Properties

Label 6027.2.a.bc.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.8.7457527933.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(1.21768\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.51387 q^{2} +1.00000 q^{3} +0.291794 q^{4} -3.80505 q^{5} -1.51387 q^{6} +2.58600 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.51387 q^{2} +1.00000 q^{3} +0.291794 q^{4} -3.80505 q^{5} -1.51387 q^{6} +2.58600 q^{8} +1.00000 q^{9} +5.76034 q^{10} +1.15660 q^{11} +0.291794 q^{12} +4.56081 q^{13} -3.80505 q^{15} -4.49844 q^{16} +6.92527 q^{17} -1.51387 q^{18} -2.40606 q^{19} -1.11029 q^{20} -1.75093 q^{22} +3.28488 q^{23} +2.58600 q^{24} +9.47840 q^{25} -6.90445 q^{26} +1.00000 q^{27} +1.28140 q^{29} +5.76034 q^{30} +0.334671 q^{31} +1.63805 q^{32} +1.15660 q^{33} -10.4839 q^{34} +0.291794 q^{36} +1.13227 q^{37} +3.64245 q^{38} +4.56081 q^{39} -9.83985 q^{40} +1.00000 q^{41} +2.12116 q^{43} +0.337487 q^{44} -3.80505 q^{45} -4.97287 q^{46} +7.39779 q^{47} -4.49844 q^{48} -14.3490 q^{50} +6.92527 q^{51} +1.33082 q^{52} -2.25189 q^{53} -1.51387 q^{54} -4.40090 q^{55} -2.40606 q^{57} -1.93987 q^{58} +12.9132 q^{59} -1.11029 q^{60} -2.57480 q^{61} -0.506648 q^{62} +6.51709 q^{64} -17.3541 q^{65} -1.75093 q^{66} -6.21525 q^{67} +2.02075 q^{68} +3.28488 q^{69} +2.30854 q^{71} +2.58600 q^{72} -11.9079 q^{73} -1.71411 q^{74} +9.47840 q^{75} -0.702072 q^{76} -6.90445 q^{78} -12.7517 q^{79} +17.1168 q^{80} +1.00000 q^{81} -1.51387 q^{82} -2.58930 q^{83} -26.3510 q^{85} -3.21115 q^{86} +1.28140 q^{87} +2.99095 q^{88} +9.21039 q^{89} +5.76034 q^{90} +0.958507 q^{92} +0.334671 q^{93} -11.1993 q^{94} +9.15516 q^{95} +1.63805 q^{96} +12.8974 q^{97} +1.15660 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.51387 −1.07047 −0.535233 0.844705i \(-0.679776\pi\)
−0.535233 + 0.844705i \(0.679776\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.291794 0.145897
\(5\) −3.80505 −1.70167 −0.850835 0.525433i \(-0.823903\pi\)
−0.850835 + 0.525433i \(0.823903\pi\)
\(6\) −1.51387 −0.618034
\(7\) 0 0
\(8\) 2.58600 0.914288
\(9\) 1.00000 0.333333
\(10\) 5.76034 1.82158
\(11\) 1.15660 0.348727 0.174363 0.984681i \(-0.444213\pi\)
0.174363 + 0.984681i \(0.444213\pi\)
\(12\) 0.291794 0.0842336
\(13\) 4.56081 1.26494 0.632470 0.774585i \(-0.282041\pi\)
0.632470 + 0.774585i \(0.282041\pi\)
\(14\) 0 0
\(15\) −3.80505 −0.982460
\(16\) −4.49844 −1.12461
\(17\) 6.92527 1.67963 0.839813 0.542876i \(-0.182665\pi\)
0.839813 + 0.542876i \(0.182665\pi\)
\(18\) −1.51387 −0.356822
\(19\) −2.40606 −0.551987 −0.275994 0.961159i \(-0.589007\pi\)
−0.275994 + 0.961159i \(0.589007\pi\)
\(20\) −1.11029 −0.248268
\(21\) 0 0
\(22\) −1.75093 −0.373300
\(23\) 3.28488 0.684944 0.342472 0.939528i \(-0.388736\pi\)
0.342472 + 0.939528i \(0.388736\pi\)
\(24\) 2.58600 0.527864
\(25\) 9.47840 1.89568
\(26\) −6.90445 −1.35407
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.28140 0.237950 0.118975 0.992897i \(-0.462039\pi\)
0.118975 + 0.992897i \(0.462039\pi\)
\(30\) 5.76034 1.05169
\(31\) 0.334671 0.0601087 0.0300544 0.999548i \(-0.490432\pi\)
0.0300544 + 0.999548i \(0.490432\pi\)
\(32\) 1.63805 0.289569
\(33\) 1.15660 0.201337
\(34\) −10.4839 −1.79798
\(35\) 0 0
\(36\) 0.291794 0.0486323
\(37\) 1.13227 0.186145 0.0930724 0.995659i \(-0.470331\pi\)
0.0930724 + 0.995659i \(0.470331\pi\)
\(38\) 3.64245 0.590883
\(39\) 4.56081 0.730313
\(40\) −9.83985 −1.55582
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 2.12116 0.323474 0.161737 0.986834i \(-0.448290\pi\)
0.161737 + 0.986834i \(0.448290\pi\)
\(44\) 0.337487 0.0508781
\(45\) −3.80505 −0.567223
\(46\) −4.97287 −0.733209
\(47\) 7.39779 1.07908 0.539540 0.841960i \(-0.318598\pi\)
0.539540 + 0.841960i \(0.318598\pi\)
\(48\) −4.49844 −0.649294
\(49\) 0 0
\(50\) −14.3490 −2.02926
\(51\) 6.92527 0.969732
\(52\) 1.33082 0.184551
\(53\) −2.25189 −0.309322 −0.154661 0.987968i \(-0.549428\pi\)
−0.154661 + 0.987968i \(0.549428\pi\)
\(54\) −1.51387 −0.206011
\(55\) −4.40090 −0.593418
\(56\) 0 0
\(57\) −2.40606 −0.318690
\(58\) −1.93987 −0.254717
\(59\) 12.9132 1.68115 0.840575 0.541696i \(-0.182218\pi\)
0.840575 + 0.541696i \(0.182218\pi\)
\(60\) −1.11029 −0.143338
\(61\) −2.57480 −0.329669 −0.164834 0.986321i \(-0.552709\pi\)
−0.164834 + 0.986321i \(0.552709\pi\)
\(62\) −0.506648 −0.0643443
\(63\) 0 0
\(64\) 6.51709 0.814637
\(65\) −17.3541 −2.15251
\(66\) −1.75093 −0.215525
\(67\) −6.21525 −0.759313 −0.379657 0.925127i \(-0.623958\pi\)
−0.379657 + 0.925127i \(0.623958\pi\)
\(68\) 2.02075 0.245052
\(69\) 3.28488 0.395453
\(70\) 0 0
\(71\) 2.30854 0.273973 0.136986 0.990573i \(-0.456258\pi\)
0.136986 + 0.990573i \(0.456258\pi\)
\(72\) 2.58600 0.304763
\(73\) −11.9079 −1.39371 −0.696855 0.717212i \(-0.745418\pi\)
−0.696855 + 0.717212i \(0.745418\pi\)
