Properties

Label 6027.2.a.bk.1.1
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 1
Dimension 14
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: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.73044\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.73044 q^{2} +1.00000 q^{3} +5.45531 q^{4} -3.67975 q^{5} -2.73044 q^{6} -9.43451 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.73044 q^{2} +1.00000 q^{3} +5.45531 q^{4} -3.67975 q^{5} -2.73044 q^{6} -9.43451 q^{8} +1.00000 q^{9} +10.0473 q^{10} -5.55413 q^{11} +5.45531 q^{12} -1.35125 q^{13} -3.67975 q^{15} +14.8498 q^{16} +5.33017 q^{17} -2.73044 q^{18} +3.13095 q^{19} -20.0742 q^{20} +15.1652 q^{22} +6.55809 q^{23} -9.43451 q^{24} +8.54056 q^{25} +3.68952 q^{26} +1.00000 q^{27} -8.35577 q^{29} +10.0473 q^{30} -3.83202 q^{31} -21.6774 q^{32} -5.55413 q^{33} -14.5537 q^{34} +5.45531 q^{36} +0.883409 q^{37} -8.54886 q^{38} -1.35125 q^{39} +34.7166 q^{40} -1.00000 q^{41} -3.78313 q^{43} -30.2995 q^{44} -3.67975 q^{45} -17.9065 q^{46} -2.25564 q^{47} +14.8498 q^{48} -23.3195 q^{50} +5.33017 q^{51} -7.37151 q^{52} +4.13650 q^{53} -2.73044 q^{54} +20.4378 q^{55} +3.13095 q^{57} +22.8149 q^{58} +4.43498 q^{59} -20.0742 q^{60} -4.50628 q^{61} +10.4631 q^{62} +29.4893 q^{64} +4.97228 q^{65} +15.1652 q^{66} -9.88169 q^{67} +29.0777 q^{68} +6.55809 q^{69} +3.25222 q^{71} -9.43451 q^{72} +6.37270 q^{73} -2.41210 q^{74} +8.54056 q^{75} +17.0803 q^{76} +3.68952 q^{78} +4.67377 q^{79} -54.6434 q^{80} +1.00000 q^{81} +2.73044 q^{82} +0.851113 q^{83} -19.6137 q^{85} +10.3296 q^{86} -8.35577 q^{87} +52.4005 q^{88} +9.60988 q^{89} +10.0473 q^{90} +35.7764 q^{92} -3.83202 q^{93} +6.15889 q^{94} -11.5211 q^{95} -21.6774 q^{96} -13.7839 q^{97} -5.55413 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73044 −1.93071 −0.965357 0.260934i \(-0.915969\pi\)
−0.965357 + 0.260934i \(0.915969\pi\)
\(3\) 1.00000 0.577350
\(4\) 5.45531 2.72765
\(5\) −3.67975 −1.64563 −0.822817 0.568306i \(-0.807599\pi\)
−0.822817 + 0.568306i \(0.807599\pi\)
\(6\) −2.73044 −1.11470
\(7\) 0 0
\(8\) −9.43451 −3.33560
\(9\) 1.00000 0.333333
\(10\) 10.0473 3.17725
\(11\) −5.55413 −1.67463 −0.837316 0.546718i \(-0.815877\pi\)
−0.837316 + 0.546718i \(0.815877\pi\)
\(12\) 5.45531 1.57481
\(13\) −1.35125 −0.374770 −0.187385 0.982287i \(-0.560001\pi\)
−0.187385 + 0.982287i \(0.560001\pi\)
\(14\) 0 0
\(15\) −3.67975 −0.950107
\(16\) 14.8498 3.71244
\(17\) 5.33017 1.29276 0.646378 0.763017i \(-0.276283\pi\)
0.646378 + 0.763017i \(0.276283\pi\)
\(18\) −2.73044 −0.643571
\(19\) 3.13095 0.718288 0.359144 0.933282i \(-0.383069\pi\)
0.359144 + 0.933282i \(0.383069\pi\)
\(20\) −20.0742 −4.48872
\(21\) 0 0
\(22\) 15.1652 3.23324
\(23\) 6.55809 1.36746 0.683728 0.729737i \(-0.260357\pi\)
0.683728 + 0.729737i \(0.260357\pi\)
\(24\) −9.43451 −1.92581
\(25\) 8.54056 1.70811
\(26\) 3.68952 0.723574
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −8.35577 −1.55163 −0.775814 0.630962i \(-0.782660\pi\)
−0.775814 + 0.630962i \(0.782660\pi\)
\(30\) 10.0473 1.83438
\(31\) −3.83202 −0.688252 −0.344126 0.938924i \(-0.611825\pi\)
−0.344126 + 0.938924i \(0.611825\pi\)
\(32\) −21.6774 −3.83206
\(33\) −5.55413 −0.966850
\(34\) −14.5537 −2.49594
\(35\) 0 0
\(36\) 5.45531 0.909218
\(37\) 0.883409 0.145232 0.0726158 0.997360i \(-0.476865\pi\)
0.0726158 + 0.997360i \(0.476865\pi\)
\(38\) −8.54886 −1.38681
\(39\) −1.35125 −0.216374
\(40\) 34.7166 5.48918
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −3.78313 −0.576922 −0.288461 0.957492i \(-0.593144\pi\)
−0.288461 + 0.957492i \(0.593144\pi\)
\(44\) −30.2995 −4.56782
\(45\) −3.67975 −0.548545
\(46\) −17.9065 −2.64017
\(47\) −2.25564 −0.329019 −0.164509 0.986376i \(-0.552604\pi\)
−0.164509 + 0.986376i \(0.552604\pi\)
\(48\) 14.8498 2.14338
\(49\) 0 0
\(50\) −23.3195 −3.29787
\(51\) 5.33017 0.746373
\(52\) −7.37151 −1.02224
\(53\) 4.13650 0.568192 0.284096 0.958796i \(-0.408307\pi\)
0.284096 + 0.958796i \(0.408307\pi\)
\(54\) −2.73044 −0.371566
\(55\) 20.4378 2.75583
\(56\) 0 0
\(57\) 3.13095 0.414704
\(58\) 22.8149 2.99575
\(59\) 4.43498 0.577386 0.288693 0.957422i \(-0.406779\pi\)
0.288693 + 0.957422i \(0.406779\pi\)
\(60\) −20.0742 −2.59156
\(61\) −4.50628 −0.576971 −0.288485 0.957484i \(-0.593152\pi\)
−0.288485 + 0.957484i \(0.593152\pi\)
\(62\) 10.4631 1.32882
\(63\) 0 0
\(64\) 29.4893 3.68616
\(65\) 4.97228 0.616735
\(66\) 15.1652 1.86671
\(67\) −9.88169 −1.20724 −0.603620 0.797272i \(-0.706276\pi\)
−0.603620 + 0.797272i \(0.706276\pi\)
\(68\) 29.0777 3.52619
\(69\) 6.55809 0.789501
\(70\) 0 0
\(71\) 3.25222 0.385968 0.192984 0.981202i \(-0.438183\pi\)
0.192984 + 0.981202i \(0.438183\pi\)
\(72\) −9.43451 −1.11187
\(73\) 6.37270 0.745868 0.372934 0.927858i \(-0.378352\pi\)
