Properties

Label 6027.2.a.bc.1.5
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 1.5
Root \(-0.169079\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.62618 q^{2} +1.00000 q^{3} +0.644462 q^{4} +1.67363 q^{5} +1.62618 q^{6} -2.20435 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.62618 q^{2} +1.00000 q^{3} +0.644462 q^{4} +1.67363 q^{5} +1.62618 q^{6} -2.20435 q^{8} +1.00000 q^{9} +2.72162 q^{10} +2.72505 q^{11} +0.644462 q^{12} -2.59232 q^{13} +1.67363 q^{15} -4.87359 q^{16} +2.49455 q^{17} +1.62618 q^{18} -0.765400 q^{19} +1.07859 q^{20} +4.43142 q^{22} +1.55115 q^{23} -2.20435 q^{24} -2.19898 q^{25} -4.21557 q^{26} +1.00000 q^{27} +9.11743 q^{29} +2.72162 q^{30} +8.26914 q^{31} -3.51664 q^{32} +2.72505 q^{33} +4.05659 q^{34} +0.644462 q^{36} -3.21502 q^{37} -1.24468 q^{38} -2.59232 q^{39} -3.68926 q^{40} +1.00000 q^{41} +11.8356 q^{43} +1.75619 q^{44} +1.67363 q^{45} +2.52244 q^{46} +5.81113 q^{47} -4.87359 q^{48} -3.57593 q^{50} +2.49455 q^{51} -1.67065 q^{52} -4.59187 q^{53} +1.62618 q^{54} +4.56071 q^{55} -0.765400 q^{57} +14.8266 q^{58} -4.77304 q^{59} +1.07859 q^{60} -0.867396 q^{61} +13.4471 q^{62} +4.02849 q^{64} -4.33857 q^{65} +4.43142 q^{66} +3.89367 q^{67} +1.60764 q^{68} +1.55115 q^{69} -10.6283 q^{71} -2.20435 q^{72} +2.23945 q^{73} -5.22820 q^{74} -2.19898 q^{75} -0.493271 q^{76} -4.21557 q^{78} +8.10443 q^{79} -8.15657 q^{80} +1.00000 q^{81} +1.62618 q^{82} +8.58566 q^{83} +4.17495 q^{85} +19.2469 q^{86} +9.11743 q^{87} -6.00695 q^{88} +1.25617 q^{89} +2.72162 q^{90} +0.999655 q^{92} +8.26914 q^{93} +9.44994 q^{94} -1.28099 q^{95} -3.51664 q^{96} +8.55514 q^{97} +2.72505 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.62618 1.14988 0.574942 0.818195i \(-0.305025\pi\)
0.574942 + 0.818195i \(0.305025\pi\)
\(3\) 1.00000 0.577350
\(4\) 0.644462 0.322231
\(5\) 1.67363 0.748468 0.374234 0.927334i \(-0.377906\pi\)
0.374234 + 0.927334i \(0.377906\pi\)
\(6\) 1.62618 0.663885
\(7\) 0 0
\(8\) −2.20435 −0.779355
\(9\) 1.00000 0.333333
\(10\) 2.72162 0.860651
\(11\) 2.72505 0.821632 0.410816 0.911718i \(-0.365244\pi\)
0.410816 + 0.911718i \(0.365244\pi\)
\(12\) 0.644462 0.186040
\(13\) −2.59232 −0.718979 −0.359490 0.933149i \(-0.617049\pi\)
−0.359490 + 0.933149i \(0.617049\pi\)
\(14\) 0 0
\(15\) 1.67363 0.432128
\(16\) −4.87359 −1.21840
\(17\) 2.49455 0.605017 0.302509 0.953147i \(-0.402176\pi\)
0.302509 + 0.953147i \(0.402176\pi\)
\(18\) 1.62618 0.383294
\(19\) −0.765400 −0.175595 −0.0877974 0.996138i \(-0.527983\pi\)
−0.0877974 + 0.996138i \(0.527983\pi\)
\(20\) 1.07859 0.241180
\(21\) 0 0
\(22\) 4.43142 0.944781
\(23\) 1.55115 0.323436 0.161718 0.986837i \(-0.448296\pi\)
0.161718 + 0.986837i \(0.448296\pi\)
\(24\) −2.20435 −0.449961
\(25\) −2.19898 −0.439795
\(26\) −4.21557 −0.826742
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 9.11743 1.69306 0.846532 0.532338i \(-0.178687\pi\)
0.846532 + 0.532338i \(0.178687\pi\)
\(30\) 2.72162 0.496897
\(31\) 8.26914 1.48518 0.742591 0.669745i \(-0.233597\pi\)
0.742591 + 0.669745i \(0.233597\pi\)
\(32\) −3.51664 −0.621660
\(33\) 2.72505 0.474370
\(34\) 4.05659 0.695699
\(35\) 0 0
\(36\) 0.644462 0.107410
\(37\) −3.21502 −0.528546 −0.264273 0.964448i \(-0.585132\pi\)
−0.264273 + 0.964448i \(0.585132\pi\)
\(38\) −1.24468 −0.201913
\(39\) −2.59232 −0.415103
\(40\) −3.68926 −0.583323
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 11.8356 1.80492 0.902458 0.430778i \(-0.141761\pi\)
0.902458 + 0.430778i \(0.141761\pi\)
\(44\) 1.75619 0.264755
\(45\) 1.67363 0.249489
\(46\) 2.52244 0.371914
\(47\) 5.81113 0.847640 0.423820 0.905746i \(-0.360689\pi\)
0.423820 + 0.905746i \(0.360689\pi\)
\(48\) −4.87359 −0.703443
\(49\) 0 0
\(50\) −3.57593 −0.505713
\(51\) 2.49455 0.349307
\(52\) −1.67065 −0.231677
\(53\) −4.59187 −0.630742 −0.315371 0.948968i \(-0.602129\pi\)
−0.315371 + 0.948968i \(0.602129\pi\)
\(54\) 1.62618 0.221295
\(55\) 4.56071 0.614966
\(56\) 0 0
\(57\) −0.765400 −0.101380
\(58\) 14.8266 1.94682
\(59\) −4.77304 −0.621397 −0.310698 0.950509i \(-0.600563\pi\)
−0.310698 + 0.950509i \(0.600563\pi\)
\(60\) 1.07859 0.139245
\(61\) −0.867396 −0.111059 −0.0555293 0.998457i \(-0.517685\pi\)
−0.0555293 + 0.998457i \(0.517685\pi\)
\(62\) 13.4471 1.70779
\(63\) 0 0
\(64\) 4.02849 0.503562
\(65\) −4.33857 −0.538133
\(66\) 4.43142 0.545470
\(67\) 3.89367 0.475688 0.237844 0.971303i \(-0.423559\pi\)
0.237844 + 0.971303i \(0.423559\pi\)
\(68\) 1.60764 0.194955
\(69\) 1.55115 0.186736
\(70\) 0 0
\(71\) −10.6283 −1.26135 −0.630675 0.776047i \(-0.717222\pi\)
−0.630675 + 0.776047i \(0.717222\pi\)
\(72\) −2.20435 −0.259785
\(73\) 2.23945 0.262107 0.131054 0.991375i \(-0.458164\pi\)
0.131054 + 0.991375i \(0.458164\pi\)
\(74\) −5.22820 −0.607766
\(75\) −2.19898 −0.253916
