LMFDB - Embedded newform 36.5.f.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.73046 + 2.92312i) q^{2} +(8.98168 + 0.573987i) q^{3} +(-1.08921 - 15.9629i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-26.2019 + 24.6872i) q^{6} +(-10.5700 + 6.10260i) q^{7} +(49.6354 + 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +O(q^{10})$	\(q+(-2.73046 + 2.92312i) q^{2} +(8.98168 + 0.573987i) q^{3} +(-1.08921 - 15.9629i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-26.2019 + 24.6872i) q^{6} +(-10.5700 + 6.10260i) q^{7} +(49.6354 + 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +(45.5763 + 149.524i) q^{10} +(96.1446 - 55.5091i) q^{11} +(-0.620447 - 143.999i) q^{12} +(-104.491 + 180.984i) q^{13} +(11.0224 - 47.5603i) q^{14} +(194.923 - 292.754i) q^{15} +(-253.627 + 34.7739i) q^{16} +93.3790 q^{17} +(-249.507 + 206.693i) q^{18} -26.8894i q^{19} +(-561.519 - 275.043i) q^{20} +(-98.4393 + 48.7446i) q^{21} +(-100.259 + 432.607i) q^{22} +(-757.577 - 437.387i) q^{23} +(422.619 + 391.368i) q^{24} +(-451.080 - 781.293i) q^{25} +(-243.728 - 799.608i) q^{26} +(715.679 + 138.723i) q^{27} +(108.928 + 162.081i) q^{28} +(650.809 + 1127.23i) q^{29} +(323.527 + 1369.13i) q^{30} +(593.492 + 342.653i) q^{31} +(590.870 - 836.330i) q^{32} +(895.401 - 443.379i) q^{33} +(-254.967 + 272.958i) q^{34} +476.966i q^{35} +(77.0808 - 1293.71i) q^{36} -1760.25 q^{37} +(78.6008 + 73.4203i) q^{38} +(-1042.39 + 1565.56i) q^{39} +(2337.19 - 890.392i) q^{40} +(-39.0421 + 67.6229i) q^{41} +(126.298 - 420.844i) q^{42} +(-1405.46 + 811.442i) q^{43} +(-990.807 - 1474.28i) q^{44} +(1918.77 - 2517.54i) q^{45} +(3347.06 - 1020.22i) q^{46} +(-1999.54 + 1154.43i) q^{47} +(-2297.96 + 166.749i) q^{48} +(-1126.02 + 1950.32i) q^{49} +(3515.46 + 814.729i) q^{50} +(838.700 + 53.5984i) q^{51} +(3002.84 + 1470.85i) q^{52} -1313.48 q^{53} +(-2359.63 + 1713.24i) q^{54} -4338.47i q^{55} +(-771.205 - 124.146i) q^{56} +(15.4342 - 241.512i) q^{57} +(-5072.04 - 1175.47i) q^{58} +(4818.38 + 2781.89i) q^{59} +(-4885.52 - 2792.66i) q^{60} +(-1090.13 - 1888.16i) q^{61} +(-2622.12 + 799.247i) q^{62} +(-912.129 + 381.305i) q^{63} +(831.345 + 4010.75i) q^{64} +(4083.39 + 7072.65i) q^{65} +(-1148.81 + 3827.99i) q^{66} +(-213.077 - 123.020i) q^{67} +(-101.709 - 1490.60i) q^{68} +(-6553.25 - 4363.31i) q^{69} +(-1394.23 - 1302.33i) q^{70} -4608.15i q^{71} +(3571.19 + 3757.72i) q^{72} +2564.79 q^{73} +(4806.29 - 5145.42i) q^{74} +(-3603.00 - 7276.24i) q^{75} +(-429.232 + 29.2882i) q^{76} +(-677.500 + 1173.46i) q^{77} +(-1730.12 - 7321.72i) q^{78} +(4486.29 - 2590.16i) q^{79} +(-3778.87 + 9263.05i) q^{80} +(6348.38 + 1656.75i) q^{81} +(-91.0669 - 298.766i) q^{82} +(-1622.37 + 936.677i) q^{83} +(885.325 + 1518.28i) q^{84} +(1824.57 - 3160.25i) q^{85} +(1465.61 - 6323.93i) q^{86} +(5198.34 + 10498.0i) q^{87} +(7014.86 + 1129.22i) q^{88} -1167.17 q^{89} +(2119.95 + 12482.8i) q^{90} -2550.67i q^{91} +(-6156.80 + 12569.5i) q^{92} +(5133.87 + 3418.25i) q^{93} +(2085.11 - 8997.00i) q^{94} +(-910.026 - 525.404i) q^{95} +(5787.05 - 7172.50i) q^{96} +(2869.58 + 4970.26i) q^{97} +(-2626.47 - 8616.73i) q^{98} +(8296.70 - 3468.34i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−2.73046	+	2.92312i	−0.682614	+	0.730779i
$2$	−2.73046	+	2.92312i	−0.682614	+	0.730779i
$3$	8.98168	+	0.573987i	0.997964	+	0.0637764i
$3$	8.98168	+	0.573987i	0.997964	+	0.0637764i
$4$	−1.08921	−	15.9629i	−0.0680757	−	0.997680i
$5$	19.5394	−	33.8433i	0.781578	−	1.35373i	−0.149444	−	0.988770i	$-0.547749\pi$
$5$	19.5394	−	33.8433i	0.781578	−	1.35373i	0.931022	−	0.364962i	$-0.118918\pi$
$6$	−26.2019	+	24.6872i	−0.727831	+	0.685757i
$7$	−10.5700	+	6.10260i	−0.215715	+	0.124543i	−0.603964	−	0.797011i	$-0.706413\pi$
$7$	−10.5700	+	6.10260i	−0.215715	+	0.124543i	0.388250	+	0.921554i	$0.373080\pi$
$8$	49.6354	+	40.4021i	0.775553	+	0.631282i
$9$	80.3411	+	10.3107i	0.991865	+	0.127293i
$10$	45.5763	+	149.524i	0.455763	+	1.49524i
$11$	96.1446	−	55.5091i	0.794583	−	0.458753i	−0.0469902	−	0.998895i	$-0.514963\pi$
$11$	96.1446	−	55.5091i	0.794583	−	0.458753i	0.841574	+	0.540142i	$0.181630\pi$
$12$	−0.620447	−	143.999i	−0.00430866	−	0.999991i
$13$	−104.491	+	180.984i	−0.618290	+	1.07091i	0.371507	+	0.928430i	$0.378841\pi$
$13$	−104.491	+	180.984i	−0.618290	+	1.07091i	−0.989798	+	0.142480i	$0.954492\pi$
$14$	11.0224	−	47.5603i	0.0562366	−	0.242654i
$15$	194.923	−	292.754i	0.866323	−	1.30113i
$16$	−253.627	+	34.7739i	−0.990731	+	0.135835i
$17$	93.3790			0.323111			0.161555	−	0.986864i	$-0.448349\pi$
$17$	93.3790			0.323111			0.161555	+	0.986864i	$0.448349\pi$
$18$	−249.507	+	206.693i	−0.770084	+	0.637942i
$19$		−	26.8894i		−	0.0744859i	−0.999306	−	0.0372429i	$-0.988142\pi$
$19$		−	26.8894i		−	0.0744859i	0.999306	−	0.0372429i	$-0.0118575\pi$
$20$	−561.519	−	275.043i	−1.40380	−	0.687608i
$21$	−98.4393	+	48.7446i	−0.223218	+	0.110532i
$22$	−100.259	+	432.607i	−0.207147	+	0.893816i
$23$	−757.577	−	437.387i	−1.43209	−	0.826819i	−0.434812	−	0.900521i	$-0.643185\pi$
$23$	−757.577	−	437.387i	−1.43209	−	0.826819i	−0.997280	+	0.0737029i	$0.976518\pi$
$24$	422.619	+	391.368i	0.733713	+	0.679459i
$25$	−451.080	−	781.293i	−0.721728	−	1.25007i
$26$	−243.728	−	799.608i	−0.360545	−	1.18285i
$27$	715.679	+	138.723i	0.981728	+	0.190292i
$28$	108.928	+	162.081i	0.138939	+	0.206736i
$29$	650.809	+	1127.23i	0.773851	+	1.34035i	0.935438	+	0.353491i	$0.115005\pi$
$29$	650.809	+	1127.23i	0.773851	+	1.34035i	−0.161587	+	0.986858i	$0.551661\pi$
$30$	323.527	+	1369.13i	0.359474	+	1.52126i
$31$	593.492	+	342.653i	0.617577	+	0.356558i	0.775925	−	0.630825i	$-0.217283\pi$
$31$	593.492	+	342.653i	0.617577	+	0.356558i	−0.158348	+	0.987383i	$0.550617\pi$
$32$	590.870	−	836.330i	0.577022	−	0.816729i
$33$	895.401	−	443.379i	0.822223	−	0.407143i
$34$	−254.967	+	272.958i	−0.220560	+	0.236122i
$35$			476.966i			0.389360i
$36$	77.0808	−	1293.71i	0.0594759	−	0.998230i
$37$	−1760.25			−1.28579			−0.642897	−	0.765953i	$-0.722268\pi$
$37$	−1760.25			−1.28579			−0.642897	+	0.765953i	$0.722268\pi$
$38$	78.6008	+	73.4203i	0.0544327	+	0.0508451i
$39$	−1042.39	+	1565.56i	−0.685330	+	1.02930i
$40$	2337.19	−	890.392i	1.46074	−	0.556495i
$41$	−39.0421	+	67.6229i	−0.0232255	+	0.0402278i	−0.877405	−	0.479751i	$-0.840727\pi$
$41$	−39.0421	+	67.6229i	−0.0232255	+	0.0402278i	0.854179	+	0.519979i	$0.174060\pi$
$42$	126.298	−	420.844i	0.0715977	−	0.238574i
$43$	−1405.46	+	811.442i	−0.760118	+	0.438855i	−0.829338	−	0.558747i	$-0.811282\pi$
$43$	−1405.46	+	811.442i	−0.760118	+	0.438855i	0.0692198	+	0.997601i	$0.477949\pi$
$44$	−990.807	−	1474.28i	−0.511780	−	0.761510i
$45$	1918.77	−	2517.54i	0.947541	−	1.24323i
$46$	3347.06	−	1020.22i	1.58179	−	0.482144i
$47$	−1999.54	+	1154.43i	−0.905177	+	0.522604i	−0.878876	−	0.477050i	$-0.841706\pi$
$47$	−1999.54	+	1154.43i	−0.905177	+	0.522604i	−0.0263007	+	0.999654i	$0.508373\pi$
$48$	−2297.96	+	166.749i	−0.997378	+	0.0723737i
$49$	−1126.02	+	1950.32i	−0.468978	+	0.812294i
$50$	3515.46	+	814.729i	1.40619	+	0.325892i
$51$	838.700	+	53.5984i	0.322453	+	0.0206068i
$52$	3002.84	+	1470.85i	1.11052	+	0.543953i
$53$	−1313.48			−0.467598			−0.233799	−	0.972285i	$-0.575116\pi$
$53$	−1313.48			−0.467598			−0.233799	+	0.972285i	$0.575116\pi$
$54$	−2359.63	+	1713.24i	−0.809202	+	0.587530i
$55$		−	4338.47i		−	1.43420i
$56$	−771.205	−	124.146i	−0.245920	−	0.0395872i
$57$	15.4342	−	241.512i	0.00475044	−	0.0743342i
$58$	−5072.04	−	1175.47i	−1.50774	−	0.349427i
$59$	4818.38	+	2781.89i	1.38419	+	0.799164i	0.992653	−	0.120997i	$-0.0386091\pi$
$59$	4818.38	+	2781.89i	1.38419	+	0.799164i	0.391540	+	0.920161i	$0.371942\pi$
$60$	−4885.52	−	2792.66i	−1.35709	−	0.775738i
$61$	−1090.13	−	1888.16i	−0.292967	−	0.507433i	0.681543	−	0.731778i	$-0.261309\pi$
$61$	−1090.13	−	1888.16i	−0.292967	−	0.507433i	−0.974510	+	0.224345i	$0.927976\pi$
$62$	−2622.12	+	799.247i	−0.682132	+	0.207921i
$63$	−912.129	+	381.305i	−0.229813	+	0.0960708i
$64$	831.345	+	4010.75i	0.202965	+	0.979186i
$65$	4083.39	+	7072.65i	0.966484	+	1.67400i
$66$	−1148.81	+	3827.99i	−0.263730	+	0.878785i
$67$	−213.077	−	123.020i	−0.0474665	−	0.0274048i	0.476079	−	0.879403i	$-0.342058\pi$
$67$	−213.077	−	123.020i	−0.0474665	−	0.0274048i	−0.523545	+	0.851998i	$0.675391\pi$
$68$	−101.709	−	1490.60i	−0.0219960	−	0.322361i
$69$	−6553.25	−	4363.31i	−1.37644	−	0.916469i
$70$	−1394.23	−	1302.33i	−0.284536	−	0.265783i
$71$		−	4608.15i		−	0.914134i	−0.889432	−	0.457067i	$-0.848900\pi$
$71$		−	4608.15i		−	0.914134i	0.889432	−	0.457067i	$-0.151100\pi$
$72$	3571.19	+	3757.72i	0.688886	+	0.724870i
$73$	2564.79			0.481290			0.240645	−	0.970613i	$-0.422641\pi$
$73$	2564.79			0.481290			0.240645	+	0.970613i	$0.422641\pi$
$74$	4806.29	−	5145.42i	0.877701	−	0.939631i
$75$	−3603.00	−	7276.24i	−0.640534	−	1.29355i
$76$	−429.232	+	29.2882i	−0.0743131	+	0.00507067i
$77$	−677.500	+	1173.46i	−0.114269	+	0.197919i
$78$	−1730.12	−	7321.72i	−0.284373	−	1.20344i
$79$	4486.29	−	2590.16i	0.718842	−	0.415023i	−0.0954846	−	0.995431i	$-0.530440\pi$
