LMFDB - Embedded newform 55.3.i.b.46.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [55,3,Mod(6,55)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(55, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 9])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("55.6"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 55 = 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	55.i (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.49864145398$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			46.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	55.46
Dual form			55.3.i.b.6.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.92705 + 0.951057i) q^{2} +(-3.73607 + 2.71441i) q^{3} +(4.42705 + 3.21644i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-13.5172 + 4.39201i) q^{6} +(6.38197 - 8.78402i) q^{7} +(2.66312 + 3.66547i) q^{8} +(3.80902 - 11.7229i) q^{9} +6.88191i q^{10} +(10.3713 + 3.66547i) q^{11} -25.2705 q^{12} +(-10.8541 - 3.52671i) q^{13} +(27.0344 - 19.6417i) q^{14} +(-8.35410 - 6.06961i) q^{15} +(-2.45492 - 7.55545i) q^{16} +(-21.4443 + 6.96767i) q^{17} +(22.2984 - 30.6911i) q^{18} +(4.96149 + 6.82891i) q^{19} +(-3.78115 + 11.6372i) q^{20} +50.1410i q^{21} +(26.8713 + 20.5927i) q^{22} +0.472136 q^{23} +(-19.8992 - 6.46564i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-28.4164 - 20.6457i) q^{26} +(4.74671 + 14.6089i) q^{27} +(56.5066 - 18.3601i) q^{28} +(-9.67376 + 13.3148i) q^{29} +(-18.6803 - 25.7113i) q^{30} +(9.96556 - 30.6708i) q^{31} -42.5730i q^{32} +(-48.6976 + 14.4576i) q^{33} -69.3951 q^{34} +(23.0902 + 7.50245i) q^{35} +(54.5689 - 39.6466i) q^{36} +(-7.18034 - 5.21682i) q^{37} +(8.02786 + 24.7072i) q^{38} +(50.1246 - 16.2865i) q^{39} +(-5.95492 + 8.19624i) q^{40} +(15.5902 + 21.4580i) q^{41} +(-47.6869 + 146.765i) q^{42} +50.0350i q^{43} +(34.1246 + 49.5860i) q^{44} +27.5623 q^{45} +(1.38197 + 0.449028i) q^{46} +(-28.3607 + 20.6052i) q^{47} +(29.6803 + 21.5640i) q^{48} +(-21.2877 - 65.5169i) q^{49} +(-14.6353 + 4.75528i) q^{50} +(61.2041 - 84.2403i) q^{51} +(-36.7082 - 50.5245i) q^{52} +(10.3951 - 31.9929i) q^{53} +47.2753i q^{54} +(-0.628677 + 24.5887i) q^{55} +49.1935 q^{56} +(-37.0729 - 12.0457i) q^{57} +(-40.9787 + 29.7728i) q^{58} +(89.4681 + 65.0024i) q^{59} +(-17.4615 - 53.7409i) q^{60} +(-71.4296 + 23.2089i) q^{61} +(58.3394 - 80.2973i) q^{62} +(-78.6656 - 108.274i) q^{63} +(30.6697 - 94.3916i) q^{64} -25.5195i q^{65} +(-156.290 - 3.99598i) q^{66} +44.4508 q^{67} +(-117.346 - 38.1280i) q^{68} +(-1.76393 + 1.28157i) q^{69} +(60.4508 + 43.9201i) q^{70} +(-16.2148 - 49.9040i) q^{71} +(53.1140 - 17.2578i) q^{72} +(-46.3197 + 63.7535i) q^{73} +(-16.0557 - 22.0988i) q^{74} +(7.13525 - 21.9601i) q^{75} +46.1903i q^{76} +(98.3870 - 67.7090i) q^{77} +162.207 q^{78} +(-121.151 - 39.3643i) q^{79} +(14.3713 - 10.4414i) q^{80} +(32.3607 + 23.5114i) q^{81} +(25.2254 + 77.6359i) q^{82} +(35.6287 - 11.5765i) q^{83} +(-161.276 + 221.977i) q^{84} +(-29.6353 - 40.7894i) q^{85} +(-47.5861 + 146.455i) q^{86} -76.0035i q^{87} +(14.1844 + 47.7773i) q^{88} +108.326 q^{89} +(80.6763 + 26.2133i) q^{90} +(-100.249 + 72.8353i) q^{91} +(2.09017 + 1.51860i) q^{92} +(46.0213 + 141.639i) q^{93} +(-102.610 + 33.3400i) q^{94} +(-11.0942 + 15.2699i) q^{95} +(115.561 + 159.056i) q^{96} +(19.1008 - 58.7863i) q^{97} -212.017i q^{98} +(82.4746 - 107.621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 5 q^{2} - 6 q^{3} + 11 q^{4} + 5 q^{5} - 25 q^{6} + 30 q^{7} - 5 q^{8} + 13 q^{9} - q^{11} - 34 q^{12} - 30 q^{13} + 50 q^{14} - 20 q^{15} - 21 q^{16} - 50 q^{17} + 40 q^{18} - 45 q^{19} + 5 q^{20}+ \cdots + 113 q^{99}+O(q^{100}) $ 4 * q + 5 * q^2 - 6 * q^3 + 11 * q^4 + 5 * q^5 - 25 * q^6 + 30 * q^7 - 5 * q^8 + 13 * q^9 - q^11 - 34 * q^12 - 30 * q^13 + 50 * q^14 - 20 * q^15 - 21 * q^16 - 50 * q^17 + 40 * q^18 - 45 * q^19 + 5 * q^20 + 65 * q^22 - 16 * q^23 - 55 * q^24 - 5 * q^25 - 60 * q^26 + 57 * q^27 + 150 * q^28 - 70 * q^29 - 30 * q^30 + 98 * q^31 - 121 * q^33 - 130 * q^34 + 70 * q^35 + 102 * q^36 + 16 * q^37 + 50 * q^38 + 120 * q^39 - 35 * q^40 + 40 * q^41 - 70 * q^42 + 56 * q^44 + 70 * q^45 + 10 * q^46 - 24 * q^47 + 74 * q^48 + 11 * q^49 - 25 * q^50 + 95 * q^51 - 120 * q^52 - 106 * q^53 - 45 * q^55 - 155 * q^57 - 70 * q^58 + 217 * q^59 - 5 * q^60 - 80 * q^61 + 50 * q^62 - 100 * q^63 + 31 * q^64 - 330 * q^66 + 66 * q^67 - 210 * q^68 - 16 * q^69 + 130 * q^70 + 38 * q^71 + 85 * q^72 - 230 * q^73 - 100 * q^74 - 5 * q^75 + 300 * q^78 - 100 * q^79 + 15 * q^80 + 40 * q^81 + 45 * q^82 + 185 * q^83 - 180 * q^84 - 85 * q^85 - 45 * q^86 + 135 * q^88 + 402 * q^89 + 155 * q^90 - 240 * q^91 - 14 * q^92 + 278 * q^93 - 160 * q^94 - 145 * q^95 + 100 * q^96 + 101 * q^97 + 113 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/55\mathbb{Z}\right)^\times$.

$n$	$12$	$46$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	2.92705	+	0.951057i	1.46353	+	0.475528i	0.929145	−	0.369716i	$-0.120545\pi$
$2$	2.92705	+	0.951057i	1.46353	+	0.475528i	0.534381	+	0.845244i	$0.320545\pi$
$3$	−3.73607	+	2.71441i	−1.24536	+	0.904804i	−0.997943	−	0.0641060i	$-0.979580\pi$
$3$	−3.73607	+	2.71441i	−1.24536	+	0.904804i	−0.247413	+	0.968910i	$0.579580\pi$
$4$	4.42705	+	3.21644i	1.10676	+	0.804110i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$6$	−13.5172	+	4.39201i	−2.25287	+	0.732002i
$7$	6.38197	−	8.78402i	0.911709	−	1.25486i	−0.0548701	−	0.998494i	$-0.517474\pi$
$7$	6.38197	−	8.78402i	0.911709	−	1.25486i	0.966580	−	0.256367i	$-0.0825255\pi$
$8$	2.66312	+	3.66547i	0.332890	+	0.458184i
$9$	3.80902	−	11.7229i	0.423224	−	1.30255i
$10$			6.88191i			0.688191i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$11$	10.3713	+	3.66547i	0.942848	+	0.333224i
$12$	−25.2705			−2.10588
$13$	−10.8541	−	3.52671i	−0.834931	−	0.271286i	−0.139810	−	0.990178i	$-0.544649\pi$
$13$	−10.8541	−	3.52671i	−0.834931	−	0.271286i	−0.695121	+	0.718893i	$0.744649\pi$
$14$	27.0344	−	19.6417i	1.93103	−	1.40298i
$15$	−8.35410	−	6.06961i	−0.556940	−	0.404641i
$16$	−2.45492	−	7.55545i	−0.153432	−	0.472216i
$17$	−21.4443	+	6.96767i	−1.26143	+	0.409863i	−0.862003	−	0.506903i	$-0.830790\pi$
$17$	−21.4443	+	6.96767i	−1.26143	+	0.409863i	−0.399425	+	0.916766i	$0.630790\pi$
$18$	22.2984	−	30.6911i	1.23880	−	1.70506i
$19$	4.96149	+	6.82891i	0.261131	+	0.359416i	0.919371	−	0.393392i	$-0.128699\pi$
$19$	4.96149	+	6.82891i	0.261131	+	0.359416i	−0.658239	+	0.752809i	$0.728699\pi$
$20$	−3.78115	+	11.6372i	−0.189058	+	0.581860i
$21$			50.1410i			2.38767i
$22$	26.8713	+	20.5927i	1.22142	+	0.936033i
$23$	0.472136			0.0205277			0.0102638	−	0.999947i	$-0.496733\pi$
$23$	0.472136			0.0205277			0.0102638	+	0.999947i	$0.496733\pi$
$24$	−19.8992	−	6.46564i	−0.829133	−	0.269402i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	−28.4164	−	20.6457i	−1.09294	−	0.794066i
$27$	4.74671	+	14.6089i	0.175804	+	0.541069i
$28$	56.5066	−	18.3601i	2.01809	−	0.655718i
$29$	−9.67376	+	13.3148i	−0.333578	+	0.459131i	−0.942552	−	0.334059i	$-0.891581\pi$
$29$	−9.67376	+	13.3148i	−0.333578	+	0.459131i	0.608974	+	0.793190i	$0.291581\pi$
$30$	−18.6803	−	25.7113i	−0.622678	−	0.857043i
$31$	9.96556	−	30.6708i	0.321470	−	0.989382i	−0.651539	−	0.758615i	$-0.725876\pi$
$31$	9.96556	−	30.6708i	0.321470	−	0.989382i	0.973009	−	0.230767i	$-0.0741235\pi$
$32$		−	42.5730i		−	1.33041i
$33$	−48.6976	+	14.4576i	−1.47568	+	0.438109i
$34$	−69.3951			−2.04103
$35$	23.0902	+	7.50245i	0.659719	+	0.214356i
$36$	54.5689	−	39.6466i	1.51580	−	1.10129i
$37$	−7.18034	−	5.21682i	−0.194063	−	0.140995i	0.486511	−	0.873675i	$-0.338269\pi$
$37$	−7.18034	−	5.21682i	−0.194063	−	0.140995i	−0.680574	+	0.732679i	$0.738269\pi$
$38$	8.02786	+	24.7072i	0.211260	+	0.650190i
$39$	50.1246	−	16.2865i	1.28525	−	0.417602i
$40$	−5.95492	+	8.19624i	−0.148873	+	0.204906i
$41$	15.5902	+	21.4580i	0.380248	+	0.523367i	0.955650	−	0.294504i	$-0.0951545\pi$
$41$	15.5902	+	21.4580i	0.380248	+	0.523367i	−0.575402	+	0.817871i	$0.695154\pi$
$42$	−47.6869	+	146.765i	−1.13540	+	3.49441i
$43$			50.0350i			1.16360i	0.813330	+	0.581802i	$0.197652\pi$
$43$			50.0350i			1.16360i	−0.813330	+	0.581802i	$0.802348\pi$
$44$	34.1246	+	49.5860i	0.775559	+	1.12695i
$45$	27.5623			0.612496
$46$	1.38197	+	0.449028i	0.0300427	+	0.00976148i
$47$	−28.3607	+	20.6052i	−0.603419	+	0.438409i	−0.847091	−	0.531448i	$-0.821648\pi$
$47$	−28.3607	+	20.6052i	−0.603419	+	0.438409i	0.243672	+	0.969858i	$0.421648\pi$
$48$	29.6803	+	21.5640i	0.618340	+	0.449251i
$49$	−21.2877	−	65.5169i	−0.434443	−	1.33708i
$50$	−14.6353	+	4.75528i	−0.292705	+	0.0951057i
$51$	61.2041	−	84.2403i	1.20008	−	1.65177i
$52$	−36.7082	−	50.5245i	−0.705927	−	0.971625i
$53$	10.3951	−	31.9929i	0.196134	−	0.603640i	−0.803827	−	0.594863i	$-0.797206\pi$
$53$	10.3951	−	31.9929i	0.196134	−	0.603640i	0.999961	−	0.00877654i	$-0.00279370\pi$
$54$			47.2753i			0.875469i
$55$	−0.628677	+	24.5887i	−0.0114305	+	0.447067i
$56$	49.1935			0.878455
$57$	−37.0729	−	12.0457i	−0.650403	−	0.211329i
$58$	−40.9787	+	29.7728i	−0.706530	+	0.513324i
$59$	89.4681	+	65.0024i	1.51641	+	1.10173i	0.963232	+	0.268670i	$0.0865842\pi$
$59$	89.4681	+	65.0024i	1.51641	+	1.10173i	0.553176	+	0.833065i	$0.313416\pi$
