Properties

Label 8046.2.a.l.1.11
Level 8046
Weight 2
Character 8046.1
Self dual Yes
Analytic conductor 64.248
Analytic rank 0
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8046 = 2 \cdot 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8046.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2476334663\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(4.11015\)
Character \(\chi\) = 8046.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+4.11015 q^{5}\) \(-3.78475 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+4.11015 q^{5}\) \(-3.78475 q^{7}\) \(-1.00000 q^{8}\) \(-4.11015 q^{10}\) \(+2.15275 q^{11}\) \(+5.55753 q^{13}\) \(+3.78475 q^{14}\) \(+1.00000 q^{16}\) \(-2.24829 q^{17}\) \(+2.44233 q^{19}\) \(+4.11015 q^{20}\) \(-2.15275 q^{22}\) \(-0.398673 q^{23}\) \(+11.8933 q^{25}\) \(-5.55753 q^{26}\) \(-3.78475 q^{28}\) \(+8.12942 q^{29}\) \(+0.810327 q^{31}\) \(-1.00000 q^{32}\) \(+2.24829 q^{34}\) \(-15.5559 q^{35}\) \(+8.17817 q^{37}\) \(-2.44233 q^{38}\) \(-4.11015 q^{40}\) \(+0.726269 q^{41}\) \(-3.96985 q^{43}\) \(+2.15275 q^{44}\) \(+0.398673 q^{46}\) \(+7.08367 q^{47}\) \(+7.32431 q^{49}\) \(-11.8933 q^{50}\) \(+5.55753 q^{52}\) \(-9.53601 q^{53}\) \(+8.84813 q^{55}\) \(+3.78475 q^{56}\) \(-8.12942 q^{58}\) \(-11.4244 q^{59}\) \(+5.54958 q^{61}\) \(-0.810327 q^{62}\) \(+1.00000 q^{64}\) \(+22.8423 q^{65}\) \(+3.37901 q^{67}\) \(-2.24829 q^{68}\) \(+15.5559 q^{70}\) \(+8.38502 q^{71}\) \(-5.85256 q^{73}\) \(-8.17817 q^{74}\) \(+2.44233 q^{76}\) \(-8.14762 q^{77}\) \(-10.4633 q^{79}\) \(+4.11015 q^{80}\) \(-0.726269 q^{82}\) \(-1.42102 q^{83}\) \(-9.24083 q^{85}\) \(+3.96985 q^{86}\) \(-2.15275 q^{88}\) \(+15.6438 q^{89}\) \(-21.0338 q^{91}\) \(-0.398673 q^{92}\) \(-7.08367 q^{94}\) \(+10.0383 q^{95}\) \(-10.0228 q^{97}\) \(-7.32431 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut +\mathstrut 12q^{4} \) \(\mathstrut +\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut -\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 10q^{11} \) \(\mathstrut -\mathstrut q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 12q^{16} \) \(\mathstrut +\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 10q^{19} \) \(\mathstrut +\mathstrut 5q^{20} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 15q^{23} \) \(\mathstrut +\mathstrut 7q^{25} \) \(\mathstrut +\mathstrut q^{26} \) \(\mathstrut -\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 33q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 13q^{37} \) \(\mathstrut +\mathstrut 10q^{38} \) \(\mathstrut -\mathstrut 5q^{40} \) \(\mathstrut +\mathstrut 20q^{41} \) \(\mathstrut -\mathstrut 11q^{43} \) \(\mathstrut +\mathstrut 10q^{44} \) \(\mathstrut -\mathstrut 15q^{46} \) \(\mathstrut +\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 33q^{58} \) \(\mathstrut +\mathstrut 10q^{59} \) \(\mathstrut -\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 6q^{62} \) \(\mathstrut +\mathstrut 12q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut -\mathstrut 19q^{67} \) \(\mathstrut +\mathstrut 6q^{68} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut -\mathstrut 15q^{79} \) \(\mathstrut +\mathstrut 5q^{80} \) \(\mathstrut -\mathstrut 20q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 11q^{86} \) \(\mathstrut -\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut -\mathstrut 3q^{91} \) \(\mathstrut +\mathstrut 15q^{92} \) \(\mathstrut -\mathstrut 15q^{94} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 25q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 4.11015 1.83812 0.919058 0.394123i \(-0.128951\pi\)
0.919058 + 0.394123i \(0.128951\pi\)
\(6\) 0 0
\(7\) −3.78475 −1.43050 −0.715250 0.698869i \(-0.753687\pi\)
−0.715250 + 0.698869i \(0.753687\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −4.11015 −1.29974
\(11\) 2.15275 0.649079 0.324539 0.945872i \(-0.394791\pi\)
0.324539 + 0.945872i \(0.394791\pi\)
\(12\) 0 0
\(13\) 5.55753 1.54138 0.770690 0.637210i \(-0.219912\pi\)
0.770690 + 0.637210i \(0.219912\pi\)
\(14\) 3.78475 1.01152
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −2.24829 −0.545292 −0.272646 0.962114i \(-0.587899\pi\)
−0.272646 + 0.962114i \(0.587899\pi\)
\(18\) 0 0
\(19\) 2.44233 0.560308 0.280154 0.959955i \(-0.409614\pi\)
0.280154 + 0.959955i \(0.409614\pi\)
\(20\) 4.11015 0.919058
\(21\) 0 0
\(22\) −2.15275 −0.458968
\(23\) −0.398673 −0.0831291 −0.0415645 0.999136i \(-0.513234\pi\)
−0.0415645 + 0.999136i \(0.513234\pi\)
\(24\) 0 0
\(25\) 11.8933 2.37867
\(26\) −5.55753 −1.08992
\(27\) 0 0
\(28\) −3.78475 −0.715250
\(29\) 8.12942 1.50959 0.754797 0.655958i \(-0.227735\pi\)
