LMFDB - Embedded newform 140.3.x.a.103.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [140,3,Mod(3,140)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(140, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("140.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 140 = 2^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	140.x (of order $12$, degree $4$, 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:	$3.81472370104$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.31
Character	$\chi$	$=$	140.103
Dual form			140.3.x.a.87.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22756 - 1.57895i) q^{2} +(-0.451084 + 1.68347i) q^{3} +(-0.986197 - 3.87652i) q^{4} +(3.35921 - 3.70347i) q^{5} +(2.10439 + 2.77880i) q^{6} +(-3.89031 - 5.81941i) q^{7} +(-7.33147 - 3.20150i) q^{8} +(5.16363 + 2.98123i) q^{9} +O(q^{10})$	\(q+(1.22756 - 1.57895i) q^{2} +(-0.451084 + 1.68347i) q^{3} +(-0.986197 - 3.87652i) q^{4} +(3.35921 - 3.70347i) q^{5} +(2.10439 + 2.77880i) q^{6} +(-3.89031 - 5.81941i) q^{7} +(-7.33147 - 3.20150i) q^{8} +(5.16363 + 2.98123i) q^{9} +(-1.72399 - 9.85027i) q^{10} +(1.87311 - 1.08144i) q^{11} +(6.97087 + 0.0884058i) q^{12} +(5.22698 - 5.22698i) q^{13} +(-13.9642 - 1.00105i) q^{14} +(4.71940 + 7.32571i) q^{15} +(-14.0548 + 7.64602i) q^{16} +(4.84903 - 18.0968i) q^{17} +(11.0459 - 4.49351i) q^{18} +(-3.24006 - 1.87065i) q^{19} +(-17.6694 - 9.36968i) q^{20} +(11.5517 - 3.92417i) q^{21} +(0.591808 - 4.28509i) q^{22} +(8.89644 + 33.2020i) q^{23} +(8.69674 - 10.8982i) q^{24} +(-2.43145 - 24.8815i) q^{25} +(-1.83674 - 14.6696i) q^{26} +(-18.4395 + 18.4395i) q^{27} +(-18.7224 + 20.8199i) q^{28} +44.0942i q^{29} +(17.3603 + 1.54101i) q^{30} +(14.0330 + 24.3059i) q^{31} +(-5.18041 + 31.5779i) q^{32} +(0.975642 + 3.64115i) q^{33} +(-22.6216 - 29.8713i) q^{34} +(-34.6204 - 5.14094i) q^{35} +(6.46442 - 22.9570i) q^{36} +(11.2746 + 42.0776i) q^{37} +(-6.93104 + 2.81958i) q^{38} +(6.44165 + 11.1573i) q^{39} +(-36.4846 + 16.3974i) q^{40} +10.7660i q^{41} +(7.98425 - 23.0567i) q^{42} +(41.7141 - 41.7141i) q^{43} +(-6.03948 - 6.19464i) q^{44} +(28.3866 - 9.10883i) q^{45} +(63.3453 + 26.7103i) q^{46} +(-9.52027 - 35.5301i) q^{47} +(-6.53194 - 27.1099i) q^{48} +(-18.7310 + 45.2786i) q^{49} +(-42.2715 - 26.7043i) q^{50} +(28.2781 + 16.3264i) q^{51} +(-25.4173 - 15.1077i) q^{52} +(8.08134 - 30.1600i) q^{53} +(6.47956 + 51.7507i) q^{54} +(2.28708 - 10.5698i) q^{55} +(9.89083 + 55.1196i) q^{56} +(4.61073 - 4.61073i) q^{57} +(69.6227 + 54.1282i) q^{58} +(12.8816 - 7.43720i) q^{59} +(23.7440 - 25.5195i) q^{60} +(30.6400 + 17.6900i) q^{61} +(55.6043 + 7.67944i) q^{62} +(-2.73916 - 41.6472i) q^{63} +(43.5008 + 46.9434i) q^{64} +(-1.79948 - 36.9165i) q^{65} +(6.94686 + 2.92923i) q^{66} +(-2.52064 + 9.40717i) q^{67} +(-74.9348 - 0.950337i) q^{68} -59.9076 q^{69} +(-50.6159 + 48.3532i) q^{70} +10.3786i q^{71} +(-28.3126 - 38.3881i) q^{72} +(-126.933 - 34.0116i) q^{73} +(80.2789 + 33.8505i) q^{74} +(42.9840 + 7.13037i) q^{75} +(-4.05628 + 14.4050i) q^{76} +(-13.5803 - 6.69325i) q^{77} +(25.5243 + 3.52513i) q^{78} +(-33.7636 + 58.4802i) q^{79} +(-18.8962 + 77.7363i) q^{80} +(4.10644 + 7.11256i) q^{81} +(16.9991 + 13.2159i) q^{82} +(-107.371 - 107.371i) q^{83} +(-26.6043 - 40.9102i) q^{84} +(-50.7322 - 78.7492i) q^{85} +(-14.6582 - 117.071i) q^{86} +(-74.2312 - 19.8902i) q^{87} +(-17.1949 + 1.93178i) q^{88} +(-2.52306 + 4.37006i) q^{89} +(20.4638 - 56.0028i) q^{90} +(-50.7525 - 10.0834i) q^{91} +(119.935 - 67.2309i) q^{92} +(-47.2484 + 12.6602i) q^{93} +(-67.7872 - 28.5833i) q^{94} +(-17.8119 + 5.71558i) q^{95} +(-50.8236 - 22.9654i) q^{96} +(101.878 + 101.878i) q^{97} +(48.4994 + 85.1576i) q^{98} +12.8961 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	$ 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/140\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.22756	−	1.57895i	0.613780	−	0.789477i
$2$	1.22756	−	1.57895i	0.613780	−	0.789477i
$3$	−0.451084	+	1.68347i	−0.150361	+	0.561157i	0.849097	+	0.528238i	$0.177147\pi$
$3$	−0.451084	+	1.68347i	−0.150361	+	0.561157i	−0.999458	+	0.0329190i	$0.989520\pi$
$4$	−0.986197	−	3.87652i	−0.246549	−	0.969130i
$5$	3.35921	−	3.70347i	0.671841	−	0.740695i
$5$	3.35921	−	3.70347i	0.671841	−	0.740695i
$6$	2.10439	+	2.77880i	0.350732	+	0.463134i
$7$	−3.89031	−	5.81941i	−0.555758	−	0.831344i
$7$	−3.89031	−	5.81941i	−0.555758	−	0.831344i
$8$	−7.33147	−	3.20150i	−0.916433	−	0.400187i
$9$	5.16363	+	2.98123i	0.573737	+	0.331247i
$10$	−1.72399	−	9.85027i	−0.172399	−	0.985027i
$11$	1.87311	−	1.08144i	0.170283	−	0.0983128i	−0.412436	−	0.910986i	$-0.635322\pi$
$11$	1.87311	−	1.08144i	0.170283	−	0.0983128i	0.582719	+	0.812674i	$0.301989\pi$
$12$	6.97087	+	0.0884058i	0.580905	+	0.00736715i
$13$	5.22698	−	5.22698i	0.402075	−	0.402075i	−0.476888	−	0.878964i	$-0.658235\pi$
$13$	5.22698	−	5.22698i	0.402075	−	0.402075i	0.878964	+	0.476888i	$0.158235\pi$
$14$	−13.9642	−	1.00105i	−0.997440	−	0.0715034i
$15$	4.71940	+	7.32571i	0.314627	+	0.488380i
$16$	−14.0548	+	7.64602i	−0.878427	+	0.477877i
$17$	4.84903	−	18.0968i	0.285237	−	1.06452i	−0.663429	−	0.748239i	$-0.730900\pi$
$17$	4.84903	−	18.0968i	0.285237	−	1.06452i	0.948666	−	0.316279i	$-0.102434\pi$
$18$	11.0459	−	4.49351i	0.613660	−	0.249640i
$19$	−3.24006	−	1.87065i	−0.170530	−	0.0984553i	0.412306	−	0.911045i	$-0.364723\pi$
$19$	−3.24006	−	1.87065i	−0.170530	−	0.0984553i	−0.582836	+	0.812590i	$0.698057\pi$
$20$	−17.6694	−	9.36968i	−0.883472	−	0.468484i
$21$	11.5517	−	3.92417i	0.550079	−	0.186865i
$22$	0.591808	−	4.28509i	0.0269003	−	0.194777i
$23$	8.89644	+	33.2020i	0.386802	+	1.44356i	0.835307	+	0.549784i	$0.185290\pi$
$23$	8.89644	+	33.2020i	0.386802	+	1.44356i	−0.448505	+	0.893780i	$0.648043\pi$
$24$	8.69674	−	10.8982i	0.362364	−	0.454090i
$25$	−2.43145	−	24.8815i	−0.0972580	−	0.995259i
$26$	−1.83674	−	14.6696i	−0.0706437	−	0.564215i
$27$	−18.4395	+	18.4395i	−0.682945	+	0.682945i
$28$	−18.7224	+	20.8199i	−0.668659	+	0.743569i
$29$			44.0942i			1.52049i	0.649637	+	0.760244i	$0.274921\pi$
$29$			44.0942i			1.52049i	−0.649637	+	0.760244i	$0.725079\pi$
$30$	17.3603	+	1.54101i	0.578677	+	0.0513671i
$31$	14.0330	+	24.3059i	0.452678	+	0.784062i	0.998551	−	0.0538059i	$-0.0171352\pi$
$31$	14.0330	+	24.3059i	0.452678	+	0.784062i	−0.545873	+	0.837868i	$0.683802\pi$
$32$	−5.18041	+	31.5779i	−0.161888	+	0.986809i
$33$	0.975642	+	3.64115i	0.0295649	+	0.110338i
$34$	−22.6216	−	29.8713i	−0.665341	−	0.878568i
$35$	−34.6204	−	5.14094i	−0.989154	−	0.146884i
$36$	6.46442	−	22.9570i	0.179567	−	0.637695i
$37$	11.2746	+	42.0776i	0.304720	+	1.13723i	0.933186	+	0.359394i	$0.117017\pi$
$37$	11.2746	+	42.0776i	0.304720	+	1.13723i	−0.628466	+	0.777837i	$0.716317\pi$
$38$	−6.93104	+	2.81958i	−0.182396	+	0.0741994i
$39$	6.44165	+	11.1573i	0.165171	+	0.286084i
$40$	−36.4846	+	16.3974i	−0.912115	+	0.409935i
$41$			10.7660i			0.262586i	0.991344	+	0.131293i	$0.0419129\pi$
$41$			10.7660i			0.262586i	−0.991344	+	0.131293i	$0.958087\pi$
$42$	7.98425	−	23.0567i	0.190101	−	0.548969i
$43$	41.7141	−	41.7141i	0.970095	−	0.970095i	−0.0294702	−	0.999566i	$-0.509382\pi$
$43$	41.7141	−	41.7141i	0.970095	−	0.970095i	0.999566	+	0.0294702i	$0.00938203\pi$
$44$	−6.03948	−	6.19464i	−0.137261	−	0.140787i
$45$	28.3866	−	9.10883i	0.630814	−	0.202419i
$46$	63.3453	+	26.7103i	1.37707	+	0.580659i
$47$	−9.52027	−	35.5301i	−0.202559	−	0.755960i	−0.990180	−	0.139800i	$-0.955354\pi$
$47$	−9.52027	−	35.5301i	−0.202559	−	0.755960i	0.787621	−	0.616160i	$-0.211313\pi$
$48$	−6.53194	−	27.1099i	−0.136082	−	0.564789i
$49$	−18.7310	+	45.2786i	−0.382266	+	0.924053i
$50$	−42.2715	−	26.7043i	−0.845430	−	0.534087i
$51$	28.2781	+	16.3264i	0.554473	+	0.320125i
$52$	−25.4173	−	15.1077i	−0.488795	−	0.290532i
$53$	8.08134	−	30.1600i	0.152478	−	0.569056i	−0.846830	−	0.531864i	$-0.821492\pi$
$53$	8.08134	−	30.1600i	0.152478	−	0.569056i	0.999308	−	0.0371924i	$-0.0118415\pi$
$54$	6.47956	+	51.7507i	0.119992	+	0.958347i
$55$	2.28708	−	10.5698i	0.0415832	−	0.192178i
$56$	9.89083	+	55.1196i	0.176622	+	0.984279i
$57$	4.61073	−	4.61073i	0.0808899	−	0.0808899i
$58$	69.6227	+	54.1282i	1.20039	+	0.933245i
$59$	12.8816	−	7.43720i	0.218332	−	0.126054i	−0.386846	−	0.922145i	$-0.626435\pi$
$59$	12.8816	−	7.43720i	0.218332	−	0.126054i	0.605178	+	0.796090i	$0.293102\pi$
$60$	23.7440	−	25.5195i	0.395733	−	0.425324i
$61$	30.6400	+	17.6900i	0.502294	+	0.290000i	0.729661	−	0.683809i	$-0.239678\pi$
$61$	30.6400	+	17.6900i	0.502294	+	0.290000i	−0.227366	+	0.973809i	$0.573011\pi$
$62$	55.6043	+	7.67944i	0.896844	+	0.123862i
$63$	−2.73916	−	41.6472i	−0.0434787	−	0.661066i
$64$	43.5008	+	46.9434i	0.679700	+	0.733490i
$65$	−1.79948	−	36.9165i	−0.0276843	−	0.567946i
$66$	6.94686	+	2.92923i	0.105256	+	0.0443822i
$67$	−2.52064	+	9.40717i	−0.0376215	+	0.140406i	−0.982182	−	0.187932i	$-0.939822\pi$
$67$	−2.52064	+	9.40717i	−0.0376215	+	0.140406i	0.944561	+	0.328337i	$0.106488\pi$
$68$	−74.9348	−	0.950337i	−1.10198	−	0.0139755i
$69$	−59.9076			−0.868226
$70$	−50.6159	+	48.3532i	−0.723084	+	0.690760i
$71$			10.3786i			0.146178i	0.997325	+	0.0730889i	$0.0232857\pi$
$71$			10.3786i			0.146178i	−0.997325	+	0.0730889i	$0.976714\pi$
$72$	−28.3126	−	38.3881i	−0.393231	−	0.533168i
$73$	−126.933	−	34.0116i	−1.73881	−	0.465912i	−0.756625	−	0.653849i	$-0.773153\pi$
$73$	−126.933	−	34.0116i	−1.73881	−	0.465912i	−0.982181	+	0.187937i	$0.939820\pi$
$74$	80.2789	+	33.8505i	1.08485	+	0.457440i
