Properties

Label 8001.2.a.u.1.16
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
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: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Root \(2.59597\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.59597 q^{2}\) \(+4.73905 q^{4}\) \(+1.63234 q^{5}\) \(+1.00000 q^{7}\) \(+7.11048 q^{8}\) \(+O(q^{10})\) \(q\)\(+2.59597 q^{2}\) \(+4.73905 q^{4}\) \(+1.63234 q^{5}\) \(+1.00000 q^{7}\) \(+7.11048 q^{8}\) \(+4.23750 q^{10}\) \(-4.79599 q^{11}\) \(+0.263712 q^{13}\) \(+2.59597 q^{14}\) \(+8.98048 q^{16}\) \(+5.12058 q^{17}\) \(+5.93565 q^{19}\) \(+7.73574 q^{20}\) \(-12.4502 q^{22}\) \(+4.10470 q^{23}\) \(-2.33547 q^{25}\) \(+0.684587 q^{26}\) \(+4.73905 q^{28}\) \(-0.459771 q^{29}\) \(-9.24495 q^{31}\) \(+9.09207 q^{32}\) \(+13.2929 q^{34}\) \(+1.63234 q^{35}\) \(+6.64452 q^{37}\) \(+15.4088 q^{38}\) \(+11.6067 q^{40}\) \(+3.43282 q^{41}\) \(+2.33770 q^{43}\) \(-22.7284 q^{44}\) \(+10.6557 q^{46}\) \(+5.69134 q^{47}\) \(+1.00000 q^{49}\) \(-6.06280 q^{50}\) \(+1.24974 q^{52}\) \(-2.55281 q^{53}\) \(-7.82868 q^{55}\) \(+7.11048 q^{56}\) \(-1.19355 q^{58}\) \(+13.3394 q^{59}\) \(+10.9442 q^{61}\) \(-23.9996 q^{62}\) \(+5.64176 q^{64}\) \(+0.430467 q^{65}\) \(+1.34491 q^{67}\) \(+24.2667 q^{68}\) \(+4.23750 q^{70}\) \(-5.05046 q^{71}\) \(-16.4455 q^{73}\) \(+17.2490 q^{74}\) \(+28.1293 q^{76}\) \(-4.79599 q^{77}\) \(-0.111124 q^{79}\) \(+14.6592 q^{80}\) \(+8.91149 q^{82}\) \(-6.65678 q^{83}\) \(+8.35852 q^{85}\) \(+6.06861 q^{86}\) \(-34.1018 q^{88}\) \(-11.2897 q^{89}\) \(+0.263712 q^{91}\) \(+19.4524 q^{92}\) \(+14.7745 q^{94}\) \(+9.68900 q^{95}\) \(-5.51451 q^{97}\) \(+2.59597 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.59597 1.83563 0.917813 0.397013i \(-0.129953\pi\)
0.917813 + 0.397013i \(0.129953\pi\)
\(3\) 0 0
\(4\) 4.73905 2.36952
\(5\) 1.63234 0.730005 0.365002 0.931007i \(-0.381068\pi\)
0.365002 + 0.931007i \(0.381068\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 7.11048 2.51393
\(9\) 0 0
\(10\) 4.23750 1.34002
\(11\) −4.79599 −1.44604 −0.723022 0.690825i \(-0.757248\pi\)
−0.723022 + 0.690825i \(0.757248\pi\)
\(12\) 0 0
\(13\) 0.263712 0.0731405 0.0365702 0.999331i \(-0.488357\pi\)
0.0365702 + 0.999331i \(0.488357\pi\)
\(14\) 2.59597 0.693802
\(15\) 0 0
\(16\) 8.98048 2.24512
\(17\) 5.12058 1.24192 0.620961 0.783841i \(-0.286742\pi\)
0.620961 + 0.783841i \(0.286742\pi\)
\(18\) 0 0
\(19\) 5.93565 1.36173 0.680866 0.732408i \(-0.261604\pi\)
0.680866 + 0.732408i \(0.261604\pi\)
\(20\) 7.73574 1.72976
\(21\) 0 0
\(22\) −12.4502 −2.65440
\(23\) 4.10470 0.855889 0.427944 0.903805i \(-0.359238\pi\)
0.427944 + 0.903805i \(0.359238\pi\)
\(24\) 0 0
\(25\) −2.33547 −0.467093
\(26\) 0.684587 0.134259
\(27\) 0 0
\(28\) 4.73905 0.895596
\(29\) −0.459771 −0.0853773 −0.0426886 0.999088i \(-0.513592\pi\)
−0.0426886 + 0.999088i \(0.513592\pi\)
\(30\) 0 0
\(31\) −9.24495 −1.66044 −0.830221 0.557434i \(-0.811786\pi\)
−0.830221 + 0.557434i \(0.811786\pi\)
\(32\) 9.09207 1.60727
\(33\) 0 0
\(34\) 13.2929 2.27971
\(35\) 1.63234 0.275916
\(36\) 0 0
\(37\) 6.64452 1.09235 0.546176 0.837670i \(-0.316083\pi\)
0.546176 + 0.837670i \(0.316083\pi\)
\(38\) 15.4088 2.49963
\(39\) 0 0
\(40\) 11.6067 1.83518
\(41\) 3.43282 0.536116 0.268058 0.963403i \(-0.413618\pi\)
0.268058 + 0.963403i \(0.413618\pi\)
\(42\) 0 0
\(43\) 2.33770 0.356497 0.178248 0.983986i \(-0.442957\pi\)
0.178248 + 0.983986i \(0.442957\pi\)
\(44\) −22.7284 −3.42644
\(45\) 0 0
\(46\) 10.6557 1.57109
\(47\) 5.69134 0.830167 0.415083 0.909783i \(-0.363752\pi\)
0.415083 + 0.909783i \(0.363752\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −6.06280 −0.857409
\(51\) 0 0
\(52\) 1.24974 0.173308
\(53\) −2.55281 −0.350656 −0.175328 0.984510i \(-0.556099\pi\)
−0.175328 + 0.984510i \(0.556099\pi\)
\(54\) 0 0
\(55\) −7.82868 −1.05562
\(56\) 7.11048 0.950178
\(57\) 0 0
\(58\) −1.19355 −0.156721
\(59\) 13.3394 1.73664 0.868320 0.496005i \(-0.165200\pi\)
0.868320 + 0.496005i \(0.165200\pi\)
\(60\) 0 0
\(61\) 10.9442 1.40126 0.700631 0.713524i \(-0.252902\pi\)
0.700631 + 0.713524i \(0.252902\pi\)
\(62\) −23.9996 −3.04795
\(63\) 0 0
\(64\) 5.64176 0.705220
\(65\) 0.430467 0.0533929
\(66\) 0 0
\(67\) 1.34491 0.164307 0.0821535 0.996620i \(-0.473820\pi\)
0.0821535 + 0.996620i \(0.473820\pi\)
\(68\) 24.2667 2.94276
\(69\) 0 0
\(70\) 4.23750 0.506478
\(71\) −5.05046 −0.599379 −0.299690 0.954037i \(-0.596883\pi\)
