Properties

Label 6003.2.a.t.1.5
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.96070 q^{2} +1.84436 q^{4} -2.84151 q^{5} -2.21458 q^{7} +0.305158 q^{8} +O(q^{10})\) \(q-1.96070 q^{2} +1.84436 q^{4} -2.84151 q^{5} -2.21458 q^{7} +0.305158 q^{8} +5.57136 q^{10} +1.29670 q^{11} -0.673949 q^{13} +4.34214 q^{14} -4.28705 q^{16} +1.19266 q^{17} -5.61616 q^{19} -5.24077 q^{20} -2.54244 q^{22} +1.00000 q^{23} +3.07417 q^{25} +1.32142 q^{26} -4.08449 q^{28} +1.00000 q^{29} -4.05642 q^{31} +7.79533 q^{32} -2.33846 q^{34} +6.29275 q^{35} +3.39113 q^{37} +11.0116 q^{38} -0.867109 q^{40} +9.19828 q^{41} +9.58517 q^{43} +2.39158 q^{44} -1.96070 q^{46} -4.53489 q^{47} -2.09562 q^{49} -6.02754 q^{50} -1.24301 q^{52} +3.31678 q^{53} -3.68457 q^{55} -0.675798 q^{56} -1.96070 q^{58} +7.04726 q^{59} -13.0676 q^{61} +7.95344 q^{62} -6.71023 q^{64} +1.91503 q^{65} +4.14971 q^{67} +2.19971 q^{68} -12.3382 q^{70} -4.40083 q^{71} -6.12240 q^{73} -6.64901 q^{74} -10.3582 q^{76} -2.87164 q^{77} +1.11103 q^{79} +12.1817 q^{80} -18.0351 q^{82} -2.93238 q^{83} -3.38897 q^{85} -18.7937 q^{86} +0.395697 q^{88} +13.3205 q^{89} +1.49252 q^{91} +1.84436 q^{92} +8.89157 q^{94} +15.9584 q^{95} +0.608559 q^{97} +4.10890 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.96070 −1.38643 −0.693214 0.720732i \(-0.743806\pi\)
−0.693214 + 0.720732i \(0.743806\pi\)
\(3\) 0 0
\(4\) 1.84436 0.922182
\(5\) −2.84151 −1.27076 −0.635381 0.772199i \(-0.719157\pi\)
−0.635381 + 0.772199i \(0.719157\pi\)
\(6\) 0 0
\(7\) −2.21458 −0.837033 −0.418517 0.908209i \(-0.637450\pi\)
−0.418517 + 0.908209i \(0.637450\pi\)
\(8\) 0.305158 0.107890
\(9\) 0 0
\(10\) 5.57136 1.76182
\(11\) 1.29670 0.390968 0.195484 0.980707i \(-0.437372\pi\)
0.195484 + 0.980707i \(0.437372\pi\)
\(12\) 0 0
\(13\) −0.673949 −0.186920 −0.0934600 0.995623i \(-0.529793\pi\)
−0.0934600 + 0.995623i \(0.529793\pi\)
\(14\) 4.34214 1.16049
\(15\) 0 0
\(16\) −4.28705 −1.07176
\(17\) 1.19266 0.289264 0.144632 0.989486i \(-0.453800\pi\)
0.144632 + 0.989486i \(0.453800\pi\)
\(18\) 0 0
\(19\) −5.61616 −1.28844 −0.644218 0.764842i \(-0.722817\pi\)
−0.644218 + 0.764842i \(0.722817\pi\)
\(20\) −5.24077 −1.17187
\(21\) 0 0
\(22\) −2.54244 −0.542049
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 3.07417 0.614834
\(26\) 1.32142 0.259151
\(27\) 0 0
\(28\) −4.08449 −0.771897
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −4.05642 −0.728555 −0.364277 0.931290i \(-0.618684\pi\)
−0.364277 + 0.931290i \(0.618684\pi\)
\(32\) 7.79533 1.37803
\(33\) 0 0
\(34\) −2.33846 −0.401043
\(35\) 6.29275 1.06367
\(36\) 0 0
\(37\) 3.39113 0.557499 0.278749 0.960364i \(-0.410080\pi\)
0.278749 + 0.960364i \(0.410080\pi\)
\(38\) 11.0116 1.78632
\(39\) 0 0
\(40\) −0.867109 −0.137102
\(41\) 9.19828 1.43653 0.718265 0.695770i \(-0.244937\pi\)
0.718265 + 0.695770i \(0.244937\pi\)
\(42\) 0 0
\(43\) 9.58517 1.46172 0.730862 0.682525i \(-0.239118\pi\)
0.730862 + 0.682525i \(0.239118\pi\)
\(44\) 2.39158 0.360544
\(45\) 0 0
\(46\) −1.96070 −0.289090
\(47\) −4.53489 −0.661481 −0.330741 0.943722i \(-0.607299\pi\)
−0.330741 + 0.943722i \(0.607299\pi\)
\(48\) 0 0
\(49\) −2.09562 −0.299375
\(50\) −6.02754 −0.852423
\(51\) 0 0
\(52\) −1.24301 −0.172374
\(53\) 3.31678 0.455595 0.227797 0.973709i \(-0.426848\pi\)
0.227797 + 0.973709i \(0.426848\pi\)
\(54\) 0 0
\(55\) −3.68457 −0.496828
\(56\) −0.675798 −0.0903073
\(57\) 0 0
\(58\) −1.96070 −0.257453
\(59\) 7.04726 0.917475 0.458738 0.888572i \(-0.348302\pi\)
0.458738 + 0.888572i \(0.348302\pi\)
\(60\) 0 0
\(61\) −13.0676 −1.67314 −0.836568 0.547864i \(-0.815441\pi\)
−0.836568 + 0.547864i \(0.815441\pi\)
\(62\) 7.95344 1.01009
\(63\) 0 0
\(64\) −6.71023 −0.838779
\(65\) 1.91503 0.237531
\(66\) 0 0
\(67\) 4.14971 0.506967 0.253484 0.967340i \(-0.418424\pi\)
0.253484 + 0.967340i \(0.418424\pi\)
\(68\) 2.19971 0.266753
\(69\) 0 0
\(70\) −12.3382 −1.47470
\(71\) −4.40083 −0.522282 −0.261141 0.965301i \(-0.584099\pi\)
−0.261141 + 0.965301i \(0.584099\pi\)
\(72\) 0 0
\(73\) −6.12240 −0.716573 −0.358287 0.933612i \(-0.616639\pi\)
−0.358287 + 0.933612i \(0.616639\pi\)
\(74\) −6.64901 −0.772932
\(75\) 0 0
\(76\) −10.3582 −1.18817
\(77\) −2.87164 −0.327254
\(78\) 0 0
\(79\) 1.11103 0.125001 0.0625005 0.998045i \(-0.480092\pi\)
0.0625005 + 0.998045i \(0.480092\pi\)
\(80\) 12.1817 1.36195
\(81\) 0 0
\(82\) −18.0351 −1.99164
