Properties

Label 8001.2.a.u.1.14
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 1.14
Root \(1.77085\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.77085 q^{2}\) \(+1.13590 q^{4}\) \(-1.38376 q^{5}\) \(+1.00000 q^{7}\) \(-1.53019 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.77085 q^{2}\) \(+1.13590 q^{4}\) \(-1.38376 q^{5}\) \(+1.00000 q^{7}\) \(-1.53019 q^{8}\) \(-2.45042 q^{10}\) \(-3.51371 q^{11}\) \(+4.71315 q^{13}\) \(+1.77085 q^{14}\) \(-4.98153 q^{16}\) \(+4.68539 q^{17}\) \(-3.74479 q^{19}\) \(-1.57181 q^{20}\) \(-6.22224 q^{22}\) \(+2.00004 q^{23}\) \(-3.08521 q^{25}\) \(+8.34626 q^{26}\) \(+1.13590 q^{28}\) \(+4.37013 q^{29}\) \(-0.875947 q^{31}\) \(-5.76115 q^{32}\) \(+8.29711 q^{34}\) \(-1.38376 q^{35}\) \(-9.02904 q^{37}\) \(-6.63146 q^{38}\) \(+2.11741 q^{40}\) \(-1.57067 q^{41}\) \(-2.16122 q^{43}\) \(-3.99122 q^{44}\) \(+3.54176 q^{46}\) \(+12.9854 q^{47}\) \(+1.00000 q^{49}\) \(-5.46344 q^{50}\) \(+5.35366 q^{52}\) \(+10.7152 q^{53}\) \(+4.86212 q^{55}\) \(-1.53019 q^{56}\) \(+7.73884 q^{58}\) \(+0.801398 q^{59}\) \(+3.10892 q^{61}\) \(-1.55117 q^{62}\) \(-0.239057 q^{64}\) \(-6.52185 q^{65}\) \(+6.63235 q^{67}\) \(+5.32214 q^{68}\) \(-2.45042 q^{70}\) \(+8.91999 q^{71}\) \(+12.3019 q^{73}\) \(-15.9891 q^{74}\) \(-4.25371 q^{76}\) \(-3.51371 q^{77}\) \(+3.05893 q^{79}\) \(+6.89323 q^{80}\) \(-2.78142 q^{82}\) \(-4.04869 q^{83}\) \(-6.48345 q^{85}\) \(-3.82719 q^{86}\) \(+5.37664 q^{88}\) \(+11.2427 q^{89}\) \(+4.71315 q^{91}\) \(+2.27184 q^{92}\) \(+22.9952 q^{94}\) \(+5.18189 q^{95}\) \(-8.60399 q^{97}\) \(+1.77085 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.77085 1.25218 0.626089 0.779752i \(-0.284655\pi\)
0.626089 + 0.779752i \(0.284655\pi\)
\(3\) 0 0
\(4\) 1.13590 0.567950
\(5\) −1.38376 −0.618835 −0.309418 0.950926i \(-0.600134\pi\)
−0.309418 + 0.950926i \(0.600134\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −1.53019 −0.541004
\(9\) 0 0
\(10\) −2.45042 −0.774892
\(11\) −3.51371 −1.05942 −0.529712 0.848178i \(-0.677700\pi\)
−0.529712 + 0.848178i \(0.677700\pi\)
\(12\) 0 0
\(13\) 4.71315 1.30719 0.653596 0.756844i \(-0.273260\pi\)
0.653596 + 0.756844i \(0.273260\pi\)
\(14\) 1.77085 0.473279
\(15\) 0 0
\(16\) −4.98153 −1.24538
\(17\) 4.68539 1.13637 0.568187 0.822899i \(-0.307645\pi\)
0.568187 + 0.822899i \(0.307645\pi\)
\(18\) 0 0
\(19\) −3.74479 −0.859114 −0.429557 0.903040i \(-0.641330\pi\)
−0.429557 + 0.903040i \(0.641330\pi\)
\(20\) −1.57181 −0.351467
\(21\) 0 0
\(22\) −6.22224 −1.32659
\(23\) 2.00004 0.417036 0.208518 0.978018i \(-0.433136\pi\)
0.208518 + 0.978018i \(0.433136\pi\)
\(24\) 0 0
\(25\) −3.08521 −0.617043
\(26\) 8.34626 1.63684
\(27\) 0 0
\(28\) 1.13590 0.214665
\(29\) 4.37013 0.811514 0.405757 0.913981i \(-0.367008\pi\)
0.405757 + 0.913981i \(0.367008\pi\)
\(30\) 0 0
\(31\) −0.875947 −0.157325 −0.0786624 0.996901i \(-0.525065\pi\)
−0.0786624 + 0.996901i \(0.525065\pi\)
\(32\) −5.76115 −1.01844
\(33\) 0 0
\(34\) 8.29711 1.42294
\(35\) −1.38376 −0.233898
\(36\) 0 0
\(37\) −9.02904 −1.48437 −0.742183 0.670198i \(-0.766209\pi\)
−0.742183 + 0.670198i \(0.766209\pi\)
\(38\) −6.63146 −1.07576
\(39\) 0 0
\(40\) 2.11741 0.334792
\(41\) −1.57067 −0.245298 −0.122649 0.992450i \(-0.539139\pi\)
−0.122649 + 0.992450i \(0.539139\pi\)
\(42\) 0 0
\(43\) −2.16122 −0.329583 −0.164791 0.986328i \(-0.552695\pi\)
−0.164791 + 0.986328i \(0.552695\pi\)
\(44\) −3.99122 −0.601700
\(45\) 0 0
\(46\) 3.54176 0.522204
\(47\) 12.9854 1.89412 0.947061 0.321054i \(-0.104037\pi\)
0.947061 + 0.321054i \(0.104037\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −5.46344 −0.772648
\(51\) 0 0
\(52\) 5.35366 0.742419
\(53\) 10.7152 1.47184 0.735922 0.677066i \(-0.236749\pi\)
0.735922 + 0.677066i \(0.236749\pi\)
\(54\) 0 0
\(55\) 4.86212 0.655609
\(56\) −1.53019 −0.204480
\(57\) 0 0
\(58\) 7.73884 1.01616
\(59\) 0.801398 0.104333 0.0521666 0.998638i \(-0.483387\pi\)
0.0521666 + 0.998638i \(0.483387\pi\)
\(60\) 0 0
\(61\) 3.10892 0.398056 0.199028 0.979994i \(-0.436222\pi\)
0.199028 + 0.979994i \(0.436222\pi\)
\(62\) −1.55117 −0.196999
\(63\) 0 0
\(64\) −0.239057 −0.0298822
\(65\) −6.52185 −0.808936
\(66\) 0 0
\(67\) 6.63235 0.810271 0.405135 0.914257i \(-0.367224\pi\)
0.405135 + 0.914257i \(0.367224\pi\)
\(68\) 5.32214 0.645404
\(69\) 0 0
\(70\) −2.45042 −0.292882
\(71\) 8.91999 1.05861 0.529304 0.848432i \(-0.322453\pi\)
0.529304 + 0.848432i \(0.322453\pi\)
