Properties

Label 15.12.a.d.1.1
Level 15
Weight 12
Character 15.1
Self dual Yes
Analytic conductor 11.525
Analytic rank 0
Dimension 3
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 15.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(11.5251477084\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\mathbb{Q}[x]/(x^{3} - \cdots)\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2\cdot 3\cdot 5 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(74.9776\)
Character \(\chi\) = 15.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-74.9776 q^{2}\) \(+243.000 q^{3}\) \(+3573.65 q^{4}\) \(+3125.00 q^{5}\) \(-18219.6 q^{6}\) \(-63061.5 q^{7}\) \(-114389. q^{8}\) \(+59049.0 q^{9}\) \(+O(q^{10})\) \(q\)\(-74.9776 q^{2}\) \(+243.000 q^{3}\) \(+3573.65 q^{4}\) \(+3125.00 q^{5}\) \(-18219.6 q^{6}\) \(-63061.5 q^{7}\) \(-114389. q^{8}\) \(+59049.0 q^{9}\) \(-234305. q^{10}\) \(+256618. q^{11}\) \(+868396. q^{12}\) \(-465623. q^{13}\) \(+4.72820e6 q^{14}\) \(+759375. q^{15}\) \(+1.25782e6 q^{16}\) \(+1.08463e7 q^{17}\) \(-4.42735e6 q^{18}\) \(+9.38335e6 q^{19}\) \(+1.11676e7 q^{20}\) \(-1.53239e7 q^{21}\) \(-1.92406e7 q^{22}\) \(-2.41377e7 q^{23}\) \(-2.77966e7 q^{24}\) \(+9.76562e6 q^{25}\) \(+3.49113e7 q^{26}\) \(+1.43489e7 q^{27}\) \(-2.25359e8 q^{28}\) \(+2.07639e8 q^{29}\) \(-5.69361e7 q^{30}\) \(+2.06141e8 q^{31}\) \(+1.39961e8 q^{32}\) \(+6.23583e7 q^{33}\) \(-8.13230e8 q^{34}\) \(-1.97067e8 q^{35}\) \(+2.11020e8 q^{36}\) \(+2.18529e8 q^{37}\) \(-7.03542e8 q^{38}\) \(-1.13146e8 q^{39}\) \(-3.57467e8 q^{40}\) \(+8.54426e8 q^{41}\) \(+1.14895e9 q^{42}\) \(-2.70952e8 q^{43}\) \(+9.17063e8 q^{44}\) \(+1.84528e8 q^{45}\) \(+1.80979e9 q^{46}\) \(-2.09625e9 q^{47}\) \(+3.05650e8 q^{48}\) \(+1.99942e9 q^{49}\) \(-7.32204e8 q^{50}\) \(+2.63565e9 q^{51}\) \(-1.66397e9 q^{52}\) \(-1.20106e9 q^{53}\) \(-1.07585e9 q^{54}\) \(+8.01933e8 q^{55}\) \(+7.21356e9 q^{56}\) \(+2.28015e9 q^{57}\) \(-1.55683e10 q^{58}\) \(+6.04665e9 q^{59}\) \(+2.71374e9 q^{60}\) \(-1.28841e10 q^{61}\) \(-1.54560e10 q^{62}\) \(-3.72372e9 q^{63}\) \(-1.30700e10 q^{64}\) \(-1.45507e9 q^{65}\) \(-4.67548e9 q^{66}\) \(+6.01919e9 q^{67}\) \(+3.87608e10 q^{68}\) \(-5.86547e9 q^{69}\) \(+1.47756e10 q^{70}\) \(+7.99639e9 q^{71}\) \(-6.75458e9 q^{72}\) \(+3.23383e10 q^{73}\) \(-1.63848e10 q^{74}\) \(+2.37305e9 q^{75}\) \(+3.35328e10 q^{76}\) \(-1.61827e10 q^{77}\) \(+8.48344e9 q^{78}\) \(+3.84151e9 q^{79}\) \(+3.93068e9 q^{80}\) \(+3.48678e9 q^{81}\) \(-6.40628e10 q^{82}\) \(-1.29073e9 q^{83}\) \(-5.47623e10 q^{84}\) \(+3.38947e10 q^{85}\) \(+2.03154e10 q^{86}\) \(+5.04563e10 q^{87}\) \(-2.93544e10 q^{88}\) \(-6.96454e10 q^{89}\) \(-1.38355e10 q^{90}\) \(+2.93628e10 q^{91}\) \(-8.62597e10 q^{92}\) \(+5.00923e10 q^{93}\) \(+1.57172e11 q^{94}\) \(+2.93230e10 q^{95}\) \(+3.40106e10 q^{96}\) \(+2.33370e10 q^{97}\) \(-1.49912e11 q^{98}\) \(+1.51531e10 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 729q^{3} \) \(\mathstrut +\mathstrut 4757q^{4} \) \(\mathstrut +\mathstrut 9375q^{5} \) \(\mathstrut -\mathstrut 243q^{6} \) \(\mathstrut -\mathstrut 14608q^{7} \) \(\mathstrut -\mathstrut 33999q^{8} \) \(\mathstrut +\mathstrut 177147q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 729q^{3} \) \(\mathstrut +\mathstrut 4757q^{4} \) \(\mathstrut +\mathstrut 9375q^{5} \) \(\mathstrut -\mathstrut 243q^{6} \) \(\mathstrut -\mathstrut 14608q^{7} \) \(\mathstrut -\mathstrut 33999q^{8} \) \(\mathstrut +\mathstrut 177147q^{9} \) \(\mathstrut -\mathstrut 3125q^{10} \) \(\mathstrut +\mathstrut 540620q^{11} \) \(\mathstrut +\mathstrut 1155951q^{12} \) \(\mathstrut +\mathstrut 840970q^{13} \) \(\mathstrut +\mathstrut 5432712q^{14} \) \(\mathstrut +\mathstrut 2278125q^{15} \) \(\mathstrut +\mathstrut 5062961q^{16} \) \(\mathstrut +\mathstrut 15165038q^{17} \) \(\mathstrut -\mathstrut 59049q^{18} \) \(\mathstrut +\mathstrut 17743756q^{19} \) \(\mathstrut +\mathstrut 14865625q^{20} \) \(\mathstrut -\mathstrut 3549744q^{21} \) \(\mathstrut +\mathstrut 11176076q^{22} \) \(\mathstrut -\mathstrut 28140816q^{23} \) \(\mathstrut -\mathstrut 8261757q^{24} \) \(\mathstrut +\mathstrut 29296875q^{25} \) \(\mathstrut -\mathstrut 52021894q^{26} \) \(\mathstrut +\mathstrut 43046721q^{27} \) \(\mathstrut -\mathstrut 277157944q^{28} \) \(\mathstrut -\mathstrut 67382798q^{29} \) \(\mathstrut -\mathstrut 759375q^{30} \) \(\mathstrut -\mathstrut 206919496q^{31} \) \(\mathstrut -\mathstrut 46592663q^{32} \) \(\mathstrut +\mathstrut 131370660q^{33} \) \(\mathstrut -\mathstrut 1230469666q^{34} \) \(\mathstrut -\mathstrut 45650000q^{35} \) \(\mathstrut +\mathstrut 280896093q^{36} \) \(\mathstrut -\mathstrut 318337278q^{37} \) \(\mathstrut +\mathstrut 653190692q^{38} \) \(\mathstrut +\mathstrut 204355710q^{39} \) \(\mathstrut -\mathstrut 106246875q^{40} \) \(\mathstrut +\mathstrut 2110085854q^{41} \) \(\mathstrut +\mathstrut 1320149016q^{42} \) \(\mathstrut +\mathstrut 418259692q^{43} \) \(\mathstrut +\mathstrut 2558131108q^{44} \) \(\mathstrut +\mathstrut 553584375q^{45} \) \(\mathstrut -\mathstrut 137169096q^{46} \) \(\mathstrut -\mathstrut 1599668584q^{47} \) \(\mathstrut +\mathstrut 1230299523q^{48} \) \(\mathstrut -\mathstrut 316107077q^{49} \) \(\mathstrut -\mathstrut 9765625q^{50} \) \(\mathstrut +\mathstrut 3685104234q^{51} \) \(\mathstrut -\mathstrut 10897289202q^{52} \) \(\mathstrut +\mathstrut 4489142234q^{53} \) \(\mathstrut -\mathstrut 14348907q^{54} \) \(\mathstrut +\mathstrut 1689437500q^{55} \) \(\mathstrut +\mathstrut 7768845960q^{56} \) \(\mathstrut +\mathstrut 4311732708q^{57} \) \(\mathstrut -\mathstrut 24168830726q^{58} \) \(\mathstrut +\mathstrut 11102167484q^{59} \) \(\mathstrut +\mathstrut 3612346875q^{60} \) \(\mathstrut -\mathstrut 3568120958q^{61} \) \(\mathstrut -\mathstrut 35509109136q^{62} \) \(\mathstrut -\mathstrut 862587792q^{63} \) \(\mathstrut -\mathstrut 35608208271q^{64} \) \(\mathstrut +\mathstrut 2628031250q^{65} \) \(\mathstrut +\mathstrut 2715786468q^{66} \) \(\mathstrut +\mathstrut 2229942788q^{67} \) \(\mathstrut -\mathstrut 1367872838q^{68} \) \(\mathstrut -\mathstrut 