LMFDB - Embedded newform 117.3.k.a.29.8

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			29.8
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.86232i q^{2} +(2.37269 - 1.83585i) q^{3} +0.531747 q^{4} +(0.895843 - 0.517215i) q^{5} +(-3.41894 - 4.41872i) q^{6} +(2.55841 + 4.43129i) q^{7} -8.43958i q^{8} +(2.25933 - 8.71180i) q^{9} +(-0.963222 - 1.66835i) q^{10} +9.70050i q^{11} +(1.26167 - 0.976206i) q^{12} +(-5.56216 + 11.7500i) q^{13} +(8.25251 - 4.76459i) q^{14} +(1.17603 - 2.87182i) q^{15} -13.5903 q^{16} +(-26.8136 - 15.4808i) q^{17} +(-16.2242 - 4.20760i) q^{18} +(-0.305781 + 0.529628i) q^{19} +(0.476361 - 0.275027i) q^{20} +(14.2055 + 5.81725i) q^{21} +18.0655 q^{22} +(23.3898 + 13.5041i) q^{23} +(-15.4938 - 20.0245i) q^{24} +(-11.9650 + 20.7239i) q^{25} +(21.8823 + 10.3585i) q^{26} +(-10.6328 - 24.8182i) q^{27} +(1.36043 + 2.35633i) q^{28} -20.6407i q^{29} +(-5.34826 - 2.19015i) q^{30} +(1.09962 + 1.90460i) q^{31} -8.44886i q^{32} +(17.8086 + 23.0163i) q^{33} +(-28.8303 + 49.9356i) q^{34} +(4.58386 + 2.64650i) q^{35} +(1.20139 - 4.63247i) q^{36} +(30.6351 + 53.0616i) q^{37} +(0.986339 + 0.569463i) q^{38} +(8.37392 + 38.0904i) q^{39} +(-4.36508 - 7.56054i) q^{40} +(30.6838 + 17.7153i) q^{41} +(10.8336 - 26.4552i) q^{42} +(-0.628105 - 1.08791i) q^{43} +5.15821i q^{44} +(-2.48187 - 8.97296i) q^{45} +(25.1491 - 43.5595i) q^{46} +(17.3684 + 10.0277i) q^{47} +(-32.2455 + 24.9496i) q^{48} +(11.4091 - 19.7611i) q^{49} +(38.5947 + 22.2827i) q^{50} +(-92.0408 + 12.4944i) q^{51} +(-2.95766 + 6.24802i) q^{52} +39.4824i q^{53} +(-46.2195 + 19.8018i) q^{54} +(5.01725 + 8.69013i) q^{55} +(37.3983 - 21.5919i) q^{56} +(0.246793 + 1.81801i) q^{57} -38.4397 q^{58} -5.72404i q^{59} +(0.625350 - 1.52708i) q^{60} +(-55.5554 - 96.2247i) q^{61} +(3.54699 - 2.04785i) q^{62} +(44.3848 - 12.2766i) q^{63} -70.0956 q^{64} +(1.09446 + 13.4030i) q^{65} +(42.8638 - 33.1655i) q^{66} +(-3.05129 + 5.28499i) q^{67} +(-14.2580 - 8.23188i) q^{68} +(80.2884 - 10.8990i) q^{69} +(4.92863 - 8.53664i) q^{70} +(-77.5112 - 44.7511i) q^{71} +(-73.5240 - 19.0678i) q^{72} +85.2365 q^{73} +(98.8180 - 57.0526i) q^{74} +(9.65681 + 71.1374i) q^{75} +(-0.162598 + 0.281628i) q^{76} +(-42.9858 + 24.8179i) q^{77} +(70.9367 - 15.5950i) q^{78} +(13.6252 - 23.5995i) q^{79} +(-12.1747 + 7.02909i) q^{80} +(-70.7909 - 39.3656i) q^{81} +(32.9917 - 57.1432i) q^{82} +(-128.236 - 74.0368i) q^{83} +(7.55373 + 3.09330i) q^{84} -32.0277 q^{85} +(-2.02604 + 1.16974i) q^{86} +(-37.8932 - 48.9740i) q^{87} +81.8682 q^{88} +(-42.7999 + 24.7105i) q^{89} +(-16.7106 + 4.62205i) q^{90} +(-66.2980 + 5.41374i) q^{91} +(12.4375 + 7.18078i) q^{92} +(6.10562 + 2.50029i) q^{93} +(18.6748 - 32.3457i) q^{94} +0.632618i q^{95} +(-15.5108 - 20.0465i) q^{96} +(36.6052 + 63.4021i) q^{97} +(-36.8016 - 21.2474i) q^{98} +(84.5088 + 21.9166i) 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 $

$2$		−	1.86232i		−	0.931162i	−0.885005	−	0.465581i	$-0.845845\pi$
$2$		−	1.86232i		−	0.931162i	0.885005	−	0.465581i	$-0.154155\pi$
$3$	2.37269	−	1.83585i	0.790897	−	0.611949i
$3$	2.37269	−	1.83585i	0.790897	−	0.611949i
$4$	0.531747			0.132937
$5$	0.895843	−	0.517215i	0.179169	−	0.103443i	−0.407733	−	0.913101i	$-0.633681\pi$
$5$	0.895843	−	0.517215i	0.179169	−	0.103443i	0.586902	+	0.809658i	$0.300347\pi$
$6$	−3.41894	−	4.41872i	−0.569824	−	0.736454i
$7$	2.55841	+	4.43129i	0.365487	+	0.633042i	0.988854	−	0.148887i	$-0.0475691\pi$
$7$	2.55841	+	4.43129i	0.365487	+	0.633042i	−0.623367	+	0.781929i	$0.714236\pi$
$8$		−	8.43958i		−	1.05495i
$9$	2.25933	−	8.71180i	0.251036	−	0.967978i
$10$	−0.963222	−	1.66835i	−0.0963222	−	0.166835i
$11$			9.70050i			0.881864i	0.897541	+	0.440932i	$0.145352\pi$
$11$			9.70050i			0.881864i	−0.897541	+	0.440932i	$0.854648\pi$
$12$	1.26167	−	0.976206i	0.105139	−	0.0813505i
$13$	−5.56216	+	11.7500i	−0.427858	+	0.903846i
$13$	−5.56216	+	11.7500i	−0.427858	+	0.903846i
$14$	8.25251	−	4.76459i	0.589465	−	0.340328i
$15$	1.17603	−	2.87182i	0.0784020	−	0.191455i
$16$	−13.5903			−0.849391
$17$	−26.8136	−	15.4808i	−1.57727	−	0.910637i	−0.995238	−	0.0974709i	$-0.968925\pi$
$17$	−26.8136	−	15.4808i	−1.57727	−	0.910637i	−0.582031	−	0.813166i	$-0.697742\pi$
$18$	−16.2242	−	4.20760i	−0.901344	−	0.233756i
$19$	−0.305781	+	0.529628i	−0.0160937	+	0.0278752i	−0.873960	−	0.485998i	$-0.838456\pi$
$19$	−0.305781	+	0.529628i	−0.0160937	+	0.0278752i	0.857866	+	0.513873i	$0.171790\pi$
$20$	0.476361	−	0.275027i	0.0238181	−	0.0137514i
$21$	14.2055	+	5.81725i	0.676452	+	0.277012i
$22$	18.0655			0.821159
$23$	23.3898	+	13.5041i	1.01695	+	0.587136i	0.913219	−	0.407469i	$-0.133589\pi$
$23$	23.3898	+	13.5041i	1.01695	+	0.587136i	0.103731	+	0.994605i	$0.466922\pi$
$24$	−15.4938	−	20.0245i	−0.645575	−	0.834355i
$25$	−11.9650	+	20.7239i	−0.478599	+	0.828958i
$26$	21.8823	+	10.3585i	0.841627	+	0.398405i
$27$	−10.6328	−	24.8182i	−0.393809	−	0.919192i
$28$	1.36043	+	2.35633i	0.0485866	+	0.0841545i
$29$		−	20.6407i		−	0.711748i	−0.934534	−	0.355874i	$-0.884183\pi$
$29$		−	20.6407i		−	0.711748i	0.934534	−	0.355874i	$-0.115817\pi$
$30$	−5.34826	−	2.19015i	−0.178275	−	0.0730050i
$31$	1.09962	+	1.90460i	0.0354717	+	0.0614388i	0.883216	−	0.468966i	$-0.155373\pi$
$31$	1.09962	+	1.90460i	0.0354717	+	0.0614388i	−0.847745	+	0.530405i	$0.822040\pi$
$32$		−	8.44886i		−	0.264027i
$33$	17.8086	+	23.0163i	0.539656	+	0.697464i
$34$	−28.8303	+	49.9356i	−0.847951	+	1.46869i
$35$	4.58386	+	2.64650i	0.130968	+	0.0756141i
$36$	1.20139	−	4.63247i	0.0333720	−	0.128680i
$37$	30.6351	+	53.0616i	0.827977	+	1.43410i	0.899623	+	0.436668i	$0.143842\pi$
$37$	30.6351	+	53.0616i	0.827977	+	1.43410i	−0.0716456	+	0.997430i	$0.522825\pi$
$38$	0.986339	+	0.569463i	0.0259563	+	0.0149859i
$39$	8.37392	+	38.0904i	0.214716	+	0.976677i
$40$	−4.36508	−	7.56054i	−0.109127	−	0.189013i
$41$	30.6838	+	17.7153i	0.748386	+	0.432081i	0.825110	−	0.564972i	$-0.191113\pi$
$41$	30.6838	+	17.7153i	0.748386	+	0.432081i	−0.0767246	+	0.997052i	$0.524446\pi$
$42$	10.8336	−	26.4552i	0.257943	−	0.629887i
$43$	−0.628105	−	1.08791i	−0.0146071	−	0.0253002i	0.858629	−	0.512597i	$-0.171316\pi$
$43$	−0.628105	−	1.08791i	−0.0146071	−	0.0253002i	−0.873237	+	0.487297i	$0.837983\pi$
$44$			5.15821i			0.117232i
$45$	−2.48187	−	8.97296i	−0.0551527	−	0.199399i
$46$	25.1491	−	43.5595i	0.546719	−	0.946945i
$47$	17.3684	+	10.0277i	0.369541	+	0.213355i	0.673258	−	0.739408i	$-0.264894\pi$
$47$	17.3684	+	10.0277i	0.369541	+	0.213355i	−0.303717	+	0.952762i	$0.598228\pi$
$48$	−32.2455	+	24.9496i	−0.671781	+	0.519784i
$49$	11.4091	−	19.7611i	0.232838	−	0.403288i
$50$	38.5947	+	22.2827i	0.771894	+	0.445653i
$51$	−92.0408	+	12.4944i	−1.80472	+	0.244989i
$52$	−2.95766	+	6.24802i	−0.0568781	+	0.120154i
$53$			39.4824i			0.744952i	0.928042	+	0.372476i	$0.121491\pi$
$53$			39.4824i			0.744952i	−0.928042	+	0.372476i	$0.878509\pi$
