LMFDB - Embedded newform 475.2.n.b.39.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.3
Character	$\chi$	$=$	475.39
Dual form			475.2.n.b.134.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47440 - 2.02934i) q^{2} +(-2.71260 - 0.881376i) q^{3} +(-1.32633 + 4.08203i) q^{4} +(-1.86244 + 1.23746i) q^{5} +(2.21085 + 6.80430i) q^{6} +0.624081i q^{7} +(5.46813 - 1.77670i) q^{8} +(4.15431 + 3.01828i) q^{9} +O(q^{10})$	\(q+(-1.47440 - 2.02934i) q^{2} +(-2.71260 - 0.881376i) q^{3} +(-1.32633 + 4.08203i) q^{4} +(-1.86244 + 1.23746i) q^{5} +(2.21085 + 6.80430i) q^{6} +0.624081i q^{7} +(5.46813 - 1.77670i) q^{8} +(4.15431 + 3.01828i) q^{9} +(5.25723 + 1.95502i) q^{10} +(-2.58624 + 1.87901i) q^{11} +(7.19562 - 9.90392i) q^{12} +(2.03442 - 2.80014i) q^{13} +(1.26647 - 0.920148i) q^{14} +(6.14273 - 1.71522i) q^{15} +(-4.72301 - 3.43147i) q^{16} +(-5.08116 + 1.65097i) q^{17} -12.8807i q^{18} +(0.309017 + 0.951057i) q^{19} +(-2.58113 - 9.24384i) q^{20} +(0.550050 - 1.69288i) q^{21} +(7.62633 + 2.47794i) q^{22} +(1.68625 + 2.32092i) q^{23} -16.3988 q^{24} +(1.93739 - 4.60940i) q^{25} -8.68202 q^{26} +(-3.57929 - 4.92648i) q^{27} +(-2.54752 - 0.827739i) q^{28} +(-2.14180 + 6.59179i) q^{29} +(-12.5376 - 9.93678i) q^{30} +(-2.73850 - 8.42823i) q^{31} +3.14491i q^{32} +(8.67155 - 2.81756i) q^{33} +(10.8421 + 7.87722i) q^{34} +(-0.772275 - 1.16231i) q^{35} +(-17.8307 + 12.9548i) q^{36} +(-3.16897 + 4.36171i) q^{37} +(1.47440 - 2.02934i) q^{38} +(-7.98655 + 5.80257i) q^{39} +(-7.98548 + 10.0756i) q^{40} +(5.74535 + 4.17424i) q^{41} +(-4.24643 + 1.37975i) q^{42} -7.29563i q^{43} +(-4.23998 - 13.0493i) q^{44} +(-11.4722 - 0.480586i) q^{45} +(2.22374 - 6.84396i) q^{46} +(1.53014 + 0.497172i) q^{47} +(9.78720 + 13.4709i) q^{48} +6.61052 q^{49} +(-12.2105 + 2.86449i) q^{50} +15.2383 q^{51} +(8.73196 + 12.0185i) q^{52} +(-4.01056 - 1.30311i) q^{53} +(-4.72019 + 14.5272i) q^{54} +(2.49152 - 6.69992i) q^{55} +(1.10881 + 3.41256i) q^{56} -2.85219i q^{57} +(16.5349 - 5.37251i) q^{58} +(-11.1458 - 8.09790i) q^{59} +(-1.14572 + 27.3498i) q^{60} +(5.45839 - 3.96575i) q^{61} +(-13.0661 + 17.9840i) q^{62} +(-1.88365 + 2.59262i) q^{63} +(-3.06392 + 2.22606i) q^{64} +(-0.323931 + 7.73262i) q^{65} +(-18.5032 - 13.4433i) q^{66} +(-6.63488 + 2.15580i) q^{67} -22.9312i q^{68} +(-2.52851 - 7.78195i) q^{69} +(-1.22009 + 3.28093i) q^{70} +(2.64273 - 8.13349i) q^{71} +(28.0789 + 9.12339i) q^{72} +(-2.82435 - 3.88738i) q^{73} +13.5237 q^{74} +(-9.31796 + 10.7959i) q^{75} -4.29211 q^{76} +(-1.17266 - 1.61402i) q^{77} +(23.5508 + 7.65212i) q^{78} +(1.98481 - 6.10861i) q^{79} +(13.0426 + 0.546375i) q^{80} +(0.606690 + 1.86720i) q^{81} -17.8138i q^{82} +(9.19729 - 2.98838i) q^{83} +(6.18084 + 4.49065i) q^{84} +(7.42036 - 9.36256i) q^{85} +(-14.8054 + 10.7567i) q^{86} +(11.6197 - 15.9931i) q^{87} +(-10.8035 + 14.8697i) q^{88} +(9.84471 - 7.15260i) q^{89} +(15.9393 + 23.9896i) q^{90} +(1.74752 + 1.26964i) q^{91} +(-11.7106 + 3.80501i) q^{92} +25.2760i q^{93} +(-1.24711 - 3.83821i) q^{94} +(-1.75242 - 1.38889i) q^{95} +(2.77185 - 8.53087i) q^{96} +(11.9315 + 3.87677i) q^{97} +(-9.74659 - 13.4150i) q^{98} -16.4154 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−1.47440	−	2.02934i	−1.04256	−	1.43496i	−0.895084	−	0.445897i	$-0.852885\pi$
$2$	−1.47440	−	2.02934i	−1.04256	−	1.43496i	−0.147477	−	0.989065i	$-0.547115\pi$
$3$	−2.71260	−	0.881376i	−1.56612	−	0.508863i	−0.607685	−	0.794178i	$-0.707902\pi$
$3$	−2.71260	−	0.881376i	−1.56612	−	0.508863i	−0.958434	+	0.285315i	$0.907902\pi$
$4$	−1.32633	+	4.08203i	−0.663167	+	2.04102i
$5$	−1.86244	+	1.23746i	−0.832910	+	0.553409i
$5$	−1.86244	+	1.23746i	−0.832910	+	0.553409i
$6$	2.21085	+	6.80430i	0.902576	+	2.77784i
$7$			0.624081i			0.235880i	0.993021	+	0.117940i	$0.0376291\pi$
$7$			0.624081i			0.235880i	−0.993021	+	0.117940i	$0.962371\pi$
$8$	5.46813	−	1.77670i	1.93328	−	0.628160i
$9$	4.15431	+	3.01828i	1.38477	+	1.00609i
$10$	5.25723	+	1.95502i	1.66248	+	0.618232i
$11$	−2.58624	+	1.87901i	−0.779781	+	0.566544i	−0.904913	−	0.425596i	$-0.860064\pi$
$11$	−2.58624	+	1.87901i	−0.779781	+	0.566544i	0.125132	+	0.992140i	$0.460064\pi$
$12$	7.19562	−	9.90392i	2.07720	−	2.85901i
$13$	2.03442	−	2.80014i	0.564248	−	0.776620i	−0.427611	−	0.903963i	$-0.640645\pi$
$13$	2.03442	−	2.80014i	0.564248	−	0.776620i	0.991859	+	0.127343i	$0.0406448\pi$
$14$	1.26647	−	0.920148i	0.338480	−	0.245920i
$15$	6.14273	−	1.71522i	1.58604	−	0.442867i
$16$	−4.72301	−	3.43147i	−1.18075	−	0.857866i
$17$	−5.08116	+	1.65097i	−1.23236	+	0.400419i	−0.851569	−	0.524242i	$-0.824349\pi$
$17$	−5.08116	+	1.65097i	−1.23236	+	0.400419i	−0.380792	+	0.924661i	$0.624349\pi$
$18$		−	12.8807i		−	3.03601i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	−2.58113	−	9.24384i	−0.577159	−	2.06699i
$21$	0.550050	−	1.69288i	0.120031	−	0.369417i
$22$	7.62633	+	2.47794i	1.62594	+	0.528300i
$23$	1.68625	+	2.32092i	0.351607	+	0.483946i	0.947787	−	0.318905i	$-0.103315\pi$
$23$	1.68625	+	2.32092i	0.351607	+	0.483946i	−0.596179	+	0.802851i	$0.703315\pi$
$24$	−16.3988			−3.34739
$25$	1.93739	−	4.60940i	0.387477	−	0.921879i
$26$	−8.68202			−1.70268
$27$	−3.57929	−	4.92648i	−0.688836	−	0.948101i
$28$	−2.54752	−	0.827739i	−0.481436	−	0.156428i
$29$	−2.14180	+	6.59179i	−0.397723	+	1.22406i	0.529098	+	0.848561i	$0.322530\pi$
$29$	−2.14180	+	6.59179i	−0.397723	+	1.22406i	−0.926821	+	0.375504i	$0.877470\pi$
$30$	−12.5376	−	9.93678i	−2.28905	−	1.81420i
$31$	−2.73850	−	8.42823i	−0.491849	−	1.51375i	−0.821811	−	0.569761i	$-0.807036\pi$
$31$	−2.73850	−	8.42823i	−0.491849	−	1.51375i	0.329962	−	0.943994i	$-0.392964\pi$
$32$			3.14491i			0.555946i
$33$	8.67155	−	2.81756i	1.50952	−	0.490474i
$34$	10.8421	+	7.87722i	1.85940	+	1.35093i
$35$	−0.772275	−	1.16231i	−0.130538	−	0.196467i
$36$	−17.8307	+	12.9548i	−2.97179	+	2.15913i
$37$	−3.16897	+	4.36171i	−0.520975	+	0.717061i	−0.985722	−	0.168383i	$-0.946145\pi$
$37$	−3.16897	+	4.36171i	−0.520975	+	0.717061i	0.464747	+	0.885444i	$0.346145\pi$
$38$	1.47440	−	2.02934i	0.239180	−	0.329203i
$39$	−7.98655	+	5.80257i	−1.27887	+	0.929155i
$40$	−7.98548	+	10.0756i	−1.26262	+	1.59309i
$41$	5.74535	+	4.17424i	0.897273	+	0.651907i	0.937764	−	0.347273i	$-0.112892\pi$
$41$	5.74535	+	4.17424i	0.897273	+	0.651907i	−0.0404909	+	0.999180i	$0.512892\pi$
$42$	−4.24643	+	1.37975i	−0.655239	+	0.212900i
$43$		−	7.29563i		−	1.11257i	−0.830990	−	0.556287i	$-0.812226\pi$
$43$		−	7.29563i		−	1.11257i	0.830990	−	0.556287i	$-0.187774\pi$
$44$	−4.23998	−	13.0493i	−0.639201	−	1.96726i
$45$	−11.4722	−	0.480586i	−1.71017	−	0.0716416i
$46$	2.22374	−	6.84396i	0.327872	−	1.00909i
$47$	1.53014	+	0.497172i	0.223193	+	0.0725199i	0.418479	−	0.908226i	$-0.362563\pi$
$47$	1.53014	+	0.497172i	0.223193	+	0.0725199i	−0.195286	+	0.980746i	$0.562563\pi$
$48$	9.78720	+	13.4709i	1.41266	+	1.94436i
$49$	6.61052			0.944360
$50$	−12.2105	+	2.86449i	−1.72683	+	0.405101i
$51$	15.2383			2.13378
$52$	8.73196	+	12.0185i	1.21090	+	1.66667i
$53$	−4.01056	−	1.30311i	−0.550893	−	0.178996i	0.0203264	−	0.999793i	$-0.493529\pi$
$53$	−4.01056	−	1.30311i	−0.550893	−	0.178996i	−0.571219	+	0.820797i	$0.693529\pi$
$54$	−4.72019	+	14.5272i	−0.642336	+	1.97691i
$55$	2.49152	−	6.69992i	0.335957	−	0.903418i
$56$	1.10881	+	3.41256i	0.148170	+	0.456022i
$57$		−	2.85219i		−	0.377782i
$58$	16.5349	−	5.37251i	2.17114	−	0.705445i
$59$	−11.1458	−	8.09790i	−1.45106	−	1.05426i	−0.985582	−	0.169196i	$-0.945883\pi$
$59$	−11.1458	−	8.09790i	−1.45106	−	1.05426i	−0.465477	−	0.885060i	$-0.654117\pi$
$60$	−1.14572	+	27.3498i	−0.147912	+	3.53084i
$61$	5.45839	−	3.96575i	0.698875	−	0.507762i	−0.180691	−	0.983540i	$-0.557833\pi$
$61$	5.45839	−	3.96575i	0.698875	−	0.507762i	0.879566	+	0.475778i	$0.157833\pi$
$62$	−13.0661	+	17.9840i	−1.65940	+	2.28397i
$63$	−1.88365	+	2.59262i	−0.237318	+	0.326640i
$64$	−3.06392	+	2.22606i	−0.382989	+	0.278258i
$65$	−0.323931	+	7.73262i	−0.0401787	+	0.959114i
$66$	−18.5032	−	13.4433i	−2.27758	−	1.65476i
$67$	−6.63488	+	2.15580i	−0.810580	+	0.263373i	−0.684843	−	0.728690i	$-0.740129\pi$
$67$	−6.63488	+	2.15580i	−0.810580	+	0.263373i	−0.125737	+	0.992064i	$0.540129\pi$
$68$		−	22.9312i		−	2.78082i
$69$	−2.52851	−	7.78195i	−0.304397	−	0.936837i
$70$	−1.22009	+	3.28093i	−0.145829	+	0.392147i
$71$	2.64273	−	8.13349i	0.313634	−	0.965268i	−0.662678	−	0.748904i	$-0.730580\pi$
$71$	2.64273	−	8.13349i	0.313634	−	0.965268i	0.976313	−	0.216364i	$-0.0694197\pi$
$72$	28.0789	+	9.12339i	3.30913	+	1.07520i
$73$	−2.82435	−	3.88738i	−0.330565	−	0.454983i	0.611091	−	0.791560i	$-0.290731\pi$
$73$	−2.82435	−	3.88738i	−0.330565	−	0.454983i	−0.941656	+	0.336577i	$0.890731\pi$
$74$	13.5237			1.57210
$75$	−9.31796	+	10.7959i	−1.07595	+	1.24660i
$76$	−4.29211			−0.492338
$77$	−1.17266	−	1.61402i	−0.133637	−	0.183935i
