LMFDB - Embedded newform 48.4.j.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,4,Mod(13,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("48.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	48.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.83209168028$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.6
Character	$\chi$	$=$	48.13
Dual form			48.4.j.a.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.716137 - 2.73627i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.97430 + 3.91908i) q^{4} +(-11.7719 + 11.7719i) q^{5} +(-4.28534 + 7.32365i) q^{6} -14.7089i q^{7} +(15.7182 + 16.2769i) q^{8} +9.00000i q^{9} +O(q^{10})$	\(q+(-0.716137 - 2.73627i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.97430 + 3.91908i) q^{4} +(-11.7719 + 11.7719i) q^{5} +(-4.28534 + 7.32365i) q^{6} -14.7089i q^{7} +(15.7182 + 16.2769i) q^{8} +9.00000i q^{9} +(40.6415 + 23.7808i) q^{10} +(-24.9380 + 24.9380i) q^{11} +(23.1083 + 6.48109i) q^{12} +(-58.1345 - 58.1345i) q^{13} +(-40.2475 + 10.5336i) q^{14} +49.9441 q^{15} +(33.2816 - 54.6657i) q^{16} -75.8798 q^{17} +(24.6264 - 6.44523i) q^{18} +(51.8464 + 51.8464i) q^{19} +(35.9658 - 128.236i) q^{20} +(-31.2023 + 31.2023i) q^{21} +(86.0960 + 50.3779i) q^{22} -149.444i q^{23} +(1.18523 - 67.8719i) q^{24} -152.157i q^{25} +(-117.439 + 200.704i) q^{26} +(19.0919 - 19.0919i) q^{27} +(57.6455 + 102.584i) q^{28} +(48.5419 + 48.5419i) q^{29} +(-35.7668 - 136.660i) q^{30} +29.6074 q^{31} +(-173.414 - 51.9192i) q^{32} +105.803 q^{33} +(54.3403 + 207.627i) q^{34} +(173.153 + 173.153i) q^{35} +(-35.2717 - 62.7687i) q^{36} +(-147.751 + 147.751i) q^{37} +(104.736 - 178.994i) q^{38} +246.644i q^{39} +(-376.645 - 6.57727i) q^{40} +225.232i q^{41} +(107.723 + 63.0327i) q^{42} +(81.7640 - 81.7640i) q^{43} +(76.1909 - 271.659i) q^{44} +(-105.947 - 105.947i) q^{45} +(-408.917 + 107.022i) q^{46} +46.5418 q^{47} +(-186.564 + 45.3625i) q^{48} +126.648 q^{49} +(-416.342 + 108.965i) q^{50} +(160.965 + 160.965i) q^{51} +(633.281 + 177.613i) q^{52} +(-156.105 + 156.105i) q^{53} +(-65.9129 - 38.5681i) q^{54} -587.137i q^{55} +(239.416 - 231.198i) q^{56} -219.965i q^{57} +(98.0609 - 167.586i) q^{58} +(-238.199 + 238.199i) q^{59} +(-348.325 + 195.735i) q^{60} +(-594.013 - 594.013i) q^{61} +(-21.2029 - 81.0137i) q^{62} +132.380 q^{63} +(-17.8765 + 511.688i) q^{64} +1368.71 q^{65} +(-75.7694 - 289.505i) q^{66} +(299.623 + 299.623i) q^{67} +(529.208 - 297.379i) q^{68} +(-317.018 + 317.018i) q^{69} +(349.790 - 597.792i) q^{70} -693.932i q^{71} +(-146.492 + 141.464i) q^{72} +462.446i q^{73} +(510.096 + 298.476i) q^{74} +(-322.774 + 322.774i) q^{75} +(-564.782 - 158.402i) q^{76} +(366.811 + 366.811i) q^{77} +(674.883 - 176.631i) q^{78} -878.797 q^{79} +(251.732 + 1035.31i) q^{80} -81.0000 q^{81} +(616.293 - 161.297i) q^{82} +(-926.380 - 926.380i) q^{83} +(95.3298 - 339.899i) q^{84} +(893.252 - 893.252i) q^{85} +(-282.282 - 165.174i) q^{86} -205.946i q^{87} +(-797.894 - 13.9335i) q^{88} -350.770i q^{89} +(-214.027 + 365.773i) q^{90} +(-855.096 + 855.096i) q^{91} +(585.682 + 1042.26i) q^{92} +(-62.8068 - 62.8068i) q^{93} +(-33.3303 - 127.351i) q^{94} -1220.66 q^{95} +(257.729 + 478.004i) q^{96} -766.194 q^{97} +(-90.6971 - 346.542i) q^{98} +(-224.442 - 224.442i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) $ 24 * q - 20 * q^4 + 84 * q^8	$ 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) $ 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.716137	−	2.73627i	−0.253193	−	0.967416i
$2$	−0.716137	−	2.73627i	−0.253193	−	0.967416i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$3$	−2.12132	−	2.12132i	−0.408248	−	0.408248i
$4$	−6.97430	+	3.91908i	−0.871787	+	0.489885i
$5$	−11.7719	+	11.7719i	−1.05291	+	1.05291i	−0.0543947	+	0.998520i	$0.517323\pi$
$5$	−11.7719	+	11.7719i	−1.05291	+	1.05291i	−0.998520	+	0.0543947i	$0.982677\pi$
$6$	−4.28534	+	7.32365i	−0.291580	+	0.498311i
$7$		−	14.7089i		−	0.794207i	−0.917774	−	0.397104i	$-0.870015\pi$
$7$		−	14.7089i		−	0.794207i	0.917774	−	0.397104i	$-0.129985\pi$
$8$	15.7182	+	16.2769i	0.694653	+	0.719345i
$9$			9.00000i			0.333333i
$10$	40.6415	+	23.7808i	1.28520	+	0.752016i
$11$	−24.9380	+	24.9380i	−0.683553	+	0.683553i	−0.960799	−	0.277246i	$-0.910578\pi$
$11$	−24.9380	+	24.9380i	−0.683553	+	0.683553i	0.277246	+	0.960799i	$0.410578\pi$
$12$	23.1083	+	6.48109i	0.555900	+	0.155911i
$13$	−58.1345	−	58.1345i	−1.24028	−	1.24028i	−0.959885	−	0.280393i	$-0.909535\pi$
$13$	−58.1345	−	58.1345i	−1.24028	−	1.24028i	−0.280393	−	0.959885i	$-0.590465\pi$
$14$	−40.2475	+	10.5336i	−0.768329	+	0.201087i
$15$	49.9441			0.859701
$16$	33.2816	−	54.6657i	0.520025	−	0.854151i
$17$	−75.8798			−1.08256			−0.541281	−	0.840842i	$-0.682060\pi$
$17$	−75.8798			−1.08256			−0.541281	+	0.840842i	$0.682060\pi$
$18$	24.6264	−	6.44523i	0.322472	−	0.0843976i
$19$	51.8464	+	51.8464i	0.626020	+	0.626020i	0.947064	−	0.321045i	$-0.104034\pi$
$19$	51.8464	+	51.8464i	0.626020	+	0.626020i	−0.321045	+	0.947064i	$0.604034\pi$
$20$	35.9658	−	128.236i	0.402110	−	1.43372i
$21$	−31.2023	+	31.2023i	−0.324234	+	0.324234i
$22$	86.0960	+	50.3779i	0.834351	+	0.488210i
$23$		−	149.444i		−	1.35483i	−0.735600	−	0.677416i	$-0.763100\pi$
$23$		−	149.444i		−	1.35483i	0.735600	−	0.677416i	$-0.236900\pi$
$24$	1.18523	−	67.8719i	0.0100806	−	0.577262i
$25$		−	152.157i		−	1.21726i
$26$	−117.439	+	200.704i	−0.885836	+	1.51389i
$27$	19.0919	−	19.0919i	0.136083	−	0.136083i
$28$	57.6455	+	102.584i	0.389070	+	0.692379i
$29$	48.5419	+	48.5419i	0.310828	+	0.310828i	0.845230	−	0.534402i	$-0.179463\pi$
$29$	48.5419	+	48.5419i	0.310828	+	0.310828i	−0.534402	+	0.845230i	$0.679463\pi$
$30$	−35.7668	−	136.660i	−0.217670	−	0.831688i
$31$	29.6074			0.171537			0.0857685	−	0.996315i	$-0.472665\pi$
$31$	29.6074			0.171537			0.0857685	+	0.996315i	$0.472665\pi$
$32$	−173.414	−	51.9192i	−0.957986	−	0.286816i
$33$	105.803			0.558119
$34$	54.3403	+	207.627i	0.274097	+	1.04729i
$35$	173.153	+	173.153i	0.836232	+	0.836232i
$36$	−35.2717	−	62.7687i	−0.163295	−	0.290596i
$37$	−147.751	+	147.751i	−0.656489	+	0.656489i	−0.954548	−	0.298058i	$-0.903661\pi$
$37$	−147.751	+	147.751i	−0.656489	+	0.656489i	0.298058	+	0.954548i	$0.403661\pi$
$38$	104.736	−	178.994i	0.447118	−	0.764125i
$39$			246.644i			1.01268i
$40$	−376.645	−	6.57727i	−1.48882	−	0.0259990i
$41$			225.232i			0.857933i	0.903320	+	0.428967i	$0.141122\pi$
$41$			225.232i			0.857933i	−0.903320	+	0.428967i	$0.858878\pi$
$42$	107.723	+	63.0327i	0.395762	+	0.231575i
$43$	81.7640	−	81.7640i	0.289974	−	0.289974i	−0.547096	−	0.837070i	$-0.684267\pi$
$43$	81.7640	−	81.7640i	0.289974	−	0.289974i	0.837070	+	0.547096i	$0.184267\pi$
$44$	76.1909	−	271.659i	0.261050	−	0.930776i
$45$	−105.947	−	105.947i	−0.350971	−	0.350971i
$46$	−408.917	+	107.022i	−1.31069	+	0.343034i
$47$	46.5418			0.144443			0.0722215	−	0.997389i	$-0.476991\pi$
$47$	46.5418			0.144443			0.0722215	+	0.997389i	$0.476991\pi$
$48$	−186.564	+	45.3625i	−0.561005	+	0.136406i
$49$	126.648			0.369235
$50$	−416.342	+	108.965i	−1.17759	+	0.308200i
$51$	160.965	+	160.965i	0.441954	+	0.441954i
$52$	633.281	+	177.613i	1.68885	+	0.473664i
$53$	−156.105	+	156.105i	−0.404578	+	0.404578i	−0.879843	−	0.475265i	$-0.842352\pi$
$53$	−156.105	+	156.105i	−0.404578	+	0.404578i	0.475265	+	0.879843i	$0.342352\pi$
$54$	−65.9129	−	38.5681i	−0.166104	−	0.0971935i
$55$		−	587.137i		−	1.43945i
$56$	239.416	−	231.198i	0.571309	−	0.551698i
$57$		−	219.965i		−	0.511143i
$58$	98.0609	−	167.586i	0.222000	−	0.379399i
$59$	−238.199	+	238.199i	−0.525608	+	0.525608i	−0.919260	−	0.393652i	$-0.871212\pi$
$59$	−238.199	+	238.199i	−0.525608	+	0.525608i	0.393652	+	0.919260i	$0.371212\pi$
$60$	−348.325	+	195.735i	−0.749476	+	0.421155i
$61$	−594.013	−	594.013i	−1.24681	−	1.24681i	−0.957120	−	0.289692i	$-0.906447\pi$
$61$	−594.013	−	594.013i	−1.24681	−	1.24681i	−0.289692	−	0.957120i	$-0.593553\pi$
$62$	−21.2029	−	81.0137i	−0.0434319	−	0.165948i
$63$	132.380			0.264736
$64$	−17.8765	+	511.688i	−0.0349150	+	0.999390i
$65$	1368.71			2.61181
$66$	−75.7694	−	289.505i	−0.141312	−	0.539933i
$67$	299.623	+	299.623i	0.546339	+	0.546339i	0.925380	−	0.379041i	$-0.123746\pi$
$67$	299.623	+	299.623i	0.546339	+	0.546339i	−0.379041	+	0.925380i	$0.623746\pi$
$68$	529.208	−	297.379i	0.943763	−	0.530331i
$69$	−317.018	+	317.018i	−0.553108	+	0.553108i
$70$	349.790	−	597.792i	0.597256	−	1.02071i
$71$		−	693.932i		−	1.15992i	−0.814644	−	0.579962i	$-0.803067\pi$
$71$		−	693.932i		−	1.15992i	0.814644	−	0.579962i	$-0.196933\pi$
$72$	−146.492	+	141.464i	−0.239782	+	0.231551i
$73$			462.446i			0.741441i	0.928745	+	0.370720i	$0.120889\pi$
$73$			462.446i			0.741441i	−0.928745	+	0.370720i	$0.879111\pi$
$74$	510.096	+	298.476i	0.801316	+	0.468880i
$75$	−322.774	+	322.774i	−0.496943	+	0.496943i
$76$	−564.782	−	158.402i	−0.852433	−	0.239078i
