LMFDB - Embedded newform 201.3.h.a.97.5

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			97.5
Character	$\chi$	$=$	201.97
Dual form			201.3.h.a.172.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.443170 + 0.255864i) q^{2} -1.73205i q^{3} +(-1.86907 + 3.23732i) q^{4} -5.57502i q^{5} +(0.443170 + 0.767593i) q^{6} +(3.11708 + 1.79965i) q^{7} -3.95982i q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.443170 + 0.255864i) q^{2} -1.73205i q^{3} +(-1.86907 + 3.23732i) q^{4} -5.57502i q^{5} +(0.443170 + 0.767593i) q^{6} +(3.11708 + 1.79965i) q^{7} -3.95982i q^{8} -3.00000 q^{9} +(1.42645 + 2.47068i) q^{10} +(-8.16117 - 4.71186i) q^{11} +(5.60720 + 3.23732i) q^{12} +(-3.89934 + 2.25129i) q^{13} -1.84186 q^{14} -9.65622 q^{15} +(-6.46309 - 11.1944i) q^{16} +(-12.0566 - 20.8826i) q^{17} +(1.32951 - 0.767593i) q^{18} +(-6.97614 - 12.0830i) q^{19} +(18.0481 + 10.4201i) q^{20} +(3.11708 - 5.39894i) q^{21} +4.82238 q^{22} +(-5.76224 - 9.98049i) q^{23} -6.85861 q^{24} -6.08087 q^{25} +(1.15205 - 1.99541i) q^{26} +5.19615i q^{27} +(-11.6521 + 6.72732i) q^{28} +(1.52213 - 2.63641i) q^{29} +(4.27935 - 2.47068i) q^{30} +(-37.2593 - 21.5117i) q^{31} +(19.4457 + 11.2270i) q^{32} +(-8.16117 + 14.1356i) q^{33} +(10.6862 + 6.16969i) q^{34} +(10.0331 - 17.3778i) q^{35} +(5.60720 - 9.71196i) q^{36} +(0.844262 + 1.46230i) q^{37} +(6.18323 + 3.56989i) q^{38} +(3.89934 + 6.75386i) q^{39} -22.0761 q^{40} +(36.4380 + 21.0375i) q^{41} +3.19020i q^{42} +46.0678i q^{43} +(30.5076 - 17.6136i) q^{44} +16.7251i q^{45} +(5.10730 + 2.94870i) q^{46} +(22.2690 - 38.5711i) q^{47} +(-19.3893 + 11.1944i) q^{48} +(-18.0225 - 31.2160i) q^{49} +(2.69486 - 1.55588i) q^{50} +(-36.1697 + 20.8826i) q^{51} -16.8312i q^{52} +29.2703i q^{53} +(-1.32951 - 2.30278i) q^{54} +(-26.2687 + 45.4987i) q^{55} +(7.12628 - 12.3431i) q^{56} +(-20.9284 + 12.0830i) q^{57} +1.55784i q^{58} +52.6250 q^{59} +(18.0481 - 31.2603i) q^{60} +(27.8368 - 16.0716i) q^{61} +22.0163 q^{62} +(-9.35124 - 5.39894i) q^{63} +40.2144 q^{64} +(12.5510 + 21.7389i) q^{65} -8.35261i q^{66} +(6.42069 + 66.6916i) q^{67} +90.1381 q^{68} +(-17.2867 + 9.98049i) q^{69} +10.2684i q^{70} +(-18.2728 + 31.6494i) q^{71} +11.8795i q^{72} +(19.0069 + 32.9210i) q^{73} +(-0.748302 - 0.432033i) q^{74} +10.5324i q^{75} +52.1555 q^{76} +(-16.9594 - 29.3745i) q^{77} +(-3.45614 - 1.99541i) q^{78} +(57.0858 + 32.9585i) q^{79} +(-62.4090 + 36.0319i) q^{80} +9.00000 q^{81} -21.5309 q^{82} +(-32.6821 - 56.6071i) q^{83} +(11.6521 + 20.1820i) q^{84} +(-116.421 + 67.2156i) q^{85} +(-11.7871 - 20.4159i) q^{86} +(-4.56639 - 2.63641i) q^{87} +(-18.6581 + 32.3168i) q^{88} +45.8085 q^{89} +(-4.27935 - 7.41204i) q^{90} -16.2061 q^{91} +43.0801 q^{92} +(-37.2593 + 64.5351i) q^{93} +22.7914i q^{94} +(-67.3632 + 38.8922i) q^{95} +(19.4457 - 33.6810i) q^{96} +(135.610 - 78.2947i) q^{97} +(15.9741 + 9.22265i) q^{98} +(24.4835 + 14.1356i) 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 $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.443170	+	0.255864i	−0.221585	+	0.127932i	−0.606684	−	0.794943i	$-0.707501\pi$
$2$	−0.443170	+	0.255864i	−0.221585	+	0.127932i	0.385099	+	0.922875i	$0.374167\pi$
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−1.86907	+	3.23732i	−0.467267	+	0.809330i
$5$		−	5.57502i		−	1.11500i	−0.830175	−	0.557502i	$-0.811760\pi$
$5$		−	5.57502i		−	1.11500i	0.830175	−	0.557502i	$-0.188240\pi$
$6$	0.443170	+	0.767593i	0.0738616	+	0.127932i
$7$	3.11708	+	1.79965i	0.445297	+	0.257092i	0.705842	−	0.708369i	$-0.250569\pi$
$7$	3.11708	+	1.79965i	0.445297	+	0.257092i	−0.260545	+	0.965462i	$0.583902\pi$
$8$		−	3.95982i		−	0.494978i
$9$	−3.00000			−0.333333
$10$	1.42645	+	2.47068i	0.142645	+	0.247068i
$11$	−8.16117	−	4.71186i	−0.741925	−	0.428351i	0.0808438	−	0.996727i	$-0.474238\pi$
$11$	−8.16117	−	4.71186i	−0.741925	−	0.428351i	−0.822769	+	0.568376i	$0.807572\pi$
$12$	5.60720	+	3.23732i	0.467267	+	0.269777i
$13$	−3.89934	+	2.25129i	−0.299950	+	0.173176i	−0.642420	−	0.766353i	$-0.722070\pi$
$13$	−3.89934	+	2.25129i	−0.299950	+	0.173176i	0.342471	+	0.939529i	$0.388736\pi$
$14$	−1.84186			−0.131561
$15$	−9.65622			−0.643748
$16$	−6.46309	−	11.1944i	−0.403943	−	0.699650i
$17$	−12.0566	−	20.8826i	−0.709210	−	1.22839i	−0.965151	−	0.261695i	$-0.915719\pi$
$17$	−12.0566	−	20.8826i	−0.709210	−	1.22839i	0.255941	−	0.966692i	$-0.417615\pi$
$18$	1.32951	−	0.767593i	0.0738616	−	0.0426440i
$19$	−6.97614	−	12.0830i	−0.367165	−	0.635949i	0.621956	−	0.783052i	$-0.286338\pi$
$19$	−6.97614	−	12.0830i	−0.367165	−	0.635949i	−0.989121	+	0.147103i	$0.953005\pi$
$20$	18.0481	+	10.4201i	0.902406	+	0.521004i
$21$	3.11708	−	5.39894i	0.148432	−	0.257092i
$22$	4.82238			0.219199
$23$	−5.76224	−	9.98049i	−0.250532	−	0.433934i	0.713140	−	0.701021i	$-0.247272\pi$
$23$	−5.76224	−	9.98049i	−0.250532	−	0.433934i	−0.963672	+	0.267087i	$0.913939\pi$
$24$	−6.85861			−0.285776
$25$	−6.08087			−0.243235
$26$	1.15205	−	1.99541i	0.0443095	−	0.0767464i
$27$			5.19615i			0.192450i
$28$	−11.6521	+	6.72732i	−0.416145	+	0.240261i
$29$	1.52213	−	2.63641i	0.0524873	−	0.0909106i	−0.838588	−	0.544766i	$-0.816618\pi$
$29$	1.52213	−	2.63641i	0.0524873	−	0.0909106i	0.891075	+	0.453855i	$0.149952\pi$
$30$	4.27935	−	2.47068i	0.142645	−	0.0823560i
$31$	−37.2593	−	21.5117i	−1.20191	−	0.693925i	−0.240934	−	0.970542i	$-0.577454\pi$
$31$	−37.2593	−	21.5117i	−1.20191	−	0.693925i	−0.960981	+	0.276616i	$0.910787\pi$
$32$	19.4457	+	11.2270i	0.607679	+	0.350844i
$33$	−8.16117	+	14.1356i	−0.247308	+	0.428351i
$34$	10.6862	+	6.16969i	0.314300	+	0.181461i
$35$	10.0331	−	17.3778i	0.286659	−	0.496508i
$36$	5.60720	−	9.71196i	0.155756	−	0.269777i
$37$	0.844262	+	1.46230i	0.0228179	+	0.0395217i	0.877209	−	0.480109i	$-0.159403\pi$
$37$	0.844262	+	1.46230i	0.0228179	+	0.0395217i	−0.854391	+	0.519631i	$0.826070\pi$
$38$	6.18323	+	3.56989i	0.162717	+	0.0939445i
$39$	3.89934	+	6.75386i	0.0999832	+	0.173176i
$40$	−22.0761			−0.551903
$41$	36.4380	+	21.0375i	0.888731	+	0.513109i	0.873527	−	0.486776i	$-0.161827\pi$
$41$	36.4380	+	21.0375i	0.888731	+	0.513109i	0.0152035	+	0.999884i	$0.495160\pi$
$42$			3.19020i			0.0759571i
$43$			46.0678i			1.07134i	0.844426	+	0.535672i	$0.179942\pi$
$43$			46.0678i			1.07134i	−0.844426	+	0.535672i	$0.820058\pi$
$44$	30.5076	−	17.6136i	0.693354	−	0.400308i
$45$			16.7251i			0.371668i
$46$	5.10730	+	2.94870i	0.111028	+	0.0641022i
$47$	22.2690	−	38.5711i	0.473810	−	0.820662i	−0.525741	−	0.850645i	$-0.676212\pi$
$47$	22.2690	−	38.5711i	0.473810	−	0.820662i	0.999550	+	0.0299826i	$0.00954517\pi$
$48$	−19.3893	+	11.1944i	−0.403943	+	0.233217i
$49$	−18.0225	−	31.2160i	−0.367807	−	0.637060i
$50$	2.69486	−	1.55588i	0.0538972	−	0.0311175i
$51$	−36.1697	+	20.8826i	−0.709210	+	0.409463i
$52$		−	16.8312i		−	0.323677i
$53$			29.2703i			0.552270i	0.961119	+	0.276135i	$0.0890537\pi$
$53$			29.2703i			0.552270i	−0.961119	+	0.276135i	$0.910946\pi$
$54$	−1.32951	−	2.30278i	−0.0246205	−	0.0426440i
$55$	−26.2687	+	45.4987i	−0.477613	+	0.827250i
$56$	7.12628	−	12.3431i	0.127255	−	0.220412i
$57$	−20.9284	+	12.0830i	−0.367165	+	0.211983i
$58$			1.55784i			0.0268592i
$59$	52.6250			0.891949			0.445975	−	0.895046i	$-0.352857\pi$
$59$	52.6250			0.891949			0.445975	+	0.895046i	$0.352857\pi$
$60$	18.0481	−	31.2603i	0.300802	−	0.521004i
$61$	27.8368	−	16.0716i	0.456342	−	0.263469i	−0.254163	−	0.967161i	$-0.581800\pi$
$61$	27.8368	−	16.0716i	0.456342	−	0.263469i	0.710505	+	0.703692i	$0.248467\pi$
$62$	22.0163			0.355101
$63$	−9.35124	−	5.39894i	−0.148432	−	0.0856975i
$64$	40.2144			0.628350
$65$	12.5510	+	21.7389i	0.193092	+	0.334445i
$66$		−	8.35261i		−	0.126555i
$67$	6.42069	+	66.6916i	0.0958312	+	0.995398i
$67$	6.42069	+	66.6916i	0.0958312	+	0.995398i
$68$	90.1381			1.32556
$69$	−17.2867	+	9.98049i	−0.250532	+	0.144645i
$70$			10.2684i			0.146692i
$71$	−18.2728	+	31.6494i	−0.257363	+	0.445766i	−0.965535	−	0.260274i	$-0.916187\pi$
$71$	−18.2728	+	31.6494i	−0.257363	+	0.445766i	0.708172	+	0.706040i	$0.249520\pi$
$72$			11.8795i			0.164993i
$73$	19.0069	+	32.9210i	0.260369	+	0.450972i	0.966340	−	0.257269i	$-0.0828225\pi$
$73$	19.0069	+	32.9210i	0.260369	+	0.450972i	−0.705971	+	0.708241i	$0.749489\pi$
$74$	−0.748302	−	0.432033i	−0.0101122	−	0.00583828i
$75$			10.5324i			0.140432i
$76$	52.1555			0.686257
$77$	−16.9594	−	29.3745i	−0.220251	−	0.381486i
