Properties

Label 8034.2.a.o.1.1
Level 8034
Weight 2
Character 8034.1
Self dual Yes
Analytic conductor 64.152
Analytic rank 1
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8034.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1518129839\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.519850\)
Character \(\chi\) = 8034.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.94146 q^{5}\) \(+1.00000 q^{6}\) \(-3.14882 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-2.94146 q^{5}\) \(+1.00000 q^{6}\) \(-3.14882 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+2.94146 q^{10}\) \(+0.137087 q^{11}\) \(-1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+3.14882 q^{14}\) \(+2.94146 q^{15}\) \(+1.00000 q^{16}\) \(-2.74850 q^{17}\) \(-1.00000 q^{18}\) \(-4.14882 q^{19}\) \(-2.94146 q^{20}\) \(+3.14882 q^{21}\) \(-0.137087 q^{22}\) \(+7.19107 q^{23}\) \(+1.00000 q^{24}\) \(+3.65220 q^{25}\) \(-1.00000 q^{26}\) \(-1.00000 q^{27}\) \(-3.14882 q^{28}\) \(-10.1077 q^{29}\) \(-2.94146 q^{30}\) \(+4.60157 q^{31}\) \(-1.00000 q^{32}\) \(-0.137087 q^{33}\) \(+2.74850 q^{34}\) \(+9.26214 q^{35}\) \(+1.00000 q^{36}\) \(-0.829880 q^{37}\) \(+4.14882 q^{38}\) \(-1.00000 q^{39}\) \(+2.94146 q^{40}\) \(+4.33657 q^{41}\) \(-3.14882 q^{42}\) \(-9.96834 q^{43}\) \(+0.137087 q^{44}\) \(-2.94146 q^{45}\) \(-7.19107 q^{46}\) \(+6.77316 q^{47}\) \(-1.00000 q^{48}\) \(+2.91507 q^{49}\) \(-3.65220 q^{50}\) \(+2.74850 q^{51}\) \(+1.00000 q^{52}\) \(+5.15156 q^{53}\) \(+1.00000 q^{54}\) \(-0.403237 q^{55}\) \(+3.14882 q^{56}\) \(+4.14882 q^{57}\) \(+10.1077 q^{58}\) \(+10.3965 q^{59}\) \(+2.94146 q^{60}\) \(-8.47985 q^{61}\) \(-4.60157 q^{62}\) \(-3.14882 q^{63}\) \(+1.00000 q^{64}\) \(-2.94146 q^{65}\) \(+0.137087 q^{66}\) \(+12.7124 q^{67}\) \(-2.74850 q^{68}\) \(-7.19107 q^{69}\) \(-9.26214 q^{70}\) \(-4.30422 q^{71}\) \(-1.00000 q^{72}\) \(+1.09602 q^{73}\) \(+0.829880 q^{74}\) \(-3.65220 q^{75}\) \(-4.14882 q^{76}\) \(-0.431663 q^{77}\) \(+1.00000 q^{78}\) \(-2.76399 q^{79}\) \(-2.94146 q^{80}\) \(+1.00000 q^{81}\) \(-4.33657 q^{82}\) \(+8.49113 q^{83}\) \(+3.14882 q^{84}\) \(+8.08460 q^{85}\) \(+9.96834 q^{86}\) \(+10.1077 q^{87}\) \(-0.137087 q^{88}\) \(+3.36617 q^{89}\) \(+2.94146 q^{90}\) \(-3.14882 q^{91}\) \(+7.19107 q^{92}\) \(-4.60157 q^{93}\) \(-6.77316 q^{94}\) \(+12.2036 q^{95}\) \(+1.00000 q^{96}\) \(-10.0536 q^{97}\) \(-2.91507 q^{98}\) \(+0.137087 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(7q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 7q^{6} \) \(\mathstrut -\mathstrut 9q^{7} \) \(\mathstrut -\mathstrut 7q^{8} \) \(\mathstrut +\mathstrut 7q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{12} \) \(\mathstrut +\mathstrut 7q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 7q^{16} \) \(\mathstrut +\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 7q^{18} \) \(\mathstrut -\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 7q^{24} \) \(\mathstrut +\mathstrut 15q^{25} \) \(\mathstrut -\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 5q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 7q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut -\mathstrut 10q^{35} \) \(\mathstrut +\mathstrut 7q^{36} \) \(\mathstrut +\mathstrut 17q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut -\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 9q^{42} \) \(\mathstrut -\mathstrut 22q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 7q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut +\mathstrut 7q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut +\mathstrut 7q^{54} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 5q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 7q^{64} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 6q^{69} \) \(\mathstrut +\mathstrut 10q^{70} \) \(\mathstrut +\mathstrut 15q^{71} \) \(\mathstrut -\mathstrut 7q^{72} \) \(\mathstrut +\mathstrut 17q^{73} \) \(\mathstrut -\mathstrut 17q^{74} \) \(\mathstrut -\mathstrut 15q^{75} \) \(\mathstrut -\mathstrut 16q^{76} \) \(\mathstrut -\mathstrut 10q^{77} \) \(\mathstrut +\mathstrut 7q^{78} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 7q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut +\mathstrut 22q^{86} \) \(\mathstrut +\mathstrut 5q^{87} \) \(\mathstrut -\mathstrut 9q^{89} \) \(\mathstrut -\mathstrut 2q^{90} \) \(\mathstrut -\mathstrut 9q^{91} \) \(\mathstrut +\mathstrut 6q^{92} \) \(\mathstrut +\mathstrut 16q^{93} \) \(\mathstrut -\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 7q^{96} \) \(\mathstrut -\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.00000 −0.577350
\(4\) 1.00000 0.500000
\(5\) −2.94146 −1.31546 −0.657731 0.753253i \(-0.728484\pi\)
−0.657731 + 0.753253i \(0.728484\pi\)
\(6\) 1.00000 0.408248
\(7\) −3.14882 −1.19014 −0.595071 0.803673i \(-0.702876\pi\)
−0.595071 + 0.803673i \(0.702876\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 2.94146 0.930172
\(11\) 0.137087 0.0413334 0.0206667 0.999786i \(-0.493421\pi\)
0.0206667 + 0.999786i \(0.493421\pi\)
\(12\) −1.00000 −0.288675
\(13\) 1.00000 0.277350
\(14\) 3.14882 0.841558
\(15\) 2.94146 0.759482
\(16\) 1.00000 0.250000
\(17\) −2.74850 −0.666609 −0.333304 0.942819i \(-0.608164\pi\)
−0.333304 + 0.942819i \(0.608164\pi\)
\(18\) −1.00000 −0.235702
\(19\) −4.14882 −0.951805 −0.475902 0.879498i \(-0.657878\pi\)
