	+	0.114336i
$58$		−	21.3499i		−	0.368102i
$59$	−15.3914			−0.260872			−0.130436	−	0.991457i	$-0.541638\pi$
$59$	−15.3914			−0.260872			−0.130436	+	0.991457i	$0.541638\pi$
$60$	−12.4714	−	21.6012i	−0.207857	−	0.360020i
$61$	−64.1168	−	37.0179i	−1.05110	−	0.606850i	−0.128140	−	0.991756i	$-0.540901\pi$
$61$	−64.1168	−	37.0179i	−1.05110	−	0.606850i	−0.922956	+	0.384906i	$0.874234\pi$
$62$	31.8981			0.514485
$63$	22.7577	−	13.1392i	0.361234	−	0.208558i
$64$	15.0283			0.234817
$65$	−37.3889	+	64.7595i	−0.575214	+	0.996300i
$66$		−	16.3651i		−	0.247956i
$67$	−66.6532	−	6.80782i	−0.994824	−	0.101609i
$67$	−66.6532	−	6.80782i	−0.994824	−	0.101609i
$68$	−10.1019			−0.148557
$69$	9.55293	+	5.51539i	0.138448	+	0.0799331i
$70$			28.0129i			0.400185i
$71$	23.3415	+	40.4287i	0.328754	+	0.569418i	0.982265	−	0.187499i	$-0.0600380\pi$
$71$	23.3415	+	40.4287i	0.328754	+	0.569418i	−0.653511	+	0.756917i	$0.726705\pi$
$72$			16.9234i			0.235047i
$73$	65.0140	−	112.607i	0.890602	−	1.54257i	0.0514474	−	0.998676i	$-0.483617\pi$
$73$	65.0140	−	112.607i	0.890602	−	1.54257i	0.839155	−	0.543893i	$-0.183050\pi$
$74$	23.6975	−	13.6818i	0.320237	−	0.184889i
$75$			12.6338i			0.168451i
$76$	−25.7545			−0.338876
$77$	54.4479	−	94.3066i	0.707116	−	1.22476i
$78$	20.2595	−	11.6968i	0.259737	−	0.149959i
$79$	96.8536	−	55.9185i	1.22600	−	0.707829i	0.259805	−	0.965661i	$-0.416342\pi$
$79$	96.8536	−	55.9185i	1.22600	−	0.707829i	0.966190	+	0.257832i	$0.0830082\pi$
$80$	34.2623	+	19.7813i	0.428279	+	0.247267i
$81$	9.00000			0.111111
$82$	−54.2239			−0.661267
$83$	29.2863	−	50.7254i	0.352847	−	0.611150i	−0.633900	−	0.773415i	$-0.718547\pi$
$83$	29.2863	−	50.7254i	0.352847	−	0.611150i	0.986747	+	0.162266i	$0.0518802\pi$
$84$	−25.9618	+	44.9672i	−0.309069	+	0.535324i
$85$	−10.7563	−	6.21015i	−0.126545	−	0.0730606i
$86$	−9.35002	+	16.1947i	−0.108721	+	0.188311i
$87$	42.1371	−	24.3279i	0.484335	−	0.279631i
$88$	35.0647	+	60.7339i	0.398463	+	0.690158i
$89$	−81.1599			−0.911910			−0.455955	−	0.890003i	$-0.650702\pi$
$89$	−81.1599			−0.911910			−0.455955	+	0.890003i	$0.650702\pi$
$90$	−4.79703	+	8.30871i	−0.0533004	+	0.0923190i
$91$	155.665			1.71061
$92$	−21.7958			−0.236911
$93$	36.3473	+	62.9554i	0.390831	+	0.676940i
$94$			18.4823i			0.196620i
$95$	−27.4230	−	15.8327i	−0.288663	−	0.166660i
$96$	−25.7299	−	44.5654i	−0.268019	−	0.464223i
$97$	17.9019	+	10.3357i	0.184555	+	0.106553i	0.589431	−	0.807819i	$-0.299352\pi$
$97$	17.9019	+	10.3357i	0.184555	+	0.106553i	−0.404876	+	0.914372i	$0.632685\pi$
$98$	18.2504	−	10.5369i	0.186229	−	0.107519i
$99$	32.2988	−	18.6477i	0.326251	−	0.188361i
$100$	−12.4816	−	21.6188i	−0.124816	−	0.216188i
$101$	−80.5706	+	46.5174i	−0.797728	+	0.460569i	−0.842676	−	0.538421i	$-0.819021\pi$
$101$	−80.5706	+	46.5174i	−0.797728	+	0.460569i	0.0449479	+	0.998989i	$0.485688\pi$
$102$	1.94280	+	3.36502i	0.0190470	+	0.0329904i
$103$	7.82247	+	13.5489i	0.0759463	+	0.131543i	0.901497	−	0.432785i	$-0.142469\pi$
$103$	7.82247	+	13.5489i	0.0759463	+	0.131543i	−0.825551	+	0.564327i	$0.809136\pi$
$104$	−50.1245	+	86.8182i	−0.481967	+	0.834791i
$105$	−55.2875	+	31.9202i	−0.526547	+	0.304002i
$106$	−17.2599	+	29.8950i	−0.162829	+	0.282029i
$107$	−190.146			−1.77707			−0.888534	−	0.458811i	$-0.848276\pi$
$107$	−190.146			−1.77707			−0.888534	+	0.458811i	$0.848276\pi$
$108$	−15.4007	+	8.89159i	−0.142599	+	0.0823295i
$109$			72.5767i			0.665841i	0.942955	+	0.332921i	$0.108034\pi$
$109$			72.5767i			0.665841i	−0.942955	+	0.332921i	$0.891966\pi$
$110$			39.7572i			0.361429i
$111$	54.0058	+	31.1803i	0.486539	+	0.280903i
$112$		−	82.3577i		−	0.735337i
$113$	116.565	−	67.2989i	1.03155	−	0.595565i	0.114121	−	0.993467i	$-0.463595\pi$
$113$	116.565	−	67.2989i	1.03155	−	0.595565i	0.917428	+	0.397902i	$0.130262\pi$
$114$	4.95313	+	8.57907i	0.0434485	+	0.0752550i
$115$	−23.2078	−	13.3990i	−0.201807	−	0.116513i
$116$	−48.0697	+	83.2591i	−0.414394	+	0.717751i
$117$	46.1707	+	26.6567i	0.394621	+	0.227835i
$118$	−10.1305	−	5.84888i	−0.0858521	−	0.0495667i
$119$			25.8554i			0.217272i
$120$		−	41.1136i		−	0.342613i
$121$	16.7750	−	29.0552i	0.138636	−	0.240125i
$122$	−28.1342	−	48.7298i	−0.230608	−	0.399425i
$123$	−61.7872	−	107.019i	−0.502335	−	0.870070i
$124$	−124.394	−	71.8190i	−1.00318	−	0.579185i
$125$		−	135.888i		−	1.08711i
$126$	19.9720			0.158508
$127$	−96.6962	−	167.483i	−0.761388	−	1.31876i	−0.942135	−	0.335233i	$-0.891185\pi$
$127$	−96.6962	−	167.483i	−0.761388	−	1.31876i	0.180748	−	0.983529i	$-0.442148\pi$
$128$	112.811	+	65.1315i	0.881336	+	0.508840i
$129$	−42.6167			−0.330362
$130$	−49.2183	+	28.4162i	−0.378602	+	0.218586i
$131$	−40.3633			−0.308117			−0.154058	−	0.988062i	$-0.549234\pi$
$131$	−40.3633			−0.308117			−0.154058	+	0.988062i	$0.549234\pi$
$132$	−36.8462	+	63.8195i	−0.279138	+	0.483481i
$133$			65.9179i			0.495623i
$134$	−41.2837	−	29.8096i	−0.308087	−	0.222460i
$135$	−21.8645			−0.161960
$136$	−14.4202	−	8.32548i	−0.106031	−	0.0612168i
$137$		−	212.148i		−	1.54853i	−0.632864	−	0.774263i	$-0.718121\pi$
$137$		−	212.148i		−	1.54853i	0.632864	−	0.774263i	$-0.281879\pi$
$138$	4.19178	+	7.26038i	0.0303752	+	0.0526115i
$139$			147.031i			1.05778i	0.848691	+	0.528888i	$0.177391\pi$
$139$			147.031i			1.05778i	−0.848691	+	0.528888i	$0.822609\pi$
$140$	63.0715	−	109.243i	0.450511	−	0.780307i
$141$	−36.4775	+	21.0603i	−0.258705	+	0.149364i
$142$			35.4799i			0.249858i
$143$	220.927			1.54494
$144$	14.1032	−	24.4275i	0.0979391	−	0.169635i
$145$	−102.368	+	59.1020i	−0.705984	+	0.407600i
$146$	85.5835	−	49.4117i	0.586189	−	0.338436i
$147$	41.5920	+	24.0132i	0.282939	+	0.163355i
$148$	−123.219			−0.832559
$149$	−183.704			−1.23291			−0.616455	−	0.787390i	$-0.711432\pi$
$149$	−183.704			−1.23291			−0.616455	+	0.787390i	$0.711432\pi$
$150$	−4.80095	+	8.31550i	−0.0320064	+	0.0554367i
$151$	−22.6577	+	39.2444i	−0.150051	+	0.259896i	−0.931246	−	0.364391i	$-0.881277\pi$
$151$	−22.6577	+	39.2444i	−0.150051	+	0.259896i	0.781195	+	0.624287i	$0.214611\pi$
$152$	−36.7640	−	21.2257i	−0.241868	−	0.139643i
$153$	−4.42756	+	7.66876i	−0.0289383	+	0.0501226i
$154$	71.6746	−	41.3813i	0.465419	−	0.268710i
$155$	−88.3019	−	152.943i	−0.569690	−	0.986732i
$156$	−105.342			−0.675271
$157$	59.7547	−	103.498i	0.380603	−	0.659224i	−0.610545	−	0.791981i	$-0.709050\pi$
$157$	59.7547	−	103.498i	0.380603	−	0.659224i	0.991149	+	0.132757i	$0.0423831\pi$
$158$	84.9979			0.537961
$159$	−78.6695			−0.494776
$160$	62.5080	+	108.267i	0.390675	+	0.676669i
$161$			55.7856i			0.346495i
$162$	5.92374	+	3.42007i	0.0365663	+	0.0211116i
$163$	−58.9721	−	102.143i	−0.361792	−	0.626642i	0.626464	−	0.779451i	$-0.284502\pi$
$163$	−58.9721	−	102.143i	−0.361792	−	0.626642i	−0.988256	+	0.152808i	$0.951168\pi$
$164$	211.459	+	122.086i	1.28938	+	0.744426i
$165$	−78.4665	+	45.3027i	−0.475555	+	0.274562i
$166$	38.5521	−	22.2581i	0.232242	−	0.134085i
$167$	−14.4865	−	25.0914i	−0.0867457	−	0.150248i	0.819388	−	0.573239i	$-0.194313\pi$
$167$	−14.4865	−	25.0914i	−0.0867457	−	0.150248i	−0.906134	+	0.422991i	$0.860980\pi$
$168$	−74.1198	+	42.7931i	−0.441189	+	0.254721i
$169$	73.4061	+	127.143i	0.434355	+	0.752326i
$170$	−4.71982	−	8.17496i	−0.0277636	−	0.0480880i
$171$	−11.2880	+	19.5514i	−0.0660118	+	0.114336i
$172$	72.9252	−	42.1034i	0.423984	−	0.244787i
$173$	78.9294	−	136.710i	0.456239	−	0.790229i	−0.542519	−	0.840043i	$-0.682530\pi$
$173$	78.9294	−	136.710i	0.456239	−	0.790229i	0.998759	+	0.0498140i	$0.0158628\pi$
$174$	36.9792			0.212524
$175$	−55.3327	+	31.9463i	−0.316187	+	0.182550i
$176$		−	116.886i		−	0.664124i
$177$		−	26.6588i		−	0.150614i
$178$	−53.4190	−	30.8414i	−0.300106	−	0.173267i
$179$			180.136i			1.00634i	0.864186	+	0.503172i	$0.167834\pi$
