LMFDB - Embedded newform 117.3.u.a.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(68,117)]

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([5, 2]))

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

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

chi := DirichletCharacter("117.68");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.u (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			68.3
Character	$\chi$	$=$	117.68
Dual form			117.3.u.a.74.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.83378 - 1.63609i) q^{2} +(0.158993 - 2.99578i) q^{3} +(3.35355 + 5.80853i) q^{4} +(-3.48512 - 2.01214i) q^{5} +(-5.35191 + 8.22928i) q^{6} -2.80059 q^{7} -8.85812i q^{8} +(-8.94944 - 0.952618i) q^{9} +(6.58406 + 11.4039i) q^{10} +(-9.14343 - 5.27896i) q^{11} +(17.9343 - 9.12301i) q^{12} +(8.36009 + 9.95535i) q^{13} +(7.93627 + 4.58201i) q^{14} +(-6.58204 + 10.1208i) q^{15} +(-1.07844 + 1.86791i) q^{16} +(13.9728 + 8.06719i) q^{17} +(23.8022 + 17.3416i) q^{18} +(-11.6456 + 20.1708i) q^{19} -26.9912i q^{20} +(-0.445274 + 8.38996i) q^{21} +(17.2737 + 29.9189i) q^{22} +11.1273i q^{23} +(-26.5370 - 1.40838i) 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} +(-21.4537 - 12.3863i) q^{29} +(35.2105 - 17.9113i) q^{30} +(4.04316 - 7.00296i) q^{31} +(-24.5733 + 14.1874i) q^{32} +(-17.2684 + 26.5524i) q^{33} +(-26.3972 - 45.7213i) q^{34} +(9.76040 + 5.63517i) q^{35} +(-24.4791 - 55.1777i) q^{36} +(-33.7864 - 58.5198i) q^{37} +(66.0022 - 38.1064i) q^{38} +(31.1533 - 23.4622i) q^{39} +(-17.8238 + 30.8716i) q^{40} -9.86048i q^{41} +(14.9885 - 23.0468i) q^{42} -3.41456 q^{43} -70.8132i q^{44} +(29.2731 + 21.3275i) q^{45} +(18.2053 - 31.5325i) q^{46} +(-80.2410 + 46.3271i) q^{47} +(5.42438 + 3.52774i) q^{48} -41.1567 q^{49} +28.8122i q^{50} +(26.3891 - 40.5768i) q^{51} +(-29.7899 + 81.9456i) q^{52} +36.1018i q^{53} +(55.7360 - 68.5491i) q^{54} +(21.2440 + 36.7957i) q^{55} +24.8080i q^{56} +(58.5757 + 38.0947i) q^{57} +(40.5301 + 70.2002i) q^{58} +(14.6081 - 8.43398i) q^{59} +(-80.8599 - 4.29142i) q^{60} -17.8181 q^{61} +(-22.9149 + 13.2299i) q^{62} +(25.0637 + 2.66789i) q^{63} +101.475 q^{64} +(-9.10442 - 51.5172i) q^{65} +(92.3769 - 46.9913i) q^{66} -54.9439 q^{67} +108.215i q^{68} +(33.3351 + 1.76917i) q^{69} +(-18.4392 - 31.9377i) q^{70} +(-76.3871 - 44.1021i) q^{71} +(-8.43840 + 79.2753i) q^{72} +86.4607 q^{73} +221.110i q^{74} +(-23.5445 + 11.9769i) q^{75} -156.217 q^{76} +(25.6070 + 14.7842i) q^{77} +(-126.668 + 15.5174i) q^{78} +(-62.9550 - 109.041i) q^{79} +(7.51696 - 4.33992i) q^{80} +(79.1850 + 17.0508i) q^{81} +(-16.1326 + 27.9425i) q^{82} +(1.94262 - 1.12157i) q^{83} +(-50.2266 + 25.5498i) q^{84} +(-32.4646 - 56.2303i) q^{85} +(9.67611 + 5.58651i) q^{86} +(-40.5177 + 62.3013i) q^{87} +(-46.7617 + 80.9937i) 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} +(-20.3365 - 13.2259i) q^{93} +303.181 q^{94} +(81.1726 - 46.8650i) q^{95} +(38.5955 + 75.8721i) q^{96} +98.9671 q^{97} +(116.629 + 67.3359i) q^{98} +(76.7998 + 55.9540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.83378	−	1.63609i	−1.41689	−	0.818043i	−0.420867	−	0.907122i	$-0.638274\pi$
$2$	−2.83378	−	1.63609i	−1.41689	−	0.818043i	−0.996025	+	0.0890792i	$0.971608\pi$
$3$	0.158993	−	2.99578i	0.0529977	−	0.998595i
$3$	0.158993	−	2.99578i	0.0529977	−	0.998595i
$4$	3.35355	+	5.80853i	0.838389	+	1.45213i
$5$	−3.48512	−	2.01214i	−0.697024	−	0.402427i	0.109214	−	0.994018i	$-0.465167\pi$
$5$	−3.48512	−	2.01214i	−0.697024	−	0.402427i	−0.806238	+	0.591591i	$0.798500\pi$
$6$	−5.35191	+	8.22928i	−0.891985	+	1.37155i
$7$	−2.80059			−0.400084			−0.200042	−	0.979787i	$-0.564108\pi$
$7$	−2.80059			−0.400084			−0.200042	+	0.979787i	$0.564108\pi$
$8$		−	8.85812i		−	1.10727i
$9$	−8.94944	−	0.952618i	−0.994382	−	0.105846i
$10$	6.58406	+	11.4039i	0.658406	+	1.14039i
$11$	−9.14343	−	5.27896i	−0.831221	−	0.479906i	0.0230495	−	0.999734i	$-0.492662\pi$
$11$	−9.14343	−	5.27896i	−0.831221	−	0.479906i	−0.854271	+	0.519829i	$0.825996\pi$
$12$	17.9343	−	9.12301i	1.49452	−	0.760251i
$13$	8.36009	+	9.95535i	0.643084	+	0.765796i
$13$	8.36009	+	9.95535i	0.643084	+	0.765796i
$14$	7.93627	+	4.58201i	0.566876	+	0.327286i
$15$	−6.58204	+	10.1208i	−0.438802	+	0.674717i
$16$	−1.07844	+	1.86791i	−0.0674022	+	0.116744i
$17$	13.9728	+	8.06719i	0.821928	+	0.474540i	0.851081	−	0.525035i	$-0.175948\pi$
$17$	13.9728	+	8.06719i	0.821928	+	0.474540i	−0.0291528	+	0.999575i	$0.509281\pi$
$18$	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	$0.956659\pi$
$20$		−	26.9912i		−	1.34956i
$21$	−0.445274	+	8.38996i	−0.0212035	+	0.399522i
$22$	17.2737	+	29.9189i	0.785167	+	1.35995i
$23$			11.1273i			0.483797i	0.970302	+	0.241899i	$0.0777701\pi$
$23$			11.1273i			0.483797i	−0.970302	+	0.241899i	$0.922230\pi$
$24$	−26.5370	−	1.40838i	−1.10571	−	0.0586825i
$25$	−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
$29$	−21.4537	−	12.3863i	−0.739783	−	0.427114i	0.0822074	−	0.996615i	$-0.473803\pi$
$29$	−21.4537	−	12.3863i	−0.739783	−	0.427114i	−0.821990	+	0.569501i	$0.807136\pi$
$30$	35.2105	−	17.9113i	1.17368	−	0.597042i
$31$	4.04316	−	7.00296i	0.130425	−	0.225902i	−0.793416	−	0.608680i	$-0.791699\pi$
$31$	4.04316	−	7.00296i	0.130425	−	0.225902i	0.923840	+	0.382778i	$0.125033\pi$
$32$	−24.5733	+	14.1874i	−0.767917	+	0.443357i
$33$	−17.2684	+	26.5524i	−0.523284	+	0.804619i
$34$	−26.3972	−	45.7213i	−0.776389	−	1.34475i
$35$	9.76040	+	5.63517i	0.278869	+	0.161005i
$36$	−24.4791	−	55.1777i	−0.679976	−	1.53271i
$37$	−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
$39$	31.1533	−	23.4622i	0.798802	−	0.601595i
$40$	−17.8238	+	30.8716i	−0.445594	+	0.771791i
$41$		−	9.86048i		−	0.240500i	−0.992744	−	0.120250i	$-0.961630\pi$
$41$		−	9.86048i		−	0.240500i	0.992744	−	0.120250i	$-0.0383696\pi$
$42$	14.9885	−	23.0468i	0.356869	−	0.548734i
$43$	−3.41456			−0.0794083			−0.0397041	−	0.999211i	$-0.512642\pi$
$43$	−3.41456			−0.0794083			−0.0397041	+	0.999211i	$0.512642\pi$
$44$		−	70.8132i		−	1.60939i
$45$	29.2731	+	21.3275i	0.650513	+	0.473944i
$46$	18.2053	−	31.5325i	0.395767	−	0.685488i
$47$	−80.2410	+	46.3271i	−1.70725	+	0.985684i	−0.769326	+	0.638857i	$0.779408\pi$
$47$	−80.2410	+	46.3271i	−1.70725	+	0.985684i	−0.937929	+	0.346827i	$0.887259\pi$
$48$	5.42438	+	3.52774i	0.113008	+	0.0734947i
$49$	−41.1567			−0.839933
$50$			28.8122i			0.576245i
$51$	26.3891	−	40.5768i	0.517434	−	0.795623i
$52$	−29.7899	+	81.9456i	−0.572882	+	1.57588i
$53$			36.1018i			0.681167i	0.940214	+	0.340583i	$0.110625\pi$
$53$			36.1018i			0.681167i	−0.940214	+	0.340583i	$0.889375\pi$
$54$	55.7360	−	68.5491i	1.03215	−	1.26943i
$55$	21.2440	+	36.7957i	0.386254	+	0.669012i
$56$			24.8080i			0.443000i
$57$	58.5757	+	38.0947i	1.02764	+	0.668328i
$58$	40.5301	+	70.2002i	0.698795	+	1.21035i
$59$	14.6081	−	8.43398i	0.247595	−	0.142949i	−0.371068	−	0.928606i	$-0.621008\pi$
$59$	14.6081	−	8.43398i	0.247595	−	0.142949i	0.618662	+	0.785657i	$0.287675\pi$
$60$	−80.8599	−	4.29142i	−1.34766	−	0.0715236i
$61$	−17.8181			−0.292100			−0.146050	−	0.989277i	$-0.546656\pi$
$61$	−17.8181			−0.292100			−0.146050	+	0.989277i	$0.546656\pi$
$62$	−22.9149	+	13.2299i	−0.369595	+	0.213386i
$63$	25.0637	+	2.66789i	0.397837	+	0.0423475i
$64$	101.475			1.58554
$65$	−9.10442	−	51.5172i	−0.140068	−	0.792573i
$66$	92.3769	−	46.9913i	1.39965	−	0.711989i
$67$	−54.9439			−0.820059			−0.410029	−	0.912072i	$-0.634482\pi$
$67$	−54.9439			−0.820059			−0.410029	+	0.912072i	$0.634482\pi$
$68$			108.215i			1.59140i
$69$	33.3351	+	1.76917i	0.483117	+	0.0256401i
$70$	−18.4392	−	31.9377i	−0.263418	−	0.456253i
$71$	−76.3871	−	44.1021i	−1.07587	−	0.621156i	−0.146094	−	0.989271i	$-0.546670\pi$
$71$	−76.3871	−	44.1021i	−1.07587	−	0.621156i	−0.929780	+	0.368115i	$0.880003\pi$
$72$	−8.43840	+	79.2753i	−0.117200	+	1.10105i
$73$	86.4607			1.18439			0.592196	−	0.805794i	$-0.298261\pi$
$73$	86.4607			1.18439			0.592196	+	0.805794i	$0.298261\pi$
$74$			221.110i			2.98797i
$75$	−23.5445	+	11.9769i	−0.313927	+	0.159692i
$76$	−156.217			−2.05548
$77$	25.6070	+	14.7842i	0.332558	+	0.192003i
$78$	−126.668	+	15.5174i	−1.62395	+	0.198941i
$79$	−62.9550	−	109.041i	−0.796899	−	1.38027i	−0.921626	−	0.388079i	$-0.873139\pi$
$79$	−62.9550	−	109.041i	−0.796899	−	1.38027i	0.124727	−	0.992191i	$-0.460195\pi$
