LMFDB - Embedded newform 117.3.k.a.29.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			29.16
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.13140i q^{2} +(-2.34643 + 1.86930i) q^{3} +2.71993 q^{4} +(-7.06649 + 4.07984i) q^{5} +(-2.11493 - 2.65475i) q^{6} +(-3.97102 - 6.87801i) q^{7} +7.60294i q^{8} +(2.01145 - 8.77235i) q^{9} +(-4.61594 - 7.99504i) q^{10} +4.00036i q^{11} +(-6.38212 + 5.08436i) q^{12} +(-12.9709 - 0.869283i) q^{13} +(7.78178 - 4.49282i) q^{14} +(8.95458 - 22.7824i) q^{15} +2.27776 q^{16} +(-1.60230 - 0.925090i) q^{17} +(9.92504 + 2.27575i) q^{18} +(-14.4514 + 25.0305i) q^{19} +(-19.2204 + 11.0969i) q^{20} +(22.1748 + 8.71573i) q^{21} -4.52601 q^{22} +(-13.0031 - 7.50735i) q^{23} +(-14.2122 - 17.8397i) q^{24} +(20.7902 - 36.0097i) q^{25} +(0.983507 - 14.6753i) q^{26} +(11.6784 + 24.3437i) q^{27} +(-10.8009 - 18.7077i) q^{28} +11.4917i q^{29} +(25.7761 + 10.1312i) q^{30} +(26.0477 + 45.1159i) q^{31} +32.9888i q^{32} +(-7.47787 - 9.38656i) q^{33} +(1.04665 - 1.81285i) q^{34} +(56.1224 + 32.4023i) q^{35} +(5.47100 - 23.8602i) q^{36} +(21.4744 + 37.1948i) q^{37} +(-28.3196 - 16.3503i) q^{38} +(32.0602 - 22.2068i) q^{39} +(-31.0188 - 53.7261i) q^{40} +(35.1449 + 20.2909i) q^{41} +(-9.86098 + 25.0885i) q^{42} +(-18.3431 - 31.7712i) q^{43} +10.8807i q^{44} +(21.5759 + 70.1961i) q^{45} +(8.49383 - 14.7117i) q^{46} +(-62.5840 - 36.1329i) q^{47} +(-5.34460 + 4.25781i) q^{48} +(-7.03800 + 12.1902i) q^{49} +(40.7414 + 23.5221i) q^{50} +(5.48896 - 0.824526i) q^{51} +(-35.2800 - 2.36439i) q^{52} +66.2582i q^{53} +(-27.5425 + 13.2130i) q^{54} +(-16.3208 - 28.2685i) q^{55} +(52.2931 - 30.1914i) q^{56} +(-12.8804 - 85.7463i) q^{57} -13.0017 q^{58} -4.32590i q^{59} +(24.3558 - 61.9667i) q^{60} +(-7.13924 - 12.3655i) q^{61} +(-51.0441 + 29.4703i) q^{62} +(-68.3238 + 21.0004i) q^{63} -28.2125 q^{64} +(95.2054 - 46.7765i) q^{65} +(10.6200 - 8.46047i) q^{66} +(44.8949 - 77.7602i) q^{67} +(-4.35816 - 2.51618i) q^{68} +(44.5444 - 6.69124i) q^{69} +(-36.6600 + 63.4969i) q^{70} +(-77.9009 - 44.9761i) q^{71} +(66.6956 + 15.2929i) q^{72} +44.6797 q^{73} +(-42.0823 + 24.2962i) q^{74} +(18.5302 + 123.357i) q^{75} +(-39.3068 + 68.0813i) q^{76} +(27.5145 - 15.8855i) q^{77} +(25.1248 + 36.2730i) q^{78} +(-10.9688 + 18.9985i) q^{79} +(-16.0958 + 9.29290i) q^{80} +(-72.9082 - 35.2902i) q^{81} +(-22.9571 + 39.7629i) q^{82} +(-101.145 - 58.3960i) q^{83} +(60.3138 + 23.7062i) q^{84} +15.0969 q^{85} +(35.9460 - 20.7534i) q^{86} +(-21.4815 - 26.9645i) q^{87} -30.4145 q^{88} +(20.9089 - 12.0718i) q^{89} +(-79.4200 + 24.4110i) q^{90} +(45.5288 + 92.6659i) q^{91} +(-35.3676 - 20.4195i) q^{92} +(-145.454 - 57.1703i) q^{93} +(40.8808 - 70.8075i) q^{94} -235.837i q^{95} +(-61.6659 - 77.4059i) q^{96} +(46.7356 + 80.9485i) q^{97} +(-13.7920 - 7.96280i) q^{98} +(35.0926 + 8.04651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$			1.13140i			0.565700i	0.959164	+	0.282850i	$0.0912799\pi$
$2$			1.13140i			0.565700i	−0.959164	+	0.282850i	$0.908720\pi$
$3$	−2.34643	+	1.86930i	−0.782143	+	0.623099i
$3$	−2.34643	+	1.86930i	−0.782143	+	0.623099i
$4$	2.71993			0.679983
$5$	−7.06649	+	4.07984i	−1.41330	+	0.815968i	−0.995698	−	0.0926619i	$-0.970462\pi$
$5$	−7.06649	+	4.07984i	−1.41330	+	0.815968i	−0.417601	+	0.908630i	$0.637129\pi$
$6$	−2.11493	−	2.65475i	−0.352488	−	0.442458i
$7$	−3.97102	−	6.87801i	−0.567289	−	0.982573i	−0.996833	−	0.0795268i	$-0.974659\pi$
$7$	−3.97102	−	6.87801i	−0.567289	−	0.982573i	0.429544	−	0.903046i	$-0.358674\pi$
$8$			7.60294i			0.950367i
$9$	2.01145	−	8.77235i	0.223494	−	0.974705i
$10$	−4.61594	−	7.99504i	−0.461594	−	0.799504i
$11$			4.00036i			0.363669i	0.983329	+	0.181835i	$0.0582036\pi$
$11$			4.00036i			0.363669i	−0.983329	+	0.181835i	$0.941796\pi$
$12$	−6.38212	+	5.08436i	−0.531844	+	0.423697i
$13$	−12.9709	−	0.869283i	−0.997762	−	0.0668679i
$13$	−12.9709	−	0.869283i	−0.997762	−	0.0668679i
$14$	7.78178	−	4.49282i	0.555842	−	0.320915i
$15$	8.95458	−	22.7824i	0.596972	−	1.51883i
$16$	2.27776			0.142360
$17$	−1.60230	−	0.925090i	−0.0942531	−	0.0544171i	0.452133	−	0.891951i	$-0.350663\pi$
$17$	−1.60230	−	0.925090i	−0.0942531	−	0.0544171i	−0.546386	+	0.837534i	$0.683997\pi$
$18$	9.92504	+	2.27575i	0.551391	+	0.126431i
$19$	−14.4514	+	25.0305i	−0.760599	+	1.31740i	0.181943	+	0.983309i	$0.441761\pi$
$19$	−14.4514	+	25.0305i	−0.760599	+	1.31740i	−0.942542	+	0.334087i	$0.891572\pi$
$20$	−19.2204	+	11.0969i	−0.961019	+	0.554845i
$21$	22.1748	+	8.71573i	1.05594	+	0.415035i
$22$	−4.52601			−0.205728
$23$	−13.0031	−	7.50735i	−0.565353	−	0.326407i	0.189938	−	0.981796i	$-0.439171\pi$
$23$	−13.0031	−	7.50735i	−0.565353	−	0.326407i	−0.755291	+	0.655389i	$0.772505\pi$
$24$	−14.2122	−	17.8397i	−0.592173	−	0.743323i
$25$	20.7902	−	36.0097i	0.831609	−	1.44039i
$26$	0.983507	−	14.6753i	0.0378272	−	0.564434i
$27$	11.6784	+	24.3437i	0.432534	+	0.901618i
$28$	−10.8009	−	18.7077i	−0.385747	−	0.668133i
$29$			11.4917i			0.396266i	0.980175	+	0.198133i	$0.0634878\pi$
$29$			11.4917i			0.396266i	−0.980175	+	0.198133i	$0.936512\pi$
$30$	25.7761	+	10.1312i	0.859202	+	0.337707i
$31$	26.0477	+	45.1159i	0.840247	+	1.45535i	0.889686	+	0.456573i	$0.150923\pi$
$31$	26.0477	+	45.1159i	0.840247	+	1.45535i	−0.0494388	+	0.998777i	$0.515743\pi$
$32$			32.9888i			1.03090i
$33$	−7.47787	−	9.38656i	−0.226602	−	0.284441i
$34$	1.04665	−	1.81285i	0.0307838	−	0.0533190i
$35$	56.1224	+	32.4023i	1.60350	+	0.925779i
$36$	5.47100	−	23.8602i	0.151972	−	0.662783i
$37$	21.4744	+	37.1948i	0.580390	+	1.00527i	0.995433	+	0.0954635i	$0.0304333\pi$
$37$	21.4744	+	37.1948i	0.580390	+	1.00527i	−0.415043	+	0.909802i	$0.636233\pi$
$38$	−28.3196	−	16.3503i	−0.745252	−	0.430271i
$39$	32.0602	−	22.2068i	0.822057	−	0.569405i
$40$	−31.0188	−	53.7261i	−0.775470	−	1.34315i
$41$	35.1449	+	20.2909i	0.857192	+	0.494900i	0.863071	−	0.505083i	$-0.168538\pi$
$41$	35.1449	+	20.2909i	0.857192	+	0.494900i	−0.00587914	+	0.999983i	$0.501871\pi$
$42$	−9.86098	+	25.0885i	−0.234785	+	0.597346i
$43$	−18.3431	−	31.7712i	−0.426584	−	0.738865i	0.569983	−	0.821657i	$-0.306950\pi$
$43$	−18.3431	−	31.7712i	−0.426584	−	0.738865i	−0.996567	+	0.0827913i	$0.973617\pi$
$44$			10.8807i			0.247289i
$45$	21.5759	+	70.1961i	0.479465	+	1.55991i
$46$	8.49383	−	14.7117i	0.184648	−	0.319820i
$47$	−62.5840	−	36.1329i	−1.33157	−	0.768784i	−0.346033	−	0.938222i	$-0.612471\pi$
$47$	−62.5840	−	36.1329i	−1.33157	−	0.768784i	−0.985541	+	0.169438i	$0.945805\pi$
$48$	−5.34460	+	4.25781i	−0.111346	+	0.0887044i
$49$	−7.03800	+	12.1902i	−0.143633	+	0.248779i
$50$	40.7414	+	23.5221i	0.814829	+	0.470442i
$51$	5.48896	−	0.824526i	0.107627	−	0.0161672i
$52$	−35.2800	−	2.36439i	−0.678461	−	0.0454690i
$53$			66.2582i			1.25016i	0.780563	+	0.625078i	$0.214933\pi$
$53$			66.2582i			1.25016i	−0.780563	+	0.625078i	$0.785067\pi$
