LMFDB - Embedded newform 45.3.h.a.14.6

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			14.6
Root			$0.315300 - 1.70311i$ of defining polynomial
Character	$\chi$	$=$	45.14
Dual form			45.3.h.a.29.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.264396 + 0.457947i) q^{2} +(2.94987 + 0.546115i) q^{3} +(1.86019 - 3.22194i) q^{4} +(-4.68146 + 1.75610i) q^{5} +(0.529842 + 1.49528i) q^{6} +(-2.39593 + 1.38329i) q^{7} +4.08247 q^{8} +(8.40352 + 3.22194i) q^{9} +O(q^{10})$	\(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}+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 $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.264396	+	0.457947i	0.132198	+	0.228973i	0.924524	−	0.381125i	$-0.124463\pi$
$2$	0.264396	+	0.457947i	0.132198	+	0.228973i	−0.792326	+	0.610098i	$0.791130\pi$
$3$	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	−0.661278	−	0.750141i	$-0.729986\pi$
$7$	−2.39593	+	1.38329i	−0.342276	+	0.197613i	0.319002	+	0.947754i	$0.396652\pi$
$8$	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	−0.817152	−	0.576422i	$-0.804449\pi$
$11$	−7.99186	+	4.61410i	−0.726533	+	0.419464i	0.0906197	+	0.995886i	$0.471115\pi$
$12$	7.24688	−	8.48845i	0.603907	−	0.707371i
$13$	−11.7678	−	6.79417i	−0.905218	−	0.522628i	−0.0263288	−	0.999653i	$-0.508382\pi$
$13$	−11.7678	−	6.79417i	−0.905218	−	0.522628i	−0.878890	+	0.477025i	$0.841715\pi$
$14$	−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	−0.890649	−	0.454692i	$-0.849749\pi$
$23$	−1.18564	+	2.05358i	−0.0515494	+	0.0892861i	0.839099	+	0.543978i	$0.183083\pi$
$24$	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	0.122020	−	0.992528i	$-0.461063\pi$
$29$	30.2349	−	17.4561i	1.04258	−	0.601936i	0.920564	+	0.390592i	$0.127730\pi$
$30$	−5.10629	−	6.06962i	−0.170210	−	0.202321i
$31$	−14.7233	+	25.5015i	−0.474945	+	0.822629i	−0.999588	−	0.0286933i	$-0.990865\pi$
$31$	−14.7233	+	25.5015i	−0.474945	+	0.822629i	0.524643	+	0.851322i	$0.324199\pi$
$32$	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
$40$	−19.1119	+	7.16923i	−0.477798	+	0.179231i
$41$	34.5195	+	19.9299i	0.841940	+	0.486094i	0.857923	−	0.513778i	$-0.171755\pi$
$41$	34.5195	+	19.9299i	0.841940	+	0.486094i	−0.0159834	+	0.999872i	$0.505088\pi$
$42$	−3.33787	−	2.84965i	−0.0794730	−	0.0678488i
$43$	58.5402	−	33.7982i	1.36140	−	0.786004i	0.371589	−	0.928397i	$-0.378813\pi$
$43$	58.5402	−	33.7982i	1.36140	−	0.786004i	0.989810	+	0.142393i	$0.0454796\pi$
$44$			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	−0.595992	−	0.802991i	$-0.703241\pi$
$47$	−46.6901	−	80.8696i	−0.993406	−	1.72063i	−0.397414	−	0.917639i	$-0.630092\pi$
$48$	−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	0.00485217	−	0.999988i	$-0.498456\pi$
$59$	−50.6655	−	29.2517i	−0.858737	−	0.495792i	−0.863589	+	0.504196i	$0.831789\pi$
$60$	−19.0194	+	52.4646i	−0.316990	+	0.874411i
$61$	7.75283	+	13.4283i	0.127096	+	0.220136i	0.922550	−	0.385877i	$-0.126101\pi$
$61$	7.75283	+	13.4283i	0.127096	+	0.220136i	−0.795455	+	0.606013i	$0.792768\pi$
$62$	−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	0.396022	−	0.918241i	$-0.370390\pi$
$67$	−13.4796	−	7.78243i	−0.201188	−	0.116156i	−0.597209	+	0.802085i	$0.703724\pi$
$68$	−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	$-0.877771\pi$
$71$		−	53.1970i		−	0.749254i	0.927176	−	0.374627i	$-0.122229\pi$
