Properties

Label 15.12.a.d.1.2
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 1.2
Root \(-1.33067\)
Character \(\chi\) = 15.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.33067 q^{2} +243.000 q^{3} -2046.23 q^{4} +3125.00 q^{5} +323.352 q^{6} +39478.9 q^{7} -5448.05 q^{8} +59049.0 q^{9} +O(q^{10})\) \(q+1.33067 q^{2} +243.000 q^{3} -2046.23 q^{4} +3125.00 q^{5} +323.352 q^{6} +39478.9 q^{7} -5448.05 q^{8} +59049.0 q^{9} +4158.33 q^{10} -137204. q^{11} -497234. q^{12} +2.54995e6 q^{13} +52533.2 q^{14} +759375. q^{15} +4.18343e6 q^{16} +1.02499e7 q^{17} +78574.5 q^{18} -1.05078e7 q^{19} -6.39447e6 q^{20} +9.59336e6 q^{21} -182572. q^{22} +2.32226e7 q^{23} -1.32388e6 q^{24} +9.76562e6 q^{25} +3.39313e6 q^{26} +1.43489e7 q^{27} -8.07828e7 q^{28} -1.59556e8 q^{29} +1.01047e6 q^{30} -1.39582e8 q^{31} +1.67243e7 q^{32} -3.33405e7 q^{33} +1.36392e7 q^{34} +1.23371e8 q^{35} -1.20828e8 q^{36} -2.50524e8 q^{37} -1.39823e7 q^{38} +6.19638e8 q^{39} -1.70252e7 q^{40} +8.03862e8 q^{41} +1.27656e7 q^{42} -6.15730e8 q^{43} +2.80750e8 q^{44} +1.84528e8 q^{45} +3.09015e7 q^{46} +1.40825e9 q^{47} +1.01657e9 q^{48} -4.18747e8 q^{49} +1.29948e7 q^{50} +2.49072e9 q^{51} -5.21779e9 q^{52} +2.24989e9 q^{53} +1.90936e7 q^{54} -4.28762e8 q^{55} -2.15083e8 q^{56} -2.55338e9 q^{57} -2.12316e8 q^{58} -5.57645e9 q^{59} -1.55386e9 q^{60} +2.46257e9 q^{61} -1.85737e8 q^{62} +2.33119e9 q^{63} -8.54541e9 q^{64} +7.96860e9 q^{65} -4.43651e7 q^{66} -9.05284e9 q^{67} -2.09736e10 q^{68} +5.64308e9 q^{69} +1.64166e8 q^{70} +2.45738e10 q^{71} -3.21702e8 q^{72} +2.54920e9 q^{73} -3.33364e8 q^{74} +2.37305e9 q^{75} +2.15013e10 q^{76} -5.41665e9 q^{77} +8.24531e8 q^{78} +1.79099e10 q^{79} +1.30732e10 q^{80} +3.48678e9 q^{81} +1.06967e9 q^{82} +1.40327e10 q^{83} -1.96302e10 q^{84} +3.20309e10 q^{85} -8.19330e8 q^{86} -3.87721e10 q^{87} +7.47493e8 q^{88} -6.35833e10 q^{89} +2.45545e8 q^{90} +1.00669e11 q^{91} -4.75187e10 q^{92} -3.39184e10 q^{93} +1.87391e9 q^{94} -3.28367e10 q^{95} +4.06402e9 q^{96} -8.52774e10 q^{97} -5.57212e8 q^{98} -8.10174e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - q^{2} + 729q^{3} + 4757q^{4} + 9375q^{5} - 243q^{6} - 14608q^{7} - 33999q^{8} + 177147q^{9} + O(q^{10}) \) \( 3q - q^{2} + 729q^{3} + 4757q^{4} + 9375q^{5} - 243q^{6} - 14608q^{7} - 33999q^{8} + 177147q^{9} - 3125q^{10} + 540620q^{11} + 1155951q^{12} + 840970q^{13} + 5432712q^{14} + 2278125q^{15} + 5062961q^{16} + 15165038q^{17} - 59049q^{18} + 17743756q^{19} + 14865625q^{20} - 3549744q^{21} + 11176076q^{22} - 28140816q^{23} - 8261757q^{24} + 29296875q^{25} - 52021894q^{26} + 43046721q^{27} - 277157944q^{28} - 67382798q^{29} - 759375q^{30} - 206919496q^{31} - 46592663q^{32} + 131370660q^{33} - 1230469666q^{34} - 45650000q^{35} + 280896093q^{36} - 318337278q^{37} + 653190692q^{38} + 204355710q^{39} - 106246875q^{40} + 2110085854q^{41} + 1320149016q^{42} + 418259692q^{43} + 2558131108q^{44} + 553584375q^{45} - 137169096q^{46} - 1599668584q^{47} + 1230299523q^{48} - 316107077q^{49} - 9765625q^{50} + 3685104234q^{51} - 10897289202q^{52} + 4489142234q^{53} - 14348907q^{54} + 1689437500q^{55} + 7768845960q^{56} + 4311732708q^{57} - 24168830726q^{58} + 11102167484q^{59} + 3612346875q^{60} - 3568120958q^{61} - 35509109136q^{62} - 862587792q^{63} - 35608208271q^{64} + 2628031250q^{65} + 2715786468q^{66} + 2229942788q^{67} - 1367872838q^{68} - 6838218288q^{69} + 16977225000q^{70} + 49842766696q^{71} - 2007606951q^{72} + 40752219934q^{73} - 37519971278q^{74} + 7119140625q^{75} + 115970329116q^{76} - 17819224896q^{77} - 12641320242q^{78} + 113159960q^{79} + 15821753125q^{80} + 10460353203q^{81} - 30171431066q^{82} + 6259660308q^{83} - 67349380392q^{84} + 47390743750q^{85} + 114296127740q^{86} - 16374019914q^{87} + 7548672276q^{88} - 59972401554q^{89} - 184528125q^{90} + 118873361824q^{91} - 221705928648q^{92} - 50281437528q^{93} + 92816682800q^{94} + 55449237500q^{95} - 11322017109q^{96} - 207831285882q^{97} - 288264739625q^{98} + 31923070380q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33067 0.0294038 0.0147019 0.999892i \(-0.495320\pi\)
0.0147019 + 0.999892i \(0.495320\pi\)
\(3\) 243.000 0.577350
\(4\) −2046.23 −0.999135
\(5\) 3125.00 0.447214
\(6\) 323.352 0.0169763
\(7\) 39478.9 0.887821 0.443910 0.896071i \(-0.353591\pi\)
0.443910 + 0.896071i \(0.353591\pi\)
\(8\) −5448.05 −0.0587822
\(9\) 59049.0 0.333333
\(10\) 4158.33 0.0131498
\(11\) −137204. −0.256866 −0.128433 0.991718i \(-0.540995\pi\)
−0.128433 + 0.991718i \(0.540995\pi\)
\(12\) −497234. −0.576851
\(13\) 2.54995e6 1.90477 0.952387 0.304891i \(-0.0986200\pi\)
0.952387 + 0.304891i \(0.0986200\pi\)
\(14\) 52533.2 0.0261053
\(15\) 759375. 0.258199
\(16\) 4.18343e6 0.997407
\(17\) 1.02499e7 1.75085 0.875426 0.483351i \(-0.160581\pi\)
0.875426 + 0.483351i \(0.160581\pi\)
\(18\) 78574.5 0.00980128
\(19\) −1.05078e7 −0.973565 −0.486783 0.873523i \(-0.661830\pi\)
−0.486783 + 0.873523i \(0.661830\pi\)
\(20\) −6.39447e6 −0.446827
\(21\) 9.59336e6 0.512584
\(22\) −182572. −0.00755283
\(23\) 2.32226e7 0.752328 0.376164 0.926553i \(-0.377243\pi\)
0.376164 + 0.926553i \(0.377243\pi\)
\(24\) −1.32388e6 −0.0339379
\(25\) 9.76562e6 0.200000
\(26\) 3.39313e6 0.0560077
\(27\) 1.43489e7 0.192450
\(28\) −8.07828e7 −0.887053
\(29\) −1.59556e8 −1.44452 −0.722261 0.691621i \(-0.756897\pi\)
−0.722261 + 0.691621i \(0.756897\pi\)
\(30\) 1.01047e6 0.00759204
\(31\) −1.39582e8 −0.875670 −0.437835 0.899055i \(-0.644255\pi\)
−0.437835 + 0.899055i \(0.644255\pi\)
\(32\) 1.67243e7 0.0881098
\(33\) −3.33405e7 −0.148301
\(34\) 1.36392e7 0.0514818
\(35\) 1.23371e8 0.397046
\(36\) −1.20828e8 −0.333045
\(37\) −2.50524e8 −0.593937 −0.296968 0.954887i \(-0.595976\pi\)
−0.296968 + 0.954887i \(0.595976\pi\)
