Properties

Label 6027.2.a.y.1.7
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
CM No
Inner twists 1

Related objects

Downloads

Learn more about

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: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
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 \(-1.69463\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.69463 q^{2} -1.00000 q^{3} +5.26102 q^{4} +2.08082 q^{5} -2.69463 q^{6} +8.78724 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.69463 q^{2} -1.00000 q^{3} +5.26102 q^{4} +2.08082 q^{5} -2.69463 q^{6} +8.78724 q^{8} +1.00000 q^{9} +5.60704 q^{10} +3.71461 q^{11} -5.26102 q^{12} +6.98882 q^{13} -2.08082 q^{15} +13.1563 q^{16} -0.439561 q^{17} +2.69463 q^{18} -0.527622 q^{19} +10.9472 q^{20} +10.0095 q^{22} -7.76264 q^{23} -8.78724 q^{24} -0.670181 q^{25} +18.8323 q^{26} -1.00000 q^{27} -2.31439 q^{29} -5.60704 q^{30} -1.64558 q^{31} +17.8769 q^{32} -3.71461 q^{33} -1.18445 q^{34} +5.26102 q^{36} +9.81901 q^{37} -1.42175 q^{38} -6.98882 q^{39} +18.2847 q^{40} -1.00000 q^{41} -8.88126 q^{43} +19.5426 q^{44} +2.08082 q^{45} -20.9174 q^{46} -9.76026 q^{47} -13.1563 q^{48} -1.80589 q^{50} +0.439561 q^{51} +36.7684 q^{52} +1.90524 q^{53} -2.69463 q^{54} +7.72944 q^{55} +0.527622 q^{57} -6.23642 q^{58} +9.36489 q^{59} -10.9472 q^{60} -1.50981 q^{61} -4.43422 q^{62} +21.8589 q^{64} +14.5425 q^{65} -10.0095 q^{66} +1.04172 q^{67} -2.31254 q^{68} +7.76264 q^{69} -9.49670 q^{71} +8.78724 q^{72} +3.01125 q^{73} +26.4586 q^{74} +0.670181 q^{75} -2.77583 q^{76} -18.8323 q^{78} -13.8353 q^{79} +27.3759 q^{80} +1.00000 q^{81} -2.69463 q^{82} -13.6009 q^{83} -0.914648 q^{85} -23.9317 q^{86} +2.31439 q^{87} +32.6412 q^{88} -9.86142 q^{89} +5.60704 q^{90} -40.8394 q^{92} +1.64558 q^{93} -26.3003 q^{94} -1.09789 q^{95} -17.8769 q^{96} +5.45564 q^{97} +3.71461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.69463 1.90539 0.952695 0.303928i \(-0.0982983\pi\)
0.952695 + 0.303928i \(0.0982983\pi\)
\(3\) −1.00000 −0.577350
\(4\) 5.26102 2.63051
\(5\) 2.08082 0.930572 0.465286 0.885160i \(-0.345952\pi\)
0.465286 + 0.885160i \(0.345952\pi\)
\(6\) −2.69463 −1.10008
\(7\) 0 0
\(8\) 8.78724 3.10676
\(9\) 1.00000 0.333333
\(10\) 5.60704 1.77310
\(11\) 3.71461 1.12000 0.559998 0.828494i \(-0.310802\pi\)
0.559998 + 0.828494i \(0.310802\pi\)
\(12\) −5.26102 −1.51873
\(13\) 6.98882 1.93835 0.969176 0.246371i \(-0.0792382\pi\)
0.969176 + 0.246371i \(0.0792382\pi\)
\(14\) 0 0
\(15\) −2.08082 −0.537266
\(16\) 13.1563 3.28908
\(17\) −0.439561 −0.106609 −0.0533046 0.998578i \(-0.516975\pi\)
−0.0533046 + 0.998578i \(0.516975\pi\)
\(18\) 2.69463 0.635130
\(19\) −0.527622 −0.121045 −0.0605224 0.998167i \(-0.519277\pi\)
−0.0605224 + 0.998167i \(0.519277\pi\)
\(20\) 10.9472 2.44788
\(21\) 0 0
\(22\) 10.0095 2.13403
\(23\) −7.76264 −1.61862 −0.809311 0.587380i \(-0.800159\pi\)
−0.809311 + 0.587380i \(0.800159\pi\)
\(24\) −8.78724 −1.79369
\(25\) −0.670181 −0.134036
\(26\) 18.8323 3.69331
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.31439 −0.429771 −0.214886 0.976639i \(-0.568938\pi\)
−0.214886 + 0.976639i \(0.568938\pi\)
\(30\) −5.60704 −1.02370
\(31\) −1.64558 −0.295555 −0.147777 0.989021i \(-0.547212\pi\)
−0.147777 + 0.989021i \(0.547212\pi\)
\(32\) 17.8769 3.16021
\(33\) −3.71461 −0.646630
\(34\) −1.18445 −0.203132
\(35\) 0 0
\(36\) 5.26102 0.876837
\(37\) 9.81901 1.61424 0.807118 0.590390i \(-0.201026\pi\)
0.807118 + 0.590390i \(0.201026\pi\)
\(38\) −1.42175 −0.230638
\(39\) −6.98882 −1.11911
\(40\) 18.2847 2.89106
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −8.88126 −1.35438 −0.677189 0.735809i \(-0.736802\pi\)
−0.677189 + 0.735809i \(0.736802\pi\)
\(44\) 19.5426 2.94616
\(45\) 2.08082 0.310191
\(46\) −20.9174 −3.08411
\(47\) −9.76026 −1.42368 −0.711840 0.702342i \(-0.752138\pi\)
−0.711840 + 0.702342i \(0.752138\pi\)
\(48\) −13.1563 −1.89895
\(49\) 0 0
\(50\) −1.80589 −0.255391
\(51\) 0.439561 0.0615509
\(52\) 36.7684 5.09885
\(53\) 1.90524 0.261705 0.130853 0.991402i \(-0.458229\pi\)
0.130853 + 0.991402i \(0.458229\pi\)
\(54\) −2.69463 −0.366692
\(55\) 7.72944 1.04224
\(56\) 0 0
\(57\) 0.527622 0.0698853
\(58\) −6.23642 −0.818882
\(59\) 9.36489 1.21920 0.609602 0.792707i \(-0.291329\pi\)
0.609602 + 0.792707i \(0.291329\pi\)
\(60\) −10.9472 −1.41328
\(61\) −1.50981 −0.193311 −0.0966555 0.995318i \(-0.530815\pi\)
−0.0966555 + 0.995318i \(0.530815\pi\)
\(62\) −4.43422 −0.563147
\(63\) 0 0
\(64\) 21.8589 2.73236
\(65\) 14.5425 1.80377
\(66\) −10.0095 −1.23208
\(67\) 1.04172 0.127266 0.0636331 0.997973i \(-0.479731\pi\)
0.0636331 + 0.997973i \(0.479731\pi\)
\(68\) −2.31254 −0.280437
\(69\) 7.76264 0.934512
\(70\) 0 0
\(71\) −9.49670 −1.12705 −0.563525 0.826099i \(-0.690555\pi\)
