LMFDB - Embedded newform 48.5.l.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,5,Mod(19,48)]

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([2, 3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$4.96175822802$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	48.43
Dual form			48.5.l.a.19.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.94725 + 0.647479i) q^{2} +(3.67423 + 3.67423i) q^{3} +(15.1615 - 5.11152i) q^{4} +(-21.2428 - 21.2428i) q^{5} +(-16.8821 - 12.1241i) q^{6} +35.6927 q^{7} +(-56.5368 + 29.9932i) q^{8} +27.0000i q^{9} +O(q^{10})$	\(q+(-3.94725 + 0.647479i) q^{2} +(3.67423 + 3.67423i) q^{3} +(15.1615 - 5.11152i) q^{4} +(-21.2428 - 21.2428i) q^{5} +(-16.8821 - 12.1241i) q^{6} +35.6927 q^{7} +(-56.5368 + 29.9932i) q^{8} +27.0000i q^{9} +(97.6049 + 70.0964i) q^{10} +(159.157 - 159.157i) q^{11} +(74.4880 + 36.9261i) q^{12} +(109.893 - 109.893i) q^{13} +(-140.888 + 23.1103i) q^{14} -156.102i q^{15} +(203.745 - 154.997i) q^{16} +252.870 q^{17} +(-17.4819 - 106.576i) q^{18} +(188.083 + 188.083i) q^{19} +(-430.657 - 213.491i) q^{20} +(131.143 + 131.143i) q^{21} +(-525.181 + 731.282i) q^{22} -841.621 q^{23} +(-317.931 - 97.5273i) q^{24} +277.514i q^{25} +(-362.622 + 504.929i) q^{26} +(-99.2043 + 99.2043i) q^{27} +(541.157 - 182.444i) q^{28} +(67.7983 - 67.7983i) q^{29} +(101.073 + 616.174i) q^{30} -1316.70i q^{31} +(-703.874 + 743.732i) q^{32} +1169.56 q^{33} +(-998.142 + 163.728i) q^{34} +(-758.214 - 758.214i) q^{35} +(138.011 + 409.362i) q^{36} +(-122.895 - 122.895i) q^{37} +(-864.189 - 620.630i) q^{38} +807.547 q^{39} +(1838.14 + 563.860i) q^{40} +1562.90i q^{41} +(-602.568 - 432.743i) q^{42} +(-1332.42 + 1332.42i) q^{43} +(1599.53 - 3226.60i) q^{44} +(573.556 - 573.556i) q^{45} +(3322.09 - 544.932i) q^{46} -1300.90i q^{47} +(1318.10 + 179.111i) q^{48} -1127.03 q^{49} +(-179.685 - 1095.42i) q^{50} +(929.104 + 929.104i) q^{51} +(1104.43 - 2227.87i) q^{52} +(3782.51 + 3782.51i) q^{53} +(327.351 - 455.817i) q^{54} -6761.88 q^{55} +(-2017.95 + 1070.54i) q^{56} +1382.12i q^{57} +(-223.719 + 311.514i) q^{58} +(2408.42 - 2408.42i) q^{59} +(-797.919 - 2366.75i) q^{60} +(454.048 - 454.048i) q^{61} +(852.536 + 5197.35i) q^{62} +963.704i q^{63} +(2296.81 - 3391.44i) q^{64} -4668.88 q^{65} +(-4616.54 + 757.265i) q^{66} +(34.6901 + 34.6901i) q^{67} +(3833.90 - 1292.55i) q^{68} +(-3092.31 - 3092.31i) q^{69} +(3483.79 + 2501.93i) q^{70} -1847.75 q^{71} +(-809.817 - 1526.49i) q^{72} +4677.04i q^{73} +(564.668 + 405.524i) q^{74} +(-1019.65 + 1019.65i) q^{75} +(3813.01 + 1890.24i) q^{76} +(5680.74 - 5680.74i) q^{77} +(-3187.59 + 522.870i) q^{78} +1136.73i q^{79} +(-7620.69 - 1035.54i) q^{80} -729.000 q^{81} +(-1011.95 - 6169.17i) q^{82} +(6428.83 + 6428.83i) q^{83} +(2658.68 + 1317.99i) q^{84} +(-5371.68 - 5371.68i) q^{85} +(4396.67 - 6122.10i) q^{86} +498.213 q^{87} +(-4224.59 + 13771.8i) q^{88} +12920.4i q^{89} +(-1892.60 + 2635.33i) q^{90} +(3922.39 - 3922.39i) q^{91} +(-12760.3 + 4301.96i) q^{92} +(4837.87 - 4837.87i) q^{93} +(842.306 + 5134.98i) q^{94} -7990.82i q^{95} +(-5318.84 + 146.449i) q^{96} -11245.3 q^{97} +(4448.67 - 729.728i) q^{98} +(4297.23 + 4297.23i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) $ 32 * q + 12 * q^4 + 180 * q^8	$ 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) $ 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−3.94725	+	0.647479i	−0.986812	+	0.161870i
$2$	−3.94725	+	0.647479i	−0.986812	+	0.161870i
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$3$	3.67423	+	3.67423i	0.408248	+	0.408248i
$4$	15.1615	−	5.11152i	0.947596	−	0.319470i
$5$	−21.2428	−	21.2428i	−0.849713	−	0.849713i	0.140384	−	0.990097i	$-0.455166\pi$
$5$	−21.2428	−	21.2428i	−0.849713	−	0.849713i	−0.990097	+	0.140384i	$0.955166\pi$
$6$	−16.8821	−	12.1241i	−0.468947	−	0.336781i
$7$	35.6927			0.728423			0.364211	−	0.931316i	$-0.381339\pi$
$7$	35.6927			0.728423			0.364211	+	0.931316i	$0.381339\pi$
$8$	−56.5368	+	29.9932i	−0.883387	+	0.468644i
$9$			27.0000i			0.333333i
$10$	97.6049	+	70.0964i	0.976049	+	0.700964i
$11$	159.157	−	159.157i	1.31535	−	1.31535i	0.397930	−	0.917416i	$-0.369729\pi$
$11$	159.157	−	159.157i	1.31535	−	1.31535i	0.917416	−	0.397930i	$-0.130271\pi$
$12$	74.4880	+	36.9261i	0.517278	+	0.256432i
$13$	109.893	−	109.893i	0.650256	−	0.650256i	−0.302799	−	0.953055i	$-0.597921\pi$
$13$	109.893	−	109.893i	0.650256	−	0.650256i	0.953055	+	0.302799i	$0.0979210\pi$
$14$	−140.888	+	23.1103i	−0.718817	+	0.117910i
$15$		−	156.102i		−	0.693787i
$16$	203.745	−	154.997i	0.795878	−	0.605457i
$17$	252.870			0.874983			0.437492	−	0.899222i	$-0.355867\pi$
$17$	252.870			0.874983			0.437492	+	0.899222i	$0.355867\pi$
$18$	−17.4819	−	106.576i	−0.0539566	−	0.328937i
$19$	188.083	+	188.083i	0.521005	+	0.521005i	0.917875	−	0.396870i	$-0.129904\pi$
$19$	188.083	+	188.083i	0.521005	+	0.521005i	−0.396870	+	0.917875i	$0.629904\pi$
$20$	−430.657	−	213.491i	−1.07664	−	0.533727i
$21$	131.143	+	131.143i	0.297377	+	0.297377i
$22$	−525.181	+	731.282i	−1.08508	+	1.51091i
$23$	−841.621			−1.59097			−0.795483	−	0.605976i	$-0.792783\pi$
$23$	−841.621			−1.59097			−0.795483	+	0.605976i	$0.792783\pi$
$24$	−317.931	−	97.5273i	−0.551964	−	0.169318i
$25$			277.514i			0.444023i
$26$	−362.622	+	504.929i	−0.536424	+	0.746937i
$27$	−99.2043	+	99.2043i	−0.136083	+	0.136083i
$28$	541.157	−	182.444i	0.690251	−	0.232709i
$29$	67.7983	−	67.7983i	0.0806162	−	0.0806162i	−0.665649	−	0.746265i	$-0.731845\pi$
$29$	67.7983	−	67.7983i	0.0806162	−	0.0806162i	0.746265	+	0.665649i	$0.231845\pi$
$30$	101.073	+	616.174i	0.112303	+	0.684638i
$31$		−	1316.70i		−	1.37014i	−0.728479	−	0.685068i	$-0.759772\pi$
$31$		−	1316.70i		−	1.37014i	0.728479	−	0.685068i	$-0.240228\pi$
$32$	−703.874	+	743.732i	−0.687377	+	0.726301i
$33$	1169.56			1.07398
$34$	−998.142	+	163.728i	−0.863444	+	0.141633i
$35$	−758.214	−	758.214i	−0.618950	−	0.618950i
$36$	138.011	+	409.362i	0.106490	+	0.315865i
$37$	−122.895	−	122.895i	−0.0897697	−	0.0897697i	0.660796	−	0.750566i	$-0.270219\pi$
$37$	−122.895	−	122.895i	−0.0897697	−	0.0897697i	−0.750566	+	0.660796i	$0.770219\pi$
$38$	−864.189	−	620.630i	−0.598469	−	0.429799i
$39$	807.547			0.530932
$40$	1838.14	+	563.860i	1.14884	+	0.352413i
$41$			1562.90i			0.929746i	0.885377	+	0.464873i	$0.153900\pi$
$41$			1562.90i			0.929746i	−0.885377	+	0.464873i	$0.846100\pi$
$42$	−602.568	−	432.743i	−0.341592	−	0.245319i
$43$	−1332.42	+	1332.42i	−0.720615	+	0.720615i	−0.968731	−	0.248115i	$-0.920189\pi$
$43$	−1332.42	+	1332.42i	−0.720615	+	0.720615i	0.248115	+	0.968731i	$0.420189\pi$
$44$	1599.53	−	3226.60i	0.826203	−	1.66663i
$45$	573.556	−	573.556i	0.283238	−	0.283238i
$46$	3322.09	−	544.932i	1.56998	−	0.257529i
$47$		−	1300.90i		−	0.588910i	−0.955665	−	0.294455i	$-0.904862\pi$
$47$		−	1300.90i		−	0.588910i	0.955665	−	0.294455i	$-0.0951381\pi$
$48$	1318.10	+	179.111i	0.572093	+	0.0777389i
$49$	−1127.03			−0.469400
$50$	−179.685	−	1095.42i	−0.0718739	−	0.438167i
$51$	929.104	+	929.104i	0.357210	+	0.357210i
$52$	1104.43	−	2227.87i	0.408443	−	0.823917i
$53$	3782.51	+	3782.51i	1.34657	+	1.34657i	0.889361	+	0.457207i	$0.151150\pi$
$53$	3782.51	+	3782.51i	1.34657	+	1.34657i	0.457207	+	0.889361i	$0.348850\pi$
$54$	327.351	−	455.817i	0.112260	−	0.156316i
$55$	−6761.88			−2.23533
$56$	−2017.95	+	1070.54i	−0.643479	+	0.341371i
$57$			1382.12i			0.425399i
$58$	−223.719	+	311.514i	−0.0665038	+	0.0926024i
$59$	2408.42	−	2408.42i	0.691876	−	0.691876i	−0.270769	−	0.962644i	$-0.587278\pi$
$59$	2408.42	−	2408.42i	0.691876	−	0.691876i	0.962644	+	0.270769i	$0.0872778\pi$
$60$	−797.919	−	2366.75i	−0.221644	−	0.657430i
$61$	454.048	−	454.048i	0.122023	−	0.122023i	−0.643458	−	0.765481i	$-0.722501\pi$
$61$	454.048	−	454.048i	0.122023	−	0.122023i	0.765481	+	0.643458i	$0.222501\pi$
$62$	852.536	+	5197.35i	0.221784	+	1.35207i
$63$			963.704i			0.242808i
$64$	2296.81	−	3391.44i	0.560746	−	0.827988i
$65$	−4668.88			−1.10506
$66$	−4616.54	+	757.265i	−1.05981	+	0.173844i
$67$	34.6901	+	34.6901i	0.00772779	+	0.00772779i	0.710960	−	0.703232i	$-0.248261\pi$
$67$	34.6901	+	34.6901i	0.00772779	+	0.00772779i	−0.703232	+	0.710960i	$0.748261\pi$
$68$	3833.90	−	1292.55i	0.829131	−	0.279531i
$69$	−3092.31	−	3092.31i	−0.649509	−	0.649509i
$70$	3483.79	+	2501.93i	0.710977	+	0.510598i
$71$	−1847.75			−0.366545			−0.183272	−	0.983062i	$-0.558669\pi$
$71$	−1847.75			−0.366545			−0.183272	+	0.983062i	$0.558669\pi$
$72$	−809.817	−	1526.49i	−0.156215	−	0.294462i
$73$			4677.04i			0.877658i	0.898571	+	0.438829i	$0.144607\pi$
$73$			4677.04i			0.877658i	−0.898571	+	0.438829i	$0.855393\pi$
$74$	564.668	+	405.524i	0.103117	+	0.0740549i
$75$	−1019.65	+	1019.65i	−0.181272	+	0.181272i
$76$	3813.01	+	1890.24i	0.660148	+	0.327257i
$77$	5680.74	−	5680.74i	0.958128	−	0.958128i
$78$	−3187.59	+	522.870i	−0.523930	+	0.0859417i