$60$	−17.4615	−	53.7409i	−0.291025	−	0.895682i
$61$	−71.4296	+	23.2089i	−1.17098	+	0.380473i	−0.829007	−	0.559238i	$-0.811094\pi$
$61$	−71.4296	+	23.2089i	−1.17098	+	0.380473i	−0.341969	+	0.939711i	$0.611094\pi$
$62$	58.3394	−	80.2973i	0.940958	−	1.29512i
$63$	−78.6656	−	108.274i	−1.24866	−	1.71863i
$64$	30.6697	−	94.3916i	0.479214	−	1.47487i
$65$		−	25.5195i		−	0.392608i
$66$	−156.290	−	3.99598i	−2.36803	−	0.0605452i
$67$	44.4508			0.663446			0.331723	−	0.943377i	$-0.392370\pi$
$67$	44.4508			0.663446			0.331723	+	0.943377i	$0.392370\pi$
$68$	−117.346	−	38.1280i	−1.72568	−	0.560706i
$69$	−1.76393	+	1.28157i	−0.0255642	+	0.0185735i
$70$	60.4508	+	43.9201i	0.863584	+	0.627430i
$71$	−16.2148	−	49.9040i	−0.228377	−	0.702873i	−0.997931	−	0.0642910i	$-0.979521\pi$
$71$	−16.2148	−	49.9040i	−0.228377	−	0.702873i	0.769554	−	0.638582i	$-0.220479\pi$
$72$	53.1140	−	17.2578i	0.737694	−	0.239691i
$73$	−46.3197	+	63.7535i	−0.634516	+	0.873336i	−0.998308	−	0.0581439i	$-0.981482\pi$
$73$	−46.3197	+	63.7535i	−0.634516	+	0.873336i	0.363792	+	0.931480i	$0.381482\pi$
$74$	−16.0557	−	22.0988i	−0.216969	−	0.298633i
$75$	7.13525	−	21.9601i	0.0951367	−	0.292801i
$76$			46.1903i			0.607767i
$77$	98.3870	−	67.7090i	1.27775	−	0.879338i
$78$	162.207			2.07957
$79$	−121.151	−	39.3643i	−1.53356	−	0.498283i	−0.583966	−	0.811778i	$-0.698500\pi$
$79$	−121.151	−	39.3643i	−1.53356	−	0.498283i	−0.949590	+	0.313495i	$0.898500\pi$
$80$	14.3713	−	10.4414i	0.179642	−	0.130517i
$81$	32.3607	+	23.5114i	0.399515	+	0.290264i
$82$	25.2254	+	77.6359i	0.307627	+	0.946779i
$83$	35.6287	−	11.5765i	0.429261	−	0.139475i	−0.0864145	−	0.996259i	$-0.527541\pi$
$83$	35.6287	−	11.5765i	0.429261	−	0.139475i	0.515676	+	0.856784i	$0.327541\pi$
$84$	−161.276	+	221.977i	−1.91995	+	2.64258i
$85$	−29.6353	−	40.7894i	−0.348650	−	0.479876i
$86$	−47.5861	+	146.455i	−0.553327	+	1.70296i
$87$		−	76.0035i		−	0.873604i
$88$	14.1844	+	47.7773i	0.161186	+	0.542924i
$89$	108.326			1.21715			0.608574	−	0.793497i	$-0.291742\pi$
$89$	108.326			1.21715			0.608574	+	0.793497i	$0.291742\pi$
$90$	80.6763	+	26.2133i	0.896403	+	0.291259i
$91$	−100.249	+	72.8353i	−1.10164	+	0.800388i
$92$	2.09017	+	1.51860i	0.0227192	+	0.0165065i
$93$	46.0213	+	141.639i	0.494853	+	1.52300i
$94$	−102.610	+	33.3400i	−1.09159	+	0.354681i
$95$	−11.0942	+	15.2699i	−0.116781	+	0.160736i
$96$	115.561	+	159.056i	1.20376	+	1.65683i
$97$	19.1008	−	58.7863i	0.196916	−	0.606044i	−0.803033	−	0.595934i	$-0.796782\pi$
$97$	19.1008	−	58.7863i	0.196916	−	0.606044i	0.999949	−	0.0101097i	$-0.00321808\pi$
$98$		−	212.017i		−	2.16344i
$99$	82.4746	−	107.621i	0.833077	−	1.08708i
$100$	−27.3607			−0.273607
$101$	54.8460	+	17.8205i	0.543029	+	0.176441i	0.567671	−	0.823255i	$-0.307845\pi$
$101$	54.8460	+	17.8205i	0.543029	+	0.176441i	−0.0246418	+	0.999696i	$0.507845\pi$
$102$	259.265	−	188.367i	2.54181	−	1.84673i
$103$	−88.9230	−	64.6063i	−0.863330	−	0.627246i	0.0654589	−	0.997855i	$-0.479149\pi$
$103$	−88.9230	−	64.6063i	−0.863330	−	0.627246i	−0.928789	+	0.370609i	$0.879149\pi$
$104$	−15.9787	−	49.1774i	−0.153641	−	0.472860i
$105$	−106.631	+	34.6466i	−1.01554	+	0.329967i
$106$	60.8541	−	83.7585i	0.574095	−	0.790174i
$107$	32.9803	+	45.3934i	0.308227	+	0.424238i	0.934827	−	0.355103i	$-0.115554\pi$
$107$	32.9803	+	45.3934i	0.308227	+	0.424238i	−0.626600	+	0.779341i	$0.715554\pi$
$108$	−25.9746	+	79.9417i	−0.240506	+	0.740201i
$109$			64.2478i			0.589430i	0.955585	+	0.294715i	$0.0952247\pi$
$109$			64.2478i			0.589430i	−0.955585	+	0.294715i	$0.904775\pi$
$110$	−25.2254	+	71.3745i	−0.229322	+	0.648859i
$111$	40.9868			0.369251
$112$	−82.0344	−	26.6546i	−0.732450	−	0.237988i
$113$	−7.25329	+	5.26982i	−0.0641884	+	0.0466356i	−0.619417	−	0.785062i	$-0.712631\pi$
$113$	−7.25329	+	5.26982i	−0.0641884	+	0.0466356i	0.555228	+	0.831698i	$0.312631\pi$
$114$	−97.0582	−	70.5169i	−0.851388	−	0.618570i
$115$	0.326238	+	1.00406i	0.00283685	+	0.00873093i
$116$	−85.6525	+	27.8302i	−0.738383	+	0.239915i
$117$	−82.6869	+	113.809i	−0.706726	+	0.972725i
$118$	200.057	+	275.354i	1.69540	+	2.33351i
$119$	−75.6525	+	232.834i	−0.635735	+	1.95659i
$120$		−	46.7858i		−	0.389882i
$121$	94.1287	+	76.0315i	0.777923	+	0.628360i
$122$	−231.151			−1.89468
$123$	−116.492	−	37.8505i	−0.947088	−	0.307728i
$124$	142.769	−	103.728i	1.15136	−	0.836514i
$125$	−9.04508	−	6.57164i	−0.0723607	−	0.0525731i
$126$	−127.284	−	391.739i	−1.01019	−	3.10904i
$127$	143.387	−	46.5893i	1.12903	−	0.366845i	0.315824	−	0.948818i	$-0.397719\pi$
$127$	143.387	−	46.5893i	1.12903	−	0.366845i	0.813208	+	0.581973i	$0.197719\pi$
$128$	79.4483	−	109.351i	0.620690	−	0.854307i
$129$	−135.816	−	186.934i	−1.05283	−	1.44910i
$130$	24.2705	−	74.6969i	0.186696	−	0.574592i
$131$		−	97.0983i		−	0.741208i	−0.928791	−	0.370604i	$-0.879151\pi$
$131$		−	97.0983i		−	0.741208i	0.928791	−	0.370604i	$-0.120849\pi$
$132$	−262.089	−	92.6283i	−1.98552	−	0.701729i
$133$	91.6494			0.689093
$134$	130.110	+	42.2753i	0.970969	+	0.315487i
$135$	−27.7877	+	20.1890i	−0.205835	+	0.149548i
$136$	−82.6484	−	60.0476i	−0.607709	−	0.441526i
$137$	64.7239	+	199.200i	0.472437	+	1.45401i	0.849383	+	0.527777i	$0.176974\pi$
$137$	64.7239	+	199.200i	0.472437	+	1.45401i	−0.376946	+	0.926235i	$0.623026\pi$
$138$	−6.38197	+	2.07363i	−0.0462461	+	0.0150263i
$139$	−4.72136	+	6.49839i	−0.0339666	+	0.0467510i	−0.825663	−	0.564164i	$-0.809198\pi$
$139$	−4.72136	+	6.49839i	−0.0339666	+	0.0467510i	0.791696	+	0.610915i	$0.209198\pi$
$140$	78.0902	+	107.482i	0.557787	+	0.767728i
$141$	50.0263	−	153.965i	0.354797	−	1.09195i
$142$		−	161.493i		−	1.13727i
$143$	−99.6443	−	76.3620i	−0.696814	−	0.534000i
$144$	−97.9230			−0.680021
$145$	−35.0000	−	11.3722i	−0.241379	−	0.0784289i
$146$	−196.213	+	142.557i	−1.34393	+	0.976420i
$147$	257.372	+	186.992i	1.75083	+	1.27205i
$148$	−15.0081	−	46.1903i	−0.101406	−	0.312096i
$149$	−44.3951	+	14.4248i	−0.297954	+	0.0968111i	−0.454179	−	0.890910i	$-0.650067\pi$
$149$	−44.3951	+	14.4248i	−0.297954	+	0.0968111i	0.156225	+	0.987721i	$0.450067\pi$
$150$	41.7705	−	57.4922i	0.278470	−	0.383281i
$151$	44.1459	+	60.7616i	0.292357	+	0.402395i	0.929778	−	0.368121i	$-0.119999\pi$
$151$	44.1459	+	60.7616i	0.292357	+	0.402395i	−0.637421	+	0.770516i	$0.719999\pi$
$152$	−11.8181	+	36.3724i	−0.0777507	+	0.239292i
$153$			277.930i			1.81654i
$154$	352.379	−	104.616i	2.28817	−	0.679326i
$155$	72.1115			0.465235
$156$	274.289	+	89.1218i	1.75826	+	0.571294i
$157$	29.9311	−	21.7462i	0.190644	−	0.138511i	−0.488369	−	0.872637i	$-0.662408\pi$
$157$	29.9311	−	21.7462i	0.190644	−	0.138511i	0.679013	+	0.734126i	$0.262408\pi$
$158$	−317.177	−	230.443i	−2.00745	−	1.45850i
$159$	48.0050	+	147.744i	0.301918	+	0.929209i
$160$	90.5370	−	29.4172i	0.565856	−	0.183858i
$161$	3.01316	−	4.14725i	0.0187153	−	0.0257593i
$162$	72.3607	+	99.5959i	0.446671	+	0.614790i
$163$	14.5263	−	44.7074i	0.0891185	−	0.274278i	−0.896558	−	0.442927i	$-0.853940\pi$
$163$	14.5263	−	44.7074i	0.0891185	−	0.274278i	0.985676	+	0.168648i	$0.0539402\pi$
$164$			145.141i			0.885004i
$165$	−64.3951	−	93.5716i	−0.390273	−	0.567101i
$166$	115.297			0.694559
$167$	45.2786	+	14.7119i	0.271130	+	0.0880953i	0.441426	−	0.897297i	$-0.354473\pi$
$167$	45.2786	+	14.7119i	0.271130	+	0.0880953i	−0.170297	+	0.985393i	$0.554473\pi$
$168$	−183.790	+	133.531i	−1.09399	+	0.794830i
$169$	−31.3500	−	22.7771i	−0.185503	−	0.134776i
$170$	−47.9508	−	147.578i	−0.282064	−	0.868103i
$171$	98.9534	−	32.1519i	0.578675	−	0.188023i
$172$	−160.935	+	221.507i	−0.935666	+	1.28783i
$173$	−112.207	−	154.439i	−0.648593	−	0.892712i	0.350444	−	0.936584i	$-0.386031\pi$
$173$	−112.207	−	154.439i	−0.648593	−	0.892712i	−0.999037	+	0.0438716i	$0.986031\pi$
$174$	72.2837	−	222.466i	0.415423	−	1.27854i
$175$			54.2882i			0.310219i
$176$	2.23356	−	87.3584i	0.0126907	−	0.496355i
$177$	−510.702			−2.88532
$178$	317.076	+	103.024i	1.78133	+	0.578789i
$179$	−208.919	+	151.788i	−1.16714	+	0.847980i	−0.990664	−	0.136324i	$-0.956471\pi$
$179$	−208.919	+	151.788i	−1.16714	+	0.847980i	−0.176480	+	0.984304i	$0.556471\pi$
$180$	122.020	+	88.6525i	0.677887	+	0.492514i
$181$	−50.8115	−	156.382i	−0.280727	−	0.863988i	−0.987647	−	0.156695i	$-0.949916\pi$
$181$	−50.8115	−	156.382i	−0.280727	−	0.863988i	0.706920	−	0.707293i	$-0.250084\pi$
$182$	−362.705	+	117.850i	−1.99289	+	0.647528i
$183$	203.867	−	280.599i	1.11403	−	1.53333i
$184$	1.25735	+	1.73060i	0.00683345	+	0.00940543i
$185$	6.13274	−	18.8746i	0.0331500	−	0.102025i
$186$			458.353i			2.46426i
$187$	−247.945	−	6.33939i	−1.32591	−	0.0339005i
$188$	−191.830			−1.02037
$189$	158.618	+	51.5381i	0.839249	+	0.272688i
$190$	−46.9959	+	34.1445i	−0.247347	+	0.179708i
$191$	30.7426	+	22.3358i	0.160956	+	0.116942i	0.665348	−	0.746533i	$-0.268283\pi$
$191$	30.7426	+	22.3358i	0.160956	+	0.116942i	−0.504392	+	0.863475i	$0.668283\pi$
$192$	141.634	+	435.904i	0.737676	+	2.27033i
$193$	4.47214	−	1.45309i	0.0231717	−	0.00752894i	−0.297408	−	0.954750i	$-0.596122\pi$
$193$	4.47214	−	1.45309i	0.0231717	−	0.00752894i	0.320580	+	0.947221i	$0.396122\pi$
$194$	111.818	−	153.904i	0.576382	−	0.793322i
$195$	69.2705	+	95.3427i	0.355233	+	0.488937i