$54$	−46.2195	+	19.8018i	−0.855917	+	0.366700i
$55$	5.01725	+	8.69013i	0.0912227	+	0.158002i
$56$	37.3983	−	21.5919i	0.667826	−	0.385570i
$57$	0.246793	+	1.81801i	0.00432970	+	0.0318949i
$58$	−38.4397			−0.662753
$59$		−	5.72404i		−	0.0970177i	−0.998823	−	0.0485089i	$-0.984553\pi$
$59$		−	5.72404i		−	0.0970177i	0.998823	−	0.0485089i	$-0.0154469\pi$
$60$	0.625350	−	1.52708i	0.0104225	−	0.0254514i
$61$	−55.5554	−	96.2247i	−0.910744	−	1.57745i	−0.813016	−	0.582241i	$-0.802176\pi$
$61$	−55.5554	−	96.2247i	−0.910744	−	1.57745i	−0.0977275	−	0.995213i	$-0.531157\pi$
$62$	3.54699	−	2.04785i	0.0572095	−	0.0330299i
$63$	44.3848	−	12.2766i	0.704521	−	0.194867i
$64$	−70.0956			−1.09524
$65$	1.09446	+	13.4030i	0.0168378	+	0.206200i
$66$	42.8638	−	33.1655i	0.649452	−	0.502507i
$67$	−3.05129	+	5.28499i	−0.0455416	+	0.0788804i	−0.887898	−	0.460041i	$-0.847835\pi$
$67$	−3.05129	+	5.28499i	−0.0455416	+	0.0788804i	0.842356	+	0.538921i	$0.181168\pi$
$68$	−14.2580	−	8.23188i	−0.209677	−	0.121057i
$69$	80.2884	−	10.8990i	1.16360	−	0.157957i
$70$	4.92863	−	8.53664i	0.0704090	−	0.121952i
$71$	−77.5112	−	44.7511i	−1.09171	−	0.630298i	−0.157677	−	0.987491i	$-0.550400\pi$
$71$	−77.5112	−	44.7511i	−1.09171	−	0.630298i	−0.934030	+	0.357193i	$0.883734\pi$
$72$	−73.5240	−	19.0678i	−1.02117	−	0.264830i
$73$	85.2365			1.16762			0.583812	−	0.811889i	$-0.301561\pi$
$73$	85.2365			1.16762			0.583812	+	0.811889i	$0.301561\pi$
$74$	98.8180	−	57.0526i	1.33538	−	0.770981i
$75$	9.65681	+	71.1374i	0.128757	+	0.948499i
$76$	−0.162598	+	0.281628i	−0.00213945	+	0.00370563i
$77$	−42.9858	+	24.8179i	−0.558257	+	0.322310i
$78$	70.9367	−	15.5950i	0.909444	−	0.199935i
$79$	13.6252	−	23.5995i	0.172471	−	0.298728i	−0.766812	−	0.641871i	$-0.778158\pi$
$79$	13.6252	−	23.5995i	0.172471	−	0.298728i	0.939283	+	0.343143i	$0.111492\pi$
$80$	−12.1747	+	7.02909i	−0.152184	+	0.0878636i
$81$	−70.7909	−	39.3656i	−0.873961	−	0.485995i
$82$	32.9917	−	57.1432i	0.402337	−	0.696869i
$83$	−128.236	−	74.0368i	−1.54501	−	0.892010i	−0.998511	−	0.0545484i	$-0.982628\pi$
$83$	−128.236	−	74.0368i	−1.54501	−	0.892010i	−0.546496	−	0.837462i	$-0.684039\pi$
$84$	7.55373	+	3.09330i	0.0899253	+	0.0368250i
$85$	−32.0277			−0.376796
$86$	−2.02604	+	1.16974i	−0.0235586	+	0.0136016i
$87$	−37.8932	−	48.9740i	−0.435554	−	0.562920i
$88$	81.8682			0.930321
$89$	−42.7999	+	24.7105i	−0.480898	+	0.277646i	−0.720790	−	0.693153i	$-0.756221\pi$
$89$	−42.7999	+	24.7105i	−0.480898	+	0.277646i	0.239893	+	0.970799i	$0.422888\pi$
$90$	−16.7106	+	4.62205i	−0.185673	+	0.0513561i
$91$	−66.2980	+	5.41374i	−0.728549	+	0.0594917i
$92$	12.4375	+	7.18078i	0.135190	+	0.0780519i
$93$	6.10562	+	2.50029i	0.0656519	+	0.0268849i
$94$	18.6748	−	32.3457i	0.198668	−	0.344103i
$95$			0.632618i			0.00665914i
$96$	−15.5108	−	20.0465i	−0.161571	−	0.208818i
$97$	36.6052	+	63.4021i	0.377373	+	0.653630i	0.990679	−	0.136216i	$-0.0434940\pi$
$97$	36.6052	+	63.4021i	0.377373	+	0.653630i	−0.613306	+	0.789846i	$0.710161\pi$
$98$	−36.8016	−	21.2474i	−0.375527	−	0.216810i
$99$	84.5088	+	21.9166i	0.853625	+	0.221380i
$100$	−6.36234	+	11.0199i	−0.0636234	+	0.110199i
$101$		−	41.6526i		−	0.412402i	−0.978510	−	0.206201i	$-0.933890\pi$
$101$		−	41.6526i		−	0.412402i	0.978510	−	0.206201i	$-0.0661101\pi$
$102$	23.2687	+	171.410i	0.228124	+	1.68049i
$103$	−42.1951	−	73.0840i	−0.409661	−	0.709554i	0.585191	−	0.810896i	$-0.301020\pi$
$103$	−42.1951	−	73.0840i	−0.409661	−	0.709554i	−0.994852	+	0.101342i	$0.967686\pi$
$104$	99.1651	+	46.9423i	0.953510	+	0.451368i
$105$	15.7347	−	2.13596i	0.149854	−	0.0203425i
$106$	73.5291			0.693671
$107$	−98.1933	+	56.6919i	−0.917695	+	0.529831i	−0.882899	−	0.469563i	$-0.844411\pi$
$107$	−98.1933	+	56.6919i	−0.917695	+	0.529831i	−0.0347958	+	0.999394i	$0.511078\pi$
$108$	−5.65398	−	13.1970i	−0.0523517	−	0.122194i
$109$	45.3665			0.416206			0.208103	−	0.978107i	$-0.433271\pi$
$109$	45.3665			0.416206			0.208103	+	0.978107i	$0.433271\pi$
$110$	16.1838	−	9.34374i	0.147126	−	0.0849431i
$111$	170.101	+	69.6574i	1.53244	+	0.627544i
$112$	−34.7694	−	60.2224i	−0.310441	−	0.537700i
$113$			73.3260i			0.648902i	0.945902	+	0.324451i	$0.105180\pi$
$113$			73.3260i			0.648902i	−0.945902	+	0.324451i	$0.894820\pi$
$114$	3.38573	−	0.459608i	0.0296994	−	0.00403165i
$115$	27.9382			0.242940
$116$		−	10.9756i		−	0.0946174i
$117$	89.7969	+	75.0035i	0.767495	+	0.641055i
$118$	−10.6600			−0.0903392
$119$		−	158.425i		−	1.33130i
$120$	−24.2370	−	9.92521i	−0.201975	−	0.0827100i
$121$	26.9002			0.222316
$122$	−179.202	+	103.462i	−1.46887	+	0.848050i
$123$	105.326	−	14.2978i	0.856308	−	0.116243i
$124$	0.584721	+	1.01277i	0.00471549	+	0.00816747i
$125$			50.6146i			0.404917i
$126$	−22.8630	−	82.6590i	−0.181452	−	0.656024i
$127$	−63.9418	−	110.750i	−0.503479	−	0.872051i	−0.999992	−	0.00402161i	$-0.998720\pi$
$127$	−63.9418	−	110.750i	−0.503479	−	0.872051i	0.496513	−	0.868029i	$-0.334613\pi$
$128$			96.7452i			0.755822i
$129$	−3.48754	−	1.42817i	−0.0270352	−	0.0110711i
$130$	24.9607	−	2.03824i	0.192005	−	0.0156787i
$131$	−57.6724	+	33.2972i	−0.440248	+	0.254177i	−0.703703	−	0.710495i	$-0.748471\pi$
$131$	−57.6724	+	33.2972i	−0.440248	+	0.254177i	0.263455	+	0.964672i	$0.415138\pi$
$132$	9.46969	+	12.2388i	0.0717401	+	0.0927185i
$133$	−3.12925			−0.0235282
$134$	9.84236	+	5.68249i	0.0734505	+	0.0424066i
$135$	−22.3617	−	16.7337i	−0.165642	−	0.123954i
$136$	−130.652	+	226.296i	−0.960675	+	1.66394i
$137$	−168.227	+	97.1257i	−1.22793	+	0.708947i	−0.966597	−	0.256301i	$-0.917496\pi$
$137$	−168.227	+	97.1257i	−1.22793	+	0.708947i	−0.261335	+	0.965248i	$0.584163\pi$
$138$	−20.2976	−	149.523i	−0.147084	−	1.08350i
$139$	240.784			1.73226			0.866130	−	0.499819i	$-0.166600\pi$
$139$	240.784			1.73226			0.866130	+	0.499819i	$0.166600\pi$
$140$	2.43746	+	1.40727i	0.0174104	+	0.0100519i
$141$	59.6192	−	8.09324i	0.422832	−	0.0573988i
$142$	−83.3411	+	144.351i	−0.586909	+	1.01656i
$143$	−113.981	−	53.9557i	−0.797069	−	0.377313i
$144$	−30.7049	+	118.396i	−0.213228	+	0.822192i
$145$	−10.6757	−	18.4908i	−0.0736254	−	0.127523i
$146$		−	158.738i		−	1.08725i
$147$	−9.20816	−	67.8324i	−0.0626405	−	0.461445i
$148$	16.2901	+	28.2154i	0.110069	+	0.190644i
$149$		−	20.0621i		−	0.134645i	−0.997731	−	0.0673223i	$-0.978554\pi$
$149$		−	20.0621i		−	0.134645i	0.997731	−	0.0673223i	$-0.0214456\pi$
$150$	132.481	−	17.9841i	0.883206	−	0.119894i
$151$	105.409	−	182.574i	0.698075	−	1.20910i	−0.271058	−	0.962563i	$-0.587373\pi$
$151$	105.409	−	182.574i	0.698075	−	1.20910i	0.969133	−	0.246539i	$-0.0792933\pi$
$152$	4.46984	+	2.58066i	0.0294068	+	0.0169781i
$153$	−195.447	+	198.618i	−1.27743	+	1.29816i
$154$	46.2189	+	80.0535i	0.300123	+	0.519828i
$155$	1.97018	+	1.13748i	0.0127108	+	0.00733860i
$156$	4.45281	+	20.2544i	0.0285436	+	0.129836i
$157$	22.5433	+	39.0461i	0.143588	+	0.248701i	0.928845	−	0.370468i	$-0.120803\pi$
