LMFDB - Embedded newform 46.4.c.a.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [46,4,Mod(3,46)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("46.3"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(46, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,-6] 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:	$2.71408786026$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	46.13
Dual form			46.4.c.a.39.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30972 - 1.51150i) q^{2} +(-4.75375 - 3.05505i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(-6.73761 + 14.7533i) q^{5} +(1.60838 + 11.1865i) q^{6} +(22.9137 + 6.72806i) q^{7} +(6.73003 - 4.32513i) q^{8} +(2.04859 + 4.48580i) q^{9} +(31.1240 - 9.13883i) q^{10} +(-43.2609 + 49.9258i) q^{11} +(14.8019 - 17.0823i) q^{12} +(-66.3140 + 19.4716i) q^{13} +(-19.8411 - 43.4459i) q^{14} +(77.1009 - 49.5498i) q^{15} +(-15.3519 - 4.50772i) q^{16} +(2.87874 + 20.0220i) q^{17} +(4.09719 - 8.97159i) q^{18} +(9.51172 - 66.1555i) q^{19} +(-54.5771 - 35.0746i) q^{20} +(-88.3713 - 101.986i) q^{21} +132.123 q^{22} +(68.6830 + 86.3113i) q^{23} -45.2063 q^{24} +(-90.4069 - 104.335i) q^{25} +(116.284 + 74.7313i) q^{26} +(-17.7473 + 123.436i) q^{27} +(-39.6821 + 86.8918i) q^{28} +(-21.4363 - 149.093i) q^{29} +(-175.875 - 51.6416i) q^{30} +(55.7410 - 35.8226i) q^{31} +(13.2933 + 29.1082i) q^{32} +(358.177 - 105.170i) q^{33} +(26.4930 - 30.5745i) q^{34} +(-253.644 + 292.721i) q^{35} +(-18.9267 + 5.55739i) q^{36} +(-46.8861 - 102.666i) q^{37} +(-112.452 + 72.2683i) q^{38} +(374.727 + 110.030i) q^{39} +(18.4656 + 128.431i) q^{40} +(-105.395 + 230.783i) q^{41} +(-38.4098 + 267.146i) q^{42} +(221.086 + 142.083i) q^{43} +(-173.044 - 199.703i) q^{44} -79.9829 q^{45} +(40.5039 - 216.858i) q^{46} -290.588 q^{47} +(59.2077 + 68.3293i) q^{48} +(191.220 + 122.890i) q^{49} +(-39.2946 + 273.300i) q^{50} +(47.4835 - 103.974i) q^{51} +(-39.3436 - 273.640i) q^{52} +(-34.6916 - 10.1864i) q^{53} +(209.817 - 134.841i) q^{54} +(-445.095 - 974.621i) q^{55} +(183.309 - 53.8245i) q^{56} +(-247.324 + 285.428i) q^{57} +(-197.278 + 227.671i) q^{58} +(110.932 - 32.5727i) q^{59} +(152.291 + 333.471i) q^{60} +(230.979 - 148.441i) q^{61} +(-127.151 - 37.3349i) q^{62} +(16.7601 + 116.569i) q^{63} +(26.5866 - 58.2164i) q^{64} +(159.528 - 1109.54i) q^{65} +(-628.077 - 403.641i) q^{66} +(476.872 + 550.339i) q^{67} -80.9117 q^{68} +(-62.8165 - 620.132i) q^{69} +774.652 q^{70} +(116.331 + 134.253i) q^{71} +(33.1887 + 21.3291i) q^{72} +(-89.6640 + 623.627i) q^{73} +(-93.7721 + 205.332i) q^{74} +(111.023 + 772.181i) q^{75} +(256.514 + 75.3192i) q^{76} +(-1327.17 + 852.921i) q^{77} +(-324.478 - 710.507i) q^{78} +(636.735 - 186.962i) q^{79} +(169.939 - 196.120i) q^{80} +(548.662 - 633.190i) q^{81} +(486.867 - 142.957i) q^{82} +(-33.4015 - 73.1391i) q^{83} +(454.098 - 291.831i) q^{84} +(-314.787 - 92.4298i) q^{85} +(-74.8023 - 520.261i) q^{86} +(-353.582 + 774.238i) q^{87} +(-75.2120 + 523.111i) q^{88} +(-704.309 - 452.632i) q^{89} +(104.755 + 120.894i) q^{90} -1650.50 q^{91} +(-380.830 + 222.802i) q^{92} -374.418 q^{93} +(380.590 + 439.224i) q^{94} +(911.925 + 586.059i) q^{95} +(25.7341 - 178.985i) q^{96} +(-533.009 + 1167.13i) q^{97} +(-64.6973 - 449.980i) q^{98} +(-312.581 - 91.7820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9} + 20 q^{10} + 64 q^{11} - 20 q^{12} + 8 q^{13} + 16 q^{14} + 252 q^{15} - 48 q^{16} - 126 q^{17} - 126 q^{18}+ \cdots + 1377 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 + 6 * q^3 - 12 * q^4 + 10 * q^5 + 12 * q^6 + 107 * q^7 - 24 * q^8 - 63 * q^9 + 20 * q^10 + 64 * q^11 - 20 * q^12 + 8 * q^13 + 16 * q^14 + 252 * q^15 - 48 * q^16 - 126 * q^17 - 126 * q^18 + 123 * q^19 - 136 * q^20 - 514 * q^21 - 356 * q^22 - 507 * q^23 + 48 * q^24 - 419 * q^25 - 94 * q^26 - 657 * q^27 + 32 * q^28 + 757 * q^29 + 240 * q^30 + 840 * q^31 - 96 * q^32 + 1948 * q^33 + 936 * q^34 - 785 * q^35 - 164 * q^36 - 444 * q^37 + 554 * q^38 + 1954 * q^39 + 80 * q^40 - 771 * q^41 + 72 * q^42 - 789 * q^43 + 256 * q^44 - 2596 * q^45 + 1230 * q^46 - 1748 * q^47 - 80 * q^48 - 720 * q^49 - 2026 * q^50 + 1641 * q^51 + 472 * q^52 - 785 * q^53 + 2030 * q^54 + 967 * q^55 + 856 * q^56 + 5918 * q^57 + 1052 * q^58 + 2307 * q^59 - 444 * q^60 + 877 * q^61 - 278 * q^62 - 5708 * q^63 - 192 * q^64 - 3846 * q^65 - 4156 * q^66 + 1763 * q^67 - 2528 * q^68 - 1970 * q^69 - 3968 * q^70 - 6362 * q^71 - 152 * q^72 - 3584 * q^73 - 888 * q^74 + 3143 * q^75 + 360 * q^76 + 6347 * q^77 - 1460 * q^78 + 2642 * q^79 + 864 * q^80 + 1043 * q^81 + 5542 * q^82 - 372 * q^83 + 2212 * q^84 + 5136 * q^85 - 2326 * q^86 + 5451 * q^87 - 104 * q^88 - 4283 * q^89 + 5104 * q^90 - 6182 * q^91 - 92 * q^92 - 8734 * q^93 - 2550 * q^94 + 9449 * q^95 + 192 * q^96 + 7599 * q^97 + 3928 * q^98 + 1377 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−1.30972	−	1.51150i	−0.463056	−	0.534396i
$2$	−1.30972	−	1.51150i	−0.463056	−	0.534396i
$3$	−4.75375	−	3.05505i	−0.914859	−	0.587944i	−0.00369747	−	0.999993i	$-0.501177\pi$
$3$	−4.75375	−	3.05505i	−0.914859	−	0.587944i	−0.911162	+	0.412049i	$0.864813\pi$
$4$	−0.569259	+	3.95929i	−0.0711574	+	0.494911i
$5$	−6.73761	+	14.7533i	−0.602630	+	1.31958i	0.324872	+	0.945758i	$0.394679\pi$
$5$	−6.73761	+	14.7533i	−0.602630	+	1.31958i	−0.927502	+	0.373817i	$0.878049\pi$
$6$	1.60838	+	11.1865i	0.109437	+	0.761148i
$7$	22.9137	+	6.72806i	1.23722	+	0.363281i	0.833971	−	0.551808i	$-0.186062\pi$
$7$	22.9137	+	6.72806i	1.23722	+	0.363281i	0.403251	+	0.915089i	$0.367880\pi$
$8$	6.73003	−	4.32513i	0.297428	−	0.191145i
$9$	2.04859	+	4.48580i	0.0758739	+	0.166141i
$10$	31.1240	−	9.13883i	0.984227	−	0.288995i
$11$	−43.2609	+	49.9258i	−1.18579	+	1.36847i	−0.271990	+	0.962300i	$0.587682\pi$
$11$	−43.2609	+	49.9258i	−1.18579	+	1.36847i	−0.913797	+	0.406171i	$0.866864\pi$
$12$	14.8019	−	17.0823i	0.356079	−	0.410937i
$13$	−66.3140	+	19.4716i	−1.41478	+	0.415418i	−0.897734	−	0.440537i	$-0.854788\pi$
$13$	−66.3140	+	19.4716i	−1.41478	+	0.415418i	−0.517050	+	0.855955i	$0.672970\pi$
$14$	−19.8411	−	43.4459i	−0.378768	−	0.829386i
$15$	77.1009	−	49.5498i	1.32716	−	0.852913i
$16$	−15.3519	−	4.50772i	−0.239873	−	0.0704331i
$17$	2.87874	+	20.0220i	0.0410703	+	0.285651i	0.999998	+	0.00199977i	$0.000636548\pi$
$17$	2.87874	+	20.0220i	0.0410703	+	0.285651i	−0.958928	+	0.283651i	$0.908454\pi$
$18$	4.09719	−	8.97159i	0.0536509	−	0.117479i
$19$	9.51172	−	66.1555i	0.114849	−	0.798795i	−0.848240	−	0.529612i	$-0.822337\pi$
$19$	9.51172	−	66.1555i	0.114849	−	0.798795i	0.963089	−	0.269183i	$-0.0867535\pi$
$20$	−54.5771	−	35.0746i	−0.610190	−	0.392146i
$21$	−88.3713	−	101.986i	−0.918295	−	1.05977i
$22$	132.123			1.28039
$23$	68.6830	+	86.3113i	0.622670	+	0.782485i
$23$	68.6830	+	86.3113i	0.622670	+	0.782485i
$24$	−45.2063			−0.384488
$25$	−90.4069	−	104.335i	−0.723255	−	0.834681i
$26$	116.284	+	74.7313i	0.877123	+	0.563693i
$27$	−17.7473	+	123.436i	−0.126499	+	0.879821i
$28$	−39.6821	+	86.8918i	−0.267829	+	0.586464i
$29$	−21.4363	−	149.093i	−0.137263	−	0.954683i	−0.935748	−	0.352669i	$-0.885274\pi$
$29$	−21.4363	−	149.093i	−0.137263	−	0.954683i	0.798486	−	0.602014i	$-0.205635\pi$
$30$	−175.875	−	51.6416i	−1.07034	−	0.314281i
$31$	55.7410	−	35.8226i	0.322948	−	0.207546i	−0.369114	−	0.929384i	$-0.620339\pi$
$31$	55.7410	−	35.8226i	0.322948	−	0.207546i	0.692062	+	0.721838i	$0.256703\pi$
$32$	13.2933	+	29.1082i	0.0734357	+	0.160802i
$33$	358.177	−	105.170i	1.88941	−	0.554782i
$34$	26.4930	−	30.5745i	0.133633	−	0.154220i
$35$	−253.644	+	292.721i	−1.22496	+	1.41368i
$36$	−18.9267	+	5.55739i	−0.0876238	+	0.0257287i
$37$	−46.8861	−	102.666i	−0.208325	−	0.456168i	0.776410	−	0.630228i	$-0.217039\pi$
$37$	−46.8861	−	102.666i	−0.208325	−	0.456168i	−0.984735	+	0.174060i	$0.944311\pi$
$38$	−112.452	+	72.2683i	−0.480054	+	0.308512i
$39$	374.727	+	110.030i	1.53857	+	0.451765i
$40$	18.4656	+	128.431i	0.0729917	+	0.507669i
$41$	−105.395	+	230.783i	−0.401462	+	0.879080i	0.595658	+	0.803238i	$0.296891\pi$
$41$	−105.395	+	230.783i	−0.401462	+	0.879080i	−0.997120	+	0.0758412i	$0.975836\pi$
$42$	−38.4098	+	267.146i	−0.141113	+	0.981466i
$43$	221.086	+	142.083i	0.784077	+	0.503896i	0.870384	−	0.492373i	$-0.163870\pi$
$43$	221.086	+	142.083i	0.784077	+	0.503896i	−0.0863072	+	0.996269i	$0.527507\pi$
$44$	−173.044	−	199.703i	−0.592894	−	0.684236i
$45$	−79.9829			−0.264959
$46$	40.5039	−	216.858i	0.129825	−	0.695087i
$47$	−290.588			−0.901844			−0.450922	−	0.892563i	$-0.648905\pi$
$47$	−290.588			−0.901844			−0.450922	+	0.892563i	$0.648905\pi$
$48$	59.2077	+	68.3293i	0.178039	+	0.205469i
$49$	191.220	+	122.890i	0.557492	+	0.358278i
$50$	−39.2946	+	273.300i	−0.111142	+	0.773009i
$51$	47.4835	−	103.974i	0.130373	−	0.285477i
$52$	−39.3436	−	273.640i	−0.104923	−	0.729752i
$53$	−34.6916	−	10.1864i	−0.0899105	−	0.0264001i	0.236468	−	0.971639i	$-0.424010\pi$
$53$	−34.6916	−	10.1864i	−0.0899105	−	0.0264001i	−0.326378	+	0.945239i	$0.605828\pi$
$54$	209.817	−	134.841i	0.528749	−	0.339806i
$55$	−445.095	−	974.621i	−1.09121	−	2.38942i
$56$	183.309	−	53.8245i	0.437424	−	0.128439i
$57$	−247.324	+	285.428i	−0.574718	+	0.663260i
$58$	−197.278	+	227.671i	−0.446618	+	0.515425i
$59$	110.932	−	32.5727i	0.244782	−	0.0718746i	−0.157040	−	0.987592i	$-0.550195\pi$
$59$	110.932	−	32.5727i	0.244782	−	0.0718746i	0.401822	+	0.915718i	$0.368377\pi$
$60$	152.291	+	333.471i	0.327679	+	0.717516i