$196$	116.489	−	358.517i	0.594333	−	1.82917i
$197$		−	107.254i		−	0.544439i	−0.962235	−	0.272219i	$-0.912242\pi$
$197$		−	107.254i		−	0.544439i	0.962235	−	0.272219i	$-0.0877576\pi$
$198$	343.761	−	236.573i	1.73617	−	1.19481i
$199$	18.5936			0.0934354			0.0467177	−	0.998908i	$-0.485124\pi$
$199$	18.5936			0.0934354			0.0467177	+	0.998908i	$0.485124\pi$
$200$	−21.5451	−	7.00042i	−0.107725	−	0.0350021i
$201$	−166.071	+	120.658i	−0.826226	+	0.600288i
$202$	143.589	+	104.323i	0.710835	+	0.516452i
$203$	55.2198	+	169.949i	0.272019	+	0.837188i
$204$	541.908	−	176.076i	2.65641	−	0.863120i
$205$	−34.8607	+	47.9816i	−0.170052	+	0.234057i
$206$	−198.838	−	273.677i	−0.965232	−	1.32853i
$207$	1.79837	−	5.53483i	0.00868780	−	0.0267383i
$208$			90.6654i			0.435891i
$209$	26.4261	+	89.0110i	0.126441	+	0.425890i
$210$	−345.066			−1.64317
$211$	−92.8829	−	30.1795i	−0.440203	−	0.143031i	0.0805260	−	0.996753i	$-0.474340\pi$
$211$	−92.8829	−	30.1795i	−0.440203	−	0.143031i	−0.520729	+	0.853722i	$0.674340\pi$
$212$	148.923	−	108.199i	0.702467	−	0.510372i
$213$	196.039	+	142.431i	0.920373	+	0.668690i
$214$	53.3632	+	164.235i	0.249361	+	0.767453i
$215$	−106.406	+	34.5733i	−0.494911	+	0.160806i
$216$	−40.9073	+	56.3041i	−0.189386	+	0.260667i
$217$	−205.813	−	283.278i	−0.948449	−	1.30543i
$218$	−61.1033	+	188.057i	−0.280290	+	0.862645i
$219$		−	363.918i		−	1.66173i
$220$	−81.8713	+	106.833i	−0.372142	+	0.485606i
$221$	257.331			1.16439
$222$	119.971	+	38.9808i	0.540408	+	0.175589i
$223$	306.920	−	222.990i	1.37632	−	0.999957i	0.379109	−	0.925352i	$-0.376230\pi$
$223$	306.920	−	222.990i	1.37632	−	0.999957i	0.997213	−	0.0746047i	$-0.0237695\pi$
$224$	−373.962	−	271.700i	−1.66948	−	1.21294i
$225$	19.0451	+	58.6147i	0.0846448	+	0.260510i
$226$	−26.2426	+	8.52675i	−0.116118	+	0.0377290i
$227$	122.513	−	168.624i	0.539703	−	0.742837i	−0.448867	−	0.893598i	$-0.648172\pi$
$227$	122.513	−	168.624i	0.539703	−	0.742837i	0.988570	+	0.150761i	$0.0481724\pi$
$228$	−125.379	−	172.570i	−0.549910	−	0.756886i
$229$	−19.2179	+	59.1466i	−0.0839209	+	0.258282i	−0.984208	−	0.177014i	$-0.943356\pi$
$229$	−19.2179	+	59.1466i	−0.0839209	+	0.258282i	0.900287	+	0.435296i	$0.143356\pi$
$230$			3.24920i			0.0141269i
$231$	−183.790	+	520.028i	−0.795629	+	2.25121i
$232$	−74.5673			−0.321411
$233$	263.488	+	85.6124i	1.13085	+	0.367435i	0.813899	−	0.581007i	$-0.197341\pi$
$233$	263.488	+	85.6124i	1.13085	+	0.367435i	0.316950	+	0.948442i	$0.397341\pi$
$234$	−350.267	+	254.484i	−1.49687	+	1.08754i
$235$	−63.4164	−	46.0747i	−0.269857	−	0.196063i
$236$	187.003	+	575.538i	0.792388	+	2.43872i
$237$	559.479	−	181.786i	2.36067	−	0.767029i
$238$	−442.877	+	609.568i	−1.86083	+	2.56121i
$239$	−87.2179	−	120.045i	−0.364928	−	0.502281i	0.586585	−	0.809888i	$-0.300472\pi$
$239$	−87.2179	−	120.045i	−0.364928	−	0.502281i	−0.951514	+	0.307607i	$0.900472\pi$
$240$	−25.3500	+	78.0194i	−0.105625	+	0.325081i
$241$		−	413.928i		−	1.71754i	−0.512358	−	0.858772i	$-0.671228\pi$
$241$		−	413.928i		−	1.71754i	0.512358	−	0.858772i	$-0.328772\pi$
$242$	203.209	+	312.070i	0.839707	+	1.28954i
$243$	−322.967			−1.32908
$244$	−390.872	−	127.002i	−1.60194	−	0.520500i
$245$	124.621	−	90.5421i	0.508655	−	0.369560i
$246$	−304.980	−	221.581i	−1.23975	−	0.900735i
$247$	−29.7690	−	91.6194i	−0.120522	−	0.370929i
$248$	138.962	−	45.1516i	0.560332	−	0.182063i
$249$	−101.688	+	139.961i	−0.408385	+	0.562094i
$250$	−20.2254	−	27.8379i	−0.0809017	−	0.111352i
$251$	115.281	−	354.797i	0.459285	−	1.41353i	−0.406745	−	0.913542i	$-0.633336\pi$
$251$	115.281	−	354.797i	0.459285	−	1.41353i	0.866030	−	0.499992i	$-0.166664\pi$
$252$		−	732.358i		−	2.90618i
$253$	4.89667	+	1.73060i	0.0193544	+	0.00684031i
$254$	464.010			1.82681
$255$	221.439	+	71.9498i	0.868387	+	0.282156i
$256$	15.3713	−	11.1679i	0.0600442	−	0.0436247i
$257$	−165.102	−	119.953i	−0.642419	−	0.466745i	0.218261	−	0.975890i	$-0.429962\pi$
$257$	−165.102	−	119.953i	−0.642419	−	0.466745i	−0.860681	+	0.509145i	$0.829962\pi$
$258$	−219.754	−	676.334i	−0.851761	−	2.62145i
$259$	−91.6494	+	29.7787i	−0.353859	+	0.114976i
$260$	82.0820	−	112.976i	0.315700	−	0.434524i
$261$	119.241	+	164.121i	0.456862	+	0.628817i
$262$	92.3460	−	284.212i	0.352466	−	1.08478i
$263$			64.2788i			0.244406i	0.992505	+	0.122203i	$0.0389959\pi$
$263$			64.2788i			0.244406i	−0.992505	+	0.122203i	$0.961004\pi$
$264$	−182.681	−	139.997i	−0.691975	−	0.530292i
$265$	75.2198			0.283848
$266$	268.262	+	87.1637i	1.00851	+	0.327683i
$267$	−404.714	+	294.042i	−1.51578	+	1.10128i
$268$	196.786	+	142.974i	0.734277	+	0.533483i
$269$	−69.0050	−	212.376i	−0.256524	−	0.789500i	−0.993526	−	0.113609i	$-0.963759\pi$
$269$	−69.0050	−	212.376i	−0.256524	−	0.789500i	0.737001	−	0.675891i	$-0.236241\pi$
$270$	−100.537	+	32.6664i	−0.372359	+	0.120987i
$271$	−165.220	+	227.406i	−0.609667	+	0.839135i	−0.996550	−	0.0829940i	$-0.973552\pi$
$271$	−165.220	+	227.406i	−0.609667	+	0.839135i	0.386883	+	0.922129i	$0.373552\pi$
$272$	105.288	+	144.916i	0.387087	+	0.532780i
$273$	176.833	−	544.235i	0.647739	−	1.99354i
$274$			644.623i			2.35264i
$275$	−52.7254	+	15.6534i	−0.191729	+	0.0569215i
$276$	−11.9311			−0.0432287
$277$	114.538	+	37.2156i	0.413494	+	0.134352i	0.508374	−	0.861136i	$-0.330247\pi$
$277$	114.538	+	37.2156i	0.413494	+	0.134352i	−0.0948799	+	0.995489i	$0.530247\pi$
$278$	−20.0000	+	14.5309i	−0.0719424	+	0.0522692i
$279$	−321.594	−	233.651i	−1.15267	−	0.837460i
$280$	33.9919	+	104.616i	0.121400	+	0.373629i
$281$	−385.665	+	125.310i	−1.37247	+	0.445944i	−0.900188	−	0.435502i	$-0.856571\pi$
$281$	−385.665	+	125.310i	−1.37247	+	0.445944i	−0.472286	+	0.881446i	$0.656571\pi$
$282$	292.859	−	403.086i	1.03851	−	1.42938i
$283$	324.259	+	446.305i	1.14579	+	1.57705i	0.753834	+	0.657065i	$0.228202\pi$
$283$	324.259	+	446.305i	1.14579	+	1.57705i	0.391959	+	0.919983i	$0.371798\pi$
$284$	88.7295	−	273.081i	0.312428	−	0.961554i
$285$		−	87.1637i		−	0.305838i
$286$	−219.039	−	318.283i	−0.765872	−	1.11288i
$287$	287.984			1.00343
$288$	−499.081	−	162.161i	−1.73292	−	0.563060i
$289$	177.503	−	128.963i	0.614196	−	0.446239i
$290$	−91.6312	−	66.5740i	−0.315970	−	0.229565i
$291$	88.2082	+	271.477i	0.303121	+	0.932910i
$292$	−410.119	+	133.256i	−1.40452	+	0.456355i
$293$	−189.259	+	260.493i	−0.645936	+	0.889055i	−0.998915	−	0.0465766i	$-0.985169\pi$
$293$	−189.259	+	260.493i	−0.645936	+	0.889055i	0.352979	+	0.935631i	$0.385169\pi$
$294$	575.502	+	792.110i	1.95749	+	2.69425i
$295$	−76.4149	+	235.181i	−0.259033	+	0.797223i
$296$		−	40.2123i		−	0.135852i
$297$	−4.31870	+	168.912i	−0.0145411	+	0.568728i
$298$	−143.666			−0.482099
$299$	−5.12461	−	1.66509i	−0.0171392	−	0.00556885i
$300$	102.221	−	74.2682i	0.340738	−	0.247561i
$301$	439.508	+	319.322i	1.46016	+	1.06087i
$302$	71.4296	+	219.838i	0.236522	+	0.727939i
$303$	−253.281	+	82.2958i	−0.835909	+	0.271603i
$304$	39.4154	−	54.2507i	0.129656	−	0.178456i
$305$	−98.7132	−	135.867i	−0.323650	−	0.445466i
$306$	−264.327	+	813.515i	−0.863814	+	2.65855i
$307$			100.126i			0.326143i	0.986614	+	0.163072i	$0.0521401\pi$
$307$			100.126i			0.326143i	−0.986614	+	0.163072i	$0.947860\pi$
$308$	653.346	+	16.7046i	2.12125	+	0.0542356i
$309$	507.591			1.64269
$310$	211.074	+	68.5821i	0.680884	+	0.221232i
$311$	159.456	−	115.851i	0.512720	−	0.372513i	−0.301135	−	0.953582i	$-0.597365\pi$
$311$	159.456	−	115.851i	0.512720	−	0.372513i	0.813854	+	0.581069i	$0.197365\pi$
$312$	193.185	+	140.357i	0.619184	+	0.449863i
$313$	−75.0886	−	231.099i	−0.239900	−	0.738335i	−0.996434	−	0.0843809i	$-0.973109\pi$
$313$	−75.0886	−	231.099i	−0.239900	−	0.738335i	0.756534	−	0.653955i	$-0.226891\pi$
$314$	108.292	−	35.1861i	0.344878	−	0.112058i
$315$	175.902	−	242.108i	0.558418	−	0.768597i
$316$	−409.728	−	563.943i	−1.29661	−	1.78463i
$317$	−174.790	+	537.949i	−0.551389	+	1.69700i	0.153906	+	0.988086i	$0.450815\pi$
$317$	−174.790	+	537.949i	−0.551389	+	1.69700i	−0.705294	+	0.708915i	$0.749185\pi$
$318$			478.111i			1.50349i
$319$	−149.135	+	102.633i	−0.467507	+	0.321734i
$320$	221.928			0.693525
$321$	−246.433	−	80.0709i	−0.767704	−	0.249442i
$322$	12.7639	−	9.27354i	0.0396395	−	0.0287998i
$323$	−153.977	−	111.871i	−0.476709	−	0.346350i
$324$	67.6393	+	208.172i	0.208763	+	0.642507i
$325$	54.2705	−	17.6336i	0.166986	−	0.0542571i
$326$	85.0385	−	117.045i	0.260854	−	0.359035i
$327$	−174.395	−	240.034i	−0.533318	−	0.734050i
$328$	−37.1353	+	114.291i	−0.113217	+	0.348447i
$329$			380.623i			1.15691i
$330$	−99.4959	−	335.132i	−0.301503	−	1.01555i
$331$	−144.353			−0.436110			−0.218055	−	0.975936i	$-0.569971\pi$
$331$	−144.353			−0.436110			−0.218055	+	0.975936i	$0.569971\pi$
$332$	194.965	+	63.3480i	0.587244	+	0.190807i
$333$	−88.5066	+	64.3038i	−0.265786	+	0.193104i
$334$	118.541	+	86.1251i	0.354913	+	0.257860i
$335$	30.7148	+	94.5304i	0.0916859	+	0.282180i
$336$	378.838	−	123.092i	1.12749	−	0.366345i
$337$	−113.715	+	156.516i	−0.337434	+	0.464439i	−0.943690	−	0.330831i	$-0.892671\pi$
$337$	−113.715	+	156.516i	−0.337434	+	0.464439i	0.606256	+	0.795270i	$0.292671\pi$
$338$	−70.1008	−	96.4855i	−0.207399	−	0.285460i
$339$	12.7943	−	39.3768i	0.0377413	−	0.116156i
$340$		−	275.897i		−	0.811462i