$77$	366.811	+	366.811i	0.542883	+	0.542883i
$78$	674.883	−	176.631i	0.979686	−	0.256404i
$79$	−878.797			−1.25155			−0.625775	−	0.780004i	$-0.715217\pi$
$79$	−878.797			−1.25155			−0.625775	+	0.780004i	$0.715217\pi$
$80$	251.732	+	1035.31i	0.351806	+	1.44689i
$81$	−81.0000			−0.111111
$82$	616.293	−	161.297i	0.829978	−	0.217222i
$83$	−926.380	−	926.380i	−1.22510	−	1.22510i	−0.965795	−	0.259306i	$-0.916506\pi$
$83$	−926.380	−	926.380i	−1.22510	−	1.22510i	−0.259306	−	0.965795i	$-0.583494\pi$
$84$	95.3298	−	339.899i	0.123825	−	0.441500i
$85$	893.252	−	893.252i	1.13984	−	1.13984i
$86$	−282.282	−	165.174i	−0.353945	−	0.207106i
$87$		−	205.946i		−	0.253790i
$88$	−797.894	−	13.9335i	−0.966543	−	0.0168786i
$89$		−	350.770i		−	0.417770i	−0.977940	−	0.208885i	$-0.933017\pi$
$89$		−	350.770i		−	0.417770i	0.977940	−	0.208885i	$-0.0669834\pi$
$90$	−214.027	+	365.773i	−0.250672	+	0.428399i
$91$	−855.096	+	855.096i	−0.985038	+	0.985038i
$92$	585.682	+	1042.26i	0.663713	+	1.18113i
$93$	−62.8068	−	62.8068i	−0.0700296	−	0.0700296i
$94$	−33.3303	−	127.351i	−0.0365719	−	0.139737i
$95$	−1220.66			−1.31829
$96$	257.729	+	478.004i	0.274004	+	0.508188i
$97$	−766.194			−0.802013			−0.401006	−	0.916075i	$-0.631339\pi$
$97$	−766.194			−0.802013			−0.401006	+	0.916075i	$0.631339\pi$
$98$	−90.6971	−	346.542i	−0.0934876	−	0.357204i
$99$	−224.442	−	224.442i	−0.227851	−	0.227851i
$100$	596.316	+	1061.19i	0.596316	+	1.06119i
$101$	−983.994	+	983.994i	−0.969417	+	0.969417i	−0.999546	−	0.0301291i	$-0.990408\pi$
$101$	−983.994	+	983.994i	−0.969417	+	0.969417i	0.0301291	+	0.999546i	$0.490408\pi$
$102$	325.170	−	555.717i	0.315654	−	0.539453i
$103$			512.291i			0.490074i	0.969514	+	0.245037i	$0.0788000\pi$
$103$			512.291i			0.490074i	−0.969514	+	0.245037i	$0.921200\pi$
$104$	32.4812	−	1860.02i	0.0306254	−	1.75375i
$105$		−	734.624i		−	0.682781i
$106$	538.937	+	315.352i	0.493832	+	0.288959i
$107$	633.097	−	633.097i	0.571998	−	0.571998i	−0.360688	−	0.932686i	$-0.617458\pi$
$107$	633.097	−	633.097i	0.571998	−	0.571998i	0.932686	+	0.360688i	$0.117458\pi$
$108$	−58.3298	+	207.975i	−0.0519702	+	0.185300i
$109$	983.894	+	983.894i	0.864587	+	0.864587i	0.991867	−	0.127280i	$-0.0406246\pi$
$109$	983.894	+	983.894i	0.864587	+	0.864587i	−0.127280	+	0.991867i	$0.540625\pi$
$110$	−1606.56	+	420.471i	−1.39254	+	0.364457i
$111$	626.854			0.536021
$112$	−804.073	−	489.536i	−0.678373	−	0.413007i
$113$	332.042			0.276424			0.138212	−	0.990403i	$-0.455864\pi$
$113$	332.042			0.276424			0.138212	+	0.990403i	$0.455864\pi$
$114$	−601.884	+	157.525i	−0.494488	+	0.129418i
$115$	1759.24	+	1759.24i	1.42652	+	1.42652i
$116$	−528.785	−	148.306i	−0.423245	−	0.118706i
$117$	523.211	−	523.211i	0.413426	−	0.413426i
$118$	822.359	+	481.193i	0.641562	+	0.375401i
$119$			1116.11i			0.859778i
$120$	785.031	+	812.936i	0.597194	+	0.618422i
$121$			87.1933i			0.0655096i
$122$	−1199.98	+	2050.77i	−0.890502	+	1.52187i
$123$	477.788	−	477.788i	0.350250	−	0.350250i
$124$	−206.491	+	116.034i	−0.149544	+	0.0840334i
$125$	319.692	+	319.692i	0.228753	+	0.228753i
$126$	−94.8024	−	362.228i	−0.0670291	−	0.256110i
$127$	712.949			0.498141			0.249071	−	0.968485i	$-0.419875\pi$
$127$	712.949			0.498141			0.249071	+	0.968485i	$0.419875\pi$
$128$	1412.92	−	317.524i	0.975666	−	0.219261i
$129$	−346.895			−0.236763
$130$	−980.186	−	3745.16i	−0.661292	−	2.52671i
$131$	−2039.63	−	2039.63i	−1.36033	−	1.36033i	−0.873489	−	0.486843i	$-0.838148\pi$
$131$	−2039.63	−	2039.63i	−1.36033	−	1.36033i	−0.486843	−	0.873489i	$-0.661852\pi$
$132$	−737.901	+	414.650i	−0.486561	+	0.273414i
$133$	762.604	−	762.604i	0.497189	−	0.497189i
$134$	605.276	−	1034.42i	0.390208	−	0.666866i
$135$			449.497i			0.286567i
$136$	−1192.69	−	1235.09i	−0.752004	−	0.778735i
$137$			761.248i			0.474728i	0.971421	+	0.237364i	$0.0762835\pi$
$137$			761.248i			0.474728i	−0.971421	+	0.237364i	$0.923717\pi$
$138$	1094.47	+	640.417i	0.675129	+	0.395043i
$139$	1277.92	−	1277.92i	0.779798	−	0.779798i	−0.199998	−	0.979796i	$-0.564094\pi$
$139$	1277.92	−	1277.92i	0.779798	−	0.779798i	0.979796	+	0.199998i	$0.0640937\pi$
$140$	−1886.22	−	529.018i	−1.13867	−	0.319358i
$141$	−98.7302	−	98.7302i	−0.0589686	−	0.0589686i
$142$	−1898.78	+	496.950i	−1.12213	+	0.293684i
$143$	2899.52			1.69559
$144$	491.991	+	299.534i	0.284717	+	0.173342i
$145$	−1142.86			−0.654550
$146$	1265.37	−	331.175i	0.717282	−	0.187727i
$147$	−268.660	−	268.660i	−0.150740	−	0.150740i
$148$	451.411	−	1609.51i	0.250714	−	0.893923i
$149$	746.651	−	746.651i	0.410524	−	0.410524i	−0.471397	−	0.881921i	$-0.656250\pi$
$149$	746.651	−	746.651i	0.410524	−	0.410524i	0.881921	+	0.471397i	$0.156250\pi$
$150$	1114.35	+	652.045i	0.606573	+	0.354928i
$151$		−	1186.11i		−	0.639234i	−0.947547	−	0.319617i	$-0.896446\pi$
$151$		−	1186.11i		−	0.639234i	0.947547	−	0.319617i	$-0.103554\pi$
$152$	−28.9678	+	1658.83i	−0.0154579	+	0.885190i
$153$		−	682.918i		−	0.360854i
$154$	741.005	−	1266.38i	0.387740	−	0.662648i
$155$	−348.536	+	348.536i	−0.180614	+	0.180614i
$156$	−966.618	−	1720.17i	−0.496098	−	0.882844i
$157$	219.416	+	219.416i	0.111537	+	0.111537i	0.760673	−	0.649136i	$-0.224869\pi$
$157$	219.416	+	219.416i	0.111537	+	0.111537i	−0.649136	+	0.760673i	$0.724869\pi$
$158$	629.339	+	2404.62i	0.316883	+	1.21077i
$159$	662.297			0.330337
$160$	2652.61	−	1430.23i	1.31067	−	0.706685i
$161$	−2198.15			−1.07602
$162$	58.0071	+	221.637i	0.0281325	+	0.107491i
$163$	1321.49	+	1321.49i	0.635011	+	0.635011i	0.949321	−	0.314309i	$-0.101773\pi$
$163$	1321.49	+	1321.49i	0.635011	+	0.635011i	−0.314309	+	0.949321i	$0.601773\pi$
$164$	−882.701	−	1570.83i	−0.420289	−	0.747935i
$165$	−1245.51	+	1245.51i	−0.587651	+	0.587651i
$166$	−1871.41	+	3198.24i	−0.874996	+	1.49537i
$167$			1180.83i			0.547160i	0.961849	+	0.273580i	$0.0882078\pi$
$167$			1180.83i			0.547160i	−0.961849	+	0.273580i	$0.911792\pi$
$168$	−998.322	−	17.4335i	−0.458466	−	0.00800610i
$169$			4562.25i			2.07658i
$170$	−3083.86	−	1804.48i	−1.39130	−	0.814103i
$171$	−466.617	+	466.617i	−0.208673	+	0.208673i
$172$	−249.807	+	890.687i	−0.110742	+	0.394850i
$173$	−1559.35	−	1559.35i	−0.685289	−	0.685289i	0.275898	−	0.961187i	$-0.411025\pi$
$173$	−1559.35	−	1559.35i	−0.685289	−	0.685289i	−0.961187	+	0.275898i	$0.911025\pi$
$174$	−563.522	+	147.485i	−0.245520	+	0.0642577i
$175$	−2238.07			−0.966754
$176$	533.276	+	2193.23i	0.228393	+	0.939323i
$177$	1010.59			0.429157
$178$	−959.799	+	251.199i	−0.404157	+	0.105776i
$179$	1718.83	+	1718.83i	0.717717	+	0.717717i	0.968137	−	0.250420i	$-0.0805687\pi$
$179$	1718.83	+	1718.83i	0.717717	+	0.717717i	−0.250420	+	0.968137i	$0.580569\pi$
$180$	1154.13	+	323.692i	0.477908	+	0.134037i
$181$	703.803	−	703.803i	0.289023	−	0.289023i	−0.547671	−	0.836694i	$-0.684485\pi$
$181$	703.803	−	703.803i	0.289023	−	0.289023i	0.836694	+	0.547671i	$0.184485\pi$
$182$	2952.14	+	1727.40i	1.20235	+	0.703537i
$183$			2520.18i			1.01802i
$184$	2432.48	−	2348.99i	0.974593	−	0.941138i
$185$		−	3478.63i		−	1.38245i
$186$	−126.878	+	216.834i	−0.0500168	+	0.0854788i
$187$	1892.29	−	1892.29i	0.739989	−	0.739989i
$188$	−324.597	+	182.401i	−0.125924	+	0.0707605i
$189$	−280.821	−	280.821i	−0.108078	−	0.108078i
$190$	874.163	+	3340.06i	0.333781	+	1.27533i
$191$	290.013			0.109867			0.0549335	−	0.998490i	$-0.482505\pi$
$191$	290.013			0.109867			0.0549335	+	0.998490i	$0.482505\pi$
$192$	1123.38	−	1047.53i	0.422253	−	0.393745i
$193$	−4295.94			−1.60222			−0.801111	−	0.598516i	$-0.795757\pi$
$193$	−4295.94			−1.60222			−0.801111	+	0.598516i	$0.795757\pi$
$194$	548.700	+	2096.51i	0.203064	+	0.775880i
$195$	−2903.48	−	2903.48i	−1.06627	−	1.06627i
$196$	−883.278	+	496.342i	−0.321894	+	0.180883i
$197$	936.690	−	936.690i	0.338764	−	0.338764i	−0.517138	−	0.855902i	$-0.673003\pi$
$197$	936.690	−	936.690i	0.338764	−	0.338764i	0.855902	+	0.517138i	$0.173003\pi$
$198$	−453.401	+	774.864i	−0.162737	+	0.278117i
$199$			3333.18i			1.18735i	0.804705	+	0.593675i	$0.202324\pi$
$199$			3333.18i			1.18735i	−0.804705	+	0.593675i	$0.797676\pi$
$200$	2476.65	−	2391.64i	0.875628	−	0.845571i
$201$		−	1271.19i		−	0.446084i
$202$	3397.14	+	1987.80i	1.18328	+	0.692380i
$203$	713.999	−	713.999i	0.246862	−	0.246862i
$204$	−1753.46	−	491.783i	−0.601796	−	0.168783i
$205$	−2651.41	−	2651.41i	−0.903330	−	0.903330i
$206$	1401.77	−	366.871i	0.474105	−	0.124083i
$207$	1344.99			0.451611
$208$	−5112.77	+	1243.15i	−1.70436	+	0.414409i
$209$	−2585.89			−0.855836
$210$	−2010.13	+	526.091i	−0.660533	+	0.172875i
$211$	−3810.99	−	3810.99i	−1.24341	−	1.24341i	−0.958578	−	0.284831i	$-0.908063\pi$
$211$	−3810.99	−	3810.99i	−1.24341	−	1.24341i	−0.284831	−	0.958578i	$-0.591937\pi$
$212$	476.934	−	1700.51i	0.154509	−	0.550903i
$213$	−1472.05	+	1472.05i	−0.473537	+	0.473537i
$214$	−2185.71	−	1278.94i	−0.698186	−	0.408534i
$215$			1925.04i			0.610636i
$216$	610.847	+	10.6671i	0.192421	+	0.00336021i