\(74\) −1.71411 −0.199262
\(75\) 9.47840 1.09447
\(76\) −0.702072 −0.0805332
\(77\) 0 0
\(78\) −6.90445 −0.781775
\(79\) −12.7517 −1.43467 −0.717337 0.696727i \(-0.754639\pi\)
−0.717337 + 0.696727i \(0.754639\pi\)
\(80\) 17.1168 1.91372
\(81\) 1.00000 0.111111
\(82\) −1.51387 −0.167179
\(83\) −2.58930 −0.284213 −0.142106 0.989851i \(-0.545388\pi\)
−0.142106 + 0.989851i \(0.545388\pi\)
\(84\) 0 0
\(85\) −26.3510 −2.85817
\(86\) −3.21115 −0.346267
\(87\) 1.28140 0.137380
\(88\) 2.99095 0.318837
\(89\) 9.21039 0.976299 0.488150 0.872760i \(-0.337672\pi\)
0.488150 + 0.872760i \(0.337672\pi\)
\(90\) 5.76034 0.607193
\(91\) 0 0
\(92\) 0.958507 0.0999312
\(93\) 0.334671 0.0347038
\(94\) −11.1993 −1.15512
\(95\) 9.15516 0.939300
\(96\) 1.63805 0.167183
\(97\) 12.8974 1.30953 0.654766 0.755832i \(-0.272767\pi\)
0.654766 + 0.755832i \(0.272767\pi\)
\(98\) 0 0
\(99\) 1.15660 0.116242
\(100\) 2.76574 0.276574
\(101\) −0.177513 −0.0176632 −0.00883162 0.999961i \(-0.502811\pi\)
−0.00883162 + 0.999961i \(0.502811\pi\)
\(102\) −10.4839 −1.03807
\(103\) 14.5341 1.43209 0.716046 0.698053i \(-0.245950\pi\)
0.716046 + 0.698053i \(0.245950\pi\)
\(104\) 11.7942 1.15652
\(105\) 0 0
\(106\) 3.40907 0.331118
\(107\) −12.0732 −1.16716 −0.583579 0.812056i \(-0.698348\pi\)
−0.583579 + 0.812056i \(0.698348\pi\)
\(108\) 0.291794 0.0280779
\(109\) 17.0080 1.62907 0.814537 0.580111i \(-0.196991\pi\)
0.814537 + 0.580111i \(0.196991\pi\)
\(110\) 6.66238 0.635233
\(111\) 1.13227 0.107471
\(112\) 0 0
\(113\) 1.63814 0.154103 0.0770516 0.997027i \(-0.475449\pi\)
0.0770516 + 0.997027i \(0.475449\pi\)
\(114\) 3.64245 0.341147
\(115\) −12.4991 −1.16555
\(116\) 0.373905 0.0347162
\(117\) 4.56081 0.421647
\(118\) −19.5488 −1.79961
\(119\) 0 0
\(120\) −9.83985 −0.898251
\(121\) −9.66229 −0.878390
\(122\) 3.89790 0.352899
\(123\) 1.00000 0.0901670
\(124\) 0.0976550 0.00876968
\(125\) −17.0405 −1.52415
\(126\) 0 0
\(127\) −20.7696 −1.84300 −0.921502 0.388374i \(-0.873037\pi\)
−0.921502 + 0.388374i \(0.873037\pi\)
\(128\) −13.1421 −1.16161
\(129\) 2.12116 0.186758
\(130\) 26.2718 2.30419
\(131\) −12.0351 −1.05151 −0.525756 0.850636i \(-0.676217\pi\)
−0.525756 + 0.850636i \(0.676217\pi\)
\(132\) 0.337487 0.0293745
\(133\) 0 0
\(134\) 9.40906 0.812819
\(135\) −3.80505 −0.327487
\(136\) 17.9087 1.53566
\(137\) −6.50063 −0.555386 −0.277693 0.960670i \(-0.589570\pi\)
−0.277693 + 0.960670i \(0.589570\pi\)
\(138\) −4.97287 −0.423318
\(139\) −23.1305 −1.96191 −0.980954 0.194243i \(-0.937775\pi\)
−0.980954 + 0.194243i \(0.937775\pi\)
\(140\) 0 0
\(141\) 7.39779 0.623007
\(142\) −3.49482 −0.293279
\(143\) 5.27501 0.441118
\(144\) −4.49844 −0.374870
\(145\) −4.87579 −0.404912
\(146\) 18.0269 1.49192
\(147\) 0 0
\(148\) 0.330391 0.0271580
\(149\) −5.20043 −0.426036 −0.213018 0.977048i \(-0.568329\pi\)
−0.213018 + 0.977048i \(0.568329\pi\)
\(150\) −14.3490 −1.17159
\(151\) −10.2898 −0.837370 −0.418685 0.908131i \(-0.637509\pi\)
−0.418685 + 0.908131i \(0.637509\pi\)
\(152\) −6.22205 −0.504675
\(153\) 6.92527 0.559875
\(154\) 0 0
\(155\) −1.27344 −0.102285
\(156\) 1.33082 0.106550
\(157\) −4.03587 −0.322097 −0.161049 0.986946i \(-0.551488\pi\)
−0.161049 + 0.986946i \(0.551488\pi\)
\(158\) 19.3043 1.53577
\(159\) −2.25189 −0.178587
\(160\) −6.23287 −0.492752
\(161\) 0 0
\(162\) −1.51387 −0.118941
\(163\) 6.84917 0.536468 0.268234 0.963354i \(-0.413560\pi\)
0.268234 + 0.963354i \(0.413560\pi\)
\(164\) 0.291794 0.0227853
\(165\) −4.40090 −0.342610
\(166\) 3.91986 0.304240
\(167\) −2.72776 −0.211080 −0.105540 0.994415i \(-0.533657\pi\)
−0.105540 + 0.994415i \(0.533657\pi\)
\(168\) 0 0
\(169\) 7.80095 0.600073
\(170\) 39.8919 3.05957
\(171\) −2.40606 −0.183996
\(172\) 0.618941 0.0471938
\(173\) 3.57517 0.271815 0.135908 0.990722i \(-0.456605\pi\)
0.135908 + 0.990722i \(0.456605\pi\)
\(174\) −1.93987 −0.147061
\(175\) 0 0
\(176\) −5.20288 −0.392182
\(177\) 12.9132 0.970612
\(178\) −13.9433 −1.04510
\(179\) 13.3401 0.997084 0.498542 0.866865i \(-0.333869\pi\)
0.498542 + 0.866865i \(0.333869\pi\)
\(180\) −1.11029 −0.0827561
\(181\) 6.15975 0.457850 0.228925 0.973444i \(-0.426479\pi\)
0.228925 + 0.973444i \(0.426479\pi\)
\(182\) 0 0
\(183\) −2.57480 −0.190334
\(184\) 8.49468 0.626236
\(185\) −4.30836 −0.316757
\(186\) −0.506648 −0.0371492
\(187\) 8.00974 0.585730
\(188\) 2.15863 0.157434
\(189\) 0 0
\(190\) −13.8597 −1.00549
\(191\) 23.8691 1.72711 0.863554 0.504256i \(-0.168233\pi\)
0.863554 + 0.504256i \(0.168233\pi\)
\(192\) 6.51709 0.470331
\(193\) −21.6807 −1.56061 −0.780304 0.625400i \(-0.784936\pi\)
−0.780304 + 0.625400i \(0.784936\pi\)
\(194\) −19.5249 −1.40181
\(195\) −17.3541 −1.24275
\(196\) 0 0
\(197\) 22.1707 1.57959 0.789797 0.613368i \(-0.210186\pi\)
0.789797 + 0.613368i \(0.210186\pi\)
