Properties

Label 6008.2.a.e.1.16
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 1.16
Character \(\chi\) = 6008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.33859 q^{3}\) \(+3.94917 q^{5}\) \(+0.220759 q^{7}\) \(-1.20816 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.33859 q^{3}\) \(+3.94917 q^{5}\) \(+0.220759 q^{7}\) \(-1.20816 q^{9}\) \(+1.87126 q^{11}\) \(+3.17517 q^{13}\) \(-5.28634 q^{15}\) \(+7.01370 q^{17}\) \(+5.00513 q^{19}\) \(-0.295507 q^{21}\) \(+1.70287 q^{23}\) \(+10.5960 q^{25}\) \(+5.63303 q^{27}\) \(+1.30440 q^{29}\) \(-4.27484 q^{31}\) \(-2.50486 q^{33}\) \(+0.871815 q^{35}\) \(+3.57462 q^{37}\) \(-4.25027 q^{39}\) \(+4.53410 q^{41}\) \(-3.45578 q^{43}\) \(-4.77125 q^{45}\) \(+1.75027 q^{47}\) \(-6.95127 q^{49}\) \(-9.38851 q^{51}\) \(-6.18967 q^{53}\) \(+7.38994 q^{55}\) \(-6.69984 q^{57}\) \(-10.8041 q^{59}\) \(+8.37748 q^{61}\) \(-0.266713 q^{63}\) \(+12.5393 q^{65}\) \(-3.87632 q^{67}\) \(-2.27945 q^{69}\) \(+3.47020 q^{71}\) \(-6.72897 q^{73}\) \(-14.1837 q^{75}\) \(+0.413098 q^{77}\) \(-6.08611 q^{79}\) \(-3.91584 q^{81}\) \(-6.03473 q^{83}\) \(+27.6983 q^{85}\) \(-1.74607 q^{87}\) \(+17.0339 q^{89}\) \(+0.700948 q^{91}\) \(+5.72227 q^{93}\) \(+19.7661 q^{95}\) \(+0.167792 q^{97}\) \(-2.26079 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(50q \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 23q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 56q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 5q^{15} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 9q^{19} \) \(\mathstrut +\mathstrut 30q^{21} \) \(\mathstrut +\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 24q^{27} \) \(\mathstrut +\mathstrut 61q^{29} \) \(\mathstrut +\mathstrut 27q^{31} \) \(\mathstrut +\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 7q^{35} \) \(\mathstrut +\mathstrut 56q^{37} \) \(\mathstrut -\mathstrut 2q^{39} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut +\mathstrut 19q^{43} \) \(\mathstrut +\mathstrut 76q^{45} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 82q^{49} \) \(\mathstrut -\mathstrut q^{51} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut +\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 35q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut +\mathstrut 67q^{61} \) \(\mathstrut +\mathstrut 25q^{63} \) \(\mathstrut +\mathstrut 27q^{65} \) \(\mathstrut +\mathstrut 46q^{67} \) \(\mathstrut +\mathstrut 68q^{69} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 62q^{73} \) \(\mathstrut +\mathstrut 27q^{75} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut +\mathstrut 7q^{79} \) \(\mathstrut +\mathstrut 74q^{81} \) \(\mathstrut -\mathstrut q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 45q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 24q^{95} \) \(\mathstrut +\mathstrut 81q^{97} \) \(\mathstrut +\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.33859 −0.772838 −0.386419 0.922323i \(-0.626288\pi\)
−0.386419 + 0.922323i \(0.626288\pi\)
\(4\) 0 0
\(5\) 3.94917 1.76612 0.883062 0.469257i \(-0.155478\pi\)
0.883062 + 0.469257i \(0.155478\pi\)
\(6\) 0 0
\(7\) 0.220759 0.0834391 0.0417195 0.999129i \(-0.486716\pi\)
0.0417195 + 0.999129i \(0.486716\pi\)
\(8\) 0 0
\(9\) −1.20816 −0.402722
\(10\) 0 0
\(11\) 1.87126 0.564207 0.282104 0.959384i \(-0.408968\pi\)
0.282104 + 0.959384i \(0.408968\pi\)
\(12\) 0 0
\(13\) 3.17517 0.880635 0.440317 0.897842i \(-0.354866\pi\)
0.440317 + 0.897842i \(0.354866\pi\)
\(14\) 0 0
\(15\) −5.28634 −1.36493
\(16\) 0 0
\(17\) 7.01370 1.70107 0.850537 0.525916i \(-0.176277\pi\)
0.850537 + 0.525916i \(0.176277\pi\)
\(18\) 0 0
\(19\) 5.00513 1.14826 0.574128 0.818766i \(-0.305341\pi\)
0.574128 + 0.818766i \(0.305341\pi\)
\(20\) 0 0
\(21\) −0.295507 −0.0644849
\(22\) 0 0
\(23\) 1.70287 0.355073 0.177536 0.984114i \(-0.443187\pi\)
0.177536 + 0.984114i \(0.443187\pi\)
\(24\) 0 0
\(25\) 10.5960 2.11919
\(26\) 0 0
\(27\) 5.63303 1.08408
\(28\) 0 0
\(29\) 1.30440 0.242222 0.121111 0.992639i \(-0.461354\pi\)
0.121111 + 0.992639i \(0.461354\pi\)
\(30\) 0 0
