LMFDB - Embedded newform 56.3.j.a.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(5,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("56.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34357 - 1.48149i) q^{2} +(-1.93494 - 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(-2.33882 + 4.05096i) q^{5} +(-7.56482 - 1.63627i) q^{6} +(6.95505 + 0.792023i) q^{7} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +O(q^{10})$	\(q+(1.34357 - 1.48149i) q^{2} +(-1.93494 - 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(-2.33882 + 4.05096i) q^{5} +(-7.56482 - 1.63627i) q^{6} +(6.95505 + 0.792023i) q^{7} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +(2.85908 + 8.90769i) q^{10} +(12.6383 - 7.29671i) q^{11} +(-12.5880 + 9.00877i) q^{12} +12.7102 q^{13} +(10.5180 - 9.23970i) q^{14} +18.1019 q^{15} +(-15.6964 + 3.10223i) q^{16} +(-16.9068 + 9.76116i) q^{17} +(3.65265 + 11.3801i) q^{18} +(-8.86233 + 15.3500i) q^{19} +(17.0380 + 7.73241i) q^{20} +(-10.8032 - 24.8418i) q^{21} +(6.17041 - 28.5271i) q^{22} +(-4.43038 + 7.67364i) q^{23} +(-3.56645 + 30.7529i) q^{24} +(1.55984 + 2.70172i) q^{25} +(17.0770 - 18.8300i) q^{26} -11.7027 q^{27} +(0.443120 - 27.9965i) q^{28} +35.4981i q^{29} +(24.3212 - 26.8178i) q^{30} +(25.1331 - 14.5106i) q^{31} +(-16.4933 + 27.4221i) q^{32} +(-48.9086 - 28.2374i) q^{33} +(-8.25445 + 38.1621i) q^{34} +(-19.4751 + 26.3222i) q^{35} +(21.7671 + 9.87861i) q^{36} +(10.5802 + 6.10847i) q^{37} +(10.8337 + 33.7533i) q^{38} +(-24.5934 - 42.5970i) q^{39} +(34.3473 - 14.8527i) q^{40} -22.0903i q^{41} +(-51.3177 - 17.3718i) q^{42} -79.8001i q^{43} +(-33.9723 - 47.4696i) q^{44} +(-13.9767 - 24.2084i) q^{45} +(5.41590 + 16.8736i) q^{46} +(-36.5041 - 21.0756i) q^{47} +(40.7684 + 46.6024i) q^{48} +(47.7454 + 11.0171i) q^{49} +(6.09833 + 1.31907i) q^{50} +(65.4273 + 37.7745i) q^{51} +(-4.95229 - 50.5989i) q^{52} +(-31.3096 + 18.0766i) q^{53} +(-15.7234 + 17.3374i) q^{54} +68.2627i q^{55} +(-40.8812 - 38.2718i) q^{56} +68.5923 q^{57} +(52.5901 + 47.6942i) q^{58} +(1.20348 + 2.08449i) q^{59} +(-7.05308 - 72.0633i) q^{60} +(-14.6224 + 25.3268i) q^{61} +(12.2708 - 56.7306i) q^{62} +(-24.8805 + 33.6282i) q^{63} +(18.4657 + 61.2782i) q^{64} +(-29.7268 + 51.4883i) q^{65} +(-107.546 + 34.5187i) q^{66} +(-35.2303 + 20.3402i) q^{67} +(45.4464 + 63.5024i) q^{68} +34.2900 q^{69} +(12.8300 + 64.2179i) q^{70} -22.6174 q^{71} +(43.8807 - 18.9752i) q^{72} +(66.1587 - 38.1967i) q^{73} +(23.2649 - 7.46728i) q^{74} +(6.03639 - 10.4553i) q^{75} +(64.5611 + 29.2999i) q^{76} +(93.6789 - 40.7391i) q^{77} +(-96.1501 - 20.7972i) q^{78} +(-68.4014 + 118.475i) q^{79} +(24.1440 - 70.8409i) q^{80} +(49.5358 + 85.7985i) q^{81} +(-32.7266 - 29.6799i) q^{82} -49.9942 q^{83} +(-94.6852 + 52.6864i) q^{84} -91.3184i q^{85} +(-118.223 - 107.217i) q^{86} +(118.969 - 68.6866i) q^{87} +(-115.970 - 13.4492i) q^{88} +(0.970023 + 0.560043i) q^{89} +(-54.6432 - 11.8193i) q^{90} +(88.3998 + 10.0667i) q^{91} +(32.2748 + 14.6473i) q^{92} +(-97.2622 - 56.1544i) q^{93} +(-80.2692 + 25.7638i) q^{94} +(-41.4548 - 71.8018i) q^{95} +(123.816 + 2.21566i) q^{96} -158.827i q^{97} +(80.4711 - 55.9321i) q^{98} +87.2097i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.34357	−	1.48149i	0.671786	−	0.740746i
$2$	1.34357	−	1.48149i	0.671786	−	0.740746i
$3$	−1.93494	−	3.35141i	−0.644980	−	1.11714i	−0.984306	−	0.176469i	$-0.943532\pi$
$3$	−1.93494	−	3.35141i	−0.644980	−	1.11714i	0.339326	−	0.940669i	$-0.389801\pi$
$4$	−0.389632	−	3.98098i	−0.0974079	−	0.995245i
$5$	−2.33882	+	4.05096i	−0.467764	+	0.810191i	−0.999322	−	0.0368311i	$-0.988274\pi$
$5$	−2.33882	+	4.05096i	−0.467764	+	0.810191i	0.531557	+	0.847022i	$0.321607\pi$
$6$	−7.56482	−	1.63627i	−1.26080	−	0.272711i
$7$	6.95505	+	0.792023i	0.993578	+	0.113146i
$7$	6.95505	+	0.792023i	0.993578	+	0.113146i
$8$	−6.42128	−	4.77149i	−0.802660	−	0.596437i
$9$	−2.98798	+	5.17534i	−0.331998	+	0.575037i
$10$	2.85908	+	8.90769i	0.285908	+	0.890769i
$11$	12.6383	−	7.29671i	1.14893	−	0.663337i	0.200306	−	0.979733i	$-0.435806\pi$
$11$	12.6383	−	7.29671i	1.14893	−	0.663337i	0.948627	+	0.316396i	$0.102473\pi$
$12$	−12.5880	+	9.00877i	−1.04900	+	0.750731i
$13$	12.7102			0.977705			0.488853	−	0.872366i	$-0.337416\pi$
$13$	12.7102			0.977705			0.488853	+	0.872366i	$0.337416\pi$
$14$	10.5180	−	9.23970i	0.751284	−	0.659979i
$15$	18.1019			1.20679
$16$	−15.6964	+	3.10223i	−0.981023	+	0.193889i
$17$	−16.9068	+	9.76116i	−0.994519	+	0.574186i	−0.906622	−	0.421944i	$-0.861348\pi$
$17$	−16.9068	+	9.76116i	−0.994519	+	0.574186i	−0.0878969	+	0.996130i	$0.528015\pi$
$18$	3.65265	+	11.3801i	0.202925	+	0.632228i
$19$	−8.86233	+	15.3500i	−0.466439	+	0.807895i	−0.999265	−	0.0383291i	$-0.987796\pi$
$19$	−8.86233	+	15.3500i	−0.466439	+	0.807895i	0.532827	+	0.846224i	$0.321130\pi$
$20$	17.0380	+	7.73241i	0.851902	+	0.386621i
$21$	−10.8032	−	24.8418i	−0.514438	−	1.18294i
$22$	6.17041	−	28.5271i	0.280473	−	1.29669i
$23$	−4.43038	+	7.67364i	−0.192625	+	0.333636i	−0.946119	−	0.323818i	$-0.895033\pi$
$23$	−4.43038	+	7.67364i	−0.192625	+	0.333636i	0.753494	+	0.657454i	$0.228367\pi$
$24$	−3.56645	+	30.7529i	−0.148602	+	1.28137i
$25$	1.55984	+	2.70172i	0.0623936	+	0.108069i
$26$	17.0770	−	18.8300i	0.656808	−	0.724231i
$27$	−11.7027			−0.433432
$28$	0.443120	−	27.9965i	0.0158257	−	0.999875i
$29$			35.4981i			1.22407i	0.790830	+	0.612036i	$0.209649\pi$
$29$			35.4981i			1.22407i	−0.790830	+	0.612036i	$0.790351\pi$
$30$	24.3212	−	26.8178i	0.810707	−	0.893927i
$31$	25.1331	−	14.5106i	0.810747	−	0.468085i	−0.0364685	−	0.999335i	$-0.511611\pi$
$31$	25.1331	−	14.5106i	0.810747	−	0.468085i	0.847215	+	0.531250i	$0.178278\pi$
$32$	−16.4933	+	27.4221i	−0.515415	+	0.856941i
$33$	−48.9086	−	28.2374i	−1.48208	−	0.855678i
$34$	−8.25445	+	38.1621i	−0.242778	+	1.12242i
$35$	−19.4751	+	26.3222i	−0.556430	+	0.752063i
$36$	21.7671	+	9.87861i	0.604642	+	0.274406i
$37$	10.5802	+	6.10847i	0.285951	+	0.165094i	0.636114	−	0.771595i	$-0.280541\pi$
$37$	10.5802	+	6.10847i	0.285951	+	0.165094i	−0.350163	+	0.936689i	$0.613874\pi$
$38$	10.8337	+	33.7533i	0.285098	+	0.888245i
$39$	−24.5934	−	42.5970i	−0.630600	−	1.09223i
$40$	34.3473	−	14.8527i	0.858683	−	0.371317i
$41$		−	22.0903i		−	0.538788i	−0.963030	−	0.269394i	$-0.913177\pi$
$41$		−	22.0903i		−	0.538788i	0.963030	−	0.269394i	$-0.0868233\pi$
$42$	−51.3177	−	17.3718i	−1.22185	−	0.413615i
$43$		−	79.8001i		−	1.85582i	−0.372809	−	0.927908i	$-0.621605\pi$
$43$		−	79.8001i		−	1.85582i	0.372809	−	0.927908i	$-0.378395\pi$
$44$	−33.9723	−	47.4696i	−0.772098	−	1.07886i
$45$	−13.9767	−	24.2084i	−0.310593	−	0.537964i
$46$	5.41590	+	16.8736i	0.117737	+	0.366818i
$47$	−36.5041	−	21.0756i	−0.776682	−	0.448418i	0.0585708	−	0.998283i	$-0.481346\pi$
$47$	−36.5041	−	21.0756i	−0.776682	−	0.448418i	−0.835253	+	0.549865i	$0.814679\pi$
$48$	40.7684	+	46.6024i	0.849342	+	0.970884i
$49$	47.7454	+	11.0171i	0.974396	+	0.224839i
$50$	6.09833	+	1.31907i	0.121967	+	0.0263813i
$51$	65.4273	+	37.7745i	1.28289	+	0.740676i
$52$	−4.95229	−	50.5989i	−0.0952363	−	0.973056i
$53$	−31.3096	+	18.0766i	−0.590748	+	0.341068i	−0.765393	−	0.643563i	$-0.777455\pi$
$53$	−31.3096	+	18.0766i	−0.590748	+	0.341068i	0.174645	+	0.984631i	$0.444122\pi$
$54$	−15.7234	+	17.3374i	−0.291173	+	0.321063i
$55$			68.2627i			1.24114i
$56$	−40.8812	−	38.2718i	−0.730021	−	0.683424i
$57$	68.5923			1.20337
$58$	52.5901	+	47.6942i	0.906726	+	0.822314i
$59$	1.20348	+	2.08449i	0.0203979	+	0.0353303i	0.876044	−	0.482231i	$-0.160173\pi$
$59$	1.20348	+	2.08449i	0.0203979	+	0.0353303i	−0.855646	+	0.517561i	$0.826840\pi$
$60$	−7.05308	−	72.0633i	−0.117551	−	1.20105i
$61$	−14.6224	+	25.3268i	−0.239712	+	0.415194i	−0.960632	−	0.277825i	$-0.910386\pi$
$61$	−14.6224	+	25.3268i	−0.239712	+	0.415194i	0.720919	+	0.693019i	$0.243720\pi$
$62$	12.2708	−	56.7306i	0.197916	−	0.915010i
$63$	−24.8805	+	33.6282i	−0.394929	+	0.533780i
$64$	18.4657	+	61.2782i	0.288527	+	0.957472i
$65$	−29.7268	+	51.4883i	−0.457335	+	0.792128i
$66$	−107.546	+	34.5187i	−1.62948	+	0.523010i
$67$	−35.2303	+	20.3402i	−0.525825	+	0.303585i	−0.739315	−	0.673360i	$-0.764850\pi$
$67$	−35.2303	+	20.3402i	−0.525825	+	0.303585i	0.213490	+	0.976945i	$0.431517\pi$
$68$	45.4464	+	63.5024i	0.668329	+	0.933859i
$69$	34.2900			0.496957
$70$	12.8300	+	64.2179i	0.183285	+	0.917398i
$71$	−22.6174			−0.318554			−0.159277	−	0.987234i	$-0.550916\pi$
$71$	−22.6174			−0.318554			−0.159277	+	0.987234i	$0.550916\pi$
$72$	43.8807	−	18.9752i	0.609455	−	0.263544i
$73$	66.1587	−	38.1967i	0.906283	−	0.523243i	0.0270498	−	0.999634i	$-0.491389\pi$
$73$	66.1587	−	38.1967i	0.906283	−	0.523243i	0.879233	+	0.476391i	$0.158055\pi$
$74$	23.2649	−	7.46728i	0.314390	−	0.100909i
$75$	6.03639	−	10.4553i	0.0804852	−	0.139404i
$76$	64.5611	+	29.2999i	0.849488	+	0.385525i
$77$	93.6789	−	40.7391i	1.21661	−	0.529080i
$78$	−96.1501	−	20.7972i	−1.23269	−	0.266631i
$79$	−68.4014	+	118.475i	−0.865840	+	1.49968i	0.000370612		1.00000i	$0.499882\pi$