\(198\) −1.75093 −0.124433
\(199\) 7.79167 0.552337 0.276168 0.961109i \(-0.410935\pi\)
0.276168 + 0.961109i \(0.410935\pi\)
\(200\) 24.5111 1.73320
\(201\) −6.21525 −0.438390
\(202\) 0.268732 0.0189079
\(203\) 0 0
\(204\) 2.02075 0.141481
\(205\) −3.80505 −0.265756
\(206\) −22.0028 −1.53301
\(207\) 3.28488 0.228315
\(208\) −20.5165 −1.42257
\(209\) −2.78283 −0.192493
\(210\) 0 0
\(211\) 7.81577 0.538060 0.269030 0.963132i \(-0.413297\pi\)
0.269030 + 0.963132i \(0.413297\pi\)
\(212\) −0.657089 −0.0451291
\(213\) 2.30854 0.158178
\(214\) 18.2772 1.24940
\(215\) −8.07111 −0.550445
\(216\) 2.58600 0.175955
\(217\) 0 0
\(218\) −25.7479 −1.74387
\(219\) −11.9079 −0.804658
\(220\) −1.28416 −0.0865778
\(221\) 31.5848 2.12463
\(222\) −1.71411 −0.115044
\(223\) −22.6963 −1.51986 −0.759929 0.650006i \(-0.774766\pi\)
−0.759929 + 0.650006i \(0.774766\pi\)
\(224\) 0 0
\(225\) 9.47840 0.631893
\(226\) −2.47992 −0.164962
\(227\) 1.16540 0.0773504 0.0386752 0.999252i \(-0.487686\pi\)
0.0386752 + 0.999252i \(0.487686\pi\)
\(228\) −0.702072 −0.0464959
\(229\) 24.8081 1.63936 0.819682 0.572819i \(-0.194150\pi\)
0.819682 + 0.572819i \(0.194150\pi\)
\(230\) 18.9220 1.24768
\(231\) 0 0
\(232\) 3.31370 0.217555
\(233\) −18.9135 −1.23906 −0.619531 0.784972i \(-0.712677\pi\)
−0.619531 + 0.784972i \(0.712677\pi\)
\(234\) −6.90445 −0.451358
\(235\) −28.1490 −1.83624
\(236\) 3.76798 0.245275
\(237\) −12.7517 −0.828309
\(238\) 0 0
\(239\) 5.69526 0.368396 0.184198 0.982889i \(-0.441031\pi\)
0.184198 + 0.982889i \(0.441031\pi\)
\(240\) 17.1168 1.10488
\(241\) −12.4796 −0.803884 −0.401942 0.915665i \(-0.631665\pi\)
−0.401942 + 0.915665i \(0.631665\pi\)
\(242\) 14.6274 0.940286
\(243\) 1.00000 0.0641500
\(244\) −0.751310 −0.0480977
\(245\) 0 0
\(246\) −1.51387 −0.0965206
\(247\) −10.9736 −0.698230
\(248\) 0.865459 0.0549567
\(249\) −2.58930 −0.164090
\(250\) 25.7971 1.63155
\(251\) 29.7508 1.87785 0.938926 0.344120i \(-0.111823\pi\)
0.938926 + 0.344120i \(0.111823\pi\)
\(252\) 0 0
\(253\) 3.79927 0.238858
\(254\) 31.4424 1.97287
\(255\) −26.3510 −1.65016
\(256\) 6.86124 0.428827
\(257\) −4.66090 −0.290739 −0.145369 0.989377i \(-0.546437\pi\)
−0.145369 + 0.989377i \(0.546437\pi\)
\(258\) −3.21115 −0.199918
\(259\) 0 0
\(260\) −5.06382 −0.314045
\(261\) 1.28140 0.0793166
\(262\) 18.2195 1.12561
\(263\) 24.2173 1.49330 0.746650 0.665217i \(-0.231661\pi\)
0.746650 + 0.665217i \(0.231661\pi\)
\(264\) 2.99095 0.184080
\(265\) 8.56857 0.526363
\(266\) 0 0
\(267\) 9.21039 0.563667
\(268\) −1.81357 −0.110782
\(269\) 26.7174 1.62899 0.814495 0.580170i \(-0.197014\pi\)
0.814495 + 0.580170i \(0.197014\pi\)
\(270\) 5.76034 0.350563
\(271\) 21.2293 1.28959 0.644795 0.764356i \(-0.276943\pi\)
0.644795 + 0.764356i \(0.276943\pi\)
\(272\) −31.1530 −1.88893
\(273\) 0 0
\(274\) 9.84108 0.594522
\(275\) 10.9627 0.661074
\(276\) 0.958507 0.0576953
\(277\) −8.30807 −0.499184 −0.249592 0.968351i \(-0.580296\pi\)
−0.249592 + 0.968351i \(0.580296\pi\)
\(278\) 35.0166 2.10015
\(279\) 0.334671 0.0200362
\(280\) 0 0
\(281\) −19.0193 −1.13460 −0.567300 0.823511i \(-0.692012\pi\)
−0.567300 + 0.823511i \(0.692012\pi\)
\(282\) −11.1993 −0.666907
\(283\) −8.80867 −0.523621 −0.261811 0.965119i \(-0.584320\pi\)
−0.261811 + 0.965119i \(0.584320\pi\)
\(284\) 0.673617 0.0399718
\(285\) 9.15516 0.542305
\(286\) −7.98566 −0.472202
\(287\) 0 0
\(288\) 1.63805 0.0965232
\(289\) 30.9594 1.82114
\(290\) 7.38130 0.433445
\(291\) 12.8974 0.756058
\(292\) −3.47464 −0.203338
\(293\) 30.0047 1.75289 0.876446 0.481500i \(-0.159908\pi\)
0.876446 + 0.481500i \(0.159908\pi\)
\(294\) 0 0
\(295\) −49.1352 −2.86076
\(296\) 2.92806 0.170190
\(297\) 1.15660 0.0671125
\(298\) 7.87276 0.456056
\(299\) 14.9817 0.866413
\(300\) 2.76574 0.159680
\(301\) 0 0
\(302\) 15.5774 0.896376
\(303\) −0.177513 −0.0101979
\(304\) 10.8235 0.620771
\(305\) 9.79723 0.560988
\(306\) −10.4839 −0.599327
\(307\) 26.3241 1.50240 0.751199 0.660076i \(-0.229476\pi\)
0.751199 + 0.660076i \(0.229476\pi\)
\(308\) 0 0
\(309\) 14.5341 0.826819
\(310\) 1.92782 0.109493
\(311\) −21.2895 −1.20721 −0.603607 0.797282i \(-0.706270\pi\)
−0.603607 + 0.797282i \(0.706270\pi\)
\(312\) 11.7942 0.667717
\(313\) 14.8092 0.837065 0.418532 0.908202i \(-0.362545\pi\)
0.418532 + 0.908202i \(0.362545\pi\)
\(314\) 6.10977 0.344794
\(315\) 0 0
\(316\) −3.72085 −0.209314
\(317\) 3.95277 0.222010 0.111005 0.993820i \(-0.464593\pi\)
0.111005 + 0.993820i \(0.464593\pi\)
\(318\) 3.40907 0.191171
\(319\) 1.48206 0.0829795
\(320\) −24.7979 −1.38624
\(321\) −12.0732 −0.673859
\(322\) 0 0
\(323\) −16.6626 −0.927132
\(324\) 0.291794 0.0162108
\(325\) 43.2291 2.39792
\(326\) −10.3687 −0.574271
\(327\) 17.0080 0.940547
\(328\) 2.58600 0.142788
\(329\) 0 0
\(330\) 6.66238 0.366752
