Properties

Label 6027.2.a.bk.1.7
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 1.7
Root \(0.442251\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.442251 q^{2} +1.00000 q^{3} -1.80441 q^{4} -4.29274 q^{5} -0.442251 q^{6} +1.68250 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.442251 q^{2} +1.00000 q^{3} -1.80441 q^{4} -4.29274 q^{5} -0.442251 q^{6} +1.68250 q^{8} +1.00000 q^{9} +1.89847 q^{10} -2.21212 q^{11} -1.80441 q^{12} -3.11687 q^{13} -4.29274 q^{15} +2.86474 q^{16} -6.92396 q^{17} -0.442251 q^{18} +7.72487 q^{19} +7.74589 q^{20} +0.978311 q^{22} +0.0381692 q^{23} +1.68250 q^{24} +13.4277 q^{25} +1.37844 q^{26} +1.00000 q^{27} +2.66709 q^{29} +1.89847 q^{30} +4.69959 q^{31} -4.63194 q^{32} -2.21212 q^{33} +3.06213 q^{34} -1.80441 q^{36} -0.0300718 q^{37} -3.41633 q^{38} -3.11687 q^{39} -7.22256 q^{40} -1.00000 q^{41} +11.0093 q^{43} +3.99158 q^{44} -4.29274 q^{45} -0.0168804 q^{46} -3.78108 q^{47} +2.86474 q^{48} -5.93839 q^{50} -6.92396 q^{51} +5.62412 q^{52} -0.546137 q^{53} -0.442251 q^{54} +9.49606 q^{55} +7.72487 q^{57} -1.17952 q^{58} -9.55909 q^{59} +7.74589 q^{60} +6.02077 q^{61} -2.07840 q^{62} -3.68100 q^{64} +13.3799 q^{65} +0.978311 q^{66} -8.97673 q^{67} +12.4937 q^{68} +0.0381692 q^{69} +15.6199 q^{71} +1.68250 q^{72} -2.42299 q^{73} +0.0132993 q^{74} +13.4277 q^{75} -13.9389 q^{76} +1.37844 q^{78} +2.16136 q^{79} -12.2976 q^{80} +1.00000 q^{81} +0.442251 q^{82} +17.0488 q^{83} +29.7228 q^{85} -4.86886 q^{86} +2.66709 q^{87} -3.72190 q^{88} -8.69193 q^{89} +1.89847 q^{90} -0.0688730 q^{92} +4.69959 q^{93} +1.67218 q^{94} -33.1609 q^{95} -4.63194 q^{96} +0.216724 q^{97} -2.21212 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} + O(q^{10}) \) \( 14q - 2q^{2} + 14q^{3} + 14q^{4} - 10q^{5} - 2q^{6} - 6q^{8} + 14q^{9} - 3q^{10} - 16q^{11} + 14q^{12} - 21q^{13} - 10q^{15} + 22q^{16} - 12q^{17} - 2q^{18} - 2q^{19} - 40q^{20} + q^{22} - 7q^{23} - 6q^{24} + 22q^{25} - 2q^{26} + 14q^{27} - 16q^{29} - 3q^{30} - 8q^{31} - 19q^{32} - 16q^{33} - 33q^{34} + 14q^{36} + q^{37} - 32q^{38} - 21q^{39} + 13q^{40} - 14q^{41} + 14q^{43} - 36q^{44} - 10q^{45} - 12q^{46} - 12q^{47} + 22q^{48} - q^{50} - 12q^{51} - 60q^{52} - 20q^{53} - 2q^{54} + 11q^{55} - 2q^{57} + 21q^{58} - 25q^{59} - 40q^{60} - 26q^{61} + 33q^{62} + 42q^{64} - 8q^{65} + q^{66} - 22q^{67} - 15q^{68} - 7q^{69} - 36q^{71} - 6q^{72} - 31q^{73} - 65q^{74} + 22q^{75} + 2q^{76} - 2q^{78} + 12q^{79} - 112q^{80} + 14q^{81} + 2q^{82} - 20q^{83} + 40q^{85} - 9q^{86} - 16q^{87} - 54q^{88} - 39q^{89} - 3q^{90} + 63q^{92} - 8q^{93} - 14q^{94} - 55q^{95} - 19q^{96} - 18q^{97} - 16q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.442251 −0.312718 −0.156359 0.987700i \(-0.549976\pi\)
−0.156359 + 0.987700i \(0.549976\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.80441 −0.902207
\(5\) −4.29274 −1.91977 −0.959887 0.280387i \(-0.909537\pi\)
−0.959887 + 0.280387i \(0.909537\pi\)
\(6\) −0.442251 −0.180548
\(7\) 0 0
\(8\) 1.68250 0.594855
\(9\) 1.00000 0.333333
\(10\) 1.89847 0.600349
\(11\) −2.21212 −0.666979 −0.333489 0.942754i \(-0.608226\pi\)
−0.333489 + 0.942754i \(0.608226\pi\)
\(12\) −1.80441 −0.520890
\(13\) −3.11687 −0.864463 −0.432231 0.901763i \(-0.642274\pi\)
−0.432231 + 0.901763i \(0.642274\pi\)
\(14\) 0 0
\(15\) −4.29274 −1.10838
\(16\) 2.86474 0.716185
\(17\) −6.92396 −1.67931 −0.839654 0.543122i \(-0.817242\pi\)
−0.839654 + 0.543122i \(0.817242\pi\)
\(18\) −0.442251 −0.104239
\(19\) 7.72487 1.77221 0.886104 0.463487i \(-0.153402\pi\)
0.886104 + 0.463487i \(0.153402\pi\)
\(20\) 7.74589 1.73203
\(21\) 0 0
\(22\) 0.978311 0.208577
\(23\) 0.0381692 0.00795883 0.00397941 0.999992i \(-0.498733\pi\)
0.00397941 + 0.999992i \(0.498733\pi\)
\(24\) 1.68250 0.343440
\(25\) 13.4277 2.68553
\(26\) 1.37844 0.270334
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 2.66709 0.495266 0.247633 0.968854i \(-0.420347\pi\)
0.247633 + 0.968854i \(0.420347\pi\)
\(30\) 1.89847 0.346612
\(31\) 4.69959 0.844072 0.422036 0.906579i \(-0.361316\pi\)
0.422036 + 0.906579i \(0.361316\pi\)
\(32\) −4.63194 −0.818820
\(33\) −2.21212 −0.385080
\(34\) 3.06213 0.525151
\(35\) 0 0
\(36\) −1.80441 −0.300736
\(37\) −0.0300718 −0.00494377 −0.00247189 0.999997i \(-0.500787\pi\)
−0.00247189 + 0.999997i \(0.500787\pi\)
\(38\) −3.41633 −0.554202
\(39\) −3.11687 −0.499098
\(40\) −7.22256 −1.14199
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 11.0093 1.67890 0.839449 0.543438i \(-0.182878\pi\)
0.839449 + 0.543438i \(0.182878\pi\)
\(44\) 3.99158 0.601753
\(45\) −4.29274 −0.639925
\(46\) −0.0168804 −0.00248887
\(47\) −3.78108 −0.551527 −0.275763 0.961226i \(-0.588931\pi\)
−0.275763 + 0.961226i \(0.588931\pi\)
\(48\) 2.86474 0.413490
\(49\) 0 0
\(50\) −5.93839 −0.839815
\(51\) −6.92396 −0.969549
\(52\) 5.62412 0.779925
\(53\) −0.546137 −0.0750176 −0.0375088 0.999296i \(-0.511942\pi\)
−0.0375088 + 0.999296i \(0.511942\pi\)
\(54\) −0.442251 −0.0601827