\(76\) −0.493271 −0.0565821
\(77\) 0 0
\(78\) −4.21557 −0.477320
\(79\) 8.10443 0.911819 0.455910 0.890026i \(-0.349314\pi\)
0.455910 + 0.890026i \(0.349314\pi\)
\(80\) −8.15657 −0.911933
\(81\) 1.00000 0.111111
\(82\) 1.62618 0.179582
\(83\) 8.58566 0.942398 0.471199 0.882027i \(-0.343821\pi\)
0.471199 + 0.882027i \(0.343821\pi\)
\(84\) 0 0
\(85\) 4.17495 0.452836
\(86\) 19.2469 2.07544
\(87\) 9.11743 0.977491
\(88\) −6.00695 −0.640343
\(89\) 1.25617 0.133154 0.0665770 0.997781i \(-0.478792\pi\)
0.0665770 + 0.997781i \(0.478792\pi\)
\(90\) 2.72162 0.286884
\(91\) 0 0
\(92\) 0.999655 0.104221
\(93\) 8.26914 0.857470
\(94\) 9.44994 0.974687
\(95\) −1.28099 −0.131427
\(96\) −3.51664 −0.358916
\(97\) 8.55514 0.868643 0.434322 0.900758i \(-0.356988\pi\)
0.434322 + 0.900758i \(0.356988\pi\)
\(98\) 0 0
\(99\) 2.72505 0.273877
\(100\) −1.41716 −0.141716
\(101\) 1.30829 0.130179 0.0650896 0.997879i \(-0.479267\pi\)
0.0650896 + 0.997879i \(0.479267\pi\)
\(102\) 4.05659 0.401662
\(103\) 15.8139 1.55819 0.779097 0.626903i \(-0.215678\pi\)
0.779097 + 0.626903i \(0.215678\pi\)
\(104\) 5.71437 0.560340
\(105\) 0 0
\(106\) −7.46721 −0.725279
\(107\) 6.65637 0.643495 0.321748 0.946825i \(-0.395730\pi\)
0.321748 + 0.946825i \(0.395730\pi\)
\(108\) 0.644462 0.0620134
\(109\) 6.62737 0.634787 0.317393 0.948294i \(-0.397192\pi\)
0.317393 + 0.948294i \(0.397192\pi\)
\(110\) 7.41653 0.707139
\(111\) −3.21502 −0.305156
\(112\) 0 0
\(113\) −17.6805 −1.66324 −0.831621 0.555343i \(-0.812587\pi\)
−0.831621 + 0.555343i \(0.812587\pi\)
\(114\) −1.24468 −0.116575
\(115\) 2.59604 0.242082
\(116\) 5.87583 0.545557
\(117\) −2.59232 −0.239660
\(118\) −7.76182 −0.714534
\(119\) 0 0
\(120\) −3.68926 −0.336781
\(121\) −3.57412 −0.324920
\(122\) −1.41054 −0.127705
\(123\) 1.00000 0.0901670
\(124\) 5.32915 0.478572
\(125\) −12.0484 −1.07764
\(126\) 0 0
\(127\) −15.6503 −1.38874 −0.694371 0.719617i \(-0.744317\pi\)
−0.694371 + 0.719617i \(0.744317\pi\)
\(128\) 13.5843 1.20070
\(129\) 11.8356 1.04207
\(130\) −7.05529 −0.618790
\(131\) 9.62811 0.841212 0.420606 0.907243i \(-0.361818\pi\)
0.420606 + 0.907243i \(0.361818\pi\)
\(132\) 1.75619 0.152857
\(133\) 0 0
\(134\) 6.33181 0.546985
\(135\) 1.67363 0.144043
\(136\) −5.49886 −0.471523
\(137\) −3.87928 −0.331429 −0.165715 0.986174i \(-0.552993\pi\)
−0.165715 + 0.986174i \(0.552993\pi\)
\(138\) 2.52244 0.214725
\(139\) 12.8314 1.08834 0.544171 0.838975i \(-0.316844\pi\)
0.544171 + 0.838975i \(0.316844\pi\)
\(140\) 0 0
\(141\) 5.81113 0.489385
\(142\) −17.2836 −1.45041
\(143\) −7.06418 −0.590737
\(144\) −4.87359 −0.406133
\(145\) 15.2592 1.26720
\(146\) 3.64174 0.301393
\(147\) 0 0
\(148\) −2.07196 −0.170314
\(149\) 0.448719 0.0367605 0.0183802 0.999831i \(-0.494149\pi\)
0.0183802 + 0.999831i \(0.494149\pi\)
\(150\) −3.57593 −0.291973
\(151\) −3.57359 −0.290815 −0.145408 0.989372i \(-0.546449\pi\)
−0.145408 + 0.989372i \(0.546449\pi\)
\(152\) 1.68721 0.136851
\(153\) 2.49455 0.201672
\(154\) 0 0
\(155\) 13.8395 1.11161
\(156\) −1.67065 −0.133759
\(157\) 8.91606 0.711579 0.355790 0.934566i \(-0.384212\pi\)
0.355790 + 0.934566i \(0.384212\pi\)
\(158\) 13.1793 1.04849
\(159\) −4.59187 −0.364159
\(160\) −5.88554 −0.465293
\(161\) 0 0
\(162\) 1.62618 0.127765
\(163\) −24.4870 −1.91797 −0.958984 0.283459i \(-0.908518\pi\)
−0.958984 + 0.283459i \(0.908518\pi\)
\(164\) 0.644462 0.0503240
\(165\) 4.56071 0.355051
\(166\) 13.9618 1.08365
\(167\) 0.708918 0.0548577 0.0274289 0.999624i \(-0.491268\pi\)
0.0274289 + 0.999624i \(0.491268\pi\)
\(168\) 0 0
\(169\) −6.27990 −0.483069
\(170\) 6.78921 0.520709
\(171\) −0.765400 −0.0585316
\(172\) 7.62761 0.581600
\(173\) 2.97877 0.226472 0.113236 0.993568i \(-0.463878\pi\)
0.113236 + 0.993568i \(0.463878\pi\)
\(174\) 14.8266 1.12400
\(175\) 0 0
\(176\) −13.2808 −1.00108
\(177\) −4.77304 −0.358764
\(178\) 2.04276 0.153111
\(179\) −20.8395 −1.55762 −0.778810 0.627260i \(-0.784176\pi\)
−0.778810 + 0.627260i \(0.784176\pi\)
\(180\) 1.07859 0.0803932
\(181\) −5.73956 −0.426618 −0.213309 0.976985i \(-0.568424\pi\)
−0.213309 + 0.976985i \(0.568424\pi\)
\(182\) 0 0
\(183\) −0.867396 −0.0641198
\(184\) −3.41927 −0.252072
\(185\) −5.38074 −0.395600
\(186\) 13.4471 0.985991
\(187\) 6.79777 0.497102
\(188\) 3.74505 0.273136
\(189\) 0 0
\(190\) −2.08313 −0.151126
\(191\) −2.63706 −0.190811 −0.0954055 0.995438i \(-0.530415\pi\)
−0.0954055 + 0.995438i \(0.530415\pi\)
\(192\) 4.02849 0.290731
\(193\) −0.711941 −0.0512467 −0.0256233 0.999672i \(-0.508157\pi\)
−0.0256233 + 0.999672i \(0.508157\pi\)
\(194\) 13.9122 0.998838
\(195\) −4.33857 −0.310691
\(196\) 0 0
\(197\) −17.2730 −1.23065 −0.615323 0.788275i \(-0.710975\pi\)
−0.615323 + 0.788275i \(0.710975\pi\)
\(198\) 4.43142 0.314927
\(199\) 3.51338 0.249057 0.124529 0.992216i \(-0.460258\pi\)