$79$			1136.73i			0.182139i	0.995845	+	0.0910694i	$0.0290285\pi$
$79$			1136.73i			0.182139i	−0.995845	+	0.0910694i	$0.970972\pi$
$80$	−7620.69	−	1035.54i	−1.19073	−	0.161803i
$81$	−729.000			−0.111111
$82$	−1011.95	−	6169.17i	−0.150498	−	0.917485i
$83$	6428.83	+	6428.83i	0.933203	+	0.933203i	0.997905	−	0.0647020i	$-0.0206097\pi$
$83$	6428.83	+	6428.83i	0.933203	+	0.933203i	−0.0647020	+	0.997905i	$0.520610\pi$
$84$	2658.68	+	1317.99i	0.376797	+	0.186791i
$85$	−5371.68	−	5371.68i	−0.743484	−	0.743484i
$86$	4396.67	−	6122.10i	0.594466	−	0.827758i
$87$	498.213			0.0658229
$88$	−4224.59	+	13771.8i	−0.545531	+	1.77839i
$89$			12920.4i			1.63116i	0.578642	+	0.815582i	$0.303583\pi$
$89$			12920.4i			1.63116i	−0.578642	+	0.815582i	$0.696417\pi$
$90$	−1892.60	+	2635.33i	−0.233655	+	0.325350i
$91$	3922.39	−	3922.39i	0.473661	−	0.473661i
$92$	−12760.3	+	4301.96i	−1.50759	+	0.508266i
$93$	4837.87	−	4837.87i	0.559356	−	0.559356i
$94$	842.306	+	5134.98i	0.0953266	+	0.581143i
$95$		−	7990.82i		−	0.885409i
$96$	−5318.84	+	146.449i	−0.577132	+	0.0158907i
$97$	−11245.3			−1.19517			−0.597584	−	0.801806i	$-0.703873\pi$
$97$	−11245.3			−1.19517			−0.597584	+	0.801806i	$0.703873\pi$
$98$	4448.67	−	729.728i	0.463210	−	0.0759816i
$99$	4297.23	+	4297.23i	0.438449	+	0.438449i
$100$	1418.52	+	4207.55i	0.141852	+	0.420755i
$101$	−4832.74	−	4832.74i	−0.473752	−	0.473752i	0.429375	−	0.903127i	$-0.358734\pi$
$101$	−4832.74	−	4832.74i	−0.473752	−	0.473752i	−0.903127	+	0.429375i	$0.858734\pi$
$102$	−4268.98	−	3065.83i	−0.410321	−	0.294678i
$103$	−4687.43			−0.441835			−0.220918	−	0.975292i	$-0.570905\pi$
$103$	−4687.43			−0.441835			−0.220918	+	0.975292i	$0.570905\pi$
$104$	−2916.96	+	9509.06i	−0.269689	+	0.879166i
$105$		−	5571.71i		−	0.505371i
$106$	−17379.6	−	12481.4i	−1.54678	−	1.11084i
$107$	6383.61	−	6383.61i	0.557569	−	0.557569i	−0.371046	−	0.928615i	$-0.621001\pi$
$107$	6383.61	−	6383.61i	0.557569	−	0.557569i	0.928615	+	0.371046i	$0.121001\pi$
$108$	−997.006	+	2011.18i	−0.0854772	+	0.172426i
$109$	8614.64	−	8614.64i	0.725077	−	0.725077i	−0.244558	−	0.969635i	$-0.578643\pi$
$109$	8614.64	−	8614.64i	0.725077	−	0.725077i	0.969635	+	0.244558i	$0.0786427\pi$
$110$	26690.8	−	4378.17i	2.20585	−	0.361832i
$111$		−	903.088i		−	0.0732967i
$112$	7272.20	−	5532.27i	0.579736	−	0.441029i
$113$	13911.1			1.08944			0.544720	−	0.838618i	$-0.316636\pi$
$113$	13911.1			1.08944			0.544720	+	0.838618i	$0.316636\pi$
$114$	−894.894	−	5455.57i	−0.0688592	−	0.419789i
$115$	17878.4	+	17878.4i	1.35186	+	1.35186i
$116$	681.374	−	1374.48i	0.0506372	−	0.102146i
$117$	2967.12	+	2967.12i	0.216752	+	0.216752i
$118$	−7947.23	+	11066.0i	−0.570758	+	0.794745i
$119$	9025.63			0.637358
$120$	4682.01	+	8825.51i	0.325139	+	0.612883i
$121$		−	36020.8i		−	2.46027i
$122$	−1498.25	+	2086.23i	−0.100662	+	0.140166i
$123$	−5742.47	+	5742.47i	−0.379567	+	0.379567i
$124$	−6730.35	−	19963.2i	−0.437718	−	1.29834i
$125$	−7381.57	+	7381.57i	−0.472421	+	0.472421i
$126$	−623.978	−	3803.98i	−0.0393032	−	0.239606i
$127$			16399.5i			1.01677i	0.861129	+	0.508387i	$0.169758\pi$
$127$			16399.5i			1.01677i	−0.861129	+	0.508387i	$0.830242\pi$
$128$	−6870.21	+	14874.0i	−0.419324	+	0.907836i
$129$	−9791.23			−0.588380
$130$	18429.2	−	3023.00i	1.09049	−	0.178876i
$131$	−10589.4	−	10589.4i	−0.617064	−	0.617064i	0.327714	−	0.944777i	$-0.393722\pi$
$131$	−10589.4	−	10589.4i	−0.617064	−	0.617064i	−0.944777	+	0.327714i	$0.893722\pi$
$132$	17732.3	−	5978.22i	1.01770	−	0.343103i
$133$	6713.19	+	6713.19i	0.379512	+	0.379512i
$134$	−159.391	−	114.469i	−0.00887678	−	0.00637498i
$135$	4214.76			0.231262
$136$	−14296.5	+	7584.39i	−0.772949	+	0.410056i
$137$			24703.3i			1.31617i	0.752942	+	0.658087i	$0.228634\pi$
$137$			24703.3i			1.31617i	−0.752942	+	0.658087i	$0.771366\pi$
$138$	14208.3	+	10203.9i	0.746079	+	0.535807i
$139$	3286.64	−	3286.64i	0.170107	−	0.170107i	−0.616919	−	0.787026i	$-0.711620\pi$
$139$	3286.64	−	3286.64i	0.170107	−	0.170107i	0.787026	+	0.616919i	$0.211620\pi$
$140$	−15371.3	−	7620.07i	−0.784251	−	0.388779i
$141$	4779.82	−	4779.82i	0.240421	−	0.240421i
$142$	7293.53	−	1196.38i	0.361711	−	0.0593325i
$143$		−	34980.5i		−	1.71062i
$144$	4184.92	+	5501.11i	0.201819	+	0.265293i
$145$	−2880.45			−0.137001
$146$	−3028.28	−	18461.4i	−0.142066	−	0.866084i
$147$	−4140.97	−	4140.97i	−0.191632	−	0.191632i
$148$	−2491.45	−	1235.10i	−0.113744	−	0.0563867i
$149$	−11812.2	−	11812.2i	−0.532055	−	0.532055i	0.389128	−	0.921184i	$-0.372776\pi$
$149$	−11812.2	−	11812.2i	−0.532055	−	0.532055i	−0.921184	+	0.389128i	$0.872776\pi$
$150$	3364.62	−	4685.03i	0.149539	−	0.208223i
$151$	1262.04			0.0553503			0.0276751	−	0.999617i	$-0.491190\pi$
$151$	1262.04			0.0553503			0.0276751	+	0.999617i	$0.491190\pi$
$152$	−16274.8	−	4992.39i	−0.704415	−	0.216083i
$153$			6827.50i			0.291661i
$154$	−18745.1	+	26101.5i	−0.790400	+	1.10058i
$155$	−27970.4	+	27970.4i	−1.16422	+	1.16422i
$156$	12243.7	−	4127.79i	0.503109	−	0.169617i
$157$	−21016.2	+	21016.2i	−0.852619	+	0.852619i	−0.990455	−	0.137836i	$-0.955985\pi$
$157$	−21016.2	+	21016.2i	−0.852619	+	0.852619i	0.137836	+	0.990455i	$0.455985\pi$
$158$	−736.007	−	4486.95i	−0.0294827	−	0.179737i
$159$			27795.6i			1.09947i
$160$	30751.2	−	846.704i	1.20122	−	0.0330744i
$161$	−30039.7			−1.15890
$162$	2877.54	−	472.012i	0.109646	−	0.0179855i
$163$	21448.9	+	21448.9i	0.807289	+	0.807289i	0.984223	−	0.176933i	$-0.0566177\pi$
$163$	21448.9	+	21448.9i	0.807289	+	0.807289i	−0.176933	+	0.984223i	$0.556618\pi$
$164$	7988.81	+	23696.0i	0.297026	+	0.881024i
$165$	−24844.7	−	24844.7i	−0.912570	−	0.912570i
$166$	−29538.7	−	21213.7i	−1.07195	−	0.769838i
$167$	−11794.1			−0.422894			−0.211447	−	0.977389i	$-0.567818\pi$
$167$	−11794.1			−0.422894			−0.211447	+	0.977389i	$0.567818\pi$
$168$	−11347.8	−	3481.01i	−0.402064	−	0.123335i
$169$			4407.96i			0.154335i
$170$	24681.4	+	17725.3i	0.854027	+	0.613332i
$171$	−5078.24	+	5078.24i	−0.173668	+	0.173668i
$172$	−13390.8	+	27012.2i	−0.452638	+	0.913067i
$173$	−25427.3	+	25427.3i	−0.849587	+	0.849587i	−0.990081	−	0.140495i	$-0.955131\pi$
$173$	−25427.3	+	25427.3i	−0.849587	+	0.849587i	0.140495	+	0.990081i	$0.455131\pi$
$174$	−1966.57	+	322.583i	−0.0649548	+	0.0106547i
$175$			9905.25i			0.323437i
$176$	7758.53	−	57096.2i	0.250469	−	1.84324i
$177$	17698.2			0.564914
$178$	−8365.71	−	51000.2i	−0.264036	−	1.60965i
$179$	−28120.2	−	28120.2i	−0.877631	−	0.877631i	0.115658	−	0.993289i	$-0.463102\pi$
$179$	−28120.2	−	28120.2i	−0.877631	−	0.877631i	−0.993289	+	0.115658i	$0.963102\pi$
$180$	5764.25	−	11627.7i	0.177909	−	0.358881i
$181$	37465.4	+	37465.4i	1.14360	+	1.14360i	0.987787	+	0.155812i	$0.0497993\pi$
$181$	37465.4	+	37465.4i	1.14360	+	1.14360i	0.155812	+	0.987787i	$0.450201\pi$
$182$	−12943.0	+	18022.3i	−0.390743	+	0.544086i
$183$	3336.56			0.0996315
$184$	47582.5	−	25242.9i	1.40544	−	0.745596i
$185$			5221.26i			0.152557i
$186$	−15963.9	+	22228.7i	−0.461437	+	0.642522i
$187$	40246.0	−	40246.0i	1.15091	−	1.15091i
$188$	−6649.58	−	19723.7i	−0.188139	−	0.558049i
$189$	−3540.87	+	3540.87i	−0.0991258	+	0.0991258i
$190$	5173.88	+	31541.7i	0.143321	+	0.873732i
$191$			11800.4i			0.323467i	0.986835	+	0.161733i	$0.0517084\pi$
$191$			11800.4i			0.323467i	−0.986835	+	0.161733i	$0.948292\pi$
$192$	20900.0	−	4021.91i	0.566948	−	0.109101i
$193$	60521.8			1.62479			0.812396	−	0.583107i	$-0.198163\pi$
$193$	60521.8			1.62479			0.812396	+	0.583107i	$0.198163\pi$
$194$	44388.1	−	7281.12i	1.17941	−	0.193462i
$195$	−17154.6	−	17154.6i	−0.451139	−	0.451139i
$196$	−17087.5	+	5760.83i	−0.444802	+	0.149959i
$197$	15590.7	+	15590.7i	0.401730	+	0.401730i	0.878842	−	0.477112i	$-0.158317\pi$
$197$	15590.7	+	15590.7i	0.401730	+	0.401730i	−0.477112	+	0.878842i	$0.658317\pi$
$198$	−19744.6	−	14179.9i	−0.503638	−	0.361695i
$199$	−49344.9			−1.24605			−0.623026	−	0.782201i	$-0.714097\pi$
$199$	−49344.9			−1.24605			−0.623026	+	0.782201i	$0.714097\pi$
$200$	−8323.55	−	15689.8i	−0.208089	−	0.392244i
$201$			254.919i			0.00630972i
$202$	22205.1	+	15946.9i	0.544190	+	0.390818i
$203$	2419.90	−	2419.90i	0.0587227	−	0.0587227i
$204$	18835.8	+	9337.52i	0.452609	+	0.224373i
$205$	33200.5	−	33200.5i	0.790017	−	0.790017i
$206$	18502.4	−	3035.01i	0.436008	−	0.0715197i
$207$		−	22723.8i		−	0.530322i
$208$	5357.04	−	39423.3i	0.123822	−	0.911226i
$209$	59869.3			1.37060
$210$	3607.57	+	21992.9i	0.0818042	+	0.498706i
$211$	−51072.5	−	51072.5i	−1.14716	−	1.14716i	−0.987110	−	0.160046i	$-0.948836\pi$
$211$	−51072.5	−	51072.5i	−1.14716	−	1.14716i	−0.160046	−	0.987110i	$-0.551164\pi$
$212$	76683.0	+	38014.3i	1.70619	+	0.845814i
$213$	−6789.07	−	6789.07i	−0.149641	−	0.149641i
$214$	−21064.4	+	29330.9i	−0.459962	+	0.640470i
$215$	56608.6			1.22463
$216$	2633.24	−	8584.15i	0.0564394	−	0.183988i
$217$		−	46996.7i		−	0.998039i
$218$	−28426.3	+	39581.9i	−0.598147	+	0.832883i
$219$	−17184.5	+	17184.5i	−0.358302	+	0.358302i
