LMFDB - Embedded newform 45.3.h.a.29.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,3,Mod(14,45)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("45.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	45.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.22616118962$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.5
Root			$-0.315300 - 1.70311i$ of defining polynomial
Character	$\chi$	$=$	45.29
Dual form			45.3.h.a.14.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264396 + 0.457947i) q^{2} +(-2.94987 + 0.546115i) q^{3} +(1.86019 + 3.22194i) q^{4} +(-0.819902 + 4.93232i) q^{5} +(0.529842 - 1.49528i) q^{6} +(2.39593 + 1.38329i) q^{7} -4.08247 q^{8} +(8.40352 - 3.22194i) q^{9} +O(q^{10})$	\(q+(-0.264396 + 0.457947i) q^{2} +(-2.94987 + 0.546115i) q^{3} +(1.86019 + 3.22194i) q^{4} +(-0.819902 + 4.93232i) q^{5} +(0.529842 - 1.49528i) q^{6} +(2.39593 + 1.38329i) q^{7} -4.08247 q^{8} +(8.40352 - 3.22194i) q^{9} +(-2.04196 - 1.67955i) q^{10} +(-7.99186 - 4.61410i) q^{11} +(-7.24688 - 8.48845i) q^{12} +(11.7678 - 6.79417i) q^{13} +(-1.26695 + 0.731472i) q^{14} +(-0.275006 - 14.9975i) q^{15} +(-6.36137 + 11.0182i) q^{16} +12.2161 q^{17} +(-0.746375 + 4.70023i) q^{18} +20.2664 q^{19} +(-17.4168 + 6.53337i) q^{20} +(-7.82313 - 2.77208i) q^{21} +(4.22603 - 2.43990i) q^{22} +(1.18564 + 2.05358i) q^{23} +(12.0428 - 2.22950i) q^{24} +(-23.6555 - 8.08804i) q^{25} +7.18539i q^{26} +(-23.0298 + 14.0936i) q^{27} +10.2927i q^{28} +(30.2349 + 17.4561i) q^{29} +(6.94076 + 3.83933i) q^{30} +(-14.7233 - 25.5015i) q^{31} +(-11.5288 - 19.9684i) q^{32} +(26.0948 + 9.24654i) q^{33} +(-3.22989 + 5.59433i) q^{34} +(-8.78726 + 10.6833i) q^{35} +(26.0131 + 21.0822i) q^{36} +64.3630i q^{37} +(-5.35836 + 9.28095i) q^{38} +(-31.0032 + 26.4685i) q^{39} +(3.34723 - 20.1360i) q^{40} +(34.5195 - 19.9299i) q^{41} +(3.33787 - 2.84965i) q^{42} +(-58.5402 - 33.7982i) q^{43} -34.3324i q^{44} +(9.00159 + 44.0905i) q^{45} -1.25391 q^{46} +(46.6901 - 80.8696i) q^{47} +(12.7480 - 35.9764i) q^{48} +(-20.6730 - 35.8067i) q^{49} +(9.95831 - 8.69452i) q^{50} +(-36.0360 + 6.67141i) q^{51} +(43.7808 + 25.2769i) q^{52} -9.82656 q^{53} +(-0.365157 - 14.2727i) q^{54} +(29.3108 - 35.6353i) q^{55} +(-9.78131 - 5.64724i) q^{56} +(-59.7834 + 11.0678i) q^{57} +(-15.9880 + 9.23066i) q^{58} +(-50.6655 + 29.2517i) q^{59} +(47.8095 - 28.7842i) q^{60} +(7.75283 - 13.4283i) q^{61} +15.5711 q^{62} +(24.5911 + 3.90496i) q^{63} -38.6984 q^{64} +(23.8625 + 63.6133i) q^{65} +(-11.1338 + 9.50529i) q^{66} +(13.4796 - 7.78243i) q^{67} +(22.7243 + 39.3596i) q^{68} +(-4.61897 - 5.41031i) q^{69} +(-2.56908 - 6.84872i) q^{70} +53.1970i q^{71} +(-34.3071 + 13.1535i) q^{72} -23.6547i q^{73} +(-29.4748 - 17.0173i) q^{74} +(74.1978 + 10.9401i) q^{75} +(37.6994 + 65.2973i) q^{76} +(-12.7653 - 22.1101i) q^{77} +(-3.92405 - 21.1960i) q^{78} +(-17.2692 + 29.9112i) q^{79} +(-49.1297 - 40.4102i) q^{80} +(60.2382 - 54.1513i) q^{81} +21.0775i q^{82} +(-37.6730 + 65.2516i) q^{83} +(-5.62102 - 30.3623i) q^{84} +(-10.0160 + 60.2538i) q^{85} +(30.9555 - 17.8722i) q^{86} +(-98.7223 - 34.9817i) q^{87} +(32.6265 + 18.8369i) q^{88} -29.1344i q^{89} +(-22.5711 - 7.53509i) q^{90} +37.5932 q^{91} +(-4.41101 + 7.64010i) q^{92} +(57.3586 + 67.1856i) q^{93} +(24.6893 + 42.7631i) q^{94} +(-16.6165 + 99.9605i) q^{95} +(44.9135 + 52.6083i) q^{96} +(54.0151 + 31.1857i) q^{97} +21.8634 q^{98} +(-82.0261 - 13.0254i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9}+O(q^{10}) $ 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9	$ 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31} - 4 q^{34} + 432 q^{36} + 240 q^{39} - 34 q^{40} + 102 q^{41} - 162 q^{45} + 116 q^{46} - 40 q^{49} - 408 q^{50} - 156 q^{51} - 270 q^{54} + 36 q^{55} - 618 q^{56} + 120 q^{59} + 330 q^{60} - 50 q^{61} + 140 q^{64} + 492 q^{65} - 768 q^{66} + 162 q^{69} - 54 q^{70} + 504 q^{74} + 276 q^{75} - 96 q^{76} - 128 q^{79} + 846 q^{81} + 450 q^{84} - 74 q^{85} + 1488 q^{86} - 990 q^{90} - 288 q^{91} + 218 q^{94} - 762 q^{95} - 474 q^{96} - 468 q^{99}+O(q^{100}) $ 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.264396	+	0.457947i	−0.132198	+	0.228973i	−0.924524	−	0.381125i	$-0.875537\pi$
$2$	−0.264396	+	0.457947i	−0.132198	+	0.228973i	0.792326	+	0.610098i	$0.208870\pi$
$3$	−2.94987	+	0.546115i	−0.983291	+	0.182038i
$3$	−2.94987	+	0.546115i	−0.983291	+	0.182038i
$4$	1.86019	+	3.22194i	0.465047	+	0.805486i
$5$	−0.819902	+	4.93232i	−0.163980	+	0.986464i
$5$	−0.819902	+	4.93232i	−0.163980	+	0.986464i
$6$	0.529842	−	1.49528i	0.0883070	−	0.249213i
$7$	2.39593	+	1.38329i	0.342276	+	0.197613i	0.661278	−	0.750141i	$-0.270014\pi$
$7$	2.39593	+	1.38329i	0.342276	+	0.197613i	−0.319002	+	0.947754i	$0.603348\pi$
$8$	−4.08247			−0.510309
$9$	8.40352	−	3.22194i	0.933724	−	0.357994i
$10$	−2.04196	−	1.67955i	−0.204196	−	0.167955i
$11$	−7.99186	−	4.61410i	−0.726533	−	0.419464i	0.0906197	−	0.995886i	$-0.471115\pi$
$11$	−7.99186	−	4.61410i	−0.726533	−	0.419464i	−0.817152	+	0.576422i	$0.804449\pi$
$12$	−7.24688	−	8.48845i	−0.603907	−	0.707371i
$13$	11.7678	−	6.79417i	0.905218	−	0.522628i	0.0263288	−	0.999653i	$-0.491618\pi$
$13$	11.7678	−	6.79417i	0.905218	−	0.522628i	0.878890	+	0.477025i	$0.158285\pi$
$14$	−1.26695	+	0.731472i	−0.0904962	+	0.0522480i
$15$	−0.275006	−	14.9975i	−0.0183337	−	0.999832i
$16$	−6.36137	+	11.0182i	−0.397586	+	0.688639i
$17$	12.2161			0.718595			0.359297	−	0.933223i	$-0.383016\pi$
$17$	12.2161			0.718595			0.359297	+	0.933223i	$0.383016\pi$
$18$	−0.746375	+	4.70023i	−0.0414653	+	0.261124i
$19$	20.2664			1.06665			0.533327	−	0.845909i	$-0.320941\pi$
$19$	20.2664			1.06665			0.533327	+	0.845909i	$0.320941\pi$
$20$	−17.4168	+	6.53337i	−0.870841	+	0.326668i
$21$	−7.82313	−	2.77208i	−0.372530	−	0.132004i
$22$	4.22603	−	2.43990i	0.192092	−	0.110904i
$23$	1.18564	+	2.05358i	0.0515494	+	0.0892861i	0.890649	−	0.454692i	$-0.150251\pi$
$23$	1.18564	+	2.05358i	0.0515494	+	0.0892861i	−0.839099	+	0.543978i	$0.816917\pi$
$24$	12.0428	−	2.22950i	0.501782	−	0.0928958i
$25$	−23.6555	−	8.08804i	−0.946221	−	0.323522i
$26$			7.18539i			0.276361i
$27$	−23.0298	+	14.0936i	−0.852954	+	0.521986i
$28$			10.2927i			0.367598i
$29$	30.2349	+	17.4561i	1.04258	+	0.601936i	0.920564	−	0.390592i	$-0.127730\pi$
$29$	30.2349	+	17.4561i	1.04258	+	0.601936i	0.122020	+	0.992528i	$0.461063\pi$
$30$	6.94076	+	3.83933i	0.231359	+	0.127978i
$31$	−14.7233	−	25.5015i	−0.474945	−	0.822629i	0.524643	−	0.851322i	$-0.324199\pi$
$31$	−14.7233	−	25.5015i	−0.474945	−	0.822629i	−0.999588	+	0.0286933i	$0.990865\pi$
$32$	−11.5288	−	19.9684i	−0.360274	−	0.624013i
$33$	26.0948	+	9.24654i	0.790752	+	0.280198i
$34$	−3.22989	+	5.59433i	−0.0949967	+	0.164539i
$35$	−8.78726	+	10.6833i	−0.251065	+	0.305238i
$36$	26.0131	+	21.0822i	0.722585	+	0.585617i
$37$			64.3630i			1.73954i	0.493457	+	0.869770i	$0.335733\pi$
$37$			64.3630i			1.73954i	−0.493457	+	0.869770i	$0.664267\pi$
$38$	−5.35836	+	9.28095i	−0.141009	+	0.244235i
$39$	−31.0032	+	26.4685i	−0.794955	+	0.678680i
$40$	3.34723	−	20.1360i	0.0836807	−	0.503401i
$41$	34.5195	−	19.9299i	0.841940	−	0.486094i	−0.0159834	−	0.999872i	$-0.505088\pi$
$41$	34.5195	−	19.9299i	0.841940	−	0.486094i	0.857923	+	0.513778i	$0.171755\pi$
$42$	3.33787	−	2.84965i	0.0794730	−	0.0678488i
$43$	−58.5402	−	33.7982i	−1.36140	−	0.786004i	−0.371589	−	0.928397i	$-0.621187\pi$
$43$	−58.5402	−	33.7982i	−1.36140	−	0.786004i	−0.989810	+	0.142393i	$0.954520\pi$
$44$		−	34.3324i		−	0.780282i
$45$	9.00159	+	44.0905i	0.200035	+	0.979789i
$46$	−1.25391			−0.0272588
$47$	46.6901	−	80.8696i	0.993406	−	1.72063i	0.397414	−	0.917639i	$-0.369908\pi$
$47$	46.6901	−	80.8696i	0.993406	−	1.72063i	0.595992	−	0.802991i	$-0.296759\pi$
$48$	12.7480	−	35.9764i	0.265584	−	0.749509i
$49$	−20.6730	−	35.8067i	−0.421898	−	0.730749i
$50$	9.95831	−	8.69452i	0.199166	−	0.173890i
$51$	−36.0360	+	6.67141i	−0.706588	+	0.130812i
$52$	43.7808	+	25.2769i	0.841939	+	0.486094i
$53$	−9.82656			−0.185407			−0.0927034	−	0.995694i	$-0.529551\pi$
$53$	−9.82656			−0.185407			−0.0927034	+	0.995694i	$0.529551\pi$
$54$	−0.365157	−	14.2727i	−0.00676216	−	0.264309i
$55$	29.3108	−	35.6353i	0.532923	−	0.647914i
$56$	−9.78131	−	5.64724i	−0.174666	−	0.100844i
$57$	−59.7834	+	11.0678i	−1.04883	+	0.194172i
$58$	−15.9880	+	9.23066i	−0.275655	+	0.159149i
$59$	−50.6655	+	29.2517i	−0.858737	+	0.495792i	−0.863589	−	0.504196i	$-0.831789\pi$
$59$	−50.6655	+	29.2517i	−0.858737	+	0.495792i	0.00485217	+	0.999988i	$0.498456\pi$
$60$	47.8095	−	28.7842i	0.796824	−	0.479737i
$61$	7.75283	−	13.4283i	0.127096	−	0.220136i	−0.795455	−	0.606013i	$-0.792768\pi$
$61$	7.75283	−	13.4283i	0.127096	−	0.220136i	0.922550	+	0.385877i	$0.126101\pi$
$62$	15.5711			0.251147
$63$	24.5911	+	3.90496i	0.390335	+	0.0619834i
$64$	−38.6984			−0.604662
$65$	23.8625	+	63.6133i	0.367115	+	0.978666i
$66$	−11.1338	+	9.50529i	−0.168694	+	0.144019i
$67$	13.4796	−	7.78243i	0.201188	−	0.116156i	−0.396022	−	0.918241i	$-0.629610\pi$
$67$	13.4796	−	7.78243i	0.201188	−	0.116156i	0.597209	+	0.802085i	$0.296276\pi$
$68$	22.7243	+	39.3596i	0.334181	+	0.578818i
$69$	−4.61897	−	5.41031i	−0.0669415	−	0.0784103i