\(331\) 30.9459 1.70094 0.850470 0.526023i \(-0.176317\pi\)
0.850470 + 0.526023i \(0.176317\pi\)
\(332\) −0.755542 −0.0414658
\(333\) 1.13227 0.0620483
\(334\) 4.12946 0.225954
\(335\) 23.6493 1.29210
\(336\) 0 0
\(337\) 32.5965 1.77564 0.887822 0.460188i \(-0.152218\pi\)
0.887822 + 0.460188i \(0.152218\pi\)
\(338\) −11.8096 −0.642357
\(339\) 1.63814 0.0889715
\(340\) −7.68906 −0.416998
\(341\) 0.387079 0.0209615
\(342\) 3.64245 0.196961
\(343\) 0 0
\(344\) 5.48531 0.295748
\(345\) −12.4991 −0.672930
\(346\) −5.41234 −0.290969
\(347\) −24.1324 −1.29549 −0.647747 0.761855i \(-0.724289\pi\)
−0.647747 + 0.761855i \(0.724289\pi\)
\(348\) 0.373905 0.0200434
\(349\) 24.9455 1.33530 0.667651 0.744474i \(-0.267300\pi\)
0.667651 + 0.744474i \(0.267300\pi\)
\(350\) 0 0
\(351\) 4.56081 0.243438
\(352\) 1.89456 0.100981
\(353\) 35.1182 1.86916 0.934578 0.355759i \(-0.115778\pi\)
0.934578 + 0.355759i \(0.115778\pi\)
\(354\) −19.5488 −1.03901
\(355\) −8.78410 −0.466211
\(356\) 2.68754 0.142439
\(357\) 0 0
\(358\) −20.1951 −1.06734
\(359\) −2.09790 −0.110723 −0.0553614 0.998466i \(-0.517631\pi\)
−0.0553614 + 0.998466i \(0.517631\pi\)
\(360\) −9.83985 −0.518605
\(361\) −13.2109 −0.695310
\(362\) −9.32504 −0.490113
\(363\) −9.66229 −0.507139
\(364\) 0 0
\(365\) 45.3100 2.37163
\(366\) 3.89790 0.203746
\(367\) −15.7507 −0.822180 −0.411090 0.911595i \(-0.634852\pi\)
−0.411090 + 0.911595i \(0.634852\pi\)
\(368\) −14.7768 −0.770295
\(369\) 1.00000 0.0520579
\(370\) 6.52229 0.339077
\(371\) 0 0
\(372\) 0.0976550 0.00506318
\(373\) −10.4347 −0.540289 −0.270144 0.962820i \(-0.587071\pi\)
−0.270144 + 0.962820i \(0.587071\pi\)
\(374\) −12.1257 −0.627004
\(375\) −17.0405 −0.879969
\(376\) 19.1307 0.986589
\(377\) 5.84421 0.300992
\(378\) 0 0
\(379\) −13.0415 −0.669895 −0.334947 0.942237i \(-0.608719\pi\)
−0.334947 + 0.942237i \(0.608719\pi\)
\(380\) 2.67142 0.137041
\(381\) −20.7696 −1.06406
\(382\) −36.1347 −1.84881
\(383\) −13.8502 −0.707714 −0.353857 0.935299i \(-0.615130\pi\)
−0.353857 + 0.935299i \(0.615130\pi\)
\(384\) −13.1421 −0.670656
\(385\) 0 0
\(386\) 32.8216 1.67058
\(387\) 2.12116 0.107825
\(388\) 3.76338 0.191057
\(389\) 29.4776 1.49458 0.747288 0.664500i \(-0.231356\pi\)
0.747288 + 0.664500i \(0.231356\pi\)
\(390\) 26.2718 1.33032
\(391\) 22.7487 1.15045
\(392\) 0 0
\(393\) −12.0351 −0.607090
\(394\) −33.5634 −1.69090
\(395\) 48.5207 2.44134
\(396\) 0.337487 0.0169594
\(397\) 25.5717 1.28341 0.641703 0.766954i \(-0.278228\pi\)
0.641703 + 0.766954i \(0.278228\pi\)
\(398\) −11.7955 −0.591257
\(399\) 0 0
\(400\) −42.6381 −2.13190
\(401\) 6.69303 0.334234 0.167117 0.985937i \(-0.446554\pi\)
0.167117 + 0.985937i \(0.446554\pi\)
\(402\) 9.40906 0.469281
\(403\) 1.52637 0.0760339
\(404\) −0.0517973 −0.00257701
\(405\) −3.80505 −0.189074
\(406\) 0 0
\(407\) 1.30958 0.0649136
\(408\) 17.9087 0.886615
\(409\) 18.9785 0.938425 0.469212 0.883085i \(-0.344538\pi\)
0.469212 + 0.883085i \(0.344538\pi\)
\(410\) 5.76034 0.284483
\(411\) −6.50063 −0.320652
\(412\) 4.24097 0.208938
\(413\) 0 0
\(414\) −4.97287 −0.244403
\(415\) 9.85242 0.483636
\(416\) 7.47084 0.366288
\(417\) −23.1305 −1.13271
\(418\) 4.21284 0.206057
\(419\) −38.3019 −1.87117 −0.935586 0.353099i \(-0.885128\pi\)
−0.935586 + 0.353099i \(0.885128\pi\)
\(420\) 0 0
\(421\) 13.7293 0.669124 0.334562 0.942374i \(-0.391412\pi\)
0.334562 + 0.942374i \(0.391412\pi\)
\(422\) −11.8320 −0.575974
\(423\) 7.39779 0.359693
\(424\) −5.82339 −0.282809
\(425\) 65.6405 3.18403
\(426\) −3.49482 −0.169325
\(427\) 0 0
\(428\) −3.52288 −0.170285
\(429\) 5.27501 0.254680
\(430\) 12.2186 0.589233
\(431\) −1.39769 −0.0673244 −0.0336622 0.999433i \(-0.510717\pi\)
−0.0336622 + 0.999433i \(0.510717\pi\)
\(432\) −4.49844 −0.216431
\(433\) −19.3022 −0.927605 −0.463802 0.885939i \(-0.653515\pi\)
−0.463802 + 0.885939i \(0.653515\pi\)
\(434\) 0 0
\(435\) −4.87579 −0.233776
\(436\) 4.96284 0.237677
\(437\) −7.90359 −0.378080
\(438\) 18.0269 0.861359
\(439\) 2.98535 0.142483 0.0712416 0.997459i \(-0.477304\pi\)
0.0712416 + 0.997459i \(0.477304\pi\)
\(440\) −11.3807 −0.542555
\(441\) 0 0
\(442\) −47.8152 −2.27434
\(443\) 35.3757 1.68075 0.840374 0.542007i \(-0.182335\pi\)
0.840374 + 0.542007i \(0.182335\pi\)
\(444\) 0.330391 0.0156797
\(445\) −35.0460 −1.66134
\(446\) 34.3592 1.62696
\(447\) −5.20043 −0.245972
\(448\) 0 0
\(449\) −24.7278 −1.16698 −0.583489 0.812121i \(-0.698313\pi\)
−0.583489 + 0.812121i \(0.698313\pi\)
\(450\) −14.3490 −0.676420
\(451\) 1.15660 0.0544619
\(452\) 0.477999 0.0224832
\(453\) −10.2898 −0.483456
\(454\) −1.76426 −0.0828010
\(455\) 0 0
\(456\) −6.22205 −0.291374
\(457\) −9.46161 −0.442595 −0.221298 0.975206i \(-0.571029\pi\)
−0.221298 + 0.975206i \(0.571029\pi\)
\(458\) −37.5561 −1.75488
\(459\) 6.92527 0.323244
\(460\) −3.64716 −0.170050
