Properties

Label 15.12.a.d.1.3
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 1.3
Root \(-72.6470\)
Character \(\chi\) = 15.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+72.6470 q^{2}\) \(+243.000 q^{3}\) \(+3229.58 q^{4}\) \(+3125.00 q^{5}\) \(+17653.2 q^{6}\) \(+8974.61 q^{7}\) \(+85838.4 q^{8}\) \(+59049.0 q^{9}\) \(+O(q^{10})\) \(q\)\(+72.6470 q^{2}\) \(+243.000 q^{3}\) \(+3229.58 q^{4}\) \(+3125.00 q^{5}\) \(+17653.2 q^{6}\) \(+8974.61 q^{7}\) \(+85838.4 q^{8}\) \(+59049.0 q^{9}\) \(+227022. q^{10}\) \(+421205. q^{11}\) \(+784789. q^{12}\) \(-1.24336e6 q^{13}\) \(+651979. q^{14}\) \(+759375. q^{15}\) \(-378284. q^{16}\) \(-5.93114e6 q^{17}\) \(+4.28973e6 q^{18}\) \(+1.88682e7 q^{19}\) \(+1.00924e7 q^{20}\) \(+2.18083e6 q^{21}\) \(+3.05993e7 q^{22}\) \(-2.72256e7 q^{23}\) \(+2.08587e7 q^{24}\) \(+9.76562e6 q^{25}\) \(-9.03263e7 q^{26}\) \(+1.43489e7 q^{27}\) \(+2.89843e7 q^{28}\) \(-1.15466e8 q^{29}\) \(+5.51663e7 q^{30}\) \(-2.73479e8 q^{31}\) \(-2.03278e8 q^{32}\) \(+1.02353e8 q^{33}\) \(-4.30879e8 q^{34}\) \(+2.80457e7 q^{35}\) \(+1.90704e8 q^{36}\) \(-2.86342e8 q^{37}\) \(+1.37071e9 q^{38}\) \(-3.02136e8 q^{39}\) \(+2.68245e8 q^{40}\) \(+4.51798e8 q^{41}\) \(+1.58431e8 q^{42}\) \(+1.30494e9 q^{43}\) \(+1.36032e9 q^{44}\) \(+1.84528e8 q^{45}\) \(-1.97786e9 q^{46}\) \(-9.11661e8 q^{47}\) \(-9.19231e7 q^{48}\) \(-1.89678e9 q^{49}\) \(+7.09443e8 q^{50}\) \(-1.44127e9 q^{51}\) \(-4.01553e9 q^{52}\) \(+3.44031e9 q^{53}\) \(+1.04240e9 q^{54}\) \(+1.31627e9 q^{55}\) \(+7.70367e8 q^{56}\) \(+4.58496e9 q^{57}\) \(-8.38824e9 q^{58}\) \(+1.06320e10 q^{59}\) \(+2.45246e9 q^{60}\) \(+6.85337e9 q^{61}\) \(-1.98674e10 q^{62}\) \(+5.29942e8 q^{63}\) \(-1.39928e10 q^{64}\) \(-3.88550e9 q^{65}\) \(+7.43563e9 q^{66}\) \(+5.26360e9 q^{67}\) \(-1.91551e10 q^{68}\) \(-6.61583e9 q^{69}\) \(+2.03743e9 q^{70}\) \(+1.72726e10 q^{71}\) \(+5.06867e9 q^{72}\) \(+5.86468e9 q^{73}\) \(-2.08019e10 q^{74}\) \(+2.37305e9 q^{75}\) \(+6.09363e10 q^{76}\) \(+3.78015e9 q^{77}\) \(-2.19493e10 q^{78}\) \(-2.16383e10 q^{79}\) \(-1.18214e9 q^{80}\) \(+3.48678e9 q^{81}\) \(+3.28217e10 q^{82}\) \(-6.48232e9 q^{83}\) \(+7.04317e9 q^{84}\) \(-1.85348e10 q^{85}\) \(+9.48001e10 q^{86}\) \(-2.80582e10 q^{87}\) \(+3.61556e10 q^{88}\) \(+7.32562e10 q^{89}\) \(+1.34054e10 q^{90}\) \(-1.11587e10 q^{91}\) \(-8.79275e10 q^{92}\) \(-6.64553e10 q^{93}\) \(-6.62294e10 q^{94}\) \(+5.89630e10 q^{95}\) \(-4.93966e10 q^{96}\) \(-1.45891e11 q^{97}\) \(-1.37796e11 q^{98}\) \(+2.48718e10 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 729q^{3} \) \(\mathstrut +\mathstrut 4757q^{4} \) \(\mathstrut +\mathstrut 9375q^{5} \) \(\mathstrut -\mathstrut 243q^{6} \) \(\mathstrut -\mathstrut 14608q^{7} \) \(\mathstrut -\mathstrut 33999q^{8} \) \(\mathstrut +\mathstrut 177147q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut +\mathstrut 729q^{3} \) \(\mathstrut +\mathstrut 4757q^{4} \) \(\mathstrut +\mathstrut 9375q^{5} \) \(\mathstrut -\mathstrut 243q^{6} \) \(\mathstrut -\mathstrut 14608q^{7} \) \(\mathstrut -\mathstrut 33999q^{8} \) \(\mathstrut +\mathstrut 177147q^{9} \) \(\mathstrut -\mathstrut 3125q^{10} \) \(\mathstrut +\mathstrut 540620q^{11} \) \(\mathstrut +\mathstrut 1155951q^{12} \) \(\mathstrut +\mathstrut 840970q^{13} \) \(\mathstrut +\mathstrut 5432712q^{14} \) \(\mathstrut +\mathstrut 2278125q^{15} \) \(\mathstrut +\mathstrut 5062961q^{16} \) \(\mathstrut +\mathstrut 15165038q^{17} \) \(\mathstrut -\mathstrut 59049q^{18} \) \(\mathstrut +\mathstrut 17743756q^{19} \) \(\mathstrut +\mathstrut 14865625q^{20} \) \(\mathstrut -\mathstrut 3549744q^{21} \) \(\mathstrut +\mathstrut 11176076q^{22} \) \(\mathstrut -\mathstrut 28140816q^{23} \) \(\mathstrut -\mathstrut 8261757q^{24} \) \(\mathstrut +\mathstrut 29296875q^{25} \) \(\mathstrut -\mathstrut 52021894q^{26} \) \(\mathstrut +\mathstrut 43046721q^{27} \) \(\mathstrut -\mathstrut 277157944q^{28} \) \(\mathstrut -\mathstrut 67382798q^{29} \) \(\mathstrut -\mathstrut 759375q^{30} \) \(\mathstrut -\mathstrut 206919496q^{31} \) \(\mathstrut -\mathstrut 46592663q^{32} \) \(\mathstrut +\mathstrut 131370660q^{33} \) \(\mathstrut -\mathstrut 1230469666q^{34} \) \(\mathstrut -\mathstrut 45650000q^{35} \) \(\mathstrut +\mathstrut 280896093q^{36} \) \(\mathstrut -\mathstrut 318337278q^{37} \) \(\mathstrut +\mathstrut 653190692q^{38} \) \(\mathstrut +\mathstrut 204355710q^{39} \) \(\mathstrut -\mathstrut 106246875q^{40} \) \(\mathstrut +\mathstrut 2110085854q^{41} \) \(\mathstrut +\mathstrut 1320149016q^{42} \) \(\mathstrut +\mathstrut 418259692q^{43} \) \(\mathstrut +\mathstrut 2558131108q^{44} \) \(\mathstrut +\mathstrut 553584375q^{45} \) \(\mathstrut -\mathstrut 137169096q^{46} \) \(\mathstrut -\mathstrut 1599668584q^{47} \) \(\mathstrut +\mathstrut 1230299523q^{48} \) \(\mathstrut -\mathstrut 316107077q^{49} \) \(\mathstrut -\mathstrut 9765625q^{50} \) \(\mathstrut +\mathstrut 3685104234q^{51} \) \(\mathstrut -\mathstrut 10897289202q^{52} \) \(\mathstrut +\mathstrut 4489142234q^{53} \) \(\mathstrut -\mathstrut 14348907q^{54} \) \(\mathstrut +\mathstrut 1689437500q^{55} \) \(\mathstrut +\mathstrut 7768845960q^{56} \) \(\mathstrut +\mathstrut 4311732708q^{57} \) \(\mathstrut -\mathstrut 24168830726q^{58} \) \(\mathstrut +\mathstrut 11102167484q^{59} \) \(\mathstrut +\mathstrut 3612346875q^{60} \) \(\mathstrut -\mathstrut 3568120958q^{61} \) \(\mathstrut -\mathstrut 35509109136q^{62} \) \(\mathstrut -\mathstrut 862587792q^{63} \) \(\mathstrut -\mathstrut 35608208271q^{64} \) \(\mathstrut +\mathstrut 2628031250q^{65} \) \(\mathstrut +\mathstrut 2715786468q^{66} \) \(\mathstrut +\mathstrut 2229942788q^{67} \) \(\mathstrut -\mathstrut 1367872838q^{68} \) \(\mathstrut -\mathstrut 6838218288q^{69} \) \(\mathstrut +\mathstrut 16977225000q^{70} \) \(\mathstrut +\mathstrut 49842766696q^{71} \) \(\mathstrut -\mathstrut 2007606951q^{72} \) \(\mathstrut +\mathstrut 40752219934q^{73} \) \(\mathstrut -\mathstrut 37519971278q^{74} \) \(\mathstrut +\mathstrut 7119140625q^{75} \) \(\mathstrut +\mathstrut 