Properties

Label 6027.2.a.bm.1.4
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(1\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.64639\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.64639 q^{2} +1.00000 q^{3} +0.710595 q^{4} +0.0457395 q^{5} -1.64639 q^{6} +2.12286 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.64639 q^{2} +1.00000 q^{3} +0.710595 q^{4} +0.0457395 q^{5} -1.64639 q^{6} +2.12286 q^{8} +1.00000 q^{9} -0.0753050 q^{10} +0.153516 q^{11} +0.710595 q^{12} +3.46056 q^{13} +0.0457395 q^{15} -4.91624 q^{16} -0.713284 q^{17} -1.64639 q^{18} -6.38590 q^{19} +0.0325023 q^{20} -0.252747 q^{22} -1.26532 q^{23} +2.12286 q^{24} -4.99791 q^{25} -5.69742 q^{26} +1.00000 q^{27} +1.30954 q^{29} -0.0753050 q^{30} +0.735747 q^{31} +3.84832 q^{32} +0.153516 q^{33} +1.17434 q^{34} +0.710595 q^{36} +9.12498 q^{37} +10.5137 q^{38} +3.46056 q^{39} +0.0970987 q^{40} +1.00000 q^{41} +2.39572 q^{43} +0.109088 q^{44} +0.0457395 q^{45} +2.08321 q^{46} +9.00229 q^{47} -4.91624 q^{48} +8.22850 q^{50} -0.713284 q^{51} +2.45905 q^{52} -14.1311 q^{53} -1.64639 q^{54} +0.00702175 q^{55} -6.38590 q^{57} -2.15600 q^{58} -11.3136 q^{59} +0.0325023 q^{60} -14.2763 q^{61} -1.21133 q^{62} +3.49665 q^{64} +0.158284 q^{65} -0.252747 q^{66} -13.3603 q^{67} -0.506856 q^{68} -1.26532 q^{69} -6.60480 q^{71} +2.12286 q^{72} +15.8710 q^{73} -15.0233 q^{74} -4.99791 q^{75} -4.53778 q^{76} -5.69742 q^{78} -6.18509 q^{79} -0.224867 q^{80} +1.00000 q^{81} -1.64639 q^{82} -2.20561 q^{83} -0.0326253 q^{85} -3.94428 q^{86} +1.30954 q^{87} +0.325893 q^{88} -14.3331 q^{89} -0.0753050 q^{90} -0.899130 q^{92} +0.735747 q^{93} -14.8213 q^{94} -0.292088 q^{95} +3.84832 q^{96} -8.42652 q^{97} +0.153516 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.64639 −1.16417 −0.582086 0.813127i \(-0.697763\pi\)
−0.582086 + 0.813127i \(0.697763\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.710595 0.355297
\(5\) 0.0457395 0.0204553 0.0102277 0.999948i \(-0.496744\pi\)
0.0102277 + 0.999948i \(0.496744\pi\)
\(6\) −1.64639 −0.672135
\(7\) 0 0
\(8\) 2.12286 0.750545
\(9\) 1.00000 0.333333
\(10\) −0.0753050 −0.0238135
\(11\) 0.153516 0.0462868 0.0231434 0.999732i \(-0.492633\pi\)
0.0231434 + 0.999732i \(0.492633\pi\)
\(12\) 0.710595 0.205131
\(13\) 3.46056 0.959786 0.479893 0.877327i \(-0.340675\pi\)
0.479893 + 0.877327i \(0.340675\pi\)
\(14\) 0 0
\(15\) 0.0457395 0.0118099
\(16\) −4.91624 −1.22906
\(17\) −0.713284 −0.172997 −0.0864984 0.996252i \(-0.527568\pi\)
−0.0864984 + 0.996252i \(0.527568\pi\)
\(18\) −1.64639 −0.388057
\(19\) −6.38590 −1.46503 −0.732513 0.680754i \(-0.761652\pi\)
−0.732513 + 0.680754i \(0.761652\pi\)
\(20\) 0.0325023 0.00726773
\(21\) 0 0
\(22\) −0.252747 −0.0538858
\(23\) −1.26532 −0.263838 −0.131919 0.991261i \(-0.542114\pi\)
−0.131919 + 0.991261i \(0.542114\pi\)
\(24\) 2.12286 0.433327
\(25\) −4.99791 −0.999582
\(26\) −5.69742 −1.11736
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.30954 0.243175 0.121587 0.992581i \(-0.461202\pi\)
0.121587 + 0.992581i \(0.461202\pi\)
\(30\) −0.0753050 −0.0137487
\(31\) 0.735747 0.132144 0.0660721 0.997815i \(-0.478953\pi\)
0.0660721 + 0.997815i \(0.478953\pi\)
\(32\) 3.84832 0.680294
\(33\) 0.153516 0.0267237
\(34\) 1.17434 0.201398
\(35\) 0 0
\(36\) 0.710595 0.118432
\(37\) 9.12498 1.50014 0.750069 0.661360i \(-0.230020\pi\)
0.750069 + 0.661360i \(0.230020\pi\)
\(38\) 10.5137 1.70554
\(39\) 3.46056 0.554133
\(40\) 0.0970987 0.0153526
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 2.39572 0.365344 0.182672 0.983174i \(-0.441525\pi\)
0.182672 + 0.983174i \(0.441525\pi\)
\(44\) 0.109088 0.0164456
\(45\) 0.0457395 0.00681844
\(46\) 2.08321 0.307152
\(47\) 9.00229 1.31312 0.656560 0.754274i \(-0.272011\pi\)
0.656560 + 0.754274i \(0.272011\pi\)
\(48\) −4.91624 −0.709599
\(49\) 0 0
\(50\) 8.22850 1.16369
\(51\) −0.713284 −0.0998798
\(52\) 2.45905 0.341009
\(53\) −14.1311 −1.94106 −0.970529 0.240985i \(-0.922529\pi\)
−0.970529 + 0.240985i \(0.922529\pi\)
\(54\) −1.64639 −0.224045
\(55\) 0.00702175 0.000946812 0
\(56\) 0 0
\(57\) −6.38590 −0.845833
\(58\) −2.15600 −0.283097
\(59\) −11.3136 −1.47291 −0.736454 0.676488i \(-0.763501\pi\)
−0.736454 + 0.676488i \(0.763501\pi\)
\(60\) 0.0325023 0.00419602
\(61\) −14.2763 −1.82789 −0.913946 0.405836i \(-0.866980\pi\)
−0.913946 + 0.405836i \(0.866980\pi\)
\(62\) −1.21133 −0.153839
\(63\) 0 0
\(64\) 3.49665 0.437081
\(65\) 0.158284 0.0196327
\(66\) −0.252747 −0.0311110
\(67\) −13.3603 −1.63222 −0.816109 0.577898i \(-0.803873\pi\)
−0.816109 + 0.577898i \(0.803873\pi\)
\(68\) −0.506856 −0.0614653
\(69\) −1.26532 −0.152327
\(70\) 0 0
\(71\) −6.60480 −0.783846 −0.391923 0.919998i \(-0.628190\pi\)
−0.391923 + 0.919998i \(0.628190\pi\)
\(72\) 2.12286 0.250182
\(73\) 15.8710 1.85756 0.928778 0.370637i \(-0.120861\pi\)
0.928778 + 0.370637i \(0.120861\pi\)
