LMFDB - Embedded newform 117.3.n.a.38.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(38,117)]

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, 3]))

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

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

chi := DirichletCharacter("117.38");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.n (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			38.3
Character	$\chi$	$=$	117.38
Dual form			117.3.n.a.77.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.68517 + 2.91881i) q^{2} +(2.36131 + 1.85046i) q^{3} +(-3.67962 - 6.37330i) q^{4} +(3.61500 + 6.26136i) q^{5} +(-9.38036 + 3.77386i) q^{6} +(-2.20723 - 1.27434i) q^{7} +11.3218 q^{8} +(2.15158 + 8.73903i) q^{9} -24.3676 q^{10} +(0.796079 - 1.37885i) q^{11} +(3.10481 - 21.8583i) q^{12} +(-1.08797 + 12.9544i) q^{13} +(7.43913 - 4.29498i) q^{14} +(-3.05028 + 21.4744i) q^{15} +(-4.36077 + 7.55307i) q^{16} -17.5218i q^{17} +(-29.1333 - 8.44675i) q^{18} -33.2052i q^{19} +(26.6037 - 46.0789i) q^{20} +(-2.85383 - 7.09352i) q^{21} +(2.68306 + 4.64720i) q^{22} +(-13.3796 + 7.72474i) q^{23} +(26.7344 + 20.9506i) q^{24} +(-13.6364 + 23.6189i) q^{25} +(-35.9780 - 25.0060i) q^{26} +(-11.0907 + 24.6170i) q^{27} +18.7564i q^{28} +(40.5355 + 23.4032i) q^{29} +(-57.5395 - 45.0913i) q^{30} +(19.7402 - 11.3970i) q^{31} +(7.94636 + 13.7635i) q^{32} +(4.43130 - 1.78278i) q^{33} +(51.1427 + 29.5272i) q^{34} -18.4270i q^{35} +(47.7794 - 45.8690i) q^{36} +40.4940i q^{37} +(96.9197 + 55.9566i) q^{38} +(-26.5407 + 28.5761i) q^{39} +(40.9284 + 70.8901i) q^{40} +(7.21611 + 12.4987i) q^{41} +(25.5138 + 3.62404i) q^{42} +(-16.2824 + 28.2019i) q^{43} -11.7171 q^{44} +(-46.9403 + 45.0634i) q^{45} -52.0701i q^{46} +(11.5162 - 19.9467i) q^{47} +(-24.2738 + 9.76572i) q^{48} +(-21.2521 - 36.8097i) q^{49} +(-45.9594 - 79.6041i) q^{50} +(32.4234 - 41.3744i) q^{51} +(86.5655 - 40.7333i) q^{52} +29.9403i q^{53} +(-53.1625 - 73.8556i) q^{54} +11.5113 q^{55} +(-24.9899 - 14.4279i) q^{56} +(61.4450 - 78.4079i) q^{57} +(-136.619 + 78.8769i) q^{58} +(33.8805 + 58.6828i) q^{59} +(148.087 - 59.5775i) q^{60} +(57.3856 - 99.3948i) q^{61} +76.8239i q^{62} +(6.38751 - 22.0309i) q^{63} -88.4502 q^{64} +(-85.0451 + 40.0179i) q^{65} +(-2.26393 + 15.9384i) q^{66} +(94.0391 - 54.2935i) q^{67} +(-111.671 + 64.4735i) q^{68} +(-45.8878 - 6.51801i) q^{69} +(53.7849 + 31.0527i) q^{70} +3.91799 q^{71} +(24.3598 + 98.9419i) q^{72} -13.3331i q^{73} +(-118.194 - 68.2395i) q^{74} +(-75.9057 + 30.5380i) q^{75} +(-211.627 + 122.183i) q^{76} +(-3.51426 + 2.02896i) q^{77} +(-38.6825 - 125.623i) q^{78} +(-17.6162 + 30.5122i) q^{79} -63.0567 q^{80} +(-71.7414 + 37.6054i) q^{81} -48.6416 q^{82} +(2.29384 - 3.97305i) q^{83} +(-34.7081 + 44.2898i) q^{84} +(109.710 - 63.3411i) q^{85} +(-54.8773 - 95.0503i) q^{86} +(52.4103 + 130.272i) q^{87} +(9.01307 - 15.6111i) q^{88} -80.5545 q^{89} +(-52.4288 - 212.949i) q^{90} +(18.9098 - 27.2069i) q^{91} +(98.4640 + 56.8482i) q^{92} +(67.7025 + 9.61662i) q^{93} +(38.8138 + 67.2274i) q^{94} +(207.910 - 120.037i) q^{95} +(-6.70501 + 47.2043i) q^{96} +(26.6439 + 15.3828i) q^{97} +143.254 q^{98} +(13.7626 + 3.99026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) $ 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Character values

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

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

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 $

$2$	−1.68517	+	2.91881i	−0.842587	+	1.45940i	0.0451132	+	0.998982i	$0.485635\pi$
$2$	−1.68517	+	2.91881i	−0.842587	+	1.45940i	−0.887700	+	0.460422i	$0.847698\pi$
$3$	2.36131	+	1.85046i	0.787104	+	0.616821i
$3$	2.36131	+	1.85046i	0.787104	+	0.616821i
$4$	−3.67962	−	6.37330i	−0.919906	−	1.59332i
$5$	3.61500	+	6.26136i	0.722999	+	1.25227i	0.959792	+	0.280711i	$0.0905704\pi$
$5$	3.61500	+	6.26136i	0.722999	+	1.25227i	−0.236793	+	0.971560i	$0.576096\pi$
$6$	−9.38036	+	3.77386i	−1.56339	+	0.628977i
$7$	−2.20723	−	1.27434i	−0.315318	−	0.182049i	0.333985	−	0.942578i	$-0.391606\pi$
$7$	−2.20723	−	1.27434i	−0.315318	−	0.182049i	−0.649304	+	0.760529i	$0.724940\pi$
$8$	11.3218			1.41523
$9$	2.15158	+	8.73903i	0.239064	+	0.971004i
$10$	−24.3676			−2.43676
$11$	0.796079	−	1.37885i	0.0723708	−	0.125350i	−0.827569	−	0.561364i	$-0.810277\pi$
$11$	0.796079	−	1.37885i	0.0723708	−	0.125350i	0.899940	+	0.436014i	$0.143610\pi$
$12$	3.10481	−	21.8583i	0.258734	−	1.82153i
$13$	−1.08797	+	12.9544i	−0.0836903	+	0.996492i
$13$	−1.08797	+	12.9544i	−0.0836903	+	0.996492i
$14$	7.43913	−	4.29498i	0.531367	−	0.306785i
$15$	−3.05028	+	21.4744i	−0.203352	+	1.43163i
$16$	−4.36077	+	7.55307i	−0.272548	+	0.472067i
$17$		−	17.5218i		−	1.03069i	−0.856982	−	0.515346i	$-0.827663\pi$
$17$		−	17.5218i		−	1.03069i	0.856982	−	0.515346i	$-0.172337\pi$
$18$	−29.1333	−	8.44675i	−1.61852	−	0.469264i
$19$		−	33.2052i		−	1.74764i	−0.486246	−	0.873822i	$-0.661634\pi$
$19$		−	33.2052i		−	1.74764i	0.486246	−	0.873822i	$-0.338366\pi$
$20$	26.6037	−	46.0789i	1.33018	−	2.30394i
$21$	−2.85383	−	7.09352i	−0.135897	−	0.337787i
$22$	2.68306	+	4.64720i	0.121957	+	0.211236i
$23$	−13.3796	+	7.72474i	−0.581723	+	0.335858i	−0.761818	−	0.647791i	$-0.775693\pi$
$23$	−13.3796	+	7.72474i	−0.581723	+	0.335858i	0.180095	+	0.983649i	$0.442360\pi$
$24$	26.7344	+	20.9506i	1.11393	+	0.872943i
$25$	−13.6364	+	23.6189i	−0.545456	+	0.944758i
$26$	−35.9780	−	25.0060i	−1.38377	−	0.961769i
$27$	−11.0907	+	24.6170i	−0.410767	+	0.911740i
$28$			18.7564i			0.669873i
$29$	40.5355	+	23.4032i	1.39778	+	0.807007i	0.994159	−	0.107921i	$-0.0344193\pi$
$29$	40.5355	+	23.4032i	1.39778	+	0.807007i	0.403618	+	0.914928i	$0.367753\pi$
$30$	−57.5395	−	45.0913i	−1.91798	−	1.50304i
$31$	19.7402	−	11.3970i	0.636781	−	0.367646i	−0.146592	−	0.989197i	$-0.546831\pi$
$31$	19.7402	−	11.3970i	0.636781	−	0.367646i	0.783374	+	0.621551i	$0.213497\pi$
$32$	7.94636	+	13.7635i	0.248324	+	0.430109i
$33$	4.43130	−	1.78278i	0.134282	−	0.0540235i
$34$	51.1427	+	29.5272i	1.50420	+	0.868448i
$35$		−	18.4270i		−	0.526486i
$36$	47.7794	−	45.8690i	1.32721	−	1.27414i
$37$			40.4940i			1.09443i	0.836991	+	0.547217i	$0.184313\pi$
$37$			40.4940i			1.09443i	−0.836991	+	0.547217i	$0.815687\pi$
$38$	96.9197	+	55.9566i	2.55052	+	1.47254i
$39$	−26.5407	+	28.5761i	−0.680530	+	0.732720i
$40$	40.9284	+	70.8901i	1.02321	+	1.77225i
$41$	7.21611	+	12.4987i	0.176003	+	0.304845i	0.940508	−	0.339772i	$-0.110350\pi$
$41$	7.21611	+	12.4987i	0.176003	+	0.304845i	−0.764505	+	0.644618i	$0.777017\pi$
$42$	25.5138	+	3.62404i	0.607472	+	0.0862867i
$43$	−16.2824	+	28.2019i	−0.378660	+	0.655859i	−0.990868	−	0.134839i	$-0.956948\pi$
$43$	−16.2824	+	28.2019i	−0.378660	+	0.655859i	0.612207	+	0.790697i	$0.290282\pi$
$44$	−11.7171			−0.266297
$45$	−46.9403	+	45.0634i	−1.04312	+	1.00141i
$46$		−	52.0701i		−	1.13196i
$47$	11.5162	−	19.9467i	0.245027	−	0.424398i	−0.717113	−	0.696957i	$-0.754537\pi$
$47$	11.5162	−	19.9467i	0.245027	−	0.424398i	0.962139	+	0.272559i	$0.0878700\pi$
