Properties

Label 6027.2.a.bc.1.7
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 1.7
Root \(-2.52358\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.07710 q^{2} +1.00000 q^{3} +2.31436 q^{4} -2.30039 q^{5} +2.07710 q^{6} +0.652949 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.07710 q^{2} +1.00000 q^{3} +2.31436 q^{4} -2.30039 q^{5} +2.07710 q^{6} +0.652949 q^{8} +1.00000 q^{9} -4.77814 q^{10} -2.24173 q^{11} +2.31436 q^{12} +4.05386 q^{13} -2.30039 q^{15} -3.27247 q^{16} +1.22520 q^{17} +2.07710 q^{18} +4.41144 q^{19} -5.32392 q^{20} -4.65630 q^{22} +6.56124 q^{23} +0.652949 q^{24} +0.291790 q^{25} +8.42028 q^{26} +1.00000 q^{27} +3.41695 q^{29} -4.77814 q^{30} -1.07464 q^{31} -8.10315 q^{32} -2.24173 q^{33} +2.54488 q^{34} +2.31436 q^{36} -1.63983 q^{37} +9.16300 q^{38} +4.05386 q^{39} -1.50204 q^{40} +1.00000 q^{41} -4.67207 q^{43} -5.18815 q^{44} -2.30039 q^{45} +13.6284 q^{46} +10.9409 q^{47} -3.27247 q^{48} +0.606078 q^{50} +1.22520 q^{51} +9.38207 q^{52} -3.43644 q^{53} +2.07710 q^{54} +5.15684 q^{55} +4.41144 q^{57} +7.09735 q^{58} +9.90021 q^{59} -5.32392 q^{60} +5.18833 q^{61} -2.23214 q^{62} -10.2861 q^{64} -9.32545 q^{65} -4.65630 q^{66} +10.9161 q^{67} +2.83556 q^{68} +6.56124 q^{69} -5.24347 q^{71} +0.652949 q^{72} +5.69973 q^{73} -3.40610 q^{74} +0.291790 q^{75} +10.2096 q^{76} +8.42028 q^{78} +3.55265 q^{79} +7.52795 q^{80} +1.00000 q^{81} +2.07710 q^{82} +2.44743 q^{83} -2.81845 q^{85} -9.70437 q^{86} +3.41695 q^{87} -1.46373 q^{88} +5.51735 q^{89} -4.77814 q^{90} +15.1850 q^{92} -1.07464 q^{93} +22.7254 q^{94} -10.1480 q^{95} -8.10315 q^{96} -3.88945 q^{97} -2.24173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.07710 1.46873 0.734367 0.678753i \(-0.237479\pi\)
0.734367 + 0.678753i \(0.237479\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.31436 1.15718
\(5\) −2.30039 −1.02877 −0.514383 0.857561i \(-0.671979\pi\)
−0.514383 + 0.857561i \(0.671979\pi\)
\(6\) 2.07710 0.847974
\(7\) 0 0
\(8\) 0.652949 0.230852
\(9\) 1.00000 0.333333
\(10\) −4.77814 −1.51098
\(11\) −2.24173 −0.675906 −0.337953 0.941163i \(-0.609735\pi\)
−0.337953 + 0.941163i \(0.609735\pi\)
\(12\) 2.31436 0.668097
\(13\) 4.05386 1.12434 0.562169 0.827022i \(-0.309967\pi\)
0.562169 + 0.827022i \(0.309967\pi\)
\(14\) 0 0
\(15\) −2.30039 −0.593958
\(16\) −3.27247 −0.818117
\(17\) 1.22520 0.297156 0.148578 0.988901i \(-0.452530\pi\)
0.148578 + 0.988901i \(0.452530\pi\)
\(18\) 2.07710 0.489578
\(19\) 4.41144 1.01205 0.506026 0.862518i \(-0.331114\pi\)
0.506026 + 0.862518i \(0.331114\pi\)
\(20\) −5.32392 −1.19046
\(21\) 0 0
\(22\) −4.65630 −0.992726
\(23\) 6.56124 1.36811 0.684056 0.729429i \(-0.260214\pi\)
0.684056 + 0.729429i \(0.260214\pi\)
\(24\) 0.652949 0.133283
\(25\) 0.291790 0.0583580
\(26\) 8.42028 1.65135
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 3.41695 0.634511 0.317255 0.948340i \(-0.397239\pi\)
0.317255 + 0.948340i \(0.397239\pi\)
\(30\) −4.77814 −0.872366
\(31\) −1.07464 −0.193011 −0.0965056 0.995332i \(-0.530767\pi\)
−0.0965056 + 0.995332i \(0.530767\pi\)
\(32\) −8.10315 −1.43245
\(33\) −2.24173 −0.390235
\(34\) 2.54488 0.436443
\(35\) 0 0
\(36\) 2.31436 0.385726
\(37\) −1.63983 −0.269587 −0.134793 0.990874i \(-0.543037\pi\)
−0.134793 + 0.990874i \(0.543037\pi\)
\(38\) 9.16300 1.48644
\(39\) 4.05386 0.649137
\(40\) −1.50204 −0.237493
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) −4.67207 −0.712484 −0.356242 0.934394i \(-0.615942\pi\)
−0.356242 + 0.934394i \(0.615942\pi\)
\(44\) −5.18815 −0.782144
\(45\) −2.30039 −0.342922
\(46\) 13.6284 2.00939
\(47\) 10.9409 1.59589 0.797947 0.602727i \(-0.205919\pi\)
0.797947 + 0.602727i \(0.205919\pi\)
\(48\) −3.27247 −0.472340
\(49\) 0 0
\(50\) 0.606078 0.0857123
\(51\) 1.22520 0.171563
\(52\) 9.38207 1.30106
\(53\) −3.43644 −0.472032 −0.236016 0.971749i \(-0.575842\pi\)
−0.236016 + 0.971749i \(0.575842\pi\)
\(54\) 2.07710 0.282658
\(55\) 5.15684 0.695349
\(56\) 0 0
\(57\) 4.41144 0.584309
\(58\) 7.09735 0.931927
\(59\) 9.90021 1.28890 0.644449 0.764648i \(-0.277087\pi\)
0.644449 + 0.764648i \(0.277087\pi\)
\(60\) −5.32392 −0.687315
\(61\) 5.18833 0.664298 0.332149 0.943227i \(-0.392226\pi\)
0.332149 + 0.943227i \(0.392226\pi\)
\(62\) −2.23214 −0.283482
\(63\) 0 0
\(64\) −10.2861 −1.28577
\(65\) −9.32545 −1.15668
\(66\) −4.65630 −0.573151
\(67\) 10.9161 1.33361 0.666806 0.745231i \(-0.267661\pi\)
0.666806 + 0.745231i \(0.267661\pi\)
\(68\) 2.83556 0.343862
\(69\) 6.56124 0.789880
\(70\) 0 0
\(71\) −5.24347 −0.622286 −0.311143 0.950363i \(-0.600712\pi\)
−0.311143 + 0.950363i \(0.600712\pi\)
\(72\) 0.652949 0.0769507
\(73\) 5.69973 0.667103 0.333551 0.942732i \(-0.391753\pi\)
0.333551 + 0.942732i \(0.391753\pi\)
\(74\) −3.40610 −0.395951
\(75\) 0.291790 0.0336930
