LMFDB - Embedded newform 117.3.k.a.29.3

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			29.3
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.27217i q^{2} +(-2.67392 - 1.36020i) q^{3} -6.70711 q^{4} +(-3.48512 + 2.01214i) q^{5} +(-4.45081 + 8.74953i) q^{6} +(1.40029 + 2.42538i) q^{7} +8.85812i q^{8} +(5.29971 + 7.27414i) q^{9} +(6.58406 + 11.4039i) q^{10} -10.5579i q^{11} +(17.9343 + 9.12301i) q^{12} +(-12.8016 + 2.26238i) q^{13} +(7.93627 - 4.58201i) q^{14} +(12.0559 - 0.639831i) q^{15} +2.15687 q^{16} +(-13.9728 - 8.06719i) q^{17} +(23.8022 - 17.3416i) q^{18} +(-11.6456 + 20.1708i) q^{19} +(23.3751 - 13.4956i) q^{20} +(-0.445274 - 8.38996i) q^{21} -34.5473 q^{22} +(9.63655 + 5.56367i) q^{23} +(12.0488 - 23.6859i) q^{24} +(-4.40262 + 7.62555i) q^{25} +(7.40288 + 41.8891i) q^{26} +(-4.27674 - 26.6591i) q^{27} +(-9.39193 - 16.2673i) q^{28} -24.7726i q^{29} +(-2.09364 - 39.4488i) q^{30} +(4.04316 + 7.00296i) q^{31} +28.3748i q^{32} +(-14.3609 + 28.2311i) q^{33} +(-26.3972 + 45.7213i) q^{34} +(-9.76040 - 5.63517i) q^{35} +(-35.5457 - 48.7884i) q^{36} +(-33.7864 - 58.5198i) q^{37} +(66.0022 + 38.1064i) q^{38} +(37.3078 + 11.3634i) q^{39} +(-17.8238 - 30.8716i) q^{40} +(-8.53943 - 4.93024i) q^{41} +(-27.4534 + 1.45701i) q^{42} +(1.70728 + 2.95709i) q^{43} +70.8132i q^{44} +(-33.1067 - 14.6875i) q^{45} +(18.2053 - 31.5325i) q^{46} +(-80.2410 - 46.3271i) q^{47} +(-5.76730 - 2.93378i) q^{48} +(20.5783 - 35.6427i) q^{49} +(24.9521 + 14.4061i) q^{50} +(26.3891 + 40.5768i) q^{51} +(85.8619 - 15.1740i) q^{52} -36.1018i q^{53} +(-87.2333 + 13.9942i) q^{54} +(21.2440 + 36.7957i) q^{55} +(-21.4843 + 12.4040i) q^{56} +(58.5757 - 38.0947i) q^{57} -81.0602 q^{58} -16.8680i q^{59} +(-80.8599 + 4.29142i) q^{60} +(8.90904 + 15.4309i) q^{61} +(22.9149 - 13.2299i) q^{62} +(-10.2214 + 23.0398i) q^{63} +101.475 q^{64} +(40.0630 - 33.6433i) q^{65} +(92.3769 + 46.9913i) q^{66} +(27.4720 - 47.5828i) q^{67} +(93.7169 + 54.1075i) q^{68} +(-18.1997 - 27.9844i) q^{69} +(-18.4392 + 31.9377i) q^{70} +(76.3871 + 44.1021i) q^{71} +(-64.4352 + 46.9455i) q^{72} +86.4607 q^{73} +(-191.487 + 110.555i) q^{74} +(22.1445 - 14.4017i) q^{75} +(78.1083 - 135.287i) q^{76} +(25.6070 - 14.7842i) q^{77} +(37.1829 - 122.078i) q^{78} +(-62.9550 + 109.041i) q^{79} +(-7.51696 + 4.33992i) q^{80} +(-24.8261 + 77.1017i) q^{81} +(-16.1326 + 27.9425i) q^{82} +(1.94262 + 1.12157i) q^{83} +(2.98650 + 56.2724i) q^{84} +64.9291 q^{85} +(9.67611 - 5.58651i) q^{86} +(-33.6957 + 66.2400i) q^{87} +93.5234 q^{88} +(-66.8494 + 38.5955i) q^{89} +(-48.0601 + 108.331i) q^{90} +(-23.4132 - 27.8808i) q^{91} +(-64.6334 - 37.3161i) q^{92} +(-1.28567 - 24.2249i) q^{93} +(-151.590 + 262.562i) q^{94} -93.7301i q^{95} +(38.5955 - 75.8721i) q^{96} +(-49.4835 - 85.7080i) q^{97} +(-116.629 - 67.3359i) q^{98} +(76.7998 - 55.9540i) 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 $

$2$		−	3.27217i		−	1.63609i	−0.575157	−	0.818043i	$-0.695059\pi$
$2$		−	3.27217i		−	1.63609i	0.575157	−	0.818043i	$-0.304941\pi$
$3$	−2.67392	−	1.36020i	−0.891307	−	0.453400i
$3$	−2.67392	−	1.36020i	−0.891307	−	0.453400i
$4$	−6.70711			−1.67678
$5$	−3.48512	+	2.01214i	−0.697024	+	0.402427i	−0.806238	−	0.591591i	$-0.798500\pi$
$5$	−3.48512	+	2.01214i	−0.697024	+	0.402427i	0.109214	+	0.994018i	$0.465167\pi$
$6$	−4.45081	+	8.74953i	−0.741801	+	1.45826i
$7$	1.40029	+	2.42538i	0.200042	+	0.346483i	0.948542	−	0.316652i	$-0.102559\pi$
$7$	1.40029	+	2.42538i	0.200042	+	0.346483i	−0.748500	+	0.663135i	$0.769225\pi$
$8$			8.85812i			1.10727i
$9$	5.29971	+	7.27414i	0.588857	+	0.808237i
$10$	6.58406	+	11.4039i	0.658406	+	1.14039i
$11$		−	10.5579i		−	0.959811i	−0.877320	−	0.479906i	$-0.840671\pi$
$11$		−	10.5579i		−	0.959811i	0.877320	−	0.479906i	$-0.159329\pi$
$12$	17.9343	+	9.12301i	1.49452	+	0.760251i
$13$	−12.8016	+	2.26238i	−0.984741	+	0.174029i
$13$	−12.8016	+	2.26238i	−0.984741	+	0.174029i
$14$	7.93627	−	4.58201i	0.566876	−	0.327286i
$15$	12.0559	−	0.639831i	0.803723	−	0.0426554i
$16$	2.15687			0.134804
$17$	−13.9728	−	8.06719i	−0.821928	−	0.474540i	0.0291528	−	0.999575i	$-0.490719\pi$
$17$	−13.9728	−	8.06719i	−0.821928	−	0.474540i	−0.851081	+	0.525035i	$0.824052\pi$
$18$	23.8022	−	17.3416i	1.32235	−	0.963421i
$19$	−11.6456	+	20.1708i	−0.612926	+	1.06162i	0.377819	+	0.925880i	$0.376674\pi$
$19$	−11.6456	+	20.1708i	−0.612926	+	1.06162i	−0.990745	+	0.135739i	$0.956659\pi$
$20$	23.3751	−	13.4956i	1.16875	−	0.674781i
$21$	−0.445274	−	8.38996i	−0.0212035	−	0.399522i
$22$	−34.5473			−1.57033
$23$	9.63655	+	5.56367i	0.418981	+	0.241899i	0.694641	−	0.719357i	$-0.255563\pi$
$23$	9.63655	+	5.56367i	0.418981	+	0.241899i	−0.275660	+	0.961255i	$0.588897\pi$
$24$	12.0488	−	23.6859i	0.502034	−	0.986914i
$25$	−4.40262	+	7.62555i	−0.176105	+	0.305022i
$26$	7.40288	+	41.8891i	0.284726	+	1.61112i
$27$	−4.27674	−	26.6591i	−0.158398	−	0.987375i
$28$	−9.39193	−	16.2673i	−0.335426	−	0.580975i
$29$		−	24.7726i		−	0.854228i	−0.904198	−	0.427114i	$-0.859530\pi$
$29$		−	24.7726i		−	0.854228i	0.904198	−	0.427114i	$-0.140470\pi$
$30$	−2.09364	−	39.4488i	−0.0697879	−	1.31496i
$31$	4.04316	+	7.00296i	0.130425	+	0.225902i	0.923840	−	0.382778i	$-0.125033\pi$
$31$	4.04316	+	7.00296i	0.130425	+	0.225902i	−0.793416	+	0.608680i	$0.791699\pi$
$32$			28.3748i			0.886714i
$33$	−14.3609	+	28.2311i	−0.435178	+	0.855487i
$34$	−26.3972	+	45.7213i	−0.776389	+	1.34475i
$35$	−9.76040	−	5.63517i	−0.278869	−	0.161005i
$36$	−35.5457	−	48.7884i	−0.987382	−	1.35523i
$37$	−33.7864	−	58.5198i	−0.913146	−	1.58162i	−0.809593	−	0.586992i	$-0.800312\pi$
$37$	−33.7864	−	58.5198i	−0.913146	−	1.58162i	−0.103553	−	0.994624i	$-0.533021\pi$
$38$	66.0022	+	38.1064i	1.73690	+	1.00280i
$39$	37.3078	+	11.3634i	0.956611	+	0.291368i
$40$	−17.8238	−	30.8716i	−0.445594	−	0.771791i
$41$	−8.53943	−	4.93024i	−0.208279	−	0.120250i	0.392232	−	0.919866i	$-0.371703\pi$
$41$	−8.53943	−	4.93024i	−0.208279	−	0.120250i	−0.600511	+	0.799616i	$0.705036\pi$
$42$	−27.4534	+	1.45701i	−0.653652	+	0.0346908i
$43$	1.70728	+	2.95709i	0.0397041	+	0.0687696i	0.885195	−	0.465221i	$-0.154025\pi$
$43$	1.70728	+	2.95709i	0.0397041	+	0.0687696i	−0.845490	+	0.533991i	$0.820692\pi$
$44$			70.8132i			1.60939i
$45$	−33.1067	−	14.6875i	−0.735704	−	0.326389i
$46$	18.2053	−	31.5325i	0.395767	−	0.685488i
$47$	−80.2410	−	46.3271i	−1.70725	−	0.985684i	−0.937929	−	0.346827i	$-0.887259\pi$
$47$	−80.2410	−	46.3271i	−1.70725	−	0.985684i	−0.769326	−	0.638857i	$-0.779408\pi$
$48$	−5.76730	−	2.93378i	−0.120152	−	0.0611203i
$49$	20.5783	−	35.6427i	0.419966	−	0.727403i
$50$	24.9521	+	14.4061i	0.499043	+	0.288122i
$51$	26.3891	+	40.5768i	0.517434	+	0.795623i
$52$	85.8619	−	15.1740i	1.65119	−	0.291808i
$53$		−	36.1018i		−	0.681167i	−0.940214	−	0.340583i	$-0.889375\pi$
$53$		−	36.1018i		−	0.681167i	0.940214	−	0.340583i	$-0.110625\pi$