\(461\) 20.5811 0.958557 0.479279 0.877663i \(-0.340898\pi\)
0.479279 + 0.877663i \(0.340898\pi\)
\(462\) 0 0
\(463\) −27.1195 −1.26035 −0.630175 0.776453i \(-0.717017\pi\)
−0.630175 + 0.776453i \(0.717017\pi\)
\(464\) −5.76430 −0.267601
\(465\) −1.27344 −0.0590544
\(466\) 28.6325 1.32637
\(467\) −6.72518 −0.311204 −0.155602 0.987820i \(-0.549732\pi\)
−0.155602 + 0.987820i \(0.549732\pi\)
\(468\) 1.33082 0.0615169
\(469\) 0 0
\(470\) 42.6138 1.96563
\(471\) −4.03587 −0.185963
\(472\) 33.3934 1.53705
\(473\) 2.45332 0.112804
\(474\) 19.3043 0.886676
\(475\) −22.8056 −1.04639
\(476\) 0 0
\(477\) −2.25189 −0.103107
\(478\) −8.62186 −0.394355
\(479\) −18.3927 −0.840382 −0.420191 0.907436i \(-0.638037\pi\)
−0.420191 + 0.907436i \(0.638037\pi\)
\(480\) −6.23287 −0.284490
\(481\) 5.16408 0.235462
\(482\) 18.8925 0.860531
\(483\) 0 0
\(484\) −2.81940 −0.128154
\(485\) −49.0752 −2.22839
\(486\) −1.51387 −0.0686704
\(487\) 8.31877 0.376960 0.188480 0.982077i \(-0.439644\pi\)
0.188480 + 0.982077i \(0.439644\pi\)
\(488\) −6.65842 −0.301412
\(489\) 6.84917 0.309730
\(490\) 0 0
\(491\) −0.703140 −0.0317323 −0.0158661 0.999874i \(-0.505051\pi\)
−0.0158661 + 0.999874i \(0.505051\pi\)
\(492\) 0.291794 0.0131551
\(493\) 8.87404 0.399667
\(494\) 16.6125 0.747432
\(495\) −4.40090 −0.197806
\(496\) −1.50550 −0.0675989
\(497\) 0 0
\(498\) 3.91986 0.175653
\(499\) −25.1798 −1.12720 −0.563601 0.826047i \(-0.690584\pi\)
−0.563601 + 0.826047i \(0.690584\pi\)
\(500\) −4.97232 −0.222369
\(501\) −2.72776 −0.121867
\(502\) −45.0387 −2.01018
\(503\) 9.10380 0.405918 0.202959 0.979187i \(-0.434944\pi\)
0.202959 + 0.979187i \(0.434944\pi\)
\(504\) 0 0
\(505\) 0.675447 0.0300570
\(506\) −5.75159 −0.255689
\(507\) 7.80095 0.346452
\(508\) −6.06044 −0.268889
\(509\) −8.52853 −0.378021 −0.189010 0.981975i \(-0.560528\pi\)
−0.189010 + 0.981975i \(0.560528\pi\)
\(510\) 39.8919 1.76644
\(511\) 0 0
\(512\) 15.8972 0.702565
\(513\) −2.40606 −0.106230
\(514\) 7.05598 0.311226
\(515\) −55.3031 −2.43695
\(516\) 0.618941 0.0272474
\(517\) 8.55625 0.376304
\(518\) 0 0
\(519\) 3.57517 0.156933
\(520\) −44.8776 −1.96801
\(521\) −29.7200 −1.30206 −0.651029 0.759053i \(-0.725662\pi\)
−0.651029 + 0.759053i \(0.725662\pi\)
\(522\) −1.93987 −0.0849058
\(523\) −23.3081 −1.01919 −0.509597 0.860413i \(-0.670205\pi\)
−0.509597 + 0.860413i \(0.670205\pi\)
\(524\) −3.51177 −0.153412
\(525\) 0 0
\(526\) −36.6617 −1.59853
\(527\) 2.31769 0.100960
\(528\) −5.20288 −0.226426
\(529\) −12.2096 −0.530852
\(530\) −12.9717 −0.563454
\(531\) 12.9132 0.560383
\(532\) 0 0
\(533\) 4.56081 0.197550
\(534\) −13.9433 −0.603386
\(535\) 45.9390 1.98612
\(536\) −16.0726 −0.694231
\(537\) 13.3401 0.575667
\(538\) −40.4466 −1.74378
\(539\) 0 0
\(540\) −1.11029 −0.0477793
\(541\) 22.9665 0.987407 0.493704 0.869630i \(-0.335643\pi\)
0.493704 + 0.869630i \(0.335643\pi\)
\(542\) −32.1384 −1.38046
\(543\) 6.15975 0.264340
\(544\) 11.3440 0.486368
\(545\) −64.7164 −2.77215
\(546\) 0 0
\(547\) −19.0779 −0.815711 −0.407856 0.913046i \(-0.633723\pi\)
−0.407856 + 0.913046i \(0.633723\pi\)
\(548\) −1.89684 −0.0810291
\(549\) −2.57480 −0.109890
\(550\) −16.5960 −0.707657
\(551\) −3.08312 −0.131345
\(552\) 8.49468 0.361558
\(553\) 0 0
\(554\) 12.5773 0.534359
\(555\) −4.30836 −0.182880
\(556\) −6.74935 −0.286236
\(557\) −1.60892 −0.0681723 −0.0340861 0.999419i \(-0.510852\pi\)
−0.0340861 + 0.999419i \(0.510852\pi\)
\(558\) −0.506648 −0.0214481
\(559\) 9.67419 0.409175
\(560\) 0 0
\(561\) 8.00974 0.338171
\(562\) 28.7928 1.21455
\(563\) −40.0650 −1.68854 −0.844268 0.535921i \(-0.819965\pi\)
−0.844268 + 0.535921i \(0.819965\pi\)
\(564\) 2.15863 0.0908948
\(565\) −6.23320 −0.262233
\(566\) 13.3352 0.560519
\(567\) 0 0
\(568\) 5.96987 0.250490
\(569\) 0.910623 0.0381753 0.0190876 0.999818i \(-0.493924\pi\)
0.0190876 + 0.999818i \(0.493924\pi\)
\(570\) −13.8597 −0.580519
\(571\) 0.733915 0.0307134 0.0153567 0.999882i \(-0.495112\pi\)
0.0153567 + 0.999882i \(0.495112\pi\)
\(572\) 1.53921 0.0643578
\(573\) 23.8691 0.997146
\(574\) 0 0
\(575\) 31.1354 1.29843
\(576\) 6.51709 0.271546
\(577\) 31.6908 1.31930 0.659652 0.751571i \(-0.270704\pi\)
0.659652 + 0.751571i \(0.270704\pi\)
\(578\) −46.8684 −1.94947
\(579\) −21.6807 −0.901017
\(580\) −1.42273 −0.0590754
\(581\) 0 0
\(582\) −19.5249 −0.809334
\(583\) −2.60453 −0.107869
\(584\) −30.7937 −1.27425
\(585\) −17.3541 −0.717503
\(586\) −45.4231 −1.87641
\(587\) 20.9045 0.862823 0.431411 0.902155i \(-0.358016\pi\)
0.431411 + 0.902155i \(0.358016\pi\)
\(588\) 0 0
\(589\) −0.805238 −0.0331792
\(590\) 74.3841 3.06235
\(591\) 22.1707 0.911979
\(592\) −5.09347 −0.209340
\(593\) −1.44402 −0.0592987 −0.0296494 0.999560i \(-0.509439\pi\)
−0.0296494 + 0.999560i \(0.509439\pi\)
\(594\) −1.75093 −0.0718416