\(55\) 9.49606 1.28045
\(56\) 0 0
\(57\) 7.72487 1.02318
\(58\) −1.17952 −0.154879
\(59\) −9.55909 −1.24449 −0.622243 0.782824i \(-0.713779\pi\)
−0.622243 + 0.782824i \(0.713779\pi\)
\(60\) 7.74589 0.999990
\(61\) 6.02077 0.770881 0.385441 0.922733i \(-0.374049\pi\)
0.385441 + 0.922733i \(0.374049\pi\)
\(62\) −2.07840 −0.263957
\(63\) 0 0
\(64\) −3.68100 −0.460125
\(65\) 13.3799 1.65957
\(66\) 0.978311 0.120422
\(67\) −8.97673 −1.09668 −0.548341 0.836255i \(-0.684741\pi\)
−0.548341 + 0.836255i \(0.684741\pi\)
\(68\) 12.4937 1.51508
\(69\) 0.0381692 0.00459503
\(70\) 0 0
\(71\) 15.6199 1.85374 0.926868 0.375386i \(-0.122490\pi\)
0.926868 + 0.375386i \(0.122490\pi\)
\(72\) 1.68250 0.198285
\(73\) −2.42299 −0.283590 −0.141795 0.989896i \(-0.545287\pi\)
−0.141795 + 0.989896i \(0.545287\pi\)
\(74\) 0.0132993 0.00154601
\(75\) 13.4277 1.55049
\(76\) −13.9389 −1.59890
\(77\) 0 0
\(78\) 1.37844 0.156077
\(79\) 2.16136 0.243172 0.121586 0.992581i \(-0.461202\pi\)
0.121586 + 0.992581i \(0.461202\pi\)
\(80\) −12.2976 −1.37491
\(81\) 1.00000 0.111111
\(82\) 0.442251 0.0488384
\(83\) 17.0488 1.87135 0.935675 0.352862i \(-0.114792\pi\)
0.935675 + 0.352862i \(0.114792\pi\)
\(84\) 0 0
\(85\) 29.7228 3.22389
\(86\) −4.86886 −0.525023
\(87\) 2.66709 0.285942
\(88\) −3.72190 −0.396756
\(89\) −8.69193 −0.921343 −0.460672 0.887571i \(-0.652391\pi\)
−0.460672 + 0.887571i \(0.652391\pi\)
\(90\) 1.89847 0.200116
\(91\) 0 0
\(92\) −0.0688730 −0.00718051
\(93\) 4.69959 0.487325
\(94\) 1.67218 0.172473
\(95\) −33.1609 −3.40224
\(96\) −4.63194 −0.472746
\(97\) 0.216724 0.0220050 0.0110025 0.999939i \(-0.496498\pi\)
0.0110025 + 0.999939i \(0.496498\pi\)
\(98\) 0 0
\(99\) −2.21212 −0.222326
\(100\) −24.2291 −2.42291
\(101\) −2.53326 −0.252069 −0.126034 0.992026i \(-0.540225\pi\)
−0.126034 + 0.992026i \(0.540225\pi\)
\(102\) 3.06213 0.303196
\(103\) −0.709634 −0.0699223 −0.0349612 0.999389i \(-0.511131\pi\)
−0.0349612 + 0.999389i \(0.511131\pi\)
\(104\) −5.24414 −0.514230
\(105\) 0 0
\(106\) 0.241529 0.0234594
\(107\) 6.42089 0.620731 0.310366 0.950617i \(-0.399549\pi\)
0.310366 + 0.950617i \(0.399549\pi\)
\(108\) −1.80441 −0.173630
\(109\) −2.52449 −0.241802 −0.120901 0.992665i \(-0.538578\pi\)
−0.120901 + 0.992665i \(0.538578\pi\)
\(110\) −4.19964 −0.400420
\(111\) −0.0300718 −0.00285429
\(112\) 0 0
\(113\) 1.71911 0.161721 0.0808603 0.996725i \(-0.474233\pi\)
0.0808603 + 0.996725i \(0.474233\pi\)
\(114\) −3.41633 −0.319969
\(115\) −0.163851 −0.0152791
\(116\) −4.81253 −0.446832
\(117\) −3.11687 −0.288154
\(118\) 4.22751 0.389174
\(119\) 0 0
\(120\) −7.22256 −0.659327
\(121\) −6.10653 −0.555139
\(122\) −2.66269 −0.241069
\(123\) −1.00000 −0.0901670
\(124\) −8.48001 −0.761527
\(125\) −36.1778 −3.23584
\(126\) 0 0
\(127\) −18.8770 −1.67506 −0.837529 0.546392i \(-0.816001\pi\)
−0.837529 + 0.546392i \(0.816001\pi\)
\(128\) 10.8918 0.962709
\(129\) 11.0093 0.969313
\(130\) −5.91727 −0.518979
\(131\) −9.69220 −0.846811 −0.423406 0.905940i \(-0.639166\pi\)
−0.423406 + 0.905940i \(0.639166\pi\)
\(132\) 3.99158 0.347422
\(133\) 0 0
\(134\) 3.96997 0.342953
\(135\) −4.29274 −0.369461
\(136\) −11.6496 −0.998945
\(137\) 6.05845 0.517608 0.258804 0.965930i \(-0.416672\pi\)
0.258804 + 0.965930i \(0.416672\pi\)
\(138\) −0.0168804 −0.00143695
\(139\) 1.67013 0.141658 0.0708291 0.997488i \(-0.477435\pi\)
0.0708291 + 0.997488i \(0.477435\pi\)
\(140\) 0 0
\(141\) −3.78108 −0.318424
\(142\) −6.90790 −0.579698
\(143\) 6.89487 0.576578
\(144\) 2.86474 0.238728
\(145\) −11.4491 −0.950798
\(146\) 1.07157 0.0886837
\(147\) 0 0
\(148\) 0.0542620 0.00446031
\(149\) 2.69542 0.220817 0.110409 0.993886i \(-0.464784\pi\)
0.110409 + 0.993886i \(0.464784\pi\)
\(150\) −5.93839 −0.484868
\(151\) −1.70580 −0.138816 −0.0694082 0.997588i \(-0.522111\pi\)
−0.0694082 + 0.997588i \(0.522111\pi\)
\(152\) 12.9971 1.05421
\(153\) −6.92396 −0.559769
\(154\) 0 0
\(155\) −20.1741 −1.62043
\(156\) 5.62412 0.450290
\(157\) −11.6850 −0.932562 −0.466281 0.884637i \(-0.654406\pi\)
−0.466281 + 0.884637i \(0.654406\pi\)
\(158\) −0.955865 −0.0760445
\(159\) −0.546137 −0.0433114
\(160\) 19.8837 1.57195
\(161\) 0 0
\(162\) −0.442251 −0.0347465
\(163\) −12.3332 −0.966009 −0.483005 0.875618i \(-0.660455\pi\)
−0.483005 + 0.875618i \(0.660455\pi\)
\(164\) 1.80441 0.140901
\(165\) 9.49606 0.739267
\(166\) −7.53985 −0.585206
\(167\) −6.35364 −0.491659 −0.245830 0.969313i \(-0.579060\pi\)
−0.245830 + 0.969313i \(0.579060\pi\)
\(168\) 0 0
\(169\) −3.28515 −0.252704
\(170\) −13.1449 −1.00817
\(171\) 7.72487 0.590736
\(172\) −19.8653 −1.51471
\(173\) 0.579038 0.0440235 0.0220117 0.999758i \(-0.492993\pi\)
0.0220117 + 0.999758i \(0.492993\pi\)
\(174\) −1.17952 −0.0894193
\(175\) 0 0
\(176\) −6.33714 −0.477680
\(177\) −9.55909 −0.718505
\(178\) 3.84401 0.288121
\(179\) 21.2907 1.59134 0.795672 0.605727i \(-0.207118\pi\)
0.795672 + 0.605727i \(0.207118\pi\)
\(180\) 7.74589 0.577345