6838218288q^{69} \) \(\mathstrut +\mathstrut 16977225000q^{70} \) \(\mathstrut +\mathstrut 49842766696q^{71} \) \(\mathstrut -\mathstrut 2007606951q^{72} \) \(\mathstrut +\mathstrut 40752219934q^{73} \) \(\mathstrut -\mathstrut 37519971278q^{74} \) \(\mathstrut +\mathstrut 7119140625q^{75} \) \(\mathstrut +\mathstrut 115970329116q^{76} \) \(\mathstrut -\mathstrut 17819224896q^{77} \) \(\mathstrut -\mathstrut 12641320242q^{78} \) \(\mathstrut +\mathstrut 113159960q^{79} \) \(\mathstrut +\mathstrut 15821753125q^{80} \) \(\mathstrut +\mathstrut 10460353203q^{81} \) \(\mathstrut -\mathstrut 30171431066q^{82} \) \(\mathstrut +\mathstrut 6259660308q^{83} \) \(\mathstrut -\mathstrut 67349380392q^{84} \) \(\mathstrut +\mathstrut 47390743750q^{85} \) \(\mathstrut +\mathstrut 114296127740q^{86} \) \(\mathstrut -\mathstrut 16374019914q^{87} \) \(\mathstrut +\mathstrut 7548672276q^{88} \) \(\mathstrut -\mathstrut 59972401554q^{89} \) \(\mathstrut -\mathstrut 184528125q^{90} \) \(\mathstrut +\mathstrut 118873361824q^{91} \) \(\mathstrut -\mathstrut 221705928648q^{92} \) \(\mathstrut -\mathstrut 50281437528q^{93} \) \(\mathstrut +\mathstrut 92816682800q^{94} \) \(\mathstrut +\mathstrut 55449237500q^{95} \) \(\mathstrut -\mathstrut 11322017109q^{96} \) \(\mathstrut -\mathstrut 207831285882q^{97} \) \(\mathstrut -\mathstrut 288264739625q^{98} \) \(\mathstrut +\mathstrut 31923070380q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −74.9776 −1.65679 −0.828394 0.560146i \(-0.810745\pi\)
−0.828394 + 0.560146i \(0.810745\pi\)
\(3\) 243.000 0.577350
\(4\) 3573.65 1.74494
\(5\) 3125.00 0.447214
\(6\) −18219.6 −0.956547
\(7\) −63061.5 −1.41816 −0.709079 0.705129i \(-0.750889\pi\)
−0.709079 + 0.705129i \(0.750889\pi\)
\(8\) −114389. −1.23421
\(9\) 59049.0 0.333333
\(10\) −234305. −0.740938
\(11\) 256618. 0.480428 0.240214 0.970720i \(-0.422782\pi\)
0.240214 + 0.970720i \(0.422782\pi\)
\(12\) 868396. 1.00744
\(13\) −465623. −0.347813 −0.173906 0.984762i \(-0.555639\pi\)
−0.173906 + 0.984762i \(0.555639\pi\)
\(14\) 4.72820e6 2.34959
\(15\) 759375. 0.258199
\(16\) 1.25782e6 0.299887
\(17\) 1.08463e7 1.85273 0.926366 0.376626i \(-0.122916\pi\)
0.926366 + 0.376626i \(0.122916\pi\)
\(18\) −4.42735e6 −0.552262
\(19\) 9.38335e6 0.869387 0.434694 0.900578i \(-0.356857\pi\)
0.434694 + 0.900578i \(0.356857\pi\)
\(20\) 1.11676e7 0.780363
\(21\) −1.53239e7 −0.818774
\(22\) −1.92406e7 −0.795967
\(23\) −2.41377e7 −0.781976 −0.390988 0.920396i \(-0.627867\pi\)
−0.390988 + 0.920396i \(0.627867\pi\)
\(24\) −2.77966e7 −0.712574
\(25\) 9.76562e6 0.200000
\(26\) 3.49113e7 0.576252
\(27\) 1.43489e7 0.192450
\(28\) −2.25359e8 −2.47461
\(29\) 2.07639e8 1.87984 0.939918 0.341402i \(-0.110902\pi\)
0.939918 + 0.341402i \(0.110902\pi\)
\(30\) −5.69361e7 −0.427781
\(31\) 2.06141e8 1.29323 0.646615 0.762817i \(-0.276184\pi\)
0.646615 + 0.762817i \(0.276184\pi\)
\(32\) 1.39961e8 0.737366
\(33\) 6.23583e7 0.277375
\(34\) −8.13230e8 −3.06958
\(35\) −1.97067e8 −0.634220
\(36\) 2.11020e8 0.581648
\(37\) 2.18529e8 0.518082 0.259041 0.965866i \(-0.416593\pi\)
0.259041 + 0.965866i \(0.416593\pi\)
\(38\) −7.03542e8 −1.44039
\(39\) −1.13146e8 −0.200810
\(40\) −3.57467e8 −0.551958
\(41\) 8.54426e8 1.15176 0.575882 0.817533i \(-0.304659\pi\)
0.575882 + 0.817533i \(0.304659\pi\)
\(42\) 1.14895e9 1.35654
\(43\) −2.70952e8 −0.281071 −0.140536 0.990076i \(-0.544882\pi\)
−0.140536 + 0.990076i \(0.544882\pi\)
\(44\) 9.17063e8 0.838320
\(45\) 1.84528e8 0.149071
\(46\) 1.80979e9 1.29557
\(47\) −2.09625e9 −1.33323 −0.666616 0.745401i \(-0.732258\pi\)
−0.666616 + 0.745401i \(0.732258\pi\)
\(48\) 3.05650e8 0.173140
\(49\) 1.99942e9 1.01117
\(50\) −7.32204e8 −0.331357
\(51\) 2.63565e9 1.06967
\(52\) −1.66397e9 −0.606914
\(53\) −1.20106e9 −0.394501 −0.197251 0.980353i \(-0.563201\pi\)
−0.197251 + 0.980353i \(0.563201\pi\)
\(54\) −1.07585e9 −0.318849
\(55\) 8.01933e8 0.214854
\(56\) 7.21356e9 1.75031
\(57\) 2.28015e9 0.501941
\(58\) −1.55683e10 −3.11449
\(59\) 6.04665e9 1.10111 0.550553 0.834800i \(-0.314417\pi\)
0.550553 + 0.834800i \(0.314417\pi\)
\(60\) 2.71374e9 0.450543
\(61\) −1.28841e10 −1.95316 −0.976581 0.215148i \(-0.930977\pi\)
−0.976581 + 0.215148i \(0.930977\pi\)
\(62\) −1.54560e10 −2.14261
\(63\) −3.72372e9 −0.472720
\(64\) −1.30700e10 −1.52155
\(65\) −1.45507e9 −0.155547
\(66\) −4.67548e9 −0.459552
\(67\) 6.01919e9 0.544661 0.272331 0.962204i \(-0.412206\pi\)
0.272331 + 0.962204i \(0.412206\pi\)
\(68\) 3.87608e10 3.23291
\(69\) −5.86547e9 −0.451474
\(70\) 1.47756e10 1.05077
\(71\) 7.99639e9 0.525984 0.262992 0.964798i \(-0.415291\pi\)
0.262992 + 0.964798i \(0.415291\pi\)
\(72\) −6.75458e9 −0.411405
\(73\) 3.23383e10 1.82575 0.912876 0.408236i \(-0.133856\pi\)
0.912876 + 0.408236i \(0.133856\pi\)
\(74\) −1.63848e10 −0.858352
\(75\) 2.37305e9 0.115470
\(76\) 3.35328e10 1.51703
\(77\) −1.61827e10 −0.681323
\(78\) 8.48344e9 0.332699
\(79\) 3.84151e9 0.140460 0.0702300 0.997531i \(-0.477627\pi\)
0.0702300 + 0.997531i \(0.477627\pi\)
\(80\) 3.93068e9 0.134114
\(81\) 3.48678e9 0.111111
\(82\) −6.40628e10 −1.90823
\(83\) −1.29073e9 −0.0359671 −0.0179836 0.999838i \(-0.505725\pi\)
−0.0179836 + 0.999838i \(0.505725\pi\)
\(84\) −5.47623e10 −1.42872
\(85\) 3.38947e10 0.828567
\(86\) 2.03154e10 0.465675
\(87\) 5.04563e10 1.08532
\(88\) −2.93544e10 −0.592951
\(89\) −6.96454e10 −1.32205 −0.661024 0.750365i \(-0.729878\pi\)
−0.661024 + 0.750365i \(0.729878\pi\)
\(90\) −1.38355e10 −0.246979
\(91\) 2.93628e10 0.493254
\(92\) −8.62597e10 −1.36450
\(93\) 5.00923e10 0.746646
\(94\) 1.57172e11 2.20888
\(95\) 2.93230e10 0.388802
\(96\) 3.40106e10 0.425718
\(97\) 2.33370e10 0.275931 0.137965 0.990437i \(-0.455944\pi\)
0.137965 + 0.990437i \(0.455944\pi\)
\(98\) −1.49912e11 −1.67530
\(99\) 1.51531e10 0.160143
\(100\) 3.48989e10 0.348989
\(101\) −6.21623e10 −0.588518 −0.294259 0.955726i \(-0.595073\pi\)
−0.294259 + 0.955726i \(0.595073\pi\)
\(102\) −1.97615e11 −1.77222
\(103\) −1.26451e11 −1.07478 −0.537389 0.843334i \(-0.680589\pi\)
−0.537389 + 0.843334i \(0.680589\pi\)
\(104\) 5.32623e10 0.429276
\(105\) −4.78873e10 −0.366167