$220$	−102520.	+	34563.5i	−2.11819	+	0.714121i
$221$	27788.7	−	27788.7i	0.568963	−	0.568963i
$222$	584.731	+	3564.71i	0.0118645	+	0.0723301i
$223$		−	11647.7i		−	0.234224i	−0.993119	−	0.117112i	$-0.962636\pi$
$223$		−	11647.7i		−	0.234224i	0.993119	−	0.117112i	$-0.0373637\pi$
$224$	−25123.2	+	26545.8i	−0.500701	+	0.529054i
$225$	−7492.89			−0.148008
$226$	−54910.4	+	9007.11i	−1.07507	+	0.176347i
$227$	−51559.8	−	51559.8i	−1.00060	−	1.00060i	−1.00000		0.000598399i	$-0.999810\pi$
$227$	−51559.8	−	51559.8i	−1.00060	−	1.00060i	−0.000598399	−	1.00000i	$-0.500190\pi$
$228$	7064.74	+	20955.1i	0.135902	+	0.403106i
$229$	56609.9	+	56609.9i	1.07950	+	1.07950i	0.996554	+	0.0829426i	$0.0264318\pi$
$229$	56609.9	+	56609.9i	1.07950	+	1.07950i	0.0829426	+	0.996554i	$0.473568\pi$
$230$	−82146.3	−	58994.6i	−1.55286	−	1.11521i
$231$	41744.7			0.782308
$232$	−1799.61	+	5866.58i	−0.0334350	+	0.108996i
$233$		−	24725.0i		−	0.455434i	−0.973727	−	0.227717i	$-0.926874\pi$
$233$		−	24725.0i		−	0.455434i	0.973727	−	0.227717i	$-0.0731260\pi$
$234$	−13633.1	−	9790.80i	−0.248979	−	0.178808i
$235$	−27634.8	+	27634.8i	−0.500404	+	0.500404i
$236$	24204.7	−	48826.1i	0.434586	−	0.876653i
$237$	−4176.60	+	4176.60i	−0.0743578	+	0.0743578i
$238$	−35626.4	+	5843.90i	−0.628953	+	0.103169i
$239$			53379.0i			0.934490i	0.884128	+	0.467245i	$0.154753\pi$
$239$			53379.0i			0.934490i	−0.884128	+	0.467245i	$0.845247\pi$
$240$	−24195.4	−	31805.0i	−0.420059	−	0.552170i
$241$	−48291.3			−0.831447			−0.415724	−	0.909491i	$-0.636472\pi$
$241$	−48291.3			−0.831447			−0.415724	+	0.909491i	$0.636472\pi$
$242$	23322.7	+	142183.i	0.398243	+	2.42782i
$243$	−2678.52	−	2678.52i	−0.0453609	−	0.0453609i
$244$	4563.20	−	9204.95i	0.0766460	−	0.154611i
$245$	23941.3	+	23941.3i	0.398855	+	0.398855i
$246$	18948.8	−	26385.1i	0.313121	−	0.436002i
$247$	41338.1			0.677573
$248$	39492.1	+	74442.1i	0.642106	+	1.21036i
$249$			47242.1i			0.761957i
$250$	24357.5	−	33916.3i	0.389720	−	0.542661i
$251$	46289.7	−	46289.7i	0.734746	−	0.734746i	−0.236810	−	0.971556i	$-0.576102\pi$
$251$	46289.7	−	46289.7i	0.734746	−	0.734746i	0.971556	+	0.236810i	$0.0761020\pi$
$252$	4925.99	+	14611.2i	0.0775697	+	0.230084i
$253$	−133950.	+	133950.i	−2.09267	+	2.09267i
$254$	−10618.4	−	64733.0i	−0.164585	−	1.00336i
$255$		−	39473.6i		−	0.607052i
$256$	17487.8	−	63159.7i	0.266843	−	0.963740i
$257$	9485.94			0.143620			0.0718099	−	0.997418i	$-0.477123\pi$
$257$	9485.94			0.143620			0.0718099	+	0.997418i	$0.477123\pi$
$258$	38648.4	−	6339.61i	0.580620	−	0.0952409i
$259$	−4386.45	−	4386.45i	−0.0653903	−	0.0653903i
$260$	−70787.5	+	23865.1i	−1.04715	+	0.353034i
$261$	1830.55	+	1830.55i	0.0268721	+	0.0268721i
$262$	48655.5	+	34942.7i	0.708810	+	0.509042i
$263$	59450.1			0.859491			0.429745	−	0.902950i	$-0.358603\pi$
$263$	59450.1			0.859491			0.429745	+	0.902950i	$0.358603\pi$
$264$	−66123.1	+	35078.8i	−0.948736	+	0.503312i
$265$		−	160702.i		−	2.28839i
$266$	−30845.3	−	22152.0i	−0.435939	−	0.313076i
$267$	−47472.7	+	47472.7i	−0.665920	+	0.665920i
$268$	703.274	+	348.636i	0.00979163	+	0.00485403i
$269$	1388.90	−	1388.90i	0.0191940	−	0.0191940i	−0.697445	−	0.716639i	$-0.745680\pi$
$269$	1388.90	−	1388.90i	0.0191940	−	0.0191940i	0.716639	+	0.697445i	$0.245680\pi$
$270$	−16636.7	+	2728.97i	−0.228213	+	0.0374344i
$271$			40663.4i			0.553688i	0.960915	+	0.276844i	$0.0892886\pi$
$271$			40663.4i			0.553688i	−0.960915	+	0.276844i	$0.910711\pi$
$272$	51521.0	−	39194.1i	0.696380	−	0.529765i
$273$	28823.6			0.386743
$274$	−15994.8	−	97509.9i	−0.213049	−	1.29882i
$275$	44168.3	+	44168.3i	0.584044	+	0.584044i
$276$	−62690.6	−	31077.8i	−0.822971	−	0.407974i
$277$	−65179.5	−	65179.5i	−0.849477	−	0.849477i	0.140591	−	0.990068i	$-0.455100\pi$
$277$	−65179.5	−	65179.5i	−0.849477	−	0.849477i	−0.990068	+	0.140591i	$0.955100\pi$
$278$	−10845.1	+	15101.2i	−0.140328	+	0.195399i
$279$	35550.9			0.456712
$280$	65608.2	+	20125.7i	0.836840	+	0.256705i
$281$		−	9048.57i		−	0.114595i	−0.998357	−	0.0572977i	$-0.981752\pi$
$281$		−	9048.57i		−	0.114595i	0.998357	−	0.0572977i	$-0.0182484\pi$
$282$	−15772.3	+	21962.0i	−0.198334	+	0.276168i
$283$	55255.4	−	55255.4i	0.689924	−	0.689924i	−0.272291	−	0.962215i	$-0.587781\pi$
$283$	55255.4	−	55255.4i	0.689924	−	0.689924i	0.962215	+	0.272291i	$0.0877812\pi$
$284$	−28014.8	+	9444.82i	−0.347336	+	0.117100i
$285$	29360.1	−	29360.1i	0.361467	−	0.361467i
$286$	22649.1	+	138077.i	0.276898	+	1.68806i
$287$			55784.3i			0.677248i
$288$	−20080.8	−	19004.6i	−0.242100	−	0.229126i
$289$	−19577.7			−0.234404
$290$	11369.9	−	1865.03i	0.135195	−	0.0221764i
$291$	−41318.0	−	41318.0i	−0.487925	−	0.487925i
$292$	23906.8	+	70911.2i	0.280385	+	0.831666i
$293$	−31065.0	−	31065.0i	−0.361857	−	0.361857i	0.502639	−	0.864496i	$-0.332362\pi$
$293$	−31065.0	−	31065.0i	−0.361857	−	0.361857i	−0.864496	+	0.502639i	$0.832362\pi$
$294$	19026.6	+	13664.2i	0.220124	+	0.158085i
$295$	−102323.			−1.17579
$296$	10634.1	+	3262.07i	0.121371	+	0.0372314i
$297$			31578.1i			0.357992i
$298$	54273.6	+	38977.4i	0.611162	+	0.438915i
$299$	−92488.4	+	92488.4i	−1.03453	+	1.03453i
$300$	−10247.5	+	20671.5i	−0.113862	+	0.229683i
$301$	−47557.6	+	47557.6i	−0.524913	+	0.524913i
$302$	−4981.59	+	817.145i	−0.0546203	+	0.00895953i
$303$		−	35513.3i		−	0.386817i
$304$	67473.2	+	9168.61i	0.730103	+	0.0992102i
$305$	−19290.5			−0.207369
$306$	−4420.66	−	26949.8i	−0.0472111	−	0.287815i
$307$	71621.7	+	71621.7i	0.759920	+	0.759920i	0.976308	−	0.216388i	$-0.0694275\pi$
$307$	71621.7	+	71621.7i	0.759920	+	0.759920i	−0.216388	+	0.976308i	$0.569428\pi$
$308$	57091.6	−	115166.i	0.601825	−	1.21401i
$309$	−17222.7	−	17222.7i	−0.180378	−	0.180378i
$310$	92296.0	−	128517.i	0.960417	−	1.33732i
$311$	−28899.4			−0.298791			−0.149395	−	0.988778i	$-0.547733\pi$
$311$	−28899.4			−0.298791			−0.149395	+	0.988778i	$0.547733\pi$
$312$	−45656.1	+	24220.9i	−0.469018	+	0.248818i
$313$			102013.i			1.04127i	0.853778	+	0.520637i	$0.174306\pi$
$313$			102013.i			1.04127i	−0.853778	+	0.520637i	$0.825694\pi$
$314$	69348.6	−	96563.7i	0.703361	−	0.979387i
$315$	20471.8	−	20471.8i	0.206317	−	0.206317i
$316$	5810.41	+	17234.5i	0.0581878	+	0.172594i
$317$	24377.7	−	24377.7i	0.242590	−	0.242590i	−0.575331	−	0.817921i	$-0.695127\pi$
$317$	24377.7	−	24377.7i	0.242590	−	0.242590i	0.817921	+	0.575331i	$0.195127\pi$
$318$	−17997.1	−	109716.i	−0.177970	−	1.08497i
$319$		−	21581.1i		−	0.212076i
$320$	−120835.	+	23252.9i	−1.18002	+	0.227079i
$321$	46909.8			0.455253
$322$	118574.	−	19450.1i	1.14361	−	0.187590i
$323$	47560.5	+	47560.5i	0.455871	+	0.455871i
$324$	−11052.8	+	3726.30i	−0.105288	+	0.0354967i
$325$	30497.0	+	30497.0i	0.288729	+	0.288729i
$326$	−98551.7	−	70776.3i	−0.927319	−	0.665967i
$327$	63304.4			0.592023
$328$	−46876.5	−	88361.5i	−0.435720	−	0.821326i
$329$		−	46432.7i		−	0.428975i
$330$	114155.	+	81981.9i	1.04825	+	0.752818i
$331$	22929.4	−	22929.4i	0.209285	−	0.209285i	−0.594679	−	0.803963i	$-0.702721\pi$
$331$	22929.4	−	22929.4i	0.209285	−	0.209285i	0.803963	+	0.594679i	$0.202721\pi$
$332$	130332.	+	64609.9i	1.18243	+	0.586169i
$333$	3318.16	−	3318.16i	0.0299232	−	0.0299232i
$334$	46554.2	−	7636.42i	0.417317	−	0.0684537i
$335$		−	1473.83i		−	0.0131328i
$336$	47046.6	+	6392.94i	0.416725	+	0.0566268i
$337$	−12020.4			−0.105842			−0.0529209	−	0.998599i	$-0.516853\pi$
$337$	−12020.4			−0.105842			−0.0529209	+	0.998599i	$0.516853\pi$
$338$	−2854.06	−	17399.3i	−0.0249821	−	0.152299i
$339$	51112.5	+	51112.5i	0.444762	+	0.444762i
$340$	−108900.	−	53985.5i	−0.942044	−	0.467002i
$341$	−209562.	−	209562.i	−1.80220	−	1.80220i
$342$	16757.0	−	23333.1i	0.143266	−	0.199490i
$343$	−125925.			−1.07034
$344$	35367.1	−	115294.i	0.298870	−	0.974294i
$345$			131379.i			1.10379i
$346$	83904.2	−	116831.i	0.700860	−	0.975905i
$347$	−116717.	+	116717.i	−0.969340	+	0.969340i	−0.999544	−	0.0302037i	$-0.990384\pi$
$347$	−116717.	+	116717.i	−0.969340	+	0.969340i	0.0302037	+	0.999544i	$0.490384\pi$
$348$	7553.68	−	2546.63i	0.0623735	−	0.0210284i
$349$	61504.5	−	61504.5i	0.504959	−	0.504959i	−0.408016	−	0.912975i	$-0.633779\pi$
$349$	61504.5	−	61504.5i	0.504959	−	0.504959i	0.912975	+	0.408016i	$0.133779\pi$
$350$	−6413.44	−	39098.5i	−0.0523546	−	0.319171i
$351$			21803.8i			0.176977i
$352$	6343.73	+	230396.i	0.0511987	+	1.85947i
$353$	−113704.			−0.912483			−0.456242	−	0.889856i	$-0.650805\pi$
$353$	−113704.			−0.912483			−0.456242	+	0.889856i	$0.650805\pi$
$354$	−69859.2	+	11459.2i	−0.557464	+	0.0914425i
$355$	39251.4	+	39251.4i	0.311458	+	0.311458i
$356$	66043.1	+	195894.i	0.521108	+	1.54568i
$357$	33162.3	+	33162.3i	0.260200	+	0.260200i
$358$	129204.	+	92790.1i	1.00812	+	0.723995i
$359$	117615.			0.912586			0.456293	−	0.889830i	$-0.349177\pi$
$359$	117615.			0.912586			0.456293	+	0.889830i	$0.349177\pi$
$360$	−15224.2	+	49629.8i	−0.117471	+	0.382946i