$48$	−24.2738	+	9.76572i	−0.505704	+	0.203452i
$49$	−21.2521	−	36.8097i	−0.433716	−	0.751218i
$50$	−45.9594	−	79.6041i	−0.919188	−	1.59208i
$51$	32.4234	−	41.3744i	0.635753	−	0.811262i
$52$	86.5655	−	40.7333i	1.66472	−	0.783333i
$53$			29.9403i			0.564911i	0.959280	+	0.282456i	$0.0911490\pi$
$53$			29.9403i			0.564911i	−0.959280	+	0.282456i	$0.908851\pi$
$54$	−53.1625	−	73.8556i	−0.984490	−	1.36770i
$55$	11.5113			0.209296
$56$	−24.9899	−	14.4279i	−0.446248	−	0.257641i
$57$	61.4450	−	78.4079i	1.07798	−	1.37558i
$58$	−136.619	+	78.8769i	−2.35550	+	1.35995i
$59$	33.8805	+	58.6828i	0.574246	+	0.994624i	0.996123	+	0.0879708i	$0.0280382\pi$
$59$	33.8805	+	58.6828i	0.574246	+	0.994624i	−0.421877	+	0.906653i	$0.638628\pi$
$60$	148.087	−	59.5775i	2.46811	−	0.992958i
$61$	57.3856	−	99.3948i	0.940748	−	1.62942i	0.176699	−	0.984265i	$-0.443458\pi$
$61$	57.3856	−	99.3948i	0.940748	−	1.62942i	0.764049	−	0.645158i	$-0.223209\pi$
$62$			76.8239i			1.23909i
$63$	6.38751	−	22.0309i	0.101389	−	0.349697i
$64$	−88.4502			−1.38203
$65$	−85.0451	+	40.0179i	−1.30839	+	0.615660i
$66$	−2.26393	+	15.9384i	−0.0343019	+	0.241491i
$67$	94.0391	−	54.2935i	1.40357	−	0.810351i	0.408812	−	0.912619i	$-0.365943\pi$
$67$	94.0391	−	54.2935i	1.40357	−	0.810351i	0.994757	+	0.102267i	$0.0326098\pi$
$68$	−111.671	+	64.4735i	−1.64223	+	0.948140i
$69$	−45.8878	−	6.51801i	−0.665041	−	0.0944639i
$70$	53.7849	+	31.0527i	0.768355	+	0.443610i
$71$	3.91799			0.0551830			0.0275915	−	0.999619i	$-0.491216\pi$
$71$	3.91799			0.0551830			0.0275915	+	0.999619i	$0.491216\pi$
$72$	24.3598	+	98.9419i	0.338331	+	1.37419i
$73$		−	13.3331i		−	0.182645i	−0.995821	−	0.0913224i	$-0.970891\pi$
$73$		−	13.3331i		−	0.182645i	0.995821	−	0.0913224i	$-0.0291094\pi$
$74$	−118.194	−	68.2395i	−1.59722	−	0.922155i
$75$	−75.9057	+	30.5380i	−1.01208	+	0.407173i
$76$	−211.627	+	122.183i	−2.78456	+	1.60767i
$77$	−3.51426	+	2.02896i	−0.0456397	+	0.0263501i
$78$	−38.6825	−	125.623i	−0.495929	−	1.61055i
$79$	−17.6162	+	30.5122i	−0.222990	+	0.386230i	−0.955715	−	0.294295i	$-0.904915\pi$
$79$	−17.6162	+	30.5122i	−0.222990	+	0.386230i	0.732724	+	0.680526i	$0.238248\pi$
$80$	−63.0567			−0.788208
$81$	−71.7414	+	37.6054i	−0.885697	+	0.464264i
$82$	−48.6416			−0.593190
$83$	2.29384	−	3.97305i	0.0276366	−	0.0478681i	−0.851876	−	0.523743i	$-0.824535\pi$
$83$	2.29384	−	3.97305i	0.0276366	−	0.0478681i	0.879513	+	0.475875i	$0.157869\pi$
$84$	−34.7081	+	44.2898i	−0.413191	+	0.527259i
$85$	109.710	−	63.3411i	1.29071	−	0.745190i
$86$	−54.8773	−	95.0503i	−0.638108	−	1.10524i
$87$	52.4103	+	130.272i	0.602417	+	1.49738i
$88$	9.01307	−	15.6111i	0.102421	−	0.177399i
$89$	−80.5545			−0.905106			−0.452553	−	0.891737i	$-0.649487\pi$
$89$	−80.5545			−0.905106			−0.452553	+	0.891737i	$0.649487\pi$
$90$	−52.4288	−	212.949i	−0.582542	−	2.36610i
$91$	18.9098	−	27.2069i	0.207800	−	0.298977i
$92$	98.4640	+	56.8482i	1.07026	+	0.617916i
$93$	67.7025	+	9.61662i	0.727984	+	0.103405i
$94$	38.8138	+	67.2274i	0.412912	+	0.715185i
$95$	207.910	−	120.037i	2.18852	−	1.26355i
$96$	−6.70501	+	47.2043i	−0.0698439	+	0.491712i
$97$	26.6439	+	15.3828i	0.274679	+	0.158586i	0.631012	−	0.775773i	$-0.282640\pi$
$97$	26.6439	+	15.3828i	0.274679	+	0.158586i	−0.356333	+	0.934359i	$0.615973\pi$
$98$	143.254			1.46177
$99$	13.7626	+	3.99026i	0.139016	+	0.0403056i
$100$	200.707			2.00707
$101$	−45.5824	−	26.3170i	−0.451311	−	0.260564i	0.257073	−	0.966392i	$-0.417242\pi$
$101$	−45.5824	−	26.3170i	−0.451311	−	0.260564i	−0.708384	+	0.705828i	$0.750575\pi$
$102$	66.1247	+	164.361i	0.648281	+	1.61138i
$103$	−19.6139	−	33.9723i	−0.190427	−	0.329828i	0.754965	−	0.655765i	$-0.227654\pi$
$103$	−19.6139	−	33.9723i	−0.190427	−	0.329828i	−0.945392	+	0.325937i	$0.894320\pi$
$104$	−12.3179	+	146.668i	−0.118441	+	1.41026i
$105$	34.0985	−	43.5119i	0.324747	−	0.414399i
$106$	−87.3899	−	50.4546i	−0.824433	−	0.475987i
$107$		−	171.598i		−	1.60372i	−0.597515	−	0.801858i	$-0.703845\pi$
$107$		−	171.598i		−	1.60372i	0.597515	−	0.801858i	$-0.296155\pi$
$108$	197.701	−	19.8969i	1.83056	−	0.184230i
$109$		−	141.755i		−	1.30050i	−0.759719	−	0.650252i	$-0.774663\pi$
$109$		−	141.755i		−	1.30050i	0.759719	−	0.650252i	$-0.225337\pi$
$110$	−19.3985	+	33.5992i	−0.176350	+	0.305448i
$111$	−74.9327	+	95.6190i	−0.675069	+	0.861432i
$112$	19.2504	−	11.1142i	0.171879	−	0.0992343i
$113$	−106.190	+	61.3089i	−0.939736	+	0.542557i	−0.889877	−	0.456200i	$-0.849210\pi$
$113$	−106.190	+	61.3089i	−0.939736	+	0.542557i	−0.0498582	+	0.998756i	$0.515877\pi$
$114$	125.312	+	311.477i	1.09923	+	2.73226i
$115$	−96.7347	−	55.8498i	−0.841171	−	0.485650i
$116$		−	344.460i		−	2.96948i
$117$	−115.550	+	18.3645i	−0.987605	+	0.156962i
$118$	−228.378			−1.93541
$119$	−22.3288	+	38.6746i	−0.187637	+	0.324996i
$120$	−34.5347	+	243.130i	−0.287789	+	2.02608i
$121$	59.2325	+	102.594i	0.489525	+	0.847882i
$122$	193.410	+	334.995i	1.58532	+	2.74586i
$123$	−6.08884	+	42.8664i	−0.0495027	+	0.348507i
$124$	−145.273	−	83.8735i	−1.17156	−	0.676399i
$125$	−16.4323			−0.131459
$126$	53.5399	+	55.7698i	0.424920	+	0.442618i
$127$	224.469			1.76747			0.883736	−	0.467985i	$-0.155020\pi$
$127$	224.469			1.76747			0.883736	+	0.467985i	$0.155020\pi$
$128$	117.268	−	203.115i	0.916160	−	1.58684i
$129$	−90.6344	+	36.4636i	−0.702592	+	0.282663i
$130$	26.5113	−	315.667i	0.203933	−	2.42821i
$131$	−43.6415	+	25.1964i	−0.333141	+	0.192339i	−0.657235	−	0.753686i	$-0.728274\pi$
$131$	−43.6415	+	25.1964i	−0.333141	+	0.192339i	0.324094	+	0.946025i	$0.394941\pi$
$132$	−27.6677	−	21.6820i	−0.209604	−	0.164258i
$133$	−42.3149	+	73.2916i	−0.318157	+	0.551064i
$134$			365.976i			2.73117i
$135$	−194.229	+	19.5474i	−1.43873	+	0.144796i
$136$		−	198.379i		−	1.45867i
$137$	−11.1350	+	19.2865i	−0.0812777	+	0.140777i	−0.903799	−	0.427957i	$-0.859233\pi$
$137$	−11.1350	+	19.2865i	−0.0812777	+	0.140777i	0.822521	+	0.568734i	$0.192567\pi$
$138$	96.3538	−	122.954i	0.698216	−	0.890969i
$139$	−49.3955	−	85.5556i	−0.355364	−	0.615508i	0.631816	−	0.775118i	$-0.282310\pi$
$139$	−49.3955	−	85.5556i	−0.355364	−	0.615508i	−0.987180	+	0.159610i	$0.948976\pi$
$140$	−117.441	+	67.8044i	−0.838862	+	0.484317i
$141$	64.1041	−	25.7900i	0.454639	−	0.182908i
$142$	−6.60250	+	11.4359i	−0.0464965	+	0.0805343i
$143$	16.9960	+	11.8129i	0.118853	+	0.0826075i
$144$	−75.3891	−	21.8579i	−0.523535	−	0.151791i
$145$			338.410i			2.33386i
$146$	38.9167	+	22.4686i	0.266553	+	0.153894i
$147$	17.9322	−	126.245i	0.121988	−	0.858812i
$148$	258.080	−	149.003i	1.74379	−	1.00678i
$149$	20.7254	+	35.8975i	0.139097	+	0.240923i	0.927155	−	0.374678i	$-0.122247\pi$
$149$	20.7254	+	35.8975i	0.139097	+	0.240923i	−0.788058	+	0.615601i	$0.788913\pi$
$150$	38.7798	−	273.016i	0.258532	−	1.82011i
$151$	−212.950	−	122.947i	−1.41026	−	0.814216i	−0.414851	−	0.909889i	$-0.636166\pi$
$151$	−212.950	−	122.947i	−1.41026	−	0.814216i	−0.995413	+	0.0956729i	$0.969500\pi$
$152$		−	375.944i		−	2.47332i
$153$	153.123	−	37.6995i	1.00081	−	0.246402i
$154$		−	13.6766i		−	0.0888090i