$179$			180.136i			1.00634i	−0.864186	+	0.503172i	$0.832166\pi$
$180$	37.4143	−	21.6012i	0.207857	−	0.120007i
$181$	−0.542190	−	0.939100i	−0.00299552	−	0.00518840i	0.864524	−	0.502592i	$-0.167620\pi$
$181$	−0.542190	−	0.939100i	−0.00299552	−	0.00518840i	−0.867519	+	0.497404i	$0.834287\pi$
$182$	102.458	+	59.1540i	0.562955	+	0.325022i
$183$	64.1168	−	111.054i	0.350365	−	0.606850i
$184$	−31.1130	−	17.9631i	−0.169092	−	0.0976255i
$185$	−131.201	−	75.7492i	−0.709197	−	0.409455i
$186$			55.2491i			0.297038i
$187$			36.6951i			0.196230i
$188$	41.6132	−	72.0762i	0.221347	−	0.383384i
$189$	22.7577	+	39.4175i	0.120411	+	0.208558i
$190$	−12.0331	−	20.8420i	−0.0633321	−	0.109694i
$191$	−168.806	−	97.4602i	−0.883802	−	0.510263i	−0.0118916	−	0.999929i	$-0.503785\pi$
$191$	−168.806	−	97.4602i	−0.883802	−	0.510263i	−0.871910	+	0.489666i	$0.837119\pi$
$192$			26.0298i			0.135572i
$193$	−28.9023			−0.149753			−0.0748765	−	0.997193i	$-0.523856\pi$
$193$	−28.9023			−0.149753			−0.0748765	+	0.997193i	$0.523856\pi$
$194$	7.85527	+	13.6057i	0.0404911	+	0.0701326i
$195$	−112.167	−	64.7595i	−0.575214	−	0.332100i
$196$	−94.8956			−0.484161
$197$	−78.1916	+	45.1439i	−0.396911	+	0.229157i	−0.685150	−	0.728402i	$-0.740264\pi$
$197$	−78.1916	+	45.1439i	−0.396911	+	0.229157i	0.288239	+	0.957558i	$0.406930\pi$
$198$	28.3451			0.143157
$199$	−103.378	+	179.056i	−0.519487	+	0.899777i	0.480257	+	0.877128i	$0.340543\pi$
$199$	−103.378	+	179.056i	−0.519487	+	0.899777i	−0.999743	+	0.0226492i	$0.992790\pi$
$200$		−	41.1472i		−	0.205736i
$201$	11.7915	−	115.447i	0.0586642	−	0.574362i
$202$	−70.7080			−0.350040
$203$	213.099	+	123.033i	1.04975	+	0.606072i
$204$		−	17.4969i		−	0.0857692i
$205$	150.105	+	259.990i	0.732222	+	1.26824i
$206$			11.8904i			0.0577204i
$207$	−9.55293	+	16.5462i	−0.0461494	+	0.0799331i
$208$	144.701	−	83.5433i	0.695679	−	0.401650i
$209$			93.5537i			0.447625i
$210$	−48.5198			−0.231047
$211$	153.589	−	266.024i	0.727911	−	1.26078i	−0.229853	−	0.973225i	$-0.573825\pi$
$211$	153.589	−	266.024i	0.727911	−	1.26078i	0.957764	−	0.287554i	$-0.0928421\pi$
$212$	134.618	−	77.7218i	0.634991	−	0.366612i
$213$	−70.0246	+	40.4287i	−0.328754	+	0.189806i
$214$	−125.153	−	72.2571i	−0.584827	−	0.337650i
$215$	103.533			0.481548
$216$	−29.3122			−0.135704
$217$	−183.818	+	318.382i	−0.847089	+	1.46720i
$218$	−27.5797	+	47.7695i	−0.126513	+	0.219126i
$219$	195.042	+	112.607i	0.890602	+	0.514189i
$220$	89.5139	−	155.043i	0.406882	−	0.704739i
$221$	−45.4275	+	26.2276i	−0.205554	+	0.118677i
$222$	23.6975	+	41.0453i	0.106746	+	0.184889i
$223$	−100.014			−0.448492			−0.224246	−	0.974533i	$-0.571992\pi$
$223$	−100.014			−0.448492			−0.224246	+	0.974533i	$0.571992\pi$
$224$	130.123	−	225.380i	0.580906	−	1.00616i
$225$	−21.8824			−0.0972552
$226$	102.296			0.452639
$227$	172.862	+	299.405i	0.761506	+	1.31897i	0.942074	+	0.335404i	$0.108873\pi$
$227$	172.862	+	299.405i	0.761506	+	1.31897i	−0.180569	+	0.983562i	$0.557794\pi$
$228$		−	44.6082i		−	0.195650i
$229$	311.609	+	179.908i	1.36074	+	0.785624i	0.989722	−	0.143002i	$-0.0456756\pi$
$229$	311.609	+	179.908i	1.36074	+	0.785624i	0.371018	+	0.928626i	$0.379009\pi$
$230$	−10.1835	−	17.6383i	−0.0442761	−	0.0766884i
$231$	163.344	+	94.3066i	0.707116	+	0.408254i
$232$	−137.237	+	79.2336i	−0.591537	+	0.341524i
$233$	−347.692	+	200.740i	−1.49224	+	0.861546i	−0.999960	−	0.00888958i	$-0.997170\pi$
$233$	−347.692	+	200.740i	−1.49224	+	0.861546i	−0.492282	+	0.870436i	$0.663837\pi$
$234$	20.2595	+	35.0905i	0.0865790	+	0.149959i
$235$	88.6181	−	51.1637i	0.377098	−	0.217718i
$236$	26.3376	+	45.6181i	0.111600	+	0.193297i
$237$	96.8536	+	167.755i	0.408665	+	0.707829i
$238$	−9.82525	+	17.0178i	−0.0412825	+	0.0715035i
$239$	368.100	−	212.523i	1.54017	−	0.889217i	0.541342	−	0.840803i	$-0.317917\pi$
$239$	368.100	−	212.523i	1.54017	−	0.889217i	0.998827	−	0.0484143i	$-0.0154168\pi$
$240$	−34.2623	+	59.3440i	−0.142760	+	0.247267i
$241$	−267.365			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$241$	−267.365			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$242$	22.0824	−	12.7493i	0.0912496	−	0.0526830i
$243$			15.5885i			0.0641500i
$244$			253.378i			1.03843i
$245$	−101.043	−	58.3374i	−0.412422	−	0.238112i
$246$		−	93.9186i		−	0.381783i
$247$	−115.817	+	66.8668i	−0.468894	+	0.270716i
$248$	−118.380	−	205.040i	−0.477338	−	0.826773i
$249$	87.8590	+	50.7254i	0.352847	+	0.203717i
$250$	51.6387	−	89.4408i	0.206555	−	0.357763i
$251$	−53.5104	−	30.8943i	−0.213189	−	0.123085i	0.389604	−	0.920983i	$-0.372612\pi$
$251$	−53.5104	−	30.8943i	−0.213189	−	0.123085i	−0.602793	+	0.797898i	$0.705945\pi$
$252$	−77.8855	−	44.9672i	−0.309069	−	0.178441i
$253$			79.1735i			0.312939i
$254$		−	146.981i		−	0.578667i
$255$	10.7563	−	18.6304i	0.0421815	−	0.0730606i
$256$	19.4444	+	33.6787i	0.0759547	+	0.131557i
$257$	23.7777	+	41.1843i	0.0925204	+	0.160250i	0.908571	−	0.417730i	$-0.137174\pi$
$257$	23.7777	+	41.1843i	0.0925204	+	0.160250i	−0.816051	+	0.577980i	$0.803841\pi$
$258$	−28.0501	−	16.1947i	−0.108721	−	0.0627702i
$259$			315.374i			1.21766i
$260$	255.918			0.984299
$261$	42.1371	+	72.9836i	0.161445	+	0.279631i
$262$	−26.5669	−	15.3384i	−0.101400	−	0.0585435i
$263$	305.448			1.16140			0.580699	−	0.814118i	$-0.302779\pi$
$263$	305.448			1.16140			0.580699	+	0.814118i	$0.302779\pi$
$264$	−105.194	+	60.7339i	−0.398463	+	0.230053i
$265$	191.119			0.721204
$266$	−25.0493	+	43.3867i	−0.0941704	+	0.163108i
$267$		−	140.573i		−	0.526491i
$268$	93.8787	+	209.201i	0.350294	+	0.780599i
$269$	59.0542			0.219532			0.109766	−	0.993957i	$-0.464990\pi$
$269$	59.0542			0.219532			0.109766	+	0.993957i	$0.464990\pi$
$270$	−14.3911	−	8.30871i	−0.0533004	−	0.0307730i
$271$		−	377.855i		−	1.39430i	−0.716926	−	0.697150i	$-0.754451\pi$
$271$		−	377.855i		−	1.39430i	0.716926	−	0.697150i	$-0.245549\pi$
$272$	13.8762	+	24.0343i	0.0510155	+	0.0883614i
$273$			269.620i			0.987619i
$274$	80.6180	−	139.635i	0.294226	−	0.509615i
$275$	−78.5306	+	45.3397i	−0.285566	+	0.164872i
$276$		−	37.7514i		−	0.136781i
$277$	−138.773			−0.500984			−0.250492	−	0.968119i	$-0.580592\pi$
$277$	−138.773			−0.500984			−0.250492	+	0.968119i	$0.580592\pi$
$278$	−55.8730	+	96.7748i	−0.200982	+	0.348111i
$279$	−109.042	+	62.9554i	−0.390831	+	0.225647i
$280$	180.066	−	103.961i	0.643093	−	0.371290i
$281$	−205.753	−	118.792i	−0.732218	−	0.422746i	0.0870148	−	0.996207i	$-0.472267\pi$
$281$	−205.753	−	118.792i	−0.732218	−	0.422746i	−0.819233	+	0.573461i	$0.805601\pi$
$282$	−32.0123			−0.113519
$283$	293.663			1.03768			0.518838	−	0.854872i	$-0.326365\pi$
$283$	293.663			1.03768			0.518838	+	0.854872i	$0.326365\pi$
$284$	79.8835	−	138.362i	0.281280	−	0.487191i
$285$	27.4230	−	47.4981i	0.0962211	−	0.166660i
$286$	145.413	+	83.9541i	0.508436	+	0.293546i
$287$	312.475	−	541.222i	1.08876	−	1.88579i
$288$	77.1896	−	44.5654i	0.268019	−	0.154741i
$289$	140.144	+	242.736i	0.484926	+	0.839917i
$290$	−89.8369			−0.309783
$291$	−17.9019	+	31.0070i	−0.0615185	+	0.106553i
$292$	−445.004			−1.52399
$293$	438.330			1.49601			0.748003	−	0.663696i	$-0.231013\pi$
$293$	438.330			1.49601			0.748003	+	0.663696i	$0.231013\pi$
$294$	18.2504	+	31.6106i	0.0620762	+	0.107519i
$295$			64.7646i			0.219541i
$296$	−175.892	−	101.551i	−0.594229	−	0.343078i
$297$	32.2988	+	55.9432i	0.108750	+	0.188361i
$298$	−120.913	−	69.8089i	−0.405747	−	0.234258i
$299$	−98.0145	+	56.5887i	−0.327808	+	0.189260i
$300$	37.4449	−	21.6188i	0.124816	−	0.0720628i
$301$	−107.762	−	186.650i	−0.358014	−	0.620098i
$302$	−29.8264	+	17.2203i	−0.0987628	+	0.0570207i
$303$	−80.5706	−	139.552i	−0.265909	−	0.460569i
$304$	35.3772	+	61.2751i	0.116372	+	0.201563i
$305$	−155.765	+	269.793i	−0.510705	+	0.884567i