0.124529 + 0.992216i \(0.460258\pi\)
\(200\) 4.84731 0.342757
\(201\) 3.89367 0.274638
\(202\) 2.12751 0.149691
\(203\) 0 0
\(204\) 1.60764 0.112558
\(205\) 1.67363 0.116891
\(206\) 25.7163 1.79174
\(207\) 1.55115 0.107812
\(208\) 12.6339 0.876003
\(209\) −2.08575 −0.144274
\(210\) 0 0
\(211\) 2.04162 0.140551 0.0702756 0.997528i \(-0.477612\pi\)
0.0702756 + 0.997528i \(0.477612\pi\)
\(212\) −2.95929 −0.203245
\(213\) −10.6283 −0.728241
\(214\) 10.8244 0.739944
\(215\) 19.8084 1.35092
\(216\) −2.20435 −0.149987
\(217\) 0 0
\(218\) 10.7773 0.729930
\(219\) 2.23945 0.151328
\(220\) 2.93920 0.198161
\(221\) −6.46666 −0.434995
\(222\) −5.22820 −0.350894
\(223\) 16.3846 1.09719 0.548597 0.836087i \(-0.315162\pi\)
0.548597 + 0.836087i \(0.315162\pi\)
\(224\) 0 0
\(225\) −2.19898 −0.146598
\(226\) −28.7517 −1.91253
\(227\) −29.8662 −1.98229 −0.991146 0.132780i \(-0.957610\pi\)
−0.991146 + 0.132780i \(0.957610\pi\)
\(228\) −0.493271 −0.0326677
\(229\) −24.3750 −1.61075 −0.805374 0.592767i \(-0.798035\pi\)
−0.805374 + 0.592767i \(0.798035\pi\)
\(230\) 4.22163 0.278366
\(231\) 0 0
\(232\) −20.0980 −1.31950
\(233\) 4.83770 0.316928 0.158464 0.987365i \(-0.449346\pi\)
0.158464 + 0.987365i \(0.449346\pi\)
\(234\) −4.21557 −0.275581
\(235\) 9.72566 0.634432
\(236\) −3.07604 −0.200233
\(237\) 8.10443 0.526439
\(238\) 0 0
\(239\) −4.59128 −0.296985 −0.148493 0.988914i \(-0.547442\pi\)
−0.148493 + 0.988914i \(0.547442\pi\)
\(240\) −8.15657 −0.526504
\(241\) 0.322023 0.0207433 0.0103717 0.999946i \(-0.496699\pi\)
0.0103717 + 0.999946i \(0.496699\pi\)
\(242\) −5.81217 −0.373620
\(243\) 1.00000 0.0641500
\(244\) −0.559004 −0.0357866
\(245\) 0 0
\(246\) 1.62618 0.103681
\(247\) 1.98416 0.126249
\(248\) −18.2281 −1.15748
\(249\) 8.58566 0.544094
\(250\) −19.5929 −1.23916
\(251\) −8.39485 −0.529878 −0.264939 0.964265i \(-0.585352\pi\)
−0.264939 + 0.964265i \(0.585352\pi\)
\(252\) 0 0
\(253\) 4.22695 0.265746
\(254\) −25.4502 −1.59689
\(255\) 4.17495 0.261445
\(256\) 14.0336 0.877100
\(257\) 21.5104 1.34178 0.670892 0.741555i \(-0.265911\pi\)
0.670892 + 0.741555i \(0.265911\pi\)
\(258\) 19.2469 1.19826
\(259\) 0 0
\(260\) −2.79604 −0.173403
\(261\) 9.11743 0.564354
\(262\) 15.6570 0.967295
\(263\) 15.4590 0.953240 0.476620 0.879109i \(-0.341862\pi\)
0.476620 + 0.879109i \(0.341862\pi\)
\(264\) −6.00695 −0.369702
\(265\) −7.68507 −0.472090
\(266\) 0 0
\(267\) 1.25617 0.0768765
\(268\) 2.50932 0.153281
\(269\) 21.3937 1.30440 0.652199 0.758048i \(-0.273847\pi\)
0.652199 + 0.758048i \(0.273847\pi\)
\(270\) 2.72162 0.165632
\(271\) −7.41776 −0.450597 −0.225298 0.974290i \(-0.572336\pi\)
−0.225298 + 0.974290i \(0.572336\pi\)
\(272\) −12.1574 −0.737152
\(273\) 0 0
\(274\) −6.30841 −0.381105
\(275\) −5.99231 −0.361350
\(276\) 0.999655 0.0601722
\(277\) −23.9735 −1.44043 −0.720215 0.693751i \(-0.755957\pi\)
−0.720215 + 0.693751i \(0.755957\pi\)
\(278\) 20.8661 1.25147
\(279\) 8.26914 0.495061
\(280\) 0 0
\(281\) 11.7067 0.698366 0.349183 0.937055i \(-0.386459\pi\)
0.349183 + 0.937055i \(0.386459\pi\)
\(282\) 9.44994 0.562736
\(283\) −13.5001 −0.802496 −0.401248 0.915969i \(-0.631423\pi\)
−0.401248 + 0.915969i \(0.631423\pi\)
\(284\) −6.84955 −0.406446
\(285\) −1.28099 −0.0758795
\(286\) −11.4876 −0.679278
\(287\) 0 0
\(288\) −3.51664 −0.207220
\(289\) −10.7772 −0.633954
\(290\) 24.8141 1.45714
\(291\) 8.55514 0.501511
\(292\) 1.44324 0.0844591
\(293\) −21.3767 −1.24884 −0.624419 0.781089i \(-0.714664\pi\)
−0.624419 + 0.781089i \(0.714664\pi\)
\(294\) 0 0
\(295\) −7.98828 −0.465096
\(296\) 7.08703 0.411925
\(297\) 2.72505 0.158123
\(298\) 0.729698 0.0422703
\(299\) −4.02106 −0.232544
\(300\) −1.41716 −0.0818195
\(301\) 0 0
\(302\) −5.81131 −0.334403
\(303\) 1.30829 0.0751590
\(304\) 3.73025 0.213944
\(305\) −1.45170 −0.0831239
\(306\) 4.05659 0.231900
\(307\) 25.7934 1.47211 0.736053 0.676924i \(-0.236688\pi\)
0.736053 + 0.676924i \(0.236688\pi\)
\(308\) 0 0
\(309\) 15.8139 0.899624
\(310\) 22.5054 1.27822
\(311\) 4.24169 0.240524 0.120262 0.992742i \(-0.461626\pi\)
0.120262 + 0.992742i \(0.461626\pi\)
\(312\) 5.71437 0.323512
\(313\) 6.77432 0.382907 0.191453 0.981502i \(-0.438680\pi\)
0.191453 + 0.981502i \(0.438680\pi\)
\(314\) 14.4991 0.818233
\(315\) 0 0
\(316\) 5.22300 0.293816
\(317\) 33.6214 1.88836 0.944182 0.329423i \(-0.106854\pi\)
0.944182 + 0.329423i \(0.106854\pi\)
\(318\) −7.46721 −0.418740
\(319\) 24.8454 1.39108
\(320\) 6.74219 0.376900
\(321\) 6.65637 0.371522
\(322\) 0 0
\(323\) −1.90933 −0.106238
\(324\) 0.644462 0.0358034
\(325\) 5.70044 0.316203
\(326\) −39.8202 −2.20544
\(327\) 6.62737 0.366494
\(328\) −2.20435 −0.121715
\(329\) 0 0
\(330\) 7.41653 0.408267
\(331\) 29.0356 1.59594 0.797970 0.602698i \(-0.205907\pi\)