0.754797 + 0.655958i \(0.227735\pi\)
\(30\) 0 0
\(31\) 0.810327 0.145539 0.0727695 0.997349i \(-0.476816\pi\)
0.0727695 + 0.997349i \(0.476816\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 2.24829 0.385579
\(35\) −15.5559 −2.62942
\(36\) 0 0
\(37\) 8.17817 1.34448 0.672241 0.740332i \(-0.265332\pi\)
0.672241 + 0.740332i \(0.265332\pi\)
\(38\) −2.44233 −0.396198
\(39\) 0 0
\(40\) −4.11015 −0.649872
\(41\) 0.726269 0.113424 0.0567121 0.998391i \(-0.481938\pi\)
0.0567121 + 0.998391i \(0.481938\pi\)
\(42\) 0 0
\(43\) −3.96985 −0.605396 −0.302698 0.953087i \(-0.597887\pi\)
−0.302698 + 0.953087i \(0.597887\pi\)
\(44\) 2.15275 0.324539
\(45\) 0 0
\(46\) 0.398673 0.0587811
\(47\) 7.08367 1.03326 0.516630 0.856209i \(-0.327186\pi\)
0.516630 + 0.856209i \(0.327186\pi\)
\(48\) 0 0
\(49\) 7.32431 1.04633
\(50\) −11.8933 −1.68197
\(51\) 0 0
\(52\) 5.55753 0.770690
\(53\) −9.53601 −1.30987 −0.654936 0.755685i \(-0.727304\pi\)
−0.654936 + 0.755685i \(0.727304\pi\)
\(54\) 0 0
\(55\) 8.84813 1.19308
\(56\) 3.78475 0.505758
\(57\) 0 0
\(58\) −8.12942 −1.06744
\(59\) −11.4244 −1.48733 −0.743664 0.668553i \(-0.766914\pi\)
−0.743664 + 0.668553i \(0.766914\pi\)
\(60\) 0 0
\(61\) 5.54958 0.710551 0.355276 0.934762i \(-0.384387\pi\)
0.355276 + 0.934762i \(0.384387\pi\)
\(62\) −0.810327 −0.102912
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 22.8423 2.83324
\(66\) 0 0
\(67\) 3.37901 0.412812 0.206406 0.978466i \(-0.433823\pi\)
0.206406 + 0.978466i \(0.433823\pi\)
\(68\) −2.24829 −0.272646
\(69\) 0 0
\(70\) 15.5559 1.85928
\(71\) 8.38502 0.995119 0.497559 0.867430i \(-0.334230\pi\)
0.497559 + 0.867430i \(0.334230\pi\)
\(72\) 0 0
\(73\) −5.85256 −0.684991 −0.342495 0.939520i \(-0.611272\pi\)
−0.342495 + 0.939520i \(0.611272\pi\)
\(74\) −8.17817 −0.950693
\(75\) 0 0
\(76\) 2.44233 0.280154
\(77\) −8.14762 −0.928507
\(78\) 0 0
\(79\) −10.4633 −1.17721 −0.588604 0.808422i \(-0.700322\pi\)
−0.588604 + 0.808422i \(0.700322\pi\)
\(80\) 4.11015 0.459529
\(81\) 0 0
\(82\) −0.726269 −0.0802030
\(83\) −1.42102 −0.155977 −0.0779886 0.996954i \(-0.524850\pi\)
−0.0779886 + 0.996954i \(0.524850\pi\)
\(84\) 0 0
\(85\) −9.24083 −1.00231
\(86\) 3.96985 0.428079
\(87\) 0 0
\(88\) −2.15275 −0.229484
\(89\) 15.6438 1.65824 0.829119 0.559072i \(-0.188842\pi\)
0.829119 + 0.559072i \(0.188842\pi\)
\(90\) 0 0
\(91\) −21.0338 −2.20494
\(92\) −0.398673 −0.0415645
\(93\) 0 0
\(94\) −7.08367 −0.730625
\(95\) 10.0383 1.02991
\(96\) 0 0
\(97\) −10.0228 −1.01766 −0.508829 0.860868i \(-0.669922\pi\)
−0.508829 + 0.860868i \(0.669922\pi\)
\(98\) −7.32431 −0.739867
\(99\) 0 0
\(100\) 11.8933 1.18933
\(101\) 6.69423 0.666101 0.333050 0.942909i \(-0.391922\pi\)
0.333050 + 0.942909i \(0.391922\pi\)
\(102\) 0 0
\(103\) −12.2037 −1.20247 −0.601233 0.799074i \(-0.705323\pi\)
−0.601233 + 0.799074i \(0.705323\pi\)
\(104\) −5.55753 −0.544960
\(105\) 0 0
\(106\) 9.53601 0.926219
\(107\) −1.15590 −0.111745 −0.0558726 0.998438i \(-0.517794\pi\)
−0.0558726 + 0.998438i \(0.517794\pi\)
\(108\) 0 0
\(109\) 10.3304 0.989476 0.494738 0.869042i \(-0.335264\pi\)
0.494738 + 0.869042i \(0.335264\pi\)
\(110\) −8.84813 −0.843636
\(111\) 0 0
\(112\) −3.78475 −0.357625
\(113\) −14.7374 −1.38638 −0.693190 0.720755i \(-0.743795\pi\)
−0.693190 + 0.720755i \(0.743795\pi\)
\(114\) 0 0
\(115\) −1.63861 −0.152801
\(116\) 8.12942 0.754797
\(117\) 0 0
\(118\) 11.4244 1.05170
\(119\) 8.50923 0.780039
\(120\) 0 0
\(121\) −6.36566 −0.578697
\(122\) −5.54958 −0.502435
\(123\) 0 0
\(124\) 0.810327 0.0727695
\(125\) 28.3327 2.53415
\(126\) 0 0
\(127\) −15.4737 −1.37307 −0.686535 0.727097i \(-0.740869\pi\)
−0.686535 + 0.727097i \(0.740869\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −22.8423 −2.00340
\(131\) −17.0676 −1.49120 −0.745600 0.666394i \(-0.767837\pi\)
−0.745600 + 0.666394i \(0.767837\pi\)
\(132\) 0 0
\(133\) −9.24359 −0.801521
\(134\) −3.37901 −0.291902
\(135\) 0 0
\(136\) 2.24829 0.192790
\(137\) −12.0167 −1.02665 −0.513327 0.858193i \(-0.671587\pi\)
−0.513327 + 0.858193i \(0.671587\pi\)
\(138\) 0 0
\(139\) 8.26244 0.700811 0.350406 0.936598i \(-0.386044\pi\)
0.350406 + 0.936598i \(0.386044\pi\)
\(140\) −15.5559 −1.31471
\(141\) 0 0
\(142\) −8.38502 −0.703655
\(143\) 11.9640 1.00048
\(144\) 0 0
\(145\) 33.4131 2.77481
\(146\) 5.85256 0.484361
\(147\) 0 0
\(148\) 8.17817 0.672241
\(149\) 1.00000 0.0819232
\(150\) 0 0
\(151\) 23.5649 1.91769 0.958843 0.283938i \(-0.0916410\pi\)
0.958843 + 0.283938i \(0.0916410\pi\)
\(152\) −2.44233 −0.198099
\(153\) 0 0
\(154\) 8.14762 0.656554
\(155\) 3.33057 0.267517
\(156\) 0 0
\(157\) 3.01390 0.240535 0.120268 0.992741i \(-0.461625\pi\)
0.120268 + 0.992741i \(0.461625\pi\)
