LMFDB - Embedded newform 31.4.g.a.10.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,4,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.82905921018$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			10.1
Character	$\chi$	$=$	31.10
Dual form			31.4.g.a.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.13779 - 3.00628i) q^{2} +(-1.02796 - 9.78042i) q^{3} +(5.61145 + 17.2703i) q^{4} +(-1.20661 - 2.08991i) q^{5} +(-25.1492 + 43.5597i) q^{6} +(9.84945 + 2.09357i) q^{7} +(16.0563 - 49.4162i) q^{8} +(-68.1899 + 14.4942i) q^{9} +(-1.29016 + 12.2750i) q^{10} +(19.7241 - 21.9059i) q^{11} +(163.142 - 72.6355i) q^{12} +(4.56919 + 2.03433i) q^{13} +(-34.4611 - 38.2729i) q^{14} +(-19.1999 + 13.9495i) q^{15} +(-97.4690 + 70.8153i) q^{16} +(-55.2442 - 61.3549i) q^{17} +(325.729 + 145.024i) q^{18} +(-74.0059 + 32.9496i) q^{19} +(29.3225 - 32.5660i) q^{20} +(10.3511 - 98.4838i) q^{21} +(-147.470 + 31.3456i) q^{22} +(4.84835 - 14.9217i) q^{23} +(-499.817 - 106.239i) q^{24} +(59.5882 - 103.210i) q^{25} +(-12.7906 - 22.1539i) q^{26} +(129.804 + 399.496i) q^{27} +(19.1133 + 181.851i) q^{28} +(110.053 + 79.9580i) q^{29} +121.381 q^{30} +(149.648 - 86.0023i) q^{31} +200.523 q^{32} +(-234.524 - 170.392i) q^{33} +(44.1389 + 419.953i) q^{34} +(-7.50910 - 23.1106i) q^{35} +(-632.963 - 1096.32i) q^{36} +(80.6505 - 139.691i) q^{37} +(405.277 + 86.1442i) q^{38} +(15.1997 - 46.7798i) q^{39} +(-122.649 + 26.0699i) q^{40} +(9.01775 - 85.7982i) q^{41} +(-338.901 + 376.387i) q^{42} +(117.051 - 52.1146i) q^{43} +(489.001 + 217.717i) q^{44} +(112.570 + 125.022i) q^{45} +(-64.9202 + 47.1673i) q^{46} +(232.979 - 169.269i) q^{47} +(792.798 + 880.492i) q^{48} +(-220.717 - 98.2697i) q^{49} +(-556.841 + 247.922i) q^{50} +(-543.288 + 603.382i) q^{51} +(-9.49371 + 90.3266i) q^{52} +(-340.216 + 72.3151i) q^{53} +(663.895 - 2043.26i) q^{54} +(-69.5808 - 14.7898i) q^{55} +(261.602 - 453.108i) q^{56} +(398.336 + 689.938i) q^{57} +(-214.999 - 661.699i) q^{58} +(0.969034 + 9.21974i) q^{59} +(-348.651 - 253.310i) q^{60} +454.393 q^{61} +(-877.760 - 94.0249i) q^{62} -701.978 q^{63} +(-49.9685 - 36.3042i) q^{64} +(-1.26166 - 12.0039i) q^{65} +(458.167 + 1410.09i) q^{66} +(127.331 + 220.543i) q^{67} +(749.615 - 1298.37i) q^{68} +(-150.924 - 32.0799i) q^{69} +(-38.4060 + 118.201i) q^{70} +(-501.762 + 106.653i) q^{71} +(-378.629 + 3602.41i) q^{72} +(695.371 - 772.288i) q^{73} +(-753.664 + 335.553i) q^{74} +(-1070.69 - 476.701i) q^{75} +(-984.328 - 1093.21i) q^{76} +(240.133 - 174.467i) q^{77} +(-203.526 + 147.870i) q^{78} +(709.187 + 787.631i) q^{79} +(265.605 + 118.255i) q^{80} +(2054.28 - 914.623i) q^{81} +(-295.247 + 327.905i) q^{82} +(-74.0500 + 704.539i) q^{83} +(1758.93 - 373.871i) q^{84} +(-61.5681 + 189.487i) q^{85} +(-641.005 - 136.250i) q^{86} +(668.893 - 1158.56i) q^{87} +(-765.809 - 1326.42i) q^{88} +(242.074 + 745.027i) q^{89} +(-89.9412 - 855.734i) q^{90} +(40.7450 + 29.6029i) q^{91} +284.908 q^{92} +(-994.972 - 1375.22i) q^{93} -1472.89 q^{94} +(158.158 + 114.909i) q^{95} +(-206.130 - 1961.19i) q^{96} +(129.563 + 398.755i) q^{97} +(617.856 + 1070.16i) q^{98} +(-1027.48 + 1779.64i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) $ 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{15}\right)$

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 $

$2$	−4.13779	−	3.00628i	−1.46293	−	1.06288i	−0.982588	−	0.185800i	$-0.940512\pi$
$2$	−4.13779	−	3.00628i	−1.46293	−	1.06288i	−0.480342	−	0.877081i	$-0.659488\pi$
$3$	−1.02796	−	9.78042i	−0.197832	−	1.88224i	−0.420419	−	0.907330i	$-0.638117\pi$
$3$	−1.02796	−	9.78042i	−0.197832	−	1.88224i	0.222588	−	0.974913i	$-0.428550\pi$
$4$	5.61145	+	17.2703i	0.701431	+	2.15878i
$5$	−1.20661	−	2.08991i	−0.107923	−	0.186928i	0.807006	−	0.590543i	$-0.201087\pi$
$5$	−1.20661	−	2.08991i	−0.107923	−	0.186928i	−0.914929	+	0.403616i	$0.867753\pi$
$6$	−25.1492	+	43.5597i	−1.71119	+	2.96386i
$7$	9.84945	+	2.09357i	0.531820	+	0.113042i	0.465992	−	0.884789i	$-0.345698\pi$
$7$	9.84945	+	2.09357i	0.531820	+	0.113042i	0.0658285	+	0.997831i	$0.479031\pi$
$8$	16.0563	−	49.4162i	0.709595	−	2.18391i
$9$	−68.1899	+	14.4942i	−2.52555	+	0.536823i
$10$	−1.29016	+	12.2750i	−0.0407984	+	0.388171i
$11$	19.7241	−	21.9059i	0.540641	−	0.600443i	−0.409482	−	0.912318i	$-0.634291\pi$
$11$	19.7241	−	21.9059i	0.540641	−	0.600443i	0.950123	+	0.311876i	$0.100957\pi$
$12$	163.142	−	72.6355i	3.92459	−	1.74734i
$13$	4.56919	+	2.03433i	0.0974819	+	0.0434017i	0.454898	−	0.890543i	$-0.349676\pi$
$13$	4.56919	+	2.03433i	0.0974819	+	0.0434017i	−0.357416	+	0.933945i	$0.616342\pi$
$14$	−34.4611	−	38.2729i	−0.657866	−	0.730634i
$15$	−19.1999	+	13.9495i	−0.330493	+	0.240117i
$16$	−97.4690	+	70.8153i	−1.52295	+	1.10649i
$17$	−55.2442	−	61.3549i	−0.788158	−	0.875338i	0.206512	−	0.978444i	$-0.433789\pi$
$17$	−55.2442	−	61.3549i	−0.788158	−	0.875338i	−0.994670	+	0.103106i	$0.967122\pi$
$18$	325.729	+	145.024i	4.26528	+	1.89903i
$19$	−74.0059	+	32.9496i	−0.893585	+	0.397850i	−0.801565	−	0.597907i	$-0.795999\pi$
$19$	−74.0059	+	32.9496i	−0.893585	+	0.397850i	−0.0920201	+	0.995757i	$0.529332\pi$
$20$	29.3225	−	32.5660i	0.327836	−	0.364099i
$21$	10.3511	−	98.4838i	0.107561	−	1.02338i
$22$	−147.470	+	31.3456i	−1.42912	+	0.303769i
$23$	4.84835	−	14.9217i	0.0439544	−	0.135278i	−0.926671	−	0.375873i	$-0.877343\pi$
$23$	4.84835	−	14.9217i	0.0439544	−	0.135278i	0.970625	+	0.240596i	$0.0773428\pi$
$24$	−499.817	−	106.239i	−4.25103	−	0.903584i
$25$	59.5882	−	103.210i	0.476705	−	0.825678i
$26$	−12.7906	−	22.1539i	−0.0964783	−	0.167105i
$27$	129.804	+	399.496i	0.925216	+	2.84752i
$28$	19.1133	+	181.851i	0.129002	+	1.22738i
$29$	110.053	+	79.9580i	0.704699	+	0.511994i	0.881459	−	0.472260i	$-0.156562\pi$
$29$	110.053	+	79.9580i	0.704699	+	0.511994i	−0.176760	+	0.984254i	$0.556562\pi$
$30$	121.381			0.738703
$31$	149.648	−	86.0023i	0.867020	−	0.498273i
$31$	149.648	−	86.0023i	0.867020	−	0.498273i
$32$	200.523			1.10774
$33$	−234.524	−	170.392i	−1.23713	−	0.898831i
$34$	44.1389	+	419.953i	0.222640	+	2.11828i
$35$	−7.50910	−	23.1106i	−0.0362648	−	0.111612i
$36$	−632.963	−	1096.32i	−2.93038	−	5.07558i
$37$	80.6505	−	139.691i	0.358348	−	0.620676i	−0.629337	−	0.777132i	$-0.716674\pi$
$37$	80.6505	−	139.691i	0.358348	−	0.620676i	0.987685	+	0.156456i	$0.0500070\pi$
$38$	405.277	+	86.1442i	1.73012	+	0.367748i
$39$	15.1997	−	46.7798i	0.0624076	−	0.192071i
$40$	−122.649	+	26.0699i	−0.484814	+	0.103050i
$41$	9.01775	−	85.7982i	0.0343497	−	0.326815i	−0.963831	−	0.266515i	$-0.914128\pi$
$41$	9.01775	−	85.7982i	0.0343497	−	0.326815i	0.998180	−	0.0602998i	$-0.0192057\pi$
$42$	−338.901	+	376.387i	−1.24508	+	1.38281i
$43$	117.051	−	52.1146i	0.415120	−	0.184823i	−0.188539	−	0.982066i	$-0.560375\pi$
$43$	117.051	−	52.1146i	0.415120	−	0.184823i	0.603659	+	0.797242i	$0.293709\pi$
$44$	489.001	+	217.717i	1.67545	+	0.745957i
$45$	112.570	+	125.022i	0.372911	+	0.414160i
$46$	−64.9202	+	47.1673i	−0.208086	+	0.151183i
$47$	232.979	−	169.269i	0.723052	−	0.525328i	−0.164306	−	0.986409i	$-0.552538\pi$
$47$	232.979	−	169.269i	0.723052	−	0.525328i	0.887358	+	0.461082i	$0.152538\pi$
$48$	792.798	+	880.492i	2.38397	+	2.64767i
$49$	−220.717	−	98.2697i	−0.643491	−	0.286501i
$50$	−556.841	+	247.922i	−1.57498	+	0.701228i
$51$	−543.288	+	603.382i	−1.49168	+	1.65667i
$52$	−9.49371	+	90.3266i	−0.0253181	+	0.240886i
$53$	−340.216	+	72.3151i	−0.881740	+	0.187420i	−0.626466	−	0.779449i	$-0.715499\pi$
$53$	−340.216	+	72.3151i	−0.881740	+	0.187420i	−0.255274	+	0.966869i	$0.582166\pi$
$54$	663.895	−	2043.26i	1.67305	−	5.14912i
$55$	−69.5808	−	14.7898i	−0.170587	−	0.0362593i
$56$	261.602	−	453.108i	0.624250	−	1.08123i
$57$	398.336	+	689.938i	0.925629	+	1.60324i
$58$	−214.999	−	661.699i	−0.486737	−	1.49802i
$59$	0.969034	+	9.21974i	0.00213826	+	0.0203442i	0.995539	−	0.0943509i	$-0.0300776\pi$
$59$	0.969034	+	9.21974i	0.00213826	+	0.0203442i	−0.993401	+	0.114695i	$0.963411\pi$
$60$	−348.651	−	253.310i	−0.750178	−	0.545036i
$61$	454.393			0.953756			0.476878	−	0.878970i	$-0.341768\pi$
$61$	454.393			0.953756			0.476878	+	0.878970i	$0.341768\pi$
$62$	−877.760	−	94.0249i	−1.79799	−	0.192600i
$63$	−701.978			−1.40382
$64$	−49.9685	−	36.3042i	−0.0975947	−	0.0709067i
$65$	−1.26166	−	12.0039i	−0.00240753	−	0.0229061i
$66$	458.167	+	1410.09i	0.854491	+	2.62985i
$67$	127.331	+	220.543i	0.232178	+	0.402144i	0.958449	−	0.285265i	$-0.0920816\pi$
$67$	127.331	+	220.543i	0.232178	+	0.402144i	−0.726271	+	0.687408i	$0.758748\pi$
$68$	749.615	−	1298.37i	1.33683	−	2.31545i
$69$	−150.924	−	32.0799i	−0.263321	−	0.0559706i
$70$	−38.4060	+	118.201i	−0.0655770	+	0.201825i
$71$	−501.762	+	106.653i	−0.838706	+	0.178273i	−0.607188	−	0.794558i	$-0.707703\pi$
$71$	−501.762	+	106.653i	−0.838706	+	0.178273i	−0.231518	+	0.972831i	$0.574369\pi$
$72$	−378.629	+	3602.41i	−0.619747	+	5.89650i
$73$	695.371	−	772.288i	1.11489	−	1.23821i	0.146383	−	0.989228i	$-0.453237\pi$
$73$	695.371	−	772.288i	1.11489	−	1.23821i	0.968508	−	0.248984i	$-0.0800966\pi$
$74$	−753.664	+	335.553i	−1.18394	+	0.527125i