\(38\) −1.39823e7 −0.0286265
\(39\) 6.19638e8 1.09972
\(40\) −1.70252e7 −0.0262882
\(41\) 8.03862e8 1.08360 0.541802 0.840506i \(-0.317742\pi\)
0.541802 + 0.840506i \(0.317742\pi\)
\(42\) 1.27656e7 0.0150719
\(43\) −6.15730e8 −0.638725 −0.319362 0.947633i \(-0.603469\pi\)
−0.319362 + 0.947633i \(0.603469\pi\)
\(44\) 2.80750e8 0.256644
\(45\) 1.84528e8 0.149071
\(46\) 3.09015e7 0.0221213
\(47\) 1.40825e9 0.895655 0.447827 0.894120i \(-0.352198\pi\)
0.447827 + 0.894120i \(0.352198\pi\)
\(48\) 1.01657e9 0.575853
\(49\) −4.18747e8 −0.211774
\(50\) 1.29948e7 0.00588077
\(51\) 2.49072e9 1.01086
\(52\) −5.21779e9 −1.90313
\(53\) 2.24989e9 0.739000 0.369500 0.929231i \(-0.379529\pi\)
0.369500 + 0.929231i \(0.379529\pi\)
\(54\) 1.90936e7 0.00565877
\(55\) −4.28762e8 −0.114874
\(56\) −2.15083e8 −0.0521881
\(57\) −2.55338e9 −0.562088
\(58\) −2.12316e8 −0.0424745
\(59\) −5.57645e9 −1.01548 −0.507740 0.861510i \(-0.669519\pi\)
−0.507740 + 0.861510i \(0.669519\pi\)
\(60\) −1.55386e9 −0.257976
\(61\) 2.46257e9 0.373314 0.186657 0.982425i \(-0.440235\pi\)
0.186657 + 0.982425i \(0.440235\pi\)
\(62\) −1.85737e8 −0.0257480
\(63\) 2.33119e9 0.295940
\(64\) −8.54541e9 −0.994816
\(65\) 7.96860e9 0.851841
\(66\) −4.43651e7 −0.00436063
\(67\) −9.05284e9 −0.819169 −0.409584 0.912272i \(-0.634326\pi\)
−0.409584 + 0.912272i \(0.634326\pi\)
\(68\) −2.09736e10 −1.74934
\(69\) 5.64308e9 0.434357
\(70\) 1.64166e8 0.0116747
\(71\) 2.45738e10 1.61641 0.808205 0.588902i \(-0.200440\pi\)
0.808205 + 0.588902i \(0.200440\pi\)
\(72\) −3.21702e8 −0.0195941
\(73\) 2.54920e9 0.143922 0.0719612 0.997407i \(-0.477074\pi\)
0.0719612 + 0.997407i \(0.477074\pi\)
\(74\) −3.33364e8 −0.0174640
\(75\) 2.37305e9 0.115470
\(76\) 2.15013e10 0.972723
\(77\) −5.41665e9 −0.228051
\(78\) 8.24531e8 0.0323360
\(79\) 1.79099e10 0.654855 0.327428 0.944876i \(-0.393818\pi\)
0.327428 + 0.944876i \(0.393818\pi\)
\(80\) 1.30732e10 0.446054
\(81\) 3.48678e9 0.111111
\(82\) 1.06967e9 0.0318621
\(83\) 1.40327e10 0.391032 0.195516 0.980701i \(-0.437362\pi\)
0.195516 + 0.980701i \(0.437362\pi\)
\(84\) −1.96302e10 −0.512140
\(85\) 3.20309e10 0.783005
\(86\) −8.19330e8 −0.0187810
\(87\) −3.87721e10 −0.833995
\(88\) 7.47493e8 0.0150991
\(89\) −6.35833e10 −1.20697 −0.603487 0.797373i \(-0.706222\pi\)
−0.603487 + 0.797373i \(0.706222\pi\)
\(90\) 2.45545e8 0.00438326
\(91\) 1.00669e11 1.69110
\(92\) −4.75187e10 −0.751677
\(93\) −3.39184e10 −0.505568
\(94\) 1.87391e9 0.0263357
\(95\) −3.28367e10 −0.435392
\(96\) 4.06402e9 0.0508702
\(97\) −8.52774e10 −1.00830 −0.504150 0.863616i \(-0.668194\pi\)
−0.504150 + 0.863616i \(0.668194\pi\)
\(98\) −5.57212e8 −0.00622697
\(99\) −8.10174e9 −0.0856219
\(100\) −1.99827e10 −0.199827
\(101\) 6.09094e10 0.576656 0.288328 0.957532i \(-0.406901\pi\)
0.288328 + 0.957532i \(0.406901\pi\)
\(102\) 3.31432e9 0.0297230
\(103\) 5.58896e10 0.475035 0.237518 0.971383i \(-0.423666\pi\)
0.237518 + 0.971383i \(0.423666\pi\)
\(104\) −1.38923e10 −0.111967
\(105\) 2.99793e10 0.229234
\(106\) 2.99385e9 0.0217294
\(107\) −2.07358e11 −1.42926 −0.714628 0.699505i \(-0.753404\pi\)
−0.714628 + 0.699505i \(0.753404\pi\)
\(108\) −2.93612e10 −0.192284
\(109\) −1.40979e11 −0.877626 −0.438813 0.898578i \(-0.644601\pi\)
−0.438813 + 0.898578i \(0.644601\pi\)
\(110\) −5.70538e8 −0.00337773
\(111\) −6.08774e10 −0.342909
\(112\) 1.65157e11 0.885519
\(113\) −1.54479e10 −0.0788749 −0.0394375 0.999222i \(-0.512557\pi\)
−0.0394375 + 0.999222i \(0.512557\pi\)
\(114\) −3.39770e9 −0.0165275
\(115\) 7.25705e10 0.336451
\(116\) 3.26488e11 1.44327
\(117\) 1.50572e11 0.634925
\(118\) −7.42038e9 −0.0298590
\(119\) 4.04654e11 1.55444
\(120\) −4.13711e9 −0.0151775
\(121\) −2.66487e11 −0.934020
\(122\) 3.27685e9 0.0109769
\(123\) 1.95338e11 0.625619
\(124\) 2.85617e11 0.874913
\(125\) 3.05176e10 0.0894427
\(126\) 3.10203e9 0.00870178
\(127\) −4.10211e10 −0.110176 −0.0550880 0.998482i \(-0.517544\pi\)
−0.0550880 + 0.998482i \(0.517544\pi\)
\(128\) −4.56225e10 −0.117361
\(129\) −1.49622e11 −0.368768
\(130\) 1.06035e10 0.0250474
\(131\) −7.51429e11 −1.70175 −0.850875 0.525368i \(-0.823928\pi\)
−0.850875 + 0.525368i \(0.823928\pi\)
\(132\) 6.82223e10 0.148173
\(133\) −4.14834e11 −0.864352
\(134\) −1.20463e10 −0.0240867
\(135\) 4.48403e10 0.0860663
\(136\) −5.58418e10 −0.102919
\(137\) 9.85433e11 1.74447 0.872236 0.489085i \(-0.162669\pi\)
0.872236 + 0.489085i \(0.162669\pi\)
\(138\) 7.50906e9 0.0127718
\(139\) −9.72813e11 −1.59019 −0.795093 0.606487i \(-0.792578\pi\)
−0.795093 + 0.606487i \(0.792578\pi\)
\(140\) −2.52446e11 −0.396702
\(141\) 3.42204e11 0.517106
\(142\) 3.26995e10 0.0475286
\(143\) −3.49863e11 −0.489271
\(144\) 2.47027e11 0.332469
\(145\) −4.98612e11 −0.646010
\(146\) 3.39213e9 0.00423187
\(147\) −1.01755e11 −0.122268
\(148\) 5.12630e11 0.593423
\(149\) 5.75994e11 0.642530 0.321265 0.946989i \(-0.395892\pi\)
0.321265 + 0.946989i \(0.395892\pi\)
\(150\) 3.15773e9 0.00339526
\(151\) −1.65471e12 −1.71534 −0.857669 0.514202i \(-0.828088\pi\)
−0.857669 + 0.514202i \(0.828088\pi\)
\(152\) 5.72468e10 0.0572283
\(153\) 6.05245e11 0.583618
\(154\) −7.20774e9 −0.00670556
\(155\) −4.36194e11 −0.391611
\(156\) −1.26792e12 −1.09877
\(157\) 2.86808e10 0.0239962 0.0119981 0.999928i \(-0.496181\pi\)
0.0119981 + 0.999928i \(0.496181\pi\)
\(158\) 2.38322e10 0.0192553
\(159\) 5.46724e11 0.426662
\(160\) 5.22636e10 0.0394039
\(161\) 9.16801e11 0.667932
\(162\) 4.63974e9 0.00326709
\(163\) 1.62245e12 1.10443 0.552216 0.833701i \(-0.313782\pi\)
0.552216 + 0.833701i \(0.313782\pi\)
\(164\) −1.64489e12 −1.08267
\(165\) −1.04189e11 −0.0663224
\(166\) 1.86728e10 0.0114978
\(167\) 2.10373e12 1.25329 0.626643 0.779307i \(-0.284429\pi\)
0.626643 + 0.779307i \(0.284429\pi\)