−0.299690 + 0.954037i \(0.596883\pi\)
\(72\) 0 0
\(73\) −16.4455 −1.92480 −0.962401 0.271634i \(-0.912436\pi\)
−0.962401 + 0.271634i \(0.912436\pi\)
\(74\) 17.2490 2.00515
\(75\) 0 0
\(76\) 28.1293 3.22666
\(77\) −4.79599 −0.546554
\(78\) 0 0
\(79\) −0.111124 −0.0125025 −0.00625124 0.999980i \(-0.501990\pi\)
−0.00625124 + 0.999980i \(0.501990\pi\)
\(80\) 14.6592 1.63895
\(81\) 0 0
\(82\) 8.91149 0.984109
\(83\) −6.65678 −0.730676 −0.365338 0.930875i \(-0.619047\pi\)
−0.365338 + 0.930875i \(0.619047\pi\)
\(84\) 0 0
\(85\) 8.35852 0.906609
\(86\) 6.06861 0.654395
\(87\) 0 0
\(88\) −34.1018 −3.63526
\(89\) −11.2897 −1.19671 −0.598353 0.801233i \(-0.704178\pi\)
−0.598353 + 0.801233i \(0.704178\pi\)
\(90\) 0 0
\(91\) 0.263712 0.0276445
\(92\) 19.4524 2.02805
\(93\) 0 0
\(94\) 14.7745 1.52388
\(95\) 9.68900 0.994070
\(96\) 0 0
\(97\) −5.51451 −0.559913 −0.279957 0.960013i \(-0.590320\pi\)
−0.279957 + 0.960013i \(0.590320\pi\)
\(98\) 2.59597 0.262232
\(99\) 0 0
\(100\) −11.0679 −1.10679
\(101\) −0.809406 −0.0805389 −0.0402694 0.999189i \(-0.512822\pi\)
−0.0402694 + 0.999189i \(0.512822\pi\)
\(102\) 0 0
\(103\) −5.13235 −0.505705 −0.252853 0.967505i \(-0.581369\pi\)
−0.252853 + 0.967505i \(0.581369\pi\)
\(104\) 1.87512 0.183870
\(105\) 0 0
\(106\) −6.62702 −0.643673
\(107\) 17.1879 1.66161 0.830807 0.556560i \(-0.187879\pi\)
0.830807 + 0.556560i \(0.187879\pi\)
\(108\) 0 0
\(109\) 8.44424 0.808812 0.404406 0.914580i \(-0.367478\pi\)
0.404406 + 0.914580i \(0.367478\pi\)
\(110\) −20.3230 −1.93772
\(111\) 0 0
\(112\) 8.98048 0.848575
\(113\) 2.27777 0.214275 0.107137 0.994244i \(-0.465832\pi\)
0.107137 + 0.994244i \(0.465832\pi\)
\(114\) 0 0
\(115\) 6.70026 0.624803
\(116\) −2.17888 −0.202303
\(117\) 0 0
\(118\) 34.6286 3.18782
\(119\) 5.12058 0.469403
\(120\) 0 0
\(121\) 12.0015 1.09105
\(122\) 28.4108 2.57219
\(123\) 0 0
\(124\) −43.8123 −3.93446
\(125\) −11.9740 −1.07098
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −3.53831 −0.312745
\(129\) 0 0
\(130\) 1.11748 0.0980094
\(131\) −7.70860 −0.673503 −0.336752 0.941593i \(-0.609328\pi\)
−0.336752 + 0.941593i \(0.609328\pi\)
\(132\) 0 0
\(133\) 5.93565 0.514686
\(134\) 3.49134 0.301606
\(135\) 0 0
\(136\) 36.4098 3.12211
\(137\) 2.92001 0.249473 0.124737 0.992190i \(-0.460191\pi\)
0.124737 + 0.992190i \(0.460191\pi\)
\(138\) 0 0
\(139\) 1.52119 0.129026 0.0645130 0.997917i \(-0.479451\pi\)
0.0645130 + 0.997917i \(0.479451\pi\)
\(140\) 7.73574 0.653789
\(141\) 0 0
\(142\) −13.1108 −1.10024
\(143\) −1.26476 −0.105764
\(144\) 0 0
\(145\) −0.750502 −0.0623258
\(146\) −42.6920 −3.53322
\(147\) 0 0
\(148\) 31.4887 2.58835
\(149\) −12.0258 −0.985195 −0.492598 0.870257i \(-0.663953\pi\)
−0.492598 + 0.870257i \(0.663953\pi\)
\(150\) 0 0
\(151\) 4.51556 0.367471 0.183736 0.982976i \(-0.441181\pi\)
0.183736 + 0.982976i \(0.441181\pi\)
\(152\) 42.2053 3.42330
\(153\) 0 0
\(154\) −12.4502 −1.00327
\(155\) −15.0909 −1.21213
\(156\) 0 0
\(157\) 2.59506 0.207109 0.103554 0.994624i \(-0.466978\pi\)
0.103554 + 0.994624i \(0.466978\pi\)
\(158\) −0.288475 −0.0229499
\(159\) 0 0
\(160\) 14.8413 1.17331
\(161\) 4.10470 0.323495
\(162\) 0 0
\(163\) 20.3837 1.59658 0.798288 0.602275i \(-0.205739\pi\)
0.798288 + 0.602275i \(0.205739\pi\)
\(164\) 16.2683 1.27034
\(165\) 0 0
\(166\) −17.2808 −1.34125
\(167\) −7.15571 −0.553726 −0.276863 0.960909i \(-0.589295\pi\)
−0.276863 + 0.960909i \(0.589295\pi\)
\(168\) 0 0
\(169\) −12.9305 −0.994650
\(170\) 21.6985 1.66420
\(171\) 0 0
\(172\) 11.0785 0.844727
\(173\) 9.08892 0.691018 0.345509 0.938415i \(-0.387706\pi\)
0.345509 + 0.938415i \(0.387706\pi\)
\(174\) 0 0
\(175\) −2.33547 −0.176545
\(176\) −43.0703 −3.24654
\(177\) 0 0
\(178\) −29.3077 −2.19670
\(179\) 19.6649 1.46982 0.734912 0.678162i \(-0.237223\pi\)
0.734912 + 0.678162i \(0.237223\pi\)
\(180\) 0 0
\(181\) 5.64241 0.419397 0.209699 0.977766i \(-0.432752\pi\)
0.209699 + 0.977766i \(0.432752\pi\)
\(182\) 0.684587 0.0507450
\(183\) 0 0
\(184\) 29.1864 2.15165
\(185\) 10.8461 0.797422
\(186\) 0 0
\(187\) −24.5582 −1.79588
\(188\) 26.9715 1.96710
\(189\) 0 0
\(190\) 25.1523 1.82474
\(191\) 14.5073 1.04971 0.524855 0.851192i \(-0.324119\pi\)
0.524855 + 0.851192i \(0.324119\pi\)
\(192\) 0 0
\(193\) −13.6112 −0.979753 −0.489877 0.871792i \(-0.662958\pi\)
−0.489877 + 0.871792i \(0.662958\pi\)
\(194\) −14.3155 −1.02779
\(195\) 0 0
\(196\) 4.73905 0.338503