\(181\) 21.3004 1.58325 0.791623 0.611010i \(-0.209237\pi\)
0.791623 + 0.611010i \(0.209237\pi\)
\(182\) 0 0
\(183\) 6.02077 0.445068
\(184\) 0.0642198 0.00473435
\(185\) 0.129091 0.00949093
\(186\) −2.07840 −0.152396
\(187\) 15.3166 1.12006
\(188\) 6.82263 0.497591
\(189\) 0 0
\(190\) 14.6654 1.06394
\(191\) −2.25947 −0.163490 −0.0817448 0.996653i \(-0.526049\pi\)
−0.0817448 + 0.996653i \(0.526049\pi\)
\(192\) −3.68100 −0.265653
\(193\) −19.8775 −1.43081 −0.715406 0.698709i \(-0.753758\pi\)
−0.715406 + 0.698709i \(0.753758\pi\)
\(194\) −0.0958464 −0.00688137
\(195\) 13.3799 0.958155
\(196\) 0 0
\(197\) −7.13650 −0.508455 −0.254227 0.967144i \(-0.581821\pi\)
−0.254227 + 0.967144i \(0.581821\pi\)
\(198\) 0.978311 0.0695255
\(199\) 13.9705 0.990343 0.495172 0.868795i \(-0.335105\pi\)
0.495172 + 0.868795i \(0.335105\pi\)
\(200\) 22.5921 1.59750
\(201\) −8.97673 −0.633170
\(202\) 1.12034 0.0788265
\(203\) 0 0
\(204\) 12.4937 0.874734
\(205\) 4.29274 0.299818
\(206\) 0.313836 0.0218660
\(207\) 0.0381692 0.00265294
\(208\) −8.92901 −0.619115
\(209\) −17.0883 −1.18202
\(210\) 0 0
\(211\) 23.3091 1.60466 0.802332 0.596878i \(-0.203592\pi\)
0.802332 + 0.596878i \(0.203592\pi\)
\(212\) 0.985457 0.0676814
\(213\) 15.6199 1.07026
\(214\) −2.83964 −0.194114
\(215\) −47.2600 −3.22311
\(216\) 1.68250 0.114480
\(217\) 0 0
\(218\) 1.11646 0.0756159
\(219\) −2.42299 −0.163731
\(220\) −17.1348 −1.15523
\(221\) 21.5811 1.45170
\(222\) 0.0132993 0.000892589 0
\(223\) −24.6795 −1.65266 −0.826330 0.563186i \(-0.809575\pi\)
−0.826330 + 0.563186i \(0.809575\pi\)
\(224\) 0 0
\(225\) 13.4277 0.895177
\(226\) −0.760279 −0.0505730
\(227\) −11.7407 −0.779259 −0.389630 0.920972i \(-0.627397\pi\)
−0.389630 + 0.920972i \(0.627397\pi\)
\(228\) −13.9389 −0.923124
\(229\) 15.4411 1.02037 0.510187 0.860063i \(-0.329576\pi\)
0.510187 + 0.860063i \(0.329576\pi\)
\(230\) 0.0724630 0.00477807
\(231\) 0 0
\(232\) 4.48739 0.294611
\(233\) −7.24116 −0.474384 −0.237192 0.971463i \(-0.576227\pi\)
−0.237192 + 0.971463i \(0.576227\pi\)
\(234\) 1.37844 0.0901112
\(235\) 16.2312 1.05881
\(236\) 17.2486 1.12279
\(237\) 2.16136 0.140396
\(238\) 0 0
\(239\) −13.7858 −0.891726 −0.445863 0.895101i \(-0.647103\pi\)
−0.445863 + 0.895101i \(0.647103\pi\)
\(240\) −12.2976 −0.793806
\(241\) −3.50900 −0.226035 −0.113017 0.993593i \(-0.536052\pi\)
−0.113017 + 0.993593i \(0.536052\pi\)
\(242\) 2.70062 0.173602
\(243\) 1.00000 0.0641500
\(244\) −10.8640 −0.695494
\(245\) 0 0
\(246\) 0.442251 0.0281969
\(247\) −24.0774 −1.53201
\(248\) 7.90709 0.502100
\(249\) 17.0488 1.08042
\(250\) 15.9997 1.01191
\(251\) −14.8746 −0.938876 −0.469438 0.882965i \(-0.655543\pi\)
−0.469438 + 0.882965i \(0.655543\pi\)
\(252\) 0 0
\(253\) −0.0844348 −0.00530837
\(254\) 8.34835 0.523822
\(255\) 29.7228 1.86131
\(256\) 2.54509 0.159068
\(257\) 21.7559 1.35709 0.678547 0.734557i \(-0.262610\pi\)
0.678547 + 0.734557i \(0.262610\pi\)
\(258\) −4.86886 −0.303122
\(259\) 0 0
\(260\) −24.1429 −1.49728
\(261\) 2.66709 0.165089
\(262\) 4.28638 0.264814
\(263\) 2.27801 0.140468 0.0702340 0.997531i \(-0.477625\pi\)
0.0702340 + 0.997531i \(0.477625\pi\)
\(264\) −3.72190 −0.229067
\(265\) 2.34442 0.144017
\(266\) 0 0
\(267\) −8.69193 −0.531938
\(268\) 16.1977 0.989435
\(269\) −2.03093 −0.123828 −0.0619141 0.998081i \(-0.519720\pi\)
−0.0619141 + 0.998081i \(0.519720\pi\)
\(270\) 1.89847 0.115537
\(271\) −15.8435 −0.962427 −0.481214 0.876603i \(-0.659804\pi\)
−0.481214 + 0.876603i \(0.659804\pi\)
\(272\) −19.8354 −1.20269
\(273\) 0 0
\(274\) −2.67935 −0.161866
\(275\) −29.7036 −1.79119
\(276\) −0.0688730 −0.00414567
\(277\) −3.50000 −0.210294 −0.105147 0.994457i \(-0.533531\pi\)
−0.105147 + 0.994457i \(0.533531\pi\)
\(278\) −0.738614 −0.0442992
\(279\) 4.69959 0.281357
\(280\) 0 0
\(281\) 26.7164 1.59377 0.796883 0.604134i \(-0.206481\pi\)
0.796883 + 0.604134i \(0.206481\pi\)
\(282\) 1.67218 0.0995771
\(283\) −15.6917 −0.932774 −0.466387 0.884581i \(-0.654445\pi\)
−0.466387 + 0.884581i \(0.654445\pi\)
\(284\) −28.1847 −1.67245
\(285\) −33.1609 −1.96428
\(286\) −3.04926 −0.180307
\(287\) 0 0
\(288\) −4.63194 −0.272940
\(289\) 30.9413 1.82007
\(290\) 5.06338 0.297332
\(291\) 0.216724 0.0127046
\(292\) 4.37208 0.255857
\(293\) −14.4844 −0.846189 −0.423095 0.906085i \(-0.639056\pi\)
−0.423095 + 0.906085i \(0.639056\pi\)
\(294\) 0 0
\(295\) 41.0347 2.38913
\(296\) −0.0505959 −0.00294083
\(297\) −2.21212 −0.128360
\(298\) −1.19205 −0.0690537
\(299\) −0.118968 −0.00688011
\(300\) −24.2291 −1.39887
\(301\) 0 0
\(302\) 0.754393 0.0434105
\(303\) −2.53326 −0.145532
\(304\) 22.1297 1.26923
\(305\) −25.8456 −1.47992
\(306\) 3.06213 0.175050
\(307\) 19.7492 1.12715 0.563573 0.826066i \(-0.309426\pi\)
0.563573 + 0.826066i \(0.309426\pi\)
\(308\) 0 0
\(309\) −0.709634 −0.0403697
\(310\) 8.92203 0.506737
\(311\) −18.1355 −1.02837 −0.514184 0.857680i \(-0.671905\pi\)
−0.514184 + 0.857680i \(0.671905\pi\)