$78$	−3.45614	−	1.99541i	−0.0443095	−	0.0255821i
$79$	57.0858	+	32.9585i	0.722605	+	0.417196i	0.815711	−	0.578460i	$-0.196346\pi$
$79$	57.0858	+	32.9585i	0.722605	+	0.417196i	−0.0931060	+	0.995656i	$0.529680\pi$
$80$	−62.4090	+	36.0319i	−0.780113	+	0.450398i
$81$	9.00000			0.111111
$82$	−21.5309			−0.262572
$83$	−32.6821	−	56.6071i	−0.393760	−	0.682013i	0.599182	−	0.800613i	$-0.295493\pi$
$83$	−32.6821	−	56.6071i	−0.393760	−	0.682013i	−0.992942	+	0.118600i	$0.962159\pi$
$84$	11.6521	+	20.1820i	0.138715	+	0.240261i
$85$	−116.421	+	67.2156i	−1.36966	+	0.790772i
$86$	−11.7871	−	20.4159i	−0.137059	−	0.237394i
$87$	−4.56639	−	2.63641i	−0.0524873	−	0.0303035i
$88$	−18.6581	+	32.3168i	−0.212024	+	0.367236i
$89$	45.8085			0.514702			0.257351	−	0.966318i	$-0.417150\pi$
$89$	45.8085			0.514702			0.257351	+	0.966318i	$0.417150\pi$
$90$	−4.27935	−	7.41204i	−0.0475483	−	0.0823560i
$91$	−16.2061			−0.178089
$92$	43.0801			0.468261
$93$	−37.2593	+	64.5351i	−0.400638	+	0.693925i
$94$			22.7914i			0.242462i
$95$	−67.3632	+	38.8922i	−0.709086	+	0.409391i
$96$	19.4457	−	33.6810i	0.202560	−	0.350844i
$97$	135.610	−	78.2947i	1.39805	−	0.807162i	0.403858	−	0.914822i	$-0.367669\pi$
$97$	135.610	−	78.2947i	1.39805	−	0.807162i	0.994188	+	0.107660i	$0.0343357\pi$
$98$	15.9741	+	9.22265i	0.163001	+	0.0941087i
$99$	24.4835	+	14.1356i	0.247308	+	0.142784i
$100$	11.3656	−	19.6857i	0.113656	−	0.196857i
$101$	−54.6887	−	31.5745i	−0.541472	−	0.312619i	0.204203	−	0.978929i	$-0.434540\pi$
$101$	−54.6887	−	31.5745i	−0.541472	−	0.312619i	−0.745676	+	0.666309i	$0.767873\pi$
$102$	10.6862	−	18.5091i	0.104767	−	0.181461i
$103$	−45.4940	+	78.7980i	−0.441690	+	0.765029i	−0.997815	−	0.0660694i	$-0.978954\pi$
$103$	−45.4940	+	78.7980i	−0.441690	+	0.765029i	0.556125	+	0.831098i	$0.312287\pi$
$104$	8.91470	+	15.4407i	0.0857183	+	0.148468i
$105$	−30.0992	−	17.3778i	−0.286659	−	0.165503i
$106$	−7.48922	−	12.9717i	−0.0706531	−	0.122375i
$107$	−160.128			−1.49652			−0.748260	−	0.663405i	$-0.769111\pi$
$107$	−160.128			−1.49652			−0.748260	+	0.663405i	$0.769111\pi$
$108$	−16.8216	−	9.71196i	−0.155756	−	0.0899255i
$109$		−	75.6403i		−	0.693948i	−0.937875	−	0.346974i	$-0.887209\pi$
$109$		−	75.6403i		−	0.693948i	0.937875	−	0.346974i	$-0.112791\pi$
$110$		−	26.8849i		−	0.244408i
$111$	2.53278	−	1.46230i	0.0228179	−	0.0131739i
$112$		−	46.5251i		−	0.415403i
$113$	−3.89035	−	2.24610i	−0.0344279	−	0.0198770i	0.482687	−	0.875793i	$-0.339661\pi$
$113$	−3.89035	−	2.24610i	−0.0344279	−	0.0198770i	−0.517115	+	0.855916i	$0.672994\pi$
$114$	6.18323	−	10.7097i	0.0542389	−	0.0939445i
$115$	−55.6415	+	32.1246i	−0.483839	+	0.279344i
$116$	5.68993	+	9.85525i	0.0490511	+	0.0849590i
$117$	11.6980	−	6.75386i	0.0999832	−	0.0577253i
$118$	−23.3218	+	13.4649i	−0.197642	+	0.114109i
$119$		−	86.7902i		−	0.729330i
$120$			38.2369i			0.318641i
$121$	−16.0968	−	27.8805i	−0.133032	−	0.230417i
$122$	−8.22430	+	14.2449i	−0.0674123	+	0.116762i
$123$	36.4380	−	63.1124i	0.296244	−	0.513109i
$124$	139.280	−	80.4136i	1.12323	−	0.648497i
$125$		−	105.475i		−	0.843797i
$126$	5.52558			0.0438538
$127$	74.1801	−	128.484i	0.584095	−	1.01168i	−0.410892	−	0.911684i	$-0.634783\pi$
$127$	74.1801	−	128.484i	0.584095	−	1.01168i	0.994988	−	0.0999987i	$-0.0318839\pi$
$128$	−95.6047	+	55.1974i	−0.746912	+	0.431230i
$129$	79.7918			0.618541
$130$	−11.1244	−	6.42269i	−0.0855725	−	0.0494053i
$131$	160.027			1.22158			0.610789	−	0.791794i	$-0.290853\pi$
$131$	160.027			1.22158			0.610789	+	0.791794i	$0.290853\pi$
$132$	−30.5076	−	52.8407i	−0.231118	−	0.400308i
$133$		−	50.2184i		−	0.377582i
$134$	−19.9095	−	27.9129i	−0.148578	−	0.208305i
$135$	28.9687			0.214583
$136$	−82.6914	+	47.7419i	−0.608025	+	0.351043i
$137$		−	214.826i		−	1.56807i	−0.620716	−	0.784036i	$-0.713158\pi$
$137$		−	214.826i		−	1.56807i	0.620716	−	0.784036i	$-0.286842\pi$
$138$	5.10730	−	8.84611i	0.0370094	−	0.0641022i
$139$		−	128.827i		−	0.926814i	−0.886145	−	0.463407i	$-0.846627\pi$
$139$		−	128.827i		−	0.926814i	0.886145	−	0.463407i	$-0.153373\pi$
$140$	37.5050	+	64.9605i	0.267893	+	0.464004i
$141$	−66.8071	−	38.5711i	−0.473810	−	0.273554i
$142$		−	18.7014i		−	0.131700i
$143$	42.4310			0.296720
$144$	19.3893	+	33.5832i	0.134648	+	0.233217i
$145$	−14.6980	−	8.48592i	−0.101366	−	0.0585236i
$146$	−16.8466	−	9.72638i	−0.115388	−	0.0666191i
$147$	−54.0676	+	31.2160i	−0.367807	+	0.212353i
$148$	−6.31193			−0.0426481
$149$	−2.53011			−0.0169806			−0.00849031	−	0.999964i	$-0.502703\pi$
$149$	−2.53011			−0.0169806			−0.00849031	+	0.999964i	$0.502703\pi$
$150$	−2.69486	−	4.66763i	−0.0179657	−	0.0311175i
$151$	−7.58197	−	13.1324i	−0.0502117	−	0.0869692i	0.839827	−	0.542854i	$-0.182656\pi$
$151$	−7.58197	−	13.1324i	−0.0502117	−	0.0869692i	−0.890039	+	0.455885i	$0.849323\pi$
$152$	−47.8467	+	27.6243i	−0.314781	+	0.181739i
$153$	36.1697	+	62.6478i	0.236403	+	0.409463i
$154$	15.0317	+	8.67858i	0.0976087	+	0.0563544i
$155$	−119.928	+	207.722i	−0.773730	+	1.34014i
$156$	−29.1525			−0.186875
$157$	−122.224	−	211.698i	−0.778496	−	1.34839i	−0.932809	−	0.360372i	$-0.882650\pi$
$157$	−122.224	−	211.698i	−0.778496	−	1.34839i	0.154313	−	0.988022i	$-0.450684\pi$
$158$	−33.7316			−0.213491
$159$	50.6977			0.318853
$160$	62.5907	−	108.410i	0.391192	−	0.677565i
$161$		−	41.4800i		−	0.257640i
$162$	−3.98853	+	2.30278i	−0.0246205	+	0.0142147i
$163$	−67.9446	+	117.684i	−0.416838	+	0.721985i	−0.995619	−	0.0934978i	$-0.970195\pi$
$163$	−67.9446	+	117.684i	−0.416838	+	0.721985i	0.578781	+	0.815483i	$0.303529\pi$
$164$	−136.210	+	78.6409i	−0.830549	+	0.479517i
$165$	78.8061	+	45.4987i	0.477613	+	0.275750i
$166$	28.9675	+	16.7244i	0.174503	+	0.100749i
$167$	−162.589	+	281.612i	−0.973584	+	1.68630i	−0.289055	+	0.957312i	$0.593341\pi$
$167$	−162.589	+	281.612i	−0.973584	+	1.68630i	−0.684529	+	0.728985i	$0.739992\pi$
$168$	−21.3788	−	12.3431i	−0.127255	−	0.0734707i
$169$	−74.3634	+	128.801i	−0.440020	+	0.762137i
$170$	34.3961	−	59.5759i	0.202330	−	0.350446i
$171$	20.9284	+	36.2491i	0.122388	+	0.211983i
$172$	−149.136	−	86.1038i	−0.867071	−	0.500604i
$173$	0.959902	+	1.66260i	0.00554856	+	0.00961039i	0.868786	−	0.495187i	$-0.164900\pi$
$173$	0.959902	+	1.66260i	0.00554856	+	0.00961039i	−0.863238	+	0.504798i	$0.831567\pi$
$174$	2.69825			0.0155072
$175$	−18.9546	−	10.9434i	−0.108312	−	0.0625338i
$176$			121.813i			0.692117i
$177$		−	91.1492i		−	0.514967i
$178$	−20.3009	+	11.7208i	−0.114050	+	0.0658469i
$179$			25.4108i			0.141960i	0.997478	+	0.0709800i	$0.0226126\pi$
$179$			25.4108i			0.141960i	−0.997478	+	0.0709800i	$0.977387\pi$
$180$	−54.1444	−	31.2603i	−0.300802	−	0.173668i
$181$	−58.9822	+	102.160i	−0.325868	+	0.564420i	−0.981688	−	0.190497i	$-0.938990\pi$
$181$	−58.9822	+	102.160i	−0.325868	+	0.564420i	0.655819	+	0.754918i	$0.272323\pi$
$182$	7.18205	−	4.14656i	0.0394618	−	0.0227833i
$183$	−27.8368	−	48.2148i	−0.152114	−	0.263469i
$184$	−39.5210	+	22.8175i	−0.214788	+	0.124008i
$185$	8.15238	−	4.70678i	0.0440669	−	0.0254420i
$186$		−	38.1333i		−	0.205018i
$187$			227.235i			1.21516i
$188$	83.2447	+	144.184i	0.442791	+	0.766936i
$189$	−9.35124	+	16.1968i	−0.0494774	+	0.0856975i
$190$	19.9022	−	34.4717i	0.104749	−	0.181430i
$191$	219.035	−	126.460i	1.14678	−	0.662095i	0.198681	−	0.980064i	$-0.436334\pi$
$191$	219.035	−	126.460i	1.14678	−	0.662095i	0.948101	+	0.317970i	$0.103001\pi$
$192$		−	69.6534i		−	0.362778i
$193$	29.2615			0.151614			0.0758071	−	0.997123i	$-0.475847\pi$
$193$	29.2615			0.151614			0.0758071	+	0.997123i	$0.475847\pi$
$194$	−40.0656	+	69.3957i	−0.206524	+	0.357710i
$195$	37.6529	−	21.7389i	0.193092	−	0.111482i
$196$	134.741			0.687456
$197$	−216.226	−	124.838i	−1.09760	−	0.633697i	−0.162007	−	0.986790i	$-0.551797\pi$
$197$	−216.226	−	124.838i	−1.09760	−	0.633697i	−0.935588	+	0.353092i	$0.885130\pi$
$198$	−14.4671			−0.0730664
$199$	181.375	+	314.150i	0.911430	+	1.57864i	0.812045	+	0.583594i	$0.198354\pi$
$199$	181.375	+	314.150i	0.911430	+	1.57864i	0.0993848	+	0.995049i	$0.468313\pi$
$200$			24.0792i			0.120396i
$201$	115.513	−	11.1210i	0.574693	−	0.0553282i
$202$	32.3152			0.159976
$203$	9.48921	−	5.47860i	0.0467449	−	0.0269882i
$204$		−	156.124i		−	0.765313i
$205$	117.284	−	203.142i	0.572119	−	0.990939i
$206$		−	46.5612i		−	0.226025i
$207$	17.2867	+	29.9415i	0.0835107	+	0.144645i
$208$	50.4036	+	29.1005i	0.242325	+	0.139906i
$209$			131.482i			0.629102i
