LMFDB - Embedded newform 110.3.l.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,3,Mod(3,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([15, 16]))

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

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

chi := DirichletCharacter("110.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.l (of order $20$, degree $8$, 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:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			37.1
Character	$\chi$	$=$	110.37
Dual form			110.3.l.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.221232 - 1.39680i) q^{2} +(-2.02588 - 3.97601i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(2.39781 - 4.38754i) q^{5} +(-5.10551 + 3.70937i) q^{6} +(0.699150 - 1.37216i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-6.41440 + 8.82867i) q^{9} +(-6.65900 - 2.37861i) q^{10} +(-9.33076 + 5.82554i) q^{11} +(6.31076 + 6.31076i) q^{12} +(-0.895765 + 0.141875i) q^{13} +(-2.07131 - 0.673009i) q^{14} +(-22.3026 - 0.645111i) q^{15} +(3.23607 - 2.35114i) q^{16} +(10.8039 + 1.71117i) q^{17} +(13.7510 + 7.00647i) q^{18} +(-7.26080 - 2.35918i) q^{19} +(-1.84926 + 9.82752i) q^{20} -6.87211 q^{21} +(10.2014 + 11.7444i) q^{22} +(22.7314 - 22.7314i) q^{23} +(7.41874 - 10.2110i) q^{24} +(-13.5010 - 21.0410i) q^{25} +(0.396343 + 1.21982i) q^{26} +(8.43072 + 1.33529i) q^{27} +(-0.481821 + 3.04210i) q^{28} +(38.8343 - 12.6180i) q^{29} +(4.03295 + 31.2950i) q^{30} +(-39.5741 - 28.7523i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(42.0654 + 25.2974i) q^{33} -15.4694i q^{34} +(-4.34397 - 6.35773i) q^{35} +(6.74450 - 20.7574i) q^{36} +(15.7806 - 30.9712i) q^{37} +(-1.68899 + 10.6638i) q^{38} +(2.37881 + 3.27415i) q^{39} +(14.1362 + 0.408896i) q^{40} +(-13.7806 + 42.4124i) q^{41} +(1.52033 + 9.59898i) q^{42} +(34.2916 - 34.2916i) q^{43} +(14.1478 - 16.8476i) q^{44} +(23.3556 + 49.3129i) q^{45} +(-36.7801 - 26.7223i) q^{46} +(-64.1369 + 32.6794i) q^{47} +(-15.9040 - 8.10351i) q^{48} +(27.4075 + 37.7231i) q^{49} +(-26.4033 + 23.5131i) q^{50} +(-15.0837 - 46.4230i) q^{51} +(1.61616 - 0.823476i) q^{52} +(24.1946 - 3.83205i) q^{53} -12.0715i q^{54} +(3.18634 + 54.9076i) q^{55} +4.35581 q^{56} +(5.32939 + 33.6484i) q^{57} +(-26.2163 - 51.4523i) q^{58} +(47.2216 - 15.3432i) q^{59} +(42.8207 - 12.5567i) q^{60} +(59.7357 - 43.4006i) q^{61} +(-31.4062 + 61.6382i) q^{62} +(7.62971 + 14.9742i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-1.52539 + 4.27039i) q^{65} +(26.0292 - 64.3536i) q^{66} +(28.4627 + 28.4627i) q^{67} +(-21.6078 + 3.42233i) q^{68} +(-136.431 - 44.3291i) q^{69} +(-7.91947 + 7.47420i) q^{70} +(-58.9825 + 42.8533i) q^{71} +(-30.4862 - 4.82853i) q^{72} +(-107.790 - 54.9219i) q^{73} +(-46.7518 - 15.1906i) q^{74} +(-56.3079 + 96.3065i) q^{75} +15.2689 q^{76} +(1.46996 + 16.8762i) q^{77} +(4.04707 - 4.04707i) q^{78} +(46.2115 - 63.6046i) q^{79} +(-2.55623 - 19.8360i) q^{80} +(18.5798 + 57.1828i) q^{81} +(62.2905 + 9.86584i) q^{82} +(-1.59272 + 10.0560i) q^{83} +(13.0715 - 4.24720i) q^{84} +(33.4135 - 43.2994i) q^{85} +(-55.4850 - 40.3122i) q^{86} +(-128.843 - 128.843i) q^{87} +(-26.6626 - 16.0344i) q^{88} +96.2499i q^{89} +(63.7134 - 43.5327i) q^{90} +(-0.431599 + 1.32832i) q^{91} +(-29.1889 + 57.2864i) q^{92} +(-34.1470 + 215.596i) q^{93} +(59.8358 + 82.3569i) q^{94} +(-27.7610 + 26.2002i) q^{95} +(-7.80053 + 24.0076i) q^{96} +(-7.79490 - 49.2151i) q^{97} +(46.6284 - 46.6284i) q^{98} +(8.41955 - 119.746i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$2$	−0.221232	−	1.39680i	−0.110616	−	0.698401i
$3$	−2.02588	−	3.97601i	−0.675293	−	1.32534i	−0.933266	−	0.359185i	$-0.883055\pi$
$3$	−2.02588	−	3.97601i	−0.675293	−	1.32534i	0.257974	−	0.966152i	$-0.416945\pi$
$4$	−1.90211	+	0.618034i	−0.475528	+	0.154508i
$5$	2.39781	−	4.38754i	0.479563	−	0.877508i
$5$	2.39781	−	4.38754i	0.479563	−	0.877508i
$6$	−5.10551	+	3.70937i	−0.850918	+	0.618228i
$7$	0.699150	−	1.37216i	0.0998786	−	0.196023i	−0.835660	−	0.549247i	$-0.814915\pi$
$7$	0.699150	−	1.37216i	0.0998786	−	0.196023i	0.935539	+	0.353224i	$0.114915\pi$
$8$	1.28408	+	2.52015i	0.160510	+	0.315018i
$9$	−6.41440	+	8.82867i	−0.712712	+	0.980963i
$10$	−6.65900	−	2.37861i	−0.665900	−	0.237861i
$11$	−9.33076	+	5.82554i	−0.848251	+	0.529594i
$11$	−9.33076	+	5.82554i	−0.848251	+	0.529594i
$12$	6.31076	+	6.31076i	0.525897	+	0.525897i
$13$	−0.895765	+	0.141875i	−0.0689050	+	0.0109135i	−0.190792	−	0.981631i	$-0.561106\pi$
$13$	−0.895765	+	0.141875i	−0.0689050	+	0.0109135i	0.121887	+	0.992544i	$0.461106\pi$
$14$	−2.07131	−	0.673009i	−0.147951	−	0.0480721i
$15$	−22.3026	−	0.645111i	−1.48684	−	0.0430074i
$16$	3.23607	−	2.35114i	0.202254	−	0.146946i
$17$	10.8039	+	1.71117i	0.635522	+	0.100657i	0.465879	−	0.884849i	$-0.345738\pi$
$17$	10.8039	+	1.71117i	0.635522	+	0.100657i	0.169644	+	0.985505i	$0.445738\pi$
$18$	13.7510	+	7.00647i	0.763943	+	0.389248i
$19$	−7.26080	−	2.35918i	−0.382148	−	0.124167i	0.111642	−	0.993748i	$-0.464389\pi$
$19$	−7.26080	−	2.35918i	−0.382148	−	0.124167i	−0.493790	+	0.869581i	$0.664389\pi$
$20$	−1.84926	+	9.82752i	−0.0924632	+	0.491376i
$21$	−6.87211			−0.327243
$22$	10.2014	+	11.7444i	0.463699	+	0.533838i
$23$	22.7314	−	22.7314i	0.988320	−	0.988320i	−0.0116127	−	0.999933i	$-0.503697\pi$
$23$	22.7314	−	22.7314i	0.988320	−	0.988320i	0.999933	+	0.0116127i	$0.00369654\pi$
$24$	7.41874	−	10.2110i	0.309114	−	0.425459i
$25$	−13.5010	−	21.0410i	−0.540039	−	0.841640i
$26$	0.396343	+	1.21982i	0.0152440	+	0.0469161i
$27$	8.43072	+	1.33529i	0.312249	+	0.0494553i
$28$	−0.481821	+	3.04210i	−0.0172079	+	0.108646i
$29$	38.8343	−	12.6180i	1.33911	−	0.435104i	0.450097	−	0.892980i	$-0.351389\pi$
$29$	38.8343	−	12.6180i	1.33911	−	0.435104i	0.889016	+	0.457875i	$0.151389\pi$
$30$	4.03295	+	31.2950i	0.134432	+	1.04317i
$31$	−39.5741	−	28.7523i	−1.27658	−	0.927493i	−0.277141	−	0.960829i	$-0.589387\pi$
$31$	−39.5741	−	28.7523i	−1.27658	−	0.927493i	−0.999444	+	0.0333361i	$0.989387\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	42.0654	+	25.2974i	1.27471	+	0.766587i
$34$		−	15.4694i		−	0.454984i
$35$	−4.34397	−	6.35773i	−0.124113	−	0.181649i
$36$	6.74450	−	20.7574i	0.187347	−	0.576596i
$37$	15.7806	−	30.9712i	0.426503	−	0.837059i	−0.573340	−	0.819318i	$-0.694352\pi$
$37$	15.7806	−	30.9712i	0.426503	−	0.837059i	0.999843	−	0.0177413i	$-0.00564752\pi$
$38$	−1.68899	+	10.6638i	−0.0444470	+	0.280627i
$39$	2.37881	+	3.27415i	0.0609951	+	0.0839526i
$40$	14.1362	+	0.408896i	0.353406	+	0.0102224i
$41$	−13.7806	+	42.4124i	−0.336113	+	1.03445i	0.630058	+	0.776548i	$0.283031\pi$
$41$	−13.7806	+	42.4124i	−0.336113	+	1.03445i	−0.966171	+	0.257902i	$0.916969\pi$
$42$	1.52033	+	9.59898i	0.0361983	+	0.228547i
$43$	34.2916	−	34.2916i	0.797479	−	0.797479i	−0.185218	−	0.982697i	$-0.559299\pi$
$43$	34.2916	−	34.2916i	0.797479	−	0.797479i	0.982697	+	0.185218i	$0.0592993\pi$
$44$	14.1478	−	16.8476i	0.321541	−	0.382899i
$45$	23.3556	+	49.3129i	0.519013	+	1.09584i
$46$	−36.7801	−	26.7223i	−0.799568	−	0.580920i
$47$	−64.1369	+	32.6794i	−1.36462	+	0.695306i	−0.974275	−	0.225364i	$-0.927643\pi$
$47$	−64.1369	+	32.6794i	−1.36462	+	0.695306i	−0.390341	+	0.920671i	$0.627643\pi$
$48$	−15.9040	−	8.10351i	−0.331334	−	0.168823i
$49$	27.4075	+	37.7231i	0.559336	+	0.769860i
$50$	−26.4033	+	23.5131i	−0.528065	+	0.470263i
$51$	−15.0837	−	46.4230i	−0.295759	−	0.910254i
$52$	1.61616	−	0.823476i	0.0310801	−	0.0158361i
$53$	24.1946	−	3.83205i	0.456502	−	0.0723028i	0.0760509	−	0.997104i	$-0.475769\pi$
$53$	24.1946	−	3.83205i	0.456502	−	0.0723028i	0.380451	+	0.924801i	$0.375769\pi$
$54$		−	12.0715i		−	0.223545i
$55$	3.18634	+	54.9076i	0.0579334	+	0.998320i
$56$	4.35581			0.0777823
$57$	5.32939	+	33.6484i	0.0934980	+	0.590323i
$58$	−26.2163	−	51.4523i	−0.452004	−	0.887109i
$59$	47.2216	−	15.3432i	0.800367	−	0.260055i	0.119854	−	0.992791i	$-0.461757\pi$
$59$	47.2216	−	15.3432i	0.800367	−	0.260055i	0.680512	+	0.732737i	$0.261757\pi$
$60$	42.8207	−	12.5567i	0.713679	−	0.209278i
$61$	59.7357	−	43.4006i	0.979274	−	0.711484i	0.0217280	−	0.999764i	$-0.493083\pi$
$61$	59.7357	−	43.4006i	0.979274	−	0.711484i	0.957546	+	0.288279i	$0.0930832\pi$
$62$	−31.4062	+	61.6382i	−0.506552	+	0.994164i
$63$	7.62971	+	14.9742i	0.121107	+	0.237685i
$64$	−4.70228	+	6.47214i	−0.0734732	+	0.101127i
$65$	−1.52539	+	4.27039i	−0.0234676	+	0.0656984i
$66$	26.0292	−	64.3536i	0.394382	−	0.975054i
$67$	28.4627	+	28.4627i	0.424816	+	0.424816i	0.886858	−	0.462042i	$-0.152883\pi$
$67$	28.4627	+	28.4627i	0.424816	+	0.424816i	−0.462042	+	0.886858i	$0.652883\pi$
$68$	−21.6078	+	3.42233i	−0.317761	+	0.0503284i
$69$	−136.431	−	44.3291i	−1.97726	−	0.642451i
$70$	−7.91947	+	7.47420i	−0.113135	+	0.106774i
$71$	−58.9825	+	42.8533i	−0.830740	+	0.603568i	−0.919768	−	0.392461i	$-0.871624\pi$
$71$	−58.9825	+	42.8533i	−0.830740	+	0.603568i	0.0890289	+	0.996029i	$0.471624\pi$
$72$	−30.4862	−	4.82853i	−0.423419	−	0.0670629i
$73$	−107.790	−	54.9219i	−1.47658	−	0.752355i	−0.484130	−	0.874996i	$-0.660864\pi$
$73$	−107.790	−	54.9219i	−1.47658	−	0.752355i	−0.992451	+	0.122641i	$0.960864\pi$
$74$	−46.7518	−	15.1906i	−0.631781	−	0.205278i
$75$	−56.3079	+	96.3065i	−0.750771	+	1.28409i
$76$	15.2689			0.200907
$77$	1.46996	+	16.8762i	0.0190904	+	0.219172i