115970329116q^{76} \) \(\mathstrut -\mathstrut 17819224896q^{77} \) \(\mathstrut -\mathstrut 12641320242q^{78} \) \(\mathstrut +\mathstrut 113159960q^{79} \) \(\mathstrut +\mathstrut 15821753125q^{80} \) \(\mathstrut +\mathstrut 10460353203q^{81} \) \(\mathstrut -\mathstrut 30171431066q^{82} \) \(\mathstrut +\mathstrut 6259660308q^{83} \) \(\mathstrut -\mathstrut 67349380392q^{84} \) \(\mathstrut +\mathstrut 47390743750q^{85} \) \(\mathstrut +\mathstrut 114296127740q^{86} \) \(\mathstrut -\mathstrut 16374019914q^{87} \) \(\mathstrut +\mathstrut 7548672276q^{88} \) \(\mathstrut -\mathstrut 59972401554q^{89} \) \(\mathstrut -\mathstrut 184528125q^{90} \) \(\mathstrut +\mathstrut 118873361824q^{91} \) \(\mathstrut -\mathstrut 221705928648q^{92} \) \(\mathstrut -\mathstrut 50281437528q^{93} \) \(\mathstrut +\mathstrut 92816682800q^{94} \) \(\mathstrut +\mathstrut 55449237500q^{95} \) \(\mathstrut -\mathstrut 11322017109q^{96} \) \(\mathstrut -\mathstrut 207831285882q^{97} \) \(\mathstrut -\mathstrut 288264739625q^{98} \) \(\mathstrut +\mathstrut 31923070380q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 72.6470 1.60529 0.802643 0.596459i \(-0.203426\pi\)
0.802643 + 0.596459i \(0.203426\pi\)
\(3\) 243.000 0.577350
\(4\) 3229.58 1.57694
\(5\) 3125.00 0.447214
\(6\) 17653.2 0.926813
\(7\) 8974.61 0.201826 0.100913 0.994895i \(-0.467824\pi\)
0.100913 + 0.994895i \(0.467824\pi\)
\(8\) 85838.4 0.926162
\(9\) 59049.0 0.333333
\(10\) 227022. 0.717906
\(11\) 421205. 0.788559 0.394279 0.918991i \(-0.370994\pi\)
0.394279 + 0.918991i \(0.370994\pi\)
\(12\) 784789. 0.910449
\(13\) −1.24336e6 −0.928770 −0.464385 0.885633i \(-0.653725\pi\)
−0.464385 + 0.885633i \(0.653725\pi\)
\(14\) 651979. 0.323988
\(15\) 759375. 0.258199
\(16\) −378284. −0.0901900
\(17\) −5.93114e6 −1.01314 −0.506569 0.862199i \(-0.669087\pi\)
−0.506569 + 0.862199i \(0.669087\pi\)
\(18\) 4.28973e6 0.535096
\(19\) 1.88682e7 1.74817 0.874087 0.485769i \(-0.161460\pi\)
0.874087 + 0.485769i \(0.161460\pi\)
\(20\) 1.00924e7 0.705231
\(21\) 2.18083e6 0.116524
\(22\) 3.05993e7 1.26586
\(23\) −2.72256e7 −0.882013 −0.441007 0.897504i \(-0.645378\pi\)
−0.441007 + 0.897504i \(0.645378\pi\)
\(24\) 2.08587e7 0.534720
\(25\) 9.76562e6 0.200000
\(26\) −9.03263e7 −1.49094
\(27\) 1.43489e7 0.192450
\(28\) 2.89843e7 0.318268
\(29\) −1.15466e8 −1.04536 −0.522678 0.852530i \(-0.675067\pi\)
−0.522678 + 0.852530i \(0.675067\pi\)
\(30\) 5.51663e7 0.414483
\(31\) −2.73479e8 −1.71567 −0.857836 0.513924i \(-0.828191\pi\)
−0.857836 + 0.513924i \(0.828191\pi\)
\(32\) −2.03278e8 −1.07094
\(33\) 1.02353e8 0.455275
\(34\) −4.30879e8 −1.62638
\(35\) 2.80457e7 0.0902592
\(36\) 1.90704e8 0.525648
\(37\) −2.86342e8 −0.678852 −0.339426 0.940633i \(-0.610233\pi\)
−0.339426 + 0.940633i \(0.610233\pi\)
\(38\) 1.37071e9 2.80632
\(39\) −3.02136e8 −0.536226
\(40\) 2.68245e8 0.414192
\(41\) 4.51798e8 0.609022 0.304511 0.952509i \(-0.401507\pi\)
0.304511 + 0.952509i \(0.401507\pi\)
\(42\) 1.58431e8 0.187055
\(43\) 1.30494e9 1.35368 0.676838 0.736132i \(-0.263350\pi\)
0.676838 + 0.736132i \(0.263350\pi\)
\(44\) 1.36032e9 1.24351
\(45\) 1.84528e8 0.149071
\(46\) −1.97786e9 −1.41588
\(47\) −9.11661e8 −0.579823 −0.289911 0.957053i \(-0.593626\pi\)
−0.289911 + 0.957053i \(0.593626\pi\)
\(48\) −9.19231e7 −0.0520712
\(49\) −1.89678e9 −0.959266
\(50\) 7.09443e8 0.321057
\(51\) −1.44127e9 −0.584936
\(52\) −4.01553e9 −1.46462
\(53\) 3.44031e9 1.13001 0.565003 0.825089i \(-0.308875\pi\)
0.565003 + 0.825089i \(0.308875\pi\)
\(54\) 1.04240e9 0.308938
\(55\) 1.31627e9 0.352654
\(56\) 7.70367e8 0.186923
\(57\) 4.58496e9 1.00931
\(58\) −8.38824e9 −1.67810
\(59\) 1.06320e10 1.93610 0.968049 0.250762i \(-0.0806812\pi\)
0.968049 + 0.250762i \(0.0806812\pi\)
\(60\) 2.45246e9 0.407165
\(61\) 6.85337e9 1.03894 0.519469 0.854489i \(-0.326130\pi\)
0.519469 + 0.854489i \(0.326130\pi\)
\(62\) −1.98674e10 −2.75414
\(63\) 5.29942e8 0.0672752
\(64\) −1.39928e10 −1.62898
\(65\) −3.88550e9 −0.415359
\(66\) 7.43563e9 0.730846
\(67\) 5.26360e9 0.476290 0.238145 0.971230i \(-0.423461\pi\)
0.238145 + 0.971230i \(0.423461\pi\)
\(68\) −1.91551e10 −1.59766
\(69\) −6.61583e9 −0.509231
\(70\) 2.03743e9 0.144892
\(71\) 1.72726e10 1.13615 0.568076 0.822976i \(-0.307688\pi\)
0.568076 + 0.822976i \(0.307688\pi\)
\(72\) 5.06867e9 0.308721
\(73\) 5.86468e9 0.331107 0.165554 0.986201i \(-0.447059\pi\)
0.165554 + 0.986201i \(0.447059\pi\)
\(74\) −2.08019e10 −1.08975
\(75\) 2.37305e9 0.115470
\(76\) 6.09363e10 2.75677
\(77\) 3.78015e9 0.159151
\(78\) −2.19493e10 −0.860796
\(79\) −2.16383e10 −0.791178 −0.395589 0.918428i \(-0.629459\pi\)
−0.395589 + 0.918428i \(0.629459\pi\)
\(80\) −1.18214e9 −0.0403342
\(81\) 3.48678e9 0.111111
\(82\) 3.28217e10 0.977655
\(83\) −6.48232e9 −0.180635 −0.0903173 0.995913i \(-0.528788\pi\)
−0.0903173 + 0.995913i \(0.528788\pi\)
\(84\) 7.04317e9 0.183752
\(85\) −1.85348e10 −0.453089
\(86\) 9.48001e10 2.17304
\(87\) −2.80582e10 −0.603537
\(88\) 3.61556e10 0.730333
\(89\) 7.32562e10 1.39059 0.695296 0.718724i \(-0.255273\pi\)
0.695296 + 0.718724i \(0.255273\pi\)
\(90\) 1.34054e10 0.239302
\(91\) −1.11587e10 −0.187450
\(92\) −8.79275e10 −1.39089
\(93\) −6.64553e10 −0.990543
\(94\) −6.62294e10 −0.930782
\(95\) 5.89630e10 0.781807
\(96\) −4.93966e10 −0.618309
\(97\) −1.45891e11 −1.72498 −0.862489 0.506076i \(-0.831096\pi\)
−0.862489 + 0.506076i \(0.831096\pi\)
\(98\) −1.37796e11 −1.53990
\(99\) 2.48718e10 0.262853
\(100\) 3.15389e10 0.315389
\(101\) −9.19701e10 −0.870721 −0.435360 0.900256i \(-0.643379\pi\)
−0.435360 + 0.900256i \(0.643379\pi\)
\(102\) −1.04704e11 −0.938990
\(103\) 1.18655e11 1.00851 0.504257 0.863553i \(-0.331766\pi\)
0.504257 + 0.863553i \(0.331766\pi\)
\(104\) −1.06728e11 −0.860191
\(105\) 6.81510e9 0.0521112
\(106\) 2.49928e11 1.81398
\(107\) 2.63515e10 0.181633 0.0908164 0.995868i \(-0.471052\pi\)
0.0908164 + 0.995868i \(0.471052\pi\)
\(108\) 4.63410e10 0.303483
\(109\) 1.24011e9 0.00771994 0.00385997 0.999993i \(-0.498771\pi\)
0.00385997 + 0.999993i \(0.498771\pi\)
