Properties

Label 8001.2.a.v.1.2
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 19
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: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.49323\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.49323 q^{2} +4.21621 q^{4} +0.262973 q^{5} +1.00000 q^{7} -5.52554 q^{8} +O(q^{10})\) \(q-2.49323 q^{2} +4.21621 q^{4} +0.262973 q^{5} +1.00000 q^{7} -5.52554 q^{8} -0.655653 q^{10} -3.55277 q^{11} -2.65719 q^{13} -2.49323 q^{14} +5.34403 q^{16} -7.62237 q^{17} -1.10257 q^{19} +1.10875 q^{20} +8.85789 q^{22} +3.50334 q^{23} -4.93085 q^{25} +6.62499 q^{26} +4.21621 q^{28} +4.14426 q^{29} +7.01796 q^{31} -2.27284 q^{32} +19.0043 q^{34} +0.262973 q^{35} -0.847404 q^{37} +2.74897 q^{38} -1.45307 q^{40} +8.88998 q^{41} -11.3921 q^{43} -14.9792 q^{44} -8.73465 q^{46} -8.26272 q^{47} +1.00000 q^{49} +12.2937 q^{50} -11.2033 q^{52} -4.21727 q^{53} -0.934282 q^{55} -5.52554 q^{56} -10.3326 q^{58} -13.5072 q^{59} +1.49849 q^{61} -17.4974 q^{62} -5.02134 q^{64} -0.698769 q^{65} -2.38846 q^{67} -32.1375 q^{68} -0.655653 q^{70} +9.51155 q^{71} -1.22482 q^{73} +2.11278 q^{74} -4.64869 q^{76} -3.55277 q^{77} +4.70270 q^{79} +1.40533 q^{80} -22.1648 q^{82} -3.89809 q^{83} -2.00448 q^{85} +28.4032 q^{86} +19.6310 q^{88} -6.98825 q^{89} -2.65719 q^{91} +14.7708 q^{92} +20.6009 q^{94} -0.289947 q^{95} -10.7226 q^{97} -2.49323 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + O(q^{10}) \) \( 19q - 4q^{2} + 22q^{4} - 5q^{5} + 19q^{7} - 9q^{8} + 9q^{11} + 24q^{13} - 4q^{14} + 20q^{16} - 17q^{17} + 23q^{19} - 5q^{20} - 3q^{22} + 17q^{23} + 38q^{25} - 28q^{26} + 22q^{28} - 2q^{29} + 16q^{31} - 17q^{32} + 29q^{34} - 5q^{35} + 56q^{37} - 2q^{38} - 13q^{40} + 7q^{41} + 19q^{43} + 29q^{44} + 10q^{46} - 25q^{47} + 19q^{49} + 9q^{50} + 16q^{52} - 18q^{53} + 10q^{55} - 9q^{56} + 31q^{58} - 11q^{59} + 26q^{61} - 26q^{62} + 45q^{64} - 27q^{65} + 24q^{67} - 14q^{68} + 32q^{71} + 51q^{73} + 12q^{76} + 9q^{77} + 30q^{79} + 30q^{80} - 52q^{82} - q^{83} + 44q^{85} + 24q^{86} - 30q^{88} - 5q^{89} + 24q^{91} + 88q^{92} + 7q^{94} + 24q^{95} + 5q^{97} - 4q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49323 −1.76298 −0.881491 0.472200i \(-0.843460\pi\)
−0.881491 + 0.472200i \(0.843460\pi\)
\(3\) 0 0
\(4\) 4.21621 2.10811
\(5\) 0.262973 0.117605 0.0588025 0.998270i \(-0.481272\pi\)
0.0588025 + 0.998270i \(0.481272\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −5.52554 −1.95357
\(9\) 0 0
\(10\) −0.655653 −0.207336
\(11\) −3.55277 −1.07120 −0.535601 0.844471i \(-0.679915\pi\)
−0.535601 + 0.844471i \(0.679915\pi\)
\(12\) 0 0
\(13\) −2.65719 −0.736972 −0.368486 0.929633i \(-0.620124\pi\)
−0.368486 + 0.929633i \(0.620124\pi\)
\(14\) −2.49323 −0.666345
\(15\) 0 0
\(16\) 5.34403 1.33601
\(17\) −7.62237 −1.84870 −0.924348 0.381551i \(-0.875390\pi\)
−0.924348 + 0.381551i \(0.875390\pi\)
\(18\) 0 0
\(19\) −1.10257 −0.252948 −0.126474 0.991970i \(-0.540366\pi\)
−0.126474 + 0.991970i \(0.540366\pi\)
\(20\) 1.10875 0.247924
\(21\) 0 0
\(22\) 8.85789 1.88851
\(23\) 3.50334 0.730497 0.365249 0.930910i \(-0.380984\pi\)
0.365249 + 0.930910i \(0.380984\pi\)
\(24\) 0 0
\(25\) −4.93085 −0.986169
\(26\) 6.62499 1.29927
\(27\) 0 0
\(28\) 4.21621 0.796790
\(29\) 4.14426 0.769570 0.384785 0.923006i \(-0.374276\pi\)
0.384785 + 0.923006i \(0.374276\pi\)
\(30\) 0 0
\(31\) 7.01796 1.26046 0.630231 0.776408i \(-0.282960\pi\)
0.630231 + 0.776408i \(0.282960\pi\)
\(32\) −2.27284 −0.401785
\(33\) 0 0
\(34\) 19.0043 3.25922
\(35\) 0.262973 0.0444505
\(36\) 0 0
\(37\) −0.847404 −0.139312 −0.0696562 0.997571i \(-0.522190\pi\)
−0.0696562 + 0.997571i \(0.522190\pi\)
\(38\) 2.74897 0.445942
\(39\) 0 0
\(40\) −1.45307 −0.229750
\(41\) 8.88998 1.38838 0.694191 0.719791i \(-0.255762\pi\)
0.694191 + 0.719791i \(0.255762\pi\)
\(42\) 0 0
\(43\) −11.3921 −1.73728 −0.868642 0.495441i \(-0.835006\pi\)
−0.868642 + 0.495441i \(0.835006\pi\)
\(44\) −14.9792 −2.25821
\(45\) 0 0
\(46\) −8.73465 −1.28785
\(47\) −8.26272 −1.20524 −0.602621 0.798028i \(-0.705877\pi\)
−0.602621 + 0.798028i \(0.705877\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 12.2937 1.73860
\(51\) 0 0
\(52\) −11.2033 −1.55362
\(53\) −4.21727 −0.579287 −0.289643 0.957135i \(-0.593537\pi\)
−0.289643 + 0.957135i \(0.593537\pi\)
\(54\) 0 0
\(55\) −0.934282 −0.125979
\(56\) −5.52554 −0.738381
\(57\) 0 0
\(58\) −10.3326 −1.35674
\(59\) −13.5072 −1.75849 −0.879244 0.476372i \(-0.841952\pi\)
−0.879244 + 0.476372i \(0.841952\pi\)