\(83\) −2.93238 −0.321871 −0.160935 0.986965i \(-0.551451\pi\)
−0.160935 + 0.986965i \(0.551451\pi\)
\(84\) 0 0
\(85\) −3.38897 −0.367585
\(86\) −18.7937 −2.02657
\(87\) 0 0
\(88\) 0.395697 0.0421815
\(89\) 13.3205 1.41197 0.705986 0.708225i \(-0.250504\pi\)
0.705986 + 0.708225i \(0.250504\pi\)
\(90\) 0 0
\(91\) 1.49252 0.156458
\(92\) 1.84436 0.192288
\(93\) 0 0
\(94\) 8.89157 0.917096
\(95\) 15.9584 1.63730
\(96\) 0 0
\(97\) 0.608559 0.0617898 0.0308949 0.999523i \(-0.490164\pi\)
0.0308949 + 0.999523i \(0.490164\pi\)
\(98\) 4.10890 0.415062
\(99\) 0 0
\(100\) 5.66989 0.566989
\(101\) −0.680930 −0.0677551 −0.0338775 0.999426i \(-0.510786\pi\)
−0.0338775 + 0.999426i \(0.510786\pi\)
\(102\) 0 0
\(103\) −2.78839 −0.274748 −0.137374 0.990519i \(-0.543866\pi\)
−0.137374 + 0.990519i \(0.543866\pi\)
\(104\) −0.205661 −0.0201667
\(105\) 0 0
\(106\) −6.50322 −0.631649
\(107\) −0.980463 −0.0947849 −0.0473924 0.998876i \(-0.515091\pi\)
−0.0473924 + 0.998876i \(0.515091\pi\)
\(108\) 0 0
\(109\) 17.2190 1.64928 0.824640 0.565658i \(-0.191378\pi\)
0.824640 + 0.565658i \(0.191378\pi\)
\(110\) 7.22436 0.688815
\(111\) 0 0
\(112\) 9.49403 0.897101
\(113\) −3.78339 −0.355912 −0.177956 0.984038i \(-0.556948\pi\)
−0.177956 + 0.984038i \(0.556948\pi\)
\(114\) 0 0
\(115\) −2.84151 −0.264972
\(116\) 1.84436 0.171245
\(117\) 0 0
\(118\) −13.8176 −1.27201
\(119\) −2.64125 −0.242123
\(120\) 0 0
\(121\) −9.31858 −0.847144
\(122\) 25.6217 2.31968
\(123\) 0 0
\(124\) −7.48151 −0.671860
\(125\) 5.47226 0.489454
\(126\) 0 0
\(127\) 15.1839 1.34736 0.673679 0.739024i \(-0.264713\pi\)
0.673679 + 0.739024i \(0.264713\pi\)
\(128\) −2.43387 −0.215126
\(129\) 0 0
\(130\) −3.75481 −0.329319
\(131\) 8.78208 0.767294 0.383647 0.923480i \(-0.374668\pi\)
0.383647 + 0.923480i \(0.374668\pi\)
\(132\) 0 0
\(133\) 12.4375 1.07846
\(134\) −8.13635 −0.702874
\(135\) 0 0
\(136\) 0.363951 0.0312086
\(137\) 6.22749 0.532050 0.266025 0.963966i \(-0.414290\pi\)
0.266025 + 0.963966i \(0.414290\pi\)
\(138\) 0 0
\(139\) 0.443368 0.0376060 0.0188030 0.999823i \(-0.494014\pi\)
0.0188030 + 0.999823i \(0.494014\pi\)
\(140\) 11.6061 0.980897
\(141\) 0 0
\(142\) 8.62873 0.724107
\(143\) −0.873907 −0.0730798
\(144\) 0 0
\(145\) −2.84151 −0.235974
\(146\) 12.0042 0.993477
\(147\) 0 0
\(148\) 6.25448 0.514115
\(149\) −1.36917 −0.112166 −0.0560832 0.998426i \(-0.517861\pi\)
−0.0560832 + 0.998426i \(0.517861\pi\)
\(150\) 0 0
\(151\) 12.8135 1.04274 0.521372 0.853329i \(-0.325420\pi\)
0.521372 + 0.853329i \(0.325420\pi\)
\(152\) −1.71382 −0.139009
\(153\) 0 0
\(154\) 5.63044 0.453714
\(155\) 11.5264 0.925819
\(156\) 0 0
\(157\) 7.07935 0.564993 0.282497 0.959268i \(-0.408837\pi\)
0.282497 + 0.959268i \(0.408837\pi\)
\(158\) −2.17841 −0.173305
\(159\) 0 0
\(160\) −22.1505 −1.75115
\(161\) −2.21458 −0.174534
\(162\) 0 0
\(163\) 18.3823 1.43982 0.719908 0.694069i \(-0.244184\pi\)
0.719908 + 0.694069i \(0.244184\pi\)
\(164\) 16.9650 1.32474
\(165\) 0 0
\(166\) 5.74953 0.446250
\(167\) −16.1543 −1.25006 −0.625030 0.780601i \(-0.714913\pi\)
−0.625030 + 0.780601i \(0.714913\pi\)
\(168\) 0 0
\(169\) −12.5458 −0.965061
\(170\) 6.64476 0.509630
\(171\) 0 0
\(172\) 17.6785 1.34797
\(173\) −4.63833 −0.352646 −0.176323 0.984332i \(-0.556420\pi\)
−0.176323 + 0.984332i \(0.556420\pi\)
\(174\) 0 0
\(175\) −6.80800 −0.514637
\(176\) −5.55900 −0.419025
\(177\) 0 0
\(178\) −26.1176 −1.95760
\(179\) 22.3814 1.67287 0.836434 0.548068i \(-0.184637\pi\)
0.836434 + 0.548068i \(0.184637\pi\)
\(180\) 0 0
\(181\) −15.0727 −1.12034 −0.560171 0.828377i \(-0.689265\pi\)
−0.560171 + 0.828377i \(0.689265\pi\)
\(182\) −2.92638 −0.216918
\(183\) 0 0
\(184\) 0.305158 0.0224966
\(185\) −9.63594 −0.708448
\(186\) 0 0
\(187\) 1.54652 0.113093
\(188\) −8.36398 −0.610006
\(189\) 0 0
\(190\) −31.2897 −2.26999
\(191\) 12.0277 0.870291 0.435146 0.900360i \(-0.356697\pi\)
0.435146 + 0.900360i \(0.356697\pi\)
\(192\) 0 0
\(193\) −10.0358 −0.722392 −0.361196 0.932490i \(-0.617632\pi\)
−0.361196 + 0.932490i \(0.617632\pi\)
\(194\) −1.19320 −0.0856671
\(195\) 0 0
\(196\) −3.86509 −0.276078
\(197\) 15.2492 1.08646 0.543229 0.839584i \(-0.317201\pi\)
0.543229 + 0.839584i \(0.317201\pi\)
\(198\) 0 0
\(199\) −14.5103 −1.02861 −0.514304 0.857608i \(-0.671950\pi\)
−0.514304 + 0.857608i \(0.671950\pi\)
\(200\) 0.938108 0.0663343
\(201\) 0 0
\(202\) 1.33510 0.0939375
\(203\) −2.21458 −0.155433
\(204\) 0 0