\(74\) −15.0233 −1.74642
\(75\) −4.99791 −0.577109
\(76\) −4.53778 −0.520520
\(77\) 0 0
\(78\) −5.69742 −0.645106
\(79\) −6.18509 −0.695877 −0.347938 0.937517i \(-0.613118\pi\)
−0.347938 + 0.937517i \(0.613118\pi\)
\(80\) −0.224867 −0.0251409
\(81\) 1.00000 0.111111
\(82\) −1.64639 −0.181813
\(83\) −2.20561 −0.242097 −0.121048 0.992647i \(-0.538626\pi\)
−0.121048 + 0.992647i \(0.538626\pi\)
\(84\) 0 0
\(85\) −0.0326253 −0.00353871
\(86\) −3.94428 −0.425323
\(87\) 1.30954 0.140397
\(88\) 0.325893 0.0347403
\(89\) −14.3331 −1.51930 −0.759651 0.650332i \(-0.774630\pi\)
−0.759651 + 0.650332i \(0.774630\pi\)
\(90\) −0.0753050 −0.00793784
\(91\) 0 0
\(92\) −0.899130 −0.0937408
\(93\) 0.735747 0.0762935
\(94\) −14.8213 −1.52870
\(95\) −0.292088 −0.0299676
\(96\) 3.84832 0.392768
\(97\) −8.42652 −0.855583 −0.427792 0.903877i \(-0.640708\pi\)
−0.427792 + 0.903877i \(0.640708\pi\)
\(98\) 0 0
\(99\) 0.153516 0.0154289
\(100\) −3.55149 −0.355149
\(101\) −4.27869 −0.425746 −0.212873 0.977080i \(-0.568282\pi\)
−0.212873 + 0.977080i \(0.568282\pi\)
\(102\) 1.17434 0.116277
\(103\) 8.86287 0.873284 0.436642 0.899635i \(-0.356168\pi\)
0.436642 + 0.899635i \(0.356168\pi\)
\(104\) 7.34629 0.720363
\(105\) 0 0
\(106\) 23.2653 2.25973
\(107\) 2.93535 0.283771 0.141886 0.989883i \(-0.454683\pi\)
0.141886 + 0.989883i \(0.454683\pi\)
\(108\) 0.710595 0.0683770
\(109\) −8.56169 −0.820061 −0.410030 0.912072i \(-0.634482\pi\)
−0.410030 + 0.912072i \(0.634482\pi\)
\(110\) −0.0115605 −0.00110225
\(111\) 9.12498 0.866105
\(112\) 0 0
\(113\) 8.56761 0.805973 0.402986 0.915206i \(-0.367972\pi\)
0.402986 + 0.915206i \(0.367972\pi\)
\(114\) 10.5137 0.984695
\(115\) −0.0578751 −0.00539688
\(116\) 0.930549 0.0863993
\(117\) 3.46056 0.319929
\(118\) 18.6266 1.71472
\(119\) 0 0
\(120\) 0.0970987 0.00886385
\(121\) −10.9764 −0.997858
\(122\) 23.5043 2.12798
\(123\) 1.00000 0.0901670
\(124\) 0.522818 0.0469505
\(125\) −0.457299 −0.0409021
\(126\) 0 0
\(127\) −0.852507 −0.0756478 −0.0378239 0.999284i \(-0.512043\pi\)
−0.0378239 + 0.999284i \(0.512043\pi\)
\(128\) −13.4535 −1.18913
\(129\) 2.39572 0.210931
\(130\) −0.260597 −0.0228559
\(131\) −10.6329 −0.928999 −0.464499 0.885573i \(-0.653766\pi\)
−0.464499 + 0.885573i \(0.653766\pi\)
\(132\) 0.109088 0.00949486
\(133\) 0 0
\(134\) 21.9962 1.90018
\(135\) 0.0457395 0.00393663
\(136\) −1.51420 −0.129842
\(137\) 21.2240 1.81329 0.906645 0.421895i \(-0.138635\pi\)
0.906645 + 0.421895i \(0.138635\pi\)
\(138\) 2.08321 0.177334
\(139\) 12.0384 1.02108 0.510541 0.859854i \(-0.329445\pi\)
0.510541 + 0.859854i \(0.329445\pi\)
\(140\) 0 0
\(141\) 9.00229 0.758130
\(142\) 10.8741 0.912531
\(143\) 0.531251 0.0444254
\(144\) −4.91624 −0.409687
\(145\) 0.0598975 0.00497422
\(146\) −26.1298 −2.16252
\(147\) 0 0
\(148\) 6.48416 0.532995
\(149\) −15.5561 −1.27441 −0.637203 0.770696i \(-0.719909\pi\)
−0.637203 + 0.770696i \(0.719909\pi\)
\(150\) 8.22850 0.671854
\(151\) 23.1467 1.88365 0.941826 0.336100i \(-0.109108\pi\)
0.941826 + 0.336100i \(0.109108\pi\)
\(152\) −13.5564 −1.09957
\(153\) −0.713284 −0.0576656
\(154\) 0 0
\(155\) 0.0336527 0.00270305
\(156\) 2.45905 0.196882
\(157\) 13.5629 1.08244 0.541219 0.840882i \(-0.317963\pi\)
0.541219 + 0.840882i \(0.317963\pi\)
\(158\) 10.1831 0.810120
\(159\) −14.1311 −1.12067
\(160\) 0.176020 0.0139156
\(161\) 0 0
\(162\) −1.64639 −0.129352
\(163\) 18.8746 1.47837 0.739184 0.673503i \(-0.235211\pi\)
0.739184 + 0.673503i \(0.235211\pi\)
\(164\) 0.710595 0.0554881
\(165\) 0.00702175 0.000546642 0
\(166\) 3.63128 0.281842
\(167\) 1.10994 0.0858894 0.0429447 0.999077i \(-0.486326\pi\)
0.0429447 + 0.999077i \(0.486326\pi\)
\(168\) 0 0
\(169\) −1.02454 −0.0788109
\(170\) 0.0537139 0.00411967
\(171\) −6.38590 −0.488342
\(172\) 1.70239 0.129806
\(173\) −21.6857 −1.64874 −0.824368 0.566054i \(-0.808469\pi\)
−0.824368 + 0.566054i \(0.808469\pi\)
\(174\) −2.15600 −0.163446
\(175\) 0 0
\(176\) −0.754722 −0.0568893
\(177\) −11.3136 −0.850383
\(178\) 23.5978 1.76873
\(179\) −7.05942 −0.527646 −0.263823 0.964571i \(-0.584983\pi\)
−0.263823 + 0.964571i \(0.584983\pi\)
\(180\) 0.0325023 0.00242258
\(181\) 13.1070 0.974234 0.487117 0.873337i \(-0.338049\pi\)
0.487117 + 0.873337i \(0.338049\pi\)
\(182\) 0 0
\(183\) −14.2763 −1.05533
\(184\) −2.68610 −0.198022
\(185\) 0.417372 0.0306858
\(186\) −1.21133 −0.0888187
\(187\) −0.109501 −0.00800747
\(188\) 6.39698 0.466548
\(189\) 0 0
\(190\) 0.480890 0.0348874
\(191\) 9.51467 0.688457 0.344229 0.938886i \(-0.388140\pi\)
0.344229 + 0.938886i \(0.388140\pi\)
\(192\) 3.49665 0.252349
\(193\) −10.1608 −0.731389 −0.365695 0.930735i \(-0.619169\pi\)
−0.365695 + 0.930735i \(0.619169\pi\)
\(194\) 13.8733 0.996047
\(195\) 0.158284 0.0113350
\(196\) 0 0
\(197\) 7.54126 0.537293 0.268646 0.963239i \(-0.413424\pi\)
0.268646 + 0.963239i \(0.413424\pi\)