$72$	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
$75$	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	0.735782	−	0.677219i	$-0.236815\pi$
$79$	−17.2692	−	29.9112i	−0.218598	−	0.378623i	−0.954380	+	0.298596i	$0.903482\pi$
$80$	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	$-0.0167020\pi$
$83$	37.6730	+	65.2516i	0.453892	+	0.786163i	−0.544732	+	0.838610i	$0.683369\pi$
$84$	−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	$0.0523352\pi$
$89$			29.1344i			0.327352i	−0.986514	+	0.163676i	$0.947665\pi$
$90$	−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	−0.751883	−	0.659296i	$-0.770854\pi$
$97$	−54.0151	+	31.1857i	−0.556857	+	0.321502i	0.195026	+	0.980798i	$0.437521\pi$
$98$	−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	−0.954989	−	0.296642i	$-0.904133\pi$
$101$	−118.734	+	68.5511i	−1.17558	+	0.678723i	−0.220595	+	0.975366i	$0.570800\pi$
$102$	−6.47261	−	18.2665i	−0.0634570	−	0.179083i
$103$	−94.2266	−	54.4017i	−0.914821	−	0.528172i	−0.0328419	−	0.999461i	$-0.510456\pi$
$103$	−94.2266	−	54.4017i	−0.914821	−	0.528172i	−0.881979	+	0.471288i	$0.843789\pi$
$104$	−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	−0.622599	−	0.782541i	$-0.713923\pi$
$113$	41.4033	−	71.7126i	0.366401	−	0.634625i	0.989000	+	0.147916i	$0.0472566\pi$
$114$	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	$-0.953810\pi$
$127$		−	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
$130$	12.6183	+	33.6381i	0.0970637	+	0.258755i
$131$	50.1743	+	28.9682i	0.383010	+	0.221131i	0.679127	−	0.734021i	$-0.262359\pi$
$131$	50.1743	+	28.9682i	0.383010	+	0.221131i	−0.296117	+	0.955152i	$0.595692\pi$
$132$	−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	0.951759	−	0.306847i	$-0.0992738\pi$
$137$	28.7895	+	49.8649i	0.210143	+	0.363978i	−0.741616	+	0.670824i	$0.765941\pi$
$138$	−3.69887	−	0.684778i	−0.0268034	−	0.00496216i
$139$	30.3246	−	52.5237i	0.218162	−	0.377868i	−0.736084	−	0.676890i	$-0.763327\pi$
$139$	30.3246	−	52.5237i	0.218162	−	0.377868i	0.954246	+	0.299022i	$0.0966605\pi$
$140$	−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	0.990907	−	0.134545i	$-0.0429572\pi$
$149$	204.106	+	117.841i	1.36984	+	0.790879i	0.378934	+	0.925424i	$0.376291\pi$
$150$	34.5638	+	19.4475i	0.230425	+	0.129650i
$151$	7.41840	+	12.8490i	0.0491285	+	0.0850930i	0.889544	−	0.456850i	$-0.151022\pi$
$151$	7.41840	+	12.8490i	0.0491285	+	0.0850930i	−0.840415	+	0.541943i	$0.817689\pi$
$152$	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	0.847654	−	0.530549i	$-0.178014\pi$
$157$	127.486	+	73.6041i	0.812013	+	0.468816i	−0.0356413	+	0.999365i	$0.511347\pi$
$158$	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	$0.00939571\pi$
$163$			9.62130i			0.0590264i	−0.999564	+	0.0295132i	$0.990604\pi$
$164$	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	−0.963176	−	0.268872i	$-0.913349\pi$
$167$	−41.5393	+	71.9482i	−0.248738	+	0.430828i	0.714438	+	0.699699i	$0.246683\pi$
$168$	−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	$-0.166263\pi$
$173$	0.219578	+	0.380321i	0.00126924	+	0.00219839i	−0.865390	+	0.501099i	$0.832929\pi$
$174$	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	$-0.907385\pi$
$179$		−	102.699i		−	0.573740i	0.957970	−	0.286870i	$-0.0926148\pi$
$180$	−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	−0.793663	−	0.608358i	$-0.791829\pi$