$155$	142.722	+	82.4004i	0.920785	+	0.531615i
$156$	279.784	+	64.0022i	1.79348	+	0.410271i
$157$	−87.9765	−	152.380i	−0.560360	−	0.970572i	−0.997465	−	0.0711615i	$-0.977329\pi$
$157$	−87.9765	−	152.380i	−0.560360	−	0.970572i	0.437105	−	0.899411i	$-0.356004\pi$
$158$	−59.3728	−	102.837i	−0.375777	−	0.650865i
$159$	−55.4034	+	70.6983i	−0.348449	+	0.444644i
$160$	−57.4521	+	99.5100i	−0.359076	+	0.621938i
$161$	39.3759			0.244571
$162$	11.1338	−	272.771i	0.0687273	−	1.68377i
$163$			120.543i			0.739529i	0.929126	+	0.369764i	$0.120562\pi$
$163$			120.543i			0.739529i	−0.929126	+	0.369764i	$0.879438\pi$
$164$	53.1051	−	91.9808i	0.323812	−	0.560858i
$165$	27.1817	+	21.3012i	0.164738	+	0.129098i
$166$	7.73104	+	13.3906i	0.0465725	+	0.0806660i
$167$	−93.4676	−	161.891i	−0.559686	−	0.969405i	−0.997522	−	0.0703500i	$-0.977588\pi$
$167$	−93.4676	−	161.891i	−0.559686	−	0.969405i	0.437836	−	0.899055i	$-0.355745\pi$
$168$	−32.3106	−	80.3116i	−0.192325	−	0.478046i
$169$	−166.633	−	28.1881i	−0.985992	−	0.166793i
$170$			426.963i			2.51155i
$171$	290.182	−	71.4436i	1.69697	−	0.417799i
$172$	239.652			1.39333
$173$	−17.5631	−	10.1401i	−0.101521	−	0.0586130i	0.448380	−	0.893843i	$-0.352001\pi$
$173$	−17.5631	−	10.1401i	−0.101521	−	0.0586130i	−0.549901	+	0.835230i	$0.685334\pi$
$174$	−468.558	−	66.5551i	−2.69286	−	0.382501i
$175$	60.1973	−	34.7549i	0.343985	−	0.198600i
$176$	6.94303	+	12.0257i	0.0394490	+	0.0683277i
$177$	−28.5879	+	201.263i	−0.161513	+	1.13708i
$178$	135.748	−	235.123i	0.762631	−	1.32092i
$179$		−	160.073i		−	0.894262i	−0.894468	−	0.447131i	$-0.852446\pi$
$179$		−	160.073i		−	0.894262i	0.894468	−	0.447131i	$-0.147554\pi$
$180$	459.925	+	133.348i	2.55514	+	0.740822i
$181$	116.492			0.643600			0.321800	−	0.946808i	$-0.395712\pi$
$181$	116.492			0.643600			0.321800	+	0.946808i	$0.395712\pi$
$182$	47.5453	+	101.042i	0.261238	+	0.555177i
$183$	319.432	−	128.512i	1.74553	−	0.702252i
$184$	−151.482	+	87.4582i	−0.823272	+	0.475316i
$185$	−253.548	+	146.386i	−1.37053	+	0.791274i
$186$	−142.160	+	181.405i	−0.764299	+	0.975296i
$187$	−24.1599	−	13.9487i	−0.129197	−	0.0745920i
$188$	−169.502			−0.901605
$189$	55.8503	−	40.2020i	0.295504	−	0.212709i
$190$			809.132i			4.25859i
$191$	−202.354	−	116.829i	−1.05944	−	0.611670i	−0.134166	−	0.990959i	$-0.542835\pi$
$191$	−202.354	−	116.829i	−1.05944	−	0.611670i	−0.925278	+	0.379289i	$0.876169\pi$
$192$	−208.858	−	163.674i	−1.08780	−	0.852467i
$193$	−194.186	+	112.113i	−1.00615	+	0.580898i	−0.910061	−	0.414475i	$-0.863965\pi$
$193$	−194.186	+	112.113i	−1.00615	+	0.580898i	−0.0960848	+	0.995373i	$0.530632\pi$
$194$	−89.7991	+	51.8455i	−0.462882	+	0.267245i
$195$	−274.870	−	62.8781i	−1.40959	−	0.322452i
$196$	−156.399	+	270.892i	−0.797956	+	1.38210i
$197$	−200.974			−1.02017			−0.510086	−	0.860124i	$-0.670386\pi$
$197$	−200.974			−1.02017			−0.510086	+	0.860124i	$0.670386\pi$
$198$	−34.8392	+	33.4462i	−0.175956	+	0.168920i
$199$	96.9630			0.487251			0.243626	−	0.969869i	$-0.421663\pi$
$199$	96.9630			0.487251			0.243626	+	0.969869i	$0.421663\pi$
$200$	−154.389	+	267.410i	−0.771945	+	1.33705i
$201$	322.524	+	45.8120i	1.60460	+	0.227920i
$202$	153.628	−	88.6974i	0.760537	−	0.439096i
$203$	−59.6475	−	103.312i	−0.293830	−	0.508928i
$204$	−382.997	−	54.4017i	−1.87744	−	0.266675i
$205$	−52.1724	+	90.3653i	−0.254500	+	0.440806i
$206$	132.212			0.641804
$207$	−96.2940	−	100.305i	−0.465189	−	0.484564i
$208$	−93.1011	−	64.7087i	−0.447601	−	0.311099i
$209$	−45.7850	−	26.4340i	−0.219067	−	0.126478i
$210$	69.5409	+	172.852i	0.331147	+	0.823105i
$211$	123.499	+	213.907i	0.585303	+	1.01378i	0.994838	+	0.101480i	$0.0323579\pi$
$211$	123.499	+	213.907i	0.585303	+	1.01378i	−0.409534	+	0.912295i	$0.634309\pi$
$212$	190.818	−	110.169i	0.900086	−	0.519665i
$213$	9.25160	+	7.25010i	0.0434347	+	0.0340380i
$214$	500.860	+	289.172i	2.34047	+	1.35127i
$215$	−235.443			−1.09508
$216$	−125.567	+	278.710i	−0.581330	+	1.29032i
$217$	−58.0949			−0.267719
$218$	413.755	+	238.882i	1.89796	+	1.09579i
$219$	24.6724	−	31.4835i	0.112659	−	0.143760i
$220$	−42.3572	−	73.3648i	−0.192533	−	0.333477i
$221$	226.984	+	19.0632i	1.02708	+	0.0862590i
$222$	−152.819	−	379.849i	−0.688373	−	1.71103i
$223$	47.8254	+	27.6120i	0.214464	+	0.123821i	0.603384	−	0.797451i	$-0.293819\pi$
$223$	47.8254	+	27.6120i	0.214464	+	0.123821i	−0.388920	+	0.921271i	$0.627152\pi$
$224$		−	40.5056i		−	0.180829i
$225$	−235.746	−	68.3510i	−1.04776	−	0.303782i
$226$		−	413.265i		−	1.82860i
$227$	66.2010	−	114.663i	0.291634	−	0.505125i	−0.682562	−	0.730828i	$-0.739134\pi$
$227$	66.2010	−	114.663i	0.291634	−	0.505125i	0.974196	+	0.225702i	$0.0724676\pi$
$228$	−725.811	−	103.096i	−3.18338	−	0.452175i
$229$	−113.797	+	65.7006i	−0.496929	+	0.286902i	−0.727445	−	0.686167i	$-0.759292\pi$
$229$	−113.797	+	65.7006i	−0.496929	+	0.286902i	0.230515	+	0.973069i	$0.425959\pi$
$230$	326.030	−	188.233i	1.41752	−	0.818405i
$231$	−12.0528	−	1.71200i	−0.0521765	−	0.00741126i
$232$	458.937	+	264.967i	1.97818	+	1.14210i
$233$		−	18.2772i		−	0.0784431i	−0.999231	−	0.0392215i	$-0.987512\pi$
$233$		−	18.2772i		−	0.0784431i	0.999231	−	0.0392215i	$-0.0124878\pi$
$234$	141.119	−	368.215i	0.603072	−	1.57357i
$235$	166.525			0.708616
$236$	249.335	−	431.861i	1.05651	−	1.82992i
$237$	−98.0591	+	39.4506i	−0.413751	+	0.166458i
$238$	−75.2557	−	130.347i	−0.316201	−	0.547676i
$239$	−153.523	−	265.909i	−0.642354	−	1.11259i	−0.984906	−	0.173091i	$-0.944625\pi$
$239$	−153.523	−	265.909i	−0.642354	−	1.11259i	0.342552	−	0.939499i	$-0.388709\pi$
$240$	−148.896	−	116.684i	−0.620402	−	0.486183i
$241$	163.378	+	94.3262i	0.677916	+	0.391395i	0.799069	−	0.601239i	$-0.205326\pi$
$241$	163.378	+	94.3262i	0.677916	+	0.391395i	−0.121154	+	0.992634i	$0.538659\pi$
$242$	−399.268			−1.64987
$243$	−238.991	−	43.9567i	−0.983503	−	0.180892i
$244$	−844.630			−3.46160
$245$	153.652	−	266.134i	0.627153	−	1.08626i
$246$	−114.858	−	90.0094i	−0.466902	−	0.365892i
$247$	430.154	+	36.1264i	1.74151	+	0.146261i
$248$	223.496	−	129.035i	0.901192	−	0.520303i
$249$	12.7684	−	5.13694i	0.0512789	−	0.0206303i
$250$	27.6914	−	47.9628i	0.110765	−	0.191851i
$251$		−	221.279i		−	0.881589i	−0.897608	−	0.440795i	$-0.854697\pi$
$251$		−	221.279i		−	0.881589i	0.897608	−	0.440795i	$-0.145303\pi$
$252$	−163.913	+	40.3559i	−0.650449	+	0.160143i
$253$			24.5980i			0.0972253i
$254$	−378.269	+	655.182i	−1.48925	+	2.57946i
$255$	376.270	+	53.4462i	1.47557	+	0.209593i
$256$	218.335	+	378.168i	0.852872	+	1.47722i
$257$	−311.454	+	179.818i	−1.21188	+	0.699682i	−0.963170	−	0.268895i	$-0.913342\pi$
$257$	−311.454	+	179.818i	−1.21188	+	0.699682i	−0.248715	+	0.968577i	$0.580008\pi$
$258$	46.3046	−	325.992i	0.179475	−	1.26353i
$259$	51.6033	−	89.3796i	0.199241	−	0.345095i
$260$	567.980	+	394.767i	2.18454	+	1.51833i
$261$	−117.306	+	404.595i	−0.449448	+	1.55017i
$262$		−	169.841i		−	0.648250i
$263$	243.053	+	140.327i	0.924156	+	0.533562i	0.884958	−	0.465670i	$-0.154187\pi$
$263$	243.053	+	140.327i	0.924156	+	0.533562i	0.0391972	+	0.999231i	$0.487520\pi$