$217$		−	435.493i		−	0.136236i
$218$	1987.59	−	3396.80i	0.617508	−	1.05532i
$219$	980.996	−	980.996i	0.302692	−	0.302692i
$220$	2301.04	+	4094.87i	0.705163	+	1.25489i
$221$	4411.23	+	4411.23i	1.34268	+	1.34268i
$222$	−448.913	−	1715.24i	−0.135717	−	0.518555i
$223$	−3093.27			−0.928882			−0.464441	−	0.885604i	$-0.653745\pi$
$223$	−3093.27			−0.928882			−0.464441	+	0.885604i	$0.653745\pi$
$224$	−763.675	+	2550.73i	−0.227791	+	0.760839i
$225$	1369.41			0.405752
$226$	−237.788	−	908.555i	−0.0699885	−	0.267417i
$227$	97.5310	+	97.5310i	0.0285170	+	0.0285170i	0.721222	−	0.692705i	$-0.243581\pi$
$227$	97.5310	+	97.5310i	0.0285170	+	0.0285170i	−0.692705	+	0.721222i	$0.743581\pi$
$228$	862.063	+	1534.10i	0.250401	+	0.445608i
$229$	2867.04	−	2867.04i	0.827334	−	0.827334i	−0.159813	−	0.987147i	$-0.551089\pi$
$229$	2867.04	−	2867.04i	0.827334	−	0.827334i	0.987147	+	0.159813i	$0.0510892\pi$
$230$	3553.89	−	6073.61i	1.01886	−	1.74123i
$231$		−	1556.25i		−	0.443262i
$232$	−27.1216	+	1553.10i	−0.00767508	+	0.439510i
$233$			260.384i			0.0732116i	0.999330	+	0.0366058i	$0.0116546\pi$
$233$			260.384i			0.0732116i	−0.999330	+	0.0366058i	$0.988345\pi$
$234$	−1806.33	−	1056.95i	−0.504631	−	0.295279i
$235$	−547.888	+	547.888i	−0.152086	+	0.152086i
$236$	727.749	−	2594.79i	0.200731	−	0.715706i
$237$	1864.21	+	1864.21i	0.510943	+	0.510943i
$238$	3053.97	−	799.287i	0.831763	−	0.217689i
$239$	1133.63			0.306814			0.153407	−	0.988163i	$-0.450975\pi$
$239$	1133.63			0.306814			0.153407	+	0.988163i	$0.450975\pi$
$240$	1662.22	−	2730.23i	0.447066	−	0.734314i
$241$	2717.65			0.726386			0.363193	−	0.931714i	$-0.381686\pi$
$241$	2717.65			0.726386			0.363193	+	0.931714i	$0.381686\pi$
$242$	238.584	−	62.4423i	0.0633750	−	0.0165866i
$243$	171.827	+	171.827i	0.0453609	+	0.0453609i
$244$	6470.80	+	1814.84i	1.69775	+	0.476160i
$245$	−1490.89	+	1490.89i	−0.388773	+	0.388773i
$246$	−1649.52	−	965.193i	−0.427518	−	0.250156i
$247$		−	6028.13i		−	1.55288i
$248$	465.375	+	481.917i	0.119159	+	0.123394i
$249$			3930.30i			1.00029i
$250$	645.818	−	1103.70i	0.163381	−	0.279218i
$251$	902.500	−	902.500i	0.226953	−	0.226953i	−0.584465	−	0.811419i	$-0.698696\pi$
$251$	902.500	−	902.500i	0.226953	−	0.226953i	0.811419	+	0.584465i	$0.198696\pi$
$252$	−923.259	+	518.809i	−0.230793	+	0.129690i
$253$	3726.82	+	3726.82i	0.926101	+	0.926101i
$254$	−510.569	−	1950.82i	−0.126126	−	0.481910i
$255$	−3789.75			−0.930679
$256$	−1880.67	−	3638.72i	−0.459148	−	0.888360i
$257$	−49.0728			−0.0119108			−0.00595541	−	0.999982i	$-0.501896\pi$
$257$	−49.0728			−0.0119108			−0.00595541	+	0.999982i	$0.501896\pi$
$258$	248.425	+	949.198i	0.0599467	+	0.229048i
$259$	2173.26	+	2173.26i	0.521388	+	0.521388i
$260$	−9545.81	+	5364.10i	−2.27695	+	1.27949i
$261$	−436.877	+	436.877i	−0.103609	+	0.103609i
$262$	−4120.32	+	7041.63i	−0.971581	+	1.66043i
$263$		−	448.347i		−	0.105119i	−0.998618	−	0.0525594i	$-0.983262\pi$
$263$		−	448.347i		−	0.105119i	0.998618	−	0.0525594i	$-0.0167379\pi$
$264$	1663.03	+	1722.15i	0.387699	+	0.401480i
$265$		−	3675.31i		−	0.851973i
$266$	−2632.82	−	1540.56i	−0.606873	−	0.355104i
$267$	−744.095	+	744.095i	−0.170554	+	0.170554i
$268$	−3263.90	−	915.411i	−0.743935	−	0.208648i
$269$	−4691.01	−	4691.01i	−1.06326	−	1.06326i	−0.997859	−	0.0653970i	$-0.979169\pi$
$269$	−4691.01	−	4691.01i	−1.06326	−	1.06326i	−0.0653970	−	0.997859i	$-0.520831\pi$
$270$	1229.94	−	321.901i	0.277229	−	0.0725567i
$271$	310.218			0.0695365			0.0347683	−	0.999395i	$-0.488931\pi$
$271$	310.218			0.0695365			0.0347683	+	0.999395i	$0.488931\pi$
$272$	−2525.40	+	4148.02i	−0.562959	+	0.924671i
$273$	3627.87			0.804280
$274$	2082.98	−	545.158i	0.459260	−	0.120198i
$275$	3794.49	+	3794.49i	0.832060	+	0.832060i
$276$	968.557	−	3453.40i	0.211233	−	0.753152i
$277$	3523.42	−	3523.42i	0.764267	−	0.764267i	−0.212823	−	0.977091i	$-0.568266\pi$
$277$	3523.42	−	3523.42i	0.764267	−	0.764267i	0.977091	+	0.212823i	$0.0682659\pi$
$278$	−4411.90	−	2581.57i	−0.951828	−	0.556950i
$279$			266.467i			0.0571790i
$280$	−96.7446	+	5540.04i	−0.0206486	+	1.18243i
$281$		−	1369.74i		−	0.290789i	−0.989374	−	0.145395i	$-0.953555\pi$
$281$		−	1369.74i		−	0.290789i	0.989374	−	0.145395i	$-0.0464452\pi$
$282$	−199.448	+	340.856i	−0.0421168	+	0.0719776i
$283$	−5575.17	+	5575.17i	−1.17106	+	1.17106i	−0.189100	+	0.981958i	$0.560557\pi$
$283$	−5575.17	+	5575.17i	−1.17106	+	1.17106i	−0.981958	+	0.189100i	$0.939443\pi$
$284$	2719.58	+	4839.69i	0.568229	+	1.01121i
$285$	2589.42	+	2589.42i	0.538190	+	0.538190i
$286$	−2076.45	−	7933.85i	−0.429312	−	1.64034i
$287$	3312.91			0.681377
$288$	467.273	−	1560.73i	0.0956052	−	0.319329i
$289$	844.738			0.171939
$290$	818.448	+	3127.18i	0.165727	+	0.633222i
$291$	1625.34	+	1625.34i	0.327420	+	0.327420i
$292$	−1812.36	−	3225.23i	−0.363221	−	0.646378i
$293$	−1651.17	+	1651.17i	−0.329222	+	0.329222i	−0.852291	−	0.523068i	$-0.824787\pi$
$293$	−1651.17	+	1651.17i	−0.329222	+	0.329222i	0.523068	+	0.852291i	$0.324787\pi$
$294$	−542.728	+	927.523i	−0.107662	+	0.183994i
$295$		−	5608.13i		−	1.10684i
$296$	−4727.31	−	82.5521i	−0.928274	−	0.0162103i
$297$			952.226i			0.186040i
$298$	−2577.74	−	1508.33i	−0.501089	−	0.293206i
$299$	−8687.84	+	8687.84i	−1.68037	+	1.68037i
$300$	986.143	−	3516.10i	0.189783	−	0.676673i
$301$	−1202.66	−	1202.66i	−0.230300	−	0.230300i
$302$	−3245.51	+	849.418i	−0.618405	+	0.161849i
$303$	4174.73			0.791526
$304$	4559.75	−	1108.69i	0.860261	−	0.209169i
$305$	13985.4			2.62557
$306$	−1868.64	+	489.063i	−0.349096	+	0.0913655i
$307$	−1930.51	−	1930.51i	−0.358892	−	0.358892i	0.504512	−	0.863404i	$-0.331672\pi$
$307$	−1930.51	−	1930.51i	−0.358892	−	0.358892i	−0.863404	+	0.504512i	$0.831672\pi$
$308$	−3995.81	−	1120.69i	−0.739229	−	0.207328i
$309$	1086.73	−	1086.73i	0.200072	−	0.200072i
$310$	1203.29	+	704.088i	0.220459	+	0.128998i
$311$			3967.14i			0.723331i	0.932308	+	0.361665i	$0.117792\pi$
$311$			3967.14i			0.723331i	−0.932308	+	0.361665i	$0.882208\pi$
$312$	−4014.60	+	3876.80i	−0.728469	+	0.703463i
$313$			7329.46i			1.32360i	0.749682	+	0.661798i	$0.230206\pi$
$313$			7329.46i			1.32360i	−0.749682	+	0.661798i	$0.769794\pi$
$314$	443.247	−	757.511i	0.0796621	−	0.136143i
$315$	−1558.37	+	1558.37i	−0.278744	+	0.278744i
$316$	6128.99	−	3444.08i	1.09108	−	0.613115i
$317$	−3264.85	−	3264.85i	−0.578461	−	0.578461i	0.356018	−	0.934479i	$-0.384134\pi$
$317$	−3264.85	−	3264.85i	−0.578461	−	0.578461i	−0.934479	+	0.356018i	$0.884134\pi$
$318$	−474.295	−	1812.22i	−0.0836389	−	0.319573i
$319$	−2421.07			−0.424935
$320$	−5813.12	−	6234.00i	−1.01551	−	1.08903i
$321$	−2686.00			−0.467035
$322$	1574.18	+	6014.74i	0.272440	+	1.04096i
$323$	−3934.09	−	3934.09i	−0.677705	−	0.677705i
$324$	564.918	−	317.446i	0.0968652	−	0.0544317i
$325$	−8845.58	+	8845.58i	−1.50974	+	1.50974i
$326$	2669.57	−	4562.30i	0.453540	−	0.775100i
$327$		−	4174.31i		−	0.705932i
$328$	−3666.08	+	3540.23i	−0.617150	+	0.595966i
$329$		−	684.580i		−	0.114718i
$330$	4299.99	+	2516.08i	0.717292	+	0.419714i
$331$	7640.33	−	7640.33i	1.26873	−	1.26873i	0.321991	−	0.946743i	$-0.395648\pi$
$331$	7640.33	−	7640.33i	1.26873	−	1.26873i	0.946743	−	0.321991i	$-0.104352\pi$
$332$	10091.4	+	2830.29i	1.66819	+	0.467868i
$333$	−1329.76	−	1329.76i	−0.218830	−	0.218830i
$334$	3231.08	−	845.639i	0.529331	−	0.138537i
$335$	−7054.28			−1.15050
$336$	667.233	+	2744.16i	0.108335	+	0.445554i
$337$	10375.8			1.67716			0.838582	−	0.544775i	$-0.183385\pi$
$337$	10375.8			1.67716			0.838582	+	0.544775i	$0.183385\pi$
$338$	12483.5	−	3267.20i	2.00892	−	0.525775i
$339$	−704.368	−	704.368i	−0.112850	−	0.112850i
$340$	−2729.08	+	9730.53i	−0.435309	+	1.55209i
$341$	−738.349	+	738.349i	−0.117255	+	0.117255i
$342$	1610.95	+	942.627i	0.254708	+	0.149039i
$343$		−	6908.01i		−	1.08746i
$344$	2616.05	+	45.6836i	0.410023	+	0.00716016i
$345$		−	7463.83i		−	1.16475i
$346$	−3150.08	+	5383.49i	−0.489449	+	0.836469i
$347$	3827.22	−	3827.22i	0.592092	−	0.592092i	−0.346104	−	0.938196i	$-0.612496\pi$
$347$	3827.22	−	3827.22i	0.592092	−	0.592092i	0.938196	+	0.346104i	$0.112496\pi$
$348$	807.119	+	1436.33i	0.124328	+	0.221251i
$349$	783.575	+	783.575i	0.120183	+	0.120183i	0.764640	−	0.644457i	$-0.222917\pi$
$349$	783.575	+	783.575i	0.120183	+	0.120183i	−0.644457	+	0.764640i	$0.722917\pi$
$350$	1602.76	+	6123.94i	0.244775	+	0.935253i
$351$	−2219.80			−0.337561
$352$	5619.36	−	3029.84i	0.850888	−	0.458781i
$353$	−9151.32			−1.37982			−0.689909	−	0.723896i	$-0.742349\pi$
$353$	−9151.32			−1.37982			−0.689909	+	0.723896i	$0.742349\pi$
$354$	−723.723	−	2765.25i	−0.108659	−	0.415173i
$355$	8168.92	+	8168.92i	1.22130	+	1.22130i
$356$	1374.70	+	2446.37i	0.204659	+	0.364206i
$357$	2367.63	−	2367.63i	0.351003	−	0.351003i
$358$	3472.26	−	5934.09i	0.512610	−	0.876052i
$359$		−	290.943i		−	0.0427727i	−0.999771	−	0.0213863i	$-0.993192\pi$