$79$	−68.4014	+	118.475i	−0.865840	+	1.49968i	−0.866211	+	0.499679i	$0.833451\pi$
$80$	24.1440	−	70.8409i	0.301800	−	0.885511i
$81$	49.5358	+	85.7985i	0.611553	+	1.05924i
$82$	−32.7266	−	29.6799i	−0.399105	−	0.361950i
$83$	−49.9942			−0.602340			−0.301170	−	0.953571i	$-0.597377\pi$
$83$	−49.9942			−0.602340			−0.301170	+	0.953571i	$0.597377\pi$
$84$	−94.6852	+	52.6864i	−1.12721	+	0.627220i
$85$		−	91.3184i		−	1.07433i
$86$	−118.223	−	107.217i	−1.37469	−	1.24671i
$87$	118.969	−	68.6866i	1.36746	−	0.789502i
$88$	−115.970	−	13.4492i	−1.31784	−	0.152832i
$89$	0.970023	+	0.560043i	0.0108991	+	0.00629262i	0.505440	−	0.862862i	$-0.331330\pi$
$89$	0.970023	+	0.560043i	0.0108991	+	0.00629262i	−0.494541	+	0.869155i	$0.664664\pi$
$90$	−54.6432	−	11.8193i	−0.607146	−	0.131326i
$91$	88.3998	+	10.0667i	0.971427	+	0.110624i
$92$	32.2748	+	14.6473i	0.350813	+	0.159210i
$93$	−97.2622	−	56.1544i	−1.04583	−	0.603810i
$94$	−80.2692	+	25.7638i	−0.853928	+	0.274083i
$95$	−41.4548	−	71.8018i	−0.436366	−	0.755809i
$96$	123.816	+	2.21566i	1.28975	+	0.0230797i
$97$		−	158.827i		−	1.63740i	−0.574225	−	0.818698i	$-0.694696\pi$
$97$		−	158.827i		−	1.63740i	0.574225	−	0.818698i	$-0.305304\pi$
$98$	80.4711	−	55.9321i	0.821134	−	0.570736i
$99$			87.2097i			0.880906i
$100$	10.1477	−	7.26236i	0.101477	−	0.0726236i
$101$	34.8122	+	60.2965i	0.344675	+	0.596995i	0.985295	−	0.170864i	$-0.0546557\pi$
$101$	34.8122	+	60.2965i	0.344675	+	0.596995i	−0.640620	+	0.767858i	$0.721322\pi$
$102$	143.869	−	46.1773i	1.41048	−	0.452719i
$103$	16.9911	+	9.80983i	0.164962	+	0.0952411i	0.580208	−	0.814468i	$-0.302971\pi$
$103$	16.9911	+	9.80983i	0.164962	+	0.0952411i	−0.415246	+	0.909709i	$0.636304\pi$
$104$	−81.6156	−	60.6465i	−0.784765	−	0.583139i
$105$	125.900	+	14.3371i	1.19904	+	0.136544i
$106$	−15.2864	+	70.6722i	−0.144211	+	0.666718i
$107$	−38.7540	−	22.3747i	−0.362187	−	0.209109i	0.307852	−	0.951434i	$-0.400390\pi$
$107$	−38.7540	−	22.3747i	−0.362187	−	0.209109i	−0.670040	+	0.742325i	$0.733723\pi$
$108$	4.55973	+	46.5880i	0.0422197	+	0.431371i
$109$	49.0210	−	28.3023i	0.449734	−	0.259654i	−0.257984	−	0.966149i	$-0.583058\pi$
$109$	49.0210	−	28.3023i	0.449734	−	0.259654i	0.707718	+	0.706495i	$0.249725\pi$
$110$	101.131	+	91.7159i	0.919369	+	0.833781i
$111$		−	47.2781i		−	0.425929i
$112$	−111.626	+	9.14427i	−0.996661	+	0.0816453i
$113$	−188.632			−1.66931			−0.834657	−	0.550770i	$-0.814334\pi$
$113$	−188.632			−1.66931			−0.834657	+	0.550770i	$0.814334\pi$
$114$	92.1587	−	101.619i	0.808409	−	0.891394i
$115$	−20.7237	−	35.8945i	−0.180206	−	0.312126i
$116$	141.317	−	13.8312i	1.21825	−	0.119234i
$117$	−37.9777	+	65.7794i	−0.324596	+	0.562217i
$118$	4.70511	+	1.01771i	0.0398738	+	0.00862469i
$119$	−125.319	+	54.4987i	−1.05310	+	0.457972i
$120$	−116.237	−	86.3731i	−0.968645	−	0.719776i
$121$	45.9838	−	79.6463i	0.380032	−	0.658234i
$122$	17.8752	+	55.6914i	0.146518	+	0.456487i
$123$	−74.0337	+	42.7434i	−0.601900	+	0.347507i
$124$	−67.5592	−	94.4007i	−0.544832	−	0.761296i
$125$	−131.534			−1.05227
$126$	16.3910	+	82.0421i	0.130088	+	0.651128i
$127$	45.8547			0.361060			0.180530	−	0.983569i	$-0.442219\pi$
$127$	45.8547			0.361060			0.180530	+	0.983569i	$0.442219\pi$
$128$	115.593	+	54.9748i	0.903071	+	0.429491i
$129$	−267.443	+	154.408i	−2.07320	+	1.19696i
$130$	36.3394	+	113.218i	0.279534	+	0.870909i
$131$	60.4982	−	104.786i	0.461818	−	0.799893i	−0.537233	−	0.843434i	$-0.680531\pi$
$131$	60.4982	−	104.786i	0.461818	−	0.799893i	0.999052	+	0.0435409i	$0.0138639\pi$
$132$	−93.3560	+	205.706i	−0.707243	+	1.55838i
$133$	−73.7955	+	99.7409i	−0.554854	+	0.749932i
$134$	−17.2006	+	79.5219i	−0.128362	+	0.593447i
$135$	27.3704	−	47.4069i	0.202744	−	0.351163i
$136$	155.139	+	17.9916i	1.14073	+	0.132291i
$137$	72.6207	+	125.783i	0.530078	+	0.918122i	0.999384	+	0.0350869i	$0.0111708\pi$
$137$	72.6207	+	125.783i	0.530078	+	0.918122i	−0.469306	+	0.883036i	$0.655496\pi$
$138$	46.0711	−	50.8004i	0.333849	−	0.368119i
$139$	86.3503			0.621225			0.310613	−	0.950537i	$-0.399466\pi$
$139$	86.3503			0.621225			0.310613	+	0.950537i	$0.399466\pi$
$140$	112.376	+	67.2738i	0.802687	+	0.480527i
$141$			163.120i			1.15688i
$142$	−30.3880	+	33.5074i	−0.214000	+	0.235968i
$143$	160.634	−	92.7424i	1.12332	−	0.648548i
$144$	30.8454	−	90.5034i	0.214204	−	0.628496i
$145$	−143.801	−	83.0236i	−0.991732	−	0.572577i
$146$	32.3008	−	149.334i	0.221238	−	1.02283i
$147$	−55.4615	−	181.332i	−0.377289	−	1.23355i
$148$	20.1953	−	44.4996i	0.136455	−	0.300673i
$149$	189.536	+	109.429i	1.27205	+	0.734421i	0.975374	−	0.220556i	$-0.0707873\pi$
$149$	189.536	+	109.429i	1.27205	+	0.734421i	0.296680	+	0.954977i	$0.404121\pi$
$150$	−7.37916	−	22.9903i	−0.0491944	−	0.153269i
$151$	−41.6552	−	72.1490i	−0.275862	−	0.477808i	0.694490	−	0.719502i	$-0.255630\pi$
$151$	−41.6552	−	72.1490i	−0.275862	−	0.477808i	−0.970352	+	0.241695i	$0.922297\pi$
$152$	130.150	−	56.2802i	0.856250	−	0.370264i
$153$		−	116.665i		−	0.762514i
$154$	65.5096	−	193.520i	0.425387	−	1.25663i
$155$			135.751i			0.875813i
$156$	−159.995	+	114.503i	−1.02561	+	0.733993i
$157$	−17.7207	−	30.6932i	−0.112871	−	0.195498i	0.804056	−	0.594554i	$-0.202671\pi$
$157$	−17.7207	−	30.6932i	−0.112871	−	0.195498i	−0.916927	+	0.399056i	$0.869338\pi$
$158$	83.6170	+	260.515i	0.529222	+	1.64883i
$159$	121.164	+	69.9543i	0.762041	+	0.439964i
$160$	−72.5109	−	130.949i	−0.453193	−	0.818431i
$161$	−36.8912	+	49.8616i	−0.229138	+	0.309699i
$162$	193.664	+	41.8896i	1.19546	+	0.258578i
$163$	−9.05412	−	5.22740i	−0.0555468	−	0.0320699i	0.471969	−	0.881615i	$-0.343543\pi$
$163$	−9.05412	−	5.22740i	−0.0555468	−	0.0320699i	−0.527516	+	0.849545i	$0.676877\pi$
$164$	−87.9410	+	8.60708i	−0.536226	+	0.0524822i
$165$	228.777	−	132.084i	1.38653	−	0.800511i
$166$	−67.1708	+	74.0659i	−0.404643	+	0.446180i
$167$			78.8843i			0.472361i	0.971709	+	0.236181i	$0.0758957\pi$
$167$			78.8843i			0.472361i	−0.971709	+	0.236181i	$0.924104\pi$
$168$	−49.1619	+	211.063i	−0.292630	+	1.25633i
$169$	−7.45163			−0.0440925
$170$	−135.287	−	122.693i	−0.795808	−	0.721722i
$171$	−52.9610	−	91.7311i	−0.309713	−	0.536439i
$172$	−317.682	+	31.0926i	−1.84699	+	0.180771i
$173$	95.9208	−	166.140i	0.554456	−	0.960345i	−0.443490	−	0.896279i	$-0.646260\pi$
$173$	95.9208	−	166.140i	0.554456	−	0.960345i	0.997946	−	0.0640660i	$-0.0204068\pi$
$174$	58.0844	−	268.537i	0.333818	−	1.54331i
$175$	8.70893	+	20.0260i	0.0497653	+	0.114434i
$176$	−175.739	+	153.739i	−0.998516	+	0.873515i
$177$	4.65732	−	8.06671i	0.0263125	−	0.0455746i
$178$	2.13299	−	0.684623i	0.0119831	−	0.00384620i
$179$	60.5426	−	34.9543i	0.338227	−	0.195275i	−0.321261	−	0.946991i	$-0.604107\pi$
$179$	60.5426	−	34.9543i	0.338227	−	0.195275i	0.659488	+	0.751715i	$0.270773\pi$
$180$	−90.9272	+	65.0733i	−0.505151	+	0.361518i
$181$	−343.635			−1.89853			−0.949267	−	0.314472i	$-0.898173\pi$
$181$	−343.635			−1.89853			−0.949267	+	0.314472i	$0.898173\pi$
$182$	133.685	−	117.438i	0.734535	−	0.645265i
$183$	113.174			0.618438
$184$	65.0634	−	28.1351i	0.353605	−	0.152908i
$185$	−49.4903	+	28.5732i	−0.267515	+	0.154450i
$186$	−213.871	+	68.6457i	−1.14984	+	0.369063i
$187$	−142.449	+	246.728i	−0.761757	+	1.31940i
$188$	−69.6785	+	153.534i	−0.370630	+	0.816668i
$189$	−81.3925	−	9.26878i	−0.430648	−	0.0490411i
$190$	−162.071	−	35.0560i	−0.853007	−	0.184505i
$191$	69.8895	−	121.052i	0.365913	−	0.633781i	−0.623009	−	0.782215i	$-0.714090\pi$
$191$	69.8895	−	121.052i	0.365913	−	0.633781i	0.988922	+	0.148434i	$0.0474233\pi$
$192$	169.639	−	180.456i	0.883534	−	0.939874i
$193$	−11.4616	−	19.8521i	−0.0593867	−	0.102861i	0.834804	−	0.550548i	$-0.185581\pi$
$193$	−11.4616	−	19.8521i	−0.0593867	−	0.102861i	−0.894190	+	0.447687i	$0.852248\pi$
$194$	−235.301	−	213.396i	−1.21289	−	1.09998i
$195$	230.078			1.17989
$196$	25.2558	−	194.366i	0.128856	−	0.991663i
$197$		−	287.788i		−	1.46085i	−0.682992	−	0.730426i	$-0.739322\pi$
$197$		−	287.788i		−	1.46085i	0.682992	−	0.730426i	$-0.260678\pi$
$198$	129.200	+	117.172i	0.652527	+	0.591780i
$199$	−56.7091	+	32.7410i	−0.284970	+	0.164528i	−0.635671	−	0.771960i	$-0.719277\pi$
$199$	−56.7091	+	32.7410i	−0.284970	+	0.164528i	0.350701	+	0.936487i	$0.385943\pi$
$200$	2.87507	−	24.7913i	0.0143754	−	0.123956i
$201$	136.337	+	78.7141i	0.678293	+	0.391613i
$202$	136.101	+	29.4387i	0.673769	+	0.145736i
$203$	−28.1153	+	246.891i	−0.138499	+	1.21621i
$204$	124.887	−	275.183i	0.612191	−	1.34894i
$205$	89.4868	+	51.6652i	0.436521	+	0.252026i
$206$	37.3620	−	11.9920i	0.181369	−	0.0582135i
$207$	−26.4758	−	45.8574i	−0.127902	−	0.221533i
$208$	−199.504	+	39.4299i	−0.959152	+	0.189567i
$209$			258.663i			1.23762i
$210$	190.395	−	167.256i	0.906645	−	0.796458i
$211$		−	17.8985i		−	0.0848270i	−0.999100	−	0.0424135i	$-0.986495\pi$
$211$		−	17.8985i		−	0.0848270i	0.999100	−	0.0424135i	$-0.0135047\pi$
$212$	84.1618	+	117.600i	0.396990	+	0.554716i
$213$	43.7632	+	75.8001i	0.205461	+	0.355869i
