Properties

Label 6027.2.a.bm.1.13
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 16
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.13
Root \(-1.49558\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.49558 q^{2} +1.00000 q^{3} +0.236756 q^{4} +1.30108 q^{5} +1.49558 q^{6} -2.63707 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.49558 q^{2} +1.00000 q^{3} +0.236756 q^{4} +1.30108 q^{5} +1.49558 q^{6} -2.63707 q^{8} +1.00000 q^{9} +1.94586 q^{10} -0.750331 q^{11} +0.236756 q^{12} -4.40274 q^{13} +1.30108 q^{15} -4.41746 q^{16} -4.00199 q^{17} +1.49558 q^{18} +5.38274 q^{19} +0.308037 q^{20} -1.12218 q^{22} +3.23452 q^{23} -2.63707 q^{24} -3.30720 q^{25} -6.58465 q^{26} +1.00000 q^{27} -3.07532 q^{29} +1.94586 q^{30} -9.02077 q^{31} -1.33252 q^{32} -0.750331 q^{33} -5.98530 q^{34} +0.236756 q^{36} +0.222437 q^{37} +8.05032 q^{38} -4.40274 q^{39} -3.43103 q^{40} +1.00000 q^{41} +0.320612 q^{43} -0.177645 q^{44} +1.30108 q^{45} +4.83747 q^{46} -3.80784 q^{47} -4.41746 q^{48} -4.94618 q^{50} -4.00199 q^{51} -1.04238 q^{52} -5.43224 q^{53} +1.49558 q^{54} -0.976237 q^{55} +5.38274 q^{57} -4.59939 q^{58} -1.91525 q^{59} +0.308037 q^{60} +10.2528 q^{61} -13.4913 q^{62} +6.84203 q^{64} -5.72830 q^{65} -1.12218 q^{66} -10.1905 q^{67} -0.947496 q^{68} +3.23452 q^{69} +0.199216 q^{71} -2.63707 q^{72} -14.2100 q^{73} +0.332673 q^{74} -3.30720 q^{75} +1.27440 q^{76} -6.58465 q^{78} -12.7948 q^{79} -5.74745 q^{80} +1.00000 q^{81} +1.49558 q^{82} -9.59023 q^{83} -5.20689 q^{85} +0.479501 q^{86} -3.07532 q^{87} +1.97868 q^{88} +4.12065 q^{89} +1.94586 q^{90} +0.765791 q^{92} -9.02077 q^{93} -5.69492 q^{94} +7.00336 q^{95} -1.33252 q^{96} -6.19741 q^{97} -0.750331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} + O(q^{10}) \) \( 16q - 4q^{2} + 16q^{3} + 12q^{4} - 12q^{5} - 4q^{6} - 12q^{8} + 16q^{9} - 4q^{10} - 4q^{11} + 12q^{12} - 12q^{15} - 8q^{17} - 4q^{18} + 4q^{19} - 20q^{20} - 16q^{22} - 12q^{23} - 12q^{24} - 8q^{25} - 8q^{26} + 16q^{27} - 16q^{29} - 4q^{30} - 4q^{31} - 48q^{32} - 4q^{33} + 16q^{34} + 12q^{36} - 48q^{37} - 4q^{38} + 56q^{40} + 16q^{41} - 16q^{43} - 12q^{45} - 4q^{46} - 36q^{47} - 8q^{50} - 8q^{51} - 60q^{53} - 4q^{54} + 8q^{55} + 4q^{57} - 36q^{58} - 36q^{59} - 20q^{60} - 4q^{61} - 12q^{62} + 52q^{64} - 36q^{65} - 16q^{66} - 52q^{67} - 8q^{68} - 12q^{69} - 12q^{71} - 12q^{72} - 16q^{73} + 4q^{74} - 8q^{75} + 16q^{76} - 8q^{78} - 36q^{79} - 68q^{80} + 16q^{81} - 4q^{82} - 32q^{83} - 28q^{85} - 8q^{86} - 16q^{87} - 36q^{88} - 12q^{89} - 4q^{90} - 36q^{92} - 4q^{93} + 24q^{94} - 20q^{95} - 48q^{96} + 48q^{97} - 4q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.49558 1.05753 0.528767 0.848767i \(-0.322655\pi\)
0.528767 + 0.848767i \(0.322655\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.236756 0.118378
\(5\) 1.30108 0.581859 0.290929 0.956745i \(-0.406036\pi\)
0.290929 + 0.956745i \(0.406036\pi\)
\(6\) 1.49558 0.610567
\(7\) 0 0
\(8\) −2.63707 −0.932345
\(9\) 1.00000 0.333333
\(10\) 1.94586 0.615335
\(11\) −0.750331 −0.226233 −0.113117 0.993582i \(-0.536083\pi\)
−0.113117 + 0.993582i \(0.536083\pi\)
\(12\) 0.236756 0.0683456
\(13\) −4.40274 −1.22110 −0.610551 0.791977i \(-0.709052\pi\)
−0.610551 + 0.791977i \(0.709052\pi\)
\(14\) 0 0
\(15\) 1.30108 0.335936
\(16\) −4.41746 −1.10436
\(17\) −4.00199 −0.970626 −0.485313 0.874341i \(-0.661294\pi\)
−0.485313 + 0.874341i \(0.661294\pi\)
\(18\) 1.49558 0.352511
\(19\) 5.38274 1.23489 0.617443 0.786616i \(-0.288169\pi\)
0.617443 + 0.786616i \(0.288169\pi\)
\(20\) 0.308037 0.0688792
\(21\) 0 0
\(22\) −1.12218 −0.239249
\(23\) 3.23452 0.674443 0.337222 0.941425i \(-0.390513\pi\)
0.337222 + 0.941425i \(0.390513\pi\)
\(24\) −2.63707 −0.538290
\(25\) −3.30720 −0.661441
\(26\) −6.58465 −1.29136
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −3.07532 −0.571073 −0.285536 0.958368i \(-0.592172\pi\)
−0.285536 + 0.958368i \(0.592172\pi\)
\(30\) 1.94586 0.355264
\(31\) −9.02077 −1.62018 −0.810089 0.586307i \(-0.800581\pi\)
−0.810089 + 0.586307i \(0.800581\pi\)
\(32\) −1.33252 −0.235558
\(33\) −0.750331 −0.130616
\(34\) −5.98530 −1.02647
\(35\) 0 0
\(36\) 0.236756 0.0394593
\(37\) 0.222437 0.0365685 0.0182842 0.999833i \(-0.494180\pi\)
0.0182842 + 0.999833i \(0.494180\pi\)
\(38\) 8.05032 1.30593
\(39\) −4.40274 −0.705003
\(40\) −3.43103 −0.542493
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 0.320612 0.0488929 0.0244465 0.999701i \(-0.492218\pi\)
0.0244465 + 0.999701i \(0.492218\pi\)
\(44\) −0.177645 −0.0267810
\(45\) 1.30108 0.193953
\(46\) 4.83747 0.713247
\(47\) −3.80784 −0.555430 −0.277715 0.960663i \(-0.589577\pi\)
−0.277715 + 0.960663i \(0.589577\pi\)
\(48\) −4.41746 −0.637605
\(49\) 0 0
\(50\) −4.94618 −0.699496
\(51\) −4.00199 −0.560391
\(52\) −1.04238 −0.144552
\(53\) −5.43224 −0.746175 −0.373088 0.927796i \(-0.621701\pi\)
−0.373088 + 0.927796i \(0.621701\pi\)
\(54\) 1.49558 0.203522