\(106\) 9.00529e10 0.653605
\(107\) 6.79291e10 0.468215 0.234107 0.972211i \(-0.424783\pi\)
0.234107 + 0.972211i \(0.424783\pi\)
\(108\) 5.12779e10 0.335815
\(109\) 1.15778e11 0.720746 0.360373 0.932808i \(-0.382649\pi\)
0.360373 + 0.932808i \(0.382649\pi\)
\(110\) −6.01270e10 −0.355967
\(111\) 5.31024e10 0.299115
\(112\) −7.93198e10 −0.425287
\(113\) −6.09916e10 −0.311414 −0.155707 0.987803i \(-0.549766\pi\)
−0.155707 + 0.987803i \(0.549766\pi\)
\(114\) −1.70961e11 −0.831609
\(115\) −7.54304e10 −0.349710
\(116\) 7.42028e11 3.28021
\(117\) −2.74945e10 −0.115938
\(118\) −4.53364e11 −1.82430
\(119\) −6.83983e11 −2.62747
\(120\) −8.68644e10 −0.318673
\(121\) −2.19459e11 −0.769189
\(122\) 9.66016e11 3.23598
\(123\) 2.07626e11 0.664971
\(124\) 7.36676e11 2.25661
\(125\) 3.05176e10 0.0894427
\(126\) 2.79196e11 0.783196
\(127\) −1.77862e11 −0.477707 −0.238853 0.971056i \(-0.576772\pi\)
−0.238853 + 0.971056i \(0.576772\pi\)
\(128\) 6.93315e11 1.78351
\(129\) −6.58414e10 −0.162277
\(130\) 1.09098e11 0.257708
\(131\) 4.59970e10 0.104169 0.0520843 0.998643i \(-0.483414\pi\)
0.0520843 + 0.998643i \(0.483414\pi\)
\(132\) 2.22846e11 0.484004
\(133\) −5.91728e11 −1.23293
\(134\) −4.51304e11 −0.902388
\(135\) 4.48403e10 0.0860663
\(136\) −1.24070e12 −2.28667
\(137\) −4.98200e10 −0.0881943 −0.0440972 0.999027i \(-0.514041\pi\)
−0.0440972 + 0.999027i \(0.514041\pi\)
\(138\) 4.39779e11 0.747997
\(139\) 1.80909e11 0.295718 0.147859 0.989008i \(-0.452762\pi\)
0.147859 + 0.989008i \(0.452762\pi\)
\(140\) −7.04248e11 −1.10668
\(141\) −5.09390e11 −0.769742
\(142\) −5.99550e11 −0.871444
\(143\) −1.19487e11 −0.167099
\(144\) 7.42728e10 0.0999623
\(145\) 6.48872e11 0.840688
\(146\) −2.42465e12 −3.02488
\(147\) 4.85860e11 0.583802
\(148\) 7.80944e11 0.904025
\(149\) 5.43337e11 0.606101 0.303051 0.952974i \(-0.401995\pi\)
0.303051 + 0.952974i \(0.401995\pi\)
\(150\) −1.77925e11 −0.191309
\(151\) −1.19411e12 −1.23786 −0.618930 0.785446i \(-0.712434\pi\)
−0.618930 + 0.785446i \(0.712434\pi\)
\(152\) −1.07336e12 −1.07301
\(153\) 6.40463e11 0.617577
\(154\) 1.21334e12 1.12881
\(155\) 6.44191e11 0.578350
\(156\) −4.04345e11 −0.350402
\(157\) 2.21075e12 1.84965 0.924827 0.380387i \(-0.124209\pi\)
0.924827 + 0.380387i \(0.124209\pi\)
\(158\) −2.88027e11 −0.232712
\(159\) −2.91858e11 −0.227765
\(160\) 4.37379e11 0.329760
\(161\) 1.52216e12 1.10897
\(162\) −2.61431e11 −0.184087
\(163\) −1.38866e12 −0.945291 −0.472645 0.881253i \(-0.656701\pi\)
−0.472645 + 0.881253i \(0.656701\pi\)
\(164\) 3.05342e12 2.00976
\(165\) 1.94870e11 0.124046
\(166\) 9.67758e10 0.0595899
\(167\) 7.93403e11 0.472665 0.236332 0.971672i \(-0.424055\pi\)
0.236332 + 0.971672i \(0.424055\pi\)
\(168\) 1.75290e12 1.01054
\(169\) −1.57536e12 −0.879026
\(170\) −2.54134e12 −1.37276
\(171\) 5.54078e11 0.289796
\(172\) −9.68288e11 −0.490454
\(173\) 2.86863e12 1.40741 0.703706 0.710491i \(-0.251527\pi\)
0.703706 + 0.710491i \(0.251527\pi\)
\(174\) −3.78309e12 −1.79815
\(175\) −6.15835e11 −0.283632
\(176\) 3.22779e11 0.144074
\(177\) 1.46934e12 0.635724
\(178\) 5.22185e12 2.19035
\(179\) 6.99004e10 0.0284307 0.0142154 0.999899i \(-0.495475\pi\)
0.0142154 + 0.999899i \(0.495475\pi\)
\(180\) 6.59438e11 0.260121
\(181\) −2.96087e12 −1.13289 −0.566445 0.824100i \(-0.691682\pi\)
−0.566445 + 0.824100i \(0.691682\pi\)
\(182\) −2.20156e12 −0.817217
\(183\) −3.13083e12 −1.12766
\(184\) 2.76110e12 0.965126
\(185\) 6.82902e11 0.231693
\(186\) −3.75580e12 −1.23703
\(187\) 2.78336e12 0.890103
\(188\) −7.49127e12 −2.32642
\(189\) −9.04863e11 −0.272925
\(190\) −2.19857e12 −0.644162
\(191\) 4.52689e12 1.28860 0.644298 0.764775i \(-0.277150\pi\)
0.644298 + 0.764775i \(0.277150\pi\)
\(192\) −3.17600e12 −0.878465
\(193\) −1.04014e12 −0.279593 −0.139796 0.990180i \(-0.544645\pi\)
−0.139796 + 0.990180i \(0.544645\pi\)
\(194\) −1.74975e12 −0.457159
\(195\) −3.53582e11 −0.0898049
\(196\) 7.14523e12 1.76444
\(197\) 5.42576e12 1.30285 0.651427 0.758711i \(-0.274170\pi\)
0.651427 + 0.758711i \(0.274170\pi\)
\(198\) −1.13614e12 −0.265322
\(199\) −7.72708e12 −1.75519 −0.877593 0.479406i \(-0.840852\pi\)
−0.877593 + 0.479406i \(0.840852\pi\)
\(200\) −1.11708e12 −0.246843
\(201\) 1.46266e12 0.314460
\(202\) 4.66078e12 0.975049
\(203\) −1.30940e13 −2.66590
\(204\) 9.41888e12 1.86652
\(205\) 2.67008e12 0.515084
\(206\) 9.48103e12 1.78068
\(207\) −1.42531e12 −0.260659
\(208\) −5.85668e11 −0.104305
\(209\) 2.40794e12 0.417678
\(210\) 3.59048e12 0.606661
\(211\) 2.66403e12 0.438517 0.219258 0.975667i \(-0.429636\pi\)
0.219258 + 0.975667i \(0.429636\pi\)
\(212\) −4.29217e12 −0.688383
\(213\) 1.94312e12 0.303677
\(214\) −5.09317e12 −0.775733
\(215\) −8.46726e11 −0.125699
\(216\) −1.64136e12 −0.237525
\(217\) −1.29996e13 −1.83400
\(218\) −8.68080e12 −1.19412
\(219\) 7.85822e12 1.05410
\(220\) 2.86582e12 0.374908
\(221\) −5.05028e12 −0.644404
\(222\) −3.98149e12 −0.495570
\(223\) 1.73148e12 0.210252 0.105126 0.994459i \(-0.466475\pi\)
0.105126 + 0.994459i \(0.466475\pi\)
\(224\) −8.82616e12 −1.04570
\(225\) 5.76650e11 0.0666667
\(226\) 4.57301e12 0.515948
\(227\) 8.49255e12 0.935181 0.467590 0.883945i \(-0.345122\pi\)
0.467590 + 0.883945i \(0.345122\pi\)
\(228\) 8.14847e12 0.875859
\(229\) 7.60395e12 0.797892 0.398946 0.916974i \(-0.369376\pi\)
0.398946 + 0.916974i \(0.369376\pi\)
\(230\) 5.65560e12 0.579396
\(231\) −3.93240e12 −0.393362
\(232\) −2.37517e13 −2.32012
\(233\) 1.09237e13 1.04210 0.521051 0.853525i \(-0.325540\pi\)
0.521051 + 0.853525i \(0.325540\pi\)
\(234\) 2.06148e12 0.192084
\(235\) −6.55079e12 −0.596240
\(236\) 2.16086e13 1.92137
\(237\) 9.33486e11 0.0810946
\(238\) 5.12835e13 4.35315
\(239\) 5.91005e12 0.490233 0.245117 0.969494i \(-0.421174\pi\)
0.245117 + 0.969494i \(0.421174\pi\)
\(240\) 9.55155e11 0.0774305
\(241\) 2.58394e12 0.204734 0.102367 0.994747i \(-0.467358\pi\)
0.102367 + 0.994747i \(0.467358\pi\)
\(242\) 1.64545e13 1.27438
\(243\) 8.47289e11 0.0641500
\(244\) −4.60431e13 −3.40816
\(245\) 6.24820e12 0.452211
\(246\) −1.55673e13 −1.10172
\(247\) −4.36910e12 −0.302384
\(248\) −2.35804e13 −1.59612