\(595\) 0 0
\(596\) −1.51745 −0.0621573
\(597\) 7.79167 0.318892
\(598\) −22.6803 −0.927465
\(599\) 10.3458 0.422719 0.211360 0.977408i \(-0.432211\pi\)
0.211360 + 0.977408i \(0.432211\pi\)
\(600\) 24.5111 1.00066
\(601\) −8.35641 −0.340865 −0.170432 0.985369i \(-0.554516\pi\)
−0.170432 + 0.985369i \(0.554516\pi\)
\(602\) 0 0
\(603\) −6.21525 −0.253104
\(604\) −3.00249 −0.122170
\(605\) 36.7655 1.49473
\(606\) 0.268732 0.0109165
\(607\) 0.600544 0.0243753 0.0121877 0.999926i \(-0.496120\pi\)
0.0121877 + 0.999926i \(0.496120\pi\)
\(608\) −3.94125 −0.159839
\(609\) 0 0
\(610\) −14.8317 −0.600518
\(611\) 33.7399 1.36497
\(612\) 2.02075 0.0816841
\(613\) −20.2750 −0.818899 −0.409449 0.912333i \(-0.634279\pi\)
−0.409449 + 0.912333i \(0.634279\pi\)
\(614\) −39.8512 −1.60827
\(615\) −3.80505 −0.153434
\(616\) 0 0
\(617\) −23.4448 −0.943854 −0.471927 0.881638i \(-0.656441\pi\)
−0.471927 + 0.881638i \(0.656441\pi\)
\(618\) −22.0028 −0.885081
\(619\) −10.3180 −0.414716 −0.207358 0.978265i \(-0.566487\pi\)
−0.207358 + 0.978265i \(0.566487\pi\)
\(620\) −0.371582 −0.0149231
\(621\) 3.28488 0.131818
\(622\) 32.2294 1.29228
\(623\) 0 0
\(624\) −20.5165 −0.821318
\(625\) 17.4481 0.697923
\(626\) −22.4191 −0.896049
\(627\) −2.78283 −0.111136
\(628\) −1.17764 −0.0469930
\(629\) 7.84131 0.312654
\(630\) 0 0
\(631\) 5.95019 0.236873 0.118437 0.992962i \(-0.462212\pi\)
0.118437 + 0.992962i \(0.462212\pi\)
\(632\) −32.9757 −1.31170
\(633\) 7.81577 0.310649
\(634\) −5.98397 −0.237654
\(635\) 79.0293 3.13618
\(636\) −0.657089 −0.0260553
\(637\) 0 0
\(638\) −2.24364 −0.0888267
\(639\) 2.30854 0.0913243
\(640\) 50.0064 1.97668
\(641\) −18.7783 −0.741697 −0.370848 0.928693i \(-0.620933\pi\)
−0.370848 + 0.928693i \(0.620933\pi\)
\(642\) 18.2772 0.721343
\(643\) 26.6022 1.04909 0.524543 0.851384i \(-0.324236\pi\)
0.524543 + 0.851384i \(0.324236\pi\)
\(644\) 0 0
\(645\) −8.07111 −0.317800
\(646\) 25.2250 0.992463
\(647\) 23.5755 0.926847 0.463424 0.886137i \(-0.346621\pi\)
0.463424 + 0.886137i \(0.346621\pi\)
\(648\) 2.58600 0.101588
\(649\) 14.9353 0.586261
\(650\) −65.4432 −2.56689
\(651\) 0 0
\(652\) 1.99855 0.0782691
\(653\) −17.2768 −0.676093 −0.338046 0.941129i \(-0.609766\pi\)
−0.338046 + 0.941129i \(0.609766\pi\)
\(654\) −25.7479 −1.00682
\(655\) 45.7941 1.78933
\(656\) −4.49844 −0.175635
\(657\) −11.9079 −0.464570
\(658\) 0 0
\(659\) 32.3358 1.25963 0.629813 0.776747i \(-0.283132\pi\)
0.629813 + 0.776747i \(0.283132\pi\)
\(660\) −1.28416 −0.0499857
\(661\) 41.8828 1.62905 0.814525 0.580128i \(-0.196998\pi\)
0.814525 + 0.580128i \(0.196998\pi\)
\(662\) −46.8480 −1.82080
\(663\) 31.5848 1.22665
\(664\) −6.69593 −0.259852
\(665\) 0 0
\(666\) −1.71411 −0.0664205
\(667\) 4.20924 0.162982
\(668\) −0.795943 −0.0307960
\(669\) −22.6963 −0.877490
\(670\) −35.8019 −1.38315
\(671\) −2.97800 −0.114964
\(672\) 0 0
\(673\) −32.0621 −1.23590 −0.617951 0.786217i \(-0.712037\pi\)
−0.617951 + 0.786217i \(0.712037\pi\)
\(674\) −49.3467 −1.90077
\(675\) 9.47840 0.364824
\(676\) 2.27627 0.0875488
\(677\) −39.2517 −1.50857 −0.754283 0.656549i \(-0.772016\pi\)
−0.754283 + 0.656549i \(0.772016\pi\)
\(678\) −2.47992 −0.0952409
\(679\) 0 0
\(680\) −68.1436 −2.61319
\(681\) 1.16540 0.0446583
\(682\) −0.585987 −0.0224386
\(683\) −15.5806 −0.596176 −0.298088 0.954538i \(-0.596349\pi\)
−0.298088 + 0.954538i \(0.596349\pi\)
\(684\) −0.702072 −0.0268444
\(685\) 24.7352 0.945084
\(686\) 0 0
\(687\) 24.8081 0.946487
\(688\) −9.54191 −0.363782
\(689\) −10.2705 −0.391273
\(690\) 18.9220 0.720348
\(691\) 18.0215 0.685569 0.342784 0.939414i \(-0.388630\pi\)
0.342784 + 0.939414i \(0.388630\pi\)
\(692\) 1.04321 0.0396570
\(693\) 0 0
\(694\) 36.5332 1.38678
\(695\) 88.0129 3.33852
\(696\) 3.31370 0.125605
\(697\) 6.92527 0.262313
\(698\) −37.7642 −1.42940
\(699\) −18.9135 −0.715373
\(700\) 0 0
\(701\) −5.16472 −0.195069 −0.0975344 0.995232i \(-0.531096\pi\)
−0.0975344 + 0.995232i \(0.531096\pi\)
\(702\) −6.90445 −0.260592
\(703\) −2.72432 −0.102750
\(704\) 7.53764 0.284086
\(705\) −28.1490 −1.06015
\(706\) −53.1643 −2.00087
\(707\) 0 0
\(708\) 3.76798 0.141609
\(709\) 11.3643 0.426796 0.213398 0.976965i \(-0.431547\pi\)
0.213398 + 0.976965i \(0.431547\pi\)
\(710\) 13.2980 0.499063
\(711\) −12.7517 −0.478224
\(712\) 23.8180 0.892619
\(713\) 1.09935 0.0411711
\(714\) 0 0
\(715\) −20.0717 −0.750637
\(716\) 3.89255 0.145472
\(717\) 5.69526 0.212693
\(718\) 3.17594 0.118525
\(719\) 30.5843 1.14060 0.570302 0.821435i \(-0.306826\pi\)
0.570302 + 0.821435i \(0.306826\pi\)
\(720\) 17.1168 0.637906
\(721\) 0 0
\(722\) 19.9995 0.744306
\(723\) −12.4796 −0.464123
\(724\) 1.79738 0.0667990
\(725\) 12.1456 0.451077
\(726\) 14.6274 0.542874
\(727\) 18.0711 0.670221 0.335111 0.942179i \(-0.391226\pi\)