$54$	−87.2333	+	13.9942i	−1.61543	+	0.259152i
$55$	21.2440	+	36.7957i	0.386254	+	0.669012i
$56$	−21.4843	+	12.4040i	−0.383649	+	0.221500i
$57$	58.5757	−	38.0947i	1.02764	−	0.668328i
$58$	−81.0602			−1.39759
$59$		−	16.8680i		−	0.285898i	−0.989730	−	0.142949i	$-0.954342\pi$
$59$		−	16.8680i		−	0.285898i	0.989730	−	0.142949i	$-0.0456584\pi$
$60$	−80.8599	+	4.29142i	−1.34766	+	0.0715236i
$61$	8.90904	+	15.4309i	0.146050	+	0.252966i	0.929764	−	0.368156i	$-0.120011\pi$
$61$	8.90904	+	15.4309i	0.146050	+	0.252966i	−0.783714	+	0.621121i	$0.786677\pi$
$62$	22.9149	−	13.2299i	0.369595	−	0.213386i
$63$	−10.2214	+	23.0398i	−0.162244	+	0.365711i
$64$	101.475			1.58554
$65$	40.0630	−	33.6433i	0.616354	−	0.517589i
$66$	92.3769	+	46.9913i	1.39965	+	0.711989i
$67$	27.4720	−	47.5828i	0.410029	−	0.710192i	−0.584863	−	0.811132i	$-0.698852\pi$
$67$	27.4720	−	47.5828i	0.410029	−	0.710192i	0.994892	+	0.100940i	$0.0321851\pi$
$68$	93.7169	+	54.1075i	1.37819	+	0.795699i
$69$	−18.1997	−	27.9844i	−0.263764	−	0.405572i
$70$	−18.4392	+	31.9377i	−0.263418	+	0.456253i
$71$	76.3871	+	44.1021i	1.07587	+	0.621156i	0.929780	−	0.368115i	$-0.119997\pi$
$71$	76.3871	+	44.1021i	1.07587	+	0.621156i	0.146094	+	0.989271i	$0.453330\pi$
$72$	−64.4352	+	46.9455i	−0.894933	+	0.652021i
$73$	86.4607			1.18439			0.592196	−	0.805794i	$-0.298261\pi$
$73$	86.4607			1.18439			0.592196	+	0.805794i	$0.298261\pi$
$74$	−191.487	+	110.555i	−2.58766	+	1.49399i
$75$	22.1445	−	14.4017i	0.295260	−	0.192023i
$76$	78.1083	−	135.287i	1.02774	−	1.78010i
$77$	25.6070	−	14.7842i	0.332558	−	0.192003i
$78$	37.1829	−	122.078i	0.476703	−	1.56510i
$79$	−62.9550	+	109.041i	−0.796899	+	1.38027i	0.124727	+	0.992191i	$0.460195\pi$
$79$	−62.9550	+	109.041i	−0.796899	+	1.38027i	−0.921626	+	0.388079i	$0.873139\pi$
$80$	−7.51696	+	4.33992i	−0.0939620	+	0.0542490i
$81$	−24.8261	+	77.1017i	−0.306495	+	0.951872i
$82$	−16.1326	+	27.9425i	−0.196739	+	0.340762i
$83$	1.94262	+	1.12157i	0.0234051	+	0.0135129i	0.511657	−	0.859190i	$-0.329032\pi$
$83$	1.94262	+	1.12157i	0.0234051	+	0.0135129i	−0.488252	+	0.872703i	$0.662365\pi$
$84$	2.98650	+	56.2724i	0.0355536	+	0.669909i
$85$	64.9291			0.763872
$86$	9.67611	−	5.58651i	0.112513	−	0.0649594i
$87$	−33.6957	+	66.2400i	−0.387307	+	0.761379i
$88$	93.5234			1.06277
$89$	−66.8494	+	38.5955i	−0.751117	+	0.433658i	−0.826098	−	0.563527i	$-0.809444\pi$
$89$	−66.8494	+	38.5955i	−0.751117	+	0.433658i	0.0749801	+	0.997185i	$0.476111\pi$
$90$	−48.0601	+	108.331i	−0.534001	+	1.20368i
$91$	−23.4132	−	27.8808i	−0.257288	−	0.306383i
$92$	−64.6334	−	37.3161i	−0.702537	−	0.405610i
$93$	−1.28567	−	24.2249i	−0.0138244	−	0.260483i
$94$	−151.590	+	262.562i	−1.61266	+	2.79322i
$95$		−	93.7301i		−	0.986632i
$96$	38.5955	−	75.8721i	0.402036	−	0.790334i
$97$	−49.4835	−	85.7080i	−0.510140	−	0.883588i	−0.999931	−	0.0117480i	$-0.996260\pi$
$97$	−49.4835	−	85.7080i	−0.510140	−	0.883588i	0.489791	−	0.871840i	$-0.337073\pi$
$98$	−116.629	−	67.3359i	−1.19009	−	0.687101i
$99$	76.7998	−	55.9540i	0.775755	−	0.565192i
$100$	29.5288	−	51.1454i	0.295288	−	0.511454i
$101$			91.5426i			0.906362i	0.891419	+	0.453181i	$0.149711\pi$
$101$			91.5426i			0.906362i	−0.891419	+	0.453181i	$0.850289\pi$
$102$	132.774	−	86.3498i	1.30171	−	0.846566i
$103$	46.6869	+	80.8641i	0.453271	+	0.785089i	0.998587	−	0.0531421i	$-0.0169236\pi$
$103$	46.6869	+	80.8641i	0.453271	+	0.785089i	−0.545316	+	0.838231i	$0.683590\pi$
$104$	−20.0404	−	113.398i	−0.192696	−	1.09037i
$105$	18.4336	+	28.3441i	0.175558	+	0.269944i
$106$	−118.131			−1.11445
$107$	66.3985	−	38.3352i	0.620547	−	0.358273i	−0.156535	−	0.987672i	$-0.550032\pi$
$107$	66.3985	−	38.3352i	0.620547	−	0.358273i	0.777082	+	0.629400i	$0.216699\pi$
$108$	28.6845	+	178.806i	0.265597	+	1.65561i
$109$	−157.860			−1.44826			−0.724128	−	0.689666i	$-0.757757\pi$
$109$	−157.860			−1.44826			−0.724128	+	0.689666i	$0.757757\pi$
$110$	120.402	−	69.5140i	1.09456	−	0.631945i
$111$	10.7436	+	202.434i	0.0967893	+	1.82373i
$112$	3.02026	+	5.23124i	0.0269666	+	0.0467075i
$113$		−	119.644i		−	1.05879i	−0.848374	−	0.529397i	$-0.822418\pi$
$113$		−	119.644i		−	1.05879i	0.848374	−	0.529397i	$-0.177582\pi$
$114$	−124.652	−	191.670i	−1.09344	−	1.68131i
$115$	−44.7794			−0.389386
$116$			166.153i			1.43235i
$117$	−84.3018	−	81.1308i	−0.720528	−	0.693426i
$118$	−55.1949			−0.467753
$119$		−	45.1858i		−	0.379712i
$120$	5.66771	+	106.792i	0.0472309	+	0.889935i
$121$	9.53021			0.0787621
$122$	50.4926	−	29.1519i	0.413874	−	0.238950i
$123$	16.1277	+	24.7984i	0.131119	+	0.201613i
$124$	−27.1179	−	46.9696i	−0.218693	−	0.378787i
$125$		−	136.041i		−	1.08833i
$126$	75.3901	+	33.4462i	0.598334	+	0.265446i
$127$	95.7996	+	165.930i	0.754327	+	1.30653i	0.945708	+	0.325017i	$0.105370\pi$
$127$	95.7996	+	165.930i	0.754327	+	1.30653i	−0.191381	+	0.981516i	$0.561296\pi$
$128$		−	218.544i		−	1.70737i
$129$	−0.542891	−	10.2293i	−0.00420845	−	0.0792967i
$130$	−110.087	−	131.093i	−0.846820	−	1.00841i
$131$	−208.472	+	120.361i	−1.59139	+	0.918789i	−0.598321	+	0.801257i	$0.704165\pi$
$131$	−208.472	+	120.361i	−1.59139	+	0.918789i	−0.993069	+	0.117533i	$0.962502\pi$
$132$	96.3200	−	189.349i	0.729697	−	1.43446i
$133$	−65.2291			−0.490444
$134$	−155.699	−	89.8930i	−1.16193	−	0.670843i
$135$	68.5468	+	84.3050i	0.507754	+	0.624481i
$136$	71.4601	−	123.773i	0.525442	−	0.910093i
$137$	−17.9933	+	10.3884i	−0.131338	+	0.0758278i	−0.564229	−	0.825618i	$-0.690827\pi$
$137$	−17.9933	+	10.3884i	−0.131338	+	0.0758278i	0.432892	+	0.901446i	$0.357493\pi$
$138$	−91.5699	+	59.5525i	−0.663550	+	0.431540i
$139$	253.990			1.82727			0.913634	−	0.406539i	$-0.133264\pi$
$139$	253.990			1.82727			0.913634	+	0.406539i	$0.133264\pi$
$140$	65.4640	+	37.7957i	0.467600	+	0.269969i
$141$	151.544	+	233.019i	1.07478	+	1.65262i
$142$	144.310	−	249.952i	1.01626	−	1.76022i
$143$	23.8860	+	135.159i	0.167035	+	0.945165i
$144$	11.4308	+	15.6894i	0.0793805	+	0.108954i
$145$	49.8459	+	86.3356i	0.343765	+	0.595418i
$146$		−	282.914i		−	1.93777i
$147$	−103.506	+	67.3152i	−0.704123	+	0.457927i
$148$	226.609	+	392.499i	1.53114	+	2.65202i
$149$		−	146.052i		−	0.980214i	−0.871662	−	0.490107i	$-0.836958\pi$
$149$		−	146.052i		−	0.980214i	0.871662	−	0.490107i	$-0.163042\pi$
$150$	−47.1248	−	72.4607i	−0.314166	−	0.483071i
$151$	140.864	−	243.983i	0.932871	−	1.61578i	0.154485	−	0.987995i	$-0.450628\pi$
$151$	140.864	−	243.983i	0.932871	−	1.61578i	0.778386	−	0.627786i	$-0.216039\pi$
$152$	−178.675	−	103.158i	−1.17549	−	0.678672i
$153$	−15.3699	−	144.394i	−0.100457	−	0.943749i
$154$	−48.3765	−	83.7905i	−0.314133	−	0.544094i
$155$	−28.1818	−	16.2708i	−0.181818	−	0.104973i
$156$	−250.228	−	76.2153i	−1.60402	−	0.488559i
$157$	−66.6730	−	115.481i	−0.424669	−	0.735548i	0.571720	−	0.820448i	$-0.306276\pi$
$157$	−66.6730	−	115.481i	−0.424669	−	0.735548i	−0.996389	+	0.0849002i	$0.972943\pi$