$157$	22.5433	+	39.0461i	0.143588	+	0.248701i	−0.785257	+	0.619170i	$0.787469\pi$
$158$	−43.9500	−	25.3745i	−0.278164	−	0.160598i
$159$	72.4837	+	93.6797i	0.455873	+	0.589180i
$160$	−4.36988	−	7.56885i	−0.0273117	−	0.0473053i
$161$			138.196i			0.858362i
$162$	−73.3116	+	131.836i	−0.452541	+	0.813800i
$163$	7.69510	−	13.3283i	0.0472092	−	0.0817688i	−0.841455	−	0.540327i	$-0.818301\pi$
$163$	7.69510	−	13.3283i	0.0472092	−	0.0817688i	0.888664	+	0.458558i	$0.151634\pi$
$164$	16.3160	+	9.42006i	0.0994879	+	0.0574394i
$165$	27.8581	+	11.4081i	0.168837	+	0.0691399i
$166$	−137.881	+	238.816i	−0.830606	+	1.43865i
$167$	76.5775	+	44.2121i	0.458548	+	0.264743i	0.711434	−	0.702753i	$-0.248046\pi$
$167$	76.5775	+	44.2121i	0.458548	+	0.264743i	−0.252886	+	0.967496i	$0.581380\pi$
$168$	49.0951	−	119.888i	0.292233	−	0.713622i
$169$	−107.125	−	130.711i	−0.633875	−	0.773436i
$170$			59.6459i			0.350858i
$171$	3.92315	+	3.86051i	0.0229424	+	0.0225761i
$172$	−0.333993	−	0.578493i	−0.00194182	−	0.00336333i
$173$	145.259	−	83.8653i	0.839647	−	0.484771i	−0.0174970	−	0.999847i	$-0.505570\pi$
$173$	145.259	−	83.8653i	0.839647	−	0.484771i	0.857144	+	0.515076i	$0.172236\pi$
$174$	−91.2055	+	70.5694i	−0.524169	+	0.405571i
$175$	−122.445			−0.699687
$176$		−	131.832i		−	0.749047i
$177$	−10.5085	−	13.5814i	−0.0593699	−	0.0767310i
$178$	46.0190	+	79.7073i	0.258534	+	0.447794i
$179$	227.604	−	131.407i	1.27153	−	0.734118i	0.296254	−	0.955109i	$-0.404263\pi$
$179$	227.604	−	131.407i	1.27153	−	0.734118i	0.975276	+	0.220991i	$0.0709292\pi$
$180$	−1.31973	−	4.77134i	−0.00733182	−	0.0265075i
$181$	−268.017			−1.48076			−0.740378	−	0.672191i	$-0.765353\pi$
$181$	−268.017			−1.48076			−0.740378	+	0.672191i	$0.765353\pi$
$182$	10.0822	+	123.468i	0.0553964	+	0.678397i
$183$	−308.470	−	126.320i	−1.68563	−	0.690275i
$184$	113.969	−	197.400i	0.619398	−	1.07283i
$185$	54.8885	+	31.6899i	0.296695	+	0.171297i
$186$	4.65636	−	11.3707i	0.0250342	−	0.0611326i
$187$	150.172	−	260.105i	0.803058	−	1.39094i
$188$	9.23562	+	5.33219i	0.0491256	+	0.0283627i
$189$	82.7735	−	110.612i	0.437955	−	0.585251i
$190$	1.17814			0.00620074
$191$	−76.4195	+	44.1208i	−0.400102	+	0.230999i	−0.686528	−	0.727103i	$-0.740866\pi$
$191$	−76.4195	+	44.1208i	−0.400102	+	0.230999i	0.286426	+	0.958102i	$0.407533\pi$
$192$	−166.315	+	128.685i	−0.866225	+	0.670233i
$193$	−50.9639	+	88.2721i	−0.264062	+	0.457368i	−0.967317	−	0.253569i	$-0.918396\pi$
$193$	−50.9639	+	88.2721i	−0.264062	+	0.457368i	0.703256	+	0.710937i	$0.251729\pi$
$194$	118.075	−	68.1708i	0.608635	−	0.351396i
$195$	27.2026	+	29.7919i	0.139501	+	0.152779i
$196$	6.06674	−	10.5079i	0.0309528	−	0.0536118i
$197$	134.270	−	77.5206i	0.681572	−	0.393506i	−0.118875	−	0.992909i	$-0.537929\pi$
$197$	134.270	−	77.5206i	0.681572	−	0.393506i	0.800447	+	0.599404i	$0.204596\pi$
$198$	40.8159	−	157.383i	0.206141	−	0.794863i
$199$	178.909	−	309.879i	0.899038	−	1.55718i	0.0703119	−	0.997525i	$-0.477601\pi$
$199$	178.909	−	309.879i	0.899038	−	1.55718i	0.828726	−	0.559654i	$-0.189066\pi$
$200$	174.902	+	100.979i	0.874508	+	0.504897i
$201$	2.46266	+	18.1413i	0.0122521	+	0.0902554i
$202$	−77.5707			−0.384014
$203$	91.4650	−	52.8073i	0.450567	−	0.260135i
$204$	−48.9424	+	6.64387i	−0.239914	+	0.0325680i
$205$	36.6505			0.178783
$206$	−136.106	+	78.5810i	−0.660710	+	0.381461i
$207$	170.491	−	173.257i	0.823626	−	0.836992i
$208$	75.5911	−	159.685i	0.363419	−	0.767719i
$209$	−5.13766	−	2.96623i	−0.0245821	−	0.0141925i
$210$	−3.97785	−	29.3030i	−0.0189421	−	0.139538i
$211$	−36.1067	+	62.5387i	−0.171122	+	0.296392i	−0.938812	−	0.344429i	$-0.888073\pi$
$211$	−36.1067	+	62.5387i	−0.171122	+	0.296392i	0.767690	+	0.640821i	$0.221406\pi$
$212$			20.9947i			0.0990314i
$213$	−266.066	+	36.1182i	−1.24914	+	0.169569i
$214$	105.579	+	182.868i	0.493359	+	0.854523i
$215$	−1.12537	−	0.649731i	−0.00523427	−	0.00302200i
$216$	−209.455	+	89.7368i	−0.969700	+	0.415448i
$217$	−5.62657	+	9.74550i	−0.0259289	+	0.0449102i
$218$		−	84.4871i		−	0.387556i
$219$	202.240	−	156.481i	0.923470	−	0.714526i
$220$	2.66790	+	4.62095i	0.0121268	+	0.0210043i
$221$	331.041	−	228.953i	1.49792	−	1.03599i
$222$	129.725	−	316.783i	0.584346	−	1.42695i
$223$	−253.078			−1.13488			−0.567439	−	0.823415i	$-0.692066\pi$
$223$	−253.078			−1.13488			−0.567439	+	0.823415i	$0.692066\pi$
$224$	37.4394	−	21.6156i	0.167140	−	0.0964984i
$225$	153.510	+	151.059i	0.682267	+	0.671372i
$226$	136.557			0.604233
$227$	70.3266	−	40.6031i	0.309809	−	0.178868i	−0.337032	−	0.941493i	$-0.609423\pi$
$227$	70.3266	−	40.6031i	0.309809	−	0.178868i	0.646841	+	0.762625i	$0.276090\pi$
$228$	0.131231	+	0.966722i	0.000575575	+	0.00424001i
$229$	212.394	+	367.878i	0.927486	+	1.60645i	0.787514	+	0.616297i	$0.211368\pi$
$229$	212.394	+	367.878i	0.927486	+	1.60645i	0.139971	+	0.990156i	$0.455299\pi$
$230$		−	52.0299i		−	0.226217i
$231$	−56.4302	+	137.800i	−0.244287	+	0.596539i
$232$	−174.199			−0.750857
$233$		−	58.9981i		−	0.253211i	−0.991953	−	0.126605i	$-0.959592\pi$
$233$		−	58.9981i		−	0.253211i	0.991953	−	0.126605i	$-0.0404082\pi$
$234$	139.681	−	167.231i	0.596927	−	0.714662i
$235$	20.7459			0.0882803
$236$		−	3.04374i		−	0.0128972i
$237$	−10.9967	−	81.0081i	−0.0463998	−	0.341806i
$238$	−295.039			−1.23966
$239$	−195.018	+	112.594i	−0.815975	+	0.471103i	−0.849027	−	0.528350i	$-0.822811\pi$
$239$	−195.018	+	112.594i	−0.815975	+	0.471103i	0.0330514	+	0.999454i	$0.489477\pi$
$240$	−15.9826	+	39.0288i	−0.0665940	+	0.162620i
$241$	−125.529	−	217.423i	−0.520867	−	0.902168i	−0.999706	−	0.0242653i	$-0.992275\pi$
$241$	−125.529	−	217.423i	−0.520867	−	0.902168i	0.478838	−	0.877903i	$-0.341058\pi$
$242$		−	50.0969i		−	0.207012i
$243$	−240.234	+	36.5588i	−0.988618	+	0.150448i
$244$	−29.5414	−	51.1672i	−0.121071	−	0.209702i
$245$		−	23.6038i		−	0.0963420i
$246$	−26.6272	−	196.151i	−0.108241	−	0.797361i
$247$	−4.52233	−	6.53880i	−0.0183090	−	0.0264729i
$248$	16.0741	−	9.28036i	0.0648147	−	0.0374208i
$249$	−440.184	+	59.7544i	−1.76781	+	0.239977i
$250$	94.2608			0.377043
$251$	−91.3518	−	52.7420i	−0.363951	−	0.210127i	0.306861	−	0.951754i	$-0.400721\pi$
$251$	−91.3518	−	52.7420i	−0.363951	−	0.210127i	−0.670813	+	0.741627i	$0.734055\pi$
$252$	23.6015	−	6.52804i	0.0936567	−	0.0259049i
$253$	−130.997	+	226.893i	−0.517774	+	0.896811i
$254$	−206.253	+	119.080i	−0.812021	+	0.468820i
$255$	−75.9918	+	58.7979i	−0.298007	+	0.230580i
$256$	−100.211			−0.391450
$257$	57.0764	+	32.9531i	0.222087	+	0.128222i	0.606916	−	0.794766i	$-0.292406\pi$
$257$	57.0764	+	32.9531i	0.222087	+	0.128222i	−0.384829	+	0.922988i	$0.625740\pi$
$258$	−2.65972	+	6.49493i	−0.0103090	+	0.0251741i
$259$	−156.754	+	271.507i	−0.605230	+	1.04829i
$260$	0.581974	+	7.12699i	0.00223836	+	0.0274115i
$261$	−179.818	−	46.6341i	−0.688956	−	0.178675i
$262$	62.0102	+	107.405i	0.236680	+	0.409942i
$263$			274.690i			1.04445i	0.852808	+	0.522225i	$0.174898\pi$