\(110\) 9.56228e10 0.566111
\(111\) −6.95810e10 −0.391935
\(112\) −3.39495e9 −0.0182027
\(113\) 1.82045e11 0.929498 0.464749 0.885443i \(-0.346145\pi\)
0.464749 + 0.885443i \(0.346145\pi\)
\(114\) 3.33084e11 1.62023
\(115\) −8.50802e10 −0.394448
\(116\) −3.72906e11 −1.64847
\(117\) −7.34191e10 −0.309590
\(118\) 7.72380e11 3.10799
\(119\) −5.32297e10 −0.204477
\(120\) 6.51836e10 0.239134
\(121\) −1.07898e11 −0.378175
\(122\) 4.97876e11 1.66779
\(123\) 1.09787e11 0.351619
\(124\) −8.83222e11 −2.70552
\(125\) 3.05176e10 0.0894427
\(126\) 3.84987e10 0.107996
\(127\) −3.53295e11 −0.948892 −0.474446 0.880285i \(-0.657351\pi\)
−0.474446 + 0.880285i \(0.657351\pi\)
\(128\) −6.00223e11 −1.54404
\(129\) 3.17101e11 0.781545
\(130\) −2.82270e11 −0.666770
\(131\) 2.61604e11 0.592451 0.296225 0.955118i \(-0.404272\pi\)
0.296225 + 0.955118i \(0.404272\pi\)
\(132\) 3.30557e11 0.717943
\(133\) 1.69334e11 0.352827
\(134\) 3.82384e11 0.764582
\(135\) 4.48403e10 0.0860663
\(136\) −5.09119e11 −0.938330
\(137\) −1.30283e11 −0.230634 −0.115317 0.993329i \(-0.536788\pi\)
−0.115317 + 0.993329i \(0.536788\pi\)
\(138\) −4.80620e11 −0.817461
\(139\) −5.52082e11 −0.902447 −0.451224 0.892411i \(-0.649012\pi\)
−0.451224 + 0.892411i \(0.649012\pi\)
\(140\) 9.05758e10 0.142334
\(141\) −2.21534e11 −0.334761
\(142\) 1.25480e12 1.82385
\(143\) −5.23710e11 −0.732390
\(144\) −2.23373e10 −0.0300633
\(145\) −3.60831e11 −0.467498
\(146\) 4.26051e11 0.531522
\(147\) −4.60918e11 −0.553833
\(148\) −9.24764e11 −1.07051
\(149\) 1.76536e12 1.96929 0.984646 0.174564i \(-0.0558517\pi\)
0.984646 + 0.174564i \(0.0558517\pi\)
\(150\) 1.72395e11 0.185363
\(151\) −3.08570e11 −0.319875 −0.159937 0.987127i \(-0.551129\pi\)
−0.159937 + 0.987127i \(0.551129\pi\)
\(152\) 1.61961e12 1.61909
\(153\) −3.50228e11 −0.337713
\(154\) 2.74617e11 0.255484
\(155\) −8.54621e11 −0.767271
\(156\) −9.75774e11 −0.845598
\(157\) −3.92737e11 −0.328590 −0.164295 0.986411i \(-0.552535\pi\)
−0.164295 + 0.986411i \(0.552535\pi\)
\(158\) −1.57196e12 −1.27007
\(159\) 8.35996e11 0.652409
\(160\) −6.35245e11 −0.478940
\(161\) −2.44340e11 −0.178013
\(162\) 2.53304e11 0.178365
\(163\) 3.08103e11 0.209732 0.104866 0.994486i \(-0.466559\pi\)
0.104866 + 0.994486i \(0.466559\pi\)
\(164\) 1.45912e12 0.960394
\(165\) 3.19853e11 0.203605
\(166\) −4.70921e11 −0.289970
\(167\) −2.05731e12 −1.22563 −0.612814 0.790227i \(-0.709962\pi\)
−0.612814 + 0.790227i \(0.709962\pi\)
\(168\) 1.87199e11 0.107920
\(169\) −2.46218e11 −0.137386
\(170\) −1.34650e12 −0.727338
\(171\) 1.11415e12 0.582725
\(172\) 4.21442e12 2.13467
\(173\) 1.53807e12 0.754610 0.377305 0.926089i \(-0.376851\pi\)
0.377305 + 0.926089i \(0.376851\pi\)
\(174\) −2.03834e12 −0.968849
\(175\) 8.76427e10 0.0403651
\(176\) −1.59335e11 −0.0711201
\(177\) 2.58357e12 1.11781
\(178\) 5.32184e12 2.23230
\(179\) 7.80906e11 0.317619 0.158810 0.987309i \(-0.449234\pi\)
0.158810 + 0.987309i \(0.449234\pi\)
\(180\) 5.95949e11 0.235077
\(181\) 3.43484e12 1.31424 0.657119 0.753787i \(-0.271775\pi\)
0.657119 + 0.753787i \(0.271775\pi\)
\(182\) −8.10644e11 −0.300911
\(183\) 1.66537e12 0.599831
\(184\) −2.33701e12 −0.816887
\(185\) −8.94818e11 −0.303592
\(186\) −4.82778e12 −1.59011
\(187\) −2.49823e12 −0.798919
\(188\) −2.94429e12 −0.914348
\(189\) 1.28776e11 0.0388414
\(190\) 4.28348e12 1.25502
\(191\) −1.22458e12 −0.348580 −0.174290 0.984694i \(-0.555763\pi\)
−0.174290 + 0.984694i \(0.555763\pi\)
\(192\) −3.40026e12 −0.940492
\(193\) −4.63699e11 −0.124644 −0.0623220 0.998056i \(-0.519851\pi\)
−0.0623220 + 0.998056i \(0.519851\pi\)
\(194\) −1.05985e13 −2.76908
\(195\) −9.44176e11 −0.239807
\(196\) −6.12582e12 −1.51271
\(197\) −3.26993e12 −0.785188 −0.392594 0.919712i \(-0.628422\pi\)
−0.392594 + 0.919712i \(0.628422\pi\)
\(198\) 1.80686e12 0.421954
\(199\) 8.62553e12 1.95927 0.979634 0.200792i \(-0.0643514\pi\)
0.979634 + 0.200792i \(0.0643514\pi\)
\(200\) 8.38266e11 0.185232
\(201\) 1.27905e12 0.274986
\(202\) −6.68135e12 −1.39776
\(203\) −1.03626e12 −0.210980
\(204\) −4.65469e12 −0.922412
\(205\) 1.41187e12 0.272363
\(206\) 8.61994e12 1.61895
\(207\) −1.60765e12 −0.294004
\(208\) 4.70343e11 0.0837658
\(209\) 7.94737e12 1.37854
\(210\) 4.95096e11 0.0836534
\(211\) −1.20136e13 −1.97752 −0.988761 0.149506i \(-0.952232\pi\)
−0.988761 + 0.149506i \(0.952232\pi\)
\(212\) 1.11108e13 1.78196
\(213\) 4.19724e12 0.655958
\(214\) 1.91436e12 0.291573
\(215\) 4.07794e12 0.605382
\(216\) 1.23169e12 0.178240
\(217\) −2.45436e12 −0.346267
\(218\) 9.00901e10 0.0123927
\(219\) 1.42512e12 0.191165
\(220\) 4.25099e12 0.556116
\(221\) 7.37454e12 0.940973
\(222\) −5.05485e12 −0.629169
\(223\) −1.23299e13 −1.49722 −0.748608 0.663013i \(-0.769277\pi\)
−0.748608 + 0.663013i \(0.769277\pi\)
\(224\) −1.82434e12 −0.216144
\(225\) 5.76650e11 0.0666667
\(226\) 1.32250e13 1.49211
\(227\) 8.62723e12 0.950012 0.475006 0.879983i \(-0.342446\pi\)
0.475006 + 0.879983i \(0.342446\pi\)
\(228\) 1.48075e13 1.59162
\(229\) 6.94039e11 0.0728264 0.0364132 0.999337i \(-0.488407\pi\)
0.0364132 + 0.999337i \(0.488407\pi\)
\(230\) −6.18082e12 −0.633203
\(231\) 9.18578e11 0.0918861
\(232\) −9.91140e12 −0.968169
\(233\) −1.07799e13 −1.02839 −0.514196 0.857673i \(-0.671910\pi\)
−0.514196 + 0.857673i \(0.671910\pi\)
\(234\) −5.33368e12 −0.496981
\(235\) −2.84894e12 −0.259305
\(236\) 3.43368e13 3.05312
\(237\) −5.25811e12 −0.456787
\(238\) −3.86697e12 −0.328245
\(239\) −2.37538e13 −1.97036 −0.985178 0.171534i \(-0.945128\pi\)
−0.985178 + 0.171534i \(0.945128\pi\)
\(240\) −2.87260e11 −0.0232870
\(241\) 2.23146e12 0.176805 0.0884026 0.996085i \(-0.471824\pi\)
0.0884026 + 0.996085i \(0.471824\pi\)
\(242\) −7.83845e12 −0.607079
\(243\) 8.47289e11 0.0641500
\(244\) 2.21335e13 1.63835
\(245\) −5.92745e12 −0.428997
\(246\) 7.97568e12 0.564449
\(247\) −2.34599e13 −1.62365
\(248\) −2.34750e13 −1.58899
\(249\) −1.57520e12 −0.104289
\(250\) 2.21701e12 0.143581
\(251\) 4.42422e12 0.280305 0.140153 0.990130i \(-0.455241\pi\)
0.140153 + 0.990130i \(0.455241\pi\)
\(252\) 1.71149e12 0.106089
\(253\) −1.14676e13 −0.695519