\(55\) −0.976237 −0.131636
\(56\) 0 0
\(57\) 5.38274 0.712962
\(58\) −4.59939 −0.603929
\(59\) −1.91525 −0.249344 −0.124672 0.992198i \(-0.539788\pi\)
−0.124672 + 0.992198i \(0.539788\pi\)
\(60\) 0.308037 0.0397674
\(61\) 10.2528 1.31274 0.656371 0.754439i \(-0.272091\pi\)
0.656371 + 0.754439i \(0.272091\pi\)
\(62\) −13.4913 −1.71339
\(63\) 0 0
\(64\) 6.84203 0.855254
\(65\) −5.72830 −0.710508
\(66\) −1.12218 −0.138131
\(67\) −10.1905 −1.24497 −0.622485 0.782632i \(-0.713877\pi\)
−0.622485 + 0.782632i \(0.713877\pi\)
\(68\) −0.947496 −0.114901
\(69\) 3.23452 0.389390
\(70\) 0 0
\(71\) 0.199216 0.0236426 0.0118213 0.999930i \(-0.496237\pi\)
0.0118213 + 0.999930i \(0.496237\pi\)
\(72\) −2.63707 −0.310782
\(73\) −14.2100 −1.66315 −0.831574 0.555413i \(-0.812560\pi\)
−0.831574 + 0.555413i \(0.812560\pi\)
\(74\) 0.332673 0.0386724
\(75\) −3.30720 −0.381883
\(76\) 1.27440 0.146183
\(77\) 0 0
\(78\) −6.58465 −0.745565
\(79\) −12.7948 −1.43953 −0.719766 0.694216i \(-0.755751\pi\)
−0.719766 + 0.694216i \(0.755751\pi\)
\(80\) −5.74745 −0.642584
\(81\) 1.00000 0.111111
\(82\) 1.49558 0.165159
\(83\) −9.59023 −1.05266 −0.526332 0.850279i \(-0.676433\pi\)
−0.526332 + 0.850279i \(0.676433\pi\)
\(84\) 0 0
\(85\) −5.20689 −0.564767
\(86\) 0.479501 0.0517060
\(87\) −3.07532 −0.329709
\(88\) 1.97868 0.210928
\(89\) 4.12065 0.436788 0.218394 0.975861i \(-0.429918\pi\)
0.218394 + 0.975861i \(0.429918\pi\)
\(90\) 1.94586 0.205112
\(91\) 0 0
\(92\) 0.765791 0.0798392
\(93\) −9.02077 −0.935410
\(94\) −5.69492 −0.587386
\(95\) 7.00336 0.718529
\(96\) −1.33252 −0.135999
\(97\) −6.19741 −0.629252 −0.314626 0.949216i \(-0.601879\pi\)
−0.314626 + 0.949216i \(0.601879\pi\)
\(98\) 0 0
\(99\) −0.750331 −0.0754111
\(100\) −0.783000 −0.0783000
\(101\) 17.1028 1.70179 0.850897 0.525332i \(-0.176059\pi\)
0.850897 + 0.525332i \(0.176059\pi\)
\(102\) −5.98530 −0.592633
\(103\) 8.58842 0.846242 0.423121 0.906073i \(-0.360934\pi\)
0.423121 + 0.906073i \(0.360934\pi\)
\(104\) 11.6103 1.13849
\(105\) 0 0
\(106\) −8.12434 −0.789106
\(107\) −16.8587 −1.62979 −0.814894 0.579610i \(-0.803205\pi\)
−0.814894 + 0.579610i \(0.803205\pi\)
\(108\) 0.236756 0.0227819
\(109\) 9.66152 0.925406 0.462703 0.886513i \(-0.346880\pi\)
0.462703 + 0.886513i \(0.346880\pi\)
\(110\) −1.46004 −0.139209
\(111\) 0.222437 0.0211128
\(112\) 0 0
\(113\) −10.5574 −0.993155 −0.496578 0.867992i \(-0.665410\pi\)
−0.496578 + 0.867992i \(0.665410\pi\)
\(114\) 8.05032 0.753981
\(115\) 4.20835 0.392431
\(116\) −0.728101 −0.0676025
\(117\) −4.40274 −0.407034
\(118\) −2.86441 −0.263690
\(119\) 0 0
\(120\) −3.43103 −0.313208
\(121\) −10.4370 −0.948818
\(122\) 15.3339 1.38827
\(123\) 1.00000 0.0901670
\(124\) −2.13572 −0.191793
\(125\) −10.8083 −0.966723
\(126\) 0 0
\(127\) 3.01008 0.267101 0.133551 0.991042i \(-0.457362\pi\)
0.133551 + 0.991042i \(0.457362\pi\)
\(128\) 12.8978 1.14002
\(129\) 0.320612 0.0282284
\(130\) −8.56713 −0.751387
\(131\) 12.9015 1.12721 0.563603 0.826046i \(-0.309415\pi\)
0.563603 + 0.826046i \(0.309415\pi\)
\(132\) −0.177645 −0.0154620
\(133\) 0 0
\(134\) −15.2407 −1.31660
\(135\) 1.30108 0.111979
\(136\) 10.5535 0.904958
\(137\) 4.96393 0.424097 0.212049 0.977259i \(-0.431986\pi\)
0.212049 + 0.977259i \(0.431986\pi\)
\(138\) 4.83747 0.411793
\(139\) 12.1564 1.03109 0.515546 0.856862i \(-0.327589\pi\)
0.515546 + 0.856862i \(0.327589\pi\)
\(140\) 0 0
\(141\) −3.80784 −0.320678
\(142\) 0.297944 0.0250029
\(143\) 3.30352 0.276254
\(144\) −4.41746 −0.368122
\(145\) −4.00123 −0.332284
\(146\) −21.2521 −1.75884
\(147\) 0 0
\(148\) 0.0526634 0.00432890
\(149\) −14.8763 −1.21872 −0.609359 0.792894i \(-0.708573\pi\)
−0.609359 + 0.792894i \(0.708573\pi\)
\(150\) −4.94618 −0.403854
\(151\) −0.301545 −0.0245394 −0.0122697 0.999925i \(-0.503906\pi\)
−0.0122697 + 0.999925i \(0.503906\pi\)
\(152\) −14.1947 −1.15134
\(153\) −4.00199 −0.323542
\(154\) 0 0
\(155\) −11.7367 −0.942714
\(156\) −1.04238 −0.0834569
\(157\) 4.70368 0.375395 0.187697 0.982227i \(-0.439898\pi\)
0.187697 + 0.982227i \(0.439898\pi\)
\(158\) −19.1357 −1.52235
\(159\) −5.43224 −0.430804
\(160\) −1.73370 −0.137061
\(161\) 0 0
\(162\) 1.49558 0.117504
\(163\) −5.64405 −0.442076 −0.221038 0.975265i \(-0.570944\pi\)
−0.221038 + 0.975265i \(0.570944\pi\)
\(164\) 0.236756 0.0184875
\(165\) −0.976237 −0.0760000
\(166\) −14.3429 −1.11323
\(167\) −14.1707 −1.09656 −0.548282 0.836293i \(-0.684718\pi\)
−0.548282 + 0.836293i \(0.684718\pi\)
\(168\) 0 0
\(169\) 6.38416 0.491089
\(170\) −7.78732 −0.597260
\(171\) 5.38274 0.411629
\(172\) 0.0759069 0.00578785
\(173\) 4.35168 0.330852 0.165426 0.986222i \(-0.447100\pi\)
0.165426 + 0.986222i \(0.447100\pi\)
\(174\) −4.59939 −0.348679
\(175\) 0 0
\(176\) 3.31456 0.249844
\(177\) −1.91525 −0.143959
\(178\) 6.16276 0.461918
\(179\) −3.44395 −0.257413 −0.128706 0.991683i \(-0.541082\pi\)
−0.128706 + 0.991683i \(0.541082\pi\)
\(180\) 0.308037 0.0229597