$210$	17.7854			0.0846924
$211$	74.7642	+	129.495i	0.354333	+	0.613723i	0.987004	−	0.160698i	$-0.0513746\pi$
$211$	74.7642	+	129.495i	0.354333	+	0.613723i	−0.632671	+	0.774421i	$0.718041\pi$
$212$	−94.7573	−	54.7082i	−0.446969	−	0.258057i
$213$	54.8183	+	31.6494i	0.257363	+	0.148589i
$214$	70.9638	−	40.9709i	0.331606	−	0.191453i
$215$	256.829			1.19455
$216$	20.5758			0.0952585
$217$	−77.4269	−	134.107i	−0.356806	−	0.618006i
$218$	19.3536	+	33.5215i	0.0887782	+	0.153768i
$219$	57.0208	−	32.9210i	0.260369	−	0.150324i
$220$	−98.1959	−	170.080i	−0.446345	−	0.773092i
$221$	94.0254	+	54.2856i	0.425454	+	0.245636i
$222$	−0.748302	+	1.29610i	−0.00337073	+	0.00583828i
$223$	217.217			0.974066			0.487033	−	0.873384i	$-0.338079\pi$
$223$	217.217			0.974066			0.487033	+	0.873384i	$0.338079\pi$
$224$	40.4092	+	69.9909i	0.180398	+	0.312459i
$225$	18.2426			0.0810783
$226$	2.29878			0.0101716
$227$	7.54912	−	13.0755i	0.0332560	−	0.0576012i	−0.848918	−	0.528524i	$-0.822746\pi$
$227$	7.54912	−	13.0755i	0.0332560	−	0.0576012i	0.882174	+	0.470923i	$0.156079\pi$
$228$		−	90.3360i		−	0.396211i
$229$	225.573	−	130.235i	0.985034	−	0.568710i	0.0812478	−	0.996694i	$-0.474109\pi$
$229$	225.573	−	130.235i	0.985034	−	0.568710i	0.903786	+	0.427984i	$0.140776\pi$
$230$	16.4391	−	28.4733i	0.0714743	−	0.123797i
$231$	−50.8781	+	29.3745i	−0.220251	+	0.127162i
$232$	−10.4397	−	6.02737i	−0.0449988	−	0.0259800i
$233$	−54.6879	−	31.5741i	−0.234712	−	0.135511i	0.378032	−	0.925793i	$-0.376601\pi$
$233$	−54.6879	−	31.5741i	−0.234712	−	0.135511i	−0.612744	+	0.790282i	$0.709934\pi$
$234$	−3.45614	+	5.98622i	−0.0147698	+	0.0255821i
$235$	−215.035	−	124.150i	−0.915042	−	0.528300i
$236$	−98.3597	+	170.364i	−0.416778	+	0.721881i
$237$	57.0858	−	98.8754i	0.240868	−	0.417196i
$238$	22.2065	+	38.4628i	0.0933047	+	0.161608i
$239$	−203.309	−	117.380i	−0.850665	−	0.491132i	0.0102103	−	0.999948i	$-0.496750\pi$
$239$	−203.309	−	117.380i	−0.850665	−	0.491132i	−0.860875	+	0.508816i	$0.830083\pi$
$240$	62.4090	+	108.096i	0.260038	+	0.450398i
$241$	348.249			1.44502			0.722509	−	0.691361i	$-0.242989\pi$
$241$	348.249			1.44502			0.722509	+	0.691361i	$0.242989\pi$
$242$	14.2673	+	8.23720i	0.0589556	+	0.0340380i
$243$		−	15.5885i		−	0.0641500i
$244$			120.156i			0.492441i
$245$	−174.030	+	100.476i	−0.710325	+	0.410106i
$246$			37.2927i			0.151596i
$247$	54.4048	+	31.4106i	0.220262	+	0.127168i
$248$	−85.1825	+	147.540i	−0.343478	+	0.594921i
$249$	−98.0464	+	56.6071i	−0.393760	+	0.227338i
$250$	26.9872	+	46.7431i	0.107949	+	0.186973i
$251$	−191.304	+	110.449i	−0.762167	+	0.440037i	−0.830073	−	0.557655i	$-0.811701\pi$
$251$	−191.304	+	110.449i	−0.762167	+	0.440037i	0.0679064	+	0.997692i	$0.478368\pi$
$252$	34.9562	−	20.1820i	0.138715	−	0.0800871i
$253$			108.603i			0.429262i
$254$			75.9201i			0.298898i
$255$	116.421	+	201.647i	0.456552	+	0.790772i
$256$	−52.1827	+	90.3831i	−0.203839	+	0.353059i
$257$	211.180	−	365.774i	0.821711	−	1.42324i	−0.0826968	−	0.996575i	$-0.526353\pi$
$257$	211.180	−	365.774i	0.821711	−	1.42324i	0.904407	−	0.426670i	$-0.140313\pi$
$258$	−35.3613	+	20.4159i	−0.137059	+	0.0791312i
$259$			6.07749i			0.0234652i
$260$	−93.8345			−0.360902
$261$	−4.56639	+	7.90923i	−0.0174958	+	0.0303035i
$262$	−70.9190	+	40.9451i	−0.270683	+	0.156279i
$263$	346.845			1.31880			0.659401	−	0.751791i	$-0.270810\pi$
$263$	346.845			1.31880			0.659401	+	0.751791i	$0.270810\pi$
$264$	55.9744	+	32.3168i	0.212024	+	0.122412i
$265$	163.183			0.615783
$266$	12.8491	+	22.2553i	0.0483048	+	0.0836664i
$267$		−	79.3427i		−	0.297163i
$268$	−227.903	−	103.865i	−0.850384	−	0.387557i
$269$	−338.653			−1.25893			−0.629467	−	0.777027i	$-0.716727\pi$
$269$	−338.653			−1.25893			−0.629467	+	0.777027i	$0.716727\pi$
$270$	−12.8380	+	7.41204i	−0.0475483	+	0.0274520i
$271$			248.291i			0.916201i	0.888900	+	0.458101i	$0.151470\pi$
$271$			248.291i			0.916201i	−0.888900	+	0.458101i	$0.848530\pi$
$272$	−155.845	+	269.932i	−0.572961	+	0.992398i
$273$			28.0698i			0.102820i
$274$	54.9662	+	95.2043i	0.200607	+	0.347461i
$275$	49.6270	+	28.6522i	0.180462	+	0.104190i
$276$		−	74.6168i		−	0.270351i
$277$	442.986			1.59923			0.799614	−	0.600515i	$-0.205038\pi$
$277$	442.986			1.59923			0.799614	+	0.600515i	$0.205038\pi$
$278$	32.9623	+	57.0923i	0.118569	+	0.205368i
$279$	111.778	+	64.5351i	0.400638	+	0.231308i
$280$	−68.8130	−	39.7292i	−0.245761	−	0.141890i
$281$	−55.5219	+	32.0556i	−0.197587	+	0.114077i	−0.595529	−	0.803333i	$-0.703058\pi$
$281$	−55.5219	+	32.0556i	−0.197587	+	0.114077i	0.397942	+	0.917410i	$0.369724\pi$
$282$	39.4759			0.139985
$283$	−436.508			−1.54243			−0.771215	−	0.636574i	$-0.780351\pi$
$283$	−436.508			−1.54243			−0.771215	+	0.636574i	$0.780351\pi$
$284$	−68.3061	−	118.310i	−0.240514	−	0.416583i
$285$	67.3632	+	116.676i	0.236362	+	0.409391i
$286$	−18.8041	+	10.8566i	−0.0657487	+	0.0379600i
$287$	75.7200	+	131.151i	0.263833	+	0.456972i
$288$	−58.3372	−	33.6810i	−0.202560	−	0.116948i
$289$	−146.222	+	253.263i	−0.505957	+	0.876344i
$290$	8.68497			0.0299482
$291$	−135.610	−	234.884i	−0.466015	−	0.807162i
$292$	−142.101			−0.486647
$293$	48.4691			0.165424			0.0827118	−	0.996574i	$-0.473642\pi$
$293$	48.4691			0.165424			0.0827118	+	0.996574i	$0.473642\pi$
$294$	15.9741	−	27.6679i	0.0543337	−	0.0941087i
$295$		−	293.386i		−	0.994527i
$296$	5.79047	−	3.34313i	0.0195624	−	0.0112943i
$297$	24.4835	−	42.4067i	0.0824361	−	0.142784i
$298$	1.12127	−	0.647365i	0.00376265	−	0.00217237i
$299$	44.9379	+	25.9449i	0.150294	+	0.0867723i
$300$	−34.0967	−	19.6857i	−0.113656	−	0.0656190i
$301$	−82.9058	+	143.597i	−0.275434	+	0.477066i
$302$	6.72020	+	3.87991i	0.0222523	+	0.0128474i
$303$	−54.6887	+	94.7236i	−0.180491	+	0.312619i
$304$	−90.1749	+	156.188i	−0.296628	+	0.513775i
$305$	−89.5996	−	155.191i	−0.293769	−	0.508823i
$306$	−32.0586	−	18.5091i	−0.104767	−	0.0604871i
$307$	139.095	+	240.920i	0.453078	+	0.784754i	0.998575	−	0.0533584i	$-0.0169926\pi$
$307$	139.095	+	240.920i	0.453078	+	0.784754i	−0.545497	+	0.838113i	$0.683659\pi$
$308$	126.793			0.411664
$309$	136.482	+	78.7980i	0.441690	+	0.255010i
$310$		−	122.741i		−	0.395940i
$311$		−	462.392i		−	1.48679i	−0.668852	−	0.743396i	$-0.733214\pi$
$311$		−	462.392i		−	1.48679i	0.668852	−	0.743396i	$-0.266786\pi$
$312$	26.7441	−	15.4407i	0.0857183	−	0.0494895i
$313$		−	547.995i		−	1.75078i	−0.483415	−	0.875391i	$-0.660604\pi$
$313$		−	547.995i		−	1.75078i	0.483415	−	0.875391i	$-0.339396\pi$
$314$	108.332	+	62.5454i	0.345006	+	0.199189i
$315$	−30.0992	+	52.1334i	−0.0955530	+	0.165503i
$316$	−213.394	+	123.203i	−0.675298	+	0.389884i
$317$	−217.212	−	376.222i	−0.685211	−	1.18682i	−0.973370	−	0.229238i	$-0.926377\pi$
$317$	−217.212	−	376.222i	−0.685211	−	1.18682i	0.288159	−	0.957582i	$-0.406957\pi$
$318$	−22.4677	+	12.9717i	−0.0706531	+	0.0407916i
$319$	−24.8448	+	14.3441i	−0.0778833	+	0.0449659i
$320$		−	224.196i		−	0.700613i
$321$			277.349i			0.864016i
$322$	10.6132	+	18.3827i	0.0329604	+	0.0570891i
$323$	−168.217	+	291.360i	−0.520795	+	0.902043i
$324$	−16.8216	+	29.1359i	−0.0519185	+	0.0899255i
$325$	23.7114	−	13.6898i	0.0729582	−	0.0421224i
$326$		−	69.5384i		−	0.213308i
$327$	−131.013			−0.400651
$328$	83.3046	−	144.288i	0.253978	−	0.439902i
$329$	138.829	−	80.1528i	0.421972	−	0.243626i
$330$	−46.5660			−0.141109
$331$	−335.965	−	193.970i	−1.01500	−	0.586011i	−0.102349	−	0.994749i	$-0.532636\pi$
$331$	−335.965	−	193.970i	−1.01500	−	0.586011i	−0.912652	+	0.408738i	$0.865969\pi$
$332$	244.340			0.735965
$333$	−2.53278	−	4.38691i	−0.00760596	−	0.0131739i
$334$		−	166.402i		−	0.498211i
$335$	371.807	−	35.7955i	1.10987	−	0.106852i
$336$	−80.5839			−0.239833
$337$	−100.418	+	57.9763i	−0.297976	+	0.172037i	−0.641533	−	0.767095i	$-0.721701\pi$
$337$	−100.418	+	57.9763i	−0.297976	+	0.172037i	0.343557	+	0.939132i	$0.388368\pi$
$338$		−	76.1077i		−	0.225171i
$339$	−3.89035	+	6.73829i	−0.0114760	+	0.0198770i
$340$		−	502.522i		−	1.47801i
$341$	202.720	+	351.121i	0.594487	+	1.02968i
$342$	−18.5497	−	10.7097i	−0.0542389	−	0.0313148i
$343$		−	306.102i		−	0.892426i
$344$	182.420			0.530292
$345$	55.6415	+	96.3738i	0.161280	+	0.279344i
$346$	−0.850799	−	0.491209i	−0.00245896	−	0.00141968i
$347$	−217.829	−	125.764i	−0.627750	−	0.362432i	0.152130	−	0.988361i	$-0.451387\pi$
$347$	−217.829	−	125.764i	−0.627750	−	0.362432i	−0.779880	+	0.625929i	$0.784720\pi$
