LMFDB - Embedded newform 112.3.u.a.51.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,3,Mod(11,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.11"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 8])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	112.u (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.05177896084$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			51.16
Character	$\chi$	$=$	112.51
Dual form			112.3.u.a.11.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0556527 + 1.99923i) q^{2} +(-5.31530 - 1.42423i) q^{3} +(-3.99381 - 0.222525i) q^{4} +(0.419571 + 1.56586i) q^{5} +(3.14317 - 10.5472i) q^{6} +(6.45786 - 2.70113i) q^{7} +(0.667143 - 7.97213i) q^{8} +(18.4298 + 10.6404i) q^{9} +(-3.15386 + 0.751673i) q^{10} +(2.85576 - 10.6579i) q^{11} +(20.9114 + 6.87089i) q^{12} +(-1.18165 - 1.18165i) q^{13} +(5.04077 + 13.0610i) q^{14} -8.92058i q^{15} +(15.9010 + 1.77744i) q^{16} +(-4.47899 - 7.75783i) q^{17} +(-22.2983 + 36.2531i) q^{18} +(-7.83562 - 29.2429i) q^{19} +(-1.32724 - 6.34710i) q^{20} +(-38.1725 + 5.15984i) q^{21} +(21.1485 + 6.30246i) q^{22} +(-5.11508 + 8.85958i) q^{23} +(-14.9002 + 41.4241i) q^{24} +(19.3748 - 11.1860i) q^{25} +(2.42816 - 2.29663i) q^{26} +(-47.7857 - 47.7857i) q^{27} +(-26.3925 + 9.35075i) q^{28} +(31.5544 + 31.5544i) q^{29} +(17.8343 + 0.496454i) q^{30} +(8.16065 - 4.71155i) q^{31} +(-4.43843 + 31.6907i) q^{32} +(-30.3585 + 52.5825i) q^{33} +(15.7589 - 8.52276i) q^{34} +(6.93912 + 8.97878i) q^{35} +(-71.2372 - 46.5969i) q^{36} +(-13.9304 - 51.9889i) q^{37} +(58.8993 - 14.0377i) q^{38} +(4.59790 + 7.96380i) q^{39} +(12.7632 - 2.30022i) q^{40} -53.2158i q^{41} +(-8.19128 - 76.6026i) q^{42} +(6.71176 + 6.71176i) q^{43} +(-13.7770 + 41.9299i) q^{44} +(-8.92883 + 33.3229i) q^{45} +(-17.4276 - 10.7193i) q^{46} +(-4.10186 - 2.36821i) q^{47} +(-81.9869 - 32.0943i) q^{48} +(34.4078 - 34.8870i) q^{49} +(21.2851 + 39.3570i) q^{50} +(12.7582 + 47.6143i) q^{51} +(4.45635 + 4.98225i) q^{52} +(-32.8247 - 8.79535i) q^{53} +(98.1938 - 92.8750i) q^{54} +17.8869 q^{55} +(-17.2255 - 53.2849i) q^{56} +166.595i q^{57} +(-64.8404 + 61.3282i) q^{58} +(-22.9411 + 85.6173i) q^{59} +(-1.98505 + 35.6271i) q^{60} +(15.4586 - 4.14213i) q^{61} +(8.96529 + 16.5772i) q^{62} +(147.758 + 18.9332i) q^{63} +(-63.1098 - 10.6371i) q^{64} +(1.35452 - 2.34609i) q^{65} +(-103.435 - 63.6198i) q^{66} +(-14.3420 - 3.84292i) q^{67} +(16.1619 + 31.9800i) q^{68} +(39.8063 - 39.8063i) q^{69} +(-18.3368 + 13.3732i) q^{70} +93.6627 q^{71} +(97.1222 - 139.826i) q^{72} +(-16.5673 + 9.56511i) q^{73} +(104.713 - 24.9567i) q^{74} +(-118.914 + 31.8630i) q^{75} +(24.7867 + 118.534i) q^{76} +(-10.3461 - 76.5407i) q^{77} +(-16.1773 + 8.74904i) q^{78} +(-102.698 - 59.2925i) q^{79} +(3.88836 + 25.6444i) q^{80} +(90.1737 + 156.185i) q^{81} +(106.390 + 2.96160i) q^{82} +(-7.54311 + 7.54311i) q^{83} +(153.602 - 12.1131i) q^{84} +(10.2684 - 10.2684i) q^{85} +(-13.7919 + 13.0448i) q^{86} +(-122.780 - 212.662i) q^{87} +(-83.0607 - 29.8768i) q^{88} +(56.1412 + 32.4131i) q^{89} +(-66.1230 - 19.7053i) q^{90} +(-10.8228 - 4.43915i) q^{91} +(22.4001 - 34.2452i) q^{92} +(-50.0866 + 13.4207i) q^{93} +(4.96286 - 8.06874i) q^{94} +(42.5027 - 24.5390i) q^{95} +(68.7265 - 162.124i) q^{96} -119.381 q^{97} +(67.8321 + 70.7305i) q^{98} +(166.035 - 166.035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{7} - 20 q^{8} + 16 q^{10} + 14 q^{11} - 2 q^{12} - 8 q^{13} + 20 q^{14} + 8 q^{16} - 4 q^{17} - 38 q^{18} - 2 q^{19} + 72 q^{20} + 14 q^{21}+ \cdots - 776 q^{99}+O(q^{100}) $ 120 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 20 * q^8 + 16 * q^10 + 14 * q^11 - 2 * q^12 - 8 * q^13 + 20 * q^14 + 8 * q^16 - 4 * q^17 - 38 * q^18 - 2 * q^19 + 72 * q^20 + 14 * q^21 + 52 * q^22 - 68 * q^23 - 142 * q^24 - 2 * q^26 - 44 * q^27 - 62 * q^28 - 40 * q^29 - 14 * q^30 + 88 * q^32 - 4 * q^33 + 168 * q^34 + 94 * q^35 - 272 * q^36 - 50 * q^37 + 138 * q^38 - 4 * q^39 - 206 * q^40 - 198 * q^42 - 104 * q^43 + 2 * q^44 - 84 * q^45 - 76 * q^46 - 856 * q^48 - 8 * q^49 - 320 * q^50 + 114 * q^51 + 76 * q^52 - 82 * q^53 + 350 * q^54 - 16 * q^55 + 8 * q^56 - 6 * q^58 + 62 * q^59 + 318 * q^60 - 2 * q^61 + 876 * q^62 + 112 * q^64 - 4 * q^65 + 162 * q^66 - 66 * q^67 + 192 * q^68 + 28 * q^69 + 112 * q^70 + 496 * q^71 + 248 * q^72 + 178 * q^74 + 12 * q^75 - 308 * q^76 + 94 * q^77 - 140 * q^78 + 204 * q^80 + 248 * q^81 + 266 * q^82 - 488 * q^83 + 620 * q^84 + 92 * q^85 - 408 * q^86 - 4 * q^87 - 370 * q^88 - 404 * q^90 - 488 * q^91 + 900 * q^92 - 38 * q^93 - 150 * q^94 + 768 * q^96 - 16 * q^97 + 432 * q^98 - 776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0556527	+	1.99923i	−0.0278263	+	0.999613i
$2$	−0.0556527	+	1.99923i	−0.0278263	+	0.999613i
$3$	−5.31530	−	1.42423i	−1.77177	−	0.474744i	−0.782724	−	0.622369i	$-0.786170\pi$
$3$	−5.31530	−	1.42423i	−1.77177	−	0.474744i	−0.989043	+	0.147626i	$0.952837\pi$
$4$	−3.99381	−	0.222525i	−0.998451	−	0.0556311i
$5$	0.419571	+	1.56586i	0.0839142	+	0.313172i	0.995106	−	0.0988096i	$-0.0315035\pi$
$5$	0.419571	+	1.56586i	0.0839142	+	0.313172i	−0.911192	+	0.411982i	$0.864837\pi$
$6$	3.14317	−	10.5472i	0.523862	−	1.75787i
$7$	6.45786	−	2.70113i	0.922551	−	0.385876i
$7$	6.45786	−	2.70113i	0.922551	−	0.385876i
$8$	0.667143	−	7.97213i	0.0833928	−	0.996517i
$9$	18.4298	+	10.6404i	2.04775	+	1.18227i
$10$	−3.15386	+	0.751673i	−0.315386	+	0.0751673i
$11$	2.85576	−	10.6579i	0.259615	−	0.968896i	−0.705850	−	0.708362i	$-0.749435\pi$
$11$	2.85576	−	10.6579i	0.259615	−	0.968896i	0.965465	−	0.260534i	$-0.0838988\pi$
$12$	20.9114	+	6.87089i	1.74261	+	0.572574i
$13$	−1.18165	−	1.18165i	−0.0908965	−	0.0908965i	0.660196	−	0.751093i	$-0.270473\pi$
$13$	−1.18165	−	1.18165i	−0.0908965	−	0.0908965i	−0.751093	+	0.660196i	$0.770473\pi$
$14$	5.04077	+	13.0610i	0.360055	+	0.932931i
$15$		−	8.92058i		−	0.594706i
$16$	15.9010	+	1.77744i	0.993810	+	0.111090i
$17$	−4.47899	−	7.75783i	−0.263470	−	0.456343i	0.703692	−	0.710505i	$-0.251534\pi$
$17$	−4.47899	−	7.75783i	−0.263470	−	0.456343i	−0.967162	+	0.254162i	$0.918200\pi$
$18$	−22.2983	+	36.2531i	−1.23879	+	2.01406i
$19$	−7.83562	−	29.2429i	−0.412401	−	1.53910i	−0.789985	−	0.613126i	$-0.789912\pi$
$19$	−7.83562	−	29.2429i	−0.412401	−	1.53910i	0.377584	−	0.925975i	$-0.376755\pi$
$20$	−1.32724	−	6.34710i	−0.0663621	−	0.317355i
$21$	−38.1725	+	5.15984i	−1.81774	+	0.245707i
$22$	21.1485	+	6.30246i	0.961297	+	0.286475i
$23$	−5.11508	+	8.85958i	−0.222395	+	0.385199i	−0.955535	−	0.294879i	$-0.904721\pi$
$23$	−5.11508	+	8.85958i	−0.222395	+	0.385199i	0.733140	+	0.680078i	$0.238054\pi$
$24$	−14.9002	+	41.4241i	−0.620843	+	1.72601i
$25$	19.3748	−	11.1860i	0.774990	−	0.447441i
$26$	2.42816	−	2.29663i	0.0933906	−	0.0883320i
$27$	−47.7857	−	47.7857i	−1.76984	−	1.76984i
$28$	−26.3925	+	9.35075i	−0.942589	+	0.333955i
$29$	31.5544	+	31.5544i	1.08808	+	1.08808i	0.995726	+	0.0923562i	$0.0294399\pi$
$29$	31.5544	+	31.5544i	1.08808	+	1.08808i	0.0923562	+	0.995726i	$0.470560\pi$
$30$	17.8343	+	0.496454i	0.594475	+	0.0165485i
$31$	8.16065	−	4.71155i	0.263247	−	0.151986i	−0.362568	−	0.931957i	$-0.618100\pi$
$31$	8.16065	−	4.71155i	0.263247	−	0.151986i	0.625815	+	0.779972i	$0.284767\pi$
$32$	−4.43843	+	31.6907i	−0.138701	+	0.990334i
$33$	−30.3585	+	52.5825i	−0.919955	+	1.59341i
$34$	15.7589	−	8.52276i	0.463498	−	0.250669i
$35$	6.93912	+	8.97878i	0.198261	+	0.256537i
$36$	−71.2372	−	46.5969i	−1.97881	−	1.29436i
$37$	−13.9304	−	51.9889i	−0.376497	−	1.40511i	−0.851146	−	0.524930i	$-0.824092\pi$
$37$	−13.9304	−	51.9889i	−0.376497	−	1.40511i	0.474649	−	0.880175i	$-0.342575\pi$
$38$	58.8993	−	14.0377i	1.54998	−	0.369414i
$39$	4.59790	+	7.96380i	0.117895	+	0.204200i
$40$	12.7632	−	2.30022i	0.319079	−	0.0575056i
$41$		−	53.2158i		−	1.29795i	−0.760811	−	0.648974i	$-0.775199\pi$
$41$		−	53.2158i		−	1.29795i	0.760811	−	0.648974i	$-0.224801\pi$
$42$	−8.19128	−	76.6026i	−0.195031	−	1.82387i
$43$	6.71176	+	6.71176i	0.156088	+	0.156088i	0.780830	−	0.624743i	$-0.214796\pi$
$43$	6.71176	+	6.71176i	0.156088	+	0.156088i	−0.624743	+	0.780830i	$0.714796\pi$
$44$	−13.7770	+	41.9299i	−0.313114	+	0.952953i
$45$	−8.92883	+	33.3229i	−0.198418	+	0.740508i
$46$	−17.4276	−	10.7193i	−0.378862	−	0.233027i
$47$	−4.10186	−	2.36821i	−0.0872735	−	0.0503874i	0.455728	−	0.890119i	$-0.349379\pi$
$47$	−4.10186	−	2.36821i	−0.0872735	−	0.0503874i	−0.543002	+	0.839732i	$0.682712\pi$
$48$	−81.9869	−	32.0943i	−1.70806	−	0.668631i
$49$	34.4078	−	34.8870i	0.702200	−	0.711980i
$50$	21.2851	+	39.3570i	0.425702	+	0.787141i
$51$	12.7582	+	47.6143i	0.250161	+	0.933614i
$52$	4.45635	+	4.98225i	0.0856991	+	0.0958124i
$53$	−32.8247	−	8.79535i	−0.619334	−	0.165950i	−0.0645090	−	0.997917i	$-0.520548\pi$
$53$	−32.8247	−	8.79535i	−0.619334	−	0.165950i	−0.554825	+	0.831967i	$0.687215\pi$
$54$	98.1938	−	92.8750i	1.81840	−	1.71991i
$55$	17.8869			0.325217
$56$	−17.2255	−	53.2849i	−0.307597	−	0.951517i
$57$			166.595i			2.92271i
$58$	−64.8404	+	61.3282i	−1.11794	+	1.05738i
$59$	−22.9411	+	85.6173i	−0.388832	+	1.45114i	0.443205	+	0.896420i	$0.353841\pi$
$59$	−22.9411	+	85.6173i	−0.388832	+	1.45114i	−0.832037	+	0.554720i	$0.812825\pi$
$60$	−1.98505	+	35.6271i	−0.0330841	+	0.593785i
$61$	15.4586	−	4.14213i	0.253420	−	0.0679037i	−0.129872	−	0.991531i	$-0.541457\pi$
$61$	15.4586	−	4.14213i	0.253420	−	0.0679037i	0.383293	+	0.923627i	$0.374790\pi$