\(197\) −6.88652 −0.490644 −0.245322 0.969442i \(-0.578894\pi\)
−0.245322 + 0.969442i \(0.578894\pi\)
\(198\) 0 0
\(199\) −25.0663 −1.77690 −0.888451 0.458972i \(-0.848218\pi\)
−0.888451 + 0.458972i \(0.848218\pi\)
\(200\) −16.6063 −1.17424
\(201\) 0 0
\(202\) −2.10119 −0.147839
\(203\) −0.459771 −0.0322696
\(204\) 0 0
\(205\) 5.60353 0.391367
\(206\) −13.3234 −0.928286
\(207\) 0 0
\(208\) 2.36826 0.164209
\(209\) −28.4673 −1.96913
\(210\) 0 0
\(211\) −22.2975 −1.53502 −0.767512 0.641035i \(-0.778505\pi\)
−0.767512 + 0.641035i \(0.778505\pi\)
\(212\) −12.0979 −0.830887
\(213\) 0 0
\(214\) 44.6192 3.05010
\(215\) 3.81593 0.260244
\(216\) 0 0
\(217\) −9.24495 −0.627588
\(218\) 21.9210 1.48468
\(219\) 0 0
\(220\) −37.1005 −2.50131
\(221\) 1.35036 0.0908348
\(222\) 0 0
\(223\) −9.15329 −0.612950 −0.306475 0.951879i \(-0.599150\pi\)
−0.306475 + 0.951879i \(0.599150\pi\)
\(224\) 9.09207 0.607489
\(225\) 0 0
\(226\) 5.91303 0.393329
\(227\) −18.4647 −1.22554 −0.612771 0.790260i \(-0.709945\pi\)
−0.612771 + 0.790260i \(0.709945\pi\)
\(228\) 0 0
\(229\) −21.5708 −1.42544 −0.712721 0.701448i \(-0.752537\pi\)
−0.712721 + 0.701448i \(0.752537\pi\)
\(230\) 17.3937 1.14690
\(231\) 0 0
\(232\) −3.26919 −0.214633
\(233\) 8.86474 0.580749 0.290374 0.956913i \(-0.406220\pi\)
0.290374 + 0.956913i \(0.406220\pi\)
\(234\) 0 0
\(235\) 9.29020 0.606026
\(236\) 63.2160 4.11501
\(237\) 0 0
\(238\) 13.2929 0.861648
\(239\) −20.1987 −1.30654 −0.653272 0.757124i \(-0.726604\pi\)
−0.653272 + 0.757124i \(0.726604\pi\)
\(240\) 0 0
\(241\) 0.276725 0.0178254 0.00891272 0.999960i \(-0.497163\pi\)
0.00891272 + 0.999960i \(0.497163\pi\)
\(242\) 31.1555 2.00275
\(243\) 0 0
\(244\) 51.8651 3.32032
\(245\) 1.63234 0.104286
\(246\) 0 0
\(247\) 1.56530 0.0995977
\(248\) −65.7360 −4.17424
\(249\) 0 0
\(250\) −31.0840 −1.96593
\(251\) 23.2801 1.46942 0.734712 0.678379i \(-0.237317\pi\)
0.734712 + 0.678379i \(0.237317\pi\)
\(252\) 0 0
\(253\) −19.6861 −1.23765
\(254\) 2.59597 0.162885
\(255\) 0 0
\(256\) −20.4689 −1.27930
\(257\) −23.4788 −1.46457 −0.732285 0.680998i \(-0.761546\pi\)
−0.732285 + 0.680998i \(0.761546\pi\)
\(258\) 0 0
\(259\) 6.64452 0.412870
\(260\) 2.04000 0.126516
\(261\) 0 0
\(262\) −20.0113 −1.23630
\(263\) 2.69710 0.166310 0.0831551 0.996537i \(-0.473500\pi\)
0.0831551 + 0.996537i \(0.473500\pi\)
\(264\) 0 0
\(265\) −4.16706 −0.255980
\(266\) 15.4088 0.944772
\(267\) 0 0
\(268\) 6.37360 0.389329
\(269\) 4.37198 0.266565 0.133282 0.991078i \(-0.457448\pi\)
0.133282 + 0.991078i \(0.457448\pi\)
\(270\) 0 0
\(271\) −8.85747 −0.538053 −0.269026 0.963133i \(-0.586702\pi\)
−0.269026 + 0.963133i \(0.586702\pi\)
\(272\) 45.9852 2.78826
\(273\) 0 0
\(274\) 7.58024 0.457939
\(275\) 11.2009 0.675438
\(276\) 0 0
\(277\) −19.4438 −1.16826 −0.584131 0.811659i \(-0.698565\pi\)
−0.584131 + 0.811659i \(0.698565\pi\)
\(278\) 3.94897 0.236843
\(279\) 0 0
\(280\) 11.6067 0.693634
\(281\) 0.140909 0.00840591 0.00420295 0.999991i \(-0.498662\pi\)
0.00420295 + 0.999991i \(0.498662\pi\)
\(282\) 0 0
\(283\) 22.7659 1.35329 0.676645 0.736309i \(-0.263433\pi\)
0.676645 + 0.736309i \(0.263433\pi\)
\(284\) −23.9344 −1.42024
\(285\) 0 0
\(286\) −3.28327 −0.194144
\(287\) 3.43282 0.202633
\(288\) 0 0
\(289\) 9.22031 0.542371
\(290\) −1.94828 −0.114407
\(291\) 0 0
\(292\) −77.9361 −4.56086
\(293\) 29.5536 1.72654 0.863271 0.504741i \(-0.168412\pi\)
0.863271 + 0.504741i \(0.168412\pi\)
\(294\) 0 0
\(295\) 21.7744 1.26775
\(296\) 47.2457 2.74610
\(297\) 0 0
\(298\) −31.2187 −1.80845
\(299\) 1.08246 0.0626001
\(300\) 0 0
\(301\) 2.33770 0.134743
\(302\) 11.7223 0.674540
\(303\) 0 0
\(304\) 53.3050 3.05725
\(305\) 17.8647 1.02293
\(306\) 0 0
\(307\) −17.4005 −0.993097 −0.496549 0.868009i \(-0.665400\pi\)
−0.496549 + 0.868009i \(0.665400\pi\)
\(308\) −22.7284 −1.29507
\(309\) 0 0
\(310\) −39.1755 −2.22502
\(311\) 17.8934 1.01464 0.507322 0.861757i \(-0.330635\pi\)
0.507322 + 0.861757i \(0.330635\pi\)
\(312\) 0 0
\(313\) −13.0691 −0.738712 −0.369356 0.929288i \(-0.620422\pi\)
−0.369356 + 0.929288i \(0.620422\pi\)
\(314\) 6.73670 0.380174
\(315\) 0 0
\(316\) −0.526624 −0.0296249
\(317\) 24.7771 1.39162 0.695809 0.718226i \(-0.255046\pi\)
0.695809 + 0.718226i \(0.255046\pi\)
\(318\) 0 0
\(319\) 2.20505 0.123459
\(320\) 9.20927 0.514814
\(321\) 0 0
\(322\) 10.6557 0.593817
\(323\) 30.3940 1.69117
\(324\) 0 0
\(325\) −0.615890 −0.0341634
\(326\) 52.9155 2.93072