$61$	230.979	−	148.441i	0.484816	−	0.311572i	−0.275301	−	0.961358i	$-0.588778\pi$
$61$	230.979	−	148.441i	0.484816	−	0.311572i	0.760118	+	0.649786i	$0.225141\pi$
$62$	−127.151	−	37.3349i	−0.260455	−	0.0764764i
$63$	16.7601	+	116.569i	0.0335171	+	0.233116i
$64$	26.5866	−	58.2164i	0.0519269	−	0.113704i
$65$	159.528	−	1109.54i	0.304416	−	2.11726i
$66$	−628.077	−	403.641i	−1.17138	−	0.752799i
$67$	476.872	+	550.339i	0.869539	+	1.00350i	0.999928	+	0.0120390i	$0.00383222\pi$
$67$	476.872	+	550.339i	0.869539	+	1.00350i	−0.130388	+	0.991463i	$0.541622\pi$
$68$	−80.9117			−0.144294
$69$	−62.8165	−	620.132i	−0.109597	−	1.08196i
$70$	774.652			1.32269
$71$	116.331	+	134.253i	0.194450	+	0.224407i	0.844599	−	0.535400i	$-0.179839\pi$
$71$	116.331	+	134.253i	0.194450	+	0.224407i	−0.650149	+	0.759807i	$0.725294\pi$
$72$	33.1887	+	21.3291i	0.0543240	+	0.0349119i
$73$	−89.6640	+	623.627i	−0.143759	+	0.999863i	0.782413	+	0.622760i	$0.213989\pi$
$73$	−89.6640	+	623.627i	−0.143759	+	0.999863i	−0.926171	+	0.377103i	$0.876920\pi$
$74$	−93.7721	+	205.332i	−0.147308	+	0.322559i
$75$	111.023	+	772.181i	0.170931	+	1.18885i
$76$	256.514	+	75.3192i	0.387160	+	0.113680i
$77$	−1327.17	+	852.921i	−1.96422	+	1.26233i
$78$	−324.478	−	710.507i	−0.471024	−	1.03140i
$79$	636.735	−	186.962i	0.906814	−	0.266265i	0.205115	−	0.978738i	$-0.434243\pi$
$79$	636.735	−	186.962i	0.906814	−	0.266265i	0.701699	+	0.712473i	$0.252425\pi$
$80$	169.939	−	196.120i	0.237497	−	0.274086i
$81$	548.662	−	633.190i	0.752623	−	0.868573i
$82$	486.867	−	142.957i	0.655676	−	0.192524i
$83$	−33.4015	−	73.1391i	−0.0441722	−	0.0967237i	0.886259	−	0.463189i	$-0.153295\pi$
$83$	−33.4015	−	73.1391i	−0.0441722	−	0.0967237i	−0.930432	+	0.366466i	$0.880568\pi$
$84$	454.098	−	291.831i	0.589835	−	0.379064i
$85$	−314.787	−	92.4298i	−0.401688	−	0.117946i
$86$	−74.8023	−	520.261i	−0.0937923	−	0.652340i
$87$	−353.582	+	774.238i	−0.435724	+	0.954103i
$88$	−75.2120	+	523.111i	−0.0911094	+	0.633679i
$89$	−704.309	−	452.632i	−0.838838	−	0.539088i	0.0492369	−	0.998787i	$-0.484321\pi$
$89$	−704.309	−	452.632i	−0.838838	−	0.539088i	−0.888075	+	0.459699i	$0.847957\pi$
$90$	104.755	+	120.894i	0.122691	+	0.141593i
$91$	−1650.50			−1.90132
$92$	−380.830	+	222.802i	−0.431568	+	0.252486i
$93$	−374.418			−0.417477
$94$	380.590	+	439.224i	0.417605	+	0.481942i
$95$	911.925	+	586.059i	0.984858	+	0.632930i
$96$	25.7341	−	178.985i	0.0273591	−	0.190287i
$97$	−533.009	+	1167.13i	−0.557926	+	1.22169i	0.395055	+	0.918657i	$0.370726\pi$
$97$	−533.009	+	1167.13i	−0.557926	+	1.22169i	−0.952981	+	0.303030i	$0.902002\pi$
$98$	−64.6973	−	449.980i	−0.0666879	−	0.463825i
$99$	−312.581	−	91.7820i	−0.317329	−	0.0931762i
$100$	464.558	−	298.553i	0.464558	−	0.298553i
$101$	317.623	+	695.497i	0.312918	+	0.685194i	0.999108	−	0.0422281i	$-0.0134456\pi$
$101$	317.623	+	695.497i	0.312918	+	0.685194i	−0.686190	+	0.727422i	$0.740718\pi$
$102$	−219.347	+	64.4062i	−0.212928	+	0.0625212i
$103$	179.983	−	207.712i	0.172177	−	0.198703i	−0.663102	−	0.748529i	$-0.730760\pi$
$103$	179.983	−	207.712i	0.172177	−	0.198703i	0.835279	+	0.549826i	$0.185306\pi$
$104$	−362.078	+	417.861i	−0.341391	+	0.393987i
$105$	2100.04	−	616.627i	1.95184	−	0.573111i
$106$	30.0396	+	65.7776i	0.0275255	+	0.0602725i
$107$	1721.98	−	1106.65i	1.55579	−	0.999848i	0.572061	−	0.820211i	$-0.306144\pi$
$107$	1721.98	−	1106.65i	1.55579	−	0.999848i	0.983733	−	0.179638i	$-0.0574925\pi$
$108$	−478.614	−	140.534i	−0.426432	−	0.125212i
$109$	84.8057	+	589.836i	0.0745221	+	0.518313i	0.992554	+	0.121806i	$0.0388686\pi$
$109$	84.8057	+	589.836i	0.0745221	+	0.518313i	−0.918032	+	0.396507i	$0.870222\pi$
$110$	−890.189	+	1949.24i	−0.771602	+	1.68957i
$111$	−90.7656	+	631.288i	−0.0776134	+	0.539813i
$112$	−321.440	−	206.577i	−0.271189	−	0.174283i
$113$	1031.06	+	1189.91i	0.858354	+	0.990594i	1.00000		0.000676364i	$0.000215293\pi$
$113$	1031.06	+	1189.91i	0.858354	+	0.990594i	−0.141645	+	0.989917i	$0.545239\pi$
$114$	755.350			0.620570
$115$	−1736.14	+	431.769i	−1.40779	+	0.350111i
$116$	602.503			0.482250
$117$	−223.196	−	257.582i	−0.176363	−	0.203534i
$118$	−194.524	−	125.013i	−0.151758	−	0.0975287i
$119$	−68.7472	+	478.147i	−0.0529583	+	0.368333i
$120$	304.582	−	666.943i	0.231704	−	0.507360i
$121$	−431.654	−	3002.22i	−0.324308	−	2.25561i
$122$	−526.886	−	154.708i	−0.391000	−	0.114808i
$123$	1206.08	−	775.097i	0.884131	−	0.568197i
$124$	110.101	+	241.087i	0.0797366	+	0.174599i
$125$	203.165	−	59.6546i	0.145373	−	0.0426854i
$126$	154.243	−	178.006i	0.109056	−	0.125857i
$127$	180.919	−	208.791i	0.126409	−	0.145884i	−0.689017	−	0.724745i	$-0.741957\pi$
$127$	180.919	−	208.791i	0.126409	−	0.145884i	0.815426	+	0.578862i	$0.196503\pi$
$128$	−122.815	+	36.0618i	−0.0848080	+	0.0249019i
$129$	−616.916	−	1350.86i	−0.421058	−	0.921988i
$130$	−1886.01	+	1212.06i	−1.27242	+	0.817732i
$131$	430.367	+	126.367i	0.287033	+	0.0842806i	0.422080	−	0.906559i	$-0.361300\pi$
$131$	430.367	+	126.367i	0.287033	+	0.0842806i	−0.135046	+	0.990839i	$0.543118\pi$
$132$	212.504	+	1477.99i	0.140122	+	0.974568i
$133$	663.047	−	1451.87i	0.432281	−	0.946564i
$134$	207.268	−	1441.58i	0.133621	−	0.929356i
$135$	−1701.51	−	1093.49i	−1.08476	−	0.697132i
$136$	105.972	+	122.298i	0.0668163	+	0.0771101i
$137$	−2830.59			−1.76521			−0.882606	−	0.470114i	$-0.844213\pi$
$137$	−2830.59			−1.76521			−0.882606	+	0.470114i	$0.844213\pi$
$138$	−855.057	+	907.148i	−0.527444	+	0.559576i
$139$	−313.605			−0.191364			−0.0956822	−	0.995412i	$-0.530503\pi$
$139$	−313.605			−0.191364			−0.0956822	+	0.995412i	$0.530503\pi$
$140$	−1014.58	−	1170.89i	−0.612482	−	0.706842i
$141$	1381.38	+	887.762i	0.825061	+	0.530234i
$142$	50.5623	−	351.668i	0.0298809	−	0.207826i
$143$	1896.67	−	4153.13i	1.10915	−	2.42869i
$144$	−11.2291	−	78.0999i	−0.00649831	−	0.0451967i
$145$	2344.04	+	688.271i	1.34249	+	0.394192i
$146$	1060.05	−	681.250i	0.600891	−	0.386169i
$147$	−533.577	−	1168.37i	−0.299379	−	0.655549i
$148$	433.175	−	127.192i	0.240586	−	0.0706425i
$149$	−753.214	+	869.256i	−0.414132	+	0.477934i	−0.924040	−	0.382295i	$-0.875134\pi$
$149$	−753.214	+	869.256i	−0.414132	+	0.477934i	0.509908	+	0.860229i	$0.329679\pi$
$150$	1021.74	−	1179.15i	0.556166	−	0.641849i
$151$	−1063.55	+	312.287i	−0.573182	+	0.168301i	−0.555463	−	0.831542i	$-0.687459\pi$
$151$	−1063.55	+	312.287i	−0.573182	+	0.168301i	−0.0177196	+	0.999843i	$0.505641\pi$
$152$	−222.117	−	486.367i	−0.118527	−	0.259537i
$153$	−83.9174	+	53.9305i	−0.0443420	+	0.0284969i
$154$	3027.41	+	888.928i	1.58413	+	0.465142i
$155$	152.940	+	1063.72i	0.0792545	+	0.551227i
$156$	−648.956	+	1421.01i	−0.333064	+	0.729309i
$157$	−473.370	+	3292.36i	−0.240631	+	1.67362i	0.408354	+	0.912823i	$0.366103\pi$
$157$	−473.370	+	3292.36i	−0.240631	+	1.67362i	−0.648985	+	0.760801i	$0.724806\pi$
$158$	−1116.54	−	717.556i	−0.562197	−	0.361302i
$159$	133.795	+	154.408i	0.0667337	+	0.0770148i
$160$	−519.007			−0.256445
$161$	993.073	+	2439.81i	0.486118	+	1.19431i
$162$	−1675.66			−0.812668
$163$	−257.174	−	296.795i	−0.123579	−	0.142618i	0.690588	−	0.723248i	$-0.257352\pi$
$163$	−257.174	−	296.795i	−0.123579	−	0.142618i	−0.814168	+	0.580630i	$0.802806\pi$
$164$	−853.739	−	548.665i	−0.406499	−	0.261241i
$165$	−861.648	+	5992.89i	−0.406540	+	2.82755i
$166$	−66.8031	+	146.278i	−0.0312345	+	0.0683940i
$167$	437.289	+	3041.41i	0.202626	+	1.40929i	0.796454	+	0.604700i	$0.206707\pi$
$167$	437.289	+	3041.41i	0.202626	+	1.40929i	−0.593828	+	0.804592i	$0.702384\pi$
$168$	−1035.84	−	304.151i	−0.475697	−	0.139677i
$169$	2170.17	−	1394.69i	0.987789	−	0.634814i
$170$	272.576	+	596.858i	0.122974	+	0.269276i
$171$	316.246	−	92.8581i	0.141426	−	0.0415265i
$172$	−688.404	+	794.461i	−0.305176	+	0.352192i
$173$	1294.19	−	1493.57i	0.568758	−	0.656382i	−0.396391	−	0.918082i	$-0.629738\pi$
$173$	1294.19	−	1493.57i	0.568758	−	0.656382i	0.965149	+	0.261700i	$0.0842831\pi$
$174$	1633.35	−	479.596i	0.711634	−	0.208954i
$175$	−1369.58	−	2998.97i	−0.591604	−	1.29543i
$176$	889.188	−	571.447i	0.380824	−	0.244741i
$177$	−626.856	−	184.061i	−0.266200	−	0.0781633i
$178$	238.296	+	1657.38i	0.100343	+	0.697900i
$179$	1323.23	−	2897.46i	0.552528	−	1.20987i	−0.403063	−	0.915172i	$-0.632054\pi$
$179$	1323.23	−	2897.46i	0.552528	−	1.20987i	0.955591	−	0.294696i	$-0.0952182\pi$
$180$	45.5310	−	316.675i	0.0188538	−	0.131131i
$181$	−1693.49	−	1088.34i	−0.695448	−	0.446938i	0.144571	−	0.989494i	$-0.453820\pi$
$181$	−1693.49	−	1088.34i	−0.695448	−	0.446938i	−0.840019	+	0.542557i	$0.817456\pi$
$182$	2161.70	+	2494.74i	0.880417	+	1.01606i
$183$	−1551.51			−0.626726
$184$	835.546	+	283.815i	0.334768	+	0.113713i
$185$	1830.56			0.727491
$186$	490.384	+	565.933i	0.193316	+	0.223098i
$187$	−1124.15	−	722.449i	−0.439605	−	0.282517i
$188$	165.420	−	1150.52i	0.0641729	−	0.446332i
$189$	−1237.14	+	2708.96i	−0.476130	+	1.04258i
$190$	−308.541	−	2145.95i	−0.117810	−	0.819386i
$191$	−1661.33	−	487.809i	−0.629368	−	0.184799i	−0.0485346	−	0.998822i	$-0.515455\pi$
$191$	−1661.33	−	487.809i	−0.629368	−	0.184799i	−0.580834	+	0.814022i	$0.697273\pi$
$192$	−304.240	+	195.523i	−0.114357	+	0.0734930i
$193$	1104.07	+	2417.59i	0.411777	+	0.901666i	0.995939	+	0.0900291i	$0.0286960\pi$
$193$	1104.07	+	2417.59i	0.411777	+	0.901666i	−0.584162	+	0.811637i	$0.698577\pi$
$194$	2462.20	−	722.968i	0.911216	−	0.267557i
$195$	−4148.06	+	4787.12i	−1.52333	+	1.75801i
$196$	−595.408	+	687.138i	−0.216986	+	0.250415i
