Properties

Label 8015.2.a.l.1.46
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.46
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.52977 q^{2} +0.0640431 q^{3} +0.340181 q^{4} -1.00000 q^{5} +0.0979709 q^{6} -1.00000 q^{7} -2.53913 q^{8} -2.99590 q^{9} +O(q^{10})\) \(q+1.52977 q^{2} +0.0640431 q^{3} +0.340181 q^{4} -1.00000 q^{5} +0.0979709 q^{6} -1.00000 q^{7} -2.53913 q^{8} -2.99590 q^{9} -1.52977 q^{10} -6.33328 q^{11} +0.0217863 q^{12} -2.98935 q^{13} -1.52977 q^{14} -0.0640431 q^{15} -4.56464 q^{16} -3.87195 q^{17} -4.58302 q^{18} +0.248126 q^{19} -0.340181 q^{20} -0.0640431 q^{21} -9.68843 q^{22} +4.03259 q^{23} -0.162614 q^{24} +1.00000 q^{25} -4.57300 q^{26} -0.383996 q^{27} -0.340181 q^{28} -2.72647 q^{29} -0.0979709 q^{30} +6.29609 q^{31} -1.90456 q^{32} -0.405603 q^{33} -5.92318 q^{34} +1.00000 q^{35} -1.01915 q^{36} -1.45340 q^{37} +0.379574 q^{38} -0.191447 q^{39} +2.53913 q^{40} -6.94726 q^{41} -0.0979709 q^{42} +3.71626 q^{43} -2.15446 q^{44} +2.99590 q^{45} +6.16892 q^{46} +0.165459 q^{47} -0.292334 q^{48} +1.00000 q^{49} +1.52977 q^{50} -0.247972 q^{51} -1.01692 q^{52} -3.32221 q^{53} -0.587424 q^{54} +6.33328 q^{55} +2.53913 q^{56} +0.0158907 q^{57} -4.17086 q^{58} -10.7987 q^{59} -0.0217863 q^{60} +2.79025 q^{61} +9.63154 q^{62} +2.99590 q^{63} +6.21575 q^{64} +2.98935 q^{65} -0.620477 q^{66} -5.18520 q^{67} -1.31717 q^{68} +0.258260 q^{69} +1.52977 q^{70} -6.62897 q^{71} +7.60698 q^{72} +8.86780 q^{73} -2.22336 q^{74} +0.0640431 q^{75} +0.0844077 q^{76} +6.33328 q^{77} -0.292869 q^{78} +15.8461 q^{79} +4.56464 q^{80} +8.96310 q^{81} -10.6277 q^{82} -13.7034 q^{83} -0.0217863 q^{84} +3.87195 q^{85} +5.68501 q^{86} -0.174612 q^{87} +16.0810 q^{88} +4.87365 q^{89} +4.58302 q^{90} +2.98935 q^{91} +1.37181 q^{92} +0.403221 q^{93} +0.253113 q^{94} -0.248126 q^{95} -0.121974 q^{96} +2.59750 q^{97} +1.52977 q^{98} +18.9739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.52977 1.08171 0.540854 0.841117i \(-0.318101\pi\)
0.540854 + 0.841117i \(0.318101\pi\)
\(3\) 0.0640431 0.0369753 0.0184877 0.999829i \(-0.494115\pi\)
0.0184877 + 0.999829i \(0.494115\pi\)
\(4\) 0.340181 0.170091
\(5\) −1.00000 −0.447214
\(6\) 0.0979709 0.0399965
\(7\) −1.00000 −0.377964
\(8\) −2.53913 −0.897719
\(9\) −2.99590 −0.998633
\(10\) −1.52977 −0.483754
\(11\) −6.33328 −1.90956 −0.954778 0.297319i \(-0.903907\pi\)
−0.954778 + 0.297319i \(0.903907\pi\)
\(12\) 0.0217863 0.00628916
\(13\) −2.98935 −0.829095 −0.414548 0.910028i \(-0.636060\pi\)
−0.414548 + 0.910028i \(0.636060\pi\)
\(14\) −1.52977 −0.408847
\(15\) −0.0640431 −0.0165359
\(16\) −4.56464 −1.14116
\(17\) −3.87195 −0.939086 −0.469543 0.882910i \(-0.655581\pi\)
−0.469543 + 0.882910i \(0.655581\pi\)
\(18\) −4.58302 −1.08023
\(19\) 0.248126 0.0569239 0.0284620 0.999595i \(-0.490939\pi\)
0.0284620 + 0.999595i \(0.490939\pi\)
\(20\) −0.340181 −0.0760669
\(21\) −0.0640431 −0.0139754
\(22\) −9.68843 −2.06558
\(23\) 4.03259 0.840853 0.420427 0.907327i \(-0.361880\pi\)
0.420427 + 0.907327i \(0.361880\pi\)
\(24\) −0.162614 −0.0331934
\(25\) 1.00000 0.200000
\(26\) −4.57300 −0.896839
\(27\) −0.383996 −0.0739001
\(28\) −0.340181 −0.0642882
\(29\) −2.72647 −0.506293 −0.253147 0.967428i \(-0.581466\pi\)
−0.253147 + 0.967428i \(0.581466\pi\)
\(30\) −0.0979709 −0.0178870
\(31\) 6.29609 1.13081 0.565405 0.824813i \(-0.308720\pi\)
0.565405 + 0.824813i \(0.308720\pi\)
\(32\) −1.90456 −0.336682
\(33\) −0.405603 −0.0706064
\(34\) −5.92318 −1.01582
\(35\) 1.00000 0.169031
\(36\) −1.01915 −0.169858
\(37\) −1.45340 −0.238938 −0.119469 0.992838i \(-0.538119\pi\)
−0.119469 + 0.992838i \(0.538119\pi\)
\(38\) 0.379574 0.0615750
\(39\) −0.191447 −0.0306561
\(40\) 2.53913 0.401472
\(41\) −6.94726 −1.08498 −0.542490 0.840063i \(-0.682518\pi\)
−0.542490 + 0.840063i \(0.682518\pi\)
\(42\) −0.0979709 −0.0151172
\(43\) 3.71626 0.566725 0.283362 0.959013i \(-0.408550\pi\)
0.283362 + 0.959013i \(0.408550\pi\)
\(44\) −2.15446 −0.324798
\(45\) 2.99590 0.446602
\(46\) 6.16892 0.909557
\(47\) 0.165459 0.0241346 0.0120673 0.999927i \(-0.496159\pi\)
0.0120673 + 0.999927i \(0.496159\pi\)
\(48\) −0.292334 −0.0421947
\(49\) 1.00000 0.142857
\(50\) 1.52977 0.216341
\(51\) −0.247972 −0.0347230
\(52\) −1.01692 −0.141021
\(53\) −3.32221 −0.456341 −0.228171 0.973621i \(-0.573274\pi\)
−0.228171 + 0.973621i \(0.573274\pi\)
\(54\) −0.587424 −0.0799382
\(55\) 6.33328 0.853980
\(56\) 2.53913 0.339306
\(57\) 0.0158907 0.00210478
\(58\) −4.17086 −0.547661
\(59\) −10.7987 −1.40587 −0.702937 0.711252i \(-0.748128\pi\)
−0.702937 + 0.711252i \(0.748128\pi\)
\(60\) −0.0217863 −0.00281260
\(61\) 2.79025 0.357255 0.178628 0.983917i \(-0.442834\pi\)
0.178628 + 0.983917i \(0.442834\pi\)
\(62\) 9.63154 1.22321
\(63\) 2.99590 0.377448
\(64\) 6.21575 0.776969
\(65\) 2.98935 0.370783
\(66\) −0.620477 −0.0763755
\(67\) −5.18520 −0.633473 −0.316736 0.948514i \(-0.602587\pi\)
−0.316736 + 0.948514i \(0.602587\pi\)
\(68\) −1.31717 −0.159730
\(69\) 0.258260 0.0310908
\(70\) 1.52977 0.182842
\(71\) −6.62897 −0.786714 −0.393357 0.919386i \(-0.628686\pi\)
−0.393357 + 0.919386i \(0.628686\pi\)
\(72\) 7.60698 0.896492