$214$	−85.2167	+	27.3518i	−0.398209	+	0.127812i
$215$	323.267	+	186.638i	1.50357	+	0.868084i
$216$	75.1461	+	55.8391i	0.347898	+	0.258515i
$217$	186.295	−	81.0161i	0.858502	−	0.373346i
$218$	23.9336	−	110.650i	0.109787	−	0.507570i
$219$	−256.026	−	147.817i	−1.16907	−	0.674962i
$220$	271.752	−	26.5973i	1.23524	−	0.120897i
$221$	−214.889	+	124.066i	−0.972346	+	0.561384i
$222$	−70.0421	−	63.5215i	−0.315505	−	0.286133i
$223$			258.973i			1.16132i	0.814148	+	0.580658i	$0.197205\pi$
$223$			258.973i			1.16132i	−0.814148	+	0.580658i	$0.802795\pi$
$224$	−136.430	+	177.659i	−0.609065	+	0.793121i
$225$	−18.6431			−0.0828581
$226$	−253.441	+	279.457i	−1.12142	+	1.23654i
$227$	−58.6721	−	101.623i	−0.258468	−	0.447679i	0.707364	−	0.706849i	$-0.249884\pi$
$227$	−58.6721	−	101.623i	−0.258468	−	0.447679i	−0.965832	+	0.259171i	$0.916551\pi$
$228$	−26.7257	−	273.065i	−0.117218	−	1.19765i
$229$	43.5475	−	75.4264i	0.190164	−	0.329373i	−0.755141	−	0.655563i	$-0.772431\pi$
$229$	43.5475	−	75.4264i	0.190164	−	0.329373i	0.945304	+	0.326190i	$0.105765\pi$
$230$	−81.0212	−	17.5249i	−0.352266	−	0.0761950i
$231$	−317.797	−	235.129i	−1.37574	−	1.01787i
$232$	169.379	−	227.943i	0.730081	−	0.982514i
$233$	155.825	−	269.897i	0.668778	−	1.15836i	−0.309468	−	0.950910i	$-0.600151\pi$
$233$	155.825	−	269.897i	0.668778	−	1.15836i	0.978246	−	0.207448i	$-0.0665159\pi$
$234$	46.4258	+	144.643i	0.198401	+	0.618132i
$235$	170.753	−	98.5843i	0.726608	−	0.419507i
$236$	7.82938	−	5.60320i	0.0331753	−	0.0237424i
$237$	529.410			2.23380
$238$	−87.6354	+	258.882i	−0.368216	+	1.08774i
$239$	−140.823			−0.589218			−0.294609	−	0.955618i	$-0.595189\pi$
$239$	−140.823			−0.589218			−0.294609	+	0.955618i	$0.595189\pi$
$240$	−284.134	+	56.1563i	−1.18389	+	0.233985i
$241$	−41.6447	+	24.0436i	−0.172799	+	0.0997658i	−0.583905	−	0.811822i	$-0.698476\pi$
$241$	−41.6447	+	24.0436i	−0.172799	+	0.0997658i	0.411106	+	0.911588i	$0.365143\pi$
$242$	−56.2128	−	175.135i	−0.232284	−	0.723699i
$243$	139.035	−	240.816i	0.572162	−	0.991014i
$244$	106.523	+	48.3435i	0.436569	+	0.198129i
$245$	−156.298	+	167.647i	−0.637950	+	0.684275i
$246$	−36.1456	+	167.109i	−0.146934	+	0.679305i
$247$	−112.642	+	195.101i	−0.456039	+	0.789883i
$248$	−230.624	−	26.7458i	−0.929937	−	0.107846i
$249$	96.7357	+	167.551i	0.388497	+	0.672896i
$250$	−176.725	+	194.866i	−0.706900	+	0.779464i
$251$	152.080			0.605895			0.302947	−	0.953007i	$-0.402029\pi$
$251$	152.080			0.605895			0.302947	+	0.953007i	$0.402029\pi$
$252$	143.567	+	85.9463i	0.569711	+	0.341057i
$253$			129.309i			0.511101i
$254$	61.6090	−	67.9333i	0.242555	−	0.267454i
$255$	−306.046	+	176.696i	−1.20018	+	0.692924i
$256$	236.752	−	97.3876i	0.924814	−	0.380420i
$257$	126.153	+	72.8347i	0.490869	+	0.283403i	0.724935	−	0.688817i	$-0.241870\pi$
$257$	126.153	+	72.8347i	0.490869	+	0.283403i	−0.234066	+	0.972221i	$0.575203\pi$
$258$	−130.574	+	603.673i	−0.506102	+	2.33982i
$259$	68.7477	+	50.8645i	0.265435	+	0.196388i
$260$	216.556	+	98.2803i	0.832909	+	0.378001i
$261$	−183.714	−	106.068i	−0.703887	−	0.406389i
$262$	−73.9558	−	230.415i	−0.282274	−	0.879446i
$263$	−176.696	−	306.047i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$263$	−176.696	−	306.047i	−0.671850	−	1.16368i	0.305529	−	0.952183i	$-0.401167\pi$
$264$	179.321	+	414.687i	0.679247	+	1.57078i
$265$		−	169.112i		−	0.638158i
$266$	48.6157	+	243.336i	0.182766	+	0.914799i
$267$		−	4.33460i		−	0.0162345i
$268$	94.7008	+	132.326i	0.353361	+	0.493753i
$269$	66.6490	+	115.439i	0.247766	+	0.429143i	0.962906	−	0.269838i	$-0.0869703\pi$
$269$	66.6490	+	115.439i	0.247766	+	0.429143i	−0.715140	+	0.698981i	$0.753637\pi$
$270$	−33.4589	−	104.244i	−0.123922	−	0.386088i
$271$	−326.342	−	188.414i	−1.20421	−	0.695253i	−0.242725	−	0.970095i	$-0.578041\pi$
$271$	−326.342	−	188.414i	−1.20421	−	0.695253i	−0.961489	+	0.274842i	$0.911375\pi$
$272$	235.094	−	205.664i	0.864318	−	0.756116i
$273$	−137.310	−	315.743i	−0.502969	−	1.15657i
$274$	283.917	+	61.4112i	1.03619	+	0.224128i
$275$	39.4273	+	22.7634i	0.143372	+	0.0827759i
$276$	−13.3605	−	136.508i	−0.0484076	−	0.494594i
$277$	−67.4788	+	38.9589i	−0.243606	+	0.140646i	−0.616833	−	0.787094i	$-0.711585\pi$
$277$	−67.4788	+	38.9589i	−0.243606	+	0.140646i	0.373227	+	0.927740i	$0.378251\pi$
$278$	116.018	−	127.927i	0.417330	−	0.460170i
$279$			173.430i			0.621613i
$280$	250.651	−	76.0971i	0.895182	−	0.271775i
$281$	324.564			1.15503			0.577516	−	0.816380i	$-0.304022\pi$
$281$	324.564			1.15503			0.577516	+	0.816380i	$0.304022\pi$
$282$	241.661	+	219.164i	0.856955	+	0.777177i
$283$	149.741	+	259.359i	0.529119	+	0.916462i	0.999423	+	0.0339572i	$0.0108110\pi$
$283$	149.741	+	259.359i	0.529119	+	0.916462i	−0.470304	+	0.882505i	$0.655856\pi$
$284$	8.81244	+	90.0392i	0.0310297	+	0.317040i
$285$	−160.425	+	277.864i	−0.562895	+	0.974963i
$286$	78.4269	−	362.585i	0.274220	−	1.26778i
$287$	17.4960	−	153.639i	0.0609618	−	0.535328i
$288$	−92.6370	−	167.295i	−0.321656	−	0.580885i
$289$	46.0604	−	79.7789i	0.159378	−	0.276052i
$290$	−316.206	+	101.492i	−1.09037	+	0.349972i
$291$	−532.296	+	307.321i	−1.82920	+	1.05609i
$292$	−177.838	−	248.494i	−0.609034	−	0.851005i
$293$	−81.7250			−0.278925			−0.139463	−	0.990227i	$-0.544537\pi$
$293$	−81.7250			−0.278925			−0.139463	+	0.990227i	$0.544537\pi$
$294$	−343.158	−	161.467i	−1.16721	−	0.549207i
$295$	−11.2589			−0.0381657
$296$	−38.7918	−	89.7075i	−0.131053	−	0.303066i
$297$	−147.901	+	85.3908i	−0.497984	+	0.287511i
$298$	416.773	−	133.771i	1.39857	−	0.448895i
$299$	−56.3108	+	97.5332i	−0.188331	+	0.326198i
$300$	−43.9744	−	19.9570i	−0.146581	−	0.0665233i
$301$	63.2035	−	555.013i	0.209979	−	1.84390i
$302$	−162.855	−	35.2254i	−0.539254	−	0.116641i
$303$	134.719	−	233.340i	0.444617	−	0.770099i
$304$	91.4872	−	268.433i	0.300945	−	0.883002i
$305$	−68.3986	−	118.470i	−0.224258	−	0.388425i
$306$	−172.838	−	156.747i	−0.564829	−	0.512246i
$307$	−361.930			−1.17892			−0.589462	−	0.807796i	$-0.700660\pi$
$307$	−361.930			−1.17892			−0.589462	+	0.807796i	$0.700660\pi$
$308$	−198.682	−	357.060i	−0.645071	−	1.15929i
$309$		−	75.9257i		−	0.245714i
$310$	201.114	+	182.391i	0.648755	+	0.588359i
$311$	163.508	−	94.4017i	0.525751	−	0.303542i	−0.213534	−	0.976936i	$-0.568497\pi$
$311$	163.508	−	94.4017i	0.525751	−	0.303542i	0.739284	+	0.673393i	$0.235164\pi$
$312$	−45.3302	+	390.875i	−0.145289	+	1.25280i
$313$	−22.2463	−	12.8439i	−0.0710745	−	0.0410349i	0.464042	−	0.885813i	$-0.346399\pi$
$313$	−22.2463	−	12.8439i	−0.0710745	−	0.0410349i	−0.535116	+	0.844779i	$0.679732\pi$
$314$	−69.2808	−	14.9854i	−0.220639	−	0.0477242i
$315$	−78.0351	−	179.440i	−0.247730	−	0.569651i
$316$	498.296	+	226.143i	1.57689	+	0.715642i
$317$	−432.257	−	249.564i	−1.36359	−	0.787268i	−0.373489	−	0.927635i	$-0.621838\pi$
$317$	−432.257	−	249.564i	−1.36359	−	0.787268i	−0.990100	+	0.140367i	$0.955172\pi$
$318$	266.430	−	85.5154i	0.837830	−	0.268916i
$319$	259.019	+	448.634i	0.811972	+	1.40638i
$320$	−291.423	−	68.5149i	−0.910698	−	0.214109i
$321$			173.174i			0.539484i
$322$	24.3035	+	121.647i	0.0754768	+	0.377784i
$323$		−	346.027i		−	1.07129i
$324$	322.261	−	230.631i	0.994633	−	0.711823i
$325$	19.8258	+	34.3393i	0.0610025	+	0.105659i
$326$	−19.9092	+	6.39022i	−0.0610712	+	0.0196019i
$327$	−189.705	−	109.526i	−0.580138	−	0.334943i
$328$	−105.404	+	141.848i	−0.321353	+	0.432464i
$329$	−237.195	−	175.494i	−0.720958	−	0.533417i
$330$	111.696	−	516.395i	0.338473	−	1.56483i
$331$	216.384	+	124.930i	0.653729	+	0.377431i	0.789883	−	0.613257i	$-0.210141\pi$
$331$	216.384	+	124.930i	0.653729	+	0.377431i	−0.136154	+	0.990688i	$0.543474\pi$
$332$	19.4793	+	199.026i	0.0586727	+	0.599475i
$333$	−63.2268	+	36.5040i	−0.189870	+	0.109622i
$334$	116.866	+	105.987i	0.349899	+	0.317326i
$335$		−	190.288i		−	0.568025i
$336$	246.636	+	356.412i	0.734036	+	1.06075i
$337$	−84.4039			−0.250457			−0.125228	−	0.992128i	$-0.539966\pi$
$337$	−84.4039			−0.250457			−0.125228	+	0.992128i	$0.539966\pi$
$338$	−10.0118	+	11.0395i	−0.0296207	+	0.0326613i
$339$	364.992	+	632.185i	1.07667	+	1.86485i
$340$	−363.536	+	35.5805i	−1.06922	+	0.104649i
$341$	211.760	−	366.778i	0.620996	−	1.07560i
$342$	−207.056	−	44.7861i	−0.605426	−	0.130953i
$343$	323.346	+	114.440i	0.942699	+	0.333645i
$344$	−380.766	+	512.419i	−1.10688	+	1.48959i
$345$	−80.1982	+	138.907i	−0.232459	+	0.402630i
$346$	−117.258	−	365.326i	−0.338896	−	1.05586i
$347$	326.707	−	188.624i	0.941518	−	0.543586i	0.0510824	−	0.998694i	$-0.483733\pi$
$347$	326.707	−	188.624i	0.941518	−	0.543586i	0.890436	+	0.455109i	$0.150400\pi$
$348$	−319.794	−	446.849i	−0.918948	−	1.28405i
$349$	400.193			1.14668			0.573342	−	0.819316i	$-0.305647\pi$
$349$	400.193			1.14668			0.573342	+	0.819316i	$0.305647\pi$
$350$	41.3694	+	14.0042i	0.118198	+	0.0400120i
$351$	−148.743			−0.423768
$352$	−8.35529	+	466.914i	−0.0237366	+	1.32646i
$353$	256.293	−	147.971i	0.726043	−	0.419181i	−0.0909296	−	0.995857i	$-0.528984\pi$