\(312\) −5.24414 −0.296891
\(313\) 3.28237 0.185531 0.0927653 0.995688i \(-0.470429\pi\)
0.0927653 + 0.995688i \(0.470429\pi\)
\(314\) 5.16769 0.291629
\(315\) 0 0
\(316\) −3.90000 −0.219392
\(317\) −0.440700 −0.0247522 −0.0123761 0.999923i \(-0.503940\pi\)
−0.0123761 + 0.999923i \(0.503940\pi\)
\(318\) 0.241529 0.0135443
\(319\) −5.89991 −0.330332
\(320\) 15.8016 0.883336
\(321\) 6.42089 0.358379
\(322\) 0 0
\(323\) −53.4867 −2.97608
\(324\) −1.80441 −0.100245
\(325\) −41.8522 −2.32154
\(326\) 5.45436 0.302089
\(327\) −2.52449 −0.139604
\(328\) −1.68250 −0.0929008
\(329\) 0 0
\(330\) −4.19964 −0.231183
\(331\) −3.26805 −0.179628 −0.0898141 0.995959i \(-0.528627\pi\)
−0.0898141 + 0.995959i \(0.528627\pi\)
\(332\) −30.7631 −1.68835
\(333\) −0.0300718 −0.00164792
\(334\) 2.80990 0.153751
\(335\) 38.5348 2.10538
\(336\) 0 0
\(337\) −18.8129 −1.02481 −0.512403 0.858745i \(-0.671244\pi\)
−0.512403 + 0.858745i \(0.671244\pi\)
\(338\) 1.45286 0.0790252
\(339\) 1.71911 0.0933694
\(340\) −53.6323 −2.90862
\(341\) −10.3961 −0.562978
\(342\) −3.41633 −0.184734
\(343\) 0 0
\(344\) 18.5232 0.998702
\(345\) −0.163851 −0.00882142
\(346\) −0.256080 −0.0137669
\(347\) −24.8798 −1.33562 −0.667809 0.744332i \(-0.732768\pi\)
−0.667809 + 0.744332i \(0.732768\pi\)
\(348\) −4.81253 −0.257979
\(349\) −34.7651 −1.86094 −0.930468 0.366374i \(-0.880599\pi\)
−0.930468 + 0.366374i \(0.880599\pi\)
\(350\) 0 0
\(351\) −3.11687 −0.166366
\(352\) 10.2464 0.546135
\(353\) 16.6295 0.885098 0.442549 0.896744i \(-0.354074\pi\)
0.442549 + 0.896744i \(0.354074\pi\)
\(354\) 4.22751 0.224690
\(355\) −67.0521 −3.55876
\(356\) 15.6839 0.831242
\(357\) 0 0
\(358\) −9.41584 −0.497643
\(359\) −25.2772 −1.33408 −0.667041 0.745021i \(-0.732439\pi\)
−0.667041 + 0.745021i \(0.732439\pi\)
\(360\) −7.22256 −0.380663
\(361\) 40.6736 2.14072
\(362\) −9.42011 −0.495110
\(363\) −6.10653 −0.320510
\(364\) 0 0
\(365\) 10.4013 0.544428
\(366\) −2.66269 −0.139181
\(367\) −33.2183 −1.73398 −0.866992 0.498322i \(-0.833950\pi\)
−0.866992 + 0.498322i \(0.833950\pi\)
\(368\) 0.109345 0.00569999
\(369\) −1.00000 −0.0520579
\(370\) −0.0570904 −0.00296799
\(371\) 0 0
\(372\) −8.48001 −0.439668
\(373\) 25.9809 1.34524 0.672619 0.739989i \(-0.265169\pi\)
0.672619 + 0.739989i \(0.265169\pi\)
\(374\) −6.77379 −0.350264
\(375\) −36.1778 −1.86821
\(376\) −6.36168 −0.328079
\(377\) −8.31295 −0.428139
\(378\) 0 0
\(379\) 10.2601 0.527028 0.263514 0.964656i \(-0.415118\pi\)
0.263514 + 0.964656i \(0.415118\pi\)
\(380\) 59.8360 3.06952
\(381\) −18.8770 −0.967096
\(382\) 0.999253 0.0511262
\(383\) 2.59188 0.132439 0.0662194 0.997805i \(-0.478906\pi\)
0.0662194 + 0.997805i \(0.478906\pi\)
\(384\) 10.8918 0.555820
\(385\) 0 0
\(386\) 8.79083 0.447441
\(387\) 11.0093 0.559633
\(388\) −0.391060 −0.0198531
\(389\) −8.65407 −0.438779 −0.219390 0.975637i \(-0.570407\pi\)
−0.219390 + 0.975637i \(0.570407\pi\)
\(390\) −5.91727 −0.299633
\(391\) −0.264282 −0.0133653
\(392\) 0 0
\(393\) −9.69220 −0.488907
\(394\) 3.15612 0.159003
\(395\) −9.27818 −0.466836
\(396\) 3.99158 0.200584
\(397\) −30.0428 −1.50780 −0.753902 0.656987i \(-0.771830\pi\)
−0.753902 + 0.656987i \(0.771830\pi\)
\(398\) −6.17847 −0.309699
\(399\) 0 0
\(400\) 38.4667 1.92334
\(401\) 12.0942 0.603955 0.301978 0.953315i \(-0.402353\pi\)
0.301978 + 0.953315i \(0.402353\pi\)
\(402\) 3.96997 0.198004
\(403\) −14.6480 −0.729669
\(404\) 4.57105 0.227418
\(405\) −4.29274 −0.213308
\(406\) 0 0
\(407\) 0.0665224 0.00329739
\(408\) −11.6496 −0.576741
\(409\) 13.5140 0.668222 0.334111 0.942534i \(-0.391564\pi\)
0.334111 + 0.942534i \(0.391564\pi\)
\(410\) −1.89847 −0.0937587
\(411\) 6.05845 0.298841
\(412\) 1.28047 0.0630844
\(413\) 0 0
\(414\) −0.0168804 −0.000829624 0
\(415\) −73.1862 −3.59257
\(416\) 14.4371 0.707839
\(417\) 1.67013 0.0817864
\(418\) 7.55733 0.369641
\(419\) −32.1763 −1.57191 −0.785957 0.618281i \(-0.787829\pi\)
−0.785957 + 0.618281i \(0.787829\pi\)
\(420\) 0 0
\(421\) −32.2673 −1.57261 −0.786307 0.617836i \(-0.788010\pi\)
−0.786307 + 0.617836i \(0.788010\pi\)
\(422\) −10.3085 −0.501808
\(423\) −3.78108 −0.183842
\(424\) −0.918877 −0.0446246
\(425\) −92.9726 −4.50983
\(426\) −6.90790 −0.334689
\(427\) 0 0
\(428\) −11.5859 −0.560028
\(429\) 6.89487 0.332888
\(430\) 20.9008 1.00792
\(431\) 10.4482 0.503271 0.251635 0.967822i \(-0.419032\pi\)
0.251635 + 0.967822i \(0.419032\pi\)
\(432\) 2.86474 0.137830
\(433\) −3.79123 −0.182195 −0.0910975 0.995842i \(-0.529037\pi\)
−0.0910975 + 0.995842i \(0.529037\pi\)
\(434\) 0 0
\(435\) −11.4491 −0.548943
\(436\) 4.55522 0.218155
\(437\) 0.294852 0.0141047
\(438\) 1.07157 0.0512016
\(439\) 4.49268 0.214424 0.107212 0.994236i \(-0.465808\pi\)
0.107212 + 0.994236i \(0.465808\pi\)
\(440\) 15.9772 0.761682
\(441\) 0 0
\(442\) −9.54424 −0.453973
\(443\) −8.19908 −0.389550 −0.194775 0.980848i \(-0.562398\pi\)
−0.194775 + 0.980848i \(0.562398\pi\)
\(444\) 0.0542620 0.00257516
