Properties

Label 6027.2.a.bn.1.20
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 1.20
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.37367 q^{2} -1.00000 q^{3} +3.63432 q^{4} +3.47491 q^{5} -2.37367 q^{6} +3.87933 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.37367 q^{2} -1.00000 q^{3} +3.63432 q^{4} +3.47491 q^{5} -2.37367 q^{6} +3.87933 q^{8} +1.00000 q^{9} +8.24830 q^{10} +1.00968 q^{11} -3.63432 q^{12} +3.69507 q^{13} -3.47491 q^{15} +1.93963 q^{16} -2.26443 q^{17} +2.37367 q^{18} -3.08267 q^{19} +12.6289 q^{20} +2.39664 q^{22} +2.97074 q^{23} -3.87933 q^{24} +7.07502 q^{25} +8.77089 q^{26} -1.00000 q^{27} +6.10211 q^{29} -8.24830 q^{30} -1.10018 q^{31} -3.15463 q^{32} -1.00968 q^{33} -5.37501 q^{34} +3.63432 q^{36} +7.80010 q^{37} -7.31725 q^{38} -3.69507 q^{39} +13.4803 q^{40} +1.00000 q^{41} +11.3610 q^{43} +3.66949 q^{44} +3.47491 q^{45} +7.05157 q^{46} -10.8405 q^{47} -1.93963 q^{48} +16.7938 q^{50} +2.26443 q^{51} +13.4291 q^{52} -3.15739 q^{53} -2.37367 q^{54} +3.50854 q^{55} +3.08267 q^{57} +14.4844 q^{58} -10.4467 q^{59} -12.6289 q^{60} -2.86665 q^{61} -2.61146 q^{62} -11.3673 q^{64} +12.8401 q^{65} -2.39664 q^{66} -7.54599 q^{67} -8.22965 q^{68} -2.97074 q^{69} +7.56311 q^{71} +3.87933 q^{72} +8.49635 q^{73} +18.5149 q^{74} -7.07502 q^{75} -11.2034 q^{76} -8.77089 q^{78} +8.24616 q^{79} +6.74004 q^{80} +1.00000 q^{81} +2.37367 q^{82} +12.4677 q^{83} -7.86870 q^{85} +26.9674 q^{86} -6.10211 q^{87} +3.91688 q^{88} +7.10936 q^{89} +8.24830 q^{90} +10.7966 q^{92} +1.10018 q^{93} -25.7317 q^{94} -10.7120 q^{95} +3.15463 q^{96} -1.37040 q^{97} +1.00968 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + O(q^{10}) \) \( 24q + 8q^{2} - 24q^{3} + 32q^{4} - 4q^{5} - 8q^{6} + 24q^{8} + 24q^{9} + 4q^{10} + 12q^{11} - 32q^{12} + 4q^{15} + 44q^{16} - 8q^{17} + 8q^{18} + 4q^{19} - 28q^{20} + 16q^{22} + 20q^{23} - 24q^{24} + 48q^{25} - 32q^{26} - 24q^{27} + 24q^{29} - 4q^{30} + 4q^{31} + 36q^{32} - 12q^{33} - 16q^{34} + 32q^{36} + 64q^{37} - 20q^{38} + 48q^{40} + 24q^{41} + 20q^{43} + 48q^{44} - 4q^{45} + 28q^{46} - 32q^{47} - 44q^{48} - 20q^{50} + 8q^{51} + 76q^{53} - 8q^{54} + 24q^{55} - 4q^{57} + 28q^{58} - 28q^{59} + 28q^{60} + 28q^{61} + 4q^{62} + 48q^{64} + 28q^{65} - 16q^{66} + 44q^{67} + 32q^{68} - 20q^{69} + 20q^{71} + 24q^{72} + 16q^{73} + 44q^{74} - 48q^{75} + 16q^{76} + 32q^{78} + 4q^{79} - 44q^{80} + 24q^{81} + 8q^{82} - 8q^{83} + 28q^{85} + 56q^{86} - 24q^{87} + 60q^{88} - 60q^{89} + 4q^{90} + 60q^{92} - 4q^{93} - 24q^{94} + 28q^{95} - 36q^{96} + 48q^{97} + 12q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.37367 1.67844 0.839220 0.543793i \(-0.183012\pi\)
0.839220 + 0.543793i \(0.183012\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.63432 1.81716
\(5\) 3.47491 1.55403 0.777014 0.629483i \(-0.216733\pi\)
0.777014 + 0.629483i \(0.216733\pi\)
\(6\) −2.37367 −0.969047
\(7\) 0 0
\(8\) 3.87933 1.37155
\(9\) 1.00000 0.333333
\(10\) 8.24830 2.60834
\(11\) 1.00968 0.304429 0.152215 0.988347i \(-0.451359\pi\)
0.152215 + 0.988347i \(0.451359\pi\)
\(12\) −3.63432 −1.04914
\(13\) 3.69507 1.02483 0.512414 0.858738i \(-0.328751\pi\)
0.512414 + 0.858738i \(0.328751\pi\)
\(14\) 0 0
\(15\) −3.47491 −0.897219
\(16\) 1.93963 0.484907
\(17\) −2.26443 −0.549205 −0.274602 0.961558i \(-0.588546\pi\)
−0.274602 + 0.961558i \(0.588546\pi\)
\(18\) 2.37367 0.559480
\(19\) −3.08267 −0.707214 −0.353607 0.935394i \(-0.615045\pi\)
−0.353607 + 0.935394i \(0.615045\pi\)
\(20\) 12.6289 2.82392
\(21\) 0 0
\(22\) 2.39664 0.510966
\(23\) 2.97074 0.619443 0.309722 0.950827i \(-0.399764\pi\)
0.309722 + 0.950827i \(0.399764\pi\)
\(24\) −3.87933 −0.791866
\(25\) 7.07502 1.41500
\(26\) 8.77089 1.72011
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 6.10211 1.13313 0.566567 0.824016i \(-0.308271\pi\)
0.566567 + 0.824016i \(0.308271\pi\)
\(30\) −8.24830 −1.50593
\(31\) −1.10018 −0.197598 −0.0987988 0.995107i \(-0.531500\pi\)
−0.0987988 + 0.995107i \(0.531500\pi\)
\(32\) −3.15463 −0.557664
\(33\) −1.00968 −0.175762
\(34\) −5.37501 −0.921807
\(35\) 0 0
\(36\) 3.63432 0.605720
\(37\) 7.80010 1.28233 0.641164 0.767404i \(-0.278452\pi\)
0.641164 + 0.767404i \(0.278452\pi\)
\(38\) −7.31725 −1.18702
\(39\) −3.69507 −0.591685
\(40\) 13.4803 2.13143
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 11.3610 1.73254 0.866271 0.499574i \(-0.166510\pi\)
0.866271 + 0.499574i \(0.166510\pi\)
\(44\) 3.66949 0.553196
\(45\) 3.47491 0.518009
\(46\) 7.05157 1.03970
\(47\) −10.8405 −1.58125 −0.790623 0.612303i \(-0.790243\pi\)
−0.790623 + 0.612303i \(0.790243\pi\)
\(48\) −1.93963 −0.279961
\(49\) 0 0
\(50\) 16.7938 2.37500
\(51\) 2.26443 0.317084
\(52\) 13.4291 1.86228
\(53\) −3.15739 −0.433701 −0.216850 0.976205i \(-0.569578\pi\)
−0.216850 + 0.976205i \(0.569578\pi\)
\(54\) −2.37367 −0.323016
\(55\) 3.50854 0.473092
\(56\) 0 0