$353$	256.293	−	147.971i	0.726043	−	0.419181i	0.816973	+	0.576676i	$0.195650\pi$
$354$	−5.69332	−	17.7380i	−0.0160828	−	0.0501073i
$355$	52.8980	−	91.6220i	0.149008	−	0.258090i
$356$	1.85157	−	4.07985i	0.00520103	−	0.0114603i
$357$	425.132	+	314.543i	1.19085	+	0.881074i
$358$	29.5588	−	136.657i	0.0825666	−	0.381723i
$359$	102.587	−	177.686i	0.285757	−	0.494946i	−0.687035	−	0.726624i	$-0.741088\pi$
$359$	102.587	−	177.686i	0.285757	−	0.494946i	0.972793	+	0.231678i	$0.0744215\pi$
$360$	−25.7617	+	222.138i	−0.0715602	+	0.617051i
$361$	23.4181	+	40.5613i	0.0648701	+	0.112358i
$362$	−461.698	+	509.092i	−1.27541	+	1.40633i
$363$	−355.904			−0.980451
$364$	5.63213	−	355.840i	0.0154729	−	0.977583i
$365$			357.341i			0.979017i
$366$	152.058	−	167.667i	0.415458	−	0.458105i
$367$	−306.216	+	176.794i	−0.834377	+	0.481728i	−0.855349	−	0.518052i	$-0.826657\pi$
$367$	−306.216	+	176.794i	−0.834377	+	0.481728i	0.0209719	+	0.999780i	$0.493324\pi$
$368$	45.7355	−	134.192i	0.124281	−	0.364653i
$369$	114.325	+	66.0054i	0.309823	+	0.178876i
$370$	−24.1628	+	111.710i	−0.0653048	+	0.301918i
$371$	−232.077	+	100.926i	−0.625545	+	0.272037i
$372$	−185.653	+	409.078i	−0.499067	+	1.09967i
$373$	310.062	+	179.014i	0.831264	+	0.479931i	0.854285	−	0.519804i	$-0.173995\pi$
$373$	310.062	+	179.014i	0.831264	+	0.479931i	−0.0230210	+	0.999735i	$0.507328\pi$
$374$	174.136	+	542.533i	0.465604	+	1.45062i
$375$	254.510	+	440.824i	0.678693	+	1.17553i
$376$	133.841	+	309.512i	0.355959	+	0.823169i
$377$			451.187i			1.19678i
$378$	−123.088	+	108.129i	−0.325630	+	0.286056i
$379$		−	514.679i		−	1.35799i	−0.734142	−	0.678996i	$-0.762415\pi$
$379$		−	514.679i		−	1.35799i	0.734142	−	0.678996i	$-0.237585\pi$
$380$	−269.689	+	193.007i	−0.709709	+	0.507913i
$381$	−88.7260	−	153.678i	−0.232877	−	0.403354i
$382$	−85.4361	−	266.183i	−0.223655	−	0.696813i
$383$	450.193	+	259.919i	1.17544	+	0.678639i	0.954955	−	0.296752i	$-0.0959033\pi$
$383$	450.193	+	259.919i	1.17544	+	0.678639i	0.220483	+	0.975391i	$0.429237\pi$
$384$	−39.4223	−	493.773i	−0.102662	−	1.28587i
$385$	−54.0657	+	474.771i	−0.140430	+	1.23317i
$386$	−44.8103	−	9.69244i	−0.116089	−	0.0251100i
$387$	412.992	+	238.441i	1.06716	+	0.616127i
$388$	−632.288	+	61.8842i	−1.62961	+	0.159495i
$389$	91.3278	−	52.7281i	0.234776	−	0.135548i	−0.377997	−	0.925807i	$-0.623387\pi$
$389$	91.3278	−	52.7281i	0.234776	−	0.135548i	0.612773	+	0.790259i	$0.290054\pi$
$390$	309.127	−	340.859i	0.792632	−	0.873997i
$391$		−	172.982i		−	0.442410i
$392$	−254.019	−	298.561i	−0.648006	−	0.761635i
$393$	−468.241			−1.19145
$394$	−426.355	−	386.663i	−1.08212	−	0.981379i
$395$	−319.957	−	554.182i	−0.810018	−	1.40299i
$396$	347.180	−	33.9797i	0.876717	−	0.0858072i
$397$	−185.762	+	321.749i	−0.467914	+	0.810450i	−0.999328	−	0.0366619i	$-0.988328\pi$
$397$	−185.762	+	321.749i	−0.467914	+	0.810450i	0.531414	+	0.847112i	$0.321661\pi$
$398$	−27.6872	+	128.004i	−0.0695659	+	0.321618i
$399$	477.063	+	54.3267i	1.19565	+	0.136157i
$400$	−32.8652	−	37.5682i	−0.0821629	−	0.0939206i
$401$	−149.636	+	259.177i	−0.373157	+	0.646327i	−0.990049	−	0.140721i	$-0.955058\pi$
$401$	−149.636	+	259.177i	−0.373157	+	0.646327i	0.616893	+	0.787047i	$0.288391\pi$
$402$	299.793	−	96.2238i	0.745753	−	0.239363i
$403$	319.446	−	184.433i	0.792671	−	0.457649i
$404$	226.475	−	162.080i	0.560582	−	0.401188i
$405$	−463.421			−1.14425
$406$	327.992	+	373.368i	0.807861	+	0.919626i
$407$	178.287			0.438052
$408$	−239.887	−	554.747i	−0.587958	−	1.35967i
$409$	−17.6410	+	10.1850i	−0.0431320	+	0.0249023i	−0.521411	−	0.853306i	$-0.674594\pi$
$409$	−17.6410	+	10.1850i	−0.0431320	+	0.0249023i	0.478279	+	0.878208i	$0.341261\pi$
$410$	196.774	−	63.1580i	0.479935	−	0.154044i
$411$	281.033	−	486.764i	0.683780	−	1.18434i
$412$	32.4324	−	71.4635i	0.0787195	−	0.173455i
$413$	6.71929	+	15.4509i	0.0162695	+	0.0374113i
$414$	−103.509	−	22.3890i	−0.250023	−	0.0540798i
$415$	116.927	−	202.524i	0.281753	−	0.488010i
$416$	−209.632	+	348.540i	−0.503924	+	0.837836i
$417$	−167.083	−	289.396i	−0.400678	−	0.693994i
$418$	383.207	+	347.533i	0.916764	+	0.831418i
$419$	−183.085			−0.436956			−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−183.085			−0.436956			−0.218478	+	0.975842i	$0.570109\pi$
$420$	8.02131	−	506.790i	0.0190984	−	1.20664i
$421$			293.022i			0.696014i	0.937492	+	0.348007i	$0.113141\pi$
$421$			293.022i			0.696014i	−0.937492	+	0.348007i	$0.886859\pi$
$422$	−26.5165	−	24.0479i	−0.0628352	−	0.0569856i
$423$	218.147	−	125.947i	0.515714	−	0.297748i
$424$	287.300	+	33.3186i	0.677595	+	0.0785815i
$425$	−52.7438	−	30.4517i	−0.124103	−	0.0716510i
$426$	171.096	+	37.0081i	0.401634	+	0.0868734i
$427$	−121.759	+	164.568i	−0.285150	+	0.385405i
$428$	−73.9732	+	162.997i	−0.172835	+	0.380834i
$429$	−621.636	−	358.902i	−1.44903	−	0.836601i
$430$	710.834	−	228.155i	1.65310	−	0.530593i
$431$	37.6108	+	65.1439i	0.0872641	+	0.151146i	0.906354	−	0.422520i	$-0.138854\pi$
$431$	37.6108	+	65.1439i	0.0872641	+	0.151146i	−0.819090	+	0.573666i	$0.805521\pi$
$432$	183.689	−	36.3043i	0.425207	−	0.0840378i
$433$		−	506.209i		−	1.16907i	−0.811367	−	0.584536i	$-0.801276\pi$
$433$		−	506.209i		−	1.16907i	0.811367	−	0.584536i	$-0.198724\pi$
$434$	130.276	−	384.845i	0.300175	−	0.886740i
$435$			642.583i			1.47720i
$436$	−131.771	−	184.124i	−0.302227	−	0.422303i
$437$	−78.5269	−	136.013i	−0.179696	−	0.311242i
$438$	−562.978	+	180.698i	−1.28534	+	0.412553i
$439$	−141.358	−	81.6130i	−0.322000	−	0.185907i	0.330284	−	0.943882i	$-0.392856\pi$
$439$	−141.358	−	81.6130i	−0.322000	−	0.185907i	−0.652284	+	0.757975i	$0.726189\pi$
$440$	325.715	−	438.334i	0.740262	−	0.996214i
$441$	−199.680	+	214.180i	−0.452788	+	0.485668i
$442$	−104.915	+	485.047i	−0.237365	+	1.09739i
$443$	−98.4732	−	56.8535i	−0.222287	−	0.128338i	0.384722	−	0.923033i	$-0.374297\pi$
$443$	−98.4732	−	56.8535i	−0.222287	−	0.128338i	−0.607009	+	0.794695i	$0.707631\pi$
$444$	−188.213	+	18.4211i	−0.423903	+	0.0414889i
$445$	−4.53742	+	2.61968i	−0.0101964	+	0.00588692i
$446$	383.667	+	347.949i	0.860239	+	0.780155i
$447$		−	846.952i		−	1.89475i
$448$	79.8962	+	440.818i	0.178340	+	0.983969i
$449$	391.120			0.871091			0.435546	−	0.900167i	$-0.356555\pi$
$449$	391.120			0.871091			0.435546	+	0.900167i	$0.356555\pi$
$450$	−25.0483	+	27.6196i	−0.0556629	+	0.0613768i
$451$	−161.186	−	279.183i	−0.357398	−	0.619031i
$452$	73.4972	+	750.942i	0.162604	+	1.66138i
$453$	−161.201	+	279.208i	−0.355851	+	0.616353i
$454$	−229.384	−	49.6157i	−0.505251	−	0.109286i
$455$	−247.531	+	334.559i	−0.544025	+	0.735296i
$456$	−440.451	−	327.288i	−0.965900	−	0.717736i
$457$	−286.893	+	496.913i	−0.627774	+	1.08734i	0.360223	+	0.932866i	$0.382701\pi$
$457$	−286.893	+	496.913i	−0.627774	+	1.08734i	−0.987997	+	0.154471i	$0.950633\pi$
$458$	−53.2345	−	165.856i	−0.116232	−	0.362131i
$459$	197.855	−	114.231i	0.431056	−	0.248870i
$460$	−134.821	+	96.4863i	−0.293088	+	0.209753i
$461$	847.131			1.83759			0.918797	−	0.394729i	$-0.129162\pi$
$461$	847.131			1.83759			0.918797	+	0.394729i	$0.129162\pi$
$462$	−775.324	+	154.900i	−1.67819	+	0.335282i
$463$	109.055			0.235539			0.117770	−	0.993041i	$-0.462426\pi$
$463$	109.055			0.235539			0.117770	+	0.993041i	$0.462426\pi$
$464$	−110.123	−	557.191i	−0.237335	−	1.20084i
$465$	454.958	−	262.670i	0.978404	−	0.564882i
$466$	−190.488	−	593.480i	−0.408773	−	1.27356i
$467$	−321.205	+	556.343i	−0.687805	+	1.19131i	0.284741	+	0.958604i	$0.408092\pi$
$467$	−321.205	+	556.343i	−0.687805	+	1.19131i	−0.972546	+	0.232709i	$0.925241\pi$
$468$	276.664	+	125.559i	0.591162	+	0.268288i
$469$	−261.138	+	113.564i	−0.556798	+	0.242141i
$470$	83.3671	−	385.424i	0.177377	−	0.820051i
$471$	−68.5771	+	118.779i	−0.145599	+	0.252185i
$472$	2.21823	−	19.1275i	0.00469965	−	0.0405243i
$473$	−582.278	−	1008.53i	−1.23103	−	2.13221i
$474$	711.300	−	784.316i	1.50063	−	1.65468i
$475$	−55.2952			−0.116411
$476$	265.786	+	477.657i	0.558375	+	1.00348i
$477$		−	216.050i		−	0.452936i
$478$	−189.206	+	208.628i	−0.395828	+	0.436461i
$479$	−367.909	+	212.412i	−0.768077	+	0.443449i	−0.832188	−	0.554493i	$-0.812912\pi$
$479$	−367.909	+	212.412i	−0.768077	+	0.443449i	0.0641112	+	0.997943i	$0.479579\pi$
$480$	−298.560	+	496.392i	−0.621999	+	1.03415i
$481$	134.476	+	77.6397i	0.279576	+	0.161413i
$482$	−20.3323	+	94.0004i	−0.0421831	+	0.195022i
$483$	238.489	+	27.1585i	0.493766	+	0.0562288i
$484$	−334.987	−	152.028i	−0.692122	−	0.314107i
$485$	643.403	+	371.469i	1.32660	+	0.765915i
$486$	−169.963	−	529.534i	−0.349719	−	1.08958i
$487$	−388.616	−	673.103i	−0.797980	−	1.38214i	−0.920929	−	0.389729i	$-0.872569\pi$
$487$	−388.616	−	673.103i	−0.797980	−	1.38214i	0.122949	−	0.992413i	$-0.460765\pi$
$488$	214.742	−	92.8598i	0.440044	−	0.190286i
$489$			40.4588i			0.0827379i
$490$	38.3709	+	456.800i	0.0783081	+	0.932245i
$491$			476.370i			0.970203i	0.874458	+	0.485102i	$0.161217\pi$
$491$			476.370i			0.970203i	−0.874458	+	0.485102i	$0.838783\pi$
$492$	199.006	+	278.072i	0.404485	+	0.565188i