$75$	42.9840	+	7.13037i	0.573120	+	0.0950717i
$76$	−4.05628	+	14.4050i	−0.0533721	+	0.189539i
$77$	−13.5803	−	6.69325i	−0.176368	−	0.0869254i
$78$	25.5243	+	3.52513i	0.327235	+	0.0451940i
$79$	−33.7636	+	58.4802i	−0.427387	+	0.740256i	−0.996640	−	0.0819065i	$-0.973899\pi$
$79$	−33.7636	+	58.4802i	−0.427387	+	0.740256i	0.569253	+	0.822162i	$0.307232\pi$
$80$	−18.8962	+	77.7363i	−0.236203	+	0.971704i
$81$	4.10644	+	7.11256i	0.0506968	+	0.0878094i
$82$	16.9991	+	13.2159i	0.207306	+	0.161170i
$83$	−107.371	−	107.371i	−1.29363	−	1.29363i	−0.932526	−	0.361103i	$-0.882400\pi$
$83$	−107.371	−	107.371i	−1.29363	−	1.29363i	−0.361103	−	0.932526i	$-0.617600\pi$
$84$	−26.6043	−	40.9102i	−0.316718	−	0.487027i
$85$	−50.7322	−	78.7492i	−0.596849	−	0.926461i
$86$	−14.6582	−	117.071i	−0.170444	−	1.36129i
$87$	−74.2312	−	19.8902i	−0.853232	−	0.228623i
$88$	−17.1949	+	1.93178i	−0.195396	+	0.0219521i
$89$	−2.52306	+	4.37006i	−0.0283490	+	0.0491018i	−0.879852	−	0.475248i	$-0.842358\pi$
$89$	−2.52306	+	4.37006i	−0.0283490	+	0.0491018i	0.851503	+	0.524350i	$0.175692\pi$
$90$	20.4638	−	56.0028i	0.227376	−	0.622253i
$91$	−50.7525	−	10.0834i	−0.557720	−	0.110806i
$92$	119.935	−	67.2309i	1.30364	−	0.730771i
$93$	−47.2484	+	12.6602i	−0.508047	+	0.136131i
$94$	−67.7872	−	28.5833i	−0.721140	−	0.304077i
$95$	−17.8119	+	5.71558i	−0.187494	+	0.0601641i
$96$	−50.8236	−	22.9654i	−0.529413	−	0.239223i
$97$	101.878	+	101.878i	1.05029	+	1.05029i	0.998667	+	0.0516185i	$0.0164380\pi$
$97$	101.878	+	101.878i	1.05029	+	1.05029i	0.0516185	+	0.998667i	$0.483562\pi$
$98$	48.4994	+	85.1576i	0.494892	+	0.868955i
$99$	12.8961			0.130263
$100$	−94.0557	+	33.9636i	−0.940557	+	0.339636i
$101$	50.4158	−	29.1076i	0.499166	−	0.288194i	−0.229203	−	0.973379i	$-0.573612\pi$
$101$	50.4158	−	29.1076i	0.499166	−	0.288194i	0.728369	+	0.685185i	$0.240279\pi$
$102$	60.4917	−	24.6083i	0.593056	−	0.241258i
$103$	91.9946	−	24.6499i	0.893152	−	0.239319i	0.217079	−	0.976154i	$-0.430347\pi$
$103$	91.9946	−	24.6499i	0.893152	−	0.239319i	0.676073	+	0.736835i	$0.263680\pi$
$104$	−55.0556	+	21.5873i	−0.529381	+	0.207570i
$105$	24.2713	−	55.9634i	0.231156	−	0.532985i
$106$	−37.7009	−	49.7832i	−0.355669	−	0.469653i
$107$	154.834	−	41.4877i	1.44705	−	0.387736i	0.552053	−	0.833809i	$-0.313845\pi$
$107$	154.834	−	41.4877i	1.44705	−	0.387736i	0.894996	+	0.446073i	$0.147178\pi$
$108$	89.6661	+	53.2962i	0.830242	+	0.493483i
$109$	10.1574	−	5.86440i	0.0931875	−	0.0538018i	−0.452682	−	0.891672i	$-0.649533\pi$
$109$	10.1574	−	5.86440i	0.0931875	−	0.0538018i	0.545870	+	0.837870i	$0.316199\pi$
$110$	−13.8817	−	16.5862i	−0.126197	−	0.150784i
$111$	−75.9221			−0.683983
$112$	99.1730	+	52.0454i	0.885473	+	0.464691i
$113$	−115.919	−	115.919i	−1.02583	−	1.02583i	−0.999658	−	0.0261700i	$-0.991669\pi$
$113$	−115.919	−	115.919i	−1.02583	−	1.02583i	−0.0261700	−	0.999658i	$-0.508331\pi$
$114$	−1.62019	−	12.9401i	−0.0142122	−	0.113509i
$115$	152.848	+	78.5846i	1.32911	+	0.683344i
$116$	170.932	−	43.4855i	1.47355	−	0.374875i
$117$	42.5730	−	11.4074i	0.363872	−	0.0974992i
$118$	4.06993	−	29.4691i	0.0344910	−	0.249738i
$119$	−124.177	+	42.1837i	−1.04350	+	0.354485i
$120$	−11.1469	−	68.8173i	−0.0928909	−	0.573478i
$121$	−58.1610	+	100.738i	−0.480669	+	0.832543i
$122$	65.5441	−	26.6636i	0.537246	−	0.218554i
$123$	−18.1243	−	4.85639i	−0.147352	−	0.0394828i
$124$	80.3831	−	78.3698i	0.648251	−	0.632014i
$125$	−100.316	−	74.5772i	−0.802525	−	0.596618i
$126$	−69.1215	−	46.7994i	−0.548583	−	0.371424i
$127$	−26.6495	−	26.6495i	−0.209839	−	0.209839i	0.594360	−	0.804199i	$-0.297405\pi$
$127$	−26.6495	−	26.6495i	−0.209839	−	0.209839i	−0.804199	+	0.594360i	$0.797405\pi$
$128$	127.521	−	11.0600i	0.996260	−	0.0864065i
$129$	51.4079	+	89.0410i	0.398511	+	0.690241i
$130$	−60.4984	−	42.4759i	−0.465373	−	0.326738i
$131$	92.0583	−	159.450i	0.702735	−	1.21717i	−0.264768	−	0.964312i	$-0.585295\pi$
$131$	92.0583	−	159.450i	0.702735	−	1.21717i	0.967503	−	0.252861i	$-0.0813714\pi$
$132$	13.1528	−	7.37298i	0.0996425	−	0.0558559i
$133$	1.71876	+	26.1327i	0.0129230	+	0.196486i
$134$	11.7593	+	15.5278i	0.0877556	+	0.115879i
$135$	6.34812	+	130.232i	0.0470231	+	0.964684i
$136$	−93.4874	+	117.152i	−0.687407	+	0.861412i
$137$	−238.734	−	63.9686i	−1.74259	−	0.466924i	−0.759567	−	0.650430i	$-0.774589\pi$
$137$	−238.734	−	63.9686i	−1.74259	−	0.466924i	−0.983019	+	0.183505i	$0.941256\pi$
$138$	−73.5401	+	94.5914i	−0.532899	+	0.685445i
$139$		−	132.896i		−	0.956089i	−0.878336	−	0.478045i	$-0.841346\pi$
$139$		−	132.896i		−	0.956089i	0.878336	−	0.478045i	$-0.158654\pi$
$140$	14.2135	+	139.277i	0.101525	+	0.994833i
$141$	64.1084			0.454669
$142$	16.3874	+	12.7404i	0.115404	+	0.0897210i
$143$	4.13804	−	15.4434i	0.0289373	−	0.107996i
$144$	−95.3685	−	2.41935i	−0.662281	−	0.0168011i
$145$	163.302	+	148.121i	1.12622	+	1.02153i
$146$	−209.520	+	158.670i	−1.43507	+	1.08678i
$147$	−67.7759	−	51.9576i	−0.461060	−	0.353453i
$148$	151.996	−	85.2032i	1.02700	−	0.575697i
$149$	21.2788	+	12.2853i	0.142811	+	0.0824520i	0.569703	−	0.821851i	$-0.307058\pi$
$149$	21.2788	+	12.2853i	0.142811	+	0.0824520i	−0.426892	+	0.904303i	$0.640392\pi$
$150$	64.0240	−	59.1169i	0.426826	−	0.394112i
$151$	−112.668	+	65.0490i	−0.746147	+	0.430788i	−0.824300	−	0.566153i	$-0.808431\pi$
$151$	−112.668	+	65.0490i	−0.746147	+	0.430788i	0.0781533	+	0.996941i	$0.475098\pi$
$152$	17.7655	+	24.0877i	0.116878	+	0.158472i
$153$	78.9893	−	78.9893i	0.516270	−	0.516270i
$154$	−27.2390	+	13.2263i	−0.176877	+	0.0858853i
$155$	137.156	+	29.6777i	0.884879	+	0.191469i
$156$	36.8987	−	35.9745i	0.236530	−	0.230606i
$157$	−49.6571	+	185.323i	−0.316287	+	1.18040i	0.606498	+	0.795085i	$0.292574\pi$
$157$	−49.6571	+	185.323i	−0.316287	+	1.18040i	−0.922785	+	0.385315i	$0.874093\pi$
$158$	50.8908	+	125.099i	0.322094	+	0.791766i
$159$	47.1281	+	27.2094i	0.296403	+	0.171128i
$160$	99.5459	+	125.262i	0.622162	+	0.782889i
$161$	158.606	−	180.938i	0.985130	−	1.12384i
$162$	16.2713	+	2.24721i	0.100440	+	0.0138717i
$163$	22.0388	+	82.2499i	0.135207	+	0.504601i	0.999997	+	0.00246634i	$0.000785060\pi$
$163$	22.0388	+	82.2499i	0.135207	+	0.504601i	−0.864790	+	0.502134i	$0.832548\pi$
$164$	41.7347	−	10.6174i	0.254480	−	0.0647404i
$165$	16.7623	+	8.61810i	0.101590	+	0.0522309i
$166$	−301.339	+	37.7298i	−1.81529	+	0.227288i
$167$	−61.8052	+	61.8052i	−0.370091	+	0.370091i	−0.867510	−	0.497419i	$-0.834281\pi$
$167$	−61.8052	+	61.8052i	−0.370091	+	0.370091i	0.497419	+	0.867510i	$0.334281\pi$
$168$	−97.2538	−	8.21268i	−0.578892	−	0.0488850i
$169$			114.357i			0.676671i
$170$	−186.618	−	16.5654i	−1.09775	−	0.0974438i
$171$	−11.1537	−	19.3187i	−0.0652261	−	0.112975i
$172$	−202.844	−	120.567i	−1.17933	−	0.700973i
$173$	18.7798	+	70.0870i	0.108554	+	0.405127i	0.998724	−	0.0505003i	$-0.0160816\pi$
$173$	18.7798	+	70.0870i	0.108554	+	0.405127i	−0.890171	+	0.455627i	$0.849415\pi$
$174$	−122.529	+	92.7914i	−0.704189	+	0.533284i
$175$	−135.336	+	110.946i	−0.773351	+	0.633978i
$176$	−18.0575	+	29.5213i	−0.102600	+	0.167735i
$177$	6.70961	+	25.0406i	0.0379074	+	0.141472i
$178$	3.80293	+	9.34831i	0.0213648	+	0.0525186i
$179$	20.3828	+	35.3040i	0.113870	+	0.197229i	0.917328	−	0.398133i	$-0.130342\pi$
$179$	20.3828	+	35.3040i	0.113870	+	0.197229i	−0.803457	+	0.595362i	$0.797008\pi$
$180$	−63.3054	−	101.058i	−0.351696	−	0.561434i
$181$		−	97.4982i		−	0.538664i	−0.963047	−	0.269332i	$-0.913197\pi$
$181$		−	97.4982i		−	0.538664i	0.963047	−	0.269332i	$-0.0868029\pi$
$182$	−78.2229	+	67.7579i	−0.429796	+	0.372296i
$183$	−43.6018	+	43.6018i	−0.238261	+	0.238261i
$184$	41.0721	−	271.901i	0.223218	−	1.47772i
$185$	193.707	+	99.5919i	1.04707	+	0.538335i
$186$	−38.0104	+	90.1442i	−0.204357	+	0.484646i
$187$	−10.4879	−	39.1413i	−0.0560849	−	0.209312i
$188$	−128.344	+	71.9452i	−0.682683	+	0.382687i
$189$	179.042	+	35.5717i	0.947314	+	0.188210i
$190$	−12.8406	+	35.1405i	−0.0675820	+	0.184950i
$191$	231.783	+	133.820i	1.21352	+	0.700628i	0.963525	−	0.267619i	$-0.0862367\pi$
$191$	231.783	+	133.820i	1.21352	+	0.700628i	0.249998	+	0.968246i	$0.419570\pi$
$192$	−98.6503	+	52.0569i	−0.513804	+	0.271130i
$193$	−9.50704	+	35.4807i	−0.0492593	+	0.183838i	−0.986172	−	0.165725i	$-0.947003\pi$
$193$	−9.50704	+	35.4807i	−0.0492593	+	0.183838i	0.936913	+	0.349564i	$0.113670\pi$
$194$	285.921	−	35.7994i	1.47382	−	0.184533i
$195$	62.9595	+	13.6231i	0.322869	+	0.0698620i
$196$	193.996	+	27.9576i	0.989775	+	0.142641i
$197$	−90.7107	+	90.7107i	−0.460460	+	0.460460i	−0.898806	−	0.438346i	$-0.855564\pi$
$197$	−90.7107	+	90.7107i	−0.460460	+	0.460460i	0.438346	+	0.898806i	$0.355564\pi$
$198$	15.8307	−	20.3623i	0.0799530	−	0.102840i
$199$	−338.103	+	195.204i	−1.69901	+	0.980924i	−0.752309	+	0.658810i	$0.771060\pi$
$199$	−338.103	+	195.204i	−1.69901	+	0.980924i	−0.946701	+	0.322114i	$0.895607\pi$
$200$	−61.8319	+	190.202i	−0.309160	+	0.951010i
$201$	−14.6997	−	8.48686i	−0.0731327	−	0.0422232i
$202$	15.9288	−	115.335i	0.0788555	−	0.570968i
$203$	256.602	−	171.540i	1.26405	−	0.845024i
$204$	35.4018	−	125.722i	0.173538	−	0.616283i
$205$	39.8717	+	36.1653i	0.194496	+	0.176416i
$206$	74.0078	−	175.515i	0.359261	−	0.852012i
$207$	−53.0446	+	197.965i	−0.256254	+	0.956354i
$208$	−33.4987	+	113.430i	−0.161051	+	0.545336i
$209$	−8.09199			−0.0387177
$210$	−58.5691	−	107.022i	−0.278901	−	0.509627i
$211$			266.839i			1.26464i	0.774708	+	0.632319i	$0.217897\pi$