\(158\) 10.4633 0.832412
\(159\) 0 0
\(160\) −4.11015 −0.324936
\(161\) 1.50888 0.118916
\(162\) 0 0
\(163\) −15.9593 −1.25003 −0.625016 0.780612i \(-0.714908\pi\)
−0.625016 + 0.780612i \(0.714908\pi\)
\(164\) 0.726269 0.0567121
\(165\) 0 0
\(166\) 1.42102 0.110292
\(167\) 25.5613 1.97799 0.988997 0.147939i \(-0.0472639\pi\)
0.988997 + 0.147939i \(0.0472639\pi\)
\(168\) 0 0
\(169\) 17.8861 1.37585
\(170\) 9.24083 0.708740
\(171\) 0 0
\(172\) −3.96985 −0.302698
\(173\) 17.7637 1.35055 0.675274 0.737567i \(-0.264025\pi\)
0.675274 + 0.737567i \(0.264025\pi\)
\(174\) 0 0
\(175\) −45.0133 −3.40269
\(176\) 2.15275 0.162270
\(177\) 0 0
\(178\) −15.6438 −1.17255
\(179\) 15.5056 1.15895 0.579473 0.814992i \(-0.303259\pi\)
0.579473 + 0.814992i \(0.303259\pi\)
\(180\) 0 0
\(181\) −14.7689 −1.09777 −0.548883 0.835899i \(-0.684947\pi\)
−0.548883 + 0.835899i \(0.684947\pi\)
\(182\) 21.0338 1.55913
\(183\) 0 0
\(184\) 0.398673 0.0293906
\(185\) 33.6135 2.47131
\(186\) 0 0
\(187\) −4.84002 −0.353937
\(188\) 7.08367 0.516630
\(189\) 0 0
\(190\) −10.0383 −0.728257
\(191\) 4.50124 0.325699 0.162849 0.986651i \(-0.447932\pi\)
0.162849 + 0.986651i \(0.447932\pi\)
\(192\) 0 0
\(193\) 11.3824 0.819325 0.409663 0.912237i \(-0.365646\pi\)
0.409663 + 0.912237i \(0.365646\pi\)
\(194\) 10.0228 0.719593
\(195\) 0 0
\(196\) 7.32431 0.523165
\(197\) 12.9512 0.922734 0.461367 0.887209i \(-0.347359\pi\)
0.461367 + 0.887209i \(0.347359\pi\)
\(198\) 0 0
\(199\) 1.67614 0.118818 0.0594092 0.998234i \(-0.481078\pi\)
0.0594092 + 0.998234i \(0.481078\pi\)
\(200\) −11.8933 −0.840987
\(201\) 0 0
\(202\) −6.69423 −0.471004
\(203\) −30.7678 −2.15947
\(204\) 0 0
\(205\) 2.98508 0.208487
\(206\) 12.2037 0.850271
\(207\) 0 0
\(208\) 5.55753 0.385345
\(209\) 5.25772 0.363684
\(210\) 0 0
\(211\) −23.0409 −1.58620 −0.793101 0.609091i \(-0.791535\pi\)
−0.793101 + 0.609091i \(0.791535\pi\)
\(212\) −9.53601 −0.654936
\(213\) 0 0
\(214\) 1.15590 0.0790158
\(215\) −16.3167 −1.11279
\(216\) 0 0
\(217\) −3.06688 −0.208193
\(218\) −10.3304 −0.699665
\(219\) 0 0
\(220\) 8.84813 0.596541
\(221\) −12.4950 −0.840502
\(222\) 0 0
\(223\) 4.24071 0.283979 0.141990 0.989868i \(-0.454650\pi\)
0.141990 + 0.989868i \(0.454650\pi\)
\(224\) 3.78475 0.252879
\(225\) 0 0
\(226\) 14.7374 0.980318
\(227\) 21.1581 1.40431 0.702156 0.712023i \(-0.252221\pi\)
0.702156 + 0.712023i \(0.252221\pi\)
\(228\) 0 0
\(229\) 9.81055 0.648299 0.324150 0.946006i \(-0.394922\pi\)
0.324150 + 0.946006i \(0.394922\pi\)
\(230\) 1.63861 0.108047
\(231\) 0 0
\(232\) −8.12942 −0.533722
\(233\) 27.6563 1.81183 0.905914 0.423462i \(-0.139185\pi\)
0.905914 + 0.423462i \(0.139185\pi\)
\(234\) 0 0
\(235\) 29.1150 1.89925
\(236\) −11.4244 −0.743664
\(237\) 0 0
\(238\) −8.50923 −0.551571
\(239\) 20.9751 1.35676 0.678382 0.734710i \(-0.262682\pi\)
0.678382 + 0.734710i \(0.262682\pi\)
\(240\) 0 0
\(241\) 16.3880 1.05565 0.527823 0.849355i \(-0.323009\pi\)
0.527823 + 0.849355i \(0.323009\pi\)
\(242\) 6.36566 0.409200
\(243\) 0 0
\(244\) 5.54958 0.355276
\(245\) 30.1040 1.92327
\(246\) 0 0
\(247\) 13.5733 0.863648
\(248\) −0.810327 −0.0514558
\(249\) 0 0
\(250\) −28.3327 −1.79192
\(251\) −1.25604 −0.0792806 −0.0396403 0.999214i \(-0.512621\pi\)
−0.0396403 + 0.999214i \(0.512621\pi\)
\(252\) 0 0
\(253\) −0.858243 −0.0539573
\(254\) 15.4737 0.970907
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −18.7145 −1.16738 −0.583688 0.811978i \(-0.698391\pi\)
−0.583688 + 0.811978i \(0.698391\pi\)
\(258\) 0 0
\(259\) −30.9523 −1.92328
\(260\) 22.8423 1.41662
\(261\) 0 0
\(262\) 17.0676 1.05444
\(263\) 24.6171 1.51796 0.758978 0.651116i \(-0.225699\pi\)
0.758978 + 0.651116i \(0.225699\pi\)
\(264\) 0 0
\(265\) −39.1944 −2.40769
\(266\) 9.24359 0.566761
\(267\) 0 0
\(268\) 3.37901 0.206406
\(269\) −16.4410 −1.00242 −0.501211 0.865325i \(-0.667112\pi\)
−0.501211 + 0.865325i \(0.667112\pi\)
\(270\) 0 0
\(271\) −7.32917 −0.445215 −0.222608 0.974908i \(-0.571457\pi\)
−0.222608 + 0.974908i \(0.571457\pi\)
\(272\) −2.24829 −0.136323
\(273\) 0 0
\(274\) 12.0167 0.725954
\(275\) 25.6034 1.54394
\(276\) 0 0
\(277\) −20.8558 −1.25310 −0.626551 0.779381i \(-0.715534\pi\)
−0.626551 + 0.779381i \(0.715534\pi\)
\(278\) −8.26244 −0.495548
\(279\) 0 0
\(280\) 15.5559 0.929642
\(281\) −17.8130 −1.06264 −0.531318 0.847172i \(-0.678303\pi\)
−0.531318 + 0.847172i \(0.678303\pi\)
\(282\) 0 0
\(283\) −27.8399 −1.65491 −0.827456 0.561531i \(-0.810213\pi\)
−0.827456 + 0.561531i \(0.810213\pi\)
\(284\) 8.38502 0.497559
\(285\) 0 0
\(286\) −11.9640 −0.707444
\(287\) −2.74874 −0.162253
\(288\) 0 0
\(289\) −11.9452 −0.702657
\(290\) −33.4131 −1.96209