$54$	−27.5425	+	13.2130i	−0.510045	+	0.244685i
$55$	−16.3208	−	28.2685i	−0.296743	−	0.513973i
$56$	52.2931	−	30.1914i	0.933805	−	0.539132i
$57$	−12.8804	−	85.7463i	−0.225972	−	1.50432i
$58$	−13.0017			−0.224168
$59$		−	4.32590i		−	0.0733203i	−0.999328	−	0.0366602i	$-0.988328\pi$
$59$		−	4.32590i		−	0.0733203i	0.999328	−	0.0366602i	$-0.0116719\pi$
$60$	24.3558	−	61.9667i	0.405931	−	1.03278i
$61$	−7.13924	−	12.3655i	−0.117037	−	0.202714i	0.801555	−	0.597921i	$-0.204006\pi$
$61$	−7.13924	−	12.3655i	−0.117037	−	0.202714i	−0.918592	+	0.395207i	$0.870673\pi$
$62$	−51.0441	+	29.4703i	−0.823292	+	0.475328i
$63$	−68.3238	+	21.0004i	−1.08450	+	0.333340i
$64$	−28.2125			−0.440821
$65$	95.2054	−	46.7765i	1.46470	−	0.719638i
$66$	10.6200	−	8.46047i	0.160909	−	0.128189i
$67$	44.8949	−	77.7602i	0.670073	−	1.16060i	−0.307810	−	0.951448i	$-0.599596\pi$
$67$	44.8949	−	77.7602i	0.670073	−	1.16060i	0.977883	−	0.209153i	$-0.0670706\pi$
$68$	−4.35816	−	2.51618i	−0.0640905	−	0.0370027i
$69$	44.5444	−	6.69124i	0.645570	−	0.0969746i
$70$	−36.6600	+	63.4969i	−0.523714	+	0.907099i
$71$	−77.9009	−	44.9761i	−1.09720	−	0.633466i	−0.161713	−	0.986838i	$-0.551702\pi$
$71$	−77.9009	−	44.9761i	−1.09720	−	0.633466i	−0.935483	+	0.353371i	$0.885035\pi$
$72$	66.6956	+	15.2929i	0.926328	+	0.212401i
$73$	44.6797			0.612050			0.306025	−	0.952023i	$-0.401001\pi$
$73$	44.6797			0.612050			0.306025	+	0.952023i	$0.401001\pi$
$74$	−42.0823	+	24.2962i	−0.568679	+	0.328327i
$75$	18.5302	+	123.357i	0.247069	+	1.64476i
$76$	−39.3068	+	68.0813i	−0.517194	+	0.895807i
$77$	27.5145	−	15.8855i	0.357331	−	0.206305i
$78$	25.1248	+	36.2730i	0.322112	+	0.465038i
$79$	−10.9688	+	18.9985i	−0.138845	+	0.240487i	−0.927060	−	0.374913i	$-0.877672\pi$
$79$	−10.9688	+	18.9985i	−0.138845	+	0.240487i	0.788214	+	0.615401i	$0.211006\pi$
$80$	−16.0958	+	9.29290i	−0.201197	+	0.116161i
$81$	−72.9082	−	35.2902i	−0.900101	−	0.435682i
$82$	−22.9571	+	39.7629i	−0.279965	+	0.484914i
$83$	−101.145	−	58.3960i	−1.21861	−	0.703566i	−0.253991	−	0.967207i	$-0.581743\pi$
$83$	−101.145	−	58.3960i	−1.21861	−	0.703566i	−0.964621	+	0.263640i	$0.915077\pi$
$84$	60.3138	+	23.7062i	0.718022	+	0.282217i
$85$	15.0969			0.177610
$86$	35.9460	−	20.7534i	0.417976	−	0.241319i
$87$	−21.4815	−	26.9645i	−0.246913	−	0.309937i
$88$	−30.4145			−0.345619
$89$	20.9089	−	12.0718i	0.234932	−	0.135638i	−0.377913	−	0.925841i	$-0.623358\pi$
$89$	20.9089	−	12.0718i	0.234932	−	0.135638i	0.612845	+	0.790203i	$0.290025\pi$
$90$	−79.4200	+	24.4110i	−0.882444	+	0.271233i
$91$	45.5288	+	92.6659i	0.500316	+	1.01831i
$92$	−35.3676	−	20.4195i	−0.384430	−	0.221951i
$93$	−145.454	−	57.1703i	−1.56402	−	0.614734i
$94$	40.8808	−	70.8075i	0.434902	−	0.753272i
$95$		−	235.837i		−	2.48250i
$96$	−61.6659	−	77.4059i	−0.642353	−	0.806311i
$97$	46.7356	+	80.9485i	0.481811	+	0.834521i	0.999782	−	0.0208774i	$-0.00664596\pi$
$97$	46.7356	+	80.9485i	0.481811	+	0.834521i	−0.517971	+	0.855398i	$0.673313\pi$
$98$	−13.7920	−	7.96280i	−0.140734	−	0.0812531i
$99$	35.0926	+	8.04651i	0.354470	+	0.0812779i
$100$	56.5480	−	97.9440i	0.565480	−	0.979440i
$101$			45.2880i			0.448396i	0.974544	+	0.224198i	$0.0719763\pi$
$101$			45.2880i			0.448396i	−0.974544	+	0.224198i	$0.928024\pi$
$102$	0.932869	+	6.21021i	0.00914577	+	0.0608844i
$103$	33.9722	+	58.8416i	0.329827	+	0.571278i	0.982477	−	0.186382i	$-0.0596761\pi$
$103$	33.9722	+	58.8416i	0.329827	+	0.571278i	−0.652650	+	0.757659i	$0.726343\pi$
$104$	6.60910	−	98.6170i	0.0635491	−	0.948240i
$105$	−192.257	+	28.8799i	−1.83102	+	0.275047i
$106$	−74.9646			−0.707213
$107$	−9.46031	+	5.46191i	−0.0884141	+	0.0510459i	−0.543555	−	0.839373i	$-0.682922\pi$
$107$	−9.46031	+	5.46191i	−0.0884141	+	0.0510459i	0.455141	+	0.890419i	$0.349589\pi$
$108$	31.7645	+	66.2131i	0.294116	+	0.613085i
$109$	−23.9383			−0.219617			−0.109809	−	0.993953i	$-0.535024\pi$
$109$	−23.9383			−0.219617			−0.109809	+	0.993953i	$0.535024\pi$
$110$	31.9830	−	18.4654i	0.290755	−	0.167867i
$111$	−119.916	−	47.1328i	−1.08033	−	0.424620i
$112$	−9.04503	−	15.6664i	−0.0807592	−	0.139879i
$113$			145.831i			1.29054i	0.763953	+	0.645271i	$0.223256\pi$
$113$			145.831i			1.29054i	−0.763953	+	0.645271i	$0.776744\pi$
$114$	97.0134	−	14.5729i	0.850995	−	0.127832i
$115$	122.515			1.06535
$116$			31.2567i			0.269454i
$117$	−33.7159	+	112.037i	−0.288170	+	0.957579i
$118$	4.89433			0.0414773
$119$			14.6942i			0.123481i
$120$	173.213	+	68.0811i	1.44345	+	0.567342i
$121$	104.997			0.867745
$122$	13.9904	−	8.07735i	0.114675	−	0.0662078i
$123$	−120.395	+	18.0851i	−0.978818	+	0.147033i
$124$	70.8479	+	122.712i	0.571354	+	0.989614i
$125$			135.291i			1.08233i
$126$	−23.7599	−	77.3016i	−0.188571	−	0.613505i
$127$	−28.2184	−	48.8757i	−0.222192	−	0.384848i	0.733281	−	0.679925i	$-0.237988\pi$
$127$	−28.2184	−	48.8757i	−0.222192	−	0.384848i	−0.955473	+	0.295078i	$0.904655\pi$
$128$			100.036i			0.781528i
$129$	102.431	+	40.2601i	0.794036	+	0.312094i
$130$	52.9229	+	107.715i	0.407099	+	0.828580i
$131$	112.286	−	64.8284i	0.857146	−	0.494873i	−0.00590977	−	0.999983i	$-0.501881\pi$
$131$	112.286	−	64.8284i	0.857146	−	0.494873i	0.863055	+	0.505109i	$0.168548\pi$
$132$	−20.3393	−	25.5308i	−0.154086	−	0.193415i
$133$	229.547			1.72592
$134$	87.9780	+	50.7941i	0.656552	+	0.379061i
$135$	−181.844	−	124.378i	−1.34699	−	0.921321i
$136$	7.03340	−	12.1822i	0.0517162	−	0.0895751i
$137$	154.418	−	89.1533i	1.12714	−	0.650754i	0.183925	−	0.982940i	$-0.441120\pi$
$137$	154.418	−	89.1533i	1.12714	−	0.650754i	0.943214	+	0.332186i	$0.107786\pi$
$138$	7.57048	+	50.3975i	0.0548585	+	0.365199i
$139$	5.92693			0.0426398			0.0213199	−	0.999773i	$-0.493213\pi$
$139$	5.92693			0.0426398			0.0213199	+	0.999773i	$0.493213\pi$
$140$	152.649	+	88.1320i	1.09035	+	0.629514i
$141$	214.392	−	32.2049i	1.52051	−	0.228404i
$142$	50.8860	−	88.1372i	0.358352	−	0.620684i
$143$	3.47745	−	51.8883i	0.0243178	−	0.362855i
$144$	4.58159	−	19.9813i	0.0318166	−	0.138759i
$145$	−46.8844	−	81.2062i	−0.323341	−	0.560043i
$146$			50.5506i			0.346237i
$147$	−6.27291	−	41.7595i	−0.0426729	−	0.284078i
$148$	58.4090	+	101.167i	0.394656	+	0.683563i
$149$		−	21.2861i		−	0.142860i	−0.997446	−	0.0714300i	$-0.977244\pi$
$149$		−	21.2861i		−	0.142860i	0.997446	−	0.0714300i	$-0.0227562\pi$
$150$	−139.567	+	20.9650i	−0.930444	+	0.139767i
$151$	−73.3882	+	127.112i	−0.486014	+	0.841802i	−0.999871	−	0.0160745i	$-0.994883\pi$
$151$	−73.3882	+	127.112i	−0.486014	+	0.841802i	0.513856	+	0.857876i	$0.328216\pi$
$152$	−190.306	−	109.873i	−1.25201	−	0.722848i
$153$	−11.3382	+	12.1952i	−0.0741056	+	0.0797071i
$154$	17.9729	+	31.1300i	0.116707	+	0.202143i
$155$	−368.131	−	212.541i	−2.37504	−	1.37123i
$156$	87.2017	−	60.4009i	0.558985	−	0.387185i
$157$	−13.6091	−	23.5716i	−0.0866820	−	0.150138i	0.819425	−	0.573187i	$-0.194293\pi$
$157$	−13.6091	−	23.5716i	−0.0866820	−	0.150138i	−0.906107	+	0.423049i	$0.860960\pi$