\(198\) −0.252747 −0.0179619
\(199\) 25.9232 1.83765 0.918823 0.394671i \(-0.129141\pi\)
0.918823 + 0.394671i \(0.129141\pi\)
\(200\) −10.6099 −0.750231
\(201\) −13.3603 −0.942361
\(202\) 7.04439 0.495641
\(203\) 0 0
\(204\) −0.506856 −0.0354870
\(205\) 0.0457395 0.00319459
\(206\) −14.5917 −1.01665
\(207\) −1.26532 −0.0879458
\(208\) −17.0129 −1.17964
\(209\) −0.980337 −0.0678113
\(210\) 0 0
\(211\) −14.2724 −0.982555 −0.491277 0.871003i \(-0.663470\pi\)
−0.491277 + 0.871003i \(0.663470\pi\)
\(212\) −10.0415 −0.689653
\(213\) −6.60480 −0.452553
\(214\) −4.83273 −0.330359
\(215\) 0.109579 0.00747322
\(216\) 2.12286 0.144442
\(217\) 0 0
\(218\) 14.0959 0.954692
\(219\) 15.8710 1.07246
\(220\) 0.00498962 0.000336400 0
\(221\) −2.46836 −0.166040
\(222\) −15.0233 −1.00830
\(223\) −15.5265 −1.03973 −0.519866 0.854248i \(-0.674018\pi\)
−0.519866 + 0.854248i \(0.674018\pi\)
\(224\) 0 0
\(225\) −4.99791 −0.333194
\(226\) −14.1056 −0.938291
\(227\) −22.0233 −1.46174 −0.730870 0.682517i \(-0.760886\pi\)
−0.730870 + 0.682517i \(0.760886\pi\)
\(228\) −4.53778 −0.300522
\(229\) −14.6238 −0.966369 −0.483184 0.875519i \(-0.660520\pi\)
−0.483184 + 0.875519i \(0.660520\pi\)
\(230\) 0.0952849 0.00628290
\(231\) 0 0
\(232\) 2.77996 0.182514
\(233\) 4.56710 0.299200 0.149600 0.988747i \(-0.452201\pi\)
0.149600 + 0.988747i \(0.452201\pi\)
\(234\) −5.69742 −0.372452
\(235\) 0.411760 0.0268603
\(236\) −8.03940 −0.523320
\(237\) −6.18509 −0.401765
\(238\) 0 0
\(239\) 15.1362 0.979079 0.489540 0.871981i \(-0.337165\pi\)
0.489540 + 0.871981i \(0.337165\pi\)
\(240\) −0.224867 −0.0145151
\(241\) −12.9806 −0.836153 −0.418077 0.908412i \(-0.637296\pi\)
−0.418077 + 0.908412i \(0.637296\pi\)
\(242\) 18.0715 1.16168
\(243\) 1.00000 0.0641500
\(244\) −10.1447 −0.649445
\(245\) 0 0
\(246\) −1.64639 −0.104970
\(247\) −22.0988 −1.40611
\(248\) 1.56189 0.0991801
\(249\) −2.20561 −0.139775
\(250\) 0.752892 0.0476171
\(251\) −21.8010 −1.37607 −0.688033 0.725679i \(-0.741526\pi\)
−0.688033 + 0.725679i \(0.741526\pi\)
\(252\) 0 0
\(253\) −0.194247 −0.0122122
\(254\) 1.40356 0.0880671
\(255\) −0.0326253 −0.00204307
\(256\) 15.1564 0.947274
\(257\) −8.80386 −0.549170 −0.274585 0.961563i \(-0.588540\pi\)
−0.274585 + 0.961563i \(0.588540\pi\)
\(258\) −3.94428 −0.245560
\(259\) 0 0
\(260\) 0.112476 0.00697546
\(261\) 1.30954 0.0810582
\(262\) 17.5058 1.08151
\(263\) −24.6440 −1.51962 −0.759808 0.650147i \(-0.774707\pi\)
−0.759808 + 0.650147i \(0.774707\pi\)
\(264\) 0.325893 0.0200573
\(265\) −0.646350 −0.0397050
\(266\) 0 0
\(267\) −14.3331 −0.877169
\(268\) −9.49375 −0.579923
\(269\) −13.5580 −0.826648 −0.413324 0.910584i \(-0.635632\pi\)
−0.413324 + 0.910584i \(0.635632\pi\)
\(270\) −0.0753050 −0.00458292
\(271\) 19.5011 1.18461 0.592305 0.805714i \(-0.298218\pi\)
0.592305 + 0.805714i \(0.298218\pi\)
\(272\) 3.50668 0.212624
\(273\) 0 0
\(274\) −34.9430 −2.11098
\(275\) −0.767259 −0.0462674
\(276\) −0.899130 −0.0541213
\(277\) 9.02931 0.542519 0.271259 0.962506i \(-0.412560\pi\)
0.271259 + 0.962506i \(0.412560\pi\)
\(278\) −19.8198 −1.18871
\(279\) 0.735747 0.0440480
\(280\) 0 0
\(281\) 0.893294 0.0532895 0.0266447 0.999645i \(-0.491518\pi\)
0.0266447 + 0.999645i \(0.491518\pi\)
\(282\) −14.8213 −0.882594
\(283\) 20.6014 1.22463 0.612313 0.790615i \(-0.290239\pi\)
0.612313 + 0.790615i \(0.290239\pi\)
\(284\) −4.69334 −0.278498
\(285\) −0.292088 −0.0173018
\(286\) −0.874645 −0.0517189
\(287\) 0 0
\(288\) 3.84832 0.226765
\(289\) −16.4912 −0.970072
\(290\) −0.0986146 −0.00579085
\(291\) −8.42652 −0.493971
\(292\) 11.2778 0.659985
\(293\) 17.0744 0.997495 0.498747 0.866747i \(-0.333794\pi\)
0.498747 + 0.866747i \(0.333794\pi\)
\(294\) 0 0
\(295\) −0.517479 −0.0301288
\(296\) 19.3711 1.12592
\(297\) 0.153516 0.00890790
\(298\) 25.6114 1.48363
\(299\) −4.37871 −0.253228
\(300\) −3.55149 −0.205045
\(301\) 0 0
\(302\) −38.1085 −2.19290
\(303\) −4.27869 −0.245804
\(304\) 31.3946 1.80061
\(305\) −0.652991 −0.0373901
\(306\) 1.17434 0.0671327
\(307\) 6.13820 0.350325 0.175163 0.984539i \(-0.443955\pi\)
0.175163 + 0.984539i \(0.443955\pi\)
\(308\) 0 0
\(309\) 8.86287 0.504191
\(310\) −0.0554055 −0.00314682
\(311\) 15.6468 0.887247 0.443624 0.896213i \(-0.353693\pi\)
0.443624 + 0.896213i \(0.353693\pi\)
\(312\) 7.34629 0.415901
\(313\) 16.9514 0.958150 0.479075 0.877774i \(-0.340972\pi\)
0.479075 + 0.877774i \(0.340972\pi\)
\(314\) −22.3298 −1.26015
\(315\) 0 0
\(316\) −4.39509 −0.247243
\(317\) −8.16987 −0.458866 −0.229433 0.973324i \(-0.573687\pi\)
−0.229433 + 0.973324i \(0.573687\pi\)
\(318\) 23.2653 1.30465
\(319\) 0.201035 0.0112558
\(320\) 0.159935 0.00894065
\(321\) 2.93535 0.163836
\(322\) 0 0
\(323\) 4.55496 0.253445
\(324\) 0.710595 0.0394775
\(325\) −17.2955 −0.959384
\(326\) −31.0748 −1.72108
\(327\) −8.56169 −0.473462
\(328\) 2.12286 0.117215
\(329\) 0 0
\(330\) −0.0115605 −0.000636386 0