0.335111 + 0.942179i \(0.391226\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −68.5933 −2.53875
\(731\) 14.6896 0.543315
\(732\) −0.751310 −0.0277692
\(733\) −49.3640 −1.82330 −0.911651 0.410966i \(-0.865192\pi\)
−0.911651 + 0.410966i \(0.865192\pi\)
\(734\) 23.8445 0.880115
\(735\) 0 0
\(736\) 5.38080 0.198339
\(737\) −7.18853 −0.264793
\(738\) −1.51387 −0.0557262
\(739\) −9.21630 −0.339027 −0.169514 0.985528i \(-0.554220\pi\)
−0.169514 + 0.985528i \(0.554220\pi\)
\(740\) −1.25715 −0.0462139
\(741\) −10.9736 −0.403124
\(742\) 0 0
\(743\) −47.8911 −1.75696 −0.878478 0.477783i \(-0.841440\pi\)
−0.878478 + 0.477783i \(0.841440\pi\)
\(744\) 0.865459 0.0317293
\(745\) 19.7879 0.724972
\(746\) 15.7968 0.578361
\(747\) −2.58930 −0.0947376
\(748\) 2.33719 0.0854562
\(749\) 0 0
\(750\) 25.7971 0.941977
\(751\) −0.992350 −0.0362114 −0.0181057 0.999836i \(-0.505764\pi\)
−0.0181057 + 0.999836i \(0.505764\pi\)
\(752\) −33.2786 −1.21354
\(753\) 29.7508 1.08418
\(754\) −8.84736 −0.322202
\(755\) 39.1531 1.42493
\(756\) 0 0
\(757\) 17.2370 0.626490 0.313245 0.949672i \(-0.398584\pi\)
0.313245 + 0.949672i \(0.398584\pi\)
\(758\) 19.7430 0.717100
\(759\) 3.79927 0.137905
\(760\) 23.6752 0.858791
\(761\) −25.0256 −0.907177 −0.453589 0.891211i \(-0.649856\pi\)
−0.453589 + 0.891211i \(0.649856\pi\)
\(762\) 31.4424 1.13904
\(763\) 0 0
\(764\) 6.96486 0.251980
\(765\) −26.3510 −0.952723
\(766\) 20.9674 0.757584
\(767\) 58.8944 2.12655
\(768\) 6.86124 0.247584
\(769\) 12.7073 0.458239 0.229119 0.973398i \(-0.426415\pi\)
0.229119 + 0.973398i \(0.426415\pi\)
\(770\) 0 0
\(771\) −4.66090 −0.167858
\(772\) −6.32628 −0.227688
\(773\) 47.3022 1.70134 0.850671 0.525699i \(-0.176196\pi\)
0.850671 + 0.525699i \(0.176196\pi\)
\(774\) −3.21115 −0.115422
\(775\) 3.17215 0.113947
\(776\) 33.3526 1.19729
\(777\) 0 0
\(778\) −44.6252 −1.59989
\(779\) −2.40606 −0.0862059
\(780\) −5.06382 −0.181314
\(781\) 2.67004 0.0955417
\(782\) −34.4385 −1.23152
\(783\) 1.28140 0.0457935
\(784\) 0 0
\(785\) 15.3567 0.548103
\(786\) 18.2195 0.649869
\(787\) 41.5945 1.48269 0.741343 0.671127i \(-0.234189\pi\)
0.741343 + 0.671127i \(0.234189\pi\)
\(788\) 6.46927 0.230458
\(789\) 24.2173 0.862158
\(790\) −73.4539 −2.61337
\(791\) 0 0
\(792\) 2.99095 0.106279
\(793\) −11.7431 −0.417011
\(794\) −38.7121 −1.37384
\(795\) 8.56857 0.303896
\(796\) 2.27356 0.0805842
\(797\) 50.4009 1.78529 0.892645 0.450760i \(-0.148847\pi\)
0.892645 + 0.450760i \(0.148847\pi\)
\(798\) 0 0
\(799\) 51.2317 1.81245
\(800\) 15.5261 0.548931
\(801\) 9.21039 0.325433
\(802\) −10.1324 −0.357786
\(803\) −13.7726 −0.486024
\(804\) −1.81357 −0.0639597
\(805\) 0 0
\(806\) −2.31072 −0.0813917
\(807\) 26.7174 0.940498
\(808\) −0.459049 −0.0161493
\(809\) 18.2063 0.640098 0.320049 0.947401i \(-0.396301\pi\)
0.320049 + 0.947401i \(0.396301\pi\)
\(810\) 5.76034 0.202398
\(811\) 47.0365 1.65168 0.825838 0.563908i \(-0.190703\pi\)
0.825838 + 0.563908i \(0.190703\pi\)
\(812\) 0 0
\(813\) 21.2293 0.744545
\(814\) −1.98254 −0.0694878
\(815\) −26.0614 −0.912892
\(816\) −31.1530 −1.09057
\(817\) −5.10363 −0.178553
\(818\) −28.7309 −1.00455
\(819\) 0 0
\(820\) −1.11029 −0.0387730
\(821\) −52.1811 −1.82113 −0.910566 0.413364i \(-0.864354\pi\)
−0.910566 + 0.413364i \(0.864354\pi\)
\(822\) 9.84108 0.343247
\(823\) −4.29085 −0.149570 −0.0747848 0.997200i \(-0.523827\pi\)
−0.0747848 + 0.997200i \(0.523827\pi\)
\(824\) 37.5853 1.30934
\(825\) 10.9627 0.381671
\(826\) 0 0
\(827\) 46.0862 1.60257 0.801287 0.598280i \(-0.204149\pi\)
0.801287 + 0.598280i \(0.204149\pi\)
\(828\) 0.958507 0.0333104
\(829\) 12.1577 0.422256 0.211128 0.977458i \(-0.432286\pi\)
0.211128 + 0.977458i \(0.432286\pi\)
\(830\) −14.9153 −0.517716
\(831\) −8.30807 −0.288204
\(832\) 29.7232 1.03047
\(833\) 0 0
\(834\) 35.0166 1.21252
\(835\) 10.3793 0.359189
\(836\) −0.812014 −0.0280841
\(837\) 0.334671 0.0115679
\(838\) 57.9840 2.00303
\(839\) 4.79517 0.165548 0.0827739 0.996568i \(-0.473622\pi\)
0.0827739 + 0.996568i \(0.473622\pi\)
\(840\) 0 0
\(841\) −27.3580 −0.943380
\(842\) −20.7843 −0.716274
\(843\) −19.0193 −0.655061
\(844\) 2.28059 0.0785012
\(845\) −29.6830 −1.02113
\(846\) −11.1993 −0.385039
\(847\) 0 0
\(848\) 10.1300 0.347866
\(849\) −8.80867 −0.302313
\(850\) −99.3710 −3.40840
\(851\) 3.71938 0.127499
\(852\) 0.673617 0.0230777
\(853\) 5.26286 0.180197 0.0900984 0.995933i \(-0.471282\pi\)
0.0900984 + 0.995933i \(0.471282\pi\)
\(854\) 0 0
\(855\) 9.15516 0.313100
\(856\) −31.2212 −1.06712
\(857\) 0.907168 0.0309883 0.0154941 0.999880i \(-0.495068\pi\)
0.0154941 + 0.999880i \(0.495068\pi\)
\(858\) −7.98566 −0.272626
\(859\) −28.1280 −0.959715 −0.479858 0.877346i \(-0.659312\pi\)
−0.479858 + 0.877346i \(0.659312\pi\)
\(860\) −2.35510 −0.0803083
\(861\) 0 0
\(862\) 2.11592 0.0720685