$70$	−2.56908	−	6.84872i	−0.0367011	−	0.0978389i
$71$			53.1970i			0.749254i	0.927176	+	0.374627i	$0.122229\pi$
$71$			53.1970i			0.749254i	−0.927176	+	0.374627i	$0.877771\pi$
$72$	−34.3071	+	13.1535i	−0.476487	+	0.182687i
$73$		−	23.6547i		−	0.324037i	−0.986788	−	0.162019i	$-0.948200\pi$
$73$		−	23.6547i		−	0.324037i	0.986788	−	0.162019i	$-0.0518005\pi$
$74$	−29.4748	−	17.0173i	−0.398308	−	0.229963i
$75$	74.1978	+	10.9401i	0.989304	+	0.145867i
$76$	37.6994	+	65.2973i	0.496045	+	0.859175i
$77$	−12.7653	−	22.1101i	−0.165783	−	0.287145i
$78$	−3.92405	−	21.1960i	−0.0503084	−	0.271744i
$79$	−17.2692	+	29.9112i	−0.218598	+	0.378623i	−0.954380	−	0.298596i	$-0.903482\pi$
$79$	−17.2692	+	29.9112i	−0.218598	+	0.378623i	0.735782	+	0.677219i	$0.236815\pi$
$80$	−49.1297	−	40.4102i	−0.614121	−	0.505127i
$81$	60.2382	−	54.1513i	0.743681	−	0.668535i
$82$			21.0775i			0.257042i
$83$	−37.6730	+	65.2516i	−0.453892	+	0.786163i	−0.998624	−	0.0524468i	$-0.983298\pi$
$83$	−37.6730	+	65.2516i	−0.453892	+	0.786163i	0.544732	+	0.838610i	$0.316631\pi$
$84$	−5.62102	−	30.3623i	−0.0669169	−	0.361456i
$85$	−10.0160	+	60.2538i	−0.117836	+	0.708868i
$86$	30.9555	−	17.8722i	0.359948	−	0.207816i
$87$	−98.7223	−	34.9817i	−1.13474	−	0.402088i
$88$	32.6265	+	18.8369i	0.370756	+	0.214056i
$89$		−	29.1344i		−	0.327352i	−0.986514	−	0.163676i	$-0.947665\pi$
$89$		−	29.1344i		−	0.327352i	0.986514	−	0.163676i	$-0.0523352\pi$
$90$	−22.5711	−	7.53509i	−0.250790	−	0.0837232i
$91$	37.5932			0.413112
$92$	−4.41101	+	7.64010i	−0.0479458	+	0.0830445i
$93$	57.3586	+	67.1856i	0.616759	+	0.722426i
$94$	24.6893	+	42.7631i	0.262652	+	0.454927i
$95$	−16.6165	+	99.9605i	−0.174911	+	1.05222i
$96$	44.9135	+	52.6083i	0.467849	+	0.548003i
$97$	54.0151	+	31.1857i	0.556857	+	0.321502i	0.751883	−	0.659296i	$-0.229146\pi$
$97$	54.0151	+	31.1857i	0.556857	+	0.321502i	−0.195026	+	0.980798i	$0.562479\pi$
$98$	21.8634			0.223096
$99$	−82.0261	−	13.0254i	−0.828546	−	0.131569i
$100$	−17.9446	−	91.2620i	−0.179446	−	0.912620i
$101$	−118.734	−	68.5511i	−1.17558	−	0.678723i	−0.220595	−	0.975366i	$-0.570800\pi$
$101$	−118.734	−	68.5511i	−1.17558	−	0.678723i	−0.954989	+	0.296642i	$0.904133\pi$
$102$	6.47261	−	18.2665i	0.0634570	−	0.179083i
$103$	94.2266	−	54.4017i	0.914821	−	0.528172i	0.0328419	−	0.999461i	$-0.489544\pi$
$103$	94.2266	−	54.4017i	0.914821	−	0.528172i	0.881979	+	0.471288i	$0.156211\pi$
$104$	−48.0418	+	27.7370i	−0.461941	+	0.266702i
$105$	20.0870	−	36.3133i	0.191305	−	0.345841i
$106$	2.59810	−	4.50004i	0.0245104	−	0.0424532i
$107$	64.0002			0.598133			0.299067	−	0.954232i	$-0.403325\pi$
$107$	64.0002			0.598133			0.299067	+	0.954232i	$0.403325\pi$
$108$	−88.2486	−	47.9838i	−0.817116	−	0.444294i
$109$	−14.8135			−0.135904			−0.0679520	−	0.997689i	$-0.521646\pi$
$109$	−14.8135			−0.135904			−0.0679520	+	0.997689i	$0.521646\pi$
$110$	8.56942	+	22.8446i	0.0779038	+	0.207678i
$111$	−35.1496	−	189.863i	−0.316663	−	1.71048i
$112$	−30.4828	+	17.5993i	−0.272168	+	0.157136i
$113$	−41.4033	−	71.7126i	−0.366401	−	0.634625i	0.622599	−	0.782541i	$-0.286077\pi$
$113$	−41.4033	−	71.7126i	−0.366401	−	0.634625i	−0.989000	+	0.147916i	$0.952743\pi$
$114$	10.7380	−	30.3039i	0.0941931	−	0.265824i
$115$	−11.1010	+	4.16419i	−0.0965306	+	0.0362104i
$116$			129.887i			1.11972i
$117$	77.0008	−	95.0102i	0.658127	−	0.812053i
$118$		−	30.9361i		−	0.262170i
$119$	29.2690	+	16.8984i	0.245958	+	0.142004i
$120$	1.12270	+	61.2267i	0.00935585	+	0.510223i
$121$	−17.9201	−	31.0386i	−0.148100	−	0.256517i
$122$	4.09963	+	7.10077i	0.0336035	+	0.0582030i
$123$	−90.9443	+	77.6422i	−0.739384	+	0.631238i
$124$	54.7763	−	94.8753i	0.441744	−	0.765123i
$125$	59.2880	−	110.045i	0.474304	−	0.880361i
$126$	−8.29005	+	10.2290i	−0.0657940	+	0.0811823i
$127$		−	36.7291i		−	0.289206i	−0.989490	−	0.144603i	$-0.953810\pi$
$127$		−	36.7291i		−	0.289206i	0.989490	−	0.144603i	$-0.0461904\pi$
$128$	56.3468	−	97.5955i	0.440209	−	0.762465i
$129$	191.144	+	67.7307i	1.48174	+	0.525044i
$130$	−35.4406	−	5.89132i	−0.272620	−	0.0453178i
$131$	50.1743	−	28.9682i	0.383010	−	0.221131i	−0.296117	−	0.955152i	$-0.595692\pi$
$131$	50.1743	−	28.9682i	0.383010	−	0.221131i	0.679127	+	0.734021i	$0.262359\pi$
$132$	18.7495	+	101.276i	0.142041	+	0.767245i
$133$	48.5570	+	28.0344i	0.365090	+	0.210785i
$134$			8.23056i			0.0614221i
$135$	−50.6320	−	125.145i	−0.375052	−	0.927004i
$136$	−49.8719			−0.366705
$137$	−28.7895	+	49.8649i	−0.210143	+	0.363978i	−0.951759	−	0.306847i	$-0.900726\pi$
$137$	−28.7895	+	49.8649i	−0.210143	+	0.363978i	0.741616	+	0.670824i	$0.234059\pi$
$138$	3.69887	−	0.684778i	0.0268034	−	0.00496216i
$139$	30.3246	+	52.5237i	0.218162	+	0.377868i	0.954246	−	0.299022i	$-0.0966605\pi$
$139$	30.3246	+	52.5237i	0.218162	+	0.377868i	−0.736084	+	0.676890i	$0.763327\pi$
$140$	−50.7670	−	8.43904i	−0.362622	−	0.0602789i
$141$	−93.5657	+	264.053i	−0.663587	+	1.87272i
$142$	−24.3614	−	14.0651i	−0.171559	−	0.0990497i
$143$	−125.396			−0.876894
$144$	−17.9578	+	113.088i	−0.124707	+	0.785332i
$145$	−110.889	+	134.816i	−0.764751	+	0.929765i
$146$	10.8326	+	6.25420i	0.0741959	+	0.0428370i
$147$	80.5374	+	94.3354i	0.547873	+	0.641738i
$148$	−207.374	+	119.727i	−1.40118	+	0.808969i
$149$	204.106	−	117.841i	1.36984	−	0.790879i	0.378934	−	0.925424i	$-0.376291\pi$
$149$	204.106	−	117.841i	1.36984	−	0.790879i	0.990907	+	0.134545i	$0.0429572\pi$
$150$	−24.6275	+	31.0861i	−0.164184	+	0.207241i
$151$	7.41840	−	12.8490i	0.0491285	−	0.0850930i	−0.840415	−	0.541943i	$-0.817689\pi$
$151$	7.41840	−	12.8490i	0.0491285	−	0.0850930i	0.889544	+	0.456850i	$0.151022\pi$
$152$	−82.7371			−0.544323
$153$	102.658	−	39.3596i	0.670969	−	0.257252i
$154$	13.5003			0.0876646
$155$	137.853	−	51.7112i	0.889375	−	0.333621i
$156$	−142.952	−	50.6542i	−0.916359	−	0.324707i
$157$	−127.486	+	73.6041i	−0.812013	+	0.468816i	−0.847654	−	0.530549i	$-0.821986\pi$
$157$	−127.486	+	73.6041i	−0.812013	+	0.468816i	0.0356413	+	0.999365i	$0.488653\pi$
$158$	−9.13182	−	15.8168i	−0.0577963	−	0.100106i
$159$	28.9871	−	5.36643i	0.182309	−	0.0337512i
$160$	107.943	−	40.4914i	0.674644	−	0.253071i
$161$			6.56031i			0.0407473i
$162$	8.87170	+	41.9032i	0.0547636	+	0.258662i
$163$			9.62130i			0.0590264i	0.999564	+	0.0295132i	$0.00939571\pi$
$163$			9.62130i			0.0590264i	−0.999564	+	0.0295132i	$0.990604\pi$
$164$	128.426	+	74.1466i	0.783084	+	0.452114i
$165$	−67.0021	+	121.127i	−0.406073	+	0.734101i
$166$	−19.9212	−	34.5045i	−0.120007	−	0.207858i
$167$	41.5393	+	71.9482i	0.248738	+	0.430828i	0.963176	−	0.268872i	$-0.0866507\pi$
$167$	41.5393	+	71.9482i	0.248738	+	0.430828i	−0.714438	+	0.699699i	$0.753317\pi$
$168$	31.9377	+	11.3169i	0.190105	+	0.0673627i
$169$	7.82136	−	13.5470i	0.0462803	−	0.0801598i
$170$	−24.9448	−	20.5176i	−0.146734	−	0.120692i
$171$	170.309	−	65.2973i	0.995961	−	0.381856i
$172$		−	251.484i		−	1.46212i
$173$	−0.219578	+	0.380321i	−0.00126924	+	0.00219839i	−0.866659	−	0.498900i	$-0.833737\pi$
$173$	−0.219578	+	0.380321i	−0.00126924	+	0.00219839i	0.865390	+	0.501099i	$0.167071\pi$
$174$	42.1215	−	35.9606i	0.242078	−	0.206670i
$175$	−45.4889	−	52.1008i	−0.259936	−	0.297719i
$176$	101.678	−	58.7040i	0.577718	−	0.333546i
$177$	133.482	−	113.958i	0.754135	−	0.643831i
$178$	13.3420	+	7.70300i	0.0749550	+	0.0432753i
$179$			102.699i			0.573740i	0.957970	+	0.286870i	$0.0926148\pi$
$179$			102.699i			0.573740i	−0.957970	+	0.286870i	$0.907385\pi$
$180$	−125.312	+	111.019i	−0.696180	+	0.616774i
$181$	−120.426			−0.665337			−0.332669	−	0.943044i	$-0.607949\pi$
$181$	−120.426			−0.665337			−0.332669	+	0.943044i	$0.607949\pi$
$182$	−9.93949	+	17.2157i	−0.0546126	+	0.0945917i
$183$	−15.5365	+	43.8457i	−0.0848988	+	0.239594i
$184$	−4.84032	−	8.38368i	−0.0263061	−	0.0455635i
$185$	−317.459	−	52.7714i	−1.71599	−	0.285251i
$186$	−45.9328	+	8.50362i	−0.246950	+	0.0457184i
$187$	−97.6295	−	56.3664i	−0.522083	−	0.301425i
$188$	347.410			1.84792
$189$	−74.6733	+	1.91046i	−0.395097	+	0.0101083i
$190$	−41.3833	−	34.0386i	−0.217807	−	0.179150i
$191$	−126.755	−	73.1823i	−0.663641	−	0.383153i	0.130022	−	0.991511i	$-0.458495\pi$
$191$	−126.755	−	73.1823i	−0.663641	−	0.383153i	−0.793663	+	0.608358i	$0.791829\pi$
$192$	114.155	−	21.1338i	0.594559	−	0.110072i
$193$	112.932	−	65.2014i	0.585141	−	0.337831i	−0.178033	−	0.984025i	$-0.556973\pi$
$193$	112.932	−	65.2014i	0.585141	−	0.337831i	0.763174	+	0.646193i	$0.223640\pi$
$194$	−28.5627	+	16.4907i	−0.147231	+	0.0850036i
$195$	−105.132	−	174.619i	−0.539136	−	0.895485i
$196$	76.9115	−	133.215i	0.392405	−	0.679666i
$197$	−186.652			−0.947470			−0.473735	−	0.880668i	$-0.657094\pi$
$197$	−186.652			−0.947470			−0.473735	+	0.880668i	$0.657094\pi$
$198$	27.6523	−	34.1197i	0.139658	−	0.172322i
$199$	45.1917			0.227094			0.113547	−	0.993533i	$-0.463779\pi$
$199$	45.1917			0.227094			0.113547	+	0.993533i	$0.463779\pi$
$200$	96.5729	+	33.0192i	0.482865	+	0.165096i
$201$	−35.5129	+	30.3186i	−0.176681	+	0.150839i
$202$	62.7855	−	36.2492i	0.310819	−	0.179451i
$203$	48.2939	+	83.6474i	0.237901	+	0.412056i
$204$	−88.5287	−	103.696i	−0.433964	−	0.508313i
$205$	69.9978	+	186.602i	0.341452	+	0.910253i
$206$			57.5343i			0.279293i
$207$	16.5800	+	13.4372i	0.0800967	+	0.0649142i