\(72\) 0 0
\(73\) 12.3019 1.43983 0.719915 0.694062i \(-0.244181\pi\)
0.719915 + 0.694062i \(0.244181\pi\)
\(74\) −15.9891 −1.85869
\(75\) 0 0
\(76\) −4.25371 −0.487934
\(77\) −3.51371 −0.400424
\(78\) 0 0
\(79\) 3.05893 0.344156 0.172078 0.985083i \(-0.444952\pi\)
0.172078 + 0.985083i \(0.444952\pi\)
\(80\) 6.89323 0.770687
\(81\) 0 0
\(82\) −2.78142 −0.307156
\(83\) −4.04869 −0.444401 −0.222201 0.975001i \(-0.571324\pi\)
−0.222201 + 0.975001i \(0.571324\pi\)
\(84\) 0 0
\(85\) −6.48345 −0.703229
\(86\) −3.82719 −0.412696
\(87\) 0 0
\(88\) 5.37664 0.573152
\(89\) 11.2427 1.19173 0.595864 0.803085i \(-0.296810\pi\)
0.595864 + 0.803085i \(0.296810\pi\)
\(90\) 0 0
\(91\) 4.71315 0.494072
\(92\) 2.27184 0.236856
\(93\) 0 0
\(94\) 22.9952 2.37178
\(95\) 5.18189 0.531650
\(96\) 0 0
\(97\) −8.60399 −0.873603 −0.436802 0.899558i \(-0.643889\pi\)
−0.436802 + 0.899558i \(0.643889\pi\)
\(98\) 1.77085 0.178883
\(99\) 0 0
\(100\) −3.50449 −0.350449
\(101\) 12.8002 1.27366 0.636832 0.771003i \(-0.280245\pi\)
0.636832 + 0.771003i \(0.280245\pi\)
\(102\) 0 0
\(103\) −15.8265 −1.55943 −0.779715 0.626134i \(-0.784636\pi\)
−0.779715 + 0.626134i \(0.784636\pi\)
\(104\) −7.21201 −0.707196
\(105\) 0 0
\(106\) 18.9750 1.84301
\(107\) −4.31000 −0.416663 −0.208332 0.978058i \(-0.566803\pi\)
−0.208332 + 0.978058i \(0.566803\pi\)
\(108\) 0 0
\(109\) −4.97624 −0.476638 −0.238319 0.971187i \(-0.576596\pi\)
−0.238319 + 0.971187i \(0.576596\pi\)
\(110\) 8.61008 0.820939
\(111\) 0 0
\(112\) −4.98153 −0.470710
\(113\) −3.01373 −0.283508 −0.141754 0.989902i \(-0.545274\pi\)
−0.141754 + 0.989902i \(0.545274\pi\)
\(114\) 0 0
\(115\) −2.76757 −0.258077
\(116\) 4.96403 0.460899
\(117\) 0 0
\(118\) 1.41915 0.130644
\(119\) 4.68539 0.429509
\(120\) 0 0
\(121\) 1.34616 0.122378
\(122\) 5.50542 0.498437
\(123\) 0 0
\(124\) −0.994988 −0.0893526
\(125\) 11.1880 1.00068
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 11.0990 0.981020
\(129\) 0 0
\(130\) −11.5492 −1.01293
\(131\) 1.80215 0.157454 0.0787271 0.996896i \(-0.474914\pi\)
0.0787271 + 0.996896i \(0.474914\pi\)
\(132\) 0 0
\(133\) −3.74479 −0.324715
\(134\) 11.7449 1.01460
\(135\) 0 0
\(136\) −7.16954 −0.614783
\(137\) −8.12738 −0.694369 −0.347184 0.937797i \(-0.612862\pi\)
−0.347184 + 0.937797i \(0.612862\pi\)
\(138\) 0 0
\(139\) 17.8232 1.51174 0.755871 0.654720i \(-0.227213\pi\)
0.755871 + 0.654720i \(0.227213\pi\)
\(140\) −1.57181 −0.132842
\(141\) 0 0
\(142\) 15.7959 1.32557
\(143\) −16.5606 −1.38487
\(144\) 0 0
\(145\) −6.04721 −0.502193
\(146\) 21.7848 1.80292
\(147\) 0 0
\(148\) −10.2561 −0.843045
\(149\) −7.44846 −0.610201 −0.305101 0.952320i \(-0.598690\pi\)
−0.305101 + 0.952320i \(0.598690\pi\)
\(150\) 0 0
\(151\) −5.07938 −0.413354 −0.206677 0.978409i \(-0.566265\pi\)
−0.206677 + 0.978409i \(0.566265\pi\)
\(152\) 5.73024 0.464784
\(153\) 0 0
\(154\) −6.22224 −0.501403
\(155\) 1.21210 0.0973581
\(156\) 0 0
\(157\) 1.60558 0.128139 0.0640695 0.997945i \(-0.479592\pi\)
0.0640695 + 0.997945i \(0.479592\pi\)
\(158\) 5.41689 0.430945
\(159\) 0 0
\(160\) 7.97204 0.630245
\(161\) 2.00004 0.157625
\(162\) 0 0
\(163\) 16.6976 1.30786 0.653928 0.756557i \(-0.273120\pi\)
0.653928 + 0.756557i \(0.273120\pi\)
\(164\) −1.78413 −0.139317
\(165\) 0 0
\(166\) −7.16961 −0.556469
\(167\) 18.4120 1.42477 0.712383 0.701791i \(-0.247616\pi\)
0.712383 + 0.701791i \(0.247616\pi\)
\(168\) 0 0
\(169\) 9.21376 0.708750
\(170\) −11.4812 −0.880567
\(171\) 0 0
\(172\) −2.45493 −0.187187
\(173\) −24.4792 −1.86112 −0.930560 0.366138i \(-0.880680\pi\)
−0.930560 + 0.366138i \(0.880680\pi\)
\(174\) 0 0
\(175\) −3.08521 −0.233220
\(176\) 17.5037 1.31939
\(177\) 0 0
\(178\) 19.9092 1.49226
\(179\) −8.54042 −0.638341 −0.319171 0.947697i \(-0.603404\pi\)
−0.319171 + 0.947697i \(0.603404\pi\)
\(180\) 0 0
\(181\) −12.2354 −0.909453 −0.454726 0.890631i \(-0.650263\pi\)
−0.454726 + 0.890631i \(0.650263\pi\)
\(182\) 8.34626 0.618666
\(183\) 0 0
\(184\) −3.06043 −0.225618
\(185\) 12.4940 0.918578
\(186\) 0 0
\(187\) −16.4631 −1.20390
\(188\) 14.7502 1.07577
\(189\) 0 0
\(190\) 9.17633 0.665721
\(191\) 23.6641 1.71227 0.856137 0.516749i \(-0.172858\pi\)
0.856137 + 0.516749i \(0.172858\pi\)
\(192\) 0 0
\(193\) 19.3057 1.38965 0.694827 0.719177i \(-0.255481\pi\)
0.694827 + 0.719177i \(0.255481\pi\)
\(194\) −15.2364 −1.09391
\(195\) 0 0
\(196\) 1.13590 0.0811357
\(197\) 15.5858 1.11044 0.555222 0.831702i \(-0.312633\pi\)