\(327\) 0 0
\(328\) 24.4090 1.34776
\(329\) 5.69134 0.313774
\(330\) 0 0
\(331\) −14.3948 −0.791210 −0.395605 0.918421i \(-0.629465\pi\)
−0.395605 + 0.918421i \(0.629465\pi\)
\(332\) −31.5468 −1.73136
\(333\) 0 0
\(334\) −18.5760 −1.01643
\(335\) 2.19535 0.119945
\(336\) 0 0
\(337\) −8.13837 −0.443325 −0.221663 0.975123i \(-0.571148\pi\)
−0.221663 + 0.975123i \(0.571148\pi\)
\(338\) −33.5670 −1.82581
\(339\) 0 0
\(340\) 39.6114 2.14823
\(341\) 44.3387 2.40107
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 16.6222 0.896209
\(345\) 0 0
\(346\) 23.5946 1.26845
\(347\) 23.6307 1.26856 0.634280 0.773103i \(-0.281297\pi\)
0.634280 + 0.773103i \(0.281297\pi\)
\(348\) 0 0
\(349\) −27.0018 −1.44537 −0.722686 0.691176i \(-0.757093\pi\)
−0.722686 + 0.691176i \(0.757093\pi\)
\(350\) −6.06280 −0.324070
\(351\) 0 0
\(352\) −43.6055 −2.32418
\(353\) −20.7847 −1.10626 −0.553130 0.833095i \(-0.686567\pi\)
−0.553130 + 0.833095i \(0.686567\pi\)
\(354\) 0 0
\(355\) −8.24406 −0.437549
\(356\) −53.5024 −2.83562
\(357\) 0 0
\(358\) 51.0495 2.69805
\(359\) 7.34347 0.387574 0.193787 0.981044i \(-0.437923\pi\)
0.193787 + 0.981044i \(0.437923\pi\)
\(360\) 0 0
\(361\) 16.2320 0.854314
\(362\) 14.6475 0.769856
\(363\) 0 0
\(364\) 1.24974 0.0655043
\(365\) −26.8447 −1.40511
\(366\) 0 0
\(367\) 3.27104 0.170747 0.0853735 0.996349i \(-0.472792\pi\)
0.0853735 + 0.996349i \(0.472792\pi\)
\(368\) 36.8621 1.92157
\(369\) 0 0
\(370\) 28.1562 1.46377
\(371\) −2.55281 −0.132535
\(372\) 0 0
\(373\) −30.7576 −1.59257 −0.796284 0.604923i \(-0.793204\pi\)
−0.796284 + 0.604923i \(0.793204\pi\)
\(374\) −63.7524 −3.29656
\(375\) 0 0
\(376\) 40.4681 2.08698
\(377\) −0.121247 −0.00624453
\(378\) 0 0
\(379\) 16.1652 0.830353 0.415176 0.909741i \(-0.363720\pi\)
0.415176 + 0.909741i \(0.363720\pi\)
\(380\) 45.9166 2.35547
\(381\) 0 0
\(382\) 37.6604 1.92688
\(383\) −10.0448 −0.513263 −0.256632 0.966509i \(-0.582613\pi\)
−0.256632 + 0.966509i \(0.582613\pi\)
\(384\) 0 0
\(385\) −7.82868 −0.398987
\(386\) −35.3341 −1.79846
\(387\) 0 0
\(388\) −26.1335 −1.32673
\(389\) −29.6168 −1.50163 −0.750816 0.660511i \(-0.770340\pi\)
−0.750816 + 0.660511i \(0.770340\pi\)
\(390\) 0 0
\(391\) 21.0184 1.06295
\(392\) 7.11048 0.359133
\(393\) 0 0
\(394\) −17.8772 −0.900640
\(395\) −0.181393 −0.00912687
\(396\) 0 0
\(397\) 0.0564815 0.00283472 0.00141736 0.999999i \(-0.499549\pi\)
0.00141736 + 0.999999i \(0.499549\pi\)
\(398\) −65.0713 −3.26173
\(399\) 0 0
\(400\) −20.9736 −1.04868
\(401\) 13.6688 0.682587 0.341294 0.939957i \(-0.389135\pi\)
0.341294 + 0.939957i \(0.389135\pi\)
\(402\) 0 0
\(403\) −2.43800 −0.121446
\(404\) −3.83581 −0.190839
\(405\) 0 0
\(406\) −1.19355 −0.0592349
\(407\) −31.8670 −1.57959
\(408\) 0 0
\(409\) −37.5240 −1.85544 −0.927722 0.373272i \(-0.878236\pi\)
−0.927722 + 0.373272i \(0.878236\pi\)
\(410\) 14.5466 0.718404
\(411\) 0 0
\(412\) −24.3224 −1.19828
\(413\) 13.3394 0.656388
\(414\) 0 0
\(415\) −10.8661 −0.533397
\(416\) 2.39769 0.117556
\(417\) 0 0
\(418\) −73.9002 −3.61458
\(419\) −9.96006 −0.486581 −0.243290 0.969954i \(-0.578227\pi\)
−0.243290 + 0.969954i \(0.578227\pi\)
\(420\) 0 0
\(421\) −0.917111 −0.0446973 −0.0223486 0.999750i \(-0.507114\pi\)
−0.0223486 + 0.999750i \(0.507114\pi\)
\(422\) −57.8836 −2.81773
\(423\) 0 0
\(424\) −18.1517 −0.881526
\(425\) −11.9589 −0.580094
\(426\) 0 0
\(427\) 10.9442 0.529627
\(428\) 81.4542 3.93724
\(429\) 0 0
\(430\) 9.90603 0.477711
\(431\) 28.8257 1.38848 0.694242 0.719741i \(-0.255740\pi\)
0.694242 + 0.719741i \(0.255740\pi\)
\(432\) 0 0
\(433\) −29.4309 −1.41436 −0.707178 0.707035i \(-0.750032\pi\)
−0.707178 + 0.707035i \(0.750032\pi\)
\(434\) −23.9996 −1.15202
\(435\) 0 0
\(436\) 40.0177 1.91650
\(437\) 24.3641 1.16549
\(438\) 0 0
\(439\) −21.0634 −1.00530 −0.502650 0.864490i \(-0.667642\pi\)
−0.502650 + 0.864490i \(0.667642\pi\)
\(440\) −55.6657 −2.65376
\(441\) 0 0
\(442\) 3.50548 0.166739
\(443\) −37.1991 −1.76738 −0.883691 0.468071i \(-0.844949\pi\)
−0.883691 + 0.468071i \(0.844949\pi\)
\(444\) 0 0
\(445\) −18.4286 −0.873600
\(446\) −23.7617 −1.12515
\(447\) 0 0
\(448\) 5.64176 0.266548
\(449\) −20.6942 −0.976621 −0.488310 0.872670i \(-0.662387\pi\)
−0.488310 + 0.872670i \(0.662387\pi\)
\(450\) 0 0
\(451\) −16.4638 −0.775248
\(452\) 10.7945 0.507729
\(453\) 0 0
\(454\) −47.9337 −2.24964
\(455\) 0.430467 0.0201806
\(456\) 0 0
\(457\) 29.9339 1.40025 0.700124 0.714021i \(-0.253128\pi\)
