Properties

Label 6027.2.a.bk.1.10
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
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: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.766355\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.766355 q^{2} +1.00000 q^{3} -1.41270 q^{4} -1.12787 q^{5} +0.766355 q^{6} -2.61534 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.766355 q^{2} +1.00000 q^{3} -1.41270 q^{4} -1.12787 q^{5} +0.766355 q^{6} -2.61534 q^{8} +1.00000 q^{9} -0.864345 q^{10} +0.505796 q^{11} -1.41270 q^{12} +6.75326 q^{13} -1.12787 q^{15} +0.821123 q^{16} -3.67233 q^{17} +0.766355 q^{18} -5.76728 q^{19} +1.59334 q^{20} +0.387619 q^{22} -4.22825 q^{23} -2.61534 q^{24} -3.72792 q^{25} +5.17539 q^{26} +1.00000 q^{27} +6.10745 q^{29} -0.864345 q^{30} +6.07935 q^{31} +5.85995 q^{32} +0.505796 q^{33} -2.81431 q^{34} -1.41270 q^{36} -3.42869 q^{37} -4.41978 q^{38} +6.75326 q^{39} +2.94975 q^{40} -1.00000 q^{41} -4.44949 q^{43} -0.714538 q^{44} -1.12787 q^{45} -3.24034 q^{46} -7.61846 q^{47} +0.821123 q^{48} -2.85691 q^{50} -3.67233 q^{51} -9.54033 q^{52} +3.36844 q^{53} +0.766355 q^{54} -0.570470 q^{55} -5.76728 q^{57} +4.68047 q^{58} +8.83914 q^{59} +1.59334 q^{60} +9.19041 q^{61} +4.65894 q^{62} +2.84856 q^{64} -7.61677 q^{65} +0.387619 q^{66} -4.42534 q^{67} +5.18790 q^{68} -4.22825 q^{69} -7.27268 q^{71} -2.61534 q^{72} -3.16427 q^{73} -2.62759 q^{74} -3.72792 q^{75} +8.14744 q^{76} +5.17539 q^{78} +9.39352 q^{79} -0.926116 q^{80} +1.00000 q^{81} -0.766355 q^{82} -15.7109 q^{83} +4.14189 q^{85} -3.40989 q^{86} +6.10745 q^{87} -1.32283 q^{88} -14.1653 q^{89} -0.864345 q^{90} +5.97325 q^{92} +6.07935 q^{93} -5.83845 q^{94} +6.50471 q^{95} +5.85995 q^{96} -10.8666 q^{97} +0.505796 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.766355 0.541895 0.270947 0.962594i \(-0.412663\pi\)
0.270947 + 0.962594i \(0.412663\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.41270 −0.706350
\(5\) −1.12787 −0.504397 −0.252198 0.967676i \(-0.581154\pi\)
−0.252198 + 0.967676i \(0.581154\pi\)
\(6\) 0.766355 0.312863
\(7\) 0 0
\(8\) −2.61534 −0.924662
\(9\) 1.00000 0.333333
\(10\) −0.864345 −0.273330
\(11\) 0.505796 0.152503 0.0762516 0.997089i \(-0.475705\pi\)
0.0762516 + 0.997089i \(0.475705\pi\)
\(12\) −1.41270 −0.407811
\(13\) 6.75326 1.87302 0.936509 0.350645i \(-0.114038\pi\)
0.936509 + 0.350645i \(0.114038\pi\)
\(14\) 0 0
\(15\) −1.12787 −0.291214
\(16\) 0.821123 0.205281
\(17\) −3.67233 −0.890670 −0.445335 0.895364i \(-0.646915\pi\)
−0.445335 + 0.895364i \(0.646915\pi\)
\(18\) 0.766355 0.180632
\(19\) −5.76728 −1.32310 −0.661552 0.749899i \(-0.730102\pi\)
−0.661552 + 0.749899i \(0.730102\pi\)
\(20\) 1.59334 0.356281
\(21\) 0 0
\(22\) 0.387619 0.0826406
\(23\) −4.22825 −0.881652 −0.440826 0.897593i \(-0.645314\pi\)
−0.440826 + 0.897593i \(0.645314\pi\)
\(24\) −2.61534 −0.533854
\(25\) −3.72792 −0.745584
\(26\) 5.17539 1.01498
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 6.10745 1.13413 0.567063 0.823675i \(-0.308080\pi\)
0.567063 + 0.823675i \(0.308080\pi\)
\(30\) −0.864345 −0.157807
\(31\) 6.07935 1.09188 0.545942 0.837823i \(-0.316172\pi\)
0.545942 + 0.837823i \(0.316172\pi\)
\(32\) 5.85995 1.03590
\(33\) 0.505796 0.0880477
\(34\) −2.81431 −0.482649
\(35\) 0 0
\(36\) −1.41270 −0.235450
\(37\) −3.42869 −0.563673 −0.281836 0.959463i \(-0.590944\pi\)
−0.281836 + 0.959463i \(0.590944\pi\)
\(38\) −4.41978 −0.716983
\(39\) 6.75326 1.08139
\(40\) 2.94975 0.466397
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.44949 −0.678541 −0.339270 0.940689i \(-0.610180\pi\)
−0.339270 + 0.940689i \(0.610180\pi\)
\(44\) −0.714538 −0.107721
\(45\) −1.12787 −0.168132
\(46\) −3.24034 −0.477762
\(47\) −7.61846 −1.11127 −0.555634 0.831427i \(-0.687524\pi\)
−0.555634 + 0.831427i \(0.687524\pi\)
\(48\) 0.821123 0.118519
\(49\) 0 0
\(50\) −2.85691 −0.404028
\(51\) −3.67233 −0.514229
\(52\) −9.54033 −1.32301
\(53\) 3.36844 0.462690 0.231345 0.972872i \(-0.425687\pi\)
0.231345 + 0.972872i \(0.425687\pi\)
\(54\) 0.766355 0.104288
\(55\) −0.570470 −0.0769221
\(56\) 0 0
\(57\) −5.76728 −0.763895
\(58\) 4.68047 0.614576
\(59\) 8.83914 1.15076 0.575379 0.817887i \(-0.304855\pi\)
0.575379 + 0.817887i \(0.304855\pi\)
\(60\) 1.59334 0.205699
\(61\) 9.19041 1.17671 0.588356 0.808602i \(-0.299776\pi\)
0.588356 + 0.808602i \(0.299776\pi\)
\(62\) 4.65894 0.591686
\(63\) 0 0
\(64\) 2.84856 0.356069
\(65\) −7.61677 −0.944744
\(66\) 0.387619 0.0477126
\(67\) −4.42534 −0.540641 −0.270321 0.962770i \(-0.587130\pi\)
−0.270321 + 0.962770i \(0.587130\pi\)
\(68\) 5.18790 0.629125
\(69\) −4.22825 −0.509022
\(70\) 0 0
\(71\) −7.27268 −0.863108 −0.431554 0.902087i \(-0.642035\pi\)
−0.431554 + 0.902087i \(0.642035\pi\)
\(72\) −2.61534 −0.308221
\(73\) −3.16427 −0.370350 −0.185175 0.982706i \(-0.559285\pi\)