$211$			266.839i			1.26464i	−0.774708	+	0.632319i	$0.782103\pi$
$212$	−124.886	−	1.58382i	−0.589083	−	0.00747086i
$213$	−17.4721	−	4.68164i	−0.0820287	−	0.0219795i
$214$	124.561	−	295.405i	0.582061	−	1.38040i
$215$	−14.3608	−	294.613i	−0.0667944	−	1.37030i
$216$	194.223	−	76.1546i	0.899179	−	0.352567i
$217$	86.8533	−	176.221i	0.400245	−	0.812080i
$218$	3.20923	−	23.2370i	0.0147213	−	0.106592i
$219$	114.515	−	198.346i	0.522899	−	0.905688i
$220$	−43.2296	+	1.55800i	−0.196498	+	0.00708181i
$221$	−69.2459	−	119.937i	−0.313330	−	0.542703i
$222$	−93.1989	+	119.878i	−0.419815	+	0.539989i
$223$	149.274	+	149.274i	0.669390	+	0.669390i	0.957575	−	0.288185i	$-0.0930517\pi$
$223$	149.274	+	149.274i	0.669390	+	0.669390i	−0.288185	+	0.957575i	$0.593052\pi$
$224$	203.918	−	92.7008i	0.910348	−	0.413843i
$225$	61.6222	−	135.728i	0.273876	−	0.603234i
$226$	−325.327	+	40.7333i	−1.43950	+	0.180236i
$227$	13.7411	+	3.68191i	0.0605334	+	0.0162199i	0.288959	−	0.957342i	$-0.406691\pi$
$227$	13.7411	+	3.68191i	0.0605334	+	0.0162199i	−0.228425	+	0.973561i	$0.573358\pi$
$228$	−22.4207	−	13.3265i	−0.0983362	−	0.0584495i
$229$	154.955	−	268.390i	0.676661	−	1.17201i	−0.299320	−	0.954153i	$-0.596760\pi$
$229$	154.955	−	268.390i	0.676661	−	1.17201i	0.975981	−	0.217858i	$-0.0699069\pi$
$230$	311.711	−	144.872i	1.35527	−	0.629880i
$231$	17.3938	−	19.8428i	0.0752977	−	0.0858997i
$232$	141.167	−	323.275i	0.608480	−	1.39343i
$233$	−106.572	+	28.5558i	−0.457389	+	0.122557i	−0.480155	−	0.877184i	$-0.659419\pi$
$233$	−106.572	+	28.5558i	−0.457389	+	0.122557i	0.0227658	+	0.999741i	$0.492753\pi$
$234$	34.2491	−	81.2241i	0.146364	−	0.347112i
$235$	−163.566	−	84.0950i	−0.696024	−	0.357851i
$236$	−41.5343	−	42.6013i	−0.175993	−	0.180514i
$237$	−83.2195	−	83.2195i	−0.351137	−	0.351137i
$238$	−85.8284	+	247.853i	−0.360623	+	1.04140i
$239$	−254.465			−1.06471			−0.532354	−	0.846522i	$-0.678692\pi$
$239$	−254.465			−1.06471			−0.532354	+	0.846522i	$0.678692\pi$
$240$	−122.343	−	66.8769i	−0.509762	−	0.278654i
$241$	−33.4920	+	19.3366i	−0.138971	+	0.0802348i	−0.567873	−	0.823116i	$-0.692234\pi$
$241$	−33.4920	+	19.3366i	−0.138971	+	0.0802348i	0.428903	+	0.903351i	$0.358900\pi$
$242$	87.6643	+	215.495i	0.362249	+	0.890476i
$243$	−240.526	+	64.4487i	−0.989818	+	0.265221i
$244$	38.3586	−	136.222i	0.157207	−	0.558288i
$245$	104.767	+	221.470i	0.427619	+	0.903959i
$246$	−29.9166	+	22.6559i	−0.121612	+	0.0920973i
$247$	−26.7136	+	7.15789i	−0.108152	+	0.0289793i
$248$	−25.0673	−	223.125i	−0.101078	−	0.899697i
$249$	229.190	−	132.323i	0.920441	−	0.531417i
$250$	−240.898	+	66.8460i	−0.963590	+	0.267384i
$251$	220.468			0.878358			0.439179	−	0.898400i	$-0.355269\pi$
$251$	220.468			0.878358			0.439179	+	0.898400i	$0.355269\pi$
$252$	−158.745	+	51.6907i	−0.629940	+	0.205122i
$253$	52.5700	+	52.5700i	0.207787	+	0.207787i
$254$	−74.7922	+	9.36452i	−0.294458	+	0.0368682i
$255$	155.456	−	49.8836i	0.609633	−	0.195622i
$256$	139.077	−	214.927i	0.543268	−	0.839559i
$257$	−269.757	+	72.2812i	−1.04964	+	0.281250i	−0.742103	−	0.670286i	$-0.766171\pi$
$257$	−269.757	+	72.2812i	−1.04964	+	0.281250i	−0.307536	+	0.951536i	$0.599505\pi$
$258$	203.698	+	28.1324i	0.789527	+	0.109040i
$259$	201.005	−	229.306i	0.776080	−	0.885353i
$260$	−141.333	+	43.3826i	−0.543588	+	0.166856i
$261$	−131.455	+	227.686i	−0.503658	+	0.872361i
$262$	−138.757	−	341.090i	−0.529606	−	1.30187i
$263$	−136.671	−	36.6208i	−0.519661	−	0.139243i	−0.0105513	−	0.999944i	$-0.503359\pi$
$263$	−136.671	−	36.6208i	−0.519661	−	0.139243i	−0.509110	+	0.860702i	$0.670025\pi$
$264$	4.50424	−	29.8185i	0.0170615	−	0.112949i
$265$	−84.5498	−	131.243i	−0.319056	−	0.495255i
$266$	43.3722	+	29.3655i	0.163053	+	0.110397i
$267$	−6.21876	−	6.21876i	−0.0232912	−	0.0232912i
$268$	38.9529	+	0.494008i	0.145347	+	0.00184331i
$269$	−199.921	−	346.273i	−0.743200	−	1.28726i	−0.951031	−	0.309096i	$-0.899974\pi$
$269$	−199.921	−	346.273i	−0.743200	−	1.28726i	0.207830	−	0.978165i	$-0.433360\pi$
$270$	213.424	+	149.845i	0.790458	+	0.554980i
$271$	67.9963	−	117.773i	0.250909	−	0.434587i	−0.712867	−	0.701299i	$-0.752604\pi$
$271$	67.9963	−	117.773i	0.250909	−	0.434587i	0.963776	+	0.266712i	$0.0859372\pi$
$272$	70.2164	+	291.423i	0.258149	+	1.07141i
$273$	39.8687	−	80.8918i	0.146039	−	0.296307i
$274$	−394.064	+	298.425i	−1.43819	+	1.08914i
$275$	−31.4622	−	43.9763i	−0.114408	−	0.159914i
$276$	59.0807	+	232.233i	0.214060	+	0.841424i
$277$	183.904	+	49.2769i	0.663913	+	0.177895i	0.575011	−	0.818145i	$-0.304998\pi$
$277$	183.904	+	49.2769i	0.663913	+	0.177895i	0.0889017	+	0.996040i	$0.471664\pi$
$278$	−209.837	−	163.138i	−0.754811	−	0.586828i
$279$			167.343i			0.599794i
$280$	237.359	+	148.528i	0.847712	+	0.530456i
$281$	38.0362			0.135360			0.0676800	−	0.997707i	$-0.478440\pi$
$281$	38.0362			0.135360			0.0676800	+	0.997707i	$0.478440\pi$
$282$	78.6968	−	101.224i	0.279067	−	0.358951i
$283$	41.5239	−	154.969i	0.146727	−	0.547594i	−0.852945	−	0.522001i	$-0.825186\pi$
$283$	41.5239	−	154.969i	0.146727	−	0.547594i	0.999672	−	0.0255936i	$-0.00814758\pi$
$284$	40.2330	−	10.2354i	0.141665	−	0.0360400i
$285$	−1.58732	−	32.5641i	−0.00556955	−	0.114260i
$286$	−19.3047	−	25.4914i	−0.0674990	−	0.0891309i
$287$	62.6519	−	41.8832i	0.218299	−	0.145934i
$288$	−120.891	+	147.613i	−0.419759	+	0.512544i
$289$	−53.7002	−	31.0038i	−0.185814	−	0.107280i
$290$	434.340	−	76.0180i	1.49772	−	0.262131i
$291$	−217.463	+	125.553i	−0.747297	+	0.431452i
$292$	−6.66576	+	525.600i	−0.0228279	+	1.80000i
$293$	2.88977	−	2.88977i	0.00986271	−	0.00986271i	−0.702158	−	0.712021i	$-0.747780\pi$
$293$	2.88977	−	2.88977i	0.00986271	−	0.00986271i	0.712021	+	0.702158i	$0.247780\pi$
$294$	−165.238	+	43.2340i	−0.562032	+	0.147055i
$295$	15.7285	−	72.6898i	0.0533170	−	0.246406i
$296$	52.0516	−	344.586i	0.175850	−	1.16414i
$297$	−14.5980	+	54.4805i	−0.0491515	+	0.183436i
$298$	45.5191	−	18.5173i	0.152749	−	0.0621388i
$299$	220.048	+	127.045i	0.735945	+	0.424898i
$300$	−14.7496	−	173.660i	−0.0491655	−	0.578868i
$301$	−405.032	−	80.4707i	−1.34562	−	0.267344i
$302$	−35.5974	+	257.749i	−0.117872	+	0.853475i
$303$	26.2599	+	98.0034i	0.0866664	+	0.323444i
$304$	59.8416	+	1.51809i	0.196847	+	0.00499371i
$305$	168.440	−	54.0500i	0.552264	−	0.177213i
$306$	−27.7565	−	221.685i	−0.0907075	−	0.724459i
$307$	−277.450	+	277.450i	−0.903747	+	0.903747i	−0.995758	−	0.0920112i	$-0.970670\pi$
$307$	−277.450	+	277.450i	−0.903747	+	0.903747i	0.0920112	+	0.995758i	$0.470670\pi$
$308$	−12.5537	+	59.2453i	−0.0407587	+	0.192355i
$309$			165.989i			0.537182i
$310$	215.227	−	180.132i	0.694281	−	0.581072i
$311$	−143.290	−	248.185i	−0.460739	−	0.798024i	0.538259	−	0.842780i	$-0.319082\pi$
$311$	−143.290	−	248.185i	−0.460739	−	0.798024i	−0.998998	+	0.0447559i	$0.985749\pi$
$312$	−11.5068	−	102.422i	−0.0368807	−	0.328276i
$313$	92.8419	+	346.491i	0.296620	+	1.10700i	0.939923	+	0.341388i	$0.110897\pi$
$313$	92.8419	+	346.491i	0.296620	+	1.10700i	−0.643303	+	0.765612i	$0.722436\pi$
$314$	231.659	+	305.901i	0.737769	+	0.974207i
$315$	−163.441	−	129.757i	−0.518859	−	0.411927i
$316$	259.997	+	73.2122i	0.822776	+	0.231684i
$317$	−72.7458	−	271.491i	−0.229482	−	0.856439i	−0.980559	−	0.196224i	$-0.937132\pi$
$317$	−72.7458	−	271.491i	−0.229482	−	0.856439i	0.751077	−	0.660215i	$-0.229535\pi$
$318$	100.815	−	41.0119i	0.317028	−	0.128968i
$319$	47.6852	+	82.5932i	0.149483	+	0.258913i
$320$	319.982	−	3.41161i	0.999943	−	0.0106613i
$321$			279.373i			0.870322i
$322$	−90.9947	−	472.544i	−0.282592	−	1.46753i
$323$	−49.5640	+	49.5640i	−0.153449	+	0.153449i
$324$	23.5222	−	22.9331i	0.0725995	−	0.0707811i
$325$	−142.764	−	117.346i	−0.439274	−	0.361064i
$326$	156.923	+	66.1684i	0.481358	+	0.202970i
$327$	5.29068	+	19.7451i	0.0161794	+	0.0603825i
$328$	34.4674	−	78.9308i	0.105084	−	0.240643i
$329$	−169.728	+	193.626i	−0.515889	+	0.588527i
$330$	34.1843	−	15.8876i	0.103589	−	0.0481444i
$331$	−488.925	−	282.281i	−1.47711	−	0.852813i	−0.477449	−	0.878659i	$-0.658438\pi$
$331$	−488.925	−	282.281i	−1.47711	−	0.852813i	−0.999666	+	0.0258468i	$0.991772\pi$
$332$	−310.338	+	522.116i	−0.934752	+	1.57264i
$333$	−67.2245	+	250.885i	−0.201875	+	0.753410i
$334$	21.7181	+	173.457i	0.0650242	+	0.519333i
$335$	26.3719	+	40.9358i	0.0787219	+	0.122196i
$336$	−132.352	+	143.478i	−0.393906	+	0.427017i
$337$	39.0473	−	39.0473i	0.115867	−	0.115867i	−0.646796	−	0.762663i	$-0.723891\pi$
$337$	39.0473	−	39.0473i	0.115867	−	0.115867i	0.762663	+	0.646796i	$0.223891\pi$
$338$	180.565	+	140.380i	0.534216	+	0.415327i
$339$	247.434	−	142.856i	0.729895	−	0.421405i
$340$	−255.241	+	274.327i	−0.750709	+	0.806843i
$341$	52.5708	+	30.3518i	0.154167	+	0.0890081i
$342$	−44.1952	−	6.10373i	−0.129226	−	0.0178472i
$343$	336.364	−	67.1442i	0.980653	−	0.195756i
$344$	−439.373	+	172.278i	−1.27725	+	0.500808i
$345$	−201.242	+	221.866i	−0.583310	+	0.643091i
$346$	133.717	+	56.3836i	0.386467	+	0.162958i
$347$	120.407	−	449.365i	0.346994	−	1.29500i	−0.543272	−	0.839557i	$-0.682815\pi$
$347$	120.407	−	449.365i	0.346994	−	1.29500i	0.890266	−	0.455442i	$-0.150519\pi$
$348$	−3.89818	+	307.375i	−0.0112017	+	0.883260i
$349$	−37.2020			−0.106596			−0.0532980	−	0.998579i	$-0.516973\pi$
$349$	−37.2020			−0.106596			−0.0532980	+	0.998579i	$0.516973\pi$
$350$	9.04564	+	349.883i	0.0258447	+	0.999666i
$351$			192.766i			0.549191i
$352$	24.4461	+	64.7512i	0.0694492	+	0.183952i
$353$	−259.120	−	69.4309i	−0.734050	−	0.196688i	−0.127618	−	0.991823i	$-0.540733\pi$
