Properties

Label 8001.2.a.v.1.11
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-0.249163\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.249163 q^{2}\) \(-1.93792 q^{4}\) \(-0.989651 q^{5}\) \(+1.00000 q^{7}\) \(-0.981182 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.249163 q^{2}\) \(-1.93792 q^{4}\) \(-0.989651 q^{5}\) \(+1.00000 q^{7}\) \(-0.981182 q^{8}\) \(-0.246584 q^{10}\) \(+2.01884 q^{11}\) \(+4.18024 q^{13}\) \(+0.249163 q^{14}\) \(+3.63136 q^{16}\) \(+7.51203 q^{17}\) \(+7.64620 q^{19}\) \(+1.91786 q^{20}\) \(+0.503020 q^{22}\) \(+2.82780 q^{23}\) \(-4.02059 q^{25}\) \(+1.04156 q^{26}\) \(-1.93792 q^{28}\) \(-5.08664 q^{29}\) \(+1.14394 q^{31}\) \(+2.86716 q^{32}\) \(+1.87172 q^{34}\) \(-0.989651 q^{35}\) \(+10.6080 q^{37}\) \(+1.90515 q^{38}\) \(+0.971028 q^{40}\) \(-8.51782 q^{41}\) \(-2.46779 q^{43}\) \(-3.91235 q^{44}\) \(+0.704583 q^{46}\) \(+0.347815 q^{47}\) \(+1.00000 q^{49}\) \(-1.00178 q^{50}\) \(-8.10096 q^{52}\) \(+4.33912 q^{53}\) \(-1.99795 q^{55}\) \(-0.981182 q^{56}\) \(-1.26740 q^{58}\) \(+9.40635 q^{59}\) \(-3.40599 q^{61}\) \(+0.285027 q^{62}\) \(-6.54833 q^{64}\) \(-4.13698 q^{65}\) \(+5.65641 q^{67}\) \(-14.5577 q^{68}\) \(-0.246584 q^{70}\) \(-4.93333 q^{71}\) \(+1.89559 q^{73}\) \(+2.64311 q^{74}\) \(-14.8177 q^{76}\) \(+2.01884 q^{77}\) \(+8.24436 q^{79}\) \(-3.59378 q^{80}\) \(-2.12232 q^{82}\) \(-9.21069 q^{83}\) \(-7.43428 q^{85}\) \(-0.614881 q^{86}\) \(-1.98085 q^{88}\) \(+1.13183 q^{89}\) \(+4.18024 q^{91}\) \(-5.48005 q^{92}\) \(+0.0866624 q^{94}\) \(-7.56707 q^{95}\) \(+18.6987 q^{97}\) \(+0.249163 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.249163 0.176185 0.0880923 0.996112i \(-0.471923\pi\)
0.0880923 + 0.996112i \(0.471923\pi\)
\(3\) 0 0
\(4\) −1.93792 −0.968959
\(5\) −0.989651 −0.442585 −0.221293 0.975207i \(-0.571028\pi\)
−0.221293 + 0.975207i \(0.571028\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −0.981182 −0.346900
\(9\) 0 0
\(10\) −0.246584 −0.0779767
\(11\) 2.01884 0.608704 0.304352 0.952560i \(-0.401560\pi\)
0.304352 + 0.952560i \(0.401560\pi\)
\(12\) 0 0
\(13\) 4.18024 1.15939 0.579695 0.814833i \(-0.303172\pi\)
0.579695 + 0.814833i \(0.303172\pi\)
\(14\) 0.249163 0.0665915
\(15\) 0 0
\(16\) 3.63136 0.907841
\(17\) 7.51203 1.82193 0.910967 0.412479i \(-0.135337\pi\)
0.910967 + 0.412479i \(0.135337\pi\)
\(18\) 0 0
\(19\) 7.64620 1.75416 0.877080 0.480345i \(-0.159488\pi\)
0.877080 + 0.480345i \(0.159488\pi\)
\(20\) 1.91786 0.428847
\(21\) 0 0
\(22\) 0.503020 0.107244
\(23\) 2.82780 0.589637 0.294819 0.955553i \(-0.404741\pi\)
0.294819 + 0.955553i \(0.404741\pi\)
\(24\) 0 0
\(25\) −4.02059 −0.804118
\(26\) 1.04156 0.204267
\(27\) 0 0
\(28\) −1.93792 −0.366232
\(29\) −5.08664 −0.944566 −0.472283 0.881447i \(-0.656570\pi\)
−0.472283 + 0.881447i \(0.656570\pi\)
\(30\) 0 0
\(31\) 1.14394 0.205457 0.102729 0.994709i \(-0.467243\pi\)
0.102729 + 0.994709i \(0.467243\pi\)
\(32\) 2.86716 0.506848
\(33\) 0 0
\(34\) 1.87172 0.320997
\(35\) −0.989651 −0.167282
\(36\) 0 0
\(37\) 10.6080 1.74394 0.871970 0.489559i \(-0.162842\pi\)
0.871970 + 0.489559i \(0.162842\pi\)
\(38\) 1.90515 0.309056
\(39\) 0 0
\(40\) 0.971028 0.153533
\(41\) −8.51782 −1.33026 −0.665130 0.746728i \(-0.731624\pi\)
−0.665130 + 0.746728i \(0.731624\pi\)
\(42\) 0 0
\(43\) −2.46779 −0.376335 −0.188167 0.982137i \(-0.560255\pi\)
−0.188167 + 0.982137i \(0.560255\pi\)
\(44\) −3.91235 −0.589810
\(45\) 0 0
\(46\) 0.704583 0.103885
\(47\) 0.347815 0.0507340 0.0253670 0.999678i \(-0.491925\pi\)
0.0253670 + 0.999678i \(0.491925\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −1.00178 −0.141673
\(51\) 0 0
\(52\) −8.10096 −1.12340
\(53\) 4.33912 0.596024 0.298012 0.954562i \(-0.403676\pi\)
0.298012 + 0.954562i \(0.403676\pi\)
\(54\) 0 0
\(55\) −1.99795 −0.269404
\(56\) −0.981182 −0.131116
\(57\) 0 0
\(58\) −1.26740 −0.166418
\(59\) 9.40635 1.22460 0.612301 0.790625i \(-0.290244\pi\)
0.612301 + 0.790625i \(0.290244\pi\)
\(60\) 0 0
\(61\) −3.40599 −0.436092 −0.218046 0.975938i \(-0.569968\pi\)
−0.218046 + 0.975938i \(0.569968\pi\)
\(62\) 0.285027 0.0361984
\(63\) 0 0
\(64\) −6.54833 −0.818542
\(65\) −4.13698 −0.513129
\(66\) 0 0
\(67\) 5.65641 0.691040 0.345520 0.938411i \(-0.387703\pi\)
0.345520 + 0.938411i \(0.387703\pi\)
\(68\) −14.5577 −1.76538
\(69\) 0 0
\(70\) −0.246584 −0.0294724
\(71\) −4.93333 −0.585479 −0.292740 0.956192i \(-0.594567\pi\)
−0.292740 + 0.956192i \(0.594567\pi\)