$197$	3437.55	−	1009.36i	1.24323	−	0.365044i	0.406999	−	0.913428i	$-0.366575\pi$
$197$	3437.55	−	1009.36i	1.24323	−	0.365044i	0.836226	+	0.548384i	$0.184757\pi$
$198$	270.665	+	592.675i	0.0971483	+	0.212725i
$199$	−2699.86	+	1735.10i	−0.961750	+	0.618079i	−0.924482	−	0.381226i	$-0.875502\pi$
$199$	−2699.86	+	1735.10i	−0.961750	+	0.618079i	−0.0372682	+	0.999305i	$0.511866\pi$
$200$	−1059.70	−	311.157i	−0.374662	−	0.110011i
$201$	−585.615	−	4073.04i	−0.205503	−	1.42930i
$202$	635.246	−	1390.99i	0.221266	−	0.484505i
$203$	511.920	−	3560.48i	0.176994	−	1.23102i
$204$	384.634	+	247.189i	0.132009	+	0.0848368i
$205$	−2694.70	−	3109.85i	−0.918079	−	1.05952i
$206$	−549.684			−0.185914
$207$	−246.471	+	484.915i	−0.0827582	+	0.162821i
$208$	1105.82			0.368628
$209$	2891.38	+	3336.83i	0.956941	+	1.10437i
$210$	−3682.50	−	2366.60i	−1.21008	−	0.777670i
$211$	−554.581	+	3857.19i	−0.180943	+	1.25848i	0.673597	+	0.739099i	$0.264748\pi$
$211$	−554.581	+	3857.19i	−0.180943	+	1.25848i	−0.854540	+	0.519386i	$0.826161\pi$
$212$	60.0793	−	131.555i	0.0194635	−	0.0426191i
$213$	−142.858	−	993.602i	−0.0459554	−	0.319627i
$214$	−3928.01	−	1153.37i	−1.25474	−	0.368423i
$215$	−3585.79	+	2304.45i	−1.13744	+	0.730986i
$216$	414.434	+	907.484i	0.130549	+	0.285863i
$217$	1518.25	−	445.798i	0.474956	−	0.139460i
$218$	780.465	−	900.705i	0.242476	−	0.279832i
$219$	2331.45	−	2690.64i	0.719382	−	0.830212i
$220$	4112.18	−	1207.44i	1.26020	−	0.370027i
$221$	−580.761	−	1271.69i	−0.176770	−	0.387073i
$222$	1073.07	−	689.620i	0.324413	−	0.208488i
$223$	2804.94	+	823.606i	0.842300	+	0.247322i	0.674293	−	0.738464i	$-0.264449\pi$
$223$	2804.94	+	823.606i	0.842300	+	0.247322i	0.168007	+	0.985786i	$0.446267\pi$
$224$	108.756	+	756.414i	0.0324400	+	0.225625i
$225$	282.819	−	619.287i	0.0837983	−	0.183493i
$226$	448.142	−	3116.90i	0.131902	−	0.917402i
$227$	−1752.10	−	1126.01i	−0.512296	−	0.329233i	0.258822	−	0.965925i	$-0.416666\pi$
$227$	−1752.10	−	1126.01i	−0.512296	−	0.329233i	−0.771118	+	0.636692i	$0.780302\pi$
$228$	−989.298	−	1141.71i	−0.287359	−	0.331630i
$229$	−1114.78			−0.321688			−0.160844	−	0.986980i	$-0.551422\pi$
$229$	−1114.78			−0.321688			−0.160844	+	0.986980i	$0.551422\pi$
$230$	2926.47	+	2058.67i	0.838982	+	0.590194i
$231$	8914.75			2.53917
$232$	−789.111	−	910.683i	−0.223309	−	0.257712i
$233$	2490.43	+	1600.50i	0.700229	+	0.450010i	0.841709	−	0.539931i	$-0.181550\pi$
$233$	2490.43	+	1600.50i	0.700229	+	0.450010i	−0.141480	+	0.989941i	$0.545186\pi$
$234$	−97.0102	+	674.721i	−0.0271015	+	0.188495i
$235$	1957.87	−	4287.14i	0.543478	−	1.19005i
$236$	65.8153	+	457.755i	0.0181534	+	0.126260i
$237$	−3598.06	−	1056.48i	−0.986156	−	0.289561i
$238$	812.758	−	522.328i	0.221358	−	0.142258i
$239$	−2366.37	−	5181.63i	−0.640451	−	1.40239i	−0.899669	−	0.436572i	$-0.856192\pi$
$239$	−2366.37	−	5181.63i	−0.640451	−	1.40239i	0.259219	−	0.965819i	$-0.416535\pi$
$240$	−1407.00	+	413.133i	−0.378423	+	0.111115i
$241$	1053.75	−	1216.10i	0.281652	−	0.325044i	−0.597241	−	0.802061i	$-0.703737\pi$
$241$	1053.75	−	1216.10i	0.281652	−	0.325044i	0.878894	+	0.477017i	$0.158282\pi$
$242$	−3972.50	+	4584.51i	−1.05522	+	1.21778i
$243$	−1311.98	+	385.233i	−0.346353	+	0.101698i
$244$	456.233	+	999.012i	0.119702	+	0.262111i
$245$	−3101.39	+	1993.14i	−0.808737	+	0.519744i
$246$	−2751.18	−	807.820i	−0.713044	−	0.209369i
$247$	657.389	+	4572.24i	0.169347	+	1.17783i
$248$	220.201	−	482.174i	0.0563823	−	0.123460i
$249$	−64.6612	+	449.728i	−0.0164568	+	0.114459i
$250$	−356.257	−	228.953i	−0.0901268	−	0.0579210i
$251$	1046.39	+	1207.60i	0.263138	+	0.303678i	0.871908	−	0.489669i	$-0.162882\pi$
$251$	1046.39	+	1207.60i	0.263138	+	0.303678i	−0.608770	+	0.793346i	$0.708337\pi$
$252$	−471.071			−0.117757
$253$	−7280.45	−	304.855i	−1.80916	−	0.0757552i
$254$	−552.541			−0.136494
$255$	1214.04	+	1401.08i	0.298142	+	0.344074i
$256$	215.361	+	138.404i	0.0525783	+	0.0337901i
$257$	839.674	−	5840.06i	0.203803	−	1.41748i	−0.589063	−	0.808087i	$-0.700503\pi$
$257$	839.674	−	5840.06i	0.203803	−	1.41748i	0.792867	−	0.609395i	$-0.208588\pi$
$258$	−1233.83	+	2701.72i	−0.297733	+	0.651944i
$259$	−383.588	−	2667.91i	−0.0920270	−	0.640062i
$260$	4302.18	+	1263.23i	1.02619	+	0.301317i
$261$	624.885	−	401.589i	0.148197	−	0.0952404i
$262$	−372.657	−	816.006i	−0.0878735	−	0.192416i
$263$	1735.28	−	509.525i	0.406852	−	0.119462i	−0.0719019	−	0.997412i	$-0.522907\pi$
$263$	1735.28	−	509.525i	0.406852	−	0.119462i	0.478754	+	0.877949i	$0.341089\pi$
$264$	1955.67	−	2256.96i	0.455920	−	0.526160i
$265$	384.021	−	443.184i	0.0890197	−	0.102734i
$266$	−3062.91	+	899.350i	−0.706010	+	0.207303i
$267$	1965.29	+	4303.39i	0.450465	+	0.986380i
$268$	−2450.41	+	1574.79i	−0.558518	+	0.358938i
$269$	−3193.48	−	937.691i	−0.723830	−	0.212536i	−0.100993	−	0.994887i	$-0.532202\pi$
$269$	−3193.48	−	937.691i	−0.723830	−	0.212536i	−0.622837	+	0.782352i	$0.714020\pi$
$270$	575.688	+	4004.00i	0.129760	+	0.902501i
$271$	−1406.83	+	3080.53i	−0.315346	+	0.690512i	−0.999236	−	0.0390728i	$-0.987560\pi$
$271$	−1406.83	+	3080.53i	−0.315346	+	0.690512i	0.683890	+	0.729585i	$0.260287\pi$
$272$	46.0598	−	320.353i	0.0102676	−	0.0714126i
$273$	7846.08	+	5042.37i	1.73944	+	1.11787i
$274$	3707.29	+	4278.44i	0.817392	+	0.943321i
$275$	9120.10			1.99986
$276$	2491.04	+	104.308i	0.543272	+	0.0227485i
$277$	−7196.61			−1.56102			−0.780510	−	0.625143i	$-0.785041\pi$
$277$	−7196.61			−1.56102			−0.780510	+	0.625143i	$0.785041\pi$
$278$	410.736	+	474.014i	0.0886125	+	0.102264i
$279$	274.883	+	176.657i	0.0589851	+	0.0379074i
$280$	−440.978	+	3067.07i	−0.0941195	+	0.654615i
$281$	440.197	−	963.897i	0.0934518	−	0.204631i	−0.857134	−	0.515094i	$-0.827757\pi$
$281$	440.197	−	963.897i	0.0934518	−	0.204631i	0.950585	+	0.310463i	$0.100484\pi$
$282$	−467.377	−	3250.68i	−0.0986948	−	0.686437i
$283$	4619.08	+	1356.29i	0.970233	+	0.284886i	0.728187	−	0.685379i	$-0.240363\pi$
$283$	4619.08	+	1356.29i	0.970233	+	0.284886i	0.242046	+	0.970265i	$0.422181\pi$
$284$	−597.769	+	384.163i	−0.124898	+	0.0802671i
$285$	−2544.62	−	5571.95i	−0.528879	−	1.15808i
$286$	−8761.57	+	2572.63i	−1.81148	+	0.531898i
$287$	−3967.71	+	4578.98i	−0.816051	+	0.941773i
$288$	−103.341	+	119.262i	−0.0211438	+	0.0244013i
$289$	4321.39	−	1268.88i	0.879584	−	0.258269i
$290$	−2029.71	−	4444.45i	−0.410996	−	0.899956i
$291$	6099.41	−	3919.86i	1.22871	−	0.789643i
$292$	−2418.07	−	710.011i	−0.484613	−	0.142295i
$293$	843.719	+	5868.19i	0.168227	+	1.17005i	0.882546	+	0.470226i	$0.155827\pi$
$293$	843.719	+	5868.19i	0.168227	+	1.17005i	−0.714319	+	0.699820i	$0.753263\pi$
$294$	−1067.15	+	2336.74i	−0.211693	+	0.463543i
$295$	−266.864	+	1856.08i	−0.0526692	+	0.366323i
$296$	−759.589	−	488.158i	−0.149156	−	0.0958568i
$297$	−5394.85	−	6225.98i	−1.05401	−	1.21639i
$298$	2300.38			0.447173
$299$	−6235.26	−	4386.29i	−1.20600	−	0.848379i
$300$	−3120.48			−0.600538
$301$	4109.95	+	4743.14i	0.787022	+	0.908272i
$302$	1864.98	+	1198.55i	0.355355	+	0.228373i
$303$	614.878	−	4276.57i	0.116580	−	0.810834i
$304$	−444.233	+	972.735i	−0.0838109	+	0.183520i
$305$	633.751	+	4407.83i	0.118979	+	0.827514i
$306$	191.424	+	56.2073i	0.0357614	+	0.0105005i
$307$	−5028.10	+	3231.36i	−0.934752	+	0.600728i	−0.916902	−	0.399112i	$-0.869318\pi$
$307$	−5028.10	+	3231.36i	−0.934752	+	0.600728i	−0.0178497	+	0.999841i	$0.505682\pi$
$308$	−2621.45	−	5740.18i	−0.484971	−	1.06194i
$309$	−1490.16	+	437.551i	−0.274344	+	0.0805548i
$310$	1407.51	−	1624.35i	0.257874	−	0.297603i
$311$	−3763.66	+	4343.49i	−0.686230	+	0.791951i	−0.986823	−	0.161801i	$-0.948270\pi$
$311$	−3763.66	+	4343.49i	−0.686230	+	0.791951i	0.300594	+	0.953752i	$0.402815\pi$
$312$	2997.81	−	880.237i	0.543967	−	0.159723i
$313$	−1088.16	−	2382.74i	−0.196507	−	0.430290i	0.785570	−	0.618773i	$-0.212370\pi$
$313$	−1088.16	−	2382.74i	−0.196507	−	0.430290i	−0.982076	+	0.188484i	$0.939643\pi$
$314$	5596.38	−	3596.58i	1.00580	−	0.646391i
$315$	−1832.70	−	538.130i	−0.327813	−	0.0962546i
$316$	377.770	+	2627.45i	0.0672507	+	0.467739i
$317$	3586.38	−	7853.08i	0.635430	−	1.39140i	−0.268318	−	0.963331i	$-0.586468\pi$
$317$	3586.38	−	7853.08i	0.635430	−	1.39140i	0.903747	−	0.428066i	$-0.140805\pi$
$318$	58.1530	−	404.463i	0.0102549	−	0.0713244i
$319$	8370.91	+	5379.66i	1.46922	+	0.944210i
$320$	679.755	+	784.479i	0.118748	+	0.137043i
$321$	−11566.7			−2.01119
$322$	2387.13	−	4696.50i	0.413135	−	0.812813i
$323$	1351.95			0.232893
$324$	2194.65	+	2532.76i	0.376311	+	0.434286i
$325$	8026.81	+	5158.52i	1.36999	+	0.880441i
$326$	−111.779	+	777.437i	−0.0189903	+	0.132081i
$327$	1398.83	−	3063.02i	0.236562	−	0.517998i
$328$	288.854	+	2009.02i	0.0486259	+	0.338201i
$329$	−6658.45	−	1955.10i	−1.11578	−	0.327623i
$330$	10186.8	−	6546.64i	1.69928	−	1.09206i
$331$	3247.47	+	7110.98i	0.539267	+	1.18083i	0.961617	+	0.274397i	$0.0884781\pi$
$331$	3247.47	+	7110.98i	0.539267	+	1.18083i	−0.422350	+	0.906433i	$0.638795\pi$
$332$	308.593	−	90.6111i	0.0510128	−	0.0149787i
$333$	364.489	−	420.643i	0.0599816	−	0.0692225i
$334$	4024.37	−	4644.37i	0.659292	−	0.760864i
$335$	−11332.3	+	3327.46i	−1.84821	+	0.542682i
$336$	896.942	+	1964.03i	0.145632	+	0.318889i
$337$	6986.59	−	4490.01i	1.12933	−	0.725775i	0.163909	−	0.986475i	$-0.447590\pi$
$337$	6986.59	−	4490.01i	1.12933	−	0.725775i	0.965420	+	0.260700i	$0.0839534\pi$
$338$	−4950.39	−	1453.57i	−0.796644	−	0.233916i
$339$	−1266.18	−	8806.46i	−0.202859	−	1.41092i