−0.475902 + 0.879498i \(0.657878\pi\)
\(20\) −2.94146 −0.657731
\(21\) 3.14882 0.687129
\(22\) −0.137087 −0.0292271
\(23\) 7.19107 1.49944 0.749721 0.661754i \(-0.230188\pi\)
0.749721 + 0.661754i \(0.230188\pi\)
\(24\) 1.00000 0.204124
\(25\) 3.65220 0.730440
\(26\) −1.00000 −0.196116
\(27\) −1.00000 −0.192450
\(28\) −3.14882 −0.595071
\(29\) −10.1077 −1.87695 −0.938475 0.345346i \(-0.887762\pi\)
−0.938475 + 0.345346i \(0.887762\pi\)
\(30\) −2.94146 −0.537035
\(31\) 4.60157 0.826467 0.413233 0.910625i \(-0.364399\pi\)
0.413233 + 0.910625i \(0.364399\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.137087 −0.0238638
\(34\) 2.74850 0.471363
\(35\) 9.26214 1.56559
\(36\) 1.00000 0.166667
\(37\) −0.829880 −0.136431 −0.0682157 0.997671i \(-0.521731\pi\)
−0.0682157 + 0.997671i \(0.521731\pi\)
\(38\) 4.14882 0.673027
\(39\) −1.00000 −0.160128
\(40\) 2.94146 0.465086
\(41\) 4.33657 0.677259 0.338630 0.940920i \(-0.390037\pi\)
0.338630 + 0.940920i \(0.390037\pi\)
\(42\) −3.14882 −0.485873
\(43\) −9.96834 −1.52016 −0.760079 0.649831i \(-0.774840\pi\)
−0.760079 + 0.649831i \(0.774840\pi\)
\(44\) 0.137087 0.0206667
\(45\) −2.94146 −0.438487
\(46\) −7.19107 −1.06027
\(47\) 6.77316 0.987967 0.493984 0.869471i \(-0.335540\pi\)
0.493984 + 0.869471i \(0.335540\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.91507 0.416438
\(50\) −3.65220 −0.516499
\(51\) 2.74850 0.384867
\(52\) 1.00000 0.138675
\(53\) 5.15156 0.707621 0.353810 0.935317i \(-0.384886\pi\)
0.353810 + 0.935317i \(0.384886\pi\)
\(54\) 1.00000 0.136083
\(55\) −0.403237 −0.0543725
\(56\) 3.14882 0.420779
\(57\) 4.14882 0.549525
\(58\) 10.1077 1.32720
\(59\) 10.3965 1.35351 0.676755 0.736208i \(-0.263386\pi\)
0.676755 + 0.736208i \(0.263386\pi\)
\(60\) 2.94146 0.379741
\(61\) −8.47985 −1.08573 −0.542867 0.839819i \(-0.682661\pi\)
−0.542867 + 0.839819i \(0.682661\pi\)
\(62\) −4.60157 −0.584400
\(63\) −3.14882 −0.396714
\(64\) 1.00000 0.125000
\(65\) −2.94146 −0.364843
\(66\) 0.137087 0.0168743
\(67\) 12.7124 1.55306 0.776532 0.630078i \(-0.216977\pi\)
0.776532 + 0.630078i \(0.216977\pi\)
\(68\) −2.74850 −0.333304
\(69\) −7.19107 −0.865703
\(70\) −9.26214 −1.10704
\(71\) −4.30422 −0.510817 −0.255409 0.966833i \(-0.582210\pi\)
−0.255409 + 0.966833i \(0.582210\pi\)
\(72\) −1.00000 −0.117851
\(73\) 1.09602 0.128280 0.0641400 0.997941i \(-0.479570\pi\)
0.0641400 + 0.997941i \(0.479570\pi\)
\(74\) 0.829880 0.0964716
\(75\) −3.65220 −0.421720
\(76\) −4.14882 −0.475902
\(77\) −0.431663 −0.0491926
\(78\) 1.00000 0.113228
\(79\) −2.76399 −0.310973 −0.155486 0.987838i \(-0.549694\pi\)
−0.155486 + 0.987838i \(0.549694\pi\)
\(80\) −2.94146 −0.328865
\(81\) 1.00000 0.111111
\(82\) −4.33657 −0.478895
\(83\) 8.49113 0.932022 0.466011 0.884779i \(-0.345691\pi\)
0.466011 + 0.884779i \(0.345691\pi\)
\(84\) 3.14882 0.343564
\(85\) 8.08460 0.876898
\(86\) 9.96834 1.07491
\(87\) 10.1077 1.08366
\(88\) −0.137087 −0.0146136
\(89\) 3.36617 0.356814 0.178407 0.983957i \(-0.442906\pi\)
0.178407 + 0.983957i \(0.442906\pi\)
\(90\) 2.94146 0.310057
\(91\) −3.14882 −0.330086
\(92\) 7.19107 0.749721
\(93\) −4.60157 −0.477161
\(94\) −6.77316 −0.698598
\(95\) 12.2036 1.25206
\(96\) 1.00000 0.102062
\(97\) −10.0536 −1.02078 −0.510392 0.859942i \(-0.670500\pi\)
−0.510392 + 0.859942i \(0.670500\pi\)
\(98\) −2.91507 −0.294466
\(99\) 0.137087 0.0137778
\(100\) 3.65220 0.365220
\(101\) 15.0153 1.49408 0.747038 0.664781i \(-0.231475\pi\)
0.747038 + 0.664781i \(0.231475\pi\)
\(102\) −2.74850 −0.272142
\(103\) 1.00000 0.0985329
\(104\) −1.00000 −0.0980581
\(105\) −9.26214 −0.903892
\(106\) −5.15156 −0.500363
\(107\) 3.93656 0.380561 0.190281 0.981730i \(-0.439060\pi\)
0.190281 + 0.981730i \(0.439060\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 12.7707 1.22322 0.611608 0.791161i \(-0.290523\pi\)
0.611608 + 0.791161i \(0.290523\pi\)
\(110\) 0.403237 0.0384472
\(111\) 0.829880 0.0787687
\(112\) −3.14882 −0.297536
\(113\) −5.01087 −0.471383 −0.235691 0.971828i \(-0.575735\pi\)
−0.235691 + 0.971828i \(0.575735\pi\)
\(114\) −4.14882 −0.388573
\(115\) −21.1523 −1.97246
\(116\) −10.1077 −0.938475
\(117\) 1.00000 0.0924500
\(118\) −10.3965 −0.957076
\(119\) 8.65452 0.793359
\(120\) −2.94146 −0.268518
\(121\) −10.9812 −0.998292
\(122\) 8.47985 0.767730
\(123\) −4.33657 −0.391016
\(124\) 4.60157 0.413233
\(125\) 3.96450 0.354596
\(126\) 3.14882 0.280519
\(127\) 8.01336 0.711071 0.355536 0.934663i \(-0.384299\pi\)
0.355536 + 0.934663i \(0.384299\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 9.96834 0.877663
\(130\) 2.94146 0.257983
\(131\) 16.7419 1.46274 0.731372 0.681979i \(-0.238880\pi\)
0.731372 + 0.681979i \(0.238880\pi\)
\(132\) −0.137087 −0.0119319
\(133\) 13.0639 1.13278
\(134\) −12.7124 −1.09818
\(135\) 2.94146 0.253161
\(136\) 2.74850 0.235682
\(137\) −6.21021 −0.530574 −0.265287 0.964169i \(-0.585467\pi\)
−0.265287 + 0.964169i \(0.585467\pi\)
\(138\) 7.19107 0.612144
\(139\) −4.22377 −0.358255 −0.179128 0.983826i \(-0.557328\pi\)
−0.179128 + 0.983826i \(0.557328\pi\)
\(140\) 9.26214 0.782793
\(141\) −6.77316 −0.570403
\(142\) 4.30422 0.361202
\(143\) 0.137087 0.0114638
\(144\) 1.00000 0.0833333
\(145\) 29.7314 2.46906
\(146\) −1.09602 −0.0907076
\(147\) −2.91507 −0.240431
\(148\) −0.829880 −0.0682157
\(149\) 12.6682 1.03782 0.518909 0.854830i \(-0.326338\pi\)
0.518909 + 0.854830i \(0.326338\pi\)
\(150\) 3.65220 0.298201