$493$	−346.502	−	600.160i	−0.702845	−	1.21736i
$494$	137.698	+	429.010i	0.278742	+	0.868442i
$495$	−353.283	−	203.968i	−0.713702	−	0.412056i
$496$	−349.484	+	305.733i	−0.704605	+	0.616397i
$497$	−157.305	−	17.9135i	−0.316509	−	0.0360432i
$498$	378.197	+	81.8039i	0.759432	+	0.164265i
$499$	−377.065	−	217.698i	−0.755641	−	0.436269i	0.0720876	−	0.997398i	$-0.477034\pi$
$499$	−377.065	−	217.698i	−0.755641	−	0.436269i	−0.827728	+	0.561129i	$0.810367\pi$
$500$	51.2497	+	523.633i	0.102499	+	1.04727i
$501$	264.374	−	152.636i	0.527693	−	0.304663i
$502$	204.330	−	225.305i	0.407031	−	0.448814i
$503$			375.404i			0.746329i	0.927765	+	0.373165i	$0.121727\pi$
$503$			375.404i			0.746329i	−0.927765	+	0.373165i	$0.878273\pi$
$504$	320.222	−	97.2186i	0.635360	−	0.192894i
$505$	−325.678			−0.644907
$506$	191.570	+	173.735i	0.378596	+	0.343351i
$507$	14.4185	+	24.9735i	0.0284388	+	0.0492574i
$508$	−17.8664	−	182.546i	−0.0351701	−	0.359343i
$509$	73.9117	−	128.019i	0.145210	−	0.251510i	−0.784242	−	0.620456i	$-0.786948\pi$
$509$	73.9117	−	128.019i	0.145210	−	0.251510i	0.929451	+	0.368945i	$0.120281\pi$
$510$	−149.421	+	690.807i	−0.292983	+	1.35452i
$511$	490.389	−	213.261i	0.959666	−	0.417340i
$512$	173.815	−	481.594i	0.339482	−	0.940613i
$513$	103.713	−	179.636i	0.202169	−	0.350167i
$514$	277.400	−	89.0365i	0.539689	−	0.173223i
$515$	−79.4784	+	45.8869i	−0.154327	+	0.0891007i
$516$	718.901	+	1004.52i	1.39322	+	1.94675i
$517$	−615.131			−1.18981
$518$	167.723	−	33.5090i	0.323789	−	0.0646892i
$519$	−742.404			−1.43045
$520$	436.560	−	188.780i	0.839539	−	0.363038i
$521$	755.302	−	436.074i	1.44972	−	0.836994i	0.451253	−	0.892396i	$-0.350977\pi$
$521$	755.302	−	436.074i	1.44972	−	0.836994i	0.998464	+	0.0554019i	$0.0176440\pi$
$522$	−403.972	+	129.662i	−0.773892	+	0.248395i
$523$	−178.600	+	309.344i	−0.341491	+	0.591480i	−0.984710	−	0.174202i	$-0.944265\pi$
$523$	−178.600	+	309.344i	−0.341491	+	0.591480i	0.643219	+	0.765683i	$0.277599\pi$
$524$	−440.723	−	200.014i	−0.841074	−	0.381706i
$525$	50.2642	−	67.9364i	0.0957414	−	0.129403i
$526$	−690.811	−	149.422i	−1.31333	−	0.284072i
$527$	−283.281	+	490.657i	−0.537535	+	0.931038i
$528$	855.286	+	291.499i	1.61986	+	0.552081i
$529$	225.244	+	390.133i	0.425791	+	0.737492i
$530$	−250.538	−	227.214i	−0.472713	−	0.428705i
$531$	−14.3839			−0.0270883
$532$	425.819	+	254.916i	0.800412	+	0.479166i
$533$		−	280.771i		−	0.526776i
$534$	−6.42167	−	5.82384i	−0.0120256	−	0.0109061i
$535$	181.278	−	104.661i	0.338836	−	0.195627i
$536$	323.277	+	37.4908i	0.603128	+	0.0699455i
$537$	−234.293	−	135.269i	−0.436299	−	0.251897i
$538$	260.570	+	56.3613i	0.484331	+	0.104761i
$539$	683.808	−	209.147i	1.26866	−	0.388028i
$540$	−199.390	−	90.4898i	−0.369241	−	0.167574i
$541$	807.198	+	466.036i	1.49205	+	0.861434i	0.999958	−	0.00911085i	$-0.00290011\pi$
$541$	807.198	+	466.036i	1.49205	+	0.861434i	0.492089	+	0.870545i	$0.336233\pi$
$542$	−717.597	+	230.326i	−1.32398	+	0.424955i
$543$	664.912	+	1151.66i	1.22452	+	2.12092i
$544$	11.1773	−	624.614i	0.0205465	−	1.14819i
$545$			264.776i			0.485827i
$546$	−652.257	−	220.799i	−1.19461	−	0.404394i
$547$			151.397i			0.276778i	0.990378	+	0.138389i	$0.0441924\pi$
$547$			151.397i			0.276778i	−0.990378	+	0.138389i	$0.955808\pi$
$548$	472.443	−	338.110i	0.862123	−	0.616990i
$549$	−87.3832	−	151.352i	−0.159168	−	0.275687i
$550$	86.6971	−	27.8270i	0.157631	−	0.0505945i
$551$	−544.896	−	314.596i	−0.988922	−	0.570954i
$552$	−220.186	−	163.615i	−0.398888	−	0.296403i
$553$	−569.569	+	769.821i	−1.02996	+	1.39208i
$554$	−32.9453	+	152.313i	−0.0594681	+	0.274934i
$555$	191.522	+	110.575i	0.345084	+	0.199234i
$556$	−33.6448	−	343.759i	−0.0605123	−	0.618271i
$557$	−775.593	+	447.789i	−1.39245	+	0.803929i	−0.993586	−	0.113082i	$-0.963928\pi$
$557$	−775.593	+	447.789i	−1.39245	+	0.803929i	−0.398861	+	0.917011i	$0.630594\pi$
$558$	256.935	+	233.016i	0.460457	+	0.417591i
$559$		−	1014.27i		−	1.81444i
$560$	224.030	−	473.579i	0.400054	−	0.845677i
$561$	1102.52			1.96527
$562$	436.075	−	480.838i	0.775933	−	0.855584i
$563$	−139.958	−	242.414i	−0.248592	−	0.430575i	0.714543	−	0.699591i	$-0.246635\pi$
$563$	−139.958	−	242.414i	−0.248592	−	0.430575i	−0.963136	+	0.269017i	$0.913301\pi$
$564$	649.378	−	63.5569i	1.15138	−	0.112689i
$565$	441.177	−	764.142i	0.780845	−	1.35246i
$566$	585.425	+	126.627i	1.03432	+	0.223723i
$567$	276.569	+	635.966i	0.487776	+	1.12163i
$568$	145.232	+	107.919i	0.255691	+	0.189998i
$569$	−160.963	+	278.796i	−0.282887	+	0.489975i	−0.972095	−	0.234589i	$-0.924626\pi$
$569$	−160.963	+	278.796i	−0.282887	+	0.489975i	0.689207	+	0.724564i	$0.257959\pi$
$570$	196.111	+	610.999i	0.344055	+	1.07193i
$571$	−712.583	+	411.410i	−1.24796	+	0.720508i	−0.970702	−	0.240288i	$-0.922758\pi$
$571$	−712.583	+	411.410i	−1.24796	+	0.720508i	−0.277255	+	0.960796i	$0.589425\pi$
$572$	−431.794	−	603.347i	−0.754884	−	1.05480i
$573$	−540.928			−0.944027
$574$	−204.108	−	232.345i	−0.355588	−	0.404783i
$575$	−27.6427			−0.0480742
$576$	−372.310	−	87.5318i	−0.646372	−	0.151965i
$577$	833.162	−	481.027i	1.44396	−	0.833668i	0.445845	−	0.895110i	$-0.352903\pi$
$577$	833.162	−	481.027i	1.44396	−	0.833668i	0.998111	+	0.0614420i	$0.0195699\pi$
$578$	−56.3064	−	175.427i	−0.0974158	−	0.303506i
$579$	−44.3551	+	76.8253i	−0.0766064	+	0.132686i
$580$	−274.486	+	604.818i	−0.473251	+	1.04279i
$581$	−347.712	−	39.5966i	−0.598472	−	0.0681524i
$582$	−259.884	+	1201.50i	−0.446536	+	2.06443i
$583$	−263.800	+	456.914i	−0.452486	+	0.783729i
$584$	−607.079	−	70.4037i	−1.03952	−	0.120554i
$585$	−177.646	−	307.692i	−0.303669	−	0.525970i
$586$	−109.803	+	121.075i	−0.187378	+	0.206612i
$587$	885.638			1.50875			0.754377	−	0.656442i	$-0.227939\pi$
$587$	885.638			1.50875			0.754377	+	0.656442i	$0.227939\pi$
$588$	−700.269	+	291.444i	−1.19093	+	0.495653i
$589$			514.392i			0.873331i
$590$	−15.1271	+	16.6799i	−0.0256392	+	0.0282711i
$591$	−964.496	+	556.852i	−1.63197	+	0.942220i
$592$	−185.020	−	63.0587i	−0.312535	−	0.106518i
$593$	290.818	+	167.904i	0.490418	+	0.283143i	0.724748	−	0.689014i	$-0.241956\pi$
$593$	290.818	+	167.904i	0.490418	+	0.283143i	−0.234330	+	0.972157i	$0.575290\pi$
$594$	−72.2102	+	333.843i	−0.121566	+	0.562025i
$595$	72.3263	−	635.124i	0.121557	−	1.06743i
$596$	361.784	−	797.176i	0.607020	−	1.33754i
$597$	219.457	+	126.704i	0.367600	+	0.212234i
$598$	68.8370	+	214.467i	0.115112	+	0.358640i
$599$	30.1532	+	52.2269i	0.0503393	+	0.0871902i	0.890097	−	0.455771i	$-0.150636\pi$
$599$	30.1532	+	52.2269i	0.0503393	+	0.0871902i	−0.839758	+	0.542961i	$0.817303\pi$
$600$	−88.6489	+	38.3340i	−0.147748	+	0.0638901i
$601$			509.153i			0.847176i	0.905855	+	0.423588i	$0.139230\pi$
$601$			509.153i			0.847176i	−0.905855	+	0.423588i	$0.860770\pi$
$602$	−737.329	−	839.336i	−1.22480	−	1.39425i
$603$		−	243.105i		−	0.403159i
$604$	−270.993	+	193.940i	−0.448664	+	0.321093i
$605$	215.096	+	372.557i	0.355530	+	0.615797i
$606$	−164.687	−	513.094i	−0.271760	−	0.846690i
$607$	−900.363	−	519.825i	−1.48330	−	0.856384i	−0.483480	−	0.875355i	$-0.660627\pi$
$607$	−900.363	−	519.825i	−1.48330	−	0.856384i	−0.999820	+	0.0189717i	$0.993961\pi$
$608$	−274.761	−	496.196i	−0.451909	−	0.816111i
$609$	881.835	−	383.493i	1.44800	−	0.629709i
$610$	−267.410	−	57.8407i	−0.438377	−	0.0948209i
$611$	−463.973	−	267.875i	−0.759366	−	0.438420i
$612$	−464.439	+	45.4562i	−0.758888	+	0.0742749i
$613$	−172.277	+	99.4641i	−0.281039	+	0.162258i	−0.633894	−	0.773420i	$-0.718544\pi$
$613$	−172.277	+	99.4641i	−0.281039	+	0.162258i	0.352855	+	0.935678i	$0.385211\pi$
$614$	−486.278	+	536.196i	−0.791984	+	0.873283i
$615$		−	399.876i		−	0.650206i
$616$	−795.925	−	185.391i	−1.29209	−	0.300959i
$617$	136.689			0.221538			0.110769	−	0.993846i	$-0.464669\pi$
$617$	136.689			0.221538			0.110769	+	0.993846i	$0.464669\pi$
$618$	−112.483	−	102.012i	−0.182012	−	0.165067i
$619$	230.938	+	399.997i	0.373083	+	0.646199i	0.990038	−	0.140799i	$-0.0449673\pi$
$619$	230.938	+	399.997i	0.373083	+	0.646199i	−0.616955	+	0.786998i	$0.711634\pi$
$620$	540.422	−	52.8929i	0.871648	−	0.0853111i
$621$	51.8472	−	89.8019i	0.0834898	−	0.144609i
$622$	79.8301	−	369.072i	0.128344	−	0.593363i
$623$	6.30299	+	4.66341i	0.0101172	+	0.00748541i
$624$	518.173	+	592.324i	0.830406	+	0.949238i
$625$	268.638	−	465.294i	0.429821	−	0.744471i
$626$	−48.9177	+	15.7010i	−0.0781432	+	0.0250815i
$627$	866.888	−	500.498i	1.38260	−	0.798242i
$628$	−115.284	+	82.5049i	−0.183574	+	0.131377i
$629$	−238.503			−0.379178
$630$	−370.685	−	125.482i	−0.588389	−	0.199179i
$631$	1042.33			1.65187			0.825933	−	0.563768i	$-0.190649\pi$
$631$	1042.33			1.65187			0.825933	+	0.563768i	$0.190649\pi$
$632$	1004.53	−	434.382i	1.58944	−	0.687314i
$633$	−59.9853	+	34.6325i	−0.0947635	+	0.0547117i
$634$	−950.495	+	305.079i	−1.49920	+	0.481196i
$635$	−107.246	+	185.755i	−0.168891	+	0.292528i
$636$	231.277	−	509.609i	0.363643	−	0.801273i
$637$	606.852	+	140.029i	0.952672	+	0.219826i
$638$	1012.66	+	219.038i	1.58724	+	0.343319i