$191$	−126.755	+	73.1823i	−0.663641	+	0.383153i	0.130022	+	0.991511i	$0.458495\pi$
$192$	−114.155	−	21.1338i	−0.594559	−	0.110072i
$193$	−112.932	−	65.2014i	−0.585141	−	0.337831i	0.178033	−	0.984025i	$-0.443027\pi$
$193$	−112.932	−	65.2014i	−0.585141	−	0.337831i	−0.763174	+	0.646193i	$0.776360\pi$
$194$	−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	−0.654504	−	0.756058i	$-0.727123\pi$
$211$	69.1054	−	119.694i	0.327514	−	0.567270i	0.982018	+	0.188788i	$0.0604559\pi$
$212$	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	−0.382703	−	0.923871i	$-0.625007\pi$
$223$	50.4072	−	29.1026i	0.226041	−	0.130505i	0.608744	+	0.793366i	$0.291673\pi$
$224$			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	0.901866	+	0.432015i	$0.142197\pi$
$227$	187.291	+	324.397i	0.825069	+	1.42906i	−0.0767971	+	0.997047i	$0.524469\pi$
$228$	146.868	−	172.031i	0.644160	−	0.754520i
$229$	−33.8418	+	58.6157i	−0.147781	+	0.255964i	−0.930407	−	0.366528i	$-0.880546\pi$
$229$	−33.8418	+	58.6157i	−0.147781	+	0.255964i	0.782626	+	0.622492i	$0.213880\pi$
$230$	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	−0.348833	−	0.937185i	$-0.613422\pi$
$239$	−319.035	−	184.195i	−1.33488	−	0.770691i	−0.986042	+	0.166494i	$0.946755\pi$
$240$	122.858	+	146.035i	0.511907	+	0.608481i
$241$	−185.554	−	321.389i	−0.769934	−	1.33357i	−0.937598	−	0.347721i	$-0.886956\pi$
$241$	−185.554	−	321.389i	−0.769934	−	1.33357i	0.167664	−	0.985844i	$-0.446378\pi$
$242$	−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	$-0.790986\pi$
$251$		−	306.449i		−	1.22091i	0.792049	−	0.610457i	$-0.209014\pi$
$252$	−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	0.398284	+	0.917262i	$0.369606\pi$
$257$	−152.974	+	264.959i	−0.595230	+	1.03097i	−0.993514	+	0.113707i	$0.963728\pi$
$258$	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	$-0.256626\pi$
$263$	−73.3426	−	127.033i	−0.278869	−	0.483016i	−0.971104	+	0.238657i	$0.923293\pi$
$264$	−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	$0.171562\pi$
$269$			276.133i			1.02652i	−0.858234	+	0.513258i	$0.828438\pi$
$270$	−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	0.306090	−	0.952003i	$-0.400979\pi$
$277$	355.555	−	205.280i	1.28359	−	0.741083i	0.977503	+	0.210920i	$0.0676460\pi$
$278$	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	−0.331387	−	0.943495i	$-0.607516\pi$
$281$	89.9230	−	51.9171i	0.320011	−	0.184758i	0.651397	+	0.758737i	$0.274183\pi$
$282$	96.1840	−	112.663i	0.341078	−	0.399513i
$283$	−243.762	−	140.736i	−0.861351	−	0.497301i	0.00311372	−	0.999995i	$-0.499009\pi$
$283$	−243.762	−	140.736i	−0.861351	−	0.497301i	−0.864464	+	0.502694i	$0.832342\pi$
$284$	−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	−0.271983	−	0.962302i	$-0.587679\pi$
$293$	204.334	−	353.917i	0.697387	−	1.20791i	0.969369	−	0.245607i	$-0.0789873\pi$
$294$	−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	$0.0915301\pi$
$307$			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
$310$	72.8955	−	27.3444i	0.235147	−	0.0882079i
$311$	237.573	+	137.163i	0.763900	+	0.441038i	0.830694	−	0.556729i	$-0.187944\pi$
$311$	237.573	+	137.163i	0.763900	+	0.441038i	−0.0667941	+	0.997767i	$0.521277\pi$
$312$	−126.570	−	108.057i	−0.405672	−	0.346336i
$313$	−184.560	+	106.555i	−0.589647	+	0.340433i	−0.764958	−	0.644080i	$-0.777240\pi$