$158$	−21.4949	−	12.4101i	−0.136044	−	0.0785449i
$159$	−123.856	−	155.470i	−0.778971	−	0.977800i
$160$	−134.589	−	233.115i	−0.841182	−	1.45697i
$161$			119.247i			0.740667i
$162$	39.9274	−	82.4884i	0.246465	−	0.509187i
$163$	−105.196	+	182.204i	−0.645371	+	1.11782i	0.338844	+	0.940843i	$0.389964\pi$
$163$	−105.196	+	182.204i	−0.645371	+	1.11782i	−0.984216	+	0.176974i	$0.943369\pi$
$164$	95.5916	+	55.1899i	0.582876	+	0.336524i
$165$	91.1380	+	35.8215i	0.552352	+	0.217100i
$166$	66.0693	−	114.435i	0.398008	−	0.689370i
$167$	38.3622	+	22.1484i	0.229714	+	0.132625i	0.610440	−	0.792062i	$-0.290993\pi$
$167$	38.3622	+	22.1484i	0.229714	+	0.132625i	−0.380726	+	0.924688i	$0.624326\pi$
$168$	−66.2651	+	168.593i	−0.394435	+	1.00353i
$169$	167.489	+	22.5508i	0.991057	+	0.133437i
$170$			17.0806i			0.100474i
$171$	190.508	+	177.120i	1.11408	+	1.03579i
$172$	−49.8920	−	86.4155i	−0.290070	−	0.502416i
$173$	51.0591	−	29.4790i	0.295139	−	0.170399i	−0.345118	−	0.938559i	$-0.612161\pi$
$173$	51.0591	−	29.4790i	0.295139	−	0.170399i	0.640257	+	0.768161i	$0.278828\pi$
$174$	30.5077	−	24.3041i	0.175331	−	0.139679i
$175$	−330.234			−1.88705
$176$			9.11186i			0.0517719i
$177$	8.08640	+	10.1504i	0.0456859	+	0.0573469i
$178$	13.6580	+	23.6564i	0.0767303	+	0.132901i
$179$	202.873	−	117.129i	1.13337	−	0.654351i	0.188589	−	0.982056i	$-0.439608\pi$
$179$	202.873	−	117.129i	1.13337	−	0.654351i	0.944780	+	0.327705i	$0.106275\pi$
$180$	58.6850	+	190.929i	0.326028	+	1.06072i
$181$	−257.758			−1.42408			−0.712040	−	0.702139i	$-0.752228\pi$
$181$	−257.758			−1.42408			−0.712040	+	0.702139i	$0.752228\pi$
$182$	−104.842	+	51.5113i	−0.576057	+	0.283029i
$183$	39.8666	+	15.6695i	0.217850	+	0.0856254i
$184$	57.0779	−	98.8619i	0.310206	−	0.537293i
$185$	−303.498	−	175.225i	−1.64053	−	0.947160i
$186$	64.6825	−	164.567i	0.347755	−	0.884767i
$187$	3.70070	−	6.40979i	0.0197898	−	0.0342770i
$188$	−170.224	−	98.2789i	−0.905447	−	0.522760i
$189$	121.061	−	176.993i	0.640533	−	0.936474i
$190$	266.827			1.40435
$191$	144.292	−	83.3072i	0.755457	−	0.436163i	−0.0722051	−	0.997390i	$-0.523004\pi$
$191$	144.292	−	83.3072i	0.755457	−	0.436163i	0.827662	+	0.561226i	$0.189670\pi$
$192$	66.1987	−	52.7376i	0.344785	−	0.274675i
$193$	−67.7322	+	117.316i	−0.350944	+	0.607852i	−0.986415	−	0.164272i	$-0.947473\pi$
$193$	−67.7322	+	117.316i	−0.350944	+	0.607852i	0.635471	+	0.772125i	$0.280806\pi$
$194$	−91.5852	+	52.8767i	−0.472089	+	0.272561i
$195$	−135.953	+	287.725i	−0.697197	+	1.47551i
$196$	−19.1429	+	33.1564i	−0.0976678	+	0.169166i
$197$	−67.0955	+	38.7376i	−0.340586	+	0.196638i	−0.660531	−	0.750798i	$-0.729669\pi$
$197$	−67.0955	+	38.7376i	−0.340586	+	0.196638i	0.319945	+	0.947436i	$0.396336\pi$
$198$	−9.10383	+	39.7038i	−0.0459790	+	0.200524i
$199$	−12.3535	+	21.3969i	−0.0620781	+	0.107522i	−0.895394	−	0.445274i	$-0.853106\pi$
$199$	−12.3535	+	21.3969i	−0.0620781	+	0.107522i	0.833316	+	0.552797i	$0.186439\pi$
$200$	273.780	+	158.067i	1.36890	+	0.790334i
$201$	40.0145	+	266.381i	0.199077	+	1.32528i
$202$	−51.2389			−0.253658
$203$	79.0402	−	45.6339i	0.389360	−	0.224797i
$204$	14.9296	−	2.24265i	0.0731843	−	0.0109934i
$205$	−331.135			−1.61529
$206$	−66.5734	+	38.4362i	−0.323172	+	0.186583i
$207$	−92.0122	+	98.9672i	−0.444503	+	0.478103i
$208$	−29.5446	−	1.98002i	−0.142041	−	0.00951931i
$209$	−100.131	−	57.8108i	−0.479097	−	0.276606i
$210$	−32.6747	−	217.519i	−0.155594	−	1.03581i
$211$	−179.209	+	310.398i	−0.849330	+	1.47108i	0.0324778	+	0.999472i	$0.489660\pi$
$211$	−179.209	+	310.398i	−0.849330	+	1.47108i	−0.881807	+	0.471610i	$0.843673\pi$
$212$			180.218i			0.850084i
$213$	266.863	−	40.0869i	1.25288	−	0.188201i
$214$	−6.17961	−	10.7034i	−0.0288767	−	0.0500159i
$215$	259.243	+	149.674i	1.20578	+	0.696158i
$216$	−185.083	+	88.7903i	−0.856868	+	0.411066i
$217$	206.872	−	358.312i	0.953325	−	1.65121i
$218$		−	27.0838i		−	0.124238i
$219$	−104.838	+	83.5197i	−0.478711	+	0.381368i
$220$	−44.3916	−	76.8885i	−0.201780	−	0.349493i
$221$	19.9792	+	13.3921i	0.0904034	+	0.0605978i
$222$	53.3261	−	135.674i	0.240208	−	0.611142i
$223$	−338.585			−1.51832			−0.759160	−	0.650904i	$-0.774390\pi$
$223$	−338.585			−1.51832			−0.759160	+	0.650904i	$0.774390\pi$
$224$	226.897	−	130.999i	1.01293	−	0.584818i
$225$	−274.071	−	254.811i	−1.21810	−	1.13249i
$226$	−164.994			−0.730061
$227$	−284.389	+	164.192i	−1.25282	+	0.723314i	−0.971668	−	0.236350i	$-0.924049\pi$
$227$	−284.389	+	164.192i	−1.25282	+	0.723314i	−0.281148	+	0.959664i	$0.590715\pi$
$228$	−35.0338	−	233.224i	−0.153657	−	1.02291i
$229$	−94.7010	−	164.027i	−0.413541	−	0.716275i	0.581733	−	0.813380i	$-0.302375\pi$
$229$	−94.7010	−	164.027i	−0.413541	−	0.716275i	−0.995274	+	0.0971052i	$0.969042\pi$
$230$			138.614i			0.602669i
$231$	−34.8661	+	88.7071i	−0.150935	+	0.384013i
$232$	−87.3708			−0.376598
$233$		−	13.4331i		−	0.0576527i	−0.999584	−	0.0288264i	$-0.990823\pi$
$233$		−	13.4331i		−	0.0576527i	0.999584	−	0.0288264i	$-0.00917699\pi$
$234$	−126.758	−	38.1462i	−0.541703	−	0.163018i
$235$	589.666			2.50922
$236$		−	11.7662i		−	0.0498566i
$237$	−9.77639	−	65.0825i	−0.0412506	−	0.274610i
$238$	−16.6250			−0.0698531
$239$	−130.900	+	75.5752i	−0.547699	+	0.316214i	−0.748193	−	0.663481i	$-0.769078\pi$
$239$	−130.900	+	75.5752i	−0.547699	+	0.316214i	0.200494	+	0.979695i	$0.435745\pi$
$240$	20.3964	−	51.8929i	0.0849849	−	0.216220i
$241$	4.55604	+	7.89130i	0.0189047	+	0.0327440i	0.875323	−	0.483539i	$-0.160649\pi$
$241$	4.55604	+	7.89130i	0.0189047	+	0.0327440i	−0.856418	+	0.516283i	$0.827315\pi$
$242$			118.794i			0.490884i
$243$	237.042	−	53.4812i	0.975480	−	0.220087i
$244$	−19.4183	−	33.6334i	−0.0795830	−	0.137842i
$245$		−	114.856i		−	0.468799i
$246$	−20.4615	−	136.215i	−0.0831769	−	0.553718i
$247$	209.206	−	312.106i	0.846988	−	1.26359i
$248$	−343.013	+	198.039i	−1.38312	+	0.798543i
$249$	346.489	−	52.0479i	1.39152	−	0.209028i
$250$	−153.069			−0.612275
$251$	−49.5787	−	28.6243i	−0.197525	−	0.114041i	0.397976	−	0.917396i	$-0.369713\pi$
$251$	−49.5787	−	28.6243i	−0.197525	−	0.114041i	−0.595500	+	0.803355i	$0.703046\pi$
$252$	−185.836	+	57.1197i	−0.737445	+	0.226666i
$253$	30.0321	−	52.0172i	0.118704	−	0.205601i
$254$	55.2980	−	31.9263i	0.217709	−	0.125694i
$255$	−35.4238	+	28.2206i	−0.138917	+	0.110669i
$256$	−226.030			−0.882931
$257$	233.785	+	134.976i	0.909668	+	0.525197i	0.880324	−	0.474373i	$-0.157325\pi$
$257$	233.785	+	134.976i	0.909668	+	0.525197i	0.0293434	+	0.999569i	$0.490658\pi$
$258$	−45.5503	+	115.890i	−0.176552	+	0.449187i
$259$	170.551	−	295.403i	0.658498	−	1.14055i
$260$	258.952	−	127.229i	0.995970	−	0.489342i
$261$	100.809	+	23.1150i	0.386243	+	0.0885632i
$262$	73.3469	+	127.041i	0.279950	+	0.484888i
$263$			423.518i			1.61034i	0.593047	+	0.805168i	$0.297925\pi$
$263$			423.518i			1.61034i	−0.593047	+	0.805168i	$0.702075\pi$
