LMFDB - Embedded newform 45.3.h.a.29.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,3,Mod(14,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

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

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

Self dual:	no
Analytic conductor:	$1.22616118962$
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			29.6
Root			$0.315300 + 1.70311i$ of defining polynomial
Character	$\chi$	$=$	45.29
Dual form			45.3.h.a.14.6

$q$-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} +(-4.68146 - 1.75610i) 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} +(-14.7688 - 2.62366i) q^{15} +(-6.36137 + 11.0182i) q^{16} -12.2161 q^{17} +(0.746375 - 4.70023i) q^{18} +20.2664 q^{19} +(-3.05035 - 18.3501i) 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} +(18.8322 + 16.4423i) q^{25} +7.18539i q^{26} +(23.0298 - 14.0936i) q^{27} -10.2927i q^{28} +(30.2349 + 17.4561i) q^{29} +(-5.10629 + 6.06962i) 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} +(-19.1119 - 7.16923i) q^{40} +(34.5195 - 19.9299i) q^{41} +(-3.33787 + 2.84965i) q^{42} +(58.5402 + 33.7982i) q^{43} -34.3324i q^{44} +(-44.9988 + 0.325975i) q^{45} -1.25391 q^{46} +(-46.6901 + 80.8696i) q^{47} +(-12.7480 + 35.9764i) q^{48} +(-20.6730 - 35.8067i) q^{49} +(12.5088 - 4.27688i) 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} +(-19.0194 - 52.4646i) q^{60} +(7.75283 - 13.4283i) q^{61} -15.5711 q^{62} +(-24.5911 - 3.90496i) q^{63} -38.6984 q^{64} +(67.0220 - 11.1411i) 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} +(7.21571 - 1.19947i) q^{70} +53.1970i q^{71} +(34.3071 - 13.1535i) q^{72} +23.6547i q^{73} +(-29.4748 - 17.0173i) q^{74} +(64.5320 + 38.2180i) 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} +(57.1893 + 21.4527i) q^{85} +(30.9555 - 17.8722i) q^{86} +(98.7223 + 34.9817i) q^{87} +(-32.6265 - 18.8369i) q^{88} -29.1344i q^{89} +(-11.7482 + 20.6932i) q^{90} +37.5932 q^{91} +(4.41101 - 7.64010i) q^{92} +(-57.3586 - 67.1856i) q^{93} +(24.6893 + 42.7631i) q^{94} +(-94.8766 - 35.5899i) 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} + 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}+ \cdots - 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

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	−0.792326	−	0.610098i	$-0.791130\pi$
$2$	0.264396	−	0.457947i	0.132198	−	0.228973i	0.924524	+	0.381125i	$0.124463\pi$
$3$	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
$5$	−4.68146	−	1.75610i	−0.936293	−	0.351221i
$5$	−4.68146	−	1.75610i	−0.936293	−	0.351221i
$6$	0.529842	−	1.49528i	0.0883070	−	0.249213i
$7$	−2.39593	−	1.38329i	−0.342276	−	0.197613i	0.319002	−	0.947754i	$-0.396652\pi$
$7$	−2.39593	−	1.38329i	−0.342276	−	0.197613i	−0.661278	+	0.750141i	$0.729986\pi$
$8$	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	−0.878890	−	0.477025i	$-0.841715\pi$
$13$	−11.7678	+	6.79417i	−0.905218	+	0.522628i	−0.0263288	+	0.999653i	$0.508382\pi$
$14$	−1.26695	+	0.731472i	−0.0904962	+	0.0522480i
$15$	−14.7688	−	2.62366i	−0.984584	−	0.174911i
$16$	−6.36137	+	11.0182i	−0.397586	+	0.688639i
$17$	−12.2161			−0.718595			−0.359297	−	0.933223i	$-0.616984\pi$
$17$	−12.2161			−0.718595			−0.359297	+	0.933223i	$0.616984\pi$
$18$	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	$0.320941\pi$
$20$	−3.05035	−	18.3501i	−0.152517	−	0.917505i
$21$	−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	0.839099	−	0.543978i	$-0.183083\pi$
$23$	−1.18564	−	2.05358i	−0.0515494	−	0.0892861i	−0.890649	+	0.454692i	$0.849749\pi$
$24$	12.0428	−	2.22950i	0.501782	−	0.0928958i
$25$	18.8322	+	16.4423i	0.753288	+	0.657690i
$26$			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	$0.461063\pi$
$30$	−5.10629	+	6.06962i	−0.170210	+	0.202321i
$31$	−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	$-0.664267\pi$
$37$		−	64.3630i		−	1.73954i	0.493457	−	0.869770i	$-0.335733\pi$
$38$	5.35836	−	9.28095i	0.141009	−	0.244235i
$39$	−31.0032	+	26.4685i	−0.794955	+	0.678680i
$40$	−19.1119	−	7.16923i	−0.477798	−	0.179231i
$41$	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	0.989810	−	0.142393i	$-0.0454796\pi$
$43$	58.5402	+	33.7982i	1.36140	+	0.786004i	0.371589	+	0.928397i	$0.378813\pi$
$44$		−	34.3324i		−	0.780282i
$45$	−44.9988	+	0.325975i	−0.999974	+	0.00724389i
$46$	−1.25391			−0.0272588
$47$	−46.6901	+	80.8696i	−0.993406	+	1.72063i	−0.397414	+	0.917639i	$0.630092\pi$
$47$	−46.6901	+	80.8696i	−0.993406	+	1.72063i	−0.595992	+	0.802991i	$0.703241\pi$
$48$	−12.7480	+	35.9764i	−0.265584	+	0.749509i
$49$	−20.6730	−	35.8067i	−0.421898	−	0.730749i
$50$	12.5088	−	4.27688i	0.250177	−	0.0855377i
$51$	−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	$-0.470449\pi$
$53$	9.82656			0.185407			0.0927034	+	0.995694i	$0.470449\pi$
$54$	−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	$0.498456\pi$