$79$	4486.29	−	2590.16i	0.718842	−	0.415023i	0.814326	+	0.580408i	$0.197107\pi$
$80$	−3778.87	+	9263.05i	−0.590449	+	1.44735i
$81$	6348.38	+	1656.75i	0.967593	+	0.252515i
$82$	−91.0669	−	298.766i	−0.0135436	−	0.0444328i
$83$	−1622.37	+	936.677i	−0.235502	+	0.135967i	−0.613108	−	0.789999i	$-0.710081\pi$
$83$	−1622.37	+	936.677i	−0.235502	+	0.135967i	0.377606	+	0.925966i	$0.376747\pi$
$84$	885.325	+	1518.28i	0.125471	+	0.215176i
$85$	1824.57	−	3160.25i	0.252536	−	0.437405i
$86$	1465.61	−	6323.93i	0.198162	−	0.855047i
$87$	5198.34	+	10498.0i	0.686793	+	1.38697i
$88$	7014.86	+	1129.22i	0.905844	+	0.145819i
$89$	−1167.17			−0.147352			−0.0736759	−	0.997282i	$-0.523473\pi$
$89$	−1167.17			−0.147352			−0.0736759	+	0.997282i	$0.523473\pi$
$90$	2119.95	+	12482.8i	0.261722	+	1.54109i
$91$		−	2550.67i		−	0.308015i
$92$	−6156.80	+	12569.5i	−0.727410	+	1.48506i
$93$	5133.87	+	3418.25i	0.593580	+	0.395219i
$94$	2085.11	−	8997.00i	0.235979	−	1.01822i
$95$	−910.026	−	525.404i	−0.100834	−	0.0582165i
$96$	5787.05	−	7172.50i	0.627935	−	0.778266i
$97$	2869.58	+	4970.26i	0.304983	+	0.528245i	0.977257	−	0.212056i	$-0.0680160\pi$
$97$	2869.58	+	4970.26i	0.304983	+	0.528245i	−0.672275	+	0.740302i	$0.734683\pi$
$98$	−2626.47	−	8616.73i	−0.273476	−	0.897203i
$99$	8296.70	−	3468.34i	0.846516	−	0.353876i
$100$	−11980.4	+	8051.53i	−1.19804	+	0.805153i
$101$	−7793.37	−	13498.5i	−0.763981	−	1.32325i	−0.940783	−	0.339008i	$-0.889909\pi$
$101$	−7793.37	−	13498.5i	−0.763981	−	1.32325i	0.176802	−	0.984246i	$-0.443425\pi$
$102$	−2446.71	+	2305.27i	−0.235170	+	0.221575i
$103$	9636.52	+	5563.65i	0.908334	+	0.524427i	0.879895	−	0.475168i	$-0.157613\pi$
$103$	9636.52	+	5563.65i	0.908334	+	0.524427i	0.0284395	+	0.999596i	$0.490946\pi$
$104$	−12498.6	+	4761.55i	−1.15556	+	0.440232i
$105$	−273.772	+	4283.95i	−0.0248320	+	0.388567i
$106$	3586.41	−	3839.46i	0.319189	−	0.341711i
$107$		−	4464.91i		−	0.389983i	−0.980805	−	0.194991i	$-0.937532\pi$
$107$		−	4464.91i		−	0.389983i	0.980805	−	0.194991i	$-0.0624679\pi$
$108$	1434.89	−	11575.4i	0.123018	−	0.992404i
$109$	−4736.05			−0.398624			−0.199312	−	0.979936i	$-0.563871\pi$
$109$	−4736.05			−0.398624			−0.199312	+	0.979936i	$0.563871\pi$
$110$	12681.8	+	11846.0i	1.04809	+	0.979008i
$111$	−15810.0	−	1010.36i	−1.28318	−	0.0820033i
$112$	2468.63	−	1915.35i	0.196798	−	0.152690i
$113$	9173.06	−	15888.2i	0.718385	−	1.24428i	−0.243254	−	0.969963i	$-0.578215\pi$
$113$	9173.06	−	15888.2i	0.718385	−	1.24428i	0.961639	−	0.274317i	$-0.0884519\pi$
$114$	663.825	+	704.554i	0.0510792	+	0.0542131i
$115$	−29605.3	+	17092.6i	−2.23858	+	1.29245i
$116$	17285.0	−	11616.6i	1.28456	−	0.863301i
$117$	−10261.0	+	13463.1i	−0.749580	+	0.983494i
$118$	−21288.2	+	6488.84i	−1.52888	+	0.466018i
$119$	−987.017	+	569.855i	−0.0696997	+	0.0402411i
$120$	21502.9	−	6655.70i	1.49326	−	0.462201i
$121$	−1157.98	+	2005.68i	−0.0790915	+	0.136990i
$122$	8495.85	+	1968.96i	0.570804	+	0.132287i
$123$	−389.479	+	584.958i	−0.0257438	+	0.0386647i
$124$	4823.29	−	9847.06i	0.313689	−	0.640417i
$125$	−10831.1			−0.693190
$126$	1375.93	−	3707.40i	0.0866673	−	0.233522i
$127$			8169.42i			0.506505i	0.967400	+	0.253252i	$0.0815003\pi$
$127$			8169.42i			0.506505i	−0.967400	+	0.253252i	$0.918500\pi$
$128$	−13993.8	−	8521.05i	−0.854115	−	0.520084i
$129$	−13089.1	+	6481.40i	−0.786560	+	0.389484i
$130$	−31823.7	−	7375.32i	−1.88306	−	0.436410i
$131$	−9131.01	−	5271.79i	−0.532079	−	0.307196i	0.209784	−	0.977748i	$-0.432724\pi$
$131$	−9131.01	−	5271.79i	−0.532079	−	0.307196i	−0.741863	+	0.670552i	$0.766057\pi$
$132$	−8052.89	−	13810.3i	−0.462172	−	0.792599i
$133$	164.095	+	284.221i	0.00927669	+	0.0160677i
$134$	941.399	−	286.948i	0.0524281	−	0.0159806i
$135$	18678.8	−	21510.4i	1.02490	−	1.18027i
$136$	4634.90	+	3772.70i	0.250589	+	0.203974i
$137$	−1612.85	−	2793.54i	−0.0859318	−	0.148838i	0.819856	−	0.572570i	$-0.194053\pi$
$137$	−1612.85	−	2793.54i	−0.0859318	−	0.148838i	−0.905788	+	0.423731i	$0.860720\pi$
$138$	30647.8	−	7242.09i	1.60932	−	0.380282i
$139$	16276.4	+	9397.17i	0.842419	+	0.486371i	0.858086	−	0.513506i	$-0.171654\pi$
$139$	16276.4	+	9397.17i	0.842419	+	0.486371i	−0.0156666	+	0.999877i	$0.504987\pi$
$140$	7613.75	−	519.516i	0.388457	−	0.0265059i
$141$	−18621.8	+	9221.03i	−0.936664	+	0.463811i
$142$	13470.2	+	12582.4i	0.668030	+	0.624001i
$143$			23200.8i			1.13457i
$144$	−20735.2	+	178.687i	−0.999963	+	0.00861724i
$145$	50865.8			2.41930
$146$	−7003.05	+	7497.18i	−0.328535	+	0.351716i
$147$	−11233.0	+	16870.8i	−0.519829	+	0.780731i
$148$	1917.28	+	28098.7i	0.0875313	+	1.28281i
$149$	3825.13	−	6625.31i	0.172295	−	0.298424i	−0.766927	−	0.641735i	$-0.778215\pi$
$149$	3825.13	−	6625.31i	0.172295	−	0.298424i	0.939222	+	0.343311i	$0.111548\pi$
$150$	31107.1	+	9335.47i	1.38254	+	0.414910i
$151$	−974.974	+	562.901i	−0.0427601	+	0.0246876i	−0.521228	−	0.853418i	$-0.674526\pi$
$151$	−974.974	+	562.901i	−0.0427601	+	0.0246876i	0.478468	+	0.878105i	$0.341192\pi$
$152$	1086.39	−	1334.67i	0.0470216	−	0.0577677i
$153$	7502.17	+	962.806i	0.320482	+	0.0411297i
$154$	−1580.29	−	5184.51i	−0.0666338	−	0.218608i
$155$	23193.0	−	13390.5i	0.965369	−	0.557356i
$156$	26126.3	+	14934.3i	1.07356	+	0.613670i
$157$	1755.81	−	3041.15i	0.0712326	−	0.123378i	−0.828209	−	0.560419i	$-0.810640\pi$
$157$	1755.81	−	3041.15i	0.0712326	−	0.123378i	0.899442	+	0.437041i	$0.143973\pi$
$158$	−4678.28	+	20186.3i	−0.187401	+	0.808615i
$159$	−11797.3	−	753.923i	−0.466646	−	0.0298217i
$160$	−16758.9	−	36338.4i	−0.654645	−	1.41947i
$161$	10676.8			0.411898
$162$	−22176.8	+	14033.4i	−0.845025	+	0.534726i
$163$		−	41947.9i		−	1.57883i	−0.613861	−	0.789414i	$-0.710385\pi$
$163$		−	41947.9i		−	1.57883i	0.613861	−	0.789414i	$-0.289615\pi$
$164$	1121.98	+	549.569i	0.0417156	+	0.0204331i
$165$	2490.23	−	38966.7i	0.0914684	−	1.43128i
$166$	1691.80	−	7299.94i	0.0613951	−	0.264913i
$167$	5900.58	+	3406.70i	0.211574	+	0.122152i	0.602043	−	0.798464i	$-0.294354\pi$
$167$	5900.58	+	3406.70i	0.211574	+	0.122152i	−0.390469	+	0.920616i	$0.627687\pi$
$168$	−6855.46	−	1557.70i	−0.242895	−	0.0551905i
$169$	−7556.26	−	13087.8i	−0.264566	−	0.458241i
$170$	4255.87	+	13962.4i	0.147262	+	0.483127i
$171$	277.250	−	2160.32i	0.00948153	−	0.0738799i
$172$	14483.8	+	21551.3i	0.489582	+	0.728480i
$173$	−7874.16	−	13638.4i	−0.263095	−	0.455693i	0.703968	−	0.710232i	$-0.251410\pi$
$173$	−7874.16	−	13638.4i	−0.263095	−	0.455693i	−0.967063	+	0.254539i	$0.918076\pi$
$174$	−44880.7	−	13469.0i	−1.48239	−	0.444874i
$175$	9535.85	+	5505.52i	0.311375	+	0.179772i
$176$	−22454.6	+	17421.9i	−0.724904	+	0.562434i
$177$	41680.3	+	27751.7i	1.33041	+	0.885816i
$178$	3186.92	−	3411.79i	0.100584	−	0.107682i
$179$		−	22497.6i		−	0.702151i	−0.936347	−	0.351075i	$-0.885816\pi$
$179$		−	22497.6i		−	0.702151i	0.936347	−	0.351075i	$-0.114184\pi$
$180$	−42277.2	−	27887.0i	−1.30485	−	0.860709i
$181$	−21847.2			−0.666867			−0.333434	−	0.942774i	$-0.608207\pi$
$181$	−21847.2			−0.666867			−0.333434	+	0.942774i	$0.608207\pi$
$182$	7455.90	+	6964.49i	0.225091	+	0.210255i
$183$	−8707.40	−	17584.5i	−0.260008	−	0.525084i
$184$	−19931.3	−	52317.5i	−0.588707	−	1.54530i
$185$	−34394.3	+	59572.7i	−1.00495	+	1.74062i
$186$	−24009.8	+	5673.51i	−0.694004	+	0.163993i
$187$	8977.88	−	5183.38i	0.256738	−	0.148228i
$188$	20606.0	+	30660.9i	0.583012	+	0.867500i
$189$	−8411.31	+	2901.21i	−0.235473	+	0.0812186i
$190$	4020.60	−	1225.52i	0.111374	−	0.0339479i
$191$	16182.1	−	9342.76i	0.443577	−	0.256099i	−0.261537	−	0.965194i	$-0.584229\pi$
$191$	16182.1	−	9342.76i	0.443577	−	0.256099i	0.705114	+	0.709094i	$0.250896\pi$
$192$	5164.76	+	36500.4i	0.140103	+	0.990137i
$193$	−23049.7	+	39923.2i	−0.618800	+	1.07179i	0.370905	+	0.928671i	$0.379048\pi$
$193$	−23049.7	+	39923.2i	−0.618800	+	1.07179i	−0.989705	+	0.143123i	$0.954286\pi$
$194$	−22363.9	−	5182.96i	−0.594216	−	0.137713i
$195$	32616.1	+	65868.1i	0.857755	+	1.73223i
$196$	32359.2	+	15850.2i	0.842336	+	0.412593i
$197$	15934.7			0.410592			0.205296	−	0.978700i	$-0.434184\pi$
$197$	15934.7			0.410592			0.205296	+	0.978700i	$0.434184\pi$
$198$	−12515.4	+	33722.4i	−0.319238	+	0.860177i
$199$		−	73733.8i		−	1.86192i	−0.365124	−	0.930959i	$-0.618974\pi$
$199$		−	73733.8i		−	1.86192i	0.365124	−	0.930959i	$-0.381026\pi$
$200$	9176.34	−	57004.4i	0.229408	−	1.42511i
$201$	−1843.18	−	1227.23i	−0.0456221	−	0.0303762i
$202$	60737.2	+	14076.2i	1.48851	+	0.344971i
$203$	−13758.1	−	7943.25i	−0.333862	−	0.192755i
$204$	−57.9367	−	13446.4i	−0.00139217	−	0.323108i
$205$	1525.72	+	2642.63i	0.0363051	+	0.0628823i
$206$	−42575.3	+	12977.4i	−1.00328	+	0.305810i
$207$	−56354.7	−	42951.3i	−1.31519	−	1.00239i
$208$	20208.3	−	49536.0i	0.467092	−	1.14497i
$209$	−1492.61	−	2585.27i	−0.0341706	−	0.0591852i
$210$	−11775.0	−	12497.4i	−0.267006	−	0.283388i
$211$	15431.2	+	8909.20i	0.346605	+	0.200112i	0.663189	−	0.748452i	$-0.269203\pi$
$211$	15431.2	+	8909.20i	0.346605	+	0.200112i	−0.316584	+	0.948564i	$0.602536\pi$