0.797970 + 0.602698i \(0.205907\pi\)
\(332\) 5.53313 0.303670
\(333\) −3.21502 −0.176182
\(334\) 1.15283 0.0630800
\(335\) 6.51655 0.356037
\(336\) 0 0
\(337\) −14.5845 −0.794471 −0.397235 0.917717i \(-0.630030\pi\)
−0.397235 + 0.917717i \(0.630030\pi\)
\(338\) −10.2122 −0.555473
\(339\) −17.6805 −0.960274
\(340\) 2.69059 0.145918
\(341\) 22.5338 1.22027
\(342\) −1.24468 −0.0673045
\(343\) 0 0
\(344\) −26.0898 −1.40667
\(345\) 2.59604 0.139766
\(346\) 4.84402 0.260416
\(347\) −19.9558 −1.07128 −0.535641 0.844446i \(-0.679930\pi\)
−0.535641 + 0.844446i \(0.679930\pi\)
\(348\) 5.87583 0.314978
\(349\) 28.9751 1.55100 0.775500 0.631348i \(-0.217498\pi\)
0.775500 + 0.631348i \(0.217498\pi\)
\(350\) 0 0
\(351\) −2.59232 −0.138368
\(352\) −9.58301 −0.510776
\(353\) 15.3168 0.815231 0.407615 0.913154i \(-0.366360\pi\)
0.407615 + 0.913154i \(0.366360\pi\)
\(354\) −7.76182 −0.412536
\(355\) −17.7878 −0.944081
\(356\) 0.809555 0.0429063
\(357\) 0 0
\(358\) −33.8888 −1.79108
\(359\) −21.6773 −1.14409 −0.572043 0.820224i \(-0.693849\pi\)
−0.572043 + 0.820224i \(0.693849\pi\)
\(360\) −3.68926 −0.194441
\(361\) −18.4142 −0.969166
\(362\) −9.33355 −0.490561
\(363\) −3.57412 −0.187593
\(364\) 0 0
\(365\) 3.74800 0.196179
\(366\) −1.41054 −0.0737302
\(367\) −14.0689 −0.734388 −0.367194 0.930144i \(-0.619681\pi\)
−0.367194 + 0.930144i \(0.619681\pi\)
\(368\) −7.55966 −0.394074
\(369\) 1.00000 0.0520579
\(370\) −8.75006 −0.454894
\(371\) 0 0
\(372\) 5.32915 0.276304
\(373\) 21.1728 1.09629 0.548143 0.836384i \(-0.315335\pi\)
0.548143 + 0.836384i \(0.315335\pi\)
\(374\) 11.0544 0.571609
\(375\) −12.0484 −0.622176
\(376\) −12.8098 −0.660613
\(377\) −23.6352 −1.21728
\(378\) 0 0
\(379\) 0.272209 0.0139824 0.00699122 0.999976i \(-0.497775\pi\)
0.00699122 + 0.999976i \(0.497775\pi\)
\(380\) −0.825551 −0.0423499
\(381\) −15.6503 −0.801790
\(382\) −4.28833 −0.219410
\(383\) −14.7319 −0.752767 −0.376384 0.926464i \(-0.622833\pi\)
−0.376384 + 0.926464i \(0.622833\pi\)
\(384\) 13.5843 0.693223
\(385\) 0 0
\(386\) −1.15774 −0.0589277
\(387\) 11.8356 0.601639
\(388\) 5.51347 0.279904
\(389\) 3.29845 0.167238 0.0836189 0.996498i \(-0.473352\pi\)
0.0836189 + 0.996498i \(0.473352\pi\)
\(390\) −7.05529 −0.357259
\(391\) 3.86941 0.195685
\(392\) 0 0
\(393\) 9.62811 0.485674
\(394\) −28.0889 −1.41510
\(395\) 13.5638 0.682468
\(396\) 1.75619 0.0882518
\(397\) −1.85602 −0.0931509 −0.0465755 0.998915i \(-0.514831\pi\)
−0.0465755 + 0.998915i \(0.514831\pi\)
\(398\) 5.71340 0.286387
\(399\) 0 0
\(400\) 10.7169 0.535846
\(401\) 15.9025 0.794133 0.397067 0.917790i \(-0.370028\pi\)
0.397067 + 0.917790i \(0.370028\pi\)
\(402\) 6.33181 0.315802
\(403\) −21.4362 −1.06781
\(404\) 0.843140 0.0419478
\(405\) 1.67363 0.0831632
\(406\) 0 0
\(407\) −8.76108 −0.434271
\(408\) −5.49886 −0.272234
\(409\) 4.62449 0.228666 0.114333 0.993442i \(-0.463527\pi\)
0.114333 + 0.993442i \(0.463527\pi\)
\(410\) 2.72162 0.134411
\(411\) −3.87928 −0.191351
\(412\) 10.1915 0.502099
\(413\) 0 0
\(414\) 2.52244 0.123971
\(415\) 14.3692 0.705355
\(416\) 9.11625 0.446961
\(417\) 12.8314 0.628354
\(418\) −3.39180 −0.165899
\(419\) −28.4534 −1.39004 −0.695019 0.718991i \(-0.744604\pi\)
−0.695019 + 0.718991i \(0.744604\pi\)
\(420\) 0 0
\(421\) −36.4418 −1.77607 −0.888033 0.459780i \(-0.847928\pi\)
−0.888033 + 0.459780i \(0.847928\pi\)
\(422\) 3.32005 0.161617
\(423\) 5.81113 0.282547
\(424\) 10.1221 0.491572
\(425\) −5.48546 −0.266084
\(426\) −17.2836 −0.837392
\(427\) 0 0
\(428\) 4.28977 0.207354
\(429\) −7.06418 −0.341062
\(430\) 32.2120 1.55340
\(431\) −7.43000 −0.357890 −0.178945 0.983859i \(-0.557268\pi\)
−0.178945 + 0.983859i \(0.557268\pi\)
\(432\) −4.87359 −0.234481
\(433\) −13.8996 −0.667972 −0.333986 0.942578i \(-0.608394\pi\)
−0.333986 + 0.942578i \(0.608394\pi\)
\(434\) 0 0
\(435\) 15.2592 0.731621
\(436\) 4.27109 0.204548
\(437\) −1.18725 −0.0567937
\(438\) 3.64174 0.174009
\(439\) 9.09943 0.434292 0.217146 0.976139i \(-0.430325\pi\)
0.217146 + 0.976139i \(0.430325\pi\)
\(440\) −10.0534 −0.479277
\(441\) 0 0
\(442\) −10.5160 −0.500193
\(443\) 26.9631 1.28106 0.640529 0.767934i \(-0.278715\pi\)
0.640529 + 0.767934i \(0.278715\pi\)
\(444\) −2.07196 −0.0983308
\(445\) 2.10236 0.0996615
\(446\) 26.6443 1.26164
\(447\) 0.448719 0.0212237
\(448\) 0 0
\(449\) 16.8277 0.794149 0.397074 0.917786i \(-0.370025\pi\)
0.397074 + 0.917786i \(0.370025\pi\)
\(450\) −3.57593 −0.168571
\(451\) 2.72505 0.128317
\(452\) −11.3944 −0.535948
\(453\) −3.57359 −0.167902
\(454\) −48.5679 −2.27940
\(455\) 0 0
\(456\) 1.68721 0.0790107
\(457\) 22.1206 1.03476 0.517379 0.855756i \(-0.326908\pi\)
0.517379 + 0.855756i \(0.326908\pi\)
\(458\) −39.6382 −1.85217
\(459\) 2.49455 0.116436
\(460\) 1.67305 0.0780063
