LMFDB - Embedded newform 171.3.i.a.103.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,3,Mod(88,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("171.88");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.i (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:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.30
Character	$\chi$	$=$	171.103
Dual form			171.3.i.a.88.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.41326i q^{2} +(-2.25389 - 1.97989i) q^{3} -1.82382 q^{4} +(3.12409 + 5.41107i) q^{5} +(4.77800 - 5.43922i) q^{6} +(-3.26441 - 5.65412i) q^{7} +5.25168i q^{8} +(1.16004 + 8.92493i) q^{9} +O(q^{10})$	\(q+2.41326i q^{2} +(-2.25389 - 1.97989i) q^{3} -1.82382 q^{4} +(3.12409 + 5.41107i) q^{5} +(4.77800 - 5.43922i) q^{6} +(-3.26441 - 5.65412i) q^{7} +5.25168i q^{8} +(1.16004 + 8.92493i) q^{9} +(-13.0583 + 7.53923i) q^{10} +(1.18250 + 2.04815i) q^{11} +(4.11070 + 3.61098i) q^{12} +17.7142i q^{13} +(13.6449 - 7.87787i) q^{14} +(3.67201 - 18.3813i) q^{15} -19.9690 q^{16} +(-6.18287 + 10.7090i) q^{17} +(-21.5382 + 2.79947i) q^{18} +(-17.8708 - 6.45239i) q^{19} +(-5.69778 - 9.86885i) q^{20} +(-3.83695 + 19.2070i) q^{21} +(-4.94272 + 2.85368i) q^{22} -18.2468 q^{23} +(10.3978 - 11.8367i) q^{24} +(-7.01982 + 12.1587i) q^{25} -42.7489 q^{26} +(15.0558 - 22.4125i) q^{27} +(5.95371 + 10.3121i) q^{28} +(20.6684 + 11.9329i) q^{29} +(44.3589 + 8.86152i) q^{30} +(36.0937 + 20.8387i) q^{31} -27.1836i q^{32} +(1.38990 - 6.95754i) q^{33} +(-25.8437 - 14.9209i) q^{34} +(20.3966 - 35.3279i) q^{35} +(-2.11570 - 16.2775i) q^{36} +17.7927i q^{37} +(15.5713 - 43.1270i) q^{38} +(35.0722 - 39.9258i) q^{39} +(-28.4172 + 16.4067i) q^{40} +(35.4070 - 20.4423i) q^{41} +(-46.3514 - 9.25955i) q^{42} -0.656571 q^{43} +(-2.15667 - 3.73547i) q^{44} +(-44.6694 + 34.1593i) q^{45} -44.0343i q^{46} +(-21.7623 + 37.6934i) q^{47} +(45.0078 + 39.5364i) q^{48} +(3.18726 - 5.52050i) q^{49} +(-29.3421 - 16.9407i) q^{50} +(35.1383 - 11.8956i) q^{51} -32.3076i q^{52} +(56.0233 - 32.3450i) q^{53} +(54.0873 + 36.3336i) q^{54} +(-7.38847 + 12.7972i) q^{55} +(29.6936 - 17.1436i) q^{56} +(27.5038 + 49.9253i) q^{57} +(-28.7972 + 49.8782i) q^{58} +(78.7916 - 45.4904i) q^{59} +(-6.69710 + 33.5243i) q^{60} +(-19.7636 + 34.2315i) q^{61} +(-50.2893 + 87.1036i) q^{62} +(46.6758 - 35.6936i) q^{63} -14.2748 q^{64} +(-95.8528 + 55.3406i) q^{65} +(16.7903 + 3.35418i) q^{66} +114.069i q^{67} +(11.2765 - 19.5314i) q^{68} +(41.1263 + 36.1268i) q^{69} +(85.2555 + 49.2223i) q^{70} +(-7.60532 - 4.39093i) q^{71} +(-46.8709 + 6.09214i) q^{72} +(68.3654 - 118.412i) q^{73} -42.9383 q^{74} +(39.8948 - 13.5058i) q^{75} +(32.5932 + 11.7680i) q^{76} +(7.72033 - 13.3720i) q^{77} +(96.3514 + 84.6384i) q^{78} -131.147i q^{79} +(-62.3847 - 108.054i) q^{80} +(-78.3086 + 20.7065i) q^{81} +(49.3325 + 85.4463i) q^{82} +(-12.4101 - 21.4949i) q^{83} +(6.99792 - 35.0301i) q^{84} -77.2633 q^{85} -1.58448i q^{86} +(-22.9584 - 67.8166i) q^{87} +(-10.7562 + 6.21012i) q^{88} +(-11.2942 + 6.52074i) q^{89} +(-82.4352 - 107.799i) q^{90} +(100.158 - 57.8264i) q^{91} +33.2790 q^{92} +(-40.0928 - 118.430i) q^{93} +(-90.9640 - 52.5181i) q^{94} +(-20.9156 - 116.858i) q^{95} +(-53.8206 + 61.2688i) q^{96} -118.488i q^{97} +(13.3224 + 7.69170i) q^{98} +(-16.9079 + 12.9297i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 3 q^{3} - 146 q^{4} + q^{5} + 7 q^{6} - 3 q^{7} - 13 q^{9}+O(q^{10}) $ 76 * q - 3 * q^3 - 146 * q^4 + q^5 + 7 * q^6 - 3 * q^7 - 13 * q^9	\( 76 q - 3 q^{3} - 146 q^{4} + q^{5} + 7 q^{6} - 3 q^{7} - 13 q^{9} - 6 q^{10} + 4 q^{11} - 15 q^{12} + 21 q^{14} - 18 q^{15} + 262 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} - 17 q^{20} + 24 q^{21} - 15 q^{22} + 46 q^{23} - 23 q^{24} - 149 q^{25} + 48 q^{26} - 63 q^{27} + 30 q^{28} - 30 q^{29} - 41 q^{30} + 48 q^{31} - 93 q^{33} + 15 q^{34} - 31 q^{35} - 51 q^{36} - 135 q^{38} + 28 q^{39} + 96 q^{40} + 123 q^{41} + 238 q^{42} + 182 q^{43} - 191 q^{44} - 289 q^{45} + 61 q^{47} + 123 q^{48} - 171 q^{49} + 243 q^{50} - 45 q^{51} - 42 q^{53} + 224 q^{54} + 23 q^{55} - 624 q^{56} - 133 q^{57} + 6 q^{58} - 390 q^{59} + 381 q^{60} - 6 q^{61} - 366 q^{62} + 323 q^{63} - 152 q^{64} + 582 q^{65} + 95 q^{66} - 74 q^{68} - 75 q^{69} - 150 q^{70} - 87 q^{71} + 99 q^{72} + 29 q^{73} + 252 q^{74} - 585 q^{75} - 3 q^{76} + 32 q^{77} - 216 q^{78} - 104 q^{80} - 5 q^{81} + 54 q^{82} - 23 q^{83} + 204 q^{84} + 98 q^{85} + 671 q^{87} + 132 q^{88} - 222 q^{89} + 249 q^{90} - 51 q^{91} + 694 q^{92} + 293 q^{93} + 24 q^{94} + 145 q^{95} + 147 q^{96} - 558 q^{98} - 92 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 146 * q^4 + q^5 + 7 * q^6 - 3 * q^7 - 13 * q^9 - 6 * q^10 + 4 * q^11 - 15 * q^12 + 21 * q^14 - 18 * q^15 + 262 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 - 17 * q^20 + 24 * q^21 - 15 * q^22 + 46 * q^23 - 23 * q^24 - 149 * q^25 + 48 * q^26 - 63 * q^27 + 30 * q^28 - 30 * q^29 - 41 * q^30 + 48 * q^31 - 93 * q^33 + 15 * q^34 - 31 * q^35 - 51 * q^36 - 135 * q^38 + 28 * q^39 + 96 * q^40 + 123 * q^41 + 238 * q^42 + 182 * q^43 - 191 * q^44 - 289 * q^45 + 61 * q^47 + 123 * q^48 - 171 * q^49 + 243 * q^50 - 45 * q^51 - 42 * q^53 + 224 * q^54 + 23 * q^55 - 624 * q^56 - 133 * q^57 + 6 * q^58 - 390 * q^59 + 381 * q^60 - 6 * q^61 - 366 * q^62 + 323 * q^63 - 152 * q^64 + 582 * q^65 + 95 * q^66 - 74 * q^68 - 75 * q^69 - 150 * q^70 - 87 * q^71 + 99 * q^72 + 29 * q^73 + 252 * q^74 - 585 * q^75 - 3 * q^76 + 32 * q^77 - 216 * q^78 - 104 * q^80 - 5 * q^81 + 54 * q^82 - 23 * q^83 + 204 * q^84 + 98 * q^85 + 671 * q^87 + 132 * q^88 - 222 * q^89 + 249 * q^90 - 51 * q^91 + 694 * q^92 + 293 * q^93 + 24 * q^94 + 145 * q^95 + 147 * q^96 - 558 * q^98 - 92 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			2.41326i			1.20663i	0.797503	+	0.603315i	$0.206154\pi$
$2$			2.41326i			1.20663i	−0.797503	+	0.603315i	$0.793846\pi$
$3$	−2.25389	−	1.97989i	−0.751297	−	0.659965i
$3$	−2.25389	−	1.97989i	−0.751297	−	0.659965i
$4$	−1.82382			−0.455956
$5$	3.12409	+	5.41107i	0.624817	+	1.08221i	0.988576	+	0.150722i	$0.0481598\pi$
$5$	3.12409	+	5.41107i	0.624817	+	1.08221i	−0.363759	+	0.931493i	$0.618507\pi$
$6$	4.77800	−	5.43922i	0.796333	−	0.906537i
$7$	−3.26441	−	5.65412i	−0.466344	−	0.807732i	0.532917	−	0.846168i	$-0.321096\pi$
$7$	−3.26441	−	5.65412i	−0.466344	−	0.807732i	−0.999261	+	0.0384358i	$0.987762\pi$
$8$			5.25168i			0.656460i
$9$	1.16004	+	8.92493i	0.128893	+	0.991659i
$10$	−13.0583	+	7.53923i	−1.30583	+	0.753923i
$11$	1.18250	+	2.04815i	0.107500	+	0.186196i	0.914757	−	0.404005i	$-0.132382\pi$
$11$	1.18250	+	2.04815i	0.107500	+	0.186196i	−0.807257	+	0.590200i	$0.799049\pi$
$12$	4.11070	+	3.61098i	0.342558	+	0.300915i
$13$			17.7142i			1.36263i	0.731990	+	0.681315i	$0.238592\pi$
$13$			17.7142i			1.36263i	−0.731990	+	0.681315i	$0.761408\pi$
$14$	13.6449	−	7.87787i	0.974633	−	0.562705i
$15$	3.67201	−	18.3813i	0.244801	−	1.22542i
$16$	−19.9690			−1.24806
$17$	−6.18287	+	10.7090i	−0.363698	+	0.629944i	−0.988566	−	0.150786i	$-0.951819\pi$
$17$	−6.18287	+	10.7090i	−0.363698	+	0.629944i	0.624868	+	0.780730i	$0.285153\pi$
$18$	−21.5382	+	2.79947i	−1.19656	+	0.155526i
$19$	−17.8708	−	6.45239i	−0.940570	−	0.339599i
$19$	−17.8708	−	6.45239i	−0.940570	−	0.339599i
$20$	−5.69778	−	9.86885i	−0.284889	−	0.493442i
$21$	−3.83695	+	19.2070i	−0.182712	+	0.914617i
$22$	−4.94272	+	2.85368i	−0.224669	+	0.129713i
$23$	−18.2468			−0.793340			−0.396670	−	0.917961i	$-0.629834\pi$
$23$	−18.2468			−0.793340			−0.396670	+	0.917961i	$0.629834\pi$
$24$	10.3978	−	11.8367i	0.433240	−	0.493196i
$25$	−7.01982	+	12.1587i	−0.280793	+	0.486347i
$26$	−42.7489			−1.64419
$27$	15.0558	−	22.4125i	0.557623	−	0.830094i
$28$	5.95371	+	10.3121i	0.212632	+	0.368290i
$29$	20.6684	+	11.9329i	0.712703	+	0.411479i	0.812061	−	0.583573i	$-0.198346\pi$
$29$	20.6684	+	11.9329i	0.712703	+	0.411479i	−0.0993583	+	0.995052i	$0.531679\pi$
$30$	44.3589	+	8.86152i	1.47863	+	0.295384i
$31$	36.0937	+	20.8387i	1.16431	+	0.672217i	0.952334	−	0.305057i	$-0.0986755\pi$
$31$	36.0937	+	20.8387i	1.16431	+	0.672217i	0.211980	+	0.977274i	$0.432009\pi$
$32$		−	27.1836i		−	0.849487i
$33$	1.38990	−	6.95754i	0.0421181	−	0.210834i
$34$	−25.8437	−	14.9209i	−0.760109	−	0.438849i
$35$	20.3966	−	35.3279i	0.582760	−	1.00937i
$36$	−2.11570	−	16.2775i	−0.0587695	−	0.452153i
$37$			17.7927i			0.480883i	0.970664	+	0.240441i	$0.0772922\pi$
$37$			17.7927i			0.480883i	−0.970664	+	0.240441i	$0.922708\pi$
$38$	15.5713	−	43.1270i	0.409771	−	1.13492i
$39$	35.0722	−	39.9258i	0.899288	−	1.02374i
$40$	−28.4172	+	16.4067i	−0.710431	+	0.410167i
$41$	35.4070	−	20.4423i	0.863586	−	0.498591i	−0.00162564	−	0.999999i	$-0.500517\pi$
$41$	35.4070	−	20.4423i	0.863586	−	0.498591i	0.865211	+	0.501407i	$0.167184\pi$
$42$	−46.3514	−	9.25955i	−1.10360	−	0.220466i
$43$	−0.656571			−0.0152691			−0.00763454	−	0.999971i	$-0.502430\pi$
$43$	−0.656571			−0.0152691			−0.00763454	+	0.999971i	$0.502430\pi$
$44$	−2.15667	−	3.73547i	−0.0490153	−	0.0848970i
$45$	−44.6694	+	34.1593i	−0.992653	+	0.759095i
$46$		−	44.0343i		−	0.957267i
$47$	−21.7623	+	37.6934i	−0.463028	+	0.801987i	−0.999110	−	0.0421782i	$-0.986570\pi$
$47$	−21.7623	+	37.6934i	−0.463028	+	0.801987i	0.536082	+	0.844166i	$0.319904\pi$
$48$	45.0078	+	39.5364i	0.937663	+	0.823676i