$306$	−5.82839	+	3.36502i	−0.0190470	+	0.0109968i
$307$	252.492	−	437.328i	0.822448	−	1.42452i	−0.0814057	−	0.996681i	$-0.525941\pi$
$307$	252.492	−	437.328i	0.822448	−	1.42452i	0.903854	−	0.427841i	$-0.140726\pi$
$308$	−372.683			−1.21001
$309$	−23.4674	+	13.5489i	−0.0759463	+	0.0438476i
$310$		−	134.222i		−	0.432974i
$311$			333.689i			1.07296i	0.843914	+	0.536478i	$0.180246\pi$
$311$			333.689i			1.07296i	−0.843914	+	0.536478i	$0.819754\pi$
$312$	−150.374	−	86.8182i	−0.481967	−	0.278264i
$313$		−	5.17753i		−	0.0165416i	−0.999966	−	0.00827081i	$-0.997367\pi$
$313$		−	5.17753i		−	0.0165416i	0.999966	−	0.00827081i	$-0.00263271\pi$
$314$	78.6603	−	45.4145i	0.250511	−	0.144632i
$315$	−55.2875	−	95.7607i	−0.175516	−	0.304002i
$316$	−331.469	−	191.374i	−1.04895	−	0.605614i
$317$	39.2559	−	67.9932i	0.123836	−	0.214490i	−0.797442	−	0.603396i	$-0.793814\pi$
$317$	39.2559	−	67.9932i	0.123836	−	0.214490i	0.921277	+	0.388907i	$0.127147\pi$
$318$	−51.7797	−	29.8950i	−0.162829	−	0.0940096i
$319$	302.440	+	174.614i	0.948086	+	0.547378i
$320$		−	63.2365i		−	0.197614i
$321$		−	329.343i		−	1.02599i
$322$	−21.1990	+	36.7177i	−0.0658354	+	0.114030i
$323$	−11.1063	−	19.2367i	−0.0343849	−	0.0595563i
$324$	−15.4007	−	26.6748i	−0.0475330	−	0.0823295i
$325$	−112.258	−	64.8124i	−0.345411	−	0.199423i
$326$		−	89.6396i		−	0.274968i
$327$	−125.706			−0.384424
$328$	201.235	+	348.549i	0.613522	+	1.06265i
$329$	−184.476	−	106.508i	−0.560719	−	0.323731i
$330$	−68.8615			−0.208671
$331$	−109.394	+	63.1589i	−0.330497	+	0.190812i	−0.656062	−	0.754707i	$-0.727779\pi$
$331$	−109.394	+	63.1589i	−0.330497	+	0.190812i	0.325565	+	0.945520i	$0.394446\pi$
$332$	−200.458			−0.603788
$333$	−54.0058	+	93.5408i	−0.162180	+	0.280903i
$334$		−	22.0200i		−	0.0659282i
$335$	−28.6462	+	280.466i	−0.0855110	+	0.837211i
$336$	142.648			0.424547
$337$	−206.088	−	118.985i	−0.611536	−	0.353070i	0.162031	−	0.986786i	$-0.448196\pi$
$337$	−206.088	−	118.985i	−0.611536	−	0.353070i	−0.773566	+	0.633715i	$0.781529\pi$
$338$			111.580i			0.330117i
$339$	116.565	+	201.897i	0.343850	+	0.595565i
$340$			42.5069i			0.125020i
$341$	−260.883	+	451.863i	−0.765053	+	1.32511i
$342$	−14.8594	+	8.57907i	−0.0434485	+	0.0250850i
$343$		−	186.331i		−	0.543239i
$344$	138.799			0.403485
$345$	23.2078	−	40.1971i	0.0672691	−	0.116513i
$346$	103.902	−	59.9876i	0.300294	−	0.173375i
$347$	−507.231	+	292.850i	−1.46176	+	0.843948i	−0.999093	−	0.0425832i	$-0.986441\pi$
$347$	−507.231	+	292.850i	−1.46176	+	0.843948i	−0.462668	+	0.886531i	$0.653108\pi$
$348$	−144.209	−	83.2591i	−0.414394	−	0.239250i
$349$	−148.011			−0.424101			−0.212051	−	0.977259i	$-0.568014\pi$
$349$	−148.011			−0.424101			−0.212051	+	0.977259i	$0.568014\pi$
$350$	−48.5595			−0.138741
$351$	−46.1707	+	79.9700i	−0.131540	+	0.227835i
$352$	184.676	−	319.869i	0.524649	−	0.908719i
$353$	−424.657	−	245.176i	−1.20299	−	0.694549i	−0.241775	−	0.970332i	$-0.577729\pi$
$353$	−424.657	−	245.176i	−1.20299	−	0.694549i	−0.961220	+	0.275783i	$0.911063\pi$
$354$	10.1305	−	17.5466i	0.0286174	−	0.0495667i
$355$	170.117	−	98.2172i	0.479204	−	0.276668i
$356$	138.880	+	240.547i	0.390112	+	0.675694i
$357$	−44.7828			−0.125442
$358$	−68.4531	+	118.564i	−0.191210	+	0.331185i
$359$	−93.8465			−0.261411			−0.130705	−	0.991421i	$-0.541724\pi$
$359$	−93.8465			−0.261411			−0.130705	+	0.991421i	$0.541724\pi$
$360$	71.2108			0.197808
$361$	152.185	+	263.591i	0.421564	+	0.730170i
$362$		−	0.824146i		−	0.00227665i
$363$	50.3250	+	29.0552i	0.138636	+	0.0800418i
$364$	−266.372	−	461.370i	−0.731792	−	1.26750i
$365$	−473.834	−	273.568i	−1.29817	−	0.749501i
$366$	84.4026	−	48.7298i	0.230608	−	0.133142i
$367$	317.125	−	183.092i	0.864102	−	0.498890i	−0.00128174	−	0.999999i	$-0.500408\pi$
$367$	317.125	−	183.092i	0.864102	−	0.498890i	0.865384	+	0.501110i	$0.167075\pi$
$368$	29.9394	+	51.8565i	0.0813570	+	0.140914i
$369$	185.362	−	107.019i	0.502335	−	0.290023i
$370$	−57.5706	−	99.7152i	−0.155596	−	0.269501i
$371$	−198.926	−	344.551i	−0.536190	−	0.928708i
$372$	124.394	−	215.457i	0.334393	−	0.579185i
$373$	−515.186	+	297.443i	−1.38120	+	0.797434i	−0.992301	−	0.123848i	$-0.960477\pi$
$373$	−515.186	+	297.443i	−1.38120	+	0.797434i	−0.388895	+	0.921282i	$0.627143\pi$
$374$	−13.9444	+	24.1525i	−0.0372846	+	0.0645788i
$375$	235.366			0.627641
$376$	118.804	−	68.5913i	0.315967	−	0.182424i
$377$			499.215i			1.32418i
$378$			34.5925i			0.0915145i
$379$	−492.749	−	284.489i	−1.30013	−	0.750631i	−0.319704	−	0.947517i	$-0.603583\pi$
$379$	−492.749	−	284.489i	−1.30013	−	0.750631i	−0.980426	+	0.196887i	$0.936917\pi$
$380$			108.371i			0.285186i
$381$	290.089	−	167.483i	0.761388	−	0.439587i
$382$	−74.0714	−	128.295i	−0.193904	−	0.335852i
$383$	251.985	+	145.484i	0.657924	+	0.379853i	0.791486	−	0.611188i	$-0.209308\pi$
$383$	251.985	+	145.484i	0.657924	+	0.379853i	−0.133561	+	0.991041i	$0.542641\pi$
$384$	−112.811	+	195.394i	−0.293779	+	0.508840i
$385$	−396.826	−	229.108i	−1.03072	−	0.595085i
$386$	−19.0233	−	10.9831i	−0.0492832	−	0.0284537i
$387$		−	73.8143i		−	0.190735i
$388$		−	70.7450i		−	0.182332i
$389$	144.705	−	250.637i	0.371993	−	0.644312i	−0.617879	−	0.786273i	$-0.712008\pi$
$389$	144.705	−	250.637i	0.371993	−	0.644312i	0.989872	+	0.141962i	$0.0453410\pi$
$390$	−49.2183	−	85.2486i	−0.126201	−	0.218586i
$391$	−9.39915	−	16.2798i	−0.0240388	−	0.0416364i
$392$	−135.461	−	78.2086i	−0.345564	−	0.199512i
$393$		−	69.9113i		−	0.177891i
$394$	−68.6202			−0.174163
$395$	−235.296	−	407.544i	−0.595685	−	1.03176i
$396$	−110.539	−	63.8195i	−0.279138	−	0.161160i
$397$	59.5469			0.149992			0.0749961	−	0.997184i	$-0.476106\pi$
$397$	59.5469			0.149992			0.0749961	+	0.997184i	$0.476106\pi$
$398$	−136.085	+	78.5688i	−0.341923	+	0.197409i
$399$	−114.173			−0.286148
$400$	−34.2903	+	59.3925i	−0.0857257	+	0.148481i
$401$			514.029i			1.28187i	0.767596	+	0.640934i	$0.221453\pi$
$401$			514.029i			1.28187i	−0.767596	+	0.640934i	$0.778547\pi$
$402$	51.6318	−	71.5055i	0.128437	−	0.177874i
$403$	−745.858			−1.85076
$404$	275.743	+	159.200i	0.682531	+	0.394060i
$405$		−	37.8705i		−	0.0935074i
$406$	93.5068	+	161.959i	0.230312	+	0.398913i
$407$			447.594i			1.09974i
$408$	14.4202	−	24.9764i	0.0353435	−	0.0612168i
$409$	582.005	−	336.021i	1.42299	−	0.821567i	0.426441	−	0.904515i	$-0.359767\pi$
$409$	582.005	−	336.021i	1.42299	−	0.821567i	0.996554	+	0.0829488i	$0.0264338\pi$
$410$			228.165i			0.556500i
$411$	367.451			0.894042
$412$	26.7714	−	46.3695i	0.0649792	−	0.112547i
$413$	116.758	−	67.4103i	0.282707	−	0.163221i
$414$	−12.5754	+	7.26038i	−0.0303752	+	0.0175372i
$415$	−213.444	−	123.232i	−0.514323	−	0.296945i
$416$	527.985			1.26919
$417$	−254.665			−0.610708
$418$	−35.5512	+	61.5764i	−0.0850506	+	0.147312i
$419$	−22.7589	+	39.4196i	−0.0543172	+	0.0940801i	−0.891906	−	0.452222i	$-0.850632\pi$
$419$	−22.7589	+	39.4196i	−0.0543172	+	0.0940801i	0.837588	+	0.546302i	$0.183965\pi$
$420$	189.214	+	109.243i	0.450511	+	0.260102i
$421$	−44.7624	+	77.5308i	−0.106324	+	0.184159i	−0.914278	−	0.405086i	$-0.867241\pi$
$421$	−44.7624	+	77.5308i	−0.106324	+	0.184159i	0.807954	+	0.589245i	$0.200575\pi$
$422$	202.183	−	116.730i	0.479107	−	0.276612i
$423$	−36.4775	−	63.1808i	−0.0862352	−	0.149364i
$424$	256.219			0.604290
$425$	10.7651	−	18.6457i	0.0253296	−	0.0438722i
$426$	−61.4530			−0.144256
$427$	648.513			1.51876
$428$	325.376	+	563.568i	0.760224	+	1.31675i
$429$			382.657i			0.891974i
$430$	68.1446	+	39.3433i	0.158476	+	0.0914961i
$431$	376.445	+	652.022i	0.873423	+	1.51281i	0.858434	+	0.512925i	$0.171438\pi$
$431$	376.445	+	652.022i	0.873423	+	1.51281i	0.0149892	+	0.999888i	$0.495229\pi$
$432$	42.3097	+	24.4275i	0.0979391	+	0.0565452i
$433$	658.189	−	380.006i	1.52007	−	0.877611i	0.520348	−	0.853955i	$-0.325802\pi$