$263$			274.690i			1.04445i	−0.852808	+	0.522225i	$0.825102\pi$
$264$	194.248	−	150.298i	0.735788	−	0.569309i
$265$	20.4209	+	35.3701i	0.0770600	+	0.133472i
$266$			5.82768i			0.0219086i
$267$	−56.1862	+	137.205i	−0.210435	+	0.513875i
$268$	−1.62251	+	2.81027i	−0.00605415	+	0.0104861i
$269$	264.200	+	152.536i	0.982157	+	0.567048i	0.902921	−	0.429808i	$-0.141419\pi$
$269$	264.200	+	152.536i	0.982157	+	0.567048i	0.0792360	+	0.996856i	$0.474752\pi$
$270$	−31.1636	+	41.6447i	−0.115421	+	0.154240i
$271$	−115.783	−	200.541i	−0.427242	−	0.740005i	0.569385	−	0.822071i	$-0.307181\pi$
$271$	−115.783	−	200.541i	−0.427242	−	0.740005i	−0.996627	+	0.0820661i	$0.973848\pi$
$272$	364.404	+	210.388i	1.33972	+	0.773487i
$273$	−147.366	+	134.558i	−0.539801	+	0.492887i
$274$	180.880	+	313.293i	0.660145	+	1.14340i
$275$	−201.033	−	116.066i	−0.731028	−	0.422059i
$276$	42.6931	−	5.79553i	0.154685	−	0.0209983i
$277$	143.454	+	248.470i	0.517885	+	0.897003i	0.999784	+	0.0207766i	$0.00661386\pi$
$277$	143.454	+	248.470i	0.517885	+	0.897003i	−0.481899	+	0.876227i	$0.660053\pi$
$278$		−	448.418i		−	1.61302i
$279$	19.0769	−	5.27657i	0.0683761	−	0.0189124i
$280$	22.3353	−	38.6859i	0.0797690	−	0.138164i
$281$	94.4645	+	54.5391i	0.336173	+	0.194089i	0.658578	−	0.752512i	$-0.271158\pi$
$281$	94.4645	+	54.5391i	0.336173	+	0.194089i	−0.322406	+	0.946602i	$0.604491\pi$
$282$	−15.0722	−	111.030i	−0.0534476	−	0.393725i
$283$	180.826	−	313.199i	0.638960	−	1.10671i	−0.346702	−	0.937975i	$-0.612698\pi$
$283$	180.826	−	313.199i	0.638960	−	1.10671i	0.985661	−	0.168735i	$-0.0539683\pi$
$284$	−41.2163	−	23.7963i	−0.145128	−	0.0837897i
$285$	1.16139	+	1.50101i	0.00407505	+	0.00526669i
$286$	−100.483	+	212.269i	−0.351339	+	0.742201i
$287$			181.292i			0.631680i
$288$	−73.6048	−	19.0888i	−0.255572	−	0.0662804i
$289$	334.812	+	579.912i	1.15852	+	2.00662i
$290$	−34.4359	+	19.8816i	−0.118744	+	0.0685572i
$291$	203.249	+	83.2320i	0.698452	+	0.286021i
$292$	45.3242			0.155220
$293$			334.721i			1.14239i	0.820814	+	0.571196i	$0.193520\pi$
$293$			334.721i			1.14239i	−0.820814	+	0.571196i	$0.806480\pi$
$294$	−126.326	+	17.1486i	−0.429680	+	0.0583285i
$295$	−2.96056	−	5.12784i	−0.0100358	−	0.0173825i
$296$	447.818	−	258.548i	1.51290	−	0.873473i
$297$	240.749	−	103.144i	0.810603	−	0.347286i
$298$	−37.3621			−0.125376
$299$	−288.771	+	199.718i	−0.965791	+	0.667955i
$300$	5.13498	+	37.8271i	0.0171166	+	0.126090i
$301$	3.21390	−	5.56664i	0.0106774	−	0.0184938i
$302$	−340.013	−	196.306i	−1.12587	−	0.650022i
$303$	−76.4679	−	98.8289i	−0.252369	−	0.326168i
$304$	4.15564	−	7.19778i	0.0136699	−	0.0236769i
$305$	−99.5377	−	57.4681i	−0.326353	−	0.188420i
$306$	369.892	+	363.985i	1.20880	+	1.18949i
$307$	−538.966			−1.75559			−0.877795	−	0.479036i	$-0.840986\pi$
$307$	−538.966			−1.75559			−0.877795	+	0.479036i	$0.840986\pi$
$308$	−22.8576	+	13.1968i	−0.0742129	+	0.0428468i
$309$	−234.287	−	95.9421i	−0.758211	−	0.310492i
$310$	2.11836	−	3.66911i	0.00683343	−	0.0118358i
$311$	437.572	−	252.632i	1.40698	−	0.812323i	0.411888	−	0.911234i	$-0.364869\pi$
$311$	437.572	−	252.632i	1.40698	−	0.812323i	0.995096	+	0.0989114i	$0.0315360\pi$
$312$	321.467	−	70.6724i	1.03034	−	0.226514i
$313$	−130.184	+	225.485i	−0.415923	+	0.720400i	−0.995525	−	0.0944999i	$-0.969875\pi$
$313$	−130.184	+	225.485i	−0.415923	+	0.720400i	0.579602	+	0.814900i	$0.303208\pi$
$314$	72.7166	−	41.9829i	0.231581	−	0.133704i
$315$	33.4122	−	33.9544i	0.106070	−	0.107792i
$316$	7.24515	−	12.5490i	0.0229277	−	0.0397119i
$317$	−378.081	−	218.285i	−1.19269	−	0.688597i	−0.233771	−	0.972292i	$-0.575107\pi$
$317$	−378.081	−	218.285i	−1.19269	−	0.688597i	−0.958915	+	0.283694i	$0.908440\pi$
$318$	174.462	−	134.988i	0.548622	−	0.424491i
$319$	200.225			0.627665
$320$	−62.7946	+	36.2545i	−0.196233	+	0.113295i
$321$	−128.905	+	314.780i	−0.401572	+	0.980625i
$322$	257.366			0.799275
$323$	16.3982	−	9.46749i	0.0507683	−	0.0293111i
$324$	−37.6428	−	20.9325i	−0.116182	−	0.0646066i
$325$	−176.955	−	255.858i	−0.544478	−	0.787256i
$326$	−24.8216	−	14.3308i	−0.0761400	−	0.0439595i
$327$	107.641	−	83.2859i	0.329176	−	0.254697i
$328$	149.510	−	258.959i	0.455823	−	0.789508i
$329$			102.620i			0.311914i
$330$	21.2456	−	51.8809i	0.0643805	−	0.157215i
$331$	178.365	+	308.937i	0.538866	+	0.933344i	0.998965	+	0.0454763i	$0.0144805\pi$
$331$	178.365	+	308.937i	0.538866	+	0.933344i	−0.460099	+	0.887868i	$0.652186\pi$
$332$	−68.1889	−	39.3689i	−0.205388	−	0.118581i
$333$	531.477	−	147.004i	1.59603	−	0.441452i
$334$	82.3372	−	142.612i	0.246519	−	0.426983i
$335$			6.31269i			0.0188438i
$336$	−193.056	−	79.0579i	−0.574573	−	0.235291i
$337$	−7.01618	−	12.1524i	−0.0208195	−	0.0360605i	0.855428	−	0.517922i	$-0.173294\pi$
$337$	−7.01618	−	12.1524i	−0.0208195	−	0.0360605i	−0.876247	+	0.481861i	$0.839961\pi$
$338$	−243.426	+	199.501i	−0.720194	+	0.590240i
$339$	134.615	+	173.980i	0.397095	+	0.513215i
$340$	−17.0306			−0.0500900
$341$	−18.4756	+	10.6669i	−0.0541807	+	0.0312812i
$342$	7.18951	−	7.30619i	0.0210220	−	0.0213631i
$343$	367.481			1.07137
$344$	−9.18151	+	5.30095i	−0.0266904	+	0.0154097i
$345$	66.2886	−	51.2902i	0.192141	−	0.148667i
$346$	−156.184	−	270.519i	−0.451400	−	0.781848i
$347$			51.5693i			0.148615i	0.997235	+	0.0743073i	$0.0236746\pi$
$347$			51.5693i			0.148615i	−0.997235	+	0.0743073i	$0.976325\pi$
$348$	−20.1496	−	26.0418i	−0.0579011	−	0.0748327i
$349$	−101.719			−0.291459			−0.145729	−	0.989325i	$-0.546553\pi$
$349$	−101.719			−0.291459			−0.145729	+	0.989325i	$0.546553\pi$
$350$			228.033i			0.651522i
$351$	350.755	+	13.1068i	0.999303	+	0.0373412i
$352$	81.9582			0.232836
$353$		−	306.151i		−	0.867284i	−0.901085	−	0.433642i	$-0.857228\pi$
$353$		−	306.151i		−	0.867284i	0.901085	−	0.433642i	$-0.142772\pi$
$354$	−25.2930	+	19.5702i	−0.0714490	+	0.0552830i
$355$	−92.5838			−0.260799
$356$	−22.7587	+	13.1397i	−0.0639289	+	0.0369094i
$357$	−290.845	−	375.894i	−0.814691	−	1.05292i
$358$	−244.723	−	423.872i	−0.683583	−	1.18400i
$359$			401.590i			1.11864i	0.828953	+	0.559318i	$0.188937\pi$
$359$			401.590i			1.11864i	−0.828953	+	0.559318i	$0.811063\pi$
$360$	−75.7280	+	20.9460i	−0.210356	+	0.0581832i
$361$	180.313	+	312.311i	0.499482	+	0.865128i
$362$			499.134i			1.37882i
$363$	63.8259	−	49.3847i	0.175829	−	0.136046i
$364$	−35.2537	+	2.87874i	−0.0968509	+	0.00790863i
$365$	76.3585	−	44.0856i	0.209201	−	0.120782i
$366$	−235.250	+	574.471i	−0.642758	+	1.56959i
$367$	−168.708			−0.459694			−0.229847	−	0.973227i	$-0.573823\pi$
$367$	−168.708			−0.459694			−0.229847	+	0.973227i	$0.573823\pi$
$368$	−317.874	−	183.525i	−0.863788	−	0.498708i
$369$	223.657	−	227.287i	0.606117	−	0.615953i
$370$	59.0169	−	102.220i	0.159505	−	0.276271i
$371$	−174.958	+	101.012i	−0.471586	+	0.272270i
$372$	3.24665	+	1.32952i	0.00872754	+	0.00357399i
$373$	−217.640			−0.583486			−0.291743	−	0.956497i	$-0.594235\pi$