\(57\) 3.08267 0.408310
\(58\) 14.4844 1.90190
\(59\) −10.4467 −1.36005 −0.680024 0.733190i \(-0.738031\pi\)
−0.680024 + 0.733190i \(0.738031\pi\)
\(60\) −12.6289 −1.63039
\(61\) −2.86665 −0.367037 −0.183518 0.983016i \(-0.558749\pi\)
−0.183518 + 0.983016i \(0.558749\pi\)
\(62\) −2.61146 −0.331656
\(63\) 0 0
\(64\) −11.3673 −1.42091
\(65\) 12.8401 1.59261
\(66\) −2.39664 −0.295006
\(67\) −7.54599 −0.921889 −0.460944 0.887429i \(-0.652489\pi\)
−0.460944 + 0.887429i \(0.652489\pi\)
\(68\) −8.22965 −0.997992
\(69\) −2.97074 −0.357636
\(70\) 0 0
\(71\) 7.56311 0.897576 0.448788 0.893638i \(-0.351856\pi\)
0.448788 + 0.893638i \(0.351856\pi\)
\(72\) 3.87933 0.457184
\(73\) 8.49635 0.994422 0.497211 0.867630i \(-0.334357\pi\)
0.497211 + 0.867630i \(0.334357\pi\)
\(74\) 18.5149 2.15231
\(75\) −7.07502 −0.816953
\(76\) −11.2034 −1.28512
\(77\) 0 0
\(78\) −8.77089 −0.993107
\(79\) 8.24616 0.927766 0.463883 0.885897i \(-0.346456\pi\)
0.463883 + 0.885897i \(0.346456\pi\)
\(80\) 6.74004 0.753559
\(81\) 1.00000 0.111111
\(82\) 2.37367 0.262128
\(83\) 12.4677 1.36851 0.684255 0.729243i \(-0.260128\pi\)
0.684255 + 0.729243i \(0.260128\pi\)
\(84\) 0 0
\(85\) −7.86870 −0.853480
\(86\) 26.9674 2.90797
\(87\) −6.10211 −0.654215
\(88\) 3.91688 0.417540
\(89\) 7.10936 0.753591 0.376795 0.926296i \(-0.377026\pi\)
0.376795 + 0.926296i \(0.377026\pi\)
\(90\) 8.24830 0.869448
\(91\) 0 0
\(92\) 10.7966 1.12563
\(93\) 1.10018 0.114083
\(94\) −25.7317 −2.65403
\(95\) −10.7120 −1.09903
\(96\) 3.15463 0.321968
\(97\) −1.37040 −0.139143 −0.0695717 0.997577i \(-0.522163\pi\)
−0.0695717 + 0.997577i \(0.522163\pi\)
\(98\) 0 0
\(99\) 1.00968 0.101476
\(100\) 25.7129 2.57129
\(101\) −3.16096 −0.314528 −0.157264 0.987557i \(-0.550267\pi\)
−0.157264 + 0.987557i \(0.550267\pi\)
\(102\) 5.37501 0.532205
\(103\) −5.03265 −0.495881 −0.247941 0.968775i \(-0.579754\pi\)
−0.247941 + 0.968775i \(0.579754\pi\)
\(104\) 14.3344 1.40560
\(105\) 0 0
\(106\) −7.49461 −0.727941
\(107\) 8.80363 0.851079 0.425540 0.904940i \(-0.360084\pi\)
0.425540 + 0.904940i \(0.360084\pi\)
\(108\) −3.63432 −0.349712
\(109\) −0.819402 −0.0784845 −0.0392422 0.999230i \(-0.512494\pi\)
−0.0392422 + 0.999230i \(0.512494\pi\)
\(110\) 8.32813 0.794056
\(111\) −7.80010 −0.740353
\(112\) 0 0
\(113\) −3.73111 −0.350994 −0.175497 0.984480i \(-0.556153\pi\)
−0.175497 + 0.984480i \(0.556153\pi\)
\(114\) 7.31725 0.685324
\(115\) 10.3231 0.962632
\(116\) 22.1770 2.05908
\(117\) 3.69507 0.341610
\(118\) −24.7971 −2.28276
\(119\) 0 0
\(120\) −13.4803 −1.23058
\(121\) −9.98055 −0.907323
\(122\) −6.80449 −0.616049
\(123\) −1.00000 −0.0901670
\(124\) −3.99839 −0.359066
\(125\) 7.21052 0.644929
\(126\) 0 0
\(127\) −4.70586 −0.417578 −0.208789 0.977961i \(-0.566952\pi\)
−0.208789 + 0.977961i \(0.566952\pi\)
\(128\) −20.6730 −1.82725
\(129\) −11.3610 −1.00028
\(130\) 30.4781 2.67310
\(131\) 5.84671 0.510829 0.255415 0.966832i \(-0.417788\pi\)
0.255415 + 0.966832i \(0.417788\pi\)
\(132\) −3.66949 −0.319388
\(133\) 0 0
\(134\) −17.9117 −1.54733
\(135\) −3.47491 −0.299073
\(136\) −8.78448 −0.753263
\(137\) −18.0997 −1.54636 −0.773181 0.634185i \(-0.781336\pi\)
−0.773181 + 0.634185i \(0.781336\pi\)
\(138\) −7.05157 −0.600270
\(139\) −5.95439 −0.505045 −0.252522 0.967591i \(-0.581260\pi\)
−0.252522 + 0.967591i \(0.581260\pi\)
\(140\) 0 0
\(141\) 10.8405 0.912933
\(142\) 17.9523 1.50653
\(143\) 3.73083 0.311988
\(144\) 1.93963 0.161636
\(145\) 21.2043 1.76092
\(146\) 20.1675 1.66908
\(147\) 0 0
\(148\) 28.3480 2.33019
\(149\) 2.81919 0.230957 0.115479 0.993310i \(-0.463160\pi\)
0.115479 + 0.993310i \(0.463160\pi\)
\(150\) −16.7938 −1.37121
\(151\) 2.17246 0.176793 0.0883963 0.996085i \(-0.471826\pi\)
0.0883963 + 0.996085i \(0.471826\pi\)
\(152\) −11.9587 −0.969980
\(153\) −2.26443 −0.183068
\(154\) 0 0
\(155\) −3.82302 −0.307072
\(156\) −13.4291 −1.07519
\(157\) −9.90769 −0.790719 −0.395360 0.918526i \(-0.629380\pi\)
−0.395360 + 0.918526i \(0.629380\pi\)
\(158\) 19.5737 1.55720
\(159\) 3.15739 0.250397
\(160\) −10.9621 −0.866626
\(161\) 0 0
\(162\) 2.37367 0.186493
\(163\) −10.6771 −0.836299 −0.418149 0.908378i \(-0.637321\pi\)
−0.418149 + 0.908378i \(0.637321\pi\)
\(164\) 3.63432 0.283793
\(165\) −3.50854 −0.273140
\(166\) 29.5943 2.29696
\(167\) −22.2093 −1.71861 −0.859305 0.511463i \(-0.829104\pi\)
−0.859305 + 0.511463i \(0.829104\pi\)
\(168\) 0 0
\(169\) 0.653556 0.0502735
\(170\) −18.6777 −1.43251
\(171\) −3.08267 −0.235738
\(172\) 41.2896 3.14830
\(173\) 2.71224 0.206208 0.103104 0.994671i \(-0.467123\pi\)
0.103104 + 0.994671i \(0.467123\pi\)
\(174\) −14.4844 −1.09806
\(175\) 0 0
\(176\) 1.95840 0.147620
\(177\) 10.4467 0.785224
\(178\) 16.8753 1.26486
\(179\) −25.9226 −1.93755 −0.968774 0.247944i \(-0.920245\pi\)
−0.968774 + 0.247944i \(0.920245\pi\)
\(180\) 12.6289 0.941305
\(181\) 14.9349 1.11011 0.555053 0.831815i \(-0.312698\pi\)