\(31\) −4.27484 −0.767783 −0.383892 0.923378i \(-0.625416\pi\)
−0.383892 + 0.923378i \(0.625416\pi\)
\(32\) 0 0
\(33\) −2.50486 −0.436041
\(34\) 0 0
\(35\) 0.871815 0.147364
\(36\) 0 0
\(37\) 3.57462 0.587664 0.293832 0.955857i \(-0.405069\pi\)
0.293832 + 0.955857i \(0.405069\pi\)
\(38\) 0 0
\(39\) −4.25027 −0.680588
\(40\) 0 0
\(41\) 4.53410 0.708107 0.354054 0.935225i \(-0.384803\pi\)
0.354054 + 0.935225i \(0.384803\pi\)
\(42\) 0 0
\(43\) −3.45578 −0.527002 −0.263501 0.964659i \(-0.584877\pi\)
−0.263501 + 0.964659i \(0.584877\pi\)
\(44\) 0 0
\(45\) −4.77125 −0.711256
\(46\) 0 0
\(47\) 1.75027 0.255302 0.127651 0.991819i \(-0.459256\pi\)
0.127651 + 0.991819i \(0.459256\pi\)
\(48\) 0 0
\(49\) −6.95127 −0.993038
\(50\) 0 0
\(51\) −9.38851 −1.31465
\(52\) 0 0
\(53\) −6.18967 −0.850216 −0.425108 0.905143i \(-0.639764\pi\)
−0.425108 + 0.905143i \(0.639764\pi\)
\(54\) 0 0
\(55\) 7.38994 0.996460
\(56\) 0 0
\(57\) −6.69984 −0.887416
\(58\) 0 0
\(59\) −10.8041 −1.40658 −0.703290 0.710903i \(-0.748287\pi\)
−0.703290 + 0.710903i \(0.748287\pi\)
\(60\) 0 0
\(61\) 8.37748 1.07263 0.536313 0.844019i \(-0.319817\pi\)
0.536313 + 0.844019i \(0.319817\pi\)
\(62\) 0 0
\(63\) −0.266713 −0.0336027
\(64\) 0 0
\(65\) 12.5393 1.55531
\(66\) 0 0
\(67\) −3.87632 −0.473567 −0.236784 0.971562i \(-0.576093\pi\)
−0.236784 + 0.971562i \(0.576093\pi\)
\(68\) 0 0
\(69\) −2.27945 −0.274414
\(70\) 0 0
\(71\) 3.47020 0.411837 0.205918 0.978569i \(-0.433982\pi\)
0.205918 + 0.978569i \(0.433982\pi\)
\(72\) 0 0
\(73\) −6.72897 −0.787566 −0.393783 0.919203i \(-0.628834\pi\)
−0.393783 + 0.919203i \(0.628834\pi\)
\(74\) 0 0
\(75\) −14.1837 −1.63779
\(76\) 0 0
\(77\) 0.413098 0.0470769
\(78\) 0 0
\(79\) −6.08611 −0.684741 −0.342371 0.939565i \(-0.611230\pi\)
−0.342371 + 0.939565i \(0.611230\pi\)
\(80\) 0 0
\(81\) −3.91584 −0.435094
\(82\) 0 0
\(83\) −6.03473 −0.662398 −0.331199 0.943561i \(-0.607453\pi\)
−0.331199 + 0.943561i \(0.607453\pi\)
\(84\) 0 0
\(85\) 27.6983 3.00431
\(86\) 0 0
\(87\) −1.74607 −0.187198
\(88\) 0 0
\(89\) 17.0339 1.80559 0.902794 0.430073i \(-0.141512\pi\)
0.902794 + 0.430073i \(0.141512\pi\)
\(90\) 0 0
\(91\) 0.700948 0.0734793
\(92\) 0 0
\(93\) 5.72227 0.593372
\(94\) 0 0
\(95\) 19.7661 2.02796
\(96\) 0 0
\(97\) 0.167792 0.0170367 0.00851834 0.999964i \(-0.497288\pi\)
0.00851834 + 0.999964i \(0.497288\pi\)
\(98\) 0 0
\(99\) −2.26079 −0.227218
\(100\) 0 0
\(101\) −3.99967 −0.397982 −0.198991 0.980001i \(-0.563766\pi\)
−0.198991 + 0.980001i \(0.563766\pi\)
\(102\) 0 0
\(103\) −3.38265 −0.333303 −0.166651 0.986016i \(-0.553295\pi\)
−0.166651 + 0.986016i \(0.553295\pi\)
\(104\) 0 0
\(105\) −1.16701 −0.113888
\(106\) 0 0
\(107\) −5.71506 −0.552496 −0.276248 0.961086i \(-0.589091\pi\)
−0.276248 + 0.961086i \(0.589091\pi\)
\(108\) 0 0
\(109\) 4.68816 0.449045 0.224522 0.974469i \(-0.427918\pi\)
0.224522 + 0.974469i \(0.427918\pi\)
\(110\) 0 0
\(111\) −4.78497 −0.454169
\(112\) 0 0
\(113\) −9.49848 −0.893542 −0.446771 0.894648i \(-0.647426\pi\)
−0.446771 + 0.894648i \(0.647426\pi\)
\(114\) 0 0
\(115\) 6.72492 0.627102
\(116\) 0 0
\(117\) −3.83613 −0.354651
\(118\) 0 0
\(119\) 1.54834 0.141936
\(120\) 0 0
\(121\) −7.49837 −0.681670
\(122\) 0 0
\(123\) −6.06932 −0.547252
\(124\) 0 0
\(125\) 22.0994 1.97663
\(126\) 0 0
\(127\) 11.2302 0.996522 0.498261 0.867027i \(-0.333972\pi\)
0.498261 + 0.867027i \(0.333972\pi\)
\(128\) 0 0
\(129\) 4.62589 0.407287
\(130\) 0 0
\(131\) 14.3712 1.25562 0.627810 0.778367i \(-0.283952\pi\)
0.627810 + 0.778367i \(0.283952\pi\)
\(132\) 0 0
\(133\) 1.10493 0.0958094
\(134\) 0 0
\(135\) 22.2458 1.91461
\(136\) 0 0
\(137\) 9.33336 0.797403 0.398701 0.917081i \(-0.369461\pi\)
0.398701 + 0.917081i \(0.369461\pi\)
\(138\) 0 0
\(139\) 7.70690 0.653690 0.326845 0.945078i \(-0.394014\pi\)
0.326845 + 0.945078i \(0.394014\pi\)
\(140\) 0 0
\(141\) −2.34290 −0.197307
\(142\) 0 0
\(143\) 5.94159 0.496860
\(144\) 0 0
\(145\) 5.15131 0.427793
\(146\) 0 0
\(147\) 9.30493 0.767457
\(148\) 0 0
\(149\) −3.02064 −0.247460 −0.123730 0.992316i \(-0.539486\pi\)
−0.123730 + 0.992316i \(0.539486\pi\)
\(150\) 0 0
\(151\) −2.76483 −0.224999 −0.112499 0.993652i \(-0.535886\pi\)