\(254\) −2.56658e13 −1.52324
\(255\) −4.50396e12 −0.261591
\(256\) −1.49470e13 −0.849641
\(257\) 1.74889e13 0.973039 0.486520 0.873670i \(-0.338266\pi\)
0.486520 + 0.873670i \(0.338266\pi\)
\(258\) 2.30364e13 1.25460
\(259\) −2.56981e12 −0.137010
\(260\) −1.25485e13 −0.654998
\(261\) −6.81814e12 −0.348452
\(262\) 1.90047e13 0.951053
\(263\) −9.99599e12 −0.489857 −0.244929 0.969541i \(-0.578765\pi\)
−0.244929 + 0.969541i \(0.578765\pi\)
\(264\) 8.78581e12 0.421658
\(265\) 1.07510e13 0.505354
\(266\) 1.23016e13 0.566388
\(267\) 1.78013e13 0.802858
\(268\) 1.69992e13 0.751083
\(269\) 3.47374e13 1.50370 0.751848 0.659336i \(-0.229163\pi\)
0.751848 + 0.659336i \(0.229163\pi\)
\(270\) 3.25751e12 0.138161
\(271\) −5.11553e12 −0.212598 −0.106299 0.994334i \(-0.533900\pi\)
−0.106299 + 0.994334i \(0.533900\pi\)
\(272\) 2.24366e12 0.0913750
\(273\) −2.71156e12 −0.108224
\(274\) −9.46464e12 −0.370234
\(275\) 4.11333e12 0.157712
\(276\) −2.13664e13 −0.803029
\(277\) 1.12045e13 0.412812 0.206406 0.978466i \(-0.433823\pi\)
0.206406 + 0.978466i \(0.433823\pi\)
\(278\) −4.01071e13 −1.44869
\(279\) −1.61486e13 −0.571890
\(280\) 2.40740e12 0.0835946
\(281\) −1.18779e13 −0.404441 −0.202220 0.979340i \(-0.564816\pi\)
−0.202220 + 0.979340i \(0.564816\pi\)
\(282\) −1.60938e13 −0.537387
\(283\) −1.81554e13 −0.594540 −0.297270 0.954793i \(-0.596076\pi\)
−0.297270 + 0.954793i \(0.596076\pi\)
\(284\) 5.57832e13 1.79165
\(285\) 1.43280e13 0.451377
\(286\) −3.80459e13 −1.17570
\(287\) 4.05471e12 0.122916
\(288\) −1.20034e13 −0.356981
\(289\) 9.06488e11 0.0264499
\(290\) −2.62133e13 −0.750467
\(291\) −3.54515e13 −0.995917
\(292\) 1.89405e13 0.522138
\(293\) 6.34023e13 1.71527 0.857637 0.514256i \(-0.171932\pi\)
0.857637 + 0.514256i \(0.171932\pi\)
\(294\) −3.34843e13 −0.889060
\(295\) 3.32249e13 0.865849
\(296\) −2.45791e13 −0.628727
\(297\) 6.04384e12 0.151758
\(298\) 1.28248e14 3.16128
\(299\) 3.38513e13 0.819188
\(300\) 7.66395e12 0.182090
\(301\) 1.17113e13 0.273207
\(302\) −2.24167e13 −0.513491
\(303\) −2.23487e13 −0.502711
\(304\) −7.13753e12 −0.157668
\(305\) 2.14168e13 0.464627
\(306\) −2.54430e13 −0.542126
\(307\) 5.09373e13 1.06604 0.533021 0.846102i \(-0.321057\pi\)
0.533021 + 0.846102i \(0.321057\pi\)
\(308\) 1.22083e13 0.250973
\(309\) 2.88332e13 0.582266
\(310\) −6.20856e13 −1.23169
\(311\) −2.18208e13 −0.425292 −0.212646 0.977129i \(-0.568208\pi\)
−0.212646 + 0.977129i \(0.568208\pi\)
\(312\) −2.59349e13 −0.496632
\(313\) 4.34705e13 0.817901 0.408950 0.912557i \(-0.365895\pi\)
0.408950 + 0.912557i \(0.365895\pi\)
\(314\) −2.85312e13 −0.527481
\(315\) 1.65607e12 0.0300864
\(316\) −6.98827e13 −1.24764
\(317\) 6.91742e12 0.121372 0.0606860 0.998157i \(-0.480671\pi\)
0.0606860 + 0.998157i \(0.480671\pi\)
\(318\) 6.07326e13 1.04730
\(319\) −4.86348e13 −0.824325
\(320\) −4.37276e13 −0.728502
\(321\) 6.40341e12 0.104866
\(322\) −1.77505e13 −0.285762
\(323\) −1.11910e14 −1.77114
\(324\) 1.12609e13 0.175216
\(325\) −1.21422e13 −0.185754
\(326\) 2.23828e13 0.336679
\(327\) 3.01346e11 0.00445711
\(328\) 3.87816e13 0.564053
\(329\) −8.18181e12 −0.117023
\(330\) 2.32363e13 0.326844
\(331\) −3.99718e13 −0.552967 −0.276484 0.961019i \(-0.589169\pi\)
−0.276484 + 0.961019i \(0.589169\pi\)
\(332\) −2.09352e13 −0.284851
\(333\) −1.69082e13 −0.226284
\(334\) −1.49457e14 −1.96748
\(335\) 1.64487e13 0.213003
\(336\) −8.24974e11 −0.0105093
\(337\) 6.16325e13 0.772405 0.386202 0.922414i \(-0.373787\pi\)
0.386202 + 0.922414i \(0.373787\pi\)
\(338\) −1.78870e13 −0.220544
\(339\) 4.42370e13 0.536646
\(340\) −5.98597e13 −0.714497
\(341\) −1.15191e14 −1.35291
\(342\) 8.09393e13 0.935440
\(343\) −3.47686e13 −0.395430
\(344\) 1.12014e14 1.25372
\(345\) −2.06745e13 −0.227735
\(346\) 1.11736e14 1.21137
\(347\) −1.69421e13 −0.180782 −0.0903912 0.995906i \(-0.528812\pi\)
−0.0903912 + 0.995906i \(0.528812\pi\)
\(348\) −9.06162e13 −0.951744
\(349\) 8.63767e13 0.893011 0.446506 0.894781i \(-0.352668\pi\)
0.446506 + 0.894781i \(0.352668\pi\)
\(350\) 6.36698e12 0.0647976
\(351\) −1.78408e13 −0.178742
\(352\) −8.56219e13 −0.844501
\(353\) −1.74597e14 −1.69541 −0.847706 0.530467i \(-0.822017\pi\)
−0.847706 + 0.530467i \(0.822017\pi\)
\(354\) 1.87688e14 1.79440
\(355\) 5.39768e13 0.508103
\(356\) 2.36587e14 2.19289
\(357\) −1.29348e13 −0.118055
\(358\) 5.67304e13 0.509870
\(359\) 4.82814e13 0.427327 0.213664 0.976907i \(-0.431460\pi\)
0.213664 + 0.976907i \(0.431460\pi\)
\(360\) 1.58396e13 0.138064
\(361\) 2.39517e14 2.05611
\(362\) 2.49530e14 2.10973
\(363\) −2.62192e13 −0.218339
\(364\) −3.60379e13 −0.295598
\(365\) 1.83271e13 0.148076
\(366\) 1.20984e14 0.962901
\(367\) −8.66249e13 −0.679171 −0.339586 0.940575i \(-0.610287\pi\)
−0.339586 + 0.940575i \(0.610287\pi\)
\(368\) 1.02990e13 0.0795488
\(369\) 2.66782e13 0.203007
\(370\) −6.50058e13 −0.487352
\(371\) 3.08755e13 0.228064
\(372\) −2.14623e14 −1.56203
\(373\) −6.19068e13 −0.443956 −0.221978 0.975052i \(-0.571251\pi\)
−0.221978 + 0.975052i \(0.571251\pi\)
\(374\) −1.81489e14 −1.28249
\(375\) 7.41577e12 0.0516398
\(376\) −7.82556e13 −0.537010
\(377\) 1.43565e14 0.970896
\(378\) 9.35518e12 0.0623515
\(379\) −1.30905e14 −0.859883 −0.429942 0.902857i \(-0.641466\pi\)
−0.429942 + 0.902857i \(0.641466\pi\)
\(380\) 1.90426e14 1.23287
\(381\) −8.58506e13 −0.547843
\(382\) −8.89617e13 −0.559570
\(383\) −1.24954e14 −0.774741 −0.387371 0.921924i \(-0.626617\pi\)
−0.387371 + 0.921924i \(0.626617\pi\)
\(384\) −1.45854e14 −0.891450
\(385\) 1.18130e13 0.0711747
\(386\) −3.36863e13 −0.200089
\(387\) 7.70555e13 0.451225
\(388\) −4.71167e14 −2.72020
\(389\) 1.96127e13 0.111639 0.0558193 0.998441i \(-0.482223\pi\)
0.0558193 + 0.998441i \(0.482223\pi\)
\(390\) −6.85915e13 −0.384960
\(391\) 1.61479e14 0.893602
\(392\) −1.62817e14 −0.888436
\(393\) 6.35698e13 0.342052
\(394\) −2.37550e14 −1.26045
\(395\) −6.76197e13 −0.353825
\(396\) 8.03254e13 0.414505
\(397\) −3.05579e14 −1.55516 −0.777580 0.628784i \(-0.783553\pi\)
−0.777580 + 0.628784i \(0.783553\pi\)
\(398\) 6.26619e14 3.14519
\(399\) 4.11483e13 0.203704