$433$	658.189	−	380.006i	1.52007	−	0.877611i	0.999720	−	0.0236569i	$-0.00753093\pi$
$434$	−241.976	+	139.705i	−0.557548	+	0.321901i
$435$	−102.368	−	177.306i	−0.235328	−	0.407600i
$436$	215.107	−	124.192i	0.493366	−	0.284845i
$437$	−23.9630	−	41.5052i	−0.0548353	−	0.0949775i
$438$	85.5835	+	148.235i	0.195396	+	0.338436i
$439$	−148.246	+	256.769i	−0.337690	+	0.584896i	−0.983998	−	0.178181i	$-0.942979\pi$
$439$	−148.246	+	256.769i	−0.337690	+	0.584896i	0.646308	+	0.763077i	$0.276312\pi$
$440$	255.558	−	147.547i	0.580814	−	0.335333i
$441$	−41.5920	+	72.0395i	−0.0943129	+	0.163355i
$442$	−39.8668			−0.0901963
$443$	−435.916	+	251.676i	−0.984009	+	0.568118i	−0.903478	−	0.428634i	$-0.858995\pi$
$443$	−435.916	+	251.676i	−0.984009	+	0.568118i	−0.0805306	+	0.996752i	$0.525661\pi$
$444$		−	213.421i		−	0.480678i
$445$			341.508i			0.767433i
$446$	−65.8284	−	38.0060i	−0.147597	−	0.0852153i
$447$		−	318.184i		−	0.711821i
$448$	−114.003	+	65.8198i	−0.254472	+	0.146919i
$449$	−80.6763	−	139.735i	−0.179680	−	0.311215i	0.762091	−	0.647470i	$-0.224173\pi$
$449$	−80.6763	−	139.735i	−0.179680	−	0.311215i	−0.941771	+	0.336255i	$0.890840\pi$
$450$	−14.4029	−	8.31550i	−0.0320064	−	0.0184789i
$451$	443.478	−	768.127i	0.983322	−	1.70316i
$452$	−398.929	−	230.322i	−0.882587	−	0.509562i
$453$	−67.9732	−	39.2444i	−0.150051	−	0.0866321i
$454$			262.756i			0.578757i
$455$		−	655.013i		−	1.43959i
$456$	36.7640	−	63.6771i	0.0806228	−	0.139643i
$457$	−392.585	−	679.977i	−0.859048	−	1.48791i	−0.872838	−	0.488009i	$-0.837723\pi$
$457$	−392.585	−	679.977i	−0.859048	−	1.48791i	0.0137906	−	0.999905i	$-0.495610\pi$
$458$	136.733	+	236.828i	0.298543	+	0.517092i
$459$	−13.2827	−	7.66876i	−0.0289383	−	0.0167075i
$460$			91.7131i			0.199376i
$461$	−255.735			−0.554739			−0.277370	−	0.960763i	$-0.589463\pi$
$461$	−255.735			−0.554739			−0.277370	+	0.960763i	$0.589463\pi$
$462$	71.6746	+	124.144i	0.155140	+	0.268710i
$463$	471.815	+	272.403i	1.01904	+	0.588342i	0.913825	−	0.406107i	$-0.133114\pi$
$463$	471.815	+	272.403i	1.01904	+	0.588342i	0.105214	+	0.994450i	$0.466447\pi$
$464$	264.120			0.569223
$465$	264.906	−	152.943i	0.569690	−	0.328911i
$466$	−305.132			−0.654789
$467$	−156.512	+	271.088i	−0.335145	+	0.580487i	−0.983513	−	0.180840i	$-0.942118\pi$
$467$	−156.512	+	271.088i	−0.335145	+	0.580487i	0.648368	+	0.761327i	$0.275452\pi$
$468$		−	182.458i		−	0.389868i
$469$	535.442	−	240.279i	1.14167	−	0.512323i
$470$	77.7705			0.165469
$471$	179.264	+	103.498i	0.380603	+	0.219741i
$472$			86.8251i			0.183951i
$473$	−152.941	−	264.902i	−0.323343	−	0.560046i
$474$			147.221i			0.310592i
$475$	27.4454	−	47.5369i	0.0577799	−	0.100078i
$476$	76.6317	−	44.2434i	0.160991	−	0.0929482i
$477$		−	136.259i		−	0.285659i
$478$	323.042			0.675820
$479$	327.652	−	567.509i	0.684033	−	1.18478i	−0.289707	−	0.957115i	$-0.593558\pi$
$479$	327.652	−	567.509i	0.684033	−	1.18478i	0.973740	−	0.227664i	$-0.0731088\pi$
$480$	−187.524	+	108.267i	−0.390675	+	0.225556i
$481$	−554.108	+	319.914i	−1.15199	+	0.665103i
$482$	−175.978	−	101.601i	−0.365100	−	0.210791i
$483$	−96.6235			−0.200049
$484$	−114.821			−0.237233
$485$	43.4907	−	75.3281i	0.0896716	−	0.155316i
$486$	−5.92374	+	10.2602i	−0.0121888	+	0.0211116i
$487$	−80.8927	−	46.7034i	−0.166104	−	0.0959002i	0.414643	−	0.909984i	$-0.363906\pi$
$487$	−80.8927	−	46.7034i	−0.166104	−	0.0959002i	−0.580748	+	0.814084i	$0.697240\pi$
$488$	−208.823	+	361.691i	−0.427915	+	0.741170i
$489$	176.916	−	102.143i	0.361792	−	0.208881i
$490$	−44.3374	−	76.7946i	−0.0904845	−	0.156724i
$491$	579.314			1.17987			0.589933	−	0.807452i	$-0.299154\pi$
$491$	579.314			1.17987			0.589933	+	0.807452i	$0.299154\pi$
$492$	−211.459	+	366.258i	−0.429795	+	0.744426i
$493$	−82.9176			−0.168190
$494$	−101.640			−0.205748
$495$	−78.4665	−	135.908i	−0.158518	−	0.274562i
$496$			394.611i			0.795586i
$497$	−354.133	−	204.459i	−0.712542	−	0.411386i
$498$	38.5521	+	66.7743i	0.0774140	+	0.134085i
$499$	409.166	+	236.232i	0.819973	+	0.473411i	0.850407	−	0.526125i	$-0.176356\pi$
$499$	409.166	+	236.232i	0.819973	+	0.473411i	−0.0304345	+	0.999537i	$0.509689\pi$
$500$	−402.755	+	232.530i	−0.805509	+	0.465061i
$501$	43.4596	−	25.0914i	0.0867457	−	0.0500827i
$502$	−23.4801	−	40.6688i	−0.0467732	−	0.0810136i
$503$	−64.2995	+	37.1233i	−0.127832	+	0.0738038i	−0.562552	−	0.826762i	$-0.690181\pi$
$503$	−64.2995	+	37.1233i	−0.127832	+	0.0738038i	0.434720	+	0.900565i	$0.356847\pi$
$504$	−74.1198	−	128.379i	−0.147063	−	0.254721i
$505$	195.738	+	339.027i	0.387599	+	0.671341i
$506$	−30.0866	+	52.1115i	−0.0594596	+	0.102987i
$507$	−220.218	+	127.143i	−0.434355	+	0.250775i
$508$	−330.931	+	573.189i	−0.651438	+	1.12832i
$509$	151.542			0.297725			0.148863	−	0.988858i	$-0.452439\pi$
$509$	151.542			0.297725			0.148863	+	0.988858i	$0.452439\pi$
$510$	14.1594	−	8.17496i	0.0277636	−	0.0160293i
$511$			1138.97i			2.22891i
$512$		−	491.496i		−	0.959952i
$513$	−33.8640	−	19.5514i	−0.0660118	−	0.0381119i
$514$			36.1430i			0.0703170i
$515$	57.0116	−	32.9156i	0.110702	−	0.0639139i
$516$	72.9252	+	126.310i	0.141328	+	0.244787i
$517$	−261.817	−	151.160i	−0.506417	−	0.292380i
$518$	−119.845	+	207.577i	−0.231361	+	0.400728i
$519$	236.788	+	136.710i	0.456239	+	0.263410i
$520$	365.317	+	210.916i	0.702532	+	0.405607i
$521$			96.2290i			0.184700i	0.995727	+	0.0923502i	$0.0294379\pi$
$521$			96.2290i			0.184700i	−0.995727	+	0.0923502i	$0.970562\pi$
$522$			64.0498i			0.122701i
$523$	130.122	−	225.378i	0.248800	−	0.430934i	−0.714393	−	0.699744i	$-0.753297\pi$
$523$	130.122	−	225.378i	0.248800	−	0.430934i	0.963193	+	0.268811i	$0.0866306\pi$
$524$	69.0692	+	119.631i	0.131811	+	0.228304i
$525$	−55.3327	−	95.8390i	−0.105396	−	0.182550i
$526$	201.044	+	116.073i	0.382213	+	0.220671i
$527$		−	123.884i		−	0.235074i
$528$	202.452			0.383432
$529$	244.220	+	423.002i	0.461664	+	0.799626i
$530$	125.793	+	72.6268i	0.237346	+	0.137032i
$531$	46.1743			0.0869573
$532$	195.372	−	112.798i	0.367240	−	0.212026i
$533$	1267.89			2.37878
$534$	53.4190	−	92.5243i	0.100035	−	0.173267i
$535$			800.104i			1.49552i
$536$	−38.4038	+	375.999i	−0.0716489	+	0.701491i
$537$	−312.004			−0.581013
$538$	38.8691	+	22.4411i	0.0722474	+	0.0417121i
$539$			344.709i			0.639535i
$540$	37.4143	+	64.8035i	0.0692858	+	0.120007i
$541$		−	67.5728i		−	0.124904i	−0.998048	−	0.0624518i	$-0.980108\pi$
$541$		−	67.5728i		−	0.124904i	0.998048	−	0.0624518i	$-0.0198920\pi$
$542$	143.588	−	248.702i	0.264923	−	0.458859i
$543$	1.62657	−	0.939100i	0.00299552	−	0.00172947i
$544$			87.6961i			0.161206i
$545$	305.391			0.560350
$546$	−102.458	+	177.462i	−0.187652	+	0.325022i
$547$	−420.819	+	242.960i	−0.769321	+	0.444168i	−0.832632	−	0.553826i	$-0.813167\pi$
$547$	−420.819	+	242.960i	−0.769321	+	0.444168i	0.0633114	+	0.997994i	$0.479834\pi$
$548$	−628.778	+	363.025i	−1.14741	+	0.662455i
$549$	192.350	+	111.054i	0.350365	+	0.202283i
$550$	−68.9178			−0.125305
$551$	−211.397			−0.383661
$552$	31.1130	−	53.8893i	0.0563641	−	0.0976255i
$553$	−489.815	+	848.385i	−0.885742	+	1.53415i
$554$	−91.3393	−	52.7347i	−0.164872	−	0.0951891i
$555$	131.201	−	227.247i	0.236399	−	0.409455i
$556$	435.780	−	251.598i	0.783777	−	0.452514i
$557$	−431.928	−	748.122i	−0.775455	−	1.34313i	−0.934538	−	0.355862i	$-0.884187\pi$
$557$	−431.928	−	748.122i	−0.775455	−	1.34313i	0.159083	−	0.987265i	$-0.449146\pi$
$558$	−95.6942			−0.171495
$559$	218.627	−	378.673i	0.391104	−	0.677412i
$560$	−346.547			−0.618835
$561$	−63.5578			−0.113294
$562$	−90.2837	−	156.376i	−0.160647	−	0.278249i
$563$		−	594.420i		−	1.05581i	−0.849304	−	0.527904i	$-0.822978\pi$
$563$		−	594.420i		−	1.05581i	0.849304	−	0.527904i	$-0.177022\pi$
$564$	124.840	+	72.0762i	0.221347	+	0.127795i