$62$	8.96529	+	16.5772i	0.144602	+	0.267374i
$63$	147.758	+	18.9332i	2.34536	+	0.300527i
$64$	−63.1098	−	10.6371i	−0.986091	−	0.166205i
$65$	1.35452	−	2.34609i	0.0208387	−	0.0360937i
$66$	−103.435	−	63.6198i	−1.56719	−	0.963937i
$67$	−14.3420	−	3.84292i	−0.214059	−	0.0573570i	0.150196	−	0.988656i	$-0.452010\pi$
$67$	−14.3420	−	3.84292i	−0.214059	−	0.0573570i	−0.364255	+	0.931299i	$0.618676\pi$
$68$	16.1619	+	31.9800i	0.237675	+	0.470294i
$69$	39.8063	−	39.8063i	0.576903	−	0.576903i
$70$	−18.3368	+	13.3732i	−0.261954	+	0.191045i
$71$	93.6627			1.31919			0.659597	−	0.751620i	$-0.270727\pi$
$71$	93.6627			1.31919			0.659597	+	0.751620i	$0.270727\pi$
$72$	97.1222	−	139.826i	1.34892	−	1.94203i
$73$	−16.5673	+	9.56511i	−0.226949	+	0.131029i	−0.609164	−	0.793045i	$-0.708495\pi$
$73$	−16.5673	+	9.56511i	−0.226949	+	0.131029i	0.382215	+	0.924073i	$0.375161\pi$
$74$	104.713	−	24.9567i	1.41504	−	0.337252i
$75$	−118.914	+	31.8630i	−1.58552	+	0.424839i
$76$	24.7867	+	118.534i	0.326140	+	1.55966i
$77$	−10.3461	−	76.5407i	−0.134365	−	0.994035i
$78$	−16.1773	+	8.74904i	−0.207401	+	0.112167i
$79$	−102.698	−	59.2925i	−1.29997	−	0.750538i	−0.319572	−	0.947562i	$-0.603539\pi$
$79$	−102.698	−	59.2925i	−1.29997	−	0.750538i	−0.980399	+	0.197024i	$0.936872\pi$
$80$	3.88836	+	25.6444i	0.0486045	+	0.320556i
$81$	90.1737	+	156.185i	1.11326	+	1.92822i
$82$	106.390	+	2.96160i	1.29744	+	0.0361171i
$83$	−7.54311	+	7.54311i	−0.0908809	+	0.0908809i	−0.751086	−	0.660205i	$-0.770469\pi$
$83$	−7.54311	+	7.54311i	−0.0908809	+	0.0908809i	0.660205	+	0.751086i	$0.270469\pi$
$84$	153.602	−	12.1131i	1.82859	−	0.144203i
$85$	10.2684	−	10.2684i	0.120805	−	0.120805i
$86$	−13.7919	+	13.0448i	−0.160370	+	0.151684i
$87$	−122.780	−	212.662i	−1.41127	−	2.44439i
$88$	−83.0607	−	29.8768i	−0.943871	−	0.339510i
$89$	56.1412	+	32.4131i	0.630800	+	0.364192i	0.781062	−	0.624454i	$-0.214678\pi$
$89$	56.1412	+	32.4131i	0.630800	+	0.364192i	−0.150262	+	0.988646i	$0.548012\pi$
$90$	−66.1230	−	19.7053i	−0.734700	−	0.218947i
$91$	−10.8228	−	4.43915i	−0.118931	−	0.0487819i
$92$	22.4001	−	34.2452i	0.243480	−	0.372231i
$93$	−50.0866	+	13.4207i	−0.538566	+	0.144308i
$94$	4.96286	−	8.06874i	0.0527964	−	0.0858376i
$95$	42.5027	−	24.5390i	0.447397	−	0.258305i
$96$	68.7265	−	162.124i	0.715901	−	1.68879i
$97$	−119.381			−1.23073			−0.615366	−	0.788242i	$-0.710992\pi$
$97$	−119.381			−1.23073			−0.615366	+	0.788242i	$0.710992\pi$
$98$	67.8321	+	70.7305i	0.692164	+	0.721740i
$99$	166.035	−	166.035i	1.67712	−	1.67712i
$100$	−79.8682	+	40.3634i	−0.798682	+	0.403634i
$101$	167.187	+	44.7977i	1.65532	+	0.443542i	0.961096	−	0.276216i	$-0.0890804\pi$
$101$	167.187	+	44.7977i	1.65532	+	0.443542i	0.694225	+	0.719758i	$0.255747\pi$
$102$	−95.9018	+	22.8567i	−0.940214	+	0.224085i
$103$	−21.0109	+	36.3920i	−0.203990	+	0.353321i	−0.949810	−	0.312826i	$-0.898724\pi$
$103$	−21.0109	+	36.3920i	−0.203990	+	0.353321i	0.745821	+	0.666147i	$0.232058\pi$
$104$	−10.2086	+	8.63198i	−0.0981600	+	0.0829998i
$105$	−24.0956	−	57.6078i	−0.229482	−	0.548646i
$106$	19.4107	−	65.1345i	0.183120	−	0.614476i
$107$	38.0354	−	10.1916i	0.355471	−	0.0952482i	−0.0766641	−	0.997057i	$-0.524427\pi$
$107$	38.0354	−	10.1916i	0.355471	−	0.0952482i	0.432135	+	0.901809i	$0.357760\pi$
$108$	180.213	+	201.480i	1.66864	+	1.86556i
$109$	32.8786	−	122.704i	0.301638	−	1.12573i	−0.634162	−	0.773200i	$-0.718655\pi$
$109$	32.8786	−	122.704i	0.301638	−	1.12573i	0.935801	−	0.352529i	$-0.114678\pi$
$110$	−0.995454	+	35.7600i	−0.00904959	+	0.325091i
$111$			296.177i			2.66826i
$112$	107.487	−	31.4721i	0.959707	−	0.281001i
$113$	−129.391			−1.14506			−0.572528	−	0.819885i	$-0.694037\pi$
$113$	−129.391			−1.14506			−0.572528	+	0.819885i	$0.694037\pi$
$114$	−333.060	−	9.27144i	−2.92158	−	0.0813284i
$115$	−16.0190	−	4.29228i	−0.139296	−	0.0373242i
$116$	−119.000	−	133.044i	−1.02587	−	1.14693i
$117$	−9.20430	−	34.3509i	−0.0786693	−	0.293598i
$118$	−169.891	−	50.6292i	−1.43976	−	0.429061i
$119$	−49.8796	−	38.0006i	−0.419156	−	0.319333i
$120$	−71.1161	−	5.95130i	−0.592634	−	0.0495942i
$121$	−0.645479	−	0.372667i	−0.00533454	−	0.00307990i
$122$	7.42073	+	31.1358i	0.0608257	+	0.255212i
$123$	−75.7916	+	282.858i	−0.616192	+	2.29966i
$124$	−33.6405	+	17.0011i	−0.271294	+	0.137105i
$125$	54.3021	+	54.3021i	0.434416	+	0.434416i
$126$	−46.0748	+	294.348i	−0.365673	+	2.33609i
$127$		−	53.1110i		−	0.418197i	−0.977895	−	0.209099i	$-0.932947\pi$
$127$		−	53.1110i		−	0.418197i	0.977895	−	0.209099i	$-0.0670530\pi$
$128$	24.7782	−	125.579i	0.193580	−	0.981085i
$129$	−26.1159	−	45.2341i	−0.202449	−	0.350652i
$130$	4.61499	+	2.83855i	0.0354999	+	0.0218350i
$131$	3.86906	+	14.4395i	0.0295348	+	0.110225i	0.979120	−	0.203285i	$-0.0651617\pi$
$131$	3.86906	+	14.4395i	0.0295348	+	0.110225i	−0.949585	+	0.313510i	$0.898495\pi$
$132$	132.947	−	203.249i	1.00717	−	1.53976i
$133$	−129.590	−	167.682i	−0.974363	−	1.26076i
$134$	8.48103	−	28.4590i	0.0632913	−	0.212380i
$135$	54.7762	−	94.8752i	0.405750	−	0.702779i
$136$	−64.8346	+	30.5315i	−0.476725	+	0.224496i
$137$	−56.0020	+	32.3328i	−0.408774	+	0.236005i	−0.690263	−	0.723559i	$-0.742505\pi$
$137$	−56.0020	+	32.3328i	−0.408774	+	0.236005i	0.281489	+	0.959564i	$0.409172\pi$
$138$	77.3664	+	81.7971i	0.560626	+	0.592732i
$139$	30.9038	+	30.9038i	0.222330	+	0.222330i	0.809479	−	0.587149i	$-0.199750\pi$
$139$	30.9038	+	30.9038i	0.222330	+	0.222330i	−0.587149	+	0.809479i	$0.699750\pi$
$140$	−25.7155	−	37.4036i	−0.183682	−	0.267169i
$141$	18.4297	+	18.4297i	0.130707	+	0.130707i
$142$	−5.21258	+	187.253i	−0.0367083	+	1.31868i
$143$	−15.9684	+	9.21938i	−0.111667	+	0.0644712i
$144$	274.138	+	201.951i	1.90374	+	1.40244i
$145$	−36.1704	+	62.6490i	−0.249451	+	0.432062i
$146$	−18.2008	−	33.6540i	−0.124663	−	0.230507i
$147$	−232.575	+	136.430i	−1.58214	+	0.928097i
$148$	44.0664	+	210.733i	0.297746	+	1.42387i
$149$	23.1621	+	86.4420i	0.155450	+	0.580148i	0.999066	+	0.0432012i	$0.0137557\pi$
$149$	23.1621	+	86.4420i	0.155450	+	0.580148i	−0.843616	+	0.536947i	$0.819578\pi$
$150$	−57.0833	−	239.509i	−0.380556	−	1.59673i
$151$	39.0685	+	67.6686i	0.258732	+	0.448136i	0.965902	−	0.258906i	$-0.0833621\pi$
$151$	39.0685	+	67.6686i	0.258732	+	0.448136i	−0.707171	+	0.707043i	$0.750029\pi$
$152$	−238.356	+	42.9574i	−1.56813	+	0.282614i
$153$		−	190.633i		−	1.24597i
$154$	153.598	−	16.4246i	0.997389	−	0.106653i
$155$	10.8016	+	10.8016i	0.0696878	+	0.0696878i
$156$	−16.5910	−	32.8290i	−0.106352	−	0.210442i
$157$	15.0915	−	56.3224i	0.0961244	−	0.358741i	−0.901063	−	0.433688i	$-0.857212\pi$
$157$	15.0915	−	56.3224i	0.0961244	−	0.358741i	0.997188	+	0.0749467i	$0.0238787\pi$
$158$	124.255	−	202.016i	0.786421	−	1.27858i
$159$	161.947	+	93.4999i	1.01853	+	0.588050i
$160$	−51.4854	+	6.34653i	−0.321784	+	0.0396658i
$161$	−9.10159	+	71.0304i	−0.0565316	+	0.441183i
$162$	−317.268	+	171.585i	−1.95845	+	1.05917i
$163$	71.1385	+	265.492i	0.436432	+	1.62879i	0.737616	+	0.675221i	$0.235952\pi$
$163$	71.1385	+	265.492i	0.436432	+	1.62879i	−0.301183	+	0.953566i	$0.597382\pi$
$164$	−11.8418	+	212.534i	−0.0722063	+	1.29594i
$165$	−95.0743	−	25.4751i	−0.576208	−	0.154394i
$166$	−14.6606	−	15.5002i	−0.0883168	−	0.0933746i
$167$	86.0202			0.515091			0.257546	−	0.966266i	$-0.417086\pi$
$167$	86.0202			0.515091			0.257546	+	0.966266i	$0.417086\pi$
$168$	15.6684	+	307.758i	0.0932645	+	1.83190i
$169$		−	166.207i		−	0.983476i
$170$	19.9574	+	21.1004i	0.117397	+	0.124120i
$171$	166.749	−	622.315i	0.975139	−	3.63927i
$172$	−25.3119	−	28.2990i	−0.147162	−	0.164529i
$173$	−79.2116	+	21.2247i	−0.457871	+	0.122686i	−0.480380	−	0.877061i	$-0.659501\pi$
$173$	−79.2116	+	21.2247i	−0.457871	+	0.122686i	0.0225092	+	0.999747i	$0.492834\pi$
$174$	431.992	−	233.630i	2.48271	−	1.34270i
$175$	94.9045	−	124.571i	0.542311	−	0.711837i
$176$	64.3531	−	164.394i	0.365643	−	0.934058i
$177$	243.877	−	422.408i	1.37784	−	2.38649i
$178$	−67.9256	+	110.435i	−0.381604	+	0.620421i
$179$	−250.556	−	67.1363i	−1.39975	−	0.375063i	−0.521498	−	0.853253i	$-0.674626\pi$
$179$	−250.556	−	67.1363i	−1.39975	−	0.375063i	−0.878257	+	0.478190i	$0.841293\pi$
$180$	43.0752	−	131.098i	0.239306	−	0.728323i
$181$	207.889	−	207.889i	1.14856	−	1.14856i	0.161722	−	0.986836i	$-0.448295\pi$
$181$	207.889	−	207.889i	1.14856	−	1.14856i	0.986836	−	0.161722i	$-0.0517049\pi$
$182$	9.47718	−	21.3901i	0.0520724	−	0.117528i
$183$	−88.0666			−0.481238
$184$	67.2173	+	46.6887i	0.365311	+	0.253743i
$185$	75.5625	−	43.6260i	0.408446	−	0.235816i
$186$	−24.0435	−	100.881i	−0.129266	−	0.542373i
$187$	−95.4728	+	25.5819i	−0.510550	+	0.136801i
$188$	15.8550	+	10.3709i	0.0843353	+	0.0551645i
$189$	−437.669	−	179.518i	−2.31571	−	0.949830i
$190$	46.6935	+	86.3382i	0.245755	+	0.454412i
$191$	−127.283	−	73.4869i	−0.666403	−	0.384748i	0.128309	−	0.991734i	$-0.459045\pi$
$191$	−127.283	−	73.4869i	−0.666403	−	0.384748i	−0.794712	+	0.606986i	$0.792378\pi$
$192$	320.298	+	146.422i	1.66822	+	0.762617i
$193$	63.9196	+	110.712i	0.331190	+	0.573637i	0.982745	−	0.184964i	$-0.0592167\pi$
$193$	63.9196	+	110.712i	0.331190	+	0.573637i	−0.651556	+	0.758601i	$0.725883\pi$
$194$	6.64387	−	238.669i	0.0342467	−	1.23025i
$195$	−10.5410	+	10.5410i	−0.0540567	+	0.0540567i
$196$	−145.181	+	131.675i	−0.740721	+	0.671813i
$197$	−98.6531	+	98.6531i	−0.500777	+	0.500777i	−0.911679	−	0.410902i	$-0.865214\pi$
$197$	−98.6531	+	98.6531i	−0.500777	+	0.500777i	0.410902	+	0.911679i	$0.365214\pi$