$340$	545.151	−	1193.72i	0.0869559	−	0.190407i
$341$	−622.938	+	4332.63i	−0.0989267	+	0.688050i
$342$	−554.548	−	356.387i	−0.0876800	−	0.0563485i
$343$	−1809.35	−	2088.10i	−0.284827	−	0.328708i
$344$	2102.45			0.329524
$345$	9572.23	+	3251.46i	1.49377	+	0.507399i
$346$	−3952.55			−0.614135
$347$	−2332.09	−	2691.37i	−0.360786	−	0.416370i	0.546117	−	0.837709i	$-0.316106\pi$
$347$	−2332.09	−	2691.37i	−0.360786	−	0.416370i	−0.906903	+	0.421339i	$0.861560\pi$
$348$	−2864.15	−	1840.68i	−0.441191	−	0.283536i
$349$	1651.92	−	11489.3i	0.253367	−	1.76221i	−0.324321	−	0.945947i	$-0.605136\pi$
$349$	1651.92	−	11489.3i	0.253367	−	1.76221i	0.577687	−	0.816258i	$-0.303955\pi$
$350$	−2739.16	+	5997.93i	−0.418327	+	0.916008i
$351$	−1226.58	−	8531.07i	−0.186525	−	1.29731i
$352$	−2028.33	−	595.571i	−0.307132	−	0.0901820i
$353$	−7189.68	+	4620.52i	−1.08404	+	0.696673i	−0.955488	−	0.295029i	$-0.904671\pi$
$353$	−7189.68	+	4620.52i	−1.08404	+	0.696673i	−0.128557	+	0.991702i	$0.541034\pi$
$354$	542.798	+	1188.56i	0.0814954	+	0.178450i
$355$	−2764.47	+	811.721i	−0.413303	+	0.121357i
$356$	2193.03	−	2530.89i	0.326490	−	0.376790i
$357$	1787.57	−	2062.96i	0.265009	−	0.305837i
$358$	−6112.57	+	1794.81i	−0.902400	+	0.264968i
$359$	589.862	+	1291.62i	0.0867179	+	0.189886i	0.948023	−	0.318203i	$-0.103079\pi$
$359$	589.862	+	1291.62i	0.0867179	+	0.189886i	−0.861305	+	0.508089i	$0.830352\pi$
$360$	−538.287	+	345.936i	−0.0788062	+	0.0506457i
$361$	2295.09	+	673.899i	0.334610	+	0.0982504i
$362$	572.976	+	3985.13i	0.0831904	+	0.578602i
$363$	−7119.94	+	15590.5i	−1.02948	+	2.25424i
$364$	939.565	−	6534.82i	0.135293	−	0.940982i
$365$	−8596.43	−	5524.59i	−1.23276	−	0.792247i
$366$	2032.04	+	2345.10i	0.290209	+	0.334920i
$367$	10523.8			1.49683			0.748417	−	0.663229i	$-0.230814\pi$
$367$	10523.8			1.49683			0.748417	+	0.663229i	$0.230814\pi$
$368$	−665.347	−	1634.65i	−0.0942489	−	0.231554i
$369$	−1251.16			−0.176511
$370$	−2397.53	−	2766.90i	−0.336869	−	0.388768i
$371$	−726.378	−	466.815i	−0.101649	−	0.0653256i
$372$	213.141	−	1482.43i	0.0297066	−	0.206614i
$373$	−831.484	+	1820.70i	−0.115422	+	0.252740i	−0.958523	−	0.285017i	$-0.908001\pi$
$373$	−831.484	+	1820.70i	−0.115422	+	0.252740i	0.843100	+	0.537757i	$0.180728\pi$
$374$	380.346	+	2645.36i	0.0525861	+	0.365745i
$375$	−1148.04	−	337.096i	−0.158092	−	0.0464201i
$376$	−1955.67	+	1256.83i	−0.268234	+	0.172383i
$377$	4324.59	+	9469.53i	0.590790	+	1.29365i
$378$	5714.89	−	1678.04i	0.777625	−	0.228331i
$379$	282.702	−	326.255i	0.0383151	−	0.0442180i	−0.736269	−	0.676689i	$-0.763414\pi$
$379$	282.702	−	326.255i	0.0383151	−	0.0442180i	0.774584	+	0.632471i	$0.217959\pi$
$380$	−2839.50	+	3276.95i	−0.383324	+	0.442379i
$381$	−1497.91	+	439.826i	−0.201418	+	0.0591416i
$382$	1438.55	+	3149.99i	0.192677	+	0.421904i
$383$	5796.74	−	3725.34i	0.773368	−	0.497013i	−0.0934589	−	0.995623i	$-0.529792\pi$
$383$	5796.74	−	3725.34i	0.773368	−	0.497013i	0.866826	+	0.498610i	$0.166156\pi$
$384$	694.002	+	203.778i	0.0922283	+	0.0270807i
$385$	−3641.44	−	25326.8i	−0.482039	−	3.35266i
$386$	2208.15	−	4835.17i	0.291170	−	0.637574i
$387$	−184.442	+	1282.82i	−0.0242266	+	0.168500i
$388$	−4317.57	−	2774.73i	−0.564926	−	0.363056i
$389$	−895.168	−	1033.08i	−0.116676	−	0.134651i	0.694407	−	0.719582i	$-0.255667\pi$
$389$	−895.168	−	1033.08i	−0.116676	−	0.134651i	−0.811083	+	0.584932i	$0.801121\pi$
$390$	12668.5			1.64486
$391$	−1530.41	+	1623.64i	−0.197944	+	0.210003i
$392$	1818.43			0.234297
$393$	−1659.80	−	1915.51i	−0.213043	−	0.245865i
$394$	−6027.88	−	3873.88i	−0.770762	−	0.495338i
$395$	−1531.76	+	10653.6i	−0.195117	+	1.35707i
$396$	541.331	−	1185.35i	0.0686942	−	0.150419i
$397$	783.232	+	5447.50i	0.0990159	+	0.688671i	0.977506	+	0.210909i	$0.0676425\pi$
$397$	783.232	+	5447.50i	0.0990159	+	0.688671i	−0.878490	+	0.477761i	$0.841448\pi$
$398$	6158.67	+	1808.35i	0.775643	+	0.227749i
$399$	−7587.49	+	4876.18i	−0.952004	+	0.611816i
$400$	917.603	+	2009.27i	0.114700	+	0.251159i
$401$	−624.769	+	183.449i	−0.0778041	+	0.0228454i	−0.320403	−	0.947281i	$-0.603818\pi$
$401$	−624.769	+	183.449i	−0.0778041	+	0.0228454i	0.242599	+	0.970127i	$0.422000\pi$
$402$	−5389.40	+	6219.70i	−0.668654	+	0.771668i
$403$	−2998.89	+	3460.90i	−0.370683	+	0.427791i
$404$	−2934.48	+	861.642i	−0.361376	+	0.106110i
$405$	5644.97	+	12360.8i	0.692594	+	1.51657i
$406$	−6052.14	+	3889.48i	−0.739810	+	0.475447i
$407$	7154.02	+	2100.61i	0.871282	+	0.255831i
$408$	−130.137	−	905.123i	−0.0157910	−	0.109829i
$409$	−3115.39	+	6821.76i	−0.376641	+	0.824729i	0.622473	+	0.782642i	$0.286128\pi$
$409$	−3115.39	+	6821.76i	−0.376641	+	0.824729i	−0.999114	+	0.0420878i	$0.986599\pi$
$410$	−1171.23	+	8146.08i	−0.141080	+	0.981234i
$411$	13455.9	+	8647.60i	1.61492	+	1.03785i
$412$	719.932	+	830.846i	0.0860886	+	0.0993516i
$413$	2761.02			0.328961
$414$	1055.76	−	262.562i	0.125332	−	0.0311696i
$415$	1304.09			0.154254
$416$	−1448.31	−	1671.44i	−0.170696	−	0.196993i
$417$	1490.80	+	958.080i	0.175072	+	0.112512i
$418$	1256.71	−	8740.62i	0.147052	−	1.02277i
$419$	−1395.69	+	3056.13i	−0.162730	+	0.356329i	−0.973378	−	0.229204i	$-0.926388\pi$
$419$	−1395.69	+	3056.13i	−0.162730	+	0.356329i	0.810648	+	0.585533i	$0.199115\pi$
$420$	1245.94	+	8665.68i	0.144751	+	1.00677i
$421$	8734.61	+	2564.71i	1.01116	+	0.296904i	0.745029	−	0.667032i	$-0.232436\pi$
$421$	8734.61	+	2564.71i	1.01116	+	0.296904i	0.266133	+	0.963936i	$0.414254\pi$
$422$	6556.49	−	4213.60i	0.756315	−	0.486054i
$423$	−595.298	−	1303.52i	−0.0684264	−	0.149833i
$424$	−277.533	+	81.4910i	−0.0317882	+	0.00933385i
$425$	1828.75	−	2110.48i	0.208723	−	0.240879i
$426$	−1314.72	+	1517.27i	−0.149527	+	0.172564i
$427$	6291.29	−	1847.29i	0.713014	−	0.209360i
$428$	3401.29	+	7447.78i	0.384129	+	0.841126i
$429$	−21704.3	+	13948.5i	−2.44265	+	1.56979i
$430$	8179.56	+	2401.74i	0.917333	+	0.269353i
$431$	−1613.73	−	11223.7i	−0.180349	−	1.25436i	−0.855939	−	0.517078i	$-0.827020\pi$
$431$	−1613.73	−	11223.7i	−0.180349	−	1.25436i	0.675589	−	0.737278i	$-0.263889\pi$
$432$	828.868	−	1814.97i	0.0923123	−	0.202136i
$433$	851.285	−	5920.81i	0.0944807	−	0.657127i	−0.886458	−	0.462809i	$-0.846841\pi$
$433$	851.285	−	5920.81i	0.0944807	−	0.657127i	0.980939	−	0.194318i	$-0.0622494\pi$
$434$	−2662.30	−	1710.96i	−0.294458	−	0.189237i
$435$	−9040.26	−	10433.0i	−0.996430	−	1.14994i
$436$	−2383.61			−0.261821
$437$	6363.26	−	3722.79i	0.696558	−	0.407517i
$438$	−7120.44			−0.776776
$439$	−1940.36	−	2239.29i	−0.210953	−	0.243452i	0.640406	−	0.768037i	$-0.278766\pi$
$439$	−1940.36	−	2239.29i	−0.210953	−	0.243452i	−0.851359	+	0.524584i	$0.824221\pi$
$440$	−7210.86	−	4634.14i	−0.781283	−	0.502100i
$441$	−159.525	+	1109.52i	−0.0172255	+	0.119806i
$442$	−1161.52	+	2543.38i	−0.124995	+	0.273702i
$443$	1435.53	+	9984.30i	0.153959	+	1.07081i	0.909499	+	0.415706i	$0.136466\pi$
$443$	1435.53	+	9984.30i	0.153959	+	1.07081i	−0.755540	+	0.655103i	$0.772625\pi$
$444$	−2447.78	−	718.734i	−0.261636	−	0.0768234i
$445$	11423.2	−	7341.22i	1.21688	−	0.782039i
$446$	−2428.82	−	5318.37i	−0.257865	−	0.564645i
$447$	6236.21	−	1831.12i	0.659872	−	0.193756i
$448$	1000.88	−	1155.08i	0.105552	−	0.121813i
$449$	−2208.83	+	2549.13i	−0.232163	+	0.267930i	−0.859863	−	0.510525i	$-0.829451\pi$
$449$	−2208.83	+	2549.13i	−0.232163	+	0.267930i	0.627700	+	0.778455i	$0.283996\pi$
$450$	−1306.47	+	383.613i	−0.136861	+	0.0401860i
$451$	−6962.53	−	15245.8i	−0.726946	−	1.59179i
$452$	−5298.13	+	3404.90i	−0.551334	+	0.354321i
$453$	6009.90	+	1764.67i	0.623333	+	0.183027i
$454$	592.807	+	4123.06i	0.0612815	+	0.426222i
$455$	11120.4	−	24350.4i	1.14579	−	2.50893i
$456$	−429.990	+	2990.65i	−0.0441582	+	0.307127i
$457$	−2574.99	−	1654.85i	−0.263573	−	0.169388i	0.402179	−	0.915561i	$-0.368253\pi$
$457$	−2574.99	−	1654.85i	−0.263573	−	0.169388i	−0.665752	+	0.746173i	$0.731889\pi$
$458$	1460.05	+	1684.98i	0.148959	+	0.171908i
$459$	−2522.52			−0.256517
$460$	−721.187	−	7119.65i	−0.0730990	−	0.721642i
$461$	−6696.11			−0.676505			−0.338253	−	0.941055i	$-0.609836\pi$
$461$	−6696.11			−0.676505			−0.338253	+	0.941055i	$0.609836\pi$
$462$	−11675.8	−	13474.6i	−1.17578	−	1.35692i
$463$	−10479.0	−	6734.42i	−1.05183	−	0.675972i	−0.103948	−	0.994583i	$-0.533147\pi$
$463$	−10479.0	−	6734.42i	−1.05183	−	0.675972i	−0.947886	+	0.318611i	$0.896784\pi$
$464$	−342.980	+	2385.48i	−0.0343157	+	0.238671i
$465$	2522.68	−	5523.91i	0.251584	−	0.550893i
$466$	−842.611	−	5860.49i	−0.0837622	−	0.582579i
$467$	5979.62	+	1755.77i	0.592513	+	0.173978i	0.564223	−	0.825622i	$-0.309176\pi$
$467$	5979.62	+	1755.77i	0.592513	+	0.173978i	0.0282898	+	0.999600i	$0.490994\pi$
$468$	1146.90	−	737.066i	0.113281	−	0.0728010i
$469$	7224.17	+	15818.7i	0.711260	+	1.55744i
$470$	−9044.27	+	2655.64i	−0.887619	+	0.260629i
$471$	12308.6	−	14204.9i	1.20414	−	1.38965i
$472$	605.697	−	699.012i	0.0590667	−	0.0681666i
$473$	−16658.0	+	4891.23i	−1.61932	+	0.475474i
$474$	3115.58	+	6822.16i	0.301905	+	0.661081i
$475$	−7762.27	+	4988.50i	−0.749805	+	0.481870i
$476$	−1853.99	−	544.379i	−0.178524	−	0.0524193i
$477$	−25.3750	−	176.487i	−0.00243573	−	0.0169409i
$478$	−4732.74	+	10363.3i	−0.452867	+	0.991640i
$479$	−491.114	+	3415.77i	−0.0468467	+	0.325826i	0.952899	+	0.303287i	$0.0980841\pi$
$479$	−491.114	+	3415.77i	−0.0468467	+	0.325826i	−0.999746	+	0.0225389i	$0.992825\pi$
$480$	2467.23	+	1585.59i	0.234611	+	0.150775i
$481$	5108.27	+	5895.26i	0.484235	+	0.558837i