\(291\) 0 0
\(292\) −5.85256 −0.342495
\(293\) 11.6167 0.678656 0.339328 0.940668i \(-0.389800\pi\)
0.339328 + 0.940668i \(0.389800\pi\)
\(294\) 0 0
\(295\) −46.9560 −2.73388
\(296\) −8.17817 −0.475346
\(297\) 0 0
\(298\) −1.00000 −0.0579284
\(299\) −2.21564 −0.128133
\(300\) 0 0
\(301\) 15.0249 0.866018
\(302\) −23.5649 −1.35601
\(303\) 0 0
\(304\) 2.44233 0.140077
\(305\) 22.8096 1.30608
\(306\) 0 0
\(307\) 15.6923 0.895607 0.447804 0.894132i \(-0.352206\pi\)
0.447804 + 0.894132i \(0.352206\pi\)
\(308\) −8.14762 −0.464253
\(309\) 0 0
\(310\) −3.33057 −0.189163
\(311\) 4.04112 0.229151 0.114576 0.993415i \(-0.463449\pi\)
0.114576 + 0.993415i \(0.463449\pi\)
\(312\) 0 0
\(313\) 4.56731 0.258160 0.129080 0.991634i \(-0.458798\pi\)
0.129080 + 0.991634i \(0.458798\pi\)
\(314\) −3.01390 −0.170084
\(315\) 0 0
\(316\) −10.4633 −0.588604
\(317\) −24.3298 −1.36650 −0.683249 0.730185i \(-0.739434\pi\)
−0.683249 + 0.730185i \(0.739434\pi\)
\(318\) 0 0
\(319\) 17.5006 0.979846
\(320\) 4.11015 0.229764
\(321\) 0 0
\(322\) −1.50888 −0.0840864
\(323\) −5.49107 −0.305531
\(324\) 0 0
\(325\) 66.0976 3.66643
\(326\) 15.9593 0.883906
\(327\) 0 0
\(328\) −0.726269 −0.0401015
\(329\) −26.8099 −1.47808
\(330\) 0 0
\(331\) 15.2814 0.839942 0.419971 0.907538i \(-0.362040\pi\)
0.419971 + 0.907538i \(0.362040\pi\)
\(332\) −1.42102 −0.0779886
\(333\) 0 0
\(334\) −25.5613 −1.39865
\(335\) 13.8883 0.758796
\(336\) 0 0
\(337\) 16.3455 0.890398 0.445199 0.895432i \(-0.353133\pi\)
0.445199 + 0.895432i \(0.353133\pi\)
\(338\) −17.8861 −0.972875
\(339\) 0 0
\(340\) −9.24083 −0.501155
\(341\) 1.74443 0.0944663
\(342\) 0 0
\(343\) −1.22742 −0.0662742
\(344\) 3.96985 0.214040
\(345\) 0 0
\(346\) −17.7637 −0.954981
\(347\) 18.2895 0.981830 0.490915 0.871207i \(-0.336663\pi\)
0.490915 + 0.871207i \(0.336663\pi\)
\(348\) 0 0
\(349\) 5.35471 0.286631 0.143316 0.989677i \(-0.454224\pi\)
0.143316 + 0.989677i \(0.454224\pi\)
\(350\) 45.0133 2.40606
\(351\) 0 0
\(352\) −2.15275 −0.114742
\(353\) 26.9483 1.43431 0.717157 0.696912i \(-0.245443\pi\)
0.717157 + 0.696912i \(0.245443\pi\)
\(354\) 0 0
\(355\) 34.4637 1.82914
\(356\) 15.6438 0.829119
\(357\) 0 0
\(358\) −15.5056 −0.819498
\(359\) −10.2380 −0.540342 −0.270171 0.962812i \(-0.587080\pi\)
−0.270171 + 0.962812i \(0.587080\pi\)
\(360\) 0 0
\(361\) −13.0350 −0.686055
\(362\) 14.7689 0.776238
\(363\) 0 0
\(364\) −21.0338 −1.10247
\(365\) −24.0549 −1.25909
\(366\) 0 0
\(367\) 6.92125 0.361287 0.180643 0.983549i \(-0.442182\pi\)
0.180643 + 0.983549i \(0.442182\pi\)
\(368\) −0.398673 −0.0207823
\(369\) 0 0
\(370\) −33.6135 −1.74748
\(371\) 36.0914 1.87377
\(372\) 0 0
\(373\) 6.70601 0.347224 0.173612 0.984814i \(-0.444456\pi\)
0.173612 + 0.984814i \(0.444456\pi\)
\(374\) 4.84002 0.250271
\(375\) 0 0
\(376\) −7.08367 −0.365312
\(377\) 45.1794 2.32686
\(378\) 0 0
\(379\) −8.87420 −0.455837 −0.227918 0.973680i \(-0.573192\pi\)
−0.227918 + 0.973680i \(0.573192\pi\)
\(380\) 10.0383 0.514956
\(381\) 0 0
\(382\) −4.50124 −0.230304
\(383\) −15.6017 −0.797212 −0.398606 0.917122i \(-0.630506\pi\)
−0.398606 + 0.917122i \(0.630506\pi\)
\(384\) 0 0
\(385\) −33.4879 −1.70670
\(386\) −11.3824 −0.579350
\(387\) 0 0
\(388\) −10.0228 −0.508829
\(389\) −1.71896 −0.0871546 −0.0435773 0.999050i \(-0.513875\pi\)
−0.0435773 + 0.999050i \(0.513875\pi\)
\(390\) 0 0
\(391\) 0.896334 0.0453296
\(392\) −7.32431 −0.369933
\(393\) 0 0
\(394\) −12.9512 −0.652472
\(395\) −43.0055 −2.16384
\(396\) 0 0
\(397\) −11.2415 −0.564196 −0.282098 0.959386i \(-0.591030\pi\)
−0.282098 + 0.959386i \(0.591030\pi\)
\(398\) −1.67614 −0.0840172
\(399\) 0 0
\(400\) 11.8933 0.594667
\(401\) −20.2914 −1.01330 −0.506651 0.862151i \(-0.669117\pi\)
−0.506651 + 0.862151i \(0.669117\pi\)
\(402\) 0 0
\(403\) 4.50341 0.224331
\(404\) 6.69423 0.333050
\(405\) 0 0
\(406\) 30.7678 1.52698
\(407\) 17.6056 0.872675
\(408\) 0 0
\(409\) −17.9113 −0.885659 −0.442829 0.896606i \(-0.646025\pi\)
−0.442829 + 0.896606i \(0.646025\pi\)
\(410\) −2.98508 −0.147422
\(411\) 0 0
\(412\) −12.2037 −0.601233
\(413\) 43.2384 2.12762
\(414\) 0 0
\(415\) −5.84061 −0.286704
\(416\) −5.55753 −0.272480
\(417\) 0 0
\(418\) −5.25772 −0.257164
\(419\) −15.7447 −0.769180 −0.384590 0.923087i \(-0.625657\pi\)
−0.384590 + 0.923087i \(0.625657\pi\)
\(420\) 0 0
\(421\) −6.80219 −0.331518 −0.165759 0.986166i \(-0.553007\pi\)
−0.165759 + 0.986166i \(0.553007\pi\)
\(422\) 23.0409 1.12161
\(423\) 0 0
\(424\) 9.53601 0.463109
\(425\) −26.7398 −1.29707
\(426\) 0 0
\(427\) −21.0038 −1.01644
\(428\) −1.15590 −0.0558726
\(429\) 0 0
\(430\) 16.3167 0.786860
\(431\) 4.88102 0.235111 0.117555 0.993066i \(-0.462494\pi\)