−0.563525 + 0.826099i \(0.690555\pi\)
\(72\) 8.78724 1.03559
\(73\) 3.01125 0.352441 0.176220 0.984351i \(-0.443613\pi\)
0.176220 + 0.984351i \(0.443613\pi\)
\(74\) 26.4586 3.07575
\(75\) 0.670181 0.0773859
\(76\) −2.77583 −0.318410
\(77\) 0 0
\(78\) −18.8323 −2.13234
\(79\) −13.8353 −1.55659 −0.778295 0.627899i \(-0.783915\pi\)
−0.778295 + 0.627899i \(0.783915\pi\)
\(80\) 27.3759 3.06072
\(81\) 1.00000 0.111111
\(82\) −2.69463 −0.297572
\(83\) −13.6009 −1.49289 −0.746445 0.665447i \(-0.768241\pi\)
−0.746445 + 0.665447i \(0.768241\pi\)
\(84\) 0 0
\(85\) −0.914648 −0.0992076
\(86\) −23.9317 −2.58062
\(87\) 2.31439 0.248129
\(88\) 32.6412 3.47956
\(89\) −9.86142 −1.04531 −0.522654 0.852545i \(-0.675058\pi\)
−0.522654 + 0.852545i \(0.675058\pi\)
\(90\) 5.60704 0.591034
\(91\) 0 0
\(92\) −40.8394 −4.25780
\(93\) 1.64558 0.170639
\(94\) −26.3003 −2.71267
\(95\) −1.09789 −0.112641
\(96\) −17.8769 −1.82455
\(97\) 5.45564 0.553937 0.276968 0.960879i \(-0.410670\pi\)
0.276968 + 0.960879i \(0.410670\pi\)
\(98\) 0 0
\(99\) 3.71461 0.373332
\(100\) −3.52584 −0.352584
\(101\) −3.12132 −0.310583 −0.155292 0.987869i \(-0.549632\pi\)
−0.155292 + 0.987869i \(0.549632\pi\)
\(102\) 1.18445 0.117278
\(103\) 13.7132 1.35120 0.675601 0.737268i \(-0.263884\pi\)
0.675601 + 0.737268i \(0.263884\pi\)
\(104\) 61.4125 6.02199
\(105\) 0 0
\(106\) 5.13392 0.498651
\(107\) −4.06184 −0.392673 −0.196337 0.980537i \(-0.562905\pi\)
−0.196337 + 0.980537i \(0.562905\pi\)
\(108\) −5.26102 −0.506242
\(109\) −8.07102 −0.773063 −0.386532 0.922276i \(-0.626327\pi\)
−0.386532 + 0.922276i \(0.626327\pi\)
\(110\) 20.8280 1.98587
\(111\) −9.81901 −0.931979
\(112\) 0 0
\(113\) −9.43020 −0.887119 −0.443559 0.896245i \(-0.646284\pi\)
−0.443559 + 0.896245i \(0.646284\pi\)
\(114\) 1.42175 0.133159
\(115\) −16.1527 −1.50624
\(116\) −12.1761 −1.13052
\(117\) 6.98882 0.646117
\(118\) 25.2349 2.32306
\(119\) 0 0
\(120\) −18.2847 −1.66916
\(121\) 2.79832 0.254393
\(122\) −4.06837 −0.368333
\(123\) 1.00000 0.0901670
\(124\) −8.65742 −0.777460
\(125\) −11.7986 −1.05530
\(126\) 0 0
\(127\) −12.0758 −1.07156 −0.535779 0.844358i \(-0.679982\pi\)
−0.535779 + 0.844358i \(0.679982\pi\)
\(128\) 23.1479 2.04600
\(129\) 8.88126 0.781951
\(130\) 39.1866 3.43689
\(131\) −12.5809 −1.09920 −0.549600 0.835428i \(-0.685220\pi\)
−0.549600 + 0.835428i \(0.685220\pi\)
\(132\) −19.5426 −1.70097
\(133\) 0 0
\(134\) 2.80704 0.242492
\(135\) −2.08082 −0.179089
\(136\) −3.86253 −0.331209
\(137\) 13.6143 1.16315 0.581573 0.813494i \(-0.302437\pi\)
0.581573 + 0.813494i \(0.302437\pi\)
\(138\) 20.9174 1.78061
\(139\) 0.750677 0.0636716 0.0318358 0.999493i \(-0.489865\pi\)
0.0318358 + 0.999493i \(0.489865\pi\)
\(140\) 0 0
\(141\) 9.76026 0.821962
\(142\) −25.5901 −2.14747
\(143\) 25.9608 2.17095
\(144\) 13.1563 1.09636
\(145\) −4.81583 −0.399933
\(146\) 8.11421 0.671537
\(147\) 0 0
\(148\) 51.6580 4.24626
\(149\) 6.69402 0.548396 0.274198 0.961673i \(-0.411588\pi\)
0.274198 + 0.961673i \(0.411588\pi\)
\(150\) 1.80589 0.147450
\(151\) 22.8919 1.86292 0.931460 0.363845i \(-0.118536\pi\)
0.931460 + 0.363845i \(0.118536\pi\)
\(152\) −4.63634 −0.376057
\(153\) −0.439561 −0.0355364
\(154\) 0 0
\(155\) −3.42416 −0.275035
\(156\) −36.7684 −2.94382
\(157\) 15.6112 1.24591 0.622955 0.782258i \(-0.285932\pi\)
0.622955 + 0.782258i \(0.285932\pi\)
\(158\) −37.2809 −2.96591
\(159\) −1.90524 −0.151096
\(160\) 37.1986 2.94081
\(161\) 0 0
\(162\) 2.69463 0.211710
\(163\) 2.98975 0.234175 0.117088 0.993122i \(-0.462644\pi\)
0.117088 + 0.993122i \(0.462644\pi\)
\(164\) −5.26102 −0.410817
\(165\) −7.72944 −0.601736
\(166\) −36.6493 −2.84454
\(167\) −23.3640 −1.80796 −0.903980 0.427576i \(-0.859368\pi\)
−0.903980 + 0.427576i \(0.859368\pi\)
\(168\) 0 0
\(169\) 35.8437 2.75721
\(170\) −2.46464 −0.189029
\(171\) −0.527622 −0.0403483
\(172\) −46.7245 −3.56271
\(173\) −0.0825921 −0.00627936 −0.00313968 0.999995i \(-0.500999\pi\)
−0.00313968 + 0.999995i \(0.500999\pi\)
\(174\) 6.23642 0.472782
\(175\) 0 0
\(176\) 48.8705 3.68375
\(177\) −9.36489 −0.703908
\(178\) −26.5729 −1.99172
\(179\) 20.6346 1.54230 0.771152 0.636651i \(-0.219681\pi\)
0.771152 + 0.636651i \(0.219681\pi\)
\(180\) 10.9472 0.815960
\(181\) −17.1001 −1.27104 −0.635520 0.772084i \(-0.719214\pi\)
−0.635520 + 0.772084i \(0.719214\pi\)
\(182\) 0 0
\(183\) 1.50981 0.111608
\(184\) −68.2122 −5.02867
\(185\) 20.4316 1.50216
\(186\) 4.43422 0.325133
\(187\) −1.63280 −0.119402
\(188\) −51.3489 −3.74501
\(189\) 0 0
\(190\) −2.95840 −0.214625
\(191\) 19.7074 1.42598 0.712990 0.701174i \(-0.247340\pi\)
0.712990 + 0.701174i \(0.247340\pi\)
\(192\) −21.8589 −1.57753
\(193\) 11.3362 0.815996 0.407998 0.912983i \(-0.366227\pi\)
0.407998 + 0.912983i \(0.366227\pi\)
\(194\) 14.7009 1.05547
\(195\) −14.5425 −1.04141
