Properties

Label 8001.2.a.v.1.13
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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 1.13
Root \(-0.782325\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.782325 q^{2}\) \(-1.38797 q^{4}\) \(+2.85652 q^{5}\) \(+1.00000 q^{7}\) \(-2.65049 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.782325 q^{2}\) \(-1.38797 q^{4}\) \(+2.85652 q^{5}\) \(+1.00000 q^{7}\) \(-2.65049 q^{8}\) \(+2.23472 q^{10}\) \(+5.95291 q^{11}\) \(-2.24308 q^{13}\) \(+0.782325 q^{14}\) \(+0.702387 q^{16}\) \(-0.355250 q^{17}\) \(+4.58452 q^{19}\) \(-3.96475 q^{20}\) \(+4.65711 q^{22}\) \(-1.77438 q^{23}\) \(+3.15968 q^{25}\) \(-1.75482 q^{26}\) \(-1.38797 q^{28}\) \(+9.18000 q^{29}\) \(-2.61888 q^{31}\) \(+5.85048 q^{32}\) \(-0.277921 q^{34}\) \(+2.85652 q^{35}\) \(+0.446439 q^{37}\) \(+3.58659 q^{38}\) \(-7.57117 q^{40}\) \(+5.55748 q^{41}\) \(-3.81437 q^{43}\) \(-8.26245 q^{44}\) \(-1.38814 q^{46}\) \(+4.89679 q^{47}\) \(+1.00000 q^{49}\) \(+2.47190 q^{50}\) \(+3.11332 q^{52}\) \(-12.9711 q^{53}\) \(+17.0046 q^{55}\) \(-2.65049 q^{56}\) \(+7.18175 q^{58}\) \(-5.34918 q^{59}\) \(+3.71025 q^{61}\) \(-2.04882 q^{62}\) \(+3.17221 q^{64}\) \(-6.40739 q^{65}\) \(+10.3248 q^{67}\) \(+0.493075 q^{68}\) \(+2.23472 q^{70}\) \(-1.31960 q^{71}\) \(-8.85675 q^{73}\) \(+0.349261 q^{74}\) \(-6.36316 q^{76}\) \(+5.95291 q^{77}\) \(+13.1696 q^{79}\) \(+2.00638 q^{80}\) \(+4.34776 q^{82}\) \(-15.2753 q^{83}\) \(-1.01478 q^{85}\) \(-2.98408 q^{86}\) \(-15.7782 q^{88}\) \(+2.60509 q^{89}\) \(-2.24308 q^{91}\) \(+2.46278 q^{92}\) \(+3.83088 q^{94}\) \(+13.0958 q^{95}\) \(-3.10938 q^{97}\) \(+0.782325 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut -\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 17q^{23} \) \(\mathstrut +\mathstrut 38q^{25} \) \(\mathstrut -\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut -\mathstrut 2q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut +\mathstrut 29q^{34} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut -\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 7q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 29q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut -\mathstrut 25q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 9q^{50} \) \(\mathstrut +\mathstrut 16q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut +\mathstrut 26q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut +\mathstrut 45q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 24q^{67} \) \(\mathstrut -\mathstrut 14q^{68} \) \(\mathstrut +\mathstrut 32q^{71} \) \(\mathstrut +\mathstrut 51q^{73} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 30q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 5q^{89} \) \(\mathstrut +\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 88q^{92} \) \(\mathstrut +\mathstrut 7q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 5q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.782325 0.553188 0.276594 0.960987i \(-0.410794\pi\)
0.276594 + 0.960987i \(0.410794\pi\)
\(3\) 0 0
\(4\) −1.38797 −0.693984
\(5\) 2.85652 1.27747 0.638736 0.769426i \(-0.279457\pi\)
0.638736 + 0.769426i \(0.279457\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.65049 −0.937091
\(9\) 0 0
\(10\) 2.23472 0.706682
\(11\) 5.95291 1.79487 0.897435 0.441146i \(-0.145428\pi\)
0.897435 + 0.441146i \(0.145428\pi\)
\(12\) 0 0
\(13\) −2.24308 −0.622118 −0.311059 0.950391i \(-0.600684\pi\)
−0.311059 + 0.950391i \(0.600684\pi\)
\(14\) 0.782325 0.209085
\(15\) 0 0
\(16\) 0.702387 0.175597
\(17\) −0.355250 −0.0861607 −0.0430803 0.999072i \(-0.513717\pi\)
−0.0430803 + 0.999072i \(0.513717\pi\)
\(18\) 0 0
\(19\) 4.58452 1.05176 0.525881 0.850558i \(-0.323736\pi\)
0.525881 + 0.850558i \(0.323736\pi\)
\(20\) −3.96475 −0.886545
\(21\) 0 0
\(22\) 4.65711 0.992900
\(23\) −1.77438 −0.369984 −0.184992 0.982740i \(-0.559226\pi\)
−0.184992 + 0.982740i \(0.559226\pi\)
\(24\) 0 0
\(25\) 3.15968 0.631936
\(26\) −1.75482 −0.344148
\(27\) 0 0
\(28\) −1.38797 −0.262301
\(29\) 9.18000 1.70468 0.852342 0.522985i \(-0.175182\pi\)
0.852342 + 0.522985i \(0.175182\pi\)
\(30\) 0 0
\(31\) −2.61888 −0.470365 −0.235183 0.971951i \(-0.575569\pi\)
−0.235183 + 0.971951i \(0.575569\pi\)
\(32\) 5.85048 1.03423
\(33\) 0 0
\(34\) −0.277921 −0.0476630
\(35\) 2.85652 0.482839
\(36\) 0 0
\(37\) 0.446439 0.0733942 0.0366971 0.999326i \(-0.488316\pi\)
0.0366971 + 0.999326i \(0.488316\pi\)
\(38\) 3.58659 0.581821
\(39\) 0 0
\(40\) −7.57117 −1.19711
\(41\) 5.55748 0.867932 0.433966 0.900929i \(-0.357114\pi\)