\(60\) 0 0
\(61\) 1.49849 0.191862 0.0959310 0.995388i \(-0.469417\pi\)
0.0959310 + 0.995388i \(0.469417\pi\)
\(62\) −17.4974 −2.22217
\(63\) 0 0
\(64\) −5.02134 −0.627667
\(65\) −0.698769 −0.0866716
\(66\) 0 0
\(67\) −2.38846 −0.291797 −0.145898 0.989300i \(-0.546607\pi\)
−0.145898 + 0.989300i \(0.546607\pi\)
\(68\) −32.1375 −3.89725
\(69\) 0 0
\(70\) −0.655653 −0.0783655
\(71\) 9.51155 1.12881 0.564407 0.825497i \(-0.309105\pi\)
0.564407 + 0.825497i \(0.309105\pi\)
\(72\) 0 0
\(73\) −1.22482 −0.143354 −0.0716771 0.997428i \(-0.522835\pi\)
−0.0716771 + 0.997428i \(0.522835\pi\)
\(74\) 2.11278 0.245605
\(75\) 0 0
\(76\) −4.64869 −0.533241
\(77\) −3.55277 −0.404876
\(78\) 0 0
\(79\) 4.70270 0.529095 0.264548 0.964373i \(-0.414777\pi\)
0.264548 + 0.964373i \(0.414777\pi\)
\(80\) 1.40533 0.157121
\(81\) 0 0
\(82\) −22.1648 −2.44769
\(83\) −3.89809 −0.427871 −0.213935 0.976848i \(-0.568628\pi\)
−0.213935 + 0.976848i \(0.568628\pi\)
\(84\) 0 0
\(85\) −2.00448 −0.217416
\(86\) 28.4032 3.06280
\(87\) 0 0
\(88\) 19.6310 2.09267
\(89\) −6.98825 −0.740753 −0.370377 0.928882i \(-0.620771\pi\)
−0.370377 + 0.928882i \(0.620771\pi\)
\(90\) 0 0
\(91\) −2.65719 −0.278549
\(92\) 14.7708 1.53997
\(93\) 0 0
\(94\) 20.6009 2.12482
\(95\) −0.289947 −0.0297479
\(96\) 0 0
\(97\) −10.7226 −1.08872 −0.544360 0.838852i \(-0.683227\pi\)
−0.544360 + 0.838852i \(0.683227\pi\)
\(98\) −2.49323 −0.251855
\(99\) 0 0
\(100\) −20.7895 −2.07895
\(101\) 7.08508 0.704992 0.352496 0.935813i \(-0.385333\pi\)
0.352496 + 0.935813i \(0.385333\pi\)
\(102\) 0 0
\(103\) 12.8326 1.26443 0.632215 0.774793i \(-0.282146\pi\)
0.632215 + 0.774793i \(0.282146\pi\)
\(104\) 14.6824 1.43973
\(105\) 0 0
\(106\) 10.5146 1.02127
\(107\) −3.49701 −0.338068 −0.169034 0.985610i \(-0.554065\pi\)
−0.169034 + 0.985610i \(0.554065\pi\)
\(108\) 0 0
\(109\) 6.77216 0.648655 0.324328 0.945945i \(-0.394862\pi\)
0.324328 + 0.945945i \(0.394862\pi\)
\(110\) 2.32938 0.222098
\(111\) 0 0
\(112\) 5.34403 0.504964
\(113\) 3.39124 0.319021 0.159511 0.987196i \(-0.449008\pi\)
0.159511 + 0.987196i \(0.449008\pi\)
\(114\) 0 0
\(115\) 0.921284 0.0859101
\(116\) 17.4731 1.62234
\(117\) 0 0
\(118\) 33.6766 3.10018
\(119\) −7.62237 −0.698741
\(120\) 0 0
\(121\) 1.62219 0.147472
\(122\) −3.73609 −0.338249
\(123\) 0 0
\(124\) 29.5892 2.65719
\(125\) −2.61154 −0.233583
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) 17.0651 1.50835
\(129\) 0 0
\(130\) 1.74219 0.152800
\(131\) 12.8441 1.12220 0.561099 0.827749i \(-0.310379\pi\)
0.561099 + 0.827749i \(0.310379\pi\)
\(132\) 0 0
\(133\) −1.10257 −0.0956052
\(134\) 5.95499 0.514432
\(135\) 0 0
\(136\) 42.1177 3.61156
\(137\) 9.68042 0.827054 0.413527 0.910492i \(-0.364297\pi\)
0.413527 + 0.910492i \(0.364297\pi\)
\(138\) 0 0
\(139\) −8.17409 −0.693317 −0.346659 0.937991i \(-0.612684\pi\)
−0.346659 + 0.937991i \(0.612684\pi\)
\(140\) 1.10875 0.0937064
\(141\) 0 0
\(142\) −23.7145 −1.99008
\(143\) 9.44039 0.789445
\(144\) 0 0
\(145\) 1.08983 0.0905053
\(146\) 3.05376 0.252731
\(147\) 0 0
\(148\) −3.57284 −0.293685
\(149\) −4.34652 −0.356081 −0.178040 0.984023i \(-0.556976\pi\)
−0.178040 + 0.984023i \(0.556976\pi\)
\(150\) 0 0
\(151\) −16.7253 −1.36108 −0.680542 0.732709i \(-0.738256\pi\)
−0.680542 + 0.732709i \(0.738256\pi\)
\(152\) 6.09231 0.494152
\(153\) 0 0
\(154\) 8.85789 0.713789
\(155\) 1.84553 0.148237
\(156\) 0 0
\(157\) 0.888372 0.0708998 0.0354499 0.999371i \(-0.488714\pi\)
0.0354499 + 0.999371i \(0.488714\pi\)
\(158\) −11.7249 −0.932786
\(159\) 0 0
\(160\) −0.597695 −0.0472520
\(161\) 3.50334 0.276102
\(162\) 0 0
\(163\) −2.55167 −0.199862 −0.0999310 0.994994i \(-0.531862\pi\)
−0.0999310 + 0.994994i \(0.531862\pi\)
\(164\) 37.4821 2.92686
\(165\) 0 0
\(166\) 9.71884 0.754328
\(167\) 18.1567 1.40500 0.702502 0.711681i \(-0.252066\pi\)
0.702502 + 0.711681i \(0.252066\pi\)
\(168\) 0 0
\(169\) −5.93934 −0.456873
\(170\) 4.99763 0.383300
\(171\) 0 0
\(172\) −48.0316 −3.66238
\(173\) 8.07410 0.613863 0.306931 0.951732i \(-0.400698\pi\)
0.306931 + 0.951732i \(0.400698\pi\)
\(174\) 0 0
\(175\) −4.93085 −0.372737
\(176\) −18.9861 −1.43113
\(177\) 0 0
\(178\) 17.4233 1.30593
\(179\) 12.3253 0.921239 0.460619 0.887598i \(-0.347627\pi\)
0.460619 + 0.887598i \(0.347627\pi\)
\(180\) 0 0
\(181\) −7.94838 −0.590798 −0.295399 0.955374i \(-0.595453\pi\)
−0.295399 + 0.955374i \(0.595453\pi\)
\(182\) 6.62499 0.491077
\(183\) 0 0
\(184\) −19.3579 −1.42708
\(185\) −0.222844 −0.0163838