\(181\) 21.0180 1.56226 0.781129 0.624370i \(-0.214644\pi\)
0.781129 + 0.624370i \(0.214644\pi\)
\(182\) 0 0
\(183\) 10.2528 0.757911
\(184\) −8.52965 −0.628814
\(185\) 0.289408 0.0212777
\(186\) −13.4913 −0.989228
\(187\) 3.00282 0.219588
\(188\) −0.901529 −0.0657507
\(189\) 0 0
\(190\) 10.4741 0.759869
\(191\) 17.6175 1.27476 0.637379 0.770551i \(-0.280019\pi\)
0.637379 + 0.770551i \(0.280019\pi\)
\(192\) 6.84203 0.493781
\(193\) −24.4497 −1.75993 −0.879964 0.475040i \(-0.842434\pi\)
−0.879964 + 0.475040i \(0.842434\pi\)
\(194\) −9.26872 −0.665455
\(195\) −5.72830 −0.410212
\(196\) 0 0
\(197\) −10.8760 −0.774880 −0.387440 0.921895i \(-0.626641\pi\)
−0.387440 + 0.921895i \(0.626641\pi\)
\(198\) −1.12218 −0.0797498
\(199\) 9.38454 0.665252 0.332626 0.943059i \(-0.392065\pi\)
0.332626 + 0.943059i \(0.392065\pi\)
\(200\) 8.72133 0.616691
\(201\) −10.1905 −0.718783
\(202\) 25.5786 1.79971
\(203\) 0 0
\(204\) −0.947496 −0.0663380
\(205\) 1.30108 0.0908710
\(206\) 12.8447 0.894930
\(207\) 3.23452 0.224814
\(208\) 19.4489 1.34854
\(209\) −4.03884 −0.279372
\(210\) 0 0
\(211\) −18.1085 −1.24664 −0.623319 0.781968i \(-0.714216\pi\)
−0.623319 + 0.781968i \(0.714216\pi\)
\(212\) −1.28611 −0.0883307
\(213\) 0.199216 0.0136501
\(214\) −25.2135 −1.72356
\(215\) 0.417141 0.0284488
\(216\) −2.63707 −0.179430
\(217\) 0 0
\(218\) 14.4496 0.978648
\(219\) −14.2100 −0.960219
\(220\) −0.231130 −0.0155828
\(221\) 17.6198 1.18523
\(222\) 0.332673 0.0223275
\(223\) −20.6736 −1.38441 −0.692203 0.721703i \(-0.743360\pi\)
−0.692203 + 0.721703i \(0.743360\pi\)
\(224\) 0 0
\(225\) −3.30720 −0.220480
\(226\) −15.7894 −1.05030
\(227\) −17.2707 −1.14629 −0.573147 0.819452i \(-0.694278\pi\)
−0.573147 + 0.819452i \(0.694278\pi\)
\(228\) 1.27440 0.0843990
\(229\) 8.57141 0.566415 0.283207 0.959059i \(-0.408602\pi\)
0.283207 + 0.959059i \(0.408602\pi\)
\(230\) 6.29392 0.415009
\(231\) 0 0
\(232\) 8.10984 0.532437
\(233\) 16.0030 1.04839 0.524196 0.851598i \(-0.324366\pi\)
0.524196 + 0.851598i \(0.324366\pi\)
\(234\) −6.58465 −0.430452
\(235\) −4.95428 −0.323182
\(236\) −0.453447 −0.0295169
\(237\) −12.7948 −0.831115
\(238\) 0 0
\(239\) 9.31197 0.602341 0.301171 0.953570i \(-0.402623\pi\)
0.301171 + 0.953570i \(0.402623\pi\)
\(240\) −5.74745 −0.370996
\(241\) 13.4089 0.863742 0.431871 0.901935i \(-0.357854\pi\)
0.431871 + 0.901935i \(0.357854\pi\)
\(242\) −15.6094 −1.00341
\(243\) 1.00000 0.0641500
\(244\) 2.42742 0.155400
\(245\) 0 0
\(246\) 1.49558 0.0953546
\(247\) −23.6988 −1.50792
\(248\) 23.7884 1.51056
\(249\) −9.59023 −0.607756
\(250\) −16.1647 −1.02234
\(251\) 0.0581644 0.00367130 0.00183565 0.999998i \(-0.499416\pi\)
0.00183565 + 0.999998i \(0.499416\pi\)
\(252\) 0 0
\(253\) −2.42696 −0.152582
\(254\) 4.50181 0.282468
\(255\) −5.20689 −0.326068
\(256\) 5.60566 0.350354
\(257\) 19.6323 1.22463 0.612314 0.790615i \(-0.290239\pi\)
0.612314 + 0.790615i \(0.290239\pi\)
\(258\) 0.479501 0.0298524
\(259\) 0 0
\(260\) −1.35621 −0.0841085
\(261\) −3.07532 −0.190358
\(262\) 19.2951 1.19206
\(263\) −1.71718 −0.105886 −0.0529431 0.998598i \(-0.516860\pi\)
−0.0529431 + 0.998598i \(0.516860\pi\)
\(264\) 1.97868 0.121779
\(265\) −7.06775 −0.434168
\(266\) 0 0
\(267\) 4.12065 0.252180
\(268\) −2.41266 −0.147377
\(269\) 13.1932 0.804404 0.402202 0.915551i \(-0.368245\pi\)
0.402202 + 0.915551i \(0.368245\pi\)
\(270\) 1.94586 0.118421
\(271\) −0.787682 −0.0478483 −0.0239241 0.999714i \(-0.507616\pi\)
−0.0239241 + 0.999714i \(0.507616\pi\)
\(272\) 17.6786 1.07192
\(273\) 0 0
\(274\) 7.42395 0.448497
\(275\) 2.48150 0.149640
\(276\) 0.765791 0.0460952
\(277\) 9.56370 0.574627 0.287314 0.957837i \(-0.407238\pi\)
0.287314 + 0.957837i \(0.407238\pi\)
\(278\) 18.1808 1.09041
\(279\) −9.02077 −0.540059
\(280\) 0 0
\(281\) 7.48602 0.446579 0.223289 0.974752i \(-0.428321\pi\)
0.223289 + 0.974752i \(0.428321\pi\)
\(282\) −5.69492 −0.339128
\(283\) 30.8025 1.83102 0.915509 0.402298i \(-0.131789\pi\)
0.915509 + 0.402298i \(0.131789\pi\)
\(284\) 0.0471656 0.00279876
\(285\) 7.00336 0.414843
\(286\) 4.94067 0.292148
\(287\) 0 0
\(288\) −1.33252 −0.0785193
\(289\) −0.984056 −0.0578856
\(290\) −5.98415 −0.351401
\(291\) −6.19741 −0.363299
\(292\) −3.36429 −0.196880
\(293\) 1.19896 0.0700440 0.0350220 0.999387i \(-0.488850\pi\)
0.0350220 + 0.999387i \(0.488850\pi\)
\(294\) 0 0
\(295\) −2.49188 −0.145083
\(296\) −0.586583 −0.0340944
\(297\) −0.750331 −0.0435386
\(298\) −22.2488 −1.28884
\(299\) −14.2407 −0.823564
\(300\) −0.783000 −0.0452065
\(301\) 0 0
\(302\) −0.450984 −0.0259512
\(303\) 17.1028 0.982532
\(304\) −23.7780 −1.36376
\(305\) 13.3397 0.763830
\(306\) −5.98530 −0.342157
\(307\) −14.2847 −0.815268 −0.407634 0.913145i \(-0.633646\pi\)
−0.407634 + 0.913145i \(0.633646\pi\)
\(308\) 0 0
\(309\) 8.58842 0.488578
\(310\) −17.5532 −0.996952
\(311\) 0.370661 0.0210183 0.0105091 0.999945i \(-0.496655\pi\)
0.0105091 + 0.999945i \(0.496655\pi\)
\(312\) 11.6103 0.657306