$361$		−	59570.7i		−	0.457108i
$362$	−172143.	−	123627.i	−1.31363	−	0.943403i
$363$	132349.	−	132349.i	1.00440	−	1.00440i
$364$	39420.1	−	79518.8i	0.297519	−	0.600160i
$365$	99353.5	−	99353.5i	0.745757	−	0.745757i
$366$	−13170.2	+	2160.35i	−0.0983176	+	0.0161273i
$367$			55259.1i			0.410272i	0.978733	+	0.205136i	$0.0657637\pi$
$367$			55259.1i			0.410272i	−0.978733	+	0.205136i	$0.934236\pi$
$368$	−171476.	+	130449.i	−1.26621	+	0.963261i
$369$	−42198.4			−0.309915
$370$	−3380.66	−	20609.6i	−0.0246943	−	0.150545i
$371$	135008.	+	135008.i	0.980870	+	0.980870i
$372$	48620.7	−	98078.5i	0.351346	−	0.708741i
$373$	57655.8	+	57655.8i	0.414405	+	0.414405i	0.883270	−	0.468865i	$-0.155337\pi$
$373$	57655.8	+	57655.8i	0.414405	+	0.414405i	−0.468865	+	0.883270i	$0.655337\pi$
$374$	−132803.	+	184919.i	−0.949431	+	1.32202i
$375$	−54243.3			−0.385730
$376$	39018.2	+	73548.8i	0.275989	+	0.520235i
$377$		−	14901.1i		−	0.104842i
$378$	11684.1	−	16269.3i	0.0817731	−	0.113864i
$379$	106918.	−	106918.i	0.744341	−	0.744341i	−0.229070	−	0.973410i	$-0.573568\pi$
$379$	106918.	−	106918.i	0.744341	−	0.744341i	0.973410	+	0.229070i	$0.0735683\pi$
$380$	−40845.2	−	121153.i	−0.282862	−	0.839010i
$381$	−60255.7	+	60255.7i	−0.415096	+	0.415096i
$382$	−7640.50	−	46579.0i	−0.0523594	−	0.319201i
$383$			19290.3i			0.131505i	0.997836	+	0.0657524i	$0.0209447\pi$
$383$			19290.3i			0.131505i	−0.997836	+	0.0657524i	$0.979055\pi$
$384$	−79893.3	+	29407.8i	−0.541811	+	0.199434i
$385$	−241350.			−1.62827
$386$	−238895.	+	39186.6i	−1.60336	+	0.263004i
$387$	−35975.3	−	35975.3i	−0.240205	−	0.240205i
$388$	−170497.	+	57480.8i	−1.13254	+	0.381820i
$389$	61378.3	+	61378.3i	0.405616	+	0.405616i	0.880207	−	0.474590i	$-0.157404\pi$
$389$	61378.3	+	61378.3i	0.405616	+	0.405616i	−0.474590	+	0.880207i	$0.657404\pi$
$390$	78820.6	+	56606.1i	0.518216	+	0.372164i
$391$	−212821.			−1.39207
$392$	63718.6	−	33803.2i	0.414662	−	0.219981i
$393$		−	77816.1i		−	0.503830i
$394$	−71635.2	−	51445.8i	−0.461460	−	0.331404i
$395$	24147.3	−	24147.3i	0.154766	−	0.154766i
$396$	87118.1	+	43187.3i	0.555543	+	0.275401i
$397$	−16169.8	+	16169.8i	−0.102594	+	0.102594i	−0.756541	−	0.653947i	$-0.773112\pi$
$397$	−16169.8	+	16169.8i	−0.102594	+	0.102594i	0.653947	+	0.756541i	$0.273112\pi$
$398$	194777.	−	31949.8i	1.22962	−	0.201698i
$399$			49331.6i			0.309870i
$400$	43013.9	+	56542.1i	0.268837	+	0.353388i
$401$	102288.			0.636116			0.318058	−	0.948071i	$-0.396969\pi$
$401$	102288.			0.636116			0.318058	+	0.948071i	$0.396969\pi$
$402$	−165.055	−	1006.23i	−0.00102135	−	0.00622651i
$403$	−144697.	−	144697.i	−0.890940	−	0.890940i
$404$	−97974.5	−	48569.2i	−0.600275	−	0.297576i
$405$	15486.0	+	15486.0i	0.0944125	+	0.0944125i
$406$	−7985.13	+	11118.8i	−0.0484429	+	0.0674537i
$407$	−39119.1			−0.236156
$408$	−80395.4	−	24661.7i	−0.482960	−	0.148151i
$409$			185560.i			1.10927i	0.832094	+	0.554635i	$0.187142\pi$
$409$			185560.i			1.10927i	−0.832094	+	0.554635i	$0.812858\pi$
$410$	−109554.	+	152547.i	−0.651718	+	0.907478i
$411$	−90765.6	+	90765.6i	−0.537326	+	0.537326i
$412$	−71068.6	+	23959.9i	−0.418681	+	0.141153i
$413$	85963.1	−	85963.1i	0.503978	−	0.503978i
$414$	14713.2	+	89696.3i	0.0858430	+	0.523328i
$415$		−	273133.i		−	1.58591i
$416$	4380.16	+	159082.i	0.0253107	+	0.919252i
$417$	24151.8			0.138892
$418$	−236319.	+	38764.1i	−1.35253	+	0.221859i
$419$	26072.9	+	26072.9i	0.148512	+	0.148512i	0.777453	−	0.628941i	$-0.216511\pi$
$419$	26072.9	+	26072.9i	0.148512	+	0.148512i	−0.628941	+	0.777453i	$0.716511\pi$
$420$	−28479.9	−	84475.7i	−0.161451	−	0.478887i
$421$	164255.	+	164255.i	0.926735	+	0.926735i	0.997493	−	0.0707585i	$-0.0225420\pi$
$421$	164255.	+	164255.i	0.926735	+	0.926735i	−0.0707585	+	0.997493i	$0.522542\pi$
$422$	234664.	+	168528.i	1.31772	+	0.946337i
$423$	35124.3			0.196303
$424$	−327300.	−	100401.i	−1.82060	−	0.558480i
$425$			70175.1i			0.388513i
$426$	31193.9	+	22402.4i	0.171890	+	0.123445i
$427$	16206.2	−	16206.2i	0.0888845	−	0.0888845i
$428$	64155.4	−	129415.i	0.350224	−	0.706477i
$429$	128527.	−	128527.i	0.698359	−	0.698359i
$430$	−223448.	+	36652.9i	−1.20848	+	0.198231i
$431$		−	239996.i		−	1.29196i	−0.763354	−	0.645980i	$-0.776449\pi$
$431$		−	239996.i		−	1.29196i	0.763354	−	0.645980i	$-0.223551\pi$
$432$	−4835.98	+	35588.7i	−0.0259130	+	0.190698i
$433$	160235.			0.854636			0.427318	−	0.904101i	$-0.359458\pi$
$433$	160235.			0.854636			0.427318	+	0.904101i	$0.359458\pi$
$434$	30429.3	+	185508.i	0.161552	+	0.984877i
$435$	−10583.5	−	10583.5i	−0.0559305	−	0.0559305i
$436$	86577.3	−	174645.i	0.455440	−	0.918721i
$437$	−158294.	−	158294.i	−0.828901	−	0.828901i
$438$	56705.0	−	78958.3i	0.295579	−	0.411576i
$439$	338022.			1.75394			0.876972	−	0.480541i	$-0.159560\pi$
$439$	338022.			1.75394			0.876972	+	0.480541i	$0.159560\pi$
$440$	382295.	−	202810.i	1.97466	−	1.04757i
$441$		−	30429.8i		−	0.156467i
$442$	−91696.4	+	127682.i	−0.469362	+	0.653557i
$443$	13035.7	−	13035.7i	0.0664245	−	0.0664245i	−0.673114	−	0.739539i	$-0.735044\pi$
$443$	13035.7	−	13035.7i	0.0664245	−	0.0664245i	0.739539	+	0.673114i	$0.235044\pi$
$444$	−4616.15	−	13692.2i	−0.0234161	−	0.0694557i
$445$	274467.	−	274467.i	1.38602	−	1.38602i
$446$	7541.66	+	45976.5i	0.0379138	+	0.231135i
$447$		−	86801.3i		−	0.434421i
$448$	81979.6	−	121050.i	0.408460	−	0.603126i
$449$	138628.			0.687635			0.343817	−	0.939037i	$-0.388280\pi$
$449$	138628.			0.687635			0.343817	+	0.939037i	$0.388280\pi$
$450$	29576.3	−	4851.49i	0.146056	−	0.0239580i
$451$	248747.	+	248747.i	1.22294	+	1.22294i
$452$	210913.	−	71106.6i	1.03235	−	0.348043i
$453$	4637.04	+	4637.04i	0.0225967	+	0.0225967i
$454$	236903.	+	170136.i	1.14937	+	0.825436i
$455$	−166645.			−0.804952
$456$	−41454.2	−	78140.6i	−0.199361	−	0.375792i
$457$		−	44132.1i		−	0.211311i	−0.994403	−	0.105656i	$-0.966306\pi$
$457$		−	44132.1i		−	0.211311i	0.994403	−	0.105656i	$-0.0336941\pi$
$458$	−260107.	−	186800.i	−1.24000	−	0.890523i
$459$	−25085.8	+	25085.8i	−0.119070	+	0.119070i
$460$	362450.	+	179678.i	1.71290	+	0.849141i
$461$	8511.94	−	8511.94i	0.0400522	−	0.0400522i	−0.686797	−	0.726849i	$-0.740984\pi$
$461$	8511.94	−	8511.94i	0.0400522	−	0.0400522i	0.726849	+	0.686797i	$0.240984\pi$
$462$	−164777.	+	27028.8i	−0.771991	+	0.126632i
$463$		−	45874.9i		−	0.214000i	−0.994259	−	0.107000i	$-0.965876\pi$
$463$		−	45874.9i		−	0.214000i	0.994259	−	0.107000i	$-0.0341244\pi$
$464$	3305.01	−	24322.1i	0.0153510	−	0.112970i
$465$	−205540.			−0.950584
$466$	16008.9	+	97595.9i	0.0737209	+	0.449427i
$467$	−214765.	−	214765.i	−0.984758	−	0.984758i	0.0151278	−	0.999886i	$-0.495184\pi$
$467$	−214765.	−	214765.i	−0.984758	−	0.984758i	−0.999886	+	0.0151278i	$0.995184\pi$
$468$	60152.6	+	29819.6i	0.274639	+	0.136148i
$469$	1238.18	+	1238.18i	0.00562910	+	0.00562910i
$470$	91188.5	−	126974.i	0.412805	−	0.574805i
$471$	−154437.			−0.696160
$472$	−63928.1	+	208401.i	−0.286951	+	0.935438i
$473$			424127.i			1.89572i
$474$	13781.8	−	19190.4i	0.0613409	−	0.0854135i
$475$	−52195.7	+	52195.7i	−0.231338	+	0.231338i
$476$	136842.	−	46134.7i	0.603958	−	0.203617i
$477$	−102128.	+	102128.i	−0.448856	+	0.448856i
$478$	−34561.8	−	210700.i	−0.151266	−	0.922166i
$479$			344286.i			1.50054i	0.661129	+	0.750272i	$0.270077\pi$
$479$			344286.i			1.50054i	−0.661129	+	0.750272i	$0.729923\pi$
$480$	116098.	+	109876.i	0.503899	+	0.476893i
$481$	−27010.6			−0.116747
$482$	190618.	−	31267.6i	0.820482	−	0.134586i
$483$	−110373.	−	110373.i	−0.473117	−	0.473117i
$484$	−184121.	−	546131.i	−0.785982	−	2.33134i
$485$	238883.	+	238883.i	1.01555	+	1.01555i
$486$	12307.1	+	8838.49i	0.0521053	+	0.0374201i
$487$	−139801.			−0.589458			−0.294729	−	0.955581i	$-0.595229\pi$
$487$	−139801.			−0.589458			−0.294729	+	0.955581i	$0.595229\pi$
$488$	−12052.1	+	39288.8i	−0.0506083	+	0.164979i
$489$			157616.i			0.659149i
$490$	−110004.	−	79000.7i	−0.458158	−	0.329033i
$491$	226343.	−	226343.i	0.938866	−	0.938866i	−0.0593703	−	0.998236i	$-0.518909\pi$
$491$	226343.	−	226343.i	0.938866	−	0.938866i	0.998236	+	0.0593703i	$0.0189093\pi$
$492$	−57712.0	+	116417.i	−0.238416	+	0.480937i
$493$	17144.2	−	17144.2i	0.0705379	−	0.0705379i
$494$	−163172.	+	26765.5i	−0.668637	+	0.109679i
$495$		−	182571.i		−	0.745111i
$496$	−204085.	−	268271.i	−0.829559	−	1.09046i
$497$	−65951.3			−0.266999
$498$	−30588.2	−	186476.i	−0.123338	−	0.751908i
$499$	87889.3	+	87889.3i	0.352968	+	0.352968i	0.861213	−	0.508245i	$-0.169706\pi$
$499$	87889.3	+	87889.3i	0.352968	+	0.352968i	−0.508245	+	0.861213i	$0.669706\pi$
$500$	−74185.0	+	149647.i	−0.296740	+	0.598588i
$501$	−43334.2	−	43334.2i	−0.172646	−	0.172646i
$502$	−152745.	+	212689.i	−0.606123	+	0.843989i
$503$	−382392.			−1.51138			−0.755689	−	0.654931i	$-0.772698\pi$
$503$	−382392.			−1.51138			−0.755689	+	0.654931i	$0.772698\pi$
$504$	−28904.6	−	54484.7i	−0.113790	−	0.214493i
$505$			205322.i			0.805106i