0.700124 + 0.714021i \(0.253128\pi\)
\(458\) −55.9972 −2.61658
\(459\) 0 0
\(460\) 31.7529 1.48048
\(461\) −22.9494 −1.06886 −0.534429 0.845213i \(-0.679473\pi\)
−0.534429 + 0.845213i \(0.679473\pi\)
\(462\) 0 0
\(463\) −14.6390 −0.680333 −0.340167 0.940365i \(-0.610484\pi\)
−0.340167 + 0.940365i \(0.610484\pi\)
\(464\) −4.12896 −0.191682
\(465\) 0 0
\(466\) 23.0126 1.06604
\(467\) −2.88366 −0.133440 −0.0667200 0.997772i \(-0.521253\pi\)
−0.0667200 + 0.997772i \(0.521253\pi\)
\(468\) 0 0
\(469\) 1.34491 0.0621022
\(470\) 24.1171 1.11244
\(471\) 0 0
\(472\) 94.8494 4.36580
\(473\) −11.2116 −0.515510
\(474\) 0 0
\(475\) −13.8625 −0.636056
\(476\) 24.2667 1.11226
\(477\) 0 0
\(478\) −52.4351 −2.39833
\(479\) −9.17227 −0.419092 −0.209546 0.977799i \(-0.567199\pi\)
−0.209546 + 0.977799i \(0.567199\pi\)
\(480\) 0 0
\(481\) 1.75224 0.0798952
\(482\) 0.718370 0.0327209
\(483\) 0 0
\(484\) 56.8757 2.58526
\(485\) −9.00155 −0.408739
\(486\) 0 0
\(487\) −26.2962 −1.19160 −0.595798 0.803134i \(-0.703164\pi\)
−0.595798 + 0.803134i \(0.703164\pi\)
\(488\) 77.8185 3.52268
\(489\) 0 0
\(490\) 4.23750 0.191431
\(491\) −14.2675 −0.643882 −0.321941 0.946760i \(-0.604335\pi\)
−0.321941 + 0.946760i \(0.604335\pi\)
\(492\) 0 0
\(493\) −2.35429 −0.106032
\(494\) 4.06347 0.182824
\(495\) 0 0
\(496\) −83.0241 −3.72789
\(497\) −5.05046 −0.226544
\(498\) 0 0
\(499\) 31.6638 1.41747 0.708734 0.705476i \(-0.249267\pi\)
0.708734 + 0.705476i \(0.249267\pi\)
\(500\) −56.7452 −2.53772
\(501\) 0 0
\(502\) 60.4343 2.69731
\(503\) 38.6248 1.72219 0.861097 0.508441i \(-0.169778\pi\)
0.861097 + 0.508441i \(0.169778\pi\)
\(504\) 0 0
\(505\) −1.32123 −0.0587937
\(506\) −51.1044 −2.27187
\(507\) 0 0
\(508\) 4.73905 0.210261
\(509\) 15.2747 0.677040 0.338520 0.940959i \(-0.390074\pi\)
0.338520 + 0.940959i \(0.390074\pi\)
\(510\) 0 0
\(511\) −16.4455 −0.727507
\(512\) −46.0599 −2.03558
\(513\) 0 0
\(514\) −60.9503 −2.68840
\(515\) −8.37773 −0.369167
\(516\) 0 0
\(517\) −27.2956 −1.20046
\(518\) 17.2490 0.757876
\(519\) 0 0
\(520\) 3.06083 0.134226
\(521\) −10.6429 −0.466273 −0.233136 0.972444i \(-0.574899\pi\)
−0.233136 + 0.972444i \(0.574899\pi\)
\(522\) 0 0
\(523\) 28.1697 1.23178 0.615888 0.787834i \(-0.288797\pi\)
0.615888 + 0.787834i \(0.288797\pi\)
\(524\) −36.5314 −1.59588
\(525\) 0 0
\(526\) 7.00158 0.305283
\(527\) −47.3395 −2.06214
\(528\) 0 0
\(529\) −6.15146 −0.267455
\(530\) −10.8175 −0.469884
\(531\) 0 0
\(532\) 28.1293 1.21956
\(533\) 0.905275 0.0392118
\(534\) 0 0
\(535\) 28.0565 1.21299
\(536\) 9.56296 0.413057
\(537\) 0 0
\(538\) 11.3495 0.489313
\(539\) −4.79599 −0.206578
\(540\) 0 0
\(541\) 11.9718 0.514708 0.257354 0.966317i \(-0.417149\pi\)
0.257354 + 0.966317i \(0.417149\pi\)
\(542\) −22.9937 −0.987664
\(543\) 0 0
\(544\) 46.5566 1.99610
\(545\) 13.7839 0.590436
\(546\) 0 0
\(547\) 38.6453 1.65235 0.826177 0.563410i \(-0.190511\pi\)
0.826177 + 0.563410i \(0.190511\pi\)
\(548\) 13.8381 0.591132
\(549\) 0 0
\(550\) 29.0771 1.23985
\(551\) −2.72904 −0.116261
\(552\) 0 0
\(553\) −0.111124 −0.00472549
\(554\) −50.4754 −2.14449
\(555\) 0 0
\(556\) 7.20901 0.305730
\(557\) 27.9185 1.18295 0.591473 0.806325i \(-0.298547\pi\)
0.591473 + 0.806325i \(0.298547\pi\)
\(558\) 0 0
\(559\) 0.616480 0.0260743
\(560\) 14.6592 0.619464
\(561\) 0 0
\(562\) 0.365794 0.0154301
\(563\) −17.5654 −0.740292 −0.370146 0.928974i \(-0.620692\pi\)
−0.370146 + 0.928974i \(0.620692\pi\)
\(564\) 0 0
\(565\) 3.71810 0.156422
\(566\) 59.0994 2.48413
\(567\) 0 0
\(568\) −35.9112 −1.50680
\(569\) 6.23445 0.261362 0.130681 0.991424i \(-0.458284\pi\)
0.130681 + 0.991424i \(0.458284\pi\)
\(570\) 0 0
\(571\) 10.2350 0.428321 0.214161 0.976798i \(-0.431298\pi\)
0.214161 + 0.976798i \(0.431298\pi\)
\(572\) −5.99375 −0.250611
\(573\) 0 0
\(574\) 8.91149 0.371958
\(575\) −9.58639 −0.399780
\(576\) 0 0
\(577\) −6.56718 −0.273395 −0.136698 0.990613i \(-0.543649\pi\)
−0.136698 + 0.990613i \(0.543649\pi\)
\(578\) 23.9356 0.995591
\(579\) 0 0
\(580\) −3.55666 −0.147682
\(581\) −6.65678 −0.276170
\(582\) 0 0
\(583\) 12.2433 0.507064
\(584\) −116.935 −4.83882
\(585\) 0 0
\(586\) 76.7202 3.16928
\(587\) 3.47722 0.143520 0.0717602 0.997422i \(-0.477138\pi\)
0.0717602 + 0.997422i \(0.477138\pi\)
\(588\) 0 0
\(589\) −54.8748 −2.26108
\(590\) 56.5256 2.32712
\(591\) 0 0
\(592\) 59.6709 2.45246
\(593\) 18.0049 0.739372 0.369686 0.929157i \(-0.379465\pi\)