$75$	−1070.69	−	476.701i	−1.64843	−	0.733930i
$76$	−984.328	−	1093.21i	−1.48566	−	1.64999i
$77$	240.133	−	174.467i	0.355399	−	0.258212i
$78$	−203.526	+	147.870i	−0.295446	+	0.214654i
$79$	709.187	+	787.631i	1.01000	+	1.12171i	0.992546	+	0.121867i	$0.0388881\pi$
$79$	709.187	+	787.631i	1.01000	+	1.12171i	0.0174500	+	0.999848i	$0.494445\pi$
$80$	265.605	+	118.255i	0.371195	+	0.165266i
$81$	2054.28	−	914.623i	2.81794	−	1.25463i
$82$	−295.247	+	327.905i	−0.397617	+	0.441598i
$83$	−74.0500	+	704.539i	−0.0979283	+	0.931725i	0.829697	+	0.558214i	$0.188513\pi$
$83$	−74.0500	+	704.539i	−0.0979283	+	0.931725i	−0.927626	+	0.373512i	$0.878154\pi$
$84$	1758.93	−	373.871i	2.28470	−	0.485628i
$85$	−61.5681	+	189.487i	−0.0785647	+	0.241797i
$86$	−641.005	−	136.250i	−0.803737	−	0.170840i
$87$	668.893	−	1158.56i	0.824285	−	1.42770i
$88$	−765.809	−	1326.42i	−0.927676	−	1.60678i
$89$	242.074	+	745.027i	0.288312	+	0.887334i	0.985386	+	0.170335i	$0.0544850\pi$
$89$	242.074	+	745.027i	0.288312	+	0.887334i	−0.697074	+	0.716999i	$0.745515\pi$
$90$	−89.9412	−	855.734i	−0.105340	−	1.00225i
$91$	40.7450	+	29.6029i	0.0469366	+	0.0341014i
$92$	284.908			0.322866
$93$	−994.972	−	1375.22i	−1.10940	−	1.53337i
$94$	−1472.89			−1.61613
$95$	158.158	+	114.909i	0.170807	+	0.124099i
$96$	−206.130	−	1961.19i	−0.219146	−	2.08504i
$97$	129.563	+	398.755i	0.135620	+	0.417396i	0.995686	−	0.0927870i	$-0.0295776\pi$
$97$	129.563	+	398.755i	0.135620	+	0.417396i	−0.860066	+	0.510183i	$0.829578\pi$
$98$	617.856	+	1070.16i	0.636866	+	1.10308i
$99$	−1027.48	+	1779.64i	−1.04309	+	1.80668i
$100$	2116.84	+	449.947i	2.11684	+	0.449947i
$101$	171.938	−	529.170i	0.169391	−	0.521330i	−0.829942	−	0.557849i	$-0.811627\pi$
$101$	171.938	−	529.170i	0.169391	−	0.521330i	0.999333	+	0.0365186i	$0.0116268\pi$
$102$	4061.95	−	863.393i	3.94306	−	0.838124i
$103$	212.605	−	2022.81i	0.203385	−	1.93508i	−0.128400	−	0.991722i	$-0.540984\pi$
$103$	212.605	−	2022.81i	0.203385	−	1.93508i	0.331785	−	0.943355i	$-0.392349\pi$
$104$	173.893	−	193.128i	0.163958	−	0.182094i
$105$	−218.313	+	97.1990i	−0.202906	+	0.0903395i
$106$	1625.14	+	723.559i	1.48913	+	0.663003i
$107$	924.439	+	1026.69i	0.835223	+	0.927609i	0.998257	−	0.0590111i	$-0.0187947\pi$
$107$	924.439	+	1026.69i	0.835223	+	0.927609i	−0.163034	+	0.986620i	$0.552128\pi$
$108$	−6171.02	+	4483.51i	−5.49821	+	3.99468i
$109$	−1201.36	+	872.838i	−1.05568	+	0.766997i	−0.973285	−	0.229602i	$-0.926258\pi$
$109$	−1201.36	+	872.838i	−1.05568	+	0.766997i	−0.0823969	+	0.996600i	$0.526258\pi$
$110$	243.448	+	270.377i	0.211017	+	0.234358i
$111$	−1449.14	−	645.199i	−1.23916	−	0.551708i
$112$	−1108.27	+	493.434i	−0.935017	+	0.416296i
$113$	−138.155	+	153.437i	−0.115014	+	0.127736i	−0.797902	−	0.602787i	$-0.794057\pi$
$113$	−138.155	+	153.437i	−0.115014	+	0.127736i	0.682888	+	0.730523i	$0.260724\pi$
$114$	425.917	−	4052.33i	0.349919	−	3.32926i
$115$	−37.0351	+	7.87205i	−0.0300308	+	0.00638324i
$116$	−763.341	+	2349.32i	−0.610986	+	1.88042i
$117$	−341.058	−	72.4942i	−0.269495	−	0.0572828i
$118$	23.7075	−	41.0626i	0.0184953	−	0.0320349i
$119$	−415.674	−	719.969i	−0.320209	−	0.554617i
$120$	381.054	+	1172.76i	0.289878	+	0.892152i
$121$	48.3017	+	459.560i	0.0362898	+	0.345274i
$122$	−1880.18	−	1366.03i	−1.39528	−	1.01373i
$123$	−848.412			−0.621941
$124$	2325.03	+	2101.87i	1.68382	+	1.52220i
$125$	−589.252			−0.421635
$126$	2904.64	+	2110.34i	2.05369	+	1.49210i
$127$	94.5784	+	899.854i	0.0660825	+	0.628733i	0.976571	+	0.215198i	$0.0690396\pi$
$127$	94.5784	+	899.854i	0.0660825	+	0.628733i	−0.910488	+	0.413535i	$0.864294\pi$
$128$	−398.100	−	1225.23i	−0.274902	−	0.846061i
$129$	−630.027	−	1091.24i	−0.430006	−	0.744793i
$130$	−30.8665	+	53.4623i	−0.0208244	+	0.0360689i
$131$	2000.20	+	425.156i	1.33403	+	0.283557i	0.819089	−	0.573666i	$-0.194479\pi$
$131$	2000.20	+	425.156i	1.33403	+	0.283557i	0.514944	+	0.857224i	$0.327813\pi$
$132$	1626.69	−	5006.44i	1.07262	−	3.30117i
$133$	−797.900	+	169.599i	−0.520201	+	0.110572i
$134$	136.147	−	1295.35i	0.0877710	−	0.835085i
$135$	678.289	−	753.317i	0.432429	−	0.480261i
$136$	−3918.95	+	1744.83i	−2.47093	+	1.10013i
$137$	−2200.25	−	979.614i	−1.37212	−	0.610905i	−0.417482	−	0.908685i	$-0.637087\pi$
$137$	−2200.25	−	979.614i	−1.37212	−	0.610905i	−0.954635	+	0.297780i	$0.903754\pi$
$138$	528.051	+	586.461i	0.325730	+	0.361760i
$139$	675.225	−	490.580i	0.412028	−	0.299356i	−0.362394	−	0.932025i	$-0.618041\pi$
$139$	675.225	−	490.580i	0.412028	−	0.299356i	0.774422	+	0.632669i	$0.218041\pi$
$140$	356.990	−	259.368i	0.215508	−	0.156576i
$141$	−1895.01	−	2104.63i	−1.13184	−	1.25703i
$142$	2396.81	+	1067.13i	1.41645	+	0.630644i
$143$	134.687	−	59.9665i	0.0787629	−	0.0350675i
$144$	5619.99	−	6241.63i	3.25231	−	3.61205i
$145$	34.3143	−	326.479i	0.0196528	−	0.186984i
$146$	−5199.01	+	1105.08i	−2.94708	+	0.626421i
$147$	−734.230	+	2259.73i	−0.411961	+	1.26789i
$148$	2865.06	+	608.988i	1.59126	+	0.338233i
$149$	434.406	−	752.413i	0.238845	−	0.413692i	−0.721538	−	0.692375i	$-0.756565\pi$
$149$	434.406	−	752.413i	0.238845	−	0.413692i	0.960383	+	0.278683i	$0.0898979\pi$
$150$	2997.19	+	5191.28i	1.63146	+	2.82578i
$151$	74.3459	+	228.813i	0.0400674	+	0.123315i	0.969089	−	0.246709i	$-0.0793493\pi$
$151$	74.3459	+	228.813i	0.0400674	+	0.123315i	−0.929022	+	0.370024i	$0.879349\pi$
$152$	439.981	+	4186.14i	0.234784	+	2.23382i
$153$	4656.39	+	3383.06i	2.46044	+	1.78761i
$154$	−1518.12			−0.794373
$155$	−360.305	−	208.980i	−0.186712	−	0.108295i
$156$	893.191			0.458414
$157$	−658.959	−	478.761i	−0.334972	−	0.243371i	0.407565	−	0.913176i	$-0.366378\pi$
$157$	−658.959	−	478.761i	−0.334972	−	0.243371i	−0.742537	+	0.669805i	$0.766378\pi$
$158$	−566.624	−	5391.07i	−0.285305	−	2.71450i
$159$	1057.00	+	3253.11i	0.527205	+	1.62257i
$160$	−241.953	−	419.075i	−0.119550	−	0.207067i
$161$	78.9931	−	136.820i	0.0386679	−	0.0669747i
$162$	−11249.8	−	2391.21i	−5.45596	−	1.15970i
$163$	−320.657	+	986.880i	−0.154084	+	0.474223i	−0.998067	−	0.0621475i	$-0.980205\pi$
$163$	−320.657	+	986.880i	−0.154084	+	0.474223i	0.843983	+	0.536371i	$0.180205\pi$
$164$	1532.36	−	325.713i	0.729617	−	0.155085i
$165$	−73.1244	+	695.733i	−0.0345014	+	0.328259i
$166$	2424.45	−	2692.62i	1.13357	−	1.25896i
$167$	−336.886	+	149.991i	−0.156102	+	0.0695011i	−0.483300	−	0.875455i	$-0.660562\pi$
$167$	−336.886	+	149.991i	−0.156102	+	0.0695011i	0.327198	+	0.944956i	$0.393895\pi$
$168$	−4700.50	−	2092.80i	−2.15864	−	0.961088i
$169$	−1453.34	−	1614.10i	−0.661512	−	0.734683i
$170$	824.408	−	598.967i	0.371936	−	0.270228i
$171$	4568.88	−	3319.48i	2.04322	−	1.48449i
$172$	1556.86	+	1729.07i	0.690172	+	0.766513i
$173$	3896.72	+	1734.93i	1.71250	+	0.762453i	0.998027	+	0.0627858i	$0.0199985\pi$
$173$	3896.72	+	1734.93i	1.71250	+	0.762453i	0.714469	+	0.699667i	$0.246668\pi$
$174$	−6250.68	+	2782.98i	−2.72335	+	1.21251i
$175$	802.987	−	891.807i	0.346858	−	0.385225i
$176$	−371.219	+	3531.91i	−0.158987	+	1.51266i
$177$	89.1768	−	18.9551i	0.0378697	−	0.00804946i
$178$	1238.11	−	3810.51i	0.521350	−	1.60455i
$179$	3526.22	+	749.521i	1.47241	+	0.312971i	0.873099	−	0.487542i	$-0.162106\pi$
$179$	3526.22	+	749.521i	1.47241	+	0.312971i	0.599315	+	0.800513i	$0.295440\pi$
$180$	−1527.48	+	2645.68i	−0.632510	+	1.09554i
$181$	−1120.25	−	1940.33i	−0.460043	−	0.796817i	0.538920	−	0.842357i	$-0.318833\pi$
$181$	−1120.25	−	1940.33i	−0.460043	−	0.796817i	−0.998963	+	0.0455399i	$0.985499\pi$
$182$	−79.5993	−	244.982i	−0.0324192	−	0.0997760i
$183$	−467.100	−	4444.16i	−0.188683	−	1.79520i
$184$	−659.527	−	479.174i	−0.264244	−	0.191985i
$185$	−389.256			−0.154695
$186$	−17.2978	+	8681.52i	−0.00681901	+	3.42236i
$187$	−2433.68			−0.951701
$188$	4230.67	+	3073.76i	1.64124	+	1.19243i
$189$	442.128	+	4206.57i	0.170159	+	1.61896i
$190$	−308.978	−	950.936i	−0.117977	−	0.363096i
$191$	−581.143	−	1006.57i	−0.220157	−	0.381324i	0.734698	−	0.678394i	$-0.237324\pi$
$191$	−581.143	−	1006.57i	−0.220157	−	0.381324i	−0.954856	+	0.297070i	$0.903990\pi$
$192$	−303.705	+	526.032i	−0.114156	+	0.197725i
$193$	−688.526	−	146.351i	−0.256794	−	0.0545832i	0.0777158	−	0.996976i	$-0.475237\pi$
$193$	−688.526	−	146.351i	−0.256794	−	0.0545832i	−0.334510	+	0.942392i	$0.608571\pi$
$194$	662.663	−	2039.47i	0.245239	−	0.754770i
$195$	−116.106	+	24.6791i	−0.0426385	+	0.00906310i
$196$	458.600	−	4363.29i	0.167128	−	1.59012i
$197$	−3126.64	+	3472.49i	−1.13078	+	1.25586i	−0.167939	+	0.985797i	$0.553711\pi$
$197$	−3126.64	+	3472.49i	−1.13078	+	1.25586i	−0.962843	+	0.270063i	$0.912955\pi$
$198$	9601.60	−	4274.91i	3.44624	−	1.53437i
$199$	2262.77	+	1007.45i	0.806047	+	0.358875i	0.768040	−	0.640402i	$-0.221232\pi$
$199$	2262.77	+	1007.45i	0.806047	+	0.358875i	0.0380071	+	0.999277i	$0.487899\pi$
$200$	−4143.47	−	4601.79i	−1.46494	−	1.62698i
$201$	2026.11	−	1472.06i	0.711000	−	0.516571i
$202$	−2302.28	+	1672.70i	−0.801919	+	0.582628i
$203$	916.562	+	1017.94i	0.316897	+	0.351949i
$204$	−13469.2	−	5996.87i	−4.62271	−	2.05816i
$205$	−190.192	+	84.6788i	−0.0647979	+	0.0288499i
$206$	−6960.84	+	7730.79i	−2.35429	+	2.61471i
$207$	−114.330	+	1087.78i	−0.0383889	+	0.365246i