\(151\) −0.585495 −0.0476469 −0.0238235 0.999716i \(-0.507584\pi\)
−0.0238235 + 0.999716i \(0.507584\pi\)
\(152\) 4.14882 0.336514
\(153\) −2.74850 −0.222203
\(154\) 0.431663 0.0347844
\(155\) −13.5353 −1.08719
\(156\) −1.00000 −0.0800641
\(157\) 6.17311 0.492668 0.246334 0.969185i \(-0.420774\pi\)
0.246334 + 0.969185i \(0.420774\pi\)
\(158\) 2.76399 0.219891
\(159\) −5.15156 −0.408545
\(160\) 2.94146 0.232543
\(161\) −22.6434 −1.78455
\(162\) −1.00000 −0.0785674
\(163\) 19.0187 1.48966 0.744829 0.667255i \(-0.232531\pi\)
0.744829 + 0.667255i \(0.232531\pi\)
\(164\) 4.33657 0.338630
\(165\) 0.403237 0.0313920
\(166\) −8.49113 −0.659039
\(167\) −14.1560 −1.09543 −0.547713 0.836666i \(-0.684502\pi\)
−0.547713 + 0.836666i \(0.684502\pi\)
\(168\) −3.14882 −0.242937
\(169\) 1.00000 0.0769231
\(170\) −8.08460 −0.620061
\(171\) −4.14882 −0.317268
\(172\) −9.96834 −0.760079
\(173\) −1.79096 −0.136164 −0.0680821 0.997680i \(-0.521688\pi\)
−0.0680821 + 0.997680i \(0.521688\pi\)
\(174\) −10.1077 −0.766262
\(175\) −11.5001 −0.869327
\(176\) 0.137087 0.0103333
\(177\) −10.3965 −0.781450
\(178\) −3.36617 −0.252305
\(179\) −16.8883 −1.26229 −0.631144 0.775666i \(-0.717414\pi\)
−0.631144 + 0.775666i \(0.717414\pi\)
\(180\) −2.94146 −0.219244
\(181\) 22.9822 1.70826 0.854129 0.520062i \(-0.174091\pi\)
0.854129 + 0.520062i \(0.174091\pi\)
\(182\) 3.14882 0.233406
\(183\) 8.47985 0.626849
\(184\) −7.19107 −0.530133
\(185\) 2.44106 0.179470
\(186\) 4.60157 0.337404
\(187\) −0.376784 −0.0275532
\(188\) 6.77316 0.493984
\(189\) 3.14882 0.229043
\(190\) −12.2036 −0.885342
\(191\) −1.01677 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 4.27406 0.307653 0.153827 0.988098i \(-0.450840\pi\)
0.153827 + 0.988098i \(0.450840\pi\)
\(194\) 10.0536 0.721803
\(195\) 2.94146 0.210642
\(196\) 2.91507 0.208219
\(197\) 22.0133 1.56838 0.784190 0.620521i \(-0.213079\pi\)
0.784190 + 0.620521i \(0.213079\pi\)
\(198\) −0.137087 −0.00974237
\(199\) −24.9686 −1.76997 −0.884987 0.465615i \(-0.845833\pi\)
−0.884987 + 0.465615i \(0.845833\pi\)
\(200\) −3.65220 −0.258250
\(201\) −12.7124 −0.896662
\(202\) −15.0153 −1.05647
\(203\) 31.8273 2.23384
\(204\) 2.74850 0.192433
\(205\) −12.7559 −0.890909
\(206\) −1.00000 −0.0696733
\(207\) 7.19107 0.499814
\(208\) 1.00000 0.0693375
\(209\) −0.568751 −0.0393413
\(210\) 9.26214 0.639148
\(211\) 4.72118 0.325020 0.162510 0.986707i \(-0.448041\pi\)
0.162510 + 0.986707i \(0.448041\pi\)
\(212\) 5.15156 0.353810
\(213\) 4.30422 0.294921
\(214\) −3.93656 −0.269098
\(215\) 29.3215 1.99971
\(216\) 1.00000 0.0680414
\(217\) −14.4895 −0.983613
\(218\) −12.7707 −0.864944
\(219\) −1.09602 −0.0740625
\(220\) −0.403237 −0.0271863
\(221\) −2.74850 −0.184884
\(222\) −0.829880 −0.0556979
\(223\) −26.6098 −1.78193 −0.890963 0.454076i \(-0.849970\pi\)
−0.890963 + 0.454076i \(0.849970\pi\)
\(224\) 3.14882 0.210389
\(225\) 3.65220 0.243480
\(226\) 5.01087 0.333318
\(227\) 0.507530 0.0336860 0.0168430 0.999858i \(-0.494638\pi\)
0.0168430 + 0.999858i \(0.494638\pi\)
\(228\) 4.14882 0.274762
\(229\) −1.12067 −0.0740556 −0.0370278 0.999314i \(-0.511789\pi\)
−0.0370278 + 0.999314i \(0.511789\pi\)
\(230\) 21.1523 1.39474
\(231\) 0.431663 0.0284014
\(232\) 10.1077 0.663602
\(233\) −3.05262 −0.199984 −0.0999920 0.994988i \(-0.531882\pi\)
−0.0999920 + 0.994988i \(0.531882\pi\)
\(234\) −1.00000 −0.0653720
\(235\) −19.9230 −1.29963
\(236\) 10.3965 0.676755
\(237\) 2.76399 0.179540
\(238\) −8.65452 −0.560989
\(239\) 1.15111 0.0744589 0.0372294 0.999307i \(-0.488147\pi\)
0.0372294 + 0.999307i \(0.488147\pi\)
\(240\) 2.94146 0.189871
\(241\) 1.40880 0.0907489 0.0453745 0.998970i \(-0.485552\pi\)
0.0453745 + 0.998970i \(0.485552\pi\)
\(242\) 10.9812 0.705899
\(243\) −1.00000 −0.0641500
\(244\) −8.47985 −0.542867
\(245\) −8.57456 −0.547809
\(246\) 4.33657 0.276490
\(247\) −4.14882 −0.263983
\(248\) −4.60157 −0.292200
\(249\) −8.49113 −0.538103
\(250\) −3.96450 −0.250737
\(251\) −3.13575 −0.197927 −0.0989634 0.995091i \(-0.531553\pi\)
−0.0989634 + 0.995091i \(0.531553\pi\)
\(252\) −3.14882 −0.198357
\(253\) 0.985804 0.0619770
\(254\) −8.01336 −0.502803
\(255\) −8.08460 −0.506277
\(256\) 1.00000 0.0625000
\(257\) 6.85244 0.427443 0.213722 0.976895i \(-0.431441\pi\)
0.213722 + 0.976895i \(0.431441\pi\)
\(258\) −9.96834 −0.620602
\(259\) 2.61314 0.162373
\(260\) −2.94146 −0.182422
\(261\) −10.1077 −0.625650
\(262\) −16.7419 −1.03432
\(263\) −18.0045 −1.11020 −0.555102 0.831782i \(-0.687321\pi\)
−0.555102 + 0.831782i \(0.687321\pi\)
\(264\) 0.137087 0.00843714
\(265\) −15.1531 −0.930848
\(266\) −13.0639 −0.800998
\(267\) −3.36617 −0.206006
\(268\) 12.7124 0.776532
\(269\) −13.9664 −0.851548 −0.425774 0.904829i \(-0.639998\pi\)
−0.425774 + 0.904829i \(0.639998\pi\)
\(270\) −2.94146 −0.179012
\(271\) −17.6408 −1.07160 −0.535801 0.844345i \(-0.679990\pi\)
−0.535801 + 0.844345i \(0.679990\pi\)
\(272\) −2.74850 −0.166652
\(273\) 3.14882 0.190575
\(274\) 6.21021 0.375173
\(275\) 0.500670 0.0301916
\(276\) −7.19107 −0.432851
\(277\) 2.39614 0.143970 0.0719849 0.997406i \(-0.477067\pi\)
0.0719849 + 0.997406i \(0.477067\pi\)
\(278\) 4.22377 0.253325
\(279\) 4.60157 0.275489
\(280\) −9.26214 −0.553518
\(281\) −2.16737 −0.129294 −0.0646472 0.997908i \(-0.520592\pi\)
−0.0646472 + 0.997908i \(0.520592\pi\)
\(282\) 6.77316 0.403336
\(283\) −6.62007 −0.393522 −0.196761 0.980451i \(-0.563042\pi\)
−0.196761 + 0.980451i \(0.563042\pi\)