\(331\) 7.85298 0.431639 0.215820 0.976433i \(-0.430758\pi\)
0.215820 + 0.976433i \(0.430758\pi\)
\(332\) −1.56729 −0.0860163
\(333\) 9.12498 0.500046
\(334\) −1.82738 −0.0999900
\(335\) −0.611093 −0.0333876
\(336\) 0 0
\(337\) −10.3559 −0.564124 −0.282062 0.959396i \(-0.591018\pi\)
−0.282062 + 0.959396i \(0.591018\pi\)
\(338\) 1.68679 0.0917495
\(339\) 8.56761 0.465328
\(340\) −0.0231834 −0.00125729
\(341\) 0.112949 0.00611653
\(342\) 10.5137 0.568514
\(343\) 0 0
\(344\) 5.08578 0.274207
\(345\) −0.0578751 −0.00311589
\(346\) 35.7032 1.91941
\(347\) −28.8340 −1.54789 −0.773944 0.633254i \(-0.781719\pi\)
−0.773944 + 0.633254i \(0.781719\pi\)
\(348\) 0.930549 0.0498827
\(349\) −2.39890 −0.128410 −0.0642051 0.997937i \(-0.520451\pi\)
−0.0642051 + 0.997937i \(0.520451\pi\)
\(350\) 0 0
\(351\) 3.46056 0.184711
\(352\) 0.590779 0.0314886
\(353\) −0.720190 −0.0383318 −0.0191659 0.999816i \(-0.506101\pi\)
−0.0191659 + 0.999816i \(0.506101\pi\)
\(354\) 18.6266 0.989993
\(355\) −0.302100 −0.0160338
\(356\) −10.1850 −0.539804
\(357\) 0 0
\(358\) 11.6225 0.614271
\(359\) −18.3701 −0.969535 −0.484767 0.874643i \(-0.661096\pi\)
−0.484767 + 0.874643i \(0.661096\pi\)
\(360\) 0.0970987 0.00511755
\(361\) 21.7797 1.14630
\(362\) −21.5792 −1.13418
\(363\) −10.9764 −0.576113
\(364\) 0 0
\(365\) 0.725930 0.0379969
\(366\) 23.5043 1.22859
\(367\) −7.81632 −0.408009 −0.204004 0.978970i \(-0.565396\pi\)
−0.204004 + 0.978970i \(0.565396\pi\)
\(368\) 6.22062 0.324272
\(369\) 1.00000 0.0520579
\(370\) −0.687157 −0.0357236
\(371\) 0 0
\(372\) 0.522818 0.0271069
\(373\) −24.2133 −1.25372 −0.626859 0.779133i \(-0.715660\pi\)
−0.626859 + 0.779133i \(0.715660\pi\)
\(374\) 0.180280 0.00932208
\(375\) −0.457299 −0.0236148
\(376\) 19.1106 0.985555
\(377\) 4.53172 0.233396
\(378\) 0 0
\(379\) −15.6238 −0.802538 −0.401269 0.915960i \(-0.631431\pi\)
−0.401269 + 0.915960i \(0.631431\pi\)
\(380\) −0.207556 −0.0106474
\(381\) −0.852507 −0.0436753
\(382\) −15.6648 −0.801483
\(383\) 32.9203 1.68215 0.841073 0.540921i \(-0.181924\pi\)
0.841073 + 0.540921i \(0.181924\pi\)
\(384\) −13.4535 −0.686546
\(385\) 0 0
\(386\) 16.7286 0.851463
\(387\) 2.39572 0.121781
\(388\) −5.98784 −0.303987
\(389\) −22.7504 −1.15349 −0.576745 0.816924i \(-0.695678\pi\)
−0.576745 + 0.816924i \(0.695678\pi\)
\(390\) −0.260597 −0.0131959
\(391\) 0.902533 0.0456431
\(392\) 0 0
\(393\) −10.6329 −0.536358
\(394\) −12.4158 −0.625501
\(395\) −0.282903 −0.0142344
\(396\) 0.109088 0.00548186
\(397\) −5.59969 −0.281040 −0.140520 0.990078i \(-0.544877\pi\)
−0.140520 + 0.990078i \(0.544877\pi\)
\(398\) −42.6796 −2.13934
\(399\) 0 0
\(400\) 24.5709 1.22855
\(401\) −24.1918 −1.20808 −0.604041 0.796953i \(-0.706444\pi\)
−0.604041 + 0.796953i \(0.706444\pi\)
\(402\) 21.9962 1.09707
\(403\) 2.54610 0.126830
\(404\) −3.04042 −0.151266
\(405\) 0.0457395 0.00227281
\(406\) 0 0
\(407\) 1.40083 0.0694366
\(408\) −1.51420 −0.0749643
\(409\) −18.2159 −0.900716 −0.450358 0.892848i \(-0.648704\pi\)
−0.450358 + 0.892848i \(0.648704\pi\)
\(410\) −0.0753050 −0.00371905
\(411\) 21.2240 1.04690
\(412\) 6.29791 0.310276
\(413\) 0 0
\(414\) 2.08321 0.102384
\(415\) −0.100883 −0.00495217
\(416\) 13.3173 0.652937
\(417\) 12.0384 0.589521
\(418\) 1.61402 0.0789441
\(419\) −39.5625 −1.93275 −0.966377 0.257128i \(-0.917224\pi\)
−0.966377 + 0.257128i \(0.917224\pi\)
\(420\) 0 0
\(421\) −33.8389 −1.64921 −0.824603 0.565712i \(-0.808601\pi\)
−0.824603 + 0.565712i \(0.808601\pi\)
\(422\) 23.4980 1.14386
\(423\) 9.00229 0.437706
\(424\) −29.9984 −1.45685
\(425\) 3.56493 0.172925
\(426\) 10.8741 0.526850
\(427\) 0 0
\(428\) 2.08585 0.100823
\(429\) 0.531251 0.0256490
\(430\) −0.180410 −0.00870012
\(431\) −16.8579 −0.812016 −0.406008 0.913869i \(-0.633080\pi\)
−0.406008 + 0.913869i \(0.633080\pi\)
\(432\) −4.91624 −0.236533
\(433\) −2.77987 −0.133592 −0.0667961 0.997767i \(-0.521278\pi\)
−0.0667961 + 0.997767i \(0.521278\pi\)
\(434\) 0 0
\(435\) 0.0598975 0.00287187
\(436\) −6.08389 −0.291365
\(437\) 8.08020 0.386529
\(438\) −26.1298 −1.24853
\(439\) −15.5531 −0.742309 −0.371154 0.928571i \(-0.621038\pi\)
−0.371154 + 0.928571i \(0.621038\pi\)
\(440\) 0.0149062 0.000710625 0
\(441\) 0 0
\(442\) 4.06388 0.193299
\(443\) −19.3228 −0.918056 −0.459028 0.888422i \(-0.651802\pi\)
−0.459028 + 0.888422i \(0.651802\pi\)
\(444\) 6.48416 0.307725
\(445\) −0.655587 −0.0310778
\(446\) 25.5627 1.21043
\(447\) −15.5561 −0.735779
\(448\) 0 0
\(449\) −29.7895 −1.40585 −0.702926 0.711263i \(-0.748124\pi\)
−0.702926 + 0.711263i \(0.748124\pi\)
\(450\) 8.22850 0.387895
\(451\) 0.153516 0.00722879
\(452\) 6.08810 0.286360
\(453\) 23.1467 1.08753
\(454\) 36.2590 1.70172
\(455\) 0 0
\(456\) −13.5564 −0.634835
\(457\) −19.4583 −0.910223 −0.455111 0.890434i \(-0.650401\pi\)
−0.455111 + 0.890434i \(0.650401\pi\)
\(458\) 24.0765 1.12502
\(459\) −0.713284 −0.0332933