$506$	442003.	−	615462.i	1.72633	−	2.40381i
$507$	−16195.9	+	16195.9i	−0.0630069	+	0.0630069i
$508$	83826.5	+	248642.i	0.324828	+	0.963491i
$509$	−237200.	+	237200.i	−0.915544	+	0.915544i	−0.996701	−	0.0811572i	$-0.974138\pi$
$509$	−237200.	+	237200.i	−0.915544	+	0.915544i	0.0811572	+	0.996701i	$0.474138\pi$
$510$	25558.3	+	155812.i	0.0982634	+	0.599047i
$511$			166936.i			0.639306i
$512$	−28134.3	+	260630.i	−0.107324	+	0.994224i
$513$	−37317.3			−0.141800
$514$	−37443.4	+	6141.95i	−0.141726	+	0.0232477i
$515$	99574.2	+	99574.2i	0.375433	+	0.375433i
$516$	−148450.	+	50048.1i	−0.557547	+	0.187970i
$517$	−207047.	−	207047.i	−0.774620	−	0.774620i
$518$	20154.5	+	14474.3i	0.0751127	+	0.0539433i
$519$	−186852.			−0.693685
$520$	263964.	−	140035.i	0.976197	−	0.517880i
$521$		−	265360.i		−	0.977599i	−0.872396	−	0.488799i	$-0.837435\pi$
$521$		−	265360.i		−	0.977599i	0.872396	−	0.488799i	$-0.162565\pi$
$522$	−8410.89	−	6040.40i	−0.0308675	−	0.0221679i
$523$	−59273.7	+	59273.7i	−0.216700	+	0.216700i	−0.807106	−	0.590406i	$-0.798968\pi$
$523$	−59273.7	+	59273.7i	−0.216700	+	0.216700i	0.590406	+	0.807106i	$0.298968\pi$
$524$	−214680.	−	106424.i	−0.781860	−	0.387594i
$525$	−36394.2	+	36394.2i	−0.132042	+	0.132042i
$526$	−234664.	+	38492.7i	−0.848156	+	0.139126i
$527$		−	332955.i		−	1.19885i
$528$	238291.	−	181278.i	0.854753	−	0.650246i
$529$	428484.			1.53117
$530$	104051.	+	634332.i	0.370421	+	2.25821i
$531$	65027.3	+	65027.3i	0.230625	+	0.230625i
$532$	136097.	+	67467.7i	0.480867	+	0.238382i
$533$	171752.	+	171752.i	0.604573	+	0.604573i
$534$	156649.	−	218124.i	0.549345	−	0.764930i
$535$	−271212.			−0.947547
$536$	−3001.73	−	920.798i	−0.0104482	−	0.00320505i
$537$		−	206640.i		−	0.716582i
$538$	−4583.03	+	6381.59i	−0.0158339	+	0.0220478i
$539$	−179374.	+	179374.i	−0.617423	+	0.617423i
$540$	63902.2	−	21543.8i	0.219143	−	0.0738814i
$541$	−316583.	+	316583.i	−1.08166	+	1.08166i	−0.0853106	+	0.996354i	$0.527188\pi$
$541$	−316583.	+	316583.i	−1.08166	+	1.08166i	−0.996354	+	0.0853106i	$0.972812\pi$
$542$	−26328.7	−	160509.i	−0.0896253	−	0.546386i
$543$			275314.i			0.933744i
$544$	−177989.	+	188068.i	−0.601443	+	0.635501i
$545$	−365998.			−1.23221
$546$	−113774.	+	18662.6i	−0.381642	+	0.0626019i
$547$	−250996.	−	250996.i	−0.838864	−	0.838864i	0.149845	−	0.988709i	$-0.452122\pi$
$547$	−250996.	−	250996.i	−0.838864	−	0.838864i	−0.988709	+	0.149845i	$0.952122\pi$
$548$	126271.	+	374540.i	0.420478	+	1.24720i
$549$	12259.3	+	12259.3i	0.0406744	+	0.0406744i
$550$	−202941.	−	145745.i	−0.670881	−	0.481803i
$551$	25503.4			0.0840029
$552$	267578.	+	82081.0i	0.878156	+	0.269379i
$553$			40572.9i			0.132674i
$554$	299482.	+	215077.i	0.975778	+	0.700769i
$555$	−19184.1	+	19184.1i	−0.0622811	+	0.0622811i
$556$	33030.8	−	66630.2i	0.106849	−	0.215537i
$557$	343535.	−	343535.i	1.10729	−	1.10729i	0.113784	−	0.993506i	$-0.463703\pi$
$557$	343535.	−	343535.i	1.10729	−	1.10729i	0.993506	−	0.113784i	$-0.0362971\pi$
$558$	−140328.	+	23018.5i	−0.450689	+	0.0739279i
$559$			292847.i			0.937169i
$560$	−272003.	−	36961.2i	−0.867357	−	0.117861i
$561$	295747.			0.939710
$562$	5858.76	+	35717.0i	0.0185495	+	0.113084i
$563$	−5443.51	−	5443.51i	−0.0171736	−	0.0171736i	0.698468	−	0.715641i	$-0.253866\pi$
$563$	−5443.51	−	5443.51i	−0.0171736	−	0.0171736i	−0.715641	+	0.698468i	$0.753866\pi$
$564$	48037.3	−	96901.5i	0.151015	−	0.304630i
$565$	−295510.	−	295510.i	−0.925710	−	0.925710i
$566$	−182330.	+	253883.i	−0.569148	+	0.792504i
$567$	−26020.0			−0.0809359
$568$	104466.	−	55420.0i	0.323801	−	0.171779i
$569$		−	88063.4i		−	0.272001i	−0.990709	−	0.136001i	$-0.956575\pi$
$569$		−	88063.4i		−	0.272001i	0.990709	−	0.136001i	$-0.0434249\pi$
$570$	−96881.7	+	134902.i	−0.298189	+	0.415210i
$571$	−164748.	+	164748.i	−0.505297	+	0.505297i	−0.913079	−	0.407782i	$-0.866302\pi$
$571$	−164748.	+	164748.i	−0.505297	+	0.505297i	0.407782	+	0.913079i	$0.366302\pi$
$572$	−178804.	−	530359.i	−0.546492	−	1.62098i
$573$	−43357.4	+	43357.4i	−0.132055	+	0.132055i
$574$	−36119.1	−	220194.i	−0.109626	−	0.668317i
$575$		−	233562.i		−	0.706425i
$576$	91568.9	+	62014.0i	0.275996	+	0.186915i
$577$	−66584.1			−0.199995			−0.0999975	−	0.994988i	$-0.531883\pi$
$577$	−66584.1			−0.199995			−0.0999975	+	0.994988i	$0.531883\pi$
$578$	77277.9	−	12676.1i	0.231313	−	0.0379429i
$579$	222371.	+	222371.i	0.663318	+	0.663318i
$580$	−43672.1	+	14723.5i	−0.129822	+	0.0437678i
$581$	229463.	+	229463.i	0.679766	+	0.679766i
$582$	189845.	+	136340.i	0.560471	+	0.402510i
$583$	1.20402e6			3.54240
$584$	−140279.	−	264425.i	−0.411309	−	0.775312i
$585$		−	126060.i		−	0.368354i
$586$	142735.	+	102507.i	0.415658	+	0.298511i
$587$	80101.9	−	80101.9i	0.232470	−	0.232470i	−0.581253	−	0.813723i	$-0.697437\pi$
$587$	80101.9	−	80101.9i	0.232470	−	0.232470i	0.813723	+	0.581253i	$0.197437\pi$
$588$	−83950.2	−	41616.9i	−0.242810	−	0.120369i
$589$	247649.	−	247649.i	0.713848	−	0.713848i
$590$	403895.	−	66252.1i	1.16029	−	0.190325i
$591$			114568.i			0.328011i
$592$	−44087.5	−	5990.84i	−0.125797	−	0.0170940i
$593$	−48436.4			−0.137741			−0.0688704	−	0.997626i	$-0.521940\pi$
$593$	−48436.4			−0.137741			−0.0688704	+	0.997626i	$0.521940\pi$
$594$	−20446.1	−	124647.i	−0.0579480	−	0.353271i
$595$	−191730.	−	191730.i	−0.541571	−	0.541571i
$596$	−239469.	−	118712.i	−0.674149	−	0.334198i
$597$	−181305.	−	181305.i	−0.508699	−	0.508699i
$598$	305190.	−	424959.i	0.853431	−	1.18835i
$599$	367451.			1.02411			0.512054	−	0.858953i	$-0.328885\pi$
$599$	367451.			1.02411			0.512054	+	0.858953i	$0.328885\pi$
$600$	27065.2	−	88230.6i	0.0751812	−	0.245085i
$601$			152192.i			0.421349i	0.977556	+	0.210675i	$0.0675661\pi$
$601$			152192.i			0.421349i	−0.977556	+	0.210675i	$0.932434\pi$
$602$	156929.	−	218514.i	0.433023	−	0.602958i
$603$	−936.632	+	936.632i	−0.00257593	+	0.00257593i
$604$	19134.5	−	6450.95i	0.0524497	−	0.0176828i
$605$	−765183.	+	765183.i	−2.09052	+	2.09052i
$606$	22994.1	+	140180.i	0.0626139	+	0.381716i
$607$		−	390742.i		−	1.06050i	−0.847840	−	0.530252i	$-0.822097\pi$
$607$		−	390742.i		−	1.06050i	0.847840	−	0.530252i	$-0.177903\pi$
$608$	−272270.	+	7496.67i	−0.736533	+	0.0202797i
$609$	17782.6			0.0479469
$610$	76144.5	−	12490.2i	0.204635	−	0.0335668i
$611$	−142960.	−	142960.i	−0.382942	−	0.382942i
$612$	34898.9	+	103515.i	0.0931770	+	0.276377i
$613$	−162671.	−	162671.i	−0.432902	−	0.432902i	0.456712	−	0.889615i	$-0.349027\pi$
$613$	−162671.	−	162671.i	−0.432902	−	0.432902i	−0.889615	+	0.456712i	$0.849027\pi$
$614$	−329082.	−	236335.i	−0.872906	−	0.626890i
$615$	243973.			0.645046
$616$	−150787.	+	491554.i	−0.397377	+	1.29542i
$617$		−	619987.i		−	1.62859i	−0.580451	−	0.814295i	$-0.697124\pi$
$617$		−	619987.i		−	1.62859i	0.580451	−	0.814295i	$-0.302876\pi$
$618$	79133.7	+	56831.0i	0.207197	+	0.148802i
$619$	−285113.	+	285113.i	−0.744108	+	0.744108i	−0.973366	−	0.229258i	$-0.926370\pi$
$619$	−285113.	+	285113.i	−0.744108	+	0.744108i	0.229258	+	0.973366i	$0.426370\pi$
$620$	−281104.	+	567047.i	−0.731279	+	1.47515i
$621$	83492.4	−	83492.4i	0.216503	−	0.216503i
$622$	114073.	−	18711.7i	0.294850	−	0.0483652i
$623$			461166.i			1.18818i
$624$	164533.	−	125167.i	0.422557	−	0.321456i
$625$	487057.			1.24687
$626$	−66051.0	−	402669.i	−0.168551	−	1.02754i
$627$	219974.	+	219974.i	0.559546	+	0.559546i
$628$	−211213.	+	426063.i	−0.535552	+	1.08032i
$629$	−31076.4	−	31076.4i	−0.0785470	−	0.0785470i
$630$	−67552.2	+	94062.2i	−0.170199	+	0.236992i
$631$	575797.			1.44614			0.723071	−	0.690774i	$-0.242730\pi$
$631$	575797.			1.44614			0.723071	+	0.690774i	$0.242730\pi$
$632$	−34094.1	−	64266.9i	−0.0853582	−	0.160899i
$633$		−	375305.i		−	0.936649i
$634$	−80440.6	+	112009.i	−0.200123	+	0.278659i
$635$	348372.	−	348372.i	0.863965	−	0.863965i
$636$	142078.	+	421425.i	0.351247	+	1.04185i
$637$	−123853.	+	123853.i	−0.305230	+	0.305230i
$638$	13973.3	+	85186.0i	0.0343287	+	0.209280i
$639$		−	49889.3i		−	0.122182i
$640$	461908.	−	170023.i	1.12771	−	0.415095i
$641$	−203282.			−0.494747			−0.247373	−	0.968920i	$-0.579567\pi$
$641$	−203282.			−0.494747			−0.247373	+	0.968920i	$0.579567\pi$
$642$	−185164.	+	30373.1i	−0.449250	+	0.0736917i
$643$	−27155.7	−	27155.7i	−0.0656809	−	0.0656809i	0.673503	−	0.739184i	$-0.264789\pi$
$643$	−27155.7	−	27155.7i	−0.0656809	−	0.0656809i	−0.739184	+	0.673503i	$0.764789\pi$
$644$	−455449.	+	153549.i	−1.09817	+	0.370232i
$645$	207993.	+	207993.i	0.499954	+	0.499954i
$646$	−218528.	−	156939.i	−0.523650	−	0.376067i
$647$	143123.			0.341900			0.170950	−	0.985280i	$-0.445316\pi$
$647$	143123.			0.341900			0.170950	+	0.985280i	$0.445316\pi$
$648$	41215.3	−	21865.1i	0.0981541	−	0.0520716i
$649$		−	766633.i		−	1.82011i
$650$	−140125.	−	100633.i	−0.331657	−	0.238184i
$651$	172677.	−	172677.i	0.407448	−	0.407448i
$652$	434834.	+	215562.i	1.02289	+	0.507080i