$313$	−184.560	+	106.555i	−0.589647	+	0.340433i	0.175311	+	0.984513i	$0.443907\pi$
$314$			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	0.609435	−	0.792836i	$-0.291396\pi$
$317$	−121.062	−	209.686i	−0.381899	−	0.661469i	−0.991334	+	0.131368i	$0.958063\pi$
$318$	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	0.976249	−	0.216653i	$-0.0695139\pi$
$331$	99.4647	+	172.278i	0.300498	+	0.520477i	−0.675751	+	0.737130i	$0.736181\pi$
$332$	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	0.847000	−	0.531592i	$-0.178406\pi$
$337$	273.013	+	157.624i	0.810128	+	0.467728i	−0.0368724	+	0.999320i	$0.511740\pi$
$338$	−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	−0.228144	−	0.973627i	$-0.573266\pi$
$347$	253.003	−	438.213i	0.729114	−	1.26286i	0.957258	−	0.289235i	$-0.0934009\pi$
$348$	70.9333	−	383.150i	0.203831	−	1.10101i
$349$	280.837	+	486.423i	0.804689	+	1.39376i	0.916501	+	0.400033i	$0.131001\pi$
$349$	280.837	+	486.423i	0.804689	+	1.39376i	−0.111811	+	0.993729i	$0.535665\pi$
$350$	−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	$-0.0553957\pi$
$353$	120.900	+	209.404i	0.342492	+	0.593213i	−0.642403	+	0.766367i	$0.722062\pi$
$354$	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	$-0.831845\pi$
$359$		−	361.904i		−	1.00809i	0.863678	−	0.504044i	$-0.168155\pi$
$360$	−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	−0.776934	−	0.629582i	$-0.783226\pi$
$367$	−227.601	+	131.406i	−0.620168	+	0.358054i	0.156767	+	0.987636i	$0.449893\pi$
$368$	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	$-0.195683\pi$
$373$	270.755	+	156.320i	0.725883	+	0.419089i	−0.0910309	+	0.995848i	$0.529016\pi$
$374$	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	−0.890257	−	0.455458i	$-0.849476\pi$
$383$	−19.4145	+	33.6269i	−0.0506906	+	0.0877986i	0.839567	+	0.543257i	$0.182809\pi$
$384$	−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	−0.117691	−	0.993050i	$-0.537549\pi$
$389$	265.870	−	153.500i	0.683469	−	0.394601i	0.801161	+	0.598449i	$0.204216\pi$
$390$	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	$-0.981142\pi$
$397$		−	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
$400$	−300.963	−	102.902i	−0.752408	−	0.257255i
$401$	−492.460	−	284.322i	−1.22808	−	0.709032i	−0.261452	−	0.965216i	$-0.584201\pi$
$401$	−492.460	−	284.322i	−1.22808	−	0.709032i	−0.966628	+	0.256184i	$0.917535\pi$
$402$	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	−0.285523	−	0.958372i	$-0.592167\pi$
$409$	281.070	−	486.828i	0.687213	−	1.19029i	0.972736	−	0.231916i	$-0.0744994\pi$
$410$	−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	0.699360	−	0.714770i	$-0.253469\pi$
$419$	180.183	+	104.029i	0.430031	+	0.248279i	−0.269329	+	0.963048i	$0.586802\pi$
$420$	−27.0047	−	152.011i	−0.0642968	−	0.361931i
$421$	197.236	+	341.622i	0.468493	+	0.811454i	0.999352	−	0.0360063i	$-0.0114636\pi$
$421$	197.236	+	341.622i	0.468493	+	0.811454i	−0.530858	+	0.847461i	$0.678130\pi$
$422$	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	$0.0808177\pi$
$431$			216.515i			0.502355i	−0.967941	+	0.251177i	$0.919182\pi$
$432$	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
$435$	−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	−0.993974	−	0.109613i	$-0.965039\pi$
$439$	−259.851	−	450.074i	−0.591915	−	1.02523i	0.402059	−	0.915614i	$-0.368295\pi$