$78$	23.5508	+	7.65212i	2.66660	+	0.866432i
$79$	1.98481	−	6.10861i	0.223308	−	0.687273i	−0.775150	−	0.631777i	$-0.782326\pi$
$79$	1.98481	−	6.10861i	0.223308	−	0.687273i	0.998459	−	0.0554961i	$-0.0176741\pi$
$80$	13.0426	+	0.546375i	1.45821	+	0.0610866i
$81$	0.606690	+	1.86720i	0.0674100	+	0.207467i
$82$		−	17.8138i		−	1.96721i
$83$	9.19729	−	2.98838i	1.00953	−	0.328017i	0.242865	−	0.970060i	$-0.421913\pi$
$83$	9.19729	−	2.98838i	1.00953	−	0.328017i	0.766669	+	0.642043i	$0.221913\pi$
$84$	6.18084	+	4.49065i	0.674385	+	0.489970i
$85$	7.42036	−	9.36256i	0.804851	−	1.01551i
$86$	−14.8054	+	10.7567i	−1.59650	+	1.15993i
$87$	11.6197	−	15.9931i	1.24576	−	1.71464i
$88$	−10.8035	+	14.8697i	−1.15165	+	1.58511i
$89$	9.84471	−	7.15260i	1.04354	−	0.758174i	0.0725645	−	0.997364i	$-0.476882\pi$
$89$	9.84471	−	7.15260i	1.04354	−	0.758174i	0.970973	+	0.239189i	$0.0768817\pi$
$90$	15.9393	+	23.9896i	1.68015	+	2.52872i
$91$	1.74752	+	1.26964i	0.183189	+	0.133095i
$92$	−11.7106	+	3.80501i	−1.22092	+	0.396700i
$93$			25.2760i			2.62100i
$94$	−1.24711	−	3.83821i	−0.128629	−	0.395881i
$95$	−1.75242	−	1.38889i	−0.179795	−	0.142497i
$96$	2.77185	−	8.53087i	0.282900	−	0.870678i
$97$	11.9315	+	3.87677i	1.21146	+	0.393627i	0.843964	−	0.536399i	$-0.180216\pi$
$97$	11.9315	+	3.87677i	1.21146	+	0.393627i	0.367494	+	0.930026i	$0.380216\pi$
$98$	−9.74659	−	13.4150i	−0.984554	−	1.35512i
$99$	−16.4154			−1.64981
$100$	16.2461	+	14.0221i	1.62461	+	1.40221i
$101$	10.0385			0.998865			0.499432	−	0.866353i	$-0.333542\pi$
$101$	10.0385			0.998865			0.499432	+	0.866353i	$0.333542\pi$
$102$	−22.4674	−	30.9237i	−2.22460	−	3.06190i
$103$	−11.2600	−	3.65860i	−1.10948	−	0.360492i	−0.303737	−	0.952756i	$-0.598234\pi$
$103$	−11.2600	−	3.65860i	−1.10948	−	0.360492i	−0.805744	+	0.592264i	$0.798234\pi$
$104$	6.14947	−	18.9261i	0.603005	−	1.85586i
$105$	1.07043	+	3.83356i	0.104464	+	0.374117i
$106$	3.26873	+	10.0601i	0.317487	+	0.977125i
$107$		−	6.28184i		−	0.607288i	−0.952786	−	0.303644i	$-0.901797\pi$
$107$		−	6.28184i		−	0.607288i	0.952786	−	0.303644i	$-0.0982033\pi$
$108$	24.8574	−	8.07665i	2.39190	−	0.777176i
$109$	10.2946	+	7.47949i	0.986048	+	0.716406i	0.959052	−	0.283230i	$-0.0914060\pi$
$109$	10.2946	+	7.47949i	0.986048	+	0.716406i	0.0269956	+	0.999636i	$0.491406\pi$
$110$	−17.2700	+	4.82225i	−1.64663	+	0.459783i
$111$	12.4404	−	9.03851i	1.18079	−	0.857897i
$112$	2.14151	−	2.94754i	0.202354	−	0.278516i
$113$	8.97647	−	12.3551i	0.844435	−	1.16227i	−0.140626	−	0.990063i	$-0.544912\pi$
$113$	8.97647	−	12.3551i	0.844435	−	1.16227i	0.985061	−	0.172203i	$-0.0550885\pi$
$114$	−5.78808	+	4.20529i	−0.542104	+	0.393861i
$115$	−6.01259	−	2.23592i	−0.560677	−	0.208501i
$116$	−24.0672	−	17.4858i	−2.23458	−	1.62352i
$117$	16.9032	−	5.49220i	1.56271	−	0.507754i
$118$			34.5582i			3.18134i
$119$	−1.03034	−	3.17105i	−0.0944509	−	0.290690i
$120$	30.5418	−	20.2928i	2.78807	−	1.85247i
$121$	−0.241240	+	0.742460i	−0.0219309	+	0.0674963i
$122$	−16.0957	−	5.22982i	−1.45724	−	0.473486i
$123$	−11.9057	−	16.3869i	−1.07351	−	1.47755i
$124$	38.0365			3.41578
$125$	2.09567	+	10.9822i	0.187443	+	0.982276i
$126$	8.03859			0.716135
$127$	7.19077	+	9.89725i	0.638078	+	0.878239i	0.998511	−	0.0545463i	$-0.0173712\pi$
$127$	7.19077	+	9.89725i	0.638078	+	0.878239i	−0.360434	+	0.932785i	$0.617371\pi$
$128$	15.0169	+	4.87928i	1.32732	+	0.431271i
$129$	−6.43020	+	19.7901i	−0.566148	+	1.74242i
$130$	16.1698	−	10.7436i	1.41818	−	0.942280i
$131$	−5.74982	−	17.6961i	−0.502364	−	1.54612i	−0.805157	−	0.593062i	$-0.797919\pi$
$131$	−5.74982	−	17.6961i	−0.502364	−	1.54612i	0.302792	−	0.953057i	$-0.402081\pi$
$132$			39.1346i			3.40623i
$133$	−0.593536	+	0.192852i	−0.0514661	+	0.0167224i
$134$	14.1574	+	10.2859i	1.22301	+	0.888569i
$135$	12.7625	+	4.74605i	1.09843	+	0.408475i
$136$	−24.8512	+	18.0554i	−2.13097	+	1.54824i
$137$	−5.46567	+	7.52285i	−0.466964	+	0.642721i	−0.975935	−	0.218063i	$-0.930026\pi$
$137$	−5.46567	+	7.52285i	−0.466964	+	0.642721i	0.508971	+	0.860784i	$0.330026\pi$
$138$	−12.0642	+	16.6050i	−1.02697	+	1.41351i
$139$	−14.7057	+	10.6843i	−1.24732	+	0.906234i	−0.998064	−	0.0622027i	$-0.980187\pi$
$139$	−14.7057	+	10.6843i	−1.24732	+	0.906234i	−0.249260	+	0.968437i	$0.580187\pi$
$140$	5.76890	−	1.61084i	0.487561	−	0.136141i
$141$	−3.71245	−	2.69725i	−0.312645	−	0.227150i
$142$	−20.4021	+	6.62905i	−1.71211	+	0.556297i
$143$			11.0646i			0.925264i
$144$	−9.26370	−	28.5107i	−0.771975	−	2.37589i
$145$	−4.16809	−	14.9272i	−0.346141	−	1.23964i
$146$	−3.72460	+	11.4631i	−0.308250	+	0.948696i
$147$	−17.9317	−	5.82636i	−1.47898	−	0.480550i
$148$	−13.6015	−	18.7209i	−1.11804	−	1.53885i
$149$	16.8950			1.38409			0.692047	−	0.721853i	$-0.256709\pi$
$149$	16.8950			1.38409			0.692047	+	0.721853i	$0.256709\pi$
$150$	35.6470	+	2.99186i	2.91056	+	0.244284i
$151$	23.4449			1.90792			0.953961	−	0.299930i	$-0.0969635\pi$
$151$	23.4449			1.90792			0.953961	+	0.299930i	$0.0969635\pi$
$152$	3.37949	+	4.65147i	0.274113	+	0.377284i
$153$	−26.0918	−	8.47774i	−2.10940	−	0.685384i
$154$	−1.54644	+	4.75945i	−0.124615	+	0.383527i
$155$	15.5299	+	12.3083i	1.24739	+	0.988628i
$156$	−13.0935	−	40.2975i	−1.04832	−	3.22638i
$157$			2.06711i			0.164974i	0.996592	+	0.0824868i	$0.0262862\pi$
$157$			2.06711i			0.164974i	−0.996592	+	0.0824868i	$0.973714\pi$
$158$	−15.3229	+	4.97871i	−1.21902	+	0.396085i
$159$	9.73051	+	7.06963i	0.771679	+	0.560658i
$160$	−3.89170	−	5.85721i	−0.307666	−	0.463053i
$161$	−1.44844	+	1.05236i	−0.114153	+	0.0829373i
$162$	2.89468	−	3.98419i	0.227428	−	0.313028i
$163$	−4.33748	+	5.97002i	−0.339737	+	0.467608i	−0.944365	−	0.328900i	$-0.893322\pi$
$163$	−4.33748	+	5.97002i	−0.339737	+	0.467608i	0.604627	+	0.796509i	$0.293322\pi$
$164$	−24.6597	+	17.9163i	−1.92560	+	1.39903i
$165$	−12.6636	+	15.9782i	−0.985863	+	1.24390i
$166$	−19.6250	−	14.2584i	−1.52319	−	1.10667i
$167$	10.6088	−	3.44699i	0.820930	−	0.266736i	0.131710	−	0.991288i	$-0.457953\pi$
$167$	10.6088	−	3.44699i	0.820930	−	0.266736i	0.689220	+	0.724552i	$0.257953\pi$
$168$		−	10.2342i		−	0.789583i
$169$	0.315295	+	0.970380i	0.0242535	+	0.0746446i
$170$	−29.9405	−	1.25425i	−2.29633	−	0.0961967i
$171$	−1.58681	+	4.88368i	−0.121346	+	0.373465i
$172$	29.7810	+	9.67644i	2.27078	+	0.737822i
$173$	−2.56757	−	3.53396i	−0.195209	−	0.268682i	0.700180	−	0.713966i	$-0.253103\pi$
$173$	−2.56757	−	3.53396i	−0.195209	−	0.268682i	−0.895390	+	0.445284i	$0.853103\pi$
$174$	−49.5877			−3.75923
$175$	2.87664	+	1.20908i	0.217453	+	0.0913982i
$176$	18.6626			1.40675
$177$	23.0968	+	31.7900i	1.73606	+	2.38948i
$178$	−29.0302	−	9.43248i	−2.17590	−	0.706994i
$179$	1.38379	−	4.25887i	0.103429	−	0.318323i	−0.885929	−	0.463820i	$-0.846478\pi$
$179$	1.38379	−	4.25887i	0.103429	−	0.318323i	0.989359	+	0.145497i	$0.0464783\pi$
$180$	17.1777	−	46.1924i	1.28035	−	3.44298i
$181$	−0.153260	−	0.471687i	−0.0113918	−	0.0350602i	0.945199	−	0.326495i	$-0.105867\pi$
$181$	−0.153260	−	0.471687i	−0.0113918	−	0.0350602i	−0.956591	+	0.291434i	$0.905867\pi$
$182$		−	5.41828i		−	0.401630i
$183$	−18.3017	+	5.94659i	−1.35290	+	0.439585i
$184$	13.3442	+	9.69515i	0.983750	+	0.714736i
$185$	0.504579	−	12.0449i	0.0370974	−	0.885559i
$186$	51.2938	−	37.2671i	3.76104	−	2.73256i
$187$	10.0389	−	13.8174i	0.734117	−	1.01043i
$188$	−4.05894	+	5.58666i	−0.296029	+	0.407449i
$189$	3.07452	−	2.23377i	0.223638	−	0.162483i
$190$	−0.234762	+	5.60405i	−0.0170314	+	0.406561i
$191$	−8.72639	−	6.34009i	−0.631419	−	0.458753i	0.225472	−	0.974250i	$-0.427607\pi$
$191$	−8.72639	−	6.34009i	−0.631419	−	0.458753i	−0.856892	+	0.515497i	$0.827607\pi$
$192$	10.2732	−	3.33795i	0.741402	−	0.240896i
$193$		−	2.23902i		−	0.161168i	−0.996748	−	0.0805840i	$-0.974321\pi$
$193$		−	2.23902i		−	0.161168i	0.996748	−	0.0805840i	$-0.0256785\pi$
$194$	−9.72453	−	29.9290i	−0.698180	−	2.14878i
$195$	7.69405	−	20.6900i	0.550982	−	1.48164i
$196$	−8.76776	+	26.9844i	−0.626268	+	1.92746i
$197$	−1.42420	−	0.462750i	−0.101470	−	0.0329695i	0.257842	−	0.966187i	$-0.416989\pi$
$197$	−1.42420	−	0.462750i	−0.101470	−	0.0329695i	−0.359312	+	0.933218i	$0.616989\pi$
$198$	24.2030	+	33.3126i	1.72003	+	2.36742i
$199$	−5.32537			−0.377506			−0.188753	−	0.982025i	$-0.560445\pi$
$199$	−5.32537			−0.377506			−0.188753	+	0.982025i	$0.560445\pi$
$200$	2.40435	−	28.6469i	0.170013	−	2.02564i
$201$	19.8978			1.40349
$202$	−14.8008	−	20.3715i	−1.04138	−	1.43333i
$203$	−4.11381	−	1.33666i	−0.288733	−	0.0938149i
$204$	−20.2110	+	62.2031i	−1.41505	+	4.35509i
$205$	−15.8658	−	0.664644i	−1.10812	−	0.0464208i
$206$	9.17725	+	28.2447i	0.639409	+	1.96790i
$207$			14.7314i			1.02390i
$208$	−19.2172	+	6.24404i	−1.33247	+	0.432947i
$209$	−2.58624	−	1.87901i	−0.178894	−	0.129974i
$210$	6.20135	−	7.82449i	0.427934	−	0.539941i