$208$	−589.416	+	125.284i	−0.196484	+	0.0417639i
$209$	−737.914	+	2271.07i	−0.244223	+	0.751641i
$210$	1195.54	+	254.120i	0.392857	+	0.0835044i
$211$	−904.644	+	1566.89i	−0.295157	+	0.511228i	−0.975022	−	0.222110i	$-0.928705\pi$
$211$	−904.644	+	1566.89i	−0.295157	+	0.511228i	0.679864	+	0.733338i	$0.262039\pi$
$212$	−3158.00	−	5469.82i	−1.02308	−	1.77202i
$213$	1558.90	+	4797.80i	0.501475	+	1.54338i
$214$	−738.606	−	7027.37i	−0.235935	−	2.24477i
$215$	−250.151	−	181.745i	−0.0793495	−	0.0576508i
$216$	21825.8			6.87526
$217$	1654.00	−	533.777i	0.517425	−	0.166982i
$218$	7594.97			2.35961
$219$	−8268.12	−	6007.14i	−2.55118	−	1.85354i
$220$	−135.024	−	1284.67i	−0.0413788	−	0.393693i
$221$	−127.605	−	392.727i	−0.0388399	−	0.119537i
$222$	4056.59	+	7026.22i	1.22640	+	2.12418i
$223$	−516.164	+	894.022i	−0.155000	+	0.268467i	−0.933059	−	0.359724i	$-0.882871\pi$
$223$	−516.164	+	894.022i	−0.155000	+	0.268467i	0.778059	+	0.628191i	$0.216204\pi$
$224$	1975.04	+	419.807i	0.589119	+	0.125221i
$225$	−2567.37	+	7901.55i	−0.760702	+	2.34120i
$226$	1032.93	−	219.557i	0.304025	−	0.0646226i
$227$	132.179	−	1257.60i	0.0386477	−	0.367709i	−0.958056	−	0.286581i	$-0.907481\pi$
$227$	132.179	−	1257.60i	0.0386477	−	0.367709i	0.996704	−	0.0811276i	$-0.0258521\pi$
$228$	−9680.17	+	10750.9i	−2.81178	+	3.12279i
$229$	−4056.70	+	1806.16i	−1.17063	+	0.521198i	−0.897602	−	0.440807i	$-0.854692\pi$
$229$	−4056.70	+	1806.16i	−1.17063	+	0.521198i	−0.273029	+	0.962006i	$0.588026\pi$
$230$	176.909	+	78.7650i	0.0507176	+	0.0225809i
$231$	−1953.21	−	2169.26i	−0.556328	−	0.617864i
$232$	5718.26	−	4154.56i	1.61820	−	1.17569i
$233$	2791.93	−	2028.46i	0.785003	−	0.570338i	−0.121474	−	0.992595i	$-0.538762\pi$
$233$	2791.93	−	2028.46i	0.785003	−	0.570338i	0.906476	+	0.422257i	$0.138762\pi$
$234$	1193.29	+	1325.28i	0.333367	+	0.370241i
$235$	−634.872	−	282.663i	−0.176232	−	0.0784635i
$236$	−153.790	+	68.4716i	−0.0424189	+	0.0188861i
$237$	6974.35	−	7745.80i	1.91153	−	2.12297i
$238$	−444.456	+	4228.72i	−0.121050	+	1.15171i
$239$	3983.77	−	846.777i	1.07820	−	0.229178i	0.365614	−	0.930767i	$-0.380859\pi$
$239$	3983.77	−	846.777i	1.07820	−	0.229178i	0.712582	+	0.701589i	$0.247526\pi$
$240$	883.552	−	2719.29i	0.237638	−	0.731373i
$241$	−5627.36	−	1196.13i	−1.50411	−	0.319708i	−0.619111	−	0.785303i	$-0.712507\pi$
$241$	−5627.36	−	1196.13i	−1.50411	−	0.319708i	−0.884998	+	0.465595i	$0.845840\pi$
$242$	1181.70	−	2046.77i	0.313896	−	0.543684i
$243$	−5386.37	−	9329.47i	−1.42196	−	2.46290i
$244$	2549.81	+	7847.50i	0.668994	+	2.05895i
$245$	60.9451	+	579.854i	0.0158924	+	0.151206i
$246$	3510.55	+	2550.57i	0.909856	+	0.661049i
$247$	−405.177			−0.104376
$248$	−1847.11	−	8775.93i	−0.472951	−	2.24707i
$249$	6966.81			1.77311
$250$	2438.20	+	1771.46i	0.616822	+	0.448147i
$251$	−211.379	−	2011.14i	−0.0531559	−	0.505744i	−0.988414	−	0.151779i	$-0.951500\pi$
$251$	−211.379	−	2011.14i	−0.0531559	−	0.505744i	0.935259	−	0.353965i	$-0.115167\pi$
$252$	−3939.11	−	12123.3i	−0.984685	−	3.03055i
$253$	−231.243	−	400.524i	−0.0574629	−	0.0995287i
$254$	2313.87	−	4007.73i	0.571594	−	0.990030i
$255$	1916.55	+	407.376i	0.470664	+	0.100043i
$256$	−2188.81	+	6736.47i	−0.534378	+	1.64465i
$257$	−1938.68	+	412.079i	−0.470551	+	0.100019i	−0.437083	−	0.899421i	$-0.643988\pi$
$257$	−1938.68	+	412.079i	−0.470551	+	0.100019i	−0.0334676	+	0.999440i	$0.510655\pi$
$258$	−673.651	+	6409.36i	−0.162557	+	1.54662i
$259$	1086.81	−	1207.03i	0.260739	−	0.289580i
$260$	200.230	−	89.1482i	0.0477606	−	0.0212644i
$261$	−8663.41	−	3857.20i	−2.05460	−	0.914769i
$262$	−6998.27	−	7772.37i	−1.65021	−	1.83274i
$263$	−2132.70	+	1549.50i	−0.500031	+	0.363294i	−0.809029	−	0.587769i	$-0.800006\pi$
$263$	−2132.70	+	1549.50i	−0.500031	+	0.363294i	0.308998	+	0.951063i	$0.400006\pi$
$264$	−12185.7	+	8853.44i	−2.84083	+	2.06398i
$265$	561.641	+	623.765i	0.130194	+	0.144595i
$266$	3811.40	+	1696.95i	0.878542	+	0.391152i
$267$	7037.84	−	3133.45i	1.61314	−	0.718217i
$268$	−3094.33	+	3436.60i	−0.705284	+	0.783297i
$269$	−380.815	+	3623.22i	−0.0863150	+	0.821232i	0.862640	+	0.505819i	$0.168810\pi$
$269$	−380.815	+	3623.22i	−0.0863150	+	0.821232i	−0.948955	+	0.315413i	$0.897857\pi$
$270$	−5071.30	+	1077.94i	−1.14307	+	0.242968i
$271$	−1617.94	+	4979.50i	−0.362667	+	1.11617i	0.588762	+	0.808306i	$0.299615\pi$
$271$	−1617.94	+	4979.50i	−0.362667	+	1.11617i	−0.951429	+	0.307868i	$0.900385\pi$
$272$	9729.46	+	2068.06i	2.16888	+	0.461010i
$273$	247.645	−	428.933i	0.0549016	−	0.0950924i
$274$	6159.17	+	10668.0i	1.35799	+	2.35211i
$275$	−1085.57	−	3341.05i	−0.238046	−	0.732629i
$276$	−292.875	−	2786.52i	−0.0638731	−	0.607712i
$277$	−1118.32	−	812.510i	−0.242576	−	0.176242i	0.459854	−	0.887994i	$-0.347902\pi$
$277$	−1118.32	−	812.510i	−0.242576	−	0.176242i	−0.702430	+	0.711753i	$0.747902\pi$
$278$	−4268.76			−0.920947
$279$	−8957.96	+	8033.52i	−1.92222	+	1.72385i
$280$	−1262.61			−0.269483
$281$	7044.82	+	5118.36i	1.49558	+	1.08660i	0.972100	+	0.234567i	$0.0753673\pi$
$281$	7044.82	+	5118.36i	1.49558	+	1.08660i	0.523482	+	0.852037i	$0.324633\pi$
$282$	1514.07	+	14405.4i	0.319723	+	3.04196i
$283$	1268.63	+	3904.45i	0.266475	+	0.820126i	0.991350	+	0.131245i	$0.0418975\pi$
$283$	1268.63	+	3904.45i	0.266475	+	0.820126i	−0.724875	+	0.688880i	$0.758102\pi$
$284$	−4657.53	−	8067.08i	−0.973146	−	1.68554i
$285$	961.274	−	1664.98i	0.199793	−	0.346051i
$286$	−737.583	−	156.778i	−0.152497	−	0.0324143i
$287$	268.444	−	826.186i	0.0552117	−	0.169924i
$288$	−13673.6	+	2906.42i	−2.79766	+	0.594660i
$289$	−198.954	+	1892.92i	−0.0404954	+	0.385288i
$290$	−1123.47	+	1247.74i	−0.227492	+	0.252655i
$291$	3766.80	−	1677.09i	0.758811	−	0.337844i
$292$	17239.7	+	7675.59i	3.45505	+	1.53829i
$293$	−766.831	−	851.652i	−0.152897	−	0.169809i	0.661830	−	0.749654i	$-0.269780\pi$
$293$	−766.831	−	851.652i	−0.152897	−	0.169809i	−0.814727	+	0.579845i	$0.803113\pi$
$294$	9831.46	−	7142.98i	1.95028	−	1.41696i
$295$	18.0992	−	13.1499i	0.00357213	−	0.00259530i
$296$	−5608.04	−	6228.36i	−1.10122	−	1.22303i
$297$	11311.6	+	5036.24i	2.20998	+	0.983948i
$298$	−4059.44	+	1807.38i	−0.789119	+	0.351338i
$299$	52.5087	−	58.3168i	0.0101560	−	0.0112794i
$300$	2224.64	−	21166.1i	0.428133	−	4.07341i
$301$	1262.00	−	268.246i	0.241662	−	0.0513669i
$302$	380.249	−	1170.29i	0.0724532	−	0.222988i
$303$	−5352.25	−	1137.66i	−1.01478	−	0.215698i
$304$	4879.95	−	8452.31i	0.920671	−	1.59465i
$305$	−548.277	−	949.643i	−0.102932	−	0.178283i
$306$	−9096.72	−	27996.8i	−1.69943	−	5.23030i
$307$	−535.737	−	5097.20i	−0.0995966	−	0.947598i	−0.924206	−	0.381895i	$-0.875272\pi$
$307$	−535.737	−	5097.20i	−0.0995966	−	0.947598i	0.824609	−	0.565703i	$-0.191395\pi$
$308$	4360.59	+	3168.15i	0.806713	+	0.586111i
$309$	−20002.4			−3.68252
$310$	862.612	+	1947.90i	0.158042	+	0.356881i
$311$	7402.52			1.34971			0.674853	−	0.737952i	$-0.264207\pi$
$311$	7402.52			1.34971			0.674853	+	0.737952i	$0.264207\pi$
$312$	−2067.63	−	1502.22i	−0.375181	−	0.272585i
$313$	−289.166	−	2751.23i	−0.0522192	−	0.496832i	−0.989107	−	0.147201i	$-0.952974\pi$
$313$	−289.166	−	2751.23i	−0.0522192	−	0.496832i	0.936887	−	0.349631i	$-0.113693\pi$
$314$	1287.34	+	3962.03i	0.231366	+	0.712071i
$315$	847.015	+	1467.07i	0.151504	+	0.262413i
$316$	−9623.04	+	16667.6i	−1.71310	+	2.96717i
$317$	−9141.24	−	1943.03i	−1.61963	−	0.344263i	−0.693206	−	0.720740i	$-0.743802\pi$
$317$	−9141.24	−	1943.03i	−1.61963	−	0.344263i	−0.926426	+	0.376476i	$0.877136\pi$
$318$	5406.13	−	16638.3i	0.953335	−	2.93406i
$319$	3922.24	−	833.699i	0.688412	−	0.146327i
$320$	−15.5801	+	148.235i	−0.00272174	+	0.0258956i
$321$	9091.20	−	10096.8i	1.58075	−	1.75560i
$322$	−738.176	+	328.657i	−0.127754	+	0.0568800i
$323$	6110.01	+	2720.35i	1.05254	+	0.468621i
$324$	27323.3	+	30345.5i	4.68506	+	5.20328i
$325$	482.232	−	350.362i	0.0823060	−	0.0597988i
$326$	4293.65	−	3119.52i	0.729457	−	0.529982i
$327$	9771.67	+	10852.5i	1.65252	+	1.83531i
$328$	−4095.03	−	1823.23i	−0.689361	−	0.306923i
$329$	2649.09	−	1179.45i	0.443917	−	0.197645i
$330$	2394.14	−	2658.96i	0.399373	−	0.443549i
$331$	−178.507	+	1698.38i	−0.0296424	+	0.282029i	0.969653	+	0.244487i	$0.0786195\pi$
$331$	−178.507	+	1698.38i	−0.0296424	+	0.282029i	−0.999295	+	0.0375421i	$0.988047\pi$
$332$	−12583.1	+	2674.62i	−2.08008	+	0.442135i
$333$	−3474.84	+	10694.5i	−0.571832	+	1.75992i
$334$	1844.88	+	392.141i	0.302238	+	0.0642426i
$335$	307.277	−	532.220i	0.0501145	−	0.0868008i
$336$	5965.26	+	10332.1i	0.968546	+	1.67757i
$337$	70.3471	+	216.506i	0.0113711	+	0.0349966i	0.956581	−	0.291466i	$-0.0941432\pi$
$337$	70.3471	+	216.506i	0.0113711	+	0.0349966i	−0.945210	+	0.326463i	$0.894143\pi$
$338$	1161.19	+	11048.0i	0.186865	+	1.77790i
$339$	1642.70	+	1193.49i	0.263183	+	0.191214i
$340$	−3617.98			−0.577096
$341$	1067.73	−	4974.50i	0.169562	−	0.789983i
$342$	−28884.4			−4.56692
$343$	−4762.42	−	3460.10i	−0.749699	−	0.544688i
$344$	−695.896	−	6621.00i	−0.109070	−	1.03773i
$345$	115.063	+	354.127i	0.0179559	+	0.0552624i
$346$	−10908.1	−	18893.4i	−1.69487	−	2.93559i