\(72\) 0 0
\(73\) 1.89559 0.221862 0.110931 0.993828i \(-0.464617\pi\)
0.110931 + 0.993828i \(0.464617\pi\)
\(74\) 2.64311 0.307255
\(75\) 0 0
\(76\) −14.8177 −1.69971
\(77\) 2.01884 0.230069
\(78\) 0 0
\(79\) 8.24436 0.927563 0.463782 0.885950i \(-0.346492\pi\)
0.463782 + 0.885950i \(0.346492\pi\)
\(80\) −3.59378 −0.401797
\(81\) 0 0
\(82\) −2.12232 −0.234371
\(83\) −9.21069 −1.01100 −0.505502 0.862825i \(-0.668693\pi\)
−0.505502 + 0.862825i \(0.668693\pi\)
\(84\) 0 0
\(85\) −7.43428 −0.806361
\(86\) −0.614881 −0.0663044
\(87\) 0 0
\(88\) −1.98085 −0.211160
\(89\) 1.13183 0.119974 0.0599869 0.998199i \(-0.480894\pi\)
0.0599869 + 0.998199i \(0.480894\pi\)
\(90\) 0 0
\(91\) 4.18024 0.438208
\(92\) −5.48005 −0.571334
\(93\) 0 0
\(94\) 0.0866624 0.00893855
\(95\) −7.56707 −0.776365
\(96\) 0 0
\(97\) 18.6987 1.89857 0.949285 0.314418i \(-0.101809\pi\)
0.949285 + 0.314418i \(0.101809\pi\)
\(98\) 0.249163 0.0251692
\(99\) 0 0
\(100\) 7.79158 0.779158
\(101\) −4.10828 −0.408790 −0.204395 0.978889i \(-0.565523\pi\)
−0.204395 + 0.978889i \(0.565523\pi\)
\(102\) 0 0
\(103\) −9.05224 −0.891944 −0.445972 0.895047i \(-0.647142\pi\)
−0.445972 + 0.895047i \(0.647142\pi\)
\(104\) −4.10158 −0.402193
\(105\) 0 0
\(106\) 1.08115 0.105010
\(107\) −13.8515 −1.33907 −0.669535 0.742780i \(-0.733507\pi\)
−0.669535 + 0.742780i \(0.733507\pi\)
\(108\) 0 0
\(109\) −9.27191 −0.888088 −0.444044 0.896005i \(-0.646457\pi\)
−0.444044 + 0.896005i \(0.646457\pi\)
\(110\) −0.497815 −0.0474648
\(111\) 0 0
\(112\) 3.63136 0.343131
\(113\) −2.81376 −0.264696 −0.132348 0.991203i \(-0.542252\pi\)
−0.132348 + 0.991203i \(0.542252\pi\)
\(114\) 0 0
\(115\) −2.79854 −0.260965
\(116\) 9.85750 0.915246
\(117\) 0 0
\(118\) 2.34371 0.215756
\(119\) 7.51203 0.688626
\(120\) 0 0
\(121\) −6.92427 −0.629479
\(122\) −0.848645 −0.0768327
\(123\) 0 0
\(124\) −2.21686 −0.199080
\(125\) 8.92724 0.798476
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −7.36593 −0.651062
\(129\) 0 0
\(130\) −1.03078 −0.0904055
\(131\) 0.239985 0.0209676 0.0104838 0.999945i \(-0.496663\pi\)
0.0104838 + 0.999945i \(0.496663\pi\)
\(132\) 0 0
\(133\) 7.64620 0.663010
\(134\) 1.40937 0.121751
\(135\) 0 0
\(136\) −7.37067 −0.632029
\(137\) −15.1732 −1.29633 −0.648165 0.761500i \(-0.724463\pi\)
−0.648165 + 0.761500i \(0.724463\pi\)
\(138\) 0 0
\(139\) 1.07164 0.0908953 0.0454477 0.998967i \(-0.485529\pi\)
0.0454477 + 0.998967i \(0.485529\pi\)
\(140\) 1.91786 0.162089
\(141\) 0 0
\(142\) −1.22920 −0.103152
\(143\) 8.43925 0.705726
\(144\) 0 0
\(145\) 5.03400 0.418051
\(146\) 0.472311 0.0390887
\(147\) 0 0
\(148\) −20.5574 −1.68981
\(149\) −7.00252 −0.573669 −0.286834 0.957980i \(-0.592603\pi\)
−0.286834 + 0.957980i \(0.592603\pi\)
\(150\) 0 0
\(151\) −3.72548 −0.303175 −0.151587 0.988444i \(-0.548439\pi\)
−0.151587 + 0.988444i \(0.548439\pi\)
\(152\) −7.50232 −0.608518
\(153\) 0 0
\(154\) 0.503020 0.0405345
\(155\) −1.13210 −0.0909325
\(156\) 0 0
\(157\) 18.6725 1.49023 0.745113 0.666938i \(-0.232396\pi\)
0.745113 + 0.666938i \(0.232396\pi\)
\(158\) 2.05419 0.163422
\(159\) 0 0
\(160\) −2.83749 −0.224323
\(161\) 2.82780 0.222862
\(162\) 0 0
\(163\) −2.99112 −0.234282 −0.117141 0.993115i \(-0.537373\pi\)
−0.117141 + 0.993115i \(0.537373\pi\)
\(164\) 16.5068 1.28897
\(165\) 0 0
\(166\) −2.29496 −0.178123
\(167\) 1.05587 0.0817054 0.0408527 0.999165i \(-0.486993\pi\)
0.0408527 + 0.999165i \(0.486993\pi\)
\(168\) 0 0
\(169\) 4.47442 0.344186
\(170\) −1.85235 −0.142068
\(171\) 0 0
\(172\) 4.78238 0.364653
\(173\) 14.4208 1.09639 0.548197 0.836349i \(-0.315314\pi\)
0.548197 + 0.836349i \(0.315314\pi\)
\(174\) 0 0
\(175\) −4.02059 −0.303928
\(176\) 7.33115 0.552606
\(177\) 0 0
\(178\) 0.282010 0.0211375
\(179\) −22.6413 −1.69229 −0.846145 0.532952i \(-0.821083\pi\)
−0.846145 + 0.532952i \(0.821083\pi\)
\(180\) 0 0
\(181\) 22.0630 1.63993 0.819964 0.572415i \(-0.193993\pi\)
0.819964 + 0.572415i \(0.193993\pi\)
\(182\) 1.04156 0.0772056
\(183\) 0 0
\(184\) −2.77459 −0.204545
\(185\) −10.4982 −0.771842
\(186\) 0 0
\(187\) 15.1656 1.10902
\(188\) −0.674036 −0.0491592
\(189\) 0 0
\(190\) −1.88543 −0.136784
\(191\) −23.2667 −1.68352 −0.841760 0.539851i \(-0.818480\pi\)
−0.841760 + 0.539851i \(0.818480\pi\)
\(192\) 0 0
\(193\) 24.1716 1.73991 0.869956 0.493130i \(-0.164147\pi\)
0.869956 + 0.493130i \(0.164147\pi\)
\(194\) 4.65903 0.334499
\(195\) 0 0
\(196\) −1.93792 −0.138423
\(197\) −1.83988 −0.131086 −0.0655430 0.997850i \(-0.520878\pi\)