$264$	71.3654	−	56.8538i	0.270324	−	0.215355i
$265$	−270.323	−	468.213i	−1.02009	−	1.76684i
$266$			259.710i			0.976352i
$267$	−26.4955	+	67.4105i	−0.0992341	+	0.252474i
$268$	122.111	−	211.503i	0.455638	−	0.789189i
$269$	31.0174	+	17.9079i	0.115306	+	0.0665722i	0.556544	−	0.830818i	$-0.312127\pi$
$269$	31.0174	+	17.9079i	0.115306	+	0.0665722i	−0.441238	+	0.897390i	$0.645460\pi$
$270$	140.722	−	205.738i	0.521192	−	0.761994i
$271$	113.086	+	195.871i	0.417292	+	0.722771i	0.995666	−	0.0930007i	$-0.0296459\pi$
$271$	113.086	+	195.871i	0.417292	+	0.722771i	−0.578374	+	0.815772i	$0.696313\pi$
$272$	−3.64966	−	2.10713i	−0.0134179	−	0.00774681i
$273$	−280.050	−	132.327i	−1.02583	−	0.484714i
$274$	100.868	+	174.709i	0.368132	+	0.637623i
$275$	144.052	+	83.1684i	0.523825	+	0.302431i
$276$	121.158	−	18.1997i	0.438977	−	0.0659411i
$277$	245.696	+	425.558i	0.886990	+	1.53631i	0.843416	+	0.537261i	$0.180541\pi$
$277$	245.696	+	425.558i	0.886990	+	1.53631i	0.0435736	+	0.999050i	$0.486126\pi$
$278$			6.70573i			0.0241213i
$279$	448.166	−	137.751i	1.60633	−	0.493731i
$280$	−246.352	+	426.695i	−0.879830	+	1.52391i
$281$	−296.149	−	170.981i	−1.05391	−	0.608475i	−0.130168	−	0.991492i	$-0.541552\pi$
$281$	−296.149	−	170.981i	−1.05391	−	0.608475i	−0.923741	+	0.383017i	$0.874885\pi$
$282$	36.4367	+	242.563i	0.129208	+	0.860153i
$283$	17.3221	−	30.0028i	0.0612089	−	0.106017i	−0.833797	−	0.552071i	$-0.813838\pi$
$283$	17.3221	−	30.0028i	0.0612089	−	0.106017i	0.895006	+	0.446054i	$0.147171\pi$
$284$	−211.885	−	122.332i	−0.746075	−	0.430746i
$285$	440.851	+	553.376i	1.54684	+	1.94167i
$286$	58.7065	+	3.93439i	0.205267	+	0.0137566i
$287$		−	322.302i		−	1.12300i
$288$	289.389	+	66.3552i	1.00482	+	0.230400i
$289$	−142.788	−	247.317i	−0.494078	−	0.855767i
$290$	91.8768	−	53.0451i	0.316816	−	0.182914i
$291$	−260.979	−	102.577i	−0.896834	−	0.352498i
$292$	121.526			0.416184
$293$		−	509.607i		−	1.73927i	−0.493691	−	0.869637i	$-0.664353\pi$
$293$		−	509.607i		−	1.73927i	0.493691	−	0.869637i	$-0.335647\pi$
$294$	47.2467	−	7.09718i	0.160703	−	0.0241401i
$295$	17.6490	+	30.5689i	0.0598271	+	0.103624i
$296$	−282.790	+	163.269i	−0.955371	+	0.551584i
$297$	−97.3835	+	46.7179i	−0.327891	+	0.157299i
$298$	24.0831			0.0808159
$299$	162.136	+	108.681i	0.542261	+	0.363480i
$300$	50.4008	+	335.524i	0.168003	+	1.11841i
$301$	−145.682	+	252.328i	−0.483993	+	0.838300i
$302$	−143.815	−	83.0315i	−0.476208	−	0.274939i
$303$	−84.6568	−	106.265i	−0.279396	−	0.350710i
$304$	−32.9168	+	57.0135i	−0.108279	+	0.187544i
$305$	100.899	+	58.2540i	0.330816	+	0.190997i
$306$	−13.7977	−	12.8280i	−0.0450904	−	0.0419216i
$307$	−71.8316			−0.233979			−0.116990	−	0.993133i	$-0.537324\pi$
$307$	−71.8316			−0.233979			−0.116990	+	0.993133i	$0.537324\pi$
$308$	74.8376	−	43.2075i	0.242979	−	0.140284i
$309$	−189.706	−	74.5634i	−0.613935	−	0.241305i
$310$	240.469	−	416.504i	0.775705	−	1.34356i
$311$	−100.786	+	58.1890i	−0.324072	+	0.187103i	−0.653206	−	0.757180i	$-0.726576\pi$
$311$	−100.786	+	58.1890i	−0.324072	+	0.187103i	0.329134	+	0.944283i	$0.393243\pi$
$312$	168.837	+	243.752i	0.541143	+	0.781256i
$313$	160.351	−	277.737i	0.512304	−	0.887337i	−0.487594	−	0.873071i	$-0.662125\pi$
$313$	160.351	−	277.737i	0.512304	−	0.887337i	0.999898	−	0.0142666i	$-0.00454135\pi$
$314$	26.6689	−	15.3973i	0.0849329	−	0.0490360i
$315$	397.131	−	427.150i	1.26073	−	1.35603i
$316$	−29.8343	+	51.6746i	−0.0944125	+	0.163527i
$317$	513.217	+	296.306i	1.61898	+	0.934719i	0.987184	+	0.159584i	$0.0510152\pi$
$317$	513.217	+	296.306i	1.61898	+	0.934719i	0.631796	+	0.775135i	$0.282318\pi$
$318$	175.899	−	140.131i	0.553142	−	0.440664i
$319$	−45.9710			−0.144110
$320$	199.364	−	115.103i	0.623011	−	0.359696i
$321$	11.9880	−	30.5001i	0.0373458	−	0.0950160i
$322$	−134.917			−0.418996
$323$	46.3110	−	26.7377i	0.143378	−	0.0827792i
$324$	−198.305	−	95.9870i	−0.612053	−	0.296256i
$325$	−300.971	+	449.006i	−0.926064	+	1.38156i
$326$	−206.146	−	119.018i	−0.632349	−	0.365087i
$327$	56.1695	−	44.7478i	0.171772	−	0.136843i
$328$	−154.270	+	267.204i	−0.470337	+	0.814647i
$329$			573.937i			1.74449i
$330$	−40.5285	+	103.114i	−0.122814	+	0.312466i
$331$	−34.2548	−	59.3310i	−0.103489	−	0.179248i	0.809631	−	0.586939i	$-0.199667\pi$
$331$	−34.2548	−	59.3310i	−0.103489	−	0.179248i	−0.913120	+	0.407691i	$0.866334\pi$
$332$	−275.107	−	158.833i	−0.828636	−	0.478413i
$333$	369.481	−	113.566i	1.10955	−	0.341039i
$334$	−25.0588	+	43.4031i	−0.0750262	+	0.129949i
$335$			732.656i			2.18703i
$336$	50.5088	+	19.8523i	0.150324	+	0.0590843i
$337$	299.382	+	518.545i	0.888373	+	1.53871i	0.841798	+	0.539793i	$0.181497\pi$
$337$	299.382	+	518.545i	0.888373	+	1.53871i	0.0465755	+	0.998915i	$0.485169\pi$
$338$	−25.5140	+	189.497i	−0.0754851	+	0.560642i
$339$	−272.602	−	342.183i	−0.804136	−	1.00939i
$340$	41.0625			0.120772
$341$	−180.480	+	104.200i	−0.529266	+	0.305572i
$342$	−200.394	+	215.541i	−0.585947	+	0.630238i
$343$	−277.368			−0.808652
$344$	241.555	−	139.462i	0.702193	−	0.405412i
$345$	−287.473	+	229.018i	−0.833256	+	0.663819i
$346$	33.3526	+	57.7683i	0.0963947	+	0.166960i
$347$		−	198.188i		−	0.571147i	−0.958357	−	0.285573i	$-0.907816\pi$
$347$		−	198.188i		−	0.571147i	0.958357	−	0.285573i	$-0.0921841\pi$
$348$	−58.4281	−	73.3416i	−0.167897	−	0.210752i
$349$	303.509			0.869653			0.434826	−	0.900514i	$-0.356810\pi$
$349$	303.509			0.869653			0.434826	+	0.900514i	$0.356810\pi$
$350$		−	373.627i		−	1.06750i
$351$	−130.318	−	325.911i	−0.371277	−	0.928522i
$352$	−131.967			−0.374907
$353$			302.626i			0.857297i	0.903471	+	0.428648i	$0.141010\pi$
$353$			302.626i			0.857297i	−0.903471	+	0.428648i	$0.858990\pi$
$354$	−11.4842	+	9.14896i	−0.0324412	+	0.0258445i
$355$	733.982			2.06755
$356$	56.8708	−	32.8344i	0.159749	−	0.0922314i
$357$	−27.4679	−	34.4789i	−0.0769408	−	0.0965795i
$358$	132.520	+	229.531i	0.370167	+	0.641148i
$359$		−	107.705i		−	0.300014i	−0.988685	−	0.150007i	$-0.952070\pi$
$359$		−	107.705i		−	0.300014i	0.988685	−	0.150007i	$-0.0479296\pi$
$360$	−533.697	+	164.040i	−1.48249	+	0.455668i
$361$	−237.185	−	410.816i	−0.657022	−	1.13800i
$362$		−	291.628i		−	0.805602i
$363$	−246.368	+	196.271i	−0.678700	+	0.540691i
$364$	123.835	+	252.045i	0.340207	+	0.692431i
$365$	−315.729	+	182.286i	−0.865010	+	0.499414i
$366$	−17.7284	+	45.1051i	−0.0484383	+	0.123238i
$367$	−64.2993			−0.175202			−0.0876012	−	0.996156i	$-0.527920\pi$
$367$	−64.2993			−0.175202			−0.0876012	+	0.996156i	$0.527920\pi$
$368$	−29.6180	−	17.0999i	−0.0804836	−	0.0464672i
$369$	248.691	−	267.489i	0.673959	−	0.724902i
$370$	198.249	−	343.378i	0.535809	−	0.928048i
$371$	455.725	−	263.113i	1.22837	−	0.709199i
$372$	−395.625	−	155.499i	−1.06351	−	0.418009i
$373$	−209.099			−0.560588			−0.280294	−	0.959914i	$-0.590432\pi$
$373$	−209.099			−0.560588			−0.280294	+	0.959914i	$0.590432\pi$