\(400\) −3.69418e12 −0.0180380
\(401\) −2.19942e14 −1.05929 −0.529645 0.848220i \(-0.677675\pi\)
−0.529645 + 0.848220i \(0.677675\pi\)
\(402\) 9.29194e13 0.441431
\(403\) 3.40032e14 1.59346
\(404\) −2.97025e14 −1.37308
\(405\) 1.08962e13 0.0496904
\(406\) −7.52812e13 −0.338683
\(407\) −1.20609e14 −0.535315
\(408\) −1.23716e14 −0.541745
\(409\) 2.96496e14 1.28098 0.640488 0.767968i \(-0.278732\pi\)
0.640488 + 0.767968i \(0.278732\pi\)
\(410\) 1.02568e14 0.437220
\(411\) −3.16587e13 −0.133157
\(412\) 3.83207e14 1.59037
\(413\) 9.54177e13 0.390754
\(414\) −1.16791e14 −0.471961
\(415\) −2.02573e13 −0.0807823
\(416\) 2.52748e14 0.994659
\(417\) −1.34156e14 −0.521028
\(418\) 5.77352e14 2.21295
\(419\) 6.30261e13 0.238420 0.119210 0.992869i \(-0.461964\pi\)
0.119210 + 0.992869i \(0.461964\pi\)
\(420\) 2.20099e13 0.0821765
\(421\) 2.35891e13 0.0869282 0.0434641 0.999055i \(-0.486161\pi\)
0.0434641 + 0.999055i \(0.486161\pi\)
\(422\) −8.72755e14 −3.17449
\(423\) −5.38327e13 −0.193274
\(424\) 2.95311e14 1.04657
\(425\) −5.79213e13 −0.202628
\(426\) 3.04917e14 1.05300
\(427\) 6.15063e13 0.209685
\(428\) 8.51043e13 0.286425
\(429\) −1.27261e14 −0.422845
\(430\) 2.96250e14 0.971812
\(431\) −2.46226e14 −0.797461 −0.398731 0.917068i \(-0.630549\pi\)
−0.398731 + 0.917068i \(0.630549\pi\)
\(432\) −5.42796e12 −0.0173571
\(433\) −5.82563e14 −1.83933 −0.919665 0.392704i \(-0.871540\pi\)
−0.919665 + 0.392704i \(0.871540\pi\)
\(434\) −1.78302e14 −0.555857
\(435\) −8.76818e13 −0.269910
\(436\) 4.00503e12 0.0121739
\(437\) −5.13698e14 −1.54191
\(438\) 1.03530e14 0.306874
\(439\) 3.32296e14 0.972681 0.486340 0.873769i \(-0.338331\pi\)
0.486340 + 0.873769i \(0.338331\pi\)
\(440\) 1.12986e14 0.326615
\(441\) −1.12003e14 −0.319755
\(442\) 5.35738e14 1.51053
\(443\) 5.20556e14 1.44960 0.724798 0.688961i \(-0.241933\pi\)
0.724798 + 0.688961i \(0.241933\pi\)
\(444\) −2.24718e14 −0.618060
\(445\) 2.28926e14 0.621891
\(446\) −8.95733e14 −2.40346
\(447\) 4.28984e14 1.13697
\(448\) −1.25580e14 −0.328770
\(449\) 1.80442e14 0.466642 0.233321 0.972400i \(-0.425041\pi\)
0.233321 + 0.972400i \(0.425041\pi\)
\(450\) 4.18919e13 0.107019
\(451\) 1.90300e14 0.480250
\(452\) 5.87931e14 1.46577
\(453\) −7.49825e13 −0.184680
\(454\) 6.26742e14 1.52504
\(455\) −3.48708e13 −0.0838301
\(456\) 3.93566e14 0.934783
\(457\) −8.24111e14 −1.93396 −0.966978 0.254861i \(-0.917970\pi\)
−0.966978 + 0.254861i \(0.917970\pi\)
\(458\) 5.04198e13 0.116907
\(459\) −8.51053e13 −0.194979
\(460\) −2.74773e14 −0.622023
\(461\) 2.21805e14 0.496153 0.248076 0.968740i \(-0.420202\pi\)
0.248076 + 0.968740i \(0.420202\pi\)
\(462\) 6.67319e13 0.147504
\(463\) −7.96390e14 −1.73952 −0.869761 0.493473i \(-0.835727\pi\)
−0.869761 + 0.493473i \(0.835727\pi\)
\(464\) 4.36789e13 0.0942807
\(465\) −2.07673e14 −0.442984
\(466\) −7.83130e14 −1.65086
\(467\) 3.19815e14 0.666280 0.333140 0.942877i \(-0.391892\pi\)
0.333140 + 0.942877i \(0.391892\pi\)
\(468\) −2.37113e14 −0.488206
\(469\) 4.72388e13 0.0961275
\(470\) −2.06967e14 −0.416258
\(471\) −9.54352e13 −0.189711
\(472\) 9.12631e14 1.79314
\(473\) 5.49648e14 1.06745
\(474\) −3.81985e14 −0.733273
\(475\) 1.84259e14 0.349635
\(476\) −1.71910e14 −0.322450
\(477\) 2.03147e14 0.376669
\(478\) −1.72564e15 −3.16299
\(479\) 9.20568e14 1.66806 0.834028 0.551722i \(-0.186029\pi\)
0.834028 + 0.551722i \(0.186029\pi\)
\(480\) −1.54364e14 −0.276516
\(481\) 3.56026e14 0.630497
\(482\) 1.62109e14 0.283823
\(483\) −5.93745e13 −0.102776
\(484\) −3.48465e14 −0.596361
\(485\) −4.55909e14 −0.771434
\(486\) 6.15530e13 0.102979
\(487\) 6.15748e13 0.101858 0.0509288 0.998702i \(-0.483782\pi\)
0.0509288 + 0.998702i \(0.483782\pi\)
\(488\) 5.88282e14 0.962225
\(489\) 7.48690e13 0.121089
\(490\) −4.30611e14 −0.688663
\(491\) 5.24202e14 0.828992 0.414496 0.910051i \(-0.363958\pi\)
0.414496 + 0.910051i \(0.363958\pi\)
\(492\) 3.54566e14 0.554484
\(493\) 6.84843e14 1.05909
\(494\) −1.70429e15 −2.60643
\(495\) 7.77242e13 0.117551
\(496\) 1.03453e14 0.154736
\(497\) 1.55015e14 0.229305
\(498\) −1.14434e14 −0.167414
\(499\) −5.82465e14 −0.842784 −0.421392 0.906878i \(-0.638458\pi\)
−0.421392 + 0.906878i \(0.638458\pi\)
\(500\) 9.85590e13 0.141046
\(501\) −4.99926e14 −0.707616
\(502\) 3.21406e14 0.449970
\(503\) 2.94219e14 0.407424 0.203712 0.979031i \(-0.434699\pi\)
0.203712 + 0.979031i \(0.434699\pi\)
\(504\) 4.54894e13 0.0623078
\(505\) −2.87407e14 −0.389398
\(506\) −8.33086e14 −1.11651
\(507\) −5.98309e13 −0.0793198
\(508\) −1.14099e15 −1.49635
\(509\) 1.77642e13 0.0230462 0.0115231 0.999934i \(-0.496332\pi\)
0.0115231 + 0.999934i \(0.496332\pi\)
\(510\) −3.27199e14 −0.419929
\(511\) 5.26332e13 0.0668259
\(512\) 1.43398e14 0.180119
\(513\) 2.70737e14 0.336436
\(514\) 1.27052e15 1.56201
\(515\) 3.70798e14 0.451021
\(516\) 1.02410e15 1.23245
\(517\) −3.83997e14 −0.457224
\(518\) −1.86689e14 −0.219940
\(519\) 3.73751e14 0.435674
\(520\) −3.33525e14 −0.384689
\(521\) −1.74393e14 −0.199031 −0.0995154 0.995036i \(-0.531729\pi\)
−0.0995154 + 0.995036i \(0.531729\pi\)
\(522\) −4.95317e14 −0.559365
\(523\) 3.37057e14 0.376656 0.188328 0.982106i \(-0.439693\pi\)
0.188328 + 0.982106i \(0.439693\pi\)
\(524\) 8.44872e14 0.934262
\(525\) 2.12972e13 0.0233048
\(526\) −7.26179e14 −0.786361
\(527\) 1.62204e15 1.73821
\(528\) −3.87185e13 −0.0410612
\(529\) −2.11574e14 −0.222052
\(530\) 7.81026e14 0.811238
\(531\) 6.27807e14 0.645366
\(532\) 5.46880e14 0.556388
\(533\) −5.61747e14 −0.565641
\(534\) 1.29321e15 1.28882
\(535\) 8.23484e13 0.0812287
\(536\) 4.51819e14 0.441121
\(537\) 1.89760e14 0.183378
\(538\) 2.52357e15 2.41386
\(539\) −7.98935e14 −0.756438
\(540\) 1.44816e14 0.135722
\(541\) 4.06015e14 0.376667 0.188333 0.982105i \(-0.439691\pi\)
0.188333 + 0.982105i \(0.439691\pi\)
\(542\) −3.71628e14 −0.341281
\(543\) 8.34665e14 0.758775
\(544\) 1.20567e15 1.08501
\(545\) 3.87534e12 0.00345246
\(546\) −1.96986e14 −0.173731
\(547\) −1.88321e15 −1.64425 −0.822125 0.569307i \(-0.807212\pi\)
−0.822125 + 0.569307i \(0.807212\pi\)
\(548\) −4.20759e14 −0.363697
\(549\) 4.04684e14 0.346313