$264$	50.1704	−	20.1843i	0.190039	−	0.0764557i
$265$	−187.467	+	108.234i	−0.707422	+	0.408430i
$266$	−142.616	−	247.018i	−0.536150	−	0.928639i
$267$	−190.214	−	149.063i	−0.712412	−	0.558288i
$268$	−692.057	−	399.559i	−2.58230	−	1.49089i
$269$			224.370i			0.834088i	0.908886	+	0.417044i	$0.136934\pi$
$269$			224.370i			0.834088i	−0.908886	+	0.417044i	$0.863066\pi$
$270$	270.254	−	599.857i	1.00094	−	2.22169i
$271$		−	69.7426i		−	0.257353i	−0.991687	−	0.128676i	$-0.958927\pi$
$271$		−	69.7426i		−	0.257353i	0.991687	−	0.128676i	$-0.0410729\pi$
$272$	132.343	+	76.4084i	0.486556	+	0.280913i
$273$	94.9971	−	29.2520i	0.347975	−	0.107150i
$274$	−37.5290	−	65.0021i	−0.136967	−	0.237234i
$275$	21.7113	+	37.6051i	0.0789502	+	0.136746i
$276$	127.309	+	316.440i	0.461263	+	1.14652i
$277$	121.631	−	210.670i	0.439099	−	0.760542i	−0.558521	−	0.829490i	$-0.688631\pi$
$277$	121.631	−	210.670i	0.439099	−	0.760542i	0.997620	+	0.0689480i	$0.0219643\pi$
$278$	332.960			1.19770
$279$	142.072	+	147.989i	0.509217	+	0.530426i
$280$		−	208.628i		−	0.745098i
$281$	115.235	−	199.593i	0.410089	−	0.710295i	−0.584810	−	0.811170i	$-0.698831\pi$
$281$	115.235	−	199.593i	0.410089	−	0.710295i	0.994899	+	0.100875i	$0.0321643\pi$
$282$	−32.7504	+	230.568i	−0.116136	+	0.817618i
$283$	−116.854	−	202.397i	−0.412912	−	0.715185i	0.582295	−	0.812978i	$-0.302155\pi$
$283$	−116.854	−	202.397i	−0.412912	−	0.715185i	−0.995207	+	0.0977929i	$0.968822\pi$
$284$	−14.4167	−	24.9705i	−0.0507632	−	0.0879244i
$285$	713.063	+	101.285i	2.50198	+	0.355386i
$286$	−63.1208	+	29.7014i	−0.220702	+	0.103851i
$287$		−	36.7832i		−	0.128165i
$288$	−103.182	+	99.0568i	−0.358273	+	0.343947i
$289$	−18.0125			−0.0623270
$290$	−987.754	−	570.280i	−3.40605	−	1.96648i
$291$	34.4491	+	85.6271i	0.118382	+	0.294251i
$292$	−84.9756	+	49.0607i	−0.291012	+	0.168016i
$293$	254.259	+	440.390i	0.867780	+	1.50304i	0.864260	+	0.503045i	$0.167787\pi$
$293$	254.259	+	440.390i	0.867780	+	1.50304i	0.00351943	+	0.999994i	$0.498880\pi$
$294$	338.267	+	265.086i	1.15057	+	0.901653i
$295$	−244.956	+	424.276i	−0.830360	+	1.43823i
$296$			458.467i			1.54887i
$297$	25.1140	+	34.8895i	0.0845590	+	0.117473i
$298$	−139.704			−0.468805
$299$	−85.5126	−	181.729i	−0.285995	−	0.607790i
$300$	473.932	+	371.401i	1.57977	+	1.23800i
$301$	71.8779	−	41.4987i	0.238797	−	0.137870i
$302$	717.715	−	414.373i	2.37654	−	1.37210i
$303$	−58.9355	−	146.491i	−0.194507	−	0.483469i
$304$	250.802	+	144.800i	0.825005	+	0.476317i
$305$	829.795			2.72064
$306$	−148.002	+	510.468i	−0.483667	+	1.66820i
$307$			9.23416i			0.0300787i	0.999887	+	0.0150394i	$0.00478736\pi$
$307$			9.23416i			0.0300787i	−0.999887	+	0.0150394i	$0.995213\pi$
$308$	25.8623	+	14.9316i	0.0839685	+	0.0484792i
$309$	16.5499	−	116.514i	0.0535596	−	0.377068i
$310$	−481.022	+	277.718i	−1.55168	+	0.895864i
$311$	−229.075	+	132.257i	−0.736576	+	0.425262i	−0.820823	−	0.571183i	$-0.806485\pi$
$311$	−229.075	+	132.257i	−0.736576	+	0.425262i	0.0842470	+	0.996445i	$0.473152\pi$
$312$	−300.489	+	323.534i	−0.963106	+	1.03697i
$313$	90.1946	−	156.222i	0.288162	−	0.499110i	−0.685209	−	0.728346i	$-0.740289\pi$
$313$	90.1946	−	156.222i	0.288162	−	0.499110i	0.973371	+	0.229236i	$0.0736227\pi$
$314$	593.023			1.88861
$315$	161.034	−	39.6471i	0.511220	−	0.125864i
$316$	259.284			0.820520
$317$	−148.339	+	256.931i	−0.467947	+	0.810508i	−0.999329	−	0.0366243i	$-0.988340\pi$
$317$	−148.339	+	256.931i	−0.467947	+	0.810508i	0.531382	+	0.847132i	$0.321673\pi$
$318$	−112.990	−	280.851i	−0.355316	−	0.883179i
$319$	64.5390	−	37.2616i	0.202316	−	0.116807i
$320$	−319.747	−	553.818i	−0.999209	−	1.73068i
$321$	317.535	−	405.195i	0.989205	−	1.26229i
$322$	−66.3552	+	114.931i	−0.206072	+	0.356927i
$323$	−581.814			−1.80128
$324$	503.652	+	318.856i	1.55448	+	0.984122i
$325$	−291.133	−	202.348i	−0.895794	−	0.622610i
$326$	−351.842	−	203.136i	−1.07927	−	0.623117i
$327$	262.312	−	334.727i	0.802178	−	1.02363i
$328$	81.6996	+	141.508i	0.249084	+	0.431426i
$329$	−50.8380	+	29.3513i	−0.154523	+	0.0892138i
$330$	−107.980	+	43.4420i	−0.327212	+	0.131642i
$331$	−16.6396	−	9.60687i	−0.0502706	−	0.0290238i	0.474654	−	0.880172i	$-0.342573\pi$
$331$	−16.6396	−	9.60687i	−0.0502706	−	0.0290238i	−0.524925	+	0.851149i	$0.675907\pi$
$332$	−33.7619			−0.101692
$333$	−353.879	+	87.1260i	−1.06270	+	0.261640i
$334$	630.037			1.88634
$335$	679.902	+	392.542i	2.02956	+	1.17177i
$336$	66.0228	+	9.37802i	0.196496	+	0.0279108i
$337$	−54.9401	−	95.1591i	−0.163027	−	0.282371i	0.772926	−	0.634496i	$-0.218792\pi$
$337$	−54.9401	−	95.1591i	−0.163027	−	0.282371i	−0.935953	+	0.352125i	$0.885459\pi$
$338$	363.081	−	438.867i	1.07420	−	1.29842i
$339$	−364.198	−	51.7315i	−1.07433	−	0.152600i
$340$	−807.384	−	466.143i	−2.37466	−	1.37101i
$341$		−	36.2917i		−	0.106427i
$342$	−280.476	+	967.379i	−0.820106	+	2.82859i
$343$			233.216i			0.679929i
$344$	−184.347	+	319.298i	−0.535891	+	0.928191i
$345$	−125.073	−	310.883i	−0.362530	−	0.901109i
$346$	59.1937	−	34.1755i	0.171080	−	0.0987731i
$347$	127.592	−	73.6654i	0.367701	−	0.212292i	−0.304753	−	0.952432i	$-0.598574\pi$
$347$	127.592	−	73.6654i	0.367701	−	0.212292i	0.672454	+	0.740139i	$0.265240\pi$
$348$	637.410	−	813.377i	1.83164	−	2.33729i
$349$	389.200	+	224.705i	1.11519	+	0.643854i	0.940168	−	0.340711i	$-0.110668\pi$
$349$	389.200	+	224.705i	1.11519	+	0.643854i	0.175019	+	0.984565i	$0.444001\pi$
$350$			234.273i			0.669350i
$351$	−306.832	−	170.456i	−0.874165	−	0.485630i
$352$	25.3037			0.0718856
$353$	−19.8373	+	34.3593i	−0.0561964	+	0.0973351i	−0.892755	−	0.450542i	$-0.851231\pi$
$353$	−19.8373	+	34.3593i	−0.0561964	+	0.0973351i	0.836559	+	0.547877i	$0.184564\pi$
$354$	−539.273	−	422.606i	−1.52337	−	1.19380i
$355$	14.1635	+	24.5320i	0.0398973	+	0.0691041i
$356$	296.410	+	513.397i	0.832613	+	1.44213i
$357$	−124.291	+	50.0041i	−0.348154	+	0.140068i
$358$	467.222	+	269.751i	1.30509	+	0.753494i
$359$	439.859			1.22524			0.612618	−	0.790379i	$-0.290117\pi$
$359$	439.859			1.22524			0.612618	+	0.790379i	$0.290117\pi$
$360$	−531.450	+	510.200i	−1.47625	+	1.41722i
$361$	−741.587			−2.05426
$362$	−196.309	+	340.017i	−0.542289	+	0.939273i
$363$	−49.9795	+	351.863i	−0.137684	+	0.969320i
$364$	−242.978	−	20.4065i	−0.667523	−	0.0560619i
$365$	83.4832	−	48.1990i	0.228721	−	0.132052i
$366$	−163.196	+	1148.92i	−0.445890	+	3.13914i
$367$	83.2209	−	144.143i	0.226760	−	0.392760i	−0.730086	−	0.683355i	$-0.760520\pi$
$367$	83.2209	−	144.143i	0.226760	−	0.392760i	0.956846	+	0.290596i	$0.0938534\pi$
$368$		−	134.743i		−	0.366150i
$369$	−93.7002	+	89.9537i	−0.253930	+	0.243777i
$370$		−	986.742i		−	2.66687i
$371$	38.1542	−	66.0851i	0.102842	−	0.178127i
$372$	−187.830	−	466.874i	−0.504920	−	1.25504i
$373$	36.2155	+	62.7271i	0.0970924	+	0.168169i	0.910480	−	0.413553i	$-0.135712\pi$
$373$	36.2155	+	62.7271i	0.0970924	+	0.168169i	−0.813388	+	0.581722i	$0.802379\pi$
$374$	81.4272	−	47.0120i	0.217720	−	0.125701i
$375$	−38.8019	−	30.4074i	−0.103472	−	0.0810865i