$373$	−217.640			−0.583486			−0.291743	+	0.956497i	$0.594235\pi$
$374$	−484.401	−	279.669i	−1.29519	−	0.747778i
$375$	92.9207	+	120.093i	0.247789	+	0.320248i
$376$	84.6294	−	146.582i	0.225078	−	0.389847i
$377$	242.528	+	114.807i	0.643311	+	0.304527i
$378$	−205.996	−	154.151i	−0.544963	−	0.407807i
$379$	316.884	+	548.859i	0.836105	+	1.44818i	0.893127	+	0.449804i	$0.148506\pi$
$379$	316.884	+	548.859i	0.836105	+	1.44818i	−0.0570221	+	0.998373i	$0.518161\pi$
$380$			0.336393i			0.000885244i
$381$	−355.035	−	145.389i	−0.931851	−	0.381599i
$382$	82.1673	+	142.318i	0.215098	+	0.372560i
$383$		−	691.711i		−	1.80603i	−0.429605	−	0.903017i	$-0.641347\pi$
$383$		−	691.711i		−	1.80603i	0.429605	−	0.903017i	$-0.358653\pi$
$384$	177.609	+	229.547i	0.462525	+	0.597778i
$385$	−25.6723	+	44.4658i	−0.0666814	+	0.115496i
$386$	164.391	+	94.9114i	0.425884	+	0.245884i
$387$	−10.8968	+	3.01398i	−0.0281570	+	0.00778806i
$388$	19.4647	+	33.7139i	0.0501668	+	0.0868914i
$389$	205.719	+	118.772i	0.528842	+	0.305327i	0.740545	−	0.672007i	$-0.234568\pi$
$389$	205.719	+	118.772i	0.528842	+	0.305327i	−0.211703	+	0.977334i	$0.567901\pi$
$390$	55.4821	−	50.6601i	0.142262	−	0.129898i
$391$	−418.110	−	724.188i	−1.06934	−	1.85214i
$392$	−166.776	−	96.2879i	−0.425448	−	0.245632i
$393$	−75.7103	+	184.882i	−0.192647	+	0.470437i
$394$	−144.369	−	250.054i	−0.366418	−	0.634654i
$395$		−	28.1886i		−	0.0713635i
$396$	44.9373	+	11.6541i	0.113478	+	0.0294295i
$397$	175.974	−	304.795i	0.443258	−	0.767746i	−0.554671	−	0.832070i	$-0.687156\pi$
$397$	175.974	−	304.795i	0.443258	−	0.767746i	0.997929	+	0.0643240i	$0.0204891\pi$
$398$	−577.095	−	333.186i	−1.44999	−	0.837150i
$399$	−7.42475	+	5.74483i	−0.0186084	+	0.0143981i
$400$	162.607	−	281.644i	0.406518	−	0.704110i
$401$	−360.251	−	207.991i	−0.898381	−	0.518681i	−0.0217068	−	0.999764i	$-0.506910\pi$
$401$	−360.251	−	207.991i	−0.898381	−	0.518681i	−0.876675	+	0.481084i	$0.840243\pi$
$402$	33.7851	−	4.58628i	0.0840425	−	0.0114087i
$403$	−28.4953	+	2.32687i	−0.0707081	+	0.00577386i
$404$		−	22.1487i		−	0.0548234i
$405$	−83.7780	+	1.34870i	−0.206859	+	0.00333012i
$406$	−98.3444	−	170.338i	−0.242228	−	0.419551i
$407$	−514.725	+	297.176i	−1.26468	+	0.730163i
$408$	105.448	+	776.786i	0.258450	+	1.90389i
$409$	−212.893			−0.520522			−0.260261	−	0.965538i	$-0.583809\pi$
$409$	−212.893			−0.520522			−0.260261	+	0.965538i	$0.583809\pi$
$410$		−	68.2551i		−	0.166476i
$411$	−220.842	+	539.288i	−0.537329	+	1.31214i
$412$	−22.4371	−	38.8622i	−0.0544590	−	0.0943257i
$413$	25.3649	−	14.6444i	0.0614163	−	0.0354587i
$414$	−322.661	−	317.509i	−0.779375	−	0.766929i
$415$	−153.172			−0.369089
$416$	99.2741	+	46.9939i	0.238640	+	0.112966i
$417$	571.307	−	442.043i	1.37004	−	1.06006i
$418$	−5.52408	+	9.56799i	−0.0132155	+	0.0228899i
$419$	−12.9141	−	7.45599i	−0.0308214	−	0.0177947i	0.484510	−	0.874786i	$-0.338998\pi$
$419$	−12.9141	−	7.45599i	−0.0308214	−	0.0177947i	−0.515332	+	0.856991i	$0.672331\pi$
$420$	8.36685	−	1.13579i	0.0199211	−	0.00270426i
$421$	381.610	−	660.969i	0.906438	−	1.57000i	0.0874627	−	0.996168i	$-0.472124\pi$
$421$	381.610	−	660.969i	0.906438	−	1.57000i	0.818975	−	0.573829i	$-0.194543\pi$
$422$	116.467	+	67.2425i	0.275989	+	0.159342i
$423$	126.600	−	128.655i	0.299291	−	0.304148i
$424$	333.215			0.785885
$425$	641.648	−	370.456i	1.50976	−	0.871660i
$426$	67.2638	+	495.502i	0.157896	+	1.16315i
$427$	284.267	−	492.364i	0.665730	−	1.15308i
$428$	−52.2140	+	30.1458i	−0.121995	+	0.0704340i
$429$	−369.496	+	81.2313i	−0.861296	+	0.189350i
$430$	−1.21001	+	2.09580i	−0.00281398	+	0.00487395i
$431$	−107.703	+	62.1822i	−0.249890	+	0.144274i	−0.619714	−	0.784828i	$-0.712751\pi$
$431$	−107.703	+	62.1822i	−0.249890	+	0.144274i	0.369824	+	0.929102i	$0.379418\pi$
$432$	144.503	+	337.286i	0.334498	+	0.780754i
$433$	−5.70944	+	9.88903i	−0.0131858	+	0.0228384i	−0.872543	−	0.488537i	$-0.837531\pi$
$433$	−5.70944	+	9.88903i	−0.0131858	+	0.0228384i	0.859357	+	0.511376i	$0.170864\pi$
$434$	18.1493	+	10.4785i	0.0418187	+	0.0241440i
$435$	−59.2764	−	24.2741i	−0.136268	−	0.0558025i
$436$	24.1235			0.0553291
$437$	−14.3043	+	8.25861i	−0.0327330	+	0.0188984i
$438$	−291.419	−	376.636i	−0.665340	−	0.859901i
$439$	171.523			0.390714			0.195357	−	0.980732i	$-0.437413\pi$
$439$	171.523			0.390714			0.195357	+	0.980732i	$0.437413\pi$
$440$	73.3410	−	42.3435i	0.166684	−	0.0962352i
$441$	−146.378	−	144.040i	−0.331923	−	0.326622i
$442$	−426.384	−	616.506i	−0.964670	−	1.39481i
$443$	654.843	+	378.074i	1.47820	+	0.853440i	0.999696	−	0.0246449i	$-0.00784551\pi$
$443$	654.843	+	378.074i	1.47820	+	0.853440i	0.478505	+	0.878085i	$0.341179\pi$
$444$	90.4506	+	37.0401i	0.203718	+	0.0834237i
$445$	−25.5613	+	44.2735i	−0.0574411	+	0.0994910i
$446$			471.313i			1.05676i
$447$	−36.8309	−	47.6011i	−0.0823957	−	0.106490i
$448$	−179.333	−	310.614i	−0.400297	−	0.693335i
$449$	7.33065	+	4.23235i	0.0163266	+	0.00942618i	0.508141	−	0.861274i	$-0.330333\pi$
$449$	7.33065	+	4.23235i	0.0163266	+	0.00942618i	−0.491814	+	0.870700i	$0.663666\pi$
$450$	281.320	−	285.886i	0.625156	−	0.635301i
$451$	−171.847	+	297.649i	−0.381036	+	0.659975i
$452$			38.9908i			0.0862629i
$453$	−85.0748	−	626.708i	−0.187803	−	1.38346i
$454$	−75.6161	−	130.971i	−0.166555	−	0.288482i
$455$	−56.5925	+	39.1402i	−0.124379	+	0.0860223i
$456$	15.3433	−	2.08283i	0.0336475	−	0.00456760i
$457$	722.488			1.58094			0.790468	−	0.612504i	$-0.209838\pi$
$457$	722.488			1.58094			0.790468	+	0.612504i	$0.209838\pi$
$458$	685.107	−	395.547i	1.49587	−	0.863640i
$459$	−99.1015	+	830.070i	−0.215907	+	1.80843i
$460$	14.8560			0.0322957
$461$	335.189	−	193.521i	0.727090	−	0.419786i	−0.0902664	−	0.995918i	$-0.528772\pi$
$461$	335.189	−	193.521i	0.727090	−	0.419786i	0.817357	+	0.576132i	$0.195439\pi$
$462$	256.629	+	105.091i	0.555475	+	0.227471i
$463$	131.549	+	227.850i	0.284124	+	0.492116i	0.972396	−	0.233336i	$-0.0749641\pi$
$463$	131.549	+	227.850i	0.284124	+	0.492116i	−0.688273	+	0.725452i	$0.741631\pi$
$464$			280.512i			0.604553i
$465$	6.76287	−	0.918051i	0.0145438	−	0.00197430i
$466$	−109.874			−0.235780
$467$			859.088i			1.83959i	0.392402	+	0.919794i	$0.371644\pi$
$467$			859.088i			1.83959i	−0.392402	+	0.919794i	$0.628356\pi$
$468$	47.7492	+	39.8829i	0.102028	+	0.0852198i
$469$	−31.2258			−0.0665795
$470$		−	38.6355i		−	0.0822033i
$471$	125.171	+	51.2584i	0.265756	+	0.108829i
$472$	−48.3086			−0.102349
$473$	10.5533	−	6.09294i	0.0223114	−	0.0128815i
$474$	−150.863	+	20.4795i	−0.318277	+	0.0432057i
$475$	−7.31732	−	12.6740i	−0.0154049	−	0.0266821i
$476$		−	84.2421i		−	0.176979i
$477$	343.963	+	89.2038i	0.721097	+	0.187010i
$478$	209.686	+	363.187i	0.438674	+	0.759805i
$479$		−	527.810i		−	1.10190i	−0.834539	−	0.550950i	$-0.814266\pi$
$479$		−	527.810i		−	1.10190i	0.834539	−	0.550950i	$-0.185734\pi$
$480$	−24.2636	−	9.93612i	−0.0505492	−	0.0207002i
$481$	−793.872	+	64.8258i	−1.65046	+	0.134773i