\(313\) 23.9391 1.35312 0.676559 0.736388i \(-0.263470\pi\)
0.676559 + 0.736388i \(0.263470\pi\)
\(314\) 7.03473 0.396993
\(315\) 0 0
\(316\) −3.02926 −0.170409
\(317\) −6.14198 −0.344968 −0.172484 0.985012i \(-0.555179\pi\)
−0.172484 + 0.985012i \(0.555179\pi\)
\(318\) −8.12434 −0.455590
\(319\) 2.30751 0.129196
\(320\) 8.90200 0.497637
\(321\) −16.8587 −0.940959
\(322\) 0 0
\(323\) −21.5417 −1.19861
\(324\) 0.236756 0.0131531
\(325\) 14.5608 0.807686
\(326\) −8.44112 −0.467510
\(327\) 9.66152 0.534283
\(328\) −2.63707 −0.145608
\(329\) 0 0
\(330\) −1.46004 −0.0803725
\(331\) −19.8031 −1.08848 −0.544239 0.838930i \(-0.683182\pi\)
−0.544239 + 0.838930i \(0.683182\pi\)
\(332\) −2.27054 −0.124612
\(333\) 0.222437 0.0121895
\(334\) −21.1935 −1.15965
\(335\) −13.2586 −0.724396
\(336\) 0 0
\(337\) 7.16733 0.390429 0.195215 0.980761i \(-0.437460\pi\)
0.195215 + 0.980761i \(0.437460\pi\)
\(338\) 9.54801 0.519343
\(339\) −10.5574 −0.573399
\(340\) −1.23276 −0.0668560
\(341\) 6.76856 0.366538
\(342\) 8.05032 0.435311
\(343\) 0 0
\(344\) −0.845478 −0.0455851
\(345\) 4.20835 0.226570
\(346\) 6.50828 0.349887
\(347\) 31.6998 1.70173 0.850867 0.525381i \(-0.176077\pi\)
0.850867 + 0.525381i \(0.176077\pi\)
\(348\) −0.728101 −0.0390303
\(349\) 34.3013 1.83611 0.918054 0.396456i \(-0.129760\pi\)
0.918054 + 0.396456i \(0.129760\pi\)
\(350\) 0 0
\(351\) −4.40274 −0.235001
\(352\) 0.999829 0.0532910
\(353\) 15.5061 0.825304 0.412652 0.910889i \(-0.364603\pi\)
0.412652 + 0.910889i \(0.364603\pi\)
\(354\) −2.86441 −0.152242
\(355\) 0.259195 0.0137567
\(356\) 0.975589 0.0517061
\(357\) 0 0
\(358\) −5.15069 −0.272223
\(359\) −27.0959 −1.43007 −0.715033 0.699091i \(-0.753588\pi\)
−0.715033 + 0.699091i \(0.753588\pi\)
\(360\) −3.43103 −0.180831
\(361\) 9.97394 0.524944
\(362\) 31.4341 1.65214
\(363\) −10.4370 −0.547801
\(364\) 0 0
\(365\) −18.4882 −0.967717
\(366\) 15.3339 0.801517
\(367\) −15.2872 −0.797987 −0.398994 0.916954i \(-0.630640\pi\)
−0.398994 + 0.916954i \(0.630640\pi\)
\(368\) −14.2883 −0.744831
\(369\) 1.00000 0.0520579
\(370\) 0.432832 0.0225019
\(371\) 0 0
\(372\) −2.13572 −0.110732
\(373\) −5.41590 −0.280424 −0.140212 0.990121i \(-0.544778\pi\)
−0.140212 + 0.990121i \(0.544778\pi\)
\(374\) 4.49095 0.232222
\(375\) −10.8083 −0.558138
\(376\) 10.0415 0.517853
\(377\) 13.5399 0.697338
\(378\) 0 0
\(379\) 31.5728 1.62179 0.810893 0.585195i \(-0.198982\pi\)
0.810893 + 0.585195i \(0.198982\pi\)
\(380\) 1.65809 0.0850580
\(381\) 3.01008 0.154211
\(382\) 26.3484 1.34810
\(383\) −18.4875 −0.944666 −0.472333 0.881420i \(-0.656588\pi\)
−0.472333 + 0.881420i \(0.656588\pi\)
\(384\) 12.8978 0.658190
\(385\) 0 0
\(386\) −36.5665 −1.86118
\(387\) 0.320612 0.0162976
\(388\) −1.46727 −0.0744896
\(389\) 0.290515 0.0147297 0.00736485 0.999973i \(-0.497656\pi\)
0.00736485 + 0.999973i \(0.497656\pi\)
\(390\) −8.56713 −0.433813
\(391\) −12.9445 −0.654632
\(392\) 0 0
\(393\) 12.9015 0.650792
\(394\) −16.2658 −0.819462
\(395\) −16.6471 −0.837604
\(396\) −0.177645 −0.00892701
\(397\) −33.5002 −1.68133 −0.840663 0.541559i \(-0.817834\pi\)
−0.840663 + 0.541559i \(0.817834\pi\)
\(398\) 14.0353 0.703527
\(399\) 0 0
\(400\) 14.6094 0.730472
\(401\) 9.39811 0.469319 0.234660 0.972078i \(-0.424602\pi\)
0.234660 + 0.972078i \(0.424602\pi\)
\(402\) −15.2407 −0.760138
\(403\) 39.7161 1.97840
\(404\) 4.04920 0.201455
\(405\) 1.30108 0.0646509
\(406\) 0 0
\(407\) −0.166902 −0.00827301
\(408\) 10.5535 0.522478
\(409\) −21.9938 −1.08752 −0.543761 0.839240i \(-0.683000\pi\)
−0.543761 + 0.839240i \(0.683000\pi\)
\(410\) 1.94586 0.0960992
\(411\) 4.96393 0.244853
\(412\) 2.03336 0.100176
\(413\) 0 0
\(414\) 4.83747 0.237749
\(415\) −12.4776 −0.612502
\(416\) 5.86673 0.287640
\(417\) 12.1564 0.595301
\(418\) −6.04040 −0.295446
\(419\) 12.5798 0.614564 0.307282 0.951619i \(-0.400581\pi\)
0.307282 + 0.951619i \(0.400581\pi\)
\(420\) 0 0
\(421\) −5.04947 −0.246096 −0.123048 0.992401i \(-0.539267\pi\)
−0.123048 + 0.992401i \(0.539267\pi\)
\(422\) −27.0826 −1.31836
\(423\) −3.80784 −0.185143
\(424\) 14.3252 0.695693
\(425\) 13.2354 0.642011
\(426\) 0.297944 0.0144354
\(427\) 0 0
\(428\) −3.99139 −0.192931
\(429\) 3.30352 0.159495
\(430\) 0.623867 0.0300855
\(431\) −12.1483 −0.585161 −0.292580 0.956241i \(-0.594514\pi\)
−0.292580 + 0.956241i \(0.594514\pi\)
\(432\) −4.41746 −0.212535
\(433\) −19.0236 −0.914217 −0.457108 0.889411i \(-0.651115\pi\)
−0.457108 + 0.889411i \(0.651115\pi\)
\(434\) 0 0
\(435\) −4.00123 −0.191844
\(436\) 2.28742 0.109548
\(437\) 17.4106 0.832861
\(438\) −21.2521 −1.01546
\(439\) −23.3222 −1.11311 −0.556553 0.830812i \(-0.687876\pi\)
−0.556553 + 0.830812i \(0.687876\pi\)
\(440\) 2.57441 0.122730
\(441\) 0 0
\(442\) 26.3517 1.25342
\(443\) 24.9061 1.18332 0.591662 0.806186i \(-0.298472\pi\)
0.591662 + 0.806186i \(0.298472\pi\)
\(444\) 0.0526634 0.00249929
\(445\) 5.36128 0.254149
\(446\) −30.9190 −1.46406