$440$	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	0.996937	+	0.0782045i	$0.0249187\pi$
$443$	250.825	+	434.441i	0.566196	+	0.980680i	−0.430742	+	0.902475i	$0.641748\pi$
$444$	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	$-0.940678\pi$
$449$		−	166.389i		−	0.370576i	0.982684	−	0.185288i	$-0.0593218\pi$
$450$	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	−0.581428	+	0.813598i	$0.697506\pi$
$457$	−720.569	+	416.021i	−1.57674	+	0.910330i	−0.995310	+	0.0967320i	$0.969161\pi$
$458$	−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	−0.0331619	−	0.999450i	$-0.510558\pi$
$461$	376.087	−	217.134i	0.815806	−	0.471006i	0.848968	+	0.528444i	$0.177224\pi$
$462$	39.8243	+	7.37275i	0.0861999	+	0.0159583i
$463$	150.734	+	87.0264i	0.325560	+	0.187962i	0.653868	−	0.756609i	$-0.273145\pi$
$463$	150.734	+	87.0264i	0.325560	+	0.187962i	−0.328308	+	0.944571i	$0.606478\pi$
$464$	−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	−0.978353	−	0.206944i	$-0.933648\pi$
$479$	−617.101	+	356.283i	−1.28831	+	0.743806i	−0.309958	+	0.950750i	$0.600315\pi$
$480$	−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	$0.0687246\pi$
$487$			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
$490$	102.353	−	38.3944i	0.208883	−	0.0783559i
$491$	−356.432	−	205.786i	−0.725931	−	0.419117i	0.0910005	−	0.995851i	$-0.470994\pi$
$491$	−356.432	−	205.786i	−0.725931	−	0.419117i	−0.816932	+	0.576734i	$0.804327\pi$
$492$	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	−0.648268	−	0.761412i	$-0.724506\pi$
$499$	167.299	−	289.770i	0.335269	−	0.580702i	0.983536	+	0.180710i	$0.0578396\pi$
$500$	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	0.633097	−	0.774073i	$-0.281784\pi$
$509$	142.153	+	82.0719i	0.279278	+	0.161241i	−0.353818	+	0.935314i	$0.615117\pi$
$510$	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	$0.368536\pi$
$521$			954.386i			1.83184i	−0.401366	+	0.915918i	$0.631464\pi$
$522$	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
$525$	−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	−0.950293	−	0.311359i	$-0.899216\pi$
$547$	−632.220	+	365.012i	−1.15579	+	0.667298i	−0.205502	+	0.978657i	$0.565883\pi$
$548$	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	−0.432385	−	0.901689i	$-0.642328\pi$
$563$	317.922	−	550.657i	0.564693	−	0.978077i	0.997078	−	0.0763882i	$-0.0243388\pi$
$564$	−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	−0.988023	−	0.154305i	$-0.950686\pi$
$569$	−767.241	+	442.967i	−1.34840	+	0.778501i	−0.360380	+	0.932806i	$0.617353\pi$
$570$	−103.486	−	123.010i	−0.181555	−	0.215806i
$571$	−463.096	+	802.105i	−0.811026	+	1.40474i	0.101121	+	0.994874i	$0.467757\pi$
$571$	−463.096	+	802.105i	−0.811026	+	1.40474i	−0.912147	+	0.409864i	$0.865576\pi$
$572$	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
$580$	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	−0.999869	−	0.0161926i	$-0.994846\pi$
$587$	−301.693	−	522.548i	−0.513958	−	0.890201i	0.485911	−	0.874008i	$-0.338488\pi$
$588$	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	0.933498	−	0.358582i	$-0.116740\pi$
$599$	652.734	+	376.856i	1.08971	+	0.629142i	0.156208	+	0.987724i	$0.450073\pi$
$600$	263.450	−	156.024i	0.439083	−	0.260040i
$601$	168.976	+	292.675i	0.281158	+	0.486979i	0.971670	−	0.236341i	$-0.0759483\pi$