$158$	356.802	+	206.000i	2.25824	+	1.30380i
$159$	−49.1057	+	96.5335i	−0.308841	+	0.607129i
$160$	−57.0941	−	98.8898i	−0.356838	−	0.618061i
$161$			31.1631i			0.193560i
$162$	252.290	+	81.2353i	1.55734	+	0.501452i
$163$	−15.9767	+	27.6724i	−0.0980163	+	0.169769i	−0.910863	−	0.412708i	$-0.864583\pi$
$163$	−15.9767	+	27.6724i	−0.0980163	+	0.169769i	0.812847	+	0.582477i	$0.197916\pi$
$164$	57.2749	+	33.0677i	0.349237	+	0.201632i
$165$	−6.75529	−	127.285i	−0.0409412	−	0.771423i
$166$	3.66998	−	6.35659i	0.0221083	−	0.0382927i
$167$	−144.425	−	83.3837i	−0.864819	−	0.499303i	0.000804162	−	1.00000i	$-0.499744\pi$
$167$	−144.425	−	83.3837i	−0.864819	−	0.499303i	−0.865623	+	0.500696i	$0.833077\pi$
$168$	74.3193	−	3.94430i	0.442377	−	0.0234779i
$169$	158.763	−	57.9242i	0.939428	−	0.342747i
$170$		−	212.459i		−	1.24976i
$171$	−208.443	+	22.1876i	−1.21897	+	0.129752i
$172$	−11.4509	−	19.8335i	−0.0665750	−	0.115311i
$173$	−57.0314	+	32.9271i	−0.329661	+	0.190330i	−0.655691	−	0.755030i	$-0.727622\pi$
$173$	−57.0314	+	32.9271i	−0.329661	+	0.190330i	0.326030	+	0.945360i	$0.394289\pi$
$174$	216.749	+	110.258i	1.24568	+	0.633667i
$175$	−24.6598			−0.140913
$176$		−	22.7721i		−	0.129387i
$177$	−22.9438	+	45.1036i	−0.129626	+	0.254823i
$178$	126.291	+	218.743i	0.709501	+	1.22889i
$179$	−210.321	+	121.429i	−1.17498	+	0.678374i	−0.954847	−	0.297097i	$-0.903982\pi$
$179$	−210.321	+	121.429i	−1.17498	+	0.678374i	−0.220130	+	0.975470i	$0.570648\pi$
$180$	222.050	+	98.5107i	1.23361	+	0.547282i
$181$	−117.666			−0.650086			−0.325043	−	0.945699i	$-0.605379\pi$
$181$	−117.666			−0.650086			−0.325043	+	0.945699i	$0.605379\pi$
$182$	−91.2309	+	76.6119i	−0.501269	+	0.420945i
$183$	−2.83295	−	53.3791i	−0.0154806	−	0.291689i
$184$	−49.2837	+	85.3618i	−0.267846	+	0.463923i
$185$	235.500	+	135.966i	1.27297	+	0.734950i
$186$	−79.2680	+	4.20693i	−0.426172	+	0.0226179i
$187$	−85.1728	+	147.524i	−0.455469	+	0.788896i
$188$	538.185	+	310.721i	2.86269	+	1.65277i
$189$	58.6699	−	47.7034i	0.310423	−	0.252399i
$190$	−306.701			−1.61422
$191$	−184.114	+	106.298i	−0.963948	+	0.556535i	−0.897386	−	0.441247i	$-0.854536\pi$
$191$	−184.114	+	106.298i	−0.963948	+	0.556535i	−0.0665619	+	0.997782i	$0.521203\pi$
$192$	−271.336	−	138.026i	−1.41321	−	0.718886i
$193$	−31.1378	+	53.9323i	−0.161336	+	0.279442i	−0.935348	−	0.353729i	$-0.884914\pi$
$193$	−31.1378	+	53.9323i	−0.161336	+	0.279442i	0.774012	+	0.633171i	$0.218247\pi$
$194$	−280.451	+	161.919i	−1.44563	+	0.834632i
$195$	−152.887	+	35.4658i	−0.784036	+	0.181876i
$196$	−138.021	+	239.060i	−0.704190	+	1.21969i
$197$	−248.948	+	143.730i	−1.26369	+	0.729594i	−0.973787	−	0.227461i	$-0.926957\pi$
$197$	−248.948	+	143.730i	−1.26369	+	0.729594i	−0.289906	+	0.957055i	$0.593624\pi$
$198$	−183.091	−	251.302i	−0.924702	−	1.26920i
$199$	−106.633	+	184.694i	−0.535845	+	0.928111i	0.463277	+	0.886214i	$0.346674\pi$
$199$	−106.633	+	184.694i	−0.535845	+	0.928111i	−0.999122	+	0.0418972i	$0.986660\pi$
$200$	−67.5481	−	38.9989i	−0.337741	−	0.194995i
$201$	−138.180	+	89.8654i	−0.687463	+	0.447092i
$202$	299.543			1.48289
$203$	60.0830	−	34.6890i	0.295976	−	0.170882i
$204$	−176.995	−	272.153i	−0.867621	−	1.33408i
$205$	39.6813			0.193567
$206$	264.601	−	152.768i	1.28447	−	0.741590i
$207$	10.6001	+	99.5834i	0.0512082	+	0.481079i
$208$	−27.6115	+	4.87965i	−0.132747	+	0.0234599i
$209$	212.961	+	122.953i	1.01895	+	0.588293i
$210$	92.7467	−	60.3178i	0.441651	−	0.287228i
$211$	177.600	−	307.613i	0.841708	−	1.45788i	−0.0467410	−	0.998907i	$-0.514884\pi$
$211$	177.600	−	307.613i	0.841708	−	1.45788i	0.888449	−	0.458975i	$-0.151783\pi$
$212$			242.139i			1.14216i
$213$	−144.265	−	221.827i	−0.677302	−	1.04144i
$214$	−125.439	−	217.267i	−0.586165	−	1.01527i
$215$	−11.9001	−	6.87055i	−0.0553495	−	0.0319560i
$216$	236.150	−	37.8839i	1.09329	−	0.175388i
$217$	−11.3232	+	19.6124i	−0.0521808	+	0.0903798i
$218$			516.545i			2.36947i
$219$	−231.189	−	117.604i	−1.05566	−	0.537004i
$220$	−142.486	−	246.792i	−0.647662	−	1.12178i
$221$	197.125	+	71.6614i	0.891970	+	0.324260i
$222$	662.397	−	35.1549i	2.98377	−	0.158356i
$223$	−26.7604			−0.120002			−0.0600008	−	0.998198i	$-0.519110\pi$
$223$	−26.7604			−0.120002			−0.0600008	+	0.998198i	$0.519110\pi$
$224$	−68.8198	+	39.7332i	−0.307231	+	0.177380i
$225$	−78.8019	+	8.38802i	−0.350231	+	0.0372801i
$226$	−391.495			−1.73228
$227$	263.953	−	152.393i	1.16279	−	0.671337i	0.210818	−	0.977525i	$-0.432387\pi$
$227$	263.953	−	152.393i	1.16279	−	0.671337i	0.951971	+	0.306189i	$0.0990538\pi$
$228$	−392.873	+	255.505i	−1.72313	+	1.12064i
$229$	4.51573	+	7.82147i	0.0197193	+	0.0341549i	0.875717	−	0.482825i	$-0.160389\pi$
$229$	4.51573	+	7.82147i	0.0197193	+	0.0341549i	−0.855997	+	0.516980i	$0.827056\pi$
$230$			146.526i			0.637069i
$231$	−88.5806	+	4.70117i	−0.383466	+	0.0203514i
$232$	219.439			0.945857
$233$			104.668i			0.449218i	0.974449	+	0.224609i	$0.0721105\pi$
$233$			104.668i			0.449218i	−0.974449	+	0.224609i	$0.927889\pi$
$234$	−265.474	+	275.850i	−1.13450	+	1.17885i
$235$	372.866			1.58666
$236$			113.135i			0.479387i
$237$	316.655	−	205.937i	1.33610	−	0.868930i
$238$	−147.856			−0.621242
$239$	97.9341	−	56.5423i	0.409766	−	0.236579i	−0.280923	−	0.959730i	$-0.590641\pi$
$239$	97.9341	−	56.5423i	0.409766	−	0.236579i	0.690689	+	0.723152i	$0.257307\pi$
$240$	26.0029	−	1.38003i	0.108345	−	0.00575014i
$241$	−83.2698	−	144.227i	−0.345518	−	0.598454i	0.639930	−	0.768433i	$-0.278963\pi$
$241$	−83.2698	−	144.227i	−0.345518	−	0.598454i	−0.985448	+	0.169979i	$0.945630\pi$
$242$		−	31.1845i		−	0.128861i
$243$	171.257	−	172.395i	0.704760	−	0.709446i
$244$	−59.7539	−	103.497i	−0.244893	−	0.424167i
$245$			165.626i			0.676023i
$246$	81.1447	−	52.7724i	0.329856	−	0.214522i
$247$	103.449	−	284.565i	0.418821	−	1.15209i
$248$	−62.0331	+	35.8148i	−0.250134	+	0.144415i
$249$	−3.66885	−	5.64135i	−0.0147344	−	0.0226560i
$250$	−445.151			−1.78060
$251$	98.5267	+	56.8844i	0.392537	+	0.226631i	0.683259	−	0.730176i	$-0.260562\pi$
$251$	98.5267	+	56.8844i	0.392537	+	0.226631i	−0.290722	+	0.956808i	$0.593895\pi$
$252$	68.5560	−	154.530i	0.272048	−	0.613215i
$253$	58.7408	−	101.742i	0.232177	−	0.402142i
$254$	542.951	−	313.473i	2.13760	−	1.23414i
$255$	−173.615	−	88.3166i	−0.680845	−	0.346340i
$256$	−309.213			−1.20786
$257$	−87.1830	−	50.3351i	−0.339233	−	0.195857i	0.320700	−	0.947181i	$-0.396082\pi$
$257$	−87.1830	−	50.3351i	−0.339233	−	0.195857i	−0.659933	+	0.751324i	$0.729415\pi$
$258$	−33.4719	+	1.77643i	−0.129736	+	0.00688539i
$259$	94.6219	−	163.890i	0.365335	−	0.632780i
$260$	−268.707	+	225.649i	−1.03349	+	0.867881i
$261$	180.199	−	131.288i	0.690419	−	0.503018i
$262$	393.843	+	682.156i	1.50322	+	2.60365i
$263$		−	57.0781i		−	0.217027i	−0.994095	−	0.108513i	$-0.965391\pi$
$263$		−	57.0781i		−	0.217027i	0.994095	−	0.108513i	$-0.0346091\pi$