−0.185175 + 0.982706i \(0.559285\pi\)
\(74\) −2.62759 −0.305451
\(75\) −3.72792 −0.430463
\(76\) 8.14744 0.934575
\(77\) 0 0
\(78\) 5.17539 0.585998
\(79\) 9.39352 1.05685 0.528427 0.848979i \(-0.322782\pi\)
0.528427 + 0.848979i \(0.322782\pi\)
\(80\) −0.926116 −0.103543
\(81\) 1.00000 0.111111
\(82\) −0.766355 −0.0846297
\(83\) −15.7109 −1.72450 −0.862250 0.506483i \(-0.830945\pi\)
−0.862250 + 0.506483i \(0.830945\pi\)
\(84\) 0 0
\(85\) 4.14189 0.449251
\(86\) −3.40989 −0.367698
\(87\) 6.10745 0.654788
\(88\) −1.32283 −0.141014
\(89\) −14.1653 −1.50152 −0.750762 0.660573i \(-0.770313\pi\)
−0.750762 + 0.660573i \(0.770313\pi\)
\(90\) −0.864345 −0.0911100
\(91\) 0 0
\(92\) 5.97325 0.622755
\(93\) 6.07935 0.630399
\(94\) −5.83845 −0.602190
\(95\) 6.50471 0.667370
\(96\) 5.85995 0.598079
\(97\) −10.8666 −1.10333 −0.551667 0.834064i \(-0.686008\pi\)
−0.551667 + 0.834064i \(0.686008\pi\)
\(98\) 0 0
\(99\) 0.505796 0.0508344
\(100\) 5.26643 0.526643
\(101\) −11.9238 −1.18646 −0.593231 0.805033i \(-0.702148\pi\)
−0.593231 + 0.805033i \(0.702148\pi\)
\(102\) −2.81431 −0.278658
\(103\) −7.24511 −0.713882 −0.356941 0.934127i \(-0.616180\pi\)
−0.356941 + 0.934127i \(0.616180\pi\)
\(104\) −17.6621 −1.73191
\(105\) 0 0
\(106\) 2.58142 0.250730
\(107\) −1.87385 −0.181152 −0.0905761 0.995890i \(-0.528871\pi\)
−0.0905761 + 0.995890i \(0.528871\pi\)
\(108\) −1.41270 −0.135937
\(109\) −2.00648 −0.192186 −0.0960931 0.995372i \(-0.530635\pi\)
−0.0960931 + 0.995372i \(0.530635\pi\)
\(110\) −0.437182 −0.0416837
\(111\) −3.42869 −0.325437
\(112\) 0 0
\(113\) −6.17017 −0.580441 −0.290221 0.956960i \(-0.593729\pi\)
−0.290221 + 0.956960i \(0.593729\pi\)
\(114\) −4.41978 −0.413950
\(115\) 4.76890 0.444702
\(116\) −8.62800 −0.801090
\(117\) 6.75326 0.624339
\(118\) 6.77391 0.623589
\(119\) 0 0
\(120\) 2.94975 0.269274
\(121\) −10.7442 −0.976743
\(122\) 7.04311 0.637654
\(123\) −1.00000 −0.0901670
\(124\) −8.58830 −0.771252
\(125\) 9.84392 0.880467
\(126\) 0 0
\(127\) 20.7420 1.84056 0.920280 0.391261i \(-0.127961\pi\)
0.920280 + 0.391261i \(0.127961\pi\)
\(128\) −9.53690 −0.842950
\(129\) −4.44949 −0.391756
\(130\) −5.83715 −0.511952
\(131\) −9.73921 −0.850919 −0.425459 0.904978i \(-0.639887\pi\)
−0.425459 + 0.904978i \(0.639887\pi\)
\(132\) −0.714538 −0.0621925
\(133\) 0 0
\(134\) −3.39138 −0.292971
\(135\) −1.12787 −0.0970712
\(136\) 9.60438 0.823569
\(137\) −12.4467 −1.06340 −0.531698 0.846934i \(-0.678446\pi\)
−0.531698 + 0.846934i \(0.678446\pi\)
\(138\) −3.24034 −0.275836
\(139\) 13.2925 1.12746 0.563728 0.825960i \(-0.309366\pi\)
0.563728 + 0.825960i \(0.309366\pi\)
\(140\) 0 0
\(141\) −7.61846 −0.641590
\(142\) −5.57345 −0.467714
\(143\) 3.41577 0.285641
\(144\) 0.821123 0.0684269
\(145\) −6.88838 −0.572049
\(146\) −2.42496 −0.200691
\(147\) 0 0
\(148\) 4.84371 0.398150
\(149\) 7.77975 0.637342 0.318671 0.947865i \(-0.396764\pi\)
0.318671 + 0.947865i \(0.396764\pi\)
\(150\) −2.85691 −0.233266
\(151\) −12.3630 −1.00609 −0.503044 0.864261i \(-0.667787\pi\)
−0.503044 + 0.864261i \(0.667787\pi\)
\(152\) 15.0834 1.22342
\(153\) −3.67233 −0.296890
\(154\) 0 0
\(155\) −6.85669 −0.550742
\(156\) −9.54033 −0.763838
\(157\) −10.5216 −0.839718 −0.419859 0.907589i \(-0.637920\pi\)
−0.419859 + 0.907589i \(0.637920\pi\)
\(158\) 7.19877 0.572703
\(159\) 3.36844 0.267134
\(160\) −6.60924 −0.522506
\(161\) 0 0
\(162\) 0.766355 0.0602105
\(163\) −14.4331 −1.13049 −0.565244 0.824924i \(-0.691218\pi\)
−0.565244 + 0.824924i \(0.691218\pi\)
\(164\) 1.41270 0.110313
\(165\) −0.570470 −0.0444110
\(166\) −12.0402 −0.934497
\(167\) −13.4981 −1.04451 −0.522257 0.852788i \(-0.674910\pi\)
−0.522257 + 0.852788i \(0.674910\pi\)
\(168\) 0 0
\(169\) 32.6065 2.50819
\(170\) 3.17416 0.243447
\(171\) −5.76728 −0.441035
\(172\) 6.28579 0.479287
\(173\) −16.5440 −1.25782 −0.628910 0.777478i \(-0.716499\pi\)
−0.628910 + 0.777478i \(0.716499\pi\)
\(174\) 4.68047 0.354826
\(175\) 0 0
\(176\) 0.415320 0.0313060
\(177\) 8.83914 0.664390
\(178\) −10.8557 −0.813668
\(179\) 23.5017 1.75660 0.878301 0.478108i \(-0.158677\pi\)
0.878301 + 0.478108i \(0.158677\pi\)
\(180\) 1.59334 0.118760
\(181\) −8.17569 −0.607694 −0.303847 0.952721i \(-0.598271\pi\)
−0.303847 + 0.952721i \(0.598271\pi\)
\(182\) 0 0
\(183\) 9.19041 0.679375
\(184\) 11.0583 0.815230
\(185\) 3.86710 0.284315
\(186\) 4.65894 0.341610
\(187\) −1.85745 −0.135830
\(188\) 10.7626 0.784944
\(189\) 0 0
\(190\) 4.98492 0.361644
\(191\) 5.20526 0.376639 0.188320 0.982108i \(-0.439696\pi\)
0.188320 + 0.982108i \(0.439696\pi\)
\(192\) 2.84856 0.205577
\(193\) −21.7422 −1.56504 −0.782518 0.622628i \(-0.786065\pi\)
−0.782518 + 0.622628i \(0.786065\pi\)
\(194\) −8.32766 −0.597891
\(195\) −7.61677 −0.545448
\(196\) 0 0
\(197\) 10.9913 0.783101 0.391550 0.920157i \(-0.371939\pi\)