$78$	4.04707	−	4.04707i	0.0518855	−	0.0518855i
$79$	46.2115	−	63.6046i	0.584955	−	0.805122i	−0.409272	−	0.912412i	$-0.634217\pi$
$79$	46.2115	−	63.6046i	0.584955	−	0.805122i	0.994228	+	0.107290i	$0.0342174\pi$
$80$	−2.55623	−	19.8360i	−0.0319529	−	0.247950i
$81$	18.5798	+	57.1828i	0.229380	+	0.705960i
$82$	62.2905	+	9.86584i	0.759640	+	0.120315i
$83$	−1.59272	+	10.0560i	−0.0191894	+	0.121157i	−0.995424	−	0.0955614i	$-0.969535\pi$
$83$	−1.59272	+	10.0560i	−0.0191894	+	0.121157i	0.976234	+	0.216718i	$0.0695354\pi$
$84$	13.0715	−	4.24720i	0.155614	−	0.0505619i
$85$	33.4135	−	43.2994i	0.393100	−	0.509404i
$86$	−55.4850	−	40.3122i	−0.645174	−	0.468746i
$87$	−128.843	−	128.843i	−1.48095	−	1.48095i
$88$	−26.6626	−	16.0344i	−0.302985	−	0.182210i
$89$			96.2499i			1.08146i	0.841196	+	0.540730i	$0.181852\pi$
$89$			96.2499i			1.08146i	−0.841196	+	0.540730i	$0.818148\pi$
$90$	63.7134	−	43.5327i	0.707927	−	0.483697i
$91$	−0.431599	+	1.32832i	−0.00474285	+	0.0145970i
$92$	−29.1889	+	57.2864i	−0.317270	+	0.622678i
$93$	−34.1470	+	215.596i	−0.367172	+	2.31823i
$94$	59.8358	+	82.3569i	0.636551	+	0.876137i
$95$	−27.7610	+	26.2002i	−0.292221	+	0.275791i
$96$	−7.80053	+	24.0076i	−0.0812555	+	0.250079i
$97$	−7.79490	−	49.2151i	−0.0803598	−	0.507372i	−0.994733	−	0.102500i	$-0.967316\pi$
$97$	−7.79490	−	49.2151i	−0.0803598	−	0.507372i	0.914373	−	0.404872i	$-0.132684\pi$
$98$	46.6284	−	46.6284i	0.475800	−	0.475800i
$99$	8.41955	−	119.746i	0.0850460	−	1.20955i
$100$	38.6844	+	31.6783i	0.386844	+	0.316783i
$101$	78.6726	+	57.1590i	0.778937	+	0.565931i	0.904660	−	0.426135i	$-0.140125\pi$
$101$	78.6726	+	57.1590i	0.778937	+	0.565931i	−0.125723	+	0.992065i	$0.540125\pi$
$102$	−61.5067	+	31.3392i	−0.603007	+	0.307247i
$103$	109.033	+	55.5551i	1.05857	+	0.539370i	0.894495	−	0.447078i	$-0.147535\pi$
$103$	109.033	+	55.5551i	1.05857	+	0.539370i	0.164078	+	0.986447i	$0.447535\pi$
$104$	−1.50778	−	2.07528i	−0.0144979	−	0.0199546i
$105$	−16.4780	+	30.1517i	−0.156934	+	0.287159i
$106$	−10.7052	−	32.9473i	−0.100993	−	0.310823i
$107$	189.494	−	96.5521i	1.77097	−	0.902356i	0.835032	−	0.550201i	$-0.185449\pi$
$107$	189.494	−	96.5521i	1.77097	−	0.902356i	0.935942	−	0.352155i	$-0.114551\pi$
$108$	−16.8614	+	2.67059i	−0.156124	+	0.0247277i
$109$			24.8050i			0.227569i	0.993505	+	0.113784i	$0.0362973\pi$
$109$			24.8050i			0.227569i	−0.993505	+	0.113784i	$0.963703\pi$
$110$	75.9902	−	16.5980i	0.690820	−	0.150891i
$111$	−155.111			−1.39740
$112$	−0.963643	−	6.08420i	−0.00860395	−	0.0543232i
$113$	−13.6972	−	26.8824i	−0.121215	−	0.237897i	0.822424	−	0.568875i	$-0.192621\pi$
$113$	−13.6972	−	26.8824i	−0.121215	−	0.237897i	−0.943638	+	0.330978i	$0.892621\pi$
$114$	45.8212	−	14.8882i	0.401940	−	0.130598i
$115$	−45.2291	−	154.240i	−0.393297	−	1.34122i
$116$	−66.0688	+	48.0018i	−0.569559	+	0.413809i
$117$	4.49323	−	8.81846i	0.0384037	−	0.0753715i
$118$	−31.8784	−	62.5649i	−0.270156	−	0.530211i
$119$	9.90153	−	13.6283i	0.0832061	−	0.114523i
$120$	−27.0125	−	57.0341i	−0.225104	−	0.475284i
$121$	53.1263	−	108.713i	0.439060	−	0.898458i
$122$	−73.8374	−	73.8374i	−0.605225	−	0.605225i
$123$	196.550	−	31.1305i	1.59797	−	0.253093i
$124$	93.0444	+	30.2319i	0.750358	+	0.243806i
$125$	−124.691	+	8.78371i	−0.997528	+	0.0702697i
$126$	19.2280	−	13.9700i	0.152603	−	0.110873i
$127$	99.3414	+	15.7341i	0.782216	+	0.123891i	0.534755	−	0.845007i	$-0.320404\pi$
$127$	99.3414	+	15.7341i	0.782216	+	0.123891i	0.247461	+	0.968898i	$0.420404\pi$
$128$	10.0806	+	5.13632i	0.0787546	+	0.0401275i
$129$	−205.814	−	66.8731i	−1.59546	−	0.518396i
$130$	6.30236	+	1.18593i	0.0484797	+	0.00912252i
$131$	159.321			1.21619			0.608097	−	0.793863i	$-0.291933\pi$
$131$	159.321			1.21619			0.608097	+	0.793863i	$0.291933\pi$
$132$	−95.6477	−	22.1206i	−0.724604	−	0.167581i
$133$	−8.31356	+	8.31356i	−0.0625080	+	0.0625080i
$134$	33.4599	−	46.0536i	0.249701	−	0.343684i
$135$	26.0739	−	33.7883i	0.193140	−	0.250284i
$136$	9.56065	+	29.4246i	0.0702989	+	0.216358i
$137$	175.619	+	27.8153i	1.28189	+	0.203031i	0.759967	−	0.649961i	$-0.225215\pi$
$137$	175.619	+	27.8153i	1.28189	+	0.203031i	0.521923	+	0.852993i	$0.325215\pi$
$138$	−31.7362	+	200.374i	−0.229972	+	1.45199i
$139$	−80.8487	+	26.2693i	−0.581645	+	0.188988i	−0.585037	−	0.811006i	$-0.698920\pi$
$139$	−80.8487	+	26.2693i	−0.581645	+	0.188988i	0.00339236	+	0.999994i	$0.498920\pi$
$140$	12.1920	+	9.40840i	0.0870858	+	0.0672029i
$141$	259.867	+	188.805i	1.84303	+	1.33904i
$142$	72.9064	+	72.9064i	0.513425	+	0.513425i
$143$	7.53167	−	6.54212i	0.0526690	−	0.0457491i
$144$			43.6513i			0.303134i
$145$	37.7553	−	200.643i	0.260381	−	1.38374i
$146$	−52.8684	+	162.712i	−0.362113	+	1.11447i
$147$	94.4634	−	185.395i	0.642608	−	1.26119i
$148$	−10.8753	+	68.6636i	−0.0734814	+	0.463944i
$149$	132.080	+	181.792i	0.886441	+	1.22008i	0.974595	+	0.223974i	$0.0719031\pi$
$149$	132.080	+	181.792i	0.886441	+	1.22008i	−0.0881546	+	0.996107i	$0.528097\pi$
$150$	146.978	+	57.3449i	0.979855	+	0.382299i
$151$	−50.9689	+	156.866i	−0.337542	+	1.03885i	0.627914	+	0.778283i	$0.283909\pi$
$151$	−50.9689	+	156.866i	−0.337542	+	1.03885i	−0.965456	+	0.260566i	$0.916091\pi$
$152$	−3.37797	−	21.3277i	−0.0222235	−	0.140314i
$153$	−84.4078	+	84.4078i	−0.551685	+	0.551685i
$154$	23.2475	−	5.78680i	0.150958	−	0.0375766i
$155$	−221.043	+	104.690i	−1.42608	+	0.675422i
$156$	−6.54830	−	4.75762i	−0.0419763	−	0.0304976i
$157$	2.40604	−	1.22594i	0.0153251	−	0.00780852i	−0.446311	−	0.894878i	$-0.647263\pi$
$157$	2.40604	−	1.22594i	0.0153251	−	0.00780852i	0.461636	+	0.887069i	$0.347263\pi$
$158$	−99.0666	−	50.4769i	−0.627003	−	0.319474i
$159$	−64.2515	−	88.4347i	−0.404098	−	0.556193i
$160$	−27.1414	+	7.95890i	−0.169634	+	0.0497431i
$161$	−15.2984	−	47.0837i	−0.0950212	−	0.292445i
$162$	75.7626	−	38.6030i	0.467670	−	0.238290i
$163$	−143.508	+	22.7294i	−0.880417	+	0.139444i	−0.580246	−	0.814441i	$-0.697044\pi$
$163$	−143.508	+	22.7294i	−0.880417	+	0.139444i	−0.300171	+	0.953886i	$0.597044\pi$
$164$		−	89.1901i		−	0.543842i
$165$	211.858	−	123.905i	1.28399	−	0.750940i
$166$	14.3987			0.0867389
$167$	20.9586	+	132.328i	0.125501	+	0.792381i	0.967494	+	0.252893i	$0.0813822\pi$
$167$	20.9586	+	132.328i	0.125501	+	0.792381i	−0.841993	+	0.539488i	$0.818618\pi$
$168$	−8.82434	−	17.3187i	−0.0525258	−	0.103088i
$169$	−159.946	+	51.9697i	−0.946428	+	0.307513i
$170$	−67.8728	−	37.0928i	−0.399252	−	0.218193i
$171$	67.4021	−	48.9705i	0.394165	−	0.286377i
$172$	−44.0331	+	86.4199i	−0.256007	+	0.502441i
$173$	−71.4367	−	140.202i	−0.412929	−	0.810419i	−1.00000		0.000883143i	$-0.999719\pi$
$173$	−71.4367	−	140.202i	−0.412929	−	0.810419i	0.587071	−	0.809536i	$-0.300281\pi$
$174$	−151.464	+	208.472i	−0.870482	+	1.19812i
$175$	−38.3108	+	3.81469i	−0.218919	+	0.0217982i
$176$	−16.4983	+	40.7898i	−0.0937405	+	0.231760i
$177$	−156.670	−	156.670i	−0.885142	−	0.885142i
$178$	134.442	−	21.2935i	0.755292	−	0.119627i
$179$	−127.010	−	41.2682i	−0.709556	−	0.230549i	−0.0680667	−	0.997681i	$-0.521683\pi$
$179$	−127.010	−	41.2682i	−0.709556	−	0.230549i	−0.641489	+	0.767132i	$0.721683\pi$
$180$	−74.9020	−	79.3643i	−0.416122	−	0.440913i
$181$	−68.9277	+	50.0789i	−0.380816	+	0.276679i	−0.761682	−	0.647951i	$-0.775626\pi$
$181$	−68.9277	+	50.0789i	−0.380816	+	0.276679i	0.380866	+	0.924630i	$0.375626\pi$
$182$	1.95089	+	0.308991i	0.0107192	+	0.00169775i
$183$	−293.578	−	149.586i	−1.60425	−	0.817408i
$184$	86.4752	+	28.0975i	0.469974	+	0.152704i
$185$	−98.0483	−	143.501i	−0.529991	−	0.775682i
$186$	308.699			1.65967
$187$	−110.777	+	46.9719i	−0.592390	+	0.251187i
$188$	101.799	−	101.799i	0.541482	−	0.541482i
$189$	7.72657	−	10.6347i	0.0408813	−	0.0562683i
$190$	42.7381	+	32.9804i	0.224937	+	0.173581i
$191$	13.1030	+	40.3269i	0.0686022	+	0.211136i	0.979480	−	0.201539i	$-0.0645944\pi$
$191$	13.1030	+	40.3269i	0.0686022	+	0.211136i	−0.910878	+	0.412675i	$0.864594\pi$
$192$	35.2595	+	5.58456i	0.183643	+	0.0290863i
$193$	17.7244	−	111.907i	0.0918361	−	0.579831i	−0.898263	−	0.439459i	$-0.855170\pi$
$193$	17.7244	−	111.907i	0.0918361	−	0.579831i	0.990099	−	0.140372i	$-0.0448298\pi$
$194$	−67.0192	+	21.7759i	−0.345460	+	0.112247i
$195$	20.0694	−	2.58632i	0.102920	−	0.0132632i
$196$	−75.4463	−	54.8149i	−0.384930	−	0.279668i
$197$	−214.060	−	214.060i	−1.08660	−	1.08660i	−0.995876	−	0.0907225i	$-0.971082\pi$
$197$	−214.060	−	214.060i	−1.08660	−	1.08660i	−0.0907225	−	0.995876i	$-0.528918\pi$
$198$	−169.124	+	14.7311i	−0.854159	+	0.0743994i
$199$			240.663i			1.20936i	0.796468	+	0.604681i	$0.206699\pi$
$199$			240.663i			1.20936i	−0.796468	+	0.604681i	$0.793301\pi$
$200$	35.6901	−	61.0428i	0.178450	−	0.305214i
$201$	55.5060	−	170.830i	0.276149	−	0.849900i
$202$	62.4349	−	122.535i	0.309084	−	0.606611i
$203$	9.83706	−	62.1087i	0.0484584	−	0.305954i
$204$	57.3819	+	78.9794i	0.281284	+	0.387154i
$205$	153.043	+	162.160i	0.746550	+	0.791025i
$206$	53.4779	−	164.588i	0.259602	−	0.798971i
$207$	54.8795	+	346.496i	0.265119	+	1.67389i
$208$	−2.56519	+	2.56519i	−0.0123326	+	0.0123326i
$209$	81.4923	−	20.2851i	0.389915	−	0.0970581i
$210$	45.7614	+	16.3461i	0.217911	+	0.0778384i
$211$	−186.222	−	135.298i	−0.882569	−	0.641224i	0.0513609	−	0.998680i	$-0.483644\pi$
$211$	−186.222	−	135.298i	−0.882569	−	0.641224i	−0.933930	+	0.357456i	$0.883644\pi$
$212$	−43.6525	+	22.2421i	−0.205908	+	0.104915i