$49$	3.18726	−	5.52050i	0.0650462	−	0.112663i
$50$	−29.3421	−	16.9407i	−0.586841	−	0.338813i
$51$	35.1383	−	11.8956i	0.688986	−	0.233247i
$52$		−	32.3076i		−	0.621299i
$53$	56.0233	−	32.3450i	1.05704	−	0.610284i	0.132430	−	0.991192i	$-0.457722\pi$
$53$	56.0233	−	32.3450i	1.05704	−	0.610284i	0.924613	+	0.380908i	$0.124389\pi$
$54$	54.0873	+	36.3336i	1.00162	+	0.672845i
$55$	−7.38847	+	12.7972i	−0.134336	+	0.232676i
$56$	29.6936	−	17.1436i	0.530244	−	0.306136i
$57$	27.5038	+	49.9253i	0.482523	+	0.875883i
$58$	−28.7972	+	49.8782i	−0.496503	+	0.859968i
$59$	78.7916	−	45.4904i	1.33545	−	0.771023i	0.349322	−	0.937003i	$-0.386412\pi$
$59$	78.7916	−	45.4904i	1.33545	−	0.771023i	0.986129	+	0.165980i	$0.0530786\pi$
$60$	−6.69710	+	33.5243i	−0.111618	+	0.558738i
$61$	−19.7636	+	34.2315i	−0.323993	+	0.561172i	−0.981308	−	0.192444i	$-0.938359\pi$
$61$	−19.7636	+	34.2315i	−0.323993	+	0.561172i	0.657315	+	0.753616i	$0.271692\pi$
$62$	−50.2893	+	87.1036i	−0.811117	+	1.40490i
$63$	46.6758	−	35.6936i	0.740886	−	0.566565i
$64$	−14.2748			−0.223044
$65$	−95.8528	+	55.3406i	−1.47466	+	0.851395i
$66$	16.7903	+	3.35418i	0.254399	+	0.0508210i
$67$			114.069i			1.70252i	0.524740	+	0.851262i	$0.324162\pi$
$67$			114.069i			1.70252i	−0.524740	+	0.851262i	$0.675838\pi$
$68$	11.2765	−	19.5314i	0.165830	−	0.287227i
$69$	41.1263	+	36.1268i	0.596033	+	0.523576i
$70$	85.2555	+	49.2223i	1.21794	+	0.703175i
$71$	−7.60532	−	4.39093i	−0.107117	−	0.0618441i	0.445484	−	0.895290i	$-0.353032\pi$
$71$	−7.60532	−	4.39093i	−0.107117	−	0.0618441i	−0.552602	+	0.833446i	$0.686365\pi$
$72$	−46.8709	+	6.09214i	−0.650984	+	0.0846130i
$73$	68.3654	−	118.412i	0.936512	−	1.62209i	0.164598	−	0.986361i	$-0.447367\pi$
$73$	68.3654	−	118.412i	0.936512	−	1.62209i	0.771914	−	0.635726i	$-0.219299\pi$
$74$	−42.9383			−0.580247
$75$	39.8948	−	13.5058i	0.531931	−	0.180078i
$76$	32.5932	+	11.7680i	0.428858	+	0.154842i
$77$	7.72033	−	13.3720i	0.100264	−	0.173662i
$78$	96.3514	+	84.6384i	1.23527	+	1.08511i
$79$		−	131.147i		−	1.66009i	−0.557697	−	0.830044i	$-0.688315\pi$
$79$		−	131.147i		−	1.66009i	0.557697	−	0.830044i	$-0.311685\pi$
$80$	−62.3847	−	108.054i	−0.779809	−	1.35067i
$81$	−78.3086	+	20.7065i	−0.966773	+	0.255635i
$82$	49.3325	+	85.4463i	0.601615	+	1.04203i
$83$	−12.4101	−	21.4949i	−0.149519	−	0.258974i	0.781531	−	0.623867i	$-0.214439\pi$
$83$	−12.4101	−	21.4949i	−0.149519	−	0.258974i	−0.931050	+	0.364892i	$0.881106\pi$
$84$	6.99792	−	35.0301i	0.0833085	−	0.417025i
$85$	−77.2633			−0.908980
$86$		−	1.58448i		−	0.0184241i
$87$	−22.9584	−	67.8166i	−0.263889	−	0.779501i
$88$	−10.7562	+	6.21012i	−0.122230	+	0.0705695i
$89$	−11.2942	+	6.52074i	−0.126902	+	0.0732667i	−0.562107	−	0.827065i	$-0.690009\pi$
$89$	−11.2942	+	6.52074i	−0.126902	+	0.0732667i	0.435205	+	0.900331i	$0.356676\pi$
$90$	−82.4352	−	107.799i	−0.915947	−	1.19777i
$91$	100.158	−	57.8264i	1.10064	−	0.635455i
$92$	33.2790			0.361728
$93$	−40.0928	−	118.430i	−0.431106	−	1.27344i
$94$	−90.9640	−	52.5181i	−0.967702	−	0.558703i
$95$	−20.9156	−	116.858i	−0.220165	−	1.23009i
$96$	−53.8206	+	61.2688i	−0.560631	+	0.638216i
$97$		−	118.488i		−	1.22153i	−0.791813	−	0.610764i	$-0.790862\pi$
$97$		−	118.488i		−	1.22153i	0.791813	−	0.610764i	$-0.209138\pi$
$98$	13.3224	+	7.69170i	0.135943	+	0.0784867i
$99$	−16.9079	+	12.9297i	−0.170786	+	0.130603i
$100$	12.8029	−	22.1753i	0.128029	−	0.221753i
$101$	−44.8880	+	77.7482i	−0.444435	+	0.769785i	−0.998013	−	0.0630132i	$-0.979929\pi$
$101$	−44.8880	+	77.7482i	−0.444435	+	0.769785i	0.553577	+	0.832798i	$0.313262\pi$
$102$	28.7071	+	84.7978i	0.281442	+	0.831351i
$103$	−35.8761	−	20.7131i	−0.348311	−	0.201098i	0.315630	−	0.948882i	$-0.397784\pi$
$103$	−35.8761	−	20.7131i	−0.348311	−	0.201098i	−0.663941	+	0.747785i	$0.731118\pi$
$104$	−93.0293			−0.894512
$105$	−115.917	+	39.2422i	−1.10397	+	0.373735i
$106$	78.0570	+	135.199i	0.736387	+	1.27546i
$107$			97.4795i			0.911024i	0.890230	+	0.455512i	$0.150544\pi$
$107$			97.4795i			0.911024i	−0.890230	+	0.455512i	$0.849456\pi$
$108$	−27.4592	+	40.8765i	−0.254251	+	0.378486i
$109$	−42.3563	−	24.4544i	−0.388590	−	0.224353i	0.292959	−	0.956125i	$-0.405360\pi$
$109$	−42.3563	−	24.4544i	−0.388590	−	0.224353i	−0.681549	+	0.731772i	$0.738693\pi$
$110$	−30.8830	−	17.8303i	−0.280754	−	0.162094i
$111$	35.2276	−	40.1027i	0.317366	−	0.361285i
$112$	65.1869	+	112.907i	0.582026	+	1.00810i
$113$	114.547	+	66.1337i	1.01369	+	0.585254i	0.912270	−	0.409589i	$-0.134328\pi$
$113$	114.547	+	66.1337i	1.01369	+	0.585254i	0.101420	+	0.994844i	$0.467661\pi$
$114$	−120.483	+	66.3739i	−1.05687	+	0.582227i
$115$	−57.0046	−	98.7349i	−0.495692	−	0.858564i
$116$	−37.6955	−	21.7635i	−0.324961	−	0.187616i
$117$	−158.098	+	20.5491i	−1.35126	+	0.175633i
$118$	109.780	+	190.145i	0.930340	+	1.61140i
$119$	80.7337			0.678434
$120$	96.5328	+	19.2842i	0.804440	+	0.160702i
$121$	57.7034	−	99.9452i	0.476887	−	0.825993i
$122$	−82.6095	−	47.6946i	−0.677127	−	0.390939i
$123$	−120.277	−	24.0276i	−0.977862	−	0.195346i
$124$	−65.8286	−	38.0062i	−0.530876	−	0.306501i
$125$	68.4822			0.547858
$126$	86.1379	+	112.641i	0.683634	+	0.893975i
$127$	−66.3187	+	38.2891i	−0.522194	+	0.301489i	−0.737832	−	0.674984i	$-0.764150\pi$
$127$	−66.3187	+	38.2891i	−0.522194	+	0.301489i	0.215638	+	0.976473i	$0.430817\pi$
$128$		−	143.183i		−	1.11862i
$129$	1.47984	+	1.29994i	0.0114716	+	0.0100771i
$130$	−133.551	−	231.318i	−1.02732	−	1.77937i
$131$	60.2999	+	104.442i	0.460304	+	0.797271i	0.998976	−	0.0452452i	$-0.0144069\pi$
$131$	60.2999	+	104.442i	0.460304	+	0.797271i	−0.538671	+	0.842516i	$0.681074\pi$
$132$	−2.53493	+	12.6893i	−0.0192040	+	0.0961312i
$133$	21.8551	+	122.107i	0.164324	+	0.918099i
$134$	−275.278			−2.05432
$135$	168.312	+	11.4495i	1.24675	+	0.0848108i
$136$	−56.2405	−	32.4705i	−0.413533	−	0.238753i
$137$	−4.79286	+	8.30148i	−0.0349844	+	0.0605948i	−0.882987	−	0.469397i	$-0.844471\pi$
$137$	−4.79286	+	8.30148i	−0.0349844	+	0.0605948i	0.848003	+	0.529991i	$0.177805\pi$
$138$	−87.1833	+	99.2484i	−0.631763	+	0.719192i
$139$	217.026			1.56134			0.780670	−	0.624943i	$-0.214878\pi$
$139$	217.026			1.56134			0.780670	+	0.624943i	$0.214878\pi$
$140$	−37.1998	+	64.4319i	−0.265713	+	0.460228i
$141$	123.679	−	41.8697i	0.877155	−	0.296948i
$142$	10.5965	−	18.3536i	0.0746230	−	0.129251i
$143$	−36.2814	+	20.9470i	−0.253716	+	0.146483i
$144$	−23.1647	−	178.222i	−0.160866	−	1.23765i
$145$			149.118i			1.02840i
$146$	285.760	+	164.984i	1.95726	+	1.13002i
$147$	−18.1138	+	6.13216i	−0.123223	+	0.0417154i
$148$		−	32.4507i		−	0.219261i
$149$	−19.1720	−	33.2069i	−0.128671	−	0.222865i	0.794491	−	0.607276i	$-0.207738\pi$
$149$	−19.1720	−	33.2069i	−0.128671	−	0.222865i	−0.923162	+	0.384411i	$0.874405\pi$
$150$	32.5931	+	96.2766i	0.217287	+	0.641844i
$151$	−118.893	+	68.6427i	−0.787369	+	0.454588i	−0.839035	−	0.544077i	$-0.816880\pi$
$151$	−118.893	+	68.6427i	−0.787369	+	0.454588i	0.0516665	+	0.998664i	$0.483547\pi$
$152$	33.8859	−	93.8519i	0.222933	−	0.617447i
$153$	−102.750	−	42.7588i	−0.671567	−	0.279469i
$154$	32.2701	+	18.6312i	0.209546	+	0.120982i
$155$			260.408i			1.68005i
$156$	−63.9656	+	72.8177i	−0.410036	+	0.466780i
$157$	23.9636	+	41.5062i	0.152635	+	0.264371i	0.932195	−	0.361956i	$-0.117891\pi$
$157$	23.9636	+	41.5062i	0.152635	+	0.264371i	−0.779561	+	0.626327i	$0.784558\pi$
$158$	316.492			2.00311
$159$	−190.310	−	38.0180i	−1.19692	−	0.239107i
$160$	147.092	−	84.9238i	0.919327	−	0.530774i
$161$	59.5651	+	103.170i	0.369969	+	0.640806i
$162$	−49.9701	−	188.979i	−0.308457	−	1.16654i
$163$	−282.924			−1.73573			−0.867863	−	0.496803i	$-0.834507\pi$
$163$	−282.924			−1.73573			−0.867863	+	0.496803i	$0.834507\pi$
$164$	−64.5762	+	37.2831i	−0.393757	+	0.227336i
$165$	41.9899	−	14.2151i	0.254484	−	0.0861521i
$166$	51.8727	−	29.9487i	0.312486	−	0.180414i
$167$			298.859i			1.78957i	0.446493	+	0.894787i	$0.352673\pi$
$167$			298.859i			1.78957i	−0.446493	+	0.894787i	$0.647327\pi$
$168$	−100.869	−	20.1504i	−0.600409	−	0.119943i
$169$	−144.793			−0.856761
$170$		−	186.456i		−	1.09680i
$171$	36.8563	−	166.981i	0.215534	−	0.976496i
$172$	1.19747			0.00696203
$173$			127.652i			0.737874i	0.929454	+	0.368937i	$0.120278\pi$
$173$			127.652i			0.737874i	−0.929454	+	0.368937i	$0.879722\pi$
$174$	163.659	−	55.4045i	0.940570	−	0.318417i
$175$	91.6623			0.523784
$176$	−23.6133	−	40.8995i	−0.134167	−	0.232383i
$177$	−267.654	−	53.4688i	−1.51217	−	0.302084i
$178$	−15.7362	−	27.2560i	−0.0884058	−	0.153123i
$179$		−	69.7934i		−	0.389907i	−0.980812	−	0.194954i	$-0.937544\pi$
$179$		−	69.7934i		−	0.389907i	0.980812	−	0.194954i	$-0.0624556\pi$
$180$	81.4691	−	62.3005i	0.452606	−	0.346114i
$181$	196.037	−	113.182i	1.08308	−	0.625316i	0.151354	−	0.988480i	$-0.451637\pi$
$181$	196.037	−	113.182i	1.08308	−	0.625316i	0.931725	+	0.363163i	$0.118303\pi$
$182$	139.550	+	241.708i	0.766759	+	1.32806i
$183$	112.320	−	38.0242i	0.613768	−	0.207783i
$184$		−	95.8264i		−	0.520796i
$185$	−96.2774	+	55.5858i	−0.520418	+	0.300464i
$186$	285.802	−	96.7544i	1.53657	−	0.520185i
$187$	−29.2450			−0.156390
$188$	39.6906	−	68.7461i	0.211120	−	0.365671i
$189$	−175.872	−	11.9637i	−0.930538	−	0.0633001i
$190$	282.009	−	50.4749i	1.48426	−	0.265657i
$191$	179.229	+	310.434i	0.938371	+	1.62531i	0.768509	+	0.639839i	$0.220999\pi$
