Properties

Label 6008.2.a.e.1.49
Level 6008
Weight 2
Character 6008.1
Self dual Yes
Analytic conductor 47.974
Analytic rank 0
Dimension 50
CM No

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Newspace parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9741215344\)
Analytic rank: \(0\)
Dimension: \(50\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.49
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.31674 q^{3} +1.75910 q^{5} +2.38162 q^{7} +8.00078 q^{9} +O(q^{10})\) \(q+3.31674 q^{3} +1.75910 q^{5} +2.38162 q^{7} +8.00078 q^{9} -3.93150 q^{11} -0.976931 q^{13} +5.83449 q^{15} -2.10948 q^{17} +6.21202 q^{19} +7.89923 q^{21} +6.40852 q^{23} -1.90555 q^{25} +16.5863 q^{27} +0.867057 q^{29} -10.0166 q^{31} -13.0398 q^{33} +4.18952 q^{35} +0.819052 q^{37} -3.24023 q^{39} +4.02372 q^{41} +6.72951 q^{43} +14.0742 q^{45} +8.59758 q^{47} -1.32788 q^{49} -6.99660 q^{51} +2.10552 q^{53} -6.91592 q^{55} +20.6037 q^{57} -5.86417 q^{59} -10.1195 q^{61} +19.0548 q^{63} -1.71852 q^{65} -3.94234 q^{67} +21.2554 q^{69} +3.41828 q^{71} -7.00064 q^{73} -6.32024 q^{75} -9.36335 q^{77} -0.747192 q^{79} +31.0102 q^{81} -1.07637 q^{83} -3.71079 q^{85} +2.87580 q^{87} +0.430535 q^{89} -2.32668 q^{91} -33.2225 q^{93} +10.9276 q^{95} +8.89693 q^{97} -31.4551 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} + O(q^{10}) \) \( 50q + 6q^{3} + 23q^{5} + 12q^{7} + 56q^{9} - 5q^{11} + 36q^{13} + 5q^{15} + 14q^{17} + 9q^{19} + 30q^{21} + 3q^{23} + 71q^{25} + 24q^{27} + 61q^{29} + 27q^{31} + 24q^{33} - 7q^{35} + 56q^{37} - 2q^{39} + 10q^{41} + 19q^{43} + 76q^{45} + 3q^{47} + 82q^{49} - q^{51} + 56q^{53} + 7q^{55} + 35q^{57} - q^{59} + 67q^{61} + 25q^{63} + 27q^{65} + 46q^{67} + 68q^{69} + 4q^{71} + 62q^{73} + 27q^{75} + 71q^{77} + 7q^{79} + 74q^{81} - q^{83} + 72q^{85} + 25q^{87} + 19q^{89} + 45q^{91} + 72q^{93} - 24q^{95} + 81q^{97} + 16q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 3.31674 1.91492 0.957461 0.288562i \(-0.0931772\pi\)
0.957461 + 0.288562i \(0.0931772\pi\)
\(4\) 0 0
\(5\) 1.75910 0.786695 0.393347 0.919390i \(-0.371317\pi\)
0.393347 + 0.919390i \(0.371317\pi\)
\(6\) 0 0
\(7\) 2.38162 0.900169 0.450084 0.892986i \(-0.351394\pi\)
0.450084 + 0.892986i \(0.351394\pi\)
\(8\) 0 0
\(9\) 8.00078 2.66693
\(10\) 0 0
\(11\) −3.93150 −1.18539 −0.592696 0.805426i \(-0.701937\pi\)
−0.592696 + 0.805426i \(0.701937\pi\)
\(12\) 0 0
\(13\) −0.976931 −0.270952 −0.135476 0.990781i \(-0.543256\pi\)
−0.135476 + 0.990781i \(0.543256\pi\)
\(14\) 0 0
\(15\) 5.83449 1.50646
\(16\) 0 0
\(17\) −2.10948 −0.511624 −0.255812 0.966727i \(-0.582343\pi\)
−0.255812 + 0.966727i \(0.582343\pi\)
\(18\) 0 0
\(19\) 6.21202 1.42513 0.712567 0.701604i \(-0.247532\pi\)
0.712567 + 0.701604i \(0.247532\pi\)
\(20\) 0 0
\(21\) 7.89923 1.72375
\(22\) 0 0
\(23\) 6.40852 1.33627 0.668135 0.744040i \(-0.267093\pi\)
0.668135 + 0.744040i \(0.267093\pi\)
\(24\) 0 0
\(25\) −1.90555 −0.381111
\(26\) 0 0
\(27\) 16.5863 3.19204
\(28\) 0 0
\(29\) 0.867057 0.161008 0.0805042 0.996754i \(-0.474347\pi\)
0.0805042 + 0.996754i \(0.474347\pi\)
\(30\) 0 0
\(31\) −10.0166 −1.79903 −0.899517 0.436885i \(-0.856082\pi\)
−0.899517 + 0.436885i \(0.856082\pi\)
\(32\) 0 0
\(33\) −13.0398 −2.26993
\(34\) 0 0
\(35\) 4.18952 0.708158
\(36\) 0 0
\(37\) 0.819052 0.134651 0.0673257 0.997731i \(-0.478553\pi\)
0.0673257 + 0.997731i \(0.478553\pi\)
\(38\) 0 0
\(39\) −3.24023 −0.518852
\(40\) 0 0
\(41\) 4.02372 0.628399 0.314200 0.949357i \(-0.398264\pi\)
0.314200 + 0.949357i \(0.398264\pi\)
\(42\) 0 0
\(43\) 6.72951 1.02624 0.513121 0.858317i \(-0.328489\pi\)
0.513121 + 0.858317i \(0.328489\pi\)
\(44\) 0 0
\(45\) 14.0742 2.09806
\(46\) 0 0
\(47\) 8.59758 1.25409 0.627043 0.778985i \(-0.284265\pi\)
0.627043 + 0.778985i \(0.284265\pi\)
\(48\) 0 0
\(49\) −1.32788 −0.189696
\(50\) 0 0
\(51\) −6.99660 −0.979720
\(52\) 0 0
\(53\) 2.10552 0.289215 0.144608 0.989489i \(-0.453808\pi\)
0.144608 + 0.989489i \(0.453808\pi\)
\(54\) 0 0
\(55\) −6.91592 −0.932542
\(56\) 0 0
\(57\) 20.6037 2.72902
\(58\) 0 0
\(59\) −5.86417 −0.763450 −0.381725 0.924276i \(-0.624670\pi\)
−0.381725 + 0.924276i \(0.624670\pi\)
\(60\) 0 0