$213$	289.877	+	147.699i	1.36092	+	0.693425i
$214$	−176.786	−	243.326i	−0.826104	−	1.13704i
$215$	−68.2308	−	232.681i	−0.317353	−	1.08224i
$216$	7.46057	+	22.9613i	0.0345397	+	0.106302i
$217$	−67.1210	+	34.1999i	−0.309313	+	0.157603i
$218$	34.6476	−	5.48765i	0.158934	−	0.0251727i
$219$			539.841i			2.46503i
$220$	−39.9955	−	102.471i	−0.181798	−	0.465778i
$221$	−9.92051			−0.0448892
$222$	34.3155	+	216.660i	0.154575	+	0.975945i
$223$	−82.0755	−	161.082i	−0.368052	−	0.722342i	0.630497	−	0.776191i	$-0.282851\pi$
$223$	−82.0755	−	161.082i	−0.368052	−	0.722342i	−0.998549	+	0.0538492i	$0.982851\pi$
$224$	−8.28524	+	2.69204i	−0.0369877	+	0.0120180i
$225$	272.365	+	15.7697i	1.21051	+	0.0700876i
$226$	−34.5191	+	25.0796i	−0.152739	+	0.110972i
$227$	−115.642	+	226.959i	−0.509434	+	0.999821i	0.482835	+	0.875712i	$0.339607\pi$
$227$	−115.642	+	226.959i	−0.509434	+	0.999821i	−0.992269	+	0.124109i	$0.960393\pi$
$228$	−30.9330	−	60.7094i	−0.135671	−	0.266269i
$229$	169.027	−	232.646i	0.738110	−	1.01592i	−0.260616	−	0.965443i	$-0.583925\pi$
$229$	169.027	−	232.646i	0.738110	−	1.01592i	0.998725	−	0.0504781i	$-0.0160745\pi$
$230$	−205.437	+	97.2990i	−0.893204	+	0.423039i
$231$	64.1221	−	40.0337i	0.277585	−	0.173306i
$232$	81.6656	+	81.6656i	0.352007	+	0.352007i
$233$	−297.711	+	47.1528i	−1.27773	+	0.202372i	−0.758167	−	0.652060i	$-0.773905\pi$
$233$	−297.711	+	47.1528i	−1.27773	+	0.202372i	−0.519562	+	0.854433i	$0.673905\pi$
$234$	−13.3117	−	4.32523i	−0.0568876	−	0.0184839i
$235$	−10.4063	+	359.762i	−0.0442820	+	1.53090i
$236$	−80.3382	+	58.3692i	−0.340416	+	0.247327i
$237$	−346.512	−	54.8820i	−1.46207	−	0.231570i
$238$	−21.2266	−	10.8155i	−0.0891872	−	0.0454431i
$239$	434.890	+	141.304i	1.81962	+	0.591232i	0.999827	+	0.0185779i	$0.00591387\pi$
$239$	434.890	+	141.304i	1.81962	+	0.591232i	0.819797	+	0.572654i	$0.194086\pi$
$240$	−73.6894	+	50.3489i	−0.307039	+	0.209787i
$241$	146.407			0.607497			0.303748	−	0.952752i	$-0.401762\pi$
$241$	146.407			0.607497			0.303748	+	0.952752i	$0.401762\pi$
$242$	−163.604	−	50.1560i	−0.676051	−	0.207256i
$243$	244.040	−	244.040i	1.00428	−	1.00428i
$244$	−86.8011	+	119.471i	−0.355742	+	0.489637i
$245$	231.230	−	29.7983i	0.943795	−	0.121626i
$246$	−86.9663	−	267.655i	−0.353521	−	1.08803i
$247$	6.83868	+	1.08314i	0.0276870	+	0.00438519i
$248$	21.6437	−	136.653i	0.0872729	−	0.551020i
$249$	43.2096	−	14.0396i	0.173532	−	0.0563841i
$250$	39.8547	+	172.225i	0.159419	+	0.688902i
$251$	102.396	+	74.3954i	0.407954	+	0.296396i	0.772773	−	0.634682i	$-0.218869\pi$
$251$	102.396	+	74.3954i	0.407954	+	0.296396i	−0.364819	+	0.931079i	$0.618869\pi$
$252$	−23.7671	−	23.7671i	−0.0943139	−	0.0943139i
$253$	−79.6786	+	344.523i	−0.314935	+	1.36175i
$254$		−	142.241i		−	0.560005i
$255$	−239.850	−	45.1331i	−0.940590	−	0.176993i
$256$	4.94427	−	15.2169i	0.0193136	−	0.0594410i
$257$	1.01065	−	1.98351i	0.00393249	−	0.00771795i	−0.889032	−	0.457845i	$-0.848621\pi$
$257$	1.01065	−	1.98351i	0.00393249	−	0.00771795i	0.892964	+	0.450127i	$0.148621\pi$
$258$	−47.8759	+	302.276i	−0.185565	+	1.17161i
$259$	−31.4644	−	43.3070i	−0.121484	−	0.167209i
$260$	0.262224	−	9.06552i	0.00100855	−	0.0348674i
$261$	−137.698	+	423.792i	−0.527580	+	1.62373i
$262$	−35.2470	−	222.541i	−0.134530	−	0.849391i
$263$	0.0549681	−	0.0549681i	0.000209004	−	0.000209004i	−0.707002	−	0.707211i	$-0.749953\pi$
$263$	0.0549681	−	0.0549681i	0.000209004	−	0.000209004i	0.707211	+	0.707002i	$0.249953\pi$
$264$	−9.73784	+	138.495i	−0.0368858	+	0.524601i
$265$	41.2008	−	115.343i	0.155475	−	0.435257i
$266$	13.4516	+	9.77318i	0.0505700	+	0.0367413i
$267$	382.690	−	194.991i	1.43330	−	0.730302i
$268$	−71.7302	−	36.5483i	−0.267650	−	0.136374i
$269$	−70.4801	−	97.0076i	−0.262008	−	0.360623i	0.657663	−	0.753312i	$-0.271545\pi$
$269$	−70.4801	−	97.0076i	−0.262008	−	0.360623i	−0.919671	+	0.392689i	$0.871545\pi$
$270$	−52.9640	−	28.9451i	−0.196163	−	0.107204i
$271$	12.6932	+	39.0657i	0.0468385	+	0.144154i	0.971741	−	0.236051i	$-0.0758533\pi$
$271$	12.6932	+	39.0657i	0.0468385	+	0.144154i	−0.924902	+	0.380205i	$0.875853\pi$
$272$	38.9853	−	19.8640i	0.143328	−	0.0730294i
$273$	6.15580	−	0.974983i	0.0225487	−	0.00357137i
$274$		−	251.459i		−	0.917732i
$275$	248.550	+	117.678i	0.903817	+	0.427920i
$276$	286.904			1.03951
$277$	17.4230	+	110.004i	0.0628988	+	0.397128i	0.998972	+	0.0453232i	$0.0144318\pi$
$277$	17.4230	+	110.004i	0.0628988	+	0.397128i	−0.936074	+	0.351804i	$0.885568\pi$
$278$	54.5793	+	107.118i	0.196329	+	0.385316i
$279$	507.689	−	164.958i	1.81967	−	0.591248i
$280$	10.4444	−	19.1113i	0.0373015	−	0.0682545i
$281$	5.81065	−	4.22168i	0.0206785	−	0.0150238i	−0.577398	−	0.816463i	$-0.695932\pi$
$281$	5.81065	−	4.22168i	0.0206785	−	0.0150238i	0.598076	+	0.801439i	$0.295932\pi$
$282$	206.232	−	404.753i	0.731318	−	1.43529i
$283$	183.107	+	359.367i	0.647020	+	1.26985i	0.948621	+	0.316414i	$0.102479\pi$
$283$	183.107	+	359.367i	0.647020	+	1.26985i	−0.301602	+	0.953434i	$0.597521\pi$
$284$	85.7066	−	117.965i	0.301784	−	0.415370i
$285$	160.413	+	57.2998i	0.562851	+	0.201052i
$286$	−10.8043	−	9.07293i	−0.0377772	−	0.0317235i
$287$	48.5619	+	48.5619i	0.169205	+	0.169205i
$288$	60.9723	−	9.65706i	0.211709	−	0.0335315i
$289$	−161.060	−	52.3314i	−0.557300	−	0.181078i
$290$	−288.611	−	8.34818i	−0.995209	−	0.0287868i
$291$	−179.888	+	130.696i	−0.618172	+	0.449128i
$292$	238.973	+	37.8496i	0.818401	+	0.129622i
$293$	79.3286	+	40.4199i	0.270746	+	0.137952i	0.584093	−	0.811687i	$-0.301450\pi$
$293$	79.3286	+	40.4199i	0.270746	+	0.137952i	−0.313347	+	0.949639i	$0.601450\pi$
$294$	−279.858	−	90.9315i	−0.951899	−	0.309291i
$295$	45.9096	−	243.977i	0.155626	−	0.827041i
$296$	98.3155			0.332147
$297$	−86.4438	+	36.6541i	−0.291057	+	0.123415i
$298$	224.707	−	224.707i	0.754051	−	0.754051i
$299$	−17.1369	+	23.5870i	−0.0573142	+	0.0788862i
$300$	47.5832	−	217.986i	0.158611	−	0.726620i
$301$	−23.0786	−	71.0285i	−0.0766730	−	0.235975i
$302$	230.387	+	36.4897i	0.762871	+	0.120827i
$303$	67.8836	−	428.600i	0.224038	−	1.41452i
$304$	−29.0432	+	9.43671i	−0.0955369	+	0.0310418i
$305$	−47.1865	−	366.159i	−0.154710	−	1.20052i
$306$	136.575	+	99.2273i	0.446322	+	0.324272i
$307$	−163.817	−	163.817i	−0.533607	−	0.533607i	0.388037	−	0.921644i	$-0.373153\pi$
$307$	−163.817	−	163.817i	−0.533607	−	0.533607i	−0.921644	+	0.388037i	$0.873153\pi$
$308$	−13.2261	−	31.1920i	−0.0429419	−	0.101273i
$309$		−	546.064i		−	1.76720i
$310$	195.134	+	285.593i	0.629463	+	0.921267i
$311$	−20.7747	+	63.9380i	−0.0667997	+	0.205588i	−0.978885	−	0.204413i	$-0.934472\pi$
$311$	−20.7747	+	63.9380i	−0.0667997	+	0.205588i	0.912085	+	0.410001i	$0.134472\pi$
$312$	−5.19676	+	10.1992i	−0.0166563	+	0.0326898i
$313$	−20.2043	+	127.565i	−0.0645505	+	0.407556i	0.934163	+	0.356847i	$0.116148\pi$
$313$	−20.2043	+	127.565i	−0.0645505	+	0.407556i	−0.998713	+	0.0507092i	$0.983852\pi$
$314$	−2.24468	−	3.08954i	−0.00714868	−	0.00983931i
$315$	83.9943	+	2.42957i	0.266649	+	0.00771291i
$316$	−48.5896	+	149.543i	−0.153765	+	0.473239i
$317$	−25.5145	−	161.092i	−0.0804875	−	0.508178i	−0.994690	−	0.102920i	$-0.967182\pi$
$317$	−25.5145	−	161.092i	−0.0804875	−	0.508178i	0.914202	−	0.405258i	$-0.132818\pi$
$318$	−109.311	+	109.311i	−0.343746	+	0.343746i
$319$	−288.847	+	343.966i	−0.905476	+	1.07826i
$320$	17.1216	+	36.1504i	0.0535048	+	0.112970i
$321$	−767.784	−	557.828i	−2.39185	−	1.73778i
$322$	−62.3821	+	31.7853i	−0.193733	+	0.0987120i
$323$	−74.4079	−	37.9127i	−0.230365	−	0.117377i
$324$	−70.6818	−	97.2851i	−0.218154	−	0.300263i
$325$	15.0789	+	16.9323i	0.0463966	+	0.0520995i
$326$	63.4970	+	195.424i	0.194776	+	0.599459i
$327$	98.6248	−	50.2519i	0.301605	−	0.153675i
$328$	−124.581	+	19.7317i	−0.379820	+	0.0601576i
$329$			110.854i			0.336942i
$330$	−219.941	−	268.512i	−0.666487	−	0.813673i
$331$	−167.863			−0.507140			−0.253570	−	0.967317i	$-0.581605\pi$
$331$	−167.863			−0.507140			−0.253570	+	0.967317i	$0.581605\pi$
$332$	−3.18544	−	20.1121i	−0.00959470	−	0.0605785i
$333$	172.211	+	337.983i	0.517151	+	1.01497i
$334$	180.199	−	58.5502i	0.539518	−	0.175300i
$335$	193.129	−	56.6329i	0.576506	−	0.169054i
$336$	−22.2386	+	16.1573i	−0.0661864	+	0.0480872i
$337$	−112.872	+	221.525i	−0.334933	+	0.657343i	−0.995638	−	0.0933026i	$-0.970258\pi$
$337$	−112.872	+	221.525i	−0.334933	+	0.657343i	0.660705	+	0.750646i	$0.270258\pi$
$338$	107.977	+	211.916i	0.319457	+	0.626970i
$339$	−79.1356	+	108.921i	−0.233438	+	0.321300i
$340$	−36.7958	+	103.011i	−0.108223	+	0.302974i
$341$	536.754	+	37.7403i	1.57406	+	0.110675i
$342$	−83.3136	−	83.3136i	−0.243607	−	0.243607i
$343$	145.456	−	23.0379i	0.424069	−	0.0671659i
$344$	130.453	+	42.3867i	0.379224	+	0.123217i
$345$	−521.632	+	492.303i	−1.51198	+	1.42697i
$346$	−180.031	+	130.800i	−0.520321	+	0.378035i
$347$	331.078	+	52.4376i	0.954114	+	0.151117i	0.614034	−	0.789280i	$-0.289546\pi$
$347$	331.078	+	52.4376i	0.954114	+	0.151117i	0.340080	+	0.940396i	$0.389546\pi$
$348$	324.703	+	165.444i	0.933055	+	0.475415i
$349$	−289.441	−	94.0452i	−0.829345	−	0.269470i	−0.136575	−	0.990630i	$-0.543610\pi$
$349$	−289.441	−	94.0452i	−0.829345	−	0.269470i	−0.692769	+	0.721159i	$0.743610\pi$
$350$	13.8039	+	52.6687i	0.0394398	+	0.150482i
$351$	−7.74139			−0.0220552
$352$	60.6252	+	14.0209i	0.172231	+	0.0398321i