\(284\) −4.30422 −0.255409
\(285\) −12.2036 −0.722879
\(286\) −0.137087 −0.00810614
\(287\) −13.6551 −0.806035
\(288\) −1.00000 −0.0589256
\(289\) −9.44576 −0.555633
\(290\) −29.7314 −1.74589
\(291\) 10.0536 0.589350
\(292\) 1.09602 0.0641400
\(293\) 17.4690 1.02055 0.510275 0.860011i \(-0.329543\pi\)
0.510275 + 0.860011i \(0.329543\pi\)
\(294\) 2.91507 0.170010
\(295\) −30.5809 −1.78049
\(296\) 0.829880 0.0482358
\(297\) −0.137087 −0.00795461
\(298\) −12.6682 −0.733848
\(299\) 7.19107 0.415870
\(300\) −3.65220 −0.210860
\(301\) 31.3885 1.80920
\(302\) 0.585495 0.0336915
\(303\) −15.0153 −0.862605
\(304\) −4.14882 −0.237951
\(305\) 24.9432 1.42824
\(306\) 2.74850 0.157121
\(307\) −21.1127 −1.20496 −0.602482 0.798132i \(-0.705822\pi\)
−0.602482 + 0.798132i \(0.705822\pi\)
\(308\) −0.431663 −0.0245963
\(309\) −1.00000 −0.0568880
\(310\) 13.5353 0.768756
\(311\) −15.4624 −0.876793 −0.438397 0.898782i \(-0.644453\pi\)
−0.438397 + 0.898782i \(0.644453\pi\)
\(312\) 1.00000 0.0566139
\(313\) 26.0600 1.47300 0.736499 0.676438i \(-0.236477\pi\)
0.736499 + 0.676438i \(0.236477\pi\)
\(314\) −6.17311 −0.348369
\(315\) 9.26214 0.521862
\(316\) −2.76399 −0.155486
\(317\) −14.1968 −0.797373 −0.398687 0.917087i \(-0.630534\pi\)
−0.398687 + 0.917087i \(0.630534\pi\)
\(318\) 5.15156 0.288885
\(319\) −1.38564 −0.0775807
\(320\) −2.94146 −0.164433
\(321\) −3.93656 −0.219717
\(322\) 22.6434 1.26187
\(323\) 11.4030 0.634481
\(324\) 1.00000 0.0555556
\(325\) 3.65220 0.202588
\(326\) −19.0187 −1.05335
\(327\) −12.7707 −0.706224
\(328\) −4.33657 −0.239447
\(329\) −21.3275 −1.17582
\(330\) −0.403237 −0.0221975
\(331\) 20.5911 1.13179 0.565896 0.824477i \(-0.308530\pi\)
0.565896 + 0.824477i \(0.308530\pi\)
\(332\) 8.49113 0.466011
\(333\) −0.829880 −0.0454772
\(334\) 14.1560 0.774583
\(335\) −37.3930 −2.04300
\(336\) 3.14882 0.171782
\(337\) −5.93953 −0.323547 −0.161773 0.986828i \(-0.551721\pi\)
−0.161773 + 0.986828i \(0.551721\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 5.01087 0.272153
\(340\) 8.08460 0.438449
\(341\) 0.630817 0.0341607
\(342\) 4.14882 0.224342
\(343\) 12.8627 0.694521
\(344\) 9.96834 0.537457
\(345\) 21.1523 1.13880
\(346\) 1.79096 0.0962827
\(347\) 8.09109 0.434353 0.217176 0.976132i \(-0.430315\pi\)
0.217176 + 0.976132i \(0.430315\pi\)
\(348\) 10.1077 0.541829
\(349\) −14.5290 −0.777719 −0.388859 0.921297i \(-0.627131\pi\)
−0.388859 + 0.921297i \(0.627131\pi\)
\(350\) 11.5001 0.614707
\(351\) −1.00000 −0.0533761
\(352\) −0.137087 −0.00730678
\(353\) 8.63553 0.459623 0.229811 0.973235i \(-0.426189\pi\)
0.229811 + 0.973235i \(0.426189\pi\)
\(354\) 10.3965 0.552568
\(355\) 12.6607 0.671961
\(356\) 3.36617 0.178407
\(357\) −8.65452 −0.458046
\(358\) 16.8883 0.892572
\(359\) −6.80238 −0.359016 −0.179508 0.983757i \(-0.557451\pi\)
−0.179508 + 0.983757i \(0.557451\pi\)
\(360\) 2.94146 0.155029
\(361\) −1.78729 −0.0940680
\(362\) −22.9822 −1.20792
\(363\) 10.9812 0.576364
\(364\) −3.14882 −0.165043
\(365\) −3.22392 −0.168747
\(366\) −8.47985 −0.443249
\(367\) −28.3418 −1.47943 −0.739714 0.672921i \(-0.765039\pi\)
−0.739714 + 0.672921i \(0.765039\pi\)
\(368\) 7.19107 0.374860
\(369\) 4.33657 0.225753
\(370\) −2.44106 −0.126905
\(371\) −16.2213 −0.842169
\(372\) −4.60157 −0.238580
\(373\) 0.827118 0.0428265 0.0214133 0.999771i \(-0.493183\pi\)
0.0214133 + 0.999771i \(0.493183\pi\)
\(374\) 0.376784 0.0194830
\(375\) −3.96450 −0.204726
\(376\) −6.77316 −0.349299
\(377\) −10.1077 −0.520572
\(378\) −3.14882 −0.161958
\(379\) −4.67824 −0.240305 −0.120153 0.992755i \(-0.538338\pi\)
−0.120153 + 0.992755i \(0.538338\pi\)
\(380\) 12.2036 0.626031
\(381\) −8.01336 −0.410537
\(382\) 1.01677 0.0520227
\(383\) 34.0161 1.73814 0.869070 0.494688i \(-0.164718\pi\)
0.869070 + 0.494688i \(0.164718\pi\)
\(384\) 1.00000 0.0510310
\(385\) 1.26972 0.0647110
\(386\) −4.27406 −0.217544
\(387\) −9.96834 −0.506719
\(388\) −10.0536 −0.510392
\(389\) −17.2938 −0.876828 −0.438414 0.898773i \(-0.644460\pi\)
−0.438414 + 0.898773i \(0.644460\pi\)
\(390\) −2.94146 −0.148947
\(391\) −19.7646 −0.999540
\(392\) −2.91507 −0.147233
\(393\) −16.7419 −0.844516
\(394\) −22.0133 −1.10901
\(395\) 8.13016 0.409073
\(396\) 0.137087 0.00688890
\(397\) −11.9604 −0.600276 −0.300138 0.953896i \(-0.597033\pi\)
−0.300138 + 0.953896i \(0.597033\pi\)
\(398\) 24.9686 1.25156
\(399\) −13.0639 −0.654012
\(400\) 3.65220 0.182610
\(401\) −3.41345 −0.170460 −0.0852298 0.996361i \(-0.527162\pi\)
−0.0852298 + 0.996361i \(0.527162\pi\)
\(402\) 12.7124 0.634035
\(403\) 4.60157 0.229221
\(404\) 15.0153 0.747038
\(405\) −2.94146 −0.146162
\(406\) −31.8273 −1.57956
\(407\) −0.113766 −0.00563918
\(408\) −2.74850 −0.136071
\(409\) −24.8064 −1.22660 −0.613298 0.789852i \(-0.710158\pi\)
−0.613298 + 0.789852i \(0.710158\pi\)
\(410\) 12.7559 0.629968
\(411\) 6.21021 0.306327
\(412\) 1.00000 0.0492665
\(413\) −32.7367 −1.61087
\(414\) −7.19107 −0.353422
\(415\) −24.9763 −1.22604
\(416\) −1.00000 −0.0490290
\(417\) 4.22377 0.206839
\(418\) 0.568751 0.0278185
\(419\) 6.00013 0.293125 0.146563 0.989201i \(-0.453179\pi\)
0.146563 + 0.989201i \(0.453179\pi\)
\(420\) −9.26214 −0.451946
\(421\) −1.38513 −0.0675070 −0.0337535 0.999430i \(-0.510746\pi\)
−0.0337535 + 0.999430i \(0.510746\pi\)
\(422\) −4.72118 −0.229824
\(423\) 6.77316 0.329322
\(424\) −5.15156 −0.250182
\(425\) −10.0381 −0.486918
\(426\) −4.30422 −0.208540