$639$	67.5803	−	117.052i	0.105759	−	0.183181i
$640$	−493.052	+	339.686i	−0.770394	+	0.530760i
$641$	−61.3334	−	106.233i	−0.0956840	−	0.165730i	0.814210	−	0.580571i	$-0.197170\pi$
$641$	−61.3334	−	106.233i	−0.0956840	−	0.165730i	−0.909894	+	0.414841i	$0.863837\pi$
$642$	256.556	+	232.672i	0.399621	+	0.362418i
$643$	720.813			1.12102			0.560508	−	0.828149i	$-0.310606\pi$
$643$	720.813			1.12102			0.560508	+	0.828149i	$0.310606\pi$
$644$	212.872	+	127.435i	0.330546	+	0.197881i
$645$		−	1444.53i		−	2.23959i
$646$	−512.635	−	464.911i	−0.793553	−	0.719677i
$647$	510.825	−	294.925i	0.789528	−	0.455834i	−0.0502683	−	0.998736i	$-0.516008\pi$
$647$	510.825	−	294.925i	0.789528	−	0.455834i	0.839796	+	0.542901i	$0.182674\pi$
$648$	91.3036	−	787.296i	0.140901	−	1.21496i
$649$	30.4198	+	17.5629i	0.0468717	+	0.0270614i
$650$	77.5108	+	16.7656i	0.119247	+	0.0257932i
$651$	−631.988	−	467.590i	−0.970796	−	0.718265i
$652$	−17.2824	+	38.0810i	−0.0265067	+	0.0584065i
$653$	−215.294	−	124.300i	−0.329700	−	0.190352i	0.326008	−	0.945367i	$-0.394296\pi$
$653$	−215.294	−	124.300i	−0.329700	−	0.190352i	−0.655708	+	0.755015i	$0.727630\pi$
$654$	−417.145	+	133.890i	−0.637836	+	0.204725i
$655$	282.989	+	490.151i	0.432044	+	0.748322i
$656$	68.5292	+	346.738i	0.104465	+	0.528563i
$657$			456.524i			0.694862i
$658$	−578.682	+	115.614i	−0.879456	+	0.175705i
$659$		−	640.918i		−	0.972562i	−0.873802	−	0.486281i	$-0.838353\pi$
$659$		−	640.918i		−	0.972562i	0.873802	−	0.486281i	$-0.161647\pi$
$660$	−614.963	−	859.291i	−0.931762	−	1.30196i
$661$	483.321	+	837.137i	0.731197	+	1.26647i	0.956372	+	0.292152i	$0.0943712\pi$
$661$	483.321	+	837.137i	0.731197	+	1.26647i	−0.225175	+	0.974318i	$0.572295\pi$
$662$	475.810	−	152.720i	0.718746	−	0.230694i
$663$	831.593	+	480.120i	1.25429	+	0.724163i
$664$	321.027	+	238.547i	0.483474	+	0.359257i
$665$	−231.451	−	532.218i	−0.348047	−	0.800328i
$666$	−30.8694	+	142.716i	−0.0463504	+	0.214288i
$667$	−272.399	−	157.270i	−0.408395	−	0.235787i
$668$	314.037	−	30.7358i	0.470115	−	0.0460117i
$669$	867.927	−	501.098i	1.29735	−	0.749025i
$670$	−281.911	−	255.666i	−0.420762	−	0.381591i
$671$			426.783i			0.636040i
$672$	859.394	+	113.475i	1.27886	+	0.168862i
$673$	−754.537			−1.12115			−0.560577	−	0.828102i	$-0.689421\pi$
$673$	−754.537			−1.12115			−0.560577	+	0.828102i	$0.689421\pi$
$674$	−113.403	+	125.044i	−0.168253	+	0.185525i
$675$	−18.2543	−	31.6173i	−0.0270433	−	0.0468404i
$676$	2.90339	+	29.6648i	0.00429496	+	0.0438828i
$677$	−380.978	+	659.874i	−0.562745	+	0.974703i	0.434511	+	0.900667i	$0.356921\pi$
$677$	−380.978	+	659.874i	−0.562745	+	0.974703i	−0.997256	+	0.0740362i	$0.976412\pi$
$678$	1426.97	+	308.653i	2.10468	+	0.455241i
$679$	125.795	−	1104.65i	0.185265	−	1.62688i
$680$	−435.725	+	586.381i	−0.640772	+	0.862325i
$681$	−227.054	+	393.269i	−0.333413	+	0.577488i
$682$	−258.865	−	806.513i	−0.379567	−	1.18257i
$683$	−657.604	+	379.668i	−0.962817	+	0.555883i	−0.897039	−	0.441952i	$-0.854286\pi$
$683$	−657.604	+	379.668i	−0.962817	+	0.555883i	−0.0657781	+	0.997834i	$0.520953\pi$
$684$	−344.544	+	246.578i	−0.503720	+	0.360494i
$685$	−679.387			−0.991806
$686$	603.980	−	325.275i	0.880437	−	0.474162i
$687$	−337.047			−0.490607
$688$	247.558	+	1252.57i	0.359823	+	1.82060i
$689$	−397.951	+	229.757i	−0.577577	+	0.333464i
$690$	98.0381	+	305.445i	0.142084	+	0.442674i
$691$	−245.076	+	424.484i	−0.354669	+	0.614304i	−0.987061	−	0.160344i	$-0.948740\pi$
$691$	−245.076	+	424.484i	−0.354669	+	0.614304i	0.632393	+	0.774648i	$0.282073\pi$
$692$	−698.773	−	317.125i	−1.00979	−	0.458274i
$693$	−69.0721	+	606.548i	−0.0996711	+	0.875249i
$694$	159.509	−	737.443i	0.229840	−	1.06260i
$695$	−201.958	+	349.801i	−0.290587	+	0.503311i
$696$	−1091.67	−	126.602i	−1.56849	−	0.181900i
$697$	215.627	+	373.477i	0.309364	+	0.535835i
$698$	537.687	−	592.882i	0.770326	−	0.849401i
$699$	−1206.05			−1.72539
$700$	76.3299	−	42.4728i	0.109043	−	0.0606755i
$701$		−	577.533i		−	0.823870i	−0.911213	−	0.411935i	$-0.864853\pi$
$701$		−	577.533i		−	0.823870i	0.911213	−	0.411935i	$-0.135147\pi$
$702$	−199.846	+	220.361i	−0.284682	+	0.313905i
$703$	−187.530	+	108.271i	−0.266757	+	0.154012i
$704$	680.504	+	639.711i	0.966624	+	0.908681i
$705$	−660.793	−	381.509i	−0.937295	−	0.541148i
$706$	125.131	−	578.506i	0.177239	−	0.819413i
$707$	194.364	+	446.937i	0.274914	+	0.632160i
$708$	−33.9280	−	15.3976i	−0.0479209	−	0.0217481i
$709$	−615.814	−	355.540i	−0.868567	−	0.501467i	−0.00169497	−	0.999999i	$-0.500540\pi$
$709$	−615.814	−	355.540i	−0.868567	−	0.501467i	−0.866872	+	0.498531i	$0.833873\pi$
$710$	−64.6649	−	201.468i	−0.0910774	−	0.283758i
$711$	−408.764	−	708.000i	−0.574914	−	0.995781i
$712$	−3.55655	−	8.22465i	−0.00499516	−	0.0115515i
$713$			257.150i			0.360659i
$714$	1037.19	−	207.218i	1.45265	−	0.290221i
$715$			867.631i			1.21347i
$716$	−162.742	−	227.399i	−0.227293	−	0.317597i
$717$	272.484	+	471.957i	0.380034	+	0.658238i
$718$	−125.407	−	390.715i	−0.174662	−	0.544171i
$719$	−150.440	−	86.8564i	−0.209235	−	0.120802i	0.391721	−	0.920084i	$-0.371880\pi$
$719$	−150.440	−	86.8564i	−0.209235	−	0.120802i	−0.600956	+	0.799282i	$0.705213\pi$
$720$	294.484	+	336.625i	0.409005	+	0.467534i
$721$	110.404	+	81.6852i	0.153127	+	0.113294i
$722$	91.5551	+	19.8033i	0.126808	+	0.0274285i
$723$	161.160	+	93.0457i	0.222904	+	0.128694i
$724$	133.891	+	1368.00i	0.184932	+	1.88951i
$725$	−95.9059	+	55.3713i	−0.132284	+	0.0763742i
$726$	−478.182	+	527.268i	−0.658653	+	0.726265i
$727$			1056.57i			1.45333i	0.686993	+	0.726664i	$0.258930\pi$
$727$			1056.57i			1.45333i	−0.686993	+	0.726664i	$0.741070\pi$
$728$	−519.607	−	486.441i	−0.713746	−	0.668188i
$729$	−184.457			−0.253028
$730$	529.398	+	480.113i	0.725202	+	0.657689i
$731$	778.941	+	1349.17i	1.06558	+	1.84564i
$732$	−44.0963	−	450.544i	−0.0602408	−	0.615497i
$733$	115.299	−	199.703i	0.157297	−	0.272446i	−0.776596	−	0.629999i	$-0.783055\pi$
$733$	115.299	−	199.703i	0.157297	−	0.272446i	0.933893	+	0.357553i	$0.116389\pi$
$734$	−149.505	+	691.192i	−0.203685	+	0.941679i
$735$	864.283	+	199.431i	1.17589	+	0.271334i
$736$	−137.356	−	248.054i	−0.186625	−	0.337029i
$737$	−296.833	+	514.130i	−0.402758	+	0.697598i
$738$	251.390	−	80.6881i	0.340637	−	0.109333i
$739$	77.4971	−	44.7430i	0.104868	−	0.0605453i	−0.446649	−	0.894709i	$-0.647383\pi$
$739$	77.4971	−	44.7430i	0.104868	−	0.0605453i	0.551517	+	0.834164i	$0.314049\pi$
$740$	133.032	+	185.887i	0.179774	+	0.251198i
$741$	871.820			1.17654
$742$	−162.291	+	479.421i	−0.218722	+	0.646120i
$743$	−236.120			−0.317793			−0.158897	−	0.987295i	$-0.550794\pi$
$743$	−236.120			−0.317793			−0.158897	+	0.987295i	$0.550794\pi$
$744$	356.608	+	824.669i	0.479312	+	1.10843i
$745$	−886.581	+	511.868i	−1.19004	+	0.687071i
$746$	681.798	−	218.835i	0.913938	−	0.293345i
$747$	149.382	−	258.737i	0.199976	−	0.346368i
$748$	1037.72	+	470.952i	1.38733	+	0.629614i
$749$	−251.815	−	186.311i	−0.336202	−	0.248746i
$750$	995.029	+	215.224i	1.32671	+	0.286966i
$751$	717.692	−	1243.08i	0.955649	−	1.65523i	0.222772	−	0.974871i	$-0.428490\pi$
$751$	717.692	−	1243.08i	0.955649	−	1.65523i	0.732877	−	0.680361i	$-0.238177\pi$
$752$	638.363	+	217.567i	0.848887	+	0.289318i
$753$	−294.265	−	509.682i	−0.390790	−	0.676868i
$754$	668.429	+	606.201i	0.886510	+	0.803981i
$755$	389.696			0.516154
$756$	−5.18568	+	327.633i	−0.00685936	+	0.433377i
$757$		−	692.645i		−	0.914987i	−0.889213	−	0.457494i	$-0.848747\pi$
$757$		−	692.645i		−	0.914987i	0.889213	−	0.457494i	$-0.151253\pi$
$758$	−762.493	−	691.508i	−1.00593	−	0.912280i
$759$	433.367	−	250.204i	0.570971	−	0.329650i
$760$	−76.4089	+	658.861i	−0.100538	+	0.866923i
$761$	−999.810	−	577.241i	−1.31381	−	0.758529i	−0.331086	−	0.943601i	$-0.607415\pi$
$761$	−999.810	−	577.241i	−1.31381	−	0.758529i	−0.982725	+	0.185071i	$0.940748\pi$
$762$	−346.882	−	75.0305i	−0.455226	−	0.0984652i
$763$	363.359	−	158.018i	0.476224	−	0.207101i
$764$	−509.137	−	231.063i	−0.666410	−	0.302438i
$765$	472.603	+	272.858i	0.617782	+	0.356677i
$766$	989.933	−	317.737i	1.29234	−	0.414800i
$767$	15.2964	+	26.4942i	0.0199432	+	0.0345426i
$768$	−784.487	−	605.016i	−1.02147	−	0.787781i
$769$		−	894.095i		−	1.16267i	−0.813663	−	0.581336i	$-0.802530\pi$
$769$		−	894.095i		−	1.16267i	0.813663	−	0.581336i	$-0.197470\pi$
$770$	630.727	+	717.986i	0.819126	+	0.932449i
$771$		−	563.723i		−	0.731158i
$772$	−74.5650	+	53.3635i	−0.0965868	+	0.0691237i
$773$	−464.538	−	804.603i	−0.600954	−	1.04088i	−0.992677	−	0.120800i	$-0.961454\pi$
$773$	−464.538	−	804.603i	−0.600954	−	1.04088i	0.391722	−	0.920083i	$-0.371879\pi$
$774$	908.133	−	291.482i	1.17330	−	0.376591i
$775$	78.4073	+	45.2685i	0.101171	+	0.0584109i
$776$	−757.844	+	1019.88i	−0.976603	+	1.31427i
$777$	37.4454	−	328.822i	0.0481922	−	0.423194i
$778$	44.5892	−	206.145i	0.0573126	−	0.264968i
$779$	339.086	+	195.772i	0.435284	+	0.251311i
$780$	−89.6458	−	915.936i	−0.114930	−	1.17428i
$781$	−285.844	+	165.032i	−0.365998	+	0.211309i