\(73\) 8.86780 1.03790 0.518949 0.854805i \(-0.326324\pi\)
0.518949 + 0.854805i \(0.326324\pi\)
\(74\) −2.22336 −0.258461
\(75\) 0.0640431 0.00739506
\(76\) 0.0844077 0.00968223
\(77\) 6.33328 0.721744
\(78\) −0.292869 −0.0331609
\(79\) 15.8461 1.78282 0.891411 0.453197i \(-0.149716\pi\)
0.891411 + 0.453197i \(0.149716\pi\)
\(80\) 4.56464 0.510342
\(81\) 8.96310 0.995900
\(82\) −10.6277 −1.17363
\(83\) −13.7034 −1.50414 −0.752070 0.659083i \(-0.770945\pi\)
−0.752070 + 0.659083i \(0.770945\pi\)
\(84\) −0.0217863 −0.00237708
\(85\) 3.87195 0.419972
\(86\) 5.68501 0.613030
\(87\) −0.174612 −0.0187204
\(88\) 16.0810 1.71424
\(89\) 4.87365 0.516606 0.258303 0.966064i \(-0.416837\pi\)
0.258303 + 0.966064i \(0.416837\pi\)
\(90\) 4.58302 0.483093
\(91\) 2.98935 0.313369
\(92\) 1.37181 0.143021
\(93\) 0.403221 0.0418121
\(94\) 0.253113 0.0261066
\(95\) −0.248126 −0.0254572
\(96\) −0.121974 −0.0124489
\(97\) 2.59750 0.263736 0.131868 0.991267i \(-0.457903\pi\)
0.131868 + 0.991267i \(0.457903\pi\)
\(98\) 1.52977 0.154530
\(99\) 18.9739 1.90695
\(100\) 0.340181 0.0340181
\(101\) −15.2588 −1.51831 −0.759153 0.650912i \(-0.774387\pi\)
−0.759153 + 0.650912i \(0.774387\pi\)
\(102\) −0.379339 −0.0375601
\(103\) −3.84827 −0.379181 −0.189591 0.981863i \(-0.560716\pi\)
−0.189591 + 0.981863i \(0.560716\pi\)
\(104\) 7.59035 0.744295
\(105\) 0.0640431 0.00624997
\(106\) −5.08221 −0.493627
\(107\) 0.128746 0.0124463 0.00622317 0.999981i \(-0.498019\pi\)
0.00622317 + 0.999981i \(0.498019\pi\)
\(108\) −0.130628 −0.0125697
\(109\) 4.66644 0.446964 0.223482 0.974708i \(-0.428258\pi\)
0.223482 + 0.974708i \(0.428258\pi\)
\(110\) 9.68843 0.923756
\(111\) −0.0930804 −0.00883480
\(112\) 4.56464 0.431318
\(113\) 1.34578 0.126600 0.0633002 0.997995i \(-0.479837\pi\)
0.0633002 + 0.997995i \(0.479837\pi\)
\(114\) 0.0243091 0.00227676
\(115\) −4.03259 −0.376041
\(116\) −0.927495 −0.0861158
\(117\) 8.95578 0.827962
\(118\) −16.5195 −1.52074
\(119\) 3.87195 0.354941
\(120\) 0.162614 0.0148446
\(121\) 29.1105 2.64641
\(122\) 4.26843 0.386446
\(123\) −0.444924 −0.0401174
\(124\) 2.14181 0.192340
\(125\) −1.00000 −0.0894427
\(126\) 4.58302 0.408288
\(127\) −2.40677 −0.213566 −0.106783 0.994282i \(-0.534055\pi\)
−0.106783 + 0.994282i \(0.534055\pi\)
\(128\) 13.3178 1.17713
\(129\) 0.238001 0.0209548
\(130\) 4.57300 0.401078
\(131\) 1.25416 0.109576 0.0547881 0.998498i \(-0.482552\pi\)
0.0547881 + 0.998498i \(0.482552\pi\)
\(132\) −0.137979 −0.0120095
\(133\) −0.248126 −0.0215152
\(134\) −7.93213 −0.685232
\(135\) 0.383996 0.0330491
\(136\) 9.83140 0.843035
\(137\) 0.743203 0.0634961 0.0317481 0.999496i \(-0.489893\pi\)
0.0317481 + 0.999496i \(0.489893\pi\)
\(138\) 0.395077 0.0336311
\(139\) 10.7094 0.908358 0.454179 0.890910i \(-0.349933\pi\)
0.454179 + 0.890910i \(0.349933\pi\)
\(140\) 0.340181 0.0287506
\(141\) 0.0105965 0.000892385 0
\(142\) −10.1408 −0.850994
\(143\) 18.9324 1.58320
\(144\) 13.6752 1.13960
\(145\) 2.72647 0.226421
\(146\) 13.5657 1.12270
\(147\) 0.0640431 0.00528219
\(148\) −0.494420 −0.0406411
\(149\) −19.5430 −1.60103 −0.800513 0.599315i \(-0.795440\pi\)
−0.800513 + 0.599315i \(0.795440\pi\)
\(150\) 0.0979709 0.00799929
\(151\) 10.4567 0.850955 0.425478 0.904969i \(-0.360106\pi\)
0.425478 + 0.904969i \(0.360106\pi\)
\(152\) −0.630024 −0.0511017
\(153\) 11.6000 0.937802
\(154\) 9.68843 0.780716
\(155\) −6.29609 −0.505714
\(156\) −0.0651267 −0.00521431
\(157\) −2.10666 −0.168130 −0.0840648 0.996460i \(-0.526790\pi\)
−0.0840648 + 0.996460i \(0.526790\pi\)
\(158\) 24.2408 1.92849
\(159\) −0.212765 −0.0168734
\(160\) 1.90456 0.150569
\(161\) −4.03259 −0.317813
\(162\) 13.7114 1.07727
\(163\) 3.71513 0.290991 0.145496 0.989359i \(-0.453522\pi\)
0.145496 + 0.989359i \(0.453522\pi\)
\(164\) −2.36333 −0.184545
\(165\) 0.405603 0.0315762
\(166\) −20.9629 −1.62704
\(167\) 17.5534 1.35832 0.679162 0.733988i \(-0.262343\pi\)
0.679162 + 0.733988i \(0.262343\pi\)
\(168\) 0.162614 0.0125459
\(169\) −4.06381 −0.312601
\(170\) 5.92318 0.454287
\(171\) −0.743359 −0.0568461
\(172\) 1.26420 0.0963946
\(173\) −18.7357 −1.42445 −0.712226 0.701950i \(-0.752313\pi\)
−0.712226 + 0.701950i \(0.752313\pi\)
\(174\) −0.267115 −0.0202499
\(175\) −1.00000 −0.0755929
\(176\) 28.9091 2.17911
\(177\) −0.691584 −0.0519826
\(178\) 7.45554 0.558816
\(179\) −25.0619 −1.87321 −0.936606 0.350384i \(-0.886051\pi\)
−0.936606 + 0.350384i \(0.886051\pi\)
\(180\) 1.01915 0.0759629
\(181\) −6.58458 −0.489428 −0.244714 0.969595i \(-0.578694\pi\)
−0.244714 + 0.969595i \(0.578694\pi\)
\(182\) 4.57300 0.338973
\(183\) 0.178697 0.0132096
\(184\) −10.2393 −0.754850
\(185\) 1.45340 0.106856
\(186\) 0.616834 0.0452284
\(187\) 24.5222 1.79324
\(188\) 0.0562860 0.00410508
\(189\) 0.383996 0.0279316
\(190\) −0.379574 −0.0275372
\(191\) 25.9927 1.88077 0.940383 0.340117i \(-0.110467\pi\)
0.940383 + 0.340117i \(0.110467\pi\)
\(192\) 0.398076 0.0287287
\(193\) −11.0098 −0.792502 −0.396251 0.918142i \(-0.629689\pi\)
−0.396251 + 0.918142i \(0.629689\pi\)
\(194\) 3.97356 0.285285
\(195\) 0.191447 0.0137098
\(196\) 0.340181 0.0242987
\(197\) 21.1177 1.50458 0.752288 0.658835i \(-0.228950\pi\)