$348$	17.0698	−	9.85525i	0.0490511	−	0.0283197i
$349$	479.259			1.37323			0.686617	−	0.727019i	$-0.259095\pi$
$349$	479.259			1.37323			0.686617	+	0.727019i	$0.259095\pi$
$350$	11.2001			0.0320003
$351$	−11.6980	−	20.2616i	−0.0333277	−	0.0577253i
$352$	−105.800	−	183.251i	−0.300568	−	0.520599i
$353$	269.721	−	155.723i	0.764082	−	0.441143i	−0.0666776	−	0.997775i	$-0.521240\pi$
$353$	269.721	−	155.723i	0.764082	−	0.441143i	0.830759	+	0.556632i	$0.187907\pi$
$354$	23.3218	+	40.3946i	0.0658808	+	0.114109i
$355$	176.446	+	101.871i	0.497031	+	0.286961i
$356$	−85.6192	+	148.297i	−0.240503	+	0.416564i
$357$	−150.325			−0.421079
$358$	−6.50172	−	11.2613i	−0.0181612	−	0.0314562i
$359$	−215.942			−0.601508			−0.300754	−	0.953702i	$-0.597238\pi$
$359$	−215.942			−0.601508			−0.300754	+	0.953702i	$0.597238\pi$
$360$	66.2283			0.183968
$361$	83.1669	−	144.049i	0.230379	−	0.399028i
$362$		−	60.3657i		−	0.166756i
$363$	−48.2905	+	27.8805i	−0.133032	+	0.0768058i
$364$	30.2903	−	52.4643i	0.0832150	−	0.144133i
$365$	183.535	−	105.964i	0.502836	−	0.290312i
$366$	24.6729	+	14.2449i	0.0674123	+	0.0389205i
$367$	−283.438	−	163.643i	−0.772311	−	0.445894i	0.0613871	−	0.998114i	$-0.480448\pi$
$367$	−283.438	−	163.643i	−0.772311	−	0.445894i	−0.833699	+	0.552220i	$0.813781\pi$
$368$	−74.4838	+	129.010i	−0.202402	+	0.350570i
$369$	−109.314	−	63.1124i	−0.296244	−	0.171036i
$370$	−2.40859	+	4.17180i	−0.00650971	+	0.0112751i
$371$	−52.6762	+	91.2379i	−0.141984	+	0.245924i
$372$	−139.280	−	241.241i	−0.374410	−	0.648497i
$373$	328.774	+	189.818i	0.881432	+	0.508895i	0.871130	−	0.491052i	$-0.163387\pi$
$373$	328.774	+	189.818i	0.881432	+	0.508895i	0.0103018	+	0.999947i	$0.496721\pi$
$374$	−58.1414	−	100.704i	−0.155458	−	0.269262i
$375$	−182.687			−0.487166
$376$	−152.735	−	88.1815i	−0.406210	−	0.234525i
$377$			13.7070i			0.0363581i
$378$		−	9.57059i		−	0.0253190i
$379$	−566.253	+	326.926i	−1.49407	+	0.862602i	−0.999977	−	0.00680690i	$-0.997833\pi$
$379$	−566.253	+	326.926i	−1.49407	+	0.862602i	−0.494093	+	0.869409i	$0.664500\pi$
$380$		−	290.768i		−	0.765179i
$381$	−222.540	−	128.484i	−0.584095	−	0.337228i
$382$	−64.7132	+	112.087i	−0.169406	+	0.293420i
$383$	57.2662	−	33.0626i	0.149520	−	0.0863254i	−0.423373	−	0.905955i	$-0.639154\pi$
$383$	57.2662	−	33.0626i	0.149520	−	0.0863254i	0.572894	+	0.819630i	$0.305821\pi$
$384$	95.6047	+	165.592i	0.248971	+	0.431230i
$385$	−163.763	+	94.5488i	−0.425359	+	0.245581i
$386$	−12.9678	+	7.48698i	−0.0335954	+	0.0193963i
$387$		−	138.203i		−	0.357115i
$388$			585.352i			1.50864i
$389$	−62.1277	−	107.608i	−0.159711	−	0.276628i	0.775053	−	0.631896i	$-0.217723\pi$
$389$	−62.1277	−	107.608i	−0.159711	−	0.276628i	−0.934765	+	0.355268i	$0.884390\pi$
$390$	−11.1244	+	19.2681i	−0.0285242	+	0.0494053i
$391$	−138.946	+	240.661i	−0.355360	+	0.615501i
$392$	−123.610	+	71.3661i	−0.315331	+	0.182056i
$393$		−	277.174i		−	0.705278i
$394$	127.767			0.324281
$395$	183.744	−	318.254i	0.465175	−	0.805707i
$396$	−91.5227	+	52.8407i	−0.231118	+	0.133436i
$397$	−350.675			−0.883312			−0.441656	−	0.897185i	$-0.645609\pi$
$397$	−350.675			−0.883312			−0.441656	+	0.897185i	$0.645609\pi$
$398$	−160.760	−	92.8145i	−0.403918	−	0.233202i
$399$	−86.9808			−0.217997
$400$	39.3012	+	68.0717i	0.0982530	+	0.170179i
$401$		−	190.295i		−	0.474550i	−0.971443	−	0.237275i	$-0.923746\pi$
$401$		−	190.295i		−	0.474550i	0.971443	−	0.237275i	$-0.0762543\pi$
$402$	−48.3466	+	34.4842i	−0.120265	+	0.0857816i
$403$	193.716			0.480685
$404$	204.434	−	118.030i	0.506024	−	0.292153i
$405$		−	50.1752i		−	0.123889i
$406$	−2.80355	+	4.85590i	−0.00690530	+	0.0119603i
$407$		−	15.9122i		−	0.0390962i
$408$	82.6914	+	143.226i	0.202675	+	0.351043i
$409$	426.844	+	246.438i	1.04363	+	0.602539i	0.920859	−	0.389896i	$-0.127489\pi$
$409$	426.844	+	246.438i	1.04363	+	0.602539i	0.122769	+	0.992435i	$0.460822\pi$
$410$			120.035i			0.292769i
$411$	−372.089			−0.905326
$412$	−170.063	−	294.557i	−0.412774	−	0.714945i
$413$	164.036	+	94.7064i	0.397182	+	0.229313i
$414$	−15.3219	−	8.84611i	−0.0370094	−	0.0213674i
$415$	−315.586	+	182.204i	−0.760448	+	0.439045i
$416$	−101.101			−0.243031
$417$	−223.135			−0.535097
$418$	−33.6416	−	58.2690i	−0.0804824	−	0.139400i
$419$	49.5559	+	85.8333i	0.118272	+	0.204853i	0.919083	−	0.394064i	$-0.128931\pi$
$419$	49.5559	+	85.8333i	0.118272	+	0.204853i	−0.800811	+	0.598917i	$0.795598\pi$
$420$	112.515	−	64.9605i	0.267893	−	0.154668i
$421$	198.065	+	343.059i	0.470464	+	0.814868i	0.999429	−	0.0337756i	$-0.0107531\pi$
$421$	198.065	+	343.059i	0.470464	+	0.814868i	−0.528965	+	0.848644i	$0.677420\pi$
$422$	−66.2665	−	38.2590i	−0.157030	−	0.0906611i
$423$	−66.8071	+	115.713i	−0.157937	+	0.273554i
$424$	115.905			0.273361
$425$	73.3144	+	126.984i	0.172504	+	0.298787i
$426$	−32.3918			−0.0760370
$427$	115.693			0.270943
$428$	299.289	−	518.384i	0.699274	−	1.21118i
$429$		−	73.4926i		−	0.171311i
$430$	−113.819	+	65.7134i	−0.264695	+	0.152822i
$431$	62.4539	−	108.173i	0.144905	−	0.250982i	−0.784433	−	0.620214i	$-0.787046\pi$
$431$	62.4539	−	108.173i	0.144905	−	0.250982i	0.929337	+	0.369232i	$0.120379\pi$
$432$	58.1678	−	33.5832i	0.134648	−	0.0777389i
$433$	−224.722	−	129.744i	−0.518989	−	0.299639i	0.217532	−	0.976053i	$-0.430199\pi$
$433$	−224.722	−	129.744i	−0.518989	−	0.299639i	−0.736521	+	0.676415i	$0.763533\pi$
$434$	68.6265	+	39.6215i	0.158126	+	0.0912939i
$435$	−14.6980	+	25.4577i	−0.0337886	+	0.0585236i
$436$	244.872	+	141.377i	0.561632	+	0.324259i
$437$	−80.3964	+	139.251i	−0.183974	+	0.318651i
$438$	−16.8466	+	29.1791i	−0.0384625	+	0.0666191i
$439$	174.434	+	302.129i	0.397344	+	0.688220i	0.993397	−	0.114725i	$-0.0365986\pi$
$439$	174.434	+	302.129i	0.397344	+	0.688220i	−0.596053	+	0.802945i	$0.703265\pi$
$440$	180.167	+	104.019i	0.409470	+	0.236408i
$441$	54.0676	+	93.6479i	0.122602	+	0.212353i
$442$	−55.5590			−0.125699
$443$	365.140	+	210.814i	0.824243	+	0.475877i	0.851878	−	0.523741i	$-0.175464\pi$
$443$	365.140	+	210.814i	0.824243	+	0.475877i	−0.0276342	+	0.999618i	$0.508797\pi$
$444$			10.9326i			0.0246229i
$445$		−	255.383i		−	0.573895i
$446$	−96.2639	+	55.5780i	−0.215838	+	0.124614i
$447$			4.38228i			0.00980377i
$448$	125.351	+	72.3717i	0.279802	+	0.161544i
$449$	−40.8431	+	70.7424i	−0.0909647	+	0.157555i	−0.907917	−	0.419149i	$-0.862328\pi$
$449$	−40.8431	+	70.7424i	−0.0909647	+	0.157555i	0.816953	+	0.576705i	$0.195662\pi$
$450$	−8.08457	+	4.66763i	−0.0179657	+	0.0103725i
$451$	−198.251	−	343.381i	−0.439581	−	0.761377i
$452$	14.5427	−	8.39621i	0.0321740	−	0.0185757i
$453$	−22.7459	+	13.1324i	−0.0502117	+	0.0289897i
$454$			7.72620i			0.0170181i
$455$			90.3493i			0.198570i
$456$	47.8467	+	82.8729i	0.104927	+	0.181739i
$457$	135.381	−	234.486i	0.296237	−	0.513098i	−0.679035	−	0.734106i	$-0.737601\pi$
$457$	135.381	−	234.486i	0.296237	−	0.513098i	0.975272	+	0.221008i	$0.0709347\pi$
$458$	−66.6447	+	115.432i	−0.145512	+	0.252035i
$459$	108.509	−	62.6478i	0.236403	−	0.136488i
$460$		−	240.172i		−	0.522114i
$461$	480.981			1.04334			0.521671	−	0.853147i	$-0.325309\pi$
$461$	480.981			1.04334			0.521671	+	0.853147i	$0.325309\pi$
$462$	15.0317	−	26.0357i	0.0325362	−	0.0563544i
$463$	−448.358	+	258.860i	−0.968376	+	0.559092i	−0.898741	−	0.438480i	$-0.855517\pi$
$463$	−448.358	+	258.860i	−0.968376	+	0.559092i	−0.0696352	+	0.997573i	$0.522184\pi$
$464$	−39.3507			−0.0848075
$465$	359.784	+	207.722i	0.773730	+	0.446713i
$466$	32.3147			0.0693448
$467$	−388.221	−	672.419i	−0.831309	−	1.43987i	−0.897000	−	0.442030i	$-0.854259\pi$
$467$	−388.221	−	672.419i	−0.831309	−	1.43987i	0.0656910	−	0.997840i	$-0.479075\pi$
$468$			50.4937i			0.107892i
$469$	−100.008	+	219.438i	−0.213236	+	0.467885i
$470$	127.063			0.270346
$471$	−366.671	+	211.698i	−0.778496	+	0.449465i
$472$		−	208.386i		−	0.441495i
$473$	217.065	−	375.967i	0.458911	−	0.794857i
$474$			58.4248i			0.123259i
$475$	42.4210	+	73.4754i	0.0893074	+	0.154685i
$476$	280.968	+	162.217i	0.590268	+	0.340792i
$477$		−	87.8109i		−	0.184090i
$478$	120.134			0.251326
$479$	195.433	+	338.500i	0.408002	+	0.706681i	0.994666	−	0.103150i	$-0.0328921\pi$
$479$	195.433	+	338.500i	0.408002	+	0.706681i	−0.586663	+	0.809831i	$0.699559\pi$
$480$	−187.772	−	108.410i	−0.391192	−	0.225855i
$481$	−6.58413	−	3.80135i	−0.0136884	−	0.00790302i
$482$	−154.334	+	89.1045i	−0.320194	+	0.184864i