$80$	7.51696	−	4.33992i	0.0939620	−	0.0542490i
$81$	79.1850	+	17.0508i	0.977593	+	0.210504i
$82$	−16.1326	+	27.9425i	−0.196739	+	0.340762i
$83$	1.94262	−	1.12157i	0.0234051	−	0.0135129i	−0.488252	−	0.872703i	$-0.662365\pi$
$83$	1.94262	−	1.12157i	0.0234051	−	0.0135129i	0.511657	+	0.859190i	$0.329032\pi$
$84$	−50.2266	+	25.5498i	−0.597935	+	0.304164i
$85$	−32.4646	−	56.2303i	−0.381936	−	0.661533i
$86$	9.67611	+	5.58651i	0.112513	+	0.0649594i
$87$	−40.5177	+	62.3013i	−0.465720	+	0.716107i
$88$	−46.7617	+	80.9937i	−0.531383	+	0.920382i
$89$	66.8494	−	38.5955i	0.751117	−	0.433658i	−0.0749801	−	0.997185i	$-0.523889\pi$
$89$	66.8494	−	38.5955i	0.751117	−	0.433658i	0.826098	+	0.563527i	$0.190556\pi$
$90$	−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
$93$	−20.3365	−	13.2259i	−0.218672	−	0.142214i
$94$	303.181			3.22533
$95$	81.1726	−	46.8650i	0.854449	−	0.493316i
$96$	38.5955	+	75.8721i	0.402036	+	0.790334i
$97$	98.9671			1.02028			0.510140	−	0.860092i	$-0.329594\pi$
$97$	98.9671			1.02028			0.510140	+	0.860092i	$0.329594\pi$
$98$	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
$101$	79.2782	+	45.7713i	0.784932	+	0.453181i	0.838175	−	0.545401i	$-0.183622\pi$
$101$	79.2782	+	45.7713i	0.784932	+	0.453181i	−0.0532431	+	0.998582i	$0.516956\pi$
$102$	−141.168	+	71.8110i	−1.38400	+	0.704029i
$103$	46.6869	−	80.8641i	0.453271	−	0.785089i	−0.545316	−	0.838231i	$-0.683590\pi$
$103$	46.6869	−	80.8641i	0.453271	−	0.785089i	0.998587	+	0.0531421i	$0.0169236\pi$
$104$	88.1857	−	74.0547i	0.847939	−	0.712064i
$105$	18.4336	−	28.3441i	0.175558	−	0.269944i
$106$	59.0657	−	102.305i	0.557224	−	0.965139i
$107$	−66.3985	+	38.3352i	−0.620547	+	0.358273i	−0.777082	−	0.629400i	$-0.783301\pi$
$107$	−66.3985	+	38.3352i	−0.620547	+	0.358273i	0.156535	+	0.987672i	$0.449968\pi$
$108$	−169.193	+	64.5613i	−1.56660	+	0.597790i
$109$	−157.860			−1.44826			−0.724128	−	0.689666i	$-0.757757\pi$
$109$	−157.860			−1.44826			−0.724128	+	0.689666i	$0.757757\pi$
$110$		−	139.028i		−	1.26389i
$111$	−180.684	+	91.9125i	−1.62779	+	0.828041i
$112$	3.02026	−	5.23124i	0.0269666	−	0.0467075i
$113$	103.615	−	59.8219i	0.916943	−	0.529397i	0.0342847	−	0.999412i	$-0.489085\pi$
$113$	103.615	−	59.8219i	0.916943	−	0.529397i	0.882659	+	0.470015i	$0.155751\pi$
$114$	−103.665	−	203.787i	−0.909339	−	1.78760i
$115$	22.3897	−	38.7801i	0.194693	−	0.337218i
$116$		−	166.153i		−	1.43235i
$117$	−65.3345	−	97.0588i	−0.558414	−	0.829562i
$118$	−55.1949			−0.467753
$119$	−39.1320	−	22.5929i	−0.328841	−	0.189856i
$120$	89.6509	+	58.3045i	0.747091	+	0.485871i
$121$	−4.76510	−	8.25340i	−0.0393810	−	0.0682099i
$122$	50.4926	+	29.1519i	0.413874	+	0.238950i
$123$	−29.5399	−	1.56775i	−0.240162	−	0.0127459i
$124$	54.2359			0.437386
$125$			136.041i			1.08833i
$126$	−66.6603	−	48.5666i	−0.529050	−	0.385449i
$127$	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	$0.561296\pi$
$128$	−189.264	−	109.272i	−1.47863	−	0.853687i
$129$	−0.542891	+	10.2293i	−0.00420845	+	0.0792967i
$130$	−58.4867	+	160.884i	−0.449897	+	1.23757i
$131$	−208.472	−	120.361i	−1.59139	−	0.918789i	−0.993069	−	0.117533i	$-0.962502\pi$
$131$	−208.472	−	120.361i	−1.59139	−	0.918789i	−0.598321	−	0.801257i	$-0.704165\pi$
$132$	−212.141	−	11.2588i	−1.60713	−	0.0852939i
$133$	32.6145	−	56.4900i	0.245222	−	0.424737i
$134$	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
$137$			20.7768i			0.151656i	0.997121	+	0.0758278i	$0.0241599\pi$
$137$			20.7768i			0.151656i	−0.997121	+	0.0758278i	$0.975840\pi$
$138$	−91.5699	−	59.5525i	−0.663550	−	0.431540i
$139$	−126.995	−	219.962i	−0.913634	−	1.58246i	−0.808890	−	0.587960i	$-0.799931\pi$
$139$	−126.995	−	219.962i	−0.913634	−	1.58246i	−0.104744	−	0.994499i	$-0.533402\pi$
$140$			75.5914i			0.539938i
$141$	126.028	+	247.750i	0.893818	+	1.75709i
$142$	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
$146$	−245.011	−	141.457i	−1.67816	−	0.968884i
$147$	−6.54363	+	123.297i	−0.0445145	+	0.838752i
$148$	226.609	−	392.499i	1.53114	−	2.65202i
$149$	126.485	−	73.0260i	0.848891	−	0.490107i	−0.0113858	−	0.999935i	$-0.503624\pi$
$149$	126.485	−	73.0260i	0.848891	−	0.490107i	0.860276	+	0.509828i	$0.170291\pi$
$150$	86.3152	+	4.58094i	0.575435	+	0.0305396i
$151$	140.864	+	243.983i	0.932871	+	1.61578i	0.778386	+	0.627786i	$0.216039\pi$
$151$	140.864	+	243.983i	0.932871	+	1.61578i	0.154485	+	0.987995i	$0.450628\pi$
$152$	178.675	+	103.158i	1.17549	+	0.678672i
$153$	−117.364	−	85.5075i	−0.767083	−	0.558873i
$154$	−48.3765	−	83.7905i	−0.314133	−	0.544094i
$155$	−28.1818	+	16.2708i	−0.181818	+	0.104973i
$156$	240.755	+	102.273i	1.54330	+	0.655595i
$157$	−66.6730	+	115.481i	−0.424669	+	0.735548i	−0.996389	−	0.0849002i	$-0.972943\pi$
$157$	−66.6730	+	115.481i	−0.424669	+	0.735548i	0.571720	+	0.820448i	$0.306276\pi$
$158$			411.999i			2.60759i
$159$	108.153	+	5.73994i	0.680209	+	0.0361002i
$160$	114.188			0.713676
$161$		−	31.1631i		−	0.193560i
$162$	−196.497	−	177.872i	−1.21294	−	1.09797i
$163$	−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
$165$	113.609	−	57.7921i	0.688542	−	0.350255i
$166$	−7.33996			−0.0442166
$167$		−	166.767i		−	0.998607i	−0.866427	−	0.499303i	$-0.833589\pi$
$167$		−	166.767i		−	0.998607i	0.866427	−	0.499303i	$-0.166411\pi$
$168$	74.3193	+	3.94430i	0.442377	+	0.0234779i
$169$	−29.2178	+	166.455i	−0.172887	+	0.984942i
$170$			212.459i			1.24976i
$171$	123.437	−	169.423i	0.721851	−	0.990779i
$172$	−11.4509	−	19.8335i	−0.0665750	−	0.115311i
$173$			65.8542i			0.380660i	0.981720	+	0.190330i	$0.0609558\pi$
$173$			65.8542i			0.380660i	−0.981720	+	0.190330i	$0.939044\pi$
$174$	216.749	−	110.258i	1.24568	−	0.633667i
$175$	12.3299	+	21.3561i	0.0704567	+	0.122035i
$176$	19.7212	−	11.3860i	0.112052	−	0.0646934i
$177$	−22.9438	−	45.1036i	−0.129626	−	0.254823i
$178$	−252.583			−1.41900
$179$	210.321	−	121.429i	1.17498	−	0.678374i	0.220130	−	0.975470i	$-0.429352\pi$
$179$	210.321	−	121.429i	1.17498	−	0.678374i	0.954847	+	0.297097i	$0.0960184\pi$
$180$	−25.7123	+	241.556i	−0.142846	+	1.34198i
$181$	−117.666			−0.650086			−0.325043	−	0.945699i	$-0.605379\pi$
$181$	−117.666			−0.650086			−0.325043	+	0.945699i	$0.605379\pi$
$182$	20.7324	+	117.314i	0.113915	+	0.644584i
$183$	−2.83295	+	53.3791i	−0.0154806	+	0.291689i
$184$	98.5673			0.535692
$185$			271.931i			1.46990i
$186$	35.9907	+	70.7515i	0.193498	+	0.380385i
$187$	−85.1728	−	147.524i	−0.455469	−	0.788896i
$188$	−538.185	−	310.721i	−2.86269	−	1.65277i
$189$	11.9774	−	74.6613i	0.0633724	−	0.395033i
$190$	−306.701			−1.61422
$191$			212.597i			1.11307i	0.830824	+	0.556535i	$0.187870\pi$
$191$			212.597i			1.11307i	−0.830824	+	0.556535i	$0.812130\pi$
$192$	16.1338	−	303.997i	0.0840302	−	1.58332i
$193$	62.2756			0.322672			0.161336	−	0.986900i	$-0.448420\pi$
$193$	62.2756			0.322672			0.161336	+	0.986900i	$0.448420\pi$
$194$	−280.451	−	161.919i	−1.44563	−	0.834632i
$195$	−155.782	+	19.0840i	−0.798882	+	0.0978666i
$196$	−138.021	−	239.060i	−0.704190	−	1.21969i
$197$	248.948	−	143.730i	1.26369	−	0.729594i	0.289906	−	0.957055i	$-0.406376\pi$
$197$	248.948	−	143.730i	1.26369	−	0.729594i	0.973787	+	0.227461i	$0.0730425\pi$
$198$	−126.088	−	284.212i	−0.636811	−	1.43542i
$199$	−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
$201$	−8.73570	+	164.600i	−0.0434612	+	0.818906i
$202$	−149.771	−	259.412i	−0.741443	−	1.28422i
$203$	60.0830	+	34.6890i	0.295976	+	0.170882i
$204$	324.189	+	17.2054i	1.58916	+	0.0843404i
$205$	−19.8406	+	34.3650i	−0.0967836	+	0.167634i
$206$	−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
$210$	−98.6102	+	50.1621i	−0.469572	+	0.238867i
$211$	−355.201			−1.68342			−0.841708	−	0.539932i	$-0.818450\pi$
$211$	−355.201			−1.68342			−0.841708	+	0.539932i	$0.818450\pi$
$212$	−209.698	+	121.069i	−0.989144	+	0.571082i
$213$	−144.265	+	221.827i	−0.677302	+	1.04144i
$214$	250.879			1.17233
$215$	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
$218$	447.341	+	258.272i	2.05202	+	1.18474i
$219$	13.7466	−	259.017i	0.0627701	−	1.18273i
$220$	−142.486	+	246.792i	−0.647662	+	1.12178i
$221$	36.5020	+	206.546i	0.165168	+	0.934598i
$222$	662.397	+	35.1549i	2.98377	+	0.158356i
$223$	13.3802	−	23.1752i	0.0600008	−	0.103925i	−0.834465	−	0.551061i	$-0.814223\pi$