\(447\) −14.8763 −0.703627
\(448\) 0 0
\(449\) −25.2477 −1.19151 −0.595756 0.803165i \(-0.703147\pi\)
−0.595756 + 0.803165i \(0.703147\pi\)
\(450\) −4.94618 −0.233165
\(451\) −0.750331 −0.0353317
\(452\) −2.49952 −0.117568
\(453\) −0.301545 −0.0141678
\(454\) −25.8296 −1.21225
\(455\) 0 0
\(456\) −14.1947 −0.664727
\(457\) −13.0645 −0.611130 −0.305565 0.952171i \(-0.598845\pi\)
−0.305565 + 0.952171i \(0.598845\pi\)
\(458\) 12.8192 0.599003
\(459\) −4.00199 −0.186797
\(460\) 0.996352 0.0464551
\(461\) −31.7275 −1.47769 −0.738847 0.673873i \(-0.764630\pi\)
−0.738847 + 0.673873i \(0.764630\pi\)
\(462\) 0 0
\(463\) −3.68283 −0.171156 −0.0855779 0.996331i \(-0.527274\pi\)
−0.0855779 + 0.996331i \(0.527274\pi\)
\(464\) 13.5851 0.630673
\(465\) −11.7367 −0.544276
\(466\) 23.9338 1.10871
\(467\) −29.4057 −1.36074 −0.680368 0.732871i \(-0.738180\pi\)
−0.680368 + 0.732871i \(0.738180\pi\)
\(468\) −1.04238 −0.0481838
\(469\) 0 0
\(470\) −7.40952 −0.341776
\(471\) 4.70368 0.216734
\(472\) 5.05065 0.232475
\(473\) −0.240566 −0.0110612
\(474\) −19.1357 −0.878932
\(475\) −17.8018 −0.816804
\(476\) 0 0
\(477\) −5.43224 −0.248725
\(478\) 13.9268 0.636996
\(479\) 17.2828 0.789670 0.394835 0.918752i \(-0.370802\pi\)
0.394835 + 0.918752i \(0.370802\pi\)
\(480\) −1.73370 −0.0791324
\(481\) −0.979335 −0.0446538
\(482\) 20.0540 0.913436
\(483\) 0 0
\(484\) −2.47102 −0.112319
\(485\) −8.06330 −0.366136
\(486\) 1.49558 0.0678408
\(487\) −40.0005 −1.81260 −0.906298 0.422640i \(-0.861104\pi\)
−0.906298 + 0.422640i \(0.861104\pi\)
\(488\) −27.0374 −1.22393
\(489\) −5.64405 −0.255233
\(490\) 0 0
\(491\) 9.17562 0.414090 0.207045 0.978331i \(-0.433615\pi\)
0.207045 + 0.978331i \(0.433615\pi\)
\(492\) 0.236756 0.0106738
\(493\) 12.3074 0.554298
\(494\) −35.4435 −1.59468
\(495\) −0.976237 −0.0438786
\(496\) 39.8489 1.78927
\(497\) 0 0
\(498\) −14.3429 −0.642723
\(499\) 33.3392 1.49247 0.746233 0.665685i \(-0.231861\pi\)
0.746233 + 0.665685i \(0.231861\pi\)
\(500\) −2.55893 −0.114439
\(501\) −14.1707 −0.633102
\(502\) 0.0869894 0.00388253
\(503\) −8.10607 −0.361432 −0.180716 0.983535i \(-0.557841\pi\)
−0.180716 + 0.983535i \(0.557841\pi\)
\(504\) 0 0
\(505\) 22.2521 0.990204
\(506\) −3.62971 −0.161360
\(507\) 6.38416 0.283530
\(508\) 0.712654 0.0316189
\(509\) −20.6817 −0.916698 −0.458349 0.888772i \(-0.651559\pi\)
−0.458349 + 0.888772i \(0.651559\pi\)
\(510\) −7.78732 −0.344828
\(511\) 0 0
\(512\) −17.4120 −0.769507
\(513\) 5.38274 0.237654
\(514\) 29.3616 1.29508
\(515\) 11.1742 0.492393
\(516\) 0.0759069 0.00334162
\(517\) 2.85714 0.125657
\(518\) 0 0
\(519\) 4.35168 0.191018
\(520\) 15.1059 0.662439
\(521\) 12.6259 0.553152 0.276576 0.960992i \(-0.410800\pi\)
0.276576 + 0.960992i \(0.410800\pi\)
\(522\) −4.59939 −0.201310
\(523\) 29.9917 1.31145 0.655724 0.755001i \(-0.272364\pi\)
0.655724 + 0.755001i \(0.272364\pi\)
\(524\) 3.05450 0.133436
\(525\) 0 0
\(526\) −2.56818 −0.111978
\(527\) 36.1010 1.57259
\(528\) 3.31456 0.144248
\(529\) −12.5379 −0.545126
\(530\) −10.5704 −0.459148
\(531\) −1.91525 −0.0831148
\(532\) 0 0
\(533\) −4.40274 −0.190704
\(534\) 6.16276 0.266689
\(535\) −21.9344 −0.948306
\(536\) 26.8731 1.16074
\(537\) −3.44395 −0.148617
\(538\) 19.7315 0.850685
\(539\) 0 0
\(540\) 0.308037 0.0132558
\(541\) 5.29585 0.227687 0.113843 0.993499i \(-0.463684\pi\)
0.113843 + 0.993499i \(0.463684\pi\)
\(542\) −1.17804 −0.0506012
\(543\) 21.0180 0.901970
\(544\) 5.33272 0.228639
\(545\) 12.5704 0.538455
\(546\) 0 0
\(547\) 18.0194 0.770452 0.385226 0.922822i \(-0.374123\pi\)
0.385226 + 0.922822i \(0.374123\pi\)
\(548\) 1.17524 0.0502038
\(549\) 10.2528 0.437580
\(550\) 3.71128 0.158249
\(551\) −16.5537 −0.705210
\(552\) −8.52965 −0.363046
\(553\) 0 0
\(554\) 14.3033 0.607688
\(555\) 0.289408 0.0122847
\(556\) 2.87810 0.122059
\(557\) 34.1481 1.44690 0.723451 0.690375i \(-0.242555\pi\)
0.723451 + 0.690375i \(0.242555\pi\)
\(558\) −13.4913 −0.571131
\(559\) −1.41157 −0.0597033
\(560\) 0 0
\(561\) 3.00282 0.126779
\(562\) 11.1959 0.472272
\(563\) 24.4327 1.02972 0.514859 0.857275i \(-0.327844\pi\)
0.514859 + 0.857275i \(0.327844\pi\)
\(564\) −0.901529 −0.0379612
\(565\) −13.7360 −0.577876
\(566\) 46.0675 1.93636
\(567\) 0 0
\(568\) −0.525347 −0.0220431
\(569\) −12.6126 −0.528746 −0.264373 0.964420i \(-0.585165\pi\)
−0.264373 + 0.964420i \(0.585165\pi\)
\(570\) 10.4741 0.438710
\(571\) −1.85956 −0.0778203 −0.0389101 0.999243i \(-0.512389\pi\)
−0.0389101 + 0.999243i \(0.512389\pi\)
\(572\) 0.782127 0.0327024
\(573\) 17.6175 0.735981
\(574\) 0 0
\(575\) −10.6972 −0.446104
\(576\) 6.84203 0.285085
\(577\) 16.1880 0.673915 0.336958 0.941520i \(-0.390602\pi\)
0.336958 + 0.941520i \(0.390602\pi\)
\(578\) −1.47173 −0.0612160
\(579\) −24.4497 −1.01610
\(580\) −0.947314 −0.0393351
\(581\) 0 0
\(582\) −9.26872 −0.384201
\(583\) 4.07598 0.168810
\(584\) 37.4726 1.55063
\(585\) −5.72830 −0.236836
\(586\) 1.79314 0.0740739