\(205\) −26.1370 −1.82549
\(206\) 5.46721 0.380919
\(207\) 0 0
\(208\) 2.88926 0.200334
\(209\) −7.28246 −0.503738
\(210\) 0 0
\(211\) 25.6728 1.76739 0.883694 0.468065i \(-0.155049\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(212\) 6.11734 0.420141
\(213\) 0 0
\(214\) 1.92240 0.131412
\(215\) −27.2363 −1.85750
\(216\) 0 0
\(217\) 8.98328 0.609825
\(218\) −33.7614 −2.28661
\(219\) 0 0
\(220\) −6.79569 −0.458165
\(221\) −0.803795 −0.0540691
\(222\) 0 0
\(223\) −12.1664 −0.814724 −0.407362 0.913267i \(-0.633551\pi\)
−0.407362 + 0.913267i \(0.633551\pi\)
\(224\) −17.2634 −1.15346
\(225\) 0 0
\(226\) 7.41811 0.493446
\(227\) −0.928537 −0.0616292 −0.0308146 0.999525i \(-0.509810\pi\)
−0.0308146 + 0.999525i \(0.509810\pi\)
\(228\) 0 0
\(229\) 19.3364 1.27779 0.638894 0.769295i \(-0.279392\pi\)
0.638894 + 0.769295i \(0.279392\pi\)
\(230\) 5.57136 0.367365
\(231\) 0 0
\(232\) 0.305158 0.0200346
\(233\) −1.34224 −0.0879334 −0.0439667 0.999033i \(-0.514000\pi\)
−0.0439667 + 0.999033i \(0.514000\pi\)
\(234\) 0 0
\(235\) 12.8859 0.840585
\(236\) 12.9977 0.846079
\(237\) 0 0
\(238\) 5.17872 0.335686
\(239\) −14.6847 −0.949874 −0.474937 0.880020i \(-0.657529\pi\)
−0.474937 + 0.880020i \(0.657529\pi\)
\(240\) 0 0
\(241\) −8.98783 −0.578957 −0.289478 0.957185i \(-0.593482\pi\)
−0.289478 + 0.957185i \(0.593482\pi\)
\(242\) 18.2710 1.17450
\(243\) 0 0
\(244\) −24.1014 −1.54293
\(245\) 5.95474 0.380434
\(246\) 0 0
\(247\) 3.78501 0.240834
\(248\) −1.23785 −0.0786035
\(249\) 0 0
\(250\) −10.7295 −0.678592
\(251\) −18.5933 −1.17360 −0.586800 0.809732i \(-0.699613\pi\)
−0.586800 + 0.809732i \(0.699613\pi\)
\(252\) 0 0
\(253\) 1.29670 0.0815226
\(254\) −29.7712 −1.86801
\(255\) 0 0
\(256\) 18.1926 1.13704
\(257\) 7.89783 0.492653 0.246327 0.969187i \(-0.420776\pi\)
0.246327 + 0.969187i \(0.420776\pi\)
\(258\) 0 0
\(259\) −7.50995 −0.466645
\(260\) 3.53202 0.219046
\(261\) 0 0
\(262\) −17.2191 −1.06380
\(263\) −17.9046 −1.10405 −0.552023 0.833829i \(-0.686144\pi\)
−0.552023 + 0.833829i \(0.686144\pi\)
\(264\) 0 0
\(265\) −9.42465 −0.578952
\(266\) −24.3862 −1.49521
\(267\) 0 0
\(268\) 7.65357 0.467516
\(269\) −17.5255 −1.06855 −0.534275 0.845311i \(-0.679415\pi\)
−0.534275 + 0.845311i \(0.679415\pi\)
\(270\) 0 0
\(271\) 19.0244 1.15565 0.577824 0.816161i \(-0.303902\pi\)
0.577824 + 0.816161i \(0.303902\pi\)
\(272\) −5.11301 −0.310022
\(273\) 0 0
\(274\) −12.2103 −0.737649
\(275\) 3.98626 0.240381
\(276\) 0 0
\(277\) −10.0189 −0.601975 −0.300987 0.953628i \(-0.597316\pi\)
−0.300987 + 0.953628i \(0.597316\pi\)
\(278\) −0.869314 −0.0521380
\(279\) 0 0
\(280\) 1.92029 0.114759
\(281\) −6.16169 −0.367575 −0.183788 0.982966i \(-0.558836\pi\)
−0.183788 + 0.982966i \(0.558836\pi\)
\(282\) 0 0
\(283\) −8.23812 −0.489705 −0.244853 0.969560i \(-0.578740\pi\)
−0.244853 + 0.969560i \(0.578740\pi\)
\(284\) −8.11673 −0.481639
\(285\) 0 0
\(286\) 1.71347 0.101320
\(287\) −20.3703 −1.20242
\(288\) 0 0
\(289\) −15.5776 −0.916327
\(290\) 5.57136 0.327161
\(291\) 0 0
\(292\) −11.2919 −0.660811
\(293\) 11.1979 0.654190 0.327095 0.944991i \(-0.393930\pi\)
0.327095 + 0.944991i \(0.393930\pi\)
\(294\) 0 0
\(295\) −20.0249 −1.16589
\(296\) 1.03483 0.0601484
\(297\) 0 0
\(298\) 2.68453 0.155511
\(299\) −0.673949 −0.0389755
\(300\) 0 0
\(301\) −21.2271 −1.22351
\(302\) −25.1234 −1.44569
\(303\) 0 0
\(304\) 24.0768 1.38090
\(305\) 37.1317 2.12616
\(306\) 0 0
\(307\) −17.4442 −0.995596 −0.497798 0.867293i \(-0.665858\pi\)
−0.497798 + 0.867293i \(0.665858\pi\)
\(308\) −5.29635 −0.301787
\(309\) 0 0
\(310\) −22.5998 −1.28358
\(311\) 33.3243 1.88965 0.944823 0.327581i \(-0.106233\pi\)
0.944823 + 0.327581i \(0.106233\pi\)
\(312\) 0 0
\(313\) −3.59645 −0.203283 −0.101642 0.994821i \(-0.532409\pi\)
−0.101642 + 0.994821i \(0.532409\pi\)
\(314\) −13.8805 −0.783322
\(315\) 0 0
\(316\) 2.04915 0.115274
\(317\) −22.9986 −1.29173 −0.645865 0.763452i \(-0.723503\pi\)
−0.645865 + 0.763452i \(0.723503\pi\)
\(318\) 0 0
\(319\) 1.29670 0.0726010
\(320\) 19.0672 1.06589
\(321\) 0 0
\(322\) 4.34214 0.241978
\(323\) −6.69820 −0.372698
\(324\) 0 0
\(325\) −2.07184 −0.114925
\(326\) −36.0424 −1.99620
\(327\) 0 0
\(328\) 2.80693 0.154987
\(329\) 10.0429 0.553682
\(330\) 0 0
\(331\) −21.5418 −1.18405 −0.592023 0.805921i \(-0.701671\pi\)
−0.592023 + 0.805921i \(0.701671\pi\)
\(332\) −5.40838 −0.296823
\(333\) 0 0
\(334\) 31.6739 1.73312