0.433966 + 0.900929i \(0.357114\pi\)
\(42\) 0 0
\(43\) −3.81437 −0.581685 −0.290843 0.956771i \(-0.593936\pi\)
−0.290843 + 0.956771i \(0.593936\pi\)
\(44\) −8.26245 −1.24561
\(45\) 0 0
\(46\) −1.38814 −0.204671
\(47\) 4.89679 0.714271 0.357135 0.934053i \(-0.383754\pi\)
0.357135 + 0.934053i \(0.383754\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 2.47190 0.349579
\(51\) 0 0
\(52\) 3.11332 0.431740
\(53\) −12.9711 −1.78171 −0.890856 0.454286i \(-0.849894\pi\)
−0.890856 + 0.454286i \(0.849894\pi\)
\(54\) 0 0
\(55\) 17.0046 2.29290
\(56\) −2.65049 −0.354187
\(57\) 0 0
\(58\) 7.18175 0.943010
\(59\) −5.34918 −0.696403 −0.348202 0.937420i \(-0.613208\pi\)
−0.348202 + 0.937420i \(0.613208\pi\)
\(60\) 0 0
\(61\) 3.71025 0.475049 0.237524 0.971382i \(-0.423664\pi\)
0.237524 + 0.971382i \(0.423664\pi\)
\(62\) −2.04882 −0.260200
\(63\) 0 0
\(64\) 3.17221 0.396526
\(65\) −6.40739 −0.794739
\(66\) 0 0
\(67\) 10.3248 1.26138 0.630689 0.776035i \(-0.282772\pi\)
0.630689 + 0.776035i \(0.282772\pi\)
\(68\) 0.493075 0.0597941
\(69\) 0 0
\(70\) 2.23472 0.267101
\(71\) −1.31960 −0.156608 −0.0783041 0.996930i \(-0.524950\pi\)
−0.0783041 + 0.996930i \(0.524950\pi\)
\(72\) 0 0
\(73\) −8.85675 −1.03660 −0.518302 0.855198i \(-0.673436\pi\)
−0.518302 + 0.855198i \(0.673436\pi\)
\(74\) 0.349261 0.0406007
\(75\) 0 0
\(76\) −6.36316 −0.729905
\(77\) 5.95291 0.678397
\(78\) 0 0
\(79\) 13.1696 1.48169 0.740847 0.671673i \(-0.234424\pi\)
0.740847 + 0.671673i \(0.234424\pi\)
\(80\) 2.00638 0.224320
\(81\) 0 0
\(82\) 4.34776 0.480129
\(83\) −15.2753 −1.67668 −0.838342 0.545145i \(-0.816475\pi\)
−0.838342 + 0.545145i \(0.816475\pi\)
\(84\) 0 0
\(85\) −1.01478 −0.110068
\(86\) −2.98408 −0.321781
\(87\) 0 0
\(88\) −15.7782 −1.68196
\(89\) 2.60509 0.276139 0.138070 0.990423i \(-0.455910\pi\)
0.138070 + 0.990423i \(0.455910\pi\)
\(90\) 0 0
\(91\) −2.24308 −0.235139
\(92\) 2.46278 0.256763
\(93\) 0 0
\(94\) 3.83088 0.395126
\(95\) 13.0958 1.34360
\(96\) 0 0
\(97\) −3.10938 −0.315709 −0.157855 0.987462i \(-0.550458\pi\)
−0.157855 + 0.987462i \(0.550458\pi\)
\(98\) 0.782325 0.0790268
\(99\) 0 0
\(100\) −4.38553 −0.438553
\(101\) −2.36661 −0.235487 −0.117743 0.993044i \(-0.537566\pi\)
−0.117743 + 0.993044i \(0.537566\pi\)
\(102\) 0 0
\(103\) 3.24902 0.320135 0.160068 0.987106i \(-0.448829\pi\)
0.160068 + 0.987106i \(0.448829\pi\)
\(104\) 5.94526 0.582981
\(105\) 0 0
\(106\) −10.1476 −0.985621
\(107\) 0.104034 0.0100573 0.00502866 0.999987i \(-0.498399\pi\)
0.00502866 + 0.999987i \(0.498399\pi\)
\(108\) 0 0
\(109\) 19.8237 1.89877 0.949383 0.314120i \(-0.101710\pi\)
0.949383 + 0.314120i \(0.101710\pi\)
\(110\) 13.3031 1.26840
\(111\) 0 0
\(112\) 0.702387 0.0663693
\(113\) 13.2923 1.25043 0.625216 0.780452i \(-0.285011\pi\)
0.625216 + 0.780452i \(0.285011\pi\)
\(114\) 0 0
\(115\) −5.06855 −0.472645
\(116\) −12.7415 −1.18302
\(117\) 0 0
\(118\) −4.18480 −0.385242
\(119\) −0.355250 −0.0325657
\(120\) 0 0
\(121\) 24.4372 2.22156
\(122\) 2.90262 0.262791
\(123\) 0 0
\(124\) 3.63492 0.326426
\(125\) −5.25690 −0.470191
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −9.21926 −0.814875
\(129\) 0 0
\(130\) −5.01266 −0.439640
\(131\) −1.48402 −0.129660 −0.0648298 0.997896i \(-0.520650\pi\)
−0.0648298 + 0.997896i \(0.520650\pi\)
\(132\) 0 0
\(133\) 4.58452 0.397528
\(134\) 8.07738 0.697779
\(135\) 0 0
\(136\) 0.941587 0.0807404
\(137\) −3.92401 −0.335251 −0.167626 0.985851i \(-0.553610\pi\)
−0.167626 + 0.985851i \(0.553610\pi\)
\(138\) 0 0
\(139\) −1.61387 −0.136887 −0.0684435 0.997655i \(-0.521803\pi\)
−0.0684435 + 0.997655i \(0.521803\pi\)
\(140\) −3.96475 −0.335082
\(141\) 0 0
\(142\) −1.03236 −0.0866337
\(143\) −13.3529 −1.11662
\(144\) 0 0
\(145\) 26.2228 2.17769
\(146\) −6.92886 −0.573437
\(147\) 0 0
\(148\) −0.619643 −0.0509343
\(149\) −9.10778 −0.746138 −0.373069 0.927804i \(-0.621695\pi\)
−0.373069 + 0.927804i \(0.621695\pi\)
\(150\) 0 0
\(151\) −9.73474 −0.792202 −0.396101 0.918207i \(-0.629637\pi\)
−0.396101 + 0.918207i \(0.629637\pi\)
\(152\) −12.1512 −0.985595
\(153\) 0 0
\(154\) 4.65711 0.375281
\(155\) −7.48088 −0.600879
\(156\) 0 0
\(157\) 10.5542 0.842315 0.421158 0.906987i \(-0.361624\pi\)
0.421158 + 0.906987i \(0.361624\pi\)
\(158\) 10.3029 0.819655
\(159\) 0 0
\(160\) 16.7120 1.32120
\(161\) −1.77438 −0.139841
\(162\) 0 0
\(163\) 6.03292 0.472534 0.236267 0.971688i \(-0.424076\pi\)
0.236267 + 0.971688i \(0.424076\pi\)
\(164\) −7.71360 −0.602331
\(165\) 0 0
\(166\) −11.9503 −0.927520
\(167\) −1.24770 −0.0965497 −0.0482748 0.998834i \(-0.515372\pi\)
−0.0482748 + 0.998834i \(0.515372\pi\)
\(168\) 0 0
\(169\) −7.96860 −0.612969