\(249\) −3.13647e11 −0.0207656
\(250\) −2.28814e12 −0.148188
\(251\) −1.89161e13 −1.19847 −0.599234 0.800574i \(-0.704528\pi\)
−0.599234 + 0.800574i \(0.704528\pi\)
\(252\) −1.33072e13 −0.824870
\(253\) −6.19419e12 −0.375683
\(254\) 1.33356e13 0.791459
\(255\) 8.23641e12 0.478373
\(256\) −2.52158e13 −1.43335
\(257\) −1.55673e13 −0.866125 −0.433062 0.901364i \(-0.642567\pi\)
−0.433062 + 0.901364i \(0.642567\pi\)
\(258\) 4.93664e12 0.268858
\(259\) −1.37807e13 −0.734723
\(260\) −5.19991e12 −0.271420
\(261\) 1.22609e13 0.626612
\(262\) −3.44874e12 −0.172585
\(263\) −2.33801e13 −1.14575 −0.572874 0.819643i \(-0.694172\pi\)
−0.572874 + 0.819643i \(0.694172\pi\)
\(264\) −7.13312e12 −0.342340
\(265\) −3.75332e12 −0.176426
\(266\) 4.43664e13 2.04270
\(267\) −1.69238e13 −0.763285
\(268\) 2.15104e13 0.950403
\(269\) 1.52689e13 0.660953 0.330476 0.943814i \(-0.392791\pi\)
0.330476 + 0.943814i \(0.392791\pi\)
\(270\) −3.36202e12 −0.142594
\(271\) −2.59439e13 −1.07821 −0.539105 0.842239i \(-0.681237\pi\)
−0.539105 + 0.842239i \(0.681237\pi\)
\(272\) 1.36427e13 0.555610
\(273\) 7.13517e12 0.284780
\(274\) 3.73539e12 0.146119
\(275\) 2.50604e12 0.0960855
\(276\) −2.09611e13 −0.787797
\(277\) 2.84140e13 1.04687 0.523436 0.852065i \(-0.324650\pi\)
0.523436 + 0.852065i \(0.324650\pi\)
\(278\) −1.35641e13 −0.489942
\(279\) 1.21724e13 0.431076
\(280\) 2.25424e13 0.782764
\(281\) 1.47578e12 0.0502500 0.0251250 0.999684i \(-0.492002\pi\)
0.0251250 + 0.999684i \(0.492002\pi\)
\(282\) 3.81928e13 1.27530
\(283\) −1.67811e13 −0.549533 −0.274767 0.961511i \(-0.588601\pi\)
−0.274767 + 0.961511i \(0.588601\pi\)
\(284\) 2.85763e13 0.917814
\(285\) 7.12548e12 0.224475
\(286\) 8.95888e12 0.276847
\(287\) −5.38814e13 −1.63338
\(288\) 8.26457e12 0.245789
\(289\) 8.33702e13 2.43261
\(290\) −4.86509e13 −1.39284
\(291\) 5.67089e12 0.159309
\(292\) 1.15566e14 3.18584
\(293\) −2.95564e13 −0.799612 −0.399806 0.916600i \(-0.630923\pi\)
−0.399806 + 0.916600i \(0.630923\pi\)
\(294\) −3.64286e13 −0.967236
\(295\) 1.88958e13 0.492429
\(296\) −2.49973e13 −0.639425
\(297\) 3.68219e12 0.0924584
\(298\) −4.07382e13 −1.00418
\(299\) 1.12391e13 0.271981
\(300\) 8.48043e12 0.201489
\(301\) 1.70867e13 0.398604
\(302\) 8.95317e13 2.05087
\(303\) −1.51054e13 −0.339781
\(304\) 1.18025e13 0.260718
\(305\) −4.02627e13 −0.873481
\(306\) −4.80204e13 −1.02319
\(307\) −2.76815e13 −0.579333 −0.289666 0.957128i \(-0.593544\pi\)
−0.289666 + 0.957128i \(0.593544\pi\)
\(308\) −5.78314e13 −1.18887
\(309\) −3.07277e13 −0.620523
\(310\) −4.82999e13 −0.958202
\(311\) −2.42772e12 −0.0473169 −0.0236585 0.999720i \(-0.507531\pi\)
−0.0236585 + 0.999720i \(0.507531\pi\)
\(312\) 1.29427e13 0.247842
\(313\) 2.50845e13 0.471967 0.235984 0.971757i \(-0.424169\pi\)
0.235984 + 0.971757i \(0.424169\pi\)
\(314\) −1.65756e14 −3.06448
\(315\) −1.16366e13 −0.211407
\(316\) 1.37282e13 0.245095
\(317\) 1.42145e11 0.00249406 0.00124703 0.999999i \(-0.499603\pi\)
0.00124703 + 0.999999i \(0.499603\pi\)
\(318\) 2.18828e13 0.377359
\(319\) 5.32840e13 0.903125
\(320\) −4.08437e13 −0.680456
\(321\) 1.65068e13 0.270324
\(322\) −1.14128e14 −1.83732
\(323\) 1.01775e14 1.61074
\(324\) 1.24605e13 0.193883
\(325\) −4.54709e12 −0.0695626
\(326\) 1.04119e14 1.56615
\(327\) 2.81342e13 0.416123
\(328\) −9.77373e13 −1.42152
\(329\) 1.32193e14 1.89073
\(330\) −1.46109e13 −0.205518
\(331\) −9.45872e13 −1.30851 −0.654257 0.756272i \(-0.727018\pi\)
−0.654257 + 0.756272i \(0.727018\pi\)
\(332\) −4.61261e12 −0.0627606
\(333\) 1.29039e13 0.172694
\(334\) −5.94875e13 −0.783105
\(335\) 1.88100e13 0.243580
\(336\) −1.92747e13 −0.245540
\(337\) 8.93839e12 0.112020 0.0560099 0.998430i \(-0.482162\pi\)
0.0560099 + 0.998430i \(0.482162\pi\)
\(338\) 1.18116e14 1.45636
\(339\) −1.48210e13 −0.179795
\(340\) 1.21128e14 1.44580
\(341\) 5.28996e13 0.621303
\(342\) −4.15434e13 −0.480130
\(343\) −1.39339e12 −0.0158473
\(344\) 3.09941e13 0.346902
\(345\) −1.83296e13 −0.201905
\(346\) −2.15083e14 −2.33178
\(347\) −1.83665e13 −0.195981 −0.0979907 0.995187i \(-0.531242\pi\)
−0.0979907 + 0.995187i \(0.531242\pi\)
\(348\) 1.80313e14 1.89383
\(349\) 1.20668e14 1.24754 0.623769 0.781609i \(-0.285601\pi\)
0.623769 + 0.781609i \(0.285601\pi\)
\(350\) 4.61738e13 0.469918
\(351\) −6.68117e12 −0.0669366
\(352\) 3.59166e13 0.354251
\(353\) −2.62988e13 −0.255373 −0.127687 0.991815i \(-0.540755\pi\)
−0.127687 + 0.991815i \(0.540755\pi\)
\(354\) −1.10167e14 −1.05326
\(355\) 2.49887e13 0.235227
\(356\) −2.48888e14 −2.30690
\(357\) −1.66208e14 −1.51697
\(358\) −5.24097e12 −0.0471037
\(359\) −7.23499e13 −0.640352 −0.320176 0.947358i \(-0.603742\pi\)
−0.320176 + 0.947358i \(0.603742\pi\)
\(360\) −2.11081e13 −0.183986
\(361\) −2.84430e13 −0.244166
\(362\) 2.21999e14 1.87696
\(363\) −5.33285e13 −0.444092
\(364\) 1.04932e14 0.860700
\(365\) 1.01057e14 0.816501
\(366\) 2.34742e14 1.86829
\(367\) −6.60414e13 −0.517789 −0.258894 0.965906i \(-0.583358\pi\)
−0.258894 + 0.965906i \(0.583358\pi\)
\(368\) −3.03609e13 −0.234504
\(369\) 5.04530e13 0.383921
\(370\) −5.12023e13 −0.383867
\(371\) 7.57408e13 0.559466
\(372\) 1.79012e14 1.30286
\(373\) −3.72124e13 −0.266864 −0.133432 0.991058i \(-0.542600\pi\)
−0.133432 + 0.991058i \(0.542600\pi\)
\(374\) −2.08690e14 −1.47471
\(375\) 7.41577e12 0.0516398
\(376\) 2.39789e14 1.64549
\(377\) −9.66813e13 −0.653831
\(378\) 6.78445e13 0.452178
\(379\) 1.91105e14 1.25533 0.627664 0.778485i \(-0.284011\pi\)
0.627664 + 0.778485i \(0.284011\pi\)
\(380\) 1.04790e14 0.678437
\(381\) −4.32203e13 −0.275804
\(382\) −3.39416e14 −2.13493
\(383\) −2.38924e14 −1.48138 −0.740689 0.671848i \(-0.765501\pi\)
−0.740689 + 0.671848i \(0.765501\pi\)
\(384\) 1.68476e14 1.02971
\(385\) −5.05710e13 −0.304697
\(386\) 7.79871e13 0.463226
\(387\) −1.59995e13 −0.0936904
\(388\) 8.33981e13 0.481484
\(389\) −9.94459e13 −0.566062 −0.283031 0.959111i \(-0.591340\pi\)
−0.283031 + 0.959111i \(0.591340\pi\)
\(390\) 2.65108e13 0.148788
\(391\) −2.61805e14 −1.44879
\(392\) −2.28713e14 −1.24801
\(393\) 1.11773e13 0.0601418
\(394\) −4.06810e14 −2.15855
\(395\) 1.20047e13 0.0628156
\(396\) 5.41517e13 0.279440