\(460\) −0.0411258 −0.00191750
\(461\) −8.86653 −0.412955 −0.206478 0.978451i \(-0.566200\pi\)
−0.206478 + 0.978451i \(0.566200\pi\)
\(462\) 0 0
\(463\) 23.0442 1.07096 0.535478 0.844549i \(-0.320131\pi\)
0.535478 + 0.844549i \(0.320131\pi\)
\(464\) −6.43800 −0.298877
\(465\) 0.0336527 0.00156061
\(466\) −7.51921 −0.348321
\(467\) −6.62006 −0.306340 −0.153170 0.988200i \(-0.548948\pi\)
−0.153170 + 0.988200i \(0.548948\pi\)
\(468\) 2.45905 0.113670
\(469\) 0 0
\(470\) −0.677918 −0.0312700
\(471\) 13.5629 0.624946
\(472\) −24.0172 −1.10548
\(473\) 0.367781 0.0169106
\(474\) 10.1831 0.467723
\(475\) 31.9161 1.46441
\(476\) 0 0
\(477\) −14.1311 −0.647019
\(478\) −24.9201 −1.13982
\(479\) 16.9788 0.775782 0.387891 0.921705i \(-0.373204\pi\)
0.387891 + 0.921705i \(0.373204\pi\)
\(480\) 0.176020 0.00803420
\(481\) 31.5775 1.43981
\(482\) 21.3711 0.973426
\(483\) 0 0
\(484\) −7.79980 −0.354536
\(485\) −0.385425 −0.0175012
\(486\) −1.64639 −0.0746817
\(487\) 18.3314 0.830677 0.415338 0.909667i \(-0.363663\pi\)
0.415338 + 0.909667i \(0.363663\pi\)
\(488\) −30.3066 −1.37192
\(489\) 18.8746 0.853537
\(490\) 0 0
\(491\) −6.45168 −0.291160 −0.145580 0.989346i \(-0.546505\pi\)
−0.145580 + 0.989346i \(0.546505\pi\)
\(492\) 0.710595 0.0320361
\(493\) −0.934072 −0.0420685
\(494\) 36.3831 1.63696
\(495\) 0.00702175 0.000315604 0
\(496\) −3.61711 −0.162413
\(497\) 0 0
\(498\) 3.63128 0.162722
\(499\) 9.71812 0.435043 0.217521 0.976056i \(-0.430203\pi\)
0.217521 + 0.976056i \(0.430203\pi\)
\(500\) −0.324955 −0.0145324
\(501\) 1.10994 0.0495882
\(502\) 35.8929 1.60198
\(503\) 19.3611 0.863269 0.431634 0.902049i \(-0.357937\pi\)
0.431634 + 0.902049i \(0.357937\pi\)
\(504\) 0 0
\(505\) −0.195705 −0.00870877
\(506\) 0.319806 0.0142171
\(507\) −1.02454 −0.0455015
\(508\) −0.605787 −0.0268775
\(509\) 4.52576 0.200601 0.100300 0.994957i \(-0.468020\pi\)
0.100300 + 0.994957i \(0.468020\pi\)
\(510\) 0.0537139 0.00237849
\(511\) 0 0
\(512\) 1.95371 0.0863426
\(513\) −6.38590 −0.281944
\(514\) 14.4946 0.639328
\(515\) 0.405383 0.0178633
\(516\) 1.70239 0.0749433
\(517\) 1.38200 0.0607801
\(518\) 0 0
\(519\) −21.6857 −0.951899
\(520\) 0.336015 0.0147353
\(521\) −6.12296 −0.268252 −0.134126 0.990964i \(-0.542823\pi\)
−0.134126 + 0.990964i \(0.542823\pi\)
\(522\) −2.15600 −0.0943658
\(523\) 12.0382 0.526394 0.263197 0.964742i \(-0.415223\pi\)
0.263197 + 0.964742i \(0.415223\pi\)
\(524\) −7.55567 −0.330071
\(525\) 0 0
\(526\) 40.5737 1.76910
\(527\) −0.524797 −0.0228605
\(528\) −0.754722 −0.0328451
\(529\) −21.3990 −0.930390
\(530\) 1.06414 0.0462234
\(531\) −11.3136 −0.490969
\(532\) 0 0
\(533\) 3.46056 0.149893
\(534\) 23.5978 1.02118
\(535\) 0.134262 0.00580464
\(536\) −28.3620 −1.22505
\(537\) −7.05942 −0.304636
\(538\) 22.3218 0.962361
\(539\) 0 0
\(540\) 0.0325023 0.00139867
\(541\) −43.0826 −1.85226 −0.926132 0.377199i \(-0.876887\pi\)
−0.926132 + 0.377199i \(0.876887\pi\)
\(542\) −32.1064 −1.37909
\(543\) 13.1070 0.562474
\(544\) −2.74495 −0.117689
\(545\) −0.391607 −0.0167746
\(546\) 0 0
\(547\) −20.8040 −0.889514 −0.444757 0.895651i \(-0.646710\pi\)
−0.444757 + 0.895651i \(0.646710\pi\)
\(548\) 15.0817 0.644257
\(549\) −14.2763 −0.609297
\(550\) 1.26321 0.0538633
\(551\) −8.36256 −0.356257
\(552\) −2.68610 −0.114328
\(553\) 0 0
\(554\) −14.8657 −0.631585
\(555\) 0.417372 0.0177165
\(556\) 8.55440 0.362787
\(557\) −17.5841 −0.745060 −0.372530 0.928020i \(-0.621510\pi\)
−0.372530 + 0.928020i \(0.621510\pi\)
\(558\) −1.21133 −0.0512795
\(559\) 8.29052 0.350652
\(560\) 0 0
\(561\) −0.109501 −0.00462312
\(562\) −1.47071 −0.0620381
\(563\) −17.7830 −0.749463 −0.374731 0.927133i \(-0.622265\pi\)
−0.374731 + 0.927133i \(0.622265\pi\)
\(564\) 6.39698 0.269362
\(565\) 0.391878 0.0164864
\(566\) −33.9179 −1.42568
\(567\) 0 0
\(568\) −14.0211 −0.588311
\(569\) −2.63154 −0.110320 −0.0551599 0.998478i \(-0.517567\pi\)
−0.0551599 + 0.998478i \(0.517567\pi\)
\(570\) 0.480890 0.0201423
\(571\) −5.24279 −0.219404 −0.109702 0.993965i \(-0.534990\pi\)
−0.109702 + 0.993965i \(0.534990\pi\)
\(572\) 0.377504 0.0157842
\(573\) 9.51467 0.397481
\(574\) 0 0
\(575\) 6.32395 0.263727
\(576\) 3.49665 0.145694
\(577\) 30.1299 1.25432 0.627162 0.778888i \(-0.284216\pi\)
0.627162 + 0.778888i \(0.284216\pi\)
\(578\) 27.1510 1.12933
\(579\) −10.1608 −0.422268
\(580\) 0.0425629 0.00176733
\(581\) 0 0
\(582\) 13.8733 0.575068
\(583\) −2.16935 −0.0898454
\(584\) 33.6919 1.39418
\(585\) 0.158284 0.00654425
\(586\) −28.1110 −1.16126
\(587\) −27.5676 −1.13784 −0.568918 0.822394i \(-0.692638\pi\)
−0.568918 + 0.822394i \(0.692638\pi\)
\(588\) 0 0
\(589\) −4.69841 −0.193594
\(590\) 0.851972 0.0350751
\(591\) 7.54126 0.310206
\(592\) −44.8606 −1.84376
\(593\) 18.6723 0.766780 0.383390 0.923586i \(-0.374756\pi\)
0.383390 + 0.923586i \(0.374756\pi\)
\(594\) −0.252747 −0.0103703