0.555222 + 0.831702i \(0.312633\pi\)
\(198\) 0 0
\(199\) 8.01019 0.567827 0.283914 0.958850i \(-0.408367\pi\)
0.283914 + 0.958850i \(0.408367\pi\)
\(200\) 4.72096 0.333822
\(201\) 0 0
\(202\) 22.6671 1.59485
\(203\) 4.37013 0.306723
\(204\) 0 0
\(205\) 2.17343 0.151799
\(206\) −28.0263 −1.95269
\(207\) 0 0
\(208\) −23.4787 −1.62795
\(209\) 13.1581 0.910166
\(210\) 0 0
\(211\) 28.6873 1.97492 0.987458 0.157881i \(-0.0504663\pi\)
0.987458 + 0.157881i \(0.0504663\pi\)
\(212\) 12.1714 0.835934
\(213\) 0 0
\(214\) −7.63235 −0.521736
\(215\) 2.99060 0.203958
\(216\) 0 0
\(217\) −0.875947 −0.0594632
\(218\) −8.81217 −0.596835
\(219\) 0 0
\(220\) 5.52289 0.372353
\(221\) 22.0829 1.48546
\(222\) 0 0
\(223\) 20.1324 1.34817 0.674083 0.738656i \(-0.264539\pi\)
0.674083 + 0.738656i \(0.264539\pi\)
\(224\) −5.76115 −0.384933
\(225\) 0 0
\(226\) −5.33685 −0.355002
\(227\) 17.6437 1.17106 0.585528 0.810652i \(-0.300887\pi\)
0.585528 + 0.810652i \(0.300887\pi\)
\(228\) 0 0
\(229\) −17.9149 −1.18385 −0.591925 0.805993i \(-0.701632\pi\)
−0.591925 + 0.805993i \(0.701632\pi\)
\(230\) −4.90094 −0.323158
\(231\) 0 0
\(232\) −6.68713 −0.439032
\(233\) 16.1065 1.05517 0.527585 0.849502i \(-0.323098\pi\)
0.527585 + 0.849502i \(0.323098\pi\)
\(234\) 0 0
\(235\) −17.9687 −1.17215
\(236\) 0.910308 0.0592560
\(237\) 0 0
\(238\) 8.29711 0.537822
\(239\) 1.89730 0.122726 0.0613631 0.998116i \(-0.480455\pi\)
0.0613631 + 0.998116i \(0.480455\pi\)
\(240\) 0 0
\(241\) 2.23972 0.144273 0.0721365 0.997395i \(-0.477018\pi\)
0.0721365 + 0.997395i \(0.477018\pi\)
\(242\) 2.38385 0.153240
\(243\) 0 0
\(244\) 3.53142 0.226076
\(245\) −1.38376 −0.0884050
\(246\) 0 0
\(247\) −17.6498 −1.12303
\(248\) 1.34037 0.0851133
\(249\) 0 0
\(250\) 19.8122 1.25303
\(251\) 6.80187 0.429330 0.214665 0.976688i \(-0.431134\pi\)
0.214665 + 0.976688i \(0.431134\pi\)
\(252\) 0 0
\(253\) −7.02755 −0.441818
\(254\) 1.77085 0.111113
\(255\) 0 0
\(256\) 20.1327 1.25829
\(257\) 19.0414 1.18777 0.593886 0.804549i \(-0.297593\pi\)
0.593886 + 0.804549i \(0.297593\pi\)
\(258\) 0 0
\(259\) −9.02904 −0.561037
\(260\) −7.40817 −0.459435
\(261\) 0 0
\(262\) 3.19132 0.197161
\(263\) 18.7401 1.15556 0.577782 0.816191i \(-0.303918\pi\)
0.577782 + 0.816191i \(0.303918\pi\)
\(264\) 0 0
\(265\) −14.8272 −0.910829
\(266\) −6.63146 −0.406601
\(267\) 0 0
\(268\) 7.53369 0.460193
\(269\) 8.31015 0.506679 0.253339 0.967377i \(-0.418471\pi\)
0.253339 + 0.967377i \(0.418471\pi\)
\(270\) 0 0
\(271\) 8.07002 0.490219 0.245110 0.969495i \(-0.421176\pi\)
0.245110 + 0.969495i \(0.421176\pi\)
\(272\) −23.3404 −1.41522
\(273\) 0 0
\(274\) −14.3923 −0.869473
\(275\) 10.8406 0.653710
\(276\) 0 0
\(277\) 1.87325 0.112553 0.0562764 0.998415i \(-0.482077\pi\)
0.0562764 + 0.998415i \(0.482077\pi\)
\(278\) 31.5621 1.89297
\(279\) 0 0
\(280\) 2.11741 0.126540
\(281\) −19.1711 −1.14365 −0.571825 0.820376i \(-0.693764\pi\)
−0.571825 + 0.820376i \(0.693764\pi\)
\(282\) 0 0
\(283\) −8.16883 −0.485587 −0.242793 0.970078i \(-0.578064\pi\)
−0.242793 + 0.970078i \(0.578064\pi\)
\(284\) 10.1322 0.601236
\(285\) 0 0
\(286\) −29.3264 −1.73410
\(287\) −1.57067 −0.0927138
\(288\) 0 0
\(289\) 4.95289 0.291347
\(290\) −10.7087 −0.628835
\(291\) 0 0
\(292\) 13.9737 0.817751
\(293\) −2.53599 −0.148154 −0.0740771 0.997253i \(-0.523601\pi\)
−0.0740771 + 0.997253i \(0.523601\pi\)
\(294\) 0 0
\(295\) −1.10894 −0.0645650
\(296\) 13.8161 0.803047
\(297\) 0 0
\(298\) −13.1901 −0.764081
\(299\) 9.42646 0.545146
\(300\) 0 0
\(301\) −2.16122 −0.124571
\(302\) −8.99481 −0.517593
\(303\) 0 0
\(304\) 18.6548 1.06993
\(305\) −4.30199 −0.246331
\(306\) 0 0
\(307\) 12.9910 0.741436 0.370718 0.928745i \(-0.379112\pi\)
0.370718 + 0.928745i \(0.379112\pi\)
\(308\) −3.99122 −0.227421
\(309\) 0 0
\(310\) 2.14644 0.121910
\(311\) −19.1662 −1.08682 −0.543408 0.839469i \(-0.682866\pi\)
−0.543408 + 0.839469i \(0.682866\pi\)
\(312\) 0 0
\(313\) −22.9716 −1.29843 −0.649216 0.760604i \(-0.724903\pi\)
−0.649216 + 0.760604i \(0.724903\pi\)
\(314\) 2.84323 0.160453
\(315\) 0 0
\(316\) 3.47464 0.195464
\(317\) −6.48402 −0.364179 −0.182089 0.983282i \(-0.558286\pi\)
−0.182089 + 0.983282i \(0.558286\pi\)
\(318\) 0 0
\(319\) −15.3554 −0.859737
\(320\) 0.330797 0.0184921
\(321\) 0 0
\(322\) 3.54176 0.197374
\(323\) −17.5458 −0.976276
\(324\) 0 0
\(325\) −14.5411 −0.806593
\(326\) 29.5689 1.63767
\(327\) 0 0
\(328\) 2.40343 0.132707
\(329\) 12.9854 0.715911