$353$	−259.120	−	69.4309i	−0.734050	−	0.196688i	−0.606432	+	0.795135i	$0.707400\pi$
$354$	47.7744	+	20.1447i	0.134956	+	0.0569058i
$355$	38.4370	+	34.8640i	0.108273	+	0.0982083i
$356$	19.4289	+	5.47094i	0.0545755	+	0.0153678i
$357$	−15.0007	−	228.077i	−0.0420189	−	0.638870i
$358$	80.7646	+	11.1543i	0.225599	+	0.0311572i
$359$	219.855	−	380.800i	0.612409	−	1.06072i	−0.378424	−	0.925632i	$-0.623534\pi$
$359$	219.855	−	380.800i	0.612409	−	1.06072i	0.990833	−	0.135092i	$-0.0431329\pi$
$360$	−237.277	−	24.0986i	−0.659104	−	0.0669406i
$361$	−173.501	−	300.513i	−0.480613	−	0.832446i
$362$	−153.945	−	119.685i	−0.425263	−	0.330621i
$363$	−143.354	−	143.354i	−0.394913	−	0.394913i
$364$	10.9636	+	206.687i	0.0301196	+	0.567822i
$365$	−552.355	+	355.841i	−1.51330	+	0.974906i
$366$	15.3215	+	122.369i	0.0418620	+	0.334342i
$367$	288.521	+	77.3091i	0.786162	+	0.210651i	0.629500	−	0.777001i	$-0.283260\pi$
$367$	288.521	+	77.3091i	0.786162	+	0.210651i	0.156662	+	0.987652i	$0.449927\pi$
$368$	−378.901	−	398.626i	−1.02962	−	1.08322i
$369$	−32.0960	+	55.5918i	−0.0869809	+	0.150655i
$370$	395.038	−	183.600i	1.06767	−	0.496216i
$371$	−206.952	+	70.3030i	−0.557822	+	0.189496i
$372$	95.6736	+	170.674i	0.257187	+	0.458801i
$373$	336.642	−	90.2030i	0.902526	−	0.241831i	0.222425	−	0.974950i	$-0.428603\pi$
$373$	336.642	−	90.2030i	0.902526	−	0.241831i	0.680101	+	0.733119i	$0.261936\pi$
$374$	−74.6767	−	31.4883i	−0.199670	−	0.0841934i
$375$	170.799	−	135.238i	0.455465	−	0.360634i
$376$	−43.9522	+	290.967i	−0.116894	+	0.773849i
$377$	230.479	+	230.479i	0.611351	+	0.611351i
$378$	275.951	−	239.034i	0.730030	−	0.632364i
$379$	−29.4521			−0.0777100			−0.0388550	−	0.999245i	$-0.512371\pi$
$379$	−29.4521			−0.0777100			−0.0388550	+	0.999245i	$0.512371\pi$
$380$	39.7227	+	63.4117i	0.104533	+	0.166873i
$381$	56.8848	−	32.8425i	0.149304	−	0.0862007i
$382$	495.823	−	201.703i	1.29797	−	0.528018i
$383$	−615.618	+	164.954i	−1.60736	+	0.430690i	−0.947254	−	0.320484i	$-0.896155\pi$
$383$	−615.618	+	164.954i	−1.60736	+	0.430690i	−0.660104	+	0.751174i	$0.729488\pi$
$384$	−38.9036	+	219.667i	−0.101312	+	0.572050i
$385$	−70.4074	+	27.8103i	−0.182876	+	0.0722346i
$386$	44.3520	+	58.5659i	0.114902	+	0.151725i
$387$	339.755	−	91.0372i	0.877921	−	0.235238i
$388$	294.460	−	495.402i	0.758916	−	1.27681i
$389$	−378.849	+	218.729i	−0.973905	+	0.562284i	−0.900425	−	0.435012i	$-0.856744\pi$
$389$	−378.849	+	218.729i	−0.973905	+	0.562284i	−0.0734807	+	0.997297i	$0.523411\pi$
$390$	98.7968	−	82.6871i	0.253325	−	0.212018i
$391$	643.989			1.64703
$392$	282.285	−	271.991i	0.720115	−	0.693855i
$393$	226.903	+	226.903i	0.577360	+	0.577360i
$394$	31.8753	+	254.581i	0.0809019	+	0.646144i
$395$	103.161	+	321.490i	0.261167	+	0.813898i
$396$	−12.7181	−	49.9919i	−0.0321163	−	0.126242i
$397$	400.216	−	107.238i	1.00810	−	0.270120i	0.283265	−	0.959042i	$-0.408582\pi$
$397$	400.216	−	107.238i	1.00810	−	0.270120i	0.724836	+	0.688922i	$0.241916\pi$
$398$	−106.823	+	773.474i	−0.268400	+	1.94340i
$399$	−44.7688	−	8.89455i	−0.112203	−	0.0222921i
$400$	224.418	+	331.114i	0.561045	+	0.827785i
$401$	−28.3227	+	49.0564i	−0.0706302	+	0.122335i	−0.899178	−	0.437584i	$-0.855834\pi$
$401$	−28.3227	+	49.0564i	−0.0706302	+	0.122335i	0.828547	+	0.559919i	$0.189168\pi$
$402$	−31.4451	+	12.7920i	−0.0782216	+	0.0318209i
$403$	200.397	+	53.6962i	0.497263	+	0.133241i
$404$	−162.556	−	166.732i	−0.402366	−	0.412703i
$405$	40.1356	+	8.68447i	0.0991002	+	0.0214431i
$406$	44.1404	−	615.738i	0.108720	−	1.51660i
$407$	66.6230	+	66.6230i	0.163693	+	0.163693i
$408$	−155.051	−	210.229i	−0.380028	−	0.515266i
$409$	−53.1735	−	92.0992i	−0.130009	−	0.225181i	0.793671	−	0.608347i	$-0.208167\pi$
$409$	−53.1735	−	92.0992i	−0.130009	−	0.225181i	−0.923680	+	0.383166i	$0.874834\pi$
$410$	106.048	−	18.5606i	0.258654	−	0.0452697i
$411$	215.379	−	373.047i	0.524035	−	0.907656i
$412$	−186.281	−	332.309i	−0.452137	−	0.806576i
$413$	−93.3935	−	46.0303i	−0.226134	−	0.111454i
$414$	247.463	+	326.769i	0.597736	+	0.789297i
$415$	−758.329	+	36.9644i	−1.82730	+	0.0890708i
$416$	137.979	+	192.135i	0.331680	+	0.461863i
$417$	223.727	+	59.9475i	0.536516	+	0.143759i
$418$	−9.93340	+	12.7769i	−0.0237641	+	0.0305667i
$419$		−	25.1968i		−	0.0601355i	−0.999548	−	0.0300677i	$-0.990428\pi$
$419$		−	25.1968i		−	0.0601355i	0.999548	−	0.0300677i	$-0.00957230\pi$
$420$	−240.880	−	38.8975i	−0.573523	−	0.0926130i
$421$	345.793			0.821361			0.410680	−	0.911779i	$-0.365291\pi$
$421$	345.793			0.821361			0.410680	+	0.911779i	$0.365291\pi$
$422$	421.326	+	327.560i	0.998404	+	0.776209i
$423$	56.7641	−	211.847i	0.134194	−	0.500820i
$424$	−155.805	+	195.244i	−0.367465	+	0.460482i
$425$	−462.066	−	76.6494i	−1.08721	−	0.180352i
$426$	−28.8401	+	21.8407i	−0.0676999	+	0.0512692i
$427$	−16.2536	−	247.126i	−0.0380647	−	0.578749i
$428$	−313.525	−	559.303i	−0.732535	−	1.30678i
$429$	24.1319	+	13.9325i	0.0562514	+	0.0324768i
$430$	−482.810	−	338.980i	−1.12281	−	0.788327i
$431$	−463.036	+	267.334i	−1.07433	+	0.620264i	−0.929361	−	0.369173i	$-0.879641\pi$
$431$	−463.036	+	267.334i	−1.07433	+	0.620264i	−0.144968	+	0.989436i	$0.546308\pi$
$432$	118.175	−	400.153i	0.273554	−	0.926281i
$433$	494.564	−	494.564i	1.14218	−	1.14218i	0.154129	−	0.988051i	$-0.450743\pi$
$433$	494.564	−	494.564i	1.14218	−	1.14218i	0.988051	−	0.154129i	$-0.0492573\pi$
$434$	−171.628	−	353.460i	−0.395457	−	0.814423i
$435$	−323.021	+	208.098i	−0.742577	+	0.478387i
$436$	−32.7507	−	33.5921i	−0.0751162	−	0.0770460i
$437$	33.2843	−	124.219i	0.0761654	−	0.284253i
$438$	−172.605	−	424.295i	−0.394075	−	0.968710i
$439$	234.445	+	135.357i	0.534044	+	0.308330i	0.742662	−	0.669667i	$-0.233563\pi$
$439$	234.445	+	135.357i	0.534044	+	0.308330i	−0.208618	+	0.977997i	$0.566896\pi$
$440$	−50.6068	+	70.1700i	−0.115016	+	0.159477i
$441$	−231.706	+	177.961i	−0.525410	+	0.403539i
$442$	−274.379	−	37.8941i	−0.620767	−	0.0857333i
$443$	140.265	+	523.477i	0.316626	+	1.18166i	0.922466	+	0.386078i	$0.126170\pi$
$443$	140.265	+	523.477i	0.316626	+	1.18166i	−0.605840	+	0.795587i	$0.707163\pi$
$444$	74.8742	+	294.314i	0.168636	+	0.662869i
$445$	7.70895	+	24.0240i	0.0173235	+	0.0539866i
$446$	418.939	−	52.4542i	0.939326	−	0.117610i
$447$	−30.2806	+	30.2806i	−0.0677418	+	0.0677418i
$448$	103.951	−	435.773i	0.232034	−	0.972708i
$449$		−	623.701i		−	1.38909i	−0.719449	−	0.694545i	$-0.755606\pi$
$449$		−	623.701i		−	1.38909i	0.719449	−	0.694545i	$-0.244394\pi$
$450$	−138.663	−	263.912i	−0.308140	−	0.586472i
$451$	11.6428	+	20.1660i	0.0258156	+	0.0447139i
$452$	−335.042	+	563.679i	−0.741244	+	1.24708i
$453$	−58.6852	−	219.016i	−0.129548	−	0.483479i
$454$	22.6816	−	17.1768i	0.0499594	−	0.0378343i
$455$	−207.832	+	154.088i	−0.456773	+	0.338656i
$456$	−48.5646	+	19.0422i	−0.106501	+	0.0417591i
$457$	−29.4850	−	110.039i	−0.0645185	−	0.240786i	0.926134	−	0.377194i	$-0.123111\pi$
$457$	−29.4850	−	110.039i	−0.0645185	−	0.240786i	−0.990653	+	0.136408i	$0.956444\pi$
$458$	−233.560	−	574.133i	−0.509955	−	1.25356i
$459$	244.283	+	423.110i	0.532206	+	0.921808i
$460$	153.897	−	670.017i	0.334559	−	1.45656i
$461$			254.159i			0.551321i	0.961255	+	0.275661i	$0.0888966\pi$
$461$			254.159i			0.551321i	−0.961255	+	0.275661i	$0.911103\pi$
$462$	−9.97907	−	51.8222i	−0.0215997	−	0.112169i
$463$	−125.284	+	125.284i	−0.270593	+	0.270593i	−0.829339	−	0.558746i	$-0.811283\pi$
$463$	−125.284	+	125.284i	−0.270593	+	0.270593i	0.558746	+	0.829339i	$0.311283\pi$
$464$	−337.145	−	619.736i	−0.726606	−	1.33564i
$465$	−111.831	+	217.511i	−0.240496	+	0.467766i
$466$	−85.7347	+	203.326i	−0.183980	+	0.436321i
$467$	171.331	+	639.415i	0.366875	+	1.36920i	0.864861	+	0.502012i	$0.167407\pi$
$467$	171.331	+	639.415i	0.366875	+	1.36920i	−0.497985	+	0.867186i	$0.665927\pi$
$468$	−86.2064	−	153.785i	−0.184202	−	0.328601i
$469$	64.5502	−	21.9281i	0.137634	−	0.0467551i
$470$	−333.569	+	155.031i	−0.709720	+	0.329853i
$471$	−289.586	−	167.192i	−0.614832	−	0.354973i
$472$	−118.251	+	13.2851i	−0.250532	+	0.0281464i
$473$	33.0238	−	123.246i	0.0698177	−	0.260563i
$474$	−233.557	+	29.2430i	−0.492735	+	0.0616940i
$475$	−38.6665	+	85.1659i	−0.0814032	+	0.179297i
$476$	285.989	+	439.773i	0.600817	+	0.923893i
$477$	131.643	−	131.643i	0.275981	−	0.275981i
$478$	−312.371	+	401.789i	−0.653496	+	0.840562i
$479$	−525.501	+	303.398i	−1.09708	+	0.633399i	−0.935452	−	0.353453i	$-0.885008\pi$
$479$	−525.501	+	303.398i	−1.09708	+	0.633399i	−0.161627	+	0.986852i	$0.551674\pi$
$480$	−255.779	+	111.079i	−0.532873	+	0.231414i
$481$	278.871	+	161.006i	0.579773	+	0.334732i
$482$	−10.5818	+	76.6191i	−0.0219539	+	0.158961i
$483$	233.059	+	348.627i	0.482524	+	0.721794i
$484$	447.870	+	126.115i	0.925352	+	0.260568i
$485$	719.530	−	35.0732i	1.48357	−	0.0723158i
$486$	−193.498	+	458.894i	−0.398144	+	0.944226i
$487$	92.4450	−	345.009i	0.189825	−	0.708438i	−0.803720	−	0.595007i	$-0.797149\pi$
$487$	92.4450	−	345.009i	0.189825	−	0.708438i	0.993546	−	0.113431i	$-0.0361841\pi$
$488$	−168.001	−	227.787i	−0.344265	−	0.466777i
$489$	−148.407			−0.303490
$490$	478.298	+	106.446i	0.976119	+	0.217236i
$491$		−	498.639i		−	1.01556i	−0.861487	−	0.507779i	$-0.830467\pi$
$491$		−	498.639i		−	1.01556i	0.861487	−	0.507779i	$-0.169533\pi$
$492$	−0.951779	+	75.0485i	−0.00193451	+	0.152538i
$493$	797.964	+	213.814i	1.61859	+	0.433699i
$494$	−21.4905	+	50.9663i	−0.0435031	+	0.103171i
$495$	43.3206	−	47.7603i	0.0875163	−	0.0964854i