\(76\) 10.2096 1.17112
\(77\) 0 0
\(78\) 8.42028 0.953409
\(79\) 3.55265 0.399704 0.199852 0.979826i \(-0.435954\pi\)
0.199852 + 0.979826i \(0.435954\pi\)
\(80\) 7.52795 0.841651
\(81\) 1.00000 0.111111
\(82\) 2.07710 0.229378
\(83\) 2.44743 0.268640 0.134320 0.990938i \(-0.457115\pi\)
0.134320 + 0.990938i \(0.457115\pi\)
\(84\) 0 0
\(85\) −2.81845 −0.305703
\(86\) −9.70437 −1.04645
\(87\) 3.41695 0.366335
\(88\) −1.46373 −0.156034
\(89\) 5.51735 0.584837 0.292419 0.956290i \(-0.405540\pi\)
0.292419 + 0.956290i \(0.405540\pi\)
\(90\) −4.77814 −0.503661
\(91\) 0 0
\(92\) 15.1850 1.58315
\(93\) −1.07464 −0.111435
\(94\) 22.7254 2.34394
\(95\) −10.1480 −1.04116
\(96\) −8.10315 −0.827025
\(97\) −3.88945 −0.394914 −0.197457 0.980312i \(-0.563268\pi\)
−0.197457 + 0.980312i \(0.563268\pi\)
\(98\) 0 0
\(99\) −2.24173 −0.225302
\(100\) 0.675306 0.0675306
\(101\) 11.7539 1.16956 0.584780 0.811192i \(-0.301181\pi\)
0.584780 + 0.811192i \(0.301181\pi\)
\(102\) 2.54488 0.251980
\(103\) −7.81801 −0.770331 −0.385165 0.922848i \(-0.625856\pi\)
−0.385165 + 0.922848i \(0.625856\pi\)
\(104\) 2.64696 0.259556
\(105\) 0 0
\(106\) −7.13785 −0.693289
\(107\) 14.9202 1.44239 0.721193 0.692734i \(-0.243594\pi\)
0.721193 + 0.692734i \(0.243594\pi\)
\(108\) 2.31436 0.222699
\(109\) −2.44790 −0.234466 −0.117233 0.993104i \(-0.537402\pi\)
−0.117233 + 0.993104i \(0.537402\pi\)
\(110\) 10.7113 1.02128
\(111\) −1.63983 −0.155646
\(112\) 0 0
\(113\) −5.66753 −0.533156 −0.266578 0.963813i \(-0.585893\pi\)
−0.266578 + 0.963813i \(0.585893\pi\)
\(114\) 9.16300 0.858194
\(115\) −15.0934 −1.40747
\(116\) 7.90803 0.734242
\(117\) 4.05386 0.374779
\(118\) 20.5637 1.89305
\(119\) 0 0
\(120\) −1.50204 −0.137116
\(121\) −5.97466 −0.543151
\(122\) 10.7767 0.975676
\(123\) 1.00000 0.0901670
\(124\) −2.48710 −0.223348
\(125\) 10.8307 0.968729
\(126\) 0 0
\(127\) 5.81071 0.515617 0.257809 0.966196i \(-0.417000\pi\)
0.257809 + 0.966196i \(0.417000\pi\)
\(128\) −5.15907 −0.456001
\(129\) −4.67207 −0.411353
\(130\) −19.3699 −1.69885
\(131\) 14.4403 1.26165 0.630826 0.775925i \(-0.282716\pi\)
0.630826 + 0.775925i \(0.282716\pi\)
\(132\) −5.18815 −0.451571
\(133\) 0 0
\(134\) 22.6738 1.95872
\(135\) −2.30039 −0.197986
\(136\) 0.799996 0.0685991
\(137\) 7.95642 0.679762 0.339881 0.940468i \(-0.389613\pi\)
0.339881 + 0.940468i \(0.389613\pi\)
\(138\) 13.6284 1.16012
\(139\) −8.96101 −0.760063 −0.380031 0.924974i \(-0.624087\pi\)
−0.380031 + 0.924974i \(0.624087\pi\)
\(140\) 0 0
\(141\) 10.9409 0.921390
\(142\) −10.8912 −0.913972
\(143\) −9.08764 −0.759947
\(144\) −3.27247 −0.272706
\(145\) −7.86030 −0.652763
\(146\) 11.8389 0.979796
\(147\) 0 0
\(148\) −3.79515 −0.311960
\(149\) −3.54749 −0.290622 −0.145311 0.989386i \(-0.546418\pi\)
−0.145311 + 0.989386i \(0.546418\pi\)
\(150\) 0.606078 0.0494860
\(151\) −8.99035 −0.731624 −0.365812 0.930689i \(-0.619209\pi\)
−0.365812 + 0.930689i \(0.619209\pi\)
\(152\) 2.88044 0.233635
\(153\) 1.22520 0.0990519
\(154\) 0 0
\(155\) 2.47209 0.198563
\(156\) 9.38207 0.751166
\(157\) −7.01626 −0.559958 −0.279979 0.960006i \(-0.590328\pi\)
−0.279979 + 0.960006i \(0.590328\pi\)
\(158\) 7.37921 0.587059
\(159\) −3.43644 −0.272528
\(160\) 18.6404 1.47365
\(161\) 0 0
\(162\) 2.07710 0.163193
\(163\) 18.5576 1.45355 0.726773 0.686878i \(-0.241019\pi\)
0.726773 + 0.686878i \(0.241019\pi\)
\(164\) 2.31436 0.180721
\(165\) 5.15684 0.401460
\(166\) 5.08356 0.394561
\(167\) 14.8071 1.14581 0.572905 0.819622i \(-0.305816\pi\)
0.572905 + 0.819622i \(0.305816\pi\)
\(168\) 0 0
\(169\) 3.43376 0.264135
\(170\) −5.85420 −0.448997
\(171\) 4.41144 0.337351
\(172\) −10.8128 −0.824470
\(173\) −21.1741 −1.60984 −0.804920 0.593383i \(-0.797792\pi\)
−0.804920 + 0.593383i \(0.797792\pi\)
\(174\) 7.09735 0.538049
\(175\) 0 0
\(176\) 7.33598 0.552971
\(177\) 9.90021 0.744145
\(178\) 11.4601 0.858970
\(179\) 7.08941 0.529887 0.264944 0.964264i \(-0.414647\pi\)
0.264944 + 0.964264i \(0.414647\pi\)
\(180\) −5.32392 −0.396821
\(181\) 24.0383 1.78675 0.893375 0.449312i \(-0.148331\pi\)
0.893375 + 0.449312i \(0.148331\pi\)
\(182\) 0 0
\(183\) 5.18833 0.383532
\(184\) 4.28415 0.315832
\(185\) 3.77225 0.277341
\(186\) −2.23214 −0.163668
\(187\) −2.74657 −0.200849
\(188\) 25.3211 1.84673
\(189\) 0 0
\(190\) −21.0785 −1.52919
\(191\) 19.7740 1.43080 0.715399 0.698716i \(-0.246245\pi\)
0.715399 + 0.698716i \(0.246245\pi\)
\(192\) −10.2861 −0.742338
\(193\) −10.7386 −0.772985 −0.386492 0.922293i \(-0.626313\pi\)
−0.386492 + 0.922293i \(0.626313\pi\)
\(194\) −8.07879 −0.580023
\(195\) −9.32545 −0.667809
\(196\) 0 0
\(197\) −25.6837 −1.82989 −0.914944 0.403580i \(-0.867766\pi\)
−0.914944 + 0.403580i \(0.867766\pi\)
\(198\) −4.65630 −0.330909
\(199\) 12.3661 0.876611 0.438305 0.898826i \(-0.355579\pi\)