$60$	−19.0194	−	52.4646i	−0.316990	−	0.874411i
$61$	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
$65$	67.0220	−	11.1411i	1.03111	−	0.171402i
$66$	−11.1338	+	9.50529i	−0.168694	+	0.144019i
$67$	−13.4796	+	7.78243i	−0.201188	+	0.116156i	−0.597209	−	0.802085i	$-0.703724\pi$
$67$	−13.4796	+	7.78243i	−0.201188	+	0.116156i	0.396022	+	0.918241i	$0.370390\pi$
$68$	−22.7243	−	39.3596i	−0.334181	−	0.578818i
$69$	−4.61897	−	5.41031i	−0.0669415	−	0.0784103i
$70$	7.21571	−	1.19947i	0.103082	−	0.0171353i
$71$			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	$0.0518005\pi$
$73$			23.6547i			0.324037i	−0.986788	+	0.162019i	$0.948200\pi$
$74$	−29.4748	−	17.0173i	−0.398308	−	0.229963i
$75$	64.5320	+	38.2180i	0.860427	+	0.509574i
$76$	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	−0.544732	−	0.838610i	$-0.683369\pi$
$83$	37.6730	−	65.2516i	0.453892	−	0.786163i	0.998624	+	0.0524468i	$0.0167020\pi$
$84$	−5.62102	−	30.3623i	−0.0669169	−	0.361456i
$85$	57.1893	+	21.4527i	0.672815	+	0.252385i
$86$	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	$-0.0523352\pi$
$90$	−11.7482	+	20.6932i	−0.130536	+	0.229925i
$91$	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
$95$	−94.8766	−	35.5899i	−0.998701	−	0.374631i
$96$	44.9135	+	52.6083i	0.467849	+	0.548003i
$97$	−54.0151	−	31.1857i	−0.556857	−	0.321502i	0.195026	−	0.980798i	$-0.437521\pi$
$97$	−54.0151	−	31.1857i	−0.556857	−	0.321502i	−0.751883	+	0.659296i	$0.770854\pi$
$98$	−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	−0.881979	−	0.471288i	$-0.843789\pi$
$103$	−94.2266	+	54.4017i	−0.914821	+	0.528172i	−0.0328419	+	0.999461i	$0.510456\pi$
$104$	−48.0418	+	27.7370i	−0.461941	+	0.266702i
$105$	31.7556	+	26.7156i	0.302435	+	0.254434i
$106$	2.59810	−	4.50004i	0.0245104	−	0.0424532i
$107$	−64.0002			−0.598133			−0.299067	−	0.954232i	$-0.596675\pi$
$107$	−64.0002			−0.598133			−0.299067	+	0.954232i	$0.596675\pi$
$108$	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	$0.521646\pi$
$110$	24.0687	−	4.00095i	0.218806	−	0.0363723i
$111$	−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	0.989000	−	0.147916i	$-0.0472566\pi$
$113$	41.4033	+	71.7126i	0.366401	+	0.634625i	−0.622599	+	0.782541i	$0.713923\pi$
$114$	10.7380	−	30.3039i	0.0941931	−	0.265824i
$115$	1.94421	+	11.6959i	0.0169062	+	0.101703i
$116$			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
$120$	−60.2930	−	10.7110i	−0.502442	−	0.0892585i
$121$	−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	$0.0461904\pi$
$127$			36.7291i			0.289206i	−0.989490	+	0.144603i	$0.953810\pi$
$128$	−56.3468	+	97.5955i	−0.440209	+	0.762465i
$129$	191.144	+	67.7307i	1.48174	+	0.525044i
$130$	12.6183	−	33.6381i	0.0970637	−	0.258755i
$131$	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
$135$	−132.563	+	25.5361i	−0.981947	+	0.189157i
$136$	−49.8719			−0.366705
$137$	28.7895	−	49.8649i	0.210143	−	0.363978i	−0.741616	−	0.670824i	$-0.765941\pi$
$137$	28.7895	−	49.8649i	0.210143	−	0.363978i	0.951759	+	0.306847i	$0.0992738\pi$
$138$	−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	$0.763327\pi$
$140$	−18.0751	+	48.1851i	−0.129108	+	0.344179i
$141$	−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	$0.0429572\pi$
$150$	34.5638	−	19.4475i	0.230425	−	0.129650i
$151$	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
$155$	24.1433	+	145.240i	0.155763	+	0.937032i
$156$	−142.952	−	50.6542i	−0.916359	−	0.324707i
$157$	127.486	−	73.6041i	0.812013	−	0.468816i	−0.0356413	−	0.999365i	$-0.511347\pi$
$157$	127.486	−	73.6041i	0.812013	−	0.468816i	0.847654	+	0.530549i	$0.178014\pi$
$158$	9.13182	+	15.8168i	0.0577963	+	0.100106i
$159$	28.9871	−	5.36643i	0.182309	−	0.0337512i
$160$	−18.9049	−	113.727i	−0.118156	−	0.710795i
$161$			6.56031i			0.0407473i
$162$	−8.87170	−	41.9032i	−0.0547636	−	0.258662i
$163$		−	9.62130i		−	0.0590264i	−0.999564	−	0.0295132i	$-0.990604\pi$
$163$		−	9.62130i		−	0.0590264i	0.999564	−	0.0295132i	$-0.00939571\pi$
$164$	128.426	+	74.1466i	0.783084	+	0.452114i
$165$	105.924	+	89.1125i	0.641964	+	0.540076i
$166$	−19.9212	−	34.5045i	−0.120007	−	0.207858i
$167$	−41.5393	−	71.9482i	−0.248738	−	0.430828i	0.714438	−	0.699699i	$-0.246683\pi$
$167$	−41.5393	−	71.9482i	−0.248738	−	0.430828i	−0.963176	+	0.268872i	$0.913349\pi$
$168$	−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	−0.865390	−	0.501099i	$-0.832929\pi$
$173$	0.219578	−	0.380321i	0.00126924	−	0.00219839i	0.866659	+	0.498900i	$0.166263\pi$
$174$	42.1215	−	35.9606i	0.242078	−	0.206670i
$175$	−22.3762	−	65.4449i	−0.127864	−	0.373971i
$176$	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	$0.907385\pi$
$180$	−84.7566	−	144.377i	−0.470870	−	0.802096i
$181$	−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
$185$	−113.028	+	301.313i	−0.610962	+	1.62872i