$482$	−404.911	+	233.776i	−0.840065	+	0.485012i
$483$	253.707	+	327.897i	0.525274	+	0.678876i
$484$	14.3041			0.0295539
$485$	65.5850	+	37.8655i	0.135227	+	0.0780733i
$486$	68.0843	+	447.394i	0.140091	+	0.920564i
$487$	224.140	−	388.222i	0.460246	−	0.797170i	−0.538727	−	0.842481i	$-0.681094\pi$
$487$	224.140	−	388.222i	0.460246	−	0.797170i	0.998973	+	0.0453105i	$0.0144277\pi$
$488$	−812.097	+	468.864i	−1.66413	+	0.960787i
$489$	−6.21064	−	45.7510i	−0.0127007	−	0.0935603i
$490$	−43.9579			−0.0897101
$491$	−717.213	−	414.083i	−1.46072	−	0.843347i	−0.461674	−	0.887049i	$-0.652751\pi$
$491$	−717.213	−	414.083i	−1.46072	−	0.843347i	−0.999045	+	0.0437029i	$0.986085\pi$
$492$	56.0067	−	7.60283i	0.113835	−	0.0154529i
$493$	−319.535	+	553.451i	−0.648144	+	1.12262i
$494$	−12.1774	+	8.42204i	−0.0246505	+	0.0170487i
$495$	87.0422	−	24.0754i	0.175843	−	0.0486372i
$496$	−14.9442	−	25.8840i	−0.0301293	−	0.0521856i
$497$		−	457.967i		−	0.921462i
$498$	111.282	+	819.765i	0.223458	+	1.64611i
$499$	278.506	+	482.386i	0.558128	+	0.966706i	0.997653	+	0.0684755i	$0.0218135\pi$
$499$	278.506	+	482.386i	0.558128	+	0.966706i	−0.439525	+	0.898230i	$0.644853\pi$
$500$			26.9142i			0.0538283i
$501$	262.861	−	35.6831i	0.524673	−	0.0712237i
$502$	−98.2227	+	170.127i	−0.195663	+	0.338898i
$503$	−592.859	−	342.287i	−1.17865	−	0.680491i	−0.222945	−	0.974831i	$-0.571567\pi$
$503$	−592.859	−	342.287i	−1.17865	−	0.680491i	−0.955701	+	0.294340i	$0.904900\pi$
$504$	−103.609	−	374.590i	−0.205574	−	0.743233i
$505$	−21.5434	−	37.3142i	−0.0426601	−	0.0738895i
$506$	422.549	+	243.959i	0.835077	+	0.482132i
$507$	−494.139	−	113.471i	−0.974633	−	0.223809i
$508$	−34.0009	−	58.8912i	−0.0669308	−	0.115928i
$509$	773.262	+	446.443i	1.51918	+	0.877098i	0.999745	+	0.0225881i	$0.00719062\pi$
$509$	773.262	+	446.443i	1.51918	+	0.877098i	0.519434	+	0.854510i	$0.326143\pi$
$510$	109.501	+	141.521i	0.214707	+	0.277493i
$511$	218.070	+	377.708i	0.426751	+	0.739155i
$512$			573.607i			1.12033i
$513$	16.3957	+	1.95748i	0.0319605	+	0.00381574i
$514$	61.3693	−	106.295i	0.119396	−	0.206799i
$515$	−75.6003	−	43.6479i	−0.146797	−	0.0847531i
$516$	−1.85449	−	0.759425i	−0.00359397	−	0.00147175i
$517$	−97.2735	+	168.483i	−0.188150	+	0.325885i
$518$	505.634	+	291.928i	0.976127	+	0.563567i
$519$	190.691	−	465.660i	0.367420	−	0.897225i
$520$	113.116	−	9.23677i	0.217530	−	0.0177630i
$521$		−	293.279i		−	0.562916i	−0.959574	−	0.281458i	$-0.909182\pi$
$521$		−	293.279i		−	0.562916i	0.959574	−	0.281458i	$-0.0908180\pi$
$522$	−86.8478	+	334.879i	−0.166375	+	0.641530i
$523$	−136.808	−	236.958i	−0.261583	−	0.453075i	0.705080	−	0.709128i	$-0.250911\pi$
$523$	−136.808	−	236.958i	−0.261583	−	0.453075i	−0.966663	+	0.256053i	$0.917578\pi$
$524$	−30.6671	+	17.7057i	−0.0585251	+	0.0337895i
$525$	−290.525	+	224.791i	−0.553380	+	0.428173i
$526$	511.562			0.972552
$527$		−	68.0923i		−	0.129207i
$528$	−242.024	−	312.797i	−0.458379	−	0.592419i
$529$	100.223	+	173.591i	0.189457	+	0.328150i
$530$	65.8705	−	38.0304i	0.124284	−	0.0717554i
$531$	−49.8667	−	12.9325i	−0.0939110	−	0.0243550i
$532$	−1.66397			−0.00312776
$533$	−378.823	+	261.999i	−0.710737	+	0.491556i
$534$	255.519	+	104.637i	0.478501	+	0.195949i
$535$	−58.6439	+	101.574i	−0.109615	+	0.189858i
$536$	44.6031	+	25.7516i	0.0832147	+	0.0480440i
$537$	298.790	−	729.634i	0.556406	−	1.35872i
$538$	284.072	−	492.026i	0.528014	−	0.914547i
$539$	191.693	+	110.674i	0.355645	+	0.205332i
$540$	−11.8908	−	8.89811i	−0.0220199	−	0.0164780i
$541$	−312.038			−0.576780			−0.288390	−	0.957513i	$-0.593120\pi$
$541$	−312.038			−0.576780			−0.288390	+	0.957513i	$0.593120\pi$
$542$	−373.473	+	215.625i	−0.689065	+	0.397832i
$543$	−635.921	+	492.038i	−1.17113	+	0.906147i
$544$	−130.795	+	226.544i	−0.240433	+	0.416442i
$545$	40.6412	−	23.4642i	0.0745711	−	0.0430536i
$546$	250.591	+	274.443i	0.458958	+	0.502643i
$547$	−359.443	+	622.574i	−0.657117	+	1.13816i	0.324241	+	0.945975i	$0.394891\pi$
$547$	−359.443	+	622.574i	−0.657117	+	1.13816i	−0.981358	+	0.192186i	$0.938442\pi$
$548$	−89.4540	+	51.6463i	−0.163237	+	0.0942451i
$549$	−963.808	+	266.584i	−1.75557	+	0.485581i
$550$	−216.153	+	374.388i	−0.393006	+	0.680706i
$551$	10.9319	+	6.31153i	0.0198401	+	0.0114547i
$552$	−91.9834	−	677.601i	−0.166637	−	1.22754i
$553$	139.435			0.252143
$554$	462.732	−	267.158i	0.835256	−	0.482235i
$555$	188.411	−	25.5766i	0.339480	−	0.0460840i
$556$	128.036			0.230281
$557$	222.259	−	128.322i	0.399029	−	0.230380i	−0.287036	−	0.957920i	$-0.592670\pi$
$557$	222.259	−	128.322i	0.399029	−	0.230380i	0.686065	+	0.727540i	$0.259336\pi$
$558$	−9.82669	−	35.5274i	−0.0176105	−	0.0636692i
$559$	16.2766	−	1.32911i	0.0291173	−	0.00237765i
$560$	−62.2959	−	35.9666i	−0.111243	−	0.0642260i
$561$	−121.202	−	892.842i	−0.216047	−	1.59152i
$562$	101.570	−	175.924i	0.180729	−	0.313031i
$563$			381.735i			0.678038i	0.940780	+	0.339019i	$0.110095\pi$
$563$			381.735i			0.678038i	−0.940780	+	0.339019i	$0.889905\pi$
$564$	31.7023	−	4.30355i	0.0562098	−	0.00763041i
$565$	37.9253	+	65.6885i	0.0671244	+	0.116263i
$566$	−583.278	−	336.756i	−1.03053	−	0.594975i
$567$	−6.67134	−	414.409i	−0.0117660	−	0.730879i
$568$	−377.681	+	654.162i	−0.664931	+	1.15169i
$569$		−	273.544i		−	0.480745i	−0.970681	−	0.240372i	$-0.922730\pi$
$569$		−	273.544i		−	0.480745i	0.970681	−	0.240372i	$-0.0772695\pi$
$570$	2.79536	−	2.16289i	0.00490414	−	0.00379454i
$571$	411.408	+	712.580i	0.720504	+	1.24795i	0.960798	+	0.277250i	$0.0894230\pi$
$571$	411.408	+	712.580i	0.720504	+	1.24795i	−0.240293	+	0.970700i	$0.577244\pi$
$572$	−60.6090	−	28.6908i	−0.105960	−	0.0501587i
$573$	−100.321	+	244.980i	−0.175080	+	0.427538i
$574$	337.625			0.588196
$575$	−559.718	+	323.153i	−0.973422	+	0.562006i
$576$	−158.369	+	610.658i	−0.274946	+	1.06017i
$577$	−1072.92			−1.85948			−0.929738	−	0.368221i	$-0.879967\pi$
$577$	−1072.92			−1.85948			−0.929738	+	0.368221i	$0.879967\pi$
$578$	1079.98	−	623.529i	1.86848	−	1.07877i
$579$	41.1325	+	303.004i	0.0710405	+	0.523324i
$580$	−5.67676	−	9.83243i	−0.00978751	−	0.0169525i
$581$		−	757.666i		−	1.30407i
$582$	155.005	−	378.516i	0.266332	−	0.650372i
$583$	−383.000			−0.656946
$584$		−	719.361i		−	1.23178i
$585$	119.237	+	20.7470i	0.203824	+	0.0354650i
$586$	623.358			1.06375
$587$		−	212.275i		−	0.361627i	−0.983517	−	0.180813i	$-0.942127\pi$
$587$		−	212.275i		−	0.361627i	0.983517	−	0.180813i	$-0.0578730\pi$
$588$	−4.89641	−	36.0696i	−0.00832722	−	0.0613429i
$589$	−1.34497			−0.00228349
$590$	−9.54971	+	5.51353i	−0.0161859	+	0.00934496i
$591$	176.264	−	430.431i	0.298248	−	0.728310i
$592$	−416.340	−	721.121i	−0.703276	−	1.21811i
$593$			437.862i			0.738384i	0.929353	+	0.369192i	$0.120366\pi$
$593$			437.862i			0.738384i	−0.929353	+	0.369192i	$0.879634\pi$
$594$	−192.088	−	448.353i	−0.323380	−	0.754803i
$595$	−81.9399	−	141.924i	−0.137714	−	0.238528i
$596$		−	10.6679i		−	0.0178992i
