Properties

Label 8001.2.a.u.1.5
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 1.5
Root \(-1.33766\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.33766 q^{2}\) \(-0.210663 q^{4}\) \(+0.660635 q^{5}\) \(+1.00000 q^{7}\) \(+2.95712 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.33766 q^{2}\) \(-0.210663 q^{4}\) \(+0.660635 q^{5}\) \(+1.00000 q^{7}\) \(+2.95712 q^{8}\) \(-0.883705 q^{10}\) \(+2.50246 q^{11}\) \(+3.59818 q^{13}\) \(-1.33766 q^{14}\) \(-3.53429 q^{16}\) \(-0.647641 q^{17}\) \(+4.90149 q^{19}\) \(-0.139171 q^{20}\) \(-3.34744 q^{22}\) \(-4.27804 q^{23}\) \(-4.56356 q^{25}\) \(-4.81314 q^{26}\) \(-0.210663 q^{28}\) \(+7.60208 q^{29}\) \(-2.73462 q^{31}\) \(-1.18655 q^{32}\) \(+0.866324 q^{34}\) \(+0.660635 q^{35}\) \(+0.693776 q^{37}\) \(-6.55653 q^{38}\) \(+1.95357 q^{40}\) \(+11.1859 q^{41}\) \(-1.57216 q^{43}\) \(-0.527175 q^{44}\) \(+5.72257 q^{46}\) \(+6.59069 q^{47}\) \(+1.00000 q^{49}\) \(+6.10450 q^{50}\) \(-0.758003 q^{52}\) \(-7.27823 q^{53}\) \(+1.65321 q^{55}\) \(+2.95712 q^{56}\) \(-10.1690 q^{58}\) \(+9.88118 q^{59}\) \(+0.382234 q^{61}\) \(+3.65799 q^{62}\) \(+8.65579 q^{64}\) \(+2.37708 q^{65}\) \(-4.37009 q^{67}\) \(+0.136434 q^{68}\) \(-0.883705 q^{70}\) \(+13.1847 q^{71}\) \(+4.43665 q^{73}\) \(-0.928037 q^{74}\) \(-1.03256 q^{76}\) \(+2.50246 q^{77}\) \(-6.44755 q^{79}\) \(-2.33488 q^{80}\) \(-14.9629 q^{82}\) \(+4.82194 q^{83}\) \(-0.427854 q^{85}\) \(+2.10301 q^{86}\) \(+7.40006 q^{88}\) \(+9.63534 q^{89}\) \(+3.59818 q^{91}\) \(+0.901226 q^{92}\) \(-8.81610 q^{94}\) \(+3.23809 q^{95}\) \(-0.182292 q^{97}\) \(-1.33766 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.33766 −0.945869 −0.472935 0.881098i \(-0.656805\pi\)
−0.472935 + 0.881098i \(0.656805\pi\)
\(3\) 0 0
\(4\) −0.210663 −0.105332
\(5\) 0.660635 0.295445 0.147722 0.989029i \(-0.452806\pi\)
0.147722 + 0.989029i \(0.452806\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.95712 1.04550
\(9\) 0 0
\(10\) −0.883705 −0.279452
\(11\) 2.50246 0.754519 0.377259 0.926108i \(-0.376867\pi\)
0.377259 + 0.926108i \(0.376867\pi\)
\(12\) 0 0
\(13\) 3.59818 0.997955 0.498977 0.866615i \(-0.333709\pi\)
0.498977 + 0.866615i \(0.333709\pi\)
\(14\) −1.33766 −0.357505
\(15\) 0 0
\(16\) −3.53429 −0.883574
\(17\) −0.647641 −0.157076 −0.0785380 0.996911i \(-0.525025\pi\)
−0.0785380 + 0.996911i \(0.525025\pi\)
\(18\) 0 0
\(19\) 4.90149 1.12448 0.562239 0.826975i \(-0.309940\pi\)
0.562239 + 0.826975i \(0.309940\pi\)
\(20\) −0.139171 −0.0311197
\(21\) 0 0
\(22\) −3.34744 −0.713676
\(23\) −4.27804 −0.892033 −0.446017 0.895025i \(-0.647158\pi\)
−0.446017 + 0.895025i \(0.647158\pi\)
\(24\) 0 0
\(25\) −4.56356 −0.912712
\(26\) −4.81314 −0.943935
\(27\) 0 0
\(28\) −0.210663 −0.0398116
\(29\) 7.60208 1.41167 0.705835 0.708376i \(-0.250572\pi\)
0.705835 + 0.708376i \(0.250572\pi\)
\(30\) 0 0
\(31\) −2.73462 −0.491152 −0.245576 0.969377i \(-0.578977\pi\)
−0.245576 + 0.969377i \(0.578977\pi\)
\(32\) −1.18655 −0.209754
\(33\) 0 0
\(34\) 0.866324 0.148573
\(35\) 0.660635 0.111668
\(36\) 0 0
\(37\) 0.693776 0.114056 0.0570280 0.998373i \(-0.481838\pi\)
0.0570280 + 0.998373i \(0.481838\pi\)
\(38\) −6.55653 −1.06361
\(39\) 0 0
\(40\) 1.95357 0.308887
\(41\) 11.1859 1.74694 0.873470 0.486878i \(-0.161864\pi\)
0.873470 + 0.486878i \(0.161864\pi\)
\(42\) 0 0
\(43\) −1.57216 −0.239751 −0.119876 0.992789i \(-0.538250\pi\)
−0.119876 + 0.992789i \(0.538250\pi\)
\(44\) −0.527175 −0.0794746
\(45\) 0 0
\(46\) 5.72257 0.843747
\(47\) 6.59069 0.961350 0.480675 0.876899i \(-0.340392\pi\)
0.480675 + 0.876899i \(0.340392\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 6.10450 0.863306
\(51\) 0 0
\(52\) −0.758003 −0.105116
\(53\) −7.27823 −0.999742 −0.499871 0.866100i \(-0.666619\pi\)
−0.499871 + 0.866100i \(0.666619\pi\)
\(54\) 0 0
\(55\) 1.65321 0.222919
\(56\) 2.95712 0.395161
\(57\) 0 0
\(58\) −10.1690 −1.33526
\(59\) 9.88118 1.28642 0.643210 0.765690i \(-0.277602\pi\)
0.643210 + 0.765690i \(0.277602\pi\)
\(60\) 0 0
\(61\) 0.382234 0.0489401 0.0244700 0.999701i \(-0.492210\pi\)
0.0244700 + 0.999701i \(0.492210\pi\)
\(62\) 3.65799 0.464566
\(63\) 0 0
\(64\) 8.65579 1.08197
\(65\) 2.37708 0.294841
\(66\) 0 0
\(67\) −4.37009 −0.533892 −0.266946 0.963712i \(-0.586015\pi\)
−0.266946 + 0.963712i \(0.586015\pi\)
\(68\) 0.136434 0.0165451
\(69\) 0 0
\(70\) −0.883705 −0.105623
\(71\) 13.1847 1.56474 0.782371 0.622813i \(-0.214010\pi\)
0.782371 + 0.622813i \(0.214010\pi\)