0.391550 + 0.920157i \(0.371939\pi\)
\(198\) 0.387619 0.0275469
\(199\) 17.5094 1.24121 0.620606 0.784123i \(-0.286887\pi\)
0.620606 + 0.784123i \(0.286887\pi\)
\(200\) 9.74977 0.689413
\(201\) −4.42534 −0.312139
\(202\) −9.13785 −0.642937
\(203\) 0 0
\(204\) 5.18790 0.363226
\(205\) 1.12787 0.0787735
\(206\) −5.55232 −0.386849
\(207\) −4.22825 −0.293884
\(208\) 5.54525 0.384494
\(209\) −2.91707 −0.201778
\(210\) 0 0
\(211\) 9.79260 0.674150 0.337075 0.941478i \(-0.390562\pi\)
0.337075 + 0.941478i \(0.390562\pi\)
\(212\) −4.75859 −0.326822
\(213\) −7.27268 −0.498316
\(214\) −1.43604 −0.0981654
\(215\) 5.01842 0.342254
\(216\) −2.61534 −0.177951
\(217\) 0 0
\(218\) −1.53768 −0.104145
\(219\) −3.16427 −0.213822
\(220\) 0.805902 0.0543339
\(221\) −24.8002 −1.66824
\(222\) −2.62759 −0.176352
\(223\) −8.69570 −0.582307 −0.291154 0.956676i \(-0.594039\pi\)
−0.291154 + 0.956676i \(0.594039\pi\)
\(224\) 0 0
\(225\) −3.72792 −0.248528
\(226\) −4.72854 −0.314538
\(227\) −27.5856 −1.83092 −0.915460 0.402410i \(-0.868173\pi\)
−0.915460 + 0.402410i \(0.868173\pi\)
\(228\) 8.14744 0.539577
\(229\) −8.18565 −0.540923 −0.270462 0.962731i \(-0.587176\pi\)
−0.270462 + 0.962731i \(0.587176\pi\)
\(230\) 3.65467 0.240982
\(231\) 0 0
\(232\) −15.9731 −1.04868
\(233\) −5.07644 −0.332569 −0.166284 0.986078i \(-0.553177\pi\)
−0.166284 + 0.986078i \(0.553177\pi\)
\(234\) 5.17539 0.338326
\(235\) 8.59260 0.560520
\(236\) −12.4870 −0.812838
\(237\) 9.39352 0.610175
\(238\) 0 0
\(239\) 17.5543 1.13550 0.567748 0.823202i \(-0.307815\pi\)
0.567748 + 0.823202i \(0.307815\pi\)
\(240\) −0.926116 −0.0597805
\(241\) −11.6130 −0.748058 −0.374029 0.927417i \(-0.622024\pi\)
−0.374029 + 0.927417i \(0.622024\pi\)
\(242\) −8.23385 −0.529292
\(243\) 1.00000 0.0641500
\(244\) −12.9833 −0.831170
\(245\) 0 0
\(246\) −0.766355 −0.0488610
\(247\) −38.9479 −2.47820
\(248\) −15.8996 −1.00962
\(249\) −15.7109 −0.995640
\(250\) 7.54393 0.477120
\(251\) −5.85349 −0.369469 −0.184735 0.982788i \(-0.559143\pi\)
−0.184735 + 0.982788i \(0.559143\pi\)
\(252\) 0 0
\(253\) −2.13863 −0.134455
\(254\) 15.8958 0.997389
\(255\) 4.14189 0.259375
\(256\) −13.0058 −0.812860
\(257\) −21.6778 −1.35223 −0.676113 0.736798i \(-0.736337\pi\)
−0.676113 + 0.736798i \(0.736337\pi\)
\(258\) −3.40989 −0.212290
\(259\) 0 0
\(260\) 10.7602 0.667320
\(261\) 6.10745 0.378042
\(262\) −7.46369 −0.461108
\(263\) −2.69289 −0.166051 −0.0830253 0.996547i \(-0.526458\pi\)
−0.0830253 + 0.996547i \(0.526458\pi\)
\(264\) −1.32283 −0.0814144
\(265\) −3.79914 −0.233380
\(266\) 0 0
\(267\) −14.1653 −0.866905
\(268\) 6.25168 0.381882
\(269\) 17.7915 1.08477 0.542383 0.840131i \(-0.317522\pi\)
0.542383 + 0.840131i \(0.317522\pi\)
\(270\) −0.864345 −0.0526024
\(271\) −2.05424 −0.124786 −0.0623931 0.998052i \(-0.519873\pi\)
−0.0623931 + 0.998052i \(0.519873\pi\)
\(272\) −3.01543 −0.182837
\(273\) 0 0
\(274\) −9.53860 −0.576248
\(275\) −1.88557 −0.113704
\(276\) 5.97325 0.359548
\(277\) 11.5640 0.694815 0.347408 0.937714i \(-0.387062\pi\)
0.347408 + 0.937714i \(0.387062\pi\)
\(278\) 10.1868 0.610963
\(279\) 6.07935 0.363961
\(280\) 0 0
\(281\) −10.7124 −0.639050 −0.319525 0.947578i \(-0.603523\pi\)
−0.319525 + 0.947578i \(0.603523\pi\)
\(282\) −5.83845 −0.347674
\(283\) −0.225414 −0.0133995 −0.00669974 0.999978i \(-0.502133\pi\)
−0.00669974 + 0.999978i \(0.502133\pi\)
\(284\) 10.2741 0.609657
\(285\) 6.50471 0.385306
\(286\) 2.61769 0.154787
\(287\) 0 0
\(288\) 5.85995 0.345301
\(289\) −3.51401 −0.206706
\(290\) −5.27895 −0.309990
\(291\) −10.8666 −0.637011
\(292\) 4.47017 0.261597
\(293\) −32.1559 −1.87857 −0.939285 0.343138i \(-0.888510\pi\)
−0.939285 + 0.343138i \(0.888510\pi\)
\(294\) 0 0
\(295\) −9.96935 −0.580438
\(296\) 8.96718 0.521207
\(297\) 0.505796 0.0293492
\(298\) 5.96205 0.345372
\(299\) −28.5545 −1.65135
\(300\) 5.26643 0.304058
\(301\) 0 0
\(302\) −9.47446 −0.545194
\(303\) −11.9238 −0.685004
\(304\) −4.73564 −0.271608
\(305\) −10.3655 −0.593529
\(306\) −2.81431 −0.160883
\(307\) −15.2207 −0.868692 −0.434346 0.900746i \(-0.643020\pi\)
−0.434346 + 0.900746i \(0.643020\pi\)
\(308\) 0 0
\(309\) −7.24511 −0.412160
\(310\) −5.25465 −0.298444
\(311\) 26.7199 1.51515 0.757575 0.652749i \(-0.226384\pi\)
0.757575 + 0.652749i \(0.226384\pi\)
\(312\) −17.6621 −0.999917
\(313\) −18.4588 −1.04335 −0.521676 0.853143i \(-0.674693\pi\)
−0.521676 + 0.853143i \(0.674693\pi\)
\(314\) −8.06330 −0.455039
\(315\) 0 0
\(316\) −13.2702 −0.746509
\(317\) −3.22714 −0.181254 −0.0906271 0.995885i \(-0.528887\pi\)
−0.0906271 + 0.995885i \(0.528887\pi\)
\(318\) 2.58142 0.144759
\(319\) 3.08912 0.172958
\(320\) −3.21279 −0.179600
\(321\) −1.87385 −0.104588
\(322\) 0 0
\(323\) 21.1793 1.17845
\(324\) −1.41270 −0.0784834
\(325\) −25.1756 −1.39649
\(326\) −11.0609 −0.612605
