Properties

Label 6027.2.a.bo.1.3
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.22021 q^{2} +1.00000 q^{3} +2.92934 q^{4} +0.165927 q^{5} -2.22021 q^{6} -2.06334 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.22021 q^{2} +1.00000 q^{3} +2.92934 q^{4} +0.165927 q^{5} -2.22021 q^{6} -2.06334 q^{8} +1.00000 q^{9} -0.368393 q^{10} +2.45014 q^{11} +2.92934 q^{12} +0.862086 q^{13} +0.165927 q^{15} -1.27763 q^{16} +4.02184 q^{17} -2.22021 q^{18} +2.72504 q^{19} +0.486057 q^{20} -5.43984 q^{22} -4.73844 q^{23} -2.06334 q^{24} -4.97247 q^{25} -1.91401 q^{26} +1.00000 q^{27} -6.41611 q^{29} -0.368393 q^{30} +4.79993 q^{31} +6.96329 q^{32} +2.45014 q^{33} -8.92935 q^{34} +2.92934 q^{36} -7.78311 q^{37} -6.05018 q^{38} +0.862086 q^{39} -0.342364 q^{40} -1.00000 q^{41} +7.56342 q^{43} +7.17732 q^{44} +0.165927 q^{45} +10.5203 q^{46} +10.2804 q^{47} -1.27763 q^{48} +11.0399 q^{50} +4.02184 q^{51} +2.52535 q^{52} +6.13697 q^{53} -2.22021 q^{54} +0.406545 q^{55} +2.72504 q^{57} +14.2451 q^{58} +8.52045 q^{59} +0.486057 q^{60} -0.773934 q^{61} -10.6569 q^{62} -12.9047 q^{64} +0.143043 q^{65} -5.43984 q^{66} +11.6535 q^{67} +11.7814 q^{68} -4.73844 q^{69} -4.99642 q^{71} -2.06334 q^{72} -15.8299 q^{73} +17.2801 q^{74} -4.97247 q^{75} +7.98259 q^{76} -1.91401 q^{78} +10.2409 q^{79} -0.211993 q^{80} +1.00000 q^{81} +2.22021 q^{82} +5.29386 q^{83} +0.667332 q^{85} -16.7924 q^{86} -6.41611 q^{87} -5.05549 q^{88} +9.60949 q^{89} -0.368393 q^{90} -13.8805 q^{92} +4.79993 q^{93} -22.8246 q^{94} +0.452158 q^{95} +6.96329 q^{96} -18.6836 q^{97} +2.45014 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{3} + 32q^{4} + 4q^{5} + 8q^{6} + 24q^{8} + 24q^{9} - 4q^{10} + 12q^{11} + 32q^{12} + 4q^{15} + 44q^{16} + 8q^{17} + 8q^{18} - 4q^{19} + 28q^{20} + 16q^{22} + 20q^{23} + 24q^{24} + 48q^{25} + 32q^{26} + 24q^{27} + 24q^{29} - 4q^{30} - 4q^{31} + 36q^{32} + 12q^{33} + 16q^{34} + 32q^{36} + 64q^{37} + 20q^{38} - 48q^{40} - 24q^{41} + 20q^{43} + 48q^{44} + 4q^{45} + 28q^{46} + 32q^{47} + 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} + 8q^{54} - 24q^{55} - 4q^{57} + 28q^{58} + 28q^{59} + 28q^{60} - 28q^{61} - 4q^{62} + 48q^{64} + 28q^{65} + 16q^{66} + 44q^{67} - 32q^{68} + 20q^{69} + 20q^{71} + 24q^{72} - 16q^{73} + 44q^{74} + 48q^{75} - 16q^{76} + 32q^{78} + 4q^{79} + 44q^{80} + 24q^{81} - 8q^{82} + 8q^{83} + 28q^{85} + 56q^{86} + 24q^{87} + 60q^{88} + 60q^{89} - 4q^{90} + 60q^{92} - 4q^{93} + 24q^{94} + 28q^{95} + 36q^{96} - 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.22021 −1.56993 −0.784964 0.619542i \(-0.787318\pi\)
−0.784964 + 0.619542i \(0.787318\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.92934 1.46467
\(5\) 0.165927 0.0742047 0.0371024 0.999311i \(-0.488187\pi\)
0.0371024 + 0.999311i \(0.488187\pi\)
\(6\) −2.22021 −0.906398
\(7\) 0 0
\(8\) −2.06334 −0.729502
\(9\) 1.00000 0.333333
\(10\) −0.368393 −0.116496
\(11\) 2.45014 0.738746 0.369373 0.929281i \(-0.379572\pi\)
0.369373 + 0.929281i \(0.379572\pi\)
\(12\) 2.92934 0.845629
\(13\) 0.862086 0.239100 0.119550 0.992828i \(-0.461855\pi\)
0.119550 + 0.992828i \(0.461855\pi\)
\(14\) 0 0
\(15\) 0.165927 0.0428421
\(16\) −1.27763 −0.319407
\(17\) 4.02184 0.975440 0.487720 0.873000i \(-0.337829\pi\)
0.487720 + 0.873000i \(0.337829\pi\)
\(18\) −2.22021 −0.523309
\(19\) 2.72504 0.625168 0.312584 0.949890i \(-0.398805\pi\)
0.312584 + 0.949890i \(0.398805\pi\)
\(20\) 0.486057 0.108686
\(21\) 0 0
\(22\) −5.43984 −1.15978
\(23\) −4.73844 −0.988033 −0.494016 0.869453i \(-0.664472\pi\)
−0.494016 + 0.869453i \(0.664472\pi\)
\(24\) −2.06334 −0.421178
\(25\) −4.97247 −0.994494
\(26\) −1.91401 −0.375369
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −6.41611 −1.19144 −0.595720 0.803192i \(-0.703133\pi\)
−0.595720 + 0.803192i \(0.703133\pi\)
\(30\) −0.368393 −0.0672590
\(31\) 4.79993 0.862094 0.431047 0.902330i \(-0.358144\pi\)
0.431047 + 0.902330i \(0.358144\pi\)
\(32\) 6.96329 1.23095
\(33\) 2.45014 0.426515
\(34\) −8.92935 −1.53137
\(35\) 0 0
\(36\) 2.92934 0.488224
\(37\) −7.78311 −1.27953 −0.639767 0.768569i \(-0.720969\pi\)
−0.639767 + 0.768569i \(0.720969\pi\)
\(38\) −6.05018 −0.981468
\(39\) 0.862086 0.138044
\(40\) −0.342364 −0.0541325
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) 7.56342 1.15341 0.576705 0.816952i \(-0.304338\pi\)
0.576705 + 0.816952i \(0.304338\pi\)
\(44\) 7.17732 1.08202
\(45\) 0.165927 0.0247349
\(46\) 10.5203 1.55114
\(47\) 10.2804 1.49955 0.749774 0.661694i \(-0.230162\pi\)
0.749774 + 0.661694i \(0.230162\pi\)
\(48\) −1.27763 −0.184410
\(49\) 0 0
\(50\) 11.0399 1.56128
\(51\) 4.02184 0.563171
\(52\) 2.52535 0.350203
\(53\) 6.13697 0.842977 0.421489 0.906834i \(-0.361508\pi\)
0.421489 + 0.906834i \(0.361508\pi\)
\(54\) −2.22021 −0.302133
\(55\) 0.406545 0.0548185
\(56\) 0 0
\(57\) 2.72504 0.360941
\(58\) 14.2451 1.87048
\(59\) 8.52045 1.10927 0.554634 0.832095i \(-0.312858\pi\)