$483$	−71.8454			−0.148748
$484$	120.344			0.248645
$485$	−436.495	−	756.031i	−0.899989	−	1.55883i
$486$	3.98853	+	6.90833i	0.00820685	+	0.0142147i
$487$	73.0732	−	42.1888i	0.150048	−	0.0866301i	−0.423096	−	0.906085i	$-0.639057\pi$
$487$	73.0732	−	42.1888i	0.150048	−	0.0866301i	0.573144	+	0.819455i	$0.305724\pi$
$488$	−63.6407	−	110.229i	−0.130411	−	0.225879i
$489$	203.834	+	117.684i	0.416838	+	0.240662i
$490$	51.4165	−	89.0559i	0.104932	−	0.181747i
$491$	267.349			0.544500			0.272250	−	0.962227i	$-0.412232\pi$
$491$	267.349			0.544500			0.272250	+	0.962227i	$0.412232\pi$
$492$	136.210	+	235.923i	0.276850	+	0.479517i
$493$	−73.4067			−0.148898
$494$	−32.1474			−0.0650757
$495$	78.8061	−	136.496i	0.159204	−	0.275750i
$496$			556.128i			1.12123i
$497$	−113.915	+	65.7691i	−0.229206	+	0.132332i
$498$	28.9675	−	50.1731i	0.0581676	−	0.100749i
$499$	163.486	−	94.3887i	0.327627	−	0.189156i	−0.327160	−	0.944969i	$-0.606092\pi$
$499$	163.486	−	94.3887i	0.327627	−	0.189156i	0.654787	+	0.755813i	$0.272758\pi$
$500$	341.455	+	197.139i	0.682910	+	0.394278i
$501$	487.766	+	281.612i	0.973584	+	0.562099i
$502$	56.5201	−	97.8956i	0.112590	−	0.195011i
$503$	296.566	+	171.223i	0.589595	+	0.340403i	0.764937	−	0.644105i	$-0.222770\pi$
$503$	296.566	+	171.223i	0.589595	+	0.340403i	−0.175342	+	0.984508i	$0.556103\pi$
$504$	−21.3788	+	37.0292i	−0.0424183	+	0.0734707i
$505$	−176.029	+	304.891i	−0.348572	+	0.603744i
$506$	−27.7877	−	48.1297i	−0.0549164	−	0.0951181i
$507$	223.090	+	128.801i	0.440020	+	0.254046i
$508$	277.295	+	480.289i	0.545857	+	0.945451i
$509$	−390.923			−0.768022			−0.384011	−	0.923328i	$-0.625458\pi$
$509$	−390.923			−0.768022			−0.384011	+	0.923328i	$0.625458\pi$
$510$	−103.188	−	59.5759i	−0.202330	−	0.116815i
$511$			136.823i			0.267755i
$512$		−	494.986i		−	0.966769i
$513$	62.7853	−	36.2491i	0.122388	−	0.0706610i
$514$			216.133i			0.420493i
$515$	439.301	+	253.630i	0.853011	+	0.492486i
$516$	−149.136	+	258.311i	−0.289024	+	0.500604i
$517$	−363.483	+	209.857i	−0.703062	+	0.405913i
$518$	−1.55501	−	2.69336i	−0.00300195	−	0.00519954i
$519$	2.87970	−	1.66260i	0.00554856	−	0.00320346i
$520$	86.0823	−	49.6996i	0.165543	−	0.0955762i
$521$		−	451.231i		−	0.866086i	−0.901373	−	0.433043i	$-0.857440\pi$
$521$		−	451.231i		−	0.866086i	0.901373	−	0.433043i	$-0.142560\pi$
$522$		−	4.67351i		−	0.00895308i
$523$	−225.705	−	390.932i	−0.431557	−	0.747479i	0.565450	−	0.824782i	$-0.308702\pi$
$523$	−225.705	−	390.932i	−0.431557	−	0.747479i	−0.997008	+	0.0773031i	$0.975369\pi$
$524$	−299.100	+	518.057i	−0.570802	+	0.988659i
$525$	−18.9546	+	32.8302i	−0.0361039	+	0.0625338i
$526$	−153.711	+	88.7452i	−0.292227	+	0.168717i
$527$			1037.43i			1.96856i
$528$	210.986			0.399594
$529$	198.093	−	343.107i	0.374467	−	0.648596i
$530$	−72.3176	+	41.7526i	−0.136448	+	0.0787785i
$531$	−157.875			−0.297316
$532$	162.573	+	93.8615i	0.305588	+	0.176431i
$533$	−189.445			−0.355432
$534$	20.3009	+	35.1623i	0.0380168	+	0.0658469i
$535$			892.715i			1.66863i
$536$	264.087	−	25.4248i	0.492700	−	0.0474343i
$537$	44.0129			0.0819606
$538$	150.081	−	86.6492i	0.278961	−	0.161058i
$539$			339.679i			0.630201i
$540$	−54.1444	+	93.7808i	−0.100267	+	0.173668i
$541$		−	382.721i		−	0.707432i	−0.935353	−	0.353716i	$-0.884918\pi$
$541$		−	382.721i		−	0.707432i	0.935353	−	0.353716i	$-0.115082\pi$
$542$	−63.5287	−	110.035i	−0.117212	−	0.203016i
$543$	176.946	+	102.160i	0.325868	+	0.188140i
$544$		−	541.436i		−	0.995287i
$545$	−421.696			−0.773755
$546$	−7.18205	−	12.4397i	−0.0131539	−	0.0227833i
$547$	−634.547	−	366.356i	−1.16005	−	0.669754i	−0.208733	−	0.977973i	$-0.566934\pi$
$547$	−634.547	−	366.356i	−1.16005	−	0.669754i	−0.951316	+	0.308218i	$0.900267\pi$
$548$	695.460	+	401.524i	1.26909	+	0.732708i
$549$	−83.5105	+	48.2148i	−0.152114	+	0.0878230i
$550$	−29.3243			−0.0533169
$551$	−42.4744			−0.0770861
$552$	39.5210	+	68.4524i	0.0715960	+	0.124008i
$553$	118.627	+	205.468i	0.214516	+	0.371552i
$554$	−196.318	+	113.344i	−0.354365	+	0.204593i
$555$	−8.15238	−	14.1203i	−0.0146890	−	0.0254420i
$556$	417.055	+	240.787i	0.750098	+	0.433070i
$557$	−99.0394	+	171.541i	−0.177809	+	0.307974i	−0.941130	−	0.338046i	$-0.890234\pi$
$557$	−99.0394	+	171.541i	−0.177809	+	0.307974i	0.763321	+	0.646019i	$0.223567\pi$
$558$	−66.0489			−0.118367
$559$	−103.712	−	179.634i	−0.185531	−	0.321349i
$560$	−259.379			−0.463176
$561$	393.583			0.701574
$562$	16.4038	−	28.4121i	0.0291882	−	0.0505554i
$563$		−	27.6406i		−	0.0490952i	−0.999699	−	0.0245476i	$-0.992185\pi$
$563$		−	27.6406i		−	0.0490952i	0.999699	−	0.0245476i	$-0.00781453\pi$
$564$	249.734	−	144.184i	0.442791	−	0.255645i
$565$	−12.5220	+	21.6888i	−0.0221629	+	0.0383873i
$566$	193.447	−	111.687i	0.341779	−	0.197326i
$567$	28.0537	+	16.1968i	0.0494774	+	0.0285658i
$568$	125.326	+	72.3570i	0.220644	+	0.127389i
$569$	−507.248	+	878.580i	−0.891474	+	1.54408i	−0.0533642	+	0.998575i	$0.516994\pi$
$569$	−507.248	+	878.580i	−0.891474	+	1.54408i	−0.838109	+	0.545502i	$0.816339\pi$
$570$	−59.7067	−	34.4717i	−0.104749	−	0.0604766i
$571$	478.056	−	828.018i	0.837227	−	1.45012i	−0.0549777	−	0.998488i	$-0.517509\pi$
$571$	478.056	−	828.018i	0.837227	−	1.45012i	0.892204	−	0.451632i	$-0.149158\pi$
$572$	−79.3063	+	137.363i	−0.138647	+	0.240144i
$573$	−219.035	−	379.380i	−0.382261	−	0.662095i
$574$	−67.1136	−	38.7481i	−0.116923	−	0.0675054i
$575$	35.0394	+	60.6901i	0.0609381	+	0.105548i
$576$	−120.643			−0.209450
$577$	38.6110	+	22.2921i	0.0669169	+	0.0386345i	0.533085	−	0.846062i	$-0.321033\pi$
$577$	38.6110	+	22.2921i	0.0669169	+	0.0386345i	−0.466168	+	0.884696i	$0.654366\pi$
$578$		−	149.652i		−	0.258913i
$579$		−	50.6825i		−	0.0875345i
$580$	54.9432	−	31.7215i	0.0947297	−	0.0546922i
$581$		−	235.265i		−	0.404931i
$582$	120.197	+	69.3957i	0.206524	+	0.119237i
$583$	137.917	−	238.880i	0.236565	−	0.409743i
$584$	130.361	−	75.2641i	0.223221	−	0.128877i
$585$	−37.6529	−	65.2168i	−0.0643640	−	0.111482i
$586$	−21.4800	+	12.4015i	−0.0366554	+	0.0211630i
$587$	140.285	−	80.9934i	0.238986	−	0.137979i	−0.375725	−	0.926731i	$-0.622606\pi$
$587$	140.285	−	80.9934i	0.238986	−	0.137979i	0.614711	+	0.788753i	$0.289273\pi$
$588$		−	233.379i		−	0.396903i
$589$			600.275i			1.01914i
$590$	75.0669	+	130.020i	0.127232	+	0.220372i
$591$	−216.226	+	374.515i	−0.365865	+	0.633697i
$592$	10.9131	−	18.9020i	0.0184343	−	0.0319291i
$593$	84.3890	−	48.7220i	0.142309	−	0.0821619i	−0.427155	−	0.904178i	$-0.640484\pi$
$593$	84.3890	−	48.7220i	0.142309	−	0.0821619i	0.569464	+	0.822016i	$0.307151\pi$
$594$			25.0578i			0.0421849i
$595$	−483.857			−0.813206
$596$	4.72895	−	8.19078i	0.00793448	−	0.0137429i
$597$	544.124	−	314.150i	0.911430	−	0.526214i
$598$	−26.5535			−0.0444038
$599$	286.966	+	165.680i	0.479076	+	0.276595i	0.720031	−	0.693942i	$-0.244127\pi$
$599$	286.966	+	165.680i	0.479076	+	0.276595i	−0.240955	+	0.970536i	$0.577461\pi$
$600$	41.7063			0.0695106
$601$	−537.393	−	930.792i	−0.894165	−	1.54874i	−0.834835	−	0.550500i	$-0.814437\pi$
$601$	−537.393	−	930.792i	−0.894165	−	1.54874i	−0.0593293	−	0.998238i	$-0.518896\pi$
$602$		−	84.8505i		−	0.140948i
$603$	−19.2621	−	200.075i	−0.0319437	−	0.331799i
$604$	56.6848			0.0938490
$605$	−155.434	+	89.7401i	−0.256916	+	0.148331i
$606$		−	55.9715i		−	0.0923623i
$607$	199.486	−	345.520i	0.328642	−	0.569225i	−0.653600	−	0.756840i	$-0.726742\pi$
$607$	199.486	−	345.520i	0.328642	−	0.569225i	0.982243	+	0.187615i	$0.0600756\pi$
$608$		−	313.284i		−	0.515271i
$609$	−9.48921	−	16.4358i	−0.0155816	−	0.0269882i
$610$	79.4156	+	45.8506i	0.130190	+	0.0751650i
$611$			200.536i			0.328210i
$612$	−270.414			−0.441854
$613$	302.271	+	523.549i	0.493102	+	0.854077i	0.999968	−	0.00794723i	$-0.00252971\pi$
$613$	302.271	+	523.549i	0.493102	+	0.854077i	−0.506867	+	0.862024i	$0.669196\pi$
$614$	−123.285	−	71.1788i	−0.200791	−	0.115926i
$615$	−351.853	−	203.142i	−0.572119	−	0.330313i
$616$	−116.318	+	67.1560i	−0.188827	+	0.109020i
$617$	27.4703			0.0445223			0.0222612	−	0.999752i	$-0.492913\pi$
$617$	27.4703			0.0445223			0.0222612	+	0.999752i	$0.492913\pi$
$618$	−80.6463			−0.130496
$619$	382.478	+	662.471i	0.617896	+	1.07023i	0.989869	+	0.141984i	$0.0453482\pi$
$619$	382.478	+	662.471i	0.617896	+	1.07023i	−0.371973	+	0.928244i	$0.621319\pi$
$620$	−448.307	−	776.491i	−0.723077	−	1.25241i
$621$	51.8602	−	29.9415i	0.0835107	−	0.0482149i