\(595\) 0 0
\(596\) −11.0541 −0.452793
\(597\) 25.9232 1.06096
\(598\) 7.20906 0.294801
\(599\) 16.7957 0.686253 0.343127 0.939289i \(-0.388514\pi\)
0.343127 + 0.939289i \(0.388514\pi\)
\(600\) −10.6099 −0.433146
\(601\) −7.92057 −0.323087 −0.161543 0.986866i \(-0.551647\pi\)
−0.161543 + 0.986866i \(0.551647\pi\)
\(602\) 0 0
\(603\) −13.3603 −0.544073
\(604\) 16.4479 0.669257
\(605\) −0.502057 −0.0204115
\(606\) 7.04439 0.286159
\(607\) 29.7076 1.20579 0.602897 0.797819i \(-0.294013\pi\)
0.602897 + 0.797819i \(0.294013\pi\)
\(608\) −24.5750 −0.996648
\(609\) 0 0
\(610\) 1.07508 0.0435286
\(611\) 31.1529 1.26031
\(612\) −0.506856 −0.0204884
\(613\) 21.3366 0.861776 0.430888 0.902406i \(-0.358200\pi\)
0.430888 + 0.902406i \(0.358200\pi\)
\(614\) −10.1059 −0.407839
\(615\) 0.0457395 0.00184440
\(616\) 0 0
\(617\) 5.34012 0.214985 0.107493 0.994206i \(-0.465718\pi\)
0.107493 + 0.994206i \(0.465718\pi\)
\(618\) −14.5917 −0.586965
\(619\) 8.18591 0.329019 0.164510 0.986375i \(-0.447396\pi\)
0.164510 + 0.986375i \(0.447396\pi\)
\(620\) 0.0239135 0.000960387 0
\(621\) −1.26532 −0.0507756
\(622\) −25.7607 −1.03291
\(623\) 0 0
\(624\) −17.0129 −0.681063
\(625\) 24.9686 0.998745
\(626\) −27.9086 −1.11545
\(627\) −0.980337 −0.0391509
\(628\) 9.63774 0.384588
\(629\) −6.50871 −0.259519
\(630\) 0 0
\(631\) 3.64661 0.145169 0.0725845 0.997362i \(-0.476875\pi\)
0.0725845 + 0.997362i \(0.476875\pi\)
\(632\) −13.1301 −0.522287
\(633\) −14.2724 −0.567278
\(634\) 13.4508 0.534199
\(635\) −0.0389933 −0.00154740
\(636\) −10.0415 −0.398171
\(637\) 0 0
\(638\) −0.330981 −0.0131037
\(639\) −6.60480 −0.261282
\(640\) −0.615356 −0.0243241
\(641\) −33.2611 −1.31373 −0.656867 0.754007i \(-0.728119\pi\)
−0.656867 + 0.754007i \(0.728119\pi\)
\(642\) −4.83273 −0.190733
\(643\) 31.6609 1.24858 0.624291 0.781192i \(-0.285388\pi\)
0.624291 + 0.781192i \(0.285388\pi\)
\(644\) 0 0
\(645\) 0.109579 0.00431467
\(646\) −7.49923 −0.295053
\(647\) −19.7459 −0.776291 −0.388146 0.921598i \(-0.626884\pi\)
−0.388146 + 0.921598i \(0.626884\pi\)
\(648\) 2.12286 0.0833939
\(649\) −1.73682 −0.0681762
\(650\) 28.4752 1.11689
\(651\) 0 0
\(652\) 13.4122 0.525261
\(653\) 12.9661 0.507403 0.253702 0.967283i \(-0.418352\pi\)
0.253702 + 0.967283i \(0.418352\pi\)
\(654\) 14.0959 0.551192
\(655\) −0.486343 −0.0190030
\(656\) −4.91624 −0.191947
\(657\) 15.8710 0.619185
\(658\) 0 0
\(659\) 4.26699 0.166218 0.0831091 0.996540i \(-0.473515\pi\)
0.0831091 + 0.996540i \(0.473515\pi\)
\(660\) 0.00498962 0.000194221 0
\(661\) 6.81866 0.265215 0.132608 0.991169i \(-0.457665\pi\)
0.132608 + 0.991169i \(0.457665\pi\)
\(662\) −12.9291 −0.502502
\(663\) −2.46836 −0.0958632
\(664\) −4.68220 −0.181704
\(665\) 0 0
\(666\) −15.0233 −0.582140
\(667\) −1.65698 −0.0641586
\(668\) 0.788714 0.0305163
\(669\) −15.5265 −0.600289
\(670\) 1.00610 0.0388689
\(671\) −2.19164 −0.0846073
\(672\) 0 0
\(673\) −35.9850 −1.38712 −0.693559 0.720400i \(-0.743958\pi\)
−0.693559 + 0.720400i \(0.743958\pi\)
\(674\) 17.0499 0.656738
\(675\) −4.99791 −0.192370
\(676\) −0.728034 −0.0280013
\(677\) 33.0463 1.27007 0.635036 0.772482i \(-0.280985\pi\)
0.635036 + 0.772482i \(0.280985\pi\)
\(678\) −14.1056 −0.541723
\(679\) 0 0
\(680\) −0.0692590 −0.00265596
\(681\) −22.0233 −0.843936
\(682\) −0.185958 −0.00712070
\(683\) 40.0689 1.53319 0.766596 0.642130i \(-0.221949\pi\)
0.766596 + 0.642130i \(0.221949\pi\)
\(684\) −4.53778 −0.173507
\(685\) 0.970776 0.0370914
\(686\) 0 0
\(687\) −14.6238 −0.557933
\(688\) −11.7779 −0.449030
\(689\) −48.9015 −1.86300
\(690\) 0.0952849 0.00362744
\(691\) −13.5466 −0.515335 −0.257668 0.966234i \(-0.582954\pi\)
−0.257668 + 0.966234i \(0.582954\pi\)
\(692\) −15.4098 −0.585792
\(693\) 0 0
\(694\) 47.4719 1.80201
\(695\) 0.550629 0.0208866
\(696\) 2.77996 0.105374
\(697\) −0.713284 −0.0270176
\(698\) 3.94952 0.149492
\(699\) 4.56710 0.172743
\(700\) 0 0
\(701\) 14.1232 0.533428 0.266714 0.963776i \(-0.414062\pi\)
0.266714 + 0.963776i \(0.414062\pi\)
\(702\) −5.69742 −0.215035
\(703\) −58.2712 −2.19774
\(704\) 0.536792 0.0202311
\(705\) 0.411760 0.0155078
\(706\) 1.18571 0.0446249
\(707\) 0 0
\(708\) −8.03940 −0.302139
\(709\) 25.2039 0.946554 0.473277 0.880914i \(-0.343071\pi\)
0.473277 + 0.880914i \(0.343071\pi\)
\(710\) 0.497374 0.0186661
\(711\) −6.18509 −0.231959
\(712\) −30.4271 −1.14030
\(713\) −0.930956 −0.0348646
\(714\) 0 0
\(715\) 0.0242992 0.000908737 0
\(716\) −5.01639 −0.187471
\(717\) 15.1362 0.565272
\(718\) 30.2443 1.12871
\(719\) 3.91519 0.146012 0.0730059 0.997332i \(-0.476741\pi\)
0.0730059 + 0.997332i \(0.476741\pi\)
\(720\) −0.224867 −0.00838028
\(721\) 0 0
\(722\) −35.8578 −1.33449
\(723\) −12.9806 −0.482753
\(724\) 9.31375 0.346143
\(725\) −6.54494 −0.243073
\(726\) 18.0715 0.670695
\(727\) 44.3489 1.64481 0.822406 0.568902i \(-0.192632\pi\)