0.554634 + 0.832095i \(0.312858\pi\)
\(60\) 0.486057 0.0627497
\(61\) −0.773934 −0.0990922 −0.0495461 0.998772i \(-0.515777\pi\)
−0.0495461 + 0.998772i \(0.515777\pi\)
\(62\) −10.6569 −1.35342
\(63\) 0 0
\(64\) −12.9047 −1.61309
\(65\) 0.143043 0.0177423
\(66\) −5.43984 −0.669598
\(67\) 11.6535 1.42370 0.711850 0.702332i \(-0.247858\pi\)
0.711850 + 0.702332i \(0.247858\pi\)
\(68\) 11.7814 1.42870
\(69\) −4.73844 −0.570441
\(70\) 0 0
\(71\) −4.99642 −0.592966 −0.296483 0.955038i \(-0.595814\pi\)
−0.296483 + 0.955038i \(0.595814\pi\)
\(72\) −2.06334 −0.243167
\(73\) −15.8299 −1.85275 −0.926376 0.376599i \(-0.877093\pi\)
−0.926376 + 0.376599i \(0.877093\pi\)
\(74\) 17.2801 2.00878
\(75\) −4.97247 −0.574171
\(76\) 7.98259 0.915666
\(77\) 0 0
\(78\) −1.91401 −0.216719
\(79\) 10.2409 1.15219 0.576097 0.817382i \(-0.304575\pi\)
0.576097 + 0.817382i \(0.304575\pi\)
\(80\) −0.211993 −0.0237015
\(81\) 1.00000 0.111111
\(82\) 2.22021 0.245181
\(83\) 5.29386 0.581076 0.290538 0.956863i \(-0.406166\pi\)
0.290538 + 0.956863i \(0.406166\pi\)
\(84\) 0 0
\(85\) 0.667332 0.0723823
\(86\) −16.7924 −1.81077
\(87\) −6.41611 −0.687879
\(88\) −5.05549 −0.538917
\(89\) 9.60949 1.01860 0.509302 0.860588i \(-0.329904\pi\)
0.509302 + 0.860588i \(0.329904\pi\)
\(90\) −0.368393 −0.0388320
\(91\) 0 0
\(92\) −13.8805 −1.44714
\(93\) 4.79993 0.497730
\(94\) −22.8246 −2.35418
\(95\) 0.452158 0.0463904
\(96\) 6.96329 0.710688
\(97\) −18.6836 −1.89703 −0.948514 0.316736i \(-0.897413\pi\)
−0.948514 + 0.316736i \(0.897413\pi\)
\(98\) 0 0
\(99\) 2.45014 0.246249
\(100\) −14.5661 −1.45661
\(101\) 9.94335 0.989400 0.494700 0.869064i \(-0.335278\pi\)
0.494700 + 0.869064i \(0.335278\pi\)
\(102\) −8.92935 −0.884137
\(103\) 8.14668 0.802716 0.401358 0.915921i \(-0.368538\pi\)
0.401358 + 0.915921i \(0.368538\pi\)
\(104\) −1.77878 −0.174424
\(105\) 0 0
\(106\) −13.6254 −1.32341
\(107\) 5.74895 0.555772 0.277886 0.960614i \(-0.410366\pi\)
0.277886 + 0.960614i \(0.410366\pi\)
\(108\) 2.92934 0.281876
\(109\) −2.62119 −0.251065 −0.125532 0.992090i \(-0.540064\pi\)
−0.125532 + 0.992090i \(0.540064\pi\)
\(110\) −0.902616 −0.0860610
\(111\) −7.78311 −0.738740
\(112\) 0 0
\(113\) −4.82467 −0.453866 −0.226933 0.973910i \(-0.572870\pi\)
−0.226933 + 0.973910i \(0.572870\pi\)
\(114\) −6.05018 −0.566651
\(115\) −0.786234 −0.0733167
\(116\) −18.7950 −1.74507
\(117\) 0.862086 0.0796998
\(118\) −18.9172 −1.74147
\(119\) 0 0
\(120\) −0.342364 −0.0312534
\(121\) −4.99679 −0.454254
\(122\) 1.71830 0.155568
\(123\) −1.00000 −0.0901670
\(124\) 14.0607 1.26268
\(125\) −1.65470 −0.148001
\(126\) 0 0
\(127\) 13.7531 1.22039 0.610193 0.792253i \(-0.291092\pi\)
0.610193 + 0.792253i \(0.291092\pi\)
\(128\) 14.7247 1.30149
\(129\) 7.56342 0.665922
\(130\) −0.317586 −0.0278541
\(131\) 0.254327 0.0222207 0.0111103 0.999938i \(-0.496463\pi\)
0.0111103 + 0.999938i \(0.496463\pi\)
\(132\) 7.17732 0.624705
\(133\) 0 0
\(134\) −25.8732 −2.23511
\(135\) 0.165927 0.0142807
\(136\) −8.29844 −0.711586
\(137\) 13.0440 1.11443 0.557214 0.830369i \(-0.311870\pi\)
0.557214 + 0.830369i \(0.311870\pi\)
\(138\) 10.5203 0.895551
\(139\) −2.08977 −0.177252 −0.0886262 0.996065i \(-0.528248\pi\)
−0.0886262 + 0.996065i \(0.528248\pi\)
\(140\) 0 0
\(141\) 10.2804 0.865764
\(142\) 11.0931 0.930914
\(143\) 2.11223 0.176634
\(144\) −1.27763 −0.106469
\(145\) −1.06460 −0.0884105
\(146\) 35.1458 2.90869
\(147\) 0 0
\(148\) −22.7994 −1.87410
\(149\) 1.42493 0.116735 0.0583674 0.998295i \(-0.481411\pi\)
0.0583674 + 0.998295i \(0.481411\pi\)
\(150\) 11.0399 0.901407
\(151\) 11.7421 0.955559 0.477779 0.878480i \(-0.341442\pi\)
0.477779 + 0.878480i \(0.341442\pi\)
\(152\) −5.62270 −0.456061
\(153\) 4.02184 0.325147
\(154\) 0 0
\(155\) 0.796438 0.0639714
\(156\) 2.52535 0.202190
\(157\) −20.9461 −1.67168 −0.835841 0.548972i \(-0.815019\pi\)
−0.835841 + 0.548972i \(0.815019\pi\)
\(158\) −22.7370 −1.80886
\(159\) 6.13697 0.486693
\(160\) 1.15540 0.0913421
\(161\) 0 0
\(162\) −2.22021 −0.174436
\(163\) −14.4528 −1.13203 −0.566015 0.824395i \(-0.691515\pi\)
−0.566015 + 0.824395i \(0.691515\pi\)
\(164\) −2.92934 −0.228743
\(165\) 0.406545 0.0316495
\(166\) −11.7535 −0.912248
\(167\) −11.7930 −0.912567 −0.456284 0.889834i \(-0.650820\pi\)
−0.456284 + 0.889834i \(0.650820\pi\)
\(168\) 0 0
\(169\) −12.2568 −0.942831
\(170\) −1.48162 −0.113635
\(171\) 2.72504 0.208389
\(172\) 22.1559 1.68937
\(173\) 20.7992 1.58133 0.790667 0.612246i \(-0.209734\pi\)
0.790667 + 0.612246i \(0.209734\pi\)
\(174\) 14.2451 1.07992
\(175\) 0 0
\(176\) −3.13037 −0.235961
\(177\) 8.52045 0.640436
\(178\) −21.3351 −1.59913
\(179\) −5.07361 −0.379220 −0.189610 0.981860i \(-0.560722\pi\)
−0.189610 + 0.981860i \(0.560722\pi\)
\(180\) 0.486057 0.0362285
\(181\) 4.61958 0.343371 0.171685 0.985152i \(-0.445079\pi\)
0.171685 + 0.985152i \(0.445079\pi\)
\(182\) 0 0