$191$	179.229	+	310.434i	0.938371	+	1.62531i	0.169862	+	0.985468i	$0.445668\pi$
$192$	32.1738	+	28.2626i	0.167572	+	0.147201i
$193$	−244.793	+	141.331i	−1.26836	+	0.732285i	−0.974677	−	0.223619i	$-0.928213\pi$
$193$	−244.793	+	141.331i	−1.26836	+	0.732285i	−0.293678	+	0.955904i	$0.594880\pi$
$194$	285.943			1.47393
$195$	325.610	+	65.0467i	1.66980	+	0.333573i
$196$	−5.81301	+	10.0684i	−0.0296582	+	0.0513695i
$197$	−239.928			−1.21791			−0.608954	−	0.793205i	$-0.708411\pi$
$197$	−239.928			−1.21791			−0.608954	+	0.793205i	$0.708411\pi$
$198$	−31.2026	−	40.8031i	−0.157589	−	0.206076i
$199$	−11.9893	−	20.7661i	−0.0602478	−	0.104352i	0.834328	−	0.551268i	$-0.185856\pi$
$199$	−11.9893	−	20.7661i	−0.0602478	−	0.104352i	−0.894576	+	0.446916i	$0.852522\pi$
$200$	−63.8535	−	36.8658i	−0.319268	−	0.184329i
$201$	225.845	−	257.099i	1.12361	−	1.27910i
$202$	−187.627	−	108.326i	−0.928845	−	0.536269i
$203$		−	155.815i		−	0.767563i
$204$	−64.0860	+	21.6954i	−0.314147	+	0.106350i
$205$	221.229	+	127.727i	1.07917	+	0.623057i
$206$	49.9860	−	86.5783i	0.242650	−	0.420283i
$207$	−21.1670	−	162.851i	−0.102256	−	0.786722i
$208$		−	353.734i		−	1.70064i
$209$	−7.91681	−	44.2321i	−0.0378795	−	0.211637i
$210$	−94.7015	−	279.738i	−0.450960	−	1.33209i
$211$	204.299	−	117.952i	0.968242	−	0.559015i	0.0695418	−	0.997579i	$-0.477846\pi$
$211$	204.299	−	117.952i	0.968242	−	0.559015i	0.898700	+	0.438565i	$0.144513\pi$
$212$	−102.177	+	58.9917i	−0.481965	+	0.278263i
$213$	8.44797	+	24.9544i	0.0396618	+	0.117157i
$214$	−235.243			−1.09927
$215$	−2.05118	−	3.55275i	−0.00954039	−	0.0165244i
$216$	117.704	+	79.0683i	0.544924	+	0.366057i
$217$		−	272.105i		−	1.25394i
$218$	59.0149	−	102.217i	0.270711	−	0.468885i
$219$	−388.532	+	131.532i	−1.77412	+	0.600603i
$220$	13.4753	−	23.3398i	0.0612512	−	0.106090i
$221$	−189.702	−	109.525i	−0.858380	−	0.495586i
$222$	96.7782	+	85.0133i	0.435938	+	0.382943i
$223$			175.122i			0.785301i	0.919688	+	0.392651i	$0.128442\pi$
$223$			175.122i			0.785301i	−0.919688	+	0.392651i	$0.871558\pi$
$224$	−153.699	+	88.7383i	−0.686157	+	0.396153i
$225$	−116.659	−	48.5469i	−0.518483	−	0.215764i
$226$	−159.598	+	276.432i	−0.706185	+	1.22315i
$227$	345.883	−	199.696i	1.52371	−	0.879717i	0.524108	−	0.851652i	$-0.324399\pi$
$227$	345.883	−	199.696i	1.52371	−	0.879717i	0.999606	−	0.0280655i	$-0.00893469\pi$
$228$	−50.1621	−	91.0550i	−0.220009	−	0.399364i
$229$	147.423	−	255.344i	0.643769	−	1.11504i	−0.340816	−	0.940130i	$-0.610703\pi$
$229$	147.423	−	255.344i	0.643769	−	1.11504i	0.984584	−	0.174910i	$-0.0559634\pi$
$230$	238.273	−	137.567i	1.03597	−	0.598117i
$231$	−43.8760	+	14.8536i	−0.189939	+	0.0643013i
$232$	−62.6677	+	108.544i	−0.270120	+	0.467861i
$233$	−37.6394	+	65.1933i	−0.161542	+	0.279800i	−0.935422	−	0.353533i	$-0.884980\pi$
$233$	−37.6394	+	65.1933i	−0.161542	+	0.279800i	0.773880	+	0.633333i	$0.218314\pi$
$234$	−49.5903	−	381.531i	−0.211924	−	1.63048i
$235$	−271.949			−1.15723
$236$	−143.702	+	82.9664i	−0.608907	+	0.351553i
$237$	−259.657	+	295.591i	−1.09560	+	1.24722i
$238$			194.831i			0.818619i
$239$	47.9338	−	83.0237i	0.200560	−	0.347380i	−0.748149	−	0.663531i	$-0.769057\pi$
$239$	47.9338	−	83.0237i	0.200560	−	0.347380i	0.948709	+	0.316151i	$0.102391\pi$
$240$	−73.3263	+	367.056i	−0.305526	+	1.52940i
$241$	199.547	+	115.208i	0.827994	+	0.478043i	0.853165	−	0.521641i	$-0.174680\pi$
$241$	199.547	+	115.208i	0.827994	+	0.478043i	−0.0251713	+	0.999683i	$0.508013\pi$
$242$	241.194	+	139.253i	0.996668	+	0.575427i
$243$	217.496	+	108.373i	0.895044	+	0.445978i
$244$	36.0452	−	62.4322i	0.147726	−	0.255870i
$245$	39.8292			0.162568
$246$	57.9848	−	290.260i	0.235711	−	1.17992i
$247$	114.299	−	316.567i	0.462748	−	1.28165i
$248$	−109.438	+	189.553i	−0.441284	+	0.764326i
$249$	−14.5867	+	73.0177i	−0.0585810	+	0.293244i
$250$			165.265i			0.661061i
$251$	−113.679	−	196.897i	−0.452903	−	0.784451i	0.545662	−	0.838005i	$-0.316278\pi$
$251$	−113.679	−	196.897i	−0.452903	−	0.784451i	−0.998565	+	0.0535544i	$0.982945\pi$
$252$	−85.1284	+	65.0988i	−0.337811	+	0.258329i
$253$	−21.5769	−	37.3722i	−0.0852841	−	0.147716i
$254$	−92.4016	−	160.044i	−0.363786	−	0.630095i
$255$	174.143	+	152.973i	0.682913	+	0.599895i
$256$	288.439			1.12671
$257$		−	13.8780i		−	0.0540000i	−0.999635	−	0.0270000i	$-0.991405\pi$
$257$		−	13.8780i		−	0.0540000i	0.999635	−	0.0270000i	$-0.00859540\pi$
$258$	−3.13709	+	3.57123i	−0.0121593	+	0.0138420i
$259$	100.602	−	58.0825i	0.388424	−	0.224257i
$260$	174.819	−	100.932i	0.672379	−	0.388198i
$261$	−82.5241	+	198.306i	−0.316184	+	0.759794i
$262$	−252.047	+	145.519i	−0.962011	+	0.555417i
$263$	−126.137			−0.479609			−0.239804	−	0.970821i	$-0.577083\pi$
$263$	−126.137			−0.479609			−0.239804	+	0.970821i	$0.577083\pi$
$264$	36.5387	+	7.29930i	0.138404	+	0.0276489i
$265$	350.043	+	202.097i	1.32092	+	0.762632i
$266$	−294.676	+	52.7421i	−1.10781	+	0.198278i
$267$	38.3664	+	7.66440i	0.143694	+	0.0287056i
$268$		−	208.042i		−	0.776276i
$269$	348.719	+	201.333i	1.29635	+	0.748450i	0.979772	−	0.200115i	$-0.0641315\pi$
$269$	348.719	+	201.333i	1.29635	+	0.748450i	0.316582	+	0.948565i	$0.397465\pi$
$270$	−27.6305	+	406.180i	−0.102335	+	1.50437i
$271$	−77.7508	+	134.668i	−0.286903	+	0.496931i	−0.973069	−	0.230514i	$-0.925959\pi$
$271$	−77.7508	+	134.668i	−0.286903	+	0.496931i	0.686166	+	0.727445i	$0.259293\pi$
$272$	123.466	−	213.849i	0.453917	−	0.786208i
$273$	−340.236	−	67.9684i	−1.24628	−	0.248969i
$274$	−20.0336	−	11.5664i	−0.0731155	−	0.0422132i
$275$	−33.2038			−0.120741
$276$	−75.0071	−	65.8888i	−0.271765	−	0.238728i
$277$	−73.7004	−	127.653i	−0.266066	−	0.460840i	0.701776	−	0.712398i	$-0.252391\pi$
$277$	−73.7004	−	127.653i	−0.266066	−	0.460840i	−0.967842	+	0.251557i	$0.919057\pi$
$278$			523.741i			1.88396i
$279$	−144.114	+	346.308i	−0.516538	+	1.24125i
$280$	185.531	+	107.116i	0.662611	+	0.382558i
$281$	−352.618	−	203.584i	−1.25487	−	0.724499i	−0.282797	−	0.959180i	$-0.591262\pi$
$281$	−352.618	−	203.584i	−1.25487	−	0.724499i	−0.972073	+	0.234680i	$0.924596\pi$
$282$	101.043	+	298.469i	0.358307	+	1.05840i
$283$	−92.6501	−	160.475i	−0.327386	−	0.567048i	0.654607	−	0.755970i	$-0.272834\pi$
$283$	−92.6501	−	160.475i	−0.327386	−	0.567048i	−0.981992	+	0.188921i	$0.939501\pi$
$284$	13.8708	+	8.00829i	0.0488407	+	0.0281982i
$285$	−184.225	+	304.796i	−0.646405	+	1.06946i
$286$	−50.5507	−	87.5563i	−0.176751	−	0.306141i
$287$	−231.166	−	133.464i	−0.805456	−	0.465030i
$288$	242.611	−	31.5339i	0.842401	−	0.109493i
$289$	68.0442	+	117.856i	0.235447	+	0.407806i
$290$	−359.859			−1.24089
$291$	−234.594	+	267.059i	−0.806166	+	0.917730i
$292$	−124.686	+	215.963i	−0.427008	+	0.739600i
$293$	−154.785	−	89.3650i	−0.528275	−	0.305000i	0.212038	−	0.977261i	$-0.431990\pi$
$293$	−154.785	−	89.3650i	−0.528275	−	0.305000i	−0.740314	+	0.672261i	$0.765323\pi$
$294$	−14.7985	−	43.7132i	−0.0503350	−	0.148684i
$295$	492.304	+	284.232i	1.66883	+	0.963497i
$296$	−93.4413			−0.315680
$297$	63.7078	+	4.33375i	0.214504	+	0.0145917i
$298$	80.1369	−	46.2670i	0.268916	−	0.155259i
$299$		−	323.228i		−	1.08103i
$300$	−72.7611	+	24.6323i	−0.242537	+	0.0821075i
$301$	2.14332	+	3.71233i	0.00712065	+	0.0123333i
$302$	−165.653	−	286.919i	−0.548519	−	0.950063i
$303$	255.106	−	86.3625i	0.841933	−	0.285025i
$304$	356.862	+	128.848i	1.17389	+	0.423841i
$305$	−246.972			−0.809745
$306$	103.188	−	247.962i	0.337216	−	0.810333i
$307$	131.586	+	75.9710i	0.428618	+	0.247463i	0.698758	−	0.715358i	$-0.253737\pi$
$307$	131.586	+	75.9710i	0.428618	+	0.247463i	−0.270140	+	0.962821i	$0.587070\pi$
$308$	−14.0805	+	24.3882i	−0.0457160	+	0.0791824i
$309$	39.8510	+	117.716i	0.128968	+	0.380957i
$310$	−628.432			−2.02720
$311$	−42.7185	+	73.9906i	−0.137359	+	0.237912i	−0.926496	−	0.376305i	$-0.877195\pi$
$311$	−42.7185	+	73.9906i	−0.137359	+	0.237912i	0.789137	+	0.614217i	$0.210528\pi$
$312$	209.678	+	184.188i	0.672044	+	0.590347i
$313$	31.1163	−	53.8951i	0.0994132	−	0.172189i	−0.812029	−	0.583617i	$-0.801637\pi$
$313$	31.1163	−	53.8951i	0.0994132	−	0.172189i	0.911442	+	0.411429i	$0.134970\pi$
$314$	−100.165	+	57.8305i	−0.318998	+	0.184174i
$315$	338.960	+	141.056i	1.07606	+	0.447798i
$316$			239.189i			0.756927i
$317$	45.1075	+	26.0428i	0.142295	+	0.0821540i	0.569457	−	0.822021i	$-0.307153\pi$
$317$	45.1075	+	26.0428i	0.142295	+	0.0821540i	−0.427162	+	0.904175i	$0.640487\pi$
$318$	91.7473	−	459.268i	0.288513	−	1.44424i
$319$			56.4426i			0.176936i
$320$	−44.5957	−	77.2421i	−0.139362	−	0.241381i
$321$	192.999	−	219.708i	0.601244	−	0.684449i
$322$	−248.975	+	143.746i	−0.773215	+	0.446416i
$323$	179.592	−	151.485i	0.556012	−	0.468995i
$324$	142.821	−	37.7649i	0.440806	−	0.116558i
$325$	−215.381	−	124.350i	−0.662712	−	0.382617i
$326$		−	682.768i		−	2.09438i
$327$	47.0493	+	138.979i	0.143882	+	0.425011i
$328$	107.356	+	185.946i	0.327305	+	0.566909i
$329$	284.164			0.863721
$330$	34.3047	+	101.333i	0.103954	+	0.307068i
$331$	79.8373	−	46.0941i	0.241200	−	0.139257i	−0.374528	−	0.927216i	$-0.622195\pi$
$331$	79.8373	−	46.0941i	0.241200	−	0.139257i	0.615728	+	0.787959i	$0.288862\pi$
$332$	22.6338	+	39.2029i	0.0681741	+	0.118081i
$333$	−158.798	+	20.6401i	−0.476871	+	0.0619824i
$334$	−721.224			−2.15935
$335$	−617.237	+	356.362i	−1.84250	+	1.06377i
$336$	76.6199	−	383.543i	0.228035	−	1.14150i