0.555053 + 0.831815i \(0.312698\pi\)
\(182\) 0 0
\(183\) 2.86665 0.211909
\(184\) 11.5245 0.849598
\(185\) 27.1047 1.99277
\(186\) 2.61146 0.191482
\(187\) −2.28634 −0.167194
\(188\) −39.3977 −2.87338
\(189\) 0 0
\(190\) −25.4268 −1.84466
\(191\) −3.25643 −0.235627 −0.117813 0.993036i \(-0.537588\pi\)
−0.117813 + 0.993036i \(0.537588\pi\)
\(192\) 11.3673 0.820364
\(193\) 21.7417 1.56500 0.782499 0.622651i \(-0.213944\pi\)
0.782499 + 0.622651i \(0.213944\pi\)
\(194\) −3.25289 −0.233544
\(195\) −12.8401 −0.919495
\(196\) 0 0
\(197\) 22.4747 1.60125 0.800626 0.599164i \(-0.204500\pi\)
0.800626 + 0.599164i \(0.204500\pi\)
\(198\) 2.39664 0.170322
\(199\) 0.769084 0.0545189 0.0272595 0.999628i \(-0.491322\pi\)
0.0272595 + 0.999628i \(0.491322\pi\)
\(200\) 27.4464 1.94075
\(201\) 7.54599 0.532253
\(202\) −7.50309 −0.527916
\(203\) 0 0
\(204\) 8.22965 0.576191
\(205\) 3.47491 0.242698
\(206\) −11.9459 −0.832307
\(207\) 2.97074 0.206481
\(208\) 7.16706 0.496947
\(209\) −3.11251 −0.215297
\(210\) 0 0
\(211\) −6.39650 −0.440354 −0.220177 0.975460i \(-0.570663\pi\)
−0.220177 + 0.975460i \(0.570663\pi\)
\(212\) −11.4750 −0.788104
\(213\) −7.56311 −0.518216
\(214\) 20.8969 1.42848
\(215\) 39.4786 2.69242
\(216\) −3.87933 −0.263955
\(217\) 0 0
\(218\) −1.94499 −0.131731
\(219\) −8.49635 −0.574130
\(220\) 12.7512 0.859683
\(221\) −8.36723 −0.562841
\(222\) −18.5149 −1.24264
\(223\) 13.5518 0.907499 0.453749 0.891129i \(-0.350086\pi\)
0.453749 + 0.891129i \(0.350086\pi\)
\(224\) 0 0
\(225\) 7.07502 0.471668
\(226\) −8.85644 −0.589121
\(227\) −11.0791 −0.735344 −0.367672 0.929955i \(-0.619845\pi\)
−0.367672 + 0.929955i \(0.619845\pi\)
\(228\) 11.2034 0.741964
\(229\) 4.05671 0.268075 0.134038 0.990976i \(-0.457206\pi\)
0.134038 + 0.990976i \(0.457206\pi\)
\(230\) 24.5036 1.61572
\(231\) 0 0
\(232\) 23.6721 1.55415
\(233\) −5.83354 −0.382168 −0.191084 0.981574i \(-0.561200\pi\)
−0.191084 + 0.981574i \(0.561200\pi\)
\(234\) 8.77089 0.573371
\(235\) −37.6697 −2.45730
\(236\) −37.9667 −2.47142
\(237\) −8.24616 −0.535646
\(238\) 0 0
\(239\) 12.8223 0.829407 0.414703 0.909957i \(-0.363885\pi\)
0.414703 + 0.909957i \(0.363885\pi\)
\(240\) −6.74004 −0.435068
\(241\) 3.16368 0.203790 0.101895 0.994795i \(-0.467509\pi\)
0.101895 + 0.994795i \(0.467509\pi\)
\(242\) −23.6906 −1.52289
\(243\) −1.00000 −0.0641500
\(244\) −10.4183 −0.666964
\(245\) 0 0
\(246\) −2.37367 −0.151340
\(247\) −11.3907 −0.724773
\(248\) −4.26795 −0.271015
\(249\) −12.4677 −0.790109
\(250\) 17.1154 1.08247
\(251\) −13.8603 −0.874851 −0.437426 0.899255i \(-0.644110\pi\)
−0.437426 + 0.899255i \(0.644110\pi\)
\(252\) 0 0
\(253\) 2.99949 0.188577
\(254\) −11.1702 −0.700879
\(255\) 7.86870 0.492757
\(256\) −26.3363 −1.64602
\(257\) −26.8020 −1.67186 −0.835931 0.548835i \(-0.815072\pi\)
−0.835931 + 0.548835i \(0.815072\pi\)
\(258\) −26.9674 −1.67892
\(259\) 0 0
\(260\) 46.6648 2.89403
\(261\) 6.10211 0.377711
\(262\) 13.8782 0.857396
\(263\) −24.5257 −1.51232 −0.756161 0.654386i \(-0.772927\pi\)
−0.756161 + 0.654386i \(0.772927\pi\)
\(264\) −3.91688 −0.241067
\(265\) −10.9717 −0.673984
\(266\) 0 0
\(267\) −7.10936 −0.435086
\(268\) −27.4245 −1.67522
\(269\) 20.3063 1.23810 0.619049 0.785353i \(-0.287518\pi\)
0.619049 + 0.785353i \(0.287518\pi\)
\(270\) −8.24830 −0.501976
\(271\) −10.3354 −0.627829 −0.313915 0.949451i \(-0.601641\pi\)
−0.313915 + 0.949451i \(0.601641\pi\)
\(272\) −4.39215 −0.266313
\(273\) 0 0
\(274\) −42.9627 −2.59547
\(275\) 7.14349 0.430769
\(276\) −10.7966 −0.649881
\(277\) 4.41311 0.265158 0.132579 0.991172i \(-0.457674\pi\)
0.132579 + 0.991172i \(0.457674\pi\)
\(278\) −14.1338 −0.847687
\(279\) −1.10018 −0.0658659
\(280\) 0 0
\(281\) 21.2364 1.26686 0.633429 0.773801i \(-0.281647\pi\)
0.633429 + 0.773801i \(0.281647\pi\)
\(282\) 25.7317 1.53230
\(283\) −14.7031 −0.874010 −0.437005 0.899459i \(-0.643961\pi\)
−0.437005 + 0.899459i \(0.643961\pi\)
\(284\) 27.4867 1.63104
\(285\) 10.7120 0.634525
\(286\) 8.85577 0.523653
\(287\) 0 0
\(288\) −3.15463 −0.185888
\(289\) −11.8724 −0.698374
\(290\) 50.3321 2.95560
\(291\) 1.37040 0.0803344
\(292\) 30.8784 1.80702
\(293\) 3.42974 0.200367 0.100184 0.994969i \(-0.468057\pi\)
0.100184 + 0.994969i \(0.468057\pi\)
\(294\) 0 0
\(295\) −36.3015 −2.11355
\(296\) 30.2592 1.75878
\(297\) −1.00968 −0.0585874
\(298\) 6.69183 0.387648
\(299\) 10.9771 0.634823
\(300\) −25.7129 −1.48453
\(301\) 0 0
\(302\) 5.15671 0.296736
\(303\) 3.16096 0.181593
\(304\) −5.97924 −0.342933
\(305\) −9.96136 −0.570386
\(306\) −5.37501 −0.307269
\(307\) −19.0304 −1.08612 −0.543062 0.839693i \(-0.682735\pi\)
−0.543062 + 0.839693i \(0.682735\pi\)
\(308\) 0 0
\(309\) 5.03265 0.286297
\(310\) −9.07460 −0.515402
\(311\) 22.3897 1.26961 0.634803 0.772674i \(-0.281081\pi\)
0.634803 + 0.772674i \(0.281081\pi\)
\(312\) −14.3344 −0.811526