0.117555 + 0.993066i \(0.462494\pi\)
\(432\) 0 0
\(433\) −33.8020 −1.62442 −0.812211 0.583364i \(-0.801736\pi\)
−0.812211 + 0.583364i \(0.801736\pi\)
\(434\) 3.06688 0.147215
\(435\) 0 0
\(436\) 10.3304 0.494738
\(437\) −0.973690 −0.0465779
\(438\) 0 0
\(439\) 0.322206 0.0153780 0.00768902 0.999970i \(-0.497552\pi\)
0.00768902 + 0.999970i \(0.497552\pi\)
\(440\) −8.84813 −0.421818
\(441\) 0 0
\(442\) 12.4950 0.594324
\(443\) 25.6552 1.21891 0.609457 0.792819i \(-0.291387\pi\)
0.609457 + 0.792819i \(0.291387\pi\)
\(444\) 0 0
\(445\) 64.2984 3.04803
\(446\) −4.24071 −0.200804
\(447\) 0 0
\(448\) −3.78475 −0.178812
\(449\) −14.1446 −0.667527 −0.333764 0.942657i \(-0.608319\pi\)
−0.333764 + 0.942657i \(0.608319\pi\)
\(450\) 0 0
\(451\) 1.56348 0.0736212
\(452\) −14.7374 −0.693190
\(453\) 0 0
\(454\) −21.1581 −0.992998
\(455\) −86.4522 −4.05294
\(456\) 0 0
\(457\) 8.82093 0.412626 0.206313 0.978486i \(-0.433854\pi\)
0.206313 + 0.978486i \(0.433854\pi\)
\(458\) −9.81055 −0.458417
\(459\) 0 0
\(460\) −1.63861 −0.0764004
\(461\) 26.3264 1.22614 0.613072 0.790027i \(-0.289934\pi\)
0.613072 + 0.790027i \(0.289934\pi\)
\(462\) 0 0
\(463\) −2.95723 −0.137434 −0.0687171 0.997636i \(-0.521891\pi\)
−0.0687171 + 0.997636i \(0.521891\pi\)
\(464\) 8.12942 0.377399
\(465\) 0 0
\(466\) −27.6563 −1.28116
\(467\) −31.9881 −1.48023 −0.740116 0.672480i \(-0.765229\pi\)
−0.740116 + 0.672480i \(0.765229\pi\)
\(468\) 0 0
\(469\) −12.7887 −0.590528
\(470\) −29.1150 −1.34297
\(471\) 0 0
\(472\) 11.4244 0.525850
\(473\) −8.54609 −0.392950
\(474\) 0 0
\(475\) 29.0474 1.33279
\(476\) 8.50923 0.390020
\(477\) 0 0
\(478\) −20.9751 −0.959377
\(479\) 1.09806 0.0501719 0.0250859 0.999685i \(-0.492014\pi\)
0.0250859 + 0.999685i \(0.492014\pi\)
\(480\) 0 0
\(481\) 45.4504 2.07236
\(482\) −16.3880 −0.746454
\(483\) 0 0
\(484\) −6.36566 −0.289348
\(485\) −41.1951 −1.87057
\(486\) 0 0
\(487\) 15.0374 0.681409 0.340704 0.940170i \(-0.389334\pi\)
0.340704 + 0.940170i \(0.389334\pi\)
\(488\) −5.54958 −0.251218
\(489\) 0 0
\(490\) −30.1040 −1.35996
\(491\) 35.2574 1.59114 0.795571 0.605860i \(-0.207171\pi\)
0.795571 + 0.605860i \(0.207171\pi\)
\(492\) 0 0
\(493\) −18.2773 −0.823169
\(494\) −13.5733 −0.610691
\(495\) 0 0
\(496\) 0.810327 0.0363847
\(497\) −31.7352 −1.42352
\(498\) 0 0
\(499\) 25.6838 1.14977 0.574883 0.818235i \(-0.305047\pi\)
0.574883 + 0.818235i \(0.305047\pi\)
\(500\) 28.3327 1.26708
\(501\) 0 0
\(502\) 1.25604 0.0560599
\(503\) −15.5146 −0.691763 −0.345882 0.938278i \(-0.612420\pi\)
−0.345882 + 0.938278i \(0.612420\pi\)
\(504\) 0 0
\(505\) 27.5143 1.22437
\(506\) 0.858243 0.0381536
\(507\) 0 0
\(508\) −15.4737 −0.686535
\(509\) 23.9031 1.05949 0.529743 0.848158i \(-0.322289\pi\)
0.529743 + 0.848158i \(0.322289\pi\)
\(510\) 0 0
\(511\) 22.1505 0.979879
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 18.7145 0.825460
\(515\) −50.1590 −2.21027
\(516\) 0 0
\(517\) 15.2494 0.670667
\(518\) 30.9523 1.35997
\(519\) 0 0
\(520\) −22.8423 −1.00170
\(521\) 16.3759 0.717442 0.358721 0.933445i \(-0.383213\pi\)
0.358721 + 0.933445i \(0.383213\pi\)
\(522\) 0 0
\(523\) −35.5618 −1.55501 −0.777505 0.628877i \(-0.783515\pi\)
−0.777505 + 0.628877i \(0.783515\pi\)
\(524\) −17.0676 −0.745600
\(525\) 0 0
\(526\) −24.6171 −1.07336
\(527\) −1.82185 −0.0793612
\(528\) 0 0
\(529\) −22.8411 −0.993090
\(530\) 39.1944 1.70250
\(531\) 0 0
\(532\) −9.24359 −0.400760
\(533\) 4.03626 0.174830
\(534\) 0 0
\(535\) −4.75093 −0.205401
\(536\) −3.37901 −0.145951
\(537\) 0 0
\(538\) 16.4410 0.708820
\(539\) 15.7674 0.679150
\(540\) 0 0
\(541\) −8.19214 −0.352208 −0.176104 0.984372i \(-0.556349\pi\)
−0.176104 + 0.984372i \(0.556349\pi\)
\(542\) 7.32917 0.314815
\(543\) 0 0
\(544\) 2.24829 0.0963948
\(545\) 42.4596 1.81877
\(546\) 0 0
\(547\) −1.42337 −0.0608588 −0.0304294 0.999537i \(-0.509687\pi\)
−0.0304294 + 0.999537i \(0.509687\pi\)
\(548\) −12.0167 −0.513327
\(549\) 0 0
\(550\) −25.6034 −1.09173
\(551\) 19.8547 0.845838
\(552\) 0 0
\(553\) 39.6008 1.68400
\(554\) 20.8558 0.886076
\(555\) 0 0
\(556\) 8.26244 0.350406
\(557\) 12.5490 0.531716 0.265858 0.964012i \(-0.414345\pi\)
0.265858 + 0.964012i \(0.414345\pi\)
\(558\) 0 0
\(559\) −22.0625 −0.933145
\(560\) −15.5559 −0.657356
\(561\) 0 0
\(562\) 17.8130 0.751397
\(563\) −30.0087 −1.26472 −0.632359 0.774676i \(-0.717913\pi\)
−0.632359 + 0.774676i \(0.717913\pi\)
\(564\) 0 0
\(565\) −60.5730 −2.54833
\(566\) 27.8399 1.17020
\(567\) 0 0
\(568\) −8.38502 −0.351828
\(569\) −33.4950 −1.40418 −0.702092 0.712087i \(-0.747750\pi\)
−0.702092 + 0.712087i \(0.747750\pi\)
\(570\) 0 0
\(571\) 2.65000 0.110899 0.0554495 0.998461i \(-0.482341\pi\)