\(327\) −2.00648 −0.110959
\(328\) 2.61534 0.144408
\(329\) 0 0
\(330\) −0.437182 −0.0240661
\(331\) −4.00194 −0.219966 −0.109983 0.993933i \(-0.535080\pi\)
−0.109983 + 0.993933i \(0.535080\pi\)
\(332\) 22.1949 1.21810
\(333\) −3.42869 −0.187891
\(334\) −10.3443 −0.566016
\(335\) 4.99119 0.272698
\(336\) 0 0
\(337\) 1.46519 0.0798139 0.0399069 0.999203i \(-0.487294\pi\)
0.0399069 + 0.999203i \(0.487294\pi\)
\(338\) 24.9882 1.35918
\(339\) −6.17017 −0.335118
\(340\) −5.85125 −0.317329
\(341\) 3.07491 0.166516
\(342\) −4.41978 −0.238994
\(343\) 0 0
\(344\) 11.6369 0.627421
\(345\) 4.76890 0.256749
\(346\) −12.6786 −0.681606
\(347\) 13.1714 0.707077 0.353539 0.935420i \(-0.384978\pi\)
0.353539 + 0.935420i \(0.384978\pi\)
\(348\) −8.62800 −0.462509
\(349\) 23.2638 1.24528 0.622642 0.782507i \(-0.286059\pi\)
0.622642 + 0.782507i \(0.286059\pi\)
\(350\) 0 0
\(351\) 6.75326 0.360462
\(352\) 2.96394 0.157978
\(353\) −32.1766 −1.71259 −0.856295 0.516487i \(-0.827239\pi\)
−0.856295 + 0.516487i \(0.827239\pi\)
\(354\) 6.77391 0.360029
\(355\) 8.20260 0.435349
\(356\) 20.0114 1.06060
\(357\) 0 0
\(358\) 18.0107 0.951893
\(359\) −20.1682 −1.06444 −0.532219 0.846606i \(-0.678642\pi\)
−0.532219 + 0.846606i \(0.678642\pi\)
\(360\) 2.94975 0.155466
\(361\) 14.2615 0.750606
\(362\) −6.26548 −0.329306
\(363\) −10.7442 −0.563923
\(364\) 0 0
\(365\) 3.56887 0.186803
\(366\) 7.04311 0.368149
\(367\) −21.6077 −1.12791 −0.563957 0.825804i \(-0.690722\pi\)
−0.563957 + 0.825804i \(0.690722\pi\)
\(368\) −3.47191 −0.180986
\(369\) −1.00000 −0.0520579
\(370\) 2.96357 0.154069
\(371\) 0 0
\(372\) −8.58830 −0.445282
\(373\) 19.8822 1.02946 0.514730 0.857352i \(-0.327892\pi\)
0.514730 + 0.857352i \(0.327892\pi\)
\(374\) −1.42346 −0.0736056
\(375\) 9.84392 0.508338
\(376\) 19.9249 1.02755
\(377\) 41.2452 2.12424
\(378\) 0 0
\(379\) −15.5450 −0.798494 −0.399247 0.916843i \(-0.630728\pi\)
−0.399247 + 0.916843i \(0.630728\pi\)
\(380\) −9.18921 −0.471397
\(381\) 20.7420 1.06265
\(382\) 3.98908 0.204099
\(383\) −13.0240 −0.665496 −0.332748 0.943016i \(-0.607976\pi\)
−0.332748 + 0.943016i \(0.607976\pi\)
\(384\) −9.53690 −0.486678
\(385\) 0 0
\(386\) −16.6622 −0.848085
\(387\) −4.44949 −0.226180
\(388\) 15.3512 0.779341
\(389\) 22.6507 1.14844 0.574218 0.818702i \(-0.305306\pi\)
0.574218 + 0.818702i \(0.305306\pi\)
\(390\) −5.83715 −0.295575
\(391\) 15.5275 0.785261
\(392\) 0 0
\(393\) −9.73921 −0.491278
\(394\) 8.42327 0.424358
\(395\) −10.5946 −0.533074
\(396\) −0.714538 −0.0359069
\(397\) −12.9295 −0.648915 −0.324458 0.945900i \(-0.605182\pi\)
−0.324458 + 0.945900i \(0.605182\pi\)
\(398\) 13.4184 0.672606
\(399\) 0 0
\(400\) −3.06108 −0.153054
\(401\) −8.28212 −0.413589 −0.206795 0.978384i \(-0.566303\pi\)
−0.206795 + 0.978384i \(0.566303\pi\)
\(402\) −3.39138 −0.169147
\(403\) 41.0554 2.04512
\(404\) 16.8447 0.838057
\(405\) −1.12787 −0.0560441
\(406\) 0 0
\(407\) −1.73421 −0.0859618
\(408\) 9.60438 0.475488
\(409\) −21.5259 −1.06439 −0.532194 0.846622i \(-0.678632\pi\)
−0.532194 + 0.846622i \(0.678632\pi\)
\(410\) 0.864345 0.0426870
\(411\) −12.4467 −0.613951
\(412\) 10.2352 0.504251
\(413\) 0 0
\(414\) −3.24034 −0.159254
\(415\) 17.7198 0.869832
\(416\) 39.5738 1.94026
\(417\) 13.2925 0.650938
\(418\) −2.23551 −0.109342
\(419\) 30.7824 1.50382 0.751910 0.659266i \(-0.229133\pi\)
0.751910 + 0.659266i \(0.229133\pi\)
\(420\) 0 0
\(421\) 25.0081 1.21882 0.609410 0.792855i \(-0.291406\pi\)
0.609410 + 0.792855i \(0.291406\pi\)
\(422\) 7.50460 0.365318
\(423\) −7.61846 −0.370422
\(424\) −8.80961 −0.427832
\(425\) 13.6901 0.664069
\(426\) −5.57345 −0.270035
\(427\) 0 0
\(428\) 2.64719 0.127957
\(429\) 3.41577 0.164915
\(430\) 3.84589 0.185465
\(431\) −3.97054 −0.191254 −0.0956271 0.995417i \(-0.530486\pi\)
−0.0956271 + 0.995417i \(0.530486\pi\)
\(432\) 0.821123 0.0395063
\(433\) −8.38679 −0.403043 −0.201522 0.979484i \(-0.564589\pi\)
−0.201522 + 0.979484i \(0.564589\pi\)
\(434\) 0 0
\(435\) −6.88838 −0.330273
\(436\) 2.83456 0.135751
\(437\) 24.3855 1.16652
\(438\) −2.42496 −0.115869
\(439\) 25.8343 1.23300 0.616502 0.787353i \(-0.288549\pi\)
0.616502 + 0.787353i \(0.288549\pi\)
\(440\) 1.49197 0.0711269
\(441\) 0 0
\(442\) −19.0057 −0.904011
\(443\) 23.0113 1.09330 0.546650 0.837361i \(-0.315903\pi\)
0.546650 + 0.837361i \(0.315903\pi\)
\(444\) 4.84371 0.229872
\(445\) 15.9766 0.757364
\(446\) −6.66400 −0.315549
\(447\) 7.77975 0.367969
\(448\) 0 0
\(449\) −20.7163 −0.977664 −0.488832 0.872378i \(-0.662577\pi\)
−0.488832 + 0.872378i \(0.662577\pi\)
\(450\) −2.85691 −0.134676
\(451\) −0.505796 −0.0238170
\(452\) 8.71661 0.409995
\(453\) −12.3630 −0.580865
\(454\) −21.1403 −0.992165
\(455\) 0 0
\(456\) 15.0834 0.706344
\(457\) −7.29796 −0.341384 −0.170692 0.985324i \(-0.554600\pi\)
−0.170692 + 0.985324i \(0.554600\pi\)