0.752288 + 0.658835i \(0.228950\pi\)
\(198\) 29.0256 2.06276
\(199\) −0.983055 −0.0696869 −0.0348434 0.999393i \(-0.511093\pi\)
−0.0348434 + 0.999393i \(0.511093\pi\)
\(200\) −2.53913 −0.179544
\(201\) −0.332076 −0.0234228
\(202\) −23.3424 −1.64236
\(203\) 2.72647 0.191361
\(204\) −0.0843554 −0.00590606
\(205\) 6.94726 0.485217
\(206\) −5.88695 −0.410163
\(207\) −12.0812 −0.839704
\(208\) 13.6453 0.946130
\(209\) −1.57145 −0.108699
\(210\) 0.0979709 0.00676064
\(211\) −13.7715 −0.948068 −0.474034 0.880507i \(-0.657203\pi\)
−0.474034 + 0.880507i \(0.657203\pi\)
\(212\) −1.13015 −0.0776194
\(213\) −0.424540 −0.0290890
\(214\) 0.196951 0.0134633
\(215\) −3.71626 −0.253447
\(216\) 0.975017 0.0663415
\(217\) −6.29609 −0.427406
\(218\) 7.13856 0.483485
\(219\) 0.567922 0.0383766
\(220\) 2.15446 0.145254
\(221\) 11.5746 0.778592
\(222\) −0.142391 −0.00955667
\(223\) −15.1545 −1.01482 −0.507411 0.861704i \(-0.669397\pi\)
−0.507411 + 0.861704i \(0.669397\pi\)
\(224\) 1.90456 0.127254
\(225\) −2.99590 −0.199727
\(226\) 2.05873 0.136945
\(227\) 11.8269 0.784978 0.392489 0.919757i \(-0.371614\pi\)
0.392489 + 0.919757i \(0.371614\pi\)
\(228\) 0.00540573 0.000358004 0
\(229\) 1.00000 0.0660819
\(230\) −6.16892 −0.406766
\(231\) 0.405603 0.0266867
\(232\) 6.92288 0.454509
\(233\) −26.1105 −1.71055 −0.855277 0.518170i \(-0.826613\pi\)
−0.855277 + 0.518170i \(0.826613\pi\)
\(234\) 13.7002 0.895612
\(235\) −0.165459 −0.0107933
\(236\) −3.67352 −0.239126
\(237\) 1.01483 0.0659204
\(238\) 5.92318 0.383942
\(239\) −8.58088 −0.555051 −0.277526 0.960718i \(-0.589514\pi\)
−0.277526 + 0.960718i \(0.589514\pi\)
\(240\) 0.292334 0.0188701
\(241\) 7.57526 0.487966 0.243983 0.969780i \(-0.421546\pi\)
0.243983 + 0.969780i \(0.421546\pi\)
\(242\) 44.5322 2.86264
\(243\) 1.72601 0.110724
\(244\) 0.949192 0.0607658
\(245\) −1.00000 −0.0638877
\(246\) −0.680629 −0.0433953
\(247\) −0.741734 −0.0471954
\(248\) −15.9866 −1.01515
\(249\) −0.877607 −0.0556161
\(250\) −1.52977 −0.0967508
\(251\) 0.889480 0.0561435 0.0280717 0.999606i \(-0.491063\pi\)
0.0280717 + 0.999606i \(0.491063\pi\)
\(252\) 1.01915 0.0642003
\(253\) −25.5395 −1.60566
\(254\) −3.68179 −0.231016
\(255\) 0.247972 0.0155286
\(256\) 7.94154 0.496346
\(257\) −8.95767 −0.558764 −0.279382 0.960180i \(-0.590130\pi\)
−0.279382 + 0.960180i \(0.590130\pi\)
\(258\) 0.364086 0.0226670
\(259\) 1.45340 0.0903100
\(260\) 1.01692 0.0630667
\(261\) 8.16824 0.505601
\(262\) 1.91856 0.118529
\(263\) −9.02758 −0.556664 −0.278332 0.960485i \(-0.589782\pi\)
−0.278332 + 0.960485i \(0.589782\pi\)
\(264\) 1.02988 0.0633847
\(265\) 3.32221 0.204082
\(266\) −0.379574 −0.0232732
\(267\) 0.312124 0.0191017
\(268\) −1.76391 −0.107748
\(269\) −3.20915 −0.195665 −0.0978325 0.995203i \(-0.531191\pi\)
−0.0978325 + 0.995203i \(0.531191\pi\)
\(270\) 0.587424 0.0357495
\(271\) 15.0040 0.911431 0.455715 0.890126i \(-0.349384\pi\)
0.455715 + 0.890126i \(0.349384\pi\)
\(272\) 17.6741 1.07165
\(273\) 0.191447 0.0115869
\(274\) 1.13693 0.0686842
\(275\) −6.33328 −0.381911
\(276\) 0.0878551 0.00528826
\(277\) 2.50666 0.150611 0.0753053 0.997161i \(-0.476007\pi\)
0.0753053 + 0.997161i \(0.476007\pi\)
\(278\) 16.3828 0.982577
\(279\) −18.8624 −1.12926
\(280\) −2.53913 −0.151742
\(281\) −8.57990 −0.511834 −0.255917 0.966699i \(-0.582377\pi\)
−0.255917 + 0.966699i \(0.582377\pi\)
\(282\) 0.0162101 0.000965300 0
\(283\) 25.9387 1.54190 0.770949 0.636897i \(-0.219782\pi\)
0.770949 + 0.636897i \(0.219782\pi\)
\(284\) −2.25505 −0.133813
\(285\) −0.0158907 −0.000941286 0
\(286\) 28.9621 1.71256
\(287\) 6.94726 0.410084
\(288\) 5.70587 0.336222
\(289\) −2.00799 −0.118117
\(290\) 4.17086 0.244922
\(291\) 0.166352 0.00975172
\(292\) 3.01666 0.176537
\(293\) 0.0470215 0.00274702 0.00137351 0.999999i \(-0.499563\pi\)
0.00137351 + 0.999999i \(0.499563\pi\)
\(294\) 0.0979709 0.00571378
\(295\) 10.7987 0.628726
\(296\) 3.69038 0.214499
\(297\) 2.43196 0.141116
\(298\) −29.8962 −1.73184
\(299\) −12.0548 −0.697147
\(300\) 0.0217863 0.00125783
\(301\) −3.71626 −0.214202
\(302\) 15.9963 0.920484
\(303\) −0.977220 −0.0561398
\(304\) −1.13260 −0.0649593
\(305\) −2.79025 −0.159769
\(306\) 17.7452 1.01443
\(307\) −28.3458 −1.61778 −0.808891 0.587958i \(-0.799932\pi\)
−0.808891 + 0.587958i \(0.799932\pi\)
\(308\) 2.15446 0.122762
\(309\) −0.246455 −0.0140203
\(310\) −9.63154 −0.547034
\(311\) 29.4770 1.67149 0.835743 0.549120i \(-0.185037\pi\)
0.835743 + 0.549120i \(0.185037\pi\)
\(312\) 0.486109 0.0275205
\(313\) −19.3373 −1.09301 −0.546503 0.837457i \(-0.684041\pi\)
−0.546503 + 0.837457i \(0.684041\pi\)
\(314\) −3.22269 −0.181867
\(315\) −2.99590 −0.168800
\(316\) 5.39053 0.303241
\(317\) −14.1393 −0.794141 −0.397071 0.917788i \(-0.629973\pi\)
−0.397071 + 0.917788i \(0.629973\pi\)
\(318\) −0.325480 −0.0182520
\(319\) 17.2675 0.966796
\(320\) −6.21575 −0.347471
\(321\) 0.00824529 0.000460207 0
\(322\) −6.16892 −0.343780
\(323\) −0.960731 −0.0534565
\(324\) 3.04908 0.169393
\(325\) −2.98935 −0.165819
\(326\) 5.68328 0.314768
\(327\) 0.298854 0.0165266
\(328\) 17.6400 0.974006
\(329\) −0.165459 −0.00912203
\(330\) 0.620477 0.0341562