0.438305 + 0.898826i \(0.355579\pi\)
\(200\) 0.190524 0.0134721
\(201\) 10.9161 0.769961
\(202\) 24.4141 1.71777
\(203\) 0 0
\(204\) 2.83556 0.198529
\(205\) −2.30039 −0.160666
\(206\) −16.2388 −1.13141
\(207\) 6.56124 0.456037
\(208\) −13.2661 −0.919840
\(209\) −9.88923 −0.684053
\(210\) 0 0
\(211\) −12.7379 −0.876916 −0.438458 0.898752i \(-0.644475\pi\)
−0.438458 + 0.898752i \(0.644475\pi\)
\(212\) −7.95315 −0.546225
\(213\) −5.24347 −0.359277
\(214\) 30.9907 2.11848
\(215\) 10.7476 0.732979
\(216\) 0.652949 0.0444275
\(217\) 0 0
\(218\) −5.08454 −0.344368
\(219\) 5.69973 0.385152
\(220\) 11.9348 0.804642
\(221\) 4.96680 0.334103
\(222\) −3.40610 −0.228602
\(223\) −14.5408 −0.973721 −0.486861 0.873480i \(-0.661858\pi\)
−0.486861 + 0.873480i \(0.661858\pi\)
\(224\) 0 0
\(225\) 0.291790 0.0194527
\(226\) −11.7720 −0.783064
\(227\) −12.7598 −0.846898 −0.423449 0.905920i \(-0.639181\pi\)
−0.423449 + 0.905920i \(0.639181\pi\)
\(228\) 10.2096 0.676149
\(229\) −16.3536 −1.08067 −0.540337 0.841448i \(-0.681703\pi\)
−0.540337 + 0.841448i \(0.681703\pi\)
\(230\) −31.3505 −2.06719
\(231\) 0 0
\(232\) 2.23109 0.146478
\(233\) 25.6813 1.68244 0.841218 0.540696i \(-0.181839\pi\)
0.841218 + 0.540696i \(0.181839\pi\)
\(234\) 8.42028 0.550451
\(235\) −25.1683 −1.64180
\(236\) 22.9126 1.49148
\(237\) 3.55265 0.230769
\(238\) 0 0
\(239\) −6.68343 −0.432315 −0.216158 0.976359i \(-0.569352\pi\)
−0.216158 + 0.976359i \(0.569352\pi\)
\(240\) 7.52795 0.485927
\(241\) −12.8119 −0.825289 −0.412645 0.910892i \(-0.635395\pi\)
−0.412645 + 0.910892i \(0.635395\pi\)
\(242\) −12.4100 −0.797744
\(243\) 1.00000 0.0641500
\(244\) 12.0076 0.768711
\(245\) 0 0
\(246\) 2.07710 0.132431
\(247\) 17.8833 1.13789
\(248\) −0.701685 −0.0445570
\(249\) 2.44743 0.155099
\(250\) 22.4965 1.42280
\(251\) −20.6747 −1.30498 −0.652488 0.757799i \(-0.726275\pi\)
−0.652488 + 0.757799i \(0.726275\pi\)
\(252\) 0 0
\(253\) −14.7085 −0.924716
\(254\) 12.0694 0.757304
\(255\) −2.81845 −0.176498
\(256\) 9.85637 0.616023
\(257\) 26.3985 1.64669 0.823345 0.567541i \(-0.192105\pi\)
0.823345 + 0.567541i \(0.192105\pi\)
\(258\) −9.70437 −0.604167
\(259\) 0 0
\(260\) −21.5824 −1.33848
\(261\) 3.41695 0.211504
\(262\) 29.9939 1.85303
\(263\) −4.26169 −0.262787 −0.131393 0.991330i \(-0.541945\pi\)
−0.131393 + 0.991330i \(0.541945\pi\)
\(264\) −1.46373 −0.0900865
\(265\) 7.90516 0.485610
\(266\) 0 0
\(267\) 5.51735 0.337656
\(268\) 25.2637 1.54323
\(269\) −14.8791 −0.907193 −0.453597 0.891207i \(-0.649859\pi\)
−0.453597 + 0.891207i \(0.649859\pi\)
\(270\) −4.77814 −0.290789
\(271\) −24.8652 −1.51045 −0.755225 0.655465i \(-0.772473\pi\)
−0.755225 + 0.655465i \(0.772473\pi\)
\(272\) −4.00944 −0.243108
\(273\) 0 0
\(274\) 16.5263 0.998390
\(275\) −0.654114 −0.0394445
\(276\) 15.1850 0.914032
\(277\) −24.1746 −1.45251 −0.726256 0.687425i \(-0.758741\pi\)
−0.726256 + 0.687425i \(0.758741\pi\)
\(278\) −18.6129 −1.11633
\(279\) −1.07464 −0.0643370
\(280\) 0 0
\(281\) −11.0063 −0.656583 −0.328291 0.944576i \(-0.606473\pi\)
−0.328291 + 0.944576i \(0.606473\pi\)
\(282\) 22.7254 1.35328
\(283\) −16.1057 −0.957387 −0.478694 0.877982i \(-0.658890\pi\)
−0.478694 + 0.877982i \(0.658890\pi\)
\(284\) −12.1353 −0.720095
\(285\) −10.1480 −0.601117
\(286\) −18.8760 −1.11616
\(287\) 0 0
\(288\) −8.10315 −0.477483
\(289\) −15.4989 −0.911698
\(290\) −16.3267 −0.958735
\(291\) −3.88945 −0.228004
\(292\) 13.1912 0.771957
\(293\) 12.6292 0.737808 0.368904 0.929467i \(-0.379733\pi\)
0.368904 + 0.929467i \(0.379733\pi\)
\(294\) 0 0
\(295\) −22.7743 −1.32597
\(296\) −1.07073 −0.0622347
\(297\) −2.24173 −0.130078
\(298\) −7.36851 −0.426846
\(299\) 26.5983 1.53822
\(300\) 0.675306 0.0389888
\(301\) 0 0
\(302\) −18.6739 −1.07456
\(303\) 11.7539 0.675246
\(304\) −14.4363 −0.827978
\(305\) −11.9352 −0.683406
\(306\) 2.54488 0.145481
\(307\) −23.2927 −1.32939 −0.664693 0.747116i \(-0.731438\pi\)
−0.664693 + 0.747116i \(0.731438\pi\)
\(308\) 0 0
\(309\) −7.81801 −0.444751
\(310\) 5.13479 0.291636
\(311\) 8.17595 0.463616 0.231808 0.972762i \(-0.425536\pi\)
0.231808 + 0.972762i \(0.425536\pi\)
\(312\) 2.64696 0.149855
\(313\) 16.9412 0.957576 0.478788 0.877931i \(-0.341076\pi\)
0.478788 + 0.877931i \(0.341076\pi\)
\(314\) −14.5735 −0.822429
\(315\) 0 0
\(316\) 8.22209 0.462529
\(317\) 10.8754 0.610824 0.305412 0.952220i \(-0.401206\pi\)
0.305412 + 0.952220i \(0.401206\pi\)
\(318\) −7.13785 −0.400271
\(319\) −7.65986 −0.428870
\(320\) 23.6621 1.32275
\(321\) 14.9202 0.832762
\(322\) 0 0
\(323\) 5.40491 0.300737
\(324\) 2.31436 0.128575
\(325\) 1.18288 0.0656141
\(326\) 38.5461 2.13487
\(327\) −2.44790 −0.135369
\(328\) 0.652949 0.0360531
\(329\) 0 0
\(330\) 10.7113 0.589637
\(331\) −12.5272 −0.688557 −0.344278 0.938868i \(-0.611876\pi\)