\(335\) −11.7914 −0.644235
\(336\) 0 0
\(337\) 4.44117 0.241926 0.120963 0.992657i \(-0.461402\pi\)
0.120963 + 0.992657i \(0.461402\pi\)
\(338\) 24.5986 1.33799
\(339\) 0 0
\(340\) −6.25048 −0.338980
\(341\) −5.25994 −0.284842
\(342\) 0 0
\(343\) 20.1430 1.08762
\(344\) 2.92499 0.157705
\(345\) 0 0
\(346\) 9.09439 0.488918
\(347\) −32.7661 −1.75898 −0.879488 0.475922i \(-0.842114\pi\)
−0.879488 + 0.475922i \(0.842114\pi\)
\(348\) 0 0
\(349\) −7.88733 −0.422199 −0.211099 0.977465i \(-0.567704\pi\)
−0.211099 + 0.977465i \(0.567704\pi\)
\(350\) 13.3485 0.713507
\(351\) 0 0
\(352\) 10.1082 0.538767
\(353\) 1.42984 0.0761027 0.0380514 0.999276i \(-0.487885\pi\)
0.0380514 + 0.999276i \(0.487885\pi\)
\(354\) 0 0
\(355\) 12.5050 0.663696
\(356\) 24.5679 1.30210
\(357\) 0 0
\(358\) −43.8834 −2.31931
\(359\) 19.6228 1.03565 0.517827 0.855486i \(-0.326741\pi\)
0.517827 + 0.855486i \(0.326741\pi\)
\(360\) 0 0
\(361\) 12.5413 0.660069
\(362\) 29.5530 1.55327
\(363\) 0 0
\(364\) 2.75274 0.144283
\(365\) 17.3969 0.910594
\(366\) 0 0
\(367\) −4.79683 −0.250392 −0.125196 0.992132i \(-0.539956\pi\)
−0.125196 + 0.992132i \(0.539956\pi\)
\(368\) −4.28705 −0.223478
\(369\) 0 0
\(370\) 18.8932 0.982212
\(371\) −7.34528 −0.381348
\(372\) 0 0
\(373\) −19.4532 −1.00725 −0.503624 0.863923i \(-0.668000\pi\)
−0.503624 + 0.863923i \(0.668000\pi\)
\(374\) −3.03227 −0.156795
\(375\) 0 0
\(376\) −1.38386 −0.0713670
\(377\) −0.673949 −0.0347102
\(378\) 0 0
\(379\) 3.96263 0.203547 0.101773 0.994808i \(-0.467548\pi\)
0.101773 + 0.994808i \(0.467548\pi\)
\(380\) 29.4330 1.50988
\(381\) 0 0
\(382\) −23.5827 −1.20660
\(383\) −21.5143 −1.09933 −0.549665 0.835385i \(-0.685244\pi\)
−0.549665 + 0.835385i \(0.685244\pi\)
\(384\) 0 0
\(385\) 8.15979 0.415861
\(386\) 19.6772 1.00154
\(387\) 0 0
\(388\) 1.12240 0.0569814
\(389\) 9.42136 0.477682 0.238841 0.971059i \(-0.423233\pi\)
0.238841 + 0.971059i \(0.423233\pi\)
\(390\) 0 0
\(391\) 1.19266 0.0603156
\(392\) −0.639497 −0.0322995
\(393\) 0 0
\(394\) −29.8991 −1.50630
\(395\) −3.15701 −0.158847
\(396\) 0 0
\(397\) −5.73525 −0.287844 −0.143922 0.989589i \(-0.545971\pi\)
−0.143922 + 0.989589i \(0.545971\pi\)
\(398\) 28.4504 1.42609
\(399\) 0 0
\(400\) −13.1791 −0.658956
\(401\) 15.1016 0.754138 0.377069 0.926185i \(-0.376932\pi\)
0.377069 + 0.926185i \(0.376932\pi\)
\(402\) 0 0
\(403\) 2.73382 0.136181
\(404\) −1.25588 −0.0624825
\(405\) 0 0
\(406\) 4.34214 0.215497
\(407\) 4.39727 0.217965
\(408\) 0 0
\(409\) −13.2492 −0.655132 −0.327566 0.944828i \(-0.606228\pi\)
−0.327566 + 0.944828i \(0.606228\pi\)
\(410\) 51.2469 2.53090
\(411\) 0 0
\(412\) −5.14281 −0.253368
\(413\) −15.6067 −0.767958
\(414\) 0 0
\(415\) 8.33239 0.409021
\(416\) −5.25365 −0.257582
\(417\) 0 0
\(418\) 14.2787 0.698396
\(419\) −1.15337 −0.0563456 −0.0281728 0.999603i \(-0.508969\pi\)
−0.0281728 + 0.999603i \(0.508969\pi\)
\(420\) 0 0
\(421\) −35.5973 −1.73491 −0.867453 0.497519i \(-0.834245\pi\)
−0.867453 + 0.497519i \(0.834245\pi\)
\(422\) −50.3368 −2.45035
\(423\) 0 0
\(424\) 1.01214 0.0491540
\(425\) 3.66645 0.177849
\(426\) 0 0
\(427\) 28.9393 1.40047
\(428\) −1.80833 −0.0874089
\(429\) 0 0
\(430\) 53.4024 2.57529
\(431\) −7.03642 −0.338932 −0.169466 0.985536i \(-0.554204\pi\)
−0.169466 + 0.985536i \(0.554204\pi\)
\(432\) 0 0
\(433\) 10.3154 0.495726 0.247863 0.968795i \(-0.420272\pi\)
0.247863 + 0.968795i \(0.420272\pi\)
\(434\) −17.6136 −0.845478
\(435\) 0 0
\(436\) 31.7581 1.52094
\(437\) −5.61616 −0.268658
\(438\) 0 0
\(439\) −27.8585 −1.32962 −0.664808 0.747015i \(-0.731486\pi\)
−0.664808 + 0.747015i \(0.731486\pi\)
\(440\) −1.12438 −0.0536026
\(441\) 0 0
\(442\) 1.57601 0.0749629
\(443\) −26.6762 −1.26742 −0.633712 0.773569i \(-0.718470\pi\)
−0.633712 + 0.773569i \(0.718470\pi\)
\(444\) 0 0
\(445\) −37.8504 −1.79428
\(446\) 23.8548 1.12956
\(447\) 0 0
\(448\) 14.8604 0.702086
\(449\) 16.4948 0.778437 0.389219 0.921145i \(-0.372745\pi\)
0.389219 + 0.921145i \(0.372745\pi\)
\(450\) 0 0
\(451\) 11.9274 0.561638
\(452\) −6.97795 −0.328215
\(453\) 0 0
\(454\) 1.82059 0.0854444
\(455\) −4.24100 −0.198821
\(456\) 0 0
\(457\) −32.6252 −1.52614 −0.763070 0.646316i \(-0.776309\pi\)
−0.763070 + 0.646316i \(0.776309\pi\)
\(458\) −37.9131 −1.77156
\(459\) 0 0
\(460\) −5.24077 −0.244352
\(461\) −39.2060 −1.82600 −0.913002 0.407956i \(-0.866242\pi\)
−0.913002 + 0.407956i \(0.866242\pi\)