$212$	1430.66	+	20967.0i	0.0318321	+	0.466513i
$213$	2645.02	−	41388.9i	0.0583001	−	0.912273i
$214$	13051.4	+	12191.2i	0.284991	+	0.266208i
$215$			63420.5i			1.37200i
$216$	29918.4	+	35800.5i	0.641254	+	0.767329i
$217$	−8364.29			−0.177627
$218$	12931.6	−	13844.0i	0.272106	−	0.291306i
$219$	23036.1	+	1472.16i	0.480310	+	0.0306949i
$220$	−69254.5	+	4725.51i	−1.43088	+	0.0976344i
$221$	−9757.27	+	16900.1i	−0.199776	+	0.346022i
$222$	46122.0	−	43455.7i	0.935840	−	0.881741i
$223$	−58353.8	+	33690.6i	−1.17344	+	0.677483i	−0.954487	−	0.298253i	$-0.903596\pi$
$223$	−58353.8	+	33690.6i	−1.17344	+	0.677483i	−0.218949	+	0.975736i	$0.570263\pi$
$224$	−1141.72	+	12445.9i	−0.0227542	+	0.248044i
$225$	−28184.5	−	67420.9i	−0.556732	−	1.33177i
$226$	21396.4	+	70196.0i	0.418914	+	1.37434i
$227$	−54381.5	+	31397.2i	−1.05536	+	0.609310i	−0.924144	−	0.382044i	$-0.875220\pi$
$227$	−54381.5	+	31397.2i	−1.05536	+	0.609310i	−0.131212	+	0.991354i	$0.541887\pi$
$228$	−3872.04	+	16.6834i	−0.0744852	+	0.000320934i
$229$	20463.2	−	35443.2i	0.390213	−	0.675868i	−0.602265	−	0.798297i	$-0.705735\pi$
$229$	20463.2	−	35443.2i	0.390213	−	0.675868i	0.992477	+	0.122428i	$0.0390681\pi$
$230$	30872.2	−	133210.i	0.583596	−	2.51815i
$231$	−6758.64	+	10150.8i	−0.126659	+	0.190229i
$232$	−13239.4	+	82244.7i	−0.245976	+	1.52803i
$233$	79254.5			1.45986			0.729932	−	0.683520i	$-0.239552\pi$
$233$	79254.5			1.45986			0.729932	+	0.683520i	$0.239552\pi$
$234$	−11336.8	−	66754.4i	−0.207043	−	1.21912i
$235$			90227.9i			1.63382i
$236$	39158.8	−	79945.2i	0.703080	−	1.43539i
$237$	41781.1	−	20688.9i	0.743847	−	0.368333i
$238$	1029.26	−	4441.13i	0.0181706	−	0.0784042i
$239$	39084.7	+	22565.5i	0.684243	+	0.395048i	0.801452	−	0.598059i	$-0.204061\pi$
$239$	39084.7	+	22565.5i	0.684243	+	0.395048i	−0.117209	+	0.993107i	$0.537395\pi$
$240$	−39257.5	+	81028.7i	−0.681554	+	1.40675i
$241$	−37826.8	−	65517.9i	−0.651276	−	1.12804i	−0.982814	−	0.184601i	$-0.940901\pi$
$241$	−37826.8	−	65517.9i	−0.651276	−	1.12804i	0.331537	−	0.943442i	$-0.392433\pi$
$242$	−2701.02	−	8861.32i	−0.0461208	−	0.151310i
$243$	56068.1	+	18524.3i	0.949519	+	0.313711i
$244$	−28953.1	+	19458.2i	−0.486312	+	0.326831i
$245$	44003.5	+	76216.3i	0.733086	+	1.26974i
$246$	−646.445	−	2735.69i	−0.0106822	−	0.0452061i
$247$	4866.55	+	2809.70i	0.0797677	+	0.0460539i
$248$	15614.3	+	40986.0i	0.253875	+	0.666395i
$249$	−15109.3	+	7481.71i	−0.243694	+	0.120671i
$250$	29573.8	−	31660.6i	0.473182	−	0.506569i
$251$		−	78270.9i		−	1.24238i	−0.783662	−	0.621188i	$-0.786650\pi$
$251$		−	78270.9i		−	1.24238i	0.783662	−	0.621188i	$-0.213350\pi$
$252$	7080.23	+	14144.9i	0.111493	+	0.222740i
$253$	−97115.9			−1.51722
$254$	−23880.2	−	22306.2i	−0.370143	−	0.345747i
$255$	18201.7	−	27337.1i	0.279918	−	0.420409i
$256$	63117.6	−	17639.2i	0.963097	−	0.269153i
$257$	11506.3	−	19929.5i	0.174209	−	0.301739i	−0.765678	−	0.643224i	$-0.777597\pi$
$257$	11506.3	−	19929.5i	0.174209	−	0.301739i	0.939887	+	0.341485i	$0.110930\pi$
$258$	16793.5	−	55958.2i	0.252290	−	0.840668i
$259$	18605.9	−	10742.1i	0.277365	−	0.160136i
$260$	108452.	−	72886.4i	1.60432	−	1.07820i
$261$	40664.1	+	97273.5i	0.596939	+	1.42795i
$262$	40341.9	−	12296.6i	0.587697	−	0.179136i
$263$	−75237.8	+	43438.5i	−1.08774	+	0.628006i	−0.932973	−	0.359945i	$-0.882795\pi$
$263$	−75237.8	+	43438.5i	−1.08774	+	0.628006i	−0.154765	+	0.987951i	$0.549462\pi$
$264$	62357.0	+	14168.8i	0.894700	+	0.203294i
$265$	−25664.7	+	44452.6i	−0.365464	+	0.633003i
$266$	−1278.87	−	296.385i	−0.0180743	−	0.00418883i
$267$	−10483.2	−	669.943i	−0.147052	−	0.00939757i
$268$	−1731.67	+	3535.32i	−0.0241099	+	0.0492220i
$269$	−54083.3			−0.747409			−0.373705	−	0.927548i	$-0.621913\pi$
$269$	−54083.3			−0.747409			−0.373705	+	0.927548i	$0.621913\pi$
$270$	11875.7	+	113334.i	0.162904	+	1.55464i
$271$			47957.3i			0.653004i	0.945197	+	0.326502i	$0.105870\pi$
$271$			47957.3i			0.653004i	−0.945197	+	0.326502i	$0.894130\pi$
$272$	−23683.5	+	3247.15i	−0.320116	+	0.0438899i
$273$	1464.05	−	22909.3i	0.0196441	−	0.307388i
$274$	12569.7	+	2913.09i	0.167426	+	0.0388019i
$275$	−86737.8	−	50078.1i	−1.14695	−	0.662190i
$276$	−62513.1	+	109361.i	−0.820641	+	1.43564i
$277$	36861.8	+	63846.5i	0.480415	+	0.832103i	0.999748	−	0.0224689i	$-0.00715269\pi$
$277$	36861.8	+	63846.5i	0.480415	+	0.832103i	−0.519332	+	0.854572i	$0.673819\pi$
$278$	−71911.0	+	21919.2i	−0.930477	+	0.283618i
$279$	44148.8	+	33648.4i	0.567166	+	0.432271i
$280$	−19270.4	+	23674.4i	−0.245796	+	0.301969i
$281$	−28062.0	−	48604.7i	−0.355390	−	0.615554i	0.631795	−	0.775136i	$-0.282319\pi$
$281$	−28062.0	−	48604.7i	−0.355390	−	0.615554i	−0.987185	+	0.159582i	$0.948985\pi$
$282$	23891.9	−	79611.4i	0.300437	−	1.00110i
$283$	−132300.	−	76383.2i	−1.65191	−	0.953730i	−0.976287	−	0.216481i	$-0.930542\pi$
$283$	−132300.	−	76383.2i	−1.65191	−	0.953730i	−0.675621	−	0.737249i	$-0.736124\pi$
$284$	−73559.3	+	5019.25i	−0.912013	+	0.0622303i
$285$	−7871.99	−	5241.35i	−0.0969158	−	0.0645288i
$286$	−67818.7	−	63348.8i	−0.829120	−	0.774474i
$287$		−	953.034i		−	0.0115703i
$288$	56094.3	−	61099.4i	0.676292	−	0.736634i
$289$	−74801.4			−0.895600
$290$	−138887.	+	148687.i	−1.65145	+	1.76797i
$291$	22920.8	+	46288.4i	0.270672	+	0.546620i
$292$	−2793.60	−	40941.5i	−0.0327641	−	0.480173i
$293$	19420.1	−	33636.7i	0.226213	−	0.391812i	−0.730470	−	0.682945i	$-0.760699\pi$
$293$	19420.1	−	33636.7i	0.226213	−	0.391812i	0.956683	+	0.291133i	$0.0940322\pi$
$294$	−18644.2	−	78900.3i	−0.215699	−	0.912818i
$295$	188297.	−	108713.i	2.16371	−	1.24922i
$296$	−87370.8	−	71117.8i	−0.997201	−	0.811699i
$297$	76509.1	−	26389.3i	0.867361	−	0.299168i
$298$	8922.21	+	29271.4i	0.100471	+	0.329618i
$299$	158320.	−	91406.1i	1.77090	−	1.02243i
$300$	−112225.	+	65439.7i	−1.24695	+	0.727107i
$301$	9903.82	−	17153.9i	0.109312	−	0.189335i
$302$	1016.70	−	4386.94i	0.0111475	−	0.0481003i
$303$	−62249.6	−	125713.i	−0.678034	−	1.36928i
$304$	935.049	+	6819.88i	0.0101178	+	0.0737955i
$305$	−85202.0			−0.915905
$306$	−23298.7	+	19300.8i	−0.248822	+	0.206126i
$307$			457.528i			0.00485446i	0.999997	+	0.00242723i	$0.000772612\pi$
$307$			457.528i			0.00485446i	−0.999997	+	0.00242723i	$0.999227\pi$
$308$	19469.8	+	9536.70i	0.205239	+	0.100530i
$309$	83358.6	+	55502.1i	0.873039	+	0.581290i
$310$	−24185.5	+	104358.i	−0.251671	+	1.08593i
$311$	−9285.82	−	5361.17i	−0.0960062	−	0.0554292i	0.451228	−	0.892409i	$-0.350986\pi$
$311$	−9285.82	−	5361.17i	−0.0960062	−	0.0554292i	−0.547234	+	0.836979i	$0.684319\pi$
$312$	−114991.	+	35592.7i	−1.18129	+	0.365638i
$313$	−8976.10	−	15547.1i	−0.0916218	−	0.158694i	0.816572	−	0.577244i	$-0.195872\pi$
$313$	−8976.10	−	15547.1i	−0.0916218	−	0.158694i	−0.908194	+	0.418550i	$0.862538\pi$
$314$	4095.48	+	13436.2i	0.0415380	+	0.136275i
$315$	−4917.87	+	38320.0i	−0.0495628	+	0.386193i
$316$	−46232.9	−	68792.9i	−0.462996	−	0.688921i
$317$	30685.9	+	53149.6i	0.305366	+	0.528909i	0.977343	−	0.211663i	$-0.0678879\pi$
$317$	30685.9	+	53149.6i	0.305366	+	0.528909i	−0.671977	+	0.740572i	$0.734555\pi$
$318$	34415.8	−	32426.3i	0.340332	−	0.320659i
$319$	125143.	+	72251.6i	1.22978	+	0.710013i
$320$	151981.	+	50232.3i	1.48419	+	0.490550i
$321$	2562.80	−	40102.4i	0.0248717	−	0.389189i
$322$	−29152.5	+	31209.5i	−0.281167	+	0.301006i
$323$		−	2510.90i		−	0.0240672i
$324$	19531.8	−	103143.i	0.186060	−	0.982538i
$325$	188535.			1.78495
$326$	122619.	+	114537.i	1.15377	+	1.07773i
$327$	−42537.7	−	2718.43i	−0.397812	−	0.0254228i
$328$	−4669.98	+	1779.11i	−0.0434077	+	0.0165369i
$329$	14090.1	−	24404.7i	0.130173	−	0.225467i
$330$	107105.	+	113676.i	0.983515	+	1.04386i
$331$	−160993.	+	92949.3i	−1.46944	+	0.848379i	−0.999412	−	0.0342747i	$-0.989088\pi$
$331$	−160993.	+	92949.3i	−1.46944	+	0.848379i	−0.470023	+	0.882654i	$0.655755\pi$
$332$	16719.2	+	24877.5i	0.151684	+	0.225700i
$333$	−141420.	−	18149.5i	−1.27533	−	0.163673i
$334$	−26069.4	+	7946.22i	−0.233689	+	0.0712308i
$335$	−8326.81	+	4807.49i	−0.0741975	+	0.0428379i
$336$	23271.9	−	15786.1i	0.206135	−	0.139828i
$337$	73998.8	−	128170.i	0.651576	−	1.12856i	−0.331165	−	0.943573i	$-0.607442\pi$
$337$	73998.8	−	128170.i	0.651576	−	1.12856i	0.982741	−	0.184989i	$-0.0592251\pi$
$338$	58889.3	+	13647.9i	0.515469	+	0.119463i
$339$	91509.1	−	137438.i	0.796279	−	1.19593i
$340$	−52434.1	−	25683.3i	−0.453582	−	0.222174i
$341$	76081.3			0.654289
$342$	5557.86	+	6709.10i	0.0475177	+	0.0573604i
$343$		−	56791.2i		−	0.482717i
$344$	−102544.	−	16507.2i	−0.866553	−	0.139494i
$345$	−275716.	+	136527.i	−2.31645	+	1.14705i
$346$	61366.8	+	14222.1i	0.512603	+	0.118799i
$347$	125556.	+	72490.0i	1.04275	+	0.602031i	0.920611	−	0.390482i	$-0.127692\pi$
$347$	125556.	+	72490.0i	1.04275	+	0.602031i	0.122138	+	0.992513i	$0.461025\pi$
$348$	161916.	−	94415.0i	1.33700	−	0.779619i
$349$	89475.8	+	154977.i	0.734606	+	1.27238i	0.954896	+	0.296941i	$0.0959664\pi$
$349$	89475.8	+	154977.i	0.734606	+	1.27238i	−0.220290	+	0.975435i	$0.570700\pi$
$350$	−42130.5	+	12841.8i	−0.343922	+	0.104831i