\(72\) 0 0
\(73\) 4.43665 0.519271 0.259635 0.965707i \(-0.416398\pi\)
0.259635 + 0.965707i \(0.416398\pi\)
\(74\) −0.928037 −0.107882
\(75\) 0 0
\(76\) −1.03256 −0.118443
\(77\) 2.50246 0.285181
\(78\) 0 0
\(79\) −6.44755 −0.725406 −0.362703 0.931905i \(-0.618146\pi\)
−0.362703 + 0.931905i \(0.618146\pi\)
\(80\) −2.33488 −0.261047
\(81\) 0 0
\(82\) −14.9629 −1.65238
\(83\) 4.82194 0.529276 0.264638 0.964348i \(-0.414747\pi\)
0.264638 + 0.964348i \(0.414747\pi\)
\(84\) 0 0
\(85\) −0.427854 −0.0464073
\(86\) 2.10301 0.226774
\(87\) 0 0
\(88\) 7.40006 0.788849
\(89\) 9.63534 1.02134 0.510672 0.859775i \(-0.329397\pi\)
0.510672 + 0.859775i \(0.329397\pi\)
\(90\) 0 0
\(91\) 3.59818 0.377191
\(92\) 0.901226 0.0939593
\(93\) 0 0
\(94\) −8.81610 −0.909312
\(95\) 3.23809 0.332221
\(96\) 0 0
\(97\) −0.182292 −0.0185089 −0.00925446 0.999957i \(-0.502946\pi\)
−0.00925446 + 0.999957i \(0.502946\pi\)
\(98\) −1.33766 −0.135124
\(99\) 0 0
\(100\) 0.961374 0.0961374
\(101\) 14.8172 1.47436 0.737181 0.675695i \(-0.236156\pi\)
0.737181 + 0.675695i \(0.236156\pi\)
\(102\) 0 0
\(103\) −4.22841 −0.416638 −0.208319 0.978061i \(-0.566799\pi\)
−0.208319 + 0.978061i \(0.566799\pi\)
\(104\) 10.6402 1.04336
\(105\) 0 0
\(106\) 9.73581 0.945625
\(107\) −3.60740 −0.348740 −0.174370 0.984680i \(-0.555789\pi\)
−0.174370 + 0.984680i \(0.555789\pi\)
\(108\) 0 0
\(109\) −10.1924 −0.976259 −0.488129 0.872771i \(-0.662321\pi\)
−0.488129 + 0.872771i \(0.662321\pi\)
\(110\) −2.21143 −0.210852
\(111\) 0 0
\(112\) −3.53429 −0.333959
\(113\) −5.90567 −0.555559 −0.277780 0.960645i \(-0.589598\pi\)
−0.277780 + 0.960645i \(0.589598\pi\)
\(114\) 0 0
\(115\) −2.82622 −0.263547
\(116\) −1.60148 −0.148693
\(117\) 0 0
\(118\) −13.2177 −1.21679
\(119\) −0.647641 −0.0593692
\(120\) 0 0
\(121\) −4.73772 −0.430702
\(122\) −0.511300 −0.0462909
\(123\) 0 0
\(124\) 0.576083 0.0517338
\(125\) −6.31802 −0.565101
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −9.20541 −0.813651
\(129\) 0 0
\(130\) −3.17973 −0.278881
\(131\) −1.15626 −0.101023 −0.0505116 0.998723i \(-0.516085\pi\)
−0.0505116 + 0.998723i \(0.516085\pi\)
\(132\) 0 0
\(133\) 4.90149 0.425013
\(134\) 5.84570 0.504992
\(135\) 0 0
\(136\) −1.91515 −0.164223
\(137\) −12.7644 −1.09054 −0.545270 0.838260i \(-0.683573\pi\)
−0.545270 + 0.838260i \(0.683573\pi\)
\(138\) 0 0
\(139\) −1.66110 −0.140892 −0.0704461 0.997516i \(-0.522442\pi\)
−0.0704461 + 0.997516i \(0.522442\pi\)
\(140\) −0.139171 −0.0117621
\(141\) 0 0
\(142\) −17.6367 −1.48004
\(143\) 9.00428 0.752976
\(144\) 0 0
\(145\) 5.02220 0.417071
\(146\) −5.93473 −0.491162
\(147\) 0 0
\(148\) −0.146153 −0.0120137
\(149\) 2.58333 0.211634 0.105817 0.994386i \(-0.466254\pi\)
0.105817 + 0.994386i \(0.466254\pi\)
\(150\) 0 0
\(151\) 14.2335 1.15831 0.579153 0.815219i \(-0.303384\pi\)
0.579153 + 0.815219i \(0.303384\pi\)
\(152\) 14.4943 1.17564
\(153\) 0 0
\(154\) −3.34744 −0.269744
\(155\) −1.80658 −0.145108
\(156\) 0 0
\(157\) −14.1240 −1.12722 −0.563611 0.826040i \(-0.690588\pi\)
−0.563611 + 0.826040i \(0.690588\pi\)
\(158\) 8.62463 0.686139
\(159\) 0 0
\(160\) −0.783874 −0.0619707
\(161\) −4.27804 −0.337157
\(162\) 0 0
\(163\) 10.0883 0.790173 0.395087 0.918644i \(-0.370715\pi\)
0.395087 + 0.918644i \(0.370715\pi\)
\(164\) −2.35645 −0.184008
\(165\) 0 0
\(166\) −6.45012 −0.500626
\(167\) −6.93188 −0.536405 −0.268203 0.963363i \(-0.586430\pi\)
−0.268203 + 0.963363i \(0.586430\pi\)
\(168\) 0 0
\(169\) −0.0531190 −0.00408608
\(170\) 0.572324 0.0438952
\(171\) 0 0
\(172\) 0.331195 0.0252534
\(173\) 9.68261 0.736155 0.368078 0.929795i \(-0.380016\pi\)
0.368078 + 0.929795i \(0.380016\pi\)
\(174\) 0 0
\(175\) −4.56356 −0.344973
\(176\) −8.84441 −0.666673
\(177\) 0 0
\(178\) −12.8888 −0.966058
\(179\) −4.48504 −0.335228 −0.167614 0.985853i \(-0.553606\pi\)
−0.167614 + 0.985853i \(0.553606\pi\)
\(180\) 0 0
\(181\) 0.293930 0.0218476 0.0109238 0.999940i \(-0.496523\pi\)
0.0109238 + 0.999940i \(0.496523\pi\)
\(182\) −4.81314 −0.356774
\(183\) 0 0
\(184\) −12.6507 −0.932620
\(185\) 0.458332 0.0336972
\(186\) 0 0
\(187\) −1.62069 −0.118517
\(188\) −1.38841 −0.101261
\(189\) 0 0
\(190\) −4.33147 −0.314238
\(191\) −13.1650 −0.952583 −0.476291 0.879287i \(-0.658019\pi\)
−0.476291 + 0.879287i \(0.658019\pi\)
\(192\) 0 0
\(193\) −6.75824 −0.486469 −0.243234 0.969968i \(-0.578208\pi\)
−0.243234 + 0.969968i \(0.578208\pi\)
\(194\) 0.243845 0.0175070
\(195\) 0 0
\(196\) −0.210663 −0.0150474