\(186\) 0 0
\(187\) 27.0805 1.98033
\(188\) −34.8374 −2.54078
\(189\) 0 0
\(190\) 0.722905 0.0524451
\(191\) 0.672554 0.0486643 0.0243321 0.999704i \(-0.492254\pi\)
0.0243321 + 0.999704i \(0.492254\pi\)
\(192\) 0 0
\(193\) 9.97229 0.717821 0.358911 0.933372i \(-0.383148\pi\)
0.358911 + 0.933372i \(0.383148\pi\)
\(194\) 26.7341 1.91939
\(195\) 0 0
\(196\) 4.21621 0.301158
\(197\) −13.3551 −0.951509 −0.475755 0.879578i \(-0.657825\pi\)
−0.475755 + 0.879578i \(0.657825\pi\)
\(198\) 0 0
\(199\) −4.93412 −0.349770 −0.174885 0.984589i \(-0.555955\pi\)
−0.174885 + 0.984589i \(0.555955\pi\)
\(200\) 27.2456 1.92655
\(201\) 0 0
\(202\) −17.6648 −1.24289
\(203\) 4.14426 0.290870
\(204\) 0 0
\(205\) 2.33782 0.163281
\(206\) −31.9946 −2.22917
\(207\) 0 0
\(208\) −14.2001 −0.984600
\(209\) 3.91719 0.270958
\(210\) 0 0
\(211\) 19.9155 1.37104 0.685518 0.728055i \(-0.259576\pi\)
0.685518 + 0.728055i \(0.259576\pi\)
\(212\) −17.7809 −1.22120
\(213\) 0 0
\(214\) 8.71885 0.596009
\(215\) −2.99582 −0.204313
\(216\) 0 0
\(217\) 7.01796 0.476410
\(218\) −16.8846 −1.14357
\(219\) 0 0
\(220\) −3.93913 −0.265576
\(221\) 20.2541 1.36244
\(222\) 0 0
\(223\) −8.03732 −0.538219 −0.269109 0.963110i \(-0.586729\pi\)
−0.269109 + 0.963110i \(0.586729\pi\)
\(224\) −2.27284 −0.151861
\(225\) 0 0
\(226\) −8.45515 −0.562428
\(227\) 8.51416 0.565104 0.282552 0.959252i \(-0.408819\pi\)
0.282552 + 0.959252i \(0.408819\pi\)
\(228\) 0 0
\(229\) −5.72906 −0.378587 −0.189294 0.981921i \(-0.560620\pi\)
−0.189294 + 0.981921i \(0.560620\pi\)
\(230\) −2.29698 −0.151458
\(231\) 0 0
\(232\) −22.8993 −1.50341
\(233\) 10.0593 0.659004 0.329502 0.944155i \(-0.393119\pi\)
0.329502 + 0.944155i \(0.393119\pi\)
\(234\) 0 0
\(235\) −2.17287 −0.141742
\(236\) −56.9492 −3.70708
\(237\) 0 0
\(238\) 19.0043 1.23187
\(239\) −13.4107 −0.867463 −0.433732 0.901042i \(-0.642803\pi\)
−0.433732 + 0.901042i \(0.642803\pi\)
\(240\) 0 0
\(241\) 8.69479 0.560080 0.280040 0.959988i \(-0.409652\pi\)
0.280040 + 0.959988i \(0.409652\pi\)
\(242\) −4.04450 −0.259991
\(243\) 0 0
\(244\) 6.31795 0.404466
\(245\) 0.262973 0.0168007
\(246\) 0 0
\(247\) 2.92975 0.186415
\(248\) −38.7780 −2.46240
\(249\) 0 0
\(250\) 6.51118 0.411803
\(251\) 20.7428 1.30927 0.654636 0.755944i \(-0.272822\pi\)
0.654636 + 0.755944i \(0.272822\pi\)
\(252\) 0 0
\(253\) −12.4466 −0.782510
\(254\) −2.49323 −0.156439
\(255\) 0 0
\(256\) −32.5045 −2.03153
\(257\) 28.4551 1.77498 0.887491 0.460825i \(-0.152446\pi\)
0.887491 + 0.460825i \(0.152446\pi\)
\(258\) 0 0
\(259\) −0.847404 −0.0526551
\(260\) −2.94616 −0.182713
\(261\) 0 0
\(262\) −32.0235 −1.97842
\(263\) −24.8938 −1.53502 −0.767508 0.641039i \(-0.778503\pi\)
−0.767508 + 0.641039i \(0.778503\pi\)
\(264\) 0 0
\(265\) −1.10903 −0.0681270
\(266\) 2.74897 0.168550
\(267\) 0 0
\(268\) −10.0703 −0.615139
\(269\) −10.3169 −0.629034 −0.314517 0.949252i \(-0.601843\pi\)
−0.314517 + 0.949252i \(0.601843\pi\)
\(270\) 0 0
\(271\) 9.92171 0.602701 0.301350 0.953513i \(-0.402563\pi\)
0.301350 + 0.953513i \(0.402563\pi\)
\(272\) −40.7342 −2.46987
\(273\) 0 0
\(274\) −24.1356 −1.45808
\(275\) 17.5182 1.05639
\(276\) 0 0
\(277\) 2.98940 0.179615 0.0898077 0.995959i \(-0.471375\pi\)
0.0898077 + 0.995959i \(0.471375\pi\)
\(278\) 20.3799 1.22231
\(279\) 0 0
\(280\) −1.45307 −0.0868373
\(281\) 30.9297 1.84511 0.922556 0.385864i \(-0.126097\pi\)
0.922556 + 0.385864i \(0.126097\pi\)
\(282\) 0 0
\(283\) 26.0239 1.54696 0.773479 0.633822i \(-0.218515\pi\)
0.773479 + 0.633822i \(0.218515\pi\)
\(284\) 40.1027 2.37966
\(285\) 0 0
\(286\) −23.5371 −1.39178
\(287\) 8.88998 0.524759
\(288\) 0 0
\(289\) 41.1005 2.41768
\(290\) −2.71720 −0.159559
\(291\) 0 0
\(292\) −5.16409 −0.302206
\(293\) −28.1794 −1.64626 −0.823128 0.567855i \(-0.807773\pi\)
−0.823128 + 0.567855i \(0.807773\pi\)
\(294\) 0 0
\(295\) −3.55203 −0.206807
\(296\) 4.68237 0.272157
\(297\) 0 0
\(298\) 10.8369 0.627764
\(299\) −9.30905 −0.538356
\(300\) 0 0
\(301\) −11.3921 −0.656631
\(302\) 41.7001 2.39957
\(303\) 0 0
\(304\) −5.89219 −0.337940
\(305\) 0.394062 0.0225639
\(306\) 0 0
\(307\) −14.2085 −0.810924 −0.405462 0.914112i \(-0.632889\pi\)
−0.405462 + 0.914112i \(0.632889\pi\)
\(308\) −14.9792 −0.853522
\(309\) 0 0
\(310\) −4.60134 −0.261339
\(311\) −19.2348 −1.09071 −0.545353 0.838206i \(-0.683605\pi\)
−0.545353 + 0.838206i \(0.683605\pi\)
\(312\) 0 0
\(313\) −21.8899 −1.23729 −0.618646 0.785670i \(-0.712318\pi\)
−0.618646 + 0.785670i \(0.712318\pi\)
\(314\) −2.21492 −0.124995