$223$	13.3802	−	23.1752i	0.0600008	−	0.103925i	0.894466	+	0.447137i	$0.147556\pi$
$224$	68.8198	−	39.7332i	0.307231	−	0.177380i
$225$	32.1367	+	72.4385i	0.142830	+	0.321949i
$226$	−391.495			−1.73228
$227$		−	304.787i		−	1.34267i	−0.741152	−	0.671337i	$-0.765720\pi$
$227$		−	304.787i		−	1.34267i	0.741152	−	0.671337i	$-0.234280\pi$
$228$	−24.8373	+	467.991i	−0.108936	+	2.05259i
$229$	4.51573	−	7.82147i	0.0197193	−	0.0341549i	−0.855997	−	0.516980i	$-0.827056\pi$
$229$	4.51573	−	7.82147i	0.0197193	−	0.0341549i	0.875717	+	0.482825i	$0.160389\pi$
$230$	−126.895	+	73.2630i	−0.551718	+	0.318535i
$231$	48.3616	−	74.3625i	0.209358	−	0.321915i
$232$	−109.719	+	190.040i	−0.472928	+	0.819136i
$233$		−	104.668i		−	0.449218i	−0.974449	−	0.224609i	$-0.927889\pi$
$233$		−	104.668i		−	0.449218i	0.974449	−	0.224609i	$-0.0721105\pi$
$234$	26.3474	+	381.936i	0.112596	+	1.63221i
$235$	372.866			1.58666
$236$	97.9780	+	56.5676i	0.415161	+	0.239693i
$237$	−336.674	+	171.263i	−1.42056	+	0.722628i
$238$	73.9278	+	128.047i	0.310621	+	0.538011i
$239$	97.9341	+	56.5423i	0.409766	+	0.236579i	0.690689	−	0.723152i	$-0.257307\pi$
$239$	97.9341	+	56.5423i	0.409766	+	0.236579i	−0.280923	+	0.959730i	$0.590641\pi$
$240$	−11.8063	−	23.2092i	−0.0491930	−	0.0967050i
$241$	166.540			0.691035			0.345518	−	0.938412i	$-0.387703\pi$
$241$	166.540			0.691035			0.345518	+	0.938412i	$0.387703\pi$
$242$			31.1845i			0.128861i
$243$	63.6704	−	234.510i	0.262018	−	0.965063i
$244$	−59.7539	−	103.497i	−0.244893	−	0.424167i
$245$	143.436	+	82.8129i	0.585454	+	0.338012i
$246$	81.1447	+	52.7724i	0.329856	+	0.214522i
$247$	−298.165	+	52.6934i	−1.20715	+	0.213334i
$248$	−62.0331	−	35.8148i	−0.250134	−	0.144415i
$249$	−3.05113	−	5.99800i	−0.0122535	−	0.0240883i
$250$	222.576	−	385.512i	0.890302	−	1.54205i
$251$	−98.5267	−	56.8844i	−0.392537	−	0.226631i	0.290722	−	0.956808i	$-0.406105\pi$
$251$	−98.5267	−	56.8844i	−0.392537	−	0.226631i	−0.683259	+	0.730176i	$0.739438\pi$
$252$	68.5560	+	154.530i	0.272048	+	0.613215i
$253$	58.7408	−	101.742i	0.232177	−	0.402142i
$254$		−	626.945i		−	2.46829i
$255$	−173.615	+	88.3166i	−0.680845	+	0.346340i
$256$	154.607	+	267.787i	0.603932	+	1.04604i
$257$		−	100.670i		−	0.391713i	−0.980633	−	0.195857i	$-0.937251\pi$
$257$		−	100.670i		−	0.391713i	0.980633	−	0.195857i	$-0.0627487\pi$
$258$	18.2744	−	28.0993i	0.0708310	−	0.108912i
$259$	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
$263$	−49.4311	−	28.5390i	−0.187951	−	0.108513i	0.403072	−	0.915168i	$-0.367942\pi$
$263$	−49.4311	−	28.5390i	−0.187951	−	0.108513i	−0.591023	+	0.806655i	$0.701276\pi$
$264$	235.205	+	152.965i	0.890927	+	0.579414i
$265$	72.6418	−	125.819i	0.274120	−	0.474790i
$266$	−184.845	+	106.720i	−0.694906	+	0.401204i
$267$	−104.995	−	206.403i	−0.393241	−	0.773045i
$268$	−184.257	−	319.143i	−0.687528	−	1.19083i
$269$	−407.684	−	235.377i	−1.51556	−	0.875006i	−0.999833	−	0.0182500i	$-0.994191\pi$
$269$	−407.684	−	235.377i	−1.51556	−	0.875006i	−0.515722	−	0.856756i	$-0.672476\pi$
$270$	−332.177	+	126.754i	−1.23028	+	0.469458i
$271$	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
$273$	−87.2475	+	65.7080i	−0.319588	+	0.240689i
$274$	33.9927	−	58.8770i	0.124061	−	0.214880i
$275$			92.9650i			0.338054i
$276$	101.515	+	199.561i	0.367807	+	0.723046i
$277$	−203.740			−0.735522			−0.367761	−	0.929920i	$-0.619876\pi$
$277$	−203.740			−0.735522			−0.367761	+	0.929920i	$0.619876\pi$
$278$			831.099i			2.98957i
$279$	−42.8552	+	58.8210i	−0.153603	+	0.210828i
$280$	49.9170	−	86.4588i	0.178275	−	0.308781i
$281$	−37.9875	+	21.9321i	−0.135187	+	0.0780502i	−0.566068	−	0.824358i	$-0.691536\pi$
$281$	−37.9875	+	21.9321i	−0.135187	+	0.0780502i	0.430881	+	0.902409i	$0.358203\pi$
$282$	48.2036	−	908.264i	0.170935	−	3.22079i
$283$	147.292			0.520468			0.260234	−	0.965546i	$-0.416200\pi$
$283$	147.292			0.520468			0.260234	+	0.965546i	$0.416200\pi$
$284$		−	591.595i		−	2.08308i
$285$	−127.492	−	250.627i	−0.447339	−	0.879393i
$286$	−153.443	+	422.090i	−0.536515	+	1.47584i
$287$			27.6152i			0.0962201i
$288$	233.433	−	103.561i	0.810531	−	0.359585i
$289$	−14.3410	−	24.8393i	−0.0496228	−	0.0859491i
$290$		−	326.208i		−	1.12486i
$291$	15.7351	−	296.484i	0.0540724	−	1.01885i
$292$	289.951	+	502.209i	0.992981	+	1.71989i
$293$	317.860	−	183.516i	1.08485	−	0.626336i	0.152646	−	0.988281i	$-0.451221\pi$
$293$	317.860	−	183.516i	1.08485	−	0.626336i	0.932199	+	0.361945i	$0.117887\pi$
$294$	220.267	−	338.690i	0.749208	−	1.15201i
$295$	−67.8813			−0.230106
$296$	−518.375	+	299.284i	−1.75127	+	1.01110i
$297$	179.837	−	221.179i	0.605511	−	0.744711i
$298$	−477.907			−1.60371
$299$	−110.776	+	93.0255i	−0.370490	+	0.311122i
$300$	−148.526	−	96.5937i	−0.495086	−	0.321979i
$301$	9.56277			0.0317700
$302$		−	921.860i		−	3.05252i
$303$	149.726	−	230.223i	0.494144	−	0.759812i
$304$	−25.1180	−	43.5057i	−0.0826251	−	0.143111i
$305$	62.0982	+	35.8524i	0.203601	+	0.117549i
$306$	192.685	+	434.327i	0.629691	+	1.41937i
$307$	−39.1332			−0.127470			−0.0637348	−	0.997967i	$-0.520301\pi$
$307$	−39.1332			−0.127470			−0.0637348	+	0.997967i	$0.520301\pi$
$308$			198.319i			0.643892i
$309$	−234.829	−	152.721i	−0.759963	−	0.494242i
$310$	106.482			0.343489
$311$	−245.318	−	141.635i	−0.788805	−	0.455417i	0.0507366	−	0.998712i	$-0.483843\pi$
$311$	−245.318	−	141.635i	−0.788805	−	0.455417i	−0.839542	+	0.543295i	$0.817176\pi$
$312$	−207.831	−	275.959i	−0.666125	−	0.884485i
$313$	−59.1441	−	102.441i	−0.188959	−	0.327286i	0.755945	−	0.654636i	$-0.227178\pi$
$313$	−59.1441	−	102.441i	−0.188959	−	0.327286i	−0.944903	+	0.327349i	$0.893845\pi$
$314$	377.874	−	218.166i	1.20342	−	0.694795i
$315$	−81.9820	−	59.7295i	−0.260260	−	0.189618i
$316$	422.246	−	731.352i	1.33622	−	2.31441i
$317$	−373.019	+	215.363i	−1.17672	+	0.679378i	−0.955253	−	0.295791i	$-0.904417\pi$
$317$	−373.019	+	215.363i	−1.17672	+	0.679378i	−0.221464	+	0.975169i	$0.571083\pi$
$318$	−297.092	−	193.214i	−0.934252	−	0.607591i
$319$	130.774	+	226.507i	0.409949	+	0.710052i
$320$	−353.652	−	204.181i	−1.10516	−	0.638066i
$321$	104.287	+	205.011i	0.324882	+	0.638662i
$322$	−50.9855	+	88.3095i	−0.158340	+	0.274253i
$323$	−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
$327$	−25.0986	+	472.914i	−0.0767542	+	1.44622i
$328$	−87.3454			−0.266297
$329$	224.722	−	129.743i	0.683046	−	0.394357i
$330$	−416.498	−	22.1045i	−1.26211	−	0.0669833i
$331$	139.751			0.422208			0.211104	−	0.977464i	$-0.432294\pi$
$331$	139.751			0.422208			0.211104	+	0.977464i	$0.432294\pi$
$332$	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
$335$	191.486	+	110.555i	0.571601	+	0.330014i
$336$	−15.1915	−	9.87976i	−0.0452127	−	0.0294041i
$337$	−58.9960	+	102.184i	−0.175062	+	0.303217i	−0.940183	−	0.340670i	$-0.889346\pi$
$337$	−58.9960	+	102.184i	−0.175062	+	0.303217i	0.765120	+	0.643887i	$0.222679\pi$
$338$	355.132	−	423.895i	1.05069	−	1.25413i
$339$	−162.740	−	319.918i	−0.480058	−	0.943712i
$340$	217.743	−	377.142i	0.640422	−	1.10924i
$341$	−73.9368	+	42.6874i	−0.216823	+	0.125183i
$342$	−626.984	+	278.156i	−1.83329	+	0.813322i
$343$	252.492			0.736128
$344$			30.2466i			0.0879260i
$345$	−112.617	−	73.2405i	−0.326426	−	0.212291i
$346$	107.743	−	186.616i	0.311396	−	0.539354i
$347$	177.144	−	102.274i	0.510503	−	0.294739i	−0.222537	−	0.974924i	$-0.571434\pi$
$347$	177.144	−	102.274i	0.510503	−	0.294739i	0.733040	+	0.680185i	$0.238101\pi$
$348$	−497.757	−	26.4171i	−1.43034	−	0.0759112i
$349$	187.605	−	324.941i	0.537550	−	0.931063i	−0.461486	−	0.887148i	$-0.652683\pi$
$349$	187.605	−	324.941i	0.537550	−	0.931063i	0.999035	−	0.0439155i	$-0.0139832\pi$
$350$		−	80.6912i		−	0.230546i
$351$	−301.155	+	180.296i	−0.857991	+	0.513665i
$352$	299.580			0.851078
$353$	40.3285	+	23.2837i	0.114245	+	0.0659594i	0.556034	−	0.831160i	$-0.312323\pi$
$353$	40.3285	+	23.2837i	0.114245	+	0.0659594i	−0.441789	+	0.897119i	$0.645656\pi$
$354$	−8.77560	+	165.352i	−0.0247898	+	0.467096i
$355$	177.479	+	307.402i	0.499940	+	0.865922i
$356$	448.367	+	258.865i	1.25946	+	0.727148i
$357$	−73.9051	+	113.639i	−0.207017	+	0.318316i
$358$	−794.672			−2.21976
$359$			18.4512i			0.0513962i	0.999670	+	0.0256981i	$0.00818086\pi$
$359$			18.4512i			0.0513962i	−0.999670	+	0.0256981i	$0.991819\pi$
$360$	188.922	−	259.305i	0.524782	−	0.720291i
$361$	−90.7397	−	157.166i	−0.251357	−	0.435362i