$601$	168.976	+	292.675i	0.281158	+	0.486979i	−0.690512	+	0.723320i	$0.742615\pi$
$602$	−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	0.150818	−	0.988562i	$-0.451809\pi$
$607$	−382.344	−	220.747i	−0.629892	−	0.363668i	−0.780710	+	0.624893i	$0.785143\pi$
$608$	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	$0.107442\pi$
$613$			406.010i			0.662332i	−0.943572	+	0.331166i	$0.892558\pi$
$614$	−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	0.232762	+	0.972534i	$0.425224\pi$
$617$	−447.854	+	775.706i	−0.725858	+	1.25722i	−0.958620	+	0.284689i	$0.908110\pi$
$618$	31.4204	−	169.719i	0.0508420	−	0.274626i
$619$	−185.811	−	321.834i	−0.300179	−	0.519925i	0.675997	−	0.736904i	$-0.263713\pi$
$619$	−185.811	−	321.834i	−0.300179	−	0.519925i	−0.976176	+	0.216979i	$0.930380\pi$
$620$	−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	−0.356424	−	0.934324i	$-0.616004\pi$
$641$	175.963	−	101.592i	0.274513	−	0.158490i	0.630937	+	0.775834i	$0.282671\pi$
$642$	−33.9100	−	95.6980i	−0.0528193	−	0.149062i
$643$	42.7186	+	24.6636i	0.0664365	+	0.0383571i	0.532850	−	0.846210i	$-0.321121\pi$
$643$	42.7186	+	24.6636i	0.0664365	+	0.0383571i	−0.466414	+	0.884567i	$0.654454\pi$
$644$	−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	−0.966578	−	0.256371i	$-0.917473\pi$
$653$	−170.606	+	295.498i	−0.261265	+	0.452524i	0.705313	+	0.708896i	$0.250806\pi$
$654$	−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	−0.724265	−	0.689522i	$-0.757821\pi$
$659$	−322.418	+	186.148i	−0.489254	+	0.282471i	0.235011	+	0.971993i	$0.424487\pi$
$660$	−90.0767	−	507.047i	−0.136480	−	0.768254i
$661$	−166.221	+	287.904i	−0.251469	+	0.435557i	−0.963931	−	0.266154i	$-0.914247\pi$
$661$	−166.221	+	287.904i	−0.251469	+	0.435557i	0.712461	+	0.701711i	$0.247580\pi$
$662$	−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	−0.346541	−	0.938035i	$-0.612644\pi$
$673$	196.887	−	113.673i	0.292551	−	0.168905i	0.639092	+	0.769130i	$0.279310\pi$
$674$			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	0.929623	+	0.368512i	$0.120133\pi$
$677$	530.736	+	919.261i	0.783952	+	1.35785i	−0.145671	+	0.989333i	$0.546534\pi$
$678$	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	−0.930318	−	0.366753i	$-0.880469\pi$
$691$	−540.899	−	936.864i	−0.782777	−	1.35581i	0.147542	−	0.989056i	$-0.452864\pi$
$692$	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	$0.0325253\pi$
$701$			143.009i			0.204007i	−0.994784	+	0.102003i	$0.967475\pi$
$702$	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	−0.993000	−	0.118113i	$-0.962315\pi$
$709$	−424.541	−	735.327i	−0.598789	−	1.03713i	0.394211	−	0.919020i	$-0.371018\pi$
$710$	−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	$0.0344867\pi$
$719$			155.493i			0.216263i	−0.994137	+	0.108131i	$0.965513\pi$
$720$	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	−0.0796259	−	0.996825i	$-0.525373\pi$
$727$	540.769	−	312.213i	0.743837	−	0.429454i	0.823463	+	0.567370i	$0.192039\pi$
$728$	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	$-0.433477\pi$
$733$	−392.871	−	226.824i	−0.535977	−	0.309447i	−0.743447	+	0.668795i	$0.766810\pi$
$734$	−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	−0.994410	−	0.105586i	$-0.966328\pi$
$743$	−301.483	+	522.184i	−0.405765	+	0.702805i	0.588645	+	0.808391i	$0.299661\pi$