$622$	118.310	+	204.918i	0.190208	+	0.329451i
$623$	142.789	+	82.4391i	0.229195	+	0.132326i
$624$	50.4036	−	87.3016i	0.0807750	−	0.139906i
$625$	−740.045			−1.18407
$626$	140.212	+	242.855i	0.223981	+	0.387947i
$627$	227.734			0.363212
$628$	913.778			1.45506
$629$	20.3578	−	35.2607i	0.0323653	−	0.0560584i
$630$		−	30.8052i		−	0.0488972i
$631$	82.7305	−	47.7645i	0.131110	−	0.0756965i	−0.433010	−	0.901389i	$-0.642549\pi$
$631$	82.7305	−	47.7645i	0.131110	−	0.0756965i	0.564121	+	0.825692i	$0.309215\pi$
$632$	130.510	−	226.050i	0.206503	−	0.357673i
$633$	224.293	−	129.495i	0.354333	−	0.204574i
$634$	192.524	+	111.153i	0.303665	+	0.175321i
$635$	−716.299	−	413.556i	−1.12803	−	0.651269i
$636$	−94.7573	+	164.125i	−0.148990	+	0.258057i
$637$	140.552	+	81.1479i	0.220647	+	0.127391i
$638$	7.34030	−	12.7138i	0.0115052	−	0.0199275i
$639$	54.8183	−	94.9481i	0.0857877	−	0.148589i
$640$	307.727	+	532.998i	0.480823	+	0.832810i
$641$	497.699	+	287.347i	0.776442	+	0.448279i	0.835168	−	0.549995i	$-0.185371\pi$
$641$	497.699	+	287.347i	0.776442	+	0.448279i	−0.0587261	+	0.998274i	$0.518704\pi$
$642$	−70.9638	−	122.913i	−0.110535	−	0.191453i
$643$	−812.669			−1.26387			−0.631936	−	0.775021i	$-0.717739\pi$
$643$	−812.669			−1.26387			−0.631936	+	0.775021i	$0.717739\pi$
$644$	134.284	+	77.5289i	0.208515	+	0.120386i
$645$		−	444.841i		−	0.689676i
$646$		−	172.163i		−	0.266505i
$647$	−510.239	+	294.586i	−0.788622	+	0.455311i	−0.839477	−	0.543395i	$-0.817139\pi$
$647$	−510.239	+	294.586i	−0.788622	+	0.455311i	0.0508550	+	0.998706i	$0.483805\pi$
$648$		−	35.6384i		−	0.0549975i
$649$	−429.482	−	247.961i	−0.661759	−	0.382067i
$650$	−7.00545	+	12.1338i	−0.0107776	+	0.0186674i
$651$	−232.281	+	134.107i	−0.356806	+	0.206002i
$652$	−253.986	−	439.917i	−0.389549	−	0.674719i
$653$	−348.327	+	201.107i	−0.533426	+	0.307973i	−0.742410	−	0.669946i	$-0.766317\pi$
$653$	−348.327	+	201.107i	−0.533426	+	0.307973i	0.208985	+	0.977919i	$0.432984\pi$
$654$	58.0609	−	33.5215i	0.0887782	−	0.0512561i
$655$		−	892.152i		−	1.36206i
$656$		−	543.868i		−	0.829067i
$657$	−57.0208	−	98.7629i	−0.0867896	−	0.150324i
$658$	−41.0165	+	71.0426i	−0.0623351	+	0.107968i
$659$	130.645	−	226.285i	0.198248	−	0.343376i	−0.749712	−	0.661764i	$-0.769808\pi$
$659$	130.645	−	226.285i	0.198248	−	0.343376i	0.947960	+	0.318388i	$0.103142\pi$
$660$	−294.588	+	170.080i	−0.446345	+	0.257697i
$661$			1007.73i			1.52455i	0.647255	+	0.762274i	$0.275917\pi$
$661$			1007.73i			1.52455i	−0.647255	+	0.762274i	$0.724083\pi$
$662$	198.520			0.299878
$663$	94.0254	−	162.857i	0.141818	−	0.245636i
$664$	−224.154	+	129.415i	−0.337581	+	0.194903i
$665$	−279.969			−0.421005
$666$	2.24491	+	1.29610i	0.00337073	+	0.00194609i
$667$	−35.0835			−0.0525990
$668$	−607.778	−	1052.70i	−0.909847	−	1.57590i
$669$		−	376.230i		−	0.562377i
$670$	−155.615	+	110.996i	−0.232261	+	0.165665i
$671$	−302.908			−0.451428
$672$	121.228	−	69.9909i	0.180398	−	0.104153i
$673$			167.562i			0.248977i	0.992221	+	0.124489i	$0.0397290\pi$
$673$			167.562i			0.248977i	−0.992221	+	0.124489i	$0.960271\pi$
$674$	29.6681	−	51.3867i	0.0440180	−	0.0762414i
$675$		−	31.5971i		−	0.0468106i
$676$	−277.980	−	481.476i	−0.411214	−	0.712243i
$677$	−929.464	−	536.626i	−1.37292	−	0.792653i	−0.381622	−	0.924319i	$-0.624634\pi$
$677$	−929.464	−	536.626i	−1.37292	−	0.792653i	−0.991294	+	0.131665i	$0.957968\pi$
$678$		−	3.98161i		−	0.00587258i
$679$	563.611			0.830061
$680$	266.162	+	461.006i	0.391415	+	0.677950i
$681$	−22.6474	−	13.0755i	−0.0332560	−	0.0192004i
$682$	−179.679	−	103.738i	−0.263459	−	0.152108i
$683$	−881.420	+	508.888i	−1.29051	+	0.745078i	−0.978745	−	0.205080i	$-0.934254\pi$
$683$	−881.420	+	508.888i	−1.29051	+	0.745078i	−0.311768	+	0.950158i	$0.600921\pi$
$684$	−156.467			−0.228752
$685$	−1197.66			−1.74841
$686$	78.3206	+	135.655i	0.114170	+	0.197748i
$687$	−225.573	−	390.704i	−0.328345	−	0.568710i
$688$	515.701	−	297.740i	0.749566	−	0.432762i
$689$	−65.8959	−	114.135i	−0.0956399	−	0.165653i
$690$	−49.3172	−	28.4733i	−0.0714743	−	0.0412657i
$691$	592.904	−	1026.94i	0.858037	−	1.48616i	−0.0157615	−	0.999876i	$-0.505017\pi$
$691$	592.904	−	1026.94i	0.858037	−	1.48616i	0.873799	−	0.486288i	$-0.161649\pi$
$692$	−7.17648			−0.0103706
$693$	50.8781	+	88.1234i	0.0734171	+	0.127162i
$694$	128.714			0.185467
$695$	−718.214			−1.03340
$696$	−10.4397	+	18.0821i	−0.0149996	+	0.0259800i
$697$		−	1014.56i		−	1.45561i
$698$	−212.393	+	122.625i	−0.304288	+	0.175681i
$699$	−54.6879	+	94.7222i	−0.0782373	+	0.135511i
$700$	70.8547	−	40.9080i	0.101221	−	0.0584399i
$701$	374.196	+	216.042i	0.533803	+	0.308191i	0.742564	−	0.669775i	$-0.233610\pi$
$701$	374.196	+	216.042i	0.533803	+	0.308191i	−0.208761	+	0.977967i	$0.566943\pi$
$702$	10.3684	+	5.98622i	0.0147698	+	0.00852737i
$703$	11.7794	−	20.4025i	0.0167559	−	0.0290220i
$704$	−328.197	−	189.484i	−0.466188	−	0.269154i
$705$	−215.035	+	372.451i	−0.305014	+	0.528300i
$706$	−79.6881	+	138.024i	−0.112873	+	0.195501i
$707$	−113.646	−	196.841i	−0.160744	−	0.278417i
$708$	295.079	+	170.364i	0.416778	+	0.240627i
$709$	634.803	+	1099.51i	0.895350	+	1.55079i	0.833371	+	0.552714i	$0.186408\pi$
$709$	634.803	+	1099.51i	0.895350	+	1.55079i	0.0619787	+	0.998077i	$0.480259\pi$
$710$	−104.261			−0.146846
$711$	−171.257	−	98.8754i	−0.240868	−	0.139065i
$712$		−	181.394i		−	0.254766i
$713$			495.822i			0.695403i
$714$	66.6196	−	38.4628i	0.0933047	−	0.0538695i
$715$		−	236.554i		−	0.330844i
$716$	−82.2630	−	47.4945i	−0.114892	−	0.0663332i
$717$	−203.309	+	352.141i	−0.283555	+	0.491132i
$718$	95.6988	−	55.2517i	0.133285	−	0.0769522i
$719$	630.334	+	1091.77i	0.876681	+	1.51846i	0.854961	+	0.518692i	$0.173581\pi$
$719$	630.334	+	1091.77i	0.876681	+	1.51846i	0.0217202	+	0.999764i	$0.493086\pi$
$720$	187.227	−	108.096i	0.260038	−	0.150133i
$721$	−283.617	+	163.746i	−0.393366	+	0.227110i
$722$			85.1177i			0.117892i
$723$		−	603.186i		−	0.834282i
$724$	−220.483	−	381.888i	−0.304535	−	0.527470i
$725$	−9.25588	+	16.0317i	−0.0127667	+	0.0221126i
$726$	14.2673	−	24.7116i	0.0196519	−	0.0340380i
$727$	643.064	−	371.273i	0.884545	−	0.510692i	0.0123909	−	0.999923i	$-0.496056\pi$
$727$	643.064	−	371.273i	0.884545	−	0.510692i	0.872154	+	0.489231i	$0.162722\pi$
$728$			64.1732i			0.0881500i
$729$	−27.0000			−0.0370370
$730$	−54.2248	+	93.9201i	−0.0742805	+	0.128658i
$731$	962.015	−	555.420i	1.31603	−	0.759808i
$732$	208.116			0.284311
$733$	−253.422	−	146.313i	−0.345733	−	0.199609i	0.317071	−	0.948402i	$-0.397301\pi$
$733$	−253.422	−	146.313i	−0.345733	−	0.199609i	−0.662804	+	0.748793i	$0.730634\pi$
$734$	167.482			0.228177
$735$	174.030	+	301.428i	0.236775	+	0.410106i
$736$		−	258.771i		−	0.351590i
$737$	261.841	−	574.535i	0.355280	−	0.779560i
$738$	64.5928			0.0875241
$739$	901.378	−	520.411i	1.21973	−	0.704210i	0.254868	−	0.966976i	$-0.417968\pi$
$739$	901.378	−	520.411i	1.21973	−	0.704210i	0.964860	+	0.262766i	$0.0846348\pi$
$740$			35.1891i			0.0475529i
$741$	54.4048	−	94.2318i	0.0734207	−	0.127168i
$742$		−	53.9118i		−	0.0726575i
$743$	683.990	+	1184.70i	0.920578	+	1.59449i	0.798522	+	0.601965i	$0.205615\pi$
$743$	683.990	+	1184.70i	0.920578	+	1.59449i	0.122056	+	0.992523i	$0.461051\pi$
$744$	255.547	+	147.540i	0.343478	+	0.198307i
$745$			14.1054i			0.0189335i
$746$	−194.270			−0.260416
$747$	98.0464	+	169.821i	0.131253	+	0.227338i
$748$	−735.633	−	424.718i	−0.983467	−	0.567805i
$749$	−499.131	−	288.173i	−0.666396	−	0.384744i
$750$	80.9615	−	46.7431i	0.107949	−	0.0623242i
$751$	679.619			0.904952			0.452476	−	0.891777i	$-0.350541\pi$
$751$	679.619			0.904952			0.452476	+	0.891777i	$0.350541\pi$
$752$	−575.708			−0.765569
$753$	191.304	+	331.348i	0.254056	+	0.440037i
$754$	−3.50714	−	6.07454i	−0.00465137	−	0.00805642i
$755$	−73.2132	+	42.2696i	−0.0969711	+	0.0559863i
$756$	−34.9562	−	60.5459i	−0.0462383	−	0.0800871i
$757$	959.306	+	553.856i	1.26725	+	0.731645i	0.974466	−	0.224534i	$-0.0720860\pi$
$757$	959.306	+	553.856i	1.26725	+	0.731645i	0.292781	+	0.956180i	$0.405419\pi$
$758$	167.297	−	289.768i	0.220709	−	0.382279i
$759$	188.107			0.247835
$760$	154.006	+	266.746i	0.202640	+	0.350982i
$761$	262.753			0.345274			0.172637	−	0.984986i	$-0.444771\pi$
$761$	262.753			0.345274			0.172637	+	0.984986i	$0.444771\pi$
$762$	131.498			0.172569
$763$	136.126	−	235.777i	0.178409	−	0.309013i
$764$			945.449i			1.23750i