0.0554495 + 0.998461i \(0.482341\pi\)
\(572\) 11.9640 0.500239
\(573\) 0 0
\(574\) 2.74874 0.114730
\(575\) −4.74156 −0.197737
\(576\) 0 0
\(577\) 29.1798 1.21477 0.607386 0.794407i \(-0.292218\pi\)
0.607386 + 0.794407i \(0.292218\pi\)
\(578\) 11.9452 0.496854
\(579\) 0 0
\(580\) 33.4131 1.38741
\(581\) 5.37820 0.223125
\(582\) 0 0
\(583\) −20.5286 −0.850210
\(584\) 5.85256 0.242181
\(585\) 0 0
\(586\) −11.6167 −0.479883
\(587\) −3.91577 −0.161621 −0.0808106 0.996729i \(-0.525751\pi\)
−0.0808106 + 0.996729i \(0.525751\pi\)
\(588\) 0 0
\(589\) 1.97908 0.0815467
\(590\) 46.9560 1.93315
\(591\) 0 0
\(592\) 8.17817 0.336121
\(593\) −33.1199 −1.36007 −0.680035 0.733180i \(-0.738035\pi\)
−0.680035 + 0.733180i \(0.738035\pi\)
\(594\) 0 0
\(595\) 34.9742 1.43380
\(596\) 1.00000 0.0409616
\(597\) 0 0
\(598\) 2.21564 0.0906041
\(599\) 22.2847 0.910527 0.455263 0.890357i \(-0.349545\pi\)
0.455263 + 0.890357i \(0.349545\pi\)
\(600\) 0 0
\(601\) 30.2514 1.23398 0.616991 0.786971i \(-0.288352\pi\)
0.616991 + 0.786971i \(0.288352\pi\)
\(602\) −15.0249 −0.612368
\(603\) 0 0
\(604\) 23.5649 0.958843
\(605\) −26.1638 −1.06371
\(606\) 0 0
\(607\) −0.504778 −0.0204883 −0.0102442 0.999948i \(-0.503261\pi\)
−0.0102442 + 0.999948i \(0.503261\pi\)
\(608\) −2.44233 −0.0990494
\(609\) 0 0
\(610\) −22.8096 −0.923535
\(611\) 39.3677 1.59265
\(612\) 0 0
\(613\) −2.30487 −0.0930928 −0.0465464 0.998916i \(-0.514822\pi\)
−0.0465464 + 0.998916i \(0.514822\pi\)
\(614\) −15.6923 −0.633290
\(615\) 0 0
\(616\) 8.14762 0.328277
\(617\) −43.7493 −1.76128 −0.880640 0.473785i \(-0.842887\pi\)
−0.880640 + 0.473785i \(0.842887\pi\)
\(618\) 0 0
\(619\) 3.25992 0.131027 0.0655136 0.997852i \(-0.479131\pi\)
0.0655136 + 0.997852i \(0.479131\pi\)
\(620\) 3.33057 0.133759
\(621\) 0 0
\(622\) −4.04112 −0.162034
\(623\) −59.2078 −2.37211
\(624\) 0 0
\(625\) 56.9850 2.27940
\(626\) −4.56731 −0.182547
\(627\) 0 0
\(628\) 3.01390 0.120268
\(629\) −18.3869 −0.733135
\(630\) 0 0
\(631\) 29.2273 1.16352 0.581761 0.813360i \(-0.302364\pi\)
0.581761 + 0.813360i \(0.302364\pi\)
\(632\) 10.4633 0.416206
\(633\) 0 0
\(634\) 24.3298 0.966260
\(635\) −63.5993 −2.52386
\(636\) 0 0
\(637\) 40.7050 1.61279
\(638\) −17.5006 −0.692856
\(639\) 0 0
\(640\) −4.11015 −0.162468
\(641\) 26.1571 1.03314 0.516571 0.856244i \(-0.327208\pi\)
0.516571 + 0.856244i \(0.327208\pi\)
\(642\) 0 0
\(643\) −18.9542 −0.747482 −0.373741 0.927533i \(-0.621925\pi\)
−0.373741 + 0.927533i \(0.621925\pi\)
\(644\) 1.50888 0.0594580
\(645\) 0 0
\(646\) 5.49107 0.216043
\(647\) −28.1286 −1.10585 −0.552925 0.833231i \(-0.686488\pi\)
−0.552925 + 0.833231i \(0.686488\pi\)
\(648\) 0 0
\(649\) −24.5939 −0.965394
\(650\) −66.0976 −2.59256
\(651\) 0 0
\(652\) −15.9593 −0.625016
\(653\) 25.8434 1.01133 0.505665 0.862730i \(-0.331247\pi\)
0.505665 + 0.862730i \(0.331247\pi\)
\(654\) 0 0
\(655\) −70.1502 −2.74100
\(656\) 0.726269 0.0283560
\(657\) 0 0
\(658\) 26.8099 1.04516
\(659\) 11.1184 0.433112 0.216556 0.976270i \(-0.430518\pi\)
0.216556 + 0.976270i \(0.430518\pi\)
\(660\) 0 0
\(661\) 10.6871 0.415680 0.207840 0.978163i \(-0.433357\pi\)
0.207840 + 0.978163i \(0.433357\pi\)
\(662\) −15.2814 −0.593929
\(663\) 0 0
\(664\) 1.42102 0.0551462
\(665\) −37.9926 −1.47329
\(666\) 0 0
\(667\) −3.24098 −0.125491
\(668\) 25.5613 0.988997
\(669\) 0 0
\(670\) −13.8883 −0.536550
\(671\) 11.9469 0.461204
\(672\) 0 0
\(673\) −8.75317 −0.337410 −0.168705 0.985667i \(-0.553959\pi\)
−0.168705 + 0.985667i \(0.553959\pi\)
\(674\) −16.3455 −0.629607
\(675\) 0 0
\(676\) 17.8861 0.687927
\(677\) 30.0676 1.15559 0.577797 0.816181i \(-0.303913\pi\)
0.577797 + 0.816181i \(0.303913\pi\)
\(678\) 0 0
\(679\) 37.9336 1.45576
\(680\) 9.24083 0.354370
\(681\) 0 0
\(682\) −1.74443 −0.0667977
\(683\) 26.4002 1.01018 0.505088 0.863068i \(-0.331460\pi\)
0.505088 + 0.863068i \(0.331460\pi\)
\(684\) 0 0
\(685\) −49.3904 −1.88711
\(686\) 1.22742 0.0468629
\(687\) 0 0
\(688\) −3.96985 −0.151349
\(689\) −52.9966 −2.01901
\(690\) 0 0
\(691\) −0.519830 −0.0197752 −0.00988762 0.999951i \(-0.503147\pi\)
−0.00988762 + 0.999951i \(0.503147\pi\)
\(692\) 17.7637 0.675274
\(693\) 0 0
\(694\) −18.2895 −0.694259
\(695\) 33.9599 1.28817
\(696\) 0 0
\(697\) −1.63287 −0.0618492
\(698\) −5.35471 −0.202679
\(699\) 0 0
\(700\) −45.0133 −1.70134
\(701\) −7.56304 −0.285652 −0.142826 0.989748i \(-0.545619\pi\)
−0.142826 + 0.989748i \(0.545619\pi\)
\(702\) 0 0
\(703\) 19.9738 0.753325
\(704\) 2.15275 0.0811348
\(705\) 0 0
\(706\) −26.9483 −1.01421
\(707\) −25.3360 −0.952857
\(708\) 0 0
\(709\) −6.02154 −0.226144 −0.113072 0.993587i \(-0.536069\pi\)
−0.113072 + 0.993587i \(0.536069\pi\)