\(587\) 16.1967 0.668511 0.334256 0.942482i \(-0.391515\pi\)
0.334256 + 0.942482i \(0.391515\pi\)
\(588\) 0 0
\(589\) −48.5565 −2.00073
\(590\) −3.72681 −0.153430
\(591\) −10.8760 −0.447377
\(592\) −0.982608 −0.0403849
\(593\) −21.0639 −0.864990 −0.432495 0.901636i \(-0.642367\pi\)
−0.432495 + 0.901636i \(0.642367\pi\)
\(594\) −1.12218 −0.0460436
\(595\) 0 0
\(596\) −3.52206 −0.144269
\(597\) 9.38454 0.384084
\(598\) −21.2982 −0.870947
\(599\) −14.7515 −0.602731 −0.301365 0.953509i \(-0.597442\pi\)
−0.301365 + 0.953509i \(0.597442\pi\)
\(600\) 8.72133 0.356047
\(601\) 29.3384 1.19674 0.598370 0.801220i \(-0.295815\pi\)
0.598370 + 0.801220i \(0.295815\pi\)
\(602\) 0 0
\(603\) −10.1905 −0.414990
\(604\) −0.0713926 −0.00290492
\(605\) −13.5793 −0.552078
\(606\) 25.5786 1.03906
\(607\) −2.93492 −0.119125 −0.0595624 0.998225i \(-0.518971\pi\)
−0.0595624 + 0.998225i \(0.518971\pi\)
\(608\) −7.17260 −0.290887
\(609\) 0 0
\(610\) 19.9506 0.807776
\(611\) 16.7649 0.678237
\(612\) −0.947496 −0.0383002
\(613\) 19.1580 0.773785 0.386892 0.922125i \(-0.373548\pi\)
0.386892 + 0.922125i \(0.373548\pi\)
\(614\) −21.3638 −0.862174
\(615\) 1.30108 0.0524644
\(616\) 0 0
\(617\) 7.15081 0.287881 0.143940 0.989586i \(-0.454023\pi\)
0.143940 + 0.989586i \(0.454023\pi\)
\(618\) 12.8447 0.516688
\(619\) 3.52506 0.141684 0.0708421 0.997488i \(-0.477431\pi\)
0.0708421 + 0.997488i \(0.477431\pi\)
\(620\) −2.77873 −0.111597
\(621\) 3.23452 0.129797
\(622\) 0.554353 0.0222275
\(623\) 0 0
\(624\) 19.4489 0.778581
\(625\) 2.47361 0.0989444
\(626\) 35.8028 1.43097
\(627\) −4.03884 −0.161296
\(628\) 1.11363 0.0444385
\(629\) −0.890193 −0.0354943
\(630\) 0 0
\(631\) 33.3841 1.32900 0.664499 0.747289i \(-0.268645\pi\)
0.664499 + 0.747289i \(0.268645\pi\)
\(632\) 33.7409 1.34214
\(633\) −18.1085 −0.719747
\(634\) −9.18581 −0.364815
\(635\) 3.91634 0.155415
\(636\) −1.28611 −0.0509978
\(637\) 0 0
\(638\) 3.45106 0.136629
\(639\) 0.199216 0.00788087
\(640\) 16.7811 0.663329
\(641\) 22.5473 0.890565 0.445282 0.895390i \(-0.353103\pi\)
0.445282 + 0.895390i \(0.353103\pi\)
\(642\) −25.2135 −0.995096
\(643\) −15.8629 −0.625572 −0.312786 0.949824i \(-0.601262\pi\)
−0.312786 + 0.949824i \(0.601262\pi\)
\(644\) 0 0
\(645\) 0.417141 0.0164249
\(646\) −32.2173 −1.26757
\(647\) 6.50471 0.255727 0.127863 0.991792i \(-0.459188\pi\)
0.127863 + 0.991792i \(0.459188\pi\)
\(648\) −2.63707 −0.103594
\(649\) 1.43707 0.0564100
\(650\) 21.7768 0.854156
\(651\) 0 0
\(652\) −1.33626 −0.0523321
\(653\) −49.5602 −1.93944 −0.969721 0.244216i \(-0.921470\pi\)
−0.969721 + 0.244216i \(0.921470\pi\)
\(654\) 14.4496 0.565023
\(655\) 16.7858 0.655874
\(656\) −4.41746 −0.172473
\(657\) −14.2100 −0.554383
\(658\) 0 0
\(659\) −27.3186 −1.06418 −0.532091 0.846687i \(-0.678593\pi\)
−0.532091 + 0.846687i \(0.678593\pi\)
\(660\) −0.231130 −0.00899672
\(661\) −25.6016 −0.995786 −0.497893 0.867239i \(-0.665893\pi\)
−0.497893 + 0.867239i \(0.665893\pi\)
\(662\) −29.6172 −1.15110
\(663\) 17.6198 0.684294
\(664\) 25.2901 0.981447
\(665\) 0 0
\(666\) 0.332673 0.0128908
\(667\) −9.94718 −0.385156
\(668\) −3.35501 −0.129809
\(669\) −20.6736 −0.799287
\(670\) −19.8293 −0.766073
\(671\) −7.69302 −0.296986
\(672\) 0 0
\(673\) −5.96774 −0.230039 −0.115020 0.993363i \(-0.536693\pi\)
−0.115020 + 0.993363i \(0.536693\pi\)
\(674\) 10.7193 0.412892
\(675\) −3.30720 −0.127294
\(676\) 1.51149 0.0581341
\(677\) 19.9773 0.767789 0.383894 0.923377i \(-0.374583\pi\)
0.383894 + 0.923377i \(0.374583\pi\)
\(678\) −15.7894 −0.606388
\(679\) 0 0
\(680\) 13.7309 0.526558
\(681\) −17.2707 −0.661813
\(682\) 10.1229 0.387627
\(683\) 23.9569 0.916686 0.458343 0.888775i \(-0.348443\pi\)
0.458343 + 0.888775i \(0.348443\pi\)
\(684\) 1.27440 0.0487278
\(685\) 6.45845 0.246765
\(686\) 0 0
\(687\) 8.57141 0.327020
\(688\) −1.41629 −0.0539956
\(689\) 23.9168 0.911156
\(690\) 6.29392 0.239605
\(691\) 40.9688 1.55853 0.779264 0.626696i \(-0.215593\pi\)
0.779264 + 0.626696i \(0.215593\pi\)
\(692\) 1.03029 0.0391656
\(693\) 0 0
\(694\) 47.4095 1.79964
\(695\) 15.8164 0.599949
\(696\) 8.10984 0.307403
\(697\) −4.00199 −0.151586
\(698\) 51.3003 1.94175
\(699\) 16.0030 0.605290
\(700\) 0 0
\(701\) 44.7542 1.69034 0.845171 0.534495i \(-0.179498\pi\)
0.845171 + 0.534495i \(0.179498\pi\)
\(702\) −6.58465 −0.248522
\(703\) 1.19732 0.0451579
\(704\) −5.13379 −0.193487
\(705\) −4.95428 −0.186589
\(706\) 23.1905 0.872787
\(707\) 0 0
\(708\) −0.453447 −0.0170416
\(709\) −41.9685 −1.57616 −0.788081 0.615572i \(-0.788925\pi\)
−0.788081 + 0.615572i \(0.788925\pi\)
\(710\) 0.387647 0.0145481
\(711\) −12.7948 −0.479844
\(712\) −10.8664 −0.407237
\(713\) −29.1778 −1.09272
\(714\) 0 0
\(715\) 4.29812 0.160741
\(716\) −0.815375 −0.0304720
\(717\) 9.31197 0.347762
\(718\) −40.5240 −1.51234
\(719\) −13.0723 −0.487516 −0.243758 0.969836i \(-0.578380\pi\)
−0.243758 + 0.969836i \(0.578380\pi\)
\(720\) −5.74745 −0.214195
\(721\) 0 0