\(462\) 0 0
\(463\) 14.6448 0.680600 0.340300 0.940317i \(-0.389471\pi\)
0.340300 + 0.940317i \(0.389471\pi\)
\(464\) −4.28705 −0.199021
\(465\) 0 0
\(466\) 2.63175 0.121913
\(467\) −12.7214 −0.588677 −0.294339 0.955701i \(-0.595099\pi\)
−0.294339 + 0.955701i \(0.595099\pi\)
\(468\) 0 0
\(469\) −9.18987 −0.424349
\(470\) −25.2655 −1.16541
\(471\) 0 0
\(472\) 2.15053 0.0989861
\(473\) 12.4290 0.571488
\(474\) 0 0
\(475\) −17.2650 −0.792175
\(476\) −4.87143 −0.223282
\(477\) 0 0
\(478\) 28.7923 1.31693
\(479\) 32.0057 1.46238 0.731190 0.682174i \(-0.238965\pi\)
0.731190 + 0.682174i \(0.238965\pi\)
\(480\) 0 0
\(481\) −2.28545 −0.104208
\(482\) 17.6225 0.802682
\(483\) 0 0
\(484\) −17.1868 −0.781220
\(485\) −1.72923 −0.0785201
\(486\) 0 0
\(487\) 0.0321749 0.00145798 0.000728991 1.00000i \(-0.499768\pi\)
0.000728991 1.00000i \(0.499768\pi\)
\(488\) −3.98769 −0.180514
\(489\) 0 0
\(490\) −11.6755 −0.527444
\(491\) 5.05865 0.228294 0.114147 0.993464i \(-0.463587\pi\)
0.114147 + 0.993464i \(0.463587\pi\)
\(492\) 0 0
\(493\) 1.19266 0.0537149
\(494\) −7.42129 −0.333900
\(495\) 0 0
\(496\) 17.3901 0.780838
\(497\) 9.74600 0.437168
\(498\) 0 0
\(499\) 34.2451 1.53302 0.766511 0.642231i \(-0.221991\pi\)
0.766511 + 0.642231i \(0.221991\pi\)
\(500\) 10.0928 0.451365
\(501\) 0 0
\(502\) 36.4560 1.62711
\(503\) −18.8257 −0.839398 −0.419699 0.907663i \(-0.637864\pi\)
−0.419699 + 0.907663i \(0.637864\pi\)
\(504\) 0 0
\(505\) 1.93487 0.0861005
\(506\) −2.54244 −0.113025
\(507\) 0 0
\(508\) 28.0047 1.24251
\(509\) −30.0086 −1.33011 −0.665054 0.746795i \(-0.731592\pi\)
−0.665054 + 0.746795i \(0.731592\pi\)
\(510\) 0 0
\(511\) 13.5586 0.599796
\(512\) −30.8025 −1.36129
\(513\) 0 0
\(514\) −15.4853 −0.683028
\(515\) 7.92324 0.349140
\(516\) 0 0
\(517\) −5.88037 −0.258618
\(518\) 14.7248 0.646970
\(519\) 0 0
\(520\) 0.584388 0.0256271
\(521\) 12.9951 0.569328 0.284664 0.958627i \(-0.408118\pi\)
0.284664 + 0.958627i \(0.408118\pi\)
\(522\) 0 0
\(523\) −14.9002 −0.651540 −0.325770 0.945449i \(-0.605623\pi\)
−0.325770 + 0.945449i \(0.605623\pi\)
\(524\) 16.1973 0.707584
\(525\) 0 0
\(526\) 35.1056 1.53068
\(527\) −4.83795 −0.210744
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 18.4790 0.802675
\(531\) 0 0
\(532\) 22.9392 0.994540
\(533\) −6.19917 −0.268516
\(534\) 0 0
\(535\) 2.78599 0.120449
\(536\) 1.26632 0.0546966
\(537\) 0 0
\(538\) 34.3624 1.48147
\(539\) −2.71739 −0.117046
\(540\) 0 0
\(541\) 8.58232 0.368983 0.184491 0.982834i \(-0.440936\pi\)
0.184491 + 0.982834i \(0.440936\pi\)
\(542\) −37.3012 −1.60222
\(543\) 0 0
\(544\) 9.29720 0.398614
\(545\) −48.9279 −2.09584
\(546\) 0 0
\(547\) −15.7984 −0.675489 −0.337744 0.941238i \(-0.609664\pi\)
−0.337744 + 0.941238i \(0.609664\pi\)
\(548\) 11.4858 0.490647
\(549\) 0 0
\(550\) −7.81589 −0.333271
\(551\) −5.61616 −0.239257
\(552\) 0 0
\(553\) −2.46048 −0.104630
\(554\) 19.6440 0.834594
\(555\) 0 0
\(556\) 0.817732 0.0346795
\(557\) 1.23748 0.0524337 0.0262169 0.999656i \(-0.491654\pi\)
0.0262169 + 0.999656i \(0.491654\pi\)
\(558\) 0 0
\(559\) −6.45992 −0.273225
\(560\) −26.9774 −1.14000
\(561\) 0 0
\(562\) 12.0812 0.509617
\(563\) −28.8167 −1.21448 −0.607239 0.794519i \(-0.707723\pi\)
−0.607239 + 0.794519i \(0.707723\pi\)
\(564\) 0 0
\(565\) 10.7505 0.452279
\(566\) 16.1525 0.678941
\(567\) 0 0
\(568\) −1.34295 −0.0563489
\(569\) 1.98271 0.0831195 0.0415597 0.999136i \(-0.486767\pi\)
0.0415597 + 0.999136i \(0.486767\pi\)
\(570\) 0 0
\(571\) 10.8248 0.453004 0.226502 0.974011i \(-0.427271\pi\)
0.226502 + 0.974011i \(0.427271\pi\)
\(572\) −1.61180 −0.0673928
\(573\) 0 0
\(574\) 39.9402 1.66707
\(575\) 3.07417 0.128202
\(576\) 0 0
\(577\) 41.9111 1.74478 0.872391 0.488809i \(-0.162569\pi\)
0.872391 + 0.488809i \(0.162569\pi\)
\(578\) 30.5430 1.27042
\(579\) 0 0
\(580\) −5.24077 −0.217611
\(581\) 6.49400 0.269417
\(582\) 0 0
\(583\) 4.30085 0.178123
\(584\) −1.86830 −0.0773109
\(585\) 0 0
\(586\) −21.9558 −0.906988
\(587\) 22.4769 0.927721 0.463860 0.885908i \(-0.346464\pi\)
0.463860 + 0.885908i \(0.346464\pi\)
\(588\) 0 0
\(589\) 22.7815 0.938697
\(590\) 39.2628 1.61642
\(591\) 0 0
\(592\) −14.5380 −0.597507
\(593\) 26.6551 1.09459 0.547297 0.836938i \(-0.315657\pi\)
0.547297 + 0.836938i \(0.315657\pi\)
\(594\) 0 0
\(595\) 7.50514 0.307681
\(596\) −2.52524 −0.103438
\(597\) 0 0
\(598\) 1.32142 0.0540367