\(863\) 4.62233 0.157346 0.0786730 0.996900i \(-0.474932\pi\)
0.0786730 + 0.996900i \(0.474932\pi\)
\(864\) 1.63805 0.0557277
\(865\) −13.6037 −0.462540
\(866\) 29.2210 0.992969
\(867\) 30.9594 1.05144
\(868\) 0 0
\(869\) −14.7485 −0.500309
\(870\) 7.38130 0.250249
\(871\) −28.3465 −0.960486
\(872\) 43.9827 1.48944
\(873\) 12.8974 0.436510
\(874\) 11.9650 0.404722
\(875\) 0 0
\(876\) −3.47464 −0.117397
\(877\) −33.5121 −1.13162 −0.565812 0.824534i \(-0.691437\pi\)
−0.565812 + 0.824534i \(0.691437\pi\)
\(878\) −4.51943 −0.152523
\(879\) 30.0047 1.01203
\(880\) 19.7972 0.667364
\(881\) −5.55431 −0.187129 −0.0935647 0.995613i \(-0.529826\pi\)
−0.0935647 + 0.995613i \(0.529826\pi\)
\(882\) 0 0
\(883\) 33.3288 1.12160 0.560802 0.827950i \(-0.310493\pi\)
0.560802 + 0.827950i \(0.310493\pi\)
\(884\) 9.21626 0.309976
\(885\) −49.1352 −1.65166
\(886\) −53.5541 −1.79918
\(887\) 31.4901 1.05733 0.528667 0.848829i \(-0.322692\pi\)
0.528667 + 0.848829i \(0.322692\pi\)
\(888\) 2.92806 0.0982592
\(889\) 0 0
\(890\) 53.0550 1.77841
\(891\) 1.15660 0.0387474
\(892\) −6.62265 −0.221743
\(893\) −17.7995 −0.595638
\(894\) 7.87276 0.263304
\(895\) −50.7597 −1.69671
\(896\) 0 0
\(897\) 14.9817 0.500224
\(898\) 37.4346 1.24921
\(899\) 0.428848 0.0143029
\(900\) 2.76574 0.0921913
\(901\) −15.5950 −0.519544
\(902\) −1.75093 −0.0582996
\(903\) 0 0
\(904\) 4.23622 0.140895
\(905\) −23.4381 −0.779110
\(906\) 15.5774 0.517523
\(907\) −24.1540 −0.802021 −0.401010 0.916074i \(-0.631341\pi\)
−0.401010 + 0.916074i \(0.631341\pi\)
\(908\) 0.340057 0.0112852
\(909\) −0.177513 −0.00588775
\(910\) 0 0
\(911\) 13.5342 0.448407 0.224203 0.974542i \(-0.428022\pi\)
0.224203 + 0.974542i \(0.428022\pi\)
\(912\) 10.8235 0.358402
\(913\) −2.99477 −0.0991126
\(914\) 14.3236 0.473783
\(915\) 9.79723 0.323886
\(916\) 7.23884 0.239178
\(917\) 0 0
\(918\) −10.4839 −0.346022
\(919\) −6.10358 −0.201339 −0.100669 0.994920i \(-0.532098\pi\)
−0.100669 + 0.994920i \(0.532098\pi\)
\(920\) −32.3227 −1.06565
\(921\) 26.3241 0.867410
\(922\) −31.1571 −1.02610
\(923\) 10.5288 0.346559
\(924\) 0 0
\(925\) 10.7322 0.352871
\(926\) 41.0553 1.34916
\(927\) 14.5341 0.477364
\(928\) 2.09900 0.0689030
\(929\) 34.5625 1.13396 0.566979 0.823732i \(-0.308112\pi\)
0.566979 + 0.823732i \(0.308112\pi\)
\(930\) 1.92782 0.0632157
\(931\) 0 0
\(932\) −5.51883 −0.180775
\(933\) −21.2895 −0.696985
\(934\) 10.1810 0.333133
\(935\) −30.4775 −0.996719
\(936\) 11.7942 0.385506
\(937\) −3.45162 −0.112759 −0.0563797 0.998409i \(-0.517956\pi\)
−0.0563797 + 0.998409i \(0.517956\pi\)
\(938\) 0 0
\(939\) 14.8092 0.483280
\(940\) −8.21370 −0.267901
\(941\) −33.2147 −1.08277 −0.541384 0.840775i \(-0.682100\pi\)
−0.541384 + 0.840775i \(0.682100\pi\)
\(942\) 6.10977 0.199067
\(943\) 3.28488 0.106970
\(944\) −58.0891 −1.89064
\(945\) 0 0
\(946\) −3.71400 −0.120753
\(947\) 29.1330 0.946694 0.473347 0.880876i \(-0.343046\pi\)
0.473347 + 0.880876i \(0.343046\pi\)
\(948\) −3.72085 −0.120848
\(949\) −54.3094 −1.76296
\(950\) 34.5246 1.12013
\(951\) 3.95277 0.128177
\(952\) 0 0
\(953\) 37.7997 1.22445 0.612226 0.790683i \(-0.290274\pi\)
0.612226 + 0.790683i \(0.290274\pi\)
\(954\) 3.40907 0.110373
\(955\) −90.8231 −2.93897
\(956\) 1.66184 0.0537478
\(957\) 1.48206 0.0479082
\(958\) 27.8440 0.899600
\(959\) 0 0
\(960\) −24.7979 −0.800348
\(961\) −30.8880 −0.996387
\(962\) −7.81774 −0.252054
\(963\) −12.0732 −0.389053
\(964\) −3.64148 −0.117284
\(965\) 82.4960 2.65564
\(966\) 0 0
\(967\) 17.1460 0.551379 0.275690 0.961247i \(-0.411094\pi\)
0.275690 + 0.961247i \(0.411094\pi\)
\(968\) −24.9866 −0.803101
\(969\) −16.6626 −0.535280
\(970\) 74.2933 2.38541
\(971\) 10.5979 0.340104 0.170052 0.985435i \(-0.445606\pi\)
0.170052 + 0.985435i \(0.445606\pi\)
\(972\) 0.291794 0.00935929
\(973\) 0 0
\(974\) −12.5935 −0.403522
\(975\) 43.2291 1.38444
\(976\) 11.5826 0.370749
\(977\) 26.8876 0.860209 0.430105 0.902779i \(-0.358477\pi\)
0.430105 + 0.902779i \(0.358477\pi\)
\(978\) −10.3687 −0.331555
\(979\) 10.6527 0.340462
\(980\) 0 0
\(981\) 17.0080 0.543025
\(982\) 1.06446 0.0339683
\(983\) 27.7596 0.885392 0.442696 0.896672i \(-0.354022\pi\)
0.442696 + 0.896672i \(0.354022\pi\)
\(984\) 2.58600 0.0824386
\(985\) −84.3605 −2.68795
\(986\) −13.4341 −0.427830
\(987\) 0 0
\(988\) −3.20202 −0.101870
\(989\) 6.96774 0.221561
\(990\) 6.66238 0.211744
\(991\) 12.1510 0.385988 0.192994 0.981200i \(-0.438180\pi\)
0.192994 + 0.981200i \(0.438180\pi\)
\(992\) 0.548209 0.0174057
\(993\) 30.9459 0.982039
\(994\) 0 0
\(995\) −29.6477 −0.939894
\(996\) −0.755542 −0.0239403
\(997\) −15.7997 −0.500382 −0.250191 0.968197i \(-0.580493\pi\)
−0.250191 + 0.968197i \(0.580493\pi\)
\(998\) 38.1188 1.20663
\(999\) 1.13227 0.0358236
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 \(a_p\))