\(330\) 0 0
\(331\) 33.4592 1.83909 0.919543 0.392990i \(-0.128559\pi\)
0.919543 + 0.392990i \(0.128559\pi\)
\(332\) −4.59890 −0.252398
\(333\) 0 0
\(334\) 32.6049 1.78406
\(335\) −9.17757 −0.501424
\(336\) 0 0
\(337\) −21.8026 −1.18766 −0.593832 0.804589i \(-0.702386\pi\)
−0.593832 + 0.804589i \(0.702386\pi\)
\(338\) 16.3162 0.887482
\(339\) 0 0
\(340\) −7.36455 −0.399399
\(341\) 3.07783 0.166674
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 3.30708 0.178306
\(345\) 0 0
\(346\) −43.3490 −2.33045
\(347\) 36.6342 1.96663 0.983314 0.181918i \(-0.0582307\pi\)
0.983314 + 0.181918i \(0.0582307\pi\)
\(348\) 0 0
\(349\) −13.6984 −0.733256 −0.366628 0.930368i \(-0.619488\pi\)
−0.366628 + 0.930368i \(0.619488\pi\)
\(350\) −5.46344 −0.292033
\(351\) 0 0
\(352\) 20.2430 1.07896
\(353\) 28.7738 1.53148 0.765738 0.643153i \(-0.222374\pi\)
0.765738 + 0.643153i \(0.222374\pi\)
\(354\) 0 0
\(355\) −12.3431 −0.655104
\(356\) 12.7706 0.676842
\(357\) 0 0
\(358\) −15.1238 −0.799317
\(359\) −32.9067 −1.73675 −0.868376 0.495907i \(-0.834836\pi\)
−0.868376 + 0.495907i \(0.834836\pi\)
\(360\) 0 0
\(361\) −4.97653 −0.261922
\(362\) −21.6671 −1.13880
\(363\) 0 0
\(364\) 5.35366 0.280608
\(365\) −17.0229 −0.891018
\(366\) 0 0
\(367\) 3.44086 0.179611 0.0898057 0.995959i \(-0.471375\pi\)
0.0898057 + 0.995959i \(0.471375\pi\)
\(368\) −9.96324 −0.519370
\(369\) 0 0
\(370\) 22.1250 1.15022
\(371\) 10.7152 0.556305
\(372\) 0 0
\(373\) −16.1404 −0.835719 −0.417859 0.908512i \(-0.637220\pi\)
−0.417859 + 0.908512i \(0.637220\pi\)
\(374\) −29.1537 −1.50750
\(375\) 0 0
\(376\) −19.8702 −1.02473
\(377\) 20.5971 1.06080
\(378\) 0 0
\(379\) −7.03351 −0.361287 −0.180644 0.983549i \(-0.557818\pi\)
−0.180644 + 0.983549i \(0.557818\pi\)
\(380\) 5.88610 0.301951
\(381\) 0 0
\(382\) 41.9055 2.14407
\(383\) −5.54087 −0.283125 −0.141563 0.989929i \(-0.545213\pi\)
−0.141563 + 0.989929i \(0.545213\pi\)
\(384\) 0 0
\(385\) 4.86212 0.247797
\(386\) 34.1874 1.74009
\(387\) 0 0
\(388\) −9.77328 −0.496163
\(389\) −9.88826 −0.501354 −0.250677 0.968071i \(-0.580653\pi\)
−0.250677 + 0.968071i \(0.580653\pi\)
\(390\) 0 0
\(391\) 9.37095 0.473909
\(392\) −1.53019 −0.0772862
\(393\) 0 0
\(394\) 27.6001 1.39047
\(395\) −4.23282 −0.212976
\(396\) 0 0
\(397\) −32.5678 −1.63453 −0.817265 0.576262i \(-0.804511\pi\)
−0.817265 + 0.576262i \(0.804511\pi\)
\(398\) 14.1848 0.711021
\(399\) 0 0
\(400\) 15.3691 0.768455
\(401\) −0.767983 −0.0383512 −0.0191756 0.999816i \(-0.506104\pi\)
−0.0191756 + 0.999816i \(0.506104\pi\)
\(402\) 0 0
\(403\) −4.12847 −0.205654
\(404\) 14.5397 0.723377
\(405\) 0 0
\(406\) 7.73884 0.384072
\(407\) 31.7254 1.57257
\(408\) 0 0
\(409\) 13.7626 0.680517 0.340258 0.940332i \(-0.389485\pi\)
0.340258 + 0.940332i \(0.389485\pi\)
\(410\) 3.84881 0.190079
\(411\) 0 0
\(412\) −17.9773 −0.885679
\(413\) 0.801398 0.0394342
\(414\) 0 0
\(415\) 5.60240 0.275011
\(416\) −27.1532 −1.33129
\(417\) 0 0
\(418\) 23.3010 1.13969
\(419\) −25.5079 −1.24614 −0.623072 0.782165i \(-0.714116\pi\)
−0.623072 + 0.782165i \(0.714116\pi\)
\(420\) 0 0
\(421\) 25.0885 1.22274 0.611370 0.791345i \(-0.290619\pi\)
0.611370 + 0.791345i \(0.290619\pi\)
\(422\) 50.8009 2.47295
\(423\) 0 0
\(424\) −16.3963 −0.796273
\(425\) −14.4554 −0.701192
\(426\) 0 0
\(427\) 3.10892 0.150451
\(428\) −4.89572 −0.236644
\(429\) 0 0
\(430\) 5.29590 0.255391
\(431\) 1.42166 0.0684788 0.0342394 0.999414i \(-0.489099\pi\)
0.0342394 + 0.999414i \(0.489099\pi\)
\(432\) 0 0
\(433\) −0.288528 −0.0138658 −0.00693288 0.999976i \(-0.502207\pi\)
−0.00693288 + 0.999976i \(0.502207\pi\)
\(434\) −1.55117 −0.0744585
\(435\) 0 0
\(436\) −5.65251 −0.270706
\(437\) −7.48972 −0.358282
\(438\) 0 0
\(439\) 5.66246 0.270254 0.135127 0.990828i \(-0.456856\pi\)
0.135127 + 0.990828i \(0.456856\pi\)
\(440\) −7.43997 −0.354687
\(441\) 0 0
\(442\) 39.1055 1.86006
\(443\) 35.1768 1.67130 0.835650 0.549263i \(-0.185091\pi\)
0.835650 + 0.549263i \(0.185091\pi\)
\(444\) 0 0
\(445\) −15.5572 −0.737483
\(446\) 35.6514 1.68814
\(447\) 0 0
\(448\) −0.239057 −0.0112944
\(449\) 10.2609 0.484244 0.242122 0.970246i \(-0.422157\pi\)
0.242122 + 0.970246i \(0.422157\pi\)
\(450\) 0 0
\(451\) 5.51889 0.259874
\(452\) −3.42329 −0.161018
\(453\) 0 0
\(454\) 31.2444 1.46637
\(455\) −6.52185 −0.305749
\(456\) 0 0
\(457\) 26.8801 1.25740 0.628700 0.777648i \(-0.283587\pi\)
0.628700 + 0.777648i \(0.283587\pi\)
\(458\) −31.7246 −1.48239