$264$	−250.074	−	127.211i	−0.947251	−	0.481858i
$265$	72.6418	+	125.819i	0.274120	+	0.474790i
$266$			213.441i			0.802409i
$267$	231.248	−	12.2728i	0.866097	−	0.0459657i
$268$	−184.257	+	319.143i	−0.687528	+	1.19083i
$269$	407.684	+	235.377i	1.51556	+	0.875006i	0.999833	+	0.0182500i	$0.00580947\pi$
$269$	407.684	+	235.377i	1.51556	+	0.875006i	0.515722	+	0.856756i	$0.327524\pi$
$270$	275.860	−	224.297i	1.02170	−	0.830729i
$271$	23.6165	+	40.9050i	0.0871457	+	0.150941i	0.906304	−	0.422627i	$-0.138892\pi$
$271$	23.6165	+	40.9050i	0.0871457	+	0.150941i	−0.819158	+	0.573568i	$0.805559\pi$
$272$	−30.1375	−	17.3999i	−0.110800	−	0.0639702i
$273$	24.6815	+	106.398i	0.0904084	+	0.389735i
$274$	33.9927	+	58.8770i	0.124061	+	0.214880i
$275$	80.5100	+	46.4825i	0.292764	+	0.169027i
$276$	122.067	+	187.695i	0.442273	+	0.680053i
$277$	101.870	+	176.444i	0.367761	+	0.636981i	0.989215	−	0.146470i	$-0.0467911\pi$
$277$	101.870	+	176.444i	0.367761	+	0.636981i	−0.621454	+	0.783451i	$0.713458\pi$
$278$		−	831.099i		−	2.98957i
$279$	−29.5129	+	66.5242i	−0.105781	+	0.238438i
$280$	49.9170	−	86.4588i	0.178275	−	0.308781i
$281$	−37.9875	−	21.9321i	−0.135187	−	0.0780502i	0.430881	−	0.902409i	$-0.358203\pi$
$281$	−37.9875	−	21.9321i	−0.135187	−	0.0780502i	−0.566068	+	0.824358i	$0.691536\pi$
$282$	762.478	−	495.878i	2.70382	−	1.75843i
$283$	−73.6462	+	127.559i	−0.260234	+	0.450739i	−0.966304	−	0.257404i	$-0.917133\pi$
$283$	−73.6462	+	127.559i	−0.260234	+	0.450739i	0.706070	+	0.708142i	$0.250466\pi$
$284$	−512.336	−	295.797i	−1.80400	−	1.04154i
$285$	−127.492	+	250.627i	−0.447339	+	0.879393i
$286$	442.262	−	78.1591i	1.54637	−	0.273284i
$287$		−	27.6152i		−	0.0962201i
$288$	−206.402	+	150.379i	−0.716675	+	0.522148i
$289$	−14.3410	−	24.8393i	−0.0496228	−	0.0859491i
$290$	282.505	−	163.104i	0.974154	−	0.562428i
$291$	15.7351	+	296.484i	0.0540724	+	1.01885i
$292$	−579.901			−1.98596
$293$		−	367.033i		−	1.25267i	−0.779553	−	0.626336i	$-0.784554\pi$
$293$		−	367.033i		−	1.25267i	0.779553	−	0.626336i	$-0.215446\pi$
$294$	220.267	+	338.690i	0.749208	+	1.15201i
$295$	33.9406	+	58.7869i	0.115053	+	0.199278i
$296$	518.375	−	299.284i	1.75127	−	1.01110i
$297$	−281.465	+	45.1535i	−0.947694	+	0.152032i
$298$	−477.907			−1.60371
$299$	−135.951	−	49.4225i	−0.454685	−	0.165293i
$300$	−148.526	+	96.5937i	−0.495086	+	0.321979i
$301$	−4.78138	+	8.28160i	−0.0158850	+	0.0275136i
$302$	−798.354	−	460.930i	−2.64356	−	1.52626i
$303$	124.516	−	244.778i	0.410944	−	0.807847i
$304$	−25.1180	+	43.5057i	−0.0826251	+	0.143111i
$305$	−62.0982	−	35.8524i	−0.203601	−	0.117549i
$306$	−472.481	+	50.2929i	−1.54406	+	0.164356i
$307$	−39.1332			−0.127470			−0.0637348	−	0.997967i	$-0.520301\pi$
$307$	−39.1332			−0.127470			−0.0637348	+	0.997967i	$0.520301\pi$
$308$	−171.749	+	99.1593i	−0.557626	+	0.321946i
$309$	−14.8458	−	279.728i	−0.0480446	−	0.905268i
$310$	−53.2408	+	92.2158i	−0.171745	+	0.297470i
$311$	−245.318	+	141.635i	−0.788805	+	0.455417i	−0.839542	−	0.543295i	$-0.817176\pi$
$311$	−245.318	+	141.635i	−0.788805	+	0.455417i	0.0507366	+	0.998712i	$0.483843\pi$
$312$	−100.658	+	330.477i	−0.322622	+	1.05922i
$313$	−59.1441	+	102.441i	−0.188959	+	0.327286i	−0.944903	−	0.327349i	$-0.893845\pi$
$313$	−59.1441	+	102.441i	−0.188959	+	0.327286i	0.755945	+	0.654636i	$0.227178\pi$
$314$	−377.874	+	218.166i	−1.20342	+	0.694795i
$315$	−10.7363	−	100.863i	−0.0340836	−	0.320201i
$316$	422.246	−	731.352i	1.33622	−	2.31441i
$317$	−373.019	−	215.363i	−1.17672	−	0.679378i	−0.221464	−	0.975169i	$-0.571083\pi$
$317$	−373.019	−	215.363i	−1.17672	−	0.679378i	−0.955253	+	0.295791i	$0.904417\pi$
$318$	315.874	+	160.682i	0.993315	+	0.505290i
$319$	−261.547			−0.819898
$320$	−353.652	+	204.181i	−1.10516	+	0.638066i
$321$	−229.688	+	12.1901i	−0.715539	+	0.0379753i
$322$	101.971			0.316680
$323$	325.443	−	187.894i	1.00756	−	0.581716i
$324$	166.511	−	517.129i	0.513924	−	1.59608i
$325$	39.1088	−	107.580i	0.120335	−	0.331015i
$326$	90.5488	+	52.2784i	0.277757	+	0.160363i
$327$	422.105	+	214.721i	1.29084	+	0.656639i
$328$	43.6727	−	75.6433i	0.133148	−	0.230620i
$329$		−	259.487i		−	0.788713i
$330$	−416.498	+	22.1045i	−1.26211	+	0.0669833i
$331$	−69.8755	−	121.028i	−0.211104	−	0.365643i	0.740956	−	0.671553i	$-0.234373\pi$
$331$	−69.8755	−	121.028i	−0.211104	−	0.365643i	−0.952060	+	0.305910i	$0.901039\pi$
$332$	−13.0294	−	7.52251i	−0.0392451	−	0.0226582i
$333$	246.623	−	555.905i	0.740608	−	1.66938i
$334$	−272.846	+	472.583i	−0.816903	+	1.41492i
$335$			221.109i			0.660028i
$336$	−0.960399	−	18.0961i	−0.00285833	−	0.0538573i
$337$	−58.9960	−	102.184i	−0.175062	−	0.303217i	0.765120	−	0.643887i	$-0.222679\pi$
$337$	−58.9960	−	102.184i	−0.175062	−	0.303217i	−0.940183	+	0.340670i	$0.889346\pi$
$338$	−189.538	−	519.501i	−0.560763	−	1.53698i
$339$	−162.740	+	319.918i	−0.480058	+	0.943712i
$340$	−435.487			−1.28084
$341$	73.9368	−	42.6874i	0.216823	−	0.125183i
$342$	72.6016	+	682.062i	0.212285	+	1.99433i
$343$	252.492			0.736128
$344$	−26.1943	+	15.1233i	−0.0761462	+	0.0439630i
$345$	119.737	+	60.9090i	0.347063	+	0.176548i
$346$	107.743	+	186.616i	0.311396	+	0.539354i
$347$		−	204.549i		−	0.589478i	−0.955578	−	0.294739i	$-0.904767\pi$
$347$		−	204.549i		−	0.589478i	0.955578	−	0.294739i	$-0.0952327\pi$
$348$	226.001	−	444.279i	0.649427	−	1.27666i
$349$	−375.210			−1.07510			−0.537550	−	0.843232i	$-0.680650\pi$
$349$	−375.210			−1.07510			−0.537550	+	0.843232i	$0.680650\pi$
$350$			80.6912i			0.230546i
$351$	115.062	+	331.605i	0.327812	+	0.944743i
$352$	299.580			0.851078
$353$			46.5674i			0.131919i	0.997822	+	0.0659594i	$0.0210108\pi$
$353$			46.5674i			0.131919i	−0.997822	+	0.0659594i	$0.978989\pi$
$354$	147.587	+	75.0761i	0.416912	+	0.212079i
$355$	−354.958			−0.999881
$356$	448.367	−	258.865i	1.25946	−	0.727148i
$357$	−61.4617	+	120.823i	−0.172162	+	0.338440i
$358$	397.336	+	688.206i	1.10988	+	1.92236i
$359$		−	18.4512i		−	0.0513962i	−0.999670	−	0.0256981i	$-0.991819\pi$
$359$		−	18.4512i		−	0.0513962i	0.999670	−	0.0256981i	$-0.00818086\pi$
$360$	130.104	−	293.263i	0.361399	−	0.814620i
$361$	−90.7397	−	157.166i	−0.251357	−	0.435362i
$362$			385.022i			1.06360i
$363$	−25.4830	−	12.9630i	−0.0702012	−	0.0357107i
$364$	157.035	+	187.000i	0.431414	+	0.513736i
$365$	−301.326	+	173.971i	−0.825551	+	0.476632i
$366$	−174.666	+	9.26990i	−0.477229	+	0.0253276i
$367$	128.775			0.350886			0.175443	−	0.984490i	$-0.443864\pi$
$367$	128.775			0.350886			0.175443	+	0.984490i	$0.443864\pi$
$368$	20.7848	+	12.0001i	0.0564804	+	0.0326090i
$369$	−9.39327	−	88.2458i	−0.0254560	−	0.239149i
$370$	444.903	−	770.595i	1.20244	−	2.08269i
$371$	87.5607	−	50.5532i	0.236013	−	0.136262i
$372$	8.62312	+	162.479i	0.0231804	+	0.436771i
$373$	−156.887			−0.420607			−0.210304	−	0.977636i	$-0.567445\pi$
$373$	−156.887			−0.420607			−0.210304	+	0.977636i	$0.567445\pi$