$341$	215.779	−	281.569i	0.632783	−	0.825715i
$342$	320.220			0.936315
$343$	−205.374	−	66.7300i	−0.598758	−	0.194548i
$344$	−183.402	+	133.249i	−0.533144	+	0.387352i
$345$	−3.94427	−	2.86568i	−0.0114327	−	0.00830632i
$346$	−181.554	−	558.766i	−0.524723	−	1.61493i
$347$	−249.410	+	81.0382i	−0.718760	+	0.233539i	−0.645486	−	0.763772i	$-0.723345\pi$
$347$	−249.410	+	81.0382i	−0.718760	+	0.233539i	−0.0732747	+	0.997312i	$0.523345\pi$
$348$	244.461	−	336.472i	0.702474	−	0.966872i
$349$	70.2310	+	96.6647i	0.201235	+	0.276976i	0.897693	−	0.440621i	$-0.145242\pi$
$349$	70.2310	+	96.6647i	0.201235	+	0.276976i	−0.696458	+	0.717597i	$0.745242\pi$
$350$	−51.6312	+	158.904i	−0.147518	+	0.454013i
$351$		−	175.306i		−	0.499449i
$352$	156.050	−	441.539i	0.443324	−	1.25437i
$353$	150.674			0.426838			0.213419	−	0.976961i	$-0.431540\pi$
$353$	150.674			0.426838			0.213419	+	0.976961i	$0.431540\pi$
$354$	−1494.85	−	485.706i	−4.22274	−	1.37205i
$355$	94.9230	−	68.9656i	0.267389	−	0.194269i
$356$	479.566	+	348.425i	1.34709	+	0.978722i
$357$	−349.366	−	1075.24i	−0.978615	−	3.01187i
$358$	−755.876	+	245.599i	−2.11138	+	0.686031i
$359$	160.143	−	220.418i	0.446080	−	0.613977i	−0.525470	−	0.850812i	$-0.676110\pi$
$359$	160.143	−	220.418i	0.446080	−	0.613977i	0.971550	+	0.236836i	$0.0761103\pi$
$360$	73.4017	+	101.029i	0.203894	+	0.280635i
$361$	89.5375	−	275.568i	0.248026	−	0.763347i
$362$		−	506.062i		−	1.39796i
$363$	−558.052	−	28.5549i	−1.53733	−	0.0786636i
$364$	−678.079			−1.86285
$365$	−167.586	−	54.4520i	−0.459140	−	0.149184i
$366$	863.596	−	627.439i	2.35955	−	1.71431i
$367$	523.912	+	380.644i	1.42755	+	1.03718i	0.990466	+	0.137758i	$0.0439897\pi$
$367$	523.912	+	380.644i	1.42755	+	1.03718i	0.437087	+	0.899419i	$0.356010\pi$
$368$	−1.15905	−	3.56720i	−0.00314960	−	0.00969348i
$369$	310.935	−	101.029i	0.842641	−	0.273791i
$370$	35.9017	−	49.4145i	0.0970316	−	0.133553i
$371$	−214.685	−	295.489i	−0.578666	−	0.796465i
$372$	−251.835	+	775.068i	−0.676975	+	2.08352i
$373$		−	402.936i		−	1.08026i	−0.841583	−	0.540129i	$-0.818376\pi$
$373$		−	402.936i		−	1.08026i	0.841583	−	0.540129i	$-0.181624\pi$
$374$	−719.719	−	254.366i	−1.92438	−	0.680122i
$375$	51.6312			0.137683
$376$	−151.056	−	49.0810i	−0.401744	−	0.130535i
$377$	151.957	−	110.404i	0.403070	−	0.292848i
$378$	415.267	+	301.709i	1.09859	+	0.798173i
$379$	41.9023	+	128.962i	0.110560	+	0.340269i	0.990995	−	0.133898i	$-0.0427494\pi$
$379$	41.9023	+	128.962i	0.110560	+	0.340269i	−0.880435	+	0.474167i	$0.842749\pi$
$380$	−98.2295	+	31.9167i	−0.258499	+	0.0839913i
$381$	−409.241	+	563.272i	−1.07412	+	1.47840i
$382$	68.7426	+	94.6161i	0.179955	+	0.247686i
$383$	−170.833	+	525.769i	−0.446039	+	1.37277i	0.435302	+	0.900285i	$0.356642\pi$
$383$	−170.833	+	525.769i	−0.446039	+	1.37277i	−0.881341	+	0.472481i	$0.843358\pi$
$384$			624.199i			1.62552i
$385$	211.976	+	162.447i	0.550586	+	0.421939i
$386$	14.4721			0.0374926
$387$	586.558	+	190.584i	1.51565	+	0.492465i
$388$	273.643	−	198.813i	0.705265	−	0.512405i
$389$	107.164	+	77.8593i	0.275486	+	0.200152i	0.716946	−	0.697129i	$-0.245539\pi$
$389$	107.164	+	77.8593i	0.275486	+	0.200152i	−0.441460	+	0.897281i	$0.645539\pi$
$390$	112.082	+	344.953i	0.287390	+	0.884495i
$391$	−10.1246	+	3.28969i	−0.0258941	+	0.00841352i
$392$	183.458	−	252.509i	0.468006	−	0.644155i
$393$	263.565	+	362.766i	0.670648	+	0.923068i
$394$	102.005	−	313.939i	0.258896	−	0.796800i
$395$		−	284.843i		−	0.721121i
$396$	711.275	−	211.167i	1.79615	−	0.533251i
$397$	−110.721			−0.278895			−0.139448	−	0.990229i	$-0.544533\pi$
$397$	−110.721			−0.278895			−0.139448	+	0.990229i	$0.544533\pi$
$398$	54.4245	+	17.6836i	0.136745	+	0.0444312i
$399$	−342.408	+	248.774i	−0.858166	+	0.623494i
$400$	32.1353	+	23.3476i	0.0803381	+	0.0583691i
$401$	9.64494	+	29.6841i	0.0240522	+	0.0740251i	0.962362	−	0.271770i	$-0.0876091\pi$
$401$	9.64494	+	29.6841i	0.0240522	+	0.0740251i	−0.938310	+	0.345795i	$0.887609\pi$
$402$	−600.852	+	195.229i	−1.49466	+	0.485643i
$403$	−216.334	+	297.759i	−0.536810	+	0.738855i
$404$	185.487	+	255.301i	0.459127	+	0.631934i
$405$	−27.6393	+	85.0651i	−0.0682452	+	0.210037i
$406$			549.967i			1.35460i
$407$	−55.3475	−	80.4247i	−0.135989	−	0.197604i
$408$	471.774			1.15631
$409$	436.217	+	141.735i	1.06654	+	0.346541i	0.789141	−	0.614212i	$-0.210526\pi$
$409$	436.217	+	141.735i	1.06654	+	0.346541i	0.277404	+	0.960753i	$0.410526\pi$
$410$	−147.672	+	107.290i	−0.360176	+	0.261683i
$411$	−782.523	−	568.536i	−1.90395	−	1.38330i
$412$	−185.864	−	572.031i	−0.451127	−	1.38842i
$413$	1141.96	−	371.047i	2.76505	−	0.898418i
$414$	10.5279	−	14.4904i	0.0254296	−	0.0350009i
$415$	49.2376	+	67.7698i	0.118645	+	0.163301i
$416$	−150.143	+	462.092i	−0.360920	+	1.11080i
$417$		−	37.0942i		−	0.0889548i
$418$	−7.30399	+	285.672i	−0.0174737	+	0.683427i
$419$	−47.0476			−0.112285			−0.0561427	−	0.998423i	$-0.517880\pi$
$419$	−47.0476			−0.112285			−0.0561427	+	0.998423i	$0.517880\pi$
$420$	−583.500	−	189.591i	−1.38929	−	0.451407i
$421$	122.931	−	89.3147i	0.291998	−	0.212149i	−0.432136	−	0.901809i	$-0.642240\pi$
$421$	122.931	−	89.3147i	0.291998	−	0.212149i	0.724134	+	0.689660i	$0.242240\pi$
$422$	−243.171	−	176.674i	−0.576234	−	0.418658i
$423$	133.528	+	410.957i	0.315669	+	0.971528i
$424$	144.952	−	47.0979i	0.341869	−	0.111080i
$425$	66.2664	−	91.2079i	0.155921	−	0.214607i
$426$	438.358	+	603.347i	1.02901	+	1.41631i
$427$	−251.994	+	775.557i	−0.590149	+	1.81629i
$428$			307.038i			0.717379i
$429$	579.556	+	14.8179i	1.35095	+	0.0345406i
$430$	−344.336			−0.800782
$431$	−492.254	−	159.943i	−1.14212	−	0.371098i	−0.323951	−	0.946074i	$-0.605011\pi$
$431$	−492.254	−	159.943i	−1.14212	−	0.371098i	−0.818170	+	0.574976i	$0.805011\pi$
$432$	98.7239	−	71.7271i	0.228527	−	0.166035i
$433$	−336.791	−	244.693i	−0.777809	−	0.565111i	0.126512	−	0.991965i	$-0.459622\pi$
$433$	−336.791	−	244.693i	−0.777809	−	0.565111i	−0.904321	+	0.426854i	$0.859622\pi$
$434$	−333.013	−	1024.91i	−0.767311	−	2.36154i
$435$	161.631	−	52.5172i	0.371566	−	0.120729i
$436$	−206.649	+	284.428i	−0.473966	+	0.652359i
$437$	2.34250	+	3.22417i	0.00536041	+	0.00737797i
$438$	346.107	−	1065.21i	0.790198	−	2.43198i
$439$		−	685.921i		−	1.56246i	−0.624242	−	0.781231i	$-0.714592\pi$
$439$		−	685.921i		−	1.56246i	0.624242	−	0.781231i	$-0.285408\pi$
$440$	−91.8034	+	63.1783i	−0.208644	+	0.143587i
$441$	−849.137			−1.92548
$442$	753.222	+	244.737i	1.70412	+	0.553703i
$443$	468.163	−	340.140i	1.05680	−	0.767810i	0.0833065	−	0.996524i	$-0.473452\pi$
$443$	468.163	−	340.140i	1.05680	−	0.767810i	0.973494	+	0.228714i	$0.0734519\pi$
$444$	181.451	+	131.832i	0.408673	+	0.296918i
$445$	74.8516	+	230.370i	0.168206	+	0.517684i
$446$	1110.45	−	360.806i	2.48979	−	0.808982i
$447$	126.708	−	174.399i	0.283464	−	0.390154i
$448$	−633.405	−	871.807i	−1.41385	−	1.94600i
$449$	−262.733	+	808.609i	−0.585151	+	1.80091i	0.0135103	+	0.999909i	$0.495699\pi$
$449$	−262.733	+	808.609i	−0.585151	+	1.80091i	−0.598662	+	0.801002i	$0.704301\pi$
$450$			189.681i			0.421514i
$451$	83.0370	+	279.693i	0.184117	+	0.620163i
$452$	−49.0608			−0.108541
$453$	−329.864	−	107.179i	−0.728177	−	0.236599i
$454$	518.972	−	377.055i	1.14311	−	0.830517i
$455$	−224.164	−	162.865i	−0.492668	−	0.357944i
$456$	−54.5764	−	167.969i	−0.119685	−	0.368353i
$457$	−387.747	+	125.987i	−0.848462	+	0.275682i	−0.700802	−	0.713356i	$-0.747174\pi$
$457$	−387.747	+	125.987i	−0.848462	+	0.275682i	−0.147660	+	0.989038i	$0.547174\pi$
$458$	−112.503	+	154.848i	−0.245641	+	0.338096i
$459$	−203.580	−	280.203i	−0.443528	−	0.610464i
$460$	−1.78522	+	5.49434i	−0.00388091	+	0.0119442i
$461$			721.774i			1.56567i	0.622229	+	0.782835i	$0.286227\pi$
$461$			721.774i			1.56567i	−0.622229	+	0.782835i	$0.713773\pi$
$462$	−1032.54	+	1347.35i	−2.23493	+	2.91635i
$463$	775.669			1.67531			0.837656	−	0.546198i	$-0.183925\pi$
$463$	775.669			1.67531			0.837656	+	0.546198i	$0.183925\pi$
$464$	124.348	+	40.4030i	0.267990	+	0.0870753i
$465$	−269.413	+	195.740i	−0.579383	+	0.420947i
$466$	689.820	+	501.184i	1.48030	+	1.07550i
$467$	144.385	+	444.372i	0.309176	+	0.951545i	0.978086	+	0.208202i	$0.0667611\pi$
$467$	144.385	+	444.372i	0.309176	+	0.951545i	−0.668910	+	0.743343i	$0.733239\pi$
$468$	−732.118	+	237.880i	−1.56436	+	0.508290i
$469$	283.684	−	390.457i	0.604870	−	0.832531i
$470$	−141.803	−	195.176i	−0.301709	−	0.415267i
$471$	−52.7965	+	162.491i	−0.112094	+	0.344991i
$472$			501.051i			1.06155i
$473$	−183.402	+	518.929i	−0.387741	+	1.09710i
$474$	1810.51			3.81965
$475$	−40.1393	−	13.0421i	−0.0845038	−	0.0274570i
$476$	−1083.82	+	787.438i	−2.27692	+	1.65428i
$477$	−335.456	−	243.723i	−0.703262	−	0.510950i
$478$	−141.122	−	434.327i	−0.295233	−	0.908635i
$479$	−8.26238	+	2.68461i	−0.0172492	+	0.00560461i	−0.317629	−	0.948215i	$-0.602887\pi$
$479$	−8.26238	+	2.68461i	−0.0172492	+	0.00560461i	0.300380	+	0.953820i	$0.402887\pi$
$480$	−258.402	+	355.659i	−0.538337	+	0.740957i
$481$	59.5379	+	81.9469i	0.123779	+	0.170368i
$482$	393.669	−	1211.59i	0.816741	−	2.51367i
$483$			23.6734i			0.0490132i
$484$	172.162	+	639.355i	0.355706	+	1.32098i
$485$	138.215			0.284979