\(315\) 0 0
\(316\) 19.8276 1.11539
\(317\) 26.0453 1.46285 0.731426 0.681921i \(-0.238855\pi\)
0.731426 + 0.681921i \(0.238855\pi\)
\(318\) 0 0
\(319\) −14.7236 −0.824365
\(320\) −1.32048 −0.0738168
\(321\) 0 0
\(322\) −8.73465 −0.486763
\(323\) 8.40422 0.467623
\(324\) 0 0
\(325\) 13.1022 0.726779
\(326\) 6.36190 0.352353
\(327\) 0 0
\(328\) −49.1219 −2.71230
\(329\) −8.26272 −0.455538
\(330\) 0 0
\(331\) 3.29836 0.181294 0.0906470 0.995883i \(-0.471106\pi\)
0.0906470 + 0.995883i \(0.471106\pi\)
\(332\) −16.4352 −0.901997
\(333\) 0 0
\(334\) −45.2688 −2.47700
\(335\) −0.628100 −0.0343168
\(336\) 0 0
\(337\) 17.1260 0.932912 0.466456 0.884545i \(-0.345531\pi\)
0.466456 + 0.884545i \(0.345531\pi\)
\(338\) 14.8082 0.805458
\(339\) 0 0
\(340\) −8.45130 −0.458336
\(341\) −24.9332 −1.35021
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 62.9476 3.39391
\(345\) 0 0
\(346\) −20.1306 −1.08223
\(347\) −14.8310 −0.796171 −0.398085 0.917348i \(-0.630325\pi\)
−0.398085 + 0.917348i \(0.630325\pi\)
\(348\) 0 0
\(349\) −13.6783 −0.732180 −0.366090 0.930579i \(-0.619304\pi\)
−0.366090 + 0.930579i \(0.619304\pi\)
\(350\) 12.2937 0.657129
\(351\) 0 0
\(352\) 8.07489 0.430393
\(353\) 30.9696 1.64835 0.824174 0.566337i \(-0.191640\pi\)
0.824174 + 0.566337i \(0.191640\pi\)
\(354\) 0 0
\(355\) 2.50128 0.132754
\(356\) −29.4640 −1.56159
\(357\) 0 0
\(358\) −30.7299 −1.62413
\(359\) 20.9788 1.10722 0.553610 0.832776i \(-0.313250\pi\)
0.553610 + 0.832776i \(0.313250\pi\)
\(360\) 0 0
\(361\) −17.7843 −0.936017
\(362\) 19.8172 1.04157
\(363\) 0 0
\(364\) −11.2033 −0.587211
\(365\) −0.322094 −0.0168592
\(366\) 0 0
\(367\) 8.13181 0.424477 0.212239 0.977218i \(-0.431925\pi\)
0.212239 + 0.977218i \(0.431925\pi\)
\(368\) 18.7220 0.975950
\(369\) 0 0
\(370\) 0.555603 0.0288844
\(371\) −4.21727 −0.218950
\(372\) 0 0
\(373\) 32.8632 1.70159 0.850795 0.525497i \(-0.176121\pi\)
0.850795 + 0.525497i \(0.176121\pi\)
\(374\) −67.5181 −3.49128
\(375\) 0 0
\(376\) 45.6560 2.35453
\(377\) −11.0121 −0.567152
\(378\) 0 0
\(379\) 16.8929 0.867731 0.433866 0.900978i \(-0.357149\pi\)
0.433866 + 0.900978i \(0.357149\pi\)
\(380\) −1.22248 −0.0627118
\(381\) 0 0
\(382\) −1.67683 −0.0857943
\(383\) −8.23533 −0.420806 −0.210403 0.977615i \(-0.567478\pi\)
−0.210403 + 0.977615i \(0.567478\pi\)
\(384\) 0 0
\(385\) −0.934282 −0.0476154
\(386\) −24.8632 −1.26551
\(387\) 0 0
\(388\) −45.2090 −2.29514
\(389\) −30.8529 −1.56430 −0.782152 0.623087i \(-0.785878\pi\)
−0.782152 + 0.623087i \(0.785878\pi\)
\(390\) 0 0
\(391\) −26.7038 −1.35047
\(392\) −5.52554 −0.279082
\(393\) 0 0
\(394\) 33.2973 1.67749
\(395\) 1.23668 0.0622242
\(396\) 0 0
\(397\) 12.4669 0.625698 0.312849 0.949803i \(-0.398717\pi\)
0.312849 + 0.949803i \(0.398717\pi\)
\(398\) 12.3019 0.616639
\(399\) 0 0
\(400\) −26.3506 −1.31753
\(401\) 11.9396 0.596237 0.298118 0.954529i \(-0.403641\pi\)
0.298118 + 0.954529i \(0.403641\pi\)
\(402\) 0 0
\(403\) −18.6480 −0.928925
\(404\) 29.8722 1.48620
\(405\) 0 0
\(406\) −10.3326 −0.512799
\(407\) 3.01064 0.149232
\(408\) 0 0
\(409\) 40.0631 1.98099 0.990497 0.137538i \(-0.0439189\pi\)
0.990497 + 0.137538i \(0.0439189\pi\)
\(410\) −5.82874 −0.287861
\(411\) 0 0
\(412\) 54.1048 2.66555
\(413\) −13.5072 −0.664646
\(414\) 0 0
\(415\) −1.02509 −0.0503197
\(416\) 6.03937 0.296104
\(417\) 0 0
\(418\) −9.76648 −0.477694
\(419\) −38.5864 −1.88507 −0.942535 0.334107i \(-0.891565\pi\)
−0.942535 + 0.334107i \(0.891565\pi\)
\(420\) 0 0
\(421\) 27.8460 1.35713 0.678566 0.734539i \(-0.262602\pi\)
0.678566 + 0.734539i \(0.262602\pi\)
\(422\) −49.6539 −2.41711
\(423\) 0 0
\(424\) 23.3027 1.13168
\(425\) 37.5847 1.82313
\(426\) 0 0
\(427\) 1.49849 0.0725170
\(428\) −14.7441 −0.712684
\(429\) 0 0
\(430\) 7.46928 0.360201
\(431\) −4.80037 −0.231226 −0.115613 0.993294i \(-0.536883\pi\)
−0.115613 + 0.993294i \(0.536883\pi\)
\(432\) 0 0
\(433\) −20.7252 −0.995992 −0.497996 0.867179i \(-0.665931\pi\)
−0.497996 + 0.867179i \(0.665931\pi\)
\(434\) −17.4974 −0.839902
\(435\) 0 0
\(436\) 28.5529 1.36743
\(437\) −3.86269 −0.184778
\(438\) 0 0
\(439\) 16.3776 0.781662 0.390831 0.920462i \(-0.372188\pi\)
0.390831 + 0.920462i \(0.372188\pi\)
\(440\) 5.16241 0.246108
\(441\) 0 0
\(442\) −50.4982 −2.40195
\(443\) −20.1883 −0.959175 −0.479588 0.877494i \(-0.659214\pi\)
−0.479588 + 0.877494i \(0.659214\pi\)
\(444\) 0 0
\(445\) −1.83772 −0.0871163
\(446\) 20.0389 0.948870
\(447\) 0 0
\(448\) −5.02134 −0.237236