$744$	−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	−0.728041	−	0.685534i	$-0.759569\pi$
$751$	172.482	−	298.747i	0.229669	−	0.397799i	0.957710	+	0.287735i	$0.0929023\pi$
$752$	−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
$760$	−387.331	+	145.295i	−0.509646	+	0.191177i
$761$	−960.298	−	554.428i	−1.26189	−	0.728552i	−0.288450	−	0.957495i	$-0.593140\pi$
$761$	−960.298	−	554.428i	−1.26189	−	0.728552i	−0.973440	+	0.228942i	$0.926473\pi$
$762$	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	−0.198949	−	0.980010i	$-0.563753\pi$
$769$	576.165	−	997.947i	0.749239	−	1.29772i	0.948188	−	0.317710i	$-0.102914\pi$
$770$	−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	−0.217967	−	0.975956i	$-0.569943\pi$
$787$	−922.485	−	532.597i	−1.17215	−	0.676743i	−0.954186	+	0.299213i	$0.903276\pi$
$788$	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	−0.800639	−	0.599147i	$-0.795507\pi$
$797$	94.4897	−	163.661i	0.118557	−	0.205346i	0.919196	+	0.393801i	$0.128840\pi$
$798$	−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	$-0.760604\pi$
$809$		−	1105.36i		−	1.36633i	0.730266	−	0.683163i	$-0.239396\pi$
$810$	−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	0.0397625	−	0.999209i	$-0.487340\pi$
$821$	759.412	−	438.447i	0.924984	−	0.534040i	0.885222	+	0.465169i	$0.154007\pi$
$822$	−59.3079	+	69.4688i	−0.0721507	+	0.0845120i
$823$	992.214	+	572.855i	1.20561	+	0.696057i	0.961796	−	0.273766i	$-0.0882693\pi$
$823$	992.214	+	572.855i	1.20561	+	0.696057i	0.243810	+	0.969823i	$0.421603\pi$
$824$	−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	−0.247154	−	0.968976i	$-0.579495\pi$
$839$	393.010	−	226.904i	0.468427	−	0.270446i	0.715581	+	0.698530i	$0.246162\pi$
$840$	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	−0.491715	−	0.870756i	$-0.663630\pi$
$853$	14.0948	−	8.13764i	0.0165238	−	0.00954002i	0.508239	+	0.861216i	$0.330297\pi$
$854$		−	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	0.989590	+	0.143912i	$0.0459683\pi$
$857$	530.849	+	919.457i	0.619427	+	1.07288i	−0.370164	+	0.928967i	$0.620698\pi$
$858$	66.4400	+	187.501i	0.0774359	+	0.218533i
$859$	−811.869	+	1406.20i	−0.945133	+	1.63702i	−0.189648	+	0.981852i	$0.560735\pi$
$859$	−811.869	+	1406.20i	−0.945133	+	1.63702i	−0.755485	+	0.655166i	$0.772599\pi$
$860$	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	0.999148	+	0.0412710i	$0.0131407\pi$
$877$	1345.72	+	776.955i	1.53446	+	0.885923i	0.535316	+	0.844652i	$0.320193\pi$
$878$	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	$-0.917396\pi$
$881$		−	452.136i		−	0.513208i	0.966517	−	0.256604i	$-0.0826036\pi$
$882$	−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
$885$	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	−0.801387	−	0.598147i	$-0.795904\pi$
$887$	104.060	−	180.237i	0.117317	−	0.203199i	0.918704	+	0.394948i	$0.129237\pi$
$888$	−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	−0.609073	−	0.793114i	$-0.708458\pi$
$907$	−205.665	+	118.741i	−0.226753	+	0.130916i	0.382320	+	0.924030i	$0.375125\pi$
$908$	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	0.304404	−	0.952543i	$-0.401543\pi$
$911$	1167.48	−	674.042i	1.28153	−	0.739893i	0.977128	+	0.212650i	$0.0682095\pi$
$912$	−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	−0.813408	−	0.581693i	$-0.802391\pi$