\(196\) 0 0
\(197\) 14.0094 0.998128 0.499064 0.866565i \(-0.333677\pi\)
0.499064 + 0.866565i \(0.333677\pi\)
\(198\) 10.0095 0.711344
\(199\) 11.0903 0.786172 0.393086 0.919502i \(-0.371407\pi\)
0.393086 + 0.919502i \(0.371407\pi\)
\(200\) −5.88904 −0.416418
\(201\) −1.04172 −0.0734772
\(202\) −8.41080 −0.591782
\(203\) 0 0
\(204\) 2.31254 0.161910
\(205\) −2.08082 −0.145331
\(206\) 36.9520 2.57456
\(207\) −7.76264 −0.539541
\(208\) 91.9471 6.37538
\(209\) −1.95991 −0.135570
\(210\) 0 0
\(211\) 22.8501 1.57306 0.786532 0.617550i \(-0.211875\pi\)
0.786532 + 0.617550i \(0.211875\pi\)
\(212\) 10.0235 0.688419
\(213\) 9.49670 0.650703
\(214\) −10.9452 −0.748196
\(215\) −18.4803 −1.26035
\(216\) −8.78724 −0.597896
\(217\) 0 0
\(218\) −21.7484 −1.47299
\(219\) −3.01125 −0.203482
\(220\) 40.6647 2.74162
\(221\) −3.07202 −0.206646
\(222\) −26.4586 −1.77578
\(223\) 14.8028 0.991267 0.495634 0.868532i \(-0.334936\pi\)
0.495634 + 0.868532i \(0.334936\pi\)
\(224\) 0 0
\(225\) −0.670181 −0.0446787
\(226\) −25.4109 −1.69031
\(227\) 15.3884 1.02137 0.510683 0.859769i \(-0.329393\pi\)
0.510683 + 0.859769i \(0.329393\pi\)
\(228\) 2.77583 0.183834
\(229\) 19.3347 1.27767 0.638836 0.769343i \(-0.279416\pi\)
0.638836 + 0.769343i \(0.279416\pi\)
\(230\) −43.5254 −2.86998
\(231\) 0 0
\(232\) −20.3371 −1.33520
\(233\) 20.7893 1.36195 0.680977 0.732305i \(-0.261556\pi\)
0.680977 + 0.732305i \(0.261556\pi\)
\(234\) 18.8323 1.23110
\(235\) −20.3094 −1.32484
\(236\) 49.2689 3.20713
\(237\) 13.8353 0.898697
\(238\) 0 0
\(239\) −3.53932 −0.228940 −0.114470 0.993427i \(-0.536517\pi\)
−0.114470 + 0.993427i \(0.536517\pi\)
\(240\) −27.3759 −1.76711
\(241\) −14.4506 −0.930842 −0.465421 0.885089i \(-0.654097\pi\)
−0.465421 + 0.885089i \(0.654097\pi\)
\(242\) 7.54044 0.484718
\(243\) −1.00000 −0.0641500
\(244\) −7.94313 −0.508507
\(245\) 0 0
\(246\) 2.69463 0.171803
\(247\) −3.68746 −0.234627
\(248\) −14.4601 −0.918217
\(249\) 13.6009 0.861920
\(250\) −31.7929 −2.01076
\(251\) −8.31897 −0.525089 −0.262545 0.964920i \(-0.584562\pi\)
−0.262545 + 0.964920i \(0.584562\pi\)
\(252\) 0 0
\(253\) −28.8352 −1.81285
\(254\) −32.5399 −2.04174
\(255\) 0.914648 0.0572775
\(256\) 18.6571 1.16607
\(257\) −3.68295 −0.229736 −0.114868 0.993381i \(-0.536645\pi\)
−0.114868 + 0.993381i \(0.536645\pi\)
\(258\) 23.9317 1.48992
\(259\) 0 0
\(260\) 76.5084 4.74485
\(261\) −2.31439 −0.143257
\(262\) −33.9009 −2.09440
\(263\) 4.39783 0.271182 0.135591 0.990765i \(-0.456707\pi\)
0.135591 + 0.990765i \(0.456707\pi\)
\(264\) −32.6412 −2.00892
\(265\) 3.96447 0.243536
\(266\) 0 0
\(267\) 9.86142 0.603509
\(268\) 5.48050 0.334775
\(269\) 7.71053 0.470119 0.235060 0.971981i \(-0.424471\pi\)
0.235060 + 0.971981i \(0.424471\pi\)
\(270\) −5.60704 −0.341234
\(271\) 5.03337 0.305756 0.152878 0.988245i \(-0.451146\pi\)
0.152878 + 0.988245i \(0.451146\pi\)
\(272\) −5.78300 −0.350646
\(273\) 0 0
\(274\) 36.6854 2.21625
\(275\) −2.48946 −0.150120
\(276\) 40.8394 2.45824
\(277\) −21.8379 −1.31211 −0.656055 0.754713i \(-0.727776\pi\)
−0.656055 + 0.754713i \(0.727776\pi\)
\(278\) 2.02280 0.121319
\(279\) −1.64558 −0.0985182
\(280\) 0 0
\(281\) 4.62047 0.275634 0.137817 0.990458i \(-0.455991\pi\)
0.137817 + 0.990458i \(0.455991\pi\)
\(282\) 26.3003 1.56616
\(283\) −21.3099 −1.26674 −0.633371 0.773848i \(-0.718329\pi\)
−0.633371 + 0.773848i \(0.718329\pi\)
\(284\) −49.9623 −2.96472
\(285\) 1.09789 0.0650333
\(286\) 69.9546 4.13650
\(287\) 0 0
\(288\) 17.8769 1.05340
\(289\) −16.8068 −0.988634
\(290\) −12.9769 −0.762028
\(291\) −5.45564 −0.319815
\(292\) 15.8423 0.927099
\(293\) 14.5844 0.852030 0.426015 0.904716i \(-0.359917\pi\)
0.426015 + 0.904716i \(0.359917\pi\)
\(294\) 0 0
\(295\) 19.4867 1.13456
\(296\) 86.2820 5.01504
\(297\) −3.71461 −0.215543
\(298\) 18.0379 1.04491
\(299\) −54.2517 −3.13746
\(300\) 3.52584 0.203564
\(301\) 0 0
\(302\) 61.6853 3.54959
\(303\) 3.12132 0.179315
\(304\) −6.94156 −0.398126
\(305\) −3.14164 −0.179890
\(306\) −1.18445 −0.0677107
\(307\) −29.0776 −1.65954 −0.829772 0.558102i \(-0.811530\pi\)
−0.829772 + 0.558102i \(0.811530\pi\)
\(308\) 0 0
\(309\) −13.7132 −0.780116
\(310\) −9.22683 −0.524048
\(311\) 16.8938 0.957959 0.478979 0.877826i \(-0.341007\pi\)
0.478979 + 0.877826i \(0.341007\pi\)
\(312\) −61.4125 −3.47680
\(313\) 7.10059 0.401349 0.200675 0.979658i \(-0.435687\pi\)
0.200675 + 0.979658i \(0.435687\pi\)
\(314\) 42.0664 2.37394
\(315\) 0 0
\(316\) −72.7877 −4.09463
\(317\) 16.3844 0.920238 0.460119 0.887857i \(-0.347807\pi\)
0.460119 + 0.887857i \(0.347807\pi\)
\(318\) −5.13392 −0.287896
\(319\) −8.59705 −0.481343
\(320\) 45.4845 2.54266
\(321\) 4.06184 0.226710
\(322\) 0 0
\(323\) 0.231922 0.0129045
\(324\) 5.26102 0.292279
\(325\) −4.68378 −0.259809
\(326\) 8.05626 0.446195