\(170\) −0.793885 −0.0608882
\(171\) 0 0
\(172\) 5.29421 0.403680
\(173\) 7.02419 0.534039 0.267020 0.963691i \(-0.413961\pi\)
0.267020 + 0.963691i \(0.413961\pi\)
\(174\) 0 0
\(175\) 3.15968 0.238849
\(176\) 4.18125 0.315173
\(177\) 0 0
\(178\) 2.03803 0.152757
\(179\) 16.0501 1.19964 0.599822 0.800134i \(-0.295238\pi\)
0.599822 + 0.800134i \(0.295238\pi\)
\(180\) 0 0
\(181\) −10.0388 −0.746181 −0.373091 0.927795i \(-0.621702\pi\)
−0.373091 + 0.927795i \(0.621702\pi\)
\(182\) −1.75482 −0.130076
\(183\) 0 0
\(184\) 4.70299 0.346709
\(185\) 1.27526 0.0937590
\(186\) 0 0
\(187\) −2.11477 −0.154647
\(188\) −6.79659 −0.495692
\(189\) 0 0
\(190\) 10.2451 0.743260
\(191\) −12.8858 −0.932386 −0.466193 0.884683i \(-0.654375\pi\)
−0.466193 + 0.884683i \(0.654375\pi\)
\(192\) 0 0
\(193\) 15.5417 1.11871 0.559357 0.828927i \(-0.311048\pi\)
0.559357 + 0.828927i \(0.311048\pi\)
\(194\) −2.43254 −0.174647
\(195\) 0 0
\(196\) −1.38797 −0.0991405
\(197\) 9.10451 0.648669 0.324335 0.945942i \(-0.394860\pi\)
0.324335 + 0.945942i \(0.394860\pi\)
\(198\) 0 0
\(199\) 20.7799 1.47305 0.736524 0.676411i \(-0.236466\pi\)
0.736524 + 0.676411i \(0.236466\pi\)
\(200\) −8.37471 −0.592181
\(201\) 0 0
\(202\) −1.85146 −0.130268
\(203\) 9.18000 0.644310
\(204\) 0 0
\(205\) 15.8750 1.10876
\(206\) 2.54179 0.177095
\(207\) 0 0
\(208\) −1.57551 −0.109242
\(209\) 27.2912 1.88778
\(210\) 0 0
\(211\) −7.23948 −0.498387 −0.249193 0.968454i \(-0.580165\pi\)
−0.249193 + 0.968454i \(0.580165\pi\)
\(212\) 18.0034 1.23648
\(213\) 0 0
\(214\) 0.0813882 0.00556358
\(215\) −10.8958 −0.743087
\(216\) 0 0
\(217\) −2.61888 −0.177781
\(218\) 15.5086 1.05037
\(219\) 0 0
\(220\) −23.6018 −1.59123
\(221\) 0.796853 0.0536021
\(222\) 0 0
\(223\) −16.9713 −1.13648 −0.568241 0.822862i \(-0.692376\pi\)
−0.568241 + 0.822862i \(0.692376\pi\)
\(224\) 5.85048 0.390902
\(225\) 0 0
\(226\) 10.3989 0.691723
\(227\) −26.3750 −1.75057 −0.875285 0.483607i \(-0.839326\pi\)
−0.875285 + 0.483607i \(0.839326\pi\)
\(228\) 0 0
\(229\) 22.6839 1.49900 0.749498 0.662006i \(-0.230295\pi\)
0.749498 + 0.662006i \(0.230295\pi\)
\(230\) −3.96525 −0.261461
\(231\) 0 0
\(232\) −24.3315 −1.59744
\(233\) −19.9035 −1.30392 −0.651960 0.758253i \(-0.726053\pi\)
−0.651960 + 0.758253i \(0.726053\pi\)
\(234\) 0 0
\(235\) 13.9878 0.912461
\(236\) 7.42448 0.483292
\(237\) 0 0
\(238\) −0.277921 −0.0180149
\(239\) −14.8701 −0.961870 −0.480935 0.876756i \(-0.659703\pi\)
−0.480935 + 0.876756i \(0.659703\pi\)
\(240\) 0 0
\(241\) 29.5656 1.90449 0.952245 0.305335i \(-0.0987685\pi\)
0.952245 + 0.305335i \(0.0987685\pi\)
\(242\) 19.1178 1.22894
\(243\) 0 0
\(244\) −5.14970 −0.329676
\(245\) 2.85652 0.182496
\(246\) 0 0
\(247\) −10.2834 −0.654320
\(248\) 6.94133 0.440775
\(249\) 0 0
\(250\) −4.11261 −0.260104
\(251\) −20.0199 −1.26364 −0.631821 0.775114i \(-0.717692\pi\)
−0.631821 + 0.775114i \(0.717692\pi\)
\(252\) 0 0
\(253\) −10.5627 −0.664074
\(254\) 0.782325 0.0490875
\(255\) 0 0
\(256\) −13.5569 −0.847305
\(257\) 26.4101 1.64742 0.823709 0.567012i \(-0.191901\pi\)
0.823709 + 0.567012i \(0.191901\pi\)
\(258\) 0 0
\(259\) 0.446439 0.0277404
\(260\) 8.89325 0.551536
\(261\) 0 0
\(262\) −1.16099 −0.0717261
\(263\) 18.5090 1.14131 0.570656 0.821189i \(-0.306689\pi\)
0.570656 + 0.821189i \(0.306689\pi\)
\(264\) 0 0
\(265\) −37.0520 −2.27609
\(266\) 3.58659 0.219908
\(267\) 0 0
\(268\) −14.3305 −0.875376
\(269\) −0.573334 −0.0349568 −0.0174784 0.999847i \(-0.505564\pi\)
−0.0174784 + 0.999847i \(0.505564\pi\)
\(270\) 0 0
\(271\) 7.26958 0.441595 0.220798 0.975320i \(-0.429134\pi\)
0.220798 + 0.975320i \(0.429134\pi\)
\(272\) −0.249523 −0.0151295
\(273\) 0 0
\(274\) −3.06986 −0.185457
\(275\) 18.8093 1.13424
\(276\) 0 0
\(277\) −16.1927 −0.972924 −0.486462 0.873702i \(-0.661713\pi\)
−0.486462 + 0.873702i \(0.661713\pi\)
\(278\) −1.26257 −0.0757242
\(279\) 0 0
\(280\) −7.57117 −0.452464
\(281\) 0.461522 0.0275321 0.0137661 0.999905i \(-0.495618\pi\)
0.0137661 + 0.999905i \(0.495618\pi\)
\(282\) 0 0
\(283\) 3.00080 0.178379 0.0891895 0.996015i \(-0.471572\pi\)
0.0891895 + 0.996015i \(0.471572\pi\)
\(284\) 1.83157 0.108683
\(285\) 0 0
\(286\) −10.4463 −0.617701
\(287\) 5.55748 0.328048
\(288\) 0 0
\(289\) −16.8738 −0.992576
\(290\) 20.5148 1.20467
\(291\) 0 0
\(292\) 12.2929 0.719386
\(293\) −14.8706 −0.868752 −0.434376 0.900732i \(-0.643031\pi\)
−0.434376 + 0.900732i \(0.643031\pi\)
\(294\) 0 0
\(295\) −15.2800 −0.889636
\(296\) −1.18328 −0.0687770
\(297\) 0 0
\(298\) −7.12524 −0.412754
\(299\) 3.98008 0.230174
\(300\) 0 0
\(301\) −3.81437 −0.219856
\(302\) −7.61573 −0.438236