0.372934 + 0.927858i \(0.378352\pi\)
\(74\) −2.41210 −0.280400
\(75\) 8.54056 0.986179
\(76\) 17.0803 1.95924
\(77\) 0 0
\(78\) 3.68952 0.417756
\(79\) 4.67377 0.525840 0.262920 0.964818i \(-0.415314\pi\)
0.262920 + 0.964818i \(0.415314\pi\)
\(80\) −54.6434 −6.10932
\(81\) 1.00000 0.111111
\(82\) 2.73044 0.301527
\(83\) 0.851113 0.0934218 0.0467109 0.998908i \(-0.485126\pi\)
0.0467109 + 0.998908i \(0.485126\pi\)
\(84\) 0 0
\(85\) −19.6137 −2.12740
\(86\) 10.3296 1.11387
\(87\) −8.35577 −0.895833
\(88\) 52.4005 5.58591
\(89\) 9.60988 1.01865 0.509323 0.860576i \(-0.329896\pi\)
0.509323 + 0.860576i \(0.329896\pi\)
\(90\) 10.0473 1.05908
\(91\) 0 0
\(92\) 35.7764 3.72995
\(93\) −3.83202 −0.397362
\(94\) 6.15889 0.635241
\(95\) −11.5211 −1.18204
\(96\) −21.6774 −2.21244
\(97\) −13.7839 −1.39955 −0.699774 0.714364i \(-0.746716\pi\)
−0.699774 + 0.714364i \(0.746716\pi\)
\(98\) 0 0
\(99\) −5.55413 −0.558211
\(100\) 46.5914 4.65914
\(101\) 2.22327 0.221224 0.110612 0.993864i \(-0.464719\pi\)
0.110612 + 0.993864i \(0.464719\pi\)
\(102\) −14.5537 −1.44103
\(103\) 2.67624 0.263698 0.131849 0.991270i \(-0.457909\pi\)
0.131849 + 0.991270i \(0.457909\pi\)
\(104\) 12.7484 1.25009
\(105\) 0 0
\(106\) −11.2945 −1.09702
\(107\) 9.72726 0.940370 0.470185 0.882568i \(-0.344187\pi\)
0.470185 + 0.882568i \(0.344187\pi\)
\(108\) 5.45531 0.524937
\(109\) 19.4402 1.86203 0.931015 0.364982i \(-0.118925\pi\)
0.931015 + 0.364982i \(0.118925\pi\)
\(110\) −55.8042 −5.32072
\(111\) 0.883409 0.0838495
\(112\) 0 0
\(113\) 5.24038 0.492973 0.246487 0.969146i \(-0.420724\pi\)
0.246487 + 0.969146i \(0.420724\pi\)
\(114\) −8.54886 −0.800674
\(115\) −24.1321 −2.25033
\(116\) −45.5833 −4.23230
\(117\) −1.35125 −0.124923
\(118\) −12.1095 −1.11477
\(119\) 0 0
\(120\) 34.7166 3.16918
\(121\) 19.8484 1.80440
\(122\) 12.3041 1.11396
\(123\) −1.00000 −0.0901670
\(124\) −20.9049 −1.87731
\(125\) −13.0284 −1.16529
\(126\) 0 0
\(127\) 11.1551 0.989854 0.494927 0.868935i \(-0.335195\pi\)
0.494927 + 0.868935i \(0.335195\pi\)
\(128\) −37.1640 −3.28486
\(129\) −3.78313 −0.333086
\(130\) −13.5765 −1.19074
\(131\) −1.22298 −0.106853 −0.0534263 0.998572i \(-0.517014\pi\)
−0.0534263 + 0.998572i \(0.517014\pi\)
\(132\) −30.2995 −2.63723
\(133\) 0 0
\(134\) 26.9814 2.33084
\(135\) −3.67975 −0.316702
\(136\) −50.2875 −4.31212
\(137\) 14.7954 1.26406 0.632029 0.774944i \(-0.282222\pi\)
0.632029 + 0.774944i \(0.282222\pi\)
\(138\) −17.9065 −1.52430
\(139\) 5.54637 0.470437 0.235219 0.971942i \(-0.424419\pi\)
0.235219 + 0.971942i \(0.424419\pi\)
\(140\) 0 0
\(141\) −2.25564 −0.189959
\(142\) −8.88000 −0.745193
\(143\) 7.50504 0.627603
\(144\) 14.8498 1.23748
\(145\) 30.7471 2.55341
\(146\) −17.4003 −1.44006
\(147\) 0 0
\(148\) 4.81927 0.396141
\(149\) 3.94934 0.323542 0.161771 0.986828i \(-0.448279\pi\)
0.161771 + 0.986828i \(0.448279\pi\)
\(150\) −23.3195 −1.90403
\(151\) 16.4925 1.34214 0.671072 0.741393i \(-0.265834\pi\)
0.671072 + 0.741393i \(0.265834\pi\)
\(152\) −29.5390 −2.39593
\(153\) 5.33017 0.430919
\(154\) 0 0
\(155\) 14.1009 1.13261
\(156\) −7.37151 −0.590193
\(157\) −11.0722 −0.883662 −0.441831 0.897098i \(-0.645671\pi\)
−0.441831 + 0.897098i \(0.645671\pi\)
\(158\) −12.7614 −1.01525
\(159\) 4.13650 0.328046
\(160\) 79.7673 6.30616
\(161\) 0 0
\(162\) −2.73044 −0.214524
\(163\) −6.41011 −0.502079 −0.251039 0.967977i \(-0.580772\pi\)
−0.251039 + 0.967977i \(0.580772\pi\)
\(164\) −5.45531 −0.425988
\(165\) 20.4378 1.59108
\(166\) −2.32391 −0.180371
\(167\) −9.75464 −0.754837 −0.377418 0.926043i \(-0.623188\pi\)
−0.377418 + 0.926043i \(0.623188\pi\)
\(168\) 0 0
\(169\) −11.1741 −0.859547
\(170\) 53.5540 4.10741
\(171\) 3.13095 0.239429
\(172\) −20.6381 −1.57364
\(173\) −6.97623 −0.530393 −0.265197 0.964194i \(-0.585437\pi\)
−0.265197 + 0.964194i \(0.585437\pi\)
\(174\) 22.8149 1.72960
\(175\) 0 0
\(176\) −82.4775 −6.21698
\(177\) 4.43498 0.333354
\(178\) −26.2392 −1.96671
\(179\) −2.84611 −0.212728 −0.106364 0.994327i \(-0.533921\pi\)
−0.106364 + 0.994327i \(0.533921\pi\)
\(180\) −20.0742 −1.49624
\(181\) −25.8260 −1.91963 −0.959814 0.280636i \(-0.909455\pi\)
−0.959814 + 0.280636i \(0.909455\pi\)
\(182\) 0 0
\(183\) −4.50628 −0.333114
\(184\) −61.8724 −4.56129
\(185\) −3.25072 −0.238998
\(186\) 10.4631 0.767193
\(187\) −29.6044 −2.16489
\(188\) −12.3052 −0.897449
\(189\) 0 0
\(190\) 31.4577 2.28218
\(191\) −21.6988 −1.57007 −0.785037 0.619449i \(-0.787356\pi\)
−0.785037 + 0.619449i \(0.787356\pi\)
\(192\) 29.4893 2.12820
\(193\) 3.38989 0.244009 0.122005 0.992530i \(-0.461068\pi\)
0.122005 + 0.992530i \(0.461068\pi\)
\(194\) 37.6363 2.70213
\(195\) 4.97228 0.356072
\(196\) 0 0
\(197\) 20.6945 1.47442 0.737211 0.675663i \(-0.236142\pi\)