$337$	−201.197	+	116.161i	−0.597025	+	0.344693i	−0.767870	−	0.640605i	$-0.778684\pi$
$337$	−201.197	+	116.161i	−0.597025	+	0.344693i	0.170845	+	0.985298i	$0.445350\pi$
$338$		−	349.422i		−	1.03379i
$339$	−127.238	−	375.849i	−0.375335	−	1.10870i
$340$	140.915			0.414455
$341$			98.5673i			0.289054i
$342$	402.968	+	88.9438i	1.17827	+	0.260070i
$343$	−361.530			−1.05402
$344$		−	3.44810i		−	0.0100235i
$345$	−67.0025	+	335.401i	−0.194210	+	0.972176i
$346$	−308.058			−0.890341
$347$	−237.371	−	411.138i	−0.684065	−	1.18484i	−0.973730	−	0.227707i	$-0.926877\pi$
$347$	−237.371	−	411.138i	−0.684065	−	1.18484i	0.289665	−	0.957128i	$-0.406456\pi$
$348$	41.8720	+	123.686i	0.120322	+	0.355418i
$349$	−173.201	−	299.993i	−0.496278	−	0.859579i	0.503713	−	0.863871i	$-0.331967\pi$
$349$	−173.201	−	299.993i	−0.496278	−	0.859579i	−0.999991	+	0.00429236i	$0.998634\pi$
$350$			221.205i			0.632014i
$351$	397.020	+	266.702i	1.13111	+	0.759834i
$352$	55.6761	−	32.1446i	0.158171	−	0.0913199i
$353$	−93.4864	−	161.923i	−0.264834	−	0.458706i	0.702686	−	0.711500i	$-0.251984\pi$
$353$	−93.4864	−	161.923i	−0.264834	−	0.458706i	−0.967520	+	0.252794i	$0.918650\pi$
$354$	129.034	−	645.918i	0.364503	−	1.82463i
$355$		−	54.8706i		−	0.154565i
$356$	20.5987	−	11.8927i	0.0578615	−	0.0334064i
$357$	−181.965	−	159.844i	−0.509705	−	0.447743i
$358$	168.430			0.470474
$359$	134.826	−	233.525i	0.375560	−	0.650489i	−0.614851	−	0.788643i	$-0.710784\pi$
$359$	134.826	−	233.525i	0.375560	−	0.650489i	0.990411	+	0.138155i	$0.0441171\pi$
$360$	−179.394	−	234.589i	−0.498315	−	0.651637i
$361$	277.733	+	230.619i	0.769344	+	0.638834i
$362$	273.138	+	473.089i	0.754525	+	1.30688i
$363$	−327.938	+	111.019i	−0.903410	+	0.305837i
$364$	−182.671	+	105.465i	−0.501843	+	0.289739i
$365$	854.318			2.34060
$366$	91.7623	+	271.056i	0.250717	+	0.740591i
$367$	−41.0283	+	71.0630i	−0.111794	+	0.193632i	−0.916493	−	0.400050i	$-0.868993\pi$
$367$	−41.0283	+	71.0630i	−0.111794	+	0.193632i	0.804700	+	0.593682i	$0.202326\pi$
$368$	364.370			0.990136
$369$	223.519	+	292.291i	0.605743	+	0.792117i
$370$	−134.143	−	232.342i	−0.362549	−	0.627952i
$371$	−365.766	−	211.175i	−0.985891	−	0.569205i
$372$	73.1222	+	215.995i	0.196565	+	0.580633i
$373$	357.217	+	206.240i	0.957687	+	0.552921i	0.895460	−	0.445141i	$-0.146846\pi$
$373$	357.217	+	206.240i	0.957687	+	0.552921i	0.0622268	+	0.998062i	$0.480180\pi$
$374$		−	70.5758i		−	0.188705i
$375$	−154.351	−	135.588i	−0.411603	−	0.361567i
$376$	−197.954	−	114.289i	−0.526473	−	0.303959i
$377$	−211.382	+	366.124i	−0.560694	+	0.971150i
$378$	28.8716	−	424.424i	0.0763799	−	1.12281i
$379$		−	5.94480i		−	0.0156855i	−0.999969	−	0.00784274i	$-0.997504\pi$
$379$		−	5.94480i		−	0.0156855i	0.999969	−	0.00784274i	$-0.00249645\pi$
$380$	38.1465	+	213.129i	0.100385	+	0.560865i
$381$	225.283	+	45.0046i	0.591295	+	0.118122i
$382$	−749.157	+	432.526i	−1.96114	+	1.13227i
$383$	415.076	−	239.644i	1.08375	−	0.625703i	0.151844	−	0.988405i	$-0.451479\pi$
$383$	415.076	−	239.644i	1.08375	−	0.625703i	0.931905	+	0.362702i	$0.118146\pi$
$384$	−283.487	+	322.719i	−0.738249	+	0.840414i
$385$	96.4759			0.250587
$386$	−341.069	−	590.748i	−0.883597	−	1.53044i
$387$	−0.761646	−	5.85985i	−0.00196808	−	0.0151417i
$388$			216.102i			0.556963i
$389$	−257.176	+	445.441i	−0.661120	+	1.14509i	0.319202	+	0.947687i	$0.396585\pi$
$389$	−257.176	+	445.441i	−0.661120	+	1.14509i	−0.980322	+	0.197406i	$0.936748\pi$
$390$	−156.975	+	785.782i	−0.402499	+	2.01483i
$391$	112.818	−	195.406i	0.288536	−	0.499759i
$392$	28.9919	+	16.7385i	0.0739590	+	0.0427002i
$393$	70.8758	−	354.789i	0.180345	−	0.902771i
$394$		−	579.009i		−	1.46956i
$395$	709.646	−	409.715i	1.79657	−	1.03725i
$396$	30.8370	−	23.5814i	0.0778711	−	0.0595491i
$397$	98.5486	−	170.691i	0.248233	−	0.429953i	−0.714802	−	0.699326i	$-0.753483\pi$
$397$	98.5486	−	170.691i	0.248233	−	0.429953i	0.963036	+	0.269374i	$0.0868167\pi$
$398$	50.1140	−	28.9333i	0.125915	−	0.0726968i
$399$	192.500	−	318.487i	0.482457	−	0.798212i
$400$	140.179	−	242.796i	0.350446	−	0.606991i
$401$	−684.083	+	394.956i	−1.70594	+	0.984927i	−0.766486	+	0.642261i	$0.777997\pi$
$401$	−684.083	+	394.956i	−1.70594	+	0.984927i	−0.939457	+	0.342666i	$0.888670\pi$
$402$	620.447	+	545.022i	1.54340	+	1.35578i
$403$	−369.141	+	639.371i	−0.915983	+	1.58653i
$404$	81.8677	−	141.799i	0.202643	−	0.350988i
$405$	−356.687	−	359.045i	−0.880709	−	0.886531i
$406$	376.023			0.926165
$407$	−36.4421	+	21.0398i	−0.0895383	+	0.0516949i
$408$	62.4717	+	184.535i	0.153117	+	0.452292i
$409$		−	479.048i		−	1.17127i	−0.810576	−	0.585633i	$-0.800846\pi$
$409$		−	479.048i		−	1.17127i	0.810576	−	0.585633i	$-0.199154\pi$
$410$	−308.238	+	533.883i	−0.751799	+	1.30215i
$411$	27.2386	−	9.22126i	0.0662741	−	0.0224362i
$412$	65.4316	+	37.7770i	0.158815	+	0.0916916i
$413$	−514.416	−	296.998i	−1.24556	−	0.719124i
$414$	393.003	−	51.0814i	0.949282	−	0.123385i
$415$	77.5403	−	134.304i	0.186844	−	0.323623i
$416$	481.535			1.15754
$417$	−489.153	−	429.689i	−1.17303	−	1.03043i
$418$	106.744	−	19.1053i	0.255368	−	0.0457065i
$419$	−72.6472	+	125.829i	−0.173382	+	0.300307i	−0.939600	−	0.342274i	$-0.888803\pi$
$419$	−72.6472	+	125.829i	−0.173382	+	0.300307i	0.766218	+	0.642581i	$0.222136\pi$
$420$	211.413	−	71.5708i	0.503363	−	0.170407i
$421$		−	416.217i		−	0.988639i	−0.869280	−	0.494319i	$-0.835417\pi$
$421$		−	416.217i		−	0.988639i	0.869280	−	0.494319i	$-0.164583\pi$
$422$	284.649	+	493.027i	0.674524	+	1.16831i
$423$	−361.656	−	150.501i	−0.854979	−	0.355795i
$424$	169.866	+	294.216i	0.400627	+	0.693906i
$425$	−86.8053	−	150.351i	−0.204248	−	0.353767i
$426$	−60.2215	+	20.3871i	−0.141365	+	0.0478571i
$427$	258.065			0.604368
$428$		−	177.785i		−	0.415387i
$429$	123.247	+	24.6209i	0.287289	+	0.0573914i
$430$	8.57372	−	4.95004i	0.0199389	−	0.0115117i
$431$	−292.931	+	169.124i	−0.679653	+	0.392398i	−0.799724	−	0.600367i	$-0.795021\pi$
$431$	−292.931	+	169.124i	−0.679653	+	0.392398i	0.120071	+	0.992765i	$0.461688\pi$
$432$	−300.649	+	447.555i	−0.695947	+	1.03601i
$433$	−615.308	+	355.248i	−1.42104	+	0.820435i	−0.996387	−	0.0849238i	$-0.972935\pi$
$433$	−615.308	+	355.248i	−1.42104	+	0.820435i	−0.424648	+	0.905359i	$0.639602\pi$
$434$	656.659			1.51304
$435$	295.237	−	336.094i	0.678706	−	0.772631i
$436$	77.2505	+	44.6006i	0.177180	+	0.102295i
$437$	326.086	+	117.736i	0.746192	+	0.269418i
$438$	−317.421	−	937.629i	−0.724706	−	2.14071i
$439$		−	19.5916i		−	0.0446279i	−0.999751	−	0.0223139i	$-0.992897\pi$
$439$		−	19.5916i		−	0.0446279i	0.999751	−	0.0223139i	$-0.00710334\pi$
$440$	−67.2068	−	38.8019i	−0.152743	−	0.0881861i
$441$	52.9674	+	22.0421i	0.120108	+	0.0499821i
$442$	264.311	−	457.800i	0.597989	−	1.03575i
$443$	403.114	−	698.214i	0.909964	−	1.57610i	0.0958515	−	0.995396i	$-0.469443\pi$
$443$	403.114	−	698.214i	0.909964	−	1.57610i	0.814112	−	0.580708i	$-0.197224\pi$
$444$	−64.2489	+	73.1402i	−0.144705	+	0.164730i
$445$	−70.5684	−	40.7427i	−0.158581	−	0.0915566i
$446$	−422.615			−0.947568
$447$	−22.5346	+	112.803i	−0.0504129	+	0.252356i
$448$	46.5988	+	80.7115i	0.104015	+	0.180160i
$449$		−	387.615i		−	0.863286i	−0.902045	−	0.431643i	$-0.857934\pi$
$449$		−	387.615i		−	0.863286i	0.902045	−	0.431643i	$-0.142066\pi$
$450$	117.156	−	281.528i	0.260347	−	0.625617i
$451$	83.7377	+	48.3460i	0.185671	+	0.107197i
$452$	−208.913	−	120.616i	−0.462198	−	0.266850i
$453$	403.876	+	80.6819i	0.891559	+	0.178106i
$454$	481.918	+	834.706i	1.06149	+	1.83856i
$455$	625.806	+	361.309i	1.37540	+	0.794086i
$456$	−262.192	+	144.441i	−0.574982	+	0.316757i
$457$	−71.2482	−	123.406i	−0.155904	−	0.270034i	0.777484	−	0.628903i	$-0.216496\pi$
$457$	−71.2482	−	123.406i	−0.155904	−	0.270034i	−0.933388	+	0.358869i	$0.883162\pi$
$458$	616.212	+	355.770i	1.34544	+	0.776791i
$459$	146.929	+	299.807i	0.320106	+	0.653175i
$460$	103.966	+	180.075i	0.226014	+	0.391467i
$461$	151.389			0.328393			0.164196	−	0.986428i	$-0.447497\pi$
$461$	151.389			0.328393			0.164196	+	0.986428i	$0.447497\pi$
$462$	−35.8456	−	105.884i	−0.0775878	−	0.229186i
$463$	−0.197010	+	0.341231i	−0.000425508	+	0.000737001i	−0.866238	−	0.499631i	$-0.833469\pi$
$463$	−0.197010	+	0.341231i	−0.000425508	+	0.000737001i	0.865813	+	0.500368i	$0.166802\pi$
$464$	−412.726	−	238.287i	−0.889496	−	0.513551i
$465$	515.580	−	586.931i	1.10877	−	1.26222i
$466$	−157.328	−	90.8336i	−0.337615	−	0.194922i
$467$	−110.723			−0.237094			−0.118547	−	0.992948i	$-0.537824\pi$
$467$	−110.723			−0.237094			−0.118547	+	0.992948i	$0.537824\pi$
$468$	288.343	−	37.4779i	0.616117	−	0.0800810i
$469$	644.961	−	372.368i	1.37518	−	0.793962i
$470$		−	656.284i		−	1.39635i
$471$	28.1666	−	140.996i	0.0598017	−	0.299354i
$472$	238.901	+	413.788i	0.506146	+	0.876670i
$473$	−0.776396	−	1.34476i	−0.00164143	−	0.00284304i
$474$	−713.338	−	626.621i	−1.50493	−	1.32198i
$475$	203.903	−	171.991i	0.429269	−	0.362087i
$476$	−147.244			−0.309336
$477$	353.666	+	462.482i	0.741439	+	0.969564i
$478$	200.358	+	115.677i	0.419159	+	0.242001i
$479$	18.2814	−	31.6643i	0.0381658	−	0.0661050i	−0.846312	−	0.532688i	$-0.821182\pi$
$479$	18.2814	−	31.6643i	0.0381658	−	0.0661050i	0.884477	+	0.466583i	$0.154515\pi$
$480$	−499.670	−	99.8185i	−1.04098	−	0.207955i
$481$	−315.183			−0.655265
$482$	−278.027	+	481.558i	−0.576821	+	0.999082i
$483$	70.0121	−	350.466i	0.144953	−	0.725602i