$374$	7.25205	+	4.18697i	0.0193905	+	0.0111951i
$375$	−252.900	−	317.451i	−0.674399	−	0.846537i
$376$	274.716	−	475.822i	0.730627	−	1.26548i
$377$	9.98956	−	149.058i	0.0264975	−	0.395379i
$378$	200.251	+	136.968i	0.529763	+	0.362350i
$379$	−105.972	−	183.549i	−0.279610	−	0.484298i	0.691678	−	0.722206i	$-0.256872\pi$
$379$	−105.972	−	183.549i	−0.279610	−	0.484298i	−0.971288	+	0.237908i	$0.923538\pi$
$380$		−	641.462i		−	1.68806i
$381$	157.576	+	61.9347i	0.413584	+	0.162558i
$382$	94.2539	+	163.252i	0.246738	+	0.427362i
$383$		−	232.095i		−	0.605991i	−0.952992	−	0.302996i	$-0.902013\pi$
$383$		−	232.095i		−	0.605991i	0.952992	−	0.302996i	$-0.0979868\pi$
$384$	−186.996	−	234.726i	−0.486970	−	0.611266i
$385$	−129.621	+	224.510i	−0.336677	+	0.583142i
$386$	−132.731	−	76.6322i	−0.343862	−	0.198529i
$387$	−315.604	+	97.0061i	−0.815515	+	0.250662i
$388$	127.118	+	220.174i	0.327623	+	0.567460i
$389$	−106.814	−	61.6691i	−0.274586	−	0.158532i	0.356384	−	0.934340i	$-0.384010\pi$
$389$	−106.814	−	61.6691i	−0.274586	−	0.158532i	−0.630970	+	0.775807i	$0.717343\pi$
$390$	−325.532	−	153.818i	−0.834698	−	0.394404i
$391$	13.8900	+	24.0581i	0.0355242	+	0.0615297i
$392$	−92.6811	−	53.5095i	−0.236431	−	0.136504i
$393$	−142.288	+	362.011i	−0.362055	+	0.921148i
$394$	−43.8278	−	75.9119i	−0.111238	−	0.192670i
$395$		−	179.004i		−	0.453174i
$396$	95.4494	+	21.8860i	0.241034	+	0.0552676i
$397$	254.354	−	440.555i	0.640691	−	1.10971i	−0.344587	−	0.938754i	$-0.611981\pi$
$397$	254.354	−	440.555i	0.640691	−	1.10971i	0.985279	−	0.170956i	$-0.0546855\pi$
$398$	−24.2085	−	13.9768i	−0.0608254	−	0.0351176i
$399$	−538.615	+	429.092i	−1.34991	+	1.07542i
$400$	47.3551	−	82.0215i	0.118388	−	0.205054i
$401$	−438.023	−	252.893i	−1.09233	−	0.630655i	−0.158132	−	0.987418i	$-0.550547\pi$
$401$	−438.023	−	252.893i	−1.09233	−	0.630655i	−0.934195	+	0.356762i	$0.883881\pi$
$402$	−301.383	+	45.2724i	−0.749710	+	0.112618i
$403$	−298.643	−	607.836i	−0.741050	−	1.50828i
$404$			123.180i			0.304902i
$405$	659.184	−	48.0757i	1.62761	−	0.118705i
$406$	51.6302	+	89.4261i	0.127168	+	0.220261i
$407$	−148.793	+	85.9055i	−0.365584	+	0.211070i
$408$	6.26882	+	41.7322i	0.0153647	+	0.102285i
$409$	368.824			0.901769			0.450885	−	0.892582i	$-0.351109\pi$
$409$	368.824			0.901769			0.450885	+	0.892582i	$0.351109\pi$
$410$		−	374.646i		−	0.913771i
$411$	−195.677	+	497.845i	−0.476099	+	1.21130i
$412$	92.4021	+	160.045i	0.224277	+	0.388459i
$413$	−29.7536	+	17.1782i	−0.0720425	+	0.0415938i
$414$	−111.972	−	104.103i	−0.270463	−	0.251456i
$415$	952.986			2.29635
$416$	28.6766	−	427.895i	0.0689342	−	1.02859i
$417$	−13.9071	+	11.0792i	−0.0333504	+	0.0265688i
$418$	65.4071	−	113.288i	0.156476	−	0.271025i
$419$	488.999	+	282.323i	1.16706	+	0.673803i	0.952986	−	0.303014i	$-0.0979929\pi$
$419$	488.999	+	282.323i	1.16706	+	0.673803i	0.214075	+	0.976817i	$0.431326\pi$
$420$	−522.925	+	78.5513i	−1.24506	+	0.187027i
$421$	−183.363	+	317.594i	−0.435541	+	0.754379i	−0.997340	−	0.0728949i	$-0.976776\pi$
$421$	−183.363	+	317.594i	−0.435541	+	0.754379i	0.561799	+	0.827274i	$0.310110\pi$
$422$	−351.185	−	202.757i	−0.832192	−	0.480466i
$423$	−442.854	+	476.329i	−1.04694	+	1.12607i
$424$	−503.757			−1.18811
$425$	−66.6245	+	38.4657i	−0.156764	+	0.0905075i
$426$	45.3543	+	301.929i	0.106466	+	0.708753i
$427$	−56.7002	+	98.2076i	−0.132787	+	0.229994i
$428$	−25.7314	+	14.8560i	−0.0601201	+	0.0347104i
$429$	88.8352	+	128.253i	0.207075	+	0.298957i
$430$	−169.341	+	293.308i	−0.393817	+	0.682111i
$431$	−55.7008	+	32.1589i	−0.129236	+	0.0746145i	−0.563224	−	0.826304i	$-0.690439\pi$
$431$	−55.7008	+	32.1589i	−0.129236	+	0.0746145i	0.433988	+	0.900919i	$0.357106\pi$
$432$	26.6006	+	55.4490i	0.0615755	+	0.128354i
$433$	−401.064	+	694.664i	−0.926246	+	1.60430i	−0.136701	+	0.990612i	$0.543650\pi$
$433$	−401.064	+	694.664i	−0.926246	+	1.60430i	−0.789545	+	0.613692i	$0.789683\pi$
$434$	405.395	+	234.055i	0.934089	+	0.539296i
$435$	261.810	+	102.903i	0.601861	+	0.236560i
$436$	−65.1105			−0.149336
$437$	375.826	−	216.983i	0.860014	−	0.496529i
$438$	−94.4942	−	118.613i	−0.215740	−	0.270807i
$439$	−384.741			−0.876403			−0.438201	−	0.898877i	$-0.644384\pi$
$439$	−384.741			−0.876403			−0.438201	+	0.898877i	$0.644384\pi$
$440$	214.924	−	124.086i	0.488463	−	0.282014i
$441$	92.7799	+	86.2597i	0.210385	+	0.195600i
$442$	−15.1518	+	22.6044i	−0.0342802	+	0.0511413i
$443$	341.114	+	196.942i	0.770010	+	0.444565i	0.832878	−	0.553457i	$-0.186692\pi$
$443$	341.114	+	196.942i	0.770010	+	0.444565i	−0.0628685	+	0.998022i	$0.520025\pi$
$444$	−326.165	−	128.198i	−0.734605	−	0.288734i
$445$	−98.5018	+	170.610i	−0.221352	+	0.383393i
$446$		−	383.076i		−	0.858914i
$447$	39.7901	+	49.9464i	0.0890159	+	0.111737i
$448$	112.033	+	194.046i	0.250073	+	0.433138i
$449$	630.717	+	364.144i	1.40471	+	0.811012i	0.994872	−	0.101144i	$-0.0322504\pi$
$449$	630.717	+	364.144i	1.40471	+	0.811012i	0.409842	+	0.912156i	$0.365584\pi$
$450$	288.293	−	310.085i	0.640651	−	0.689077i
$451$	−81.1709	+	140.592i	−0.179980	+	0.311734i
$452$			396.651i			0.877547i
$453$	−65.4103	−	435.444i	−0.144394	−	0.961244i
$454$	−185.767	−	321.758i	−0.409179	−	0.708719i
$455$	−699.791	−	469.073i	−1.53800	−	1.03093i
$456$	651.924	−	97.9289i	1.42966	−	0.214756i
$457$	−452.813			−0.990837			−0.495419	−	0.868654i	$-0.664985\pi$
$457$	−452.813			−0.990837			−0.495419	+	0.868654i	$0.664985\pi$
$458$	185.580	−	107.145i	0.405197	−	0.233941i
$459$	3.80772	−	49.8095i	0.00829569	−	0.108518i
$460$	333.233			0.724420
$461$	−198.203	+	114.432i	−0.429940	+	0.248226i	−0.699321	−	0.714808i	$-0.746514\pi$
$461$	−198.203	+	114.432i	−0.429940	+	0.248226i	0.269381	+	0.963034i	$0.413181\pi$
$462$	−100.363	−	39.4475i	−0.217236	−	0.0853842i
$463$	129.217	+	223.811i	0.279087	+	0.483393i	0.971158	−	0.238436i	$-0.0766348\pi$
$463$	129.217	+	223.811i	0.279087	+	0.483393i	−0.692071	+	0.721830i	$0.743301\pi$
$464$			26.1754i			0.0564124i
$465$	1261.10	−	189.436i	2.71203	−	0.407389i
$466$	15.1982			0.0326142
$467$		−	363.509i		−	0.778393i	−0.921155	−	0.389196i	$-0.872753\pi$
$467$		−	363.509i		−	0.778393i	0.921155	−	0.389196i	$-0.127247\pi$
$468$	−91.7050	+	304.732i	−0.195951	+	0.651138i
$469$	−713.114			−1.52050
$470$			667.148i			1.41946i
$471$	75.9950	+	29.8696i	0.161348	+	0.0634175i
$472$	32.8895			0.0696812
$473$	127.096	−	73.3791i	0.268703	−	0.155136i
$474$	73.6344	−	11.0610i	0.155347	−	0.0233355i
$475$	600.895	+	1040.78i	1.26504	+	2.19112i
$476$			39.9672i			0.0839648i
$477$	581.240	+	133.275i	1.21853	+	0.279402i
$478$	−85.5058	−	148.100i	−0.178882	−	0.309834i
$479$		−	649.207i		−	1.35534i	−0.735367	−	0.677669i	$-0.762990\pi$
$479$		−	649.207i		−	1.35534i	0.735367	−	0.677669i	$-0.237010\pi$
$480$	751.566	+	295.401i	1.56576	+	0.615418i
$481$	−246.210	−	501.118i	−0.511871	−	1.04182i