$351$	−99888.6	+	115031.i	−0.810778	+	0.933687i
$352$	10385.0	−	113207.i	0.0838150	−	0.913670i
$353$	−13197.7	−	22859.1i	−0.105913	−	0.183446i	0.808198	−	0.588911i	$-0.200443\pi$
$353$	−13197.7	−	22859.1i	−0.105913	−	0.183446i	−0.914111	+	0.405465i	$0.867110\pi$
$354$	−194928.	+	46061.5i	−1.55549	+	0.367563i
$355$	−155955.	−	90040.7i	−1.23749	−	0.714467i
$356$	1271.30	+	18631.5i	0.0100311	+	0.147010i
$357$	−9192.16	+	4551.72i	−0.0721242	+	0.0357140i
$358$	65763.1	+	61428.8i	0.513117	+	0.479298i
$359$			181364.i			1.40722i	0.710587	+	0.703609i	$0.248429\pi$
$359$			181364.i			1.40722i	−0.710587	+	0.703609i	$0.751571\pi$
$360$	196953.	−	47436.9i	1.51970	−	0.366026i
$361$	129598.			0.994452
$362$	59652.9	−	63862.0i	0.455213	−	0.487333i
$363$	−11551.8	+	17349.7i	−0.0876672	+	0.131667i
$364$	−40716.0	+	2778.22i	−0.307300	+	0.0209683i
$365$	50114.6	−	86801.1i	0.376165	−	0.651537i
$366$	75176.8	+	22561.1i	0.561206	+	0.168422i
$367$	181000.	−	104500.i	1.34383	−	0.775863i	0.356467	−	0.934308i	$-0.383981\pi$
$367$	181000.	−	104500.i	1.34383	−	0.775863i	0.987368	+	0.158445i	$0.0506481\pi$
$368$	207352.	+	84589.4i	1.53113	+	0.624626i
$369$	−3833.93	+	5030.35i	−0.0281573	+	0.0369441i
$370$	−80225.8	−	263199.i	−0.586017	−	1.92257i
$371$	13883.5	−	8015.67i	0.100868	−	0.0582360i
$372$	48973.3	−	85674.6i	0.353894	−	0.619108i
$373$	38298.0	−	66334.0i	0.275269	−	0.476781i	−0.694934	−	0.719074i	$-0.744566\pi$
$373$	38298.0	−	66334.0i	0.275269	−	0.476781i	0.970203	+	0.242293i	$0.0778996\pi$
$374$	−9362.09	+	40396.4i	−0.0669314	+	0.288801i
$375$	−97281.4	−	6216.91i	−0.691779	−	0.0442092i
$376$	−145889.	−	23484.7i	−1.03192	−	0.166115i
$377$	−272015.			−1.91386
$378$	14486.2	−	32508.9i	0.101384	−	0.227519i
$379$			232118.i			1.61596i	0.589211	+	0.807979i	$0.299439\pi$
$379$			232118.i			1.61596i	−0.589211	+	0.807979i	$0.700561\pi$
$380$	−7395.75	+	15098.9i	−0.0512171	+	0.104563i
$381$	−4689.14	+	73375.1i	−0.0323030	+	0.505474i
$382$	−16874.7	+	72812.3i	−0.115640	+	0.498974i
$383$	74119.1	+	42792.7i	0.505280	+	0.291724i	0.730891	−	0.682494i	$-0.239105\pi$
$383$	74119.1	+	42792.7i	0.505280	+	0.291724i	−0.225611	+	0.974217i	$0.572438\pi$
$384$	−120797.	−	84565.6i	−0.819207	−	0.573497i
$385$	26476.0	+	45857.7i	0.178620	+	0.309379i
$386$	−53764.1	−	176386.i	−0.360842	−	1.18383i
$387$	−121283.	+	50700.8i	−0.809798	+	0.338527i
$388$	76214.1	−	51220.4i	0.506258	−	0.340236i
$389$	−60869.2	−	105429.i	−0.402252	−	0.696721i	0.591745	−	0.806125i	$-0.298439\pi$
$389$	−60869.2	−	105429.i	−0.402252	−	0.696721i	−0.993997	+	0.109404i	$0.965106\pi$
$390$	−281597.	−	84509.2i	−1.85139	−	0.555616i
$391$	−70741.7	−	40842.8i	−0.462724	−	0.267154i
$392$	−134687.	+	51311.4i	−0.876504	+	0.333919i
$393$	−78985.8	−	52590.6i	−0.511404	−	0.340505i
$394$	−43508.9	+	46578.9i	−0.280276	+	0.300052i
$395$		−	202441.i		−	1.29749i
$396$	−64401.5	−	128661.i	−0.410682	−	0.820462i
$397$	−71690.8			−0.454865			−0.227432	−	0.973794i	$-0.573033\pi$
$397$	−71690.8			−0.454865			−0.227432	+	0.973794i	$0.573033\pi$
$398$	215532.	+	201327.i	1.36065	+	1.27097i
$399$	1310.71	+	2646.97i	0.00823306	+	0.0166266i
$400$	141575.	+	182471.i	0.884842	+	1.14045i
$401$	43140.3	−	74721.1i	0.268283	−	0.464681i	−0.700135	−	0.714010i	$-0.746877\pi$
$401$	43140.3	−	74721.1i	0.268283	−	0.464681i	0.968419	+	0.249330i	$0.0802103\pi$
$402$	8620.05	−	2036.92i	0.0533406	−	0.0126044i
$403$	−124029.	+	71608.3i	−0.763684	+	0.440913i
$404$	−206987.	+	139107.i	−1.26818	+	0.852291i
$405$	180114.	−	182478.i	1.09809	−	1.11250i
$406$	60785.0	−	18527.9i	0.368761	−	0.112402i
$407$	−169239.	+	97710.0i	−1.02167	+	0.589862i
$408$	39463.7	+	36545.6i	0.237071	+	0.219540i
$409$	−115231.	+	199585.i	−0.688844	+	1.19311i	0.283368	+	0.959011i	$0.408548\pi$
$409$	−115231.	+	199585.i	−0.688844	+	1.19311i	−0.972212	+	0.234102i	$0.924785\pi$
$410$	−11890.6	−	2755.72i	−0.0707355	−	0.0163933i
$411$	−12882.7	−	26016.5i	−0.0762645	−	0.154016i
$412$	78315.6	−	159887.i	0.461375	−	0.941928i
$413$	−67907.1			−0.398121
$414$	279426.	−	47454.7i	1.63029	−	0.276872i
$415$			73208.6i			0.425075i
$416$	89621.6	+	194327.i	0.517876	+	1.12291i
$417$	140795.	+	93744.8i	0.809685	+	0.539107i
$418$	11632.5	+	2695.91i	0.0665767	+	0.0154295i
$419$	48172.3	+	27812.3i	0.274391	+	0.158420i	0.630881	−	0.775879i	$-0.282693\pi$
$419$	48172.3	+	27812.3i	0.274391	+	0.158420i	−0.356491	+	0.934299i	$0.616027\pi$
$420$	68682.5	−	295.932i	0.389356	−	0.00167762i
$421$	−70485.7	−	122085.i	−0.397683	−	0.688807i	0.595757	−	0.803165i	$-0.296852\pi$
$421$	−70485.7	−	122085.i	−0.397683	−	0.688807i	−0.993440	+	0.114358i	$0.963519\pi$
$422$	−68176.8	+	20781.0i	−0.382835	+	0.116692i
$423$	−172548.	+	72131.7i	−0.964337	+	0.403130i
$424$	−65195.3	−	53067.4i	−0.362647	−	0.295186i
$425$	−42121.4	−	72956.4i	−0.233198	−	0.403911i
$426$	113762.	+	120742.i	0.626873	+	0.665335i
$427$	23045.4	+	13305.2i	0.126394	+	0.0729738i
$428$	−71272.8	+	4863.23i	−0.389078	+	0.0265483i
$429$	−13317.0	+	208382.i	−0.0723588	+	1.13226i
$430$	−185386.	−	173167.i	−1.00263	−	0.936544i
$431$		−	191015.i		−	1.02828i	−0.857705	−	0.514142i	$-0.828111\pi$
$431$		−	191015.i		−	1.02828i	0.857705	−	0.514142i	$-0.171889\pi$
$432$	−186340.	−	10296.9i	−0.998477	−	0.0551743i
$433$	48243.4			0.257313			0.128657	−	0.991689i	$-0.458933\pi$
$433$	48243.4			0.257313			0.128657	+	0.991689i	$0.458933\pi$
$434$	22838.3	−	24449.8i	0.121251	−	0.129806i
$435$	456860.	+	29196.3i	2.41437	+	0.154294i
$436$	5158.56	+	75601.0i	0.0271366	+	0.397699i
$437$	−11761.1	+	20370.8i	−0.0615863	+	0.106671i
$438$	−67202.5	+	63317.6i	−0.350297	+	0.330047i
$439$	227081.	−	131105.i	1.17829	−	0.680285i	0.222670	−	0.974894i	$-0.428523\pi$
$439$	227081.	−	131105.i	1.17829	−	0.680285i	0.955618	+	0.294609i	$0.0951893\pi$
$440$	175283.	−	215342.i	0.905388	−	1.11230i
$441$	−110575.	+	145081.i	−0.568562	+	0.745988i
$442$	−22759.1	−	74666.6i	−0.116496	−	0.382192i
$443$	−78793.6	+	45491.5i	−0.401498	+	0.231805i	−0.687130	−	0.726534i	$-0.741130\pi$
$443$	−78793.6	+	45491.5i	−0.401498	+	0.231805i	0.285632	+	0.958339i	$0.407796\pi$
$444$	1092.14	+	253474.i	0.00554005	+	1.28578i
$445$	−22805.9	+	39501.0i	−0.115167	+	0.199475i
$446$	60851.0	−	262566.i	0.305913	−	1.31998i
$447$	38158.9	−	57310.8i	0.190977	−	0.286828i
$448$	−33263.3	−	37320.3i	−0.165733	−	0.185947i
$449$	283350.			1.40550			0.702748	−	0.711438i	$-0.251956\pi$
$449$	283350.			1.40550			0.702748	+	0.711438i	$0.251956\pi$
$450$	274036.	+	101703.i	1.35326	+	0.502238i
$451$			8668.77i			0.0426191i
$452$	−263613.	−	129123.i	−1.29030	−	0.632014i
$453$	−9080.00	+	4496.18i	−0.0442476	+	0.0219102i
$454$	56708.7	−	244692.i	0.275130	−	1.18716i
$455$	−86323.1	−	49838.7i	−0.416970	−	0.240737i
$456$	10523.7	−	11364.0i	0.0506101	−	0.0546513i
$457$	−99226.7	−	171866.i	−0.475112	−	0.822918i	0.524482	−	0.851422i	$-0.324259\pi$
$457$	−99226.7	−	171866.i	−0.475112	−	0.822918i	−0.999594	+	0.0285035i	$0.990926\pi$
$458$	47730.9	+	156592.i	0.227546	+	0.746517i
$459$	66829.4	+	12953.8i	0.317207	+	0.0614852i
$460$	305094.	+	453968.i	1.44184	+	2.14541i
$461$	104347.	+	180735.i	0.490998	+	0.850433i	0.999946	−	0.0103639i	$-0.00329898\pi$
$461$	104347.	+	180735.i	0.490998	+	0.850433i	−0.508949	+	0.860797i	$0.669966\pi$
$462$	−11217.8	−	47472.6i	−0.0525562	−	0.222413i
$463$	−22687.9	−	13098.9i	−0.105836	−	0.0611044i	0.446148	−	0.894959i	$-0.352796\pi$
$463$	−22687.9	−	13098.9i	−0.105836	−	0.0611044i	−0.551984	+	0.833855i	$0.686129\pi$
$464$	−204261.	−	263266.i	−0.948746	−	1.22281i
$465$	215998.	−	106957.i	0.998950	−	0.494654i
$466$	−216401.	+	231670.i	−0.996524	+	1.06684i
$467$		−	96607.8i		−	0.442974i	−0.975163	−	0.221487i	$-0.928909\pi$
$467$		−	96607.8i		−	0.442974i	0.975163	−	0.221487i	$-0.0710911\pi$
$468$	226086.	+	149131.i	1.03224	+	0.680889i
$469$	3002.97			0.0136523
$470$	−263747.	−	246363.i	−1.19396	−	1.11527i
$471$	17515.7	−	26306.9i	0.0789562	−	0.118584i
$472$	126768.	+	332753.i	0.569017	+	1.49361i
$473$	−90084.9	+	156032.i	−0.402652	+	0.697413i
$474$	−53605.5	+	178621.i	−0.238590	+	0.795017i
$475$	−21008.5	+	12129.3i	−0.0931125	+	0.0537585i
$476$	10171.6	+	15135.0i	0.0448926	+	0.0667986i
$477$	−105527.	−	13543.0i	−0.463794	−	0.0595220i
$478$	−172681.	+	52634.7i	−0.755767	+	0.230365i
$479$	−29664.3	+	17126.7i	−0.129289	+	0.0746453i	−0.563250	−	0.826287i	$-0.690449\pi$
$479$	−29664.3	+	17126.7i	−0.129289	+	0.0746453i	0.433960	+	0.900932i	$0.357116\pi$
$480$	−129665.	−	336000.i	−0.562784	−	1.45833i
$481$	183931.	−	318577.i	0.794994	−	1.37697i
$482$	294801.	+	68321.7i	1.26892	+	0.294080i
$483$	95895.6	+	6128.35i	0.411059	+	0.0262693i
$484$	33277.7	+	16300.1i	0.142057	+	0.0695823i
$485$	224280.			0.953470
$486$	−207240.	+	113314.i	−0.877408	+	0.479745i
$487$			69521.4i			0.293130i	0.989201	+	0.146565i	$0.0468218\pi$
$487$			69521.4i			0.293130i	−0.989201	+	0.146565i	$0.953178\pi$
$488$	22176.5	−	137763.i	0.0931224	−	0.578486i
$489$	24077.6	−	376762.i	0.100692	−	1.57561i
$490$	−342939.	−	79477.9i	−1.42832	−	0.331020i