$486$	−945.342	−	307.160i	−1.94515	−	0.632017i
$487$	645.822	−	469.217i	1.32612	−	0.963484i	0.326288	−	0.945270i	$-0.394202\pi$
$487$	645.822	−	469.217i	1.32612	−	0.963484i	0.999834	−	0.0182139i	$-0.00579800\pi$
$488$	−275.297	−	200.015i	−0.564133	−	0.409866i
$489$	67.0830	+	206.460i	0.137184	+	0.422209i
$490$	450.881	−	146.500i	0.920166	−	0.298980i
$491$	−87.5364	+	120.483i	−0.178282	+	0.245384i	−0.888800	−	0.458295i	$-0.848460\pi$
$491$	−87.5364	+	120.483i	−0.178282	+	0.245384i	0.710519	+	0.703678i	$0.248460\pi$
$492$	−393.972	−	542.255i	−0.800755	−	1.10214i
$493$	114.674	−	352.930i	0.232604	−	0.715881i
$494$		−	296.487i		−	0.600176i
$495$	285.858	+	101.029i	0.577490	+	0.204099i
$496$	−256.197			−0.516525
$497$	−541.840	−	176.054i	−1.09022	−	0.354234i
$498$	−430.757	+	312.963i	−0.864973	+	0.628440i
$499$	−493.030	−	358.207i	−0.988036	−	0.717850i	−0.0285456	−	0.999592i	$-0.509088\pi$
$499$	−493.030	−	358.207i	−0.988036	−	0.717850i	−0.959490	+	0.281743i	$0.909088\pi$
$500$	−18.9058	−	58.1860i	−0.0378115	−	0.116372i
$501$	−209.098	+	67.9402i	−0.417362	+	0.135609i
$502$	674.864	−	928.871i	1.34435	−	1.85034i
$503$	−88.0720	−	121.221i	−0.175093	−	0.240995i	0.712446	−	0.701727i	$-0.247587\pi$
$503$	−88.0720	−	121.221i	−0.175093	−	0.240995i	−0.887540	+	0.460731i	$0.847587\pi$
$504$	187.379	−	576.693i	0.371783	−	1.14423i
$505$			128.951i			0.255348i
$506$	12.6869	+	9.72257i	0.0250730	+	0.0192146i
$507$	178.952			0.352963
$508$	784.633	+	254.943i	1.54455	+	0.501856i
$509$	−256.395	+	186.282i	−0.503723	+	0.365976i	−0.810437	−	0.585825i	$-0.800770\pi$
$509$	−256.395	+	186.282i	−0.503723	+	0.365976i	0.306714	+	0.951802i	$0.400770\pi$
$510$	579.734	+	421.201i	1.13673	+	0.825885i
$511$	264.402	+	813.746i	0.517421	+	1.59246i
$512$	−458.586	+	149.004i	−0.895677	+	0.291023i
$513$	−76.2119	+	104.897i	−0.148561	+	0.204477i
$514$	−369.179	−	508.131i	−0.718247	−	0.988582i
$515$	75.9493	−	233.748i	0.147474	−	0.453879i
$516$		−	1264.41i		−	2.45041i
$517$	−369.666	+	109.748i	−0.715021	+	0.212279i
$518$	−296.584			−0.572555
$519$	838.423	+	272.420i	1.61546	+	0.524895i
$520$	93.5410	−	67.9615i	0.179887	−	0.130695i
$521$	−298.555	−	216.913i	−0.573042	−	0.416340i	0.263167	−	0.964750i	$-0.415233\pi$
$521$	−298.555	−	216.913i	−0.573042	−	0.416340i	−0.836209	+	0.548411i	$0.815233\pi$
$522$	192.936	+	593.796i	0.369609	+	1.13754i
$523$	466.990	−	151.734i	0.892907	−	0.290123i	0.173601	−	0.984816i	$-0.444460\pi$
$523$	466.990	−	151.734i	0.892907	−	0.290123i	0.719306	+	0.694693i	$0.244460\pi$
$524$	312.311	−	429.859i	0.596013	−	0.820342i
$525$	−147.361	−	202.825i	−0.280687	−	0.386333i
$526$	−61.1327	+	188.147i	−0.116222	+	0.357694i
$527$			727.150i			1.37979i
$528$	228.782	+	332.440i	0.433299	+	0.629621i
$529$	−528.777			−0.999579
$530$	220.172	+	71.5383i	0.415419	+	0.134978i
$531$	1102.80	−	801.235i	2.07685	−	1.50892i
$532$	405.736	+	294.785i	0.762662	+	0.554107i
$533$	−93.5410	−	287.890i	−0.175499	−	0.540131i
$534$	−1464.27	+	475.770i	−2.74208	+	0.890955i
$535$	−73.7461	+	101.503i	−0.137843	+	0.189725i
$536$	118.378	+	162.933i	0.220854	+	0.303980i
$537$	368.519	−	1134.18i	0.686255	−	2.11207i
$538$		−	687.262i		−	1.27744i
$539$	19.3682	−	757.526i	0.0359336	−	1.40543i
$540$	−187.954			−0.348064
$541$	−418.618	−	136.017i	−0.773786	−	0.251418i	−0.104601	−	0.994514i	$-0.533357\pi$
$541$	−418.618	−	136.017i	−0.773786	−	0.251418i	−0.669185	+	0.743096i	$0.733357\pi$
$542$	−699.882	+	508.494i	−1.29130	+	0.938181i
$543$	614.320	+	446.330i	1.13134	+	0.821970i
$544$	296.635	+	912.948i	0.545284	+	1.67821i
$545$	−136.631	+	44.3942i	−0.250699	+	0.0814572i
$546$	1035.20	−	1424.83i	1.89597	−	2.60957i
$547$	350.478	+	482.392i	0.640728	+	0.881886i	0.998654	−	0.0518636i	$-0.0165161\pi$
$547$	350.478	+	482.392i	0.640728	+	0.881886i	−0.357926	+	0.933750i	$0.616516\pi$
$548$	−354.178	+	1090.05i	−0.646310	+	1.98914i
$549$			925.768i			1.68628i
$550$	−169.217	−	4.32650i	−0.307668	−	0.00786636i
$551$	−138.922			−0.252127
$552$	−9.39512	−	3.05266i	−0.0170201	−	0.00553018i
$553$	−1118.96	+	812.971i	−2.02343	+	1.47011i
$554$	299.864	+	217.864i	0.541271	+	0.393256i
$555$	28.3212	+	87.1637i	0.0510292	+	0.157052i
$556$	−41.8034	+	13.5827i	−0.0751860	+	0.0244294i
$557$	−352.889	+	485.709i	−0.633552	+	0.872010i	−0.998251	−	0.0591158i	$-0.981172\pi$
$557$	−352.889	+	485.709i	−0.633552	+	0.872010i	0.364699	+	0.931125i	$0.381172\pi$
$558$	−719.105	−	989.763i	−1.28872	−	1.77377i
$559$	176.459	−	543.085i	0.315669	−	0.971529i
$560$		−	192.875i		−	0.344419i
$561$	943.548	−	649.341i	1.68190	−	1.15747i
$562$	−1248.04			−2.22071
$563$	−632.047	−	205.365i	−1.12264	−	0.364768i	−0.311866	−	0.950126i	$-0.600954\pi$
$563$	−632.047	−	205.365i	−1.12264	−	0.364768i	−0.810775	+	0.585358i	$0.800954\pi$
$564$	716.689	−	520.705i	1.27072	−	0.923236i
$565$	−16.2188	−	11.7837i	−0.0287059	−	0.0208561i
$566$	524.663	+	1614.75i	0.926966	+	2.85291i
$567$	413.050	−	134.208i	0.728482	−	0.236698i
$568$	139.740	−	192.335i	0.246020	−	0.338618i
$569$	−255.449	−	351.595i	−0.448943	−	0.617917i	0.523227	−	0.852193i	$-0.324728\pi$
$569$	−255.449	−	351.595i	−0.448943	−	0.617917i	−0.972170	+	0.234276i	$0.924728\pi$
$570$	82.8976	−	255.133i	0.145434	−	0.447601i
$571$		−	807.082i		−	1.41345i	−0.707487	−	0.706727i	$-0.750171\pi$
$571$		−	807.082i		−	1.41345i	0.707487	−	0.706727i	$-0.249829\pi$
$572$	−195.517	−	658.559i	−0.341812	−	1.15133i
$573$	−175.485			−0.306257
$574$	842.943	+	273.889i	1.46854	+	0.477158i
$575$	−1.90983	+	1.38757i	−0.00332144	+	0.00241317i
$576$	−989.727	−	719.079i	−1.71828	−	1.24840i
$577$	−224.288	−	690.288i	−0.388715	−	1.19634i	−0.933750	−	0.357927i	$-0.883484\pi$
$577$	−224.288	−	690.288i	−0.388715	−	1.19634i	0.545035	−	0.838413i	$-0.316516\pi$
$578$	642.210	−	208.667i	1.11109	−	0.361015i
$579$	−12.7639	+	17.5680i	−0.0220448	+	0.0303420i
$580$	−118.369	−	162.921i	−0.204084	−	0.280898i
$581$	125.693	−	386.844i	0.216339	−	0.665824i
$582$			878.518i			1.50948i
$583$	225.080	−	293.706i	0.386072	−	0.503783i
$584$	−357.041			−0.611372
$585$	−299.164	−	97.2043i	−0.511392	−	0.166161i
$586$	−801.715	+	582.480i	−1.36811	+	0.993993i
$587$	153.232	+	111.330i	0.261043	+	0.189659i	0.710607	−	0.703590i	$-0.248421\pi$
$587$	153.232	+	111.330i	0.261043	+	0.189659i	−0.449564	+	0.893248i	$0.648421\pi$
$588$	537.952	+	1655.65i	0.914884	+	2.81572i
$589$	258.892	−	84.1192i	0.439546	−	0.142817i
$590$	−447.340	+	615.711i	−0.758204	+	1.04358i
$591$	291.133	+	400.710i	0.492610	+	0.678020i
$592$	−21.7883	+	67.0576i	−0.0368046	+	0.113273i
$593$			216.058i			0.364348i	0.983266	+	0.182174i	$0.0583134\pi$
$593$			216.058i			0.364348i	−0.983266	+	0.182174i	$0.941687\pi$
$594$	−173.286	+	490.308i	−0.291728	+	0.825434i
$595$	−547.426			−0.920044
$596$	−242.936	−	78.9347i	−0.407611	−	0.132441i
$597$	−69.4671	+	50.4708i	−0.116360	+	0.0845407i
$598$	−13.4164	−	9.74759i	−0.0224355	−	0.0163003i
$599$	−309.617	−	952.903i	−0.516890	−	1.59082i	−0.779817	−	0.626007i	$-0.784688\pi$
$599$	−309.617	−	952.903i	−0.516890	−	1.59082i	0.262928	−	0.964815i	$-0.415312\pi$
$600$	99.4959	−	32.3282i	0.165827	−	0.0538803i
$601$	230.744	−	317.592i	0.383934	−	0.528440i	−0.572688	−	0.819774i	$-0.694099\pi$
$601$	230.744	−	317.592i	0.383934	−	0.528440i	0.956621	+	0.291334i	$0.0940992\pi$
$602$	982.771	+	1352.67i	1.63251	+	2.24696i
$603$	169.314	−	521.095i	0.280786	−	0.864171i
$604$			410.987i			0.680443i
$605$	−96.6494	+	252.713i	−0.159751	+	0.417708i
$606$	−819.633			−1.35253
$607$	−501.620	−	162.986i	−0.826392	−	0.268511i	−0.134867	−	0.990864i	$-0.543061\pi$
$607$	−501.620	−	162.986i	−0.826392	−	0.268511i	−0.691525	+	0.722353i	$0.743061\pi$
$608$	290.727	−	211.226i	0.478170	−	0.347411i
$609$	−667.617	−	485.052i	−1.09625	−	0.796473i
$610$	−159.721	−	491.572i	−0.261838	−	0.805855i
$611$	380.498	−	123.631i	0.622747	−	0.202343i
$612$	−893.946	+	1230.41i	−1.46070	+	2.01047i
$613$	157.852	+	217.265i	0.257508	+	0.354429i	0.918123	−	0.396296i	$-0.129705\pi$
$613$	157.852	+	217.265i	0.257508	+	0.354429i	−0.660615	+	0.750725i	$0.729705\pi$
$614$	−95.2254	+	293.074i	−0.155090	+	0.477319i
$615$		−	273.889i		−	0.445348i
$616$	510.202	+	180.317i	0.828249	+	0.292723i
$617$	623.989			1.01133			0.505664	−	0.862731i	$-0.331248\pi$
$617$	623.989			1.01133			0.505664	+	0.862731i	$0.331248\pi$
$618$	1485.74	+	482.747i	2.40412	+	0.781144i
$619$	−727.247	+	528.376i	−1.17487	+	0.853596i	−0.991584	−	0.129463i	$-0.958675\pi$
$619$	−727.247	+	528.376i	−1.17487	+	0.853596i	−0.183290	+	0.983059i	$0.558675\pi$
$620$	319.241	+	231.942i	0.514905	+	0.374100i
$621$	2.24109	+	6.89737i	0.00360885	+	0.0111069i
$622$	576.917	−	187.452i	0.927519	−	0.301369i
$623$	691.334	−	951.540i	1.10969	−	1.52735i
$624$	−246.103	−	338.732i	−0.394396	−	0.542840i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$		−	747.852i		−	1.19465i
$627$	−340.342	−	260.820i	−0.542811	−	0.415981i
$628$	202.452			0.322376
$629$	190.326	+	61.8407i	0.302585	+	0.0983160i
$630$	745.132	−	541.370i	1.18275	−	0.859317i
$631$	861.325	+	625.789i	1.36502	+	0.991742i	0.998108	+	0.0614849i	$0.0195836\pi$
$631$	861.325	+	625.789i	1.36502	+	0.991742i	0.366908	+	0.930257i	$0.380416\pi$