$186$	−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	−0.763174	−	0.646193i	$-0.776360\pi$
$193$	−112.932	+	65.2014i	−0.585141	+	0.337831i	0.178033	+	0.984025i	$0.443027\pi$
$194$	−28.5627	+	16.4907i	−0.147231	+	0.0850036i
$195$	191.622	−	69.4666i	0.982677	−	0.356239i
$196$	76.9115	−	133.215i	0.392405	−	0.679666i
$197$	186.652			0.947470			0.473735	−	0.880668i	$-0.342906\pi$
$197$	186.652			0.947470			0.473735	+	0.880668i	$0.342906\pi$
$198$	−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	$0.463779\pi$
$200$	76.8819	+	67.1250i	0.384410	+	0.335625i
$201$	−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
$205$	−196.601	+	32.6811i	−0.959028	+	0.159420i
$206$			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
$210$	20.6304	−	7.47890i	0.0982399	−	0.0356138i
$211$	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
$220$	−60.2913	+	160.726i	−0.274051	+	0.730573i
$221$	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	0.608744	−	0.793366i	$-0.291673\pi$
$223$	50.4072	+	29.1026i	0.226041	+	0.130505i	−0.382703	+	0.923871i	$0.625007\pi$
$224$		−	63.7906i		−	0.284780i
$225$	211.233	+	77.4965i	0.938812	+	0.344429i
$226$	43.7874			0.193750
$227$	187.291	−	324.397i	0.825069	−	1.42906i	−0.0767971	−	0.997047i	$-0.524469\pi$
$227$	187.291	−	324.397i	0.825069	−	1.42906i	0.901866	−	0.432015i	$-0.142197\pi$
$228$	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	$0.880546\pi$
$230$	5.87012	+	2.20199i	0.0255223	+	0.00957387i
$231$	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	$-0.292789\pi$
$233$	282.378			1.21192			0.605961	+	0.795495i	$0.292789\pi$
$234$	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	$0.613422\pi$
$240$	122.858	−	146.035i	0.511907	−	0.608481i
$241$	−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
$245$	33.8997	+	203.932i	0.138366	+	0.832374i
$246$	−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
$250$	−66.0703	−	1.94471i	−0.264281	−	0.00777886i
$251$			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
$255$	180.417	+	32.0510i	0.707517	+	0.125690i
$256$	−47.6010	−	82.4474i	−0.185941	−	0.322060i
$257$	−152.974	−	264.959i	−0.595230	−	1.03097i	−0.993514	−	0.113707i	$-0.963728\pi$
$257$	−152.974	−	264.959i	−0.595230	−	1.03097i	0.398284	−	0.917262i	$-0.369606\pi$
$258$	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	−0.971104	−	0.238657i	$-0.923293\pi$
$263$	−73.3426	+	127.033i	−0.278869	+	0.483016i	0.692235	+	0.721672i	$0.256626\pi$
$264$	−106.531	−	37.7487i	−0.403528	−	0.142988i
$265$	−46.0027	−	17.2564i	−0.173595	−	0.0651187i
$266$	−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	$-0.171562\pi$
$270$	−23.3548	+	67.4583i	−0.0864994	+	0.249846i
$271$	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
$275$	−74.6381	−	218.298i	−0.271411	−	0.793811i
$276$	8.83956	−	24.9463i	0.0320274	−	0.0903850i
$277$	355.555	+	205.280i	1.28359	+	0.741083i	0.977503	−	0.210920i	$-0.0676460\pi$
$277$	355.555	+	205.280i	1.28359	+	0.741083i	0.306090	+	0.952003i	$0.400979\pi$
$278$	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	−0.864464	−	0.502694i	$-0.832342\pi$
$283$	−243.762	+	140.736i	−0.861351	+	0.497301i	0.00311372	+	0.999995i	$0.499009\pi$
$284$	−171.398	+	98.9566i	−0.603513	+	0.348439i
$285$	−299.310	−	53.1723i	−1.05021	−	0.186569i
$286$	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
$290$	−91.0571	+	15.1365i	−0.313990	+	0.0521947i
$291$	−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	$0.0789873\pi$
$293$	204.334	+	353.917i	0.697387	+	1.20791i	−0.271983	+	0.962302i	$0.587679\pi$
$294$	−64.4943	+	11.9399i	−0.219368	+	0.0406121i
$295$	288.558	−	47.9671i	0.978162	−	0.162600i
$296$		−	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
$300$	−3.09458	+	279.011i	−0.0103153	+	0.930038i
$301$	−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	$-0.908470\pi$
$307$		−	174.133i		−	0.567208i	0.958941	−	0.283604i	$-0.0915301\pi$
$308$	−47.4917	+	82.2581i	−0.154194	+	0.267072i
$309$	−248.247	+	211.937i	−0.803388	+	0.685880i
$310$	72.8955	+	27.3444i	0.235147	+	0.0882079i
$311$	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	0.175311	−	0.984513i	$-0.443907\pi$
$313$	−184.560	−	106.555i	−0.589647	−	0.340433i	−0.764958	+	0.644080i	$0.777240\pi$
$314$		−	77.8424i		−	0.247906i
$315$	108.265	+	61.4654i	0.343698	+	0.195128i
$316$	−128.496			−0.406634
$317$	−121.062	+	209.686i	−0.381899	+	0.661469i	−0.991334	−	0.131368i	$-0.958063\pi$
$317$	−121.062	+	209.686i	−0.381899	+	0.661469i	0.609435	+	0.792836i	$0.291396\pi$
$318$	5.20652	−	14.6934i	0.0163727	−	0.0462057i
$319$	−161.089	−	279.014i	−0.504981	−	0.874653i
$320$	181.165	+	67.9583i	0.566140	+	0.212370i
$321$	−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
$330$	68.8146	−	24.9466i	0.208529	−	0.0755957i
$331$	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
$335$	76.7709	−	12.7617i	0.229167	−	0.0380945i