$491$	−174305.	−	100635.i	−0.723016	−	0.417433i	0.0928458	−	0.995681i	$-0.470404\pi$
$491$	−174305.	−	100635.i	−0.723016	−	0.417433i	−0.815862	+	0.578247i	$0.803737\pi$
$492$	9761.84	+	5580.06i	0.0403275	+	0.0230520i
$493$	60771.9	+	105260.i	0.250040	+	0.433081i
$494$	−21501.0	+	6553.71i	−0.0881057	+	0.0268555i
$495$	44732.8	−	348557.i	0.182564	−	1.42254i
$496$	−162441.	−	66268.0i	−0.660286	−	0.269365i
$497$	28121.7	+	48708.2i	0.113849	+	0.197192i
$498$	19385.3	−	64594.6i	0.0781653	−	0.260458i
$499$	46850.8	+	27049.3i	0.188155	+	0.108631i	0.591119	−	0.806585i	$-0.298687\pi$
$499$	46850.8	+	27049.3i	0.188155	+	0.108631i	−0.402964	+	0.915216i	$0.632020\pi$
$500$	11797.3	+	172896.i	0.0471894	+	0.691582i
$501$	51041.7	+	33984.7i	0.203352	+	0.135397i
$502$	228795.	+	213715.i	0.907902	+	0.848064i
$503$			239548.i			0.946795i	0.880849	+	0.473397i	$0.156973\pi$
$503$			239548.i			0.946795i	−0.880849	+	0.473397i	$0.843027\pi$
$504$	−60679.4	−	17925.7i	−0.238880	−	0.0705691i
$505$	−609113.			−2.38844
$506$	265171.	−	283881.i	1.03568	−	1.10875i
$507$	−60355.7	−	121888.i	−0.234802	−	0.474181i
$508$	130407.	−	8898.22i	0.505330	−	0.0344807i
$509$	−57738.0	+	100005.i	−0.222857	+	0.386000i	−0.955674	−	0.294426i	$-0.904872\pi$
$509$	−57738.0	+	100005.i	−0.222857	+	0.386000i	0.732817	+	0.680425i	$0.238205\pi$
$510$	30210.6	+	127848.i	0.116150	+	0.491535i
$511$	−27109.9	+	15651.9i	−0.103821	+	0.0599412i
$512$	−120778.	+	232663.i	−0.460733	+	0.887539i
$513$	3730.16	−	19244.2i	0.0141740	−	0.0731248i
$514$	26838.8	+	88051.1i	0.101587	+	0.333279i
$515$	376584.	−	217421.i	1.41987	−	0.819761i
$516$	117719.	+	201881.i	0.442126	+	0.758221i
$517$	−128163.	+	221985.i	−0.479492	+	0.830505i
$518$	−19402.1	+	83718.1i	−0.0723086	+	0.312004i
$519$	−62894.8	−	127016.i	−0.233496	−	0.471545i
$520$	−83068.7	+	516031.i	−0.307207	+	1.90840i
$521$	217267.			0.800420			0.400210	−	0.916424i	$-0.368937\pi$
$521$	217267.			0.800420			0.400210	+	0.916424i	$0.368937\pi$
$522$	−395373.	−	146735.i	−1.45100	−	0.538510i
$523$		−	39683.4i		−	0.145079i	−0.997366	−	0.0725397i	$-0.976890\pi$
$523$		−	39683.4i		−	0.145079i	0.997366	−	0.0725397i	$-0.0231104\pi$
$524$	−74207.4	+	151499.i	−0.270262	+	0.551757i
$525$	82487.8	+	54922.3i	0.299275	+	0.199265i
$526$	78457.6	−	338536.i	0.283572	−	1.22358i
$527$	55419.6	+	31996.5i	0.199546	+	0.115208i
$528$	−211680.	+	143590.i	−0.759298	+	0.515057i
$529$	242694.	+	420359.i	0.867258	+	1.50213i
$530$	−59863.7	−	196397.i	−0.213114	−	0.699170i
$531$	358430.	+	273181.i	1.27120	+	0.968861i
$532$	4358.26	−	2929.01i	0.0153989	−	0.0103490i
$533$	−8159.11	−	14132.0i	−0.0287202	−	0.0497449i
$534$	30582.2	−	28814.3i	0.107247	−	0.101048i
$535$	−151107.	−	87241.9i	−0.527932	−	0.304802i
$536$	−5605.90	−	14714.9i	−0.0195126	−	0.0512186i
$537$	12913.3	−	202066.i	0.0447806	−	0.700721i
$538$	147672.	−	158092.i	0.510192	−	0.546191i
$539$			250017.i			0.860580i
$540$	−363713.	−	274738.i	−1.24730	−	0.942175i
$541$	−194992.			−0.666228			−0.333114	−	0.942887i	$-0.608099\pi$
$541$	−194992.			−0.666228			−0.333114	+	0.942887i	$0.608099\pi$
$542$	−140185.	−	130945.i	−0.477201	−	0.445750i
$543$	−196225.	−	12540.0i	−0.665510	−	0.0425304i
$544$	55174.8	−	78095.7i	0.186442	−	0.263894i
$545$	−92539.8	+	160284.i	−0.311556	+	0.539630i
$546$	62969.0	+	66832.4i	0.211223	+	0.224183i
$547$	81637.9	−	47133.6i	0.272846	−	0.157527i	−0.357335	−	0.933976i	$-0.616314\pi$
$547$	81637.9	−	47133.6i	0.272846	−	0.157527i	0.630180	+	0.776449i	$0.282981\pi$
$548$	−42836.3	+	28788.5i	−0.142643	+	0.0958647i
$549$	−68113.8	−	162937.i	−0.225991	−	0.540598i
$550$	383218.	−	116809.i	1.26684	−	0.386144i
$551$	30310.6	−	17499.9i	0.0998371	−	0.0576410i
$552$	−148987.	−	481340.i	−0.488955	−	1.57970i
$553$	−31613.4	+	54756.1i	−0.103376	+	0.179053i
$554$	−287280.	−	66578.8i	−0.936022	−	0.216928i
$555$	−343113.	+	515321.i	−1.11391	+	1.67299i
$556$	132278.	−	270053.i	0.427894	−	0.873575i
$557$	−563587.			−1.81656			−0.908282	−	0.418358i	$-0.862606\pi$
$557$	−563587.			−1.81656			−0.908282	+	0.418358i	$0.862606\pi$
$558$	−218904.	+	37176.4i	−0.703050	+	0.119398i
$559$		−	339154.i		−	1.08536i
$560$	−16586.0	−	120972.i	−0.0528889	−	0.385751i
$561$	83611.6	−	41402.3i	0.265669	−	0.131552i
$562$	218699.	+	50684.8i	0.692428	+	0.160474i
$563$	−543509.	−	313795.i	−1.71471	−	0.989986i	−0.927935	−	0.372741i	$-0.878418\pi$
$563$	−543509.	−	313795.i	−1.71471	−	0.989986i	−0.786771	−	0.617245i	$-0.788249\pi$
$564$	167477.	+	287214.i	0.526499	+	0.902917i
$565$	−358473.	−	620894.i	−1.12295	−	1.94500i
$566$	584516.	−	178166.i	1.82458	−	0.556150i
$567$	−77213.0	+	21229.7i	−0.240173	+	0.0660356i
$568$	186179.	−	228727.i	0.577077	−	0.708959i
$569$	38859.9	+	67307.3i	0.120026	+	0.207892i	0.919778	−	0.392439i	$-0.128369\pi$
$569$	38859.9	+	67307.3i	0.120026	+	0.207892i	−0.799751	+	0.600331i	$0.795035\pi$
$570$	36815.2	−	8699.44i	0.113312	−	0.0267758i
$571$	−276094.	−	159403.i	−0.846809	−	0.488905i	0.0127640	−	0.999919i	$-0.495937\pi$
$571$	−276094.	−	159403.i	−0.846809	−	0.488905i	−0.859573	+	0.511013i	$0.829270\pi$
$572$	370352.	−	25270.6i	1.13194	−	0.0772366i
$573$	150705.	−	74625.4i	0.459007	−	0.227288i
$574$	2785.83	+	2602.22i	0.00845533	+	0.00789805i
$575$			789186.i			2.38695i
$576$	25437.4	+	330799.i	0.0766704	+	0.997056i
$577$	40053.7			0.120307			0.0601534	−	0.998189i	$-0.480841\pi$
$577$	40053.7			0.120307			0.0601534	+	0.998189i	$0.480841\pi$
$578$	204242.	−	218653.i	0.611349	−	0.654485i
$579$	−229940.	+	345348.i	−0.685896	+	1.03015i
$580$	−55403.5	−	811964.i	−0.164695	−	2.41369i
$581$	11432.3	−	19801.4i	0.0338675	−	0.0586602i
$582$	−197890.	−	59388.3i	−0.584223	−	0.175329i
$583$	−126284.	+	72910.3i	−0.371546	+	0.214512i
$584$	127304.	+	103623.i	0.373266	+	0.303830i
$585$	255140.	+	610327.i	0.745533	+	1.78341i
$586$	45298.0	+	148611.i	0.131912	+	0.432768i
$587$	−11894.5	+	6867.28i	−0.0345199	+	0.0199301i	−0.517161	−	0.855888i	$-0.673011\pi$
$587$	−11894.5	+	6867.28i	−0.0345199	+	0.0199301i	0.482641	+	0.875818i	$0.339678\pi$
$588$	281542.	+	160935.i	0.814307	+	0.465474i
$589$	9213.72	−	15958.6i	0.0265586	−	0.0460008i
$590$	−196355.	+	847250.i	−0.564076	+	2.43393i
$591$	143120.	+	9146.29i	0.409756	+	0.0261861i
$592$	446448.	−	61210.8i	1.27388	−	0.174656i
$593$	537582.			1.52875			0.764373	−	0.644775i	$-0.223049\pi$
$593$	537582.			1.52875			0.764373	+	0.644775i	$0.223049\pi$
$594$	−131766.	+	295700.i	−0.373447	+	0.838066i
$595$			44538.6i			0.125806i
$596$	−109925.	−	53843.7i	−0.309461	−	0.151580i
$597$	42322.3	−	662253.i	0.118746	−	1.85813i
$598$	−165095.	+	712368.i	−0.461671	+	1.99206i
$599$	394401.	+	227708.i	1.09922	+	0.634635i	0.936016	−	0.351958i	$-0.114484\pi$
$599$	394401.	+	227708.i	1.09922	+	0.634635i	0.163204	+	0.986592i	$0.447817\pi$
$600$	115139.	−	506728.i	0.319830	−	1.40758i
$601$	118996.	+	206108.i	0.329446	+	0.570618i	0.982402	−	0.186778i	$-0.0598046\pi$
$601$	118996.	+	206108.i	0.329446	+	0.570618i	−0.652956	+	0.757396i	$0.726471\pi$
$602$	23100.9	+	75788.0i	0.0637436	+	0.209126i
$603$	−15850.4	−	12080.5i	−0.0435919	−	0.0332240i
$604$	10047.5	+	14950.3i	0.0275412	+	0.0409803i
$605$	45252.5	+	78379.7i	0.123632	+	0.214137i
$606$	537443.	+	161290.i	1.46348	+	0.439200i
$607$	516142.	+	297995.i	1.40085	+	0.808781i	0.994480	−	0.104927i	$-0.0334608\pi$
$607$	516142.	+	297995.i	1.40085	+	0.808781i	0.406371	+	0.913708i	$0.366794\pi$
$608$	−22488.4	−	15888.1i	−0.0608347	−	0.0429799i
$609$	−119012.	−	79240.7i	−0.320889	−	0.213655i
$610$	232640.	−	249055.i	0.625209	−	0.669324i
$611$		−	482511.i		−	1.29248i
$612$	7197.72	−	120805.i	0.0192173	−	0.322539i
$613$	547275.			1.45641			0.728206	−	0.685358i	$-0.240354\pi$
$613$	547275.			1.45641			0.728206	+	0.685358i	$0.240354\pi$
$614$	−1337.41	−	1249.26i	−0.00354754	−	0.00331372i
$615$	12186.7	+	24611.0i	0.0322208	+	0.0650697i
$616$	−81038.4	+	30873.0i	−0.213565	+	0.0813611i
$617$	−259077.	+	448735.i	−0.680549	+	1.17874i	0.294265	+	0.955724i	$0.404925\pi$
$617$	−259077.	+	448735.i	−0.680549	+	1.17874i	−0.974814	+	0.223021i	$0.928408\pi$
$618$	−389846.	+	92120.8i	−1.02074	+	0.241202i
$619$	176869.	−	102115.i	0.461605	−	0.266508i	−0.251114	−	0.967958i	$-0.580797\pi$
$619$	176869.	−	102115.i	0.461605	−	0.266508i	0.712719	+	0.701450i	$0.247463\pi$
$620$	−239013.	−	355642.i	−0.621781	−	0.925187i
$621$	−481507.	−	418122.i	−1.24859	−	1.08423i
$622$	41025.8	−	12505.1i	0.106042	−	0.0323226i
$623$	12337.1	−	7122.80i	0.0317860	−	0.0183516i
$624$	209937.	−	433317.i	0.539163	−	1.11285i
$625$	70291.3	−	121748.i	0.179946	−	0.311675i
$626$	69954.7	+	16212.4i	0.178512	+	0.0413712i
$627$	−11922.2	−	24076.8i	−0.0303264	−	0.0612440i
$628$	−50458.0	−	24715.4i	−0.127941	−	0.0626683i
$629$	−164370.			−0.415454
$630$	−98585.6	−	119006.i	−0.248389	−	0.299840i
$631$			177036.i			0.444633i	0.974975	+	0.222317i	$0.0713618\pi$
$631$			177036.i			0.444633i	−0.974975	+	0.222317i	$0.928638\pi$
$632$	327327.	+	52691.8i	0.819497	+	0.131919i