\(327\) 8.07102 0.446328
\(328\) −8.78724 −0.485194
\(329\) 0 0
\(330\) −20.8280 −1.14654
\(331\) −6.23633 −0.342780 −0.171390 0.985203i \(-0.554826\pi\)
−0.171390 + 0.985203i \(0.554826\pi\)
\(332\) −71.5545 −3.92706
\(333\) 9.81901 0.538079
\(334\) −62.9572 −3.44487
\(335\) 2.16763 0.118430
\(336\) 0 0
\(337\) −24.1319 −1.31455 −0.657273 0.753653i \(-0.728290\pi\)
−0.657273 + 0.753653i \(0.728290\pi\)
\(338\) 96.5854 5.25355
\(339\) 9.43020 0.512178
\(340\) −4.81199 −0.260967
\(341\) −6.11268 −0.331020
\(342\) −1.42175 −0.0768792
\(343\) 0 0
\(344\) −78.0417 −4.20773
\(345\) 16.1527 0.869630
\(346\) −0.222555 −0.0119646
\(347\) −18.8453 −1.01167 −0.505834 0.862631i \(-0.668815\pi\)
−0.505834 + 0.862631i \(0.668815\pi\)
\(348\) 12.1761 0.652705
\(349\) −22.1852 −1.18755 −0.593774 0.804632i \(-0.702363\pi\)
−0.593774 + 0.804632i \(0.702363\pi\)
\(350\) 0 0
\(351\) −6.98882 −0.373036
\(352\) 66.4056 3.53943
\(353\) −17.7563 −0.945075 −0.472537 0.881311i \(-0.656662\pi\)
−0.472537 + 0.881311i \(0.656662\pi\)
\(354\) −25.2349 −1.34122
\(355\) −19.7609 −1.04880
\(356\) −51.8812 −2.74970
\(357\) 0 0
\(358\) 55.6027 2.93869
\(359\) −26.6141 −1.40464 −0.702319 0.711862i \(-0.747852\pi\)
−0.702319 + 0.711862i \(0.747852\pi\)
\(360\) 18.2847 0.963687
\(361\) −18.7216 −0.985348
\(362\) −46.0784 −2.42183
\(363\) −2.79832 −0.146874
\(364\) 0 0
\(365\) 6.26588 0.327971
\(366\) 4.06837 0.212657
\(367\) 28.4341 1.48425 0.742124 0.670263i \(-0.233819\pi\)
0.742124 + 0.670263i \(0.233819\pi\)
\(368\) −102.128 −5.32377
\(369\) −1.00000 −0.0520579
\(370\) 55.0556 2.86220
\(371\) 0 0
\(372\) 8.65742 0.448867
\(373\) −14.4792 −0.749702 −0.374851 0.927085i \(-0.622306\pi\)
−0.374851 + 0.927085i \(0.622306\pi\)
\(374\) −4.39978 −0.227507
\(375\) 11.7986 0.609279
\(376\) −85.7658 −4.42303
\(377\) −16.1749 −0.833048
\(378\) 0 0
\(379\) 27.0992 1.39199 0.695996 0.718046i \(-0.254963\pi\)
0.695996 + 0.718046i \(0.254963\pi\)
\(380\) −5.77601 −0.296303
\(381\) 12.0758 0.618664
\(382\) 53.1042 2.71705
\(383\) 25.7679 1.31668 0.658339 0.752722i \(-0.271259\pi\)
0.658339 + 0.752722i \(0.271259\pi\)
\(384\) −23.1479 −1.18126
\(385\) 0 0
\(386\) 30.5468 1.55479
\(387\) −8.88126 −0.451460
\(388\) 28.7023 1.45714
\(389\) −10.8688 −0.551069 −0.275535 0.961291i \(-0.588855\pi\)
−0.275535 + 0.961291i \(0.588855\pi\)
\(390\) −39.1866 −1.98429
\(391\) 3.41215 0.172560
\(392\) 0 0
\(393\) 12.5809 0.634623
\(394\) 37.7501 1.90182
\(395\) −28.7887 −1.44852
\(396\) 19.5426 0.982055
\(397\) −18.4731 −0.927138 −0.463569 0.886061i \(-0.653431\pi\)
−0.463569 + 0.886061i \(0.653431\pi\)
\(398\) 29.8843 1.49797
\(399\) 0 0
\(400\) −8.81711 −0.440855
\(401\) −14.7562 −0.736889 −0.368445 0.929650i \(-0.620110\pi\)
−0.368445 + 0.929650i \(0.620110\pi\)
\(402\) −2.80704 −0.140003
\(403\) −11.5007 −0.572889
\(404\) −16.4213 −0.816992
\(405\) 2.08082 0.103397
\(406\) 0 0
\(407\) 36.4738 1.80794
\(408\) 3.86253 0.191224
\(409\) 11.0730 0.547523 0.273761 0.961798i \(-0.411732\pi\)
0.273761 + 0.961798i \(0.411732\pi\)
\(410\) −5.60704 −0.276912
\(411\) −13.6143 −0.671543
\(412\) 72.1454 3.55435
\(413\) 0 0
\(414\) −20.9174 −1.02804
\(415\) −28.3010 −1.38924
\(416\) 124.938 6.12560
\(417\) −0.750677 −0.0367608
\(418\) −5.28123 −0.258313
\(419\) 7.32759 0.357976 0.178988 0.983851i \(-0.442718\pi\)
0.178988 + 0.983851i \(0.442718\pi\)
\(420\) 0 0
\(421\) 1.38217 0.0673629 0.0336815 0.999433i \(-0.489277\pi\)
0.0336815 + 0.999433i \(0.489277\pi\)
\(422\) 61.5724 2.99730
\(423\) −9.76026 −0.474560
\(424\) 16.7418 0.813055
\(425\) 0.294586 0.0142895
\(426\) 25.5901 1.23984
\(427\) 0 0
\(428\) −21.3694 −1.03293
\(429\) −25.9608 −1.25340
\(430\) −49.7976 −2.40145
\(431\) 6.69985 0.322720 0.161360 0.986896i \(-0.448412\pi\)
0.161360 + 0.986896i \(0.448412\pi\)
\(432\) −13.1563 −0.632983
\(433\) 35.4887 1.70548 0.852739 0.522337i \(-0.174940\pi\)
0.852739 + 0.522337i \(0.174940\pi\)
\(434\) 0 0
\(435\) 4.81583 0.230901
\(436\) −42.4618 −2.03355
\(437\) 4.09574 0.195926
\(438\) −8.11421 −0.387712
\(439\) −17.5082 −0.835619 −0.417810 0.908535i \(-0.637202\pi\)
−0.417810 + 0.908535i \(0.637202\pi\)
\(440\) 67.9204 3.23798
\(441\) 0 0
\(442\) −8.27794 −0.393742
\(443\) −27.0536 −1.28535 −0.642677 0.766137i \(-0.722176\pi\)
−0.642677 + 0.766137i \(0.722176\pi\)
\(444\) −51.6580 −2.45158
\(445\) −20.5199 −0.972735
\(446\) 39.8880 1.88875
\(447\) −6.69402 −0.316616
\(448\) 0 0
\(449\) 35.3056 1.66617 0.833087 0.553142i \(-0.186571\pi\)
0.833087 + 0.553142i \(0.186571\pi\)
\(450\) −1.80589 −0.0851304
\(451\) −3.71461 −0.174914
\(452\) −49.6125 −2.33358
\(453\) −22.8919 −1.07556
\(454\) 41.4661 1.94610
\(455\) 0 0
\(456\) 4.63634 0.217117
\(457\) −2.67112 −0.124950 −0.0624749 0.998047i \(-0.519899\pi\)