\(61\) −10.1195 −1.29567 −0.647837 0.761779i \(-0.724326\pi\)
−0.647837 + 0.761779i \(0.724326\pi\)
\(62\) 0 0
\(63\) 19.0548 2.40068
\(64\) 0 0
\(65\) −1.71852 −0.213156
\(66\) 0 0
\(67\) −3.94234 −0.481634 −0.240817 0.970571i \(-0.577415\pi\)
−0.240817 + 0.970571i \(0.577415\pi\)
\(68\) 0 0
\(69\) 21.2554 2.55885
\(70\) 0 0
\(71\) 3.41828 0.405675 0.202838 0.979212i \(-0.434984\pi\)
0.202838 + 0.979212i \(0.434984\pi\)
\(72\) 0 0
\(73\) −7.00064 −0.819363 −0.409682 0.912229i \(-0.634360\pi\)
−0.409682 + 0.912229i \(0.634360\pi\)
\(74\) 0 0
\(75\) −6.32024 −0.729798
\(76\) 0 0
\(77\) −9.36335 −1.06705
\(78\) 0 0
\(79\) −0.747192 −0.0840656 −0.0420328 0.999116i \(-0.513383\pi\)
−0.0420328 + 0.999116i \(0.513383\pi\)
\(80\) 0 0
\(81\) 31.0102 3.44557
\(82\) 0 0
\(83\) −1.07637 −0.118147 −0.0590734 0.998254i \(-0.518815\pi\)
−0.0590734 + 0.998254i \(0.518815\pi\)
\(84\) 0 0
\(85\) −3.71079 −0.402492
\(86\) 0 0
\(87\) 2.87580 0.308319
\(88\) 0 0
\(89\) 0.430535 0.0456366 0.0228183 0.999740i \(-0.492736\pi\)
0.0228183 + 0.999740i \(0.492736\pi\)
\(90\) 0 0
\(91\) −2.32668 −0.243902
\(92\) 0 0
\(93\) −33.2225 −3.44501
\(94\) 0 0
\(95\) 10.9276 1.12115
\(96\) 0 0
\(97\) 8.89693 0.903346 0.451673 0.892183i \(-0.350827\pi\)
0.451673 + 0.892183i \(0.350827\pi\)
\(98\) 0 0
\(99\) −31.4551 −3.16136
\(100\) 0 0
\(101\) 5.66563 0.563752 0.281876 0.959451i \(-0.409043\pi\)
0.281876 + 0.959451i \(0.409043\pi\)
\(102\) 0 0
\(103\) −8.05381 −0.793566 −0.396783 0.917913i \(-0.629873\pi\)
−0.396783 + 0.917913i \(0.629873\pi\)
\(104\) 0 0
\(105\) 13.8956 1.35607
\(106\) 0 0
\(107\) −8.64530 −0.835773 −0.417886 0.908499i \(-0.637229\pi\)
−0.417886 + 0.908499i \(0.637229\pi\)
\(108\) 0 0
\(109\) 8.06456 0.772445 0.386222 0.922406i \(-0.373780\pi\)
0.386222 + 0.922406i \(0.373780\pi\)
\(110\) 0 0
\(111\) 2.71658 0.257847
\(112\) 0 0
\(113\) 9.85519 0.927098 0.463549 0.886071i \(-0.346576\pi\)
0.463549 + 0.886071i \(0.346576\pi\)
\(114\) 0 0
\(115\) 11.2733 1.05124
\(116\) 0 0
\(117\) −7.81621 −0.722609
\(118\) 0 0
\(119\) −5.02398 −0.460548
\(120\) 0 0
\(121\) 4.45671 0.405155
\(122\) 0 0
\(123\) 13.3456 1.20334
\(124\) 0 0
\(125\) −12.1476 −1.08651
\(126\) 0 0
\(127\) 2.75273 0.244265 0.122133 0.992514i \(-0.461027\pi\)
0.122133 + 0.992514i \(0.461027\pi\)
\(128\) 0 0
\(129\) 22.3201 1.96517
\(130\) 0 0
\(131\) 2.96331 0.258905 0.129453 0.991586i \(-0.458678\pi\)
0.129453 + 0.991586i \(0.458678\pi\)
\(132\) 0 0
\(133\) 14.7947 1.28286
\(134\) 0 0
\(135\) 29.1770 2.51116
\(136\) 0 0
\(137\) 3.96540 0.338787 0.169393 0.985549i \(-0.445819\pi\)
0.169393 + 0.985549i \(0.445819\pi\)
\(138\) 0 0
\(139\) −8.63154 −0.732118 −0.366059 0.930592i \(-0.619293\pi\)
−0.366059 + 0.930592i \(0.619293\pi\)
\(140\) 0 0
\(141\) 28.5160 2.40148
\(142\) 0 0
\(143\) 3.84081 0.321184
\(144\) 0 0
\(145\) 1.52524 0.126665
\(146\) 0 0
\(147\) −4.40422 −0.363254
\(148\) 0 0
\(149\) −4.71319 −0.386120 −0.193060 0.981187i \(-0.561841\pi\)
−0.193060 + 0.981187i \(0.561841\pi\)
\(150\) 0 0
\(151\) 5.26744 0.428659 0.214329 0.976761i \(-0.431243\pi\)
0.214329 + 0.976761i \(0.431243\pi\)
\(152\) 0 0
\(153\) −16.8775 −1.36446
\(154\) 0 0
\(155\) −17.6202 −1.41529
\(156\) 0 0
\(157\) 15.1946 1.21266 0.606330 0.795213i \(-0.292641\pi\)
0.606330 + 0.795213i \(0.292641\pi\)
\(158\) 0 0
\(159\) 6.98347 0.553825
\(160\) 0 0
\(161\) 15.2627 1.20287
\(162\) 0 0
\(163\) 19.9251 1.56065 0.780325 0.625374i \(-0.215054\pi\)
0.780325 + 0.625374i \(0.215054\pi\)
\(164\) 0 0
\(165\) −22.9383 −1.78575
\(166\) 0 0
\(167\) −17.7038 −1.36996 −0.684980 0.728562i \(-0.740189\pi\)
−0.684980 + 0.728562i \(0.740189\pi\)
\(168\) 0 0
\(169\) −12.0456 −0.926585
\(170\) 0 0
\(171\) 49.7010 3.80073
\(172\) 0 0
\(173\) −6.26071 −0.475993 −0.237996 0.971266i \(-0.576491\pi\)
−0.237996 + 0.971266i \(0.576491\pi\)
\(174\) 0 0
\(175\) −4.53831 −0.343064
\(176\) 0 0
\(177\) −19.4500 −1.46195
\(178\) 0 0
\(179\) −25.1668 −1.88106 −0.940529 0.339713i \(-0.889670\pi\)
−0.940529 + 0.339713i \(0.889670\pi\)
\(180\) 0 0
\(181\) 0.982740 0.0730465 0.0365232 0.999333i \(-0.488372\pi\)
0.0365232 + 0.999333i \(0.488372\pi\)
\(182\) 0 0