$336$	80.3092	−	68.5627i	0.239016	−	0.204056i
$337$	273.013	−	157.624i	0.810128	−	0.467728i	−0.0368724	−	0.999320i	$-0.511740\pi$
$337$	273.013	−	157.624i	0.810128	−	0.467728i	0.847000	+	0.531592i	$0.178406\pi$
$338$	−4.13587	−	7.16353i	−0.0122363	−	0.0211939i
$339$	161.298	+	188.932i	0.475805	+	0.557322i
$340$	37.2634	+	224.167i	0.109598	+	0.659314i
$341$			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
$345$	12.1225	+	33.4395i	0.0351376	+	0.0969262i
$346$	−0.116111	−	0.201110i	−0.000335581	−	0.000581244i
$347$	253.003	+	438.213i	0.729114	+	1.26286i	0.957258	+	0.289235i	$0.0934009\pi$
$347$	253.003	+	438.213i	0.729114	+	1.26286i	−0.228144	+	0.973627i	$0.573266\pi$
$348$	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	−0.642403	−	0.766367i	$-0.722062\pi$
$353$	120.900	−	209.404i	0.342492	−	0.593213i	0.984895	+	0.173154i	$0.0553957\pi$
$354$	16.8947	+	91.2576i	0.0477251	+	0.257790i
$355$	93.4194	−	249.040i	0.263153	−	0.701521i
$356$	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	$0.831845\pi$
$360$	−183.706	+	1.33078i	−0.510295	+	0.00369662i
$361$	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
$365$	41.5401	−	110.739i	0.113809	−	0.303394i
$366$	−15.9712	−	18.7075i	−0.0436372	−	0.0511134i
$367$	−227.601	−	131.406i	−0.620168	−	0.358054i	0.156767	−	0.987636i	$-0.449893\pi$
$367$	−227.601	−	131.406i	−0.620168	−	0.358054i	−0.776934	+	0.629582i	$0.783226\pi$
$368$	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	−0.0910309	−	0.995848i	$-0.529016\pi$
$373$	270.755	−	156.320i	0.725883	−	0.419089i	0.816914	+	0.576759i	$0.195683\pi$
$374$	51.6256	−	29.8061i	0.138036	−	0.0796953i
$375$	−234.989	−	292.241i	−0.626639	−	0.779310i
$376$	−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	$0.390109\pi$
$380$	−61.8197	−	371.891i	−0.162683	−	0.978661i
$381$	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	0.839567	−	0.543257i	$-0.182809\pi$
$383$	−19.4145	−	33.6269i	−0.0506906	−	0.0877986i	−0.890257	+	0.455458i	$0.849476\pi$
$384$	−112.918	+	318.666i	−0.294056	+	0.829860i
$385$	−20.9326	−	125.925i	−0.0543704	−	0.327078i
$386$			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	$0.537549\pi$
$390$	18.8520	−	106.119i	0.0483386	−	0.272101i
$391$	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	$0.0188582\pi$
$397$			47.0129i			0.118420i	−0.998246	+	0.0592102i	$0.981142\pi$
$398$	11.9485	−	20.6954i	0.0300213	−	0.0519985i
$399$	−158.547	−	56.1802i	−0.397361	−	0.140802i
$400$	−300.963	+	102.902i	−0.752408	+	0.257255i
$401$	−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
$405$	−377.098	+	147.723i	−0.931106	+	0.364748i
$406$	−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	$0.592167\pi$
$410$	−37.0142	+	98.6734i	−0.0902785	+	0.240667i
$411$	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	$0.253469\pi$
$420$	−27.0047	+	152.011i	−0.0642968	+	0.361931i
$421$	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
$425$	−230.056	−	200.861i	−0.541309	−	0.472613i
$426$	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
$430$	−176.303	+	29.3069i	−0.410006	+	0.0681556i
$431$		−	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	$0.250869\pi$
$433$			614.024i			1.41807i	−0.705173	+	0.709035i	$0.749131\pi$
$434$	37.3073	+	21.5394i	0.0859614	+	0.0496299i
$435$	−400.734	−	337.132i	−0.921227	−	0.775016i
$436$	−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	$-0.641748\pi$
$443$	250.825	−	434.441i	0.566196	−	0.980680i	0.996937	−	0.0782045i	$-0.0249187\pi$
$444$	546.342	−	466.431i	1.23050	−	1.05052i
$445$	−51.1629	+	136.391i	−0.114973	+	0.306498i
$446$	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	$0.940678\pi$
$450$	91.3383	−	76.2436i	0.202974	−	0.169430i
$451$	−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
$455$	−175.991	−	66.0176i	−0.386794	−	0.145094i
$456$	244.064	−	45.1840i	0.535228	−	0.0990877i
$457$	−720.569	−	416.021i	−1.57674	−	0.910330i	−0.995310	−	0.0967320i	$-0.969161\pi$
$457$	−720.569	−	416.021i	−1.57674	−	0.910330i	−0.581428	−	0.813598i	$-0.697506\pi$
$458$	−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	−0.328308	−	0.944571i	$-0.606478\pi$
$463$	150.734	−	87.0264i	0.325560	−	0.187962i	0.653868	+	0.756609i	$0.273145\pi$
$464$	−384.671	+	222.090i	−0.829033	+	0.478643i
$465$	150.538	+	415.255i	0.323737	+	0.893021i
$466$	74.6594	−	129.314i	0.160213	−	0.277498i
$467$	134.443			0.287886			0.143943	−	0.989586i	$-0.454022\pi$
$467$	134.443			0.287886			0.143943	+	0.989586i	$0.454022\pi$
$468$	−449.354	−	71.3553i	−0.960157	−	0.152469i
$469$	43.0615			0.0918155
$470$	−40.4856	−	243.551i	−0.0861397	−	0.518194i
$471$	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
$475$	381.662	+	333.226i	0.803498	+	0.701529i
$476$			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	$0.933648\pi$