\(461\) −35.2027 −1.63955 −0.819776 0.572684i \(-0.805902\pi\)
−0.819776 + 0.572684i \(0.805902\pi\)
\(462\) 0 0
\(463\) −20.0710 −0.932777 −0.466389 0.884580i \(-0.654445\pi\)
−0.466389 + 0.884580i \(0.654445\pi\)
\(464\) −44.4346 −2.06283
\(465\) 13.8395 0.641789
\(466\) 7.86698 0.364431
\(467\) −22.8854 −1.05901 −0.529505 0.848307i \(-0.677622\pi\)
−0.529505 + 0.848307i \(0.677622\pi\)
\(468\) −1.67065 −0.0772258
\(469\) 0 0
\(470\) 15.8157 0.729523
\(471\) 8.91606 0.410831
\(472\) 10.5214 0.484289
\(473\) 32.2526 1.48298
\(474\) 13.1793 0.605344
\(475\) 1.68309 0.0772257
\(476\) 0 0
\(477\) −4.59187 −0.210247
\(478\) −7.46625 −0.341498
\(479\) −20.5080 −0.937036 −0.468518 0.883454i \(-0.655212\pi\)
−0.468518 + 0.883454i \(0.655212\pi\)
\(480\) −5.88554 −0.268637
\(481\) 8.33435 0.380014
\(482\) 0.523668 0.0238524
\(483\) 0 0
\(484\) −2.30339 −0.104699
\(485\) 14.3181 0.650152
\(486\) 1.62618 0.0737650
\(487\) −4.07372 −0.184598 −0.0922989 0.995731i \(-0.529422\pi\)
−0.0922989 + 0.995731i \(0.529422\pi\)
\(488\) 1.91204 0.0865542
\(489\) −24.4870 −1.10734
\(490\) 0 0
\(491\) −6.31242 −0.284876 −0.142438 0.989804i \(-0.545494\pi\)
−0.142438 + 0.989804i \(0.545494\pi\)
\(492\) 0.644462 0.0290546
\(493\) 22.7439 1.02433
\(494\) 3.22660 0.145172
\(495\) 4.56071 0.204989
\(496\) −40.3004 −1.80954
\(497\) 0 0
\(498\) 13.9618 0.625644
\(499\) 37.4975 1.67862 0.839310 0.543653i \(-0.182959\pi\)
0.839310 + 0.543653i \(0.182959\pi\)
\(500\) −7.76473 −0.347249
\(501\) 0.708918 0.0316721
\(502\) −13.6515 −0.609298
\(503\) 28.7997 1.28411 0.642056 0.766657i \(-0.278081\pi\)
0.642056 + 0.766657i \(0.278081\pi\)
\(504\) 0 0
\(505\) 2.18958 0.0974351
\(506\) 6.87378 0.305577
\(507\) −6.27990 −0.278900
\(508\) −10.0860 −0.447496
\(509\) 2.76539 0.122574 0.0612869 0.998120i \(-0.480480\pi\)
0.0612869 + 0.998120i \(0.480480\pi\)
\(510\) 6.78921 0.300631
\(511\) 0 0
\(512\) −4.34752 −0.192135
\(513\) −0.765400 −0.0337932
\(514\) 34.9798 1.54289
\(515\) 26.4666 1.16626
\(516\) 7.62761 0.335787
\(517\) 15.8356 0.696449
\(518\) 0 0
\(519\) 2.97877 0.130754
\(520\) 9.56372 0.419397
\(521\) −4.05204 −0.177523 −0.0887616 0.996053i \(-0.528291\pi\)
−0.0887616 + 0.996053i \(0.528291\pi\)
\(522\) 14.8266 0.648942
\(523\) 4.28644 0.187433 0.0937165 0.995599i \(-0.470125\pi\)
0.0937165 + 0.995599i \(0.470125\pi\)
\(524\) 6.20495 0.271064
\(525\) 0 0
\(526\) 25.1391 1.09611
\(527\) 20.6278 0.898561
\(528\) −13.2808 −0.577971
\(529\) −20.5939 −0.895389
\(530\) −12.4973 −0.542849
\(531\) −4.77304 −0.207132
\(532\) 0 0
\(533\) −2.59232 −0.112286
\(534\) 2.04276 0.0883989
\(535\) 11.1403 0.481636
\(536\) −8.58301 −0.370730
\(537\) −20.8395 −0.899292
\(538\) 34.7900 1.49991
\(539\) 0 0
\(540\) 1.07859 0.0464151
\(541\) −41.5910 −1.78814 −0.894069 0.447929i \(-0.852162\pi\)
−0.894069 + 0.447929i \(0.852162\pi\)
\(542\) −12.0626 −0.518134
\(543\) −5.73956 −0.246308
\(544\) −8.77244 −0.376115
\(545\) 11.0917 0.475118
\(546\) 0 0
\(547\) −33.4461 −1.43005 −0.715025 0.699099i \(-0.753585\pi\)
−0.715025 + 0.699099i \(0.753585\pi\)
\(548\) −2.50005 −0.106797
\(549\) −0.867396 −0.0370196
\(550\) −9.74458 −0.415510
\(551\) −6.97847 −0.297293
\(552\) −3.41927 −0.145534
\(553\) 0 0
\(554\) −38.9853 −1.65633
\(555\) −5.38074 −0.228400
\(556\) 8.26932 0.350697
\(557\) 21.7753 0.922651 0.461326 0.887231i \(-0.347374\pi\)
0.461326 + 0.887231i \(0.347374\pi\)
\(558\) 13.4471 0.569262
\(559\) −30.6817 −1.29770
\(560\) 0 0
\(561\) 6.79777 0.287002
\(562\) 19.0373 0.803039
\(563\) −41.0426 −1.72974 −0.864871 0.501995i \(-0.832600\pi\)
−0.864871 + 0.501995i \(0.832600\pi\)
\(564\) 3.74505 0.157695
\(565\) −29.5906 −1.24488
\(566\) −21.9536 −0.922777
\(567\) 0 0
\(568\) 23.4285 0.983040
\(569\) 12.9575 0.543206 0.271603 0.962409i \(-0.412446\pi\)
0.271603 + 0.962409i \(0.412446\pi\)
\(570\) −2.08313 −0.0872525
\(571\) 36.8468 1.54199 0.770994 0.636842i \(-0.219760\pi\)
0.770994 + 0.636842i \(0.219760\pi\)
\(572\) −4.55260 −0.190354
\(573\) −2.63706 −0.110165
\(574\) 0 0
\(575\) −3.41093 −0.142246
\(576\) 4.02849 0.167854
\(577\) −46.7470 −1.94610 −0.973051 0.230589i \(-0.925935\pi\)
−0.973051 + 0.230589i \(0.925935\pi\)
\(578\) −17.5257 −0.728973
\(579\) −0.711941 −0.0295873
\(580\) 9.83395 0.408333
\(581\) 0 0
\(582\) 13.9122 0.576680
\(583\) −12.5131 −0.518238
\(584\) −4.93652 −0.204275
\(585\) −4.33857 −0.179378
\(586\) −34.7623 −1.43602
\(587\) −23.0958 −0.953266 −0.476633 0.879102i \(-0.658143\pi\)
−0.476633 + 0.879102i \(0.658143\pi\)
\(588\) 0 0
\(589\) −6.32920 −0.260790
\(590\) −12.9904 −0.534806
\(591\) −17.2730 −0.710514
\(592\) 15.6687 0.643980
\(593\) 37.8823 1.55564 0.777820 0.628487i \(-0.216326\pi\)
0.777820 + 0.628487i \(0.216326\pi\)
\(594\) 4.43142 0.181823
\(595\) 0 0
\(596\) 0.289182 0.0118454