\(168\) −5.22651e10 −0.0301308
\(169\) 4.71009e12 2.62817
\(170\) 4.26224e10 0.0230234
\(171\) −6.20472e11 −0.324522
\(172\) 1.25992e12 0.638172
\(173\) −1.71071e12 −0.839309 −0.419655 0.907684i \(-0.637849\pi\)
−0.419655 + 0.907684i \(0.637849\pi\)
\(174\) −5.15927e10 −0.0245226
\(175\) 3.85536e11 0.177564
\(176\) −5.73982e11 −0.256200
\(177\) −1.35508e12 −0.586288
\(178\) −8.46080e10 −0.0354896
\(179\) −2.72138e10 −0.0110687 −0.00553437 0.999985i \(-0.501762\pi\)
−0.00553437 + 0.999985i \(0.501762\pi\)
\(180\) −3.77587e11 −0.148942
\(181\) −3.13821e11 −0.120074 −0.0600372 0.998196i \(-0.519122\pi\)
−0.0600372 + 0.998196i \(0.519122\pi\)
\(182\) 1.33957e11 0.0497248
\(183\) 5.98404e11 0.215533
\(184\) −1.26518e11 −0.0442235
\(185\) −7.82888e11 −0.265617
\(186\) −4.51341e10 −0.0148656
\(187\) −1.40632e12 −0.449734
\(188\) −2.88160e12 −0.894880
\(189\) 5.66478e11 0.170861
\(190\) −4.36947e10 −0.0128022
\(191\) 1.26211e12 0.359265 0.179632 0.983734i \(-0.442509\pi\)
0.179632 + 0.983734i \(0.442509\pi\)
\(192\) −2.07653e12 −0.574357
\(193\) −3.20540e11 −0.0861623 −0.0430811 0.999072i \(-0.513717\pi\)
−0.0430811 + 0.999072i \(0.513717\pi\)
\(194\) −1.13476e11 −0.0296479
\(195\) 1.93637e12 0.491811
\(196\) 8.56851e11 0.211591
\(197\) 1.89617e12 0.455316 0.227658 0.973741i \(-0.426893\pi\)
0.227658 + 0.973741i \(0.426893\pi\)
\(198\) −1.07807e10 −0.00251761
\(199\) −7.48355e12 −1.69987 −0.849935 0.526888i \(-0.823359\pi\)
−0.849935 + 0.526888i \(0.823359\pi\)
\(200\) −5.32036e10 −0.0117564
\(201\) −2.19984e12 −0.472947
\(202\) 8.10500e10 0.0169559
\(203\) −6.29909e12 −1.28248
\(204\) −5.09659e12 −1.00998
\(205\) 2.51207e12 0.484602
\(206\) 7.43703e10 0.0139679
\(207\) 1.37127e12 0.250776
\(208\) 1.06675e13 1.89984
\(209\) 1.44170e12 0.250075
\(210\) 3.98924e10 0.00674037
\(211\) 2.50767e12 0.412778 0.206389 0.978470i \(-0.433829\pi\)
0.206389 + 0.978470i \(0.433829\pi\)
\(212\) −4.60379e12 −0.738361
\(213\) 5.97143e12 0.933234
\(214\) −2.75924e11 −0.0420256
\(215\) −1.92416e12 −0.285646
\(216\) −7.81736e10 −0.0113126
\(217\) −5.51054e12 −0.777438
\(218\) −1.87596e11 −0.0258056
\(219\) 6.19456e11 0.0830936
\(220\) 8.77345e11 0.114775
\(221\) 2.61367e13 3.33498
\(222\) −8.10074e10 −0.0100829
\(223\) −8.01223e12 −0.972919 −0.486459 0.873703i \(-0.661712\pi\)
−0.486459 + 0.873703i \(0.661712\pi\)
\(224\) 6.60258e11 0.0782257
\(225\) 5.76650e11 0.0666667
\(226\) −2.05560e10 −0.00231922
\(227\) −5.66743e12 −0.624085 −0.312042 0.950068i \(-0.601013\pi\)
−0.312042 + 0.950068i \(0.601013\pi\)
\(228\) 5.22481e12 0.561602
\(229\) −7.16799e11 −0.0752146 −0.0376073 0.999293i \(-0.511974\pi\)
−0.0376073 + 0.999293i \(0.511974\pi\)
\(230\) 9.65671e10 0.00989296
\(231\) −1.31624e12 −0.131665
\(232\) 8.69269e11 0.0849122
\(233\) −1.04161e13 −0.993678 −0.496839 0.867843i \(-0.665506\pi\)
−0.496839 + 0.867843i \(0.665506\pi\)
\(234\) 2.00361e11 0.0186692
\(235\) 4.40077e12 0.400549
\(236\) 1.14107e13 1.01460
\(237\) 4.35212e12 0.378081
\(238\) 5.38458e11 0.0457066
\(239\) 1.21825e13 1.01053 0.505263 0.862965i \(-0.331395\pi\)
0.505263 + 0.862965i \(0.331395\pi\)
\(240\) 3.17679e12 0.257529
\(241\) −1.76035e13 −1.39478 −0.697388 0.716694i \(-0.745654\pi\)
−0.697388 + 0.716694i \(0.745654\pi\)
\(242\) −3.54605e11 −0.0274638
\(243\) 8.47289e11 0.0641500
\(244\) −5.03898e12 −0.372991
\(245\) −1.30858e12 −0.0947082
\(246\) 2.59930e11 0.0183956
\(247\) −2.67943e13 −1.85442
\(248\) 7.60450e11 0.0514738
\(249\) 3.40995e12 0.225762
\(250\) 4.06087e10 0.00262996
\(251\) −2.12972e12 −0.134933 −0.0674664 0.997722i \(-0.521492\pi\)
−0.0674664 + 0.997722i \(0.521492\pi\)
\(252\) −4.77014e12 −0.295684
\(253\) −3.18622e12 −0.193247
\(254\) −5.45854e10 −0.00323960
\(255\) 7.78350e12 0.452068
\(256\) 1.74403e13 0.991365
\(257\) −3.24559e12 −0.180577 −0.0902884 0.995916i \(-0.528779\pi\)
−0.0902884 + 0.995916i \(0.528779\pi\)
\(258\) −1.99097e11 −0.0108432
\(259\) −9.89041e12 −0.527309
\(260\) −1.63056e13 −0.851105
\(261\) −9.42162e12 −0.481507
\(262\) −9.99901e11 −0.0500380
\(263\) −3.00325e13 −1.47175 −0.735875 0.677117i \(-0.763229\pi\)
−0.735875 + 0.677117i \(0.763229\pi\)
\(264\) 1.81641e11 0.00871749
\(265\) 7.03091e12 0.330491
\(266\) −5.52005e11 −0.0254152
\(267\) −1.54507e13 −0.696846
\(268\) 1.85242e13 0.818461
\(269\) −8.34873e12 −0.361396 −0.180698 0.983539i \(-0.557836\pi\)
−0.180698 + 0.983539i \(0.557836\pi\)
\(270\) 5.96675e10 0.00253068
\(271\) −2.77454e13 −1.15308 −0.576541 0.817068i \(-0.695598\pi\)
−0.576541 + 0.817068i \(0.695598\pi\)
\(272\) 4.28796e13 1.74631
\(273\) 2.44626e13 0.976356
\(274\) 1.31128e12 0.0512942
\(275\) −1.33988e12 −0.0513731
\(276\) −1.15470e13 −0.433981
\(277\) 4.32947e13 1.59513 0.797565 0.603234i \(-0.206121\pi\)
0.797565 + 0.603234i \(0.206121\pi\)
\(278\) −1.29449e12 −0.0467576
\(279\) −8.24218e12 −0.291890
\(280\) −6.72134e11 −0.0233392
\(281\) 3.83147e13 1.30461 0.652304 0.757957i \(-0.273802\pi\)
0.652304 + 0.757957i \(0.273802\pi\)
\(282\) 4.55359e11 0.0152049
\(283\) 3.32374e13 1.08843 0.544216 0.838945i \(-0.316827\pi\)
0.544216 + 0.838945i \(0.316827\pi\)
\(284\) −5.02836e13 −1.61501
\(285\) −7.97932e12 −0.251373
\(286\) −4.65550e11 −0.0143864
\(287\) 3.17356e13 0.962046
\(288\) 9.87556e11 0.0293699
\(289\) 7.07881e13 2.06549
\(290\) −6.63486e11 −0.0189952
\(291\) −2.07224e13 −0.582142
\(292\) −5.21625e12 −0.143798
\(293\) −5.40732e13 −1.46288 −0.731442 0.681904i \(-0.761152\pi\)
−0.731442 + 0.681904i \(0.761152\pi\)
\(294\) −1.35402e11 −0.00359514
\(295\) −1.74264e13 −0.454136
\(296\) 1.36487e12 0.0349129
\(297\) −1.96872e12 −0.0494338
\(298\) 7.66455e11 0.0188928
\(299\) 5.92164e13 1.43302
\(300\) −4.85580e12 −0.115370
\(301\) −2.43083e13 −0.567073
\(302\) −2.20187e12 −0.0504375