$482$	−3218.25			−0.304123
$483$	2732.93	−	14632.1i	0.257459	−	1.37844i
$484$	12132.4			1.13940
$485$	−13627.8	−	15727.3i	−1.27589	−	1.47245i
$486$	2300.61	+	1478.51i	0.214728	+	0.137997i
$487$	−289.551	+	2013.87i	−0.0269421	+	0.187386i	−0.998848	−	0.0479826i	$-0.984721\pi$
$487$	−289.551	+	2013.87i	−0.0269421	+	0.187386i	0.971906	+	0.235369i	$0.0756299\pi$
$488$	912.467	−	1998.02i	0.0846423	−	0.185341i
$489$	315.819	+	2196.57i	0.0292062	+	0.203133i
$490$	7074.59	+	2077.29i	0.652240	+	0.191515i
$491$	1523.63	−	979.179i	0.140042	−	0.0899994i	−0.468744	−	0.883334i	$-0.655293\pi$
$491$	1523.63	−	979.179i	0.140042	−	0.0899994i	0.608786	+	0.793335i	$0.291657\pi$
$492$	2382.26	+	5216.43i	0.218294	+	0.477997i
$493$	2923.43	−	858.396i	0.267068	−	0.0784183i
$494$	6049.94	−	6982.01i	0.551012	−	0.635901i
$495$	3460.13	−	3993.21i	0.314185	−	0.362589i
$496$	−1017.21	+	298.679i	−0.0920846	+	0.0270385i
$497$	1762.31	+	3858.91i	0.159055	+	0.348282i
$498$	764.452	−	491.284i	0.0687870	−	0.0442067i
$499$	6504.21	+	1909.81i	0.583504	+	0.171332i	0.560145	−	0.828395i	$-0.310746\pi$
$499$	6504.21	+	1909.81i	0.583504	+	0.171332i	0.0233595	+	0.999727i	$0.492564\pi$
$500$	120.536	+	838.347i	0.0107811	+	0.0749840i
$501$	7212.90	−	15794.1i	0.643211	−	1.40844i
$502$	454.805	−	3163.24i	0.0404362	−	0.281240i
$503$	6042.05	+	3882.99i	0.535590	+	0.344203i	0.780312	−	0.625391i	$-0.215060\pi$
$503$	6042.05	+	3882.99i	0.535590	+	0.344203i	−0.244722	+	0.969593i	$0.578697\pi$
$504$	616.972	+	712.024i	0.0545280	+	0.0629287i
$505$	−12400.9			−1.09274
$506$	9074.57	+	11403.7i	0.797261	+	1.00189i
$507$	−14577.3			−1.27692
$508$	723.674	+	835.165i	0.0632044	+	0.0729418i
$509$	14031.1	+	9017.22i	1.22184	+	0.785229i	0.982600	−	0.185732i	$-0.0594656\pi$
$509$	14031.1	+	9017.22i	1.22184	+	0.785229i	0.239239	+	0.970961i	$0.423102\pi$
$510$	527.672	−	3670.04i	0.0458152	−	0.318651i
$511$	−6250.33	+	13686.3i	−0.541093	+	1.18483i
$512$	−72.8652	−	506.789i	−0.00628949	−	0.0437443i
$513$	7997.12	+	2348.17i	0.688268	+	0.202094i
$514$	−9926.98	+	6379.69i	−0.851869	+	0.547463i
$515$	1851.78	+	4054.82i	0.158445	+	0.346945i
$516$	5699.62	−	1673.56i	0.486263	−	0.142780i
$517$	12571.1	−	14507.8i	1.06940	−	1.23415i
$518$	−3530.15	+	4074.01i	−0.299433	+	0.345564i
$519$	−10715.2	+	3146.26i	−0.906250	+	0.266099i
$520$	−3725.28	−	8157.23i	−0.314162	−	0.687920i
$521$	3417.16	−	2196.07i	0.287348	−	0.184667i	−0.389024	−	0.921228i	$-0.627188\pi$
$521$	3417.16	−	2196.07i	0.287348	−	0.184667i	0.676372	+	0.736560i	$0.263551\pi$
$522$	−1425.43	−	418.543i	−0.119520	−	0.0350941i
$523$	−496.730	−	3454.83i	−0.0415305	−	0.288851i	−0.999993	−	0.00363385i	$-0.998843\pi$
$523$	−496.730	−	3454.83i	−0.0415305	−	0.288851i	0.958463	−	0.285217i	$-0.0920658\pi$
$524$	−745.315	+	1632.01i	−0.0621359	+	0.136059i
$525$	−2651.34	+	18440.5i	−0.220407	+	1.53297i
$526$	−3042.88	−	1955.54i	−0.252236	−	0.162102i
$527$	877.705	+	1012.93i	0.0725492	+	0.0837262i
$528$	−5972.77			−0.492295
$529$	−2732.29	+	11856.2i	−0.224565	+	0.974459i
$530$	−1172.83			−0.0961219
$531$	373.370	+	430.892i	0.0305139	+	0.0352149i
$532$	5370.92	+	3451.68i	0.437705	+	0.281296i
$533$	2495.47	−	17356.4i	0.202797	−	1.41048i
$534$	3930.59	−	8606.79i	0.318527	−	0.697476i
$535$	4724.70	+	32861.0i	0.381807	+	2.65553i
$536$	5589.65	+	1641.27i	0.450440	+	0.132261i
$537$	−15142.2	+	9731.28i	−1.21682	+	0.782003i
$538$	2765.25	+	6055.06i	0.221596	+	0.485227i
$539$	−14407.7	+	4230.48i	−1.15136	+	0.338070i
$540$	5298.04	−	6114.27i	0.422207	−	0.487252i
$541$	5538.21	−	6391.43i	0.440122	−	0.507928i	−0.491739	−	0.870743i	$-0.663639\pi$
$541$	5538.21	−	6391.43i	0.440122	−	0.507928i	0.931861	+	0.362814i	$0.118184\pi$
$542$	6498.77	−	1908.21i	0.515030	−	0.151226i
$543$	4725.50	+	10347.4i	0.373463	+	0.817770i
$544$	−544.538	+	349.954i	−0.0429171	+	0.0275811i
$545$	−9273.42	−	2722.92i	−0.728862	−	0.214013i
$546$	−2654.64	−	18463.4i	−0.208074	−	1.44718i
$547$	−3496.75	+	7656.82i	−0.273328	+	0.598505i	−0.995662	−	0.0930391i	$-0.970342\pi$
$547$	−3496.75	+	7656.82i	−0.273328	+	0.598505i	0.722334	+	0.691544i	$0.243069\pi$
$548$	1611.34	−	11207.1i	0.125608	−	0.873622i
$549$	1139.06	+	732.028i	0.0885497	+	0.0569074i
$550$	−11944.8	−	13785.0i	−0.926050	−	1.06872i
$551$	−10067.2			−0.778360
$552$	−3104.91	−	3901.82i	−0.239409	−	0.300856i
$553$	15847.8			1.21866
$554$	9425.56	+	10877.7i	0.722840	+	0.834202i
$555$	−8702.04	−	5592.46i	−0.665552	−	0.427724i
$556$	178.523	−	1241.65i	0.0136170	−	0.0947083i
$557$	−74.0739	+	162.199i	−0.00563485	+	0.0123386i	−0.912428	−	0.409236i	$-0.865795\pi$
$557$	−74.0739	+	162.199i	−0.00563485	+	0.0123386i	0.906794	+	0.421575i	$0.138522\pi$
$558$	−93.0041	−	646.857i	−0.00705587	−	0.0490747i
$559$	−17427.7	−	5117.23i	−1.31863	−	0.387184i
$560$	5213.43	−	3350.47i	0.393406	−	0.252827i
$561$	3136.82	+	6868.68i	0.236073	+	0.516927i
$562$	−2033.47	+	597.079i	−0.152627	+	0.0448154i
$563$	−2114.70	+	2440.49i	−0.158302	+	0.182690i	−0.829360	−	0.558715i	$-0.811295\pi$
$563$	−2114.70	+	2440.49i	−0.158302	+	0.182690i	0.671058	+	0.741405i	$0.265840\pi$
$564$	−4301.27	+	4963.93i	−0.321128	+	0.370601i
$565$	−24501.9	+	7194.42i	−1.82443	+	0.535702i
$566$	−3999.69	−	8758.10i	−0.297031	−	0.650407i
$567$	16832.0	−	10817.3i	1.24670	−	0.801204i
$568$	1363.57	+	400.381i	0.100729	+	0.0295768i
$569$	2248.38	+	15637.8i	0.165654	+	1.15215i	0.887740	+	0.460345i	$0.152274\pi$
$569$	2248.38	+	15637.8i	0.165654	+	1.15215i	−0.722086	+	0.691803i	$0.756817\pi$
$570$	−5089.25	+	11143.9i	−0.373974	+	0.818889i
$571$	−2340.67	+	16279.7i	−0.171548	+	1.19314i	0.704067	+	0.710133i	$0.251365\pi$
$571$	−2340.67	+	16279.7i	−0.171548	+	1.19314i	−0.875615	+	0.483009i	$0.839544\pi$
$572$	15363.7	+	9873.68i	1.12306	+	0.721747i
$573$	6407.24	+	7394.35i	0.467132	+	0.539099i
$574$	12117.7			0.881157
$575$	2795.88	−	14969.2i	0.202776	−	1.08567i
$576$	315.612			0.0228307
$577$	7153.32	+	8255.37i	0.516112	+	0.595625i	0.952653	−	0.304060i	$-0.0983422\pi$
$577$	7153.32	+	8255.37i	0.516112	+	0.595625i	−0.436541	+	0.899684i	$0.643797\pi$
$578$	−7577.73	−	4869.91i	−0.545315	−	0.350452i
$579$	2137.35	−	14865.6i	0.153411	−	1.06700i
$580$	−4059.43	+	8888.91i	−0.290618	+	0.636365i
$581$	−273.267	−	1900.61i	−0.0195130	−	0.135716i
$582$	−13913.4	−	4085.34i	−0.990943	−	0.290967i
$583$	2009.35	−	1291.33i	0.142743	−	0.0917351i
$584$	2093.82	+	4584.83i	0.148361	+	0.324866i
$585$	5303.99	−	1557.39i	0.374860	−	0.110069i
$586$	7764.73	−	8960.98i	0.547369	−	0.631697i
$587$	10131.2	−	11692.0i	0.712364	−	0.822112i	−0.278003	−	0.960580i	$-0.589673\pi$
$587$	10131.2	−	11692.0i	0.712364	−	0.822112i	0.990367	+	0.138469i	$0.0442180\pi$
$588$	4929.66	−	1447.48i	0.345741	−	0.101519i
$589$	−1839.67	−	4028.31i	−0.128696	−	0.281806i
$590$	3154.98	−	2027.58i	0.220150	−	0.141482i
$591$	−19424.9	−	5703.66i	−1.35200	−	0.396984i
$592$	256.999	+	1787.47i	0.0178422	+	0.124095i
$593$	−7408.51	+	16222.4i	−0.513037	+	1.12340i	0.458971	+	0.888451i	$0.348218\pi$
$593$	−7408.51	+	16222.4i	−0.513037	+	1.12340i	−0.972009	+	0.234944i	$0.924509\pi$
$594$	−2344.82	+	16308.6i	−0.161968	+	1.12652i
$595$	−6591.05	−	4235.81i	−0.454129	−	0.291851i
$596$	−3012.86	−	3477.02i	−0.207066	−	0.238967i
$597$	18135.3			1.24326
$598$	1536.59	+	15169.4i	0.105077	+	1.03733i
$599$	−1955.72			−0.133403			−0.0667017	−	0.997773i	$-0.521248\pi$
$599$	−1955.72			−0.133403			−0.0667017	+	0.997773i	$0.521248\pi$
$600$	4086.97	+	4716.61i	0.278083	+	0.320925i
$601$	−16310.9	−	10482.4i	−1.10705	−	0.711456i	−0.146400	−	0.989226i	$-0.546769\pi$
$601$	−16310.9	−	10482.4i	−1.10705	−	0.711456i	−0.960648	+	0.277769i	$0.910405\pi$
$602$	1786.36	−	12424.4i	0.120941	−	0.841162i
$603$	−1491.79	+	3266.57i	−0.100747	+	0.220605i
$604$	−630.996	−	4388.67i	−0.0425080	−	0.295650i
$605$	47200.9	+	13859.4i	3.17188	+	0.931349i
$606$	−7269.36	+	4671.73i	−0.487289	+	0.313162i
$607$	−9628.83	−	21084.2i	−0.643859	−	1.40985i	−0.896828	−	0.442380i	$-0.854134\pi$
$607$	−9628.83	−	21084.2i	−0.643859	−	1.40985i	0.252969	−	0.967474i	$-0.418593\pi$
$608$	2052.11	−	602.554i	0.136882	−	0.0401921i
$609$	−13311.0	+	15361.7i	−0.885696	+	1.02215i
$610$	5832.40	−	6730.95i	0.387126	−	0.446767i
$611$	19270.1	−	5658.21i	1.27592	−	0.374643i
$612$	−165.755	−	362.954i	−0.0109481	−	0.0239731i
$613$	−10661.4	+	6851.67i	−0.702463	+	0.451446i	−0.842497	−	0.538701i	$-0.818915\pi$
$613$	−10661.4	+	6851.67i	−0.702463	+	0.451446i	0.140034	+	0.990147i	$0.455279\pi$
$614$	11469.6	+	3367.78i	0.753870	+	0.221356i
$615$	3309.19	+	23015.9i	0.216974	+	1.50909i
$616$	−5242.90	+	11480.4i	−0.342926	+	0.750904i
$617$	3085.24	−	21458.3i	0.201308	−	1.40013i	−0.599101	−	0.800674i	$-0.704475\pi$
$617$	3085.24	−	21458.3i	0.201308	−	1.40013i	0.800409	−	0.599455i	$-0.204616\pi$
$618$	2613.06	+	1679.31i	0.170085	+	0.109307i
$619$	−10356.1	−	11951.6i	−0.672449	−	0.776047i	0.312308	−	0.949981i	$-0.398898\pi$
$619$	−10356.1	−	11951.6i	−0.672449	−	0.776047i	−0.984757	+	0.173933i	$0.944352\pi$
$620$	−4298.64			−0.278448
$621$	−11872.8	+	6946.13i	−0.767214	+	0.448854i
$622$	11494.5			0.740978
$623$	−13093.0	−	15110.1i	−0.841988	−	0.971706i
$624$	−5256.78	−	3378.33i	−0.337243	−	0.216733i
$625$	1967.17	−	13682.0i	0.125899	−	0.875646i
$626$	−2176.33	+	4765.49i	−0.138951	+	0.304261i
$627$	−3550.71	−	24695.7i	−0.226159	−	1.57297i
$628$	−12765.9	−	3748.42i	−0.811172	−	0.238182i
$629$	1920.61	−	1234.30i	0.121749	−	0.0782431i
