LMFDB - Embedded newform 177.3.g.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,3,Mod(10,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("177.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.g (of order $58$, degree $28$, 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:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$560$
Relative dimension:	$20$ over $\Q(\zeta_{58})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{58}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	177.10
Dual form			177.3.g.a.124.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.55013 - 1.41450i) q^{2} +(1.72190 + 0.187268i) q^{3} +(7.69866 + 7.29256i) q^{4} +(2.93856 - 3.45954i) q^{5} +(-5.84808 - 3.10045i) q^{6} +(-1.56353 - 0.940746i) q^{7} +(-10.5974 - 22.9059i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})$	\(q+(-3.55013 - 1.41450i) q^{2} +(1.72190 + 0.187268i) q^{3} +(7.69866 + 7.29256i) q^{4} +(2.93856 - 3.45954i) q^{5} +(-5.84808 - 3.10045i) q^{6} +(-1.56353 - 0.940746i) q^{7} +(-10.5974 - 22.9059i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-15.3258 + 8.12523i) q^{10} +(10.9074 + 0.591384i) q^{11} +(11.8906 + 13.9987i) q^{12} +(4.46929 + 20.3042i) q^{13} +(4.22006 + 5.55139i) q^{14} +(5.70776 - 5.40668i) q^{15} +(2.92532 + 53.9543i) q^{16} +(0.955471 - 0.574888i) q^{17} +(-9.48918 - 6.43382i) q^{18} +(9.43301 - 33.9746i) q^{19} +(47.8519 - 5.20420i) q^{20} +(-2.51607 - 1.91267i) q^{21} +(-37.8864 - 17.5281i) q^{22} +(-7.43857 + 5.04347i) q^{23} +(-13.9581 - 41.4262i) q^{24} +(0.711266 + 4.33853i) q^{25} +(12.8538 - 78.4045i) q^{26} +(4.92415 + 1.65914i) q^{27} +(-5.17665 - 18.6446i) q^{28} +(-9.55023 - 23.9693i) q^{29} +(-27.9111 + 11.1208i) q^{30} +(40.1078 - 11.1359i) q^{31} +(33.6984 - 100.013i) q^{32} +(18.6707 + 3.06091i) q^{33} +(-4.20523 + 0.689413i) q^{34} +(-7.84908 + 2.64466i) q^{35} +(17.8529 + 26.3311i) q^{36} +(4.90077 - 10.5928i) q^{37} +(-81.5457 + 107.272i) q^{38} +(3.89335 + 35.7987i) q^{39} +(-110.385 - 30.6483i) q^{40} +(39.0248 - 57.5573i) q^{41} +(6.22691 + 10.3492i) q^{42} +(38.3648 - 2.08008i) q^{43} +(79.6599 + 84.0960i) q^{44} +(10.8407 - 8.24086i) q^{45} +(33.5419 - 7.38314i) q^{46} +(-29.0723 + 24.6942i) q^{47} +(-5.06680 + 93.4516i) q^{48} +(-21.3924 - 40.3503i) q^{49} +(3.61177 - 16.4085i) q^{50} +(1.75288 - 0.810969i) q^{51} +(-113.662 + 188.908i) q^{52} +(-10.8157 + 20.4006i) q^{53} +(-15.1345 - 12.8554i) q^{54} +(34.0981 - 35.9969i) q^{55} +(-4.97927 + 45.7836i) q^{56} +(22.6050 - 56.7343i) q^{57} +98.6029i q^{58} +(-42.5400 + 40.8821i) q^{59} +83.3706 q^{60} +(24.4696 + 9.74958i) q^{61} +(-158.140 - 17.1987i) q^{62} +(-3.97423 - 3.76459i) q^{63} +(-121.181 + 142.665i) q^{64} +(83.3765 + 44.2034i) q^{65} +(-61.9540 - 37.2765i) q^{66} +(30.2240 + 65.3280i) q^{67} +(11.5482 + 2.54196i) q^{68} +(-13.7529 + 7.29134i) q^{69} +(31.6062 + 1.71364i) q^{70} +(48.4549 + 57.0455i) q^{71} +(-16.2767 - 73.9456i) q^{72} +(-62.7409 - 82.5342i) q^{73} +(-32.3820 + 30.6738i) q^{74} +(0.412261 + 7.60370i) q^{75} +(320.383 - 192.768i) q^{76} +(-16.4978 - 11.1858i) q^{77} +(36.8155 - 132.597i) q^{78} +(-53.6622 + 5.83612i) q^{79} +(195.253 + 148.428i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-219.959 + 149.136i) q^{82} +(-7.56720 - 22.4586i) q^{83} +(-5.42213 - 33.0735i) q^{84} +(0.818861 - 4.99483i) q^{85} +(-139.142 - 46.8825i) q^{86} +(-11.9558 - 43.0611i) q^{87} +(-102.044 - 256.112i) q^{88} +(-123.255 + 49.1094i) q^{89} +(-50.1426 + 13.9220i) q^{90} +(12.1132 - 35.9507i) q^{91} +(-94.0468 - 15.4182i) q^{92} +(71.1469 - 11.6639i) q^{93} +(138.141 - 46.5450i) q^{94} +(-89.8171 - 132.470i) q^{95} +(76.7544 - 165.902i) q^{96} +(-8.54672 + 11.2430i) q^{97} +(18.8702 + 173.509i) q^{98} +(31.5759 + 8.76700i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9}+O(q^{10}) $ 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9	$ 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9} + 24 q^{12} - 24 q^{15} + 8 q^{16} - 16 q^{17} + 60 q^{19} + 164 q^{20} - 40 q^{22} - 100 q^{25} + 156 q^{26} - 200 q^{28} + 60 q^{29} + 32 q^{35} + 120 q^{36} - 28 q^{41} - 1572 q^{46} - 638 q^{47} + 96 q^{48} - 1328 q^{49} - 1856 q^{50} + 24 q^{51} - 1392 q^{52} - 572 q^{53} - 522 q^{55} - 928 q^{56} - 24 q^{57} + 268 q^{59} + 72 q^{60} + 348 q^{61} + 472 q^{62} + 24 q^{63} + 2580 q^{64} + 1218 q^{65} + 120 q^{66} + 1044 q^{67} + 1936 q^{68} + 2784 q^{70} + 1416 q^{71} + 870 q^{73} + 1752 q^{74} - 240 q^{75} - 120 q^{76} + 468 q^{78} + 420 q^{79} - 376 q^{80} - 180 q^{81} - 168 q^{84} + 348 q^{85} - 232 q^{86} - 144 q^{87} + 212 q^{88} - 152 q^{94} - 788 q^{95} - 3306 q^{98}+O(q^{100}) $ 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9 + 24 * q^12 - 24 * q^15 + 8 * q^16 - 16 * q^17 + 60 * q^19 + 164 * q^20 - 40 * q^22 - 100 * q^25 + 156 * q^26 - 200 * q^28 + 60 * q^29 + 32 * q^35 + 120 * q^36 - 28 * q^41 - 1572 * q^46 - 638 * q^47 + 96 * q^48 - 1328 * q^49 - 1856 * q^50 + 24 * q^51 - 1392 * q^52 - 572 * q^53 - 522 * q^55 - 928 * q^56 - 24 * q^57 + 268 * q^59 + 72 * q^60 + 348 * q^61 + 472 * q^62 + 24 * q^63 + 2580 * q^64 + 1218 * q^65 + 120 * q^66 + 1044 * q^67 + 1936 * q^68 + 2784 * q^70 + 1416 * q^71 + 870 * q^73 + 1752 * q^74 - 240 * q^75 - 120 * q^76 + 468 * q^78 + 420 * q^79 - 376 * q^80 - 180 * q^81 - 168 * q^84 + 348 * q^85 - 232 * q^86 - 144 * q^87 + 212 * q^88 - 152 * q^94 - 788 * q^95 - 3306 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{7}{58}\right)$	$1$

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 $

$2$	−3.55013	−	1.41450i	−1.77507	−	0.707252i	−0.996855	−	0.0792508i	$-0.974747\pi$
$2$	−3.55013	−	1.41450i	−1.77507	−	0.707252i	−0.778213	−	0.628001i	$-0.783873\pi$
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$3$	1.72190	+	0.187268i	0.573966	+	0.0624225i
$4$	7.69866	+	7.29256i	1.92466	+	1.82314i
$5$	2.93856	−	3.45954i	0.587712	−	0.691908i	−0.385266	−	0.922806i	$-0.625890\pi$
$5$	2.93856	−	3.45954i	0.587712	−	0.691908i	0.972978	+	0.230897i	$0.0741662\pi$
$6$	−5.84808	−	3.10045i	−0.974680	−	0.516742i
$7$	−1.56353	−	0.940746i	−0.223362	−	0.134392i	0.399475	−	0.916744i	$-0.369192\pi$
$7$	−1.56353	−	0.940746i	−0.223362	−	0.134392i	−0.622837	+	0.782352i	$0.714020\pi$
$8$	−10.5974	−	22.9059i	−1.32468	−	2.86324i
$9$	2.92986	+	0.644911i	0.325540	+	0.0716568i
$10$	−15.3258	+	8.12523i	−1.53258	+	0.812523i
$11$	10.9074	+	0.591384i	0.991585	+	0.0537622i	0.542787	−	0.839871i	$-0.317369\pi$
$11$	10.9074	+	0.591384i	0.991585	+	0.0537622i	0.448799	+	0.893633i	$0.351852\pi$
$12$	11.8906	+	13.9987i	0.990887	+	1.16656i
$13$	4.46929	+	20.3042i	0.343792	+	1.56186i	0.758355	+	0.651842i	$0.226003\pi$
$13$	4.46929	+	20.3042i	0.343792	+	1.56186i	−0.414563	+	0.910021i	$0.636066\pi$
$14$	4.22006	+	5.55139i	0.301433	+	0.396528i
$15$	5.70776	−	5.40668i	0.380517	−	0.360445i
$16$	2.92532	+	53.9543i	0.182832	+	3.37215i
$17$	0.955471	−	0.574888i	0.0562042	−	0.0338169i	−0.487174	−	0.873305i	$-0.661972\pi$
$17$	0.955471	−	0.574888i	0.0562042	−	0.0338169i	0.543379	+	0.839488i	$0.317145\pi$
$18$	−9.48918	−	6.43382i	−0.527176	−	0.357434i
$19$	9.43301	−	33.9746i	0.496474	−	1.78814i	−0.111024	−	0.993818i	$-0.535413\pi$
$19$	9.43301	−	33.9746i	0.496474	−	1.78814i	0.607499	−	0.794321i	$-0.292173\pi$
$20$	47.8519	−	5.20420i	2.39259	−	0.260210i
$21$	−2.51607	−	1.91267i	−0.119813	−	0.0910793i
$22$	−37.8864	−	17.5281i	−1.72211	−	0.796732i
$23$	−7.43857	+	5.04347i	−0.323416	+	0.219281i	−0.712080	−	0.702098i	$-0.752247\pi$
$23$	−7.43857	+	5.04347i	−0.323416	+	0.219281i	0.388664	+	0.921379i	$0.372937\pi$
$24$	−13.9581	−	41.4262i	−0.581588	−	1.72609i
$25$	0.711266	+	4.33853i	0.0284506	+	0.173541i
$26$	12.8538	−	78.4045i	0.494376	−	3.01556i
$27$	4.92415	+	1.65914i	0.182376	+	0.0614496i
$28$	−5.17665	−	18.6446i	−0.184880	−	0.665879i
$29$	−9.55023	−	23.9693i	−0.329318	−	0.826526i	−0.996651	−	0.0817670i	$-0.973944\pi$
$29$	−9.55023	−	23.9693i	−0.329318	−	0.826526i	0.667333	−	0.744759i	$-0.267436\pi$
$30$	−27.9111	+	11.1208i	−0.930369	+	0.370693i
$31$	40.1078	−	11.1359i	1.29380	−	0.359222i	0.448629	−	0.893718i	$-0.351912\pi$
$31$	40.1078	−	11.1359i	1.29380	−	0.359222i	0.845171	+	0.534496i	$0.179499\pi$
$32$	33.6984	−	100.013i	1.05307	−	3.12541i
$33$	18.6707	+	3.06091i	0.565780	+	0.0927549i
$34$	−4.20523	+	0.689413i	−0.123683	+	0.0202768i
$35$	−7.84908	+	2.64466i	−0.224259	+	0.0755618i
$36$	17.8529	+	26.3311i	0.495915	+	0.731420i
$37$	4.90077	−	10.5928i	0.132453	−	0.286293i	−0.829989	−	0.557780i	$-0.811653\pi$
$37$	4.90077	−	10.5928i	0.132453	−	0.286293i	0.962442	+	0.271487i	$0.0875154\pi$
$38$	−81.5457	+	107.272i	−2.14594	+	2.82293i
$39$	3.89335	+	35.7987i	0.0998294	+	0.917916i
$40$	−110.385	−	30.6483i	−2.75963	−	0.766207i
$41$	39.0248	−	57.5573i	0.951826	−	1.40384i	0.0373025	−	0.999304i	$-0.488124\pi$
$41$	39.0248	−	57.5573i	0.951826	−	1.40384i	0.914523	−	0.404534i	$-0.132566\pi$
$42$	6.22691	+	10.3492i	0.148260	+	0.246410i
$43$	38.3648	−	2.08008i	0.892204	−	0.0483739i	0.397667	−	0.917530i	$-0.369820\pi$
$43$	38.3648	−	2.08008i	0.892204	−	0.0483739i	0.494538	+	0.869156i	$0.335337\pi$
$44$	79.6599	+	84.0960i	1.81045	+	1.91127i
$45$	10.8407	−	8.24086i	0.240904	−	0.183130i
$46$	33.5419	−	7.38314i	0.729172	−	0.160503i
$47$	−29.0723	+	24.6942i	−0.618560	+	0.525409i	−0.900968	−	0.433885i	$-0.857142\pi$
$47$	−29.0723	+	24.6942i	−0.618560	+	0.525409i	0.282409	+	0.959294i	$0.408867\pi$
$48$	−5.06680	+	93.4516i	−0.105558	+	1.94691i
$49$	−21.3924	−	40.3503i	−0.436579	−	0.823476i
$50$	3.61177	−	16.4085i	0.0722355	−	0.328169i
$51$	1.75288	−	0.810969i	0.0343702	−	0.0159014i
$52$	−113.662	+	188.908i	−2.18581	+	3.63284i
$53$	−10.8157	+	20.4006i	−0.204070	+	0.384917i	−0.964330	−	0.264702i	$-0.914726\pi$