\(303\) 1.48010e13 0.332932
\(304\) −4.39584e13 −0.971041
\(305\) 7.69552e12 0.166951
\(306\) 8.05379e11 0.0171606
\(307\) 1.94547e13 0.407158 0.203579 0.979059i \(-0.434743\pi\)
0.203579 + 0.979059i \(0.434743\pi\)
\(308\) 1.10837e13 0.227854
\(309\) 1.35812e13 0.274262
\(310\) −5.80428e11 −0.0115149
\(311\) −9.16290e13 −1.78587 −0.892937 0.450182i \(-0.851359\pi\)
−0.892937 + 0.450182i \(0.851359\pi\)
\(312\) −3.37582e12 −0.0646441
\(313\) 6.48161e13 1.21952 0.609760 0.792586i \(-0.291266\pi\)
0.609760 + 0.792586i \(0.291266\pi\)
\(314\) 3.81645e10 0.000705581 0
\(315\) 7.28496e12 0.132349
\(316\) −3.66479e13 −0.654289
\(317\) 3.88357e13 0.681405 0.340703 0.940171i \(-0.389335\pi\)
0.340703 + 0.940171i \(0.389335\pi\)
\(318\) 7.27506e11 0.0125455
\(319\) 2.18917e13 0.371048
\(320\) −2.67044e13 −0.444895
\(321\) −5.03880e13 −0.825181
\(322\) 1.21995e12 0.0196398
\(323\) −1.07703e14 −1.70457
\(324\) −7.13476e12 −0.111015
\(325\) 2.49019e13 0.380955
\(326\) 2.15894e12 0.0324745
\(327\) −3.42580e13 −0.506698
\(328\) −4.37948e12 −0.0636966
\(329\) 5.55960e13 0.795181
\(330\) −1.38641e11 −0.00195013
\(331\) −6.54579e12 −0.0905541 −0.0452770 0.998974i \(-0.514417\pi\)
−0.0452770 + 0.998974i \(0.514417\pi\)
\(332\) −2.87141e13 −0.390694
\(333\) −1.47932e13 −0.197979
\(334\) 2.79936e12 0.0368514
\(335\) −2.82901e13 −0.366343
\(336\) 4.01331e13 0.511254
\(337\) −5.75811e13 −0.721632 −0.360816 0.932637i \(-0.617502\pi\)
−0.360816 + 0.932637i \(0.617502\pi\)
\(338\) 6.26756e12 0.0772781
\(339\) −3.75385e12 −0.0455385
\(340\) −6.55425e13 −0.782328
\(341\) 1.91512e13 0.224930
\(342\) −8.25641e11 −0.00954218
\(343\) −9.45942e13 −1.07584
\(344\) 3.35453e12 0.0375457
\(345\) 1.76346e13 0.194250
\(346\) −2.27638e12 −0.0246789
\(347\) 7.86562e13 0.839307 0.419654 0.907684i \(-0.362152\pi\)
0.419654 + 0.907684i \(0.362152\pi\)
\(348\) 7.93366e13 0.833274
\(349\) 4.91495e13 0.508135 0.254067 0.967187i \(-0.418231\pi\)
0.254067 + 0.967187i \(0.418231\pi\)
\(350\) 5.13019e11 0.00522107
\(351\) 3.65890e13 0.366574
\(352\) −2.29464e12 −0.0226324
\(353\) 1.94841e14 1.89200 0.945998 0.324174i \(-0.105086\pi\)
0.945998 + 0.324174i \(0.105086\pi\)
\(354\) −1.80315e12 −0.0172391
\(355\) 7.67931e13 0.722880
\(356\) 1.30106e14 1.20593
\(357\) 9.83308e13 0.897459
\(358\) −3.62125e10 −0.000325463 0
\(359\) −9.40355e13 −0.832285 −0.416143 0.909299i \(-0.636618\pi\)
−0.416143 + 0.909299i \(0.636618\pi\)
\(360\) −1.00532e12 −0.00876274
\(361\) −6.07739e12 −0.0521708
\(362\) −4.17591e11 −0.00353065
\(363\) −6.47563e13 −0.539257
\(364\) −2.05992e14 −1.68964
\(365\) 7.96625e12 0.0643641
\(366\) 7.96275e11 0.00633749
\(367\) 5.83807e13 0.457726 0.228863 0.973459i \(-0.426499\pi\)
0.228863 + 0.973459i \(0.426499\pi\)
\(368\) 9.71500e13 0.750377
\(369\) 4.74672e13 0.361201
\(370\) −1.04176e12 −0.00781014
\(371\) 8.88232e13 0.656100
\(372\) 6.94049e13 0.505131
\(373\) −1.13817e14 −0.816220 −0.408110 0.912933i \(-0.633812\pi\)
−0.408110 + 0.912933i \(0.633812\pi\)
\(374\) −1.87134e12 −0.0132239
\(375\) 7.41577e12 0.0516398
\(376\) −7.67220e12 −0.0526486
\(377\) −4.06860e14 −2.75149
\(378\) 7.53793e11 0.00502397
\(379\) −7.48279e13 −0.491528 −0.245764 0.969330i \(-0.579039\pi\)
−0.245764 + 0.969330i \(0.579039\pi\)
\(380\) 6.71915e13 0.435015
\(381\) −9.96814e12 −0.0636102
\(382\) 1.67945e12 0.0105638
\(383\) −4.61436e13 −0.286100 −0.143050 0.989715i \(-0.545691\pi\)
−0.143050 + 0.989715i \(0.545691\pi\)
\(384\) −1.10863e13 −0.0677585
\(385\) −1.69270e13 −0.101987
\(386\) −4.26532e11 −0.00253350
\(387\) −3.63582e13 −0.212908
\(388\) 1.74497e14 1.00743
\(389\) 1.20305e14 0.684793 0.342397 0.939555i \(-0.388761\pi\)
0.342397 + 0.939555i \(0.388761\pi\)
\(390\) 2.57666e12 0.0144611
\(391\) 2.38029e14 1.31722
\(392\) 2.28135e12 0.0124486
\(393\) −1.82597e14 −0.982506
\(394\) 2.52317e12 0.0133880
\(395\) 5.59686e13 0.292860
\(396\) 1.65780e13 0.0855479
\(397\) −1.50625e14 −0.766567 −0.383283 0.923631i \(-0.625207\pi\)
−0.383283 + 0.923631i \(0.625207\pi\)
\(398\) −9.95810e12 −0.0499827
\(399\) −1.00805e14 −0.499034
\(400\) 4.08538e13 0.199481
\(401\) −1.98448e14 −0.955767 −0.477883 0.878423i \(-0.658596\pi\)
−0.477883 + 0.878423i \(0.658596\pi\)
\(402\) −2.92725e12 −0.0139065
\(403\) −3.55928e14 −1.66795
\(404\) −1.24635e14 −0.576157
\(405\) 1.08962e13 0.0496904
\(406\) −8.38198e12 −0.0377097
\(407\) 3.43728e13 0.152562
\(408\) −1.35696e13 −0.0594203
\(409\) 1.69188e14 0.730956 0.365478 0.930820i \(-0.380906\pi\)
0.365478 + 0.930820i \(0.380906\pi\)
\(410\) 3.34272e12 0.0142492
\(411\) 2.39460e14 1.00717
\(412\) −1.14363e14 −0.474625
\(413\) −2.20152e14 −0.901564
\(414\) 1.82470e12 0.00737377
\(415\) 4.38522e13 0.174875
\(416\) 4.26463e13 0.167829
\(417\) −2.36394e14 −0.918094
\(418\) 1.91842e12 0.00735318
\(419\) 6.56169e13 0.248221 0.124110 0.992268i \(-0.460392\pi\)
0.124110 + 0.992268i \(0.460392\pi\)
\(420\) −6.13444e13 −0.229036
\(421\) 3.48634e14 1.28475 0.642375 0.766390i \(-0.277949\pi\)
0.642375 + 0.766390i \(0.277949\pi\)
\(422\) 3.33687e12 0.0121373
\(423\) 8.31556e13 0.298552
\(424\) −1.22575e13 −0.0434401
\(425\) 1.00096e14 0.350171
\(426\) 7.94598e12 0.0274407
\(427\) 9.72193e13 0.331436
\(428\) 4.24302e14 1.42802
\(429\) −8.50167e13 −0.282481
\(430\) −2.56041e12 −0.00839910
\(431\) −4.33114e14 −1.40274 −0.701370 0.712798i \(-0.747428\pi\)
−0.701370 + 0.712798i \(0.747428\pi\)
\(432\) 6.00276e13 0.191951
\(433\) 4.86768e14 1.53688 0.768438 0.639924i \(-0.221034\pi\)
0.768438 + 0.639924i \(0.221034\pi\)
\(434\) −7.33269e12 −0.0228597
\(435\) −1.21163e14 −0.372974
\(436\) 2.88476e14 0.876867
\(437\) −2.44017e14 −0.732440
\(438\) 8.24289e11 0.00244327
\(439\) 3.32318e14 0.972745 0.486372 0.873752i \(-0.338320\pi\)