0.369686 + 0.929157i \(0.379465\pi\)
\(594\) 0 0
\(595\) 8.35852 0.342666
\(596\) −56.9910 −2.33444
\(597\) 0 0
\(598\) 2.81002 0.114910
\(599\) −5.91219 −0.241565 −0.120783 0.992679i \(-0.538540\pi\)
−0.120783 + 0.992679i \(0.538540\pi\)
\(600\) 0 0
\(601\) −8.32532 −0.339597 −0.169799 0.985479i \(-0.554312\pi\)
−0.169799 + 0.985479i \(0.554312\pi\)
\(602\) 6.06861 0.247338
\(603\) 0 0
\(604\) 21.3995 0.870732
\(605\) 19.5905 0.796468
\(606\) 0 0
\(607\) 12.2488 0.497163 0.248581 0.968611i \(-0.420036\pi\)
0.248581 + 0.968611i \(0.420036\pi\)
\(608\) 53.9673 2.18867
\(609\) 0 0
\(610\) 46.3761 1.87771
\(611\) 1.50087 0.0607188
\(612\) 0 0
\(613\) 5.93637 0.239768 0.119884 0.992788i \(-0.461748\pi\)
0.119884 + 0.992788i \(0.461748\pi\)
\(614\) −45.1711 −1.82296
\(615\) 0 0
\(616\) −34.1018 −1.37400
\(617\) 44.2173 1.78012 0.890061 0.455841i \(-0.150662\pi\)
0.890061 + 0.455841i \(0.150662\pi\)
\(618\) 0 0
\(619\) −30.2653 −1.21647 −0.608233 0.793759i \(-0.708121\pi\)
−0.608233 + 0.793759i \(0.708121\pi\)
\(620\) −71.5165 −2.87217
\(621\) 0 0
\(622\) 46.4508 1.86251
\(623\) −11.2897 −0.452312
\(624\) 0 0
\(625\) −7.86826 −0.314730
\(626\) −33.9271 −1.35600
\(627\) 0 0
\(628\) 12.2981 0.490749
\(629\) 34.0238 1.35662
\(630\) 0 0
\(631\) 37.4959 1.49269 0.746344 0.665561i \(-0.231808\pi\)
0.746344 + 0.665561i \(0.231808\pi\)
\(632\) −0.790148 −0.0314304
\(633\) 0 0
\(634\) 64.3205 2.55449
\(635\) 1.63234 0.0647774
\(636\) 0 0
\(637\) 0.263712 0.0104486
\(638\) 5.72425 0.226625
\(639\) 0 0
\(640\) −5.77572 −0.228305
\(641\) −20.9319 −0.826762 −0.413381 0.910558i \(-0.635652\pi\)
−0.413381 + 0.910558i \(0.635652\pi\)
\(642\) 0 0
\(643\) 42.0230 1.65723 0.828613 0.559821i \(-0.189130\pi\)
0.828613 + 0.559821i \(0.189130\pi\)
\(644\) 19.4524 0.766530
\(645\) 0 0
\(646\) 78.9017 3.10435
\(647\) −7.99073 −0.314148 −0.157074 0.987587i \(-0.550206\pi\)
−0.157074 + 0.987587i \(0.550206\pi\)
\(648\) 0 0
\(649\) −63.9755 −2.51126
\(650\) −1.59883 −0.0627113
\(651\) 0 0
\(652\) 96.5995 3.78313
\(653\) 6.91364 0.270552 0.135276 0.990808i \(-0.456808\pi\)
0.135276 + 0.990808i \(0.456808\pi\)
\(654\) 0 0
\(655\) −12.5831 −0.491661
\(656\) 30.8284 1.20364
\(657\) 0 0
\(658\) 14.7745 0.575971
\(659\) −29.0812 −1.13284 −0.566421 0.824116i \(-0.691672\pi\)
−0.566421 + 0.824116i \(0.691672\pi\)
\(660\) 0 0
\(661\) −30.8242 −1.19892 −0.599461 0.800404i \(-0.704618\pi\)
−0.599461 + 0.800404i \(0.704618\pi\)
\(662\) −37.3685 −1.45237
\(663\) 0 0
\(664\) −47.3329 −1.83687
\(665\) 9.68900 0.375723
\(666\) 0 0
\(667\) −1.88722 −0.0730734
\(668\) −33.9113 −1.31207
\(669\) 0 0
\(670\) 5.69906 0.220174
\(671\) −52.4883 −2.02629
\(672\) 0 0
\(673\) 25.7018 0.990733 0.495366 0.868684i \(-0.335034\pi\)
0.495366 + 0.868684i \(0.335034\pi\)
\(674\) −21.1270 −0.813780
\(675\) 0 0
\(676\) −61.2780 −2.35685
\(677\) 21.9171 0.842342 0.421171 0.906981i \(-0.361619\pi\)
0.421171 + 0.906981i \(0.361619\pi\)
\(678\) 0 0
\(679\) −5.51451 −0.211627
\(680\) 59.4331 2.27916
\(681\) 0 0
\(682\) 115.102 4.40747
\(683\) −16.0446 −0.613931 −0.306966 0.951721i \(-0.599314\pi\)
−0.306966 + 0.951721i \(0.599314\pi\)
\(684\) 0 0
\(685\) 4.76644 0.182116
\(686\) 2.59597 0.0991145
\(687\) 0 0
\(688\) 20.9937 0.800377
\(689\) −0.673207 −0.0256471
\(690\) 0 0
\(691\) −11.0457 −0.420199 −0.210099 0.977680i \(-0.567379\pi\)
−0.210099 + 0.977680i \(0.567379\pi\)
\(692\) 43.0728 1.63738
\(693\) 0 0
\(694\) 61.3444 2.32860
\(695\) 2.48310 0.0941895
\(696\) 0 0
\(697\) 17.5780 0.665815
\(698\) −70.0958 −2.65316
\(699\) 0 0
\(700\) −11.0679 −0.418327
\(701\) 7.99153 0.301836 0.150918 0.988546i \(-0.451777\pi\)
0.150918 + 0.988546i \(0.451777\pi\)
\(702\) 0 0
\(703\) 39.4395 1.48749
\(704\) −27.0578 −1.01978
\(705\) 0 0
\(706\) −53.9565 −2.03068
\(707\) −0.809406 −0.0304408
\(708\) 0 0
\(709\) 10.5416 0.395900 0.197950 0.980212i \(-0.436572\pi\)
0.197950 + 0.980212i \(0.436572\pi\)
\(710\) −21.4013 −0.803177
\(711\) 0 0
\(712\) −80.2751 −3.00844
\(713\) −37.9477 −1.42115
\(714\) 0 0
\(715\) −2.06452 −0.0772085
\(716\) 93.1929 3.48278
\(717\) 0 0
\(718\) 19.0634 0.711440
\(719\) 25.0664 0.934820 0.467410 0.884041i \(-0.345187\pi\)
0.467410 + 0.884041i \(0.345187\pi\)
\(720\) 0 0
\(721\) −5.13235 −0.191139
\(722\) 42.1376 1.56820
\(723\) 0 0
\(724\) 26.7397 0.993771
\(725\) 1.07378 0.0398792
\(726\) 0 0
\(727\) −21.6940 −0.804588 −0.402294 0.915511i \(-0.631787\pi\)