−0.112499 + 0.993652i \(0.535886\pi\)
\(152\) 0 0
\(153\) −8.47371 −0.685059
\(154\) 0 0
\(155\) −16.8821 −1.35600
\(156\) 0 0
\(157\) −13.8352 −1.10417 −0.552083 0.833789i \(-0.686167\pi\)
−0.552083 + 0.833789i \(0.686167\pi\)
\(158\) 0 0
\(159\) 8.28545 0.657079
\(160\) 0 0
\(161\) 0.375923 0.0296269
\(162\) 0 0
\(163\) −16.7370 −1.31094 −0.655472 0.755220i \(-0.727530\pi\)
−0.655472 + 0.755220i \(0.727530\pi\)
\(164\) 0 0
\(165\) −9.89214 −0.770102
\(166\) 0 0
\(167\) −10.6390 −0.823269 −0.411635 0.911349i \(-0.635042\pi\)
−0.411635 + 0.911349i \(0.635042\pi\)
\(168\) 0 0
\(169\) −2.91827 −0.224482
\(170\) 0 0
\(171\) −6.04702 −0.462427
\(172\) 0 0
\(173\) −2.15546 −0.163877 −0.0819385 0.996637i \(-0.526111\pi\)
−0.0819385 + 0.996637i \(0.526111\pi\)
\(174\) 0 0
\(175\) 2.33915 0.176823
\(176\) 0 0
\(177\) 14.4624 1.08706
\(178\) 0 0
\(179\) −19.6925 −1.47189 −0.735945 0.677041i \(-0.763262\pi\)
−0.735945 + 0.677041i \(0.763262\pi\)
\(180\) 0 0
\(181\) 17.5173 1.30205 0.651027 0.759054i \(-0.274338\pi\)
0.651027 + 0.759054i \(0.274338\pi\)
\(182\) 0 0
\(183\) −11.2140 −0.828966
\(184\) 0 0
\(185\) 14.1168 1.03789
\(186\) 0 0
\(187\) 13.1245 0.959758
\(188\) 0 0
\(189\) 1.24354 0.0904543
\(190\) 0 0
\(191\) 10.5635 0.764345 0.382173 0.924091i \(-0.375176\pi\)
0.382173 + 0.924091i \(0.375176\pi\)
\(192\) 0 0
\(193\) 11.9677 0.861454 0.430727 0.902482i \(-0.358257\pi\)
0.430727 + 0.902482i \(0.358257\pi\)
\(194\) 0 0
\(195\) −16.7850 −1.20200
\(196\) 0 0
\(197\) −5.88879 −0.419559 −0.209779 0.977749i \(-0.567275\pi\)
−0.209779 + 0.977749i \(0.567275\pi\)
\(198\) 0 0
\(199\) −13.9917 −0.991847 −0.495924 0.868366i \(-0.665170\pi\)
−0.495924 + 0.868366i \(0.665170\pi\)
\(200\) 0 0
\(201\) 5.18882 0.365991
\(202\) 0 0
\(203\) 0.287959 0.0202107
\(204\) 0 0
\(205\) 17.9059 1.25060
\(206\) 0 0
\(207\) −2.05734 −0.142995
\(208\) 0 0
\(209\) 9.36592 0.647854
\(210\) 0 0
\(211\) −9.47202 −0.652081 −0.326040 0.945356i \(-0.605715\pi\)
−0.326040 + 0.945356i \(0.605715\pi\)
\(212\) 0 0
\(213\) −4.64519 −0.318283
\(214\) 0 0
\(215\) −13.6475 −0.930750
\(216\) 0 0
\(217\) −0.943709 −0.0640631
\(218\) 0 0
\(219\) 9.00736 0.608661
\(220\) 0 0
\(221\) 22.2697 1.49802
\(222\) 0 0
\(223\) 2.02819 0.135817 0.0679087 0.997692i \(-0.478367\pi\)
0.0679087 + 0.997692i \(0.478367\pi\)
\(224\) 0 0
\(225\) −12.8017 −0.853444
\(226\) 0 0
\(227\) −9.68842 −0.643043 −0.321522 0.946902i \(-0.604194\pi\)
−0.321522 + 0.946902i \(0.604194\pi\)
\(228\) 0 0
\(229\) −16.4929 −1.08988 −0.544940 0.838475i \(-0.683448\pi\)
−0.544940 + 0.838475i \(0.683448\pi\)
\(230\) 0 0
\(231\) −0.552971 −0.0363828
\(232\) 0 0
\(233\) 4.43586 0.290603 0.145301 0.989387i \(-0.453585\pi\)
0.145301 + 0.989387i \(0.453585\pi\)
\(234\) 0 0
\(235\) 6.91210 0.450896
\(236\) 0 0
\(237\) 8.14684 0.529194
\(238\) 0 0
\(239\) 19.0023 1.22915 0.614577 0.788857i \(-0.289327\pi\)
0.614577 + 0.788857i \(0.289327\pi\)
\(240\) 0 0
\(241\) 9.84615 0.634246 0.317123 0.948384i \(-0.397283\pi\)
0.317123 + 0.948384i \(0.397283\pi\)
\(242\) 0 0
\(243\) −11.6574 −0.747819
\(244\) 0 0
\(245\) −27.4517 −1.75383
\(246\) 0 0
\(247\) 15.8922 1.01119
\(248\) 0 0
\(249\) 8.07806 0.511926
\(250\) 0 0
\(251\) −0.204291 −0.0128948 −0.00644738 0.999979i \(-0.502052\pi\)
−0.00644738 + 0.999979i \(0.502052\pi\)
\(252\) 0 0
\(253\) 3.18652 0.200334
\(254\) 0 0
\(255\) −37.0768 −2.32184
\(256\) 0 0
\(257\) 11.3238 0.706359 0.353180 0.935556i \(-0.385100\pi\)
0.353180 + 0.935556i \(0.385100\pi\)
\(258\) 0 0
\(259\) 0.789130 0.0490341
\(260\) 0 0
\(261\) −1.57593 −0.0975479
\(262\) 0 0
\(263\) 11.8634 0.731530 0.365765 0.930707i \(-0.380807\pi\)
0.365765 + 0.930707i \(0.380807\pi\)
\(264\) 0 0
\(265\) −24.4441 −1.50159
\(266\) 0 0
\(267\) −22.8015 −1.39543
\(268\) 0 0
\(269\) −6.98712 −0.426012 −0.213006 0.977051i \(-0.568325\pi\)
−0.213006 + 0.977051i \(0.568325\pi\)
\(270\) 0 0
\(271\) −18.9261 −1.14968 −0.574840 0.818266i \(-0.694936\pi\)
−0.574840 + 0.818266i \(0.694936\pi\)
\(272\) 0 0
\(273\) −0.938285 −0.0567876
\(274\) 0 0
\(275\) 19.8278 1.19566
\(276\) 0 0