−0.0624749 + 0.998047i \(0.519899\pi\)
\(458\) 52.0998 2.43446
\(459\) 0.439561 0.0205170
\(460\) −84.9795 −3.96219
\(461\) 10.2093 0.475493 0.237747 0.971327i \(-0.423591\pi\)
0.237747 + 0.971327i \(0.423591\pi\)
\(462\) 0 0
\(463\) −33.0579 −1.53633 −0.768166 0.640250i \(-0.778831\pi\)
−0.768166 + 0.640250i \(0.778831\pi\)
\(464\) −30.4488 −1.41355
\(465\) 3.42416 0.158791
\(466\) 56.0195 2.59505
\(467\) 11.3902 0.527077 0.263538 0.964649i \(-0.415110\pi\)
0.263538 + 0.964649i \(0.415110\pi\)
\(468\) 36.7684 1.69962
\(469\) 0 0
\(470\) −54.7262 −2.52433
\(471\) −15.6112 −0.719326
\(472\) 82.2915 3.78777
\(473\) −32.9904 −1.51690
\(474\) 37.2809 1.71237
\(475\) 0.353602 0.0162244
\(476\) 0 0
\(477\) 1.90524 0.0872351
\(478\) −9.53715 −0.436219
\(479\) 15.3666 0.702119 0.351060 0.936353i \(-0.385821\pi\)
0.351060 + 0.936353i \(0.385821\pi\)
\(480\) −37.1986 −1.69787
\(481\) 68.6234 3.12896
\(482\) −38.9389 −1.77362
\(483\) 0 0
\(484\) 14.7220 0.669183
\(485\) 11.3522 0.515478
\(486\) −2.69463 −0.122231
\(487\) 19.3061 0.874844 0.437422 0.899256i \(-0.355892\pi\)
0.437422 + 0.899256i \(0.355892\pi\)
\(488\) −13.2670 −0.600570
\(489\) −2.98975 −0.135201
\(490\) 0 0
\(491\) −9.74439 −0.439758 −0.219879 0.975527i \(-0.570566\pi\)
−0.219879 + 0.975527i \(0.570566\pi\)
\(492\) 5.26102 0.237185
\(493\) 1.01732 0.0458176
\(494\) −9.93633 −0.447057
\(495\) 7.72944 0.347412
\(496\) −21.6497 −0.972102
\(497\) 0 0
\(498\) 36.6493 1.64229
\(499\) 34.5879 1.54837 0.774184 0.632960i \(-0.218160\pi\)
0.774184 + 0.632960i \(0.218160\pi\)
\(500\) −62.0729 −2.77598
\(501\) 23.3640 1.04383
\(502\) −22.4165 −1.00050
\(503\) −11.6232 −0.518254 −0.259127 0.965843i \(-0.583435\pi\)
−0.259127 + 0.965843i \(0.583435\pi\)
\(504\) 0 0
\(505\) −6.49491 −0.289020
\(506\) −77.7001 −3.45419
\(507\) −35.8437 −1.59187
\(508\) −63.5313 −2.81874
\(509\) −22.9053 −1.01526 −0.507629 0.861576i \(-0.669478\pi\)
−0.507629 + 0.861576i \(0.669478\pi\)
\(510\) 2.46464 0.109136
\(511\) 0 0
\(512\) 3.97829 0.175817
\(513\) 0.527622 0.0232951
\(514\) −9.92419 −0.437737
\(515\) 28.5347 1.25739
\(516\) 46.7245 2.05693
\(517\) −36.2556 −1.59452
\(518\) 0 0
\(519\) 0.0825921 0.00362539
\(520\) 127.788 5.60389
\(521\) −23.6522 −1.03622 −0.518110 0.855314i \(-0.673364\pi\)
−0.518110 + 0.855314i \(0.673364\pi\)
\(522\) −6.23642 −0.272961
\(523\) −20.5658 −0.899279 −0.449639 0.893210i \(-0.648447\pi\)
−0.449639 + 0.893210i \(0.648447\pi\)
\(524\) −66.1885 −2.89146
\(525\) 0 0
\(526\) 11.8505 0.516707
\(527\) 0.723332 0.0315089
\(528\) −48.8705 −2.12682
\(529\) 37.2585 1.61994
\(530\) 10.6828 0.464030
\(531\) 9.36489 0.406401
\(532\) 0 0
\(533\) −6.98882 −0.302720
\(534\) 26.5729 1.14992
\(535\) −8.45197 −0.365411
\(536\) 9.15383 0.395385
\(537\) −20.6346 −0.890450
\(538\) 20.7770 0.895761
\(539\) 0 0
\(540\) −10.9472 −0.471095
\(541\) 0.768732 0.0330504 0.0165252 0.999863i \(-0.494740\pi\)
0.0165252 + 0.999863i \(0.494740\pi\)
\(542\) 13.5631 0.582583
\(543\) 17.1001 0.733836
\(544\) −7.85798 −0.336908
\(545\) −16.7943 −0.719391
\(546\) 0 0
\(547\) 25.6661 1.09740 0.548701 0.836019i \(-0.315123\pi\)
0.548701 + 0.836019i \(0.315123\pi\)
\(548\) 71.6250 3.05967
\(549\) −1.50981 −0.0644370
\(550\) −6.70817 −0.286037
\(551\) 1.22112 0.0520216
\(552\) 68.2122 2.90330
\(553\) 0 0
\(554\) −58.8450 −2.50008
\(555\) −20.4316 −0.867274
\(556\) 3.94933 0.167489
\(557\) −26.2390 −1.11178 −0.555890 0.831256i \(-0.687622\pi\)
−0.555890 + 0.831256i \(0.687622\pi\)
\(558\) −4.43422 −0.187716
\(559\) −62.0695 −2.62526
\(560\) 0 0
\(561\) 1.63280 0.0689368
\(562\) 12.4505 0.525191
\(563\) −13.9758 −0.589009 −0.294505 0.955650i \(-0.595155\pi\)
−0.294505 + 0.955650i \(0.595155\pi\)
\(564\) 51.3489 2.16218
\(565\) −19.6226 −0.825528
\(566\) −57.4223 −2.41364
\(567\) 0 0
\(568\) −83.4498 −3.50148
\(569\) −6.10863 −0.256087 −0.128044 0.991769i \(-0.540870\pi\)
−0.128044 + 0.991769i \(0.540870\pi\)
\(570\) 2.95840 0.123914
\(571\) 11.4910 0.480885 0.240442 0.970663i \(-0.422707\pi\)
0.240442 + 0.970663i \(0.422707\pi\)
\(572\) 136.580 5.71070
\(573\) −19.7074 −0.823290
\(574\) 0 0
\(575\) 5.20237 0.216954
\(576\) 21.8589 0.910788
\(577\) 33.2316 1.38345 0.691725 0.722161i \(-0.256851\pi\)
0.691725 + 0.722161i \(0.256851\pi\)
\(578\) −45.2880 −1.88373
\(579\) −11.3362 −0.471115
\(580\) −25.3362 −1.05203
\(581\) 0 0
\(582\) −14.7009 −0.609373
\(583\) 7.07724 0.293109
\(584\) 26.4606 1.09495
\(585\) 14.5425 0.601258
\(586\) 39.2995 1.62345
\(587\) 22.5690 0.931521 0.465760 0.884911i \(-0.345781\pi\)
0.465760 + 0.884911i \(0.345781\pi\)
\(588\) 0 0
\(589\) 0.868244 0.0357754
\(590\) 52.5093 2.16177
\(591\) −14.0094 −0.576270
\(592\) 129.182 5.30934
\(593\) −7.69128 −0.315843 −0.157921 0.987452i \(-0.550479\pi\)
−0.157921 + 0.987452i \(0.550479\pi\)