\(597\) 3.51338 0.143793
\(598\) −6.53897 −0.267398
\(599\) −23.6611 −0.966767 −0.483384 0.875409i \(-0.660592\pi\)
−0.483384 + 0.875409i \(0.660592\pi\)
\(600\) 4.84731 0.197891
\(601\) −47.3526 −1.93155 −0.965776 0.259377i \(-0.916483\pi\)
−0.965776 + 0.259377i \(0.916483\pi\)
\(602\) 0 0
\(603\) 3.89367 0.158563
\(604\) −2.30305 −0.0937096
\(605\) −5.98175 −0.243193
\(606\) 2.12751 0.0864241
\(607\) 11.0182 0.447216 0.223608 0.974679i \(-0.428216\pi\)
0.223608 + 0.974679i \(0.428216\pi\)
\(608\) 2.69164 0.109160
\(609\) 0 0
\(610\) −2.36072 −0.0955828
\(611\) −15.0643 −0.609436
\(612\) 1.60764 0.0649851
\(613\) 28.6531 1.15729 0.578643 0.815581i \(-0.303582\pi\)
0.578643 + 0.815581i \(0.303582\pi\)
\(614\) 41.9447 1.69275
\(615\) 1.67363 0.0674871
\(616\) 0 0
\(617\) −19.7501 −0.795109 −0.397554 0.917579i \(-0.630141\pi\)
−0.397554 + 0.917579i \(0.630141\pi\)
\(618\) 25.7163 1.03446
\(619\) 23.5838 0.947912 0.473956 0.880549i \(-0.342826\pi\)
0.473956 + 0.880549i \(0.342826\pi\)
\(620\) 8.91900 0.358196
\(621\) 1.55115 0.0622454
\(622\) 6.89776 0.276575
\(623\) 0 0
\(624\) 12.6339 0.505760
\(625\) −9.16963 −0.366785
\(626\) 11.0163 0.440298
\(627\) −2.08575 −0.0832968
\(628\) 5.74606 0.229293
\(629\) −8.02003 −0.319780
\(630\) 0 0
\(631\) −9.59187 −0.381846 −0.190923 0.981605i \(-0.561148\pi\)
−0.190923 + 0.981605i \(0.561148\pi\)
\(632\) −17.8650 −0.710631
\(633\) 2.04162 0.0811473
\(634\) 54.6744 2.17140
\(635\) −26.1928 −1.03943
\(636\) −2.95929 −0.117343
\(637\) 0 0
\(638\) 40.4031 1.59957
\(639\) −10.6283 −0.420450
\(640\) 22.7351 0.898684
\(641\) −30.4344 −1.20208 −0.601042 0.799217i \(-0.705248\pi\)
−0.601042 + 0.799217i \(0.705248\pi\)
\(642\) 10.8244 0.427207
\(643\) 30.7646 1.21324 0.606619 0.794993i \(-0.292526\pi\)
0.606619 + 0.794993i \(0.292526\pi\)
\(644\) 0 0
\(645\) 19.8084 0.779955
\(646\) −3.10491 −0.122161
\(647\) −42.2810 −1.66224 −0.831120 0.556094i \(-0.812300\pi\)
−0.831120 + 0.556094i \(0.812300\pi\)
\(648\) −2.20435 −0.0865950
\(649\) −13.0068 −0.510560
\(650\) 9.26994 0.363597
\(651\) 0 0
\(652\) −15.7809 −0.618029
\(653\) −41.1413 −1.60998 −0.804992 0.593286i \(-0.797830\pi\)
−0.804992 + 0.593286i \(0.797830\pi\)
\(654\) 10.7773 0.421426
\(655\) 16.1139 0.629620
\(656\) −4.87359 −0.190282
\(657\) 2.23945 0.0873691
\(658\) 0 0
\(659\) 8.33455 0.324668 0.162334 0.986736i \(-0.448098\pi\)
0.162334 + 0.986736i \(0.448098\pi\)
\(660\) 2.93920 0.114408
\(661\) −5.15510 −0.200510 −0.100255 0.994962i \(-0.531966\pi\)
−0.100255 + 0.994962i \(0.531966\pi\)
\(662\) 47.2171 1.83514
\(663\) −6.46666 −0.251144
\(664\) −18.9258 −0.734463
\(665\) 0 0
\(666\) −5.22820 −0.202589
\(667\) 14.1425 0.547598
\(668\) 0.456871 0.0176769
\(669\) 16.3846 0.633465
\(670\) 10.5971 0.409401
\(671\) −2.36369 −0.0912494
\(672\) 0 0
\(673\) 15.0044 0.578379 0.289189 0.957272i \(-0.406614\pi\)
0.289189 + 0.957272i \(0.406614\pi\)
\(674\) −23.7171 −0.913548
\(675\) −2.19898 −0.0846386
\(676\) −4.04715 −0.155660
\(677\) −15.0477 −0.578332 −0.289166 0.957279i \(-0.593378\pi\)
−0.289166 + 0.957279i \(0.593378\pi\)
\(678\) −28.7517 −1.10420
\(679\) 0 0
\(680\) −9.20304 −0.352920
\(681\) −29.8662 −1.14448
\(682\) 36.6440 1.40317
\(683\) −16.4374 −0.628958 −0.314479 0.949264i \(-0.601830\pi\)
−0.314479 + 0.949264i \(0.601830\pi\)
\(684\) −0.493271 −0.0188607
\(685\) −6.49247 −0.248064
\(686\) 0 0
\(687\) −24.3750 −0.929966
\(688\) −57.6820 −2.19911
\(689\) 11.9036 0.453490
\(690\) 4.22163 0.160715
\(691\) 0.939242 0.0357304 0.0178652 0.999840i \(-0.494313\pi\)
0.0178652 + 0.999840i \(0.494313\pi\)
\(692\) 1.91970 0.0729762
\(693\) 0 0
\(694\) −32.4517 −1.23185
\(695\) 21.4749 0.814589
\(696\) −20.0980 −0.761812
\(697\) 2.49455 0.0944878
\(698\) 47.1187 1.78347
\(699\) 4.83770 0.182979
\(700\) 0 0
\(701\) 9.38248 0.354371 0.177186 0.984177i \(-0.443301\pi\)
0.177186 + 0.984177i \(0.443301\pi\)
\(702\) −4.21557 −0.159107
\(703\) 2.46078 0.0928099
\(704\) 10.9778 0.413742
\(705\) 9.72566 0.366290
\(706\) 24.9079 0.937420
\(707\) 0 0
\(708\) −3.07604 −0.115605
\(709\) 21.5870 0.810716 0.405358 0.914158i \(-0.367147\pi\)
0.405358 + 0.914158i \(0.367147\pi\)
\(710\) −28.9262 −1.08558
\(711\) 8.10443 0.303940
\(712\) −2.76904 −0.103774
\(713\) 12.8267 0.480362
\(714\) 0 0
\(715\) −11.8228 −0.442148
\(716\) −13.4303 −0.501913
\(717\) −4.59128 −0.171465
\(718\) −35.2512 −1.31556
\(719\) 31.3926 1.17074 0.585372 0.810765i \(-0.300948\pi\)
0.585372 + 0.810765i \(0.300948\pi\)
\(720\) −8.15657 −0.303978
\(721\) 0 0
\(722\) −29.9447 −1.11443
\(723\) 0.322023 0.0119762
\(724\) −3.69893 −0.137469
\(725\) −20.0490 −0.744601
\(726\) −5.81217 −0.215710
\(727\) 19.3083 0.716103 0.358052 0.933702i \(-0.383441\pi\)
0.358052 + 0.933702i \(0.383441\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 6.09492 0.225583