−0.344278 + 0.938868i \(0.611876\pi\)
\(332\) 5.66422 0.310864
\(333\) −1.63983 −0.0898622
\(334\) 30.7559 1.68289
\(335\) −25.1112 −1.37197
\(336\) 0 0
\(337\) 15.0009 0.817152 0.408576 0.912724i \(-0.366026\pi\)
0.408576 + 0.912724i \(0.366026\pi\)
\(338\) 7.13227 0.387944
\(339\) −5.66753 −0.307818
\(340\) −6.52289 −0.353753
\(341\) 2.40905 0.130457
\(342\) 9.16300 0.495479
\(343\) 0 0
\(344\) −3.05062 −0.164478
\(345\) −15.0934 −0.812601
\(346\) −43.9809 −2.36443
\(347\) −35.5777 −1.90991 −0.954955 0.296752i \(-0.904097\pi\)
−0.954955 + 0.296752i \(0.904097\pi\)
\(348\) 7.90803 0.423915
\(349\) −24.7802 −1.32646 −0.663228 0.748418i \(-0.730814\pi\)
−0.663228 + 0.748418i \(0.730814\pi\)
\(350\) 0 0
\(351\) 4.05386 0.216379
\(352\) 18.1651 0.968201
\(353\) −8.42011 −0.448157 −0.224079 0.974571i \(-0.571937\pi\)
−0.224079 + 0.974571i \(0.571937\pi\)
\(354\) 20.5637 1.09295
\(355\) 12.0620 0.640186
\(356\) 12.7691 0.676761
\(357\) 0 0
\(358\) 14.7254 0.778263
\(359\) 20.6533 1.09004 0.545019 0.838424i \(-0.316522\pi\)
0.545019 + 0.838424i \(0.316522\pi\)
\(360\) −1.50204 −0.0791642
\(361\) 0.460761 0.0242506
\(362\) 49.9299 2.62426
\(363\) −5.97466 −0.313588
\(364\) 0 0
\(365\) −13.1116 −0.686292
\(366\) 10.7767 0.563307
\(367\) 29.3148 1.53022 0.765111 0.643898i \(-0.222684\pi\)
0.765111 + 0.643898i \(0.222684\pi\)
\(368\) −21.4714 −1.11928
\(369\) 1.00000 0.0520579
\(370\) 7.83535 0.407340
\(371\) 0 0
\(372\) −2.48710 −0.128950
\(373\) −25.6244 −1.32678 −0.663391 0.748273i \(-0.730883\pi\)
−0.663391 + 0.748273i \(0.730883\pi\)
\(374\) −5.70492 −0.294994
\(375\) 10.8307 0.559296
\(376\) 7.14385 0.368416
\(377\) 13.8518 0.713405
\(378\) 0 0
\(379\) −9.09331 −0.467092 −0.233546 0.972346i \(-0.575033\pi\)
−0.233546 + 0.972346i \(0.575033\pi\)
\(380\) −23.4861 −1.20481
\(381\) 5.81071 0.297692
\(382\) 41.0727 2.10146
\(383\) −10.4624 −0.534603 −0.267302 0.963613i \(-0.586132\pi\)
−0.267302 + 0.963613i \(0.586132\pi\)
\(384\) −5.15907 −0.263272
\(385\) 0 0
\(386\) −22.3053 −1.13531
\(387\) −4.67207 −0.237495
\(388\) −9.00158 −0.456986
\(389\) −22.4569 −1.13861 −0.569304 0.822127i \(-0.692787\pi\)
−0.569304 + 0.822127i \(0.692787\pi\)
\(390\) −19.3699 −0.980834
\(391\) 8.03886 0.406542
\(392\) 0 0
\(393\) 14.4403 0.728415
\(394\) −53.3477 −2.68762
\(395\) −8.17247 −0.411202
\(396\) −5.18815 −0.260715
\(397\) 34.0978 1.71132 0.855659 0.517540i \(-0.173152\pi\)
0.855659 + 0.517540i \(0.173152\pi\)
\(398\) 25.6857 1.28751
\(399\) 0 0
\(400\) −0.954874 −0.0477437
\(401\) 26.2661 1.31167 0.655833 0.754906i \(-0.272318\pi\)
0.655833 + 0.754906i \(0.272318\pi\)
\(402\) 22.6738 1.13087
\(403\) −4.35644 −0.217010
\(404\) 27.2028 1.35339
\(405\) −2.30039 −0.114307
\(406\) 0 0
\(407\) 3.67605 0.182215
\(408\) 0.799996 0.0396057
\(409\) −13.7222 −0.678517 −0.339259 0.940693i \(-0.610176\pi\)
−0.339259 + 0.940693i \(0.610176\pi\)
\(410\) −4.77814 −0.235976
\(411\) 7.95642 0.392461
\(412\) −18.0936 −0.891410
\(413\) 0 0
\(414\) 13.6284 0.669797
\(415\) −5.63004 −0.276368
\(416\) −32.8490 −1.61056
\(417\) −8.96101 −0.438823
\(418\) −20.5410 −1.00469
\(419\) −5.03172 −0.245815 −0.122908 0.992418i \(-0.539222\pi\)
−0.122908 + 0.992418i \(0.539222\pi\)
\(420\) 0 0
\(421\) 35.3421 1.72247 0.861234 0.508209i \(-0.169692\pi\)
0.861234 + 0.508209i \(0.169692\pi\)
\(422\) −26.4580 −1.28796
\(423\) 10.9409 0.531965
\(424\) −2.24382 −0.108970
\(425\) 0.357502 0.0173414
\(426\) −10.8912 −0.527682
\(427\) 0 0
\(428\) 34.5305 1.66910
\(429\) −9.08764 −0.438755
\(430\) 22.3238 1.07655
\(431\) −10.0032 −0.481838 −0.240919 0.970545i \(-0.577449\pi\)
−0.240919 + 0.970545i \(0.577449\pi\)
\(432\) −3.27247 −0.157447
\(433\) 0.228599 0.0109858 0.00549289 0.999985i \(-0.498252\pi\)
0.00549289 + 0.999985i \(0.498252\pi\)
\(434\) 0 0
\(435\) −7.86030 −0.376873
\(436\) −5.66531 −0.271319
\(437\) 28.9445 1.38460
\(438\) 11.8389 0.565686
\(439\) −6.63796 −0.316812 −0.158406 0.987374i \(-0.550636\pi\)
−0.158406 + 0.987374i \(0.550636\pi\)
\(440\) 3.36715 0.160523
\(441\) 0 0
\(442\) 10.3166 0.490709
\(443\) −34.2893 −1.62913 −0.814567 0.580069i \(-0.803025\pi\)
−0.814567 + 0.580069i \(0.803025\pi\)
\(444\) −3.79515 −0.180110
\(445\) −12.6920 −0.601660
\(446\) −30.2026 −1.43014
\(447\) −3.54749 −0.167791
\(448\) 0 0
\(449\) −23.8006 −1.12322 −0.561609 0.827403i \(-0.689817\pi\)
−0.561609 + 0.827403i \(0.689817\pi\)
\(450\) 0.606078 0.0285708
\(451\) −2.24173 −0.105559
\(452\) −13.1167 −0.616956
\(453\) −8.99035 −0.422403
\(454\) −26.5034 −1.24387
\(455\) 0 0
\(456\) 2.88044 0.134889
\(457\) 3.89804 0.182343 0.0911713 0.995835i \(-0.470939\pi\)
0.0911713 + 0.995835i \(0.470939\pi\)
\(458\) −33.9681 −1.58722
\(459\) 1.22520 0.0571876
\(460\) −34.9315 −1.62869