$359$		−	290.943i		−	0.0427727i	0.999771	−	0.0213863i	$-0.00680800\pi$
$360$	59.1955	−	3389.80i	0.00866632	−	0.496273i
$361$		−	1482.91i		−	0.216199i
$362$	−2429.81	−	1421.77i	−0.352784	−	0.206427i
$363$	184.965	−	184.965i	0.0267442	−	0.0267442i
$364$	2612.50	−	9314.89i	0.376188	−	1.34130i
$365$	−5443.88	−	5443.88i	−0.780674	−	0.780674i
$366$	6895.89	−	1804.80i	0.984846	−	0.257755i
$367$	−5526.68			−0.786077			−0.393039	−	0.919522i	$-0.628576\pi$
$367$	−5526.68			−0.786077			−0.393039	+	0.919522i	$0.628576\pi$
$368$	−8169.44	−	4973.72i	−1.15723	−	0.704547i
$369$	−2027.08			−0.285978
$370$	−9518.45	+	2491.18i	−1.33741	+	0.350027i
$371$	2296.13	+	2296.13i	0.321319	+	0.321319i
$372$	684.178	+	191.888i	0.0953574	+	0.0267444i
$373$	−978.030	+	978.030i	−0.135765	+	0.135765i	−0.771724	−	0.635958i	$-0.780605\pi$
$373$	−978.030	+	978.030i	−0.135765	+	0.135765i	0.635958	+	0.771724i	$0.280605\pi$
$374$	−6532.94	−	3822.67i	−0.903236	−	0.528517i
$375$		−	1356.34i		−	0.186776i
$376$	731.554	+	757.558i	0.100338	+	0.103904i
$377$		−	5643.92i		−	0.771026i
$378$	−567.294	+	969.507i	−0.0771917	+	0.131921i
$379$	−4408.79	+	4408.79i	−0.597531	+	0.597531i	−0.939655	−	0.342124i	$-0.888854\pi$
$379$	−4408.79	+	4408.79i	−0.597531	+	0.597531i	0.342124	+	0.939655i	$0.388854\pi$
$380$	8513.27	−	4783.88i	1.14927	−	0.645811i
$381$	−1512.39	−	1512.39i	−0.203365	−	0.203365i
$382$	−207.689	−	793.553i	−0.0278175	−	0.106287i
$383$	6799.13			0.907101			0.453550	−	0.891231i	$-0.350157\pi$
$383$	6799.13			0.907101			0.453550	+	0.891231i	$0.350157\pi$
$384$	−3670.82	−	2323.68i	−0.487827	−	0.308801i
$385$	−8636.15			−1.14322
$386$	3076.48	+	11754.8i	0.405671	+	1.55001i
$387$	735.876	+	735.876i	0.0966581	+	0.0966581i
$388$	5343.66	−	3002.78i	0.699184	−	0.392894i
$389$	−5520.37	+	5520.37i	−0.719521	+	0.719521i	−0.968507	−	0.248986i	$-0.919903\pi$
$389$	−5520.37	+	5520.37i	−0.719521	+	0.719521i	0.248986	+	0.968507i	$0.419903\pi$
$390$	−5865.40	+	10024.0i	−0.761554	+	1.30150i
$391$			11339.7i			1.46669i
$392$	1990.67	+	2061.43i	0.256490	+	0.265607i
$393$			8653.43i			1.11071i
$394$	−3233.83	−	1892.23i	−0.413498	−	0.241953i
$395$	10345.1	−	10345.1i	1.31777	−	1.31777i
$396$	2444.93	+	685.718i	0.310259	+	0.0870167i
$397$	−4743.70	−	4743.70i	−0.599696	−	0.599696i	0.340536	−	0.940232i	$-0.389392\pi$
$397$	−4743.70	−	4743.70i	−0.599696	−	0.599696i	−0.940232	+	0.340536i	$0.889392\pi$
$398$	9120.46	−	2387.01i	1.14866	−	0.300628i
$399$	−3235.45			−0.405953
$400$	−8317.77	−	5064.03i	−1.03972	−	0.633004i
$401$	−1674.92			−0.208582			−0.104291	−	0.994547i	$-0.533257\pi$
$401$	−1674.92			−0.208582			−0.104291	+	0.994547i	$0.533257\pi$
$402$	−3478.32	+	910.347i	−0.431549	+	0.112945i
$403$	−1721.21	−	1721.21i	−0.212754	−	0.212754i
$404$	3006.31	−	10719.0i	0.370222	−	1.32003i
$405$	953.527	−	953.527i	0.116990	−	0.116990i
$406$	−2465.01	−	1442.37i	−0.301321	−	0.176314i
$407$		−	7369.22i		−	0.897491i
$408$	−89.9353	+	5150.10i	−0.0109129	+	0.624922i
$409$		−	11918.0i		−	1.44084i	−0.693536	−	0.720422i	$-0.743948\pi$
$409$		−	11918.0i		−	1.44084i	0.693536	−	0.720422i	$-0.256052\pi$
$410$	−5356.19	+	9153.74i	−0.645179	+	1.10261i
$411$	1614.85	−	1614.85i	0.193807	−	0.193807i
$412$	−2007.71	−	3572.87i	−0.240080	−	0.427240i
$413$	3503.65	+	3503.65i	0.417442	+	0.417442i
$414$	−963.199	−	3680.26i	−0.114345	−	0.436896i
$415$	21810.6			2.57985
$416$	7063.04	+	13099.6i	0.832438	+	1.54390i
$417$	−5421.76			−0.636702
$418$	1851.85	+	7075.68i	0.216691	+	0.827949i
$419$	4342.25	+	4342.25i	0.506284	+	0.506284i	0.913384	−	0.407100i	$-0.133460\pi$
$419$	4342.25	+	4342.25i	0.506284	+	0.506284i	−0.407100	+	0.913384i	$0.633460\pi$
$420$	2879.05	+	5123.48i	0.334484	+	0.595239i
$421$	−8933.14	+	8933.14i	−1.03414	+	1.03414i	−0.0347474	+	0.999396i	$0.511063\pi$
$421$	−8933.14	+	8933.14i	−1.03414	+	1.03414i	−0.999396	+	0.0347474i	$0.988937\pi$
$422$	−7698.69	+	13157.1i	−0.888071	+	1.51772i
$423$			418.877i			0.0481477i
$424$	−4994.59	−	87.2197i	−0.572073	−	0.00999000i
$425$			11545.6i			1.31776i
$426$	5082.12	+	2973.73i	0.578003	+	0.338211i
$427$	−8737.28	+	8737.28i	−0.990227	+	0.990227i
$428$	−1934.25	+	6896.57i	−0.218447	+	0.778874i
$429$	−6150.80	−	6150.80i	−0.692223	−	0.692223i
$430$	5267.43	−	1378.59i	0.590739	−	0.154609i
$431$	−6175.68			−0.690191			−0.345095	−	0.938568i	$-0.612153\pi$
$431$	−6175.68			−0.690191			−0.345095	+	0.938568i	$0.612153\pi$
$432$	−408.262	−	1679.08i	−0.0454688	−	0.187002i
$433$	7.68815			0.000853276			0.000426638	−	1.00000i	$-0.499864\pi$
$433$	7.68815			0.000853276			0.000426638		1.00000i	$0.499864\pi$
$434$	−1191.62	+	311.872i	−0.131797	+	0.0344939i
$435$	2424.38	+	2424.38i	0.267219	+	0.267219i
$436$	−10717.9	−	3006.01i	−1.17728	−	0.330187i
$437$	7748.11	−	7748.11i	0.848152	−	0.848152i
$438$	−3386.79	−	1981.74i	−0.369468	−	0.216190i
$439$			15185.1i			1.65090i	0.564477	+	0.825449i	$0.309078\pi$
$439$			15185.1i			1.65090i	−0.564477	+	0.825449i	$0.690922\pi$
$440$	9556.78	−	9228.74i	1.03546	−	0.999915i
$441$			1139.83i			0.123078i
$442$	8911.26	−	15229.4i	0.958971	−	1.63888i
$443$	−3404.98	+	3404.98i	−0.365182	+	0.365182i	−0.865716	−	0.500535i	$-0.833137\pi$
$443$	−3404.98	+	3404.98i	−0.365182	+	0.365182i	0.500535	+	0.865716i	$0.333137\pi$
$444$	−4371.87	+	2456.69i	−0.467296	+	0.262589i
$445$	4129.24	+	4129.24i	0.439876	+	0.439876i
$446$	2215.21	+	8464.01i	0.235186	+	0.898615i
$447$	−3167.77			−0.335191
$448$	7526.38	+	262.944i	0.793723	+	0.0277297i
$449$	6766.99			0.711257			0.355628	−	0.934627i	$-0.384267\pi$
$449$	6766.99			0.711257			0.355628	+	0.934627i	$0.384267\pi$
$450$	−980.688	−	3747.08i	−0.102733	−	0.392531i
$451$	−5616.82	−	5616.82i	−0.586443	−	0.586443i
$452$	−2315.76	+	1301.30i	−0.240983	+	0.135416i
$453$	−2516.12	+	2516.12i	−0.260966	+	0.260966i
$454$	197.025	−	336.716i	0.0203675	−	0.0348081i
$455$		−	20132.3i		−	2.07432i
$456$	3580.36	−	3457.46i	0.367688	−	0.355067i
$457$			7528.20i			0.770578i	0.922796	+	0.385289i	$0.125898\pi$
$457$			7528.20i			0.770578i	−0.922796	+	0.385289i	$0.874102\pi$
$458$	−9898.18	−	5791.79i	−1.00985	−	0.590901i
$459$	−1448.69	+	1448.69i	−0.147318	+	0.147318i
$460$	−19164.1	−	5374.86i	−1.94246	−	0.544792i
$461$	9029.85	+	9029.85i	0.912282	+	0.912282i	0.996451	−	0.0841690i	$-0.0268236\pi$
$461$	9029.85	+	9029.85i	0.912282	+	0.912282i	−0.0841690	+	0.996451i	$0.526824\pi$
$462$	−4258.30	+	1114.49i	−0.428819	+	0.112231i
$463$	8555.19			0.858733			0.429367	−	0.903130i	$-0.358737\pi$
$463$	8555.19			0.858733			0.429367	+	0.903130i	$0.358737\pi$
$464$	4269.13	−	1038.02i	0.427132	−	0.103856i
$465$	1478.71			0.147470
$466$	712.479	−	186.470i	0.0708261	−	0.0185366i
$467$	1326.73	+	1326.73i	0.131464	+	0.131464i	0.769777	−	0.638313i	$-0.220368\pi$
$467$	1326.73	+	1326.73i	0.131464	+	0.131464i	−0.638313	+	0.769777i	$0.720368\pi$
$468$	−1598.52	+	5699.53i	−0.157888	+	0.562951i
$469$	4407.13	−	4407.13i	0.433907	−	0.433907i
$470$	1891.53	+	1106.80i	0.185638	+	0.108623i
$471$		−	930.901i		−	0.0910693i
$472$	−7621.21	−	133.088i	−0.743209	−	0.0129785i
$473$			4078.06i			0.396426i
$474$	3765.94	−	6436.00i	0.364927	−	0.623661i
$475$	7888.79	−	7888.79i	0.762027	−	0.762027i
$476$	−4374.12	−	7784.08i	−0.421193	−	0.749543i
$477$	−1404.94	−	1404.94i	−0.134859	−	0.134859i
$478$	−811.835	−	3101.91i	−0.0776830	−	0.296816i
$479$	−6121.90			−0.583960			−0.291980	−	0.956424i	$-0.594314\pi$
$479$	−6121.90			−0.583960			−0.291980	+	0.956424i	$0.594314\pi$
$480$	−8661.01	−	2593.06i	−0.823581	−	0.246576i
$481$	17178.9			1.62846
$482$	−1946.21	−	7436.21i	−0.183916	−	0.702718i
$483$	4662.99	+	4662.99i	0.439282	+	0.439282i
$484$	−341.718	−	608.112i	−0.0320922	−	0.0571104i
$485$	9019.59	−	9019.59i	0.844450	−	0.844450i
$486$	347.112	−	593.216i	0.0323978	−	0.0553679i
$487$			6508.23i			0.605577i	0.953058	+	0.302789i	$0.0979177\pi$
$487$			6508.23i			0.605577i	−0.953058	+	0.302789i	$0.902082\pi$
$488$	331.890	−	19005.5i	0.0307867	−	1.76299i
$489$		−	5606.59i		−	0.518484i
$490$	5147.15	+	3011.79i	0.474540	+	0.277671i
$491$	−8093.67	+	8093.67i	−0.743915	+	0.743915i	−0.973329	−	0.229414i	$-0.926319\pi$
$491$	−8093.67	+	8093.67i	−0.743915	+	0.743915i	0.229414	+	0.973329i	$0.426319\pi$
$492$	−1459.75	+	5204.73i	−0.133761	+	0.476925i
$493$	−3683.35	−	3683.35i	−0.336490	−	0.336490i
$494$	−16494.6	+	4316.97i	−1.50228	+	0.393177i
$495$	5284.23			0.479815
$496$	985.381	−	1618.51i	0.0892035	−	0.146518i
$497$	−10207.0			−0.921219
$498$	10754.3	−	2814.63i	0.967697	−	0.253266i
$499$	−6772.14	−	6772.14i	−0.607540	−	0.607540i	0.334762	−	0.942303i	$-0.391344\pi$
$499$	−6772.14	−	6772.14i	−0.607540	−	0.607540i	−0.942303	+	0.334762i	$0.891344\pi$
$500$	−3482.52	−	976.727i	−0.311486	−	0.0873611i
$501$	2504.93	−	2504.93i	0.223377	−	0.223377i
$502$	−3115.79	−	1823.17i	−0.277021	−	0.162095i
$503$			3296.12i			0.292180i	0.989271	+	0.146090i	$0.0466689\pi$