$353$	−139.239	+	139.239i	−0.394445	+	0.394445i	−0.876268	−	0.481823i	$-0.839975\pi$
$353$	−139.239	+	139.239i	−0.394445	+	0.394445i	0.481823	+	0.876268i	$0.339975\pi$
$354$	−184.177	+	253.498i	−0.520274	+	0.716095i
$355$	46.5915	+	361.542i	0.131244	+	1.01843i
$356$	−59.4857	−	183.078i	−0.167095	−	0.514264i
$357$	−74.2455	−	11.7593i	−0.207971	−	0.0329393i
$358$	−29.5448	+	186.538i	−0.0825273	+	0.521057i
$359$	529.672	−	172.101i	1.47541	−	0.479390i	0.542672	−	0.839945i	$-0.317413\pi$
$359$	529.672	−	172.101i	1.47541	−	0.479390i	0.932738	+	0.360555i	$0.117413\pi$
$360$	−94.2855	+	122.181i	−0.261904	+	0.339392i
$361$	−244.902	−	177.931i	−0.678398	−	0.492885i
$362$	85.1994	+	85.1994i	0.235357	+	0.235357i
$363$	−539.873	+	9.00953i	−1.48725	+	0.0248196i
$364$		−	2.79337i		−	0.00767408i
$365$	−499.433	+	341.242i	−1.36831	+	0.934909i
$366$	−143.993	+	443.164i	−0.393423	+	1.21083i
$367$	−154.586	+	303.391i	−0.421214	+	0.826679i	0.578724	+	0.815524i	$0.303551\pi$
$367$	−154.586	+	303.391i	−0.421214	+	0.826679i	−0.999938	+	0.0111557i	$0.996449\pi$
$368$	20.1156	−	127.005i	0.0546619	−	0.345122i
$369$	−286.051	−	393.715i	−0.775205	−	1.06698i
$370$	−178.751	+	168.701i	−0.483112	+	0.455949i
$371$	11.6575	−	35.8780i	0.0314218	−	0.0967062i
$372$	−68.2940	−	431.192i	−0.183586	−	1.15912i
$373$	8.31841	−	8.31841i	0.0223014	−	0.0223014i	−0.695868	−	0.718170i	$-0.744980\pi$
$373$	8.31841	−	8.31841i	0.0223014	−	0.0223014i	0.718170	+	0.695868i	$0.244980\pi$
$374$	90.1178	+	144.342i	0.240957	+	0.385941i
$375$	287.533	+	477.978i	0.766754	+	1.27461i
$376$	−164.714	−	119.672i	−0.438068	−	0.318275i
$377$	−32.9962	+	16.8124i	−0.0875231	+	0.0445953i
$378$	−16.5640	−	8.43976i	−0.0438200	−	0.0223274i
$379$	−332.491	−	457.635i	−0.877286	−	1.20748i	−0.977165	−	0.212481i	$-0.931846\pi$
$379$	−332.491	−	457.635i	−0.877286	−	1.20748i	0.0998796	−	0.995000i	$-0.468154\pi$
$380$	36.6120	−	66.9930i	0.0963474	−	0.176297i
$381$	−138.694	−	426.858i	−0.364028	−	1.12036i
$382$	53.4299	−	27.2239i	0.139869	−	0.0712668i
$383$	−7.98774	+	1.26513i	−0.0208557	+	0.00330322i	−0.166854	−	0.985982i	$-0.553361\pi$
$383$	−7.98774	+	1.26513i	−0.0208557	+	0.00330322i	0.145998	+	0.989285i	$0.453361\pi$
$384$		−	50.4861i		−	0.131474i
$385$	77.5697	+	34.0165i	0.201480	+	0.0883546i
$386$	−160.234			−0.415113
$387$	82.7890	+	522.709i	0.213925	+	1.35067i
$388$	45.2434	+	88.7951i	0.116607	+	0.228853i
$389$	81.5567	−	26.4994i	0.209657	−	0.0681218i	−0.202305	−	0.979322i	$-0.564843\pi$
$389$	81.5567	−	26.4994i	0.209657	−	0.0681218i	0.411963	+	0.911201i	$0.364843\pi$
$390$	−8.05256	−	27.4608i	−0.0206476	−	0.0704123i
$391$	284.484	−	206.690i	0.727581	−	0.528618i
$392$	−59.8745	+	117.510i	−0.152741	+	0.299771i
$393$	−322.766	−	633.464i	−0.821287	−	1.61187i
$394$	−251.643	+	346.356i	−0.638687	+	0.879077i
$395$	−168.261	−	355.267i	−0.425978	−	0.899409i
$396$	57.9919	+	232.973i	0.146444	+	0.588316i
$397$	272.268	+	272.268i	0.685814	+	0.685814i	0.961304	−	0.275490i	$-0.0888400\pi$
$397$	272.268	+	272.268i	0.685814	+	0.685814i	−0.275490	+	0.961304i	$0.588840\pi$
$398$	336.159	−	53.2423i	0.844619	−	0.133775i
$399$	49.8971	+	16.2125i	0.125055	+	0.0406329i
$400$	−93.1604	−	36.3474i	−0.232901	−	0.0908684i
$401$	295.194	−	214.471i	0.736145	−	0.534840i	−0.155357	−	0.987858i	$-0.549653\pi$
$401$	295.194	−	214.471i	0.736145	−	0.534840i	0.891501	+	0.453018i	$0.149653\pi$
$402$	−250.895	−	39.7379i	−0.624118	−	0.0988505i
$403$	39.5284	+	20.1407i	0.0980853	+	0.0499770i
$404$	−184.970	−	60.1005i	−0.457848	−	0.148764i
$405$	295.442	+	55.5940i	0.729488	+	0.137269i
$406$	−88.9299			−0.219039
$407$	33.1786	+	380.915i	0.0815200	+	0.935910i
$408$	97.6240	−	97.6240i	0.239274	−	0.239274i
$409$	83.7618	−	115.288i	0.204797	−	0.281878i	−0.694248	−	0.719736i	$-0.744263\pi$
$409$	83.7618	−	115.288i	0.204797	−	0.281878i	0.899044	+	0.437858i	$0.144263\pi$
$410$	192.648	−	249.645i	0.469872	−	0.608891i
$411$	−245.189	−	754.613i	−0.596566	−	1.83604i
$412$	−241.728	−	38.2860i	−0.586718	−	0.0929271i
$413$	11.9616	−	75.5228i	0.0289628	−	0.182864i
$414$	471.845	−	153.312i	1.13972	−	0.370318i
$415$	40.3022	+	31.1006i	0.0971137	+	0.0749412i
$416$	4.15056	+	3.01556i	0.00997731	+	0.00724894i
$417$	268.237	+	268.237i	0.643253	+	0.643253i
$418$	−46.3630	−	109.341i	−0.110916	−	0.261581i
$419$		−	95.5286i		−	0.227992i	−0.993481	−	0.113996i	$-0.963635\pi$
$419$		−	95.5286i		−	0.227992i	0.993481	−	0.113996i	$-0.0363651\pi$
$420$	12.7083	−	67.5358i	0.0302580	−	0.160800i
$421$	−21.4703	+	66.0789i	−0.0509984	+	0.156957i	−0.973312	−	0.229485i	$-0.926296\pi$
$421$	−21.4703	+	66.0789i	−0.0509984	+	0.156957i	0.922314	+	0.386442i	$0.126296\pi$
$422$	−147.787	+	290.048i	−0.350205	+	0.687317i
$423$	122.885	−	775.862i	0.290507	−	1.83419i
$424$	40.7251	+	56.0533i	0.0960497	+	0.132201i
$425$	−109.858	−	250.427i	−0.258490	−	0.589240i
$426$	142.177	−	437.576i	0.333749	−	1.02717i
$427$	−17.7882	−	112.310i	−0.0416586	−	0.263022i
$428$	−300.767	+	300.767i	−0.702726	+	0.702726i
$429$	−41.2698	−	16.6925i	−0.0961999	−	0.0389102i
$430$	−309.914	+	146.781i	−0.720730	+	0.341352i
$431$	499.151	+	362.654i	1.15812	+	0.841426i	0.989540	−	0.144262i	$-0.0460807\pi$
$431$	499.151	+	362.654i	1.15812	+	0.841426i	0.168583	+	0.985687i	$0.446081\pi$
$432$	30.4218	−	15.5007i	0.0704209	−	0.0358813i
$433$	379.560	+	193.396i	0.876583	+	0.446641i	0.833558	−	0.552433i	$-0.186300\pi$
$433$	379.560	+	193.396i	0.876583	+	0.446641i	0.0430254	+	0.999074i	$0.486300\pi$
$434$	62.6197	+	86.1887i	0.144285	+	0.198591i
$435$	−874.244	+	256.362i	−2.00976	+	0.589338i
$436$	−15.3303	−	47.1819i	−0.0351613	−	0.108215i
$437$	−218.675	+	111.421i	−0.500401	+	0.254967i
$438$	754.051	−	119.430i	1.72158	−	0.272671i
$439$			424.322i			0.966565i	0.875465	+	0.483282i	$0.160556\pi$
$439$			424.322i			0.966565i	−0.875465	+	0.483282i	$0.839444\pi$
$440$	−134.284	+	78.5358i	−0.305190	+	0.178490i
$441$	−508.848			−1.15385
$442$	2.19473	+	13.8570i	0.00496546	+	0.0313507i
$443$	20.1896	+	39.6243i	0.0455746	+	0.0894453i	0.912671	−	0.408696i	$-0.134016\pi$
$443$	20.1896	+	39.6243i	0.0455746	+	0.0894453i	−0.867096	+	0.498141i	$0.834016\pi$
$444$	295.039	−	95.8641i	0.664503	−	0.215910i
$445$	422.300	+	230.789i	0.948989	+	0.518628i
$446$	−206.842	+	150.280i	−0.463772	+	0.336950i
$447$	455.230	−	893.438i	1.01841	−	1.99874i
$448$	5.59320	+	10.9773i	0.0124848	+	0.0245028i
$449$	459.898	−	632.995i	1.02427	−	1.40979i	0.115105	−	0.993353i	$-0.463279\pi$
$449$	459.898	−	632.995i	1.02427	−	1.40979i	0.909166	−	0.416435i	$-0.136721\pi$
$450$	−38.2286	−	383.929i	−0.0849524	−	0.853174i
$451$	−118.491	−	476.020i	−0.262730	−	1.05548i
$452$	42.6679	+	42.6679i	0.0943980	+	0.0943980i
$453$	726.958	−	115.139i	1.60476	−	0.254170i
$454$	342.601	+	111.318i	0.754627	+	0.245193i
$455$	4.79318	+	5.07873i	0.0105345	+	0.0111620i
$456$	−77.9556	+	56.6381i	−0.170955	+	0.124206i
$457$	−365.395	−	57.8729i	−0.799552	−	0.126637i	−0.256729	−	0.966483i	$-0.582645\pi$
$457$	−365.395	−	57.8729i	−0.799552	−	0.126637i	−0.542823	+	0.839847i	$0.682645\pi$
$458$	−362.354	−	184.629i	−0.791167	−	0.403120i
$459$	88.7995	+	28.8527i	0.193463	+	0.0628600i
$460$	181.357	+	265.429i	0.394254	+	0.577020i
$461$	−781.018			−1.69418			−0.847091	−	0.531447i	$-0.821648\pi$
$461$	−781.018			−1.69418			−0.847091	+	0.531447i	$0.821648\pi$
$462$	−70.1050	−	80.7091i	−0.151743	−	0.174695i
$463$	−283.220	+	283.220i	−0.611707	+	0.611707i	−0.943391	−	0.331684i	$-0.892383\pi$
$463$	−283.220	+	283.220i	−0.611707	+	0.611707i	0.331684	+	0.943391i	$0.392383\pi$
$464$	96.0036	−	132.138i	0.206904	−	0.284779i
$465$	864.057	+	666.780i	1.85819	+	1.43393i
$466$	131.726	+	405.412i	0.282674	+	0.869982i
$467$	−739.091	−	117.060i	−1.58264	−	0.250665i	−0.697704	−	0.716386i	$-0.745795\pi$
$467$	−739.091	−	117.060i	−1.58264	−	0.250665i	−0.884932	+	0.465721i	$0.845795\pi$
$468$	−3.09652	+	19.5507i	−0.00661650	+	0.0417750i
$469$	58.9551	−	19.1557i	0.125704	−	0.0408436i
$470$	504.819	−	65.0553i	1.07408	−	0.138416i
$471$	−9.74868	−	7.08283i	−0.0206978	−	0.0150379i
$472$	99.3035	+	99.3035i	0.210389	+	0.210389i
$473$	−120.200	+	519.734i	−0.254122	+	1.09880i
$474$			496.150i			1.04673i
$475$	48.3885	+	184.626i	0.101871	+	0.388686i
$476$	−10.4111	+	32.0420i	−0.0218720	+	0.0673152i
$477$	−121.362	+	238.186i	−0.254428	+	0.499342i
$478$	101.163	−	638.717i	0.211638	−	1.33623i
$479$	146.787	+	202.035i	0.306444	+	0.421784i	0.934268	−	0.356571i	$-0.116054\pi$
$479$	146.787	+	202.035i	0.306444	+	0.421784i	−0.627824	+	0.778355i	$0.716054\pi$
$480$	86.6298	+	91.7907i	0.180479	+	0.191231i
$481$	−9.74167	+	29.9818i	−0.0202530	+	0.0623322i
$482$	−32.3898	−	204.501i	−0.0671988	−	0.424276i
$483$	−156.212	+	156.212i	−0.323421	+	0.323421i
$484$	−33.8636	+	239.619i	−0.0699661	+	0.495081i
$485$	−234.624	−	83.8081i	−0.483760	−	0.172800i
$486$	−394.866	−	286.887i	−0.812481	−	0.590302i
$487$	−204.960	+	104.432i	−0.420863	+	0.214440i	−0.651579	−	0.758581i	$-0.725893\pi$
$487$	−204.960	+	104.432i	−0.420863	+	0.214440i	0.230716	+	0.973021i	$0.425893\pi$
$488$	186.081	+	94.8131i	0.381314	+	0.194289i
$489$	381.102	+	524.542i	0.779350	+	1.07268i
$490$	−92.7776	−	316.390i	−0.189342	−	0.645694i
$491$	261.577	+	805.050i	0.532743	+	1.63961i	0.748476	+	0.663162i	$0.230786\pi$
$491$	261.577	+	805.050i	0.532743	+	1.63961i	−0.215733	+	0.976452i	$0.569214\pi$