$53$	−10.8157	+	20.4006i	−0.204070	+	0.384917i	0.760260	+	0.649618i	$0.225071\pi$
$54$	−15.1345	−	12.8554i	−0.280269	−	0.238063i
$55$	34.0981	−	35.9969i	0.619965	−	0.654489i
$56$	−4.97927	+	45.7836i	−0.0889155	+	0.817565i
$57$	22.6050	−	56.7343i	0.396579	−	0.995339i
$58$			98.6029i			1.70005i
$59$	−42.5400	+	40.8821i	−0.721018	+	0.692917i
$59$	−42.5400	+	40.8821i	−0.721018	+	0.692917i
$60$	83.3706			1.38951
$61$	24.4696	+	9.74958i	0.401141	+	0.159829i	0.561979	−	0.827152i	$-0.310040\pi$
$61$	24.4696	+	9.74958i	0.401141	+	0.159829i	−0.160838	+	0.986981i	$0.551420\pi$
$62$	−158.140	−	17.1987i	−2.55064	−	0.277399i
$63$	−3.97423	−	3.76459i	−0.0630831	−	0.0597555i
$64$	−121.181	+	142.665i	−1.89345	+	2.22914i
$65$	83.3765	+	44.2034i	1.28272	+	0.680053i
$66$	−61.9540	−	37.2765i	−0.938697	−	0.564795i
$67$	30.2240	+	65.3280i	0.451104	+	0.975045i	0.991068	+	0.133357i	$0.0425757\pi$
$67$	30.2240	+	65.3280i	0.451104	+	0.975045i	−0.539964	+	0.841688i	$0.681562\pi$
$68$	11.5482	+	2.54196i	0.169827	+	0.0373818i
$69$	−13.7529	+	7.29134i	−0.199318	+	0.105672i
$70$	31.6062	+	1.71364i	0.451517	+	0.0244805i
$71$	48.4549	+	57.0455i	0.682463	+	0.803457i	0.988924	−	0.148426i	$-0.0474207\pi$
$71$	48.4549	+	57.0455i	0.682463	+	0.803457i	−0.306461	+	0.951883i	$0.599145\pi$
$72$	−16.2767	−	73.9456i	−0.226065	−	1.02702i
$73$	−62.7409	−	82.5342i	−0.859464	−	1.13061i	−0.990265	−	0.139197i	$-0.955548\pi$
$73$	−62.7409	−	82.5342i	−0.859464	−	1.13061i	0.130801	−	0.991409i	$-0.458245\pi$
$74$	−32.3820	+	30.6738i	−0.437594	+	0.414511i
$75$	0.412261	+	7.60370i	0.00549681	+	0.101383i
$76$	320.383	−	192.768i	4.21557	−	2.53642i
$77$	−16.4978	−	11.1858i	−0.214257	−	0.145270i
$78$	36.8155	−	132.597i	0.471994	−	1.69997i
$79$	−53.6622	+	5.83612i	−0.679269	+	0.0738749i	−0.441248	−	0.897385i	$-0.645464\pi$
$79$	−53.6622	+	5.83612i	−0.679269	+	0.0738749i	−0.238021	+	0.971260i	$0.576499\pi$
$80$	195.253	+	148.428i	2.44067	+	1.85535i
$81$	8.16818	+	3.77900i	0.100842	+	0.0466543i
$82$	−219.959	+	149.136i	−2.68242	+	1.81873i
$83$	−7.56720	−	22.4586i	−0.0911710	−	0.270586i	0.892360	−	0.451324i	$-0.149048\pi$
$83$	−7.56720	−	22.4586i	−0.0911710	−	0.270586i	−0.983531	+	0.180738i	$0.942151\pi$
$84$	−5.42213	−	33.0735i	−0.0645492	−	0.393733i
$85$	0.818861	−	4.99483i	0.00963366	−	0.0587627i
$86$	−139.142	−	46.8825i	−1.61794	−	0.545146i
$87$	−11.9558	−	43.0611i	−0.137423	−	0.494955i
$88$	−102.044	−	256.112i	−1.15960	−	2.91037i
$89$	−123.255	+	49.1094i	−1.38489	+	0.551791i	−0.939192	−	0.343392i	$-0.888424\pi$
$89$	−123.255	+	49.1094i	−1.38489	+	0.551791i	−0.445698	+	0.895183i	$0.647045\pi$
$90$	−50.1426	+	13.9220i	−0.557140	+	0.154689i
$91$	12.1132	−	35.9507i	0.133112	−	0.395063i
$92$	−94.0468	−	15.4182i	−1.02225	−	0.167589i
$93$	71.1469	−	11.6639i	0.765020	−	0.125419i
$94$	138.141	−	46.5450i	1.46958	−	0.495160i
$95$	−89.8171	−	132.470i	−0.945444	−	1.39442i
$96$	76.7544	−	165.902i	0.799525	−	1.72815i
$97$	−8.54672	+	11.2430i	−0.0881105	+	0.115907i	−0.838036	−	0.545615i	$-0.816296\pi$
$97$	−8.54672	+	11.2430i	−0.0881105	+	0.115907i	0.749926	+	0.661522i	$0.230089\pi$
$98$	18.8702	+	173.509i	0.192553	+	1.77050i
$99$	31.5759	+	8.76700i	0.318948	+	0.0885556i
$100$	−26.1632	+	38.5878i	−0.261632	+	0.385878i
$101$	−13.8044	−	22.9431i	−0.136677	−	0.227159i	0.780958	−	0.624584i	$-0.214731\pi$
$101$	−13.8044	−	22.9431i	−0.136677	−	0.227159i	−0.917635	+	0.397425i	$0.869904\pi$
$102$	−7.37008	+	0.399594i	−0.0722557	+	0.00391759i
$103$	114.792	+	121.185i	1.11449	+	1.17655i	0.982687	+	0.185275i	$0.0593175\pi$
$103$	114.792	+	121.185i	1.11449	+	1.17655i	0.131802	+	0.991276i	$0.457924\pi$
$104$	417.724	−	317.545i	4.01658	−	3.05332i
$105$	−14.0106	+	3.08396i	−0.133434	+	0.0293710i
$106$	67.2539	−	57.1260i	0.634471	−	0.538924i
$107$	−5.06462	+	93.4113i	−0.0473329	+	0.873003i	0.874407	+	0.485194i	$0.161251\pi$
$107$	−5.06462	+	93.4113i	−0.0473329	+	0.873003i	−0.921740	+	0.387809i	$0.873232\pi$
$108$	25.8100	+	48.6828i	0.238981	+	0.450767i
$109$	−33.4255	+	151.853i	−0.306656	+	1.39315i	0.531195	+	0.847250i	$0.321743\pi$
$109$	−33.4255	+	151.853i	−0.306656	+	1.39315i	−0.837850	+	0.545900i	$0.816188\pi$
$110$	−171.970	+	79.5620i	−1.56337	+	0.723291i
$111$	10.4223	−	17.3220i	0.0938947	−	0.156054i
$112$	46.1835	−	87.1113i	0.412352	−	0.777779i
$113$	−83.1268	−	70.6085i	−0.735635	−	0.624854i	0.199191	−	0.979961i	$-0.436169\pi$
$113$	−83.1268	−	70.6085i	−0.735635	−	0.624854i	−0.934826	+	0.355107i	$0.884445\pi$
$114$	−160.502	+	169.440i	−1.40791	+	1.48631i
$115$	−4.41058	+	40.5546i	−0.0383528	+	0.352648i
$116$	101.273	−	254.177i	0.873045	−	2.19118i
$117$			62.3708i			0.533084i
$118$	208.851	−	84.9639i	1.76992	−	0.720033i
$119$	−2.03473			−0.0170986
$120$	−184.332	−	73.4448i	−1.53610	−	0.612040i
$121$	−1.66824	−	0.181432i	−0.0137871	−	0.00149944i
$122$	−73.0796	−	69.2246i	−0.599013	−	0.567415i
$123$	77.9754	−	91.7998i	0.633946	−	0.746339i
$124$	389.985	+	206.757i	3.14504	+	1.66740i
$125$	114.334	+	68.7923i	0.914670	+	0.550339i
$126$	8.78403	+	18.9864i	0.0697146	+	0.150686i
$127$	−82.8775	−	18.2427i	−0.652579	−	0.143643i	−0.123672	−	0.992323i	$-0.539467\pi$
$127$	−82.8775	−	18.2427i	−0.652579	−	0.143643i	−0.528907	+	0.848680i	$0.677398\pi$
$128$	259.031	−	137.330i	2.02368	−	1.07289i
$129$	66.4498	+	3.60280i	0.515114	+	0.0279287i
$130$	−233.472	−	274.864i	−1.79594	−	2.11434i
$131$	40.0242	+	181.832i	0.305528	+	1.38803i	0.839883	+	0.542768i	$0.182624\pi$
$131$	40.0242	+	181.832i	0.305528	+	1.38803i	−0.534354	+	0.845260i	$0.679445\pi$
$132$	121.418	+	159.722i	0.919832	+	1.21002i
$133$	−46.7103	+	44.2463i	−0.351205	+	0.332679i
$134$	−14.8925	−	274.675i	−0.111138	−	2.04981i
$135$	20.2098	−	12.1598i	0.149702	−	0.0900727i
$136$	−23.2939	−	15.7936i	−0.171278	−	0.116130i
$137$	−18.8605	+	67.9294i	−0.137668	+	0.495835i	−0.999944	−	0.0106039i	$-0.996625\pi$
$137$	−18.8605	+	67.9294i	−0.137668	+	0.495835i	0.862276	+	0.506439i	$0.169038\pi$
$138$	59.1384	−	6.43169i	0.428539	−	0.0466064i
$139$	−131.590	−	100.032i	−0.946689	−	0.719654i	0.0132357	−	0.999912i	$-0.495787\pi$
$139$	−131.590	−	100.032i	−0.946689	−	0.719654i	−0.959925	+	0.280258i	$0.909580\pi$
$140$	−79.7137	−	36.8795i	−0.569384	−	0.263425i
$141$	−54.6840	+	37.0766i	−0.387830	+	0.262955i
$142$	−91.3303	−	271.059i	−0.643171	−	1.90886i
$143$	36.7410	+	224.110i	0.256930	+	1.56720i
$144$	−26.2250	+	159.965i	−0.182118	+	1.11087i
$145$	−110.987	−	37.3957i	−0.765424	−	0.257901i
$146$	105.994	+	381.755i	0.725984	+	2.61476i
$147$	−29.2792	−	73.4852i	−0.199178	−	0.499899i
$148$	114.978	−	45.8115i	0.776879	−	0.309537i
$149$	−70.2751	+	19.5118i	−0.471645	+	0.130952i	−0.495215	−	0.868771i	$-0.664911\pi$
$149$	−70.2751	+	19.5118i	−0.471645	+	0.130952i	0.0235697	+	0.999722i	$0.492497\pi$
$150$	9.29188	−	27.5773i	0.0619459	−	0.183849i
$151$	−52.8013	−	8.65633i	−0.349677	−	0.0573267i	−0.0156161	−	0.999878i	$-0.504971\pi$
$151$	−52.8013	−	8.65633i	−0.349677	−	0.0573267i	−0.334061	+	0.942551i	$0.608419\pi$
$152$	−878.186	+	143.971i	−5.77754	+	0.947180i
$153$	3.17015	−	1.06815i	0.0207199	−	0.00698136i
$154$	42.7470	+	63.0472i	0.277578	+	0.409397i
$155$	79.3341	−	171.478i	0.511833	−	1.10631i
$156$	−231.091	+	303.995i	−1.48135	+	1.94868i
$157$	−28.4125	−	261.249i	−0.180972	−	1.66401i	−0.634619	−	0.772825i	$-0.718843\pi$
$157$	−28.4125	−	261.249i	−0.180972	−	1.66401i	0.453648	−	0.891181i	$-0.350122\pi$
$158$	198.763	+	55.1864i	1.25800	+	0.349281i
$159$	−22.4439	+	33.1023i	−0.141157	+	0.208190i
$160$	−246.975	−	410.476i	−1.54359	−	2.56547i
$161$	16.3751	−	0.887830i	0.101708	−	0.00551447i
$162$	−23.6527	−	24.9699i	−0.146004	−	0.154135i
$163$	−73.4348	+	55.8237i	−0.450520	+	0.342477i	−0.805702	−	0.592321i	$-0.798212\pi$
$163$	−73.4348	+	55.8237i	−0.450520	+	0.342477i	0.355182	+	0.934797i	$0.384419\pi$
$164$	720.179	−	158.523i	4.39134	−	0.966606i
$165$	65.4544	−	55.5975i	0.396694	−	0.336955i
$166$	−4.90324	+	90.4350i	−0.0295376	+	0.544789i
$167$	−117.882	−	222.349i	−0.705881	−	1.33143i	−0.933815	−	0.357756i	$-0.883542\pi$
$167$	−117.882	−	222.349i	−0.705881	−	1.33143i	0.227934	−	0.973677i	$-0.426803\pi$
$168$	−17.1476	+	77.9022i	−0.102069	+	0.463704i
$169$	−238.906	+	110.530i	−1.41365	+	0.654022i
$170$	−9.97227	+	16.5740i	−0.0586604	+	0.0974944i
$171$	49.5480	−	93.4575i	0.289755	−	0.546535i
$172$	310.526	+	263.764i	1.80539	+	1.53351i
$173$	−164.825	+	174.004i	−0.952747	+	1.00580i	0.0472288	+	0.998884i	$0.484961\pi$
$173$	−164.825	+	174.004i	−0.952747	+	1.00580i	−0.999976	+	0.00691899i	$0.997798\pi$
$174$	−18.4651	+	169.784i	−0.106121	+	0.975771i
$175$	2.96937	−	7.45255i	0.0169678	−	0.0425860i
$176$			590.233i			3.35360i
$177$	−80.9055	+	62.4284i	−0.457093	+	0.352703i
$178$	507.038			2.84853
$179$	127.068	+	50.6284i	0.709876	+	0.282840i	0.696994	−	0.717077i	$-0.254520\pi$
$179$	127.068	+	50.6284i	0.709876	+	0.282840i	0.0128814	+	0.999917i	$0.495900\pi$
$180$	143.556	+	15.6126i	0.797531	+	0.0867367i
$181$	190.876	+	180.807i	1.05456	+	0.998934i	1.00000		0.000423599i	$0.000134836\pi$
$181$	190.876	+	180.807i	1.05456	+	0.998934i	0.0545619	+	0.998510i	$0.482624\pi$
$182$	−93.8560	+	110.496i	−0.515692	+	0.607120i
$183$	40.3084	+	21.3701i	0.220264	+	0.116777i
$184$	194.355	+	116.940i	1.05628	+	0.635541i
$185$	−22.2451	−	48.0821i	−0.120244	−	0.259903i
$186$	−269.080	−	59.2289i	−1.44667	−	0.318435i
$187$	10.7617	−	5.70550i	0.0575493	−	0.0305107i
$188$	−403.902	−	21.8989i	−2.14841	−	0.116484i
$189$	−6.13824	−	7.22649i	−0.0324774	−	0.0382354i
$190$	131.483	+	597.334i	0.692017	+	3.14386i
$191$	−3.20287	−	4.21330i	−0.0167689	−	0.0220592i	0.787632	−	0.616146i	$-0.211307\pi$
$191$	−3.20287	−	4.21330i	−0.0167689	−	0.0220592i	−0.804401	+	0.594087i	$0.797514\pi$