$632$	−178.351	−	548.907i	−0.282200	−	0.868523i
$633$	428.937	−	139.370i	0.677625	−	0.220174i
$634$	−1023.24	+	1408.37i	−1.61394	+	2.22140i
$635$	198.156	+	272.738i	0.312057	+	0.429509i
$636$	−262.690	+	808.477i	−0.413035	+	1.27119i
$637$			786.203i			1.23423i
$638$	−534.135	+	158.577i	−0.837202	+	0.248553i
$639$	−646.784			−1.01218
$640$	287.447	+	93.3971i	0.449136	+	0.145933i
$641$	717.550	−	521.330i	1.11942	−	0.813308i	0.135301	−	0.990805i	$-0.456800\pi$
$641$	717.550	−	521.330i	1.11942	−	0.813308i	0.984121	+	0.177497i	$0.0568000\pi$
$642$	−645.170	−	468.743i	−1.00494	−	0.730130i
$643$	−323.852	−	996.713i	−0.503657	−	1.55010i	−0.803016	−	0.595957i	$-0.796773\pi$
$643$	−323.852	−	996.713i	−0.503657	−	1.55010i	0.299359	−	0.954141i	$-0.403227\pi$
$644$	26.6788	−	8.66846i	0.0414267	−	0.0134603i
$645$	303.693	−	417.997i	0.470842	−	0.648058i
$646$	−344.303	−	473.893i	−0.532977	−	0.733580i
$647$	388.461	−	1195.56i	0.600403	−	1.84785i	0.0746578	−	0.997209i	$-0.476214\pi$
$647$	388.461	−	1195.56i	0.600403	−	1.84785i	0.525745	−	0.850642i	$-0.323786\pi$
$648$			181.231i			0.279677i
$649$	689.638	+	1002.10i	1.06262	+	1.54407i
$650$	175.623			0.270189
$651$	1537.87	+	499.683i	2.36231	+	0.767562i
$652$	208.107	−	151.199i	0.319183	−	0.231900i
$653$	139.031	+	101.012i	0.212912	+	0.154689i	0.689130	−	0.724638i	$-0.257993\pi$
$653$	139.031	+	101.012i	0.212912	+	0.154689i	−0.476218	+	0.879327i	$0.657993\pi$
$654$	−282.177	−	868.452i	−0.431464	−	1.32791i
$655$	206.492	−	67.0933i	0.315255	−	0.102432i
$656$	123.853	−	170.468i	0.188800	−	0.259860i
$657$	570.947	+	785.841i	0.869022	+	1.19611i
$658$	−361.994	+	1114.10i	−0.550143	+	1.69316i
$659$			719.550i			1.09188i	0.837824	+	0.545941i	$0.183828\pi$
$659$			719.550i			1.09188i	−0.837824	+	0.545941i	$0.816172\pi$
$660$	15.8870	−	621.369i	0.0240712	−	0.941469i
$661$	655.240			0.991286			0.495643	−	0.868526i	$-0.334932\pi$
$661$	655.240			0.991286			0.495643	+	0.868526i	$0.334932\pi$
$662$	−422.527	−	137.287i	−0.638259	−	0.207383i
$663$	−961.407	+	698.503i	−1.45009	+	1.05355i
$664$	137.317	+	99.7663i	0.206802	+	0.150250i
$665$	63.3282	+	194.904i	0.0952303	+	0.293089i
$666$	−320.220	+	104.046i	−0.480811	+	0.156225i
$667$	−4.56733	+	6.28639i	−0.00684757	+	0.00942488i
$668$	153.131	+	210.766i	0.229238	+	0.315519i
$669$	−541.386	+	1666.21i	−0.809246	+	2.49060i
$670$			305.907i			0.456577i
$671$	−825.890	−	21.1161i	−1.23084	−	0.0314696i
$672$	2134.65			3.17657
$673$	−650.235	−	211.274i	−0.966173	−	0.313929i	−0.216903	−	0.976193i	$-0.569596\pi$
$673$	−650.235	−	211.274i	−0.966173	−	0.313929i	−0.749270	+	0.662264i	$0.769596\pi$
$674$	−481.706	+	349.980i	−0.714697	+	0.519258i
$675$	−62.1353	−	45.1439i	−0.0920522	−	0.0668799i
$676$	−65.5269	−	201.671i	−0.0969333	−	0.298330i
$677$	−719.490	+	233.777i	−1.06276	+	0.345313i	−0.787665	−	0.616104i	$-0.788710\pi$
$677$	−719.490	+	233.777i	−1.06276	+	0.345313i	−0.275098	+	0.961416i	$0.588710\pi$
$678$	74.8992	−	103.090i	0.110471	−	0.152050i
$679$	−394.479	−	542.954i	−0.580971	−	0.799638i
$680$	70.5902	−	217.254i	0.103809	−	0.319491i
$681$			962.541i			1.41342i
$682$	899.384	−	618.948i	1.31874	−	0.907548i
$683$	−781.639			−1.14442			−0.572210	−	0.820107i	$-0.693914\pi$
$683$	−781.639			−1.14442			−0.572210	+	0.820107i	$0.693914\pi$
$684$	541.486	+	175.940i	0.791647	+	0.257222i
$685$	−378.900	+	275.287i	−0.553139	+	0.401879i
$686$	−537.676	−	390.644i	−0.783784	−	0.569452i
$687$	−88.7489	−	273.141i	−0.129183	−	0.397585i
$688$	378.037	−	122.832i	0.549472	−	0.178534i
$689$	−225.659	+	310.594i	−0.327517	+	0.450789i
$690$	−8.81966	−	12.1392i	−0.0127821	−	0.0175931i
$691$	−290.643	+	894.507i	−0.420612	+	1.29451i	0.486522	+	0.873668i	$0.338265\pi$
$691$	−290.643	+	894.507i	−0.420612	+	1.29451i	−0.907134	+	0.420842i	$0.861735\pi$
$692$		−	1044.62i		−	1.50956i
$693$	−418.992	−	1411.29i	−0.604606	−	2.03649i
$694$	−807.107			−1.16298
$695$	−17.0820	−	5.55029i	−0.0245785	−	0.00798603i
$696$	278.589	−	202.406i	0.400271	−	0.290814i
$697$	−483.832	−	351.525i	−0.694164	−	0.504340i
$698$	113.636	+	349.736i	0.162803	+	0.501055i
$699$	−1216.80	+	395.361i	−1.74077	+	0.565609i
$700$	−174.615	+	240.337i	−0.249450	+	0.343338i
$701$	−3.94427	−	5.42882i	−0.00562664	−	0.00774440i	0.806194	−	0.591651i	$-0.201524\pi$
$701$	−3.94427	−	5.42882i	−0.00562664	−	0.00774440i	−0.811821	+	0.583906i	$0.801524\pi$
$702$	166.726	−	513.131i	0.237502	−	0.730956i
$703$		−	74.9171i		−	0.106568i
$704$	664.075	−	866.547i	0.943288	−	1.23089i
$705$	361.994			0.513466
$706$	441.030	+	143.299i	0.624688	+	0.202973i
$707$	506.561	−	368.038i	0.716494	−	0.520563i
$708$	−2260.90	−	1642.64i	−3.19337	−	2.32012i
$709$	−307.854	−	947.478i	−0.434209	−	1.33636i	−0.893895	−	0.448276i	$-0.852038\pi$
$709$	−307.854	−	947.478i	−0.434209	−	1.33636i	0.459686	−	0.888081i	$-0.347962\pi$
$710$	343.435	−	111.589i	0.483711	−	0.157167i
$711$	−922.932	+	1270.31i	−1.29808	+	1.78665i
$712$	288.486	+	397.066i	0.405176	+	0.557678i
$713$	4.70510	−	14.4808i	0.00659902	−	0.0203097i
$714$		−	3479.54i		−	4.87331i
$715$	93.5410	−	264.671i	0.130827	−	0.370170i
$716$	−1413.11			−1.97362
$717$	651.704	+	211.751i	0.908932	+	0.295330i
$718$	678.376	−	492.869i	0.944813	−	0.686447i
$719$	478.315	+	347.516i	0.665250	+	0.483333i	0.868432	−	0.495808i	$-0.165128\pi$
$719$	478.315	+	347.516i	0.665250	+	0.483333i	−0.203182	+	0.979141i	$0.565128\pi$
$720$	−67.6631	−	208.246i	−0.0939766	−	0.289230i
$721$	−1135.01	+	368.786i	−1.57421	+	0.511493i
$722$	524.162	−	721.447i	0.725986	−	0.999234i
$723$	1123.57	+	1546.46i	1.55404	+	2.13895i
$724$	278.048	−	855.743i	0.384044	−	1.18196i
$725$		−	82.2899i		−	0.113503i
$726$	−1606.29	−	614.321i	−2.21252	−	0.846172i
$727$	−1276.13			−1.75534			−0.877670	−	0.479266i	$-0.840903\pi$
$727$	−1276.13			−1.75534			−0.877670	+	0.479266i	$0.840903\pi$
$728$	−533.951	−	173.491i	−0.733449	−	0.238312i
$729$	915.382	−	665.064i	1.25567	−	0.912297i
$730$	−438.746	−	318.768i	−0.601022	−	0.436668i
$731$	−348.627	−	1072.96i	−0.476918	−	1.46780i
$732$	1805.06	−	586.500i	2.46593	−	0.801230i
$733$	19.8208	−	27.2811i	0.0270407	−	0.0372184i	−0.795283	−	0.606239i	$-0.792678\pi$
$733$	19.8208	−	27.2811i	0.0270407	−	0.0372184i	0.822323	+	0.569021i	$0.192678\pi$
$734$	1171.50	+	1612.43i	1.59605	+	2.19678i
$735$	−219.822	+	676.543i	−0.299078	+	0.920467i
$736$		−	20.1003i		−	0.0273101i
$737$	461.014	+	162.933i	0.625528	+	0.221076i
$738$	1006.21			1.36342
$739$	1127.54	+	366.361i	1.52577	+	0.495752i	0.947408	−	0.320028i	$-0.103692\pi$
$739$	1127.54	+	366.361i	1.52577	+	0.495752i	0.578361	+	0.815781i	$0.303692\pi$
$740$	87.8591	−	63.8334i	0.118729	−	0.0862613i
$741$	359.912	+	261.491i	0.485711	+	0.352890i
$742$	−347.368	−	1069.09i	−0.468150	−	1.44082i
$743$	−1302.85	+	423.321i	−1.75350	+	0.569746i	−0.996494	−	0.0836663i	$-0.973337\pi$
$743$	−1302.85	+	423.321i	−1.75350	+	0.569746i	−0.757003	+	0.653412i	$0.773337\pi$
$744$	−396.613	+	545.891i	−0.533082	+	0.733724i
$745$	−61.3525	−	84.4445i	−0.0823524	−	0.113348i
$746$	383.215	−	1179.41i	0.513693	−	1.58098i
$747$		−	461.768i		−	0.618163i
$748$	−1077.28	−	825.566i	−1.44021	−	1.10370i
$749$	609.216			0.813372
$750$	151.127	+	49.1042i	0.201503	+	0.0654722i
$751$	316.835	−	230.194i	0.421884	−	0.306517i	−0.356512	−	0.934291i	$-0.616034\pi$
$751$	316.835	−	230.194i	0.421884	−	0.306517i	0.778395	+	0.627774i	$0.216034\pi$
$752$	225.305	+	163.694i	0.299608	+	0.217678i
$753$	532.370	+	1638.46i	0.706998	+	2.17592i
$754$	549.787	−	178.637i	0.729161	−	0.236919i
$755$	−98.7132	+	135.867i	−0.130746	+	0.179956i
$756$	536.441	+	738.347i	0.709578	+	0.976650i
$757$	−73.9880	+	227.712i	−0.0977385	+	0.300808i	−0.987958	−	0.154724i	$-0.950551\pi$
$757$	−73.9880	+	227.712i	−0.0977385	+	0.300808i	0.890219	+	0.455532i	$0.150551\pi$
$758$			417.330i			0.550567i
$759$	−22.9919	+	6.82596i	−0.0302923	+	0.00899335i
$760$	−85.5166			−0.112522
$761$	31.0228	+	10.0799i	0.0407659	+	0.0132456i	0.329329	−	0.944215i	$-0.393177\pi$
$761$	31.0228	+	10.0799i	0.0407659	+	0.0132456i	−0.288563	+	0.957461i	$0.593177\pi$
$762$	−1733.57	+	1259.51i	−2.27503	+	1.65291i
$763$	564.354	+	410.028i	0.739652	+	0.537389i
$764$	64.2574	+	197.764i	0.0841065	+	0.258853i
$765$	−591.054	+	192.045i	−0.772619	+	0.251039i
$766$	−1000.07	+	1376.48i	−1.30558	+	1.79697i
$767$	−741.851	−	1021.07i	−0.967211	−	1.33125i
$768$	−27.1140	+	83.4482i	−0.0353046	+	0.108657i
$769$		−	80.9870i		−	0.105315i	−0.998613	−	0.0526573i	$-0.983231\pi$
$769$		−	80.9870i		−	0.105315i	0.998613	−	0.0526573i	$-0.0167691\pi$
$770$	465.967	+	677.090i	0.605153	+	0.879338i
$771$	942.435			1.22235
$772$	24.4721	+	7.95148i	0.0316997	+	0.0102998i
$773$	−232.654	+	169.033i	−0.300976	+	0.218672i	−0.728015	−	0.685561i	$-0.759557\pi$
$773$	−232.654	+	169.033i	−0.300976	+	0.218672i	0.427039	+	0.904233i	$0.359557\pi$
$774$	1535.63	+	1115.70i	1.98402	+	1.44147i
$775$	49.8278	+	153.354i	0.0642939	+	0.197876i
$776$	266.347	−	86.5414i	0.343231	−	0.111522i
$777$	261.577	−	360.029i	0.336649	−	0.463358i
$778$	239.626	+	329.817i	0.308003	+	0.423929i
$779$	−69.1844	+	212.928i	−0.0888118	+	0.273335i
$780$			644.891i			0.826784i
$781$	14.7527	−	577.005i	0.0188895	−	0.738803i