\(197\) −16.8067 −1.19743 −0.598714 0.800963i \(-0.704321\pi\)
−0.598714 + 0.800963i \(0.704321\pi\)
\(198\) 0 0
\(199\) 4.39126 0.311288 0.155644 0.987813i \(-0.450255\pi\)
0.155644 + 0.987813i \(0.450255\pi\)
\(200\) −13.4950 −0.954240
\(201\) 0 0
\(202\) −19.8203 −1.39455
\(203\) 7.60208 0.533561
\(204\) 0 0
\(205\) 7.38977 0.516124
\(206\) 5.65618 0.394085
\(207\) 0 0
\(208\) −12.7170 −0.881767
\(209\) 12.2658 0.848440
\(210\) 0 0
\(211\) 0.300003 0.0206530 0.0103265 0.999947i \(-0.496713\pi\)
0.0103265 + 0.999947i \(0.496713\pi\)
\(212\) 1.53326 0.105304
\(213\) 0 0
\(214\) 4.82547 0.329863
\(215\) −1.03862 −0.0708333
\(216\) 0 0
\(217\) −2.73462 −0.185638
\(218\) 13.6340 0.923413
\(219\) 0 0
\(220\) −0.348270 −0.0234804
\(221\) −2.33033 −0.156755
\(222\) 0 0
\(223\) −25.5960 −1.71404 −0.857018 0.515286i \(-0.827686\pi\)
−0.857018 + 0.515286i \(0.827686\pi\)
\(224\) −1.18655 −0.0792795
\(225\) 0 0
\(226\) 7.89979 0.525486
\(227\) 8.55148 0.567582 0.283791 0.958886i \(-0.408408\pi\)
0.283791 + 0.958886i \(0.408408\pi\)
\(228\) 0 0
\(229\) 13.2641 0.876518 0.438259 0.898849i \(-0.355595\pi\)
0.438259 + 0.898849i \(0.355595\pi\)
\(230\) 3.78053 0.249281
\(231\) 0 0
\(232\) 22.4802 1.47590
\(233\) −9.75984 −0.639389 −0.319694 0.947521i \(-0.603580\pi\)
−0.319694 + 0.947521i \(0.603580\pi\)
\(234\) 0 0
\(235\) 4.35403 0.284026
\(236\) −2.08160 −0.135501
\(237\) 0 0
\(238\) 0.866324 0.0561555
\(239\) 3.32098 0.214816 0.107408 0.994215i \(-0.465745\pi\)
0.107408 + 0.994215i \(0.465745\pi\)
\(240\) 0 0
\(241\) −13.1150 −0.844812 −0.422406 0.906407i \(-0.638814\pi\)
−0.422406 + 0.906407i \(0.638814\pi\)
\(242\) 6.33746 0.407387
\(243\) 0 0
\(244\) −0.0805226 −0.00515493
\(245\) 0.660635 0.0422064
\(246\) 0 0
\(247\) 17.6364 1.12218
\(248\) −8.08659 −0.513499
\(249\) 0 0
\(250\) 8.45137 0.534511
\(251\) 27.6002 1.74211 0.871056 0.491184i \(-0.163436\pi\)
0.871056 + 0.491184i \(0.163436\pi\)
\(252\) 0 0
\(253\) −10.7056 −0.673056
\(254\) −1.33766 −0.0839323
\(255\) 0 0
\(256\) −4.99785 −0.312366
\(257\) 7.72105 0.481626 0.240813 0.970572i \(-0.422586\pi\)
0.240813 + 0.970572i \(0.422586\pi\)
\(258\) 0 0
\(259\) 0.693776 0.0431091
\(260\) −0.500763 −0.0310560
\(261\) 0 0
\(262\) 1.54669 0.0955547
\(263\) −18.2383 −1.12462 −0.562310 0.826926i \(-0.690087\pi\)
−0.562310 + 0.826926i \(0.690087\pi\)
\(264\) 0 0
\(265\) −4.80825 −0.295369
\(266\) −6.55653 −0.402007
\(267\) 0 0
\(268\) 0.920618 0.0562357
\(269\) 12.9944 0.792284 0.396142 0.918189i \(-0.370349\pi\)
0.396142 + 0.918189i \(0.370349\pi\)
\(270\) 0 0
\(271\) 19.1311 1.16213 0.581065 0.813857i \(-0.302636\pi\)
0.581065 + 0.813857i \(0.302636\pi\)
\(272\) 2.28895 0.138788
\(273\) 0 0
\(274\) 17.0745 1.03151
\(275\) −11.4201 −0.688659
\(276\) 0 0
\(277\) 21.3254 1.28132 0.640660 0.767825i \(-0.278661\pi\)
0.640660 + 0.767825i \(0.278661\pi\)
\(278\) 2.22198 0.133266
\(279\) 0 0
\(280\) 1.95357 0.116748
\(281\) 30.3475 1.81038 0.905189 0.425009i \(-0.139729\pi\)
0.905189 + 0.425009i \(0.139729\pi\)
\(282\) 0 0
\(283\) 3.32015 0.197362 0.0986811 0.995119i \(-0.468538\pi\)
0.0986811 + 0.995119i \(0.468538\pi\)
\(284\) −2.77754 −0.164817
\(285\) 0 0
\(286\) −12.0447 −0.712216
\(287\) 11.1859 0.660281
\(288\) 0 0
\(289\) −16.5806 −0.975327
\(290\) −6.71800 −0.394494
\(291\) 0 0
\(292\) −0.934639 −0.0546956
\(293\) 8.00402 0.467600 0.233800 0.972285i \(-0.424884\pi\)
0.233800 + 0.972285i \(0.424884\pi\)
\(294\) 0 0
\(295\) 6.52785 0.380066
\(296\) 2.05158 0.119245
\(297\) 0 0
\(298\) −3.45562 −0.200179
\(299\) −15.3932 −0.890209
\(300\) 0 0
\(301\) −1.57216 −0.0906175
\(302\) −19.0396 −1.09561
\(303\) 0 0
\(304\) −17.3233 −0.993560
\(305\) 0.252517 0.0144591
\(306\) 0 0
\(307\) −3.27243 −0.186768 −0.0933838 0.995630i \(-0.529768\pi\)
−0.0933838 + 0.995630i \(0.529768\pi\)
\(308\) −0.527175 −0.0300386
\(309\) 0 0
\(310\) 2.41660 0.137253
\(311\) −23.9348 −1.35722 −0.678608 0.734500i \(-0.737417\pi\)
−0.678608 + 0.734500i \(0.737417\pi\)
\(312\) 0 0
\(313\) −11.9219 −0.673866 −0.336933 0.941529i \(-0.609390\pi\)
−0.336933 + 0.941529i \(0.609390\pi\)
\(314\) 18.8932 1.06620
\(315\) 0 0
\(316\) 1.35826 0.0764081
\(317\) 13.8807 0.779620 0.389810 0.920895i \(-0.372541\pi\)
0.389810 + 0.920895i \(0.372541\pi\)
\(318\) 0 0
\(319\) 19.0239 1.06513
\(320\) 5.71831 0.319663
\(321\) 0 0
\(322\) 5.72257 0.318906
\(323\) −3.17441 −0.176629
\(324\) 0 0
\(325\) −16.4205 −0.910846
\(326\) −13.4947 −0.747400