$633$	133484.	+	88876.8i	0.333137	+	0.221810i
$634$	−239149.	−	55424.1i	−0.594963	−	0.137886i
$635$	276480.	+	159626.i	0.685672	+	0.395873i
$636$	814.947	+	189140.i	0.00201472	+	0.467594i
$637$	−235317.	−	407582.i	−0.579929	−	1.00447i
$638$	−552899.	+	168529.i	−1.35833	+	0.414031i
$639$	47513.4	−	370224.i	0.116363	−	0.906698i
$640$	−561812.	+	307101.i	−1.37161	+	0.749758i
$641$	−109444.	−	189562.i	−0.266364	−	0.461356i	0.701556	−	0.712614i	$-0.252489\pi$
$641$	−109444.	−	189562.i	−0.266364	−	0.461356i	−0.967920	+	0.251258i	$0.919156\pi$
$642$	110226.	+	116989.i	0.267433	+	0.283841i
$643$	298938.	+	172592.i	0.723035	+	0.417445i	0.815869	−	0.578237i	$-0.196259\pi$
$643$	298938.	+	172592.i	0.723035	+	0.417445i	−0.0928336	+	0.995682i	$0.529592\pi$
$644$	−11629.3	−	170432.i	−0.0280402	−	0.410942i
$645$	−36402.6	+	569623.i	−0.0875009	+	1.36920i
$646$	7339.66	+	6855.91i	0.0175878	+	0.0164286i
$647$		−	398251.i		−	0.951366i	−0.879617	−	0.475683i	$-0.842201\pi$
$647$		−	398251.i		−	0.951366i	0.879617	−	0.475683i	$-0.157799\pi$
$648$	248168.	+	338721.i	0.591011	+	0.806663i
$649$	617681.			1.46648
$650$	−514787.	+	551110.i	−1.21843	+	1.30440i
$651$	−75125.4	−	4801.00i	−0.177266	−	0.0113284i
$652$	−669609.	+	45690.1i	−1.57517	+	0.107480i
$653$	171144.	−	296430.i	0.401361	−	0.695178i	−0.592529	−	0.805549i	$-0.701871\pi$
$653$	171144.	−	296430.i	0.401361	−	0.695178i	0.993890	+	0.110371i	$0.0352040\pi$
$654$	124094.	−	116920.i	0.290131	−	0.273359i
$655$	−356830.	+	206016.i	−0.831722	+	0.480195i
$656$	7550.63	−	18508.7i	0.0175459	−	0.0430098i
$657$	206058.	+	26444.9i	0.477374	+	0.0612648i
$658$	32865.5	+	107823.i	0.0759082	+	0.249035i
$659$	−452868.	+	261464.i	−1.04280	+	0.602061i	−0.920625	−	0.390447i	$-0.872320\pi$
$659$	−452868.	+	261464.i	−1.04280	+	0.602061i	−0.122175	+	0.992509i	$0.538987\pi$
$660$	−624734.	+	2691.79i	−1.43419	+	0.00617950i
$661$	−154294.	+	267245.i	−0.353140	+	0.611656i	−0.986798	−	0.161957i	$-0.948219\pi$
$661$	−154294.	+	267245.i	−0.353140	+	0.611656i	0.633658	+	0.773613i	$0.281553\pi$
$662$	167883.	−	724395.i	0.383080	−	1.65295i
$663$	−97337.1	+	146191.i	−0.221438	+	0.332577i
$664$	−118371.	−	19054.9i	−0.268478	−	0.0432185i
$665$	12825.3			0.0290018
$666$	439196.	−	363832.i	0.990170	−	0.820262i
$667$		−	1.13862e6i		−	2.55934i
$668$	47953.8	−	97900.8i	0.107466	−	0.219398i
$669$	−543453.	+	269104.i	−1.21425	+	0.601267i
$670$	8683.16	−	37466.9i	0.0193432	−	0.0834637i
$671$	−209620.	−	121024.i	−0.465573	−	0.268798i
$672$	−17398.3	+	111129.i	−0.0385273	+	0.246088i
$673$	124260.	+	215225.i	0.274348	+	0.475184i	0.969970	−	0.243223i	$-0.0782047\pi$
$673$	124260.	+	215225.i	0.274348	+	0.475184i	−0.695623	+	0.718407i	$0.744871\pi$
$674$	172604.	+	566269.i	0.379955	+	1.24653i
$675$	−214446.	−	621730.i	−0.470663	−	1.36457i
$676$	−200689.	+	134875.i	−0.439168	+	0.295147i
$677$	−134761.	−	233413.i	−0.294027	−	0.509270i	0.680731	−	0.732533i	$-0.261662\pi$
$677$	−134761.	−	233413.i	−0.294027	−	0.509270i	−0.974758	+	0.223264i	$0.928329\pi$
$678$	151884.	+	642759.i	0.330410	+	1.39826i
$679$	−60663.0	−	35023.8i	−0.131578	−	0.0759668i
$680$	218244.	−	83143.9i	0.471981	−	0.179809i
$681$	−506458.	+	250785.i	−1.09207	+	0.540763i
$682$	−207737.	+	222395.i	−0.446627	+	0.478140i
$683$		−	124482.i		−	0.266848i	−0.991059	−	0.133424i	$-0.957403\pi$
$683$		−	124482.i		−	0.266848i	0.991059	−	0.133424i	$-0.0425972\pi$
$684$	−34787.0	−	2072.65i	−0.0743540	−	0.00443011i
$685$	−126057.			−0.268649
$686$	166007.	+	155066.i	0.352760	+	0.329510i
$687$	204137.	−	306594.i	0.432523	−	0.649606i
$688$	328246.	−	254677.i	0.693461	−	0.538038i
$689$	137247.	−	237719.i	0.289111	−	0.500756i
$690$	353745.	−	1.17873e6i	0.743006	−	2.47580i
$691$	−771402.	+	445369.i	−1.61557	+	0.932747i	−0.627518	+	0.778602i	$0.715929\pi$
$691$	−771402.	+	445369.i	−1.61557	+	0.932747i	−0.988048	+	0.154145i	$0.950738\pi$
$692$	−209132.	+	140549.i	−0.436726	+	0.293506i
$693$	−66530.4	+	87291.9i	−0.138533	+	0.181764i
$694$	−554723.	+	169085.i	−1.15175	+	0.351064i
$695$	636063.	−	367231.i	1.31683	−	0.760274i
$696$	−166120.	+	731096.i	−0.342928	+	1.50923i
$697$	−3645.71	+	6314.56i	−0.00750442	+	0.0129980i
$698$	−697324.	−	161609.i	−1.43128	−	0.331707i
$699$	711839.	+	45491.1i	1.45689	+	0.0931048i
$700$	77497.5	−	158216.i	0.158158	−	0.322890i
$701$	−170934.			−0.347851			−0.173925	−	0.984759i	$-0.555645\pi$
$701$	−170934.			−0.347851			−0.173925	+	0.984759i	$0.555645\pi$
$702$	−63507.7	−	606074.i	−0.128870	−	1.22985i
$703$			47332.1i			0.0957734i
$704$	302562.	+	339464.i	0.610477	+	0.684934i
$705$	−51789.7	+	810398.i	−0.104199	+	1.63050i
$706$	102855.	+	23837.3i	0.206356	+	0.0478242i
$707$	164752.	+	95119.7i	0.329604	+	0.190297i
$708$	397599.	−	695566.i	0.793193	−	1.38762i
$709$	350963.	+	607886.i	0.698183	+	1.20929i	0.969096	+	0.246684i	$0.0793410\pi$
$709$	350963.	+	607886.i	0.698183	+	1.20929i	−0.270913	+	0.962604i	$0.587326\pi$
$710$	689028.	−	210022.i	1.36685	−	0.416628i
$711$	387140.	−	161839.i	0.765823	−	0.320144i
$712$	−57933.2	−	47156.3i	−0.114279	−	0.0930206i
$713$	−299744.	−	519171.i	−0.589618	−	1.02125i
$714$	11793.6	−	39298.0i	0.0231340	−	0.0770858i
$715$	785193.	+	453331.i	1.53590	+	0.886755i
$716$	−359127.	+	24504.6i	−0.700522	+	0.0477994i
$717$	338093.	+	225110.i	0.657655	+	0.437882i
$718$	−530147.	−	495206.i	−1.02837	−	0.960587i
$719$		−	768366.i		−	1.48631i	−0.669117	−	0.743157i	$-0.733328\pi$
$719$		−	768366.i		−	1.48631i	0.669117	−	0.743157i	$-0.266672\pi$
$720$	−399108.	+	705240.i	−0.769883	+	1.36042i
$721$	−135811.			−0.261255
$722$	−353862.	+	378830.i	−0.678827	+	0.726724i
$723$	−302141.	−	610173.i	−0.578008	−	1.16728i
$724$	23796.2	+	348745.i	0.0453974	+	0.665320i
$725$	587133.	−	1.01695e6i	1.11702	−	1.93473i
$726$	−19173.4	−	81139.9i	−0.0363769	−	0.153943i
$727$	−221493.	+	127879.i	−0.419074	+	0.241952i	−0.694681	−	0.719318i	$-0.744454\pi$
$727$	−221493.	+	127879.i	−0.419074	+	0.241952i	0.275607	+	0.961270i	$0.411121\pi$
$728$	103052.	−	126604.i	0.194444	−	0.238882i
$729$	492953.	+	198562.i	0.927578	+	0.373629i
$730$	116894.	+	383497.i	0.219354	+	0.719642i
$731$	−131240.	+	75771.6i	−0.245602	+	0.141799i
$732$	−271216.	+	158149.i	−0.506166	+	0.295150i
$733$	−184829.	+	320133.i	−0.344003	+	0.595831i	−0.985172	−	0.171569i	$-0.945116\pi$
$733$	−184829.	+	320133.i	−0.344003	+	0.595831i	0.641169	+	0.767400i	$0.278450\pi$
$734$	−188746.	+	814416.i	−0.350336	+	1.51166i
$735$	351478.	+	709807.i	0.650614	+	1.31391i
$736$	−813429.	+	375145.i	−1.50163	+	0.692539i
$737$	−27314.9			−0.0502881
$738$	−4235.91	−	24942.2i	−0.00777739	−	0.0457954i
$739$			1.03557e6i			1.89623i	0.317932	+	0.948114i	$0.397012\pi$
$739$			1.03557e6i			1.89623i	−0.317932	+	0.948114i	$0.602988\pi$
$740$	988415.	+	484146.i	1.80500	+	0.884123i
$741$	42097.0	+	28029.2i	0.0766681	+	0.0510474i
$742$	−14477.7	+	62469.6i	−0.0262961	+	0.113465i
$743$	486002.	+	280593.i	0.880360	+	0.508276i	0.870777	−	0.491678i	$-0.163616\pi$
$743$	486002.	+	280593.i	0.880360	+	0.508276i	0.00958322	+	0.999954i	$0.496950\pi$
$744$	116717.	+	377085.i	0.210858	+	0.681230i
$745$	−149482.	−	258910.i	−0.269324	−	0.466483i
$746$	89331.1	+	293072.i	0.160518	+	0.526618i
$747$	−140001.	+	58525.8i	−0.250894	+	0.104883i
$748$	−92520.5	−	137667.i	−0.165362	−	0.246052i
$749$	27247.6	+	47194.2i	0.0485696	+	0.0841250i
$750$	283796.	−	267390.i	0.504525	−	0.475360i
$751$	−164898.	−	95204.1i	−0.292372	−	0.168801i	0.346639	−	0.937999i	$-0.387323\pi$
$751$	−164898.	−	95204.1i	−0.292372	−	0.168801i	−0.639011	+	0.769197i	$0.720656\pi$
$752$	466993.	−	362327.i	0.825799	−	0.640715i
$753$	44926.5	−	703004.i	0.0792342	−	1.23985i
$754$	742725.	−	795131.i	1.30643	−	1.39861i
$755$			43995.1i			0.0771810i
$756$	55473.3	+	131109.i	0.0970601	+	0.229397i
$757$	523077.			0.912797			0.456398	−	0.889776i	$-0.349139\pi$
$757$	523077.			0.912797			0.456398	+	0.889776i	$0.349139\pi$
$758$	−678508.	−	633788.i	−1.18091	−	1.10308i
$759$	−872263.	−	55743.3i	−1.51413	−	0.0967629i
$760$	−23942.1	−	62845.6i	−0.0414510	−	0.108805i
$761$	80448.7	−	139341.i	0.138915	−	0.240608i	−0.788171	−	0.615456i	$-0.788972\pi$
$761$	80448.7	−	139341.i	0.138915	−	0.240608i	0.927086	+	0.374848i	$0.122305\pi$
$762$	−201680.	−	214054.i	−0.347339	−	0.368650i
$763$	50060.1	−	28902.2i	0.0859890	−	0.0496458i
$764$	−166763.	−	248137.i	−0.285702	−	0.425114i
$765$	179173.	−	235085.i	0.306160	−	0.401701i
$766$	−327467.	+	99815.1i	−0.558097	+	0.170113i
$767$	−1.00695e6	+	581365.i	−1.71167	+	0.988231i
$768$	577026.	−	122201.i	0.978302	−	0.207182i
$769$	297804.	−	515812.i	0.503591	−	0.872246i	−0.496400	−	0.868094i	$-0.665345\pi$
$769$	297804.	−	515812.i	0.503591	−	0.872246i	0.999991	−	0.00415186i	$-0.00132158\pi$
$770$	−206339.	−	47820.2i	−0.348016	−	0.0806547i
$771$	114785.	−	172396.i	0.193098	−	0.290014i
$772$	662396.	+	324455.i	1.11143	+	0.544402i
$773$	−583394.			−0.976345			−0.488172	−	0.872747i	$-0.662336\pi$
$773$	−583394.			−0.976345			−0.488172	+	0.872747i	$0.662336\pi$
$774$	182953.	−	492960.i	0.305392	−	0.822867i