\(427\) 26.7015 1.29218
\(428\) 3.93656 0.190281
\(429\) −0.137087 −0.00661864
\(430\) −29.3215 −1.41401
\(431\) −23.5209 −1.13296 −0.566481 0.824075i \(-0.691696\pi\)
−0.566481 + 0.824075i \(0.691696\pi\)
\(432\) −1.00000 −0.0481125
\(433\) −13.5308 −0.650249 −0.325125 0.945671i \(-0.605406\pi\)
−0.325125 + 0.945671i \(0.605406\pi\)
\(434\) 14.4895 0.695519
\(435\) −29.7314 −1.42551
\(436\) 12.7707 0.611608
\(437\) −29.8344 −1.42718
\(438\) 1.09602 0.0523701
\(439\) −29.4705 −1.40655 −0.703275 0.710918i \(-0.748280\pi\)
−0.703275 + 0.710918i \(0.748280\pi\)
\(440\) 0.403237 0.0192236
\(441\) 2.91507 0.138813
\(442\) 2.74850 0.130733
\(443\) −38.0382 −1.80725 −0.903625 0.428324i \(-0.859104\pi\)
−0.903625 + 0.428324i \(0.859104\pi\)
\(444\) 0.829880 0.0393844
\(445\) −9.90147 −0.469375
\(446\) 26.6098 1.26001
\(447\) −12.6682 −0.599184
\(448\) −3.14882 −0.148768
\(449\) 21.2124 1.00108 0.500538 0.865715i \(-0.333136\pi\)
0.500538 + 0.865715i \(0.333136\pi\)
\(450\) −3.65220 −0.172166
\(451\) 0.594489 0.0279934
\(452\) −5.01087 −0.235691
\(453\) 0.585495 0.0275090
\(454\) −0.507530 −0.0238196
\(455\) 9.26214 0.434216
\(456\) −4.14882 −0.194286
\(457\) 28.9591 1.35465 0.677324 0.735684i \(-0.263139\pi\)
0.677324 + 0.735684i \(0.263139\pi\)
\(458\) 1.12067 0.0523652
\(459\) 2.74850 0.128289
\(460\) −21.1523 −0.986229
\(461\) −15.5870 −0.725960 −0.362980 0.931797i \(-0.618241\pi\)
−0.362980 + 0.931797i \(0.618241\pi\)
\(462\) −0.431663 −0.0200828
\(463\) −15.6494 −0.727290 −0.363645 0.931538i \(-0.618468\pi\)
−0.363645 + 0.931538i \(0.618468\pi\)
\(464\) −10.1077 −0.469238
\(465\) 13.5353 0.627687
\(466\) 3.05262 0.141410
\(467\) 28.3998 1.31419 0.657093 0.753809i \(-0.271786\pi\)
0.657093 + 0.753809i \(0.271786\pi\)
\(468\) 1.00000 0.0462250
\(469\) −40.0290 −1.84837
\(470\) 19.9230 0.918980
\(471\) −6.17311 −0.284442
\(472\) −10.3965 −0.478538
\(473\) −1.36653 −0.0628333
\(474\) −2.76399 −0.126954
\(475\) −15.1523 −0.695236
\(476\) 8.65452 0.396679
\(477\) 5.15156 0.235874
\(478\) −1.15111 −0.0526504
\(479\) 33.2339 1.51850 0.759249 0.650801i \(-0.225567\pi\)
0.759249 + 0.650801i \(0.225567\pi\)
\(480\) −2.94146 −0.134259
\(481\) −0.829880 −0.0378393
\(482\) −1.40880 −0.0641692
\(483\) 22.6434 1.03031
\(484\) −10.9812 −0.499146
\(485\) 29.5722 1.34280
\(486\) 1.00000 0.0453609
\(487\) −34.4329 −1.56031 −0.780153 0.625589i \(-0.784859\pi\)
−0.780153 + 0.625589i \(0.784859\pi\)
\(488\) 8.47985 0.383865
\(489\) −19.0187 −0.860055
\(490\) 8.57456 0.387359
\(491\) 27.1694 1.22614 0.613070 0.790029i \(-0.289934\pi\)
0.613070 + 0.790029i \(0.289934\pi\)
\(492\) −4.33657 −0.195508
\(493\) 27.7810 1.25119
\(494\) 4.14882 0.186664
\(495\) −0.403237 −0.0181242
\(496\) 4.60157 0.206617
\(497\) 13.5532 0.607945
\(498\) 8.49113 0.380496
\(499\) −18.9505 −0.848343 −0.424171 0.905582i \(-0.639435\pi\)
−0.424171 + 0.905582i \(0.639435\pi\)
\(500\) 3.96450 0.177298
\(501\) 14.1560 0.632445
\(502\) 3.13575 0.139955
\(503\) 28.6947 1.27943 0.639717 0.768610i \(-0.279052\pi\)
0.639717 + 0.768610i \(0.279052\pi\)
\(504\) 3.14882 0.140260
\(505\) −44.1669 −1.96540
\(506\) −0.985804 −0.0438244
\(507\) −1.00000 −0.0444116
\(508\) 8.01336 0.355536
\(509\) 12.8280 0.568590 0.284295 0.958737i \(-0.408240\pi\)
0.284295 + 0.958737i \(0.408240\pi\)
\(510\) 8.08460 0.357992
\(511\) −3.45118 −0.152671
\(512\) −1.00000 −0.0441942
\(513\) 4.14882 0.183175
\(514\) −6.85244 −0.302248
\(515\) −2.94146 −0.129616
\(516\) 9.96834 0.438832
\(517\) 0.928515 0.0408360
\(518\) −2.61314 −0.114815
\(519\) 1.79096 0.0786145
\(520\) 2.94146 0.128992
\(521\) −15.9227 −0.697587 −0.348793 0.937200i \(-0.613408\pi\)
−0.348793 + 0.937200i \(0.613408\pi\)
\(522\) 10.1077 0.442402
\(523\) 14.6818 0.641989 0.320995 0.947081i \(-0.395983\pi\)
0.320995 + 0.947081i \(0.395983\pi\)
\(524\) 16.7419 0.731372
\(525\) 11.5001 0.501906
\(526\) 18.0045 0.785032
\(527\) −12.6474 −0.550930
\(528\) −0.137087 −0.00596596
\(529\) 28.7115 1.24832
\(530\) 15.1531 0.658209
\(531\) 10.3965 0.451170
\(532\) 13.0639 0.566391
\(533\) 4.33657 0.187838
\(534\) 3.36617 0.145669
\(535\) −11.5792 −0.500614
\(536\) −12.7124 −0.549091
\(537\) 16.8883 0.728782
\(538\) 13.9664 0.602136
\(539\) 0.399619 0.0172128
\(540\) 2.94146 0.126580
\(541\) 15.0939 0.648936 0.324468 0.945897i \(-0.394815\pi\)
0.324468 + 0.945897i \(0.394815\pi\)
\(542\) 17.6408 0.757736
\(543\) −22.9822 −0.986263
\(544\) 2.74850 0.117841
\(545\) −37.5647 −1.60909
\(546\) −3.14882 −0.134757
\(547\) −17.7084 −0.757157 −0.378579 0.925569i \(-0.623587\pi\)
−0.378579 + 0.925569i \(0.623587\pi\)
\(548\) −6.21021 −0.265287
\(549\) −8.47985 −0.361911
\(550\) −0.500670 −0.0213487
\(551\) 41.9350 1.78649
\(552\) 7.19107 0.306072
\(553\) 8.70330 0.370102
\(554\) −2.39614 −0.101802
\(555\) −2.44106 −0.103617
\(556\) −4.22377 −0.179128
\(557\) −11.4351 −0.484521 −0.242260 0.970211i \(-0.577889\pi\)
−0.242260 + 0.970211i \(0.577889\pi\)
\(558\) −4.60157 −0.194800
\(559\) −9.96834 −0.421616
\(560\) 9.26214 0.391397
\(561\) 0.376784 0.0159078
\(562\) 2.16737 0.0914249
\(563\) 16.6028 0.699726 0.349863 0.936801i \(-0.386228\pi\)
0.349863 + 0.936801i \(0.386228\pi\)
\(564\) −6.77316 −0.285202
\(565\) 14.7393 0.620086
\(566\) 6.62007 0.278262
\(567\) −3.14882 −0.132238
\(568\) 4.30422 0.180601
\(569\) −13.7295 −0.575571 −0.287785 0.957695i \(-0.592919\pi\)
−0.287785 + 0.957695i \(0.592919\pi\)