$347$	1607.03	−	2783.46i	0.248617	−	0.430616i	−0.714526	−	0.699609i	$-0.753357\pi$
$347$	1607.03	−	2783.46i	0.248617	−	0.430616i	0.963142	+	0.268993i	$0.0866908\pi$
$348$	23762.0	+	5050.78i	3.66028	+	0.778017i
$349$	1711.39	−	5267.11i	0.262488	−	0.807856i	−0.729773	−	0.683690i	$-0.760374\pi$
$349$	1711.39	−	5267.11i	0.262488	−	0.807856i	0.992261	−	0.124167i	$-0.0396257\pi$
$350$	−6003.62	+	1276.11i	−0.916876	+	0.194888i
$351$	−219.609	+	2089.44i	−0.0333956	+	0.317738i
$352$	3955.13	−	4392.62i	0.598890	−	0.665135i
$353$	−2334.52	+	1039.39i	−0.351994	+	0.156718i	−0.575114	−	0.818073i	$-0.695042\pi$
$353$	−2334.52	+	1039.39i	−0.351994	+	0.156718i	0.223120	+	0.974791i	$0.428376\pi$
$354$	−425.979	−	189.658i	−0.0639564	−	0.0284752i
$355$	828.327	+	919.950i	0.123839	+	0.137538i
$356$	−11508.4	+	8361.37i	−1.71333	+	1.24481i
$357$	−6614.30	+	4805.57i	−0.980577	+	0.712431i
$358$	−12337.5	−	13702.2i	−1.82139	−	2.02286i
$359$	−2739.36	−	1219.64i	−0.402723	−	0.179304i	0.195372	−	0.980729i	$-0.437409\pi$
$359$	−2739.36	−	1219.64i	−0.402723	−	0.179304i	−0.598095	+	0.801425i	$0.704075\pi$
$360$	7985.59	−	3555.41i	1.16910	−	0.520519i
$361$	−198.364	+	220.306i	−0.0289203	+	0.0321192i
$362$	−1197.82	+	11396.5i	−0.173912	+	1.65466i
$363$	4445.04	−	944.822i	0.642711	−	0.136612i
$364$	−282.612	+	869.792i	−0.0406948	+	0.125246i
$365$	−2453.06	−	521.414i	−0.351778	−	0.0747727i
$366$	−11427.6	+	19793.2i	−1.63205	+	2.82680i
$367$	1094.13	+	1895.10i	0.155622	+	0.269545i	0.933285	−	0.359136i	$-0.116928\pi$
$367$	1094.13	+	1895.10i	0.155622	+	0.269545i	−0.777663	+	0.628681i	$0.783595\pi$
$368$	584.120	+	1797.74i	0.0827429	+	0.254656i
$369$	628.657	+	5981.28i	0.0886900	+	0.843829i
$370$	1610.66	+	1170.21i	0.226308	+	0.164423i
$371$	−3502.33			−0.490113
$372$	18167.1	−	24900.4i	2.53204	−	3.47050i
$373$	1213.39			0.168437			0.0842183	−	0.996447i	$-0.473161\pi$
$373$	1213.39			0.168437			0.0842183	+	0.996447i	$0.473161\pi$
$374$	10070.0	+	7316.31i	1.39227	+	1.01154i
$375$	605.730	+	5763.14i	0.0834127	+	0.793619i
$376$	−4623.85	−	14230.8i	−0.634194	−	1.95185i
$377$	340.190	+	589.227i	0.0464740	+	0.0804953i
$378$	10816.7	−	18735.1i	1.47183	−	2.54928i
$379$	−1427.26	−	303.373i	−0.193439	−	0.0411166i	0.110173	−	0.993912i	$-0.464859\pi$
$379$	−1427.26	−	303.373i	−0.193439	−	0.0411166i	−0.303612	+	0.952796i	$0.598193\pi$
$380$	−1097.01	+	3376.24i	−0.148093	+	0.455783i
$381$	8703.72	−	1850.03i	1.17035	−	0.248767i
$382$	−621.382	+	5912.06i	−0.0832269	+	0.791851i
$383$	314.445	−	349.226i	0.0419513	−	0.0465917i	−0.721804	−	0.692098i	$-0.756687\pi$
$383$	314.445	−	349.226i	0.0419513	−	0.0465917i	0.763755	+	0.645506i	$0.223353\pi$
$384$	−11574.0	+	5153.08i	−1.53811	+	0.684810i
$385$	−654.369	−	291.344i	−0.0866226	−	0.0385669i
$386$	2409.01	+	2675.47i	0.317656	+	0.352793i
$387$	−7226.36	+	5250.26i	−0.949190	+	0.689627i
$388$	−6159.57	+	4475.19i	−0.805940	+	0.585550i
$389$	−1870.60	−	2077.51i	−0.243812	−	0.270781i	0.608801	−	0.793323i	$-0.291651\pi$
$389$	−1870.60	−	2077.51i	−0.243812	−	0.270781i	−0.852614	+	0.522542i	$0.824984\pi$
$390$	554.614	+	246.930i	0.0720101	+	0.0320610i
$391$	−1183.36	+	526.866i	−0.153057	+	0.0681452i
$392$	−8400.03	+	9329.18i	−1.08231	+	1.20203i
$393$	2102.07	−	19999.8i	0.269810	−	2.56707i
$394$	23376.7	−	4968.86i	2.98908	−	0.635350i
$395$	790.369	−	2432.50i	0.100678	−	0.309855i
$396$	−36500.6	−	7758.44i	−4.63188	−	0.984536i
$397$	4216.32	−	7302.87i	0.533025	−	0.923226i	−0.466231	−	0.884663i	$-0.654389\pi$
$397$	4216.32	−	7302.87i	0.533025	−	0.923226i	0.999256	−	0.0385632i	$-0.0122781\pi$
$398$	−6334.18	−	10971.1i	−0.797748	−	1.38174i
$399$	2478.96	+	7629.45i	0.311036	+	0.957269i
$400$	1500.84	+	14279.5i	0.187605	+	1.78494i
$401$	593.483	+	431.191i	0.0739081	+	0.0536974i	0.624126	−	0.781324i	$-0.285455\pi$
$401$	593.483	+	431.191i	0.0739081	+	0.0536974i	−0.550218	+	0.835021i	$0.685455\pi$
$402$	−12809.0			−1.58920
$403$	858.728	−	88.5264i	0.106145	−	0.0109425i
$404$	10103.7			1.24426
$405$	−4390.20	−	3189.67i	−0.538644	−	0.391348i
$406$	−732.312	−	6967.48i	−0.0895173	−	0.851701i
$407$	−1469.29	−	4522.00i	−0.178943	−	0.550730i
$408$	21093.7	+	36535.3i	2.55954	+	4.43325i
$409$	917.776	−	1589.64i	0.110956	−	0.192182i	−0.805200	−	0.593004i	$-0.797942\pi$
$409$	917.776	−	1589.64i	0.110956	−	0.192182i	0.916156	+	0.400822i	$0.131275\pi$
$410$	1041.54	+	221.387i	0.125459	+	0.0266671i
$411$	−7319.26	+	22526.4i	−0.878424	+	2.70351i
$412$	36127.4	−	7679.12i	4.32007	−	0.918260i
$413$	−9.75768	+	92.8381i	−0.00116258	+	0.0110612i
$414$	3743.25	−	4157.30i	0.444374	−	0.493527i
$415$	1561.78	−	695.347i	0.184734	−	0.0822488i
$416$	916.225	+	407.929i	0.107985	+	0.0480779i
$417$	−5492.19	−	6099.69i	−0.644972	−	0.716314i
$418$	9880.79	−	7178.82i	1.15619	−	0.840018i
$419$	7879.54	−	5724.82i	0.918713	−	0.667484i	−0.0244905	−	0.999700i	$-0.507796\pi$
$419$	7879.54	−	5724.82i	0.918713	−	0.667484i	0.943203	+	0.332216i	$0.107796\pi$
$420$	−2903.70	−	3224.89i	−0.337348	−	0.374663i
$421$	6740.08	+	3000.88i	0.780264	+	0.347396i	0.757914	−	0.652354i	$-0.226218\pi$
$421$	6740.08	+	3000.88i	0.780264	+	0.347396i	0.0223501	+	0.999750i	$0.492885\pi$
$422$	8453.73	−	3763.84i	0.975169	−	0.434173i
$423$	−13433.4	+	14919.3i	−1.54410	+	1.71489i
$424$	−1889.07	+	17973.3i	−0.216371	+	2.05863i
$425$	−9624.32	+	2045.71i	−1.09847	+	0.233486i
$426$	7973.14	−	24538.8i	0.906807	−	2.79087i
$427$	4475.52	+	951.302i	0.507227	+	0.107814i
$428$	−12543.8	+	21726.5i	−1.41666	+	2.45372i
$429$	−724.951	−	1255.65i	−0.0815874	−	0.141313i
$430$	488.694	+	1504.05i	0.0548068	+	0.168678i
$431$	−1114.67	−	10605.4i	−0.124575	−	1.18525i	−0.860955	−	0.508681i	$-0.830133\pi$
$431$	−1114.67	−	10605.4i	−0.124575	−	1.18525i	0.736381	−	0.676568i	$-0.236533\pi$
$432$	−40942.3	−	29746.3i	−4.55981	−	3.31290i
$433$	10928.4			1.21290			0.606451	−	0.795121i	$-0.292593\pi$
$433$	10928.4			1.21290			0.606451	+	0.795121i	$0.292593\pi$
$434$	−8448.61	−	2763.74i	−0.934438	−	0.305677i
$435$	−3228.38			−0.355836
$436$	−21815.5	−	15849.9i	−2.39627	−	1.74099i
$437$	132.856	+	1264.04i	0.0145432	+	0.138369i
$438$	16152.6	+	49712.6i	1.76210	+	5.42319i
$439$	3190.51	+	5526.13i	0.346867	+	0.600792i	0.985691	−	0.168561i	$-0.0539120\pi$
$439$	3190.51	+	5526.13i	0.346867	+	0.600792i	−0.638824	+	0.769353i	$0.720579\pi$
$440$	−1848.07	+	3200.95i	−0.200235	+	0.346816i
$441$	16475.0	+	3501.88i	1.77897	+	0.378132i
$442$	−652.646	+	2008.64i	−0.0702335	+	0.216156i
$443$	−12626.3	+	2683.81i	−1.35417	+	0.287837i	−0.827132	−	0.562007i	$-0.810029\pi$
$443$	−12626.3	+	2683.81i	−1.35417	+	0.287837i	−0.527034	+	0.849844i	$0.676696\pi$
$444$	3010.98	−	28647.5i	0.321835	−	3.06205i
$445$	1264.95	−	1404.87i	0.134752	−	0.149657i
$446$	4823.46	−	2147.54i	0.512102	−	0.228003i
$447$	−7805.47	−	3475.22i	−0.825919	−	0.367723i
$448$	−416.157	−	462.189i	−0.0438874	−	0.0487419i
$449$	−9544.84	+	6934.73i	−1.00323	+	0.728887i	−0.962778	−	0.270295i	$-0.912879\pi$
$449$	−9544.84	+	6934.73i	−1.00323	+	0.728887i	−0.0404488	+	0.999182i	$0.512879\pi$
$450$	34377.5	−	24976.7i	3.60127	−	2.61647i
$451$	−1701.62	−	1889.84i	−0.177663	−	0.197315i
$452$	−3425.15	−	1524.98i	−0.356429	−	0.158692i
$453$	2161.46	−	962.346i	0.224182	−	0.0998122i
$454$	−4327.63	+	4806.32i	−0.447369	+	0.496854i
$455$	12.7042	−	120.873i	0.00130898	−	0.0124541i
$456$	40489.9	−	8606.40i	4.15815	−	0.883841i
$457$	−2247.60	+	6917.40i	−0.230062	+	0.708058i	0.767676	+	0.640838i	$0.221413\pi$
$457$	−2247.60	+	6917.40i	−0.230062	+	0.708058i	−0.997738	+	0.0672201i	$0.978587\pi$
$458$	22215.6	+	4722.07i	2.26652	+	0.481764i
$459$	17340.1	−	30034.0i	1.76333	−	3.05417i
$460$	−343.773	−	595.433i	−0.0348446	−	0.0603526i
$461$	3982.97	+	12258.3i	0.402398	+	1.23845i	0.923049	+	0.384683i	$0.125689\pi$
$461$	3982.97	+	12258.3i	0.402398	+	1.23845i	−0.520651	+	0.853769i	$0.674311\pi$
$462$	1560.57	+	14847.8i	0.157152	+	1.49520i
$463$	−12209.6	−	8870.77i	−1.22554	−	0.890410i	−0.228996	−	0.973427i	$-0.573544\pi$
$463$	−12209.6	−	8870.77i	−1.22554	−	0.890410i	−0.996548	+	0.0830176i	$0.973544\pi$
$464$	−16389.0			−1.63974
$465$	−1673.54	+	3738.76i	−0.166900	+	0.372862i
$466$	−17650.5			−1.75460
$467$	−5680.08	−	4126.82i	−0.562832	−	0.408922i	0.269662	−	0.962955i	$-0.413088\pi$
$467$	−5680.08	−	4126.82i	−0.562832	−	0.408922i	−0.832495	+	0.554033i	$0.813088\pi$
$468$	−661.838	−	6296.97i	−0.0653707	−	0.621960i
$469$	792.415	+	2438.80i	0.0780177	+	0.240114i
$470$	1777.20	+	3078.21i	0.174418	+	0.302100i
$471$	−4005.10	+	6937.04i	−0.391816	+	0.678645i
$472$	471.164	+	100.149i	0.0459472	+	0.00976638i
$473$	1167.12	−	3592.03i	0.113455	−	0.349179i
$474$	−52144.4	+	11083.6i	−5.05290	+	1.07403i
$475$	−1009.16	+	9601.54i	−0.0974811	+	0.927471i
$476$	10101.5	−	11218.9i	0.972695	−	1.08029i
$477$	22151.1	−	9862.32i	2.12627	−	0.946676i
$478$	−19029.7	−	8472.55i	−1.82091	−	0.810723i
$479$	−1551.12	−	1722.69i	−0.147959	−	0.164325i	0.664609	−	0.747191i	$-0.268598\pi$
$479$	−1551.12	−	1722.69i	−0.147959	−	0.164325i	−0.812568	+	0.582866i	$0.801931\pi$
$480$	−3850.01	+	2797.19i	−0.366100	+	0.265987i
$481$	652.685	−	474.203i	0.0618708	−	0.0449518i