0.486372 + 0.873752i \(0.338320\pi\)
\(440\) 2.33591e12 0.00675254
\(441\) −2.47266e13 −0.0705914
\(442\) 3.47792e13 0.0980612
\(443\) 5.06080e14 1.40928 0.704642 0.709563i \(-0.251108\pi\)
0.704642 + 0.709563i \(0.251108\pi\)
\(444\) 1.24569e14 0.342613
\(445\) −1.98698e14 −0.539775
\(446\) −1.06616e13 −0.0286075
\(447\) 1.39967e14 0.370965
\(448\) −3.37363e14 −0.883219
\(449\) −2.81912e14 −0.729051 −0.364526 0.931193i \(-0.618769\pi\)
−0.364526 + 0.931193i \(0.618769\pi\)
\(450\) 7.67329e11 0.00196026
\(451\) −1.10293e14 −0.278340
\(452\) 3.16100e13 0.0788067
\(453\) −4.02095e14 −0.990351
\(454\) −7.54145e12 −0.0183505
\(455\) 3.14591e14 0.756282
\(456\) 1.39110e13 0.0330408
\(457\) 5.24810e14 1.23158 0.615791 0.787910i \(-0.288837\pi\)
0.615791 + 0.787910i \(0.288837\pi\)
\(458\) −9.53820e11 −0.00221160
\(459\) 1.47075e14 0.336952
\(460\) −1.48496e14 −0.336160
\(461\) −8.51699e12 −0.0190516 −0.00952579 0.999955i \(-0.503032\pi\)
−0.00952579 + 0.999955i \(0.503032\pi\)
\(462\) −1.75148e12 −0.00387146
\(463\) 4.58576e13 0.100165 0.0500825 0.998745i \(-0.484052\pi\)
0.0500825 + 0.998745i \(0.484052\pi\)
\(464\) −6.67491e14 −1.44078
\(465\) −1.05995e14 −0.226097
\(466\) −1.38603e13 −0.0292179
\(467\) 3.09542e14 0.644877 0.322439 0.946590i \(-0.395497\pi\)
0.322439 + 0.946590i \(0.395497\pi\)
\(468\) −3.08105e14 −0.634376
\(469\) −3.57396e14 −0.727275
\(470\) 5.85596e12 0.0117777
\(471\) 6.96943e12 0.0138542
\(472\) 3.03808e13 0.0596922
\(473\) 8.44804e13 0.164066
\(474\) 5.79121e12 0.0111170
\(475\) −1.02615e14 −0.194713
\(476\) −8.28014e14 −1.55310
\(477\) 1.32854e14 0.246333
\(478\) 1.62108e13 0.0297134
\(479\) 4.55623e14 0.825582 0.412791 0.910826i \(-0.364554\pi\)
0.412791 + 0.910826i \(0.364554\pi\)
\(480\) 1.27001e13 0.0227499
\(481\) −6.38824e14 −1.13132
\(482\) −2.34243e13 −0.0410117
\(483\) 2.22783e14 0.385631
\(484\) 5.45293e14 0.933212
\(485\) −2.66492e14 −0.450925
\(486\) 1.12746e12 0.00188626
\(487\) −9.55622e13 −0.158080 −0.0790400 0.996871i \(-0.525185\pi\)
−0.0790400 + 0.996871i \(0.525185\pi\)
\(488\) −1.34162e13 −0.0219442
\(489\) 3.94255e14 0.637644
\(490\) −1.74129e12 −0.00278478
\(491\) −4.55027e14 −0.719596 −0.359798 0.933030i \(-0.617154\pi\)
−0.359798 + 0.933030i \(0.617154\pi\)
\(492\) −3.99707e14 −0.625078
\(493\) −1.63543e15 −2.52914
\(494\) −3.56542e13 −0.0545271
\(495\) −2.53179e13 −0.0382913
\(496\) −5.83932e14 −0.873399
\(497\) 9.70145e14 1.43508
\(498\) 4.53750e12 0.00663828
\(499\) −6.34865e13 −0.0918604 −0.0459302 0.998945i \(-0.514625\pi\)
−0.0459302 + 0.998945i \(0.514625\pi\)
\(500\) −6.24460e13 −0.0893654
\(501\) 5.11207e14 0.723585
\(502\) −2.83395e12 −0.00396754
\(503\) 1.12403e15 1.55652 0.778258 0.627945i \(-0.216104\pi\)
0.778258 + 0.627945i \(0.216104\pi\)
\(504\) −1.27004e13 −0.0173960
\(505\) 1.90342e14 0.257888
\(506\) −4.23980e12 −0.00568221
\(507\) 1.14455e15 1.51737
\(508\) 8.39387e13 0.110081
\(509\) 2.97012e14 0.385324 0.192662 0.981265i \(-0.438288\pi\)
0.192662 + 0.981265i \(0.438288\pi\)
\(510\) 1.03572e13 0.0132925
\(511\) 1.00640e14 0.127777
\(512\) 1.16642e14 0.146511
\(513\) −1.50775e14 −0.187363
\(514\) −4.31880e12 −0.00530965
\(515\) 1.74655e14 0.212442
\(516\) 3.06162e14 0.368449
\(517\) −1.93217e14 −0.230063
\(518\) −1.31608e13 −0.0155049
\(519\) −4.15702e14 −0.484575
\(520\) −4.34133e13 −0.0500731
\(521\) −1.02780e15 −1.17301 −0.586503 0.809947i \(-0.699496\pi\)
−0.586503 + 0.809947i \(0.699496\pi\)
\(522\) −1.25370e13 −0.0141582
\(523\) 6.06669e14 0.677941 0.338971 0.940797i \(-0.389921\pi\)
0.338971 + 0.940797i \(0.389921\pi\)
\(524\) 1.53760e15 1.70028
\(525\) 9.36852e13 0.102517
\(526\) −3.99632e13 −0.0432751
\(527\) −1.43070e15 −1.53317
\(528\) −1.39478e14 −0.147917
\(529\) −4.13522e14 −0.434003
\(530\) 9.35579e12 0.00971769
\(531\) −3.29284e14 −0.338493
\(532\) 8.48846e14 0.863604
\(533\) 2.04981e15 2.06402
\(534\) −2.05598e13 −0.0204900
\(535\) −6.47994e14 −0.639183
\(536\) 4.93203e13 0.0481526
\(537\) −6.61296e12 −0.00639053
\(538\) −1.11094e13 −0.0106264
\(539\) 5.74536e13 0.0543975
\(540\) −9.17536e13 −0.0859919
\(541\) 3.69341e14 0.342644 0.171322 0.985215i \(-0.445196\pi\)
0.171322 + 0.985215i \(0.445196\pi\)
\(542\) −3.69199e13 −0.0339050
\(543\) −7.62586e13 −0.0693250
\(544\) 1.71423e14 0.154267
\(545\) −4.40560e14 −0.392486
\(546\) 3.25516e13 0.0287086
\(547\) 6.26128e14 0.546680 0.273340 0.961918i \(-0.411872\pi\)
0.273340 + 0.961918i \(0.411872\pi\)
\(548\) −2.01642e15 −1.74296
\(549\) 1.45412e14 0.124438
\(550\) −1.78293e12 −0.00151057
\(551\) 1.67657e15 1.40634
\(552\) −3.07438e13 −0.0255325
\(553\) 7.07064e14 0.581394
\(554\) 5.76107e13 0.0469029
\(555\) −1.90242e14 −0.153354
\(556\) 1.99060e15 1.58881
\(557\) −2.28023e15 −1.80209 −0.901043 0.433729i \(-0.857198\pi\)
−0.901043 + 0.433729i \(0.857198\pi\)
\(558\) −1.09676e13 −0.00858268
\(559\) −1.57008e15 −1.21663
\(560\) 5.16116e14 0.396016
\(561\) −3.41736e14 −0.259654
\(562\) 5.09840e13 0.0383605
\(563\) −9.78191e14 −0.728832 −0.364416 0.931236i \(-0.618731\pi\)
−0.364416 + 0.931236i \(0.618731\pi\)
\(564\) −7.00228e14 −0.516659
\(565\) −4.82748e13 −0.0352739
\(566\) 4.42278e13 0.0320041
\(567\) 1.37654e14 0.0986468
\(568\) −1.33879e14 −0.0950161
\(569\) −2.07694e15 −1.45984 −0.729922 0.683531i \(-0.760443\pi\)
−0.729922 + 0.683531i \(0.760443\pi\)
\(570\) −1.06178e13 −0.00739134
\(571\) −2.02806e15 −1.39824 −0.699120 0.715005i \(-0.746425\pi\)
−0.699120 + 0.715005i \(0.746425\pi\)
\(572\) 7.15900e14 0.488848
\(573\) 3.06693e14 0.207422
\(574\) 4.22294e13 0.0282878
\(575\) 2.26783e14 0.150466
\(576\) −5.04598e14 −0.331605
\(577\) −1.99153e15 −1.29635 −0.648173 0.761493i \(-0.724466\pi\)
−0.648173 + 0.761493i \(0.724466\pi\)
\(578\) 9.41953e13 0.0607332