$630$	1586.95	+	3474.93i	0.100358	+	0.219753i
$631$	−7552.05	+	2217.48i	−0.476454	+	0.139899i	−0.511138	−	0.859499i	$-0.670776\pi$
$631$	−7552.05	+	2217.48i	−0.476454	+	0.139899i	0.0346839	+	0.999398i	$0.488958\pi$
$632$	3476.61	−	4012.22i	0.218817	−	0.252528i
$633$	14420.2	−	16641.9i	0.905456	−	1.04495i
$634$	−16567.1	+	4864.53i	−1.03780	+	0.304724i
$635$	1861.40	+	4075.90i	0.116327	+	0.254720i
$636$	−687.510	+	441.836i	−0.0428640	+	0.0275470i
$637$	−15073.4	−	4425.95i	−0.937567	−	0.275294i
$638$	−2832.21	−	19698.5i	−0.175750	−	1.22237i
$639$	−363.917	+	796.867i	−0.0225295	+	0.0493327i
$640$	295.450	−	2054.90i	0.0182479	−	0.126917i
$641$	4680.06	+	3007.69i	0.288379	+	0.185330i	0.676830	−	0.736139i	$-0.263353\pi$
$641$	4680.06	+	3007.69i	0.288379	+	0.185330i	−0.388451	+	0.921470i	$0.626990\pi$
$642$	15149.2	+	17483.1i	0.931294	+	1.07477i
$643$	20606.6			1.26383			0.631915	−	0.775037i	$-0.282269\pi$
$643$	20606.6			1.26383			0.631915	+	0.775037i	$0.282269\pi$
$644$	−10225.2	+	2542.97i	−0.625669	+	0.155601i
$645$	24086.1			1.47037
$646$	−1770.68	−	2043.47i	−0.107843	−	0.124457i
$647$	14779.5	+	9498.20i	0.898055	+	0.577145i	0.906213	−	0.422822i	$-0.138960\pi$
$647$	14779.5	+	9498.20i	0.898055	+	0.577145i	−0.00815776	+	0.999967i	$0.502597\pi$
$648$	953.885	−	6634.42i	0.0578274	−	0.402198i
$649$	−3172.82	+	6947.51i	−0.191902	+	0.420206i
$650$	−2715.79	−	18888.7i	−0.163880	−	1.13981i
$651$	−8579.30	−	2519.11i	−0.516512	−	0.151662i
$652$	1321.49	−	849.273i	0.0793769	−	0.0510124i
$653$	−8853.22	−	19385.8i	−0.530556	−	1.16176i	−0.965286	−	0.261195i	$-0.915883\pi$
$653$	−8853.22	−	19385.8i	−0.530556	−	1.16176i	0.434730	−	0.900561i	$-0.356844\pi$
$654$	−6461.83	+	1897.37i	−0.386357	+	0.113445i
$655$	−4763.98	+	5497.93i	−0.284190	+	0.327972i
$656$	2658.32	−	3067.86i	0.158216	−	0.182591i
$657$	−2981.15	+	875.344i	−0.177025	+	0.0519793i
$658$	5765.59	+	12624.9i	0.341590	+	0.747977i
$659$	22896.5	−	14714.7i	1.35345	−	0.869808i	0.355552	−	0.934657i	$-0.384293\pi$
$659$	22896.5	−	14714.7i	1.35345	−	0.869808i	0.997895	+	0.0648489i	$0.0206565\pi$
$660$	−23237.1	−	6823.02i	−1.37046	−	0.402402i
$661$	−2397.09	−	16672.1i	−0.141053	−	0.981045i	−0.930256	−	0.366912i	$-0.880415\pi$
$661$	−2397.09	−	16672.1i	−0.141053	−	0.981045i	0.789203	−	0.614133i	$-0.210494\pi$
$662$	6494.95	−	14222.0i	0.381319	−	0.834972i
$663$	−1124.28	+	7819.54i	−0.0658573	+	0.458048i
$664$	−541.129	−	347.763i	−0.0316263	−	0.0203250i
$665$	16952.5	+	19564.2i	0.988557	+	1.14086i
$666$	−1113.18			−0.0647671
$667$	11396.1	−	12090.3i	0.661556	−	0.701858i
$668$	−12290.8			−0.711892
$669$	−10817.8	−	12484.5i	−0.625175	−	0.721490i
$670$	19871.6	+	12770.7i	1.14583	+	0.736381i
$671$	−2581.32	+	17953.5i	−0.148511	+	1.03292i
$672$	1793.88	−	3928.06i	0.102977	−	0.225488i
$673$	1054.14	+	7331.73i	0.0603778	+	0.419937i	0.997484	+	0.0708925i	$0.0225847\pi$
$673$	1054.14	+	7331.73i	0.0603778	+	0.419937i	−0.937106	+	0.349045i	$0.886506\pi$
$674$	−15937.1	−	4679.56i	−0.910794	−	0.267433i
$675$	14483.1	−	9307.75i	0.825862	−	0.530749i
$676$	4286.57	+	9386.27i	0.243888	+	0.534039i
$677$	−33609.1	+	9868.51i	−1.90798	+	0.560233i	−0.923857	+	0.382738i	$0.874981\pi$
$677$	−33609.1	+	9868.51i	−1.90798	+	0.560233i	−0.984122	+	0.177495i	$0.943201\pi$
$678$	−11652.6	+	13447.8i	−0.660053	+	0.761742i
$679$	−20065.7	+	23157.0i	−1.13409	+	1.30881i
$680$	−2518.30	+	739.438i	−0.142018	+	0.0417003i
$681$	4889.05	+	10705.5i	0.275108	+	0.602404i
$682$	7364.64	−	4732.97i	0.413500	−	0.265740i
$683$	23517.1	+	6905.23i	1.31750	+	0.386854i	0.863591	−	0.504192i	$-0.168210\pi$
$683$	23517.1	+	6905.23i	1.31750	+	0.386854i	0.453912	+	0.891046i	$0.350028\pi$
$684$	187.626	+	1304.97i	0.0104884	+	0.0729483i
$685$	19071.4	−	41760.6i	1.06377	−	2.32933i
$686$	−786.418	+	5469.66i	−0.0437691	+	0.304421i
$687$	5299.36	+	3405.69i	0.294299	+	0.189134i
$688$	−2753.62	−	3177.84i	−0.152588	−	0.176096i
$689$	2498.88			0.138171
$690$	−7622.38	−	18726.9i	−0.420549	−	1.03322i
$691$	−24549.2			−1.35151			−0.675755	−	0.737126i	$-0.736182\pi$
$691$	−24549.2			−1.35151			−0.675755	+	0.737126i	$0.736182\pi$
$692$	5176.74	+	5974.28i	0.284379	+	0.328191i
$693$	−6544.86	−	4206.13i	−0.358757	−	0.230559i
$694$	−1013.62	+	7049.89i	−0.0554417	+	0.385605i
$695$	2112.95	−	4626.71i	0.115322	−	0.252520i
$696$	969.055	+	6739.93i	0.0527758	+	0.367064i
$697$	−4924.15	−	1445.86i	−0.267598	−	0.0785738i
$698$	−19529.7	+	12550.9i	−1.05904	+	0.680602i
$699$	−6949.26	−	15216.7i	−0.376030	−	0.823391i
$700$	12653.4	−	3715.38i	0.683220	−	0.200611i
$701$	−5055.34	+	5834.17i	−0.272379	+	0.314342i	−0.875415	−	0.483372i	$-0.839412\pi$
$701$	−5055.34	+	5834.17i	−0.272379	+	0.314342i	0.603036	+	0.797714i	$0.293957\pi$
$702$	−11288.2	+	13027.3i	−0.606904	+	0.700405i
$703$	−7237.90	+	2125.24i	−0.388311	+	0.114018i
$704$	1756.34	+	3845.85i	0.0940264	+	0.205889i
$705$	−22404.6	+	14398.6i	−1.19689	+	0.769195i
$706$	16400.4	+	4815.59i	0.874273	+	0.256710i
$707$	2598.56	+	18073.4i	0.138230	+	0.961414i
$708$	1085.60	−	2377.12i	0.0576259	−	0.126183i
$709$	3294.43	−	22913.3i	0.174506	−	1.21372i	−0.694711	−	0.719289i	$-0.744468\pi$
$709$	3294.43	−	22913.3i	0.174506	−	1.21372i	0.869217	−	0.494430i	$-0.164623\pi$
$710$	4847.60	+	3115.36i	0.256235	+	0.164673i
$711$	2143.09	+	2473.25i	0.113041	+	0.130456i
$712$	−6697.71			−0.352538
$713$	6920.35	+	2350.68i	0.363491	+	0.123469i
$714$	−5459.39			−0.286152
$715$	48493.4	+	55964.4i	2.53643	+	2.92720i
$716$	10718.6	+	6888.43i	0.559460	+	0.359543i
$717$	−4580.99	+	31861.5i	−0.238606	+	1.65954i
$718$	1179.72	−	2583.23i	0.0613188	−	0.134269i
$719$	−2303.44	−	16020.8i	−0.119477	−	0.830980i	−0.958134	−	0.286320i	$-0.907568\pi$
$719$	−2303.44	−	16020.8i	−0.119477	−	0.830980i	0.838657	−	0.544660i	$-0.183341\pi$
$720$	1227.89	+	360.541i	0.0635565	+	0.0186619i
$721$	5521.57	−	3548.50i	0.285207	−	0.183291i
$722$	−1987.33	−	4351.65i	−0.102439	−	0.224310i
$723$	−8724.51	+	2561.75i	−0.448780	+	0.131774i
$724$	5273.09	−	6085.47i	0.270680	−	0.312382i
$725$	−13617.6	+	15715.6i	−0.697580	+	0.805050i
$726$	32890.2	−	9657.43i	1.68136	−	0.493692i
$727$	−5228.60	−	11449.0i	−0.266737	−	0.584074i	0.728110	−	0.685461i	$-0.240399\pi$
$727$	−5228.60	−	11449.0i	−0.266737	−	0.584074i	−0.994847	+	0.101387i	$0.967672\pi$
$728$	−11107.9	+	7138.64i	−0.565505	+	0.363428i
$729$	−14291.3	−	4196.32i	−0.726075	−	0.213195i
$730$	2908.52	+	20229.2i	0.147464	+	1.02564i
$731$	−2208.35	+	4835.62i	−0.111736	+	0.244667i
$732$	883.211	−	6142.87i	0.0445962	−	0.310173i
$733$	3689.07	+	2370.82i	0.185892	+	0.119466i	0.630277	−	0.776370i	$-0.282941\pi$
$733$	3689.07	+	2370.82i	0.185892	+	0.119466i	−0.444385	+	0.895836i	$0.646578\pi$
$734$	−13783.2	−	15906.7i	−0.693118	−	0.799901i
$735$	20832.4			1.04546
$736$	−1599.35	+	3146.60i	−0.0800988	+	0.157589i
$737$	−48106.0			−2.40435
$738$	1638.67	+	1891.12i	0.0817347	+	0.0943269i
$739$	11031.7	+	7089.66i	0.549132	+	0.352906i	0.785601	−	0.618733i	$-0.212354\pi$
$739$	11031.7	+	7089.66i	0.549132	+	0.352906i	−0.236469	+	0.971639i	$0.575990\pi$
$740$	−1042.07	+	7247.73i	−0.0517664	+	0.360043i
$741$	10843.4	−	23743.6i	0.537572	−	1.17712i
$742$	245.763	+	1709.32i	0.0121593	+	0.0845701i
$743$	−10057.2	−	2953.07i	−0.496587	−	0.145811i	0.0238426	−	0.999716i	$-0.492410\pi$
$743$	−10057.2	−	2953.07i	−0.496587	−	0.145811i	−0.520429	+	0.853905i	$0.674228\pi$
$744$	−2519.85	+	1619.41i	−0.124169	+	0.0797988i
$745$	−7749.53	−	16969.1i	−0.381102	−	0.834496i
$746$	3840.99	−	1127.82i	0.188510	−	0.0553516i
$747$	259.661	−	299.665i	0.0127182	−	0.0146776i
$748$	3500.32	−	4039.58i	0.171102	−	0.197462i
$749$	46902.5	−	13771.8i	2.28809	−	0.671844i
$750$	994.096	+	2176.77i	0.0483990	+	0.105979i
$751$	−1436.31	+	923.061i	−0.0697893	+	0.0448508i	−0.575070	−	0.818104i	$-0.695025\pi$
$751$	−1436.31	+	923.061i	−0.0697893	+	0.0448508i	0.505281	+	0.862955i	$0.331389\pi$
$752$	4461.08	+	1309.89i	0.216328	+	0.0635197i
$753$	−1285.00	−	8937.40i	−0.0621888	−	0.432533i
$754$	8649.18	−	18939.1i	0.417751	−	0.914748i
$755$	2558.53	−	17794.9i	0.123330	−	0.857781i
$756$	−10021.3	−	6440.28i	−0.482104	−	0.309829i
$757$	13990.4	+	16145.7i	0.671715	+	0.775201i	0.984644	−	0.174576i	$-0.0558554\pi$
$757$	13990.4	+	16145.7i	0.671715	+	0.775201i	−0.312928	+	0.949777i	$0.601310\pi$
$758$	−863.395			−0.0413719
$759$	33678.1	+	23691.3i	1.61059	+	1.13299i
$760$	8672.06			0.413906
$761$	−5256.76	−	6066.62i	−0.250404	−	0.288981i	0.616607	−	0.787271i	$-0.288507\pi$
$761$	−5256.76	−	6066.62i	−0.250404	−	0.288981i	−0.867010	+	0.498290i	$0.833961\pi$
$762$	2626.64	+	1688.04i	0.124873	+	0.0802509i
$763$	−2025.25	+	14085.9i	−0.0960928	+	0.668340i
$764$	2877.10	−	6299.97i	0.136243	−	0.298331i
$765$	−230.250	−	1601.42i	−0.0108820	−	0.0756856i
$766$	−13223.0	−	3882.61i	−0.623714	−	0.183139i
$767$	−6722.13	+	4320.05i	−0.316456	+	0.203374i
$768$	−600.940	−	1315.88i	−0.0282351	−	0.0618263i
$769$	30655.9	−	9001.39i	1.43756	−	0.422105i	0.532150	−	0.846650i	$-0.321384\pi$
$769$	30655.9	−	9001.39i	1.43756	−	0.422105i	0.905407	+	0.424545i	$0.139566\pi$
$770$	−33512.1	+	38675.1i	−1.56843	+	1.81007i
$771$	−21833.3	+	25196.9i	−1.01985	+	1.17697i
$772$	−10200.4	+	2995.11i	−0.475545	+	0.139633i
$773$	−10183.2	−	22298.0i	−0.473820	−	1.03752i	−0.984117	−	0.177523i	$-0.943192\pi$
$773$	−10183.2	−	22298.0i	−0.473820	−	1.03752i	0.510297	−	0.859998i	$-0.329536\pi$
$774$	2180.55	−	1401.35i	0.101264	−	0.0650782i
$775$	−8776.93	−	2577.14i	−0.406808	−	0.119450i