\(458\) −6.27312 −0.293123
\(459\) −3.67233 −0.171410
\(460\) −6.73703 −0.314115
\(461\) −1.10706 −0.0515607 −0.0257804 0.999668i \(-0.508207\pi\)
−0.0257804 + 0.999668i \(0.508207\pi\)
\(462\) 0 0
\(463\) 30.0638 1.39718 0.698592 0.715521i \(-0.253810\pi\)
0.698592 + 0.715521i \(0.253810\pi\)
\(464\) 5.01497 0.232814
\(465\) −6.85669 −0.317971
\(466\) −3.89036 −0.180217
\(467\) 14.1573 0.655121 0.327560 0.944830i \(-0.393773\pi\)
0.327560 + 0.944830i \(0.393773\pi\)
\(468\) −9.54033 −0.441002
\(469\) 0 0
\(470\) 6.58498 0.303743
\(471\) −10.5216 −0.484811
\(472\) −23.1173 −1.06406
\(473\) −2.25053 −0.103480
\(474\) 7.19877 0.330650
\(475\) 21.5000 0.986485
\(476\) 0 0
\(477\) 3.36844 0.154230
\(478\) 13.4529 0.615319
\(479\) −12.8215 −0.585830 −0.292915 0.956138i \(-0.594625\pi\)
−0.292915 + 0.956138i \(0.594625\pi\)
\(480\) −6.60924 −0.301669
\(481\) −23.1548 −1.05577
\(482\) −8.89967 −0.405369
\(483\) 0 0
\(484\) 15.1783 0.689922
\(485\) 12.2560 0.556518
\(486\) 0.766355 0.0347626
\(487\) 23.6224 1.07043 0.535216 0.844715i \(-0.320230\pi\)
0.535216 + 0.844715i \(0.320230\pi\)
\(488\) −24.0360 −1.08806
\(489\) −14.4331 −0.652687
\(490\) 0 0
\(491\) 9.40811 0.424582 0.212291 0.977207i \(-0.431908\pi\)
0.212291 + 0.977207i \(0.431908\pi\)
\(492\) 1.41270 0.0636894
\(493\) −22.4286 −1.01013
\(494\) −29.8479 −1.34292
\(495\) −0.570470 −0.0256407
\(496\) 4.99189 0.224143
\(497\) 0 0
\(498\) −12.0402 −0.539532
\(499\) 15.2824 0.684134 0.342067 0.939676i \(-0.388873\pi\)
0.342067 + 0.939676i \(0.388873\pi\)
\(500\) −13.9065 −0.621918
\(501\) −13.4981 −0.603050
\(502\) −4.48585 −0.200213
\(503\) −34.4513 −1.53611 −0.768053 0.640387i \(-0.778774\pi\)
−0.768053 + 0.640387i \(0.778774\pi\)
\(504\) 0 0
\(505\) 13.4484 0.598447
\(506\) −1.63895 −0.0728603
\(507\) 32.6065 1.44811
\(508\) −29.3023 −1.30008
\(509\) 31.8857 1.41331 0.706655 0.707558i \(-0.250203\pi\)
0.706655 + 0.707558i \(0.250203\pi\)
\(510\) 3.17416 0.140554
\(511\) 0 0
\(512\) 9.10677 0.402466
\(513\) −5.76728 −0.254632
\(514\) −16.6129 −0.732764
\(515\) 8.17151 0.360080
\(516\) 6.28579 0.276717
\(517\) −3.85339 −0.169472
\(518\) 0 0
\(519\) −16.5440 −0.726203
\(520\) 19.9204 0.873569
\(521\) −3.51414 −0.153957 −0.0769786 0.997033i \(-0.524527\pi\)
−0.0769786 + 0.997033i \(0.524527\pi\)
\(522\) 4.68047 0.204859
\(523\) 32.0761 1.40259 0.701294 0.712872i \(-0.252606\pi\)
0.701294 + 0.712872i \(0.252606\pi\)
\(524\) 13.7586 0.601046
\(525\) 0 0
\(526\) −2.06371 −0.0899820
\(527\) −22.3254 −0.972508
\(528\) 0.415320 0.0180745
\(529\) −5.12188 −0.222690
\(530\) −2.91149 −0.126467
\(531\) 8.83914 0.383586
\(532\) 0 0
\(533\) −6.75326 −0.292516
\(534\) −10.8557 −0.469771
\(535\) 2.11345 0.0913726
\(536\) 11.5738 0.499911
\(537\) 23.5017 1.01417
\(538\) 13.6346 0.587829
\(539\) 0 0
\(540\) 1.59334 0.0685663
\(541\) −8.05835 −0.346456 −0.173228 0.984882i \(-0.555420\pi\)
−0.173228 + 0.984882i \(0.555420\pi\)
\(542\) −1.57428 −0.0676210
\(543\) −8.17569 −0.350853
\(544\) −21.5197 −0.922648
\(545\) 2.26304 0.0969381
\(546\) 0 0
\(547\) −9.63509 −0.411967 −0.205983 0.978556i \(-0.566039\pi\)
−0.205983 + 0.978556i \(0.566039\pi\)
\(548\) 17.5835 0.751129
\(549\) 9.19041 0.392237
\(550\) −1.44501 −0.0616155
\(551\) −35.2234 −1.50057
\(552\) 11.0583 0.470673
\(553\) 0 0
\(554\) 8.86215 0.376517
\(555\) 3.86710 0.164149
\(556\) −18.7783 −0.796379
\(557\) 25.9730 1.10051 0.550256 0.834996i \(-0.314530\pi\)
0.550256 + 0.834996i \(0.314530\pi\)
\(558\) 4.65894 0.197229
\(559\) −30.0486 −1.27092
\(560\) 0 0
\(561\) −1.85745 −0.0784215
\(562\) −8.20952 −0.346298
\(563\) −16.1320 −0.679882 −0.339941 0.940447i \(-0.610407\pi\)
−0.339941 + 0.940447i \(0.610407\pi\)
\(564\) 10.7626 0.453187
\(565\) 6.95913 0.292773
\(566\) −0.172747 −0.00726111
\(567\) 0 0
\(568\) 19.0205 0.798084
\(569\) 18.7660 0.786711 0.393356 0.919386i \(-0.371314\pi\)
0.393356 + 0.919386i \(0.371314\pi\)
\(570\) 4.98492 0.208795
\(571\) −20.3044 −0.849712 −0.424856 0.905261i \(-0.639675\pi\)
−0.424856 + 0.905261i \(0.639675\pi\)
\(572\) −4.82546 −0.201763
\(573\) 5.20526 0.217453
\(574\) 0 0
\(575\) 15.7626 0.657345
\(576\) 2.84856 0.118690
\(577\) 1.59700 0.0664841 0.0332421 0.999447i \(-0.489417\pi\)
0.0332421 + 0.999447i \(0.489417\pi\)
\(578\) −2.69298 −0.112013
\(579\) −21.7422 −0.903574
\(580\) 9.73122 0.404067
\(581\) 0 0
\(582\) −8.32766 −0.345193
\(583\) 1.70374 0.0705618
\(584\) 8.27564 0.342449
\(585\) −7.61677 −0.314915
\(586\) −24.6429 −1.01799
\(587\) 27.8719 1.15040 0.575198 0.818015i \(-0.304925\pi\)
0.575198 + 0.818015i \(0.304925\pi\)
\(588\) 0 0
\(589\) −35.0613 −1.44468
\(590\) −7.64006 −0.314536
\(591\) 10.9913 0.452123
\(592\) −2.81537 −0.115711
\(593\) −9.09010 −0.373286 −0.186643 0.982428i \(-0.559761\pi\)
−0.186643 + 0.982428i \(0.559761\pi\)