0.822406 + 0.568902i \(0.192632\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −1.19516 −0.0442350
\(731\) −1.70883 −0.0632033
\(732\) −10.1447 −0.374957
\(733\) 48.1470 1.77835 0.889175 0.457568i \(-0.151279\pi\)
0.889175 + 0.457568i \(0.151279\pi\)
\(734\) 12.8687 0.474993
\(735\) 0 0
\(736\) −4.86936 −0.179487
\(737\) −2.05102 −0.0755502
\(738\) −1.64639 −0.0606044
\(739\) 34.4634 1.26776 0.633878 0.773433i \(-0.281462\pi\)
0.633878 + 0.773433i \(0.281462\pi\)
\(740\) 0.296583 0.0109026
\(741\) −22.0988 −0.811818
\(742\) 0 0
\(743\) −28.7819 −1.05591 −0.527953 0.849273i \(-0.677040\pi\)
−0.527953 + 0.849273i \(0.677040\pi\)
\(744\) 1.56189 0.0572617
\(745\) −0.711529 −0.0260684
\(746\) 39.8645 1.45954
\(747\) −2.20561 −0.0806989
\(748\) −0.0778105 −0.00284503
\(749\) 0 0
\(750\) 0.752892 0.0274917
\(751\) −45.4779 −1.65951 −0.829756 0.558127i \(-0.811520\pi\)
−0.829756 + 0.558127i \(0.811520\pi\)
\(752\) −44.2575 −1.61390
\(753\) −21.8010 −0.794472
\(754\) −7.46098 −0.271713
\(755\) 1.05872 0.0385307
\(756\) 0 0
\(757\) −32.6583 −1.18699 −0.593493 0.804839i \(-0.702252\pi\)
−0.593493 + 0.804839i \(0.702252\pi\)
\(758\) 25.7228 0.934293
\(759\) −0.194247 −0.00705071
\(760\) −0.620062 −0.0224920
\(761\) 22.5014 0.815676 0.407838 0.913054i \(-0.366283\pi\)
0.407838 + 0.913054i \(0.366283\pi\)
\(762\) 1.40356 0.0508456
\(763\) 0 0
\(764\) 6.76108 0.244607
\(765\) −0.0326253 −0.00117957
\(766\) −54.1995 −1.95831
\(767\) −39.1514 −1.41368
\(768\) 15.1564 0.546909
\(769\) 6.24290 0.225125 0.112562 0.993645i \(-0.464094\pi\)
0.112562 + 0.993645i \(0.464094\pi\)
\(770\) 0 0
\(771\) −8.80386 −0.317063
\(772\) −7.22020 −0.259861
\(773\) −21.8999 −0.787684 −0.393842 0.919178i \(-0.628854\pi\)
−0.393842 + 0.919178i \(0.628854\pi\)
\(774\) −3.94428 −0.141774
\(775\) −3.67720 −0.132089
\(776\) −17.8883 −0.642154
\(777\) 0 0
\(778\) 37.4560 1.34286
\(779\) −6.38590 −0.228798
\(780\) 0.112476 0.00402728
\(781\) −1.01394 −0.0362817
\(782\) −1.48592 −0.0531364
\(783\) 1.30954 0.0467990
\(784\) 0 0
\(785\) 0.620361 0.0221416
\(786\) 17.5058 0.624413
\(787\) 37.6171 1.34090 0.670452 0.741953i \(-0.266100\pi\)
0.670452 + 0.741953i \(0.266100\pi\)
\(788\) 5.35878 0.190899
\(789\) −24.6440 −0.877351
\(790\) 0.465768 0.0165713
\(791\) 0 0
\(792\) 0.325893 0.0115801
\(793\) −49.4039 −1.75438
\(794\) 9.21926 0.327179
\(795\) −0.646350 −0.0229237
\(796\) 18.4209 0.652911
\(797\) −20.5650 −0.728449 −0.364224 0.931311i \(-0.618666\pi\)
−0.364224 + 0.931311i \(0.618666\pi\)
\(798\) 0 0
\(799\) −6.42119 −0.227166
\(800\) −19.2336 −0.680009
\(801\) −14.3331 −0.506434
\(802\) 39.8292 1.40642
\(803\) 2.43645 0.0859803
\(804\) −9.49375 −0.334819
\(805\) 0 0
\(806\) −4.19186 −0.147652
\(807\) −13.5580 −0.477265
\(808\) −9.08307 −0.319541
\(809\) −43.8207 −1.54065 −0.770327 0.637649i \(-0.779907\pi\)
−0.770327 + 0.637649i \(0.779907\pi\)
\(810\) −0.0753050 −0.00264595
\(811\) −28.5288 −1.00178 −0.500891 0.865511i \(-0.666994\pi\)
−0.500891 + 0.865511i \(0.666994\pi\)
\(812\) 0 0
\(813\) 19.5011 0.683935
\(814\) −2.30631 −0.0808362
\(815\) 0.863313 0.0302405
\(816\) 3.50668 0.122758
\(817\) −15.2988 −0.535238
\(818\) 29.9904 1.04859
\(819\) 0 0
\(820\) 0.0325023 0.00113503
\(821\) 36.1062 1.26012 0.630058 0.776548i \(-0.283031\pi\)
0.630058 + 0.776548i \(0.283031\pi\)
\(822\) −34.9430 −1.21878
\(823\) 42.3799 1.47727 0.738635 0.674106i \(-0.235471\pi\)
0.738635 + 0.674106i \(0.235471\pi\)
\(824\) 18.8146 0.655439
\(825\) −0.767259 −0.0267125
\(826\) 0 0
\(827\) −52.9489 −1.84121 −0.920606 0.390492i \(-0.872305\pi\)
−0.920606 + 0.390492i \(0.872305\pi\)
\(828\) −0.899130 −0.0312469
\(829\) −9.16919 −0.318459 −0.159230 0.987242i \(-0.550901\pi\)
−0.159230 + 0.987242i \(0.550901\pi\)
\(830\) 0.166093 0.00576518
\(831\) 9.02931 0.313223
\(832\) 12.1004 0.419505
\(833\) 0 0
\(834\) −19.8198 −0.686305
\(835\) 0.0507679 0.00175690
\(836\) −0.696622 −0.0240932
\(837\) 0.735747 0.0254312
\(838\) 65.1352 2.25006
\(839\) −42.6983 −1.47411 −0.737055 0.675833i \(-0.763784\pi\)
−0.737055 + 0.675833i \(0.763784\pi\)
\(840\) 0 0
\(841\) −27.2851 −0.940866
\(842\) 55.7119 1.91996
\(843\) 0.893294 0.0307667
\(844\) −10.1419 −0.349099
\(845\) −0.0468620 −0.00161210
\(846\) −14.8213 −0.509566
\(847\) 0 0
\(848\) 69.4720 2.38568
\(849\) 20.6014 0.707039
\(850\) −5.86926 −0.201314
\(851\) −11.5460 −0.395793
\(852\) −4.69334 −0.160791
\(853\) 12.6282 0.432381 0.216190 0.976351i \(-0.430637\pi\)
0.216190 + 0.976351i \(0.430637\pi\)
\(854\) 0 0
\(855\) −0.292088 −0.00998919
\(856\) 6.23135 0.212983
\(857\) −55.6169 −1.89984 −0.949919 0.312497i \(-0.898835\pi\)
−0.949919 + 0.312497i \(0.898835\pi\)
\(858\) −0.874645 −0.0298599
\(859\) −6.63053 −0.226231 −0.113115 0.993582i \(-0.536083\pi\)
−0.113115 + 0.993582i \(0.536083\pi\)
\(860\) 0.0778663 0.00265522
\(861\) 0 0
\(862\) 27.7546 0.945327