−0.0655430 + 0.997850i \(0.520878\pi\)
\(198\) 0 0
\(199\) 8.75745 0.620799 0.310400 0.950606i \(-0.399537\pi\)
0.310400 + 0.950606i \(0.399537\pi\)
\(200\) 3.94493 0.278949
\(201\) 0 0
\(202\) −1.02363 −0.0720224
\(203\) −5.08664 −0.357012
\(204\) 0 0
\(205\) 8.42967 0.588753
\(206\) −2.25548 −0.157147
\(207\) 0 0
\(208\) 15.1800 1.05254
\(209\) 15.4365 1.06776
\(210\) 0 0
\(211\) 1.51979 0.104626 0.0523132 0.998631i \(-0.483341\pi\)
0.0523132 + 0.998631i \(0.483341\pi\)
\(212\) −8.40886 −0.577523
\(213\) 0 0
\(214\) −3.45126 −0.235924
\(215\) 2.44225 0.166560
\(216\) 0 0
\(217\) 1.14394 0.0776556
\(218\) −2.31021 −0.156467
\(219\) 0 0
\(220\) 3.87186 0.261041
\(221\) 31.4021 2.11233
\(222\) 0 0
\(223\) 16.8448 1.12801 0.564005 0.825771i \(-0.309260\pi\)
0.564005 + 0.825771i \(0.309260\pi\)
\(224\) 2.86716 0.191570
\(225\) 0 0
\(226\) −0.701084 −0.0466354
\(227\) 12.6662 0.840684 0.420342 0.907366i \(-0.361910\pi\)
0.420342 + 0.907366i \(0.361910\pi\)
\(228\) 0 0
\(229\) −17.1710 −1.13469 −0.567347 0.823479i \(-0.692030\pi\)
−0.567347 + 0.823479i \(0.692030\pi\)
\(230\) −0.697291 −0.0459780
\(231\) 0 0
\(232\) 4.99092 0.327670
\(233\) 10.5646 0.692110 0.346055 0.938214i \(-0.387521\pi\)
0.346055 + 0.938214i \(0.387521\pi\)
\(234\) 0 0
\(235\) −0.344215 −0.0224541
\(236\) −18.2287 −1.18659
\(237\) 0 0
\(238\) 1.87172 0.121325
\(239\) 26.4159 1.70870 0.854352 0.519695i \(-0.173955\pi\)
0.854352 + 0.519695i \(0.173955\pi\)
\(240\) 0 0
\(241\) −12.0042 −0.773261 −0.386631 0.922235i \(-0.626361\pi\)
−0.386631 + 0.922235i \(0.626361\pi\)
\(242\) −1.72527 −0.110905
\(243\) 0 0
\(244\) 6.60052 0.422555
\(245\) −0.989651 −0.0632265
\(246\) 0 0
\(247\) 31.9630 2.03376
\(248\) −1.12241 −0.0712732
\(249\) 0 0
\(250\) 2.22433 0.140679
\(251\) 26.9138 1.69878 0.849391 0.527764i \(-0.176970\pi\)
0.849391 + 0.527764i \(0.176970\pi\)
\(252\) 0 0
\(253\) 5.70889 0.358915
\(254\) 0.249163 0.0156339
\(255\) 0 0
\(256\) 11.2614 0.703835
\(257\) 15.2607 0.951934 0.475967 0.879463i \(-0.342098\pi\)
0.475967 + 0.879463i \(0.342098\pi\)
\(258\) 0 0
\(259\) 10.6080 0.659147
\(260\) 8.01713 0.497201
\(261\) 0 0
\(262\) 0.0597953 0.00369416
\(263\) −8.60088 −0.530353 −0.265176 0.964200i \(-0.585430\pi\)
−0.265176 + 0.964200i \(0.585430\pi\)
\(264\) 0 0
\(265\) −4.29422 −0.263792
\(266\) 1.90515 0.116812
\(267\) 0 0
\(268\) −10.9617 −0.669590
\(269\) 11.7574 0.716862 0.358431 0.933556i \(-0.383312\pi\)
0.358431 + 0.933556i \(0.383312\pi\)
\(270\) 0 0
\(271\) −15.0495 −0.914191 −0.457095 0.889418i \(-0.651110\pi\)
−0.457095 + 0.889418i \(0.651110\pi\)
\(272\) 27.2789 1.65403
\(273\) 0 0
\(274\) −3.78059 −0.228393
\(275\) −8.11694 −0.489470
\(276\) 0 0
\(277\) −21.7389 −1.30616 −0.653082 0.757287i \(-0.726524\pi\)
−0.653082 + 0.757287i \(0.726524\pi\)
\(278\) 0.267013 0.0160144
\(279\) 0 0
\(280\) 0.971028 0.0580300
\(281\) −7.64133 −0.455844 −0.227922 0.973679i \(-0.573193\pi\)
−0.227922 + 0.973679i \(0.573193\pi\)
\(282\) 0 0
\(283\) 17.9456 1.06675 0.533377 0.845878i \(-0.320923\pi\)
0.533377 + 0.845878i \(0.320923\pi\)
\(284\) 9.56040 0.567305
\(285\) 0 0
\(286\) 2.10275 0.124338
\(287\) −8.51782 −0.502791
\(288\) 0 0
\(289\) 39.4305 2.31944
\(290\) 1.25429 0.0736542
\(291\) 0 0
\(292\) −3.67350 −0.214976
\(293\) 13.9233 0.813407 0.406704 0.913560i \(-0.366678\pi\)
0.406704 + 0.913560i \(0.366678\pi\)
\(294\) 0 0
\(295\) −9.30901 −0.541991
\(296\) −10.4084 −0.604973
\(297\) 0 0
\(298\) −1.74477 −0.101072
\(299\) 11.8209 0.683620
\(300\) 0 0
\(301\) −2.46779 −0.142241
\(302\) −0.928250 −0.0534148
\(303\) 0 0
\(304\) 27.7661 1.59250
\(305\) 3.37074 0.193008
\(306\) 0 0
\(307\) 10.1985 0.582057 0.291029 0.956714i \(-0.406003\pi\)
0.291029 + 0.956714i \(0.406003\pi\)
\(308\) −3.91235 −0.222927
\(309\) 0 0
\(310\) −0.282077 −0.0160209
\(311\) −17.8032 −1.00953 −0.504765 0.863257i \(-0.668421\pi\)
−0.504765 + 0.863257i \(0.668421\pi\)
\(312\) 0 0
\(313\) −24.9298 −1.40912 −0.704559 0.709646i \(-0.748855\pi\)
−0.704559 + 0.709646i \(0.748855\pi\)
\(314\) 4.65248 0.262555
\(315\) 0 0
\(316\) −15.9769 −0.898771
\(317\) 11.8136 0.663518 0.331759 0.943364i \(-0.392358\pi\)
0.331759 + 0.943364i \(0.392358\pi\)
\(318\) 0 0
\(319\) −10.2691 −0.574961
\(320\) 6.48057 0.362275
\(321\) 0 0
\(322\) 0.704583 0.0392648
\(323\) 57.4385 3.19596
\(324\) 0 0
\(325\) −16.8070 −0.932287
\(326\) −0.745275 −0.0412770
\(327\) 0 0
\(328\) 8.35753 0.461467