$211$	−12.5895	+	9.14682i	−0.866698	+	0.629693i	−0.929699	−	0.368321i	$-0.879933\pi$
$211$	−12.5895	+	9.14682i	−0.866698	+	0.629693i	0.0630009	+	0.998013i	$0.479933\pi$
$212$	10.6387	−	14.6429i	0.730668	−	1.00568i
$213$	−14.3373	+	19.7336i	−0.982378	+	1.35213i
$214$	−12.7480	+	9.26197i	−0.871436	+	0.633135i
$215$	9.02806	+	13.5877i	0.615708	+	0.926674i
$216$	−28.3249	−	20.5793i	−1.92727	−	1.40024i
$217$	5.25990	−	1.70904i	0.357065	−	0.116017i
$218$		−	31.9192i		−	2.16184i
$219$	4.23507	+	13.0342i	0.286179	+	0.880770i
$220$	24.0447	+	19.0568i	1.62110	+	1.28481i
$221$	−5.71428	+	17.5867i	−0.384384	+	1.18301i
$222$	−36.6845	−	11.9195i	−2.46210	−	0.799985i
$223$	6.45351	+	8.88250i	0.432159	+	0.594816i	0.968447	−	0.249219i	$-0.0801739\pi$
$223$	6.45351	+	8.88250i	0.432159	+	0.594816i	−0.536288	+	0.844035i	$0.680174\pi$
$224$	−1.96268			−0.131137
$225$	21.9610	−	13.3013i	1.46406	−	0.886752i
$226$	−38.3076			−2.54818
$227$	6.53498	+	8.99463i	0.433742	+	0.596995i	0.968807	−	0.247816i	$-0.0797129\pi$
$227$	6.53498	+	8.99463i	0.433742	+	0.596995i	−0.535065	+	0.844811i	$0.679713\pi$
$228$	11.6428	+	3.78296i	0.771060	+	0.250533i
$229$	4.67641	−	14.3925i	0.309026	−	0.951084i	−0.669118	−	0.743156i	$-0.733328\pi$
$229$	4.67641	−	14.3925i	0.309026	−	0.951084i	0.978144	−	0.207928i	$-0.0666721\pi$
$230$	4.32754	+	15.4983i	0.285350	+	1.02193i
$231$	1.75838	+	5.41175i	0.115693	+	0.356067i
$232$			39.8501i			2.61629i
$233$	−20.0023	+	6.49915i	−1.31040	+	0.425774i	−0.879186	−	0.476478i	$-0.841913\pi$
$233$	−20.0023	+	6.49915i	−1.31040	+	0.425774i	−0.431210	+	0.902252i	$0.641913\pi$
$234$	−36.0678	−	26.2048i	−2.35783	−	1.71306i
$235$	−3.46502	+	0.967530i	−0.226033	+	0.0631147i
$236$	47.8389	−	34.7570i	3.11405	−	2.26249i
$237$	−10.7680	+	14.8208i	−0.699455	+	0.962718i
$238$	−4.91602	+	6.76632i	−0.318658	+	0.438596i
$239$	3.34118	−	2.42751i	0.216123	−	0.157022i	−0.474457	−	0.880279i	$-0.657356\pi$
$239$	3.34118	−	2.42751i	0.216123	−	0.157022i	0.690580	+	0.723256i	$0.257356\pi$
$240$	−34.8978	−	12.9776i	−2.25265	−	0.837698i
$241$	5.47428	+	3.97730i	0.352630	+	0.256200i	0.749971	−	0.661470i	$-0.230067\pi$
$241$	5.47428	+	3.97730i	0.352630	+	0.256200i	−0.397342	+	0.917671i	$0.630067\pi$
$242$	1.86239	−	0.605128i	0.119719	−	0.0388991i
$243$			12.6687i			0.812697i
$244$	8.94869	+	27.5412i	0.572881	+	1.76315i
$245$	−12.3117	+	8.18026i	−0.786567	+	0.522618i
$246$	−15.7007	+	48.3217i	−1.00104	+	3.08088i
$247$	3.29177	+	1.06956i	0.209450	+	0.0680545i
$248$	−29.9489	−	41.2212i	−1.90176	−	2.61755i
$249$	−27.5824			−1.74797
$250$	19.1967	−	20.4450i	1.21411	−	1.29306i
$251$	19.2753			1.21665			0.608324	−	0.793689i	$-0.291842\pi$
$251$	19.2753			1.21665			0.608324	+	0.793689i	$0.291842\pi$
$252$	−8.08483	−	11.1278i	−0.509297	−	0.700987i
$253$	−8.72210	−	2.83398i	−0.548353	−	0.178171i
$254$	9.48281	−	29.1851i	0.595005	−	1.83124i
$255$	−28.3804	+	18.8567i	−1.77725	+	1.18085i
$256$	−9.89859	−	30.4647i	−0.618662	−	1.90405i
$257$		−	17.2913i		−	1.07860i	−0.842114	−	0.539300i	$-0.818689\pi$
$257$		−	17.2913i		−	1.07860i	0.842114	−	0.539300i	$-0.181311\pi$
$258$	49.6417	−	16.1296i	3.09056	−	1.00418i
$259$	−2.72206	−	1.97769i	−0.169141	−	0.122888i
$260$	−31.1352	−	11.5783i	−1.93092	−	0.718058i
$261$	−28.7936	+	20.9198i	−1.78228	+	1.29490i
$262$	−27.4340	+	37.7596i	−1.69488	+	2.33280i
$263$	−0.231203	+	0.318223i	−0.0142566	+	0.0196225i	−0.816086	−	0.577931i	$-0.803860\pi$
$263$	−0.231203	+	0.318223i	−0.0142566	+	0.0196225i	0.801829	+	0.597553i	$0.203860\pi$
$264$	42.4112	−	30.8135i	2.61023	−	1.89644i
$265$	9.08199	−	2.53594i	0.557902	−	0.155782i
$266$	1.26647	+	0.920148i	0.0776525	+	0.0564179i
$267$	−33.0089	+	10.7252i	−2.02011	+	0.656374i
$268$		−	29.9431i		−	1.82907i
$269$	−4.05301	−	12.4739i	−0.247116	−	0.760545i	−0.995281	−	0.0970326i	$-0.969065\pi$
$269$	−4.05301	−	12.4739i	−0.247116	−	0.760545i	0.748165	−	0.663513i	$-0.230935\pi$
$270$	−9.18580	−	32.8972i	−0.559030	−	2.00206i
$271$	3.01381	−	9.27555i	0.183076	−	0.563449i	−0.816834	−	0.576873i	$-0.804273\pi$
$271$	3.01381	−	9.27555i	0.183076	−	0.563449i	0.999910	+	0.0134233i	$0.00427291\pi$
$272$	29.6636	+	9.63828i	1.79862	+	0.584407i
$273$	−3.62127	−	4.98425i	−0.219169	−	0.301661i
$274$	23.3251			1.40912
$275$	3.65057	+	15.5614i	0.220138	+	0.938387i
$276$	35.1199			2.11397
$277$	1.94360	+	2.67513i	0.116779	+	0.160733i	0.863405	−	0.504511i	$-0.168327\pi$
$277$	1.94360	+	2.67513i	0.116779	+	0.160733i	−0.746626	+	0.665244i	$0.768327\pi$
$278$	43.3644	+	14.0899i	2.60082	+	0.845059i
$279$	14.0622	−	43.2790i	0.841883	−	2.59105i
$280$	−6.28799	−	4.98358i	−0.375779	−	0.297826i
$281$	−0.0176623	−	0.0543590i	−0.00105365	−	0.00324279i	0.950528	−	0.310638i	$-0.100543\pi$
$281$	−0.0176623	−	0.0543590i	−0.00105365	−	0.00324279i	−0.951582	+	0.307395i	$0.900543\pi$
$282$			11.5107i			0.685451i
$283$	5.78488	−	1.87962i	0.343875	−	0.111732i	−0.131988	−	0.991251i	$-0.542136\pi$
$283$	5.78488	−	1.87962i	0.343875	−	0.111732i	0.475863	+	0.879520i	$0.342136\pi$
$284$	29.6960	+	21.5754i	1.76214	+	1.28027i
$285$	3.52948	+	5.31205i	0.209068	+	0.314659i
$286$	22.4538	−	16.3136i	1.32772	−	0.964645i
$287$	−2.60506	+	3.58556i	−0.153772	+	0.211649i
$288$	−9.49222	+	13.0649i	−0.559334	+	0.769858i
$289$	9.33918	−	6.78531i	0.549363	−	0.399136i
$290$	−24.1470	+	30.4673i	−1.41796	+	1.78910i
$291$	−28.9484	−	21.0323i	−1.69699	−	1.23293i
$292$	19.6144	−	6.37312i	1.14785	−	0.372958i
$293$		−	27.7334i		−	1.62020i	−0.586291	−	0.810100i	$-0.699413\pi$
$293$		−	27.7334i		−	1.62020i	0.586291	−	0.810100i	$-0.300587\pi$
$294$	14.6149	+	44.9800i	0.852357	+	2.62329i
$295$	30.7792	+	1.28939i	1.79204	+	0.0750711i
$296$	−9.57886	+	29.4807i	−0.556760	+	1.71353i
$297$	18.5138	+	6.01551i	1.07428	+	0.349055i
$298$	−24.9101	−	34.2858i	−1.44300	−	1.98612i
$299$	9.92947			0.574236
$300$	−31.7104	−	52.3552i	−1.83080	−	3.02273i
$301$	4.55307			0.262434
$302$	−34.5673	−	47.5778i	−1.98913	−	2.73780i
$303$	−27.2303	−	8.84767i	−1.56434	−	0.508285i
$304$	1.80403	−	5.55223i	0.103468	−	0.318442i
$305$	−5.25847	+	14.1405i	−0.301099	+	0.809684i
$306$	21.2656	+	65.4488i	1.21567	+	3.74146i
$307$		−	27.9403i		−	1.59464i	−0.603557	−	0.797320i	$-0.706250\pi$
$307$		−	27.9403i		−	1.59464i	0.603557	−	0.797320i	$-0.293750\pi$
$308$	8.14383	−	2.64609i	0.464038	−	0.150775i
$309$	27.3193	+	19.8486i	1.55414	+	1.12915i
$310$	2.08045	−	49.6629i	0.118162	−	2.82066i
$311$	9.47042	−	6.88066i	0.537018	−	0.390167i	−0.285958	−	0.958242i	$-0.592312\pi$
$311$	9.47042	−	6.88066i	0.537018	−	0.390167i	0.822976	+	0.568076i	$0.192312\pi$
$312$	−33.3621	+	45.9189i	−1.88876	+	2.59965i
$313$	3.47538	−	4.78345i	0.196440	−	0.270376i	−0.699422	−	0.714709i	$-0.746559\pi$
$313$	3.47538	−	4.78345i	0.196440	−	0.270376i	0.895862	+	0.444333i	$0.146559\pi$
$314$	4.19488	−	3.04776i	0.236731	−	0.171995i
$315$	0.299925	−	7.15956i	0.0168988	−	0.403395i
$316$	22.3031	+	16.2041i	1.25465	+	0.911553i
$317$	−31.1203	+	10.1116i	−1.74789	+	0.567924i	−0.995835	−	0.0911740i	$-0.970938\pi$
$317$	−31.1203	+	10.1116i	−1.74789	+	0.567924i	−0.752057	+	0.659098i	$0.770938\pi$
$318$		−	30.1700i		−	1.69185i
$319$	−6.84685	−	21.0724i	−0.383350	−	1.17983i
$320$	2.95170	−	7.93739i	0.165005	−	0.443714i
$321$	−5.53666	+	17.0401i	−0.309026	+	0.951085i
$322$	4.27118	+	1.38779i	0.238024	+	0.0773386i
$323$	−3.14033	−	4.32229i	−0.174733	−	0.240499i
$324$	−8.42665			−0.468147
$325$	−8.96551	−	14.8024i	−0.497317	−	0.821091i
$326$	18.5104			1.02520
$327$	−21.3330	−	29.3623i	−1.17972	−	1.62374i
$328$	38.8327	+	12.6175i	2.14418	+	0.696686i
$329$	−0.310275	+	0.954929i	−0.0171060	+	0.0526469i
$330$	51.0967	+	2.14052i	2.81278	+	0.117832i
$331$	0.538286	+	1.65667i	0.0295869	+	0.0910591i	0.964760	−	0.263133i	$-0.0847559\pi$
$331$	0.538286	+	1.65667i	0.0295869	+	0.0910591i	−0.935173	+	0.354192i	$0.884756\pi$
$332$			41.5073i			2.27801i
$333$	−26.3297	+	8.55505i	−1.44286	+	0.468814i
$334$	−22.6367	−	16.4466i	−1.23863	−	0.899915i
$335$	9.68937	−	12.2255i	0.529387	−	0.667948i
$336$	−8.40695	+	6.10801i	−0.458637	+	0.333219i
$337$	5.29904	−	7.29350i	0.288657	−	0.397303i	−0.639920	−	0.768441i	$-0.721033\pi$
$337$	5.29904	−	7.29350i	0.288657	−	0.397303i	0.928577	+	0.371139i	$0.121033\pi$
$338$	1.50436	−	2.07058i	0.0818264	−	0.112624i
$339$	−35.2390	+	25.6026i	−1.91392	+	1.39054i
$340$	28.3764	+	42.7080i	1.53893	+	2.31617i
$341$	22.9192	+	16.6518i	1.24114	+	0.901743i
$342$	12.2503	−	3.98035i	0.662419	−	0.215233i
$343$			8.49407i			0.458636i
$344$	−12.9622	−	39.8935i	−0.698874	−	2.15091i
$345$	14.3391	+	11.3645i	0.771989	+	0.611845i
$346$	−3.38598	+	10.4210i	−0.182032	+	0.560236i
$347$	13.9497	+	4.53253i	0.748859	+	0.243319i	0.658490	−	0.752590i	$-0.271195\pi$
$347$	13.9497	+	4.53253i	0.748859	+	0.243319i	0.0903686	+	0.995908i	$0.471195\pi$