\(449\) 10.0200 0.472873 0.236437 0.971647i \(-0.424020\pi\)
0.236437 + 0.971647i \(0.424020\pi\)
\(450\) 0 0
\(451\) −31.5841 −1.48724
\(452\) 14.2982 0.672530
\(453\) 0 0
\(454\) −21.2278 −0.996269
\(455\) −0.698769 −0.0327588
\(456\) 0 0
\(457\) −12.2395 −0.572538 −0.286269 0.958149i \(-0.592415\pi\)
−0.286269 + 0.958149i \(0.592415\pi\)
\(458\) 14.2839 0.667442
\(459\) 0 0
\(460\) 3.88433 0.181108
\(461\) −33.2139 −1.54693 −0.773464 0.633840i \(-0.781478\pi\)
−0.773464 + 0.633840i \(0.781478\pi\)
\(462\) 0 0
\(463\) 1.80160 0.0837272 0.0418636 0.999123i \(-0.486671\pi\)
0.0418636 + 0.999123i \(0.486671\pi\)
\(464\) 22.1471 1.02815
\(465\) 0 0
\(466\) −25.0801 −1.16181
\(467\) 26.2032 1.21254 0.606270 0.795259i \(-0.292665\pi\)
0.606270 + 0.795259i \(0.292665\pi\)
\(468\) 0 0
\(469\) −2.38846 −0.110289
\(470\) 5.41747 0.249889
\(471\) 0 0
\(472\) 74.6346 3.43533
\(473\) 40.4736 1.86098
\(474\) 0 0
\(475\) 5.43662 0.249449
\(476\) −32.1375 −1.47302
\(477\) 0 0
\(478\) 33.4359 1.52932
\(479\) 21.1860 0.968013 0.484007 0.875064i \(-0.339181\pi\)
0.484007 + 0.875064i \(0.339181\pi\)
\(480\) 0 0
\(481\) 2.25171 0.102669
\(482\) −21.6781 −0.987412
\(483\) 0 0
\(484\) 6.83951 0.310887
\(485\) −2.81976 −0.128039
\(486\) 0 0
\(487\) 6.70021 0.303615 0.151808 0.988410i \(-0.451491\pi\)
0.151808 + 0.988410i \(0.451491\pi\)
\(488\) −8.27996 −0.374816
\(489\) 0 0
\(490\) −0.655653 −0.0296194
\(491\) 28.8514 1.30204 0.651022 0.759059i \(-0.274340\pi\)
0.651022 + 0.759059i \(0.274340\pi\)
\(492\) 0 0
\(493\) −31.5891 −1.42270
\(494\) −7.30454 −0.328647
\(495\) 0 0
\(496\) 37.5042 1.68399
\(497\) 9.51155 0.426651
\(498\) 0 0
\(499\) −19.4113 −0.868971 −0.434485 0.900679i \(-0.643070\pi\)
−0.434485 + 0.900679i \(0.643070\pi\)
\(500\) −11.0108 −0.492419
\(501\) 0 0
\(502\) −51.7166 −2.30822
\(503\) −31.6324 −1.41042 −0.705209 0.708999i \(-0.749147\pi\)
−0.705209 + 0.708999i \(0.749147\pi\)
\(504\) 0 0
\(505\) 1.86318 0.0829105
\(506\) 31.0322 1.37955
\(507\) 0 0
\(508\) 4.21621 0.187064
\(509\) −2.59835 −0.115170 −0.0575848 0.998341i \(-0.518340\pi\)
−0.0575848 + 0.998341i \(0.518340\pi\)
\(510\) 0 0
\(511\) −1.22482 −0.0541828
\(512\) 46.9112 2.07320
\(513\) 0 0
\(514\) −70.9453 −3.12926
\(515\) 3.37461 0.148703
\(516\) 0 0
\(517\) 29.3556 1.29106
\(518\) 2.11278 0.0928301
\(519\) 0 0
\(520\) 3.86107 0.169319
\(521\) −34.5776 −1.51487 −0.757436 0.652909i \(-0.773548\pi\)
−0.757436 + 0.652909i \(0.773548\pi\)
\(522\) 0 0
\(523\) 10.4040 0.454935 0.227467 0.973786i \(-0.426955\pi\)
0.227467 + 0.973786i \(0.426955\pi\)
\(524\) 54.1537 2.36571
\(525\) 0 0
\(526\) 62.0660 2.70621
\(527\) −53.4934 −2.33021
\(528\) 0 0
\(529\) −10.7266 −0.466374
\(530\) 2.76506 0.120107
\(531\) 0 0
\(532\) −4.64869 −0.201546
\(533\) −23.6224 −1.02320
\(534\) 0 0
\(535\) −0.919618 −0.0397585
\(536\) 13.1975 0.570046
\(537\) 0 0
\(538\) 25.7225 1.10898
\(539\) −3.55277 −0.153029
\(540\) 0 0
\(541\) −22.7755 −0.979196 −0.489598 0.871948i \(-0.662856\pi\)
−0.489598 + 0.871948i \(0.662856\pi\)
\(542\) −24.7371 −1.06255
\(543\) 0 0
\(544\) 17.3244 0.742779
\(545\) 1.78089 0.0762851
\(546\) 0 0
\(547\) 25.2963 1.08159 0.540796 0.841154i \(-0.318123\pi\)
0.540796 + 0.841154i \(0.318123\pi\)
\(548\) 40.8147 1.74352
\(549\) 0 0
\(550\) −43.6769 −1.86239
\(551\) −4.56935 −0.194661
\(552\) 0 0
\(553\) 4.70270 0.199979
\(554\) −7.45326 −0.316659
\(555\) 0 0
\(556\) −34.4637 −1.46159
\(557\) −36.4909 −1.54617 −0.773085 0.634302i \(-0.781288\pi\)
−0.773085 + 0.634302i \(0.781288\pi\)
\(558\) 0 0
\(559\) 30.2710 1.28033
\(560\) 1.40533 0.0593862
\(561\) 0 0
\(562\) −77.1150 −3.25290
\(563\) −31.8227 −1.34116 −0.670582 0.741835i \(-0.733956\pi\)
−0.670582 + 0.741835i \(0.733956\pi\)
\(564\) 0 0
\(565\) 0.891804 0.0375185
\(566\) −64.8836 −2.72726
\(567\) 0 0
\(568\) −52.5565 −2.20522
\(569\) 25.3998 1.06482 0.532408 0.846488i \(-0.321287\pi\)
0.532408 + 0.846488i \(0.321287\pi\)
\(570\) 0 0
\(571\) 34.2769 1.43444 0.717222 0.696845i \(-0.245413\pi\)
0.717222 + 0.696845i \(0.245413\pi\)
\(572\) 39.8027 1.66423
\(573\) 0 0
\(574\) −22.1648 −0.925141
\(575\) −17.2744 −0.720394
\(576\) 0 0
\(577\) 30.4223 1.26650 0.633248 0.773949i \(-0.281721\pi\)
0.633248 + 0.773949i \(0.281721\pi\)
\(578\) −102.473 −4.26232
\(579\) 0 0
\(580\) 4.59495 0.190795
\(581\) −3.89809 −0.161720
\(582\) 0 0
\(583\) 14.9830 0.620533
\(584\) 6.76778 0.280053
\(585\) 0 0
\(586\) 70.2578 2.90232
\(587\) −9.57137 −0.395053 −0.197526 0.980298i \(-0.563291\pi\)