\(183\) −33.5639 −2.48111
\(184\) 0 0
\(185\) 1.44080 0.105930
\(186\) 0 0
\(187\) 8.29342 0.606475
\(188\) 0 0
\(189\) 39.5023 2.87337
\(190\) 0 0
\(191\) 16.3117 1.18028 0.590138 0.807302i \(-0.299073\pi\)
0.590138 + 0.807302i \(0.299073\pi\)
\(192\) 0 0
\(193\) −12.2187 −0.879519 −0.439760 0.898116i \(-0.644936\pi\)
−0.439760 + 0.898116i \(0.644936\pi\)
\(194\) 0 0
\(195\) −5.69990 −0.408178
\(196\) 0 0
\(197\) −21.1349 −1.50580 −0.752900 0.658135i \(-0.771346\pi\)
−0.752900 + 0.658135i \(0.771346\pi\)
\(198\) 0 0
\(199\) 0.128325 0.00909672 0.00454836 0.999990i \(-0.498552\pi\)
0.00454836 + 0.999990i \(0.498552\pi\)
\(200\) 0 0
\(201\) −13.0757 −0.922292
\(202\) 0 0
\(203\) 2.06500 0.144935
\(204\) 0 0
\(205\) 7.07814 0.494358
\(206\) 0 0
\(207\) 51.2732 3.56373
\(208\) 0 0
\(209\) −24.4226 −1.68934
\(210\) 0 0
\(211\) 26.6665 1.83580 0.917898 0.396815i \(-0.129885\pi\)
0.917898 + 0.396815i \(0.129885\pi\)
\(212\) 0 0
\(213\) 11.3376 0.776837
\(214\) 0 0
\(215\) 11.8379 0.807339
\(216\) 0 0
\(217\) −23.8558 −1.61943
\(218\) 0 0
\(219\) −23.2193 −1.56902
\(220\) 0 0
\(221\) 2.06082 0.138625
\(222\) 0 0
\(223\) −13.3628 −0.894838 −0.447419 0.894324i \(-0.647657\pi\)
−0.447419 + 0.894324i \(0.647657\pi\)
\(224\) 0 0
\(225\) −15.2459 −1.01640
\(226\) 0 0
\(227\) −10.6812 −0.708939 −0.354469 0.935068i \(-0.615338\pi\)
−0.354469 + 0.935068i \(0.615338\pi\)
\(228\) 0 0
\(229\) 24.8347 1.64113 0.820563 0.571557i \(-0.193660\pi\)
0.820563 + 0.571557i \(0.193660\pi\)
\(230\) 0 0
\(231\) −31.0558 −2.04332
\(232\) 0 0
\(233\) −19.7268 −1.29234 −0.646172 0.763192i \(-0.723631\pi\)
−0.646172 + 0.763192i \(0.723631\pi\)
\(234\) 0 0
\(235\) 15.1240 0.986583
\(236\) 0 0
\(237\) −2.47824 −0.160979
\(238\) 0 0
\(239\) 4.32680 0.279878 0.139939 0.990160i \(-0.455309\pi\)
0.139939 + 0.990160i \(0.455309\pi\)
\(240\) 0 0
\(241\) −2.28751 −0.147351 −0.0736757 0.997282i \(-0.523473\pi\)
−0.0736757 + 0.997282i \(0.523473\pi\)
\(242\) 0 0
\(243\) 53.0938 3.40597
\(244\) 0 0
\(245\) −2.33587 −0.149233
\(246\) 0 0
\(247\) −6.06871 −0.386143
\(248\) 0 0
\(249\) −3.57004 −0.226242
\(250\) 0 0
\(251\) −6.75842 −0.426588 −0.213294 0.976988i \(-0.568419\pi\)
−0.213294 + 0.976988i \(0.568419\pi\)
\(252\) 0 0
\(253\) −25.1951 −1.58400
\(254\) 0 0
\(255\) −12.3077 −0.770741
\(256\) 0 0
\(257\) −22.6495 −1.41284 −0.706420 0.707793i \(-0.749691\pi\)
−0.706420 + 0.707793i \(0.749691\pi\)
\(258\) 0 0
\(259\) 1.95067 0.121209
\(260\) 0 0
\(261\) 6.93713 0.429398
\(262\) 0 0
\(263\) 3.12946 0.192971 0.0964853 0.995334i \(-0.469240\pi\)
0.0964853 + 0.995334i \(0.469240\pi\)
\(264\) 0 0
\(265\) 3.70383 0.227524
\(266\) 0 0
\(267\) 1.42797 0.0873906
\(268\) 0 0
\(269\) −16.6793 −1.01695 −0.508477 0.861076i \(-0.669791\pi\)
−0.508477 + 0.861076i \(0.669791\pi\)
\(270\) 0 0
\(271\) 14.4276 0.876413 0.438207 0.898874i \(-0.355614\pi\)
0.438207 + 0.898874i \(0.355614\pi\)
\(272\) 0 0
\(273\) −7.71700 −0.467054
\(274\) 0 0
\(275\) 7.49169 0.451766
\(276\) 0 0
\(277\) −10.3553 −0.622190 −0.311095 0.950379i \(-0.600696\pi\)
−0.311095 + 0.950379i \(0.600696\pi\)
\(278\) 0 0
\(279\) −80.1407 −4.79790
\(280\) 0 0
\(281\) −23.5233 −1.40328 −0.701642 0.712530i \(-0.747549\pi\)
−0.701642 + 0.712530i \(0.747549\pi\)
\(282\) 0 0
\(283\) −24.4995 −1.45634 −0.728171 0.685395i \(-0.759630\pi\)
−0.728171 + 0.685395i \(0.759630\pi\)
\(284\) 0 0
\(285\) 36.2440 2.14691
\(286\) 0 0
\(287\) 9.58298 0.565665
\(288\) 0 0
\(289\) −12.5501 −0.738241
\(290\) 0 0
\(291\) 29.5088 1.72984
\(292\) 0 0
\(293\) 13.9689 0.816073 0.408036 0.912966i \(-0.366214\pi\)
0.408036 + 0.912966i \(0.366214\pi\)
\(294\) 0 0
\(295\) −10.3157 −0.600603
\(296\) 0 0
\(297\) −65.2091 −3.78382
\(298\) 0 0
\(299\) −6.26068 −0.362065
\(300\) 0 0
\(301\) 16.0272 0.923790
\(302\) 0 0
\(303\) 18.7914 1.07954
\(304\) 0 0
\(305\) −17.8013 −1.01930
\(306\) 0 0
\(307\) −11.0671 −0.631633 −0.315816 0.948820i \(-0.602278\pi\)
−0.315816 + 0.948820i \(0.602278\pi\)
\(308\) 0 0
\(309\) −26.7124 −1.51962
\(310\) 0 0
\(311\) 10.7238 0.608093 0.304047 0.952657i \(-0.401662\pi\)
0.304047 + 0.952657i \(0.401662\pi\)
\(312\) 0 0
\(313\) 29.8106 1.68500 0.842498 0.538699i \(-0.181084\pi\)