\(397\) 2.55979e14 1.30274 0.651369 0.758762i \(-0.274195\pi\)
0.651369 + 0.758762i \(0.274195\pi\)
\(398\) 5.79358e14 2.90797
\(399\) −1.43790e14 −0.711832
\(400\) 1.22834e13 0.0599774
\(401\) 3.75203e13 0.180706 0.0903529 0.995910i \(-0.471201\pi\)
0.0903529 + 0.995910i \(0.471201\pi\)
\(402\) −1.09667e14 −0.520994
\(403\) −9.59840e13 −0.449802
\(404\) −2.22146e14 −1.02693
\(405\) 1.08962e13 0.0496904
\(406\) 9.81758e14 4.41684
\(407\) 5.60784e13 0.248901
\(408\) −3.01490e14 −1.32021
\(409\) −1.93512e14 −0.836044 −0.418022 0.908437i \(-0.637276\pi\)
−0.418022 + 0.908437i \(0.637276\pi\)
\(410\) −2.00196e14 −0.853385
\(411\) −1.21063e13 −0.0509190
\(412\) −4.51892e14 −1.87543
\(413\) −3.81311e14 −1.56154
\(414\) 1.06866e14 0.431856
\(415\) −4.03353e12 −0.0160850
\(416\) −6.51691e13 −0.256465
\(417\) 4.39608e13 0.170733
\(418\) −1.80542e14 −0.692003
\(419\) −1.29993e14 −0.491748 −0.245874 0.969302i \(-0.579075\pi\)
−0.245874 + 0.969302i \(0.579075\pi\)
\(420\) −1.71132e14 −0.638941
\(421\) −8.72362e13 −0.321474 −0.160737 0.986997i \(-0.551387\pi\)
−0.160737 + 0.986997i \(0.551387\pi\)
\(422\) −1.99743e14 −0.726529
\(423\) −1.23782e14 −0.444411
\(424\) 1.37389e14 0.486899
\(425\) 1.05921e14 0.370546
\(426\) −1.45691e14 −0.503129
\(427\) 8.12487e14 2.76990
\(428\) 2.42755e14 0.817009
\(429\) −2.90354e13 −0.0964746
\(430\) 6.34855e13 0.208256
\(431\) 2.21393e14 0.717033 0.358516 0.933523i \(-0.383283\pi\)
0.358516 + 0.933523i \(0.383283\pi\)
\(432\) 1.80483e13 0.0577133
\(433\) −4.37191e14 −1.38035 −0.690173 0.723644i \(-0.742466\pi\)
−0.690173 + 0.723644i \(0.742466\pi\)
\(434\) 9.74677e14 3.03856
\(435\) 1.57676e14 0.485371
\(436\) 4.13751e14 1.25766
\(437\) −2.26493e14 −0.679840
\(438\) −5.89191e14 −1.74642
\(439\) 1.77794e14 0.520430 0.260215 0.965551i \(-0.416207\pi\)
0.260215 + 0.965551i \(0.416207\pi\)
\(440\) −9.17326e13 −0.265176
\(441\) 1.18064e14 0.337058
\(442\) 3.78658e14 1.06764
\(443\) 5.57996e14 1.55386 0.776928 0.629590i \(-0.216777\pi\)
0.776928 + 0.629590i \(0.216777\pi\)
\(444\) 1.89769e14 0.521939
\(445\) −2.17642e14 −0.591238
\(446\) −1.29822e14 −0.348343
\(447\) 1.32031e14 0.349933
\(448\) 8.24212e14 2.15779
\(449\) 5.52221e14 1.42810 0.714049 0.700096i \(-0.246860\pi\)
0.714049 + 0.700096i \(0.246860\pi\)
\(450\) −4.32359e13 −0.110452
\(451\) 2.19261e14 0.553339
\(452\) −2.17963e14 −0.543401
\(453\) −2.90169e14 −0.714679
\(454\) −6.36751e14 −1.54940
\(455\) 9.17589e13 0.220590
\(456\) −2.60825e14 −0.619503
\(457\) −2.57493e13 −0.0604263 −0.0302132 0.999543i \(-0.509619\pi\)
−0.0302132 + 0.999543i \(0.509619\pi\)
\(458\) −5.70126e14 −1.32194
\(459\) 1.55632e14 0.356558
\(460\) −2.69562e14 −0.610225
\(461\) −4.26715e14 −0.954515 −0.477257 0.878764i \(-0.658369\pi\)
−0.477257 + 0.878764i \(0.658369\pi\)
\(462\) 2.94842e14 0.651717
\(463\) 1.13760e14 0.248481 0.124241 0.992252i \(-0.460351\pi\)
0.124241 + 0.992252i \(0.460351\pi\)
\(464\) 2.61172e14 0.563738
\(465\) 1.56538e14 0.333910
\(466\) −8.19030e14 −1.72654
\(467\) −1.60119e14 −0.333580 −0.166790 0.985992i \(-0.553340\pi\)
−0.166790 + 0.985992i \(0.553340\pi\)
\(468\) −9.82558e13 −0.202305
\(469\) −3.79579e14 −0.772416
\(470\) 4.91163e14 0.987842
\(471\) 5.37211e14 1.06790
\(472\) −6.91673e14 −1.35900
\(473\) −6.95314e13 −0.135034
\(474\) −6.99906e13 −0.134357
\(475\) 9.16343e13 0.173877
\(476\) −2.44431e15 −4.58478
\(477\) −7.09216e13 −0.131500
\(478\) −4.43122e14 −0.812212
\(479\) −7.66095e14 −1.38815 −0.694077 0.719901i \(-0.744187\pi\)
−0.694077 + 0.719901i \(0.744187\pi\)
\(480\) 1.06283e14 0.190387
\(481\) −1.01752e14 −0.180196
\(482\) −1.93738e14 −0.339200
\(483\) 3.69885e14 0.640262
\(484\) −7.84268e14 −1.34219
\(485\) 7.29281e13 0.123400
\(486\) −6.35277e13 −0.106283
\(487\) 9.61903e14 1.59119 0.795595 0.605829i \(-0.207158\pi\)
0.795595 + 0.605829i \(0.207158\pi\)
\(488\) 1.47380e15 2.41062
\(489\) −3.37445e14 −0.545764
\(490\) −4.68475e14 −0.749218
\(491\) 2.32694e14 0.367991 0.183996 0.982927i \(-0.441097\pi\)
0.183996 + 0.982927i \(0.441097\pi\)
\(492\) 7.41980e14 1.16034
\(493\) 2.25211e15 3.48283
\(494\) 3.27585e14 0.500986
\(495\) 4.73533e13 0.0716179
\(496\) 2.59288e14 0.387823
\(497\) −5.04264e14 −0.745929
\(498\) 2.35165e13 0.0344042
\(499\) −3.26636e14 −0.472619 −0.236309 0.971678i \(-0.575938\pi\)
−0.236309 + 0.971678i \(0.575938\pi\)
\(500\) 1.09059e14 0.156073
\(501\) 1.92797e14 0.272893
\(502\) 1.41829e15 1.98561
\(503\) −1.47765e14 −0.204620 −0.102310 0.994753i \(-0.532623\pi\)
−0.102310 + 0.994753i \(0.532623\pi\)
\(504\) 4.25954e14 0.583438
\(505\) −1.94257e14 −0.263193
\(506\) 4.64426e14 0.622427
\(507\) −3.82812e14 −0.507506
\(508\) −6.35614e14 −0.833572
\(509\) −1.76808e14 −0.229379 −0.114689 0.993401i \(-0.536587\pi\)
−0.114689 + 0.993401i \(0.536587\pi\)
\(510\) −6.17546e14 −0.792563
\(511\) −2.03930e15 −2.58921
\(512\) 4.70714e14 0.591251
\(513\) 1.34641e14 0.167314
\(514\) 1.16720e15 1.43498
\(515\) −3.95161e14 −0.480655
\(516\) −2.35294e14 −0.283164
\(517\) −5.37937e14 −0.640522
\(518\) 1.03325e15 1.21728
\(519\) 6.97078e14 0.812570
\(520\) 1.66445e14 0.191978
\(521\) −4.91557e14 −0.561004 −0.280502 0.959853i \(-0.590501\pi\)
−0.280502 + 0.959853i \(0.590501\pi\)
\(522\) −9.19291e14 −1.03816
\(523\) −1.63875e15 −1.83127 −0.915637 0.402007i \(-0.868313\pi\)
−0.915637 + 0.402007i \(0.868313\pi\)
\(524\) 1.64377e14 0.181769
\(525\) −1.49648e14 −0.163755
\(526\) 1.75298e15 1.89826
\(527\) 2.23587e15 2.39601
\(528\) 7.84353e13 0.0831812
\(529\) −3.70179e14 −0.388514
\(530\) 2.81415e14 0.292301
\(531\) 3.57049e14 0.367035
\(532\) −2.11463e15 −2.15139
\(533\) −3.97840e14 −0.400598
\(534\) 1.26891e15 1.26460
\(535\) 2.12279e14 0.209392
\(536\) −6.88531e14 −0.672229
\(537\) 1.69858e13 0.0164145
\(538\) −1.14483e15 −1.09506
\(539\) 5.13089e14 0.485796
\(540\) 1.60244e14 0.150181
\(541\) −2.49179e14 −0.231168 −0.115584 0.993298i \(-0.536874\pi\)
−0.115584 + 0.993298i \(0.536874\pi\)
\(542\) 1.94521e15 1.78636
\(543\) −7.19492e14 −0.654074
\(544\) 1.51806e15 1.36614
\(545\) 3.61808e14 0.322327
\(546\) −5.34978e14 −0.471820