−0.197526 + 0.980298i \(0.563291\pi\)
\(588\) 0 0
\(589\) −7.73781 −0.318831
\(590\) 8.85603 0.364597
\(591\) 0 0
\(592\) −4.52856 −0.186123
\(593\) 30.8249 1.26583 0.632914 0.774222i \(-0.281859\pi\)
0.632914 + 0.774222i \(0.281859\pi\)
\(594\) 0 0
\(595\) −2.00448 −0.0821755
\(596\) −18.3259 −0.750657
\(597\) 0 0
\(598\) 23.2096 0.949112
\(599\) 35.6568 1.45690 0.728449 0.685100i \(-0.240241\pi\)
0.728449 + 0.685100i \(0.240241\pi\)
\(600\) 0 0
\(601\) 32.9469 1.34393 0.671967 0.740582i \(-0.265450\pi\)
0.671967 + 0.740582i \(0.265450\pi\)
\(602\) 28.4032 1.15763
\(603\) 0 0
\(604\) −70.5174 −2.86931
\(605\) 0.426592 0.0173434
\(606\) 0 0
\(607\) 8.81706 0.357873 0.178937 0.983861i \(-0.442734\pi\)
0.178937 + 0.983861i \(0.442734\pi\)
\(608\) 2.50597 0.101631
\(609\) 0 0
\(610\) −0.982489 −0.0397798
\(611\) 21.9556 0.888229
\(612\) 0 0
\(613\) −42.7883 −1.72820 −0.864102 0.503316i \(-0.832113\pi\)
−0.864102 + 0.503316i \(0.832113\pi\)
\(614\) 35.4252 1.42964
\(615\) 0 0
\(616\) 19.6310 0.790955
\(617\) −1.39640 −0.0562170 −0.0281085 0.999605i \(-0.508948\pi\)
−0.0281085 + 0.999605i \(0.508948\pi\)
\(618\) 0 0
\(619\) 9.82893 0.395058 0.197529 0.980297i \(-0.436708\pi\)
0.197529 + 0.980297i \(0.436708\pi\)
\(620\) 7.78115 0.312499
\(621\) 0 0
\(622\) 47.9569 1.92290
\(623\) −6.98825 −0.279978
\(624\) 0 0
\(625\) 23.9675 0.958698
\(626\) 54.5767 2.18132
\(627\) 0 0
\(628\) 3.74557 0.149464
\(629\) 6.45923 0.257546
\(630\) 0 0
\(631\) −4.16758 −0.165909 −0.0829544 0.996553i \(-0.526436\pi\)
−0.0829544 + 0.996553i \(0.526436\pi\)
\(632\) −25.9850 −1.03363
\(633\) 0 0
\(634\) −64.9371 −2.57898
\(635\) 0.262973 0.0104358
\(636\) 0 0
\(637\) −2.65719 −0.105282
\(638\) 36.7094 1.45334
\(639\) 0 0
\(640\) 4.48764 0.177390
\(641\) 0.957332 0.0378123 0.0189062 0.999821i \(-0.493982\pi\)
0.0189062 + 0.999821i \(0.493982\pi\)
\(642\) 0 0
\(643\) −12.6509 −0.498905 −0.249452 0.968387i \(-0.580251\pi\)
−0.249452 + 0.968387i \(0.580251\pi\)
\(644\) 14.7708 0.582053
\(645\) 0 0
\(646\) −20.9537 −0.824412
\(647\) −26.6327 −1.04704 −0.523519 0.852014i \(-0.675381\pi\)
−0.523519 + 0.852014i \(0.675381\pi\)
\(648\) 0 0
\(649\) 47.9880 1.88369
\(650\) −32.6668 −1.28130
\(651\) 0 0
\(652\) −10.7584 −0.421331
\(653\) −8.00679 −0.313330 −0.156665 0.987652i \(-0.550074\pi\)
−0.156665 + 0.987652i \(0.550074\pi\)
\(654\) 0 0
\(655\) 3.37766 0.131976
\(656\) 47.5083 1.85489
\(657\) 0 0
\(658\) 20.6009 0.803106
\(659\) −9.88982 −0.385253 −0.192626 0.981272i \(-0.561701\pi\)
−0.192626 + 0.981272i \(0.561701\pi\)
\(660\) 0 0
\(661\) 28.6257 1.11341 0.556706 0.830709i \(-0.312065\pi\)
0.556706 + 0.830709i \(0.312065\pi\)
\(662\) −8.22357 −0.319618
\(663\) 0 0
\(664\) 21.5390 0.835876
\(665\) −0.289947 −0.0112437
\(666\) 0 0
\(667\) 14.5188 0.562169
\(668\) 76.5524 2.96190
\(669\) 0 0
\(670\) 1.56600 0.0604998
\(671\) −5.32379 −0.205523
\(672\) 0 0
\(673\) 40.8176 1.57340 0.786701 0.617335i \(-0.211788\pi\)
0.786701 + 0.617335i \(0.211788\pi\)
\(674\) −42.6991 −1.64471
\(675\) 0 0
\(676\) −25.0415 −0.963136
\(677\) 37.1987 1.42966 0.714831 0.699297i \(-0.246503\pi\)
0.714831 + 0.699297i \(0.246503\pi\)
\(678\) 0 0
\(679\) −10.7226 −0.411497
\(680\) 11.0758 0.424738
\(681\) 0 0
\(682\) 62.1643 2.38039
\(683\) 10.1783 0.389461 0.194731 0.980857i \(-0.437617\pi\)
0.194731 + 0.980857i \(0.437617\pi\)
\(684\) 0 0
\(685\) 2.54569 0.0972657
\(686\) −2.49323 −0.0951921
\(687\) 0 0
\(688\) −60.8799 −2.32102
\(689\) 11.2061 0.426918
\(690\) 0 0
\(691\) −18.8159 −0.715789 −0.357895 0.933762i \(-0.616505\pi\)
−0.357895 + 0.933762i \(0.616505\pi\)
\(692\) 34.0421 1.29409
\(693\) 0 0
\(694\) 36.9772 1.40363
\(695\) −2.14956 −0.0815376
\(696\) 0 0
\(697\) −67.7627 −2.56670
\(698\) 34.1031 1.29082
\(699\) 0 0
\(700\) −20.7895 −0.785769
\(701\) 40.7417 1.53879 0.769396 0.638772i \(-0.220557\pi\)
0.769396 + 0.638772i \(0.220557\pi\)
\(702\) 0 0
\(703\) 0.934326 0.0352388
\(704\) 17.8397 0.672358
\(705\) 0 0
\(706\) −77.2145 −2.90601
\(707\) 7.08508 0.266462
\(708\) 0 0
\(709\) 24.0156 0.901925 0.450962 0.892543i \(-0.351081\pi\)
0.450962 + 0.892543i \(0.351081\pi\)
\(710\) −6.23627 −0.234043
\(711\) 0 0
\(712\) 38.6139 1.44712
\(713\) 24.5863 0.920764
\(714\) 0 0
\(715\) 2.48257 0.0928427
\(716\) 51.9662 1.94207
\(717\) 0 0
\(718\) −52.3051 −1.95201
\(719\) 2.05844 0.0767667 0.0383834 0.999263i \(-0.487779\pi\)
0.0383834 + 0.999263i \(0.487779\pi\)
\(720\) 0 0
\(721\) 12.8326 0.477909
\(722\) 44.3405 1.65018
\(723\) 0 0