0.737211 + 0.675663i \(0.236142\pi\)
\(198\) 15.1652 1.07775
\(199\) 23.0318 1.63268 0.816340 0.577572i \(-0.196000\pi\)
0.816340 + 0.577572i \(0.196000\pi\)
\(200\) −80.5760 −5.69758
\(201\) −9.88169 −0.697001
\(202\) −6.07050 −0.427119
\(203\) 0 0
\(204\) 29.0777 2.03585
\(205\) 3.67975 0.257005
\(206\) −7.30732 −0.509125
\(207\) 6.55809 0.455819
\(208\) −20.0658 −1.39131
\(209\) −17.3897 −1.20287
\(210\) 0 0
\(211\) −1.90091 −0.130864 −0.0654322 0.997857i \(-0.520843\pi\)
−0.0654322 + 0.997857i \(0.520843\pi\)
\(212\) 22.5659 1.54983
\(213\) 3.25222 0.222839
\(214\) −26.5597 −1.81558
\(215\) 13.9210 0.949403
\(216\) −9.43451 −0.641937
\(217\) 0 0
\(218\) −53.0802 −3.59504
\(219\) 6.37270 0.430627
\(220\) 111.495 7.51696
\(221\) −7.20241 −0.484487
\(222\) −2.41210 −0.161889
\(223\) −20.1422 −1.34882 −0.674410 0.738357i \(-0.735602\pi\)
−0.674410 + 0.738357i \(0.735602\pi\)
\(224\) 0 0
\(225\) 8.54056 0.569371
\(226\) −14.3085 −0.951790
\(227\) 12.3852 0.822032 0.411016 0.911628i \(-0.365174\pi\)
0.411016 + 0.911628i \(0.365174\pi\)
\(228\) 17.0803 1.13117
\(229\) −22.6986 −1.49997 −0.749984 0.661456i \(-0.769939\pi\)
−0.749984 + 0.661456i \(0.769939\pi\)
\(230\) 65.8914 4.34475
\(231\) 0 0
\(232\) 78.8326 5.17562
\(233\) −10.4318 −0.683409 −0.341704 0.939808i \(-0.611004\pi\)
−0.341704 + 0.939808i \(0.611004\pi\)
\(234\) 3.68952 0.241191
\(235\) 8.30019 0.541445
\(236\) 24.1942 1.57491
\(237\) 4.67377 0.303594
\(238\) 0 0
\(239\) −18.7536 −1.21307 −0.606535 0.795057i \(-0.707441\pi\)
−0.606535 + 0.795057i \(0.707441\pi\)
\(240\) −54.6434 −3.52722
\(241\) 19.4561 1.25327 0.626637 0.779311i \(-0.284431\pi\)
0.626637 + 0.779311i \(0.284431\pi\)
\(242\) −54.1947 −3.48377
\(243\) 1.00000 0.0641500
\(244\) −24.5832 −1.57378
\(245\) 0 0
\(246\) 2.73044 0.174087
\(247\) −4.23070 −0.269193
\(248\) 36.1533 2.29573
\(249\) 0.851113 0.0539371
\(250\) 35.5732 2.24985
\(251\) 4.46572 0.281874 0.140937 0.990019i \(-0.454989\pi\)
0.140937 + 0.990019i \(0.454989\pi\)
\(252\) 0 0
\(253\) −36.4245 −2.28999
\(254\) −30.4583 −1.91112
\(255\) −19.6137 −1.22826
\(256\) 42.4954 2.65596
\(257\) −15.8522 −0.988830 −0.494415 0.869226i \(-0.664618\pi\)
−0.494415 + 0.869226i \(0.664618\pi\)
\(258\) 10.3296 0.643094
\(259\) 0 0
\(260\) 27.1253 1.68224
\(261\) −8.35577 −0.517209
\(262\) 3.33929 0.206302
\(263\) −17.0228 −1.04967 −0.524836 0.851203i \(-0.675873\pi\)
−0.524836 + 0.851203i \(0.675873\pi\)
\(264\) 52.4005 3.22503
\(265\) −15.2213 −0.935037
\(266\) 0 0
\(267\) 9.60988 0.588115
\(268\) −53.9077 −3.29294
\(269\) −15.1029 −0.920838 −0.460419 0.887702i \(-0.652301\pi\)
−0.460419 + 0.887702i \(0.652301\pi\)
\(270\) 10.0473 0.611462
\(271\) −14.8353 −0.901183 −0.450591 0.892730i \(-0.648787\pi\)
−0.450591 + 0.892730i \(0.648787\pi\)
\(272\) 79.1518 4.79928
\(273\) 0 0
\(274\) −40.3980 −2.44054
\(275\) −47.4354 −2.86046
\(276\) 35.7764 2.15349
\(277\) −5.78658 −0.347682 −0.173841 0.984774i \(-0.555618\pi\)
−0.173841 + 0.984774i \(0.555618\pi\)
\(278\) −15.1440 −0.908279
\(279\) −3.83202 −0.229417
\(280\) 0 0
\(281\) −10.7954 −0.644000 −0.322000 0.946740i \(-0.604355\pi\)
−0.322000 + 0.946740i \(0.604355\pi\)
\(282\) 6.15889 0.366757
\(283\) −14.1172 −0.839178 −0.419589 0.907714i \(-0.637826\pi\)
−0.419589 + 0.907714i \(0.637826\pi\)
\(284\) 17.7419 1.05279
\(285\) −11.5211 −0.682451
\(286\) −20.4921 −1.21172
\(287\) 0 0
\(288\) −21.6774 −1.27735
\(289\) 11.4107 0.671218
\(290\) −83.9533 −4.92991
\(291\) −13.7839 −0.808029
\(292\) 34.7650 2.03447
\(293\) −31.9086 −1.86412 −0.932061 0.362300i \(-0.881991\pi\)
−0.932061 + 0.362300i \(0.881991\pi\)
\(294\) 0 0
\(295\) −16.3196 −0.950166
\(296\) −8.33453 −0.484435
\(297\) −5.55413 −0.322283
\(298\) −10.7834 −0.624668
\(299\) −8.86165 −0.512482
\(300\) 46.5914 2.68995
\(301\) 0 0
\(302\) −45.0319 −2.59129
\(303\) 2.22327 0.127723
\(304\) 46.4938 2.66660
\(305\) 16.5820 0.949483
\(306\) −14.5537 −0.831980
\(307\) −20.8950 −1.19254 −0.596271 0.802783i \(-0.703352\pi\)
−0.596271 + 0.802783i \(0.703352\pi\)
\(308\) 0 0
\(309\) 2.67624 0.152246
\(310\) −38.5016 −2.18675
\(311\) 22.2101 1.25942 0.629709 0.776831i \(-0.283174\pi\)
0.629709 + 0.776831i \(0.283174\pi\)
\(312\) 12.7484 0.721737
\(313\) 7.85546 0.444017 0.222008 0.975045i \(-0.428739\pi\)
0.222008 + 0.975045i \(0.428739\pi\)
\(314\) 30.2321 1.70610
\(315\) 0 0
\(316\) 25.4968 1.43431
\(317\) 24.1210 1.35477 0.677386 0.735628i \(-0.263113\pi\)
0.677386 + 0.735628i \(0.263113\pi\)
\(318\) −11.2945 −0.633363
\(319\) 46.4090 2.59841
\(320\) −108.513 −6.06607
\(321\) 9.72726 0.542923
\(322\) 0 0
\(323\) 16.6885 0.928571
\(324\) 5.45531 0.303073
\(325\) −11.5405 −0.640150
\(326\) 17.5024 0.969370
\(327\) 19.4402 1.07504
\(328\) 9.43451 0.520934
\(329\) 0 0