\(277\) −25.8130 −1.55095 −0.775476 0.631377i \(-0.782490\pi\)
−0.775476 + 0.631377i \(0.782490\pi\)
\(278\) 0 0
\(279\) 5.16471 0.309203
\(280\) 0 0
\(281\) 1.42272 0.0848723 0.0424362 0.999099i \(-0.486488\pi\)
0.0424362 + 0.999099i \(0.486488\pi\)
\(282\) 0 0
\(283\) −2.61426 −0.155402 −0.0777009 0.996977i \(-0.524758\pi\)
−0.0777009 + 0.996977i \(0.524758\pi\)
\(284\) 0 0
\(285\) −26.4588 −1.56729
\(286\) 0 0
\(287\) 1.00094 0.0590838
\(288\) 0 0
\(289\) 32.1921 1.89365
\(290\) 0 0
\(291\) −0.224605 −0.0131666
\(292\) 0 0
\(293\) 11.9357 0.697293 0.348646 0.937254i \(-0.386641\pi\)
0.348646 + 0.937254i \(0.386641\pi\)
\(294\) 0 0
\(295\) −42.6674 −2.48419
\(296\) 0 0
\(297\) 10.5409 0.611644
\(298\) 0 0
\(299\) 5.40690 0.312689
\(300\) 0 0
\(301\) −0.762895 −0.0439725
\(302\) 0 0
\(303\) 5.35393 0.307575
\(304\) 0 0
\(305\) 33.0841 1.89439
\(306\) 0 0
\(307\) −3.80063 −0.216914 −0.108457 0.994101i \(-0.534591\pi\)
−0.108457 + 0.994101i \(0.534591\pi\)
\(308\) 0 0
\(309\) 4.52800 0.257589
\(310\) 0 0
\(311\) 15.7353 0.892266 0.446133 0.894967i \(-0.352801\pi\)
0.446133 + 0.894967i \(0.352801\pi\)
\(312\) 0 0
\(313\) −9.56109 −0.540425 −0.270212 0.962801i \(-0.587094\pi\)
−0.270212 + 0.962801i \(0.587094\pi\)
\(314\) 0 0
\(315\) −1.05330 −0.0593465
\(316\) 0 0
\(317\) 14.6210 0.821198 0.410599 0.911816i \(-0.365320\pi\)
0.410599 + 0.911816i \(0.365320\pi\)
\(318\) 0 0
\(319\) 2.44088 0.136663
\(320\) 0 0
\(321\) 7.65015 0.426990
\(322\) 0 0
\(323\) 35.1045 1.95327
\(324\) 0 0
\(325\) 33.6440 1.86623
\(326\) 0 0
\(327\) −6.27555 −0.347039
\(328\) 0 0
\(329\) 0.386387 0.0213022
\(330\) 0 0
\(331\) 11.0239 0.605927 0.302964 0.953002i \(-0.402024\pi\)
0.302964 + 0.953002i \(0.402024\pi\)
\(332\) 0 0
\(333\) −4.31873 −0.236665
\(334\) 0 0
\(335\) −15.3082 −0.836378
\(336\) 0 0
\(337\) 28.8377 1.57089 0.785444 0.618933i \(-0.212435\pi\)
0.785444 + 0.618933i \(0.212435\pi\)
\(338\) 0 0
\(339\) 12.7146 0.690563
\(340\) 0 0
\(341\) −7.99935 −0.433189
\(342\) 0 0
\(343\) −3.07987 −0.166297
\(344\) 0 0
\(345\) −9.00194 −0.484648
\(346\) 0 0
\(347\) 32.9419 1.76842 0.884208 0.467093i \(-0.154699\pi\)
0.884208 + 0.467093i \(0.154699\pi\)
\(348\) 0 0
\(349\) 9.05627 0.484771 0.242385 0.970180i \(-0.422070\pi\)
0.242385 + 0.970180i \(0.422070\pi\)
\(350\) 0 0
\(351\) 17.8858 0.954675
\(352\) 0 0
\(353\) −8.15793 −0.434203 −0.217101 0.976149i \(-0.569660\pi\)
−0.217101 + 0.976149i \(0.569660\pi\)
\(354\) 0 0
\(355\) 13.7044 0.727355
\(356\) 0 0
\(357\) −2.07260 −0.109693
\(358\) 0 0
\(359\) −19.1463 −1.01050 −0.505250 0.862973i \(-0.668600\pi\)
−0.505250 + 0.862973i \(0.668600\pi\)
\(360\) 0 0
\(361\) 6.05135 0.318492
\(362\) 0 0
\(363\) 10.0373 0.526821
\(364\) 0 0
\(365\) −26.5739 −1.39094
\(366\) 0 0
\(367\) −1.10651 −0.0577592 −0.0288796 0.999583i \(-0.509194\pi\)
−0.0288796 + 0.999583i \(0.509194\pi\)
\(368\) 0 0
\(369\) −5.47794 −0.285170
\(370\) 0 0
\(371\) −1.36642 −0.0709412
\(372\) 0 0
\(373\) 5.10511 0.264333 0.132166 0.991228i \(-0.457807\pi\)
0.132166 + 0.991228i \(0.457807\pi\)
\(374\) 0 0
\(375\) −29.5821 −1.52762
\(376\) 0 0
\(377\) 4.14171 0.213309
\(378\) 0 0
\(379\) 17.7155 0.909986 0.454993 0.890495i \(-0.349642\pi\)
0.454993 + 0.890495i \(0.349642\pi\)
\(380\) 0 0
\(381\) −15.0327 −0.770150
\(382\) 0 0
\(383\) −36.3290 −1.85632 −0.928161 0.372178i \(-0.878611\pi\)
−0.928161 + 0.372178i \(0.878611\pi\)
\(384\) 0 0
\(385\) 1.63140 0.0831436
\(386\) 0 0
\(387\) 4.17515 0.212235
\(388\) 0 0
\(389\) 12.3601 0.626684 0.313342 0.949640i \(-0.398551\pi\)
0.313342 + 0.949640i \(0.398551\pi\)
\(390\) 0 0
\(391\) 11.9434 0.604004
\(392\) 0 0
\(393\) −19.2372 −0.970390
\(394\) 0 0
\(395\) −24.0351 −1.20934
\(396\) 0 0
\(397\) −11.4293 −0.573623 −0.286811 0.957987i \(-0.592595\pi\)
−0.286811 + 0.957987i \(0.592595\pi\)
\(398\) 0 0
\(399\) −1.47905 −0.0740451
\(400\) 0 0
\(401\) 0.0721583 0.00360342 0.00180171 0.999998i \(-0.499426\pi\)
0.00180171 + 0.999998i \(0.499426\pi\)
\(402\) 0 0
\(403\) −13.5733 −0.676137
\(404\) 0 0
\(405\) −15.4643 −0.768429
\(406\) 0 0
\(407\) 6.68906 0.331564
\(408\) 0 0
\(409\) 11.1992 0.553766 0.276883 0.960904i \(-0.410699\pi\)