\(331\) 5.63435 0.309692 0.154846 0.987939i \(-0.450512\pi\)
0.154846 + 0.987939i \(0.450512\pi\)
\(332\) −4.66163 −0.255840
\(333\) 4.35424 0.238611
\(334\) 26.8526 1.46931
\(335\) 5.18520 0.283298
\(336\) 0.292334 0.0159481
\(337\) 8.30947 0.452646 0.226323 0.974052i \(-0.427330\pi\)
0.226323 + 0.974052i \(0.427330\pi\)
\(338\) −6.21667 −0.338143
\(339\) 0.0861880 0.00468109
\(340\) 1.31717 0.0714333
\(341\) −39.8749 −2.15935
\(342\) −1.13717 −0.0614909
\(343\) −1.00000 −0.0539949
\(344\) −9.43608 −0.508759
\(345\) −0.258260 −0.0139042
\(346\) −28.6613 −1.54084
\(347\) −3.02638 −0.162464 −0.0812322 0.996695i \(-0.525886\pi\)
−0.0812322 + 0.996695i \(0.525886\pi\)
\(348\) −0.0593997 −0.00318416
\(349\) 0.603670 0.0323137 0.0161569 0.999869i \(-0.494857\pi\)
0.0161569 + 0.999869i \(0.494857\pi\)
\(350\) −1.52977 −0.0817694
\(351\) 1.14790 0.0612702
\(352\) 12.0621 0.642913
\(353\) 0.153802 0.00818607 0.00409304 0.999992i \(-0.498697\pi\)
0.00409304 + 0.999992i \(0.498697\pi\)
\(354\) −1.05796 −0.0562300
\(355\) 6.62897 0.351829
\(356\) 1.65792 0.0878698
\(357\) 0.247972 0.0131241
\(358\) −38.3388 −2.02627
\(359\) 8.18487 0.431981 0.215990 0.976395i \(-0.430702\pi\)
0.215990 + 0.976395i \(0.430702\pi\)
\(360\) −7.60698 −0.400923
\(361\) −18.9384 −0.996760
\(362\) −10.0729 −0.529418
\(363\) 1.86432 0.0978517
\(364\) 1.01692 0.0533011
\(365\) −8.86780 −0.464162
\(366\) 0.273364 0.0142890
\(367\) 15.1388 0.790240 0.395120 0.918629i \(-0.370703\pi\)
0.395120 + 0.918629i \(0.370703\pi\)
\(368\) −18.4073 −0.959548
\(369\) 20.8133 1.08350
\(370\) 2.22336 0.115587
\(371\) 3.32221 0.172481
\(372\) 0.137168 0.00711184
\(373\) −32.6744 −1.69182 −0.845909 0.533327i \(-0.820941\pi\)
−0.845909 + 0.533327i \(0.820941\pi\)
\(374\) 37.5131 1.93976
\(375\) −0.0640431 −0.00330717
\(376\) −0.420122 −0.0216661
\(377\) 8.15037 0.419766
\(378\) 0.587424 0.0302138
\(379\) −11.1445 −0.572455 −0.286228 0.958162i \(-0.592401\pi\)
−0.286228 + 0.958162i \(0.592401\pi\)
\(380\) −0.0844077 −0.00433003
\(381\) −0.154137 −0.00789667
\(382\) 39.7627 2.03444
\(383\) 1.36490 0.0697431 0.0348715 0.999392i \(-0.488898\pi\)
0.0348715 + 0.999392i \(0.488898\pi\)
\(384\) 0.852911 0.0435249
\(385\) −6.33328 −0.322774
\(386\) −16.8424 −0.857255
\(387\) −11.1335 −0.565950
\(388\) 0.883620 0.0448590
\(389\) 16.8374 0.853688 0.426844 0.904325i \(-0.359625\pi\)
0.426844 + 0.904325i \(0.359625\pi\)
\(390\) 0.292869 0.0148300
\(391\) −15.6140 −0.789633
\(392\) −2.53913 −0.128246
\(393\) 0.0803201 0.00405161
\(394\) 32.3052 1.62751
\(395\) −15.8461 −0.797302
\(396\) 6.45456 0.324354
\(397\) −0.437439 −0.0219544 −0.0109772 0.999940i \(-0.503494\pi\)
−0.0109772 + 0.999940i \(0.503494\pi\)
\(398\) −1.50384 −0.0753808
\(399\) −0.0158907 −0.000795532 0
\(400\) −4.56464 −0.228232
\(401\) 5.85288 0.292279 0.146139 0.989264i \(-0.453315\pi\)
0.146139 + 0.989264i \(0.453315\pi\)
\(402\) −0.507999 −0.0253367
\(403\) −18.8212 −0.937550
\(404\) −5.19075 −0.258250
\(405\) −8.96310 −0.445380
\(406\) 4.17086 0.206997
\(407\) 9.20480 0.456265
\(408\) 0.629633 0.0311715
\(409\) 22.6847 1.12169 0.560844 0.827922i \(-0.310477\pi\)
0.560844 + 0.827922i \(0.310477\pi\)
\(410\) 10.6277 0.524863
\(411\) 0.0475971 0.00234779
\(412\) −1.30911 −0.0644952
\(413\) 10.7987 0.531370
\(414\) −18.4814 −0.908313
\(415\) 13.7034 0.672672
\(416\) 5.69339 0.279141
\(417\) 0.685862 0.0335868
\(418\) −2.40395 −0.117581
\(419\) −3.34462 −0.163395 −0.0816976 0.996657i \(-0.526034\pi\)
−0.0816976 + 0.996657i \(0.526034\pi\)
\(420\) 0.0217863 0.00106306
\(421\) −21.3930 −1.04263 −0.521315 0.853364i \(-0.674558\pi\)
−0.521315 + 0.853364i \(0.674558\pi\)
\(422\) −21.0671 −1.02553
\(423\) −0.495697 −0.0241016
\(424\) 8.43554 0.409666
\(425\) −3.87195 −0.187817
\(426\) −0.649446 −0.0314658
\(427\) −2.79025 −0.135030
\(428\) 0.0437969 0.00211700
\(429\) 1.21249 0.0585395
\(430\) −5.68501 −0.274155
\(431\) 8.21306 0.395609 0.197805 0.980241i \(-0.436619\pi\)
0.197805 + 0.980241i \(0.436619\pi\)
\(432\) 1.75280 0.0843318
\(433\) 14.5906 0.701181 0.350591 0.936529i \(-0.385981\pi\)
0.350591 + 0.936529i \(0.385981\pi\)
\(434\) −9.63154 −0.462328
\(435\) 0.174612 0.00837200
\(436\) 1.58744 0.0760245
\(437\) 1.00059 0.0478647
\(438\) 0.868787 0.0415122
\(439\) −2.38669 −0.113910 −0.0569552 0.998377i \(-0.518139\pi\)
−0.0569552 + 0.998377i \(0.518139\pi\)
\(440\) −16.0810 −0.766634
\(441\) −2.99590 −0.142662
\(442\) 17.7064 0.842209
\(443\) −25.8584 −1.22857 −0.614284 0.789085i \(-0.710555\pi\)
−0.614284 + 0.789085i \(0.710555\pi\)
\(444\) −0.0316642 −0.00150272
\(445\) −4.87365 −0.231033
\(446\) −23.1829 −1.09774
\(447\) −1.25160 −0.0591984
\(448\) −6.21575 −0.293666
\(449\) 10.9602 0.517246 0.258623 0.965978i \(-0.416731\pi\)
0.258623 + 0.965978i \(0.416731\pi\)
\(450\) −4.58302 −0.216046
\(451\) 43.9989 2.07183
\(452\) 0.457810 0.0215336
\(453\) 0.669680 0.0314643
\(454\) 18.0924 0.849116
\(455\) −2.98935 −0.140143
\(456\) −0.0403487 −0.00188950
\(457\) 3.61489 0.169097 0.0845487 0.996419i \(-0.473055\pi\)
0.0845487 + 0.996419i \(0.473055\pi\)
\(458\) 1.52977 0.0714812
\(459\) 1.48681 0.0693985
\(460\) −1.37181 −0.0639611