$480$	−117.875	−	325.157i	−0.245574	−	0.677410i
$481$	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	$-0.931275\pi$
$487$		−	208.661i		−	0.428462i	0.976783	−	0.214231i	$-0.0687246\pi$
$488$	31.6507	−	54.8206i	0.0648580	−	0.112337i
$489$	−5.25434	−	28.3816i	−0.0107451	−	0.0580402i
$490$	102.353	+	38.3944i	0.208883	+	0.0783559i
$491$	−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
$495$	361.128	+	205.024i	0.729552	+	0.414190i
$496$	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	$0.724506\pi$
$500$	244.272	−	395.727i	0.488545	−	0.791455i
$501$	−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	$-0.472926\pi$
$503$	85.4624			0.169905			0.0849527	+	0.996385i	$0.472926\pi$
$504$	−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	$0.281784\pi$
$510$	62.3791	−	74.1472i	0.122312	−	0.145387i
$511$	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
$515$	536.653	−	89.2082i	1.04205	−	0.173220i
$516$	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
$520$	273.615	−	45.4832i	0.526183	−	0.0874677i
$521$		−	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	$-0.983687\pi$
$523$		−	53.5836i		−	0.102454i	0.998687	−	0.0512271i	$-0.0163132\pi$
$524$	186.668	+	107.773i	0.356236	+	0.205673i
$525$	−101.748	−	180.834i	−0.193805	−	0.344446i
$526$	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
$535$	299.615	+	112.391i	0.560028	+	0.210077i
$536$	−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
$540$	−328.868	−	379.608i	−0.609015	−	0.702978i
$541$	−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
$545$	69.3491	+	26.0141i	0.127246	+	0.0477323i
$546$	19.9185	−	56.2122i	0.0364807	−	0.102953i
$547$	−632.220	−	365.012i	−1.15579	−	0.667298i	−0.205502	−	0.978657i	$-0.565883\pi$
$547$	−632.220	−	365.012i	−1.15579	−	0.667298i	−0.950293	+	0.311359i	$0.899216\pi$
$548$	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
$555$	−168.867	+	950.562i	−0.304264	+	1.71272i
$556$	−112.819	+	195.408i	−0.202912	+	0.351453i
$557$	−419.491			−0.753125			−0.376562	−	0.926391i	$-0.622894\pi$
$557$	−419.491			−0.753125			−0.376562	+	0.926391i	$0.622894\pi$
$558$	−130.852	+	50.1692i	−0.234502	+	0.0899090i
$559$	−918.522			−1.64315
$560$	−173.610	+	28.8594i	−0.310018	+	0.0515346i
$561$	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	$0.0243388\pi$
$563$	317.922	+	550.657i	0.564693	+	0.978077i	−0.432385	+	0.901689i	$0.642328\pi$
$564$	−1024.81	+	189.726i	−1.81705	+	0.336393i
$565$	−67.8933	−	408.428i	−0.120165	−	0.722882i
$566$			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	$0.950686\pi$
$570$	−103.486	+	123.010i	−0.181555	+	0.215806i
$571$	−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	$0.0727016\pi$
$577$			261.287i			0.452837i	−0.974030	+	0.226418i	$0.927298\pi$
$578$	−36.9537	+	64.0056i	−0.0639337	+	0.110736i
$579$	−297.528	+	254.010i	−0.513866	+	0.438705i
$580$	228.095	−	608.061i	0.393267	−	1.04838i
$581$	−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
$585$	527.324	−	309.565i	0.901409	−	0.529172i
$586$	216.100			0.368772
$587$	−301.693	+	522.548i	−0.513958	+	0.890201i	0.485911	+	0.874008i	$0.338488\pi$
$587$	−301.693	+	522.548i	−0.513958	+	0.890201i	−0.999869	+	0.0161926i	$0.994846\pi$
$588$	154.129	−	434.969i	0.262123	−	0.739743i
$589$	−298.389	−	516.825i	−0.506602	−	0.877461i
$590$	54.3270	−	144.826i	0.0920797	−	0.245468i
$591$	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	$-0.414709\pi$
$593$	314.000			0.529511			0.264756	+	0.964316i	$0.414709\pi$
$594$	−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	$0.116740\pi$
$600$	263.450	+	156.024i	0.439083	+	0.260040i
$601$	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
$605$	29.3855	+	176.775i	0.0485711	+	0.292191i
$606$	−165.413	+	141.219i	−0.272959	+	0.233034i
$607$	−382.344	+	220.747i	−0.629892	+	0.363668i	−0.780710	−	0.624893i	$-0.785143\pi$
$607$	−382.344	+	220.747i	−0.629892	+	0.363668i	0.150818	+	0.988562i	$0.451809\pi$
$608$	233.647	+	404.689i	0.384288	+	0.665607i
$609$	−188.142	−	220.375i	−0.308936	−	0.361864i
$610$	6.72259	+	40.4414i	0.0110206	+	0.0662973i
$611$		−	1268.88i		−	2.07673i
$612$	−317.778	−	257.543i	−0.519246	−	0.420822i
$613$		−	406.010i		−	0.662332i	−0.943572	−	0.331166i	$-0.892558\pi$
$613$		−	406.010i		−	0.662332i	0.943572	−	0.331166i	$-0.107442\pi$
$614$	−79.7436	−	46.0400i	−0.129876	−	0.0749837i
$615$	−562.100	+	203.772i	−0.913984	+	0.331336i
$616$	52.1139	+	90.2639i	0.0846005	+	0.146532i
$617$	−447.854	−	775.706i	−0.725858	−	1.25722i	−0.958620	−	0.284689i	$-0.908110\pi$
$617$	−447.854	−	775.706i	−0.725858	−	1.25722i	0.232762	−	0.972534i	$-0.425224\pi$
$618$	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
$625$	84.3040	+	619.288i	0.134886	+	0.990861i
$626$	−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
$630$	56.7727	−	33.3284i	0.0901154	−	0.0529022i