$503$			3296.12i			0.292180i	−0.989271	+	0.146090i	$0.953331\pi$
$504$	2080.78	+	2154.74i	0.183899	+	0.190436i
$505$		−	23167.0i		−	2.04143i
$506$	7528.66	−	12866.5i	0.661443	−	1.13041i
$507$	9677.99	−	9677.99i	0.847761	−	0.847761i
$508$	−4972.31	+	2794.10i	−0.434273	+	0.244032i
$509$	6445.02	+	6445.02i	0.561239	+	0.561239i	0.929659	−	0.368421i	$-0.120101\pi$
$509$	6445.02	+	6445.02i	0.561239	+	0.561239i	−0.368421	+	0.929659i	$0.620101\pi$
$510$	2713.98	+	10369.8i	0.235641	+	0.900354i
$511$	6802.08			0.588858
$512$	−8609.69	+	7751.84i	−0.743160	+	0.669113i
$513$	1979.69			0.170381
$514$	35.1429	+	134.276i	0.00301573	+	0.0115227i
$515$	−6030.66	−	6030.66i	−0.516005	−	0.516005i
$516$	2419.35	−	1359.51i	0.206407	−	0.115987i
$517$	−1160.66	+	1160.66i	−0.0987346	+	0.0987346i
$518$	4390.26	−	7502.96i	0.372388	−	0.636411i
$519$			6615.75i			0.559536i
$520$	21513.7	+	22278.4i	1.81430	+	1.87880i
$521$			15572.4i			1.30948i	0.755854	+	0.654740i	$0.227222\pi$
$521$			15572.4i			1.30948i	−0.755854	+	0.654740i	$0.772778\pi$
$522$	1508.28	+	882.548i	0.126466	+	0.0740001i
$523$	2333.98	−	2333.98i	0.195139	−	0.195139i	−0.602773	−	0.797913i	$-0.705938\pi$
$523$	2333.98	−	2333.98i	0.195139	−	0.195139i	0.797913	+	0.602773i	$0.205938\pi$
$524$	22218.5	+	6231.52i	1.85233	+	0.519513i
$525$	4747.66	+	4747.66i	0.394676	+	0.394676i
$526$	−1226.80	+	321.078i	−0.101694	+	0.0266153i
$527$	−2246.60			−0.185699
$528$	3521.29	−	5783.79i	0.290236	−	0.476718i
$529$	−10166.4			−0.835572
$530$	−10056.6	+	2632.03i	−0.824212	+	0.215713i
$531$	−2143.79	−	2143.79i	−0.175203	−	0.175203i
$532$	−2329.92	+	8307.33i	−0.189877	+	0.677009i
$533$	13093.7	−	13093.7i	1.06408	−	1.06408i
$534$	2568.92	+	1503.17i	0.208179	+	0.121814i
$535$			14905.6i			1.20453i
$536$	−167.407	+	9586.46i	−0.0134904	+	0.772523i
$537$		−	7292.38i		−	0.586014i
$538$	−9476.44	+	16195.3i	−0.759402	+	1.29782i
$539$	−3158.34	+	3158.34i	−0.252392	+	0.252392i
$540$	−1761.62	−	3134.92i	−0.140385	−	0.249825i
$541$	8320.06	+	8320.06i	0.661196	+	0.661196i	0.955662	−	0.294466i	$-0.0951417\pi$
$541$	8320.06	+	8320.06i	0.661196	+	0.661196i	−0.294466	+	0.955662i	$0.595142\pi$
$542$	−222.159	−	848.839i	−0.0176061	−	0.0672707i
$543$	−2985.98			−0.235987
$544$	13158.6	+	3939.61i	1.03708	+	0.310496i
$545$	−23164.7			−1.82067
$546$	−2598.05	−	9926.80i	−0.203638	−	0.778073i
$547$	−10206.5	−	10206.5i	−0.797801	−	0.797801i	0.184947	−	0.982748i	$-0.440789\pi$
$547$	−10206.5	−	10206.5i	−0.797801	−	0.797801i	−0.982748	+	0.184947i	$0.940789\pi$
$548$	−2983.39	−	5309.17i	−0.232562	−	0.413862i
$549$	5346.11	−	5346.11i	0.415604	−	0.415604i
$550$	7665.36	−	13100.1i	0.594277	−	1.01562i
$551$			5033.44i			0.389168i
$552$	−10143.0	−	177.126i	−0.782094	−	0.0136576i
$553$			12926.2i			0.993989i
$554$	−12164.3	−	7117.77i	−0.932871	−	0.545858i
$555$	−7379.29	+	7379.29i	−0.564384	+	0.564384i
$556$	−3904.32	+	13920.9i	−0.297806	+	1.06183i
$557$	9984.48	+	9984.48i	0.759526	+	0.759526i	0.976236	−	0.216710i	$-0.0695325\pi$
$557$	9984.48	+	9984.48i	0.759526	+	0.759526i	−0.216710	+	0.976236i	$0.569533\pi$
$558$	729.123	−	190.827i	0.0553158	−	0.0144773i
$559$	−9506.63			−0.719298
$560$	15228.3	−	3702.71i	1.14913	−	0.279407i
$561$	−8028.30			−0.604198
$562$	−3747.97	+	980.921i	−0.281314	+	0.0736257i
$563$	−12193.3	−	12193.3i	−0.912761	−	0.912761i	0.0837279	−	0.996489i	$-0.473317\pi$
$563$	−12193.3	−	12193.3i	−0.912761	−	0.912761i	−0.996489	+	0.0837279i	$0.973317\pi$
$564$	1075.50	+	301.642i	0.0802960	+	0.0225202i
$565$	−3908.78	+	3908.78i	−0.291051	+	0.291051i
$566$	19247.7	+	11262.6i	1.42940	+	0.836397i
$567$			1191.42i			0.0882452i
$568$	11295.1	−	10907.4i	0.834385	−	0.805744i
$569$		−	4990.14i		−	0.367659i	−0.982958	−	0.183829i	$-0.941151\pi$
$569$		−	4990.14i		−	0.367659i	0.982958	−	0.183829i	$-0.0588494\pi$
$570$	5230.96	−	8939.72i	0.384387	−	0.656919i
$571$	6896.58	−	6896.58i	0.505451	−	0.505451i	−0.407676	−	0.913127i	$-0.633661\pi$
$571$	6896.58	−	6896.58i	0.505451	−	0.505451i	0.913127	+	0.407676i	$0.133661\pi$
$572$	−20222.1	+	11363.4i	−1.47820	+	0.830646i
$573$	−615.211	−	615.211i	−0.0448530	−	0.0448530i
$574$	−2372.50	−	9065.01i	−0.172520	−	0.659174i
$575$	−22738.9			−1.64918
$576$	−4605.19	−	160.888i	−0.333130	−	0.0116383i
$577$	−12824.7			−0.925299			−0.462649	−	0.886541i	$-0.653101\pi$
$577$	−12824.7			−0.925299			−0.462649	+	0.886541i	$0.653101\pi$
$578$	−604.948	−	2311.43i	−0.0435338	−	0.166337i
$579$	9113.07	+	9113.07i	0.654104	+	0.654104i
$580$	7970.67	−	4478.98i	0.570628	−	0.320654i
$581$	−13626.0	+	13626.0i	−0.972984	+	0.972984i
$582$	3283.40	−	5611.34i	0.233851	−	0.399652i
$583$		−	7785.88i		−	0.553102i
$584$	−7527.19	+	7268.81i	−0.533352	+	0.515044i
$585$			12318.4i			0.870605i
$586$	5700.49	+	3335.57i	0.401852	+	0.235138i
$587$	15610.1	−	15610.1i	1.09761	−	1.09761i	0.102920	−	0.994690i	$-0.467181\pi$
$587$	15610.1	−	15610.1i	1.09761	−	1.09761i	0.994690	−	0.102920i	$-0.0328186\pi$
$588$	2926.62	+	820.814i	0.205258	+	0.0575677i
$589$	1535.04	+	1535.04i	0.107385	+	0.107385i
$590$	−15345.3	+	4016.19i	−1.07077	+	0.280244i
$591$	−3974.04			−0.276599
$592$	3159.52	+	12994.3i	0.219350	+	0.902132i
$593$	16469.9			1.14054			0.570268	−	0.821458i	$-0.306839\pi$
$593$	16469.9			1.14054			0.570268	+	0.821458i	$0.306839\pi$
$594$	2605.54	−	681.925i	0.179978	−	0.0471039i
$595$	−13138.8	−	13138.8i	−0.905272	−	0.905272i
$596$	−2281.18	+	8133.55i	−0.156780	+	0.558999i
$597$	7070.74	−	7070.74i	0.484734	−	0.484734i
$598$	29993.9	+	17550.5i	2.05107	+	1.20016i
$599$			10220.6i			0.697164i	0.937278	+	0.348582i	$0.113337\pi$
$599$			10220.6i			0.697164i	−0.937278	+	0.348582i	$0.886663\pi$
$600$	−10327.2	−	180.342i	−0.702676	−	0.0122707i
$601$		−	16286.3i		−	1.10538i	−0.833387	−	0.552690i	$-0.813601\pi$
$601$		−	16286.3i		−	1.10538i	0.833387	−	0.552690i	$-0.186399\pi$
$602$	−2429.53	+	4152.07i	−0.164485	+	0.281106i
$603$	−2696.60	+	2696.60i	−0.182113	+	0.182113i
$604$	4648.47	+	8272.29i	0.313151	+	0.557276i
$605$	−1026.43	−	1026.43i	−0.0689760	−	0.0689760i
$606$	−2989.68	−	11423.2i	−0.200408	−	0.765734i
$607$	−21362.6			−1.42847			−0.714235	−	0.699906i	$-0.753225\pi$
$607$	−21362.6			−1.42847			−0.714235	+	0.699906i	$0.753225\pi$
$608$	−6299.06	−	11682.7i	−0.420166	−	0.779270i
$609$	−3029.24			−0.201562
$610$	−10015.4	−	38267.7i	−0.664776	−	2.54002i
$611$	−2705.69	−	2705.69i	−0.179150	−	0.179150i
$612$	2676.41	+	4762.87i	0.176777	+	0.314588i
$613$	1189.98	−	1189.98i	0.0784057	−	0.0784057i	−0.666816	−	0.745222i	$-0.732343\pi$
$613$	1189.98	−	1189.98i	0.0784057	−	0.0784057i	0.745222	+	0.666816i	$0.232343\pi$
$614$	−3899.87	+	6664.89i	−0.256329	+	0.438067i
$615$			11249.0i			0.737566i
$616$	−204.946	+	11736.2i	−0.0134051	+	0.767635i
$617$			1361.21i			0.0888173i	0.999013	+	0.0444087i	$0.0141404\pi$
$617$			1361.21i			0.0888173i	−0.999013	+	0.0444087i	$0.985860\pi$
$618$	−3751.84	−	2195.34i	−0.244209	−	0.142896i
$619$	−5468.68	+	5468.68i	−0.355097	+	0.355097i	−0.862002	−	0.506905i	$-0.830789\pi$
$619$	−5468.68	+	5468.68i	−0.355097	+	0.355097i	0.506905	+	0.862002i	$0.330789\pi$
$620$	1064.85	−	3796.74i	0.0689767	−	0.245937i
$621$	−2853.16	−	2853.16i	−0.184369	−	0.184369i
$622$	10855.1	−	2841.02i	0.699762	−	0.183142i
$623$	−5159.44			−0.331796
$624$	13483.0	+	8208.70i	0.864984	+	0.526620i
$625$	11492.9			0.735543
$626$	20055.4	−	5248.90i	1.28047	−	0.335125i
$627$	5485.50	+	5485.50i	0.349393	+	0.349393i
$628$	−2390.18	−	670.361i	−0.151876	−	0.0425961i
$629$	11211.3	−	11211.3i	0.710690	−	0.710690i
$630$	5380.13	+	3148.11i	0.340237	+	0.199085i
$631$		−	11369.6i		−	0.717303i	−0.933472	−	0.358651i	$-0.883237\pi$
$631$		−	11369.6i		−	0.717303i	0.933472	−	0.358651i	$-0.116763\pi$
$632$	−13813.1	−	14304.1i	−0.869392	−	0.900296i
$633$			16168.7i			1.01524i
$634$	−6595.42	+	11271.6i	−0.413151	+	0.706075i
$635$	−8392.79	+	8392.79i	−0.524500	+	0.524500i
$636$	−4619.05	+	2595.60i	−0.287983	+	0.161827i
$637$	−7362.60	−	7362.60i	−0.457954	−	0.457954i
$638$	1733.82	+	6624.70i	0.107590	+	0.411089i
$639$	6245.39			0.386641
$640$	−12894.9	+	20370.6i	−0.796430	+	1.25816i
$641$	9280.18			0.571833			0.285917	−	0.958255i	$-0.407702\pi$
$641$	9280.18			0.571833			0.285917	+	0.958255i	$0.407702\pi$
$642$	1923.55	+	7349.62i	0.118250	+	0.451817i
$643$	−9377.81	−	9377.81i	−0.575155	−	0.575155i	0.358409	−	0.933565i	$-0.383319\pi$
$643$	−9377.81	−	9377.81i	−0.575155	−	0.575155i	−0.933565	+	0.358409i	$0.883319\pi$
$644$	15330.6	−	8614.75i	0.938058	−	0.527125i
$645$	4083.63	−	4083.63i	0.249291	−	0.249291i
$646$	−7947.37	+	13582.1i	−0.484032	+	0.827212i
$647$			1950.32i			0.118508i	0.998243	+	0.0592542i	$0.0188723\pi$
$647$			1950.32i			0.118508i	−0.998243	+	0.0592542i	$0.981128\pi$
$648$	−1273.17	−	1318.43i	−0.0771836	−	0.0799272i
$649$		−	11880.4i		−	0.718562i
$650$	30538.5	+	17869.2i	1.84280	+	1.07829i
$651$	−923.820	+	923.820i	−0.0556180	+	0.0556180i