\(547\) −1.63969e15 −1.43163 −0.715817 0.698287i \(-0.753946\pi\)
−0.715817 + 0.698287i \(0.753946\pi\)
\(548\) −1.78039e14 −0.153894
\(549\) −7.60791e14 −0.651054
\(550\) −1.87897e14 −0.159193
\(551\) 1.94835e15 1.63430
\(552\) 6.70947e14 0.557216
\(553\) −2.42251e14 −0.199195
\(554\) −2.13042e15 −1.73445
\(555\) 1.65945e14 0.133768
\(556\) 6.46503e14 0.516011
\(557\) −1.62476e15 −1.28406 −0.642032 0.766678i \(-0.721909\pi\)
−0.642032 + 0.766678i \(0.721909\pi\)
\(558\) −9.12660e14 −0.714202
\(559\) 1.26162e14 0.0977602
\(560\) −2.47874e14 −0.190194
\(561\) 6.76356e14 0.513901
\(562\) −1.10650e14 −0.0832536
\(563\) 1.06403e15 0.792791 0.396395 0.918080i \(-0.370261\pi\)
0.396395 + 0.918080i \(0.370261\pi\)
\(564\) −1.82038e15 −1.34316
\(565\) −1.90599e14 −0.139269
\(566\) 1.25820e15 0.910459
\(567\) −2.19882e14 −0.157573
\(568\) −9.14702e14 −0.649178
\(569\) −2.37736e14 −0.167100 −0.0835501 0.996504i \(-0.526626\pi\)
−0.0835501 + 0.996504i \(0.526626\pi\)
\(570\) −5.34252e14 −0.371907
\(571\) 8.27986e14 0.570853 0.285427 0.958401i \(-0.407865\pi\)
0.285427 + 0.958401i \(0.407865\pi\)
\(572\) −4.27005e14 −0.291578
\(573\) 1.10003e15 0.743971
\(574\) 4.03990e15 2.70617
\(575\) −2.35720e14 −0.156395
\(576\) −7.71769e14 −0.507182
\(577\) 2.25265e15 1.46632 0.733158 0.680058i \(-0.238045\pi\)
0.733158 + 0.680058i \(0.238045\pi\)
\(578\) −6.25090e15 −4.03032
\(579\) −2.52753e14 −0.161423
\(580\) 2.31884e15 1.46695
\(581\) 8.13953e13 0.0510071
\(582\) −4.25190e14 −0.263941
\(583\) −3.08215e14 −0.189529
\(584\) −3.69916e15 −2.25337
\(585\) −8.59204e13 −0.0518489
\(586\) 2.21607e15 1.32479
\(587\) −1.18033e15 −0.699029 −0.349514 0.936931i \(-0.613653\pi\)
−0.349514 + 0.936931i \(0.613653\pi\)
\(588\) 1.73629e15 1.01870
\(589\) 1.93430e15 1.12432
\(590\) −1.41676e15 −0.815851
\(591\) 1.31846e15 0.752204
\(592\) 2.74869e14 0.155366
\(593\) 2.29778e15 1.28679 0.643394 0.765535i \(-0.277526\pi\)
0.643394 + 0.765535i \(0.277526\pi\)
\(594\) −2.76082e14 −0.153184
\(595\) −2.13745e15 −1.17504
\(596\) 1.94170e15 1.05761
\(597\) −1.87768e15 −1.01336
\(598\) −8.42679e14 −0.450615
\(599\) −9.39685e14 −0.497891 −0.248946 0.968517i \(-0.580084\pi\)
−0.248946 + 0.968517i \(0.580084\pi\)
\(600\) −2.71451e14 −0.142515
\(601\) −3.30569e15 −1.71970 −0.859850 0.510547i \(-0.829443\pi\)
−0.859850 + 0.510547i \(0.829443\pi\)
\(602\) −1.28112e15 −0.660402
\(603\) 3.55427e14 0.181554
\(604\) −4.26733e15 −2.16000
\(605\) −6.85808e14 −0.343992
\(606\) 1.13257e15 0.562945
\(607\) 1.51796e15 0.747690 0.373845 0.927491i \(-0.378039\pi\)
0.373845 + 0.927491i \(0.378039\pi\)
\(608\) 1.31331e15 0.641056
\(609\) −3.18185e15 −1.53916
\(610\) 3.01880e15 1.44717
\(611\) 9.76063e14 0.463715
\(612\) 2.28879e15 1.07764
\(613\) −1.78314e15 −0.832055 −0.416028 0.909352i \(-0.636578\pi\)
−0.416028 + 0.909352i \(0.636578\pi\)
\(614\) 2.07549e15 0.959831
\(615\) 6.48830e14 0.297384
\(616\) 1.85113e15 0.840899
\(617\) −2.06098e15 −0.927911 −0.463955 0.885859i \(-0.653570\pi\)
−0.463955 + 0.885859i \(0.653570\pi\)
\(618\) 2.30389e15 1.02808
\(619\) −1.05386e15 −0.466105 −0.233052 0.972464i \(-0.574871\pi\)
−0.233052 + 0.972464i \(0.574871\pi\)
\(620\) 2.30211e15 1.00919
\(621\) −3.46350e14 −0.150491
\(622\) 1.82025e14 0.0783941
\(623\) 4.39194e15 1.87487
\(624\) −1.42317e14 −0.0602202
\(625\) 9.53674e13 0.0400000
\(626\) −1.88078e15 −0.781950
\(627\) 5.85130e14 0.241146
\(628\) 7.90042e15 3.22755
\(629\) 2.37022e15 0.959867
\(630\) 8.72486e14 0.350256
\(631\) −1.51057e15 −0.601146 −0.300573 0.953759i \(-0.597178\pi\)
−0.300573 + 0.953759i \(0.597178\pi\)
\(632\) −4.39428e14 −0.173358
\(633\) 6.47360e14 0.253178
\(634\) −1.06577e13 −0.00413212
\(635\) −5.55817e14 −0.213637
\(636\) −1.04300e15 −0.397438
\(637\) −9.30976e14 −0.351699
\(638\) −3.99511e15 −1.49629
\(639\) 4.72179e14 0.175328
\(640\) 2.16661e15 0.797611
\(641\) 4.65958e15 1.70070 0.850350 0.526218i \(-0.176390\pi\)
0.850350 + 0.526218i \(0.176390\pi\)
\(642\) −1.23764e15 −0.447869
\(643\) 2.11472e15 0.758739 0.379369 0.925245i \(-0.376141\pi\)
0.379369 + 0.925245i \(0.376141\pi\)
\(644\) 5.43967e15 1.93508
\(645\) −2.05755e14 −0.0725723
\(646\) −7.63082e15 −2.66865
\(647\) −4.70348e15 −1.63097 −0.815485 0.578778i \(-0.803530\pi\)
−0.815485 + 0.578778i \(0.803530\pi\)
\(648\) −3.98851e14 −0.137135
\(649\) 1.55168e15 0.529002
\(650\) 3.40930e14 0.115250
\(651\) −3.15889e15 −1.05886
\(652\) −4.96260e15 −1.64948
\(653\) −3.62919e15 −1.19615 −0.598077 0.801439i \(-0.704068\pi\)
−0.598077 + 0.801439i \(0.704068\pi\)
\(654\) −2.10943e15 −0.689427
\(655\) 1.43741e14 0.0465856
\(656\) 1.07471e15 0.345399
\(657\) 1.90955e15 0.608584
\(658\) −9.91151e15 −3.13255
\(659\) −1.26034e14 −0.0395020 −0.0197510 0.999805i \(-0.506287\pi\)
−0.0197510 + 0.999805i \(0.506287\pi\)
\(660\) 6.96395e14 0.216453
\(661\) 4.45748e15 1.37398 0.686991 0.726666i \(-0.258931\pi\)
0.686991 + 0.726666i \(0.258931\pi\)
\(662\) 7.09192e15 2.16793
\(663\) −1.22722e15 −0.372047
\(664\) 1.47646e14 0.0443912
\(665\) −1.84915e15 −0.551383
\(666\) −9.67503e14 −0.286117
\(667\) −5.01193e15 −1.46999
\(668\) 2.83534e15 0.824774
\(669\) 4.20750e14 0.121389
\(670\) −1.41033e15 −0.403560
\(671\) −3.30629e15 −0.938353
\(672\) −2.14476e15 −0.603736
\(673\) 4.32745e15 1.20823 0.604115 0.796897i \(-0.293527\pi\)
0.604115 + 0.796897i \(0.293527\pi\)
\(674\) −6.70180e14 −0.185593
\(675\) 1.40126e14 0.0384900
\(676\) −5.62977e15 −1.53385
\(677\) −1.61874e15 −0.437460 −0.218730 0.975785i \(-0.570191\pi\)
−0.218730 + 0.975785i \(0.570191\pi\)
\(678\) 1.11124e15 0.297882
\(679\) −1.47166e15 −0.391314
\(680\) −3.87719e15 −1.02263
\(681\) 2.06369e15 0.539927
\(682\) −3.96629e15 −1.02937
\(683\) 2.93595e15 0.755849 0.377924 0.925836i \(-0.376638\pi\)
0.377924 + 0.925836i \(0.376638\pi\)
\(684\) 1.98008e15 0.505677
\(685\) −1.55688e14 −0.0394417
\(686\) 1.04473e14 0.0262556
\(687\) 1.84776e15 0.460663
\(688\) −3.40809e14 −0.0842896
\(689\) 5.59242e14 0.137213
\(690\) 1.37431e15 0.334514
\(691\) −4.57286e14 −0.110423 −0.0552114 0.998475i \(-0.517583\pi\)
−0.0552114 + 0.998475i \(0.517583\pi\)