\(445\) 37.3123 1.76877
\(446\) 10.9145 0.516817
\(447\) 2.69542 0.127489
\(448\) 0 0
\(449\) 32.0190 1.51107 0.755535 0.655109i \(-0.227377\pi\)
0.755535 + 0.655109i \(0.227377\pi\)
\(450\) −5.93839 −0.279938
\(451\) 2.21212 0.104165
\(452\) −3.10199 −0.145906
\(453\) −1.70580 −0.0801457
\(454\) 5.19234 0.243689
\(455\) 0 0
\(456\) 12.9971 0.608647
\(457\) 3.92379 0.183547 0.0917736 0.995780i \(-0.470746\pi\)
0.0917736 + 0.995780i \(0.470746\pi\)
\(458\) −6.82882 −0.319090
\(459\) −6.92396 −0.323183
\(460\) 0.295654 0.0137850
\(461\) −26.4099 −1.23003 −0.615016 0.788514i \(-0.710851\pi\)
−0.615016 + 0.788514i \(0.710851\pi\)
\(462\) 0 0
\(463\) 5.27988 0.245377 0.122688 0.992445i \(-0.460848\pi\)
0.122688 + 0.992445i \(0.460848\pi\)
\(464\) 7.64051 0.354702
\(465\) −20.1741 −0.935554
\(466\) 3.20241 0.148349
\(467\) −20.1035 −0.930280 −0.465140 0.885237i \(-0.653996\pi\)
−0.465140 + 0.885237i \(0.653996\pi\)
\(468\) 5.62412 0.259975
\(469\) 0 0
\(470\) −7.17826 −0.331108
\(471\) −11.6850 −0.538415
\(472\) −16.0832 −0.740290
\(473\) −24.3538 −1.11979
\(474\) −0.955865 −0.0439043
\(475\) 103.727 4.75932
\(476\) 0 0
\(477\) −0.546137 −0.0250059
\(478\) 6.09676 0.278859
\(479\) 23.4552 1.07170 0.535848 0.844315i \(-0.319992\pi\)
0.535848 + 0.844315i \(0.319992\pi\)
\(480\) 19.8837 0.907565
\(481\) 0.0937297 0.00427371
\(482\) 1.55186 0.0706852
\(483\) 0 0
\(484\) 11.0187 0.500851
\(485\) −0.930341 −0.0422446
\(486\) −0.442251 −0.0200609
\(487\) 39.6797 1.79806 0.899030 0.437886i \(-0.144273\pi\)
0.899030 + 0.437886i \(0.144273\pi\)
\(488\) 10.1300 0.458563
\(489\) −12.3332 −0.557726
\(490\) 0 0
\(491\) 42.0432 1.89738 0.948691 0.316204i \(-0.102408\pi\)
0.948691 + 0.316204i \(0.102408\pi\)
\(492\) 1.80441 0.0813493
\(493\) −18.4668 −0.831703
\(494\) 10.6482 0.479087
\(495\) 9.49606 0.426816
\(496\) 13.4631 0.604511
\(497\) 0 0
\(498\) −7.53985 −0.337869
\(499\) −5.70934 −0.255585 −0.127793 0.991801i \(-0.540789\pi\)
−0.127793 + 0.991801i \(0.540789\pi\)
\(500\) 65.2797 2.91940
\(501\) −6.35364 −0.283860
\(502\) 6.57830 0.293604
\(503\) −5.71736 −0.254924 −0.127462 0.991843i \(-0.540683\pi\)
−0.127462 + 0.991843i \(0.540683\pi\)
\(504\) 0 0
\(505\) 10.8746 0.483915
\(506\) 0.0373413 0.00166002
\(507\) −3.28515 −0.145899
\(508\) 34.0618 1.51125
\(509\) −35.4392 −1.57081 −0.785407 0.618980i \(-0.787546\pi\)
−0.785407 + 0.618980i \(0.787546\pi\)
\(510\) −13.1449 −0.582067
\(511\) 0 0
\(512\) −22.9092 −1.01245
\(513\) 7.72487 0.341061
\(514\) −9.62155 −0.424388
\(515\) 3.04628 0.134235
\(516\) −19.8653 −0.874521
\(517\) 8.36419 0.367857
\(518\) 0 0
\(519\) 0.579038 0.0254170
\(520\) 22.5118 0.987206
\(521\) 4.21069 0.184474 0.0922368 0.995737i \(-0.470598\pi\)
0.0922368 + 0.995737i \(0.470598\pi\)
\(522\) −1.17952 −0.0516262
\(523\) −12.4112 −0.542703 −0.271352 0.962480i \(-0.587471\pi\)
−0.271352 + 0.962480i \(0.587471\pi\)
\(524\) 17.4887 0.763999
\(525\) 0 0
\(526\) −1.00745 −0.0439269
\(527\) −32.5398 −1.41746
\(528\) −6.33714 −0.275789
\(529\) −22.9985 −0.999937
\(530\) −1.03682 −0.0450367
\(531\) −9.55909 −0.414829
\(532\) 0 0
\(533\) 3.11687 0.135006
\(534\) 3.84401 0.166347
\(535\) −27.5632 −1.19166
\(536\) −15.1034 −0.652367
\(537\) 21.2907 0.918763
\(538\) 0.898182 0.0387234
\(539\) 0 0
\(540\) 7.74589 0.333330
\(541\) 29.7330 1.27832 0.639162 0.769072i \(-0.279282\pi\)
0.639162 + 0.769072i \(0.279282\pi\)
\(542\) 7.00682 0.300969
\(543\) 21.3004 0.914087
\(544\) 32.0714 1.37505
\(545\) 10.8370 0.464205
\(546\) 0 0
\(547\) −1.76774 −0.0755829 −0.0377915 0.999286i \(-0.512032\pi\)
−0.0377915 + 0.999286i \(0.512032\pi\)
\(548\) −10.9320 −0.466990
\(549\) 6.02077 0.256960
\(550\) 13.1364 0.560139
\(551\) 20.6029 0.877713
\(552\) 0.0642198 0.00273338
\(553\) 0 0
\(554\) 1.54788 0.0657630
\(555\) 0.129091 0.00547959
\(556\) −3.01360 −0.127805
\(557\) −37.5462 −1.59088 −0.795442 0.606029i \(-0.792761\pi\)
−0.795442 + 0.606029i \(0.792761\pi\)
\(558\) −2.07840 −0.0879856
\(559\) −34.3144 −1.45135
\(560\) 0 0
\(561\) 15.3166 0.646668
\(562\) −11.8153 −0.498400
\(563\) 7.50392 0.316253 0.158126 0.987419i \(-0.449455\pi\)
0.158126 + 0.987419i \(0.449455\pi\)
\(564\) 6.82263 0.287284
\(565\) −7.37972 −0.310467
\(566\) 6.93966 0.291696
\(567\) 0 0
\(568\) 26.2805 1.10271
\(569\) −2.92823 −0.122758 −0.0613790 0.998115i \(-0.519550\pi\)
−0.0613790 + 0.998115i \(0.519550\pi\)
\(570\) 14.6654 0.614267
\(571\) 14.3396 0.600095 0.300047 0.953924i \(-0.402997\pi\)
0.300047 + 0.953924i \(0.402997\pi\)
\(572\) −12.4412 −0.520193
\(573\) −2.25947 −0.0943908
\(574\) 0 0
\(575\) 0.512523 0.0213737
\(576\) −3.68100 −0.153375
\(577\) 15.3261 0.638036 0.319018 0.947749i \(-0.396647\pi\)
0.319018 + 0.947749i \(0.396647\pi\)
\(578\) −13.6838 −0.569171
\(579\) −19.8775 −0.826080
\(580\) 20.6590 0.857817
\(581\) 0 0
\(582\) −0.0958464 −0.00397296
\(583\) 1.20812 0.0500352
\(584\) −4.07670 −0.168695
\(585\) 13.3799 0.553191