\(550\) 2.98821e14 0.253173
\(551\) −2.17863e15 −1.82746
\(552\) −5.67893e14 −0.471630
\(553\) −1.94195e14 −0.159680
\(554\) 8.13970e14 0.662681
\(555\) −2.17441e14 −0.175279
\(556\) −1.78299e15 −1.42311
\(557\) −1.68243e15 −1.32964 −0.664818 0.747005i \(-0.731491\pi\)
−0.664818 + 0.747005i \(0.731491\pi\)
\(558\) −1.17315e15 −0.918048
\(559\) −1.62251e15 −1.25725
\(560\) −1.06092e13 −0.00814048
\(561\) −6.07069e14 −0.461256
\(562\) −8.62894e14 −0.649243
\(563\) −2.54683e14 −0.189760 −0.0948798 0.995489i \(-0.530247\pi\)
−0.0948798 + 0.995489i \(0.530247\pi\)
\(564\) −7.15461e14 −0.527899
\(565\) 5.68892e14 0.415684
\(566\) −1.31894e15 −0.954407
\(567\) 3.12925e13 0.0224251
\(568\) 1.48265e15 1.05226
\(569\) −1.14053e15 −0.801656 −0.400828 0.916153i \(-0.631277\pi\)
−0.400828 + 0.916153i \(0.631277\pi\)
\(570\) 1.04089e15 0.724589
\(571\) 5.33268e14 0.367660 0.183830 0.982958i \(-0.441150\pi\)
0.183830 + 0.982958i \(0.441150\pi\)
\(572\) −1.69136e15 −1.15494
\(573\) −2.97572e14 −0.201253
\(574\) 2.94562e14 0.197316
\(575\) −2.65875e14 −0.176403
\(576\) −8.26262e14 −0.542993
\(577\) 1.94156e15 1.26382 0.631909 0.775043i \(-0.282272\pi\)
0.631909 + 0.775043i \(0.282272\pi\)
\(578\) 6.58536e13 0.0424597
\(579\) −1.12679e14 −0.0719632
\(580\) −1.16533e15 −0.737218
\(581\) −5.81763e13 −0.0364567
\(582\) −2.57544e15 −1.59873
\(583\) 1.44908e15 0.891076
\(584\) 5.03415e14 0.306659
\(585\) −2.29435e14 −0.138453
\(586\) 4.60599e15 2.75350
\(587\) 1.35103e15 0.800123 0.400062 0.916488i \(-0.368989\pi\)
0.400062 + 0.916488i \(0.368989\pi\)
\(588\) −1.48857e15 −0.873364
\(589\) −5.16004e15 −2.99929
\(590\) 2.41369e15 1.38994
\(591\) −7.94592e14 −0.453329
\(592\) 1.08319e14 0.0612256
\(593\) 1.05549e15 0.591089 0.295544 0.955329i \(-0.404499\pi\)
0.295544 + 0.955329i \(0.404499\pi\)
\(594\) 4.39066e14 0.243615
\(595\) −1.66343e14 −0.0914451
\(596\) 5.70139e15 3.10546
\(597\) 2.09600e15 1.13118
\(598\) 2.45919e15 1.31503
\(599\) −8.49546e14 −0.450132 −0.225066 0.974344i \(-0.572260\pi\)
−0.225066 + 0.974344i \(0.572260\pi\)
\(600\) 2.03699e14 0.106944
\(601\) 1.43534e15 0.746696 0.373348 0.927691i \(-0.378210\pi\)
0.373348 + 0.927691i \(0.378210\pi\)
\(602\) 8.50794e14 0.438575
\(603\) 3.10810e14 0.158763
\(604\) −9.96552e14 −0.504425
\(605\) −3.37181e14 −0.169125
\(606\) −1.62357e15 −0.806995
\(607\) −8.76288e14 −0.431627 −0.215814 0.976435i \(-0.569240\pi\)
−0.215814 + 0.976435i \(0.569240\pi\)
\(608\) −3.83549e15 −1.87219
\(609\) −2.51811e14 −0.121809
\(610\) 1.55586e15 0.745860
\(611\) 1.13352e15 0.538522
\(612\) −1.13109e15 −0.532555
\(613\) 3.29080e14 0.153557 0.0767784 0.997048i \(-0.475537\pi\)
0.0767784 + 0.997048i \(0.475537\pi\)
\(614\) 3.70044e15 1.71130
\(615\) 3.43084e14 0.157249
\(616\) 3.24483e14 0.147400
\(617\) −1.42160e15 −0.640041 −0.320021 0.947411i \(-0.603690\pi\)
−0.320021 + 0.947411i \(0.603690\pi\)
\(618\) 2.09465e15 0.934704
\(619\) −2.67970e15 −1.18519 −0.592595 0.805501i \(-0.701896\pi\)
−0.592595 + 0.805501i \(0.701896\pi\)
\(620\) −2.76007e15 −1.20994
\(621\) −3.90658e14 −0.169744
\(622\) −1.58521e15 −0.682716
\(623\) 6.57446e14 0.280657
\(624\) 1.14293e14 0.0483622
\(625\) 9.53674e13 0.0400000
\(626\) 3.15800e15 1.31296
\(627\) 1.93121e15 0.795899
\(628\) −1.26838e15 −0.518168
\(629\) 1.69833e15 0.687771
\(630\) 1.20308e14 0.0482973
\(631\) 3.85938e15 1.53588 0.767939 0.640523i \(-0.221283\pi\)
0.767939 + 0.640523i \(0.221283\pi\)
\(632\) −1.85740e15 −0.732758
\(633\) −2.91932e15 −1.14172
\(634\) 5.02530e14 0.194837
\(635\) −1.10405e15 −0.424357
\(636\) 2.69992e15 1.02881
\(637\) 2.35838e15 0.890938
\(638\) −3.53317e15 −1.32328
\(639\) 1.01993e15 0.378717
\(640\) −1.87570e15 −0.690514
\(641\) −9.95208e14 −0.363241 −0.181620 0.983369i \(-0.558134\pi\)
−0.181620 + 0.983369i \(0.558134\pi\)
\(642\) 4.65188e14 0.168340
\(643\) −4.37182e15 −1.56856 −0.784282 0.620404i \(-0.786968\pi\)
−0.784282 + 0.620404i \(0.786968\pi\)
\(644\) −7.89115e14 −0.280717
\(645\) 9.90940e14 0.349518
\(646\) −8.12990e15 −2.84319
\(647\) 1.50021e14 0.0520208 0.0260104 0.999662i \(-0.491720\pi\)
0.0260104 + 0.999662i \(0.491720\pi\)
\(648\) 2.99300e14 0.102907
\(649\) 4.47824e15 1.52673
\(650\) −8.82093e14 −0.298188
\(651\) −5.96411e14 −0.199917
\(652\) 9.95044e14 0.330735
\(653\) −3.11485e15 −1.02663 −0.513315 0.858200i \(-0.671583\pi\)
−0.513315 + 0.858200i \(0.671583\pi\)
\(654\) 2.18919e13 0.00715493
\(655\) 8.17513e14 0.264952
\(656\) −1.70908e14 −0.0549277
\(657\) 3.46303e14 0.110369
\(658\) −5.94384e14 −0.187856
\(659\) 1.93056e15 0.605079 0.302540 0.953137i \(-0.402166\pi\)
0.302540 + 0.953137i \(0.402166\pi\)
\(660\) 1.03299e15 0.321074
\(661\) 2.24334e15 0.691491 0.345745 0.938328i \(-0.387626\pi\)
0.345745 + 0.938328i \(0.387626\pi\)
\(662\) −2.90383e15 −0.887671
\(663\) 1.79201e15 0.543271
\(664\) −5.56432e14 −0.167297
\(665\) 5.29170e14 0.157789
\(666\) −1.22833e15 −0.363251
\(667\) 3.14363e15 0.922018
\(668\) −6.64424e15 −1.93275
\(669\) −2.99618e15 −0.864418
\(670\) 1.19495e15 0.341931
\(671\) 2.88667e15 0.819264
\(672\) −4.43316e14 −0.124791
\(673\) 6.77758e15 1.89231 0.946154 0.323716i \(-0.104932\pi\)
0.946154 + 0.323716i \(0.104932\pi\)
\(674\) 4.47741e15 1.23993
\(675\) 1.40126e14 0.0384900
\(676\) −7.95180e14 −0.216650
\(677\) 3.35870e15 0.907682 0.453841 0.891083i \(-0.350053\pi\)
0.453841 + 0.891083i \(0.350053\pi\)
\(678\) 3.21369e15 0.861470
\(679\) −1.30931e15 −0.348145
\(680\) −1.59100e15 −0.419634
\(681\) 2.09642e15 0.548490
\(682\) −8.36825e15 −2.17180
\(683\) 8.39057e14 0.216012 0.108006 0.994150i \(-0.465553\pi\)
0.108006 + 0.994150i \(0.465553\pi\)
\(684\) 3.59823e15 0.918925
\(685\) −4.07133e14 −0.103143
\(686\) −2.52584e15 −0.634779
\(687\) 1.68651e14 0.0420463
\(688\) −4.93639e14 −0.122088
\(689\) −4.27755e15 −1.04952
\(690\) −1.50194e15 −0.365580
\(691\) −7.05750e15 −1.70421 −0.852103 0.523375i \(-0.824673\pi\)
−0.852103 + 0.523375i \(0.824673\pi\)
\(692\) 4.96732e15 1.18998
\(693\) 2.23214e14 0.0530505
\(694\) −1.23080e15 −0.290208
\(695\) −1.72525e15 −0.403587