\(330\) −55.8042 −3.07192
\(331\) 28.2994 1.55548 0.777738 0.628588i \(-0.216367\pi\)
0.777738 + 0.628588i \(0.216367\pi\)
\(332\) 4.64308 0.254822
\(333\) 0.883409 0.0484105
\(334\) 26.6345 1.45737
\(335\) 36.3622 1.98668
\(336\) 0 0
\(337\) 29.6052 1.61270 0.806348 0.591441i \(-0.201441\pi\)
0.806348 + 0.591441i \(0.201441\pi\)
\(338\) 30.5103 1.65954
\(339\) 5.24038 0.284618
\(340\) −106.999 −5.80282
\(341\) 21.2835 1.15257
\(342\) −8.54886 −0.462270
\(343\) 0 0
\(344\) 35.6920 1.92438
\(345\) −24.1321 −1.29923
\(346\) 19.0482 1.02404
\(347\) −8.17662 −0.438944 −0.219472 0.975619i \(-0.570433\pi\)
−0.219472 + 0.975619i \(0.570433\pi\)
\(348\) −45.5833 −2.44352
\(349\) −12.5666 −0.672675 −0.336338 0.941741i \(-0.609188\pi\)
−0.336338 + 0.941741i \(0.609188\pi\)
\(350\) 0 0
\(351\) −1.35125 −0.0721246
\(352\) 120.399 6.41729
\(353\) −26.5257 −1.41182 −0.705911 0.708301i \(-0.749462\pi\)
−0.705911 + 0.708301i \(0.749462\pi\)
\(354\) −12.1095 −0.643611
\(355\) −11.9674 −0.635162
\(356\) 52.4248 2.77851
\(357\) 0 0
\(358\) 7.77114 0.410717
\(359\) 21.3802 1.12841 0.564203 0.825636i \(-0.309184\pi\)
0.564203 + 0.825636i \(0.309184\pi\)
\(360\) 34.7166 1.82973
\(361\) −9.19718 −0.484062
\(362\) 70.5163 3.70625
\(363\) 19.8484 1.04177
\(364\) 0 0
\(365\) −23.4499 −1.22743
\(366\) 12.3041 0.643148
\(367\) −18.2387 −0.952051 −0.476026 0.879431i \(-0.657923\pi\)
−0.476026 + 0.879431i \(0.657923\pi\)
\(368\) 97.3861 5.07660
\(369\) −1.00000 −0.0520579
\(370\) 8.87591 0.461437
\(371\) 0 0
\(372\) −20.9049 −1.08387
\(373\) −20.4799 −1.06041 −0.530205 0.847870i \(-0.677885\pi\)
−0.530205 + 0.847870i \(0.677885\pi\)
\(374\) 80.8332 4.17978
\(375\) −13.0284 −0.672782
\(376\) 21.2809 1.09748
\(377\) 11.2908 0.581504
\(378\) 0 0
\(379\) −21.2995 −1.09408 −0.547040 0.837106i \(-0.684246\pi\)
−0.547040 + 0.837106i \(0.684246\pi\)
\(380\) −62.8511 −3.22420
\(381\) 11.1551 0.571492
\(382\) 59.2474 3.03136
\(383\) 4.25583 0.217463 0.108731 0.994071i \(-0.465321\pi\)
0.108731 + 0.994071i \(0.465321\pi\)
\(384\) −37.1640 −1.89652
\(385\) 0 0
\(386\) −9.25589 −0.471112
\(387\) −3.78313 −0.192307
\(388\) −75.1957 −3.81748
\(389\) 1.64453 0.0833810 0.0416905 0.999131i \(-0.486726\pi\)
0.0416905 + 0.999131i \(0.486726\pi\)
\(390\) −13.5765 −0.687473
\(391\) 34.9557 1.76779
\(392\) 0 0
\(393\) −1.22298 −0.0616914
\(394\) −56.5051 −2.84669
\(395\) −17.1983 −0.865340
\(396\) −30.2995 −1.52261
\(397\) −22.7752 −1.14306 −0.571528 0.820582i \(-0.693649\pi\)
−0.571528 + 0.820582i \(0.693649\pi\)
\(398\) −62.8869 −3.15224
\(399\) 0 0
\(400\) 126.825 6.34126
\(401\) −39.5907 −1.97706 −0.988532 0.151015i \(-0.951746\pi\)
−0.988532 + 0.151015i \(0.951746\pi\)
\(402\) 26.9814 1.34571
\(403\) 5.17804 0.257936
\(404\) 12.1286 0.603421
\(405\) −3.67975 −0.182848
\(406\) 0 0
\(407\) −4.90657 −0.243209
\(408\) −50.2875 −2.48960
\(409\) 17.2670 0.853800 0.426900 0.904299i \(-0.359606\pi\)
0.426900 + 0.904299i \(0.359606\pi\)
\(410\) −10.0473 −0.496203
\(411\) 14.7954 0.729805
\(412\) 14.5997 0.719277
\(413\) 0 0
\(414\) −17.9065 −0.880055
\(415\) −3.13188 −0.153738
\(416\) 29.2916 1.43614
\(417\) 5.54637 0.271607
\(418\) 47.4815 2.32240
\(419\) 25.4768 1.24462 0.622312 0.782769i \(-0.286193\pi\)
0.622312 + 0.782769i \(0.286193\pi\)
\(420\) 0 0
\(421\) 19.0527 0.928572 0.464286 0.885685i \(-0.346311\pi\)
0.464286 + 0.885685i \(0.346311\pi\)
\(422\) 5.19033 0.252662
\(423\) −2.25564 −0.109673
\(424\) −39.0259 −1.89526
\(425\) 45.5226 2.20817
\(426\) −8.88000 −0.430237
\(427\) 0 0
\(428\) 53.0652 2.56500
\(429\) 7.50504 0.362347
\(430\) −38.0104 −1.83302
\(431\) −7.72119 −0.371917 −0.185958 0.982558i \(-0.559539\pi\)
−0.185958 + 0.982558i \(0.559539\pi\)
\(432\) 14.8498 0.714460
\(433\) −20.3059 −0.975839 −0.487919 0.872889i \(-0.662244\pi\)
−0.487919 + 0.872889i \(0.662244\pi\)
\(434\) 0 0
\(435\) 30.7471 1.47421
\(436\) 106.052 5.07897
\(437\) 20.5330 0.982228
\(438\) −17.4003 −0.831418
\(439\) −14.4835 −0.691261 −0.345630 0.938371i \(-0.612335\pi\)
−0.345630 + 0.938371i \(0.612335\pi\)
\(440\) −192.821 −9.19237
\(441\) 0 0
\(442\) 19.6658 0.935405
\(443\) 25.0987 1.19247 0.596237 0.802809i \(-0.296662\pi\)
0.596237 + 0.802809i \(0.296662\pi\)
\(444\) 4.81927 0.228712
\(445\) −35.3620 −1.67632
\(446\) 54.9970 2.60418
\(447\) 3.94934 0.186797
\(448\) 0 0
\(449\) 25.3481 1.19625 0.598126 0.801402i \(-0.295912\pi\)
0.598126 + 0.801402i \(0.295912\pi\)
\(450\) −23.3195 −1.09929
\(451\) 5.55413 0.261534
\(452\) 28.5879 1.34466
\(453\) 16.4925 0.774887
\(454\) −33.8169 −1.58711
\(455\) 0 0
\(456\) −29.5390 −1.38329
\(457\) −16.3052 −0.762726 −0.381363 0.924425i \(-0.624545\pi\)
−0.381363 + 0.924425i \(0.624545\pi\)
\(458\) 61.9773 2.89601
\(459\) 5.33017 0.248791