$192$	−235.377	+	222.961i	−1.22592	+	1.16125i
$193$	−7.84519	−	144.696i	−0.0406487	−	0.749720i	−0.945824	−	0.324681i	$-0.894743\pi$
$193$	−7.84519	−	144.696i	−0.0406487	−	0.749720i	0.905175	−	0.425039i	$-0.139740\pi$
$194$	46.2453	−	27.8249i	0.238378	−	0.143427i
$195$	135.288	+	91.7275i	0.693784	+	0.470397i
$196$	129.564	−	466.648i	0.661042	−	2.38086i
$197$	120.746	−	13.1320i	0.612926	−	0.0666597i	0.203610	−	0.979052i	$-0.434733\pi$
$197$	120.746	−	13.1320i	0.612926	−	0.0666597i	0.409317	+	0.912392i	$0.365767\pi$
$198$	−99.6977	−	75.7882i	−0.503524	−	0.382769i
$199$	120.780	+	55.8788i	0.606935	+	0.280798i	0.699188	−	0.714937i	$-0.253545\pi$
$199$	120.780	+	55.8788i	0.606935	+	0.280798i	−0.0922533	+	0.995736i	$0.529407\pi$
$200$	91.8405	−	62.2694i	0.459203	−	0.311347i
$201$	39.8087	+	118.148i	0.198053	+	0.587802i
$202$	16.5544	+	100.977i	0.0819524	+	0.499888i
$203$	−7.61690	+	46.4610i	−0.0375217	+	0.228872i
$204$	19.4089	+	6.53961i	0.0951415	+	0.0320569i
$205$	−84.4451	−	304.144i	−0.411927	−	1.48363i
$206$	−236.112	−	592.596i	−1.14617	−	2.87668i
$207$	−25.0466	+	9.97947i	−0.120998	+	0.0482100i
$208$	−1082.43	+	300.534i	−5.20397	+	1.44488i
$209$	122.982	−	364.998i	0.588431	−	1.74640i
$210$	54.1017	+	8.86952i	0.257627	+	0.0422358i
$211$	−334.942	+	54.9110i	−1.58740	+	0.260242i	−0.889837	−	0.456278i	$-0.849182\pi$
$211$	−334.942	+	54.9110i	−1.58740	+	0.260242i	−0.697567	+	0.716520i	$0.745734\pi$
$212$	−232.039	+	78.1830i	−1.09452	+	0.368788i
$213$	72.7515	+	107.300i	0.341556	+	0.503758i
$214$	150.111	−	324.459i	0.701452	−	1.51616i
$215$	105.541	−	138.837i	0.490889	−	0.645753i
$216$	−14.1791	−	130.375i	−0.0656441	−	0.603587i
$217$	−73.1858	−	20.3199i	−0.337262	−	0.0936403i
$218$	333.462	−	491.820i	1.52964	−	2.25605i
$219$	−92.5773	−	153.865i	−0.422728	−	0.702579i
$220$	525.019	−	28.4657i	2.38645	−	0.129390i
$221$	15.9429	+	16.8307i	0.0721399	+	0.0761572i
$222$	−61.5027	+	46.7531i	−0.277039	+	0.210600i
$223$	133.280	−	29.3372i	0.597669	−	0.131557i	0.0941751	−	0.995556i	$-0.469979\pi$
$223$	133.280	−	29.3372i	0.597669	−	0.131557i	0.503494	+	0.863999i	$0.332048\pi$
$224$	−146.776	+	124.672i	−0.655248	+	0.556573i
$225$	−0.714057	+	13.1700i	−0.00317358	+	0.0585333i
$226$	195.235	+	368.253i	0.863873	+	1.62944i
$227$	−49.4498	+	224.653i	−0.217841	+	0.989660i	0.733060	+	0.680164i	$0.238091\pi$
$227$	−49.4498	+	224.653i	−0.217841	+	0.989660i	−0.950901	+	0.309496i	$0.899840\pi$
$228$	587.767	−	271.930i	2.57792	−	1.19267i
$229$	99.1061	−	164.716i	0.432778	−	0.719282i	−0.561340	−	0.827585i	$-0.689714\pi$
$229$	99.1061	−	164.716i	0.432778	−	0.719282i	0.994118	+	0.108303i	$0.0345417\pi$
$230$	73.0227	−	137.735i	0.317490	−	0.598850i
$231$	−26.3127	−	22.3503i	−0.113908	−	0.0967543i
$232$	−447.831	+	472.769i	−1.93030	+	2.03780i
$233$	41.6292	−	382.774i	0.178666	−	1.64281i	−0.470673	−	0.882308i	$-0.655989\pi$
$233$	41.6292	−	382.774i	0.178666	−	1.64281i	0.649339	−	0.760499i	$-0.275046\pi$
$234$	88.2237	−	221.425i	0.377024	−	0.946260i
$235$			173.142i			0.736776i
$236$	−625.636	+	4.51159i	−2.65100	+	0.0191169i
$237$	−93.4938			−0.394489
$238$	7.22357	+	2.87813i	0.0303511	+	0.0120930i
$239$	374.049	+	40.6803i	1.56506	+	0.170210i	0.849213	−	0.528050i	$-0.177077\pi$
$239$	374.049	+	40.6803i	1.56506	+	0.170210i	0.715844	+	0.698260i	$0.246042\pi$
$240$	308.411	+	292.142i	1.28504	+	1.21726i
$241$	−198.276	+	233.428i	−0.822721	+	0.968582i	−0.999878	−	0.0156005i	$-0.995034\pi$
$241$	−198.276	+	233.428i	−0.822721	+	0.968582i	0.177157	+	0.984183i	$0.443310\pi$
$242$	5.66583	+	3.00383i	0.0234125	+	0.0124125i
$243$	13.3571	+	8.03669i	0.0549674	+	0.0330728i
$244$	117.284	+	253.505i	0.480671	+	1.03895i
$245$	−202.456	−	44.5640i	−0.826352	−	0.181894i
$246$	−406.674	+	215.605i	−1.65315	+	0.876443i
$247$	731.987	+	39.6872i	2.96351	+	0.160677i
$248$	−680.116	−	800.695i	−2.74240	−	3.22861i
$249$	−8.82416	−	40.0886i	−0.0354384	−	0.160998i
$250$	−308.593	−	405.947i	−1.23437	−	1.62379i
$251$	201.928	−	191.276i	0.804494	−	0.762057i	−0.170246	−	0.985402i	$-0.554456\pi$
$251$	201.928	−	191.276i	0.804494	−	0.762057i	0.974740	+	0.223344i	$0.0716975\pi$
$252$	−3.14275	−	57.9646i	−0.0124712	−	0.230018i
$253$	−84.1183	+	50.6123i	−0.332484	+	0.200049i
$254$	268.422	+	181.995i	1.05678	+	0.716514i
$255$	2.34536	−	8.44724i	0.00919751	−	0.0331264i
$256$	−369.500	+	40.1856i	−1.44336	+	0.156975i
$257$	30.5342	+	23.2115i	0.118810	+	0.0903170i	0.662892	−	0.748715i	$-0.269329\pi$
$257$	30.5342	+	23.2115i	0.118810	+	0.0903170i	−0.544082	+	0.839032i	$0.683122\pi$
$258$	−230.809	−	106.784i	−0.894610	−	0.413891i
$259$	−17.6277	+	11.9519i	−0.0680605	+	0.0461462i
$260$	319.531	+	948.335i	1.22897	+	3.64744i
$261$	−12.5228	−	76.3857i	−0.0479800	−	0.292665i
$262$	115.110	−	702.142i	0.439352	−	2.67993i
$263$	219.537	+	73.9705i	0.834740	+	0.281257i	0.704036	−	0.710165i	$-0.251379\pi$
$263$	219.537	+	73.9705i	0.834740	+	0.281257i	0.130705	+	0.991421i	$0.458276\pi$
$264$	−127.749	−	460.109i	−0.483896	−	1.74284i
$265$	38.7940	+	97.3657i	0.146393	+	0.367418i
$266$	228.414	−	91.0086i	0.858701	−	0.342138i
$267$	−221.430	+	61.4796i	−0.829324	+	0.230261i
$268$	−243.724	+	723.348i	−0.909419	+	2.69906i
$269$	−187.130	−	30.6784i	−0.695651	−	0.114046i	−0.196426	−	0.980519i	$-0.562934\pi$
$269$	−187.130	−	30.6784i	−0.695651	−	0.114046i	−0.499225	+	0.866472i	$0.666382\pi$
$270$	−88.9475	+	14.5822i	−0.329435	+	0.0540082i
$271$	−132.945	+	44.7944i	−0.490573	+	0.165293i	−0.553706	−	0.832712i	$-0.686787\pi$
$271$	−132.945	+	44.7944i	−0.490573	+	0.165293i	0.0631339	+	0.998005i	$0.479890\pi$
$272$	33.8127	+	49.8701i	0.124312	+	0.183346i
$273$	27.5901	−	59.6351i	0.101063	−	0.218443i
$274$	163.044	−	214.480i	0.595050	−	0.782775i
$275$	5.19235	+	47.7429i	0.0188813	+	0.173610i
$276$	−159.052	−	44.1605i	−0.576274	−	0.160002i
$277$	−37.8841	+	55.8749i	−0.136766	+	0.201714i	−0.889904	−	0.456148i	$-0.849229\pi$
$277$	−37.8841	+	55.8749i	−0.136766	+	0.201714i	0.753138	+	0.657862i	$0.228539\pi$
$278$	325.666	+	541.261i	1.17146	+	1.94698i
$279$	124.692	−	6.76060i	0.446924	−	0.0242315i
$280$	143.758	+	151.764i	0.513423	+	0.542014i
$281$	−213.801	+	162.527i	−0.760856	+	0.578388i	−0.912032	−	0.410119i	$-0.865487\pi$
$281$	−213.801	+	162.527i	−0.760856	+	0.578388i	0.151176	+	0.988507i	$0.451694\pi$
$282$	246.580	−	54.2765i	0.874399	−	0.192470i
$283$	−102.203	+	86.8118i	−0.361140	+	0.306755i	−0.809525	−	0.587085i	$-0.800275\pi$
$283$	−102.203	+	86.8118i	−0.361140	+	0.306755i	0.448385	+	0.893841i	$0.351999\pi$
$284$	−42.9699	+	792.533i	−0.151302	+	2.79061i
$285$	−129.848	−	244.920i	−0.455609	−	0.859369i
$286$	186.569	−	847.591i	0.652339	−	2.96360i
$287$	−115.163	+	53.2803i	−0.401266	+	0.185645i
$288$	163.231	−	271.293i	0.566775	−	0.941988i
$289$	−134.788	+	254.236i	−0.466393	+	0.879711i
$290$	341.121	+	289.751i	1.17628	+	0.999140i
$291$	−16.8220	+	17.7588i	−0.0578076	+	0.0610268i
$292$	118.865	−	1092.94i	0.407071	−	3.74296i
$293$	−18.1682	+	45.5988i	−0.0620076	+	0.155627i	−0.956716	−	0.291024i	$-0.906004\pi$
$293$	−18.1682	+	45.5988i	−0.0620076	+	0.155627i	0.894708	+	0.446651i	$0.147383\pi$
$294$			302.298i			1.02822i
$295$	16.4268	+	267.303i	0.0556840	+	0.906113i
$296$	−294.574			−0.995183
$297$	52.7287	+	21.0090i	0.177538	+	0.0707375i
$298$	277.086	+	30.1349i	0.929817	+	0.101124i
$299$	−135.649	−	128.493i	−0.453675	−	0.429744i
$300$	−52.2766	+	61.5447i	−0.174255	+	0.205149i
$301$	−61.9414	−	32.8392i	−0.205785	−	0.109100i
$302$	175.207	+	105.419i	0.580157	+	0.349069i
$303$	−19.4732	−	42.0907i	−0.0642681	−	0.138913i
$304$	1860.67	+	409.565i	6.12063	+	1.34725i
$305$	105.634	−	56.0038i	0.346342	−	0.183619i
$306$	−12.7654	−	0.692117i	−0.0417168	−	0.00226182i
$307$	−224.821	−	264.680i	−0.732316	−	0.862149i	0.262385	−	0.964963i	$-0.415491\pi$
$307$	−224.821	−	264.680i	−0.732316	−	0.862149i	−0.994701	+	0.102814i	$0.967215\pi$
$308$	−45.4379	−	206.426i	−0.147526	−	0.670215i
$309$	174.967	+	230.165i	0.566235	+	0.744869i
$310$	−524.203	+	496.551i	−1.69098	+	1.60178i
$311$	6.13735	+	113.197i	0.0197343	+	0.363977i	0.991676	+	0.128756i	$0.0410985\pi$
$311$	6.13735	+	113.197i	0.0197343	+	0.363977i	−0.971942	+	0.235221i	$0.924419\pi$
$312$	778.744	−	468.555i	2.49597	−	1.50178i
$313$	−493.904	−	334.875i	−1.57797	−	1.06989i	−0.958587	−	0.284799i	$-0.908073\pi$
$313$	−493.904	−	334.875i	−1.57797	−	1.06989i	−0.619381	−	0.785090i	$-0.712617\pi$
$314$	−268.669	+	967.659i	−0.855634	+	3.08172i
$315$	−24.7023	+	2.68654i	−0.0784199	+	0.00852868i
$316$	−455.687	−	346.405i	−1.44205	−	1.09622i
$317$	−337.436	−	156.115i	−1.06447	−	0.492475i	−0.192125	−	0.981370i	$-0.561538\pi$
$317$	−337.436	−	156.115i	−1.06447	−	0.492475i	−0.872342	+	0.488896i	$0.837400\pi$
$318$	126.502	−	85.7706i	0.397805	−	0.269719i
$319$	−89.9934	−	267.091i	−0.282111	−	0.837276i
$320$	137.458	+	838.458i	0.429557	+	2.62018i
$321$	−26.2137	+	159.896i	−0.0816625	+	0.498119i
$322$	−59.3895	−	20.0107i	−0.184439	−	0.0621449i
$323$	−10.5186	−	37.8847i	−0.0325654	−	0.117290i
$324$	35.3254	+	88.6601i	0.109029	+	0.273642i
$325$	−84.9116	+	33.8319i	−0.261266	+	0.104098i
$326$	339.666	−	94.3078i	1.04192	−	0.289288i
$327$	−85.9924	+	255.216i	−0.262974	+	0.780478i
$328$	−1731.97	−	283.942i	−5.28039	−	0.865676i
$329$	68.6865	−	11.2606i	0.208773	−	0.0342267i
$330$	−311.015	+	104.793i	−0.942470	+	0.317555i
$331$	316.804	+	467.250i	0.957111	+	1.41163i	0.910866	+	0.412702i	$0.135415\pi$
$331$	316.804	+	467.250i	0.957111	+	1.41163i	0.0462445	+	0.998930i	$0.485275\pi$
$332$	105.524	−	228.086i	0.317842	−	0.687005i
$333$	21.1900	−	27.8750i	0.0636337	−	0.0837087i
$334$	103.984	+	956.114i	0.311328	+	2.86262i
$335$	314.820	+	87.4093i	0.939761	+	0.260923i
$336$	95.8363	−	141.348i	0.285227	−	0.420679i