\(461\) 32.1627 1.49797 0.748984 0.662588i \(-0.230542\pi\)
0.748984 + 0.662588i \(0.230542\pi\)
\(462\) 0.620477 0.0288672
\(463\) 14.6125 0.679103 0.339551 0.940588i \(-0.389725\pi\)
0.339551 + 0.940588i \(0.389725\pi\)
\(464\) 12.4454 0.577762
\(465\) −0.403221 −0.0186989
\(466\) −39.9429 −1.85032
\(467\) 15.1468 0.700912 0.350456 0.936579i \(-0.386027\pi\)
0.350456 + 0.936579i \(0.386027\pi\)
\(468\) 3.04659 0.140829
\(469\) 5.18520 0.239430
\(470\) −0.253113 −0.0116752
\(471\) −0.134917 −0.00621665
\(472\) 27.4194 1.26208
\(473\) −23.5361 −1.08219
\(474\) 1.55245 0.0713065
\(475\) 0.248126 0.0113848
\(476\) 1.31717 0.0603722
\(477\) 9.95301 0.455717
\(478\) −13.1267 −0.600403
\(479\) −6.58694 −0.300965 −0.150482 0.988613i \(-0.548083\pi\)
−0.150482 + 0.988613i \(0.548083\pi\)
\(480\) 0.121974 0.00556733
\(481\) 4.34472 0.198102
\(482\) 11.5884 0.527836
\(483\) −0.258260 −0.0117512
\(484\) 9.90284 0.450129
\(485\) −2.59750 −0.117946
\(486\) 2.64039 0.119771
\(487\) 30.5299 1.38344 0.691722 0.722164i \(-0.256852\pi\)
0.691722 + 0.722164i \(0.256852\pi\)
\(488\) −7.08483 −0.320715
\(489\) 0.237929 0.0107595
\(490\) −1.52977 −0.0691077
\(491\) −10.8096 −0.487829 −0.243914 0.969797i \(-0.578432\pi\)
−0.243914 + 0.969797i \(0.578432\pi\)
\(492\) −0.151355 −0.00682360
\(493\) 10.5568 0.475453
\(494\) −1.13468 −0.0510516
\(495\) −18.9739 −0.852812
\(496\) −28.7394 −1.29044
\(497\) 6.62897 0.297350
\(498\) −1.34253 −0.0601603
\(499\) −12.3086 −0.551006 −0.275503 0.961300i \(-0.588844\pi\)
−0.275503 + 0.961300i \(0.588844\pi\)
\(500\) −0.340181 −0.0152134
\(501\) 1.12418 0.0502245
\(502\) 1.36069 0.0607308
\(503\) 28.5889 1.27471 0.637357 0.770568i \(-0.280028\pi\)
0.637357 + 0.770568i \(0.280028\pi\)
\(504\) −7.60698 −0.338842
\(505\) 15.2588 0.679007
\(506\) −39.0695 −1.73685
\(507\) −0.260259 −0.0115585
\(508\) −0.818737 −0.0363256
\(509\) −28.0096 −1.24150 −0.620752 0.784007i \(-0.713173\pi\)
−0.620752 + 0.784007i \(0.713173\pi\)
\(510\) 0.379339 0.0167974
\(511\) −8.86780 −0.392288
\(512\) −14.4868 −0.640233
\(513\) −0.0952793 −0.00420668
\(514\) −13.7031 −0.604419
\(515\) 3.84827 0.169575
\(516\) 0.0809635 0.00356422
\(517\) −1.04790 −0.0460864
\(518\) 2.22336 0.0976890
\(519\) −1.19990 −0.0526696
\(520\) −7.59035 −0.332859
\(521\) 0.868896 0.0380670 0.0190335 0.999819i \(-0.493941\pi\)
0.0190335 + 0.999819i \(0.493941\pi\)
\(522\) 12.4955 0.546913
\(523\) −5.82730 −0.254810 −0.127405 0.991851i \(-0.540665\pi\)
−0.127405 + 0.991851i \(0.540665\pi\)
\(524\) 0.426641 0.0186379
\(525\) −0.0640431 −0.00279507
\(526\) −13.8101 −0.602148
\(527\) −24.3781 −1.06193
\(528\) 1.85143 0.0805732
\(529\) −6.73822 −0.292966
\(530\) 5.08221 0.220757
\(531\) 32.3519 1.40395
\(532\) −0.0844077 −0.00365954
\(533\) 20.7678 0.899551
\(534\) 0.477476 0.0206624
\(535\) −0.128746 −0.00556617
\(536\) 13.1659 0.568680
\(537\) −1.60504 −0.0692626
\(538\) −4.90924 −0.211652
\(539\) −6.33328 −0.272794
\(540\) 0.130628 0.00562135
\(541\) 25.1358 1.08067 0.540336 0.841449i \(-0.318297\pi\)
0.540336 + 0.841449i \(0.318297\pi\)
\(542\) 22.9527 0.985901
\(543\) −0.421697 −0.0180967
\(544\) 7.37437 0.316173
\(545\) −4.66644 −0.199889
\(546\) 0.292869 0.0125336
\(547\) 18.6768 0.798560 0.399280 0.916829i \(-0.369260\pi\)
0.399280 + 0.916829i \(0.369260\pi\)
\(548\) 0.252824 0.0108001
\(549\) −8.35932 −0.356767
\(550\) −9.68843 −0.413116
\(551\) −0.676508 −0.0288202
\(552\) −0.655755 −0.0279108
\(553\) −15.8461 −0.673843
\(554\) 3.83460 0.162917
\(555\) 0.0930804 0.00395104
\(556\) 3.64313 0.154503
\(557\) 28.3835 1.20265 0.601325 0.799005i \(-0.294640\pi\)
0.601325 + 0.799005i \(0.294640\pi\)
\(558\) −28.8551 −1.22153
\(559\) −11.1092 −0.469869
\(560\) −4.56464 −0.192891
\(561\) 1.57048 0.0663055
\(562\) −13.1252 −0.553654
\(563\) −4.23600 −0.178526 −0.0892630 0.996008i \(-0.528451\pi\)
−0.0892630 + 0.996008i \(0.528451\pi\)
\(564\) 0.00360473 0.000151786 0
\(565\) −1.34578 −0.0566174
\(566\) 39.6802 1.66788
\(567\) −8.96310 −0.376415
\(568\) 16.8318 0.706248
\(569\) 8.53818 0.357939 0.178970 0.983855i \(-0.442724\pi\)
0.178970 + 0.983855i \(0.442724\pi\)
\(570\) −0.0243091 −0.00101820
\(571\) −3.36599 −0.140862 −0.0704311 0.997517i \(-0.522437\pi\)
−0.0704311 + 0.997517i \(0.522437\pi\)
\(572\) 6.44044 0.269288
\(573\) 1.66465 0.0695419
\(574\) 10.6277 0.443590
\(575\) 4.03259 0.168171
\(576\) −18.6218 −0.775906
\(577\) −25.2986 −1.05320 −0.526598 0.850114i \(-0.676533\pi\)
−0.526598 + 0.850114i \(0.676533\pi\)
\(578\) −3.07176 −0.127768
\(579\) −0.705101 −0.0293030
\(580\) 0.927495 0.0385122
\(581\) 13.7034 0.568512
\(582\) 0.254479 0.0105485
\(583\) 21.0405 0.871409
\(584\) −22.5165 −0.931740
\(585\) −8.95578 −0.370276
\(586\) 0.0719318 0.00297147
\(587\) −28.4316 −1.17350 −0.586749 0.809769i \(-0.699593\pi\)
−0.586749 + 0.809769i \(0.699593\pi\)
\(588\) 0.0217863 0.000898451 0
\(589\) 1.56222 0.0643702
\(590\) 16.5195 0.680097
\(591\) 1.35244 0.0556321
\(592\) 6.63426 0.272666
\(593\) −8.04631 −0.330422 −0.165211 0.986258i \(-0.552831\pi\)
−0.165211 + 0.986258i \(0.552831\pi\)
\(594\) 3.72032 0.152647
\(595\) −3.87195 −0.158735
\(596\) −6.64817 −0.272320