$198$	322.702	+	341.182i	1.62981	+	1.72314i
$199$	191.079	+	330.958i	0.960195	+	1.66311i	0.722004	+	0.691889i	$0.243221\pi$
$199$	191.079	+	330.958i	0.960195	+	1.66311i	0.238191	+	0.971218i	$0.423445\pi$
$200$	−76.2507	−	161.921i	−0.381254	−	0.809604i
$201$	70.7587	+	40.8525i	0.352033	+	0.203246i
$202$	−98.8652	+	331.752i	−0.489432	+	1.64234i
$203$	289.006	+	118.541i	1.42368	+	0.583947i
$204$	−40.3585	−	193.001i	−0.197836	−	0.946085i
$205$	83.3285	−	22.3278i	0.406481	−	0.108916i
$206$	−71.5866	−	44.0309i	−0.347508	−	0.213742i
$207$	−188.540	+	108.853i	−0.910819	+	0.525862i
$208$	−16.6891	−	20.8898i	−0.0802362	−	0.100432i
$209$	−334.044			−1.59830
$210$	116.512	−	44.9666i	0.554819	−	0.214127i
$211$	7.41591	−	7.41591i	0.0351465	−	0.0351465i	−0.689315	−	0.724462i	$-0.742088\pi$
$211$	7.41591	−	7.41591i	0.0351465	−	0.0351465i	0.724462	+	0.689315i	$0.242088\pi$
$212$	129.138	+	42.4312i	0.609143	+	0.200147i
$213$	−497.846	−	133.397i	−2.33730	−	0.626278i
$214$	18.2585	+	76.6086i	0.0853199	+	0.357984i
$215$	−7.69362	+	13.3257i	−0.0357843	+	0.0619802i
$216$	−412.834	+	349.074i	−1.91127	+	1.61608i
$217$	39.9738	−	52.4695i	0.184211	−	0.241795i
$218$	243.484	+	72.5605i	1.11690	+	0.332846i
$219$	101.683	−	27.2459i	0.464306	−	0.124410i
$220$	−71.4368	−	3.98028i	−0.324713	−	0.0180922i
$221$	−3.87446	+	14.4597i	−0.0175315	+	0.0654285i
$222$	−592.124	−	16.4830i	−2.66723	−	0.0742479i
$223$		−	102.258i		−	0.458557i	−0.973361	−	0.229278i	$-0.926363\pi$
$223$		−	102.258i		−	0.458557i	0.973361	−	0.229278i	$-0.0736366\pi$
$224$	56.9379	+	216.643i	0.254187	+	0.967155i
$225$	476.096			2.11598
$226$	7.20098	−	258.683i	0.0318627	−	1.14461i
$227$	311.782	+	83.5418i	1.37349	+	0.368026i	0.868752	−	0.495247i	$-0.164922\pi$
$227$	311.782	+	83.5418i	1.37349	+	0.368026i	0.504738	+	0.863272i	$0.331589\pi$
$228$	37.0714	−	665.347i	0.162594	−	2.91819i
$229$	49.3064	+	184.014i	0.215312	+	0.803554i	0.986057	+	0.166410i	$0.0532176\pi$
$229$	49.3064	+	184.014i	0.215312	+	0.803554i	−0.770745	+	0.637144i	$0.780116\pi$
$230$	9.47273	−	31.7867i	0.0411858	−	0.138203i
$231$	−54.0188	+	421.572i	−0.233848	+	1.82499i
$232$	272.607	−	230.505i	1.17503	−	0.993554i
$233$	84.9300	+	49.0344i	0.364506	+	0.210448i	0.671056	−	0.741407i	$-0.265841\pi$
$233$	84.9300	+	49.0344i	0.364506	+	0.210448i	−0.306549	+	0.951855i	$0.599174\pi$
$234$	69.1875	−	16.4898i	0.295673	−	0.0704691i
$235$	1.98726	−	7.41656i	0.00845643	−	0.0315598i
$236$	110.674	−	336.834i	0.468958	−	1.42726i
$237$	461.423	+	461.423i	1.94693	+	1.94693i
$238$	78.7478	−	97.6057i	0.330873	−	0.410108i
$239$			158.330i			0.662468i	0.943549	+	0.331234i	$0.107465\pi$
$239$			158.330i			0.662468i	−0.943549	+	0.331234i	$0.892535\pi$
$240$	15.8558	−	141.846i	0.0660658	−	0.591025i
$241$	−45.5171	−	78.8379i	−0.188868	−	0.327128i	0.756005	−	0.654565i	$-0.227148\pi$
$241$	−45.5171	−	78.8379i	−0.188868	−	0.327128i	−0.944873	+	0.327437i	$0.893815\pi$
$242$	0.780969	−	1.26972i	0.00322714	−	0.00524677i
$243$	−99.4393	−	371.112i	−0.409215	−	1.52721i
$244$	−62.6605	+	13.1029i	−0.256805	+	0.0537005i
$245$	69.0647	+	39.2402i	0.281897	+	0.160164i
$246$	−561.279	−	167.266i	−2.28162	−	0.679945i
$247$	−25.2960	+	43.8140i	−0.102413	+	0.177385i
$248$	−32.1168	−	68.2011i	−0.129503	−	0.275004i
$249$	50.8371	−	29.3508i	0.204165	−	0.117875i
$250$	−111.584	+	105.540i	−0.446336	+	0.422160i
$251$	149.092	+	149.092i	0.593992	+	0.593992i	0.938707	−	0.344715i	$-0.112025\pi$
$251$	149.092	+	149.092i	0.593992	+	0.593992i	−0.344715	+	0.938707i	$0.612025\pi$
$252$	−585.904	−	108.495i	−2.32501	−	0.430537i
$253$	79.8167	+	79.8167i	0.315481	+	0.315481i
$254$	106.181	+	2.95577i	0.418035	+	0.0116369i
$255$	−69.2044	+	39.9552i	−0.271390	+	0.156687i
$256$	249.681	+	56.5260i	0.975318	+	0.220805i
$257$	−104.527	+	181.046i	−0.406720	+	0.704460i	−0.994520	−	0.104547i	$-0.966661\pi$
$257$	−104.527	+	181.046i	−0.406720	+	0.704460i	0.587800	+	0.809006i	$0.299994\pi$
$258$	91.8867	−	49.6943i	0.356150	−	0.192613i
$259$	−230.389	−	298.109i	−0.889533	−	1.15100i
$260$	−5.93174	+	9.06843i	−0.0228144	+	0.0348786i
$261$	245.788	+	917.292i	0.941715	+	3.51453i
$262$	−29.0832	+	6.93152i	−0.111004	+	0.0264562i
$263$	−140.474	−	243.308i	−0.534122	−	0.925126i	−0.999205	−	0.0398590i	$-0.987309\pi$
$263$	−140.474	−	243.308i	−0.534122	−	0.925126i	0.465084	−	0.885267i	$-0.346024\pi$
$264$	398.941	+	277.102i	1.51114	+	1.04963i
$265$		−	55.0892i		−	0.207884i
$266$	342.445	−	249.748i	1.28739	−	0.938903i
$267$	−252.244	−	252.244i	−0.944732	−	0.944732i
$268$	56.4239	+	18.5393i	0.210537	+	0.0691765i
$269$	−111.294	+	415.356i	−0.413733	+	1.54407i	0.373626	+	0.927579i	$0.378114\pi$
$269$	−111.294	+	415.356i	−0.413733	+	1.54407i	−0.787359	+	0.616494i	$0.788552\pi$
$270$	186.629	+	114.790i	0.691217	+	0.425149i
$271$	−109.682	−	63.3247i	−0.404729	−	0.233671i	0.283793	−	0.958885i	$-0.408407\pi$
$271$	−109.682	−	63.3247i	−0.404729	−	0.233671i	−0.688523	+	0.725215i	$0.741740\pi$
$272$	−57.4311	−	131.318i	−0.211144	−	0.482787i
$273$	51.2038	+	39.0095i	0.187560	+	0.142892i
$274$	−61.5238	−	113.760i	−0.224539	−	0.415182i
$275$	−63.8893	−	238.438i	−0.232325	−	0.867048i
$276$	−167.836	+	150.121i	−0.608103	+	0.543916i
$277$	342.955	+	91.8945i	1.23810	+	0.331749i	0.817730	−	0.575602i	$-0.195232\pi$
$277$	342.955	+	91.8945i	1.23810	+	0.331749i	0.420374	+	0.907351i	$0.361899\pi$
$278$	−63.5036	+	60.0638i	−0.228430	+	0.216057i
$279$	200.532			0.718752
$280$	76.2094	−	49.3295i	0.272177	−	0.176177i
$281$			203.996i			0.725966i	0.931796	+	0.362983i	$0.118242\pi$
$281$			203.996i			0.725966i	−0.931796	+	0.362983i	$0.881758\pi$
$282$	−37.8708	+	35.8195i	−0.134294	+	0.127020i
$283$	−1.93030	+	7.20400i	−0.00682086	+	0.0254558i	−0.969252	−	0.246069i	$-0.920861\pi$
$283$	−1.93030	+	7.20400i	−0.00682086	+	0.0254558i	0.962432	+	0.271524i	$0.0875278\pi$
$284$	−374.071	−	20.8422i	−1.31715	−	0.0733882i
$285$	−260.864	+	69.8983i	−0.915312	+	0.245257i
$286$	−17.5429	−	32.4376i	−0.0613389	−	0.113418i
$287$	−143.743	−	343.660i	−0.500846	−	1.19742i
$288$	−419.002	+	536.825i	−1.45487	+	1.86398i
$289$	104.377	−	180.787i	0.361167	−	0.625560i
$290$	−123.237	−	75.7995i	−0.424954	−	0.261377i
$291$	634.546	+	170.026i	2.18057	+	0.584282i
$292$	68.2949	−	34.5146i	0.233887	−	0.118201i
$293$	−67.6489	+	67.6489i	−0.230884	+	0.230884i	−0.813061	−	0.582178i	$-0.802201\pi$
$293$	−67.6489	+	67.6489i	−0.230884	+	0.230884i	0.582178	+	0.813061i	$0.302201\pi$
$294$	−259.812	−	472.563i	−0.883713	−	1.60736i
$295$	−143.690			−0.487085
$296$	−423.756	+	76.3709i	−1.43161	+	0.258010i
$297$	−645.758	+	372.829i	−2.17427	+	1.25532i
$298$	−174.106	+	41.4955i	−0.584249	+	0.139247i
$299$	16.5132	−	4.42470i	0.0552282	−	0.0147983i
$300$	482.010	−	100.793i	1.60670	−	0.335977i
$301$	61.4729	+	25.2143i	0.204229	+	0.0837683i
$302$	−137.459	+	74.3408i	−0.455162	+	0.246162i
$303$	−824.849	−	476.227i	−2.72227	−	1.57171i
$304$	−72.6164	−	478.918i	−0.238870	−	1.57539i
$305$	12.9720	+	22.4681i	0.0425311	+	0.0736660i
$306$	381.119	+	10.6093i	1.24549	+	0.0346708i
$307$	−200.976	+	200.976i	−0.654644	+	0.654644i	−0.954108	−	0.299463i	$-0.903192\pi$
$307$	−200.976	+	200.976i	−0.654644	+	0.654644i	0.299463	+	0.954108i	$0.403192\pi$
$308$	24.2883	+	307.991i	0.0788580	+	0.999971i
$309$	163.510	−	163.510i	0.529159	−	0.529159i
$310$	−22.1960	+	20.9937i	−0.0715999	+	0.0677216i
$311$	−117.586	−	203.665i	−0.378090	−	0.654871i	0.612694	−	0.790320i	$-0.290086\pi$
$311$	−117.586	−	203.665i	−0.378090	−	0.654871i	−0.990784	+	0.135449i	$0.956752\pi$
$312$	66.5559	−	31.3421i	0.213320	−	0.100455i
$313$	−133.891	−	77.3022i	−0.427768	−	0.246972i	0.270627	−	0.962684i	$-0.412769\pi$
$313$	−133.891	−	77.3022i	−0.427768	−	0.246972i	−0.698395	+	0.715712i	$0.746102\pi$
$314$	111.761	+	33.3059i	0.355928	+	0.106070i
$315$	32.3482	+	239.312i	0.102693	+	0.759721i
$316$	396.960	+	259.656i	1.25620	+	0.821695i
$317$	179.323	−	48.0495i	0.565688	−	0.151576i	0.0353699	−	0.999374i	$-0.488739\pi$
$317$	179.323	−	48.0495i	0.565688	−	0.151576i	0.530318	+	0.847799i	$0.322072\pi$
$318$	−195.940	+	318.564i	−0.616164	+	1.00177i
$319$	426.414	−	246.190i	1.33672	−	0.771756i
$320$	−9.82284	−	103.284i	−0.0306964	−	0.322763i
$321$	−216.685			−0.675031
$322$	−141.499	−	22.1492i	−0.439439	−	0.0687862i
$323$	−191.766	+	191.766i	−0.593703	+	0.593703i
$324$	−325.381	−	643.840i	−1.00426	−	1.98716i
$325$	−36.1123	−	9.67626i	−0.111115	−	0.0297731i
$326$	−534.738	+	127.446i	−1.64030	+	0.390940i
$327$	−349.519	+	605.385i	−1.06887	+	1.85133i
$328$	−424.244	−	35.5026i	−1.29343	−	0.108239i
$329$	−32.8860	−	4.21390i	−0.0999575	−	0.0128082i
$330$	56.2216	−	188.657i	0.170368	−	0.571689i
$331$	−192.182	+	51.4949i	−0.580609	+	0.155574i	−0.537158	−	0.843482i	$-0.680502\pi$
$331$	−192.182	+	51.4949i	−0.580609	+	0.155574i	−0.0434513	+	0.999056i	$0.513835\pi$
$332$	31.8043	−	28.4472i	0.0957960	−	0.0856844i
$333$	296.451	−	1106.37i	0.890242	−	3.32243i
$334$	−4.78726	+	171.974i	−0.0143331	+	0.514892i
$335$		−	24.0699i		−	0.0718504i
$336$	−616.151	+	14.1972i	−1.83378	+	0.0422535i
$337$	9.29790			0.0275902			0.0137951	−	0.999905i	$-0.495609\pi$
$337$	9.29790			0.0275902			0.0137951	+	0.999905i	$0.495609\pi$
$338$	332.286	+	9.24989i	0.983095	+	0.0273665i
$339$	687.754	+	184.283i	2.02877	+	0.543608i
$340$	−43.2951	+	38.7251i	−0.127338	+	0.113897i
$341$	−26.9102	−	100.430i	−0.0789155	−	0.294516i