\(586\) 6.40575 0.264619
\(587\) 18.1300 0.748306 0.374153 0.927367i \(-0.377934\pi\)
0.374153 + 0.927367i \(0.377934\pi\)
\(588\) 0 0
\(589\) 36.3037 1.49587
\(590\) −18.1476 −0.747126
\(591\) −7.13650 −0.293556
\(592\) −0.0861479 −0.00354066
\(593\) 14.6521 0.601691 0.300845 0.953673i \(-0.402731\pi\)
0.300845 + 0.953673i \(0.402731\pi\)
\(594\) 0.978311 0.0401406
\(595\) 0 0
\(596\) −4.86366 −0.199223
\(597\) 13.9705 0.571775
\(598\) 0.0526138 0.00215154
\(599\) 4.58262 0.187241 0.0936205 0.995608i \(-0.470156\pi\)
0.0936205 + 0.995608i \(0.470156\pi\)
\(600\) 22.5921 0.922319
\(601\) −0.579777 −0.0236496 −0.0118248 0.999930i \(-0.503764\pi\)
−0.0118248 + 0.999930i \(0.503764\pi\)
\(602\) 0 0
\(603\) −8.97673 −0.365561
\(604\) 3.07798 0.125241
\(605\) 26.2138 1.06574
\(606\) 1.12034 0.0455105
\(607\) −11.2678 −0.457345 −0.228672 0.973503i \(-0.573438\pi\)
−0.228672 + 0.973503i \(0.573438\pi\)
\(608\) −35.7812 −1.45112
\(609\) 0 0
\(610\) 11.4303 0.462798
\(611\) 11.7851 0.476774
\(612\) 12.4937 0.505028
\(613\) 41.6317 1.68149 0.840745 0.541431i \(-0.182117\pi\)
0.840745 + 0.541431i \(0.182117\pi\)
\(614\) −8.73410 −0.352479
\(615\) 4.29274 0.173100
\(616\) 0 0
\(617\) −14.5914 −0.587427 −0.293713 0.955894i \(-0.594891\pi\)
−0.293713 + 0.955894i \(0.594891\pi\)
\(618\) 0.313836 0.0126243
\(619\) −20.3756 −0.818965 −0.409482 0.912318i \(-0.634291\pi\)
−0.409482 + 0.912318i \(0.634291\pi\)
\(620\) 36.4025 1.46196
\(621\) 0.0381692 0.00153168
\(622\) 8.02043 0.321590
\(623\) 0 0
\(624\) −8.92901 −0.357446
\(625\) 88.1637 3.52655
\(626\) −1.45163 −0.0580189
\(627\) −17.0883 −0.682442
\(628\) 21.0845 0.841364
\(629\) 0.208216 0.00830212
\(630\) 0 0
\(631\) 9.23277 0.367551 0.183775 0.982968i \(-0.441168\pi\)
0.183775 + 0.982968i \(0.441168\pi\)
\(632\) 3.63651 0.144652
\(633\) 23.3091 0.926453
\(634\) 0.194900 0.00774047
\(635\) 81.0339 3.21573
\(636\) 0.985457 0.0390759
\(637\) 0 0
\(638\) 2.60924 0.103301
\(639\) 15.6199 0.617912
\(640\) −46.7558 −1.84818
\(641\) 5.12329 0.202358 0.101179 0.994868i \(-0.467739\pi\)
0.101179 + 0.994868i \(0.467739\pi\)
\(642\) −2.83964 −0.112072
\(643\) −15.5518 −0.613302 −0.306651 0.951822i \(-0.599208\pi\)
−0.306651 + 0.951822i \(0.599208\pi\)
\(644\) 0 0
\(645\) −47.2600 −1.86086
\(646\) 23.6545 0.930675
\(647\) −20.5466 −0.807768 −0.403884 0.914810i \(-0.632340\pi\)
−0.403884 + 0.914810i \(0.632340\pi\)
\(648\) 1.68250 0.0660950
\(649\) 21.1458 0.830046
\(650\) 18.5092 0.725989
\(651\) 0 0
\(652\) 22.2542 0.871540
\(653\) 22.6686 0.887091 0.443546 0.896252i \(-0.353720\pi\)
0.443546 + 0.896252i \(0.353720\pi\)
\(654\) 1.11646 0.0436569
\(655\) 41.6061 1.62569
\(656\) −2.86474 −0.111849
\(657\) −2.42299 −0.0945299
\(658\) 0 0
\(659\) −38.2328 −1.48934 −0.744669 0.667434i \(-0.767393\pi\)
−0.744669 + 0.667434i \(0.767393\pi\)
\(660\) −17.1348 −0.666972
\(661\) −25.8102 −1.00390 −0.501951 0.864896i \(-0.667384\pi\)
−0.501951 + 0.864896i \(0.667384\pi\)
\(662\) 1.44530 0.0561731
\(663\) 21.5811 0.838139
\(664\) 28.6847 1.11318
\(665\) 0 0
\(666\) 0.0132993 0.000515336 0
\(667\) 0.101801 0.00394173
\(668\) 11.4646 0.443579
\(669\) −24.6795 −0.954164
\(670\) −17.0421 −0.658392
\(671\) −13.3187 −0.514161
\(672\) 0 0
\(673\) −7.21950 −0.278291 −0.139146 0.990272i \(-0.544436\pi\)
−0.139146 + 0.990272i \(0.544436\pi\)
\(674\) 8.32003 0.320476
\(675\) 13.4277 0.516831
\(676\) 5.92777 0.227991
\(677\) −11.7898 −0.453119 −0.226560 0.973997i \(-0.572748\pi\)
−0.226560 + 0.973997i \(0.572748\pi\)
\(678\) −0.760279 −0.0291983
\(679\) 0 0
\(680\) 50.0088 1.91775
\(681\) −11.7407 −0.449906
\(682\) 4.59766 0.176054
\(683\) 27.1434 1.03861 0.519307 0.854588i \(-0.326190\pi\)
0.519307 + 0.854588i \(0.326190\pi\)
\(684\) −13.9389 −0.532966
\(685\) −26.0074 −0.993691
\(686\) 0 0
\(687\) 15.4411 0.589114
\(688\) 31.5387 1.20240
\(689\) 1.70223 0.0648500
\(690\) 0.0724630 0.00275862
\(691\) 2.26956 0.0863380 0.0431690 0.999068i \(-0.486255\pi\)
0.0431690 + 0.999068i \(0.486255\pi\)
\(692\) −1.04482 −0.0397183
\(693\) 0 0
\(694\) 11.0031 0.417673
\(695\) −7.16943 −0.271952
\(696\) 4.48739 0.170094
\(697\) 6.92396 0.262264
\(698\) 15.3749 0.581949
\(699\) −7.24116 −0.273886
\(700\) 0 0
\(701\) 31.9632 1.20723 0.603616 0.797275i \(-0.293726\pi\)
0.603616 + 0.797275i \(0.293726\pi\)
\(702\) 1.37844 0.0520257
\(703\) −0.232301 −0.00876139
\(704\) 8.14281 0.306894
\(705\) 16.2312 0.611302
\(706\) −7.35440 −0.276786
\(707\) 0 0
\(708\) 17.2486 0.648240
\(709\) −17.4623 −0.655812 −0.327906 0.944710i \(-0.606343\pi\)
−0.327906 + 0.944710i \(0.606343\pi\)
\(710\) 29.6538 1.11289
\(711\) 2.16136 0.0810575
\(712\) −14.6242 −0.548066
\(713\) 0.179380 0.00671782
\(714\) 0 0
\(715\) −29.5979 −1.10690
\(716\) −38.4173 −1.43572
\(717\) −13.7858 −0.514838
\(718\) 11.1789 0.417192
\(719\) 15.8378 0.590649 0.295325 0.955397i \(-0.404572\pi\)
0.295325 + 0.955397i \(0.404572\pi\)
\(720\) −12.2976 −0.458304
\(721\) 0 0