\(722\) 14.9168 0.555146
\(723\) 13.4089 0.498682
\(724\) 4.97614 0.184937
\(725\) 10.1707 0.377731
\(726\) −15.6094 −0.579318
\(727\) −12.7634 −0.473367 −0.236683 0.971587i \(-0.576060\pi\)
−0.236683 + 0.971587i \(0.576060\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −27.6506 −1.02339
\(731\) −1.28309 −0.0474568
\(732\) 2.42742 0.0897200
\(733\) −28.9108 −1.06785 −0.533923 0.845533i \(-0.679283\pi\)
−0.533923 + 0.845533i \(0.679283\pi\)
\(734\) −22.8633 −0.843899
\(735\) 0 0
\(736\) −4.31005 −0.158870
\(737\) 7.64626 0.281653
\(738\) 1.49558 0.0550530
\(739\) −23.0344 −0.847336 −0.423668 0.905818i \(-0.639258\pi\)
−0.423668 + 0.905818i \(0.639258\pi\)
\(740\) 0.0685190 0.00251881
\(741\) −23.6988 −0.870599
\(742\) 0 0
\(743\) −20.6971 −0.759304 −0.379652 0.925129i \(-0.623956\pi\)
−0.379652 + 0.925129i \(0.623956\pi\)
\(744\) 23.7884 0.872125
\(745\) −19.3552 −0.709121
\(746\) −8.09990 −0.296558
\(747\) −9.59023 −0.350888
\(748\) 0.710935 0.0259944
\(749\) 0 0
\(750\) −16.1647 −0.590250
\(751\) 12.8521 0.468980 0.234490 0.972118i \(-0.424658\pi\)
0.234490 + 0.972118i \(0.424658\pi\)
\(752\) 16.8210 0.613398
\(753\) 0.0581644 0.00211963
\(754\) 20.2499 0.737459
\(755\) −0.392333 −0.0142784
\(756\) 0 0
\(757\) 20.1896 0.733805 0.366902 0.930259i \(-0.380418\pi\)
0.366902 + 0.930259i \(0.380418\pi\)
\(758\) 47.2196 1.71509
\(759\) −2.42696 −0.0880930
\(760\) −18.4683 −0.669917
\(761\) −29.9222 −1.08468 −0.542339 0.840160i \(-0.682461\pi\)
−0.542339 + 0.840160i \(0.682461\pi\)
\(762\) 4.50181 0.163083
\(763\) 0 0
\(764\) 4.17105 0.150903
\(765\) −5.20689 −0.188256
\(766\) −27.6495 −0.999016
\(767\) 8.43235 0.304475
\(768\) 5.60566 0.202277
\(769\) 38.0982 1.37386 0.686929 0.726725i \(-0.258959\pi\)
0.686929 + 0.726725i \(0.258959\pi\)
\(770\) 0 0
\(771\) 19.6323 0.707039
\(772\) −5.78861 −0.208337
\(773\) −42.3581 −1.52352 −0.761758 0.647861i \(-0.775664\pi\)
−0.761758 + 0.647861i \(0.775664\pi\)
\(774\) 0.479501 0.0172353
\(775\) 29.8335 1.07165
\(776\) 16.3430 0.586680
\(777\) 0 0
\(778\) 0.434489 0.0155772
\(779\) 5.38274 0.192857
\(780\) −1.35621 −0.0485601
\(781\) −0.149478 −0.00534875
\(782\) −19.3595 −0.692296
\(783\) −3.07532 −0.109903
\(784\) 0 0
\(785\) 6.11985 0.218427
\(786\) 19.2951 0.688235
\(787\) 28.1447 1.00325 0.501625 0.865085i \(-0.332736\pi\)
0.501625 + 0.865085i \(0.332736\pi\)
\(788\) −2.57495 −0.0917287
\(789\) −1.71718 −0.0611334
\(790\) −24.8970 −0.885795
\(791\) 0 0
\(792\) 1.97868 0.0703092
\(793\) −45.1406 −1.60299
\(794\) −50.1022 −1.77806
\(795\) −7.06775 −0.250667
\(796\) 2.22185 0.0787512
\(797\) −6.52825 −0.231242 −0.115621 0.993293i \(-0.536886\pi\)
−0.115621 + 0.993293i \(0.536886\pi\)
\(798\) 0 0
\(799\) 15.2389 0.539115
\(800\) 4.40690 0.155808
\(801\) 4.12065 0.145596
\(802\) 14.0556 0.496321
\(803\) 10.6622 0.376260
\(804\) −2.41266 −0.0850881
\(805\) 0 0
\(806\) 59.3986 2.09223
\(807\) 13.1932 0.464423
\(808\) −45.1014 −1.58666
\(809\) −10.0066 −0.351813 −0.175906 0.984407i \(-0.556286\pi\)
−0.175906 + 0.984407i \(0.556286\pi\)
\(810\) 1.94586 0.0683706
\(811\) −40.0564 −1.40657 −0.703286 0.710907i \(-0.748284\pi\)
−0.703286 + 0.710907i \(0.748284\pi\)
\(812\) 0 0
\(813\) −0.787682 −0.0276252
\(814\) −0.249615 −0.00874899
\(815\) −7.34333 −0.257226
\(816\) 17.6786 0.618876
\(817\) 1.72578 0.0603772
\(818\) −32.8934 −1.15009
\(819\) 0 0
\(820\) 0.308037 0.0107571
\(821\) −33.9009 −1.18315 −0.591574 0.806250i \(-0.701493\pi\)
−0.591574 + 0.806250i \(0.701493\pi\)
\(822\) 7.42395 0.258940
\(823\) 24.9240 0.868797 0.434399 0.900721i \(-0.356961\pi\)
0.434399 + 0.900721i \(0.356961\pi\)
\(824\) −22.6483 −0.788990
\(825\) 2.48150 0.0863947
\(826\) 0 0
\(827\) −27.7154 −0.963759 −0.481880 0.876237i \(-0.660046\pi\)
−0.481880 + 0.876237i \(0.660046\pi\)
\(828\) 0.765791 0.0266131
\(829\) 6.18951 0.214971 0.107485 0.994207i \(-0.465720\pi\)
0.107485 + 0.994207i \(0.465720\pi\)
\(830\) −18.6612 −0.647741
\(831\) 9.56370 0.331761
\(832\) −30.1237 −1.04435
\(833\) 0 0
\(834\) 18.1808 0.629551
\(835\) −18.4372 −0.638045
\(836\) −0.956220 −0.0330715
\(837\) −9.02077 −0.311803
\(838\) 18.8141 0.649922
\(839\) 5.58456 0.192801 0.0964003 0.995343i \(-0.469267\pi\)
0.0964003 + 0.995343i \(0.469267\pi\)
\(840\) 0 0
\(841\) −19.5424 −0.673876
\(842\) −7.55188 −0.260255
\(843\) 7.48602 0.257832
\(844\) −4.28729 −0.147574
\(845\) 8.30627 0.285744
\(846\) −5.69492 −0.195795
\(847\) 0 0
\(848\) 23.9967 0.824049
\(849\) 30.8025 1.05714
\(850\) 19.7946 0.678949
\(851\) 0.719477 0.0246634
\(852\) 0.0471656 0.00161587
\(853\) 16.2181 0.555299 0.277649 0.960683i \(-0.410445\pi\)
0.277649 + 0.960683i \(0.410445\pi\)
\(854\) 0 0
\(855\) 7.00336 0.239510
\(856\) 44.4575 1.51953
\(857\) −54.1267 −1.84893 −0.924466 0.381265i \(-0.875489\pi\)
−0.924466 + 0.381265i \(0.875489\pi\)
\(858\) 4.94067 0.168672
\(859\) 47.8992 1.63430 0.817149 0.576426i \(-0.195553\pi\)
0.817149 + 0.576426i \(0.195553\pi\)