\(731\) 29.5246 1.09201
\(732\) −0.559004 −0.0206614
\(733\) 48.3152 1.78456 0.892281 0.451481i \(-0.149104\pi\)
0.892281 + 0.451481i \(0.149104\pi\)
\(734\) −22.8785 −0.844460
\(735\) 0 0
\(736\) −5.45483 −0.201068
\(737\) 10.6104 0.390841
\(738\) 1.62618 0.0598605
\(739\) 5.73102 0.210819 0.105409 0.994429i \(-0.466385\pi\)
0.105409 + 0.994429i \(0.466385\pi\)
\(740\) −3.46768 −0.127475
\(741\) 1.98416 0.0728899
\(742\) 0 0
\(743\) 31.0816 1.14027 0.570136 0.821550i \(-0.306890\pi\)
0.570136 + 0.821550i \(0.306890\pi\)
\(744\) −18.2281 −0.668274
\(745\) 0.750988 0.0275141
\(746\) 34.4308 1.26060
\(747\) 8.58566 0.314133
\(748\) 4.38090 0.160182
\(749\) 0 0
\(750\) −19.5929 −0.715430
\(751\) −34.7572 −1.26831 −0.634153 0.773207i \(-0.718651\pi\)
−0.634153 + 0.773207i \(0.718651\pi\)
\(752\) −28.3211 −1.03276
\(753\) −8.39485 −0.305925
\(754\) −38.4352 −1.39973
\(755\) −5.98086 −0.217666
\(756\) 0 0
\(757\) −4.67741 −0.170003 −0.0850017 0.996381i \(-0.527090\pi\)
−0.0850017 + 0.996381i \(0.527090\pi\)
\(758\) 0.442661 0.0160782
\(759\) 4.22695 0.153428
\(760\) 2.82376 0.102428
\(761\) 31.7007 1.14915 0.574575 0.818452i \(-0.305167\pi\)
0.574575 + 0.818452i \(0.305167\pi\)
\(762\) −25.4502 −0.921965
\(763\) 0 0
\(764\) −1.69948 −0.0614852
\(765\) 4.17495 0.150945
\(766\) −23.9568 −0.865594
\(767\) 12.3732 0.446771
\(768\) 14.0336 0.506394
\(769\) −25.4093 −0.916282 −0.458141 0.888880i \(-0.651484\pi\)
−0.458141 + 0.888880i \(0.651484\pi\)
\(770\) 0 0
\(771\) 21.5104 0.774679
\(772\) −0.458819 −0.0165133
\(773\) 39.9382 1.43648 0.718239 0.695797i \(-0.244948\pi\)
0.718239 + 0.695797i \(0.244948\pi\)
\(774\) 19.2469 0.691814
\(775\) −18.1836 −0.653176
\(776\) −18.8585 −0.676982
\(777\) 0 0
\(778\) 5.36387 0.192304
\(779\) −0.765400 −0.0274233
\(780\) −2.79604 −0.100114
\(781\) −28.9627 −1.03637
\(782\) 6.29236 0.225014
\(783\) 9.11743 0.325830
\(784\) 0 0
\(785\) 14.9222 0.532595
\(786\) 15.6570 0.558468
\(787\) −50.8086 −1.81113 −0.905565 0.424207i \(-0.860553\pi\)
−0.905565 + 0.424207i \(0.860553\pi\)
\(788\) −11.1318 −0.396553
\(789\) 15.4590 0.550354
\(790\) 22.0572 0.784758
\(791\) 0 0
\(792\) −6.00695 −0.213448
\(793\) 2.24857 0.0798489
\(794\) −3.01822 −0.107113
\(795\) −7.68507 −0.272561
\(796\) 2.26424 0.0802540
\(797\) 47.0831 1.66777 0.833884 0.551939i \(-0.186112\pi\)
0.833884 + 0.551939i \(0.186112\pi\)
\(798\) 0 0
\(799\) 14.4962 0.512837
\(800\) 7.73301 0.273403
\(801\) 1.25617 0.0443847
\(802\) 25.8603 0.913161
\(803\) 6.10259 0.215356
\(804\) 2.50932 0.0884970
\(805\) 0 0
\(806\) −34.8592 −1.22786
\(807\) 21.3937 0.753095
\(808\) −2.88392 −0.101456
\(809\) 17.7015 0.622353 0.311176 0.950352i \(-0.399277\pi\)
0.311176 + 0.950352i \(0.399277\pi\)
\(810\) 2.72162 0.0956279
\(811\) 23.0207 0.808365 0.404183 0.914678i \(-0.367556\pi\)
0.404183 + 0.914678i \(0.367556\pi\)
\(812\) 0 0
\(813\) −7.41776 −0.260152
\(814\) −14.2471 −0.499361
\(815\) −40.9821 −1.43554
\(816\) −12.1574 −0.425595
\(817\) −9.05898 −0.316934
\(818\) 7.52026 0.262940
\(819\) 0 0
\(820\) 1.07859 0.0376659
\(821\) −7.63363 −0.266416 −0.133208 0.991088i \(-0.542528\pi\)
−0.133208 + 0.991088i \(0.542528\pi\)
\(822\) −6.30841 −0.220031
\(823\) −46.1379 −1.60827 −0.804133 0.594450i \(-0.797370\pi\)
−0.804133 + 0.594450i \(0.797370\pi\)
\(824\) −34.8595 −1.21439
\(825\) −5.99231 −0.208625
\(826\) 0 0
\(827\) −8.79619 −0.305874 −0.152937 0.988236i \(-0.548873\pi\)
−0.152937 + 0.988236i \(0.548873\pi\)
\(828\) 0.999655 0.0347404
\(829\) −18.9774 −0.659112 −0.329556 0.944136i \(-0.606899\pi\)
−0.329556 + 0.944136i \(0.606899\pi\)
\(830\) 23.3669 0.811076
\(831\) −23.9735 −0.831633
\(832\) −10.4431 −0.362050
\(833\) 0 0
\(834\) 20.8661 0.722534
\(835\) 1.18646 0.0410593
\(836\) −1.34419 −0.0464897
\(837\) 8.26914 0.285823
\(838\) −46.2703 −1.59838
\(839\) 25.8131 0.891167 0.445584 0.895240i \(-0.352996\pi\)
0.445584 + 0.895240i \(0.352996\pi\)
\(840\) 0 0
\(841\) 54.1274 1.86646
\(842\) −59.2610 −2.04227
\(843\) 11.7067 0.403202
\(844\) 1.31575 0.0452899
\(845\) −10.5102 −0.361562
\(846\) 9.44994 0.324896
\(847\) 0 0
\(848\) 22.3789 0.768495
\(849\) −13.5001 −0.463321
\(850\) −8.92034 −0.305965
\(851\) −4.98697 −0.170951
\(852\) −6.84955 −0.234662
\(853\) −23.5448 −0.806160 −0.403080 0.915165i \(-0.632060\pi\)
−0.403080 + 0.915165i \(0.632060\pi\)
\(854\) 0 0
\(855\) −1.28099 −0.0438090
\(856\) −14.6730 −0.501511
\(857\) 15.4073 0.526304 0.263152 0.964754i \(-0.415238\pi\)
0.263152 + 0.964754i \(0.415238\pi\)
\(858\) −11.4876 −0.392181
\(859\) 10.2841 0.350887 0.175444 0.984489i \(-0.443864\pi\)
0.175444 + 0.984489i \(0.443864\pi\)
\(860\) 12.7658 0.435309
\(861\) 0 0
\(862\) −12.0825 −0.411532