$496$	−383.076	−	234.319i	−0.772330	−	0.472417i
$497$	60.3975	−	40.3761i	0.121524	−	0.0812395i
$498$	72.4123	−	524.314i	0.145406	−	1.05284i
$499$	115.618	−	200.256i	0.231699	−	0.401315i	−0.726609	−	0.687051i	$-0.758905\pi$
$499$	115.618	−	200.256i	0.231699	−	0.401315i	0.958308	+	0.285736i	$0.0922382\pi$
$500$	−190.169	+	462.424i	−0.380338	+	0.924847i
$501$	−76.1679	−	131.927i	−0.152032	−	0.263327i
$502$	270.637	−	348.109i	0.539118	−	0.693444i
$503$	−222.363	−	222.363i	−0.442073	−	0.442073i	0.450635	−	0.892708i	$-0.351197\pi$
$503$	−222.363	−	222.363i	−0.442073	−	0.442073i	−0.892708	+	0.450635i	$0.851197\pi$
$504$	−113.251	+	314.104i	−0.224705	+	0.623223i
$505$	61.5579	−	284.492i	0.121897	−	0.563350i
$506$	147.538	−	18.4729i	0.291578	−	0.0365076i
$507$	−192.517	−	51.5848i	−0.379718	−	0.101745i
$508$	−77.0257	+	129.589i	−0.151625	+	0.255097i
$509$	111.029	−	192.309i	0.218132	−	0.377816i	−0.736105	−	0.676868i	$-0.763337\pi$
$509$	111.029	−	192.309i	0.218132	−	0.377816i	0.954237	+	0.299051i	$0.0966702\pi$
$510$	112.068	−	306.694i	0.219741	−	0.601360i
$511$	295.881	+	870.990i	0.579023	+	1.70448i
$512$	−168.636	−	483.432i	−0.329366	−	0.944202i
$513$	94.2391	−	25.2513i	0.183702	−	0.0492228i
$514$	−217.014	+	514.664i	−0.422207	+	1.00129i
$515$	217.739	−	423.504i	0.422794	−	0.822337i
$516$	294.471	−	287.096i	0.570681	−	0.556387i
$517$	−56.2562	−	56.2562i	−0.108813	−	0.108813i
$518$	−115.319	−	598.864i	−0.222624	−	1.15611i
$519$	−126.461			−0.243662
$520$	−104.995	+	276.413i	−0.201914	+	0.531564i
$521$	559.257	−	322.887i	1.07343	−	0.619745i	0.144314	−	0.989532i	$-0.453903\pi$
$521$	559.257	−	322.887i	1.07343	−	0.619745i	0.929117	+	0.369787i	$0.120569\pi$
$522$	198.138	+	487.059i	0.379574	+	0.933064i
$523$	−726.018	+	194.536i	−1.38818	+	0.371962i	−0.874086	−	0.485772i	$-0.838539\pi$
$523$	−726.018	+	194.536i	−1.38818	+	0.371962i	−0.514095	+	0.857734i	$0.671872\pi$
$524$	−708.897	−	199.617i	−1.35286	−	0.380949i
$525$	−125.727	−	277.881i	−0.239479	−	0.529297i
$526$	−225.594	+	170.843i	−0.428886	+	0.324796i
$527$	507.906	−	136.093i	0.963769	−	0.258241i
$528$	−41.5528	−	43.7159i	−0.0786984	−	0.0827953i
$529$	−565.097	+	326.259i	−1.06824	+	0.616747i
$530$	−311.016	−	27.6078i	−0.586823	−	0.0520902i
$531$	88.6879			0.167020
$532$	99.6087	−	32.4347i	0.187234	−	0.0609676i
$533$	56.2738	+	56.2738i	0.105579	+	0.105579i
$534$	−17.4530	+	2.18525i	−0.0326836	+	0.00409222i
$535$	366.472	−	712.791i	0.684994	−	1.33232i
$536$	48.5971	−	60.8985i	0.0906662	−	0.113617i
$537$	−68.6277	+	18.3887i	−0.127798	+	0.0342434i
$538$	−792.165	−	109.405i	−1.47242	−	0.203355i
$539$	13.8808	+	105.068i	0.0257530	+	0.194932i
$540$	498.588	−	153.043i	0.923311	−	0.283414i
$541$	138.942	−	240.655i	0.256825	−	0.444833i	−0.708565	−	0.705646i	$-0.750657\pi$
$541$	138.942	−	240.655i	0.256825	−	0.444833i	0.965390	+	0.260812i	$0.0839904\pi$
$542$	−102.489	−	251.937i	−0.189094	−	0.464828i
$543$	164.135	+	43.9799i	0.302275	+	0.0809943i
$544$	546.339	+	246.871i	1.00430	+	0.453807i
$545$	12.4023	−	57.3175i	0.0227565	−	0.105170i
$546$	−78.7834	−	162.250i	−0.144292	−	0.297162i
$547$	−304.412	−	304.412i	−0.556512	−	0.556512i	0.371800	−	0.928313i	$-0.378741\pi$
$547$	−304.412	−	304.412i	−0.556512	−	0.556512i	−0.928313	+	0.371800i	$0.878741\pi$
$548$	−12.5369	+	988.544i	−0.0228775	+	1.80391i
$549$	105.476	+	182.689i	0.192123	+	0.332767i
$550$	−108.058	−	4.30607i	−0.196470	−	0.00782922i
$551$	82.4848	−	142.868i	0.149700	−	0.259288i
$552$	439.211	+	191.794i	0.795671	+	0.347453i
$553$	471.671	−	31.0221i	0.852931	−	0.0560978i
$554$	303.559	−	229.886i	0.547940	−	0.414956i
$555$	−255.038	+	281.176i	−0.459528	+	0.506623i
$556$	−515.176	+	131.062i	−0.926575	+	0.235723i
$557$	569.245	+	152.529i	1.02198	+	0.273840i	0.730628	−	0.682775i	$-0.239227\pi$
$557$	569.245	+	152.529i	1.02198	+	0.273840i	0.291355	+	0.956615i	$0.405894\pi$
$558$	264.226	+	205.423i	0.473524	+	0.368141i
$559$		−	436.077i		−	0.780103i
$560$	525.891	−	192.453i	0.939092	−	0.343666i
$561$	70.6240			0.125890
$562$	46.6916	−	60.0574i	0.0830812	−	0.106864i
$563$	−210.166	+	784.349i	−0.373296	+	1.39316i	0.482522	+	0.875884i	$0.339721\pi$
$563$	−210.166	+	784.349i	−0.373296	+	1.39316i	−0.855818	+	0.517276i	$0.826946\pi$
$564$	−63.2235	−	248.517i	−0.112098	−	0.440634i
$565$	−818.696	+	39.9070i	−1.44902	+	0.0706318i
$566$	−193.716	−	255.798i	−0.342255	−	0.451940i
$567$	25.4156	−	51.5671i	0.0448247	−	0.0909472i
$568$	33.2272	−	76.0906i	0.0584985	−	0.133962i
$569$	−125.729	−	72.5899i	−0.220966	−	0.127575i	0.385432	−	0.922736i	$-0.374053\pi$
$569$	−125.729	−	72.5899i	−0.220966	−	0.127575i	−0.606397	+	0.795162i	$0.707386\pi$
$570$	−53.3658	−	37.4680i	−0.0936242	−	0.0657334i
$571$	770.742	−	444.988i	1.34981	−	0.779314i	0.361588	−	0.932338i	$-0.382235\pi$
$571$	770.742	−	444.988i	1.34981	−	0.779314i	0.988222	+	0.153024i	$0.0489012\pi$
$572$	−63.9475	−	0.810994i	−0.111796	−	0.00141782i
$573$	−329.835	+	329.835i	−0.575629	+	0.575629i
$574$	10.7773	−	150.339i	0.0187758	−	0.261914i
$575$	804.483	−	302.086i	1.39910	−	0.525366i
$576$	84.6735	+	372.084i	0.147003	+	0.645979i
$577$	−50.0130	+	186.651i	−0.0866777	+	0.323486i	−0.995627	−	0.0934219i	$-0.970219\pi$
$577$	−50.0130	+	186.651i	−0.0866777	+	0.323486i	0.908949	+	0.416908i	$0.136886\pi$
$578$	−114.874	+	46.7312i	−0.198744	+	0.0808498i
$579$	−55.4423	−	32.0096i	−0.0957553	−	0.0552843i
$580$	413.148	−	779.119i	0.712325	−	1.34331i
$581$	−207.130	+	1042.54i	−0.356506	+	1.79440i
$582$	−68.7074	+	497.488i	−0.118054	+	0.854791i
$583$	−17.4790	−	65.2324i	−0.0299811	−	0.111891i
$584$	821.716	+	655.730i	1.40705	+	1.12283i
$585$	100.765	−	195.988i	0.172247	−	0.335022i
$586$	−1.01545	−	8.11019i	−0.00173286	−	0.0138399i
$587$	−194.926	+	194.926i	−0.332072	+	0.332072i	−0.853373	−	0.521301i	$-0.825447\pi$
$587$	−194.926	+	194.926i	−0.332072	+	0.332072i	0.521301	+	0.853373i	$0.325447\pi$
$588$	−134.574	+	313.975i	−0.228868	+	0.533971i
$589$		−	105.004i		−	0.178274i
$590$	−95.4662	−	114.066i	−0.161807	−	0.193332i
$591$	−111.791	−	193.627i	−0.189155	−	0.327626i
$592$	−480.189	−	505.187i	−0.811131	−	0.853356i
$593$	−34.5742	−	129.033i	−0.0583040	−	0.217593i	0.930627	−	0.365969i	$-0.119262\pi$
$593$	−34.5742	−	129.033i	−0.0583040	−	0.217593i	−0.988931	+	0.148375i	$0.952596\pi$
$594$	68.1023	+	89.9276i	0.114650	+	0.151393i
$595$	−260.910	+	601.590i	−0.438504	+	1.01108i
$596$	26.6393	−	94.6037i	0.0446968	−	0.158731i
$597$	−176.107	−	657.240i	−0.294986	−	1.10090i
$598$	470.719	−	191.491i	0.787156	−	0.320218i
$599$	130.487	+	226.011i	0.217842	+	0.377314i	0.954148	−	0.299335i	$-0.0967649\pi$
$599$	130.487	+	226.011i	0.217842	+	0.377314i	−0.736306	+	0.676649i	$0.763432\pi$
$600$	−292.308	−	189.889i	−0.487180	−	0.316482i
$601$			169.367i			0.281809i	0.990023	+	0.140904i	$0.0450010\pi$
$601$			169.367i			0.281809i	−0.990023	+	0.140904i	$0.954999\pi$
$602$	−624.260	+	540.745i	−1.03698	+	0.898247i
$603$	−41.0606	+	41.0606i	−0.0680938	+	0.0680938i
$604$	363.277	+	372.609i	0.601451	+	0.616903i
$605$	177.705	+	553.797i	0.293727	+	0.915366i
$606$	186.979	+	78.8417i	0.308545	+	0.130102i
$607$	301.087	+	1123.67i	0.496025	+	1.85119i	0.524213	+	0.851587i	$0.324360\pi$
$607$	301.087	+	1123.67i	0.496025	+	1.85119i	−0.0281881	+	0.999603i	$0.508974\pi$
$608$	75.8561	−	92.6236i	0.124763	−	0.152341i
$609$	173.033	+	509.361i	0.284127	+	0.836389i
$610$	121.428	−	332.309i	0.199063	−	0.544769i
$611$	−235.478	−	135.953i	−0.385397	−	0.222509i
$612$	−384.103	−	228.305i	−0.627619	−	0.373047i
$613$	−241.494	+	901.270i	−0.393955	+	1.47026i	0.429597	+	0.903021i	$0.358655\pi$
$613$	−241.494	+	901.270i	−0.393955	+	1.47026i	−0.823553	+	0.567240i	$0.808011\pi$
$614$	97.4948	+	778.668i	0.158786	+	1.26819i
$615$	−78.8687	+	50.8092i	−0.128242	+	0.0826166i
$616$	78.1352	+	92.5487i	0.126843	+	0.150241i
$617$	−167.964	+	167.964i	−0.272227	+	0.272227i	−0.829996	−	0.557769i	$-0.811657\pi$
$617$	−167.964	+	167.964i	−0.272227	+	0.272227i	0.557769	+	0.829996i	$0.311657\pi$
$618$	262.090	+	203.762i	0.424093	+	0.329712i
$619$	−332.254	+	191.827i	−0.536759	+	0.309898i	−0.743765	−	0.668442i	$-0.766962\pi$
$619$	−332.254	+	191.827i	−0.536759	+	0.309898i	0.207005	+	0.978340i	$0.433628\pi$
$620$	−20.2169	−	560.957i	−0.0326080	−	0.904769i
$621$	−776.274	−	448.182i	−1.25004	−	0.721710i
$622$	−567.770	−	78.4140i	−0.912814	−	0.126067i
$623$	35.2467	−	2.31819i	0.0565757	−	0.00372102i
$624$	−175.845	−	107.561i	−0.281803	−	0.172373i
$625$	−613.176	+	120.996i	−0.981082	+	0.193594i
$626$	661.062	+	278.745i	1.05601	+	0.445279i
$627$	3.65017	−	13.6226i	0.00582164	−	0.0217267i
$628$	767.379	+	9.73205i	1.22194	+	0.0154969i
$629$	816.141			1.29752
$630$	−405.514	+	98.7809i	−0.643673	+	0.156795i
$631$		−	845.639i		−	1.34016i	−0.742290	−	0.670079i	$-0.766260\pi$
$631$		−	845.639i		−	1.34016i	0.742290	−	0.670079i	$-0.233740\pi$
$632$	434.761	−	320.652i	0.687913	−	0.507360i
$633$	−449.215	−	120.367i	−0.709660	−	0.190153i
$634$	−517.972	−	218.409i	−0.816991	−	0.344494i
$635$	−188.217	+	9.17456i	−0.296405	+	0.0144481i
$636$	59.0003	−	209.527i	0.0927677	−	0.329444i
$637$	138.764	+	334.577i	0.217839	+	0.525238i
$638$	188.947	+	26.0953i	0.296156	+	0.0409017i
$639$	−30.9410	+	53.5914i	−0.0484210	+	0.0838677i
$640$	387.410	−	509.425i	0.605328	−	0.795976i
$641$	−4.97322	−	8.61387i	−0.00775853	−	0.0134382i	0.862120	−	0.506704i	$-0.169136\pi$
$641$	−4.97322	−	8.61387i	−0.00775853	−	0.0134382i	−0.869879	+	0.493266i	$0.835803\pi$