\(461\) 8.82325 0.410940 0.205470 0.978663i \(-0.434128\pi\)
0.205470 + 0.978663i \(0.434128\pi\)
\(462\) 0 0
\(463\) −27.1088 −1.25985 −0.629925 0.776656i \(-0.716915\pi\)
−0.629925 + 0.776656i \(0.716915\pi\)
\(464\) −11.1819 −0.519104
\(465\) 2.47209 0.114640
\(466\) 53.3426 2.47105
\(467\) 39.6617 1.83532 0.917662 0.397361i \(-0.130074\pi\)
0.917662 + 0.397361i \(0.130074\pi\)
\(468\) 9.38207 0.433686
\(469\) 0 0
\(470\) −52.2772 −2.41137
\(471\) −7.01626 −0.323292
\(472\) 6.46433 0.297545
\(473\) 10.4735 0.481572
\(474\) 7.37921 0.338938
\(475\) 1.28721 0.0590614
\(476\) 0 0
\(477\) −3.43644 −0.157344
\(478\) −13.8822 −0.634956
\(479\) −0.661325 −0.0302167 −0.0151084 0.999886i \(-0.504809\pi\)
−0.0151084 + 0.999886i \(0.504809\pi\)
\(480\) 18.6404 0.850814
\(481\) −6.64764 −0.303106
\(482\) −26.6117 −1.21213
\(483\) 0 0
\(484\) −13.8275 −0.628522
\(485\) 8.94725 0.406274
\(486\) 2.07710 0.0942193
\(487\) −12.0841 −0.547582 −0.273791 0.961789i \(-0.588278\pi\)
−0.273791 + 0.961789i \(0.588278\pi\)
\(488\) 3.38771 0.153355
\(489\) 18.5576 0.839205
\(490\) 0 0
\(491\) −5.89624 −0.266094 −0.133047 0.991110i \(-0.542476\pi\)
−0.133047 + 0.991110i \(0.542476\pi\)
\(492\) 2.31436 0.104339
\(493\) 4.18646 0.188549
\(494\) 37.1455 1.67126
\(495\) 5.15684 0.231783
\(496\) 3.51673 0.157906
\(497\) 0 0
\(498\) 5.08356 0.227800
\(499\) −9.66766 −0.432784 −0.216392 0.976307i \(-0.569429\pi\)
−0.216392 + 0.976307i \(0.569429\pi\)
\(500\) 25.0661 1.12099
\(501\) 14.8071 0.661534
\(502\) −42.9435 −1.91666
\(503\) −35.1796 −1.56858 −0.784290 0.620395i \(-0.786972\pi\)
−0.784290 + 0.620395i \(0.786972\pi\)
\(504\) 0 0
\(505\) −27.0386 −1.20320
\(506\) −30.5511 −1.35816
\(507\) 3.43376 0.152499
\(508\) 13.4481 0.596661
\(509\) 2.79729 0.123988 0.0619938 0.998077i \(-0.480254\pi\)
0.0619938 + 0.998077i \(0.480254\pi\)
\(510\) −5.85420 −0.259228
\(511\) 0 0
\(512\) 30.7908 1.36078
\(513\) 4.41144 0.194770
\(514\) 54.8323 2.41855
\(515\) 17.9845 0.792490
\(516\) −10.8128 −0.476008
\(517\) −24.5265 −1.07867
\(518\) 0 0
\(519\) −21.1741 −0.929442
\(520\) −6.08904 −0.267022
\(521\) −29.5199 −1.29329 −0.646645 0.762791i \(-0.723829\pi\)
−0.646645 + 0.762791i \(0.723829\pi\)
\(522\) 7.09735 0.310642
\(523\) −29.5127 −1.29050 −0.645250 0.763971i \(-0.723247\pi\)
−0.645250 + 0.763971i \(0.723247\pi\)
\(524\) 33.4199 1.45995
\(525\) 0 0
\(526\) −8.85196 −0.385964
\(527\) −1.31665 −0.0573544
\(528\) 7.33598 0.319258
\(529\) 20.0498 0.871732
\(530\) 16.4198 0.713232
\(531\) 9.90021 0.429632
\(532\) 0 0
\(533\) 4.05386 0.175592
\(534\) 11.4601 0.495927
\(535\) −34.3222 −1.48388
\(536\) 7.12764 0.307867
\(537\) 7.08941 0.305930
\(538\) −30.9054 −1.33242
\(539\) 0 0
\(540\) −5.32392 −0.229105
\(541\) 35.9810 1.54695 0.773473 0.633830i \(-0.218518\pi\)
0.773473 + 0.633830i \(0.218518\pi\)
\(542\) −51.6475 −2.21845
\(543\) 24.0383 1.03158
\(544\) −9.92802 −0.425660
\(545\) 5.63112 0.241211
\(546\) 0 0
\(547\) 19.5998 0.838028 0.419014 0.907980i \(-0.362376\pi\)
0.419014 + 0.907980i \(0.362376\pi\)
\(548\) 18.4140 0.786606
\(549\) 5.18833 0.221433
\(550\) −1.35866 −0.0579335
\(551\) 15.0736 0.642158
\(552\) 4.28415 0.182346
\(553\) 0 0
\(554\) −50.2131 −2.13335
\(555\) 3.77225 0.160123
\(556\) −20.7390 −0.879528
\(557\) 14.9938 0.635306 0.317653 0.948207i \(-0.397105\pi\)
0.317653 + 0.948207i \(0.397105\pi\)
\(558\) −2.23214 −0.0944939
\(559\) −18.9399 −0.801072
\(560\) 0 0
\(561\) −2.74657 −0.115960
\(562\) −22.8613 −0.964345
\(563\) 35.7951 1.50858 0.754291 0.656540i \(-0.227981\pi\)
0.754291 + 0.656540i \(0.227981\pi\)
\(564\) 25.3211 1.06621
\(565\) 13.0375 0.548492
\(566\) −33.4533 −1.40615
\(567\) 0 0
\(568\) −3.42372 −0.143656
\(569\) 25.4501 1.06692 0.533461 0.845825i \(-0.320891\pi\)
0.533461 + 0.845825i \(0.320891\pi\)
\(570\) −21.0785 −0.882880
\(571\) −22.1799 −0.928200 −0.464100 0.885783i \(-0.653622\pi\)
−0.464100 + 0.885783i \(0.653622\pi\)
\(572\) −21.0320 −0.879393
\(573\) 19.7740 0.826072
\(574\) 0 0
\(575\) 1.91450 0.0798403
\(576\) −10.2861 −0.428589
\(577\) 30.2462 1.25917 0.629583 0.776933i \(-0.283226\pi\)
0.629583 + 0.776933i \(0.283226\pi\)
\(578\) −32.1928 −1.33904
\(579\) −10.7386 −0.446283
\(580\) −18.1915 −0.755363
\(581\) 0 0
\(582\) −8.07879 −0.334877
\(583\) 7.70357 0.319049
\(584\) 3.72163 0.154002
\(585\) −9.32545 −0.385560
\(586\) 26.2322 1.08364
\(587\) −2.37388 −0.0979804 −0.0489902 0.998799i \(-0.515600\pi\)
−0.0489902 + 0.998799i \(0.515600\pi\)
\(588\) 0 0
\(589\) −4.74071 −0.195337
\(590\) −47.3046 −1.94750
\(591\) −25.6837 −1.05649
\(592\) 5.36630 0.220553
\(593\) 11.6657 0.479051 0.239525 0.970890i \(-0.423008\pi\)
0.239525 + 0.970890i \(0.423008\pi\)
\(594\) −4.65630 −0.191050
\(595\) 0 0
\(596\) −8.21016 −0.336301
\(597\) 12.3661 0.506112
\(598\) 55.2474 2.25924