\(696\) −2.40847e15 −0.558973
\(697\) −2.67967e15 −0.617024
\(698\) 6.27501e15 1.43354
\(699\) −2.61953e15 −0.593743
\(700\) 2.83049e14 0.0636536
\(701\) 4.30034e15 0.959519 0.479760 0.877400i \(-0.340724\pi\)
0.479760 + 0.877400i \(0.340724\pi\)
\(702\) −1.29608e15 −0.286932
\(703\) −5.40274e15 −1.18675
\(704\) −5.89385e15 −1.28455
\(705\) −6.92293e14 −0.149710
\(706\) −1.26839e16 −2.72162
\(707\) −8.25396e14 −0.175734
\(708\) 8.34384e15 1.76272
\(709\) 2.30816e15 0.483850 0.241925 0.970295i \(-0.422221\pi\)
0.241925 + 0.970295i \(0.422221\pi\)
\(710\) 3.92125e15 0.815650
\(711\) −1.27772e15 −0.263726
\(712\) 6.28820e15 1.28791
\(713\) 7.44563e15 1.51324
\(714\) −9.39675e14 −0.189512
\(715\) −1.63659e15 −0.327535
\(716\) 2.52200e15 0.500868
\(717\) −5.77218e15 −1.13759
\(718\) 3.50750e15 0.685983
\(719\) 2.20705e14 0.0428354 0.0214177 0.999771i \(-0.493182\pi\)
0.0214177 + 0.999771i \(0.493182\pi\)
\(720\) −6.98041e13 −0.0134447
\(721\) 1.06488e15 0.203544
\(722\) 1.74002e16 3.30065
\(723\) 5.42244e14 0.102079
\(724\) 1.10931e16 2.07248
\(725\) −1.12760e15 −0.209071
\(726\) −1.90474e15 −0.350497
\(727\) −2.09923e15 −0.383373 −0.191686 0.981456i \(-0.561396\pi\)
−0.191686 + 0.981456i \(0.561396\pi\)
\(728\) −9.57843e14 −0.173609
\(729\) 2.05891e14 0.0370370
\(730\) 1.33141e15 0.237704
\(731\) −7.73979e15 −1.37146
\(732\) 5.37844e15 0.945901
\(733\) 6.86229e15 1.19784 0.598918 0.800810i \(-0.295597\pi\)
0.598918 + 0.800810i \(0.295597\pi\)
\(734\) −6.29304e15 −1.09026
\(735\) −1.44037e15 −0.247682
\(736\) 5.53438e15 0.944585
\(737\) 2.21706e15 0.375582
\(738\) 1.93809e15 0.325885
\(739\) 4.84418e14 0.0808493 0.0404246 0.999183i \(-0.487129\pi\)
0.0404246 + 0.999183i \(0.487129\pi\)
\(740\) −2.88989e15 −0.478748
\(741\) −5.70076e15 −0.937416
\(742\) 2.24301e15 0.366109
\(743\) 5.18709e15 0.840398 0.420199 0.907432i \(-0.361960\pi\)
0.420199 + 0.907432i \(0.361960\pi\)
\(744\) −5.70442e15 −0.917403
\(745\) 5.51677e15 0.880694
\(746\) −4.49734e15 −0.712677
\(747\) −3.82775e14 −0.0602115
\(748\) −8.06823e15 −1.25985
\(749\) 2.36494e14 0.0366582
\(750\) 5.38733e14 0.0828966
\(751\) −5.82780e15 −0.890195 −0.445098 0.895482i \(-0.646831\pi\)
−0.445098 + 0.895482i \(0.646831\pi\)
\(752\) 3.44867e14 0.0522942
\(753\) 1.07508e15 0.161834
\(754\) 1.04296e16 1.55857
\(755\) −9.64281e14 −0.143052
\(756\) 4.15892e14 0.0612507
\(757\) −5.62401e14 −0.0822277 −0.0411139 0.999154i \(-0.513091\pi\)
−0.0411139 + 0.999154i \(0.513091\pi\)
\(758\) −9.50983e15 −1.38036
\(759\) −2.78662e15 −0.401558
\(760\) 5.06129e15 0.724080
\(761\) 5.86147e15 0.832512 0.416256 0.909247i \(-0.363342\pi\)
0.416256 + 0.909247i \(0.363342\pi\)
\(762\) −6.23679e15 −0.879445
\(763\) 1.11295e13 0.00155808
\(764\) −3.95487e15 −0.549691
\(765\) −1.09446e15 −0.151030
\(766\) −9.07752e15 −1.24368
\(767\) −1.32193e16 −1.79819
\(768\) −3.63213e15 −0.490541
\(769\) 5.18352e15 0.695072 0.347536 0.937667i \(-0.387018\pi\)
0.347536 + 0.937667i \(0.387018\pi\)
\(770\) 8.58178e14 0.114256
\(771\) 4.24980e15 0.561785
\(772\) −1.49756e15 −0.196557
\(773\) −1.29318e16 −1.68528 −0.842640 0.538478i \(-0.819000\pi\)
−0.842640 + 0.538478i \(0.819000\pi\)
\(774\) 5.59785e15 0.724346
\(775\) −2.67069e15 −0.343134
\(776\) −1.25230e16 −1.59761
\(777\) −6.24463e14 −0.0791026
\(778\) 1.42480e15 0.179212
\(779\) 8.52459e15 1.06468
\(780\) −3.04929e15 −0.378163
\(781\) 7.27530e15 0.895923
\(782\) 1.17310e16 1.43449
\(783\) −1.65681e15 −0.201179
\(784\) 7.17523e14 0.0865162
\(785\) −1.22730e15 −0.146950
\(786\) 4.61815e15 0.549091
\(787\) −2.08385e15 −0.246040 −0.123020 0.992404i \(-0.539258\pi\)
−0.123020 + 0.992404i \(0.539258\pi\)
\(788\) −1.05605e16 −1.23820
\(789\) −2.42903e15 −0.282819
\(790\) −4.91236e15 −0.567991
\(791\) 1.63379e15 0.187597
\(792\) 2.13495e15 0.243444
\(793\) −8.52120e15 −0.964935
\(794\) −2.21994e16 −2.49648
\(795\) 2.61249e15 0.291766
\(796\) 2.78569e16 3.08966
\(797\) −1.37867e16 −1.51859 −0.759293 0.650749i \(-0.774455\pi\)
−0.759293 + 0.650749i \(0.774455\pi\)
\(798\) 2.98930e15 0.327004
\(799\) 5.40719e15 0.587441
\(800\) −1.98514e15 −0.214188
\(801\) 4.32571e15 0.463530
\(802\) −1.59781e16 −1.70046
\(803\) 2.47023e15 0.261097
\(804\) 4.13081e15 0.433638
\(805\) −7.63562e14 −0.0796098
\(806\) 2.47023e16 2.55797
\(807\) 8.44119e15 0.868159
\(808\) −7.89457e15 −0.806428
\(809\) 1.04031e16 1.05547 0.527737 0.849408i \(-0.323041\pi\)
0.527737 + 0.849408i \(0.323041\pi\)
\(810\) 7.91576e14 0.0797673
\(811\) −1.01334e16 −1.01424 −0.507118 0.861877i \(-0.669289\pi\)
−0.507118 + 0.861877i \(0.669289\pi\)
\(812\) −3.34669e15 −0.332703
\(813\) −1.24307e15 −0.122744
\(814\) −8.76185e15 −0.859333
\(815\) 9.62822e14 0.0937949
\(816\) 5.45208e14 0.0527554
\(817\) 2.46218e16 2.36646
\(818\) 2.15396e16 2.05634
\(819\) −6.58908e14 −0.0624832
\(820\) 4.55975e15 0.429501
\(821\) −2.71594e15 −0.254116 −0.127058 0.991895i \(-0.540553\pi\)
−0.127058 + 0.991895i \(0.540553\pi\)
\(822\) −2.29991e15 −0.213755
\(823\) −2.37956e15 −0.219683 −0.109842 0.993949i \(-0.535034\pi\)
−0.109842 + 0.993949i \(0.535034\pi\)
\(824\) 1.01852e16 0.934047
\(825\) 9.99540e14 0.0910549
\(826\) 6.93181e15 0.627273
\(827\) −1.53241e16 −1.37751 −0.688757 0.724992i \(-0.741843\pi\)
−0.688757 + 0.724992i \(0.741843\pi\)
\(828\) −5.19203e15 −0.463629
\(829\) 6.12649e15 0.543453 0.271727 0.962375i \(-0.412405\pi\)
0.271727 + 0.962375i \(0.412405\pi\)
\(830\) −1.47163e15 −0.129679
\(831\) 2.72268e15 0.238337
\(832\) 1.73981e16 1.51295
\(833\) 1.12501e16 0.971870
\(834\) −9.74601e15 −0.836399
\(835\) −6.42908e15 −0.548117
\(836\) 2.56667e16 2.17388
\(837\) −3.92412e15 −0.330181
\(838\) 4.57866e15 0.382733
\(839\) 9.29081e15 0.771547 0.385774 0.922593i \(-0.373935\pi\)
0.385774 + 0.922593i \(0.373935\pi\)
\(840\) 5.84997e14 0.0482634
\(841\) 1.13184e15 0.0927697
\(842\) 1.71368e15 0.139545
\(843\) −2.88633e15 −0.233504
\(844\) −3.87991e16 −3.11844
\(845\) −7.69430e14 −0.0614409
\(846\) −3.91078e15 −0.310261
\(847\) −9.68341e14 −0.0763255
\(848\) −1.30142e15 −0.101915
\(849\) −4.41177e15 −0.343258