\(599\) −36.8292 −1.50480 −0.752400 0.658707i \(-0.771104\pi\)
−0.752400 + 0.658707i \(0.771104\pi\)
\(600\) 0 0
\(601\) −0.888255 −0.0362327 −0.0181163 0.999836i \(-0.505767\pi\)
−0.0181163 + 0.999836i \(0.505767\pi\)
\(602\) 41.6202 1.69631
\(603\) 0 0
\(604\) 23.6327 0.961599
\(605\) 26.4788 1.07652
\(606\) 0 0
\(607\) −22.3048 −0.905322 −0.452661 0.891683i \(-0.649525\pi\)
−0.452661 + 0.891683i \(0.649525\pi\)
\(608\) −43.7798 −1.77551
\(609\) 0 0
\(610\) −72.8043 −2.94776
\(611\) 3.05628 0.123644
\(612\) 0 0
\(613\) −30.2562 −1.22204 −0.611018 0.791617i \(-0.709240\pi\)
−0.611018 + 0.791617i \(0.709240\pi\)
\(614\) 34.2030 1.38032
\(615\) 0 0
\(616\) −0.876304 −0.0353073
\(617\) −3.71829 −0.149693 −0.0748464 0.997195i \(-0.523847\pi\)
−0.0748464 + 0.997195i \(0.523847\pi\)
\(618\) 0 0
\(619\) 21.8048 0.876409 0.438205 0.898875i \(-0.355615\pi\)
0.438205 + 0.898875i \(0.355615\pi\)
\(620\) 21.2588 0.853773
\(621\) 0 0
\(622\) −65.3391 −2.61986
\(623\) −29.4994 −1.18187
\(624\) 0 0
\(625\) −30.9203 −1.23681
\(626\) 7.05157 0.281837
\(627\) 0 0
\(628\) 13.0569 0.521026
\(629\) 4.04448 0.161264
\(630\) 0 0
\(631\) 4.62402 0.184079 0.0920396 0.995755i \(-0.470661\pi\)
0.0920396 + 0.995755i \(0.470661\pi\)
\(632\) 0.339041 0.0134863
\(633\) 0 0
\(634\) 45.0934 1.79089
\(635\) −43.1453 −1.71217
\(636\) 0 0
\(637\) 1.41234 0.0559591
\(638\) −2.54244 −0.100656
\(639\) 0 0
\(640\) 6.91587 0.273374
\(641\) 29.0724 1.14829 0.574145 0.818754i \(-0.305335\pi\)
0.574145 + 0.818754i \(0.305335\pi\)
\(642\) 0 0
\(643\) −26.8775 −1.05994 −0.529972 0.848015i \(-0.677797\pi\)
−0.529972 + 0.848015i \(0.677797\pi\)
\(644\) −4.08449 −0.160952
\(645\) 0 0
\(646\) 13.1332 0.516718
\(647\) −4.89089 −0.192281 −0.0961404 0.995368i \(-0.530650\pi\)
−0.0961404 + 0.995368i \(0.530650\pi\)
\(648\) 0 0
\(649\) 9.13815 0.358704
\(650\) 4.06226 0.159335
\(651\) 0 0
\(652\) 33.9037 1.32777
\(653\) −26.8174 −1.04945 −0.524723 0.851273i \(-0.675831\pi\)
−0.524723 + 0.851273i \(0.675831\pi\)
\(654\) 0 0
\(655\) −24.9544 −0.975047
\(656\) −39.4335 −1.53962
\(657\) 0 0
\(658\) −19.6911 −0.767640
\(659\) 36.0236 1.40328 0.701641 0.712531i \(-0.252451\pi\)
0.701641 + 0.712531i \(0.252451\pi\)
\(660\) 0 0
\(661\) −28.4082 −1.10495 −0.552476 0.833529i \(-0.686317\pi\)
−0.552476 + 0.833529i \(0.686317\pi\)
\(662\) 42.2372 1.64159
\(663\) 0 0
\(664\) −0.894840 −0.0347265
\(665\) −35.3411 −1.37047
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −29.7944 −1.15278
\(669\) 0 0
\(670\) 23.1195 0.893185
\(671\) −16.9447 −0.654143
\(672\) 0 0
\(673\) 9.35661 0.360671 0.180335 0.983605i \(-0.442282\pi\)
0.180335 + 0.983605i \(0.442282\pi\)
\(674\) −8.70782 −0.335413
\(675\) 0 0
\(676\) −23.1390 −0.889961
\(677\) −44.4912 −1.70994 −0.854968 0.518681i \(-0.826423\pi\)
−0.854968 + 0.518681i \(0.826423\pi\)
\(678\) 0 0
\(679\) −1.34770 −0.0517201
\(680\) −1.03417 −0.0396586
\(681\) 0 0
\(682\) 10.3132 0.394913
\(683\) −15.2249 −0.582563 −0.291281 0.956637i \(-0.594082\pi\)
−0.291281 + 0.956637i \(0.594082\pi\)
\(684\) 0 0
\(685\) −17.6955 −0.676109
\(686\) −39.4945 −1.50791
\(687\) 0 0
\(688\) −41.0921 −1.56662
\(689\) −2.23534 −0.0851597
\(690\) 0 0
\(691\) −38.8543 −1.47809 −0.739044 0.673657i \(-0.764722\pi\)
−0.739044 + 0.673657i \(0.764722\pi\)
\(692\) −8.55476 −0.325203
\(693\) 0 0
\(694\) 64.2446 2.43869
\(695\) −1.25983 −0.0477882
\(696\) 0 0
\(697\) 10.9705 0.415536
\(698\) 15.4647 0.585348
\(699\) 0 0
\(700\) −12.5564 −0.474589
\(701\) −8.97613 −0.339024 −0.169512 0.985528i \(-0.554219\pi\)
−0.169512 + 0.985528i \(0.554219\pi\)
\(702\) 0 0
\(703\) −19.0452 −0.718302
\(704\) −8.70112 −0.327936
\(705\) 0 0
\(706\) −2.80350 −0.105511
\(707\) 1.50798 0.0567133
\(708\) 0 0
\(709\) 22.6591 0.850979 0.425489 0.904963i \(-0.360102\pi\)
0.425489 + 0.904963i \(0.360102\pi\)
\(710\) −24.5186 −0.920167
\(711\) 0 0
\(712\) 4.06487 0.152337
\(713\) −4.05642 −0.151914
\(714\) 0 0
\(715\) 2.48321 0.0928670
\(716\) 41.2795 1.54269
\(717\) 0 0
\(718\) −38.4746 −1.43586
\(719\) −2.58167 −0.0962802 −0.0481401 0.998841i \(-0.515329\pi\)
−0.0481401 + 0.998841i \(0.515329\pi\)
\(720\) 0 0
\(721\) 6.17512 0.229974
\(722\) −24.5898 −0.915137
\(723\) 0 0
\(724\) −27.7995 −1.03316
\(725\) 3.07417 0.114172
\(726\) 0 0
\(727\) −15.2473 −0.565490 −0.282745 0.959195i \(-0.591245\pi\)
−0.282745 + 0.959195i \(0.591245\pi\)
\(728\) 0.455453 0.0168802
\(729\) 0 0