\(860\) 0.0987606 0.00336771
\(861\) 0 0
\(862\) −18.1687 −0.618827
\(863\) 54.5776 1.85784 0.928922 0.370275i \(-0.120737\pi\)
0.928922 + 0.370275i \(0.120737\pi\)
\(864\) −1.33252 −0.0453331
\(865\) 5.66186 0.192509
\(866\) −28.4513 −0.966815
\(867\) −0.984056 −0.0334203
\(868\) 0 0
\(869\) 9.60037 0.325670
\(870\) −5.98415 −0.202882
\(871\) 44.8662 1.52023
\(872\) −25.4781 −0.862798
\(873\) −6.19741 −0.209751
\(874\) 26.0389 0.880778
\(875\) 0 0
\(876\) −3.36429 −0.113669
\(877\) −8.01308 −0.270582 −0.135291 0.990806i \(-0.543197\pi\)
−0.135291 + 0.990806i \(0.543197\pi\)
\(878\) −34.8801 −1.17715
\(879\) 1.19896 0.0404399
\(880\) 4.31249 0.145374
\(881\) 16.7655 0.564842 0.282421 0.959291i \(-0.408862\pi\)
0.282421 + 0.959291i \(0.408862\pi\)
\(882\) 0 0
\(883\) −44.5687 −1.49986 −0.749928 0.661520i \(-0.769912\pi\)
−0.749928 + 0.661520i \(0.769912\pi\)
\(884\) 4.17158 0.140305
\(885\) −2.49188 −0.0837638
\(886\) 37.2490 1.25141
\(887\) 16.0532 0.539015 0.269508 0.962998i \(-0.413139\pi\)
0.269508 + 0.962998i \(0.413139\pi\)
\(888\) −0.586583 −0.0196844
\(889\) 0 0
\(890\) 8.01821 0.268771
\(891\) −0.750331 −0.0251370
\(892\) −4.89460 −0.163883
\(893\) −20.4966 −0.685893
\(894\) −22.2488 −0.744110
\(895\) −4.48083 −0.149778
\(896\) 0 0
\(897\) −14.2407 −0.475485
\(898\) −37.7599 −1.26006
\(899\) 27.7418 0.925240
\(900\) −0.783000 −0.0261000
\(901\) 21.7398 0.724257
\(902\) −1.12218 −0.0373645
\(903\) 0 0
\(904\) 27.8406 0.925964
\(905\) 27.3460 0.909013
\(906\) −0.450984 −0.0149829
\(907\) 0.619038 0.0205548 0.0102774 0.999947i \(-0.496729\pi\)
0.0102774 + 0.999947i \(0.496729\pi\)
\(908\) −4.08893 −0.135696
\(909\) 17.1028 0.567265
\(910\) 0 0
\(911\) −13.0071 −0.430944 −0.215472 0.976510i \(-0.569129\pi\)
−0.215472 + 0.976510i \(0.569129\pi\)
\(912\) −23.7780 −0.787370
\(913\) 7.19585 0.238148
\(914\) −19.5389 −0.646290
\(915\) 13.3397 0.440997
\(916\) 2.02933 0.0670510
\(917\) 0 0
\(918\) −5.98530 −0.197544
\(919\) 25.0989 0.827936 0.413968 0.910291i \(-0.364142\pi\)
0.413968 + 0.910291i \(0.364142\pi\)
\(920\) −11.0977 −0.365881
\(921\) −14.2847 −0.470695
\(922\) −47.4509 −1.56271
\(923\) −0.877098 −0.0288700
\(924\) 0 0
\(925\) −0.735646 −0.0241879
\(926\) −5.50797 −0.181003
\(927\) 8.58842 0.282081
\(928\) 4.09792 0.134521
\(929\) 57.5537 1.88828 0.944138 0.329551i \(-0.106897\pi\)
0.944138 + 0.329551i \(0.106897\pi\)
\(930\) −17.5532 −0.575591
\(931\) 0 0
\(932\) 3.78881 0.124107
\(933\) 0.370661 0.0121349
\(934\) −43.9786 −1.43902
\(935\) 3.90689 0.127769
\(936\) 11.6103 0.379496
\(937\) 55.4319 1.81088 0.905440 0.424474i \(-0.139541\pi\)
0.905440 + 0.424474i \(0.139541\pi\)
\(938\) 0 0
\(939\) 23.9391 0.781223
\(940\) −1.17296 −0.0382576
\(941\) −28.9348 −0.943247 −0.471623 0.881800i \(-0.656332\pi\)
−0.471623 + 0.881800i \(0.656332\pi\)
\(942\) 7.03473 0.229204
\(943\) 3.23452 0.105330
\(944\) 8.46054 0.275367
\(945\) 0 0
\(946\) −0.359785 −0.0116976
\(947\) 19.5413 0.635006 0.317503 0.948257i \(-0.397156\pi\)
0.317503 + 0.948257i \(0.397156\pi\)
\(948\) −3.02926 −0.0983857
\(949\) 62.5628 2.03087
\(950\) −26.6240 −0.863798
\(951\) −6.14198 −0.199167
\(952\) 0 0
\(953\) −30.2403 −0.979580 −0.489790 0.871840i \(-0.662927\pi\)
−0.489790 + 0.871840i \(0.662927\pi\)
\(954\) −8.12434 −0.263035
\(955\) 22.9217 0.741728
\(956\) 2.20466 0.0713040
\(957\) 2.30751 0.0745912
\(958\) 25.8478 0.835103
\(959\) 0 0
\(960\) 8.90200 0.287311
\(961\) 50.3742 1.62498
\(962\) −1.46467 −0.0472229
\(963\) −16.8587 −0.543263
\(964\) 3.17463 0.102248
\(965\) −31.8109 −1.02403
\(966\) 0 0
\(967\) 37.3054 1.19966 0.599831 0.800127i \(-0.295234\pi\)
0.599831 + 0.800127i \(0.295234\pi\)
\(968\) 27.5231 0.884626
\(969\) −21.5417 −0.692019
\(970\) −12.0593 −0.387201
\(971\) −14.7476 −0.473274 −0.236637 0.971598i \(-0.576045\pi\)
−0.236637 + 0.971598i \(0.576045\pi\)
\(972\) 0.236756 0.00759395
\(973\) 0 0
\(974\) −59.8239 −1.91688
\(975\) 14.5608 0.466318
\(976\) −45.2915 −1.44974
\(977\) −29.6133 −0.947413 −0.473706 0.880683i \(-0.657084\pi\)
−0.473706 + 0.880683i \(0.657084\pi\)
\(978\) −8.44112 −0.269917
\(979\) −3.09185 −0.0988160
\(980\) 0 0
\(981\) 9.66152 0.308469
\(982\) 13.7229 0.437914
\(983\) −43.6571 −1.39245 −0.696223 0.717826i \(-0.745137\pi\)
−0.696223 + 0.717826i \(0.745137\pi\)
\(984\) −2.63707 −0.0840667
\(985\) −14.1504 −0.450870
\(986\) 18.4067 0.586189
\(987\) 0 0
\(988\) −5.61084 −0.178505
\(989\) 1.03703 0.0329755
\(990\) −1.46004 −0.0464031
\(991\) −34.3757 −1.09198 −0.545990 0.837792i \(-0.683846\pi\)
−0.545990 + 0.837792i \(0.683846\pi\)
\(992\) 12.0203 0.381646
\(993\) −19.8031 −0.628434
\(994\) 0 0
\(995\) 12.2100 0.387083
\(996\) −2.27054 −0.0719449
\(997\) −8.09059 −0.256232 −0.128116 0.991759i \(-0.540893\pi\)
−0.128116 + 0.991759i \(0.540893\pi\)
\(998\) 49.8613 1.57833
\(999\) 0.222437 0.00703761
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 \(a_p\))