\(692\) 1.02515e16 2.45586
\(693\) −9.55574e14 −0.227108
\(694\) 1.37708e15 0.324699
\(695\) 5.65339e14 0.132249
\(696\) −5.77166e15 −1.33952
\(697\) 9.26736e15 2.13391
\(698\) −9.04743e15 −2.06690
\(699\) 2.65445e15 0.601658
\(700\) −2.20078e15 −0.494922
\(701\) 6.08159e15 1.35696 0.678481 0.734618i \(-0.262639\pi\)
0.678481 + 0.734618i \(0.262639\pi\)
\(702\) 5.00939e14 0.110900
\(703\) 2.05053e15 0.450414
\(704\) −3.35400e15 −0.730993
\(705\) −1.59184e15 −0.344239
\(706\) 1.97182e15 0.423099
\(707\) 3.92005e15 0.834612
\(708\) 5.25089e15 1.10930
\(709\) −5.51751e15 −1.15661 −0.578307 0.815819i \(-0.696286\pi\)
−0.578307 + 0.815819i \(0.696286\pi\)
\(710\) −1.87359e15 −0.389722
\(711\) 2.26837e14 0.0468200
\(712\) 7.96669e15 1.63169
\(713\) −4.97578e15 −1.01127
\(714\) 1.24619e16 2.51329
\(715\) −3.73398e14 −0.0747289
\(716\) 2.49799e14 0.0496100
\(717\) 1.43614e15 0.283036
\(718\) 5.42463e15 1.06093
\(719\) −5.30420e15 −1.02946 −0.514732 0.857351i \(-0.672109\pi\)
−0.514732 + 0.857351i \(0.672109\pi\)
\(720\) 2.32103e14 0.0447045
\(721\) 7.97421e15 1.52421
\(722\) 2.13259e15 0.404531
\(723\) 6.27898e14 0.118203
\(724\) −1.05811e16 −1.97683
\(725\) 2.02772e15 0.375967
\(726\) 3.99844e15 0.735765
\(727\) 7.44972e15 1.36051 0.680254 0.732977i \(-0.261870\pi\)
0.680254 + 0.732977i \(0.261870\pi\)
\(728\) −3.35880e15 −0.608781
\(729\) 2.05891e14 0.0370370
\(730\) −7.57704e15 −1.35277
\(731\) −2.93883e15 −0.520750
\(732\) −1.11885e16 −1.96770
\(733\) 5.45148e15 0.951574 0.475787 0.879561i \(-0.342163\pi\)
0.475787 + 0.879561i \(0.342163\pi\)
\(734\) 4.95162e15 0.857866
\(735\) 1.51831e15 0.261084
\(736\) −3.37835e15 −0.576602
\(737\) 1.54463e15 0.261670
\(738\) −3.78285e15 −0.636076
\(739\) 1.63560e15 0.272980 0.136490 0.990641i \(-0.456418\pi\)
0.136490 + 0.990641i \(0.456418\pi\)
\(740\) 2.44045e15 0.404292
\(741\) −1.06169e15 −0.174581
\(742\) −5.67887e15 −0.926916
\(743\) −9.47083e15 −1.53444 −0.767219 0.641385i \(-0.778360\pi\)
−0.767219 + 0.641385i \(0.778360\pi\)
\(744\) −5.73003e15 −0.921522
\(745\) 1.69793e15 0.271057
\(746\) 2.79010e15 0.442136
\(747\) −7.62163e13 −0.0119890
\(748\) 9.94674e15 1.55318
\(749\) −4.28371e15 −0.664003
\(750\) −5.56017e14 −0.0855561
\(751\) −9.72786e15 −1.48593 −0.742964 0.669331i \(-0.766581\pi\)
−0.742964 + 0.669331i \(0.766581\pi\)
\(752\) −2.63670e15 −0.399819
\(753\) −4.59661e15 −0.691936
\(754\) 7.24894e15 1.08326
\(755\) −3.73160e15 −0.553588
\(756\) −3.23366e15 −0.476239
\(757\) 1.91854e15 0.280507 0.140253 0.990116i \(-0.455208\pi\)
0.140253 + 0.990116i \(0.455208\pi\)
\(758\) −1.43286e16 −2.07981
\(759\) −1.50519e15 −0.216901
\(760\) −3.35424e15 −0.479865
\(761\) −1.17913e16 −1.67474 −0.837369 0.546638i \(-0.815907\pi\)
−0.837369 + 0.546638i \(0.815907\pi\)
\(762\) 3.24056e15 0.456949
\(763\) −7.30116e15 −1.02213
\(764\) 1.61775e16 2.24853
\(765\) 2.00145e15 0.276189
\(766\) 1.79139e16 2.45433
\(767\) −2.81546e15 −0.382979
\(768\) −6.12745e15 −0.827547
\(769\) 8.15564e15 1.09361 0.546806 0.837259i \(-0.315844\pi\)
0.546806 + 0.837259i \(0.315844\pi\)
\(770\) 3.79170e15 0.504818
\(771\) −3.78285e15 −0.500057
\(772\) −3.71708e15 −0.487874
\(773\) −5.26080e15 −0.685590 −0.342795 0.939410i \(-0.611374\pi\)
−0.342795 + 0.939410i \(0.611374\pi\)
\(774\) 1.19960e15 0.155225
\(775\) 2.01310e15 0.258646
\(776\) −2.66950e15 −0.340558
\(777\) −3.34872e15 −0.424192
\(778\) 7.45622e15 0.937845
\(779\) 8.01738e15 1.00133
\(780\) −1.26358e15 −0.156705
\(781\) 2.05202e15 0.252697
\(782\) 1.96295e16 2.40034
\(783\) 2.97939e15 0.361774
\(784\) 2.51491e15 0.303238
\(785\) 6.90858e15 0.827191
\(786\) −8.38045e14 −0.0996422
\(787\) −9.41032e15 −1.11108 −0.555538 0.831491i \(-0.687488\pi\)
−0.555538 + 0.831491i \(0.687488\pi\)
\(788\) 1.93897e16 2.27341
\(789\) −5.68136e15 −0.661498
\(790\) −9.00085e14 −0.104072
\(791\) 3.84622e15 0.441635
\(792\) −1.73335e15 −0.197650
\(793\) 5.99911e15 0.679335
\(794\) −1.91927e16 −2.15836
\(795\) −9.12057e14 −0.101860
\(796\) −2.76138e16 −3.06270
\(797\) 3.36292e15 0.370421 0.185210 0.982699i \(-0.440703\pi\)
0.185210 + 0.982699i \(0.440703\pi\)
\(798\) 1.07810e16 1.17935
\(799\) −2.27366e16 −2.47012
\(800\) 1.36681e15 0.147473
\(801\) −4.11249e15 −0.440683
\(802\) −2.81318e15 −0.299391
\(803\) 8.29861e15 0.877142
\(804\) 5.22704e15 0.548716
\(805\) 4.75675e15 0.495945
\(806\) 7.19665e15 0.745226
\(807\) 3.71035e15 0.381601
\(808\) 7.11071e15 0.726358
\(809\) 8.02144e15 0.813834 0.406917 0.913465i \(-0.366604\pi\)
0.406917 + 0.913465i \(0.366604\pi\)
\(810\) −8.16971e14 −0.0823264
\(811\) −3.16415e15 −0.316695 −0.158348 0.987383i \(-0.550617\pi\)
−0.158348 + 0.987383i \(0.550617\pi\)
\(812\) −4.67934e16 −4.65186
\(813\) −6.30436e15 −0.622505
\(814\) −4.20463e15 −0.412376
\(815\) −4.33958e15 −0.422747
\(816\) 3.31517e15 0.320782
\(817\) −2.54244e15 −0.244360
\(818\) 1.45091e16 1.38515
\(819\) 1.73385e15 0.164418
\(820\) 9.54193e15 0.898793
\(821\) −1.47257e16 −1.37781 −0.688903 0.724853i \(-0.741908\pi\)
−0.688903 + 0.724853i \(0.741908\pi\)
\(822\) 9.07699e14 0.0843620
\(823\) −1.36058e16 −1.25610 −0.628052 0.778171i \(-0.716148\pi\)
−0.628052 + 0.778171i \(0.716148\pi\)
\(824\) 1.44647e16 1.32651
\(825\) 6.08968e14 0.0554750
\(826\) 2.85898e16 2.58714
\(827\) −1.63615e16 −1.47077 −0.735384 0.677651i \(-0.762998\pi\)
−0.735384 + 0.677651i \(0.762998\pi\)
\(828\) −5.09355e15 −0.454835
\(829\) −1.63816e16 −1.45313 −0.726567 0.687096i \(-0.758885\pi\)
−0.726567 + 0.687096i \(0.758885\pi\)
\(830\) 3.02425e14 0.0266494
\(831\) 6.90461e15 0.604412
\(832\) 6.08567e15 0.529213
\(833\) 2.16863e16 1.87343
\(834\) −3.29607e15 −0.282868
\(835\) 2.47939e15 0.211382
\(836\) 8.60513e15 0.728824
\(837\) 2.95790e15 0.248882
\(838\) 9.74656e15 0.814722
\(839\) 1.30757e16 1.08586 0.542929 0.839779i \(-0.317315\pi\)
0.542929 + 0.839779i \(0.317315\pi\)
\(840\) 5.47780e15 0.451929
\(841\) 3.09134e16 2.53378
\(842\) 6.54076e15 0.532613
\(843\) 3.58614e14 0.0290119
\(844\) 9.52031e15 0.765187
\(845\) −4.92299e15 −0.393113
\(846\) 9.28086e15 0.736294
\(847\) 1.38394e16 1.09083
\(848\) −1.51072e15 −0.118306