$775$		−	618255.i		−	1.02935i
$776$	−58376.0	+	362638.i	−0.0969418	+	0.602212i
$777$	173278.	−	85802.7i	0.287013	−	0.142121i
$778$	474381.	+	109940.i	0.783732	+	0.181634i
$779$	1818.34	+	1049.82i	0.00299640	+	0.00172997i
$780$	1.01592e6	−	592392.i	1.66982	−	0.973688i
$781$	−255794.	−	443049.i	−0.419362	−	0.726356i
$782$	312545.	−	95266.9i	0.511092	−	0.155786i
$783$	309398.	+	897020.i	0.504654	+	1.46312i
$784$	217768.	−	533810.i	0.354293	−	0.868469i
$785$	−68615.2	−	118845.i	−0.111348	−	0.192860i
$786$	369396.	−	87288.3i	0.597925	−	0.141290i
$787$	151046.	+	87206.2i	0.243870	+	0.140798i	0.616954	−	0.786999i	$-0.288366\pi$
$787$	151046.	+	87206.2i	0.243870	+	0.140798i	−0.373084	+	0.927798i	$0.621700\pi$
$788$	−17356.2	−	254363.i	−0.0279513	−	0.409639i
$789$	−700695.	+	346966.i	−1.12558	+	0.557355i
$790$	591759.	+	552757.i	0.948180	+	0.885687i
$791$			223918.i			0.357879i
$792$	551938.	+	163051.i	0.879914	+	0.259941i
$793$	455635.			0.724553
$794$	195749.	−	209560.i	0.310497	−	0.332406i
$795$	−256028.	+	384528.i	−0.405091	+	0.608406i
$796$	−1.17700e6	+	80311.6i	−1.85760	+	0.126751i
$797$	−423576.	+	733655.i	−0.666829	+	1.15498i	0.311957	+	0.950096i	$0.399016\pi$
$797$	−423576.	+	733655.i	−0.666829	+	1.15498i	−0.978786	+	0.204886i	$0.934318\pi$
$798$	−11316.3	−	3396.09i	−0.0177704	−	0.00533302i
$799$	−186715.	+	107800.i	−0.292472	+	0.168859i
$800$	−919949.	−	84391.1i	−1.43742	−	0.131861i
$801$	−93772.0	−	12034.4i	−0.146153	−	0.0187569i
$802$	100626.	+	330127.i	0.156445	+	0.513254i
$803$	246591.	−	142369.i	0.382425	−	0.220793i
$804$	−17582.5	+	30759.1i	−0.0272000	+	0.0475841i
$805$	208619.	−	361338.i	0.321930	−	0.557599i
$806$	129337.	−	558075.i	0.199091	−	0.859058i
$807$	−485759.	−	31043.1i	−0.745888	−	0.0476671i
$808$	158541.	−	984873.i	0.242839	−	1.50854i
$809$	43118.8			0.0658824			0.0329412	−	0.999457i	$-0.489513\pi$
$809$	43118.8			0.0658824			0.0329412	+	0.999457i	$0.489513\pi$
$810$	41611.8	+	1.02474e6i	0.0634230	+	1.56187i
$811$		−	372984.i		−	0.567085i	−0.958960	−	0.283543i	$-0.908490\pi$
$811$		−	372984.i		−	0.567085i	0.958960	−	0.283543i	$-0.0915097\pi$
$812$	−111812.	+	228271.i	−0.169580	+	0.346209i
$813$	−27526.9	+	430737.i	−0.0416462	+	0.651674i
$814$	176481.	−	761497.i	0.266348	−	1.14926i
$815$	−1.41966e6	−	819638.i	−2.13731	−	1.23398i
$816$	−214581.	+	15570.9i	−0.322263	+	0.0233847i
$817$	21819.2	+	37791.9i	0.0326885	+	0.0566181i
$818$	−268778.	−	881791.i	−0.401687	−	1.31783i
$819$	26299.3	−	204924.i	0.0392081	−	0.305509i
$820$	40522.2	−	27233.3i	0.0602650	−	0.0405017i
$821$	665022.	+	1.15185e6i	0.986620	+	1.70888i	0.634504	+	0.772920i	$0.281204\pi$
$821$	665022.	+	1.15185e6i	0.986620	+	1.70888i	0.352116	+	0.935956i	$0.385462\pi$
$822$	111225.	+	33379.3i	0.164611	+	0.0494008i
$823$	636230.	+	367328.i	0.939322	+	0.542318i	0.889748	−	0.456452i	$-0.150880\pi$
$823$	636230.	+	367328.i	0.939322	+	0.542318i	0.0495745	+	0.998770i	$0.484213\pi$
$824$	253530.	+	665489.i	0.373400	+	0.980136i
$825$	−750307.	−	499572.i	−1.10238	−	0.733990i
$826$	185417.	−	198500.i	0.271763	−	0.290938i
$827$			1.27112e6i			1.85856i	0.369375	+	0.929281i	$0.379572\pi$
$827$			1.27112e6i			1.85856i	−0.369375	+	0.929281i	$0.620428\pi$
$828$	−624245.	+	946367.i	−0.910530	+	1.38038i
$829$	−427267.			−0.621714			−0.310857	−	0.950457i	$-0.600616\pi$
$829$	−427267.			−0.621714			−0.310857	+	0.950457i	$0.600616\pi$
$830$	−213997.	−	199893.i	−0.310636	−	0.290163i
$831$	294433.	+	594607.i	0.426369	+	0.861049i
$832$	−812748.	−	268627.i	−1.17411	−	0.388064i
$833$	−105146.	+	182119.i	−0.151532	+	0.262461i
$834$	−658463.	+	155595.i	−0.946671	+	0.223699i
$835$	230588.	−	133130.i	0.330723	−	0.190943i
$836$	−39642.6	+	26642.2i	−0.0567217	+	0.0381204i
$837$	377216.	+	327560.i	0.538443	+	0.467563i
$838$	−212831.	+	64873.0i	−0.303073	+	0.0923796i
$839$	601815.	−	347458.i	0.854947	−	0.493604i	−0.00737025	−	0.999973i	$-0.502346\pi$
$839$	601815.	−	347458.i	0.854947	−	0.493604i	0.862317	+	0.506369i	$0.169013\pi$
$840$	−186669.	+	201575.i	−0.264554	+	0.285679i
$841$	−493464.	+	854704.i	−0.697691	+	1.20844i
$842$	549327.	+	127310.i	0.774830	+	0.179571i
$843$	−224145.	−	452659.i	−0.315409	−	0.636966i
$844$	125409.	−	256030.i	0.176053	−	0.359423i
$845$	−590581.			−0.827115
$846$	260285.	−	701330.i	0.363671	−	0.979900i
$847$		−	28266.7i		−	0.0394011i
$848$	333135.	−	45674.9i	0.463264	−	0.0635164i
$849$	−1.14443e6	−	761988.i	−1.58772	−	1.05714i
$850$	328270.	+	76078.5i	0.454354	+	0.105299i
$851$	1.33353e6	+	769911.i	1.84137	+	1.06312i
$852$	−663567.	+	2859.11i	−0.914125	+	0.00393869i
$853$	−72314.7	−	125253.i	−0.0993867	−	0.172143i	0.812044	−	0.583596i	$-0.198355\pi$
$853$	−72314.7	−	125253.i	−0.0993867	−	0.172143i	−0.911431	+	0.411453i	$0.865021\pi$
$854$	−101817.	+	31034.8i	−0.139606	+	0.0425534i
$855$	−67695.2	−	51594.6i	−0.0926031	−	0.0705784i
$856$	180392.	−	221618.i	0.246189	−	0.302452i
$857$	318005.	+	550800.i	0.432984	+	0.749951i	0.997129	−	0.0757255i	$-0.0241273\pi$
$857$	318005.	+	550800.i	0.432984	+	0.749951i	−0.564145	+	0.825676i	$0.690794\pi$
$858$	−572764.	−	607906.i	−0.778039	−	0.825775i
$859$	−1.16908e6	−	674970.i	−1.58438	−	0.914741i	−0.994209	−	0.107460i	$-0.965728\pi$
$859$	−1.16908e6	−	674970.i	−1.58438	−	0.914741i	−0.590168	−	0.807281i	$-0.700938\pi$
$860$	1.01237e6	−	69078.3i	1.36881	−	0.0933996i
$861$	547.030	−	8559.85i	0.000737912	−	0.0115467i
$862$	558359.	+	521558.i	0.751448	+	0.701921i
$863$		−	916363.i		−	1.23040i	−0.788372	−	0.615199i	$-0.789076\pi$
$863$		−	916363.i		−	1.23040i	0.788372	−	0.615199i	$-0.210924\pi$
$864$	538891.	−	516577.i	0.721895	−	0.692003i
$865$	−615427.			−0.822515
$866$	−131727.	+	141021.i	−0.175646	+	0.188039i
$867$	−671842.	−	42935.0i	−0.893776	−	0.0571181i
$868$	9110.47	+	133518.i	0.0120921	+	0.177215i
$869$	287555.	−	498060.i	0.380786	−	0.659541i
$870$	−1.33278e6	+	1.25574e6i	−1.76084	+	1.65905i
$871$	44529.3	−	25709.0i	0.0586961	−	0.0338882i
$872$	−235076.	−	191346.i	−0.309154	−	0.251644i
$873$	179298.	+	428903.i	0.235260	+	0.562770i
$874$	−27433.0	−	90000.5i	−0.0359129	−	0.117821i
$875$	114485.	−	66097.9i	0.149531	−	0.0863319i
$876$	−1591.32	−	369327.i	−0.00207371	−	0.481285i
$877$	273128.	−	473071.i	0.355113	−	0.615074i	−0.632024	−	0.774949i	$-0.717776\pi$
$877$	273128.	−	473071.i	0.355113	−	0.615074i	0.987137	+	0.159875i	$0.0511090\pi$
$878$	−236799.	+	1.02176e6i	−0.307178	+	1.32544i
$879$	193732.	−	290967.i	0.250741	−	0.376587i
$880$	150865.	+	1.10035e6i	0.194816	+	1.42091i
$881$	446863.			0.575735			0.287867	−	0.957670i	$-0.407054\pi$
$881$	446863.			0.575735			0.287867	+	0.957670i	$0.407054\pi$
$882$	−122168.	−	719359.i	−0.157044	−	0.924716i
$883$			140436.i			0.180119i	0.995936	+	0.0900593i	$0.0287056\pi$
$883$			140436.i			0.180119i	−0.995936	+	0.0900593i	$0.971294\pi$
$884$	280402.	+	137346.i	0.358820	+	0.175757i
$885$	1.75362e6	−	868347.i	2.23897	−	1.10868i
$886$	82165.5	−	354535.i	0.104670	−	0.451639i
$887$	−307169.	−	177344.i	−0.390418	−	0.225408i	0.291923	−	0.956442i	$-0.405705\pi$
$887$	−307169.	−	177344.i	−0.390418	−	0.225408i	−0.682341	+	0.731034i	$0.739038\pi$
$888$	−743915.	−	688907.i	−0.943404	−	0.873644i
$889$	−49854.7	−	86350.9i	−0.0630816	−	0.109261i
$890$	−53195.5	−	174520.i	−0.0671575	−	0.220326i
$891$	702327.	−	193105.i	0.884675	−	0.243242i
$892$	601358.	+	894798.i	0.755794	+	1.12459i
$893$	31042.0	+	53766.3i	0.0389266	+	0.0674229i
$894$	63335.0	+	268028.i	0.0792445	+	0.335355i
$895$	−761394.	−	439591.i	−0.950525	−	0.548786i
$896$	199916.	+	4668.90i	0.249018	+	0.00581565i
$897$	1.47444e6	−	730106.i	1.83250	−	0.907405i
$898$	−773674.	+	828264.i	−0.959412	+	1.02711i
$899$			892005.i			1.10369i
$900$	−1.04553e6	+	523342.i	−1.29078	+	0.646101i
$901$	−122652.			−0.151086
$902$	−25339.8	−	23669.7i	−0.0311452	−	0.0290924i
$903$	98799.0	−	148386.i	0.121165	−	0.181978i
$904$	1.09723e6	−	418007.i	1.34264	−	0.511501i
$905$	−426883.	+	739383.i	−0.521209	+	0.902760i
$906$	11649.7	−	38818.5i	0.0141925	−	0.0472914i
$907$	1.27955e6	−	738746.i	1.55540	−	0.898008i	0.557709	−	0.830037i	$-0.311681\pi$
$907$	1.27955e6	−	738746.i	1.55540	−	0.898008i	0.997687	−	0.0679717i	$-0.0216528\pi$
$908$	560422.	+	833887.i	0.679741	+	1.01143i
$909$	−486948.	−	1.16484e6i	−0.589325	−	1.40974i
$910$	381386.	−	116250.i	0.460555	−	0.140382i
$911$	41701.0	−	24076.1i	0.0502470	−	0.0290101i	−0.474666	−	0.880166i	$-0.657431\pi$
$911$	41701.0	−	24076.1i	0.0502470	−	0.0290101i	0.524913	+	0.851156i	$0.324098\pi$
$912$	4483.78	+	61790.7i	0.00539082	+	0.0742905i
$913$	−103988.	+	180113.i	−0.124751	+	0.216074i
$914$	773317.	+	179221.i	0.925690	+	0.214534i
$915$	−765257.	−	48904.9i	−0.914040	−	0.0584131i
$916$	−588065.	−	288046.i	−0.700865	−	0.343297i
$917$	128687.			0.153036
$918$	−220340.	+	159980.i	−0.261462	+	0.189837i
$919$		−	346372.i		−	0.410120i	−0.978749	−	0.205060i	$-0.934261\pi$
$919$		−	346372.i		−	0.410120i	0.978749	−	0.205060i	$-0.0657390\pi$
$920$	−2.16004e6	−	347716.i	−2.55204	−	0.410817i