$208$			172.881i			0.831158i
$209$	−161.967	−	93.5114i	−0.774959	−	0.447423i
$210$	11.3187	+	18.7999i	0.0538984	+	0.0895231i
$211$	69.1054	+	119.694i	0.327514	+	0.567270i	0.982018	−	0.188788i	$-0.0604559\pi$
$211$	69.1054	+	119.694i	0.327514	+	0.567270i	−0.654504	+	0.756058i	$0.727123\pi$
$212$	−18.2793	−	31.6606i	−0.0862229	−	0.149343i
$213$	−29.0517	−	156.925i	−0.136393	−	0.736735i
$214$	−16.9214	+	29.3087i	−0.0790719	+	0.136957i
$215$	214.701	−	261.028i	0.998608	−	1.21408i
$216$	94.0183	−	57.5368i	0.435270	−	0.266374i
$217$		−	81.4664i		−	0.375421i
$218$	3.91664	−	6.78381i	0.0179662	−	0.0311184i
$219$	12.9182	+	69.7784i	0.0589872	+	0.318623i
$220$	169.338	+	28.1492i	0.769720	+	0.127951i
$221$	143.757	−	82.9983i	0.650485	−	0.375558i
$222$	96.2404	+	34.1022i	0.433515	+	0.153614i
$223$	−50.4072	−	29.1026i	−0.226041	−	0.130505i	0.382703	−	0.923871i	$-0.374993\pi$
$223$	−50.4072	−	29.1026i	−0.226041	−	0.130505i	−0.608744	+	0.793366i	$0.708327\pi$
$224$		−	63.7906i		−	0.284780i
$225$	−224.849	+	8.24879i	−0.999328	+	0.0366613i
$226$	43.7874			0.193750
$227$	−187.291	+	324.397i	−0.825069	+	1.42906i	0.0767971	+	0.997047i	$0.475531\pi$
$227$	−187.291	+	324.397i	−0.825069	+	1.42906i	−0.901866	+	0.432015i	$0.857803\pi$
$228$	−146.868	−	172.031i	−0.644160	−	0.754520i
$229$	−33.8418	−	58.6157i	−0.147781	−	0.255964i	0.782626	−	0.622492i	$-0.213880\pi$
$229$	−33.8418	−	58.6157i	−0.147781	−	0.255964i	−0.930407	+	0.366528i	$0.880546\pi$
$230$	1.02808	−	6.18467i	0.00446992	−	0.0268899i
$231$	49.7307	+	58.2508i	0.215284	+	0.252168i
$232$	−123.433	−	71.2642i	−0.532040	−	0.307173i
$233$	−282.378			−1.21192			−0.605961	−	0.795495i	$-0.707211\pi$
$233$	−282.378			−1.21192			−0.605961	+	0.795495i	$0.707211\pi$
$234$	23.1509	+	60.3825i	0.0989356	+	0.258045i
$235$	360.593	+	296.596i	1.53444	+	1.26211i
$236$	−188.495	−	108.828i	−0.798707	−	0.461134i
$237$	34.6071	−	97.6653i	0.146022	−	0.412090i
$238$	−15.4772	+	8.93575i	−0.0650301	+	0.0375452i
$239$	−319.035	+	184.195i	−1.33488	+	0.770691i	−0.986042	−	0.166494i	$-0.946755\pi$
$239$	−319.035	+	184.195i	−1.33488	+	0.770691i	−0.348833	+	0.937185i	$0.613422\pi$
$240$	166.995	+	92.3745i	0.695812	+	0.384894i
$241$	−185.554	+	321.389i	−0.769934	+	1.33357i	0.167664	+	0.985844i	$0.446378\pi$
$241$	−185.554	+	321.389i	−0.769934	+	1.33357i	−0.937598	+	0.347721i	$0.886956\pi$
$242$	18.9520			0.0783141
$243$	−148.122	+	192.637i	−0.609556	+	0.792743i
$244$	57.6870			0.236422
$245$	193.560	−	72.6079i	0.790040	−	0.296359i
$246$	−11.5107	−	62.1759i	−0.0467916	−	0.252747i
$247$	238.492	−	137.694i	0.965555	−	0.557464i
$248$	60.1074	+	104.109i	0.242369	+	0.419795i
$249$	75.4957	−	213.058i	0.303196	−	0.855653i
$250$	34.7193	+	56.2462i	0.138877	+	0.224985i
$251$			306.449i			1.22091i	0.792049	+	0.610457i	$0.209014\pi$
$251$			306.449i			1.22091i	−0.792049	+	0.610457i	$0.790986\pi$
$252$	33.1626	+	86.4952i	0.131598	+	0.343235i
$253$		−	21.8826i		−	0.0864924i
$254$	16.8200	+	9.71102i	0.0662204	+	0.0382323i
$255$	−3.35950	−	183.211i	−0.0131745	−	0.718474i
$256$	−47.6010	−	82.4474i	−0.185941	−	0.322060i
$257$	152.974	+	264.959i	0.595230	+	1.03097i	0.993514	+	0.113707i	$0.0362724\pi$
$257$	152.974	+	264.959i	0.595230	+	1.03097i	−0.398284	+	0.917262i	$0.630394\pi$
$258$	−81.5547	+	69.6260i	−0.316103	+	0.269868i
$259$	−89.0328	+	154.209i	−0.343756	+	0.595403i
$260$	−160.570	+	195.216i	−0.617575	+	0.750832i
$261$	310.322	+	49.2778i	1.18898	+	0.188804i
$262$			30.6362i			0.116932i
$263$	73.3426	−	127.033i	0.278869	−	0.483016i	−0.692235	−	0.721672i	$-0.743374\pi$
$263$	73.3426	−	127.033i	0.278869	−	0.483016i	0.971104	+	0.238657i	$0.0767070\pi$
$264$	−106.531	−	37.7487i	−0.403528	−	0.142988i
$265$	8.05682	−	48.4677i	0.0304031	−	0.182897i
$266$	−25.6765	+	14.8243i	−0.0965282	+	0.0557306i
$267$	15.9107	+	85.9427i	0.0595907	+	0.321883i
$268$	50.1491	+	28.9536i	0.187124	+	0.108036i
$269$		−	276.133i		−	1.02652i	−0.858234	−	0.513258i	$-0.828438\pi$
$269$		−	276.133i		−	1.02652i	0.858234	−	0.513258i	$-0.171562\pi$
$270$	70.6969	+	9.90115i	0.261840	+	0.0366709i
$271$	304.822			1.12480			0.562402	−	0.826864i	$-0.309877\pi$
$271$	304.822			1.12480			0.562402	+	0.826864i	$0.309877\pi$
$272$	−77.7112	+	134.600i	−0.285703	+	0.494852i
$273$	−110.895	+	20.5302i	−0.406210	+	0.0752024i
$274$	−15.2237	−	26.3681i	−0.0555608	−	0.0962341i
$275$	151.733	+	173.787i	0.551755	+	0.631954i
$276$	8.83956	−	24.9463i	0.0320274	−	0.0903850i
$277$	−355.555	−	205.280i	−1.28359	−	0.741083i	−0.306090	−	0.952003i	$-0.599021\pi$
$277$	−355.555	−	205.280i	−1.28359	−	0.741083i	−0.977503	+	0.210920i	$0.932354\pi$
$278$	−32.0707			−0.115362
$279$	−205.892	−	166.865i	−0.737964	−	0.598081i
$280$	35.8737	−	43.6144i	0.128120	−	0.155766i
$281$	89.9230	+	51.9171i	0.320011	+	0.184758i	0.651397	−	0.758737i	$-0.274183\pi$
$281$	89.9230	+	51.9171i	0.320011	+	0.184758i	−0.331387	+	0.943495i	$0.607516\pi$
$282$	−96.1840	−	112.663i	−0.341078	−	0.399513i
$283$	243.762	−	140.736i	0.861351	−	0.497301i	−0.00311372	−	0.999995i	$-0.500991\pi$
$283$	243.762	−	140.736i	0.861351	−	0.497301i	0.864464	+	0.502694i	$0.167658\pi$
$284$	−171.398	+	98.9566i	−0.603513	+	0.348439i
$285$	−5.57339	−	303.945i	−0.0195557	−	1.06648i
$286$	33.1541	−	57.4246i	0.115924	−	0.200785i
$287$	110.275			0.384234
$288$	−161.219	−	130.660i	−0.559790	−	0.453680i
$289$	−139.767			−0.483621
$290$	−32.4200	−	86.4260i	−0.111793	−	0.298021i
$291$	−176.369	−	62.4953i	−0.606078	−	0.214760i
$292$	76.2142	−	44.0023i	0.261007	−	0.150693i
$293$	−204.334	−	353.917i	−0.697387	−	1.20791i	−0.969369	−	0.245607i	$-0.921013\pi$
$293$	−204.334	−	353.917i	−0.697387	−	1.20791i	0.271983	−	0.962302i	$-0.412321\pi$
$294$	−64.4943	+	11.9399i	−0.219368	+	0.0406121i
$295$	−102.738	−	273.882i	−0.348265	−	0.928413i
$296$		−	262.760i		−	0.887703i
$297$	249.080	−	6.37253i	0.838653	−	0.0214563i
$298$			124.626i			0.418210i
$299$	27.9047	+	16.1108i	0.0933268	+	0.0538823i
$300$	102.774	+	259.412i	0.342579	+	0.864706i
$301$	−93.5055	−	161.956i	−0.310649	−	0.538060i
$302$	3.92278	+	6.79446i	0.0129893	+	0.0224982i
$303$	387.687	+	137.375i	1.27949	+	0.453381i
$304$	−128.922	+	223.300i	−0.424087	+	0.734540i
$305$	59.8761	+	49.2493i	0.196315	+	0.161473i
$306$	−9.11780	+	57.4185i	−0.0297967	+	0.187642i
$307$			174.133i			0.567208i	0.958941	+	0.283604i	$0.0915301\pi$
$307$			174.133i			0.567208i	−0.958941	+	0.283604i	$0.908470\pi$
$308$	47.4917	−	82.2581i	0.154194	−	0.267072i
$309$	−248.247	+	211.937i	−0.803388	+	0.685880i
$310$	−12.7668	+	76.8016i	−0.0411832	+	0.247747i
$311$	237.573	−	137.163i	0.763900	−	0.441038i	−0.0667941	−	0.997767i	$-0.521277\pi$
$311$	237.573	−	137.163i	0.763900	−	0.441038i	0.830694	+	0.556729i	$0.187944\pi$
$312$	126.570	−	108.057i	0.405672	−	0.346336i
$313$	184.560	+	106.555i	0.589647	+	0.340433i	0.764958	−	0.644080i	$-0.222760\pi$
$313$	184.560	+	106.555i	0.589647	+	0.340433i	−0.175311	+	0.984513i	$0.556093\pi$
$314$		−	77.8424i		−	0.247906i
$315$	−39.4228	+	118.090i	−0.125152	+	0.374887i
$316$	−128.496			−0.406634
$317$	121.062	−	209.686i	0.381899	−	0.661469i	−0.609435	−	0.792836i	$-0.708604\pi$
$317$	121.062	−	209.686i	0.381899	−	0.661469i	0.991334	+	0.131368i	$0.0419368\pi$
$318$	−5.20652	+	14.6934i	−0.0163727	+	0.0462057i
$319$	−161.089	−	279.014i	−0.504981	−	0.874653i
$320$	31.7289	−	190.873i	0.0991527	−	0.596477i
$321$	−188.793	+	34.9515i	−0.588139	+	0.108883i
$322$	−3.00427	−	1.73452i	−0.00933004	−	0.00538670i
$323$	247.577			0.766493
$324$	286.527	+	93.3522i	0.884342	+	0.288124i
$325$	−333.326	+	65.5408i	−1.02562	+	0.201664i
$326$	−4.40604	−	2.54383i	−0.0135155	−	0.00780316i
$327$	43.6981	−	8.08990i	0.133633	−	0.0247398i
$328$	−140.925	+	81.3630i	−0.429649	+	0.248058i
$329$	223.732	−	129.172i	0.680038	−	0.392620i
$330$	−37.7545	−	62.7087i	−0.114408	−	0.190026i
$331$	99.4647	−	172.278i	0.300498	−	0.520477i	−0.675751	−	0.737130i	$-0.736181\pi$
$331$	99.4647	−	172.278i	0.300498	−	0.520477i	0.976249	+	0.216653i	$0.0695139\pi$
$332$	−280.316			−0.844325
$333$	207.374	+	540.875i	0.622745	+	1.62425i
$334$	−43.9313			−0.131531
$335$	27.3335	+	72.8664i	0.0815925	+	0.217512i
$336$	80.3092	−	68.5627i	0.239016	−	0.204056i
$337$	−273.013	+	157.624i	−0.810128	+	0.467728i	−0.847000	−	0.531592i	$-0.821594\pi$
$337$	−273.013	+	157.624i	−0.810128	+	0.467728i	0.0368724	+	0.999320i	$0.488260\pi$
$338$	4.13587	+	7.16353i	0.0122363	+	0.0211939i
$339$	161.298	+	188.932i	0.475805	+	0.557322i
$340$	−212.766	+	79.8124i	−0.625782	+	0.234742i
$341$			271.739i			0.796889i
$342$	−15.1264	+	95.2569i	−0.0442291	+	0.278529i
$343$		−	249.950i		−	0.728716i
$344$	238.988	+	137.980i	0.694734	+	0.401105i
$345$	30.4725	−	18.3463i	0.0883260	−	0.0531776i
$346$	−0.116111	−	0.201110i	−0.000335581	−	0.000581244i
$347$	−253.003	−	438.213i	−0.729114	−	1.26286i	−0.957258	−	0.289235i	$-0.906599\pi$
$347$	−253.003	−	438.213i	−0.729114	−	1.26286i	0.228144	−	0.973627i	$-0.426734\pi$
$348$	−70.9333	−	383.150i	−0.203831	−	1.10101i
$349$	280.837	−	486.423i	0.804689	−	1.39376i	−0.111811	−	0.993729i	$-0.535665\pi$
$349$	280.837	−	486.423i	0.804689	−	1.39376i	0.916501	−	0.400033i	$-0.131001\pi$
$350$	35.8865	−	7.05624i	0.102533	−	0.0201607i