\(722\) −17.9879 −0.669442
\(723\) −3.50900 −0.130501
\(724\) −38.4347 −1.42842
\(725\) 35.8127 1.33005
\(726\) 2.70062 0.100229
\(727\) 14.3866 0.533568 0.266784 0.963756i \(-0.414039\pi\)
0.266784 + 0.963756i \(0.414039\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −4.59998 −0.170253
\(731\) −76.2278 −2.81939
\(732\) −10.8640 −0.401544
\(733\) −43.3409 −1.60083 −0.800416 0.599444i \(-0.795388\pi\)
−0.800416 + 0.599444i \(0.795388\pi\)
\(734\) 14.6908 0.542249
\(735\) 0 0
\(736\) −0.176798 −0.00651684
\(737\) 19.8576 0.731464
\(738\) 0.442251 0.0162795
\(739\) 7.73562 0.284560 0.142280 0.989826i \(-0.454557\pi\)
0.142280 + 0.989826i \(0.454557\pi\)
\(740\) −0.232933 −0.00856278
\(741\) −24.0774 −0.884505
\(742\) 0 0
\(743\) 29.4859 1.08173 0.540867 0.841108i \(-0.318096\pi\)
0.540867 + 0.841108i \(0.318096\pi\)
\(744\) 7.90709 0.289888
\(745\) −11.5708 −0.423920
\(746\) −11.4901 −0.420681
\(747\) 17.0488 0.623783
\(748\) −27.6375 −1.01053
\(749\) 0 0
\(750\) 15.9997 0.584225
\(751\) −16.3584 −0.596926 −0.298463 0.954421i \(-0.596474\pi\)
−0.298463 + 0.954421i \(0.596474\pi\)
\(752\) −10.8318 −0.394995
\(753\) −14.8746 −0.542060
\(754\) 3.67641 0.133887
\(755\) 7.32259 0.266496
\(756\) 0 0
\(757\) −47.1225 −1.71270 −0.856349 0.516397i \(-0.827273\pi\)
−0.856349 + 0.516397i \(0.827273\pi\)
\(758\) −4.53755 −0.164811
\(759\) −0.0844348 −0.00306479
\(760\) −55.7934 −2.02384
\(761\) 39.2835 1.42403 0.712013 0.702166i \(-0.247784\pi\)
0.712013 + 0.702166i \(0.247784\pi\)
\(762\) 8.34835 0.302429
\(763\) 0 0
\(764\) 4.07702 0.147502
\(765\) 29.7228 1.07463
\(766\) −1.14626 −0.0414161
\(767\) 29.7944 1.07581
\(768\) 2.54509 0.0918380
\(769\) 25.4482 0.917687 0.458843 0.888517i \(-0.348264\pi\)
0.458843 + 0.888517i \(0.348264\pi\)
\(770\) 0 0
\(771\) 21.7559 0.783519
\(772\) 35.8672 1.29089
\(773\) −1.77505 −0.0638440 −0.0319220 0.999490i \(-0.510163\pi\)
−0.0319220 + 0.999490i \(0.510163\pi\)
\(774\) −4.86886 −0.175008
\(775\) 63.1045 2.26678
\(776\) 0.364639 0.0130898
\(777\) 0 0
\(778\) 3.82727 0.137214
\(779\) −7.72487 −0.276772
\(780\) −24.1429 −0.864454
\(781\) −34.5530 −1.23640
\(782\) 0.116879 0.00417958
\(783\) 2.66709 0.0953139
\(784\) 0 0
\(785\) 50.1606 1.79031
\(786\) 4.28638 0.152890
\(787\) −48.7760 −1.73868 −0.869338 0.494218i \(-0.835455\pi\)
−0.869338 + 0.494218i \(0.835455\pi\)
\(788\) 12.8772 0.458731
\(789\) 2.27801 0.0810992
\(790\) 4.10328 0.145988
\(791\) 0 0
\(792\) −3.72190 −0.132252
\(793\) −18.7659 −0.666398
\(794\) 13.2864 0.471518
\(795\) 2.34442 0.0831482
\(796\) −25.2086 −0.893495
\(797\) −12.9486 −0.458665 −0.229332 0.973348i \(-0.573654\pi\)
−0.229332 + 0.973348i \(0.573654\pi\)
\(798\) 0 0
\(799\) 26.1800 0.926183
\(800\) −62.1961 −2.19897
\(801\) −8.69193 −0.307114
\(802\) −5.34866 −0.188868
\(803\) 5.35994 0.189148
\(804\) 16.1977 0.571251
\(805\) 0 0
\(806\) 6.47809 0.228181
\(807\) −2.03093 −0.0714923
\(808\) −4.26222 −0.149944
\(809\) −34.2717 −1.20493 −0.602464 0.798146i \(-0.705814\pi\)
−0.602464 + 0.798146i \(0.705814\pi\)
\(810\) 1.89847 0.0667054
\(811\) −39.7411 −1.39550 −0.697749 0.716342i \(-0.745815\pi\)
−0.697749 + 0.716342i \(0.745815\pi\)
\(812\) 0 0
\(813\) −15.8435 −0.555657
\(814\) −0.0294196 −0.00103116
\(815\) 52.9432 1.85452
\(816\) −19.8354 −0.694376
\(817\) 85.0452 2.97536
\(818\) −5.97656 −0.208965
\(819\) 0 0
\(820\) −7.74589 −0.270498
\(821\) −42.6305 −1.48782 −0.743908 0.668282i \(-0.767030\pi\)
−0.743908 + 0.668282i \(0.767030\pi\)
\(822\) −2.67935 −0.0934532
\(823\) 11.8760 0.413973 0.206986 0.978344i \(-0.433634\pi\)
0.206986 + 0.978344i \(0.433634\pi\)
\(824\) −1.19396 −0.0415937
\(825\) −29.7036 −1.03415
\(826\) 0 0
\(827\) −18.5702 −0.645751 −0.322875 0.946442i \(-0.604649\pi\)
−0.322875 + 0.946442i \(0.604649\pi\)
\(828\) −0.0688730 −0.00239350
\(829\) 45.5475 1.58193 0.790966 0.611860i \(-0.209579\pi\)
0.790966 + 0.611860i \(0.209579\pi\)
\(830\) 32.3667 1.12346
\(831\) −3.50000 −0.121414
\(832\) 11.4732 0.397761
\(833\) 0 0
\(834\) −0.738614 −0.0255761
\(835\) 27.2745 0.943875
\(836\) 30.8344 1.06643
\(837\) 4.69959 0.162442
\(838\) 14.2300 0.491566
\(839\) 0.520222 0.0179601 0.00898004 0.999960i \(-0.497142\pi\)
0.00898004 + 0.999960i \(0.497142\pi\)
\(840\) 0 0
\(841\) −21.8866 −0.754712
\(842\) 14.2703 0.491785
\(843\) 26.7164 0.920161
\(844\) −42.0593 −1.44774
\(845\) 14.1023 0.485134
\(846\) 1.67218 0.0574909
\(847\) 0 0
\(848\) −1.56454 −0.0537265
\(849\) −15.6917 −0.538537
\(850\) 41.1172 1.41031
\(851\) −0.00114782 −3.93466e−5 0
\(852\) −28.1847 −0.965592
\(853\) 26.2375 0.898356 0.449178 0.893442i \(-0.351717\pi\)
0.449178 + 0.893442i \(0.351717\pi\)
\(854\) 0 0
\(855\) −33.1609 −1.13408
\(856\) 10.8032 0.369245
\(857\) 37.6320 1.28548 0.642742 0.766083i \(-0.277797\pi\)
0.642742 + 0.766083i \(0.277797\pi\)
\(858\) −3.04926 −0.104100
\(859\) 21.6450 0.738518 0.369259 0.929327i \(-0.379612\pi\)