\(594\) −10.0095 −0.410694
\(595\) 0 0
\(596\) 35.2174 1.44256
\(597\) −11.0903 −0.453897
\(598\) −146.188 −5.97808
\(599\) −35.7330 −1.46001 −0.730005 0.683442i \(-0.760482\pi\)
−0.730005 + 0.683442i \(0.760482\pi\)
\(600\) 5.88904 0.240419
\(601\) −12.9595 −0.528628 −0.264314 0.964437i \(-0.585146\pi\)
−0.264314 + 0.964437i \(0.585146\pi\)
\(602\) 0 0
\(603\) 1.04172 0.0424221
\(604\) 120.435 4.90043
\(605\) 5.82281 0.236731
\(606\) 8.41080 0.341665
\(607\) −9.41614 −0.382189 −0.191095 0.981572i \(-0.561204\pi\)
−0.191095 + 0.981572i \(0.561204\pi\)
\(608\) −9.43223 −0.382528
\(609\) 0 0
\(610\) −8.46555 −0.342760
\(611\) −68.2127 −2.75959
\(612\) −2.31254 −0.0934789
\(613\) −5.53895 −0.223716 −0.111858 0.993724i \(-0.535680\pi\)
−0.111858 + 0.993724i \(0.535680\pi\)
\(614\) −78.3532 −3.16208
\(615\) 2.08082 0.0839068
\(616\) 0 0
\(617\) 3.96556 0.159647 0.0798237 0.996809i \(-0.474564\pi\)
0.0798237 + 0.996809i \(0.474564\pi\)
\(618\) −36.9520 −1.48643
\(619\) 1.11331 0.0447478 0.0223739 0.999750i \(-0.492878\pi\)
0.0223739 + 0.999750i \(0.492878\pi\)
\(620\) −18.0146 −0.723482
\(621\) 7.76264 0.311504
\(622\) 45.5225 1.82528
\(623\) 0 0
\(624\) −91.9471 −3.68083
\(625\) −21.2000 −0.847998
\(626\) 19.1335 0.764727
\(627\) 1.95991 0.0782713
\(628\) 82.1309 3.27738
\(629\) −4.31606 −0.172092
\(630\) 0 0
\(631\) −11.4270 −0.454903 −0.227451 0.973789i \(-0.573039\pi\)
−0.227451 + 0.973789i \(0.573039\pi\)
\(632\) −121.574 −4.83595
\(633\) −22.8501 −0.908209
\(634\) 44.1498 1.75341
\(635\) −25.1277 −0.997161
\(636\) −10.0235 −0.397459
\(637\) 0 0
\(638\) −23.1659 −0.917145
\(639\) −9.49670 −0.375684
\(640\) 48.1666 1.90395
\(641\) −24.4778 −0.966815 −0.483407 0.875395i \(-0.660601\pi\)
−0.483407 + 0.875395i \(0.660601\pi\)
\(642\) 10.9452 0.431971
\(643\) −15.1314 −0.596724 −0.298362 0.954453i \(-0.596440\pi\)
−0.298362 + 0.954453i \(0.596440\pi\)
\(644\) 0 0
\(645\) 18.4803 0.727662
\(646\) 0.624944 0.0245881
\(647\) 39.3656 1.54762 0.773811 0.633417i \(-0.218348\pi\)
0.773811 + 0.633417i \(0.218348\pi\)
\(648\) 8.78724 0.345195
\(649\) 34.7869 1.36551
\(650\) −12.6210 −0.495038
\(651\) 0 0
\(652\) 15.7291 0.616001
\(653\) 38.8681 1.52102 0.760512 0.649323i \(-0.224948\pi\)
0.760512 + 0.649323i \(0.224948\pi\)
\(654\) 21.7484 0.850429
\(655\) −26.1787 −1.02288
\(656\) −13.1563 −0.513667
\(657\) 3.01125 0.117480
\(658\) 0 0
\(659\) −1.24009 −0.0483072 −0.0241536 0.999708i \(-0.507689\pi\)
−0.0241536 + 0.999708i \(0.507689\pi\)
\(660\) −40.6647 −1.58287
\(661\) −14.1249 −0.549395 −0.274697 0.961531i \(-0.588578\pi\)
−0.274697 + 0.961531i \(0.588578\pi\)
\(662\) −16.8046 −0.653129
\(663\) 3.07202 0.119307
\(664\) −119.514 −4.63805
\(665\) 0 0
\(666\) 26.4586 1.02525
\(667\) 17.9658 0.695637
\(668\) −122.918 −4.75586
\(669\) −14.8028 −0.572309
\(670\) 5.84096 0.225656
\(671\) −5.60834 −0.216508
\(672\) 0 0
\(673\) −26.4023 −1.01773 −0.508867 0.860845i \(-0.669936\pi\)
−0.508867 + 0.860845i \(0.669936\pi\)
\(674\) −65.0264 −2.50472
\(675\) 0.670181 0.0257953
\(676\) 188.574 7.25286
\(677\) −22.2652 −0.855722 −0.427861 0.903844i \(-0.640733\pi\)
−0.427861 + 0.903844i \(0.640733\pi\)
\(678\) 25.4109 0.975899
\(679\) 0 0
\(680\) −8.03724 −0.308214
\(681\) −15.3884 −0.589685
\(682\) −16.4714 −0.630723
\(683\) −6.88159 −0.263317 −0.131658 0.991295i \(-0.542030\pi\)
−0.131658 + 0.991295i \(0.542030\pi\)
\(684\) −2.77583 −0.106137
\(685\) 28.3289 1.08239
\(686\) 0 0
\(687\) −19.3347 −0.737664
\(688\) −116.845 −4.45466
\(689\) 13.3154 0.507277
\(690\) 43.5254 1.65698
\(691\) −1.91499 −0.0728496 −0.0364248 0.999336i \(-0.511597\pi\)
−0.0364248 + 0.999336i \(0.511597\pi\)
\(692\) −0.434519 −0.0165179
\(693\) 0 0
\(694\) −50.7811 −1.92762
\(695\) 1.56203 0.0592510
\(696\) 20.3371 0.770876
\(697\) 0.439561 0.0166496
\(698\) −59.7810 −2.26274
\(699\) −20.7893 −0.786324
\(700\) 0 0
\(701\) 6.28267 0.237293 0.118647 0.992937i \(-0.462144\pi\)
0.118647 + 0.992937i \(0.462144\pi\)
\(702\) −18.8323 −0.710779
\(703\) −5.18073 −0.195395
\(704\) 81.1973 3.06024
\(705\) 20.3094 0.764895
\(706\) −47.8467 −1.80074
\(707\) 0 0
\(708\) −49.2689 −1.85164
\(709\) −12.3470 −0.463700 −0.231850 0.972752i \(-0.574478\pi\)
−0.231850 + 0.972752i \(0.574478\pi\)
\(710\) −53.2484 −1.99838
\(711\) −13.8353 −0.518863
\(712\) −86.6547 −3.24752
\(713\) 12.7740 0.478391
\(714\) 0 0
\(715\) 54.0197 2.02022
\(716\) 108.559 4.05705
\(717\) 3.53932 0.132178
\(718\) −71.7151 −2.67638
\(719\) −40.6197 −1.51486 −0.757429 0.652917i \(-0.773545\pi\)
−0.757429 + 0.652917i \(0.773545\pi\)
\(720\) 27.3759 1.02024
\(721\) 0 0
\(722\) −50.4478 −1.87747
\(723\) 14.4506 0.537422
\(724\) −89.9640 −3.34349
\(725\) 1.55106 0.0576049
\(726\) −7.54044 −0.279852