\(850\) −4.20780e15 −0.325276
\(851\) 7.79584e15 0.598756
\(852\) 1.35553e16 1.03441
\(853\) −4.51480e15 −0.342310 −0.171155 0.985244i \(-0.554750\pi\)
−0.171155 + 0.985244i \(0.554750\pi\)
\(854\) 4.46825e15 0.336604
\(855\) 3.48171e15 0.260602
\(856\) 2.26197e15 0.168221
\(857\) −1.35507e16 −1.00131 −0.500653 0.865648i \(-0.666907\pi\)
−0.500653 + 0.865648i \(0.666907\pi\)
\(858\) −9.24516e15 −0.678788
\(859\) −4.51231e15 −0.329182 −0.164591 0.986362i \(-0.552630\pi\)
−0.164591 + 0.986362i \(0.552630\pi\)
\(860\) 1.31701e16 0.954654
\(861\) 9.85295e14 0.0709658
\(862\) −1.78876e16 −1.28015
\(863\) 1.85534e15 0.131937 0.0659683 0.997822i \(-0.478986\pi\)
0.0659683 + 0.997822i \(0.478986\pi\)
\(864\) −2.91682e15 −0.206103
\(865\) 4.80647e15 0.337472
\(866\) −4.23214e16 −2.95265
\(867\) 2.20277e14 0.0152709
\(868\) −7.92657e15 −0.546043
\(869\) −9.11417e15 −0.623890
\(870\) −6.36982e15 −0.433283
\(871\) −6.54454e15 −0.442364
\(872\) 1.06449e14 0.00714991
\(873\) −8.61471e15 −0.574993
\(874\) −3.73186e16 −2.47521
\(875\) 2.73883e14 0.0180518
\(876\) 4.60253e15 0.301456
\(877\) −1.67204e16 −1.08830 −0.544150 0.838988i \(-0.683148\pi\)
−0.544150 + 0.838988i \(0.683148\pi\)
\(878\) 2.41403e16 1.56143
\(879\) 1.54068e16 0.990313
\(880\) −4.97923e14 −0.0318059
\(881\) −2.06898e16 −1.31337 −0.656687 0.754163i \(-0.728043\pi\)
−0.656687 + 0.754163i \(0.728043\pi\)
\(882\) −8.13669e15 −0.513299
\(883\) 1.78687e16 1.12024 0.560118 0.828413i \(-0.310756\pi\)
0.560118 + 0.828413i \(0.310756\pi\)
\(884\) 2.38167e16 1.48386
\(885\) 8.07364e15 0.499898
\(886\) 3.78168e16 2.32702
\(887\) −1.14519e16 −0.700323 −0.350161 0.936689i \(-0.613873\pi\)
−0.350161 + 0.936689i \(0.613873\pi\)
\(888\) −5.97273e15 −0.362995
\(889\) −3.17068e15 −0.191511
\(890\) 1.66308e16 0.998314
\(891\) 1.46865e15 0.0876176
\(892\) −3.98206e16 −2.36103
\(893\) −1.72014e16 −1.01363
\(894\) 3.11644e16 1.82516
\(895\) 2.44033e15 0.142044
\(896\) −5.38677e15 −0.311626
\(897\) 8.22586e15 0.472958
\(898\) 1.31086e16 0.749094
\(899\) 3.15774e16 1.79349
\(900\) 1.86234e15 0.105130
\(901\) −2.04050e16 −1.14485
\(902\) 1.38247e16 0.770938
\(903\) 2.84586e15 0.157736
\(904\) 1.56265e16 0.860865
\(905\) 1.07339e16 0.587745
\(906\) −5.44725e15 −0.296464
\(907\) 2.79226e16 1.51048 0.755242 0.655447i \(-0.227520\pi\)
0.755242 + 0.655447i \(0.227520\pi\)
\(908\) 2.78623e16 1.49812
\(909\) −5.43074e15 −0.290240
\(910\) −2.53326e15 −0.134571
\(911\) 6.98498e15 0.368820 0.184410 0.982849i \(-0.440963\pi\)
0.184410 + 0.982849i \(0.440963\pi\)
\(912\) −1.73442e15 −0.0910295
\(913\) −2.73039e15 −0.142441
\(914\) −5.98691e16 −3.10455
\(915\) 5.20428e15 0.268253
\(916\) 2.24146e15 0.114843
\(917\) 2.34780e15 0.119572
\(918\) −6.18264e15 −0.312997
\(919\) −7.45215e15 −0.375013 −0.187506 0.982263i \(-0.560041\pi\)
−0.187506 + 0.982263i \(0.560041\pi\)
\(920\) −7.30315e15 −0.365323
\(921\) 1.23778e16 0.615480
\(922\) 1.61134e16 0.796467
\(923\) −2.14760e16 −1.05522
\(924\) 2.96662e15 0.144899
\(925\) −2.79631e15 −0.135770
\(926\) −5.78553e16 −2.79243
\(927\) 7.00647e15 0.336172
\(928\) 2.34717e16 1.11952
\(929\) 6.90338e15 0.327322 0.163661 0.986517i \(-0.447670\pi\)
0.163661 + 0.986517i \(0.447670\pi\)
\(930\) −1.50868e16 −0.711117
\(931\) −3.57888e16 −1.67696
\(932\) −3.48147e16 −1.62172
\(933\) −5.30244e15 −0.245543
\(934\) 2.32336e16 1.06957
\(935\) −7.80696e15 −0.357288
\(936\) −6.30218e15 −0.286730
\(937\) 3.61273e16 1.63406 0.817030 0.576596i \(-0.195619\pi\)
0.817030 + 0.576596i \(0.195619\pi\)
\(938\) 3.43175e15 0.154312
\(939\) 1.05633e16 0.472215
\(940\) −9.20089e15 −0.408909
\(941\) 2.07857e16 0.918380 0.459190 0.888338i \(-0.348140\pi\)
0.459190 + 0.888338i \(0.348140\pi\)
\(942\) −6.93308e15 −0.304541
\(943\) −1.23005e16 −0.537165
\(944\) −4.02190e15 −0.174617
\(945\) 4.02425e14 0.0173704
\(946\) 3.99303e16 1.71357
\(947\) 3.77508e16 1.61065 0.805326 0.592833i \(-0.201990\pi\)
0.805326 + 0.592833i \(0.201990\pi\)
\(948\) −1.69815e16 −0.720327
\(949\) −7.29190e15 −0.307522
\(950\) 1.33859e16 0.561264
\(951\) 1.68093e15 0.0700741
\(952\) −4.56915e15 −0.189379
\(953\) 2.01734e16 0.831319 0.415659 0.909520i \(-0.363551\pi\)
0.415659 + 0.909520i \(0.363551\pi\)
\(954\) 1.47580e16 0.604661
\(955\) −3.82680e15 −0.155890
\(956\) −7.67149e16 −3.10714
\(957\) −1.18183e16 −0.475924
\(958\) 6.68765e16 2.67771
\(959\) −1.16924e15 −0.0465479
\(960\) −1.06258e16 −0.420601
\(961\) 4.93821e16 1.94353
\(962\) 2.58642e16 1.01213
\(963\) 1.55603e15 0.0605443
\(964\) 7.20668e15 0.278812
\(965\) −1.44906e15 −0.0557425
\(966\) −4.31338e15 −0.164985
\(967\) −2.86737e15 −0.109053 −0.0545266 0.998512i \(-0.517365\pi\)
−0.0545266 + 0.998512i \(0.517365\pi\)
\(968\) −9.26177e15 −0.350251
\(969\) −2.71940e16 −1.02257
\(970\) −3.31204e16 −1.23837
\(971\) 4.06331e16 1.51069 0.755344 0.655329i \(-0.227470\pi\)
0.755344 + 0.655329i \(0.227470\pi\)
\(972\) 2.73639e15 0.101161
\(973\) −4.95472e15 −0.182137
\(974\) 4.47322e15 0.163511
\(975\) −2.95055e15 −0.107245
\(976\) −2.59252e15 −0.0937018
\(977\) −4.73358e16 −1.70126 −0.850628 0.525768i \(-0.823778\pi\)
−0.850628 + 0.525768i \(0.823778\pi\)
\(978\) 5.43901e15 0.194382
\(979\) 3.08559e16 1.09656
\(980\) −1.91432e16 −0.676505
\(981\) 7.32271e13 0.00257331
\(982\) 3.80817e16 1.33077
\(983\) 3.36593e16 1.16966 0.584831 0.811155i \(-0.301161\pi\)
0.584831 + 0.811155i \(0.301161\pi\)
\(984\) 9.42393e15 0.325656
\(985\) −1.02185e16 −0.351147
\(986\) 4.97518e16 1.70014
\(987\) −1.98818e15 −0.0675633
\(988\) −7.57657e16 −2.56041
\(989\) −3.55279e16 −1.19396
\(990\) 5.64643e15 0.188704
\(991\) −4.96944e16 −1.65159 −0.825795 0.563970i \(-0.809273\pi\)
−0.825795 + 0.563970i \(0.809273\pi\)
\(992\) 5.55923e16 1.83738
\(993\) −9.71314e15 −0.319256
\(994\) 1.12614e16 0.368100
\(995\) 2.69548e16 0.876211
\(996\) −5.08725e15 −0.164459
\(997\) 6.41698e15 0.206304 0.103152 0.994666i \(-0.467107\pi\)
0.103152 + 0.994666i \(0.467107\pi\)
\(998\) −4.23143e16 −1.35291
\(999\) −4.10869e15 −0.130645
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 \(a_p\))