\(579\) −7.78913e13 −0.0497458
\(580\) 1.02027e15 0.645451
\(581\) 5.53995e14 0.347166
\(582\) −2.75746e13 −0.0171172
\(583\) −3.08693e14 −0.189824
\(584\) −1.38882e13 −0.00846008
\(585\) 4.70538e14 0.283947
\(586\) −7.19533e13 −0.0430144
\(587\) 4.80682e14 0.284674 0.142337 0.989818i \(-0.454538\pi\)
0.142337 + 0.989818i \(0.454538\pi\)
\(588\) 2.08215e14 0.122162
\(589\) 1.46669e15 0.852522
\(590\) −2.31887e13 −0.0133534
\(591\) 4.60769e14 0.262877
\(592\) −1.04805e15 −0.592396
\(593\) −9.25262e14 −0.518160 −0.259080 0.965856i \(-0.583419\pi\)
−0.259080 + 0.965856i \(0.583419\pi\)
\(594\) −2.61971e12 −0.00145354
\(595\) 1.26454e15 0.695168
\(596\) −1.17862e15 −0.641975
\(597\) −1.81850e15 −0.981420
\(598\) 7.87973e13 0.0421361
\(599\) 4.76978e14 0.252727 0.126363 0.991984i \(-0.459669\pi\)
0.126363 + 0.991984i \(0.459669\pi\)
\(600\) −1.29285e13 −0.00678759
\(601\) 3.84374e15 1.99960 0.999802 0.0198854i \(-0.00633014\pi\)
0.999802 + 0.0198854i \(0.00633014\pi\)
\(602\) −3.23462e13 −0.0166741
\(603\) −5.34561e14 −0.273056
\(604\) 3.38592e15 1.71385
\(605\) −8.32771e14 −0.417706
\(606\) 1.96951e13 0.00978948
\(607\) 1.63143e15 0.803584 0.401792 0.915731i \(-0.368387\pi\)
0.401792 + 0.915731i \(0.368387\pi\)
\(608\) −1.75735e14 −0.0857807
\(609\) −1.53068e15 −0.740438
\(610\) 1.02402e13 0.00490900
\(611\) 3.59096e15 1.70602
\(612\) −1.23847e15 −0.583113
\(613\) 1.71111e15 0.798444 0.399222 0.916854i \(-0.369280\pi\)
0.399222 + 0.916854i \(0.369280\pi\)
\(614\) 2.58877e13 0.0119720
\(615\) 6.10433e14 0.279785
\(616\) 2.95102e13 0.0134053
\(617\) 2.03932e15 0.918158 0.459079 0.888395i \(-0.348179\pi\)
0.459079 + 0.888395i \(0.348179\pi\)
\(618\) 1.80720e13 0.00806435
\(619\) −4.21849e15 −1.86577 −0.932885 0.360174i \(-0.882717\pi\)
−0.932885 + 0.360174i \(0.882717\pi\)
\(620\) 8.92553e14 0.391273
\(621\) 3.33218e14 0.144786
\(622\) −1.21928e14 −0.0525115
\(623\) −2.51019e15 −1.07158
\(624\) 2.59221e15 1.09687
\(625\) 9.53674e13 0.0400000
\(626\) 8.62486e13 0.0358586
\(627\) 3.50334e14 0.144381
\(628\) −5.86875e13 −0.0239755
\(629\) −2.56784e15 −1.03990
\(630\) 9.69384e12 0.00389155
\(631\) −6.39185e14 −0.254370 −0.127185 0.991879i \(-0.540594\pi\)
−0.127185 + 0.991879i \(0.540594\pi\)
\(632\) −9.75743e13 −0.0384939
\(633\) 6.09364e14 0.238318
\(634\) 5.16774e13 0.0200359
\(635\) −1.28191e14 −0.0492722
\(636\) −1.11872e15 −0.426293
\(637\) −1.06778e15 −0.403382
\(638\) 2.91305e13 0.0109102
\(639\) 1.45106e15 0.538803
\(640\) −1.42570e14 −0.0524855
\(641\) 2.44244e15 0.891467 0.445734 0.895166i \(-0.352943\pi\)
0.445734 + 0.895166i \(0.352943\pi\)
\(642\) −6.70496e13 −0.0242635
\(643\) 1.28261e15 0.460187 0.230094 0.973168i \(-0.426097\pi\)
0.230094 + 0.973168i \(0.426097\pi\)
\(644\) −1.87598e15 −0.667355
\(645\) −4.67570e14 −0.164918
\(646\) −1.43317e14 −0.0501209
\(647\) 7.98862e14 0.277012 0.138506 0.990362i \(-0.455770\pi\)
0.138506 + 0.990362i \(0.455770\pi\)
\(648\) −1.89962e13 −0.00653136
\(649\) 7.65109e14 0.260842
\(650\) 3.31361e13 0.0112015
\(651\) −1.33906e15 −0.448854
\(652\) −3.31990e15 −1.10348
\(653\) −9.26161e13 −0.0305256 −0.0152628 0.999884i \(-0.504858\pi\)
−0.0152628 + 0.999884i \(0.504858\pi\)
\(654\) −4.55859e13 −0.0148989
\(655\) −2.34822e15 −0.761046
\(656\) 3.36290e15 1.08079
\(657\) 1.50528e14 0.0479741
\(658\) 7.39797e13 0.0233814
\(659\) 1.66430e15 0.521628 0.260814 0.965389i \(-0.416009\pi\)
0.260814 + 0.965389i \(0.416009\pi\)
\(660\) 2.13195e14 0.0662651
\(661\) −1.34094e15 −0.413335 −0.206668 0.978411i \(-0.566262\pi\)
−0.206668 + 0.978411i \(0.566262\pi\)
\(662\) −8.71026e12 −0.00266264
\(663\) 6.35122e15 1.92545
\(664\) −7.64509e13 −0.0229857
\(665\) −1.29636e15 −0.386550
\(666\) −1.96848e13 −0.00582134
\(667\) −3.70530e15 −1.08675
\(668\) −4.30472e15 −1.25220
\(669\) −1.94697e15 −0.561715
\(670\) −3.76447e13 −0.0107719
\(671\) −3.37873e14 −0.0958915
\(672\) 1.60443e14 0.0451637
\(673\) 9.84151e14 0.274776 0.137388 0.990517i \(-0.456129\pi\)
0.137388 + 0.990517i \(0.456129\pi\)
\(674\) −7.66212e13 −0.0212187
\(675\) 1.40126e14 0.0384900
\(676\) −9.63793e15 −2.62589
\(677\) 9.02593e14 0.243924 0.121962 0.992535i \(-0.461081\pi\)
0.121962 + 0.992535i \(0.461081\pi\)
\(678\) −4.99512e12 −0.00133901
\(679\) −3.36665e15 −0.895189
\(680\) −1.74506e14 −0.0460268
\(681\) −1.37718e15 −0.360316
\(682\) 2.54838e13 0.00661379
\(683\) −1.26720e15 −0.326235 −0.163117 0.986607i \(-0.552155\pi\)
−0.163117 + 0.986607i \(0.552155\pi\)
\(684\) 1.26963e15 0.324241
\(685\) 3.07948e15 0.780152
\(686\) −1.25873e14 −0.0316338
\(687\) −1.74182e14 −0.0434252
\(688\) −2.57586e15 −0.637068
\(689\) 5.73712e15 1.40763
\(690\) 2.34658e13 0.00571170
\(691\) −3.21589e14 −0.0776555 −0.0388278 0.999246i \(-0.512362\pi\)
−0.0388278 + 0.999246i \(0.512362\pi\)
\(692\) 3.50050e15 0.838584
\(693\) −3.19848e14 −0.0760169
\(694\) 1.04665e14 0.0246788
\(695\) −3.04004e15 −0.711153
\(696\) 2.11232e14 0.0490241
\(697\) 8.23949e15 1.89723
\(698\) 6.54015e13 0.0149411
\(699\) −2.53110e15 −0.573700
\(700\) −7.88895e14 −0.177411
\(701\) −2.00911e15 −0.448286 −0.224143 0.974556i \(-0.571958\pi\)
−0.224143 + 0.974556i \(0.571958\pi\)
\(702\) 4.86878e13 0.0107787
\(703\) 2.63245e15 0.578236
\(704\) 1.17246e15 0.255534
\(705\) 1.06939e15 0.231257
\(706\) 2.59269e14 0.0556319
\(707\) 2.40463e15 0.511967
\(708\) 2.77280e15 0.585781
\(709\) 3.84612e15 0.806247 0.403124 0.915146i \(-0.367924\pi\)
0.403124 + 0.915146i \(0.367924\pi\)
\(710\) 1.02186e14 0.0212554
\(711\) 1.05756e15 0.218285
\(712\) 3.46405e14 0.0709486
\(713\) −3.24145e15 −0.658791
\(714\) 1.30845e14 0.0263887
\(715\) −1.09332e15 −0.218809
\(716\) 5.56857e13 0.0110592
\(717\) 2.96035e15 0.583428
\(718\) −1.25130e14 −0.0244724