0.842498 + 0.538699i \(0.181084\pi\)
\(314\) 0 0
\(315\) 33.5194 1.88861
\(316\) 0 0
\(317\) −0.0880663 −0.00494630 −0.00247315 0.999997i \(-0.500787\pi\)
−0.00247315 + 0.999997i \(0.500787\pi\)
\(318\) 0 0
\(319\) −3.40884 −0.190858
\(320\) 0 0
\(321\) −28.6742 −1.60044
\(322\) 0 0
\(323\) −13.1041 −0.729133
\(324\) 0 0
\(325\) 1.86160 0.103263
\(326\) 0 0
\(327\) 26.7481 1.47917
\(328\) 0 0
\(329\) 20.4762 1.12889
\(330\) 0 0
\(331\) −27.5927 −1.51663 −0.758315 0.651888i \(-0.773977\pi\)
−0.758315 + 0.651888i \(0.773977\pi\)
\(332\) 0 0
\(333\) 6.55306 0.359105
\(334\) 0 0
\(335\) −6.93499 −0.378899
\(336\) 0 0
\(337\) 17.3623 0.945787 0.472894 0.881120i \(-0.343210\pi\)
0.472894 + 0.881120i \(0.343210\pi\)
\(338\) 0 0
\(339\) 32.6871 1.77532
\(340\) 0 0
\(341\) 39.3803 2.13256
\(342\) 0 0
\(343\) −19.8339 −1.07093
\(344\) 0 0
\(345\) 37.3905 2.01304
\(346\) 0 0
\(347\) 8.92927 0.479348 0.239674 0.970853i \(-0.422959\pi\)
0.239674 + 0.970853i \(0.422959\pi\)
\(348\) 0 0
\(349\) 34.3940 1.84107 0.920535 0.390660i \(-0.127753\pi\)
0.920535 + 0.390660i \(0.127753\pi\)
\(350\) 0 0
\(351\) −16.2037 −0.864888
\(352\) 0 0
\(353\) −32.0268 −1.70461 −0.852307 0.523041i \(-0.824797\pi\)
−0.852307 + 0.523041i \(0.824797\pi\)
\(354\) 0 0
\(355\) 6.01311 0.319143
\(356\) 0 0
\(357\) −16.6633 −0.881913
\(358\) 0 0
\(359\) −25.6851 −1.35561 −0.677804 0.735242i \(-0.737068\pi\)
−0.677804 + 0.735242i \(0.737068\pi\)
\(360\) 0 0
\(361\) 19.5892 1.03101
\(362\) 0 0
\(363\) 14.7818 0.775841
\(364\) 0 0
\(365\) −12.3149 −0.644589
\(366\) 0 0
\(367\) 7.51232 0.392140 0.196070 0.980590i \(-0.437182\pi\)
0.196070 + 0.980590i \(0.437182\pi\)
\(368\) 0 0
\(369\) 32.1929 1.67589
\(370\) 0 0
\(371\) 5.01455 0.260343
\(372\) 0 0
\(373\) −5.60492 −0.290212 −0.145106 0.989416i \(-0.546352\pi\)
−0.145106 + 0.989416i \(0.546352\pi\)
\(374\) 0 0
\(375\) −40.2904 −2.08059
\(376\) 0 0
\(377\) −0.847055 −0.0436255
\(378\) 0 0
\(379\) 11.1734 0.573938 0.286969 0.957940i \(-0.407352\pi\)
0.286969 + 0.957940i \(0.407352\pi\)
\(380\) 0 0
\(381\) 9.13010 0.467749
\(382\) 0 0
\(383\) 15.8231 0.808523 0.404261 0.914644i \(-0.367529\pi\)
0.404261 + 0.914644i \(0.367529\pi\)
\(384\) 0 0
\(385\) −16.4711 −0.839445
\(386\) 0 0
\(387\) 53.8414 2.73691
\(388\) 0 0
\(389\) −21.6769 −1.09906 −0.549532 0.835473i \(-0.685194\pi\)
−0.549532 + 0.835473i \(0.685194\pi\)
\(390\) 0 0
\(391\) −13.5186 −0.683667
\(392\) 0 0
\(393\) 9.82853 0.495784
\(394\) 0 0
\(395\) −1.31439 −0.0661340
\(396\) 0 0
\(397\) 14.2200 0.713682 0.356841 0.934165i \(-0.383854\pi\)
0.356841 + 0.934165i \(0.383854\pi\)
\(398\) 0 0
\(399\) 49.0702 2.45658
\(400\) 0 0
\(401\) 28.3284 1.41466 0.707328 0.706886i \(-0.249901\pi\)
0.707328 + 0.706886i \(0.249901\pi\)
\(402\) 0 0
\(403\) 9.78553 0.487452
\(404\) 0 0
\(405\) 54.5501 2.71062
\(406\) 0 0
\(407\) −3.22010 −0.159615
\(408\) 0 0
\(409\) 34.2008 1.69112 0.845559 0.533881i \(-0.179267\pi\)
0.845559 + 0.533881i \(0.179267\pi\)
\(410\) 0 0
\(411\) 13.1522 0.648751
\(412\) 0 0
\(413\) −13.9662 −0.687234
\(414\) 0 0
\(415\) −1.89344 −0.0929455
\(416\) 0 0
\(417\) −28.6286 −1.40195
\(418\) 0 0
\(419\) −28.1099 −1.37326 −0.686630 0.727007i \(-0.740911\pi\)
−0.686630 + 0.727007i \(0.740911\pi\)
\(420\) 0 0
\(421\) 5.21924 0.254370 0.127185 0.991879i \(-0.459406\pi\)
0.127185 + 0.991879i \(0.459406\pi\)
\(422\) 0 0
\(423\) 68.7874 3.34456
\(424\) 0 0
\(425\) 4.01973 0.194985
\(426\) 0 0
\(427\) −24.1009 −1.16633
\(428\) 0 0
\(429\) 12.7390 0.615043
\(430\) 0 0
\(431\) 20.1671 0.971414 0.485707 0.874122i \(-0.338562\pi\)
0.485707 + 0.874122i \(0.338562\pi\)
\(432\) 0 0
\(433\) −4.58909 −0.220538 −0.110269 0.993902i \(-0.535171\pi\)
−0.110269 + 0.993902i \(0.535171\pi\)
\(434\) 0 0
\(435\) 5.05884 0.242553
\(436\) 0 0
\(437\) 39.8099 1.90436
\(438\) 0 0
\(439\) −25.5197 −1.21799 −0.608993 0.793175i \(-0.708426\pi\)
−0.608993 + 0.793175i \(0.708426\pi\)
\(440\) 0 0
\(441\) −10.6240 −0.505907
\(442\) 0 0
\(443\) −36.6426 −1.74094 −0.870472 0.492219i \(-0.836186\pi\)
−0.870472 + 0.492219i \(0.836186\pi\)
\(444\) 0 0
\(445\) 0.757356 0.0359021
\(446\) 0 0