\(597\) −0.0629579 −0.00257669
\(598\) −18.4410 −0.754110
\(599\) 33.0646 1.35098 0.675492 0.737367i \(-0.263931\pi\)
0.675492 + 0.737367i \(0.263931\pi\)
\(600\) −0.162614 −0.00663869
\(601\) −8.12871 −0.331577 −0.165788 0.986161i \(-0.553017\pi\)
−0.165788 + 0.986161i \(0.553017\pi\)
\(602\) −5.68501 −0.231704
\(603\) 15.5343 0.632607
\(604\) 3.55718 0.144740
\(605\) −29.1105 −1.18351
\(606\) −1.49492 −0.0607269
\(607\) −29.3624 −1.19178 −0.595891 0.803065i \(-0.703201\pi\)
−0.595891 + 0.803065i \(0.703201\pi\)
\(608\) −0.472571 −0.0191653
\(609\) 0.174612 0.00707563
\(610\) −4.26843 −0.172824
\(611\) −0.494613 −0.0200099
\(612\) 3.94609 0.159511
\(613\) 19.7545 0.797875 0.398938 0.916978i \(-0.369379\pi\)
0.398938 + 0.916978i \(0.369379\pi\)
\(614\) −43.3625 −1.74997
\(615\) 0.444924 0.0179411
\(616\) −16.0810 −0.647924
\(617\) 3.67101 0.147789 0.0738947 0.997266i \(-0.476457\pi\)
0.0738947 + 0.997266i \(0.476457\pi\)
\(618\) −0.377018 −0.0151659
\(619\) 18.2966 0.735402 0.367701 0.929944i \(-0.380145\pi\)
0.367701 + 0.929944i \(0.380145\pi\)
\(620\) −2.14181 −0.0860172
\(621\) −1.54850 −0.0621391
\(622\) 45.0929 1.80806
\(623\) −4.87365 −0.195259
\(624\) 0.873887 0.0349835
\(625\) 1.00000 0.0400000
\(626\) −29.5815 −1.18231
\(627\) −0.100641 −0.00401920
\(628\) −0.716646 −0.0285973
\(629\) 5.62750 0.224383
\(630\) −4.58302 −0.182592
\(631\) −3.13058 −0.124626 −0.0623132 0.998057i \(-0.519848\pi\)
−0.0623132 + 0.998057i \(0.519848\pi\)
\(632\) −40.2353 −1.60047
\(633\) −0.881969 −0.0350551
\(634\) −21.6298 −0.859029
\(635\) 2.40677 0.0955097
\(636\) −0.0723786 −0.00287000
\(637\) −2.98935 −0.118442
\(638\) 26.4153 1.04579
\(639\) 19.8597 0.785639
\(640\) −13.3178 −0.526431
\(641\) −41.1908 −1.62694 −0.813470 0.581607i \(-0.802424\pi\)
−0.813470 + 0.581607i \(0.802424\pi\)
\(642\) 0.0126133 0.000497809 0
\(643\) −23.4393 −0.924355 −0.462178 0.886787i \(-0.652932\pi\)
−0.462178 + 0.886787i \(0.652932\pi\)
\(644\) −1.37181 −0.0540570
\(645\) −0.238001 −0.00937128
\(646\) −1.46969 −0.0578243
\(647\) 38.3034 1.50586 0.752931 0.658100i \(-0.228639\pi\)
0.752931 + 0.658100i \(0.228639\pi\)
\(648\) −22.7585 −0.894039
\(649\) 68.3914 2.68460
\(650\) −4.57300 −0.179368
\(651\) −0.403221 −0.0158035
\(652\) 1.26382 0.0494949
\(653\) 5.59820 0.219074 0.109537 0.993983i \(-0.465063\pi\)
0.109537 + 0.993983i \(0.465063\pi\)
\(654\) 0.457176 0.0178770
\(655\) −1.25416 −0.0490039
\(656\) 31.7117 1.23813
\(657\) −26.5670 −1.03648
\(658\) −0.253113 −0.00986737
\(659\) −30.7787 −1.19897 −0.599483 0.800387i \(-0.704627\pi\)
−0.599483 + 0.800387i \(0.704627\pi\)
\(660\) 0.137979 0.00537081
\(661\) 3.01579 0.117301 0.0586504 0.998279i \(-0.481320\pi\)
0.0586504 + 0.998279i \(0.481320\pi\)
\(662\) 8.61923 0.334996
\(663\) 0.741274 0.0287887
\(664\) 34.7947 1.35030
\(665\) 0.248126 0.00962190
\(666\) 6.66097 0.258107
\(667\) −10.9947 −0.425718
\(668\) 5.97135 0.231038
\(669\) −0.970542 −0.0375233
\(670\) 7.93213 0.306445
\(671\) −17.6715 −0.682199
\(672\) 0.121974 0.00470525
\(673\) 11.8958 0.458549 0.229275 0.973362i \(-0.426365\pi\)
0.229275 + 0.973362i \(0.426365\pi\)
\(674\) 12.7115 0.489630
\(675\) −0.383996 −0.0147800
\(676\) −1.38243 −0.0531705
\(677\) 35.1701 1.35170 0.675848 0.737041i \(-0.263777\pi\)
0.675848 + 0.737041i \(0.263777\pi\)
\(678\) 0.131847 0.00506357
\(679\) −2.59750 −0.0996828
\(680\) −9.83140 −0.377017
\(681\) 0.757430 0.0290248
\(682\) −60.9992 −2.33578
\(683\) 6.82111 0.261002 0.130501 0.991448i \(-0.458341\pi\)
0.130501 + 0.991448i \(0.458341\pi\)
\(684\) −0.252877 −0.00966900
\(685\) −0.743203 −0.0283963
\(686\) −1.52977 −0.0584067
\(687\) 0.0640431 0.00244340
\(688\) −16.9634 −0.646723
\(689\) 9.93124 0.378350
\(690\) −0.395077 −0.0150403
\(691\) −4.35901 −0.165825 −0.0829123 0.996557i \(-0.526422\pi\)
−0.0829123 + 0.996557i \(0.526422\pi\)
\(692\) −6.37355 −0.242286
\(693\) −18.9739 −0.720758
\(694\) −4.62965 −0.175739
\(695\) −10.7094 −0.406230
\(696\) 0.443363 0.0168056
\(697\) 26.8994 1.01889
\(698\) 0.923473 0.0349540
\(699\) −1.67220 −0.0632483
\(700\) −0.340181 −0.0128576
\(701\) 1.07652 0.0406598 0.0203299 0.999793i \(-0.493528\pi\)
0.0203299 + 0.999793i \(0.493528\pi\)
\(702\) 1.75601 0.0662764
\(703\) −0.360626 −0.0136013
\(704\) −39.3661 −1.48367
\(705\) −0.0105965 −0.000399087 0
\(706\) 0.235281 0.00885493
\(707\) 15.2588 0.573866
\(708\) −0.235264 −0.00884176
\(709\) 27.5885 1.03611 0.518053 0.855348i \(-0.326657\pi\)
0.518053 + 0.855348i \(0.326657\pi\)
\(710\) 10.1408 0.380576
\(711\) −47.4732 −1.78038
\(712\) −12.3748 −0.463767
\(713\) 25.3895 0.950846
\(714\) 0.379339 0.0141964
\(715\) −18.9324 −0.708031
\(716\) −8.52558 −0.318616
\(717\) −0.549546 −0.0205232
\(718\) 12.5209 0.467277
\(719\) 47.2367 1.76163 0.880816 0.473458i \(-0.156994\pi\)
0.880816 + 0.473458i \(0.156994\pi\)
\(720\) −13.6752 −0.509644
\(721\) 3.84827 0.143317
\(722\) −28.9714 −1.07820
\(723\) 0.485143 0.0180427
\(724\) −2.23995 −0.0832471
\(725\) −2.72647 −0.101259
\(726\) 2.85198 0.105847
\(727\) −12.9829 −0.481510 −0.240755 0.970586i \(-0.577395\pi\)
−0.240755 + 0.970586i \(0.577395\pi\)
\(728\) −7.59035 −0.281317