$351$	−175.256	+	322.319i	−0.499305	+	0.918289i
$352$			212.780i			0.604488i
$353$	−120.900	+	209.404i	−0.342492	+	0.593213i	−0.984895	−	0.173154i	$-0.944604\pi$
$353$	−120.900	+	209.404i	−0.342492	+	0.593213i	0.642403	+	0.766367i	$0.277938\pi$
$354$	16.8947	+	91.2576i	0.0477251	+	0.257790i
$355$	−262.385	−	43.6164i	−0.739112	−	0.122863i
$356$	93.8693	−	54.1955i	0.263678	−	0.152234i
$357$	−95.5682	−	33.8640i	−0.267698	−	0.0948573i
$358$	−47.0309	−	27.1533i	−0.131371	−	0.0758472i
$359$			361.904i			1.00809i	0.863678	+	0.504044i	$0.168155\pi$
$359$			361.904i			1.00809i	−0.863678	+	0.504044i	$0.831845\pi$
$360$	−36.7487	−	179.998i	−0.102080	−	0.499995i
$361$	49.7285			0.137752
$362$	31.8401	−	55.1487i	0.0879561	−	0.152344i
$363$	69.8127	+	81.7734i	0.192322	+	0.225271i
$364$	69.9305	+	121.123i	0.192117	+	0.332756i
$365$	116.673	+	19.3946i	0.319651	+	0.0531358i
$366$	−15.9712	−	18.7075i	−0.0436372	−	0.0511134i
$367$	227.601	+	131.406i	0.620168	+	0.358054i	0.776934	−	0.629582i	$-0.216774\pi$
$367$	227.601	+	131.406i	0.620168	+	0.358054i	−0.156767	+	0.987636i	$0.550107\pi$
$368$	−30.1691			−0.0819812
$369$	225.873	−	278.701i	0.612121	−	0.755287i
$370$	108.101	−	131.427i	0.292165	−	0.355207i
$371$	−23.5437	−	13.5930i	−0.0634602	−	0.0366388i
$372$	−109.770	+	309.784i	−0.295081	+	0.832753i
$373$	−270.755	+	156.320i	−0.725883	+	0.419089i	−0.816914	−	0.576759i	$-0.804317\pi$
$373$	−270.755	+	156.320i	−0.725883	+	0.419089i	0.0910309	+	0.995848i	$0.470984\pi$
$374$	51.6256	−	29.8061i	0.138036	−	0.0796953i
$375$	−114.795	+	356.997i	−0.306119	+	0.951993i
$376$	−190.611	+	330.148i	−0.506944	+	0.878052i
$377$	474.400			1.25835
$378$	18.8684	−	34.7015i	0.0499164	−	0.0918029i
$379$	256.518			0.676830			0.338415	−	0.940997i	$-0.390109\pi$
$379$	256.518			0.676830			0.338415	+	0.940997i	$0.390109\pi$
$380$	−352.977	+	132.408i	−0.928887	+	0.348442i
$381$	20.0583	+	108.346i	0.0526465	+	0.284373i
$382$	67.0272	−	38.6982i	0.175464	−	0.101304i
$383$	19.4145	+	33.6269i	0.0506906	+	0.0877986i	0.890257	−	0.455458i	$-0.150524\pi$
$383$	19.4145	+	33.6269i	0.0506906	+	0.0877986i	−0.839567	+	0.543257i	$0.817191\pi$
$384$	−112.918	+	318.666i	−0.294056	+	0.829860i
$385$	119.521	−	44.8343i	0.310443	−	0.116453i
$386$			68.9559i			0.178642i
$387$	−600.839	−	95.4105i	−1.55256	−	0.246539i
$388$			232.045i			0.598054i
$389$	265.870	+	153.500i	0.683469	+	0.394601i	0.801161	−	0.598449i	$-0.204216\pi$
$389$	265.870	+	153.500i	0.683469	+	0.394601i	−0.117691	+	0.993050i	$0.537549\pi$
$390$	107.763	−	1.97602i	0.276315	−	0.00506673i
$391$	14.4839	+	25.0868i	0.0370431	+	0.0641605i
$392$	84.3969	+	146.180i	0.215298	+	0.372908i
$393$	−132.188	+	112.853i	−0.336356	+	0.287159i
$394$	49.3498	−	85.4764i	0.125253	−	0.216945i
$395$	−133.372	−	109.702i	−0.337652	−	0.277726i
$396$	−110.617	−	288.513i	−0.279336	−	0.728568i
$397$		−	47.0129i		−	0.118420i	−0.998246	−	0.0592102i	$-0.981142\pi$
$397$		−	47.0129i		−	0.118420i	0.998246	−	0.0592102i	$-0.0188582\pi$
$398$	−11.9485	+	20.6954i	−0.0300213	+	0.0519985i
$399$	−158.547	−	56.1802i	−0.397361	−	0.140802i
$400$	239.597	−	209.191i	0.598993	−	0.522977i
$401$	−492.460	+	284.322i	−1.22808	+	0.709032i	−0.966628	−	0.256184i	$-0.917535\pi$
$401$	−492.460	+	284.322i	−1.22808	+	0.709032i	−0.261452	+	0.965216i	$0.584201\pi$
$402$	−4.49484	−	24.2791i	−0.0111812	−	0.0603958i
$403$	−346.523	−	200.065i	−0.859858	−	0.496439i
$404$		−	510.072i		−	1.26255i
$405$	217.702	+	341.513i	0.537536	+	0.843241i
$406$	−51.0747			−0.125800
$407$	296.977	−	514.380i	0.729674	−	1.26383i
$408$	147.116	−	27.2358i	0.360578	−	0.0667544i
$409$	281.070	+	486.828i	0.687213	+	1.19029i	0.972736	+	0.231916i	$0.0744994\pi$
$409$	281.070	+	486.828i	0.687213	+	1.19029i	−0.285523	+	0.958372i	$0.592167\pi$
$410$	−103.961	−	17.2815i	−0.253563	−	0.0421499i
$411$	57.6935	−	162.818i	0.140373	−	0.396150i
$412$	350.559	+	202.395i	0.850870	+	0.491250i
$413$	−161.855			−0.391900
$414$	−10.5372	+	4.04002i	−0.0254522	+	0.00975850i
$415$	−290.953	−	239.315i	−0.701092	−	0.576663i
$416$	−271.338	−	156.657i	−0.652254	−	0.376579i
$417$	−118.138	−	138.378i	−0.283304	−	0.331841i
$418$	85.6465	−	49.4480i	0.204896	−	0.118297i
$419$	180.183	−	104.029i	0.430031	−	0.248279i	−0.269329	−	0.963048i	$-0.586802\pi$
$419$	180.183	−	104.029i	0.430031	−	0.248279i	0.699360	+	0.714770i	$0.253469\pi$
$420$	154.365	−	2.83056i	0.367536	−	0.00673943i
$421$	197.236	−	341.622i	0.468493	−	0.811454i	−0.530858	−	0.847461i	$-0.678130\pi$
$421$	197.236	−	341.622i	0.468493	−	0.811454i	0.999352	+	0.0360063i	$0.0114636\pi$
$422$	−73.0846			−0.173186
$423$	131.804	−	830.022i	0.311592	−	1.96223i
$424$	40.1166			0.0946147
$425$	−288.979	−	98.8044i	−0.679949	−	0.232481i
$426$	79.5442	+	28.1860i	0.186723	+	0.0661644i
$427$	37.1505	−	21.4488i	0.0870035	−	0.0502315i
$428$	119.053	+	206.205i	0.278160	+	0.481788i
$429$	369.902	−	68.4806i	0.862243	−	0.159629i
$430$	62.7708	+	167.336i	0.145979	+	0.389153i
$431$		−	216.515i		−	0.502355i	−0.967941	−	0.251177i	$-0.919182\pi$
$431$		−	216.515i		−	0.502355i	0.967941	−	0.251177i	$-0.0808177\pi$
$432$	−8.78569	−	343.402i	−0.0203372	−	0.794911i
$433$		−	614.024i		−	1.41807i	−0.705173	−	0.709035i	$-0.749131\pi$
$433$		−	614.024i		−	1.41807i	0.705173	−	0.709035i	$-0.250869\pi$
$434$	37.3073	+	21.5394i	0.0859614	+	0.0496299i
$435$	253.483	−	458.248i	0.582721	−	1.05344i
$436$	−27.5560	−	47.7284i	−0.0632018	−	0.109469i
$437$	24.0286	+	41.6188i	0.0549854	+	0.0952374i
$438$	−35.3703	−	12.5333i	−0.0807541	−	0.0286148i
$439$	−259.851	+	450.074i	−0.591915	+	1.02523i	0.402059	+	0.915614i	$0.368295\pi$
$439$	−259.851	+	450.074i	−0.591915	+	1.02523i	−0.993974	+	0.109613i	$0.965039\pi$
$440$	−119.660	+	145.480i	−0.271955	+	0.330636i
$441$	−289.093	−	234.295i	−0.655540	−	0.531281i
$442$			87.7775i			0.198592i
$443$	−250.825	+	434.441i	−0.566196	+	0.980680i	0.430742	+	0.902475i	$0.358252\pi$
$443$	−250.825	+	434.441i	−0.566196	+	0.980680i	−0.996937	+	0.0782045i	$0.975081\pi$
$444$	546.342	−	466.431i	1.23050	−	1.05052i
$445$	143.700	+	23.8873i	0.322921	+	0.0536794i
$446$	26.6549	−	15.3892i	0.0597643	−	0.0345049i
$447$	−537.734	+	459.082i	−1.20298	+	1.02703i
$448$	−92.7186	−	53.5311i	−0.206961	−	0.119489i
$449$			166.389i			0.370576i	0.982684	+	0.185288i	$0.0593218\pi$
$449$			166.389i			0.370576i	−0.982684	+	0.185288i	$0.940678\pi$
$450$	55.6715	−	105.150i	0.123714	−	0.233666i
$451$	−367.834			−0.815596
$452$	154.036	−	266.798i	0.340788	−	0.590261i
$453$	−14.8663	+	41.9543i	−0.0328174	+	0.0926145i
$454$	−99.0377	−	171.538i	−0.218145	−	0.377838i
$455$	−30.8228	+	185.422i	−0.0677424	+	0.407520i
$456$	244.064	−	45.1840i	0.535228	−	0.0990877i
$457$	720.569	+	416.021i	1.57674	+	0.910330i	0.995310	+	0.0967320i	$0.0308390\pi$
$457$	720.569	+	416.021i	1.57674	+	0.910330i	0.581428	+	0.813598i	$0.302494\pi$
$458$	35.7905			0.0781452
$459$	−281.334	+	172.169i	−0.612928	+	0.375096i
$460$	−34.0668	−	28.0207i	−0.0740582	−	0.0609145i
$461$	376.087	+	217.134i	0.815806	+	0.471006i	0.848968	−	0.528444i	$-0.177224\pi$
$461$	376.087	+	217.134i	0.815806	+	0.471006i	−0.0331619	+	0.999450i	$0.510558\pi$
$462$	−39.8243	+	7.37275i	−0.0861999	+	0.0159583i
$463$	−150.734	+	87.0264i	−0.325560	+	0.187962i	−0.653868	−	0.756609i	$-0.726855\pi$
$463$	−150.734	+	87.0264i	−0.325560	+	0.187962i	0.328308	+	0.944571i	$0.393522\pi$
$464$	−384.671	+	222.090i	−0.829033	+	0.478643i
$465$	−378.409	+	227.825i	−0.813783	+	0.489947i
$466$	74.6594	−	129.314i	0.160213	−	0.277498i
$467$	−134.443			−0.287886			−0.143943	−	0.989586i	$-0.545978\pi$
$467$	−134.443			−0.287886			−0.143943	+	0.989586i	$0.545978\pi$
$468$	449.354	+	71.3553i	0.960157	+	0.152469i
$469$	43.0615			0.0918155
$470$	−231.164	+	86.7139i	−0.491839	+	0.184498i
$471$	335.872	−	286.745i	0.713103	−	0.608800i
$472$	206.840	−	119.419i	0.438221	−	0.253007i
$473$	311.897	+	540.221i	0.659401	+	1.14212i
$474$	35.5755	+	41.6705i	0.0750538	+	0.0879124i
$475$	−479.413	−	163.916i	−1.00929	−	0.345086i
$476$			125.737i			0.264154i
$477$	−82.5776	+	31.6606i	−0.173119	+	0.0663744i
$478$		−	194.802i		−	0.407535i
$479$	−617.101	−	356.283i	−1.28831	−	0.743806i	−0.309958	−	0.950750i	$-0.600315\pi$
$479$	−617.101	−	356.283i	−1.28831	−	0.743806i	−0.978353	+	0.206944i	$0.933648\pi$
$480$	−296.306	+	178.394i	−0.617303	+	0.371654i
$481$	437.293	+	757.413i	0.909133	+	1.57466i
$482$	−98.1194	−	169.948i	−0.203567	−	0.352589i
$483$	−3.58269	−	19.3521i	−0.00741757	−	0.0400665i
$484$	66.6697	−	115.475i	0.137747	−	0.238585i
$485$	−198.105	+	240.851i	−0.408463	+	0.496599i
$486$	−49.0544	−	118.764i	−0.100935	−	0.244371i
$487$			208.661i			0.428462i	0.976783	+	0.214231i	$0.0687246\pi$
$487$			208.661i			0.428462i	−0.976783	+	0.214231i	$0.931275\pi$
$488$	−31.6507	+	54.8206i	−0.0648580	+	0.112337i
$489$	−5.25434	−	28.3816i	−0.0107451	−	0.0580402i
$490$	−17.9259	+	107.837i	−0.0365834	+	0.220076i
$491$	−356.432	+	205.786i	−0.725931	+	0.419117i	−0.816932	−	0.576734i	$-0.804327\pi$
$491$	−356.432	+	205.786i	−0.725931	+	0.419117i	0.0910005	+	0.995851i	$0.470994\pi$
$492$	−419.332	−	148.588i	−0.852302	−	0.302008i
$493$	369.353	+	213.246i	0.749195	+	0.432548i
$494$			145.622i			0.294782i