$374$	482.722	+	278.700i	1.29070	+	0.745187i
$375$	−185.044	+	363.764i	−0.493450	+	0.970038i
$376$	410.372	−	710.785i	1.09141	−	1.89038i
$377$	56.0450	+	317.130i	0.148660	+	0.841193i
$378$	−156.094	−	191.978i	−0.412946	−	0.507878i
$379$	−148.248	−	256.773i	−0.391156	−	0.677501i	0.601447	−	0.798913i	$-0.294591\pi$
$379$	−148.248	−	256.773i	−0.391156	−	0.677501i	−0.992602	+	0.121412i	$0.961258\pi$
$380$			628.658i			1.65436i
$381$	−30.4629	−	573.990i	−0.0799552	−	1.50653i
$382$	347.826	+	602.453i	0.910540	+	1.57710i
$383$			207.337i			0.541350i	0.962671	+	0.270675i	$0.0872469\pi$
$383$			207.337i			0.541350i	−0.962671	+	0.270675i	$0.912753\pi$
$384$	−297.263	+	584.369i	−0.774123	+	1.52179i
$385$	−59.4957	+	103.050i	−0.154534	+	0.267661i
$386$	176.476	+	101.888i	0.457191	+	0.263959i
$387$	−12.4622	+	28.0907i	−0.0322021	+	0.0725858i
$388$	331.891	+	574.853i	0.855390	+	1.48158i
$389$	116.285	+	67.1372i	0.298933	+	0.172589i	0.641964	−	0.766735i	$-0.278120\pi$
$389$	116.285	+	67.1372i	0.298933	+	0.172589i	−0.343030	+	0.939324i	$0.611453\pi$
$390$	116.050	+	500.272i	0.297564	+	1.28275i
$391$	−89.7663	−	155.480i	−0.229581	−	0.397646i
$392$	315.728	+	182.286i	0.805428	+	0.465014i
$393$	721.153	−	38.2732i	1.83500	−	0.0973874i
$394$	470.309	+	814.599i	1.19368	+	2.06751i
$395$		−	506.696i		−	1.28278i
$396$	−515.104	+	375.289i	−1.30077	+	0.947700i
$397$	−244.628	+	423.709i	−0.616192	+	1.06728i	0.373982	+	0.927436i	$0.377992\pi$
$397$	−244.628	+	423.709i	−0.616192	+	1.06728i	−0.990174	+	0.139841i	$0.955341\pi$
$398$	604.351	+	348.922i	1.51847	+	0.876688i
$399$	174.417	+	88.7246i	0.437136	+	0.222367i
$400$	−9.49588	+	16.4473i	−0.0237397	+	0.0411183i
$401$	664.384	+	383.583i	1.65682	+	0.956565i	0.974169	+	0.225819i	$0.0725058\pi$
$401$	664.384	+	383.583i	1.65682	+	0.956565i	0.682650	+	0.730746i	$0.260828\pi$
$402$	294.055	+	452.149i	0.731480	+	1.12475i
$403$	−67.6024	−	80.5022i	−0.167748	−	0.199757i
$404$		−	613.986i		−	1.51977i
$405$	−68.6170	−	318.662i	−0.169425	−	0.786820i
$406$	−113.508	−	196.602i	−0.279577	−	0.484241i
$407$	−617.847	+	356.714i	−1.51805	+	0.876448i
$408$	−359.434	+	233.758i	−0.880966	+	0.572937i
$409$	−258.247			−0.631412			−0.315706	−	0.948857i	$-0.602241\pi$
$409$	−258.247			−0.631412			−0.315706	+	0.948857i	$0.602241\pi$
$410$		−	129.844i		−	0.316693i
$411$	62.2429	−	3.30337i	0.151442	−	0.00803740i
$412$	−313.134	−	542.364i	−0.760035	−	1.31642i
$413$	40.9113	−	23.6201i	0.0990587	−	0.0571916i
$414$	325.854	−	34.6853i	0.787087	−	0.0837810i
$415$	−9.02703			−0.0217519
$416$	−64.1946	−	363.244i	−0.154314	−	0.873183i
$417$	−679.150	−	345.477i	−1.62866	−	0.828483i
$418$	402.324	−	696.846i	0.962499	−	1.66710i
$419$	323.004	+	186.486i	0.770892	+	0.445075i	0.833193	−	0.552983i	$-0.186510\pi$
$419$	323.004	+	186.486i	0.770892	+	0.445075i	−0.0623005	+	0.998057i	$0.519844\pi$
$420$	−123.636	−	190.107i	−0.294372	−	0.452635i
$421$	−211.181	+	365.776i	−0.501617	+	0.868826i	0.498381	+	0.866958i	$0.333928\pi$
$421$	−211.181	+	365.776i	−0.501617	+	0.868826i	−0.999998	+	0.00186824i	$0.999405\pi$
$422$	−1006.56	−	581.139i	−2.38522	−	1.37711i
$423$	−88.2641	−	829.204i	−0.208662	−	1.96029i
$424$	319.794			0.754232
$425$	123.034	−	71.0335i	0.289491	−	0.167138i
$426$	−725.857	+	472.061i	−1.70389	+	1.10812i
$427$	−24.9506	+	43.2157i	−0.0584322	+	0.101208i
$428$	−445.342	+	257.118i	−1.04052	+	0.600744i
$429$	119.973	−	393.893i	0.279658	−	0.918166i
$430$	−22.4816	+	38.9393i	−0.0522828	+	0.0905565i
$431$	353.148	−	203.890i	0.819369	−	0.473063i	−0.0308300	−	0.999525i	$-0.509815\pi$
$431$	353.148	−	203.890i	0.819369	−	0.473063i	0.850199	+	0.526462i	$0.176482\pi$
$432$	−9.22437	−	57.5003i	−0.0213527	−	0.133103i
$433$	228.343	−	395.502i	0.527351	−	0.913399i	−0.472141	−	0.881523i	$-0.656519\pi$
$433$	228.343	−	395.502i	0.527351	−	0.913399i	0.999492	−	0.0318757i	$-0.0101481\pi$
$434$	64.1752	+	37.0516i	0.147869	+	0.0853723i
$435$	−15.8503	−	298.655i	−0.0364374	−	0.686563i
$436$	1058.78			2.42840
$437$	−224.447	+	129.584i	−0.513608	+	0.296532i
$438$	−384.820	+	756.490i	−0.878584	+	1.72715i
$439$	413.430			0.941755			0.470877	−	0.882199i	$-0.343937\pi$
$439$	413.430			0.941755			0.470877	+	0.882199i	$0.343937\pi$
$440$	−325.941	+	188.182i	−0.740774	+	0.427686i
$441$	368.329	−	39.2066i	0.835214	−	0.0889038i
$442$	234.489	−	645.028i	0.530517	−	1.45934i
$443$	−469.005	−	270.780i	−1.05870	−	0.611242i	−0.133629	−	0.991031i	$-0.542663\pi$
$443$	−469.005	−	270.780i	−1.05870	−	0.611242i	−0.925073	+	0.379790i	$0.875996\pi$
$444$	−72.0585	−	1357.74i	−0.162294	−	3.05798i
$445$	155.319	−	269.020i	0.349031	−	0.604540i
$446$			87.5646i			0.196333i
$447$	−198.660	+	390.531i	−0.444429	+	0.873672i
$448$	142.095	+	246.115i	0.317176	+	0.549364i
$449$	−462.566	−	267.062i	−1.03021	−	0.594794i	−0.113167	−	0.993576i	$-0.536100\pi$
$449$	−462.566	−	267.062i	−1.03021	−	0.594794i	−0.917046	+	0.398782i	$0.869433\pi$
$450$	27.4470	+	257.853i	0.0609934	+	0.573008i
$451$	−52.0531	+	90.1587i	−0.115417	+	0.199908i
$452$			802.464i			1.77536i
$453$	−708.524	+	460.788i	−1.56407	+	1.01719i
$454$	−498.658	−	863.700i	−1.09836	−	1.90242i
$455$	137.698	+	50.0576i	0.302633	+	0.110017i
$456$	337.448	+	518.871i	0.740017	+	1.13787i
$457$	−647.581			−1.41703			−0.708513	−	0.705697i	$-0.750634\pi$
$457$	−647.581			−1.41703			−0.708513	+	0.705697i	$0.750634\pi$
$458$	25.5932	−	14.7762i	0.0558803	−	0.0322625i
$459$	−155.306	+	407.003i	−0.338358	+	0.886718i
$460$	300.340			0.652914
$461$	−217.137	+	125.364i	−0.471013	+	0.271940i	−0.716664	−	0.697419i	$-0.754332\pi$
$461$	−217.137	+	125.364i	−0.471013	+	0.271940i	0.245651	+	0.969358i	$0.420998\pi$
$462$	15.3830	+	289.851i	0.0332966	+	0.627383i
$463$	16.3357	+	28.2943i	0.0352823	+	0.0611108i	0.883127	−	0.469133i	$-0.155434\pi$
$463$	16.3357	+	28.2943i	0.0352823	+	0.0611108i	−0.847845	+	0.530244i	$0.822100\pi$
$464$		−	53.4313i		−	0.115154i
$465$	53.2245	+	81.8397i	0.114461	+	0.175999i
$466$	342.491			0.734960
$467$			102.067i			0.218560i	0.994011	+	0.109280i	$0.0348545\pi$
$467$			102.067i			0.218560i	−0.994011	+	0.109280i	$0.965146\pi$
$468$	565.421	+	544.153i	1.20816	+	1.16272i
$469$	153.875			0.328093
$470$		−	1220.08i		−	2.59592i
$471$	21.2011	+	399.476i	0.0450129	+	0.848144i
$472$	149.419			0.316565
$473$	31.2208	−	18.0253i	0.0660058	−	0.0381085i
$474$	−673.860	−	1036.15i	−1.42164	−	2.18597i
$475$	−102.542	−	177.608i	−0.215878	−	0.373912i
$476$			303.066i			0.636693i
$477$	262.610	−	191.329i	0.550544	−	0.401110i
$478$	−185.016	−	320.457i	−0.387063	−	0.670413i
$479$		−	568.796i		−	1.18746i	−0.804663	−	0.593732i	$-0.797654\pi$
$479$		−	568.796i		−	1.18746i	0.804663	−	0.593732i	$-0.202346\pi$
$480$	18.1551	+	342.083i	0.0378232	+	0.712673i
$481$	564.915	+	672.711i	1.17446	+	1.39857i
$482$	−471.937	+	272.473i	−0.979122	+	0.565297i