\(303\) 0 0
\(304\) 3.22011 0.184686
\(305\) 10.5984 0.606862
\(306\) 0 0
\(307\) 20.0380 1.14363 0.571815 0.820383i \(-0.306240\pi\)
0.571815 + 0.820383i \(0.306240\pi\)
\(308\) −8.26245 −0.470797
\(309\) 0 0
\(310\) −5.85248 −0.332399
\(311\) 1.42299 0.0806904 0.0403452 0.999186i \(-0.487154\pi\)
0.0403452 + 0.999186i \(0.487154\pi\)
\(312\) 0 0
\(313\) 8.24182 0.465855 0.232928 0.972494i \(-0.425170\pi\)
0.232928 + 0.972494i \(0.425170\pi\)
\(314\) 8.25680 0.465958
\(315\) 0 0
\(316\) −18.2790 −1.02827
\(317\) −22.8267 −1.28208 −0.641038 0.767509i \(-0.721496\pi\)
−0.641038 + 0.767509i \(0.721496\pi\)
\(318\) 0 0
\(319\) 54.6477 3.05969
\(320\) 9.06145 0.506551
\(321\) 0 0
\(322\) −1.38814 −0.0773582
\(323\) −1.62865 −0.0906205
\(324\) 0 0
\(325\) −7.08741 −0.393139
\(326\) 4.71970 0.261400
\(327\) 0 0
\(328\) −14.7301 −0.813331
\(329\) 4.89679 0.269969
\(330\) 0 0
\(331\) 23.7844 1.30731 0.653656 0.756792i \(-0.273235\pi\)
0.653656 + 0.756792i \(0.273235\pi\)
\(332\) 21.2016 1.16359
\(333\) 0 0
\(334\) −0.976105 −0.0534101
\(335\) 29.4930 1.61138
\(336\) 0 0
\(337\) −6.16356 −0.335750 −0.167875 0.985808i \(-0.553691\pi\)
−0.167875 + 0.985808i \(0.553691\pi\)
\(338\) −6.23403 −0.339087
\(339\) 0 0
\(340\) 1.40848 0.0763853
\(341\) −15.5900 −0.844245
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 10.1099 0.545092
\(345\) 0 0
\(346\) 5.49520 0.295424
\(347\) 10.9479 0.587716 0.293858 0.955849i \(-0.405061\pi\)
0.293858 + 0.955849i \(0.405061\pi\)
\(348\) 0 0
\(349\) −4.35089 −0.232898 −0.116449 0.993197i \(-0.537151\pi\)
−0.116449 + 0.993197i \(0.537151\pi\)
\(350\) 2.47190 0.132129
\(351\) 0 0
\(352\) 34.8274 1.85631
\(353\) 23.5716 1.25459 0.627294 0.778782i \(-0.284162\pi\)
0.627294 + 0.778782i \(0.284162\pi\)
\(354\) 0 0
\(355\) −3.76947 −0.200063
\(356\) −3.61578 −0.191636
\(357\) 0 0
\(358\) 12.5564 0.663628
\(359\) 10.7509 0.567412 0.283706 0.958911i \(-0.408436\pi\)
0.283706 + 0.958911i \(0.408436\pi\)
\(360\) 0 0
\(361\) 2.01782 0.106201
\(362\) −7.85364 −0.412778
\(363\) 0 0
\(364\) 3.11332 0.163182
\(365\) −25.2995 −1.32423
\(366\) 0 0
\(367\) 13.4042 0.699694 0.349847 0.936807i \(-0.386234\pi\)
0.349847 + 0.936807i \(0.386234\pi\)
\(368\) −1.24630 −0.0649680
\(369\) 0 0
\(370\) 0.997669 0.0518663
\(371\) −12.9711 −0.673424
\(372\) 0 0
\(373\) 2.43314 0.125983 0.0629915 0.998014i \(-0.479936\pi\)
0.0629915 + 0.998014i \(0.479936\pi\)
\(374\) −1.65444 −0.0855490
\(375\) 0 0
\(376\) −12.9789 −0.669336
\(377\) −20.5915 −1.06051
\(378\) 0 0
\(379\) 1.12262 0.0576652 0.0288326 0.999584i \(-0.490821\pi\)
0.0288326 + 0.999584i \(0.490821\pi\)
\(380\) −18.1765 −0.932433
\(381\) 0 0
\(382\) −10.0809 −0.515784
\(383\) 12.1235 0.619484 0.309742 0.950821i \(-0.399757\pi\)
0.309742 + 0.950821i \(0.399757\pi\)
\(384\) 0 0
\(385\) 17.0046 0.866634
\(386\) 12.1586 0.618858
\(387\) 0 0
\(388\) 4.31571 0.219097
\(389\) 7.49818 0.380173 0.190086 0.981767i \(-0.439123\pi\)
0.190086 + 0.981767i \(0.439123\pi\)
\(390\) 0 0
\(391\) 0.630349 0.0318781
\(392\) −2.65049 −0.133870
\(393\) 0 0
\(394\) 7.12268 0.358836
\(395\) 37.6191 1.89282
\(396\) 0 0
\(397\) 2.60531 0.130757 0.0653785 0.997861i \(-0.479175\pi\)
0.0653785 + 0.997861i \(0.479175\pi\)
\(398\) 16.2566 0.814872
\(399\) 0 0
\(400\) 2.21932 0.110966
\(401\) 34.5142 1.72356 0.861778 0.507285i \(-0.169351\pi\)
0.861778 + 0.507285i \(0.169351\pi\)
\(402\) 0 0
\(403\) 5.87436 0.292623
\(404\) 3.28478 0.163424
\(405\) 0 0
\(406\) 7.18175 0.356424
\(407\) 2.65761 0.131733
\(408\) 0 0
\(409\) −18.5829 −0.918864 −0.459432 0.888213i \(-0.651947\pi\)
−0.459432 + 0.888213i \(0.651947\pi\)
\(410\) 12.4194 0.613352
\(411\) 0 0
\(412\) −4.50953 −0.222168
\(413\) −5.34918 −0.263216
\(414\) 0 0
\(415\) −43.6342 −2.14192
\(416\) −13.1231 −0.643412
\(417\) 0 0
\(418\) 21.3506 1.04429
\(419\) 34.4281 1.68192 0.840962 0.541094i \(-0.181990\pi\)
0.840962 + 0.541094i \(0.181990\pi\)
\(420\) 0 0
\(421\) 10.5543 0.514383 0.257191 0.966360i \(-0.417203\pi\)
0.257191 + 0.966360i \(0.417203\pi\)
\(422\) −5.66363 −0.275701
\(423\) 0 0
\(424\) 34.3797 1.66963
\(425\) −1.12248 −0.0544481
\(426\) 0 0
\(427\) 3.71025 0.179552
\(428\) −0.144395 −0.00697961
\(429\) 0 0
\(430\) −8.52406 −0.411067
\(431\) −23.7306 −1.14306 −0.571531 0.820581i \(-0.693650\pi\)
−0.571531 + 0.820581i \(0.693650\pi\)
\(432\) 0 0
\(433\) 3.32779 0.159923 0.0799617 0.996798i \(-0.474520\pi\)
0.0799617 + 0.996798i \(0.474520\pi\)
\(434\) −2.04882 −0.0983464
\(435\) 0 0
\(436\) −27.5146 −1.31771
\(437\) −8.13469 −0.389135
\(438\) 0 0
\(439\) 20.6852 0.987252 0.493626 0.869674i \(-0.335671\pi\)