$348$	49.8729	+	68.6442i	2.67347	+	3.67972i
$349$	−30.9214			−1.65518			−0.827591	−	0.561331i	$-0.810289\pi$
$349$	−30.9214			−1.65518			−0.827591	+	0.561331i	$0.810289\pi$
$350$	−1.78768	−	7.62036i	−0.0955553	−	0.407326i
$351$	−21.0766			−1.12499
$352$	−5.90932	−	8.13349i	−0.314968	−	0.433516i
$353$	25.5046	+	8.28696i	1.35748	+	0.441070i	0.895199	−	0.445666i	$-0.147033\pi$
$353$	25.5046	+	8.28696i	1.35748	+	0.441070i	0.462276	+	0.886736i	$0.347033\pi$
$354$	30.4588	−	93.7426i	1.61887	−	4.98236i
$355$	5.14293	+	18.4184i	0.272959	+	0.977549i
$356$	16.1398	+	49.6732i	0.855408	+	2.63267i
$357$			9.50990i			0.503317i
$358$	−10.6830	+	3.47111i	−0.564613	+	0.183454i
$359$	−12.0139	−	8.72861i	−0.634069	−	0.460678i	0.223738	−	0.974649i	$-0.428174\pi$
$359$	−12.0139	−	8.72861i	−0.634069	−	0.460678i	−0.857808	+	0.513971i	$0.828174\pi$
$360$	−63.5852	+	17.7547i	−3.35123	+	0.935756i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−0.731247	+	1.00648i	−0.0384335	+	0.0528992i
$363$	1.30877	−	1.80137i	0.0686928	−	0.0945475i
$364$	−7.50052	+	5.44945i	−0.393134	+	0.285629i
$365$	10.0707	+	3.74500i	0.527122	+	0.196022i
$366$	39.0518	+	28.3728i	2.04127	+	1.48307i
$367$	26.6403	−	8.65597i	1.39061	−	0.451838i	0.484470	−	0.874808i	$-0.339012\pi$
$367$	26.6403	−	8.65597i	1.39061	−	0.451838i	0.906144	+	0.422970i	$0.139012\pi$
$368$		−	16.7480i		−	0.873052i
$369$	11.2689	+	34.6822i	0.586637	+	1.80548i
$370$	−25.1872	+	16.7351i	−1.30942	+	0.870016i
$371$	0.813246	−	2.50291i	0.0422216	−	0.129945i
$372$	−103.178	−	33.5245i	−5.34951	−	1.73816i
$373$	16.7966	+	23.1185i	0.869694	+	1.19703i	0.979170	+	0.203041i	$0.0650825\pi$
$373$	16.7966	+	23.1185i	0.869694	+	1.19703i	−0.109477	+	0.993989i	$0.534917\pi$
$374$	−42.8416			−2.21529
$375$	3.99471	−	31.6373i	0.206286	−	1.63374i
$376$	9.25032			0.477049
$377$	14.1006	+	19.4078i	0.726219	+	0.999555i
$378$	−9.06617	−	2.94578i	−0.466313	−	0.151514i
$379$	−3.34705	+	10.3012i	−0.171927	+	0.529136i	−0.999480	−	0.0322517i	$-0.989732\pi$
$379$	−3.34705	+	10.3012i	−0.171927	+	0.529136i	0.827553	+	0.561387i	$0.189732\pi$
$380$	7.99380	−	5.31131i	0.410073	−	0.272464i
$381$	−10.7825	−	33.1850i	−0.552403	−	1.70012i
$382$			27.0567i			1.38434i
$383$	16.6779	−	5.41897i	0.852200	−	0.276897i	0.149833	−	0.988711i	$-0.452126\pi$
$383$	16.6779	−	5.41897i	0.852200	−	0.276897i	0.702367	+	0.711815i	$0.252126\pi$
$384$	−36.4342	−	26.4710i	−1.85928	−	1.35084i
$385$	4.18129	+	1.55491i	0.213098	+	0.0792455i
$386$	−4.54374	+	3.30122i	−0.231270	+	0.168028i
$387$	22.0203	−	30.3083i	1.11935	−	1.54066i
$388$	−31.6503	+	43.5628i	−1.60680	+	2.21157i
$389$	−13.5134	+	9.81803i	−0.685154	+	0.497794i	−0.875064	−	0.484008i	$-0.839181\pi$
$389$	−13.5134	+	9.81803i	−0.685154	+	0.497794i	0.189909	+	0.981802i	$0.439181\pi$
$390$	−53.3312	+	14.8916i	−2.70053	+	0.754063i
$391$	−12.3999	−	9.00904i	−0.627089	−	0.455606i
$392$	36.1472	−	11.7449i	1.82571	−	0.593209i
$393$			53.0703i			2.67704i
$394$	1.16076	+	3.57246i	0.0584785	+	0.179978i
$395$	3.86257	+	13.8331i	0.194347	+	0.696017i
$396$	21.7723	−	67.0084i	1.09410	−	3.36730i
$397$	−8.44780	−	2.74486i	−0.423983	−	0.137760i	0.0892511	−	0.996009i	$-0.471553\pi$
$397$	−8.44780	−	2.74486i	−0.423983	−	0.137760i	−0.513234	+	0.858249i	$0.671553\pi$
$398$	7.85176	+	10.8070i	0.393573	+	0.541707i
$399$	1.78000			0.0891114
$400$	−24.9673	+	15.1221i	−1.24836	+	0.756107i
$401$	−3.07417			−0.153517			−0.0767583	−	0.997050i	$-0.524457\pi$
$401$	−3.07417			−0.153517			−0.0767583	+	0.997050i	$0.524457\pi$
$402$	−29.3375	−	40.3796i	−1.46322	−	2.01395i
$403$	−29.1715	−	9.47840i	−1.45314	−	0.472153i
$404$	−13.3144	+	40.9774i	−0.662414	+	2.03870i
$405$	−3.44051	−	2.72680i	−0.170960	−	0.135496i
$406$	3.35288	+	10.3191i	0.166401	+	0.512129i
$407$		−	17.2350i		−	0.854305i
$408$	83.3248	−	27.0739i	4.12519	−	1.34036i
$409$	−14.5784	−	10.5918i	−0.720857	−	0.523733i	0.165801	−	0.986159i	$-0.446979\pi$
$409$	−14.5784	−	10.5918i	−0.720857	−	0.523733i	−0.886658	+	0.462426i	$0.846979\pi$
$410$	22.0439	+	33.1772i	1.08867	+	1.63851i
$411$	21.4566	−	15.5892i	1.05838	−	0.768956i
$412$	29.8690	−	41.1112i	1.47154	−	2.02540i
$413$	5.05374	−	6.95588i	0.248678	−	0.342276i
$414$	29.8951	−	21.7201i	1.46926	−	1.06748i
$415$	−13.4314	+	16.9470i	−0.659323	+	0.831894i
$416$	8.80619	+	6.39807i	0.431759	+	0.313691i
$417$	49.3077	−	16.0210i	2.41461	−	0.784553i
$418$			8.01880i			0.392212i
$419$	5.36089	+	16.4991i	0.261897	+	0.806035i	0.992392	+	0.123118i	$0.0392892\pi$
$419$	5.36089	+	16.4991i	0.261897	+	0.806035i	−0.730495	+	0.682918i	$0.760711\pi$
$420$	−17.0685	−	0.715023i	−0.832856	−	0.0348896i
$421$	11.0588	−	34.0356i	0.538974	−	1.65879i	−0.195927	−	0.980618i	$-0.562772\pi$
$421$	11.0588	−	34.0356i	0.538974	−	1.65879i	0.734901	−	0.678174i	$-0.237228\pi$
$422$	37.1241	+	12.0623i	1.80717	+	0.587186i
$423$	4.85606	+	6.68379i	0.236110	+	0.324977i
$424$	−24.2455			−1.17747
$425$	−2.23419	+	26.6196i	−0.108374	+	1.29124i
$426$	61.1854			2.96444
$427$	2.47495	+	3.40647i	0.119771	+	0.164851i
$428$	25.6427	+	8.33181i	1.23949	+	0.402733i
$429$	9.75204	−	30.0137i	0.470833	−	1.44907i
$430$	14.2631	−	38.3548i	0.687828	−	1.84963i
$431$	−0.542871	−	1.67078i	−0.0261492	−	0.0804788i	0.937130	−	0.348980i	$-0.113472\pi$
$431$	−0.542871	−	1.67078i	−0.0261492	−	0.0804788i	−0.963279	+	0.268501i	$0.913472\pi$
$432$			35.5500i			1.71040i
$433$	31.8024	−	10.3332i	1.52833	−	0.496583i	0.580199	−	0.814475i	$-0.302975\pi$
$433$	31.8024	−	10.3332i	1.52833	−	0.496583i	0.948127	+	0.317892i	$0.102975\pi$
$434$	−11.2235	−	8.15432i	−0.538743	−	0.391420i
$435$	−1.85015	+	44.1652i	−0.0887077	+	2.11756i
$436$	−44.1857	+	32.1028i	−2.11611	+	1.53744i
$437$	−1.68625	+	2.32092i	−0.0806643	+	0.111025i
$438$	20.2067	−	27.8121i	0.965512	−	1.32891i
$439$	−6.02649	+	4.37850i	−0.287629	+	0.208974i	−0.722238	−	0.691645i	$-0.756886\pi$
$439$	−6.02649	+	4.37850i	−0.287629	+	0.208974i	0.434609	+	0.900619i	$0.356886\pi$
$440$	1.72018	−	41.0628i	0.0820064	−	1.95759i
$441$	27.4622	+	19.9524i	1.30772	+	0.950116i
$442$	44.1147	−	14.3337i	2.09832	−	0.681786i
$443$		−	9.57730i		−	0.455031i	−0.973774	−	0.227516i	$-0.926940\pi$
$443$		−	9.57730i		−	0.455031i	0.973774	−	0.227516i	$-0.0730603\pi$
$444$	20.3953	+	62.7704i	0.967920	+	2.97895i
$445$	−9.48415	+	25.5037i	−0.449592	+	1.20899i
$446$	8.51055	−	26.1928i	0.402986	−	1.24026i
$447$	−45.8294	−	14.8909i	−2.16765	−	0.704314i
$448$	−1.38924	−	1.91213i	−0.0656356	−	0.0903397i
$449$	−6.46160			−0.304942			−0.152471	−	0.988308i	$-0.548723\pi$
$449$	−6.46160			−0.304942			−0.152471	+	0.988308i	$0.548723\pi$
$450$	−59.3722	−	24.9549i	−2.79883	−	1.17638i
$451$	−22.7023			−1.06901
$452$	38.5280	+	53.0292i	1.81220	+	2.49428i
$453$	−63.5967	−	20.6638i	−2.98803	−	0.970871i
$454$	8.61799	−	26.5234i	0.404462	−	1.24481i
$455$	−4.82578	−	0.202159i	−0.226236	−	0.00947737i
$456$	−5.06750	−	15.5962i	−0.237308	−	0.730357i
$457$			34.9122i			1.63312i	0.577258	+	0.816562i	$0.304123\pi$
$457$			34.9122i			1.63312i	−0.577258	+	0.816562i	$0.695877\pi$
$458$	−36.1023	+	11.7303i	−1.68695	+	0.548123i
$459$	26.3204	+	19.1229i	1.22853	+	0.892580i
$460$	17.1018	−	21.5780i	0.797376	−	1.00608i
$461$	−10.5792	+	7.68624i	−0.492722	+	0.357984i	−0.806230	−	0.591602i	$-0.798496\pi$
$461$	−10.5792	+	7.68624i	−0.492722	+	0.357984i	0.313508	+	0.949586i	$0.398496\pi$
$462$	8.38972	−	11.5475i	0.390325	−	0.537237i
$463$	−15.7811	+	21.7208i	−0.733409	+	1.00945i	0.265562	+	0.964094i	$0.414442\pi$
$463$	−15.7811	+	21.7208i	−0.733409	+	1.00945i	−0.998971	+	0.0453567i	$0.985558\pi$
$464$	32.7352	−	23.7835i	1.51970	−	1.10412i
$465$	−31.2781	−	47.0752i	−1.45049	−	2.18306i
$466$	42.6805	+	31.0092i	1.97714	+	1.43647i
$467$	18.4515	−	5.99527i	0.853835	−	0.277428i	0.150784	−	0.988567i	$-0.451820\pi$
$467$	18.4515	−	5.99527i	0.853835	−	0.277428i	0.703052	+	0.711139i	$0.251820\pi$
$468$			76.2841i			3.52624i
$469$	−1.34540	−	4.14070i	−0.0621246	−	0.191200i
$470$	7.07229	+	5.60519i	0.326221	+	0.258548i
$471$	1.82191	−	5.60725i	0.0839490	−	0.258368i
$472$	−75.3342	−	24.4776i	−3.46754	−	1.12667i
$473$	13.7086	+	18.8683i	0.630322	+	0.867564i
$474$	45.9530			2.11069
$475$	4.98248	+	0.418181i	0.228612	+	0.0191875i
$476$	14.3109			0.655940
$477$	−12.7280	−	17.5185i	−0.582773	−	0.802118i
$478$	−9.85249	−	3.20127i	−0.450642	−	0.146423i
$479$	1.15554	−	3.55639i	0.0527980	−	0.162495i	−0.921181	−	0.389135i	$-0.872774\pi$
$479$	1.15554	−	3.55639i	0.0527980	−	0.162495i	0.973979	+	0.226640i	$0.0727739\pi$
$480$	5.39420	+	19.3183i	0.246211	+	0.881756i
$481$	5.76639	+	17.7471i	0.262925	+	0.809199i
$482$		−	16.9733i		−	0.773115i
$483$	4.85657	−	1.57799i	0.220981	−	0.0718012i
$484$	−2.71078	−	1.96950i	−0.123217	−	0.0895227i
$485$	−27.0191	+	7.54446i	−1.22687	+	0.342576i