\(594\) 0.387619 0.0159042
\(595\) 0 0
\(596\) −10.9904 −0.450186
\(597\) 17.5094 0.716614
\(598\) −21.8829 −0.894857
\(599\) −7.64371 −0.312314 −0.156157 0.987732i \(-0.549911\pi\)
−0.156157 + 0.987732i \(0.549911\pi\)
\(600\) 9.74977 0.398033
\(601\) 27.7148 1.13051 0.565256 0.824916i \(-0.308778\pi\)
0.565256 + 0.824916i \(0.308778\pi\)
\(602\) 0 0
\(603\) −4.42534 −0.180214
\(604\) 17.4652 0.710650
\(605\) 12.1180 0.492666
\(606\) −9.13785 −0.371200
\(607\) 39.2113 1.59154 0.795768 0.605601i \(-0.207067\pi\)
0.795768 + 0.605601i \(0.207067\pi\)
\(608\) −33.7960 −1.37061
\(609\) 0 0
\(610\) −7.94369 −0.321630
\(611\) −51.4495 −2.08142
\(612\) 5.18790 0.209708
\(613\) 46.2473 1.86791 0.933955 0.357390i \(-0.116333\pi\)
0.933955 + 0.357390i \(0.116333\pi\)
\(614\) −11.6645 −0.470740
\(615\) 1.12787 0.0454799
\(616\) 0 0
\(617\) 26.2002 1.05478 0.527391 0.849623i \(-0.323170\pi\)
0.527391 + 0.849623i \(0.323170\pi\)
\(618\) −5.55232 −0.223347
\(619\) −3.17574 −0.127644 −0.0638218 0.997961i \(-0.520329\pi\)
−0.0638218 + 0.997961i \(0.520329\pi\)
\(620\) 9.68644 0.389017
\(621\) −4.22825 −0.169674
\(622\) 20.4770 0.821051
\(623\) 0 0
\(624\) 5.54525 0.221988
\(625\) 7.53698 0.301479
\(626\) −14.1460 −0.565387
\(627\) −2.91707 −0.116496
\(628\) 14.8639 0.593135
\(629\) 12.5913 0.502046
\(630\) 0 0
\(631\) 43.4535 1.72986 0.864928 0.501895i \(-0.167364\pi\)
0.864928 + 0.501895i \(0.167364\pi\)
\(632\) −24.5672 −0.977232
\(633\) 9.79260 0.389221
\(634\) −2.47313 −0.0982207
\(635\) −23.3942 −0.928372
\(636\) −4.75859 −0.188690
\(637\) 0 0
\(638\) 2.36736 0.0937248
\(639\) −7.27268 −0.287703
\(640\) 10.7563 0.425181
\(641\) −40.0592 −1.58224 −0.791122 0.611658i \(-0.790503\pi\)
−0.791122 + 0.611658i \(0.790503\pi\)
\(642\) −1.43604 −0.0566758
\(643\) 32.7442 1.29130 0.645652 0.763632i \(-0.276586\pi\)
0.645652 + 0.763632i \(0.276586\pi\)
\(644\) 0 0
\(645\) 5.01842 0.197600
\(646\) 16.2309 0.638596
\(647\) −4.12798 −0.162288 −0.0811438 0.996702i \(-0.525857\pi\)
−0.0811438 + 0.996702i \(0.525857\pi\)
\(648\) −2.61534 −0.102740
\(649\) 4.47080 0.175494
\(650\) −19.2934 −0.756751
\(651\) 0 0
\(652\) 20.3896 0.798520
\(653\) 7.69886 0.301279 0.150640 0.988589i \(-0.451867\pi\)
0.150640 + 0.988589i \(0.451867\pi\)
\(654\) −1.53768 −0.0601279
\(655\) 10.9845 0.429201
\(656\) −0.821123 −0.0320595
\(657\) −3.16427 −0.123450
\(658\) 0 0
\(659\) 31.5274 1.22813 0.614067 0.789254i \(-0.289532\pi\)
0.614067 + 0.789254i \(0.289532\pi\)
\(660\) 0.805902 0.0313697
\(661\) 7.77588 0.302447 0.151223 0.988500i \(-0.451679\pi\)
0.151223 + 0.988500i \(0.451679\pi\)
\(662\) −3.06690 −0.119199
\(663\) −24.8002 −0.963159
\(664\) 41.0894 1.59458
\(665\) 0 0
\(666\) −2.62759 −0.101817
\(667\) −25.8238 −0.999903
\(668\) 19.0688 0.737792
\(669\) −8.69570 −0.336195
\(670\) 3.82502 0.147773
\(671\) 4.64847 0.179452
\(672\) 0 0
\(673\) −3.55165 −0.136906 −0.0684531 0.997654i \(-0.521806\pi\)
−0.0684531 + 0.997654i \(0.521806\pi\)
\(674\) 1.12285 0.0432507
\(675\) −3.72792 −0.143488
\(676\) −46.0632 −1.77166
\(677\) −33.2487 −1.27785 −0.638925 0.769269i \(-0.720621\pi\)
−0.638925 + 0.769269i \(0.720621\pi\)
\(678\) −4.72854 −0.181599
\(679\) 0 0
\(680\) −10.8325 −0.415406
\(681\) −27.5856 −1.05708
\(682\) 2.35647 0.0902339
\(683\) −42.8834 −1.64089 −0.820443 0.571728i \(-0.806273\pi\)
−0.820443 + 0.571728i \(0.806273\pi\)
\(684\) 8.14744 0.311525
\(685\) 14.0382 0.536373
\(686\) 0 0
\(687\) −8.18565 −0.312302
\(688\) −3.65358 −0.139291
\(689\) 22.7479 0.866627
\(690\) 3.65467 0.139131
\(691\) 35.1976 1.33898 0.669489 0.742822i \(-0.266513\pi\)
0.669489 + 0.742822i \(0.266513\pi\)
\(692\) 23.3718 0.888461
\(693\) 0 0
\(694\) 10.0940 0.383161
\(695\) −14.9922 −0.568686
\(696\) −15.9731 −0.605457
\(697\) 3.67233 0.139099
\(698\) 17.8283 0.674812
\(699\) −5.07644 −0.192009
\(700\) 0 0
\(701\) −25.4326 −0.960577 −0.480289 0.877111i \(-0.659468\pi\)
−0.480289 + 0.877111i \(0.659468\pi\)
\(702\) 5.17539 0.195333
\(703\) 19.7742 0.745798
\(704\) 1.44079 0.0543017
\(705\) 8.59260 0.323616
\(706\) −24.6587 −0.928043
\(707\) 0 0
\(708\) −12.4870 −0.469292
\(709\) −30.5452 −1.14715 −0.573575 0.819153i \(-0.694444\pi\)
−0.573575 + 0.819153i \(0.694444\pi\)
\(710\) 6.28611 0.235913
\(711\) 9.39352 0.352285
\(712\) 37.0472 1.38840
\(713\) −25.7050 −0.962660
\(714\) 0 0
\(715\) −3.85253 −0.144076
\(716\) −33.2009 −1.24078
\(717\) 17.5543 0.655579
\(718\) −15.4560 −0.576814
\(719\) 7.38127 0.275275 0.137637 0.990483i \(-0.456049\pi\)
0.137637 + 0.990483i \(0.456049\pi\)
\(720\) −0.926116 −0.0345143
\(721\) 0 0
\(722\) 10.9294 0.406749
\(723\) −11.6130 −0.431892
\(724\) 11.5498 0.429245
\(725\) −22.7681 −0.845586
\(726\) −8.23385 −0.305587
\(727\) 20.6700 0.766606 0.383303 0.923623i \(-0.374786\pi\)