\(863\) −35.9010 −1.22208 −0.611042 0.791598i \(-0.709250\pi\)
−0.611042 + 0.791598i \(0.709250\pi\)
\(864\) 3.84832 0.130923
\(865\) −0.991895 −0.0337255
\(866\) 4.57675 0.155524
\(867\) −16.4912 −0.560071
\(868\) 0 0
\(869\) −0.949510 −0.0322099
\(870\) −0.0986146 −0.00334335
\(871\) −46.2340 −1.56658
\(872\) −18.1753 −0.615492
\(873\) −8.42652 −0.285194
\(874\) −13.3032 −0.449986
\(875\) 0 0
\(876\) 11.2778 0.381042
\(877\) −34.1017 −1.15153 −0.575766 0.817615i \(-0.695296\pi\)
−0.575766 + 0.817615i \(0.695296\pi\)
\(878\) 25.6064 0.864175
\(879\) 17.0744 0.575904
\(880\) −0.0345206 −0.00116369
\(881\) −4.69337 −0.158124 −0.0790619 0.996870i \(-0.525192\pi\)
−0.0790619 + 0.996870i \(0.525192\pi\)
\(882\) 0 0
\(883\) 20.6223 0.693995 0.346998 0.937866i \(-0.387201\pi\)
0.346998 + 0.937866i \(0.387201\pi\)
\(884\) −1.75401 −0.0589936
\(885\) −0.517479 −0.0173949
\(886\) 31.8129 1.06878
\(887\) −4.96347 −0.166657 −0.0833285 0.996522i \(-0.526555\pi\)
−0.0833285 + 0.996522i \(0.526555\pi\)
\(888\) 19.3711 0.650051
\(889\) 0 0
\(890\) 1.07935 0.0361799
\(891\) 0.153516 0.00514298
\(892\) −11.0331 −0.369414
\(893\) −57.4877 −1.92375
\(894\) 25.6114 0.856573
\(895\) −0.322894 −0.0107932
\(896\) 0 0
\(897\) −4.37871 −0.146201
\(898\) 49.0451 1.63665
\(899\) 0.963488 0.0321341
\(900\) −3.55149 −0.118383
\(901\) 10.0795 0.335797
\(902\) −0.252747 −0.00841555
\(903\) 0 0
\(904\) 18.1878 0.604919
\(905\) 0.599507 0.0199283
\(906\) −38.1085 −1.26607
\(907\) −46.7190 −1.55128 −0.775640 0.631176i \(-0.782573\pi\)
−0.775640 + 0.631176i \(0.782573\pi\)
\(908\) −15.6497 −0.519353
\(909\) −4.27869 −0.141915
\(910\) 0 0
\(911\) −7.07687 −0.234467 −0.117234 0.993104i \(-0.537403\pi\)
−0.117234 + 0.993104i \(0.537403\pi\)
\(912\) 31.3946 1.03958
\(913\) −0.338596 −0.0112059
\(914\) 32.0360 1.05966
\(915\) −0.652991 −0.0215872
\(916\) −10.3916 −0.343348
\(917\) 0 0
\(918\) 1.17434 0.0387591
\(919\) 12.9722 0.427914 0.213957 0.976843i \(-0.431365\pi\)
0.213957 + 0.976843i \(0.431365\pi\)
\(920\) −0.122861 −0.00405060
\(921\) 6.13820 0.202261
\(922\) 14.5977 0.480751
\(923\) −22.8563 −0.752324
\(924\) 0 0
\(925\) −45.6058 −1.49951
\(926\) −37.9398 −1.24678
\(927\) 8.86287 0.291095
\(928\) 5.03952 0.165430
\(929\) 17.1271 0.561921 0.280961 0.959719i \(-0.409347\pi\)
0.280961 + 0.959719i \(0.409347\pi\)
\(930\) −0.0554055 −0.00181682
\(931\) 0 0
\(932\) 3.24536 0.106305
\(933\) 15.6468 0.512253
\(934\) 10.8992 0.356633
\(935\) −0.00500850 −0.000163796 0
\(936\) 7.34629 0.240121
\(937\) 51.2625 1.67467 0.837337 0.546687i \(-0.184111\pi\)
0.837337 + 0.546687i \(0.184111\pi\)
\(938\) 0 0
\(939\) 16.9514 0.553188
\(940\) 0.292595 0.00954339
\(941\) 35.2503 1.14913 0.574564 0.818460i \(-0.305172\pi\)
0.574564 + 0.818460i \(0.305172\pi\)
\(942\) −22.3298 −0.727545
\(943\) −1.26532 −0.0412045
\(944\) 55.6205 1.81029
\(945\) 0 0
\(946\) −0.605510 −0.0196868
\(947\) −36.1653 −1.17521 −0.587607 0.809146i \(-0.699930\pi\)
−0.587607 + 0.809146i \(0.699930\pi\)
\(948\) −4.39509 −0.142746
\(949\) 54.9224 1.78286
\(950\) −52.5463 −1.70483
\(951\) −8.16987 −0.264926
\(952\) 0 0
\(953\) −19.7601 −0.640093 −0.320046 0.947402i \(-0.603699\pi\)
−0.320046 + 0.947402i \(0.603699\pi\)
\(954\) 23.2653 0.753242
\(955\) 0.435196 0.0140826
\(956\) 10.7557 0.347864
\(957\) 0.201035 0.00649853
\(958\) −27.9537 −0.903144
\(959\) 0 0
\(960\) 0.159935 0.00516188
\(961\) −30.4587 −0.982538
\(962\) −51.9889 −1.67619
\(963\) 2.93535 0.0945905
\(964\) −9.22394 −0.297083
\(965\) −0.464749 −0.0149608
\(966\) 0 0
\(967\) −16.4406 −0.528695 −0.264347 0.964428i \(-0.585157\pi\)
−0.264347 + 0.964428i \(0.585157\pi\)
\(968\) −23.3014 −0.748937
\(969\) 4.55496 0.146326
\(970\) 0.634559 0.0203745
\(971\) 41.5017 1.33185 0.665926 0.746018i \(-0.268037\pi\)
0.665926 + 0.746018i \(0.268037\pi\)
\(972\) 0.710595 0.0227923
\(973\) 0 0
\(974\) −30.1807 −0.967051
\(975\) −17.2955 −0.553901
\(976\) 70.1857 2.24659
\(977\) −10.0675 −0.322089 −0.161044 0.986947i \(-0.551486\pi\)
−0.161044 + 0.986947i \(0.551486\pi\)
\(978\) −31.0748 −0.993664
\(979\) −2.20035 −0.0703236
\(980\) 0 0
\(981\) −8.56169 −0.273354
\(982\) 10.6220 0.338961
\(983\) 49.9216 1.59225 0.796126 0.605132i \(-0.206879\pi\)
0.796126 + 0.605132i \(0.206879\pi\)
\(984\) 2.12286 0.0676744
\(985\) 0.344934 0.0109905
\(986\) 1.53784 0.0489750
\(987\) 0 0
\(988\) −15.7033 −0.499587
\(989\) −3.03135 −0.0963913
\(990\) −0.0115605 −0.000367417 0
\(991\) −27.4632 −0.872397 −0.436199 0.899850i \(-0.643675\pi\)
−0.436199 + 0.899850i \(0.643675\pi\)
\(992\) 2.83140 0.0898969
\(993\) 7.85298 0.249207
\(994\) 0 0
\(995\) 1.18571 0.0375896
\(996\) −1.56729 −0.0496615
\(997\) 15.3608 0.486482 0.243241 0.969966i \(-0.421789\pi\)
0.243241 + 0.969966i \(0.421789\pi\)
\(998\) −15.9998 −0.506465
\(999\) 9.12498 0.288702
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 \(a_p\))