$362$	333.439	+	192.511i	0.921102	+	0.531798i
$363$	−25.4830	+	12.9630i	−0.0702012	+	0.0357107i
$364$	83.4292	−	229.496i	0.229201	−	0.630483i
$365$	−301.326	−	173.971i	−0.825551	−	0.476632i
$366$	95.3608	−	146.630i	0.260549	−	0.400628i
$367$	−64.3876	+	111.523i	−0.175443	+	0.303876i	−0.940314	−	0.340307i	$-0.889469\pi$
$367$	−64.3876	+	111.523i	−0.175443	+	0.303876i	0.764872	+	0.644183i	$0.222802\pi$
$368$	−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
$371$		−	101.106i		−	0.272524i
$372$	8.62312	−	162.479i	0.0231804	−	0.436771i
$373$	78.4433	+	135.868i	0.210304	+	0.364257i	0.951810	−	0.306690i	$-0.0992214\pi$
$373$	78.4433	+	135.868i	0.210304	+	0.364257i	−0.741506	+	0.670946i	$0.765888\pi$
$374$			557.400i			1.49037i
$375$	407.551	+	21.6296i	1.08680	+	0.0576791i
$376$	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	$0.961258\pi$
$380$	544.434	+	314.329i	1.43272	+	0.827181i
$381$	512.321	−	260.613i	1.34467	−	0.684024i
$382$	347.826	−	602.453i	0.910540	−	1.57710i
$383$	−179.559	+	103.669i	−0.468823	+	0.270675i	−0.715747	−	0.698360i	$-0.753914\pi$
$383$	−179.559	+	103.669i	−0.468823	+	0.270675i	0.246924	+	0.969035i	$0.420580\pi$
$384$	−357.447	+	549.622i	−0.930851	+	1.43131i
$385$	−59.4957	−	103.050i	−0.154534	−	0.267661i
$386$	−176.476	−	101.888i	−0.457191	−	0.263959i
$387$	30.5584	+	3.25277i	0.0789622	+	0.00840508i
$388$	331.891	+	574.853i	0.855390	+	1.48158i
$389$	116.285	−	67.1372i	0.298933	−	0.172589i	−0.343030	−	0.939324i	$-0.611453\pi$
$389$	116.285	−	67.1372i	0.298933	−	0.172589i	0.641964	+	0.766735i	$0.278120\pi$
$390$	472.676	+	200.793i	1.21199	+	0.514854i
$391$	−89.7663	+	155.480i	−0.229581	+	0.397646i
$392$			364.571i			0.930028i
$393$	−393.722	+	605.401i	−1.00184	+	1.54046i
$394$	−940.618			−2.38736
$395$			506.696i			1.28278i
$396$	−67.4579	+	633.738i	−0.170348	+	1.60035i
$397$	−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
$399$	−164.046	−	106.688i	−0.411144	−	0.267388i
$400$	18.9918			0.0474794
$401$			767.165i			1.91313i	0.291520	+	0.956565i	$0.405839\pi$
$401$			767.165i			1.91313i	−0.291520	+	0.956565i	$0.594161\pi$
$402$	294.055	−	452.149i	0.731480	−	1.12475i
$403$	103.518	−	18.2943i	0.256869	−	0.0453953i
$404$			613.986i			1.51977i
$405$	−241.661	−	218.755i	−0.596694	−	0.540136i
$406$	−113.508	−	196.602i	−0.279577	−	0.484241i
$407$			713.429i			1.75290i
$408$	−359.434	−	233.758i	−0.880966	−	0.572937i
$409$	129.124	+	223.649i	0.315706	+	0.546819i	0.979587	−	0.201019i	$-0.0644254\pi$
$409$	129.124	+	223.649i	0.315706	+	0.546819i	−0.663881	+	0.747838i	$0.731092\pi$
$410$	112.448	−	64.9220i	0.274264	−	0.158346i
$411$	62.2429	+	3.30337i	0.151442	+	0.00803740i
$412$	626.268			1.52007
$413$	−40.9113	+	23.6201i	−0.0990587	+	0.0571916i
$414$	−192.965	+	264.855i	−0.466100	+	0.639747i
$415$	−9.02703			−0.0217519
$416$	−346.676	−	126.028i	−0.833356	−	0.302952i
$417$	−679.150	+	345.477i	−1.62866	+	0.828483i
$418$	−804.649			−1.92500
$419$			372.973i			0.890150i	0.895493	+	0.445075i	$0.146823\pi$
$419$			372.973i			0.890150i	−0.895493	+	0.445075i	$0.853177\pi$
$420$	226.455	+	12.0185i	0.539180	+	0.0286155i
$421$	−211.181	−	365.776i	−0.501617	−	0.868826i	−0.999998	−	0.00186824i	$-0.999405\pi$
$421$	−211.181	−	365.776i	−0.501617	−	0.868826i	0.498381	−	0.866958i	$-0.333928\pi$
$422$	1006.56	+	581.139i	2.38522	+	1.37711i
$423$	762.244	−	338.163i	1.80200	−	0.799440i
$424$	319.794			0.754232
$425$		−	142.067i		−	0.334275i
$426$	771.745	−	392.580i	1.81161	−	0.921549i
$427$	49.9011			0.116864
$428$	−445.342	−	257.118i	−1.04052	−	0.600744i
$429$	−408.704	+	50.0680i	−0.952689	+	0.116709i
$430$	−22.4816	−	38.9393i	−0.0522828	−	0.0905565i
$431$	−353.148	+	203.890i	−0.819369	+	0.473063i	−0.850199	−	0.526462i	$-0.823518\pi$
$431$	−353.148	+	203.890i	−0.819369	+	0.473063i	0.0308300	+	0.999525i	$0.490185\pi$
$432$	−45.1846	−	36.7387i	−0.104594	−	0.0850433i
$433$	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
$435$	266.568	−	135.601i	0.612800	−	0.311726i
$436$	−529.392	−	916.933i	−1.21420	−	2.10306i
$437$	−224.447	−	129.584i	−0.513608	−	0.296532i
$438$	−462.730	+	711.509i	−1.05646	+	1.62445i
$439$	−206.715	+	358.041i	−0.470877	+	0.815584i	−0.999445	−	0.0333076i	$-0.989396\pi$
$439$	−206.715	+	358.041i	−0.470877	+	0.815584i	0.528568	+	0.848891i	$0.322729\pi$
$440$	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	−0.925073	−	0.379790i	$-0.875996\pi$
$443$	−469.005	+	270.780i	−1.05870	+	0.611242i	−0.133629	+	0.991031i	$0.542663\pi$
$444$	−1139.81	−	741.276i	−2.56714	−	1.66954i
$445$	−310.638			−0.698063
$446$	−75.8331	+	43.7823i	−0.170029	+	0.0981665i
$447$	−198.660	−	390.531i	−0.444429	−	0.873672i
$448$	−284.189			−0.634351
$449$	462.566	+	267.062i	1.03021	+	0.594794i	0.917046	−	0.398782i	$-0.130567\pi$
$449$	462.566	+	267.062i	1.03021	+	0.594794i	0.113167	+	0.993576i	$0.463900\pi$
$450$	27.4470	−	257.853i	0.0609934	−	0.573008i
$451$	−52.0531	+	90.1587i	−0.115417	+	0.199908i
$452$	694.954	+	401.232i	1.53751	+	0.887682i
$453$	753.316	−	383.205i	1.66295	−	0.845928i
$454$	−498.658	+	863.700i	−1.09836	+	1.90242i
$455$	25.4977	+	144.279i	0.0560390	+	0.317096i
$456$	337.448	−	518.871i	0.740017	−	1.13787i
$457$	323.791	−	560.822i	0.708513	−	1.22718i	−0.256895	−	0.966439i	$-0.582700\pi$
$457$	323.791	−	560.822i	0.708513	−	1.22718i	0.965409	−	0.260742i	$-0.0839672\pi$
$458$	−25.5932	+	14.7762i	−0.0558803	+	0.0322625i
$459$	−274.822	+	338.001i	−0.598741	+	0.736386i
$460$	300.340			0.652914
$461$			250.728i			0.543879i	0.962314	+	0.271940i	$0.0876651\pi$
$461$			250.728i			0.543879i	−0.962314	+	0.271940i	$0.912335\pi$
$462$	−258.710	+	131.603i	−0.559978	+	0.284856i
$463$	16.3357	−	28.2943i	0.0352823	−	0.0611108i	−0.847845	−	0.530244i	$-0.822100\pi$
$463$	16.3357	−	28.2943i	0.0352823	−	0.0611108i	0.883127	+	0.469133i	$0.155434\pi$
$464$	46.2729	−	26.7157i	0.0997260	−	0.0575768i
$465$	44.2630	+	87.0136i	0.0951893	+	0.187126i
$466$	−171.246	+	296.606i	−0.367480	+	0.636494i
$467$		−	102.067i		−	0.218560i	−0.994011	−	0.109280i	$-0.965146\pi$
$467$		−	102.067i		−	0.218560i	0.994011	−	0.109280i	$-0.0348545\pi$
$468$	344.666	−	704.989i	0.736465	−	1.50639i
$469$	153.875			0.328093
$470$	−1056.62	−	610.041i	−2.24813	−	1.29796i
$471$	335.356	+	218.099i	0.712008	+	0.463055i
$472$	−74.7093	−	129.400i	−0.158282	−	0.274153i
$473$	31.2208	+	18.0253i	0.0660058	+	0.0381085i
$474$	1234.26	+	65.5050i	2.60393	+	0.138196i
$475$	205.084			0.431756
$476$		−	303.066i		−	0.636693i
$477$	34.3912	−	323.091i	0.0720990	−	0.677340i
$478$	−185.016	−	320.457i	−0.387063	−	0.670413i
$479$	−492.592	−	284.398i	−1.02837	−	0.593732i	−0.111856	−	0.993724i	$-0.535680\pi$
$479$	−492.592	−	284.398i	−1.02837	−	0.593732i	−0.916519	+	0.399992i	$0.869013\pi$
$480$	18.1551	−	342.083i	0.0378232	−	0.712673i
$481$	300.127	−	825.586i	0.623965	−	1.71639i
$482$	−471.937	−	272.473i	−0.979122	−	0.565297i
$483$	−93.3579	−	4.95472i	−0.193288	−	0.0102582i
$484$	31.9601	−	55.3565i	0.0660332	−	0.114373i
$485$	−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	$0.284212\pi$
$488$			157.835i			0.323432i
$489$	80.3603	+	52.2623i	0.164336	+	0.106876i
$490$	−270.978	−	469.348i	−0.553016	−	0.957852i
$491$		−	665.890i		−	1.35619i	−0.734973	−	0.678096i	$-0.762805\pi$
$491$		−	665.890i		−	1.35619i	0.734973	−	0.678096i	$-0.237195\pi$
$492$	−89.9573	−	176.841i	−0.182840	−	0.359432i
$493$	−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
$497$	213.929	+	123.512i	0.430440	+	0.248515i
$498$	−1.16700	+	21.9889i	−0.00234338	+	0.0441545i
$499$	284.011	−	491.922i	0.569161	−	0.985816i	−0.427488	−	0.904021i	$-0.640601\pi$
$499$	284.011	−	491.922i	0.569161	−	0.985816i	0.996649	−	0.0817951i	$-0.0260653\pi$
$500$	−790.200	+	456.222i	−1.58040	+	0.912445i
$501$	−499.599	−	26.5148i	−0.997203	−	0.0529238i
$502$	186.136	+	322.396i	0.370788	+	0.642224i
$503$	−424.010	−	244.802i	−0.842961	−	0.486684i	0.0153084	−	0.999883i	$-0.495127\pi$
$503$	−424.010	−	244.802i	−0.842961	−	0.486684i	−0.858270	+	0.513199i	$0.828460\pi$
$504$	23.6325	−	222.018i	0.0468899	−	0.440511i
$505$	−184.196	−	319.037i	−0.364745	−	0.631756i
$506$	−332.917	+	192.210i	−0.657939	+	0.379862i
$507$	494.018	+	113.996i	0.974395	+	0.224843i
$508$	−642.538	+	1112.91i	−1.26484	+	2.19077i