$492$	−354.621	+	180.688i	−0.720774	+	0.367253i
$493$	441.153	−	69.8717i	0.894833	−	0.141728i
$494$		−	9.79192i		−	0.0198217i
$495$	−505.200	−	324.069i	−1.02061	−	0.654684i
$496$	−195.665			−0.394486
$497$	17.5639	+	110.894i	0.0353399	+	0.223127i
$498$	−29.1699	−	57.2492i	−0.0585741	−	0.114958i
$499$	238.041	−	77.3444i	0.477037	−	0.154999i	−0.0606225	−	0.998161i	$-0.519309\pi$
$499$	238.041	−	77.3444i	0.477037	−	0.154999i	0.537660	+	0.843162i	$0.319309\pi$
$500$	231.748	−	93.7709i	0.463496	−	0.187542i
$501$	483.677	−	351.412i	0.965422	−	0.701420i
$502$	81.2623	−	159.486i	0.161877	−	0.317702i
$503$	−344.891	−	676.886i	−0.685667	−	1.34570i	−0.926929	−	0.375238i	$-0.877561\pi$
$503$	−344.891	−	676.886i	−0.685667	−	1.34570i	0.241261	−	0.970460i	$-0.422439\pi$
$504$	−27.9399	+	38.4560i	−0.0554363	+	0.0763016i
$505$	439.430	−	208.123i	0.870158	−	0.412124i
$506$	498.858	+	35.0757i	0.985886	+	0.0693196i
$507$	530.664	+	530.664i	1.04667	+	1.04667i
$508$	−198.683	+	31.4683i	−0.391108	+	0.0619454i
$509$	129.521	+	42.0840i	0.254462	+	0.0826798i	0.433470	−	0.901168i	$-0.357289\pi$
$509$	129.521	+	42.0840i	0.254462	+	0.0826798i	−0.179008	+	0.983848i	$0.557289\pi$
$510$	−9.97951	+	345.009i	−0.0195677	+	0.676487i
$511$	−150.723	+	109.507i	−0.294958	+	0.214299i
$512$	−22.3488	−	3.53971i	−0.0436501	−	0.00691349i
$513$	−58.0636	−	29.5849i	−0.113184	−	0.0576703i
$514$	−2.99416	−	0.972863i	−0.00582522	−	0.00189273i
$515$	505.191	−	345.176i	0.980953	−	0.670244i
$516$	432.812			0.838783
$517$	408.071	−	678.555i	0.789306	−	1.31249i
$518$	−53.5304	+	53.5304i	−0.103341	+	0.103341i
$519$	−412.724	+	568.066i	−0.795230	+	1.09454i
$520$	−12.7208	+	1.63931i	−0.0244630	+	0.00315251i
$521$	−221.876	−	682.865i	−0.425866	−	1.31068i	−0.902162	−	0.431396i	$-0.858021\pi$
$521$	−221.876	−	682.865i	−0.425866	−	1.31068i	0.476296	−	0.879285i	$-0.341979\pi$
$522$	622.417	+	98.5812i	1.19237	+	0.188853i
$523$	−10.3880	+	65.5870i	−0.0198623	+	0.125405i	−0.995627	−	0.0934162i	$-0.970221\pi$
$523$	−10.3880	+	65.5870i	−0.0198623	+	0.125405i	0.975765	+	0.218822i	$0.0702213\pi$
$524$	−303.047	+	98.4660i	−0.578335	+	0.187912i
$525$	92.7803	+	144.596i	0.176724	+	0.275421i
$526$	−0.0889403	−	0.0646189i	−0.000169088	−	0.000122850i
$527$	−378.354	−	378.354i	−0.717940	−	0.717940i
$528$	195.604	−	17.0376i	0.370462	−	0.0322682i
$529$		−	504.429i		−	0.953552i
$530$	−170.227	−	32.0319i	−0.321182	−	0.0604375i
$531$	−167.438	+	515.322i	−0.315326	+	0.970475i
$532$	10.6753	−	20.9514i	0.0200663	−	0.0393823i
$533$	6.32694	−	39.9467i	0.0118704	−	0.0749469i
$534$	−357.027	−	491.405i	−0.668589	−	0.920234i
$535$	30.7456	−	1062.93i	0.0574684	−	1.98678i
$536$	−35.1818	+	108.279i	−0.0656377	+	0.202012i
$537$	93.2250	+	588.599i	0.173603	+	1.09609i
$538$	−119.908	+	119.908i	−0.222877	+	0.222877i
$539$	−475.490	−	192.323i	−0.882171	−	0.356814i
$540$	−28.7133	+	80.3838i	−0.0531727	+	0.148859i
$541$	611.297	+	444.133i	1.12994	+	0.820948i	0.985686	−	0.168593i	$-0.0539222\pi$
$541$	611.297	+	444.133i	1.12994	+	0.820948i	0.144253	+	0.989541i	$0.453922\pi$
$542$	51.7589	−	26.3725i	0.0954962	−	0.0486577i
$543$	338.754	+	172.604i	0.623856	+	0.317870i
$544$	−36.3709	−	50.0602i	−0.0668582	−	0.0920224i
$545$	108.833	+	59.4777i	0.199693	+	0.109133i
$546$	−2.72372	−	8.38274i	−0.00498849	−	0.0153530i
$547$	301.593	−	153.669i	0.551358	−	0.280931i	−0.156035	−	0.987752i	$-0.549871\pi$
$547$	301.593	−	153.669i	0.551358	−	0.280931i	0.707393	+	0.706820i	$0.249871\pi$
$548$	−351.238	+	55.6306i	−0.640945	+	0.101516i
$549$			805.776i			1.46772i
$550$	109.386	−	373.209i	0.198883	−	0.678561i
$551$	−311.736			−0.565765
$552$	−63.4723	−	400.748i	−0.114986	−	0.725994i
$553$	−54.9669	−	107.879i	−0.0993977	−	0.195079i
$554$	149.800	−	48.6729i	0.270397	−	0.0878572i
$555$	−371.928	+	680.557i	−0.670140	+	1.22623i
$556$	137.548	−	99.9344i	0.247388	−	0.179738i
$557$	−462.269	+	907.253i	−0.829926	+	1.62882i	−0.0535381	+	0.998566i	$0.517050\pi$
$557$	−462.269	+	907.253i	−0.829926	+	1.62882i	−0.776388	+	0.630256i	$0.782950\pi$
$558$	−342.731	−	672.647i	−0.614213	−	1.20546i
$559$	−25.8521	+	35.5824i	−0.0462470	+	0.0636536i
$560$	−29.0053	−	10.3608i	−0.0517952	−	0.0185014i
$561$	411.181	+	345.291i	0.732943	+	0.615491i
$562$	−7.18236	−	7.18236i	−0.0127800	−	0.0127800i
$563$	13.8206	−	2.18898i	0.0245482	−	0.00388806i	−0.144148	−	0.989556i	$-0.546044\pi$
$563$	13.8206	−	2.18898i	0.0245482	−	0.00388806i	0.168696	+	0.985668i	$0.446044\pi$
$564$	−610.984	−	198.521i	−1.08331	−	0.351987i
$565$	−150.791	−	4.36168i	−0.266886	−	0.00771979i
$566$	461.456	−	335.267i	0.815292	−	0.592345i
$567$	91.4539	+	14.4849i	0.161294	+	0.0255465i
$568$	−183.735	−	93.6176i	−0.323477	−	0.164820i
$569$	−253.390	−	82.3313i	−0.445324	−	0.144695i	0.0777664	−	0.996972i	$-0.475221\pi$
$569$	−253.390	−	82.3313i	−0.445324	−	0.144695i	−0.523091	+	0.852277i	$0.675221\pi$
$570$	44.5481	−	236.741i	0.0781545	−	0.415336i
$571$	780.290			1.36653			0.683266	−	0.730169i	$-0.260559\pi$
$571$	780.290			1.36653			0.683266	+	0.730169i	$0.260559\pi$
$572$	−10.2828	+	17.0987i	−0.0179770	+	0.0298928i
$573$	133.795	−	133.795i	0.233499	−	0.233499i
$574$	57.0879	−	78.5748i	0.0994563	−	0.136890i
$575$	−785.186	−	171.395i	−1.36554	−	0.298078i
$576$	−26.9780	−	83.0298i	−0.0468368	−	0.144149i
$577$	−746.977	−	118.310i	−1.29459	−	0.205043i	−0.529137	−	0.848537i	$-0.677484\pi$
$577$	−746.977	−	118.310i	−1.29459	−	0.205043i	−0.765451	+	0.643494i	$0.777484\pi$
$578$	−37.4652	+	236.546i	−0.0648186	+	0.409249i
$579$	−480.852	+	156.238i	−0.830487	+	0.269842i
$580$	52.1891	+	404.979i	0.0899812	+	0.698240i
$581$	12.6849	+	9.21615i	0.0218329	+	0.0158626i
$582$	222.354	+	222.354i	0.382051	+	0.382051i
$583$	−203.430	+	176.702i	−0.348937	+	0.303092i
$584$		−	342.172i		−	0.585911i
$585$	−27.9174	−	40.8592i	−0.0477221	−	0.0698449i
$586$	38.9087	−	119.749i	0.0663970	−	0.204349i
$587$	264.864	−	519.825i	0.451217	−	0.885562i	−0.547591	−	0.836746i	$-0.684455\pi$
$587$	264.864	−	519.825i	0.451217	−	0.885562i	0.998808	−	0.0488164i	$-0.0155449\pi$
$588$	−65.0997	+	411.024i	−0.110714	+	0.699020i
$589$	219.508	+	302.127i	0.372680	+	0.512949i
$590$	−350.944	−	10.1512i	−0.594821	−	0.0172054i
$591$	−417.445	+	1284.76i	−0.706337	+	2.17388i
$592$	−21.7505	−	137.327i	−0.0367407	−	0.231972i
$593$	−331.993	+	331.993i	−0.559854	+	0.559854i	−0.929266	−	0.369412i	$-0.879559\pi$
$593$	−331.993	+	331.993i	−0.559854	+	0.559854i	0.369412	+	0.929266i	$0.379559\pi$
$594$	70.3227	+	112.636i	0.118388	+	0.189623i
$595$	−36.0526	−	76.1214i	−0.0605926	−	0.127935i
$596$	−363.584	−	264.159i	−0.610040	−	0.443220i
$597$	956.878	−	487.554i	1.60281	−	0.816673i
$598$	36.7376	+	18.7187i	0.0614341	+	0.0313022i
$599$	331.288	+	455.979i	0.553069	+	0.761234i	0.990425	−	0.138054i	$-0.0440849\pi$
$599$	331.288	+	455.979i	0.553069	+	0.761234i	−0.437356	+	0.899289i	$0.644085\pi$
$600$	−315.010	−	18.2389i	−0.525017	−	0.0303981i
$601$	20.7864	+	63.9739i	0.0345863	+	0.106446i	0.966859	−	0.255310i	$-0.0821775\pi$
$601$	20.7864	+	63.9739i	0.0345863	+	0.106446i	−0.932273	+	0.361756i	$0.882177\pi$
$602$	−94.1071	+	47.9499i	−0.156324	+	0.0796511i
$603$	−433.859	+	68.7165i	−0.719501	+	0.113958i
$604$		−	329.878i		−	0.546155i
$605$	−349.597	−	493.768i	−0.577847	−	0.816145i
$606$	−613.688			−1.01269
$607$	−88.9500	−	561.608i	−0.146540	−	0.925220i	−0.945922	−	0.324395i	$-0.894839\pi$
$607$	−88.9500	−	561.608i	−0.146540	−	0.925220i	0.799381	−	0.600824i	$-0.205161\pi$
$608$	19.6065	+	38.4799i	0.0322475	+	0.0632894i
$609$	−266.874	+	86.7125i	−0.438216	+	0.142385i
$610$	−501.013	+	146.916i	−0.821333	+	0.240846i
$611$	52.8152	−	38.3725i	0.0864406	−	0.0628028i
$612$	108.386	−	212.720i	0.177102	−	0.347582i
$613$	276.294	+	542.257i	0.450724	+	0.884595i	0.998838	+	0.0481920i	$0.0153459\pi$
$613$	276.294	+	542.257i	0.450724	+	0.884595i	−0.548114	+	0.836404i	$0.684654\pi$
$614$	−192.579	+	265.062i	−0.313646	+	0.431697i
$615$	334.704	−	937.016i	0.544235	−	1.52360i
$616$	−40.6430	+	25.3749i	−0.0659789	+	0.0411930i
$617$	285.830	+	285.830i	0.463258	+	0.463258i	0.899722	−	0.436464i	$-0.143769\pi$
$617$	285.830	+	285.830i	0.463258	+	0.463258i	−0.436464	+	0.899722i	$0.643769\pi$
$618$	−762.744	+	120.807i	−1.23421	+	0.195480i
$619$	−562.331	−	182.712i	−0.908451	−	0.295174i	−0.182730	−	0.983163i	$-0.558493\pi$
$619$	−562.331	−	182.712i	−0.908451	−	0.295174i	−0.725721	+	0.687990i	$0.758493\pi$
$620$	355.747	−	335.745i	0.573785	−	0.541524i
$621$	221.995	−	161.289i	0.357479	−	0.259724i
$622$	93.9047	+	14.8730i	0.150972	+	0.0239116i
$623$	132.070	+	67.2931i	0.211991	+	0.108015i
$624$	15.3960	+	5.00246i	0.0246730	+	0.00801676i
$625$	−260.447	+	568.148i	−0.416715	+	0.909037i
$626$	182.653			0.291778
$627$	−245.747	−	282.919i	−0.391942	−	0.451226i
$628$	−3.81888	+	3.81888i	−0.00608103	+	0.00608103i
$629$	223.489	−	307.606i	0.355308	−	0.489039i
$630$	−15.1886	−	117.861i	−0.0241089	−	0.187081i
$631$	−203.637	−	626.731i	−0.322722	−	0.993235i	−0.972459	−	0.233076i	$-0.925121\pi$
$631$	−203.637	−	626.731i	−0.322722	−	0.993235i	0.649737	−	0.760159i	$-0.274879\pi$
$632$	219.632	+	34.7863i	0.347519	+	0.0550417i
$633$	−160.684	+	1014.52i	−0.253845	+	1.60271i
$634$	−219.370	+	71.2775i	−0.346009	+	0.112425i
$635$	307.236	−	398.137i	0.483836	−	0.626987i