$765$	349.263	−	201.647i	0.456552	−	0.263591i
$766$	−16.9191	+	29.3047i	−0.0220876	+	0.0382568i
$767$	−205.203	+	118.474i	−0.267540	+	0.154464i
$768$	156.548	+	90.3831i	0.203839	+	0.117686i
$769$	−826.852	−	477.383i	−1.07523	−	0.620785i	−0.145625	−	0.989340i	$-0.546519\pi$
$769$	−826.852	−	477.383i	−1.07523	−	0.620785i	−0.929606	+	0.368555i	$0.879853\pi$
$770$	48.3833	−	83.8023i	0.0628354	−	0.108834i
$771$	−633.539	−	365.774i	−0.821711	−	0.474415i
$772$	−54.6918	+	94.7290i	−0.0708443	+	0.122706i
$773$	−546.048	+	945.783i	−0.706401	+	1.22352i	0.259782	+	0.965667i	$0.416349\pi$
$773$	−546.048	+	945.783i	−0.706401	+	1.22352i	−0.966183	+	0.257856i	$0.916984\pi$
$774$	35.3613	+	61.2476i	0.0456864	+	0.0791312i
$775$	226.569	+	130.810i	0.292347	+	0.168787i
$776$	−310.033	−	536.993i	−0.399527	−	0.692002i
$777$	10.5265			0.0135476
$778$	55.0663	+	31.7925i	0.0707793	+	0.0408644i
$779$		−	587.041i		−	0.753583i
$780$			162.526i			0.208367i
$781$	298.255	−	172.197i	0.381888	−	0.220483i
$782$		−	142.205i		−	0.181848i
$783$	13.6992	+	7.90923i	0.0174958	+	0.0101012i
$784$	−232.963	+	403.503i	−0.297146	+	0.514672i
$785$	−1180.22	+	681.401i	−1.50347	+	0.868026i
$786$	70.9190	+	122.835i	0.0902277	+	0.156279i
$787$	896.571	−	517.636i	1.13923	−	0.657733i	0.192987	−	0.981201i	$-0.438182\pi$
$787$	896.571	−	517.636i	1.13923	−	0.657733i	0.946239	+	0.323469i	$0.104849\pi$
$788$	808.283	−	466.662i	1.02574	−	0.592211i
$789$		−	600.753i		−	0.761411i
$790$			188.054i			0.238043i
$791$	−8.08436	−	14.0025i	−0.0102204	−	0.0177023i
$792$	55.9744	−	96.9504i	0.0706747	−	0.122412i
$793$	−72.3636	+	125.337i	−0.0912530	+	0.158055i
$794$	155.408	−	89.7251i	0.195729	−	0.113004i
$795$		−	282.641i		−	0.355523i
$796$	−1356.01			−1.70352
$797$	−766.725	+	1328.01i	−0.962014	+	1.66626i	−0.244583	+	0.969628i	$0.578651\pi$
$797$	−766.725	+	1328.01i	−0.962014	+	1.66626i	−0.717432	+	0.696629i	$0.754682\pi$
$798$	38.5473	−	22.2553i	0.0483048	−	0.0278888i
$799$	−1073.95			−1.34412
$800$	−118.247	−	68.2699i	−0.147809	−	0.0853373i
$801$	−137.426			−0.171567
$802$	48.6896	+	84.3328i	0.0607102	+	0.105153i
$803$		−	358.232i		−	0.446117i
$804$	−179.900	+	394.739i	−0.223756	+	0.490969i
$805$	−231.252			−0.287269
$806$	−85.8491	+	49.5650i	−0.106512	+	0.0614950i
$807$			586.565i			0.726846i
$808$	−125.030	+	216.558i	−0.154740	+	0.268017i
$809$		−	1464.34i		−	1.81006i	−0.425346	−	0.905031i	$-0.639847\pi$
$809$		−	1464.34i		−	1.81006i	0.425346	−	0.905031i	$-0.360153\pi$
$810$	12.8380	+	22.2361i	0.0158494	+	0.0274520i
$811$	−388.799	−	224.473i	−0.479407	−	0.276786i	0.240762	−	0.970584i	$-0.422603\pi$
$811$	−388.799	−	224.473i	−0.479407	−	0.276786i	−0.720169	+	0.693798i	$0.755936\pi$
$812$			40.9595i			0.0504427i
$813$	430.052			0.528969
$814$	4.07135	+	7.05179i	0.00500166	+	0.00866313i
$815$	656.088	+	378.793i	0.805016	+	0.464776i
$816$	467.536	+	269.932i	0.572961	+	0.330799i
$817$	556.639	−	321.376i	0.681320	−	0.393361i
$818$	−252.219			−0.308336
$819$	48.6183			0.0593630
$820$	438.425	+	759.374i	0.534664	+	0.926065i
$821$	−561.681	−	972.859i	−0.684142	−	1.18497i	−0.973706	−	0.227810i	$-0.926844\pi$
$821$	−561.681	−	972.859i	−0.684142	−	1.18497i	0.289564	−	0.957159i	$-0.406490\pi$
$822$	164.899	−	95.2043i	0.200607	−	0.115820i
$823$	263.524	+	456.437i	0.320200	+	0.554602i	0.980529	−	0.196374i	$-0.0629167\pi$
$823$	263.524	+	456.437i	0.320200	+	0.554602i	−0.660329	+	0.750976i	$0.729583\pi$
$824$	312.026	+	180.148i	0.378672	+	0.218627i
$825$	49.6270	−	85.9565i	0.0601540	−	0.104190i
$826$	−96.9279			−0.117346
$827$	698.054	+	1209.07i	0.844080	+	1.46199i	0.886417	+	0.462887i	$0.153186\pi$
$827$	698.054	+	1209.07i	0.844080	+	1.46199i	−0.0423370	+	0.999103i	$0.513480\pi$
$828$	−129.240			−0.156087
$829$	616.174			0.743273			0.371637	−	0.928378i	$-0.378797\pi$
$829$	616.174			0.743273			0.371637	+	0.928378i	$0.378797\pi$
$830$	93.2387	−	161.494i	0.112336	−	0.194571i
$831$		−	767.274i		−	0.923314i
$832$	−156.810	+	90.5341i	−0.188473	+	0.108815i
$833$	−434.580	+	752.715i	−0.521705	+	0.903619i
$834$	98.8868	−	57.0923i	0.118569	−	0.0684560i
$835$	1569.99	+	906.435i	1.88023	+	1.08555i
$836$	−425.650	−	245.749i	−0.509151	−	0.293958i
$837$	111.778	−	193.605i	0.133546	−	0.231308i
$838$	−43.9234	−	25.3592i	−0.0524145	−	0.0302615i
$839$	−56.4911	+	97.8454i	−0.0673315	+	0.116621i	−0.897726	−	0.440555i	$-0.854782\pi$
$839$	−56.4911	+	97.8454i	−0.0673315	+	0.116621i	0.830394	+	0.557176i	$0.188115\pi$
$840$	−68.8130	+	119.188i	−0.0819202	+	0.141890i
$841$	415.866	+	720.301i	0.494490	+	0.856482i
$842$	−175.553	−	101.356i	−0.208496	−	0.120375i
$843$	55.5219	+	96.1668i	0.0658623	+	0.114077i
$844$	−558.958			−0.662272
$845$	718.070	+	414.578i	0.849786	+	0.490624i
$846$		−	68.3742i		−	0.0808206i
$847$		−	115.874i		−	0.136806i
$848$	327.664	−	189.177i	0.386396	−	0.223086i
$849$			756.054i			0.890523i
$850$	−64.9815	−	37.5171i	−0.0764488	−	0.0441377i
$851$	9.72968	−	16.8523i	0.0114332	−	0.0198029i
$852$	−204.918	+	118.310i	−0.240514	+	0.138861i
$853$	118.071	+	204.504i	0.138418	+	0.239747i	0.926898	−	0.375313i	$-0.122465\pi$
$853$	118.071	+	204.504i	0.138418	+	0.239747i	−0.788480	+	0.615060i	$0.789132\pi$
$854$	−51.2716	+	29.6017i	−0.0600370	+	0.0346624i
$855$	202.090	−	116.676i	0.236362	−	0.136464i
$856$			634.077i			0.740744i
$857$		−	558.717i		−	0.651945i	−0.945379	−	0.325972i	$-0.894308\pi$
$857$		−	558.717i		−	0.651945i	0.945379	−	0.325972i	$-0.105692\pi$
$858$	18.8041	+	32.5697i	0.0219162	+	0.0379600i
$859$	3.74077	−	6.47921i	0.00435480	−	0.00754273i	−0.863840	−	0.503767i	$-0.831947\pi$
$859$	3.74077	−	6.47921i	0.00435480	−	0.00754273i	0.868195	+	0.496224i	$0.165280\pi$
$860$	−480.031	+	831.437i	−0.558175	+	0.966788i
$861$	227.160	−	131.151i	0.263833	−	0.152324i
$862$			63.9189i			0.0741519i
$863$	−408.577			−0.473438			−0.236719	−	0.971578i	$-0.576072\pi$
$863$	−408.577			−0.473438			−0.236719	+	0.971578i	$0.576072\pi$
$864$	−58.3372	+	101.043i	−0.0675199	+	0.116948i
$865$	9.26902	−	5.35147i	0.0107156	−	0.00618667i
$866$	132.787			0.153334
$867$	438.665	+	253.263i	0.505957	+	0.292115i
$868$	578.864			0.666894
$869$	−310.591	−	537.960i	−0.357412	−	0.619056i
$870$		−	15.0428i		−	0.0172906i
$871$	−175.179	−	245.599i	−0.201123	−	0.281973i
$872$	−299.522			−0.343489
$873$	−406.831	+	234.884i	−0.466015	+	0.269054i
$874$		−	82.2823i		−	0.0941445i
$875$	189.817	−	328.773i	0.216934	−	0.375740i
$876$			246.126i			0.280966i
$877$	−669.513	−	1159.63i	−0.763413	−	1.32227i	−0.941082	−	0.338179i	$-0.890189\pi$
$877$	−669.513	−	1159.63i	−0.763413	−	1.32227i	0.177669	−	0.984090i	$-0.443144\pi$
$878$	−154.608	−	89.2629i	−0.176091	−	0.101666i
$879$		−	83.9509i		−	0.0955073i
$880$	679.108			0.771714
$881$	506.554	+	877.378i	0.574977	+	0.995889i	0.996044	+	0.0888594i	$0.0283222\pi$
$881$	506.554	+	877.378i	0.574977	+	0.995889i	−0.421068	+	0.907029i	$0.638344\pi$
$882$	−47.9223	−	27.6679i	−0.0543337	−	0.0313696i
$883$	−693.731	−	400.526i	−0.785652	−	0.453596i	0.0527777	−	0.998606i	$-0.483193\pi$
$883$	−693.731	−	400.526i	−0.785652	−	0.453596i	−0.838430	+	0.545010i	$0.816526\pi$
$884$	−351.480	+	202.927i	−0.397601	+	0.229555i
$885$	−508.159			−0.574191
$886$	−215.759			−0.243520
$887$	357.464	+	619.146i	0.403004	+	0.698023i	0.994087	−	0.108588i	$-0.0346328\pi$
$887$	357.464	+	619.146i	0.403004	+	0.698023i	−0.591083	+	0.806611i	$0.701299\pi$
$888$	−5.79047	−	10.0294i	−0.00652079	−	0.0112943i
$889$	462.450	−	266.996i	0.520192	−	0.300333i
$890$	65.3435	+	113.178i	0.0734196	+	0.127167i
$891$	−73.4506	−	42.4067i	−0.0824361	−	0.0475945i
$892$	−405.993	+	703.200i	−0.455149	+	0.788340i
$893$	−621.408			−0.695866
$894$	−1.12127	−	1.94210i	−0.00125422	−	0.00217237i
$895$	141.666			0.158286
$896$	−397.343			−0.443463
$897$	44.9379	−	77.8347i	0.0500980	−	0.0867723i
$898$		−	41.8012i		−	0.0465492i
$899$	−113.427	+	65.4872i	−0.126170	+	0.0728445i
$900$	−34.0967	+	59.0571i	−0.0378852	+	0.0656190i
$901$	611.240	−	352.899i	0.678402	−	0.391675i
$902$	175.718	+	101.451i	0.194809	+	0.112473i
$903$	248.717	+	143.597i	0.275434	+	0.159022i
$904$	−8.89415	+	15.4051i	−0.00983866	+	0.0170411i
$905$	569.545	+	328.827i	0.629331	+	0.363345i
$906$	6.72020	−	11.6397i	0.00741744	−	0.0128474i
$907$	210.501	−	364.599i	0.232085	−	0.401984i	−0.726336	−	0.687339i	$-0.758778\pi$
$907$	210.501	−	364.599i	0.232085	−	0.401984i	0.958422	+	0.285356i	$0.0921118\pi$