\(459\) 0 0
\(460\) −3.14368 −0.146575
\(461\) −34.5198 −1.60775 −0.803873 0.594800i \(-0.797231\pi\)
−0.803873 + 0.594800i \(0.797231\pi\)
\(462\) 0 0
\(463\) 23.9679 1.11388 0.556941 0.830552i \(-0.311975\pi\)
0.556941 + 0.830552i \(0.311975\pi\)
\(464\) −21.7700 −1.01065
\(465\) 0 0
\(466\) 28.5221 1.32126
\(467\) −32.7795 −1.51686 −0.758428 0.651757i \(-0.774032\pi\)
−0.758428 + 0.651757i \(0.774032\pi\)
\(468\) 0 0
\(469\) 6.63235 0.306253
\(470\) −31.8198 −1.46774
\(471\) 0 0
\(472\) −1.22629 −0.0564446
\(473\) 7.59390 0.349168
\(474\) 0 0
\(475\) 11.5535 0.530110
\(476\) 5.32214 0.243940
\(477\) 0 0
\(478\) 3.35983 0.153675
\(479\) −6.54768 −0.299171 −0.149586 0.988749i \(-0.547794\pi\)
−0.149586 + 0.988749i \(0.547794\pi\)
\(480\) 0 0
\(481\) −42.5552 −1.94035
\(482\) 3.96620 0.180656
\(483\) 0 0
\(484\) 1.52911 0.0695048
\(485\) 11.9058 0.540617
\(486\) 0 0
\(487\) −18.2161 −0.825451 −0.412726 0.910855i \(-0.635423\pi\)
−0.412726 + 0.910855i \(0.635423\pi\)
\(488\) −4.75723 −0.215350
\(489\) 0 0
\(490\) −2.45042 −0.110699
\(491\) −43.7839 −1.97594 −0.987969 0.154650i \(-0.950575\pi\)
−0.987969 + 0.154650i \(0.950575\pi\)
\(492\) 0 0
\(493\) 20.4758 0.922183
\(494\) −31.2550 −1.40623
\(495\) 0 0
\(496\) 4.36356 0.195930
\(497\) 8.91999 0.400116
\(498\) 0 0
\(499\) 11.9415 0.534574 0.267287 0.963617i \(-0.413873\pi\)
0.267287 + 0.963617i \(0.413873\pi\)
\(500\) 12.7084 0.568338
\(501\) 0 0
\(502\) 12.0451 0.537598
\(503\) −12.6088 −0.562197 −0.281098 0.959679i \(-0.590699\pi\)
−0.281098 + 0.959679i \(0.590699\pi\)
\(504\) 0 0
\(505\) −17.7123 −0.788188
\(506\) −12.4447 −0.553235
\(507\) 0 0
\(508\) 1.13590 0.0503974
\(509\) −7.41939 −0.328859 −0.164429 0.986389i \(-0.552578\pi\)
−0.164429 + 0.986389i \(0.552578\pi\)
\(510\) 0 0
\(511\) 12.3019 0.544205
\(512\) 13.4540 0.594588
\(513\) 0 0
\(514\) 33.7195 1.48730
\(515\) 21.9000 0.965031
\(516\) 0 0
\(517\) −45.6271 −2.00668
\(518\) −15.9891 −0.702519
\(519\) 0 0
\(520\) 9.97967 0.437638
\(521\) −15.8190 −0.693044 −0.346522 0.938042i \(-0.612637\pi\)
−0.346522 + 0.938042i \(0.612637\pi\)
\(522\) 0 0
\(523\) −17.9670 −0.785643 −0.392821 0.919615i \(-0.628501\pi\)
−0.392821 + 0.919615i \(0.628501\pi\)
\(524\) 2.04706 0.0894261
\(525\) 0 0
\(526\) 33.1858 1.44697
\(527\) −4.10416 −0.178780
\(528\) 0 0
\(529\) −18.9999 −0.826081
\(530\) −26.2567 −1.14052
\(531\) 0 0
\(532\) −4.25371 −0.184422
\(533\) −7.40281 −0.320651
\(534\) 0 0
\(535\) 5.96399 0.257846
\(536\) −10.1488 −0.438359
\(537\) 0 0
\(538\) 14.7160 0.634452
\(539\) −3.51371 −0.151346
\(540\) 0 0
\(541\) −23.0200 −0.989706 −0.494853 0.868977i \(-0.664778\pi\)
−0.494853 + 0.868977i \(0.664778\pi\)
\(542\) 14.2908 0.613842
\(543\) 0 0
\(544\) −26.9933 −1.15733
\(545\) 6.88591 0.294960
\(546\) 0 0
\(547\) 29.1769 1.24752 0.623758 0.781617i \(-0.285605\pi\)
0.623758 + 0.781617i \(0.285605\pi\)
\(548\) −9.23188 −0.394367
\(549\) 0 0
\(550\) 19.1970 0.818561
\(551\) −16.3652 −0.697183
\(552\) 0 0
\(553\) 3.05893 0.130079
\(554\) 3.31724 0.140936
\(555\) 0 0
\(556\) 20.2454 0.858594
\(557\) −35.5947 −1.50819 −0.754097 0.656763i \(-0.771925\pi\)
−0.754097 + 0.656763i \(0.771925\pi\)
\(558\) 0 0
\(559\) −10.1861 −0.430828
\(560\) 6.89323 0.291292
\(561\) 0 0
\(562\) −33.9490 −1.43205
\(563\) 16.3319 0.688307 0.344154 0.938913i \(-0.388166\pi\)
0.344154 + 0.938913i \(0.388166\pi\)
\(564\) 0 0
\(565\) 4.17027 0.175445
\(566\) −14.4658 −0.608041
\(567\) 0 0
\(568\) −13.6493 −0.572711
\(569\) −39.0238 −1.63596 −0.817981 0.575245i \(-0.804907\pi\)
−0.817981 + 0.575245i \(0.804907\pi\)
\(570\) 0 0
\(571\) −13.5080 −0.565291 −0.282646 0.959224i \(-0.591212\pi\)
−0.282646 + 0.959224i \(0.591212\pi\)
\(572\) −18.8112 −0.786537
\(573\) 0 0
\(574\) −2.78142 −0.116094
\(575\) −6.17054 −0.257329
\(576\) 0 0
\(577\) 23.3145 0.970595 0.485298 0.874349i \(-0.338711\pi\)
0.485298 + 0.874349i \(0.338711\pi\)
\(578\) 8.77082 0.364818
\(579\) 0 0
\(580\) −6.86902 −0.285221
\(581\) −4.04869 −0.167968
\(582\) 0 0
\(583\) −37.6501 −1.55931
\(584\) −18.8243 −0.778953
\(585\) 0 0
\(586\) −4.49085 −0.185515
\(587\) −31.1722 −1.28661 −0.643307 0.765609i \(-0.722438\pi\)
−0.643307 + 0.765609i \(0.722438\pi\)
\(588\) 0 0
\(589\) 3.28024 0.135160
\(590\) −1.96376 −0.0808469
\(591\) 0 0
\(592\) 44.9785 1.84860
\(593\) 4.36484 0.179242 0.0896211 0.995976i \(-0.471434\pi\)
0.0896211 + 0.995976i \(0.471434\pi\)
\(594\) 0 0