$636$	176.869	+	128.503i	0.278096	+	0.202049i
$637$	−29.9026	−	29.9026i	−0.0469429	−	0.0469429i
$638$	544.355	+	327.366i	0.853221	+	0.513112i
$639$		−	795.616i		−	1.24509i
$640$	46.7072	−	31.9130i	0.0729799	−	0.0498641i
$641$	−140.379	+	432.041i	−0.219000	+	0.674011i	0.779846	+	0.625972i	$0.215297\pi$
$641$	−140.379	+	432.041i	−0.219000	+	0.674011i	−0.998845	+	0.0480398i	$0.984703\pi$
$642$	−609.317	+	1195.85i	−0.949092	+	1.86270i
$643$	8.91164	−	56.2658i	0.0138595	−	0.0875052i	−0.979789	−	0.200034i	$-0.935895\pi$
$643$	8.91164	−	56.2658i	0.0138595	−	0.0875052i	0.993649	+	0.112528i	$0.0358949\pi$
$644$	58.1986	+	80.1035i	0.0903705	+	0.124384i
$645$	−786.913	+	742.669i	−1.22002	+	1.15142i
$646$	−36.4952	+	112.321i	−0.0564941	+	0.173871i
$647$	46.7289	+	295.035i	0.0722240	+	0.456004i	0.997124	+	0.0757929i	$0.0241488\pi$
$647$	46.7289	+	295.035i	0.0722240	+	0.456004i	−0.924900	+	0.380211i	$0.875851\pi$
$648$	−120.251	+	120.251i	−0.185573	+	0.185573i
$649$	−351.231	+	418.255i	−0.541188	+	0.644461i
$650$	20.3152	−	24.8082i	0.0312541	−	0.0381665i
$651$	271.958	+	197.589i	0.417754	+	0.303516i
$652$	258.921	−	131.927i	0.397118	−	0.202342i
$653$	−564.522	−	287.638i	−0.864505	−	0.440488i	−0.0352640	−	0.999378i	$-0.511227\pi$
$653$	−564.522	−	287.638i	−0.864505	−	0.440488i	−0.829241	+	0.558890i	$0.811227\pi$
$654$	−92.0108	−	126.642i	−0.140689	−	0.193642i
$655$	382.023	−	699.029i	0.583241	−	1.06722i
$656$	55.1225	+	169.650i	0.0840283	+	0.258612i
$657$	1176.30	−	599.354i	1.79041	−	0.912259i
$658$	154.841	−	24.5244i	0.235321	−	0.0372711i
$659$		−	521.579i		−	0.791470i	−0.918365	−	0.395735i	$-0.870490\pi$
$659$		−	521.579i		−	0.791470i	0.918365	−	0.395735i	$-0.129510\pi$
$660$	−326.401	+	366.617i	−0.494546	+	0.555480i
$661$	118.286			0.178950			0.0894749	−	0.995989i	$-0.471481\pi$
$661$	118.286			0.178950			0.0894749	+	0.995989i	$0.471481\pi$
$662$	37.1367	+	234.472i	0.0560977	+	0.354187i
$663$	20.0978	+	39.4441i	0.0303134	+	0.0594933i
$664$	−27.3879	+	8.89886i	−0.0412468	+	0.0134019i
$665$	16.5417	+	56.4104i	0.0248747	+	0.0848277i
$666$	433.998	−	315.318i	0.651648	−	0.473450i
$667$	595.931	−	1169.58i	0.893450	−	1.75349i
$668$	−121.649	−	238.749i	−0.182109	−	0.357409i
$669$	−474.190	+	652.666i	−0.708804	+	0.975585i
$670$	−121.831	−	257.235i	−0.181838	−	0.383932i
$671$	−304.548	+	752.953i	−0.453873	+	1.12214i
$672$	27.4884	+	27.4884i	0.0409054	+	0.0409054i
$673$	−40.0010	+	6.33554i	−0.0594369	+	0.00941387i	−0.186082	−	0.982534i	$-0.559579\pi$
$673$	−40.0010	+	6.33554i	−0.0594369	+	0.00941387i	0.126645	+	0.991948i	$0.459579\pi$
$674$	334.397	+	108.652i	0.496138	+	0.161205i
$675$	−85.7271	−	195.418i	−0.127003	−	0.289509i
$676$	272.117	−	197.704i	0.402540	−	0.292462i
$677$	−986.088	−	156.181i	−1.45656	−	0.230696i	−0.622606	−	0.782536i	$-0.713926\pi$
$677$	−986.088	−	156.181i	−1.45656	−	0.230696i	−0.833950	+	0.551840i	$0.813926\pi$
$678$	169.648	+	86.4400i	0.250218	+	0.127493i
$679$	−72.9807	−	23.7129i	−0.107483	−	0.0349232i
$680$	152.026	+	28.6071i	0.223568	+	0.0420693i
$681$	1136.67			1.66912
$682$	−66.0314	−	758.089i	−0.0968202	−	1.11157i
$683$	763.451	−	763.451i	1.11779	−	1.11779i	0.125726	−	0.992065i	$-0.459874\pi$
$683$	763.451	−	763.451i	1.11779	−	1.11779i	0.992065	−	0.125726i	$-0.0401261\pi$
$684$	−97.9410	+	134.804i	−0.143189	+	0.197082i
$685$	543.142	−	703.839i	0.792908	−	1.02750i
$686$	−64.3588	−	198.076i	−0.0938175	−	0.288740i
$687$	−1267.43	−	200.741i	−1.84488	−	0.292200i
$688$	30.3456	−	191.594i	0.0441069	−	0.278480i
$689$	−21.1290	+	6.86523i	−0.0306662	+	0.00996405i
$690$	803.052	+	619.704i	1.16384	+	0.898121i
$691$	−327.706	−	238.092i	−0.474249	−	0.344562i	0.324846	−	0.945767i	$-0.394687\pi$
$691$	−327.706	−	238.092i	−0.474249	−	0.344562i	−0.799095	+	0.601205i	$0.794687\pi$
$692$	222.531	+	222.531i	0.321576	+	0.321576i
$693$	−158.423	−	95.2731i	−0.228605	−	0.137479i
$694$		−	474.051i		−	0.683070i
$695$	−78.6023	+	417.716i	−0.113097	+	0.601030i
$696$	159.259	−	490.148i	0.228820	−	0.704235i
$697$	−221.459	+	434.638i	−0.317732	+	0.623584i
$698$	−67.3289	+	425.098i	−0.0964598	+	0.609023i
$699$	790.606	+	1088.18i	1.13105	+	1.55676i
$700$	70.5139	−	30.9334i	0.100734	−	0.0441905i
$701$	−325.761	+	1002.59i	−0.464709	+	1.43023i	0.394638	+	0.918837i	$0.370870\pi$
$701$	−325.761	+	1002.59i	−0.464709	+	1.43023i	−0.859348	+	0.511392i	$0.829130\pi$
$702$	1.71264	+	10.8132i	0.00243966	+	0.0154034i
$703$	−187.646	+	187.646i	−0.266922	+	0.266922i
$704$	6.17222	−	87.7833i	0.00876735	−	0.124692i
$705$	1451.50	−	687.459i	2.05887	−	0.975119i
$706$	225.294	+	163.686i	0.319113	+	0.231849i
$707$	133.435	−	67.9887i	0.188734	−	0.0961650i
$708$	394.832	+	201.177i	0.557672	+	0.284148i
$709$	226.904	+	312.307i	0.320034	+	0.440489i	0.938478	−	0.345340i	$-0.112237\pi$
$709$	226.904	+	312.307i	0.320034	+	0.440489i	−0.618444	+	0.785829i	$0.712237\pi$
$710$	494.695	−	145.064i	0.696754	−	0.204315i
$711$	265.125	+	815.972i	0.372891	+	1.14764i
$712$	−242.564	+	123.592i	−0.340680	+	0.173585i
$713$	−1553.15	+	245.995i	−2.17833	+	0.345014i
$714$			106.308i			0.148890i
$715$	−10.6442	−	48.7323i	−0.0148871	−	0.0681570i
$716$	267.093			0.373036
$717$	−319.207	−	2015.39i	−0.445198	−	2.81087i
$718$	−357.571	−	701.773i	−0.498010	−	0.977399i
$719$	290.505	−	94.3907i	0.404040	−	0.131281i	−0.0999451	−	0.994993i	$-0.531867\pi$
$719$	290.505	−	94.3907i	0.404040	−	0.131281i	0.503985	+	0.863712i	$0.331867\pi$
$720$	191.522	+	104.668i	0.266003	+	0.145372i
$721$	152.461	−	110.769i	0.211458	−	0.153633i
$722$	−194.355	+	381.443i	−0.269190	+	0.528315i
$723$	−296.602	−	582.114i	−0.410238	−	0.805138i
$724$	100.158	−	137.855i	0.138340	−	0.190408i
$725$	−789.797	−	646.756i	−1.08937	−	0.892078i
$726$	132.022	+	752.102i	0.181848	+	1.03595i
$727$	353.713	+	353.713i	0.486537	+	0.486537i	0.907212	−	0.420674i	$-0.138207\pi$
$727$	353.713	+	353.713i	0.486537	+	0.486537i	−0.420674	+	0.907212i	$0.638207\pi$
$728$	−3.90178	+	0.617981i	−0.00535959	+	0.000848876i
$729$	−950.058	−	308.693i	−1.30323	−	0.423447i
$730$	587.138	+	622.116i	0.804299	+	0.852214i
$731$	429.161	−	311.804i	0.587087	−	0.426544i
$732$	650.868	+	103.087i	0.889164	+	0.140830i
$733$	888.158	+	452.539i	1.21168	+	0.617380i	0.938731	−	0.344650i	$-0.112002\pi$
$733$	888.158	+	452.539i	1.21168	+	0.617380i	0.272945	+	0.962030i	$0.412002\pi$
$734$	457.977	+	148.806i	0.623947	+	0.202733i
$735$	−586.921	−	859.004i	−0.798533	−	1.16871i
$736$	−181.851			−0.247080
$737$	−431.389	−	99.7682i	−0.585331	−	0.135371i
$738$	−486.659	+	486.659i	−0.659429	+	0.659429i
$739$	−338.831	+	466.361i	−0.458500	+	0.631071i	−0.974197	−	0.225700i	$-0.927533\pi$
$739$	−338.831	+	466.361i	−0.458500	+	0.631071i	0.515697	+	0.856771i	$0.327533\pi$
$740$	275.188	+	212.358i	0.371875	+	0.286971i
$741$	−9.54776	−	29.3850i	−0.0128850	−	0.0396559i
$742$	−52.6935	−	8.34583i	−0.0710155	−	0.0112477i
$743$	−157.538	+	994.656i	−0.212030	+	1.33870i	0.620275	+	0.784384i	$0.287021\pi$
$743$	−157.538	+	994.656i	−0.212030	+	1.33870i	−0.832305	+	0.554318i	$0.812979\pi$
$744$	−587.181	+	190.787i	−0.789221	+	0.256434i
$745$	1114.32	−	143.601i	1.49573	−	0.192753i
$746$	−13.4595	−	9.77887i	−0.0180422	−	0.0131084i
$747$	−78.5651	−	78.5651i	−0.105174	−	0.105174i
$748$	181.680	−	157.810i	0.242888	−	0.210976i
$749$		−	327.521i		−	0.437277i
$750$	604.029	−	507.371i	0.805372	−	0.676494i
$751$	35.4409	−	109.076i	0.0471917	−	0.145241i	−0.924684	−	0.380735i	$-0.875671\pi$
$751$	35.4409	−	109.076i	0.0471917	−	0.145241i	0.971876	+	0.235494i	$0.0756709\pi$
$752$	−130.718	+	256.548i	−0.173827	+	0.341154i
$753$	88.3541	−	557.846i	0.117336	−	0.740831i
$754$	30.7834	+	42.3698i	0.0408268	+	0.0561933i
$755$	566.042	+	599.764i	0.749725	+	0.794389i
$756$	−8.12420	+	25.0037i	−0.0107463	+	0.0330737i
$757$	80.8859	+	510.693i	0.106851	+	0.674628i	0.981729	+	0.190285i	$0.0609413\pi$
$757$	80.8859	+	510.693i	0.106851	+	0.674628i	−0.874878	+	0.484343i	$0.839059\pi$
$758$	−565.668	+	565.668i	−0.746264	+	0.746264i
$759$	1531.25	−	381.159i	2.01745	−	0.502186i
$760$	−101.676	−	36.3188i	−0.133784	−	0.0477879i
$761$	415.331	+	301.756i	0.545770	+	0.396525i	0.826224	−	0.563342i	$-0.190485\pi$
$761$	415.331	+	301.756i	0.545770	+	0.396525i	−0.280453	+	0.959868i	$0.590485\pi$
$762$	−565.552	+	288.163i	−0.742195	+	0.378167i
$763$	34.0364	+	17.3424i	0.0446086	+	0.0227292i
$764$	−49.8468	−	68.6083i	−0.0652445	−	0.0898014i
$765$	167.948	+	572.737i	0.219540	+	0.748675i
$766$	3.53428	+	10.8774i	0.00461395	+	0.0142003i
$767$	−40.1227	+	20.4435i	−0.0523112	+	0.0266539i
$768$	−70.5191	+	11.1691i	−0.0918217	+	0.0145431i
$769$		−	162.316i		−	0.211074i	−0.994415	−	0.105537i	$-0.966344\pi$
$769$		−	162.316i		−	0.211074i	0.994415	−	0.105537i	$-0.0336561\pi$
$770$	30.3535	−	115.875i	0.0394201	−	0.150487i
$771$	−9.93393			−0.0128845
$772$	35.4487	+	223.815i	0.0459181	+	0.289915i
$773$	−575.280	−	1129.05i	−0.744217	−	1.46061i	−0.882548	−	0.470223i	$-0.844174\pi$
$773$	−575.280	−	1129.05i	−0.744217	−	1.46061i	0.138331	−	0.990386i	$-0.455826\pi$
$774$	711.806	−	231.280i	0.919646	−	0.298811i
$775$	−70.6870	+	1220.86i	−0.0912091	+	1.57531i
$776$	114.020	−	82.8403i	0.146933	−	0.106753i
$777$	−108.446	+	212.837i	−0.139570	+	0.273922i
$778$	−55.0573	−	108.056i	−0.0707677	−	0.138889i
$779$	200.117	−	275.437i	0.256890	−	0.353578i