$486$	25.7091	−	18.6788i	1.16619	−	0.847287i
$487$	0.988835	−	1.36101i	0.0448084	−	0.0616735i	−0.786025	−	0.618195i	$-0.787864\pi$
$487$	0.988835	−	1.36101i	0.0448084	−	0.0616735i	0.830833	+	0.556521i	$0.187864\pi$
$488$	22.8012	−	31.3832i	1.03216	−	1.42065i
$489$	17.0277	−	12.3713i	0.770018	−	0.559451i
$490$	34.7530	+	12.9237i	1.56998	+	0.583833i
$491$	−13.2868	−	9.65341i	−0.599624	−	0.435652i	0.246121	−	0.969239i	$-0.420844\pi$
$491$	−13.2868	−	9.65341i	−0.599624	−	0.435652i	−0.845745	+	0.533587i	$0.820844\pi$
$492$	82.6827	−	26.8652i	3.72763	−	1.21118i
$493$		−	37.0300i		−	1.66775i
$494$	−2.68289	−	8.25709i	−0.120709	−	0.371504i
$495$	30.5728	−	20.3134i	1.37415	−	0.913022i
$496$	−15.9872	+	49.2037i	−0.717848	+	2.20931i
$497$	5.07595	+	1.64928i	0.227688	+	0.0739802i
$498$	40.6677	+	55.9743i	1.82236	+	2.50827i
$499$	40.1537			1.79753			0.898764	−	0.438433i	$-0.144466\pi$
$499$	40.1537			1.79753			0.898764	+	0.438433i	$0.144466\pi$
$500$	−47.6092	−	6.01141i	−2.12915	−	0.268838i
$501$	−31.8154			−1.42141
$502$	−28.4196	−	39.1162i	−1.26843	−	1.74584i
$503$	−8.02116	−	2.60623i	−0.357646	−	0.116206i	0.124683	−	0.992197i	$-0.460209\pi$
$503$	−8.02116	−	2.60623i	−0.357646	−	0.116206i	−0.482328	+	0.875991i	$0.660209\pi$
$504$	−5.69373	+	17.5235i	−0.253619	+	0.780559i
$505$	−18.6961	+	12.4222i	−0.831964	+	0.552781i
$506$	7.10878	+	21.8786i	0.316024	+	0.972621i
$507$		−	2.91014i		−	0.129244i
$508$	−49.9383	+	16.2259i	−2.21565	+	0.719909i
$509$	−32.6109	−	23.6932i	−1.44545	−	1.05018i	−0.986868	−	0.161531i	$-0.948357\pi$
$509$	−32.6109	−	23.6932i	−1.44545	−	1.05018i	−0.458584	−	0.888651i	$-0.651643\pi$
$510$	80.1110	+	29.7911i	3.54737	+	1.31917i
$511$	2.42604	−	1.76262i	0.107322	−	0.0779737i
$512$	−28.6670	+	39.4567i	−1.26691	+	1.74376i
$513$	3.57929	−	4.92648i	0.158030	−	0.217509i
$514$	−35.0900	+	25.4943i	−1.54775	+	1.12451i
$515$	25.4985	−	7.11988i	1.12360	−	0.313739i
$516$	−72.2554	−	52.4966i	−3.18087	−	2.31103i
$517$	−4.89149	+	1.58934i	−0.215128	+	0.0698992i
$518$			8.43991i			0.370828i
$519$	3.85004	+	11.8492i	0.168998	+	0.520123i
$520$	11.9673	+	42.8585i	0.524800	+	1.87947i
$521$	−1.36754	+	4.20885i	−0.0599129	+	0.184393i	−0.976534	−	0.215365i	$-0.930906\pi$
$521$	−1.36754	+	4.20885i	−0.0599129	+	0.184393i	0.916621	+	0.399758i	$0.130906\pi$
$522$	84.9068	+	27.5879i	3.71627	+	1.20749i
$523$	−0.771589	−	1.06200i	−0.0337392	−	0.0464381i	0.791814	−	0.610762i	$-0.209137\pi$
$523$	−0.771589	−	1.06200i	−0.0337392	−	0.0464381i	−0.825553	+	0.564324i	$0.809137\pi$
$524$	79.8624			3.48881
$525$	−6.73750	−	5.81516i	−0.294048	−	0.253794i
$526$	0.986671			0.0430209
$527$	27.8295	+	38.3040i	1.21227	+	1.66855i
$528$	−50.6241	−	16.4488i	−2.20313	−	0.715841i
$529$	4.56414	−	14.0470i	0.198441	−	0.610738i
$530$	−18.5368	−	14.6915i	−0.805188	−	0.638157i
$531$	−21.8614	−	67.2823i	−0.948702	−	2.91980i
$532$		−	2.67862i		−	0.116133i
$533$	23.3770	−	7.59563i	1.01257	−	0.329003i
$534$	70.4336	+	51.1730i	3.04796	+	2.21447i
$535$	7.77352	+	11.6996i	0.336079	+	0.505816i
$536$	−32.4502	+	23.5764i	−1.40163	+	1.01835i
$537$	−7.50734	+	10.3330i	−0.323966	+	0.445900i
$538$	−19.3380	+	26.6165i	−0.833720	+	1.14752i
$539$	−17.0964	+	12.4213i	−0.736394	+	0.535022i
$540$	−36.3009	+	45.8023i	−1.56214	+	1.97102i
$541$	0.0591013	+	0.0429396i	0.00254096	+	0.00184612i	0.589055	−	0.808093i	$-0.299500\pi$
$541$	0.0591013	+	0.0429396i	0.00254096	+	0.00184612i	−0.586514	+	0.809939i	$0.699500\pi$
$542$	−23.2668	+	7.55986i	−0.999396	+	0.324724i
$543$			1.41458i			0.0607053i
$544$	−5.19214	−	15.9798i	−0.222611	−	0.685127i
$545$	−28.4288	−	1.19092i	−1.21775	−	0.0510135i
$546$	−4.77554	+	14.6976i	−0.204374	+	0.629000i
$547$	−39.6269	−	12.8756i	−1.69432	−	0.550519i	−0.706722	−	0.707492i	$-0.749827\pi$
$547$	−39.6269	−	12.8756i	−1.69432	−	0.550519i	−0.987603	+	0.156972i	$0.949827\pi$
$548$	−23.4592	−	32.2889i	−1.00213	−	1.37931i
$549$	34.6456			1.47864
$550$	26.1970	−	30.3520i	1.11704	−	1.29422i
$551$	−6.93102			−0.295271
$552$	−27.6524	−	38.0603i	−1.17697	−	1.61996i
$553$	3.81227	+	1.23868i	0.162114	+	0.0526741i
$554$	2.56311	−	7.88846i	0.108896	−	0.335148i
$555$	−11.9848	+	32.2283i	−0.508727	+	1.36801i
$556$	−24.1091	−	74.2003i	−1.02246	−	3.14679i
$557$		−	31.6693i		−	1.34187i	−0.741515	−	0.670936i	$-0.765892\pi$
$557$		−	31.6693i		−	1.34187i	0.741515	−	0.670936i	$-0.234108\pi$
$558$	−108.561	+	35.2738i	−4.59577	+	1.49326i
$559$	−20.4288	−	14.8424i	−0.864047	−	0.627767i
$560$	−0.340982	+	8.13965i	−0.0144091	+	0.343963i
$561$	−39.4098	+	28.6329i	−1.66388	+	1.20888i
$562$	−0.0842717	+	0.115990i	−0.00355479	+	0.00489275i
$563$	5.86450	−	8.07180i	0.247159	−	0.340186i	−0.667355	−	0.744740i	$-0.732573\pi$
$563$	5.86450	−	8.07180i	0.247159	−	0.340186i	0.914514	+	0.404555i	$0.132573\pi$
$564$	15.9342	−	11.5769i	0.670952	−	0.487475i
$565$	−1.42928	+	34.1186i	−0.0601302	+	1.43538i
$566$	−12.3436	−	8.96818i	−0.518842	−	0.376961i
$567$	−1.16528	+	0.378624i	−0.0489373	+	0.0159007i
$568$		−	49.1703i		−	2.06314i
$569$	−2.88548	−	8.88060i	−0.120966	−	0.372294i	0.872179	−	0.489187i	$-0.162707\pi$
$569$	−2.88548	−	8.88060i	−0.120966	−	0.372294i	−0.993145	+	0.116893i	$0.962707\pi$
$570$	5.57610	−	14.9946i	0.233557	−	0.628056i
$571$	5.68720	−	17.5034i	0.238002	−	0.732495i	−0.758707	−	0.651432i	$-0.774169\pi$
$571$	5.68720	−	17.5034i	0.238002	−	0.732495i	0.996709	−	0.0810628i	$-0.0258314\pi$
$572$	−45.1659	−	14.6753i	−1.88848	−	0.613605i
$573$	18.0832	+	24.8894i	0.755435	+	1.03977i
$574$	11.1173			0.464026
$575$	13.9650	−	3.27607i	0.582380	−	0.136622i
$576$	−19.4473			−0.810306
$577$	−2.88587	−	3.97205i	−0.120140	−	0.165359i	0.744711	−	0.667387i	$-0.232587\pi$
$577$	−2.88587	−	3.97205i	−0.120140	−	0.165359i	−0.864851	+	0.502028i	$0.832587\pi$
$578$	−27.5394	−	8.94811i	−1.14549	−	0.372192i
$579$	−1.97342	+	6.07355i	−0.0820124	+	0.252408i
$580$	66.4617	+	2.78418i	2.75967	+	0.115607i
$581$	1.86499	+	5.73985i	0.0773729	+	0.238129i
$582$			89.7563i			3.72052i
$583$	12.8208	−	4.16574i	0.530985	−	0.172527i
$584$	−22.3506	−	16.2387i	−0.924875	−	0.671961i
$585$	−24.6850	+	31.1460i	−1.02060	+	1.28773i
$586$	−56.2805	+	40.8902i	−2.32493	+	1.68916i
$587$	−17.1334	+	23.5821i	−0.707172	+	0.973339i	0.292681	+	0.956210i	$0.405453\pi$
$587$	−17.1334	+	23.5821i	−0.707172	+	0.973339i	−0.999853	+	0.0171289i	$0.994547\pi$
$588$	47.5668	−	65.4701i	1.96162	−	2.69994i
$589$	7.16948	−	5.20893i	0.295413	−	0.214630i
$590$	−42.7644	−	64.3627i	−1.76058	−	2.64977i
$591$	3.45542	+	2.51051i	0.142137	+	0.103268i
$592$	29.9341	−	9.72618i	1.23028	−	0.399744i
$593$		−	4.00086i		−	0.164296i	−0.996620	−	0.0821478i	$-0.973822\pi$
$593$		−	4.00086i		−	0.164296i	0.996620	−	0.0821478i	$-0.0261780\pi$
$594$	−15.0893	−	46.4402i	−0.619123	−	1.90547i
$595$	5.84300	+	4.63090i	0.239539	+	0.189848i
$596$	−22.4084	+	68.9660i	−0.917885	+	2.82496i
$597$	14.4456	+	4.69366i	0.591219	+	0.192099i
$598$	−14.6401	−	20.1503i	−0.598676	−	0.824007i
$599$	−38.9677			−1.59218			−0.796089	−	0.605180i	$-0.793101\pi$
$599$	−38.9677			−1.59218			−0.796089	+	0.605180i	$0.793101\pi$
$600$	−31.7708	+	75.5885i	−1.29704	+	3.08589i
$601$	−33.3755			−1.36141			−0.680707	−	0.732556i	$-0.738327\pi$
$601$	−33.3755			−1.36141			−0.680707	+	0.732556i	$0.738327\pi$
$602$	−6.71306	−	9.23973i	−0.273604	−	0.376583i
$603$	−34.0702	−	11.0701i	−1.38745	−	0.450808i
$604$	−31.0958	+	95.7031i	−1.26527	+	3.89410i
$605$	−0.469469	−	1.68131i	−0.0190866	−	0.0683551i
$606$	22.1935	+	68.3047i	0.901551	+	2.77469i
$607$			22.2776i			0.904220i	0.891962	+	0.452110i	$0.149329\pi$
$607$			22.2776i			0.904220i	−0.891962	+	0.452110i	$0.850671\pi$
$608$	−2.99098	+	0.971830i	−0.121300	+	0.0394129i
$609$	9.98101	+	7.25163i	0.404451	+	0.293851i
$610$	36.4491	−	10.1776i	1.47578	−	0.412078i
$611$	4.50510	−	3.27315i	0.182257	−	0.132417i
$612$	69.2128	−	95.2633i	2.79776	−	3.85079i
$613$	−3.38634	+	4.66090i	−0.136773	+	0.188252i	−0.871909	−	0.489667i	$-0.837118\pi$
$613$	−3.38634	+	4.66090i	−0.136773	+	0.188252i	0.735136	+	0.677919i	$0.237118\pi$
$614$	−56.7006	+	41.1954i	−2.28825	+	1.66251i
$615$	42.4519	+	15.7867i	1.71182	+	0.636581i
$616$	−9.27988	−	6.74223i	−0.373897	−	0.271652i
$617$	45.8937	−	14.9118i	1.84761	−	0.600325i	0.850363	−	0.526197i	$-0.176383\pi$
$617$	45.8937	−	14.9118i	1.84761	−	0.600325i	0.997249	−	0.0741284i	$-0.0236175\pi$
$618$		−	84.7050i		−	3.40734i
$619$	−1.64803	−	5.07211i	−0.0662398	−	0.203865i	0.912458	−	0.409170i	$-0.134182\pi$
$619$	−1.64803	−	5.07211i	−0.0662398	−	0.203865i	−0.978698	+	0.205304i	$0.934182\pi$
$620$	−70.8408	+	47.0686i	−2.84503	+	1.89032i
$621$	5.39839	−	16.6145i	0.216630	−	0.666719i
$622$	−27.9265	−	9.07386i	−1.11975	−	0.363828i
$623$	4.46380	+	6.14390i	0.178838	+	0.246150i
$624$	57.6319			2.30712
$625$	−17.4931	−	17.8604i	−0.699723	−	0.714414i