$631$	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
$635$	64.5001	−	171.946i	0.101575	−	0.270781i
$636$	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	−0.466414	−	0.884567i	$-0.654454\pi$
$643$	42.7186	−	24.6636i	0.0664365	−	0.0383571i	0.532850	+	0.846210i	$0.321121\pi$
$644$	−21.1370	+	12.2034i	−0.0328214	+	0.0189494i
$645$	−775.891	−	652.747i	−1.20293	−	1.01201i
$646$	−65.4583	+	113.377i	−0.101329	+	0.175506i
$647$	1189.39			1.83832			0.919159	−	0.393887i	$-0.128870\pi$
$647$	1189.39			1.83832			0.919159	+	0.393887i	$0.128870\pi$
$648$	245.920	−	221.071i	0.379507	−	0.341159i
$649$	539.882			0.831867
$650$	−118.144	+	135.317i	−0.181760	+	0.208180i
$651$	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	0.705313	−	0.708896i	$-0.250806\pi$
$653$	−170.606	−	295.498i	−0.261265	−	0.452524i	−0.966578	+	0.256371i	$0.917473\pi$
$654$	−7.84884	+	22.1503i	−0.0120013	+	0.0338690i
$655$	−285.760	+	47.5021i	−0.436275	+	0.0725223i
$656$			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	$0.757821\pi$
$660$	−90.0767	+	507.047i	−0.136480	+	0.768254i
$661$	−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
$670$	14.4537	−	38.5311i	0.0215727	−	0.0575091i
$671$	−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	0.639092	−	0.769130i	$-0.279310\pi$
$673$	196.887	+	113.673i	0.292551	+	0.168905i	−0.346541	+	0.938035i	$0.612644\pi$
$674$		−	166.701i		−	0.247330i
$675$	665.432	+	113.247i	0.985825	+	0.167774i
$676$	58.1969			0.0860901
$677$	530.736	−	919.261i	0.783952	−	1.35785i	−0.145671	−	0.989333i	$-0.546534\pi$
$677$	530.736	−	919.261i	0.783952	−	1.35785i	0.929623	−	0.368512i	$-0.120133\pi$
$678$	129.167	−	23.9130i	0.190512	−	0.0352699i
$679$	86.2777	+	149.437i	0.127066	+	0.220084i
$680$	233.474	+	87.5802i	0.343343	+	0.128794i
$681$	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	$-0.653515\pi$
$683$	−633.553			−0.927604			−0.463802	+	0.885939i	$0.653515\pi$
$684$	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
$690$	18.5187	+	3.28983i	0.0268386	+	0.00476787i
$691$	−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
$695$	−49.7264	−	299.141i	−0.0715487	−	0.430418i
$696$	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
$700$	169.236	−	193.835i	0.241766	−	0.276907i
$701$		−	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
$705$	901.729	−	1071.85i	1.27905	−	1.52035i
$706$	−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
$715$	−587.036	−	220.208i	−0.821030	−	0.307983i
$716$	−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	$-0.0344867\pi$
$720$	282.663	−	497.881i	0.392587	−	0.691501i
$721$	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
$725$	282.372	+	825.869i	0.389479	+	1.13913i
$726$	−55.9060	+	10.3500i	−0.0770056	+	0.0142562i
$727$	540.769	+	312.213i	0.743837	+	0.429454i	0.823463	−	0.567370i	$-0.192039\pi$
$727$	540.769	+	312.213i	0.743837	+	0.429454i	−0.0796259	+	0.996825i	$0.525373\pi$
$728$	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	−0.743447	−	0.668795i	$-0.766810\pi$
$733$	−392.871	+	226.824i	−0.535977	+	0.309447i	0.207470	+	0.978241i	$0.433477\pi$
$734$	−120.354	+	69.4862i	−0.163970	+	0.0946679i
$735$	211.370	+	583.060i	0.287578	+	0.793279i
$736$	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	$0.310945\pi$
$740$	−1181.07	+	196.330i	−1.59604	+	0.265310i
$741$	−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	0.588645	−	0.808391i	$-0.299661\pi$
$743$	−301.483	−	522.184i	−0.405765	−	0.702805i	−0.994410	+	0.105586i	$0.966328\pi$
$744$	−234.165	−	274.283i	−0.314738	−	0.368660i
$745$	−1162.46	+	193.236i	−1.56035	+	0.259377i
$746$		−	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
$750$	−195.961	+	30.3453i	−0.261281	+	0.0404605i
$751$	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	$0.308683\pi$
$757$			1248.67i			1.64950i	−0.565501	+	0.824748i	$0.691317\pi$
$758$	67.8223	−	117.472i	0.0894754	−	0.154976i
$759$	11.9504	+	64.5508i	0.0157449	+	0.0850472i
$760$	−387.331	−	145.295i	−0.509646	−	0.191177i
$761$	−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
$765$	549.711	−	3.98215i	0.718576	−	0.00520542i
$766$	−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	$0.563753\pi$
$770$	−63.2014	−	23.7080i	−0.0820797	−	0.0307896i
$771$	−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	$-0.756961\pi$
$773$	−1116.83			−1.44480			−0.722399	+	0.691476i	$0.756961\pi$
$774$	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
$780$	580.271	+	488.174i	0.743937	+	0.625865i
$781$	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
$785$	−726.078	+	120.696i	−0.924940	+	0.153753i
$786$	−16.7309	−	90.3730i	−0.0212861	−	0.114978i
$787$	−922.485	+	532.597i	−1.17215	+	0.676743i	−0.954186	−	0.299213i	$-0.903276\pi$
$787$	−922.485	+	532.597i	−1.17215	+	0.676743i	−0.217967	+	0.975956i	$0.569943\pi$
$788$	347.207	+	601.381i	0.440618	+	0.763173i