\(460\) −131.648 −6.13813
\(461\) −2.12664 −0.0990473 −0.0495237 0.998773i \(-0.515770\pi\)
−0.0495237 + 0.998773i \(0.515770\pi\)
\(462\) 0 0
\(463\) −38.8841 −1.80710 −0.903549 0.428485i \(-0.859048\pi\)
−0.903549 + 0.428485i \(0.859048\pi\)
\(464\) −124.081 −5.76033
\(465\) 14.1009 0.653913
\(466\) 28.4834 1.31947
\(467\) −16.8086 −0.777809 −0.388904 0.921278i \(-0.627146\pi\)
−0.388904 + 0.921278i \(0.627146\pi\)
\(468\) −7.37151 −0.340748
\(469\) 0 0
\(470\) −22.6632 −1.04537
\(471\) −11.0722 −0.510182
\(472\) −41.8419 −1.92593
\(473\) 21.0120 0.966133
\(474\) −12.7614 −0.586153
\(475\) 26.7400 1.22692
\(476\) 0 0
\(477\) 4.13650 0.189397
\(478\) 51.2056 2.34209
\(479\) 11.4663 0.523909 0.261954 0.965080i \(-0.415633\pi\)
0.261954 + 0.965080i \(0.415633\pi\)
\(480\) 79.7673 3.64086
\(481\) −1.19371 −0.0544285
\(482\) −53.1236 −2.41971
\(483\) 0 0
\(484\) 108.279 4.92177
\(485\) 50.7215 2.30314
\(486\) −2.73044 −0.123855
\(487\) −15.9414 −0.722373 −0.361187 0.932494i \(-0.617628\pi\)
−0.361187 + 0.932494i \(0.617628\pi\)
\(488\) 42.5146 1.92455
\(489\) −6.41011 −0.289875
\(490\) 0 0
\(491\) −16.1502 −0.728850 −0.364425 0.931233i \(-0.618734\pi\)
−0.364425 + 0.931233i \(0.618734\pi\)
\(492\) −5.45531 −0.245944
\(493\) −44.5377 −2.00588
\(494\) 11.5517 0.519735
\(495\) 20.4378 0.918611
\(496\) −56.9046 −2.55509
\(497\) 0 0
\(498\) −2.32391 −0.104137
\(499\) 7.64664 0.342311 0.171155 0.985244i \(-0.445250\pi\)
0.171155 + 0.985244i \(0.445250\pi\)
\(500\) −71.0738 −3.17852
\(501\) −9.75464 −0.435805
\(502\) −12.1934 −0.544217
\(503\) −27.8382 −1.24124 −0.620621 0.784111i \(-0.713120\pi\)
−0.620621 + 0.784111i \(0.713120\pi\)
\(504\) 0 0
\(505\) −8.18107 −0.364053
\(506\) 99.4549 4.42131
\(507\) −11.1741 −0.496260
\(508\) 60.8544 2.69998
\(509\) −36.9734 −1.63882 −0.819408 0.573211i \(-0.805698\pi\)
−0.819408 + 0.573211i \(0.805698\pi\)
\(510\) 53.5540 2.37141
\(511\) 0 0
\(512\) −41.7034 −1.84305
\(513\) 3.13095 0.138235
\(514\) 43.2834 1.90915
\(515\) −9.84790 −0.433950
\(516\) −20.6381 −0.908544
\(517\) 12.5281 0.550986
\(518\) 0 0
\(519\) −6.97623 −0.306223
\(520\) −46.9110 −2.05718
\(521\) −4.43422 −0.194267 −0.0971333 0.995271i \(-0.530967\pi\)
−0.0971333 + 0.995271i \(0.530967\pi\)
\(522\) 22.8149 0.998583
\(523\) −17.3405 −0.758246 −0.379123 0.925346i \(-0.623774\pi\)
−0.379123 + 0.925346i \(0.623774\pi\)
\(524\) −6.67176 −0.291457
\(525\) 0 0
\(526\) 46.4798 2.02662
\(527\) −20.4253 −0.889741
\(528\) −82.4775 −3.58937
\(529\) 20.0086 0.869937
\(530\) 41.5608 1.80529
\(531\) 4.43498 0.192462
\(532\) 0 0
\(533\) 1.35125 0.0585293
\(534\) −26.2392 −1.13548
\(535\) −35.7939 −1.54750
\(536\) 93.2290 4.02688
\(537\) −2.84611 −0.122819
\(538\) 41.2375 1.77787
\(539\) 0 0
\(540\) −20.0742 −0.863855
\(541\) −42.0364 −1.80728 −0.903642 0.428288i \(-0.859117\pi\)
−0.903642 + 0.428288i \(0.859117\pi\)
\(542\) 40.5070 1.73993
\(543\) −25.8260 −1.10830
\(544\) −115.544 −4.95391
\(545\) −71.5349 −3.06422
\(546\) 0 0
\(547\) 12.9805 0.555004 0.277502 0.960725i \(-0.410493\pi\)
0.277502 + 0.960725i \(0.410493\pi\)
\(548\) 80.7136 3.44792
\(549\) −4.50628 −0.192324
\(550\) 129.519 5.52273
\(551\) −26.1615 −1.11452
\(552\) −61.8724 −2.63346
\(553\) 0 0
\(554\) 15.7999 0.671275
\(555\) −3.25072 −0.137986
\(556\) 30.2572 1.28319
\(557\) 4.30459 0.182391 0.0911957 0.995833i \(-0.470931\pi\)
0.0911957 + 0.995833i \(0.470931\pi\)
\(558\) 10.4631 0.442939
\(559\) 5.11197 0.216213
\(560\) 0 0
\(561\) −29.6044 −1.24990
\(562\) 29.4762 1.24338
\(563\) −20.1598 −0.849634 −0.424817 0.905279i \(-0.639662\pi\)
−0.424817 + 0.905279i \(0.639662\pi\)
\(564\) −12.3052 −0.518143
\(565\) −19.2833 −0.811254
\(566\) 38.5461 1.62021
\(567\) 0 0
\(568\) −30.6831 −1.28744
\(569\) −14.3572 −0.601887 −0.300943 0.953642i \(-0.597301\pi\)
−0.300943 + 0.953642i \(0.597301\pi\)
\(570\) 31.4577 1.31762
\(571\) 9.18316 0.384303 0.192152 0.981365i \(-0.438453\pi\)
0.192152 + 0.981365i \(0.438453\pi\)
\(572\) 40.9423 1.71188
\(573\) −21.6988 −0.906482
\(574\) 0 0
\(575\) 56.0098 2.33577
\(576\) 29.4893 1.22872
\(577\) 17.0124 0.708235 0.354117 0.935201i \(-0.384781\pi\)
0.354117 + 0.935201i \(0.384781\pi\)
\(578\) −31.1562 −1.29593
\(579\) 3.38989 0.140879
\(580\) 167.735 6.96482
\(581\) 0 0
\(582\) 37.6363 1.56007
\(583\) −22.9747 −0.951513
\(584\) −60.1233 −2.48792
\(585\) 4.97228 0.205578
\(586\) 87.1247 3.59909
\(587\) −9.69119 −0.399998 −0.199999 0.979796i \(-0.564094\pi\)
−0.199999 + 0.979796i \(0.564094\pi\)
\(588\) 0 0
\(589\) −11.9979 −0.494363
\(590\) 44.5598 1.83450
\(591\) 20.6945 0.851258
\(592\) 13.1184 0.539163
\(593\) −5.02658 −0.206417 −0.103208 0.994660i \(-0.532911\pi\)
−0.103208 + 0.994660i \(0.532911\pi\)
\(594\) 15.1652 0.622237
\(595\) 0 0