\(183\) −0.773934 −0.0572109
\(184\) 9.77702 0.720772
\(185\) −1.29143 −0.0949475
\(186\) −10.6569 −0.781400
\(187\) 9.85410 0.720603
\(188\) 30.1148 2.19635
\(189\) 0 0
\(190\) −1.00389 −0.0728296
\(191\) 23.6825 1.71361 0.856803 0.515644i \(-0.172447\pi\)
0.856803 + 0.515644i \(0.172447\pi\)
\(192\) −12.9047 −0.931319
\(193\) −1.20281 −0.0865802 −0.0432901 0.999063i \(-0.513784\pi\)
−0.0432901 + 0.999063i \(0.513784\pi\)
\(194\) 41.4815 2.97820
\(195\) 0.143043 0.0102435
\(196\) 0 0
\(197\) 8.05510 0.573902 0.286951 0.957945i \(-0.407358\pi\)
0.286951 + 0.957945i \(0.407358\pi\)
\(198\) −5.43984 −0.386593
\(199\) 7.58393 0.537610 0.268805 0.963195i \(-0.413371\pi\)
0.268805 + 0.963195i \(0.413371\pi\)
\(200\) 10.2599 0.725485
\(201\) 11.6535 0.821974
\(202\) −22.0763 −1.55329
\(203\) 0 0
\(204\) 11.7814 0.824861
\(205\) −0.165927 −0.0115888
\(206\) −18.0874 −1.26021
\(207\) −4.73844 −0.329344
\(208\) −1.10143 −0.0763701
\(209\) 6.67675 0.461841
\(210\) 0 0
\(211\) 3.58783 0.246997 0.123498 0.992345i \(-0.460589\pi\)
0.123498 + 0.992345i \(0.460589\pi\)
\(212\) 17.9773 1.23469
\(213\) −4.99642 −0.342349
\(214\) −12.7639 −0.872521
\(215\) 1.25497 0.0855885
\(216\) −2.06334 −0.140393
\(217\) 0 0
\(218\) 5.81961 0.394154
\(219\) −15.8299 −1.06969
\(220\) 1.19091 0.0802911
\(221\) 3.46717 0.233227
\(222\) 17.2801 1.15977
\(223\) 6.85227 0.458862 0.229431 0.973325i \(-0.426313\pi\)
0.229431 + 0.973325i \(0.426313\pi\)
\(224\) 0 0
\(225\) −4.97247 −0.331498
\(226\) 10.7118 0.712537
\(227\) −12.4504 −0.826364 −0.413182 0.910648i \(-0.635583\pi\)
−0.413182 + 0.910648i \(0.635583\pi\)
\(228\) 7.98259 0.528660
\(229\) −19.0902 −1.26152 −0.630758 0.775979i \(-0.717256\pi\)
−0.630758 + 0.775979i \(0.717256\pi\)
\(230\) 1.74561 0.115102
\(231\) 0 0
\(232\) 13.2386 0.869159
\(233\) 9.45836 0.619638 0.309819 0.950796i \(-0.399732\pi\)
0.309819 + 0.950796i \(0.399732\pi\)
\(234\) −1.91401 −0.125123
\(235\) 1.70579 0.111273
\(236\) 24.9593 1.62471
\(237\) 10.2409 0.665219
\(238\) 0 0
\(239\) 13.9203 0.900429 0.450215 0.892920i \(-0.351347\pi\)
0.450215 + 0.892920i \(0.351347\pi\)
\(240\) −0.211993 −0.0136841
\(241\) 0.583754 0.0376029 0.0188014 0.999823i \(-0.494015\pi\)
0.0188014 + 0.999823i \(0.494015\pi\)
\(242\) 11.0939 0.713145
\(243\) 1.00000 0.0641500
\(244\) −2.26712 −0.145138
\(245\) 0 0
\(246\) 2.22021 0.141556
\(247\) 2.34922 0.149477
\(248\) −9.90391 −0.628899
\(249\) 5.29386 0.335485
\(250\) 3.67378 0.232351
\(251\) −0.426212 −0.0269023 −0.0134511 0.999910i \(-0.504282\pi\)
−0.0134511 + 0.999910i \(0.504282\pi\)
\(252\) 0 0
\(253\) −11.6099 −0.729906
\(254\) −30.5347 −1.91592
\(255\) 0.667332 0.0417899
\(256\) −6.88244 −0.430152
\(257\) 9.16194 0.571506 0.285753 0.958303i \(-0.407756\pi\)
0.285753 + 0.958303i \(0.407756\pi\)
\(258\) −16.7924 −1.04545
\(259\) 0 0
\(260\) 0.419023 0.0259867
\(261\) −6.41611 −0.397147
\(262\) −0.564661 −0.0348848
\(263\) 8.97300 0.553299 0.276649 0.960971i \(-0.410776\pi\)
0.276649 + 0.960971i \(0.410776\pi\)
\(264\) −5.05549 −0.311144
\(265\) 1.01829 0.0625529
\(266\) 0 0
\(267\) 9.60949 0.588091
\(268\) 34.1371 2.08525
\(269\) −8.74443 −0.533157 −0.266579 0.963813i \(-0.585893\pi\)
−0.266579 + 0.963813i \(0.585893\pi\)
\(270\) −0.368393 −0.0224197
\(271\) −17.6472 −1.07199 −0.535996 0.844221i \(-0.680064\pi\)
−0.535996 + 0.844221i \(0.680064\pi\)
\(272\) −5.13842 −0.311563
\(273\) 0 0
\(274\) −28.9606 −1.74957
\(275\) −12.1833 −0.734679
\(276\) −13.8805 −0.835509
\(277\) 10.8785 0.653625 0.326812 0.945089i \(-0.394025\pi\)
0.326812 + 0.945089i \(0.394025\pi\)
\(278\) 4.63974 0.278273
\(279\) 4.79993 0.287365
\(280\) 0 0
\(281\) −20.2375 −1.20727 −0.603633 0.797263i \(-0.706281\pi\)
−0.603633 + 0.797263i \(0.706281\pi\)
\(282\) −22.8246 −1.35919
\(283\) 6.49723 0.386220 0.193110 0.981177i \(-0.438143\pi\)
0.193110 + 0.981177i \(0.438143\pi\)
\(284\) −14.6362 −0.868502
\(285\) 0.452158 0.0267835
\(286\) −4.68961 −0.277302
\(287\) 0 0
\(288\) 6.96329 0.410316
\(289\) −0.824772 −0.0485160
\(290\) 2.36365 0.138798
\(291\) −18.6836 −1.09525
\(292\) −46.3713 −2.71368
\(293\) 5.51194 0.322011 0.161005 0.986954i \(-0.448526\pi\)
0.161005 + 0.986954i \(0.448526\pi\)
\(294\) 0 0
\(295\) 1.41377 0.0823129
\(296\) 16.0592 0.933423
\(297\) 2.45014 0.142172
\(298\) −3.16365 −0.183265
\(299\) −4.08494 −0.236238
\(300\) −14.5661 −0.840973
\(301\) 0 0
\(302\) −26.0700 −1.50016
\(303\) 9.94335 0.571230
\(304\) −3.48159 −0.199683
\(305\) −0.128416 −0.00735310
\(306\) −8.92935 −0.510457
\(307\) −2.22394 −0.126927 −0.0634634 0.997984i \(-0.520215\pi\)
−0.0634634 + 0.997984i \(0.520215\pi\)
\(308\) 0 0
\(309\) 8.14668 0.463448
\(310\) −1.76826 −0.100430
\(311\) 22.5977 1.28140 0.640698 0.767793i \(-0.278645\pi\)
0.640698 + 0.767793i \(0.278645\pi\)
\(312\) −1.77878 −0.100704
\(313\) 11.7856 0.666161 0.333080 0.942898i \(-0.391912\pi\)