0.276883 + 0.960904i \(0.410699\pi\)
\(410\) 0 0
\(411\) −12.4936 −0.616263
\(412\) 0 0
\(413\) −2.38511 −0.117364
\(414\) 0 0
\(415\) −23.8322 −1.16988
\(416\) 0 0
\(417\) −10.3164 −0.505197
\(418\) 0 0
\(419\) −9.70567 −0.474153 −0.237076 0.971491i \(-0.576189\pi\)
−0.237076 + 0.971491i \(0.576189\pi\)
\(420\) 0 0
\(421\) 7.09943 0.346005 0.173002 0.984921i \(-0.444653\pi\)
0.173002 + 0.984921i \(0.444653\pi\)
\(422\) 0 0
\(423\) −2.11461 −0.102816
\(424\) 0 0
\(425\) 74.3169 3.60490
\(426\) 0 0
\(427\) 1.84940 0.0894989
\(428\) 0 0
\(429\) −7.95338 −0.383993
\(430\) 0 0
\(431\) 23.0353 1.10957 0.554787 0.831993i \(-0.312800\pi\)
0.554787 + 0.831993i \(0.312800\pi\)
\(432\) 0 0
\(433\) 9.68490 0.465427 0.232713 0.972545i \(-0.425240\pi\)
0.232713 + 0.972545i \(0.425240\pi\)
\(434\) 0 0
\(435\) −6.89552 −0.330615
\(436\) 0 0
\(437\) 8.52308 0.407714
\(438\) 0 0
\(439\) 19.4680 0.929156 0.464578 0.885532i \(-0.346206\pi\)
0.464578 + 0.885532i \(0.346206\pi\)
\(440\) 0 0
\(441\) 8.39827 0.399918
\(442\) 0 0
\(443\) 12.5356 0.595583 0.297791 0.954631i \(-0.403750\pi\)
0.297791 + 0.954631i \(0.403750\pi\)
\(444\) 0 0
\(445\) 67.2698 3.18889
\(446\) 0 0
\(447\) 4.04341 0.191247
\(448\) 0 0
\(449\) 8.76851 0.413812 0.206906 0.978361i \(-0.433661\pi\)
0.206906 + 0.978361i \(0.433661\pi\)
\(450\) 0 0
\(451\) 8.48450 0.399519
\(452\) 0 0
\(453\) 3.70099 0.173888
\(454\) 0 0
\(455\) 2.76816 0.129774
\(456\) 0 0
\(457\) −23.9543 −1.12053 −0.560267 0.828312i \(-0.689301\pi\)
−0.560267 + 0.828312i \(0.689301\pi\)
\(458\) 0 0
\(459\) 39.5084 1.84409
\(460\) 0 0
\(461\) −15.5606 −0.724731 −0.362366 0.932036i \(-0.618031\pi\)
−0.362366 + 0.932036i \(0.618031\pi\)
\(462\) 0 0
\(463\) −22.4131 −1.04162 −0.520812 0.853671i \(-0.674371\pi\)
−0.520812 + 0.853671i \(0.674371\pi\)
\(464\) 0 0
\(465\) 22.5982 1.04797
\(466\) 0 0
\(467\) 36.1132 1.67112 0.835559 0.549401i \(-0.185144\pi\)
0.835559 + 0.549401i \(0.185144\pi\)
\(468\) 0 0
\(469\) −0.855732 −0.0395140
\(470\) 0 0
\(471\) 18.5197 0.853341
\(472\) 0 0
\(473\) −6.46668 −0.297338
\(474\) 0 0
\(475\) 53.0342 2.43337
\(476\) 0 0
\(477\) 7.47813 0.342400
\(478\) 0 0
\(479\) −14.6880 −0.671114 −0.335557 0.942020i \(-0.608924\pi\)
−0.335557 + 0.942020i \(0.608924\pi\)
\(480\) 0 0
\(481\) 11.3500 0.517517
\(482\) 0 0
\(483\) −0.503209 −0.0228968
\(484\) 0 0
\(485\) 0.662639 0.0300889
\(486\) 0 0
\(487\) −5.44267 −0.246631 −0.123315 0.992368i \(-0.539353\pi\)
−0.123315 + 0.992368i \(0.539353\pi\)
\(488\) 0 0
\(489\) 22.4041 1.01315
\(490\) 0 0
\(491\) 0.113956 0.00514276 0.00257138 0.999997i \(-0.499182\pi\)
0.00257138 + 0.999997i \(0.499182\pi\)
\(492\) 0 0
\(493\) 9.14870 0.412037
\(494\) 0 0
\(495\) −8.92827 −0.401296
\(496\) 0 0
\(497\) 0.766078 0.0343633
\(498\) 0 0
\(499\) −34.9379 −1.56404 −0.782018 0.623256i \(-0.785809\pi\)
−0.782018 + 0.623256i \(0.785809\pi\)
\(500\) 0 0
\(501\) 14.2413 0.636254
\(502\) 0 0
\(503\) 8.40784 0.374887 0.187444 0.982275i \(-0.439980\pi\)
0.187444 + 0.982275i \(0.439980\pi\)
\(504\) 0 0
\(505\) −15.7954 −0.702885
\(506\) 0 0
\(507\) 3.90638 0.173489
\(508\) 0 0
\(509\) 15.2112 0.674225 0.337113 0.941464i \(-0.390550\pi\)
0.337113 + 0.941464i \(0.390550\pi\)
\(510\) 0 0
\(511\) −1.48548 −0.0657138
\(512\) 0 0
\(513\) 28.1940 1.24480
\(514\) 0 0
\(515\) −13.3587 −0.588654
\(516\) 0 0
\(517\) 3.27521 0.144044
\(518\) 0 0
\(519\) 2.88529 0.126650
\(520\) 0 0
\(521\) −32.1593 −1.40893 −0.704463 0.709740i \(-0.748812\pi\)
−0.704463 + 0.709740i \(0.748812\pi\)
\(522\) 0 0
\(523\) −3.96769 −0.173495 −0.0867476 0.996230i \(-0.527647\pi\)
−0.0867476 + 0.996230i \(0.527647\pi\)
\(524\) 0 0
\(525\) −3.13118 −0.136656
\(526\) 0 0
\(527\) −29.9824 −1.30606
\(528\) 0 0
\(529\) −20.1002 −0.873923
\(530\) 0 0
\(531\) 13.0532 0.566460
\(532\) 0 0
\(533\) 14.3966 0.623584
\(534\) 0 0
\(535\) −22.5698 −0.975776
\(536\) 0 0
\(537\) 26.3603 1.13753
\(538\) 0 0
\(539\) −13.0077 −0.560279
\(540\) 0 0
\(541\) −15.5362 −0.667955 −0.333978 0.942581i \(-0.608391\pi\)
−0.333978 + 0.942581i \(0.608391\pi\)
\(542\) 0 0
\(543\) −23.4486 −1.00628
\(544\) 0 0