\(599\) 15.5533 0.635489 0.317744 0.948176i \(-0.397075\pi\)
0.317744 + 0.948176i \(0.397075\pi\)
\(600\) 0.190524 0.00777811
\(601\) −22.3375 −0.911166 −0.455583 0.890193i \(-0.650569\pi\)
−0.455583 + 0.890193i \(0.650569\pi\)
\(602\) 0 0
\(603\) 10.9161 0.444537
\(604\) −20.8069 −0.846619
\(605\) 13.7440 0.558775
\(606\) 24.4141 0.991756
\(607\) −37.4654 −1.52067 −0.760337 0.649528i \(-0.774966\pi\)
−0.760337 + 0.649528i \(0.774966\pi\)
\(608\) −35.7465 −1.44971
\(609\) 0 0
\(610\) −24.7906 −1.00374
\(611\) 44.3528 1.79432
\(612\) 2.83556 0.114621
\(613\) 47.2820 1.90970 0.954852 0.297083i \(-0.0960139\pi\)
0.954852 + 0.297083i \(0.0960139\pi\)
\(614\) −48.3814 −1.95251
\(615\) −2.30039 −0.0927606
\(616\) 0 0
\(617\) −6.52799 −0.262807 −0.131404 0.991329i \(-0.541948\pi\)
−0.131404 + 0.991329i \(0.541948\pi\)
\(618\) −16.2388 −0.653220
\(619\) 43.1677 1.73506 0.867528 0.497389i \(-0.165708\pi\)
0.867528 + 0.497389i \(0.165708\pi\)
\(620\) 5.72130 0.229773
\(621\) 6.56124 0.263293
\(622\) 16.9823 0.680928
\(623\) 0 0
\(624\) −13.2661 −0.531070
\(625\) −26.3738 −1.05495
\(626\) 35.1887 1.40642
\(627\) −9.88923 −0.394938
\(628\) −16.2381 −0.647971
\(629\) −2.00913 −0.0801092
\(630\) 0 0
\(631\) 34.2725 1.36437 0.682183 0.731182i \(-0.261031\pi\)
0.682183 + 0.731182i \(0.261031\pi\)
\(632\) 2.31970 0.0922725
\(633\) −12.7379 −0.506288
\(634\) 22.5893 0.897137
\(635\) −13.3669 −0.530449
\(636\) −7.95315 −0.315363
\(637\) 0 0
\(638\) −15.9103 −0.629895
\(639\) −5.24347 −0.207429
\(640\) 11.8679 0.469118
\(641\) 29.6706 1.17192 0.585960 0.810340i \(-0.300718\pi\)
0.585960 + 0.810340i \(0.300718\pi\)
\(642\) 30.9907 1.22311
\(643\) 0.491928 0.0193997 0.00969987 0.999953i \(-0.496912\pi\)
0.00969987 + 0.999953i \(0.496912\pi\)
\(644\) 0 0
\(645\) 10.7476 0.423185
\(646\) 11.2266 0.441703
\(647\) −17.2939 −0.679895 −0.339948 0.940444i \(-0.610409\pi\)
−0.339948 + 0.940444i \(0.610409\pi\)
\(648\) 0.652949 0.0256502
\(649\) −22.1936 −0.871174
\(650\) 2.45695 0.0963696
\(651\) 0 0
\(652\) 42.9489 1.68201
\(653\) −5.95097 −0.232879 −0.116440 0.993198i \(-0.537148\pi\)
−0.116440 + 0.993198i \(0.537148\pi\)
\(654\) −5.08454 −0.198821
\(655\) −33.2182 −1.29794
\(656\) −3.27247 −0.127768
\(657\) 5.69973 0.222368
\(658\) 0 0
\(659\) 48.3637 1.88398 0.941992 0.335635i \(-0.108951\pi\)
0.941992 + 0.335635i \(0.108951\pi\)
\(660\) 11.9348 0.464560
\(661\) −15.9158 −0.619054 −0.309527 0.950891i \(-0.600171\pi\)
−0.309527 + 0.950891i \(0.600171\pi\)
\(662\) −26.0203 −1.01131
\(663\) 4.96680 0.192895
\(664\) 1.59804 0.0620162
\(665\) 0 0
\(666\) −3.40610 −0.131984
\(667\) 22.4194 0.868082
\(668\) 34.2690 1.32591
\(669\) −14.5408 −0.562178
\(670\) −52.1586 −2.01506
\(671\) −11.6308 −0.449003
\(672\) 0 0
\(673\) −21.6199 −0.833387 −0.416693 0.909047i \(-0.636811\pi\)
−0.416693 + 0.909047i \(0.636811\pi\)
\(674\) 31.1584 1.20018
\(675\) 0.291790 0.0112310
\(676\) 7.94694 0.305651
\(677\) −10.1041 −0.388331 −0.194166 0.980969i \(-0.562200\pi\)
−0.194166 + 0.980969i \(0.562200\pi\)
\(678\) −11.7720 −0.452102
\(679\) 0 0
\(680\) −1.84030 −0.0705723
\(681\) −12.7598 −0.488957
\(682\) 5.00385 0.191607
\(683\) −44.1322 −1.68867 −0.844336 0.535813i \(-0.820005\pi\)
−0.844336 + 0.535813i \(0.820005\pi\)
\(684\) 10.2096 0.390375
\(685\) −18.3029 −0.699316
\(686\) 0 0
\(687\) −16.3536 −0.623928
\(688\) 15.2892 0.582895
\(689\) −13.9309 −0.530723
\(690\) −31.3505 −1.19349
\(691\) −6.85734 −0.260865 −0.130433 0.991457i \(-0.541637\pi\)
−0.130433 + 0.991457i \(0.541637\pi\)
\(692\) −49.0045 −1.86287
\(693\) 0 0
\(694\) −73.8985 −2.80515
\(695\) 20.6138 0.781926
\(696\) 2.23109 0.0845693
\(697\) 1.22520 0.0464079
\(698\) −51.4711 −1.94821
\(699\) 25.6813 0.971355
\(700\) 0 0
\(701\) 49.8246 1.88185 0.940925 0.338615i \(-0.109958\pi\)
0.940925 + 0.338615i \(0.109958\pi\)
\(702\) 8.42028 0.317803
\(703\) −7.23401 −0.272836
\(704\) 23.0587 0.869058
\(705\) −25.1683 −0.947894
\(706\) −17.4894 −0.658223
\(707\) 0 0
\(708\) 22.9126 0.861108
\(709\) −46.7512 −1.75578 −0.877889 0.478865i \(-0.841048\pi\)
−0.877889 + 0.478865i \(0.841048\pi\)
\(710\) 25.0541 0.940263
\(711\) 3.55265 0.133235
\(712\) 3.60254 0.135011
\(713\) −7.05097 −0.264061
\(714\) 0 0
\(715\) 20.9051 0.781807
\(716\) 16.4074 0.613174
\(717\) −6.68343 −0.249597
\(718\) 42.8990 1.60098
\(719\) −17.2085 −0.641769 −0.320884 0.947118i \(-0.603980\pi\)
−0.320884 + 0.947118i \(0.603980\pi\)
\(720\) 7.52795 0.280550
\(721\) 0 0
\(722\) 0.957049 0.0356177
\(723\) −12.8119 −0.476481
\(724\) 55.6331 2.06759
\(725\) 0.997031 0.0370288
\(726\) −12.4100 −0.460578
\(727\) −14.0624 −0.521547 −0.260773 0.965400i \(-0.583978\pi\)
−0.260773 + 0.965400i \(0.583978\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −27.2341 −1.00798