\(724\) −33.5121 −1.24547
\(725\) −20.4347 −0.758926
\(726\) 0 0
\(727\) 23.1073 0.857004 0.428502 0.903541i \(-0.359042\pi\)
0.428502 + 0.903541i \(0.359042\pi\)
\(728\) 14.6824 0.544166
\(729\) 0 0
\(730\) 0.803055 0.0297224
\(731\) 86.8350 3.21171
\(732\) 0 0
\(733\) 8.13013 0.300293 0.150147 0.988664i \(-0.452025\pi\)
0.150147 + 0.988664i \(0.452025\pi\)
\(734\) −20.2745 −0.748346
\(735\) 0 0
\(736\) −7.96254 −0.293503
\(737\) 8.48565 0.312573
\(738\) 0 0
\(739\) 18.6947 0.687695 0.343848 0.939025i \(-0.388270\pi\)
0.343848 + 0.939025i \(0.388270\pi\)
\(740\) −0.939559 −0.0345389
\(741\) 0 0
\(742\) 10.5146 0.386005
\(743\) 6.23303 0.228668 0.114334 0.993442i \(-0.463527\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(744\) 0 0
\(745\) −1.14302 −0.0418769
\(746\) −81.9356 −2.99987
\(747\) 0 0
\(748\) 114.177 4.17474
\(749\) −3.49701 −0.127778
\(750\) 0 0
\(751\) −11.2328 −0.409889 −0.204945 0.978774i \(-0.565701\pi\)
−0.204945 + 0.978774i \(0.565701\pi\)
\(752\) −44.1562 −1.61021
\(753\) 0 0
\(754\) 27.4557 0.999878
\(755\) −4.39830 −0.160070
\(756\) 0 0
\(757\) 35.0765 1.27488 0.637439 0.770501i \(-0.279994\pi\)
0.637439 + 0.770501i \(0.279994\pi\)
\(758\) −42.1180 −1.52980
\(759\) 0 0
\(760\) 1.60211 0.0581147
\(761\) −12.1870 −0.441779 −0.220890 0.975299i \(-0.570896\pi\)
−0.220890 + 0.975299i \(0.570896\pi\)
\(762\) 0 0
\(763\) 6.77216 0.245169
\(764\) 2.83563 0.102589
\(765\) 0 0
\(766\) 20.5326 0.741873
\(767\) 35.8912 1.29596
\(768\) 0 0
\(769\) 3.45765 0.124686 0.0623430 0.998055i \(-0.480143\pi\)
0.0623430 + 0.998055i \(0.480143\pi\)
\(770\) 2.32938 0.0839452
\(771\) 0 0
\(772\) 42.0453 1.51324
\(773\) 13.7406 0.494215 0.247108 0.968988i \(-0.420520\pi\)
0.247108 + 0.968988i \(0.420520\pi\)
\(774\) 0 0
\(775\) −34.6045 −1.24303
\(776\) 59.2484 2.12689
\(777\) 0 0
\(778\) 76.9235 2.75784
\(779\) −9.80186 −0.351188
\(780\) 0 0
\(781\) −33.7924 −1.20919
\(782\) 66.5787 2.38085
\(783\) 0 0
\(784\) 5.34403 0.190858
\(785\) 0.233618 0.00833817
\(786\) 0 0
\(787\) −33.2567 −1.18547 −0.592736 0.805397i \(-0.701952\pi\)
−0.592736 + 0.805397i \(0.701952\pi\)
\(788\) −56.3078 −2.00588
\(789\) 0 0
\(790\) −3.08334 −0.109700
\(791\) 3.39124 0.120579
\(792\) 0 0
\(793\) −3.98177 −0.141397
\(794\) −31.0830 −1.10309
\(795\) 0 0
\(796\) −20.8033 −0.737353
\(797\) −40.0553 −1.41883 −0.709416 0.704790i \(-0.751041\pi\)
−0.709416 + 0.704790i \(0.751041\pi\)
\(798\) 0 0
\(799\) 62.9815 2.22812
\(800\) 11.2070 0.396228
\(801\) 0 0
\(802\) −29.7683 −1.05115
\(803\) 4.35150 0.153561
\(804\) 0 0
\(805\) 0.921284 0.0324710
\(806\) 46.4939 1.63768
\(807\) 0 0
\(808\) −39.1489 −1.37725
\(809\) 34.2875 1.20548 0.602742 0.797936i \(-0.294075\pi\)
0.602742 + 0.797936i \(0.294075\pi\)
\(810\) 0 0
\(811\) 13.9247 0.488963 0.244481 0.969654i \(-0.421382\pi\)
0.244481 + 0.969654i \(0.421382\pi\)
\(812\) 17.4731 0.613186
\(813\) 0 0
\(814\) −7.50622 −0.263093
\(815\) −0.671019 −0.0235048
\(816\) 0 0
\(817\) 12.5607 0.439442
\(818\) −99.8867 −3.49246
\(819\) 0 0
\(820\) 9.85676 0.344213
\(821\) −11.5694 −0.403775 −0.201888 0.979409i \(-0.564708\pi\)
−0.201888 + 0.979409i \(0.564708\pi\)
\(822\) 0 0
\(823\) −29.7145 −1.03578 −0.517891 0.855447i \(-0.673283\pi\)
−0.517891 + 0.855447i \(0.673283\pi\)
\(824\) −70.9068 −2.47015
\(825\) 0 0
\(826\) 33.6766 1.17176
\(827\) −9.76698 −0.339631 −0.169816 0.985476i \(-0.554317\pi\)
−0.169816 + 0.985476i \(0.554317\pi\)
\(828\) 0 0
\(829\) −32.2336 −1.11952 −0.559759 0.828655i \(-0.689106\pi\)
−0.559759 + 0.828655i \(0.689106\pi\)
\(830\) 2.55579 0.0887128
\(831\) 0 0
\(832\) 13.3426 0.462573
\(833\) −7.62237 −0.264099
\(834\) 0 0
\(835\) 4.77471 0.165236
\(836\) 16.5157 0.571208
\(837\) 0 0
\(838\) 96.2050 3.32335
\(839\) 39.8825 1.37690 0.688448 0.725286i \(-0.258292\pi\)
0.688448 + 0.725286i \(0.258292\pi\)
\(840\) 0 0
\(841\) −11.8251 −0.407762
\(842\) −69.4267 −2.39260
\(843\) 0 0
\(844\) 83.9678 2.89029
\(845\) −1.56189 −0.0537305
\(846\) 0 0
\(847\) 1.62219 0.0557392
\(848\) −22.5372 −0.773932
\(849\) 0 0
\(850\) −93.7075 −3.21414
\(851\) −2.96875 −0.101767
\(852\) 0 0
\(853\) 26.2567 0.899011 0.449505 0.893278i \(-0.351600\pi\)
0.449505 + 0.893278i \(0.351600\pi\)
\(854\) −3.73609 −0.127846
\(855\) 0 0
\(856\) 19.3228 0.660441
\(857\) −14.4750 −0.494458 −0.247229 0.968957i \(-0.579520\pi\)
−0.247229 + 0.968957i \(0.579520\pi\)
\(858\) 0 0
\(859\) −1.76811 −0.0603271 −0.0301636 0.999545i \(-0.509603\pi\)
−0.0301636 + 0.999545i \(0.509603\pi\)