$483$	42.3880	−	83.3277i	0.0877599	−	0.172521i
$484$	−63.9201			−0.132066
$485$	344.912	+	199.135i	0.711159	+	0.410588i
$486$	−564.107	−	560.381i	−1.16071	−	1.15305i
$487$	−175.779	+	304.458i	−0.360942	+	0.625171i	−0.988116	−	0.153709i	$-0.950878\pi$
$487$	−175.779	+	304.458i	−0.360942	+	0.625171i	0.627174	+	0.778879i	$0.284212\pi$
$488$	−136.689	+	78.9174i	−0.280100	+	0.161716i
$489$	80.3603	−	52.2623i	0.164336	−	0.106876i
$490$	541.956			1.10603
$491$	−576.678	−	332.945i	−1.17450	−	0.678096i	−0.219761	−	0.975554i	$-0.570528\pi$
$491$	−576.678	−	332.945i	−1.17450	−	0.678096i	−0.954735	+	0.297458i	$0.903861\pi$
$492$	−108.170	−	166.326i	−0.219858	−	0.338060i
$493$	−199.845	+	346.142i	−0.405366	+	0.702114i
$494$	−931.146	−	338.502i	−1.88491	−	0.685227i
$495$	−155.070	+	349.538i	−0.313272	+	0.706137i
$496$	8.72058	+	15.1045i	0.0175818	+	0.0304526i
$497$			247.024i			0.497030i
$498$	−18.4595	+	12.0051i	−0.0370672	+	0.0241067i
$499$	284.011	+	491.922i	0.569161	+	0.985816i	0.996649	+	0.0817951i	$0.0260653\pi$
$499$	284.011	+	491.922i	0.569161	+	0.985816i	−0.427488	+	0.904021i	$0.640601\pi$
$500$			912.445i			1.82489i
$501$	272.762	+	419.408i	0.544435	+	0.837142i
$502$	186.136	−	322.396i	0.370788	−	0.642224i
$503$	424.010	+	244.802i	0.842961	+	0.486684i	0.858270	−	0.513199i	$-0.171540\pi$
$503$	424.010	+	244.802i	0.842961	+	0.486684i	−0.0153084	+	0.999883i	$0.504873\pi$
$504$	−204.089	−	90.5424i	−0.404939	−	0.179648i
$505$	−184.196	−	319.037i	−0.364745	−	0.631756i
$506$	−332.917	−	192.210i	−0.657939	−	0.379862i
$507$	−503.309	−	61.0651i	−0.992720	−	0.120444i
$508$	−642.538	−	1112.91i	−1.26484	−	2.19077i
$509$	596.533	+	344.408i	1.17197	+	0.676637i	0.954143	−	0.299350i	$-0.0967698\pi$
$509$	596.533	+	344.408i	1.17197	+	0.676637i	0.217827	+	0.975987i	$0.430103\pi$
$510$	−288.987	+	568.099i	−0.566641	+	1.11392i
$511$	121.070	+	209.700i	0.236928	+	0.410372i
$512$			137.624i			0.268797i
$513$	587.540	+	224.196i	1.14530	+	0.437030i
$514$	−164.705	+	285.278i	−0.320438	+	0.555015i
$515$	−325.419	−	187.881i	−0.631882	−	0.364817i
$516$	3.64123	+	68.6088i	0.00705664	+	0.132963i
$517$	−489.119	+	847.178i	−0.946071	+	1.63864i
$518$	−536.276	−	309.619i	−1.03528	−	0.597720i
$519$	197.285	−	10.4704i	0.380125	−	0.0201741i
$520$	298.016	+	354.883i	0.573108	+	0.682468i
$521$			248.194i			0.476379i	0.971219	+	0.238190i	$0.0765540\pi$
$521$			248.194i			0.476379i	−0.971219	+	0.238190i	$0.923446\pi$
$522$	−429.596	−	589.643i	−0.822981	−	1.12958i
$523$	241.642	+	418.536i	0.462031	+	0.800261i	0.999062	−	0.0433015i	$-0.0137876\pi$
$523$	241.642	+	418.536i	0.462031	+	0.800261i	−0.537031	+	0.843562i	$0.680454\pi$
$524$	1398.24	−	807.277i	2.66841	−	1.54060i
$525$	65.9385	+	33.5423i	0.125597	+	0.0638901i
$526$	−186.769			−0.355075
$527$		−	130.468i		−	0.247567i
$528$	−30.9746	+	60.8908i	−0.0586640	+	0.115323i
$529$	−202.591	−	350.898i	−0.382970	−	0.663324i
$530$	411.702	−	237.696i	0.776797	−	0.448484i
$531$	122.700	−	89.3953i	0.231073	−	0.168353i
$532$	437.498			0.822365
$533$	120.473	+	43.7957i	0.226028	+	0.0821683i
$534$	−40.1589	−	756.683i	−0.0752039	−	1.41701i
$535$	−154.271	+	267.206i	−0.288358	+	0.499450i
$536$	421.495	+	243.350i	0.786371	+	0.454011i
$537$	727.549	−	38.6127i	1.35484	−	0.0719045i
$538$	770.193	−	1334.01i	1.43159	−	2.47958i
$539$	−376.313	−	217.265i	−0.698170	−	0.403088i
$540$	−459.751	−	565.443i	−0.851390	−	1.04712i
$541$	−64.9904			−0.120130			−0.0600650	−	0.998194i	$-0.519131\pi$
$541$	−64.9904			−0.120130			−0.0600650	+	0.998194i	$0.519131\pi$
$542$	133.848	−	77.2772i	0.246952	−	0.142578i
$543$	314.629	+	160.049i	0.579426	+	0.294749i
$544$	228.905	−	396.475i	0.420782	−	0.728815i
$545$	550.161	−	317.636i	1.00947	−	0.582817i
$546$	348.152	−	80.7621i	0.637641	−	0.147916i
$547$	219.952	−	380.968i	0.402106	−	0.696467i	−0.591874	−	0.806030i	$-0.701612\pi$
$547$	219.952	−	380.968i	0.402106	−	0.696467i	0.993980	+	0.109563i	$0.0349452\pi$
$548$	120.683	−	69.6762i	0.220224	−	0.127146i
$549$	−65.0312	+	146.585i	−0.118454	+	0.267004i
$550$	152.099	−	263.443i	0.276543	−	0.478987i
$551$	499.682	+	288.492i	0.906864	+	0.523578i
$552$	247.890	−	161.215i	0.449076	−	0.292056i
$553$	−352.622			−0.637654
$554$	577.354	−	333.336i	1.04216	−	0.601689i
$555$	−444.767	−	683.888i	−0.801381	−	1.23223i
$556$	−1703.54			−3.06392
$557$	−365.644	+	211.105i	−0.656452	+	0.379003i	−0.790924	−	0.611915i	$-0.790400\pi$
$557$	−365.644	+	211.105i	−0.656452	+	0.379003i	0.134472	+	0.990917i	$0.457066\pi$
$558$	217.679	+	96.5713i	0.390105	+	0.173067i
$559$	−28.5460	−	33.9931i	−0.0510662	−	0.0608105i
$560$	−21.0519	−	12.1543i	−0.0375927	−	0.0217042i
$561$	428.407	−	278.614i	0.763649	−	0.496639i
$562$	−71.7657	+	124.302i	−0.127697	+	0.221178i
$563$		−	762.156i		−	1.35374i	−0.736103	−	0.676870i	$-0.763336\pi$
$563$		−	762.156i		−	1.35374i	0.736103	−	0.676870i	$-0.236664\pi$
$564$	−1016.42	−	1562.88i	−1.80217	−	2.77107i
$565$	240.740	+	416.973i	0.426088	+	0.738006i
$566$	417.395	+	240.983i	0.737447	+	0.425765i
$567$	−221.765	+	47.7523i	−0.391120	+	0.0842192i
$568$	−390.662	+	676.646i	−0.687785	+	1.19128i
$569$		−	264.660i		−	0.465131i	−0.972581	−	0.232566i	$-0.925288\pi$
$569$		−	264.660i		−	0.465131i	0.972581	−	0.232566i	$-0.0747121\pi$
$570$	820.094	+	417.175i	1.43876	+	0.731885i
$571$	200.357	+	347.029i	0.350889	+	0.607757i	0.986405	−	0.164330i	$-0.0525462\pi$
$571$	200.357	+	347.029i	0.350889	+	0.607757i	−0.635517	+	0.772087i	$0.719213\pi$
$572$	−160.206	−	906.524i	−0.280080	−	1.58483i
$573$	636.893	−	33.8014i	1.11151	−	0.0589902i
$574$	−90.3616			−0.157424
$575$	−84.8521	+	48.9894i	−0.147569	+	0.0851989i
$576$	537.788	+	738.142i	0.933659	+	1.28150i
$577$	−1041.61			−1.80522			−0.902610	−	0.430460i	$-0.858351\pi$
$577$	−1041.61			−1.80522			−0.902610	+	0.430460i	$0.858351\pi$
$578$	−81.2784	+	46.9261i	−0.140620	+	0.0811871i
$579$	156.619	−	101.857i	0.270499	−	0.175919i
$580$	−334.322	−	579.062i	−0.576416	−	0.998383i
$581$			6.28213i			0.0108126i
$582$	970.146	−	51.4879i	1.66692	−	0.0884671i
$583$	−381.160			−0.653791
$584$			765.879i			1.31144i
$585$	457.048	+	113.124i	0.781279	+	0.193375i
$586$	−1200.99			−2.04948
$587$		−	19.6411i		−	0.0334602i	−0.999860	−	0.0167301i	$-0.994674\pi$
$587$		−	19.6411i		−	0.0334602i	0.999860	−	0.0167301i	$-0.00532560\pi$
$588$	694.227	−	451.491i	1.18066	−	0.767841i
$589$	−188.340			−0.319762
$590$	192.361	−	111.060i	0.326035	−	0.188237i
$591$	861.168	−	45.7041i	1.45714	−	0.0773336i
$592$	−72.8729	−	126.220i	−0.123096	−	0.213209i
$593$			221.793i			0.374019i	0.982358	+	0.187010i	$0.0598795\pi$
$593$			221.793i			0.374019i	−0.982358	+	0.187010i	$0.940120\pi$
$594$	147.750	+	921.002i	0.248737	+	1.55051i
$595$	90.9199	+	157.478i	0.152807	+	0.264669i
$596$			979.586i			1.64360i
$597$	536.349	−	348.815i	0.898408	−	0.584280i