$376$	130.385	−	225.834i	0.346769	−	0.600621i
$377$	−347.276	+	499.651i	−0.921156	+	1.32533i
$378$	23.2243	+	230.763i	0.0614401	+	0.610485i
$379$			474.167i			1.25110i	0.780184	+	0.625550i	$0.215125\pi$
$379$			474.167i			1.25110i	−0.780184	+	0.625550i	$0.784875\pi$
$380$	−1530.06	−	883.381i	−4.02647	−	2.32469i
$381$	530.041	+	415.371i	1.39118	+	1.09021i
$382$	682.003	−	393.754i	1.78535	−	1.03077i
$383$	271.368	+	470.022i	0.708532	+	1.22721i	0.965402	+	0.260767i	$0.0839754\pi$
$383$	271.368	+	470.022i	0.708532	+	1.22721i	−0.256870	+	0.966446i	$0.582691\pi$
$384$	652.764	−	262.617i	1.69991	−	0.683898i
$385$	−25.4081	−	14.6693i	−0.0659949	−	0.0381022i
$386$		−	755.722i		−	1.95783i
$387$	−281.490	−	81.6137i	−0.727365	−	0.210888i
$388$		−	226.412i		−	0.583537i
$389$	−284.122	−	164.038i	−0.730391	−	0.421691i	0.0881744	−	0.996105i	$-0.471897\pi$
$389$	−284.122	−	164.038i	−0.730391	−	0.421691i	−0.818565	+	0.574414i	$0.805230\pi$
$390$	646.732	−	696.331i	1.65829	−	1.78546i
$391$	135.351	+	234.435i	0.346166	+	0.599578i
$392$	−240.613	−	416.753i	−0.613808	−	1.06315i
$393$	−149.676	−	21.2603i	−0.380855	−	0.0540976i
$394$	338.676	−	586.604i	0.859583	−	1.48884i
$395$	−254.730			−0.644887
$396$	−25.2102	−	102.396i	−0.0636622	−	0.258576i
$397$		−	518.469i		−	1.30597i	−0.757372	−	0.652983i	$-0.773517\pi$
$397$		−	518.469i		−	1.30597i	0.757372	−	0.652983i	$-0.226483\pi$
$398$	−163.400	+	283.016i	−0.410552	+	0.711096i
$399$	−235.542	+	94.7620i	−0.590331	+	0.237499i
$400$	−118.930	−	205.993i	−0.297326	−	0.514984i
$401$	−294.320	−	509.777i	−0.733965	−	1.27126i	−0.955176	−	0.296039i	$-0.904334\pi$
$401$	−294.320	−	509.777i	−0.733965	−	1.27126i	0.221211	−	0.975226i	$-0.428999\pi$
$402$	−677.225	+	864.183i	−1.68464	+	2.14971i
$403$	126.165	+	268.122i	0.313064	+	0.665316i
$404$			387.346i			0.958778i
$405$	−494.806	−	313.255i	−1.22174	−	0.773470i
$406$	402.066			0.990309
$407$	55.8351	+	32.2364i	0.137187	+	0.0792050i
$408$	367.092	−	468.434i	0.899736	−	1.14812i
$409$	−217.840	+	125.770i	−0.532617	+	0.307506i	−0.742081	−	0.670310i	$-0.766161\pi$
$409$	−217.840	+	125.770i	−0.532617	+	0.307506i	0.209465	+	0.977816i	$0.432828\pi$
$410$	−175.839	−	304.562i	−0.428876	−	0.742835i
$411$	−61.9822	+	24.9363i	−0.150808	+	0.0606724i
$412$	−144.344	+	250.011i	−0.350349	+	0.606822i
$413$		−	172.702i		−	0.418164i
$414$	455.042	−	112.033i	1.09914	−	0.270611i
$415$	33.1689			0.0799251
$416$	−186.943	+	87.9659i	−0.449383	+	0.211457i
$417$	41.6792	−	293.428i	0.0999501	−	0.703664i
$418$	154.311	−	89.0917i	0.369166	−	0.213138i
$419$	−103.394	+	59.6943i	−0.246763	+	0.142469i	−0.618281	−	0.785957i	$-0.712171\pi$
$419$	−103.394	+	59.6943i	−0.246763	+	0.142469i	0.371518	+	0.928426i	$0.378837\pi$
$420$	−402.784	−	57.2123i	−0.959009	−	0.136220i
$421$	−511.679	−	295.418i	−1.21539	−	0.701706i	−0.251462	−	0.967867i	$-0.580911\pi$
$421$	−511.679	−	295.418i	−1.21539	−	0.701706i	−0.963928	+	0.266161i	$0.914245\pi$
$422$	−832.469			−1.97268
$423$	199.093	+	57.7239i	0.470669	+	0.136463i
$424$			338.979i			0.799479i
$425$	413.846	+	238.934i	0.973755	+	0.562197i
$426$	−36.7522	+	14.7860i	−0.0862728	+	0.0347088i
$427$	−253.326	+	146.258i	−0.593270	+	0.342525i
$428$	−1093.64	+	631.415i	−2.55524	+	1.47527i
$429$	18.2737	+	59.3444i	0.0425959	+	0.138332i
$430$	396.763	−	687.213i	0.922704	−	1.59817i
$431$	−226.873			−0.526387			−0.263194	−	0.964743i	$-0.584776\pi$
$431$	−226.873			−0.526387			−0.263194	+	0.964743i	$0.584776\pi$
$432$	−137.570	−	191.118i	−0.318449	−	0.442403i
$433$	462.970			1.06922			0.534608	−	0.845100i	$-0.320459\pi$
$433$	462.970			1.06922			0.534608	+	0.845100i	$0.320459\pi$
$434$	97.9001	−	169.568i	0.225576	−	0.390709i
$435$	−626.215	+	799.091i	−1.43957	+	1.83699i
$436$	−903.446	+	521.605i	−2.07212	+	1.19634i
$437$	256.502	+	444.274i	0.586960	+	1.01664i
$438$	50.3172	+	125.069i	0.114879	+	0.285546i
$439$	−53.3374	+	92.3831i	−0.121497	+	0.210440i	−0.920358	−	0.391076i	$-0.872103\pi$
$439$	−53.3374	+	92.3831i	−0.121497	+	0.210440i	0.798861	+	0.601516i	$0.205436\pi$
$440$	130.329			0.296202
$441$	275.956	−	264.922i	0.625750	−	0.600729i
$442$	−438.149	+	630.397i	−0.991288	+	1.42624i
$443$	285.885	+	165.056i	0.645338	+	0.372586i	0.786668	−	0.617376i	$-0.211804\pi$
$443$	285.885	+	165.056i	0.645338	+	0.372586i	−0.141330	+	0.989963i	$0.545138\pi$
$444$	885.132	+	125.726i	1.99354	+	0.283167i
$445$	−291.204	−	504.380i	−0.654391	−	1.13344i
$446$	−161.188	+	93.0622i	−0.361409	+	0.208660i
$447$	−17.4878	+	123.117i	−0.0391226	+	0.275429i
$448$	195.230	+	112.716i	0.435781	+	0.251598i
$449$	198.847			0.442867			0.221434	−	0.975175i	$-0.428926\pi$
$449$	198.847			0.442867			0.221434	+	0.975175i	$0.428926\pi$
$450$	596.777	−	572.915i	1.32617	−	1.27315i
$451$	22.9784			0.0509498
$452$	781.479	+	451.187i	1.72894	+	0.998202i
$453$	−275.333	−	684.371i	−0.607798	−	1.51075i
$454$	223.120	+	386.456i	0.491455	+	0.851224i
$455$	238.711	+	20.0481i	0.524639	+	0.0440618i
$456$	695.671	−	887.721i	1.52559	−	1.94676i
$457$	−111.800	−	64.5475i	−0.244638	−	0.141242i	0.372669	−	0.927965i	$-0.378443\pi$
$457$	−111.800	−	64.5475i	−0.244638	−	0.141242i	−0.617307	+	0.786723i	$0.711776\pi$
$458$		−	442.868i		−	0.966960i
$459$	431.333	+	194.329i	0.939724	+	0.423374i
$460$			822.025i			1.78701i
$461$	50.5581	−	87.5692i	0.109671	−	0.189955i	−0.805966	−	0.591961i	$-0.798354\pi$
$461$	50.5581	−	87.5692i	0.109671	−	0.189955i	0.915637	+	0.402007i	$0.131687\pi$
$462$	25.3080	−	32.2947i	0.0547792	−	0.0699019i
$463$	98.9027	−	57.1015i	0.213613	−	0.123329i	−0.389377	−	0.921079i	$-0.627310\pi$
$463$	98.9027	−	57.1015i	0.213613	−	0.123329i	0.602989	+	0.797749i	$0.293976\pi$
$464$	−353.532	+	204.112i	−0.761923	+	0.439896i
$465$	184.531	+	458.674i	0.396842	+	0.986396i
$466$	53.3477	+	30.8003i	0.114480	+	0.0660951i
$467$		−	197.924i		−	0.423820i	−0.977289	−	0.211910i	$-0.932032\pi$
$467$		−	197.924i		−	0.423820i	0.977289	−	0.211910i	$-0.0679684\pi$
$468$	542.222	+	668.858i	1.15859	+	1.42918i
$469$	−276.755			−0.590095
$470$	−280.623	+	486.054i	−0.597071	+	1.03416i
$471$	74.2332	−	522.613i	0.157608	−	1.10958i
$472$	383.590	+	664.397i	0.812691	+	1.40762i
$473$	25.9241	+	44.9019i	0.0548079	+	0.0949300i
$474$	50.0978	−	352.697i	0.105692	−	0.744086i
$475$	784.272	+	452.800i	1.65110	+	0.953263i
$476$	328.646			0.690433
$477$	−261.649	+	64.4189i	−0.548531	+	0.135050i
$478$	1034.85			2.16496
$479$	−297.011	+	514.438i	−0.620065	+	1.07398i	0.369408	+	0.929267i	$0.379560\pi$
$479$	−297.011	+	514.438i	−0.620065	+	1.07398i	−0.989473	+	0.144716i	$0.953773\pi$
$480$	−319.802	+	128.661i	−0.666254	+	0.268044i
$481$	−524.576	−	44.0565i	−1.09059	−	0.0915935i
$482$	−550.640	+	317.912i	−1.14241	+	0.659569i
$483$	92.9787	+	72.8636i	0.192503	+	0.150856i
$484$	435.907	−	755.013i	0.900634	−	1.55994i
$485$			222.436i			0.458630i
$486$	531.043	−	623.495i	1.09268	−	1.28291i
$487$			40.9619i			0.0841106i	0.999115	+	0.0420553i	$0.0133906\pi$
$487$			40.9619i			0.0841106i	−0.999115	+	0.0420553i	$0.986609\pi$