$652$	−14395.5	−	4037.42i	−0.864677	−	0.242512i
$653$	−8699.36	−	8699.36i	−0.521336	−	0.521336i	0.396639	−	0.917975i	$-0.370177\pi$
$653$	−8699.36	−	8699.36i	−0.521336	−	0.521336i	−0.917975	+	0.396639i	$0.870177\pi$
$654$	−11422.0	+	2989.38i	−0.682930	+	0.178737i
$655$	48020.9			2.86463
$656$	12312.4	+	7496.06i	0.732804	+	0.446147i
$657$	−4162.01			−0.247147
$658$	−1873.19	+	490.253i	−0.110980	+	0.0290457i
$659$	7958.47	+	7958.47i	0.470437	+	0.470437i	0.902056	−	0.431619i	$-0.142058\pi$
$659$	7958.47	+	7958.47i	0.470437	+	0.470437i	−0.431619	+	0.902056i	$0.642058\pi$
$660$	3805.29	−	13567.8i	0.224425	−	0.800189i
$661$	7483.62	−	7483.62i	0.440362	−	0.440362i	−0.451772	−	0.892134i	$-0.649208\pi$
$661$	7483.62	−	7483.62i	0.440362	−	0.440362i	0.892134	+	0.451772i	$0.149208\pi$
$662$	−26377.5	−	15434.5i	−1.54863	−	0.906159i
$663$		−	18715.3i		−	1.09629i
$664$	517.591	−	29639.6i	0.0302507	−	1.73229i
$665$			17954.7i			1.04700i
$666$	−2686.28	+	4590.86i	−0.156293	+	0.267105i
$667$	7254.28	−	7254.28i	0.421120	−	0.421120i
$668$	−4627.79	−	8235.49i	−0.268046	−	0.477007i
$669$	6561.82	+	6561.82i	0.379215	+	0.379215i
$670$	5051.83	+	19302.4i	0.291297	+	1.11301i
$671$	29627.0			1.70452
$672$	7030.92	−	3790.92i	0.403607	−	0.217616i
$673$	3592.82			0.205785			0.102892	−	0.994692i	$-0.467190\pi$
$673$	3592.82			0.205785			0.102892	+	0.994692i	$0.467190\pi$
$674$	−7430.48	−	28390.9i	−0.424646	−	1.62252i
$675$	−2904.97	−	2904.97i	−0.165648	−	0.165648i
$676$	−17879.8	−	31818.5i	−1.01729	−	1.81034i
$677$	−16494.8	+	16494.8i	−0.936408	+	0.936408i	−0.998096	−	0.0616872i	$-0.980352\pi$
$677$	−16494.8	+	16494.8i	−0.936408	+	0.936408i	0.0616872	+	0.998096i	$0.480352\pi$
$678$	−1422.91	+	2431.76i	−0.0805998	+	0.137745i
$679$			11269.9i			0.636964i
$680$	28579.7	+	499.082i	1.61174	+	0.0281455i
$681$		−	413.789i		−	0.0232840i
$682$	2549.08	+	1491.56i	0.143122	+	0.0837460i
$683$	20875.1	−	20875.1i	1.16949	−	1.16949i	0.187166	−	0.982328i	$-0.440070\pi$
$683$	20875.1	−	20875.1i	1.16949	−	1.16949i	0.982328	−	0.187166i	$-0.0599302\pi$
$684$	1425.62	−	5083.04i	0.0796926	−	0.284144i
$685$	−8961.36	−	8961.36i	−0.499848	−	0.499848i
$686$	−18902.1	+	4947.08i	−1.05202	+	0.275336i
$687$	−12163.8			−0.675515
$688$	−1748.45	−	7190.92i	−0.0968880	−	0.398476i
$689$	18150.2			1.00358
$690$	−20423.0	+	5345.13i	−1.12680	+	0.294906i
$691$	22267.3	+	22267.3i	1.22589	+	1.22589i	0.965506	+	0.260382i	$0.0838487\pi$
$691$	22267.3	+	22267.3i	1.22589	+	1.22589i	0.260382	+	0.965506i	$0.416151\pi$
$692$	16986.6	+	4764.14i	0.933138	+	0.261713i
$693$	−3301.30	+	3301.30i	−0.180961	+	0.180961i
$694$	−13213.1	−	7731.47i	−0.722712	−	0.422886i
$695$			30087.2i			1.64212i
$696$	3352.16	−	3237.10i	0.182562	−	0.176296i
$697$		−	17090.5i		−	0.928765i
$698$	1582.92	−	2705.21i	0.0858373	−	0.146696i
$699$	552.357	−	552.357i	0.0298885	−	0.0298885i
$700$	15608.9	−	8771.17i	0.842803	−	0.473598i
$701$	−12419.0	−	12419.0i	−0.669129	−	0.669129i	0.288385	−	0.957515i	$-0.406882\pi$
$701$	−12419.0	−	12419.0i	−0.669129	−	0.669129i	−0.957515	+	0.288385i	$0.906882\pi$
$702$	1589.68	+	6073.95i	0.0854680	+	0.326562i
$703$	−15320.7			−0.821950
$704$	−12314.7	−	13206.3i	−0.659270	−	0.707003i
$705$	2324.49			0.124178
$706$	6553.60	+	25040.4i	0.349360	+	1.33486i
$707$	14473.5	+	14473.5i	0.769918	+	0.769918i
$708$	−7048.17	+	3960.60i	−0.374134	+	0.210238i
$709$	−17027.9	+	17027.9i	−0.901970	+	0.901970i	−0.995606	−	0.0936362i	$-0.970151\pi$
$709$	−17027.9	+	17027.9i	−0.901970	+	0.901970i	0.0936362	+	0.995606i	$0.470151\pi$
$710$	16502.3	−	28202.4i	0.872281	−	1.49073i
$711$		−	7909.17i		−	0.417183i
$712$	5709.45	−	5513.47i	0.300521	−	0.290205i
$713$		−	4424.64i		−	0.232404i
$714$	−8174.00	−	4782.91i	−0.428437	−	0.250694i
$715$	−34132.9	+	34132.9i	−1.78531	+	1.78531i
$716$	−18723.9	−	5251.39i	−0.977296	−	0.274097i
$717$	−2404.79	−	2404.79i	−0.125256	−	0.125256i
$718$	−796.097	+	208.355i	−0.0413790	+	0.0108297i
$719$	9987.52			0.518041			0.259021	−	0.965872i	$-0.416600\pi$
$719$	9987.52			0.518041			0.259021	+	0.965872i	$0.416600\pi$
$720$	−9317.79	+	2265.59i	−0.482296	+	0.117269i
$721$	7535.25			0.389220
$722$	−4057.63	+	1061.97i	−0.209154	+	0.0547400i
$723$	−5765.00	−	5765.00i	−0.296546	−	0.296546i
$724$	−2150.27	+	7666.79i	−0.110379	+	0.393555i
$725$	7385.99	−	7385.99i	0.378357	−	0.378357i
$726$	−638.573	−	373.653i	−0.0326442	−	0.0191013i
$727$		−	18495.4i		−	0.943545i	−0.881720	−	0.471772i	$-0.843614\pi$
$727$		−	18495.4i		−	0.943545i	0.881720	−	0.471772i	$-0.156386\pi$
$728$	−27358.9	−	477.763i	−1.39284	−	0.0243229i
$729$		−	729.000i		−	0.0370370i
$730$	−10997.3	+	18794.5i	−0.557575	+	0.952897i
$731$	−6204.24	+	6204.24i	−0.313915	+	0.313915i
$732$	−9876.80	−	17576.5i	−0.498712	−	0.887494i
$733$	3852.08	+	3852.08i	0.194106	+	0.194106i	0.797468	−	0.603362i	$-0.206172\pi$
$733$	3852.08	+	3852.08i	0.194106	+	0.194106i	−0.603362	+	0.797468i	$0.706172\pi$
$734$	3957.86	+	15122.5i	0.199029	+	0.760464i
$735$	6325.30			0.317432
$736$	−7758.99	+	25915.6i	−0.388587	+	1.29791i
$737$	−14944.0			−0.746904
$738$	1451.67	+	5546.64i	0.0724075	+	0.276659i
$739$	16168.9	+	16168.9i	0.804846	+	0.804846i	0.983849	−	0.179003i	$-0.0572871\pi$
$739$	16168.9	+	16168.9i	0.804846	+	0.804846i	−0.179003	+	0.983849i	$0.557287\pi$
$740$	13633.0	+	24261.0i	0.677244	+	1.20521i
$741$	−12787.6	+	12787.6i	−0.633959	+	0.633959i
$742$	4638.49	−	7927.18i	0.229493	−	0.392205i
$743$		−	36990.3i		−	1.82644i	−0.407471	−	0.913218i	$-0.633589\pi$
$743$		−	36990.3i		−	1.82644i	0.407471	−	0.913218i	$-0.366411\pi$
$744$	35.0917	−	2009.51i	0.00172920	−	0.0990218i
$745$			17579.1i			0.864492i
$746$	3376.55	+	1975.75i	0.165716	+	0.0969667i
$747$	8337.42	−	8337.42i	0.408367	−	0.408367i
$748$	−5781.35	+	20613.4i	−0.282603	+	1.00762i
$749$	−9312.18	−	9312.18i	−0.454285	−	0.454285i
$750$	−3711.30	+	971.323i	−0.180690	+	0.0472903i
$751$	−10125.3			−0.491981			−0.245990	−	0.969272i	$-0.579113\pi$
$751$	−10125.3			−0.491981			−0.245990	+	0.969272i	$0.579113\pi$
$752$	1548.99	−	2544.24i	0.0751140	−	0.123376i
$753$	−3828.98			−0.185307
$754$	−15443.3	+	4041.82i	−0.745903	+	0.195218i
$755$	13962.8	+	13962.8i	0.673059	+	0.673059i
$756$	3059.09	+	857.968i	0.147167	+	0.0412751i
$757$	−8998.60	+	8998.60i	−0.432047	+	0.432047i	−0.889324	−	0.457277i	$-0.848825\pi$
$757$	−8998.60	+	8998.60i	−0.432047	+	0.432047i	0.457277	+	0.889324i	$0.348825\pi$
$758$	15220.9	+	8906.32i	0.729351	+	0.426770i
$759$		−	15811.6i		−	0.756158i
$760$	−19186.6	−	19868.7i	−0.915754	−	0.948305i
$761$		−	25265.9i		−	1.20353i	−0.798672	−	0.601766i	$-0.794464\pi$
$761$		−	25265.9i		−	1.20353i	0.798672	−	0.601766i	$-0.205536\pi$
$762$	−3055.23	+	5221.39i	−0.145248	+	0.248230i
$763$	14472.0	−	14472.0i	0.686661	−	0.686661i
$764$	−2022.64	+	1136.58i	−0.0957807	+	0.0538222i
$765$	8039.27	+	8039.27i	0.379948	+	0.379948i
$766$	−4869.11	−	18604.2i	−0.229671	−	0.877544i
$767$	27695.2			1.30380
$768$	−3729.39	+	11708.4i	−0.175225	+	0.550118i
$769$	−28077.3			−1.31664			−0.658318	−	0.752740i	$-0.728732\pi$
$769$	−28077.3			−1.31664			−0.658318	+	0.752740i	$0.728732\pi$
$770$	6184.67	+	23630.8i	0.289455	+	1.10597i
$771$	104.099	+	104.099i	0.00486257	+	0.00486257i
$772$	29961.2	−	16836.2i	1.39680	−	0.784905i
$773$	−8413.75	+	8413.75i	−0.391490	+	0.391490i	−0.875218	−	0.483728i	$-0.839282\pi$
$773$	−8413.75	+	8413.75i	−0.391490	+	0.391490i	0.483728	+	0.875218i	$0.339282\pi$
$774$	1486.56	−	2540.54i	0.0690355	−	0.117982i
$775$		−	4504.97i		−	0.208804i
$776$	−12043.2	−	12471.3i	−0.557120	−	0.576924i
$777$		−	9220.35i		−	0.425712i
$778$	19058.5	+	11151.9i	0.878254	+	0.513899i
$779$	−11677.4	+	11677.4i	−0.537083	+	0.537083i
$780$	31628.7	+	8870.74i	1.45191	+	0.407210i
$781$	17305.3	+	17305.3i	0.792870	+	0.792870i
$782$	31028.6	−	8120.81i	1.41890	−	0.371355i
$783$	1853.51			0.0845966
$784$	4215.04	−	6923.28i	0.192011	−	0.315383i
$785$	−5165.89			−0.234877
$786$	23678.1	−	6197.04i	1.07452	−	0.281223i
$787$	8677.71	+	8677.71i	0.393046	+	0.393046i	0.875772	−	0.482726i	$-0.160353\pi$
$787$	8677.71	+	8677.71i	0.393046	+	0.393046i	−0.482726	+	0.875772i	$0.660353\pi$
$788$	−2861.79	+	10203.7i	−0.129374	+	0.461285i
$789$	−951.088	+	951.088i	−0.0429146	+	0.0429146i
$790$	−35715.6	−	20898.5i	−1.60849	−	0.941185i
$791$		−	4883.98i		−	0.219538i
$792$	125.401	−	7181.05i	0.00562619	−	0.322181i
$793$			69065.3i			3.09279i
$794$	−9582.88	+	16377.1i	−0.428317	+	0.731994i
$795$	−7796.52	+	7796.52i	−0.347816	+	0.347816i
$796$	−13063.0	−	23246.6i	−0.581665	−	1.03512i
$797$	16951.1	+	16951.1i	0.753374	+	0.753374i	0.975107	−	0.221733i	$-0.0711715\pi$
$797$	16951.1	+	16951.1i	0.753374	+	0.753374i	−0.221733	+	0.975107i	$0.571171\pi$
$798$	2317.03	+	8853.06i	0.102784	+	0.392726i
$799$	−3531.58			−0.156369
$800$	−7899.87	+	26386.2i	−0.349128	+	1.16611i
$801$	3156.93			0.139257
$802$	1199.47	+	4583.01i	0.0528114	+	0.201785i