\(329\) 0.347815 0.0191756
\(330\) 0 0
\(331\) −16.4087 −0.901905 −0.450952 0.892548i \(-0.648916\pi\)
−0.450952 + 0.892548i \(0.648916\pi\)
\(332\) 17.8496 0.979622
\(333\) 0 0
\(334\) 0.263083 0.0143952
\(335\) −5.59787 −0.305844
\(336\) 0 0
\(337\) 33.8302 1.84285 0.921424 0.388559i \(-0.127027\pi\)
0.921424 + 0.388559i \(0.127027\pi\)
\(338\) 1.11486 0.0606403
\(339\) 0 0
\(340\) 14.4070 0.781331
\(341\) 2.30943 0.125063
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 2.42135 0.130551
\(345\) 0 0
\(346\) 3.59313 0.193168
\(347\) 0.903135 0.0484828 0.0242414 0.999706i \(-0.492283\pi\)
0.0242414 + 0.999706i \(0.492283\pi\)
\(348\) 0 0
\(349\) −15.6244 −0.836356 −0.418178 0.908365i \(-0.637331\pi\)
−0.418178 + 0.908365i \(0.637331\pi\)
\(350\) −1.00178 −0.0535474
\(351\) 0 0
\(352\) 5.78836 0.308520
\(353\) −2.70320 −0.143877 −0.0719384 0.997409i \(-0.522919\pi\)
−0.0719384 + 0.997409i \(0.522919\pi\)
\(354\) 0 0
\(355\) 4.88228 0.259124
\(356\) −2.19339 −0.116250
\(357\) 0 0
\(358\) −5.64137 −0.298156
\(359\) 26.8365 1.41638 0.708188 0.706024i \(-0.249513\pi\)
0.708188 + 0.706024i \(0.249513\pi\)
\(360\) 0 0
\(361\) 39.4644 2.07708
\(362\) 5.49727 0.288930
\(363\) 0 0
\(364\) −8.10096 −0.424606
\(365\) −1.87598 −0.0981931
\(366\) 0 0
\(367\) −29.8366 −1.55746 −0.778729 0.627361i \(-0.784135\pi\)
−0.778729 + 0.627361i \(0.784135\pi\)
\(368\) 10.2688 0.535297
\(369\) 0 0
\(370\) −2.61576 −0.135987
\(371\) 4.33912 0.225276
\(372\) 0 0
\(373\) −3.76444 −0.194915 −0.0974577 0.995240i \(-0.531071\pi\)
−0.0974577 + 0.995240i \(0.531071\pi\)
\(374\) 3.77870 0.195392
\(375\) 0 0
\(376\) −0.341270 −0.0175996
\(377\) −21.2634 −1.09512
\(378\) 0 0
\(379\) −22.4272 −1.15201 −0.576004 0.817447i \(-0.695389\pi\)
−0.576004 + 0.817447i \(0.695389\pi\)
\(380\) 14.6644 0.752266
\(381\) 0 0
\(382\) −5.79720 −0.296610
\(383\) 7.38438 0.377324 0.188662 0.982042i \(-0.439585\pi\)
0.188662 + 0.982042i \(0.439585\pi\)
\(384\) 0 0
\(385\) −1.99795 −0.101825
\(386\) 6.02267 0.306546
\(387\) 0 0
\(388\) −36.2366 −1.83964
\(389\) −31.3727 −1.59066 −0.795328 0.606179i \(-0.792702\pi\)
−0.795328 + 0.606179i \(0.792702\pi\)
\(390\) 0 0
\(391\) 21.2425 1.07428
\(392\) −0.981182 −0.0495572
\(393\) 0 0
\(394\) −0.458429 −0.0230953
\(395\) −8.15904 −0.410526
\(396\) 0 0
\(397\) −4.82272 −0.242045 −0.121023 0.992650i \(-0.538617\pi\)
−0.121023 + 0.992650i \(0.538617\pi\)
\(398\) 2.18203 0.109375
\(399\) 0 0
\(400\) −14.6002 −0.730011
\(401\) −9.35881 −0.467357 −0.233678 0.972314i \(-0.575076\pi\)
−0.233678 + 0.972314i \(0.575076\pi\)
\(402\) 0 0
\(403\) 4.78194 0.238205
\(404\) 7.96152 0.396100
\(405\) 0 0
\(406\) −1.26740 −0.0629001
\(407\) 21.4158 1.06154
\(408\) 0 0
\(409\) −7.09685 −0.350917 −0.175458 0.984487i \(-0.556141\pi\)
−0.175458 + 0.984487i \(0.556141\pi\)
\(410\) 2.10036 0.103729
\(411\) 0 0
\(412\) 17.5425 0.864257
\(413\) 9.40635 0.462856
\(414\) 0 0
\(415\) 9.11537 0.447456
\(416\) 11.9854 0.587634
\(417\) 0 0
\(418\) 3.84620 0.188124
\(419\) −17.5160 −0.855715 −0.427857 0.903846i \(-0.640731\pi\)
−0.427857 + 0.903846i \(0.640731\pi\)
\(420\) 0 0
\(421\) 13.4704 0.656507 0.328254 0.944590i \(-0.393540\pi\)
0.328254 + 0.944590i \(0.393540\pi\)
\(422\) 0.378674 0.0184336
\(423\) 0 0
\(424\) −4.25747 −0.206761
\(425\) −30.2028 −1.46505
\(426\) 0 0
\(427\) −3.40599 −0.164827
\(428\) 26.8430 1.29750
\(429\) 0 0
\(430\) 0.608518 0.0293453
\(431\) −10.2490 −0.493677 −0.246839 0.969057i \(-0.579392\pi\)
−0.246839 + 0.969057i \(0.579392\pi\)
\(432\) 0 0
\(433\) 13.8600 0.666071 0.333035 0.942914i \(-0.391927\pi\)
0.333035 + 0.942914i \(0.391927\pi\)
\(434\) 0.285027 0.0136817
\(435\) 0 0
\(436\) 17.9682 0.860521
\(437\) 21.6219 1.03432
\(438\) 0 0
\(439\) −29.2215 −1.39467 −0.697333 0.716748i \(-0.745630\pi\)
−0.697333 + 0.716748i \(0.745630\pi\)
\(440\) 1.96035 0.0934562
\(441\) 0 0
\(442\) 7.82423 0.372160
\(443\) 32.0230 1.52146 0.760729 0.649070i \(-0.224842\pi\)
0.760729 + 0.649070i \(0.224842\pi\)
\(444\) 0 0
\(445\) −1.12012 −0.0530986
\(446\) 4.19709 0.198738
\(447\) 0 0
\(448\) −6.54833 −0.309380
\(449\) −27.7086 −1.30765 −0.653824 0.756647i \(-0.726836\pi\)
−0.653824 + 0.756647i \(0.726836\pi\)
\(450\) 0 0
\(451\) −17.1961 −0.809735
\(452\) 5.45284 0.256480
\(453\) 0 0
\(454\) 3.15594 0.148116
\(455\) −4.13698 −0.193945
\(456\) 0 0
\(457\) −18.9872 −0.888184 −0.444092 0.895981i \(-0.646474\pi\)
−0.444092 + 0.895981i \(0.646474\pi\)