\(570\) 12.2036 0.511152
\(571\) −30.7554 −1.28707 −0.643536 0.765416i \(-0.722533\pi\)
−0.643536 + 0.765416i \(0.722533\pi\)
\(572\) 0.137087 0.00573191
\(573\) 1.01677 0.0424764
\(574\) 13.6551 0.569953
\(575\) 26.2632 1.09525
\(576\) 1.00000 0.0416667
\(577\) 39.7020 1.65282 0.826408 0.563072i \(-0.190380\pi\)
0.826408 + 0.563072i \(0.190380\pi\)
\(578\) 9.44576 0.392892
\(579\) −4.27406 −0.177624
\(580\) 29.7314 1.23453
\(581\) −26.7370 −1.10924
\(582\) −10.0536 −0.416733
\(583\) 0.706213 0.0292484
\(584\) −1.09602 −0.0453538
\(585\) −2.94146 −0.121614
\(586\) −17.4690 −0.721638
\(587\) −41.6041 −1.71718 −0.858592 0.512659i \(-0.828661\pi\)
−0.858592 + 0.512659i \(0.828661\pi\)
\(588\) −2.91507 −0.120215
\(589\) −19.0911 −0.786635
\(590\) 30.5809 1.25900
\(591\) −22.0133 −0.905505
\(592\) −0.829880 −0.0341079
\(593\) −2.62330 −0.107726 −0.0538630 0.998548i \(-0.517153\pi\)
−0.0538630 + 0.998548i \(0.517153\pi\)
\(594\) 0.137087 0.00562476
\(595\) −25.4570 −1.04363
\(596\) 12.6682 0.518909
\(597\) 24.9686 1.02190
\(598\) −7.19107 −0.294065
\(599\) −10.0121 −0.409084 −0.204542 0.978858i \(-0.565570\pi\)
−0.204542 + 0.978858i \(0.565570\pi\)
\(600\) 3.65220 0.149100
\(601\) −7.82992 −0.319389 −0.159694 0.987166i \(-0.551051\pi\)
−0.159694 + 0.987166i \(0.551051\pi\)
\(602\) −31.3885 −1.27930
\(603\) 12.7124 0.517688
\(604\) −0.585495 −0.0238235
\(605\) 32.3008 1.31321
\(606\) 15.0153 0.609954
\(607\) −32.5823 −1.32248 −0.661238 0.750176i \(-0.729969\pi\)
−0.661238 + 0.750176i \(0.729969\pi\)
\(608\) 4.14882 0.168257
\(609\) −31.8273 −1.28971
\(610\) −24.9432 −1.00992
\(611\) 6.77316 0.274013
\(612\) −2.74850 −0.111101
\(613\) 36.6489 1.48023 0.740117 0.672479i \(-0.234770\pi\)
0.740117 + 0.672479i \(0.234770\pi\)
\(614\) 21.1127 0.852039
\(615\) 12.7559 0.514366
\(616\) 0.431663 0.0173922
\(617\) 11.2017 0.450962 0.225481 0.974248i \(-0.427605\pi\)
0.225481 + 0.974248i \(0.427605\pi\)
\(618\) 1.00000 0.0402259
\(619\) −32.1143 −1.29078 −0.645390 0.763853i \(-0.723305\pi\)
−0.645390 + 0.763853i \(0.723305\pi\)
\(620\) −13.5353 −0.543593
\(621\) −7.19107 −0.288568
\(622\) 15.4624 0.619986
\(623\) −10.5995 −0.424659
\(624\) −1.00000 −0.0400320
\(625\) −29.9224 −1.19690
\(626\) −26.0600 −1.04157
\(627\) 0.568751 0.0227137
\(628\) 6.17311 0.246334
\(629\) 2.28092 0.0909464
\(630\) −9.26214 −0.369012
\(631\) −0.248116 −0.00987734 −0.00493867 0.999988i \(-0.501572\pi\)
−0.00493867 + 0.999988i \(0.501572\pi\)
\(632\) 2.76399 0.109946
\(633\) −4.72118 −0.187650
\(634\) 14.1968 0.563828
\(635\) −23.5710 −0.935387
\(636\) −5.15156 −0.204272
\(637\) 2.91507 0.115499
\(638\) 1.38564 0.0548579
\(639\) −4.30422 −0.170272
\(640\) 2.94146 0.116272
\(641\) 9.62837 0.380298 0.190149 0.981755i \(-0.439103\pi\)
0.190149 + 0.981755i \(0.439103\pi\)
\(642\) 3.93656 0.155364
\(643\) 19.8045 0.781014 0.390507 0.920600i \(-0.372300\pi\)
0.390507 + 0.920600i \(0.372300\pi\)
\(644\) −22.6434 −0.892274
\(645\) −29.3215 −1.15453
\(646\) −11.4030 −0.448646
\(647\) −7.50452 −0.295033 −0.147517 0.989060i \(-0.547128\pi\)
−0.147517 + 0.989060i \(0.547128\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 1.42523 0.0559452
\(650\) −3.65220 −0.143251
\(651\) 14.4895 0.567889
\(652\) 19.0187 0.744829
\(653\) 6.80345 0.266239 0.133120 0.991100i \(-0.457501\pi\)
0.133120 + 0.991100i \(0.457501\pi\)
\(654\) 12.7707 0.499376
\(655\) −49.2456 −1.92418
\(656\) 4.33657 0.169315
\(657\) 1.09602 0.0427600
\(658\) 21.3275 0.831431
\(659\) −17.2877 −0.673433 −0.336717 0.941606i \(-0.609316\pi\)
−0.336717 + 0.941606i \(0.609316\pi\)
\(660\) 0.403237 0.0156960
\(661\) 46.3068 1.80112 0.900562 0.434727i \(-0.143155\pi\)
0.900562 + 0.434727i \(0.143155\pi\)
\(662\) −20.5911 −0.800298
\(663\) 2.74850 0.106743
\(664\) −8.49113 −0.329520
\(665\) −38.4269 −1.49013
\(666\) 0.829880 0.0321572
\(667\) −72.6851 −2.81438
\(668\) −14.1560 −0.547713
\(669\) 26.6098 1.02880
\(670\) 37.3930 1.44462
\(671\) −1.16248 −0.0448771
\(672\) −3.14882 −0.121468
\(673\) 17.3880 0.670257 0.335129 0.942172i \(-0.391220\pi\)
0.335129 + 0.942172i \(0.391220\pi\)
\(674\) 5.93953 0.228782
\(675\) −3.65220 −0.140573
\(676\) 1.00000 0.0384615
\(677\) 32.6958 1.25660 0.628300 0.777971i \(-0.283751\pi\)
0.628300 + 0.777971i \(0.283751\pi\)
\(678\) −5.01087 −0.192441
\(679\) 31.6568 1.21488
\(680\) −8.08460 −0.310030
\(681\) −0.507530 −0.0194486
\(682\) −0.630817 −0.0241552
\(683\) 30.8958 1.18219 0.591097 0.806601i \(-0.298695\pi\)
0.591097 + 0.806601i \(0.298695\pi\)
\(684\) −4.14882 −0.158634
\(685\) 18.2671 0.697950
\(686\) −12.8627 −0.491101
\(687\) 1.12067 0.0427560
\(688\) −9.96834 −0.380039
\(689\) 5.15156 0.196259
\(690\) −21.1523 −0.805253
\(691\) 4.36777 0.166158 0.0830789 0.996543i \(-0.473525\pi\)
0.0830789 + 0.996543i \(0.473525\pi\)
\(692\) −1.79096 −0.0680821
\(693\) −0.431663 −0.0163975
\(694\) −8.09109 −0.307134
\(695\) 12.4241 0.471271
\(696\) −10.1077 −0.383131
\(697\) −11.9191 −0.451467
\(698\) 14.5290 0.549930
\(699\) 3.05262 0.115461
\(700\) −11.5001 −0.434664
\(701\) 17.1484 0.647684 0.323842 0.946111i \(-0.395025\pi\)
0.323842 + 0.946111i \(0.395025\pi\)
\(702\) 1.00000 0.0377426
\(703\) 3.44302 0.129856
\(704\) 0.137087 0.00516667
\(705\) 19.9230 0.750344
\(706\) −8.63553 −0.325002
\(707\) −47.2804 −1.77816
\(708\) −10.3965 −0.390725
\(709\) −41.8599 −1.57208 −0.786040 0.618175i \(-0.787872\pi\)
−0.786040 + 0.618175i \(0.787872\pi\)