\(729\) −26.7788 −0.991806
\(730\) −13.5657 −0.502087
\(731\) −14.3892 −0.532203
\(732\) 0.0607892 0.00224684
\(733\) 34.5887 1.27756 0.638781 0.769389i \(-0.279439\pi\)
0.638781 + 0.769389i \(0.279439\pi\)
\(734\) 23.1589 0.854809
\(735\) −0.0640431 −0.00236227
\(736\) −7.68031 −0.283100
\(737\) 32.8393 1.20965
\(738\) 31.8394 1.17203
\(739\) −22.5558 −0.829728 −0.414864 0.909883i \(-0.636171\pi\)
−0.414864 + 0.909883i \(0.636171\pi\)
\(740\) 0.494420 0.0181752
\(741\) −0.0475029 −0.00174506
\(742\) 5.08221 0.186574
\(743\) −27.7281 −1.01725 −0.508623 0.860989i \(-0.669845\pi\)
−0.508623 + 0.860989i \(0.669845\pi\)
\(744\) −1.02383 −0.0375355
\(745\) 19.5430 0.716001
\(746\) −49.9842 −1.83005
\(747\) 41.0539 1.50208
\(748\) 8.34198 0.305013
\(749\) −0.128746 −0.00470427
\(750\) −0.0979709 −0.00357739
\(751\) 27.1351 0.990174 0.495087 0.868843i \(-0.335136\pi\)
0.495087 + 0.868843i \(0.335136\pi\)
\(752\) −0.755259 −0.0275415
\(753\) 0.0569650 0.00207592
\(754\) 12.4682 0.454063
\(755\) −10.4567 −0.380559
\(756\) 0.130628 0.00475090
\(757\) −5.58521 −0.202998 −0.101499 0.994836i \(-0.532364\pi\)
−0.101499 + 0.994836i \(0.532364\pi\)
\(758\) −17.0485 −0.619229
\(759\) −1.63563 −0.0593696
\(760\) 0.630024 0.0228534
\(761\) 22.4624 0.814263 0.407131 0.913370i \(-0.366529\pi\)
0.407131 + 0.913370i \(0.366529\pi\)
\(762\) −0.235793 −0.00854189
\(763\) −4.66644 −0.168937
\(764\) 8.84223 0.319901
\(765\) −11.6000 −0.419398
\(766\) 2.08797 0.0754416
\(767\) 32.2811 1.16560
\(768\) 0.508601 0.0183526
\(769\) 44.4172 1.60172 0.800862 0.598849i \(-0.204375\pi\)
0.800862 + 0.598849i \(0.204375\pi\)
\(770\) −9.68843 −0.349147
\(771\) −0.573677 −0.0206605
\(772\) −3.74532 −0.134797
\(773\) −27.0456 −0.972763 −0.486381 0.873747i \(-0.661683\pi\)
−0.486381 + 0.873747i \(0.661683\pi\)
\(774\) −17.0317 −0.612192
\(775\) 6.29609 0.226162
\(776\) −6.59539 −0.236761
\(777\) 0.0930804 0.00333924
\(778\) 25.7572 0.923441
\(779\) −1.72379 −0.0617613
\(780\) 0.0651267 0.00233191
\(781\) 41.9831 1.50227
\(782\) −23.8857 −0.854152
\(783\) 1.04695 0.0374151
\(784\) −4.56464 −0.163023
\(785\) 2.10666 0.0751899
\(786\) 0.122871 0.00438266
\(787\) 28.6325 1.02064 0.510319 0.859985i \(-0.329527\pi\)
0.510319 + 0.859985i \(0.329527\pi\)
\(788\) 7.18385 0.255914
\(789\) −0.578154 −0.0205828
\(790\) −24.2408 −0.862447
\(791\) −1.34578 −0.0478505
\(792\) −48.1772 −1.71190
\(793\) −8.34104 −0.296199
\(794\) −0.669179 −0.0237483
\(795\) 0.212765 0.00754599
\(796\) −0.334417 −0.0118531
\(797\) 46.1960 1.63635 0.818173 0.574972i \(-0.194987\pi\)
0.818173 + 0.574972i \(0.194987\pi\)
\(798\) −0.0243091 −0.000860533 0
\(799\) −0.640648 −0.0226645
\(800\) −1.90456 −0.0673364
\(801\) −14.6010 −0.515899
\(802\) 8.95353 0.316160
\(803\) −56.1623 −1.98192
\(804\) −0.112966 −0.00398401
\(805\) 4.03259 0.142130
\(806\) −28.7920 −1.01415
\(807\) −0.205524 −0.00723478
\(808\) 38.7441 1.36301
\(809\) −11.1772 −0.392970 −0.196485 0.980507i \(-0.562953\pi\)
−0.196485 + 0.980507i \(0.562953\pi\)
\(810\) −13.7114 −0.481771
\(811\) −7.73040 −0.271451 −0.135726 0.990746i \(-0.543337\pi\)
−0.135726 + 0.990746i \(0.543337\pi\)
\(812\) 0.927495 0.0325487
\(813\) 0.960906 0.0337004
\(814\) 14.0812 0.493545
\(815\) −3.71513 −0.130135
\(816\) 1.13190 0.0396245
\(817\) 0.922100 0.0322602
\(818\) 34.7023 1.21334
\(819\) −8.95578 −0.312940
\(820\) 2.36333 0.0825310
\(821\) 46.5304 1.62392 0.811960 0.583713i \(-0.198401\pi\)
0.811960 + 0.583713i \(0.198401\pi\)
\(822\) 0.0728123 0.00253962
\(823\) −40.0678 −1.39668 −0.698338 0.715768i \(-0.746077\pi\)
−0.698338 + 0.715768i \(0.746077\pi\)
\(824\) 9.77126 0.340398
\(825\) −0.405603 −0.0141213
\(826\) 16.5195 0.574787
\(827\) −29.0423 −1.00990 −0.504951 0.863148i \(-0.668489\pi\)
−0.504951 + 0.863148i \(0.668489\pi\)
\(828\) −4.10981 −0.142826
\(829\) 14.4423 0.501603 0.250801 0.968039i \(-0.419306\pi\)
0.250801 + 0.968039i \(0.419306\pi\)
\(830\) 20.9629 0.727634
\(831\) 0.160534 0.00556888
\(832\) −18.5810 −0.644181
\(833\) −3.87195 −0.134155
\(834\) 1.04921 0.0363311
\(835\) −17.5534 −0.607461
\(836\) −0.534578 −0.0184888
\(837\) −2.41767 −0.0835670
\(838\) −5.11648 −0.176746
\(839\) −9.18480 −0.317094 −0.158547 0.987351i \(-0.550681\pi\)
−0.158547 + 0.987351i \(0.550681\pi\)
\(840\) −0.162614 −0.00561071
\(841\) −21.5663 −0.743667
\(842\) −32.7262 −1.12782
\(843\) −0.549483 −0.0189252
\(844\) −4.68480 −0.161258
\(845\) 4.06381 0.139799
\(846\) −0.758301 −0.0260709
\(847\) −29.1105 −1.00025
\(848\) 15.1647 0.520758
\(849\) 1.66120 0.0570122
\(850\) −5.92318 −0.203163
\(851\) −5.86097 −0.200912
\(852\) −0.144421 −0.00494777
\(853\) −12.7417 −0.436268 −0.218134 0.975919i \(-0.569997\pi\)
−0.218134 + 0.975919i \(0.569997\pi\)
\(854\) −4.26843 −0.146063
\(855\) 0.743359 0.0254224
\(856\) −0.326903 −0.0111733
\(857\) 3.82422 0.130633 0.0653165 0.997865i \(-0.479194\pi\)
0.0653165 + 0.997865i \(0.479194\pi\)
\(858\) 1.85482 0.0633226
\(859\) 7.09447 0.242060 0.121030 0.992649i \(-0.461380\pi\)
0.121030 + 0.992649i \(0.461380\pi\)
\(860\) −1.26420 −0.0431090
\(861\) 0.444924 0.0151630
\(862\) 12.5641 0.427934