$342$	1234.87	+	368.002i	3.61072	+	1.07603i
$343$	127.966	−	318.235i	0.373080	−	0.927799i
$344$	57.9848	−	49.0294i	0.168560	−	0.142527i
$345$	79.0326	+	45.6295i	0.229080	+	0.132259i
$346$	−38.0246	−	159.543i	−0.109898	−	0.461107i
$347$	106.135	−	396.103i	0.305866	−	1.14151i	−0.626332	−	0.779557i	$-0.715444\pi$
$347$	106.135	−	396.103i	0.305866	−	1.14151i	0.932197	−	0.361950i	$-0.117889\pi$
$348$	443.038	+	876.652i	1.27310	+	2.51911i
$349$	−241.381	−	241.381i	−0.691636	−	0.691636i	0.270956	−	0.962592i	$-0.412660\pi$
$349$	−241.381	−	241.381i	−0.691636	−	0.691636i	−0.962592	+	0.270956i	$0.912660\pi$
$350$	243.765	+	196.668i	0.696471	+	0.561909i
$351$			112.932i			0.321745i
$352$	325.080	+	137.805i	0.923522	+	0.391493i
$353$	14.3559	+	24.8651i	0.0406682	+	0.0704394i	0.885643	−	0.464367i	$-0.153718\pi$
$353$	14.3559	+	24.8651i	0.0406682	+	0.0704394i	−0.844975	+	0.534806i	$0.820385\pi$
$354$	830.917	+	511.074i	2.34722	+	1.44371i
$355$	39.2981	+	146.663i	0.110699	+	0.413134i
$356$	−217.004	−	141.945i	−0.609563	−	0.398721i
$357$	211.003	+	273.025i	0.591045	+	0.764776i
$358$	148.165	−	497.182i	0.413868	−	1.38878i
$359$	197.795	−	342.591i	0.550962	−	0.954294i	−0.447244	−	0.894412i	$-0.647594\pi$
$359$	197.795	−	342.591i	0.550962	−	0.954294i	0.998205	−	0.0598817i	$-0.0190723\pi$
$360$	259.697	+	93.4129i	0.721382	+	0.259480i
$361$	−481.117	+	277.773i	−1.33273	+	0.769454i
$362$	404.048	+	427.187i	1.11615	+	1.18007i
$363$	2.90015	+	2.90015i	0.00798939	+	0.00798939i
$364$	42.2362	+	20.1374i	0.116033	+	0.0553226i
$365$	−21.9288	−	21.9288i	−0.0600788	−	0.0600788i
$366$	4.90114	−	176.065i	0.0133911	−	0.481052i
$367$	437.898	−	252.821i	1.19318	−	0.688885i	0.234157	−	0.972199i	$-0.424767\pi$
$367$	437.898	−	252.821i	1.19318	−	0.688885i	0.959027	+	0.283314i	$0.0914338\pi$
$368$	−97.0821	+	131.784i	−0.263810	+	0.358109i
$369$	566.239	−	980.755i	1.53452	−	2.65787i
$370$	83.0131	+	153.494i	0.224360	+	0.414850i
$371$	−235.735	+	31.8646i	−0.635403	+	0.0858885i
$372$	203.023	−	42.4541i	0.545760	−	0.114124i
$373$	−55.4367	−	206.892i	−0.148624	−	0.554671i	−0.999567	−	0.0294143i	$-0.990636\pi$
$373$	−55.4367	−	206.892i	−0.148624	−	0.554671i	0.850944	−	0.525257i	$-0.176031\pi$
$374$	−45.8306	−	192.295i	−0.122542	−	0.514159i
$375$	−211.293	−	365.970i	−0.563448	−	0.975921i
$376$	−21.6162	+	31.1206i	−0.0574899	+	0.0827676i
$377$		−	74.5728i		−	0.197806i
$378$	383.254	−	865.008i	1.01390	−	2.28838i
$379$	335.553	+	335.553i	0.885364	+	0.885364i	0.994074	−	0.108709i	$-0.0346718\pi$
$379$	335.553	+	335.553i	0.885364	+	0.885364i	−0.108709	+	0.994074i	$0.534672\pi$
$380$	−175.208	+	88.5460i	−0.461074	+	0.233016i
$381$	−75.6424	+	282.301i	−0.198536	+	0.740948i
$382$	154.000	−	250.378i	0.403142	−	0.655439i
$383$	−48.3341	−	27.9057i	−0.126199	−	0.0728609i	0.435572	−	0.900154i	$-0.356546\pi$
$383$	−48.3341	−	27.9057i	−0.126199	−	0.0728609i	−0.561770	+	0.827293i	$0.689880\pi$
$384$	−310.557	+	632.199i	−0.808742	+	1.64635i
$385$	115.511	−	48.3148i	0.300029	−	0.125493i
$386$	−224.895	+	121.628i	−0.582631	+	0.315099i
$387$	52.2802	+	195.112i	0.135091	+	0.504166i
$388$	476.784	+	26.5652i	1.22883	+	0.0684670i
$389$	−80.4320	−	21.5517i	−0.206766	−	0.0554028i	0.153949	−	0.988079i	$-0.450801\pi$
$389$	−80.4320	−	21.5517i	−0.206766	−	0.0554028i	−0.360715	+	0.932676i	$0.617467\pi$
$390$	−20.4873	−	21.6606i	−0.0525315	−	0.0555399i
$391$	91.6415			0.234377
$392$	−255.169	−	297.578i	−0.650941	−	0.759128i
$393$		−	82.2608i		−	0.209315i
$394$	−191.739	−	202.720i	−0.486648	−	0.514518i
$395$	49.7548	−	185.688i	0.125962	−	0.470095i
$396$	−700.060	+	626.166i	−1.76783	+	1.58123i
$397$	338.804	−	90.7823i	0.853411	−	0.228671i	0.194510	−	0.980901i	$-0.437688\pi$
$397$	338.804	−	90.7823i	0.853411	−	0.228671i	0.658901	+	0.752230i	$0.271022\pi$
$398$	−672.294	+	363.591i	−1.68918	+	0.913545i
$399$	449.994	+	1075.84i	1.12780	+	2.69635i
$400$	327.960	−	143.431i	0.819900	−	0.358578i
$401$	−199.672	+	345.842i	−0.497934	+	0.862448i	−0.999997	−	0.00238351i	$-0.999241\pi$
$401$	−199.672	+	345.842i	−0.497934	+	0.862448i	0.502063	+	0.864831i	$0.332575\pi$
$402$	−85.6114	+	139.189i	−0.212964	+	0.346241i
$403$	−15.2105	−	4.07564i	−0.0377432	−	0.0101132i
$404$	−657.746	−	216.117i	−1.62808	−	0.534942i
$405$	−206.730	+	206.730i	−0.510445	+	0.510445i
$406$	−253.075	+	571.191i	−0.623336	+	1.40688i
$407$	−593.872			−1.45915
$408$	388.099	−	69.9447i	0.951224	−	0.171433i
$409$	−499.745	+	288.528i	−1.22187	+	0.705448i	−0.965317	−	0.261082i	$-0.915921\pi$
$409$	−499.745	+	288.528i	−1.22187	+	0.705448i	−0.256555	+	0.966530i	$0.582587\pi$
$410$	40.0009	+	167.835i	0.0975631	+	0.409354i
$411$	343.717	−	92.0986i	0.836294	−	0.224084i
$412$	92.0118	−	140.667i	0.223330	−	0.341425i
$413$	83.1131	+	614.871i	0.201242	+	1.48879i
$414$	−207.130	−	382.991i	−0.500313	−	0.925099i
$415$	−14.9763	−	8.64659i	−0.0360875	−	0.0208352i
$416$	42.6922	−	32.2028i	0.102625	−	0.0774105i
$417$	−120.249	−	208.277i	−0.288367	−	0.499466i
$418$	18.5904	−	667.829i	0.0444747	−	1.59768i
$419$	104.114	−	104.114i	0.248482	−	0.248482i	−0.571865	−	0.820348i	$-0.693780\pi$
$419$	104.114	−	104.114i	0.248482	−	0.248482i	0.820348	+	0.571865i	$0.193780\pi$
$420$	83.4142	+	235.436i	0.198605	+	0.560563i
$421$	70.1243	−	70.1243i	0.166566	−	0.166566i	−0.618902	−	0.785468i	$-0.712422\pi$
$421$	70.1243	−	70.1243i	0.166566	−	0.166566i	0.785468	+	0.618902i	$0.212422\pi$
$422$	14.4134	+	15.2388i	0.0341549	+	0.0361109i
$423$	−50.3975	−	87.2910i	−0.119143	−	0.206362i
$424$	−92.0165	+	255.815i	−0.217020	+	0.603338i
$425$	−173.559	−	100.204i	−0.408373	−	0.235774i
$426$	294.398	−	987.882i	0.691075	−	2.31897i
$427$	88.6412	−	68.5050i	0.207591	−	0.160433i
$428$	−154.174	+	32.2393i	−0.360220	+	0.0753255i
$429$	98.0076	−	26.2610i	0.228456	−	0.0612146i
$430$	−26.2130	−	16.1229i	−0.0609604	−	0.0374951i
$431$	−395.520	+	228.353i	−0.917679	+	0.529822i	−0.882894	−	0.469573i	$-0.844408\pi$
$431$	−395.520	+	228.353i	−0.917679	+	0.529822i	−0.0347851	+	0.999395i	$0.511075\pi$
$432$	−674.903	−	844.775i	−1.56227	−	1.95550i
$433$	−42.2284			−0.0975253			−0.0487626	−	0.998810i	$-0.515528\pi$
$433$	−42.2284			−0.0975253			−0.0487626	+	0.998810i	$0.515528\pi$
$434$	102.674	+	82.8367i	0.236575	+	0.190868i
$435$	281.484	−	281.484i	0.647089	−	0.647089i
$436$	−158.615	+	482.742i	−0.363797	+	1.10721i
$437$	299.160	+	80.1597i	0.684577	+	0.183432i
$438$	48.8117	+	204.803i	0.111442	+	0.467588i
$439$	−145.062	+	251.256i	−0.330438	+	0.572336i	−0.982598	−	0.185746i	$-0.940530\pi$
$439$	−145.062	+	251.256i	−0.330438	+	0.572336i	0.652159	+	0.758082i	$0.273863\pi$
$440$	11.9331	−	142.597i	0.0271207	−	0.324084i
$441$	1005.34	−	276.846i	2.27968	−	0.627768i
$442$	−28.6926	−	8.55065i	−0.0649153	−	0.0193454i
$443$	−19.1795	+	5.13914i	−0.0432947	+	0.0116008i	−0.280401	−	0.959883i	$-0.590468\pi$
$443$	−19.1795	+	5.13914i	−0.0432947	+	0.0116008i	0.237107	+	0.971484i	$0.423801\pi$
$444$	65.9066	−	1182.87i	0.148438	−	2.66413i
$445$	−27.1992	+	101.509i	−0.0611218	+	0.228110i
$446$	204.437	+	5.69094i	0.458379	+	0.0127600i
$447$		−	492.454i		−	1.10169i
$448$	−436.286	+	101.775i	−0.973854	+	0.227176i
$449$	−552.102			−1.22963			−0.614813	−	0.788673i	$-0.710769\pi$
$449$	−552.102			−1.22963			−0.614813	+	0.788673i	$0.710769\pi$
$450$	−26.4960	+	951.824i	−0.0588801	+	2.11516i
$451$	−567.167	−	151.972i	−1.25758	−	0.336966i
$452$	516.764	+	28.7928i	1.14328	+	0.0637008i
$453$	−111.285	−	415.322i	−0.245662	−	0.916825i
$454$	−184.371	+	618.674i	−0.406102	+	1.36272i
$455$	2.41018	−	18.8095i	0.00529709	−	0.0413395i
$456$	1328.12	+	111.142i	2.91253	+	0.243733i
$457$	271.165	+	156.557i	0.593359	+	0.342576i	0.766424	−	0.642335i	$-0.222034\pi$
$457$	271.165	+	156.557i	0.593359	+	0.342576i	−0.173066	+	0.984910i	$0.555367\pi$
$458$	−370.629	+	88.3337i	−0.809234	+	0.192868i
$459$	−156.682	+	584.745i	−0.341355	+	1.27395i
$460$	63.0216	+	20.7071i	0.137004	+	0.0450155i
$461$	−122.341	−	122.341i	−0.265381	−	0.265381i	0.561855	−	0.827236i	$-0.310088\pi$
$461$	−122.341	−	122.341i	−0.265381	−	0.265381i	−0.827236	+	0.561855i	$0.810088\pi$
$462$	−839.812	−	131.457i	−1.81777	−	0.284540i
$463$		−	125.988i		−	0.272111i	−0.990701	−	0.136056i	$-0.956557\pi$
$463$		−	125.988i		−	0.272111i	0.990701	−	0.136056i	$-0.0434426\pi$
$464$	445.659	+	557.831i	0.960472	+	1.20222i
$465$	−42.0298	−	72.7977i	−0.0903867	−	0.156554i
$466$	−102.757	+	167.065i	−0.220509	+	0.358509i
$467$	−91.3037	−	340.750i	−0.195511	−	0.729657i	−0.992134	−	0.125181i	$-0.960049\pi$
$467$	−91.3037	−	340.750i	−0.195511	−	0.729657i	0.796623	−	0.604477i	$-0.206618\pi$
$468$	29.1163	+	139.239i	0.0622143	+	0.297520i
$469$	−102.999	+	13.9225i	−0.219613	+	0.0296855i
$470$	14.7168	+	4.38574i	0.0313123	+	0.00933135i
$471$	−160.432	+	277.877i	−0.340620	+	0.589972i
$472$	667.247	+	240.008i	1.41366	+	0.508492i
$473$	90.7002	−	52.3658i	0.191755	−	0.110710i
$474$	−948.168	+	896.809i	−2.00035	+	1.89200i
$475$	−478.925	−	478.925i	−1.00826	−	1.00826i
$476$	190.753	+	162.867i	0.400742	+	0.342157i
$477$	−511.365	−	511.365i	−1.07204	−	1.07204i
$478$	−316.537	−	8.81148i	−0.662211	−	0.0184341i
$479$	179.861	−	103.843i	0.375492	−	0.216791i	−0.300363	−	0.953825i	$-0.597108\pi$
$479$	179.861	−	103.843i	0.375492	−	0.216791i	0.675855	+	0.737034i	$0.263774\pi$
$480$	282.700	+	39.5934i	0.588957	+	0.0824863i
$481$	−44.9720	+	77.8938i	−0.0934969	+	0.161941i
$482$	160.148	−	86.6114i	0.332257	−	0.179692i