\(731\) −5.72424 −0.211719
\(732\) 12.0076 0.443815
\(733\) 44.3042 1.63641 0.818206 0.574925i \(-0.194969\pi\)
0.818206 + 0.574925i \(0.194969\pi\)
\(734\) 60.8899 2.24749
\(735\) 0 0
\(736\) −53.1667 −1.95975
\(737\) −24.4709 −0.901397
\(738\) 2.07710 0.0764592
\(739\) 37.1616 1.36701 0.683506 0.729945i \(-0.260455\pi\)
0.683506 + 0.729945i \(0.260455\pi\)
\(740\) 8.73033 0.320933
\(741\) 17.8833 0.656960
\(742\) 0 0
\(743\) 17.6676 0.648161 0.324080 0.946030i \(-0.394945\pi\)
0.324080 + 0.946030i \(0.394945\pi\)
\(744\) −0.701685 −0.0257250
\(745\) 8.16062 0.298982
\(746\) −53.2246 −1.94869
\(747\) 2.44743 0.0895467
\(748\) −6.35655 −0.232418
\(749\) 0 0
\(750\) 22.4965 0.821456
\(751\) 23.3385 0.851635 0.425817 0.904809i \(-0.359987\pi\)
0.425817 + 0.904809i \(0.359987\pi\)
\(752\) −35.8038 −1.30563
\(753\) −20.6747 −0.753428
\(754\) 28.7716 1.04780
\(755\) 20.6813 0.752670
\(756\) 0 0
\(757\) −2.81661 −0.102371 −0.0511857 0.998689i \(-0.516300\pi\)
−0.0511857 + 0.998689i \(0.516300\pi\)
\(758\) −18.8877 −0.686034
\(759\) −14.7085 −0.533885
\(760\) −6.62613 −0.240355
\(761\) −25.8866 −0.938389 −0.469194 0.883095i \(-0.655456\pi\)
−0.469194 + 0.883095i \(0.655456\pi\)
\(762\) 12.0694 0.437230
\(763\) 0 0
\(764\) 45.7641 1.65569
\(765\) −2.81845 −0.101901
\(766\) −21.7315 −0.785189
\(767\) 40.1340 1.44916
\(768\) 9.85637 0.355661
\(769\) 21.1931 0.764243 0.382121 0.924112i \(-0.375194\pi\)
0.382121 + 0.924112i \(0.375194\pi\)
\(770\) 0 0
\(771\) 26.3985 0.950717
\(772\) −24.8530 −0.894481
\(773\) −30.2026 −1.08631 −0.543155 0.839632i \(-0.682771\pi\)
−0.543155 + 0.839632i \(0.682771\pi\)
\(774\) −9.70437 −0.348816
\(775\) −0.313569 −0.0112637
\(776\) −2.53961 −0.0911668
\(777\) 0 0
\(778\) −46.6452 −1.67231
\(779\) 4.41144 0.158056
\(780\) −21.5824 −0.772774
\(781\) 11.7544 0.420607
\(782\) 16.6975 0.597102
\(783\) 3.41695 0.122112
\(784\) 0 0
\(785\) 16.1401 0.576066
\(786\) 29.9939 1.06985
\(787\) −22.0228 −0.785027 −0.392513 0.919746i \(-0.628394\pi\)
−0.392513 + 0.919746i \(0.628394\pi\)
\(788\) −59.4412 −2.11751
\(789\) −4.26169 −0.151720
\(790\) −16.9751 −0.603945
\(791\) 0 0
\(792\) −1.46373 −0.0520115
\(793\) 21.0328 0.746895
\(794\) 70.8245 2.51347
\(795\) 7.90516 0.280367
\(796\) 28.6196 1.01439
\(797\) −16.6446 −0.589583 −0.294791 0.955562i \(-0.595250\pi\)
−0.294791 + 0.955562i \(0.595250\pi\)
\(798\) 0 0
\(799\) 13.4048 0.474229
\(800\) −2.36442 −0.0835948
\(801\) 5.51735 0.194946
\(802\) 54.5573 1.92649
\(803\) −12.7772 −0.450899
\(804\) 25.2637 0.890982
\(805\) 0 0
\(806\) −9.04877 −0.318729
\(807\) −14.8791 −0.523768
\(808\) 7.67472 0.269996
\(809\) −20.1468 −0.708323 −0.354162 0.935184i \(-0.615234\pi\)
−0.354162 + 0.935184i \(0.615234\pi\)
\(810\) −4.77814 −0.167887
\(811\) 34.5884 1.21456 0.607282 0.794487i \(-0.292260\pi\)
0.607282 + 0.794487i \(0.292260\pi\)
\(812\) 0 0
\(813\) −24.8652 −0.872059
\(814\) 7.63554 0.267626
\(815\) −42.6898 −1.49536
\(816\) −4.00944 −0.140359
\(817\) −20.6105 −0.721071
\(818\) −28.5024 −0.996561
\(819\) 0 0
\(820\) −5.32392 −0.185919
\(821\) −31.8361 −1.11109 −0.555543 0.831488i \(-0.687490\pi\)
−0.555543 + 0.831488i \(0.687490\pi\)
\(822\) 16.5263 0.576421
\(823\) 3.12481 0.108924 0.0544620 0.998516i \(-0.482656\pi\)
0.0544620 + 0.998516i \(0.482656\pi\)
\(824\) −5.10476 −0.177833
\(825\) −0.654114 −0.0227733
\(826\) 0 0
\(827\) 9.35195 0.325199 0.162600 0.986692i \(-0.448012\pi\)
0.162600 + 0.986692i \(0.448012\pi\)
\(828\) 15.1850 0.527716
\(829\) 12.0702 0.419215 0.209608 0.977786i \(-0.432781\pi\)
0.209608 + 0.977786i \(0.432781\pi\)
\(830\) −11.6942 −0.405910
\(831\) −24.1746 −0.838608
\(832\) −41.6985 −1.44564
\(833\) 0 0
\(834\) −18.6129 −0.644513
\(835\) −34.0622 −1.17877
\(836\) −22.8872 −0.791570
\(837\) −1.07464 −0.0371450
\(838\) −10.4514 −0.361037
\(839\) 14.1488 0.488472 0.244236 0.969716i \(-0.421463\pi\)
0.244236 + 0.969716i \(0.421463\pi\)
\(840\) 0 0
\(841\) −17.3245 −0.597396
\(842\) 73.4091 2.52985
\(843\) −11.0063 −0.379078
\(844\) −29.4801 −1.01475
\(845\) −7.89898 −0.271733
\(846\) 22.7254 0.781314
\(847\) 0 0
\(848\) 11.2457 0.386178
\(849\) −16.1057 −0.552748
\(850\) 0.742569 0.0254699
\(851\) −10.7593 −0.368825
\(852\) −12.1353 −0.415747
\(853\) 51.9016 1.77708 0.888538 0.458804i \(-0.151722\pi\)
0.888538 + 0.458804i \(0.151722\pi\)
\(854\) 0 0
\(855\) −10.1480 −0.347055
\(856\) 9.74210 0.332978
\(857\) 26.5421 0.906662 0.453331 0.891342i \(-0.350236\pi\)
0.453331 + 0.891342i \(0.350236\pi\)
\(858\) −18.8760 −0.644415
\(859\) 24.1629 0.824427 0.412214 0.911087i \(-0.364756\pi\)
0.412214 + 0.911087i \(0.364756\pi\)
\(860\) 24.8737 0.848187
\(861\) 0 0
\(862\) −20.7777 −0.707692
\(863\) 49.6475 1.69002 0.845011 0.534749i \(-0.179594\pi\)