$482$	−8.92822	+	5.15471i	−0.0185233	+	0.0106944i
$483$	−222.909	−	279.805i	−0.461509	−	0.579307i
$484$	285.585			0.590052
$485$	−660.514	−	381.348i	−1.36188	−	0.786285i
$486$	60.5086	+	268.189i	0.124503	+	0.551830i
$487$	238.062	−	412.335i	0.488833	−	0.846684i	−0.511084	−	0.859531i	$-0.670756\pi$
$487$	238.062	−	412.335i	0.488833	−	0.846684i	0.999917	+	0.0128467i	$0.00408935\pi$
$488$	94.0144	−	54.2792i	0.192652	−	0.111228i
$489$	−93.7600	−	624.170i	−0.191738	−	1.27642i
$490$	129.948			0.265200
$491$	−526.634	−	304.052i	−1.07257	−	0.619251i	−0.143691	−	0.989623i	$-0.545897\pi$
$491$	−526.634	−	304.052i	−1.07257	−	0.619251i	−0.928884	+	0.370371i	$0.879230\pi$
$492$	−327.465	+	49.1903i	−0.665580	+	0.0999802i
$493$	10.6309	−	18.4132i	0.0215637	−	0.0373493i
$494$	353.117	+	236.696i	0.714812	+	0.479142i
$495$	−280.810	+	86.3115i	−0.567293	+	0.174367i
$496$	59.3303	+	102.763i	0.119618	+	0.207184i
$497$			714.404i			1.43743i
$498$	58.8870	+	392.017i	0.118247	+	0.787184i
$499$	41.7382	+	72.2927i	0.0836437	+	0.144875i	0.904812	−	0.425810i	$-0.140011\pi$
$499$	41.7382	+	72.2927i	0.0836437	+	0.144875i	−0.821169	+	0.570685i	$0.806678\pi$
$500$			367.983i			0.735966i
$501$	−131.416	+	19.7407i	−0.262308	+	0.0394027i
$502$	32.3855	−	56.0933i	0.0645130	−	0.111740i
$503$	294.128	+	169.815i	0.584747	+	0.337604i	0.763018	−	0.646378i	$-0.223717\pi$
$503$	294.128	+	169.815i	0.584747	+	0.337604i	−0.178270	+	0.983982i	$0.557050\pi$
$504$	−159.665	−	519.461i	−0.316795	−	1.03068i
$505$	−184.768	−	320.028i	−0.365877	−	0.633718i
$506$	58.8523	+	33.9784i	0.116309	+	0.0671509i
$507$	−435.154	+	260.173i	−0.858292	+	0.513161i
$508$	−76.7521	−	132.939i	−0.151087	−	0.261690i
$509$	60.3639	+	34.8511i	0.118593	+	0.0684698i	0.558123	−	0.829758i	$-0.311522\pi$
$509$	60.3639	+	34.8511i	0.118593	+	0.0684698i	−0.439530	+	0.898228i	$0.644855\pi$
$510$	−31.9288	−	40.0785i	−0.0626055	−	0.0785852i
$511$	−177.424	−	307.307i	−0.347209	−	0.601384i
$512$			144.411i			0.282053i
$513$	−778.104	−	59.4827i	−1.51677	−	0.115951i
$514$	−152.711	+	264.504i	−0.297104	+	0.514599i
$515$	−480.129	−	277.203i	−0.932289	−	0.538257i
$516$	278.604	+	109.505i	0.539931	+	0.212218i
$517$	144.545	−	250.358i	0.279583	−	0.484252i
$518$	334.219	+	192.961i	0.645210	+	0.372512i
$519$	−64.7015	+	164.615i	−0.124666	+	0.317177i
$520$	355.638	+	723.840i	0.683920	+	1.39200i
$521$			256.792i			0.492884i	0.969158	+	0.246442i	$0.0792614\pi$
$521$			256.792i			0.492884i	−0.969158	+	0.246442i	$0.920739\pi$
$522$	−26.1523	+	114.056i	−0.0501002	+	0.218498i
$523$	207.295	+	359.045i	0.396357	+	0.686511i	0.993273	−	0.115793i	$-0.0369409\pi$
$523$	207.295	+	359.045i	0.396357	+	0.686511i	−0.596916	+	0.802303i	$0.703608\pi$
$524$	305.411	−	176.329i	0.582844	−	0.336505i
$525$	774.869	−	617.305i	1.47594	−	1.17582i
$526$	−479.169			−0.910967
$527$		−	96.3857i		−	0.182895i
$528$	−17.0328	−	21.3803i	−0.0322591	−	0.0404930i
$529$	−151.779	−	262.889i	−0.286917	−	0.496956i
$530$	529.737	−	305.844i	0.999504	−	0.577064i
$531$	−37.9483	−	8.70132i	−0.0714657	−	0.0163867i
$532$	624.352			1.17359
$533$	−438.222	−	293.742i	−0.822180	−	0.551111i
$534$	−76.2683	−	29.9770i	−0.142825	−	0.0561368i
$535$	44.5675	−	77.1931i	0.0833037	−	0.144286i
$536$	591.206	+	341.333i	1.10300	+	0.636815i
$537$	−257.078	+	654.065i	−0.478731	+	1.21800i
$538$	−20.2610	+	35.0931i	−0.0376599	+	0.0652289i
$539$	−48.7651	−	28.1545i	−0.0904733	−	0.0522348i
$540$	−494.603	−	338.301i	−0.915931	−	0.626483i
$541$	262.571			0.485344			0.242672	−	0.970108i	$-0.421976\pi$
$541$	262.571			0.485344			0.242672	+	0.970108i	$0.421976\pi$
$542$	−221.609	+	127.946i	−0.408872	+	0.236062i
$543$	604.811	−	481.827i	1.11383	−	0.887343i
$544$	30.5176	−	52.8581i	0.0560986	−	0.0971656i
$545$	169.160	−	97.6645i	0.310385	−	0.179201i
$546$	149.715	−	316.849i	0.274203	−	0.580310i
$547$	341.315	−	591.174i	0.623976	−	1.08076i	−0.364762	−	0.931101i	$-0.618850\pi$
$547$	341.315	−	591.174i	0.623976	−	1.08076i	0.988738	−	0.149657i	$-0.0478169\pi$
$548$	420.007	−	242.491i	0.766435	−	0.442502i
$549$	−122.835	+	37.7553i	−0.223743	+	0.0687711i
$550$	−94.0968	+	162.980i	−0.171085	+	0.296328i
$551$	−287.644	−	166.071i	−0.522040	−	0.301400i
$552$	50.8731	+	338.668i	0.0921614	+	0.613529i
$553$	174.229			0.315061
$554$	−481.477	+	277.981i	−0.869092	+	0.501770i
$555$	1039.68	−	156.176i	1.87330	−	0.281399i
$556$	16.1208			0.0289943
$557$	−88.9427	+	51.3511i	−0.159682	+	0.0921923i	−0.577711	−	0.816241i	$-0.696054\pi$
$557$	−88.9427	+	51.3511i	−0.159682	+	0.0921923i	0.418030	+	0.908433i	$0.362721\pi$
$558$	155.852	+	507.055i	0.279304	+	0.908700i
$559$	210.309	+	428.047i	0.376223	+	0.765736i
$560$	127.833	+	73.8046i	0.228274	+	0.131794i
$561$	3.29840	+	21.9578i	0.00587950	+	0.0391405i
$562$	193.449	−	335.063i	0.344214	−	0.596197i
$563$			546.016i			0.969834i	0.874560	+	0.484917i	$0.161150\pi$
$563$			546.016i			0.969834i	−0.874560	+	0.484917i	$0.838850\pi$
$564$	583.131	−	87.5952i	1.03392	−	0.155311i
$565$	−594.969	−	1030.52i	−1.05304	−	1.82392i
$566$	33.9452	+	19.5983i	0.0599738	+	0.0346259i
$567$	46.7934	+	641.601i	0.0825280	+	1.13157i
$568$	341.951	−	592.276i	0.602026	−	1.04274i
$569$			469.135i			0.824491i	0.911073	+	0.412245i	$0.135255\pi$
$569$			469.135i			0.824491i	−0.911073	+	0.412245i	$0.864745\pi$
$570$	−626.090	+	498.779i	−1.09840	+	0.875050i
$571$	56.3026	+	97.5189i	0.0986035	+	0.170786i	0.911107	−	0.412170i	$-0.135229\pi$
$571$	56.3026	+	97.5189i	0.0986035	+	0.170786i	−0.812503	+	0.582957i	$0.801896\pi$
$572$	9.45842	−	141.133i	0.0165357	−	0.246735i
$573$	−182.845	+	465.200i	−0.319102	+	0.811867i
$574$	364.653			0.635284
$575$	−540.675	+	312.159i	−0.940305	+	0.542885i
$576$	−56.7480	+	247.490i	−0.0985208	+	0.429670i
$577$	369.071			0.639638			0.319819	−	0.947479i	$-0.396378\pi$
$577$	369.071			0.639638			0.319819	+	0.947479i	$0.396378\pi$
$578$	279.814	−	161.551i	0.484108	−	0.279500i
$579$	−60.3691	−	401.884i	−0.104264	−	0.694100i
$580$	−127.522	−	220.875i	−0.219866	−	0.380820i
$581$			927.567i			1.59650i
$582$	116.056	−	295.272i	0.199408	−	0.507339i
$583$	−265.057			−0.454643
$584$			339.697i			0.581673i
$585$	−218.839	−	929.263i	−0.374084	−	1.58848i
$586$	576.570			0.983908
$587$		−	304.408i		−	0.518582i	−0.965799	−	0.259291i	$-0.916511\pi$
$587$		−	304.408i		−	0.518582i	0.965799	−	0.259291i	$-0.0834889\pi$
$588$	−17.0619	−	113.583i	−0.0290168	−	0.193168i
$589$	−1505.70			−2.55636
$590$	−34.5857	+	19.9681i	−0.0586199	+	0.0338442i
$591$	85.0226	−	216.317i	0.143862	−	0.366018i
$592$	48.9136	+	84.7208i	0.0826243	+	0.143110i
$593$			812.895i			1.37082i	0.728158	+	0.685409i	$0.240377\pi$
$593$			812.895i			1.37082i	−0.728158	+	0.685409i	$0.759623\pi$
$594$	−52.8567	−	110.180i	−0.0889843	−	0.185488i
$595$	−59.9501	−	103.837i	−0.100756	−	0.174515i
$596$		−	57.8968i		−	0.0971423i
$597$	−11.0106	−	73.2988i	−0.0184432	−	0.122779i