$782$	−256.272	−	232.414i	−0.327713	−	0.297205i
$783$		−	415.422i		−	0.530552i
$784$	−783.607	−	24.8116i	−0.999499	−	0.0316474i
$785$	165.782			0.211188
$786$	−629.116	+	693.695i	−0.800402	+	0.882564i
$787$	−693.013	−	1200.33i	−0.880576	−	1.52520i	−0.850702	−	0.525649i	$-0.823823\pi$
$787$	−693.013	−	1200.33i	−0.880576	−	1.52520i	−0.0298746	−	0.999554i	$-0.509511\pi$
$788$	−1145.68	+	112.131i	−1.45390	+	0.142299i
$789$	−683.794	+	1184.37i	−0.866659	+	1.50110i
$790$	−1250.90	−	270.569i	−1.58342	−	0.342493i
$791$	−1311.95	−	149.401i	−1.65859	−	0.188876i
$792$	416.120	−	559.998i	0.525405	−	0.707068i
$793$	−185.854	+	321.908i	−0.234368	+	0.405937i
$794$	227.084	+	707.497i	0.286000	+	0.891054i
$795$	−566.764	+	327.221i	−0.712910	+	0.411599i
$796$	152.437	+	213.001i	0.191504	+	0.267589i
$797$	388.524			0.487484			0.243742	−	0.969840i	$-0.421625\pi$
$797$	388.524			0.487484			0.243742	+	0.969840i	$0.421625\pi$
$798$	721.453	−	633.773i	0.904076	−	0.794201i
$799$	822.890			1.02990
$800$	−99.8137	−	1.78614i	−0.124767	−	0.00223267i
$801$	−5.79682	+	3.34680i	−0.00723698	+	0.00417827i
$802$	182.922	+	569.907i	0.228082	+	0.710607i
$803$	557.421	−	965.481i	0.694173	−	1.20234i
$804$	260.238	−	573.424i	0.323679	−	0.713214i
$805$	−115.705	−	266.062i	−0.143733	−	0.330512i
$806$	155.964	−	721.055i	0.193504	−	0.894610i
$807$	257.924	−	446.737i	0.319608	−	0.553577i
$808$	64.1653	−	553.287i	0.0794125	−	0.684761i
$809$	−255.112	−	441.867i	−0.315342	−	0.546189i	0.664168	−	0.747583i	$-0.268786\pi$
$809$	−255.112	−	441.867i	−0.315342	−	0.546189i	−0.979510	+	0.201395i	$0.935453\pi$
$810$	−622.639	+	686.554i	−0.768690	+	0.847598i
$811$	54.8689			0.0676558			0.0338279	−	0.999428i	$-0.489230\pi$
$811$	54.8689			0.0676558			0.0338279	+	0.999428i	$0.489230\pi$
$812$	993.822	+	15.7299i	1.22392	+	0.0193718i
$813$			1458.28i			1.79370i
$814$	239.541	−	264.131i	0.294277	−	0.324485i
$815$	42.3519	−	24.4519i	0.0519656	−	0.0300023i
$816$	−1144.16	−	389.952i	−1.40215	−	0.477882i
$817$	1224.93	+	707.215i	1.49931	+	0.865624i
$818$	−8.61291	+	39.8193i	−0.0105292	+	0.0486789i
$819$	−316.236	+	427.420i	−0.386124	+	0.521880i
$820$	170.811	−	376.375i	0.208306	−	0.458995i
$821$	167.045	+	96.4438i	0.203466	+	0.117471i	0.598271	−	0.801294i	$-0.295855\pi$
$821$	167.045	+	96.4438i	0.203466	+	0.117471i	−0.394805	+	0.918765i	$0.629188\pi$
$822$	−343.548	−	1070.35i	−0.417942	−	1.30213i
$823$	−71.3241	−	123.537i	−0.0866636	−	0.150106i	0.819435	−	0.573172i	$-0.194287\pi$
$823$	−71.3241	−	123.537i	−0.0866636	−	0.150106i	−0.906099	+	0.423066i	$0.860954\pi$
$824$	−62.2973	−	144.065i	−0.0756035	−	0.174836i
$825$		−	176.183i		−	0.213555i
$826$	31.9182	+	10.8048i	0.0386419	+	0.0130809i
$827$		−	91.3639i		−	0.110476i	−0.998473	−	0.0552382i	$-0.982408\pi$
$827$		−	91.3639i		−	0.110476i	0.998473	−	0.0552382i	$-0.0175918\pi$
$828$	−172.241	+	123.267i	−0.208021	+	0.148873i
$829$	−232.999	−	403.567i	−0.281061	−	0.486812i	0.690586	−	0.723251i	$-0.257353\pi$
$829$	−232.999	−	403.567i	−0.281061	−	0.486812i	−0.971646	+	0.236439i	$0.924020\pi$
$830$	−142.938	−	445.333i	−0.172214	−	0.536545i
$831$	261.135	+	150.766i	0.314242	+	0.181428i
$832$	234.702	+	778.856i	0.282094	+	0.936125i
$833$	−914.763	+	279.786i	−1.09815	+	0.335877i
$834$	−653.224	−	141.292i	−0.783243	−	0.169415i
$835$	−319.557	−	184.496i	−0.382703	−	0.220954i
$836$	1029.73	−	100.783i	1.23174	−	0.120554i
$837$	−294.125	+	169.813i	−0.351403	+	0.202883i
$838$	−245.987	+	271.238i	−0.293541	+	0.323674i
$839$			24.9426i			0.0297289i	0.999890	+	0.0148645i	$0.00473168\pi$
$839$			24.9426i			0.0297289i	−0.999890	+	0.0148645i	$0.995268\pi$
$840$	−740.027	−	692.792i	−0.880985	−	0.824752i
$841$	−419.114			−0.498352
$842$	434.109	+	393.696i	0.515569	+	0.467572i
$843$	−628.011	−	1087.75i	−0.744972	−	1.29033i
$844$	−71.2535	+	6.97382i	−0.0844236	+	0.00826282i
$845$	17.4280	−	30.1862i	0.0206249	−	0.0357234i
$846$	106.506	−	492.402i	0.125894	−	0.582035i
$847$	382.901	−	517.524i	0.452068	−	0.611008i
$848$	435.370	−	380.867i	0.513408	−	0.449136i
$849$	579.479	−	1003.69i	0.682543	−	1.18220i
$850$	−115.979	+	37.2255i	−0.136446	+	0.0437947i
$851$	−93.7484	+	54.1257i	−0.110163	+	0.0636025i
$852$	284.707	−	203.755i	0.334163	−	0.239149i
$853$	1642.90			1.92603			0.963016	−	0.269445i	$-0.0868403\pi$
$853$	1642.90			1.92603			0.963016	+	0.269445i	$0.0868403\pi$
$854$	80.2137	+	401.494i	0.0939270	+	0.470134i
$855$	495.465			0.579491
$856$	142.090	+	328.589i	0.165993	+	0.383865i
$857$	−130.888	+	75.5681i	−0.152728	+	0.0881775i	−0.574416	−	0.818563i	$-0.694771\pi$
$857$	−130.888	+	75.5681i	−0.152728	+	0.0881775i	0.421688	+	0.906741i	$0.361438\pi$
$858$	−1366.92	+	438.738i	−1.59315	+	0.511350i
$859$	450.007	−	779.435i	0.523873	−	0.907374i	−0.475741	−	0.879585i	$-0.657820\pi$
$859$	450.007	−	779.435i	0.523873	−	0.907374i	0.999614	−	0.0277890i	$-0.00884664\pi$
$860$	617.047	−	1359.64i	0.717497	−	1.58097i
$861$	−548.762	+	238.646i	−0.637354	+	0.277173i
$862$	147.043	+	31.8053i	0.170583	+	0.0368971i
$863$	−207.932	+	360.149i	−0.240941	+	0.417322i	−0.960983	−	0.276609i	$-0.910789\pi$
$863$	−207.932	+	360.149i	−0.240941	+	0.417322i	0.720042	+	0.693931i	$0.244123\pi$
$864$	193.015	−	320.911i	0.223397	−	0.371425i
$865$	448.683	+	777.142i	0.518709	+	0.898430i
$866$	−749.943	−	680.127i	−0.865986	−	0.785366i
$867$	−356.496			−0.411184
$868$	−395.110	−	710.070i	−0.455196	−	0.818053i
$869$			1996.42i			2.29737i
$870$	951.981	+	863.356i	1.09423	+	0.992363i
$871$	−447.783	+	258.527i	−0.514102	+	0.296817i
$872$	−449.821	−	52.1663i	−0.515850	−	0.0598238i
$873$	821.985	+	474.573i	0.941564	+	0.543612i
$874$	−307.008	−	66.4058i	−0.351268	−	0.0759791i
$875$	−914.824	−	104.178i	−1.04551	−	0.119060i
$876$	−488.699	+	1076.83i	−0.557876	+	1.22926i
$877$	−1488.56	−	859.419i	−1.69733	−	0.979954i	−0.948278	−	0.317442i	$-0.897176\pi$
$877$	−1488.56	−	859.419i	−1.69733	−	0.979954i	−0.749052	−	0.662511i	$-0.769491\pi$
$878$	−310.833	+	99.7675i	−0.354024	+	0.113630i
$879$	158.133	+	273.894i	0.179901	+	0.311598i
$880$	−211.767	−	1071.48i	−0.240644	−	1.21759i
$881$			1094.47i			1.24231i	0.783689	+	0.621153i	$0.213336\pi$
$881$			1094.47i			1.24231i	−0.783689	+	0.621153i	$0.786664\pi$
$882$	49.0212	+	583.589i	0.0555795	+	0.661666i
$883$			527.301i			0.597170i	0.954383	+	0.298585i	$0.0965146\pi$
$883$			527.301i			0.597170i	−0.954383	+	0.298585i	$0.903485\pi$
$884$	577.631	+	807.126i	0.653429	+	0.913039i
$885$	21.7853	+	37.7332i	0.0246161	+	0.0426363i
$886$	−216.534	+	69.5004i	−0.244395	+	0.0784429i
$887$	1459.99	+	842.925i	1.64599	+	0.950310i	0.978645	+	0.205558i	$0.0659010\pi$
$887$	1459.99	+	842.925i	1.64599	+	0.950310i	0.667341	+	0.744752i	$0.267432\pi$
$888$	−225.587	+	303.586i	−0.254040	+	0.341876i
$889$	318.921	+	36.3180i	0.358742	+	0.0408526i
$890$	−2.21531	+	10.2419i	−0.00248912	+	0.0115077i
$891$	1252.09	+	722.896i	1.40527	+	0.811331i
$892$	1030.97	−	100.904i	1.15579	−	0.113121i
$893$	647.023	−	373.559i	0.724549	−	0.418319i
$894$	−1254.75	−	1137.94i	−1.40352	−	1.27286i
$895$			327.007i			0.365371i
$896$	760.414	+	473.905i	0.848677	+	0.528912i
$897$	435.832			0.485878
$898$	525.498	−	579.441i	0.585187	−	0.645257i
$899$	515.099	+	892.178i	0.572969	+	0.992412i
$900$	7.26394	+	74.2177i	0.00807104	+	0.0824641i
$901$	352.897	−	611.236i	0.391673	−	0.678398i
$902$	−630.173	−	136.306i	−0.698639	−	0.151115i
$903$	−1982.37	+	862.096i	−2.19532	+	0.954702i
$904$	1211.26	+	900.058i	1.33989	+	0.995640i
$905$	803.700	−	1392.05i	0.888066	−	1.53818i
$906$	197.059	+	613.953i	0.217505	+	0.677652i
$907$	1439.38	−	831.024i	1.58696	−	0.916234i	0.593160	−	0.805085i	$-0.297880\pi$
$907$	1439.38	−	831.024i	1.58696	−	0.916234i	0.993804	−	0.111149i	$-0.0354530\pi$
$908$	−381.699	+	273.168i	−0.420373	+	0.300846i
$909$	−416.073			−0.457726
$910$	163.071	+	816.220i	0.179199	+	0.896945i
$911$	−1220.19			−1.33940			−0.669698	−	0.742633i	$-0.733577\pi$
$911$	−1220.19			−1.33940			−0.669698	+	0.742633i	$0.733577\pi$
$912$	−1076.65	+	212.789i	−1.18054	+	0.233321i
$913$	−631.840	+	364.793i	−0.692048	+	0.399554i
$914$	350.711	+	1092.67i	0.383710	+	1.19548i
$915$	−264.694	+	458.464i	−0.289283	+	0.501053i
$916$	−317.238	−	143.973i	−0.346330	−	0.157176i
$917$	503.761	−	680.875i	0.549357	−	0.742503i
$918$	96.5990	−	446.598i	0.105228	−	0.486490i
$919$	38.1217	−	66.0288i	0.0414817	−	0.0718485i	−0.844539	−	0.535494i	$-0.820125\pi$
$919$	38.1217	−	66.0288i	0.0414817	−	0.0718485i	0.886021	+	0.463645i	$0.153459\pi$
$920$	−38.1976	+	329.372i	−0.0415192	+	0.358013i
$921$	700.312	+	1212.98i	0.760382	+	1.31702i
$922$	1138.18	−	1255.02i	1.23447	−	1.36119i
$923$	−287.471			−0.311452
$924$	−812.220	+	1356.76i	−0.879026	+	1.46835i
$925$			38.1129i			0.0412032i
$926$	146.523	−	161.564i	0.158232	−	0.174475i
$927$	−101.538	+	58.6232i	−0.109534	+	0.0632397i
$928$	−973.432	−	585.479i	−1.04896	−	0.630905i
$929$	200.762	+	115.910i	0.216106	+	0.124769i	0.604146	−	0.796874i	$-0.293514\pi$