\(727\) 27.7416 1.02888 0.514439 0.857527i \(-0.328000\pi\)
0.514439 + 0.857527i \(0.328000\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 16.8842 0.624913
\(731\) 3.90386 0.144389
\(732\) 7.94313 0.293586
\(733\) 0.517287 0.0191064 0.00955322 0.999954i \(-0.496959\pi\)
0.00955322 + 0.999954i \(0.496959\pi\)
\(734\) 76.6193 2.82807
\(735\) 0 0
\(736\) −138.772 −5.11519
\(737\) 3.86958 0.142538
\(738\) −2.69463 −0.0991906
\(739\) −49.2528 −1.81179 −0.905897 0.423498i \(-0.860802\pi\)
−0.905897 + 0.423498i \(0.860802\pi\)
\(740\) 107.491 3.95145
\(741\) 3.68746 0.135462
\(742\) 0 0
\(743\) 4.31629 0.158349 0.0791747 0.996861i \(-0.474771\pi\)
0.0791747 + 0.996861i \(0.474771\pi\)
\(744\) 14.4601 0.530133
\(745\) 13.9291 0.510321
\(746\) −39.0159 −1.42847
\(747\) −13.6009 −0.497630
\(748\) −8.59019 −0.314088
\(749\) 0 0
\(750\) 31.7929 1.16091
\(751\) 23.1864 0.846084 0.423042 0.906110i \(-0.360962\pi\)
0.423042 + 0.906110i \(0.360962\pi\)
\(752\) −128.409 −4.68259
\(753\) 8.31897 0.303160
\(754\) −43.5852 −1.58728
\(755\) 47.6340 1.73358
\(756\) 0 0
\(757\) −26.8333 −0.975274 −0.487637 0.873046i \(-0.662141\pi\)
−0.487637 + 0.873046i \(0.662141\pi\)
\(758\) 73.0222 2.65229
\(759\) 28.8352 1.04665
\(760\) −9.64740 −0.349948
\(761\) 28.9939 1.05103 0.525514 0.850785i \(-0.323873\pi\)
0.525514 + 0.850785i \(0.323873\pi\)
\(762\) 32.5399 1.17880
\(763\) 0 0
\(764\) 103.681 3.75106
\(765\) −0.914648 −0.0330692
\(766\) 69.4349 2.50878
\(767\) 65.4496 2.36325
\(768\) −18.6571 −0.673232
\(769\) 28.5947 1.03115 0.515576 0.856844i \(-0.327578\pi\)
0.515576 + 0.856844i \(0.327578\pi\)
\(770\) 0 0
\(771\) 3.68295 0.132638
\(772\) 59.6399 2.14649
\(773\) 21.4137 0.770197 0.385099 0.922875i \(-0.374167\pi\)
0.385099 + 0.922875i \(0.374167\pi\)
\(774\) −23.9317 −0.860207
\(775\) 1.10284 0.0396150
\(776\) 47.9401 1.72095
\(777\) 0 0
\(778\) −29.2873 −1.05000
\(779\) 0.527622 0.0189040
\(780\) −76.5084 −2.73944
\(781\) −35.2765 −1.26229
\(782\) 9.19449 0.328794
\(783\) 2.31439 0.0827095
\(784\) 0 0
\(785\) 32.4841 1.15941
\(786\) 33.9009 1.20921
\(787\) 37.1432 1.32401 0.662006 0.749499i \(-0.269705\pi\)
0.662006 + 0.749499i \(0.269705\pi\)
\(788\) 73.7038 2.62559
\(789\) −4.39783 −0.156567
\(790\) −77.5749 −2.75999
\(791\) 0 0
\(792\) 32.6412 1.15985
\(793\) −10.5518 −0.374705
\(794\) −49.7781 −1.76656
\(795\) −3.96447 −0.140605
\(796\) 58.3464 2.06804
\(797\) 29.1409 1.03222 0.516111 0.856521i \(-0.327379\pi\)
0.516111 + 0.856521i \(0.327379\pi\)
\(798\) 0 0
\(799\) 4.29023 0.151777
\(800\) −11.9807 −0.423583
\(801\) −9.86142 −0.348436
\(802\) −39.7625 −1.40406
\(803\) 11.1856 0.394732
\(804\) −5.48050 −0.193282
\(805\) 0 0
\(806\) −30.9900 −1.09158
\(807\) −7.71053 −0.271424
\(808\) −27.4278 −0.964907
\(809\) 22.1729 0.779558 0.389779 0.920908i \(-0.372551\pi\)
0.389779 + 0.920908i \(0.372551\pi\)
\(810\) 5.60704 0.197011
\(811\) −10.4493 −0.366923 −0.183462 0.983027i \(-0.558730\pi\)
−0.183462 + 0.983027i \(0.558730\pi\)
\(812\) 0 0
\(813\) −5.03337 −0.176528
\(814\) 98.2833 3.44483
\(815\) 6.22114 0.217917
\(816\) 5.78300 0.202446
\(817\) 4.68595 0.163941
\(818\) 29.8375 1.04324
\(819\) 0 0
\(820\) −10.9472 −0.382294
\(821\) −31.8282 −1.11081 −0.555405 0.831580i \(-0.687437\pi\)
−0.555405 + 0.831580i \(0.687437\pi\)
\(822\) −36.6854 −1.27955
\(823\) −6.19583 −0.215973 −0.107987 0.994152i \(-0.534440\pi\)
−0.107987 + 0.994152i \(0.534440\pi\)
\(824\) 120.501 4.19786
\(825\) 2.48946 0.0866719
\(826\) 0 0
\(827\) −47.1531 −1.63967 −0.819837 0.572597i \(-0.805936\pi\)
−0.819837 + 0.572597i \(0.805936\pi\)
\(828\) −40.8394 −1.41927
\(829\) −18.5572 −0.644520 −0.322260 0.946651i \(-0.604442\pi\)
−0.322260 + 0.946651i \(0.604442\pi\)
\(830\) −76.2606 −2.64705
\(831\) 21.8379 0.757548
\(832\) 152.768 5.29628
\(833\) 0 0
\(834\) −2.02280 −0.0700437
\(835\) −48.6163 −1.68244
\(836\) −10.3111 −0.356618
\(837\) 1.64558 0.0568795
\(838\) 19.7451 0.682084
\(839\) −38.4981 −1.32910 −0.664551 0.747243i \(-0.731377\pi\)
−0.664551 + 0.747243i \(0.731377\pi\)
\(840\) 0 0
\(841\) −23.6436 −0.815297
\(842\) 3.72444 0.128353
\(843\) −4.62047 −0.159138
\(844\) 120.215 4.13796
\(845\) 74.5843 2.56578
\(846\) −26.3003 −0.904222
\(847\) 0 0
\(848\) 25.0660 0.860769
\(849\) 21.3099 0.731354
\(850\) 0.793799 0.0272271
\(851\) −76.2214 −2.61284
\(852\) 49.9623 1.71168
\(853\) −34.7856 −1.19104 −0.595518 0.803342i \(-0.703053\pi\)
−0.595518 + 0.803342i \(0.703053\pi\)
\(854\) 0 0
\(855\) −1.09789 −0.0375470
\(856\) −35.6924 −1.21994
\(857\) 45.7319 1.56217 0.781086 0.624423i \(-0.214666\pi\)
0.781086 + 0.624423i \(0.214666\pi\)
\(858\) −69.9546 −2.38821
\(859\) 27.0766 0.923843 0.461921 0.886921i \(-0.347160\pi\)
0.461921 + 0.886921i \(0.347160\pi\)
\(860\) −97.2253 −3.31536
\(861\) 0 0
\(862\) 18.0536 0.614908