$653$	−205013.	+	205013.i	−0.480790	+	0.480790i	−0.905384	−	0.424594i	$-0.860417\pi$
$653$	−205013.	+	205013.i	−0.480790	+	0.480790i	0.424594	+	0.905384i	$0.360417\pi$
$654$	−249878.	+	40988.3i	−0.584215	+	0.0958306i
$655$			449899.i			1.04865i
$656$	242245.	+	318433.i	0.562921	+	0.739964i
$657$	−126280.			−0.292553
$658$	30064.2	+	183282.i	0.0694381	+	0.423318i
$659$	−203153.	−	203153.i	−0.467792	−	0.467792i	0.433407	−	0.901199i	$-0.357311\pi$
$659$	−203153.	−	203153.i	−0.467792	−	0.467792i	−0.901199	+	0.433407i	$0.857311\pi$
$660$	−503679.	−	249690.i	−1.15629	−	0.573210i
$661$	35970.3	+	35970.3i	0.0823267	+	0.0823267i	0.747071	−	0.664744i	$-0.231460\pi$
$661$	35970.3	+	35970.3i	0.0823267	+	0.0823267i	−0.664744	+	0.747071i	$0.731460\pi$
$662$	−75661.8	+	105354.i	−0.172648	+	0.240401i
$663$	204205.			0.464556
$664$	−556287.	−	170644.i	−1.26172	−	0.387039i
$665$		−	285214.i		−	0.644952i
$666$	−10949.2	+	15246.0i	−0.0246850	+	0.0343723i
$667$	−57060.4	+	57060.4i	−0.128258	+	0.128258i
$668$	−178817.	+	60285.7i	−0.400733	+	0.135102i
$669$	42796.5	−	42796.5i	0.0956216	−	0.0956216i
$670$	954.273	+	5817.57i	0.00212580	+	0.0129596i
$671$		−	144530.i		−	0.321005i
$672$	−189844.	+	5227.16i	−0.420396	+	0.0115752i
$673$	−762152.			−1.68272			−0.841359	−	0.540477i	$-0.818244\pi$
$673$	−762152.			−1.68272			−0.841359	+	0.540477i	$0.818244\pi$
$674$	47447.3	−	7782.92i	0.104446	−	0.0171326i
$675$	−27530.6	−	27530.6i	−0.0604239	−	0.0604239i
$676$	22531.4	+	66831.4i	0.0493053	+	0.146247i
$677$	56218.1	+	56218.1i	0.122659	+	0.122659i	0.765772	−	0.643113i	$-0.222357\pi$
$677$	56218.1	+	56218.1i	0.122659	+	0.122659i	−0.643113	+	0.765772i	$0.722357\pi$
$678$	−234848.	−	168659.i	−0.510890	−	0.366903i
$679$	−401377.			−0.870588
$680$	464811.	+	142583.i	1.00521	+	0.308355i
$681$		−	378886.i		−	0.816985i
$682$	962880.	+	691507.i	2.07016	+	1.48671i
$683$	558062.	−	558062.i	1.19630	−	1.19630i	0.221036	−	0.975266i	$-0.429056\pi$
$683$	558062.	−	558062.i	1.19630	−	1.19630i	0.975266	−	0.221036i	$-0.0709440\pi$
$684$	−51036.4	+	102951.i	−0.109086	+	0.220049i
$685$	524767.	−	524767.i	1.11837	−	1.11837i
$686$	497057.	−	81533.8i	1.05623	−	0.173256i
$687$			415996.i			0.881406i
$688$	−64952.3	+	477994.i	−0.137220	+	1.00982i
$689$	831344.			1.75123
$690$	−85065.0	−	518585.i	−0.178670	−	1.08924i
$691$	22548.2	+	22548.2i	0.0472232	+	0.0472232i	0.730324	−	0.683101i	$-0.239369\pi$
$691$	22548.2	+	22548.2i	0.0472232	+	0.0472232i	−0.683101	+	0.730324i	$0.739369\pi$
$692$	−255545.	+	515489.i	−0.533648	+	1.07648i
$693$	153380.	+	153380.i	0.319376	+	0.319376i
$694$	385140.	−	536284.i	0.799650	−	1.11346i
$695$	−139635.			−0.289084
$696$	−28167.4	+	14943.0i	−0.0581471	+	0.0308475i
$697$			395212.i			0.813512i
$698$	−202951.	+	282596.i	−0.416562	+	0.580037i
$699$	90845.6	−	90845.6i	0.185930	−	0.185930i
$700$	50630.9	+	150179.i	0.103328	+	0.306487i
$701$	19663.8	−	19663.8i	0.0400158	−	0.0400158i	−0.686816	−	0.726832i	$-0.740992\pi$
$701$	19663.8	−	19663.8i	0.0400158	−	0.0400158i	0.726832	+	0.686816i	$0.240992\pi$
$702$	−14117.5	−	86064.9i	−0.0286472	−	0.174643i
$703$		−	46228.8i		−	0.0935410i
$704$	−174217.	−	905324.i	−0.351516	−	1.82666i
$705$	−203074.			−0.408578
$706$	448817.	−	73620.7i	0.900450	−	0.147703i
$707$	−172494.	−	172494.i	−0.345092	−	0.345092i
$708$	268332.	−	90464.7i	0.535311	−	0.180473i
$709$	−236325.	−	236325.i	−0.470130	−	0.470130i	0.431827	−	0.901957i	$-0.357869\pi$
$709$	−236325.	−	236325.i	−0.470130	−	0.470130i	−0.901957	+	0.431827i	$0.857869\pi$
$710$	−180350.	−	129521.i	−0.357766	−	0.256935i
$711$	−30691.6			−0.0607129
$712$	−387526.	−	730480.i	−0.764435	−	1.44095i
$713$			1.10816e6i			2.17984i
$714$	−152372.	−	109428.i	−0.298887	−	0.214650i
$715$	−743085.	+	743085.i	−1.45354	+	1.45354i
$716$	−570082.	−	282608.i	−1.11202	−	0.551263i
$717$	−196127.	+	196127.i	−0.381504	+	0.381504i
$718$	−464256.	+	76153.2i	−0.900551	+	0.147720i
$719$			493411.i			0.954444i	0.878783	+	0.477222i	$0.158356\pi$
$719$			493411.i			0.954444i	−0.878783	+	0.477222i	$0.841644\pi$
$720$	27959.5	−	205759.i	0.0539343	−	0.396911i
$721$	−167307.			−0.321843
$722$	38570.8	+	235140.i	0.0739919	+	0.451079i
$723$	−177433.	−	177433.i	−0.339437	−	0.339437i
$724$	759539.	+	376528.i	1.44902	+	0.718325i
$725$	18815.0	+	18815.0i	0.0357955	+	0.0357955i
$726$	−436721.	+	608107.i	−0.828572	+	1.15374i
$727$	−192070.			−0.363405			−0.181702	−	0.983354i	$-0.558161\pi$
$727$	−192070.			−0.363405			−0.181702	+	0.983354i	$0.558161\pi$
$728$	−104114.	+	339404.i	−0.196448	+	0.640405i
$729$		−	19683.0i		−	0.0370370i
$730$	−327844.	+	456502.i	−0.615207	+	0.856638i
$731$	−336929.	+	336929.i	−0.630526	+	0.630526i
$732$	50587.4	−	17054.9i	0.0944105	−	0.0318293i
$733$	−411803.	+	411803.i	−0.766446	+	0.766446i	−0.977479	−	0.211033i	$-0.932317\pi$
$733$	−411803.	+	411803.i	−0.766446	+	0.766446i	0.211033	+	0.977479i	$0.432317\pi$
$734$	−35779.1	−	218121.i	−0.0664106	−	0.404861i
$735$			175932.i			0.325664i
$736$	592395.	−	625940.i	1.09359	−	1.15552i
$737$	11042.3			0.0203294
$738$	166567.	−	27322.6i	0.305828	−	0.0501659i
$739$	−326187.	−	326187.i	−0.597280	−	0.597280i	0.342308	−	0.939588i	$-0.388791\pi$
$739$	−326187.	−	326187.i	−0.597280	−	0.597280i	−0.939588	+	0.342308i	$0.888791\pi$
$740$	26688.6	+	79162.4i	0.0487374	+	0.144562i
$741$	151886.	+	151886.i	0.276618	+	0.276618i
$742$	−620325.	−	445495.i	−1.12671	−	0.809162i
$743$	−140393.			−0.254312			−0.127156	−	0.991883i	$-0.540585\pi$
$743$	−140393.			−0.254312			−0.127156	+	0.991883i	$0.540585\pi$
$744$	−128414.	+	418621.i	−0.231989	+	0.756267i
$745$			501847.i			0.904188i
$746$	−264913.	−	190251.i	−0.476020	−	0.341861i
$747$	−173578.	+	173578.i	−0.311068	+	0.311068i
$748$	404473.	−	815910.i	0.722914	−	1.45827i
$749$	227848.	−	227848.i	0.406146	−	0.406146i
$750$	214112.	−	35121.4i	0.380643	−	0.0624380i
$751$			370707.i			0.657281i	0.944455	+	0.328641i	$0.106590\pi$
$751$			370707.i			0.657281i	−0.944455	+	0.328641i	$0.893410\pi$
$752$	−201636.	−	265052.i	−0.356560	−	0.468700i
$753$	340158.			0.599917
$754$	9648.17	+	58818.5i	0.0169708	+	0.103460i
$755$	−26809.3	−	26809.3i	−0.0470318	−	0.0470318i
$756$	−35585.9	+	71784.3i	−0.0622635	+	0.125599i
$757$	−512987.	−	512987.i	−0.895188	−	0.895188i	0.0998176	−	0.995006i	$-0.468174\pi$
$757$	−512987.	−	512987.i	−0.895188	−	0.895188i	−0.995006	+	0.0998176i	$0.968174\pi$
$758$	−352804.	+	491258.i	−0.614038	+	0.855010i
$759$	−984325.			−1.70866
$760$	239670.	+	451775.i	0.414942	+	0.782159i
$761$			113278.i			0.195603i	0.995206	+	0.0978017i	$0.0311811\pi$
$761$			113278.i			0.195603i	−0.995206	+	0.0978017i	$0.968819\pi$
$762$	198830.	−	276859.i	0.342430	−	0.476813i
$763$	307480.	−	307480.i	0.528163	−	0.528163i
$764$	60317.9	+	178912.i	0.103338	+	0.306516i
$765$	145035.	−	145035.i	0.247828	−	0.247828i
$766$	−12490.1	−	76143.6i	−0.0212866	−	0.129771i
$767$		−	529338.i		−	0.899793i
$768$	296318.	−	167809.i	0.502383	−	0.284507i
$769$	−77114.0			−0.130401			−0.0652004	−	0.997872i	$-0.520769\pi$
$769$	−77114.0			−0.130401			−0.0652004	+	0.997872i	$0.520769\pi$
$770$	952668.	−	156269.i	1.60679	−	0.263567i
$771$	34853.6	+	34853.6i	0.0586325	+	0.0586325i
$772$	917604.	−	309359.i	1.53965	−	0.519072i
$773$	−34699.9	−	34699.9i	−0.0580724	−	0.0580724i	0.677474	−	0.735547i	$-0.263075\pi$
$773$	−34699.9	−	34699.9i	−0.0580724	−	0.0580724i	−0.735547	+	0.677474i	$0.763075\pi$
$774$	165297.	+	118710.i	0.275919	+	0.198155i
$775$	365404.			0.608372
$776$	635775.	−	337284.i	1.05580	−	0.560108i
$777$		−	32233.7i		−	0.0533910i
$778$	−282016.	−	202534.i	−0.465924	−	0.334610i
$779$	−293955.	+	293955.i	−0.484402	+	0.484402i
$780$	−347776.	−	172404.i	−0.571623	−	0.283373i
$781$	−294082.	+	294082.i	−0.482133	+	0.482133i
$782$	840057.	−	137797.i	1.37371	−	0.225334i
$783$			13451.8i			0.0219410i
$784$	−229626.	+	174686.i	−0.373585	+	0.284202i
$785$	892886.			1.44896
$786$	50384.3	+	307159.i	0.0815549	+	0.497186i
$787$	−472957.	−	472957.i	−0.763611	−	0.763611i	0.213362	−	0.976973i	$-0.431559\pi$
$787$	−472957.	−	472957.i	−0.763611	−	0.763611i	−0.976973	+	0.213362i	$0.931559\pi$
$788$	316072.	+	156687.i	0.509018	+	0.252337i
$789$	218434.	+	218434.i	0.350886	+	0.350886i
$790$	−79680.5	+	110950.i	−0.127673	+	0.177776i
$791$	496523.			0.793573
$792$	−371840.	−	114064.i	−0.592796	−	0.181844i
$793$		−	99793.7i		−	0.158693i
$794$	53356.5	−	74295.7i	0.0846343	−	0.117848i
$795$	590458.	−	590458.i	0.934231	−	0.934231i
$796$	−748145.	+	252227.i	−1.18075	+	0.398076i
$797$	−233582.	+	233582.i	−0.367725	+	0.367725i	−0.866647	−	0.498922i	$-0.833729\pi$
$797$	−233582.	+	233582.i	−0.367725	+	0.367725i	0.498922	+	0.866647i	$0.333729\pi$
$798$	−31941.2	−	194724.i	−0.0501586	−	0.305784i
$799$		−	328959.i		−	0.515286i
$800$	−206396.	−	195335.i	−0.322494	−	0.305211i
$801$	−348852.			−0.543721
$802$	−403757.	+	66229.4i	−0.627727	+	0.102968i