\(710\) −34.4637 −1.29340
\(711\) 0 0
\(712\) −15.6438 −0.586276
\(713\) −0.323055 −0.0120985
\(714\) 0 0
\(715\) 49.1737 1.83899
\(716\) 15.5056 0.579473
\(717\) 0 0
\(718\) 10.2380 0.382079
\(719\) −31.8340 −1.18721 −0.593604 0.804757i \(-0.702296\pi\)
−0.593604 + 0.804757i \(0.702296\pi\)
\(720\) 0 0
\(721\) 46.1879 1.72013
\(722\) 13.0350 0.485114
\(723\) 0 0
\(724\) −14.7689 −0.548883
\(725\) 96.6860 3.59083
\(726\) 0 0
\(727\) 44.3884 1.64627 0.823137 0.567843i \(-0.192222\pi\)
0.823137 + 0.567843i \(0.192222\pi\)
\(728\) 21.0338 0.779565
\(729\) 0 0
\(730\) 24.0549 0.890312
\(731\) 8.92538 0.330117
\(732\) 0 0
\(733\) 51.3963 1.89837 0.949183 0.314724i \(-0.101912\pi\)
0.949183 + 0.314724i \(0.101912\pi\)
\(734\) −6.92125 −0.255468
\(735\) 0 0
\(736\) 0.398673 0.0146953
\(737\) 7.27417 0.267948
\(738\) 0 0
\(739\) 39.8302 1.46518 0.732589 0.680671i \(-0.238312\pi\)
0.732589 + 0.680671i \(0.238312\pi\)
\(740\) 33.6135 1.23566
\(741\) 0 0
\(742\) −36.0914 −1.32496
\(743\) 27.0929 0.993941 0.496971 0.867767i \(-0.334446\pi\)
0.496971 + 0.867767i \(0.334446\pi\)
\(744\) 0 0
\(745\) 4.11015 0.150584
\(746\) −6.70601 −0.245525
\(747\) 0 0
\(748\) −4.84002 −0.176969
\(749\) 4.37479 0.159851
\(750\) 0 0
\(751\) −38.4389 −1.40265 −0.701327 0.712840i \(-0.747409\pi\)
−0.701327 + 0.712840i \(0.747409\pi\)
\(752\) 7.08367 0.258315
\(753\) 0 0
\(754\) −45.1794 −1.64534
\(755\) 96.8554 3.52493
\(756\) 0 0
\(757\) −36.7309 −1.33501 −0.667503 0.744607i \(-0.732637\pi\)
−0.667503 + 0.744607i \(0.732637\pi\)
\(758\) 8.87420 0.322325
\(759\) 0 0
\(760\) −10.0383 −0.364129
\(761\) −7.93102 −0.287499 −0.143750 0.989614i \(-0.545916\pi\)
−0.143750 + 0.989614i \(0.545916\pi\)
\(762\) 0 0
\(763\) −39.0981 −1.41545
\(764\) 4.50124 0.162849
\(765\) 0 0
\(766\) 15.6017 0.563714
\(767\) −63.4913 −2.29254
\(768\) 0 0
\(769\) −10.4124 −0.375482 −0.187741 0.982219i \(-0.560117\pi\)
−0.187741 + 0.982219i \(0.560117\pi\)
\(770\) 33.4879 1.20682
\(771\) 0 0
\(772\) 11.3824 0.409663
\(773\) 28.1383 1.01206 0.506031 0.862515i \(-0.331112\pi\)
0.506031 + 0.862515i \(0.331112\pi\)
\(774\) 0 0
\(775\) 9.63750 0.346189
\(776\) 10.0228 0.359797
\(777\) 0 0
\(778\) 1.71896 0.0616276
\(779\) 1.77379 0.0635525
\(780\) 0 0
\(781\) 18.0509 0.645911
\(782\) −0.896334 −0.0320528
\(783\) 0 0
\(784\) 7.32431 0.261582
\(785\) 12.3876 0.442132
\(786\) 0 0
\(787\) −20.5218 −0.731524 −0.365762 0.930708i \(-0.619192\pi\)
−0.365762 + 0.930708i \(0.619192\pi\)
\(788\) 12.9512 0.461367
\(789\) 0 0
\(790\) 43.0055 1.53007
\(791\) 55.7774 1.98322
\(792\) 0 0
\(793\) 30.8419 1.09523
\(794\) 11.2415 0.398947
\(795\) 0 0
\(796\) 1.67614 0.0594092
\(797\) −11.5545 −0.409282 −0.204641 0.978837i \(-0.565603\pi\)
−0.204641 + 0.978837i \(0.565603\pi\)
\(798\) 0 0
\(799\) −15.9262 −0.563428
\(800\) −11.8933 −0.420493
\(801\) 0 0
\(802\) 20.2914 0.716513
\(803\) −12.5991 −0.444613
\(804\) 0 0
\(805\) 6.20171 0.218582
\(806\) −4.50341 −0.158626
\(807\) 0 0
\(808\) −6.69423 −0.235502
\(809\) −0.554547 −0.0194968 −0.00974842 0.999952i \(-0.503103\pi\)
−0.00974842 + 0.999952i \(0.503103\pi\)
\(810\) 0 0
\(811\) 15.8752 0.557454 0.278727 0.960370i \(-0.410088\pi\)
0.278727 + 0.960370i \(0.410088\pi\)
\(812\) −30.7678 −1.07974
\(813\) 0 0
\(814\) −17.6056 −0.617074
\(815\) −65.5953 −2.29770
\(816\) 0 0
\(817\) −9.69566 −0.339208
\(818\) 17.9113 0.626255
\(819\) 0 0
\(820\) 2.98508 0.104243
\(821\) 49.0204 1.71082 0.855411 0.517949i \(-0.173304\pi\)
0.855411 + 0.517949i \(0.173304\pi\)
\(822\) 0 0
\(823\) −0.949756 −0.0331064 −0.0165532 0.999863i \(-0.505269\pi\)
−0.0165532 + 0.999863i \(0.505269\pi\)
\(824\) 12.2037 0.425136
\(825\) 0 0
\(826\) −43.2384 −1.50446
\(827\) −20.9351 −0.727986 −0.363993 0.931402i \(-0.618587\pi\)
−0.363993 + 0.931402i \(0.618587\pi\)
\(828\) 0 0
\(829\) −0.932727 −0.0323950 −0.0161975 0.999869i \(-0.505156\pi\)
−0.0161975 + 0.999869i \(0.505156\pi\)
\(830\) 5.84061 0.202730
\(831\) 0 0
\(832\) 5.55753 0.192673
\(833\) −16.4672 −0.570555
\(834\) 0 0
\(835\) 105.061 3.63578
\(836\) 5.25772 0.181842
\(837\) 0 0
\(838\) 15.7447 0.543893
\(839\) −28.0932 −0.969884 −0.484942 0.874546i \(-0.661159\pi\)
−0.484942 + 0.874546i \(0.661159\pi\)
\(840\) 0 0
\(841\) 37.0874 1.27888
\(842\) 6.80219 0.234419
\(843\) 0 0
\(844\) −23.0409 −0.793101
\(845\) 73.5146 2.52898
\(846\) 0 0
\(847\) 24.0924 0.827826
\(848\) −9.53601 −0.327468
\(849\) 0 0
\(850\) 26.7398 0.917166
\(851\) −3.26041 −0.111766
\(852\) 0 0
\(853\) −30.7394 −1.05250 −0.526249 0.850330i \(-0.676402\pi\)
−0.526249 + 0.850330i \(0.676402\pi\)
\(854\) 21.0038 0.718734
\(855\) 0 0
\(856\) 1.15590 0.0395079