\(730\) −34.1101 −1.26247
\(731\) 11.4319 0.422823
\(732\) 0 0
\(733\) −35.5375 −1.31261 −0.656303 0.754497i \(-0.727881\pi\)
−0.656303 + 0.754497i \(0.727881\pi\)
\(734\) 9.40516 0.347151
\(735\) 0 0
\(736\) 7.79533 0.287339
\(737\) 5.38091 0.198208
\(738\) 0 0
\(739\) −37.2272 −1.36942 −0.684712 0.728814i \(-0.740072\pi\)
−0.684712 + 0.728814i \(0.740072\pi\)
\(740\) −17.7722 −0.653318
\(741\) 0 0
\(742\) 14.4019 0.528711
\(743\) 7.10823 0.260776 0.130388 0.991463i \(-0.458378\pi\)
0.130388 + 0.991463i \(0.458378\pi\)
\(744\) 0 0
\(745\) 3.89049 0.142537
\(746\) 38.1419 1.39648
\(747\) 0 0
\(748\) 2.85235 0.104292
\(749\) 2.17132 0.0793381
\(750\) 0 0
\(751\) 5.55783 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(752\) 19.4413 0.708951
\(753\) 0 0
\(754\) 1.32142 0.0481231
\(755\) −36.4095 −1.32508
\(756\) 0 0
\(757\) −10.0525 −0.365365 −0.182683 0.983172i \(-0.558478\pi\)
−0.182683 + 0.983172i \(0.558478\pi\)
\(758\) −7.76955 −0.282203
\(759\) 0 0
\(760\) 4.86983 0.176647
\(761\) −31.3006 −1.13465 −0.567324 0.823495i \(-0.692021\pi\)
−0.567324 + 0.823495i \(0.692021\pi\)
\(762\) 0 0
\(763\) −38.1329 −1.38050
\(764\) 22.1834 0.802567
\(765\) 0 0
\(766\) 42.1832 1.52414
\(767\) −4.74950 −0.171494
\(768\) 0 0
\(769\) 47.2084 1.70238 0.851190 0.524858i \(-0.175881\pi\)
0.851190 + 0.524858i \(0.175881\pi\)
\(770\) −15.9989 −0.576562
\(771\) 0 0
\(772\) −18.5096 −0.666177
\(773\) −0.309737 −0.0111405 −0.00557023 0.999984i \(-0.501773\pi\)
−0.00557023 + 0.999984i \(0.501773\pi\)
\(774\) 0 0
\(775\) −12.4701 −0.447940
\(776\) 0.185707 0.00666648
\(777\) 0 0
\(778\) −18.4725 −0.662272
\(779\) −51.6590 −1.85088
\(780\) 0 0
\(781\) −5.70654 −0.204196
\(782\) −2.33846 −0.0836232
\(783\) 0 0
\(784\) 8.98405 0.320859
\(785\) −20.1160 −0.717972
\(786\) 0 0
\(787\) −12.1845 −0.434330 −0.217165 0.976135i \(-0.569681\pi\)
−0.217165 + 0.976135i \(0.569681\pi\)
\(788\) 28.1250 1.00191
\(789\) 0 0
\(790\) 6.18997 0.220229
\(791\) 8.37863 0.297910
\(792\) 0 0
\(793\) 8.80690 0.312742
\(794\) 11.2451 0.399074
\(795\) 0 0
\(796\) −26.7623 −0.948563
\(797\) −1.87618 −0.0664576 −0.0332288 0.999448i \(-0.510579\pi\)
−0.0332288 + 0.999448i \(0.510579\pi\)
\(798\) 0 0
\(799\) −5.40860 −0.191342
\(800\) 23.9642 0.847261
\(801\) 0 0
\(802\) −29.6098 −1.04556
\(803\) −7.93890 −0.280158
\(804\) 0 0
\(805\) 6.29275 0.221790
\(806\) −5.36022 −0.188806
\(807\) 0 0
\(808\) −0.207791 −0.00731007
\(809\) −2.02618 −0.0712369 −0.0356184 0.999365i \(-0.511340\pi\)
−0.0356184 + 0.999365i \(0.511340\pi\)
\(810\) 0 0
\(811\) 1.11691 0.0392201 0.0196101 0.999808i \(-0.493758\pi\)
0.0196101 + 0.999808i \(0.493758\pi\)
\(812\) −4.08449 −0.143338
\(813\) 0 0
\(814\) −8.62175 −0.302192
\(815\) −52.2336 −1.82966
\(816\) 0 0
\(817\) −53.8319 −1.88334
\(818\) 25.9778 0.908293
\(819\) 0 0
\(820\) −48.2061 −1.68343
\(821\) −3.23186 −0.112793 −0.0563964 0.998408i \(-0.517961\pi\)
−0.0563964 + 0.998408i \(0.517961\pi\)
\(822\) 0 0
\(823\) −9.69183 −0.337836 −0.168918 0.985630i \(-0.554027\pi\)
−0.168918 + 0.985630i \(0.554027\pi\)
\(824\) −0.850900 −0.0296425
\(825\) 0 0
\(826\) 30.6002 1.06472
\(827\) 40.6735 1.41436 0.707178 0.707036i \(-0.249968\pi\)
0.707178 + 0.707036i \(0.249968\pi\)
\(828\) 0 0
\(829\) −17.7723 −0.617257 −0.308629 0.951183i \(-0.599870\pi\)
−0.308629 + 0.951183i \(0.599870\pi\)
\(830\) −16.3373 −0.567078
\(831\) 0 0
\(832\) 4.52235 0.156784
\(833\) −2.49938 −0.0865983
\(834\) 0 0
\(835\) 45.9027 1.58853
\(836\) −13.4315 −0.464538
\(837\) 0 0
\(838\) 2.26141 0.0781191
\(839\) 1.41911 0.0489932 0.0244966 0.999700i \(-0.492202\pi\)
0.0244966 + 0.999700i \(0.492202\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 69.7958 2.40532
\(843\) 0 0
\(844\) 47.3499 1.62985
\(845\) 35.6490 1.22636
\(846\) 0 0
\(847\) 20.6368 0.709088
\(848\) −14.2192 −0.488289
\(849\) 0 0
\(850\) −7.18883 −0.246575
\(851\) 3.39113 0.116247
\(852\) 0 0
\(853\) −22.9878 −0.787086 −0.393543 0.919306i \(-0.628751\pi\)
−0.393543 + 0.919306i \(0.628751\pi\)
\(854\) −56.7414 −1.94165
\(855\) 0 0
\(856\) −0.299196 −0.0102263
\(857\) −9.16185 −0.312963 −0.156481 0.987681i \(-0.550015\pi\)
−0.156481 + 0.987681i \(0.550015\pi\)
\(858\) 0 0
\(859\) −44.1195 −1.50534 −0.752670 0.658398i \(-0.771234\pi\)
−0.752670 + 0.658398i \(0.771234\pi\)
\(860\) −50.2337 −1.71295
\(861\) 0 0
\(862\) 13.7963 0.469905