$626$	−14.8314			−0.592781
$627$	5.35931	+	7.37646i	0.214030	+	0.294587i
$628$	−8.43803	−	2.74168i	−0.336714	−	0.109405i
$629$	8.90098	−	27.3944i	0.354905	−	1.09229i
$630$	−14.9714	+	9.94744i	−0.596476	+	0.396315i
$631$	−0.134103	−	0.412727i	−0.00533856	−	0.0164304i	0.948352	−	0.317221i	$-0.102750\pi$
$631$	−0.134103	−	0.412727i	−0.00533856	−	0.0164304i	−0.953690	+	0.300790i	$0.902750\pi$
$632$		−	36.9291i		−	1.46896i
$633$	42.2121	−	13.7155i	1.67778	−	0.545144i
$634$	66.4039	+	48.2452i	2.63723	+	1.91606i
$635$	−25.6398	−	9.53476i	−1.01749	−	0.378376i
$636$	−41.7644	+	30.3436i	−1.65606	+	1.20320i
$637$	13.4486	−	18.5104i	0.532853	−	0.733409i
$638$	−32.6682	+	44.9639i	−1.29335	+	1.78014i
$639$	35.5279	−	25.8125i	1.40546	−	1.02113i
$640$	−34.0060	+	9.49540i	−1.34420	+	0.375339i
$641$	−21.6664	−	15.7416i	−0.855772	−	0.621755i	0.0709596	−	0.997479i	$-0.477394\pi$
$641$	−21.6664	−	15.7416i	−0.855772	−	0.621755i	−0.926731	+	0.375725i	$0.877394\pi$
$642$	42.7435	−	13.8882i	1.68695	−	0.548124i
$643$			2.45226i			0.0967076i	0.998830	+	0.0483538i	$0.0153975\pi$
$643$			2.45226i			0.0967076i	−0.998830	+	0.0483538i	$0.984603\pi$
$644$	−2.37463	−	7.30837i	−0.0935737	−	0.287990i
$645$	−12.5136	−	44.8151i	−0.492723	−	1.76459i
$646$	−4.14130	+	12.7456i	−0.162937	+	0.501469i
$647$	16.4900	+	5.35792i	0.648288	+	0.210642i	0.614659	−	0.788793i	$-0.289294\pi$
$647$	16.4900	+	5.35792i	0.648288	+	0.210642i	0.0336291	+	0.999434i	$0.489294\pi$
$648$	6.63492	+	9.13219i	0.260644	+	0.358746i
$649$	44.0418			1.72879
$650$	−16.8204	+	40.0189i	−0.659751	+	1.56967i
$651$	−15.7743			−0.618243
$652$	−18.6169	−	25.6240i	−0.729094	−	1.00351i
$653$	23.9350	+	7.77695i	0.936648	+	0.304335i	0.737278	−	0.675589i	$-0.236111\pi$
$653$	23.9350	+	7.77695i	0.936648	+	0.304335i	0.199370	+	0.979924i	$0.436111\pi$
$654$	−28.1328	+	86.5838i	−1.10008	+	3.38570i
$655$	32.6070	+	25.8429i	1.27406	+	1.00976i
$656$	−12.8116	−	39.4300i	−0.500208	−	1.53948i
$657$		−	24.6740i		−	0.962626i
$658$	2.39535	−	0.778297i	0.0933805	−	0.0303412i
$659$	18.1786	+	13.2075i	0.708136	+	0.514491i	0.882572	−	0.470177i	$-0.155810\pi$
$659$	18.1786	+	13.2075i	0.708136	+	0.514491i	−0.174436	+	0.984669i	$0.555810\pi$
$660$	−48.4275	−	72.8859i	−1.88504	−	2.83708i
$661$	25.1626	−	18.2817i	0.978710	−	0.711075i	0.0212903	−	0.999773i	$-0.493223\pi$
$661$	25.1626	−	18.2817i	0.978710	−	0.711075i	0.957420	+	0.288699i	$0.0932226\pi$
$662$	2.56831	−	3.53498i	0.0998202	−	0.137391i
$663$	31.0011	−	42.6693i	1.20398	−	1.65714i
$664$	44.9825	−	32.6817i	1.74566	−	1.26830i
$665$	0.866781	−	1.09365i	0.0336123	−	0.0424100i
$666$	56.1818	+	40.8185i	2.17700	+	1.58168i
$667$	−18.9107	+	6.14444i	−0.732223	+	0.237914i
$668$			47.8772i			1.85242i
$669$	−9.67696	−	29.7826i	−0.374133	−	1.15146i
$670$	−39.0957	−	1.63778i	−1.51040	−	0.0632729i
$671$	−6.66500	+	20.5128i	−0.257299	+	0.791886i
$672$	5.32395	+	1.72986i	0.205376	+	0.0667307i
$673$	−12.8229	−	17.6492i	−0.494287	−	0.680327i	0.486885	−	0.873466i	$-0.338133\pi$
$673$	−12.8229	−	17.6492i	−0.494287	−	0.680327i	−0.981171	+	0.193139i	$0.938133\pi$
$674$	−22.6140			−0.871057
$675$	−29.6426	+	6.95390i	−1.14094	+	0.267656i
$676$	−4.37931			−0.168435
$677$	−3.00753	−	4.13950i	−0.115589	−	0.159094i	0.747302	−	0.664484i	$-0.231349\pi$
$677$	−3.00753	−	4.13950i	−0.115589	−	0.159094i	−0.862891	+	0.505390i	$0.831349\pi$
$678$	103.913	+	33.7634i	3.99076	+	1.29668i
$679$	−2.41942	+	7.44621i	−0.0928488	+	0.285759i
$680$	23.9410	−	64.3795i	0.918095	−	2.46884i
$681$	−9.79912	−	30.1586i	−0.375503	−	1.15568i
$682$		−	71.0623i		−	2.72112i
$683$	−0.877311	+	0.285056i	−0.0335694	+	0.0109074i	−0.325754	−	0.945455i	$-0.605618\pi$
$683$	−0.877311	+	0.285056i	−0.0335694	+	0.0109074i	0.292184	+	0.956362i	$0.405618\pi$
$684$	−17.8307	−	12.9548i	−0.681775	−	0.495339i
$685$	0.870272	−	20.7744i	0.0332514	−	0.793750i
$686$	17.2374	−	12.5237i	0.658126	−	0.478157i
$687$	−25.3705	+	34.9194i	−0.967943	+	1.33226i
$688$	−25.0347	+	34.4573i	−0.954440	+	1.31367i
$689$	−11.8081	+	8.57907i	−0.449852	+	0.326837i
$690$	1.92093	−	45.8548i	0.0731284	−	1.74566i
$691$	21.3950	+	15.5444i	0.813906	+	0.591337i	0.914960	−	0.403544i	$-0.132222\pi$
$691$	21.3950	+	15.5444i	0.813906	+	0.591337i	−0.101055	+	0.994881i	$0.532222\pi$
$692$	17.8312	−	5.79372i	0.677841	−	0.220244i
$693$		−	10.2446i		−	0.389159i
$694$	−11.3694	−	34.9915i	−0.431578	−	1.32826i
$695$	14.1671	−	38.0967i	0.537390	−	1.44509i
$696$	35.1229	−	108.097i	1.33133	−	4.09742i
$697$	−36.0846	−	11.7246i	−1.36680	−	0.444101i
$698$	45.5906	+	62.7501i	1.72563	+	2.37513i
$699$	59.9865			2.26890
$700$	−8.75090	+	10.1389i	−0.330753	+	0.383214i
$701$	−9.09277			−0.343429			−0.171715	−	0.985147i	$-0.554931\pi$
$701$	−9.09277			−0.343429			−0.171715	+	0.985147i	$0.554931\pi$
$702$	31.0755	+	42.7717i	1.17287	+	1.61432i
$703$	−5.12750	−	1.66602i	−0.193387	−	0.0628353i
$704$	3.74122	−	11.5143i	0.141002	−	0.433961i
$705$	10.2520	+	0.429470i	0.386111	+	0.0161748i
$706$	−20.7871	−	63.9760i	−0.782332	−	2.40777i
$707$			6.26481i			0.235613i
$708$	−160.402	+	52.1177i	−6.02827	+	1.95870i
$709$	10.1513	+	7.37532i	0.381238	+	0.276986i	0.761856	−	0.647747i	$-0.224288\pi$
$709$	10.1513	+	7.37532i	0.381238	+	0.276986i	−0.380617	+	0.924733i	$0.624288\pi$
$710$	29.7946	−	37.5930i	1.11817	−	1.41084i
$711$	26.6830	−	19.3864i	1.00069	−	0.727045i
$712$	41.1241	−	56.6025i	1.54119	−	2.12127i
$713$	14.9435	−	20.5680i	0.559638	−	0.770276i
$714$	19.2989	−	14.0214i	0.722242	−	0.524739i
$715$	−13.6919	−	20.6071i	−0.512050	−	0.770662i
$716$	15.5495	+	11.2974i	0.581112	+	0.422202i
$717$	−11.2028	+	3.64001i	−0.418377	+	0.135939i
$718$			37.2498i			1.39015i
$719$	13.8409	+	42.5980i	0.516180	+	1.58864i	0.781125	+	0.624375i	$0.214646\pi$
$719$	13.8409	+	42.5980i	0.516180	+	1.58864i	−0.264945	+	0.964264i	$0.585354\pi$
$720$	52.5340	+	41.6362i	1.95783	+	1.55169i
$721$	2.28326	−	7.02715i	0.0850330	−	0.261705i
$722$	2.38564	+	0.775140i	0.0887842	+	0.0288477i
$723$	−11.3440	−	15.6137i	−0.421889	−	0.580680i
$724$	2.12872			0.0791131
$725$	26.2347	+	22.6432i	0.974331	+	0.840949i
$726$	−5.58526			−0.207289
$727$	−16.8847	−	23.2398i	−0.626220	−	0.861917i	0.371568	−	0.928406i	$-0.378820\pi$
$727$	−16.8847	−	23.2398i	−0.626220	−	0.861917i	−0.997787	+	0.0664886i	$0.978820\pi$
$728$	11.8114	+	3.83776i	0.437761	+	0.142237i
$729$	12.9860	−	39.9667i	0.480961	−	1.48025i
$730$	−7.24832	−	25.9585i	−0.268272	−	0.960766i
$731$	12.0449	+	37.0703i	0.445495	+	1.37109i
$732$		−	82.5954i		−	3.05281i
$733$	23.7960	−	7.73178i	0.878924	−	0.285580i	0.165413	−	0.986224i	$-0.447104\pi$
$733$	23.7960	−	7.73178i	0.878924	−	0.285580i	0.713510	+	0.700645i	$0.247104\pi$
$734$	−56.8446	−	41.3000i	−2.09817	−	1.52441i
$735$	40.6066	−	11.3385i	1.49780	−	0.418226i
$736$	−7.29909	+	5.30310i	−0.269048	+	0.195475i
$737$	13.1086	−	18.0425i	0.482862	−	0.664603i
$738$	53.7671	−	74.0041i	1.97920	−	2.72413i
$739$	−8.94097	+	6.49600i	−0.328899	+	0.238959i	−0.739963	−	0.672647i	$-0.765157\pi$
$739$	−8.94097	+	6.49600i	−0.328899	+	0.238959i	0.411064	+	0.911606i	$0.365157\pi$
$740$	48.4985	+	18.0353i	1.78284	+	0.662990i
$741$	−7.98655	−	5.80257i	−0.293393	−	0.213163i
$742$	−6.27833	+	2.03995i	−0.230485	+	0.0748890i
$743$		−	26.2178i		−	0.961837i	−0.876765	−	0.480918i	$-0.840303\pi$
$743$		−	26.2178i		−	0.961837i	0.876765	−	0.480918i	$-0.159697\pi$
$744$	44.9080	+	138.213i	1.64641	+	5.06712i
$745$	−31.4660	+	20.9069i	−1.15282	+	0.765970i
$746$	22.1504	−	68.1720i	0.810985	−	2.49596i
$747$	47.2282	+	15.3454i	1.72799	+	0.561458i
$748$	43.0880	+	59.3056i	1.57545	+	2.16843i
$749$	3.92037			0.143247
$750$	−70.0928	+	38.5395i	−2.55943	+	1.40727i
$751$	17.9201			0.653912			0.326956	−	0.945040i	$-0.393977\pi$
$751$	17.9201			0.653912			0.326956	+	0.945040i	$0.393977\pi$
$752$	−5.52082	−	7.59876i	−0.201324	−	0.277098i
$753$	−52.2862	−	16.9888i	−1.90541	−	0.619107i
$754$	18.5952	−	57.2300i	0.677196	−	2.08419i
$755$	−43.6649	+	29.0122i	−1.58913	+	1.05586i
$756$	5.04048	+	15.5130i	0.183321	+	0.564203i
$757$		−	17.6048i		−	0.639859i	−0.947441	−	0.319930i	$-0.896341\pi$
$757$		−	17.6048i		−	0.639859i	0.947441	−	0.319930i	$-0.103659\pi$
$758$	25.8395	−	8.39577i	0.938534	−	0.304948i
$759$	21.1617	+	15.3749i	0.768122	+	0.558073i
$760$	−12.0501	−	4.48111i	−0.437104	−	0.162547i
$761$	−40.3746	+	29.3339i	−1.46358	+	1.06335i	−0.481164	+	0.876630i	$0.659786\pi$
$761$	−40.3746	+	29.3339i	−1.46358	+	1.06335i	−0.982413	+	0.186721i	$0.940214\pi$
$762$	−51.4461	+	70.8095i	−1.86370	+	2.56516i
$763$	−4.66781	+	6.42469i	−0.168986	+	0.232589i
$764$	37.4546	−	27.2123i	1.35506	−	0.984508i
$765$	59.0853	−	16.4982i	2.13623	−	0.596495i
$766$	−35.5869	−	25.8554i	−1.28581	−	0.934194i
$767$	−45.3505	+	14.7353i	−1.63751	+	0.532060i
$768$			91.3629i			3.29678i