$488$	649.711	−	1125.33i	1.33137	−	2.30601i
$489$	−223.061	+	284.640i	−0.456157	+	0.582086i
$490$	517.862	+	896.964i	1.05686	+	1.83054i
$491$	−577.968	+	333.690i	−1.17713	+	0.679614i	−0.955348	−	0.295484i	$-0.904519\pi$
$491$	−577.968	+	333.690i	−1.17713	+	0.679614i	−0.221777	+	0.975097i	$0.571186\pi$
$492$	295.605	−	118.926i	0.600822	−	0.241720i
$493$	410.066	−	710.254i	0.831776	−	1.44068i
$494$	−830.330	+	1194.66i	−1.68083	+	2.41833i
$495$	24.7674	+	100.598i	0.0500352	+	0.203227i
$496$			198.799i			0.400805i
$497$	−8.64791	−	4.99287i	−0.0174002	−	0.0100460i
$498$	−6.52333	+	45.9253i	−0.0130991	+	0.0922194i
$499$	−132.293	+	76.3792i	−0.265116	+	0.153065i	−0.626666	−	0.779288i	$-0.715581\pi$
$499$	−132.293	+	76.3792i	−0.265116	+	0.153065i	0.361550	+	0.932353i	$0.382248\pi$
$500$	60.4648	+	104.728i	0.120930	+	0.209456i
$501$	78.8664	−	555.232i	0.157418	−	1.10825i
$502$	645.871	+	372.894i	1.28659	+	0.742816i
$503$		−	50.5446i		−	0.100486i	−0.998737	−	0.0502431i	$-0.984000\pi$
$503$		−	50.5446i		−	0.100486i	0.998737	−	0.0502431i	$-0.0159996\pi$
$504$	72.3184	−	249.430i	0.143489	−	0.494901i
$505$		−	380.543i		−	0.753551i
$506$	−71.7968	−	41.4519i	−0.141891	−	0.0819207i
$507$	−341.310	−	374.908i	−0.673196	−	0.739464i
$508$	−825.961	−	1430.61i	−1.62591	−	2.81616i
$509$	229.592	+	397.665i	0.451064	+	0.781267i	0.998452	−	0.0556124i	$-0.0177111\pi$
$509$	229.592	+	397.665i	0.451064	+	0.781267i	−0.547388	+	0.836879i	$0.684378\pi$
$510$	−790.080	+	1008.19i	−1.54918	+	1.97685i
$511$	−16.9909	+	29.4292i	−0.0332504	+	0.0575913i
$512$	−533.584			−1.04216
$513$	817.413	+	368.270i	1.59340	+	0.717874i
$514$		−	1212.10i		−	2.35817i
$515$	141.809	−	245.620i	0.275357	−	0.476931i
$516$	565.893	+	443.467i	1.09669	+	0.859433i
$517$	−18.3357	−	31.7583i	−0.0354655	−	0.0614281i
$518$	173.921	+	301.240i	0.335755	+	0.581545i
$519$	−22.7081	−	56.4436i	−0.0437536	−	0.108755i
$520$	−962.867	+	453.076i	−1.85167	+	0.871300i
$521$		−	255.226i		−	0.489877i	−0.969539	−	0.244938i	$-0.921232\pi$
$521$		−	255.226i		−	0.489877i	0.969539	−	0.244938i	$-0.0787677\pi$
$522$	−983.254	−	1024.21i	−1.88363	−	1.96208i
$523$	−298.364			−0.570485			−0.285243	−	0.958455i	$-0.592074\pi$
$523$	−298.364			−0.570485			−0.285243	+	0.958455i	$0.592074\pi$
$524$	321.169	+	185.427i	0.612917	+	0.353868i
$525$	206.457	+	29.3257i	0.393252	+	0.0558584i
$526$	−819.173	+	472.950i	−1.55736	+	0.899144i
$527$	−199.696	−	345.884i	−0.378930	−	0.656326i
$528$	−5.85842	+	41.2442i	−0.0110955	+	0.0781140i
$529$	−145.157	+	251.419i	−0.274399	+	0.475273i
$530$		−	729.573i		−	1.37655i
$531$	−439.935	+	422.344i	−0.828502	+	0.795375i
$532$	622.812			1.17070
$533$	−169.764	+	79.8821i	−0.318506	+	0.149873i
$534$	755.630	−	304.001i	1.41504	−	0.569291i
$535$	1074.43	−	620.325i	2.00829	−	1.15949i
$536$	1064.70	−	614.702i	1.98637	−	1.14683i
$537$	296.209	−	377.982i	0.551600	−	0.703877i
$538$	−654.892	−	378.102i	−1.21727	−	0.702792i
$539$	−67.6734			−0.125554
$540$	839.270	+	1165.95i	1.55420	+	2.15917i
$541$		−	575.956i		−	1.06461i	−0.846552	−	0.532307i	$-0.821325\pi$
$541$		−	575.956i		−	1.06461i	0.846552	−	0.532307i	$-0.178675\pi$
$542$	203.565	+	117.528i	0.375582	+	0.216842i
$543$	275.073	+	215.563i	0.506580	+	0.396986i
$544$	241.161	−	139.234i	0.443310	−	0.255945i
$545$	887.578	−	512.444i	1.62858	−	0.940263i
$546$	−74.7056	+	326.573i	−0.136823	+	0.598119i
$547$	−349.284	+	604.978i	−0.638545	+	1.10599i	0.347207	+	0.937789i	$0.387130\pi$
$547$	−349.284	+	604.978i	−0.638545	+	1.10599i	−0.985752	+	0.168204i	$0.946203\pi$
$548$	163.891			0.299071
$549$	992.084	+	287.639i	1.80708	+	0.523933i
$550$	−146.349			−0.266090
$551$	777.109	−	1345.99i	1.41036	−	2.44282i
$552$	−519.534	−	73.7958i	−0.941185	−	0.133688i
$553$	77.7661	−	44.8983i	0.140626	−	0.0811904i
$554$	409.937	+	710.032i	0.739959	+	1.28165i
$555$	−869.586	−	123.518i	−1.56682	−	0.222555i
$556$	−363.514	+	629.625i	−0.653802	+	1.13242i
$557$	832.902			1.49534			0.747668	−	0.664073i	$-0.231174\pi$
$557$	832.902			1.49534			0.747668	+	0.664073i	$0.231174\pi$
$558$	−671.366	+	165.293i	−1.20317	+	0.296223i
$559$	−347.624	−	241.611i	−0.621868	−	0.432221i
$560$	139.181	+	80.3559i	0.248537	+	0.143493i
$561$	−31.2374	−	77.6442i	−0.0556817	−	0.138403i
$562$	388.382	+	672.697i	0.691071	+	1.19697i
$563$	−181.376	+	104.717i	−0.322159	+	0.185999i	−0.652355	−	0.757914i	$-0.726219\pi$
$563$	−181.376	+	104.717i	−0.322159	+	0.185999i	0.330195	+	0.943913i	$0.392885\pi$
$564$	−400.246	−	313.657i	−0.709657	−	0.556129i
$565$	−767.754	−	443.263i	−1.35886	−	0.784536i
$566$	787.679			1.39166
$567$	206.272	+	8.41950i	0.363795	+	0.0148492i
$568$	44.3589			0.0780966
$569$	−306.715	−	177.082i	−0.539042	−	0.311216i	0.205649	−	0.978626i	$-0.434070\pi$
$569$	−306.715	−	177.082i	−0.539042	−	0.311216i	−0.744691	+	0.667410i	$0.767403\pi$
$570$	−1497.27	+	1910.61i	−2.62679	+	3.35195i
$571$	−21.2844	−	36.8657i	−0.0372757	−	0.0645635i	0.846786	−	0.531934i	$-0.178535\pi$
$571$	−21.2844	−	36.8657i	−0.0372757	−	0.0645635i	−0.884061	+	0.467371i	$0.845201\pi$
$572$	12.7479	−	151.788i	0.0222865	−	0.265363i
$573$	−261.633	−	650.318i	−0.456601	−	1.13493i
$574$	107.363	+	61.9861i	0.187044	+	0.107990i
$575$		−	421.350i		−	0.732783i
$576$	−190.307	−	772.969i	−0.330395	−	1.34196i
$577$			564.679i			0.978646i	0.872103	+	0.489323i	$0.162756\pi$
$577$			564.679i			0.978646i	−0.872103	+	0.489323i	$0.837244\pi$
$578$	30.3542	−	52.5750i	0.0525159	−	0.0909602i
$579$	−665.995	−	94.5995i	−1.15025	−	0.163384i
$580$	2156.79	−	1245.22i	3.71860	−	2.14693i
$581$	−10.1261	+	5.84629i	−0.0174287	+	0.0100625i
$582$	−307.982	−	43.7464i	−0.529178	−	0.0751657i
$583$	41.2831	+	23.8348i	0.0708116	+	0.0408831i
$584$		−	150.955i		−	0.258484i
$585$	−532.699	−	657.111i	−0.910596	−	1.12327i
$586$	−1713.89			−2.92472
$587$	−217.901	+	377.415i	−0.371211	+	0.642956i	−0.989752	−	0.142796i	$-0.954391\pi$
$587$	−217.901	+	377.415i	−0.371211	+	0.642956i	0.618541	+	0.785752i	$0.287724\pi$
$588$	−870.583	+	350.248i	−1.48058	+	0.595660i
$589$	−378.441	−	655.479i	−0.642514	−	1.11287i
$590$	−825.587	−	1429.96i	−1.39930	−	2.42366i
$591$	−474.562	−	371.894i	−0.802981	−	0.629263i
$592$	−305.854	−	176.585i	−0.516646	−	0.298286i
$593$	55.6224			0.0937984			0.0468992	−	0.998900i	$-0.485066\pi$
$593$	55.6224			0.0937984			0.0468992	+	0.998900i	$0.485066\pi$
$594$	−144.157	+	14.5082i	−0.242689	+	0.0244245i
$595$	−322.874			−0.542645
$596$	152.524	−	264.179i	0.255912	−	0.443253i
$597$	228.960	+	179.426i	0.383517	+	0.300547i
$598$	674.537	+	56.6509i	1.12799	+	0.0947340i
$599$	763.317	−	440.701i	1.27432	−	0.735728i	0.298521	−	0.954403i	$-0.403507\pi$
$599$	763.317	−	440.701i	1.27432	−	0.735728i	0.975798	+	0.218675i	$0.0701734\pi$
$600$	−859.392	+	345.746i	−1.43232	+	0.576244i
$601$	−19.0786	+	33.0451i	−0.0317447	+	0.0549835i	−0.881461	−	0.472256i	$-0.843440\pi$
$601$	−19.0786	+	33.0451i	−0.0317447	+	0.0549835i	0.849717	+	0.527240i	$0.176773\pi$
$602$			279.730i			0.464668i
$603$	676.805	+	704.994i	1.12240	+	1.16915i
$604$			1809.59i			2.99601i