\(327\) 0 0
\(328\) 33.0779 1.82642
\(329\) 6.59069 0.363356
\(330\) 0 0
\(331\) 7.63180 0.419482 0.209741 0.977757i \(-0.432738\pi\)
0.209741 + 0.977757i \(0.432738\pi\)
\(332\) −1.01580 −0.0557495
\(333\) 0 0
\(334\) 9.27251 0.507369
\(335\) −2.88703 −0.157736
\(336\) 0 0
\(337\) −0.476513 −0.0259573 −0.0129786 0.999916i \(-0.504131\pi\)
−0.0129786 + 0.999916i \(0.504131\pi\)
\(338\) 0.0710552 0.00386489
\(339\) 0 0
\(340\) 0.0901331 0.00488815
\(341\) −6.84326 −0.370583
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −4.64905 −0.250660
\(345\) 0 0
\(346\) −12.9520 −0.696307
\(347\) −1.27343 −0.0683613 −0.0341806 0.999416i \(-0.510882\pi\)
−0.0341806 + 0.999416i \(0.510882\pi\)
\(348\) 0 0
\(349\) −9.92179 −0.531101 −0.265551 0.964097i \(-0.585554\pi\)
−0.265551 + 0.964097i \(0.585554\pi\)
\(350\) 6.10450 0.326299
\(351\) 0 0
\(352\) −2.96928 −0.158263
\(353\) −21.2141 −1.12911 −0.564556 0.825395i \(-0.690952\pi\)
−0.564556 + 0.825395i \(0.690952\pi\)
\(354\) 0 0
\(355\) 8.71030 0.462295
\(356\) −2.02981 −0.107580
\(357\) 0 0
\(358\) 5.99947 0.317082
\(359\) 19.1882 1.01271 0.506356 0.862324i \(-0.330992\pi\)
0.506356 + 0.862324i \(0.330992\pi\)
\(360\) 0 0
\(361\) 5.02459 0.264452
\(362\) −0.393179 −0.0206650
\(363\) 0 0
\(364\) −0.758003 −0.0397302
\(365\) 2.93100 0.153416
\(366\) 0 0
\(367\) 33.0463 1.72500 0.862501 0.506055i \(-0.168897\pi\)
0.862501 + 0.506055i \(0.168897\pi\)
\(368\) 15.1199 0.788177
\(369\) 0 0
\(370\) −0.613093 −0.0318732
\(371\) −7.27823 −0.377867
\(372\) 0 0
\(373\) −8.79344 −0.455307 −0.227654 0.973742i \(-0.573105\pi\)
−0.227654 + 0.973742i \(0.573105\pi\)
\(374\) 2.16794 0.112101
\(375\) 0 0
\(376\) 19.4894 1.00509
\(377\) 27.3536 1.40878
\(378\) 0 0
\(379\) −14.9657 −0.768735 −0.384368 0.923180i \(-0.625580\pi\)
−0.384368 + 0.923180i \(0.625580\pi\)
\(380\) −0.682147 −0.0349934
\(381\) 0 0
\(382\) 17.6103 0.901019
\(383\) 1.59337 0.0814172 0.0407086 0.999171i \(-0.487038\pi\)
0.0407086 + 0.999171i \(0.487038\pi\)
\(384\) 0 0
\(385\) 1.65321 0.0842553
\(386\) 9.04023 0.460136
\(387\) 0 0
\(388\) 0.0384021 0.00194957
\(389\) 23.3352 1.18314 0.591570 0.806254i \(-0.298509\pi\)
0.591570 + 0.806254i \(0.298509\pi\)
\(390\) 0 0
\(391\) 2.77064 0.140117
\(392\) 2.95712 0.149357
\(393\) 0 0
\(394\) 22.4817 1.13261
\(395\) −4.25947 −0.214317
\(396\) 0 0
\(397\) 18.8324 0.945171 0.472586 0.881285i \(-0.343321\pi\)
0.472586 + 0.881285i \(0.343321\pi\)
\(398\) −5.87402 −0.294438
\(399\) 0 0
\(400\) 16.1290 0.806449
\(401\) −25.1525 −1.25606 −0.628029 0.778190i \(-0.716138\pi\)
−0.628029 + 0.778190i \(0.716138\pi\)
\(402\) 0 0
\(403\) −9.83964 −0.490148
\(404\) −3.12143 −0.155297
\(405\) 0 0
\(406\) −10.1690 −0.504679
\(407\) 1.73614 0.0860574
\(408\) 0 0
\(409\) −3.86404 −0.191064 −0.0955322 0.995426i \(-0.530455\pi\)
−0.0955322 + 0.995426i \(0.530455\pi\)
\(410\) −9.88501 −0.488186
\(411\) 0 0
\(412\) 0.890771 0.0438851
\(413\) 9.88118 0.486221
\(414\) 0 0
\(415\) 3.18554 0.156372
\(416\) −4.26941 −0.209325
\(417\) 0 0
\(418\) −16.4074 −0.802513
\(419\) 1.66627 0.0814028 0.0407014 0.999171i \(-0.487041\pi\)
0.0407014 + 0.999171i \(0.487041\pi\)
\(420\) 0 0
\(421\) 23.9101 1.16531 0.582653 0.812721i \(-0.302015\pi\)
0.582653 + 0.812721i \(0.302015\pi\)
\(422\) −0.401302 −0.0195351
\(423\) 0 0
\(424\) −21.5226 −1.04523
\(425\) 2.95555 0.143365
\(426\) 0 0
\(427\) 0.382234 0.0184976
\(428\) 0.759945 0.0367333
\(429\) 0 0
\(430\) 1.38932 0.0669990
\(431\) −14.2316 −0.685513 −0.342757 0.939424i \(-0.611361\pi\)
−0.342757 + 0.939424i \(0.611361\pi\)
\(432\) 0 0
\(433\) 15.4071 0.740420 0.370210 0.928948i \(-0.379286\pi\)
0.370210 + 0.928948i \(0.379286\pi\)
\(434\) 3.65799 0.175589
\(435\) 0 0
\(436\) 2.14717 0.102831
\(437\) −20.9688 −1.00307
\(438\) 0 0
\(439\) 12.7032 0.606291 0.303145 0.952944i \(-0.401963\pi\)
0.303145 + 0.952944i \(0.401963\pi\)
\(440\) 4.88873 0.233061
\(441\) 0 0
\(442\) 3.11719 0.148270
\(443\) 13.1778 0.626098 0.313049 0.949737i \(-0.398650\pi\)
0.313049 + 0.949737i \(0.398650\pi\)
\(444\) 0 0
\(445\) 6.36544 0.301751
\(446\) 34.2388 1.62125
\(447\) 0 0
\(448\) 8.65579 0.408948
\(449\) −13.5598 −0.639928 −0.319964 0.947430i \(-0.603671\pi\)
−0.319964 + 0.947430i \(0.603671\pi\)
\(450\) 0 0
\(451\) 27.9921 1.31810
\(452\) 1.24411 0.0585179
\(453\) 0 0
\(454\) −11.4390 −0.536858
\(455\) 2.37708 0.111439
\(456\) 0 0
\(457\) −15.3099 −0.716168 −0.358084 0.933689i \(-0.616570\pi\)