0.493626 + 0.869674i \(0.335671\pi\)
\(440\) −45.0705 −2.14865
\(441\) 0 0
\(442\) 0.623398 0.0296520
\(443\) 40.0896 1.90472 0.952358 0.304981i \(-0.0986503\pi\)
0.952358 + 0.304981i \(0.0986503\pi\)
\(444\) 0 0
\(445\) 7.44149 0.352760
\(446\) −13.2771 −0.628687
\(447\) 0 0
\(448\) 3.17221 0.149873
\(449\) 20.3346 0.959648 0.479824 0.877365i \(-0.340700\pi\)
0.479824 + 0.877365i \(0.340700\pi\)
\(450\) 0 0
\(451\) 33.0832 1.55783
\(452\) −18.4492 −0.867779
\(453\) 0 0
\(454\) −20.6338 −0.968394
\(455\) −6.40739 −0.300383
\(456\) 0 0
\(457\) −11.4154 −0.533991 −0.266996 0.963698i \(-0.586031\pi\)
−0.266996 + 0.963698i \(0.586031\pi\)
\(458\) 17.7462 0.829226
\(459\) 0 0
\(460\) 7.03498 0.328008
\(461\) 35.1107 1.63527 0.817634 0.575738i \(-0.195285\pi\)
0.817634 + 0.575738i \(0.195285\pi\)
\(462\) 0 0
\(463\) −9.61602 −0.446894 −0.223447 0.974716i \(-0.571731\pi\)
−0.223447 + 0.974716i \(0.571731\pi\)
\(464\) 6.44791 0.299337
\(465\) 0 0
\(466\) −15.5710 −0.721313
\(467\) −32.7492 −1.51545 −0.757725 0.652574i \(-0.773689\pi\)
−0.757725 + 0.652574i \(0.773689\pi\)
\(468\) 0 0
\(469\) 10.3248 0.476756
\(470\) 10.9430 0.504762
\(471\) 0 0
\(472\) 14.1780 0.652593
\(473\) −22.7066 −1.04405
\(474\) 0 0
\(475\) 14.4856 0.664646
\(476\) 0.493075 0.0226000
\(477\) 0 0
\(478\) −11.6333 −0.532095
\(479\) −4.11326 −0.187940 −0.0939698 0.995575i \(-0.529956\pi\)
−0.0939698 + 0.995575i \(0.529956\pi\)
\(480\) 0 0
\(481\) −1.00140 −0.0456598
\(482\) 23.1299 1.05354
\(483\) 0 0
\(484\) −33.9180 −1.54173
\(485\) −8.88199 −0.403310
\(486\) 0 0
\(487\) −10.3942 −0.471007 −0.235504 0.971873i \(-0.575674\pi\)
−0.235504 + 0.971873i \(0.575674\pi\)
\(488\) −9.83399 −0.445164
\(489\) 0 0
\(490\) 2.23472 0.100955
\(491\) −11.6309 −0.524895 −0.262447 0.964946i \(-0.584530\pi\)
−0.262447 + 0.964946i \(0.584530\pi\)
\(492\) 0 0
\(493\) −3.26119 −0.146877
\(494\) −8.04500 −0.361961
\(495\) 0 0
\(496\) −1.83947 −0.0825946
\(497\) −1.31960 −0.0591923
\(498\) 0 0
\(499\) 18.6834 0.836384 0.418192 0.908359i \(-0.362664\pi\)
0.418192 + 0.908359i \(0.362664\pi\)
\(500\) 7.29640 0.326305
\(501\) 0 0
\(502\) −15.6620 −0.699031
\(503\) 37.2918 1.66276 0.831380 0.555705i \(-0.187551\pi\)
0.831380 + 0.555705i \(0.187551\pi\)
\(504\) 0 0
\(505\) −6.76026 −0.300828
\(506\) −8.26350 −0.367357
\(507\) 0 0
\(508\) −1.38797 −0.0615811
\(509\) −30.3885 −1.34695 −0.673474 0.739211i \(-0.735199\pi\)
−0.673474 + 0.739211i \(0.735199\pi\)
\(510\) 0 0
\(511\) −8.85675 −0.391800
\(512\) 7.83264 0.346157
\(513\) 0 0
\(514\) 20.6613 0.911331
\(515\) 9.28086 0.408964
\(516\) 0 0
\(517\) 29.1502 1.28202
\(518\) 0.349261 0.0153456
\(519\) 0 0
\(520\) 16.9827 0.744742
\(521\) −13.9497 −0.611146 −0.305573 0.952169i \(-0.598848\pi\)
−0.305573 + 0.952169i \(0.598848\pi\)
\(522\) 0 0
\(523\) −22.2163 −0.971450 −0.485725 0.874112i \(-0.661444\pi\)
−0.485725 + 0.874112i \(0.661444\pi\)
\(524\) 2.05977 0.0899816
\(525\) 0 0
\(526\) 14.4800 0.631360
\(527\) 0.930357 0.0405270
\(528\) 0 0
\(529\) −19.8516 −0.863112
\(530\) −28.9867 −1.25910
\(531\) 0 0
\(532\) −6.36316 −0.275878
\(533\) −12.4659 −0.539957
\(534\) 0 0
\(535\) 0.297174 0.0128479
\(536\) −27.3659 −1.18203
\(537\) 0 0
\(538\) −0.448534 −0.0193377
\(539\) 5.95291 0.256410
\(540\) 0 0
\(541\) 25.9878 1.11730 0.558651 0.829403i \(-0.311319\pi\)
0.558651 + 0.829403i \(0.311319\pi\)
\(542\) 5.68718 0.244285
\(543\) 0 0
\(544\) −2.07838 −0.0891098
\(545\) 56.6267 2.42562
\(546\) 0 0
\(547\) −38.7425 −1.65651 −0.828254 0.560352i \(-0.810666\pi\)
−0.828254 + 0.560352i \(0.810666\pi\)
\(548\) 5.44640 0.232659
\(549\) 0 0
\(550\) 14.7150 0.627450
\(551\) 42.0859 1.79292
\(552\) 0 0
\(553\) 13.1696 0.560028
\(554\) −12.6679 −0.538209
\(555\) 0 0
\(556\) 2.24000 0.0949973
\(557\) 13.2224 0.560252 0.280126 0.959963i \(-0.409624\pi\)
0.280126 + 0.959963i \(0.409624\pi\)
\(558\) 0 0
\(559\) 8.55592 0.361877
\(560\) 2.00638 0.0847850
\(561\) 0 0
\(562\) 0.361061 0.0152304
\(563\) 12.5799 0.530180 0.265090 0.964224i \(-0.414598\pi\)
0.265090 + 0.964224i \(0.414598\pi\)
\(564\) 0 0
\(565\) 37.9696 1.59739
\(566\) 2.34760 0.0986771
\(567\) 0 0
\(568\) 3.49760 0.146756
\(569\) −22.4858 −0.942653 −0.471326 0.881959i \(-0.656225\pi\)
−0.471326 + 0.881959i \(0.656225\pi\)
\(570\) 0 0
\(571\) 10.9617 0.458733 0.229366 0.973340i \(-0.426335\pi\)
0.229366 + 0.973340i \(0.426335\pi\)
\(572\) 18.5333 0.774917
\(573\) 0 0
\(574\) 4.34776 0.181472
\(575\) −5.60648 −0.233806
\(576\) 0 0
\(577\) −7.86167 −0.327286 −0.163643 0.986520i \(-0.552324\pi\)
−0.163643 + 0.986520i \(0.552324\pi\)