\(458\) −4.27838 −0.199916
\(459\) 0 0
\(460\) 5.42333 0.252864
\(461\) −20.9874 −0.977481 −0.488740 0.872429i \(-0.662544\pi\)
−0.488740 + 0.872429i \(0.662544\pi\)
\(462\) 0 0
\(463\) −21.5933 −1.00353 −0.501763 0.865005i \(-0.667315\pi\)
−0.501763 + 0.865005i \(0.667315\pi\)
\(464\) −18.4714 −0.857515
\(465\) 0 0
\(466\) 2.63231 0.121939
\(467\) −24.6377 −1.14010 −0.570048 0.821611i \(-0.693075\pi\)
−0.570048 + 0.821611i \(0.693075\pi\)
\(468\) 0 0
\(469\) 5.65641 0.261189
\(470\) −0.0857656 −0.00395607
\(471\) 0 0
\(472\) −9.22934 −0.424815
\(473\) −4.98209 −0.229077
\(474\) 0 0
\(475\) −30.7423 −1.41055
\(476\) −14.5577 −0.667251
\(477\) 0 0
\(478\) 6.58186 0.301047
\(479\) 20.7967 0.950226 0.475113 0.879925i \(-0.342407\pi\)
0.475113 + 0.879925i \(0.342407\pi\)
\(480\) 0 0
\(481\) 44.3439 2.02191
\(482\) −2.99101 −0.136237
\(483\) 0 0
\(484\) 13.4187 0.609939
\(485\) −18.5052 −0.840279
\(486\) 0 0
\(487\) 15.7043 0.711628 0.355814 0.934557i \(-0.384204\pi\)
0.355814 + 0.934557i \(0.384204\pi\)
\(488\) 3.34189 0.151280
\(489\) 0 0
\(490\) −0.246584 −0.0111395
\(491\) 36.7734 1.65956 0.829781 0.558089i \(-0.188465\pi\)
0.829781 + 0.558089i \(0.188465\pi\)
\(492\) 0 0
\(493\) −38.2110 −1.72094
\(494\) 7.96398 0.358316
\(495\) 0 0
\(496\) 4.15406 0.186523
\(497\) −4.93333 −0.221290
\(498\) 0 0
\(499\) −13.7782 −0.616796 −0.308398 0.951257i \(-0.599793\pi\)
−0.308398 + 0.951257i \(0.599793\pi\)
\(500\) −17.3003 −0.773691
\(501\) 0 0
\(502\) 6.70590 0.299299
\(503\) −4.77246 −0.212793 −0.106397 0.994324i \(-0.533931\pi\)
−0.106397 + 0.994324i \(0.533931\pi\)
\(504\) 0 0
\(505\) 4.06577 0.180924
\(506\) 1.42244 0.0632353
\(507\) 0 0
\(508\) −1.93792 −0.0859812
\(509\) 40.0552 1.77541 0.887707 0.460409i \(-0.152297\pi\)
0.887707 + 0.460409i \(0.152297\pi\)
\(510\) 0 0
\(511\) 1.89559 0.0838561
\(512\) 17.5378 0.775067
\(513\) 0 0
\(514\) 3.80239 0.167716
\(515\) 8.95856 0.394761
\(516\) 0 0
\(517\) 0.702184 0.0308820
\(518\) 2.64311 0.116132
\(519\) 0 0
\(520\) 4.05913 0.178005
\(521\) −30.7739 −1.34823 −0.674114 0.738627i \(-0.735474\pi\)
−0.674114 + 0.738627i \(0.735474\pi\)
\(522\) 0 0
\(523\) 28.3386 1.23916 0.619580 0.784933i \(-0.287303\pi\)
0.619580 + 0.784933i \(0.287303\pi\)
\(524\) −0.465071 −0.0203167
\(525\) 0 0
\(526\) −2.14302 −0.0934400
\(527\) 8.59330 0.374330
\(528\) 0 0
\(529\) −15.0035 −0.652328
\(530\) −1.06996 −0.0464760
\(531\) 0 0
\(532\) −14.8177 −0.642429
\(533\) −35.6065 −1.54229
\(534\) 0 0
\(535\) 13.7081 0.592653
\(536\) −5.54997 −0.239722
\(537\) 0 0
\(538\) 2.92951 0.126300
\(539\) 2.01884 0.0869578
\(540\) 0 0
\(541\) −16.3417 −0.702585 −0.351292 0.936266i \(-0.614258\pi\)
−0.351292 + 0.936266i \(0.614258\pi\)
\(542\) −3.74977 −0.161066
\(543\) 0 0
\(544\) 21.5382 0.923443
\(545\) 9.17596 0.393055
\(546\) 0 0
\(547\) −22.5444 −0.963930 −0.481965 0.876191i \(-0.660077\pi\)
−0.481965 + 0.876191i \(0.660077\pi\)
\(548\) 29.4043 1.25609
\(549\) 0 0
\(550\) −2.02244 −0.0862371
\(551\) −38.8935 −1.65692
\(552\) 0 0
\(553\) 8.24436 0.350586
\(554\) −5.41652 −0.230126
\(555\) 0 0
\(556\) −2.07675 −0.0880738
\(557\) 18.6953 0.792147 0.396074 0.918219i \(-0.370372\pi\)
0.396074 + 0.918219i \(0.370372\pi\)
\(558\) 0 0
\(559\) −10.3160 −0.436319
\(560\) −3.59378 −0.151865
\(561\) 0 0
\(562\) −1.90393 −0.0803126
\(563\) 19.7540 0.832530 0.416265 0.909243i \(-0.363339\pi\)
0.416265 + 0.909243i \(0.363339\pi\)
\(564\) 0 0
\(565\) 2.78464 0.117151
\(566\) 4.47137 0.187946
\(567\) 0 0
\(568\) 4.84050 0.203103
\(569\) −26.0936 −1.09390 −0.546950 0.837165i \(-0.684211\pi\)
−0.546950 + 0.837165i \(0.684211\pi\)
\(570\) 0 0
\(571\) −36.6941 −1.53560 −0.767801 0.640688i \(-0.778649\pi\)
−0.767801 + 0.640688i \(0.778649\pi\)
\(572\) −16.3546 −0.683819
\(573\) 0 0
\(574\) −2.12232 −0.0885840
\(575\) −11.3694 −0.474138
\(576\) 0 0
\(577\) −39.8155 −1.65754 −0.828771 0.559589i \(-0.810959\pi\)
−0.828771 + 0.559589i \(0.810959\pi\)
\(578\) 9.82462 0.408650
\(579\) 0 0
\(580\) −9.75548 −0.405074
\(581\) −9.21069 −0.382124
\(582\) 0 0
\(583\) 8.76001 0.362803
\(584\) −1.85992 −0.0769641
\(585\) 0 0
\(586\) 3.46916 0.143310
\(587\) 34.3425 1.41747 0.708734 0.705476i \(-0.249267\pi\)
0.708734 + 0.705476i \(0.249267\pi\)
\(588\) 0 0
\(589\) 8.74679 0.360405
\(590\) −2.31946 −0.0954905
\(591\) 0 0
\(592\) 38.5214 1.58322
\(593\) 12.0324 0.494111 0.247055 0.969001i \(-0.420537\pi\)
0.247055 + 0.969001i \(0.420537\pi\)