−0.358084 + 0.933689i \(0.616570\pi\)
\(458\) −17.7429 −0.829071
\(459\) 0 0
\(460\) 0.595381 0.0277598
\(461\) −14.0827 −0.655897 −0.327948 0.944696i \(-0.606357\pi\)
−0.327948 + 0.944696i \(0.606357\pi\)
\(462\) 0 0
\(463\) −15.6093 −0.725424 −0.362712 0.931901i \(-0.618149\pi\)
−0.362712 + 0.931901i \(0.618149\pi\)
\(464\) −26.8680 −1.24732
\(465\) 0 0
\(466\) 13.0554 0.604778
\(467\) −37.3868 −1.73005 −0.865027 0.501725i \(-0.832699\pi\)
−0.865027 + 0.501725i \(0.832699\pi\)
\(468\) 0 0
\(469\) −4.37009 −0.201792
\(470\) −5.82422 −0.268651
\(471\) 0 0
\(472\) 29.2198 1.34495
\(473\) −3.93425 −0.180897
\(474\) 0 0
\(475\) −22.3682 −1.02633
\(476\) 0.136434 0.00625345
\(477\) 0 0
\(478\) −4.44234 −0.203188
\(479\) −28.4334 −1.29915 −0.649577 0.760296i \(-0.725054\pi\)
−0.649577 + 0.760296i \(0.725054\pi\)
\(480\) 0 0
\(481\) 2.49633 0.113823
\(482\) 17.5434 0.799082
\(483\) 0 0
\(484\) 0.998062 0.0453665
\(485\) −0.120428 −0.00546836
\(486\) 0 0
\(487\) 37.0313 1.67805 0.839024 0.544095i \(-0.183127\pi\)
0.839024 + 0.544095i \(0.183127\pi\)
\(488\) 1.13031 0.0511668
\(489\) 0 0
\(490\) −0.883705 −0.0399217
\(491\) −15.7040 −0.708711 −0.354356 0.935111i \(-0.615300\pi\)
−0.354356 + 0.935111i \(0.615300\pi\)
\(492\) 0 0
\(493\) −4.92342 −0.221740
\(494\) −23.5916 −1.06143
\(495\) 0 0
\(496\) 9.66495 0.433969
\(497\) 13.1847 0.591417
\(498\) 0 0
\(499\) 32.0326 1.43398 0.716989 0.697085i \(-0.245520\pi\)
0.716989 + 0.697085i \(0.245520\pi\)
\(500\) 1.33097 0.0595230
\(501\) 0 0
\(502\) −36.9198 −1.64781
\(503\) 3.50362 0.156219 0.0781093 0.996945i \(-0.475112\pi\)
0.0781093 + 0.996945i \(0.475112\pi\)
\(504\) 0 0
\(505\) 9.78873 0.435593
\(506\) 14.3205 0.636623
\(507\) 0 0
\(508\) −0.210663 −0.00934667
\(509\) 33.3038 1.47616 0.738082 0.674711i \(-0.235732\pi\)
0.738082 + 0.674711i \(0.235732\pi\)
\(510\) 0 0
\(511\) 4.43665 0.196266
\(512\) 25.0963 1.10911
\(513\) 0 0
\(514\) −10.3281 −0.455555
\(515\) −2.79344 −0.123093
\(516\) 0 0
\(517\) 16.4929 0.725357
\(518\) −0.928037 −0.0407756
\(519\) 0 0
\(520\) 7.02931 0.308255
\(521\) 3.99571 0.175055 0.0875276 0.996162i \(-0.472103\pi\)
0.0875276 + 0.996162i \(0.472103\pi\)
\(522\) 0 0
\(523\) 3.41299 0.149240 0.0746199 0.997212i \(-0.476226\pi\)
0.0746199 + 0.997212i \(0.476226\pi\)
\(524\) 0.243582 0.0106409
\(525\) 0 0
\(526\) 24.3966 1.06374
\(527\) 1.77105 0.0771482
\(528\) 0 0
\(529\) −4.69836 −0.204276
\(530\) 6.43181 0.279380
\(531\) 0 0
\(532\) −1.03256 −0.0447673
\(533\) 40.2488 1.74337
\(534\) 0 0
\(535\) −2.38317 −0.103033
\(536\) −12.9229 −0.558183
\(537\) 0 0
\(538\) −17.3821 −0.749397
\(539\) 2.50246 0.107788
\(540\) 0 0
\(541\) −28.7529 −1.23618 −0.618092 0.786106i \(-0.712094\pi\)
−0.618092 + 0.786106i \(0.712094\pi\)
\(542\) −25.5909 −1.09922
\(543\) 0 0
\(544\) 0.768457 0.0329473
\(545\) −6.73348 −0.288431
\(546\) 0 0
\(547\) 9.81775 0.419777 0.209888 0.977725i \(-0.432690\pi\)
0.209888 + 0.977725i \(0.432690\pi\)
\(548\) 2.68900 0.114868
\(549\) 0 0
\(550\) 15.2762 0.651381
\(551\) 37.2615 1.58739
\(552\) 0 0
\(553\) −6.44755 −0.274178
\(554\) −28.5262 −1.21196
\(555\) 0 0
\(556\) 0.349932 0.0148404
\(557\) 11.4402 0.484735 0.242368 0.970184i \(-0.422076\pi\)
0.242368 + 0.970184i \(0.422076\pi\)
\(558\) 0 0
\(559\) −5.65689 −0.239261
\(560\) −2.33488 −0.0986666
\(561\) 0 0
\(562\) −40.5946 −1.71238
\(563\) 19.8032 0.834605 0.417303 0.908768i \(-0.362975\pi\)
0.417303 + 0.908768i \(0.362975\pi\)
\(564\) 0 0
\(565\) −3.90149 −0.164137
\(566\) −4.44123 −0.186679
\(567\) 0 0
\(568\) 38.9888 1.63594
\(569\) 9.19690 0.385554 0.192777 0.981243i \(-0.438251\pi\)
0.192777 + 0.981243i \(0.438251\pi\)
\(570\) 0 0
\(571\) 34.6547 1.45026 0.725128 0.688615i \(-0.241781\pi\)
0.725128 + 0.688615i \(0.241781\pi\)
\(572\) −1.89687 −0.0793121
\(573\) 0 0
\(574\) −14.9629 −0.624540
\(575\) 19.5231 0.814170
\(576\) 0 0
\(577\) 11.7858 0.490648 0.245324 0.969441i \(-0.421106\pi\)
0.245324 + 0.969441i \(0.421106\pi\)
\(578\) 22.1792 0.922532
\(579\) 0 0
\(580\) −1.05799 −0.0439307
\(581\) 4.82194 0.200048
\(582\) 0 0
\(583\) −18.2135 −0.754324
\(584\) 13.1197 0.542897
\(585\) 0 0
\(586\) −10.7067 −0.442288
\(587\) 12.7673 0.526961 0.263480 0.964665i \(-0.415130\pi\)
0.263480 + 0.964665i \(0.415130\pi\)
\(588\) 0 0
\(589\) −13.4037 −0.552290
\(590\) −8.73205 −0.359493
\(591\) 0 0
\(592\) −2.45201 −0.100777
\(593\) 31.8244 1.30687 0.653435 0.756983i \(-0.273327\pi\)
0.653435 + 0.756983i \(0.273327\pi\)