\(578\) −13.2008 −0.549081
\(579\) 0 0
\(580\) −36.3964 −1.51128
\(581\) −15.2753 −0.633727
\(582\) 0 0
\(583\) −77.2156 −3.19794
\(584\) 23.4748 0.971392
\(585\) 0 0
\(586\) −11.6337 −0.480583
\(587\) −45.8628 −1.89296 −0.946479 0.322764i \(-0.895388\pi\)
−0.946479 + 0.322764i \(0.895388\pi\)
\(588\) 0 0
\(589\) −12.0063 −0.494712
\(590\) −11.9539 −0.492136
\(591\) 0 0
\(592\) 0.313573 0.0128878
\(593\) −19.8056 −0.813319 −0.406660 0.913580i \(-0.633307\pi\)
−0.406660 + 0.913580i \(0.633307\pi\)
\(594\) 0 0
\(595\) −1.01478 −0.0416018
\(596\) 12.6413 0.517808
\(597\) 0 0
\(598\) 3.11372 0.127329
\(599\) −34.5952 −1.41352 −0.706761 0.707452i \(-0.749844\pi\)
−0.706761 + 0.707452i \(0.749844\pi\)
\(600\) 0 0
\(601\) 10.5867 0.431840 0.215920 0.976411i \(-0.430725\pi\)
0.215920 + 0.976411i \(0.430725\pi\)
\(602\) −2.98408 −0.121622
\(603\) 0 0
\(604\) 13.5115 0.549775
\(605\) 69.8052 2.83798
\(606\) 0 0
\(607\) −28.2830 −1.14797 −0.573986 0.818865i \(-0.694604\pi\)
−0.573986 + 0.818865i \(0.694604\pi\)
\(608\) 26.8216 1.08776
\(609\) 0 0
\(610\) 8.29138 0.335708
\(611\) −10.9839 −0.444361
\(612\) 0 0
\(613\) −8.39067 −0.338896 −0.169448 0.985539i \(-0.554198\pi\)
−0.169448 + 0.985539i \(0.554198\pi\)
\(614\) 15.6762 0.632642
\(615\) 0 0
\(616\) −15.7782 −0.635720
\(617\) −1.54113 −0.0620437 −0.0310219 0.999519i \(-0.509876\pi\)
−0.0310219 + 0.999519i \(0.509876\pi\)
\(618\) 0 0
\(619\) −18.5681 −0.746313 −0.373157 0.927768i \(-0.621725\pi\)
−0.373157 + 0.927768i \(0.621725\pi\)
\(620\) 10.3832 0.417000
\(621\) 0 0
\(622\) 1.11324 0.0446369
\(623\) 2.60509 0.104371
\(624\) 0 0
\(625\) −30.8148 −1.23259
\(626\) 6.44778 0.257705
\(627\) 0 0
\(628\) −14.6489 −0.584553
\(629\) −0.158597 −0.00632369
\(630\) 0 0
\(631\) 34.2361 1.36292 0.681459 0.731857i \(-0.261346\pi\)
0.681459 + 0.731857i \(0.261346\pi\)
\(632\) −34.9059 −1.38848
\(633\) 0 0
\(634\) −17.8579 −0.709229
\(635\) 2.85652 0.113357
\(636\) 0 0
\(637\) −2.24308 −0.0888740
\(638\) 42.7523 1.69258
\(639\) 0 0
\(640\) −26.3350 −1.04098
\(641\) −0.674416 −0.0266378 −0.0133189 0.999911i \(-0.504240\pi\)
−0.0133189 + 0.999911i \(0.504240\pi\)
\(642\) 0 0
\(643\) 29.7807 1.17444 0.587219 0.809428i \(-0.300223\pi\)
0.587219 + 0.809428i \(0.300223\pi\)
\(644\) 2.46278 0.0970473
\(645\) 0 0
\(646\) −1.27413 −0.0501301
\(647\) −19.3926 −0.762401 −0.381200 0.924492i \(-0.624489\pi\)
−0.381200 + 0.924492i \(0.624489\pi\)
\(648\) 0 0
\(649\) −31.8432 −1.24995
\(650\) −5.54466 −0.217480
\(651\) 0 0
\(652\) −8.37349 −0.327931
\(653\) 7.50126 0.293547 0.146773 0.989170i \(-0.453111\pi\)
0.146773 + 0.989170i \(0.453111\pi\)
\(654\) 0 0
\(655\) −4.23913 −0.165637
\(656\) 3.90350 0.152406
\(657\) 0 0
\(658\) 3.83088 0.149343
\(659\) 1.97123 0.0767882 0.0383941 0.999263i \(-0.487776\pi\)
0.0383941 + 0.999263i \(0.487776\pi\)
\(660\) 0 0
\(661\) −24.4180 −0.949750 −0.474875 0.880053i \(-0.657507\pi\)
−0.474875 + 0.880053i \(0.657507\pi\)
\(662\) 18.6072 0.723188
\(663\) 0 0
\(664\) 40.4871 1.57120
\(665\) 13.0958 0.507831
\(666\) 0 0
\(667\) −16.2888 −0.630706
\(668\) 1.73176 0.0670039
\(669\) 0 0
\(670\) 23.0732 0.891394
\(671\) 22.0868 0.852651
\(672\) 0 0
\(673\) −39.0533 −1.50539 −0.752697 0.658367i \(-0.771247\pi\)
−0.752697 + 0.658367i \(0.771247\pi\)
\(674\) −4.82191 −0.185733
\(675\) 0 0
\(676\) 11.0601 0.425390
\(677\) 37.5231 1.44213 0.721065 0.692868i \(-0.243653\pi\)
0.721065 + 0.692868i \(0.243653\pi\)
\(678\) 0 0
\(679\) −3.10938 −0.119327
\(680\) 2.68966 0.103144
\(681\) 0 0
\(682\) −12.1964 −0.467026
\(683\) 42.5582 1.62845 0.814223 0.580552i \(-0.197163\pi\)
0.814223 + 0.580552i \(0.197163\pi\)
\(684\) 0 0
\(685\) −11.2090 −0.428274
\(686\) 0.782325 0.0298693
\(687\) 0 0
\(688\) −2.67916 −0.102142
\(689\) 29.0951 1.10844
\(690\) 0 0
\(691\) 8.50252 0.323451 0.161726 0.986836i \(-0.448294\pi\)
0.161726 + 0.986836i \(0.448294\pi\)
\(692\) −9.74934 −0.370614
\(693\) 0 0
\(694\) 8.56485 0.325117
\(695\) −4.61006 −0.174869
\(696\) 0 0
\(697\) −1.97429 −0.0747817
\(698\) −3.40381 −0.128836
\(699\) 0 0
\(700\) −4.38553 −0.165758
\(701\) −41.0282 −1.54962 −0.774808 0.632197i \(-0.782153\pi\)
−0.774808 + 0.632197i \(0.782153\pi\)
\(702\) 0 0
\(703\) 2.04671 0.0771931
\(704\) 18.8839 0.711712
\(705\) 0 0
\(706\) 18.4406 0.694023
\(707\) −2.36661 −0.0890055
\(708\) 0 0
\(709\) −27.8419 −1.04563 −0.522813 0.852448i \(-0.675117\pi\)
−0.522813 + 0.852448i \(0.675117\pi\)
\(710\) −2.94895 −0.110672
\(711\) 0 0
\(712\) −6.90478 −0.258767
\(713\) 4.64690 0.174028
\(714\) 0 0
\(715\) −38.1426 −1.42645
\(716\) −22.2771 −0.832533
\(717\) 0 0