$769$	−10.0431	−	30.9096i	−0.362165	−	1.11463i	−0.951737	−	0.306913i	$-0.900704\pi$
$769$	−10.0431	−	30.9096i	−0.362165	−	1.11463i	0.589573	−	0.807715i	$-0.299296\pi$
$770$	−3.00947	−	10.7778i	−0.108454	−	0.388407i
$771$	−15.2401	+	46.9043i	−0.548860	+	1.68922i
$772$	9.13975	+	2.96968i	0.328947	+	0.106881i
$773$	16.9632	+	23.3479i	0.610126	+	0.839766i	0.996588	−	0.0825395i	$-0.0263031\pi$
$773$	16.9632	+	23.3479i	0.610126	+	0.839766i	−0.386462	+	0.922305i	$0.626303\pi$
$774$	−93.9728			−3.37778
$775$	−44.1546	−	3.70591i	−1.58608	−	0.133120i
$776$	72.1308			2.58934
$777$	5.64076	+	7.76384i	0.202361	+	0.278526i
$778$	39.8483	+	12.9475i	1.42863	+	0.464190i
$779$	−2.19453	+	6.75407i	−0.0786272	+	0.241990i
$780$	74.2524	+	58.8492i	2.65866	+	2.10714i
$781$	8.44820	+	26.0009i	0.302300	+	0.930385i
$782$			38.4466i			1.37485i
$783$	40.1404	−	13.0424i	1.43450	−	0.466098i
$784$	−31.2215	−	22.6838i	−1.11506	−	0.810135i
$785$	−2.55797	−	3.84988i	−0.0912979	−	0.137408i
$786$	107.698	−	78.2470i	3.84145	−	2.79098i
$787$	−25.9278	+	35.6865i	−0.924225	+	1.27209i	0.0378454	+	0.999284i	$0.487951\pi$
$787$	−25.9278	+	35.6865i	−0.924225	+	1.27209i	−0.962070	+	0.272803i	$0.912049\pi$
$788$	3.77792	−	5.19986i	0.134583	−	0.185237i
$789$	0.907634	−	0.659435i	0.0323126	−	0.0234765i
$790$	22.3771	−	28.2340i	0.796140	−	1.00452i
$791$	7.71055	+	5.60204i	0.274156	+	0.199186i
$792$	−89.7618	+	29.1654i	−3.18955	+	1.03635i
$793$		−	23.3523i		−	0.829264i
$794$	6.88521	+	21.1905i	0.244347	+	0.752023i
$795$	−26.8709	−	1.12566i	−0.953012	−	0.0399231i
$796$	7.06322	−	21.7384i	0.250349	−	0.770496i
$797$	−34.8191	−	11.3134i	−1.23335	−	0.400741i	−0.381426	−	0.924399i	$-0.624567\pi$
$797$	−34.8191	−	11.3134i	−1.23335	−	0.400741i	−0.851929	+	0.523658i	$0.824567\pi$
$798$	−2.62444	−	3.61223i	−0.0929041	−	0.127872i
$799$	−8.59568			−0.304093
$800$	14.4961	+	6.09290i	0.512515	+	0.215416i
$801$	62.4866			2.20785
$802$	4.53256	+	6.23854i	0.160050	+	0.220291i
$803$	14.6089	+	4.74671i	0.515536	+	0.167508i
$804$	−26.3912	+	81.2237i	−0.930745	+	2.86454i
$805$	1.39540	−	3.75234i	0.0491812	−	0.132253i
$806$	23.7757	+	73.1740i	0.837463	+	2.57745i
$807$			37.4088i			1.31685i
$808$	54.8916	−	17.8354i	1.93108	−	0.627446i
$809$	39.2520	+	28.5183i	1.38003	+	1.00265i	0.996878	+	0.0789633i	$0.0251610\pi$
$809$	39.2520	+	28.5183i	1.38003	+	1.00265i	0.383151	+	0.923686i	$0.374839\pi$
$810$	−0.460906	+	11.0024i	−0.0161946	+	0.386584i
$811$	39.8172	−	28.9289i	1.39817	−	1.01583i	0.403259	−	0.915086i	$-0.367877\pi$
$811$	39.8172	−	28.9289i	1.39817	−	1.01583i	0.994912	−	0.100745i	$-0.0321225\pi$
$812$	10.9126	−	15.0199i	0.382956	−	0.527094i
$813$	−16.3505	+	22.5045i	−0.573437	+	0.789268i
$814$	−34.9757	+	25.4113i	−1.22590	+	0.890666i
$815$	0.690635	−	16.4863i	0.0241919	−	0.577489i
$816$	−71.9704	−	52.2896i	−2.51947	−	1.83050i
$817$	6.93856	−	2.25448i	0.242750	−	0.0788741i
$818$			45.2013i			1.58043i
$819$	3.42758	+	10.5490i	0.119769	+	0.368612i
$820$	23.7565	−	63.8834i	0.829613	−	2.23091i
$821$	−2.57752	+	7.93279i	−0.0899561	+	0.276856i	−0.985906	−	0.167298i	$-0.946496\pi$
$821$	−2.57752	+	7.93279i	−0.0899561	+	0.276856i	0.895950	+	0.444154i	$0.146496\pi$
$822$	−63.2715	−	20.5582i	−2.20685	−	0.717048i
$823$	12.0218	+	16.5466i	0.419053	+	0.576777i	0.965397	−	0.260784i	$-0.0839809\pi$
$823$	12.0218	+	16.5466i	0.419053	+	0.576777i	−0.546344	+	0.837561i	$0.683981\pi$
$824$	−68.0714			−2.37138
$825$	3.81289	−	45.4293i	0.132748	−	1.58164i
$826$	−21.5671			−0.750416
$827$	3.34856	+	4.60890i	0.116441	+	0.160267i	0.863259	−	0.504761i	$-0.168419\pi$
$827$	3.34856	+	4.60890i	0.116441	+	0.160267i	−0.746818	+	0.665028i	$0.768419\pi$
$828$	−60.1342	−	19.5388i	−2.08981	−	0.679019i
$829$	0.743398	−	2.28794i	0.0258193	−	0.0794636i	−0.937317	−	0.348479i	$-0.886698\pi$
$829$	0.743398	−	2.28794i	0.0258193	−	0.0794636i	0.963136	+	0.269015i	$0.0866983\pi$
$830$	54.1946	+	2.27029i	1.88112	+	0.0788030i
$831$	−2.91440	−	8.96960i	−0.101099	−	0.311152i
$832$			13.1082i			0.454444i
$833$	−33.5891	+	10.9138i	−1.16379	+	0.378139i
$834$	−105.212	−	76.4407i	−3.64318	−	2.64693i
$835$	−15.4927	+	19.5477i	−0.536147	+	0.676478i
$836$	11.1004	−	8.06492i	0.383916	−	0.278931i
$837$	−31.7196	+	43.6583i	−1.09639	+	1.50905i
$838$	25.5783	−	35.2055i	0.883587	−	1.21615i
$839$	−23.5901	+	17.1392i	−0.814419	+	0.591710i	−0.915108	−	0.403208i	$-0.867895\pi$
$839$	−23.5901	+	17.1392i	−0.814419	+	0.591710i	0.100689	+	0.994918i	$0.467895\pi$
$840$	12.6644	+	19.0605i	0.436962	+	0.657651i
$841$	−15.4029	−	11.1908i	−0.531133	−	0.385891i
$842$	−85.3751	+	27.7400i	−2.94222	+	0.955985i
$843$			0.163021i			0.00561475i
$844$	−20.6397	−	63.5226i	−0.710449	−	2.18654i
$845$	−1.78803	−	1.41711i	−0.0615100	−	0.0487501i
$846$	6.40391	−	19.7092i	0.220171	−	0.677617i
$847$	−0.463355	−	0.150553i	−0.0159211	−	0.00517307i
$848$	14.4703	+	19.9167i	0.496913	+	0.683942i
$849$	−17.3487			−0.595406
$850$	57.3145	−	34.7142i	1.96587	−	1.19069i
$851$	−15.4669			−0.530197
$852$	−61.5373	−	84.6989i	−2.10823	−	2.90174i
$853$	−2.97118	−	0.965395i	−0.101731	−	0.0330545i	0.257709	−	0.966223i	$-0.417032\pi$
$853$	−2.97118	−	0.965395i	−0.101731	−	0.0330545i	−0.359440	+	0.933168i	$0.617032\pi$
$854$	3.26383	−	10.0450i	0.111686	−	0.343734i
$855$	−3.08803	−	11.0592i	−0.105608	−	0.378216i
$856$	−11.1610	−	34.3499i	−0.381474	−	1.17406i
$857$		−	9.37459i		−	0.320230i	−0.987098	−	0.160115i	$-0.948814\pi$
$857$		−	9.37459i		−	0.320230i	0.987098	−	0.160115i	$-0.0511865\pi$
$858$	−75.2865	+	24.4621i	−2.57024	+	0.835121i
$859$	4.95300	+	3.59857i	0.168994	+	0.122781i	0.669068	−	0.743202i	$-0.266694\pi$
$859$	4.95300	+	3.59857i	0.168994	+	0.122781i	−0.500073	+	0.865983i	$0.666694\pi$
$860$	−67.4397	+	18.8310i	−2.29967	+	0.642132i
$861$	10.2267	−	7.43015i	0.348526	−	0.253219i
$862$	−2.59018	+	3.56508i	−0.0882220	+	0.121427i
$863$	9.38078	−	12.9115i	0.319325	−	0.439514i	−0.618936	−	0.785442i	$-0.712436\pi$
$863$	9.38078	−	12.9115i	0.319325	−	0.439514i	0.938261	+	0.345928i	$0.112436\pi$
$864$	15.4933	−	11.2565i	0.527093	−	0.382956i
$865$	9.15510	+	3.40453i	0.311283	+	0.115758i
$866$	−67.8593	−	49.3026i	−2.30595	−	1.67537i
$867$	−31.3138	+	10.1745i	−1.06347	+	0.345544i
$868$			23.7378i			0.805715i
$869$	6.34498	+	19.5278i	0.215239	+	0.662436i
$870$	92.3542	−	61.3628i	3.13110	−	2.08039i
$871$	−7.46160	+	22.9644i	−0.252827	+	0.778120i
$872$	69.5813	+	22.6083i	2.35632	+	0.765615i
$873$	37.8659	+	52.1179i	1.28157	+	1.76392i
$874$	7.19617			0.243414
$875$	−6.85376	+	1.30787i	−0.231699	+	0.0442141i
$876$	−58.8232			−1.98745
$877$	0.793516	+	1.09218i	0.0267951	+	0.0368803i	0.822204	−	0.569192i	$-0.192744\pi$
$877$	0.793516	+	1.09218i	0.0267951	+	0.0368803i	−0.795409	+	0.606073i	$0.792744\pi$
$878$	17.7710	+	5.77414i	0.599741	+	0.194868i
$879$	−24.4435	+	75.2295i	−0.824460	+	2.53743i
$880$	−34.7580	+	23.0942i	−1.17169	+	0.778506i
$881$	−4.68657	−	14.4238i	−0.157895	−	0.485950i	0.840548	−	0.541737i	$-0.182233\pi$
$881$	−4.68657	−	14.4238i	−0.157895	−	0.485950i	−0.998443	+	0.0557874i	$0.982233\pi$
$882$		−	85.1481i		−	2.86709i
$883$	11.8914	−	3.86374i	0.400177	−	0.130025i	−0.102012	−	0.994783i	$-0.532528\pi$
$883$	11.8914	−	3.86374i	0.400177	−	0.130025i	0.502189	+	0.864758i	$0.332528\pi$
$884$	−64.2106	−	46.6518i	−2.15964	−	1.56907i
$885$	−82.3552	−	30.6257i	−2.76834	−	1.02947i
$886$	−19.4356	+	14.1208i	−0.652953	+	0.474398i
$887$	4.37113	−	6.01635i	0.146768	−	0.202009i	−0.729303	−	0.684191i	$-0.760155\pi$
$887$	4.37113	−	6.01635i	0.146768	−	0.202009i	0.876071	+	0.482182i	$0.160155\pi$
$888$	51.9672	−	71.5267i	1.74391	−	2.40028i
$889$	−6.17668	+	4.48762i	−0.207159	+	0.150510i
$890$	65.7394	−	18.3562i	2.20359	−	0.615302i
$891$	−5.07754	−	3.68905i	−0.170104	−	0.123588i
$892$	−44.8182	+	14.5623i	−1.50062	+	0.487582i
$893$			1.60888i			0.0538392i
$894$	37.3523	+	114.959i	1.24925	+	3.84479i
$895$	2.69295	+	9.64429i	0.0900154	+	0.322373i
$896$	−3.04506	+	9.37174i	−0.101728	+	0.313088i
$897$	−26.9346	−	8.75160i	−0.899322	−	0.292207i
$898$	9.52701	+	13.1128i	0.317920	+	0.437580i
$899$	61.4224			2.04855
$900$	25.1687	+	107.287i	0.838958	+	3.57624i
$901$	22.5297			0.750573
$902$	33.4724	+	46.0708i	1.11451	+	1.53399i
$903$	−12.3506	−	4.01296i	−0.411003	−	0.133543i
$904$	27.1333	−	83.5076i	0.902439	−	2.77742i
$905$	0.869132	+	0.688836i	0.0288909	+	0.0228977i
$906$	51.8333	+	159.526i	1.72204	+	5.29991i
$907$			1.58677i			0.0526877i	0.999653	+	0.0263438i	$0.00838647\pi$
$907$			1.58677i			0.0526877i	−0.999653	+	0.0263438i	$0.991614\pi$
$908$	−45.3840	+	14.7461i	−1.50612	+	0.489368i
$909$	41.7029	+	30.2989i	1.38320	+	1.00495i
$910$	6.70490	+	10.0912i	0.222265	+	0.334521i
$911$	−39.8938	+	28.9846i	−1.32174	+	0.960302i	−0.321833	+	0.946796i	$0.604299\pi$