0.383303 + 0.923623i \(0.374786\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 2.73502 0.101228
\(731\) 16.3400 0.604356
\(732\) −12.9833 −0.479876
\(733\) 8.97288 0.331421 0.165710 0.986174i \(-0.447008\pi\)
0.165710 + 0.986174i \(0.447008\pi\)
\(734\) −16.5592 −0.611211
\(735\) 0 0
\(736\) −24.7773 −0.913305
\(737\) −2.23832 −0.0824495
\(738\) −0.766355 −0.0282099
\(739\) −15.2740 −0.561862 −0.280931 0.959728i \(-0.590643\pi\)
−0.280931 + 0.959728i \(0.590643\pi\)
\(740\) −5.46305 −0.200826
\(741\) −38.9479 −1.43079
\(742\) 0 0
\(743\) 11.4640 0.420572 0.210286 0.977640i \(-0.432560\pi\)
0.210286 + 0.977640i \(0.432560\pi\)
\(744\) −15.8996 −0.582906
\(745\) −8.77451 −0.321473
\(746\) 15.2368 0.557859
\(747\) −15.7109 −0.574833
\(748\) 2.62402 0.0959436
\(749\) 0 0
\(750\) 7.54393 0.275466
\(751\) −8.10088 −0.295605 −0.147803 0.989017i \(-0.547220\pi\)
−0.147803 + 0.989017i \(0.547220\pi\)
\(752\) −6.25569 −0.228122
\(753\) −5.85349 −0.213313
\(754\) 31.6085 1.15111
\(755\) 13.9438 0.507468
\(756\) 0 0
\(757\) 21.9298 0.797053 0.398526 0.917157i \(-0.369522\pi\)
0.398526 + 0.917157i \(0.369522\pi\)
\(758\) −11.9130 −0.432700
\(759\) −2.13863 −0.0776274
\(760\) −17.0120 −0.617091
\(761\) 21.8802 0.793156 0.396578 0.918001i \(-0.370198\pi\)
0.396578 + 0.918001i \(0.370198\pi\)
\(762\) 15.8958 0.575843
\(763\) 0 0
\(764\) −7.35347 −0.266039
\(765\) 4.14189 0.149750
\(766\) −9.98102 −0.360629
\(767\) 59.6930 2.15539
\(768\) −13.0058 −0.469305
\(769\) −11.2832 −0.406883 −0.203441 0.979087i \(-0.565213\pi\)
−0.203441 + 0.979087i \(0.565213\pi\)
\(770\) 0 0
\(771\) −21.6778 −0.780708
\(772\) 30.7152 1.10546
\(773\) 42.3674 1.52385 0.761924 0.647666i \(-0.224255\pi\)
0.761924 + 0.647666i \(0.224255\pi\)
\(774\) −3.40989 −0.122566
\(775\) −22.6633 −0.814090
\(776\) 28.4198 1.02021
\(777\) 0 0
\(778\) 17.3585 0.622332
\(779\) 5.76728 0.206634
\(780\) 10.7602 0.385277
\(781\) −3.67849 −0.131627
\(782\) 11.8996 0.425529
\(783\) 6.10745 0.218263
\(784\) 0 0
\(785\) 11.8670 0.423551
\(786\) −7.46369 −0.266221
\(787\) 4.87155 0.173652 0.0868261 0.996223i \(-0.472328\pi\)
0.0868261 + 0.996223i \(0.472328\pi\)
\(788\) −15.5275 −0.553143
\(789\) −2.69289 −0.0958694
\(790\) −8.11924 −0.288870
\(791\) 0 0
\(792\) −1.32283 −0.0470046
\(793\) 62.0652 2.20400
\(794\) −9.90862 −0.351644
\(795\) −3.79914 −0.134742
\(796\) −24.7356 −0.876730
\(797\) −42.5408 −1.50687 −0.753435 0.657522i \(-0.771605\pi\)
−0.753435 + 0.657522i \(0.771605\pi\)
\(798\) 0 0
\(799\) 27.9775 0.989773
\(800\) −21.8454 −0.772352
\(801\) −14.1653 −0.500508
\(802\) −6.34704 −0.224122
\(803\) −1.60048 −0.0564795
\(804\) 6.25168 0.220480
\(805\) 0 0
\(806\) 31.4630 1.10824
\(807\) 17.7915 0.626290
\(808\) 31.1848 1.09708
\(809\) −31.9362 −1.12282 −0.561408 0.827539i \(-0.689740\pi\)
−0.561408 + 0.827539i \(0.689740\pi\)
\(810\) −0.864345 −0.0303700
\(811\) −14.0158 −0.492162 −0.246081 0.969249i \(-0.579143\pi\)
−0.246081 + 0.969249i \(0.579143\pi\)
\(812\) 0 0
\(813\) −2.05424 −0.0720454
\(814\) −1.32902 −0.0465823
\(815\) 16.2786 0.570214
\(816\) −3.01543 −0.105561
\(817\) 25.6614 0.897780
\(818\) −16.4965 −0.576787
\(819\) 0 0
\(820\) −1.59334 −0.0556417
\(821\) −4.67367 −0.163112 −0.0815560 0.996669i \(-0.525989\pi\)
−0.0815560 + 0.996669i \(0.525989\pi\)
\(822\) −9.53860 −0.332697
\(823\) 38.9460 1.35757 0.678786 0.734336i \(-0.262506\pi\)
0.678786 + 0.734336i \(0.262506\pi\)
\(824\) 18.9484 0.660099
\(825\) −1.88557 −0.0656470
\(826\) 0 0
\(827\) −34.5225 −1.20046 −0.600232 0.799826i \(-0.704925\pi\)
−0.600232 + 0.799826i \(0.704925\pi\)
\(828\) 5.97325 0.207585
\(829\) −15.9543 −0.554115 −0.277057 0.960853i \(-0.589359\pi\)
−0.277057 + 0.960853i \(0.589359\pi\)
\(830\) 13.5797 0.471357
\(831\) 11.5640 0.401152
\(832\) 19.2370 0.666924
\(833\) 0 0
\(834\) 10.1868 0.352740
\(835\) 15.2240 0.526849
\(836\) 4.12094 0.142526
\(837\) 6.07935 0.210133
\(838\) 23.5903 0.814912
\(839\) 52.8191 1.82352 0.911759 0.410725i \(-0.134724\pi\)
0.911759 + 0.410725i \(0.134724\pi\)
\(840\) 0 0
\(841\) 8.30096 0.286240
\(842\) 19.1651 0.660472
\(843\) −10.7124 −0.368956
\(844\) −13.8340 −0.476186
\(845\) −36.7758 −1.26512
\(846\) −5.83845 −0.200730
\(847\) 0 0
\(848\) 2.76590 0.0949814
\(849\) −0.225414 −0.00773620
\(850\) 10.4915 0.359856
\(851\) 14.4974 0.496963
\(852\) 10.2741 0.351985
\(853\) −17.3241 −0.593165 −0.296583 0.955007i \(-0.595847\pi\)
−0.296583 + 0.955007i \(0.595847\pi\)
\(854\) 0 0
\(855\) 6.50471 0.222457
\(856\) 4.90076 0.167505
\(857\) −29.9479 −1.02300 −0.511501 0.859283i \(-0.670910\pi\)
−0.511501 + 0.859283i \(0.670910\pi\)
\(858\) 2.61769 0.0893665
\(859\) 46.9646 1.60241 0.801206 0.598388i \(-0.204192\pi\)
0.801206 + 0.598388i \(0.204192\pi\)
\(860\) −7.08953 −0.241751
\(861\) 0 0
\(862\) −3.04284 −0.103640