$509$			688.817i			1.35327i	0.736316	+	0.676637i	$0.236563\pi$
$509$			688.817i			1.35327i	−0.736316	+	0.676637i	$0.763437\pi$
$510$	636.482	+	33.7795i	1.24800	+	0.0662344i
$511$	−242.141			−0.473857
$512$		−	137.624i		−	0.268797i
$513$	−487.930	−	396.726i	−0.951130	−	0.773346i
$514$	−164.705	+	285.278i	−0.320438	+	0.555015i
$515$	−325.419	+	187.881i	−0.631882	+	0.364817i
$516$	−61.2376	+	31.1510i	−0.118678	+	0.0603702i
$517$	978.237			1.89214
$518$		−	619.238i		−	1.19544i
$519$	197.285	+	10.4704i	0.380125	+	0.0201741i
$520$	−456.346	+	80.6481i	−0.877589	+	0.155092i
$521$		−	248.194i		−	0.476379i	−0.971219	−	0.238190i	$-0.923446\pi$
$521$		−	248.194i		−	0.476379i	0.971219	−	0.238190i	$-0.0765540\pi$
$522$	−295.848	−	666.862i	−0.566758	−	1.27751i
$523$	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	$0.680454\pi$
$524$		−	1614.55i		−	3.08121i
$525$	65.9385	−	33.5423i	0.125597	−	0.0638901i
$526$	93.3847	+	161.747i	0.177537	+	0.307504i
$527$	112.988	−	65.2339i	0.214399	−	0.123783i
$528$	−30.9746	−	60.8908i	−0.0586640	−	0.115323i
$529$	405.182			0.765940
$530$	−411.702	+	237.696i	−0.776797	+	0.448484i
$531$	−138.769	+	61.5635i	−0.261334	+	0.115939i
$532$	437.498			0.822365
$533$	98.1645	−	82.4345i	0.184174	−	0.154661i
$534$	−40.1589	+	756.683i	−0.0752039	+	1.41701i
$535$	308.543			0.576715
$536$			486.700i			0.908023i
$537$	−330.335	−	649.383i	−0.615149	−	1.20928i
$538$	770.193	+	1334.01i	1.43159	+	2.47958i
$539$	376.313	+	217.265i	0.698170	+	0.403088i
$540$	719.563	+	115.434i	1.33252	+	0.213767i
$541$	−64.9904			−0.120130			−0.0600650	−	0.998194i	$-0.519131\pi$
$541$	−64.9904			−0.120130			−0.0600650	+	0.998194i	$0.519131\pi$
$542$		−	154.554i		−	0.285156i
$543$	−18.7080	+	352.501i	−0.0344531	+	0.649172i
$544$	−457.810			−0.841563
$545$	550.161	+	317.636i	1.00947	+	0.582817i
$546$	354.744	−	43.4578i	0.649715	−	0.0795930i
$547$	219.952	+	380.968i	0.402106	+	0.696467i	0.993980	−	0.109563i	$-0.0349452\pi$
$547$	219.952	+	380.968i	0.402106	+	0.696467i	−0.591874	+	0.806030i	$0.701612\pi$
$548$	−120.683	+	69.6762i	−0.220224	+	0.127146i
$549$	159.462	+	16.9738i	0.290459	+	0.0309177i
$550$	152.099	−	263.443i	0.276543	−	0.478987i
$551$	499.682	−	288.492i	0.906864	−	0.523578i
$552$	15.6715	−	295.286i	0.0283904	−	0.534939i
$553$	176.311	+	305.380i	0.318827	+	0.552224i
$554$	577.354	+	333.336i	1.04216	+	0.601689i
$555$	814.648	+	43.2352i	1.46783	+	0.0779013i
$556$	851.770	−	1475.31i	1.53196	−	2.65343i
$557$	365.644	−	211.105i	0.656452	−	0.379003i	−0.134472	−	0.990917i	$-0.542934\pi$
$557$	365.644	−	211.105i	0.656452	−	0.379003i	0.790924	+	0.611915i	$0.209600\pi$
$558$	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
$561$	−455.491	+	231.704i	−0.811926	+	0.413020i
$562$	143.531			0.255394
$563$	660.046	−	381.078i	1.17237	−	0.676870i	0.218135	−	0.975919i	$-0.430003\pi$
$563$	660.046	−	381.078i	1.17237	−	0.676870i	0.954238	+	0.299049i	$0.0966693\pi$
$564$	−1016.42	+	1562.88i	−1.80217	+	2.77107i
$565$	−481.479			−0.852176
$566$	−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
$569$	−229.202	−	132.330i	−0.402816	−	0.232566i	0.284883	−	0.958562i	$-0.408045\pi$
$569$	−229.202	−	132.330i	−0.402816	−	0.232566i	−0.687698	+	0.725997i	$0.741379\pi$
$570$	−48.7633	+	918.810i	−0.0855497	+	1.61195i
$571$	200.357	−	347.029i	0.350889	−	0.607757i	−0.635517	−	0.772087i	$-0.719213\pi$
$571$	200.357	−	347.029i	0.350889	−	0.607757i	0.986405	+	0.164330i	$0.0525462\pi$
$572$	704.969	−	592.004i	1.23246	−	1.03497i
$573$	636.893	+	33.8014i	1.11151	+	0.0589902i
$574$	45.1808	−	78.2554i	0.0787122	−	0.136334i
$575$	84.8521	−	48.9894i	0.147569	−	0.0851989i
$576$	−908.143	−	96.6667i	−1.57664	−	0.167824i
$577$	−1041.61			−1.80522			−0.902610	−	0.430460i	$-0.858351\pi$
$577$	−1041.61			−1.80522			−0.902610	+	0.430460i	$0.858351\pi$
$578$			93.8523i			0.162374i
$579$	9.90139	−	186.564i	0.0171009	−	0.322218i
$580$	−334.322	+	579.062i	−0.576416	+	0.998383i
$581$	−5.44049	+	3.14107i	−0.00936400	+	0.00540631i
$582$	−529.663	+	814.428i	−0.910074	+	1.39936i
$583$	190.580	−	330.095i	0.326896	−	0.566200i
$584$		−	765.879i		−	1.31144i
$585$	32.4032	+	469.724i	0.0553902	+	0.802946i
$586$	−1200.99			−2.04948
$587$	−17.0097	−	9.82055i	−0.0289773	−	0.0167301i	0.485441	−	0.874269i	$-0.338659\pi$
$587$	−17.0097	−	9.82055i	−0.0289773	−	0.0167301i	−0.514419	+	0.857539i	$0.671992\pi$
$588$	−738.116	+	375.473i	−1.25530	+	0.638559i
$589$	94.1700	+	163.107i	0.159881	+	0.276922i
$590$	192.361	+	111.060i	0.326035	+	0.188237i
$591$	−391.003	−	768.645i	−0.661596	−	1.30058i
$592$	145.746			0.246192
$593$		−	221.793i		−	0.374019i	−0.982358	−	0.187010i	$-0.940120\pi$
$593$		−	221.793i		−	0.374019i	0.982358	−	0.187010i	$-0.0598795\pi$
$594$	−871.486	+	332.546i	−1.46715	+	0.559842i
$595$	90.9199	+	157.478i	0.152807	+	0.264669i
$596$	848.347	+	489.793i	1.42340	+	0.821801i
$597$	536.349	+	348.815i	0.898408	+	0.584280i
$598$	466.114	−	82.3744i	0.779455	−	0.137750i
$599$	−2.12724	−	1.22816i	−0.00355132	−	0.00205035i	0.498223	−	0.867049i	$-0.333986\pi$
$599$	−2.12724	−	1.22816i	−0.00355132	−	0.00205035i	−0.501775	+	0.864998i	$0.667319\pi$
$600$	106.093	+	208.560i	0.176821	+	0.347600i
$601$	256.742	−	444.690i	0.427191	−	0.739916i	−0.569431	−	0.822039i	$-0.692837\pi$
$601$	256.742	−	444.690i	0.427191	−	0.739916i	0.996622	+	0.0821226i	$0.0261699\pi$
$602$	−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
$605$			38.3522i			0.0633920i
$606$	−800.954	+	407.438i	−1.32171	+	0.672340i
$607$	−5.10830	−	8.84784i	−0.00841565	−	0.0145763i	0.861787	−	0.507270i	$-0.169345\pi$
$607$	−5.10830	−	8.84784i	−0.00841565	−	0.0145763i	−0.870203	+	0.492694i	$0.836012\pi$
$608$		−	660.884i		−	1.08698i
$609$	113.473	−	174.480i	0.186327	−	0.286503i
$610$	−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	$0.927359\pi$
$614$	110.895	+	64.0252i	0.180611	+	0.104276i
$615$	99.7956	+	64.9021i	0.162269	+	0.105532i
$616$	130.960	−	226.830i	0.212598	−	0.368231i
$617$	−543.144	+	313.584i	−0.880298	+	0.508240i	−0.870757	−	0.491714i	$-0.836370\pi$
$617$	−543.144	+	313.584i	−0.880298	+	0.508240i	−0.00954104	+	0.999954i	$0.503037\pi$
$618$	415.589	+	816.977i	0.672474	+	1.32197i
$619$	438.414	+	759.355i	0.708261	+	1.22674i	0.965502	+	0.260397i	$0.0838533\pi$
$619$	438.414	+	759.355i	0.708261	+	1.22674i	−0.257241	+	0.966347i	$0.582813\pi$
$620$	−189.019	−	109.130i	−0.304869	−	0.176016i
$621$	−296.645	−	47.5887i	−0.477689	−	0.0766323i
$622$	463.453	+	802.724i	0.745101	+	1.29055i
$623$	−187.218	+	108.090i	−0.300510	+	0.173500i
$624$	10.2284	+	83.4938i	0.0163916	+	0.133804i
$625$	163.669	−	283.482i	0.261870	−	0.453572i
$626$			387.060i			0.618306i
$627$	−334.482	−	657.535i	−0.533464	−	1.04870i
$628$	−894.367			−1.42415
$629$		−	1090.25i		−	1.73330i
$630$	134.596	+	303.390i	0.213645	+	0.481572i
$631$	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
$633$	−56.4745	+	1064.11i	−0.0892172	+	1.68105i
$634$	1409.41			2.22304
$635$		−	771.047i		−	1.21425i
$636$	329.357	+	647.460i	0.517857	+	1.01802i
$637$	−344.074	−	409.729i	−0.540147	−	0.643217i
$638$		−	855.828i		−	1.34142i
$639$	641.609	+	467.457i	1.00408	+	0.731544i
$640$	439.740	+	761.652i	0.687093	+	1.19008i
$641$		−	357.039i		−	0.557003i	−0.960436	−	0.278501i	$-0.910162\pi$
$641$		−	357.039i		−	0.557003i	0.960436	−	0.278501i	$-0.0898377\pi$
$642$	39.8880	−	751.578i	0.0621308	−	1.17068i
$643$	92.4981	+	160.211i	0.143854	+	0.249162i	0.928945	−	0.370218i	$-0.120717\pi$
$643$	92.4981	+	160.211i	0.143854	+	0.249162i	−0.785091	+	0.619381i	$0.787384\pi$
$644$	181.012	−	104.507i	0.281074	−	0.162278i
$645$	22.4747	−	34.5579i	0.0348445	−	0.0535781i
$646$	1229.65			1.90348
$647$	−714.972	+	412.789i	−1.10506	+	0.638005i	−0.937545	−	0.347865i	$-0.886907\pi$
$647$	−714.972	+	412.789i	−1.10506	+	0.638005i	−0.167512	+	0.985870i	$0.553573\pi$
$648$	151.038	−	701.431i	0.233083	−	1.08246i
$649$	−178.091			−0.274408
$650$	−286.836	+	240.873i	−0.441286	+	0.370574i
$651$	56.9543	+	37.0402i	0.0874874	+	0.0568974i
$652$	−214.314			−0.328703
$653$		−	355.596i		−	0.544558i	−0.962218	−	0.272279i	$-0.912223\pi$
$653$		−	355.596i		−	0.544558i	0.962218	−	0.272279i	$-0.0877773\pi$
$654$	844.852	−	1299.07i	1.29182	−	1.98635i
$655$	484.367	+	838.948i	0.739492	+	1.28084i
$656$	18.4184	+	10.6339i	0.0280769	+	0.0162102i