\(545\) 18.5144 0.793068
\(546\) 0 0
\(547\) 38.4936 1.64587 0.822934 0.568137i \(-0.192336\pi\)
0.822934 + 0.568137i \(0.192336\pi\)
\(548\) 0 0
\(549\) −10.1214 −0.431970
\(550\) 0 0
\(551\) 6.52871 0.278132
\(552\) 0 0
\(553\) −1.34356 −0.0571342
\(554\) 0 0
\(555\) −18.8967 −0.802119
\(556\) 0 0
\(557\) −15.3414 −0.650036 −0.325018 0.945708i \(-0.605370\pi\)
−0.325018 + 0.945708i \(0.605370\pi\)
\(558\) 0 0
\(559\) −10.9727 −0.464096
\(560\) 0 0
\(561\) −17.5684 −0.741737
\(562\) 0 0
\(563\) 41.1512 1.73432 0.867158 0.498034i \(-0.165944\pi\)
0.867158 + 0.498034i \(0.165944\pi\)
\(564\) 0 0
\(565\) −37.5111 −1.57811
\(566\) 0 0
\(567\) −0.864458 −0.0363038
\(568\) 0 0
\(569\) −27.0512 −1.13404 −0.567022 0.823703i \(-0.691905\pi\)
−0.567022 + 0.823703i \(0.691905\pi\)
\(570\) 0 0
\(571\) 19.7641 0.827104 0.413552 0.910481i \(-0.364288\pi\)
0.413552 + 0.910481i \(0.364288\pi\)
\(572\) 0 0
\(573\) −14.1402 −0.590715
\(574\) 0 0
\(575\) 18.0435 0.752467
\(576\) 0 0
\(577\) −15.3608 −0.639477 −0.319739 0.947506i \(-0.603595\pi\)
−0.319739 + 0.947506i \(0.603595\pi\)
\(578\) 0 0
\(579\) −16.0199 −0.665764
\(580\) 0 0
\(581\) −1.33222 −0.0552699
\(582\) 0 0
\(583\) −11.5825 −0.479698
\(584\) 0 0
\(585\) −15.1495 −0.626357
\(586\) 0 0
\(587\) 15.7039 0.648169 0.324085 0.946028i \(-0.394944\pi\)
0.324085 + 0.946028i \(0.394944\pi\)
\(588\) 0 0
\(589\) −21.3961 −0.881612
\(590\) 0 0
\(591\) 7.88270 0.324251
\(592\) 0 0
\(593\) 34.0904 1.39992 0.699962 0.714180i \(-0.253200\pi\)
0.699962 + 0.714180i \(0.253200\pi\)
\(594\) 0 0
\(595\) 6.11465 0.250676
\(596\) 0 0
\(597\) 18.7293 0.766537
\(598\) 0 0
\(599\) 6.54803 0.267545 0.133773 0.991012i \(-0.457291\pi\)
0.133773 + 0.991012i \(0.457291\pi\)
\(600\) 0 0
\(601\) −26.8217 −1.09408 −0.547039 0.837107i \(-0.684245\pi\)
−0.547039 + 0.837107i \(0.684245\pi\)
\(602\) 0 0
\(603\) 4.68323 0.190716
\(604\) 0 0
\(605\) −29.6124 −1.20391
\(606\) 0 0
\(607\) 25.8143 1.04777 0.523885 0.851789i \(-0.324482\pi\)
0.523885 + 0.851789i \(0.324482\pi\)
\(608\) 0 0
\(609\) −0.385460 −0.0156196
\(610\) 0 0
\(611\) 5.55740 0.224828
\(612\) 0 0
\(613\) 3.54189 0.143056 0.0715278 0.997439i \(-0.477213\pi\)
0.0715278 + 0.997439i \(0.477213\pi\)
\(614\) 0 0
\(615\) −23.9688 −0.966515
\(616\) 0 0
\(617\) −9.07073 −0.365174 −0.182587 0.983190i \(-0.558447\pi\)
−0.182587 + 0.983190i \(0.558447\pi\)
\(618\) 0 0
\(619\) −36.2957 −1.45885 −0.729423 0.684063i \(-0.760211\pi\)
−0.729423 + 0.684063i \(0.760211\pi\)
\(620\) 0 0
\(621\) 9.59230 0.384926
\(622\) 0 0
\(623\) 3.76038 0.150657
\(624\) 0 0
\(625\) 34.2946 1.37178
\(626\) 0 0
\(627\) −12.5372 −0.500686
\(628\) 0 0
\(629\) 25.0713 0.999659
\(630\) 0 0
\(631\) 16.7823 0.668091 0.334046 0.942557i \(-0.391586\pi\)
0.334046 + 0.942557i \(0.391586\pi\)
\(632\) 0 0
\(633\) 12.6792 0.503953
\(634\) 0 0
\(635\) 44.3501 1.75998
\(636\) 0 0
\(637\) −22.0715 −0.874504
\(638\) 0 0
\(639\) −4.19257 −0.165856
\(640\) 0 0
\(641\) 25.9725 1.02585 0.512925 0.858433i \(-0.328562\pi\)
0.512925 + 0.858433i \(0.328562\pi\)
\(642\) 0 0
\(643\) −21.0960 −0.831947 −0.415973 0.909377i \(-0.636559\pi\)
−0.415973 + 0.909377i \(0.636559\pi\)
\(644\) 0 0
\(645\) 18.2684 0.719319
\(646\) 0 0
\(647\) 5.25249 0.206497 0.103248 0.994656i \(-0.467076\pi\)
0.103248 + 0.994656i \(0.467076\pi\)
\(648\) 0 0
\(649\) −20.2174 −0.793603
\(650\) 0 0
\(651\) 1.26324 0.0495104
\(652\) 0 0
\(653\) −27.2221 −1.06528 −0.532642 0.846340i \(-0.678801\pi\)
−0.532642 + 0.846340i \(0.678801\pi\)
\(654\) 0 0
\(655\) 56.7544 2.21758
\(656\) 0 0
\(657\) 8.12970 0.317170
\(658\) 0 0
\(659\) 16.4501 0.640804 0.320402 0.947282i \(-0.396182\pi\)
0.320402 + 0.947282i \(0.396182\pi\)
\(660\) 0 0
\(661\) −10.3556 −0.402787 −0.201393 0.979510i \(-0.564547\pi\)
−0.201393 + 0.979510i \(0.564547\pi\)
\(662\) 0 0
\(663\) −29.8101 −1.15773
\(664\) 0 0
\(665\) 4.36355 0.169211
\(666\) 0 0
\(667\) 2.22123 0.0860063
\(668\) 0 0
\(669\) −2.71492 −0.104965
\(670\) 0 0
\(671\) 15.6765 0.605183
\(672\) 0 0
\(673\) 0.912732 0.0351832 0.0175916 0.999845i \(-0.494400\pi\)
0.0175916 + 0.999845i \(0.494400\pi\)
\(674\) 0 0