\(710\) −12.6607 −0.475148
\(711\) −2.76399 −0.103658
\(712\) −3.36617 −0.126153
\(713\) 33.0902 1.23924
\(714\) 8.65452 0.323887
\(715\) −0.403237 −0.0150802
\(716\) −16.8883 −0.631144
\(717\) −1.15111 −0.0429889
\(718\) 6.80238 0.253863
\(719\) −35.0705 −1.30791 −0.653955 0.756533i \(-0.726892\pi\)
−0.653955 + 0.756533i \(0.726892\pi\)
\(720\) −2.94146 −0.109622
\(721\) −3.14882 −0.117268
\(722\) 1.78729 0.0665161
\(723\) −1.40880 −0.0523939
\(724\) 22.9822 0.854129
\(725\) −36.9153 −1.37100
\(726\) −10.9812 −0.407551
\(727\) 38.5964 1.43146 0.715732 0.698376i \(-0.246093\pi\)
0.715732 + 0.698376i \(0.246093\pi\)
\(728\) 3.14882 0.116703
\(729\) 1.00000 0.0370370
\(730\) 3.22392 0.119322
\(731\) 27.3980 1.01335
\(732\) 8.47985 0.313424
\(733\) −44.4750 −1.64272 −0.821361 0.570409i \(-0.806785\pi\)
−0.821361 + 0.570409i \(0.806785\pi\)
\(734\) 28.3418 1.04611
\(735\) 8.57456 0.316278
\(736\) −7.19107 −0.265066
\(737\) 1.74271 0.0641934
\(738\) −4.33657 −0.159632
\(739\) 31.4615 1.15733 0.578664 0.815566i \(-0.303574\pi\)
0.578664 + 0.815566i \(0.303574\pi\)
\(740\) 2.44106 0.0897352
\(741\) 4.14882 0.152411
\(742\) 16.2213 0.595503
\(743\) 2.00052 0.0733919 0.0366959 0.999326i \(-0.488317\pi\)
0.0366959 + 0.999326i \(0.488317\pi\)
\(744\) 4.60157 0.168702
\(745\) −37.2630 −1.36521
\(746\) −0.827118 −0.0302829
\(747\) 8.49113 0.310674
\(748\) −0.376784 −0.0137766
\(749\) −12.3955 −0.452922
\(750\) 3.96450 0.144763
\(751\) −21.1577 −0.772055 −0.386027 0.922487i \(-0.626153\pi\)
−0.386027 + 0.922487i \(0.626153\pi\)
\(752\) 6.77316 0.246992
\(753\) 3.13575 0.114273
\(754\) 10.1077 0.368100
\(755\) 1.72221 0.0626777
\(756\) 3.14882 0.114521
\(757\) 1.41669 0.0514906 0.0257453 0.999669i \(-0.491804\pi\)
0.0257453 + 0.999669i \(0.491804\pi\)
\(758\) 4.67824 0.169921
\(759\) −0.985804 −0.0357824
\(760\) −12.2036 −0.442671
\(761\) −12.0808 −0.437929 −0.218964 0.975733i \(-0.570268\pi\)
−0.218964 + 0.975733i \(0.570268\pi\)
\(762\) 8.01336 0.290294
\(763\) −40.2128 −1.45580
\(764\) −1.01677 −0.0367856
\(765\) 8.08460 0.292299
\(766\) −34.0161 −1.22905
\(767\) 10.3965 0.375396
\(768\) −1.00000 −0.0360844
\(769\) −22.6133 −0.815458 −0.407729 0.913103i \(-0.633679\pi\)
−0.407729 + 0.913103i \(0.633679\pi\)
\(770\) −1.26972 −0.0457576
\(771\) −6.85244 −0.246784
\(772\) 4.27406 0.153827
\(773\) −17.5110 −0.629828 −0.314914 0.949120i \(-0.601976\pi\)
−0.314914 + 0.949120i \(0.601976\pi\)
\(774\) 9.96834 0.358305
\(775\) 16.8059 0.603684
\(776\) 10.0536 0.360902
\(777\) −2.61314 −0.0937460
\(778\) 17.2938 0.620011
\(779\) −17.9917 −0.644618
\(780\) 2.94146 0.105321
\(781\) −0.590055 −0.0211138
\(782\) 19.7646 0.706782
\(783\) 10.1077 0.361219
\(784\) 2.91507 0.104110
\(785\) −18.1580 −0.648086
\(786\) 16.7419 0.597163
\(787\) −5.13840 −0.183164 −0.0915821 0.995798i \(-0.529192\pi\)
−0.0915821 + 0.995798i \(0.529192\pi\)
\(788\) 22.0133 0.784190
\(789\) 18.0045 0.640976
\(790\) −8.13016 −0.289258
\(791\) 15.7783 0.561013
\(792\) −0.137087 −0.00487119
\(793\) −8.47985 −0.301128
\(794\) 11.9604 0.424459
\(795\) 15.1531 0.537425
\(796\) −24.9686 −0.884987
\(797\) 49.0785 1.73845 0.869225 0.494417i \(-0.164618\pi\)
0.869225 + 0.494417i \(0.164618\pi\)
\(798\) 13.0639 0.462457
\(799\) −18.6160 −0.658587
\(800\) −3.65220 −0.129125
\(801\) 3.36617 0.118938
\(802\) 3.41345 0.120533
\(803\) 0.150251 0.00530225
\(804\) −12.7124 −0.448331
\(805\) 66.6046 2.34751
\(806\) −4.60157 −0.162083
\(807\) 13.9664 0.491642
\(808\) −15.0153 −0.528236
\(809\) −25.8699 −0.909537 −0.454769 0.890610i \(-0.650278\pi\)
−0.454769 + 0.890610i \(0.650278\pi\)
\(810\) 2.94146 0.103352
\(811\) 24.3422 0.854771 0.427385 0.904070i \(-0.359435\pi\)
0.427385 + 0.904070i \(0.359435\pi\)
\(812\) 31.8273 1.11692
\(813\) 17.6408 0.618689
\(814\) 0.113766 0.00398750
\(815\) −55.9428 −1.95959
\(816\) 2.74850 0.0962167
\(817\) 41.3569 1.44689
\(818\) 24.8064 0.867334
\(819\) −3.14882 −0.110029
\(820\) −12.7559 −0.445454
\(821\) −35.0414 −1.22295 −0.611477 0.791262i \(-0.709424\pi\)
−0.611477 + 0.791262i \(0.709424\pi\)
\(822\) −6.21021 −0.216606
\(823\) 7.32602 0.255369 0.127685 0.991815i \(-0.459245\pi\)
0.127685 + 0.991815i \(0.459245\pi\)
\(824\) −1.00000 −0.0348367
\(825\) −0.500670 −0.0174311
\(826\) 32.7367 1.13906
\(827\) −13.6740 −0.475493 −0.237746 0.971327i \(-0.576409\pi\)
−0.237746 + 0.971327i \(0.576409\pi\)
\(828\) 7.19107 0.249907
\(829\) 0.164027 0.00569690 0.00284845 0.999996i \(-0.499093\pi\)
0.00284845 + 0.999996i \(0.499093\pi\)
\(830\) 24.9763 0.866941
\(831\) −2.39614 −0.0831210
\(832\) 1.00000 0.0346688
\(833\) −8.01206 −0.277601
\(834\) −4.22377 −0.146257
\(835\) 41.6394 1.44099
\(836\) −0.568751 −0.0196707
\(837\) −4.60157 −0.159054
\(838\) −6.00013 −0.207271
\(839\) −38.6390 −1.33397 −0.666983 0.745073i \(-0.732415\pi\)
−0.666983 + 0.745073i \(0.732415\pi\)
\(840\) 9.26214 0.319574
\(841\) 73.1654 2.52294
\(842\) 1.38513 0.0477346
\(843\) 2.16737 0.0746481
\(844\) 4.72118 0.162510
\(845\) −2.94146 −0.101189
\(846\) −6.77316 −0.232866
\(847\) 34.5778 1.18811
\(848\) 5.15156 0.176905
\(849\) 6.62007 0.227200
\(850\) 10.0381 0.344303
\(851\) −5.96773 −0.204571
\(852\) 4.30422 0.147460
\(853\) −45.2760 −1.55022 −0.775110 0.631827i \(-0.782305\pi\)
−0.775110 + 0.631827i \(0.782305\pi\)
\(854\) −26.7015 −0.913708
\(855\) 12.2036 0.417354
\(856\) −3.93656 −0.134549