$337$	45.2053	+	75.1318i	0.134140	+	0.222943i	0.916646	−	0.399701i	$-0.130886\pi$
$337$	45.2053	+	75.1318i	0.134140	+	0.222943i	−0.782505	+	0.622644i	$0.786058\pi$
$338$	1004.49	−	54.4621i	2.97187	−	0.161130i
$339$	−129.913	−	137.148i	−0.383224	−	0.404565i
$340$	42.7292	−	32.4819i	0.125674	−	0.0955350i
$341$	444.059	−	97.7447i	1.30223	−	0.286641i
$342$	−308.098	+	261.701i	−0.900872	+	0.765207i
$343$	−9.35237	+	172.494i	−0.0272664	+	0.502899i
$344$	−454.214	−	856.738i	−1.32039	−	2.49052i
$345$	−15.1891	+	69.0049i	−0.0440264	+	0.200014i
$346$	831.281	−	384.592i	2.40255	−	1.11154i
$347$	−74.3524	+	123.575i	−0.214272	+	0.356123i	−0.945288	−	0.326238i	$-0.894219\pi$
$347$	−74.3524	+	123.575i	−0.214272	+	0.356123i	0.731016	+	0.682361i	$0.239047\pi$
$348$	221.981	−	418.701i	0.637877	−	1.20316i
$349$	−40.7267	−	34.5936i	−0.116696	−	0.0991221i	0.587139	−	0.809486i	$-0.300254\pi$
$349$	−40.7267	−	34.5936i	−0.116696	−	0.0991221i	−0.703834	+	0.710364i	$0.748530\pi$
$350$	−21.0833	+	22.2574i	−0.0602380	+	0.0635925i
$351$	−11.6800	+	107.396i	−0.0332765	+	0.305972i
$352$	426.709	−	1070.96i	1.21224	−	3.04250i
$353$			106.660i			0.302154i	0.988522	+	0.151077i	$0.0482742\pi$
$353$			106.660i			0.302154i	−0.988522	+	0.151077i	$0.951726\pi$
$354$	375.531	−	107.188i	1.06082	−	0.302791i
$355$	339.739			0.957010
$356$	−1307.03	−	520.769i	−3.67144	−	1.46284i
$357$	−3.50360	−	0.381039i	−0.00981400	−	0.00106734i
$358$	−379.494	−	359.475i	−1.06004	−	1.00412i
$359$	116.237	−	136.845i	0.323781	−	0.381184i	−0.576057	−	0.817410i	$-0.695409\pi$
$359$	116.237	−	136.845i	0.323781	−	0.381184i	0.899837	+	0.436226i	$0.143685\pi$
$360$	−303.648	−	160.984i	−0.843466	−	0.447177i
$361$	−755.968	−	454.851i	−2.09410	−	1.25998i
$362$	−421.882	−	911.884i	−1.16542	−	2.51902i
$363$	−2.83856	−	0.624814i	−0.00781972	−	0.00172125i
$364$	355.428	−	188.436i	0.976451	−	0.517682i
$365$	−469.898	−	25.4771i	−1.28739	−	0.0698004i
$366$	−112.872	−	132.883i	−0.308393	−	0.363069i
$367$	−20.5090	−	93.1734i	−0.0558829	−	0.253879i	0.940394	−	0.340086i	$-0.110456\pi$
$367$	−20.5090	−	93.1734i	−0.0558829	−	0.253879i	−0.996277	+	0.0862076i	$0.972525\pi$
$368$	−293.877	−	386.589i	−0.798580	−	1.05051i
$369$	151.457	−	143.467i	0.410452	−	0.388801i
$370$	10.9610	+	202.164i	0.0296243	+	0.546388i
$371$	36.1024	−	21.7221i	0.0973112	−	0.0585502i
$372$	632.795	+	429.046i	1.70106	+	1.15335i
$373$	−7.11976	+	25.6431i	−0.0190878	+	0.0687482i	−0.972481	−	0.232984i	$-0.925151\pi$
$373$	−7.11976	+	25.6431i	−0.0190878	+	0.0687482i	0.953393	+	0.301732i	$0.0975648\pi$
$374$	−46.2760	+	5.03282i	−0.123733	+	0.0134567i
$375$	183.988	+	139.864i	0.490636	+	0.372972i
$376$	873.736	+	404.233i	2.32377	+	1.07509i
$377$	443.994	−	301.035i	1.17770	−	0.798503i
$378$	11.5697	+	34.3376i	0.0306076	+	0.0908401i
$379$	−65.2802	−	398.192i	−0.172243	−	1.05064i	−0.921506	−	0.388364i	$-0.873040\pi$
$379$	−65.2802	−	398.192i	−0.172243	−	1.05064i	0.749263	−	0.662273i	$-0.230408\pi$
$380$	274.576	−	1674.84i	0.722569	−	4.40747i
$381$	−139.290	−	46.9324i	−0.365591	−	0.123182i
$382$	5.41089	+	19.4882i	0.0141646	+	0.0510164i
$383$	42.3555	+	106.304i	0.110589	+	0.277557i	0.973847	−	0.227206i	$-0.0729591\pi$
$383$	42.3555	+	106.304i	0.110589	+	0.277557i	−0.863258	+	0.504763i	$0.831580\pi$
$384$	471.742	−	187.959i	1.22850	−	0.489477i
$385$	−87.1773	+	24.2047i	−0.226435	+	0.0628693i
$386$	−176.822	+	524.788i	−0.458087	+	1.35955i
$387$	113.745	+	18.6475i	0.293915	+	0.0481849i
$388$	−147.789	+	24.2287i	−0.380898	+	0.0624451i
$389$	17.8778	−	6.02372i	0.0459582	−	0.0154851i	−0.296229	−	0.955117i	$-0.595729\pi$
$389$	17.8778	−	6.02372i	0.0459582	−	0.0154851i	0.342187	+	0.939632i	$0.388832\pi$
$390$	−350.542	−	517.010i	−0.898825	−	1.32567i
$391$	−4.20790	+	9.09523i	−0.0107619	+	0.0232615i
$392$	−697.558	+	917.622i	−1.77948	+	2.34087i
$393$	34.8664	+	320.591i	0.0887185	+	0.815753i
$394$	−447.241	−	124.176i	−1.13513	−	0.315167i
$395$	−137.499	+	202.796i	−0.348100	+	0.513409i
$396$	179.158	+	297.763i	0.452419	+	0.751927i
$397$	−91.3025	+	4.95028i	−0.229981	+	0.0124692i	−0.168769	−	0.985656i	$-0.553979\pi$
$397$	−91.3025	+	4.95028i	−0.229981	+	0.0124692i	−0.0612118	+	0.998125i	$0.519497\pi$
$398$	−349.745	−	369.221i	−0.878756	−	0.927691i
$399$	−88.7162	+	67.4403i	−0.222346	+	0.169023i
$400$	−232.002	+	51.0675i	−0.580005	+	0.127669i
$401$	92.7687	−	78.7984i	0.231343	−	0.196505i	−0.524215	−	0.851586i	$-0.675641\pi$
$401$	92.7687	−	78.7984i	0.231343	−	0.196505i	0.755559	+	0.655081i	$0.227365\pi$
$402$	25.7945	−	475.751i	0.0641654	−	1.18346i
$403$	405.359	+	764.588i	1.00585	+	1.89724i
$404$	61.0383	−	277.300i	0.151085	−	0.686386i
$405$	37.0763	−	17.1533i	0.0915464	−	0.0423539i
$406$	92.7603	−	154.169i	0.228474	−	0.379726i
$407$	59.7192	−	112.642i	0.146730	−	0.276763i
$408$	−37.1520	−	31.5572i	−0.0910588	−	0.0773461i
$409$	286.461	−	302.414i	0.700394	−	0.739397i	−0.274617	−	0.961554i	$-0.588551\pi$
$409$	286.461	−	302.414i	0.700394	−	0.739397i	0.975011	+	0.222156i	$0.0713095\pi$
$410$	−130.421	+	1199.20i	−0.318099	+	2.92488i
$411$	−45.1968	+	113.435i	−0.109968	+	0.275999i
$412$			1770.09i			4.29633i
$413$	104.972	−	23.9011i	0.254170	−	0.0578718i
$414$	103.035			0.248876
$415$	−99.9332	−	39.8170i	−0.240803	−	0.0959447i
$416$	2181.30	+	237.230i	5.24351	+	0.570266i
$417$	−207.851	−	196.887i	−0.498444	−	0.472152i
$418$	−952.893	+	1121.83i	−2.27965	+	2.68381i
$419$	−84.9127	−	45.0178i	−0.202656	−	0.107441i	0.363990	−	0.931403i	$-0.381414\pi$
$419$	−84.9127	−	45.0178i	−0.202656	−	0.107441i	−0.566645	+	0.823962i	$0.691759\pi$
$420$	−130.352	−	78.4305i	−0.310363	−	0.186739i
$421$	−228.118	−	493.070i	−0.541849	−	1.17119i	−0.964303	−	0.264803i	$-0.914693\pi$
$421$	−228.118	−	493.070i	−0.541849	−	1.17119i	0.422453	−	0.906385i	$-0.361169\pi$
$422$	1266.76	+	278.835i	3.00181	+	0.660748i
$423$	−101.103	+	53.6016i	−0.239015	+	0.126718i
$424$	581.913	+	31.5504i	1.37244	+	0.0744113i
$425$	3.17376	+	3.73644i	0.00746768	+	0.00879163i
$426$	−106.501	−	483.838i	−0.250002	−	1.13577i
$427$	−29.0871	−	38.2634i	−0.0681197	−	0.0896099i
$428$	−720.198	+	682.208i	−1.68271	+	1.59394i
$429$	21.2956	+	392.775i	0.0496402	+	0.915559i
$430$	−571.070	+	343.602i	−1.32807	+	0.799074i
$431$	525.135	+	356.050i	1.21841	+	0.826103i	0.989099	−	0.147250i	$-0.0470422\pi$
$431$	525.135	+	356.050i	1.21841	+	0.826103i	0.229311	+	0.973353i	$0.426353\pi$
$432$	−75.1130	+	270.533i	−0.173873	+	0.626233i
$433$	389.610	−	42.3726i	0.899791	−	0.0978582i	0.353481	−	0.935442i	$-0.384998\pi$
$433$	389.610	−	42.3726i	0.899791	−	0.0978582i	0.546310	+	0.837583i	$0.316032\pi$
$434$	231.077	+	175.660i	0.532435	+	0.404747i
$435$	−184.104	−	85.1758i	−0.423229	−	0.195806i
$436$	−1364.73	+	925.310i	−3.13012	+	2.12227i
$437$	101.182	+	300.298i	0.231538	+	0.687180i
$438$	111.020	+	677.191i	0.253470	+	1.54610i
$439$	−9.82494	+	59.9295i	−0.0223803	+	0.136514i	−0.995653	−	0.0931377i	$-0.970310\pi$
$439$	−9.82494	+	59.9295i	−0.0223803	+	0.136514i	0.973273	+	0.229651i	$0.0737586\pi$
$440$	−1185.89	−	399.574i	−2.69521	−	0.908123i
$441$	−36.6544	−	132.017i	−0.0831164	−	0.299358i
$442$	−32.7924	−	82.3027i	−0.0741909	−	0.186205i
$443$	314.578	−	125.339i	0.710109	−	0.282933i	0.0130171	−	0.999915i	$-0.495856\pi$
$443$	314.578	−	125.339i	0.710109	−	0.282933i	0.697092	+	0.716982i	$0.254477\pi$
$444$	206.560	−	57.3510i	0.465224	−	0.129169i
$445$	−192.297	+	570.717i	−0.432128	+	1.28251i
$446$	−514.660	−	84.3743i	−1.15395	−	0.189180i
$447$	−124.660	+	20.4370i	−0.278882	+	0.0457205i
$448$	323.681	−	109.061i	0.722502	−	0.243439i
$449$	48.5419	+	71.5939i	0.108111	+	0.159452i	0.877896	−	0.478852i	$-0.158947\pi$
$449$	48.5419	+	71.5939i	0.108111	+	0.159452i	−0.769785	+	0.638304i	$0.779636\pi$
$450$	21.1640	−	45.7452i	0.0470311	−	0.101656i
$451$	459.700	−	604.724i	1.01929	−	1.34085i
$452$	−125.048	−	1149.80i	−0.276655	−	2.54380i
$453$	−89.2973	−	24.7933i	−0.197124	−	0.0547313i
$454$	493.326	−	727.601i	1.08662	−	1.60264i
$455$	−88.7776	−	147.550i	−0.195116	−	0.324285i
$456$	−1539.11	+	83.4480i	−3.37524	+	0.183000i
$457$	−50.5509	−	53.3660i	−0.110615	−	0.116775i	0.668336	−	0.743859i	$-0.267007\pi$
$457$	−50.5509	−	53.3660i	−0.110615	−	0.116775i	−0.778951	+	0.627085i	$0.784248\pi$
$458$	−584.831	+	444.577i	−1.27692	+	0.970692i
$459$	5.65870	−	1.24557i	0.0123283	−	0.00271367i
$460$	−329.702	+	280.051i	−0.716743	+	0.608807i
$461$	−33.6502	+	620.642i	−0.0729940	+	1.34630i	0.701027	+	0.713135i	$0.252725\pi$
$461$	−33.6502	+	620.642i	−0.0729940	+	1.34630i	−0.774021	+	0.633160i	$0.781757\pi$
$462$	61.7993	+	116.566i	0.133765	+	0.252307i
$463$	−83.2459	+	378.190i	−0.179797	+	0.816825i	0.797224	+	0.603683i	$0.206301\pi$
$463$	−83.2459	+	378.190i	−0.179797	+	0.816825i	−0.977021	+	0.213142i	$0.931630\pi$
$464$	1265.31	−	585.394i	2.72696	−	1.26162i
$465$	168.718	−	280.411i	0.362833	−	0.603034i
$466$	−689.224	+	1300.01i	−1.47902	+	2.78973i
$467$	−564.375	−	479.384i	−1.20851	−	1.02652i	−0.998811	−	0.0487525i	$-0.984475\pi$
$467$	−564.375	−	479.384i	−1.20851	−	1.02652i	−0.209700	−	0.977766i	$-0.567249\pi$
$468$	−454.843	+	480.172i	−0.971886	+	1.02601i
$469$	14.2009	−	130.575i	0.0302792	−	0.278412i
$470$	244.910	−	614.679i	0.521086	−	1.30783i
$471$		−	455.165i		−	0.966379i
$472$	1387.26	+	541.175i	2.93910	+	1.14656i
$473$	419.692			0.887297
$474$	331.916	+	132.247i	0.700244	+	0.279003i
$475$	154.109	+	16.7604i	0.324441	+	0.0352851i
$476$	−15.6647	−	14.8384i	−0.0329090	−	0.0311731i
$477$	−44.8451	+	52.7957i	−0.0940148	+	0.110683i
$478$	−1270.38	−	673.513i	−2.65770	−	1.40902i
$479$	−500.681	−	301.250i	−1.04526	−	0.628914i	−0.114083	−	0.993471i	$-0.536393\pi$
$479$	−500.681	−	301.250i	−1.04526	−	0.628914i	−0.931181	+	0.364557i	$0.881221\pi$