\(594\) 0 0
\(595\) −7.43428 −0.304776
\(596\) 13.5703 0.555861
\(597\) 0 0
\(598\) 2.94533 0.120443
\(599\) 41.4773 1.69472 0.847358 0.531021i \(-0.178192\pi\)
0.847358 + 0.531021i \(0.178192\pi\)
\(600\) 0 0
\(601\) 9.46716 0.386174 0.193087 0.981182i \(-0.438150\pi\)
0.193087 + 0.981182i \(0.438150\pi\)
\(602\) −0.614881 −0.0250607
\(603\) 0 0
\(604\) 7.21967 0.293764
\(605\) 6.85261 0.278598
\(606\) 0 0
\(607\) −15.9801 −0.648613 −0.324306 0.945952i \(-0.605131\pi\)
−0.324306 + 0.945952i \(0.605131\pi\)
\(608\) 21.9229 0.889092
\(609\) 0 0
\(610\) 0.839862 0.0340050
\(611\) 1.45395 0.0588205
\(612\) 0 0
\(613\) 0.360332 0.0145537 0.00727683 0.999974i \(-0.497684\pi\)
0.00727683 + 0.999974i \(0.497684\pi\)
\(614\) 2.54108 0.102550
\(615\) 0 0
\(616\) −1.98085 −0.0798109
\(617\) 5.97404 0.240506 0.120253 0.992743i \(-0.461629\pi\)
0.120253 + 0.992743i \(0.461629\pi\)
\(618\) 0 0
\(619\) −3.06486 −0.123187 −0.0615935 0.998101i \(-0.519618\pi\)
−0.0615935 + 0.998101i \(0.519618\pi\)
\(620\) 2.19392 0.0881098
\(621\) 0 0
\(622\) −4.43590 −0.177863
\(623\) 1.13183 0.0453458
\(624\) 0 0
\(625\) 11.2681 0.450724
\(626\) −6.21158 −0.248265
\(627\) 0 0
\(628\) −36.1857 −1.44397
\(629\) 79.6874 3.17734
\(630\) 0 0
\(631\) 18.2128 0.725041 0.362521 0.931976i \(-0.381916\pi\)
0.362521 + 0.931976i \(0.381916\pi\)
\(632\) −8.08922 −0.321772
\(633\) 0 0
\(634\) 2.94351 0.116902
\(635\) −0.989651 −0.0392731
\(636\) 0 0
\(637\) 4.18024 0.165627
\(638\) −2.55869 −0.101299
\(639\) 0 0
\(640\) 7.28970 0.288151
\(641\) 12.4263 0.490808 0.245404 0.969421i \(-0.421079\pi\)
0.245404 + 0.969421i \(0.421079\pi\)
\(642\) 0 0
\(643\) 30.7289 1.21183 0.605914 0.795530i \(-0.292807\pi\)
0.605914 + 0.795530i \(0.292807\pi\)
\(644\) −5.48005 −0.215944
\(645\) 0 0
\(646\) 14.3115 0.563079
\(647\) −29.0224 −1.14099 −0.570493 0.821302i \(-0.693248\pi\)
−0.570493 + 0.821302i \(0.693248\pi\)
\(648\) 0 0
\(649\) 18.9900 0.745421
\(650\) −4.18769 −0.164255
\(651\) 0 0
\(652\) 5.79654 0.227010
\(653\) 37.0748 1.45085 0.725424 0.688302i \(-0.241644\pi\)
0.725424 + 0.688302i \(0.241644\pi\)
\(654\) 0 0
\(655\) −0.237501 −0.00927994
\(656\) −30.9313 −1.20766
\(657\) 0 0
\(658\) 0.0866624 0.00337845
\(659\) 22.7194 0.885021 0.442511 0.896763i \(-0.354088\pi\)
0.442511 + 0.896763i \(0.354088\pi\)
\(660\) 0 0
\(661\) 12.5855 0.489519 0.244759 0.969584i \(-0.421291\pi\)
0.244759 + 0.969584i \(0.421291\pi\)
\(662\) −4.08844 −0.158902
\(663\) 0 0
\(664\) 9.03737 0.350718
\(665\) −7.56707 −0.293439
\(666\) 0 0
\(667\) −14.3840 −0.556951
\(668\) −2.04618 −0.0791692
\(669\) 0 0
\(670\) −1.39478 −0.0538851
\(671\) −6.87616 −0.265451
\(672\) 0 0
\(673\) 42.2339 1.62800 0.813999 0.580866i \(-0.197286\pi\)
0.813999 + 0.580866i \(0.197286\pi\)
\(674\) 8.42922 0.324681
\(675\) 0 0
\(676\) −8.67105 −0.333502
\(677\) −8.92244 −0.342917 −0.171459 0.985191i \(-0.554848\pi\)
−0.171459 + 0.985191i \(0.554848\pi\)
\(678\) 0 0
\(679\) 18.6987 0.717592
\(680\) 7.29439 0.279727
\(681\) 0 0
\(682\) 0.575425 0.0220341
\(683\) 29.9500 1.14600 0.573002 0.819554i \(-0.305779\pi\)
0.573002 + 0.819554i \(0.305779\pi\)
\(684\) 0 0
\(685\) 15.0161 0.573737
\(686\) 0.249163 0.00951307
\(687\) 0 0
\(688\) −8.96144 −0.341652
\(689\) 18.1386 0.691025
\(690\) 0 0
\(691\) −11.8529 −0.450905 −0.225453 0.974254i \(-0.572386\pi\)
−0.225453 + 0.974254i \(0.572386\pi\)
\(692\) −27.9463 −1.06236
\(693\) 0 0
\(694\) 0.225027 0.00854192
\(695\) −1.06055 −0.0402289
\(696\) 0 0
\(697\) −63.9861 −2.42364
\(698\) −3.89302 −0.147353
\(699\) 0 0
\(700\) 7.79158 0.294494
\(701\) 35.9250 1.35687 0.678434 0.734662i \(-0.262659\pi\)
0.678434 + 0.734662i \(0.262659\pi\)
\(702\) 0 0
\(703\) 81.1107 3.05915
\(704\) −13.2201 −0.498250
\(705\) 0 0
\(706\) −0.673537 −0.0253489
\(707\) −4.10828 −0.154508
\(708\) 0 0
\(709\) 4.74062 0.178038 0.0890189 0.996030i \(-0.471627\pi\)
0.0890189 + 0.996030i \(0.471627\pi\)
\(710\) 1.21648 0.0456537
\(711\) 0 0
\(712\) −1.11053 −0.0416189
\(713\) 3.23483 0.121145
\(714\) 0 0
\(715\) −8.35192 −0.312344
\(716\) 43.8770 1.63976
\(717\) 0 0
\(718\) 6.68665 0.249544
\(719\) −24.3352 −0.907551 −0.453776 0.891116i \(-0.649923\pi\)
−0.453776 + 0.891116i \(0.649923\pi\)
\(720\) 0 0
\(721\) −9.05224 −0.337123
\(722\) 9.83306 0.365949
\(723\) 0 0
\(724\) −42.7563 −1.58902
\(725\) 20.4513 0.759543
\(726\) 0 0
\(727\) −3.13742 −0.116360 −0.0581802 0.998306i \(-0.518530\pi\)
−0.0581802 + 0.998306i \(0.518530\pi\)