\(313\) 29.2085 1.65096 0.825482 0.564429i \(-0.190903\pi\)
0.825482 + 0.564429i \(0.190903\pi\)
\(314\) −23.5176 −1.32717
\(315\) 0 0
\(316\) 29.9692 1.68590
\(317\) −14.5913 −0.819527 −0.409764 0.912192i \(-0.634389\pi\)
−0.409764 + 0.912192i \(0.634389\pi\)
\(318\) 7.49461 0.420277
\(319\) 6.16117 0.344959
\(320\) −39.5004 −2.20814
\(321\) −8.80363 −0.491371
\(322\) 0 0
\(323\) 6.98050 0.388405
\(324\) 3.63432 0.201907
\(325\) 26.1427 1.45014
\(326\) −25.3440 −1.40368
\(327\) 0.819402 0.0453130
\(328\) 3.87933 0.214200
\(329\) 0 0
\(330\) −8.32813 −0.458448
\(331\) 11.5685 0.635862 0.317931 0.948114i \(-0.397012\pi\)
0.317931 + 0.948114i \(0.397012\pi\)
\(332\) 45.3116 2.48680
\(333\) 7.80010 0.427443
\(334\) −52.7177 −2.88458
\(335\) −26.2216 −1.43264
\(336\) 0 0
\(337\) 9.96558 0.542860 0.271430 0.962458i \(-0.412504\pi\)
0.271430 + 0.962458i \(0.412504\pi\)
\(338\) 1.55133 0.0843811
\(339\) 3.73111 0.202646
\(340\) −28.5973 −1.55091
\(341\) −1.11082 −0.0601545
\(342\) −7.31725 −0.395672
\(343\) 0 0
\(344\) 44.0732 2.37627
\(345\) −10.3231 −0.555776
\(346\) 6.43797 0.346108
\(347\) 14.1125 0.757598 0.378799 0.925479i \(-0.376337\pi\)
0.378799 + 0.925479i \(0.376337\pi\)
\(348\) −22.1770 −1.18881
\(349\) 8.09565 0.433350 0.216675 0.976244i \(-0.430479\pi\)
0.216675 + 0.976244i \(0.430479\pi\)
\(350\) 0 0
\(351\) −3.69507 −0.197228
\(352\) −3.18516 −0.169769
\(353\) 26.0876 1.38850 0.694252 0.719732i \(-0.255735\pi\)
0.694252 + 0.719732i \(0.255735\pi\)
\(354\) 24.7971 1.31795
\(355\) 26.2811 1.39486
\(356\) 25.8377 1.36939
\(357\) 0 0
\(358\) −61.5318 −3.25206
\(359\) 34.2480 1.80754 0.903770 0.428019i \(-0.140788\pi\)
0.903770 + 0.428019i \(0.140788\pi\)
\(360\) 13.4803 0.710477
\(361\) −9.49713 −0.499849
\(362\) 35.4507 1.86325
\(363\) 9.98055 0.523843
\(364\) 0 0
\(365\) 29.5241 1.54536
\(366\) 6.80449 0.355676
\(367\) 18.9226 0.987751 0.493876 0.869532i \(-0.335580\pi\)
0.493876 + 0.869532i \(0.335580\pi\)
\(368\) 5.76214 0.300372
\(369\) 1.00000 0.0520579
\(370\) 64.3376 3.34475
\(371\) 0 0
\(372\) 3.99839 0.207307
\(373\) −30.9953 −1.60487 −0.802437 0.596736i \(-0.796464\pi\)
−0.802437 + 0.596736i \(0.796464\pi\)
\(374\) −5.42703 −0.280625
\(375\) −7.21052 −0.372350
\(376\) −42.0538 −2.16876
\(377\) 22.5477 1.16127
\(378\) 0 0
\(379\) 1.74457 0.0896124 0.0448062 0.998996i \(-0.485733\pi\)
0.0448062 + 0.998996i \(0.485733\pi\)
\(380\) −38.9309 −1.99711
\(381\) 4.70586 0.241089
\(382\) −7.72969 −0.395485
\(383\) −35.0490 −1.79092 −0.895461 0.445140i \(-0.853154\pi\)
−0.895461 + 0.445140i \(0.853154\pi\)
\(384\) 20.6730 1.05496
\(385\) 0 0
\(386\) 51.6076 2.62676
\(387\) 11.3610 0.577514
\(388\) −4.98048 −0.252845
\(389\) 28.5924 1.44969 0.724846 0.688911i \(-0.241911\pi\)
0.724846 + 0.688911i \(0.241911\pi\)
\(390\) −30.4781 −1.54332
\(391\) −6.72704 −0.340201
\(392\) 0 0
\(393\) −5.84671 −0.294927
\(394\) 53.3475 2.68761
\(395\) 28.6547 1.44177
\(396\) 3.66949 0.184399
\(397\) 7.20191 0.361453 0.180727 0.983533i \(-0.442155\pi\)
0.180727 + 0.983533i \(0.442155\pi\)
\(398\) 1.82555 0.0915067
\(399\) 0 0
\(400\) 13.7229 0.686146
\(401\) 2.25286 0.112502 0.0562512 0.998417i \(-0.482085\pi\)
0.0562512 + 0.998417i \(0.482085\pi\)
\(402\) 17.9117 0.893354
\(403\) −4.06523 −0.202504
\(404\) −11.4879 −0.571547
\(405\) 3.47491 0.172670
\(406\) 0 0
\(407\) 7.87559 0.390378
\(408\) 8.78448 0.434896
\(409\) −20.8350 −1.03023 −0.515113 0.857122i \(-0.672250\pi\)
−0.515113 + 0.857122i \(0.672250\pi\)
\(410\) 8.24830 0.407355
\(411\) 18.0997 0.892792
\(412\) −18.2902 −0.901095
\(413\) 0 0
\(414\) 7.05157 0.346566
\(415\) 43.3242 2.12670
\(416\) −11.6566 −0.571510
\(417\) 5.95439 0.291588
\(418\) −7.38807 −0.361362
\(419\) −36.6553 −1.79073 −0.895363 0.445336i \(-0.853084\pi\)
−0.895363 + 0.445336i \(0.853084\pi\)
\(420\) 0 0
\(421\) −38.8563 −1.89374 −0.946870 0.321616i \(-0.895774\pi\)
−0.946870 + 0.321616i \(0.895774\pi\)
\(422\) −15.1832 −0.739107
\(423\) −10.8405 −0.527082
\(424\) −12.2486 −0.594843
\(425\) −16.0209 −0.777127
\(426\) −17.9523 −0.869793
\(427\) 0 0
\(428\) 31.9952 1.54655
\(429\) −3.73083 −0.180126
\(430\) 93.7093 4.51906
\(431\) 5.46635 0.263305 0.131652 0.991296i \(-0.457972\pi\)
0.131652 + 0.991296i \(0.457972\pi\)
\(432\) −1.93963 −0.0933204
\(433\) −13.4046 −0.644184 −0.322092 0.946708i \(-0.604386\pi\)
−0.322092 + 0.946708i \(0.604386\pi\)
\(434\) 0 0
\(435\) −21.2043 −1.01667
\(436\) −2.97797 −0.142619
\(437\) −9.15783 −0.438079
\(438\) −20.1675 −0.963642
\(439\) 13.9165 0.664201 0.332100 0.943244i \(-0.392243\pi\)
0.332100 + 0.943244i \(0.392243\pi\)
\(440\) 13.6108 0.648870
\(441\) 0 0
\(442\) −19.8611 −0.944694
\(443\) 18.5861 0.883052 0.441526 0.897248i \(-0.354437\pi\)
0.441526 + 0.897248i \(0.354437\pi\)
\(444\) −28.3480 −1.34534
\(445\) 24.7044 1.17110
\(446\) 32.1676 1.52318
\(447\) −2.81919 −0.133343
\(448\) 0 0