\(447\) −15.6325 −0.739390
\(448\) 0 0
\(449\) 1.32124 0.0623534 0.0311767 0.999514i \(-0.490075\pi\)
0.0311767 + 0.999514i \(0.490075\pi\)
\(450\) 0 0
\(451\) −15.8193 −0.744900
\(452\) 0 0
\(453\) 17.4708 0.820848
\(454\) 0 0
\(455\) −4.09287 −0.191877
\(456\) 0 0
\(457\) −12.4209 −0.581025 −0.290512 0.956871i \(-0.593826\pi\)
−0.290512 + 0.956871i \(0.593826\pi\)
\(458\) 0 0
\(459\) −34.9885 −1.63312
\(460\) 0 0
\(461\) 10.9915 0.511924 0.255962 0.966687i \(-0.417608\pi\)
0.255962 + 0.966687i \(0.417608\pi\)
\(462\) 0 0
\(463\) 4.06277 0.188813 0.0944065 0.995534i \(-0.469905\pi\)
0.0944065 + 0.995534i \(0.469905\pi\)
\(464\) 0 0
\(465\) −58.4418 −2.71017
\(466\) 0 0
\(467\) 18.5621 0.858950 0.429475 0.903079i \(-0.358699\pi\)
0.429475 + 0.903079i \(0.358699\pi\)
\(468\) 0 0
\(469\) −9.38917 −0.433552
\(470\) 0 0
\(471\) 50.3966 2.32215
\(472\) 0 0
\(473\) −26.4571 −1.21650
\(474\) 0 0
\(475\) −11.8373 −0.543135
\(476\) 0 0
\(477\) 16.8458 0.771316
\(478\) 0 0
\(479\) −27.3434 −1.24935 −0.624675 0.780885i \(-0.714769\pi\)
−0.624675 + 0.780885i \(0.714769\pi\)
\(480\) 0 0
\(481\) −0.800157 −0.0364840
\(482\) 0 0
\(483\) 50.6224 2.30340
\(484\) 0 0
\(485\) 15.6506 0.710658
\(486\) 0 0
\(487\) 26.9825 1.22269 0.611347 0.791363i \(-0.290628\pi\)
0.611347 + 0.791363i \(0.290628\pi\)
\(488\) 0 0
\(489\) 66.0863 2.98852
\(490\) 0 0
\(491\) −21.7215 −0.980280 −0.490140 0.871644i \(-0.663054\pi\)
−0.490140 + 0.871644i \(0.663054\pi\)
\(492\) 0 0
\(493\) −1.82904 −0.0823757
\(494\) 0 0
\(495\) −55.3328 −2.48702
\(496\) 0 0
\(497\) 8.14106 0.365176
\(498\) 0 0
\(499\) 3.91201 0.175126 0.0875629 0.996159i \(-0.472092\pi\)
0.0875629 + 0.996159i \(0.472092\pi\)
\(500\) 0 0
\(501\) −58.7189 −2.62337
\(502\) 0 0
\(503\) −31.8132 −1.41848 −0.709240 0.704967i \(-0.750962\pi\)
−0.709240 + 0.704967i \(0.750962\pi\)
\(504\) 0 0
\(505\) 9.96644 0.443501
\(506\) 0 0
\(507\) −39.9522 −1.77434
\(508\) 0 0
\(509\) −17.8562 −0.791462 −0.395731 0.918367i \(-0.629509\pi\)
−0.395731 + 0.918367i \(0.629509\pi\)
\(510\) 0 0
\(511\) −16.6729 −0.737565
\(512\) 0 0
\(513\) 103.034 4.54908
\(514\) 0 0
\(515\) −14.1675 −0.624294
\(516\) 0 0
\(517\) −33.8014 −1.48658
\(518\) 0 0
\(519\) −20.7651 −0.911489
\(520\) 0 0
\(521\) −29.4351 −1.28957 −0.644787 0.764363i \(-0.723054\pi\)
−0.644787 + 0.764363i \(0.723054\pi\)
\(522\) 0 0
\(523\) 16.4946 0.721259 0.360630 0.932709i \(-0.382562\pi\)
0.360630 + 0.932709i \(0.382562\pi\)
\(524\) 0 0
\(525\) −15.0524 −0.656941
\(526\) 0 0
\(527\) 21.1298 0.920429
\(528\) 0 0
\(529\) 18.0692 0.785617
\(530\) 0 0
\(531\) −46.9180 −2.03607
\(532\) 0 0
\(533\) −3.93089 −0.170266
\(534\) 0 0
\(535\) −15.2080 −0.657498
\(536\) 0 0
\(537\) −83.4719 −3.60208
\(538\) 0 0
\(539\) 5.22054 0.224865
\(540\) 0 0
\(541\) 21.5430 0.926207 0.463103 0.886304i \(-0.346736\pi\)
0.463103 + 0.886304i \(0.346736\pi\)
\(542\) 0 0
\(543\) 3.25949 0.139878
\(544\) 0 0
\(545\) 14.1864 0.607678
\(546\) 0 0
\(547\) −5.82669 −0.249131 −0.124566 0.992211i \(-0.539754\pi\)
−0.124566 + 0.992211i \(0.539754\pi\)
\(548\) 0 0
\(549\) −80.9642 −3.45547
\(550\) 0 0
\(551\) 5.38617 0.229459
\(552\) 0 0
\(553\) −1.77953 −0.0756732
\(554\) 0 0
\(555\) 4.77875 0.202847
\(556\) 0 0
\(557\) 40.6603 1.72283 0.861416 0.507900i \(-0.169578\pi\)
0.861416 + 0.507900i \(0.169578\pi\)
\(558\) 0 0
\(559\) −6.57427 −0.278062
\(560\) 0 0
\(561\) 27.5071 1.16135
\(562\) 0 0
\(563\) −23.1065 −0.973824 −0.486912 0.873451i \(-0.661877\pi\)
−0.486912 + 0.873451i \(0.661877\pi\)
\(564\) 0 0
\(565\) 17.3363 0.729343
\(566\) 0 0
\(567\) 73.8545 3.10160
\(568\) 0 0
\(569\) −3.53525 −0.148205 −0.0741027 0.997251i \(-0.523609\pi\)
−0.0741027 + 0.997251i \(0.523609\pi\)
\(570\) 0 0
\(571\) −22.1162 −0.925533 −0.462767 0.886480i \(-0.653143\pi\)
−0.462767 + 0.886480i \(0.653143\pi\)
\(572\) 0 0
\(573\) 54.1019 2.26014
\(574\) 0 0
\(575\) −12.2118 −0.509267
\(576\) 0 0
\(577\) 13.8217 0.575404 0.287702 0.957720i \(-0.407109\pi\)
0.287702 + 0.957720i \(0.407109\pi\)
\(578\) 0 0
\(579\) −40.5262 −1.68421
\(580\) 0 0
\(581\) −2.56350 −0.106352
\(582\) 0 0
\(583\) −8.27786 −0.342834
\(584\) 0 0
\(585\) −13.7495 −0.568473
\(586\) 0 0