$780$	−36.5758	+	17.3230i	−0.0468921	+	0.0222090i
$781$	300.708	−	743.459i	0.385030	−	0.951932i
$782$	−351.642	−	351.642i	−0.449670	−	0.449670i
$783$	344.250	−	54.5238i	0.439655	−	0.0696345i
$784$	177.385	+	57.6358i	0.226256	+	0.0735151i
$785$	0.390381	−	13.4962i	0.000497301	−	0.0171926i
$786$	−813.417	+	590.982i	−1.03488	+	0.751886i
$787$	90.7450	+	14.3726i	0.115305	+	0.0182625i	0.213820	−	0.976873i	$-0.431409\pi$
$787$	90.7450	+	14.3726i	0.115305	+	0.0182625i	−0.0985153	+	0.995136i	$0.531409\pi$
$788$	539.463	+	274.870i	0.684597	+	0.348820i
$789$	−0.329913	−	0.107195i	−0.000418140	−	0.000135862i
$790$	−459.013	+	313.624i	−0.581029	+	0.396992i
$791$	−46.4633			−0.0587400
$792$	312.588	−	132.544i	0.394682	−	0.167354i
$793$	−47.3517	+	47.3517i	−0.0597121	+	0.0597121i
$794$	320.071	−	440.539i	0.403112	−	0.554836i
$795$	−542.074	+	69.8563i	−0.681854	+	0.0878696i
$796$	−148.738	−	457.768i	−0.186857	−	0.575086i
$797$	584.789	+	92.6215i	0.733738	+	0.116213i	0.512111	−	0.858919i	$-0.328863\pi$
$797$	584.789	+	92.6215i	0.733738	+	0.116213i	0.221626	+	0.975132i	$0.428863\pi$
$798$	11.6069	−	73.2831i	0.0145450	−	0.0918334i
$799$	−748.847	+	243.315i	−0.937231	+	0.304525i
$800$	−30.1600	+	138.168i	−0.0377001	+	0.172710i
$801$	−849.759	−	617.386i	−1.06087	−	0.770769i
$802$	−364.880	−	364.880i	−0.454962	−	0.454962i
$803$	1325.72	−	115.473i	1.65095	−	0.143802i
$804$			359.242i			0.446819i
$805$	−243.264	−	45.7755i	−0.302192	−	0.0568640i
$806$	19.3877	−	59.6691i	0.0240542	−	0.0740311i
$807$	−242.919	+	476.755i	−0.301015	+	0.590775i
$808$	−43.0272	+	271.663i	−0.0532515	+	0.336217i
$809$	51.3648	+	70.6976i	0.0634917	+	0.0873889i	0.839582	−	0.543233i	$-0.182800\pi$
$809$	51.3648	+	70.6976i	0.0634917	+	0.0873889i	−0.776090	+	0.630622i	$0.782800\pi$
$810$	12.2925	−	424.974i	0.0151760	−	0.524659i
$811$	229.640	−	706.760i	0.283157	−	0.871467i	−0.703788	−	0.710410i	$-0.748510\pi$
$811$	229.640	−	706.760i	0.283157	−	0.871467i	0.986945	−	0.161057i	$-0.0514904\pi$
$812$	19.6741	+	124.217i	0.0242292	+	0.152977i
$813$	129.611	−	129.611i	0.159423	−	0.159423i
$814$	524.723	−	130.615i	0.644623	−	0.160460i
$815$	−244.379	+	684.147i	−0.299851	+	0.839445i
$816$	−157.959	−	114.764i	−0.193577	−	0.140642i
$817$	−329.885	+	168.085i	−0.403775	+	0.205734i
$818$	−179.566	−	91.4932i	−0.219518	−	0.111850i
$819$	−8.95889	−	12.3309i	−0.0109388	−	0.0150560i
$820$	−391.325	−	213.861i	−0.477226	−	0.260806i
$821$	193.312	+	594.953i	0.235459	+	0.724668i	0.997060	+	0.0766222i	$0.0244135\pi$
$821$	193.312	+	594.953i	0.235459	+	0.724668i	−0.761601	+	0.648046i	$0.775586\pi$
$822$	−999.802	+	509.424i	−1.21630	+	0.619738i
$823$	−409.861	+	64.9156i	−0.498008	+	0.0788767i	−0.400386	−	0.916347i	$-0.631124\pi$
$823$	−409.861	+	64.9156i	−0.498008	+	0.0788767i	−0.0976226	+	0.995224i	$0.531124\pi$
$824$			346.116i			0.420044i
$825$	−35.6420	−	1226.64i	−0.0432024	−	1.48683i
$826$	−108.137			−0.130916
$827$	15.0191	+	94.8271i	0.0181610	+	0.114664i	0.995103	−	0.0988387i	$-0.0315128\pi$
$827$	15.0191	+	94.8271i	0.0181610	+	0.114664i	−0.976942	+	0.213503i	$0.931513\pi$
$828$	−318.533	−	625.157i	−0.384702	−	0.755020i
$829$	−1003.82	+	326.160i	−1.21088	+	0.393438i	−0.843752	−	0.536733i	$-0.819658\pi$
$829$	−1003.82	+	326.160i	−1.21088	+	0.393438i	−0.367127	+	0.930171i	$0.619658\pi$
$830$	34.5253	−	63.1746i	0.0415967	−	0.0761140i
$831$	402.082	−	292.129i	0.483853	−	0.351540i
$832$	3.29390	−	6.46465i	0.00395902	−	0.00777001i
$833$	231.556	+	454.455i	0.277979	+	0.545564i
$834$	315.331	−	434.016i	0.378095	−	0.520403i
$835$	630.848	+	225.340i	0.755506	+	0.269869i
$836$	−142.471	+	88.9496i	−0.170419	+	0.106399i
$837$	−295.246	−	295.246i	−0.352743	−	0.352743i
$838$	−133.434	+	21.1339i	−0.159230	+	0.0252195i
$839$	214.646	+	69.7426i	0.255835	+	0.0831259i	0.434127	−	0.900852i	$-0.357057\pi$
$839$	214.646	+	69.7426i	0.255835	+	0.0831259i	−0.178292	+	0.983978i	$0.557057\pi$
$840$	−97.1457	−	2.80998i	−0.115650	−	0.00334521i
$841$	668.504	−	485.696i	0.794892	−	0.577523i
$842$	97.0490	+	15.3711i	0.115260	+	0.0182554i
$843$	−28.5571	−	14.5506i	−0.0338756	−	0.0172605i
$844$	437.834	+	142.261i	0.518761	+	0.168556i
$845$	−155.502	+	826.384i	−0.184026	+	0.977969i
$846$	−1110.91			−1.31314
$847$	−112.029	−	148.905i	−0.132265	−	0.175802i
$848$	69.2856	−	69.2856i	0.0817048	−	0.0817048i
$849$	1057.89	−	1456.07i	1.24605	−	1.71504i
$850$	−325.493	+	208.853i	−0.382932	+	0.245709i
$851$	−345.302	−	1062.73i	−0.405761	−	1.24880i
$852$	−642.661	−	101.788i	−0.754297	−	0.119469i
$853$	33.0446	−	208.636i	0.0387393	−	0.244590i	−0.960718	−	0.277526i	$-0.910486\pi$
$853$	33.0446	−	208.636i	0.0387393	−	0.244590i	0.999457	+	0.0329355i	$0.0104856\pi$
$854$	−152.940	+	49.6933i	−0.179087	+	0.0581888i
$855$	−53.2423	−	413.152i	−0.0622717	−	0.483218i
$856$	486.651	+	353.573i	0.568518	+	0.413052i
$857$	844.018	+	844.018i	0.984852	+	0.984852i	0.999887	−	0.0150350i	$-0.00478598\pi$
$857$	844.018	+	844.018i	0.984852	+	0.984852i	−0.0150350	+	0.999887i	$0.504786\pi$
$858$	−14.1859	+	61.3386i	−0.0165337	+	0.0714902i
$859$			257.187i			0.299403i	0.988731	+	0.149701i	$0.0478312\pi$
$859$			257.187i			0.299403i	−0.988731	+	0.149701i	$0.952169\pi$
$860$	273.587	+	400.416i	0.318125	+	0.465600i
$861$	94.7021	−	291.463i	0.109991	−	0.338517i
$862$	396.128	−	777.446i	0.459546	−	0.901909i
$863$	224.105	−	1414.94i	0.259681	−	1.63956i	−0.421056	−	0.907035i	$-0.638340\pi$
$863$	224.105	−	1414.94i	0.259681	−	1.63956i	0.680737	−	0.732528i	$-0.261660\pi$
$864$	−28.3817	−	39.0640i	−0.0328492	−	0.0452130i
$865$	−786.436	−	22.7480i	−0.909174	−	0.0262982i
$866$	186.165	−	572.956i	0.214971	−	0.661612i
$867$	118.217	+	746.392i	0.136352	+	0.860890i
$868$	106.535	−	106.535i	0.122736	−	0.122736i
$869$	−60.6572	+	862.686i	−0.0698012	+	0.992735i
$870$	551.498	+	1164.43i	0.633905	+	1.33843i
$871$	−29.5340	−	21.4577i	−0.0339082	−	0.0246358i
$872$	−62.5122	+	31.8515i	−0.0716883	+	0.0365270i
$873$	484.503	+	246.867i	0.554986	+	0.282780i
$874$	204.010	+	280.796i	0.233422	+	0.321277i
$875$	−75.1251	+	177.237i	−0.0858572	+	0.202557i
$876$	−333.640	−	1026.84i	−0.380868	−	1.17219i
$877$	−389.295	+	198.356i	−0.443894	+	0.226175i	−0.661627	−	0.749833i	$-0.730134\pi$
$877$	−389.295	+	198.356i	−0.443894	+	0.226175i	0.217733	+	0.976008i	$0.430134\pi$
$878$	592.694	−	93.8735i	0.675050	−	0.106917i
$879$		−	397.297i		−	0.451988i
$880$	139.407	+	170.193i	0.158417	+	0.193401i
$881$	−1156.90			−1.31316			−0.656581	−	0.754255i	$-0.727998\pi$
$881$	−1156.90			−1.31316			−0.656581	+	0.754255i	$0.727998\pi$
$882$	112.573	+	710.760i	0.127634	+	0.805850i
$883$	−153.251	−	300.772i	−0.173557	−	0.340625i	0.787799	−	0.615932i	$-0.211221\pi$
$883$	−153.251	−	300.772i	−0.173557	−	0.340625i	−0.961356	+	0.275307i	$0.911221\pi$
$884$	18.8699	−	6.13121i	0.0213461	−	0.00693576i
$885$	−1063.06	+	311.731i	−1.20120	+	0.352238i
$886$	50.8807	−	36.9670i	0.0574274	−	0.0417235i
$887$	−57.8774	+	113.591i	−0.0652508	+	0.128062i	−0.921328	−	0.388786i	$-0.872895\pi$
$887$	−57.8774	+	113.591i	−0.0652508	+	0.128062i	0.856077	+	0.516848i	$0.172895\pi$
$888$	−199.175	−	390.903i	−0.224296	−	0.440206i
$889$	91.0443	−	125.312i	0.102412	−	0.140958i
$890$	228.941	−	640.928i	0.257237	−	0.720143i
$891$	−506.484	−	425.321i	−0.568444	−	0.477353i
$892$	255.671	+	255.671i	0.286627	+	0.286627i
$893$	542.782	−	85.9682i	0.607819	−	0.0962690i
$894$	−1348.67	−	438.209i	−1.50858	−	0.490166i
$895$	−485.613	+	458.310i	−0.542585	+	0.512078i
$896$	14.0957	−	10.2411i	0.0157318	−	0.0114298i
$897$	128.499	+	20.3523i	0.143255	+	0.0226893i
$898$	−985.913	−	502.348i	−1.09790	−	0.559407i
$899$	−1899.63	−	617.227i	−2.11305	−	0.686571i
$900$	−527.815	+	138.335i	−0.586461	+	0.153705i
$901$	267.953			0.297395
$902$	−638.692	+	270.820i	−0.708084	+	0.300243i
$903$	−235.656	+	235.656i	−0.260970	+	0.260970i
$904$	50.1591	−	69.0381i	0.0554858	−	0.0763696i
$905$	54.4474	+	422.503i	0.0601629	+	0.466854i
$906$	−321.652	−	989.945i	−0.355025	−	1.09265i
$907$	1541.49	+	244.148i	1.69955	+	0.269182i	0.929505	−	0.368811i	$-0.120235\pi$
$907$	1541.49	+	244.148i	1.69955	+	0.269182i	0.770043	+	0.637992i	$0.220235\pi$
$908$	79.6947	−	503.173i	0.0877695	−	0.554155i
$909$	−1009.28	+	327.934i	−1.11031	+	0.360763i
$910$	6.03358	−	7.81871i	0.00663031	−	0.00859198i
$911$	−32.5398	−	23.6416i	−0.0357188	−	0.0259512i	0.569783	−	0.821795i	$-0.307027\pi$
$911$	−32.5398	−	23.6416i	−0.0357188	−	0.0259512i	−0.605501	+	0.795844i	$0.707027\pi$
$912$	96.3585	+	96.3585i	0.105656	+	0.105656i
$913$	−43.7205	−	103.109i	−0.0478867	−	0.112934i
$914$			523.188i			0.572416i
$915$	−1360.26	+	929.408i	−1.48662	+	1.01575i
$916$	−177.726	+	546.983i	−0.194024	+	0.597143i
$917$	111.390	−	218.614i	0.121472	−	0.238402i
$918$	20.6563	−	130.419i	0.0225014	−	0.142068i
$919$	254.636	+	350.477i	0.277080	+	0.381367i	0.924764	−	0.380542i	$-0.124262\pi$
$919$	254.636	+	350.477i	0.277080	+	0.381367i	−0.647684	+	0.761909i	$0.724262\pi$
$920$	330.630	−	312.041i	0.359381	−	0.339175i
$921$	−319.465	+	983.213i	−0.346868	+	1.06755i
$922$	172.786	+	1090.93i	0.187403	+	1.18322i
$923$	46.7547	−	46.7547i	0.0506551	−	0.0506551i
$924$	−97.2252	+	115.778i	−0.105222	+	0.125301i
$925$	−864.718	+	86.1018i	−0.934830	+	0.0930830i
$926$	458.260	+	332.946i	0.494882	+	0.359552i