\(594\) 0 0
\(595\) −0.427854 −0.0175403
\(596\) −0.544212 −0.0222918
\(597\) 0 0
\(598\) 20.5908 0.842021
\(599\) −19.8627 −0.811570 −0.405785 0.913969i \(-0.633002\pi\)
−0.405785 + 0.913969i \(0.633002\pi\)
\(600\) 0 0
\(601\) 29.6711 1.21031 0.605154 0.796108i \(-0.293111\pi\)
0.605154 + 0.796108i \(0.293111\pi\)
\(602\) 2.10301 0.0857123
\(603\) 0 0
\(604\) −2.99847 −0.122006
\(605\) −3.12990 −0.127249
\(606\) 0 0
\(607\) −17.8654 −0.725136 −0.362568 0.931957i \(-0.618100\pi\)
−0.362568 + 0.931957i \(0.618100\pi\)
\(608\) −5.81585 −0.235864
\(609\) 0 0
\(610\) −0.337782 −0.0136764
\(611\) 23.7145 0.959384
\(612\) 0 0
\(613\) 21.2972 0.860186 0.430093 0.902785i \(-0.358481\pi\)
0.430093 + 0.902785i \(0.358481\pi\)
\(614\) 4.37740 0.176658
\(615\) 0 0
\(616\) 7.40006 0.298157
\(617\) −27.3251 −1.10007 −0.550034 0.835142i \(-0.685385\pi\)
−0.550034 + 0.835142i \(0.685385\pi\)
\(618\) 0 0
\(619\) −10.2893 −0.413562 −0.206781 0.978387i \(-0.566299\pi\)
−0.206781 + 0.978387i \(0.566299\pi\)
\(620\) 0.380581 0.0152845
\(621\) 0 0
\(622\) 32.0166 1.28375
\(623\) 9.63534 0.386032
\(624\) 0 0
\(625\) 18.6439 0.745756
\(626\) 15.9475 0.637389
\(627\) 0 0
\(628\) 2.97542 0.118732
\(629\) −0.449318 −0.0179155
\(630\) 0 0
\(631\) 26.6828 1.06223 0.531113 0.847301i \(-0.321774\pi\)
0.531113 + 0.847301i \(0.321774\pi\)
\(632\) −19.0662 −0.758411
\(633\) 0 0
\(634\) −18.5677 −0.737419
\(635\) 0.660635 0.0262165
\(636\) 0 0
\(637\) 3.59818 0.142565
\(638\) −25.4475 −1.00748
\(639\) 0 0
\(640\) −6.08141 −0.240389
\(641\) 24.1029 0.952005 0.476003 0.879444i \(-0.342085\pi\)
0.476003 + 0.879444i \(0.342085\pi\)
\(642\) 0 0
\(643\) −15.6694 −0.617940 −0.308970 0.951072i \(-0.599984\pi\)
−0.308970 + 0.951072i \(0.599984\pi\)
\(644\) 0.901226 0.0355133
\(645\) 0 0
\(646\) 4.24628 0.167068
\(647\) −5.20075 −0.204463 −0.102231 0.994761i \(-0.532598\pi\)
−0.102231 + 0.994761i \(0.532598\pi\)
\(648\) 0 0
\(649\) 24.7272 0.970628
\(650\) 21.9651 0.861541
\(651\) 0 0
\(652\) −2.12522 −0.0832302
\(653\) −14.1774 −0.554804 −0.277402 0.960754i \(-0.589473\pi\)
−0.277402 + 0.960754i \(0.589473\pi\)
\(654\) 0 0
\(655\) −0.763867 −0.0298468
\(656\) −39.5342 −1.54355
\(657\) 0 0
\(658\) −8.81610 −0.343687
\(659\) 5.06889 0.197456 0.0987280 0.995114i \(-0.468523\pi\)
0.0987280 + 0.995114i \(0.468523\pi\)
\(660\) 0 0
\(661\) −44.1647 −1.71781 −0.858905 0.512136i \(-0.828855\pi\)
−0.858905 + 0.512136i \(0.828855\pi\)
\(662\) −10.2088 −0.396775
\(663\) 0 0
\(664\) 14.2590 0.553358
\(665\) 3.23809 0.125568
\(666\) 0 0
\(667\) −32.5220 −1.25926
\(668\) 1.46029 0.0565004
\(669\) 0 0
\(670\) 3.86187 0.149197
\(671\) 0.956524 0.0369262
\(672\) 0 0
\(673\) 34.6780 1.33674 0.668369 0.743830i \(-0.266993\pi\)
0.668369 + 0.743830i \(0.266993\pi\)
\(674\) 0.637412 0.0245522
\(675\) 0 0
\(676\) 0.0111902 0.000430393 0
\(677\) 31.0973 1.19517 0.597583 0.801807i \(-0.296128\pi\)
0.597583 + 0.801807i \(0.296128\pi\)
\(678\) 0 0
\(679\) −0.182292 −0.00699571
\(680\) −1.26522 −0.0485188
\(681\) 0 0
\(682\) 9.15396 0.350523
\(683\) 49.0636 1.87736 0.938682 0.344783i \(-0.112047\pi\)
0.938682 + 0.344783i \(0.112047\pi\)
\(684\) 0 0
\(685\) −8.43263 −0.322194
\(686\) −1.33766 −0.0510721
\(687\) 0 0
\(688\) 5.55646 0.211838
\(689\) −26.1884 −0.997698
\(690\) 0 0
\(691\) 8.63843 0.328621 0.164311 0.986409i \(-0.447460\pi\)
0.164311 + 0.986409i \(0.447460\pi\)
\(692\) −2.03977 −0.0775404
\(693\) 0 0
\(694\) 1.70342 0.0646608
\(695\) −1.09738 −0.0416259
\(696\) 0 0
\(697\) −7.24443 −0.274402
\(698\) 13.2720 0.502352
\(699\) 0 0
\(700\) 0.961374 0.0363365
\(701\) −3.58228 −0.135301 −0.0676505 0.997709i \(-0.521550\pi\)
−0.0676505 + 0.997709i \(0.521550\pi\)
\(702\) 0 0
\(703\) 3.40053 0.128254
\(704\) 21.6607 0.816369
\(705\) 0 0
\(706\) 28.3772 1.06799
\(707\) 14.8172 0.557257
\(708\) 0 0
\(709\) −19.5844 −0.735509 −0.367755 0.929923i \(-0.619873\pi\)
−0.367755 + 0.929923i \(0.619873\pi\)
\(710\) −11.6514 −0.437270
\(711\) 0 0
\(712\) 28.4928 1.06781
\(713\) 11.6988 0.438124
\(714\) 0 0
\(715\) 5.94854 0.222463
\(716\) 0.944833 0.0353101
\(717\) 0 0
\(718\) −25.6673 −0.957894
\(719\) −35.2147 −1.31329 −0.656643 0.754201i \(-0.728024\pi\)
−0.656643 + 0.754201i \(0.728024\pi\)
\(720\) 0 0
\(721\) −4.22841 −0.157474
\(722\) −6.72120 −0.250137
\(723\) 0 0
\(724\) −0.0619202 −0.00230125
\(725\) −34.6926 −1.28845
\(726\) 0 0
\(727\) −0.146995 −0.00545173 −0.00272587 0.999996i \(-0.500868\pi\)