$484$	−105.241	+	182.282i	−0.217440	+	0.376617i
$485$	641.149	−	370.167i	1.32196	−	0.763232i
$486$	−261.532	+	524.873i	−0.538131	+	1.07999i
$487$			637.723i			1.30949i	0.755849	+	0.654746i	$0.227225\pi$
$487$			637.723i			1.30949i	−0.755849	+	0.654746i	$0.772775\pi$
$488$	−179.773	−	103.792i	−0.368387	−	0.212688i
$489$	637.678	+	560.159i	1.30405	+	1.14552i
$490$			96.1181i			0.196159i
$491$	346.655	+	600.424i	0.706018	+	1.22286i	0.966323	+	0.257333i	$0.0828436\pi$
$491$	346.655	+	600.424i	0.706018	+	1.22286i	−0.260305	+	0.965526i	$0.583823\pi$
$492$	219.364	+	43.8221i	0.445862	+	0.0890692i
$493$	−255.580	+	147.559i	−0.518417	+	0.299308i
$494$	763.959	+	275.833i	1.54648	+	0.558366i
$495$	−122.785	−	51.0963i	−0.248050	−	0.103225i
$496$	−720.755	−	416.128i	−1.45313	−	0.838967i
$497$			57.3352i			0.115363i
$498$	−176.211	−	35.2014i	−0.353837	−	0.0706855i
$499$	89.5132	+	155.041i	0.179385	+	0.310704i	0.941670	−	0.336537i	$-0.109256\pi$
$499$	89.5132	+	155.041i	0.179385	+	0.310704i	−0.762285	+	0.647242i	$0.775922\pi$
$500$	−124.899			−0.249799
$501$	591.709	−	673.595i	1.18106	−	1.34450i
$502$	475.164	−	274.336i	0.946542	−	0.546486i
$503$	124.296	+	215.287i	0.247109	+	0.428006i	0.962723	−	0.270491i	$-0.0871860\pi$
$503$	124.296	+	215.287i	0.247109	+	0.428006i	−0.715613	+	0.698497i	$0.753853\pi$
$504$	187.451	+	245.126i	0.371927	+	0.486362i
$505$	−560.935			−1.11076
$506$	90.1889	−	52.0706i	0.178239	−	0.102906i
$507$	326.346	+	286.674i	0.643681	+	0.565432i
$508$	120.954	−	69.8326i	0.238098	−	0.137466i
$509$			923.573i			1.81448i	0.420608	+	0.907242i	$0.361817\pi$
$509$			923.573i			1.81448i	−0.420608	+	0.907242i	$0.638183\pi$
$510$	−369.164	+	420.252i	−0.723851	+	0.824024i
$511$	−892.691			−1.74695
$512$			123.345i			0.240909i
$513$	−413.675	+	303.385i	−0.806383	+	0.591394i
$514$	33.4912			0.0651580
$515$		−	258.837i		−	0.502597i
$516$	−2.69896	−	2.37086i	−0.00523055	−	0.00459469i
$517$	−102.936			−0.199102
$518$	140.168	+	242.778i	0.270595	+	0.468684i
$519$	252.738	−	287.714i	0.486971	−	0.554362i
$520$	−290.631	−	503.388i	−0.558906	−	0.968054i
$521$			6.66801i			0.0127985i	0.999980	+	0.00639924i	$0.00203695\pi$
$521$			6.66801i			0.0127985i	−0.999980	+	0.00639924i	$0.997963\pi$
$522$	−478.565	−	199.152i	−0.916791	−	0.381518i
$523$	880.359	−	508.275i	1.68329	−	0.971846i	0.723834	−	0.689974i	$-0.242378\pi$
$523$	880.359	−	508.275i	1.68329	−	0.971846i	0.959452	−	0.281872i	$-0.0909552\pi$
$524$	−109.976	−	190.485i	−0.209879	−	0.363520i
$525$	−206.597	−	181.482i	−0.393517	−	0.345679i
$526$		−	304.402i		−	0.578710i
$527$	−446.326	+	257.686i	−0.846918	+	0.488968i
$528$	−27.7548	+	138.935i	−0.0525659	+	0.263134i
$529$	−196.054			−0.370612
$530$	−487.714	+	844.745i	−0.920214	+	1.59386i
$531$	497.399	+	650.439i	0.936722	+	1.22493i
$532$	−39.8599	−	222.702i	−0.0749246	−	0.418612i
$533$	362.118	+	627.207i	0.679396	+	1.17675i
$534$	−18.4962	+	92.5880i	−0.0346370	+	0.173386i
$535$	−527.469	+	304.534i	−0.985924	+	0.569223i
$536$	−599.055			−1.11764
$537$	−138.184	+	157.307i	−0.257325	+	0.292936i
$538$	−485.869	+	841.550i	−0.903103	+	1.56422i
$539$	15.0758			0.0279699
$540$	−306.971	−	20.8818i	−0.568464	−	0.0386700i
$541$	81.8795	+	141.819i	0.151348	+	0.262143i	0.931723	−	0.363169i	$-0.118305\pi$
$541$	81.8795	+	141.819i	0.151348	+	0.262143i	−0.780375	+	0.625312i	$0.784972\pi$
$542$	−324.990	−	187.633i	−0.599612	−	0.346186i
$543$	−665.935	−	133.033i	−1.22640	−	0.244996i
$544$	291.110	+	168.073i	0.535129	+	0.308957i
$545$		−	305.591i		−	0.560717i
$546$	164.026	−	821.077i	0.300413	−	1.50380i
$547$	−334.368	−	193.047i	−0.611276	−	0.352920i	0.162189	−	0.986760i	$-0.448145\pi$
$547$	−334.368	−	193.047i	−0.611276	−	0.352920i	−0.773465	+	0.633840i	$0.781478\pi$
$548$	8.74134	−	15.1404i	0.0159513	−	0.0276285i
$549$	−328.440	−	136.679i	−0.598251	−	0.248959i
$550$		−	80.1294i		−	0.145690i
$551$	−292.365	−	346.611i	−0.530609	−	0.629058i
$552$	−189.726	+	215.982i	−0.343707	+	0.391272i
$553$	−741.521	+	428.118i	−1.34091	+	0.774173i
$554$	308.059	−	177.858i	0.556064	−	0.321044i
$555$	327.053	+	65.3349i	0.589284	+	0.117721i
$556$	−395.818			−0.711903
$557$	−63.3352	−	109.700i	−0.113708	−	0.196948i	0.803555	−	0.595231i	$-0.202939\pi$
$557$	−63.3352	−	109.700i	−0.113708	−	0.196948i	−0.917262	+	0.398283i	$0.869606\pi$
$558$	−835.730	−	347.785i	−1.49772	−	0.623270i
$559$		−	11.6306i		−	0.0208061i
$560$	−407.299	+	705.462i	−0.727319	+	1.25975i
$561$	65.9150	+	57.9020i	0.117496	+	0.103212i
$562$	491.302	−	850.960i	0.874203	−	1.51416i
$563$	−939.362	−	542.341i	−1.66849	−	0.963305i	−0.968451	−	0.249205i	$-0.919831\pi$
$563$	−939.362	−	542.341i	−1.66849	−	0.963305i	−0.700043	−	0.714101i	$-0.746836\pi$
$564$	−225.568	+	76.3630i	−0.399944	+	0.135395i
$565$			826.430i			1.46271i
$566$	387.267	−	223.589i	0.684217	−	0.395033i
$567$	372.708	+	375.172i	0.657334	+	0.661679i
$568$	23.0598	−	39.9407i	0.0405982	−	0.0703182i
$569$	325.702	−	188.044i	0.572411	−	0.330482i	−0.185701	−	0.982606i	$-0.559456\pi$
$569$	325.702	−	188.044i	0.572411	−	0.330482i	0.758112	+	0.652125i	$0.226122\pi$
$570$	−735.553	−	444.584i	−1.29044	−	0.779972i
$571$	254.864	−	441.438i	0.446347	−	0.773096i	−0.551798	−	0.833978i	$-0.686058\pi$
$571$	254.864	−	441.438i	0.446347	−	0.773096i	0.998145	+	0.0608819i	$0.0193913\pi$
$572$	66.1708	−	38.2037i	0.115683	−	0.0667897i
$573$	210.664	−	1054.54i	0.367650	−	1.84038i
$574$	322.083	−	557.864i	0.561120	−	0.971888i
$575$	128.089	−	221.857i	0.222764	−	0.385839i
$576$	−16.5593	−	127.402i	−0.0287488	−	0.221183i
$577$	567.614			0.983734			0.491867	−	0.870670i	$-0.336315\pi$
$577$	567.614			0.983734			0.491867	+	0.870670i	$0.336315\pi$
$578$	−284.417	+	164.208i	−0.492071	+	0.284098i
$579$	831.556	+	166.119i	1.43619	+	0.286906i
$580$		−	271.964i		−	0.468904i
$581$	−81.0231	+	140.336i	−0.139455	+	0.241542i
$582$	−644.484	−	566.137i	−1.10736	−	0.972744i
$583$	132.495	+	76.4961i	0.227264	+	0.131211i
$584$	621.864	+	359.033i	1.06484	+	0.614783i
$585$	−605.104	−	791.282i	−1.03437	−	1.35262i
$586$	215.661	−	373.536i	0.368022	−	0.637433i
$587$	−486.330			−0.828502			−0.414251	−	0.910163i	$-0.635956\pi$
$587$	−486.330			−0.828502			−0.414251	+	0.910163i	$0.635956\pi$
$588$	33.0363	−	11.1840i	0.0561842	−	0.0190204i
$589$	−510.566	−	605.296i	−0.866835	−	1.02767i
$590$	−685.925	+	1188.06i	−1.16258	+	2.01365i
$591$	540.771	+	475.032i	0.915010	+	0.803777i
$592$		−	355.301i		−	0.600170i
$593$	401.928	+	696.160i	0.677788	+	1.17396i	0.975646	+	0.219353i	$0.0703946\pi$
$593$	401.928	+	696.160i	0.677788	+	1.17396i	−0.297858	+	0.954610i	$0.596272\pi$
$594$	−10.4585	+	153.744i	−0.0176068	+	0.258828i
$595$	252.219	+	436.856i	0.423897	+	0.734212i
$596$	34.9664	+	60.5635i	0.0586684	+	0.101617i
$597$	−14.0921	+	70.5421i	−0.0236049	+	0.118161i
$598$	780.032			1.30440
$599$		−	790.397i		−	1.31953i	−0.751473	−	0.659764i	$-0.770656\pi$
$599$		−	790.397i		−	1.31953i	0.751473	−	0.659764i	$-0.229344\pi$
$600$	70.9283	+	209.515i	0.118214	+	0.349191i
$601$	242.439	−	139.972i	0.403393	−	0.232899i	−0.284554	−	0.958660i	$-0.591846\pi$
$601$	242.439	−	139.972i	0.403393	−	0.232899i	0.687947	+	0.725761i	$0.258512\pi$
$602$	−8.95882	+	5.17238i	−0.0148818	+	0.00859199i
$603$	−1018.06	+	132.324i	−1.68832	+	0.219443i
$604$	216.839	−	125.192i	0.359006	−	0.207272i
$605$	721.081			1.19187
$606$	208.415	+	615.637i	0.343919	+	1.01590i
$607$	0.792003	+	0.457263i	0.00130478	+	0.000753316i	0.500652	−	0.865648i	$-0.333094\pi$
$607$	0.792003	+	0.457263i	0.00130478	+	0.000753316i	−0.499347	+	0.866402i	$0.666427\pi$
$608$	−175.399	+	485.793i	−0.288485	+	0.799002i
$609$	−308.498	+	351.191i	−0.506565	+	0.576668i
$610$		−	596.008i		−	0.977062i
$611$	−667.708	−	385.502i	−1.09281	−	0.630935i
$612$	187.398	+	77.9845i	0.306205	+	0.127426i
$613$	329.736	−	571.120i	0.537906	−	0.931680i	−0.461111	−	0.887342i	$-0.652549\pi$
$613$	329.736	−	571.120i	0.537906	−	0.931680i	0.999017	−	0.0443374i	$-0.0141177\pi$
$614$	−183.338	+	317.550i	−0.298596	+	0.517183i
$615$	−245.741	−	725.892i	−0.399578	−	1.18031i
$616$	70.2255	+	40.5447i	0.114002	+	0.0658194i
$617$	321.493			0.521059			0.260529	−	0.965466i	$-0.416103\pi$
$617$	321.493			0.521059			0.260529	+	0.965466i	$0.416103\pi$
$618$	−284.079	+	96.1709i	−0.459674	+	0.155616i
$619$	−77.6706	−	134.529i	−0.125477	−	0.217333i	0.796442	−	0.604715i	$-0.206713\pi$
$619$	−77.6706	−	134.529i	−0.125477	−	0.217333i	−0.921919	+	0.387382i	$0.873380\pi$
$620$		−	474.938i		−	0.766029i
$621$	−274.721	+	408.958i	−0.442384	+	0.658547i
$622$	−178.559	−	103.091i	−0.287072	−	0.165741i
$623$	73.7381	+	42.5727i	0.118360	+	0.0683350i
$624$	−700.356	+	797.277i	−1.12237	+	1.27769i
$625$	389.440	+	674.529i	0.623104	+	1.07925i
$626$	130.063	+	75.0918i	0.207768	+	0.119955i
$627$	−69.7314	+	115.369i	−0.111214	+	0.184001i
$628$	−43.7054	−	75.7001i	−0.0695947	−	0.120541i
$629$	−190.542	−	110.010i	−0.302929	−	0.174896i
$630$	−340.406	+	817.998i	−0.540327	+	1.29841i
$631$	−264.891	−	458.805i	−0.419796	−	0.727108i	0.576123	−	0.817363i	$-0.304565\pi$
$631$	−264.891	−	458.805i	−0.419796	−	0.727108i	−0.995919	+	0.0902553i	$0.971232\pi$
$632$	688.742			1.08978
$633$	−694.000	−	138.639i	−1.09637	−	0.219020i
$634$	−62.8481	+	108.856i	−0.0991295	+	0.171697i
$635$	−414.370	−	239.237i	−0.652552	−	0.376751i
$636$	347.092	+	69.3381i	0.545742	+	0.109022i