0.845011 + 0.534749i \(0.179594\pi\)
\(864\) −8.10315 −0.275675
\(865\) 48.7088 1.65615
\(866\) 0.474824 0.0161352
\(867\) −15.4989 −0.526369
\(868\) 0 0
\(869\) −7.96406 −0.270162
\(870\) −16.3267 −0.553526
\(871\) 44.2523 1.49943
\(872\) −1.59835 −0.0541270
\(873\) −3.88945 −0.131638
\(874\) 60.1206 2.03361
\(875\) 0 0
\(876\) 13.1912 0.445689
\(877\) −0.127968 −0.00432118 −0.00216059 0.999998i \(-0.500688\pi\)
−0.00216059 + 0.999998i \(0.500688\pi\)
\(878\) −13.7877 −0.465313
\(879\) 12.6292 0.425974
\(880\) −16.8756 −0.568877
\(881\) −35.9413 −1.21089 −0.605446 0.795886i \(-0.707005\pi\)
−0.605446 + 0.795886i \(0.707005\pi\)
\(882\) 0 0
\(883\) 12.5574 0.422590 0.211295 0.977422i \(-0.432232\pi\)
0.211295 + 0.977422i \(0.432232\pi\)
\(884\) 11.4949 0.386617
\(885\) −22.7743 −0.765551
\(886\) −71.2224 −2.39276
\(887\) −13.9193 −0.467364 −0.233682 0.972313i \(-0.575078\pi\)
−0.233682 + 0.972313i \(0.575078\pi\)
\(888\) −1.07073 −0.0359312
\(889\) 0 0
\(890\) −26.3627 −0.883679
\(891\) −2.24173 −0.0751007
\(892\) −33.6525 −1.12677
\(893\) 48.2651 1.61513
\(894\) −7.36851 −0.246440
\(895\) −16.3084 −0.545129
\(896\) 0 0
\(897\) 26.5983 0.888092
\(898\) −49.4362 −1.64971
\(899\) −3.67199 −0.122468
\(900\) 0.675306 0.0225102
\(901\) −4.21035 −0.140267
\(902\) −4.65630 −0.155038
\(903\) 0 0
\(904\) −3.70060 −0.123080
\(905\) −55.2974 −1.83815
\(906\) −18.6739 −0.620398
\(907\) −44.7454 −1.48575 −0.742874 0.669431i \(-0.766538\pi\)
−0.742874 + 0.669431i \(0.766538\pi\)
\(908\) −29.5307 −0.980011
\(909\) 11.7539 0.389853
\(910\) 0 0
\(911\) −10.4251 −0.345400 −0.172700 0.984975i \(-0.555249\pi\)
−0.172700 + 0.984975i \(0.555249\pi\)
\(912\) −14.4363 −0.478033
\(913\) −5.48647 −0.181576
\(914\) 8.09663 0.267813
\(915\) −11.9352 −0.394565
\(916\) −37.8480 −1.25053
\(917\) 0 0
\(918\) 2.54488 0.0839934
\(919\) 24.6925 0.814532 0.407266 0.913310i \(-0.366482\pi\)
0.407266 + 0.913310i \(0.366482\pi\)
\(920\) −9.85521 −0.324917
\(921\) −23.2927 −0.767522
\(922\) 18.3268 0.603561
\(923\) −21.2563 −0.699659
\(924\) 0 0
\(925\) −0.478486 −0.0157325
\(926\) −56.3077 −1.85039
\(927\) −7.81801 −0.256777
\(928\) −27.6880 −0.908904
\(929\) 0.159923 0.00524692 0.00262346 0.999997i \(-0.499165\pi\)
0.00262346 + 0.999997i \(0.499165\pi\)
\(930\) 5.13479 0.168376
\(931\) 0 0
\(932\) 59.4356 1.94688
\(933\) 8.17595 0.267669
\(934\) 82.3814 2.69560
\(935\) 6.31819 0.206627
\(936\) 2.64696 0.0865186
\(937\) −28.2710 −0.923572 −0.461786 0.886991i \(-0.652791\pi\)
−0.461786 + 0.886991i \(0.652791\pi\)
\(938\) 0 0
\(939\) 16.9412 0.552857
\(940\) −58.2485 −1.89986
\(941\) −12.0075 −0.391434 −0.195717 0.980660i \(-0.562703\pi\)
−0.195717 + 0.980660i \(0.562703\pi\)
\(942\) −14.5735 −0.474830
\(943\) 6.56124 0.213663
\(944\) −32.3981 −1.05447
\(945\) 0 0
\(946\) 21.7545 0.707301
\(947\) 1.30006 0.0422463 0.0211232 0.999777i \(-0.493276\pi\)
0.0211232 + 0.999777i \(0.493276\pi\)
\(948\) 8.22209 0.267041
\(949\) 23.1059 0.750049
\(950\) 2.67367 0.0867454
\(951\) 10.8754 0.352659
\(952\) 0 0
\(953\) −58.2749 −1.88771 −0.943854 0.330363i \(-0.892829\pi\)
−0.943854 + 0.330363i \(0.892829\pi\)
\(954\) −7.13785 −0.231096
\(955\) −45.4880 −1.47196
\(956\) −15.4678 −0.500265
\(957\) −7.65986 −0.247608
\(958\) −1.37364 −0.0443803
\(959\) 0 0
\(960\) 23.6621 0.763692
\(961\) −29.8451 −0.962747
\(962\) −13.8078 −0.445182
\(963\) 14.9202 0.480795
\(964\) −29.6514 −0.955006
\(965\) 24.7031 0.795220
\(966\) 0 0
\(967\) 39.2902 1.26349 0.631743 0.775178i \(-0.282340\pi\)
0.631743 + 0.775178i \(0.282340\pi\)
\(968\) −3.90115 −0.125388
\(969\) 5.40491 0.173631
\(970\) 18.5844 0.596708
\(971\) 56.1663 1.80246 0.901232 0.433338i \(-0.142664\pi\)
0.901232 + 0.433338i \(0.142664\pi\)
\(972\) 2.31436 0.0742330
\(973\) 0 0
\(974\) −25.0999 −0.804251
\(975\) 1.18288 0.0378823
\(976\) −16.9787 −0.543474
\(977\) −14.6676 −0.469259 −0.234629 0.972085i \(-0.575388\pi\)
−0.234629 + 0.972085i \(0.575388\pi\)
\(978\) 38.5461 1.23257
\(979\) −12.3684 −0.395295
\(980\) 0 0
\(981\) −2.44790 −0.0781554
\(982\) −12.2471 −0.390821
\(983\) −29.8488 −0.952027 −0.476014 0.879438i \(-0.657919\pi\)
−0.476014 + 0.879438i \(0.657919\pi\)
\(984\) 0.652949 0.0208152
\(985\) 59.0825 1.88253
\(986\) 8.69570 0.276928
\(987\) 0 0
\(988\) 41.3884 1.31674
\(989\) −30.6546 −0.974758
\(990\) 10.7113 0.340427
\(991\) −48.8390 −1.55142 −0.775710 0.631089i \(-0.782608\pi\)
−0.775710 + 0.631089i \(0.782608\pi\)
\(992\) 8.70797 0.276478
\(993\) −12.5272 −0.397539
\(994\) 0 0
\(995\) −28.4469 −0.901827
\(996\) 5.66422 0.179478
\(997\) −43.4145 −1.37495 −0.687475 0.726208i \(-0.741281\pi\)
−0.687475 + 0.726208i \(0.741281\pi\)
\(998\) −20.0807 −0.635644
\(999\) −1.63983 −0.0518820
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 \(a_p\))