$482$	19688.9	+	21866.8i	1.86059	+	2.06640i
$483$	−1419.36	−	631.939i	−0.133712	−	0.0595326i
$484$	−7665.68	+	3412.98i	−0.719918	+	0.320528i
$485$	677.031	−	751.919i	0.0633864	−	0.0703977i
$486$	−5759.33	+	54796.3i	−0.537548	+	5.11443i
$487$	13946.1	−	2964.33i	1.29765	−	0.275825i	0.493240	−	0.869893i	$-0.335812\pi$
$487$	13946.1	−	2964.33i	1.29765	−	0.275825i	0.804415	+	0.594068i	$0.202479\pi$
$488$	7295.88	−	22454.4i	0.676781	−	2.08292i
$489$	9981.72	+	2121.68i	0.923086	+	0.196208i
$490$	1491.03	−	2582.53i	0.137465	−	0.238096i
$491$	809.325	+	1401.79i	0.0743876	+	0.128843i	0.900820	−	0.434193i	$-0.142966\pi$
$491$	809.325	+	1401.79i	0.0743876	+	0.128843i	−0.826432	+	0.563036i	$0.809633\pi$
$492$	−4760.82	−	14652.3i	−0.436249	−	1.34264i
$493$	−1173.96	−	11169.5i	−0.107247	−	1.02038i
$494$	1676.54	+	1218.08i	0.152694	+	0.110939i
$495$	4959.07			0.450290
$496$	−8495.77	+	18979.9i	−0.769096	+	1.71820i
$497$	−5165.36			−0.466193
$498$	−28827.2	−	20944.2i	−2.59393	−	1.88460i
$499$	697.354	+	6634.88i	0.0625608	+	0.595227i	0.980227	+	0.197875i	$0.0634040\pi$
$499$	697.354	+	6634.88i	0.0625608	+	0.595227i	−0.917666	+	0.397352i	$0.869929\pi$
$500$	−3306.56	−	10176.5i	−0.295748	−	0.910218i
$501$	1813.28	+	3140.70i	0.161700	+	0.280072i
$502$	−5171.40	+	8957.13i	−0.459783	+	0.796367i
$503$	−3825.57	−	813.150i	−0.339113	−	0.0720806i	0.0352078	−	0.999380i	$-0.488791\pi$
$503$	−3825.57	−	813.150i	−0.339113	−	0.0720806i	−0.374321	+	0.927299i	$0.622124\pi$
$504$	−11271.2	+	34689.1i	−0.996146	+	3.06582i
$505$	−1313.38	+	279.168i	−0.115732	+	0.0245996i
$506$	−247.254	+	2352.47i	−0.0217229	+	0.206680i
$507$	−14292.6	+	15873.5i	−1.25198	+	1.39047i
$508$	−15010.0	+	6682.88i	−1.31095	+	0.583671i
$509$	5635.41	+	2509.05i	0.490737	+	0.218490i	0.637160	−	0.770732i	$-0.280109\pi$
$509$	5635.41	+	2509.05i	0.490737	+	0.218490i	−0.146422	+	0.989222i	$0.546776\pi$
$510$	−6705.61	−	7447.34i	−0.582215	−	0.646615i
$511$	8465.86	−	6150.81i	0.732891	−	0.532477i
$512$	20970.6	−	15236.1i	1.81012	−	1.31513i
$513$	−22769.5	−	25288.1i	−1.95965	−	2.17641i
$514$	9260.67	+	4123.12i	0.794690	+	0.353819i
$515$	−4484.02	+	1996.42i	−0.383669	+	0.170821i
$516$	15310.6	−	17004.2i	1.30623	−	1.45071i
$517$	887.319	−	8442.28i	0.0754821	−	0.718165i
$518$	−8125.68	+	1727.17i	−0.689232	+	0.146501i
$519$	12962.7	−	39895.0i	1.09633	−	3.37417i
$520$	−613.443	−	130.391i	−0.0517332	−	0.0109962i
$521$	−7262.86	+	12579.6i	−0.610733	+	1.05782i	0.380384	+	0.924829i	$0.375792\pi$
$521$	−7262.86	+	12579.6i	−0.610733	+	1.05782i	−0.991117	+	0.132992i	$0.957542\pi$
$522$	24251.6	+	42004.9i	2.03345	+	3.52204i
$523$	4347.20	+	13379.3i	0.363461	+	1.11862i	0.950939	+	0.309377i	$0.100121\pi$
$523$	4347.20	+	13379.3i	0.363461	+	1.11862i	−0.587479	+	0.809240i	$0.699879\pi$
$524$	3881.47	+	36929.7i	0.323593	+	3.07878i
$525$	−9547.69	−	6936.80i	−0.793706	−	0.576661i
$526$	13482.9			1.11765
$527$	−13543.9	−	4430.52i	−1.11951	−	0.366217i
$528$	34925.2			2.87864
$529$	9644.16	+	7006.89i	0.792649	+	0.575893i
$530$	−448.738	−	4269.46i	−0.0367773	−	0.349912i
$531$	−199.711	−	614.648i	−0.0163215	−	0.0502325i
$532$	−7406.39	−	12828.2i	−0.603586	−	1.04544i
$533$	215.746	−	373.683i	0.0175328	−	0.0303677i
$534$	−38541.1	−	8192.17i	−3.12329	−	0.663876i
$535$	1030.26	−	3170.82i	0.0832562	−	0.256236i
$536$	12942.9	−	2751.09i	1.04300	−	0.221696i
$537$	3705.81	−	35258.4i	0.297798	−	2.83336i
$538$	12468.1	−	13847.3i	0.999145	−	1.10966i
$539$	−6506.15	+	2896.72i	−0.519925	+	0.231485i
$540$	16816.2	+	7487.04i	1.34010	+	0.596650i
$541$	13145.4	+	14599.4i	1.04467	+	1.16022i	0.986808	+	0.161894i	$0.0517603\pi$
$541$	13145.4	+	14599.4i	1.04467	+	1.16022i	0.0578577	+	0.998325i	$0.481573\pi$
$542$	21664.5	−	15740.2i	1.71692	−	1.24741i
$543$	−17825.7	+	12951.1i	−1.40879	+	1.02355i
$544$	−11077.7	−	12303.0i	−0.873075	−	0.969648i
$545$	3273.73	+	1457.56i	0.257305	+	0.114560i
$546$	−2314.20	+	1030.35i	−0.181389	+	0.0807597i
$547$	−15184.7	+	16864.4i	−1.18693	+	1.31822i	−0.250193	+	0.968196i	$0.580494\pi$
$547$	−15184.7	+	16864.4i	−1.18693	+	1.31822i	−0.936740	+	0.350026i	$0.886173\pi$
$548$	4571.61	−	43495.9i	0.356367	−	3.39061i
$549$	−30985.0	+	6586.07i	−2.40876	+	0.511998i
$550$	−5552.27	+	17088.1i	−0.430454	+	1.32480i
$551$	−10779.1	−	2291.18i	−0.833406	−	0.177146i
$552$	−4008.55	+	6943.02i	−0.309086	+	0.535352i
$553$	5336.14	+	9242.46i	0.410336	+	0.710722i
$554$	2184.76	+	6723.99i	0.167548	+	0.515659i
$555$	400.141	+	3807.08i	0.0306036	+	0.291174i
$556$	12261.4	+	8908.46i	0.935254	+	0.679502i
$557$	8975.95			0.682806			0.341403	−	0.939917i	$-0.389098\pi$
$557$	8975.95			0.682806			0.341403	+	0.939917i	$0.389098\pi$
$558$	61217.2	−	6310.89i	4.64432	−	0.478784i
$559$	640.848			0.0484883
$560$	2368.49	+	1720.81i	0.178727	+	0.129853i
$561$	2501.73	+	23802.4i	0.188277	+	1.79133i
$562$	−13762.8	−	42357.4i	−1.03300	−	3.17925i
$563$	7194.14	+	12460.6i	0.538538	+	0.932775i	0.998983	+	0.0450865i	$0.0143564\pi$
$563$	7194.14	+	12460.6i	0.538538	+	0.932775i	−0.460445	+	0.887688i	$0.652310\pi$
$564$	25713.7	−	44537.4i	1.91975	−	3.32511i
$565$	487.371	+	103.594i	0.0362900	+	0.00771367i
$566$	6488.54	−	19969.7i	0.481862	−	1.48302i
$567$	22148.3	−	4707.77i	1.64046	−	0.348691i
$568$	−2786.06	+	26507.6i	−0.205811	+	1.95816i
$569$	1547.06	−	1718.18i	0.113982	−	0.126590i	−0.683453	−	0.729994i	$-0.739523\pi$
$569$	1547.06	−	1718.18i	0.113982	−	0.126590i	0.797436	+	0.603404i	$0.206189\pi$
$570$	−8982.93	+	3999.46i	−0.660094	+	0.293893i
$571$	−8699.70	−	3873.36i	−0.637603	−	0.283879i	0.0623652	−	0.998053i	$-0.480136\pi$
$571$	−8699.70	−	3873.36i	−0.637603	−	0.283879i	−0.699968	+	0.714174i	$0.746802\pi$
$572$	1791.43	+	1989.58i	0.130950	+	0.145435i
$573$	−9247.28	+	6718.54i	−0.674190	+	0.489828i
$574$	−3594.51	+	2611.57i	−0.261380	+	0.189904i
$575$	−1251.16	−	1389.55i	−0.0907425	−	0.100780i
$576$	3933.55	+	1751.33i	0.284545	+	0.126688i
$577$	−8926.01	+	3974.11i	−0.644011	+	0.286732i	−0.702638	−	0.711548i	$-0.747995\pi$
$577$	−8926.01	+	3974.11i	−0.644011	+	0.286732i	0.0586265	+	0.998280i	$0.481328\pi$
$578$	6513.87	−	7234.39i	0.468757	−	0.520607i
$579$	−723.592	+	6884.52i	−0.0519369	+	0.494147i
$580$	5830.94	−	1239.40i	0.417442	−	0.0887301i
$581$	−2204.35	+	6784.29i	−0.157404	+	0.484440i
$582$	−20628.0	−	4384.63i	−1.46918	−	0.312283i
$583$	−5126.34	+	8879.07i	−0.364170	+	0.630761i
$584$	−26998.5	−	46762.7i	−1.91302	−	3.31345i
$585$	260.019	+	800.255i	0.0183768	+	0.0565581i
$586$	612.681	+	5829.27i	0.0431904	+	0.410930i
$587$	835.375	+	606.936i	0.0587387	+	0.0426762i	0.616767	−	0.787146i	$-0.288442\pi$
$587$	835.375	+	606.936i	0.0587387	+	0.0426762i	−0.558028	+	0.829822i	$0.688442\pi$
$588$	−43146.2			−3.02605
$589$	−8241.12	+	11295.5i	−0.576518	+	0.790194i
$590$	−114.423			−0.00798427
$591$	37176.5	+	27010.3i	2.58754	+	1.87996i
$592$	2031.33	+	19326.8i	0.141026	+	1.34177i
$593$	−782.071	−	2406.97i	−0.0541582	−	0.166682i	0.920319	−	0.391169i	$-0.127929\pi$
$593$	−782.071	−	2406.97i	−0.0541582	−	0.166682i	−0.974477	+	0.224487i	$0.927929\pi$
$594$	−31664.6	−	54844.7i	−2.18723	−	3.78839i
$595$	−1003.12	+	1737.45i	−0.0691155	+	0.119712i
$596$	15432.0	+	3280.18i	1.06060	+	0.225438i
$597$	7527.23	−	23166.4i	0.516028	−	1.58817i
$598$	−392.586	+	83.4468i	−0.0268462	+	0.00570634i
$599$	2101.00	−	19989.7i	0.143313	−	1.36353i	−0.652408	−	0.757868i	$-0.726241\pi$
$599$	2101.00	−	19989.7i	0.143313	−	1.36353i	0.795721	−	0.605663i	$-0.207092\pi$
$600$	−40748.1	+	45255.3i	−2.77256	+	3.07924i
$601$	11461.8	−	5103.13i	0.777933	−	0.346358i	0.0209396	−	0.999781i	$-0.493334\pi$
$601$	11461.8	−	5103.13i	0.777933	−	0.346358i	0.756993	+	0.653423i	$0.226668\pi$
$602$	−6028.30	−	2683.97i	−0.408131	−	0.181712i
$603$	−11879.3	−	13193.3i	−0.802257	−	0.890996i
$604$	−3534.48	+	2567.95i	−0.238106	+	0.172994i
$605$	902.159	−	655.457i	0.0606248	−	0.0440465i
$606$	18726.4	+	20797.7i	1.25529	+	1.39414i
$607$	−6414.57	−	2855.95i	−0.428928	−	0.190971i	0.180906	−	0.983500i	$-0.442097\pi$
$607$	−6414.57	−	2855.95i	−0.428928	−	0.190971i	−0.609834	+	0.792529i	$0.708764\pi$
$608$	−14839.9	+	6607.13i	−0.989861	+	0.440715i
$609$	9013.74	−	10010.8i	0.599762	−	0.666103i
$610$	−586.240	+	5577.70i	−0.0389117	+	0.370220i
$611$	1408.87	−	299.465i	0.0932845	−	0.0198282i
$612$	−32297.3	+	99401.0i	−2.13324	+	6.56543i
$613$	−13719.5	−	2916.17i	−0.903955	−	0.192142i	−0.267593	−	0.963532i	$-0.586228\pi$
$613$	−13719.5	−	2916.17i	−0.903955	−	0.192142i	−0.636362	+	0.771390i	$0.719562\pi$
$614$	−13106.8	+	22701.7i	−0.861481	+	1.49213i
$615$	1023.70	+	1773.11i	0.0671216	+	0.116258i
$616$	−4765.85	−	14667.8i	−0.311723	−	0.959385i
$617$	538.561	+	5124.07i	0.0351405	+	0.334339i	0.997942	+	0.0641284i	$0.0204267\pi$
$617$	538.561	+	5124.07i	0.0351405	+	0.334339i	−0.962801	+	0.270211i	$0.912907\pi$
$618$	82765.9	+	60132.9i	5.38727	+	3.91408i
$619$	23399.9			1.51942			0.759712	−	0.650260i	$-0.225340\pi$
$619$	23399.9			1.51942			0.759712	+	0.650260i	$0.225340\pi$
$620$	1587.32	−	7395.25i	0.102820	−	0.479033i
$621$	6590.49			0.425873
$622$	−30630.1	−	22254.1i	−1.97452	−	1.43458i