\(449\) −17.8861 −0.844095 −0.422047 0.906574i \(-0.638688\pi\)
−0.422047 + 0.906574i \(0.638688\pi\)
\(450\) 16.7938 0.791666
\(451\) 1.00968 0.0475439
\(452\) −13.5600 −0.637811
\(453\) −2.17246 −0.102071
\(454\) −26.2981 −1.23423
\(455\) 0 0
\(456\) 11.9587 0.560018
\(457\) −32.9497 −1.54132 −0.770662 0.637244i \(-0.780074\pi\)
−0.770662 + 0.637244i \(0.780074\pi\)
\(458\) 9.62930 0.449948
\(459\) 2.26443 0.105695
\(460\) 37.5173 1.74926
\(461\) −17.5230 −0.816126 −0.408063 0.912954i \(-0.633796\pi\)
−0.408063 + 0.912954i \(0.633796\pi\)
\(462\) 0 0
\(463\) 1.74652 0.0811677 0.0405839 0.999176i \(-0.487078\pi\)
0.0405839 + 0.999176i \(0.487078\pi\)
\(464\) 11.8358 0.549465
\(465\) 3.82302 0.177288
\(466\) −13.8469 −0.641446
\(467\) 28.1306 1.30173 0.650865 0.759194i \(-0.274407\pi\)
0.650865 + 0.759194i \(0.274407\pi\)
\(468\) 13.4291 0.620759
\(469\) 0 0
\(470\) −89.4156 −4.12443
\(471\) 9.90769 0.456522
\(472\) −40.5263 −1.86538
\(473\) 11.4710 0.527437
\(474\) −19.5737 −0.899049
\(475\) −21.8100 −1.00071
\(476\) 0 0
\(477\) −3.15739 −0.144567
\(478\) 30.4360 1.39211
\(479\) −23.7456 −1.08497 −0.542483 0.840067i \(-0.682516\pi\)
−0.542483 + 0.840067i \(0.682516\pi\)
\(480\) 10.9621 0.500347
\(481\) 28.8219 1.31417
\(482\) 7.50953 0.342050
\(483\) 0 0
\(484\) −36.2725 −1.64875
\(485\) −4.76203 −0.216233
\(486\) −2.37367 −0.107672
\(487\) −9.71321 −0.440147 −0.220074 0.975483i \(-0.570630\pi\)
−0.220074 + 0.975483i \(0.570630\pi\)
\(488\) −11.1207 −0.503410
\(489\) 10.6771 0.482837
\(490\) 0 0
\(491\) 16.4411 0.741977 0.370988 0.928638i \(-0.379019\pi\)
0.370988 + 0.928638i \(0.379019\pi\)
\(492\) −3.63432 −0.163848
\(493\) −13.8178 −0.622323
\(494\) −27.0378 −1.21649
\(495\) 3.50854 0.157697
\(496\) −2.13393 −0.0958165
\(497\) 0 0
\(498\) −29.5943 −1.32615
\(499\) −41.1165 −1.84063 −0.920314 0.391180i \(-0.872067\pi\)
−0.920314 + 0.391180i \(0.872067\pi\)
\(500\) 26.2053 1.17194
\(501\) 22.2093 0.992240
\(502\) −32.8997 −1.46838
\(503\) −14.0518 −0.626537 −0.313269 0.949665i \(-0.601424\pi\)
−0.313269 + 0.949665i \(0.601424\pi\)
\(504\) 0 0
\(505\) −10.9841 −0.488785
\(506\) 7.11981 0.316514
\(507\) −0.653556 −0.0290254
\(508\) −17.1026 −0.758805
\(509\) −6.46752 −0.286668 −0.143334 0.989674i \(-0.545782\pi\)
−0.143334 + 0.989674i \(0.545782\pi\)
\(510\) 18.6777 0.827062
\(511\) 0 0
\(512\) −21.1677 −0.935490
\(513\) 3.08267 0.136103
\(514\) −63.6191 −2.80612
\(515\) −17.4880 −0.770614
\(516\) −41.2896 −1.81767
\(517\) −10.9454 −0.481378
\(518\) 0 0
\(519\) −2.71224 −0.119054
\(520\) 49.8108 2.18435
\(521\) 24.9703 1.09397 0.546984 0.837143i \(-0.315776\pi\)
0.546984 + 0.837143i \(0.315776\pi\)
\(522\) 14.4844 0.633966
\(523\) −14.3767 −0.628648 −0.314324 0.949316i \(-0.601778\pi\)
−0.314324 + 0.949316i \(0.601778\pi\)
\(524\) 21.2488 0.928257
\(525\) 0 0
\(526\) −58.2160 −2.53834
\(527\) 2.49127 0.108522
\(528\) −1.95840 −0.0852284
\(529\) −14.1747 −0.616290
\(530\) −26.0431 −1.13124
\(531\) −10.4467 −0.453350
\(532\) 0 0
\(533\) 3.69507 0.160051
\(534\) −16.8753 −0.730265
\(535\) 30.5919 1.32260
\(536\) −29.2734 −1.26442
\(537\) 25.9226 1.11864
\(538\) 48.2005 2.07807
\(539\) 0 0
\(540\) −12.6289 −0.543463
\(541\) 19.9925 0.859543 0.429771 0.902938i \(-0.358594\pi\)
0.429771 + 0.902938i \(0.358594\pi\)
\(542\) −24.5328 −1.05377
\(543\) −14.9349 −0.640920
\(544\) 7.14343 0.306272
\(545\) −2.84735 −0.121967
\(546\) 0 0
\(547\) 25.3349 1.08324 0.541621 0.840623i \(-0.317811\pi\)
0.541621 + 0.840623i \(0.317811\pi\)
\(548\) −65.7801 −2.80998
\(549\) −2.86665 −0.122346
\(550\) 16.9563 0.723019
\(551\) −18.8108 −0.801368
\(552\) −11.5245 −0.490516
\(553\) 0 0
\(554\) 10.4753 0.445052
\(555\) −27.1047 −1.15053
\(556\) −21.6401 −0.917746
\(557\) −25.8533 −1.09544 −0.547719 0.836662i \(-0.684504\pi\)
−0.547719 + 0.836662i \(0.684504\pi\)
\(558\) −2.61146 −0.110552
\(559\) 41.9798 1.77556
\(560\) 0 0
\(561\) 2.28634 0.0965295
\(562\) 50.4082 2.12634
\(563\) −13.7843 −0.580938 −0.290469 0.956884i \(-0.593811\pi\)
−0.290469 + 0.956884i \(0.593811\pi\)
\(564\) 39.3977 1.65894
\(565\) −12.9653 −0.545454
\(566\) −34.9004 −1.46697
\(567\) 0 0
\(568\) 29.3398 1.23107
\(569\) 46.5561 1.95173 0.975867 0.218365i \(-0.0700722\pi\)
0.975867 + 0.218365i \(0.0700722\pi\)
\(570\) 25.4268 1.06501
\(571\) −31.0198 −1.29814 −0.649069 0.760729i \(-0.724841\pi\)
−0.649069 + 0.760729i \(0.724841\pi\)
\(572\) 13.5590 0.566931
\(573\) 3.25643 0.136039
\(574\) 0 0
\(575\) 21.0181 0.876515
\(576\) −11.3673 −0.473638
\(577\) 16.4966 0.686761 0.343380 0.939196i \(-0.388428\pi\)
0.343380 + 0.939196i \(0.388428\pi\)
\(578\) −28.1811 −1.17218
\(579\) −21.7417 −0.903553
\(580\) 77.0632 3.19988
\(581\) 0 0
\(582\) 3.25289 0.134836
\(583\) −3.18795 −0.132031
\(584\) 32.9602 1.36390
\(585\) 12.8401 0.530871
\(586\) 8.14107 0.336305
\(587\) −42.7305 −1.76368 −0.881838 0.471552i \(-0.843694\pi\)