\(728\) −4.10158 −0.152015
\(729\) 0 0
\(730\) −0.467423 −0.0173001
\(731\) −18.5381 −0.685657
\(732\) 0 0
\(733\) 31.0961 1.14856 0.574280 0.818659i \(-0.305282\pi\)
0.574280 + 0.818659i \(0.305282\pi\)
\(734\) −7.43416 −0.274400
\(735\) 0 0
\(736\) 8.10777 0.298856
\(737\) 11.4194 0.420639
\(738\) 0 0
\(739\) 30.3763 1.11741 0.558705 0.829367i \(-0.311299\pi\)
0.558705 + 0.829367i \(0.311299\pi\)
\(740\) 20.3446 0.747884
\(741\) 0 0
\(742\) 1.08115 0.0396902
\(743\) 33.5807 1.23196 0.615979 0.787763i \(-0.288761\pi\)
0.615979 + 0.787763i \(0.288761\pi\)
\(744\) 0 0
\(745\) 6.93005 0.253897
\(746\) −0.937959 −0.0343411
\(747\) 0 0
\(748\) −29.3897 −1.07459
\(749\) −13.8515 −0.506121
\(750\) 0 0
\(751\) −20.1545 −0.735447 −0.367723 0.929935i \(-0.619863\pi\)
−0.367723 + 0.929935i \(0.619863\pi\)
\(752\) 1.26304 0.0460584
\(753\) 0 0
\(754\) −5.29804 −0.192943
\(755\) 3.68692 0.134181
\(756\) 0 0
\(757\) −19.0444 −0.692182 −0.346091 0.938201i \(-0.612491\pi\)
−0.346091 + 0.938201i \(0.612491\pi\)
\(758\) −5.58802 −0.202966
\(759\) 0 0
\(760\) 7.42468 0.269321
\(761\) −28.3840 −1.02892 −0.514459 0.857515i \(-0.672007\pi\)
−0.514459 + 0.857515i \(0.672007\pi\)
\(762\) 0 0
\(763\) −9.27191 −0.335666
\(764\) 45.0890 1.63126
\(765\) 0 0
\(766\) 1.83991 0.0664787
\(767\) 39.3208 1.41979
\(768\) 0 0
\(769\) −48.5905 −1.75222 −0.876110 0.482112i \(-0.839870\pi\)
−0.876110 + 0.482112i \(0.839870\pi\)
\(770\) −0.497815 −0.0179400
\(771\) 0 0
\(772\) −46.8426 −1.68590
\(773\) −28.9932 −1.04281 −0.521407 0.853308i \(-0.674592\pi\)
−0.521407 + 0.853308i \(0.674592\pi\)
\(774\) 0 0
\(775\) −4.59931 −0.165212
\(776\) −18.3469 −0.658614
\(777\) 0 0
\(778\) −7.81689 −0.280249
\(779\) −65.1290 −2.33349
\(780\) 0 0
\(781\) −9.95963 −0.356384
\(782\) 5.29284 0.189272
\(783\) 0 0
\(784\) 3.63136 0.129692
\(785\) −18.4792 −0.659552
\(786\) 0 0
\(787\) −23.2829 −0.829946 −0.414973 0.909834i \(-0.636209\pi\)
−0.414973 + 0.909834i \(0.636209\pi\)
\(788\) 3.56554 0.127017
\(789\) 0 0
\(790\) −2.03293 −0.0723283
\(791\) −2.81376 −0.100046
\(792\) 0 0
\(793\) −14.2378 −0.505601
\(794\) −1.20164 −0.0426446
\(795\) 0 0
\(796\) −16.9712 −0.601529
\(797\) 38.6556 1.36925 0.684625 0.728895i \(-0.259966\pi\)
0.684625 + 0.728895i \(0.259966\pi\)
\(798\) 0 0
\(799\) 2.61279 0.0924340
\(800\) −11.5277 −0.407565
\(801\) 0 0
\(802\) −2.33187 −0.0823411
\(803\) 3.82691 0.135049
\(804\) 0 0
\(805\) −2.79854 −0.0986355
\(806\) 1.19148 0.0419681
\(807\) 0 0
\(808\) 4.03098 0.141809
\(809\) 34.9165 1.22760 0.613799 0.789463i \(-0.289641\pi\)
0.613799 + 0.789463i \(0.289641\pi\)
\(810\) 0 0
\(811\) −21.9951 −0.772354 −0.386177 0.922425i \(-0.626205\pi\)
−0.386177 + 0.922425i \(0.626205\pi\)
\(812\) 9.85750 0.345930
\(813\) 0 0
\(814\) 5.33603 0.187028
\(815\) 2.96016 0.103690
\(816\) 0 0
\(817\) −18.8692 −0.660151
\(818\) −1.76827 −0.0618261
\(819\) 0 0
\(820\) −16.3360 −0.570478
\(821\) −22.7829 −0.795128 −0.397564 0.917574i \(-0.630144\pi\)
−0.397564 + 0.917574i \(0.630144\pi\)
\(822\) 0 0
\(823\) 21.4790 0.748711 0.374355 0.927285i \(-0.377864\pi\)
0.374355 + 0.927285i \(0.377864\pi\)
\(824\) 8.88190 0.309416
\(825\) 0 0
\(826\) 2.34371 0.0815481
\(827\) −46.5756 −1.61959 −0.809795 0.586712i \(-0.800422\pi\)
−0.809795 + 0.586712i \(0.800422\pi\)
\(828\) 0 0
\(829\) 8.19813 0.284733 0.142366 0.989814i \(-0.454529\pi\)
0.142366 + 0.989814i \(0.454529\pi\)
\(830\) 2.27121 0.0788348
\(831\) 0 0
\(832\) −27.3736 −0.949009
\(833\) 7.51203 0.260276
\(834\) 0 0
\(835\) −1.04494 −0.0361616
\(836\) −29.9147 −1.03462
\(837\) 0 0
\(838\) −4.36434 −0.150764
\(839\) 9.68783 0.334461 0.167230 0.985918i \(-0.446518\pi\)
0.167230 + 0.985918i \(0.446518\pi\)
\(840\) 0 0
\(841\) −3.12607 −0.107795
\(842\) 3.35632 0.115666
\(843\) 0 0
\(844\) −2.94522 −0.101379
\(845\) −4.42811 −0.152332
\(846\) 0 0
\(847\) −6.92427 −0.237921
\(848\) 15.7569 0.541095
\(849\) 0 0
\(850\) −7.52541 −0.258119
\(851\) 29.9972 1.02829
\(852\) 0 0
\(853\) −6.08607 −0.208383 −0.104192 0.994557i \(-0.533225\pi\)
−0.104192 + 0.994557i \(0.533225\pi\)
\(854\) −0.848645 −0.0290400
\(855\) 0 0
\(856\) 13.5908 0.464524
\(857\) 7.84241 0.267892 0.133946 0.990989i \(-0.457235\pi\)
0.133946 + 0.990989i \(0.457235\pi\)
\(858\) 0 0
\(859\) −7.86004 −0.268181 −0.134091 0.990969i \(-0.542811\pi\)
−0.134091 + 0.990969i \(0.542811\pi\)
\(860\) −4.73288 −0.161390
\(861\) 0 0
\(862\) −2.55367 −0.0869784