$642$	441.118	+	342.947i	0.687100	+	0.534186i
$643$	−242.772	−	242.772i	−0.377562	−	0.377562i	0.492660	−	0.870222i	$-0.336025\pi$
$643$	−242.772	−	242.772i	−0.377562	−	0.377562i	−0.870222	+	0.492660i	$0.836025\pi$
$644$	−857.826	−	436.399i	−1.33203	−	0.677638i
$645$	502.451	+	108.720i	0.778994	+	0.168557i
$646$	17.4166	+	139.102i	0.0269606	+	0.215328i
$647$	154.830	+	41.4865i	0.239304	+	0.0641213i	0.376478	−	0.926426i	$-0.377135\pi$
$647$	154.830	+	41.4865i	0.239304	+	0.0641213i	−0.137174	+	0.990547i	$0.543802\pi$
$648$	−7.33536	−	65.2923i	−0.0113200	−	0.100760i
$649$	16.0858	−	27.8614i	0.0247855	−	0.0429297i
$650$	−360.535	+	81.3691i	−0.554670	+	0.125183i
$651$	257.485	+	225.706i	0.395523	+	0.346706i
$652$	297.109	−	166.548i	0.455689	−	0.255442i
$653$	573.337	−	153.625i	0.878004	−	0.235260i	0.208458	−	0.978031i	$-0.433155\pi$
$653$	573.337	−	153.625i	0.878004	−	0.235260i	0.669546	+	0.742771i	$0.266489\pi$
$654$	37.6712	+	15.8845i	0.0576012	+	0.0242882i
$655$	−281.275	−	876.560i	−0.429427	−	1.33826i
$656$	−82.3173	−	151.315i	−0.125484	−	0.230663i
$657$	−554.039	−	554.039i	−0.843286	−	0.843286i
$658$	97.3753	+	505.679i	0.147987	+	0.768509i
$659$	1189.73			1.80535			0.902675	−	0.430323i	$-0.141601\pi$
$659$	1189.73			1.80535			0.902675	+	0.430323i	$0.141601\pi$
$660$	16.8773	−	73.4785i	0.0255717	−	0.111331i
$661$	−65.9680	+	38.0866i	−0.0998002	+	0.0576197i	−0.549069	−	0.835777i	$-0.685018\pi$
$661$	−65.9680	+	38.0866i	−0.0998002	+	0.0576197i	0.449269	+	0.893396i	$0.351684\pi$
$662$	−1045.89	+	425.474i	−1.57990	+	0.642710i
$663$	233.147	−	62.4715i	0.351654	−	0.0942255i
$664$	443.440	+	1130.94i	0.667831	+	1.70322i
$665$	102.555	+	81.4196i	0.154218	+	0.122436i
$666$	313.615	+	414.121i	0.470893	+	0.621804i
$667$	−1464.01	+	392.281i	−2.19492	+	0.588128i
$668$	300.541	+	178.637i	0.449912	+	0.267421i
$669$	−318.633	+	183.963i	−0.476283	+	0.274982i
$670$	97.0087	+	8.61113i	0.144789	+	0.0128524i
$671$	76.5227			0.114043
$672$	64.0748	+	385.106i	0.0953494	+	0.573074i
$673$	−443.135	−	443.135i	−0.658447	−	0.658447i	0.296566	−	0.955012i	$-0.404159\pi$
$673$	−443.135	−	443.135i	−0.658447	−	0.658447i	−0.955012	+	0.296566i	$0.904159\pi$
$674$	−13.7210	−	109.587i	−0.0203576	−	0.162592i
$675$	503.637	+	413.968i	0.746129	+	0.613285i
$676$	443.309	−	112.779i	0.655782	−	0.166833i
$677$	−347.381	+	93.0805i	−0.513118	+	0.137490i	−0.506082	−	0.862486i	$-0.668907\pi$
$677$	−347.381	+	93.0805i	−0.513118	+	0.137490i	−0.00703675	+	0.999975i	$0.502240\pi$
$678$	78.1767	−	566.052i	0.115305	−	0.834885i
$679$	196.532	−	989.203i	0.289444	−	1.45685i
$680$	119.826	+	739.766i	0.176215	+	1.08789i
$681$	−12.3968	+	21.4719i	−0.0182038	+	0.0315299i
$682$	112.458	−	45.7483i	0.164894	−	0.0670797i
$683$	479.531	+	128.490i	0.702095	+	0.188126i	0.592169	−	0.805814i	$-0.298272\pi$
$683$	479.531	+	128.490i	0.702095	+	0.188126i	0.109926	+	0.993940i	$0.464938\pi$
$684$	−63.8897	+	62.2895i	−0.0934060	+	0.0910665i
$685$	−1038.86	+	669.262i	−1.51659	+	0.977025i
$686$	306.889	−	613.527i	0.447360	−	0.894354i
$687$	381.929	+	381.929i	0.555938	+	0.555938i
$688$	−267.338	+	905.232i	−0.388572	+	1.31574i
$689$	−115.405	−	199.887i	−0.167496	−	0.290111i
$690$	103.280	+	590.106i	0.149682	+	0.855226i
$691$	−569.887	+	987.073i	−0.824728	+	1.42847i	0.0773991	+	0.997000i	$0.475338\pi$
$691$	−569.887	+	987.073i	−0.824728	+	1.42847i	−0.902127	+	0.431471i	$0.857995\pi$
$692$	253.173	−	141.920i	0.365857	−	0.205086i
$693$	−50.1697	−	75.0475i	−0.0723949	−	0.108294i
$694$	−561.720	−	741.739i	−0.809394	−	1.06879i
$695$	−492.178	−	446.427i	−0.708170	−	0.642340i
$696$	480.545	+	383.476i	0.690439	+	0.550971i
$697$	194.831	+	52.2047i	0.279528	+	0.0748992i
$698$	−45.6676	+	58.7402i	−0.0654264	+	0.0841551i
$699$		−	192.291i		−	0.275095i
$700$	563.554	+	415.220i	0.805077	+	0.593171i
$701$	102.497			0.146216			0.0731080	−	0.997324i	$-0.476708\pi$
$701$	102.497			0.146216			0.0731080	+	0.997324i	$0.476708\pi$
$702$	304.369	+	236.632i	0.433574	+	0.337082i
$703$	42.1819	−	157.425i	0.0600027	−	0.223933i
$704$	132.248	+	40.8866i	0.187853	+	0.0580775i
$705$	215.353	−	237.424i	0.305466	−	0.336771i
$706$	−427.713	+	323.908i	−0.605826	+	0.458793i
$707$	−365.522	−	180.153i	−0.517004	−	0.254813i
$708$	90.4534	−	50.7049i	0.127759	−	0.0716171i
$709$	−249.824	−	144.236i	−0.352362	−	0.203436i	0.313363	−	0.949633i	$-0.398544\pi$
$709$	−249.824	−	144.236i	−0.352362	−	0.203436i	−0.665725	+	0.746197i	$0.731878\pi$
$710$	102.232	−	17.8927i	0.143989	−	0.0252010i
$711$	−348.685	+	201.314i	−0.490415	+	0.283141i
$712$	32.4885	−	23.9614i	0.0456299	−	0.0336537i
$713$	−682.161	+	682.161i	−0.956747	+	0.956747i
$714$	−378.537	−	256.292i	−0.530164	−	0.358952i
$715$	−43.2936	−	67.2026i	−0.0605505	−	0.0939897i
$716$	116.755	−	113.831i	0.163066	−	0.158982i
$717$	114.785	−	428.384i	0.160091	−	0.597468i
$718$	−331.381	−	814.595i	−0.461533	−	1.13453i
$719$	−617.469	−	356.496i	−0.858789	−	0.495822i	0.00481747	−	0.999988i	$-0.498467\pi$
$719$	−617.469	−	356.496i	−0.858789	−	0.495822i	−0.863607	+	0.504166i	$0.831800\pi$
$720$	−329.323	+	345.068i	−0.457393	+	0.479261i
$721$	−501.335	−	439.459i	−0.695333	−	0.609513i
$722$	−687.480	−	94.9469i	−0.952188	−	0.131505i
$723$	−17.4449	−	65.1051i	−0.0241284	−	0.0900486i
$724$	−377.954	+	96.1524i	−0.522035	+	0.132807i
$725$	1097.13	−	107.213i	1.51328	−	0.147880i
$726$	−402.324	+	50.3738i	−0.554165	+	0.0693854i
$727$	473.258	−	473.258i	0.650974	−	0.650974i	−0.302253	−	0.953228i	$-0.597739\pi$
$727$	473.258	−	473.258i	0.650974	−	0.650974i	0.953228	+	0.302253i	$0.0977389\pi$
$728$	339.808	+	236.410i	0.466770	+	0.324739i
$729$		−	360.074i		−	0.493928i
$730$	−116.192	+	1308.96i	−0.159167	+	1.79309i
$731$	−552.620	−	957.165i	−0.755977	−	1.30939i
$732$	212.023	+	126.023i	0.289649	+	0.172163i
$733$	−298.640	−	1114.54i	−0.407421	−	1.52052i	−0.799547	−	0.600604i	$-0.794927\pi$
$733$	−298.640	−	1114.54i	−0.407421	−	1.52052i	0.392126	−	0.919912i	$-0.371740\pi$
$734$	476.245	−	360.661i	0.648835	−	0.491364i
$735$	−420.097	+	76.4700i	−0.571560	+	0.104041i
$736$	−1094.54	+	108.931i	−1.48714	+	0.148004i
$737$	5.45185	+	20.3466i	0.00739736	+	0.0276073i
$738$	48.3773	+	118.920i	0.0655519	+	0.161139i
$739$	187.857	+	325.378i	0.254204	+	0.440295i	0.964679	−	0.263428i	$-0.0848531\pi$
$739$	187.857	+	325.378i	0.254204	+	0.440295i	−0.710475	+	0.703723i	$0.751520\pi$
$740$	195.037	−	849.127i	0.263563	−	1.14747i
$741$		−	48.2003i		−	0.0650477i
$742$	−143.041	+	413.069i	−0.192777	+	0.556697i
$743$	1046.57	−	1046.57i	1.40857	−	1.40857i	0.641163	−	0.767405i	$-0.278452\pi$
$743$	1046.57	−	1046.57i	1.40857	−	1.40857i	0.767405	−	0.641163i	$-0.221548\pi$
$744$	386.931	+	58.4481i	0.520069	+	0.0785592i
$745$	116.979	−	37.5366i	0.157018	−	0.0503848i
$746$	270.822	−	642.272i	0.363032	−	0.860955i
$747$	−234.328	−	874.523i	−0.313692	−	1.17071i
$748$	−141.389	+	79.2574i	−0.189022	+	0.105959i
$749$	−843.787	−	739.644i	−1.12655	−	0.987508i
$750$	−3.86803	−	435.697i	−0.00515738	−	0.580929i
$751$	879.301	+	507.665i	1.17084	+	0.675985i	0.953878	−	0.300195i	$-0.0970517\pi$
$751$	879.301	+	507.665i	1.17084	+	0.675985i	0.216963	+	0.976180i	$0.430385\pi$
$752$	405.470	+	426.578i	0.539189	+	0.567258i
$753$	−99.4496	+	371.151i	−0.132071	+	0.492897i
$754$	646.843	−	80.9894i	0.857882	−	0.107413i
$755$	−137.568	+	635.777i	−0.182210	+	0.842088i
$756$	−38.6767	−	729.142i	−0.0511597	−	0.964474i
$757$	−270.760	+	270.760i	−0.357675	+	0.357675i	−0.862955	−	0.505280i	$-0.831389\pi$
$757$	−270.760	+	270.760i	−0.357675	+	0.357675i	0.505280	+	0.862955i	$0.331389\pi$
$758$	−36.1542	+	46.5035i	−0.0476968	+	0.0613503i
$759$	−112.214	+	64.7865i	−0.147844	+	0.0853577i
$760$	148.886	+	15.1213i	0.195903	+	0.0198965i
$761$	699.047	+	403.595i	0.918590	+	0.530348i	0.883185	−	0.469025i	$-0.155394\pi$
$761$	699.047	+	403.595i	0.918590	+	0.530348i	0.0354052	+	0.999373i	$0.488728\pi$
$762$	17.9727	−	130.135i	0.0235862	−	0.170780i
$763$	−73.6429	−	36.2959i	−0.0965175	−	0.0475700i
$764$	290.172	−	1030.48i	0.379807	−	1.34880i
$765$	−27.1934	−	557.876i	−0.0355470	−	0.729250i
$766$	−495.252	+	1174.52i	−0.646544	+	1.53332i
$767$	28.4578	−	106.206i	0.0371027	−	0.138469i
$768$	299.088	+	331.082i	0.389438	+	0.431096i
$769$	458.649			0.596422			0.298211	−	0.954500i	$-0.403610\pi$
$769$	458.649			0.596422			0.298211	+	0.954500i	$0.403610\pi$
$770$	−42.5180	+	145.309i	−0.0552182	+	0.188713i
$771$		−	486.733i		−	0.631301i
$772$	146.918	+	1.86324i	0.190308	+	0.00241352i
$773$	−1477.67	−	395.942i	−1.91161	−	0.512214i	−0.993174	−	0.116645i	$-0.962786\pi$
$773$	−1477.67	−	395.942i	−1.91161	−	0.512214i	−0.918436	−	0.395570i	$-0.870547\pi$
$774$	273.326	−	648.212i	0.353135	−	0.837483i
$775$	570.647	−	408.261i	0.736318	−	0.526789i
$776$	−420.751	−	1073.07i	−0.542206	−	1.38283i
$777$	295.361	+	441.822i	0.380129	+	0.568625i
$778$	−119.697	+	866.688i	−0.153852	+	1.11399i
$779$	20.1395	−	34.8826i	0.0258530	−	0.0447787i
$780$	−9.28029	−	257.499i	−0.0118978	−	0.330127i
$781$	11.2239	+	19.4403i	0.0143711	+	0.0248916i
$782$	790.535	−	1016.83i	1.01091	−	1.30029i
$783$	−813.075	−	813.075i	−1.03841	−	1.03841i
$784$	−82.9399	−	779.601i	−0.105791	−	0.994388i
$785$	519.530	+	806.442i	0.661821	+	1.02731i
$786$	636.805	−	79.7326i	0.810185	−	0.101441i
$787$	−608.862	−	163.144i	−0.773650	−	0.207299i	−0.149666	−	0.988737i	$-0.547820\pi$
$787$	−608.862	−	163.144i	−0.773650	−	0.207299i	−0.623983	+	0.781438i	$0.714487\pi$