\(863\) −17.2631 −0.587644 −0.293822 0.955860i \(-0.594927\pi\)
−0.293822 + 0.955860i \(0.594927\pi\)
\(864\) −3.51664 −0.119639
\(865\) 4.98535 0.169507
\(866\) −22.6032 −0.768090
\(867\) −10.7772 −0.366013
\(868\) 0 0
\(869\) 22.0849 0.749180
\(870\) 24.8141 0.841278
\(871\) −10.0936 −0.342010
\(872\) −14.6090 −0.494724
\(873\) 8.55514 0.289548
\(874\) −1.93068 −0.0653061
\(875\) 0 0
\(876\) 1.44324 0.0487625
\(877\) 32.1608 1.08599 0.542997 0.839735i \(-0.317290\pi\)
0.542997 + 0.839735i \(0.317290\pi\)
\(878\) 14.7973 0.499385
\(879\) −21.3767 −0.721017
\(880\) −22.2270 −0.749273
\(881\) −8.00714 −0.269767 −0.134884 0.990861i \(-0.543066\pi\)
−0.134884 + 0.990861i \(0.543066\pi\)
\(882\) 0 0
\(883\) −11.9191 −0.401108 −0.200554 0.979683i \(-0.564274\pi\)
−0.200554 + 0.979683i \(0.564274\pi\)
\(884\) −4.16752 −0.140169
\(885\) −7.98828 −0.268523
\(886\) 43.8469 1.47307
\(887\) −55.2315 −1.85449 −0.927247 0.374450i \(-0.877831\pi\)
−0.927247 + 0.374450i \(0.877831\pi\)
\(888\) 7.08703 0.237825
\(889\) 0 0
\(890\) 3.41882 0.114599
\(891\) 2.72505 0.0912925
\(892\) 10.5592 0.353550
\(893\) −4.44784 −0.148841
\(894\) 0.729698 0.0244048
\(895\) −34.8776 −1.16583
\(896\) 0 0
\(897\) −4.02106 −0.134259
\(898\) 27.3649 0.913178
\(899\) 75.3933 2.51451
\(900\) −1.41716 −0.0472385
\(901\) −11.4547 −0.381610
\(902\) 4.43142 0.147550
\(903\) 0 0
\(904\) 38.9740 1.29626
\(905\) −9.60587 −0.319310
\(906\) −5.81131 −0.193068
\(907\) −29.6769 −0.985405 −0.492703 0.870198i \(-0.663991\pi\)
−0.492703 + 0.870198i \(0.663991\pi\)
\(908\) −19.2476 −0.638756
\(909\) 1.30829 0.0433931
\(910\) 0 0
\(911\) 43.6581 1.44646 0.723228 0.690609i \(-0.242657\pi\)
0.723228 + 0.690609i \(0.242657\pi\)
\(912\) 3.73025 0.123521
\(913\) 23.3963 0.774305
\(914\) 35.9721 1.18985
\(915\) −1.45170 −0.0479916
\(916\) −15.7088 −0.519033
\(917\) 0 0
\(918\) 4.05659 0.133887
\(919\) −23.6652 −0.780642 −0.390321 0.920679i \(-0.627636\pi\)
−0.390321 + 0.920679i \(0.627636\pi\)
\(920\) −5.72258 −0.188668
\(921\) 25.7934 0.849920
\(922\) −57.2459 −1.88529
\(923\) 27.5520 0.906885
\(924\) 0 0
\(925\) 7.06975 0.232452
\(926\) −32.6390 −1.07258
\(927\) 15.8139 0.519398
\(928\) −32.0627 −1.05251
\(929\) −41.0050 −1.34533 −0.672665 0.739947i \(-0.734851\pi\)
−0.672665 + 0.739947i \(0.734851\pi\)
\(930\) 22.5054 0.737983
\(931\) 0 0
\(932\) 3.11772 0.102124
\(933\) 4.24169 0.138867
\(934\) −37.2158 −1.21774
\(935\) 11.3769 0.372065
\(936\) 5.71437 0.186780
\(937\) 17.7022 0.578305 0.289153 0.957283i \(-0.406627\pi\)
0.289153 + 0.957283i \(0.406627\pi\)
\(938\) 0 0
\(939\) 6.77432 0.221071
\(940\) 6.26782 0.204434
\(941\) −33.0063 −1.07598 −0.537988 0.842953i \(-0.680815\pi\)
−0.537988 + 0.842953i \(0.680815\pi\)
\(942\) 14.4991 0.472407
\(943\) 1.55115 0.0505123
\(944\) 23.2619 0.757109
\(945\) 0 0
\(946\) 52.4486 1.70525
\(947\) 49.0378 1.59352 0.796758 0.604299i \(-0.206547\pi\)
0.796758 + 0.604299i \(0.206547\pi\)
\(948\) 5.22300 0.169635
\(949\) −5.80535 −0.188450
\(950\) 2.73702 0.0888005
\(951\) 33.6214 1.09025
\(952\) 0 0
\(953\) −20.5062 −0.664260 −0.332130 0.943234i \(-0.607767\pi\)
−0.332130 + 0.943234i \(0.607767\pi\)
\(954\) −7.46721 −0.241760
\(955\) −4.41345 −0.142816
\(956\) −2.95891 −0.0956979
\(957\) 24.8454 0.803138
\(958\) −33.3498 −1.07748
\(959\) 0 0
\(960\) 6.74219 0.217603
\(961\) 37.3787 1.20577
\(962\) 13.5532 0.436971
\(963\) 6.65637 0.214498
\(964\) 0.207532 0.00668415
\(965\) −1.19152 −0.0383565
\(966\) 0 0
\(967\) −50.9026 −1.63692 −0.818459 0.574566i \(-0.805171\pi\)
−0.818459 + 0.574566i \(0.805171\pi\)
\(968\) 7.87861 0.253228
\(969\) −1.90933 −0.0613365
\(970\) 23.2838 0.747599
\(971\) −5.25431 −0.168619 −0.0843095 0.996440i \(-0.526868\pi\)
−0.0843095 + 0.996440i \(0.526868\pi\)
\(972\) 0.644462 0.0206711
\(973\) 0 0
\(974\) −6.62460 −0.212266
\(975\) 5.70044 0.182560
\(976\) 4.22734 0.135314
\(977\) 6.91693 0.221292 0.110646 0.993860i \(-0.464708\pi\)
0.110646 + 0.993860i \(0.464708\pi\)
\(978\) −39.8202 −1.27331
\(979\) 3.42313 0.109404
\(980\) 0 0
\(981\) 6.62737 0.211596
\(982\) −10.2651 −0.327574
\(983\) 30.1743 0.962410 0.481205 0.876608i \(-0.340199\pi\)
0.481205 + 0.876608i \(0.340199\pi\)
\(984\) −2.20435 −0.0702721
\(985\) −28.9085 −0.921100
\(986\) 36.9856 1.17786
\(987\) 0 0
\(988\) 1.27871 0.0406813
\(989\) 18.3588 0.583775
\(990\) 7.41653 0.235713
\(991\) −4.07409 −0.129418 −0.0647089 0.997904i \(-0.520612\pi\)
−0.0647089 + 0.997904i \(0.520612\pi\)
\(992\) −29.0796 −0.923279
\(993\) 29.0356 0.921416
\(994\) 0 0
\(995\) 5.88009 0.186411
\(996\) 5.53313 0.175324
\(997\) 32.1123 1.01701 0.508503 0.861060i \(-0.330199\pi\)
0.508503 + 0.861060i \(0.330199\pi\)
\(998\) 60.9778 1.93022
\(999\) −3.21502 −0.101719
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 \(a_p\))