$597$	−144.395	−	1063.70i	−0.241868	−	1.78173i
$598$	371.941	+	537.786i	0.621974	+	0.899308i
$599$	738.737	−	426.510i	1.23328	−	0.712037i	0.265571	−	0.964091i	$-0.414439\pi$
$599$	738.737	−	426.510i	1.23328	−	0.712037i	0.967713	+	0.252054i	$0.0811061\pi$
$600$	600.370	−	81.4995i	1.00062	−	0.135832i
$601$	−582.456			−0.969144			−0.484572	−	0.874751i	$-0.661025\pi$
$601$	−582.456			−0.969144			−0.484572	+	0.874751i	$0.661025\pi$
$602$	−10.3669	−	5.98533i	−0.0172207	−	0.00994240i
$603$	39.1479	+	38.5227i	0.0649219	+	0.0638851i
$604$	56.0511	−	97.0834i	0.0927998	−	0.160734i
$605$	24.0984	−	13.9132i	0.0398320	−	0.0229970i
$606$	−184.051	+	142.408i	−0.303715	+	0.234997i
$607$	653.869			1.07721			0.538607	−	0.842557i	$-0.318951\pi$
$607$	653.869			1.07721			0.538607	+	0.842557i	$0.318951\pi$
$608$	4.47476	+	2.58350i	0.00735979	+	0.00424918i
$609$	120.072	−	293.211i	0.197163	−	0.481464i
$610$	−107.024	+	185.372i	−0.175450	+	0.303888i
$611$	−214.431	+	148.304i	−0.350951	+	0.242723i
$612$	−103.928	+	105.615i	−0.169817	+	0.172573i
$613$	447.367	+	774.862i	0.729799	+	1.26405i	0.956968	+	0.290194i	$0.0937199\pi$
$613$	447.367	+	774.862i	0.729799	+	1.26405i	−0.227168	+	0.973855i	$0.572947\pi$
$614$			1003.73i			1.63474i
$615$	86.9603	−	67.2847i	0.141399	−	0.109406i
$616$	209.452	+	362.782i	0.340020	+	0.588932i
$617$			1121.77i			1.81810i	0.416684	+	0.909051i	$0.363192\pi$
$617$			1121.77i			1.81810i	−0.416684	+	0.909051i	$0.636808\pi$
$618$	−178.675	+	436.319i	−0.289119	+	0.706017i
$619$	275.899	−	477.870i	0.445717	−	0.772004i	−0.552385	−	0.833589i	$-0.686282\pi$
$619$	275.899	−	477.870i	0.445717	−	0.772004i	0.998102	+	0.0615852i	$0.0196156\pi$
$620$	1.04764	+	0.604853i	0.00168974	+	0.000975569i
$621$	86.4475	−	724.081i	0.139207	−	1.16599i
$622$	−470.484	−	814.902i	−0.756405	−	1.31013i
$623$	−218.999	−	126.439i	−0.351524	−	0.202952i
$624$	−113.804	−	517.658i	−0.182378	−	0.829580i
$625$	−272.946	−	472.756i	−0.436713	−	0.756410i
$626$	419.927	+	242.445i	0.670809	+	0.387292i
$627$	−17.6356	+	2.39401i	−0.0281270	+	0.00381820i
$628$	11.9873	+	20.7627i	0.0190881	+	0.0330616i
$629$		−	1897.03i		−	3.01595i
$630$	−63.2341	−	62.2243i	−0.100372	−	0.0987688i
$631$	79.6513	−	137.960i	0.126230	−	0.218637i	−0.795983	−	0.605319i	$-0.793046\pi$
$631$	79.6513	−	137.960i	0.126230	−	0.218637i	0.922213	+	0.386682i	$0.126379\pi$
$632$	−199.170	−	114.991i	−0.315143	−	0.181948i
$633$	29.1414	+	214.672i	0.0460369	+	0.339134i
$634$	−406.518	+	704.110i	−0.641196	+	1.11058i
$635$	−114.564	−	66.1433i	−0.180415	−	0.104163i
$636$	38.5430	+	49.8139i	0.0606022	+	0.0783237i
$637$	168.734	+	243.971i	0.264888	+	0.383000i
$638$		−	372.884i		−	0.584458i
$639$	−564.986	+	574.155i	−0.884172	+	0.898521i
$640$	50.0381	+	86.6685i	0.0781845	+	0.135420i
$641$	240.198	−	138.678i	0.374724	−	0.216347i	−0.300796	−	0.953688i	$-0.597252\pi$
$641$	240.198	−	138.678i	0.374724	−	0.216347i	0.675520	+	0.737341i	$0.263919\pi$
$642$	586.223	+	240.062i	0.913121	+	0.373929i
$643$	345.928			0.537991			0.268995	−	0.963141i	$-0.413308\pi$
$643$	345.928			0.537991			0.268995	+	0.963141i	$0.413308\pi$
$644$			73.4855i			0.114108i
$645$	−3.86296	+	0.524391i	−0.00598908	+	0.000813010i
$646$	−17.6315	−	30.5387i	−0.0272934	−	0.0472735i
$647$	−447.421	+	258.319i	−0.691531	+	0.399256i	−0.804185	−	0.594378i	$-0.797398\pi$
$647$	−447.421	+	258.319i	−0.691531	+	0.399256i	0.112654	+	0.993634i	$0.464065\pi$
$648$	−332.229	+	597.446i	−0.512700	+	0.921984i
$649$	55.5261			0.0855564
$650$	−476.491	+	329.548i	−0.733063	+	0.506997i
$651$	4.54115	+	33.4526i	0.00697565	+	0.0513865i
$652$	4.09185	−	7.08729i	0.00627584	−	0.0108701i
$653$	65.1556	+	37.6176i	0.0997789	+	0.0576074i	0.549059	−	0.835784i	$-0.314986\pi$
$653$	65.1556	+	37.6176i	0.0997789	+	0.0576074i	−0.449280	+	0.893391i	$0.648320\pi$
$654$	−155.105	−	200.462i	−0.237164	−	0.306517i
$655$	−34.4436	+	59.6581i	−0.0525857	+	0.0910811i
$656$	−417.001	−	240.756i	−0.635672	−	0.367006i
$657$	192.577	−	742.563i	0.293116	−	1.13023i
$658$	191.111			0.290442
$659$	−215.753	+	124.565i	−0.327395	+	0.189022i	−0.654684	−	0.755903i	$-0.727198\pi$
$659$	−215.753	+	124.565i	−0.327395	+	0.189022i	0.327289	+	0.944924i	$0.393865\pi$
$660$	14.8135	+	6.06621i	0.0224446	+	0.00919123i
$661$	−251.738	+	436.024i	−0.380845	+	0.659643i	−0.991183	−	0.132498i	$-0.957700\pi$
$661$	−251.738	+	436.024i	−0.380845	+	0.659643i	0.610338	+	0.792141i	$0.291033\pi$
$662$	575.341	−	332.173i	0.869095	−	0.501772i
$663$	365.136	−	1150.98i	0.550733	−	1.73601i
$664$	−624.840	+	1082.25i	−0.941024	+	1.62990i
$665$	−2.80332	+	1.61850i	−0.00421551	+	0.00243383i
$666$	−273.768	−	989.783i	−0.411064	−	1.48616i
$667$	278.735	−	482.782i	0.417893	−	0.723812i
$668$	40.7199	+	23.5096i	0.0609579	+	0.0351940i
$669$	−600.476	+	464.612i	−0.897572	+	0.694488i
$670$	11.7563			0.0175467
$671$	933.428	−	538.915i	1.39110	−	0.803152i
$672$	49.1491	−	120.020i	0.0731386	−	0.178602i
$673$	465.144			0.691150			0.345575	−	0.938391i	$-0.387684\pi$
$673$	465.144			0.691150			0.345575	+	0.938391i	$0.387684\pi$
$674$	−22.6317	+	13.0664i	−0.0335782	+	0.0193864i
$675$	641.553	+	76.5945i	0.950448	+	0.113473i
$676$	−56.9633	−	69.5050i	−0.0842652	−	0.102818i
$677$	562.294	+	324.641i	0.830567	+	0.479528i	0.854047	−	0.520196i	$-0.174141\pi$
$677$	562.294	+	324.641i	0.830567	+	0.479528i	−0.0234796	+	0.999724i	$0.507474\pi$
$678$	324.007	−	250.697i	0.477886	−	0.369760i
$679$	−187.302	+	324.417i	−0.275850	+	0.477786i
$680$			270.300i			0.397500i
$681$	92.3222	−	225.447i	0.135569	−	0.331054i
$682$	19.8652	+	34.4076i	0.0291279	+	0.0504510i
$683$	715.727	+	413.225i	1.04792	+	0.605015i	0.922066	−	0.387034i	$-0.126500\pi$
$683$	715.727	+	413.225i	1.04792	+	0.605015i	0.125852	+	0.992049i	$0.459834\pi$
$684$	2.08612	+	2.05281i	0.00304989	+	0.00300119i
$685$	−100.470	+	174.019i	−0.146671	+	0.254042i
$686$		−	684.368i		−	0.997621i
$687$	1179.31	+	482.936i	1.71661	+	0.702964i
$688$	8.53611	+	14.7850i	0.0124071	+	0.0214898i
$689$	−463.919	−	219.608i	−0.673322	−	0.318734i
$690$	−95.5190	−	123.451i	−0.138433	−	0.178914i
$691$	−494.329			−0.715382			−0.357691	−	0.933840i	$-0.616436\pi$
$691$	−494.329			−0.715382			−0.357691	+	0.933840i	$0.616436\pi$
$692$	77.2410	−	44.5951i	0.111620	−	0.0644438i
$693$	119.089	+	430.555i	0.171846	+	0.621292i
$694$	96.0388			0.138384
$695$	215.705	−	124.537i	0.310367	−	0.179190i
$696$	−413.320	+	319.803i	−0.593851	+	0.459486i
$697$	−548.495	−	950.022i	−0.786938	−	1.36302i
$698$			189.434i			0.271395i
$699$	−108.312	−	139.984i	−0.154952	−	0.200264i
$700$	−65.1099			−0.0930141
$701$			788.764i			1.12520i	0.826730	+	0.562599i	$0.190198\pi$
$701$			788.764i			1.12520i	−0.826730	+	0.562599i	$0.809802\pi$
$702$	24.4090	−	653.220i	0.0347707	−	0.930513i
$703$	−37.4706			−0.0533010
$704$		−	679.962i		−	0.965856i
$705$	49.2235	−	38.0862i	0.0698206	−	0.0540230i