$483$	149.541	−	364.585i	0.309609	−	0.754835i
$484$	2.49499	+	1.63200i	0.00515494	+	0.00337189i
$485$	−50.0888	−	186.934i	−0.103276	−	0.385431i
$486$	747.471	−	178.148i	1.53801	−	0.366560i
$487$	228.856	+	396.390i	0.469930	+	0.813943i	0.999409	−	0.0343802i	$-0.0109457\pi$
$487$	228.856	+	396.390i	0.469930	+	0.813943i	−0.529479	+	0.848323i	$0.677612\pi$
$488$	−22.7085	−	126.002i	−0.0465338	−	0.258200i
$489$		−	1512.49i		−	3.09303i
$490$	−82.2937	+	135.892i	−0.167946	+	0.277331i
$491$	−217.040	−	217.040i	−0.442037	−	0.442037i	0.450659	−	0.892696i	$-0.351189\pi$
$491$	−217.040	−	217.040i	−0.442037	−	0.442037i	−0.892696	+	0.450659i	$0.851189\pi$
$492$	365.640	−	1112.82i	0.743171	−	2.26182i
$493$	103.462	−	386.125i	0.209862	−	0.783216i
$494$	−86.1863	−	53.0109i	−0.174466	−	0.107309i
$495$	329.652	+	190.324i	0.665963	+	0.384494i
$496$	138.137	−	60.4132i	0.278501	−	0.121801i
$497$	604.860	−	252.995i	1.21702	−	0.509044i
$498$	55.8496	+	103.268i	0.112148	+	0.207366i
$499$	−89.8535	−	335.338i	−0.180067	−	0.672019i	−0.995633	−	0.0933551i	$-0.970241\pi$
$499$	−89.8535	−	335.338i	−0.180067	−	0.672019i	0.815566	−	0.578664i	$-0.196426\pi$
$500$	−204.788	−	228.955i	−0.409577	−	0.457911i
$501$	−457.223	−	122.513i	−0.912622	−	0.244536i
$502$	−306.366	+	289.771i	−0.610290	+	0.577233i
$503$	862.625			1.71496			0.857480	−	0.514517i	$-0.172029\pi$
$503$	862.625			1.71496			0.857480	+	0.514517i	$0.172029\pi$
$504$	249.514	−	1165.32i	0.495067	−	2.31213i
$505$			280.588i			0.555620i
$506$	−164.014	+	155.130i	−0.324138	+	0.306580i
$507$	−236.718	+	883.442i	−0.466899	+	1.74249i
$508$	−11.8185	+	212.115i	−0.0232648	+	0.417550i
$509$	−819.225	+	219.511i	−1.60948	+	0.431259i	−0.947887	−	0.318606i	$-0.896785\pi$
$509$	−819.225	+	219.511i	−1.60948	+	0.431259i	−0.661592	+	0.749864i	$0.730119\pi$
$510$	−76.0280	−	140.579i	−0.149075	−	0.275645i
$511$	−81.1524	+	106.520i	−0.158811	+	0.208455i
$512$	−126.904	+	496.024i	−0.247859	+	0.968796i
$513$	−1022.96	+	1771.82i	−1.99408	+	3.45385i
$514$	−356.135	−	219.049i	−0.692869	−	0.426165i
$515$	−65.8004	−	17.6312i	−0.127768	−	0.0342353i
$516$	94.2363	+	186.468i	0.182629	+	0.361372i
$517$	−36.9539	+	36.9539i	−0.0714777	+	0.0714777i
$518$	608.809	−	444.009i	1.17531	−	0.857161i
$519$	451.262			0.869485
$520$	−17.7997	−	12.3636i	−0.0342302	−	0.0237761i
$521$	703.365	−	406.088i	1.35003	−	0.779439i	0.361775	−	0.932265i	$-0.382171\pi$
$521$	703.365	−	406.088i	1.35003	−	0.779439i	0.988253	+	0.152826i	$0.0488376\pi$
$522$	−1847.55	+	440.335i	−3.53937	+	0.843554i
$523$	534.377	−	143.186i	1.02175	−	0.273778i	0.291221	−	0.956656i	$-0.405938\pi$
$523$	534.377	−	143.186i	1.02175	−	0.273778i	0.730533	+	0.682878i	$0.239272\pi$
$524$	−12.2391	−	58.5296i	−0.0233571	−	0.111698i
$525$	−681.865	+	526.969i	−1.29879	+	1.00375i
$526$	494.245	−	267.298i	0.939630	−	0.508172i
$527$	−73.1029	−	42.2060i	−0.138715	−	0.0800872i
$528$	−576.192	+	782.152i	−1.09127	+	1.48135i
$529$	212.172	+	367.492i	0.401081	+	0.694693i
$530$	110.136	+	3.06586i	0.207803	+	0.00578464i
$531$	−1333.80	+	1333.80i	−2.51187	+	2.51187i
$532$	480.245	+	698.525i	0.902716	+	1.31302i
$533$	−62.8827	+	62.8827i	−0.117979	+	0.117979i
$534$	518.330	−	490.254i	0.970655	−	0.918078i
$535$	31.9171	+	55.2821i	0.0596582	+	0.103331i
$536$	−40.2044	+	111.772i	−0.0750082	+	0.208530i
$537$	1236.16	+	713.699i	2.30198	+	1.32905i
$538$	−824.196	−	245.618i	−1.53196	−	0.456539i
$539$	−273.560	−	466.343i	−0.507533	−	0.865200i
$540$	−239.878	+	366.724i	−0.444218	+	0.679119i
$541$	753.067	−	201.784i	1.39199	−	0.372983i	0.516528	−	0.856270i	$-0.327224\pi$
$541$	753.067	−	201.784i	1.39199	−	0.372983i	0.875462	+	0.483288i	$0.160557\pi$
$542$	132.705	−	215.754i	0.244842	−	0.398070i
$543$	−1401.08	+	808.911i	−2.58025	+	1.48971i
$544$	265.731	−	107.510i	0.488476	−	0.197628i
$545$	205.933			0.377859
$546$	−80.8385	+	100.197i	−0.148056	+	0.183511i
$547$	−587.801	+	587.801i	−1.07459	+	1.07459i	−0.0776074	+	0.996984i	$0.524728\pi$
$547$	−587.801	+	587.801i	−1.07459	+	1.07459i	−0.996984	+	0.0776074i	$0.975272\pi$
$548$	230.856	−	116.669i	0.421270	−	0.212899i
$549$	328.973	+	88.1481i	0.599222	+	0.160561i
$550$	480.247	−	114.459i	0.873177	−	0.208108i
$551$	675.495	−	1169.99i	1.22594	−	2.12340i
$552$	−290.785	−	343.898i	−0.526784	−	0.623003i
$553$	−823.363	−	105.503i	−1.48890	−	0.190783i
$554$	−202.804	+	680.530i	−0.366072	+	1.22839i
$555$	−463.771	+	124.267i	−0.835624	+	0.223905i
$556$	−116.547	−	130.301i	−0.209617	−	0.234354i
$557$	−93.7657	+	349.938i	−0.168341	+	0.628256i	0.829250	+	0.558878i	$0.188768\pi$
$557$	−93.7657	+	349.938i	−0.168341	+	0.628256i	−0.997590	+	0.0693776i	$0.977899\pi$
$558$	−11.1601	+	400.908i	−0.0200002	+	0.718474i
$559$		−	15.8620i		−	0.0283756i
$560$	94.3794	+	155.105i	0.168535	+	0.276974i
$561$	543.901			0.969521
$562$	−407.835	−	11.3529i	−0.725684	−	0.0202010i
$563$	539.397	+	144.531i	0.958076	+	0.256716i	0.703786	−	0.710412i	$-0.251492\pi$
$563$	539.397	+	144.531i	0.958076	+	0.256716i	0.254290	+	0.967128i	$0.418158\pi$
$564$	−69.5037	−	77.7058i	−0.123233	−	0.137776i
$565$	−54.2889	−	202.609i	−0.0960865	−	0.358600i
$566$	−14.2950	−	4.26004i	−0.0252562	−	0.00752657i
$567$	1004.21	+	765.052i	1.77109	+	1.34930i
$568$	62.4864	−	746.692i	0.110011	−	1.31460i
$569$	−45.7744	−	26.4279i	−0.0804471	−	0.0464462i	0.459237	−	0.888314i	$-0.348123\pi$
$569$	−45.7744	−	26.4279i	−0.0804471	−	0.0464462i	−0.539684	+	0.841868i	$0.681456\pi$
$570$	−125.225	−	525.416i	−0.219692	−	0.921782i
$571$	144.565	−	539.525i	0.253179	−	0.944878i	−0.715915	−	0.698187i	$-0.753990\pi$
$571$	144.565	−	539.525i	0.253179	−	0.944878i	0.969094	−	0.246690i	$-0.0793431\pi$
$572$	65.8264	−	33.2670i	0.115081	−	0.0581592i
$573$	571.885	+	571.885i	0.998054	+	0.998054i
$574$	695.054	−	268.249i	1.21090	−	0.467332i
$575$			228.870i			0.398034i
$576$	−1049.92	−	867.555i	−1.82277	−	1.50617i
$577$	484.594	+	839.341i	0.839851	+	1.45466i	0.890019	+	0.455923i	$0.150691\pi$
$577$	484.594	+	839.341i	0.839851	+	1.45466i	−0.0501683	+	0.998741i	$0.515976\pi$
$578$	355.625	+	218.735i	0.615268	+	0.378434i
$579$	−182.072	−	679.504i	−0.314460	−	1.17358i
$580$	158.399	−	242.159i	0.273101	−	0.417516i
$581$	−28.3374	+	69.0873i	−0.0487735	+	0.118911i
$582$	−375.235	+	1259.14i	−0.644733	+	2.16347i
$583$	−187.479	+	324.724i	−0.321577	+	0.556987i
$584$	65.2016	+	138.458i	0.111647	+	0.237085i
$585$	49.9269	−	28.8253i	0.0853451	−	0.0492740i
$586$	−131.481	−	139.010i	−0.224369	−	0.237219i
$587$	532.999	+	532.999i	0.908005	+	0.908005i	0.996111	−	0.0881061i	$-0.0280815\pi$
$587$	532.999	+	532.999i	0.908005	+	0.908005i	−0.0881061	+	0.996111i	$0.528081\pi$
$588$	959.218	−	493.122i	1.63132	−	0.838644i
$589$	−201.723	−	201.723i	−0.342484	−	0.342484i
$590$	7.99674	−	287.269i	0.0135538	−	0.486896i
$591$	664.876	−	383.866i	1.12500	−	0.649520i
$592$	−129.099	−	851.434i	−0.218073	−	1.43823i
$593$	74.2290	−	128.568i	0.125175	−	0.216810i	−0.796626	−	0.604472i	$-0.793384\pi$
$593$	74.2290	−	128.568i	0.125175	−	0.216810i	0.921801	+	0.387662i	$0.126717\pi$
$594$	−709.430	−	1311.76i	−1.19433	−	2.20836i
$595$	38.5757	−	94.0484i	0.0648331	−	0.158064i
$596$	−73.2693	−	350.387i	−0.122935	−	0.587897i
$597$	−544.281	−	2031.28i	−0.911693	−	3.40249i
$598$	7.92698	+	33.2599i	0.0132558	+	0.0556186i
$599$	−104.219	−	180.513i	−0.173988	−	0.301357i	0.765822	−	0.643052i	$-0.222332\pi$
$599$	−104.219	−	180.513i	−0.173988	−	0.301357i	−0.939811	+	0.341695i	$0.888999\pi$
$600$	174.683	+	969.257i	0.291138	+	1.61543i
$601$			295.838i			0.492244i	0.969239	+	0.246122i	$0.0791563\pi$
$601$			295.838i			0.492244i	−0.969239	+	0.246122i	$0.920844\pi$
$602$	−53.8301	+	121.495i	−0.0894188	+	0.201819i
$603$	−223.429	−	223.429i	−0.370529	−	0.370529i
$604$	−140.974	−	278.949i	−0.233401	−	0.461836i
$605$	0.312721	−	1.16709i	0.000516894	−	0.00192907i
$606$	997.990	−	1622.56i	1.64685	−	2.67749i
$607$	841.395	+	485.780i	1.38615	+	0.800296i	0.992879	−	0.119126i	$-0.0380091\pi$
$607$	841.395	+	485.780i	1.38615	+	0.800296i	0.393274	+	0.919421i	$0.371342\pi$
$608$	961.507	−	118.523i	1.58143	−	0.194940i
$609$	−1367.32	−	1041.69i	−2.24520	−	1.71050i
$610$	−45.6408	+	24.6835i	−0.0748210	+	0.0404648i
$611$	2.04857	+	7.64538i	0.00335282	+	0.0125129i
$612$	−42.4206	+	761.353i	−0.0693147	+	1.24404i
$613$	432.868	+	115.987i	0.706147	+	0.189212i	0.593982	−	0.804478i	$-0.297555\pi$
$613$	432.868	+	115.987i	0.706147	+	0.189212i	0.112165	+	0.993690i	$0.464222\pi$
$614$	−390.611	−	412.981i	−0.636175	−	0.672607i
$615$	−474.716			−0.771896
$616$	−617.095	+	31.4172i	−1.00178	+	0.0510020i
$617$		−	135.380i		−	0.219416i	−0.993964	−	0.109708i	$-0.965008\pi$
$617$		−	135.380i		−	0.219416i	0.993964	−	0.109708i	$-0.0349916\pi$
$618$	317.794	+	335.994i	0.514230	+	0.543679i
$619$	−227.265	+	848.164i	−0.367149	+	1.37022i	0.497336	+	0.867558i	$0.334312\pi$
$619$	−227.265	+	848.164i	−0.367149	+	1.37022i	−0.864485	+	0.502659i	$0.832355\pi$
$620$	−40.7359	−	45.5431i	−0.0657030	−	0.0734566i
$621$	667.789	−	178.934i	1.07534	−	0.288138i
$622$	413.716	−	223.746i	0.665138	−	0.359721i
$623$	450.104	+	57.6747i	0.722478	+	0.0925758i
$624$	58.9559	+	134.805i	0.0944806	+	0.216033i
$625$	217.405	−	376.556i	0.347848	−	0.602490i
$626$	161.996	−	263.377i	0.258780	−	0.420730i
$627$	1775.54	+	475.755i	2.83181	+	0.758780i
$628$	−72.8058	+	221.582i	−0.115933	+	0.352838i
$629$	−340.927	+	340.927i	−0.542015	+	0.542015i