0.369259 + 0.929327i \(0.379612\pi\)
\(860\) 85.2766 2.90791
\(861\) 0 0
\(862\) −4.62071 −0.157382
\(863\) −33.1370 −1.12800 −0.563998 0.825776i \(-0.690737\pi\)
−0.563998 + 0.825776i \(0.690737\pi\)
\(864\) −4.63194 −0.157582
\(865\) −2.48566 −0.0845151
\(866\) 1.67668 0.0569757
\(867\) 30.9413 1.05082
\(868\) 0 0
\(869\) −4.78119 −0.162191
\(870\) 5.06338 0.171665
\(871\) 27.9793 0.948041
\(872\) −4.24746 −0.143837
\(873\) 0.216724 0.00733500
\(874\) −0.130399 −0.00441080
\(875\) 0 0
\(876\) 4.37208 0.147719
\(877\) 2.91954 0.0985857 0.0492929 0.998784i \(-0.484303\pi\)
0.0492929 + 0.998784i \(0.484303\pi\)
\(878\) −1.98689 −0.0670544
\(879\) −14.4844 −0.488548
\(880\) 27.2037 0.917038
\(881\) 24.7028 0.832258 0.416129 0.909306i \(-0.363387\pi\)
0.416129 + 0.909306i \(0.363387\pi\)
\(882\) 0 0
\(883\) 6.69015 0.225141 0.112571 0.993644i \(-0.464092\pi\)
0.112571 + 0.993644i \(0.464092\pi\)
\(884\) −38.9412 −1.30973
\(885\) 41.0347 1.37937
\(886\) 3.62605 0.121819
\(887\) 9.40760 0.315876 0.157938 0.987449i \(-0.449515\pi\)
0.157938 + 0.987449i \(0.449515\pi\)
\(888\) −0.0505959 −0.00169789
\(889\) 0 0
\(890\) −16.5014 −0.553127
\(891\) −2.21212 −0.0741088
\(892\) 44.5320 1.49104
\(893\) −29.2083 −0.977419
\(894\) −1.19205 −0.0398682
\(895\) −91.3957 −3.05502
\(896\) 0 0
\(897\) −0.118968 −0.00397223
\(898\) −14.1604 −0.472539
\(899\) 12.5342 0.418040
\(900\) −24.2291 −0.807635
\(901\) 3.78143 0.125978
\(902\) −0.978311 −0.0325742
\(903\) 0 0
\(904\) 2.89242 0.0962004
\(905\) −91.4371 −3.03947
\(906\) 0.754393 0.0250630
\(907\) 21.7567 0.722421 0.361210 0.932484i \(-0.382364\pi\)
0.361210 + 0.932484i \(0.382364\pi\)
\(908\) 21.1851 0.703053
\(909\) −2.53326 −0.0840229
\(910\) 0 0
\(911\) −38.9801 −1.29147 −0.645734 0.763562i \(-0.723449\pi\)
−0.645734 + 0.763562i \(0.723449\pi\)
\(912\) 22.1297 0.732789
\(913\) −37.7140 −1.24815
\(914\) −1.73530 −0.0573986
\(915\) −25.8456 −0.854431
\(916\) −27.8621 −0.920589
\(917\) 0 0
\(918\) 3.06213 0.101065
\(919\) −57.3909 −1.89315 −0.946576 0.322480i \(-0.895483\pi\)
−0.946576 + 0.322480i \(0.895483\pi\)
\(920\) −0.275679 −0.00908888
\(921\) 19.7492 0.650758
\(922\) 11.6798 0.384654
\(923\) −48.6850 −1.60249
\(924\) 0 0
\(925\) −0.403794 −0.0132767
\(926\) −2.33503 −0.0767338
\(927\) −0.709634 −0.0233074
\(928\) −12.3538 −0.405533
\(929\) 35.3944 1.16125 0.580627 0.814170i \(-0.302808\pi\)
0.580627 + 0.814170i \(0.302808\pi\)
\(930\) 8.92203 0.292565
\(931\) 0 0
\(932\) 13.0661 0.427993
\(933\) −18.1355 −0.593729
\(934\) 8.89079 0.290916
\(935\) −65.7504 −2.15027
\(936\) −5.24414 −0.171410
\(937\) 33.9294 1.10842 0.554212 0.832376i \(-0.313020\pi\)
0.554212 + 0.832376i \(0.313020\pi\)
\(938\) 0 0
\(939\) 3.28237 0.107116
\(940\) −29.2878 −0.955263
\(941\) 18.0053 0.586955 0.293477 0.955966i \(-0.405187\pi\)
0.293477 + 0.955966i \(0.405187\pi\)
\(942\) 5.16769 0.168372
\(943\) −0.0381692 −0.00124296
\(944\) −27.3843 −0.891283
\(945\) 0 0
\(946\) 10.7705 0.350179
\(947\) −28.6412 −0.930714 −0.465357 0.885123i \(-0.654074\pi\)
−0.465357 + 0.885123i \(0.654074\pi\)
\(948\) −3.90000 −0.126666
\(949\) 7.55214 0.245153
\(950\) −45.8733 −1.48833
\(951\) −0.440700 −0.0142907
\(952\) 0 0
\(953\) 10.2041 0.330544 0.165272 0.986248i \(-0.447150\pi\)
0.165272 + 0.986248i \(0.447150\pi\)
\(954\) 0.241529 0.00781980
\(955\) 9.69934 0.313863
\(956\) 24.8752 0.804522
\(957\) −5.89991 −0.190717
\(958\) −10.3731 −0.335139
\(959\) 0 0
\(960\) 15.8016 0.509994
\(961\) −8.91384 −0.287543
\(962\) −0.0414520 −0.00133647
\(963\) 6.42089 0.206910
\(964\) 6.33169 0.203930
\(965\) 85.3289 2.74684
\(966\) 0 0
\(967\) −49.6045 −1.59517 −0.797587 0.603204i \(-0.793891\pi\)
−0.797587 + 0.603204i \(0.793891\pi\)
\(968\) −10.2743 −0.330228
\(969\) −53.4867 −1.71824
\(970\) 0.411444 0.0132107
\(971\) −26.3030 −0.844102 −0.422051 0.906572i \(-0.638690\pi\)
−0.422051 + 0.906572i \(0.638690\pi\)
\(972\) −1.80441 −0.0578766
\(973\) 0 0
\(974\) −17.5484 −0.562287
\(975\) −41.8522 −1.34034
\(976\) 17.2480 0.552093
\(977\) 32.8265 1.05021 0.525106 0.851037i \(-0.324026\pi\)
0.525106 + 0.851037i \(0.324026\pi\)
\(978\) 5.45436 0.174411
\(979\) 19.2276 0.614516
\(980\) 0 0
\(981\) −2.52449 −0.0806006
\(982\) −18.5936 −0.593347
\(983\) 12.6918 0.404805 0.202403 0.979302i \(-0.435125\pi\)
0.202403 + 0.979302i \(0.435125\pi\)
\(984\) −1.68250 −0.0536363
\(985\) 30.6352 0.976118
\(986\) 8.16696 0.260089
\(987\) 0 0
\(988\) 43.4456 1.38219
\(989\) 0.420215 0.0133621
\(990\) −4.19964 −0.133473
\(991\) −52.5027 −1.66780 −0.833902 0.551912i \(-0.813898\pi\)
−0.833902 + 0.551912i \(0.813898\pi\)
\(992\) −21.7682 −0.691142
\(993\) −3.26805 −0.103708
\(994\) 0 0
\(995\) −59.9718 −1.90123
\(996\) −30.7631 −0.974767
\(997\) −24.7134 −0.782683 −0.391341 0.920246i \(-0.627989\pi\)
−0.391341 + 0.920246i \(0.627989\pi\)
\(998\) 2.52496 0.0799262
\(999\) −0.0300718 −0.000951430 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))