$788$	441.101	+	262.183i	0.559772	+	0.332720i
$789$	123.300	−	213.562i	0.156274	−	0.270675i
$790$	634.254	+	231.761i	0.802853	+	0.293368i
$791$	−223.618	+	1125.54i	−0.282703	+	1.42293i
$792$	−94.5471	−	41.2868i	−0.119378	−	0.0521298i
$793$	252.620	−	67.6892i	0.318562	−	0.0853584i
$794$	321.966	−	763.564i	0.405498	−	0.961667i
$795$	259.082	−	83.1356i	0.325890	−	0.104573i
$796$	1090.15	+	1118.15i	1.36953	+	1.40472i
$797$	50.9226	+	50.9226i	0.0638928	+	0.0638928i	0.738331	−	0.674438i	$-0.235614\pi$
$797$	50.9226	+	50.9226i	0.0638928	+	0.0638928i	−0.674438	+	0.738331i	$0.735614\pi$
$798$	−69.0005	+	59.7694i	−0.0864668	+	0.0748990i
$799$	−689.146			−0.862511
$800$	798.301	+	52.1162i	0.997876	+	0.0651453i
$801$	−26.0563	+	15.0436i	−0.0325297	+	0.0187810i
$802$	42.6900	+	104.940i	0.0532294	+	0.130848i
$803$	−274.541	+	73.5630i	−0.341894	+	0.0916102i
$804$	−18.4027	+	65.3533i	−0.0228890	+	0.0812852i
$805$	−137.309	−	1195.20i	−0.170570	−	1.48472i
$806$	330.783	−	250.502i	0.410401	−	0.310797i
$807$	673.122	−	180.362i	0.834104	−	0.223497i
$808$	−462.809	+	51.9950i	−0.572784	+	0.0643503i
$809$	1371.38	−	791.765i	1.69515	−	0.978696i	0.744917	−	0.667157i	$-0.232489\pi$
$809$	1371.38	−	791.765i	1.69515	−	0.978696i	0.950233	−	0.311539i	$-0.100844\pi$
$810$	62.9812	−	52.7115i	0.0777545	−	0.0650760i
$811$	377.227			0.465138			0.232569	−	0.972580i	$-0.425287\pi$
$811$	377.227			0.465138			0.232569	+	0.972580i	$0.425287\pi$
$812$	−918.038	−	825.551i	−1.13059	−	1.01669i
$813$	167.595	+	167.595i	0.206144	+	0.206144i
$814$	186.978	−	23.4110i	0.229703	−	0.0287605i
$815$	378.643	+	194.674i	0.464593	+	0.238864i
$816$	−522.276	−	13.2493i	−0.640044	−	0.0162369i
$817$	−213.189	+	57.1238i	−0.260941	+	0.0699189i
$818$	−210.694	−	29.0987i	−0.257572	−	0.0355729i
$819$	−232.006	−	203.371i	−0.283280	−	0.248317i
$820$	100.874	−	190.230i	0.123017	−	0.231987i
$821$	337.590	−	584.723i	0.411194	−	0.712209i	−0.583827	−	0.811878i	$-0.698445\pi$
$821$	337.590	−	584.723i	0.411194	−	0.712209i	0.995021	+	0.0996696i	$0.0317786\pi$
$822$	−324.634	−	798.010i	−0.394932	−	0.970815i
$823$	1462.55	+	391.890i	1.77710	+	0.476173i	0.990050	−	0.140715i	$-0.0449401\pi$
$823$	1462.55	+	391.890i	1.77710	+	0.476173i	0.787051	+	0.616888i	$0.211607\pi$
$824$	−753.372	−	113.801i	−0.914286	−	0.138108i
$825$	88.2249	−	33.1287i	0.106939	−	0.0401560i
$826$	−187.326	+	90.9592i	−0.226787	+	0.110120i
$827$	−389.611	−	389.611i	−0.471114	−	0.471114i	0.431161	−	0.902275i	$-0.358104\pi$
$827$	−389.611	−	389.611i	−0.471114	−	0.471114i	−0.902275	+	0.431161i	$0.858104\pi$
$828$	819.729	+	10.3960i	0.990010	+	0.0125555i
$829$	346.671	+	600.451i	0.418179	+	0.724308i	0.995756	−	0.0920282i	$-0.0293350\pi$
$829$	346.671	+	600.451i	0.418179	+	0.724308i	−0.577577	+	0.816336i	$0.696002\pi$
$830$	−872.528	+	1242.74i	−1.05124	+	1.49728i
$831$	−165.912	+	287.369i	−0.199654	+	0.345811i
$832$	472.750	+	17.9942i	0.568209	+	0.0216277i
$833$	728.571	+	558.529i	0.874635	+	0.670503i
$834$	369.293	−	279.666i	0.442797	−	0.335331i
$835$	21.2775	+	436.511i	0.0254821	+	0.522767i
$836$	7.98029	+	31.3688i	0.00954581	+	0.0375225i
$837$	−706.952	−	189.427i	−0.844625	−	0.226317i
$838$	−39.7846	−	30.9305i	−0.0474756	−	0.0369099i
$839$			150.282i			0.179120i	0.995981	+	0.0895600i	$0.0285461\pi$
$839$			150.282i			0.179120i	−0.995981	+	0.0895600i	$0.971454\pi$
$840$	−357.111	+	332.589i	−0.425132	+	0.395939i
$841$	−1103.30			−1.31189
$842$	424.481	−	545.991i	0.504135	−	0.648446i
$843$	−17.1575	+	64.0328i	−0.0203529	+	0.0759582i
$844$	1034.41	−	263.155i	1.22560	−	0.311796i
$845$	423.520	+	384.150i	0.501207	+	0.454616i
$846$	−264.815	−	349.682i	−0.313020	−	0.413336i
$847$	812.498	−	53.4385i	0.959266	−	0.0630915i
$848$	117.022	+	485.684i	0.137998	+	0.572740i
$849$	242.155	+	139.808i	0.285224	+	0.164674i
$850$	−688.239	+	635.489i	−0.809693	+	0.747634i
$851$	−1296.75	+	748.681i	−1.52380	+	0.879767i
$852$	−0.917531	+	72.3480i	−0.00107691	+	0.0849155i
$853$	329.812	−	329.812i	0.386649	−	0.386649i	−0.486841	−	0.873490i	$-0.661851\pi$
$853$	329.812	−	329.812i	0.386649	−	0.386649i	0.873490	+	0.486841i	$0.161851\pi$
$854$	−410.153	−	277.698i	−0.480273	−	0.325173i
$855$	−109.014	−	23.5883i	−0.127502	−	0.0275886i
$856$	−1267.99	−	191.536i	−1.48129	−	0.223757i
$857$	−78.3886	+	292.550i	−0.0914686	+	0.341365i	−0.996460	−	0.0840636i	$-0.973210\pi$
$857$	−78.3886	+	292.550i	−0.0914686	+	0.341365i	0.904992	+	0.425429i	$0.139877\pi$
$858$	51.6221	−	21.0001i	0.0601656	−	0.0244756i
$859$	416.640	+	240.547i	0.485029	+	0.280032i	0.722510	−	0.691360i	$-0.242988\pi$
$859$	416.640	+	240.547i	0.485029	+	0.280032i	−0.237481	+	0.971392i	$0.576322\pi$
$860$	−1127.91	+	346.217i	−1.31153	+	0.402578i
$861$	42.2477	+	124.365i	0.0490682	+	0.144443i
$862$	−146.296	+	1059.28i	−0.169717	+	1.22886i
$863$	−225.744	−	842.489i	−0.261581	−	0.976233i	−0.964310	−	0.264776i	$-0.914702\pi$
$863$	−225.744	−	842.489i	−0.261581	−	0.976233i	0.702729	−	0.711457i	$-0.251965\pi$
$864$	−486.757	−	677.805i	−0.563376	−	0.784497i
$865$	322.651	+	165.886i	0.373006	+	0.191776i
$866$	−173.788	−	1388.00i	−0.200679	−	1.60277i
$867$	76.4174	−	76.4174i	0.0881400	−	0.0881400i
$868$	−768.781	−	162.899i	−0.885692	−	0.187672i
$869$			146.053i			0.168070i
$870$	−67.9497	+	765.488i	−0.0781031	+	0.879872i
$871$	35.9957	+	62.3464i	0.0413269	+	0.0715803i
$872$	−93.2437	+	10.4756i	−0.106931	+	0.0120133i
$873$	222.339	+	829.779i	0.254684	+	0.950492i
$874$	−155.277	−	205.040i	−0.177663	−	0.234600i
$875$	−43.7365	+	873.906i	−0.0499845	+	0.998750i
$876$	−881.825	−	248.312i	−1.00665	−	0.283461i
$877$	390.516	+	1457.43i	0.445286	+	1.66183i	0.715179	+	0.698941i	$0.246345\pi$
$877$	390.516	+	1457.43i	0.445286	+	1.66183i	−0.269893	+	0.962890i	$0.586988\pi$
$878$	501.518	−	204.020i	0.571205	−	0.232369i
$879$	3.56131	+	6.16838i	0.00405155	+	0.00701749i
$880$	48.6725	+	166.044i	0.0553096	+	0.188686i
$881$		−	381.549i		−	0.433086i	−0.976273	−	0.216543i	$-0.930522\pi$
$881$		−	381.549i		−	0.433086i	0.976273	−	0.216543i	$-0.0694782\pi$
$882$	−3.44072	+	584.310i	−0.00390105	+	0.662483i
$883$	−587.289	+	587.289i	−0.665107	+	0.665107i	−0.956579	−	0.291473i	$-0.905855\pi$
$883$	−587.289	+	587.289i	−0.665107	+	0.665107i	0.291473	+	0.956579i	$0.405855\pi$
$884$	−396.650	+	386.715i	−0.448699	+	0.437461i
$885$	115.276	+	59.2677i	0.130256	+	0.0669692i
$886$	998.731	+	421.127i	1.12724	+	0.475313i
$887$	95.7426	+	357.316i	0.107940	+	0.402837i	0.998662	−	0.0517112i	$-0.0164675\pi$
$887$	95.7426	+	357.316i	0.107940	+	0.402837i	−0.890722	+	0.454548i	$0.849801\pi$
$888$	556.621	+	243.065i	0.626825	+	0.273721i
$889$	−51.4096	+	258.759i	−0.0578285	+	0.291068i
$890$	47.3961	+	17.3188i	0.0532540	+	0.0194594i
$891$	15.3836	+	8.88174i	0.0172656	+	0.00996828i
$892$	431.450	−	725.877i	0.483689	−	0.813764i
$893$	−35.6182	+	132.929i	−0.0398860	+	0.148857i
$894$	10.6405	+	84.9829i	0.0119021	+	0.0950591i
$895$	199.218	+	43.1064i	0.222590	+	0.0481636i
$896$	−560.460	−	699.071i	−0.625513	−	0.780214i
$897$	−313.136	+	313.136i	−0.349092	+	0.349092i
$898$	−984.796	−	765.630i	−1.09665	−	0.852595i
$899$	−1071.75	+	618.775i	−1.19216	+	0.688292i
$900$	−586.922	−	105.026i	−0.652136	−	0.116695i
$901$	−506.613	−	292.493i	−0.562278	−	0.324632i
$902$	46.1334	+	6.37142i	0.0511456	+	0.00706365i
$903$	318.174	−	645.560i	0.352352	−	0.714906i
$904$	478.740	+	1220.97i	0.529579	+	1.35063i
$905$	−361.082	−	327.517i	−0.398986	−	0.361897i
$906$	−417.856	−	176.194i	−0.461210	−	0.194475i
$907$	−92.7888	+	346.292i	−0.102303	+	0.381800i	−0.998025	−	0.0628141i	$-0.979992\pi$
$907$	−92.7888	+	346.292i	−0.102303	+	0.381800i	0.895722	+	0.444614i	$0.146659\pi$
$908$	0.721600	−	56.8987i	0.000794713	−	0.0626638i
$909$	347.105			0.381853
$910$	−11.8269	+	517.309i	−0.0129966	+	0.568472i
$911$			1212.72i			1.33120i	0.746310	+	0.665598i	$0.231824\pi$
$911$			1212.72i			1.33120i	−0.746310	+	0.665598i	$0.768176\pi$
$912$	−29.5493	+	100.057i	−0.0324005	+	0.109711i
$913$	−317.234	−	85.0025i	−0.347463	−	0.0931024i
$914$	−209.942	−	88.5245i	−0.229696	−	0.0968539i
$915$	15.0107	+	307.946i	0.0164051	+	0.336553i
$916$	−1193.24	−	336.002i	−1.30266	−	0.366814i
$917$	−1286.04	+	84.5834i	−1.40244	+	0.0922393i
$918$	967.943	+	133.681i	1.05440	+	0.145622i
$919$	−320.822	+	555.679i	−0.349099	+	0.604657i	−0.986090	−	0.166215i	$-0.946846\pi$
$919$	−320.822	+	555.679i	−0.349099	+	0.604657i	0.636991	+	0.770871i	$0.280179\pi$
$920$	−869.009	−	1065.48i	−0.944575	−	1.15813i
$921$	−341.926	−	592.233i	−0.371255	−	0.643032i
$922$	401.306	+	311.995i	0.435256	+	0.338390i
$923$	54.2489	+	54.2489i	0.0587745	+	0.0587745i
$924$	−94.0748	−	47.8584i	−0.101813	−	0.0517948i
$925$	1019.54	−	382.839i	1.10220	−	0.413881i
$926$	44.0244	+	351.613i	0.0475425	+	0.379711i
$927$	548.513	+	146.974i	0.591708	+	0.158548i
$928$	−1392.40	−	228.426i	−1.50043	−	0.246149i
$929$	−569.174	+	985.838i	−0.612674	+	1.06118i	0.378114	+	0.925759i	$0.376573\pi$
$929$	−569.174	+	985.838i	−0.612674	+	1.06118i	−0.990788	+	0.135423i	$0.956761\pi$
$930$	206.162	+	443.583i	0.221680	+	0.476971i
$931$	145.390	−	111.666i	0.156165	−	0.119942i
$932$	215.798	+	384.966i	0.231543	+	0.413053i
$933$	482.449	−	129.272i	0.517094	−	0.138555i
$934$	1219.93	+	514.397i	1.30613	+	0.550746i
$935$	−180.190	−	92.6420i	−0.192716	−	0.0990824i
$936$	−348.643	−	52.6645i	−0.372482	−	0.0562655i
$937$	−620.950	−	620.950i	−0.662700	−	0.662700i	0.293316	−	0.956016i	$-0.405241\pi$