\(675\) 59.6873 2.29737
\(676\) 0 0
\(677\) −13.3888 −0.514573 −0.257287 0.966335i \(-0.582828\pi\)
−0.257287 + 0.966335i \(0.582828\pi\)
\(678\) 0 0
\(679\) 0.0370416 0.00142152
\(680\) 0 0
\(681\) 12.9689 0.496968
\(682\) 0 0
\(683\) −22.3662 −0.855818 −0.427909 0.903822i \(-0.640750\pi\)
−0.427909 + 0.903822i \(0.640750\pi\)
\(684\) 0 0
\(685\) 36.8591 1.40831
\(686\) 0 0
\(687\) 22.0773 0.842301
\(688\) 0 0
\(689\) −19.6533 −0.748730
\(690\) 0 0
\(691\) −15.4244 −0.586773 −0.293386 0.955994i \(-0.594782\pi\)
−0.293386 + 0.955994i \(0.594782\pi\)
\(692\) 0 0
\(693\) −0.499091 −0.0189589
\(694\) 0 0
\(695\) 30.4359 1.15450
\(696\) 0 0
\(697\) 31.8008 1.20454
\(698\) 0 0
\(699\) −5.93782 −0.224589
\(700\) 0 0
\(701\) 19.0396 0.719116 0.359558 0.933123i \(-0.382927\pi\)
0.359558 + 0.933123i \(0.382927\pi\)
\(702\) 0 0
\(703\) 17.8914 0.674789
\(704\) 0 0
\(705\) −9.25250 −0.348469
\(706\) 0 0
\(707\) −0.882963 −0.0332072
\(708\) 0 0
\(709\) 5.64775 0.212106 0.106053 0.994360i \(-0.466179\pi\)
0.106053 + 0.994360i \(0.466179\pi\)
\(710\) 0 0
\(711\) 7.35303 0.275760
\(712\) 0 0
\(713\) −7.27948 −0.272619
\(714\) 0 0
\(715\) 23.4643 0.877517
\(716\) 0 0
\(717\) −25.4363 −0.949937
\(718\) 0 0
\(719\) −21.4226 −0.798927 −0.399463 0.916749i \(-0.630804\pi\)
−0.399463 + 0.916749i \(0.630804\pi\)
\(720\) 0 0
\(721\) −0.746751 −0.0278105
\(722\) 0 0
\(723\) −13.1800 −0.490170
\(724\) 0 0
\(725\) 13.8214 0.513314
\(726\) 0 0
\(727\) 13.2070 0.489821 0.244911 0.969546i \(-0.421241\pi\)
0.244911 + 0.969546i \(0.421241\pi\)
\(728\) 0 0
\(729\) 27.3520 1.01304
\(730\) 0 0
\(731\) −24.2378 −0.896469
\(732\) 0 0
\(733\) 34.7367 1.28303 0.641515 0.767111i \(-0.278306\pi\)
0.641515 + 0.767111i \(0.278306\pi\)
\(734\) 0 0
\(735\) 36.7468 1.35542
\(736\) 0 0
\(737\) −7.25361 −0.267190
\(738\) 0 0
\(739\) 37.1757 1.36753 0.683765 0.729702i \(-0.260341\pi\)
0.683765 + 0.729702i \(0.260341\pi\)
\(740\) 0 0
\(741\) −21.2732 −0.781489
\(742\) 0 0
\(743\) 43.0654 1.57992 0.789959 0.613160i \(-0.210102\pi\)
0.789959 + 0.613160i \(0.210102\pi\)
\(744\) 0 0
\(745\) −11.9290 −0.437046
\(746\) 0 0
\(747\) 7.29095 0.266762
\(748\) 0 0
\(749\) −1.26165 −0.0460998
\(750\) 0 0
\(751\) −1.00000 −0.0364905
\(752\) 0 0
\(753\) 0.273463 0.00996556
\(754\) 0 0
\(755\) −10.9188 −0.397376
\(756\) 0 0
\(757\) −43.8148 −1.59248 −0.796238 0.604984i \(-0.793180\pi\)
−0.796238 + 0.604984i \(0.793180\pi\)
\(758\) 0 0
\(759\) −4.26545 −0.154826
\(760\) 0 0
\(761\) −1.72407 −0.0624975 −0.0312488 0.999512i \(-0.509948\pi\)
−0.0312488 + 0.999512i \(0.509948\pi\)
\(762\) 0 0
\(763\) 1.03495 0.0374679
\(764\) 0 0
\(765\) −33.4641 −1.20990
\(766\) 0 0
\(767\) −34.3050 −1.23868
\(768\) 0 0
\(769\) 36.3950 1.31244 0.656218 0.754571i \(-0.272155\pi\)
0.656218 + 0.754571i \(0.272155\pi\)
\(770\) 0 0
\(771\) −15.1580 −0.545901
\(772\) 0 0
\(773\) 6.21741 0.223625 0.111812 0.993729i \(-0.464334\pi\)
0.111812 + 0.993729i \(0.464334\pi\)
\(774\) 0 0
\(775\) −45.2960 −1.62708
\(776\) 0 0
\(777\) −1.05632 −0.0378954
\(778\) 0 0
\(779\) 22.6938 0.813089
\(780\) 0 0
\(781\) 6.49366 0.232361
\(782\) 0 0
\(783\) 7.34774 0.262587
\(784\) 0 0
\(785\) −54.6374 −1.95009
\(786\) 0 0
\(787\) −28.6165 −1.02007 −0.510034 0.860154i \(-0.670367\pi\)
−0.510034 + 0.860154i \(0.670367\pi\)
\(788\) 0 0
\(789\) −15.8803 −0.565354
\(790\) 0 0
\(791\) −2.09688 −0.0745563
\(792\) 0 0
\(793\) 26.5999 0.944592
\(794\) 0 0
\(795\) 32.7207 1.16048
\(796\) 0 0
\(797\) 51.0966 1.80994 0.904968 0.425480i \(-0.139895\pi\)
0.904968 + 0.425480i \(0.139895\pi\)
\(798\) 0 0
\(799\) 12.2758 0.434288
\(800\) 0 0
\(801\) −20.5797 −0.727149
\(802\) 0 0
\(803\) −12.5917 −0.444351
\(804\) 0 0
\(805\) 1.48459 0.0523248
\(806\) 0 0
\(807\) 9.35291 0.329238
\(808\) 0 0
\(809\) −40.1193 −1.41052 −0.705259 0.708949i \(-0.749169\pi\)
−0.705259 + 0.708949i \(0.749169\pi\)
\(810\) 0 0
\(811\) 33.2049 1.16598 0.582991 0.812479i \(-0.301882\pi\)
0.582991 + 0.812479i \(0.301882\pi\)
\(812\) 0 0
\(813\) 25.3344 0.888516
\(814\) 0 0
\(815\) −66.0973 −2.31529
\(816\) 0 0
\(817\) −17.2966 −0.605133
\(818\) 0 0
\(819\) −0.846861 −0.0295917