$623$	824.533	+	7844.91i	0.0530244	+	0.504494i
$624$	1831.23	+	5635.94i	0.117481	+	0.361568i
$625$	−6737.52	−	11669.7i	−0.431201	−	0.746863i
$626$	−7074.45	+	12253.3i	−0.451681	+	0.782334i
$627$	22970.5	+	4882.54i	1.46308	+	0.310988i
$628$	4570.62	−	14066.9i	0.290426	−	0.893841i
$629$	−13026.2	+	2768.80i	−0.825736	+	0.175516i
$630$	905.663	−	8616.80i	0.0572737	−	0.544923i
$631$	13770.9	−	15294.1i	0.868797	−	0.964897i	−0.130852	−	0.991402i	$-0.541771\pi$
$631$	13770.9	−	15294.1i	0.868797	−	0.964897i	0.999649	+	0.0265054i	$0.00843792\pi$
$632$	50308.7	−	22398.9i	3.16641	−	1.40978i
$633$	16254.8	+	7237.09i	1.02065	+	0.454421i
$634$	31983.3	+	35521.0i	2.00350	+	2.22511i
$635$	1766.50	−	1283.44i	0.110396	−	0.0802072i
$636$	−50250.9	+	36509.4i	−3.13298	+	2.27624i
$637$	−808.586	−	898.025i	−0.0502941	−	0.0558572i
$638$	−18735.8	−	8341.70i	−1.16263	−	0.517635i
$639$	32669.2	−	14545.3i	2.02250	−	0.900473i
$640$	−2080.27	+	2310.37i	−0.128484	+	0.142696i
$641$	1610.84	−	15326.1i	0.0992581	−	0.944378i	−0.825649	−	0.564184i	$-0.809191\pi$
$641$	1610.84	−	15326.1i	0.0992581	−	0.944378i	0.924907	−	0.380194i	$-0.124143\pi$
$642$	−67971.3	+	14447.7i	−4.17853	+	0.888173i
$643$	−72.9494	+	224.515i	−0.00447410	+	0.0137699i	−0.953269	−	0.302124i	$-0.902304\pi$
$643$	−72.9494	+	224.515i	−0.00447410	+	0.0137699i	0.948795	+	0.315894i	$0.102304\pi$
$644$	2806.18	+	596.473i	0.171707	+	0.0364974i
$645$	−1520.40	+	2633.41i	−0.0928149	+	0.160760i
$646$	−17103.8	−	29624.7i	−1.04170	−	1.80428i
$647$	−5919.95	−	18219.7i	−0.359718	−	1.10710i	−0.953223	−	0.302267i	$-0.902256\pi$
$647$	−5919.95	−	18219.7i	−0.359718	−	1.10710i	0.593505	−	0.804830i	$-0.297744\pi$
$648$	−12213.1	−	116200.i	−0.740396	−	7.04440i
$649$	221.080	+	160.624i	0.0133716	+	0.00971501i
$650$	−3048.66			−0.183967
$651$	−6920.82	−	15628.2i	−0.416664	−	0.940884i
$652$	−18843.0			−1.13182
$653$	7360.41	+	5347.65i	0.441095	+	0.320474i	0.786070	−	0.618138i	$-0.212113\pi$
$653$	7360.41	+	5347.65i	0.441095	+	0.320474i	−0.344975	+	0.938612i	$0.612113\pi$
$654$	−7807.35	−	74282.0i	−0.466807	−	4.44137i
$655$	−1524.93	−	4693.25i	−0.0909677	−	0.279970i
$656$	5196.88	+	9001.26i	0.309305	+	0.535732i
$657$	−36223.6	+	62741.1i	−2.15101	+	3.72567i
$658$	−14507.1	−	3083.58i	−0.859493	−	0.182691i
$659$	−2927.59	+	9010.19i	−0.173054	+	0.532606i	−0.999539	−	0.0303529i	$-0.990337\pi$
$659$	−2927.59	+	9010.19i	−0.173054	+	0.532606i	0.826485	+	0.562958i	$0.190337\pi$
$660$	−12425.8	+	2641.19i	−0.732840	+	0.155770i
$661$	1476.75	−	14050.4i	0.0868971	−	0.826771i	−0.861088	−	0.508456i	$-0.830216\pi$
$661$	1476.75	−	14050.4i	0.0868971	−	0.826771i	0.947985	−	0.318315i	$-0.103117\pi$
$662$	5844.44	−	6490.91i	0.343128	−	0.381082i
$663$	−3709.86	+	1651.74i	−0.217314	+	0.0967544i
$664$	33626.7	+	14971.6i	1.96531	+	0.875014i
$665$	1317.20	+	1462.90i	0.0768104	+	0.0853066i
$666$	46528.7	−	33805.1i	2.70713	−	1.96685i
$667$	1726.68	−	1254.51i	0.100236	−	0.0728257i
$668$	−4480.81	−	4976.44i	−0.259533	−	0.288240i
$669$	9274.51	+	4129.28i	0.535984	+	0.238635i
$670$	−2871.45	+	1278.45i	−0.165573	+	0.0737178i
$671$	8962.52	−	9953.88i	0.515639	−	0.572676i
$672$	2075.62	−	19748.2i	0.119150	−	1.13364i
$673$	9310.50	−	1979.01i	0.533274	−	0.113351i	0.0665991	−	0.997780i	$-0.478785\pi$
$673$	9310.50	−	1979.01i	0.533274	−	0.113351i	0.466675	+	0.884429i	$0.345452\pi$
$674$	359.797	−	1107.34i	0.0205621	−	0.0632836i
$675$	48966.7	+	10408.2i	2.79219	+	0.593498i
$676$	19720.6	−	34157.0i	1.12202	−	1.94339i
$677$	5607.59	+	9712.62i	0.318341	+	0.551383i	0.980142	−	0.198296i	$-0.0635409\pi$
$677$	5607.59	+	9712.62i	0.318341	+	0.551383i	−0.661801	+	0.749680i	$0.730208\pi$
$678$	−3209.18	−	9876.83i	−0.181781	−	0.559465i
$679$	441.308	+	4198.77i	0.0249423	+	0.237311i
$680$	8375.19	+	6084.93i	0.472314	+	0.343156i
$681$	−12435.7			−0.699763
$682$	−19372.8	+	17373.5i	−1.08771	+	0.975465i
$683$	−5984.17			−0.335253			−0.167627	−	0.985851i	$-0.553610\pi$
$683$	−5984.17			−0.335253			−0.167627	+	0.985851i	$0.553610\pi$
$684$	82966.4	+	60278.6i	4.63787	+	3.36961i
$685$	607.539	+	5780.34i	0.0338874	+	0.322417i
$686$	9303.87	+	28634.4i	0.517818	+	1.59368i
$687$	21835.1	+	37819.6i	1.21261	+	2.10030i
$688$	−7718.36	+	13368.6i	−0.427703	+	0.740803i
$689$	−1701.62	−	361.691i	−0.0940880	−	0.0199990i
$690$	588.499	−	1811.21i	0.0324692	−	0.0999300i
$691$	1047.35	−	222.622i	0.0576602	−	0.0122561i	−0.178991	−	0.983851i	$-0.557283\pi$
$691$	1047.35	−	222.622i	0.0576602	−	0.0122561i	0.236651	+	0.971595i	$0.423950\pi$
$692$	−8096.47	+	77032.8i	−0.444771	+	4.23172i
$693$	−13845.9	+	15377.4i	−0.758964	+	0.842915i
$694$	−15017.4	+	6686.18i	−0.821403	+	0.365712i
$695$	−1840.01	−	819.223i	−0.100425	−	0.0447121i
$696$	−46511.5	−	51656.3i	−2.53307	−	2.81326i
$697$	−5762.32	+	4186.57i	−0.313147	+	0.227515i
$698$	−22915.8	+	16649.3i	−1.24266	+	0.902843i
$699$	−22709.2	−	25221.1i	−1.22881	−	1.36473i
$700$	19907.7	+	8863.47i	1.07491	+	0.478582i
$701$	−28728.1	+	12790.6i	−1.54785	+	0.689148i	−0.990036	−	0.140816i	$-0.955027\pi$
$701$	−28728.1	+	12790.6i	−1.54785	+	0.689148i	−0.557817	+	0.829964i	$0.688361\pi$
$702$	7190.13	−	7985.45i	0.386573	−	0.429332i
$703$	−1365.87	+	12995.3i	−0.0732782	+	0.697196i
$704$	−1780.86	+	378.534i	−0.0953391	+	0.0202650i
$705$	−2111.94	+	6499.88i	−0.112823	+	0.347234i
$706$	12784.5	+	2717.42i	0.681515	+	0.144860i
$707$	2801.34	−	4852.07i	0.149017	−	0.258106i
$708$	827.771	+	1433.74i	0.0439400	+	0.0761064i
$709$	−7076.98	−	21780.7i	−0.374868	−	1.15373i	−0.943568	−	0.331180i	$-0.892553\pi$
$709$	−7076.98	−	21780.7i	−0.374868	−	1.15373i	0.568700	−	0.822545i	$-0.307447\pi$
$710$	−661.814	−	6296.74i	−0.0349823	−	0.332835i
$711$	−59775.5	−	43429.4i	−3.15296	−	2.29076i
$712$	40703.3			2.14244
$713$	−557.753	−	2649.97i	−0.0292959	−	0.139190i
$714$	41815.5			2.19174
$715$	−287.840	−	209.128i	−0.0150554	−	0.0109384i
$716$	6842.78	+	65104.7i	0.357160	+	3.39815i
$717$	−12377.0	−	38092.5i	−0.644669	−	1.98409i
$718$	7668.30	+	13281.9i	0.398577	+	0.690356i
$719$	12635.2	−	21884.8i	0.655372	−	1.13514i	−0.326429	−	0.945222i	$-0.605845\pi$
$719$	12635.2	−	21884.8i	0.655372	−	1.13514i	0.981800	−	0.189915i	$-0.0608213\pi$
$720$	−19825.6	−	4214.06i	−1.02619	−	0.218123i
$721$	6328.92	−	19478.4i	0.326909	−	1.00612i
$722$	1483.09	−	315.240i	0.0764472	−	0.0162494i
$723$	−5913.96	+	56267.6i	−0.304208	+	2.89435i
$724$	27223.8	−	30235.1i	1.39747	−	1.55204i
$725$	14810.3	−	6593.96i	0.758676	−	0.337784i
$726$	−21233.0	−	9453.55i	−1.08544	−	0.483270i
$727$	−20800.5	−	23101.4i	−1.06114	−	1.17852i	−0.983383	−	0.181545i	$-0.941890\pi$
$727$	−20800.5	−	23101.4i	−1.06114	−	1.17852i	−0.0777585	−	0.996972i	$-0.524776\pi$
$728$	2117.08	−	1538.15i	0.107780	−	0.0783071i
$729$	−36590.1	+	26584.2i	−1.85897	+	1.35062i
$730$	8582.73	+	9532.08i	0.435152	+	0.483285i
$731$	−9663.90	−	4302.64i	−0.488963	−	0.217700i
$732$	74130.7	−	33005.1i	3.74310	−	1.66654i
$733$	7516.81	−	8348.26i	0.378772	−	0.420669i	−0.523372	−	0.852104i	$-0.675326\pi$
$733$	7516.81	−	8348.26i	0.378772	−	0.420669i	0.902144	+	0.431436i	$0.141993\pi$
$734$	1169.89	−	11130.8i	0.0588304	−	0.559734i
$735$	5608.57	−	1192.14i	0.281463	−	0.0598267i
$736$	972.203	−	2992.13i	0.0486900	−	0.149853i
$737$	7342.67	+	1560.73i	0.366989	+	0.0780059i
$738$	15380.1	−	26639.2i	0.767142	−	1.32873i
$739$	1971.62	+	3414.95i	0.0981426	+	0.169988i	0.910916	−	0.412592i	$-0.135377\pi$
$739$	1971.62	+	3414.95i	0.0981426	+	0.169988i	−0.812773	+	0.582580i	$0.802043\pi$
$740$	−2184.29	−	6722.55i	−0.108508	−	0.333954i
$741$	416.507	+	3962.80i	0.0206488	+	0.196460i
$742$	14491.9	+	10529.0i	0.717002	+	0.520932i
$743$	22259.0			1.09906			0.549530	−	0.835474i	$-0.314807\pi$
$743$	22259.0			1.09906			0.549530	+	0.835474i	$0.314807\pi$
$744$	−83933.5	+	27086.9i	−4.13596	+	1.33475i
$745$	−2096.64			−0.103107
$746$	−5020.75	−	3647.79i	−0.246411	−	0.179028i
$747$	−5162.27	−	49115.7i	−0.252848	−	2.40569i
$748$	−13656.5	−	42030.2i	−0.667553	−	2.05452i
$749$	6955.76	+	12047.7i	0.339330	+	0.587737i
$750$	14819.2	−	25667.6i	0.721495	−	1.24967i
$751$	−37247.2	−	7917.13i	−1.80981	−	0.384688i	−0.825969	−	0.563716i	$-0.809371\pi$
$751$	−37247.2	−	7917.13i	−1.80981	−	0.384688i	−0.983844	+	0.179028i	$0.942705\pi$
$752$	−10721.3	+	32996.9i	−0.519903	+	1.60010i
$753$	−19452.5	+	4134.75i	−0.941417	+	0.200104i
$754$	363.745	−	3460.80i	0.0175687	−	0.167155i
$755$	388.493	−	431.465i	0.0187268	−	0.0207982i
$756$	−70167.6	+	31240.6i	−3.37562	+	1.50292i
$757$	27040.0	+	12039.0i	1.29826	+	0.578024i	0.935325	−	0.353790i	$-0.115107\pi$
$757$	27040.0	+	12039.0i	1.29826	+	0.578024i	0.362937	+	0.931814i	$0.381774\pi$
$758$	4993.66	+	5546.03i	0.239285	+	0.265753i
$759$	−3679.59	+	2673.38i	−0.175969	+	0.127849i
$760$	8217.79	−	5970.57i	0.392224	−	0.284968i
$761$	7892.67	+	8765.70i	0.375965	+	0.417551i	0.901198	−	0.433407i	$-0.142689\pi$
$761$	7892.67	+	8765.70i	0.375965	+	0.417551i	−0.525234	+	0.850958i	$0.676022\pi$
$762$	−41575.9	−	18510.8i	−1.97656	−	0.880020i
$763$	−13660.1	+	6081.85i	−0.648136	+	0.288569i
$764$	14122.7	−	15684.8i	0.668770	−	0.742745i