\(863\) −49.2481 −1.67642 −0.838212 0.545344i \(-0.816399\pi\)
−0.838212 + 0.545344i \(0.816399\pi\)
\(864\) 5.85995 0.199360
\(865\) 18.6595 0.634440
\(866\) −6.42726 −0.218407
\(867\) −3.51401 −0.119342
\(868\) 0 0
\(869\) 4.75120 0.161174
\(870\) −5.27895 −0.178973
\(871\) −29.8855 −1.01263
\(872\) 5.24763 0.177707
\(873\) −10.8666 −0.367778
\(874\) 18.6880 0.632129
\(875\) 0 0
\(876\) 4.47017 0.151033
\(877\) 2.98663 0.100851 0.0504256 0.998728i \(-0.483942\pi\)
0.0504256 + 0.998728i \(0.483942\pi\)
\(878\) 19.7983 0.668159
\(879\) −32.1559 −1.08459
\(880\) −0.468426 −0.0157906
\(881\) 10.5761 0.356318 0.178159 0.984002i \(-0.442986\pi\)
0.178159 + 0.984002i \(0.442986\pi\)
\(882\) 0 0
\(883\) 4.43587 0.149279 0.0746394 0.997211i \(-0.476219\pi\)
0.0746394 + 0.997211i \(0.476219\pi\)
\(884\) 35.0352 1.17836
\(885\) −9.96935 −0.335116
\(886\) 17.6348 0.592454
\(887\) 43.0609 1.44584 0.722922 0.690930i \(-0.242799\pi\)
0.722922 + 0.690930i \(0.242799\pi\)
\(888\) 8.96718 0.300919
\(889\) 0 0
\(890\) 12.2437 0.410411
\(891\) 0.505796 0.0169448
\(892\) 12.2844 0.411313
\(893\) 43.9378 1.47032
\(894\) 5.96205 0.199401
\(895\) −26.5068 −0.886024
\(896\) 0 0
\(897\) −28.5545 −0.953407
\(898\) −15.8761 −0.529791
\(899\) 37.1293 1.23833
\(900\) 5.26643 0.175548
\(901\) −12.3700 −0.412105
\(902\) −0.387619 −0.0129063
\(903\) 0 0
\(904\) 16.1371 0.536712
\(905\) 9.22108 0.306519
\(906\) −9.47446 −0.314768
\(907\) −17.4450 −0.579251 −0.289626 0.957140i \(-0.593531\pi\)
−0.289626 + 0.957140i \(0.593531\pi\)
\(908\) 38.9702 1.29327
\(909\) −11.9238 −0.395487
\(910\) 0 0
\(911\) −0.711180 −0.0235624 −0.0117812 0.999931i \(-0.503750\pi\)
−0.0117812 + 0.999931i \(0.503750\pi\)
\(912\) −4.73564 −0.156813
\(913\) −7.94653 −0.262992
\(914\) −5.59282 −0.184994
\(915\) −10.3655 −0.342674
\(916\) 11.5639 0.382081
\(917\) 0 0
\(918\) −2.81431 −0.0928859
\(919\) 28.8745 0.952480 0.476240 0.879315i \(-0.341999\pi\)
0.476240 + 0.879315i \(0.341999\pi\)
\(920\) −12.4723 −0.411199
\(921\) −15.2207 −0.501539
\(922\) −0.848397 −0.0279405
\(923\) −49.1143 −1.61662
\(924\) 0 0
\(925\) 12.7819 0.420265
\(926\) 23.0395 0.757126
\(927\) −7.24511 −0.237961
\(928\) 35.7894 1.17484
\(929\) 20.7438 0.680583 0.340291 0.940320i \(-0.389474\pi\)
0.340291 + 0.940320i \(0.389474\pi\)
\(930\) −5.25465 −0.172307
\(931\) 0 0
\(932\) 7.17149 0.234910
\(933\) 26.7199 0.874772
\(934\) 10.8495 0.355007
\(935\) 2.09495 0.0685122
\(936\) −17.6621 −0.577303
\(937\) 43.4982 1.42102 0.710512 0.703685i \(-0.248463\pi\)
0.710512 + 0.703685i \(0.248463\pi\)
\(938\) 0 0
\(939\) −18.4588 −0.602380
\(940\) −12.1388 −0.395923
\(941\) 32.9060 1.07270 0.536352 0.843995i \(-0.319802\pi\)
0.536352 + 0.843995i \(0.319802\pi\)
\(942\) −8.06330 −0.262717
\(943\) 4.22825 0.137691
\(944\) 7.25802 0.236228
\(945\) 0 0
\(946\) −1.72471 −0.0560750
\(947\) 0.757409 0.0246125 0.0123062 0.999924i \(-0.496083\pi\)
0.0123062 + 0.999924i \(0.496083\pi\)
\(948\) −13.2702 −0.430997
\(949\) −21.3691 −0.693672
\(950\) 16.4766 0.534571
\(951\) −3.22714 −0.104647
\(952\) 0 0
\(953\) −41.8630 −1.35607 −0.678037 0.735028i \(-0.737169\pi\)
−0.678037 + 0.735028i \(0.737169\pi\)
\(954\) 2.58142 0.0835765
\(955\) −5.87083 −0.189976
\(956\) −24.7990 −0.802058
\(957\) 3.08912 0.0998572
\(958\) −9.82584 −0.317458
\(959\) 0 0
\(960\) −3.21279 −0.103692
\(961\) 5.95847 0.192209
\(962\) −17.7448 −0.572115
\(963\) −1.87385 −0.0603841
\(964\) 16.4057 0.528391
\(965\) 24.5223 0.789399
\(966\) 0 0
\(967\) −42.2716 −1.35936 −0.679682 0.733507i \(-0.737882\pi\)
−0.679682 + 0.733507i \(0.737882\pi\)
\(968\) 28.0997 0.903157
\(969\) 21.1793 0.680378
\(970\) 9.39248 0.301574
\(971\) 25.2095 0.809012 0.404506 0.914535i \(-0.367444\pi\)
0.404506 + 0.914535i \(0.367444\pi\)
\(972\) −1.41270 −0.0453124
\(973\) 0 0
\(974\) 18.1031 0.580062
\(975\) −25.1756 −0.806265
\(976\) 7.54645 0.241556
\(977\) 8.16412 0.261193 0.130597 0.991436i \(-0.458311\pi\)
0.130597 + 0.991436i \(0.458311\pi\)
\(978\) −11.0609 −0.353688
\(979\) −7.16477 −0.228987
\(980\) 0 0
\(981\) −2.00648 −0.0640620
\(982\) 7.20995 0.230079
\(983\) −33.5430 −1.06986 −0.534928 0.844897i \(-0.679661\pi\)
−0.534928 + 0.844897i \(0.679661\pi\)
\(984\) 2.61534 0.0833740
\(985\) −12.3968 −0.394994
\(986\) −17.1882 −0.547385
\(987\) 0 0
\(988\) 55.0217 1.75048
\(989\) 18.8136 0.598237
\(990\) −0.437182 −0.0138946
\(991\) −35.1267 −1.11584 −0.557918 0.829896i \(-0.688399\pi\)
−0.557918 + 0.829896i \(0.688399\pi\)
\(992\) 35.6247 1.13108
\(993\) −4.00194 −0.126998
\(994\) 0 0
\(995\) −19.7483 −0.626063
\(996\) 22.1949 0.703271
\(997\) −26.5951 −0.842274 −0.421137 0.906997i \(-0.638369\pi\)
−0.421137 + 0.906997i \(0.638369\pi\)
\(998\) 11.7117 0.370729
\(999\) −3.42869 −0.108479
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 \(a_p\))