$782$	−32.7639			−0.0418976
$783$	−240.433	−	78.1213i	−0.307066	−	0.0997718i
$784$	−442.750	+	321.677i	−0.564732	+	0.410302i
$785$	66.9280	+	48.6260i	0.0852586	+	0.0619440i
$786$	426.457	+	1312.50i	0.542566	+	1.66985i
$787$	−75.9709	+	24.6845i	−0.0965323	+	0.0313653i	−0.356885	−	0.934148i	$-0.616161\pi$
$787$	−75.9709	+	24.6845i	−0.0965323	+	0.0313653i	0.260353	+	0.965514i	$0.416161\pi$
$788$	344.978	−	474.821i	0.437789	−	0.602565i
$789$	−174.479	−	240.150i	−0.221140	−	0.304372i
$790$	270.902	−	833.750i	0.342914	−	1.05538i
$791$			97.3449i			0.123066i
$792$	614.120	+	15.7016i	0.775404	+	0.0198253i
$793$	857.155			1.08090
$794$	−324.087	−	105.302i	−0.408170	−	0.132623i
$795$	−281.026	+	204.178i	−0.353492	+	0.256827i
$796$	82.3150	+	59.8053i	0.103411	+	0.0751323i
$797$	267.409	+	823.002i	0.335520	+	1.03262i	0.966465	+	0.256797i	$0.0826672\pi$
$797$	267.409	+	823.002i	0.335520	+	1.03262i	−0.630945	+	0.775827i	$0.717333\pi$
$798$	−1238.84	+	402.525i	−1.55244	+	0.504417i
$799$	464.604	−	639.472i	0.581481	−	0.800341i
$800$	125.119	+	172.212i	0.156399	+	0.215264i
$801$	412.616	−	1269.90i	0.515127	−	1.58540i
$802$			96.0597i			0.119775i
$803$	−714.083	+	491.425i	−0.889269	+	0.611987i
$804$	−1123.30			−1.39713
$805$	10.9017	+	3.54218i	0.0135425	+	0.00440022i
$806$	−916.407	+	665.809i	−1.13698	+	0.826065i
$807$	834.282	+	606.142i	1.03381	+	0.751105i
$808$	80.7407	+	248.494i	0.0999266	+	0.307543i
$809$	−164.498	+	53.4487i	−0.203335	+	0.0660676i	−0.408914	−	0.912573i	$-0.634092\pi$
$809$	−164.498	+	53.4487i	−0.203335	+	0.0660676i	0.205579	+	0.978641i	$0.434092\pi$
$810$	−161.803	+	222.703i	−0.199757	+	0.274942i
$811$	−508.782	−	700.279i	−0.627352	−	0.863476i	0.370510	−	0.928828i	$-0.379183\pi$
$811$	−508.782	−	700.279i	−0.627352	−	0.863476i	−0.997862	+	0.0653524i	$0.979183\pi$
$812$	−302.170	+	929.985i	−0.372131	+	1.14530i
$813$		−	1298.08i		−	1.59665i
$814$	−85.5166	−	288.046i	−0.105057	−	0.353865i
$815$	105.113			0.128973
$816$	−786.724	−	255.622i	−0.964123	−	0.313263i
$817$	−341.684	+	248.248i	−0.418218	+	0.303853i
$818$	1142.03	+	829.733i	1.39612	+	1.01434i
$819$	471.994	+	1452.65i	0.576305	+	1.77368i
$820$	−308.660	+	100.290i	−0.376415	+	0.122305i
$821$	−66.2686	+	91.2109i	−0.0807169	+	0.111097i	−0.847466	−	0.530849i	$-0.821873\pi$
$821$	−66.2686	+	91.2109i	−0.0807169	+	0.111097i	0.766749	+	0.641947i	$0.221873\pi$
$822$	−1749.77	−	2408.36i	−2.12868	−	2.92987i
$823$	−123.479	+	380.030i	−0.150035	+	0.461761i	−0.997624	−	0.0688924i	$-0.978053\pi$
$823$	−123.479	+	380.030i	−0.150035	+	0.461761i	0.847589	+	0.530654i	$0.178053\pi$
$824$		−	497.999i		−	0.604367i
$825$	154.496	−	201.601i	0.187268	−	0.244365i
$826$	3695.47			4.47394
$827$	698.603	+	226.990i	0.844744	+	0.274474i	0.699243	−	0.714884i	$-0.253521\pi$
$827$	698.603	+	226.990i	0.844744	+	0.274474i	0.145501	+	0.989358i	$0.453521\pi$
$828$	25.7639	−	18.7186i	0.0311159	−	0.0226070i
$829$	251.233	+	182.531i	0.303055	+	0.220183i	0.728911	−	0.684609i	$-0.240027\pi$
$829$	251.233	+	182.531i	0.303055	+	0.220183i	−0.425856	+	0.904791i	$0.640027\pi$
$830$	79.6681	+	245.193i	0.0959857	+	0.295414i
$831$	−528.940	+	171.863i	−0.636510	+	0.206815i
$832$	−665.784	+	916.373i	−0.800221	+	1.10141i
$833$	913.000	+	1256.64i	1.09604	+	1.50857i
$834$	35.2786	−	108.576i	0.0423005	−	0.130188i
$835$			106.456i			0.127493i
$836$	−169.309	+	479.054i	−0.202523	+	0.573031i
$837$	495.370			0.591840
$838$	−137.711	−	44.7449i	−0.164333	−	0.0533949i
$839$	534.323	−	388.208i	0.636857	−	0.462704i	−0.221912	−	0.975067i	$-0.571230\pi$
$839$	534.323	−	388.208i	0.636857	−	0.462704i	0.858769	+	0.512363i	$0.171230\pi$
$840$	−410.967	−	298.585i	−0.489247	−	0.355459i
$841$	176.181	+	542.230i	0.209490	+	0.644745i
$842$	444.769	−	144.514i	0.528229	−	0.171632i
$843$	1100.73	−	1515.02i	1.30573	−	1.79718i
$844$	−314.127	−	432.359i	−0.372188	−	0.512273i
$845$	26.7761	−	82.4084i	0.0316877	−	0.0975248i
$846$			1329.88i			1.57197i
$847$	1268.59	−	341.598i	1.49774	−	0.403303i
$848$	−267.240			−0.315141
$849$	−2422.91	−	787.251i	−2.85384	−	0.927269i
$850$	280.709	−	203.947i	0.330246	−	0.239938i
$851$	−3.39010	−	2.46305i	−0.00398366	−	0.00289430i
$852$	409.756	+	1261.10i	0.480934	+	1.48016i
$853$	−464.919	+	151.061i	−0.545040	+	0.177094i	−0.568579	−	0.822629i	$-0.692507\pi$
$853$	−464.919	+	151.061i	−0.545040	+	0.177094i	0.0235392	+	0.999723i	$0.492507\pi$
$854$	−1475.20	+	2030.43i	−1.72740	+	2.37756i
$855$	136.750	+	188.220i	0.159942	+	0.220141i
$856$	−78.5579	+	241.776i	−0.0917732	+	0.282449i
$857$		−	433.345i		−	0.505653i	−0.967512	−	0.252827i	$-0.918640\pi$
$857$		−	433.345i		−	0.505653i	0.967512	−	0.252827i	$-0.0813602\pi$
$858$	1682.30	+	594.563i	1.96072	+	0.692964i
$859$	−199.533			−0.232285			−0.116143	−	0.993233i	$-0.537053\pi$
$859$	−199.533			−0.232285			−0.116143	+	0.993233i	$0.537053\pi$
$860$	−582.267	−	189.190i	−0.677054	−	0.219988i
$861$	−1075.93	+	781.707i	−1.24962	+	0.907905i
$862$	−1288.74	−	936.323i	−1.49506	−	1.08622i
$863$	−295.364	−	909.036i	−0.342252	−	1.05334i	−0.963038	−	0.269364i	$-0.913186\pi$
$863$	−295.364	−	909.036i	−0.342252	−	1.05334i	0.620786	−	0.783980i	$-0.286814\pi$
$864$	621.944	−	202.082i	0.719843	−	0.233891i
$865$	250.902	−	345.337i	0.290060	−	0.399233i
$866$	−753.088	−	1036.54i	−0.869617	−	1.19692i
$867$	−313.102	+	963.630i	−0.361133	+	1.11145i
$868$		−	1916.07i		−	2.20746i
$869$	−1112.21	−	852.335i	−1.27987	−	0.980823i
$870$	523.050			0.601206
$871$	−482.474	−	156.765i	−0.553931	−	0.179983i
$872$	−235.498	+	171.100i	−0.270067	+	0.196215i
$873$	−616.393	−	447.836i	−0.706063	−	0.512985i
$874$	3.79024	+	11.6652i	0.00433666	+	0.0133469i
$875$	−115.451	+	37.5123i	−0.131944	+	0.0428711i
$876$	1170.52	−	1611.08i	1.33621	−	1.83914i
$877$	184.805	+	254.363i	0.210724	+	0.290037i	0.901276	−	0.433246i	$-0.142632\pi$
$877$	184.805	+	254.363i	0.210724	+	0.290037i	−0.690551	+	0.723284i	$0.742632\pi$
$878$	652.349	−	2007.73i	0.742995	−	2.28670i
$879$		−	1486.95i		−	1.69164i
$880$	187.322	−	55.6133i	0.212866	−	0.0631969i
$881$	330.178			0.374777			0.187388	−	0.982286i	$-0.439998\pi$
$881$	330.178			0.374777			0.187388	+	0.982286i	$0.439998\pi$
$882$	−2485.47	−	807.577i	−2.81799	−	0.915620i
$883$	817.950	−	594.275i	0.926330	−	0.673018i	−0.0187613	−	0.999824i	$-0.505972\pi$
$883$	817.950	−	594.275i	0.926330	−	0.673018i	0.945092	+	0.326806i	$0.105972\pi$
$884$	1139.22	+	827.691i	1.28871	+	0.936302i
$885$	−352.886	−	1086.07i	−0.398742	−	1.22720i
$886$	1693.83	−	550.358i	1.91177	−	0.621172i
$887$	−135.458	+	186.442i	−0.152715	+	0.210194i	−0.878519	−	0.477708i	$-0.841468\pi$
$887$	−135.458	+	186.442i	−0.152715	+	0.210194i	0.725804	+	0.687901i	$0.241468\pi$
$888$	109.153	+	150.236i	0.122920	+	0.169185i
$889$	505.850	−	1556.85i	0.569010	−	1.75123i
$890$			745.491i			0.837631i
$891$	249.443	+	362.461i	0.279958	+	0.406803i
$892$	2075.99			2.32734
$893$	−281.423	−	91.4398i	−0.315143	−	0.102396i
$894$	536.745	−	389.968i	0.600385	−	0.436206i
$895$	−467.157	−	339.409i	−0.521963	−	0.379228i
$896$	−453.507	−	1395.75i	−0.506147	−	1.55776i
$897$	23.6656	−	7.68943i	0.0263831	−	0.00857239i
$898$	−1538.07	+	2116.97i	−1.71277	+	2.35742i
$899$	311.971	+	429.392i	0.347020	+	0.477633i
$900$	−104.217	+	320.748i	−0.115797	+	0.356387i
$901$			758.494i			0.841836i
$902$	−22.9508	+	897.650i	−0.0254444	+	0.995177i
$903$	−2508.80			−2.77830
$904$	−38.6327	−	12.5525i	−0.0427353	−	0.0138856i
$905$	297.456	−	216.114i	0.328681	−	0.238800i
$906$	−863.596	−	627.439i	−0.953196	−	0.692537i
$907$	356.661	+	1097.69i	0.393232	+	1.21024i	0.930330	+	0.366723i	$0.119520\pi$
$907$	356.661	+	1097.69i	0.393232	+	1.21024i	−0.537099	+	0.843519i	$0.680480\pi$
$908$	1084.74	−	352.453i	1.19465	−	0.388164i
$909$	417.818	−	575.078i	0.459646	−	0.632649i
$910$	−501.246	−	689.906i	−0.550820	−	0.758139i
$911$	187.421	−	576.824i	0.205732	−	0.633177i	−0.793951	−	0.607982i	$-0.791979\pi$
$911$	187.421	−	576.824i	0.205732	−	0.633177i	0.999683	−	0.0251948i	$-0.00802062\pi$
$912$			309.674i			0.339555i
$913$	411.950	+	10.5326i	0.451204	+	0.0115363i
$914$	−1254.78			−1.37284
$915$	737.599	+	239.660i	0.806119	+	0.261924i
$916$	−275.320	+	200.032i	−0.300568	+	0.218375i
$917$	−852.914	−	619.678i	−0.930113	−	0.675767i
$918$	−329.399	−	1013.78i	−0.358822	−	1.10434i
$919$	−1094.16	+	355.514i	−1.19060	+	0.386849i	−0.836294	−	0.548281i	$-0.815282\pi$
$919$	−1094.16	+	355.514i	−1.19060	+	0.386849i	−0.354304	+	0.935130i	$0.615282\pi$
$920$	−2.81153	+	3.86974i	−0.00305601	+	0.00420624i
$921$	−271.783	−	374.077i	−0.295096	−	0.406164i
$922$	−686.448	+	2112.67i	−0.744520	+	2.29140i
$923$			598.848i			0.648806i
$924$	−2486.29	+	1711.04i	−2.69079	+	1.85178i
$925$	44.3769			0.0479751
$926$	2270.42	+	737.706i	2.45186	+	0.796658i
$927$	−1096.09	+	796.353i	−1.18240	+	0.859065i
$928$	566.851	+	411.841i	0.610831	+	0.443795i
$929$	444.730	+	1368.74i	0.478719	+	1.47335i	0.840876	+	0.541228i	$0.182040\pi$
$929$	444.730	+	1368.74i	0.478719	+	1.47335i	−0.362157	+	0.932117i	$0.617960\pi$
$930$	−974.746	+	316.714i	−1.04811	+	0.340553i
$931$	341.790	−	470.434i	0.367121	−	0.505299i
$932$	891.107	+	1226.50i	0.956123	+	1.31599i