$803$	744383.	+	744383.i	1.15442	+	1.15442i
$804$	1303.02	+	3864.96i	0.00201576	+	0.00597907i
$805$	638129.	+	638129.i	0.984728	+	0.984728i
$806$	664841.	+	477465.i	1.02341	+	0.734974i
$807$	10206.3			0.0156718
$808$	418177.	+	128278.i	0.640527	+	0.196485i
$809$		−	984634.i		−	1.50445i	−0.658906	−	0.752225i	$-0.728981\pi$
$809$		−	984634.i		−	1.50445i	0.658906	−	0.752225i	$-0.271019\pi$
$810$	−71154.0	−	51100.3i	−0.108450	−	0.0778849i
$811$	211876.	−	211876.i	0.322136	−	0.322136i	−0.527450	−	0.849586i	$-0.676852\pi$
$811$	211876.	−	211876.i	0.322136	−	0.322136i	0.849586	+	0.527450i	$0.176852\pi$
$812$	24320.1	−	49058.9i	0.0368853	−	0.0744056i
$813$	−149407.	+	149407.i	−0.226042	+	0.226042i
$814$	154413.	−	25328.8i	0.233042	−	0.0382266i
$815$		−	911269.i		−	1.37193i
$816$	333309.	+	45291.7i	0.500572	+	0.0680203i
$817$	−501210.			−0.750888
$818$	−120146.	−	732450.i	−0.179557	−	1.09464i
$819$	105904.	+	105904.i	0.157887	+	0.157887i
$820$	333665.	−	673075.i	0.496231	−	1.00100i
$821$	539279.	+	539279.i	0.800068	+	0.800068i	0.983106	−	0.183038i	$-0.0585931\pi$
$821$	539279.	+	539279.i	0.800068	+	0.800068i	−0.183038	+	0.983106i	$0.558593\pi$
$822$	299506.	−	417043.i	0.443263	−	0.617216i
$823$	−143161.			−0.211361			−0.105680	−	0.994400i	$-0.533702\pi$
$823$	−143161.			−0.211361			−0.105680	+	0.994400i	$0.533702\pi$
$824$	265012.	−	140591.i	0.390311	−	0.207063i
$825$			324569.i			0.476870i
$826$	−283658.	+	394977.i	−0.415753	+	0.578911i
$827$	−110346.	+	110346.i	−0.161342	+	0.161342i	−0.783161	−	0.621819i	$-0.786394\pi$
$827$	−110346.	+	110346.i	−0.161342	+	0.161342i	0.621819	+	0.783161i	$0.286394\pi$
$828$	−116153.	−	344527.i	−0.169422	−	0.502531i
$829$	198552.	−	198552.i	0.288911	−	0.288911i	−0.547738	−	0.836650i	$-0.684511\pi$
$829$	198552.	−	198552.i	0.288911	−	0.288911i	0.836650	+	0.547738i	$0.184511\pi$
$830$	176848.	+	1.07812e6i	0.256710	+	1.56499i
$831$		−	478970.i		−	0.693595i
$832$	−120292.	−	625101.i	−0.173776	−	0.903032i
$833$	−284992.			−0.410717
$834$	−95333.0	+	15637.7i	−0.137060	+	0.0224824i
$835$	250540.	+	250540.i	0.359338	+	0.359338i
$836$	907711.	−	306023.i	1.29878	−	0.437867i
$837$	130623.	+	130623.i	0.186452	+	0.186452i
$838$	−119798.	−	86034.7i	−0.170593	−	0.122514i
$839$	−810283.			−1.15110			−0.575550	−	0.817767i	$-0.695212\pi$
$839$	−810283.			−1.15110			−0.575550	+	0.817767i	$0.695212\pi$
$840$	167114.	+	315007.i	0.236839	+	0.446438i
$841$			698088.i			0.987002i
$842$	−754709.	−	542005.i	−1.06452	−	0.764503i
$843$	33246.6	−	33246.6i	0.0467834	−	0.0467834i
$844$	−1.03540e6	−	513280.i	−1.45352	−	0.720559i
$845$	93637.4	−	93637.4i	0.131140	−	0.131140i
$846$	−138645.	+	22742.3i	−0.193714	+	0.0317755i
$847$		−	1.28568e6i		−	1.79212i
$848$	1.35694e6	+	184389.i	1.88699	+	0.256414i
$849$	406042.			0.563321
$850$	−45436.9	−	276999.i	−0.0628885	−	0.383389i
$851$	103431.	+	103431.i	0.142821	+	0.142821i
$852$	−137635.	−	68230.3i	−0.189605	−	0.0939936i
$853$	−898052.	−	898052.i	−1.23425	−	1.23425i	−0.962316	−	0.271935i	$-0.912336\pi$
$853$	−898052.	−	898052.i	−1.23425	−	1.23425i	−0.271935	−	0.962316i	$-0.587664\pi$
$854$	−53476.8	+	74463.2i	−0.0733246	+	0.102100i
$855$	215752.			0.295136
$856$	−169444.	+	552374.i	−0.231248	+	0.753851i
$857$			773474.i			1.05313i	0.850133	+	0.526567i	$0.176521\pi$
$857$			773474.i			1.05313i	−0.850133	+	0.526567i	$0.823479\pi$
$858$	−424108.	+	590545.i	−0.576106	+	0.802192i
$859$	−693267.	+	693267.i	−0.939538	+	0.939538i	−0.998274	−	0.0587358i	$-0.981293\pi$
$859$	−693267.	+	693267.i	−0.939538	+	0.939538i	0.0587358	+	0.998274i	$0.481293\pi$
$860$	858274.	−	289356.i	1.16046	−	0.391233i
$861$	−204964.	+	204964.i	−0.276485	+	0.276485i
$862$	155392.	+	947323.i	0.209129	+	1.27492i
$863$			555165.i			0.745419i	0.927948	+	0.372710i	$0.121571\pi$
$863$			555165.i			0.745419i	−0.927948	+	0.372710i	$0.878429\pi$
$864$	−3954.12	−	143609.i	−0.00529691	−	0.192377i
$865$	1.08029e6			1.44381
$866$	−632487.	+	103749.i	−0.843365	+	0.138340i
$867$	−71932.9	−	71932.9i	−0.0956951	−	0.0956951i
$868$	−240224.	−	712542.i	−0.318844	−	0.945738i
$869$	180918.	+	180918.i	0.239575	+	0.239575i
$870$	48628.1	+	34923.0i	0.0642464	+	0.0461395i
$871$	7624.41			0.0100501
$872$	−228663.	+	745425.i	−0.300721	+	0.980327i
$873$		−	303624.i		−	0.398389i
$874$	727319.	+	522335.i	0.952143	+	0.683796i
$875$	−263468.	+	263468.i	−0.344122	+	0.344122i
$876$	−172705.	+	348383.i	−0.225059	+	0.453993i
$877$	919985.	−	919985.i	1.19614	−	1.19614i	0.220825	−	0.975313i	$-0.429125\pi$
$877$	919985.	−	919985.i	1.19614	−	1.19614i	0.975313	−	0.220825i	$-0.0708751\pi$
$878$	−1.33426e6	+	218862.i	−1.73081	+	0.283910i
$879$		−	228280.i		−	0.295455i
$880$	−1.37770e6	+	1.04807e6i	−1.77905	+	1.35340i
$881$	−1.21698e6			−1.56795			−0.783974	−	0.620793i	$-0.786811\pi$
$881$	−1.21698e6			−1.56795			−0.783974	+	0.620793i	$0.786811\pi$
$882$	19702.6	+	120114.i	0.0253272	+	0.154403i
$883$	−83837.1	−	83837.1i	−0.107526	−	0.107526i	0.651297	−	0.758823i	$-0.274225\pi$
$883$	−83837.1	−	83837.1i	−0.107526	−	0.107526i	−0.758823	+	0.651297i	$0.774225\pi$
$884$	279277.	−	563362.i	0.357381	−	0.720914i
$885$	−375960.	−	375960.i	−0.480015	−	0.480015i
$886$	−43015.0	+	59895.7i	−0.0547964	+	0.0763007i
$887$	177618.			0.225757			0.112878	−	0.993609i	$-0.463993\pi$
$887$	177618.			0.225757			0.112878	+	0.993609i	$0.463993\pi$
$888$	27086.5	+	51057.7i	0.0343500	+	0.0647493i
$889$			585344.i			0.740641i
$890$	−905677.	+	1.26110e6i	−1.14339	+	1.59210i
$891$	−116025.	+	116025.i	−0.146150	+	0.146150i
$892$	−59537.6	−	176597.i	−0.0748275	−	0.221950i
$893$	244677.	−	244677.i	0.306825	−	0.306825i
$894$	56202.0	+	342626.i	0.0703196	+	0.428692i
$895$			1.19470e6i			1.49147i
$896$	−245217.	+	530893.i	−0.305446	+	0.661289i
$897$	−679648.			−0.844694
$898$	−547199.	+	89758.6i	−0.678567	+	0.111307i
$899$	−89270.1	−	89270.1i	−0.110455	−	0.110455i
$900$	−113604.	+	38300.0i	−0.140252	+	0.0472840i
$901$	956483.	+	956483.i	1.17822	+	1.17822i
$902$	−1.14292e6	−	820807.i	−1.40477	−	1.00885i
$903$	−349476.			−0.428589
$904$	−786486.	+	417237.i	−0.962397	+	0.510559i
$905$		−	1.59174e6i		−	1.94346i
$906$	−21305.9	−	15301.2i	−0.0259564	−	0.0186409i
$907$	986572.	−	986572.i	1.19926	−	1.19926i	0.224875	−	0.974388i	$-0.427803\pi$
$907$	986572.	−	986572.i	1.19926	−	1.19926i	0.974388	−	0.224875i	$-0.0721974\pi$
$908$	−1.04528e6	−	518177.i	−1.26782	−	0.628502i
$909$	130484.	−	130484.i	0.157917	−	0.157917i
$910$	657790.	−	107899.i	0.794336	−	0.130297i
$911$		−	520547.i		−	0.627225i	−0.949551	−	0.313612i	$-0.898461\pi$
$911$		−	520547.i		−	0.627225i	0.949551	−	0.313612i	$-0.101539\pi$
$912$	214225.	+	281600.i	0.257561	+	0.338565i
$913$	2.04639e6			2.45497
$914$	28574.6	+	174200.i	0.0342049	+	0.208524i
$915$	−70877.9	−	70877.9i	−0.0846581	−	0.0846581i
$916$	1.14766e6	+	568931.i	1.36779	+	0.678061i
$917$	−377966.	−	377966.i	−0.449483	−	0.449483i
$918$	82777.4	−	115263.i	0.0982260	−	0.136774i
$919$	−333572.			−0.394965			−0.197483	−	0.980306i	$-0.563277\pi$
$919$	−333572.			−0.394965			−0.197483	+	0.980306i	$0.563277\pi$
$920$	−1.54702e6	−	474556.i	−1.82776	−	0.560676i
$921$			526310.i			0.620472i
$922$	−28087.4	+	39110.1i	−0.0330408	+	0.0460073i
$923$	−203055.	+	203055.i	−0.238348	+	0.238348i
$924$	632915.	−	213379.i	0.741312	−	0.249924i
$925$	34105.1	−	34105.1i	0.0398598	−	0.0398598i
$926$	29703.0	+	181079.i	0.0346400	+	0.211177i
$927$		−	126561.i		−	0.147278i
$928$	2702.33	+	98145.2i	0.00313792	+	0.113965i
$929$	−424029.			−0.491319			−0.245660	−	0.969356i	$-0.579005\pi$
$929$	−424029.			−0.491319			−0.245660	+	0.969356i	$0.579005\pi$
$930$	811317.	−	133083.i	0.938048	−	0.153871i
$931$	−211975.	−	211975.i	−0.244560	−	0.244560i
$932$	−126382.	−	374870.i	−0.145497	−	0.431567i
$933$	−106183.	−	106183.i	−0.121981	−	0.121981i
$934$	986786.	+	708674.i	1.13117	+	0.812368i
$935$	−1.70988e6			−1.95588
$936$	−256745.	−	78757.9i	−0.293055	−	0.0898964i
$937$			972676.i			1.10787i	0.832560	+	0.553935i	$0.186875\pi$
$937$			972676.i			1.10787i	−0.832560	+	0.553935i	$0.813125\pi$
$938$	−5689.11	−	4085.72i	−0.00646605	−	0.00464369i
$939$	−374818.	+	374818.i	−0.425098	+	0.425098i
$940$	−277731.	+	560242.i	−0.314317	+	0.634045i
$941$	629440.	−	629440.i	0.710845	−	0.710845i	−0.255867	−	0.966712i	$-0.582361\pi$
$941$	629440.	−	629440.i	0.710845	−	0.710845i	0.966712	+	0.255867i	$0.0823609\pi$
$942$	609601.	−	99994.6i	0.686979	−	0.112687i
$943$		−	1.31537e6i		−	1.47919i
$944$	117405.	−	864001.i	0.131748	−	0.969550i
$945$	150436.			0.168457
$946$	−274613.	−	1.67413e6i	−0.306859	−	1.87072i
$947$	155548.	+	155548.i	0.173446	+	0.173446i	0.788491	−	0.615046i	$-0.210862\pi$
$947$	155548.	+	155548.i	0.173446	+	0.173446i	−0.615046	+	0.788491i	$0.710862\pi$
$948$	−41975.0	+	84672.6i	−0.0467061	+	0.0942163i
$949$	513975.	+	513975.i	0.570702	+	0.570702i
$950$	172234.	−	239825.i	0.190841	−	0.265734i