$927$	−1189.86	+	606.264i	−1.28356	+	0.654006i
$928$	−205.809	−	104.865i	−0.221777	−	0.113001i
$929$	636.895	+	876.611i	0.685571	+	0.943607i	0.999984	−	0.00567914i	$-0.00180774\pi$
$929$	636.895	+	876.611i	0.685571	+	0.943607i	−0.314413	+	0.949286i	$0.601808\pi$
$930$	740.203	−	1354.43i	0.795917	−	1.45638i
$931$	−110.005	−	338.559i	−0.118157	−	0.363651i
$932$	537.138	−	273.685i	0.576328	−	0.293654i
$933$	296.305	−	46.9301i	0.317583	−	0.0503002i
$934$			1058.26i			1.13304i
$935$	−59.5313	+	598.668i	−0.0636698	+	0.640286i
$936$	27.9935			0.0299076
$937$	−256.526	−	1619.64i	−0.273774	−	1.72854i	−0.614971	−	0.788550i	$-0.710832\pi$
$937$	−256.526	−	1619.64i	−0.273774	−	1.72854i	0.341197	−	0.939992i	$-0.389168\pi$
$938$	−39.7994	−	78.1107i	−0.0424301	−	0.0832737i
$939$	548.131	−	178.099i	0.583739	−	0.189668i
$940$	−202.551	−	690.740i	−0.215480	−	0.734830i
$941$	−1380.25	+	1002.81i	−1.46679	+	1.06569i	−0.485268	+	0.874366i	$0.661278\pi$
$941$	−1380.25	+	1002.81i	−1.46679	+	1.06569i	−0.981527	+	0.191323i	$0.938722\pi$
$942$	−7.73660	+	15.1839i	−0.00821295	+	0.0161188i
$943$	650.840	+	1277.34i	0.690180	+	1.35455i
$944$	116.738	−	160.676i	0.123663	−	0.170208i
$945$	−28.1333	−	59.4007i	−0.0297707	−	0.0628579i
$946$	752.557	+	52.9138i	0.795515	+	0.0559342i
$947$	312.794	+	312.794i	0.330300	+	0.330300i	0.852700	−	0.522401i	$-0.174963\pi$
$947$	312.794	+	312.794i	0.330300	+	0.330300i	−0.522401	+	0.852700i	$0.674963\pi$
$948$	693.023	−	109.764i	0.731037	−	0.115785i
$949$	104.347	+	33.9044i	0.109955	+	0.0357264i
$950$	247.181	−	108.434i	0.260190	−	0.114141i
$951$	−588.816	+	427.800i	−0.619155	+	0.449842i
$952$	47.0596	+	7.45351i	0.0494324	+	0.00782932i
$953$	483.095	+	246.149i	0.506921	+	0.258289i	0.688695	−	0.725051i	$-0.258184\pi$
$953$	483.095	+	246.149i	0.506921	+	0.258289i	−0.181774	+	0.983340i	$0.558184\pi$
$954$	359.548	+	116.824i	0.376885	+	0.122457i
$955$	208.355	+	39.2065i	0.218172	+	0.0410539i
$956$	−914.541			−0.956633
$957$	1952.78	+	451.624i	2.04052	+	0.471916i
$958$	249.729	−	249.729i	0.260677	−	0.260677i
$959$	160.951	−	221.530i	0.167832	−	0.231001i
$960$	109.048	−	141.312i	0.113592	−	0.147200i
$961$	442.452	+	1361.73i	0.460408	+	1.41699i
$962$	44.0338	+	6.97427i	0.0457732	+	0.00724976i
$963$	−363.066	+	2292.31i	−0.377015	+	2.38038i
$964$	−278.482	+	90.4843i	−0.288882	+	0.0938634i
$965$	−448.498	−	346.099i	−0.464765	−	0.358652i
$966$	252.757	+	183.639i	0.261653	+	0.190102i
$967$	276.935	+	276.935i	0.286385	+	0.286385i	0.835649	−	0.549264i	$-0.185092\pi$
$967$	276.935	+	276.935i	0.286385	+	0.286385i	−0.549264	+	0.835649i	$0.685092\pi$
$968$	342.192	−	5.71059i	0.353504	−	0.00589937i
$969$			372.653i			0.384575i
$970$	−65.1571	+	346.264i	−0.0671723	+	0.356973i
$971$	−27.1253	+	83.4830i	−0.0279354	+	0.0859763i	−0.964052	−	0.265713i	$-0.914393\pi$
$971$	−27.1253	+	83.4830i	−0.0279354	+	0.0859763i	0.936117	+	0.351689i	$0.114393\pi$
$972$	−313.367	+	615.018i	−0.322394	+	0.632734i
$973$	−20.4797	+	129.303i	−0.0210479	+	0.132892i
$974$	191.215	+	263.185i	0.196320	+	0.270211i
$975$	36.7751	−	94.2567i	0.0377181	−	0.0966736i
$976$	91.2681	−	280.894i	0.0935124	−	0.287802i
$977$	−51.5985	−	325.780i	−0.0528132	−	0.333450i	−0.999921	−	0.0125353i	$-0.996010\pi$
$977$	−51.5985	−	325.780i	−0.0528132	−	0.333450i	0.947108	−	0.320914i	$-0.103990\pi$
$978$	648.369	−	648.369i	0.662954	−	0.662954i
$979$	−560.707	−	898.085i	−0.572735	−	0.917349i
$980$	−421.409	+	199.587i	−0.430009	+	0.203661i
$981$	−218.995	−	159.109i	−0.223236	−	0.162191i
$982$	1066.63	−	543.474i	1.08618	−	0.553436i
$983$	1049.75	+	534.875i	1.06791	+	0.544125i	0.897394	−	0.441230i	$-0.145458\pi$
$983$	1049.75	+	534.875i	1.06791	+	0.544125i	0.170512	+	0.985356i	$0.445458\pi$
$984$	330.839	+	455.361i	0.336219	+	0.462765i
$985$	−1452.47	+	425.920i	−1.47459	+	0.432407i
$986$	−195.194	−	600.745i	−0.197965	−	0.609275i
$987$	440.756	−	224.576i	0.446561	−	0.227534i
$988$	−13.6774	+	2.16628i	−0.0138435	+	0.00219259i
$989$		−	1558.99i		−	1.57633i
$990$	−340.894	+	777.358i	−0.344337	+	0.785211i
$991$	−1370.75			−1.38320			−0.691601	−	0.722280i	$-0.743094\pi$
$991$	−1370.75			−1.38320			−0.691601	+	0.722280i	$0.743094\pi$
$992$	43.2874	+	273.306i	0.0436365	+	0.275510i
$993$	340.071	+	667.426i	0.342468	+	0.672131i
$994$	151.012	−	49.0667i	0.151923	−	0.0493629i
$995$	1055.92	+	577.065i	1.06122	+	0.579965i
$996$	−73.5125	+	53.4100i	−0.0738077	+	0.0536244i
$997$	358.904	−	704.388i	0.359984	−	0.706507i	−0.637996	−	0.770039i	$-0.720236\pi$
$997$	358.904	−	704.388i	0.359984	−	0.706507i	0.997980	+	0.0635320i	$0.0202365\pi$
$998$	−160.697	−	315.386i	−0.161019	−	0.316018i
$999$	174.397	−	240.038i	0.174572	−	0.240278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.l.a.37.1	yes	48
5.3	odd	4	inner	110.3.l.a.103.6	yes	48
11.3	even	5	inner	110.3.l.a.47.6	yes	48
55.3	odd	20	inner	110.3.l.a.3.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.l.a.3.1	✓	48	55.3	odd	20	inner
110.3.l.a.37.1	yes	48	1.1	even	1	trivial
110.3.l.a.47.6	yes	48	11.3	even	5	inner
110.3.l.a.103.6	yes	48	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.221232 - 1.39680i) q^{2} +(-2.02588 - 3.97601i) q^{3} +(-1.90211 + 0.618034i) q^{4} +(2.39781 - 4.38754i) q^{5} +(-5.10551 + 3.70937i) q^{6} +(0.699150 - 1.37216i) q^{7} +(1.28408 + 2.52015i) q^{8} +(-6.41440 + 8.82867i) q^{9} +(-6.65900 - 2.37861i) q^{10} +(-9.33076 + 5.82554i) q^{11} +(6.31076 + 6.31076i) q^{12} +(-0.895765 + 0.141875i) q^{13} +(-2.07131 - 0.673009i) q^{14} +(-22.3026 - 0.645111i) q^{15} +(3.23607 - 2.35114i) q^{16} +(10.8039 + 1.71117i) q^{17} +(13.7510 + 7.00647i) q^{18} +(-7.26080 - 2.35918i) q^{19} +(-1.84926 + 9.82752i) q^{20} -6.87211 q^{21} +(10.2014 + 11.7444i) q^{22} +(22.7314 - 22.7314i) q^{23} +(7.41874 - 10.2110i) q^{24} +(-13.5010 - 21.0410i) q^{25} +(0.396343 + 1.21982i) q^{26} +(8.43072 + 1.33529i) q^{27} +(-0.481821 + 3.04210i) q^{28} +(38.8343 - 12.6180i) q^{29} +(4.03295 + 31.2950i) q^{30} +(-39.5741 - 28.7523i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(42.0654 + 25.2974i) q^{33} -15.4694i q^{34} +(-4.34397 - 6.35773i) q^{35} +(6.74450 - 20.7574i) q^{36} +(15.7806 - 30.9712i) q^{37} +(-1.68899 + 10.6638i) q^{38} +(2.37881 + 3.27415i) q^{39} +(14.1362 + 0.408896i) q^{40} +(-13.7806 + 42.4124i) q^{41} +(1.52033 + 9.59898i) q^{42} +(34.2916 - 34.2916i) q^{43} +(14.1478 - 16.8476i) q^{44} +(23.3556 + 49.3129i) q^{45} +(-36.7801 - 26.7223i) q^{46} +(-64.1369 + 32.6794i) q^{47} +(-15.9040 - 8.10351i) q^{48} +(27.4075 + 37.7231i) q^{49} +(-26.4033 + 23.5131i) q^{50} +(-15.0837 - 46.4230i) q^{51} +(1.61616 - 0.823476i) q^{52} +(24.1946 - 3.83205i) q^{53} -12.0715i q^{54} +(3.18634 + 54.9076i) q^{55} +4.35581 q^{56} +(5.32939 + 33.6484i) q^{57} +(-26.2163 - 51.4523i) q^{58} +(47.2216 - 15.3432i) q^{59} +(42.8207 - 12.5567i) q^{60} +(59.7357 - 43.4006i) q^{61} +(-31.4062 + 61.6382i) q^{62} +(7.62971 + 14.9742i) q^{63} +(-4.70228 + 6.47214i) q^{64} +(-1.52539 + 4.27039i) q^{65} +(26.0292 - 64.3536i) q^{66} +(28.4627 + 28.4627i) q^{67} +(-21.6078 + 3.42233i) q^{68} +(-136.431 - 44.3291i) q^{69} +(-7.91947 + 7.47420i) q^{70} +(-58.9825 + 42.8533i) q^{71} +(-30.4862 - 4.82853i) q^{72} +(-107.790 - 54.9219i) q^{73} +(-46.7518 - 15.1906i) q^{74} +(-56.3079 + 96.3065i) q^{75} +15.2689 q^{76} +(1.46996 + 16.8762i) q^{77} +(4.04707 - 4.04707i) q^{78} +(46.2115 - 63.6046i) q^{79} +(-2.55623 - 19.8360i) q^{80} +(18.5798 + 57.1828i) q^{81} +(62.2905 + 9.86584i) q^{82} +(-1.59272 + 10.0560i) q^{83} +(13.0715 - 4.24720i) q^{84} +(33.4135 - 43.2994i) q^{85} +(-55.4850 - 40.3122i) q^{86} +(-128.843 - 128.843i) q^{87} +(-26.6626 - 16.0344i) q^{88} +96.2499i q^{89} +(63.7134 - 43.5327i) q^{90} +(-0.431599 + 1.32832i) q^{91} +(-29.1889 + 57.2864i) q^{92} +(-34.1470 + 215.596i) q^{93} +(59.8358 + 82.3569i) q^{94} +(-27.7610 + 26.2002i) q^{95} +(-7.80053 + 24.0076i) q^{96} +(-7.79490 - 49.2151i) q^{97} +(46.6284 - 46.6284i) q^{98} +(8.41955 - 119.746i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} + 2 q^{3} + 4 q^{5} + 4 q^{6} + 38 q^{7} + 24 q^{8} + 36 q^{10} + 80 q^{11} - 16 q^{12} - 16 q^{13} + 38 q^{15} + 48 q^{16} - 18 q^{17} - 44 q^{18} + 4 q^{20} + 24 q^{21} + 64 q^{23} + 70 q^{25}+ \cdots - 440 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 + 2 * q^3 + 4 * q^5 + 4 * q^6 + 38 * q^7 + 24 * q^8 + 36 * q^10 + 80 * q^11 - 16 * q^12 - 16 * q^13 + 38 * q^15 + 48 * q^16 - 18 * q^17 - 44 * q^18 + 4 * q^20 + 24 * q^21 + 64 * q^23 + 70 * q^25 + 8 * q^26 - 82 * q^27 + 64 * q^28 - 14 * q^30 - 116 * q^31 - 192 * q^32 - 312 * q^33 - 288 * q^35 - 88 * q^36 + 22 * q^37 - 72 * q^38 - 24 * q^40 - 196 * q^41 - 96 * q^42 - 484 * q^43 - 56 * q^45 - 132 * q^46 - 310 * q^47 - 8 * q^48 - 128 * q^50 + 256 * q^51 + 8 * q^52 - 82 * q^53 - 264 * q^55 + 48 * q^56 + 744 * q^57 + 168 * q^58 + 196 * q^60 + 528 * q^61 + 144 * q^62 + 814 * q^63 + 840 * q^65 + 436 * q^66 + 192 * q^67 + 36 * q^68 + 230 * q^70 - 292 * q^71 - 48 * q^72 - 108 * q^73 + 258 * q^75 + 96 * q^76 - 200 * q^77 + 88 * q^78 + 24 * q^80 + 628 * q^81 + 24 * q^82 + 360 * q^83 - 368 * q^85 + 532 * q^86 - 328 * q^87 - 40 * q^88 - 766 * q^90 + 72 * q^91 + 68 * q^92 - 66 * q^93 - 232 * q^95 - 16 * q^96 + 6 * q^97 - 440 * q^98

Introduction

L-functions

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