$911$	−39.8938	+	28.9846i	−1.32174	+	0.960302i	−0.999909	+	0.0135053i	$0.995701\pi$
$912$	−9.78720	+	13.4709i	−0.324087	+	0.446067i
$913$	−18.1712	+	25.0105i	−0.601379	+	0.827727i
$914$	70.8488	−	51.4747i	2.34347	−	1.70263i
$915$	26.7272	−	33.7228i	0.883575	−	1.11484i
$916$	52.5483	+	38.1786i	1.73624	+	1.26146i
$917$	11.0438	−	3.58835i	0.364699	−	0.118498i
$918$		−	81.6081i		−	2.69347i
$919$	−5.77223	−	17.7651i	−0.190408	−	0.586016i	0.809591	−	0.586994i	$-0.199689\pi$
$919$	−5.77223	−	17.7651i	−0.190408	−	0.586016i	−1.00000		0.000977779i	$0.999689\pi$
$920$	−36.8502	−	1.54371i	−1.21492	−	0.0508946i
$921$	−24.6260	+	75.7909i	−0.811453	+	2.49740i
$922$	31.1960	+	10.1362i	1.02739	+	0.333818i
$923$	−17.3985	−	23.9470i	−0.572679	−	0.788225i
$924$	−24.4231			−0.803462
$925$	13.9653	+	23.0573i	0.459177	+	0.758121i
$926$	67.3466			2.21315
$927$	−35.7349	−	49.1848i	−1.17369	−	1.61544i
$928$	−20.7306	−	6.73577i	−0.680514	−	0.221112i
$929$	−7.75664	+	23.8725i	−0.254487	+	0.783231i	0.739443	+	0.673219i	$0.235089\pi$
$929$	−7.75664	+	23.8725i	−0.254487	+	0.783231i	−0.993930	+	0.110012i	$0.964911\pi$
$930$	−49.4152	+	132.882i	−1.62039	+	4.35737i
$931$	2.04276	+	6.28698i	0.0669489	+	0.206047i
$932$		−	90.2703i		−	2.95690i
$933$	−31.7539	+	10.3175i	−1.03958	+	0.337779i
$934$	−39.3715	−	28.6051i	−1.28827	−	0.935986i
$935$	−1.59845	+	38.1568i	−0.0522747	+	1.24786i
$936$	82.6712	−	60.0641i	2.70219	−	1.96326i
$937$	−14.1246	+	19.4408i	−0.461431	+	0.635105i	−0.974805	−	0.223060i	$-0.928395\pi$
$937$	−14.1246	+	19.4408i	−0.461431	+	0.635105i	0.513374	+	0.858165i	$0.328395\pi$
$938$	−6.41925	+	8.83534i	−0.209596	+	0.288484i
$939$	−13.6433	+	9.91245i	−0.445233	+	0.323481i
$940$	0.646286	−	15.4276i	0.0210795	−	0.503193i
$941$	−1.68798	−	1.22639i	−0.0550266	−	0.0399792i	0.559932	−	0.828539i	$-0.310827\pi$
$941$	−1.68798	−	1.22639i	−0.0550266	−	0.0399792i	−0.614959	+	0.788559i	$0.710827\pi$
$942$	−14.0653	+	4.57008i	−0.458271	+	0.148901i
$943$			20.3733i			0.663447i
$944$	24.8540	+	76.4928i	0.808930	+	2.48963i
$945$	−2.96192	+	7.96486i	−0.0963511	+	0.259097i
$946$	18.0782	−	55.6389i	0.587772	−	1.80898i
$947$	−5.57438	−	1.81123i	−0.181143	−	0.0588570i	0.217041	−	0.976162i	$-0.430359\pi$
$947$	−5.57438	−	1.81123i	−0.181143	−	0.0588570i	−0.398184	+	0.917306i	$0.630359\pi$
$948$	−46.2173	−	63.6126i	−1.50107	−	2.06604i
$949$	−16.6311			−0.539869
$950$	−6.49756	−	10.7277i	−0.210809	−	0.348054i
$951$	93.3290			3.02640
$952$	−11.2680	−	15.5091i	−0.365199	−	0.502654i
$953$	34.7990	+	11.3069i	1.12725	+	0.366266i	0.812531	−	0.582919i	$-0.198089\pi$
$953$	34.7990	+	11.3069i	1.12725	+	0.366266i	0.314720	+	0.949185i	$0.398089\pi$
$954$	−16.7850	+	51.6588i	−0.543433	+	1.67252i
$955$	24.0980	+	1.00950i	0.779793	+	0.0326667i
$956$	5.47765	+	16.8585i	0.177160	+	0.545242i
$957$			63.1956i			2.04283i
$958$	−8.92087	+	2.89856i	−0.288220	+	0.0936484i
$959$	−4.69487	−	3.41102i	−0.151605	−	0.110148i
$960$	−15.0026	+	18.9294i	−0.484207	+	0.610943i
$961$	−38.4562	+	27.9400i	−1.24052	+	0.901292i
$962$	27.5130	−	37.8684i	0.887056	−	1.22093i
$963$	18.9604	−	26.0967i	0.610989	−	0.840954i
$964$	−23.4962	+	17.0710i	−0.756762	+	0.549819i
$965$	2.77070	+	4.17004i	0.0891918	+	0.134238i
$966$	−10.3628	−	7.52904i	−0.333419	−	0.242243i
$967$	−12.8119	+	4.16283i	−0.412002	+	0.133868i	−0.507682	−	0.861545i	$-0.669497\pi$
$967$	−12.8119	+	4.16283i	−0.412002	+	0.133868i	0.0956798	+	0.995412i	$0.469497\pi$
$968$			4.48848i			0.144265i
$969$	4.70888	+	14.4924i	0.151271	+	0.465564i
$970$	55.1473	+	43.7074i	1.77067	+	1.40336i
$971$	14.8587	−	45.7304i	0.476839	−	1.46756i	−0.366623	−	0.930369i	$-0.619486\pi$
$971$	14.8587	−	45.7304i	0.476839	−	1.46756i	0.843462	−	0.537189i	$-0.180514\pi$
$972$	−51.7140	−	16.8029i	−1.65873	−	0.538954i
$973$	−6.66789	−	9.17756i	−0.213763	−	0.294219i
$974$	−4.21991			−0.135215
$975$	11.2733	+	48.0550i	0.361035	+	1.53899i
$976$	−39.3883			−1.26079
$977$	6.80528	+	9.36667i	0.217720	+	0.299666i	0.903881	−	0.427783i	$-0.140705\pi$
$977$	6.80528	+	9.36667i	0.217720	+	0.299666i	−0.686161	+	0.727450i	$0.740705\pi$
$978$	−50.2113	−	16.3147i	−1.60558	−	0.521685i
$979$	−12.0210	+	36.9967i	−0.384191	+	1.18242i
$980$	−17.0627	−	61.1066i	−0.545046	−	1.95198i
$981$	20.1919	+	62.1443i	0.644678	+	1.98411i
$982$			41.1965i			1.31463i
$983$	16.8895	−	5.48773i	0.538691	−	0.175031i	−0.0270198	−	0.999635i	$-0.508602\pi$
$983$	16.8895	−	5.48773i	0.538691	−	0.175031i	0.565711	+	0.824603i	$0.308602\pi$
$984$	−94.2168	−	68.4525i	−3.00352	−	2.18219i
$985$	3.22512	−	0.900542i	0.102761	−	0.0286937i
$986$	−75.1465	+	54.5971i	−2.39315	+	1.73873i
$987$	1.68330	−	2.31687i	0.0535801	−	0.0737467i
$988$	−8.73196	+	12.0185i	−0.277801	+	0.382360i
$989$	16.9326	−	12.3023i	0.538426	−	0.391189i
$990$	−86.2997	−	32.0925i	−2.74278	−	1.01997i
$991$	13.7592	+	9.99661i	0.437074	+	0.317553i	0.784471	−	0.620165i	$-0.212934\pi$
$991$	13.7592	+	9.99661i	0.437074	+	0.317553i	−0.347397	+	0.937718i	$0.612934\pi$
$992$	26.5060	−	8.61232i	0.841567	−	0.273442i
$993$		−	4.96832i		−	0.157665i
$994$	−4.13706	−	12.7326i	−0.131220	−	0.403852i
$995$	9.91820	−	6.58994i	0.314428	−	0.208915i
$996$	36.5835	−	112.592i	1.15919	−	3.56763i
$997$	19.3822	+	6.29767i	0.613842	+	0.199449i	0.599404	−	0.800446i	$-0.295404\pi$
$997$	19.3822	+	6.29767i	0.613842	+	0.199449i	0.0144376	+	0.999896i	$0.495404\pi$
$998$	−59.2028	−	81.4857i	−1.87403	−	2.57939i
$999$	32.8305			1.03871

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.b.39.3	✓	96
25.9	even	10	inner	475.2.n.b.134.3	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.b.39.3	✓	96	1.1	even	1	trivial
475.2.n.b.134.3	yes	96	25.9	even	10	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47440 - 2.02934i) q^{2} +(-2.71260 - 0.881376i) q^{3} +(-1.32633 + 4.08203i) q^{4} +(-1.86244 + 1.23746i) q^{5} +(2.21085 + 6.80430i) q^{6} +0.624081i q^{7} +(5.46813 - 1.77670i) q^{8} +(4.15431 + 3.01828i) q^{9} +O(q^{10})\)	\(q+(-1.47440 - 2.02934i) q^{2} +(-2.71260 - 0.881376i) q^{3} +(-1.32633 + 4.08203i) q^{4} +(-1.86244 + 1.23746i) q^{5} +(2.21085 + 6.80430i) q^{6} +0.624081i q^{7} +(5.46813 - 1.77670i) q^{8} +(4.15431 + 3.01828i) q^{9} +(5.25723 + 1.95502i) q^{10} +(-2.58624 + 1.87901i) q^{11} +(7.19562 - 9.90392i) q^{12} +(2.03442 - 2.80014i) q^{13} +(1.26647 - 0.920148i) q^{14} +(6.14273 - 1.71522i) q^{15} +(-4.72301 - 3.43147i) q^{16} +(-5.08116 + 1.65097i) q^{17} -12.8807i q^{18} +(0.309017 + 0.951057i) q^{19} +(-2.58113 - 9.24384i) q^{20} +(0.550050 - 1.69288i) q^{21} +(7.62633 + 2.47794i) q^{22} +(1.68625 + 2.32092i) q^{23} -16.3988 q^{24} +(1.93739 - 4.60940i) q^{25} -8.68202 q^{26} +(-3.57929 - 4.92648i) q^{27} +(-2.54752 - 0.827739i) q^{28} +(-2.14180 + 6.59179i) q^{29} +(-12.5376 - 9.93678i) q^{30} +(-2.73850 - 8.42823i) q^{31} +3.14491i q^{32} +(8.67155 - 2.81756i) q^{33} +(10.8421 + 7.87722i) q^{34} +(-0.772275 - 1.16231i) q^{35} +(-17.8307 + 12.9548i) q^{36} +(-3.16897 + 4.36171i) q^{37} +(1.47440 - 2.02934i) q^{38} +(-7.98655 + 5.80257i) q^{39} +(-7.98548 + 10.0756i) q^{40} +(5.74535 + 4.17424i) q^{41} +(-4.24643 + 1.37975i) q^{42} -7.29563i q^{43} +(-4.23998 - 13.0493i) q^{44} +(-11.4722 - 0.480586i) q^{45} +(2.22374 - 6.84396i) q^{46} +(1.53014 + 0.497172i) q^{47} +(9.78720 + 13.4709i) q^{48} +6.61052 q^{49} +(-12.2105 + 2.86449i) q^{50} +15.2383 q^{51} +(8.73196 + 12.0185i) q^{52} +(-4.01056 - 1.30311i) q^{53} +(-4.72019 + 14.5272i) q^{54} +(2.49152 - 6.69992i) q^{55} +(1.10881 + 3.41256i) q^{56} -2.85219i q^{57} +(16.5349 - 5.37251i) q^{58} +(-11.1458 - 8.09790i) q^{59} +(-1.14572 + 27.3498i) q^{60} +(5.45839 - 3.96575i) q^{61} +(-13.0661 + 17.9840i) q^{62} +(-1.88365 + 2.59262i) q^{63} +(-3.06392 + 2.22606i) q^{64} +(-0.323931 + 7.73262i) q^{65} +(-18.5032 - 13.4433i) q^{66} +(-6.63488 + 2.15580i) q^{67} -22.9312i q^{68} +(-2.52851 - 7.78195i) q^{69} +(-1.22009 + 3.28093i) q^{70} +(2.64273 - 8.13349i) q^{71} +(28.0789 + 9.12339i) q^{72} +(-2.82435 - 3.88738i) q^{73} +13.5237 q^{74} +(-9.31796 + 10.7959i) q^{75} -4.29211 q^{76} +(-1.17266 - 1.61402i) q^{77} +(23.5508 + 7.65212i) q^{78} +(1.98481 - 6.10861i) q^{79} +(13.0426 + 0.546375i) q^{80} +(0.606690 + 1.86720i) q^{81} -17.8138i q^{82} +(9.19729 - 2.98838i) q^{83} +(6.18084 + 4.49065i) q^{84} +(7.42036 - 9.36256i) q^{85} +(-14.8054 + 10.7567i) q^{86} +(11.6197 - 15.9931i) q^{87} +(-10.8035 + 14.8697i) q^{88} +(9.84471 - 7.15260i) q^{89} +(15.9393 + 23.9896i) q^{90} +(1.74752 + 1.26964i) q^{91} +(-11.7106 + 3.80501i) q^{92} +25.2760i q^{93} +(-1.24711 - 3.83821i) q^{94} +(-1.75242 - 1.38889i) q^{95} +(2.77185 - 8.53087i) q^{96} +(11.9315 + 3.87677i) q^{97} +(-9.74659 - 13.4150i) q^{98} -16.4154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

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