−0.881838 + 0.471552i \(0.843694\pi\)
\(588\) 0 0
\(589\) 3.39149 0.139744
\(590\) −86.1678 −3.54747
\(591\) −22.4747 −0.924484
\(592\) 15.1293 0.621810
\(593\) −2.65943 −0.109210 −0.0546049 0.998508i \(-0.517390\pi\)
−0.0546049 + 0.998508i \(0.517390\pi\)
\(594\) −2.39664 −0.0983355
\(595\) 0 0
\(596\) 10.2458 0.419686
\(597\) −0.769084 −0.0314765
\(598\) 26.0561 1.06551
\(599\) 31.5643 1.28968 0.644842 0.764316i \(-0.276923\pi\)
0.644842 + 0.764316i \(0.276923\pi\)
\(600\) −27.4464 −1.12049
\(601\) 15.8856 0.647988 0.323994 0.946059i \(-0.394974\pi\)
0.323994 + 0.946059i \(0.394974\pi\)
\(602\) 0 0
\(603\) −7.54599 −0.307296
\(604\) 7.89542 0.321260
\(605\) −34.6815 −1.41001
\(606\) 7.50309 0.304792
\(607\) −23.0792 −0.936757 −0.468378 0.883528i \(-0.655162\pi\)
−0.468378 + 0.883528i \(0.655162\pi\)
\(608\) 9.72468 0.394388
\(609\) 0 0
\(610\) −23.6450 −0.957358
\(611\) −40.0564 −1.62051
\(612\) −8.22965 −0.332664
\(613\) −13.4943 −0.545028 −0.272514 0.962152i \(-0.587855\pi\)
−0.272514 + 0.962152i \(0.587855\pi\)
\(614\) −45.1720 −1.82299
\(615\) −3.47491 −0.140122
\(616\) 0 0
\(617\) −14.7047 −0.591991 −0.295995 0.955189i \(-0.595651\pi\)
−0.295995 + 0.955189i \(0.595651\pi\)
\(618\) 11.9459 0.480533
\(619\) −12.1213 −0.487196 −0.243598 0.969876i \(-0.578328\pi\)
−0.243598 + 0.969876i \(0.578328\pi\)
\(620\) −13.8941 −0.557999
\(621\) −2.97074 −0.119212
\(622\) 53.1459 2.13096
\(623\) 0 0
\(624\) −7.16706 −0.286912
\(625\) −10.3192 −0.412767
\(626\) 69.3315 2.77104
\(627\) 3.11251 0.124302
\(628\) −36.0077 −1.43686
\(629\) −17.6628 −0.704261
\(630\) 0 0
\(631\) −8.11700 −0.323132 −0.161566 0.986862i \(-0.551655\pi\)
−0.161566 + 0.986862i \(0.551655\pi\)
\(632\) 31.9896 1.27248
\(633\) 6.39650 0.254238
\(634\) −34.6349 −1.37553
\(635\) −16.3525 −0.648927
\(636\) 11.4750 0.455012
\(637\) 0 0
\(638\) 14.6246 0.578993
\(639\) 7.56311 0.299192
\(640\) −71.8369 −2.83960
\(641\) −17.4968 −0.691083 −0.345541 0.938403i \(-0.612305\pi\)
−0.345541 + 0.938403i \(0.612305\pi\)
\(642\) −20.8969 −0.824736
\(643\) 43.4568 1.71377 0.856884 0.515510i \(-0.172397\pi\)
0.856884 + 0.515510i \(0.172397\pi\)
\(644\) 0 0
\(645\) −39.4786 −1.55447
\(646\) 16.5694 0.651914
\(647\) 30.3127 1.19171 0.595857 0.803091i \(-0.296813\pi\)
0.595857 + 0.803091i \(0.296813\pi\)
\(648\) 3.87933 0.152395
\(649\) −10.5478 −0.414039
\(650\) 62.0542 2.43397
\(651\) 0 0
\(652\) −38.8042 −1.51969
\(653\) 7.99710 0.312951 0.156475 0.987682i \(-0.449987\pi\)
0.156475 + 0.987682i \(0.449987\pi\)
\(654\) 1.94499 0.0760552
\(655\) 20.3168 0.793843
\(656\) 1.93963 0.0757298
\(657\) 8.49635 0.331474
\(658\) 0 0
\(659\) −40.9761 −1.59620 −0.798102 0.602523i \(-0.794162\pi\)
−0.798102 + 0.602523i \(0.794162\pi\)
\(660\) −12.7512 −0.496338
\(661\) −44.8953 −1.74622 −0.873112 0.487519i \(-0.837902\pi\)
−0.873112 + 0.487519i \(0.837902\pi\)
\(662\) 27.4598 1.06726
\(663\) 8.36723 0.324956
\(664\) 48.3664 1.87698
\(665\) 0 0
\(666\) 18.5149 0.717437
\(667\) 18.1278 0.701912
\(668\) −80.7158 −3.12299
\(669\) −13.5518 −0.523945
\(670\) −62.2416 −2.40460
\(671\) −2.89439 −0.111737
\(672\) 0 0
\(673\) −19.5146 −0.752232 −0.376116 0.926573i \(-0.622741\pi\)
−0.376116 + 0.926573i \(0.622741\pi\)
\(674\) 23.6550 0.911157
\(675\) −7.07502 −0.272318
\(676\) 2.37523 0.0913550
\(677\) −0.111472 −0.00428421 −0.00214210 0.999998i \(-0.500682\pi\)
−0.00214210 + 0.999998i \(0.500682\pi\)
\(678\) 8.85644 0.340129
\(679\) 0 0
\(680\) −30.5253 −1.17059
\(681\) 11.0791 0.424551
\(682\) −2.63673 −0.100966
\(683\) 7.36917 0.281973 0.140987 0.990011i \(-0.454973\pi\)
0.140987 + 0.990011i \(0.454973\pi\)
\(684\) −11.2034 −0.428373
\(685\) −62.8949 −2.40309
\(686\) 0 0
\(687\) −4.05671 −0.154773
\(688\) 22.0362 0.840122
\(689\) −11.6668 −0.444469
\(690\) −24.5036 −0.932836
\(691\) 7.90027 0.300540 0.150270 0.988645i \(-0.451986\pi\)
0.150270 + 0.988645i \(0.451986\pi\)
\(692\) 9.85715 0.374713
\(693\) 0 0
\(694\) 33.4984 1.27158
\(695\) −20.6910 −0.784854
\(696\) −23.6721 −0.897290
\(697\) −2.26443 −0.0857714
\(698\) 19.2164 0.727352
\(699\) 5.83354 0.220645
\(700\) 0 0
\(701\) −21.7000 −0.819596 −0.409798 0.912176i \(-0.634401\pi\)
−0.409798 + 0.912176i \(0.634401\pi\)
\(702\) −8.77089 −0.331036
\(703\) −24.0452 −0.906880
\(704\) −11.4773 −0.432567
\(705\) 37.6697 1.41872
\(706\) 61.9234 2.33052
\(707\) 0 0
\(708\) 37.9667 1.42688
\(709\) −1.67315 −0.0628365 −0.0314182 0.999506i \(-0.510002\pi\)
−0.0314182 + 0.999506i \(0.510002\pi\)
\(710\) 62.3828 2.34118
\(711\) 8.24616 0.309255
\(712\) 27.5796 1.03359
\(713\) −3.26835 −0.122401
\(714\) 0 0
\(715\) 12.9643 0.484838
\(716\) −94.2111 −3.52083
\(717\) −12.8223 −0.478858
\(718\) 81.2935 3.03385
\(719\) −34.7636 −1.29646 −0.648232 0.761443i \(-0.724491\pi\)
−0.648232 + 0.761443i \(0.724491\pi\)
\(720\) 6.74004 0.251186
\(721\) 0 0