$929$	200.762	+	115.910i	0.216106	+	0.124769i	−0.388040	+	0.921643i	$0.626848\pi$
$930$	222.125	−	1026.93i	0.238844	−	1.10423i
$931$	−592.249	+	635.255i	−0.636142	+	0.682336i
$932$	−1135.17	−	515.177i	−1.21799	−	0.552765i
$933$	−632.758	−	365.323i	−0.678197	−	0.391557i
$934$	392.656	+	1223.35i	0.420403	+	1.30980i
$935$	−666.323	−	1154.11i	−0.712645	−	1.23434i
$936$	557.732	−	241.177i	0.595867	−	0.257668i
$937$		−	985.061i		−	1.05129i	−0.850703	−	0.525646i	$-0.823824\pi$
$937$		−	985.061i		−	1.05129i	0.850703	−	0.525646i	$-0.176176\pi$
$938$	−182.614	+	539.455i	−0.194684	+	0.575112i
$939$			99.4088i			0.105867i
$940$	−458.993	−	641.352i	−0.488290	−	0.682290i
$941$	−704.239	−	1219.78i	−0.748394	−	1.29626i	−0.948592	−	0.316501i	$-0.897492\pi$
$941$	−704.239	−	1219.78i	−0.748394	−	1.29626i	0.200198	−	0.979756i	$-0.435842\pi$
$942$	83.8318	+	261.184i	0.0889934	+	0.277266i
$943$	169.513	+	97.8683i	0.179759	+	0.103784i
$944$	−25.3568	−	28.9854i	−0.0268610	−	0.0307049i
$945$	227.910	−	308.040i	0.241175	−	0.325968i
$946$	−2276.47	−	492.399i	−2.40641	−	0.520506i
$947$	144.121	+	83.2085i	0.152187	+	0.0878654i	0.574160	−	0.818743i	$-0.305329\pi$
$947$	144.121	+	83.2085i	0.152187	+	0.0878654i	−0.421972	+	0.906609i	$0.638662\pi$
$948$	−206.275	−	2107.57i	−0.217590	−	2.22317i
$949$	840.888	−	485.487i	0.886078	−	0.511577i
$950$	−74.2931	+	81.9194i	−0.0782033	+	0.0862310i
$951$			1931.56i			2.03109i
$952$	1064.75	+	248.006i	1.11843	+	0.260511i
$953$	815.618			0.855843			0.427921	−	0.903816i	$-0.359246\pi$
$953$	815.618			0.855843			0.427921	+	0.903816i	$0.359246\pi$
$954$	−320.077	−	290.279i	−0.335510	−	0.304276i
$955$	326.918	+	566.238i	0.342322	+	0.592920i
$956$	54.8692	+	560.614i	0.0573945	+	0.586416i
$957$	1002.37	−	1736.16i	1.04741	−	1.81417i
$958$	−179.625	+	830.445i	−0.187500	+	0.866853i
$959$	405.458	+	932.343i	0.422792	+	0.972203i
$960$	334.265	+	1109.25i	0.348192	+	1.15547i
$961$	−59.3833	+	102.855i	−0.0617933	+	0.107029i
$962$	295.701	−	94.9104i	0.307381	−	0.0986595i
$963$	231.593	−	133.710i	0.240491	−	0.138848i
$964$	111.943	+	156.418i	0.116123	+	0.162260i
$965$	107.227			0.111116
$966$	360.662	−	316.830i	0.373356	−	0.327981i
$967$	−86.3395			−0.0892860			−0.0446430	−	0.999003i	$-0.514215\pi$
$967$	−86.3395			−0.0892860			−0.0446430	+	0.999003i	$0.514215\pi$
$968$	−675.307	+	292.020i	−0.697631	+	0.301674i
$969$	−1159.68	+	669.540i	−1.19678	+	0.690960i
$970$	1414.78	−	454.101i	1.45854	−	0.468145i
$971$	339.651	−	588.292i	0.349795	−	0.605862i	−0.636418	−	0.771344i	$-0.719585\pi$
$971$	339.651	−	588.292i	0.349795	−	0.605862i	0.986213	+	0.165482i	$0.0529180\pi$
$972$	−1012.86	−	459.667i	−1.04203	−	0.472909i
$973$	600.571	+	68.3915i	0.617236	+	0.0702893i
$974$	−1519.33	−	328.631i	−1.55989	−	0.337403i
$975$	76.7235	−	132.889i	0.0786908	−	0.136296i
$976$	150.950	−	442.901i	0.154662	−	0.453792i
$977$	107.029	+	185.379i	0.109548	+	0.189743i	0.915587	−	0.402119i	$-0.131726\pi$
$977$	107.029	+	185.379i	0.109548	+	0.189743i	−0.806039	+	0.591862i	$0.798393\pi$
$978$	59.9394	+	54.3593i	0.0612877	+	0.0555821i
$979$	16.3459			0.0166965
$980$	728.299	+	556.897i	0.743163	+	0.568263i
$981$			338.267i			0.344818i
$982$	705.738	+	640.037i	0.718674	+	0.651769i
$983$	1559.10	−	900.146i	1.58606	−	0.915713i	0.592114	−	0.805854i	$-0.298293\pi$
$983$	1559.10	−	900.146i	1.58606	−	0.915713i	0.993947	−	0.109859i	$-0.0350399\pi$
$984$	679.341	+	78.7840i	0.690387	+	0.0800650i
$985$	1165.82	+	673.084i	1.18357	+	0.683334i
$986$	−1354.68	−	293.017i	−1.37392	−	0.297178i
$987$	−129.195	+	1134.51i	−0.130897	+	1.14945i
$988$	820.583	+	372.407i	0.830549	+	0.376930i
$989$	612.357	+	353.544i	0.619168	+	0.357477i
$990$	−776.837	+	249.340i	−0.784684	+	0.251858i
$991$	−205.714	−	356.306i	−0.207582	−	0.359542i	0.743370	−	0.668880i	$-0.233226\pi$
$991$	−205.714	−	356.306i	−0.207582	−	0.359542i	−0.950952	+	0.309338i	$0.899893\pi$
$992$	−16.6158	+	928.532i	−0.0167498	+	0.936020i
$993$		−	966.925i		−	0.973741i
$994$	−237.889	+	208.978i	−0.239325	+	0.210239i
$995$		−	306.302i		−	0.307841i
$996$	629.326	−	450.386i	0.631854	−	0.452195i
$997$	806.000	+	1396.03i	0.808425	+	1.40023i	0.913954	+	0.405817i	$0.133013\pi$
$997$	806.000	+	1396.03i	0.808425	+	1.40023i	−0.105529	+	0.994416i	$0.533654\pi$
$998$	−829.132	+	266.125i	−0.830793	+	0.266658i
$999$	−123.816	−	71.4854i	−0.123940	−	0.0715569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.5.11	yes	28
4.3	odd	2		224.3.n.a.145.12		28
7.2	even	3		392.3.h.a.293.2		28
7.3	odd	6	inner	56.3.j.a.45.9	yes	28
7.4	even	3		392.3.j.e.325.9		28
7.5	odd	6		392.3.h.a.293.1		28
7.6	odd	2		392.3.j.e.117.11		28
8.3	odd	2		224.3.n.a.145.3		28
8.5	even	2	inner	56.3.j.a.5.9	✓	28
28.3	even	6		224.3.n.a.17.3		28
28.19	even	6		1568.3.h.a.881.24		28
28.23	odd	6		1568.3.h.a.881.6		28
56.3	even	6		224.3.n.a.17.12		28
56.5	odd	6		392.3.h.a.293.4		28
56.13	odd	2		392.3.j.e.117.9		28
56.19	even	6		1568.3.h.a.881.5		28
56.37	even	6		392.3.h.a.293.3		28
56.45	odd	6	inner	56.3.j.a.45.11	yes	28
56.51	odd	6		1568.3.h.a.881.23		28
56.53	even	6		392.3.j.e.325.11		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.9	✓	28	8.5	even	2	inner
56.3.j.a.5.11	yes	28	1.1	even	1	trivial
56.3.j.a.45.9	yes	28	7.3	odd	6	inner
56.3.j.a.45.11	yes	28	56.45	odd	6	inner
224.3.n.a.17.3		28	28.3	even	6
224.3.n.a.17.12		28	56.3	even	6
224.3.n.a.145.3		28	8.3	odd	2
224.3.n.a.145.12		28	4.3	odd	2
392.3.h.a.293.1		28	7.5	odd	6
392.3.h.a.293.2		28	7.2	even	3
392.3.h.a.293.3		28	56.37	even	6
392.3.h.a.293.4		28	56.5	odd	6
392.3.j.e.117.9		28	56.13	odd	2
392.3.j.e.117.11		28	7.6	odd	2
392.3.j.e.325.9		28	7.4	even	3
392.3.j.e.325.11		28	56.53	even	6
1568.3.h.a.881.5		28	56.19	even	6
1568.3.h.a.881.6		28	28.23	odd	6
1568.3.h.a.881.23		28	56.51	odd	6
1568.3.h.a.881.24		28	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34357 - 1.48149i) q^{2} +(-1.93494 - 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(-2.33882 + 4.05096i) q^{5} +(-7.56482 - 1.63627i) q^{6} +(6.95505 + 0.792023i) q^{7} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +O(q^{10})\)	\(q+(1.34357 - 1.48149i) q^{2} +(-1.93494 - 3.35141i) q^{3} +(-0.389632 - 3.98098i) q^{4} +(-2.33882 + 4.05096i) q^{5} +(-7.56482 - 1.63627i) q^{6} +(6.95505 + 0.792023i) q^{7} +(-6.42128 - 4.77149i) q^{8} +(-2.98798 + 5.17534i) q^{9} +(2.85908 + 8.90769i) q^{10} +(12.6383 - 7.29671i) q^{11} +(-12.5880 + 9.00877i) q^{12} +12.7102 q^{13} +(10.5180 - 9.23970i) q^{14} +18.1019 q^{15} +(-15.6964 + 3.10223i) q^{16} +(-16.9068 + 9.76116i) q^{17} +(3.65265 + 11.3801i) q^{18} +(-8.86233 + 15.3500i) q^{19} +(17.0380 + 7.73241i) q^{20} +(-10.8032 - 24.8418i) q^{21} +(6.17041 - 28.5271i) q^{22} +(-4.43038 + 7.67364i) q^{23} +(-3.56645 + 30.7529i) q^{24} +(1.55984 + 2.70172i) q^{25} +(17.0770 - 18.8300i) q^{26} -11.7027 q^{27} +(0.443120 - 27.9965i) q^{28} +35.4981i q^{29} +(24.3212 - 26.8178i) q^{30} +(25.1331 - 14.5106i) q^{31} +(-16.4933 + 27.4221i) q^{32} +(-48.9086 - 28.2374i) q^{33} +(-8.25445 + 38.1621i) q^{34} +(-19.4751 + 26.3222i) q^{35} +(21.7671 + 9.87861i) q^{36} +(10.5802 + 6.10847i) q^{37} +(10.8337 + 33.7533i) q^{38} +(-24.5934 - 42.5970i) q^{39} +(34.3473 - 14.8527i) q^{40} -22.0903i q^{41} +(-51.3177 - 17.3718i) q^{42} -79.8001i q^{43} +(-33.9723 - 47.4696i) q^{44} +(-13.9767 - 24.2084i) q^{45} +(5.41590 + 16.8736i) q^{46} +(-36.5041 - 21.0756i) q^{47} +(40.7684 + 46.6024i) q^{48} +(47.7454 + 11.0171i) q^{49} +(6.09833 + 1.31907i) q^{50} +(65.4273 + 37.7745i) q^{51} +(-4.95229 - 50.5989i) q^{52} +(-31.3096 + 18.0766i) q^{53} +(-15.7234 + 17.3374i) q^{54} +68.2627i q^{55} +(-40.8812 - 38.2718i) q^{56} +68.5923 q^{57} +(52.5901 + 47.6942i) q^{58} +(1.20348 + 2.08449i) q^{59} +(-7.05308 - 72.0633i) q^{60} +(-14.6224 + 25.3268i) q^{61} +(12.2708 - 56.7306i) q^{62} +(-24.8805 + 33.6282i) q^{63} +(18.4657 + 61.2782i) q^{64} +(-29.7268 + 51.4883i) q^{65} +(-107.546 + 34.5187i) q^{66} +(-35.2303 + 20.3402i) q^{67} +(45.4464 + 63.5024i) q^{68} +34.2900 q^{69} +(12.8300 + 64.2179i) q^{70} -22.6174 q^{71} +(43.8807 - 18.9752i) q^{72} +(66.1587 - 38.1967i) q^{73} +(23.2649 - 7.46728i) q^{74} +(6.03639 - 10.4553i) q^{75} +(64.5611 + 29.2999i) q^{76} +(93.6789 - 40.7391i) q^{77} +(-96.1501 - 20.7972i) q^{78} +(-68.4014 + 118.475i) q^{79} +(24.1440 - 70.8409i) q^{80} +(49.5358 + 85.7985i) q^{81} +(-32.7266 - 29.6799i) q^{82} -49.9942 q^{83} +(-94.6852 + 52.6864i) q^{84} -91.3184i q^{85} +(-118.223 - 107.217i) q^{86} +(118.969 - 68.6866i) q^{87} +(-115.970 - 13.4492i) q^{88} +(0.970023 + 0.560043i) q^{89} +(-54.6432 - 11.8193i) q^{90} +(88.3998 + 10.0667i) q^{91} +(32.2748 + 14.6473i) q^{92} +(-97.2622 - 56.1544i) q^{93} +(-80.2692 + 25.7638i) q^{94} +(-41.4548 - 71.8018i) q^{95} +(123.816 + 2.21566i) q^{96} -158.827i q^{97} +(80.4711 - 55.9321i) q^{98} +87.2097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

Introduction

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