$605$	−428.251	+	741.752i	−0.707852	+	1.22604i
$606$	526.896	+	74.8415i	0.869465	+	0.123501i
$607$	−94.0210	−	162.849i	−0.154895	−	0.268285i	0.778126	−	0.628108i	$-0.216170\pi$
$607$	−94.0210	−	162.849i	−0.154895	−	0.268285i	−0.933021	+	0.359823i	$0.882837\pi$
$608$	457.020	−	263.861i	0.751678	−	0.433981i
$609$	50.3296	−	354.328i	0.0826430	−	0.581820i
$610$	−1398.35	+	2422.01i	−2.29238	+	3.97051i
$611$	245.868	+	170.888i	0.402403	+	0.279685i
$612$	−803.706	−	837.181i	−1.31325	−	1.36794i
$613$			728.653i			1.18867i	0.804218	+	0.594334i	$0.202584\pi$
$613$			728.653i			1.18867i	−0.804218	+	0.594334i	$0.797416\pi$
$614$	−26.9527	−	15.5612i	−0.0438970	−	0.0253439i
$615$	−290.413	+	116.837i	−0.472216	+	0.189979i
$616$	−39.7878	+	22.9715i	−0.0645906	+	0.0372914i
$617$	−538.990	−	933.559i	−0.873566	−	1.51306i	−0.858282	−	0.513178i	$-0.828468\pi$
$617$	−538.990	−	933.559i	−0.873566	−	1.51306i	−0.0152844	−	0.999883i	$-0.504865\pi$
$618$	312.193	+	244.653i	0.505166	+	0.395878i
$619$	−317.751	−	183.454i	−0.513330	−	0.296371i	0.220871	−	0.975303i	$-0.429110\pi$
$619$	−317.751	−	183.454i	−0.513330	−	0.296371i	−0.734201	+	0.678932i	$0.762443\pi$
$620$		−	1212.81i		−	1.95614i
$621$	−41.7701	−	415.039i	−0.0672626	−	0.668340i
$622$		−	891.502i		−	1.43328i
$623$	177.802	+	102.654i	0.285397	+	0.164774i
$624$	−100.100	−	325.077i	−0.160416	−	0.520957i
$625$	281.507	+	487.585i	0.450411	+	0.780136i
$626$	303.987	+	526.521i	0.485602	+	0.841088i
$627$	−59.1975	−	147.142i	−0.0944139	−	0.234677i
$628$	−647.441	+	1121.40i	−1.03096	+	1.78567i
$629$	709.527			1.12802
$630$	−155.648	+	536.840i	−0.247061	+	0.852127i
$631$			79.7699i			0.126418i	0.998000	+	0.0632091i	$0.0201335\pi$
$631$			79.7699i			0.126418i	−0.998000	+	0.0632091i	$0.979866\pi$
$632$	−199.448	+	345.454i	−0.315582	+	0.546605i
$633$	−104.206	+	733.630i	−0.164623	+	1.15897i
$634$	−499.955	−	865.947i	−0.788572	−	1.36585i
$635$	811.455	+	1405.48i	1.27788	+	2.21336i
$636$	654.445	+	92.9589i	1.02900	+	0.146162i
$637$	499.969	−	235.260i	0.784881	−	0.369325i
$638$			251.169i			0.393682i
$639$	8.42987	+	34.2395i	0.0131923	+	0.0535829i
$640$	1695.70			2.64953
$641$	362.313	+	209.182i	0.565231	+	0.326336i	0.755242	−	0.655446i	$-0.227519\pi$
$641$	362.313	+	209.182i	0.565231	+	0.326336i	−0.190011	+	0.981782i	$0.560852\pi$
$642$	647.585	+	1609.65i	1.00870	+	2.50724i
$643$	−99.3380	+	57.3528i	−0.154491	+	0.0891957i	−0.575253	−	0.817976i	$-0.695096\pi$
$643$	−99.3380	+	57.3528i	−0.154491	+	0.0891957i	0.420761	+	0.907171i	$0.361763\pi$
$644$	−144.888	−	250.954i	−0.224982	−	0.389680i
$645$	−555.954	−	435.679i	−0.861945	−	0.675471i
$646$	980.459	−	1698.20i	1.51774	−	2.62880i
$647$			31.4954i			0.0486792i	0.999704	+	0.0243396i	$0.00774830\pi$
$647$			31.4954i			0.0486792i	−0.999704	+	0.0243396i	$0.992252\pi$
$648$	−812.245	+	425.762i	−1.25346	+	0.657041i
$649$	107.886			0.166235
$650$	1081.22	−	508.769i	1.66342	−	0.782722i
$651$	−137.180	−	107.502i	−0.210722	−	0.165134i
$652$	768.257	−	443.554i	1.17831	−	0.680297i
$653$	−507.638	+	293.085i	−0.777393	+	0.448828i	−0.835506	−	0.549482i	$-0.814825\pi$
$653$	−507.638	+	293.085i	−0.777393	+	0.448828i	0.0581125	+	0.998310i	$0.481492\pi$
$654$	534.963	+	1329.71i	0.817986	+	2.03320i
$655$	−315.528	−	182.170i	−0.481722	−	0.278122i
$656$	−125.871			−0.191877
$657$	116.518	−	28.6872i	0.177349	−	0.0436639i
$658$		−	197.848i		−	0.300681i
$659$	−730.478	−	421.741i	−1.10846	−	0.639972i	−0.170033	−	0.985438i	$-0.554387\pi$
$659$	−730.478	−	421.741i	−1.10846	−	0.639972i	−0.938431	+	0.345466i	$0.887721\pi$
$660$	35.7403	−	251.618i	0.0541520	−	0.381239i
$661$	−299.887	+	173.140i	−0.453686	+	0.261936i	−0.709386	−	0.704820i	$-0.751028\pi$
$661$	−299.887	+	173.140i	−0.453686	+	0.261936i	0.255699	+	0.966756i	$0.417694\pi$
$662$	56.0812	−	32.3785i	0.0847148	−	0.0489101i
$663$	500.704	+	465.039i	0.755209	+	0.701417i
$664$	25.9705	−	44.9822i	0.0391122	−	0.0677443i
$665$	−611.873			−0.920110
$666$	342.043	−	1179.73i	0.513578	−	1.77136i
$667$	−723.134			−1.08416
$668$	−687.851	+	1191.39i	−1.02972	+	1.78352i
$669$	61.8357	+	153.700i	0.0924301	+	0.229746i
$670$	−2291.51	+	1323.00i	−3.42016	+	1.97463i
$671$	−91.3670	−	158.252i	−0.136165	−	0.235845i
$672$	74.9541	−	95.6463i	0.111539	−	0.142331i
$673$	393.093	−	680.857i	0.584090	−	1.01167i	−0.410898	−	0.911681i	$-0.634785\pi$
$673$	393.093	−	680.857i	0.584090	−	1.01167i	0.994988	−	0.0999926i	$-0.0318819\pi$
$674$	370.335			0.549458
$675$	−430.190	−	597.638i	−0.637318	−	0.885390i
$676$	433.494	+	1165.72i	0.641264	+	1.72444i
$677$	534.737	+	308.730i	0.789862	+	0.456027i	0.839914	−	0.542720i	$-0.182605\pi$
$677$	534.737	+	308.730i	0.789862	+	0.456027i	−0.0500520	+	0.998747i	$0.515939\pi$
$678$	764.731	−	975.846i	1.12792	−	1.43930i
$679$	−39.2061	−	67.9069i	−0.0577409	−	0.100010i
$680$	1242.12	−	717.138i	1.82665	−	1.05461i
$681$	368.502	−	148.254i	0.541118	−	0.217700i
$682$	105.928	+	61.1578i	0.155320	+	0.0896743i
$683$	−1039.61			−1.52213			−0.761063	−	0.648678i	$-0.775322\pi$
$683$	−1039.61			−1.52213			−0.761063	+	0.648678i	$0.775322\pi$
$684$	−1523.09	−	1586.53i	−2.22674	−	2.31948i
$685$	−161.013			−0.235055
$686$	−680.712	−	393.009i	−0.992291	−	0.572900i
$687$	−390.286	−	55.4371i	−0.568102	−	0.0806945i
$688$	−142.007	−	245.964i	−0.206406	−	0.357506i
$689$	−387.858	−	32.5743i	−0.562929	−	0.0472776i
$690$	1118.18	+	158.828i	1.62054	+	0.230186i
$691$	390.293	+	225.336i	0.564823	+	0.326101i	0.755079	−	0.655634i	$-0.227598\pi$
$691$	390.293	+	225.336i	0.564823	+	0.326101i	−0.190256	+	0.981735i	$0.560932\pi$
$692$			149.246i			0.215674i
$693$	−25.2923	−	26.3458i	−0.0364969	−	0.0380170i
$694$			496.556i			0.715499i
$695$	357.129	−	618.566i	0.513855	−	0.890024i
$696$	593.380	+	1474.92i	0.852558	+	2.11913i
$697$	218.999	−	126.439i	0.314202	−	0.181405i
$698$	−1311.74	+	757.334i	−1.87928	+	1.08501i
$699$	33.8213	−	43.1582i	0.0483853	−	0.0617428i
$700$	−443.007	−	255.770i	−0.632867	−	0.365386i
$701$			1193.94i			1.70319i	0.524199	+	0.851596i	$0.324365\pi$
$701$			1193.94i			1.70319i	−0.524199	+	0.851596i	$0.675635\pi$
$702$	1014.59	−	608.335i	1.44529	−	0.866574i
$703$	1344.61			1.91268
$704$	−70.4133	+	121.959i	−0.100019	+	0.173238i
$705$	393.217	+	308.148i	0.557754	+	0.437089i
$706$	−66.8587	−	115.803i	−0.0947008	−	0.164027i
$707$	67.0738	+	116.175i	0.0948710	+	0.164321i
$708$	1387.90	−	558.373i	1.96031	−	0.788663i
$709$	836.882	+	483.174i	1.18037	+	0.681486i	0.956100	−	0.293041i	$-0.0946673\pi$
$709$	836.882	+	483.174i	1.18037	+	0.681486i	0.224269	+	0.974527i	$0.428001\pi$
$710$	−95.4721			−0.134468
$711$	−304.550	−	88.2994i	−0.428340	−	0.124190i
$712$	−912.024			−1.28093
$713$	−176.078	+	304.976i	−0.246954	+	0.427736i
$714$	63.4996	−	447.047i	0.0889350	−	0.626116i
$715$	−12.5240	+	149.122i	−0.0175161	+	0.208562i
$716$	−1020.19	+	589.008i	−1.42485	+	0.822637i
$717$	129.540	−	911.982i	0.180669	−	1.27194i
$718$	−741.240	+	1283.86i	−1.03237	+	1.78811i
$719$			108.172i			0.150448i	0.997167	+	0.0752241i	$0.0239672\pi$