0.333080 + 0.942898i \(0.391912\pi\)
\(314\) 46.5048 2.62442
\(315\) 0 0
\(316\) 29.9992 1.68759
\(317\) −5.48705 −0.308183 −0.154092 0.988057i \(-0.549245\pi\)
−0.154092 + 0.988057i \(0.549245\pi\)
\(318\) −13.6254 −0.764073
\(319\) −15.7204 −0.880173
\(320\) −2.14124 −0.119699
\(321\) 5.74895 0.320875
\(322\) 0 0
\(323\) 10.9597 0.609814
\(324\) 2.92934 0.162741
\(325\) −4.28669 −0.237783
\(326\) 32.0883 1.77720
\(327\) −2.62119 −0.144952
\(328\) 2.06334 0.113929
\(329\) 0 0
\(330\) −0.902616 −0.0496874
\(331\) −27.8774 −1.53228 −0.766141 0.642673i \(-0.777825\pi\)
−0.766141 + 0.642673i \(0.777825\pi\)
\(332\) 15.5075 0.851086
\(333\) −7.78311 −0.426512
\(334\) 26.1829 1.43266
\(335\) 1.93363 0.105645
\(336\) 0 0
\(337\) 33.3457 1.81645 0.908227 0.418478i \(-0.137436\pi\)
0.908227 + 0.418478i \(0.137436\pi\)
\(338\) 27.2127 1.48018
\(339\) −4.82467 −0.262040
\(340\) 1.95484 0.106016
\(341\) 11.7605 0.636869
\(342\) −6.05018 −0.327156
\(343\) 0 0
\(344\) −15.6059 −0.841415
\(345\) −0.786234 −0.0423294
\(346\) −46.1787 −2.48258
\(347\) −14.1721 −0.760800 −0.380400 0.924822i \(-0.624214\pi\)
−0.380400 + 0.924822i \(0.624214\pi\)
\(348\) −18.7950 −1.00752
\(349\) 2.16435 0.115855 0.0579275 0.998321i \(-0.481551\pi\)
0.0579275 + 0.998321i \(0.481551\pi\)
\(350\) 0 0
\(351\) 0.862086 0.0460147
\(352\) 17.0611 0.909359
\(353\) 33.5484 1.78560 0.892800 0.450453i \(-0.148737\pi\)
0.892800 + 0.450453i \(0.148737\pi\)
\(354\) −18.9172 −1.00544
\(355\) −0.829041 −0.0440009
\(356\) 28.1495 1.49192
\(357\) 0 0
\(358\) 11.2645 0.595347
\(359\) 17.8178 0.940386 0.470193 0.882563i \(-0.344184\pi\)
0.470193 + 0.882563i \(0.344184\pi\)
\(360\) −0.342364 −0.0180442
\(361\) −11.5741 −0.609165
\(362\) −10.2565 −0.539067
\(363\) −4.99679 −0.262263
\(364\) 0 0
\(365\) −2.62661 −0.137483
\(366\) 1.71830 0.0898169
\(367\) 2.57938 0.134643 0.0673213 0.997731i \(-0.478555\pi\)
0.0673213 + 0.997731i \(0.478555\pi\)
\(368\) 6.05396 0.315585
\(369\) −1.00000 −0.0520579
\(370\) 2.86724 0.149061
\(371\) 0 0
\(372\) 14.0607 0.729011
\(373\) 20.4331 1.05799 0.528993 0.848626i \(-0.322570\pi\)
0.528993 + 0.848626i \(0.322570\pi\)
\(374\) −21.8782 −1.13129
\(375\) −1.65470 −0.0854483
\(376\) −21.2120 −1.09392
\(377\) −5.53123 −0.284873
\(378\) 0 0
\(379\) −13.6675 −0.702051 −0.351025 0.936366i \(-0.614167\pi\)
−0.351025 + 0.936366i \(0.614167\pi\)
\(380\) 1.32453 0.0679467
\(381\) 13.7531 0.704590
\(382\) −52.5802 −2.69024
\(383\) −31.0004 −1.58405 −0.792024 0.610490i \(-0.790973\pi\)
−0.792024 + 0.610490i \(0.790973\pi\)
\(384\) 14.7247 0.751415
\(385\) 0 0
\(386\) 2.67049 0.135925
\(387\) 7.56342 0.384470
\(388\) −54.7306 −2.77852
\(389\) 25.5540 1.29564 0.647819 0.761794i \(-0.275681\pi\)
0.647819 + 0.761794i \(0.275681\pi\)
\(390\) −0.317586 −0.0160816
\(391\) −19.0573 −0.963767
\(392\) 0 0
\(393\) 0.254327 0.0128291
\(394\) −17.8840 −0.900985
\(395\) 1.69924 0.0854982
\(396\) 7.17732 0.360674
\(397\) 10.7669 0.540375 0.270187 0.962808i \(-0.412914\pi\)
0.270187 + 0.962808i \(0.412914\pi\)
\(398\) −16.8379 −0.844009
\(399\) 0 0
\(400\) 6.35297 0.317648
\(401\) −21.3162 −1.06448 −0.532241 0.846593i \(-0.678650\pi\)
−0.532241 + 0.846593i \(0.678650\pi\)
\(402\) −25.8732 −1.29044
\(403\) 4.13795 0.206126
\(404\) 29.1275 1.44915
\(405\) 0.165927 0.00824497
\(406\) 0 0
\(407\) −19.0697 −0.945252
\(408\) −8.29844 −0.410834
\(409\) 21.2963 1.05303 0.526517 0.850165i \(-0.323498\pi\)
0.526517 + 0.850165i \(0.323498\pi\)
\(410\) 0.368393 0.0181936
\(411\) 13.0440 0.643415
\(412\) 23.8644 1.17572
\(413\) 0 0
\(414\) 10.5203 0.517047
\(415\) 0.878393 0.0431186
\(416\) 6.00296 0.294319
\(417\) −2.08977 −0.102337
\(418\) −14.8238 −0.725056
\(419\) 6.18534 0.302174 0.151087 0.988520i \(-0.451723\pi\)
0.151087 + 0.988520i \(0.451723\pi\)
\(420\) 0 0
\(421\) 18.2006 0.887041 0.443521 0.896264i \(-0.353729\pi\)
0.443521 + 0.896264i \(0.353729\pi\)
\(422\) −7.96575 −0.387767
\(423\) 10.2804 0.499849
\(424\) −12.6627 −0.614954
\(425\) −19.9985 −0.970069
\(426\) 11.0931 0.537464
\(427\) 0 0
\(428\) 16.8407 0.814024
\(429\) 2.11223 0.101980
\(430\) −2.78631 −0.134368
\(431\) −22.7537 −1.09601 −0.548004 0.836475i \(-0.684612\pi\)
−0.548004 + 0.836475i \(0.684612\pi\)
\(432\) −1.27763 −0.0614699
\(433\) −29.0237 −1.39479 −0.697396 0.716686i \(-0.745658\pi\)
−0.697396 + 0.716686i \(0.745658\pi\)
\(434\) 0 0
\(435\) −1.06460 −0.0510438
\(436\) −7.67838 −0.367728
\(437\) −12.9125 −0.617686
\(438\) 35.1458 1.67933
\(439\) −22.6255 −1.07986 −0.539928 0.841711i \(-0.681549\pi\)
−0.539928 + 0.841711i \(0.681549\pi\)
\(440\) −0.838841 −0.0399902
\(441\) 0 0
\(442\) −7.69786 −0.366150
\(443\) 13.3204 0.632870 0.316435 0.948614i \(-0.397514\pi\)
0.316435 + 0.948614i \(0.397514\pi\)
\(444\) −22.7994 −1.08201
\(445\) 1.59447 0.0755852
\(446\) −15.2135 −0.720380
\(447\) 1.42493 0.0673969
\(448\) 0 0