$637$	97.7913	+	56.4598i	0.153518	+	0.0886339i
$638$	−136.211			−0.213496
$639$	30.3663	−	72.9706i	0.0475216	−	0.114195i
$640$	774.775	−	447.316i	1.21059	−	0.698932i
$641$			484.278i			0.755503i	0.925907	+	0.377752i	$0.123303\pi$
$641$			484.278i			0.755503i	−0.925907	+	0.377752i	$0.876697\pi$
$642$	530.213	+	465.757i	0.825877	+	0.725479i
$643$	279.720	+	484.490i	0.435024	+	0.753484i	0.997298	−	0.0734676i	$-0.0234065\pi$
$643$	279.720	+	484.490i	0.435024	+	0.753484i	−0.562274	+	0.826951i	$0.690073\pi$
$644$	−108.636	−	188.163i	−0.168690	−	0.292179i
$645$	−2.41094	+	12.0686i	−0.00373789	+	0.0187111i
$646$	365.573	+	433.402i	0.565903	+	0.670901i
$647$	857.934			1.32602			0.663009	−	0.748611i	$-0.269279\pi$
$647$	857.934			1.32602			0.663009	+	0.748611i	$0.269279\pi$
$648$	−108.744	−	411.252i	−0.167814	−	0.634648i
$649$	186.342	+	107.585i	0.287122	+	0.165770i
$650$	300.090	−	519.771i	0.461677	−	0.799648i
$651$	−538.738	+	613.294i	−0.827555	+	0.942079i
$652$	516.003			0.791415
$653$	484.995	−	840.036i	0.742718	−	1.28643i	−0.208535	−	0.978015i	$-0.566870\pi$
$653$	484.995	−	840.036i	0.742718	−	1.28643i	0.951253	−	0.308411i	$-0.0997971\pi$
$654$	−335.392	+	113.542i	−0.512831	+	0.173612i
$655$	−376.764	+	652.574i	−0.575212	+	0.996297i
$656$	−707.041	+	408.211i	−1.07781	+	0.622272i
$657$	1136.13	+	472.794i	1.72927	+	0.719625i
$658$			685.762i			1.04219i
$659$	−704.667	−	406.839i	−1.06930	−	0.617359i	−0.141308	−	0.989966i	$-0.545131\pi$
$659$	−704.667	−	406.839i	−1.06930	−	0.617359i	−0.927989	+	0.372607i	$0.878464\pi$
$660$	−76.5822	+	25.9258i	−0.116034	+	0.0392815i
$661$			296.517i			0.448589i	0.974521	+	0.224294i	$0.0720077\pi$
$661$			296.517i			0.448589i	−0.974521	+	0.224294i	$0.927992\pi$
$662$	111.237	+	192.668i	0.168032	+	0.291040i
$663$	210.720	+	622.446i	0.317829	+	0.938833i
$664$	112.884	−	65.1737i	0.170006	−	0.0981532i
$665$	−592.454	+	499.733i	−0.890908	+	0.751478i
$666$	−49.8100	−	383.221i	−0.0747898	−	0.575407i
$667$	−377.132	−	217.737i	−0.565415	−	0.326443i
$668$		−	545.066i		−	0.815967i
$669$	346.723	−	394.706i	0.518271	−	0.589994i
$670$	−859.994	−	1489.55i	−1.28357	−	2.22321i
$671$	−93.4817			−0.139317
$672$	522.114	+	104.302i	0.776955	+	0.155211i
$673$	820.838	−	473.911i	1.21967	−	0.704177i	0.254822	−	0.966988i	$-0.417983\pi$
$673$	820.838	−	473.911i	1.21967	−	0.704177i	0.964847	+	0.262811i	$0.0846497\pi$
$674$	−280.328	−	485.542i	−0.415916	−	0.720388i
$675$	166.818	+	340.391i	0.247138	+	0.504283i
$676$	264.076			0.390645
$677$	−631.891	+	364.822i	−0.933369	+	0.538881i	−0.887875	−	0.460084i	$-0.847819\pi$
$677$	−631.891	+	364.822i	−0.933369	+	0.538881i	−0.0454934	+	0.998965i	$0.514486\pi$
$678$	907.021	−	307.059i	1.33779	−	0.452890i
$679$	−669.947	+	386.794i	−0.986667	+	0.569653i
$680$		−	405.762i		−	0.596709i
$681$	−1174.96	−	234.720i	−1.72534	−	0.344670i
$682$	−237.868			−0.348781
$683$		−	1180.43i		−	1.72830i	−0.503231	−	0.864152i	$-0.667856\pi$
$683$		−	1180.43i		−	1.72830i	0.503231	−	0.864152i	$-0.332144\pi$
$684$	−67.2194	+	304.544i	−0.0982739	+	0.445239i
$685$	−59.8933			−0.0874354
$686$		−	872.466i		−	1.27182i
$687$	−837.830	+	283.635i	−1.21955	+	0.412861i
$688$	13.1110			0.0190567
$689$	572.966	+	992.407i	0.831591	+	1.44036i
$690$	−809.409	−	161.695i	−1.17306	−	0.234340i
$691$	452.976	+	784.577i	0.655537	+	1.13542i	0.981759	+	0.190130i	$0.0608909\pi$
$691$	452.976	+	784.577i	0.655537	+	1.13542i	−0.326222	+	0.945293i	$0.605776\pi$
$692$		−	232.815i		−	0.336438i
$693$	128.300	+	53.3914i	0.185137	+	0.0770439i
$694$	992.183	−	572.837i	1.42966	−	0.825413i
$695$	678.009	+	1174.35i	0.975552	+	1.68971i
$696$	356.151	−	120.570i	0.511712	−	0.173233i
$697$			505.567i			0.725347i
$698$	723.961	−	417.979i	1.03719	−	0.598824i
$699$	213.911	−	72.4165i	0.306024	−	0.103600i
$700$	−167.176			−0.238823
$701$	−330.664	+	572.726i	−0.471703	+	0.817014i	−0.999476	−	0.0323720i	$-0.989694\pi$
$701$	−330.664	+	572.726i	−0.471703	+	0.817014i	0.527773	+	0.849386i	$0.323027\pi$
$702$	−643.620	+	958.113i	−0.916838	+	1.36483i
$703$	114.805	−	317.970i	0.163307	−	0.452304i
$704$	−16.8800	−	29.2370i	−0.0239772	−	0.0415298i
$705$	612.943	+	538.431i	0.869423	+	0.763731i
$706$	390.763	−	225.607i	0.553488	−	0.319556i
$707$	586.131			0.829039
$708$	488.153	+	97.5177i	0.689482	+	0.137737i
$709$	632.184	−	1094.97i	0.891655	−	1.54439i	0.0537648	−	0.998554i	$-0.482878\pi$
$709$	632.184	−	1094.97i	0.891655	−	1.54439i	0.837890	−	0.545838i	$-0.183789\pi$
$710$	132.417			0.186503
$711$	1170.48	−	152.135i	1.64624	−	0.213974i
$712$	−34.2448	−	59.3138i	−0.0480967	−	0.0833058i
$713$	−658.596	−	380.240i	−0.923697	−	0.533297i
$714$	385.746	−	439.128i	0.540260	−	0.615026i
$715$	−226.692	−	130.881i	−0.317052	−	0.183050i
$716$			127.291i			0.177780i
$717$	−272.416	+	92.2225i	−0.379938	+	0.128623i
$718$	563.558	+	325.370i	0.784899	+	0.453162i
$719$	−90.3845	+	156.551i	−0.125709	+	0.217734i	−0.922010	−	0.387167i	$-0.873454\pi$
$719$	−90.3845	+	156.551i	−0.125709	+	0.217734i	0.796301	+	0.604900i	$0.206787\pi$
$720$	892.001	−	682.125i	1.23889	−	0.947396i
$721$			270.464i			0.375123i
$722$	−556.544	+	670.243i	−0.770836	+	0.928314i
$723$	−221.656	−	654.748i	−0.306578	−	0.905599i
$724$	−357.538	+	206.424i	−0.493836	+	0.285117i
$725$	−290.177	+	167.534i	−0.400244	+	0.231081i
$726$	−267.917	−	791.400i	−0.369032	−	1.09008i
$727$	1034.82			1.42341			0.711706	−	0.702478i	$-0.247923\pi$
$727$	1034.82			1.42341			0.711706	+	0.702478i	$0.247923\pi$
$728$	303.686	+	525.999i	0.417150	+	0.722526i
$729$	−275.645	−	674.879i	−0.378113	−	0.925759i
$730$			2061.69i			2.82423i
$731$	4.05949	−	7.03125i	0.00555334	−	0.00961867i
$732$	−204.851	+	69.3495i	−0.279851	+	0.0947397i
$733$	309.187	−	535.527i	0.421810	−	0.730597i	−0.574307	−	0.818640i	$-0.694728\pi$
$733$	309.187	−	535.527i	0.421810	−	0.730597i	0.996117	+	0.0880439i	$0.0280616\pi$
$734$	−171.494	−	99.0119i	−0.233642	−	0.134894i
$735$	−89.7705	−	78.8575i	−0.122137	−	0.107289i
$736$			496.014i			0.673932i
$737$	−233.631	+	134.887i	−0.317003	+	0.183022i
$738$	−705.375	+	539.409i	−0.955793	+	0.730907i
$739$	−529.527	+	917.167i	−0.716545	+	1.24109i	0.245815	+	0.969317i	$0.420944\pi$
$739$	−529.527	+	917.167i	−0.716545	+	1.24109i	−0.962361	+	0.271776i	$0.912389\pi$
$740$	175.593	−	101.379i	0.237288	−	0.136998i
$741$	−884.387	+	487.208i	−1.19350	+	0.657501i
$742$	509.620	−	882.688i	0.686819	−	1.18961i
$743$	115.977	−	66.9591i	0.156092	−	0.0901199i	−0.419919	−	0.907561i	$-0.637942\pi$
$743$	115.977	−	66.9591i	0.156092	−	0.0901199i	0.576012	+	0.817442i	$0.304608\pi$
$744$	621.956	−	210.555i	0.835963	−	0.283004i
$745$	119.790	−	207.482i	0.160792	−	0.278500i
$746$	−497.710	+	862.058i	−0.667171	+	1.15557i
$747$	177.444	−	135.694i	0.237542	−	0.181652i
$748$	53.3377			0.0713071
$749$	551.161	−	318.213i	0.735863	−	0.424851i
$750$	327.208	−	372.490i	0.436277	−	0.496653i
$751$		−	136.849i		−	0.182222i	−0.995841	−	0.0911111i	$-0.970958\pi$
$751$		−	136.849i		−	0.182222i	0.995841	−	0.0911111i	$-0.0290418\pi$
$752$	434.571	−	752.698i	0.577886	−	1.00093i
$753$	−133.617	+	668.856i	−0.177446	+	0.888255i
$754$	−883.551	−	510.119i	−1.17182	−	0.676550i
$755$	−742.862	−	428.892i	−0.983923	−	0.568068i
$756$	320.759	+	21.8197i	0.424284	+	0.0288621i
$757$	590.185	−	1022.23i	0.779637	−	1.35037i	−0.152515	−	0.988301i	$-0.548737\pi$
$757$	590.185	−	1022.23i	0.779637	−	1.35037i	0.932151	−	0.362069i	$-0.117930\pi$
$758$	14.3463			0.0189266
$759$	−25.3612	+	126.953i	−0.0334140	+	0.167263i
$760$	613.702	−	109.842i	0.807503	−	0.144529i
$761$	−334.129	+	578.729i	−0.439066	+	0.760485i	−0.997618	−	0.0689848i	$-0.978024\pi$
$761$	−334.129	+	578.729i	−0.439066	+	0.760485i	0.558551	+	0.829470i	$0.311357\pi$
$762$	−108.608	+	543.667i	−0.142530	+	0.713474i
$763$			319.317i			0.418502i
$764$	−326.882	−	566.176i	−0.427856	−	0.741068i
$765$	−89.6282	−	689.569i	−0.117161	−	0.901397i
$766$	578.324	+	1001.69i	0.754992	+	1.30768i
$767$	805.825	+	1395.73i	1.05062	+	1.81973i
$768$	−650.109	−	571.079i	−0.846497	−	0.743592i
$769$	−629.819			−0.819011			−0.409506	−	0.912308i	$-0.634299\pi$
$769$	−629.819			−0.819011			−0.409506	+	0.912308i	$0.634299\pi$
$770$			232.822i			0.302366i
$771$	−27.4770	+	31.2795i	−0.0356381	+	0.0405700i
$772$	446.458	−	257.763i	0.578314	−	0.333890i
$773$	1039.00	−	599.868i	1.34412	−	0.776026i	0.356708	−	0.934216i	$-0.383899\pi$
$773$	1039.00	−	599.868i	1.34412	−	0.776026i	0.987409	+	0.158190i	$0.0505659\pi$
$774$	14.1413	−	1.83805i	0.0182705	−	0.00237474i
$775$	−506.743	+	292.568i	−0.653862	+	0.377508i
$776$	622.262			0.801884
$777$	−341.743	−	68.2695i	−0.439823	−	0.0878630i
$778$	−1074.97	−	620.632i	−1.38170	−	0.797727i
$779$	−764.654	+	136.860i	−0.981584	+	0.175687i
$780$	−593.856	−	118.634i	−0.761353	−	0.152095i
$781$		−	20.7691i		−	0.0265930i
$782$	471.565	+	272.258i	0.603025	+	0.348156i
$783$	578.626	−	283.571i	0.738986	−	0.362160i
$784$	−63.6464	+	110.239i	−0.0811816	+	0.140611i
$785$	−149.729	+	259.338i	−0.190737	+	0.330367i
$786$	856.198	+	171.042i	1.08931	+	0.217610i
$787$	596.562	+	344.425i	0.758021	+	0.437643i	0.828585	−	0.559864i	$-0.189147\pi$
$787$	596.562	+	344.425i	0.758021	+	0.437643i	−0.0705640	+	0.997507i	$0.522480\pi$
$788$	437.586			0.555312
$789$	284.299	+	249.738i	0.360328	+	0.316525i