$719$			108.172i			0.150448i	−0.997167	+	0.0752241i	$0.976033\pi$
$720$	−135.671	−	551.054i	−0.188432	−	0.765353i
$721$			99.9796i			0.138668i
$722$	1249.70	−	2164.55i	1.73089	−	2.99799i
$723$	211.239	+	525.058i	0.292169	+	0.726221i
$724$	−428.646	−	742.436i	−0.592052	−	1.02546i
$725$	−1105.52	+	638.271i	−1.52485	+	0.880374i
$726$	−942.797	−	738.831i	−1.29862	−	1.01767i
$727$	−78.3223	+	135.658i	−0.107734	+	0.186600i	−0.914852	−	0.403790i	$-0.867693\pi$
$727$	−78.3223	+	135.658i	−0.107734	+	0.186600i	0.807118	+	0.590390i	$0.201026\pi$
$728$	214.093	−	308.032i	0.294084	−	0.423120i
$729$	−482.992	−	546.040i	−0.662541	−	0.749026i
$730$			324.895i			0.445062i
$731$	494.148	+	285.296i	0.675989	+	0.390282i
$732$	−1994.43	−	1562.96i	−2.72464	−	2.13519i
$733$	−581.233	+	335.575i	−0.792951	+	0.457811i	−0.841001	−	0.541034i	$-0.818033\pi$
$733$	−581.233	+	335.575i	−0.792951	+	0.457811i	0.0480491	+	0.998845i	$0.484700\pi$
$734$	280.483	+	485.811i	0.382130	+	0.661868i
$735$	855.292	−	344.097i	1.16366	−	0.468159i
$736$	−212.639	−	122.767i	−0.288911	−	0.166803i
$737$		−	172.888i		−	0.234583i
$738$	−104.656	−	425.081i	−0.141811	−	0.575990i
$739$		−	1012.63i		−	1.37027i	−0.728418	−	0.685133i	$-0.759744\pi$
$739$		−	1012.63i		−	1.37027i	0.728418	−	0.685133i	$-0.240256\pi$
$740$	1865.92	+	1077.29i	2.52151	+	1.45580i
$741$	948.876	+	881.289i	1.28053	+	1.18932i
$742$	128.593	+	222.730i	0.173306	+	0.300175i
$743$	−399.361	−	691.714i	−0.537498	−	0.930974i	−0.999038	−	0.0438545i	$-0.986036\pi$
$743$	−399.361	−	691.714i	−0.537498	−	0.930974i	0.461540	−	0.887119i	$-0.347297\pi$
$744$	766.517	+	108.878i	1.03026	+	0.146341i
$745$	−149.845	+	259.539i	−0.201134	+	0.348374i
$746$	−244.118			−0.327235
$747$	39.6560	+	11.4976i	0.0530870	+	0.0153917i
$748$			205.304i			0.274471i
$749$	−218.674	+	378.755i	−0.291955	+	0.505681i
$750$	154.141	−	62.0134i	0.205522	−	0.0826845i
$751$	169.930	+	294.327i	0.226272	+	0.391914i	0.956700	−	0.291075i	$-0.0940130\pi$
$751$	169.930	+	294.327i	0.226272	+	0.391914i	−0.730429	+	0.682989i	$0.760680\pi$
$752$	100.439	+	173.966i	0.133563	+	0.231338i
$753$	409.468	−	522.508i	0.543783	−	0.693902i
$754$	−873.165	−	1855.63i	−1.15804	−	2.46105i
$755$		−	1777.81i		−	2.35471i
$756$	−461.727	−	208.022i	−0.610750	−	0.275162i
$757$	7.45770			0.00985165			0.00492583	−	0.999988i	$-0.498432\pi$
$757$	7.45770			0.00985165			0.00492583	+	0.999988i	$0.498432\pi$
$758$	−1384.00	−	799.054i	−1.82586	−	1.05416i
$759$	−45.5177	+	58.0835i	−0.0599706	+	0.0765264i
$760$	2353.92	−	1359.04i	3.09726	−	1.78821i
$761$	−174.991	−	303.093i	−0.229949	−	0.398283i	0.727844	−	0.685743i	$-0.240522\pi$
$761$	−174.991	−	303.093i	−0.229949	−	0.398283i	−0.957793	+	0.287460i	$0.907189\pi$
$762$	−2105.60	+	847.114i	−2.76326	+	1.11170i
$763$	−180.645	+	312.886i	−0.236756	+	0.410073i
$764$			1719.55i			2.25072i
$765$	789.590	+	822.477i	1.03214	+	1.07513i
$766$	−1829.21			−2.38800
$767$	−797.062	+	375.056i	−1.03919	+	0.488992i
$768$	−184.228	+	1296.99i	−0.239880	+	1.68879i
$769$	349.165	−	201.591i	0.454051	−	0.262147i	−0.255488	−	0.966812i	$-0.582236\pi$
$769$	349.165	−	201.591i	0.454051	−	0.262147i	0.709540	+	0.704665i	$0.248903\pi$
$770$	85.6340	−	49.4408i	0.111213	−	0.0642088i
$771$	−1068.19	−	151.728i	−1.38546	−	0.196794i

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.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.68517 + 2.91881i) q^{2} +(2.36131 + 1.85046i) q^{3} +(-3.67962 - 6.37330i) q^{4} +(3.61500 + 6.26136i) q^{5} +(-9.38036 + 3.77386i) q^{6} +(-2.20723 - 1.27434i) q^{7} +11.3218 q^{8} +(2.15158 + 8.73903i) q^{9} -24.3676 q^{10} +(0.796079 - 1.37885i) q^{11} +(3.10481 - 21.8583i) q^{12} +(-1.08797 + 12.9544i) q^{13} +(7.43913 - 4.29498i) q^{14} +(-3.05028 + 21.4744i) q^{15} +(-4.36077 + 7.55307i) q^{16} -17.5218i q^{17} +(-29.1333 - 8.44675i) q^{18} -33.2052i q^{19} +(26.6037 - 46.0789i) q^{20} +(-2.85383 - 7.09352i) q^{21} +(2.68306 + 4.64720i) q^{22} +(-13.3796 + 7.72474i) q^{23} +(26.7344 + 20.9506i) q^{24} +(-13.6364 + 23.6189i) q^{25} +(-35.9780 - 25.0060i) q^{26} +(-11.0907 + 24.6170i) q^{27} +18.7564i q^{28} +(40.5355 + 23.4032i) q^{29} +(-57.5395 - 45.0913i) q^{30} +(19.7402 - 11.3970i) q^{31} +(7.94636 + 13.7635i) q^{32} +(4.43130 - 1.78278i) q^{33} +(51.1427 + 29.5272i) q^{34} -18.4270i q^{35} +(47.7794 - 45.8690i) q^{36} +40.4940i q^{37} +(96.9197 + 55.9566i) q^{38} +(-26.5407 + 28.5761i) q^{39} +(40.9284 + 70.8901i) q^{40} +(7.21611 + 12.4987i) q^{41} +(25.5138 + 3.62404i) q^{42} +(-16.2824 + 28.2019i) q^{43} -11.7171 q^{44} +(-46.9403 + 45.0634i) q^{45} -52.0701i q^{46} +(11.5162 - 19.9467i) q^{47} +(-24.2738 + 9.76572i) q^{48} +(-21.2521 - 36.8097i) q^{49} +(-45.9594 - 79.6041i) q^{50} +(32.4234 - 41.3744i) q^{51} +(86.5655 - 40.7333i) q^{52} +29.9403i q^{53} +(-53.1625 - 73.8556i) q^{54} +11.5113 q^{55} +(-24.9899 - 14.4279i) q^{56} +(61.4450 - 78.4079i) q^{57} +(-136.619 + 78.8769i) q^{58} +(33.8805 + 58.6828i) q^{59} +(148.087 - 59.5775i) q^{60} +(57.3856 - 99.3948i) q^{61} +76.8239i q^{62} +(6.38751 - 22.0309i) q^{63} -88.4502 q^{64} +(-85.0451 + 40.0179i) q^{65} +(-2.26393 + 15.9384i) q^{66} +(94.0391 - 54.2935i) q^{67} +(-111.671 + 64.4735i) q^{68} +(-45.8878 - 6.51801i) q^{69} +(53.7849 + 31.0527i) q^{70} +3.91799 q^{71} +(24.3598 + 98.9419i) q^{72} -13.3331i q^{73} +(-118.194 - 68.2395i) q^{74} +(-75.9057 + 30.5380i) q^{75} +(-211.627 + 122.183i) q^{76} +(-3.51426 + 2.02896i) q^{77} +(-38.6825 - 125.623i) q^{78} +(-17.6162 + 30.5122i) q^{79} -63.0567 q^{80} +(-71.7414 + 37.6054i) q^{81} -48.6416 q^{82} +(2.29384 - 3.97305i) q^{83} +(-34.7081 + 44.2898i) q^{84} +(109.710 - 63.3411i) q^{85} +(-54.8773 - 95.0503i) q^{86} +(52.4103 + 130.272i) q^{87} +(9.01307 - 15.6111i) q^{88} -80.5545 q^{89} +(-52.4288 - 212.949i) q^{90} +(18.9098 - 27.2069i) q^{91} +(98.4640 + 56.8482i) q^{92} +(67.7025 + 9.61662i) q^{93} +(38.8138 + 67.2274i) q^{94} +(207.910 - 120.037i) q^{95} +(-6.70501 + 47.2043i) q^{96} +(26.6439 + 15.3828i) q^{97} +143.254 q^{98} +(13.7626 + 3.99026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 4 q^{3} - 50 q^{4} + 4 q^{9} + 8 q^{10} - 38 q^{12} - 6 q^{13} - 6 q^{14} - 90 q^{16} + 14 q^{22} + 138 q^{23} - 92 q^{25} - 76 q^{27} + 48 q^{29} + 186 q^{30} - 154 q^{36} + 324 q^{38} - 2 q^{39}+ \cdots + 504 q^{95}+O(q^{100}) \) 52 * q - 4 * q^3 - 50 * q^4 + 4 * q^9 + 8 * q^10 - 38 * q^12 - 6 * q^13 - 6 * q^14 - 90 * q^16 + 14 * q^22 + 138 * q^23 - 92 * q^25 - 76 * q^27 + 48 * q^29 + 186 * q^30 - 154 * q^36 + 324 * q^38 - 2 * q^39 - 68 * q^40 - 216 * q^42 + 62 * q^43 + 230 * q^48 + 70 * q^49 + 90 * q^51 - 4 * q^52 + 92 * q^55 - 276 * q^56 + 12 * q^61 + 12 * q^64 - 588 * q^65 + 762 * q^66 - 144 * q^68 - 414 * q^69 + 342 * q^74 - 620 * q^75 - 510 * q^77 - 162 * q^78 - 24 * q^79 + 532 * q^81 - 292 * q^82 - 330 * q^87 - 62 * q^88 + 258 * q^90 + 264 * q^91 - 396 * q^92 - 160 * q^94 + 504 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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