−0.402294 + 0.915511i \(0.631787\pi\)
\(728\) 1.87512 0.0694964
\(729\) 0 0
\(730\) −69.6879 −2.57926
\(731\) 11.9704 0.442741
\(732\) 0 0
\(733\) 21.1204 0.780099 0.390050 0.920794i \(-0.372458\pi\)
0.390050 + 0.920794i \(0.372458\pi\)
\(734\) 8.49152 0.313428
\(735\) 0 0
\(736\) 37.3202 1.37564
\(737\) −6.45018 −0.237595
\(738\) 0 0
\(739\) −30.2759 −1.11372 −0.556858 0.830608i \(-0.687993\pi\)
−0.556858 + 0.830608i \(0.687993\pi\)
\(740\) 51.4002 1.88951
\(741\) 0 0
\(742\) −6.62702 −0.243286
\(743\) 46.3530 1.70053 0.850264 0.526356i \(-0.176442\pi\)
0.850264 + 0.526356i \(0.176442\pi\)
\(744\) 0 0
\(745\) −19.6303 −0.719197
\(746\) −79.8457 −2.92336
\(747\) 0 0
\(748\) −116.383 −4.25537
\(749\) 17.1879 0.628031
\(750\) 0 0
\(751\) 28.3709 1.03527 0.517634 0.855602i \(-0.326813\pi\)
0.517634 + 0.855602i \(0.326813\pi\)
\(752\) 51.1109 1.86382
\(753\) 0 0
\(754\) −0.314753 −0.0114626
\(755\) 7.37094 0.268256
\(756\) 0 0
\(757\) −29.1551 −1.05966 −0.529831 0.848103i \(-0.677745\pi\)
−0.529831 + 0.848103i \(0.677745\pi\)
\(758\) 41.9644 1.52422
\(759\) 0 0
\(760\) 68.8934 2.49903
\(761\) 51.7911 1.87743 0.938713 0.344700i \(-0.112019\pi\)
0.938713 + 0.344700i \(0.112019\pi\)
\(762\) 0 0
\(763\) 8.44424 0.305702
\(764\) 68.7507 2.48731
\(765\) 0 0
\(766\) −26.0759 −0.942160
\(767\) 3.51775 0.127019
\(768\) 0 0
\(769\) 44.8361 1.61683 0.808415 0.588613i \(-0.200326\pi\)
0.808415 + 0.588613i \(0.200326\pi\)
\(770\) −20.3230 −0.732390
\(771\) 0 0
\(772\) −64.5040 −2.32155
\(773\) 45.1243 1.62301 0.811504 0.584347i \(-0.198649\pi\)
0.811504 + 0.584347i \(0.198649\pi\)
\(774\) 0 0
\(775\) 21.5913 0.775582
\(776\) −39.2108 −1.40758
\(777\) 0 0
\(778\) −76.8843 −2.75644
\(779\) 20.3760 0.730047
\(780\) 0 0
\(781\) 24.2219 0.866729
\(782\) 54.5631 1.95117
\(783\) 0 0
\(784\) 8.98048 0.320731
\(785\) 4.23603 0.151190
\(786\) 0 0
\(787\) −31.6116 −1.12683 −0.563416 0.826173i \(-0.690513\pi\)
−0.563416 + 0.826173i \(0.690513\pi\)
\(788\) −32.6355 −1.16259
\(789\) 0 0
\(790\) −0.470890 −0.0167535
\(791\) 2.27777 0.0809883
\(792\) 0 0
\(793\) 2.88611 0.102489
\(794\) 0.146624 0.00520349
\(795\) 0 0
\(796\) −118.790 −4.21041
\(797\) −9.37863 −0.332208 −0.166104 0.986108i \(-0.553119\pi\)
−0.166104 + 0.986108i \(0.553119\pi\)
\(798\) 0 0
\(799\) 29.1429 1.03100
\(800\) −21.2342 −0.750743
\(801\) 0 0
\(802\) 35.4838 1.25297
\(803\) 78.8725 2.78335
\(804\) 0 0
\(805\) 6.70026 0.236153
\(806\) −6.32897 −0.222929
\(807\) 0 0
\(808\) −5.75526 −0.202469
\(809\) −30.7716 −1.08187 −0.540935 0.841064i \(-0.681930\pi\)
−0.540935 + 0.841064i \(0.681930\pi\)
\(810\) 0 0
\(811\) 5.29510 0.185936 0.0929681 0.995669i \(-0.470365\pi\)
0.0929681 + 0.995669i \(0.470365\pi\)
\(812\) −2.17888 −0.0764635
\(813\) 0 0
\(814\) −82.7258 −2.89954
\(815\) 33.2732 1.16551
\(816\) 0 0
\(817\) 13.8758 0.485453
\(818\) −97.4111 −3.40590
\(819\) 0 0
\(820\) 26.5554 0.927354
\(821\) 46.7930 1.63309 0.816543 0.577284i \(-0.195888\pi\)
0.816543 + 0.577284i \(0.195888\pi\)
\(822\) 0 0
\(823\) −9.35491 −0.326092 −0.163046 0.986618i \(-0.552132\pi\)
−0.163046 + 0.986618i \(0.552132\pi\)
\(824\) −36.4934 −1.27131
\(825\) 0 0
\(826\) 34.6286 1.20488
\(827\) −40.5945 −1.41161 −0.705805 0.708406i \(-0.749414\pi\)
−0.705805 + 0.708406i \(0.749414\pi\)
\(828\) 0 0
\(829\) −11.2936 −0.392243 −0.196121 0.980580i \(-0.562835\pi\)
−0.196121 + 0.980580i \(0.562835\pi\)
\(830\) −28.2081 −0.979118
\(831\) 0 0
\(832\) 1.48780 0.0515801
\(833\) 5.12058 0.177417
\(834\) 0 0
\(835\) −11.6806 −0.404222
\(836\) −134.908 −4.66589
\(837\) 0 0
\(838\) −25.8560 −0.893180
\(839\) −6.00322 −0.207254 −0.103627 0.994616i \(-0.533045\pi\)
−0.103627 + 0.994616i \(0.533045\pi\)
\(840\) 0 0
\(841\) −28.7886 −0.992711
\(842\) −2.38079 −0.0820475
\(843\) 0 0
\(844\) −105.669 −3.63727
\(845\) −21.1069 −0.726099
\(846\) 0 0
\(847\) 12.0015 0.412377
\(848\) −22.9255 −0.787264
\(849\) 0 0
\(850\) −31.0450 −1.06484
\(851\) 27.2737 0.934932
\(852\) 0 0
\(853\) 43.1151 1.47623 0.738116 0.674674i \(-0.235716\pi\)
0.738116 + 0.674674i \(0.235716\pi\)
\(854\) 28.4108 0.972197
\(855\) 0 0
\(856\) 122.214 4.17719
\(857\) −14.7372 −0.503414 −0.251707 0.967803i \(-0.580992\pi\)
−0.251707 + 0.967803i \(0.580992\pi\)
\(858\) 0 0
\(859\) −31.1822 −1.06392 −0.531961 0.846769i \(-0.678545\pi\)
−0.531961 + 0.846769i \(0.678545\pi\)
\(860\) 18.0839 0.616655
\(861\) 0 0
\(862\) 74.8305 2.54874