\(857\) −11.2952 −0.385837 −0.192918 0.981215i \(-0.561795\pi\)
−0.192918 + 0.981215i \(0.561795\pi\)
\(858\) 0 0
\(859\) −6.02701 −0.205639 −0.102819 0.994700i \(-0.532786\pi\)
−0.102819 + 0.994700i \(0.532786\pi\)
\(860\) −16.3167 −0.556394
\(861\) 0 0
\(862\) −4.88102 −0.166248
\(863\) 14.2444 0.484884 0.242442 0.970166i \(-0.422052\pi\)
0.242442 + 0.970166i \(0.422052\pi\)
\(864\) 0 0
\(865\) 73.0114 2.48246
\(866\) 33.8020 1.14864
\(867\) 0 0
\(868\) −3.06688 −0.104097
\(869\) −22.5248 −0.764101
\(870\) 0 0
\(871\) 18.7790 0.636300
\(872\) −10.3304 −0.349833
\(873\) 0 0
\(874\) 0.973690 0.0329355
\(875\) −107.232 −3.62511
\(876\) 0 0
\(877\) 7.36741 0.248780 0.124390 0.992233i \(-0.460303\pi\)
0.124390 + 0.992233i \(0.460303\pi\)
\(878\) −0.322206 −0.0108739
\(879\) 0 0
\(880\) 8.84813 0.298270
\(881\) 39.8625 1.34300 0.671501 0.741004i \(-0.265650\pi\)
0.671501 + 0.741004i \(0.265650\pi\)
\(882\) 0 0
\(883\) 43.3786 1.45980 0.729902 0.683551i \(-0.239565\pi\)
0.729902 + 0.683551i \(0.239565\pi\)
\(884\) −12.4950 −0.420251
\(885\) 0 0
\(886\) −25.6552 −0.861903
\(887\) 18.0823 0.607144 0.303572 0.952808i \(-0.401821\pi\)
0.303572 + 0.952808i \(0.401821\pi\)
\(888\) 0 0
\(889\) 58.5641 1.96418
\(890\) −64.2984 −2.15529
\(891\) 0 0
\(892\) 4.24071 0.141990
\(893\) 17.3006 0.578944
\(894\) 0 0
\(895\) 63.7305 2.13028
\(896\) 3.78475 0.126440
\(897\) 0 0
\(898\) 14.1446 0.472013
\(899\) 6.58748 0.219705
\(900\) 0 0
\(901\) 21.4398 0.714262
\(902\) −1.56348 −0.0520580
\(903\) 0 0
\(904\) 14.7374 0.490159
\(905\) −60.7025 −2.01782
\(906\) 0 0
\(907\) −5.55440 −0.184431 −0.0922155 0.995739i \(-0.529395\pi\)
−0.0922155 + 0.995739i \(0.529395\pi\)
\(908\) 21.1581 0.702156
\(909\) 0 0
\(910\) 86.4522 2.86586
\(911\) 17.6798 0.585757 0.292878 0.956150i \(-0.405387\pi\)
0.292878 + 0.956150i \(0.405387\pi\)
\(912\) 0 0
\(913\) −3.05910 −0.101241
\(914\) −8.82093 −0.291770
\(915\) 0 0
\(916\) 9.81055 0.324150
\(917\) 64.5964 2.13316
\(918\) 0 0
\(919\) −50.7230 −1.67320 −0.836598 0.547817i \(-0.815459\pi\)
−0.836598 + 0.547817i \(0.815459\pi\)
\(920\) 1.63861 0.0540233
\(921\) 0 0
\(922\) −26.3264 −0.867014
\(923\) 46.6000 1.53386
\(924\) 0 0
\(925\) 97.2658 3.19808
\(926\) 2.95723 0.0971806
\(927\) 0 0
\(928\) −8.12942 −0.266861
\(929\) 1.25154 0.0410616 0.0205308 0.999789i \(-0.493464\pi\)
0.0205308 + 0.999789i \(0.493464\pi\)
\(930\) 0 0
\(931\) 17.8883 0.586267
\(932\) 27.6563 0.905914
\(933\) 0 0
\(934\) 31.9881 1.04668
\(935\) −19.8932 −0.650578
\(936\) 0 0
\(937\) 37.2661 1.21743 0.608714 0.793389i \(-0.291686\pi\)
0.608714 + 0.793389i \(0.291686\pi\)
\(938\) 12.7887 0.417566
\(939\) 0 0
\(940\) 29.1150 0.949625
\(941\) 60.3111 1.96608 0.983042 0.183380i \(-0.0587039\pi\)
0.983042 + 0.183380i \(0.0587039\pi\)
\(942\) 0 0
\(943\) −0.289544 −0.00942884
\(944\) −11.4244 −0.371832
\(945\) 0 0
\(946\) 8.54609 0.277857
\(947\) 20.2775 0.658930 0.329465 0.944168i \(-0.393132\pi\)
0.329465 + 0.944168i \(0.393132\pi\)
\(948\) 0 0
\(949\) −32.5258 −1.05583
\(950\) −29.0474 −0.942424
\(951\) 0 0
\(952\) −8.50923 −0.275786
\(953\) 15.2560 0.494191 0.247095 0.968991i \(-0.420524\pi\)
0.247095 + 0.968991i \(0.420524\pi\)
\(954\) 0 0
\(955\) 18.5008 0.598672
\(956\) 20.9751 0.678382
\(957\) 0 0
\(958\) −1.09806 −0.0354769
\(959\) 45.4801 1.46863
\(960\) 0 0
\(961\) −30.3434 −0.978818
\(962\) −45.4504 −1.46538
\(963\) 0 0
\(964\) 16.3880 0.527823
\(965\) 46.7835 1.50601
\(966\) 0 0
\(967\) −61.0089 −1.96192 −0.980958 0.194222i \(-0.937782\pi\)
−0.980958 + 0.194222i \(0.937782\pi\)
\(968\) 6.36566 0.204600
\(969\) 0 0
\(970\) 41.1951 1.32270
\(971\) 5.18080 0.166260 0.0831300 0.996539i \(-0.473508\pi\)
0.0831300 + 0.996539i \(0.473508\pi\)
\(972\) 0 0
\(973\) −31.2712 −1.00251
\(974\) −15.0374 −0.481829
\(975\) 0 0
\(976\) 5.54958 0.177638
\(977\) 39.1613 1.25288 0.626441 0.779469i \(-0.284511\pi\)
0.626441 + 0.779469i \(0.284511\pi\)
\(978\) 0 0
\(979\) 33.6772 1.07633
\(980\) 30.1040 0.961637
\(981\) 0 0
\(982\) −35.2574 −1.12511
\(983\) −47.3920 −1.51157 −0.755785 0.654820i \(-0.772744\pi\)
−0.755785 + 0.654820i \(0.772744\pi\)
\(984\) 0 0
\(985\) 53.2314 1.69609
\(986\) 18.2773 0.582069
\(987\) 0 0
\(988\) 13.5733 0.431824
\(989\) 1.58267 0.0503260
\(990\) 0 0
\(991\) 48.4544 1.53920 0.769602 0.638524i \(-0.220455\pi\)
0.769602 + 0.638524i \(0.220455\pi\)
\(992\) −0.810327 −0.0257279
\(993\) 0 0
\(994\) 31.7352 1.00658
\(995\) 6.88918 0.218402
\(996\) 0 0
\(997\) 29.6563 0.939224 0.469612 0.882873i \(-0.344394\pi\)
0.469612 + 0.882873i \(0.344394\pi\)
\(998\) −25.6838 −0.813008
\(999\) 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 \(a_p\))