$630$	−480.239	+	51.3530i	−0.762284	+	0.0815128i
$631$	−215.205			−0.341053			−0.170527	−	0.985353i	$-0.554547\pi$
$631$	−215.205			−0.341053			−0.170527	+	0.985353i	$0.554547\pi$
$632$	−541.202	+	779.163i	−0.856332	+	1.23285i
$633$	−49.9798	+	28.8558i	−0.0789570	+	0.0455859i
$634$	86.0820	+	361.182i	0.135776	+	0.569687i
$635$	83.1644	−	22.2838i	0.130968	−	0.0350927i
$636$	−625.977	−	409.457i	−0.984241	−	0.643801i
$637$	−81.8825	+	0.566253i	−0.128544	+	0.000888938i
$638$	468.459	+	866.199i	0.734261	+	1.35768i
$639$	1726.18	+	996.612i	2.70138	+	1.55964i
$640$	207.035	−	13.8900i	0.323492	−	0.0217032i
$641$	268.660	+	465.334i	0.419127	+	0.725949i	0.995852	−	0.0909890i	$-0.0290028\pi$
$641$	268.660	+	465.334i	0.419127	+	0.725949i	−0.576725	+	0.816939i	$0.695669\pi$
$642$	12.0591	−	433.202i	0.0187836	−	0.674769i
$643$	−175.115	+	175.115i	−0.272341	+	0.272341i	−0.830042	−	0.557701i	$-0.811684\pi$
$643$	−175.115	+	175.115i	−0.272341	+	0.272341i	0.557701	+	0.830042i	$0.311684\pi$
$644$	52.1560	−	281.656i	0.0809875	−	0.437354i
$645$	59.8728	−	59.8728i	0.0928261	−	0.0928261i
$646$	−372.711	−	394.056i	−0.576953	−	0.609994i
$647$	113.321	+	196.278i	0.175149	+	0.303367i	0.940213	−	0.340587i	$-0.110626\pi$
$647$	113.321	+	196.278i	0.175149	+	0.303367i	−0.765064	+	0.643954i	$0.777293\pi$
$648$	1305.29	−	614.679i	2.01434	−	0.948578i
$649$	846.982	+	489.005i	1.30506	+	0.753475i
$650$	21.3548	−	71.6581i	0.0328535	−	0.110243i
$651$	−287.201	+	221.959i	−0.441170	+	0.340951i
$652$	−225.035	−	1076.15i	−0.345145	−	1.65054i
$653$	186.622	−	50.0052i	0.285792	−	0.0765777i	−0.113075	−	0.993586i	$-0.536070\pi$
$653$	186.622	−	50.0052i	0.285792	−	0.0765777i	0.398867	+	0.917009i	$0.369403\pi$
$654$	−1190.85	−	732.459i	−1.82087	−	1.11997i
$655$	−20.9869	+	12.1168i	−0.0320411	+	0.0184989i
$656$	94.5879	−	846.183i	0.144189	−	1.28991i
$657$	−407.108			−0.619646
$658$	10.2547	−	65.5121i	0.0155847	−	0.0995624i
$659$	695.484	−	695.484i	1.05536	−	1.05536i	0.0569882	−	0.998375i	$-0.481850\pi$
$659$	695.484	−	695.484i	1.05536	−	1.05536i	0.998375	−	0.0569882i	$-0.0181497\pi$
$660$	374.039	+	122.899i	0.566726	+	0.186210i
$661$	−959.171	−	257.009i	−1.45109	−	0.388819i	−0.554688	−	0.832059i	$-0.687162\pi$
$661$	−959.171	−	257.009i	−1.45109	−	0.388819i	−0.896403	+	0.443240i	$0.853829\pi$
$662$	−92.2545	−	387.080i	−0.139357	−	0.584713i
$663$	41.1879	−	71.3395i	0.0621235	−	0.107601i
$664$	55.1024	+	65.1671i	0.0829855	+	0.0981432i
$665$	208.194	−	273.274i	0.313073	−	0.410939i
$666$	2195.38	+	654.244i	3.29637	+	0.982348i
$667$	−440.962	+	118.155i	−0.661112	+	0.177144i
$668$	−343.548	−	19.1416i	−0.514294	−	0.0286551i
$669$	−145.639	+	543.533i	−0.217697	+	0.812456i
$670$	48.1211	+	1.33955i	0.0718226	+	0.00199933i
$671$		−	176.585i		−	0.263167i
$672$	5.90711	−	1232.61i	0.00879034	−	1.83425i
$673$	−432.324			−0.642383			−0.321192	−	0.947014i	$-0.604083\pi$
$673$	−432.324			−0.642383			−0.321192	+	0.947014i	$0.604083\pi$
$674$	−0.517453	+	18.5886i	−0.000767735	+	0.0275795i
$675$	−1460.37	−	391.305i	−2.16351	−	0.579711i
$676$	−36.9852	+	663.800i	−0.0547119	+	0.981953i
$677$	−26.4003	−	98.5271i	−0.0389960	−	0.145535i	0.943683	−	0.330851i	$-0.107336\pi$
$677$	−26.4003	−	98.5271i	−0.0389960	−	0.145535i	−0.982679	+	0.185316i	$0.940669\pi$
$678$	−406.699	+	1364.72i	−0.599851	+	2.01286i
$679$	−770.945	+	322.463i	−1.13541	+	0.474909i
$680$	−75.0108	−	88.7118i	−0.110310	−	0.130459i
$681$	−1538.23	−	888.100i	−2.25879	−	1.30411i
$682$	202.280	−	48.2103i	0.296598	−	0.0706896i
$683$	−72.8281	+	271.798i	−0.106630	+	0.397947i	−0.998525	−	0.0542946i	$-0.982709\pi$
$683$	−72.8281	+	271.798i	−0.106630	+	0.397947i	0.891895	+	0.452242i	$0.149376\pi$
$684$	−804.442	+	2448.30i	−1.17609	+	3.57938i
$685$	−74.1254	−	74.1254i	−0.108212	−	0.108212i
$686$	629.102	+	273.544i	0.917059	+	0.398752i
$687$		−	1048.31i		−	1.52593i
$688$	94.7938	+	118.653i	0.137782	+	0.172461i
$689$	28.3944	+	49.1805i	0.0412110	+	0.0713796i
$690$	−95.6221	+	155.465i	−0.138583	+	0.225311i
$691$	28.9159	+	107.916i	0.0418464	+	0.156173i	0.983688	−	0.179885i	$-0.0575727\pi$
$691$	28.9159	+	107.916i	0.0418464	+	0.156173i	−0.941841	+	0.336058i	$0.890906\pi$
$692$	321.079	−	67.1408i	0.463987	−	0.0970242i
$693$	623.749	−	1520.71i	0.900071	−	2.19439i
$694$	785.992	+	234.233i	1.13255	+	0.337511i
$695$	−35.4247	+	61.3574i	−0.0509708	+	0.0882840i
$696$	−1777.28	+	836.946i	−2.55356	+	1.20251i
$697$	−412.840	+	238.353i	−0.592309	+	0.341970i
$698$	496.009	−	469.142i	0.710614	−	0.672123i
$699$	−381.592	−	381.592i	−0.545912	−	0.545912i
$700$	−406.750	+	476.396i	−0.581072	+	0.680565i
$701$	−35.1689	−	35.1689i	−0.0501696	−	0.0501696i	0.681577	−	0.731747i	$-0.261295\pi$
$701$	−35.1689	−	35.1689i	−0.0501696	−	0.0501696i	−0.731747	+	0.681577i	$0.761295\pi$
$702$	−225.777	−	6.28499i	−0.321620	−	0.00895298i
$703$	−1411.15	+	814.730i	−2.00733	+	1.15893i
$704$	−293.596	+	642.239i	−0.417039	+	0.912271i
$705$	−21.1258	+	36.5909i	−0.0299657	+	0.0519020i
$706$	−50.5099	+	27.3168i	−0.0715437	+	0.0386924i
$707$	1200.68	−	162.298i	1.69827	−	0.229558i
$708$	−1068.00	+	1632.75i	−1.50847	+	2.30614i
$709$	185.103	+	690.815i	0.261076	+	0.974351i	0.964608	+	0.263687i	$0.0849386\pi$
$709$	185.103	+	690.815i	0.261076	+	0.974351i	−0.703532	+	0.710664i	$0.748395\pi$
$710$	−295.399	+	70.4037i	−0.416055	+	0.0991601i
$711$	−1261.80	−	2185.49i	−1.77468	−	3.07383i
$712$	295.856	−	425.941i	0.415528	−	0.598232i
$713$			96.3999i			0.135203i
$714$	−557.581	+	406.648i	−0.780926	+	0.569536i
$715$	−21.1361	−	21.1361i	−0.0295610	−	0.0295610i
$716$	985.733	+	323.884i	1.37672	+	0.452352i
$717$	225.498	−	841.571i	0.314502	−	1.17374i
$718$	673.910	+	414.504i	0.938593	+	0.577303i
$719$	−140.229	−	80.9613i	−0.195033	−	0.112603i	0.399303	−	0.916819i	$-0.369252\pi$
$719$	−140.229	−	80.9613i	−0.195033	−	0.112603i	−0.594337	+	0.804216i	$0.702585\pi$
$720$	−201.206	+	513.995i	−0.279453	+	0.713882i
$721$	−37.3861	+	291.768i	−0.0518531	+	0.404671i
$722$	−528.555	−	977.320i	−0.732071	−	1.35363i
$723$	129.654	+	483.874i	0.179327	+	0.669259i
$724$	−876.529	+	784.008i	−1.21068	+	1.08288i
$725$	964.327	+	258.391i	1.33011	+	0.356401i
$726$	−5.95946	+	5.63665i	−0.00820862	+	0.00776399i
$727$	714.589			0.982929			0.491464	−	0.870898i	$-0.336462\pi$
$727$	714.589			0.982929			0.491464	+	0.870898i	$0.336462\pi$
$728$	−42.6098	+	83.3189i	−0.0585300	+	0.114449i
$729$			491.072i			0.673624i
$730$	45.0609	−	42.6202i	0.0617273	−	0.0583838i
$731$	22.0068	−	82.1306i	0.0301051	−	0.112354i
$732$	351.721	+	19.5970i	0.480493	+	0.0267718i
$733$	−715.708	+	191.773i	−0.976409	+	0.261628i	−0.711532	−	0.702654i	$-0.751998\pi$
$733$	−715.708	+	191.773i	−0.976409	+	0.261628i	−0.264878	+	0.964282i	$0.585332\pi$
$734$	481.076	+	889.528i	0.655416	+	1.21189i
$735$	−311.212	−	306.938i	−0.423418	−	0.417602i
$736$	−258.063	−	201.423i	−0.350630	−	0.273673i
$737$	−81.9146	+	141.880i	−0.111146	+	0.192510i
$738$	1929.24	+	1186.62i	2.61414	+	1.60789i
$739$	−648.596	−	173.791i	−0.877668	−	0.235170i	−0.208267	−	0.978072i	$-0.566782\pi$
$739$	−648.596	−	173.791i	−0.877668	−	0.235170i	−0.669401	+	0.742902i	$0.733449\pi$
$740$	−311.490	+	157.419i	−0.420932	+	0.212729i
$741$	196.857	−	196.857i	0.265665	−	0.265665i
$742$	−50.5853	−	473.060i	−0.0681743	−	0.637547i
$743$	−881.354			−1.18621			−0.593105	−	0.805125i	$-0.702098\pi$
$743$	−881.354			−1.18621			−0.593105	+	0.805125i	$0.702098\pi$
$744$	73.5765	+	408.251i	0.0988931	+	0.548724i
$745$	−125.638	+	72.5371i	−0.168642	+	0.0973652i
$746$	416.710	−	99.3163i	0.558592	−	0.133132i
$747$	−219.280	+	58.7559i	−0.293547	+	0.0786558i
$748$	386.992	−	80.9240i	0.517370	−	0.108187i
$749$	218.099	−	168.554i	0.291186	−	0.225039i
$750$	743.416	−	402.055i	0.991222	−	0.536074i
$751$	1172.11	+	676.719i	1.56074	+	0.901091i	0.997183	+	0.0750109i	$0.0238992\pi$
$751$	1172.11	+	676.719i	1.56074	+	0.901091i	0.563553	+	0.826080i	$0.309434\pi$
$752$	−61.0141	−	44.9476i	−0.0811358	−	0.0597707i
$753$	−580.127	−	1004.81i	−0.770421	−	1.33441i
$754$	149.088	+	4.15017i	0.197729	+	0.00550421i
$755$	−89.5676	+	89.5676i	−0.118633	+	0.118633i
$756$	1708.02	+	814.351i	2.25928	+	1.07718i
$757$	−973.785	+	973.785i	−1.28637	+	1.28637i	−0.349400	+	0.936974i	$0.613614\pi$
$757$	−973.785	+	973.785i	−1.28637	+	1.28637i	−0.936974	+	0.349400i	$0.886386\pi$
$758$	−689.521	+	652.172i	−0.909658	+	0.860385i
$759$	−310.572	−	537.927i	−0.409186	−	0.708731i
$760$	−167.273	−	355.208i	−0.220095	−	0.467380i
$761$	303.447	+	175.195i	0.398748	+	0.230217i	0.685944	−	0.727655i	$-0.259390\pi$
$761$	303.447	+	175.195i	0.398748	+	0.230217i	−0.287195	+	0.957872i	$0.592723\pi$
$762$	−560.174	−	166.937i	−0.735136	−	0.219077i
$763$	−119.116	−	881.217i	−0.156115	−	1.15494i
$764$	491.991	+	321.816i	0.643967	+	0.421225i
$765$	298.505	−	79.9842i	0.390203	−	0.104555i
$766$	58.4798	−	95.0778i	0.0763444	−	0.124122i
$767$	128.278	−	74.0616i	0.167247	−	0.0965601i
$768$	−1246.63	−	656.057i	−1.62321	−	0.854241i
$769$	1006.65			1.30904			0.654518	−	0.756046i	$-0.272872\pi$
$769$	1006.65			1.30904			0.654518	+	0.756046i	$0.272872\pi$
$770$	90.1638	+	233.622i	0.117096	+	0.303405i
$771$	813.444	−	813.444i	1.05505	−	1.05505i
$772$	−230.646	−	456.386i	−0.298765	−	0.591173i
$773$	693.677	+	185.870i	0.897383	+	0.240453i	0.677892	−	0.735162i	$-0.262894\pi$
$773$	693.677	+	185.870i	0.897383	+	0.240453i	0.219491	+	0.975615i	$0.429560\pi$