$598$	−161.719	+	444.854i	−0.270433	+	0.743903i
$599$	−2.12724	+	1.22816i	−0.00355132	+	0.00205035i	−0.501775	−	0.864998i	$-0.667319\pi$
$599$	−2.12724	+	1.22816i	−0.00355132	+	0.00205035i	0.498223	+	0.867049i	$0.333986\pi$
$600$	127.572	+	196.159i	0.212620	+	0.326932i
$601$	−513.483			−0.854382			−0.427191	−	0.904161i	$-0.640497\pi$
$601$	−513.483			−0.854382			−0.427191	+	0.904161i	$0.640497\pi$
$602$	27.0988	+	15.6455i	0.0450147	+	0.0259892i
$603$	491.717	−	52.3405i	0.815452	−	0.0868002i
$604$	−944.787	+	1636.42i	−1.56422	+	2.70930i
$605$	−33.2139	+	19.1761i	−0.0548991	+	0.0316960i
$606$	−800.954	−	407.438i	−1.32171	−	0.672340i
$607$	10.2166			0.0168313			0.00841565	−	0.999965i	$-0.497321\pi$
$607$	10.2166			0.0168313			0.00841565	+	0.999965i	$0.497321\pi$
$608$	−572.342	−	330.442i	−0.941352	−	0.543490i
$609$	−207.841	+	11.0306i	−0.341283	+	0.0181127i
$610$	−117.315	+	203.196i	−0.192320	+	0.333108i
$611$	1132.02	+	411.528i	1.85274	+	0.673531i
$612$	103.088	+	968.464i	0.168444	+	1.58246i
$613$	−178.452	−	309.088i	−0.291113	−	0.504222i	0.682960	−	0.730456i	$-0.260692\pi$
$613$	−178.452	−	309.088i	−0.291113	−	0.504222i	−0.974073	+	0.226233i	$0.927359\pi$
$614$			128.050i			0.208551i
$615$	−106.105	−	53.9745i	−0.172528	−	0.0877634i
$616$	130.960	+	226.830i	0.212598	+	0.368231i
$617$			627.168i			1.01648i	0.861215	+	0.508240i	$0.169704\pi$
$617$			627.168i			1.01648i	−0.861215	+	0.508240i	$0.830296\pi$
$618$	−915.318	+	48.5780i	−1.48110	+	0.0786051i
$619$	438.414	−	759.355i	0.708261	−	1.22674i	−0.257241	−	0.966347i	$-0.582813\pi$
$619$	438.414	−	759.355i	0.708261	−	1.22674i	0.965502	−	0.260397i	$-0.0838533\pi$
$620$	189.019	+	109.130i	0.304869	+	0.176016i
$621$	107.110	−	280.697i	0.172479	−	0.452007i
$622$	463.453	+	802.724i	0.745101	+	1.29055i
$623$	−187.218	−	108.090i	−0.300510	−	0.173500i
$624$	80.4682	+	24.5093i	0.128955	+	0.0392777i
$625$	163.669	+	283.482i	0.261870	+	0.453572i
$626$	335.203	+	193.530i	0.535469	+	0.309153i
$627$	−402.201	−	618.438i	−0.641469	−	0.986344i
$628$	447.183	+	774.544i	0.712075	+	1.23335i
$629$			1090.25i			1.73330i
$630$	−330.042	+	35.1311i	−0.523876	+	0.0557636i
$631$	182.381	−	315.894i	0.289035	−	0.500624i	−0.684544	−	0.728971i	$-0.739999\pi$
$631$	182.381	−	315.894i	0.289035	−	0.500624i	0.973580	+	0.228347i	$0.0733322\pi$
$632$	−965.902	−	557.664i	−1.52833	−	0.882379i
$633$	−893.305	+	580.961i	−1.41122	+	0.917790i
$634$	−704.704	+	1220.58i	−1.11152	+	1.92521i
$635$	−667.746	−	385.524i	−1.05157	−	0.607124i
$636$	329.357	−	647.460i	0.517857	−	1.01802i
$637$	−182.799	+	502.841i	−0.286969	+	0.789389i
$638$			855.828i			1.34142i
$639$	84.0248	+	789.378i	0.131494	+	1.23533i
$640$	439.740	+	761.652i	0.687093	+	1.19008i
$641$	309.205	−	178.519i	0.482379	−	0.278501i	−0.239029	−	0.971013i	$-0.576829\pi$
$641$	309.205	−	178.519i	0.482379	−	0.278501i	0.721407	+	0.692511i	$0.243496\pi$
$642$	39.8880	+	751.578i	0.0621308	+	1.17068i
$643$	−184.996			−0.287708			−0.143854	−	0.989599i	$-0.545950\pi$
$643$	−184.996			−0.287708			−0.143854	+	0.989599i	$0.545950\pi$
$644$		−	209.014i		−	0.324556i
$645$	22.4747	+	34.5579i	0.0348445	+	0.0535781i
$646$	−614.823	−	1064.90i	−0.951738	−	1.64846i
$647$	714.972	−	412.789i	1.10506	−	0.638005i	0.167512	−	0.985870i	$-0.446427\pi$
$647$	714.972	−	412.789i	1.10506	−	0.638005i	0.937545	+	0.347865i	$0.113093\pi$
$648$	−682.976	−	219.913i	−1.05398	−	0.339371i
$649$	−178.091			−0.274408
$650$	−352.020	−	127.971i	−0.541569	−	0.196878i
$651$	56.9543	−	37.0402i	0.0874874	−	0.0568974i
$652$	107.157	−	185.602i	0.164352	−	0.284665i
$653$	−307.955	−	177.798i	−0.471601	−	0.272279i	0.245309	−	0.969445i	$-0.421111\pi$
$653$	−307.955	−	177.798i	−0.471601	−	0.272279i	−0.716910	+	0.697166i	$0.754444\pi$
$654$	702.604	−	1381.20i	1.07432	−	2.11193i
$655$	484.367	−	838.948i	0.739492	−	1.28084i
$656$	−18.4184	−	10.6339i	−0.0280769	−	0.0162102i
$657$	458.217	+	628.927i	0.697438	+	0.957270i
$658$	−849.085			−1.29040
$659$	−176.256	+	101.761i	−0.267459	+	0.154418i	−0.627732	−	0.778429i	$-0.716017\pi$
$659$	−176.256	+	101.761i	−0.267459	+	0.154418i	0.360273	+	0.932847i	$0.382683\pi$
$660$	45.3085	+	853.713i	0.0686492	+	1.29350i
$661$	178.791	−	309.676i	0.270486	−	0.468496i	−0.698500	−	0.715610i	$-0.746149\pi$
$661$	178.791	−	309.676i	0.270486	−	0.468496i	0.968986	+	0.247114i	$0.0794822\pi$
$662$	−396.024	+	228.645i	−0.598224	+	0.345385i
$663$	−429.624	−	459.747i	−0.648000	−	0.693434i
$664$	−9.93503	+	17.2080i	−0.0149624	+	0.0259156i
$665$	227.331	−	131.250i	0.341852	−	0.197368i
$666$	−1819.02	−	806.991i	−2.73126	−	1.21170i
$667$	137.827	−	238.723i	0.206636	−	0.357905i
$668$	968.672	+	559.263i	1.45011	+	0.837221i
$669$	71.5551	+	36.3995i	0.106958	+	0.0544088i
$670$	723.508			1.07986
$671$	162.918	−	94.0610i	0.242799	−	0.140180i
$672$	238.064	−	12.6346i	0.354262	−	0.0188015i
$673$	1113.09			1.65393			0.826965	−	0.562254i	$-0.190066\pi$
$673$	1113.09			1.65393			0.826965	+	0.562254i	$0.190066\pi$
$674$	−334.364	+	193.045i	−0.496089	+	0.286417i
$675$	222.120	+	84.7575i	0.329066	+	0.125567i
$676$	−1064.84	+	388.504i	−1.57521	+	0.574710i
$677$	702.163	+	405.394i	1.03717	+	0.598809i	0.919030	−	0.394188i	$-0.128974\pi$
$677$	702.163	+	405.394i	1.03717	+	0.598809i	0.118138	+	0.992997i	$0.462307\pi$
$678$	1046.83	+	532.512i	1.54399	+	0.785415i
$679$	138.583	−	240.033i	0.204099	−	0.353509i
$680$			575.150i			0.845809i
$681$	−913.076	+	48.4590i	−1.34079	+	0.0711586i
$682$	−139.681	−	241.934i	−0.204810	−	0.354742i
$683$	−710.444	−	410.175i	−1.04018	−	0.600549i	−0.120297	−	0.992738i	$-0.538385\pi$
$683$	−710.444	−	410.175i	−1.04018	−	0.600549i	−0.919885	+	0.392189i	$0.871718\pi$
$684$	1398.05	−	148.815i	2.04393	−	0.217565i
$685$	41.8058	−	72.4097i	0.0610303	−	0.105708i
$686$		−	826.197i		−	1.20437i
$687$	−1.43594	−	27.0563i	−0.00209016	−	0.0393832i
$688$	3.68238	+	6.37807i	0.00535229	+	0.00927044i
$689$	81.6759	+	462.162i	0.118543	+	0.670772i
$690$	199.305	−	391.799i	0.288847	−	0.567825i
$691$	−737.645			−1.06750			−0.533752	−	0.845641i	$-0.679218\pi$
$691$	−737.645			−1.06750			−0.533752	+	0.845641i	$0.679218\pi$
$692$	382.516	−	220.845i	0.552768	−	0.319141i
$693$	243.252	+	107.917i	0.351013	+	0.155724i
$694$	−669.319			−0.964437
$695$	−885.187	+	511.063i	−1.27365	+	0.735342i
$696$	−586.762	−	298.481i	−0.843049	−	0.428852i
$697$	79.5464	+	137.778i	0.114127	+	0.197673i
$698$			1227.75i			1.75895i
$699$	142.369	−	279.874i	0.203676	−	0.400391i
$700$	165.396			0.236280
$701$		−	1169.94i		−	1.66896i	−0.551039	−	0.834480i	$-0.685768\pi$
$701$		−	1169.94i		−	1.66896i	0.551039	−	0.834480i	$-0.314232\pi$
$702$	1085.07	−	376.503i	1.54568	−	0.536329i
$703$	1573.85			2.23876
$704$		−	1071.36i		−	1.52182i
$705$	−997.015	−	507.172i	−1.41421	−	0.719394i
$706$	152.376			0.215831
$707$	−222.026	+	128.187i	−0.314039	+	0.181311i