\(863\) 24.4449 0.832113 0.416056 0.909339i \(-0.363412\pi\)
0.416056 + 0.909339i \(0.363412\pi\)
\(864\) −17.8769 −0.608183
\(865\) −0.171860 −0.00584340
\(866\) 95.6289 3.24960
\(867\) 16.8068 0.570788
\(868\) 0 0
\(869\) −51.3926 −1.74338
\(870\) 12.9769 0.439957
\(871\) 7.28039 0.246687
\(872\) −70.9220 −2.40172
\(873\) 5.45564 0.184646
\(874\) 11.0365 0.373315
\(875\) 0 0
\(876\) −15.8423 −0.535261
\(877\) −8.03269 −0.271245 −0.135622 0.990761i \(-0.543303\pi\)
−0.135622 + 0.990761i \(0.543303\pi\)
\(878\) −47.1780 −1.59218
\(879\) −14.5844 −0.491920
\(880\) 101.691 3.42800
\(881\) 35.4114 1.19304 0.596520 0.802598i \(-0.296550\pi\)
0.596520 + 0.802598i \(0.296550\pi\)
\(882\) 0 0
\(883\) 8.19851 0.275902 0.137951 0.990439i \(-0.455948\pi\)
0.137951 + 0.990439i \(0.455948\pi\)
\(884\) −16.1619 −0.543585
\(885\) −19.4867 −0.655037
\(886\) −72.8994 −2.44910
\(887\) −31.3125 −1.05137 −0.525685 0.850679i \(-0.676191\pi\)
−0.525685 + 0.850679i \(0.676191\pi\)
\(888\) −86.2820 −2.89544
\(889\) 0 0
\(890\) −55.2934 −1.85344
\(891\) 3.71461 0.124444
\(892\) 77.8777 2.60754
\(893\) 5.14973 0.172329
\(894\) −18.0379 −0.603278
\(895\) 42.9370 1.43523
\(896\) 0 0
\(897\) 54.2517 1.81141
\(898\) 95.1355 3.17471
\(899\) 3.80851 0.127021
\(900\) −3.52584 −0.117528
\(901\) −0.837471 −0.0279002
\(902\) −10.0095 −0.333280
\(903\) 0 0
\(904\) −82.8655 −2.75606
\(905\) −35.5823 −1.18279
\(906\) −61.6853 −2.04936
\(907\) 2.33978 0.0776911 0.0388456 0.999245i \(-0.487632\pi\)
0.0388456 + 0.999245i \(0.487632\pi\)
\(908\) 80.9588 2.68671
\(909\) −3.12132 −0.103528
\(910\) 0 0
\(911\) 2.17707 0.0721295 0.0360647 0.999349i \(-0.488518\pi\)
0.0360647 + 0.999349i \(0.488518\pi\)
\(912\) 6.94156 0.229858
\(913\) −50.5219 −1.67203
\(914\) −7.19768 −0.238078
\(915\) 3.14164 0.103859
\(916\) 101.720 3.36093
\(917\) 0 0
\(918\) 1.18445 0.0390928
\(919\) 4.85889 0.160280 0.0801400 0.996784i \(-0.474463\pi\)
0.0801400 + 0.996784i \(0.474463\pi\)
\(920\) −141.937 −4.67954
\(921\) 29.0776 0.958138
\(922\) 27.5102 0.906000
\(923\) −66.3708 −2.18462
\(924\) 0 0
\(925\) −6.58052 −0.216366
\(926\) −89.0789 −2.92731
\(927\) 13.7132 0.450400
\(928\) −41.3740 −1.35817
\(929\) 20.6103 0.676202 0.338101 0.941110i \(-0.390215\pi\)
0.338101 + 0.941110i \(0.390215\pi\)
\(930\) 9.22683 0.302560
\(931\) 0 0
\(932\) 109.373 3.58263
\(933\) −16.8938 −0.553078
\(934\) 30.6924 1.00429
\(935\) −3.39756 −0.111112
\(936\) 61.4125 2.00733
\(937\) −12.8694 −0.420424 −0.210212 0.977656i \(-0.567415\pi\)
−0.210212 + 0.977656i \(0.567415\pi\)
\(938\) 0 0
\(939\) −7.10059 −0.231719
\(940\) −106.848 −3.48500
\(941\) −40.3678 −1.31595 −0.657976 0.753039i \(-0.728587\pi\)
−0.657976 + 0.753039i \(0.728587\pi\)
\(942\) −42.0664 −1.37060
\(943\) 7.76264 0.252786
\(944\) 123.207 4.01006
\(945\) 0 0
\(946\) −88.8969 −2.89029
\(947\) 37.4055 1.21552 0.607758 0.794122i \(-0.292069\pi\)
0.607758 + 0.794122i \(0.292069\pi\)
\(948\) 72.7877 2.36403
\(949\) 21.0451 0.683154
\(950\) 0.952827 0.0309138
\(951\) −16.3844 −0.531300
\(952\) 0 0
\(953\) −41.4445 −1.34252 −0.671260 0.741222i \(-0.734247\pi\)
−0.671260 + 0.741222i \(0.734247\pi\)
\(954\) 5.13392 0.166217
\(955\) 41.0077 1.32698
\(956\) −18.6204 −0.602228
\(957\) 8.59705 0.277903
\(958\) 41.4074 1.33781
\(959\) 0 0
\(960\) −45.4845 −1.46801
\(961\) −28.2921 −0.912647
\(962\) 184.914 5.96188
\(963\) −4.06184 −0.130891
\(964\) −76.0247 −2.44859
\(965\) 23.5886 0.759343
\(966\) 0 0
\(967\) 52.3364 1.68303 0.841513 0.540237i \(-0.181665\pi\)
0.841513 + 0.540237i \(0.181665\pi\)
\(968\) 24.5895 0.790337
\(969\) −0.231922 −0.00745042
\(970\) 30.5900 0.982186
\(971\) −51.5362 −1.65387 −0.826937 0.562295i \(-0.809919\pi\)
−0.826937 + 0.562295i \(0.809919\pi\)
\(972\) −5.26102 −0.168747
\(973\) 0 0
\(974\) 52.0228 1.66692
\(975\) 4.68378 0.150001
\(976\) −19.8635 −0.635814
\(977\) 8.48831 0.271565 0.135783 0.990739i \(-0.456645\pi\)
0.135783 + 0.990739i \(0.456645\pi\)
\(978\) −8.05626 −0.257611
\(979\) −36.6313 −1.17074
\(980\) 0 0
\(981\) −8.07102 −0.257688
\(982\) −26.2575 −0.837911
\(983\) 11.1950 0.357066 0.178533 0.983934i \(-0.442865\pi\)
0.178533 + 0.983934i \(0.442865\pi\)
\(984\) 8.78724 0.280127
\(985\) 29.1511 0.928830
\(986\) 2.74129 0.0873004
\(987\) 0 0
\(988\) −19.3998 −0.617190
\(989\) 68.9420 2.19223
\(990\) 20.8280 0.661956
\(991\) −29.2972 −0.930656 −0.465328 0.885138i \(-0.654064\pi\)
−0.465328 + 0.885138i \(0.654064\pi\)
\(992\) −29.4178 −0.934016
\(993\) 6.23633 0.197904
\(994\) 0 0
\(995\) 23.0770 0.731590
\(996\) 71.5545 2.26729
\(997\) 48.6205 1.53983 0.769913 0.638149i \(-0.220300\pi\)
0.769913 + 0.638149i \(0.220300\pi\)
\(998\) 93.2016 2.95025
\(999\) −9.81901 −0.310660
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 \(a_p\))