\(722\) −22.5431 −0.838966
\(723\) −3.16368 −0.117658
\(724\) 54.2783 2.01724
\(725\) 43.1726 1.60339
\(726\) 23.6906 0.879239
\(727\) −48.8728 −1.81259 −0.906297 0.422642i \(-0.861103\pi\)
−0.906297 + 0.422642i \(0.861103\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 70.0804 2.59379
\(731\) −25.7263 −0.951520
\(732\) 10.4183 0.385072
\(733\) −43.0612 −1.59050 −0.795250 0.606281i \(-0.792661\pi\)
−0.795250 + 0.606281i \(0.792661\pi\)
\(734\) 44.9160 1.65788
\(735\) 0 0
\(736\) −9.37159 −0.345441
\(737\) −7.61901 −0.280650
\(738\) 2.37367 0.0873761
\(739\) −46.9948 −1.72873 −0.864366 0.502862i \(-0.832280\pi\)
−0.864366 + 0.502862i \(0.832280\pi\)
\(740\) 98.5070 3.62119
\(741\) 11.3907 0.418448
\(742\) 0 0
\(743\) −24.9341 −0.914745 −0.457372 0.889275i \(-0.651209\pi\)
−0.457372 + 0.889275i \(0.651209\pi\)
\(744\) 4.26795 0.156471
\(745\) 9.79644 0.358914
\(746\) −73.5726 −2.69368
\(747\) 12.4677 0.456170
\(748\) −8.30930 −0.303818
\(749\) 0 0
\(750\) −17.1154 −0.624967
\(751\) −13.1644 −0.480375 −0.240187 0.970727i \(-0.577209\pi\)
−0.240187 + 0.970727i \(0.577209\pi\)
\(752\) −21.0265 −0.766758
\(753\) 13.8603 0.505096
\(754\) 53.5209 1.94912
\(755\) 7.54912 0.274741
\(756\) 0 0
\(757\) −19.3243 −0.702353 −0.351177 0.936309i \(-0.614218\pi\)
−0.351177 + 0.936309i \(0.614218\pi\)
\(758\) 4.14103 0.150409
\(759\) −2.99949 −0.108875
\(760\) −41.5555 −1.50738
\(761\) 43.6803 1.58341 0.791705 0.610903i \(-0.209193\pi\)
0.791705 + 0.610903i \(0.209193\pi\)
\(762\) 11.1702 0.404652
\(763\) 0 0
\(764\) −11.8349 −0.428171
\(765\) −7.86870 −0.284493
\(766\) −83.1949 −3.00595
\(767\) −38.6014 −1.39382
\(768\) 26.3363 0.950329
\(769\) 53.1969 1.91833 0.959165 0.282848i \(-0.0912790\pi\)
0.959165 + 0.282848i \(0.0912790\pi\)
\(770\) 0 0
\(771\) 26.8020 0.965250
\(772\) 79.0161 2.84385
\(773\) 26.0683 0.937613 0.468807 0.883301i \(-0.344684\pi\)
0.468807 + 0.883301i \(0.344684\pi\)
\(774\) 26.9674 0.969322
\(775\) −7.78378 −0.279602
\(776\) −5.31625 −0.190842
\(777\) 0 0
\(778\) 67.8690 2.43322
\(779\) −3.08267 −0.110448
\(780\) −46.6648 −1.67087
\(781\) 7.63630 0.273248
\(782\) −15.9678 −0.571007
\(783\) −6.10211 −0.218072
\(784\) 0 0
\(785\) −34.4283 −1.22880
\(786\) −13.8782 −0.495018
\(787\) 39.5826 1.41097 0.705483 0.708727i \(-0.250730\pi\)
0.705483 + 0.708727i \(0.250730\pi\)
\(788\) 81.6800 2.90973
\(789\) 24.5257 0.873139
\(790\) 68.0168 2.41993
\(791\) 0 0
\(792\) 3.91688 0.139180
\(793\) −10.5925 −0.376150
\(794\) 17.0950 0.606677
\(795\) 10.9717 0.389125
\(796\) 2.79510 0.0990695
\(797\) 27.2314 0.964584 0.482292 0.876011i \(-0.339804\pi\)
0.482292 + 0.876011i \(0.339804\pi\)
\(798\) 0 0
\(799\) 24.5475 0.868428
\(800\) −22.3190 −0.789098
\(801\) 7.10936 0.251197
\(802\) 5.34755 0.188828
\(803\) 8.57857 0.302731
\(804\) 27.4245 0.967188
\(805\) 0 0
\(806\) −9.64953 −0.339890
\(807\) −20.3063 −0.714816
\(808\) −12.2624 −0.431391
\(809\) −53.5166 −1.88154 −0.940771 0.339042i \(-0.889897\pi\)
−0.940771 + 0.339042i \(0.889897\pi\)
\(810\) 8.24830 0.289816
\(811\) 14.5348 0.510387 0.255194 0.966890i \(-0.417861\pi\)
0.255194 + 0.966890i \(0.417861\pi\)
\(812\) 0 0
\(813\) 10.3354 0.362477
\(814\) 18.6941 0.655226
\(815\) −37.1022 −1.29963
\(816\) 4.39215 0.153756
\(817\) −35.0224 −1.22528
\(818\) −49.4555 −1.72917
\(819\) 0 0
\(820\) 12.6289 0.441022
\(821\) −40.8286 −1.42493 −0.712463 0.701710i \(-0.752420\pi\)
−0.712463 + 0.701710i \(0.752420\pi\)
\(822\) 42.9627 1.49850
\(823\) 7.47635 0.260609 0.130305 0.991474i \(-0.458405\pi\)
0.130305 + 0.991474i \(0.458405\pi\)
\(824\) −19.5233 −0.680127
\(825\) −7.14349 −0.248705
\(826\) 0 0
\(827\) 0.331933 0.0115424 0.00577122 0.999983i \(-0.498163\pi\)
0.00577122 + 0.999983i \(0.498163\pi\)
\(828\) 10.7966 0.375209
\(829\) 46.9778 1.63161 0.815803 0.578330i \(-0.196295\pi\)
0.815803 + 0.578330i \(0.196295\pi\)
\(830\) 102.837 3.56954
\(831\) −4.41311 −0.153089
\(832\) −42.0030 −1.45619
\(833\) 0 0
\(834\) 14.1338 0.489412
\(835\) −77.1755 −2.67077
\(836\) −11.3118 −0.391228
\(837\) 1.10018 0.0380277
\(838\) −87.0076 −3.00563
\(839\) −34.8772 −1.20409 −0.602047 0.798461i \(-0.705648\pi\)
−0.602047 + 0.798461i \(0.705648\pi\)
\(840\) 0 0
\(841\) 8.23579 0.283993
\(842\) −92.2321 −3.17853
\(843\) −21.2364 −0.731421
\(844\) −23.2469 −0.800192
\(845\) 2.27105 0.0781265
\(846\) −25.7317 −0.884676
\(847\) 0 0
\(848\) −6.12416 −0.210305
\(849\) 14.7031 0.504610
\(850\) −38.0283 −1.30436
\(851\) 23.1721 0.794329
\(852\) −27.4867 −0.941680
\(853\) 38.5842 1.32110 0.660549 0.750783i \(-0.270323\pi\)
0.660549 + 0.750783i \(0.270323\pi\)
\(854\) 0 0
\(855\) −10.7120 −0.366343
\(856\) 34.1522 1.16730
\(857\) 49.3368 1.68531 0.842656 0.538452i \(-0.180991\pi\)
0.842656 + 0.538452i \(0.180991\pi\)
\(858\) −8.85577 −0.302331
\(859\) 14.0395 0.479021 0.239511 0.970894i \(-0.423013\pi\)