$774$	−392.983	+	93.6614i	−0.507730	+	0.121010i
$775$	105.407	−	182.570i	0.136009	−	0.235575i
$776$	−79.6441	+	951.721i	−0.102634	+	1.22644i
$777$	800.012	+	1912.67i	1.02962	+	2.46160i
$778$	47.5629	−	159.602i	0.0611349	−	0.205144i
$779$	−1556.19	+	416.979i	−1.99767	+	0.535275i
$780$	44.4445	−	39.7533i	0.0569802	−	0.0509657i
$781$	267.479	−	998.244i	0.342482	−	1.27816i
$782$	−5.10010	+	183.212i	−0.00652186	+	0.234287i
$783$		−	3015.70i		−	3.85147i
$784$	609.127	−	493.579i	0.776947	−	0.629565i
$785$	94.5249			0.120414
$786$	164.458	+	4.57803i	0.209234	+	0.00582447i
$787$	−382.652	−	102.531i	−0.486215	−	0.130281i	0.00737982	−	0.999973i	$-0.497651\pi$
$787$	−382.652	−	102.531i	−0.486215	−	0.130281i	−0.493595	+	0.869692i	$0.664318\pi$
$788$	415.954	−	372.048i	0.527860	−	0.472143i
$789$	400.135	+	1493.32i	0.507142	+	1.89268i
$790$	368.462	+	109.805i	0.466408	+	0.138994i
$791$	−835.591	+	349.503i	−1.05637	+	0.441850i
$792$	−1212.89	−	1434.42i	−1.53142	−	1.81114i
$793$	−23.1613	−	13.3722i	−0.0292072	−	0.0168628i
$794$	162.639	+	682.398i	0.204835	+	0.859444i
$795$	−78.4597	+	292.815i	−0.0986914	+	0.368321i
$796$	−689.486	−	1364.30i	−0.866188	−	1.71395i
$797$	−955.509	−	955.509i	−1.19888	−	1.19888i	−0.974502	−	0.224381i	$-0.927964\pi$
$797$	−955.509	−	955.509i	−1.19888	−	1.19888i	−0.224381	−	0.974502i	$-0.572036\pi$
$798$	−2175.90	+	839.766i	−2.72669	+	1.05234i
$799$			42.4287i			0.0531022i
$800$	268.499	+	663.648i	0.335624	+	0.829560i
$801$	689.779	+	1194.73i	0.861148	+	1.49155i
$802$	−680.303	−	418.436i	−0.848258	−	0.521740i
$803$	54.6314	+	203.887i	0.0680341	+	0.253907i
$804$	−273.506	−	178.903i	−0.340181	−	0.222516i
$805$	−115.042	+	15.5505i	−0.142910	+	0.0193174i
$806$	8.99463	−	30.1824i	0.0111596	−	0.0374471i
$807$	1183.13	−	2049.23i	1.46608	−	2.53932i
$808$	468.671	−	1302.95i	0.580039	−	1.61257i
$809$	−895.301	+	516.902i	−1.10668	+	0.638939i	−0.937966	−	0.346726i	$-0.887293\pi$
$809$	−895.301	+	516.902i	−1.10668	+	0.638939i	−0.168709	+	0.985666i	$0.553960\pi$
$810$	−401.795	−	424.805i	−0.496044	−	0.524451i
$811$	861.473	+	861.473i	1.06224	+	1.06224i	0.997930	+	0.0643058i	$0.0204833\pi$
$811$	861.473	+	861.473i	1.06224	+	1.06224i	0.0643058	+	0.997930i	$0.479517\pi$
$812$	−1127.86	−	537.741i	−1.38899	−	0.662243i
$813$	492.802	+	492.802i	0.606153	+	0.606153i
$814$	33.0506	−	1187.28i	0.0406027	−	1.45858i
$815$	−385.876	+	222.786i	−0.473468	+	0.273357i
$816$	118.236	+	779.791i	0.144898	+	0.955626i
$817$	143.681	−	248.862i	0.175864	−	0.304605i
$818$	−549.021	−	1015.16i	−0.671174	−	1.24103i
$819$	−152.226	−	196.971i	−0.185869	−	0.240502i
$820$	−337.766	+	70.6303i	−0.411910	+	0.0861345i
$821$	−165.341	−	617.062i	−0.201390	−	0.751598i	−0.990520	−	0.137371i	$-0.956135\pi$
$821$	−165.341	−	617.062i	−0.201390	−	0.751598i	0.789129	−	0.614227i	$-0.210532\pi$
$822$	164.997	+	692.293i	0.200726	+	0.842205i
$823$	613.463	+	1062.55i	0.745399	+	1.29107i	0.950008	+	0.312225i	$0.101074\pi$
$823$	613.463	+	1062.55i	0.745399	+	1.29107i	−0.204609	+	0.978844i	$0.565592\pi$
$824$	276.105	+	191.781i	0.335079	+	0.232744i
$825$			1358.36i			1.64650i
$826$	−1233.89	+	131.943i	−1.49381	+	0.159737i
$827$	105.313	+	105.313i	0.127343	+	0.127343i	0.767906	−	0.640563i	$-0.221299\pi$
$827$	105.313	+	105.313i	0.127343	+	0.127343i	−0.640563	+	0.767906i	$0.721299\pi$
$828$	777.213	−	392.784i	0.938663	−	0.474377i
$829$	319.537	−	1192.53i	0.385448	−	1.43851i	−0.452011	−	0.892012i	$-0.649293\pi$
$829$	319.537	−	1192.53i	0.385448	−	1.43851i	0.837459	−	0.546500i	$-0.184040\pi$
$830$	18.1200	−	29.4599i	0.0218313	−	0.0354938i
$831$	−1692.03	−	976.894i	−2.03614	−	1.17556i
$832$	62.0046	+	87.1434i	0.0745248	+	0.104740i
$833$	−424.760	−	110.672i	−0.509916	−	0.132859i
$834$	423.085	−	228.814i	0.507297	−	0.274357i
$835$	36.0916	+	134.696i	0.0432235	+	0.161312i
$836$	1334.11	+	74.3329i	1.59582	+	0.0889150i
$837$	−615.107	−	164.818i	−0.734895	−	0.196915i
$838$	202.353	+	213.942i	0.241472	+	0.255300i
$839$	275.728			0.328639			0.164319	−	0.986407i	$-0.447457\pi$
$839$	275.728			0.328639			0.164319	+	0.986407i	$0.447457\pi$
$840$	−475.333	+	153.661i	−0.565872	+	0.182930i
$841$			1150.36i			1.36785i
$842$	136.292	+	144.097i	0.161867	+	0.171136i
$843$	290.538	−	1084.30i	0.344647	−	1.28624i
$844$	−31.2679	+	27.9675i	−0.0370473	+	0.0331368i
$845$	260.257	−	69.7358i	0.307997	−	0.0825275i
$846$	177.319	−	95.8980i	0.209597	−	0.113355i
$847$	−5.17503	−	0.663110i	−0.00610984	−	0.000782893i
$848$	−506.311	−	198.198i	−0.597065	−	0.233725i
$849$	20.5203	−	35.5422i	0.0241700	−	0.0418636i
$850$	209.990	−	341.406i	0.247047	−	0.401654i
$851$	531.855	+	142.510i	0.624976	+	0.167462i
$852$	1958.61	+	643.546i	2.29884	+	0.755335i
$853$	−0.857543	+	0.857543i	−0.00100533	+	0.00100533i	−0.707609	−	0.706604i	$-0.750226\pi$
$853$	−0.857543	+	0.857543i	−0.00100533	+	0.00100533i	0.706604	+	0.707609i	$0.250226\pi$
$854$	132.024	+	181.026i	0.154595	+	0.211975i
$855$	1044.42			1.22154
$856$	−55.8734	−	310.023i	−0.0652727	−	0.362176i
$857$	1066.44	−	615.711i	1.24439	−	0.718449i	0.274406	−	0.961614i	$-0.411519\pi$
$857$	1066.44	−	615.711i	1.24439	−	0.718449i	0.969985	+	0.243165i	$0.0781855\pi$
$858$	47.0474	+	197.401i	0.0548338	+	0.230071i
$859$	−1238.89	+	331.959i	−1.44224	+	0.386448i	−0.893318	−	0.449425i	$-0.851629\pi$
$859$	−1238.89	+	331.959i	−1.44224	+	0.386448i	−0.548924	+	0.835872i	$0.684962\pi$
$860$	33.6921	−	51.5084i	0.0391769	−	0.0598935i
$861$	274.585	+	2031.38i	0.318914	+	2.35933i
$862$	−434.518	−	803.441i	−0.504081	−	0.932067i
$863$	98.8495	+	57.0708i	0.114542	+	0.0661307i	0.556176	−	0.831064i	$-0.312268\pi$
$863$	98.8495	+	57.0708i	0.114542	+	0.0661307i	−0.441635	+	0.897195i	$0.645601\pi$
$864$	1726.46	−	1302.27i	1.99821	−	1.50726i
$865$	−66.4698	−	115.129i	−0.0768437	−	0.133097i
$866$	2.35013	−	84.4242i	0.00271377	−	0.0974875i
$867$	−812.279	+	812.279i	−0.936885	+	0.936885i
$868$	−171.323	+	200.658i	−0.197377	+	0.231173i
$869$	−925.212	+	925.212i	−1.06469	+	1.06469i
$870$	547.084	+	578.414i	0.628832	+	0.664844i
$871$	12.4062	+	21.4883i	0.0142437	+	0.0246708i
$872$	−956.282	−	343.974i	−1.09665	−	0.394465i
$873$	−2200.16	−	1270.26i	−2.52023	−	1.45506i
$874$	−176.906	+	593.627i	−0.202410	+	0.679207i
$875$	497.352	+	203.998i	0.568402	+	0.233141i
$876$	−412.165	+	86.1877i	−0.470508	+	0.0983878i
$877$	575.594	−	154.230i	0.656321	−	0.175861i	0.0847361	−	0.996403i	$-0.472995\pi$
$877$	575.594	−	154.230i	0.656321	−	0.175861i	0.571585	+	0.820543i	$0.306329\pi$
$878$	−494.243	−	303.996i	−0.562920	−	0.346236i
$879$	455.922	−	263.227i	0.518682	−	0.299461i
$880$	284.419	+	31.7929i	0.323204	+	0.0361283i
$881$	−722.266			−0.819825			−0.409912	−	0.912125i	$-0.634441\pi$
$881$	−722.266			−0.819825			−0.409912	+	0.912125i	$0.634441\pi$
$882$	497.527	+	2025.31i	0.564089	+	2.29627i
$883$	384.133	−	384.133i	0.435032	−	0.435032i	−0.455304	−	0.890336i	$-0.650469\pi$
$883$	384.133	−	384.133i	0.435032	−	0.435032i	0.890336	+	0.455304i	$0.150469\pi$
$884$	18.6915	−	56.8870i	0.0211442	−	0.0643519i
$885$	763.756	+	204.648i	0.863001	+	0.231240i
$886$	−9.20691	−	38.6302i	−0.0103915	−	0.0436007i
$887$	−464.363	+	804.300i	−0.523521	+	0.906765i	0.476104	+	0.879389i	$0.342048\pi$
$887$	−464.363	+	804.300i	−0.523521	+	0.906765i	−0.999625	+	0.0273760i	$0.991285\pi$
$888$	2361.16	+	197.592i	2.65896	+	0.222514i
$889$	−143.460	−	342.983i	−0.161372	−	0.385808i
$890$	−201.425	−	60.0266i	−0.226321	−	0.0674456i
$891$	1922.12	−	515.030i	2.15726	−	0.578036i
$892$	−22.7550	+	408.399i	−0.0255100	+	0.457847i
$893$	−37.1127	+	138.507i	−0.0415596	+	0.155103i
$894$	984.526	+	27.4064i	1.10126	+	0.0306559i
$895$		−	420.504i		−	0.469837i
$896$	−179.191	−	877.899i	−0.199990	−	0.979798i
$897$	−94.0746			−0.104877
$898$	30.7260	−	1103.78i	0.0342160	−	1.22915i
$899$	406.174	+	108.834i	0.451807	+	0.121061i
$900$	−1901.44	−	105.943i	−2.11271	−	0.117715i
$901$	78.7885	+	294.043i	0.0874457	+	0.326352i
$902$	335.390	−	1125.44i	0.371830	−	1.24771i
$903$	−290.836	−	221.573i	−0.322078	−	0.245374i
$904$	−86.3225	+	1031.53i	−0.0954895	+	1.14107i
$905$	412.749	+	238.301i	0.456077	+	0.263316i
$906$	836.515	−	199.370i	0.923306	−	0.220055i
$907$	310.386	−	1158.38i	0.342212	−	1.27715i	−0.553624	−	0.832767i	$-0.686756\pi$
$907$	310.386	−	1158.38i	0.342212	−	1.27715i	0.895836	−	0.444385i	$-0.146578\pi$
$908$	−1226.61	−	403.029i	−1.35089	−	0.443865i
$909$	2604.56	+	2604.56i	2.86530	+	2.86530i
$910$	37.4702	+	5.86529i	0.0411761	+	0.00644537i
$911$			1018.76i			1.11829i	0.829069	+	0.559146i	$0.188871\pi$
$911$			1018.76i			1.11829i	−0.829069	+	0.559146i	$0.811129\pi$
$912$	−296.112	+	2649.02i	−0.324684	+	2.90462i
$913$	58.8521	+	101.935i	0.0644601	+	0.111648i
$914$	−328.084	+	533.407i	−0.358954	+	0.583596i
$915$	−36.9502	−	137.900i	−0.0403827	−	0.150710i
$916$	−155.972	−	745.887i	−0.170276	−	0.814288i
$917$	63.9888	+	82.7975i	0.0697806	+	0.0902917i
$918$	−1160.32	−	345.785i	−1.26396	−	0.376672i
$919$	−567.923	+	983.672i	−0.617979	+	1.07037i	0.371874	+	0.928283i	$0.378715\pi$
$919$	−567.923	+	983.672i	−0.617979	+	1.07037i	−0.989854	+	0.142089i	$0.954618\pi$
$920$	−44.9056	+	124.842i	−0.0488104	+	0.135698i
$921$	1354.48	−	782.011i	1.47067	−	0.849089i
$922$	251.395	−	237.778i	0.272663	−	0.257894i
$923$	−110.677	−	110.677i	−0.119910	−	0.119910i
$924$	309.551	−	1671.66i	0.335012	−	1.80915i
$925$	−851.447	−	851.447i	−0.920483	−	0.920483i
$926$	251.877	+	7.01154i	0.272006	+	0.00757186i