\(863\) −0.941391 −0.0320453 −0.0160227 0.999872i \(-0.505100\pi\)
−0.0160227 + 0.999872i \(0.505100\pi\)
\(864\) 0 0
\(865\) −14.2716 −0.485248
\(866\) 3.45340 0.117351
\(867\) 0 0
\(868\) −2.21686 −0.0752451
\(869\) 16.6441 0.564612
\(870\) 0 0
\(871\) 23.6452 0.801185
\(872\) 9.09743 0.308078
\(873\) 0 0
\(874\) 5.38738 0.182231
\(875\) 8.92724 0.301796
\(876\) 0 0
\(877\) 18.9307 0.639245 0.319622 0.947545i \(-0.396444\pi\)
0.319622 + 0.947545i \(0.396444\pi\)
\(878\) −7.28090 −0.245719
\(879\) 0 0
\(880\) −7.25528 −0.244576
\(881\) 11.4488 0.385720 0.192860 0.981226i \(-0.438224\pi\)
0.192860 + 0.981226i \(0.438224\pi\)
\(882\) 0 0
\(883\) −12.2769 −0.413150 −0.206575 0.978431i \(-0.566232\pi\)
−0.206575 + 0.978431i \(0.566232\pi\)
\(884\) −60.8547 −2.04676
\(885\) 0 0
\(886\) 7.97893 0.268057
\(887\) −46.7593 −1.57002 −0.785012 0.619481i \(-0.787343\pi\)
−0.785012 + 0.619481i \(0.787343\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −0.279091 −0.00935516
\(891\) 0 0
\(892\) −32.6438 −1.09300
\(893\) 2.65946 0.0889955
\(894\) 0 0
\(895\) 22.4070 0.748983
\(896\) −7.36593 −0.246078
\(897\) 0 0
\(898\) −6.90394 −0.230387
\(899\) −5.81881 −0.194068
\(900\) 0 0
\(901\) 32.5956 1.08592
\(902\) −4.28464 −0.142663
\(903\) 0 0
\(904\) 2.76081 0.0918232
\(905\) −21.8347 −0.725808
\(906\) 0 0
\(907\) −32.9186 −1.09305 −0.546523 0.837444i \(-0.684049\pi\)
−0.546523 + 0.837444i \(0.684049\pi\)
\(908\) −24.5460 −0.814588
\(909\) 0 0
\(910\) −1.03078 −0.0341701
\(911\) 35.2054 1.16641 0.583204 0.812326i \(-0.301799\pi\)
0.583204 + 0.812326i \(0.301799\pi\)
\(912\) 0 0
\(913\) −18.5949 −0.615403
\(914\) −4.73090 −0.156484
\(915\) 0 0
\(916\) 33.2761 1.09947
\(917\) 0.239985 0.00792500
\(918\) 0 0
\(919\) −6.74081 −0.222359 −0.111179 0.993800i \(-0.535463\pi\)
−0.111179 + 0.993800i \(0.535463\pi\)
\(920\) 2.74587 0.0905288
\(921\) 0 0
\(922\) −5.22928 −0.172217
\(923\) −20.6225 −0.678799
\(924\) 0 0
\(925\) −42.6503 −1.40233
\(926\) −5.38024 −0.176806
\(927\) 0 0
\(928\) −14.5842 −0.478751
\(929\) −2.08267 −0.0683303 −0.0341652 0.999416i \(-0.510877\pi\)
−0.0341652 + 0.999416i \(0.510877\pi\)
\(930\) 0 0
\(931\) 7.64620 0.250594
\(932\) −20.4733 −0.670627
\(933\) 0 0
\(934\) −6.13879 −0.200867
\(935\) −15.0087 −0.490836
\(936\) 0 0
\(937\) 19.5135 0.637479 0.318739 0.947842i \(-0.396741\pi\)
0.318739 + 0.947842i \(0.396741\pi\)
\(938\) 1.40937 0.0460174
\(939\) 0 0
\(940\) 0.667061 0.0217571
\(941\) −29.9195 −0.975347 −0.487673 0.873026i \(-0.662154\pi\)
−0.487673 + 0.873026i \(0.662154\pi\)
\(942\) 0 0
\(943\) −24.0867 −0.784371
\(944\) 34.1579 1.11174
\(945\) 0 0
\(946\) −1.24135 −0.0403598
\(947\) −2.17516 −0.0706831 −0.0353415 0.999375i \(-0.511252\pi\)
−0.0353415 + 0.999375i \(0.511252\pi\)
\(948\) 0 0
\(949\) 7.92404 0.257225
\(950\) −7.65982 −0.248517
\(951\) 0 0
\(952\) −7.37067 −0.238885
\(953\) −36.1891 −1.17228 −0.586140 0.810210i \(-0.699353\pi\)
−0.586140 + 0.810210i \(0.699353\pi\)
\(954\) 0 0
\(955\) 23.0259 0.745102
\(956\) −51.1919 −1.65566
\(957\) 0 0
\(958\) 5.18177 0.167415
\(959\) −15.1732 −0.489967
\(960\) 0 0
\(961\) −29.6914 −0.957787
\(962\) 11.0488 0.356229
\(963\) 0 0
\(964\) 23.2632 0.749259
\(965\) −23.9215 −0.770060
\(966\) 0 0
\(967\) −44.8359 −1.44183 −0.720913 0.693026i \(-0.756277\pi\)
−0.720913 + 0.693026i \(0.756277\pi\)
\(968\) 6.79397 0.218366
\(969\) 0 0
\(970\) −4.61081 −0.148044
\(971\) −43.3703 −1.39182 −0.695910 0.718129i \(-0.744999\pi\)
−0.695910 + 0.718129i \(0.744999\pi\)
\(972\) 0 0
\(973\) 1.07164 0.0343552
\(974\) 3.91291 0.125378
\(975\) 0 0
\(976\) −12.3684 −0.395902
\(977\) 27.9074 0.892837 0.446419 0.894824i \(-0.352699\pi\)
0.446419 + 0.894824i \(0.352699\pi\)
\(978\) 0 0
\(979\) 2.28499 0.0730285
\(980\) 1.91786 0.0612639
\(981\) 0 0
\(982\) 9.16257 0.292389
\(983\) −44.0231 −1.40412 −0.702059 0.712118i \(-0.747736\pi\)
−0.702059 + 0.712118i \(0.747736\pi\)
\(984\) 0 0
\(985\) 1.82084 0.0580168
\(986\) −9.52075 −0.303203
\(987\) 0 0
\(988\) −61.9416 −1.97063
\(989\) −6.97842 −0.221901
\(990\) 0 0
\(991\) 37.6198 1.19503 0.597516 0.801857i \(-0.296154\pi\)
0.597516 + 0.801857i \(0.296154\pi\)
\(992\) 3.27986 0.104136
\(993\) 0 0
\(994\) −1.22920 −0.0389879
\(995\) −8.66682 −0.274757
\(996\) 0 0
\(997\) 52.6691 1.66805 0.834023 0.551729i \(-0.186032\pi\)
0.834023 + 0.551729i \(0.186032\pi\)
\(998\) −3.43301 −0.108670
\(999\) 0 0
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 \(a_p\))