$803$	−11532.5	−	11532.5i	−0.506814	−	0.506814i
$804$	4981.90	+	8865.66i	0.218530	+	0.388890i
$805$	25876.5	−	25876.5i	1.13295	−	1.13295i
$806$	−3477.07	+	5942.32i	−0.151954	+	0.259689i
$807$			19902.3i			0.868145i
$808$	−31483.0	−	549.782i	−1.37075	−	0.0239372i
$809$		−	39305.4i		−	1.70816i	−0.520138	−	0.854082i	$-0.674120\pi$
$809$		−	39305.4i		−	1.70816i	0.520138	−	0.854082i	$-0.325880\pi$
$810$	−3291.96	−	1926.25i	−0.142800	−	0.0835573i
$811$	25524.4	−	25524.4i	1.10516	−	1.10516i	0.111378	−	0.993778i	$-0.464474\pi$
$811$	25524.4	−	25524.4i	1.10516	−	1.10516i	0.993778	−	0.111378i	$-0.0355263\pi$
$812$	−2181.42	+	7777.86i	−0.0942769	+	0.336145i
$813$	−658.072	−	658.072i	−0.0283882	−	0.0283882i
$814$	−20164.1	+	5277.37i	−0.868247	+	0.227238i
$815$	−31112.9			−1.33722
$816$	14156.5	−	3442.09i	0.607322	−	0.147668i
$817$	8478.34			0.363059
$818$	−32610.7	+	8534.89i	−1.39389	+	0.364811i
$819$	−7695.87	−	7695.87i	−0.328346	−	0.328346i
$820$	28882.8	+	8100.63i	1.23004	+	0.344983i
$821$	−20817.5	+	20817.5i	−0.884939	+	0.884939i	−0.994032	−	0.109093i	$-0.965206\pi$
$821$	−20817.5	+	20817.5i	−0.884939	+	0.884939i	0.109093	+	0.994032i	$0.465206\pi$
$822$	−5575.11	−	3262.20i	−0.236563	−	0.138421i
$823$			8625.74i			0.365339i	0.983174	+	0.182670i	$0.0584739\pi$
$823$			8625.74i			0.365339i	−0.983174	+	0.182670i	$0.941526\pi$
$824$	−8338.53	+	8052.30i	−0.352532	+	0.340431i
$825$		−	16098.7i		−	0.679374i
$826$	7077.82	−	12096.0i	0.298147	−	0.509533i
$827$	−16592.0	+	16592.0i	−0.697654	+	0.697654i	−0.963904	−	0.266250i	$-0.914215\pi$
$827$	−16592.0	+	16592.0i	−0.697654	+	0.697654i	0.266250	+	0.963904i	$0.414215\pi$
$828$	−9380.38	+	5271.14i	−0.393709	+	0.221238i
$829$	−11523.3	−	11523.3i	−0.482777	−	0.482777i	0.423240	−	0.906018i	$-0.360893\pi$
$829$	−11523.3	−	11523.3i	−0.482777	−	0.482777i	−0.906018	+	0.423240i	$0.860893\pi$
$830$	−15619.4	−	59679.5i	−0.653200	−	2.49579i
$831$	−14948.6			−0.624022
$832$	30786.0	−	28707.5i	1.28283	−	1.19622i
$833$	−9609.99			−0.399720
$834$	3882.72	+	14835.4i	0.161208	+	0.615956i
$835$	−13900.7	−	13900.7i	−0.576112	−	0.576112i
$836$	18034.7	−	10134.3i	0.746106	−	0.419261i
$837$	565.261	−	565.261i	0.0233432	−	0.0233432i
$838$	8771.91	−	14991.2i	0.361600	−	0.617975i
$839$		−	1709.60i		−	0.0703482i	−0.999381	−	0.0351741i	$-0.988801\pi$
$839$		−	1709.60i		−	0.0703482i	0.999381	−	0.0351741i	$-0.0111986\pi$
$840$	11957.4	−	11547.0i	0.491155	−	0.474295i
$841$		−	19676.4i		−	0.806772i
$842$	30840.8	+	18046.1i	1.26228	+	0.738609i
$843$	−2905.66	+	2905.66i	−0.118714	+	0.118714i
$844$	41514.5	+	11643.4i	1.69312	+	0.474860i
$845$	−53706.5	−	53706.5i	−2.18646	−	2.18646i
$846$	1146.16	−	299.973i	0.0465788	−	0.0121906i
$847$	1282.52			0.0520282
$848$	3338.16	+	13729.0i	0.135180	+	0.555962i
$849$	23653.4			0.956165
$850$	31591.9	−	8268.26i	1.27482	−	0.333646i
$851$	22080.4	+	22080.4i	0.889433	+	0.889433i
$852$	4497.43	−	16035.6i	0.180845	−	0.644802i
$853$	−27950.1	+	27950.1i	−1.12191	+	1.12191i	−0.130462	+	0.991453i	$0.541646\pi$
$853$	−27950.1	+	27950.1i	−1.12191	+	1.12191i	−0.991453	+	0.130462i	$0.958354\pi$
$854$	30164.6	+	17650.4i	1.20868	+	0.707243i
$855$		−	10986.0i		−	0.439430i
$856$	20256.0	+	353.727i	0.808805	+	0.0141240i
$857$		−	20208.0i		−	0.805477i	−0.915315	−	0.402739i	$-0.868058\pi$
$857$		−	20208.0i		−	0.805477i	0.915315	−	0.402739i	$-0.131942\pi$
$858$	−12425.4	+	21235.1i	−0.494402	+	0.844933i
$859$	−6906.75	+	6906.75i	−0.274337	+	0.274337i	−0.830843	−	0.556507i	$-0.812141\pi$
$859$	−6906.75	+	6906.75i	−0.274337	+	0.274337i	0.556507	+	0.830843i	$0.312141\pi$
$860$	−7544.40	−	13425.8i	−0.299142	−	0.532345i
$861$	−7027.75	−	7027.75i	−0.278171	−	0.278171i
$862$	4422.64	+	16898.3i	0.174751	+	0.667702i
$863$	16342.0			0.644599			0.322300	−	0.946638i	$-0.395544\pi$
$863$	16342.0			0.644599			0.322300	+	0.946638i	$0.395544\pi$
$864$	−4302.03	+	2319.56i	−0.169396	+	0.0913347i
$865$	36713.1			1.44310
$866$	−5.50577	−	21.0368i	−0.000216043	−	0.000825473i
$867$	−1791.96	−	1791.96i	−0.0701939	−	0.0701939i
$868$	1706.73	+	3037.26i	0.0667399	+	0.118769i
$869$	21915.4	−	21915.4i	0.855501	−	0.855501i
$870$	4897.56	−	8369.94i	0.190854	−	0.326170i
$871$		−	34836.9i		−	1.35523i
$872$	−549.726	+	31479.8i	−0.0213487	+	1.22252i
$873$		−	6895.75i		−	0.267338i
$874$	−26749.6	−	15652.2i	−1.03526	−	0.605770i
$875$	4702.32	−	4702.32i	0.181677	−	0.181677i
$876$	−2997.15	+	10686.4i	−0.115599	+	0.412167i
$877$	517.041	+	517.041i	0.0199079	+	0.0199079i	0.716991	−	0.697083i	$-0.245519\pi$
$877$	517.041	+	517.041i	0.0199079	+	0.0199079i	−0.697083	+	0.716991i	$0.745519\pi$
$878$	41550.4	−	10874.6i	1.59710	−	0.417995i
$879$	7005.31			0.268809
$880$	−32096.2	−	19540.9i	−1.22950	−	0.748548i
$881$	−22171.2			−0.847861			−0.423931	−	0.905695i	$-0.639350\pi$
$881$	−22171.2			−0.847861			−0.423931	+	0.905695i	$0.639350\pi$
$882$	3118.87	−	816.274i	0.119068	−	0.0311625i
$883$	589.293	+	589.293i	0.0224590	+	0.0224590i	0.718247	−	0.695788i	$-0.244945\pi$
$883$	589.293	+	589.293i	0.0224590	+	0.0224590i	−0.695788	+	0.718247i	$0.744945\pi$
$884$	−48053.2	−	13477.3i	−1.82829	−	0.512771i
$885$	−11896.6	+	11896.6i	−0.451866	+	0.451866i
$886$	11755.4	+	6878.50i	0.445744	+	0.260821i
$887$		−	13685.0i		−	0.518034i	−0.965873	−	0.259017i	$-0.916601\pi$
$887$		−	13685.0i		−	0.518034i	0.965873	−	0.259017i	$-0.0833985\pi$
$888$	9853.02	+	10203.3i	0.372349	+	0.385584i
$889$		−	10486.7i		−	0.395627i
$890$	8341.60	−	14255.8i	0.314170	−	0.536916i
$891$	2019.98	−	2019.98i	0.0759504	−	0.0759504i
$892$	21573.4	−	12122.8i	0.809787	−	0.455046i
$893$	2413.03	+	2413.03i	0.0904242	+	0.0904242i
$894$	2268.56	+	8667.86i	0.0848679	+	0.324269i
$895$	−40467.9			−1.51139
$896$	−4670.43	−	20782.5i	−0.174139	−	0.774881i
$897$	36859.4			1.37202
$898$	−4846.10	−	18516.3i	−0.180085	−	0.688081i
$899$	1437.20	+	1437.20i	0.0533184	+	0.0533184i
$900$	−9550.70	+	5366.84i	−0.353730	+	0.198772i
$901$	11845.2	−	11845.2i	0.437981	−	0.437981i
$902$	−11346.7	+	19391.5i	−0.418851	+	0.715817i
$903$			5102.46i			0.188039i
$904$	5219.10	+	5404.62i	0.192019	+	0.198844i
$905$			16570.2i			0.608634i
$906$	8686.66	+	5082.89i	0.318538	+	0.186388i
$907$	−32330.9	+	32330.9i	−1.18361	+	1.18361i	−0.204804	+	0.978803i	$0.565656\pi$
$907$	−32330.9	+	32330.9i	−1.18361	+	1.18361i	−0.978803	+	0.204804i	$0.934344\pi$
$908$	−1062.44	−	297.978i	−0.0388308	−	0.0108907i
$909$	−8855.95	−	8855.95i	−0.323139	−	0.323139i
$910$	−55087.3	+	14417.5i	−2.00673	+	0.525203i
$911$	−36436.3			−1.32513			−0.662563	−	0.749006i	$-0.730531\pi$
$911$	−36436.3			−1.32513			−0.662563	+	0.749006i	$0.730531\pi$
$912$	−12024.6	−	7320.80i	−0.436593	−	0.265807i
$913$	46204.1			1.67484
$914$	20599.1	−	5391.22i	0.745469	−	0.195105i
$915$	−29667.4	−	29667.4i	−1.07189	−	1.07189i
$916$	−8759.43	+	31231.8i	−0.315960	+	1.12656i
$917$	−30000.8	+	30000.8i	−1.08039	+	1.08039i
$918$	5001.45	+	2926.53i	0.179818	+	0.105218i
$919$		−	18351.8i		−	0.658726i	−0.944203	−	0.329363i	$-0.893166\pi$
$919$		−	18351.8i		−	0.658726i	0.944203	−	0.329363i	$-0.106834\pi$
$920$	−982.932	+	56287.2i	−0.0352242	+	2.01710i
$921$			8190.45i			0.293034i
$922$	18241.5	−	31174.7i	0.651573	−	1.11354i
$923$	−40341.4	+	40341.4i	−1.43863	+	1.43863i
$924$	6099.06	+	10853.7i	0.217148	+	0.386430i
$925$	22481.4	+	22481.4i	0.799116	+	0.799116i
$926$	−6126.69	−	23409.3i	−0.217425	−	0.830752i
$927$	−4610.62			−0.163358
$928$	−5897.59	−	10938.1i	−0.208618	−	0.386919i
$929$	25908.3			0.914989			0.457495	−	0.889212i	$-0.348747\pi$
$929$	25908.3			0.914989			0.457495	+	0.889212i	$0.348747\pi$
$930$	−1058.96	−	4046.16i	−0.0373384	−	0.142665i
$931$	6566.22	+	6566.22i	0.231148	+	0.231148i
$932$	−1020.47	−	1815.99i	−0.0358653	−	0.0638249i
$933$	8415.58	−	8415.58i	0.295299	−	0.295299i
$934$	2680.16	−	4580.39i	0.0938944	−	0.160466i
$935$			44551.8i			1.55829i
$936$	16740.2	+	292.331i	0.584584	+	0.0102085i
$937$			41822.4i			1.45814i	0.684438	+	0.729071i	$0.260047\pi$
$937$			41822.4i			1.45814i	−0.684438	+	0.729071i	$0.739953\pi$
$938$	−15215.2	−	8902.96i	−0.529630	−	0.309906i
$939$	15548.1	−	15548.1i	0.540356	−	0.540356i
$940$	1673.91	−	5968.35i	0.0580820	−	0.207092i
$941$	35805.6	+	35805.6i	1.24041	+	1.24041i	0.959829	+	0.280585i	$0.0905285\pi$
$941$	35805.6	+	35805.6i	1.24041	+	1.24041i	0.280585	+	0.959829i	$0.409471\pi$
$942$	−2547.19	+	666.653i	−0.0881019	+	0.0230581i
$943$	33659.4			1.16236
$944$	5093.67	+	20949.0i	0.175619	+	0.722278i
$945$	6611.62			0.227594
$946$	11158.7	−	2920.45i	0.383509	−	0.100372i
$947$	4833.07	+	4833.07i	0.165844	+	0.165844i	0.785150	−	0.619306i	$-0.212586\pi$
$947$	4833.07	+	4833.07i	0.165844	+	0.165844i	−0.619306	+	0.785150i	$0.712586\pi$
$948$	−20307.5	−	5695.56i	−0.695737	−	0.195130i
$949$	26884.1	−	26884.1i	0.919593	−	0.919593i
$950$	−27235.3	−	15936.4i	−0.930136	−	0.544257i
$951$			13851.6i			0.472312i