\(449\) 12.6589 0.597412 0.298706 0.954345i \(-0.403445\pi\)
0.298706 + 0.954345i \(0.403445\pi\)
\(450\) 11.0399 0.520428
\(451\) −2.45014 −0.115373
\(452\) −14.1331 −0.664766
\(453\) 11.7421 0.551692
\(454\) 27.6426 1.29733
\(455\) 0 0
\(456\) −5.62270 −0.263307
\(457\) −10.1104 −0.472943 −0.236471 0.971638i \(-0.575991\pi\)
−0.236471 + 0.971638i \(0.575991\pi\)
\(458\) 42.3843 1.98049
\(459\) 4.02184 0.187724
\(460\) −2.30315 −0.107385
\(461\) 10.9322 0.509161 0.254580 0.967052i \(-0.418063\pi\)
0.254580 + 0.967052i \(0.418063\pi\)
\(462\) 0 0
\(463\) 25.7020 1.19447 0.597237 0.802064i \(-0.296265\pi\)
0.597237 + 0.802064i \(0.296265\pi\)
\(464\) 8.19740 0.380555
\(465\) 0.796438 0.0369339
\(466\) −20.9996 −0.972787
\(467\) −21.4674 −0.993395 −0.496697 0.867924i \(-0.665454\pi\)
−0.496697 + 0.867924i \(0.665454\pi\)
\(468\) 2.52535 0.116734
\(469\) 0 0
\(470\) −3.78722 −0.174691
\(471\) −20.9461 −0.965146
\(472\) −17.5806 −0.809213
\(473\) 18.5315 0.852078
\(474\) −22.7370 −1.04435
\(475\) −13.5502 −0.621726
\(476\) 0 0
\(477\) 6.13697 0.280992
\(478\) −30.9060 −1.41361
\(479\) 3.81420 0.174275 0.0871376 0.996196i \(-0.472228\pi\)
0.0871376 + 0.996196i \(0.472228\pi\)
\(480\) 1.15540 0.0527364
\(481\) −6.70970 −0.305936
\(482\) −1.29606 −0.0590338
\(483\) 0 0
\(484\) −14.6373 −0.665333
\(485\) −3.10010 −0.140768
\(486\) −2.22021 −0.100711
\(487\) 35.2293 1.59639 0.798197 0.602396i \(-0.205787\pi\)
0.798197 + 0.602396i \(0.205787\pi\)
\(488\) 1.59689 0.0722879
\(489\) −14.4528 −0.653577
\(490\) 0 0
\(491\) −28.8483 −1.30190 −0.650952 0.759119i \(-0.725630\pi\)
−0.650952 + 0.759119i \(0.725630\pi\)
\(492\) −2.92934 −0.132065
\(493\) −25.8046 −1.16218
\(494\) −5.21577 −0.234669
\(495\) 0.406545 0.0182728
\(496\) −6.13253 −0.275359
\(497\) 0 0
\(498\) −11.7535 −0.526686
\(499\) −6.51441 −0.291625 −0.145813 0.989312i \(-0.546580\pi\)
−0.145813 + 0.989312i \(0.546580\pi\)
\(500\) −4.84719 −0.216773
\(501\) −11.7930 −0.526871
\(502\) 0.946282 0.0422346
\(503\) 15.2400 0.679516 0.339758 0.940513i \(-0.389655\pi\)
0.339758 + 0.940513i \(0.389655\pi\)
\(504\) 0 0
\(505\) 1.64987 0.0734181
\(506\) 25.7764 1.14590
\(507\) −12.2568 −0.544344
\(508\) 40.2874 1.78747
\(509\) −32.4515 −1.43839 −0.719193 0.694810i \(-0.755489\pi\)
−0.719193 + 0.694810i \(0.755489\pi\)
\(510\) −1.48162 −0.0656071
\(511\) 0 0
\(512\) −14.1689 −0.626182
\(513\) 2.72504 0.120314
\(514\) −20.3415 −0.897223
\(515\) 1.35175 0.0595653
\(516\) 22.1559 0.975357
\(517\) 25.1884 1.10779
\(518\) 0 0
\(519\) 20.7992 0.912984
\(520\) −0.295147 −0.0129431
\(521\) −8.46956 −0.371058 −0.185529 0.982639i \(-0.559400\pi\)
−0.185529 + 0.982639i \(0.559400\pi\)
\(522\) 14.2451 0.623492
\(523\) −40.6091 −1.77571 −0.887857 0.460120i \(-0.847806\pi\)
−0.887857 + 0.460120i \(0.847806\pi\)
\(524\) 0.745012 0.0325460
\(525\) 0 0
\(526\) −19.9220 −0.868639
\(527\) 19.3046 0.840921
\(528\) −3.13037 −0.136232
\(529\) −0.547203 −0.0237914
\(530\) −2.26081 −0.0982035
\(531\) 8.52045 0.369756
\(532\) 0 0
\(533\) −0.862086 −0.0373411
\(534\) −21.3351 −0.923261
\(535\) 0.953904 0.0412409
\(536\) −24.0451 −1.03859
\(537\) −5.07361 −0.218943
\(538\) 19.4145 0.837019
\(539\) 0 0
\(540\) 0.486057 0.0209166
\(541\) 38.7394 1.66554 0.832768 0.553622i \(-0.186755\pi\)
0.832768 + 0.553622i \(0.186755\pi\)
\(542\) 39.1806 1.68295
\(543\) 4.61958 0.198245
\(544\) 28.0053 1.20072
\(545\) −0.434926 −0.0186302
\(546\) 0 0
\(547\) −11.6384 −0.497623 −0.248811 0.968552i \(-0.580040\pi\)
−0.248811 + 0.968552i \(0.580040\pi\)
\(548\) 38.2105 1.63227
\(549\) −0.773934 −0.0330307
\(550\) 27.0494 1.15339
\(551\) −17.4842 −0.744851
\(552\) 9.77702 0.416138
\(553\) 0 0
\(554\) −24.1526 −1.02614
\(555\) −1.29143 −0.0548180
\(556\) −6.12167 −0.259617
\(557\) 0.391654 0.0165949 0.00829746 0.999966i \(-0.497359\pi\)
0.00829746 + 0.999966i \(0.497359\pi\)
\(558\) −10.6569 −0.451142
\(559\) 6.52031 0.275780
\(560\) 0 0
\(561\) 9.85410 0.416040
\(562\) 44.9315 1.89532
\(563\) 22.6577 0.954907 0.477453 0.878657i \(-0.341560\pi\)
0.477453 + 0.878657i \(0.341560\pi\)
\(564\) 30.1148 1.26806
\(565\) −0.800541 −0.0336790
\(566\) −14.4252 −0.606338
\(567\) 0 0
\(568\) 10.3093 0.432570
\(569\) −5.50248 −0.230676 −0.115338 0.993326i \(-0.536795\pi\)
−0.115338 + 0.993326i \(0.536795\pi\)
\(570\) −1.00389 −0.0420482
\(571\) −28.9417 −1.21117 −0.605586 0.795780i \(-0.707061\pi\)
−0.605586 + 0.795780i \(0.707061\pi\)
\(572\) 6.18746 0.258711
\(573\) 23.6825 0.989351
\(574\) 0 0
\(575\) 23.5617 0.982592
\(576\) −12.9047 −0.537697
\(577\) 25.4503 1.05951 0.529754 0.848151i \(-0.322284\pi\)
0.529754 + 0.848151i \(0.322284\pi\)
\(578\) 1.83117 0.0761666
\(579\) −1.20281 −0.0499871
\(580\) −3.11859 −0.129492
\(581\) 0 0
\(582\) 41.4815 1.71946
\(583\) 15.0365 0.622747
\(584\) 32.6626 1.35159
\(585\) 0.143043 0.00591410
\(586\) −12.2377 −0.505534
\(587\) 12.9184 0.533199 0.266600 0.963807i \(-0.414100\pi\)