$790$	988.748	+	1712.56i	1.25158	+	2.16780i
$791$		−	863.550i		−	1.09172i
$792$	−67.9025	−	88.7947i	−0.0857354	−	0.112114i
$793$	−606.383	−	350.095i	−0.764670	−	0.441482i
$794$	411.922	+	237.823i	0.518794	+	0.299526i
$795$	−388.827	−	1148.55i	−0.489090	−	1.44472i
$796$	21.8664	+	37.8737i	0.0274703	+	0.0475800i
$797$	788.094	+	455.006i	0.988825	+	0.570899i	0.904923	−	0.425575i	$-0.139928\pi$
$797$	788.094	+	455.006i	0.988825	+	0.570899i	0.0839024	+	0.996474i	$0.473262\pi$
$798$	768.591	+	464.553i	0.963147	+	0.582147i
$799$	−269.107	−	466.107i	−0.336805	−	0.583363i
$800$	330.517	+	190.824i	0.413146	+	0.238530i
$801$	−71.2988	−	93.2360i	−0.0890123	−	0.116400i
$802$	−953.131	−	1650.87i	−1.18844	−	2.05844i
$803$	323.369			0.402701
$804$	−411.901	+	468.904i	−0.512315	+	0.583213i
$805$	−372.173	+	644.622i	−0.462326	+	0.800773i
$806$	−1542.97	−	890.834i	−1.91435	−	1.10525i
$807$	−387.356	−	1144.21i	−0.479995	−	1.41786i
$808$	−408.309	−	235.737i	−0.505333	−	0.291754i
$809$	33.9467			0.0419613			0.0209807	−	0.999780i	$-0.493321\pi$
$809$	33.9467			0.0419613			0.0209807	+	0.999780i	$0.493321\pi$
$810$	866.469	−	860.779i	1.06971	−	1.06269i
$811$	−943.967	+	545.000i	−1.16395	+	0.672009i	−0.952248	−	0.305324i	$-0.901235\pi$
$811$	−943.967	+	545.000i	−1.16395	+	0.672009i	−0.211706	+	0.977333i	$0.567902\pi$
$812$			284.180i			0.349975i
$813$	441.871	−	149.589i	0.543507	−	0.183997i
$814$	−50.7746	−	87.9442i	−0.0623767	−	0.108040i
$815$	−883.877	−	1530.92i	−1.08451	−	1.87843i
$816$	−701.675	+	237.542i	−0.859896	+	0.291106i
$817$	11.7335	+	4.23645i	0.0143616	+	0.00518537i
$818$	1156.07			1.41328
$819$	632.283	+	826.824i	0.772019	+	1.00955i
$820$	−403.483	−	232.951i	−0.492052	−	0.284086i
$821$	207.375	−	359.184i	0.252588	−	0.437495i	−0.711650	−	0.702535i	$-0.752052\pi$
$821$	207.375	−	359.184i	0.252588	−	0.437495i	0.964238	+	0.265039i	$0.0853849\pi$
$822$	22.2533	+	65.7339i	0.0270721	+	0.0799683i
$823$	−391.688			−0.475927			−0.237963	−	0.971274i	$-0.576480\pi$
$823$	−391.688			−0.475927			−0.237963	+	0.971274i	$0.576480\pi$
$824$	108.778	−	188.410i	0.132013	−	0.228652i
$825$	74.8377	+	65.7400i	0.0907123	+	0.0796848i
$826$	716.734	−	1241.42i	0.867717	−	1.50293i
$827$	58.3968	−	33.7154i	0.0706128	−	0.0407683i	−0.464278	−	0.885690i	$-0.653686\pi$
$827$	58.3968	−	33.7154i	0.0706128	−	0.0407683i	0.534891	+	0.844921i	$0.320353\pi$
$828$	38.6048	+	297.012i	0.0466241	+	0.358711i
$829$		−	1177.54i		−	1.42044i	−0.703982	−	0.710218i	$-0.748596\pi$
$829$		−	1177.54i		−	1.42044i	0.703982	−	0.710218i	$-0.251404\pi$
$830$	324.110	+	187.125i	0.390494	+	0.225452i
$831$	−86.6266	+	433.634i	−0.104244	+	0.521822i
$832$		−	252.867i		−	0.303926i
$833$	39.4129	+	68.2651i	0.0473144	+	0.0819509i
$834$	1036.95	−	1180.45i	1.24335	−	1.41541i
$835$	−1617.15	+	933.661i	−1.93670	+	1.11816i
$836$	14.4389	+	80.6716i	0.0172714	+	0.0964971i
$837$	1010.47	−	495.209i	1.20725	−	0.591647i
$838$	−303.657	−	175.317i	−0.362360	−	0.209208i
$839$		−	517.358i		−	0.616636i	−0.951283	−	0.308318i	$-0.900234\pi$
$839$		−	517.358i		−	0.616636i	0.951283	−	0.308318i	$-0.0997661\pi$
$840$	−206.087	−	608.760i	−0.245342	−	0.724714i
$841$	−135.712	−	235.060i	−0.161370	−	0.279501i
$842$	1004.44			1.19292
$843$	391.687	+	1157.00i	0.464635	+	1.37248i
$844$	−372.605	+	215.124i	−0.441475	+	0.254886i
$845$	−452.344	−	783.483i	−0.535319	−	0.927199i
$846$	363.199	−	872.770i	0.429313	−	1.03164i
$847$	−753.470			−0.889575
$848$	−1118.73	+	645.897i	−1.31925	+	0.761671i
$849$	−108.900	+	545.130i	−0.128268	+	0.642084i
$850$	362.836	−	209.484i	0.426866	−	0.246451i
$851$		−	324.659i		−	0.381503i
$852$	−15.4076	−	45.5124i	−0.0180840	−	0.0534184i
$853$	−44.3715			−0.0520182			−0.0260091	−	0.999662i	$-0.508280\pi$
$853$	−44.3715			−0.0520182			−0.0260091	+	0.999662i	$0.508280\pi$
$854$			622.779i			0.729249i
$855$	1018.69	−	322.230i	1.19145	−	0.376878i
$856$	−511.931			−0.598051
$857$		−	731.950i		−	0.854084i	−0.904232	−	0.427042i	$-0.859556\pi$
$857$		−	731.950i		−	0.854084i	0.904232	−	0.427042i	$-0.140444\pi$
$858$	−59.4167	+	297.427i	−0.0692502	+	0.346652i
$859$	−1396.82			−1.62610			−0.813051	−	0.582193i	$-0.802195\pi$
$859$	−1396.82			−1.62610			−0.813051	+	0.582193i	$0.802195\pi$
$860$	3.74100	+	6.47959i	0.00434999	+	0.00753441i
$861$	256.778	+	758.497i	0.298233	+	0.880949i
$862$	−408.139	−	706.918i	−0.473479	−	0.820090i
$863$			901.886i			1.04506i	0.852621	+	0.522530i	$0.175012\pi$
$863$			901.886i			1.04506i	−0.852621	+	0.522530i	$0.824988\pi$
$864$	−609.253	−	409.271i	−0.705154	−	0.473693i
$865$	−690.735	+	398.796i	−0.798538	+	0.461036i
$866$	−857.307	−	1484.90i	−0.989961	−	1.71466i
$867$	79.9784	−	400.355i	0.0922473	−	0.461770i
$868$			496.271i			0.571741i
$869$	268.609	−	155.081i	0.309101	−	0.178460i
$870$	811.083	+	712.483i	0.932280	+	0.818947i
$871$	−2020.64			−2.31991
$872$	128.427	−	222.442i	0.147279	−	0.255094i
$873$	1057.50	−	137.451i	1.21134	−	0.157446i
$874$	−284.126	+	786.930i	−0.325087	+	0.900377i
$875$	−223.554	−	387.207i	−0.255490	−	0.442522i
$876$	708.614	−	239.891i	0.808920	−	0.273849i
$877$	−981.184	+	566.487i	−1.11880	+	0.645937i	−0.941093	−	0.338147i	$-0.890200\pi$
$877$	−981.184	+	566.487i	−1.11880	+	0.645937i	−0.177703	+	0.984084i	$0.556867\pi$
$878$	47.2797			0.0538493
$879$	171.934	+	507.876i	0.195602	+	0.577789i
$880$	147.540	−	255.547i	0.167659	−	0.290394i
$881$	−844.605			−0.958688			−0.479344	−	0.877627i	$-0.659125\pi$
$881$	−844.605			−0.958688			−0.479344	+	0.877627i	$0.659125\pi$
$882$	−53.1934	+	127.824i	−0.0603099	+	0.144925i
$883$	548.084	+	949.309i	0.620707	+	1.07510i	0.989354	+	0.145526i	$0.0464875\pi$
$883$	548.084	+	949.309i	0.620707	+	1.07510i	−0.368648	+	0.929569i	$0.620179\pi$
$884$	345.983	+	199.753i	0.391384	+	0.225965i
$885$	−546.849	−	1615.34i	−0.617909	−	1.82524i
$886$	1684.97	+	972.819i	1.90177	+	1.09799i
$887$		−	100.966i		−	0.113829i	−0.998379	−	0.0569144i	$-0.981874\pi$
$887$		−	100.966i		−	0.113829i	0.998379	−	0.0569144i	$-0.0181262\pi$
$888$	210.606	+	185.004i	0.237169	+	0.208338i
$889$	432.983	+	249.983i	0.487045	+	0.281195i
$890$	98.3227	−	170.300i	0.110475	−	0.191348i
$891$	−135.010	−	135.903i	−0.151526	−	0.152528i
$892$		−	319.392i		−	0.358063i
$893$	632.123	−	533.194i	0.707865	−	0.597082i
$894$	−272.224	−	54.3817i	−0.304501	−	0.0608297i
$895$	377.657	−	218.040i	0.421963	−	0.243621i
$896$	−809.575	+	467.408i	−0.903544	+	0.521661i
$897$	−639.956	+	728.519i	−0.713441	+	0.812173i
$898$	935.416			1.04167
$899$	497.333	+	861.406i	0.553207	+	0.958182i
$900$	212.765	+	88.5409i	0.236405	+	0.0983788i
$901$			799.941i			0.887837i
$902$	−116.671	+	202.081i	−0.129347	+	0.224036i
$903$	2.51923	−	12.6107i	0.00278984	−	0.0139654i
$904$	−347.313	+	601.564i	−0.384196	+	0.665447i
$905$	1224.87	+	707.182i	1.35345	+	0.781416i
$906$	−194.706	+	974.659i	−0.214908	+	1.07578i
$907$		−	458.679i		−	0.505710i	−0.967504	−	0.252855i	$-0.918630\pi$
$907$		−	458.679i		−	0.505710i	0.967504	−	0.252855i	$-0.0813695\pi$
$908$	−630.830	+	364.210i	−0.694747	+	0.401112i
$909$	−745.969	−	310.431i	−0.820648	−	0.341508i
$910$	−871.933	+	1510.23i	−0.958168	+	1.65960i
$911$	−194.625	+	112.367i	−0.213639	+	0.123344i	−0.603001	−	0.797740i	$-0.706029\pi$
$911$	−194.625	+	112.367i	−0.213639	+	0.123344i	0.389363	+	0.921085i	$0.372695\pi$
$912$	−549.223	−	996.957i	−0.602218	−	1.09315i
$913$	29.3499	−	50.8354i	0.0321466	−	0.0556796i
$914$	297.810	−	171.941i	0.325831	−	0.188119i
$915$	556.648	+	488.979i	0.608358	+	0.534403i
$916$	−268.874	+	465.703i	−0.293530	+	0.508409i
$917$	393.687	−	681.886i	0.429321	−	0.743605i
$918$	−723.513	+	354.577i	−0.788141	+	0.386250i
$919$	−32.2961			−0.0351427			−0.0175713	−	0.999846i	$-0.505593\pi$
$919$	−32.2961			−0.0351427			−0.0175713	+	0.999846i	$0.505593\pi$
$920$	518.524	−	299.370i	0.563613	−	0.325402i
$921$	−146.165	−	431.756i	−0.158702	−	0.468790i
$922$			365.341i			0.396249i
$923$	77.7819	−	134.722i	0.0842707	−	0.145961i
$924$	80.0220	−	27.0903i	0.0866039	−	0.0293185i
$925$	−216.335	−	124.901i	−0.233876	−	0.135028i
$926$	−0.823480	−	0.475436i	−0.000889287	−	0.000513430i
$927$	143.245	−	344.219i	0.154525	−	0.371326i
$928$	324.379	−	561.840i	0.349546	−	0.605432i
$929$	−1249.07			−1.34454			−0.672268	−	0.740308i	$-0.734680\pi$
$929$	−1249.07			−1.34454			−0.672268	+	0.740308i	$0.734680\pi$
$930$	1416.42	+	1244.23i	1.52303	+	1.33788i
$931$	−92.5795	+	78.0905i	−0.0994409	+	0.0838781i
$932$	68.6476	−	118.901i	0.0736562	−	0.127576i
$933$	242.776	−	82.1886i	0.260211	−	0.0880907i
$934$		−	267.204i		−	0.286085i
$935$	−91.3639	−	158.247i	−0.0977154	−	0.169248i
$936$	−107.917	−	830.279i	−0.115296	−	0.887051i
$937$	−116.513	−	201.806i	−0.124347	−	0.215374i	0.797131	−	0.603807i	$-0.206350\pi$
$937$	−116.513	−	201.806i	−0.124347	−	0.215374i	−0.921477	+	0.388432i	$0.873017\pi$
$938$	898.622	+	1556.46i	0.958019	+	1.65934i
$939$	−176.839	+	59.8665i	−0.188327	+	0.0637556i
$940$	495.987			0.527646
$941$			1064.53i			1.13128i	0.824654	+	0.565638i	$0.191370\pi$
$941$			1064.53i			1.13128i	−0.824654	+	0.565638i	$0.808630\pi$
$942$	340.260	+	67.9733i	0.361210	+	0.0721585i
$943$	−646.065	+	373.006i	−0.685117	+	0.395552i
$944$	−1573.39	+	908.395i	−1.66672	+	0.962283i
$945$	−484.701	−	989.030i	−0.512912	−	1.04659i
$946$	3.24525	−	1.87364i	0.00343049	−	0.00198060i