\(587\) 6.83707 0.282196 0.141098 0.989996i \(-0.454937\pi\)
0.141098 + 0.989996i \(0.454937\pi\)
\(588\) 0 0
\(589\) −62.2233 −2.56387
\(590\) 0 0
\(591\) −70.0991 −2.88349
\(592\) 0 0
\(593\) −38.6406 −1.58678 −0.793390 0.608713i \(-0.791686\pi\)
−0.793390 + 0.608713i \(0.791686\pi\)
\(594\) 0 0
\(595\) −8.83771 −0.362311
\(596\) 0 0
\(597\) 0.425621 0.0174195
\(598\) 0 0
\(599\) 1.98783 0.0812206 0.0406103 0.999175i \(-0.487070\pi\)
0.0406103 + 0.999175i \(0.487070\pi\)
\(600\) 0 0
\(601\) 1.95243 0.0796411 0.0398206 0.999207i \(-0.487321\pi\)
0.0398206 + 0.999207i \(0.487321\pi\)
\(602\) 0 0
\(603\) −31.5418 −1.28448
\(604\) 0 0
\(605\) 7.83981 0.318734
\(606\) 0 0
\(607\) −17.3571 −0.704503 −0.352252 0.935905i \(-0.614584\pi\)
−0.352252 + 0.935905i \(0.614584\pi\)
\(608\) 0 0
\(609\) 6.84908 0.277539
\(610\) 0 0
\(611\) −8.39924 −0.339797
\(612\) 0 0
\(613\) −26.8090 −1.08280 −0.541402 0.840764i \(-0.682106\pi\)
−0.541402 + 0.840764i \(0.682106\pi\)
\(614\) 0 0
\(615\) 23.4764 0.946658
\(616\) 0 0
\(617\) −13.6812 −0.550786 −0.275393 0.961332i \(-0.588808\pi\)
−0.275393 + 0.961332i \(0.588808\pi\)
\(618\) 0 0
\(619\) −11.8080 −0.474603 −0.237301 0.971436i \(-0.576263\pi\)
−0.237301 + 0.971436i \(0.576263\pi\)
\(620\) 0 0
\(621\) 106.294 4.26542
\(622\) 0 0
\(623\) 1.02537 0.0410807
\(624\) 0 0
\(625\) −11.8411 −0.473643
\(626\) 0 0
\(627\) −81.0034 −3.23496
\(628\) 0 0
\(629\) −1.72777 −0.0688908
\(630\) 0 0
\(631\) −23.9873 −0.954920 −0.477460 0.878654i \(-0.658442\pi\)
−0.477460 + 0.878654i \(0.658442\pi\)
\(632\) 0 0
\(633\) 88.4459 3.51541
\(634\) 0 0
\(635\) 4.84234 0.192162
\(636\) 0 0
\(637\) 1.29724 0.0513986
\(638\) 0 0
\(639\) 27.3489 1.08191
\(640\) 0 0
\(641\) −12.5436 −0.495443 −0.247721 0.968831i \(-0.579682\pi\)
−0.247721 + 0.968831i \(0.579682\pi\)
\(642\) 0 0
\(643\) 33.1718 1.30817 0.654085 0.756421i \(-0.273054\pi\)
0.654085 + 0.756421i \(0.273054\pi\)
\(644\) 0 0
\(645\) 39.2633 1.54599
\(646\) 0 0
\(647\) 14.0134 0.550923 0.275461 0.961312i \(-0.411169\pi\)
0.275461 + 0.961312i \(0.411169\pi\)
\(648\) 0 0
\(649\) 23.0550 0.904988
\(650\) 0 0
\(651\) −79.1234 −3.10109
\(652\) 0 0
\(653\) 12.5815 0.492354 0.246177 0.969225i \(-0.420826\pi\)
0.246177 + 0.969225i \(0.420826\pi\)
\(654\) 0 0
\(655\) 5.21277 0.203680
\(656\) 0 0
\(657\) −56.0106 −2.18518
\(658\) 0 0
\(659\) 25.9476 1.01077 0.505387 0.862893i \(-0.331350\pi\)
0.505387 + 0.862893i \(0.331350\pi\)
\(660\) 0 0
\(661\) 25.8290 1.00463 0.502317 0.864684i \(-0.332481\pi\)
0.502317 + 0.864684i \(0.332481\pi\)
\(662\) 0 0
\(663\) 6.83519 0.265457
\(664\) 0 0
\(665\) 26.0254 1.00922
\(666\) 0 0
\(667\) 5.55655 0.215151
\(668\) 0 0
\(669\) −44.3209 −1.71355
\(670\) 0 0
\(671\) 39.7850 1.53588
\(672\) 0 0
\(673\) 34.5375 1.33132 0.665662 0.746254i \(-0.268149\pi\)
0.665662 + 0.746254i \(0.268149\pi\)
\(674\) 0 0
\(675\) −31.6061 −1.21652
\(676\) 0 0
\(677\) 24.4793 0.940817 0.470408 0.882449i \(-0.344107\pi\)
0.470408 + 0.882449i \(0.344107\pi\)
\(678\) 0 0
\(679\) 21.1891 0.813164
\(680\) 0 0
\(681\) −35.4269 −1.35756
\(682\) 0 0
\(683\) −35.2697 −1.34956 −0.674779 0.738020i \(-0.735761\pi\)
−0.674779 + 0.738020i \(0.735761\pi\)
\(684\) 0 0
\(685\) 6.97555 0.266522
\(686\) 0 0
\(687\) 82.3704 3.14263
\(688\) 0 0
\(689\) −2.05695 −0.0783635
\(690\) 0 0
\(691\) −11.3110 −0.430292 −0.215146 0.976582i \(-0.569023\pi\)
−0.215146 + 0.976582i \(0.569023\pi\)
\(692\) 0 0
\(693\) −74.9141 −2.84575
\(694\) 0 0
\(695\) −15.1838 −0.575954
\(696\) 0 0
\(697\) −8.48795 −0.321504
\(698\) 0 0
\(699\) −65.4287 −2.47474
\(700\) 0 0
\(701\) 35.1281 1.32677 0.663385 0.748278i \(-0.269119\pi\)
0.663385 + 0.748278i \(0.269119\pi\)
\(702\) 0 0
\(703\) 5.08797 0.191896
\(704\) 0 0
\(705\) 50.1625 1.88923
\(706\) 0 0
\(707\) 13.4934 0.507472
\(708\) 0 0
\(709\) 31.8815 1.19734 0.598668 0.800998i \(-0.295697\pi\)
0.598668 + 0.800998i \(0.295697\pi\)
\(710\) 0 0
\(711\) −5.97812 −0.224197
\(712\) 0 0
\(713\) −64.1916 −2.40400
\(714\) 0 0
\(715\) 6.75637 0.252674
\(716\) 0 0
\(717\) 14.3509 0.535944
\(718\) 0 0
\(719\) 23.0895 0.861094 0.430547 0.902568i \(-0.358321\pi\)
0.430547 + 0.902568i \(0.358321\pi\)