$657$	−773.775	−	82.3640i	−1.17774	−	0.125364i
$658$	−849.085			−1.29040
$659$			203.522i			0.308835i	0.988006	+	0.154418i	$0.0493501\pi$
$659$			203.522i			0.308835i	−0.988006	+	0.154418i	$0.950650\pi$
$660$	716.683	+	466.095i	1.08588	+	0.706204i
$661$	−357.583			−0.540972			−0.270486	−	0.962724i	$-0.587184\pi$
$661$	−357.583			−0.540972			−0.270486	+	0.962724i	$0.587184\pi$
$662$	−396.024	−	228.645i	−0.598224	−	0.345385i
$663$	624.571	−	76.5128i	0.942038	−	0.115404i
$664$	−9.93503	−	17.2080i	−0.0149624	−	0.0259156i
$665$	−227.331	+	131.250i	−0.341852	+	0.197368i
$666$	210.633	−	1978.81i	0.316266	−	2.97119i
$667$	137.827	−	238.723i	0.206636	−	0.357905i
$668$	968.672	−	559.263i	1.45011	−	0.837221i
$669$	−67.3004	−	43.7688i	−0.100599	−	0.0654243i
$670$	−361.754	−	626.576i	−0.539931	−	0.935188i
$671$	162.918	+	94.0610i	0.242799	+	0.140180i
$672$	−108.090	−	212.487i	−0.160848	−	0.316200i
$673$	−556.547	+	963.968i	−0.826965	+	1.43234i	0.0734440	+	0.997299i	$0.476601\pi$
$673$	−556.547	+	963.968i	−0.826965	+	1.43234i	−0.900409	+	0.435045i	$0.856732\pi$
$674$	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	0.118138	−	0.992997i	$-0.462307\pi$
$677$	702.163	−	405.394i	1.03717	−	0.598809i	0.919030	+	0.394188i	$0.128974\pi$
$678$	−62.2450	+	1172.83i	−0.0918068	+	1.72985i
$679$	−277.166			−0.408198
$680$	−498.095	+	287.575i	−0.732492	+	0.422905i
$681$	−913.076	−	48.4590i	−1.34079	−	0.0711586i
$682$	279.361			0.409620
$683$	710.444	+	410.175i	1.04018	+	0.600549i	0.919885	−	0.392189i	$-0.128282\pi$
$683$	710.444	+	410.175i	1.04018	+	0.600549i	0.120297	+	0.992738i	$0.461615\pi$
$684$	1398.05	+	148.815i	2.04393	+	0.217565i
$685$	41.8058	−	72.4097i	0.0610303	−	0.105708i
$686$	−715.508	−	413.098i	−1.04301	−	0.602184i
$687$	−22.7135	−	14.7717i	−0.0330618	−	0.0215017i
$688$	3.68238	−	6.37807i	0.00535229	−	0.00927044i
$689$	−359.406	+	301.815i	−0.521635	+	0.438047i
$690$	199.305	+	391.799i	0.288847	+	0.567825i
$691$	368.823	−	638.820i	0.533752	−	0.924486i	−0.465470	−	0.885063i	$-0.654115\pi$
$691$	368.823	−	638.820i	0.533752	−	0.924486i	0.999223	−	0.0394225i	$-0.0125518\pi$
$692$	−382.516	+	220.845i	−0.552768	+	0.319141i
$693$	−215.085	−	156.704i	−0.310368	−	0.226124i
$694$	−669.319			−0.964437
$695$			1022.13i			1.47068i
$696$	551.873	+	358.911i	0.792921	+	0.515676i
$697$	79.5464	−	137.778i	0.114127	−	0.197673i
$698$	−1063.26	+	613.875i	−1.52330	+	0.879477i
$699$	−313.562	−	16.6415i	−0.448587	−	0.0238075i
$700$	−82.6981	+	143.237i	−0.118140	+	0.204625i
$701$			1169.94i			1.66896i	0.551039	+	0.834480i	$0.314232\pi$
$701$			1169.94i			1.66896i	−0.551039	+	0.834480i	$0.685768\pi$
$702$	1148.39	−	18.2058i	1.63588	−	0.0259342i
$703$	1573.85			2.23876
$704$	−927.828	−	535.682i	−1.31794	−	0.760912i
$705$	59.2831	−	1117.03i	0.0840895	−	1.58443i
$706$	−76.1882	−	131.962i	−0.107915	−	0.186915i
$707$	−222.026	−	128.187i	−0.314039	−	0.181311i
$708$	185.042	−	284.527i	0.261359	−	0.401874i
$709$	−1053.52			−1.48593			−0.742964	−	0.669331i	$-0.766581\pi$
$709$	−1053.52			−1.48593			−0.742964	+	0.669331i	$0.766581\pi$
$710$		−	1161.48i		−	1.63589i
$711$	459.538	+	1035.83i	0.646326	+	1.45687i
$712$	−341.884	−	592.161i	−0.480174	−	0.831686i
$713$	77.9243	+	44.9896i	0.109291	+	0.0630990i
$714$	395.354	−	201.113i	0.553717	−	0.281671i
$715$	−188.712	+	519.106i	−0.263933	+	0.726023i
$716$	1410.65	+	814.437i	1.97018	+	1.13748i
$717$	184.959	−	284.400i	0.257963	−	0.396652i
$718$	30.1878	−	52.2868i	0.0420443	−	0.0728228i
$719$	895.444	+	516.985i	1.24540	+	0.719033i	0.970189	−	0.242350i	$-0.0779184\pi$
$719$	895.444	+	516.985i	1.24540	+	0.719033i	0.275213	+	0.961383i	$0.411252\pi$
$720$	−71.4069	+	31.6791i	−0.0991762	+	0.0439987i
$721$	−130.751	+	226.467i	−0.181347	+	0.314102i
$722$			593.832i			0.822482i
$723$	26.4786	−	498.916i	0.0366233	−	0.690064i
$724$	−394.598	−	683.464i	−0.545025	−	0.944010i
$725$			218.129i			0.300867i
$726$	93.4220	+	4.95812i	0.128680	+	0.00682936i
$727$	334.678	+	579.679i	0.460355	+	0.797358i	0.998978	−	0.0451886i	$-0.0143889\pi$
$727$	334.678	+	579.679i	0.460355	+	0.797358i	−0.538624	+	0.842546i	$0.681056\pi$
$728$	−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
$731$	−47.7108	−	27.5459i	−0.0652679	−	0.0376824i
$732$	−319.554	+	162.555i	−0.436550	+	0.222069i
$733$	−409.264	+	708.867i	−0.558342	+	0.967076i	0.439294	+	0.898344i	$0.355229\pi$
$733$	−409.264	+	708.867i	−0.558342	+	0.967076i	−0.997635	+	0.0687324i	$0.978105\pi$
$734$	364.921	−	210.687i	0.497167	−	0.287040i
$735$	270.895	−	416.537i	0.368564	−	0.566717i
$736$	−157.868	−	273.436i	−0.214495	−	0.371516i
$737$	502.376	+	290.047i	0.681650	+	0.393551i
$738$	170.996	−	234.701i	0.231702	−	0.318024i
$739$	−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
$741$	110.452	+	901.616i	0.149058	+	1.21676i
$742$	−165.419	+	286.514i	−0.222936	+	0.386137i
$743$			207.085i			0.278714i	0.990242	+	0.139357i	$0.0445036\pi$
$743$			207.085i			0.278714i	−0.990242	+	0.139357i	$0.955496\pi$
$744$	−117.156	+	180.143i	−0.157468	+	0.242128i
$745$	−587.753			−0.788930
$746$		−	513.360i		−	0.688150i
$747$	−18.4538	+	8.18688i	−0.0247039	+	0.0109597i
$748$	571.263	−	989.456i	0.763721	−	1.32280i
$749$	185.955	−	107.361i	0.248271	−	0.143339i
$750$	−1119.52	−	728.082i	−1.49270	−	0.970776i
$751$	909.331			1.21083			0.605414	−	0.795911i	$-0.293008\pi$
$751$	909.331			1.21083			0.605414	+	0.795911i	$0.293008\pi$
$752$		−	199.843i		−	0.265749i
$753$	−186.079	+	286.121i	−0.247116	+	0.379974i
$754$	−360.032	+	990.371i	−0.477496	+	1.31349i
$755$		−	1133.75i		−	1.50165i
$756$	473.839	−	180.810i	0.626771	−	0.239166i
$757$	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	$0.772679\pi$
$758$			970.186i			1.27993i
$759$	−295.458	−	192.151i	−0.389272	−	0.253163i
$760$	−415.136	−	719.037i	−0.546232	−	0.946102i
$761$	57.1790	−	33.0123i	0.0751367	−	0.0433802i	−0.461961	−	0.886900i	$-0.652854\pi$
$761$	57.1790	−	33.0123i	0.0751367	−	0.0433802i	0.537098	+	0.843520i	$0.319521\pi$
$762$	−1878.19	−	99.6799i	−2.46482	−	0.130814i
$763$	442.101			0.579424
$764$	−1234.87	+	712.954i	−1.61633	+	0.933186i
$765$	236.974	+	534.156i	0.309770	+	0.698243i
$766$	678.443			0.885696
$767$	206.088	+	74.9197i	0.268694	+	0.0976789i
$768$	826.812	−	420.592i	1.07658	−	0.547646i
$769$	−993.806			−1.29234			−0.646168	−	0.763196i	$-0.723629\pi$
$769$	−993.806			−1.29234			−0.646168	+	0.763196i	$0.723629\pi$
$770$			389.360i			0.505663i
$771$	−301.586	−	16.0059i	−0.391163	−	0.0207599i
$772$	208.845	+	361.730i	0.270524	+	0.468562i
$773$	−229.750	−	132.646i	−0.297219	−	0.171600i	0.343974	−	0.938979i	$-0.388227\pi$
$773$	−229.750	−	132.646i	−0.297219	−	0.171600i	−0.641193	+	0.767380i	$0.721560\pi$
$774$	−81.2740	−	59.2137i	−0.105005	−	0.0765036i
$775$	−71.2020			−0.0918735
$776$		−	876.663i		−	1.12972i
$777$	506.023	−	257.409i	0.651252	−	0.331286i
$778$	−439.369			−0.564742
$779$	198.893	+	114.831i	0.255319	+	0.147408i
$780$	−633.273	−	840.865i	−0.811889	−	1.07803i
$781$	465.627	+	806.489i	0.596193	+	1.03264i
$782$	508.757	−	293.731i	0.650584	−	0.375615i
$783$	421.960	−	518.964i	0.538902	−	0.662790i
$784$	44.3848	−	76.8768i	0.0566133	−	0.0980571i
$785$	464.727	−	268.310i	0.592009	−	0.341797i
$786$	2106.21	−	1071.41i	2.67966	−	1.36312i
$787$	−136.093	−	235.720i	−0.172927	−	0.299518i	0.766515	−	0.642226i	$-0.221989\pi$
$787$	−136.093	−	235.720i	−0.172927	−	0.299518i	−0.939442	+	0.342709i	$0.888656\pi$
$788$	1669.72	+	964.013i	2.11893	+	1.22337i
$789$	−93.3560	+	143.547i	−0.118322	+	0.181936i
$790$	828.999	−	1435.87i	1.04937	−	1.81755i
$791$	−290.182	+	167.537i	−0.366855	+	0.211804i
$792$	495.647	−	680.302i	0.625817	−	0.858967i
$793$	−148.961	−	177.385i	−0.187845	−	0.223689i
$794$	1386.45	−	800.466i	1.74616	−	1.00814i
$795$	−365.378	−	237.624i	−0.459595	−	0.298898i
$796$	−1430.40			−1.79699
$797$	−321.746	+	185.760i	−0.403696	+	0.233074i	−0.688078	−	0.725637i	$-0.741545\pi$
$797$	−321.746	+	185.760i	−0.403696	+	0.233074i	0.284381	+	0.958711i	$0.408212\pi$
$798$	290.322	+	570.724i	0.363812	+	0.715193i
$799$	−1494.92			−1.87099
$800$	216.374	+	124.924i	0.270467	+	0.156154i
$801$	−635.032	+	281.727i	−0.792799	+	0.351719i
$802$	1255.15	−	2173.98i	1.56502	−	2.71070i
$803$	−790.547	−	456.423i	−0.984492	−	0.568397i