$598$	−122.961	+	183.441i	−0.205621	+	0.306758i
$599$	714.222	−	412.356i	1.19236	−	0.688407i	0.233516	−	0.972353i	$-0.424977\pi$
$599$	714.222	−	412.356i	1.19236	−	0.688407i	0.958840	+	0.283946i	$0.0916435\pi$
$600$	−937.878	+	140.884i	−1.56313	+	0.234806i
$601$	14.8864			0.0247694			0.0123847	−	0.999923i	$-0.496058\pi$
$601$	14.8864			0.0247694			0.0123847	+	0.999923i	$0.496058\pi$
$602$	−285.484	−	164.824i	−0.474227	−	0.273795i
$603$	−591.836	−	550.244i	−0.981486	−	0.912511i
$604$	−199.611	+	345.736i	−0.330482	+	0.572411i
$605$	−741.961	+	428.372i	−1.22638	+	0.708052i
$606$	120.228	−	95.7808i	0.198397	−	0.158054i
$607$	425.032			0.700218			0.350109	−	0.936709i	$-0.386144\pi$
$607$	425.032			0.700218			0.350109	+	0.936709i	$0.386144\pi$
$608$	−825.727	−	476.734i	−1.35810	−	0.784102i
$609$	−100.159	+	254.826i	−0.164464	+	0.418434i
$610$	−65.9086	+	114.157i	−0.108047	+	0.187143i
$611$	780.361	+	523.079i	1.27719	+	0.856103i
$612$	−30.8390	+	33.1701i	−0.0503906	+	0.0541995i
$613$	−353.559	−	612.383i	−0.576769	−	0.998993i	−0.995847	−	0.0910431i	$-0.970980\pi$
$613$	−353.559	−	612.383i	−0.576769	−	0.998993i	0.419078	−	0.907950i	$-0.362353\pi$
$614$		−	81.2703i		−	0.132362i
$615$	776.983	−	618.989i	1.26339	−	1.00649i
$616$	120.777	+	209.191i	0.196066	+	0.339596i
$617$			340.821i			0.552384i	0.961102	+	0.276192i	$0.0890726\pi$
$617$			340.821i			0.552384i	−0.961102	+	0.276192i	$0.910927\pi$
$618$	84.3610	−	214.633i	0.136507	−	0.347303i
$619$	−209.801	+	363.386i	−0.338935	+	0.587053i	−0.984233	−	0.176878i	$-0.943400\pi$
$619$	−209.801	+	363.386i	−0.338935	+	0.587053i	0.645297	+	0.763931i	$0.276733\pi$
$620$	−1001.29	−	578.096i	−1.61499	−	0.932413i
$621$	30.9007	−	404.218i	0.0497595	−	0.650914i
$622$	−65.8351	−	114.030i	−0.105844	−	0.183328i
$623$	−166.059	−	95.8744i	−0.266548	−	0.153892i
$624$	73.0255	−	50.5817i	0.117028	−	0.0810604i
$625$	−32.2114	−	55.7918i	−0.0515383	−	0.0892669i
$626$	314.231	+	181.422i	0.501967	+	0.289811i
$627$	343.016	−	51.5263i	0.547075	−	0.0821791i
$628$	−37.0157	−	64.1131i	−0.0589423	−	0.102091i
$629$		−	79.4632i		−	0.126333i
$630$	483.277	+	449.315i	0.767107	+	0.713198i
$631$	−12.5405	+	21.7208i	−0.0198740	+	0.0344228i	−0.875791	−	0.482690i	$-0.839660\pi$
$631$	−12.5405	+	21.7208i	−0.0198740	+	0.0344228i	0.855917	+	0.517113i	$0.172993\pi$
$632$	−144.444	−	83.3949i	−0.228551	−	0.131954i
$633$	−159.727	−	1063.32i	−0.252334	−	1.67981i
$634$	−335.241	+	580.654i	−0.528771	+	0.915858i
$635$	398.810	+	230.253i	0.628047	+	0.362603i
$636$	−336.881	−	422.868i	−0.529687	−	0.664887i
$637$	101.886	−	152.000i	0.159947	−	0.238618i
$638$		−	52.0117i		−	0.0815230i
$639$	−551.240	+	592.907i	−0.862660	+	0.927867i
$640$	−408.129	−	706.901i	−0.637702	−	1.10453i
$641$	950.859	−	548.978i	1.48340	−	0.856441i	0.483577	−	0.875302i	$-0.339337\pi$
$641$	950.859	−	548.978i	1.48340	−	0.856441i	0.999822	+	0.0188614i	$0.00600411\pi$
$642$	34.5079	+	13.5632i	0.0537506	+	0.0211265i
$643$	−221.450			−0.344401			−0.172200	−	0.985062i	$-0.555088\pi$
$643$	−221.450			−0.344401			−0.172200	+	0.985062i	$0.555088\pi$
$644$			324.345i			0.503641i
$645$	−888.081	+	133.403i	−1.37687	+	0.206827i
$646$	30.2510	+	52.3963i	0.0468282	+	0.0811088i
$647$	33.9957	−	19.6274i	0.0525436	−	0.0303361i	−0.473498	−	0.880795i	$-0.657009\pi$
$647$	33.9957	−	19.6274i	0.0525436	−	0.0303361i	0.526042	+	0.850459i	$0.323676\pi$
$648$	268.309	−	554.316i	0.414058	−	0.855426i
$649$	17.3052			0.0266643
$650$	−508.006	−	340.518i	−0.781548	−	0.523875i
$651$	184.383	+	1227.46i	0.283230	+	1.88550i
$652$	−286.125	+	495.583i	−0.438842	+	0.760096i
$653$	79.9523	+	46.1605i	0.122438	+	0.0706898i	0.559968	−	0.828514i	$-0.310813\pi$
$653$	79.9523	+	46.1605i	0.122438	+	0.0706898i	−0.437530	+	0.899204i	$0.644147\pi$
$654$	50.6277	+	63.5502i	0.0774124	+	0.0971716i
$655$	−528.979	+	916.219i	−0.807602	+	1.39881i
$656$	80.0515	+	46.2178i	0.122030	+	0.0704539i
$657$	89.8708	−	391.946i	0.136790	−	0.596569i
$658$	−649.353			−0.986859
$659$	−638.277	+	368.509i	−0.968554	+	0.559195i	−0.898795	−	0.438369i	$-0.855556\pi$
$659$	−638.277	+	368.509i	−0.968554	+	0.559195i	−0.0697589	+	0.997564i	$0.522223\pi$
$660$	247.889	+	97.4322i	0.375590	+	0.147624i
$661$	293.632	−	508.586i	0.444224	−	0.769419i	−0.553774	−	0.832667i	$-0.686813\pi$
$661$	293.632	−	508.586i	0.444224	−	0.769419i	0.997998	+	0.0632484i	$0.0201460\pi$
$662$	67.1271	−	38.7559i	0.101400	−	0.0585436i
$663$	−71.9135	+	5.92338i	−0.108467	+	0.00893422i
$664$	443.981	−	768.998i	0.668646	−	1.15813i
$665$	−1622.09	+	936.515i	−2.43924	+	1.40829i
$666$	128.489	+	418.031i	0.192926	+	0.627674i
$667$	86.2724	−	149.428i	0.129344	−	0.224030i
$668$	104.343	+	60.2423i	0.156202	+	0.0901830i
$669$	794.466	−	632.917i	1.18754	−	0.946064i
$670$	−828.928			−1.23721
$671$	49.4666	−	28.5596i	0.0737207	−	0.0425627i
$672$	−287.521	+	731.519i	−0.427859	+	1.08857i
$673$	117.694			0.174880			0.0874399	−	0.996170i	$-0.472131\pi$
$673$	117.694			0.174880			0.0874399	+	0.996170i	$0.472131\pi$
$674$	−586.682	+	338.721i	−0.870448	+	0.502553i
$675$	1119.41	+	85.5737i	1.65838	+	0.126776i
$676$	455.558	+	61.3366i	0.673902	+	0.0907346i
$677$	−638.175	−	368.450i	−0.942651	−	0.544240i	−0.0518606	−	0.998654i	$-0.516515\pi$
$677$	−638.175	−	368.450i	−0.942651	−	0.544240i	−0.890790	+	0.454415i	$0.849848\pi$
$678$	387.146	−	308.422i	0.571011	−	0.454900i
$679$	371.176	−	642.896i	0.546651	−	0.946828i
$680$			114.781i			0.168795i
$681$	360.375	−	916.874i	0.529185	−	1.34636i
$682$	−117.892	−	204.195i	−0.172862	−	0.299406i
$683$	495.258	+	285.937i	0.725122	+	0.418649i	0.816635	−	0.577155i	$-0.195837\pi$
$683$	495.258	+	285.937i	0.725122	+	0.418649i	−0.0915131	+	0.995804i	$0.529170\pi$
$684$	518.170	+	481.755i	0.757558	+	0.704320i
$685$	−727.463	+	1260.00i	−1.06199	+	1.83942i
$686$		−	313.814i		−	0.457455i
$687$	528.824	+	207.853i	0.769759	+	0.302552i
$688$	−41.7812	−	72.3672i	−0.0607285	−	0.105185i
$689$	57.5971	−	859.429i	0.0835953	−	1.24736i
$690$	−259.111	−	325.247i	−0.375523	−	0.471373i
$691$	729.078			1.05511			0.527553	−	0.849522i	$-0.323110\pi$
$691$	729.078			1.05511			0.527553	+	0.849522i	$0.323110\pi$
$692$	138.877	−	80.1809i	0.200690	−	0.115868i
$693$	−84.0093	−	273.320i	−0.121226	−	0.394401i
$694$	224.230			0.323098
$695$	−41.8826	+	24.1809i	−0.0602627	+	0.0347927i
$696$	205.009	−	163.322i	0.294554	−	0.234658i
$697$	−37.5418	−	65.0243i	−0.0538620	−	0.0932917i
$698$			343.390i			0.491963i
$699$	25.1105	+	31.5198i	0.0359234	+	0.0450927i
$700$	−898.213			−1.28316
$701$			179.270i			0.255735i	0.991791	+	0.127868i	$0.0408133\pi$
$701$			179.270i			0.255735i	−0.991791	+	0.127868i	$0.959187\pi$
$702$	368.736	−	147.442i	0.525265	−	0.210031i
$703$	−1241.34			−1.76578
$704$		−	112.860i		−	0.160313i
$705$	−1383.61	+	1102.26i	−1.96256	+	1.56349i
$706$	−342.391			−0.484973