0.266600 + 0.963807i \(0.414100\pi\)
\(588\) 0 0
\(589\) 13.0800 0.538953
\(590\) −3.13887 −0.129225
\(591\) 8.05510 0.331342
\(592\) 9.94392 0.408692
\(593\) 20.5182 0.842581 0.421291 0.906926i \(-0.361577\pi\)
0.421291 + 0.906926i \(0.361577\pi\)
\(594\) −5.43984 −0.223199
\(595\) 0 0
\(596\) 4.17411 0.170978
\(597\) 7.58393 0.310390
\(598\) 9.06944 0.370877
\(599\) 46.2714 1.89060 0.945299 0.326206i \(-0.105770\pi\)
0.945299 + 0.326206i \(0.105770\pi\)
\(600\) 10.2599 0.418859
\(601\) −32.3347 −1.31896 −0.659480 0.751722i \(-0.729224\pi\)
−0.659480 + 0.751722i \(0.729224\pi\)
\(602\) 0 0
\(603\) 11.6535 0.474567
\(604\) 34.3967 1.39958
\(605\) −0.829101 −0.0337078
\(606\) −22.0763 −0.896790
\(607\) 26.6961 1.08356 0.541781 0.840520i \(-0.317750\pi\)
0.541781 + 0.840520i \(0.317750\pi\)
\(608\) 18.9753 0.769549
\(609\) 0 0
\(610\) 0.285112 0.0115438
\(611\) 8.86257 0.358541
\(612\) 11.7814 0.476234
\(613\) 13.3137 0.537737 0.268868 0.963177i \(-0.413350\pi\)
0.268868 + 0.963177i \(0.413350\pi\)
\(614\) 4.93761 0.199266
\(615\) −0.165927 −0.00669081
\(616\) 0 0
\(617\) 20.4322 0.822569 0.411284 0.911507i \(-0.365080\pi\)
0.411284 + 0.911507i \(0.365080\pi\)
\(618\) −18.0874 −0.727580
\(619\) 25.4517 1.02299 0.511495 0.859286i \(-0.329092\pi\)
0.511495 + 0.859286i \(0.329092\pi\)
\(620\) 2.33304 0.0936971
\(621\) −4.73844 −0.190147
\(622\) −50.1716 −2.01170
\(623\) 0 0
\(624\) −1.10143 −0.0440923
\(625\) 24.5878 0.983511
\(626\) −26.1665 −1.04582
\(627\) 6.67675 0.266644
\(628\) −61.3584 −2.44847
\(629\) −31.3024 −1.24811
\(630\) 0 0
\(631\) 45.4277 1.80845 0.904225 0.427057i \(-0.140450\pi\)
0.904225 + 0.427057i \(0.140450\pi\)
\(632\) −21.1305 −0.840527
\(633\) 3.58783 0.142604
\(634\) 12.1824 0.483825
\(635\) 2.28200 0.0905584
\(636\) 17.9773 0.712846
\(637\) 0 0
\(638\) 34.9026 1.38181
\(639\) −4.99642 −0.197655
\(640\) 2.44322 0.0965767
\(641\) 24.3972 0.963633 0.481816 0.876272i \(-0.339977\pi\)
0.481816 + 0.876272i \(0.339977\pi\)
\(642\) −12.7639 −0.503750
\(643\) 24.3477 0.960180 0.480090 0.877219i \(-0.340604\pi\)
0.480090 + 0.877219i \(0.340604\pi\)
\(644\) 0 0
\(645\) 1.25497 0.0494145
\(646\) −24.3329 −0.957364
\(647\) −21.7620 −0.855552 −0.427776 0.903885i \(-0.640703\pi\)
−0.427776 + 0.903885i \(0.640703\pi\)
\(648\) −2.06334 −0.0810558
\(649\) 20.8763 0.819468
\(650\) 9.51737 0.373302
\(651\) 0 0
\(652\) −42.3372 −1.65805
\(653\) 5.37080 0.210176 0.105088 0.994463i \(-0.466488\pi\)
0.105088 + 0.994463i \(0.466488\pi\)
\(654\) 5.81961 0.227565
\(655\) 0.0421997 0.00164888
\(656\) 1.27763 0.0498830
\(657\) −15.8299 −0.617584
\(658\) 0 0
\(659\) −26.7004 −1.04010 −0.520049 0.854136i \(-0.674086\pi\)
−0.520049 + 0.854136i \(0.674086\pi\)
\(660\) 1.19091 0.0463561
\(661\) 35.6937 1.38832 0.694161 0.719820i \(-0.255775\pi\)
0.694161 + 0.719820i \(0.255775\pi\)
\(662\) 61.8938 2.40557
\(663\) 3.46717 0.134654
\(664\) −10.9230 −0.423896
\(665\) 0 0
\(666\) 17.2801 0.669592
\(667\) 30.4023 1.17718
\(668\) −34.5457 −1.33661
\(669\) 6.85227 0.264924
\(670\) −4.29306 −0.165855
\(671\) −1.89625 −0.0732040
\(672\) 0 0
\(673\) 27.9802 1.07856 0.539280 0.842127i \(-0.318697\pi\)
0.539280 + 0.842127i \(0.318697\pi\)
\(674\) −74.0345 −2.85170
\(675\) −4.97247 −0.191390
\(676\) −35.9044 −1.38094
\(677\) −8.16920 −0.313968 −0.156984 0.987601i \(-0.550177\pi\)
−0.156984 + 0.987601i \(0.550177\pi\)
\(678\) 10.7118 0.411384
\(679\) 0 0
\(680\) −1.37693 −0.0528030
\(681\) −12.4504 −0.477101
\(682\) −26.1109 −0.999838
\(683\) −10.3176 −0.394791 −0.197396 0.980324i \(-0.563248\pi\)
−0.197396 + 0.980324i \(0.563248\pi\)
\(684\) 7.98259 0.305222
\(685\) 2.16436 0.0826958
\(686\) 0 0
\(687\) −19.0902 −0.728337
\(688\) −9.66324 −0.368407
\(689\) 5.29059 0.201556
\(690\) 1.74561 0.0664541
\(691\) −2.89735 −0.110220 −0.0551101 0.998480i \(-0.517551\pi\)
−0.0551101 + 0.998480i \(0.517551\pi\)
\(692\) 60.9280 2.31614
\(693\) 0 0
\(694\) 31.4652 1.19440
\(695\) −0.346750 −0.0131530
\(696\) 13.2386 0.501809
\(697\) −4.02184 −0.152338
\(698\) −4.80532 −0.181884
\(699\) 9.45836 0.357748
\(700\) 0 0
\(701\) 33.2272 1.25497 0.627487 0.778627i \(-0.284084\pi\)
0.627487 + 0.778627i \(0.284084\pi\)
\(702\) −1.91401 −0.0722398
\(703\) −21.2093 −0.799924
\(704\) −31.6185 −1.19167
\(705\) 1.70579 0.0642438
\(706\) −74.4846 −2.80326
\(707\) 0 0
\(708\) 24.9593 0.938029
\(709\) 44.1099 1.65658 0.828291 0.560298i \(-0.189313\pi\)
0.828291 + 0.560298i \(0.189313\pi\)
\(710\) 1.84065 0.0690782
\(711\) 10.2409 0.384064
\(712\) −19.8277 −0.743074
\(713\) −22.7442 −0.851777
\(714\) 0 0
\(715\) 0.350476 0.0131071
\(716\) −14.8624 −0.555433
\(717\) 13.9203 0.519863
\(718\) −39.5593 −1.47634
\(719\) −1.17550 −0.0438388 −0.0219194 0.999760i \(-0.506978\pi\)
−0.0219194 + 0.999760i \(0.506978\pi\)
\(720\) −0.211993 −0.00790050
\(721\) 0 0
\(722\) 25.6970 0.956345