$804$	−985.380	+	501.254i	−1.22560	+	0.623450i
$805$	−62.7044	+	108.607i	−0.0778937	+	0.134916i
$806$	−323.279	−	117.522i	−0.401091	−	0.145809i
$807$	−769.957	+	1183.91i	−0.954097	+	1.46705i
$808$	405.448	−	702.256i	0.501792	−	0.869129i
$809$	−286.077	+	165.167i	−0.353618	+	0.204161i	−0.666278	−	0.745704i	$-0.732113\pi$
$809$	−286.077	+	165.167i	−0.353618	+	0.204161i	0.312660	+	0.949865i	$0.398780\pi$
$810$	326.913	+	1015.28i	0.403596	+	1.25344i
$811$	−222.419			−0.274252			−0.137126	−	0.990554i	$-0.543787\pi$
$811$	−222.419			−0.274252			−0.137126	+	0.990554i	$0.543787\pi$
$812$			465.325i			0.573061i
$813$	126.297	−	64.2463i	0.155347	−	0.0790237i
$814$	1167.23	−	2021.70i	1.43394	−	2.48366i
$815$	111.361	−	64.2944i	0.136640	−	0.0788889i
$816$	47.3346	+	93.0518i	0.0580081	+	0.114034i
$817$	39.7645	−	68.8742i	0.0486714	−	0.0843013i
$818$		−	845.030i		−	1.03304i
$819$	182.975	+	271.822i	0.223413	+	0.331895i
$820$	−266.147			−0.324569
$821$	1100.23	+	635.216i	1.34010	+	0.773710i	0.986822	−	0.161807i	$-0.0517323\pi$
$821$	1100.23	+	635.216i	1.34010	+	0.773710i	0.353282	+	0.935517i	$0.385066\pi$
$822$	−170.978	−	111.196i	−0.208003	−	0.135275i
$823$	417.915	+	723.851i	0.507795	+	0.879527i	0.999959	+	0.00902451i	$0.00287263\pi$
$823$	417.915	+	723.851i	0.507795	+	0.879527i	−0.492164	+	0.870502i	$0.663794\pi$
$824$	−716.304	−	413.559i	−0.869301	−	0.501891i
$825$	278.503	+	14.7808i	0.337579	+	0.0179161i
$826$	154.578			0.187141
$827$		−	85.0888i		−	0.102889i	−0.998676	−	0.0514443i	$-0.983618\pi$
$827$		−	85.0888i		−	0.102889i	0.998676	−	0.0514443i	$-0.0163825\pi$
$828$	613.981	−	272.388i	0.741523	−	0.328970i
$829$	−363.540	−	629.670i	−0.438528	−	0.759553i	0.559048	−	0.829135i	$-0.311167\pi$
$829$	−363.540	−	629.670i	−0.438528	−	0.759553i	−0.997576	+	0.0695820i	$0.977833\pi$
$830$	25.5807	+	14.7690i	0.0308201	+	0.0177940i
$831$	−32.3932	+	610.360i	−0.0389810	+	0.734488i
$832$	848.339	+	1010.22i	1.01964	+	1.21420i
$833$	−575.073	−	332.019i	−0.690364	−	0.398582i
$834$	2489.79	+	132.139i	2.98536	+	0.158440i
$835$	−335.559	+	581.205i	−0.401867	+	0.696053i
$836$	1428.36	+	824.661i	1.70856	+	0.986437i
$837$	169.401	+	137.737i	0.202391	+	0.164560i
$838$	610.215	−	1056.92i	0.728181	−	1.26125i
$839$			543.622i			0.647940i	0.946067	+	0.323970i	$0.105018\pi$
$839$			543.622i			0.647940i	−0.946067	+	0.323970i	$0.894982\pi$
$840$	−251.075	−	163.287i	−0.298899	−	0.194389i
$841$	−113.659	−	196.863i	−0.135147	−	0.234082i
$842$			1382.04i			1.64138i
$843$	59.6641	+	117.290i	0.0707759	+	0.139133i
$844$	−1191.19	−	2063.19i	−1.41136	−	2.44454i
$845$	436.758	−	521.326i	0.516874	−	0.616954i
$846$	−2713.30	−	288.815i	−3.20721	−	0.341389i
$847$	13.3451	+	23.1144i	0.0157557	+	0.0272897i
$848$	−67.4348	−	38.9335i	−0.0795222	−	0.0459121i
$849$	23.4185	−	441.256i	0.0275836	−	0.519737i
$850$	−232.434	+	402.587i	−0.273451	+	0.473632i
$851$	651.169	−	375.953i	0.765181	−	0.441778i
$852$	−1772.29	−	94.0595i	−2.08015	−	0.110398i
$853$	176.933	+	306.458i	0.207425	+	0.359270i	0.950903	−	0.309490i	$-0.100158\pi$
$853$	176.933	+	306.458i	0.207425	+	0.359270i	−0.743478	+	0.668761i	$0.766825\pi$
$854$	−141.409	−	81.6425i	−0.165584	−	0.0956002i
$855$	−771.094	+	342.090i	−0.901865	+	0.400105i
$856$	339.578	+	588.166i	0.396703	+	0.687110i
$857$	−901.625	+	520.553i	−1.05207	+	0.607413i	−0.923228	−	0.384252i	$-0.874459\pi$
$857$	−901.625	+	520.553i	−1.05207	+	0.607413i	−0.128842	+	0.991665i	$0.541126\pi$
$858$	1240.09	+	526.792i	1.44533	+	0.613977i
$859$	−433.002	+	749.982i	−0.504077	+	0.873087i	0.495912	+	0.868373i	$0.334834\pi$
$859$	−433.002	+	749.982i	−0.504077	+	0.873087i	−0.999989	+	0.00471431i	$0.998499\pi$
$860$			92.1631i			0.107166i
$861$	82.7291	+	4.39062i	0.0960849	+	0.00509944i
$862$	1334.33			1.54794
$863$		−	1037.10i		−	1.20174i	−0.799349	−	0.600868i	$-0.794822\pi$
$863$		−	1037.10i		−	1.20174i	0.799349	−	0.600868i	$-0.205178\pi$
$864$	−273.131	−	715.780i	−0.316124	−	0.828449i
$865$	132.508	−	229.510i	0.153188	−	0.265329i
$866$	−1294.15	+	747.178i	−1.49440	+	0.862792i
$867$	−76.6933	+	39.0132i	−0.0884582	+	0.0449979i
$868$	−151.892			−0.174991
$869$			1329.35i			1.52975i
$870$	−977.250	−	51.8649i	−1.12328	−	0.0596148i
$871$	−459.336	−	546.986i	−0.527366	−	0.627997i
$872$			1398.34i			1.60360i
$873$	−885.700	−	94.2778i	−1.01455	−	0.107993i
$874$	424.022	+	734.428i	0.485152	+	0.840307i
$875$		−	380.996i		−	0.435424i
$876$	1550.61	−	788.781i	1.77010	−	0.900435i
$877$	−305.670	−	529.435i	−0.348540	−	0.603689i	0.637450	−	0.770491i	$-0.279989\pi$
$877$	−305.670	−	529.435i	−0.348540	−	0.603689i	−0.985990	+	0.166802i	$0.946656\pi$
$878$	1171.57	−	676.408i	1.33436	−	0.770396i
$879$	−499.238	−	981.417i	−0.567961	−	1.11652i
$880$	−91.6411			−0.104138
$881$	1054.10	−	608.586i	1.19648	−	0.690791i	0.236715	−	0.971579i	$-0.423929\pi$
$881$	1054.10	−	608.586i	1.19648	−	0.690791i	0.959770	+	0.280789i	$0.0905960\pi$
$882$	−979.621	−	713.722i	−1.11068	−	0.809208i
$883$	−915.155			−1.03642			−0.518208	−	0.855255i	$-0.673401\pi$
$883$	−915.155			−1.03642			−0.518208	+	0.855255i	$0.673401\pi$
$884$	−1077.32	+	904.687i	−1.21869	+	1.02340i
$885$	−10.7926	+	203.358i	−0.0121951	+	0.229783i
$886$	1772.08			2.00009
$887$		−	182.716i		−	0.205993i	−0.994682	−	0.102997i	$-0.967157\pi$
$887$		−	182.716i		−	0.205993i	0.994682	−	0.102997i	$-0.0328431\pi$
$888$	814.173	+	1600.53i	0.916861	+	1.80239i
$889$	−268.295	−	464.701i	−0.301795	−	0.522723i
$890$	880.281	+	508.230i	0.989080	+	0.571045i
$891$	−634.013	−	573.918i	−0.711574	−	0.644128i
$892$	179.485			0.201216
$893$		−	2158.03i		−	2.41661i
$894$	−75.9839	+	1431.71i	−0.0849932	+	1.60146i
$895$	−977.326			−1.09198
$896$	530.052	+	306.026i	0.591576	+	0.341547i
$897$	261.072	+	346.653i	0.291050	+	0.386458i
$898$	−873.874	−	1513.59i	−0.973134	−	1.68552i
$899$	−173.482	+	100.160i	−0.192972	+	0.111412i
$900$	−312.989	+	429.593i	−0.347765	+	0.477326i
$901$	−291.240	+	504.443i	−0.323241	+	0.559870i
$902$	295.015	−	170.327i	0.327067	−	0.188832i
$903$	1.52041	−	28.6480i	0.00168374	−	0.0317254i
$904$	−529.910	−	917.831i	−0.586184	−	1.01530i
$905$	410.079	+	236.759i	0.453126	+	0.261612i
$906$	−2761.69	−	146.569i	−3.04823	−	0.161776i
$907$	−526.315	+	911.605i	−0.580281	+	1.00508i	0.415164	+	0.909746i	$0.363724\pi$
$907$	−526.315	+	911.605i	−0.580281	+	1.00508i	−0.995446	+	0.0953304i	$0.969609\pi$
$908$	1770.36	−	1022.12i	1.94974	−	1.12568i
$909$	−665.893	−	485.149i	−0.732555	−	0.533717i
$910$	163.797	−	450.571i	0.179997	−	0.495133i
$911$	−821.248	+	474.148i	−0.901479	+	0.520469i	−0.877680	−	0.479247i	$-0.840910\pi$
$911$	−821.248	+	474.148i	−0.901479	+	0.520469i	−0.0237996	+	0.999717i	$0.507576\pi$
$912$	−134.327	+	68.3311i	−0.147289	+	0.0749245i
$913$	−23.6830			−0.0259397
$914$	−1835.11	+	1059.50i	−2.00777	+	1.15919i
$915$	117.279	−	180.332i	0.128174	−	0.197085i
$916$	60.5749			0.0661298
$917$	583.845	+	337.083i	0.636690	+	0.367593i
$918$	1331.79	−	508.189i	1.45075	−	0.553583i
$919$	−155.014	+	268.492i	−0.168677	+	0.292156i	−0.937955	−	0.346758i	$-0.887283\pi$
$919$	−155.014	+	268.492i	−0.168677	+	0.292156i	0.769278	+	0.638914i	$0.220616\pi$
$920$	−343.519	−	198.331i	−0.373390	−	0.215577i
$921$	−6.22190	+	117.234i	−0.00675559	+	0.127290i
$922$	410.213	−	710.510i	0.444916	−	0.770618i
$923$	−199.551	−	1129.16i	−0.216198	−	1.22336i
$924$	594.120	+	31.5313i	0.642987	+	0.0341248i
$925$	−297.497	+	515.280i	−0.321619	+	0.557060i
$926$	−92.5837	+	53.4533i	−0.0999825	+	0.0577249i
$927$	−494.854	+	679.214i	−0.533824	+	0.732701i
$928$	702.919			0.757456
$929$		−	1252.17i		−	1.34787i	−0.738790	−	0.673935i	$-0.764603\pi$
$929$		−	1252.17i		−	1.34787i	0.738790	−	0.673935i	$-0.235397\pi$
$930$	16.9298	−	318.996i	0.0182041	−	0.343006i
$931$	479.294	−	830.162i	0.514817	−	0.891688i
$932$	607.966	−	351.009i	0.652324	−	0.376619i
$933$	−463.311	+	712.402i	−0.496582	+	0.763561i
$934$	−166.991	+	289.237i	−0.178791	+	0.309675i
$935$			685.517i			0.733173i
$936$	−859.759	+	578.741i	−0.918546	+	0.618313i
$937$	1387.64			1.48094			0.740471	−	0.672088i	$-0.234602\pi$
$937$	1387.64			1.48094			0.740471	+	0.672088i	$0.234602\pi$
$938$	−436.050	−	251.753i	−0.464872	−	0.268394i
$939$	−316.294	+	160.896i	−0.336841	+	0.171348i
$940$	1250.43	+	2165.80i	1.33024	+	2.30405i