$480$	−348.397	−	753.048i	−0.725827	−	1.56885i
$481$	236.982	+	52.1637i	0.492686	+	0.108448i
$482$	1034.09	−	548.240i	2.14542	−	1.13743i
$483$	28.3624	+	1.53777i	0.0587214	+	0.00318378i
$484$	−11.5201	−	13.5625i	−0.0238018	−	0.0280217i
$485$	13.7806	+	62.6060i	0.0284136	+	0.129085i
$486$	−36.0515	−	47.4250i	−0.0741801	−	0.0975822i
$487$	−301.239	+	285.348i	−0.618560	+	0.585931i	−0.931455	−	0.363857i	$-0.881460\pi$
$487$	−301.239	+	285.348i	−0.618560	+	0.585931i	0.312895	+	0.949788i	$0.398701\pi$
$488$	−35.9912	−	663.819i	−0.0737525	−	1.36029i
$489$	−136.901	+	82.3707i	−0.279961	+	0.168447i
$490$	655.711	+	444.583i	1.33819	+	0.907313i
$491$	56.7440	−	204.373i	0.115568	−	0.416239i	−0.883021	−	0.469333i	$-0.844494\pi$
$491$	56.7440	−	204.373i	0.115568	−	0.416239i	0.998590	+	0.0530938i	$0.0169082\pi$
$492$	1269.76	−	138.095i	2.58081	−	0.280680i
$493$	−22.9046	−	17.4116i	−0.0464596	−	0.0353177i
$494$	−2542.51	−	1176.29i	−5.14679	−	2.38116i
$495$	123.117	−	83.4757i	0.248722	−	0.168638i
$496$	718.157	+	2131.41i	1.44790	+	4.29720i
$497$	−22.0954	−	134.776i	−0.0444576	−	0.271179i
$498$	−25.3784	+	154.802i	−0.0509607	+	0.310847i
$499$	531.731	+	179.161i	1.06559	+	0.359040i	0.796853	−	0.604173i	$-0.206496\pi$
$499$	531.731	+	179.161i	1.06559	+	0.359040i	0.268740	+	0.963213i	$0.413393\pi$
$500$	378.544	+	1363.39i	0.757089	+	2.72679i
$501$	−161.342	−	404.938i	−0.322040	−	0.808260i
$502$	−987.433	+	393.429i	−1.96700	+	0.783723i
$503$	−392.104	+	108.867i	−0.779531	+	0.216436i	−0.634429	−	0.772981i	$-0.718765\pi$
$503$	−392.104	+	108.867i	−0.779531	+	0.216436i	−0.145102	+	0.989417i	$0.546351\pi$
$504$	−44.1149	+	130.928i	−0.0875296	+	0.259779i
$505$	−119.937	−	19.6627i	−0.237500	−	0.0389361i
$506$	370.223	−	60.6949i	0.731666	−	0.119950i
$507$	−432.070	+	145.581i	−0.852210	+	0.287143i
$508$	−505.010	−	744.833i	−0.994113	−	1.46621i
$509$	−35.5370	+	76.8120i	−0.0698173	+	0.150908i	−0.939342	−	0.342982i	$-0.888563\pi$
$509$	−35.5370	+	76.8120i	−0.0698173	+	0.150908i	0.869525	+	0.493889i	$0.164425\pi$
$510$	−20.2750	+	26.6713i	−0.0397549	+	0.0522967i
$511$	20.4536	+	188.068i	0.0400267	+	0.368039i
$512$	238.632	+	66.2558i	0.466078	+	0.129406i
$513$	102.818	−	151.646i	0.200425	−	0.295605i
$514$	−75.5677	−	125.594i	−0.147019	−	0.244347i
$515$	756.568	−	41.0199i	1.46906	−	0.0796503i
$516$	485.300	+	512.325i	0.940504	+	0.992878i
$517$	−331.708	+	252.158i	−0.641602	+	0.487733i
$518$	79.4865	−	17.4963i	0.153449	−	0.0337767i
$519$	−316.398	+	268.750i	−0.609629	+	0.517824i
$520$	128.945	−	2378.26i	0.247972	−	4.57358i
$521$	−274.012	−	516.841i	−0.525934	−	0.992017i	−0.994109	−	0.108382i	$-0.965433\pi$
$521$	−274.012	−	516.841i	−0.525934	−	0.992017i	0.468175	−	0.883636i	$-0.344912\pi$
$522$	−63.5901	+	288.893i	−0.121820	+	0.553435i
$523$	253.344	−	117.209i	0.484405	−	0.224109i	−0.162459	−	0.986715i	$-0.551942\pi$
$523$	253.344	−	117.209i	0.484405	−	0.224109i	0.646863	+	0.762606i	$0.276080\pi$
$524$	−1017.89	+	1691.74i	−1.94253	+	3.22851i
$525$	6.50857	−	12.2765i	0.0123973	−	0.0233837i
$526$	−674.754	−	573.141i	−1.28280	−	1.08962i
$527$	31.9199	−	33.6975i	0.0605692	−	0.0639421i
$528$	−110.532	+	1016.32i	−0.209340	+	1.92485i
$529$	−165.907	+	416.396i	−0.313625	+	0.787138i
$530$		−	400.536i		−	0.755728i
$531$	−151.002	+	92.3443i	−0.284372	+	0.173906i
$532$	−682.275			−1.28247
$533$	1343.07	+	535.128i	2.51983	+	1.00399i
$534$	873.068	+	94.9518i	1.63496	+	0.177812i
$535$	308.278	+	292.016i	0.576220	+	0.545824i
$536$	1176.10	−	1384.62i	2.19422	−	2.58324i
$537$	209.317	+	110.973i	0.389789	+	0.206653i
$538$	620.942	+	373.609i	1.15417	+	0.694440i
$539$	−209.474	−	452.770i	−0.388634	−	0.840018i
$540$	244.264	+	53.7666i	0.452341	+	0.0995678i
$541$	707.752	−	375.226i	1.30823	−	0.693579i	0.339244	−	0.940699i	$-0.389829\pi$
$541$	707.752	−	375.226i	1.30823	−	0.693579i	0.968985	+	0.247120i	$0.0794840\pi$
$542$	535.335	+	29.0250i	0.987703	+	0.0535517i
$543$	294.809	+	347.076i	0.542926	+	0.639182i
$544$	−25.2986	−	114.933i	−0.0465047	−	0.211273i
$545$	427.120	+	561.867i	0.783707	+	1.03095i
$546$	−182.303	+	172.686i	−0.333888	+	0.316275i
$547$	−9.66239	−	178.212i	−0.0176643	−	0.325799i	−0.993988	−	0.109486i	$-0.965079\pi$
$547$	−9.66239	−	178.212i	−0.0176643	−	0.325799i	0.976324	−	0.216313i	$-0.0694033\pi$
$548$	−640.579	+	385.424i	−1.16894	+	0.703328i
$549$	65.4049	+	44.3456i	0.119135	+	0.0807753i
$550$	49.0989	−	176.838i	0.0892707	−	0.321524i
$551$	−904.434	+	98.3631i	−1.64144	+	0.178517i
$552$	312.760	+	237.754i	0.566595	+	0.430714i
$553$	89.3929	+	41.3576i	0.161651	+	0.0747876i
$554$	213.529	−	144.776i	0.385431	−	0.261329i
$555$	−29.2996	−	86.9582i	−0.0527921	−	0.156681i
$556$	−283.576	−	1729.74i	−0.510029	−	3.11104i
$557$	12.8972	−	78.6695i	0.0231548	−	0.141238i	−0.972719	−	0.231986i	$-0.925478\pi$
$557$	12.8972	−	78.6695i	0.0231548	−	0.141238i	0.995874	+	0.0907483i	$0.0289259\pi$
$558$	−452.236	−	152.376i	−0.810459	−	0.273075i
$559$	213.698	+	769.670i	0.382286	+	1.37687i
$560$	−165.652	−	415.755i	−0.295807	−	0.742420i
$561$	19.5990	−	7.80897i	0.0349359	−	0.0139197i
$562$	988.916	−	274.571i	1.75964	−	0.488561i
$563$	6.52722	−	19.3721i	0.0115936	−	0.0344087i	−0.941700	−	0.336453i	$-0.890773\pi$
$563$	6.52722	−	19.3721i	0.0115936	−	0.0344087i	0.953294	+	0.302045i	$0.0976691\pi$
$564$	−691.377	−	113.345i	−1.22584	−	0.200967i
$565$	−488.546	+	80.0930i	−0.864683	+	0.141758i
$566$	485.629	−	163.627i	0.858002	−	0.289094i
$567$	−9.21612	−	13.5928i	−0.0162542	−	0.0239731i
$568$	793.184	−	1714.44i	1.39645	−	3.01838i
$569$	−255.100	+	335.578i	−0.448331	+	0.589769i	−0.963630	−	0.267242i	$-0.913888\pi$
$569$	−255.100	+	335.578i	−0.448331	+	0.589769i	0.515299	+	0.857011i	$0.327681\pi$
$570$	114.539	+	1053.17i	0.200946	+	1.84767i
$571$	−86.9795	−	24.1497i	−0.152328	−	0.0422938i	0.190527	−	0.981682i	$-0.438980\pi$
$571$	−86.9795	−	24.1497i	−0.152328	−	0.0422938i	−0.342855	+	0.939388i	$0.611394\pi$
$572$	−1351.48	+	1993.28i	−2.36272	+	3.48476i
$573$	−4.72599	−	7.85466i	−0.00824781	−	0.0137080i
$574$	484.211	−	26.2531i	0.843573	−	0.0457372i
$575$	−27.1721	−	28.6852i	−0.0472558	−	0.0498873i
$576$	−447.048	+	339.837i	−0.776125	+	0.589995i
$577$	372.358	−	81.9622i	0.645335	−	0.142049i	0.119769	−	0.992802i	$-0.461785\pi$
$577$	372.358	−	81.9622i	0.645335	−	0.142049i	0.525566	+	0.850753i	$0.323854\pi$
$578$	838.132	−	711.916i	1.45006	−	1.23169i
$579$	13.5883	−	250.621i	0.0234685	−	0.432851i
$580$	−581.737	−	1097.27i	−1.00299	−	1.89185i
$581$	−9.29632	+	42.2336i	−0.0160005	+	0.0726912i
$582$	84.8403	−	39.2513i	0.145774	−	0.0674421i
$583$	−130.036	+	216.122i	−0.223047	+	0.370706i
$584$	−1225.63	+	2311.79i	−2.09868	+	3.95854i
$585$	215.774	+	183.280i	0.368845	+	0.313300i
$586$	128.999	−	136.183i	0.220135	−	0.232394i
$587$	71.1234	−	653.968i	0.121164	−	1.11409i	−0.762834	−	0.646595i	$-0.776192\pi$
$587$	71.1234	−	653.968i	0.121164	−	1.11409i	0.883998	−	0.467491i	$-0.154842\pi$
$588$	310.485	−	779.258i	0.528035	−	1.32527i
$589$		−	1467.69i		−	2.49184i
$590$	319.784	−	972.199i	0.542007	−	1.64779i
$591$	210.372			0.355960
$592$	585.866	+	233.430i	0.989638	+	0.394308i
$593$	410.179	+	44.6097i	0.691702	+	0.0752271i	0.447216	−	0.894426i	$-0.352415\pi$
$593$	410.179	+	44.6097i	0.691702	+	0.0752271i	0.244486	+	0.969653i	$0.421381\pi$
$594$	−157.477	−	149.170i	−0.265112	−	0.251127i
$595$	−5.97918	+	7.03924i	−0.0100490	+	0.0118306i
$596$	−683.315	−	362.271i	−1.14650	−	0.607837i
$597$	197.507	+	118.836i	0.330832	+	0.199055i
$598$	299.818	+	648.045i	0.501367	+	1.08369i
$599$	−375.606	−	82.6771i	−0.627055	−	0.138025i	−0.109936	−	0.993939i	$-0.535065\pi$
$599$	−375.606	−	82.6771i	−0.627055	−	0.138025i	−0.517119	+	0.855913i	$0.672996\pi$
$600$	169.801	−	90.0228i	0.283002	−	0.150038i
$601$	185.811	+	10.0744i	0.309170	+	0.0167627i	0.208071	−	0.978114i	$-0.433281\pi$
$601$	185.811	+	10.0744i	0.309170	+	0.0167627i	0.101099	+	0.994876i	$0.467764\pi$
$602$	173.449	+	204.200i	0.288121	+	0.339203i
$603$	46.4212	+	210.894i	0.0769838	+	0.349741i
$604$	−343.372	−	451.698i	−0.568497	−	0.747845i
$605$	−5.52989	+	5.23819i	−0.00914031	+	0.00865816i
$606$	9.59518	+	176.973i	0.0158336	+	0.292034i
$607$	199.336	−	119.936i	0.328395	−	0.197589i	−0.341802	−	0.939772i	$-0.611037\pi$
$607$	199.336	−	119.936i	0.328395	−	0.197589i	0.670197	+	0.742183i	$0.266210\pi$
$608$	−3080.04	−	2088.32i	−5.06585	−	3.43473i
$609$	−21.8162	+	78.5747i	−0.0358229	+	0.129023i
$610$	−454.234	+	49.4009i	−0.744646	+	0.0809851i
$611$	−631.330	−	479.924i	−1.03327	−	0.785474i
$612$	32.1954	+	14.8952i	0.0526069	+	0.0243385i
$613$	352.788	−	239.196i	0.575511	−	0.390206i	−0.238425	−	0.971161i	$-0.576631\pi$
$613$	352.788	−	239.196i	0.575511	−	0.390206i	0.813936	+	0.580955i	$0.197321\pi$
$614$	423.755	+	1257.66i	0.690154	+	2.04830i
$615$	−88.4495	−	539.518i	−0.143820	−	0.877265i
$616$	−81.3868	+	496.437i	−0.132121	+	0.805905i
$617$	−371.473	−	125.164i	−0.602063	−	0.202859i	0.00173193	−	0.999999i	$-0.499449\pi$
$617$	−371.473	−	125.164i	−0.602063	−	0.202859i	−0.603795	+	0.797140i	$0.706345\pi$
$618$	−295.586	−	1064.61i	−0.478295	−	1.72266i
$619$	−141.656	−	355.530i	−0.228847	−	0.574362i	0.769050	−	0.639189i	$-0.220730\pi$
$619$	−141.656	−	355.530i	−0.228847	−	0.574362i	−0.997897	+	0.0648267i	$0.979351\pi$
$620$	1861.28	−	741.601i	3.00206	−	1.19613i
$621$	−44.9965	+	12.4932i	−0.0724581	+	0.0201179i
$622$	138.329	−	410.545i	0.222394	−	0.660041i
$623$	238.913	+	39.1678i	0.383488	+	0.0628696i
$624$	−1920.11	+	314.786i	−3.07709	+	0.504464i
$625$	469.809	−	158.297i	0.751694	−	0.253275i
$626$	1279.74	+	1887.48i	2.04432	+	3.01515i
$627$	280.115	−	605.458i	0.446754	−	0.965643i
$628$	1686.43	−	2218.47i	2.68540	−	3.53259i
$629$	−1.40715	−	12.9385i	−0.00223712	−	0.0205700i