\(723\) 0.583754 0.0217100
\(724\) 13.5323 0.502926
\(725\) 31.9039 1.18488
\(726\) 11.0939 0.411735
\(727\) 38.3481 1.42225 0.711126 0.703064i \(-0.248185\pi\)
0.711126 + 0.703064i \(0.248185\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 5.83163 0.215838
\(731\) 30.4189 1.12508
\(732\) −2.26712 −0.0837952
\(733\) −8.22560 −0.303820 −0.151910 0.988394i \(-0.548542\pi\)
−0.151910 + 0.988394i \(0.548542\pi\)
\(734\) −5.72677 −0.211379
\(735\) 0 0
\(736\) −32.9951 −1.21622
\(737\) 28.5527 1.05175
\(738\) 2.22021 0.0817272
\(739\) −27.9329 −1.02753 −0.513765 0.857931i \(-0.671750\pi\)
−0.513765 + 0.857931i \(0.671750\pi\)
\(740\) −3.78303 −0.139067
\(741\) 2.34922 0.0863008
\(742\) 0 0
\(743\) −33.8794 −1.24291 −0.621457 0.783448i \(-0.713459\pi\)
−0.621457 + 0.783448i \(0.713459\pi\)
\(744\) −9.90391 −0.363095
\(745\) 0.236434 0.00866227
\(746\) −45.3658 −1.66096
\(747\) 5.29386 0.193692
\(748\) 28.8661 1.05545
\(749\) 0 0
\(750\) 3.67378 0.134148
\(751\) 29.1721 1.06450 0.532252 0.846586i \(-0.321346\pi\)
0.532252 + 0.846586i \(0.321346\pi\)
\(752\) −13.1345 −0.478966
\(753\) −0.426212 −0.0155320
\(754\) 12.2805 0.447230
\(755\) 1.94833 0.0709070
\(756\) 0 0
\(757\) −2.85953 −0.103932 −0.0519658 0.998649i \(-0.516549\pi\)
−0.0519658 + 0.998649i \(0.516549\pi\)
\(758\) 30.3447 1.10217
\(759\) −11.6099 −0.421411
\(760\) −0.932957 −0.0338419
\(761\) −33.5286 −1.21541 −0.607706 0.794162i \(-0.707910\pi\)
−0.607706 + 0.794162i \(0.707910\pi\)
\(762\) −30.5347 −1.10616
\(763\) 0 0
\(764\) 69.3742 2.50987
\(765\) 0.667332 0.0241274
\(766\) 68.8276 2.48684
\(767\) 7.34535 0.265225
\(768\) −6.88244 −0.248349
\(769\) −47.9449 −1.72894 −0.864469 0.502686i \(-0.832345\pi\)
−0.864469 + 0.502686i \(0.832345\pi\)
\(770\) 0 0
\(771\) 9.16194 0.329959
\(772\) −3.52345 −0.126812
\(773\) 21.1871 0.762046 0.381023 0.924566i \(-0.375572\pi\)
0.381023 + 0.924566i \(0.375572\pi\)
\(774\) −16.7924 −0.603590
\(775\) −23.8675 −0.857347
\(776\) 38.5506 1.38389
\(777\) 0 0
\(778\) −56.7353 −2.03406
\(779\) −2.72504 −0.0976348
\(780\) 0.419023 0.0150034
\(781\) −12.2420 −0.438052
\(782\) 42.3112 1.51304
\(783\) −6.41611 −0.229293
\(784\) 0 0
\(785\) −3.47552 −0.124047
\(786\) −0.564661 −0.0201408
\(787\) 14.7694 0.526473 0.263236 0.964731i \(-0.415210\pi\)
0.263236 + 0.964731i \(0.415210\pi\)
\(788\) 23.5962 0.840578
\(789\) 8.97300 0.319447
\(790\) −3.77268 −0.134226
\(791\) 0 0
\(792\) −5.05549 −0.179639
\(793\) −0.667198 −0.0236929
\(794\) −23.9048 −0.848349
\(795\) 1.01829 0.0361149
\(796\) 22.2159 0.787423
\(797\) −30.0351 −1.06390 −0.531949 0.846776i \(-0.678540\pi\)
−0.531949 + 0.846776i \(0.678540\pi\)
\(798\) 0 0
\(799\) 41.3461 1.46272
\(800\) −34.6248 −1.22417
\(801\) 9.60949 0.339535
\(802\) 47.3266 1.67116
\(803\) −38.7856 −1.36871
\(804\) 34.1371 1.20392
\(805\) 0 0
\(806\) −9.18714 −0.323603
\(807\) −8.74443 −0.307819
\(808\) −20.5165 −0.721769
\(809\) 26.5142 0.932191 0.466095 0.884734i \(-0.345660\pi\)
0.466095 + 0.884734i \(0.345660\pi\)
\(810\) −0.368393 −0.0129440
\(811\) −32.3215 −1.13496 −0.567481 0.823386i \(-0.692082\pi\)
−0.567481 + 0.823386i \(0.692082\pi\)
\(812\) 0 0
\(813\) −17.6472 −0.618915
\(814\) 42.3389 1.48398
\(815\) −2.39810 −0.0840019
\(816\) −5.13842 −0.179881
\(817\) 20.6106 0.721075
\(818\) −47.2823 −1.65319
\(819\) 0 0
\(820\) −0.486057 −0.0169738
\(821\) 41.1997 1.43788 0.718939 0.695073i \(-0.244628\pi\)
0.718939 + 0.695073i \(0.244628\pi\)
\(822\) −28.9606 −1.01012
\(823\) −9.13478 −0.318418 −0.159209 0.987245i \(-0.550894\pi\)
−0.159209 + 0.987245i \(0.550894\pi\)
\(824\) −16.8094 −0.585583
\(825\) −12.1833 −0.424167
\(826\) 0 0
\(827\) 45.1279 1.56925 0.784626 0.619970i \(-0.212855\pi\)
0.784626 + 0.619970i \(0.212855\pi\)
\(828\) −13.8805 −0.482381
\(829\) 0.645036 0.0224030 0.0112015 0.999937i \(-0.496434\pi\)
0.0112015 + 0.999937i \(0.496434\pi\)
\(830\) −1.95022 −0.0676931
\(831\) 10.8785 0.377370
\(832\) −11.1250 −0.385690
\(833\) 0 0
\(834\) 4.63974 0.160661
\(835\) −1.95677 −0.0677168
\(836\) 19.5585 0.676445
\(837\) 4.79993 0.165910
\(838\) −13.7328 −0.474391
\(839\) 31.9401 1.10269 0.551347 0.834276i \(-0.314114\pi\)
0.551347 + 0.834276i \(0.314114\pi\)
\(840\) 0 0
\(841\) 12.1664 0.419531
\(842\) −40.4091 −1.39259
\(843\) −20.2375 −0.697015
\(844\) 10.5100 0.361769
\(845\) −2.03373 −0.0699625
\(846\) −22.8246 −0.784727
\(847\) 0 0
\(848\) −7.84077 −0.269253
\(849\) 6.49723 0.222984
\(850\) 44.4009 1.52294
\(851\) 36.8798 1.26422
\(852\) −14.6362 −0.501430
\(853\) 20.0907 0.687893 0.343947 0.938989i \(-0.388236\pi\)
0.343947 + 0.938989i \(0.388236\pi\)
\(854\) 0 0
\(855\) 0.452158 0.0154635
\(856\) −11.8621 −0.405437
\(857\) 5.17839 0.176890 0.0884452 0.996081i \(-0.471810\pi\)
0.0884452 + 0.996081i \(0.471810\pi\)
\(858\) −4.68961 −0.160101
\(859\) 41.7012 1.42283 0.711413 0.702775i \(-0.248056\pi\)