\(863\) 26.3519 0.897028 0.448514 0.893776i \(-0.351953\pi\)
0.448514 + 0.893776i \(0.351953\pi\)
\(864\) 0 0
\(865\) 14.8362 0.504446
\(866\) −76.4016 −2.59623
\(867\) 0 0
\(868\) −43.8123 −1.48709
\(869\) 0.532952 0.0180791
\(870\) 0 0
\(871\) 0.354669 0.0120175
\(872\) 60.0426 2.03330
\(873\) 0 0
\(874\) 63.2483 2.13941
\(875\) −11.9740 −0.404794
\(876\) 0 0
\(877\) −44.9642 −1.51833 −0.759167 0.650896i \(-0.774393\pi\)
−0.759167 + 0.650896i \(0.774393\pi\)
\(878\) −54.6798 −1.84536
\(879\) 0 0
\(880\) −70.3053 −2.36999
\(881\) −11.3353 −0.381897 −0.190949 0.981600i \(-0.561156\pi\)
−0.190949 + 0.981600i \(0.561156\pi\)
\(882\) 0 0
\(883\) 37.7221 1.26945 0.634724 0.772739i \(-0.281114\pi\)
0.634724 + 0.772739i \(0.281114\pi\)
\(884\) 6.39940 0.215235
\(885\) 0 0
\(886\) −96.5676 −3.24425
\(887\) −5.00523 −0.168059 −0.0840295 0.996463i \(-0.526779\pi\)
−0.0840295 + 0.996463i \(0.526779\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −47.8401 −1.60360
\(891\) 0 0
\(892\) −43.3779 −1.45240
\(893\) 33.7818 1.13046
\(894\) 0 0
\(895\) 32.0998 1.07298
\(896\) −3.53831 −0.118207
\(897\) 0 0
\(898\) −53.7215 −1.79271
\(899\) 4.25056 0.141764
\(900\) 0 0
\(901\) −13.0719 −0.435487
\(902\) −42.7394 −1.42307
\(903\) 0 0
\(904\) 16.1961 0.538673
\(905\) 9.21033 0.306162
\(906\) 0 0
\(907\) −1.70559 −0.0566333 −0.0283166 0.999599i \(-0.509015\pi\)
−0.0283166 + 0.999599i \(0.509015\pi\)
\(908\) −87.5049 −2.90395
\(909\) 0 0
\(910\) 1.11748 0.0370441
\(911\) 49.3674 1.63561 0.817807 0.575493i \(-0.195190\pi\)
0.817807 + 0.575493i \(0.195190\pi\)
\(912\) 0 0
\(913\) 31.9258 1.05659
\(914\) 77.7074 2.57033
\(915\) 0 0
\(916\) −102.225 −3.37762
\(917\) −7.70860 −0.254560
\(918\) 0 0
\(919\) −40.1970 −1.32598 −0.662989 0.748629i \(-0.730712\pi\)
−0.662989 + 0.748629i \(0.730712\pi\)
\(920\) 47.6421 1.57071
\(921\) 0 0
\(922\) −59.5758 −1.96202
\(923\) −1.33186 −0.0438389
\(924\) 0 0
\(925\) −15.5181 −0.510230
\(926\) −38.0024 −1.24884
\(927\) 0 0
\(928\) −4.18027 −0.137224
\(929\) −23.2396 −0.762465 −0.381233 0.924479i \(-0.624500\pi\)
−0.381233 + 0.924479i \(0.624500\pi\)
\(930\) 0 0
\(931\) 5.93565 0.194533
\(932\) 42.0104 1.37610
\(933\) 0 0
\(934\) −7.48590 −0.244946
\(935\) −40.0874 −1.31100
\(936\) 0 0
\(937\) 32.6176 1.06557 0.532785 0.846251i \(-0.321146\pi\)
0.532785 + 0.846251i \(0.321146\pi\)
\(938\) 3.49134 0.113996
\(939\) 0 0
\(940\) 44.0267 1.43599
\(941\) −0.939169 −0.0306160 −0.0153080 0.999883i \(-0.504873\pi\)
−0.0153080 + 0.999883i \(0.504873\pi\)
\(942\) 0 0
\(943\) 14.0907 0.458856
\(944\) 119.794 3.89896
\(945\) 0 0
\(946\) −29.1050 −0.946284
\(947\) 3.25233 0.105686 0.0528432 0.998603i \(-0.483172\pi\)
0.0528432 + 0.998603i \(0.483172\pi\)
\(948\) 0 0
\(949\) −4.33687 −0.140781
\(950\) −35.9866 −1.16756
\(951\) 0 0
\(952\) 36.4098 1.18005
\(953\) −20.1286 −0.652029 −0.326015 0.945365i \(-0.605706\pi\)
−0.326015 + 0.945365i \(0.605706\pi\)
\(954\) 0 0
\(955\) 23.6808 0.766293
\(956\) −95.7225 −3.09589
\(957\) 0 0
\(958\) −23.8109 −0.769296
\(959\) 2.92001 0.0942919
\(960\) 0 0
\(961\) 54.4691 1.75707
\(962\) 4.54875 0.146658
\(963\) 0 0
\(964\) 1.31141 0.0422378
\(965\) −22.2180 −0.715224
\(966\) 0 0
\(967\) −46.0528 −1.48096 −0.740479 0.672080i \(-0.765401\pi\)
−0.740479 + 0.672080i \(0.765401\pi\)
\(968\) 85.3364 2.74282
\(969\) 0 0
\(970\) −23.3677 −0.750292
\(971\) −15.1771 −0.487055 −0.243527 0.969894i \(-0.578305\pi\)
−0.243527 + 0.969894i \(0.578305\pi\)
\(972\) 0 0
\(973\) 1.52119 0.0487672
\(974\) −68.2641 −2.18732
\(975\) 0 0
\(976\) 98.2841 3.14600
\(977\) 36.8954 1.18039 0.590194 0.807261i \(-0.299051\pi\)
0.590194 + 0.807261i \(0.299051\pi\)
\(978\) 0 0
\(979\) 54.1452 1.73049
\(980\) 7.73574 0.247109
\(981\) 0 0
\(982\) −37.0379 −1.18193
\(983\) −13.2244 −0.421794 −0.210897 0.977508i \(-0.567638\pi\)
−0.210897 + 0.977508i \(0.567638\pi\)
\(984\) 0 0
\(985\) −11.2411 −0.358173
\(986\) −6.11166 −0.194635
\(987\) 0 0
\(988\) 7.41804 0.235999
\(989\) 9.59557 0.305121
\(990\) 0 0
\(991\) 23.1367 0.734960 0.367480 0.930031i \(-0.380221\pi\)
0.367480 + 0.930031i \(0.380221\pi\)
\(992\) −84.0557 −2.66877
\(993\) 0 0
\(994\) −13.1108 −0.415850
\(995\) −40.9167 −1.29715
\(996\) 0 0
\(997\) −39.4462 −1.24927 −0.624637 0.780915i \(-0.714753\pi\)
−0.624637 + 0.780915i \(0.714753\pi\)
\(998\) 82.1982 2.60194
\(999\) 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 \(a_p\))