$927$	−774.454	+	447.131i	−0.835441	+	0.482342i
$928$	−1140.03	+	859.928i	−1.22848	+	0.926647i
$929$	813.052	−	1408.25i	0.875191	−	1.51587i	0.0186309	−	0.999826i	$-0.494069\pi$
$929$	813.052	−	1408.25i	0.875191	−	1.51587i	0.856560	−	0.516048i	$-0.172597\pi$
$930$	147.878	−	79.9757i	0.159009	−	0.0859953i
$931$	−1289.80	−	732.824i	−1.38540	−	0.787136i
$932$	−328.283	−	214.733i	−0.352235	−	0.230400i
$933$	334.939	+	1250.01i	0.358992	+	1.33977i
$934$	686.317	−	163.573i	0.734815	−	0.175132i
$935$	−80.1152	−	138.764i	−0.0856847	−	0.148410i
$936$	−279.991	+	50.4610i	−0.299136	+	0.0539113i
$937$		−	1091.45i		−	1.16484i	−0.812888	−	0.582419i	$-0.802106\pi$
$937$		−	1091.45i		−	1.16484i	0.812888	−	0.582419i	$-0.197894\pi$
$938$	−22.1021	−	206.692i	−0.0235630	−	0.220354i
$939$	601.577	+	601.577i	0.640657	+	0.640657i
$940$	−9.58710	+	29.1781i	−0.0101990	+	0.0310405i
$941$	−78.2976	+	292.211i	−0.0832068	+	0.310532i	−0.994969	−	0.100187i	$-0.968056\pi$
$941$	−78.2976	+	292.211i	−0.0832068	+	0.310532i	0.911762	+	0.410719i	$0.134722\pi$
$942$	−546.610	−	336.205i	−0.580265	−	0.356905i
$943$	471.470	+	272.203i	0.499968	+	0.288657i
$944$	−516.965	+	1320.62i	−0.547632	+	1.39896i
$945$	97.4668	−	760.648i	0.103139	−	0.804919i
$946$	99.6433	+	184.245i	0.105331	+	0.194762i
$947$	−17.3017	−	64.5709i	−0.0182700	−	0.0681847i	0.956189	−	0.292750i	$-0.0945704\pi$
$947$	−17.3017	−	64.5709i	−0.0182700	−	0.0681847i	−0.974459	+	0.224565i	$0.927904\pi$
$948$	−1740.16	−	1945.51i	−1.83561	−	2.05223i
$949$	30.8794	+	8.27412i	0.0325389	+	0.00871878i
$950$	984.133	−	930.826i	1.03593	−	0.979817i
$951$	−1021.59			−1.07423
$952$	−336.223	+	372.295i	−0.353175	+	0.391066i
$953$		−	964.031i		−	1.01157i	−0.862658	−	0.505787i	$-0.831202\pi$
$953$		−	964.031i		−	1.01157i	0.862658	−	0.505787i	$-0.168798\pi$
$954$	1050.79	−	993.876i	1.10146	−	1.04180i
$955$	61.6659	−	230.140i	0.0645716	−	0.240985i
$956$	35.2323	−	632.338i	0.0368538	−	0.661442i
$957$	−2617.15	+	701.264i	−2.73475	+	0.732773i
$958$	197.595	+	365.362i	0.206258	+	0.381380i
$959$	−274.318	+	360.069i	−0.286046	+	0.375463i
$960$	−94.8891	+	562.977i	−0.0988429	+	0.586434i
$961$	−436.103	+	755.352i	−0.453801	+	0.786006i
$962$	−153.224	−	94.2442i	−0.159277	−	0.0979669i
$963$	809.427	+	216.885i	0.840526	+	0.225218i
$964$	164.243	+	324.992i	0.170377	+	0.337128i
$965$	−146.541	+	146.541i	−0.151856	+	0.151856i
$966$	720.566	+	319.257i	0.745927	+	0.330494i
$967$	1600.68			1.65531			0.827653	−	0.561241i	$-0.189676\pi$
$967$	1600.68			1.65531			0.827653	+	0.561241i	$0.189676\pi$
$968$	−3.40158	+	4.89722i	−0.00351403	+	0.00505911i
$969$	1292.41	−	746.176i	1.33376	−	0.770047i
$970$	376.510	−	89.7354i	0.388155	−	0.0925107i
$971$	−789.680	+	211.594i	−0.813265	+	0.217914i	−0.641400	−	0.767207i	$-0.721646\pi$
$971$	−789.680	+	211.594i	−0.813265	+	0.217914i	−0.171865	+	0.985121i	$0.554979\pi$
$972$	314.559	+	1504.28i	0.323621	+	1.54761i
$973$	283.048	+	116.097i	0.290902	+	0.119319i
$974$	−805.210	+	435.475i	−0.826704	+	0.447099i
$975$	178.166	+	102.864i	0.182735	+	0.105502i
$976$	253.170	−	38.3871i	0.259395	−	0.0393310i
$977$	71.5575	+	123.941i	0.0732421	+	0.126859i	0.900320	−	0.435228i	$-0.143332\pi$
$977$	71.5575	+	123.941i	0.0732421	+	0.126859i	−0.827078	+	0.562087i	$0.809999\pi$
$978$	3023.81	+	84.1741i	3.09183	+	0.0860676i
$979$	505.781	−	505.781i	0.516630	−	0.516630i
$980$	−267.099	−	172.086i	−0.272550	−	0.175598i
$981$	1911.57	−	1911.57i	1.94860	−	1.94860i
$982$	445.991	−	421.834i	0.454166	−	0.429566i
$983$	305.104	+	528.455i	0.310380	+	0.537594i	0.978445	−	0.206509i	$-0.0662104\pi$
$983$	305.104	+	528.455i	0.310380	+	0.537594i	−0.668065	+	0.744103i	$0.732877\pi$
$984$	2204.42	+	792.928i	2.24026	+	0.805821i
$985$	−195.869	−	113.085i	−0.198852	−	0.114807i
$986$	766.194	+	228.333i	0.777073	+	0.231575i
$987$	168.798	+	69.2354i	0.171021	+	0.0701473i
$988$	110.777	−	169.356i	0.112123	−	0.171413i
$989$	−93.7946	+	25.1322i	−0.0948378	+	0.0254117i
$990$	−398.847	+	648.456i	−0.402876	+	0.655006i
$991$	465.910	−	268.993i	0.470141	−	0.271436i	−0.246158	−	0.969230i	$-0.579168\pi$
$991$	465.910	−	268.993i	0.470141	−	0.271436i	0.716299	+	0.697794i	$0.245835\pi$
$992$	113.092	+	279.529i	0.114004	+	0.281783i
$993$	1094.84			1.10256
$994$	472.132	+	1223.33i	0.474982	+	1.23072i
$995$	−438.063	+	438.063i	−0.440265	+	0.440265i
$996$	−209.565	+	105.909i	−0.210406	+	0.106334i
$997$	−1224.31	−	328.053i	−1.22800	−	0.329040i	−0.414197	−	0.910187i	$-0.635937\pi$
$997$	−1224.31	−	328.053i	−1.22800	−	0.329040i	−0.813799	+	0.581147i	$0.802604\pi$
$998$	675.416	−	160.975i	0.676770	−	0.161297i
$999$	−1818.65	+	3150.00i	−1.82047	+	3.15315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.3.u.a.51.16	yes	120
7.4	even	3	inner	112.3.u.a.67.5	yes	120
16.11	odd	4	inner	112.3.u.a.107.5	yes	120
112.11	odd	12	inner	112.3.u.a.11.16	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.3.u.a.11.16	✓	120	112.11	odd	12	inner
112.3.u.a.51.16	yes	120	1.1	even	1	trivial
112.3.u.a.67.5	yes	120	7.4	even	3	inner
112.3.u.a.107.5	yes	120	16.11	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	112.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0556527 + 1.99923i) q^{2} +(-5.31530 - 1.42423i) q^{3} +(-3.99381 - 0.222525i) q^{4} +(0.419571 + 1.56586i) q^{5} +(3.14317 - 10.5472i) q^{6} +(6.45786 - 2.70113i) q^{7} +(0.667143 - 7.97213i) q^{8} +(18.4298 + 10.6404i) q^{9} +(-3.15386 + 0.751673i) q^{10} +(2.85576 - 10.6579i) q^{11} +(20.9114 + 6.87089i) q^{12} +(-1.18165 - 1.18165i) q^{13} +(5.04077 + 13.0610i) q^{14} -8.92058i q^{15} +(15.9010 + 1.77744i) q^{16} +(-4.47899 - 7.75783i) q^{17} +(-22.2983 + 36.2531i) q^{18} +(-7.83562 - 29.2429i) q^{19} +(-1.32724 - 6.34710i) q^{20} +(-38.1725 + 5.15984i) q^{21} +(21.1485 + 6.30246i) q^{22} +(-5.11508 + 8.85958i) q^{23} +(-14.9002 + 41.4241i) q^{24} +(19.3748 - 11.1860i) q^{25} +(2.42816 - 2.29663i) q^{26} +(-47.7857 - 47.7857i) q^{27} +(-26.3925 + 9.35075i) q^{28} +(31.5544 + 31.5544i) q^{29} +(17.8343 + 0.496454i) q^{30} +(8.16065 - 4.71155i) q^{31} +(-4.43843 + 31.6907i) q^{32} +(-30.3585 + 52.5825i) q^{33} +(15.7589 - 8.52276i) q^{34} +(6.93912 + 8.97878i) q^{35} +(-71.2372 - 46.5969i) q^{36} +(-13.9304 - 51.9889i) q^{37} +(58.8993 - 14.0377i) q^{38} +(4.59790 + 7.96380i) q^{39} +(12.7632 - 2.30022i) q^{40} -53.2158i q^{41} +(-8.19128 - 76.6026i) q^{42} +(6.71176 + 6.71176i) q^{43} +(-13.7770 + 41.9299i) q^{44} +(-8.92883 + 33.3229i) q^{45} +(-17.4276 - 10.7193i) q^{46} +(-4.10186 - 2.36821i) q^{47} +(-81.9869 - 32.0943i) q^{48} +(34.4078 - 34.8870i) q^{49} +(21.2851 + 39.3570i) q^{50} +(12.7582 + 47.6143i) q^{51} +(4.45635 + 4.98225i) q^{52} +(-32.8247 - 8.79535i) q^{53} +(98.1938 - 92.8750i) q^{54} +17.8869 q^{55} +(-17.2255 - 53.2849i) q^{56} +166.595i q^{57} +(-64.8404 + 61.3282i) q^{58} +(-22.9411 + 85.6173i) q^{59} +(-1.98505 + 35.6271i) q^{60} +(15.4586 - 4.14213i) q^{61} +(8.96529 + 16.5772i) q^{62} +(147.758 + 18.9332i) q^{63} +(-63.1098 - 10.6371i) q^{64} +(1.35452 - 2.34609i) q^{65} +(-103.435 - 63.6198i) q^{66} +(-14.3420 - 3.84292i) q^{67} +(16.1619 + 31.9800i) q^{68} +(39.8063 - 39.8063i) q^{69} +(-18.3368 + 13.3732i) q^{70} +93.6627 q^{71} +(97.1222 - 139.826i) q^{72} +(-16.5673 + 9.56511i) q^{73} +(104.713 - 24.9567i) q^{74} +(-118.914 + 31.8630i) q^{75} +(24.7867 + 118.534i) q^{76} +(-10.3461 - 76.5407i) q^{77} +(-16.1773 + 8.74904i) q^{78} +(-102.698 - 59.2925i) q^{79} +(3.88836 + 25.6444i) q^{80} +(90.1737 + 156.185i) q^{81} +(106.390 + 2.96160i) q^{82} +(-7.54311 + 7.54311i) q^{83} +(153.602 - 12.1131i) q^{84} +(10.2684 - 10.2684i) q^{85} +(-13.7919 + 13.0448i) q^{86} +(-122.780 - 212.662i) q^{87} +(-83.0607 - 29.8768i) q^{88} +(56.1412 + 32.4131i) q^{89} +(-66.1230 - 19.7053i) q^{90} +(-10.8228 - 4.43915i) q^{91} +(22.4001 - 34.2452i) q^{92} +(-50.0866 + 13.4207i) q^{93} +(4.96286 - 8.06874i) q^{94} +(42.5027 - 24.5390i) q^{95} +(68.7265 - 162.124i) q^{96} -119.381 q^{97} +(67.8321 + 70.7305i) q^{98} +(166.035 - 166.035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 8 q^{6} - 8 q^{7} - 20 q^{8} + 16 q^{10} + 14 q^{11} - 2 q^{12} - 8 q^{13} + 20 q^{14} + 8 q^{16} - 4 q^{17} - 38 q^{18} - 2 q^{19} + 72 q^{20} + 14 q^{21}+ \cdots - 776 q^{99}+O(q^{100}) \) 120 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 8 * q^6 - 8 * q^7 - 20 * q^8 + 16 * q^10 + 14 * q^11 - 2 * q^12 - 8 * q^13 + 20 * q^14 + 8 * q^16 - 4 * q^17 - 38 * q^18 - 2 * q^19 + 72 * q^20 + 14 * q^21 + 52 * q^22 - 68 * q^23 - 142 * q^24 - 2 * q^26 - 44 * q^27 - 62 * q^28 - 40 * q^29 - 14 * q^30 + 88 * q^32 - 4 * q^33 + 168 * q^34 + 94 * q^35 - 272 * q^36 - 50 * q^37 + 138 * q^38 - 4 * q^39 - 206 * q^40 - 198 * q^42 - 104 * q^43 + 2 * q^44 - 84 * q^45 - 76 * q^46 - 856 * q^48 - 8 * q^49 - 320 * q^50 + 114 * q^51 + 76 * q^52 - 82 * q^53 + 350 * q^54 - 16 * q^55 + 8 * q^56 - 6 * q^58 + 62 * q^59 + 318 * q^60 - 2 * q^61 + 876 * q^62 + 112 * q^64 - 4 * q^65 + 162 * q^66 - 66 * q^67 + 192 * q^68 + 28 * q^69 + 112 * q^70 + 496 * q^71 + 248 * q^72 + 178 * q^74 + 12 * q^75 - 308 * q^76 + 94 * q^77 - 140 * q^78 + 204 * q^80 + 248 * q^81 + 266 * q^82 - 488 * q^83 + 620 * q^84 + 92 * q^85 - 408 * q^86 - 4 * q^87 - 370 * q^88 - 404 * q^90 - 488 * q^91 + 900 * q^92 - 38 * q^93 - 150 * q^94 + 768 * q^96 - 16 * q^97 + 432 * q^98 - 776 * q^99

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