−0.00272587 + 0.999996i \(0.500868\pi\)
\(728\) 10.6402 0.394353
\(729\) 0 0
\(730\) −3.92069 −0.145111
\(731\) 1.01819 0.0376592
\(732\) 0 0
\(733\) −12.9512 −0.478364 −0.239182 0.970975i \(-0.576879\pi\)
−0.239182 + 0.970975i \(0.576879\pi\)
\(734\) −44.2047 −1.63163
\(735\) 0 0
\(736\) 5.07610 0.187108
\(737\) −10.9360 −0.402831
\(738\) 0 0
\(739\) −33.8631 −1.24567 −0.622836 0.782352i \(-0.714020\pi\)
−0.622836 + 0.782352i \(0.714020\pi\)
\(740\) −0.0965537 −0.00354938
\(741\) 0 0
\(742\) 9.73581 0.357413
\(743\) −18.3992 −0.675001 −0.337500 0.941325i \(-0.609581\pi\)
−0.337500 + 0.941325i \(0.609581\pi\)
\(744\) 0 0
\(745\) 1.70664 0.0625263
\(746\) 11.7626 0.430661
\(747\) 0 0
\(748\) 0.341420 0.0124836
\(749\) −3.60740 −0.131811
\(750\) 0 0
\(751\) −19.8382 −0.723904 −0.361952 0.932197i \(-0.617890\pi\)
−0.361952 + 0.932197i \(0.617890\pi\)
\(752\) −23.2934 −0.849424
\(753\) 0 0
\(754\) −36.5899 −1.33252
\(755\) 9.40314 0.342215
\(756\) 0 0
\(757\) 20.6741 0.751413 0.375706 0.926739i \(-0.377400\pi\)
0.375706 + 0.926739i \(0.377400\pi\)
\(758\) 20.0190 0.727123
\(759\) 0 0
\(760\) 9.57542 0.347337
\(761\) −1.94280 −0.0704264 −0.0352132 0.999380i \(-0.511211\pi\)
−0.0352132 + 0.999380i \(0.511211\pi\)
\(762\) 0 0
\(763\) −10.1924 −0.368991
\(764\) 2.77337 0.100337
\(765\) 0 0
\(766\) −2.13138 −0.0770100
\(767\) 35.5542 1.28379
\(768\) 0 0
\(769\) −26.6560 −0.961241 −0.480621 0.876929i \(-0.659589\pi\)
−0.480621 + 0.876929i \(0.659589\pi\)
\(770\) −2.21143 −0.0796945
\(771\) 0 0
\(772\) 1.42371 0.0512405
\(773\) 5.12985 0.184508 0.0922540 0.995736i \(-0.470593\pi\)
0.0922540 + 0.995736i \(0.470593\pi\)
\(774\) 0 0
\(775\) 12.4796 0.448281
\(776\) −0.539058 −0.0193511
\(777\) 0 0
\(778\) −31.2145 −1.11909
\(779\) 54.8274 1.96440
\(780\) 0 0
\(781\) 32.9942 1.18063
\(782\) −3.70617 −0.132532
\(783\) 0 0
\(784\) −3.53429 −0.126225
\(785\) −9.33083 −0.333032
\(786\) 0 0
\(787\) 35.0310 1.24872 0.624360 0.781137i \(-0.285360\pi\)
0.624360 + 0.781137i \(0.285360\pi\)
\(788\) 3.54055 0.126127
\(789\) 0 0
\(790\) 5.69773 0.202716
\(791\) −5.90567 −0.209982
\(792\) 0 0
\(793\) 1.37535 0.0488400
\(794\) −25.1914 −0.894008
\(795\) 0 0
\(796\) −0.925076 −0.0327885
\(797\) 30.9196 1.09523 0.547614 0.836731i \(-0.315536\pi\)
0.547614 + 0.836731i \(0.315536\pi\)
\(798\) 0 0
\(799\) −4.26840 −0.151005
\(800\) 5.41488 0.191445
\(801\) 0 0
\(802\) 33.6456 1.18807
\(803\) 11.1025 0.391799
\(804\) 0 0
\(805\) −2.82622 −0.0996112
\(806\) 13.1621 0.463615
\(807\) 0 0
\(808\) 43.8161 1.54144
\(809\) −29.9617 −1.05340 −0.526699 0.850052i \(-0.676570\pi\)
−0.526699 + 0.850052i \(0.676570\pi\)
\(810\) 0 0
\(811\) −23.8090 −0.836045 −0.418023 0.908437i \(-0.637277\pi\)
−0.418023 + 0.908437i \(0.637277\pi\)
\(812\) −1.60148 −0.0562009
\(813\) 0 0
\(814\) −2.32237 −0.0813990
\(815\) 6.66465 0.233452
\(816\) 0 0
\(817\) −7.70590 −0.269595
\(818\) 5.16877 0.180722
\(819\) 0 0
\(820\) −1.55675 −0.0543642
\(821\) 45.4733 1.58703 0.793514 0.608552i \(-0.208249\pi\)
0.793514 + 0.608552i \(0.208249\pi\)
\(822\) 0 0
\(823\) 16.4083 0.571958 0.285979 0.958236i \(-0.407681\pi\)
0.285979 + 0.958236i \(0.407681\pi\)
\(824\) −12.5039 −0.435594
\(825\) 0 0
\(826\) −13.2177 −0.459902
\(827\) 14.0064 0.487049 0.243524 0.969895i \(-0.421696\pi\)
0.243524 + 0.969895i \(0.421696\pi\)
\(828\) 0 0
\(829\) 15.3602 0.533480 0.266740 0.963768i \(-0.414053\pi\)
0.266740 + 0.963768i \(0.414053\pi\)
\(830\) −4.26117 −0.147907
\(831\) 0 0
\(832\) 31.1451 1.07976
\(833\) −0.647641 −0.0224394
\(834\) 0 0
\(835\) −4.57944 −0.158478
\(836\) −2.58394 −0.0893675
\(837\) 0 0
\(838\) −2.22891 −0.0769964
\(839\) 40.9499 1.41375 0.706874 0.707339i \(-0.250105\pi\)
0.706874 + 0.707339i \(0.250105\pi\)
\(840\) 0 0
\(841\) 28.7916 0.992814
\(842\) −31.9836 −1.10223
\(843\) 0 0
\(844\) −0.0631995 −0.00217542
\(845\) −0.0350922 −0.00120721
\(846\) 0 0
\(847\) −4.73772 −0.162790
\(848\) 25.7234 0.883346
\(849\) 0 0
\(850\) −3.95352 −0.135605
\(851\) −2.96800 −0.101742
\(852\) 0 0
\(853\) −34.1821 −1.17037 −0.585186 0.810899i \(-0.698979\pi\)
−0.585186 + 0.810899i \(0.698979\pi\)
\(854\) −0.511300 −0.0174963
\(855\) 0 0
\(856\) −10.6675 −0.364607
\(857\) −8.93481 −0.305207 −0.152604 0.988287i \(-0.548766\pi\)
−0.152604 + 0.988287i \(0.548766\pi\)
\(858\) 0 0
\(859\) 3.55658 0.121349 0.0606745 0.998158i \(-0.480675\pi\)
0.0606745 + 0.998158i \(0.480675\pi\)
\(860\) 0.218799 0.00746098
\(861\) 0 0