$565$	−283.182	−	490.486i	−0.501208	−	0.868117i
$566$	193.287	+	111.594i	0.341496	+	0.197163i
$567$	−68.2732	+	39.4175i	−0.120411	+	0.0695195i
$568$	228.063	−	131.673i	0.401520	−	0.231818i
$569$	138.243	+	239.443i	0.242957	+	0.420814i	0.961555	−	0.274612i	$-0.0885493\pi$
$569$	138.243	+	239.443i	0.242957	+	0.420814i	−0.718598	+	0.695426i	$0.755216\pi$
$570$	36.0993	−	20.8420i	0.0633321	−	0.0365648i
$571$	−275.461	−	477.113i	−0.482419	−	0.835574i	0.517377	−	0.855757i	$-0.326908\pi$
$571$	−275.461	−	477.113i	−0.482419	−	0.835574i	−0.999796	+	0.0201830i	$0.993575\pi$
$572$	−378.048	−	654.798i	−0.660922	−	1.14475i
$573$	168.806	−	292.381i	0.294601	−	0.510263i
$574$	411.338	−	237.486i	0.716616	−	0.413738i
$575$	23.2268	−	40.2300i	0.0403944	−	0.0699652i
$576$	−45.0849			−0.0782723
$577$	68.8416	−	39.7457i	0.119310	−	0.0688834i	−0.439158	−	0.898410i	$-0.644723\pi$
$577$	68.8416	−	39.7457i	0.119310	−	0.0688834i	0.558467	+	0.829527i	$0.311390\pi$
$578$			213.023i			0.368552i
$579$		−	50.0603i		−	0.0864600i
$580$	350.340	+	202.269i	0.604035	+	0.348740i
$581$			513.064i			0.883071i
$582$	−23.5658	+	13.6057i	−0.0404911	+	0.0233775i
$583$	−282.325	−	489.002i	−0.484263	−	0.838768i
$584$	−635.233	−	366.752i	−1.08773	−	0.628000i
$585$	112.167	−	194.279i	0.191738	−	0.332100i
$586$	288.506	+	166.569i	0.492331	+	0.284247i
$587$	−238.088	−	137.460i	−0.405602	−	0.234174i	0.283296	−	0.959032i	$-0.408572\pi$
$587$	−238.088	−	137.460i	−0.405602	−	0.234174i	−0.688898	+	0.724858i	$0.741905\pi$
$588$		−	164.364i		−	0.279531i
$589$		−	315.840i		−	0.536232i
$590$	−24.6111	+	42.6277i	−0.0417137	+	0.0722503i
$591$	−78.1916	−	135.432i	−0.132304	−	0.229157i
$592$	169.257	+	293.162i	0.285907	+	0.495205i
$593$	421.537	+	243.375i	0.710855	+	0.410412i	0.811378	−	0.584522i	$-0.198718\pi$
$593$	421.537	+	243.375i	0.710855	+	0.410412i	−0.100523	+	0.994935i	$0.532051\pi$
$594$			49.0952i			0.0826519i
$595$	108.795			0.182849
$596$	314.352	+	544.473i	0.527435	+	0.913545i
$597$	−310.133	−	179.056i	−0.519487	−	0.299926i
$598$	−86.0167			−0.143841
$599$	303.971	−	175.498i	0.507463	−	0.292984i	−0.224327	−	0.974514i	$-0.572018\pi$
$599$	303.971	−	175.498i	0.507463	−	0.292984i	0.731790	+	0.681530i	$0.238685\pi$
$600$	71.2690			0.118782
$601$	326.867	−	566.150i	0.543871	−	0.942013i	−0.454806	−	0.890591i	$-0.650291\pi$
$601$	326.867	−	566.150i	0.543871	−	0.942013i	0.998677	−	0.0514220i	$-0.0163754\pi$
$602$		−	163.802i		−	0.272096i
$603$	199.960	+	20.4235i	0.331608	+	0.0338698i
$604$	155.087			0.256766
$605$	−122.259	−	70.5864i	−0.202081	−	0.116672i
$606$		−	122.470i		−	0.202096i
$607$	−342.096	−	592.528i	−0.563585	−	0.976158i	−0.997180	−	0.0750503i	$-0.976088\pi$
$607$	−342.096	−	592.528i	−0.563585	−	0.976158i	0.433594	−	0.901108i	$-0.357245\pi$
$608$			223.580i			0.367730i
$609$	−213.099	+	369.098i	−0.349916	+	0.606072i
$610$	−205.047	+	118.384i	−0.336143	+	0.194072i
$611$		−	432.163i		−	0.707305i
$612$	30.3056			0.0495189
$613$	374.816	−	649.201i	0.611446	−	1.05906i	−0.379551	−	0.925171i	$-0.623922\pi$
$613$	374.816	−	649.201i	0.611446	−	1.05906i	0.990997	−	0.133884i	$-0.0427451\pi$
$614$	332.377	−	191.898i	0.541330	−	0.312537i
$615$	−450.316	+	259.990i	−0.732222	+	0.422748i
$616$	−531.996	−	307.148i	−0.863629	−	0.498616i
$617$	1088.59			1.76432			0.882161	−	0.470948i	$-0.156088\pi$
$617$	1088.59			1.76432			0.882161	+	0.470948i	$0.156088\pi$
$618$	−20.5948			−0.0333249
$619$	−481.987	+	834.826i	−0.778655	+	1.34867i	0.154062	+	0.988061i	$0.450764\pi$
$619$	−481.987	+	834.826i	−0.778655	+	1.34867i	−0.932717	+	0.360609i	$0.882569\pi$
$620$	−302.202	+	523.430i	−0.487423	+	0.844241i
$621$	−28.6588	−	16.5462i	−0.0461494	−	0.0266444i
$622$	−126.805	+	219.632i	−0.203866	+	0.353106i
$623$	615.672	−	355.458i	0.988237	−	0.570559i
$624$	144.701	+	250.630i	0.231893	+	0.401650i
$625$	−389.442			−0.623107
$626$	1.96750	−	3.40781i	0.00314298	−	0.00544379i
$627$	−162.040			−0.258436
$628$	−409.006			−0.651283
$629$	−53.1365	−	92.0351i	−0.0844777	−	0.146320i
$630$		−	84.0388i		−	0.133395i
$631$	−125.846	−	72.6573i	−0.199439	−	0.115146i	0.396955	−	0.917838i	$-0.370067\pi$
$631$	−125.846	−	72.6573i	−0.199439	−	0.115146i	−0.596394	+	0.802692i	$0.703400\pi$
$632$	−315.443	−	546.364i	−0.499119	−	0.864499i
$633$	460.768	+	266.024i	0.727911	+	0.420260i
$634$	51.6760	−	29.8351i	0.0815078	−	0.0470586i
$635$	−704.740	+	406.882i	−1.10983	+	0.640758i
$636$	134.618	+	233.166i	0.211664	+	0.366612i
$637$	−426.740	+	246.379i	−0.669922	+	0.386780i
$638$	132.709	+	229.859i	0.208008	+	0.360281i
$639$	−70.0246	−	121.286i	−0.109585	−	0.189806i
$640$	274.062	−	474.690i	0.428222	−	0.741703i
$641$	−700.515	+	404.442i	−1.09285	+	0.630955i	−0.934333	−	0.356402i	$-0.884004\pi$
$641$	−700.515	+	404.442i	−1.09285	+	0.630955i	−0.158514	+	0.987357i	$0.550670\pi$
$642$	125.153	−	216.771i	0.194942	−	0.337650i
$643$	−75.0971			−0.116792			−0.0583959	−	0.998294i	$-0.518599\pi$
$643$	−75.0971			−0.116792			−0.0583959	+	0.998294i	$0.518599\pi$
$644$	165.341	−	95.4597i	0.256741	−	0.148229i
$645$			179.324i			0.278022i
$646$		−	16.8820i		−	0.0261331i
$647$	631.658	+	364.688i	0.976288	+	0.563660i	0.901147	−	0.433513i	$-0.142726\pi$
$647$	631.658	+	364.688i	0.976288	+	0.563660i	0.0751407	+	0.997173i	$0.476059\pi$
$648$		−	50.7701i		−	0.0783490i
$649$	165.708	−	95.6718i	0.255329	−	0.147414i
$650$	−49.2585	−	85.3183i	−0.0757823	−	0.131259i
$651$	−551.455	−	318.382i	−0.847089	−	0.489067i
$652$	−201.825	+	349.571i	−0.309547	+	0.536151i
$653$	−855.104	−	493.694i	−1.30950	−	0.756041i	−0.327488	−	0.944855i	$-0.606202\pi$
$653$	−855.104	−	493.694i	−1.30950	−	0.756041i	−0.982013	+	0.188815i	$0.939535\pi$
$654$	−82.7392	−	47.7695i	−0.126513	−	0.0730421i
$655$			169.842i			0.259301i
$656$		−	670.803i		−	1.02257i
$657$	−195.042	+	337.822i	−0.296867	+	0.514189i
$658$	−80.9475	−	140.205i	−0.123021	−	0.213078i
$659$	149.616	+	259.142i	0.227034	+	0.393235i	0.956928	−	0.290326i	$-0.0937637\pi$
$659$	149.616	+	259.142i	0.227034	+	0.393235i	−0.729894	+	0.683561i	$0.760430\pi$
$660$	268.542	+	155.043i	0.406882	+	0.234913i
$661$		−	446.582i		−	0.675615i	−0.941215	−	0.337808i	$-0.890315\pi$
$661$		−	446.582i		−	0.675615i	0.941215	−	0.337808i	$-0.109685\pi$
$662$	−96.0036			−0.145021
$663$	−45.4275	−	78.6827i	−0.0685181	−	0.118677i
$664$	−286.149	−	165.208i	−0.430947	−	0.248807i
$665$	277.371			0.417100
$666$	−71.0926	+	41.0453i	−0.106746	+	0.0616296i
$667$	−178.903			−0.268221
$668$	−49.5783	+	85.8722i	−0.0742191	+	0.128551i
$669$		−	173.229i		−	0.258937i
$670$	−125.434	+	173.715i	−0.187215	+	0.259276i
$671$	920.399			1.37168
$672$	390.369	+	225.380i	0.580906	+	0.335386i
$673$			1057.86i			1.57186i	0.618314	+	0.785931i	$0.287816\pi$
$673$			1057.86i			1.57186i	−0.618314	+	0.785931i	$0.712184\pi$
$674$	−90.4303	−	156.630i	−0.134170	−	0.232389i
$675$		−	37.9015i		−	0.0561503i
$676$	251.223	−	435.131i	0.371632	−	0.643685i
$677$	41.5740	−	24.0027i	0.0614091	−	0.0354546i	−0.468981	−	0.883208i	$-0.655379\pi$
$677$	41.5740	−	24.0027i	0.0614091	−	0.0354546i	0.530390	+	0.847754i	$0.322045\pi$
$678$			177.183i			0.261331i
$679$	−181.069			−0.266671
$680$	−35.0322	+	60.6776i	−0.0515180	+	0.0892318i
$681$	−518.585	+	299.405i	−0.761506	+	0.439655i
$682$	−343.423	+	198.276i	−0.503553	+	0.290727i
$683$	−472.675	−	272.899i	−0.692057	−	0.399559i	0.112325	−	0.993671i	$-0.464170\pi$
$683$	−472.675	−	272.899i	−0.692057	−	0.399559i	−0.804382	+	0.594112i	$0.797503\pi$
$684$	77.2636			0.112959
$685$	−892.684			−1.30319
$686$	70.8073	−	122.642i	0.103218	−	0.178778i
$687$	−311.609	+	539.723i	−0.453580	+	0.785624i
$688$	−200.344	−	115.669i	−0.291198	−	0.168123i
$689$	403.580	−	699.021i	0.585748	−	1.01454i