\(720\) 0 0
\(721\) −19.1811 −0.714343
\(722\) 0 0
\(723\) −7.58707 −0.282166
\(724\) 0 0
\(725\) −1.65222 −0.0613621
\(726\) 0 0
\(727\) −8.94416 −0.331721 −0.165860 0.986149i \(-0.553040\pi\)
−0.165860 + 0.986149i \(0.553040\pi\)
\(728\) 0 0
\(729\) 83.0680 3.07659
\(730\) 0 0
\(731\) −14.1958 −0.525049
\(732\) 0 0
\(733\) 33.0905 1.22223 0.611113 0.791543i \(-0.290722\pi\)
0.611113 + 0.791543i \(0.290722\pi\)
\(734\) 0 0
\(735\) −7.74748 −0.285770
\(736\) 0 0
\(737\) 15.4993 0.570925
\(738\) 0 0
\(739\) −14.9793 −0.551022 −0.275511 0.961298i \(-0.588847\pi\)
−0.275511 + 0.961298i \(0.588847\pi\)
\(740\) 0 0
\(741\) −20.1284 −0.739434
\(742\) 0 0
\(743\) 6.35093 0.232993 0.116497 0.993191i \(-0.462834\pi\)
0.116497 + 0.993191i \(0.462834\pi\)
\(744\) 0 0
\(745\) −8.29100 −0.303759
\(746\) 0 0
\(747\) −8.61179 −0.315089
\(748\) 0 0
\(749\) −20.5898 −0.752336
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) −22.4160 −0.816883
\(754\) 0 0
\(755\) 9.26598 0.337223
\(756\) 0 0
\(757\) 8.17076 0.296971 0.148486 0.988915i \(-0.452560\pi\)
0.148486 + 0.988915i \(0.452560\pi\)
\(758\) 0 0
\(759\) −83.5658 −3.03324
\(760\) 0 0
\(761\) 49.0768 1.77903 0.889516 0.456905i \(-0.151042\pi\)
0.889516 + 0.456905i \(0.151042\pi\)
\(762\) 0 0
\(763\) 19.2067 0.695330
\(764\) 0 0
\(765\) −29.6892 −1.07342
\(766\) 0 0
\(767\) 5.72889 0.206858
\(768\) 0 0
\(769\) 40.4042 1.45701 0.728507 0.685038i \(-0.240215\pi\)
0.728507 + 0.685038i \(0.240215\pi\)
\(770\) 0 0
\(771\) −75.1227 −2.70548
\(772\) 0 0
\(773\) 54.2891 1.95264 0.976322 0.216322i \(-0.0694060\pi\)
0.976322 + 0.216322i \(0.0694060\pi\)
\(774\) 0 0
\(775\) 19.0872 0.685632
\(776\) 0 0
\(777\) 6.46988 0.232106
\(778\) 0 0
\(779\) 24.9954 0.895553
\(780\) 0 0
\(781\) −13.4390 −0.480885
\(782\) 0 0
\(783\) 14.3813 0.513945
\(784\) 0 0
\(785\) 26.7289 0.953994
\(786\) 0 0
\(787\) −25.6894 −0.915727 −0.457863 0.889023i \(-0.651385\pi\)
−0.457863 + 0.889023i \(0.651385\pi\)
\(788\) 0 0
\(789\) 10.3796 0.369524
\(790\) 0 0
\(791\) 23.4713 0.834544
\(792\) 0 0
\(793\) 9.88609 0.351065
\(794\) 0 0
\(795\) 12.2846 0.435691
\(796\) 0 0
\(797\) −27.0237 −0.957229 −0.478615 0.878025i \(-0.658861\pi\)
−0.478615 + 0.878025i \(0.658861\pi\)
\(798\) 0 0
\(799\) −18.1364 −0.641620
\(800\) 0 0
\(801\) 3.44462 0.121710
\(802\) 0 0
\(803\) 27.5230 0.971267
\(804\) 0 0
\(805\) 26.8486 0.946290
\(806\) 0 0
\(807\) −55.3209 −1.94739
\(808\) 0 0
\(809\) 0.659111 0.0231731 0.0115866 0.999933i \(-0.496312\pi\)
0.0115866 + 0.999933i \(0.496312\pi\)
\(810\) 0 0
\(811\) 49.5394 1.73956 0.869781 0.493437i \(-0.164260\pi\)
0.869781 + 0.493437i \(0.164260\pi\)
\(812\) 0 0
\(813\) 47.8526 1.67826
\(814\) 0 0
\(815\) 35.0502 1.22776
\(816\) 0 0
\(817\) 41.8039 1.46253
\(818\) 0 0
\(819\) −18.6153 −0.650470
\(820\) 0 0
\(821\) −25.4018 −0.886528 −0.443264 0.896391i \(-0.646180\pi\)
−0.443264 + 0.896391i \(0.646180\pi\)
\(822\) 0 0
\(823\) −0.895245 −0.0312063 −0.0156031 0.999878i \(-0.504967\pi\)
−0.0156031 + 0.999878i \(0.504967\pi\)
\(824\) 0 0
\(825\) 24.8480 0.865097
\(826\) 0 0
\(827\) −35.9582 −1.25039 −0.625195 0.780468i \(-0.714981\pi\)
−0.625195 + 0.780468i \(0.714981\pi\)
\(828\) 0 0
\(829\) 32.2894 1.12146 0.560728 0.828000i \(-0.310521\pi\)
0.560728 + 0.828000i \(0.310521\pi\)
\(830\) 0 0
\(831\) −34.3459 −1.19145
\(832\) 0 0
\(833\) 2.80113 0.0970532
\(834\) 0 0
\(835\) −31.1428 −1.07774
\(836\) 0 0
\(837\) −166.138 −5.74258
\(838\) 0 0
\(839\) 0.481597 0.0166266 0.00831330 0.999965i \(-0.497354\pi\)
0.00831330 + 0.999965i \(0.497354\pi\)
\(840\) 0 0
\(841\) −28.2482 −0.974076
\(842\) 0 0
\(843\) −78.0208 −2.68718
\(844\) 0 0
\(845\) −21.1895 −0.728940
\(846\) 0 0
\(847\) 10.6142 0.364708
\(848\) 0 0
\(849\) −81.2585 −2.78878
\(850\) 0 0
\(851\) 5.24891 0.179930
\(852\) 0 0
\(853\) −14.2214 −0.486932 −0.243466 0.969909i \(-0.578284\pi\)
−0.243466 + 0.969909i \(0.578284\pi\)
\(854\) 0 0
\(855\) 87.4292 2.99002
\(856\) 0 0
\(857\) 33.1043 1.13082 0.565411 0.824809i \(-0.308718\pi\)
0.565411 + 0.824809i \(0.308718\pi\)
\(858\) 0 0
\(859\) −37.6551 −1.28478 −0.642388 0.766380i \(-0.722056\pi\)