$495$	131.499	−	393.899i	0.265654	−	0.795756i
$496$	374.641			0.755326
$497$	−73.5870	+	127.456i	−0.148062	+	0.256451i
$498$	77.6083	+	90.9045i	0.155840	+	0.182539i
$499$	167.299	+	289.770i	0.335269	+	0.580702i	0.983536	−	0.180710i	$-0.0578396\pi$
$499$	167.299	+	289.770i	0.335269	+	0.580702i	−0.648268	+	0.761412i	$0.724506\pi$
$500$	464.846	−	13.6823i	0.929692	−	0.0273646i
$501$	−161.828	−	189.553i	−0.323010	−	0.378349i
$502$	−140.337	−	81.0239i	−0.279557	−	0.161402i
$503$	−85.4624			−0.169905			−0.0849527	−	0.996385i	$-0.527074\pi$
$503$	−85.4624			−0.169905			−0.0849527	+	0.996385i	$0.527074\pi$
$504$	−100.393	−	15.9419i	−0.199191	−	0.0316307i
$505$	435.466	−	529.428i	0.862309	−	1.04837i
$506$	10.0210	+	5.78565i	0.0198044	+	0.0114341i
$507$	−15.6738	+	44.2333i	−0.0309148	+	0.0872452i
$508$	118.339	−	68.3231i	0.232951	−	0.134494i
$509$	142.153	−	82.0719i	0.279278	−	0.161241i	−0.353818	−	0.935314i	$-0.615117\pi$
$509$	142.153	−	82.0719i	0.279278	−	0.161241i	0.633097	+	0.774073i	$0.281784\pi$
$510$	84.7890	+	46.9017i	0.166253	+	0.0919641i
$511$	32.7214	−	56.6750i	0.0640340	−	0.110910i
$512$	501.116			0.978743
$513$	−466.731	+	285.627i	−0.909808	+	0.556779i
$514$	−161.783			−0.314752
$515$	191.070	+	509.359i	0.371010	+	0.989048i
$516$	137.339	+	741.847i	0.266162	+	1.43769i
$517$	−746.281	+	430.866i	−1.44348	+	0.833396i
$518$	−47.0797	−	81.5445i	−0.0908875	−	0.157422i
$519$	0.440030	−	1.24181i	0.000847841	−	0.00239271i
$520$	−97.4179	−	259.699i	−0.187342	−	0.499422i
$521$		−	954.386i		−	1.83184i	−0.401366	−	0.915918i	$-0.631464\pi$
$521$		−	954.386i		−	1.83184i	0.401366	−	0.915918i	$-0.368536\pi$
$522$	−104.614	+	129.082i	−0.200411	+	0.247284i
$523$			53.5836i			0.102454i	0.998687	+	0.0512271i	$0.0163132\pi$
$523$			53.5836i			0.102454i	−0.998687	+	0.0512271i	$0.983687\pi$
$524$	186.668	+	107.773i	0.356236	+	0.205673i
$525$	162.640	+	128.849i	0.309790	+	0.245426i
$526$	38.7829	+	67.1740i	0.0737318	+	0.127707i
$527$	−179.861	−	311.529i	−0.341293	−	0.591137i
$528$	−267.879	+	228.698i	−0.507347	+	0.433140i
$529$	261.689	−	453.258i	0.494685	−	0.856820i
$530$	20.0654	+	16.5042i	0.0378593	+	0.0311401i
$531$	−331.521	+	409.059i	−0.624333	+	0.770355i
$532$			208.597i			0.392100i
$533$	270.814	−	469.063i	0.508093	−	0.880043i
$534$	−43.5639	−	15.4366i	−0.0815803	−	0.0289075i
$535$	−52.4739	+	315.669i	−0.0980821	+	0.590036i
$536$	−55.0299	+	31.7715i	−0.102668	+	0.0592753i
$537$	−56.0857	−	302.950i	−0.104443	−	0.564154i
$538$	126.454	+	73.0083i	0.235045	+	0.135703i
$539$			381.550i			0.707884i
$540$	309.027	−	395.928i	0.572271	−	0.733200i
$541$	−502.886			−0.929549			−0.464774	−	0.885429i	$-0.653865\pi$
$541$	−502.886			−0.929549			−0.464774	+	0.885429i	$0.653865\pi$
$542$	−80.5935	+	139.592i	−0.148697	+	0.257550i
$543$	355.242	−	65.7665i	0.654220	−	0.121117i
$544$	−140.837	−	243.937i	−0.258891	−	0.448413i
$545$	12.1457	−	73.0651i	0.0222856	−	0.134064i
$546$	19.9185	−	56.2122i	0.0364807	−	0.102953i
$547$	632.220	+	365.012i	1.15579	+	0.667298i	0.950293	−	0.311359i	$-0.100784\pi$
$547$	632.220	+	365.012i	1.15579	+	0.667298i	0.205502	+	0.978657i	$0.434117\pi$
$548$	−214.216			−0.390905
$549$	21.8858	−	137.824i	0.0398649	−	0.251046i
$550$	−119.703	+	23.5368i	−0.217641	+	0.0427941i
$551$	612.754	+	353.774i	1.11208	+	0.642058i
$552$	18.8568	+	22.0874i	0.0341608	+	0.0400134i
$553$	−82.7518	+	47.7768i	−0.149642	+	0.0863956i
$554$	188.014	−	108.550i	0.339376	−	0.195939i
$555$	965.283	−	17.7002i	1.73925	−	0.0318922i
$556$	−112.819	+	195.408i	−0.202912	+	0.351453i
$557$	419.491			0.753125			0.376562	−	0.926391i	$-0.377106\pi$
$557$	419.491			0.753125			0.376562	+	0.926391i	$0.377106\pi$
$558$	130.852	−	50.1692i	0.234502	−	0.0899090i
$559$	−918.522			−1.64315
$560$	−61.8122	−	164.781i	−0.110379	−	0.294251i
$561$	318.777	+	112.957i	0.568230	+	0.201349i
$562$	−47.5505	+	27.4533i	−0.0846094	+	0.0488493i
$563$	−317.922	−	550.657i	−0.564693	−	0.978077i	−0.997078	−	0.0763882i	$-0.975661\pi$
$563$	−317.922	−	550.657i	−0.564693	−	0.978077i	0.432385	−	0.901689i	$-0.357672\pi$
$564$	−1024.81	+	189.726i	−1.81705	+	0.336393i
$565$	387.656	−	145.417i	0.686117	−	0.257375i
$566$			148.840i			0.262968i
$567$	219.233	−	46.4159i	0.386655	−	0.0818622i
$568$		−	217.175i		−	0.382351i
$569$	−767.241	−	442.967i	−1.34840	−	0.778501i	−0.360380	−	0.932806i	$-0.617353\pi$
$569$	−767.241	−	442.967i	−1.34840	−	0.778501i	−0.988023	+	0.154305i	$0.950686\pi$
$570$	140.664	+	77.8095i	0.246780	+	0.136508i
$571$	−463.096	−	802.105i	−0.811026	−	1.40474i	−0.912147	−	0.409864i	$-0.865576\pi$
$571$	−463.096	−	802.105i	−0.811026	−	1.40474i	0.101121	−	0.994874i	$-0.467757\pi$
$572$	−233.260	−	404.018i	−0.407798	−	0.706326i
$573$	413.879	+	146.655i	0.722301	+	0.255943i
$574$	−29.1563	+	50.5001i	−0.0507949	+	0.0879794i
$575$	−11.4374	−	58.1680i	−0.0198911	−	0.101162i
$576$	−325.202	+	124.684i	−0.564587	+	0.216465i
$577$		−	261.287i		−	0.452837i	−0.974030	−	0.226418i	$-0.927298\pi$
$577$		−	261.287i		−	0.452837i	0.974030	−	0.226418i	$-0.0727016\pi$
$578$	36.9537	−	64.0056i	0.0639337	−	0.110736i
$579$	−297.528	+	254.010i	−0.513866	+	0.438705i
$580$	−640.644	−	106.495i	−1.10456	−	0.183611i
$581$	−180.524	+	104.225i	−0.310712	+	0.179390i
$582$	75.2506	−	64.2440i	0.129297	−	0.110385i
$583$	78.5325	+	45.3407i	0.134704	+	0.0777714i
$584$			96.5696i			0.165359i
$585$	405.487	+	457.692i	0.693141	+	0.782379i
$586$	216.100			0.368772
$587$	301.693	−	522.548i	0.513958	−	0.890201i	−0.485911	−	0.874008i	$-0.661512\pi$
$587$	301.693	−	522.548i	0.513958	−	0.890201i	0.999869	−	0.0161926i	$-0.00515450\pi$
$588$	−154.129	+	434.969i	−0.262123	+	0.739743i
$589$	−298.389	−	516.825i	−0.506602	−	0.877461i
$590$	152.587	+	25.3646i	0.258622	+	0.0429908i
$591$	550.599	−	101.933i	0.931639	−	0.172476i
$592$	−709.166	−	409.437i	−1.19792	−	0.691617i
$593$	−314.000			−0.529511			−0.264756	−	0.964316i	$-0.585291\pi$
$593$	−314.000			−0.529511			−0.264756	+	0.964316i	$0.585291\pi$
$594$	−62.9374	+	115.750i	−0.105955	+	0.194866i
$595$	−107.346	+	130.509i	−0.180414	+	0.219342i
$596$	759.354	+	438.413i	1.27408	+	0.735592i
$597$	−133.310	+	24.6799i	−0.223300	+	0.0413398i
$598$	−14.7558	+	8.51925i	−0.0246752	+	0.0142462i
$599$	652.734	−	376.856i	1.08971	−	0.629142i	0.156208	−	0.987724i	$-0.450073\pi$
$599$	652.734	−	376.856i	1.08971	−	0.629142i	0.933498	+	0.358582i	$0.116740\pi$
$600$	−302.910	−	44.6624i	−0.504850	−	0.0744374i
$601$	168.976	−	292.675i	0.281158	−	0.486979i	−0.690512	−	0.723320i	$-0.742615\pi$
$601$	168.976	−	292.675i	0.281158	−	0.486979i	0.971670	+	0.236341i	$0.0759483\pi$
$602$	98.8897			0.164269
$603$	88.2012	−	108.830i	0.146271	−	0.180481i
$604$	55.1985			0.0913883
$605$	167.785	−	62.9391i	0.277330	−	0.104032i
$606$	−165.413	+	141.219i	−0.272959	+	0.233034i
$607$	382.344	−	220.747i	0.629892	−	0.363668i	−0.150818	−	0.988562i	$-0.548191\pi$
$607$	382.344	−	220.747i	0.629892	−	0.363668i	0.780710	+	0.624893i	$0.214857\pi$
$608$	−233.647	−	404.689i	−0.384288	−	0.665607i
$609$	−188.142	−	220.375i	−0.308936	−	0.361864i
$610$	−38.3845	+	14.3987i	−0.0629255	+	0.0236045i
$611$		−	1268.88i		−	2.07673i
$612$	317.778	+	257.543i	0.519246	+	0.420822i
$613$			406.010i			0.662332i	0.943572	+	0.331166i	$0.107442\pi$
$613$			406.010i			0.662332i	−0.943572	+	0.331166i	$0.892558\pi$
$614$	−79.7436	−	46.0400i	−0.129876	−	0.0749837i
$615$	−308.391	−	512.225i	−0.501448	−	0.832886i
$616$	52.1139	+	90.2639i	0.0846005	+	0.146532i
$617$	447.854	+	775.706i	0.725858	+	1.25722i	0.958620	+	0.284689i	$0.0918903\pi$
$617$	447.854	+	775.706i	0.725858	+	1.25722i	−0.232762	+	0.972534i	$0.574776\pi$
$618$	−31.4204	−	169.719i	−0.0508420	−	0.274626i
$619$	−185.811	+	321.834i	−0.300179	+	0.519925i	−0.976176	−	0.216979i	$-0.930380\pi$
$619$	−185.811	+	321.834i	−0.300179	+	0.519925i	0.675997	+	0.736904i	$0.263713\pi$
$620$	423.044	+	347.962i	0.682329	+	0.561230i
$621$	−56.2473	−	30.5836i	−0.0905753	−	0.0492489i
$622$			145.061i			0.233217i
$623$	40.3013	−	69.8039i	0.0646891	−	0.112045i
$624$	−94.4129	−	509.977i	−0.151303	−	0.817271i
$625$	494.167	+	382.654i	0.790668	+	0.612246i
$626$	−97.5935	+	56.3456i	−0.155900	+	0.0900090i
$627$	528.849	+	187.395i	0.843459	+	0.298875i
$628$	−474.297	−	273.835i	−0.755249	−	0.436043i
$629$			786.266i			1.25002i
$630$	−43.6555	−	49.2759i	−0.0692944	−	0.0782157i
$631$	150.820			0.239017			0.119508	−	0.992833i	$-0.461868\pi$
$631$	150.820			0.239017			0.119508	+	0.992833i	$0.461868\pi$
$632$	70.5011	−	122.112i	0.111552	−	0.193214i
$633$	−269.219	−	315.343i	−0.425306	−	0.498172i
$634$	64.0165	+	110.880i	0.100972	+	0.174889i
$635$	181.160	+	30.1143i	0.285291	+	0.0474241i
$636$	71.2119	+	83.4122i	0.111968	+	0.131151i
$637$	−486.553	−	280.912i	−0.763820	−	0.440992i
$638$	170.365			0.267029
$639$	171.398	+	447.042i	0.268228	+	0.699596i
$640$	435.173	+	357.939i	0.679958	+	0.559280i
$641$	175.963	+	101.592i	0.274513	+	0.158490i	0.630937	−	0.775834i	$-0.282671\pi$
$641$	175.963	+	101.592i	0.274513	+	0.158490i	−0.356424	+	0.934324i	$0.616004\pi$
$642$	33.9100	−	95.6980i	0.0528193	−	0.149062i
$643$	−42.7186	+	24.6636i	−0.0664365	+	0.0383571i	−0.532850	−	0.846210i	$-0.678879\pi$