$765$	1451.86	−	13813.5i	0.0686170	−	0.652847i
$766$	−2350.98	+	499.716i	−0.110893	+	0.0235711i
$767$	−14.3283	+	44.0981i	−0.000674532	+	0.00207600i
$768$	68135.5	+	14482.6i	3.20134	+	0.680465i
$769$	7490.20	−	12973.4i	0.351240	−	0.608365i	−0.635227	−	0.772325i	$-0.719094\pi$
$769$	7490.20	−	12973.4i	0.351240	−	0.608365i	0.986467	+	0.163960i	$0.0524268\pi$
$770$	1831.78	+	3172.74i	0.0857309	+	0.148490i
$771$	6023.20	+	18537.5i	0.281349	+	0.865903i
$772$	−1336.11	−	12712.3i	−0.0622899	−	0.592649i
$773$	12377.0	+	8992.43i	0.575900	+	0.418416i	0.837244	−	0.546830i	$-0.184166\pi$
$773$	12377.0	+	8992.43i	0.575900	+	0.418416i	−0.261344	+	0.965246i	$0.584166\pi$
$774$	45684.9			2.12159
$775$	40.9852	−	20569.9i	0.00189965	−	0.953409i
$776$	21785.3			1.00779
$777$	−12922.5	−	9388.72i	−0.596642	−	0.433486i
$778$	1494.56	+	14219.8i	0.0688724	+	0.655277i
$779$	2159.65	+	6646.71i	0.0993291	+	0.305703i
$780$	−1077.74	−	1866.69i	−0.0494732	−	0.0856902i
$781$	−7560.49	+	13095.2i	−0.346396	+	0.599976i
$782$	6480.41	+	1377.45i	0.296341	+	0.0629893i
$783$	−17657.6	+	54344.5i	−0.805915	+	2.48035i
$784$	28472.1	−	6051.93i	1.29702	−	0.275689i
$785$	−205.463	+	1954.85i	−0.00934175	+	0.0888808i
$786$	−68823.1	+	76435.8i	−3.12320	+	3.46867i
$787$	−39276.5	+	17487.0i	−1.77898	+	0.792051i	−0.796761	+	0.604295i	$0.793455\pi$
$787$	−39276.5	+	17487.0i	−1.77898	+	0.792051i	−0.982216	+	0.187756i	$0.939878\pi$
$788$	−77515.8	−	34512.3i	−3.50430	−	1.56021i
$789$	17347.1	+	19265.9i	0.782729	+	0.869308i
$790$	−10583.2	+	7689.12i	−0.476623	+	0.346287i
$791$	−1681.99	+	1222.03i	−0.0756063	+	0.0549312i
$792$	71445.8	+	79348.6i	3.20545	+	3.56001i
$793$	2076.21	+	924.387i	0.0929739	+	0.0413946i
$794$	−39400.7	+	17542.3i	−1.76106	+	0.784073i
$795$	5523.34	−	6134.29i	0.246406	−	0.273661i
$796$	−4701.51	+	44731.8i	−0.209347	+	1.99181i
$797$	32722.0	−	6955.28i	1.45430	−	0.309120i	0.588085	−	0.808799i	$-0.299882\pi$
$797$	32722.0	−	6955.28i	1.45430	−	0.309120i	0.866211	+	0.499679i	$0.166549\pi$
$798$	12678.9	−	39021.5i	0.562440	−	1.73101i
$799$	−23256.2	−	4943.26i	−1.02972	−	0.218873i
$800$	11948.8	−	20695.9i	0.528066	−	0.914637i
$801$	−27305.6	−	47294.7i	−1.20449	−	2.08624i
$802$	−1159.43	−	3568.36i	−0.0510485	−	0.157111i
$803$	−3202.04	−	30465.4i	−0.140719	−	1.33886i
$804$	36792.2	+	26731.1i	1.61388	+	1.17255i
$805$	−381.256			−0.0166926
$806$	−3819.37	−	2215.27i	−0.166913	−	0.0968110i
$807$	35828.0			1.56283
$808$	−23388.9	−	16993.0i	−1.01834	−	0.739867i
$809$	−1946.39	−	18518.6i	−0.0845875	−	0.804797i	−0.951771	−	0.306808i	$-0.900739\pi$
$809$	−1946.39	−	18518.6i	−0.0845875	−	0.804797i	0.867184	−	0.497988i	$-0.165928\pi$
$810$	8576.69	+	26396.3i	0.372042	+	1.14503i
$811$	1362.64	+	2360.17i	0.0589998	+	0.102191i	0.894017	−	0.448034i	$-0.147876\pi$
$811$	1362.64	+	2360.17i	0.0589998	+	0.102191i	−0.835017	+	0.550224i	$0.814542\pi$
$812$	−12436.9	+	21541.4i	−0.537501	+	0.930980i
$813$	50364.8	+	10705.4i	2.17266	+	0.461812i
$814$	−7514.80	+	23128.2i	−0.323579	+	0.995875i
$815$	2449.40	−	520.636i	0.105275	−	0.0223768i
$816$	10225.0	−	97284.1i	0.438659	−	4.17356i
$817$	−6945.34	+	7713.58i	−0.297413	+	0.330311i
$818$	−8576.46	+	3818.48i	−0.366588	+	0.163215i
$819$	−3207.47	−	1428.06i	−0.136847	−	0.0609283i
$820$	−2529.68	−	2809.49i	−0.107732	−	0.119648i
$821$	−3167.20	+	2301.10i	−0.134636	+	0.0978186i	−0.653065	−	0.757302i	$-0.726517\pi$
$821$	−3167.20	+	2301.10i	−0.134636	+	0.0978186i	0.518429	+	0.855121i	$0.326517\pi$
$822$	98006.1	−	71205.6i	4.15858	−	3.02139i
$823$	15756.8	+	17499.7i	0.667373	+	0.741193i	0.977831	−	0.209394i	$-0.0671492\pi$
$823$	15756.8	+	17499.7i	0.667373	+	0.741193i	−0.310458	+	0.950587i	$0.600483\pi$
$824$	−96545.8	−	42984.9i	−4.08171	−	1.81730i
$825$	−31561.0	+	14051.9i	−1.33189	+	0.592997i
$826$	319.473	−	354.810i	0.0134575	−	0.0149460i
$827$	4589.14	−	43662.8i	0.192963	−	1.83592i	−0.286175	−	0.958177i	$-0.592384\pi$
$827$	4589.14	−	43662.8i	0.192963	−	1.83592i	0.479137	−	0.877740i	$-0.340950\pi$
$828$	−19427.8	+	4129.51i	−0.815415	+	0.173322i
$829$	−7000.51	+	21545.4i	−0.293291	+	0.902656i	0.690500	+	0.723333i	$0.257391\pi$
$829$	−7000.51	+	21545.4i	−0.293291	+	0.902656i	−0.983790	+	0.179323i	$0.942609\pi$
$830$	−8552.71	−	1817.93i	−0.357673	−	0.0760258i
$831$	−6797.09	+	11772.9i	−0.283741	+	0.491453i
$832$	−154.460	−	267.533i	−0.00643624	−	0.0111479i
$833$	6164.03	+	18970.9i	0.256388	+	0.789080i
$834$	4388.13	+	41750.3i	0.182193	+	1.73345i
$835$	719.960	+	523.082i	0.0298386	+	0.0216790i
$836$	−43362.7			−1.79393
$837$	53782.6	+	48620.4i	2.22102	+	2.00785i
$838$	−49814.3			−2.05347
$839$	−27000.8	−	19617.2i	−1.11105	−	0.807225i	−0.128221	−	0.991746i	$-0.540927\pi$
$839$	−27000.8	−	19617.2i	−1.11105	−	0.807225i	−0.982829	+	0.184520i	$0.940927\pi$
$840$	1297.92	+	12348.8i	0.0533123	+	0.507233i
$841$	−1818.29	−	5596.12i	−0.0745537	−	0.229453i
$842$	−18867.6	−	32679.6i	−0.772231	−	1.33754i
$843$	42817.9	−	74162.7i	1.74938	−	3.03001i
$844$	−32136.9	−	6830.92i	−1.31066	−	0.278590i
$845$	−1619.71	+	4984.95i	−0.0659404	+	0.202944i
$846$	100436.	−	21348.3i	4.08163	−	0.867578i
$847$	−486.374	+	4627.54i	−0.0197308	+	0.187726i
$848$	28039.5	−	31141.0i	1.13547	−	1.26107i
$849$	36883.1	−	16421.4i	1.49096	−	0.663817i
$850$	45973.4	+	20468.7i	1.85515	+	0.825965i
$851$	−1693.40	−	1880.71i	−0.0682127	−	0.0757578i
$852$	−74111.6	+	53845.3i	−2.98007	+	2.16515i
$853$	7619.51	−	5535.90i	0.305846	−	0.222210i	−0.424266	−	0.905538i	$-0.639468\pi$
$853$	7619.51	−	5535.90i	0.305846	−	0.222210i	0.730112	+	0.683327i	$0.239468\pi$
$854$	−15658.9	−	17391.0i	−0.627443	−	0.696846i
$855$	−12450.3	−	5543.23i	−0.498002	−	0.221725i
$856$	65578.4	−	29197.4i	2.61849	−	1.16582i
$857$	−11488.3	+	12759.0i	−0.457914	+	0.508565i	−0.927244	−	0.374458i	$-0.877829\pi$
$857$	−11488.3	+	12759.0i	−0.457914	+	0.508565i	0.469330	+	0.883023i	$0.344496\pi$
$858$	−775.147	+	7375.03i	−0.0308428	+	0.293449i
$859$	29132.2	−	6192.24i	1.15713	−	0.245956i	0.410925	−	0.911669i	$-0.365206\pi$
$859$	29132.2	−	6192.24i	1.15713	−	0.245956i	0.746208	+	0.665713i	$0.231872\pi$
$860$	1735.08	−	5340.02i	0.0687973	−	0.211736i
$861$	−8356.39	−	1776.21i	−0.330761	−	0.0703054i
$862$	−27270.4	+	47233.7i	−1.07753	+	1.86634i
$863$	17287.8	+	29943.3i	0.681903	+	1.18109i	0.974399	+	0.224824i	$0.0721806\pi$
$863$	17287.8	+	29943.3i	0.681903	+	1.18109i	−0.292497	+	0.956267i	$0.594486\pi$
$864$	26028.7	+	80108.0i	1.02490	+	3.15432i
$865$	−1075.97	−	10237.2i	−0.0422938	−	0.402399i
$866$	−45219.5	−	32853.9i	−1.77439	−	1.28917i
$867$	18718.1			0.733216
$868$	18499.8	+	25569.8i	0.723416	+	0.999881i
$869$	31241.8			1.21957
$870$	13358.3	+	9705.41i	0.520564	+	0.378212i
$871$	133.139	+	1266.73i	0.00517939	+	0.0492786i
$872$	23843.0	+	73381.2i	0.925947	+	2.84977i
$873$	−14614.6	−	25313.1i	−0.566584	−	0.981352i
$874$	3250.34	−	5629.75i	0.125794	−	0.217882i
$875$	−5803.81	−	1233.64i	−0.224234	−	0.0476624i
$876$	57348.8	−	176501.i	2.21191	−	6.80757i
$877$	−34544.9	+	7342.74i	−1.33010	+	0.282722i	−0.817511	−	0.575913i	$-0.804647\pi$
$877$	−34544.9	+	7342.74i	−1.33010	+	0.282722i	−0.512589	+	0.858634i	$0.671314\pi$
$878$	3411.42	−	32457.5i	0.131128	−	1.24760i
$879$	−7541.24	+	8375.39i	−0.289374	+	0.321382i
$880$	7829.31	−	3485.83i	0.299916	−	0.133531i
$881$	20328.3	+	9050.73i	0.777386	+	0.346114i	0.756777	−	0.653673i	$-0.226773\pi$
$881$	20328.3	+	9050.73i	0.777386	+	0.346114i	0.0206088	+	0.999788i	$0.493440\pi$
$882$	−57642.7	−	64018.6i	−2.20060	−	2.44401i
$883$	−25370.3	+	18432.6i	−0.966908	+	0.702500i	−0.954745	−	0.297426i	$-0.903872\pi$
$883$	−25370.3	+	18432.6i	−0.966908	+	0.702500i	−0.0121632	+	0.999926i	$0.503872\pi$
$884$	6066.45	−	4407.54i	0.230811	−	0.167694i
$885$	−147.216	−	163.500i	−0.00559167	−	0.00621018i
$886$	60313.4	+	26853.3i	2.28699	+	1.01823i
$887$	15478.3	−	6891.38i	0.585919	−	0.260868i	−0.0922956	−	0.995732i	$-0.529420\pi$
$887$	15478.3	−	6891.38i	0.585919	−	0.260868i	0.678215	+	0.734864i	$0.262754\pi$
$888$	−55151.1	+	61251.5i	−2.08418	+	2.31471i
$889$	−952.357	+	9061.07i	−0.0359292	+	0.341843i
$890$	−9457.56	+	2010.27i	−0.356200	+	0.0757127i
$891$	20483.2	−	63040.9i	0.770161	−	2.37031i
$892$	−18336.4	−	3897.53i	−0.688284	−	0.146299i
$893$	−11664.5	+	20203.4i	−0.437107	+	0.757091i
$894$	21849.9	+	37845.1i	0.817416	+	1.41581i
$895$	−2688.35	−	8273.88i	−0.100404	−	0.309012i
$896$	−1355.98	−	12901.3i	−0.0505581	−	0.481028i
$897$	−624.339	−	453.609i	−0.0232398	−	0.0168847i
$898$	60342.3			2.24237
$899$	23345.8	+	2500.78i	0.866101	+	0.0927761i
$900$	−150868.			−5.58772
$901$	23231.8	+	16878.9i	0.859006	+	0.624104i
$902$	1359.55	+	12935.3i	0.0501865	+	0.477492i
$903$	−3920.84	−	12067.1i	−0.144493	−	0.444705i
$904$	5364.02	+	9290.76i	0.197350	+	0.341821i
$905$	−2703.42	+	4682.46i	−0.0992981	+	0.171989i
$906$	−11836.8	−	2515.98i	−0.434051	−	0.0922604i
$907$	−9277.57	+	28553.4i	−0.339643	+	1.04531i	0.624746	+	0.780828i	$0.285203\pi$
$907$	−9277.57	+	28553.4i	−0.339643	+	1.04531i	−0.964389	+	0.264487i	$0.914797\pi$
$908$	22460.8	−	4774.19i	0.820912	−	0.174490i