$929$	−665.491	+	384.221i	−0.716352	+	0.413586i	0.0970567	+	0.995279i	$0.469057\pi$
$930$	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	$-0.938545\pi$
$937$		−	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
$940$	1626.39	−	610.087i	1.73020	−	0.649029i
$941$	183.507	+	105.948i	0.195013	+	0.112591i	0.594327	−	0.804223i	$-0.297418\pi$
$941$	183.507	+	105.948i	0.195013	+	0.112591i	−0.399314	+	0.916814i	$0.630752\pi$
$942$	−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	−0.908062	−	0.418837i	$-0.862438\pi$
$947$	−773.466	−	1339.68i	−0.816754	−	1.41466i	0.0913074	−	0.995823i	$-0.470895\pi$
$948$	−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	0.318795	−	0.947824i	$-0.396722\pi$
$967$	−331.339	−	191.299i	−0.342646	−	0.197827i	−0.661442	+	0.749997i	$0.730055\pi$
$968$	−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	$-0.725442\pi$
$971$		−	1474.96i		−	1.51901i	0.650503	−	0.759504i	$-0.274558\pi$
$972$	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	0.233136	+	0.972444i	$0.425101\pi$
$977$	−708.905	+	1227.86i	−0.725593	+	1.25676i	−0.958729	+	0.284320i	$0.908232\pi$
$978$	−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	$-0.239232\pi$
$983$	−222.160	−	384.792i	−0.226002	−	0.391447i	−0.956620	+	0.291340i	$0.905899\pi$
$984$	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	−0.455399	−	0.890287i	$-0.650503\pi$
$997$	87.6487	−	50.6040i	0.0879125	−	0.0507563i	0.543312	+	0.839531i	$0.317170\pi$
$998$	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.14.6	yes	20
3.2	odd	2		135.3.h.a.44.5		20
5.2	odd	4		225.3.j.e.176.5		20
5.3	odd	4		225.3.j.e.176.6		20
5.4	even	2	inner	45.3.h.a.14.5	✓	20
9.2	odd	6	inner	45.3.h.a.29.5	yes	20
9.4	even	3		405.3.d.a.404.10		20
9.5	odd	6		405.3.d.a.404.11		20
9.7	even	3		135.3.h.a.89.6		20
15.2	even	4		675.3.j.e.476.6		20
15.8	even	4		675.3.j.e.476.5		20
15.14	odd	2		135.3.h.a.44.6		20
45.2	even	12		225.3.j.e.101.5		20
45.4	even	6		405.3.d.a.404.12		20
45.7	odd	12		675.3.j.e.251.6		20
45.14	odd	6		405.3.d.a.404.9		20
45.29	odd	6	inner	45.3.h.a.29.6	yes	20
45.34	even	6		135.3.h.a.89.5		20
45.38	even	12		225.3.j.e.101.6		20
45.43	odd	12		675.3.j.e.251.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.5	✓	20	5.4	even	2	inner
45.3.h.a.14.6	yes	20	1.1	even	1	trivial
45.3.h.a.29.5	yes	20	9.2	odd	6	inner
45.3.h.a.29.6	yes	20	45.29	odd	6	inner
135.3.h.a.44.5		20	3.2	odd	2
135.3.h.a.44.6		20	15.14	odd	2
135.3.h.a.89.5		20	45.34	even	6
135.3.h.a.89.6		20	9.7	even	3
225.3.j.e.101.5		20	45.2	even	12
225.3.j.e.101.6		20	45.38	even	12
225.3.j.e.176.5		20	5.2	odd	4
225.3.j.e.176.6		20	5.3	odd	4
405.3.d.a.404.9		20	45.14	odd	6
405.3.d.a.404.10		20	9.4	even	3
405.3.d.a.404.11		20	9.5	odd	6
405.3.d.a.404.12		20	45.4	even	6
675.3.j.e.251.5		20	45.43	odd	12
675.3.j.e.251.6		20	45.7	odd	12
675.3.j.e.476.5		20	15.8	even	4
675.3.j.e.476.6		20	15.2	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.264396 + 0.457947i) q^{2} +(2.94987 + 0.546115i) q^{3} +(1.86019 - 3.22194i) q^{4} +(-4.68146 + 1.75610i) q^{5} +(0.529842 + 1.49528i) q^{6} +(-2.39593 + 1.38329i) q^{7} +4.08247 q^{8} +(8.40352 + 3.22194i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} - 12 q^{5} + 12 q^{6} - 18 q^{9}+O(q^{10}) \) 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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