$951$	179138.			0.198074
$952$	−510280.	+	270708.i	−0.563034	+	0.298694i
$953$			1.42631e6i			1.57047i	0.619201	+	0.785233i	$0.287457\pi$
$953$			1.42631e6i			1.57047i	−0.619201	+	0.785233i	$0.712543\pi$
$954$	336998.	−	469249.i	0.370280	−	0.515592i
$955$	250673.	−	250673.i	0.274854	−	0.274854i
$956$	272848.	+	809308.i	0.298541	+	0.885519i
$957$	79294.1	−	79294.1i	0.0865798	−	0.0865798i
$958$	−222918.	−	1.35898e6i	−0.242893	−	1.48076i
$959$			881727.i			0.958731i
$960$	−529411.	−	358538.i	−0.574448	−	0.389038i
$961$	−810182.			−0.877275
$962$	106618.	−	17488.8i	0.115207	−	0.0188977i
$963$	172357.	+	172357.i	0.185856	+	0.185856i
$964$	−732170.	+	246842.i	−0.787876	+	0.265622i
$965$	−1.28565e6	−	1.28565e6i	−1.38061	−	1.38061i
$966$	507134.	+	364206.i	0.543461	+	0.390294i
$967$	547046.			0.585020			0.292510	−	0.956262i	$-0.405510\pi$
$967$	547046.			0.585020			0.292510	+	0.956262i	$0.405510\pi$
$968$	1.08038e6	+	2.03650e6i	1.15299	+	2.17337i
$969$			349497.i			0.372217i
$970$	−1.09760e6	−	788258.i	−1.16654	−	0.837770i
$971$	1.22086e6	−	1.22086e6i	1.29487	−	1.29487i	0.363135	−	0.931737i	$-0.381707\pi$
$971$	1.22086e6	−	1.22086e6i	1.29487	−	1.29487i	0.931737	−	0.363135i	$-0.118293\pi$
$972$	−54301.7	−	26919.2i	−0.0574753	−	0.0284924i
$973$	117309.	−	117309.i	0.123910	−	0.123910i
$974$	551830.	−	90518.3i	0.581684	−	0.0954154i
$975$			224106.i			0.235746i
$976$	22133.8	−	162886.i	0.0232357	−	0.170995i
$977$	−696637.			−0.729823			−0.364911	−	0.931042i	$-0.618901\pi$
$977$	−696637.			−0.729823			−0.364911	+	0.931042i	$0.618901\pi$
$978$	−102053.	−	622151.i	−0.106696	−	0.650456i
$979$	2.05638e6	+	2.05638e6i	2.14554	+	2.14554i
$980$	485363.	+	240610.i	0.505376	+	0.250531i
$981$	232595.	+	232595.i	0.241692	+	0.241692i
$982$	−746879.	+	1.03998e6i	−0.774510	+	1.07846i
$983$	−76639.7			−0.0793134			−0.0396567	−	0.999213i	$-0.512626\pi$
$983$	−76639.7			−0.0793134			−0.0396567	+	0.999213i	$0.512626\pi$
$984$	152426.	−	496896.i	0.157423	−	0.513187i
$985$		−	662382.i		−	0.682710i
$986$	−56571.8	+	78772.7i	−0.0581897	+	0.0810256i
$987$	170605.	−	170605.i	0.175128	−	0.175128i
$988$	626749.	−	211300.i	0.642066	−	0.216464i
$989$	1.12139e6	−	1.12139e6i	1.14647	−	1.14647i
$990$	118211.	+	720652.i	0.120611	+	0.735284i
$991$		−	209837.i		−	0.213665i	−0.994277	−	0.106833i	$-0.965929\pi$
$991$		−	209837.i		−	0.213665i	0.994277	−	0.106833i	$-0.0340709\pi$
$992$	979273.	+	926792.i	0.995132	+	0.941800i
$993$	168496.			0.170880
$994$	260326.	−	42702.0i	0.263478	−	0.0432191i
$995$	1.04822e6	+	1.04822e6i	1.05879	+	1.05879i
$996$	241479.	+	716263.i	0.243422	+	0.722027i
$997$	385457.	+	385457.i	0.387781	+	0.387781i	0.873895	−	0.486114i	$-0.161586\pi$
$997$	385457.	+	385457.i	0.387781	+	0.387781i	−0.486114	+	0.873895i	$0.661586\pi$
$998$	−403827.	−	290015.i	−0.405448	−	0.291178i
$999$	24383.4			0.0244322

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.5.l.a.43.2	yes	32
3.2	odd	2		144.5.m.c.91.15		32
4.3	odd	2		192.5.l.a.79.5		32
8.3	odd	2		384.5.l.a.31.12		32
8.5	even	2		384.5.l.b.31.5		32
12.11	even	2		576.5.m.b.271.14		32
16.3	odd	4	inner	48.5.l.a.19.2	✓	32
16.5	even	4		384.5.l.a.223.12		32
16.11	odd	4		384.5.l.b.223.5		32
16.13	even	4		192.5.l.a.175.5		32
48.29	odd	4		576.5.m.b.559.14		32
48.35	even	4		144.5.m.c.19.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.5.l.a.19.2	✓	32	16.3	odd	4	inner
48.5.l.a.43.2	yes	32	1.1	even	1	trivial
144.5.m.c.19.15		32	48.35	even	4
144.5.m.c.91.15		32	3.2	odd	2
192.5.l.a.79.5		32	4.3	odd	2
192.5.l.a.175.5		32	16.13	even	4
384.5.l.a.31.12		32	8.3	odd	2
384.5.l.a.223.12		32	16.5	even	4
384.5.l.b.31.5		32	8.5	even	2
384.5.l.b.223.5		32	16.11	odd	4
576.5.m.b.271.14		32	12.11	even	2
576.5.m.b.559.14		32	48.29	odd	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.94725 + 0.647479i) q^{2} +(3.67423 + 3.67423i) q^{3} +(15.1615 - 5.11152i) q^{4} +(-21.2428 - 21.2428i) q^{5} +(-16.8821 - 12.1241i) q^{6} +35.6927 q^{7} +(-56.5368 + 29.9932i) q^{8} +27.0000i q^{9} +O(q^{10})\)	\(q+(-3.94725 + 0.647479i) q^{2} +(3.67423 + 3.67423i) q^{3} +(15.1615 - 5.11152i) q^{4} +(-21.2428 - 21.2428i) q^{5} +(-16.8821 - 12.1241i) q^{6} +35.6927 q^{7} +(-56.5368 + 29.9932i) q^{8} +27.0000i q^{9} +(97.6049 + 70.0964i) q^{10} +(159.157 - 159.157i) q^{11} +(74.4880 + 36.9261i) q^{12} +(109.893 - 109.893i) q^{13} +(-140.888 + 23.1103i) q^{14} -156.102i q^{15} +(203.745 - 154.997i) q^{16} +252.870 q^{17} +(-17.4819 - 106.576i) q^{18} +(188.083 + 188.083i) q^{19} +(-430.657 - 213.491i) q^{20} +(131.143 + 131.143i) q^{21} +(-525.181 + 731.282i) q^{22} -841.621 q^{23} +(-317.931 - 97.5273i) q^{24} +277.514i q^{25} +(-362.622 + 504.929i) q^{26} +(-99.2043 + 99.2043i) q^{27} +(541.157 - 182.444i) q^{28} +(67.7983 - 67.7983i) q^{29} +(101.073 + 616.174i) q^{30} -1316.70i q^{31} +(-703.874 + 743.732i) q^{32} +1169.56 q^{33} +(-998.142 + 163.728i) q^{34} +(-758.214 - 758.214i) q^{35} +(138.011 + 409.362i) q^{36} +(-122.895 - 122.895i) q^{37} +(-864.189 - 620.630i) q^{38} +807.547 q^{39} +(1838.14 + 563.860i) q^{40} +1562.90i q^{41} +(-602.568 - 432.743i) q^{42} +(-1332.42 + 1332.42i) q^{43} +(1599.53 - 3226.60i) q^{44} +(573.556 - 573.556i) q^{45} +(3322.09 - 544.932i) q^{46} -1300.90i q^{47} +(1318.10 + 179.111i) q^{48} -1127.03 q^{49} +(-179.685 - 1095.42i) q^{50} +(929.104 + 929.104i) q^{51} +(1104.43 - 2227.87i) q^{52} +(3782.51 + 3782.51i) q^{53} +(327.351 - 455.817i) q^{54} -6761.88 q^{55} +(-2017.95 + 1070.54i) q^{56} +1382.12i q^{57} +(-223.719 + 311.514i) q^{58} +(2408.42 - 2408.42i) q^{59} +(-797.919 - 2366.75i) q^{60} +(454.048 - 454.048i) q^{61} +(852.536 + 5197.35i) q^{62} +963.704i q^{63} +(2296.81 - 3391.44i) q^{64} -4668.88 q^{65} +(-4616.54 + 757.265i) q^{66} +(34.6901 + 34.6901i) q^{67} +(3833.90 - 1292.55i) q^{68} +(-3092.31 - 3092.31i) q^{69} +(3483.79 + 2501.93i) q^{70} -1847.75 q^{71} +(-809.817 - 1526.49i) q^{72} +4677.04i q^{73} +(564.668 + 405.524i) q^{74} +(-1019.65 + 1019.65i) q^{75} +(3813.01 + 1890.24i) q^{76} +(5680.74 - 5680.74i) q^{77} +(-3187.59 + 522.870i) q^{78} +1136.73i q^{79} +(-7620.69 - 1035.54i) q^{80} -729.000 q^{81} +(-1011.95 - 6169.17i) q^{82} +(6428.83 + 6428.83i) q^{83} +(2658.68 + 1317.99i) q^{84} +(-5371.68 - 5371.68i) q^{85} +(4396.67 - 6122.10i) q^{86} +498.213 q^{87} +(-4224.59 + 13771.8i) q^{88} +12920.4i q^{89} +(-1892.60 + 2635.33i) q^{90} +(3922.39 - 3922.39i) q^{91} +(-12760.3 + 4301.96i) q^{92} +(4837.87 - 4837.87i) q^{93} +(842.306 + 5134.98i) q^{94} -7990.82i q^{95} +(-5318.84 + 146.449i) q^{96} -11245.3 q^{97} +(4448.67 - 729.728i) q^{98} +(4297.23 + 4297.23i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 12 q^{4} + 180 q^{8}+O(q^{10}) \) 32 * q + 12 * q^4 + 180 * q^8	\( 32 q + 12 q^{4} + 180 q^{8} + 296 q^{10} - 192 q^{11} + 360 q^{12} - 156 q^{14} + 352 q^{16} - 324 q^{18} + 704 q^{19} - 1200 q^{20} - 1568 q^{22} - 2304 q^{23} + 1188 q^{24} + 2700 q^{26} + 4680 q^{28} - 1728 q^{29} + 1512 q^{30} - 3360 q^{32} - 9312 q^{34} - 5184 q^{35} - 756 q^{36} + 3648 q^{37} - 5880 q^{38} + 5232 q^{40} + 4500 q^{42} + 1088 q^{43} + 18840 q^{44} + 680 q^{46} + 2160 q^{48} + 10976 q^{49} - 25884 q^{50} - 4032 q^{51} - 25584 q^{52} + 960 q^{53} + 972 q^{54} + 11776 q^{55} + 15456 q^{56} + 12624 q^{58} + 13056 q^{59} + 7992 q^{60} + 3776 q^{61} + 21852 q^{62} - 8664 q^{64} + 4032 q^{65} - 8856 q^{66} - 896 q^{67} - 17280 q^{68} - 9792 q^{69} - 18240 q^{70} - 39936 q^{71} + 4860 q^{72} + 24204 q^{74} - 1152 q^{75} + 16776 q^{76} + 9408 q^{77} - 3780 q^{78} - 14232 q^{80} - 23328 q^{81} - 33800 q^{82} + 24000 q^{83} - 11448 q^{84} - 11200 q^{85} - 1200 q^{86} - 11424 q^{88} + 4104 q^{90} + 30528 q^{91} - 11664 q^{92} - 8040 q^{94} + 10080 q^{96} + 52968 q^{98} - 5184 q^{99}+O(q^{100}) \) 32 * q + 12 * q^4 + 180 * q^8 + 296 * q^10 - 192 * q^11 + 360 * q^12 - 156 * q^14 + 352 * q^16 - 324 * q^18 + 704 * q^19 - 1200 * q^20 - 1568 * q^22 - 2304 * q^23 + 1188 * q^24 + 2700 * q^26 + 4680 * q^28 - 1728 * q^29 + 1512 * q^30 - 3360 * q^32 - 9312 * q^34 - 5184 * q^35 - 756 * q^36 + 3648 * q^37 - 5880 * q^38 + 5232 * q^40 + 4500 * q^42 + 1088 * q^43 + 18840 * q^44 + 680 * q^46 + 2160 * q^48 + 10976 * q^49 - 25884 * q^50 - 4032 * q^51 - 25584 * q^52 + 960 * q^53 + 972 * q^54 + 11776 * q^55 + 15456 * q^56 + 12624 * q^58 + 13056 * q^59 + 7992 * q^60 + 3776 * q^61 + 21852 * q^62 - 8664 * q^64 + 4032 * q^65 - 8856 * q^66 - 896 * q^67 - 17280 * q^68 - 9792 * q^69 - 18240 * q^70 - 39936 * q^71 + 4860 * q^72 + 24204 * q^74 - 1152 * q^75 + 16776 * q^76 + 9408 * q^77 - 3780 * q^78 - 14232 * q^80 - 23328 * q^81 - 33800 * q^82 + 24000 * q^83 - 11448 * q^84 - 11200 * q^85 - 1200 * q^86 - 11424 * q^88 + 4104 * q^90 + 30528 * q^91 - 11664 * q^92 - 8040 * q^94 + 10080 * q^96 + 52968 * q^98 - 5184 * q^99

Introduction

L-functions

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