$690$	30.5505	−	17.6383i	0.0442761	−	0.0255628i
$691$	1.61426	+	2.79599i	0.00233613	+	0.00404629i	0.867191	−	0.497975i	$-0.165923\pi$
$691$	1.61426	+	2.79599i	0.00233613	+	0.00404629i	−0.864855	+	0.502022i	$0.832590\pi$
$692$	−540.252			−0.780711
$693$	−163.344	+	282.920i	−0.235705	+	0.408254i
$694$	−445.142			−0.641415
$695$	618.682			0.890190
$696$	−137.237	−	237.701i	−0.197179	−	0.341524i
$697$			210.592i			0.302140i
$698$	−97.4201	−	56.2455i	−0.139570	−	0.0805810i
$699$	−347.692	−	602.221i	−0.497414	−	0.861546i
$700$	189.369	+	109.332i	0.270527	+	0.156189i
$701$	1049.02	−	605.654i	1.49647	−	0.863985i	0.496474	−	0.868051i	$-0.334628\pi$
$701$	1049.02	−	605.654i	1.49647	−	0.863985i	0.999992	+	0.00406644i	$0.00129439\pi$
$702$	−60.7785	+	35.0905i	−0.0865790	+	0.0499864i
$703$	−135.471	−	234.642i	−0.192704	−	0.333773i
$704$	−161.799	+	93.4145i	−0.229828	+	0.132691i
$705$	88.6181	+	153.491i	0.125699	+	0.217718i
$706$	−186.338	−	322.746i	−0.263934	−	0.457148i
$707$	407.467	−	705.754i	0.576333	−	0.998237i
$708$	−79.0129	+	45.6181i	−0.111600	+	0.0644324i
$709$	−293.199	+	507.836i	−0.413539	+	0.716271i	−0.995274	−	0.0971078i	$-0.969041\pi$
$709$	−293.199	+	507.836i	−0.413539	+	0.716271i	0.581735	+	0.813379i	$0.302374\pi$
$710$	149.293			0.210272
$711$	−290.561	+	167.755i	−0.408665	+	0.235943i
$712$			457.834i			0.643025i
$713$		−	267.293i		−	0.374884i
$714$	−29.4757	−	17.0178i	−0.0412825	−	0.0238345i
$715$		−	929.624i		−	1.30017i
$716$	533.898	−	308.246i	0.745667	−	0.430511i
$717$	368.100	+	637.569i	0.513390	+	0.889217i
$718$	−61.7692	−	35.6624i	−0.0860295	−	0.0496691i
$719$	−419.749	+	727.026i	−0.583795	+	1.01116i	0.411229	+	0.911532i	$0.365100\pi$
$719$	−419.749	+	727.026i	−0.583795	+	1.01116i	−0.995024	+	0.0996310i	$0.968234\pi$
$720$	−102.787	−	59.3440i	−0.142760	−	0.0824223i
$721$	−118.681	−	68.5205i	−0.164606	−	0.0950354i
$722$			231.326i			0.320396i
$723$		−	463.090i		−	0.640512i
$724$	−1.85558	+	3.21395i	−0.00256295	+	0.00443916i
$725$	−102.451	−	177.451i	−0.141312	−	0.244760i
$726$	22.0824	+	38.2478i	0.0304165	+	0.0526830i
$727$	929.192	+	536.469i	1.27812	+	0.737922i	0.976502	−	0.215508i	$-0.0691406\pi$
$727$	929.192	+	536.469i	1.27812	+	0.737922i	0.301616	+	0.953429i	$0.402474\pi$
$728$		−	878.127i		−	1.20622i
$729$	−27.0000			−0.0370370
$730$	−207.916	−	360.121i	−0.284817	−	0.493317i
$731$	62.8961	+	36.3131i	0.0860412	+	0.0496759i
$732$	−438.864			−0.599541
$733$	919.877	−	531.091i	1.25495	−	0.724545i	0.282860	−	0.959161i	$-0.408717\pi$
$733$	919.877	−	531.091i	1.25495	−	0.724545i	0.972088	+	0.234616i	$0.0753834\pi$
$734$	278.307			0.379164
$735$	101.043	−	175.012i	0.137474	−	0.238112i
$736$			189.214i			0.257084i
$737$	759.923	−	341.015i	1.03110	−	0.462708i
$738$	162.672			0.220422
$739$	−437.222	−	252.430i	−0.591641	−	0.341584i	0.174105	−	0.984727i	$-0.444297\pi$
$739$	−437.222	−	252.430i	−0.591641	−	0.341584i	−0.765746	+	0.643143i	$0.777630\pi$
$740$			518.484i			0.700654i
$741$	−115.817	−	200.600i	−0.156298	−	0.270716i
$742$		−	302.375i		−	0.407513i
$743$	−366.246	+	634.357i	−0.492929	+	0.853777i	−0.999967	−	0.00814616i	$-0.997407\pi$
$743$	−366.246	+	634.357i	−0.492929	+	0.853777i	0.507038	+	0.861924i	$0.330740\pi$
$744$	355.139	−	205.040i	0.477338	−	0.275591i
$745$			772.995i			1.03758i
$746$	−452.123			−0.606063
$747$	−87.8590	+	152.176i	−0.117616	+	0.203717i
$748$	108.759	−	62.7922i	0.145400	−	0.0839468i
$749$	1442.43	−	832.789i	1.92581	−	1.11187i
$750$	154.916	+	89.4408i	0.206555	+	0.119254i
$751$	29.9490			0.0398789			0.0199394	−	0.999801i	$-0.493653\pi$
$751$	29.9490			0.0398789			0.0199394	+	0.999801i	$0.493653\pi$
$752$	−228.644			−0.304048
$753$	53.5104	−	92.6828i	0.0710630	−	0.123085i
$754$	−189.706	+	328.580i	−0.251599	+	0.435783i
$755$	165.134	+	95.3400i	0.218720	+	0.126278i
$756$	77.8855	−	134.902i	0.103023	−	0.178441i
$757$	−1051.82	+	607.267i	−1.38946	+	0.802202i	−0.993254	−	0.115961i	$-0.963005\pi$
$757$	−1051.82	+	607.267i	−1.38946	+	0.802202i	−0.396202	+	0.918164i	$0.629672\pi$
$758$	−216.216	−	374.498i	−0.285246	−	0.494060i
$759$	−137.133			−0.180675
$760$	−89.3142	+	154.697i	−0.117519	+	0.203548i
$761$	−1223.39			−1.60761			−0.803804	−	0.594895i	$-0.797194\pi$
$761$	−1223.39			−1.60761			−0.803804	+	0.594895i	$0.797194\pi$
$762$	254.579			0.334094
$763$	−317.866	−	550.560i	−0.416600	−	0.721573i
$764$			667.091i			0.873156i
$765$	32.2689	+	18.6304i	0.0421815	+	0.0243535i
$766$	110.570	+	191.513i	0.144347	+	0.250017i
$767$	236.878	+	136.761i	0.308837	+	0.178307i
$768$	−58.3332	+	33.6787i	−0.0759547	+	0.0438525i
$769$	1329.41	−	767.533i	1.72875	−	0.998093i	0.833506	−	0.552511i	$-0.186330\pi$
$769$	1329.41	−	767.533i	1.72875	−	0.998093i	0.895241	−	0.445582i	$-0.147003\pi$
$770$	−174.126	−	301.595i	−0.226137	−	0.391681i
$771$	−71.3332	+	41.1843i	−0.0925204	+	0.0534167i
$772$	49.4573	+	85.6626i	0.0640639	+	0.110962i
$773$	−610.295	−	1057.06i	−0.789515	−	1.36748i	−0.926264	−	0.376875i	$-0.876999\pi$
$773$	−610.295	−	1057.06i	−0.789515	−	1.36748i	0.136749	−	0.990606i	$-0.456335\pi$
$774$	28.0501	−	48.5841i	0.0362404	−	0.0627702i
$775$	265.122	−	153.068i	0.342093	−	0.197508i
$776$	58.3047	−	100.987i	0.0751350	−	0.130138i
$777$	−546.244			−0.703017
$778$	190.488	−	109.979i	0.244844	−	0.141361i
$779$			536.901i			0.689218i
$780$			443.263i			0.568285i
$781$	−502.602	−	290.178i	−0.643537	−	0.371546i
$782$		−	14.2870i		−	0.0182699i
$783$	−126.411	+	72.9836i	−0.161445	+	0.0932102i
$784$	130.351	+	225.775i	0.166265	+	0.287979i
$785$	−435.503	−	251.438i	−0.554781	−	0.320303i
$786$	26.5669	−	46.0152i	0.0338001	−	0.0585435i
$787$	−121.268	−	70.0138i	−0.154088	−	0.0889630i	0.420973	−	0.907073i	$-0.361689\pi$
$787$	−121.268	−	70.0138i	−0.154088	−	0.0889630i	−0.575062	+	0.818110i	$0.695022\pi$
$788$	267.601	+	154.499i	0.339595	+	0.196065i
$789$			529.051i			0.670534i
$790$		−	357.657i		−	0.452730i
$791$	−589.501	+	1021.05i	−0.745261	+	1.29083i
$792$	−105.194	−	182.202i	−0.132821	−	0.230053i
$793$	657.848	+	1139.43i	0.829569	+	1.43686i
$794$	39.1934	+	22.6283i	0.0493620	+	0.0284992i
$795$			331.028i			0.416387i
$796$	707.595			0.888939
$797$	−429.835	−	744.495i	−0.539316	−	0.934122i	−0.998941	−	0.0460092i	$-0.985350\pi$
$797$	−429.835	−	744.495i	−0.539316	−	0.934122i	0.459625	−	0.888113i	$-0.347984\pi$
$798$	−75.1480	−	43.3867i	−0.0941704	−	0.0543693i
$799$	71.7806			0.0898380
$800$	−187.677	+	108.356i	−0.234597	+	0.135444i
$801$	243.480			0.303970
$802$	−195.335	+	338.330i	−0.243560	+	0.421858i
$803$			1616.48i			2.01305i
$804$	−362.346	+	162.603i	−0.450679	+	0.202242i
$805$	234.737			0.291598
$806$	−490.919	−	283.432i	−0.609080	−	0.351653i
$807$			102.285i			0.126747i
$808$	262.411	+	454.509i	0.324766	+	0.562511i
$809$		−	246.524i		−	0.304727i	−0.988325	−	0.152363i	$-0.951312\pi$
$809$		−	246.524i		−	0.304727i	0.988325	−	0.152363i	$-0.0486884\pi$
$810$	14.3911	−	24.9261i	0.0177668	−	0.0307730i
$811$	−309.780	+	178.851i	−0.381972	+	0.220532i	−0.678676	−	0.734438i	$-0.737446\pi$
$811$	−309.780	+	178.851i	−0.381972	+	0.220532i	0.296704	+	0.954970i	$0.404113\pi$
$812$		−	842.128i		−	1.03710i
$813$	654.464			0.804999
$814$	−170.089	+	294.603i	−0.208955	+	0.361920i
$815$	−429.799	+	248.145i	−0.527361	+	0.304472i
$816$	−41.6286	+	24.0343i	−0.0510155	+	0.0294538i
$817$	160.353	+	92.5797i	0.196270	+	0.113317i
$818$	510.762			0.624404
$819$	−466.995			−0.570202
$820$	513.717	−	889.784i	0.626484	−	1.08510i
$821$	−253.034	+	438.269i	−0.308203	+	0.533823i	−0.977969	−	0.208749i	$-0.933061\pi$
$821$	−253.034	+	438.269i	−0.308203	+	0.533823i	0.669767	+	0.742572i	$0.266394\pi$
$822$	241.854	+	139.635i	0.294226	+	0.169872i
$823$	125.195	−	216.845i	0.152121	−	0.263481i	−0.779886	−	0.625921i	$-0.784723\pi$