$921$	−262.615	+	4109.37i	−0.000309600	+	0.00484458i
$922$	−813225.	−	188469.i	−0.956641	−	0.221707i
$923$	834000.	+	481510.i	0.978955	+	0.565200i
$924$	169398.	+	96831.0i	0.198410	+	0.113415i
$925$	794014.	+	1.37527e6i	0.927993	+	1.60733i
$926$	100238.	−	30553.5i	0.116899	−	0.0356319i
$927$	716843.	+	546349.i	0.834189	+	0.635786i
$928$	1.32728e6	+	121758.i	1.54123	+	0.141384i
$929$	−435392.	−	754120.i	−0.504485	−	0.873794i	−0.999987	−	0.00518706i	$-0.998349\pi$
$929$	−435392.	−	754120.i	−0.504485	−	0.873794i	0.495501	−	0.868607i	$-0.334984\pi$
$930$	−277127.	+	923427.i	−0.320415	+	1.06767i
$931$	52442.9	+	30277.9i	0.0605044	+	0.0349322i
$932$	−86324.9	−	1.26513e6i	−0.0993812	−	1.45648i
$933$	−80325.0	−	53482.2i	−0.0922757	−	0.0614393i
$934$	282396.	+	263783.i	0.323716	+	0.302380i
$935$		−	405122.i		−	0.463407i
$936$	−1.05324e6	+	253678.i	−1.20220	+	0.289555i
$937$	−1.00280e6			−1.14219			−0.571094	−	0.820885i	$-0.693481\pi$
$937$	−1.00280e6			−1.14219			−0.571094	+	0.820885i	$0.693481\pi$
$938$	−8199.48	+	8778.03i	−0.00931924	+	0.00997680i
$939$	−71696.6	−	144791.i	−0.0813144	−	0.164214i
$940$	1.44030e6	−	98277.2i	1.63003	−	0.111224i
$941$	630949.	−	1.09284e6i	0.712550	−	1.23417i	−0.251348	−	0.967897i	$-0.580874\pi$
$941$	630949.	−	1.09284e6i	0.712550	−	1.23417i	0.963897	−	0.266275i	$-0.0857930\pi$
$942$	29072.1	+	123030.i	0.0327623	+	0.138647i
$943$	59154.8	−	34153.0i	0.0665222	−	0.0384066i
$944$	−1.31881e6	−	538010.i	−1.47992	−	0.603735i
$945$	−66165.9	+	341355.i	−0.0740919	+	0.382245i
$946$	−210125.	−	689366.i	−0.234799	−	0.770314i
$947$	−162072.	+	93572.3i	−0.180721	+	0.104339i	−0.587631	−	0.809129i	$-0.699939\pi$
$947$	−162072.	+	93572.3i	−0.180721	+	0.104339i	0.406910	+	0.913468i	$0.366606\pi$
$948$	−375763.	−	644413.i	−0.418117	−	0.717047i
$949$	−267998.	+	464186.i	−0.297577	+	0.515418i
$950$	21907.6	−	94528.7i	0.0242743	−	0.104741i
$951$	245104.	+	494986.i	0.271012	+	0.547308i
$952$	−72014.3	−	11592.6i	−0.0794593	−	0.0127911i
$953$	194925.			0.214626			0.107313	−	0.994225i	$-0.465775\pi$
$953$	194925.			0.214626			0.107313	+	0.994225i	$0.465775\pi$
$954$	327724.	−	271488.i	0.360090	−	0.298301i
$955$		−	730210.i		−	0.800647i
$956$	317640.	−	648482.i	0.347551	−	0.709549i
$957$	1.08253e6	+	720772.i	1.18199	+	0.786998i
$958$	30933.8	−	133476.i	0.0337056	−	0.145436i
$959$	34095.8	+	19685.2i	0.0370735	+	0.0214044i
$960$	1.33621e6	+	538405.i	1.44988	+	0.584207i
$961$	−226939.	−	393070.i	−0.245732	−	0.425621i
$962$	429023.	+	1.40751e6i	0.463586	+	1.52090i
$963$	46036.5	−	358716.i	0.0496421	−	0.386810i
$964$	−1.00465e6	+	675187.i	−1.08109	+	0.726557i
$965$	900757.	+	1.56016e6i	0.967281	+	1.67538i
$966$	−279753.	+	263581.i	−0.299792	+	0.282461i
$967$	374342.	+	216127.i	0.400328	+	0.231129i	0.686625	−	0.727011i	$-0.259091\pi$
$967$	374342.	+	216127.i	0.400328	+	0.231129i	−0.286298	+	0.958141i	$0.592425\pi$
$968$	−138510.	+	52767.9i	−0.147819	+	0.0563143i
$969$	1441.23	−	22552.1i	0.00153492	−	0.0240182i
$970$	−612387.	+	655597.i	−0.650852	+	0.696776i
$971$		−	756598.i		−	0.802467i	−0.915976	−	0.401233i	$-0.868582\pi$
$971$		−	756598.i		−	0.802467i	0.915976	−	0.401233i	$-0.131418\pi$
$972$	234631.	−	915186.i	0.248344	−	0.968672i
$973$	−229389.			−0.242296
$974$	−203219.	−	189825.i	−0.214213	−	0.200095i
$975$	1.69336e6	+	108217.i	1.78132	+	0.113838i
$976$	342145.	+	440980.i	0.359179	+	0.462934i
$977$	−903593.	+	1.56507e6i	−0.946638	+	1.63962i	−0.194200	+	0.980962i	$0.562211\pi$
$977$	−903593.	+	1.56507e6i	−0.946638	+	1.63962i	−0.752438	+	0.658663i	$0.771122\pi$
$978$	1.03558e6	+	1.09911e6i	1.08269	+	1.14912i
$979$	−112217.	+	64788.8i	−0.117083	+	0.0675981i
$980$	1.16870e6	−	785438.i	1.21689	−	0.817824i
$981$	−380499.	−	48832.2i	−0.395381	−	0.0507421i
$982$	770102.	−	234735.i	0.798593	−	0.243419i
$983$	181852.	−	104992.i	0.188196	−	0.108655i	−0.402942	−	0.915226i	$-0.632012\pi$
$983$	181852.	−	104992.i	0.188196	−	0.108655i	0.591138	+	0.806570i	$0.298679\pi$
$984$	−42965.4	+	13298.9i	−0.0443740	+	0.0137349i
$985$	311354.	−	539282.i	0.320910	−	0.555832i
$986$	−473622.	−	109765.i	−0.487167	−	0.112904i
$987$	140561.	−	211108.i	0.144288	−	0.216706i
$988$	39550.2	−	80744.4i	0.0405168	−	0.0827178i
$989$	1.41966e6			1.45141
$990$	896732.	+	1.08248e6i	0.914939	+	1.10446i
$991$			1.66713e6i			1.69755i	0.528754	+	0.848775i	$0.322659\pi$
$991$			1.66713e6i			1.69755i	−0.528754	+	0.848775i	$0.677341\pi$
$992$	637247.	−	293892.i	0.647567	−	0.298651i
$993$	−1.49934e6	+	742433.i	−1.52055	+	0.752937i
$994$	−219165.	−	50792.7i	−0.221819	−	0.0514077i
$995$	−2.49540e6	−	1.44072e6i	−2.52054	−	1.45523i
$996$	135887.	+	233038.i	0.136981	+	0.234914i
$997$	−671417.	−	1.16293e6i	−0.675464	−	1.16994i	−0.976333	−	0.216273i	$-0.930610\pi$
$997$	−671417.	−	1.16293e6i	−0.675464	−	1.16994i	0.300869	−	0.953666i	$-0.402723\pi$
$998$	−206992.	+	63093.3i	−0.207823	+	0.0633464i
$999$	−1.25978e6	−	244187.i	−1.26230	−	0.244676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.6	yes	44
3.2	odd	2		108.5.f.a.91.17		44
4.3	odd	2	inner	36.5.f.a.31.21	yes	44
9.2	odd	6		108.5.f.a.19.2		44
9.4	even	3		324.5.d.f.163.9		22
9.5	odd	6		324.5.d.e.163.14		22
9.7	even	3	inner	36.5.f.a.7.21	yes	44
12.11	even	2		108.5.f.a.91.2		44
36.7	odd	6	inner	36.5.f.a.7.6	✓	44
36.11	even	6		108.5.f.a.19.17		44
36.23	even	6		324.5.d.e.163.13		22
36.31	odd	6		324.5.d.f.163.10		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.6	✓	44	36.7	odd	6	inner
36.5.f.a.7.21	yes	44	9.7	even	3	inner
36.5.f.a.31.6	yes	44	1.1	even	1	trivial
36.5.f.a.31.21	yes	44	4.3	odd	2	inner
108.5.f.a.19.2		44	9.2	odd	6
108.5.f.a.19.17		44	36.11	even	6
108.5.f.a.91.2		44	12.11	even	2
108.5.f.a.91.17		44	3.2	odd	2
324.5.d.e.163.13		22	36.23	even	6
324.5.d.e.163.14		22	9.5	odd	6
324.5.d.f.163.9		22	9.4	even	3
324.5.d.f.163.10		22	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.73046 + 2.92312i) q^{2} +(8.98168 + 0.573987i) q^{3} +(-1.08921 - 15.9629i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-26.2019 + 24.6872i) q^{6} +(-10.5700 + 6.10260i) q^{7} +(49.6354 + 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +O(q^{10})\)	\(q+(-2.73046 + 2.92312i) q^{2} +(8.98168 + 0.573987i) q^{3} +(-1.08921 - 15.9629i) q^{4} +(19.5394 - 33.8433i) q^{5} +(-26.2019 + 24.6872i) q^{6} +(-10.5700 + 6.10260i) q^{7} +(49.6354 + 40.4021i) q^{8} +(80.3411 + 10.3107i) q^{9} +(45.5763 + 149.524i) q^{10} +(96.1446 - 55.5091i) q^{11} +(-0.620447 - 143.999i) q^{12} +(-104.491 + 180.984i) q^{13} +(11.0224 - 47.5603i) q^{14} +(194.923 - 292.754i) q^{15} +(-253.627 + 34.7739i) q^{16} +93.3790 q^{17} +(-249.507 + 206.693i) q^{18} -26.8894i q^{19} +(-561.519 - 275.043i) q^{20} +(-98.4393 + 48.7446i) q^{21} +(-100.259 + 432.607i) q^{22} +(-757.577 - 437.387i) q^{23} +(422.619 + 391.368i) q^{24} +(-451.080 - 781.293i) q^{25} +(-243.728 - 799.608i) q^{26} +(715.679 + 138.723i) q^{27} +(108.928 + 162.081i) q^{28} +(650.809 + 1127.23i) q^{29} +(323.527 + 1369.13i) q^{30} +(593.492 + 342.653i) q^{31} +(590.870 - 836.330i) q^{32} +(895.401 - 443.379i) q^{33} +(-254.967 + 272.958i) q^{34} +476.966i q^{35} +(77.0808 - 1293.71i) q^{36} -1760.25 q^{37} +(78.6008 + 73.4203i) q^{38} +(-1042.39 + 1565.56i) q^{39} +(2337.19 - 890.392i) q^{40} +(-39.0421 + 67.6229i) q^{41} +(126.298 - 420.844i) q^{42} +(-1405.46 + 811.442i) q^{43} +(-990.807 - 1474.28i) q^{44} +(1918.77 - 2517.54i) q^{45} +(3347.06 - 1020.22i) q^{46} +(-1999.54 + 1154.43i) q^{47} +(-2297.96 + 166.749i) q^{48} +(-1126.02 + 1950.32i) q^{49} +(3515.46 + 814.729i) q^{50} +(838.700 + 53.5984i) q^{51} +(3002.84 + 1470.85i) q^{52} -1313.48 q^{53} +(-2359.63 + 1713.24i) q^{54} -4338.47i q^{55} +(-771.205 - 124.146i) q^{56} +(15.4342 - 241.512i) q^{57} +(-5072.04 - 1175.47i) q^{58} +(4818.38 + 2781.89i) q^{59} +(-4885.52 - 2792.66i) q^{60} +(-1090.13 - 1888.16i) q^{61} +(-2622.12 + 799.247i) q^{62} +(-912.129 + 381.305i) q^{63} +(831.345 + 4010.75i) q^{64} +(4083.39 + 7072.65i) q^{65} +(-1148.81 + 3827.99i) q^{66} +(-213.077 - 123.020i) q^{67} +(-101.709 - 1490.60i) q^{68} +(-6553.25 - 4363.31i) q^{69} +(-1394.23 - 1302.33i) q^{70} -4608.15i q^{71} +(3571.19 + 3757.72i) q^{72} +2564.79 q^{73} +(4806.29 - 5145.42i) q^{74} +(-3603.00 - 7276.24i) q^{75} +(-429.232 + 29.2882i) q^{76} +(-677.500 + 1173.46i) q^{77} +(-1730.12 - 7321.72i) q^{78} +(4486.29 - 2590.16i) q^{79} +(-3778.87 + 9263.05i) q^{80} +(6348.38 + 1656.75i) q^{81} +(-91.0669 - 298.766i) q^{82} +(-1622.37 + 936.677i) q^{83} +(885.325 + 1518.28i) q^{84} +(1824.57 - 3160.25i) q^{85} +(1465.61 - 6323.93i) q^{86} +(5198.34 + 10498.0i) q^{87} +(7014.86 + 1129.22i) q^{88} -1167.17 q^{89} +(2119.95 + 12482.8i) q^{90} -2550.67i q^{91} +(-6156.80 + 12569.5i) q^{92} +(5133.87 + 3418.25i) q^{93} +(2085.11 - 8997.00i) q^{94} +(-910.026 - 525.404i) q^{95} +(5787.05 - 7172.50i) q^{96} +(2869.58 + 4970.26i) q^{97} +(-2626.47 - 8616.73i) q^{98} +(8296.70 - 3468.34i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more