$706$	−570.153			−0.807582
$707$	184.575	−	106.565i	0.261068	−	0.150728i
$708$	−5.58785	−	7.22186i	−0.00789244	−	0.0102004i
$709$	−11.7312	−	20.3191i	−0.0165461	−	0.0286587i	0.857634	−	0.514261i	$-0.171934\pi$
$709$	−11.7312	−	20.3191i	−0.0165461	−	0.0286587i	−0.874180	+	0.485602i	$0.838600\pi$
$710$			172.421i			0.242847i
$711$	−174.810	−	172.019i	−0.245866	−	0.241939i
$712$	208.547	+	361.213i	0.292902	+	0.507322i
$713$			59.3978i			0.0833069i
$714$	−700.037	+	541.647i	−0.980444	+	0.758609i
$715$	−130.016	+	10.6168i	−0.181840	+	0.0148487i
$716$	121.028	−	69.8753i	0.169033	−	0.0975912i
$717$	−256.013	+	625.174i	−0.357061	+	0.871930i
$718$	747.892			1.04163
$719$	−276.402	−	159.581i	−0.384425	−	0.221948i	0.295317	−	0.955399i	$-0.404575\pi$
$719$	−276.402	−	159.581i	−0.384425	−	0.221948i	−0.679742	+	0.733451i	$0.737908\pi$
$720$	33.7293	+	121.945i	0.0468462	+	0.169368i
$721$	215.905	−	373.958i	0.299452	−	0.518665i
$722$	581.625	−	335.801i	0.805575	−	0.465099i
$723$	−696.996	−	285.425i	−0.964033	−	0.394778i
$724$	−142.517			−0.196847
$725$	427.757	+	246.965i	0.590009	+	0.340642i
$726$	−91.9703	−	118.865i	−0.126681	−	0.163725i
$727$	329.091	−	570.002i	0.452669	−	0.784046i	−0.545882	−	0.837862i	$-0.683805\pi$
$727$	329.091	−	570.002i	0.452669	−	0.784046i	0.998551	+	0.0538162i	$0.0171385\pi$
$728$	45.6898	+	559.527i	0.0627606	+	0.768581i
$729$	−502.885	+	527.776i	−0.689829	+	0.723973i
$730$	−82.1017	−	142.204i	−0.112468	−	0.194800i
$731$			38.8944i			0.0532071i
$732$	−164.028	−	67.1705i	−0.224082	−	0.0917629i
$733$	231.565	+	401.082i	0.315913	+	0.547178i	0.979631	−	0.200805i	$-0.0643557\pi$
$733$	231.565	+	401.082i	0.315913	+	0.547178i	−0.663718	+	0.747983i	$0.731022\pi$
$734$			314.189i			0.428050i
$735$	−43.3330	−	56.0045i	−0.0589564	−	0.0761966i
$736$	114.095	−	197.618i	0.155020	−	0.268502i
$737$	−51.2670	−	29.5990i	−0.0695618	−	0.0401615i
$738$	−423.281	−	416.522i	−0.573552	−	0.564393i
$739$	−498.613	−	863.622i	−0.674713	−	1.16864i	−0.976553	−	0.215278i	$-0.930934\pi$
$739$	−498.613	−	863.622i	−0.674713	−	1.16864i	0.301840	−	0.953359i	$-0.402399\pi$
$740$	29.1868	+	16.8510i	0.0394416	+	0.0227716i
$741$	−22.7343	−	7.21225i	−0.0306806	−	0.00973313i
$742$	188.118	+	325.829i	0.253528	+	0.439123i
$743$	−111.800	−	64.5478i	−0.150471	−	0.0868745i	0.422874	−	0.906188i	$-0.361021\pi$
$743$	−111.800	−	64.5478i	−0.150471	−	0.0868745i	−0.573345	+	0.819314i	$0.694355\pi$
$744$	21.1014	−	51.5289i	0.0283622	−	0.0692593i
$745$	−10.3764	−	17.9724i	−0.0139280	−	0.0241241i
$746$			405.317i			0.543320i
$747$	−934.720	+	949.889i	−1.25130	+	1.27161i
$748$	79.8534	−	138.310i	0.106756	−	0.184907i
$749$	−502.437	−	290.082i	−0.670811	−	0.387293i
$750$	223.652	−	173.049i	0.298203	−	0.230731i
$751$	−177.897	+	308.126i	−0.236880	+	0.410288i	−0.959817	−	0.280626i	$-0.909458\pi$
$751$	−177.897	+	308.126i	−0.236880	+	0.410288i	0.722938	+	0.690913i	$0.242791\pi$
$752$	−236.042	−	136.279i	−0.313885	−	0.181222i
$753$	−313.576	+	42.5675i	−0.416435	+	0.0565306i
$754$	213.807	−	451.666i	0.283564	−	0.599027i
$755$		−	218.077i		−	0.288844i
$756$	44.0146	−	58.8178i	0.0582203	−	0.0778013i
$757$	134.999	+	233.825i	0.178334	+	0.308884i	0.941310	−	0.337543i	$-0.109596\pi$
$757$	134.999	+	233.825i	0.178334	+	0.308884i	−0.762976	+	0.646427i	$0.776263\pi$
$758$	1022.15	−	590.141i	1.34849	−	0.778550i
$759$	105.726	+	778.838i	0.139297	+	1.02614i
$760$	5.33903			0.00702504
$761$			1215.03i			1.59662i	0.602245	+	0.798311i	$0.294273\pi$
$761$			1215.03i			1.59662i	−0.602245	+	0.798311i	$0.705727\pi$
$762$	−270.762	+	661.191i	−0.355331	+	0.867704i
$763$	116.066	+	201.032i	0.152118	+	0.263476i
$764$	−40.6358	+	23.4611i	−0.0531882	+	0.0307082i
$765$	−72.3610	+	279.019i	−0.0945896	+	0.364730i
$766$	−1288.19			−1.68171
$767$	67.2575	+	31.8380i	0.0876891	+	0.0415098i
$768$	−237.770	+	183.972i	−0.309597	+	0.239547i
$769$	158.059	−	273.767i	0.205539	−	0.356004i	−0.744765	−	0.667326i	$-0.767439\pi$
$769$	158.059	−	273.767i	0.205539	−	0.356004i	0.950304	+	0.311323i	$0.100772\pi$

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-1.86232i q^{2} +(2.37269 - 1.83585i) q^{3} +0.531747 q^{4} +(0.895843 - 0.517215i) q^{5} +(-3.41894 - 4.41872i) q^{6} +(2.55841 + 4.43129i) q^{7} -8.43958i q^{8} +(2.25933 - 8.71180i) q^{9} +(-0.963222 - 1.66835i) q^{10} +9.70050i q^{11} +(1.26167 - 0.976206i) q^{12} +(-5.56216 + 11.7500i) q^{13} +(8.25251 - 4.76459i) q^{14} +(1.17603 - 2.87182i) q^{15} -13.5903 q^{16} +(-26.8136 - 15.4808i) q^{17} +(-16.2242 - 4.20760i) q^{18} +(-0.305781 + 0.529628i) q^{19} +(0.476361 - 0.275027i) q^{20} +(14.2055 + 5.81725i) q^{21} +18.0655 q^{22} +(23.3898 + 13.5041i) q^{23} +(-15.4938 - 20.0245i) q^{24} +(-11.9650 + 20.7239i) q^{25} +(21.8823 + 10.3585i) q^{26} +(-10.6328 - 24.8182i) q^{27} +(1.36043 + 2.35633i) q^{28} -20.6407i q^{29} +(-5.34826 - 2.19015i) q^{30} +(1.09962 + 1.90460i) q^{31} -8.44886i q^{32} +(17.8086 + 23.0163i) q^{33} +(-28.8303 + 49.9356i) q^{34} +(4.58386 + 2.64650i) q^{35} +(1.20139 - 4.63247i) q^{36} +(30.6351 + 53.0616i) q^{37} +(0.986339 + 0.569463i) q^{38} +(8.37392 + 38.0904i) q^{39} +(-4.36508 - 7.56054i) q^{40} +(30.6838 + 17.7153i) q^{41} +(10.8336 - 26.4552i) q^{42} +(-0.628105 - 1.08791i) q^{43} +5.15821i q^{44} +(-2.48187 - 8.97296i) q^{45} +(25.1491 - 43.5595i) q^{46} +(17.3684 + 10.0277i) q^{47} +(-32.2455 + 24.9496i) q^{48} +(11.4091 - 19.7611i) q^{49} +(38.5947 + 22.2827i) q^{50} +(-92.0408 + 12.4944i) q^{51} +(-2.95766 + 6.24802i) q^{52} +39.4824i q^{53} +(-46.2195 + 19.8018i) q^{54} +(5.01725 + 8.69013i) q^{55} +(37.3983 - 21.5919i) q^{56} +(0.246793 + 1.81801i) q^{57} -38.4397 q^{58} -5.72404i q^{59} +(0.625350 - 1.52708i) q^{60} +(-55.5554 - 96.2247i) q^{61} +(3.54699 - 2.04785i) q^{62} +(44.3848 - 12.2766i) q^{63} -70.0956 q^{64} +(1.09446 + 13.4030i) q^{65} +(42.8638 - 33.1655i) q^{66} +(-3.05129 + 5.28499i) q^{67} +(-14.2580 - 8.23188i) q^{68} +(80.2884 - 10.8990i) q^{69} +(4.92863 - 8.53664i) q^{70} +(-77.5112 - 44.7511i) q^{71} +(-73.5240 - 19.0678i) q^{72} +85.2365 q^{73} +(98.8180 - 57.0526i) q^{74} +(9.65681 + 71.1374i) q^{75} +(-0.162598 + 0.281628i) q^{76} +(-42.9858 + 24.8179i) q^{77} +(70.9367 - 15.5950i) q^{78} +(13.6252 - 23.5995i) q^{79} +(-12.1747 + 7.02909i) q^{80} +(-70.7909 - 39.3656i) q^{81} +(32.9917 - 57.1432i) q^{82} +(-128.236 - 74.0368i) q^{83} +(7.55373 + 3.09330i) q^{84} -32.0277 q^{85} +(-2.02604 + 1.16974i) q^{86} +(-37.8932 - 48.9740i) q^{87} +81.8682 q^{88} +(-42.7999 + 24.7105i) q^{89} +(-16.7106 + 4.62205i) q^{90} +(-66.2980 + 5.41374i) q^{91} +(12.4375 + 7.18078i) q^{92} +(6.10562 + 2.50029i) q^{93} +(18.6748 - 32.3457i) q^{94} +0.632618i q^{95} +(-15.5108 - 20.0465i) q^{96} +(36.6052 + 63.4021i) q^{97} +(-36.8016 - 21.2474i) q^{98} +(84.5088 + 21.9166i) 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

Related objects

Downloads

Learn more