\(596\) 21.5449 0.882512
\(597\) 23.0318 0.942628
\(598\) 24.1962 0.989456
\(599\) 2.15715 0.0881389 0.0440694 0.999028i \(-0.485968\pi\)
0.0440694 + 0.999028i \(0.485968\pi\)
\(600\) −80.5760 −3.28950
\(601\) 7.95644 0.324550 0.162275 0.986746i \(-0.448117\pi\)
0.162275 + 0.986746i \(0.448117\pi\)
\(602\) 0 0
\(603\) −9.88169 −0.402414
\(604\) 89.9718 3.66090
\(605\) −73.0370 −2.96937
\(606\) −6.07050 −0.246597
\(607\) 44.2143 1.79460 0.897302 0.441418i \(-0.145524\pi\)
0.897302 + 0.441418i \(0.145524\pi\)
\(608\) −67.8707 −2.75252
\(609\) 0 0
\(610\) −45.2762 −1.83318
\(611\) 3.04794 0.123307
\(612\) 29.0777 1.17540
\(613\) −4.98381 −0.201294 −0.100647 0.994922i \(-0.532091\pi\)
−0.100647 + 0.994922i \(0.532091\pi\)
\(614\) 57.0526 2.30246
\(615\) 3.67975 0.148382
\(616\) 0 0
\(617\) −17.4210 −0.701344 −0.350672 0.936498i \(-0.614047\pi\)
−0.350672 + 0.936498i \(0.614047\pi\)
\(618\) −7.30732 −0.293944
\(619\) 10.6621 0.428547 0.214274 0.976774i \(-0.431262\pi\)
0.214274 + 0.976774i \(0.431262\pi\)
\(620\) 76.9247 3.08937
\(621\) 6.55809 0.263167
\(622\) −60.6433 −2.43158
\(623\) 0 0
\(624\) −20.0658 −0.803275
\(625\) 5.23835 0.209534
\(626\) −21.4489 −0.857269
\(627\) −17.3897 −0.694477
\(628\) −60.4025 −2.41032
\(629\) 4.70872 0.187749
\(630\) 0 0
\(631\) −9.76022 −0.388548 −0.194274 0.980947i \(-0.562235\pi\)
−0.194274 + 0.980947i \(0.562235\pi\)
\(632\) −44.0947 −1.75399
\(633\) −1.90091 −0.0755546
\(634\) −65.8611 −2.61568
\(635\) −41.0479 −1.62894
\(636\) 22.5659 0.894796
\(637\) 0 0
\(638\) −126.717 −5.01678
\(639\) 3.25222 0.128656
\(640\) 136.754 5.40568
\(641\) −21.8459 −0.862863 −0.431431 0.902146i \(-0.641991\pi\)
−0.431431 + 0.902146i \(0.641991\pi\)
\(642\) −26.5597 −1.04823
\(643\) 11.0414 0.435430 0.217715 0.976012i \(-0.430140\pi\)
0.217715 + 0.976012i \(0.430140\pi\)
\(644\) 0 0
\(645\) 13.9210 0.548138
\(646\) −45.5669 −1.79281
\(647\) −31.7070 −1.24653 −0.623266 0.782010i \(-0.714194\pi\)
−0.623266 + 0.782010i \(0.714194\pi\)
\(648\) −9.43451 −0.370623
\(649\) −24.6325 −0.966909
\(650\) 31.5106 1.23595
\(651\) 0 0
\(652\) −34.9691 −1.36950
\(653\) 9.21123 0.360463 0.180232 0.983624i \(-0.442315\pi\)
0.180232 + 0.983624i \(0.442315\pi\)
\(654\) −53.0802 −2.07560
\(655\) 4.50028 0.175840
\(656\) −14.8498 −0.579786
\(657\) 6.37270 0.248623
\(658\) 0 0
\(659\) 0.175225 0.00682579 0.00341289 0.999994i \(-0.498914\pi\)
0.00341289 + 0.999994i \(0.498914\pi\)
\(660\) 111.495 4.33992
\(661\) 3.12750 0.121646 0.0608229 0.998149i \(-0.480628\pi\)
0.0608229 + 0.998149i \(0.480628\pi\)
\(662\) −77.2699 −3.00318
\(663\) −7.20241 −0.279719
\(664\) −8.02983 −0.311618
\(665\) 0 0
\(666\) −2.41210 −0.0934668
\(667\) −54.7979 −2.12178
\(668\) −53.2145 −2.05893
\(669\) −20.1422 −0.778742
\(670\) −99.2847 −3.83570
\(671\) 25.0285 0.966214
\(672\) 0 0
\(673\) −7.59268 −0.292676 −0.146338 0.989235i \(-0.546749\pi\)
−0.146338 + 0.989235i \(0.546749\pi\)
\(674\) −80.8352 −3.11365
\(675\) 8.54056 0.328726
\(676\) −60.9582 −2.34455
\(677\) 4.91162 0.188769 0.0943844 0.995536i \(-0.469912\pi\)
0.0943844 + 0.995536i \(0.469912\pi\)
\(678\) −14.3085 −0.549516
\(679\) 0 0
\(680\) 185.046 7.09617
\(681\) 12.3852 0.474600
\(682\) −58.1135 −2.22528
\(683\) −17.7094 −0.677632 −0.338816 0.940853i \(-0.610026\pi\)
−0.338816 + 0.940853i \(0.610026\pi\)
\(684\) 17.0803 0.653081
\(685\) −54.4435 −2.08018
\(686\) 0 0
\(687\) −22.6986 −0.866007
\(688\) −56.1786 −2.14179
\(689\) −5.58947 −0.212942
\(690\) 65.8914 2.50844
\(691\) −37.6487 −1.43223 −0.716113 0.697985i \(-0.754080\pi\)
−0.716113 + 0.697985i \(0.754080\pi\)
\(692\) −38.0575 −1.44673
\(693\) 0 0
\(694\) 22.3258 0.847475
\(695\) −20.4093 −0.774167
\(696\) 78.8326 2.98814
\(697\) −5.33017 −0.201895
\(698\) 34.3124 1.29874
\(699\) −10.4318 −0.394566
\(700\) 0 0
\(701\) 44.1615 1.66796 0.833979 0.551796i \(-0.186057\pi\)
0.833979 + 0.551796i \(0.186057\pi\)
\(702\) 3.68952 0.139252
\(703\) 2.76591 0.104318
\(704\) −163.787 −6.17296
\(705\) 8.30019 0.312603
\(706\) 72.4269 2.72582
\(707\) 0 0
\(708\) 24.1942 0.909274
\(709\) 27.0428 1.01561 0.507806 0.861471i \(-0.330457\pi\)
0.507806 + 0.861471i \(0.330457\pi\)
\(710\) 32.6762 1.22632
\(711\) 4.67377 0.175280
\(712\) −90.6645 −3.39780
\(713\) −25.1308 −0.941154
\(714\) 0 0
\(715\) −27.6167 −1.03280
\(716\) −15.5264 −0.580249
\(717\) −18.7536 −0.700367
\(718\) −58.3774 −2.17863
\(719\) −21.4573 −0.800223 −0.400112 0.916466i \(-0.631029\pi\)
−0.400112 + 0.916466i \(0.631029\pi\)
\(720\) −54.6434 −2.03644
\(721\) 0 0
\(722\) 25.1123 0.934585
\(723\) 19.4561 0.723578
\(724\) −140.889 −5.23608
\(725\) −71.3630 −2.65035
\(726\) −54.1947 −2.01136
\(727\) 31.0064 1.14996 0.574982 0.818166i \(-0.305009\pi\)