\(595\) −6.48345 −0.265795
\(596\) −8.46070 −0.346564
\(597\) 0 0
\(598\) 16.6928 0.682620
\(599\) 11.6431 0.475724 0.237862 0.971299i \(-0.423553\pi\)
0.237862 + 0.971299i \(0.423553\pi\)
\(600\) 0 0
\(601\) −45.2104 −1.84417 −0.922086 0.386986i \(-0.873516\pi\)
−0.922086 + 0.386986i \(0.873516\pi\)
\(602\) −3.82719 −0.155985
\(603\) 0 0
\(604\) −5.76967 −0.234765
\(605\) −1.86276 −0.0757321
\(606\) 0 0
\(607\) −17.6142 −0.714938 −0.357469 0.933925i \(-0.616360\pi\)
−0.357469 + 0.933925i \(0.616360\pi\)
\(608\) 21.5743 0.874954
\(609\) 0 0
\(610\) −7.61817 −0.308451
\(611\) 61.2023 2.47598
\(612\) 0 0
\(613\) −3.47398 −0.140313 −0.0701563 0.997536i \(-0.522350\pi\)
−0.0701563 + 0.997536i \(0.522350\pi\)
\(614\) 23.0051 0.928410
\(615\) 0 0
\(616\) 5.37664 0.216631
\(617\) 12.7145 0.511867 0.255934 0.966694i \(-0.417617\pi\)
0.255934 + 0.966694i \(0.417617\pi\)
\(618\) 0 0
\(619\) −17.1760 −0.690360 −0.345180 0.938536i \(-0.612182\pi\)
−0.345180 + 0.938536i \(0.612182\pi\)
\(620\) 1.37682 0.0552945
\(621\) 0 0
\(622\) −33.9404 −1.36089
\(623\) 11.2427 0.450431
\(624\) 0 0
\(625\) −0.0553790 −0.00221516
\(626\) −40.6792 −1.62587
\(627\) 0 0
\(628\) 1.82378 0.0727766
\(629\) −42.3046 −1.68679
\(630\) 0 0
\(631\) 15.7815 0.628252 0.314126 0.949381i \(-0.398289\pi\)
0.314126 + 0.949381i \(0.398289\pi\)
\(632\) −4.68074 −0.186190
\(633\) 0 0
\(634\) −11.4822 −0.456017
\(635\) −1.38376 −0.0549128
\(636\) 0 0
\(637\) 4.71315 0.186742
\(638\) −27.1920 −1.07654
\(639\) 0 0
\(640\) −15.3583 −0.607090
\(641\) −0.538037 −0.0212512 −0.0106256 0.999944i \(-0.503382\pi\)
−0.0106256 + 0.999944i \(0.503382\pi\)
\(642\) 0 0
\(643\) −24.7771 −0.977112 −0.488556 0.872532i \(-0.662476\pi\)
−0.488556 + 0.872532i \(0.662476\pi\)
\(644\) 2.27184 0.0895231
\(645\) 0 0
\(646\) −31.0710 −1.22247
\(647\) 14.8933 0.585517 0.292758 0.956186i \(-0.405427\pi\)
0.292758 + 0.956186i \(0.405427\pi\)
\(648\) 0 0
\(649\) −2.81588 −0.110533
\(650\) −25.7500 −1.01000
\(651\) 0 0
\(652\) 18.9668 0.742796
\(653\) 5.43582 0.212720 0.106360 0.994328i \(-0.466080\pi\)
0.106360 + 0.994328i \(0.466080\pi\)
\(654\) 0 0
\(655\) −2.49373 −0.0974382
\(656\) 7.82435 0.305490
\(657\) 0 0
\(658\) 22.9952 0.896448
\(659\) −11.5047 −0.448158 −0.224079 0.974571i \(-0.571937\pi\)
−0.224079 + 0.974571i \(0.571937\pi\)
\(660\) 0 0
\(661\) 3.46362 0.134719 0.0673596 0.997729i \(-0.478543\pi\)
0.0673596 + 0.997729i \(0.478543\pi\)
\(662\) 59.2512 2.30286
\(663\) 0 0
\(664\) 6.19526 0.240423
\(665\) 5.18189 0.200945
\(666\) 0 0
\(667\) 8.74043 0.338431
\(668\) 20.9142 0.809195
\(669\) 0 0
\(670\) −16.2521 −0.627872
\(671\) −10.9238 −0.421710
\(672\) 0 0
\(673\) −25.4769 −0.982063 −0.491032 0.871142i \(-0.663380\pi\)
−0.491032 + 0.871142i \(0.663380\pi\)
\(674\) −38.6091 −1.48717
\(675\) 0 0
\(676\) 10.4659 0.402535
\(677\) 13.2125 0.507799 0.253900 0.967231i \(-0.418287\pi\)
0.253900 + 0.967231i \(0.418287\pi\)
\(678\) 0 0
\(679\) −8.60399 −0.330191
\(680\) 9.92090 0.380449
\(681\) 0 0
\(682\) 5.45036 0.208705
\(683\) 31.7115 1.21341 0.606704 0.794928i \(-0.292491\pi\)
0.606704 + 0.794928i \(0.292491\pi\)
\(684\) 0 0
\(685\) 11.2463 0.429700
\(686\) 1.77085 0.0676113
\(687\) 0 0
\(688\) 10.7662 0.410457
\(689\) 50.5023 1.92398
\(690\) 0 0
\(691\) −31.5039 −1.19847 −0.599233 0.800575i \(-0.704528\pi\)
−0.599233 + 0.800575i \(0.704528\pi\)
\(692\) −27.8059 −1.05702
\(693\) 0 0
\(694\) 64.8736 2.46257
\(695\) −24.6630 −0.935520
\(696\) 0 0
\(697\) −7.35921 −0.278750
\(698\) −24.2577 −0.918168
\(699\) 0 0
\(700\) −3.50449 −0.132457
\(701\) −0.903370 −0.0341198 −0.0170599 0.999854i \(-0.505431\pi\)
−0.0170599 + 0.999854i \(0.505431\pi\)
\(702\) 0 0
\(703\) 33.8119 1.27524
\(704\) 0.839978 0.0316579
\(705\) 0 0
\(706\) 50.9540 1.91768
\(707\) 12.8002 0.481399
\(708\) 0 0
\(709\) 46.7863 1.75710 0.878549 0.477653i \(-0.158512\pi\)
0.878549 + 0.477653i \(0.158512\pi\)
\(710\) −21.8578 −0.820307
\(711\) 0 0
\(712\) −17.2035 −0.644729
\(713\) −1.75193 −0.0656101
\(714\) 0 0
\(715\) 22.9159 0.857006
\(716\) −9.70106 −0.362546
\(717\) 0 0
\(718\) −58.2728 −2.17472
\(719\) −5.39158 −0.201072 −0.100536 0.994933i \(-0.532056\pi\)
−0.100536 + 0.994933i \(0.532056\pi\)
\(720\) 0 0
\(721\) −15.8265 −0.589409
\(722\) −8.81267 −0.327974
\(723\) 0 0
\(724\) −13.8982 −0.516524
\(725\) −13.4828 −0.500739
\(726\) 0 0
\(727\) −2.00859 −0.0744946 −0.0372473 0.999306i \(-0.511859\pi\)