$941$	−234.617	−	135.456i	−0.249328	−	0.143949i	0.370129	−	0.928980i	$-0.379314\pi$
$941$	−234.617	−	135.456i	−0.249328	−	0.143949i	−0.619456	+	0.785031i	$0.712647\pi$
$942$	−593.498	−	1166.72i	−0.630040	−	1.23855i
$943$	109.721			0.116353
$944$			36.3820i			0.0385403i
$945$	−191.971	+	236.104i	−0.203144	+	0.249845i
$946$	−58.9819	−	102.160i	−0.0623487	−	0.107991i
$947$	−532.423	−	307.394i	−0.562220	−	0.324598i	0.191816	−	0.981431i	$-0.438562\pi$
$947$	−532.423	−	307.394i	−0.562220	−	0.324598i	−0.754036	+	0.656833i	$0.771896\pi$
$948$	−2123.84	−	1381.24i	−2.24034	−	1.45700i
$949$	722.819	+	860.746i	0.761664	+	0.907003i
$950$	−581.165	−	335.536i	−0.611752	−	0.353195i
$951$	585.873	+	1151.73i	0.616060	+	1.21107i
$952$	−200.131	+	346.636i	−0.210221	+	0.364114i
$953$	1053.34	+	608.146i	1.10529	+	0.638139i	0.937605	−	0.347702i	$-0.113038\pi$
$953$	1053.34	+	608.146i	1.10529	+	0.638139i	0.167684	+	0.985841i	$0.446371\pi$
$954$	−626.062	+	859.304i	−0.656250	+	0.900738i
$955$	427.773	−	740.925i	0.447930	−	0.775838i
$956$			758.470i			0.793379i
$957$	699.357	−	355.757i	0.730781	−	0.371742i
$958$	930.599	+	1611.84i	0.971397	+	1.68251i
$959$		−	58.1873i		−	0.0606750i
$960$	−667.911	+	1027.00i	−0.695741	+	1.06979i
$961$	447.806	+	775.622i	0.465979	+	0.807099i
$962$	−2201.23	+	1848.50i	−2.28818	+	1.92152i
$963$	630.748	−	279.826i	0.654983	−	0.290578i
$964$	558.499	+	967.349i	0.579356	+	1.00347i
$965$	−217.038	−	125.307i	−0.224910	−	0.129852i
$966$	256.450	+	166.782i	0.265476	+	0.172652i
$967$	−18.8742	+	32.6911i	−0.0195183	+	0.0338067i	−0.875620	−	0.483001i	$-0.839547\pi$
$967$	−18.8742	+	32.6911i	−0.0195183	+	0.0338067i	0.856101	+	0.516808i	$0.172880\pi$
$968$	−73.1097	+	42.2099i	−0.0755265	+	0.0436053i
$969$	511.148	+	1004.83i	0.527500	+	1.03698i
$970$	651.605	+	1128.61i	0.671757	+	1.16352i
$971$	989.598	+	571.345i	1.01915	+	0.588408i	0.913859	−	0.406033i	$-0.133088\pi$
$971$	989.598	+	571.345i	1.01915	+	0.588408i	0.105295	+	0.994441i	$0.466421\pi$
$972$	1575.68	−	416.612i	1.62107	−	0.428613i
$973$	355.661	+	616.023i	0.365530	+	0.633117i
$974$	996.239	−	575.179i	1.02283	−	0.590533i
$975$	−316.068	−	134.266i	−0.324172	−	0.137709i
$976$	19.2157	−	33.2825i	0.0196882	−	0.0341009i
$977$		−	945.089i		−	0.967338i	−0.875251	−	0.483669i	$-0.839304\pi$
$977$		−	945.089i		−	0.967338i	0.875251	−	0.483669i	$-0.160696\pi$
$978$	−142.218	−	279.577i	−0.145417	−	0.285866i
$979$	−814.978			−0.832459
$980$			1110.87i			1.13354i
$981$	1412.76	+	150.380i	1.44012	+	0.153293i
$982$	−1089.45	+	1886.99i	−1.10942	+	1.92158i
$983$	−98.2105	+	56.7018i	−0.0999089	+	0.0576824i	−0.549122	−	0.835742i	$-0.685038\pi$
$983$	−98.2105	+	56.7018i	−0.0999089	+	0.0576824i	0.449213	+	0.893425i	$0.351704\pi$
$984$	−13.8873	+	261.668i	−0.0141131	+	0.265923i
$985$	−1156.82			−1.17443
$986$			1307.86i			1.32643i
$987$	−352.954	−	693.847i	−0.357603	−	0.702986i
$988$	−1305.98	−	1555.19i	−1.32185	−	1.57408i
$989$		−	37.9949i		−	0.0384175i
$990$	−132.440	+	1244.22i	−0.133778	+	1.25679i
$991$	548.175	+	949.467i	0.553153	+	0.958090i	0.998045	+	0.0625050i	$0.0199090\pi$
$991$	548.175	+	949.467i	0.553153	+	0.958090i	−0.444891	+	0.895585i	$0.646758\pi$
$992$			229.448i			0.231299i
$993$	22.2194	−	418.664i	0.0223761	−	0.421615i
$994$	−404.152	−	700.012i	−0.406592	−	0.704237i
$995$	743.259	−	429.121i	0.746994	−	0.431277i
$996$	24.6074	−	37.8372i	0.0247062	−	0.0379891i
$997$	876.332			0.878969			0.439484	−	0.898250i	$-0.355161\pi$
$997$	876.332			0.878969			0.439484	+	0.898250i	$0.355161\pi$
$998$	−1609.65	+	929.334i	−1.61288	+	0.931197i
$999$	1704.58	−	650.443i	1.70629	−	0.651094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.u.a.68.3	yes	52
3.2	odd	2		351.3.u.a.341.24		52
9.2	odd	6		117.3.k.a.29.3	✓	52
9.7	even	3		351.3.k.a.224.24		52
13.9	even	3		117.3.k.a.113.24	yes	52
39.35	odd	6		351.3.k.a.152.3		52
117.61	even	3		351.3.u.a.35.24		52
117.74	odd	6	inner	117.3.u.a.74.3	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.3	✓	52	9.2	odd	6
117.3.k.a.113.24	yes	52	13.9	even	3
117.3.u.a.68.3	yes	52	1.1	even	1	trivial
117.3.u.a.74.3	yes	52	117.74	odd	6	inner
351.3.k.a.152.3		52	39.35	odd	6
351.3.k.a.224.24		52	9.7	even	3
351.3.u.a.35.24		52	117.61	even	3
351.3.u.a.341.24		52	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+(-2.83378 - 1.63609i) q^{2} +(0.158993 - 2.99578i) q^{3} +(3.35355 + 5.80853i) q^{4} +(-3.48512 - 2.01214i) q^{5} +(-5.35191 + 8.22928i) q^{6} -2.80059 q^{7} -8.85812i q^{8} +(-8.94944 - 0.952618i) q^{9} +(6.58406 + 11.4039i) q^{10} +(-9.14343 - 5.27896i) q^{11} +(17.9343 - 9.12301i) q^{12} +(8.36009 + 9.95535i) q^{13} +(7.93627 + 4.58201i) q^{14} +(-6.58204 + 10.1208i) q^{15} +(-1.07844 + 1.86791i) q^{16} +(13.9728 + 8.06719i) q^{17} +(23.8022 + 17.3416i) q^{18} +(-11.6456 + 20.1708i) q^{19} -26.9912i q^{20} +(-0.445274 + 8.38996i) q^{21} +(17.2737 + 29.9189i) q^{22} +11.1273i q^{23} +(-26.5370 - 1.40838i) 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} +(-21.4537 - 12.3863i) q^{29} +(35.2105 - 17.9113i) q^{30} +(4.04316 - 7.00296i) q^{31} +(-24.5733 + 14.1874i) q^{32} +(-17.2684 + 26.5524i) q^{33} +(-26.3972 - 45.7213i) q^{34} +(9.76040 + 5.63517i) q^{35} +(-24.4791 - 55.1777i) q^{36} +(-33.7864 - 58.5198i) q^{37} +(66.0022 - 38.1064i) q^{38} +(31.1533 - 23.4622i) q^{39} +(-17.8238 + 30.8716i) q^{40} -9.86048i q^{41} +(14.9885 - 23.0468i) q^{42} -3.41456 q^{43} -70.8132i q^{44} +(29.2731 + 21.3275i) q^{45} +(18.2053 - 31.5325i) q^{46} +(-80.2410 + 46.3271i) q^{47} +(5.42438 + 3.52774i) q^{48} -41.1567 q^{49} +28.8122i q^{50} +(26.3891 - 40.5768i) q^{51} +(-29.7899 + 81.9456i) q^{52} +36.1018i q^{53} +(55.7360 - 68.5491i) q^{54} +(21.2440 + 36.7957i) q^{55} +24.8080i q^{56} +(58.5757 + 38.0947i) q^{57} +(40.5301 + 70.2002i) q^{58} +(14.6081 - 8.43398i) q^{59} +(-80.8599 - 4.29142i) q^{60} -17.8181 q^{61} +(-22.9149 + 13.2299i) q^{62} +(25.0637 + 2.66789i) q^{63} +101.475 q^{64} +(-9.10442 - 51.5172i) q^{65} +(92.3769 - 46.9913i) q^{66} -54.9439 q^{67} +108.215i q^{68} +(33.3351 + 1.76917i) q^{69} +(-18.4392 - 31.9377i) q^{70} +(-76.3871 - 44.1021i) q^{71} +(-8.43840 + 79.2753i) q^{72} +86.4607 q^{73} +221.110i q^{74} +(-23.5445 + 11.9769i) q^{75} -156.217 q^{76} +(25.6070 + 14.7842i) q^{77} +(-126.668 + 15.5174i) q^{78} +(-62.9550 - 109.041i) q^{79} +(7.51696 - 4.33992i) q^{80} +(79.1850 + 17.0508i) q^{81} +(-16.1326 + 27.9425i) q^{82} +(1.94262 - 1.12157i) q^{83} +(-50.2266 + 25.5498i) q^{84} +(-32.4646 - 56.2303i) q^{85} +(9.67611 + 5.58651i) q^{86} +(-40.5177 + 62.3013i) q^{87} +(-46.7617 + 80.9937i) 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} +(-20.3365 - 13.2259i) q^{93} +303.181 q^{94} +(81.1726 - 46.8650i) q^{95} +(38.5955 + 75.8721i) q^{96} +98.9671 q^{97} +(116.629 + 67.3359i) q^{98} +(76.7998 + 55.9540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{2} - q^{3} + 49 q^{4} - 6 q^{5} - 3 q^{6} + 2 q^{7} - 3 q^{9} - 6 q^{10} + 33 q^{11} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 28 q^{15} - 83 q^{16} + 34 q^{18} + 5 q^{19} - 91 q^{21} - 15 q^{22}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - 3 * q^2 - q^3 + 49 * q^4 - 6 * q^5 - 3 * q^6 + 2 * q^7 - 3 * q^9 - 6 * q^10 + 33 * q^11 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 28 * q^15 - 83 * q^16 + 34 * q^18 + 5 * q^19 - 91 * q^21 - 15 * q^22 + 36 * q^24 + 88 * q^25 + 132 * q^26 - 34 * q^27 - 22 * q^28 - 30 * q^29 + 31 * q^30 + 14 * q^31 - 63 * q^32 - 112 * q^33 - 6 * q^34 - 228 * q^35 + 47 * q^36 - 13 * q^37 - 192 * q^38 + 147 * q^39 + 72 * q^40 - 84 * q^42 + 62 * q^43 - 107 * q^45 + 6 * q^46 - 69 * q^47 - 58 * q^48 + 246 * q^49 + 235 * q^51 + 112 * q^52 + 444 * q^54 - 27 * q^55 + 189 * q^57 - 105 * q^58 - 435 * q^59 + 213 * q^60 - 16 * q^61 - 471 * q^62 - 170 * q^63 - 98 * q^64 - 435 * q^65 - 576 * q^66 + 68 * q^67 + 152 * q^69 - 57 * q^70 - 144 * q^71 + 513 * q^72 - 106 * q^73 + 98 * q^75 + 158 * q^76 + 282 * q^77 - 433 * q^78 - 25 * q^79 + 1050 * q^80 + 9 * q^81 + 81 * q^82 + 219 * q^83 - 172 * q^84 + 54 * q^85 - 24 * q^86 + 325 * q^87 - 15 * q^88 - 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 - 171 * q^93 - 606 * q^94 - 258 * q^95 - 439 * q^96 - 424 * q^97 + 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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