\(719\) 9.01348e15 1.74938 0.874688 0.484686i \(-0.161066\pi\)
0.874688 + 0.484686i \(0.161066\pi\)
\(720\) 7.71960e14 0.148685
\(721\) 2.20646e15 0.421746
\(722\) −8.08698e12 −0.00153402
\(723\) −4.27764e15 −0.805274
\(724\) 6.42150e14 0.119971
\(725\) −1.55816e15 −0.288904
\(726\) −8.61690e13 −0.0158562
\(727\) 1.88120e15 0.343554 0.171777 0.985136i \(-0.445049\pi\)
0.171777 + 0.985136i \(0.445049\pi\)
\(728\) −5.48451e14 −0.0994066
\(729\) 2.05891e14 0.0370370
\(730\) 1.06004e13 0.00189255
\(731\) −6.31116e15 −1.11831
\(732\) −1.22447e15 −0.215346
\(733\) 4.79831e15 0.837561 0.418781 0.908087i \(-0.362458\pi\)
0.418781 + 0.908087i \(0.362458\pi\)
\(734\) 7.76852e13 0.0134589
\(735\) −3.17986e14 −0.0546798
\(736\) 3.88382e14 0.0662875
\(737\) 1.24208e15 0.210416
\(738\) 6.31630e13 0.0106207
\(739\) −2.84214e15 −0.474352 −0.237176 0.971467i \(-0.576222\pi\)
−0.237176 + 0.971467i \(0.576222\pi\)
\(740\) 1.60197e15 0.265387
\(741\) −6.51101e15 −1.07065
\(742\) 1.18194e14 0.0192918
\(743\) −1.59424e15 −0.258295 −0.129148 0.991625i \(-0.541224\pi\)
−0.129148 + 0.991625i \(0.541224\pi\)
\(744\) 1.84789e14 0.0297184
\(745\) 1.79998e15 0.287348
\(746\) −1.51452e14 −0.0240000
\(747\) 8.28618e14 0.130344
\(748\) 2.87766e15 0.449345
\(749\) −8.18626e15 −1.26892
\(750\) 9.86791e12 0.00151841
\(751\) −9.17835e15 −1.40199 −0.700995 0.713166i \(-0.747261\pi\)
−0.700995 + 0.713166i \(0.747261\pi\)
\(752\) 5.89130e15 0.893332
\(753\) −5.17523e14 −0.0779035
\(754\) −5.41394e14 −0.0809043
\(755\) −5.17098e15 −0.767122
\(756\) −1.15914e15 −0.170713
\(757\) 8.13105e15 1.18883 0.594414 0.804159i \(-0.297384\pi\)
0.594414 + 0.804159i \(0.297384\pi\)
\(758\) −9.95710e13 −0.0144528
\(759\) −7.74252e14 −0.111571
\(760\) 1.78896e14 0.0255933
\(761\) 1.11540e16 1.58421 0.792106 0.610384i \(-0.208985\pi\)
0.792106 + 0.610384i \(0.208985\pi\)
\(762\) −1.32643e13 −0.00187038
\(763\) −5.56570e15 −0.779175
\(764\) −2.58257e15 −0.358954
\(765\) 1.89139e15 0.261002
\(766\) −6.14016e13 −0.00841244
\(767\) −1.42197e16 −1.93426
\(768\) 4.23799e15 0.572365
\(769\) 3.33975e15 0.447836 0.223918 0.974608i \(-0.428115\pi\)
0.223918 + 0.974608i \(0.428115\pi\)
\(770\) −2.25242e13 −0.00299882
\(771\) −7.88679e14 −0.104256
\(772\) 6.55899e14 0.0860878
\(773\) 8.01173e15 1.04409 0.522046 0.852917i \(-0.325169\pi\)
0.522046 + 0.852917i \(0.325169\pi\)
\(774\) −4.83806e13 −0.00626032
\(775\) −1.36311e15 −0.175134
\(776\) 4.64595e14 0.0592701
\(777\) −2.40337e15 −0.304442
\(778\) 1.60085e14 0.0201355
\(779\) −8.44678e15 −1.05496
\(780\) −3.96226e15 −0.491385
\(781\) −3.37162e15 −0.415200
\(782\) 3.16736e14 0.0387312
\(783\) −2.28945e15 −0.277998
\(784\) −1.75180e15 −0.211225
\(785\) 8.96274e13 0.0107314
\(786\) −2.42976e14 −0.0288894
\(787\) −9.06378e15 −1.07016 −0.535080 0.844802i \(-0.679718\pi\)
−0.535080 + 0.844802i \(0.679718\pi\)
\(788\) −3.88000e15 −0.454923
\(789\) −7.29789e15 −0.849716
\(790\) 7.44755e13 0.00861121
\(791\) −6.09867e14 −0.0700268
\(792\) 4.41387e13 0.00503305
\(793\) 6.27943e15 0.711078
\(794\) −2.00432e14 −0.0225400
\(795\) 1.70851e15 0.190809
\(796\) 1.53131e16 1.69840
\(797\) −1.77063e16 −1.95032 −0.975160 0.221502i \(-0.928904\pi\)
−0.975160 + 0.221502i \(0.928904\pi\)
\(798\) −1.34137e14 −0.0146735
\(799\) 1.44344e16 1.56816
\(800\) 1.63324e14 0.0176220
\(801\) −3.75453e15 −0.402324
\(802\) −2.64067e14 −0.0281032
\(803\) −3.49760e14 −0.0369687
\(804\) 4.50138e15 0.472538
\(805\) 2.86500e15 0.298708
\(806\) −4.73621e14 −0.0490442
\(807\) −2.02874e15 −0.208652
\(808\) −3.31837e14 −0.0338971
\(809\) 5.23445e15 0.531073 0.265536 0.964101i \(-0.414451\pi\)
0.265536 + 0.964101i \(0.414451\pi\)
\(810\) 1.44992e13 0.00146109
\(811\) 9.67229e15 0.968088 0.484044 0.875044i \(-0.339168\pi\)
0.484044 + 0.875044i \(0.339168\pi\)
\(812\) 1.28894e16 1.28137
\(813\) −6.74214e15 −0.665732
\(814\) 4.57387e13 0.00448590
\(815\) 5.07015e15 0.493917
\(816\) 1.04198e16 1.00823
\(817\) 6.46994e15 0.621840
\(818\) 2.25133e14 0.0214929
\(819\) 5.94442e15 0.563700
\(820\) −5.14027e15 −0.484183
\(821\) −2.57787e15 −0.241198 −0.120599 0.992701i \(-0.538482\pi\)
−0.120599 + 0.992701i \(0.538482\pi\)
\(822\) 3.18642e14 0.0296147
\(823\) −7.92171e15 −0.731341 −0.365671 0.930744i \(-0.619160\pi\)
−0.365671 + 0.930744i \(0.619160\pi\)
\(824\) −3.04489e14 −0.0279236
\(825\) −3.25591e14 −0.0296603
\(826\) −2.92948e14 −0.0265094
\(827\) 1.96551e16 1.76683 0.883415 0.468591i \(-0.155238\pi\)
0.883415 + 0.468591i \(0.155238\pi\)
\(828\) −2.80593e15 −0.250559
\(829\) −1.47602e16 −1.30931 −0.654655 0.755928i \(-0.727186\pi\)
−0.654655 + 0.755928i \(0.727186\pi\)
\(830\) 5.83526e13 0.00514199
\(831\) 1.05206e16 0.920948
\(832\) −2.17904e16 −1.89490
\(833\) −4.29210e15 −0.370785
\(834\) −3.14561e14 −0.0269955
\(835\) 6.57417e15 0.560486
\(836\) −2.95005e15 −0.249859
\(837\) −2.00285e15 −0.168523
\(838\) 8.73141e13 0.00729864
\(839\) 1.02277e16 0.849351 0.424675 0.905346i \(-0.360388\pi\)
0.424675 + 0.905346i \(0.360388\pi\)
\(840\) −1.63328e14 −0.0134749
\(841\) 1.32576e16 1.08664
\(842\) 4.63916e14 0.0377766
\(843\) 9.31046e15 0.753216
\(844\) −5.13127e15 −0.412421
\(845\) 1.47190e16 1.17535
\(846\) 1.10652e14 0.00877856
\(847\) −1.05206e16 −0.829242
\(848\) 9.41226e15 0.737084
\(849\) 8.07668e15 0.628407
\(850\) 1.33195e14 0.0102964
\(851\) −5.81781e15 −0.446835
\(852\) −1.22189e16 −0.932427
\(853\) −1.09890e16 −0.833177 −0.416589 0.909095i \(-0.636774\pi\)
−0.416589 + 0.909095i \(0.636774\pi\)
\(854\) 1.29366e14 0.00974548
\(855\) −1.93898e15 −0.145131
\(856\) 1.12970e15 0.0840149
\(857\) −2.28648e16 −1.68956 −0.844780 0.535114i \(-0.820269\pi\)
−0.844780 + 0.535114i \(0.820269\pi\)
\(858\) −1.13129e14 −0.00830602
\(859\) −5.41310e15 −0.394897 −0.197449 0.980313i \(-0.563266\pi\)