$789$	−146.977	+	414.785i	−0.186282	+	0.525710i
$790$	−14.9744	−	90.0821i	−0.0189549	−	0.114028i
$791$		−	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
$795$	−145.126	−	25.7816i	−0.182549	−	0.0324296i
$796$	84.0651	+	145.605i	0.105609	+	0.182921i
$797$	94.4897	+	163.661i	0.118557	+	0.205346i	0.919196	−	0.393801i	$-0.128840\pi$
$797$	94.4897	+	163.661i	0.118557	+	0.205346i	−0.800639	+	0.599147i	$0.795507\pi$
$798$	−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
$805$	11.5206	−	30.7119i	0.0143113	−	0.0381514i
$806$	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	$0.760604\pi$
$810$	−32.0538	+	211.748i	−0.0395726	+	0.261417i
$811$	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
$815$	−16.8960	+	45.0418i	−0.0207313	+	0.0552660i
$816$	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	0.243810	−	0.969823i	$-0.421603\pi$
$823$	992.214	−	572.855i	1.20561	−	0.696057i	0.961796	+	0.273766i	$0.0882693\pi$
$824$	−384.677	+	222.093i	−0.466841	+	0.269531i
$825$	−339.389	−	603.191i	−0.411380	−	0.731140i
$826$	42.7937	−	74.1208i	0.0518083	−	0.0897346i
$827$	255.412			0.308841			0.154421	−	0.988005i	$-0.450649\pi$
$827$	255.412			0.308841			0.154421	+	0.988005i	$0.450649\pi$
$828$	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	$0.666701\pi$
$830$	32.6668	+	196.515i	0.0393576	+	0.236765i
$831$	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
$835$	68.1164	+	409.770i	0.0815765	+	0.490743i
$836$		−	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	$0.579495\pi$
$840$	129.641	+	109.066i	0.154335	+	0.129840i
$841$	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
$850$	−152.809	+	52.2469i	−0.179776	+	0.0614669i
$851$	−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	0.508239	−	0.861216i	$-0.330297\pi$
$853$	14.0948	+	8.13764i	0.0165238	+	0.00954002i	−0.491715	+	0.870756i	$0.663630\pi$
$854$			22.6839i			0.0265620i
$855$	−911.966	+	6.60636i	−1.06663	+	0.00772673i
$856$	−261.279			−0.305232
$857$	530.849	−	919.457i	0.619427	−	1.07288i	−0.370164	−	0.928967i	$-0.620698\pi$
$857$	530.849	−	919.457i	0.619427	−	1.07288i	0.989590	−	0.143912i	$-0.0459683\pi$
$858$	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	$-0.560735\pi$
$860$	441.632	−	1177.31i	0.513526	−	1.36897i
$861$	−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	$-0.369622\pi$
$863$	687.358			0.796475			0.398238	+	0.917282i	$0.369622\pi$
$864$	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
$870$	−260.341	+	94.3784i	−0.299242	+	0.108481i
$871$	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
$875$	−10.1745	+	345.673i	−0.0116281	+	0.395055i
$876$	−200.792	+	171.423i	−0.229214	+	0.195688i
$877$	1345.72	−	776.955i	1.53446	−	0.885923i	0.535316	−	0.844652i	$-0.320193\pi$
$877$	1345.72	−	776.955i	1.53446	−	0.885923i	0.999148	−	0.0412710i	$-0.0131407\pi$
$878$	137.407	+	237.995i	0.156500	+	0.271065i
$879$	796.040	+	932.422i	0.905620	+	1.06078i
$880$	−579.094	+	96.2632i	−0.658061	+	0.109390i
$881$			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	$-0.805219\pi$
$883$		−	1014.46i		−	1.14888i	0.818546	−	0.574441i	$-0.194781\pi$
$884$	534.832	+	308.785i	0.605013	+	0.349304i
$885$	825.013	−	299.083i	0.932218	−	0.337947i
$886$	−132.634	−	229.729i	−0.149700	−	0.259287i
$887$	104.060	+	180.237i	0.117317	+	0.203199i	0.918704	−	0.394948i	$-0.129237\pi$
$887$	104.060	+	180.237i	0.117317	+	0.203199i	−0.801387	+	0.598147i	$0.795904\pi$
$888$	−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
$895$	180.351	−	480.784i	0.201509	−	0.537189i
$896$	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
$900$	143.244	+	824.738i	0.159160	+	0.916376i
$901$	−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
$905$	563.770	+	211.480i	0.622950	+	0.233680i
$906$	−15.2823	−	17.9005i	−0.0168679	−	0.0197577i
$907$	−205.665	−	118.741i	−0.226753	−	0.130916i	0.382320	−	0.924030i	$-0.375125\pi$
$907$	−205.665	−	118.741i	−0.226753	−	0.130916i	−0.609073	+	0.793114i	$0.708458\pi$
$908$	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
$915$	−149.731	+	177.979i	−0.163641	+	0.194512i
$916$	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	$0.526682\pi$
$920$	7.93718	+	47.7480i	0.00862737	+	0.0519000i
$921$	−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
$925$	1058.27	−	1212.10i	1.14408	−	1.31038i
$926$		−	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	$0.802391\pi$
$930$	229.966	+	40.8533i	0.247275	+	0.0439283i
$931$	−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	$0.0614549\pi$
$937$			359.563i			0.383738i	−0.981421	+	0.191869i	$0.938545\pi$
$938$	11.3853	−	19.7199i	0.0121378	−	0.0210233i
$939$	−602.619	−	213.534i	−0.641767	−	0.227406i
$940$	1626.39	+	610.087i	1.73020	+	0.649029i
$941$	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
$945$	352.935	+	122.190i	0.373476	+	0.129302i