\(849\) −4.07780e15 −0.317273
\(850\) −7.94170e15 −0.613916
\(851\) −5.27478e15 −0.405128
\(852\) 6.94403e15 0.529900
\(853\) −1.24432e16 −0.943433 −0.471716 0.881750i \(-0.656365\pi\)
−0.471716 + 0.881750i \(0.656365\pi\)
\(854\) −6.09184e16 −4.58913
\(855\) 1.73149e15 0.129601
\(856\) −7.77037e15 −0.577878
\(857\) −3.66106e15 −0.270528 −0.135264 0.990810i \(-0.543188\pi\)
−0.135264 + 0.990810i \(0.543188\pi\)
\(858\) 2.17701e15 0.159838
\(859\) 1.38206e16 1.00824 0.504122 0.863632i \(-0.331816\pi\)
0.504122 + 0.863632i \(0.331816\pi\)
\(860\) −3.02590e15 −0.219338
\(861\) −1.30932e16 −0.943034
\(862\) −1.65995e16 −1.18797
\(863\) 1.52984e16 1.08789 0.543946 0.839120i \(-0.316929\pi\)
0.543946 + 0.839120i \(0.316929\pi\)
\(864\) 2.00829e15 0.141906
\(865\) 8.96448e15 0.629414
\(866\) 3.27796e16 2.28694
\(867\) 2.02590e16 1.40447
\(868\) −4.64559e16 −3.20024
\(869\) 9.85801e14 0.0674809
\(870\) −1.18222e16 −0.804157
\(871\) −2.80267e15 −0.189440
\(872\) −1.32438e16 −0.889555
\(873\) 1.37803e15 0.0919769
\(874\) 1.69819e16 1.12635
\(875\) −1.92448e15 −0.126844
\(876\) 2.80825e16 1.83934
\(877\) 1.90870e14 0.0124234 0.00621169 0.999981i \(-0.498023\pi\)
0.00621169 + 0.999981i \(0.498023\pi\)
\(878\) −1.33306e16 −0.862241
\(879\) −7.18220e15 −0.461656
\(880\) 1.00868e15 0.0644319
\(881\) 7.60210e15 0.482577 0.241288 0.970453i \(-0.422430\pi\)
0.241288 + 0.970453i \(0.422430\pi\)
\(882\) −8.85215e15 −0.558434
\(883\) −2.08677e16 −1.30825 −0.654125 0.756386i \(-0.726963\pi\)
−0.654125 + 0.756386i \(0.726963\pi\)
\(884\) −1.80479e16 −1.12445
\(885\) 4.59168e15 0.284304
\(886\) −4.18372e16 −2.57441
\(887\) 3.05601e16 1.86885 0.934427 0.356154i \(-0.115912\pi\)
0.934427 + 0.356154i \(0.115912\pi\)
\(888\) −6.07435e15 −0.369172
\(889\) 1.12162e16 0.677464
\(890\) 1.63183e16 0.979555
\(891\) 8.94773e14 0.0533809
\(892\) 6.18770e15 0.366879
\(893\) −1.96699e16 −1.15909
\(894\) −9.89937e15 −0.579764
\(895\) 2.18439e14 0.0127146
\(896\) −4.37215e16 −2.52930
\(897\) 2.73109e15 0.157028
\(898\) −4.14042e16 −2.36605
\(899\) 4.28029e16 2.43106
\(900\) 2.06074e15 0.116330
\(901\) −1.30271e16 −0.730905
\(902\) −1.64397e16 −0.916765
\(903\) 4.15206e15 0.230134
\(904\) 6.97679e15 0.384352
\(905\) −9.25273e15 −0.506644
\(906\) 2.17562e16 1.18407
\(907\) −2.96304e16 −1.60287 −0.801434 0.598083i \(-0.795929\pi\)
−0.801434 + 0.598083i \(0.795929\pi\)
\(908\) 3.03494e16 1.63184
\(909\) −3.67062e15 −0.196173
\(910\) −6.87986e15 −0.365470
\(911\) 1.41726e16 0.748342 0.374171 0.927360i \(-0.377927\pi\)
0.374171 + 0.927360i \(0.377927\pi\)
\(912\) 2.86802e15 0.150526
\(913\) −3.31225e14 −0.0172796
\(914\) 1.93062e15 0.100114
\(915\) −9.78383e15 −0.504304
\(916\) 2.71738e16 1.39228
\(917\) −2.90064e15 −0.147728
\(918\) −1.16690e16 −0.590741
\(919\) 2.73944e16 1.37856 0.689281 0.724494i \(-0.257927\pi\)
0.689281 + 0.724494i \(0.257927\pi\)
\(920\) 8.62844e15 0.431618
\(921\) −6.72660e15 −0.334478
\(922\) 3.19941e16 1.58143
\(923\) −3.72330e15 −0.182944
\(924\) −1.40530e16 −0.686395
\(925\) 2.13407e15 0.103616
\(926\) −8.52944e15 −0.411681
\(927\) −7.46683e15 −0.358259
\(928\) 2.90614e16 1.38613
\(929\) −1.04825e16 −0.497024 −0.248512 0.968629i \(-0.579942\pi\)
−0.248512 + 0.968629i \(0.579942\pi\)
\(930\) −1.17369e16 −0.553218
\(931\) 1.87613e16 0.879102
\(932\) 3.90373e16 1.81841
\(933\) −5.89936e14 −0.0273184
\(934\) 1.20053e16 0.552671
\(935\) 8.69800e15 0.398066
\(936\) 3.14508e15 0.143092
\(937\) −2.52576e16 −1.14241 −0.571207 0.820806i \(-0.693525\pi\)
−0.571207 + 0.820806i \(0.693525\pi\)
\(938\) 2.84599e16 1.27973
\(939\) 6.09554e15 0.272490
\(940\) −2.34102e16 −1.04040
\(941\) 8.81490e14 0.0389471 0.0194735 0.999810i \(-0.493801\pi\)
0.0194735 + 0.999810i \(0.493801\pi\)
\(942\) −4.02788e16 −1.76928
\(943\) −2.06239e16 −0.900651
\(944\) 7.60558e15 0.330207
\(945\) −2.82770e15 −0.122056
\(946\) 5.21330e15 0.223723
\(947\) 7.90204e15 0.337143 0.168572 0.985689i \(-0.446085\pi\)
0.168572 + 0.985689i \(0.446085\pi\)
\(948\) 3.33595e15 0.141506
\(949\) −1.50575e16 −0.635020
\(950\) −6.87052e15 −0.288078
\(951\) 3.45413e13 0.00143994
\(952\) 7.82404e16 3.24286
\(953\) −3.64310e15 −0.150127 −0.0750637 0.997179i \(-0.523916\pi\)
−0.0750637 + 0.997179i \(0.523916\pi\)
\(954\) 5.31753e15 0.217868
\(955\) 1.41465e16 0.576277
\(956\) 2.11204e16 0.855430
\(957\) 1.29480e16 0.521419
\(958\) 5.74400e16 2.29987
\(959\) 3.14172e15 0.125074
\(960\) −9.92501e15 −0.392861
\(961\) 1.70857e16 0.672441
\(962\) 7.62911e15 0.298546
\(963\) 4.01115e15 0.156072
\(964\) 9.23410e15 0.357249
\(965\) −3.25043e15 −0.125038
\(966\) −2.77331e16 −1.06078
\(967\) −1.26495e16 −0.481092 −0.240546 0.970638i \(-0.577326\pi\)
−0.240546 + 0.970638i \(0.577326\pi\)
\(968\) 2.51037e16 0.949345
\(969\) 2.47312e16 0.929961
\(970\) −5.46798e15 −0.204448
\(971\) −3.31816e16 −1.23365 −0.616824 0.787101i \(-0.711581\pi\)
−0.616824 + 0.787101i \(0.711581\pi\)
\(972\) 3.02791e15 0.111938
\(973\) −1.14084e16 −0.419375
\(974\) −7.21212e16 −2.63626
\(975\) −1.10494e15 −0.0401620
\(976\) −1.62058e16 −0.585728
\(977\) −4.86678e16 −1.74913 −0.874565 0.484909i \(-0.838853\pi\)
−0.874565 + 0.484909i \(0.838853\pi\)
\(978\) 2.53009e16 0.904215
\(979\) −1.78723e16 −0.635148
\(980\) 2.23288e16 0.789083
\(981\) 6.83660e15 0.240249
\(982\) −1.74469e16 −0.609683
\(983\) −6.89914e15 −0.239746 −0.119873 0.992789i \(-0.538249\pi\)
−0.119873 + 0.992789i \(0.538249\pi\)
\(984\) −2.37502e16 −0.820717
\(985\) 1.69555e16 0.582654
\(986\) −1.68858e17 −5.77031
\(987\) 3.21229e16 1.09162
\(988\) −1.56136e16 −0.527643
\(989\) 6.54018e15 0.219791
\(990\) −3.55044e15 −0.118656
\(991\) −4.39787e16 −1.46163 −0.730814 0.682577i \(-0.760859\pi\)
−0.730814 + 0.682577i \(0.760859\pi\)
\(992\) 2.88518e16 0.953583
\(993\) −2.29847e16 −0.755471
\(994\) 3.78085e16 1.23585
\(995\) −2.41471e16 −0.784943
\(996\) −1.12086e15 −0.0362349
\(997\) −2.80611e16 −0.902157 −0.451078 0.892484i \(-0.648961\pi\)
−0.451078 + 0.892484i \(0.648961\pi\)
\(998\) 2.44904e16 0.783029
\(999\) 3.13565e15 0.0997050
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 \(a_p\))