−0.0372473 + 0.999306i \(0.511859\pi\)
\(728\) −7.21201 −0.267295
\(729\) 0 0
\(730\) −30.1449 −1.11571
\(731\) −10.1262 −0.374530
\(732\) 0 0
\(733\) −51.9571 −1.91908 −0.959540 0.281571i \(-0.909144\pi\)
−0.959540 + 0.281571i \(0.909144\pi\)
\(734\) 6.09324 0.224906
\(735\) 0 0
\(736\) −11.5225 −0.424725
\(737\) −23.3042 −0.858420
\(738\) 0 0
\(739\) 49.8689 1.83446 0.917229 0.398360i \(-0.130421\pi\)
0.917229 + 0.398360i \(0.130421\pi\)
\(740\) 14.1919 0.521706
\(741\) 0 0
\(742\) 18.9750 0.696593
\(743\) 37.0545 1.35940 0.679699 0.733491i \(-0.262110\pi\)
0.679699 + 0.733491i \(0.262110\pi\)
\(744\) 0 0
\(745\) 10.3069 0.377614
\(746\) −28.5822 −1.04647
\(747\) 0 0
\(748\) −18.7004 −0.683756
\(749\) −4.31000 −0.157484
\(750\) 0 0
\(751\) 17.8645 0.651886 0.325943 0.945389i \(-0.394318\pi\)
0.325943 + 0.945389i \(0.394318\pi\)
\(752\) −64.6874 −2.35891
\(753\) 0 0
\(754\) 36.4743 1.32832
\(755\) 7.02864 0.255798
\(756\) 0 0
\(757\) 18.7291 0.680722 0.340361 0.940295i \(-0.389451\pi\)
0.340361 + 0.940295i \(0.389451\pi\)
\(758\) −12.4553 −0.452396
\(759\) 0 0
\(760\) −7.92927 −0.287625
\(761\) 36.5839 1.32616 0.663082 0.748546i \(-0.269248\pi\)
0.663082 + 0.748546i \(0.269248\pi\)
\(762\) 0 0
\(763\) −4.97624 −0.180152
\(764\) 26.8800 0.972486
\(765\) 0 0
\(766\) −9.81204 −0.354523
\(767\) 3.77711 0.136383
\(768\) 0 0
\(769\) 24.9186 0.898589 0.449295 0.893384i \(-0.351675\pi\)
0.449295 + 0.893384i \(0.351675\pi\)
\(770\) 8.61008 0.310286
\(771\) 0 0
\(772\) 21.9293 0.789254
\(773\) −30.9862 −1.11450 −0.557249 0.830346i \(-0.688143\pi\)
−0.557249 + 0.830346i \(0.688143\pi\)
\(774\) 0 0
\(775\) 2.70249 0.0970761
\(776\) 13.1657 0.472623
\(777\) 0 0
\(778\) −17.5106 −0.627785
\(779\) 5.88184 0.210739
\(780\) 0 0
\(781\) −31.3423 −1.12151
\(782\) 16.5945 0.593419
\(783\) 0 0
\(784\) −4.98153 −0.177912
\(785\) −2.22173 −0.0792970
\(786\) 0 0
\(787\) 21.0310 0.749675 0.374837 0.927091i \(-0.377699\pi\)
0.374837 + 0.927091i \(0.377699\pi\)
\(788\) 17.7039 0.630676
\(789\) 0 0
\(790\) −7.49567 −0.266684
\(791\) −3.01373 −0.107156
\(792\) 0 0
\(793\) 14.6528 0.520336
\(794\) −57.6726 −2.04672
\(795\) 0 0
\(796\) 9.09877 0.322497
\(797\) 37.2731 1.32028 0.660141 0.751142i \(-0.270496\pi\)
0.660141 + 0.751142i \(0.270496\pi\)
\(798\) 0 0
\(799\) 60.8419 2.15243
\(800\) 17.7744 0.628420
\(801\) 0 0
\(802\) −1.35998 −0.0480226
\(803\) −43.2254 −1.52539
\(804\) 0 0
\(805\) −2.76757 −0.0975439
\(806\) −7.31089 −0.257515
\(807\) 0 0
\(808\) −19.5867 −0.689056
\(809\) 16.9337 0.595357 0.297678 0.954666i \(-0.403788\pi\)
0.297678 + 0.954666i \(0.403788\pi\)
\(810\) 0 0
\(811\) 20.6275 0.724329 0.362165 0.932114i \(-0.382038\pi\)
0.362165 + 0.932114i \(0.382038\pi\)
\(812\) 4.96403 0.174203
\(813\) 0 0
\(814\) 56.1809 1.96914
\(815\) −23.1054 −0.809347
\(816\) 0 0
\(817\) 8.09332 0.283149
\(818\) 24.3715 0.852128
\(819\) 0 0
\(820\) 2.46880 0.0862142
\(821\) −16.7244 −0.583685 −0.291842 0.956466i \(-0.594268\pi\)
−0.291842 + 0.956466i \(0.594268\pi\)
\(822\) 0 0
\(823\) −4.86071 −0.169434 −0.0847168 0.996405i \(-0.526999\pi\)
−0.0847168 + 0.996405i \(0.526999\pi\)
\(824\) 24.2175 0.843658
\(825\) 0 0
\(826\) 1.41915 0.0493787
\(827\) 37.6413 1.30892 0.654458 0.756098i \(-0.272897\pi\)
0.654458 + 0.756098i \(0.272897\pi\)
\(828\) 0 0
\(829\) −20.1585 −0.700133 −0.350067 0.936725i \(-0.613841\pi\)
−0.350067 + 0.936725i \(0.613841\pi\)
\(830\) 9.92100 0.344363
\(831\) 0 0
\(832\) −1.12671 −0.0390617
\(833\) 4.68539 0.162339
\(834\) 0 0
\(835\) −25.4778 −0.881695
\(836\) 14.9463 0.516929
\(837\) 0 0
\(838\) −45.1706 −1.56039
\(839\) −29.9945 −1.03553 −0.517763 0.855524i \(-0.673235\pi\)
−0.517763 + 0.855524i \(0.673235\pi\)
\(840\) 0 0
\(841\) −9.90193 −0.341446
\(842\) 44.4279 1.53109
\(843\) 0 0
\(844\) 32.5859 1.12165
\(845\) −12.7496 −0.438600
\(846\) 0 0
\(847\) 1.34616 0.0462547
\(848\) −53.3780 −1.83301
\(849\) 0 0
\(850\) −25.5984 −0.878017
\(851\) −18.0584 −0.619034
\(852\) 0 0
\(853\) −17.6458 −0.604182 −0.302091 0.953279i \(-0.597685\pi\)
−0.302091 + 0.953279i \(0.597685\pi\)
\(854\) 5.50542 0.188392
\(855\) 0 0
\(856\) 6.59511 0.225416
\(857\) 33.4988 1.14430 0.572149 0.820149i \(-0.306110\pi\)
0.572149 + 0.820149i \(0.306110\pi\)
\(858\) 0 0
\(859\) 3.95415 0.134914 0.0674569 0.997722i \(-0.478511\pi\)
0.0674569 + 0.997722i \(0.478511\pi\)
\(860\) 3.39703 0.115838
\(861\) 0 0
\(862\) 2.51754 0.0857476