0.574982 + 0.818166i \(0.305009\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 64.0287 2.36981
\(731\) −20.1647 −0.745819
\(732\) −24.5832 −0.908620
\(733\) −33.7922 −1.24814 −0.624071 0.781368i \(-0.714522\pi\)
−0.624071 + 0.781368i \(0.714522\pi\)
\(734\) 49.7996 1.83814
\(735\) 0 0
\(736\) −142.162 −5.24017
\(737\) 54.8842 2.02169
\(738\) 2.73044 0.100509
\(739\) 10.6144 0.390458 0.195229 0.980758i \(-0.437455\pi\)
0.195229 + 0.980758i \(0.437455\pi\)
\(740\) −17.7337 −0.651904
\(741\) −4.23070 −0.155419
\(742\) 0 0
\(743\) −19.6192 −0.719759 −0.359879 0.932999i \(-0.617182\pi\)
−0.359879 + 0.932999i \(0.617182\pi\)
\(744\) 36.1533 1.32544
\(745\) −14.5326 −0.532432
\(746\) 55.9192 2.04735
\(747\) 0.851113 0.0311406
\(748\) −161.501 −5.90507
\(749\) 0 0
\(750\) 35.5732 1.29895
\(751\) −7.30875 −0.266700 −0.133350 0.991069i \(-0.542573\pi\)
−0.133350 + 0.991069i \(0.542573\pi\)
\(752\) −33.4957 −1.22146
\(753\) 4.46572 0.162740
\(754\) −30.8288 −1.12272
\(755\) −60.6884 −2.20868
\(756\) 0 0
\(757\) 26.3503 0.957719 0.478860 0.877891i \(-0.341050\pi\)
0.478860 + 0.877891i \(0.341050\pi\)
\(758\) 58.1570 2.11236
\(759\) −36.4245 −1.32213
\(760\) 108.696 3.94282
\(761\) 22.3112 0.808779 0.404390 0.914587i \(-0.367484\pi\)
0.404390 + 0.914587i \(0.367484\pi\)
\(762\) −30.4583 −1.10339
\(763\) 0 0
\(764\) −118.374 −4.28262
\(765\) −19.6137 −0.709134
\(766\) −11.6203 −0.419858
\(767\) −5.99279 −0.216387
\(768\) 42.4954 1.53342
\(769\) 54.2290 1.95555 0.977774 0.209663i \(-0.0672368\pi\)
0.977774 + 0.209663i \(0.0672368\pi\)
\(770\) 0 0
\(771\) −15.8522 −0.570902
\(772\) 18.4929 0.665573
\(773\) −34.4225 −1.23809 −0.619046 0.785354i \(-0.712481\pi\)
−0.619046 + 0.785354i \(0.712481\pi\)
\(774\) 10.3296 0.371290
\(775\) −32.7276 −1.17561
\(776\) 130.045 4.66834
\(777\) 0 0
\(778\) −4.49029 −0.160985
\(779\) −3.13095 −0.112178
\(780\) 27.1253 0.971242
\(781\) −18.0633 −0.646354
\(782\) −95.4446 −3.41309
\(783\) −8.35577 −0.298611
\(784\) 0 0
\(785\) 40.7431 1.45418
\(786\) 3.33929 0.119108
\(787\) −27.4575 −0.978753 −0.489376 0.872073i \(-0.662776\pi\)
−0.489376 + 0.872073i \(0.662776\pi\)
\(788\) 112.895 4.02171
\(789\) −17.0228 −0.606029
\(790\) 46.9589 1.67072
\(791\) 0 0
\(792\) 52.4005 1.86197
\(793\) 6.08914 0.216232
\(794\) 62.1865 2.20692
\(795\) −15.2213 −0.539844
\(796\) 125.645 4.45338
\(797\) −6.82635 −0.241802 −0.120901 0.992665i \(-0.538578\pi\)
−0.120901 + 0.992665i \(0.538578\pi\)
\(798\) 0 0
\(799\) −12.0229 −0.425341
\(800\) −185.137 −6.54558
\(801\) 9.60988 0.339548
\(802\) 108.100 3.81714
\(803\) −35.3948 −1.24906
\(804\) −53.9077 −1.90118
\(805\) 0 0
\(806\) −14.1383 −0.498001
\(807\) −15.1029 −0.531646
\(808\) −20.9755 −0.737914
\(809\) 8.61638 0.302936 0.151468 0.988462i \(-0.451600\pi\)
0.151468 + 0.988462i \(0.451600\pi\)
\(810\) 10.0473 0.353028
\(811\) 1.71360 0.0601727 0.0300863 0.999547i \(-0.490422\pi\)
0.0300863 + 0.999547i \(0.490422\pi\)
\(812\) 0 0
\(813\) −14.8353 −0.520298
\(814\) 13.3971 0.469568
\(815\) 23.5876 0.826238
\(816\) 79.1518 2.77087
\(817\) −11.8448 −0.414396
\(818\) −47.1466 −1.64844
\(819\) 0 0
\(820\) 20.0742 0.701020
\(821\) 40.5547 1.41537 0.707685 0.706528i \(-0.249740\pi\)
0.707685 + 0.706528i \(0.249740\pi\)
\(822\) −40.3980 −1.40904
\(823\) −50.4076 −1.75710 −0.878550 0.477651i \(-0.841489\pi\)
−0.878550 + 0.477651i \(0.841489\pi\)
\(824\) −25.2490 −0.879592
\(825\) −47.4354 −1.65149
\(826\) 0 0
\(827\) −55.9884 −1.94691 −0.973454 0.228883i \(-0.926493\pi\)
−0.973454 + 0.228883i \(0.926493\pi\)
\(828\) 35.7764 1.24332
\(829\) 35.2244 1.22339 0.611697 0.791092i \(-0.290487\pi\)
0.611697 + 0.791092i \(0.290487\pi\)
\(830\) 8.55142 0.296824
\(831\) −5.78658 −0.200734
\(832\) −39.8475 −1.38146
\(833\) 0 0
\(834\) −15.1440 −0.524395
\(835\) 35.8946 1.24218
\(836\) −94.8660 −3.28101
\(837\) −3.83202 −0.132454
\(838\) −69.5630 −2.40301
\(839\) 6.15670 0.212553 0.106276 0.994337i \(-0.466107\pi\)
0.106276 + 0.994337i \(0.466107\pi\)
\(840\) 0 0
\(841\) 40.8189 1.40755
\(842\) −52.0223 −1.79281
\(843\) −10.7954 −0.371814
\(844\) −10.3701 −0.356953
\(845\) 41.1179 1.41450
\(846\) 6.15889 0.211747
\(847\) 0 0
\(848\) 61.4261 2.10938
\(849\) −14.1172 −0.484500
\(850\) −124.297 −4.26335
\(851\) 5.79348 0.198598
\(852\) 17.7419 0.607826
\(853\) −31.1759 −1.06744 −0.533722 0.845660i \(-0.679207\pi\)
−0.533722 + 0.845660i \(0.679207\pi\)
\(854\) 0 0
\(855\) −11.5211 −0.394013
\(856\) −91.7720 −3.13670
\(857\) −50.4433 −1.72311 −0.861555 0.507664i \(-0.830509\pi\)
−0.861555 + 0.507664i \(0.830509\pi\)
\(858\) −20.4921 −0.699588
\(859\) 33.3703 1.13858 0.569290 0.822137i \(-0.307218\pi\)
0.569290 + 0.822137i \(0.307218\pi\)
\(860\) 75.9432 2.58964
\(861\) 0 0
\(862\) 21.0823 0.718064