$630$	91.4966	+	25.4039i	0.145233	+	0.0403236i
$631$	123.222	−	181.739i	0.195280	−	0.288017i	−0.717425	−	0.696636i	$-0.754679\pi$
$631$	123.222	−	181.739i	0.195280	−	0.288017i	0.912705	+	0.408619i	$0.133990\pi$
$632$	702.363	+	1167.34i	1.11133	+	1.84705i
$633$	−587.019	+	31.8273i	−0.927361	+	0.0502800i
$634$	977.119	+	1031.53i	1.54120	+	1.62702i
$635$	−306.652	+	233.111i	−0.482917	+	0.367104i
$636$	−414.188	+	91.1697i	−0.651239	+	0.143349i
$637$	723.672	−	614.693i	1.13606	−	0.964981i
$638$	−58.3122	+	1075.51i	−0.0913984	+	1.68574i
$639$	105.177	+	198.384i	0.164596	+	0.310461i
$640$	286.081	−	1299.68i	0.447002	−	2.03075i
$641$	−485.112	+	224.437i	−0.756805	+	0.350135i	−0.760054	−	0.649860i	$-0.774828\pi$
$641$	−485.112	+	224.437i	−0.756805	+	0.350135i	0.00324952	+	0.999995i	$0.498966\pi$
$642$	319.236	−	530.574i	0.497252	−	0.826439i
$643$	540.957	−	1020.35i	0.841301	−	1.58686i	0.0319854	−	0.999488i	$-0.489817\pi$
$643$	540.957	−	1020.35i	0.841301	−	1.58686i	0.809316	−	0.587374i	$-0.199838\pi$
$644$	132.541	+	112.581i	0.205808	+	0.174815i
$645$	207.731	−	219.299i	0.322063	−	0.339998i
$646$	−16.2454	+	149.374i	−0.0251477	+	0.231230i
$647$	−148.456	+	372.596i	−0.229453	+	0.575882i	−0.997952	−	0.0639681i	$-0.979624\pi$
$647$	−148.456	+	372.596i	−0.229453	+	0.575882i	0.768499	+	0.639850i	$0.221004\pi$
$648$		−	227.147i		−	0.350536i
$649$	−488.180	+	420.761i	−0.752203	+	0.648323i
$650$	349.303			0.537389
$651$	−122.213	−	48.6942i	−0.187731	−	0.0747991i
$652$	−972.447	−	105.760i	−1.49148	−	0.162208i
$653$	−252.757	−	239.424i	−0.387071	−	0.366653i	0.469278	−	0.883050i	$-0.344514\pi$
$653$	−252.757	−	239.424i	−0.387071	−	0.366653i	−0.856349	+	0.516397i	$0.827273\pi$
$654$	666.289	−	784.416i	1.01879	−	1.19941i
$655$	746.668	+	395.858i	1.13995	+	0.604364i
$656$	3219.63	+	1937.19i	4.90797	+	2.95303i
$657$	−130.595	−	282.276i	−0.198774	−	0.429644i
$658$	−259.774	−	57.1806i	−0.394794	−	0.0869007i
$659$	−561.060	+	297.455i	−0.851381	+	0.451374i	−0.836144	−	0.548510i	$-0.815195\pi$
$659$	−561.060	+	297.455i	−0.851381	+	0.451374i	−0.0152373	+	0.999884i	$0.504850\pi$
$660$	909.359	+	49.3040i	1.37782	+	0.0747031i
$661$	−439.071	−	516.915i	−0.664253	−	0.782019i	0.322092	−	0.946708i	$-0.395614\pi$
$661$	−439.071	−	516.915i	−0.664253	−	0.782019i	−0.986346	+	0.164689i	$0.947338\pi$
$662$	−463.768	−	2106.92i	−0.700557	−	3.18266i
$663$	24.3002	+	31.9664i	0.0366519	+	0.0482148i
$664$	−434.243	+	411.337i	−0.653981	+	0.619484i
$665$	15.8110	+	291.617i	0.0237759	+	0.438521i
$666$	−114.657	+	68.9866i	−0.172157	+	0.103583i
$667$	191.928	+	130.131i	0.287749	+	0.195098i
$668$	713.960	−	2571.45i	1.06880	−	3.84948i
$669$	234.989	−	25.5566i	0.351254	−	0.0382011i
$670$	−994.012	−	755.628i	−1.48360	−	1.12780i
$671$	261.135	+	120.814i	0.389173	+	0.180050i
$672$	−276.079	+	187.187i	−0.410833	+	0.278551i
$673$	57.9763	+	172.067i	0.0861460	+	0.255672i	0.982064	−	0.188547i	$-0.0603777\pi$
$673$	57.9763	+	172.067i	0.0861460	+	0.255672i	−0.895918	+	0.444219i	$0.853481\pi$
$674$	−54.2108	−	330.671i	−0.0804314	−	0.490610i
$675$	−3.69585	+	22.5437i	−0.00547533	+	0.0333980i
$676$	−2645.30	−	891.305i	−3.91317	−	1.31850i
$677$	226.582	+	816.076i	0.334686	+	1.20543i	0.919116	+	0.393986i	$0.128904\pi$
$677$	226.582	+	816.076i	0.334686	+	1.20543i	−0.584430	+	0.811444i	$0.698682\pi$
$678$	267.213	+	670.655i	0.394120	+	0.989166i
$679$	23.9399	−	9.53852i	0.0352576	−	0.0140479i
$680$	−123.089	+	34.1755i	−0.181013	+	0.0502581i
$681$	−127.218	+	377.569i	−0.186810	+	0.554433i
$682$	−1714.73	−	281.116i	−2.51427	−	0.412193i
$683$	551.777	−	90.4593i	0.807873	−	0.132444i	0.256329	−	0.966590i	$-0.417487\pi$
$683$	551.777	−	90.4593i	0.807873	−	0.132444i	0.551544	+	0.834146i	$0.314039\pi$
$684$	1063.00	−	358.166i	1.55409	−	0.523634i
$685$	179.582	+	264.863i	0.262163	+	0.386662i
$686$	277.196	−	599.149i	0.404076	−	0.873395i
$687$	201.496	−	265.064i	0.293299	−	0.385828i
$688$	224.458	+	2063.86i	0.326248	+	2.99980i
$689$	−462.556	−	128.428i	−0.671344	−	0.186398i
$690$	151.531	−	223.492i	0.219610	−	0.323901i
$691$	−467.068	−	776.274i	−0.675931	−	1.12341i	−0.985031	−	0.172377i	$-0.944855\pi$
$691$	−467.068	−	776.274i	−0.675931	−	1.12341i	0.309100	−	0.951030i	$-0.399972\pi$
$692$	−2537.87	+	137.599i	−3.66744	+	0.198843i
$693$	−41.1224	−	43.4124i	−0.0593396	−	0.0626441i
$694$	438.758	−	333.535i	0.632216	−	0.480598i
$695$	−732.749	+	161.290i	−1.05432	+	0.232072i
$696$	−859.653	+	730.195i	−1.23513	+	1.04913i
$697$	4.19809	−	77.4293i	0.00602309	−	0.111089i
$698$	95.6527	+	180.420i	0.137038	+	0.258481i
$699$	143.362	−	651.302i	0.205096	−	0.931762i
$700$	77.2083	−	35.7203i	0.110298	−	0.0510291i
$701$	−202.847	+	337.134i	−0.289368	+	0.480933i	−0.967107	−	0.254369i	$-0.918132\pi$
$701$	−202.847	+	337.134i	−0.289368	+	0.480933i	0.677740	+	0.735302i	$0.262960\pi$
$702$	193.378	−	364.749i	0.275467	−	0.519586i
$703$	−313.659	−	266.424i	−0.446172	−	0.378982i
$704$	−1406.14	+	1484.44i	−1.99736	+	2.10858i
$705$	−32.4240	+	298.133i	−0.0459914	+	0.422884i
$706$	150.871	−	378.659i	0.213699	−	0.536344i
$707$			48.8586i			0.0691069i
$708$	−1078.13	−	109.393i	−1.52278	−	0.154510i
$709$	−239.872			−0.338324			−0.169162	−	0.985588i	$-0.554106\pi$
$709$	−239.872			−0.338324			−0.169162	+	0.985588i	$0.554106\pi$
$710$	−1206.12	−	480.561i	−1.69876	−	0.676847i
$711$	−160.987	−	17.5084i	−0.226423	−	0.0246250i
$712$	2431.08	+	2302.84i	3.41444	+	3.23433i
$713$	−242.181	+	285.118i	−0.339665	+	0.399884i
$714$	11.8993	+	6.30859i	0.0166656	+	0.00883556i
$715$	883.283	+	531.454i	1.23536	+	0.743292i
$716$	609.040	+	1316.42i	0.850615	+	1.83857i
$717$	636.455	+	140.094i	0.887665	+	0.195390i
$718$	−606.226	+	321.401i	−0.844326	+	0.447633i
$719$	−195.200	−	10.5834i	−0.271488	−	0.0147197i	−0.0821077	−	0.996623i	$-0.526165\pi$
$719$	−195.200	−	10.5834i	−0.271488	−	0.0147197i	−0.189380	+	0.981904i	$0.560648\pi$
$720$	476.343	+	560.794i	0.661587	+	0.778880i
$721$	−65.4773	−	297.466i	−0.0908146	−	0.412575i
$722$	2040.40	+	2684.10i	2.82604	+	3.71759i
$723$	−385.124	+	364.809i	−0.532675	+	0.504577i
$724$	150.941	+	2783.94i	0.208482	+	3.84523i
$725$	97.1986	−	58.4825i	0.134067	−	0.0806655i
$726$	9.19346	+	6.23332i	0.0126632	+	0.00858584i
$727$	−171.015	+	615.939i	−0.235233	+	0.847233i	0.747818	+	0.663904i	$0.231101\pi$
$727$	−171.015	+	615.939i	−0.235233	+	0.847233i	−0.983051	+	0.183330i	$0.941312\pi$
$728$	−951.854	+	103.520i	−1.30749	+	0.142198i
$729$	21.4945	+	16.3397i	0.0294849	+	0.0224139i
$730$	1632.16	+	755.120i	2.23584	+	1.03441i
$731$	35.4606	−	24.0429i	0.0485097	−	0.0328904i
$732$	154.477	+	458.472i	0.211035	+	0.626328i
$733$	76.0480	+	463.872i	0.103749	+	0.632841i	0.986596	+	0.163180i	$0.0521753\pi$
$733$	76.0480	+	463.872i	0.103749	+	0.632841i	−0.882847	+	0.469660i	$0.844376\pi$
$734$	−58.9843	+	359.788i	−0.0803601	+	0.490175i
$735$	−340.264	−	114.648i	−0.462944	−	0.155984i
$736$	253.747	+	913.912i	0.344764	+	1.24173i
$737$	291.032	+	730.435i	0.394887	+	0.991093i
$738$	−740.627	+	295.093i	−1.00356	+	0.399855i
$739$	−184.607	+	51.2559i	−0.249807	+	0.0693585i	−0.390174	−	0.920741i	$-0.627585\pi$
$739$	−184.607	+	51.2559i	−0.249807	+	0.0693585i	0.140368	+	0.990099i	$0.455171\pi$
$740$	179.384	−	532.391i	0.242410	−	0.719448i
$741$	1252.97	+	205.415i	1.69092	+	0.277213i
$742$	−158.895	+	26.0494i	−0.214144	+	0.0351071i
$743$	1257.67	−	423.760i	1.69270	−	0.570336i	0.702708	−	0.711478i	$-0.251974\pi$
$743$	1257.67	−	423.760i	1.69270	−	0.570336i	0.989989	+	0.141142i	$0.0450774\pi$
$744$	−1021.15	−	1506.08i	−1.37251	−	2.02430i
$745$	−139.006	+	300.456i	−0.186585	+	0.403297i
$746$	61.5483	−	80.9654i	0.0825045	−	0.108533i
$747$	−7.68701	−	70.6809i	−0.0102905	−	0.0946197i
$748$	124.458	+	34.5557i	0.166388	+	0.0461975i
$749$	95.7950	−	141.287i	0.127897	−	0.188634i
$750$	−455.345	−	756.789i	−0.607127	−	1.00905i
$751$	−638.895	+	34.6399i	−0.850726	+	0.0461250i	−0.474344	−	0.880340i	$-0.657315\pi$
$751$	−638.895	+	34.6399i	−0.850726	+	0.0461250i	−0.376382	+	0.926465i	$0.622832\pi$
$752$	−1417.41	−	1496.34i	−1.88485	−	1.98981i
$753$	383.519	−	291.544i	0.509322	−	0.387176i
$754$	−2002.05	+	440.685i	−2.65524	+	0.584464i
$755$	−185.107	+	157.231i	−0.245174	+	0.208253i
$756$	5.44340	−	100.398i	0.00720027	−	0.132801i
$757$	289.182	+	545.455i	0.382010	+	0.720548i	0.997725	−	0.0674216i	$-0.0214772\pi$
$757$	289.182	+	545.455i	0.382010	+	0.720548i	−0.615714	+	0.787970i	$0.711132\pi$
$758$	−331.490	+	1505.97i	−0.437322	+	1.98677i
$759$	−154.321	+	71.3966i	−0.203322	+	0.0940667i
$760$	−2082.53	+	3461.19i	−2.74017	+	4.55420i
$761$	193.810	−	365.564i	0.254678	−	0.480373i	−0.722899	−	0.690954i	$-0.757191\pi$
$761$	193.810	−	365.564i	0.254678	−	0.480373i	0.977576	+	0.210581i	$0.0675355\pi$
$762$	428.113	+	363.643i	0.561829	+	0.477222i
$763$	195.117	−	205.983i	0.255724	−	0.269964i
$764$	6.06795	−	55.7938i	0.00794234	−	0.0730286i
$765$	5.62037	−	14.1061i	0.00734689	−	0.0184393i
$766$		−	437.307i		−	0.570896i
$767$	−1020.20	−	681.028i	−1.33012	−	0.887911i
$768$	−643.767			−0.838239
$769$	813.647	+	324.187i	1.05806	+	0.421569i	0.833286	−	0.552842i	$-0.186457\pi$
$769$	813.647	+	324.187i	1.05806	+	0.421569i	0.224773	+	0.974411i	$0.427836\pi$
$770$	343.729	+	37.3828i	0.446401	+	0.0485490i
$771$	48.2299	+	45.6858i	0.0625550	+	0.0592553i
$772$	994.806	−	1171.18i	1.28861	−	1.51707i
$773$	750.014	+	397.633i	0.970265	+	0.514402i	0.876609	−	0.481203i	$-0.159800\pi$
$773$	750.014	+	397.633i	0.970265	+	0.514402i	0.0936553	+	0.995605i	$0.470145\pi$
$774$	−377.433	−	227.094i	−0.487640	−	0.293403i
$775$	76.8406	+	166.088i	0.0991492	+	0.214308i
$776$	348.105	+	76.6237i	0.448589	+	0.0987418i
$777$	−32.5912	+	17.2788i	−0.0419450	+	0.0222378i