\(862\) 19.0371 0.648406
\(863\) 1.17289 0.0399258 0.0199629 0.999801i \(-0.493645\pi\)
0.0199629 + 0.999801i \(0.493645\pi\)
\(864\) 0 0
\(865\) 6.39667 0.217493
\(866\) −20.6095 −0.700340
\(867\) 0 0
\(868\) 0.576083 0.0195535
\(869\) −16.1347 −0.547332
\(870\) 0 0
\(871\) −15.7244 −0.532800
\(872\) −30.1402 −1.02068
\(873\) 0 0
\(874\) 28.0491 0.948775
\(875\) −6.31802 −0.213588
\(876\) 0 0
\(877\) 29.5713 0.998553 0.499276 0.866443i \(-0.333599\pi\)
0.499276 + 0.866443i \(0.333599\pi\)
\(878\) −16.9926 −0.573472
\(879\) 0 0
\(880\) −5.84293 −0.196965
\(881\) 17.2056 0.579673 0.289837 0.957076i \(-0.406399\pi\)
0.289837 + 0.957076i \(0.406399\pi\)
\(882\) 0 0
\(883\) 39.9725 1.34518 0.672592 0.740014i \(-0.265181\pi\)
0.672592 + 0.740014i \(0.265181\pi\)
\(884\) 0.490914 0.0165112
\(885\) 0 0
\(886\) −17.6275 −0.592207
\(887\) −45.9422 −1.54259 −0.771294 0.636479i \(-0.780390\pi\)
−0.771294 + 0.636479i \(0.780390\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −8.51480 −0.285417
\(891\) 0 0
\(892\) 5.39214 0.180542
\(893\) 32.3042 1.08102
\(894\) 0 0
\(895\) −2.96297 −0.0990413
\(896\) −9.20541 −0.307531
\(897\) 0 0
\(898\) 18.1385 0.605288
\(899\) −20.7888 −0.693345
\(900\) 0 0
\(901\) 4.71368 0.157036
\(902\) −37.4440 −1.24675
\(903\) 0 0
\(904\) −17.4638 −0.580836
\(905\) 0.194180 0.00645477
\(906\) 0 0
\(907\) −40.3826 −1.34088 −0.670441 0.741963i \(-0.733895\pi\)
−0.670441 + 0.741963i \(0.733895\pi\)
\(908\) −1.80148 −0.0597843
\(909\) 0 0
\(910\) −3.17973 −0.105407
\(911\) 24.9950 0.828122 0.414061 0.910249i \(-0.364110\pi\)
0.414061 + 0.910249i \(0.364110\pi\)
\(912\) 0 0
\(913\) 12.0667 0.399349
\(914\) 20.4795 0.677401
\(915\) 0 0
\(916\) −2.79426 −0.0923250
\(917\) −1.15626 −0.0381832
\(918\) 0 0
\(919\) −32.3880 −1.06838 −0.534190 0.845364i \(-0.679383\pi\)
−0.534190 + 0.845364i \(0.679383\pi\)
\(920\) −8.35747 −0.275538
\(921\) 0 0
\(922\) 18.8379 0.620393
\(923\) 47.4410 1.56154
\(924\) 0 0
\(925\) −3.16609 −0.104100
\(926\) 20.8799 0.686156
\(927\) 0 0
\(928\) −9.02023 −0.296103
\(929\) 24.9473 0.818495 0.409248 0.912423i \(-0.365791\pi\)
0.409248 + 0.912423i \(0.365791\pi\)
\(930\) 0 0
\(931\) 4.90149 0.160640
\(932\) 2.05604 0.0673478
\(933\) 0 0
\(934\) 50.0108 1.63640
\(935\) −1.07069 −0.0350152
\(936\) 0 0
\(937\) −47.5858 −1.55456 −0.777280 0.629155i \(-0.783401\pi\)
−0.777280 + 0.629155i \(0.783401\pi\)
\(938\) 5.84570 0.190869
\(939\) 0 0
\(940\) −0.917234 −0.0299169
\(941\) 18.8073 0.613101 0.306550 0.951854i \(-0.400825\pi\)
0.306550 + 0.951854i \(0.400825\pi\)
\(942\) 0 0
\(943\) −47.8536 −1.55833
\(944\) −34.9230 −1.13665
\(945\) 0 0
\(946\) 5.26269 0.171105
\(947\) 20.7650 0.674773 0.337387 0.941366i \(-0.390457\pi\)
0.337387 + 0.941366i \(0.390457\pi\)
\(948\) 0 0
\(949\) 15.9639 0.518209
\(950\) 29.9211 0.970770
\(951\) 0 0
\(952\) −1.91515 −0.0620704
\(953\) 57.6890 1.86873 0.934365 0.356316i \(-0.115967\pi\)
0.934365 + 0.356316i \(0.115967\pi\)
\(954\) 0 0
\(955\) −8.69723 −0.281436
\(956\) −0.699607 −0.0226269
\(957\) 0 0
\(958\) 38.0342 1.22883
\(959\) −12.7644 −0.412186
\(960\) 0 0
\(961\) −23.5219 −0.758770
\(962\) −3.33924 −0.107661
\(963\) 0 0
\(964\) 2.76285 0.0889854
\(965\) −4.46473 −0.143725
\(966\) 0 0
\(967\) −11.8196 −0.380093 −0.190046 0.981775i \(-0.560864\pi\)
−0.190046 + 0.981775i \(0.560864\pi\)
\(968\) −14.0100 −0.450298
\(969\) 0 0
\(970\) 0.161092 0.00517236
\(971\) 6.79796 0.218157 0.109078 0.994033i \(-0.465210\pi\)
0.109078 + 0.994033i \(0.465210\pi\)
\(972\) 0 0
\(973\) −1.66110 −0.0532523
\(974\) −49.5353 −1.58721
\(975\) 0 0
\(976\) −1.35093 −0.0432422
\(977\) −37.7861 −1.20889 −0.604443 0.796649i \(-0.706604\pi\)
−0.604443 + 0.796649i \(0.706604\pi\)
\(978\) 0 0
\(979\) 24.1120 0.770623
\(980\) −0.139171 −0.00444567
\(981\) 0 0
\(982\) 21.0066 0.670348
\(983\) 34.4511 1.09882 0.549409 0.835554i \(-0.314853\pi\)
0.549409 + 0.835554i \(0.314853\pi\)
\(984\) 0 0
\(985\) −11.1031 −0.353774
\(986\) 6.58587 0.209737
\(987\) 0 0
\(988\) −3.71534 −0.118201
\(989\) 6.72575 0.213866
\(990\) 0 0
\(991\) 44.8723 1.42542 0.712708 0.701461i \(-0.247468\pi\)
0.712708 + 0.701461i \(0.247468\pi\)
\(992\) 3.24475 0.103021
\(993\) 0 0
\(994\) −17.6367 −0.559403
\(995\) 2.90102 0.0919684
\(996\) 0 0
\(997\) −48.8594 −1.54739 −0.773696 0.633557i \(-0.781594\pi\)
−0.773696 + 0.633557i \(0.781594\pi\)
\(998\) −42.8488 −1.35635
\(999\) 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 \(a_p\))