$952$	−18166.8	+	17543.2i	−0.618477	+	0.597247i
$953$			54695.5i			1.85914i	0.368645	+	0.929570i	$0.379822\pi$
$953$			54695.5i			1.85914i	−0.368645	+	0.929570i	$0.620178\pi$
$954$	−2838.17	+	4850.43i	−0.0963198	+	0.164611i
$955$	−3414.02	+	3414.02i	−0.115681	+	0.115681i
$956$	−7906.28	+	4442.79i	−0.267476	+	0.150304i
$957$	5135.87	+	5135.87i	0.173479	+	0.173479i
$958$	4384.12	+	16751.2i	0.147854	+	0.564932i
$959$	11197.1			0.377033
$960$	−892.824	+	25555.8i	−0.0300164	+	0.859177i
$961$	−28914.4			−0.970575
$962$	−12302.4	−	47005.9i	−0.412314	−	1.57540i
$963$	5697.88	+	5697.88i	0.190666	+	0.190666i
$964$	−18953.7	+	10650.7i	−0.633254	+	0.355846i
$965$	50571.6	−	50571.6i	1.68700	−	1.68700i
$966$	9419.84	−	16098.5i	0.313746	−	0.536192i
$967$			11587.6i			0.385350i	0.981263	+	0.192675i	$0.0617163\pi$
$967$			11587.6i			0.385350i	−0.981263	+	0.192675i	$0.938284\pi$
$968$	−1419.24	+	1370.52i	−0.0471240	+	0.0455064i
$969$			16690.9i			0.553343i
$970$	−31139.3	−	18220.7i	−1.03074	−	0.603126i
$971$	36545.7	−	36545.7i	1.20784	−	1.20784i	0.236109	−	0.971727i	$-0.424128\pi$
$971$	36545.7	−	36545.7i	1.20784	−	1.20784i	0.971727	−	0.236109i	$-0.0758723\pi$
$972$	−1871.78	−	524.968i	−0.0617667	−	0.0173234i
$973$	−18796.8	−	18796.8i	−0.619321	−	0.619321i
$974$	17808.3	−	4660.79i	0.585845	−	0.153328i
$975$	37528.6			1.23270
$976$	−52241.8	+	12702.4i	−1.71334	+	0.416592i
$977$	11161.4			0.365490			0.182745	−	0.983160i	$-0.441502\pi$
$977$	11161.4			0.365490			0.182745	+	0.983160i	$0.441502\pi$
$978$	−15341.1	+	4015.09i	−0.501590	+	0.131276i
$979$	8747.49	+	8747.49i	0.285568	+	0.285568i
$980$	4554.98	−	16240.8i	0.148473	−	0.529381i
$981$	−8855.05	+	8855.05i	−0.288196	+	0.288196i
$982$	27942.6	+	16350.2i	0.908028	+	0.531321i
$983$		−	52855.9i		−	1.71500i	−0.514486	−	0.857499i	$-0.672017\pi$
$983$		−	52855.9i		−	1.71500i	0.514486	−	0.857499i	$-0.327983\pi$
$984$	15286.9	+	266.952i	0.495252	+	0.00864850i
$985$			22053.3i			0.713378i
$986$	−7440.83	+	12716.4i	−0.240329	+	0.410723i
$987$	−1452.21	+	1452.21i	−0.0468333	+	0.0468333i
$988$	23624.7	+	42041.9i	0.760732	+	1.35378i
$989$	−12219.1	−	12219.1i	−0.392867	−	0.392867i
$990$	−3784.23	−	14459.1i	−0.121486	−	0.464181i
$991$	−50245.9			−1.61061			−0.805305	−	0.592861i	$-0.797998\pi$
$991$	−50245.9			−1.61061			−0.805305	+	0.592861i	$0.797998\pi$
$992$	−5134.33	−	1537.19i	−0.164330	−	0.0491995i
$993$	−32415.2			−1.03592
$994$	7309.60	+	27929.0i	0.233246	+	0.891202i
$995$	−39238.0	−	39238.0i	−1.25018	−	1.25018i
$996$	−15403.2	−	27411.1i	−0.490028	−	0.872041i
$997$	−3886.25	+	3886.25i	−0.123449	+	0.123449i	−0.766132	−	0.642683i	$-0.777821\pi$
$997$	−3886.25	+	3886.25i	−0.123449	+	0.123449i	0.642683	+	0.766132i	$0.277821\pi$
$998$	−13680.6	+	23380.2i	−0.433919	+	0.741569i
$999$			5641.69i			0.178674i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.4.j.a.13.6	✓	24
3.2	odd	2		144.4.k.b.109.7		24
4.3	odd	2		192.4.j.a.145.7		24
8.3	odd	2		384.4.j.a.289.1		24
8.5	even	2		384.4.j.b.289.12		24
12.11	even	2		576.4.k.b.145.11		24
16.3	odd	4		384.4.j.a.97.1		24
16.5	even	4	inner	48.4.j.a.37.6	yes	24
16.11	odd	4		192.4.j.a.49.7		24
16.13	even	4		384.4.j.b.97.12		24
48.5	odd	4		144.4.k.b.37.7		24
48.11	even	4		576.4.k.b.433.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.4.j.a.13.6	✓	24	1.1	even	1	trivial
48.4.j.a.37.6	yes	24	16.5	even	4	inner
144.4.k.b.37.7		24	48.5	odd	4
144.4.k.b.109.7		24	3.2	odd	2
192.4.j.a.49.7		24	16.11	odd	4
192.4.j.a.145.7		24	4.3	odd	2
384.4.j.a.97.1		24	16.3	odd	4
384.4.j.a.289.1		24	8.3	odd	2
384.4.j.b.97.12		24	16.13	even	4
384.4.j.b.289.12		24	8.5	even	2
576.4.k.b.145.11		24	12.11	even	2
576.4.k.b.433.11		24	48.11	even	4

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:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	48.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.716137 - 2.73627i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.97430 + 3.91908i) q^{4} +(-11.7719 + 11.7719i) q^{5} +(-4.28534 + 7.32365i) q^{6} -14.7089i q^{7} +(15.7182 + 16.2769i) q^{8} +9.00000i q^{9} +O(q^{10})\)	\(q+(-0.716137 - 2.73627i) q^{2} +(-2.12132 - 2.12132i) q^{3} +(-6.97430 + 3.91908i) q^{4} +(-11.7719 + 11.7719i) q^{5} +(-4.28534 + 7.32365i) q^{6} -14.7089i q^{7} +(15.7182 + 16.2769i) q^{8} +9.00000i q^{9} +(40.6415 + 23.7808i) q^{10} +(-24.9380 + 24.9380i) q^{11} +(23.1083 + 6.48109i) q^{12} +(-58.1345 - 58.1345i) q^{13} +(-40.2475 + 10.5336i) q^{14} +49.9441 q^{15} +(33.2816 - 54.6657i) q^{16} -75.8798 q^{17} +(24.6264 - 6.44523i) q^{18} +(51.8464 + 51.8464i) q^{19} +(35.9658 - 128.236i) q^{20} +(-31.2023 + 31.2023i) q^{21} +(86.0960 + 50.3779i) q^{22} -149.444i q^{23} +(1.18523 - 67.8719i) q^{24} -152.157i q^{25} +(-117.439 + 200.704i) q^{26} +(19.0919 - 19.0919i) q^{27} +(57.6455 + 102.584i) q^{28} +(48.5419 + 48.5419i) q^{29} +(-35.7668 - 136.660i) q^{30} +29.6074 q^{31} +(-173.414 - 51.9192i) q^{32} +105.803 q^{33} +(54.3403 + 207.627i) q^{34} +(173.153 + 173.153i) q^{35} +(-35.2717 - 62.7687i) q^{36} +(-147.751 + 147.751i) q^{37} +(104.736 - 178.994i) q^{38} +246.644i q^{39} +(-376.645 - 6.57727i) q^{40} +225.232i q^{41} +(107.723 + 63.0327i) q^{42} +(81.7640 - 81.7640i) q^{43} +(76.1909 - 271.659i) q^{44} +(-105.947 - 105.947i) q^{45} +(-408.917 + 107.022i) q^{46} +46.5418 q^{47} +(-186.564 + 45.3625i) q^{48} +126.648 q^{49} +(-416.342 + 108.965i) q^{50} +(160.965 + 160.965i) q^{51} +(633.281 + 177.613i) q^{52} +(-156.105 + 156.105i) q^{53} +(-65.9129 - 38.5681i) q^{54} -587.137i q^{55} +(239.416 - 231.198i) q^{56} -219.965i q^{57} +(98.0609 - 167.586i) q^{58} +(-238.199 + 238.199i) q^{59} +(-348.325 + 195.735i) q^{60} +(-594.013 - 594.013i) q^{61} +(-21.2029 - 81.0137i) q^{62} +132.380 q^{63} +(-17.8765 + 511.688i) q^{64} +1368.71 q^{65} +(-75.7694 - 289.505i) q^{66} +(299.623 + 299.623i) q^{67} +(529.208 - 297.379i) q^{68} +(-317.018 + 317.018i) q^{69} +(349.790 - 597.792i) q^{70} -693.932i q^{71} +(-146.492 + 141.464i) q^{72} +462.446i q^{73} +(510.096 + 298.476i) q^{74} +(-322.774 + 322.774i) q^{75} +(-564.782 - 158.402i) q^{76} +(366.811 + 366.811i) q^{77} +(674.883 - 176.631i) q^{78} -878.797 q^{79} +(251.732 + 1035.31i) q^{80} -81.0000 q^{81} +(616.293 - 161.297i) q^{82} +(-926.380 - 926.380i) q^{83} +(95.3298 - 339.899i) q^{84} +(893.252 - 893.252i) q^{85} +(-282.282 - 165.174i) q^{86} -205.946i q^{87} +(-797.894 - 13.9335i) q^{88} -350.770i q^{89} +(-214.027 + 365.773i) q^{90} +(-855.096 + 855.096i) q^{91} +(585.682 + 1042.26i) q^{92} +(-62.8068 - 62.8068i) q^{93} +(-33.3303 - 127.351i) q^{94} -1220.66 q^{95} +(257.729 + 478.004i) q^{96} -766.194 q^{97} +(-90.6971 - 346.542i) q^{98} +(-224.442 - 224.442i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 20 q^{4} + 84 q^{8}+O(q^{10}) \) 24 * q - 20 * q^4 + 84 * q^8	\( 24 q - 20 q^{4} + 84 q^{8} + 72 q^{10} - 40 q^{11} - 24 q^{12} - 348 q^{14} + 120 q^{15} - 192 q^{16} - 36 q^{18} + 24 q^{19} + 80 q^{20} + 704 q^{22} + 228 q^{24} - 20 q^{26} - 344 q^{28} + 400 q^{29} - 408 q^{30} - 744 q^{31} - 960 q^{32} - 704 q^{34} - 456 q^{35} + 108 q^{36} + 16 q^{37} + 1256 q^{38} + 1744 q^{40} + 660 q^{42} + 1240 q^{43} - 200 q^{44} - 1432 q^{46} - 528 q^{48} - 1176 q^{49} + 708 q^{50} + 744 q^{51} + 1008 q^{52} + 752 q^{53} + 108 q^{54} + 1344 q^{56} + 1936 q^{58} - 1376 q^{59} - 1224 q^{60} - 912 q^{61} - 996 q^{62} - 504 q^{63} - 56 q^{64} + 976 q^{65} - 1368 q^{66} - 2256 q^{67} - 1568 q^{68} - 528 q^{69} - 1760 q^{70} - 612 q^{72} - 2740 q^{74} + 1104 q^{75} - 1880 q^{76} + 1904 q^{77} + 1692 q^{78} + 5992 q^{79} + 712 q^{80} - 1944 q^{81} - 40 q^{82} + 2680 q^{83} + 1800 q^{84} - 240 q^{85} - 1712 q^{86} - 3936 q^{88} + 648 q^{90} - 3496 q^{91} + 5296 q^{92} + 5272 q^{94} - 7728 q^{95} + 2880 q^{96} + 6760 q^{98} - 360 q^{99}+O(q^{100}) \) 24 * q - 20 * q^4 + 84 * q^8 + 72 * q^10 - 40 * q^11 - 24 * q^12 - 348 * q^14 + 120 * q^15 - 192 * q^16 - 36 * q^18 + 24 * q^19 + 80 * q^20 + 704 * q^22 + 228 * q^24 - 20 * q^26 - 344 * q^28 + 400 * q^29 - 408 * q^30 - 744 * q^31 - 960 * q^32 - 704 * q^34 - 456 * q^35 + 108 * q^36 + 16 * q^37 + 1256 * q^38 + 1744 * q^40 + 660 * q^42 + 1240 * q^43 - 200 * q^44 - 1432 * q^46 - 528 * q^48 - 1176 * q^49 + 708 * q^50 + 744 * q^51 + 1008 * q^52 + 752 * q^53 + 108 * q^54 + 1344 * q^56 + 1936 * q^58 - 1376 * q^59 - 1224 * q^60 - 912 * q^61 - 996 * q^62 - 504 * q^63 - 56 * q^64 + 976 * q^65 - 1368 * q^66 - 2256 * q^67 - 1568 * q^68 - 528 * q^69 - 1760 * q^70 - 612 * q^72 - 2740 * q^74 + 1104 * q^75 - 1880 * q^76 + 1904 * q^77 + 1692 * q^78 + 5992 * q^79 + 712 * q^80 - 1944 * q^81 - 40 * q^82 + 2680 * q^83 + 1800 * q^84 - 240 * q^85 - 1712 * q^86 - 3936 * q^88 + 648 * q^90 - 3496 * q^91 + 5296 * q^92 + 5272 * q^94 - 7728 * q^95 + 2880 * q^96 + 6760 * q^98 - 360 * q^99

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