$778$	−71.9890	−	3.90313i	−0.0925308	−	0.00501688i
$779$	−1587.37	−	1868.79i	−2.03770	−	2.39897i
$780$	372.608	+	1692.77i	0.477702	+	2.17022i
$781$	494.783	+	650.875i	0.633524	+	0.833387i
$782$	27.8039	−	26.3372i	0.0355548	−	0.0336793i
$783$	−7.25840	−	133.873i	−0.00926999	−	0.170975i
$784$	2114.49	−	1272.25i	2.69706	−	1.62277i
$785$	−987.293	−	669.401i	−1.25770	−	0.852741i
$786$	329.696	−	1187.46i	0.419461	−	1.51076i
$787$	401.267	−	43.6404i	0.509869	−	0.0554516i	0.150431	−	0.988621i	$-0.451934\pi$
$787$	401.267	−	43.6404i	0.509869	−	0.0554516i	0.359438	+	0.933169i	$0.382968\pi$
$788$	1025.35	+	779.451i	1.30121	+	0.989152i
$789$	364.167	+	168.482i	0.461556	+	0.213538i
$790$	774.998	−	525.461i	0.981010	−	0.665141i
$791$	63.5466	+	188.600i	0.0803371	+	0.238432i
$792$	−133.806	−	816.183i	−0.168947	−	1.03053i
$793$	−88.5956	+	540.410i	−0.111722	+	0.681475i
$794$	331.138	+	111.573i	0.417051	+	0.140521i
$795$	48.5659	+	174.919i	0.0610892	+	0.220023i
$796$	522.345	+	1310.99i	0.656212	+	1.64697i
$797$	−1076.68	+	428.987i	−1.35091	+	0.538253i	−0.929569	−	0.368649i	$-0.879821\pi$
$797$	−1076.68	+	428.987i	−1.35091	+	0.538253i	−0.421343	+	0.906901i	$0.638441\pi$
$798$	410.349	−	113.933i	0.514222	−	0.142773i
$799$	−13.5813	+	40.3079i	−0.0169979	+	0.0504480i
$800$	457.879	+	75.0655i	0.572349	+	0.0938318i
$801$	−392.792	+	64.3950i	−0.490377	+	0.0803932i
$802$	−440.802	+	148.523i	−0.549628	+	0.185191i
$803$	−635.533	−	937.340i	−0.791448	−	1.16730i
$804$	−555.128	+	1199.89i	−0.690458	+	1.49240i
$805$	45.0476	−	59.2591i	0.0559598	−	0.0736138i
$806$	−357.567	−	3287.77i	−0.443631	−	4.07912i
$807$	−316.474	−	87.8685i	−0.392161	−	0.108883i
$808$	−379.242	+	559.339i	−0.469358	+	0.692252i
$809$	239.969	+	398.832i	0.296625	+	0.492994i	0.968948	−	0.247263i	$-0.0795312\pi$
$809$	239.969	+	398.832i	0.296625	+	0.492994i	−0.672324	+	0.740257i	$0.734704\pi$
$810$	−155.889	+	8.45207i	−0.192456	+	0.0104347i
$811$	−189.181	−	199.716i	−0.233269	−	0.246259i	0.598843	−	0.800866i	$-0.295627\pi$
$811$	−189.181	−	199.716i	−0.233269	−	0.246259i	−0.832112	+	0.554607i	$0.812869\pi$
$812$	−397.459	+	302.141i	−0.489482	+	0.372095i
$813$	−237.307	+	52.2351i	−0.291890	+	0.0642498i
$814$	−371.344	+	315.423i	−0.456197	+	0.387497i
$815$	−22.6683	+	418.092i	−0.0278138	+	0.512996i
$816$	48.8830	+	92.2031i	0.0599057	+	0.112994i
$817$	291.226	−	1323.05i	0.356457	−	1.61940i
$818$	−1444.74	+	668.408i	−1.76619	+	0.817125i
$819$	58.6751	−	97.5187i	0.0716423	−	0.119070i
$820$	1567.87	−	2957.32i	1.91204	−	3.60649i
$821$	−376.356	−	319.680i	−0.458412	−	0.389379i	0.388212	−	0.921570i	$-0.373093\pi$
$821$	−376.356	−	319.680i	−0.458412	−	0.389379i	−0.846624	+	0.532192i	$0.821369\pi$
$822$	320.910	−	338.780i	0.390401	−	0.412141i
$823$	0.728163	−	6.69535i	0.000884767	−	0.00813529i	−0.993687	−	0.112186i	$-0.964215\pi$
$823$	0.728163	−	6.69535i	0.000884767	−	0.00813529i	0.994572	+	0.104050i	$0.0331803\pi$
$824$	1559.35	−	3913.67i	1.89241	−	4.74960i
$825$			83.1807i			0.100825i
$826$	−406.474	−	63.6316i	−0.492099	−	0.0770359i
$827$	−170.249			−0.205863			−0.102932	−	0.994688i	$-0.532822\pi$
$827$	−170.249			−0.205863			−0.102932	+	0.994688i	$0.532822\pi$
$828$	−265.601	−	105.825i	−0.320774	−	0.127808i
$829$	−831.755	−	90.4588i	−1.00332	−	0.109118i	−0.408318	−	0.912840i	$-0.633885\pi$
$829$	−831.755	−	90.4588i	−1.00332	−	0.109118i	−0.595005	+	0.803722i	$0.702850\pi$
$830$	298.455	+	282.712i	0.359584	+	0.340617i
$831$	−75.6961	+	89.1163i	−0.0910904	+	0.107240i
$832$	−3438.29	−	1822.86i	−4.13256	−	2.19094i
$833$	−43.6367	−	26.2553i	−0.0523850	−	0.0315190i
$834$	459.403	+	992.983i	0.550843	+	1.19063i
$835$	−1115.63	−	245.569i	−1.33608	−	0.294094i
$836$	3608.56	−	1913.14i	4.31646	−	2.28844i
$837$	215.973	+	11.7097i	0.258032	+	0.0139901i
$838$	237.774	+	279.929i	0.283739	+	0.334044i
$839$	324.718	+	1475.21i	0.387030	+	1.75830i	0.618822	+	0.785531i	$0.287610\pi$
$839$	324.718	+	1475.21i	0.387030	+	1.75830i	−0.231792	+	0.972765i	$0.574459\pi$
$840$	219.117	+	288.243i	0.260853	+	0.343147i
$841$	127.244	−	120.532i	0.151300	−	0.143319i
$842$	112.402	+	2073.14i	0.133494	+	2.46216i
$843$	−398.579	+	239.817i	−0.472810	+	0.284480i
$844$	−2979.05	−	2019.84i	−3.52968	−	2.39318i
$845$	−319.658	+	1151.30i	−0.378293	+	1.36249i
$846$	434.750	−	47.2820i	0.513889	−	0.0558888i
$847$	2.43766	+	1.85306i	0.00287799	+	0.00218779i
$848$	−1132.34	−	523.876i	−1.33531	−	0.617778i
$849$	−192.240	+	130.342i	−0.226431	+	0.153524i
$850$	−5.98208	−	17.7542i	−0.00703774	−	0.0208873i
$851$	16.9700	+	103.512i	0.0199412	+	0.121636i
$852$	−222.406	+	1356.61i	−0.261039	+	1.59227i
$853$	−1275.59	−	429.795i	−1.49541	−	0.503863i	−0.551533	−	0.834153i	$-0.685957\pi$
$853$	−1275.59	−	429.795i	−1.49541	−	0.503863i	−0.943880	+	0.330290i	$0.892854\pi$
$854$	49.1394	+	176.984i	0.0575403	+	0.207241i
$855$	−177.720	−	446.044i	−0.207860	−	0.521689i
$856$	2193.35	−	873.909i	2.56232	−	1.02092i
$857$	1073.85	−	298.154i	1.25304	−	0.347904i	0.423265	−	0.906006i	$-0.360884\pi$
$857$	1073.85	−	298.154i	1.25304	−	0.347904i	0.829773	+	0.558101i	$0.188470\pi$
$858$	479.979	−	1424.53i	0.559416	−	1.66029i
$859$	1527.64	+	250.444i	1.77839	+	0.291553i	0.959358	−	0.282192i	$-0.0910616\pi$
$859$	1527.64	+	250.444i	1.77839	+	0.291553i	0.819034	+	0.573745i	$0.194510\pi$
$860$	1825.00	−	299.194i	2.12209	−	0.347900i
$861$	−208.277	+	70.1768i	−0.241902	+	0.0815061i
$862$	−1360.67	−	2006.83i	−1.57850	−	2.32811i
$863$	−504.512	+	1090.49i	−0.584603	+	1.26360i	0.359253	+	0.933240i	$0.383032\pi$
$863$	−504.512	+	1090.49i	−0.584603	+	1.26360i	−0.943856	+	0.330358i	$0.892831\pi$
$864$	331.872	−	436.570i	0.384111	−	0.505289i
$865$	117.625	+	1081.54i	0.135982	+	1.25034i
$866$	−1443.10	−	400.675i	−1.66640	−	0.462674i
$867$	−279.701	+	412.528i	−0.322607	+	0.475810i
$868$	−415.248	−	690.148i	−0.478397	−	0.795101i
$869$	−588.769	+	31.9221i	−0.677525	+	0.0367343i
$870$	533.114	+	562.802i	0.612775	+	0.646898i
$871$	−1191.35	+	905.644i	−1.36780	+	1.03977i
$872$	3832.57	−	843.612i	4.39515	−	0.967445i
$873$	−32.2914	+	27.4286i	−0.0369891	+	0.0314188i
$874$	65.5620	−	1209.22i	0.0750137	−	1.38355i
$875$	−114.048	−	215.118i	−0.130341	−	0.245849i
$876$	409.346	−	1859.68i	0.467290	−	2.12292i
$877$	−352.886	+	163.262i	−0.402378	+	0.186160i	−0.610631	−	0.791915i	$-0.709084\pi$
$877$	−352.886	+	163.262i	−0.402378	+	0.186160i	0.208253	+	0.978075i	$0.433222\pi$
$878$	119.650	−	198.860i	0.136276	−	0.226492i
$879$	−39.8230	+	75.1142i	−0.0453049	+	0.0854541i
$880$	2041.94	+	1734.44i	2.32038	+	1.97095i
$881$	604.842	−	638.524i	0.686540	−	0.724771i	−0.285814	−	0.958285i	$-0.592264\pi$
$881$	604.842	−	638.524i	0.686540	−	0.724771i	0.972353	+	0.233514i	$0.0750224\pi$
$882$	−56.6106	+	520.526i	−0.0641844	+	0.590166i
$883$	509.655	−	1279.14i	0.577186	−	1.44863i	−0.293101	−	0.956082i	$-0.594687\pi$
$883$	509.655	−	1279.14i	0.577186	−	1.44863i	0.870287	−	0.492546i	$-0.163934\pi$
$884$			245.839i			0.278098i
$885$	−21.7721	+	463.345i	−0.0246012	+	0.523554i
$886$	−1294.09			−1.46060
$887$	−455.220	−	181.376i	−0.513213	−	0.204483i	0.0991308	−	0.995074i	$-0.468394\pi$
$887$	−455.220	−	181.376i	−0.513213	−	0.204483i	−0.612344	+	0.790592i	$0.709773\pi$
$888$	−507.227	−	55.1642i	−0.571201	−	0.0621219i
$889$	112.420	+	106.490i	0.126457	+	0.119786i
$890$	1489.96	−	1754.12i	1.67411	−	1.97092i
$891$	86.8591	+	46.0498i	0.0974849	+	0.0516832i
$892$	1240.02	+	746.096i	1.39016	+	0.836431i
$893$	564.738	+	1220.66i	0.632406	+	1.36692i
$894$	471.470	+	103.778i	0.527371	+	0.116083i
$895$	548.547	−	290.821i	0.612902	−	0.324940i
$896$	−534.195	−	28.9632i	−0.596200	−	0.0323250i
$897$	−209.511	−	246.655i	−0.233568	−	0.274978i
$898$	−71.0604	−	322.831i	−0.0791319	−	0.359500i
$899$	−649.957	−	855.004i	−0.722978	−	0.951061i
$900$	−101.540	+	96.1840i	−0.112822	+	0.106871i
$901$	1.39395	+	25.7100i	0.00154712	+	0.0285349i
$902$	−2487.38	+	1496.61i	−2.75763	+	1.65921i
$903$	−100.507	−	68.1454i	−0.111303	−	0.0754656i
$904$	−736.425	+	2652.36i	−0.814629	+	2.93403i
$905$	1186.41	−	129.030i	1.31095	−	0.142574i
$906$	281.947	+	214.331i	0.311200	+	0.236568i
$907$	−89.5564	−	41.4332i	−0.0987391	−	0.0456816i	0.369898	−	0.929072i	$-0.379393\pi$
$907$	−89.5564	−	41.4332i	−0.0987391	−	0.0456816i	−0.468637	+	0.883391i	$0.655255\pi$
$908$	−2018.99	+	1368.91i	−2.22356	+	1.50761i
$909$	−25.6487	−	76.1226i	−0.0282164	−	0.0837432i
$910$	106.463	+	649.397i	0.116993	+	0.713623i
$911$	−176.104	+	1074.18i	−0.193308	+	1.17913i	0.694700	+	0.719299i	$0.255537\pi$
$911$	−176.104	+	1074.18i	−0.193308	+	1.17913i	−0.888008	+	0.459827i	$0.847911\pi$
$912$	3127.19	+	1053.67i	3.42894	+	1.15534i
$913$	−69.2570	−	249.441i	−0.0758566	−	0.273211i
$914$	103.976	+	260.961i	0.113760	+	0.285515i
$915$	192.379	−	76.6509i	0.210251	−	0.0837715i
$916$	1964.18	−	545.352i	2.14430	−	0.595363i
$917$	108.478	−	321.952i	0.118297	−	0.351093i
$918$	−21.8510	−	3.58229i	−0.0238029	−	0.00390228i
$919$	602.007	−	98.6940i	0.655067	−	0.107393i	0.174922	−	0.984582i	$-0.444033\pi$
$919$	602.007	−	98.6940i	0.655067	−	0.107393i	0.480144	+	0.877189i	$0.340584\pi$
$920$	975.681	−	328.745i	1.06052	−	0.357332i
$921$	−337.553	−	497.853i	−0.366507	−	0.540557i
$922$	997.363	−	2155.76i	1.08174	−	2.33814i
$923$	−941.704	+	1238.79i	−1.02026	+	1.34213i
$924$	−39.5824	−	363.954i	−0.0428381	−	0.393890i
$925$	49.4431	+	13.7278i	0.0534520	+	0.0148409i
$926$	830.485	−	1224.87i	0.896852	−	1.32276i
$927$	258.172	+	429.085i	0.278503	+	0.462875i
$928$	−2719.07	+	147.424i	−2.93003	+	0.158862i
$929$	−340.663	−	359.634i	−0.366699	−	0.387119i	0.516368	−	0.856367i	$-0.327284\pi$
$929$	−340.663	−	359.634i	−0.366699	−	0.387119i	−0.883067	+	0.469248i	$0.844525\pi$
$930$	−995.612	+	756.844i	−1.07055	+	0.813811i