\(863\) −16.6210 −0.565786 −0.282893 0.959151i \(-0.591294\pi\)
−0.282893 + 0.959151i \(0.591294\pi\)
\(864\) −21.6774 −0.737479
\(865\) 25.6708 0.872833
\(866\) 55.4440 1.88406
\(867\) 11.4107 0.387528
\(868\) 0 0
\(869\) −25.9587 −0.880589
\(870\) −83.9533 −2.84628
\(871\) 13.3527 0.452438
\(872\) −183.408 −6.21099
\(873\) −13.7839 −0.466516
\(874\) −56.0642 −1.89640
\(875\) 0 0
\(876\) 34.7650 1.17460
\(877\) −19.4275 −0.656020 −0.328010 0.944674i \(-0.606378\pi\)
−0.328010 + 0.944674i \(0.606378\pi\)
\(878\) 39.5464 1.33463
\(879\) −31.9086 −1.07625
\(880\) 303.497 10.2309
\(881\) 24.7456 0.833702 0.416851 0.908975i \(-0.363134\pi\)
0.416851 + 0.908975i \(0.363134\pi\)
\(882\) 0 0
\(883\) −9.21151 −0.309992 −0.154996 0.987915i \(-0.549536\pi\)
−0.154996 + 0.987915i \(0.549536\pi\)
\(884\) −39.2914 −1.32151
\(885\) −16.3196 −0.548578
\(886\) −68.5304 −2.30232
\(887\) 27.3860 0.919532 0.459766 0.888040i \(-0.347933\pi\)
0.459766 + 0.888040i \(0.347933\pi\)
\(888\) −8.33453 −0.279689
\(889\) 0 0
\(890\) 96.5537 3.23649
\(891\) −5.55413 −0.186070
\(892\) −109.882 −3.67911
\(893\) −7.06229 −0.236330
\(894\) −10.7834 −0.360652
\(895\) 10.4730 0.350073
\(896\) 0 0
\(897\) −8.86165 −0.295882
\(898\) −69.2116 −2.30962
\(899\) 32.0195 1.06791
\(900\) 46.5914 1.55305
\(901\) 22.0483 0.734534
\(902\) −15.1652 −0.504947
\(903\) 0 0
\(904\) −49.4404 −1.64436
\(905\) 95.0331 3.15901
\(906\) −45.0319 −1.49608
\(907\) 1.19783 0.0397734 0.0198867 0.999802i \(-0.493669\pi\)
0.0198867 + 0.999802i \(0.493669\pi\)
\(908\) 67.5648 2.24222
\(909\) 2.22327 0.0737412
\(910\) 0 0
\(911\) −52.9657 −1.75483 −0.877416 0.479730i \(-0.840734\pi\)
−0.877416 + 0.479730i \(0.840734\pi\)
\(912\) 46.4938 1.53956
\(913\) −4.72719 −0.156447
\(914\) 44.5204 1.47260
\(915\) 16.5820 0.548184
\(916\) −123.828 −4.09139
\(917\) 0 0
\(918\) −14.5537 −0.480344
\(919\) 24.4543 0.806672 0.403336 0.915052i \(-0.367851\pi\)
0.403336 + 0.915052i \(0.367851\pi\)
\(920\) 227.675 7.50622
\(921\) −20.8950 −0.688514
\(922\) 5.80665 0.191232
\(923\) −4.39458 −0.144649
\(924\) 0 0
\(925\) 7.54480 0.248072
\(926\) 106.171 3.48899
\(927\) 2.67624 0.0878993
\(928\) 181.131 5.94592
\(929\) 3.18991 0.104657 0.0523287 0.998630i \(-0.483336\pi\)
0.0523287 + 0.998630i \(0.483336\pi\)
\(930\) −38.5016 −1.26252
\(931\) 0 0
\(932\) −56.9086 −1.86410
\(933\) 22.2101 0.727126
\(934\) 45.8949 1.50173
\(935\) 108.937 3.56262
\(936\) 12.7484 0.416695
\(937\) 22.6297 0.739279 0.369640 0.929175i \(-0.379481\pi\)
0.369640 + 0.929175i \(0.379481\pi\)
\(938\) 0 0
\(939\) 7.85546 0.256353
\(940\) 45.2801 1.47687
\(941\) −24.5821 −0.801353 −0.400677 0.916220i \(-0.631225\pi\)
−0.400677 + 0.916220i \(0.631225\pi\)
\(942\) 30.2321 0.985016
\(943\) −6.55809 −0.213561
\(944\) 65.8585 2.14351
\(945\) 0 0
\(946\) −57.3720 −1.86533
\(947\) 56.2875 1.82910 0.914550 0.404474i \(-0.132545\pi\)
0.914550 + 0.404474i \(0.132545\pi\)
\(948\) 25.4968 0.828099
\(949\) −8.61114 −0.279529
\(950\) −73.0121 −2.36882
\(951\) 24.1210 0.782178
\(952\) 0 0
\(953\) 41.0106 1.32847 0.664233 0.747526i \(-0.268758\pi\)
0.664233 + 0.747526i \(0.268758\pi\)
\(954\) −11.2945 −0.365672
\(955\) 79.8463 2.58377
\(956\) −102.307 −3.30884
\(957\) 46.4090 1.50019
\(958\) −31.3081 −1.01152
\(959\) 0 0
\(960\) −108.513 −3.50225
\(961\) −16.3156 −0.526310
\(962\) 3.25935 0.105086
\(963\) 9.72726 0.313457
\(964\) 106.139 3.41850
\(965\) −12.4739 −0.401550
\(966\) 0 0
\(967\) 5.56198 0.178861 0.0894306 0.995993i \(-0.471495\pi\)
0.0894306 + 0.995993i \(0.471495\pi\)
\(968\) −187.260 −6.01875
\(969\) 16.6885 0.536111
\(970\) −138.492 −4.44671
\(971\) 4.71602 0.151344 0.0756722 0.997133i \(-0.475890\pi\)
0.0756722 + 0.997133i \(0.475890\pi\)
\(972\) 5.45531 0.174979
\(973\) 0 0
\(974\) 43.5270 1.39470
\(975\) −11.5405 −0.369591
\(976\) −66.9173 −2.14197
\(977\) −17.3670 −0.555620 −0.277810 0.960636i \(-0.589609\pi\)
−0.277810 + 0.960636i \(0.589609\pi\)
\(978\) 17.5024 0.559666
\(979\) −53.3745 −1.70586
\(980\) 0 0
\(981\) 19.4402 0.620676
\(982\) 44.0972 1.40720
\(983\) −1.97887 −0.0631162 −0.0315581 0.999502i \(-0.510047\pi\)
−0.0315581 + 0.999502i \(0.510047\pi\)
\(984\) 9.43451 0.300761
\(985\) −76.1506 −2.42636
\(986\) 121.607 3.87277
\(987\) 0 0
\(988\) −23.0798 −0.734266
\(989\) −24.8101 −0.788916
\(990\) −55.8042 −1.77357
\(991\) 2.04528 0.0649704 0.0324852 0.999472i \(-0.489658\pi\)
0.0324852 + 0.999472i \(0.489658\pi\)
\(992\) 83.0682 2.63742
\(993\) 28.2994 0.898055
\(994\) 0 0
\(995\) −84.7512 −2.68679
\(996\) 4.64308 0.147122
\(997\) −40.9434 −1.29669 −0.648345 0.761346i \(-0.724539\pi\)
−0.648345 + 0.761346i \(0.724539\pi\)
\(998\) −20.8787 −0.660904
\(999\) 0.883409 0.0279498
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 \(a_p\))