$946$	−329.856			−0.348685
$947$	−773.466	+	1339.68i	−0.816754	+	1.41466i	0.0913074	+	0.995823i	$0.470895\pi$
$947$	−773.466	+	1339.68i	−0.816754	+	1.41466i	−0.908062	+	0.418837i	$0.862438\pi$
$948$	−379.048	+	70.1738i	−0.399839	+	0.0740230i
$949$	−160.714	−	278.365i	−0.169351	−	0.293324i
$950$	253.509	−	86.6772i	0.266852	−	0.0912392i
$951$	−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	$-0.776195\pi$
$953$	−1453.97			−1.52568			−0.762838	+	0.646589i	$0.776195\pi$
$954$	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
$960$	571.527	+	101.531i	0.595340	+	0.105762i
$961$	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
$965$	643.188	−	106.918i	0.666517	−	0.110795i
$966$	9.80948	+	3.47593i	0.0101547	+	0.00359827i
$967$	−331.339	+	191.299i	−0.342646	+	0.197827i	−0.661442	−	0.749997i	$-0.730055\pi$
$967$	−331.339	+	191.299i	−0.342646	+	0.197827i	0.318795	+	0.947824i	$0.396722\pi$
$968$	−73.1583	−	126.714i	−0.0755768	−	0.130903i
$969$	−730.321	+	135.206i	−0.753686	+	0.139531i
$970$	162.675	−	27.0415i	0.167706	−	0.0278779i
$971$			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
$975$	−1019.06	−	11.3027i	−1.04519	−	0.0115925i
$976$	98.6373	+	170.845i	0.101063	+	0.175046i
$977$	−708.905	−	1227.86i	−0.725593	−	1.25676i	−0.958729	−	0.284320i	$-0.908232\pi$
$977$	−708.905	−	1227.86i	−0.725593	−	1.25676i	0.233136	−	0.972444i	$-0.425101\pi$
$978$	−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	−0.956620	−	0.291340i	$-0.905899\pi$
$983$	−222.160	+	384.792i	−0.226002	+	0.391447i	0.730618	+	0.682787i	$0.239232\pi$
$984$	371.277	−	316.972i	0.377314	−	0.322126i
$985$	−873.802	−	327.779i	−0.887109	−	0.332771i
$986$	−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
$990$	189.371	−	111.170i	0.191284	−	0.112293i
$991$	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
$995$	−211.563	−	79.3613i	−0.212626	−	0.0797601i
$996$	826.896	−	153.085i	0.830217	−	0.153700i
$997$	87.6487	+	50.6040i	0.0879125	+	0.0507563i	0.543312	−	0.839531i	$-0.317170\pi$
$997$	87.6487	+	50.6040i	0.0879125	+	0.0507563i	−0.455399	+	0.890287i	$0.650503\pi$
$998$	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.29.6	yes	20
3.2	odd	2		135.3.h.a.89.5		20
5.2	odd	4		225.3.j.e.101.6		20
5.3	odd	4		225.3.j.e.101.5		20
5.4	even	2	inner	45.3.h.a.29.5	yes	20
9.2	odd	6		405.3.d.a.404.12		20
9.4	even	3		135.3.h.a.44.6		20
9.5	odd	6	inner	45.3.h.a.14.5	✓	20
9.7	even	3		405.3.d.a.404.9		20
15.2	even	4		675.3.j.e.251.5		20
15.8	even	4		675.3.j.e.251.6		20
15.14	odd	2		135.3.h.a.89.6		20
45.4	even	6		135.3.h.a.44.5		20
45.13	odd	12		675.3.j.e.476.6		20
45.14	odd	6	inner	45.3.h.a.14.6	yes	20
45.22	odd	12		675.3.j.e.476.5		20
45.23	even	12		225.3.j.e.176.5		20
45.29	odd	6		405.3.d.a.404.10		20
45.32	even	12		225.3.j.e.176.6		20
45.34	even	6		405.3.d.a.404.11		20

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

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} +(-4.68146 - 1.75610i) 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} +(-14.7688 - 2.62366i) q^{15} +(-6.36137 + 11.0182i) q^{16} -12.2161 q^{17} +(0.746375 - 4.70023i) q^{18} +20.2664 q^{19} +(-3.05035 - 18.3501i) 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} +(18.8322 + 16.4423i) q^{25} +7.18539i q^{26} +(23.0298 - 14.0936i) q^{27} -10.2927i q^{28} +(30.2349 + 17.4561i) q^{29} +(-5.10629 + 6.06962i) 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} +(-19.1119 - 7.16923i) q^{40} +(34.5195 - 19.9299i) q^{41} +(-3.33787 + 2.84965i) q^{42} +(58.5402 + 33.7982i) q^{43} -34.3324i q^{44} +(-44.9988 + 0.325975i) q^{45} -1.25391 q^{46} +(-46.6901 + 80.8696i) q^{47} +(-12.7480 + 35.9764i) q^{48} +(-20.6730 - 35.8067i) q^{49} +(12.5088 - 4.27688i) 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} +(-19.0194 - 52.4646i) q^{60} +(7.75283 - 13.4283i) q^{61} -15.5711 q^{62} +(-24.5911 - 3.90496i) q^{63} -38.6984 q^{64} +(67.0220 - 11.1411i) 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} +(7.21571 - 1.19947i) q^{70} +53.1970i q^{71} +(34.3071 - 13.1535i) q^{72} +23.6547i q^{73} +(-29.4748 - 17.0173i) q^{74} +(64.5320 + 38.2180i) 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} +(57.1893 + 21.4527i) q^{85} +(30.9555 - 17.8722i) q^{86} +(98.7223 + 34.9817i) q^{87} +(-32.6265 - 18.8369i) q^{88} -29.1344i q^{89} +(-11.7482 + 20.6932i) q^{90} +37.5932 q^{91} +(4.41101 - 7.64010i) q^{92} +(-57.3586 - 67.1856i) q^{93} +(24.6893 + 42.7631i) q^{94} +(-94.8766 - 35.5899i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9} + 4 q^{10} - 24 q^{11} + 30 q^{14} + 24 q^{15} - 26 q^{16} - 8 q^{19} + 144 q^{20} - 96 q^{21} - 102 q^{24} + 2 q^{25} - 114 q^{29} - 48 q^{30} + 28 q^{31}+ \cdots - 468 q^{99}+O(q^{100}) \) 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

L-functions

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