−0.642388 + 0.766380i \(0.722056\pi\)
\(860\) 0 0
\(861\) 31.7843 1.08320
\(862\) 0 0
\(863\) 6.60273 0.224759 0.112380 0.993665i \(-0.464153\pi\)
0.112380 + 0.993665i \(0.464153\pi\)
\(864\) 0 0
\(865\) −11.0132 −0.374461
\(866\) 0 0
\(867\) −41.6254 −1.41367
\(868\) 0 0
\(869\) 2.93759 0.0996508
\(870\) 0 0
\(871\) 3.85140 0.130500
\(872\) 0 0
\(873\) 71.1824 2.40916
\(874\) 0 0
\(875\) −28.9310 −0.978045
\(876\) 0 0
\(877\) −23.7712 −0.802696 −0.401348 0.915926i \(-0.631458\pi\)
−0.401348 + 0.915926i \(0.631458\pi\)
\(878\) 0 0
\(879\) 46.3313 1.56272
\(880\) 0 0
\(881\) −39.0187 −1.31457 −0.657286 0.753641i \(-0.728296\pi\)
−0.657286 + 0.753641i \(0.728296\pi\)
\(882\) 0 0
\(883\) −55.6421 −1.87251 −0.936253 0.351326i \(-0.885731\pi\)
−0.936253 + 0.351326i \(0.885731\pi\)
\(884\) 0 0
\(885\) −34.2145 −1.15011
\(886\) 0 0
\(887\) −24.0861 −0.808731 −0.404366 0.914597i \(-0.632508\pi\)
−0.404366 + 0.914597i \(0.632508\pi\)
\(888\) 0 0
\(889\) 6.55597 0.219880
\(890\) 0 0
\(891\) −121.917 −4.08436
\(892\) 0 0
\(893\) 53.4083 1.78724
\(894\) 0 0
\(895\) −44.2711 −1.47982
\(896\) 0 0
\(897\) −20.7651 −0.693326
\(898\) 0 0
\(899\) −8.68496 −0.289660
\(900\) 0 0
\(901\) −4.44155 −0.147970
\(902\) 0 0
\(903\) 53.1580 1.76899
\(904\) 0 0
\(905\) 1.72874 0.0574653
\(906\) 0 0
\(907\) 2.35558 0.0782157 0.0391079 0.999235i \(-0.487548\pi\)
0.0391079 + 0.999235i \(0.487548\pi\)
\(908\) 0 0
\(909\) 45.3295 1.50348
\(910\) 0 0
\(911\) 45.9853 1.52356 0.761781 0.647835i \(-0.224325\pi\)
0.761781 + 0.647835i \(0.224325\pi\)
\(912\) 0 0
\(913\) 4.23175 0.140050
\(914\) 0 0
\(915\) −59.0424 −1.95188
\(916\) 0 0
\(917\) 7.05748 0.233059
\(918\) 0 0
\(919\) 8.45619 0.278944 0.139472 0.990226i \(-0.455459\pi\)
0.139472 + 0.990226i \(0.455459\pi\)
\(920\) 0 0
\(921\) −36.7067 −1.20953
\(922\) 0 0
\(923\) −3.33942 −0.109919
\(924\) 0 0
\(925\) −1.56075 −0.0513171
\(926\) 0 0
\(927\) −64.4368 −2.11638
\(928\) 0 0
\(929\) −6.89207 −0.226122 −0.113061 0.993588i \(-0.536065\pi\)
−0.113061 + 0.993588i \(0.536065\pi\)
\(930\) 0 0
\(931\) −8.24879 −0.270343
\(932\) 0 0
\(933\) 35.5682 1.16445
\(934\) 0 0
\(935\) 14.5890 0.477111
\(936\) 0 0
\(937\) 7.87803 0.257364 0.128682 0.991686i \(-0.458925\pi\)
0.128682 + 0.991686i \(0.458925\pi\)
\(938\) 0 0
\(939\) 98.8742 3.22664
\(940\) 0 0
\(941\) 23.9771 0.781633 0.390816 0.920469i \(-0.372193\pi\)
0.390816 + 0.920469i \(0.372193\pi\)
\(942\) 0 0
\(943\) 25.7861 0.839711
\(944\) 0 0
\(945\) 69.4887 2.26047
\(946\) 0 0
\(947\) 24.7491 0.804239 0.402119 0.915587i \(-0.368274\pi\)
0.402119 + 0.915587i \(0.368274\pi\)
\(948\) 0 0
\(949\) 6.83914 0.222008
\(950\) 0 0
\(951\) −0.292093 −0.00947178
\(952\) 0 0
\(953\) 21.4022 0.693285 0.346643 0.937997i \(-0.387322\pi\)
0.346643 + 0.937997i \(0.387322\pi\)
\(954\) 0 0
\(955\) 28.6940 0.928517
\(956\) 0 0
\(957\) −11.3062 −0.365479
\(958\) 0 0
\(959\) 9.44408 0.304965
\(960\) 0 0
\(961\) 69.3323 2.23653
\(962\) 0 0
\(963\) −69.1692 −2.22895
\(964\) 0 0
\(965\) −21.4939 −0.691913
\(966\) 0 0
\(967\) −25.4482 −0.818359 −0.409179 0.912454i \(-0.634185\pi\)
−0.409179 + 0.912454i \(0.634185\pi\)
\(968\) 0 0
\(969\) −43.4630 −1.39623
\(970\) 0 0
\(971\) 43.8012 1.40565 0.702823 0.711365i \(-0.251923\pi\)
0.702823 + 0.711365i \(0.251923\pi\)
\(972\) 0 0
\(973\) −20.5571 −0.659030
\(974\) 0 0
\(975\) 6.17443 0.197740
\(976\) 0 0
\(977\) −4.93318 −0.157826 −0.0789132 0.996881i \(-0.525145\pi\)
−0.0789132 + 0.996881i \(0.525145\pi\)
\(978\) 0 0
\(979\) −1.69265 −0.0540973
\(980\) 0 0
\(981\) 64.5228 2.06005
\(982\) 0 0
\(983\) 56.0776 1.78860 0.894299 0.447469i \(-0.147675\pi\)
0.894299 + 0.447469i \(0.147675\pi\)
\(984\) 0 0
\(985\) −37.1785 −1.18461
\(986\) 0 0
\(987\) 67.9142 2.16173
\(988\) 0 0
\(989\) 43.1263 1.37133
\(990\) 0 0
\(991\) 31.5887 1.00345 0.501725 0.865027i \(-0.332699\pi\)
0.501725 + 0.865027i \(0.332699\pi\)
\(992\) 0 0
\(993\) −91.5178 −2.90423
\(994\) 0 0
\(995\) 0.225737 0.00715634
\(996\) 0 0
\(997\) 57.7241 1.82814 0.914070 0.405557i \(-0.132922\pi\)
0.914070 + 0.405557i \(0.132922\pi\)
\(998\) 0 0
\(999\) 13.5850 0.429812
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 \(a_p\))