$909$	−4054.52	+	38576.1i	−0.147943	+	1.40758i
$910$	−415.945	+	461.954i	−0.0151521	+	0.0168281i
$911$	304.213	−	135.445i	0.0110637	−	0.00492588i	−0.401197	−	0.915992i	$-0.631406\pi$
$911$	304.213	−	135.445i	0.0110637	−	0.00492588i	0.412261	+	0.911066i	$0.364739\pi$
$912$	−87683.6	−	39039.2i	−3.18365	−	1.41745i
$913$	13973.0	+	15518.5i	0.506503	+	0.562529i
$914$	30095.8	−	21865.9i	1.08915	−	0.791311i
$915$	−8724.30	+	6338.57i	−0.315209	+	0.229013i
$916$	−53956.9	−	59925.2i	−1.94627	−	2.16155i
$917$	18810.8	+	8375.10i	0.677412	+	0.301603i
$918$	−162040.	+	72145.0i	−5.82585	+	2.59383i
$919$	8577.75	−	9526.56i	0.307893	−	0.341950i	−0.569263	−	0.822156i	$-0.692771\pi$
$919$	8577.75	−	9526.56i	0.307893	−	0.341950i	0.877156	+	0.480206i	$0.159438\pi$
$920$	−205.640	+	1956.53i	−0.00736928	+	0.0701141i
$921$	−49302.0	+	10479.5i	−1.76391	+	0.374930i
$922$	20371.2	−	62696.2i	0.727648	−	2.23947i
$923$	−2509.61	−	533.434i	−0.0894960	−	0.0190230i
$924$	26503.3	−	45905.1i	0.943610	−	1.63438i
$925$	−9611.63	−	16647.8i	−0.341652	−	0.591759i
$926$	23852.6	+	73410.8i	0.846485	+	2.60521i
$927$	14821.4	+	141016.i	0.525134	+	4.99632i
$928$	22068.1	+	16033.4i	0.780624	+	0.567157i
$929$	−34508.5			−1.21872			−0.609359	−	0.792895i	$-0.708573\pi$
$929$	−34508.5			−1.21872			−0.609359	+	0.792895i	$0.708573\pi$
$930$	18164.5	−	10439.1i	0.640470	−	0.368076i
$931$	19572.3			0.688999
$932$	50698.8	+	36834.8i	1.78186	+	1.29460i
$933$	−7609.52	−	72399.7i	−0.267014	−	2.54047i
$934$	11096.6	+	34151.8i	0.388749	+	1.19645i
$935$	2936.50	+	5086.17i	0.102710	+	0.177899i
$936$	−9058.53	+	15689.8i	−0.316333	+	0.547904i
$937$	−50040.9	−	10636.5i	−1.74468	−	0.370843i	−0.778285	−	0.627911i	$-0.783910\pi$
$937$	−50040.9	−	10636.5i	−1.74468	−	0.370843i	−0.966393	+	0.257068i	$0.917243\pi$
$938$	4052.88	−	12473.5i	0.141078	−	0.434193i
$939$	−26610.9	+	5656.32i	−0.924829	+	0.196578i
$940$	1319.12	−	12550.6i	0.0457711	−	0.435483i
$941$	15432.4	−	17139.4i	0.534624	−	0.593761i	−0.413956	−	0.910297i	$-0.635853\pi$
$941$	15432.4	−	17139.4i	0.534624	−	0.593761i	0.948580	+	0.316536i	$0.102520\pi$
$942$	37427.0	−	16663.6i	1.29452	−	0.576357i
$943$	−1236.53	−	550.540i	−0.0427010	−	0.0190117i
$944$	−747.350	−	830.016i	−0.0257671	−	0.0286173i
$945$	8257.89	−	5999.71i	0.284264	−	0.206530i
$946$	−15627.9	+	11354.4i	−0.537112	+	0.390235i
$947$	22288.7	+	24754.2i	0.764822	+	0.849421i	0.992235	−	0.124377i	$-0.0396932\pi$
$947$	22288.7	+	24754.2i	0.764822	+	0.849421i	−0.227413	+	0.973799i	$0.573027\pi$
$948$	172908.	+	76983.7i	5.92384	+	2.63746i
$949$	4748.37	−	2114.11i	0.162422	−	0.0723150i
$950$	33040.6	−	36695.3i	1.12840	−	1.25321i
$951$	−9606.80	+	91402.6i	−0.327573	+	3.11665i
$952$	−42252.4	+	8981.02i	−1.43845	+	0.305753i
$953$	−12242.5	+	37678.5i	−0.416132	+	1.28072i	0.495103	+	0.868834i	$0.335130\pi$
$953$	−12242.5	+	37678.5i	−0.416132	+	1.28072i	−0.911235	+	0.411887i	$0.864870\pi$
$954$	−121306.	−	25784.3i	−4.11679	−	0.875050i
$955$	−1402.43	+	2429.08i	−0.0475200	+	0.0823070i
$956$	36978.8	+	64049.2i	1.25103	+	2.16684i
$957$	−12185.8	−	37504.2i	−0.411612	−	1.26681i
$958$	1239.31	+	11791.2i	0.0417957	+	0.397659i
$959$	−19620.4	−	14255.0i	−0.660661	−	0.479999i
$960$	1465.82			0.0492802
$961$	14998.2	−	25740.2i	0.503447	−	0.864026i
$962$	−4126.26			−0.138291
$963$	−77918.5	−	56611.1i	−2.60736	−	1.89436i
$964$	−10920.1	−	103898.i	−0.364848	−	3.47130i
$965$	524.924	+	1615.55i	0.0175108	+	0.0538926i
$966$	3973.22	+	6881.82i	0.132336	+	0.229212i
$967$	−16194.0	+	28048.8i	−0.538536	+	0.932771i	0.460447	+	0.887687i	$0.347689\pi$
$967$	−16194.0	+	28048.8i	−0.538536	+	0.932771i	−0.998983	+	0.0450843i	$0.985644\pi$
$968$	23485.3	+	4991.95i	0.779799	+	0.165751i
$969$	20325.3	−	62554.9i	0.673832	−	2.07384i
$970$	−5061.89	+	1075.94i	−0.167554	+	0.0356147i
$971$	−5629.92	+	53565.1i	−0.186069	+	1.77033i	0.360354	+	0.932816i	$0.382656\pi$
$971$	−5629.92	+	53565.1i	−0.186069	+	1.77033i	−0.546423	+	0.837510i	$0.684011\pi$
$972$	130897.	−	145376.i	4.31947	−	4.79726i
$973$	7677.66	−	3418.31i	0.252965	−	0.112627i
$974$	−66617.6	−	29660.1i	−2.19155	−	0.975740i
$975$	−3922.41	−	4356.27i	−0.128839	−	0.143090i
$976$	−44289.2	+	32178.0i	−1.45252	+	1.05532i
$977$	−26474.2	+	19234.6i	−0.866922	+	0.629856i	−0.929759	−	0.368168i	$-0.879985\pi$
$977$	−26474.2	+	19234.6i	−0.866922	+	0.629856i	0.0628370	+	0.998024i	$0.479985\pi$
$978$	−34923.9	−	38786.9i	−1.14186	−	1.26817i
$979$	21095.2	+	9392.18i	0.688667	+	0.306614i
$980$	−9672.24	+	4306.36i	−0.315274	+	0.140369i
$981$	69269.4	−	76931.5i	2.25444	−	2.50381i
$982$	865.363	−	8233.38i	0.0281210	−	0.267554i
$983$	8452.69	−	1796.67i	0.274261	−	0.0582961i	−0.0687276	−	0.997635i	$-0.521894\pi$
$983$	8452.69	−	1796.67i	0.274261	−	0.0582961i	0.342989	+	0.939339i	$0.388561\pi$
$984$	−13622.4	+	41925.3i	−0.441326	+	1.35826i
$985$	11029.8	+	2344.47i	0.356792	+	0.0758385i
$986$	−28721.0	+	49746.3i	−0.927651	+	1.60674i
$987$	−14258.7	−	24696.7i	−0.459836	−	0.796460i
$988$	−2273.63	−	6997.52i	−0.0732124	−	0.225325i
$989$	−210.132	−	1999.27i	−0.00675613	−	0.0642803i
$990$	−20519.6	−	14908.4i	−0.658743	−	0.478605i
$991$	−7311.82			−0.234377			−0.117188	−	0.993110i	$-0.537388\pi$
$991$	−7311.82			−0.234377			−0.117188	+	0.993110i	$0.537388\pi$
$992$	30007.8	−	17245.4i	0.960433	−	0.551958i
$993$	16794.4			0.536711
$994$	21373.2	+	15528.5i	0.682008	+	0.495508i
$995$	−624.801	−	5944.59i	−0.0199071	−	0.189403i
$996$	39093.9	+	120319.i	1.24371	+	3.82775i
$997$	−31004.8	−	53702.0i	−0.984888	−	1.70588i	−0.642433	−	0.766342i	$-0.722075\pi$
$997$	−31004.8	−	53702.0i	−0.984888	−	1.70588i	−0.342455	−	0.939534i	$-0.611258\pi$
$998$	17060.8	−	29550.2i	0.541133	−	0.937269i
$999$	66274.7	+	14087.1i	2.09894	+	0.446143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.10.1	✓	56
31.11	odd	30		961.4.a.l.1.27		28
31.20	even	15		961.4.a.m.1.27		28
31.28	even	15	inner	31.4.g.a.28.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.10.1	✓	56	1.1	even	1	trivial
31.4.g.a.28.1	yes	56	31.28	even	15	inner
961.4.a.l.1.27		28	31.11	odd	30
961.4.a.m.1.27		28	31.20	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.13779 - 3.00628i) q^{2} +(-1.02796 - 9.78042i) q^{3} +(5.61145 + 17.2703i) q^{4} +(-1.20661 - 2.08991i) q^{5} +(-25.1492 + 43.5597i) q^{6} +(9.84945 + 2.09357i) q^{7} +(16.0563 - 49.4162i) q^{8} +(-68.1899 + 14.4942i) q^{9} +(-1.29016 + 12.2750i) q^{10} +(19.7241 - 21.9059i) q^{11} +(163.142 - 72.6355i) q^{12} +(4.56919 + 2.03433i) q^{13} +(-34.4611 - 38.2729i) q^{14} +(-19.1999 + 13.9495i) q^{15} +(-97.4690 + 70.8153i) q^{16} +(-55.2442 - 61.3549i) q^{17} +(325.729 + 145.024i) q^{18} +(-74.0059 + 32.9496i) q^{19} +(29.3225 - 32.5660i) q^{20} +(10.3511 - 98.4838i) q^{21} +(-147.470 + 31.3456i) q^{22} +(4.84835 - 14.9217i) q^{23} +(-499.817 - 106.239i) q^{24} +(59.5882 - 103.210i) q^{25} +(-12.7906 - 22.1539i) q^{26} +(129.804 + 399.496i) q^{27} +(19.1133 + 181.851i) q^{28} +(110.053 + 79.9580i) q^{29} +121.381 q^{30} +(149.648 - 86.0023i) q^{31} +200.523 q^{32} +(-234.524 - 170.392i) q^{33} +(44.1389 + 419.953i) q^{34} +(-7.50910 - 23.1106i) q^{35} +(-632.963 - 1096.32i) q^{36} +(80.6505 - 139.691i) q^{37} +(405.277 + 86.1442i) q^{38} +(15.1997 - 46.7798i) q^{39} +(-122.649 + 26.0699i) q^{40} +(9.01775 - 85.7982i) q^{41} +(-338.901 + 376.387i) q^{42} +(117.051 - 52.1146i) q^{43} +(489.001 + 217.717i) q^{44} +(112.570 + 125.022i) q^{45} +(-64.9202 + 47.1673i) q^{46} +(232.979 - 169.269i) q^{47} +(792.798 + 880.492i) q^{48} +(-220.717 - 98.2697i) q^{49} +(-556.841 + 247.922i) q^{50} +(-543.288 + 603.382i) q^{51} +(-9.49371 + 90.3266i) q^{52} +(-340.216 + 72.3151i) q^{53} +(663.895 - 2043.26i) q^{54} +(-69.5808 - 14.7898i) q^{55} +(261.602 - 453.108i) q^{56} +(398.336 + 689.938i) q^{57} +(-214.999 - 661.699i) q^{58} +(0.969034 + 9.21974i) q^{59} +(-348.651 - 253.310i) q^{60} +454.393 q^{61} +(-877.760 - 94.0249i) q^{62} -701.978 q^{63} +(-49.9685 - 36.3042i) q^{64} +(-1.26166 - 12.0039i) q^{65} +(458.167 + 1410.09i) q^{66} +(127.331 + 220.543i) q^{67} +(749.615 - 1298.37i) q^{68} +(-150.924 - 32.0799i) q^{69} +(-38.4060 + 118.201i) q^{70} +(-501.762 + 106.653i) q^{71} +(-378.629 + 3602.41i) q^{72} +(695.371 - 772.288i) q^{73} +(-753.664 + 335.553i) q^{74} +(-1070.69 - 476.701i) q^{75} +(-984.328 - 1093.21i) q^{76} +(240.133 - 174.467i) q^{77} +(-203.526 + 147.870i) q^{78} +(709.187 + 787.631i) q^{79} +(265.605 + 118.255i) q^{80} +(2054.28 - 914.623i) q^{81} +(-295.247 + 327.905i) q^{82} +(-74.0500 + 704.539i) q^{83} +(1758.93 - 373.871i) q^{84} +(-61.5681 + 189.487i) q^{85} +(-641.005 - 136.250i) q^{86} +(668.893 - 1158.56i) q^{87} +(-765.809 - 1326.42i) q^{88} +(242.074 + 745.027i) q^{89} +(-89.9412 - 855.734i) q^{90} +(40.7450 + 29.6029i) q^{91} +284.908 q^{92} +(-994.972 - 1375.22i) q^{93} -1472.89 q^{94} +(158.158 + 114.909i) q^{95} +(-206.130 - 1961.19i) q^{96} +(129.563 + 398.755i) q^{97} +(617.856 + 1070.16i) q^{98} +(-1027.48 + 1779.64i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Introduction

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