$933$	−281.269	+	865.658i	−0.301468	+	0.927822i
$934$			1438.02i			1.53963i
$935$	−157.844	−	531.667i	−0.168818	−	0.568628i
$936$	−637.368			−0.680948
$937$	467.559	+	151.919i	0.498996	+	0.162133i	0.547692	−	0.836680i	$-0.315507\pi$
$937$	467.559	+	151.919i	0.498996	+	0.162133i	−0.0486963	+	0.998814i	$0.515507\pi$
$938$	1201.70	−	873.089i	1.28113	−	0.930799i
$939$	907.834	+	659.580i	0.966810	+	0.702428i
$940$	−132.551	−	407.950i	−0.141012	−	0.433990i
$941$	1702.39	−	553.141i	1.80913	−	0.587822i	0.809132	−	0.587628i	$-0.199938\pi$
$941$	1702.39	−	553.141i	1.80913	−	0.587822i	1.00000		0.000194881i	$-6.20325e-5\pi$
$942$	−309.076	+	425.406i	−0.328106	+	0.451599i
$943$	7.36068	+	10.1311i	0.00780560	+	0.0107435i
$944$	271.486	−	835.547i	0.287591	−	0.885113i
$945$			372.933i			0.394638i
$946$	−1030.36	+	1344.51i	−1.08917	+	1.42125i
$947$	−1111.85			−1.17407			−0.587037	−	0.809560i	$-0.699706\pi$
$947$	−1111.85			−1.17407			−0.587037	+	0.809560i	$0.699706\pi$
$948$	3061.55	+	994.756i	3.22948	+	1.04932i
$949$	727.599	−	528.631i	0.766700	−	0.557040i
$950$	−105.086	−	76.3495i	−0.110617	−	0.0803679i
$951$	−807.187	−	2484.27i	−0.848777	−	2.61227i
$952$	−1054.92	+	342.764i	−1.10811	+	0.360046i
$953$	175.776	−	241.935i	0.184445	−	0.253867i	−0.706775	−	0.707439i	$-0.749850\pi$
$953$	175.776	−	241.935i	0.184445	−	0.253867i	0.891220	+	0.453572i	$0.149850\pi$
$954$	−750.102	−	1032.43i	−0.786271	−	1.08221i
$955$	−26.2574	+	80.8118i	−0.0274946	+	0.0846197i
$956$		−	811.977i		−	0.849348i
$957$	278.589	−	788.257i	0.291106	−	0.823675i
$958$	−26.7376			−0.0279098
$959$	2162.84	+	702.749i	2.25531	+	0.732794i
$960$	−829.138	+	602.404i	−0.863686	+	0.627504i
$961$	−63.9224	−	46.4423i	−0.0665165	−	0.0483271i
$962$	96.3344	+	296.487i	0.100140	+	0.308198i
$963$	657.767	−	213.722i	0.683040	−	0.221933i
$964$	1331.38	−	1832.48i	1.38109	−	1.90091i
$965$	6.18034	+	8.50651i	0.00640450	+	0.00881503i
$966$	−22.5147	+	69.2931i	−0.0233072	+	0.0717320i
$967$		−	246.770i		−	0.255191i	−0.991826	−	0.127596i	$-0.959274\pi$
$967$		−	246.770i		−	0.255191i	0.991826	−	0.127596i	$-0.0407259\pi$
$968$	−28.0153	+	547.507i	−0.0289414	+	0.565606i
$969$	878.933			0.907052
$970$	404.562	+	131.450i	0.417074	+	0.135516i
$971$	−161.120	+	117.060i	−0.165932	+	0.120556i	−0.667652	−	0.744473i	$-0.732701\pi$
$971$	−161.120	+	117.060i	−0.165932	+	0.120556i	0.501720	+	0.865030i	$0.332701\pi$
$972$	−1429.79	−	1038.81i	−1.47098	−	1.06873i
$973$	26.9505	+	82.9451i	0.0276983	+	0.0852467i
$974$	2336.60	−	759.209i	2.39898	−	0.779475i
$975$	−154.894	+	213.193i	−0.158865	+	0.218659i
$976$	350.707	+	482.707i	0.359331	+	0.494577i
$977$	−72.9462	+	224.505i	−0.0746635	+	0.229790i	−0.981423	−	0.191858i	$-0.938549\pi$
$977$	−72.9462	+	224.505i	−0.0746635	+	0.229790i	0.906759	+	0.421649i	$0.138549\pi$
$978$			668.119i			0.683149i
$979$	1123.49	+	397.066i	1.14759	+	0.405584i
$980$	842.925			0.860127
$981$	753.174	+	244.721i	0.767762	+	0.249461i
$982$	−370.810	+	269.409i	−0.377607	+	0.274347i
$983$	−301.034	−	218.714i	−0.306241	−	0.222497i	0.424041	−	0.905643i	$-0.360611\pi$
$983$	−301.034	−	218.714i	−0.306241	−	0.222497i	−0.730282	+	0.683146i	$0.760611\pi$
$984$	−171.492	−	527.798i	−0.174280	−	0.536380i
$985$	228.090	−	74.1110i	0.231564	−	0.0752396i
$986$	671.312	−	923.982i	0.680844	−	0.937101i
$987$	−1033.17	−	1422.03i	−1.04678	−	1.44076i
$988$	162.900	−	501.354i	0.164878	−	0.507443i
$989$			23.6233i			0.0238861i
$990$	740.636	+	567.583i	0.748117	+	0.573316i
$991$	−759.033			−0.765927			−0.382963	−	0.923764i	$-0.625096\pi$
$991$	−759.033			−0.765927			−0.382963	+	0.923764i	$0.625096\pi$
$992$	−1305.75	−	424.264i	−1.31628	−	0.427685i
$993$	539.311	−	391.832i	0.543113	−	0.394594i
$994$	−1418.55	−	1030.64i	−1.42712	−	1.03686i
$995$	12.8479	+	39.5417i	0.0129125	+	0.0397404i
$996$	−900.355	+	292.543i	−0.903971	+	0.293718i
$997$	−415.743	+	572.222i	−0.416994	+	0.573944i	−0.964907	−	0.262592i	$-0.915423\pi$
$997$	−415.743	+	572.222i	−0.416994	+	0.573944i	0.547913	+	0.836536i	$0.315423\pi$
$998$	−1102.45	−	1517.39i	−1.10466	−	1.52043i
$999$	42.1289	−	129.659i	0.0421711	−	0.129789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	55.3.i.b.46.1	yes	4
5.2	odd	4		275.3.q.a.24.1		8
5.3	odd	4		275.3.q.a.24.2		8
5.4	even	2		275.3.x.a.101.1		4
11.4	even	5		605.3.c.b.241.4		4
11.6	odd	10	inner	55.3.i.b.6.1	✓	4
11.7	odd	10		605.3.c.b.241.1		4
55.17	even	20		275.3.q.a.149.2		8
55.28	even	20		275.3.q.a.149.1		8
55.39	odd	10		275.3.x.a.226.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.3.i.b.6.1	✓	4	11.6	odd	10	inner
55.3.i.b.46.1	yes	4	1.1	even	1	trivial
275.3.q.a.24.1		8	5.2	odd	4
275.3.q.a.24.2		8	5.3	odd	4
275.3.q.a.149.1		8	55.28	even	20
275.3.q.a.149.2		8	55.17	even	20
275.3.x.a.101.1		4	5.4	even	2
275.3.x.a.226.1		4	55.39	odd	10
605.3.c.b.241.1		4	11.7	odd	10
605.3.c.b.241.4		4	11.4	even	5

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:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.i (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.92705 + 0.951057i) q^{2} +(-3.73607 + 2.71441i) q^{3} +(4.42705 + 3.21644i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-13.5172 + 4.39201i) q^{6} +(6.38197 - 8.78402i) q^{7} +(2.66312 + 3.66547i) q^{8} +(3.80902 - 11.7229i) q^{9} +6.88191i q^{10} +(10.3713 + 3.66547i) q^{11} -25.2705 q^{12} +(-10.8541 - 3.52671i) q^{13} +(27.0344 - 19.6417i) q^{14} +(-8.35410 - 6.06961i) q^{15} +(-2.45492 - 7.55545i) q^{16} +(-21.4443 + 6.96767i) q^{17} +(22.2984 - 30.6911i) q^{18} +(4.96149 + 6.82891i) q^{19} +(-3.78115 + 11.6372i) q^{20} +50.1410i q^{21} +(26.8713 + 20.5927i) q^{22} +0.472136 q^{23} +(-19.8992 - 6.46564i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-28.4164 - 20.6457i) q^{26} +(4.74671 + 14.6089i) q^{27} +(56.5066 - 18.3601i) q^{28} +(-9.67376 + 13.3148i) q^{29} +(-18.6803 - 25.7113i) q^{30} +(9.96556 - 30.6708i) q^{31} -42.5730i q^{32} +(-48.6976 + 14.4576i) q^{33} -69.3951 q^{34} +(23.0902 + 7.50245i) q^{35} +(54.5689 - 39.6466i) q^{36} +(-7.18034 - 5.21682i) q^{37} +(8.02786 + 24.7072i) q^{38} +(50.1246 - 16.2865i) q^{39} +(-5.95492 + 8.19624i) q^{40} +(15.5902 + 21.4580i) q^{41} +(-47.6869 + 146.765i) q^{42} +50.0350i q^{43} +(34.1246 + 49.5860i) q^{44} +27.5623 q^{45} +(1.38197 + 0.449028i) q^{46} +(-28.3607 + 20.6052i) q^{47} +(29.6803 + 21.5640i) q^{48} +(-21.2877 - 65.5169i) q^{49} +(-14.6353 + 4.75528i) q^{50} +(61.2041 - 84.2403i) q^{51} +(-36.7082 - 50.5245i) q^{52} +(10.3951 - 31.9929i) q^{53} +47.2753i q^{54} +(-0.628677 + 24.5887i) q^{55} +49.1935 q^{56} +(-37.0729 - 12.0457i) q^{57} +(-40.9787 + 29.7728i) q^{58} +(89.4681 + 65.0024i) q^{59} +(-17.4615 - 53.7409i) q^{60} +(-71.4296 + 23.2089i) q^{61} +(58.3394 - 80.2973i) q^{62} +(-78.6656 - 108.274i) q^{63} +(30.6697 - 94.3916i) q^{64} -25.5195i q^{65} +(-156.290 - 3.99598i) q^{66} +44.4508 q^{67} +(-117.346 - 38.1280i) q^{68} +(-1.76393 + 1.28157i) q^{69} +(60.4508 + 43.9201i) q^{70} +(-16.2148 - 49.9040i) q^{71} +(53.1140 - 17.2578i) q^{72} +(-46.3197 + 63.7535i) q^{73} +(-16.0557 - 22.0988i) q^{74} +(7.13525 - 21.9601i) q^{75} +46.1903i q^{76} +(98.3870 - 67.7090i) q^{77} +162.207 q^{78} +(-121.151 - 39.3643i) q^{79} +(14.3713 - 10.4414i) q^{80} +(32.3607 + 23.5114i) q^{81} +(25.2254 + 77.6359i) q^{82} +(35.6287 - 11.5765i) q^{83} +(-161.276 + 221.977i) q^{84} +(-29.6353 - 40.7894i) q^{85} +(-47.5861 + 146.455i) q^{86} -76.0035i q^{87} +(14.1844 + 47.7773i) q^{88} +108.326 q^{89} +(80.6763 + 26.2133i) q^{90} +(-100.249 + 72.8353i) q^{91} +(2.09017 + 1.51860i) q^{92} +(46.0213 + 141.639i) q^{93} +(-102.610 + 33.3400i) q^{94} +(-11.0942 + 15.2699i) q^{95} +(115.561 + 159.056i) q^{96} +(19.1008 - 58.7863i) q^{97} -212.017i q^{98} +(82.4746 - 107.621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 5 q^{2} - 6 q^{3} + 11 q^{4} + 5 q^{5} - 25 q^{6} + 30 q^{7} - 5 q^{8} + 13 q^{9} - q^{11} - 34 q^{12} - 30 q^{13} + 50 q^{14} - 20 q^{15} - 21 q^{16} - 50 q^{17} + 40 q^{18} - 45 q^{19} + 5 q^{20}+ \cdots + 113 q^{99}+O(q^{100}) \) 4 * q + 5 * q^2 - 6 * q^3 + 11 * q^4 + 5 * q^5 - 25 * q^6 + 30 * q^7 - 5 * q^8 + 13 * q^9 - q^11 - 34 * q^12 - 30 * q^13 + 50 * q^14 - 20 * q^15 - 21 * q^16 - 50 * q^17 + 40 * q^18 - 45 * q^19 + 5 * q^20 + 65 * q^22 - 16 * q^23 - 55 * q^24 - 5 * q^25 - 60 * q^26 + 57 * q^27 + 150 * q^28 - 70 * q^29 - 30 * q^30 + 98 * q^31 - 121 * q^33 - 130 * q^34 + 70 * q^35 + 102 * q^36 + 16 * q^37 + 50 * q^38 + 120 * q^39 - 35 * q^40 + 40 * q^41 - 70 * q^42 + 56 * q^44 + 70 * q^45 + 10 * q^46 - 24 * q^47 + 74 * q^48 + 11 * q^49 - 25 * q^50 + 95 * q^51 - 120 * q^52 - 106 * q^53 - 45 * q^55 - 155 * q^57 - 70 * q^58 + 217 * q^59 - 5 * q^60 - 80 * q^61 + 50 * q^62 - 100 * q^63 + 31 * q^64 - 330 * q^66 + 66 * q^67 - 210 * q^68 - 16 * q^69 + 130 * q^70 + 38 * q^71 + 85 * q^72 - 230 * q^73 - 100 * q^74 - 5 * q^75 + 300 * q^78 - 100 * q^79 + 15 * q^80 + 40 * q^81 + 45 * q^82 + 185 * q^83 - 180 * q^84 - 85 * q^85 - 45 * q^86 + 135 * q^88 + 402 * q^89 + 155 * q^90 - 240 * q^91 - 14 * q^92 + 278 * q^93 - 160 * q^94 - 145 * q^95 + 100 * q^96 + 101 * q^97 + 113 * q^99

Introduction

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