\(718\) 8.41072 0.313885
\(719\) −35.7992 −1.33509 −0.667543 0.744572i \(-0.732654\pi\)
−0.667543 + 0.744572i \(0.732654\pi\)
\(720\) 0 0
\(721\) 3.24902 0.121000
\(722\) 1.57859 0.0587492
\(723\) 0 0
\(724\) 13.9336 0.517838
\(725\) 29.0059 1.07725
\(726\) 0 0
\(727\) 28.1120 1.04262 0.521308 0.853369i \(-0.325444\pi\)
0.521308 + 0.853369i \(0.325444\pi\)
\(728\) 5.94526 0.220346
\(729\) 0 0
\(730\) −19.7924 −0.732550
\(731\) 1.35505 0.0501184
\(732\) 0 0
\(733\) −3.35859 −0.124053 −0.0620263 0.998075i \(-0.519756\pi\)
−0.0620263 + 0.998075i \(0.519756\pi\)
\(734\) 10.4865 0.387062
\(735\) 0 0
\(736\) −10.3810 −0.382648
\(737\) 61.4628 2.26401
\(738\) 0 0
\(739\) −8.81699 −0.324338 −0.162169 0.986763i \(-0.551849\pi\)
−0.162169 + 0.986763i \(0.551849\pi\)
\(740\) −1.77002 −0.0650672
\(741\) 0 0
\(742\) −10.1476 −0.372530
\(743\) 33.5929 1.23240 0.616201 0.787589i \(-0.288671\pi\)
0.616201 + 0.787589i \(0.288671\pi\)
\(744\) 0 0
\(745\) −26.0165 −0.953171
\(746\) 1.90350 0.0696922
\(747\) 0 0
\(748\) 2.93523 0.107323
\(749\) 0.104034 0.00380131
\(750\) 0 0
\(751\) 38.7986 1.41578 0.707891 0.706321i \(-0.249647\pi\)
0.707891 + 0.706321i \(0.249647\pi\)
\(752\) 3.43944 0.125424
\(753\) 0 0
\(754\) −16.1092 −0.586663
\(755\) −27.8074 −1.01202
\(756\) 0 0
\(757\) 13.6304 0.495406 0.247703 0.968836i \(-0.420324\pi\)
0.247703 + 0.968836i \(0.420324\pi\)
\(758\) 0.878256 0.0318997
\(759\) 0 0
\(760\) −34.7102 −1.25907
\(761\) 7.00438 0.253909 0.126954 0.991909i \(-0.459480\pi\)
0.126954 + 0.991909i \(0.459480\pi\)
\(762\) 0 0
\(763\) 19.8237 0.717666
\(764\) 17.8851 0.647061
\(765\) 0 0
\(766\) 9.48456 0.342691
\(767\) 11.9986 0.433245
\(768\) 0 0
\(769\) −25.3807 −0.915251 −0.457625 0.889145i \(-0.651300\pi\)
−0.457625 + 0.889145i \(0.651300\pi\)
\(770\) 13.3031 0.479411
\(771\) 0 0
\(772\) −21.5713 −0.776368
\(773\) −45.1789 −1.62497 −0.812485 0.582982i \(-0.801886\pi\)
−0.812485 + 0.582982i \(0.801886\pi\)
\(774\) 0 0
\(775\) −8.27483 −0.297241
\(776\) 8.24138 0.295848
\(777\) 0 0
\(778\) 5.86601 0.210307
\(779\) 25.4784 0.912857
\(780\) 0 0
\(781\) −7.85548 −0.281091
\(782\) 0.493138 0.0176346
\(783\) 0 0
\(784\) 0.702387 0.0250852
\(785\) 30.1482 1.07603
\(786\) 0 0
\(787\) 17.2345 0.614344 0.307172 0.951654i \(-0.400617\pi\)
0.307172 + 0.951654i \(0.400617\pi\)
\(788\) −12.6368 −0.450166
\(789\) 0 0
\(790\) 29.4304 1.04709
\(791\) 13.2923 0.472619
\(792\) 0 0
\(793\) −8.32238 −0.295536
\(794\) 2.03820 0.0723331
\(795\) 0 0
\(796\) −28.8418 −1.02227
\(797\) −11.1590 −0.395273 −0.197636 0.980275i \(-0.563327\pi\)
−0.197636 + 0.980275i \(0.563327\pi\)
\(798\) 0 0
\(799\) −1.73958 −0.0615420
\(800\) 18.4856 0.653566
\(801\) 0 0
\(802\) 27.0013 0.953450
\(803\) −52.7235 −1.86057
\(804\) 0 0
\(805\) −5.06855 −0.178643
\(806\) 4.59566 0.161875
\(807\) 0 0
\(808\) 6.27268 0.220672
\(809\) 8.81764 0.310012 0.155006 0.987914i \(-0.450460\pi\)
0.155006 + 0.987914i \(0.450460\pi\)
\(810\) 0 0
\(811\) 23.6575 0.830726 0.415363 0.909656i \(-0.363655\pi\)
0.415363 + 0.909656i \(0.363655\pi\)
\(812\) −12.7415 −0.447140
\(813\) 0 0
\(814\) 2.07912 0.0728731
\(815\) 17.2331 0.603650
\(816\) 0 0
\(817\) −17.4870 −0.611794
\(818\) −14.5379 −0.508304
\(819\) 0 0
\(820\) −22.0340 −0.769461
\(821\) 10.4013 0.363006 0.181503 0.983390i \(-0.441904\pi\)
0.181503 + 0.983390i \(0.441904\pi\)
\(822\) 0 0
\(823\) −55.3493 −1.92935 −0.964677 0.263434i \(-0.915145\pi\)
−0.964677 + 0.263434i \(0.915145\pi\)
\(824\) −8.61149 −0.299996
\(825\) 0 0
\(826\) −4.18480 −0.145608
\(827\) −48.9737 −1.70298 −0.851491 0.524369i \(-0.824301\pi\)
−0.851491 + 0.524369i \(0.824301\pi\)
\(828\) 0 0
\(829\) 13.1541 0.456859 0.228430 0.973560i \(-0.426641\pi\)
0.228430 + 0.973560i \(0.426641\pi\)
\(830\) −34.1361 −1.18488
\(831\) 0 0
\(832\) −7.11551 −0.246686
\(833\) −0.355250 −0.0123087
\(834\) 0 0
\(835\) −3.56407 −0.123340
\(836\) −37.8794 −1.31008
\(837\) 0 0
\(838\) 26.9340 0.930420
\(839\) 22.3972 0.773237 0.386618 0.922240i \(-0.373643\pi\)
0.386618 + 0.922240i \(0.373643\pi\)
\(840\) 0 0
\(841\) 55.2724 1.90594
\(842\) 8.25686 0.284550
\(843\) 0 0
\(844\) 10.0482 0.345872
\(845\) −22.7624 −0.783051
\(846\) 0 0
\(847\) 24.4372 0.839671
\(848\) −9.11070 −0.312863
\(849\) 0 0
\(850\) −0.878141 −0.0301200
\(851\) −0.792154 −0.0271547
\(852\) 0 0
\(853\) 6.45732 0.221094 0.110547 0.993871i \(-0.464740\pi\)
0.110547 + 0.993871i \(0.464740\pi\)
\(854\) 2.90262 0.0993257
\(855\) 0 0
\(856\) −0.275741 −0.00942462
\(857\) 2.95220 0.100845 0.0504226 0.998728i \(-0.483943\pi\)
0.0504226 + 0.998728i \(0.483943\pi\)
\(858\) 0 0