0.239511 + 0.970894i \(0.423013\pi\)
\(860\) 143.478 4.89255
\(861\) 0 0
\(862\) 12.9753 0.441941
\(863\) −41.4234 −1.41007 −0.705034 0.709174i \(-0.749068\pi\)
−0.705034 + 0.709174i \(0.749068\pi\)
\(864\) 3.15463 0.107323
\(865\) 9.42481 0.320453
\(866\) −31.8181 −1.08122
\(867\) 11.8724 0.403206
\(868\) 0 0
\(869\) 8.32597 0.282439
\(870\) −50.3321 −1.70642
\(871\) −27.8830 −0.944778
\(872\) −3.17873 −0.107645
\(873\) −1.37040 −0.0463811
\(874\) −21.7377 −0.735288
\(875\) 0 0
\(876\) −30.8784 −1.04329
\(877\) 11.2172 0.378779 0.189389 0.981902i \(-0.439349\pi\)
0.189389 + 0.981902i \(0.439349\pi\)
\(878\) 33.0333 1.11482
\(879\) −3.42974 −0.115682
\(880\) 6.80527 0.229406
\(881\) −13.9187 −0.468932 −0.234466 0.972124i \(-0.575334\pi\)
−0.234466 + 0.972124i \(0.575334\pi\)
\(882\) 0 0
\(883\) 49.1531 1.65413 0.827066 0.562104i \(-0.190008\pi\)
0.827066 + 0.562104i \(0.190008\pi\)
\(884\) −30.4092 −1.02277
\(885\) 36.3015 1.22026
\(886\) 44.1173 1.48215
\(887\) 14.7228 0.494343 0.247172 0.968972i \(-0.420499\pi\)
0.247172 + 0.968972i \(0.420499\pi\)
\(888\) −30.2592 −1.01543
\(889\) 0 0
\(890\) 58.6402 1.96562
\(891\) 1.00968 0.0338255
\(892\) 49.2517 1.64907
\(893\) 33.4177 1.11828
\(894\) −6.69183 −0.223808
\(895\) −90.0789 −3.01101
\(896\) 0 0
\(897\) −10.9771 −0.366515
\(898\) −42.4556 −1.41676
\(899\) −6.71341 −0.223905
\(900\) 25.7129 0.857096
\(901\) 7.14969 0.238191
\(902\) 2.39664 0.0797995
\(903\) 0 0
\(904\) −14.4742 −0.481406
\(905\) 51.8976 1.72514
\(906\) −5.15671 −0.171320
\(907\) −26.6311 −0.884271 −0.442136 0.896948i \(-0.645779\pi\)
−0.442136 + 0.896948i \(0.645779\pi\)
\(908\) −40.2649 −1.33624
\(909\) −3.16096 −0.104843
\(910\) 0 0
\(911\) 22.5241 0.746257 0.373129 0.927780i \(-0.378285\pi\)
0.373129 + 0.927780i \(0.378285\pi\)
\(912\) 5.97924 0.197992
\(913\) 12.5884 0.416614
\(914\) −78.2119 −2.58702
\(915\) 9.96136 0.329312
\(916\) 14.7434 0.487135
\(917\) 0 0
\(918\) 5.37501 0.177402
\(919\) 48.4583 1.59849 0.799247 0.601003i \(-0.205232\pi\)
0.799247 + 0.601003i \(0.205232\pi\)
\(920\) 40.0467 1.32030
\(921\) 19.0304 0.627074
\(922\) −41.5938 −1.36982
\(923\) 27.9462 0.919861
\(924\) 0 0
\(925\) 55.1859 1.81450
\(926\) 4.14567 0.136235
\(927\) −5.03265 −0.165294
\(928\) −19.2499 −0.631908
\(929\) 28.9304 0.949177 0.474588 0.880208i \(-0.342597\pi\)
0.474588 + 0.880208i \(0.342597\pi\)
\(930\) 9.07460 0.297568
\(931\) 0 0
\(932\) −21.2009 −0.694460
\(933\) −22.3897 −0.733007
\(934\) 66.7728 2.18487
\(935\) −7.94485 −0.259824
\(936\) 14.3344 0.468535
\(937\) −16.6500 −0.543933 −0.271967 0.962307i \(-0.587674\pi\)
−0.271967 + 0.962307i \(0.587674\pi\)
\(938\) 0 0
\(939\) −29.2085 −0.953184
\(940\) −136.904 −4.46531
\(941\) −48.0871 −1.56759 −0.783797 0.621018i \(-0.786719\pi\)
−0.783797 + 0.621018i \(0.786719\pi\)
\(942\) 23.5176 0.766245
\(943\) 2.97074 0.0967407
\(944\) −20.2628 −0.659497
\(945\) 0 0
\(946\) 27.2284 0.885270
\(947\) 57.4521 1.86694 0.933471 0.358653i \(-0.116764\pi\)
0.933471 + 0.358653i \(0.116764\pi\)
\(948\) −29.9692 −0.973353
\(949\) 31.3946 1.01911
\(950\) −51.7697 −1.67963
\(951\) 14.5913 0.473154
\(952\) 0 0
\(953\) −44.9002 −1.45446 −0.727230 0.686393i \(-0.759193\pi\)
−0.727230 + 0.686393i \(0.759193\pi\)
\(954\) −7.49461 −0.242647
\(955\) −11.3158 −0.366171
\(956\) 46.6004 1.50716
\(957\) −6.16117 −0.199162
\(958\) −56.3643 −1.82105
\(959\) 0 0
\(960\) 39.5004 1.27487
\(961\) −29.7896 −0.960955
\(962\) 68.4138 2.20575
\(963\) 8.80363 0.283693
\(964\) 11.4978 0.370319
\(965\) 75.5504 2.43205
\(966\) 0 0
\(967\) 29.1975 0.938928 0.469464 0.882952i \(-0.344447\pi\)
0.469464 + 0.882952i \(0.344447\pi\)
\(968\) −38.7179 −1.24444
\(969\) −6.98050 −0.224246
\(970\) −11.3035 −0.362933
\(971\) 13.4009 0.430057 0.215028 0.976608i \(-0.431016\pi\)
0.215028 + 0.976608i \(0.431016\pi\)
\(972\) −3.63432 −0.116571
\(973\) 0 0
\(974\) −23.0560 −0.738761
\(975\) −26.1427 −0.837237
\(976\) −5.56024 −0.177979
\(977\) 23.3819 0.748052 0.374026 0.927418i \(-0.377977\pi\)
0.374026 + 0.927418i \(0.377977\pi\)
\(978\) 25.3440 0.810413
\(979\) 7.17817 0.229415
\(980\) 0 0
\(981\) −0.819402 −0.0261615
\(982\) 39.0258 1.24536
\(983\) −48.9655 −1.56176 −0.780878 0.624683i \(-0.785228\pi\)
−0.780878 + 0.624683i \(0.785228\pi\)
\(984\) −3.87933 −0.123669
\(985\) 78.0975 2.48839
\(986\) −32.7989 −1.04453
\(987\) 0 0
\(988\) −41.3974 −1.31703
\(989\) 33.7507 1.07321
\(990\) 8.32813 0.264685
\(991\) −11.6616 −0.370443 −0.185221 0.982697i \(-0.559300\pi\)
−0.185221 + 0.982697i \(0.559300\pi\)
\(992\) 3.47065 0.110193
\(993\) −11.5685 −0.367115
\(994\) 0 0
\(995\) 2.67250 0.0847240
\(996\) −45.3116 −1.43575
\(997\) 0.480867 0.0152292 0.00761460 0.999971i \(-0.497576\pi\)
0.00761460 + 0.999971i \(0.497576\pi\)
\(998\) −97.5971 −3.08938
\(999\) −7.80010 −0.246784
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 \(a_p\))