$643$	−42.7186	+	24.6636i	−0.0664365	+	0.0383571i	0.466414	+	0.884567i	$0.345546\pi$
$644$	−21.1370	+	12.2034i	−0.0328214	+	0.0189494i
$645$	−490.789	+	887.250i	−0.760913	+	1.37558i
$646$	−65.4583	+	113.377i	−0.101329	+	0.175506i
$647$	−1189.39			−1.83832			−0.919159	−	0.393887i	$-0.871130\pi$
$647$	−1189.39			−1.83832			−0.919159	+	0.393887i	$0.871130\pi$
$648$	−245.920	+	221.071i	−0.379507	+	0.341159i
$649$	539.882			0.831867
$650$	58.1157	−	169.974i	0.0894088	−	0.261499i
$651$	44.4901	+	240.316i	0.0683411	+	0.369148i
$652$	−30.9993	+	17.8975i	−0.0475449	+	0.0274501i
$653$	170.606	+	295.498i	0.261265	+	0.452524i	0.966578	−	0.256371i	$-0.0825270\pi$
$653$	170.606	+	295.498i	0.261265	+	0.452524i	−0.705313	+	0.708896i	$0.749194\pi$
$654$	−7.84884	+	22.1503i	−0.0120013	+	0.0338690i
$655$	101.742	+	271.227i	0.155331	+	0.414087i
$656$			507.125i			0.773056i
$657$	−76.2142	−	198.783i	−0.116003	−	0.302561i
$658$			136.610i			0.207614i
$659$	−322.418	−	186.148i	−0.489254	−	0.282471i	0.235011	−	0.971993i	$-0.424487\pi$
$659$	−322.418	−	186.148i	−0.489254	−	0.282471i	−0.724265	+	0.689522i	$0.757821\pi$
$660$	−514.900	+	9.44161i	−0.780151	+	0.0143055i
$661$	−166.221	−	287.904i	−0.251469	−	0.435557i	0.712461	−	0.701711i	$-0.247580\pi$
$661$	−166.221	−	287.904i	−0.251469	−	0.435557i	−0.963931	+	0.266154i	$0.914247\pi$
$662$	52.5961	+	91.0991i	0.0794502	+	0.137612i
$663$	−378.739	+	323.343i	−0.571251	+	0.487696i
$664$	153.799	−	266.387i	0.231625	−	0.401186i
$665$	−178.086	+	216.513i	−0.267799	+	0.325583i
$666$	−302.521	−	48.0389i	−0.454236	−	0.0721305i
$667$			82.7865i			0.124118i
$668$	−154.542	+	267.675i	−0.231350	+	0.400711i
$669$	164.588	+	58.3209i	0.246021	+	0.0871762i
$670$	−40.5958	−	6.74826i	−0.0605907	−	0.0100720i
$671$	−123.919	+	71.5447i	−0.184678	+	0.106624i
$672$	34.8370	+	188.174i	0.0518408	+	0.280021i
$673$	−196.887	−	113.673i	−0.292551	−	0.168905i	0.346541	−	0.938035i	$-0.387356\pi$
$673$	−196.887	−	113.673i	−0.292551	−	0.168905i	−0.639092	+	0.769130i	$0.720690\pi$
$674$		−	166.701i		−	0.247330i
$675$	658.771	−	147.126i	0.975957	−	0.217965i
$676$	58.1969			0.0860901
$677$	−530.736	+	919.261i	−0.783952	+	1.35785i	0.145671	+	0.989333i	$0.453466\pi$
$677$	−530.736	+	919.261i	−0.783952	+	1.35785i	−0.929623	+	0.368512i	$0.879867\pi$
$678$	−129.167	+	23.9130i	−0.190512	+	0.0352699i
$679$	86.2777	+	149.437i	0.127066	+	0.220084i
$680$	40.8901	−	245.984i	0.0601325	−	0.361741i
$681$	375.326	−	1059.21i	0.551139	−	1.55538i
$682$	−124.442	−	71.8466i	−0.182466	−	0.105347i
$683$	633.553			0.927604			0.463802	−	0.885939i	$-0.346485\pi$
$683$	633.553			0.927604			0.463802	+	0.885939i	$0.346485\pi$
$684$	527.192	+	427.262i	0.770749	+	0.624652i
$685$	−222.345	−	182.884i	−0.324591	−	0.266983i
$686$	114.464	+	66.0856i	0.166857	+	0.0963347i
$687$	131.840	+	154.428i	0.191907	+	0.224785i
$688$	744.792	−	430.006i	1.08255	−	0.625008i
$689$	−115.637	+	66.7633i	−0.167834	+	0.0968988i
$690$	0.344832	+	18.8054i	0.000499756	+	0.0272543i
$691$	−540.899	+	936.864i	−0.782777	+	1.35581i	0.147542	+	0.989056i	$0.452864\pi$
$691$	−540.899	+	936.864i	−0.782777	+	1.35581i	−0.930318	+	0.366753i	$0.880469\pi$
$692$	−1.63383			−0.00236103
$693$	−178.511	−	144.674i	−0.257592	−	0.208765i
$694$	267.571			0.385549
$695$	−283.927	+	106.506i	−0.408528	+	0.153246i
$696$	403.031	+	142.812i	0.579067	+	0.205189i
$697$	421.694	−	243.465i	0.605014	−	0.349305i
$698$	148.504	+	257.216i	0.212756	+	0.368505i
$699$	832.979	−	154.211i	1.19167	−	0.220616i
$700$	83.2480	−	243.480i	0.118926	−	0.347829i
$701$		−	143.009i		−	0.204007i	−0.994784	−	0.102003i	$-0.967475\pi$
$701$		−	143.009i		−	0.204007i	0.994784	−	0.102003i	$-0.0325253\pi$
$702$	−101.268	−	165.478i	−0.144257	−	0.235723i
$703$			1304.41i			1.85549i
$704$	309.272	+	178.558i	0.439306	+	0.253634i
$705$	−1225.68	−	677.994i	−1.73855	−	0.961694i
$706$	−63.9307	−	110.731i	−0.0905534	−	0.156843i
$707$	−189.652	−	328.487i	−0.268249	−	0.464621i
$708$	615.468	+	218.088i	0.869306	+	0.308033i
$709$	−424.541	+	735.327i	−0.598789	+	1.03713i	0.394211	+	0.919020i	$0.371018\pi$
$709$	−424.541	+	735.327i	−0.598789	+	1.03713i	−0.993000	+	0.118113i	$0.962315\pi$
$710$	89.3473	−	108.626i	0.125841	−	0.152995i
$711$	−48.7501	+	307.000i	−0.0685656	+	0.431786i
$712$			118.940i			0.167051i
$713$	34.9129	−	60.4709i	0.0489662	−	0.0848120i
$714$	40.7757	−	34.8116i	0.0571089	−	0.0487558i
$715$	102.812	−	618.492i	0.143794	−	0.865024i
$716$	−330.892	+	191.040i	−0.462139	+	0.266816i
$717$	840.522	−	717.582i	1.17228	−	1.00081i
$718$	−165.733	−	95.6858i	−0.230825	−	0.133267i
$719$		−	155.493i		−	0.216263i	−0.994137	−	0.108131i	$-0.965513\pi$
$719$		−	155.493i		−	0.216263i	0.994137	−	0.108131i	$-0.0344867\pi$
$720$	−543.061	−	181.295i	−0.754252	−	0.251798i
$721$	301.014			0.417495
$722$	−13.1480	+	22.7730i	−0.0182105	+	0.0315416i
$723$	371.846	−	1049.39i	0.514310	−	1.45144i
$724$	−224.015	−	388.006i	−0.309413	−	0.535920i
$725$	−574.037	−	657.476i	−0.791775	−	0.906863i
$726$	−55.9060	+	10.3500i	−0.0770056	+	0.0142562i
$727$	−540.769	−	312.213i	−0.743837	−	0.429454i	0.0796259	−	0.996825i	$-0.474627\pi$
$727$	−540.769	−	312.213i	−0.743837	−	0.429454i	−0.823463	+	0.567370i	$0.807961\pi$
$728$	−153.473			−0.210815
$729$	331.740	−	649.145i	0.455062	−	0.890460i
$730$	−39.7294	+	48.3020i	−0.0544238	+	0.0661671i
$731$	−715.133	−	412.882i	−0.978295	−	0.564819i
$732$	−170.169	+	31.5037i	−0.232472	+	0.0430379i
$733$	392.871	−	226.824i	0.535977	−	0.309447i	−0.207470	−	0.978241i	$-0.566523\pi$
$733$	392.871	−	226.824i	0.535977	−	0.309447i	0.743447	+	0.668795i	$0.233190\pi$
$734$	−120.354	+	69.4862i	−0.163970	+	0.0946679i
$735$	−531.325	+	319.890i	−0.722891	+	0.435225i
$736$	27.3378	−	47.3505i	0.0371438	−	0.0643350i
$737$	−143.636			−0.194892
$738$	67.9104	+	177.125i	0.0920195	+	0.240007i
$739$	827.126			1.11925			0.559625	−	0.828746i	$-0.310945\pi$
$739$	827.126			1.11925			0.559625	+	0.828746i	$0.310945\pi$
$740$	−420.507	−	1121.00i	−0.568253	−	1.51486i
$741$	−628.325	+	536.423i	−0.847943	+	0.723917i
$742$	12.4497	−	7.18785i	0.0167786	−	0.00968713i
$743$	301.483	+	522.184i	0.405765	+	0.702805i	0.994410	−	0.105586i	$-0.0336719\pi$
$743$	301.483	+	522.184i	0.405765	+	0.702805i	−0.588645	+	0.808391i	$0.700339\pi$
$744$	−234.165	−	274.283i	−0.314738	−	0.368660i
$745$	413.881	+	1103.34i	0.555546	+	1.48099i
$746$		−	165.321i		−	0.221611i
$747$	−106.349	+	669.723i	−0.142368	+	0.896550i
$748$		−	419.409i		−	0.560707i
$749$	153.340	+	88.5309i	0.204726	+	0.118199i
$750$	−133.135	−	146.958i	−0.177513	−	0.195945i
$751$	172.482	+	298.747i	0.229669	+	0.397799i	0.957710	−	0.287735i	$-0.0929023\pi$
$751$	172.482	+	298.747i	0.229669	+	0.397799i	−0.728041	+	0.685534i	$0.759569\pi$
$752$	594.026	+	1028.88i	0.789928	+	1.36820i
$753$	−167.357	−	903.987i	−0.222253	−	1.20051i
$754$	−125.429	+	217.250i	−0.166352	+	0.288130i
$755$	57.2932	+	47.1248i	0.0758850	+	0.0624170i
$756$	−145.062	−	237.039i	−0.191881	−	0.313544i
$757$		−	1248.67i		−	1.64950i	−0.565501	−	0.824748i	$-0.691317\pi$
$757$		−	1248.67i		−	1.64950i	0.565501	−	0.824748i	$-0.308683\pi$
$758$	−67.8223	+	117.472i	−0.0894754	+	0.154976i
$759$	11.9504	+	64.5508i	0.0157449	+	0.0850472i
$760$	67.8364	−	408.086i	0.0892584	−	0.536955i
$761$	−960.298	+	554.428i	−1.26189	+	0.728552i	−0.973440	−	0.228942i	$-0.926473\pi$
$761$	−960.298	+	554.428i	−1.26189	+	0.728552i	−0.288450	+	0.957495i	$0.593140\pi$
$762$	−54.9201	−	19.4606i	−0.0720737	−	0.0255389i
$763$	−35.4922	−	20.4914i	−0.0465167	−	0.0268564i
$764$		−	544.532i		−	0.712738i
$765$	109.964	+	538.614i	0.143744	+	0.704071i
$766$	−20.5324			−0.0268047
$767$	−397.482	+	688.459i	−0.518230	+	0.897600i
$768$	185.443	+	217.214i	0.241462	+	0.282830i
$769$	576.165	+	997.947i	0.749239	+	1.29772i	0.948188	+	0.317710i	$0.102914\pi$
$769$	576.165	+	997.947i	0.749239	+	1.29772i	−0.198949	+	0.980010i	$0.563753\pi$
$770$	−11.0690	+	66.5880i	−0.0143753	+	0.0864779i
$771$	−595.952	−	698.054i	−0.772960	−	0.905388i
$772$	420.151	+	242.574i	0.544237	+	0.314215i
$773$	1116.83			1.44480			0.722399	−	0.691476i	$-0.243039\pi$
$773$	1116.83			1.44480			0.722399	+	0.691476i	$0.243039\pi$
$774$	202.552	−	249.926i	0.261695	−	0.322902i
$775$	142.030	+	722.334i	0.183265	+	0.932044i
$776$	−220.515	−	127.314i	−0.284169	−	0.164065i
$777$	178.419	−	503.520i	0.229626	−	0.648031i
$778$	−140.590	+	81.1694i	−0.180706	+	0.104331i
$779$	699.588	−	403.907i	0.898059	−	0.518495i
$780$	367.049	−	663.553i	0.470576	−	0.850709i
$781$	245.456	−	425.143i	0.314285	−	0.544357i
$782$	−15.3179			−0.0195881
$783$	−942.324	+	24.1087i	−1.20348	+	0.0307901i
$784$	526.035			0.670963
$785$	−258.513	−	689.150i	−0.329316	−	0.877898i
$786$	−16.7309	−	90.3730i	−0.0212861	−	0.114978i
$787$	922.485	−	532.597i	1.17215	−	0.676743i	0.217967	−	0.975956i	$-0.430057\pi$
$787$	922.485	−	532.597i	1.17215	−	0.676743i	0.954186	+	0.299213i	$0.0967241\pi$
$788$	−347.207	−	601.381i	−0.440618	−	0.763173i
$789$	−146.977	+	414.785i	−0.186282	+	0.525710i
$790$	85.5006	−	32.0728i	0.108229	−	0.0405985i
$791$		−	229.091i		−	0.289622i
$792$	334.869	+	53.1756i	0.422814	+	0.0671410i
$793$		−	210.696i		−	0.265695i
$794$	21.5294	+	12.4300i	0.0271151	+	0.0156549i