$937$	−620.950	−	620.950i	−0.662700	−	0.662700i	−0.956016	+	0.293316i	$0.905241\pi$
$938$	44.6157	−	128.840i	0.0475647	−	0.137356i
$939$	−625.186			−0.665800
$940$	−164.688	+	716.999i	−0.175200	+	0.762765i
$941$	1366.48	−	788.939i	1.45216	−	0.838405i	0.453557	−	0.891228i	$-0.350155\pi$
$941$	1366.48	−	788.939i	1.45216	−	0.838405i	0.998604	+	0.0528223i	$0.0168217\pi$
$942$	−619.473	+	252.004i	−0.657615	+	0.267521i
$943$	−357.453	+	95.7794i	−0.379060	+	0.101569i
$944$	−124.184	+	203.022i	−0.131551	+	0.215065i
$945$	733.179	−	543.586i	0.775851	−	0.575224i
$946$	−154.062	−	203.435i	−0.162856	−	0.215048i
$947$	−142.951	+	38.3036i	−0.150952	+	0.0404473i	−0.333503	−	0.942749i	$-0.608231\pi$
$947$	−142.951	+	38.3036i	−0.150952	+	0.0404473i	0.182552	+	0.983196i	$0.441564\pi$
$948$	−240.531	+	404.673i	−0.253725	+	0.426870i
$949$	−841.253	+	485.698i	−0.886463	+	0.511800i
$950$	87.0077	+	165.599i	0.0915871	+	0.174315i
$951$	489.862			0.515102
$952$	1045.45	+	88.2839i	1.09816	+	0.0927352i
$953$	179.288	+	179.288i	0.188130	+	0.188130i	0.794887	−	0.606757i	$-0.207530\pi$
$953$	179.288	+	179.288i	0.188130	+	0.188130i	−0.606757	+	0.794887i	$0.707530\pi$
$954$	−46.2587	−	369.457i	−0.0484892	−	0.387272i
$955$	1274.21	−	408.873i	1.33425	−	0.428139i
$956$	250.953	+	986.439i	0.262503	+	1.03184i
$957$	−160.553	+	43.0201i	−0.167767	+	0.0449531i
$958$	−166.032	+	1202.18i	−0.173311	+	1.25489i
$959$	556.490	+	1638.15i	0.580281	+	1.70818i
$960$	−138.595	+	540.219i	−0.144370	+	0.562728i
$961$	86.6481	−	150.079i	0.0901645	−	0.156170i
$962$	596.552	−	242.680i	0.620116	−	0.252266i
$963$	923.192	+	247.368i	0.958662	+	0.256873i
$964$	107.988	+	110.763i	0.112021	+	0.114899i
$965$	99.4659	+	154.396i	0.103074	+	0.159996i
$966$	836.560	+	59.9703i	0.866004	+	0.0620811i
$967$	−368.609	−	368.609i	−0.381188	−	0.381188i	0.490342	−	0.871530i	$-0.336872\pi$
$967$	−368.609	−	368.609i	−0.381188	−	0.381188i	−0.871530	+	0.490342i	$0.836872\pi$
$968$	748.917	−	552.353i	0.773675	−	0.570613i
$969$	−61.0819	−	105.797i	−0.0630360	−	0.109182i
$970$	827.886	−	1179.16i	0.853491	−	1.21563i
$971$	746.719	−	1293.35i	0.769020	−	1.33198i	−0.169074	−	0.985603i	$-0.554078\pi$
$971$	746.719	−	1293.35i	0.769020	−	1.33198i	0.938095	−	0.346379i	$-0.112589\pi$
$972$	487.042	+	868.844i	0.501072	+	0.893872i
$973$	−773.378	+	517.008i	−0.794839	+	0.531354i
$974$	−431.273	−	569.486i	−0.442785	−	0.584688i
$975$	261.947	−	187.406i	0.268663	−	0.192212i
$976$	−565.898	−	14.3559i	−0.579813	−	0.0147090i
$977$	971.449	+	260.299i	0.994318	+	0.266427i	0.719063	−	0.694944i	$-0.244571\pi$
$977$	971.449	+	260.299i	0.994318	+	0.266427i	0.275255	+	0.961371i	$0.411238\pi$
$978$	−182.178	+	234.327i	−0.186276	+	0.239599i
$979$			10.9141i			0.0111483i
$980$	755.212	−	624.543i	0.770625	−	0.637289i
$981$	69.9324			0.0712868
$982$	−787.329	−	612.109i	−0.801761	−	0.623329i
$983$	58.1411	−	216.985i	0.0591465	−	0.220738i	−0.930026	−	0.367493i	$-0.880216\pi$
$983$	58.1411	−	216.985i	0.0591465	−	0.220738i	0.989173	+	0.146755i	$0.0468829\pi$
$984$	117.330	+	93.6293i	0.119238	+	0.0951518i
$985$	31.2287	+	640.661i	0.0317043	+	0.650417i
$986$	1317.15	−	997.480i	1.33585	−	1.01164i
$987$	−249.401	−	373.073i	−0.252686	−	0.377987i
$988$	54.0925	+	96.4967i	0.0547495	+	0.0976687i
$989$	1756.10	+	1013.88i	1.77563	+	1.02516i
$990$	−22.2327	−	127.030i	−0.0224573	−	0.128313i
$991$	225.110	−	129.967i	0.227154	−	0.131148i	−0.382104	−	0.924119i	$-0.624801\pi$
$991$	225.110	−	129.967i	0.227154	−	0.131148i	0.609259	+	0.792972i	$0.291467\pi$
$992$	−840.227	+	317.219i	−0.847003	+	0.319777i
$993$	695.758	−	695.758i	0.700663	−	0.700663i
$994$	10.3895	−	144.929i	0.0104522	−	0.145804i
$995$	−412.826	+	1907.89i	−0.414900	+	1.91747i
$996$	−738.978	−	757.962i	−0.741946	−	0.761007i
$997$	−252.116	+	940.908i	−0.252874	+	0.943739i	0.716387	+	0.697704i	$0.245795\pi$
$997$	−252.116	+	940.908i	−0.252874	+	0.943739i	−0.969261	+	0.246036i	$0.920872\pi$
$998$	−174.267	−	428.382i	−0.174617	−	0.429240i
$999$	−983.789	−	567.991i	−0.984773	−	0.568559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	140.3.x.a.103.31	yes	176
4.3	odd	2	inner	140.3.x.a.103.7	yes	176
5.2	odd	4	inner	140.3.x.a.47.35	yes	176
7.3	odd	6	inner	140.3.x.a.3.29	✓	176
20.7	even	4	inner	140.3.x.a.47.29	yes	176
28.3	even	6	inner	140.3.x.a.3.35	yes	176
35.17	even	12	inner	140.3.x.a.87.7	yes	176
140.87	odd	12	inner	140.3.x.a.87.31	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.x.a.3.29	✓	176	7.3	odd	6	inner
140.3.x.a.3.35	yes	176	28.3	even	6	inner
140.3.x.a.47.29	yes	176	20.7	even	4	inner
140.3.x.a.47.35	yes	176	5.2	odd	4	inner
140.3.x.a.87.7	yes	176	35.17	even	12	inner
140.3.x.a.87.31	yes	176	140.87	odd	12	inner
140.3.x.a.103.7	yes	176	4.3	odd	2	inner
140.3.x.a.103.31	yes	176	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 140 = 2^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	140.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22756 - 1.57895i) q^{2} +(-0.451084 + 1.68347i) q^{3} +(-0.986197 - 3.87652i) q^{4} +(3.35921 - 3.70347i) q^{5} +(2.10439 + 2.77880i) q^{6} +(-3.89031 - 5.81941i) q^{7} +(-7.33147 - 3.20150i) q^{8} +(5.16363 + 2.98123i) q^{9} +O(q^{10})\)	\(q+(1.22756 - 1.57895i) q^{2} +(-0.451084 + 1.68347i) q^{3} +(-0.986197 - 3.87652i) q^{4} +(3.35921 - 3.70347i) q^{5} +(2.10439 + 2.77880i) q^{6} +(-3.89031 - 5.81941i) q^{7} +(-7.33147 - 3.20150i) q^{8} +(5.16363 + 2.98123i) q^{9} +(-1.72399 - 9.85027i) q^{10} +(1.87311 - 1.08144i) q^{11} +(6.97087 + 0.0884058i) q^{12} +(5.22698 - 5.22698i) q^{13} +(-13.9642 - 1.00105i) q^{14} +(4.71940 + 7.32571i) q^{15} +(-14.0548 + 7.64602i) q^{16} +(4.84903 - 18.0968i) q^{17} +(11.0459 - 4.49351i) q^{18} +(-3.24006 - 1.87065i) q^{19} +(-17.6694 - 9.36968i) q^{20} +(11.5517 - 3.92417i) q^{21} +(0.591808 - 4.28509i) q^{22} +(8.89644 + 33.2020i) q^{23} +(8.69674 - 10.8982i) q^{24} +(-2.43145 - 24.8815i) q^{25} +(-1.83674 - 14.6696i) q^{26} +(-18.4395 + 18.4395i) q^{27} +(-18.7224 + 20.8199i) q^{28} +44.0942i q^{29} +(17.3603 + 1.54101i) q^{30} +(14.0330 + 24.3059i) q^{31} +(-5.18041 + 31.5779i) q^{32} +(0.975642 + 3.64115i) q^{33} +(-22.6216 - 29.8713i) q^{34} +(-34.6204 - 5.14094i) q^{35} +(6.46442 - 22.9570i) q^{36} +(11.2746 + 42.0776i) q^{37} +(-6.93104 + 2.81958i) q^{38} +(6.44165 + 11.1573i) q^{39} +(-36.4846 + 16.3974i) q^{40} +10.7660i q^{41} +(7.98425 - 23.0567i) q^{42} +(41.7141 - 41.7141i) q^{43} +(-6.03948 - 6.19464i) q^{44} +(28.3866 - 9.10883i) q^{45} +(63.3453 + 26.7103i) q^{46} +(-9.52027 - 35.5301i) q^{47} +(-6.53194 - 27.1099i) q^{48} +(-18.7310 + 45.2786i) q^{49} +(-42.2715 - 26.7043i) q^{50} +(28.2781 + 16.3264i) q^{51} +(-25.4173 - 15.1077i) q^{52} +(8.08134 - 30.1600i) q^{53} +(6.47956 + 51.7507i) q^{54} +(2.28708 - 10.5698i) q^{55} +(9.89083 + 55.1196i) q^{56} +(4.61073 - 4.61073i) q^{57} +(69.6227 + 54.1282i) q^{58} +(12.8816 - 7.43720i) q^{59} +(23.7440 - 25.5195i) q^{60} +(30.6400 + 17.6900i) q^{61} +(55.6043 + 7.67944i) q^{62} +(-2.73916 - 41.6472i) q^{63} +(43.5008 + 46.9434i) q^{64} +(-1.79948 - 36.9165i) q^{65} +(6.94686 + 2.92923i) q^{66} +(-2.52064 + 9.40717i) q^{67} +(-74.9348 - 0.950337i) q^{68} -59.9076 q^{69} +(-50.6159 + 48.3532i) q^{70} +10.3786i q^{71} +(-28.3126 - 38.3881i) q^{72} +(-126.933 - 34.0116i) q^{73} +(80.2789 + 33.8505i) q^{74} +(42.9840 + 7.13037i) q^{75} +(-4.05628 + 14.4050i) q^{76} +(-13.5803 - 6.69325i) q^{77} +(25.5243 + 3.52513i) q^{78} +(-33.7636 + 58.4802i) q^{79} +(-18.8962 + 77.7363i) q^{80} +(4.10644 + 7.11256i) q^{81} +(16.9991 + 13.2159i) q^{82} +(-107.371 - 107.371i) q^{83} +(-26.6043 - 40.9102i) q^{84} +(-50.7322 - 78.7492i) q^{85} +(-14.6582 - 117.071i) q^{86} +(-74.2312 - 19.8902i) q^{87} +(-17.1949 + 1.93178i) q^{88} +(-2.52306 + 4.37006i) q^{89} +(20.4638 - 56.0028i) q^{90} +(-50.7525 - 10.0834i) q^{91} +(119.935 - 67.2309i) q^{92} +(-47.2484 + 12.6602i) q^{93} +(-67.7872 - 28.5833i) q^{94} +(-17.8119 + 5.71558i) q^{95} +(-50.8236 - 22.9654i) q^{96} +(101.878 + 101.878i) q^{97} +(48.4994 + 85.1576i) q^{98} +12.8961 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8	\( 176 q - 2 q^{2} - 12 q^{5} + 4 q^{8} - 6 q^{10} - 6 q^{12} - 28 q^{16} - 12 q^{17} - 36 q^{18} - 32 q^{21} - 24 q^{22} - 4 q^{25} - 12 q^{26} + 114 q^{28} + 28 q^{30} + 58 q^{32} - 156 q^{33} - 144 q^{36} - 4 q^{37} + 192 q^{38} + 54 q^{40} - 218 q^{42} - 12 q^{45} + 68 q^{46} - 332 q^{50} - 264 q^{52} - 4 q^{53} - 300 q^{56} - 24 q^{57} - 146 q^{58} - 434 q^{60} - 24 q^{61} + 92 q^{65} - 660 q^{66} - 72 q^{68} + 488 q^{70} - 80 q^{72} - 12 q^{73} - 156 q^{77} + 688 q^{78} + 588 q^{80} + 288 q^{81} + 798 q^{82} + 272 q^{85} - 72 q^{86} + 588 q^{88} + 524 q^{92} + 164 q^{93} + 1080 q^{96} - 766 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 12 * q^5 + 4 * q^8 - 6 * q^10 - 6 * q^12 - 28 * q^16 - 12 * q^17 - 36 * q^18 - 32 * q^21 - 24 * q^22 - 4 * q^25 - 12 * q^26 + 114 * q^28 + 28 * q^30 + 58 * q^32 - 156 * q^33 - 144 * q^36 - 4 * q^37 + 192 * q^38 + 54 * q^40 - 218 * q^42 - 12 * q^45 + 68 * q^46 - 332 * q^50 - 264 * q^52 - 4 * q^53 - 300 * q^56 - 24 * q^57 - 146 * q^58 - 434 * q^60 - 24 * q^61 + 92 * q^65 - 660 * q^66 - 72 * q^68 + 488 * q^70 - 80 * q^72 - 12 * q^73 - 156 * q^77 + 688 * q^78 + 588 * q^80 + 288 * q^81 + 798 * q^82 + 272 * q^85 - 72 * q^86 + 588 * q^88 + 524 * q^92 + 164 * q^93 + 1080 * q^96 - 766 * q^98

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