\(863\) 45.9769 1.56507 0.782536 0.622605i \(-0.213926\pi\)
0.782536 + 0.622605i \(0.213926\pi\)
\(864\) 0.731344 0.0248808
\(865\) 18.7357 0.637034
\(866\) 22.3202 0.758473
\(867\) −0.128598 −0.00436742
\(868\) −2.14181 −0.0726978
\(869\) −100.358 −3.40440
\(870\) 0.267115 0.00905605
\(871\) 15.5003 0.525209
\(872\) −11.8487 −0.401248
\(873\) −7.78184 −0.263375
\(874\) 1.53067 0.0517756
\(875\) 1.00000 0.0338062
\(876\) 0.193196 0.00652750
\(877\) 31.9887 1.08018 0.540091 0.841607i \(-0.318390\pi\)
0.540091 + 0.841607i \(0.318390\pi\)
\(878\) −3.65107 −0.123218
\(879\) 0.00301140 0.000101572 0
\(880\) −28.9091 −0.974527
\(881\) 0.341666 0.0115110 0.00575552 0.999983i \(-0.498168\pi\)
0.00575552 + 0.999983i \(0.498168\pi\)
\(882\) −4.58302 −0.154318
\(883\) 10.3447 0.348127 0.174063 0.984734i \(-0.444310\pi\)
0.174063 + 0.984734i \(0.444310\pi\)
\(884\) 3.93746 0.132431
\(885\) 0.691584 0.0232473
\(886\) −39.5572 −1.32895
\(887\) 20.3583 0.683565 0.341783 0.939779i \(-0.388969\pi\)
0.341783 + 0.939779i \(0.388969\pi\)
\(888\) 0.236343 0.00793117
\(889\) 2.40677 0.0807204
\(890\) −7.45554 −0.249910
\(891\) −56.7659 −1.90173
\(892\) −5.15528 −0.172612
\(893\) 0.0410546 0.00137384
\(894\) −1.91465 −0.0640354
\(895\) 25.0619 0.837726
\(896\) −13.3178 −0.444915
\(897\) −0.772027 −0.0257772
\(898\) 16.7666 0.559509
\(899\) −17.1661 −0.572522
\(900\) −1.01915 −0.0339716
\(901\) 12.8634 0.428544
\(902\) 67.3080 2.24111
\(903\) −0.238001 −0.00792018
\(904\) −3.41712 −0.113652
\(905\) 6.58458 0.218879
\(906\) 1.02445 0.0340352
\(907\) 25.1621 0.835492 0.417746 0.908564i \(-0.362820\pi\)
0.417746 + 0.908564i \(0.362820\pi\)
\(908\) 4.02328 0.133517
\(909\) 45.7138 1.51623
\(910\) −4.57300 −0.151593
\(911\) −18.1865 −0.602547 −0.301274 0.953538i \(-0.597412\pi\)
−0.301274 + 0.953538i \(0.597412\pi\)
\(912\) −0.0725355 −0.00240189
\(913\) 86.7873 2.87224
\(914\) 5.52993 0.182914
\(915\) −0.178697 −0.00590753
\(916\) 0.340181 0.0112399
\(917\) −1.25416 −0.0414159
\(918\) 2.27448 0.0750689
\(919\) 26.5004 0.874168 0.437084 0.899421i \(-0.356011\pi\)
0.437084 + 0.899421i \(0.356011\pi\)
\(920\) 10.2393 0.337579
\(921\) −1.81536 −0.0598180
\(922\) 49.2014 1.62036
\(923\) 19.8163 0.652261
\(924\) 0.137979 0.00453916
\(925\) −1.45340 −0.0477876
\(926\) 22.3538 0.734590
\(927\) 11.5290 0.378663
\(928\) 5.19273 0.170460
\(929\) −25.5300 −0.837613 −0.418806 0.908076i \(-0.637551\pi\)
−0.418806 + 0.908076i \(0.637551\pi\)
\(930\) −0.616834 −0.0202268
\(931\) 0.248126 0.00813199
\(932\) −8.88230 −0.290949
\(933\) 1.88780 0.0618037
\(934\) 23.1711 0.758181
\(935\) −24.5222 −0.801960
\(936\) −22.7399 −0.743277
\(937\) 1.00053 0.0326858 0.0163429 0.999866i \(-0.494798\pi\)
0.0163429 + 0.999866i \(0.494798\pi\)
\(938\) 7.93213 0.258993
\(939\) −1.23842 −0.0404142
\(940\) −0.0562860 −0.00183585
\(941\) 34.1333 1.11271 0.556356 0.830944i \(-0.312199\pi\)
0.556356 + 0.830944i \(0.312199\pi\)
\(942\) −0.206391 −0.00672459
\(943\) −28.0154 −0.912308
\(944\) 49.2923 1.60433
\(945\) −0.383996 −0.0124914
\(946\) −36.0048 −1.17062
\(947\) −35.2983 −1.14704 −0.573520 0.819192i \(-0.694422\pi\)
−0.573520 + 0.819192i \(0.694422\pi\)
\(948\) 0.345227 0.0112124
\(949\) −26.5089 −0.860516
\(950\) 0.379574 0.0123150
\(951\) −0.905524 −0.0293636
\(952\) −9.83140 −0.318637
\(953\) 29.4600 0.954302 0.477151 0.878821i \(-0.341669\pi\)
0.477151 + 0.878821i \(0.341669\pi\)
\(954\) 15.2258 0.492953
\(955\) −25.9927 −0.841104
\(956\) −2.91906 −0.0944090
\(957\) 1.10587 0.0357476
\(958\) −10.0765 −0.325556
\(959\) −0.743203 −0.0239993
\(960\) −0.398076 −0.0128478
\(961\) 8.64072 0.278733
\(962\) 6.64640 0.214289
\(963\) −0.385709 −0.0124293
\(964\) 2.57696 0.0829984
\(965\) 11.0098 0.354418
\(966\) −0.395077 −0.0127114
\(967\) −17.8398 −0.573690 −0.286845 0.957977i \(-0.592607\pi\)
−0.286845 + 0.957977i \(0.592607\pi\)
\(968\) −73.9153 −2.37573
\(969\) −0.0615282 −0.00197657
\(970\) −3.97356 −0.127583
\(971\) −38.5055 −1.23570 −0.617851 0.786296i \(-0.711996\pi\)
−0.617851 + 0.786296i \(0.711996\pi\)
\(972\) 0.587157 0.0188331
\(973\) −10.7094 −0.343327
\(974\) 46.7036 1.49648
\(975\) −0.191447 −0.00613121
\(976\) −12.7365 −0.407686
\(977\) 6.13402 0.196245 0.0981223 0.995174i \(-0.468716\pi\)
0.0981223 + 0.995174i \(0.468716\pi\)
\(978\) 0.363975 0.0116386
\(979\) −30.8662 −0.986487
\(980\) −0.340181 −0.0108667
\(981\) −13.9802 −0.446353
\(982\) −16.5361 −0.527688
\(983\) 40.4504 1.29017 0.645084 0.764112i \(-0.276822\pi\)
0.645084 + 0.764112i \(0.276822\pi\)
\(984\) 1.12972 0.0360142
\(985\) −21.1177 −0.672867
\(986\) 16.1494 0.514301
\(987\) −0.0105965 −0.000337290 0
\(988\) −0.252324 −0.00802749
\(989\) 14.9862 0.476532
\(990\) −29.0256 −0.922493
\(991\) −59.0067 −1.87441 −0.937205 0.348780i \(-0.886596\pi\)
−0.937205 + 0.348780i \(0.886596\pi\)
\(992\) −11.9913 −0.380724
\(993\) 0.360841 0.0114510
\(994\) 10.1408 0.321646
\(995\) 0.983055 0.0311649
\(996\) −0.298545 −0.00945977
\(997\) 56.7998 1.79887 0.899434 0.437056i \(-0.143979\pi\)
0.899434 + 0.437056i \(0.143979\pi\)
\(998\) −18.8292 −0.596028
\(999\) 0.558101 0.0176575
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 \(a_p\))