$776$	1460.80	+	10160.1i	0.0675771	+	0.470009i
$777$	−6327.12	+	13854.5i	−0.292129	+	0.639673i
$778$	−389.077	+	2706.09i	−0.0179294	+	0.124702i
$779$	14265.1	+	9167.60i	0.656097	+	0.421648i
$780$	−16592.2	−	19148.5i	−0.761664	−	0.879007i
$781$	−11735.3			−0.537671
$782$	4458.54	+	186.693i	0.203884	+	0.00853725i
$783$	18783.8			0.857314
$784$	−2381.63	−	2748.55i	−0.108493	−	0.125207i
$785$	−45383.8	−	29166.4i	−2.06346	−	1.32611i
$786$	−721.418	+	5017.57i	−0.0327381	+	0.227698i
$787$	−5713.90	+	12511.7i	−0.258804	+	0.566701i	−0.993776	−	0.111396i	$-0.964468\pi$
$787$	−5713.90	+	12511.7i	−0.258804	+	0.566701i	0.734972	+	0.678097i	$0.237195\pi$
$788$	2039.47	+	14184.8i	0.0921995	+	0.641261i
$789$	−9805.71	−	2879.22i	−0.442449	−	0.129915i
$790$	18109.1	−	11638.0i	0.815561	−	0.524130i
$791$	15619.6	+	34202.2i	0.702111	+	1.53741i
$792$	−2500.65	+	734.256i	−0.112193	+	0.0329427i
$793$	−12426.7	+	14341.2i	−0.556477	+	0.642209i
$794$	7208.08	−	8318.56i	0.322173	−	0.371807i
$795$	−3179.49	+	933.582i	−0.141843	+	0.0416487i
$796$	−5332.82	−	11677.3i	−0.237458	−	0.519961i
$797$	12107.5	−	7781.02i	0.538105	−	0.345819i	−0.243192	−	0.969978i	$-0.578195\pi$
$797$	12107.5	−	7781.02i	0.538105	−	0.345819i	0.781297	+	0.624159i	$0.214558\pi$
$798$	17307.8	+	5082.04i	0.767783	+	0.225441i
$799$	−836.527	−	5818.17i	−0.0370391	−	0.257612i
$800$	1835.21	−	4018.54i	0.0811054	−	0.177596i
$801$	587.571	−	4086.64i	0.0259186	−	0.180268i
$802$	1095.56	+	704.071i	0.0482362	+	0.0309995i
$803$	−27256.1	−	31455.2i	−1.19782	−	1.38235i
$804$	16459.7			0.722001
$805$	−42686.2	−	1787.41i	−1.86893	−	0.0782581i
$806$	9158.86			0.400257
$807$	12316.3	+	14213.8i	0.537243	+	0.620012i
$808$	5145.73	+	3306.96i	0.224042	+	0.143983i
$809$	1011.01	−	7031.72i	0.0439372	−	0.305590i	−0.955989	−	0.293404i	$-0.905212\pi$
$809$	1011.01	−	7031.72i	0.0439372	−	0.305590i	0.999926	−	0.0121858i	$-0.00387895\pi$
$810$	11289.9	−	24721.5i	0.489738	−	1.07238i
$811$	−2215.81	−	15411.3i	−0.0959404	−	0.667280i	−0.979867	−	0.199654i	$-0.936018\pi$
$811$	−2215.81	−	15411.3i	−0.0959404	−	0.667280i	0.883926	−	0.467627i	$-0.154891\pi$
$812$	13805.6	+	4053.68i	0.596650	+	0.175192i
$813$	16098.9	−	10346.1i	0.694480	−	0.446315i
$814$	−6194.71	−	13564.5i	−0.266737	−	0.584074i
$815$	6111.44	−	1794.48i	0.262668	−	0.0771263i
$816$	−1197.65	+	1382.16i	−0.0513800	+	0.0592957i
$817$	11502.5	−	13274.6i	0.492560	−	0.568445i
$818$	14391.4	−	4225.69i	0.615138	−	0.180621i
$819$	−3381.21	−	7403.82i	−0.144260	−	0.315886i
$820$	13846.8	−	8898.78i	0.589695	−	0.378974i
$821$	38852.6	+	11408.2i	1.65160	+	0.484954i	0.969252	−	0.246070i	$-0.0791394\pi$
$821$	38852.6	+	11408.2i	1.65160	+	0.484954i	0.682351	+	0.731025i	$0.260958\pi$
$822$	−4552.68	−	31664.6i	−0.193179	−	1.34359i
$823$	−6039.90	+	13225.5i	−0.255817	+	0.560162i	−0.993348	−	0.115152i	$-0.963265\pi$
$823$	−6039.90	+	13225.5i	−0.255817	+	0.560162i	0.737531	+	0.675314i	$0.235992\pi$
$824$	312.912	−	2176.35i	0.0132292	−	0.0920108i
$825$	−43354.7	−	27862.3i	−1.82959	−	1.17581i
$826$	−3616.17	−	4173.28i	−0.152328	−	0.175795i
$827$	−33401.2			−1.40444			−0.702221	−	0.711959i	$-0.747808\pi$
$827$	−33401.2			−1.40444			−0.702221	+	0.711959i	$0.747808\pi$
$828$	−1779.61	−	1251.89i	−0.0746929	−	0.0525438i
$829$	29827.2			1.24963			0.624813	−	0.780774i	$-0.285175\pi$
$829$	29827.2			1.24963			0.624813	+	0.780774i	$0.285175\pi$
$830$	−1707.99	−	1971.13i	−0.0714282	−	0.0824325i
$831$	34210.9	+	21986.0i	1.42811	+	0.917793i
$832$	−629.497	+	4378.25i	−0.0262306	+	0.182438i
$833$	−1910.03	+	4182.38i	−0.0794460	+	0.173963i
$834$	−504.397	−	3508.16i	−0.0209423	−	0.145657i
$835$	−47817.2	−	14040.4i	−1.98177	−	0.581901i
$836$	−14857.4	+	9548.26i	−0.614657	+	0.395016i
$837$	3432.52	+	7516.17i	0.141751	+	0.310391i
$838$	6447.31	−	1893.10i	0.265774	−	0.0780382i
$839$	−10739.6	+	12394.1i	−0.441920	+	0.510003i	−0.932389	−	0.361455i	$-0.882280\pi$
$839$	−10739.6	+	12394.1i	−0.441920	+	0.510003i	0.490469	+	0.871459i	$0.336825\pi$
$840$	11466.3	−	13232.9i	0.470984	−	0.543544i
$841$	1631.99	−	479.194i	0.0669148	−	0.0196480i
$842$	−7563.35	−	16561.4i	−0.309561	−	0.677844i
$843$	−5037.34	+	3237.30i	−0.205807	+	0.132264i
$844$	−14956.0	−	4391.49i	−0.609962	−	0.179101i
$845$	5954.44	+	41414.1i	0.242413	+	1.68602i
$846$	−1190.60	+	2607.04i	−0.0483848	+	0.105948i
$847$	10308.3	−	71696.0i	0.418180	−	2.90851i
$848$	486.664	+	312.760i	0.0197077	+	0.0126654i
$849$	−17814.4	−	20559.0i	−0.720130	−	0.831074i
$850$	−5585.14			−0.225375
$851$	5640.98	−	11098.2i	0.227227	−	0.447053i
$852$	4015.28			0.161457
$853$	994.985	+	1148.27i	0.0399386	+	0.0460916i	0.775367	−	0.631510i	$-0.217565\pi$
$853$	994.985	+	1148.27i	0.0399386	+	0.0460916i	−0.735429	+	0.677602i	$0.763019\pi$
$854$	−11032.0	−	7089.84i	−0.442047	−	0.284086i
$855$	−760.775	+	5291.31i	−0.0304304	+	0.211648i
$856$	6802.57	−	14895.6i	0.271620	−	0.594766i
$857$	3333.27	+	23183.4i	0.132862	+	0.924072i	0.941799	+	0.336177i	$0.109134\pi$
$857$	3333.27	+	23183.4i	0.132862	+	0.924072i	−0.808937	+	0.587895i	$0.799957\pi$
$858$	49509.8	+	14537.4i	1.96997	+	0.578436i
$859$	18010.5	−	11574.6i	0.715377	−	0.459745i	−0.131649	−	0.991296i	$-0.542027\pi$
$859$	18010.5	−	11574.6i	0.715377	−	0.459745i	0.847026	+	0.531551i	$0.178391\pi$
$860$	−7082.72	−	15509.0i	−0.280836	−	0.614945i
$861$	32850.5	−	9645.78i	1.30028	−	0.381797i
$862$	−14851.1	+	17139.1i	−0.586810	+	0.677215i
$863$	−19889.1	+	22953.3i	−0.784512	+	0.905375i	−0.997427	−	0.0716955i	$-0.977159\pi$
$863$	−19889.1	+	22953.3i	−0.784512	+	0.905375i	0.212914	+	0.977071i	$0.431704\pi$
$864$	−3828.91	+	1124.27i	−0.150766	+	0.0442690i
$865$	13315.4	+	29156.6i	0.523395	+	1.14607i
$866$	−10064.3	+	6467.90i	−0.394916	+	0.253797i
$867$	−24419.3	−	7170.15i	−0.956543	−	0.280866i
$868$	900.764	+	6264.95i	0.0352234	+	0.244984i
$869$	−18211.5	+	39877.6i	−0.710913	+	1.55668i
$870$	−3929.27	+	27328.7i	−0.153120	+	1.06498i
$871$	−42339.2	−	27209.8i	−1.64708	−	1.05852i
$872$	3121.86	+	3602.82i	0.121238	+	0.139916i
$873$	−6327.41			−0.245304
$874$	−13961.1	−	4742.24i	−0.540321	−	0.183534i
$875$	5056.62			0.195366
$876$	9325.80	+	10762.5i	0.359691	+	0.415106i
$877$	−15821.3	−	10167.7i	−0.609175	−	0.391493i	0.199372	−	0.979924i	$-0.436110\pi$
$877$	−15821.3	−	10167.7i	−0.609175	−	0.391493i	−0.808548	+	0.588431i	$0.799746\pi$
$878$	−843.360	+	5865.70i	−0.0324169	+	0.225464i
$879$	13916.8	−	30473.5i	0.534018	−	1.16934i
$880$	2439.72	+	16968.6i	0.0934580	+	0.650015i
$881$	−34363.7	−	10090.1i	−1.31412	−	0.385861i	−0.451754	−	0.892142i	$-0.649202\pi$
$881$	−34363.7	−	10090.1i	−1.31412	−	0.385861i	−0.862369	+	0.506281i	$0.831020\pi$
$882$	1885.98	−	1212.04i	0.0720002	−	0.0462717i
$883$	9121.70	+	19973.7i	0.347644	+	0.761234i	0.999994	+	0.00331684i	$0.00105579\pi$
$883$	9121.70	+	19973.7i	0.347644	+	0.761234i	−0.652350	+	0.757917i	$0.726217\pi$
$884$	5365.58	−	1575.48i	0.204145	−	0.0599423i
$885$	6939.02	−	8008.06i	0.263562	−	0.304167i
$886$	13211.1	−	15246.4i	0.500944	−	0.578120i
$887$	25076.6	−	7363.16i	0.949256	−	0.278727i	0.229779	−	0.973243i	$-0.426200\pi$
$887$	25076.6	−	7363.16i	0.949256	−	0.278727i	0.719477	+	0.694516i	$0.244382\pi$
$888$	2119.55	+	4641.16i	0.0800984	+	0.175391i
$889$	5550.27	−	3566.94i	0.209393	−	0.134568i
$890$	−26057.4	−	7651.15i	−0.981401	−	0.288165i
$891$	7876.85	+	54784.7i	0.296167	+	2.05988i
$892$	−4857.63	+	10636.7i	−0.182338	+	0.399265i
$893$	−2764.00	+	19224.0i	−0.103576	+	0.720389i
$894$	−10935.4	−	7027.77i	−0.409100	−	0.262913i
$895$	33831.7	+	39043.9i	1.26354	+	1.45820i
$896$	−3056.77			−0.113973
$897$	16240.5	+	39900.3i	0.604522	+	1.48521i
$898$	6745.95			0.250685
$899$	−6535.76	−	7542.67i	−0.242469	−	0.279824i
$900$	2290.94	+	1472.30i	0.0848496	+	0.0545295i
$901$	104.084	−	723.921i	0.00384855	−	0.0267673i
$902$	−13925.1	+	30491.6i	−0.514029	+	1.12557i
$903$	−5047.16	−	35103.8i	−0.186001	−	1.29367i
$904$	12085.6	+	3548.64i	0.444646	+	0.130560i
$905$	27466.7	−	17651.8i	1.00887	−	0.648359i
$906$	−5204.01	−	11395.2i	−0.190829	−	0.417858i
$907$	28996.7	−	8514.21i	1.06154	−	0.311698i	0.296072	−	0.955166i	$-0.404323\pi$
$907$	28996.7	−	8514.21i	1.06154	−	0.311698i	0.765473	+	0.643468i	$0.222505\pi$
$908$	5455.60	−	6296.09i	0.199395	−	0.230114i
$909$	−2469.18	+	2849.58i	−0.0900962	+	0.103977i
$910$	−51370.3	+	15083.7i	−1.87133	+	0.549471i
$911$	2611.23	+	5717.80i	0.0949660	+	0.207947i	0.951153	−	0.308719i	$-0.0999003\pi$
$911$	2611.23	+	5717.80i	0.0949660	+	0.207947i	−0.856187	+	0.516666i	$0.827173\pi$
$912$	5083.52	−	3266.98i	0.184575	−	0.118619i
$913$	5096.51	+	1496.47i	0.184742	+	0.0542453i
$914$	871.222	+	6059.48i	0.0315290	+	0.219289i
$915$	10453.5	−	22889.9i	0.377684	−	0.827012i
$916$	634.596	−	4413.71i	0.0228905	−	0.159207i
$917$	9011.09	+	5791.08i	0.324507	+	0.208548i
$918$	3303.80	+	3812.79i	0.118782	+	0.137081i
$919$	47690.0			1.71181			0.855903	−	0.517137i	$-0.173002\pi$
$919$	47690.0			1.71181			0.855903	+	0.517137i	$0.173002\pi$
$920$	−9816.79	+	10414.8i	−0.351793	+	0.373225i
$921$	33774.3			1.20836
$922$	8770.04	+	10121.2i	0.313260	+	0.361521i
$923$	−10328.5	−	6637.72i	−0.368328	−	0.236710i
$924$	−5074.80	+	35296.0i	−0.180680	+	1.25666i
$925$	−6472.87	+	14173.6i	−0.230083	+	0.503811i
$926$	3545.45	+	24659.2i	0.125822	+	0.875108i
$927$	1300.46	+	381.851i	0.0460764	+	0.0135293i
$928$	4054.86	−	2605.90i	0.143435	−	0.0921799i