$795$	2.70236	+	147.374i	0.00339919	+	0.185376i
$796$	84.0651	+	145.605i	0.105609	+	0.182921i
$797$	−94.4897	−	163.661i	−0.118557	−	0.205346i	0.800639	−	0.599147i	$-0.204493\pi$
$797$	−94.4897	−	163.661i	−0.118557	−	0.205346i	−0.919196	+	0.393801i	$0.871160\pi$
$798$	67.6467	−	57.7523i	0.0847702	−	0.0723713i
$799$	570.371	−	987.912i	0.713857	−	1.23644i
$800$	111.214	+	565.609i	0.139017	+	0.707011i
$801$	−93.8693	−	244.831i	−0.117190	−	0.305657i
$802$		−	300.694i		−	0.374930i
$803$	−109.145	+	189.045i	−0.135922	+	0.235424i
$804$	−163.746	−	58.0223i	−0.203664	−	0.0721670i
$805$	−32.3576	−	5.37882i	−0.0401957	−	0.00668176i
$806$	183.238	−	105.793i	0.227343	−	0.131256i
$807$	150.800	+	814.557i	0.186865	+	1.00936i
$808$	484.728	+	279.858i	0.599910	+	0.346358i
$809$			1105.36i			1.36633i	0.730266	+	0.683163i	$0.239396\pi$
$809$			1105.36i			1.36633i	−0.730266	+	0.683163i	$0.760604\pi$
$810$	−213.954	+	9.40150i	−0.264141	+	0.0116068i
$811$	4.70248			0.00579838			0.00289919	−	0.999996i	$-0.499077\pi$
$811$	4.70248			0.00579838			0.00289919	+	0.999996i	$0.499077\pi$
$812$	−179.672	+	311.200i	−0.221270	+	0.383251i
$813$	−899.186	+	166.468i	−1.10601	+	0.204758i
$814$	157.039	+	272.000i	0.192923	+	0.334152i
$815$	−47.4553	−	7.88853i	−0.0582274	−	0.00967918i
$816$	155.731	−	439.492i	0.190847	−	0.538593i
$817$	−1186.40	−	684.969i	−1.45214	−	0.838395i
$818$	−297.255			−0.363392
$819$	315.915	−	121.123i	0.385733	−	0.147892i
$820$	−471.011	+	572.644i	−0.574404	+	0.698346i
$821$	759.412	+	438.447i	0.924984	+	0.534040i	0.885222	−	0.465169i	$-0.154007\pi$
$821$	759.412	+	438.447i	0.924984	+	0.534040i	0.0397625	+	0.999209i	$0.487340\pi$
$822$	59.3079	+	69.4688i	0.0721507	+	0.0845120i
$823$	−992.214	+	572.855i	−1.20561	+	0.696057i	−0.961796	−	0.273766i	$-0.911731\pi$
$823$	−992.214	+	572.855i	−1.20561	+	0.696057i	−0.243810	+	0.969823i	$0.578397\pi$
$824$	−384.677	+	222.093i	−0.466841	+	0.269531i
$825$	−542.500	−	429.788i	−0.657576	−	0.520955i
$826$	42.7937	−	74.1208i	0.0518083	−	0.0897346i
$827$	−255.412			−0.308841			−0.154421	−	0.988005i	$-0.549351\pi$
$827$	−255.412			−0.308841			−0.154421	+	0.988005i	$0.549351\pi$
$828$	−12.4521	+	78.4157i	−0.0150387	+	0.0947050i
$829$	−829.155			−1.00019			−0.500093	−	0.865971i	$-0.666701\pi$
$829$	−829.155			−1.00019			−0.500093	+	0.865971i	$0.666701\pi$
$830$	186.520	−	69.9672i	0.224723	−	0.0842978i
$831$	1160.95	+	411.376i	1.39705	+	0.495037i
$832$	−455.396	+	262.923i	−0.547351	+	0.316013i
$833$	−252.544	−	437.419i	−0.303174	−	0.525113i
$834$	94.6046	−	17.5143i	0.113435	−	0.0210004i
$835$	−388.930	+	145.895i	−0.465784	+	0.174724i
$836$		−	695.796i		−	0.832292i
$837$	698.482	+	379.789i	0.834507	+	0.453750i
$838$			110.019i			0.131288i
$839$	393.010	+	226.904i	0.468427	+	0.270446i	0.715581	−	0.698530i	$-0.246162\pi$
$839$	393.010	+	226.904i	0.468427	+	0.270446i	−0.247154	+	0.968976i	$0.579495\pi$
$840$	−82.0045	+	148.248i	−0.0976244	+	0.176486i
$841$	188.934	+	327.244i	0.224654	+	0.389113i
$842$	104.297	+	180.647i	0.123868	+	0.214545i
$843$	−293.614	−	104.040i	−0.348297	−	0.123417i
$844$	−257.098	+	445.307i	−0.304619	+	0.527615i
$845$	60.4054	+	49.6847i	0.0714856	+	0.0587984i
$846$	345.257	+	279.813i	0.408106	+	0.330748i
$847$		−	99.1550i		−	0.117066i
$848$	62.5104	−	108.271i	0.0737151	−	0.127678i
$849$	−642.210	+	548.276i	−0.756431	+	0.645791i
$850$	121.652	−	106.213i	0.143120	−	0.124957i
$851$	−132.175	+	76.3110i	−0.155317	+	0.0896722i
$852$	451.560	−	385.512i	0.530000	−	0.452479i
$853$	−14.0948	−	8.13764i	−0.0165238	−	0.00954002i	0.491715	−	0.870756i	$-0.336370\pi$
$853$	−14.0948	−	8.13764i	−0.0165238	−	0.00954002i	−0.508239	+	0.861216i	$0.669703\pi$
$854$			22.6839i			0.0265620i
$855$	182.430	+	893.557i	0.213369	+	1.04510i
$856$	−261.279			−0.305232
$857$	−530.849	+	919.457i	−0.619427	+	1.07288i	0.370164	+	0.928967i	$0.379302\pi$
$857$	−530.849	+	919.457i	−0.619427	+	1.07288i	−0.989590	+	0.143912i	$0.954032\pi$
$858$	−66.4400	+	187.501i	−0.0774359	+	0.218533i
$859$	−811.869	−	1406.20i	−0.945133	−	1.63702i	−0.755485	−	0.655166i	$-0.772599\pi$
$859$	−811.869	−	1406.20i	−0.945133	−	1.63702i	−0.189648	−	0.981852i	$-0.560735\pi$
$860$	1240.40	+	206.193i	1.44233	+	0.239759i
$861$	−325.298	+	60.2230i	−0.377814	+	0.0699454i
$862$	99.1522	+	57.2456i	0.115026	+	0.0664102i
$863$	−687.358			−0.796475			−0.398238	−	0.917282i	$-0.630378\pi$
$863$	−687.358			−0.796475			−0.398238	+	0.917282i	$0.630378\pi$
$864$	546.932	+	297.386i	0.633024	+	0.344197i
$865$	−1.69583	−	1.39486i	−0.00196050	−	0.00161255i
$866$	281.190	+	162.345i	0.324700	+	0.187466i
$867$	412.294	−	76.3287i	0.475541	−	0.0880377i
$868$	262.480	−	151.543i	0.302397	−	0.174589i
$869$	276.027	−	159.364i	0.317637	−	0.183388i
$870$	142.833	+	237.241i	0.164176	+	0.272690i
$871$	105.750	−	183.165i	0.121412	−	0.210293i
$872$	60.4758			0.0693530
$873$	554.395	+	88.0354i	0.635046	+	0.100842i
$874$	−25.4122			−0.0290758
$875$	294.274	−	181.648i	0.336314	−	0.207598i
$876$	−200.792	+	171.423i	−0.229214	+	0.195688i
$877$	−1345.72	+	776.955i	−1.53446	+	0.885923i	−0.535316	+	0.844652i	$0.679807\pi$
$877$	−1345.72	+	776.955i	−1.53446	+	0.885923i	−0.999148	+	0.0412710i	$0.986859\pi$
$878$	−137.407	−	237.995i	−0.156500	−	0.271065i
$879$	796.040	+	932.422i	0.905620	+	1.06078i
$880$	206.181	+	549.642i	0.234296	+	0.624593i
$881$			452.136i			0.513208i	0.966517	+	0.256604i	$0.0826036\pi$
$881$			452.136i			0.513208i	−0.966517	+	0.256604i	$0.917396\pi$
$882$	183.730	−	70.4427i	0.208310	−	0.0798670i
$883$			1014.46i			1.14888i	0.818546	+	0.574441i	$0.194781\pi$
$883$			1014.46i			1.14888i	−0.818546	+	0.574441i	$0.805219\pi$
$884$	534.832	+	308.785i	0.605013	+	0.349304i
$885$	452.635	+	751.810i	0.511453	+	0.849503i
$886$	−132.634	−	229.729i	−0.149700	−	0.259287i
$887$	−104.060	−	180.237i	−0.117317	−	0.203199i	0.801387	−	0.598147i	$-0.204096\pi$
$887$	−104.060	−	180.237i	−0.117317	−	0.203199i	−0.918704	+	0.394948i	$0.870763\pi$
$888$	143.497	+	775.109i	0.161596	+	0.872870i
$889$	50.8071	−	88.0004i	0.0571508	−	0.0989881i
$890$	−48.9328	+	59.4912i	−0.0549806	+	0.0668441i
$891$	−731.275	+	154.825i	−0.820735	+	0.173765i
$892$		−	216.545i		−	0.242764i
$893$	946.242	−	1638.94i	1.05962	−	1.83532i
$894$	−68.0604	−	367.632i	−0.0761302	−	0.411222i
$895$	−506.546	−	84.2035i	−0.565974	−	0.0940821i
$896$	270.006	−	155.888i	0.301346	−	0.173982i
$897$	−91.1138	−	32.2856i	−0.101576	−	0.0359929i
$898$	−76.1971	−	43.9924i	−0.0848521	−	0.0489894i
$899$		−	1028.05i		−	1.14355i
$900$	−444.838	−	709.106i	−0.494265	−	0.787895i
$901$	−120.042			−0.133232
$902$	97.2536	−	168.448i	0.107820	−	0.186750i
$903$	364.276	+	426.686i	0.403407	+	0.472520i
$904$	169.028	+	292.765i	0.186978	+	0.323855i
$905$	98.7376	−	593.980i	0.109102	−	0.656331i
$906$	−15.2823	−	17.9005i	−0.0168679	−	0.0197577i
$907$	205.665	+	118.741i	0.226753	+	0.130916i	0.609073	−	0.793114i	$-0.291542\pi$
$907$	205.665	+	118.741i	0.226753	+	0.130916i	−0.382320	+	0.924030i	$0.624875\pi$
$908$	−1393.59			−1.53479
$909$	−1218.65	−	193.516i	−1.34065	−	0.212889i
$910$	−76.7639	−	63.1399i	−0.0843559	−	0.0693845i
$911$	1167.48	+	674.042i	1.28153	+	0.739893i	0.977128	−	0.212650i	$-0.0682095\pi$
$911$	1167.48	+	674.042i	1.28153	+	0.739893i	0.304404	+	0.952543i	$0.401543\pi$
$912$	258.357	−	729.114i	0.283286	−	0.799467i
$913$	602.155	−	347.654i	0.659534	−	0.380782i
$914$	−381.031	+	219.988i	−0.416883	+	0.240687i
$915$	−203.523	−	112.580i	−0.222429	−	0.123038i
$916$	125.904	−	218.073i	0.137450	−	0.238071i
$917$	160.286			0.174793
$918$	−4.46079	−	174.357i	−0.00485925	−	0.189931i
$919$	−153.887			−0.167450			−0.0837250	−	0.996489i	$-0.526682\pi$
$919$	−153.887			−0.167450			−0.0837250	+	0.996489i	$0.526682\pi$
$920$	45.3196	−	17.0002i	0.0492604	−	0.0184785i
$921$	−95.0967	−	513.670i	−0.103254	−	0.557731i
$922$	−198.871	+	114.818i	−0.215696	+	0.124532i
$923$	361.429	+	626.014i	0.391581	+	0.678238i
$924$	−95.1722	+	268.587i	−0.103000	+	0.290679i
$925$	520.570	−	1522.54i	0.562779	−	1.64599i
$926$		−	92.0376i		−	0.0993926i
$927$	616.555	−	760.759i	0.665108	−	0.820667i
$928$		−	804.992i		−	0.867448i
$929$	−665.491	−	384.221i	−0.716352	−	0.413586i	0.0970567	−	0.995279i	$-0.469057\pi$
$929$	−665.491	−	384.221i	−0.716352	−	0.413586i	−0.813408	+	0.581693i	$0.802391\pi$
$930$	−4.28214	−	233.527i	−0.00460445	−	0.251105i
$931$	−418.968	−	725.674i	−0.450020	−	0.779457i
$932$	−525.276	−	909.805i	−0.563601	−	0.976186i
$933$	−625.904	+	534.355i	−0.670851	+	0.572728i
$934$	35.5461	−	61.5677i	0.0380579	−	0.0659183i
$935$	358.064	−	435.325i	0.382956	−	0.465588i
$936$	−314.353	+	387.876i	−0.335848	+	0.414398i
$937$		−	359.563i		−	0.383738i	−0.981421	−	0.191869i	$-0.938545\pi$
$937$		−	359.563i		−	0.383738i	0.981421	−	0.191869i	$-0.0614549\pi$
$938$	−11.3853	+	19.7199i	−0.0121378	+	0.0210233i
$939$	−602.619	−	213.534i	−0.641767	−	0.227406i
$940$	−284.842	+	1713.54i	−0.303023	+	1.82291i
$941$	183.507	−	105.948i	0.195013	−	0.112591i	−0.399314	−	0.916814i	$-0.630752\pi$
$941$	183.507	−	105.948i	0.195013	−	0.112591i	0.594327	+	0.804223i	$0.297418\pi$
$942$	42.5109	+	229.625i	0.0451284	+	0.243764i
$943$	81.8551	+	47.2591i	0.0868029	+	0.0501157i