$707$	311.491	−	179.840i	0.440582	−	0.254370i
$708$	21.9944	+	27.6084i	0.0310656	+	0.0389950i
$709$	−295.470	−	511.768i	−0.416741	−	0.721817i	0.578868	−	0.815421i	$-0.303495\pi$
$709$	−295.470	−	511.768i	−0.416741	−	0.721817i	−0.995610	+	0.0936039i	$0.970161\pi$
$710$			830.428i			1.16962i
$711$	144.598	+	134.436i	0.203373	+	0.189081i
$712$	91.7808	+	158.969i	0.128906	+	0.223271i
$713$		−	782.196i		−	1.09705i
$714$	39.0095	−	31.0772i	0.0546351	−	0.0435254i
$715$	187.123	+	380.856i	0.261710	+	0.532666i
$716$	551.801	−	318.583i	0.770672	−	0.444948i
$717$	165.875	−	422.023i	0.231346	−	0.588596i
$718$	121.857			0.169718
$719$	513.432	+	296.430i	0.714092	+	0.412281i	0.812574	−	0.582858i	$-0.198065\pi$
$719$	513.432	+	296.430i	0.714092	+	0.412281i	−0.0984823	+	0.995139i	$0.531399\pi$
$720$	49.1447	+	159.890i	0.0682566	+	0.222069i
$721$	269.809	−	467.322i	0.374215	−	0.648159i
$722$	464.798	−	268.351i	0.643765	−	0.371678i
$723$	−25.4416	−	9.99976i	−0.0351890	−	0.0138309i
$724$	−701.085			−0.968350
$725$	413.814	+	238.916i	0.570778	+	0.329539i
$726$	−222.061	−	278.741i	−0.305869	−	0.383941i
$727$	223.764	−	387.571i	0.307791	−	0.533110i	−0.670088	−	0.742282i	$-0.733744\pi$
$727$	223.764	−	387.571i	0.307791	−	0.533110i	0.977879	+	0.209172i	$0.0670769\pi$
$728$	−704.533	+	346.152i	−0.967765	+	0.475484i
$729$	−456.229	+	568.591i	−0.625828	+	0.779961i
$730$	−206.239	−	357.216i	−0.282519	−	0.489337i
$731$			67.8762i			0.0928538i
$732$	108.434	+	42.6198i	0.148134	+	0.0582238i
$733$	−239.454	−	414.746i	−0.326677	−	0.565820i	0.655174	−	0.755478i	$-0.272595\pi$
$733$	−239.454	−	414.746i	−0.326677	−	0.565820i	−0.981850	+	0.189658i	$0.939262\pi$
$734$		−	72.7482i		−	0.0991121i
$735$	214.700	+	269.501i	0.292108	+	0.366668i
$736$	247.659	−	428.957i	0.336493	−	0.582822i
$737$	311.069	+	179.596i	0.422075	+	0.243685i
$738$	302.637	+	281.369i	0.410077	+	0.381259i
$739$	−102.545	−	177.613i	−0.138762	−	0.240343i	0.788266	−	0.615334i	$-0.210979\pi$
$739$	−102.545	−	177.613i	−0.138762	−	0.240343i	−0.927028	+	0.374991i	$0.877646\pi$
$740$	−825.494	−	476.599i	−1.11553	−	0.644053i
$741$	92.5327	+	1123.40i	0.124875	+	1.51606i
$742$	297.686	+	515.607i	0.401194	+	0.694888i
$743$	1218.62	+	703.570i	1.64013	+	0.946932i	0.980784	+	0.195095i	$0.0625015\pi$
$743$	1218.62	+	703.570i	1.64013	+	0.946932i	0.659349	+	0.751837i	$0.270832\pi$
$744$	434.662	−	1105.88i	0.584223	−	1.48639i
$745$	86.8440	+	150.418i	0.116569	+	0.201904i
$746$		−	236.575i		−	0.317125i
$747$	−715.717	+	769.817i	−0.958122	+	1.03054i
$748$	10.0656	−	17.4342i	0.0134567	−	0.0233078i
$749$	75.1342	+	43.3787i	0.100313	+	0.0579155i
$750$	359.165	−	286.131i	0.478886	−	0.381508i
$751$	−657.236	+	1138.37i	−0.875148	+	1.51580i	−0.0185422	+	0.999828i	$0.505903\pi$
$751$	−657.236	+	1138.37i	−0.875148	+	1.51580i	−0.856605	+	0.515972i	$0.827431\pi$
$752$	−142.551	−	82.3020i	−0.189563	−	0.109444i
$753$	169.840	−	25.5126i	0.225551	−	0.0338812i
$754$	168.644	+	11.3022i	0.223666	+	0.0149896i
$755$		−	1197.65i		−	1.58629i
$756$	329.277	−	481.410i	0.435552	−	0.636786i
$757$	−76.2314	−	132.037i	−0.100702	−	0.174421i	0.811272	−	0.584669i	$-0.198776\pi$
$757$	−76.2314	−	132.037i	−0.100702	−	0.174421i	−0.911974	+	0.410248i	$0.865442\pi$
$758$	207.668	−	119.897i	0.273968	−	0.158175i
$759$	26.7674	+	178.194i	0.0352667	+	0.234774i
$760$	1793.06			2.35929
$761$		−	375.644i		−	0.493619i	−0.969064	−	0.246810i	$-0.920618\pi$
$761$		−	375.644i		−	0.493619i	0.969064	−	0.246810i	$-0.0793823\pi$
$762$	−70.0729	+	178.281i	−0.0919592	+	0.233965i
$763$	95.0594	+	164.648i	0.124586	+	0.215790i
$764$	392.465	−	226.590i	0.513698	−	0.296584i
$765$	30.3666	−	132.435i	0.0396949	−	0.173118i
$766$	262.592			0.342810
$767$	−3.76043	+	56.1108i	−0.00490278	+	0.0731562i
$768$	530.364	−	422.518i	0.690578	−	0.550154i
$769$	16.3675	−	28.3494i	0.0212842	−	0.0368653i	−0.855187	−	0.518319i	$-0.826558\pi$
$769$	16.3675	−	28.3494i	0.0212842	−	0.0368653i	0.876471	+	0.481454i	$0.159891\pi$
$770$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.13140i q^{2} +(-2.34643 + 1.86930i) q^{3} +2.71993 q^{4} +(-7.06649 + 4.07984i) q^{5} +(-2.11493 - 2.65475i) q^{6} +(-3.97102 - 6.87801i) q^{7} +7.60294i q^{8} +(2.01145 - 8.77235i) q^{9} +(-4.61594 - 7.99504i) q^{10} +4.00036i q^{11} +(-6.38212 + 5.08436i) q^{12} +(-12.9709 - 0.869283i) q^{13} +(7.78178 - 4.49282i) q^{14} +(8.95458 - 22.7824i) q^{15} +2.27776 q^{16} +(-1.60230 - 0.925090i) q^{17} +(9.92504 + 2.27575i) q^{18} +(-14.4514 + 25.0305i) q^{19} +(-19.2204 + 11.0969i) q^{20} +(22.1748 + 8.71573i) q^{21} -4.52601 q^{22} +(-13.0031 - 7.50735i) q^{23} +(-14.2122 - 17.8397i) q^{24} +(20.7902 - 36.0097i) q^{25} +(0.983507 - 14.6753i) q^{26} +(11.6784 + 24.3437i) q^{27} +(-10.8009 - 18.7077i) q^{28} +11.4917i q^{29} +(25.7761 + 10.1312i) q^{30} +(26.0477 + 45.1159i) q^{31} +32.9888i q^{32} +(-7.47787 - 9.38656i) q^{33} +(1.04665 - 1.81285i) q^{34} +(56.1224 + 32.4023i) q^{35} +(5.47100 - 23.8602i) q^{36} +(21.4744 + 37.1948i) q^{37} +(-28.3196 - 16.3503i) q^{38} +(32.0602 - 22.2068i) q^{39} +(-31.0188 - 53.7261i) q^{40} +(35.1449 + 20.2909i) q^{41} +(-9.86098 + 25.0885i) q^{42} +(-18.3431 - 31.7712i) q^{43} +10.8807i q^{44} +(21.5759 + 70.1961i) q^{45} +(8.49383 - 14.7117i) q^{46} +(-62.5840 - 36.1329i) q^{47} +(-5.34460 + 4.25781i) q^{48} +(-7.03800 + 12.1902i) q^{49} +(40.7414 + 23.5221i) q^{50} +(5.48896 - 0.824526i) q^{51} +(-35.2800 - 2.36439i) q^{52} +66.2582i q^{53} +(-27.5425 + 13.2130i) q^{54} +(-16.3208 - 28.2685i) q^{55} +(52.2931 - 30.1914i) q^{56} +(-12.8804 - 85.7463i) q^{57} -13.0017 q^{58} -4.32590i q^{59} +(24.3558 - 61.9667i) q^{60} +(-7.13924 - 12.3655i) q^{61} +(-51.0441 + 29.4703i) q^{62} +(-68.3238 + 21.0004i) q^{63} -28.2125 q^{64} +(95.2054 - 46.7765i) q^{65} +(10.6200 - 8.46047i) q^{66} +(44.8949 - 77.7602i) q^{67} +(-4.35816 - 2.51618i) q^{68} +(44.5444 - 6.69124i) q^{69} +(-36.6600 + 63.4969i) q^{70} +(-77.9009 - 44.9761i) q^{71} +(66.6956 + 15.2929i) q^{72} +44.6797 q^{73} +(-42.0823 + 24.2962i) q^{74} +(18.5302 + 123.357i) q^{75} +(-39.3068 + 68.0813i) q^{76} +(27.5145 - 15.8855i) q^{77} +(25.1248 + 36.2730i) q^{78} +(-10.9688 + 18.9985i) q^{79} +(-16.0958 + 9.29290i) q^{80} +(-72.9082 - 35.2902i) q^{81} +(-22.9571 + 39.7629i) q^{82} +(-101.145 - 58.3960i) q^{83} +(60.3138 + 23.7062i) q^{84} +15.0969 q^{85} +(35.9460 - 20.7534i) q^{86} +(-21.4815 - 26.9645i) q^{87} -30.4145 q^{88} +(20.9089 - 12.0718i) q^{89} +(-79.4200 + 24.4110i) q^{90} +(45.5288 + 92.6659i) q^{91} +(-35.3676 - 20.4195i) q^{92} +(-145.454 - 57.1703i) q^{93} +(40.8808 - 70.8075i) q^{94} -235.837i q^{95} +(-61.6659 - 77.4059i) q^{96} +(46.7356 + 80.9485i) q^{97} +(-13.7920 - 7.96280i) q^{98} +(35.0926 + 8.04651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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