$908$	28.2196	+	48.8778i	0.0310789	+	0.0538302i
$909$	164.066	+	94.7236i	0.180491	+	0.104206i
$910$	−23.1171	−	40.0401i	−0.0254035	−	0.0440001i
$911$	1345.03			1.47644			0.738218	−	0.674563i	$-0.235668\pi$
$911$	1345.03			1.47644			0.738218	+	0.674563i	$0.235668\pi$
$912$	270.525	+	156.188i	0.296628	+	0.171258i
$913$			615.974i			0.674670i
$914$			138.556i			0.151593i
$915$	−268.799	+	155.191i	−0.293769	+	0.169608i
$916$			973.668i			1.06296i
$917$	498.816	+	287.991i	0.543965	+	0.314058i
$918$	−32.0586	+	55.5272i	−0.0349223	+	0.0604871i
$919$	96.9653	−	55.9829i	0.105512	−	0.0609172i	−0.446316	−	0.894876i	$-0.647264\pi$
$919$	96.9653	−	55.9829i	0.105512	−	0.0609172i	0.551827	+	0.833958i	$0.313931\pi$
$920$	127.208	+	220.330i	0.138269	+	0.239490i
$921$	417.285	−	240.920i	0.453078	−	0.261585i
$922$	−213.156	+	123.066i	−0.231189	+	0.133477i
$923$		−	164.549i		−	0.178276i
$924$		−	219.611i		−	0.237675i
$925$	−5.13384	−	8.89208i	−0.00555010	−	0.00961306i
$926$	132.466	−	229.438i	0.143052	−	0.247773i
$927$	136.482	−	236.394i	0.147230	−	0.255010i
$928$	59.1979	−	34.1779i	0.0637908	−	0.0368297i
$929$			1631.75i			1.75646i	0.478240	+	0.878229i	$0.341275\pi$
$929$			1631.75i			1.75646i	−0.478240	+	0.878229i	$0.658725\pi$
$930$	−212.594			−0.228596
$931$	−251.456	+	435.534i	−0.270092	+	0.467813i
$932$	204.431	−	118.028i	0.219346	−	0.126640i
$933$	−800.887			−0.858400
$934$	344.096	+	198.664i	0.368411	+	0.212702i
$935$	1266.84			1.35491
$936$	−26.7441	−	46.3221i	−0.0285728	−	0.0494895i
$937$			324.347i			0.346155i	0.984908	+	0.173077i	$0.0553711\pi$
$937$			324.347i			0.346155i	−0.984908	+	0.173077i	$0.944629\pi$
$938$	−11.8260	−	122.837i	−0.0126077	−	0.130956i
$939$	−949.155			−1.01081
$940$	803.829	−	464.091i	0.855137	−	0.493714i
$941$		−	1416.08i		−	1.50486i	−0.658670	−	0.752432i	$-0.728881\pi$
$941$		−	1416.08i		−	1.50486i	0.658670	−	0.752432i	$-0.271119\pi$
$942$	108.332	−	187.636i	0.115002	−	0.199189i
$943$		−	484.892i		−	0.514201i
$944$	−340.120	−	589.105i	−0.360297	−	0.624052i
$945$	90.2976	+	52.1334i	0.0955530	+	0.0551676i
$946$			222.157i			0.234838i
$947$	−741.456			−0.782953			−0.391476	−	0.920188i	$-0.628036\pi$
$947$	−741.456			−0.782953			−0.391476	+	0.920188i	$0.628036\pi$
$948$	213.394	+	369.610i	0.225099	+	0.389884i
$949$	−148.229	−	85.5801i	−0.156195	−	0.0901792i
$950$	−37.5994	−	21.7080i	−0.0395783	−	0.0228506i
$951$	−651.636	+	376.222i	−0.685211	+	0.395607i
$952$	−343.674			−0.361002
$953$	15.9042			0.0166886			0.00834431	−	0.999965i	$-0.497344\pi$
$953$	15.9042			0.0166886			0.00834431	+	0.999965i	$0.497344\pi$
$954$	22.4677	+	38.9152i	0.0235510	+	0.0407916i
$955$	−705.018	−	1221.13i	−0.738238	−	1.27867i
$956$	759.996	−	438.784i	0.794975	−	0.458979i
$957$	24.8448	+	43.0324i	0.0259611	+	0.0449659i
$958$	−173.220	−	100.009i	−0.180814	−	0.104393i
$959$	386.610	−	669.629i	0.403139	−	0.698258i
$960$	−388.319			−0.404499
$961$	445.006	+	770.772i	0.463065	+	0.802052i
$962$	3.89052			0.00404420
$963$	480.383			0.498840
$964$	−650.901	+	1127.39i	−0.675209	+	1.16950i
$965$		−	163.134i		−	0.169051i
$966$	31.8397	−	18.3827i	0.0329604	−	0.0190297i
$967$	−626.090	+	1084.42i	−0.647456	+	1.12143i	0.336273	+	0.941765i	$0.390834\pi$
$967$	−626.090	+	1084.42i	−0.647456	+	1.12143i	−0.983729	+	0.179661i	$0.942500\pi$
$968$	−110.402	+	63.7406i	−0.114052	+	0.0658477i
$969$	504.650	+	291.360i	0.520795	+	0.300681i
$970$	386.883	+	223.367i	0.398848	+	0.230275i
$971$	425.113	−	736.318i	0.437810	−	0.758309i	−0.559711	−	0.828688i	$-0.689088\pi$
$971$	425.113	−	736.318i	0.437810	−	0.758309i	0.997520	+	0.0703795i	$0.0224210\pi$
$972$	50.4648	+	29.1359i	0.0519185	+	0.0299752i
$973$	231.843	−	401.565i	0.238277	−	0.412708i
$974$	−21.5892	+	37.3936i	−0.0221655	+	0.0383918i
$975$	−23.7114	−	41.0694i	−0.0243194	−	0.0421224i
$976$	−359.824	−	207.745i	−0.368672	−	0.212853i
$977$	−35.8262	−	62.0528i	−0.0366696	−	0.0635136i	0.847108	−	0.531421i	$-0.178342\pi$
$977$	−35.8262	−	62.0528i	−0.0366696	−	0.0635136i	−0.883778	+	0.467907i	$0.845008\pi$
$978$	−120.444			−0.123153
$979$	−373.851	−	215.843i	−0.381870	−	0.220473i
$980$		−	751.186i		−	0.766516i
$981$			226.921i			0.231316i
$982$	−118.481	+	68.4051i	−0.120653	+	0.0696590i
$983$			463.426i			0.471441i	0.971821	+	0.235720i	$0.0757450\pi$
$983$			463.426i			0.471441i	−0.971821	+	0.235720i	$0.924255\pi$
$984$	−249.914	−	144.288i	−0.253978	−	0.146634i
$985$	−695.976	+	1205.47i	−0.706575	+	1.22382i
$986$	32.5316	−	18.7822i	0.0329936	−	0.0190488i
$987$	−138.829	−	240.459i	−0.140657	−	0.243626i
$988$	−203.372	+	117.417i	−0.205842	+	0.118843i
$989$	459.779	−	265.454i	0.464893	−	0.268406i
$990$			80.6547i			0.0814693i
$991$			713.363i			0.719842i	0.932983	+	0.359921i	$0.117196\pi$
$991$			713.363i			0.719842i	−0.932983	+	0.359921i	$0.882804\pi$
$992$	−483.023	−	836.621i	−0.486919	−	0.843368i
$993$	−335.965	+	581.909i	−0.338334	+	0.586011i
$994$	33.6559	−	58.2937i	0.0338591	−	0.0586456i
$995$	1751.39	−	1011.17i	1.76019	−	1.01625i
$996$		−	423.210i		−	0.424909i
$997$	1221.49			1.22517			0.612583	−	0.790407i	$-0.290131\pi$
$997$	1221.49			1.22517			0.612583	+	0.790407i	$0.290131\pi$
$998$	−48.3014	+	83.6604i	−0.0483982	+	0.0838281i
$999$	−7.59835	+	4.38691i	−0.00760596	+	0.00439130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.3.h.a.97.5	✓	22
67.38	odd	6	inner	201.3.h.a.172.5	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.3.h.a.97.5	✓	22	1.1	even	1	trivial
201.3.h.a.172.5	yes	22	67.38	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.443170 + 0.255864i) q^{2} -1.73205i q^{3} +(-1.86907 + 3.23732i) q^{4} -5.57502i q^{5} +(0.443170 + 0.767593i) q^{6} +(3.11708 + 1.79965i) q^{7} -3.95982i q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.443170 + 0.255864i) q^{2} -1.73205i q^{3} +(-1.86907 + 3.23732i) q^{4} -5.57502i q^{5} +(0.443170 + 0.767593i) q^{6} +(3.11708 + 1.79965i) q^{7} -3.95982i q^{8} -3.00000 q^{9} +(1.42645 + 2.47068i) q^{10} +(-8.16117 - 4.71186i) q^{11} +(5.60720 + 3.23732i) q^{12} +(-3.89934 + 2.25129i) q^{13} -1.84186 q^{14} -9.65622 q^{15} +(-6.46309 - 11.1944i) q^{16} +(-12.0566 - 20.8826i) q^{17} +(1.32951 - 0.767593i) q^{18} +(-6.97614 - 12.0830i) q^{19} +(18.0481 + 10.4201i) q^{20} +(3.11708 - 5.39894i) q^{21} +4.82238 q^{22} +(-5.76224 - 9.98049i) q^{23} -6.85861 q^{24} -6.08087 q^{25} +(1.15205 - 1.99541i) q^{26} +5.19615i q^{27} +(-11.6521 + 6.72732i) q^{28} +(1.52213 - 2.63641i) q^{29} +(4.27935 - 2.47068i) q^{30} +(-37.2593 - 21.5117i) q^{31} +(19.4457 + 11.2270i) q^{32} +(-8.16117 + 14.1356i) q^{33} +(10.6862 + 6.16969i) q^{34} +(10.0331 - 17.3778i) q^{35} +(5.60720 - 9.71196i) q^{36} +(0.844262 + 1.46230i) q^{37} +(6.18323 + 3.56989i) q^{38} +(3.89934 + 6.75386i) q^{39} -22.0761 q^{40} +(36.4380 + 21.0375i) q^{41} +3.19020i q^{42} +46.0678i q^{43} +(30.5076 - 17.6136i) q^{44} +16.7251i q^{45} +(5.10730 + 2.94870i) q^{46} +(22.2690 - 38.5711i) q^{47} +(-19.3893 + 11.1944i) q^{48} +(-18.0225 - 31.2160i) q^{49} +(2.69486 - 1.55588i) q^{50} +(-36.1697 + 20.8826i) q^{51} -16.8312i q^{52} +29.2703i q^{53} +(-1.32951 - 2.30278i) q^{54} +(-26.2687 + 45.4987i) q^{55} +(7.12628 - 12.3431i) q^{56} +(-20.9284 + 12.0830i) q^{57} +1.55784i q^{58} +52.6250 q^{59} +(18.0481 - 31.2603i) q^{60} +(27.8368 - 16.0716i) q^{61} +22.0163 q^{62} +(-9.35124 - 5.39894i) q^{63} +40.2144 q^{64} +(12.5510 + 21.7389i) q^{65} -8.35261i q^{66} +(6.42069 + 66.6916i) q^{67} +90.1381 q^{68} +(-17.2867 + 9.98049i) q^{69} +10.2684i q^{70} +(-18.2728 + 31.6494i) q^{71} +11.8795i q^{72} +(19.0069 + 32.9210i) q^{73} +(-0.748302 - 0.432033i) q^{74} +10.5324i q^{75} +52.1555 q^{76} +(-16.9594 - 29.3745i) q^{77} +(-3.45614 - 1.99541i) q^{78} +(57.0858 + 32.9585i) q^{79} +(-62.4090 + 36.0319i) q^{80} +9.00000 q^{81} -21.5309 q^{82} +(-32.6821 - 56.6071i) q^{83} +(11.6521 + 20.1820i) q^{84} +(-116.421 + 67.2156i) q^{85} +(-11.7871 - 20.4159i) q^{86} +(-4.56639 - 2.63641i) q^{87} +(-18.6581 + 32.3168i) q^{88} +45.8085 q^{89} +(-4.27935 - 7.41204i) q^{90} -16.2061 q^{91} +43.0801 q^{92} +(-37.2593 + 64.5351i) q^{93} +22.7914i q^{94} +(-67.3632 + 38.8922i) q^{95} +(19.4457 - 33.6810i) q^{96} +(135.610 - 78.2947i) q^{97} +(15.9741 + 9.22265i) q^{98} +(24.4835 + 14.1356i) 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

Related objects

Downloads

Learn more