$823$	125.195	−	216.845i	0.152121	−	0.263481i	0.932007	+	0.362441i	$0.118056\pi$
$824$	76.4311	−	44.1275i	0.0927562	−	0.0535528i
$825$	−78.5306	−	136.019i	−0.0951887	−	0.164872i
$826$	102.466			0.124051
$827$	329.117	−	570.047i	0.397965	−	0.689295i	−0.595510	−	0.803348i	$-0.703050\pi$
$827$	329.117	−	570.047i	0.397965	−	0.689295i	0.993475	+	0.114053i	$0.0363833\pi$
$828$	65.3874			0.0789703
$829$	770.181			0.929048			0.464524	−	0.885561i	$-0.346225\pi$
$829$	770.181			0.929048			0.464524	+	0.885561i	$0.346225\pi$
$830$	−93.6583	−	162.221i	−0.112841	−	0.195447i
$831$		−	240.361i		−	0.289243i
$832$	−231.289	−	133.535i	−0.277991	−	0.160498i
$833$	−40.9225	−	70.8798i	−0.0491266	−	0.0850898i
$834$	−167.619	−	96.7748i	−0.200982	−	0.116037i
$835$	−105.580	+	60.9569i	−0.126444	+	0.0730023i
$836$	277.280	−	160.088i	0.331675	−	0.191493i
$837$	−109.042	−	188.866i	−0.130277	−	0.225647i
$838$	−29.9595	+	17.2971i	−0.0357512	+	0.0206410i
$839$	756.871	+	1310.94i	0.902110	+	1.56250i	0.824750	+	0.565498i	$0.191316\pi$
$839$	756.871	+	1310.94i	0.902110	+	1.56250i	0.0773606	+	0.997003i	$0.475351\pi$
$840$	180.066	+	311.884i	0.214364	+	0.371290i
$841$	25.9364	−	44.9232i	0.0308400	−	0.0534165i
$842$	−58.9247	+	34.0202i	−0.0699818	+	0.0404040i
$843$	205.753	−	356.375i	0.244073	−	0.422746i
$844$	−1051.28			−1.24559
$845$	534.997	−	308.880i	0.633132	−	0.365539i
$846$		−	55.4470i		−	0.0655401i
$847$			293.880i			0.346965i
$848$	−369.831	−	213.522i	−0.436122	−	0.251795i
$849$			508.638i			0.599103i
$850$	14.1710	−	8.18164i	0.0166718	−	0.00962546i
$851$	−114.647	−	198.575i	−0.134721	−	0.233343i
$852$	239.650	+	138.362i	0.281280	+	0.162397i
$853$	−211.274	+	365.937i	−0.247683	+	0.429000i	−0.962883	−	0.269921i	$-0.913003\pi$
$853$	−211.274	+	365.937i	−0.247683	+	0.429000i	0.715199	+	0.698920i	$0.246336\pi$
$854$	426.847	+	246.440i	0.499821	+	0.288572i
$855$	82.2691	+	47.4981i	0.0962211	+	0.0555533i
$856$			1072.64i			1.25308i
$857$		−	390.360i		−	0.455496i	−0.973720	−	0.227748i	$-0.926864\pi$
$857$		−	390.360i		−	0.455496i	0.973720	−	0.227748i	$-0.0731363\pi$
$858$	−145.413	+	251.862i	−0.169479	+	0.293546i
$859$	−443.135	−	767.532i	−0.515873	−	0.893518i	−0.999830	−	0.0184262i	$-0.994134\pi$
$859$	−443.135	−	767.532i	−0.515873	−	0.893518i	0.483958	−	0.875091i	$-0.339199\pi$
$860$	−177.164	−	306.857i	−0.206005	−	0.356811i
$861$	937.424	+	541.222i	1.08876	+	0.628597i
$862$			572.209i			0.663816i
$863$	−869.580			−1.00762			−0.503812	−	0.863813i	$-0.668070\pi$
$863$	−869.580			−1.00762			−0.503812	+	0.863813i	$0.668070\pi$
$864$	77.1896	+	133.696i	0.0893398	+	0.154741i
$865$	−575.251	−	332.122i	−0.665031	−	0.383956i
$866$	577.621			0.666999
$867$	−420.431	+	242.736i	−0.484926	+	0.279972i
$868$	1258.19			1.44953
$869$	−695.168	+	1204.07i	−0.799963	+	1.38558i
$870$		−	155.602i		−	0.178853i
$871$	965.317	+	697.025i	1.10829	+	0.800258i
$872$	409.414			0.469512
$873$	−53.7056	−	31.0070i	−0.0615185	−	0.0355177i
$874$		−	36.4246i		−	0.0416757i
$875$	595.154	+	1030.84i	0.680176	+	1.17810i
$876$		−	770.770i		−	0.879875i
$877$	167.252	−	289.688i	0.190709	−	0.330317i	−0.754777	−	0.655982i	$-0.772255\pi$
$877$	167.252	−	289.688i	0.190709	−	0.330317i	0.945485	+	0.325665i	$0.105588\pi$
$878$	−195.149	+	112.669i	−0.222265	+	0.128325i
$879$			759.209i			0.863719i
$880$	−491.836			−0.558905
$881$	469.758	−	813.644i	0.533210	−	0.923546i	−0.466038	−	0.884765i	$-0.654319\pi$
$881$	469.758	−	813.644i	0.533210	−	0.923546i	0.999248	−	0.0387816i	$-0.0123477\pi$
$882$	−54.7512	+	31.6106i	−0.0620762	+	0.0358397i
$883$	−3.38044	+	1.95170i	−0.00382836	+	0.00221030i	−0.501913	−	0.864918i	$-0.667370\pi$
$883$	−3.38044	+	1.95170i	−0.00382836	+	0.00221030i	0.498085	+	0.867128i	$0.334037\pi$
$884$	155.470	+	89.7605i	0.175871	+	0.101539i
$885$	−112.176			−0.126752
$886$	−382.556			−0.431779
$887$	−187.398	+	324.584i	−0.211272	+	0.365934i	−0.952113	−	0.305747i	$-0.901094\pi$
$887$	−187.398	+	324.584i	−0.211272	+	0.365934i	0.740841	+	0.671681i	$0.234427\pi$
$888$	175.892	−	304.654i	0.198076	−	0.343078i
$889$	1467.06	+	847.006i	1.65023	+	0.952763i
$890$	−129.776	+	224.778i	−0.145815	+	0.252560i
$891$	−96.8964	+	55.9432i	−0.108750	+	0.0627869i
$892$	171.142	+	296.427i	0.191864	+	0.332317i
$893$	183.004			0.204931
$894$	120.913	−	209.427i	0.135249	−	0.234258i
$895$	757.981			0.846906
$896$	−1141.03			−1.27347
$897$	−98.0145	−	169.766i	−0.109269	−	0.189260i
$898$		−	122.631i		−	0.136560i
$899$	−1021.05	−	589.502i	−1.13576	−	0.655730i
$900$	37.4449	+	64.8565i	0.0416055	+	0.0720628i
$901$	116.105	+	67.0331i	0.128862	+	0.0743985i
$902$	583.789	−	337.051i	0.647216	−	0.373670i
$903$	323.287	−	186.650i	0.358014	−	0.206699i
$904$	−379.641	−	657.558i	−0.419957	−	0.727387i
$905$	−3.95158	+	2.28144i	−0.00436638	+	0.00252093i
$906$	−29.8264	−	51.6608i	−0.0329209	−	0.0570207i
$907$	−235.627	−	408.118i	−0.259787	−	0.449964i	0.706398	−	0.707815i	$-0.250319\pi$
$907$	−235.627	−	408.118i	−0.259787	−	0.449964i	−0.966185	+	0.257851i	$0.916986\pi$
$908$	591.598	−	1024.68i	0.651539	−	1.12850i
$909$	241.712	−	139.552i	0.265909	−	0.153523i
$910$	248.910	−	431.125i	0.273528	−	0.473764i
$911$	70.2894			0.0771564			0.0385782	−	0.999256i	$-0.487717\pi$
$911$	70.2894			0.0771564			0.0385782	+	0.999256i	$0.487717\pi$
$912$	−106.132	+	61.2751i	−0.116372	+	0.0671876i
$913$			728.165i			0.797551i
$914$		−	596.742i		−	0.652890i
$915$	−467.295	−	269.793i	−0.510705	−	0.294856i
$916$		−	1231.42i		−	1.34435i
$917$	306.192	−	176.780i	0.333907	−	0.192781i
$918$	−5.82839	−	10.0951i	−0.00634901	−	0.0109968i
$919$	−1249.27	−	721.265i	−1.35938	−	0.784837i	−0.369837	−	0.929097i	$-0.620586\pi$
$919$	−1249.27	−	721.265i	−1.35938	−	0.784837i	−0.989540	+	0.144260i	$0.953920\pi$
$920$	−75.5857	+	130.918i	−0.0821584	+	0.142302i
$921$	757.475	+	437.328i	0.822448	+	0.474841i
$922$	−168.323	−	97.1813i	−0.182563	−	0.105403i
$923$		−	829.609i		−	0.898818i
$924$		−	645.505i		−	0.698599i
$925$	131.309	−	227.433i	0.141955	−	0.245874i
$926$	207.030	+	358.587i	0.223575	+	0.387243i
$927$	−23.4674	−	40.6467i	−0.0253154	−	0.0438476i
$928$	722.788	+	417.302i	0.778867	+	0.449679i
$929$		−	1086.60i		−	1.16965i	−0.811161	−	0.584823i	$-0.801164\pi$
$929$		−	1086.60i		−	1.16965i	0.811161	−	0.584823i	$-0.198836\pi$
$930$	232.479			0.249977
$931$	−104.331	−	180.707i	−0.112064	−	0.194100i
$932$	1189.93	+	687.009i	1.27675	+	0.737134i
$933$	−577.967			−0.619472
$934$	−206.031	+	118.952i	−0.220590	+	0.127358i
$935$	154.407			0.165141
$936$	150.374	−	260.455i	0.160656	−	0.278264i
$937$			794.625i			0.848052i	0.905650	+	0.424026i	$0.139384\pi$
$937$			794.625i			0.848052i	−0.905650	+	0.424026i	$0.860616\pi$
$938$	443.732	+	45.3219i	0.473062	+	0.0483176i
$939$	8.96774			0.00955031
$940$	−303.285	−	175.101i	−0.322643	−	0.186278i
$941$			1589.30i			1.68895i	0.535597	+	0.844474i	$0.320087\pi$
$941$			1589.30i			1.68895i	−0.535597	+	0.844474i	$0.679913\pi$
$942$	78.6603	+	136.244i	0.0835035	+	0.144632i
$943$			454.374i			0.481838i
$944$	72.3563	−	125.325i	0.0766487	−	0.132759i
$945$	165.862	−	95.7607i	0.175516	−	0.101334i
$946$		−	232.475i		−	0.245746i
$947$	1119.04			1.18167			0.590834	−	0.806793i	$-0.298799\pi$
$947$	1119.04			1.18167			0.590834	+	0.806793i	$0.298799\pi$
$948$	331.469	−	574.122i	0.349651	−	0.605614i
$949$	−2001.16	+	1155.37i	−2.10870	+	1.21746i
$950$	36.1288	−	20.8590i	0.0380303	−	0.0219568i
$951$	117.768	+	67.9932i	0.123836	+	0.0714966i
$952$	145.853			0.153207
$953$	1687.76			1.77100			0.885498	−	0.464643i	$-0.153817\pi$
$953$	1687.76			1.77100			0.885498	+	0.464643i	$0.153817\pi$
$954$	51.7797	−	89.6851i	0.0542764	−	0.0940096i
$955$	−410.096	+	710.308i	−0.429420	+	0.743778i