$944$		−	744.325i		−	0.788479i
$945$	51.8018	−	369.879i	0.0548167	−	0.391406i
$946$	−329.856			−0.348685
$947$	773.466	−	1339.68i	0.816754	−	1.41466i	−0.0913074	−	0.995823i	$-0.529105\pi$
$947$	773.466	−	1339.68i	0.816754	−	1.41466i	0.908062	−	0.418837i	$-0.137562\pi$
$948$	379.048	−	70.1738i	0.399839	−	0.0740230i
$949$	−160.714	−	278.365i	−0.169351	−	0.293324i
$950$	201.819	−	176.207i	0.212441	−	0.185481i
$951$	−242.605	+	684.660i	−0.255105	+	0.719937i
$952$	−119.490	−	68.9874i	−0.125514	−	0.0724657i
$953$	1453.97			1.52568			0.762838	−	0.646589i	$-0.223805\pi$
$953$	1453.97			1.52568			0.762838	+	0.646589i	$0.223805\pi$
$954$	7.33429	−	46.1871i	0.00768794	−	0.0484141i
$955$	464.885	−	565.196i	0.486791	−	0.591828i
$956$	−1186.93	−	685.276i	−1.24156	−	0.716816i
$957$	627.566	+	735.084i	0.655764	+	0.768112i
$958$	326.317	−	188.399i	0.340624	−	0.196659i
$959$	−137.955	+	79.6486i	−0.143853	+	0.0830538i
$960$	10.6423	+	580.378i	0.0110857	+	0.604560i
$961$	46.9491	−	81.3183i	0.0488544	−	0.0846184i
$962$	−462.473			−0.480741
$963$	537.827	−	206.205i	0.558491	−	0.214128i
$964$	−1380.66			−1.43222
$965$	229.001	+	610.476i	0.237307	+	0.632618i
$966$	9.80948	+	3.47593i	0.0101547	+	0.00359827i
$967$	331.339	−	191.299i	0.342646	−	0.197827i	−0.318795	−	0.947824i	$-0.603278\pi$
$967$	331.339	−	191.299i	0.342646	−	0.197827i	0.661442	+	0.749997i	$0.269945\pi$
$968$	73.1583	+	126.714i	0.0755768	+	0.130903i
$969$	−730.321	+	135.206i	−0.753686	+	0.139531i
$970$	−57.9187	−	154.401i	−0.0597100	−	0.159177i
$971$			1474.96i			1.51901i	0.650503	+	0.759504i	$0.274558\pi$
$971$			1474.96i			1.51901i	−0.650503	+	0.759504i	$0.725442\pi$
$972$	−896.199	−	118.901i	−0.922016	−	0.122326i
$973$			167.791i			0.172447i
$974$	−95.5557	−	55.1691i	−0.0981064	−	0.0566418i
$975$	947.476	−	375.371i	0.971771	−	0.384996i
$976$	98.6373	+	170.845i	0.101063	+	0.175046i
$977$	708.905	+	1227.86i	0.725593	+	1.25676i	0.958729	+	0.284320i	$0.0917680\pi$
$977$	708.905	+	1227.86i	0.725593	+	1.25676i	−0.233136	+	0.972444i	$0.574899\pi$
$978$	14.3865	+	5.09777i	0.0147101	+	0.00521245i
$979$	−134.429	+	232.838i	−0.137313	+	0.237832i
$980$	593.997	+	488.575i	0.606119	+	0.498546i
$981$	−124.486	+	47.7284i	−0.126897	+	0.0486528i
$982$		−	217.636i		−	0.221625i
$983$	222.160	−	384.792i	0.226002	−	0.391447i	−0.730618	−	0.682787i	$-0.760768\pi$
$983$	222.160	−	384.792i	0.226002	−	0.391447i	0.956620	+	0.291340i	$0.0941011\pi$
$984$	371.277	−	316.972i	0.377314	−	0.322126i
$985$	153.036	−	920.625i	0.155367	−	0.934644i
$986$	−195.311	+	112.763i	−0.198084	+	0.114364i
$987$	−589.440	+	503.225i	−0.597203	+	0.509853i
$988$	887.282	+	512.272i	0.898058	+	0.518494i
$989$		−	160.289i		−	0.162072i
$990$	145.617	+	164.365i	0.147088	+	0.166025i
$991$	1177.77			1.18847			0.594235	−	0.804291i	$-0.297455\pi$
$991$	1177.77			1.18847			0.594235	+	0.804291i	$0.297455\pi$
$992$	−339.483	+	588.002i	−0.342221	+	0.592744i
$993$	−199.325	+	562.517i	−0.200730	+	0.566483i
$994$	−38.9121	−	67.3978i	−0.0391470	−	0.0678046i
$995$	−37.0528	+	222.900i	−0.0372390	+	0.224020i
$996$	826.896	−	153.085i	0.830217	−	0.153700i
$997$	−87.6487	−	50.6040i	−0.0879125	−	0.0507563i	0.455399	−	0.890287i	$-0.349497\pi$
$997$	−87.6487	−	50.6040i	−0.0879125	−	0.0507563i	−0.543312	+	0.839531i	$0.682830\pi$
$998$	−176.933			−0.177287
$999$	−907.107	−	1482.26i	−0.908016	−	1.48375i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.3.h.a.29.5	yes	20
3.2	odd	2		135.3.h.a.89.6		20
5.2	odd	4		225.3.j.e.101.5		20
5.3	odd	4		225.3.j.e.101.6		20
5.4	even	2	inner	45.3.h.a.29.6	yes	20
9.2	odd	6		405.3.d.a.404.10		20
9.4	even	3		135.3.h.a.44.5		20
9.5	odd	6	inner	45.3.h.a.14.6	yes	20
9.7	even	3		405.3.d.a.404.11		20
15.2	even	4		675.3.j.e.251.6		20
15.8	even	4		675.3.j.e.251.5		20
15.14	odd	2		135.3.h.a.89.5		20
45.4	even	6		135.3.h.a.44.6		20
45.13	odd	12		675.3.j.e.476.5		20
45.14	odd	6	inner	45.3.h.a.14.5	✓	20
45.22	odd	12		675.3.j.e.476.6		20
45.23	even	12		225.3.j.e.176.6		20
45.29	odd	6		405.3.d.a.404.12		20
45.32	even	12		225.3.j.e.176.5		20
45.34	even	6		405.3.d.a.404.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.5	✓	20	45.14	odd	6	inner
45.3.h.a.14.6	yes	20	9.5	odd	6	inner
45.3.h.a.29.5	yes	20	1.1	even	1	trivial
45.3.h.a.29.6	yes	20	5.4	even	2	inner
135.3.h.a.44.5		20	9.4	even	3
135.3.h.a.44.6		20	45.4	even	6
135.3.h.a.89.5		20	15.14	odd	2
135.3.h.a.89.6		20	3.2	odd	2
225.3.j.e.101.5		20	5.2	odd	4
225.3.j.e.101.6		20	5.3	odd	4
225.3.j.e.176.5		20	45.32	even	12
225.3.j.e.176.6		20	45.23	even	12
405.3.d.a.404.9		20	45.34	even	6
405.3.d.a.404.10		20	9.2	odd	6
405.3.d.a.404.11		20	9.7	even	3
405.3.d.a.404.12		20	45.29	odd	6
675.3.j.e.251.5		20	15.8	even	4
675.3.j.e.251.6		20	15.2	even	4
675.3.j.e.476.5		20	45.13	odd	12
675.3.j.e.476.6		20	45.22	odd	12

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:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.264396 + 0.457947i) q^{2} +(-2.94987 + 0.546115i) q^{3} +(1.86019 + 3.22194i) q^{4} +(-0.819902 + 4.93232i) q^{5} +(0.529842 - 1.49528i) q^{6} +(2.39593 + 1.38329i) q^{7} -4.08247 q^{8} +(8.40352 - 3.22194i) q^{9} +O(q^{10})\)	\(q+(-0.264396 + 0.457947i) q^{2} +(-2.94987 + 0.546115i) q^{3} +(1.86019 + 3.22194i) q^{4} +(-0.819902 + 4.93232i) q^{5} +(0.529842 - 1.49528i) q^{6} +(2.39593 + 1.38329i) q^{7} -4.08247 q^{8} +(8.40352 - 3.22194i) q^{9} +(-2.04196 - 1.67955i) q^{10} +(-7.99186 - 4.61410i) q^{11} +(-7.24688 - 8.48845i) q^{12} +(11.7678 - 6.79417i) q^{13} +(-1.26695 + 0.731472i) q^{14} +(-0.275006 - 14.9975i) q^{15} +(-6.36137 + 11.0182i) q^{16} +12.2161 q^{17} +(-0.746375 + 4.70023i) q^{18} +20.2664 q^{19} +(-17.4168 + 6.53337i) q^{20} +(-7.82313 - 2.77208i) q^{21} +(4.22603 - 2.43990i) q^{22} +(1.18564 + 2.05358i) q^{23} +(12.0428 - 2.22950i) q^{24} +(-23.6555 - 8.08804i) q^{25} +7.18539i q^{26} +(-23.0298 + 14.0936i) q^{27} +10.2927i q^{28} +(30.2349 + 17.4561i) q^{29} +(6.94076 + 3.83933i) q^{30} +(-14.7233 - 25.5015i) q^{31} +(-11.5288 - 19.9684i) q^{32} +(26.0948 + 9.24654i) q^{33} +(-3.22989 + 5.59433i) q^{34} +(-8.78726 + 10.6833i) q^{35} +(26.0131 + 21.0822i) q^{36} +64.3630i q^{37} +(-5.35836 + 9.28095i) q^{38} +(-31.0032 + 26.4685i) q^{39} +(3.34723 - 20.1360i) q^{40} +(34.5195 - 19.9299i) q^{41} +(3.33787 - 2.84965i) q^{42} +(-58.5402 - 33.7982i) q^{43} -34.3324i q^{44} +(9.00159 + 44.0905i) q^{45} -1.25391 q^{46} +(46.6901 - 80.8696i) q^{47} +(12.7480 - 35.9764i) q^{48} +(-20.6730 - 35.8067i) q^{49} +(9.95831 - 8.69452i) q^{50} +(-36.0360 + 6.67141i) q^{51} +(43.7808 + 25.2769i) q^{52} -9.82656 q^{53} +(-0.365157 - 14.2727i) q^{54} +(29.3108 - 35.6353i) q^{55} +(-9.78131 - 5.64724i) q^{56} +(-59.7834 + 11.0678i) q^{57} +(-15.9880 + 9.23066i) q^{58} +(-50.6655 + 29.2517i) q^{59} +(47.8095 - 28.7842i) q^{60} +(7.75283 - 13.4283i) q^{61} +15.5711 q^{62} +(24.5911 + 3.90496i) q^{63} -38.6984 q^{64} +(23.8625 + 63.6133i) q^{65} +(-11.1338 + 9.50529i) q^{66} +(13.4796 - 7.78243i) q^{67} +(22.7243 + 39.3596i) q^{68} +(-4.61897 - 5.41031i) q^{69} +(-2.56908 - 6.84872i) q^{70} +53.1970i q^{71} +(-34.3071 + 13.1535i) q^{72} -23.6547i q^{73} +(-29.4748 - 17.0173i) q^{74} +(74.1978 + 10.9401i) q^{75} +(37.6994 + 65.2973i) q^{76} +(-12.7653 - 22.1101i) q^{77} +(-3.92405 - 21.1960i) q^{78} +(-17.2692 + 29.9112i) q^{79} +(-49.1297 - 40.4102i) q^{80} +(60.2382 - 54.1513i) q^{81} +21.0775i q^{82} +(-37.6730 + 65.2516i) q^{83} +(-5.62102 - 30.3623i) q^{84} +(-10.0160 + 60.2538i) q^{85} +(30.9555 - 17.8722i) q^{86} +(-98.7223 - 34.9817i) q^{87} +(32.6265 + 18.8369i) q^{88} -29.1344i q^{89} +(-22.5711 - 7.53509i) q^{90} +37.5932 q^{91} +(-4.41101 + 7.64010i) q^{92} +(57.3586 + 67.1856i) q^{93} +(24.6893 + 42.7631i) q^{94} +(-16.6165 + 99.9605i) q^{95} +(44.9135 + 52.6083i) q^{96} +(54.0151 + 31.1857i) q^{97} +21.8634 q^{98} +(-82.0261 - 13.0254i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9}+O(q^{10}) \) 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31} - 4 q^{34} + 432 q^{36} + 240 q^{39} - 34 q^{40} + 102 q^{41} - 162 q^{45} + 116 q^{46} - 40 q^{49} - 408 q^{50} - 156 q^{51} - 270 q^{54} + 36 q^{55} - 618 q^{56} + 120 q^{59} + 330 q^{60} - 50 q^{61} + 140 q^{64} + 492 q^{65} - 768 q^{66} + 162 q^{69} - 54 q^{70} + 504 q^{74} + 276 q^{75} - 96 q^{76} - 128 q^{79} + 846 q^{81} + 450 q^{84} - 74 q^{85} + 1488 q^{86} - 990 q^{90} - 288 q^{91} + 218 q^{94} - 762 q^{95} - 474 q^{96} - 468 q^{99}+O(q^{100}) \) 20 * q - 18 * q^4 - 12 * q^5 + 12 * q^6 - 18 * q^9 + 4 * q^10 - 24 * q^11 + 30 * q^14 + 24 * q^15 - 26 * q^16 - 8 * q^19 + 144 * q^20 - 96 * q^21 - 102 * q^24 + 2 * q^25 - 114 * q^29 - 48 * q^30 + 28 * q^31 - 4 * q^34 + 432 * q^36 + 240 * q^39 - 34 * q^40 + 102 * q^41 - 162 * q^45 + 116 * q^46 - 40 * q^49 - 408 * q^50 - 156 * q^51 - 270 * q^54 + 36 * q^55 - 618 * q^56 + 120 * q^59 + 330 * q^60 - 50 * q^61 + 140 * q^64 + 492 * q^65 - 768 * q^66 + 162 * q^69 - 54 * q^70 + 504 * q^74 + 276 * q^75 - 96 * q^76 - 128 * q^79 + 846 * q^81 + 450 * q^84 - 74 * q^85 + 1488 * q^86 - 990 * q^90 - 288 * q^91 + 218 * q^94 - 762 * q^95 - 474 * q^96 - 468 * q^99

Introduction

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