−0.197449 + 0.980313i \(0.563266\pi\)
\(860\) 3.93726e15 0.285399
\(861\) 7.71174e15 0.555437
\(862\) −5.76329e14 −0.0412459
\(863\) 1.26068e16 0.896491 0.448246 0.893910i \(-0.352049\pi\)
0.448246 + 0.893910i \(0.352049\pi\)
\(864\) 2.39976e14 0.0169567
\(865\) −5.34596e15 −0.375350
\(866\) 6.47726e14 0.0451900
\(867\) 1.72015e16 1.19251
\(868\) 1.12758e16 0.776766
\(869\) −2.45731e15 −0.168210
\(870\) −1.61227e14 −0.0109669
\(871\) −2.30843e16 −1.56033
\(872\) 7.68062e14 0.0515888
\(873\) −5.03554e15 −0.336100
\(874\) −3.24705e14 −0.0215365
\(875\) 1.20480e15 0.0794091
\(876\) −1.26755e15 −0.0830218
\(877\) −1.24037e15 −0.0807337 −0.0403669 0.999185i \(-0.512853\pi\)
−0.0403669 + 0.999185i \(0.512853\pi\)
\(878\) 4.42204e14 0.0286024
\(879\) −1.31398e16 −0.844597
\(880\) −1.79369e15 −0.114576
\(881\) 1.97903e16 1.25627 0.628136 0.778103i \(-0.283818\pi\)
0.628136 + 0.778103i \(0.283818\pi\)
\(882\) −3.29028e13 −0.00207566
\(883\) −2.76313e16 −1.73228 −0.866139 0.499803i \(-0.833406\pi\)
−0.866139 + 0.499803i \(0.833406\pi\)
\(884\) −5.34817e16 −3.33210
\(885\) −4.23461e15 −0.262196
\(886\) 6.73423e14 0.0414383
\(887\) −1.89670e15 −0.115990 −0.0579949 0.998317i \(-0.518471\pi\)
−0.0579949 + 0.998317i \(0.518471\pi\)
\(888\) 3.31663e14 0.0201570
\(889\) −1.61947e15 −0.0978166
\(890\) −2.64400e14 −0.0158715
\(891\) −4.78400e14 −0.0285406
\(892\) 1.63949e16 0.972077
\(893\) −1.47975e16 −0.871978
\(894\) 1.86249e14 0.0109078
\(895\) −8.50432e13 −0.00495009
\(896\) −1.80113e15 −0.104196
\(897\) 1.43896e16 0.827352
\(898\) −3.75130e14 −0.0214369
\(899\) 2.22711e16 1.26492
\(900\) −1.17996e15 −0.0666090
\(901\) 2.30611e16 1.29388
\(902\) −1.46763e14 −0.00818428
\(903\) −5.90692e15 −0.327400
\(904\) 8.41611e13 0.00463644
\(905\) −9.80692e14 −0.0536989
\(906\) −5.35055e14 −0.0291201
\(907\) 1.35383e15 0.0732360 0.0366180 0.999329i \(-0.488342\pi\)
0.0366180 + 0.999329i \(0.488342\pi\)
\(908\) 1.15969e16 0.623545
\(909\) 3.59664e15 0.192219
\(910\) 4.18616e14 0.0222376
\(911\) −2.23682e16 −1.18108 −0.590542 0.807007i \(-0.701086\pi\)
−0.590542 + 0.807007i \(0.701086\pi\)
\(912\) −1.06819e16 −0.560631
\(913\) −1.92534e15 −0.100443
\(914\) 6.98347e14 0.0362132
\(915\) 1.87001e15 0.0963892
\(916\) 1.46674e15 0.0751496
\(917\) −2.96656e16 −1.51085
\(918\) 1.95707e14 0.00990767
\(919\) 2.89368e15 0.145618 0.0728089 0.997346i \(-0.476804\pi\)
0.0728089 + 0.997346i \(0.476804\pi\)
\(920\) −3.95368e14 −0.0197774
\(921\) 4.72749e15 0.235073
\(922\) −1.13333e13 −0.000560189 0
\(923\) 6.26620e16 3.07889
\(924\) 2.69334e15 0.131551
\(925\) −2.44652e15 −0.118787
\(926\) 6.10211e13 0.00294523
\(927\) 3.30022e15 0.158345
\(928\) −2.66847e15 −0.127277
\(929\) 3.33789e16 1.58265 0.791326 0.611394i \(-0.209391\pi\)
0.791326 + 0.611394i \(0.209391\pi\)
\(930\) −1.41044e14 −0.00664812
\(931\) 4.40008e15 0.206176
\(932\) 2.13136e16 0.992819
\(933\) −2.22658e16 −1.03107
\(934\) 4.11897e14 0.0189619
\(935\) −4.39475e15 −0.201127
\(936\) −8.20324e14 −0.0373223
\(937\) 1.52926e16 0.691694 0.345847 0.938291i \(-0.387592\pi\)
0.345847 + 0.938291i \(0.387592\pi\)
\(938\) −4.75574e14 −0.0213847
\(939\) 1.57503e16 0.704091
\(940\) −9.00499e15 −0.400203
\(941\) −3.93559e16 −1.73887 −0.869435 0.494047i \(-0.835517\pi\)
−0.869435 + 0.494047i \(0.835517\pi\)
\(942\) 9.27398e12 0.000407367 0
\(943\) 1.86677e16 0.815225
\(944\) −2.33287e16 −1.01285
\(945\) 1.77025e15 0.0764115
\(946\) 1.12415e14 0.00482418
\(947\) −4.01756e15 −0.171411 −0.0857053 0.996321i \(-0.527314\pi\)
−0.0857053 + 0.996321i \(0.527314\pi\)
\(948\) −8.90543e15 −0.377754
\(949\) 6.50034e15 0.274140
\(950\) −1.36546e14 −0.00572531
\(951\) 9.43708e15 0.393409
\(952\) −2.20457e15 −0.0913737
\(953\) 6.33511e15 0.261062 0.130531 0.991444i \(-0.458332\pi\)
0.130531 + 0.991444i \(0.458332\pi\)
\(954\) 1.76784e14 0.00724314
\(955\) 3.94410e15 0.160668
\(956\) −2.49282e16 −1.00965
\(957\) 5.31967e15 0.214225
\(958\) 6.06282e14 0.0242753
\(959\) 3.89038e16 1.54878
\(960\) −6.48917e15 −0.256860
\(961\) −5.92532e15 −0.233202
\(962\) −8.50062e14 −0.0332650
\(963\) −1.22443e16 −0.476419
\(964\) 3.60207e16 1.39357
\(965\) −1.00169e15 −0.0385330
\(966\) 2.96449e14 0.0113390
\(967\) 4.66836e16 1.77549 0.887747 0.460332i \(-0.152270\pi\)
0.887747 + 0.460332i \(0.152270\pi\)
\(968\) 1.45183e15 0.0549038
\(969\) −2.61719e16 −0.984134
\(970\) −3.54611e14 −0.0132589
\(971\) −1.52755e16 −0.567923 −0.283961 0.958836i \(-0.591649\pi\)
−0.283961 + 0.958836i \(0.591649\pi\)
\(972\) −1.73375e15 −0.0640946
\(973\) −3.84055e16 −1.41180
\(974\) −1.27161e14 −0.00464816
\(975\) 6.05116e15 0.219944
\(976\) 1.03020e16 0.372346
\(977\) −3.74521e15 −0.134603 −0.0673016 0.997733i \(-0.521439\pi\)
−0.0673016 + 0.997733i \(0.521439\pi\)
\(978\) 5.24621e14 0.0187492
\(979\) 8.72386e15 0.310030
\(980\) 2.67766e15 0.0946264
\(981\) −8.32469e15 −0.292542
\(982\) −6.05489e14 −0.0211589
\(983\) −2.52155e15 −0.0876242 −0.0438121 0.999040i \(-0.513950\pi\)
−0.0438121 + 0.999040i \(0.513950\pi\)
\(984\) −1.06421e15 −0.0367753
\(985\) 5.92553e15 0.203624
\(986\) −2.17621e15 −0.0743665
\(987\) 1.35098e16 0.459098
\(988\) 5.48272e16 1.85282
\(989\) −1.42988e16 −0.480530
\(990\) −3.36897e13 −0.00112591
\(991\) −3.99971e16 −1.32930 −0.664650 0.747155i \(-0.731419\pi\)
−0.664650 + 0.747155i \(0.731419\pi\)
\(992\) −2.33442e15 −0.0771551
\(993\) −1.59063e15 −0.0522814
\(994\) 1.29094e15 0.0421969
\(995\) −2.33861e16 −0.760205
\(996\) −6.97754e15 −0.225567
\(997\) −6.16247e15 −0.198121 −0.0990607 0.995081i \(-0.531584\pi\)
−0.0990607 + 0.995081i \(0.531584\pi\)
\(998\) −8.44792e13 −0.00270105
\(999\) −3.59475e15 −0.114303
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 \(a_p\))