\(860\) −12.6310 −0.430714
\(861\) 0 0
\(862\) 11.9685 0.407647
\(863\) 51.3029 1.74637 0.873186 0.487388i \(-0.162050\pi\)
0.873186 + 0.487388i \(0.162050\pi\)
\(864\) 0 0
\(865\) 2.12327 0.0721933
\(866\) 51.6729 1.75592
\(867\) 0 0
\(868\) 29.5892 1.00432
\(869\) −16.7076 −0.566767
\(870\) 0 0
\(871\) 6.34659 0.215046
\(872\) −37.4198 −1.26720
\(873\) 0 0
\(874\) 9.63060 0.325760
\(875\) −2.61154 −0.0882862
\(876\) 0 0
\(877\) 58.7886 1.98515 0.992575 0.121633i \(-0.0388130\pi\)
0.992575 + 0.121633i \(0.0388130\pi\)
\(878\) −40.8333 −1.37806
\(879\) 0 0
\(880\) −4.99283 −0.168308
\(881\) 6.41629 0.216170 0.108085 0.994142i \(-0.465528\pi\)
0.108085 + 0.994142i \(0.465528\pi\)
\(882\) 0 0
\(883\) −15.8316 −0.532776 −0.266388 0.963866i \(-0.585830\pi\)
−0.266388 + 0.963866i \(0.585830\pi\)
\(884\) 85.3955 2.87216
\(885\) 0 0
\(886\) 50.3341 1.69101
\(887\) −33.1828 −1.11417 −0.557084 0.830456i \(-0.688080\pi\)
−0.557084 + 0.830456i \(0.688080\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 4.58186 0.153584
\(891\) 0 0
\(892\) −33.8871 −1.13462
\(893\) 9.11025 0.304863
\(894\) 0 0
\(895\) 3.24123 0.108342
\(896\) 17.0651 0.570103
\(897\) 0 0
\(898\) −24.9822 −0.833667
\(899\) 29.0843 0.970014
\(900\) 0 0
\(901\) 32.1456 1.07092
\(902\) 78.7465 2.62197
\(903\) 0 0
\(904\) −18.7384 −0.623231
\(905\) −2.09021 −0.0694808
\(906\) 0 0
\(907\) −37.1547 −1.23370 −0.616851 0.787080i \(-0.711592\pi\)
−0.616851 + 0.787080i \(0.711592\pi\)
\(908\) 35.8975 1.19130
\(909\) 0 0
\(910\) 1.74219 0.0577531
\(911\) 14.3754 0.476279 0.238139 0.971231i \(-0.423462\pi\)
0.238139 + 0.971231i \(0.423462\pi\)
\(912\) 0 0
\(913\) 13.8490 0.458335
\(914\) 30.5159 1.00938
\(915\) 0 0
\(916\) −24.1549 −0.798102
\(917\) 12.8441 0.424151
\(918\) 0 0
\(919\) 17.1784 0.566662 0.283331 0.959022i \(-0.408560\pi\)
0.283331 + 0.959022i \(0.408560\pi\)
\(920\) −5.09059 −0.167832
\(921\) 0 0
\(922\) 82.8101 2.72721
\(923\) −25.2740 −0.831904
\(924\) 0 0
\(925\) 4.17842 0.137386
\(926\) −4.49180 −0.147610
\(927\) 0 0
\(928\) −9.41925 −0.309202
\(929\) −2.11145 −0.0692745 −0.0346373 0.999400i \(-0.511028\pi\)
−0.0346373 + 0.999400i \(0.511028\pi\)
\(930\) 0 0
\(931\) −1.10257 −0.0361354
\(932\) 42.4120 1.38925
\(933\) 0 0
\(934\) −65.3308 −2.13769
\(935\) 7.12145 0.232896
\(936\) 0 0
\(937\) 9.84177 0.321516 0.160758 0.986994i \(-0.448606\pi\)
0.160758 + 0.986994i \(0.448606\pi\)
\(938\) 5.95499 0.194437
\(939\) 0 0
\(940\) −9.16128 −0.298808
\(941\) −50.6893 −1.65242 −0.826211 0.563360i \(-0.809508\pi\)
−0.826211 + 0.563360i \(0.809508\pi\)
\(942\) 0 0
\(943\) 31.1446 1.01421
\(944\) −72.1829 −2.34935
\(945\) 0 0
\(946\) −100.910 −3.28087
\(947\) −25.5880 −0.831497 −0.415748 0.909480i \(-0.636480\pi\)
−0.415748 + 0.909480i \(0.636480\pi\)
\(948\) 0 0
\(949\) 3.25457 0.105648
\(950\) −13.5548 −0.439775
\(951\) 0 0
\(952\) 42.1177 1.36504
\(953\) 14.8512 0.481077 0.240539 0.970640i \(-0.422676\pi\)
0.240539 + 0.970640i \(0.422676\pi\)
\(954\) 0 0
\(955\) 0.176863 0.00572316
\(956\) −56.5422 −1.82871
\(957\) 0 0
\(958\) −52.8216 −1.70659
\(959\) 9.68042 0.312597
\(960\) 0 0
\(961\) 18.2517 0.588765
\(962\) −5.61405 −0.181004
\(963\) 0 0
\(964\) 36.6591 1.18071
\(965\) 2.62244 0.0844194
\(966\) 0 0
\(967\) −35.2407 −1.13326 −0.566632 0.823971i \(-0.691754\pi\)
−0.566632 + 0.823971i \(0.691754\pi\)
\(968\) −8.96349 −0.288097
\(969\) 0 0
\(970\) 7.03033 0.225730
\(971\) 23.7014 0.760614 0.380307 0.924860i \(-0.375818\pi\)
0.380307 + 0.924860i \(0.375818\pi\)
\(972\) 0 0
\(973\) −8.17409 −0.262049
\(974\) −16.7052 −0.535269
\(975\) 0 0
\(976\) 8.00798 0.256329
\(977\) −40.3025 −1.28939 −0.644696 0.764439i \(-0.723016\pi\)
−0.644696 + 0.764439i \(0.723016\pi\)
\(978\) 0 0
\(979\) 24.8277 0.793496
\(980\) 1.10875 0.0354177
\(981\) 0 0
\(982\) −71.9332 −2.29548
\(983\) −21.8967 −0.698395 −0.349197 0.937049i \(-0.613546\pi\)
−0.349197 + 0.937049i \(0.613546\pi\)
\(984\) 0 0
\(985\) −3.51202 −0.111902
\(986\) 78.7590 2.50820
\(987\) 0 0
\(988\) 12.3524 0.392983
\(989\) −39.9105 −1.26908
\(990\) 0 0
\(991\) 14.7659 0.469054 0.234527 0.972110i \(-0.424646\pi\)
0.234527 + 0.972110i \(0.424646\pi\)
\(992\) −15.9507 −0.506435
\(993\) 0 0
\(994\) −23.7145 −0.752179
\(995\) −1.29754 −0.0411347
\(996\) 0 0
\(997\) 29.3782 0.930416 0.465208 0.885201i \(-0.345980\pi\)
0.465208 + 0.885201i \(0.345980\pi\)
\(998\) 48.3970 1.53198
\(999\) 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 \(a_p\))