0.711413 + 0.702775i \(0.248056\pi\)
\(860\) 3.67625 0.125359
\(861\) 0 0
\(862\) 50.5181 1.72065
\(863\) −23.7810 −0.809514 −0.404757 0.914424i \(-0.632644\pi\)
−0.404757 + 0.914424i \(0.632644\pi\)
\(864\) 6.96329 0.236896
\(865\) 3.45114 0.117342
\(866\) 64.4389 2.18972
\(867\) −0.824772 −0.0280107
\(868\) 0 0
\(869\) 25.0917 0.851179
\(870\) 2.36365 0.0801351
\(871\) 10.0463 0.340406
\(872\) 5.40842 0.183152
\(873\) −18.6836 −0.632342
\(874\) 28.6684 0.969723
\(875\) 0 0
\(876\) −46.3713 −1.56674
\(877\) 41.2107 1.39159 0.695793 0.718242i \(-0.255053\pi\)
0.695793 + 0.718242i \(0.255053\pi\)
\(878\) 50.2335 1.69530
\(879\) 5.51194 0.185913
\(880\) −0.519413 −0.0175094
\(881\) −40.0194 −1.34829 −0.674143 0.738601i \(-0.735487\pi\)
−0.674143 + 0.738601i \(0.735487\pi\)
\(882\) 0 0
\(883\) 37.5006 1.26200 0.630998 0.775785i \(-0.282646\pi\)
0.630998 + 0.775785i \(0.282646\pi\)
\(884\) 10.1565 0.341602
\(885\) 1.41377 0.0475234
\(886\) −29.5740 −0.993560
\(887\) 6.99132 0.234745 0.117373 0.993088i \(-0.462553\pi\)
0.117373 + 0.993088i \(0.462553\pi\)
\(888\) 16.0592 0.538912
\(889\) 0 0
\(890\) −3.54007 −0.118663
\(891\) 2.45014 0.0820829
\(892\) 20.0727 0.672082
\(893\) 28.0145 0.937469
\(894\) −3.16365 −0.105808
\(895\) −0.841848 −0.0281399
\(896\) 0 0
\(897\) −4.08494 −0.136392
\(898\) −28.1055 −0.937893
\(899\) −30.7969 −1.02713
\(900\) −14.5661 −0.485536
\(901\) 24.6819 0.822274
\(902\) 5.43984 0.181127
\(903\) 0 0
\(904\) 9.95494 0.331096
\(905\) 0.766512 0.0254797
\(906\) −26.0700 −0.866117
\(907\) 17.5799 0.583730 0.291865 0.956460i \(-0.405724\pi\)
0.291865 + 0.956460i \(0.405724\pi\)
\(908\) −36.4716 −1.21035
\(909\) 9.94335 0.329800
\(910\) 0 0
\(911\) −3.56905 −0.118248 −0.0591240 0.998251i \(-0.518831\pi\)
−0.0591240 + 0.998251i \(0.518831\pi\)
\(912\) −3.48159 −0.115287
\(913\) 12.9707 0.429268
\(914\) 22.4472 0.742486
\(915\) −0.128416 −0.00424532
\(916\) −55.9218 −1.84771
\(917\) 0 0
\(918\) −8.92935 −0.294712
\(919\) −56.3987 −1.86042 −0.930210 0.367026i \(-0.880376\pi\)
−0.930210 + 0.367026i \(0.880376\pi\)
\(920\) 1.62227 0.0534847
\(921\) −2.22394 −0.0732812
\(922\) −24.2717 −0.799346
\(923\) −4.30735 −0.141778
\(924\) 0 0
\(925\) 38.7012 1.27249
\(926\) −57.0640 −1.87524
\(927\) 8.14668 0.267572
\(928\) −44.6772 −1.46660
\(929\) −35.5398 −1.16602 −0.583011 0.812464i \(-0.698126\pi\)
−0.583011 + 0.812464i \(0.698126\pi\)
\(930\) −1.76826 −0.0579836
\(931\) 0 0
\(932\) 27.7068 0.907567
\(933\) 22.5977 0.739814
\(934\) 47.6623 1.55956
\(935\) 1.63506 0.0534721
\(936\) −1.77878 −0.0581412
\(937\) −8.98177 −0.293422 −0.146711 0.989179i \(-0.546869\pi\)
−0.146711 + 0.989179i \(0.546869\pi\)
\(938\) 0 0
\(939\) 11.7856 0.384608
\(940\) 4.99685 0.162979
\(941\) 39.4769 1.28691 0.643455 0.765484i \(-0.277500\pi\)
0.643455 + 0.765484i \(0.277500\pi\)
\(942\) 46.5048 1.51521
\(943\) 4.73844 0.154305
\(944\) −10.8860 −0.354308
\(945\) 0 0
\(946\) −41.1438 −1.33770
\(947\) −30.4765 −0.990353 −0.495176 0.868792i \(-0.664897\pi\)
−0.495176 + 0.868792i \(0.664897\pi\)
\(948\) 29.9992 0.974328
\(949\) −13.6468 −0.442992
\(950\) 30.0843 0.976064
\(951\) −5.48705 −0.177930
\(952\) 0 0
\(953\) −38.1639 −1.23625 −0.618125 0.786080i \(-0.712107\pi\)
−0.618125 + 0.786080i \(0.712107\pi\)
\(954\) −13.6254 −0.441138
\(955\) 3.92956 0.127158
\(956\) 40.7774 1.31883
\(957\) −15.7204 −0.508168
\(958\) −8.46834 −0.273600
\(959\) 0 0
\(960\) −2.14124 −0.0691083
\(961\) −7.96063 −0.256795
\(962\) 14.8970 0.480298
\(963\) 5.74895 0.185257
\(964\) 1.71002 0.0550759
\(965\) −0.199578 −0.00642465
\(966\) 0 0
\(967\) 12.7300 0.409368 0.204684 0.978828i \(-0.434383\pi\)
0.204684 + 0.978828i \(0.434383\pi\)
\(968\) 10.3101 0.331379
\(969\) 10.9597 0.352076
\(970\) 6.88288 0.220996
\(971\) 15.8759 0.509482 0.254741 0.967009i \(-0.418010\pi\)
0.254741 + 0.967009i \(0.418010\pi\)
\(972\) 2.92934 0.0939588
\(973\) 0 0
\(974\) −78.2166 −2.50622
\(975\) −4.28669 −0.137284
\(976\) 0.988801 0.0316507
\(977\) 11.6369 0.372298 0.186149 0.982522i \(-0.440399\pi\)
0.186149 + 0.982522i \(0.440399\pi\)
\(978\) 32.0883 1.02607
\(979\) 23.5446 0.752490
\(980\) 0 0
\(981\) −2.62119 −0.0836883
\(982\) 64.0493 2.04389
\(983\) 43.2367 1.37904 0.689518 0.724268i \(-0.257822\pi\)
0.689518 + 0.724268i \(0.257822\pi\)
\(984\) 2.06334 0.0657770
\(985\) 1.33656 0.0425862
\(986\) 57.2916 1.82454
\(987\) 0 0
\(988\) 6.88168 0.218935
\(989\) −35.8388 −1.13961
\(990\) −0.902616 −0.0286870
\(991\) −34.6510 −1.10072 −0.550362 0.834926i \(-0.685510\pi\)
−0.550362 + 0.834926i \(0.685510\pi\)
\(992\) 33.4234 1.06119
\(993\) −27.8774 −0.884663
\(994\) 0 0
\(995\) 1.25838 0.0398932
\(996\) 15.5075 0.491375
\(997\) 16.9551 0.536973 0.268486 0.963284i \(-0.413477\pi\)
0.268486 + 0.963284i \(0.413477\pi\)
\(998\) 14.4634 0.457830
\(999\) −7.78311 −0.246247
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 \(a_p\))