\(859\) −36.7317 −1.25327 −0.626634 0.779314i \(-0.715568\pi\)
−0.626634 + 0.779314i \(0.715568\pi\)
\(860\) 15.1230 0.515690
\(861\) 0 0
\(862\) −18.5650 −0.632327
\(863\) −20.3620 −0.693131 −0.346565 0.938026i \(-0.612652\pi\)
−0.346565 + 0.938026i \(0.612652\pi\)
\(864\) 0 0
\(865\) 20.0647 0.682220
\(866\) 2.60342 0.0884677
\(867\) 0 0
\(868\) 3.63492 0.123377
\(869\) 78.3974 2.65945
\(870\) 0 0
\(871\) −23.1594 −0.784727
\(872\) −52.5426 −1.77932
\(873\) 0 0
\(874\) −6.36397 −0.215265
\(875\) −5.25690 −0.177716
\(876\) 0 0
\(877\) 24.0567 0.812338 0.406169 0.913798i \(-0.366864\pi\)
0.406169 + 0.913798i \(0.366864\pi\)
\(878\) 16.1826 0.546136
\(879\) 0 0
\(880\) 11.9438 0.402625
\(881\) −46.6478 −1.57161 −0.785803 0.618477i \(-0.787750\pi\)
−0.785803 + 0.618477i \(0.787750\pi\)
\(882\) 0 0
\(883\) 25.3836 0.854225 0.427112 0.904198i \(-0.359531\pi\)
0.427112 + 0.904198i \(0.359531\pi\)
\(884\) −1.10601 −0.0371990
\(885\) 0 0
\(886\) 31.3631 1.05367
\(887\) −25.9636 −0.871771 −0.435886 0.900002i \(-0.643565\pi\)
−0.435886 + 0.900002i \(0.643565\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 5.82166 0.195143
\(891\) 0 0
\(892\) 23.5556 0.788699
\(893\) 22.4494 0.751242
\(894\) 0 0
\(895\) 45.8475 1.53251
\(896\) −9.21926 −0.307994
\(897\) 0 0
\(898\) 15.9083 0.530866
\(899\) −24.0413 −0.801824
\(900\) 0 0
\(901\) 4.60796 0.153514
\(902\) 25.8818 0.861770
\(903\) 0 0
\(904\) −35.2310 −1.17177
\(905\) −28.6761 −0.953226
\(906\) 0 0
\(907\) −16.6421 −0.552591 −0.276296 0.961073i \(-0.589107\pi\)
−0.276296 + 0.961073i \(0.589107\pi\)
\(908\) 36.6076 1.21487
\(909\) 0 0
\(910\) −5.01266 −0.166168
\(911\) −23.3831 −0.774717 −0.387358 0.921929i \(-0.626612\pi\)
−0.387358 + 0.921929i \(0.626612\pi\)
\(912\) 0 0
\(913\) −90.9326 −3.00943
\(914\) −8.93058 −0.295397
\(915\) 0 0
\(916\) −31.4845 −1.04028
\(917\) −1.48402 −0.0490067
\(918\) 0 0
\(919\) 24.1039 0.795114 0.397557 0.917578i \(-0.369858\pi\)
0.397557 + 0.917578i \(0.369858\pi\)
\(920\) 13.4342 0.442911
\(921\) 0 0
\(922\) 27.4680 0.904610
\(923\) 2.95997 0.0974288
\(924\) 0 0
\(925\) 1.41061 0.0463804
\(926\) −7.52286 −0.247216
\(927\) 0 0
\(928\) 53.7074 1.76303
\(929\) 11.7991 0.387117 0.193559 0.981089i \(-0.437997\pi\)
0.193559 + 0.981089i \(0.437997\pi\)
\(930\) 0 0
\(931\) 4.58452 0.150252
\(932\) 27.6254 0.904899
\(933\) 0 0
\(934\) −25.6205 −0.838328
\(935\) −6.04087 −0.197558
\(936\) 0 0
\(937\) −13.8473 −0.452371 −0.226186 0.974084i \(-0.572626\pi\)
−0.226186 + 0.974084i \(0.572626\pi\)
\(938\) 8.07738 0.263736
\(939\) 0 0
\(940\) −19.4146 −0.633233
\(941\) −44.6036 −1.45404 −0.727018 0.686618i \(-0.759095\pi\)
−0.727018 + 0.686618i \(0.759095\pi\)
\(942\) 0 0
\(943\) −9.86109 −0.321121
\(944\) −3.75719 −0.122286
\(945\) 0 0
\(946\) −17.7639 −0.577555
\(947\) −23.5909 −0.766601 −0.383301 0.923624i \(-0.625213\pi\)
−0.383301 + 0.923624i \(0.625213\pi\)
\(948\) 0 0
\(949\) 19.8664 0.644891
\(950\) 11.3325 0.367674
\(951\) 0 0
\(952\) 0.941587 0.0305170
\(953\) −22.2076 −0.719374 −0.359687 0.933073i \(-0.617116\pi\)
−0.359687 + 0.933073i \(0.617116\pi\)
\(954\) 0 0
\(955\) −36.8086 −1.19110
\(956\) 20.6393 0.667522
\(957\) 0 0
\(958\) −3.21791 −0.103966
\(959\) −3.92401 −0.126713
\(960\) 0 0
\(961\) −24.1415 −0.778757
\(962\) −0.783419 −0.0252585
\(963\) 0 0
\(964\) −41.0361 −1.32168
\(965\) 44.3950 1.42913
\(966\) 0 0
\(967\) −15.9265 −0.512161 −0.256081 0.966655i \(-0.582431\pi\)
−0.256081 + 0.966655i \(0.582431\pi\)
\(968\) −64.7705 −2.08180
\(969\) 0 0
\(970\) −6.94860 −0.223106
\(971\) 34.2446 1.09896 0.549480 0.835507i \(-0.314826\pi\)
0.549480 + 0.835507i \(0.314826\pi\)
\(972\) 0 0
\(973\) −1.61387 −0.0517384
\(974\) −8.13166 −0.260555
\(975\) 0 0
\(976\) 2.60603 0.0834170
\(977\) −6.04555 −0.193414 −0.0967072 0.995313i \(-0.530831\pi\)
−0.0967072 + 0.995313i \(0.530831\pi\)
\(978\) 0 0
\(979\) 15.5079 0.495634
\(980\) −3.96475 −0.126649
\(981\) 0 0
\(982\) −9.09914 −0.290365
\(983\) −50.1818 −1.60055 −0.800275 0.599633i \(-0.795313\pi\)
−0.800275 + 0.599633i \(0.795313\pi\)
\(984\) 0 0
\(985\) 26.0072 0.828657
\(986\) −2.55131 −0.0812504
\(987\) 0 0
\(988\) 14.2731 0.454087
\(989\) 6.76814 0.215214
\(990\) 0 0
\(991\) 34.7358 1.10342 0.551710 0.834036i \(-0.313976\pi\)
0.551710 + 0.834036i \(0.313976\pi\)
\(992\) −15.3217 −0.486465
\(993\) 0 0
\(994\) −1.03236 −0.0327444
\(995\) 59.3581 1.88178
\(996\) 0 0
\(997\) −28.1054 −0.890108 −0.445054 0.895504i \(-0.646815\pi\)
−0.445054 + 0.895504i \(0.646815\pi\)
\(998\) 14.6165 0.462677
\(999\) 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 \(a_p\))