$931$	−1572.68	+	346.173i	−1.68924	+	0.371830i
$932$	3111.89	−	2643.26i	3.33894	−	2.83612i
$933$	−10.6302	+	196.063i	−0.0113936	+	0.210142i
$934$	1325.52	+	2500.19i	1.41918	+	2.67686i
$935$	11.8855	−	53.9965i	0.0127118	−	0.0577503i
$936$	1428.66	−	660.969i	1.52635	−	0.706164i
$937$	−260.822	+	433.489i	−0.278358	+	0.462635i	−0.964222	−	0.265094i	$-0.914597\pi$
$937$	−260.822	+	433.489i	−0.278358	+	0.462635i	0.685864	+	0.727730i	$0.259424\pi$
$938$	−235.115	+	443.473i	−0.250655	+	0.472786i
$939$	−787.741	−	669.113i	−0.838915	−	0.712581i
$940$	−1262.65	+	1332.96i	−1.34324	+	1.41805i
$941$	−51.2864	+	471.571i	−0.0545020	+	0.501138i	0.934791	+	0.355197i	$0.115586\pi$
$941$	−51.2864	+	471.571i	−0.0545020	+	0.501138i	−0.989293	+	0.145940i	$0.953379\pi$
$942$	−643.832	+	1615.90i	−0.683473	+	1.71539i
$943$			624.965i			0.662741i
$944$	−2330.21	−	2175.63i	−2.46844	−	2.30469i
$945$	−43.0379			−0.0455428
$946$	−1489.96	−	593.655i	−1.57501	−	0.627542i
$947$	−108.000	−	11.7457i	−0.114044	−	0.0124030i	0.0509190	−	0.998703i	$-0.483785\pi$
$947$	−108.000	−	11.7457i	−0.114044	−	0.0124030i	−0.164963	+	0.986300i	$0.552750\pi$
$948$	−719.777	−	681.809i	−0.759258	−	0.719207i
$949$	1395.38	−	1642.77i	1.47037	−	1.73106i
$950$	−523.401	−	277.490i	−0.550949	−	0.292095i
$951$	−551.795	−	332.004i	−0.580226	−	0.349111i
$952$	21.5629	+	46.6074i	0.0226501	+	0.0489574i
$953$	−1187.24	−	261.332i	−1.24579	−	0.274220i	−0.457328	−	0.889298i	$-0.651194\pi$
$953$	−1187.24	−	261.332i	−1.24579	−	0.274220i	−0.788466	+	0.615078i	$0.789125\pi$
$954$	233.886	−	123.998i	0.245163	−	0.129977i
$955$	−23.9879	−	1.30059i	−0.0251182	−	0.00136187i
$956$	2583.01	+	3040.95i	2.70189	+	3.18091i
$957$	−104.942	−	476.756i	−0.109657	−	0.498178i
$958$	1351.37	+	1777.69i	1.41061	+	1.85563i
$959$	93.3932	−	88.4668i	0.0973861	−	0.0922490i
$960$	79.6729	+	1469.48i	0.0829926	+	1.53071i
$961$	661.188	−	397.823i	0.688020	−	0.413968i
$962$	−767.533	−	520.400i	−0.797851	−	0.540956i
$963$	−75.0807	+	270.416i	−0.0779654	+	0.280806i
$964$	−3228.75	+	351.147i	−3.34932	+	0.364261i
$965$	−523.635	−	398.057i	−0.542627	−	0.412495i
$966$	−98.5153	−	45.5780i	−0.101983	−	0.0471822i
$967$	82.5377	−	55.9619i	0.0853544	−	0.0578717i	−0.517763	−	0.855524i	$-0.673235\pi$
$967$	82.5377	−	55.9619i	0.0853544	−	0.0578717i	0.603118	+	0.797652i	$0.293925\pi$
$968$	13.5231	+	40.1352i	0.0139702	+	0.0414620i
$969$	−11.0174	−	67.2033i	−0.0113699	−	0.0693533i
$970$	39.6333	−	241.752i	0.0408591	−	0.249229i
$971$	−117.186	−	39.4847i	−0.120686	−	0.0406640i	0.258310	−	0.966062i	$-0.416834\pi$
$971$	−117.186	−	39.4847i	−0.120686	−	0.0406640i	−0.378997	+	0.925398i	$0.623731\pi$
$972$	44.2236	+	159.279i	0.0454975	+	0.163867i
$973$	111.640	+	280.196i	0.114738	+	0.287971i
$974$	1473.06	−	586.922i	1.51239	−	0.602590i
$975$	−152.545	+	42.3538i	−0.156456	+	0.0434398i
$976$	−454.451	+	1348.76i	−0.465626	+	1.38193i
$977$	−887.383	−	145.479i	−0.908273	−	0.148904i	−0.310504	−	0.950572i	$-0.600498\pi$
$977$	−887.383	−	145.479i	−0.908273	−	0.148904i	−0.597769	+	0.801668i	$0.703946\pi$
$978$	602.531	−	98.7800i	0.616085	−	0.101002i
$979$	−1373.44	+	462.766i	−1.40290	+	0.472693i
$980$	−1233.66	−	1819.51i	−1.25883	−	1.85664i
$981$	−195.864	+	423.353i	−0.199657	+	0.431552i
$982$	−490.536	+	645.289i	−0.499527	+	0.657117i
$983$	3.68304	+	33.8650i	0.00374674	+	0.0344507i	0.995862	−	0.0908774i	$-0.0289672\pi$
$983$	3.68304	+	33.8650i	0.00374674	+	0.0344507i	−0.992115	+	0.125328i	$0.960002\pi$
$984$	−2929.10	−	813.260i	−2.97672	−	0.826483i
$985$	309.390	−	456.316i	0.314102	−	0.463265i
$986$	56.6856	+	94.2122i	0.0574905	+	0.0955499i
$987$	120.380	−	6.52680i	0.121965	−	0.00661277i
$988$	5345.90	+	5643.59i	5.41083	+	5.71214i
$989$	−274.888	+	208.965i	−0.277946	+	0.211289i
$990$	−555.160	+	122.200i	−0.560768	+	0.123434i
$991$	−537.982	+	456.966i	−0.542868	+	0.461116i	−0.876374	−	0.481632i	$-0.840044\pi$
$991$	−537.982	+	456.966i	−0.542868	+	0.461116i	0.333506	+	0.942748i	$0.391768\pi$
$992$	237.833	−	4386.57i	0.239751	−	4.42195i
$993$	458.002	+	863.884i	0.461231	+	0.869974i
$994$	−112.199	+	509.727i	−0.112877	+	0.512804i
$995$	548.235	−	253.640i	0.550989	−	0.254915i
$996$	224.414	−	372.979i	0.225315	−	0.374477i
$997$	−256.958	+	484.675i	−0.257732	+	0.486134i	−0.978285	−	0.207267i	$-0.933543\pi$
$997$	−256.958	+	484.675i	−0.257732	+	0.486134i	0.720553	+	0.693400i	$0.243888\pi$
$998$	−1634.29	−	1388.18i	−1.63757	−	1.39096i
$999$	41.7071	−	44.0297i	0.0417489	−	0.0440737i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.3.g.a.10.1	✓	560
59.6	odd	58	inner	177.3.g.a.124.1	yes	560

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.3.g.a.10.1	✓	560	1.1	even	1	trivial
177.3.g.a.124.1	yes	560	59.6	odd	58	inner

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.g (of order \(58\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.55013 - 1.41450i) q^{2} +(1.72190 + 0.187268i) q^{3} +(7.69866 + 7.29256i) q^{4} +(2.93856 - 3.45954i) q^{5} +(-5.84808 - 3.10045i) q^{6} +(-1.56353 - 0.940746i) q^{7} +(-10.5974 - 22.9059i) q^{8} +(2.92986 + 0.644911i) q^{9} +O(q^{10})\)	\(q+(-3.55013 - 1.41450i) q^{2} +(1.72190 + 0.187268i) q^{3} +(7.69866 + 7.29256i) q^{4} +(2.93856 - 3.45954i) q^{5} +(-5.84808 - 3.10045i) q^{6} +(-1.56353 - 0.940746i) q^{7} +(-10.5974 - 22.9059i) q^{8} +(2.92986 + 0.644911i) q^{9} +(-15.3258 + 8.12523i) q^{10} +(10.9074 + 0.591384i) q^{11} +(11.8906 + 13.9987i) q^{12} +(4.46929 + 20.3042i) q^{13} +(4.22006 + 5.55139i) q^{14} +(5.70776 - 5.40668i) q^{15} +(2.92532 + 53.9543i) q^{16} +(0.955471 - 0.574888i) q^{17} +(-9.48918 - 6.43382i) q^{18} +(9.43301 - 33.9746i) q^{19} +(47.8519 - 5.20420i) q^{20} +(-2.51607 - 1.91267i) q^{21} +(-37.8864 - 17.5281i) q^{22} +(-7.43857 + 5.04347i) q^{23} +(-13.9581 - 41.4262i) q^{24} +(0.711266 + 4.33853i) q^{25} +(12.8538 - 78.4045i) q^{26} +(4.92415 + 1.65914i) q^{27} +(-5.17665 - 18.6446i) q^{28} +(-9.55023 - 23.9693i) q^{29} +(-27.9111 + 11.1208i) q^{30} +(40.1078 - 11.1359i) q^{31} +(33.6984 - 100.013i) q^{32} +(18.6707 + 3.06091i) q^{33} +(-4.20523 + 0.689413i) q^{34} +(-7.84908 + 2.64466i) q^{35} +(17.8529 + 26.3311i) q^{36} +(4.90077 - 10.5928i) q^{37} +(-81.5457 + 107.272i) q^{38} +(3.89335 + 35.7987i) q^{39} +(-110.385 - 30.6483i) q^{40} +(39.0248 - 57.5573i) q^{41} +(6.22691 + 10.3492i) q^{42} +(38.3648 - 2.08008i) q^{43} +(79.6599 + 84.0960i) q^{44} +(10.8407 - 8.24086i) q^{45} +(33.5419 - 7.38314i) q^{46} +(-29.0723 + 24.6942i) q^{47} +(-5.06680 + 93.4516i) q^{48} +(-21.3924 - 40.3503i) q^{49} +(3.61177 - 16.4085i) q^{50} +(1.75288 - 0.810969i) q^{51} +(-113.662 + 188.908i) q^{52} +(-10.8157 + 20.4006i) q^{53} +(-15.1345 - 12.8554i) q^{54} +(34.0981 - 35.9969i) q^{55} +(-4.97927 + 45.7836i) q^{56} +(22.6050 - 56.7343i) q^{57} +98.6029i q^{58} +(-42.5400 + 40.8821i) q^{59} +83.3706 q^{60} +(24.4696 + 9.74958i) q^{61} +(-158.140 - 17.1987i) q^{62} +(-3.97423 - 3.76459i) q^{63} +(-121.181 + 142.665i) q^{64} +(83.3765 + 44.2034i) q^{65} +(-61.9540 - 37.2765i) q^{66} +(30.2240 + 65.3280i) q^{67} +(11.5482 + 2.54196i) q^{68} +(-13.7529 + 7.29134i) q^{69} +(31.6062 + 1.71364i) q^{70} +(48.4549 + 57.0455i) q^{71} +(-16.2767 - 73.9456i) q^{72} +(-62.7409 - 82.5342i) q^{73} +(-32.3820 + 30.6738i) q^{74} +(0.412261 + 7.60370i) q^{75} +(320.383 - 192.768i) q^{76} +(-16.4978 - 11.1858i) q^{77} +(36.8155 - 132.597i) q^{78} +(-53.6622 + 5.83612i) q^{79} +(195.253 + 148.428i) q^{80} +(8.16818 + 3.77900i) q^{81} +(-219.959 + 149.136i) q^{82} +(-7.56720 - 22.4586i) q^{83} +(-5.42213 - 33.0735i) q^{84} +(0.818861 - 4.99483i) q^{85} +(-139.142 - 46.8825i) q^{86} +(-11.9558 - 43.0611i) q^{87} +(-102.044 - 256.112i) q^{88} +(-123.255 + 49.1094i) q^{89} +(-50.1426 + 13.9220i) q^{90} +(12.1132 - 35.9507i) q^{91} +(-94.0468 - 15.4182i) q^{92} +(71.1469 - 11.6639i) q^{93} +(138.141 - 46.5450i) q^{94} +(-89.8171 - 132.470i) q^{95} +(76.7544 - 165.902i) q^{96} +(-8.54672 + 11.2430i) q^{97} +(18.8702 + 173.509i) q^{98} +(31.5759 + 8.76700i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9}+O(q^{10}) \) 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9	\( 560 q + 40 q^{4} + 8 q^{7} - 60 q^{9} + 24 q^{12} - 24 q^{15} + 8 q^{16} - 16 q^{17} + 60 q^{19} + 164 q^{20} - 40 q^{22} - 100 q^{25} + 156 q^{26} - 200 q^{28} + 60 q^{29} + 32 q^{35} + 120 q^{36} - 28 q^{41} - 1572 q^{46} - 638 q^{47} + 96 q^{48} - 1328 q^{49} - 1856 q^{50} + 24 q^{51} - 1392 q^{52} - 572 q^{53} - 522 q^{55} - 928 q^{56} - 24 q^{57} + 268 q^{59} + 72 q^{60} + 348 q^{61} + 472 q^{62} + 24 q^{63} + 2580 q^{64} + 1218 q^{65} + 120 q^{66} + 1044 q^{67} + 1936 q^{68} + 2784 q^{70} + 1416 q^{71} + 870 q^{73} + 1752 q^{74} - 240 q^{75} - 120 q^{76} + 468 q^{78} + 420 q^{79} - 376 q^{80} - 180 q^{81} - 168 q^{84} + 348 q^{85} - 232 q^{86} - 144 q^{87} + 212 q^{88} - 152 q^{94} - 788 q^{95} - 3306 q^{98}+O(q^{100}) \) 560 * q + 40 * q^4 + 8 * q^7 - 60 * q^9 + 24 * q^12 - 24 * q^15 + 8 * q^16 - 16 * q^17 + 60 * q^19 + 164 * q^20 - 40 * q^22 - 100 * q^25 + 156 * q^26 - 200 * q^28 + 60 * q^29 + 32 * q^35 + 120 * q^36 - 28 * q^41 - 1572 * q^46 - 638 * q^47 + 96 * q^48 - 1328 * q^49 - 1856 * q^50 + 24 * q^51 - 1392 * q^52 - 572 * q^53 - 522 * q^55 - 928 * q^56 - 24 * q^57 + 268 * q^59 + 72 * q^60 + 348 * q^61 + 472 * q^62 + 24 * q^63 + 2580 * q^64 + 1218 * q^65 + 120 * q^66 + 1044 * q^67 + 1936 * q^68 + 2784 * q^70 + 1416 * q^71 + 870 * q^73 + 1752 * q^74 - 240 * q^75 - 120 * q^76 + 468 * q^78 + 420 * q^79 - 376 * q^80 - 180 * q^81 - 168 * q^84 + 348 * q^85 - 232 * q^86 - 144 * q^87 + 212 * q^88 - 152 * q^94 - 788 * q^95 - 3306 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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