\(863\) 28.8938 0.983557 0.491778 0.870720i \(-0.336347\pi\)
0.491778 + 0.870720i \(0.336347\pi\)
\(864\) 0 0
\(865\) 33.8733 1.15173
\(866\) −0.510938 −0.0173624
\(867\) 0 0
\(868\) −0.994988 −0.0337721
\(869\) −10.7482 −0.364607
\(870\) 0 0
\(871\) 31.2592 1.05918
\(872\) 7.61459 0.257863
\(873\) 0 0
\(874\) −13.2632 −0.448633
\(875\) 11.1880 0.378223
\(876\) 0 0
\(877\) −2.53706 −0.0856703 −0.0428352 0.999082i \(-0.513639\pi\)
−0.0428352 + 0.999082i \(0.513639\pi\)
\(878\) 10.0273 0.338407
\(879\) 0 0
\(880\) −24.2208 −0.816484
\(881\) −7.31984 −0.246612 −0.123306 0.992369i \(-0.539350\pi\)
−0.123306 + 0.992369i \(0.539350\pi\)
\(882\) 0 0
\(883\) −38.0071 −1.27904 −0.639521 0.768774i \(-0.720867\pi\)
−0.639521 + 0.768774i \(0.720867\pi\)
\(884\) 25.0840 0.843666
\(885\) 0 0
\(886\) 62.2927 2.09276
\(887\) 20.9072 0.701993 0.350997 0.936377i \(-0.385843\pi\)
0.350997 + 0.936377i \(0.385843\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −27.5495 −0.923460
\(891\) 0 0
\(892\) 22.8684 0.765691
\(893\) −48.6278 −1.62727
\(894\) 0 0
\(895\) 11.8179 0.395028
\(896\) 11.0990 0.370791
\(897\) 0 0
\(898\) 18.1706 0.606359
\(899\) −3.82801 −0.127671
\(900\) 0 0
\(901\) 50.2048 1.67257
\(902\) 9.77311 0.325409
\(903\) 0 0
\(904\) 4.61158 0.153379
\(905\) 16.9309 0.562801
\(906\) 0 0
\(907\) 26.8915 0.892918 0.446459 0.894804i \(-0.352685\pi\)
0.446459 + 0.894804i \(0.352685\pi\)
\(908\) 20.0415 0.665101
\(909\) 0 0
\(910\) −11.5492 −0.382852
\(911\) −39.7733 −1.31775 −0.658875 0.752253i \(-0.728967\pi\)
−0.658875 + 0.752253i \(0.728967\pi\)
\(912\) 0 0
\(913\) 14.2259 0.470809
\(914\) 47.6006 1.57449
\(915\) 0 0
\(916\) −20.3495 −0.672368
\(917\) 1.80215 0.0595121
\(918\) 0 0
\(919\) −13.4951 −0.445161 −0.222580 0.974914i \(-0.571448\pi\)
−0.222580 + 0.974914i \(0.571448\pi\)
\(920\) 4.23490 0.139620
\(921\) 0 0
\(922\) −61.1293 −2.01319
\(923\) 42.0412 1.38380
\(924\) 0 0
\(925\) 27.8565 0.915917
\(926\) 42.4435 1.39478
\(927\) 0 0
\(928\) −25.1770 −0.826476
\(929\) −19.7078 −0.646592 −0.323296 0.946298i \(-0.604791\pi\)
−0.323296 + 0.946298i \(0.604791\pi\)
\(930\) 0 0
\(931\) −3.74479 −0.122731
\(932\) 18.2953 0.599284
\(933\) 0 0
\(934\) −58.0475 −1.89937
\(935\) 22.7810 0.745017
\(936\) 0 0
\(937\) −2.82515 −0.0922935 −0.0461467 0.998935i \(-0.514694\pi\)
−0.0461467 + 0.998935i \(0.514694\pi\)
\(938\) 11.7449 0.383484
\(939\) 0 0
\(940\) −20.4107 −0.665722
\(941\) −7.68921 −0.250661 −0.125331 0.992115i \(-0.539999\pi\)
−0.125331 + 0.992115i \(0.539999\pi\)
\(942\) 0 0
\(943\) −3.14140 −0.102298
\(944\) −3.99219 −0.129935
\(945\) 0 0
\(946\) 13.4476 0.437220
\(947\) −38.9226 −1.26482 −0.632408 0.774636i \(-0.717933\pi\)
−0.632408 + 0.774636i \(0.717933\pi\)
\(948\) 0 0
\(949\) 57.9807 1.88213
\(950\) 20.4595 0.663793
\(951\) 0 0
\(952\) −7.16954 −0.232366
\(953\) 1.05657 0.0342257 0.0171129 0.999854i \(-0.494553\pi\)
0.0171129 + 0.999854i \(0.494553\pi\)
\(954\) 0 0
\(955\) −32.7454 −1.05962
\(956\) 2.15514 0.0697024
\(957\) 0 0
\(958\) −11.5949 −0.374616
\(959\) −8.12738 −0.262447
\(960\) 0 0
\(961\) −30.2327 −0.975249
\(962\) −75.3588 −2.42966
\(963\) 0 0
\(964\) 2.54410 0.0819399
\(965\) −26.7144 −0.859967
\(966\) 0 0
\(967\) −17.3565 −0.558148 −0.279074 0.960270i \(-0.590027\pi\)
−0.279074 + 0.960270i \(0.590027\pi\)
\(968\) −2.05988 −0.0662071
\(969\) 0 0
\(970\) 21.0834 0.676948
\(971\) −0.389374 −0.0124956 −0.00624780 0.999980i \(-0.501989\pi\)
−0.00624780 + 0.999980i \(0.501989\pi\)
\(972\) 0 0
\(973\) 17.8232 0.571385
\(974\) −32.2580 −1.03361
\(975\) 0 0
\(976\) −15.4872 −0.495732
\(977\) 44.1149 1.41136 0.705680 0.708531i \(-0.250642\pi\)
0.705680 + 0.708531i \(0.250642\pi\)
\(978\) 0 0
\(979\) −39.5037 −1.26254
\(980\) −1.57181 −0.0502096
\(981\) 0 0
\(982\) −77.5346 −2.47423
\(983\) 30.6578 0.977833 0.488917 0.872331i \(-0.337392\pi\)
0.488917 + 0.872331i \(0.337392\pi\)
\(984\) 0 0
\(985\) −21.5670 −0.687182
\(986\) 36.2595 1.15474
\(987\) 0 0
\(988\) −20.0484 −0.637823
\(989\) −4.32252 −0.137448
\(990\) 0 0
\(991\) 13.2935 0.422281 0.211140 0.977456i \(-0.432282\pi\)
0.211140 + 0.977456i \(0.432282\pi\)
\(992\) 5.04647 0.160225
\(993\) 0 0
\(994\) 15.7959 0.501017
\(995\) −11.0842 −0.351392
\(996\) 0 0
\(997\) −41.6510 −1.31910 −0.659551 0.751660i \(-0.729254\pi\)
−0.659551 + 0.751660i \(0.729254\pi\)
\(998\) 21.1465 0.669382
\(999\) 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 \(a_p\))