$708$	153.887	−	302.515i	0.217354	−	0.427281i
$709$	526.762	+	912.378i	0.742964	+	1.28685i	0.951140	+	0.308760i	$0.0999141\pi$
$709$	526.762	+	912.378i	0.742964	+	1.28685i	−0.208176	+	0.978091i	$0.566753\pi$
$710$			1161.48i			1.63589i
$711$	−1126.83	+	119.944i	−1.58485	+	0.168698i
$712$	−341.884	−	592.161i	−0.480174	−	0.831686i
$713$			89.9792i			0.126198i
$714$	395.354	+	201.113i	0.553717	+	0.281671i
$715$	−355.203	−	422.982i	−0.496788	−	0.591584i
$716$	1410.65	−	814.437i	1.97018	−	1.13748i
$717$	−338.777	+	17.9797i	−0.472492	+	0.0250762i
$718$	−60.3756			−0.0840886
$719$	−895.444	−	516.985i	−1.24540	−	0.719033i	−0.275213	−	0.961383i	$-0.588748\pi$
$719$	−895.444	−	516.985i	−1.24540	−	0.719033i	−0.970189	+	0.242350i	$0.922082\pi$
$720$	−71.4069	−	31.6791i	−0.0991762	−	0.0439987i
$721$	−130.751	+	226.467i	−0.181347	+	0.314102i
$722$	−514.274	+	296.916i	−0.712290	+	0.411241i
$723$	26.4786	+	498.916i	0.0366233	+	0.690064i
$724$	789.196			1.09005
$725$	188.905	+	109.064i	0.260558	+	0.150433i
$726$	−42.4171	+	83.3848i	−0.0584258	+	0.114855i
$727$	334.678	−	579.679i	0.460355	−	0.797358i	−0.538624	−	0.842546i	$-0.681056\pi$
$727$	334.678	−	579.679i	0.460355	−	0.797358i	0.998978	+	0.0451886i	$0.0143889\pi$
$728$	246.972	−	207.397i	0.339247	−	0.284886i
$729$	−692.419	+	228.028i	−0.949820	+	0.312796i
$730$	569.262	+	985.990i	0.779811	+	1.35067i
$731$		−	55.0917i		−	0.0753649i
$732$	19.0009	+	358.020i	0.0259575	+	0.489098i
$733$	−409.264	−	708.867i	−0.558342	−	0.967076i	−0.997635	−	0.0687324i	$-0.978105\pi$
$733$	−409.264	−	708.867i	−0.558342	−	0.967076i	0.439294	−	0.898344i	$-0.355229\pi$
$734$		−	421.374i		−	0.574079i
$735$	225.284	−	442.870i	0.306509	−	0.602545i
$736$	−157.868	+	273.436i	−0.214495	+	0.371516i
$737$	−502.376	−	290.047i	−0.681650	−	0.393551i
$738$	−288.756	+	30.7364i	−0.391268	+	0.0416482i
$739$	−616.781	−	1068.30i	−0.834616	−	1.44560i	−0.894343	−	0.447383i	$-0.852356\pi$
$739$	−616.781	−	1068.30i	−0.834616	−	1.44560i	0.0597263	−	0.998215i	$-0.480977\pi$
$740$	−1579.52	−	911.937i	−2.13449	−	1.23235i
$741$	−663.679	+	620.194i	−0.895654	+	0.836969i
$742$	−165.419	−	286.514i	−0.222936	−	0.386137i
$743$	179.341	+	103.542i	0.241374	+	0.139357i	0.615808	−	0.787896i	$-0.288830\pi$
$743$	179.341	+	103.542i	0.241374	+	0.139357i	−0.374434	+	0.927253i	$0.622163\pi$
$744$	214.587	−	11.3886i	0.288423	−	0.0153073i
$745$	293.876	+	509.009i	0.394465	+	0.683233i
$746$			513.360i			0.688150i
$747$	2.13686	+	20.0749i	0.00286059	+	0.0268740i
$748$	571.263	−	989.456i	0.763721	−	1.32280i
$749$	185.955	+	107.361i	0.248271	+	0.143339i
$750$	1190.30	+	605.494i	1.58707	+	0.807326i
$751$	−454.666	+	787.504i	−0.605414	+	1.04861i	0.386572	+	0.922259i	$0.373659\pi$
$751$	−454.666	+	787.504i	−0.605414	+	1.04861i	−0.991986	+	0.126348i	$0.959674\pi$
$752$	−173.069	−	99.9217i	−0.230146	−	0.132875i
$753$	−186.079	−	286.121i	−0.247116	−	0.379974i
$754$	1037.70	−	183.389i	1.37626	−	0.243221i
$755$			1133.75i			1.50165i
$756$	−393.505	+	319.952i	−0.520510	+	0.423217i
$757$	143.376	+	248.334i	0.189400	+	0.328050i	0.945050	−	0.326925i	$-0.106012\pi$
$757$	143.376	+	248.334i	0.189400	+	0.328050i	−0.755650	+	0.654975i	$0.772679\pi$
$758$	−840.205	+	485.093i	−1.10845	+	0.639964i
$759$	−295.458	+	192.151i	−0.389272	+	0.253163i
$760$	830.273			1.09246
$761$		−	66.0246i		−	0.0867604i	−0.999059	−	0.0433802i	$-0.986187\pi$
$761$		−	66.0246i		−	0.0867604i	0.999059	−	0.0433802i	$-0.0138127\pi$
$762$	−1878.19	+	99.6799i	−2.46482	+	0.130814i
$763$	−221.050	−	382.870i	−0.289712	−	0.501796i
$764$	1234.87	−	712.954i	1.61633	−	0.933186i
$765$	344.106	+	472.303i	0.449811	+	0.617390i
$766$	678.443			0.885696
$767$	38.1617	+	215.937i	0.0497545	+	0.281535i
$768$	826.812	+	420.592i	1.07658	+	0.547646i
$769$	496.903	−	860.661i	0.646168	−	1.11920i	−0.337863	−	0.941195i	$-0.609704\pi$
$769$	496.903	−	860.661i	0.646168	−	1.11920i	0.984031	−	0.178000i	$-0.0569626\pi$
$770$

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.27217i q^{2} +(-2.67392 - 1.36020i) q^{3} -6.70711 q^{4} +(-3.48512 + 2.01214i) q^{5} +(-4.45081 + 8.74953i) q^{6} +(1.40029 + 2.42538i) q^{7} +8.85812i q^{8} +(5.29971 + 7.27414i) q^{9} +(6.58406 + 11.4039i) q^{10} -10.5579i q^{11} +(17.9343 + 9.12301i) q^{12} +(-12.8016 + 2.26238i) q^{13} +(7.93627 - 4.58201i) q^{14} +(12.0559 - 0.639831i) q^{15} +2.15687 q^{16} +(-13.9728 - 8.06719i) q^{17} +(23.8022 - 17.3416i) q^{18} +(-11.6456 + 20.1708i) q^{19} +(23.3751 - 13.4956i) q^{20} +(-0.445274 - 8.38996i) q^{21} -34.5473 q^{22} +(9.63655 + 5.56367i) q^{23} +(12.0488 - 23.6859i) q^{24} +(-4.40262 + 7.62555i) q^{25} +(7.40288 + 41.8891i) q^{26} +(-4.27674 - 26.6591i) q^{27} +(-9.39193 - 16.2673i) q^{28} -24.7726i q^{29} +(-2.09364 - 39.4488i) q^{30} +(4.04316 + 7.00296i) q^{31} +28.3748i q^{32} +(-14.3609 + 28.2311i) q^{33} +(-26.3972 + 45.7213i) q^{34} +(-9.76040 - 5.63517i) q^{35} +(-35.5457 - 48.7884i) q^{36} +(-33.7864 - 58.5198i) q^{37} +(66.0022 + 38.1064i) q^{38} +(37.3078 + 11.3634i) q^{39} +(-17.8238 - 30.8716i) q^{40} +(-8.53943 - 4.93024i) q^{41} +(-27.4534 + 1.45701i) q^{42} +(1.70728 + 2.95709i) q^{43} +70.8132i q^{44} +(-33.1067 - 14.6875i) q^{45} +(18.2053 - 31.5325i) q^{46} +(-80.2410 - 46.3271i) q^{47} +(-5.76730 - 2.93378i) q^{48} +(20.5783 - 35.6427i) q^{49} +(24.9521 + 14.4061i) q^{50} +(26.3891 + 40.5768i) q^{51} +(85.8619 - 15.1740i) q^{52} -36.1018i q^{53} +(-87.2333 + 13.9942i) q^{54} +(21.2440 + 36.7957i) q^{55} +(-21.4843 + 12.4040i) q^{56} +(58.5757 - 38.0947i) q^{57} -81.0602 q^{58} -16.8680i q^{59} +(-80.8599 + 4.29142i) q^{60} +(8.90904 + 15.4309i) q^{61} +(22.9149 - 13.2299i) q^{62} +(-10.2214 + 23.0398i) q^{63} +101.475 q^{64} +(40.0630 - 33.6433i) q^{65} +(92.3769 + 46.9913i) q^{66} +(27.4720 - 47.5828i) q^{67} +(93.7169 + 54.1075i) q^{68} +(-18.1997 - 27.9844i) q^{69} +(-18.4392 + 31.9377i) q^{70} +(76.3871 + 44.1021i) q^{71} +(-64.4352 + 46.9455i) q^{72} +86.4607 q^{73} +(-191.487 + 110.555i) q^{74} +(22.1445 - 14.4017i) q^{75} +(78.1083 - 135.287i) q^{76} +(25.6070 - 14.7842i) q^{77} +(37.1829 - 122.078i) q^{78} +(-62.9550 + 109.041i) q^{79} +(-7.51696 + 4.33992i) q^{80} +(-24.8261 + 77.1017i) q^{81} +(-16.1326 + 27.9425i) q^{82} +(1.94262 + 1.12157i) q^{83} +(2.98650 + 56.2724i) q^{84} +64.9291 q^{85} +(9.67611 - 5.58651i) q^{86} +(-33.6957 + 66.2400i) q^{87} +93.5234 q^{88} +(-66.8494 + 38.5955i) q^{89} +(-48.0601 + 108.331i) q^{90} +(-23.4132 - 27.8808i) q^{91} +(-64.6334 - 37.3161i) q^{92} +(-1.28567 - 24.2249i) q^{93} +(-151.590 + 262.562i) q^{94} -93.7301i q^{95} +(38.5955 - 75.8721i) q^{96} +(-49.4835 - 85.7080i) q^{97} +(-116.629 - 67.3359i) q^{98} +(76.7998 - 55.9540i) 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

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Database

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