\(857\) 8.54449 0.291874 0.145937 0.989294i \(-0.453380\pi\)
0.145937 + 0.989294i \(0.453380\pi\)
\(858\) 0.137087 0.00468008
\(859\) −51.2047 −1.74708 −0.873540 0.486752i \(-0.838182\pi\)
−0.873540 + 0.486752i \(0.838182\pi\)
\(860\) 29.3215 0.999855
\(861\) 13.6551 0.465364
\(862\) 23.5209 0.801126
\(863\) 11.8317 0.402755 0.201378 0.979514i \(-0.435458\pi\)
0.201378 + 0.979514i \(0.435458\pi\)
\(864\) 1.00000 0.0340207
\(865\) 5.26804 0.179119
\(866\) 13.5308 0.459796
\(867\) 9.44576 0.320795
\(868\) −14.4895 −0.491806
\(869\) −0.378908 −0.0128536
\(870\) 29.7314 1.00799
\(871\) 12.7124 0.430742
\(872\) −12.7707 −0.432472
\(873\) −10.0536 −0.340261
\(874\) 29.8344 1.00917
\(875\) −12.4835 −0.422019
\(876\) −1.09602 −0.0370312
\(877\) −9.41928 −0.318067 −0.159033 0.987273i \(-0.550838\pi\)
−0.159033 + 0.987273i \(0.550838\pi\)
\(878\) 29.4705 0.994582
\(879\) −17.4690 −0.589215
\(880\) −0.403237 −0.0135931
\(881\) −44.7004 −1.50600 −0.752998 0.658023i \(-0.771393\pi\)
−0.752998 + 0.658023i \(0.771393\pi\)
\(882\) −2.91507 −0.0981555
\(883\) 38.4515 1.29400 0.646998 0.762492i \(-0.276024\pi\)
0.646998 + 0.762492i \(0.276024\pi\)
\(884\) −2.74850 −0.0924420
\(885\) 30.5809 1.02797
\(886\) 38.0382 1.27792
\(887\) −18.0261 −0.605259 −0.302629 0.953108i \(-0.597864\pi\)
−0.302629 + 0.953108i \(0.597864\pi\)
\(888\) −0.829880 −0.0278490
\(889\) −25.2326 −0.846276
\(890\) 9.90147 0.331898
\(891\) 0.137087 0.00459260
\(892\) −26.6098 −0.890963
\(893\) −28.1006 −0.940352
\(894\) 12.6682 0.423687
\(895\) 49.6762 1.66049
\(896\) 3.14882 0.105195
\(897\) −7.19107 −0.240103
\(898\) −21.2124 −0.707867
\(899\) −46.5112 −1.55124
\(900\) 3.65220 0.121740
\(901\) −14.1590 −0.471706
\(902\) −0.594489 −0.0197943
\(903\) −31.3885 −1.04454
\(904\) 5.01087 0.166659
\(905\) −67.6014 −2.24715
\(906\) −0.585495 −0.0194518
\(907\) 23.7118 0.787338 0.393669 0.919252i \(-0.371206\pi\)
0.393669 + 0.919252i \(0.371206\pi\)
\(908\) 0.507530 0.0168430
\(909\) 15.0153 0.498025
\(910\) −9.26214 −0.307037
\(911\) 45.2061 1.49774 0.748872 0.662714i \(-0.230596\pi\)
0.748872 + 0.662714i \(0.230596\pi\)
\(912\) 4.14882 0.137381
\(913\) 1.16403 0.0385236
\(914\) −28.9591 −0.957881
\(915\) −24.9432 −0.824596
\(916\) −1.12067 −0.0370278
\(917\) −52.7171 −1.74087
\(918\) −2.74850 −0.0907139
\(919\) −30.0324 −0.990677 −0.495339 0.868700i \(-0.664956\pi\)
−0.495339 + 0.868700i \(0.664956\pi\)
\(920\) 21.1523 0.697369
\(921\) 21.1127 0.695687
\(922\) 15.5870 0.513331
\(923\) −4.30422 −0.141675
\(924\) 0.431663 0.0142007
\(925\) −3.03089 −0.0996550
\(926\) 15.6494 0.514272
\(927\) 1.00000 0.0328443
\(928\) 10.1077 0.331801
\(929\) 3.27154 0.107336 0.0536678 0.998559i \(-0.482909\pi\)
0.0536678 + 0.998559i \(0.482909\pi\)
\(930\) −13.5353 −0.443842
\(931\) −12.0941 −0.396368
\(932\) −3.05262 −0.0999920
\(933\) 15.4624 0.506217
\(934\) −28.3998 −0.929270
\(935\) 1.10830 0.0362452
\(936\) −1.00000 −0.0326860
\(937\) −13.6534 −0.446036 −0.223018 0.974814i \(-0.571591\pi\)
−0.223018 + 0.974814i \(0.571591\pi\)
\(938\) 40.0290 1.30699
\(939\) −26.0600 −0.850436
\(940\) −19.9230 −0.649817
\(941\) −7.40560 −0.241416 −0.120708 0.992688i \(-0.538516\pi\)
−0.120708 + 0.992688i \(0.538516\pi\)
\(942\) 6.17311 0.201131
\(943\) 31.1846 1.01551
\(944\) 10.3965 0.338378
\(945\) −9.26214 −0.301297
\(946\) 1.36653 0.0444298
\(947\) 29.3314 0.953143 0.476572 0.879136i \(-0.341879\pi\)
0.476572 + 0.879136i \(0.341879\pi\)
\(948\) 2.76399 0.0897701
\(949\) 1.09602 0.0355785
\(950\) 15.1523 0.491606
\(951\) 14.1968 0.460364
\(952\) −8.65452 −0.280495
\(953\) −24.9809 −0.809209 −0.404605 0.914492i \(-0.632591\pi\)
−0.404605 + 0.914492i \(0.632591\pi\)
\(954\) −5.15156 −0.166788
\(955\) 2.99080 0.0967801
\(956\) 1.15111 0.0372294
\(957\) 1.38564 0.0447913
\(958\) −33.2339 −1.07374
\(959\) 19.5548 0.631459
\(960\) 2.94146 0.0949353
\(961\) −9.82555 −0.316953
\(962\) 0.829880 0.0267564
\(963\) 3.93656 0.126854
\(964\) 1.40880 0.0453745
\(965\) −12.5720 −0.404706
\(966\) −22.6434 −0.728539
\(967\) −21.5596 −0.693308 −0.346654 0.937993i \(-0.612682\pi\)
−0.346654 + 0.937993i \(0.612682\pi\)
\(968\) 10.9812 0.352949
\(969\) −11.4030 −0.366318
\(970\) −29.5722 −0.949505
\(971\) −5.37257 −0.172414 −0.0862070 0.996277i \(-0.527475\pi\)
−0.0862070 + 0.996277i \(0.527475\pi\)
\(972\) −1.00000 −0.0320750
\(973\) 13.2999 0.426375
\(974\) 34.4329 1.10330
\(975\) −3.65220 −0.116964
\(976\) −8.47985 −0.271433
\(977\) −10.9763 −0.351162 −0.175581 0.984465i \(-0.556180\pi\)
−0.175581 + 0.984465i \(0.556180\pi\)
\(978\) 19.0187 0.608151
\(979\) 0.461460 0.0147483
\(980\) −8.57456 −0.273904
\(981\) 12.7707 0.407739
\(982\) −27.1694 −0.867012
\(983\) 32.6451 1.04122 0.520609 0.853795i \(-0.325705\pi\)
0.520609 + 0.853795i \(0.325705\pi\)
\(984\) 4.33657 0.138245
\(985\) −64.7512 −2.06314
\(986\) −27.7810 −0.884726
\(987\) 21.3275 0.678861
\(988\) −4.14882 −0.131992
\(989\) −71.6830 −2.27939
\(990\) 0.403237 0.0128157
\(991\) −47.8870 −1.52118 −0.760590 0.649233i \(-0.775090\pi\)
−0.760590 + 0.649233i \(0.775090\pi\)
\(992\) −4.60157 −0.146100
\(993\) −20.5911 −0.653440
\(994\) −13.5532 −0.429882
\(995\) 73.4441 2.32833
\(996\) −8.49113 −0.269052
\(997\) 23.8769 0.756190 0.378095 0.925767i \(-0.376579\pi\)
0.378095 + 0.925767i \(0.376579\pi\)
\(998\) 18.9505 0.599869
\(999\) 0.829880 0.0262562
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 \(a_p\))