$947$	−171.074			−0.180649			−0.0903244	−	0.995912i	$-0.528790\pi$
$947$	−171.074			−0.180649			−0.0903244	+	0.995912i	$0.528790\pi$
$948$	473.569	−	539.106i	0.499545	−	0.568677i
$949$	2097.58	+	1211.04i	2.21030	+	1.27612i
$950$	415.060	+	492.070i	0.436905	+	0.517968i
$951$	−50.1053	−	148.006i	−0.0526869	−	0.155632i
$952$			423.987i			0.445365i
$953$	−289.764	−	167.295i	−0.304055	−	0.175546i	0.340208	−	0.940350i	$-0.389502\pi$
$953$	−289.764	−	167.295i	−0.304055	−	0.175546i	−0.644263	+	0.764804i	$0.722836\pi$
$954$	−1116.09	+	853.488i	−1.16991	+	0.894642i
$955$	−1119.85	+	1939.64i	−1.17262	+	2.03104i
$956$	−87.4227	+	151.421i	−0.0914464	+	0.158390i
$957$	111.750	−	127.215i	0.116772	−	0.132932i
$958$	76.4142	+	44.1178i	0.0797643	+	0.0460519i
$959$	62.5835			0.0652591
$960$	−52.4173	+	262.390i	−0.0546013	+	0.273323i
$961$	388.006	+	672.045i	0.403752	+	0.699319i
$962$		−	760.617i		−	0.790663i
$963$	−869.998	+	113.080i	−0.903425	+	0.117424i
$964$	−363.938	−	210.120i	−0.377529	−	0.217966i
$965$	−1529.51	−	883.060i	−1.58498	−	0.915089i
$966$	845.765	+	168.957i	0.875533	+	0.174904i
$967$	−564.227	−	977.269i	−0.583482	−	1.01062i	−0.995063	−	0.0992467i	$-0.968357\pi$
$967$	−564.227	−	977.269i	−0.583482	−	1.01062i	0.411581	−	0.911373i	$-0.364977\pi$
$968$	524.880	+	303.040i	0.542232	+	0.313058i
$969$	−704.705	−	14.1421i	−0.727250	−	0.0145945i
$970$	893.310	+	1547.26i	0.920938	+	1.59511i
$971$	−455.201	−	262.810i	−0.468796	−	0.270660i	0.246940	−	0.969031i	$-0.420575\pi$
$971$	−455.201	−	262.810i	−0.468796	−	0.270660i	−0.715736	+	0.698371i	$0.753908\pi$
$972$	−396.674	−	197.653i	−0.408100	−	0.203346i
$973$	−708.463	−	1227.09i	−0.728122	−	1.26114i
$974$	−1538.99			−1.58007
$975$	239.245	+	706.704i	0.245379	+	0.724825i
$976$	394.658	−	683.567i	0.404362	−	0.700376i
$977$	497.860	+	287.440i	0.509580	+	0.294206i	0.732661	−	0.680594i	$-0.238278\pi$
$977$	497.860	+	287.440i	0.509580	+	0.294206i	−0.223081	+	0.974800i	$0.571611\pi$
$978$	−1351.81	+	1538.88i	−1.38222	+	1.57350i
$979$	−26.7109	−	15.4216i	−0.0272839	−	0.0157524i
$980$	−72.6413			−0.0741238
$981$	169.119	−	406.395i	0.172395	−	0.414266i
$982$	−1448.98	+	836.568i	−1.47554	+	0.851902i
$983$			1118.88i			1.13823i	0.822259	+	0.569114i	$0.192714\pi$
$983$			1118.88i			1.13823i	−0.822259	+	0.569114i	$0.807286\pi$
$984$	126.185	−	631.656i	0.128237	−	0.641927i
$985$	−749.555	−	1298.27i	−0.760970	−	1.31804i
$986$	−356.098	−	616.781i	−0.361155	−	0.625538i
$987$	−640.475	−	562.615i	−0.648911	−	0.570026i
$988$	−208.461	+	577.363i	−0.210993	+	0.584375i
$989$	11.9803			0.0121136
$990$	123.309	−	296.312i	0.124554	−	0.299305i
$991$	−26.3311	−	15.2023i	−0.0265703	−	0.0153404i	0.486656	−	0.873594i	$-0.338217\pi$
$991$	−26.3311	−	15.2023i	−0.0265703	−	0.0153404i	−0.513226	+	0.858253i	$0.671550\pi$
$992$	566.471	−	981.157i	0.571040	−	0.989070i
$993$	−271.206	−	54.1785i	−0.273118	−	0.0545604i
$994$	−138.365			−0.139200
$995$	74.9113	−	129.750i	0.0752877	−	0.130402i
$996$	26.6035	−	133.171i	0.0267103	−	0.133706i
$997$	287.520	−	498.000i	0.288386	−	0.499499i	−0.685039	−	0.728506i	$-0.740215\pi$
$997$	287.520	−	498.000i	0.288386	−	0.499499i	0.973425	+	0.229008i	$0.0735482\pi$
$998$	−374.155	+	216.019i	−0.374905	+	0.216452i
$999$	398.779	+	267.883i	0.399178	+	0.268151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.3.i.a.103.30	yes	76
3.2	odd	2		513.3.i.a.388.9		76
9.2	odd	6		513.3.s.a.46.9		76
9.7	even	3		171.3.s.a.160.30	yes	76
19.12	odd	6		171.3.s.a.31.30	yes	76
57.50	even	6		513.3.s.a.145.9		76
171.88	odd	6	inner	171.3.i.a.88.9	✓	76
171.164	even	6		513.3.i.a.316.30		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.3.i.a.88.9	✓	76	171.88	odd	6	inner
171.3.i.a.103.30	yes	76	1.1	even	1	trivial
171.3.s.a.31.30	yes	76	19.12	odd	6
171.3.s.a.160.30	yes	76	9.7	even	3
513.3.i.a.316.30		76	171.164	even	6
513.3.i.a.388.9		76	3.2	odd	2
513.3.s.a.46.9		76	9.2	odd	6
513.3.s.a.145.9		76	57.50	even	6

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.41326i q^{2} +(-2.25389 - 1.97989i) q^{3} -1.82382 q^{4} +(3.12409 + 5.41107i) q^{5} +(4.77800 - 5.43922i) q^{6} +(-3.26441 - 5.65412i) q^{7} +5.25168i q^{8} +(1.16004 + 8.92493i) q^{9} +O(q^{10})\)	\(q+2.41326i q^{2} +(-2.25389 - 1.97989i) q^{3} -1.82382 q^{4} +(3.12409 + 5.41107i) q^{5} +(4.77800 - 5.43922i) q^{6} +(-3.26441 - 5.65412i) q^{7} +5.25168i q^{8} +(1.16004 + 8.92493i) q^{9} +(-13.0583 + 7.53923i) q^{10} +(1.18250 + 2.04815i) q^{11} +(4.11070 + 3.61098i) q^{12} +17.7142i q^{13} +(13.6449 - 7.87787i) q^{14} +(3.67201 - 18.3813i) q^{15} -19.9690 q^{16} +(-6.18287 + 10.7090i) q^{17} +(-21.5382 + 2.79947i) q^{18} +(-17.8708 - 6.45239i) q^{19} +(-5.69778 - 9.86885i) q^{20} +(-3.83695 + 19.2070i) q^{21} +(-4.94272 + 2.85368i) q^{22} -18.2468 q^{23} +(10.3978 - 11.8367i) q^{24} +(-7.01982 + 12.1587i) q^{25} -42.7489 q^{26} +(15.0558 - 22.4125i) q^{27} +(5.95371 + 10.3121i) q^{28} +(20.6684 + 11.9329i) q^{29} +(44.3589 + 8.86152i) q^{30} +(36.0937 + 20.8387i) q^{31} -27.1836i q^{32} +(1.38990 - 6.95754i) q^{33} +(-25.8437 - 14.9209i) q^{34} +(20.3966 - 35.3279i) q^{35} +(-2.11570 - 16.2775i) q^{36} +17.7927i q^{37} +(15.5713 - 43.1270i) q^{38} +(35.0722 - 39.9258i) q^{39} +(-28.4172 + 16.4067i) q^{40} +(35.4070 - 20.4423i) q^{41} +(-46.3514 - 9.25955i) q^{42} -0.656571 q^{43} +(-2.15667 - 3.73547i) q^{44} +(-44.6694 + 34.1593i) q^{45} -44.0343i q^{46} +(-21.7623 + 37.6934i) q^{47} +(45.0078 + 39.5364i) q^{48} +(3.18726 - 5.52050i) q^{49} +(-29.3421 - 16.9407i) q^{50} +(35.1383 - 11.8956i) q^{51} -32.3076i q^{52} +(56.0233 - 32.3450i) q^{53} +(54.0873 + 36.3336i) q^{54} +(-7.38847 + 12.7972i) q^{55} +(29.6936 - 17.1436i) q^{56} +(27.5038 + 49.9253i) q^{57} +(-28.7972 + 49.8782i) q^{58} +(78.7916 - 45.4904i) q^{59} +(-6.69710 + 33.5243i) q^{60} +(-19.7636 + 34.2315i) q^{61} +(-50.2893 + 87.1036i) q^{62} +(46.6758 - 35.6936i) q^{63} -14.2748 q^{64} +(-95.8528 + 55.3406i) q^{65} +(16.7903 + 3.35418i) q^{66} +114.069i q^{67} +(11.2765 - 19.5314i) q^{68} +(41.1263 + 36.1268i) q^{69} +(85.2555 + 49.2223i) q^{70} +(-7.60532 - 4.39093i) q^{71} +(-46.8709 + 6.09214i) q^{72} +(68.3654 - 118.412i) q^{73} -42.9383 q^{74} +(39.8948 - 13.5058i) q^{75} +(32.5932 + 11.7680i) q^{76} +(7.72033 - 13.3720i) q^{77} +(96.3514 + 84.6384i) q^{78} -131.147i q^{79} +(-62.3847 - 108.054i) q^{80} +(-78.3086 + 20.7065i) q^{81} +(49.3325 + 85.4463i) q^{82} +(-12.4101 - 21.4949i) q^{83} +(6.99792 - 35.0301i) q^{84} -77.2633 q^{85} -1.58448i q^{86} +(-22.9584 - 67.8166i) q^{87} +(-10.7562 + 6.21012i) q^{88} +(-11.2942 + 6.52074i) q^{89} +(-82.4352 - 107.799i) q^{90} +(100.158 - 57.8264i) q^{91} +33.2790 q^{92} +(-40.0928 - 118.430i) q^{93} +(-90.9640 - 52.5181i) q^{94} +(-20.9156 - 116.858i) q^{95} +(-53.8206 + 61.2688i) q^{96} -118.488i q^{97} +(13.3224 + 7.69170i) q^{98} +(-16.9079 + 12.9297i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 3 q^{3} - 146 q^{4} + q^{5} + 7 q^{6} - 3 q^{7} - 13 q^{9}+O(q^{10}) \) 76 * q - 3 * q^3 - 146 * q^4 + q^5 + 7 * q^6 - 3 * q^7 - 13 * q^9	\( 76 q - 3 q^{3} - 146 q^{4} + q^{5} + 7 q^{6} - 3 q^{7} - 13 q^{9} - 6 q^{10} + 4 q^{11} - 15 q^{12} + 21 q^{14} - 18 q^{15} + 262 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} - 17 q^{20} + 24 q^{21} - 15 q^{22} + 46 q^{23} - 23 q^{24} - 149 q^{25} + 48 q^{26} - 63 q^{27} + 30 q^{28} - 30 q^{29} - 41 q^{30} + 48 q^{31} - 93 q^{33} + 15 q^{34} - 31 q^{35} - 51 q^{36} - 135 q^{38} + 28 q^{39} + 96 q^{40} + 123 q^{41} + 238 q^{42} + 182 q^{43} - 191 q^{44} - 289 q^{45} + 61 q^{47} + 123 q^{48} - 171 q^{49} + 243 q^{50} - 45 q^{51} - 42 q^{53} + 224 q^{54} + 23 q^{55} - 624 q^{56} - 133 q^{57} + 6 q^{58} - 390 q^{59} + 381 q^{60} - 6 q^{61} - 366 q^{62} + 323 q^{63} - 152 q^{64} + 582 q^{65} + 95 q^{66} - 74 q^{68} - 75 q^{69} - 150 q^{70} - 87 q^{71} + 99 q^{72} + 29 q^{73} + 252 q^{74} - 585 q^{75} - 3 q^{76} + 32 q^{77} - 216 q^{78} - 104 q^{80} - 5 q^{81} + 54 q^{82} - 23 q^{83} + 204 q^{84} + 98 q^{85} + 671 q^{87} + 132 q^{88} - 222 q^{89} + 249 q^{90} - 51 q^{91} + 694 q^{92} + 293 q^{93} + 24 q^{94} + 145 q^{95} + 147 q^{96} - 558 q^{98} - 92 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 146 * q^4 + q^5 + 7 * q^6 - 3 * q^7 - 13 * q^9 - 6 * q^10 + 4 * q^11 - 15 * q^12 + 21 * q^14 - 18 * q^15 + 262 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 - 17 * q^20 + 24 * q^21 - 15 * q^22 + 46 * q^23 - 23 * q^24 - 149 * q^25 + 48 * q^26 - 63 * q^27 + 30 * q^28 - 30 * q^29 - 41 * q^30 + 48 * q^31 - 93 * q^33 + 15 * q^34 - 31 * q^35 - 51 * q^36 - 135 * q^38 + 28 * q^39 + 96 * q^40 + 123 * q^41 + 238 * q^42 + 182 * q^43 - 191 * q^44 - 289 * q^45 + 61 * q^47 + 123 * q^48 - 171 * q^49 + 243 * q^50 - 45 * q^51 - 42 * q^53 + 224 * q^54 + 23 * q^55 - 624 * q^56 - 133 * q^57 + 6 * q^58 - 390 * q^59 + 381 * q^60 - 6 * q^61 - 366 * q^62 + 323 * q^63 - 152 * q^64 + 582 * q^65 + 95 * q^66 - 74 * q^68 - 75 * q^69 - 150 * q^70 - 87 * q^71 + 99 * q^72 + 29 * q^73 + 252 * q^74 - 585 * q^75 - 3 * q^76 + 32 * q^77 - 216 * q^78 - 104 * q^80 - 5 * q^81 + 54 * q^82 - 23 * q^83 + 204 * q^84 + 98 * q^85 + 671 * q^87 + 132 * q^88 - 222 * q^89 + 249 * q^90 - 51 * q^91 + 694 * q^92 + 293 * q^93 + 24 * q^94 + 145 * q^95 + 147 * q^96 - 558 * q^98 - 92 * q^99

Introduction

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