$929$	9171.31	+	20082.4i	0.323898	+	0.709237i	0.999610	−	0.0279286i	$-0.00889112\pi$
$929$	9171.31	+	20082.4i	0.323898	+	0.709237i	−0.675712	+	0.737165i	$0.736164\pi$
$930$	−11653.4	+	3421.74i	−0.410892	+	0.120649i
$931$	9948.64	−	11481.3i	0.350219	−	0.404174i
$932$	−7754.53	+	8949.21i	−0.272541	+	0.314529i
$933$	31161.1	−	9149.71i	1.09343	−	0.321059i
$934$	−5177.78	−	11337.8i	−0.181394	−	0.397198i
$935$	18232.6	−	11717.4i	0.637722	−	0.409839i
$936$	−2616.19	−	768.182i	−0.0913598	−	0.0268257i
$937$	4060.67	+	28242.6i	0.141576	+	0.984680i	0.929477	+	0.368879i	$0.120258\pi$
$937$	4060.67	+	28242.6i	0.141576	+	0.984680i	−0.787902	+	0.615801i	$0.788833\pi$
$938$	14448.3	−	31637.4i	0.502937	−	1.10128i
$939$	−2106.55	+	14651.4i	−0.0732104	+	0.509190i
$940$	15859.5	+	10192.3i	0.550297	+	0.353654i
$941$	6089.76	+	7027.95i	0.210967	+	0.243469i	0.851364	−	0.524575i	$-0.175776\pi$
$941$	6089.76	+	7027.95i	0.210967	+	0.243469i	−0.640397	+	0.768044i	$0.721230\pi$
$942$	−37591.5			−1.30021
$943$	−27158.0	+	6754.09i	−0.937845	+	0.233238i
$944$	−1849.85			−0.0637791
$945$	−31630.7	−	36503.8i	−1.08883	−	1.25658i
$946$	29210.5	+	18772.4i	1.00393	+	0.645184i
$947$	−6838.05	+	47559.7i	−0.234643	+	1.63198i	0.442955	+	0.896544i	$0.353930\pi$
$947$	−6838.05	+	47559.7i	−0.234643	+	1.63198i	−0.677598	+	0.735432i	$0.736979\pi$
$948$	6231.15	−	13644.3i	0.213479	−	0.467455i
$949$	−6197.00	−	43101.1i	−0.211974	−	1.47431i
$950$	17706.5	+	5199.11i	0.604711	+	0.177559i
$951$	−41040.3	+	26375.0i	−1.39939	+	0.899335i
$952$	1605.38	+	3515.28i	0.0546539	+	0.119675i
$953$	−22003.8	+	6460.89i	−0.747924	+	0.219610i	−0.633415	−	0.773812i	$-0.718348\pi$
$953$	−22003.8	+	6460.89i	−0.747924	+	0.219610i	−0.114509	+	0.993422i	$0.536529\pi$
$954$	−233.526	+	269.503i	−0.00792525	+	0.00914622i
$955$	18390.2	−	21223.4i	0.623132	−	0.719133i
$956$	21862.6	−	6419.44i	0.739631	−	0.217175i
$957$	−23358.1	−	51147.1i	−0.788986	−	1.72764i
$958$	5806.16	−	3731.39i	0.195813	−	0.125841i
$959$	−64859.3	−	19044.4i	−2.18396	−	0.641268i
$960$	−834.762	−	5805.90i	−0.0280644	−	0.195192i
$961$	−10551.8	+	23105.3i	−0.354195	+	0.775579i
$962$	2220.27	−	15442.3i	0.0744120	−	0.517547i
$963$	8491.84	+	5457.37i	0.284160	+	0.182618i
$964$	4215.01	+	4864.39i	0.140826	+	0.162522i
$965$	−43106.2			−1.43797
$966$	−25695.8	+	15033.2i	−0.855849	+	0.500710i
$967$	−47232.2			−1.57072			−0.785359	−	0.619041i	$-0.787521\pi$
$967$	−47232.2			−1.57072			−0.785359	+	0.619041i	$0.787521\pi$
$968$	−15890.0	−	18338.0i	−0.527608	−	0.608892i
$969$	−6426.83	−	4130.27i	−0.213064	−	0.136928i
$970$	−5923.19	+	41196.7i	−0.196064	+	1.36366i
$971$	−16273.7	+	35634.5i	−0.537847	+	1.17772i	0.424383	+	0.905483i	$0.360491\pi$
$971$	−16273.7	+	35634.5i	−0.537847	+	1.17772i	−0.962230	+	0.272237i	$0.912236\pi$
$972$	−778.389	−	5413.81i	−0.0256860	−	0.178650i
$973$	−7185.85	−	2109.96i	−0.236760	−	0.0695191i
$974$	3423.20	−	2199.95i	0.112614	−	0.0723728i
$975$	−22397.9	−	49044.6i	−0.735700	−	1.61096i
$976$	−4215.09	+	1237.66i	−0.138239	+	0.0405908i
$977$	28541.7	−	32938.9i	0.934627	−	1.07862i	−0.0621236	−	0.998068i	$-0.519787\pi$
$977$	28541.7	−	32938.9i	0.934627	−	1.07862i	0.996751	−	0.0805487i	$-0.0256673\pi$
$978$	2906.48	−	3354.25i	0.0950295	−	0.109670i
$979$	53067.0	−	15581.9i	1.73241	−	0.508682i
$980$	−6125.92	−	13413.9i	−0.199679	−	0.437236i
$981$	−2472.15	+	1588.76i	−0.0804585	+	0.0517075i
$982$	−3475.56	−	1020.52i	−0.112943	−	0.0331629i
$983$	−3680.50	−	25598.5i	−0.119420	−	0.830584i	−0.958197	−	0.286109i	$-0.907638\pi$
$983$	−3680.50	−	25598.5i	−0.119420	−	0.830584i	0.838777	−	0.544475i	$-0.183271\pi$
$984$	4764.53	−	10432.9i	0.154357	−	0.337995i
$985$	−8269.54	+	57515.9i	−0.267502	+	1.86052i
$986$	−5126.34	−	3294.50i	−0.165574	−	0.106408i
$987$	25679.7	+	29635.9i	0.828159	+	0.955747i
$988$	−18477.0			−0.594973
$989$	2921.45	+	28841.0i	0.0939301	+	0.927289i
$990$	−10567.5			−0.339251
$991$	−14280.2	−	16480.2i	−0.457744	−	0.528265i	0.479218	−	0.877696i	$-0.340920\pi$
$991$	−14280.2	−	16480.2i	−0.457744	−	0.528265i	−0.936962	+	0.349431i	$0.886375\pi$
$992$	1783.71	+	1146.32i	0.0570896	+	0.0366893i
$993$	6286.70	−	43725.0i	0.200909	−	1.39735i
$994$	3524.61	−	7717.83i	0.112469	−	0.246272i
$995$	−7407.79	−	51522.3i	−0.236023	−	1.64157i
$996$	−1743.79	−	512.024i	−0.0554761	−	0.0162893i
$997$	22635.1	−	14546.7i	0.719018	−	0.462085i	−0.129277	−	0.991609i	$-0.541266\pi$
$997$	22635.1	−	14546.7i	0.719018	−	0.462085i	0.848295	+	0.529524i	$0.177629\pi$
$998$	−5632.03	−	12332.4i	−0.178636	−	0.391158i
$999$	13504.8	−	3965.35i	0.427699	−	0.125584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.a.13.1	✓	30
23.4	even	11		1058.4.a.v.1.4		15
23.16	even	11	inner	46.4.c.a.39.1	yes	30
23.19	odd	22		1058.4.a.w.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.a.13.1	✓	30	1.1	even	1	trivial
46.4.c.a.39.1	yes	30	23.16	even	11	inner
1058.4.a.v.1.4		15	23.4	even	11
1058.4.a.w.1.4		15	23.19	odd	22

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:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30972 - 1.51150i) q^{2} +(-4.75375 - 3.05505i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(-6.73761 + 14.7533i) q^{5} +(1.60838 + 11.1865i) q^{6} +(22.9137 + 6.72806i) q^{7} +(6.73003 - 4.32513i) q^{8} +(2.04859 + 4.48580i) q^{9} +(31.1240 - 9.13883i) q^{10} +(-43.2609 + 49.9258i) q^{11} +(14.8019 - 17.0823i) q^{12} +(-66.3140 + 19.4716i) q^{13} +(-19.8411 - 43.4459i) q^{14} +(77.1009 - 49.5498i) q^{15} +(-15.3519 - 4.50772i) q^{16} +(2.87874 + 20.0220i) q^{17} +(4.09719 - 8.97159i) q^{18} +(9.51172 - 66.1555i) q^{19} +(-54.5771 - 35.0746i) q^{20} +(-88.3713 - 101.986i) q^{21} +132.123 q^{22} +(68.6830 + 86.3113i) q^{23} -45.2063 q^{24} +(-90.4069 - 104.335i) q^{25} +(116.284 + 74.7313i) q^{26} +(-17.7473 + 123.436i) q^{27} +(-39.6821 + 86.8918i) q^{28} +(-21.4363 - 149.093i) q^{29} +(-175.875 - 51.6416i) q^{30} +(55.7410 - 35.8226i) q^{31} +(13.2933 + 29.1082i) q^{32} +(358.177 - 105.170i) q^{33} +(26.4930 - 30.5745i) q^{34} +(-253.644 + 292.721i) q^{35} +(-18.9267 + 5.55739i) q^{36} +(-46.8861 - 102.666i) q^{37} +(-112.452 + 72.2683i) q^{38} +(374.727 + 110.030i) q^{39} +(18.4656 + 128.431i) q^{40} +(-105.395 + 230.783i) q^{41} +(-38.4098 + 267.146i) q^{42} +(221.086 + 142.083i) q^{43} +(-173.044 - 199.703i) q^{44} -79.9829 q^{45} +(40.5039 - 216.858i) q^{46} -290.588 q^{47} +(59.2077 + 68.3293i) q^{48} +(191.220 + 122.890i) q^{49} +(-39.2946 + 273.300i) q^{50} +(47.4835 - 103.974i) q^{51} +(-39.3436 - 273.640i) q^{52} +(-34.6916 - 10.1864i) q^{53} +(209.817 - 134.841i) q^{54} +(-445.095 - 974.621i) q^{55} +(183.309 - 53.8245i) q^{56} +(-247.324 + 285.428i) q^{57} +(-197.278 + 227.671i) q^{58} +(110.932 - 32.5727i) q^{59} +(152.291 + 333.471i) q^{60} +(230.979 - 148.441i) q^{61} +(-127.151 - 37.3349i) q^{62} +(16.7601 + 116.569i) q^{63} +(26.5866 - 58.2164i) q^{64} +(159.528 - 1109.54i) q^{65} +(-628.077 - 403.641i) q^{66} +(476.872 + 550.339i) q^{67} -80.9117 q^{68} +(-62.8165 - 620.132i) q^{69} +774.652 q^{70} +(116.331 + 134.253i) q^{71} +(33.1887 + 21.3291i) q^{72} +(-89.6640 + 623.627i) q^{73} +(-93.7721 + 205.332i) q^{74} +(111.023 + 772.181i) q^{75} +(256.514 + 75.3192i) q^{76} +(-1327.17 + 852.921i) q^{77} +(-324.478 - 710.507i) q^{78} +(636.735 - 186.962i) q^{79} +(169.939 - 196.120i) q^{80} +(548.662 - 633.190i) q^{81} +(486.867 - 142.957i) q^{82} +(-33.4015 - 73.1391i) q^{83} +(454.098 - 291.831i) q^{84} +(-314.787 - 92.4298i) q^{85} +(-74.8023 - 520.261i) q^{86} +(-353.582 + 774.238i) q^{87} +(-75.2120 + 523.111i) q^{88} +(-704.309 - 452.632i) q^{89} +(104.755 + 120.894i) q^{90} -1650.50 q^{91} +(-380.830 + 222.802i) q^{92} -374.418 q^{93} +(380.590 + 439.224i) q^{94} +(911.925 + 586.059i) q^{95} +(25.7341 - 178.985i) q^{96} +(-533.009 + 1167.13i) q^{97} +(-64.6973 - 449.980i) q^{98} +(-312.581 - 91.7820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9} + 20 q^{10} + 64 q^{11} - 20 q^{12} + 8 q^{13} + 16 q^{14} + 252 q^{15} - 48 q^{16} - 126 q^{17} - 126 q^{18}+ \cdots + 1377 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 + 6 * q^3 - 12 * q^4 + 10 * q^5 + 12 * q^6 + 107 * q^7 - 24 * q^8 - 63 * q^9 + 20 * q^10 + 64 * q^11 - 20 * q^12 + 8 * q^13 + 16 * q^14 + 252 * q^15 - 48 * q^16 - 126 * q^17 - 126 * q^18 + 123 * q^19 - 136 * q^20 - 514 * q^21 - 356 * q^22 - 507 * q^23 + 48 * q^24 - 419 * q^25 - 94 * q^26 - 657 * q^27 + 32 * q^28 + 757 * q^29 + 240 * q^30 + 840 * q^31 - 96 * q^32 + 1948 * q^33 + 936 * q^34 - 785 * q^35 - 164 * q^36 - 444 * q^37 + 554 * q^38 + 1954 * q^39 + 80 * q^40 - 771 * q^41 + 72 * q^42 - 789 * q^43 + 256 * q^44 - 2596 * q^45 + 1230 * q^46 - 1748 * q^47 - 80 * q^48 - 720 * q^49 - 2026 * q^50 + 1641 * q^51 + 472 * q^52 - 785 * q^53 + 2030 * q^54 + 967 * q^55 + 856 * q^56 + 5918 * q^57 + 1052 * q^58 + 2307 * q^59 - 444 * q^60 + 877 * q^61 - 278 * q^62 - 5708 * q^63 - 192 * q^64 - 3846 * q^65 - 4156 * q^66 + 1763 * q^67 - 2528 * q^68 - 1970 * q^69 - 3968 * q^70 - 6362 * q^71 - 152 * q^72 - 3584 * q^73 - 888 * q^74 + 3143 * q^75 + 360 * q^76 + 6347 * q^77 - 1460 * q^78 + 2642 * q^79 + 864 * q^80 + 1043 * q^81 + 5542 * q^82 - 372 * q^83 + 2212 * q^84 + 5136 * q^85 - 2326 * q^86 + 5451 * q^87 - 104 * q^88 - 4283 * q^89 + 5104 * q^90 - 6182 * q^91 - 92 * q^92 - 8734 * q^93 - 2550 * q^94 + 9449 * q^95 + 192 * q^96 + 7599 * q^97 + 3928 * q^98 + 1377 * q^99

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