$956$	−1259.78	−	727.333i	−1.31776	−	0.760809i
$957$	−302.440	+	523.841i	−0.316029	+	0.547378i
$958$	431.316	−	249.021i	0.450226	−	0.259938i
$959$	929.151	+	1609.34i	0.968875	+	1.67814i
$960$	109.529			0.114093
$961$	400.251	−	693.255i	0.416494	−	0.721389i
$962$	−486.280			−0.505489
$963$	570.439			0.592356
$964$	457.512	+	792.435i	0.474598	+	0.822028i
$965$			121.616i			0.126027i
$966$	−63.5970	−	36.7177i	−0.0658354	−	0.0380101i
$967$	538.628	+	932.932i	0.557010	+	0.964769i	0.997744	+	0.0671316i	$0.0213847\pi$
$967$	538.628	+	932.932i	0.557010	+	0.964769i	−0.440734	+	0.897638i	$0.645282\pi$
$968$	−163.904	−	94.6300i	−0.169322	−	0.0977582i
$969$	33.3189	−	19.2367i	0.0343849	−	0.0198521i
$970$	57.2506	−	33.0537i	0.0590212	−	0.0340759i
$971$	513.513	+	889.431i	0.528850	+	0.915995i	0.999434	+	0.0336399i	$0.0107099\pi$
$971$	513.513	+	889.431i	0.528850	+	0.915995i	−0.470584	+	0.882355i	$0.655957\pi$
$972$	46.2021	−	26.6748i	0.0475330	−	0.0274432i
$973$	−643.955	−	1115.36i	−0.661825	−	1.14631i
$974$	−35.4954	−	61.4798i	−0.0364429	−	0.0631209i
$975$	112.258	−	194.437i	0.115137	−	0.199423i
$976$	602.836	−	348.048i	0.617660	−	0.356606i
$977$	82.2163	−	142.403i	0.0841518	−	0.145755i	−0.820878	−	0.571104i	$-0.806515\pi$
$977$	82.2163	−	142.403i	0.0841518	−	0.145755i	0.905029	+	0.425349i	$0.139849\pi$
$978$	155.260			0.158753
$979$	873.790	−	504.483i	0.892533	−	0.515304i
$980$			399.305i			0.407454i
$981$		−	217.730i		−	0.221947i
$982$	381.301	+	220.144i	0.388290	+	0.224179i
$983$			938.305i			0.954532i	0.878759	+	0.477266i	$0.158372\pi$
$983$			938.305i			0.954532i	−0.878759	+	0.477266i	$0.841628\pi$
$984$	−603.705	+	348.549i	−0.613522	+	0.354217i
$985$	189.958	+	329.017i	0.192851	+	0.334027i
$986$	−54.5759	−	31.5094i	−0.0553508	−	0.0319568i
$987$	184.476	−	319.523i	0.186906	−	0.323731i
$988$	396.368	+	228.843i	0.401182	+	0.231623i
$989$	135.705	+	78.3492i	0.137214	+	0.0792207i
$990$		−	119.272i		−	0.120476i
$991$		−	133.644i		−	0.134858i	−0.997724	−	0.0674288i	$-0.978520\pi$
$991$		−	133.644i		−	0.134858i	0.997724	−	0.0674288i	$-0.0214795\pi$
$992$	−623.474	+	1079.89i	−0.628502	+	1.08860i
$993$	−109.394	−	189.477i	−0.110166	−	0.190812i
$994$	−155.392	−	269.147i	−0.156330	−	0.270772i
$995$	753.436	+	434.997i	0.757222	+	0.437183i
$996$		−	347.203i		−	0.348597i
$997$	238.969			0.239688			0.119844	−	0.992793i	$-0.461761\pi$
$997$	238.969			0.239688			0.119844	+	0.992793i	$0.461761\pi$
$998$	179.540	+	310.973i	0.179900	+	0.311596i
$999$	−162.017	−	93.5408i	−0.162180	−	0.0936345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.172.7	yes	22
67.30	odd	6	inner	201.3.h.a.97.7	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.7	✓	22	67.30	odd	6	inner
201.3.h.a.172.7	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	201.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.658194 + 0.380008i) q^{2} +1.73205i q^{3} +(-1.71119 - 2.96386i) q^{4} -4.20783i q^{5} +(-0.658194 + 1.14002i) q^{6} +(-7.58591 + 4.37973i) q^{7} -5.64113i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.658194 + 0.380008i) q^{2} +1.73205i q^{3} +(-1.71119 - 2.96386i) q^{4} -4.20783i q^{5} +(-0.658194 + 1.14002i) q^{6} +(-7.58591 + 4.37973i) q^{7} -5.64113i q^{8} -3.00000 q^{9} +(1.59901 - 2.76957i) q^{10} +(-10.7663 + 6.21591i) q^{11} +(5.13356 - 2.96386i) q^{12} +(-15.3902 - 8.88555i) q^{13} -6.65733 q^{14} +7.28818 q^{15} +(-4.70108 + 8.14250i) q^{16} +(1.47585 - 2.55625i) q^{17} +(-1.97458 - 1.14002i) q^{18} +(3.76267 - 6.51714i) q^{19} +(-12.4714 + 7.20039i) q^{20} +(-7.58591 - 13.1392i) q^{21} -9.44838 q^{22} +(3.18431 - 5.51539i) q^{23} +9.77072 q^{24} +7.29414 q^{25} +(-6.75317 - 11.6968i) q^{26} -5.19615i q^{27} +(25.9618 + 14.9891i) q^{28} +(-14.0457 - 24.3279i) q^{29} +(4.79703 + 2.76957i) q^{30} +(36.3473 - 20.9851i) q^{31} +(-25.7299 + 14.8551i) q^{32} +(-10.7663 - 18.6477i) q^{33} +(1.94280 - 1.12167i) q^{34} +(18.4292 + 31.9202i) q^{35} +(5.13356 + 8.89159i) q^{36} +(18.0019 - 31.1803i) q^{37} +(4.95313 - 2.85969i) q^{38} +(15.3902 - 26.6567i) q^{39} -23.7369 q^{40} +(-61.7872 + 35.6729i) q^{41} -11.5308i q^{42} +24.6048i q^{43} +(36.8462 + 21.2732i) q^{44} +12.6235i q^{45} +(4.19178 - 2.42013i) q^{46} +(12.1592 + 21.0603i) q^{47} +(-14.1032 - 8.14250i) q^{48} +(13.8640 - 24.0132i) q^{49} +(4.80095 + 2.77183i) q^{50} +(4.42756 + 2.55625i) q^{51} +60.8194i q^{52} +45.4198i q^{53} +(1.97458 - 3.42007i) q^{54} +(26.1555 + 45.3027i) q^{55} +(24.7066 + 42.7931i) q^{56} +(11.2880 + 6.51714i) q^{57} -21.3499i q^{58} -15.3914 q^{59} +(-12.4714 - 21.6012i) q^{60} +(-64.1168 - 37.0179i) q^{61} +31.8981 q^{62} +(22.7577 - 13.1392i) q^{63} +15.0283 q^{64} +(-37.3889 + 64.7595i) q^{65} -16.3651i q^{66} +(-66.6532 - 6.80782i) q^{67} -10.1019 q^{68} +(9.55293 + 5.51539i) q^{69} +28.0129i q^{70} +(23.3415 + 40.4287i) q^{71} +16.9234i q^{72} +(65.0140 - 112.607i) q^{73} +(23.6975 - 13.6818i) q^{74} +12.6338i q^{75} -25.7545 q^{76} +(54.4479 - 94.3066i) q^{77} +(20.2595 - 11.6968i) q^{78} +(96.8536 - 55.9185i) q^{79} +(34.2623 + 19.7813i) q^{80} +9.00000 q^{81} -54.2239 q^{82} +(29.2863 - 50.7254i) q^{83} +(-25.9618 + 44.9672i) q^{84} +(-10.7563 - 6.21015i) q^{85} +(-9.35002 + 16.1947i) q^{86} +(42.1371 - 24.3279i) q^{87} +(35.0647 + 60.7339i) q^{88} -81.1599 q^{89} +(-4.79703 + 8.30871i) q^{90} +155.665 q^{91} -21.7958 q^{92} +(36.3473 + 62.9554i) q^{93} +18.4823i q^{94} +(-27.4230 - 15.8327i) q^{95} +(-25.7299 - 44.5654i) q^{96} +(17.9019 + 10.3357i) q^{97} +(18.2504 - 10.5369i) q^{98} +(32.2988 - 18.6477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9}+O(q^{10}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9	\( 22 q + 26 q^{4} - 15 q^{7} - 66 q^{9} + 6 q^{10} + 30 q^{11} - 78 q^{12} - 27 q^{13} + 6 q^{14} - 6 q^{15} - 58 q^{16} - 8 q^{17} + q^{19} - 12 q^{20} - 15 q^{21} + 14 q^{22} - q^{23} - 56 q^{25} + 71 q^{26} - 75 q^{28} + 42 q^{29} + 18 q^{30} + 120 q^{31} - 105 q^{32} + 30 q^{33} - 24 q^{34} + 3 q^{35} - 78 q^{36} + 13 q^{37} + 108 q^{38} + 27 q^{39} + 82 q^{40} - 159 q^{41} + 189 q^{44} + 372 q^{46} - 35 q^{47} - 174 q^{48} - 40 q^{49} + 285 q^{50} - 24 q^{51} - 212 q^{55} - 113 q^{56} + 3 q^{57} + 136 q^{59} - 12 q^{60} + 63 q^{61} - 150 q^{62} + 45 q^{63} - 284 q^{64} - 20 q^{65} + 94 q^{67} + 154 q^{68} - 3 q^{69} - 41 q^{71} - 16 q^{73} + 441 q^{74} - 390 q^{76} - 84 q^{77} - 213 q^{78} - 615 q^{79} + 267 q^{80} + 198 q^{81} - 302 q^{82} - 154 q^{83} + 75 q^{84} + 633 q^{85} + 221 q^{86} - 126 q^{87} + 410 q^{88} + 56 q^{89} - 18 q^{90} + 272 q^{91} + 636 q^{92} + 120 q^{93} + 588 q^{95} - 105 q^{96} - 441 q^{97} + 780 q^{98} - 90 q^{99}+O(q^{100}) \) 22 * q + 26 * q^4 - 15 * q^7 - 66 * q^9 + 6 * q^10 + 30 * q^11 - 78 * q^12 - 27 * q^13 + 6 * q^14 - 6 * q^15 - 58 * q^16 - 8 * q^17 + q^19 - 12 * q^20 - 15 * q^21 + 14 * q^22 - q^23 - 56 * q^25 + 71 * q^26 - 75 * q^28 + 42 * q^29 + 18 * q^30 + 120 * q^31 - 105 * q^32 + 30 * q^33 - 24 * q^34 + 3 * q^35 - 78 * q^36 + 13 * q^37 + 108 * q^38 + 27 * q^39 + 82 * q^40 - 159 * q^41 + 189 * q^44 + 372 * q^46 - 35 * q^47 - 174 * q^48 - 40 * q^49 + 285 * q^50 - 24 * q^51 - 212 * q^55 - 113 * q^56 + 3 * q^57 + 136 * q^59 - 12 * q^60 + 63 * q^61 - 150 * q^62 + 45 * q^63 - 284 * q^64 - 20 * q^65 + 94 * q^67 + 154 * q^68 - 3 * q^69 - 41 * q^71 - 16 * q^73 + 441 * q^74 - 390 * q^76 - 84 * q^77 - 213 * q^78 - 615 * q^79 + 267 * q^80 + 198 * q^81 - 302 * q^82 - 154 * q^83 + 75 * q^84 + 633 * q^85 + 221 * q^86 - 126 * q^87 + 410 * q^88 + 56 * q^89 - 18 * q^90 + 272 * q^91 + 636 * q^92 + 120 * q^93 + 588 * q^95 - 105 * q^96 - 441 * q^97 + 780 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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