\(863\) −25.6405 −0.872813 −0.436406 0.899750i \(-0.643749\pi\)
−0.436406 + 0.899750i \(0.643749\pi\)
\(864\) 0 0
\(865\) 13.1799 0.448128
\(866\) −20.2254 −0.687288
\(867\) 0 0
\(868\) 16.5684 0.562369
\(869\) 1.44067 0.0488715
\(870\) 0 0
\(871\) −2.79669 −0.0947623
\(872\) 5.25451 0.177940
\(873\) 0 0
\(874\) 11.0116 0.372474
\(875\) −12.1188 −0.409689
\(876\) 0 0
\(877\) −17.5935 −0.594091 −0.297045 0.954863i \(-0.596001\pi\)
−0.297045 + 0.954863i \(0.596001\pi\)
\(878\) 54.6224 1.84342
\(879\) 0 0
\(880\) 15.7959 0.532481
\(881\) −33.7623 −1.13748 −0.568741 0.822517i \(-0.692569\pi\)
−0.568741 + 0.822517i \(0.692569\pi\)
\(882\) 0 0
\(883\) 9.69578 0.326289 0.163145 0.986602i \(-0.447836\pi\)
0.163145 + 0.986602i \(0.447836\pi\)
\(884\) −1.48249 −0.0498615
\(885\) 0 0
\(886\) 52.3041 1.75719
\(887\) 28.1087 0.943796 0.471898 0.881653i \(-0.343569\pi\)
0.471898 + 0.881653i \(0.343569\pi\)
\(888\) 0 0
\(889\) −33.6261 −1.12778
\(890\) 74.2134 2.48764
\(891\) 0 0
\(892\) −22.4393 −0.751324
\(893\) 25.4687 0.852276
\(894\) 0 0
\(895\) −63.5970 −2.12581
\(896\) 5.39001 0.180068
\(897\) 0 0
\(898\) −32.3414 −1.07925
\(899\) −4.05642 −0.135289
\(900\) 0 0
\(901\) 3.95580 0.131787
\(902\) −23.3860 −0.778670
\(903\) 0 0
\(904\) −1.15453 −0.0383992
\(905\) 42.8291 1.42369
\(906\) 0 0
\(907\) 10.5584 0.350585 0.175292 0.984516i \(-0.443913\pi\)
0.175292 + 0.984516i \(0.443913\pi\)
\(908\) −1.71256 −0.0568333
\(909\) 0 0
\(910\) 8.31534 0.275651
\(911\) −36.6663 −1.21481 −0.607405 0.794393i \(-0.707789\pi\)
−0.607405 + 0.794393i \(0.707789\pi\)
\(912\) 0 0
\(913\) −3.80241 −0.125841
\(914\) 63.9683 2.11588
\(915\) 0 0
\(916\) 35.6634 1.17835
\(917\) −19.4486 −0.642251
\(918\) 0 0
\(919\) −43.8602 −1.44681 −0.723407 0.690422i \(-0.757425\pi\)
−0.723407 + 0.690422i \(0.757425\pi\)
\(920\) −0.867109 −0.0285878
\(921\) 0 0
\(922\) 76.8713 2.53162
\(923\) 2.96594 0.0976250
\(924\) 0 0
\(925\) 10.4249 0.342769
\(926\) −28.7141 −0.943602
\(927\) 0 0
\(928\) 7.79533 0.255894
\(929\) 31.9067 1.04683 0.523413 0.852079i \(-0.324658\pi\)
0.523413 + 0.852079i \(0.324658\pi\)
\(930\) 0 0
\(931\) 11.7694 0.385726
\(932\) −2.47559 −0.0810905
\(933\) 0 0
\(934\) 24.9429 0.816158
\(935\) −4.39446 −0.143714
\(936\) 0 0
\(937\) 42.0133 1.37251 0.686257 0.727359i \(-0.259252\pi\)
0.686257 + 0.727359i \(0.259252\pi\)
\(938\) 18.0186 0.588329
\(939\) 0 0
\(940\) 23.7663 0.775172
\(941\) 30.3371 0.988963 0.494481 0.869188i \(-0.335358\pi\)
0.494481 + 0.869188i \(0.335358\pi\)
\(942\) 0 0
\(943\) 9.19828 0.299537
\(944\) −30.2120 −0.983316
\(945\) 0 0
\(946\) −24.3697 −0.792327
\(947\) 15.9902 0.519610 0.259805 0.965661i \(-0.416342\pi\)
0.259805 + 0.965661i \(0.416342\pi\)
\(948\) 0 0
\(949\) 4.12619 0.133942
\(950\) 33.8517 1.09829
\(951\) 0 0
\(952\) −0.806000 −0.0261226
\(953\) −27.9450 −0.905228 −0.452614 0.891707i \(-0.649508\pi\)
−0.452614 + 0.891707i \(0.649508\pi\)
\(954\) 0 0
\(955\) −34.1767 −1.10593
\(956\) −27.0839 −0.875956
\(957\) 0 0
\(958\) −62.7538 −2.02748
\(959\) −13.7913 −0.445344
\(960\) 0 0
\(961\) −14.5454 −0.469208
\(962\) 4.48110 0.144476
\(963\) 0 0
\(964\) −16.5768 −0.533903
\(965\) 28.5168 0.917988
\(966\) 0 0
\(967\) −24.3686 −0.783642 −0.391821 0.920041i \(-0.628155\pi\)
−0.391821 + 0.920041i \(0.628155\pi\)
\(968\) −2.84364 −0.0913981
\(969\) 0 0
\(970\) 3.39050 0.108862
\(971\) 11.2336 0.360503 0.180251 0.983621i \(-0.442309\pi\)
0.180251 + 0.983621i \(0.442309\pi\)
\(972\) 0 0
\(973\) −0.981875 −0.0314775
\(974\) −0.0630854 −0.00202139
\(975\) 0 0
\(976\) 56.0215 1.79320
\(977\) 7.55369 0.241664 0.120832 0.992673i \(-0.461444\pi\)
0.120832 + 0.992673i \(0.461444\pi\)
\(978\) 0 0
\(979\) 17.2727 0.552037
\(980\) 10.9827 0.350829
\(981\) 0 0
\(982\) −9.91852 −0.316513
\(983\) −11.8587 −0.378233 −0.189116 0.981955i \(-0.560562\pi\)
−0.189116 + 0.981955i \(0.560562\pi\)
\(984\) 0 0
\(985\) −43.3307 −1.38063
\(986\) −2.33846 −0.0744718
\(987\) 0 0
\(988\) 6.98093 0.222093
\(989\) 9.58517 0.304791
\(990\) 0 0
\(991\) 7.70198 0.244662 0.122331 0.992489i \(-0.460963\pi\)
0.122331 + 0.992489i \(0.460963\pi\)
\(992\) −31.6211 −1.00397
\(993\) 0 0
\(994\) −19.1090 −0.606101
\(995\) 41.2311 1.30711
\(996\) 0 0
\(997\) 41.9155 1.32748 0.663738 0.747965i \(-0.268969\pi\)
0.663738 + 0.747965i \(0.268969\pi\)
\(998\) −67.1445 −2.12542
\(999\) 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 \(a_p\))