\(820\) 0 0
\(821\) −0.533428 −0.0186168 −0.00930838 0.999957i \(-0.502963\pi\)
−0.00930838 + 0.999957i \(0.502963\pi\)
\(822\) 0 0
\(823\) −31.8473 −1.11013 −0.555063 0.831808i \(-0.687306\pi\)
−0.555063 + 0.831808i \(0.687306\pi\)
\(824\) 0 0
\(825\) −26.5414 −0.924054
\(826\) 0 0
\(827\) 19.5264 0.678998 0.339499 0.940606i \(-0.389742\pi\)
0.339499 + 0.940606i \(0.389742\pi\)
\(828\) 0 0
\(829\) −39.1148 −1.35851 −0.679257 0.733901i \(-0.737698\pi\)
−0.679257 + 0.733901i \(0.737698\pi\)
\(830\) 0 0
\(831\) 34.5531 1.19863
\(832\) 0 0
\(833\) −48.7541 −1.68923
\(834\) 0 0
\(835\) −42.0152 −1.45400
\(836\) 0 0
\(837\) −24.0803 −0.832336
\(838\) 0 0
\(839\) 22.9760 0.793221 0.396610 0.917987i \(-0.370186\pi\)
0.396610 + 0.917987i \(0.370186\pi\)
\(840\) 0 0
\(841\) −27.2985 −0.941329
\(842\) 0 0
\(843\) −1.90444 −0.0655925
\(844\) 0 0
\(845\) −11.5248 −0.396464
\(846\) 0 0
\(847\) −1.65533 −0.0568779
\(848\) 0 0
\(849\) 3.49944 0.120100
\(850\) 0 0
\(851\) 6.08711 0.208663
\(852\) 0 0
\(853\) 54.2863 1.85873 0.929363 0.369166i \(-0.120357\pi\)
0.929363 + 0.369166i \(0.120357\pi\)
\(854\) 0 0
\(855\) −23.8807 −0.816704
\(856\) 0 0
\(857\) −45.7939 −1.56429 −0.782145 0.623096i \(-0.785875\pi\)
−0.782145 + 0.623096i \(0.785875\pi\)
\(858\) 0 0
\(859\) −0.226434 −0.00772583 −0.00386291 0.999993i \(-0.501230\pi\)
−0.00386291 + 0.999993i \(0.501230\pi\)
\(860\) 0 0
\(861\) −1.33986 −0.0456622
\(862\) 0 0
\(863\) 48.7597 1.65980 0.829900 0.557912i \(-0.188397\pi\)
0.829900 + 0.557912i \(0.188397\pi\)
\(864\) 0 0
\(865\) −8.51230 −0.289427
\(866\) 0 0
\(867\) −43.0921 −1.46348
\(868\) 0 0
\(869\) −11.3887 −0.386336
\(870\) 0 0
\(871\) −12.3080 −0.417040
\(872\) 0 0
\(873\) −0.202720 −0.00686104
\(874\) 0 0
\(875\) 4.87864 0.164928
\(876\) 0 0
\(877\) 19.3293 0.652706 0.326353 0.945248i \(-0.394180\pi\)
0.326353 + 0.945248i \(0.394180\pi\)
\(878\) 0 0
\(879\) −15.9771 −0.538894
\(880\) 0 0
\(881\) −48.6138 −1.63784 −0.818920 0.573908i \(-0.805427\pi\)
−0.818920 + 0.573908i \(0.805427\pi\)
\(882\) 0 0
\(883\) −10.8725 −0.365888 −0.182944 0.983123i \(-0.558563\pi\)
−0.182944 + 0.983123i \(0.558563\pi\)
\(884\) 0 0
\(885\) 57.1144 1.91988
\(886\) 0 0
\(887\) −24.5323 −0.823715 −0.411858 0.911248i \(-0.635120\pi\)
−0.411858 + 0.911248i \(0.635120\pi\)
\(888\) 0 0
\(889\) 2.47917 0.0831488
\(890\) 0 0
\(891\) −7.32758 −0.245483
\(892\) 0 0
\(893\) 8.76031 0.293153
\(894\) 0 0
\(895\) −77.7693 −2.59954
\(896\) 0 0
\(897\) −7.23765 −0.241658
\(898\) 0 0
\(899\) −5.57611 −0.185974
\(900\) 0 0
\(901\) −43.4125 −1.44628
\(902\) 0 0
\(903\) 1.02121 0.0339837
\(904\) 0 0
\(905\) 69.1790 2.29959
\(906\) 0 0
\(907\) 26.2391 0.871254 0.435627 0.900127i \(-0.356527\pi\)
0.435627 + 0.900127i \(0.356527\pi\)
\(908\) 0 0
\(909\) 4.83226 0.160276
\(910\) 0 0
\(911\) −33.9371 −1.12439 −0.562193 0.827006i \(-0.690042\pi\)
−0.562193 + 0.827006i \(0.690042\pi\)
\(912\) 0 0
\(913\) −11.2926 −0.373730
\(914\) 0 0
\(915\) −44.2862 −1.46406
\(916\) 0 0
\(917\) 3.17258 0.104768
\(918\) 0 0
\(919\) 6.62477 0.218531 0.109265 0.994013i \(-0.465150\pi\)
0.109265 + 0.994013i \(0.465150\pi\)
\(920\) 0 0
\(921\) 5.08751 0.167639
\(922\) 0 0
\(923\) 11.0185 0.362678
\(924\) 0 0
\(925\) 37.8765 1.24537
\(926\) 0 0
\(927\) 4.08680 0.134228
\(928\) 0 0
\(929\) −48.5220 −1.59196 −0.795978 0.605326i \(-0.793043\pi\)
−0.795978 + 0.605326i \(0.793043\pi\)
\(930\) 0 0
\(931\) −34.7920 −1.14026
\(932\) 0 0
\(933\) −21.0632 −0.689577
\(934\) 0 0
\(935\) 51.8309 1.69505
\(936\) 0 0
\(937\) 2.56125 0.0836722 0.0418361 0.999124i \(-0.486679\pi\)
0.0418361 + 0.999124i \(0.486679\pi\)
\(938\) 0 0
\(939\) 12.7984 0.417661
\(940\) 0 0
\(941\) 11.1766 0.364346 0.182173 0.983266i \(-0.441687\pi\)
0.182173 + 0.983266i \(0.441687\pi\)
\(942\) 0 0
\(943\) 7.72097 0.251429
\(944\) 0 0
\(945\) 4.91096 0.159753
\(946\) 0 0
\(947\) 25.6807 0.834509 0.417255 0.908790i \(-0.362992\pi\)
0.417255 + 0.908790i \(0.362992\pi\)
\(948\) 0 0
\(949\) −21.3656 −0.693558
\(950\) 0 0
\(951\) −19.5716 −0.634653
\(952\) 0 0
\(953\) 29.6835 0.961541 0.480771 0.876846i \(-0.340357\pi\)
0.480771 + 0.876846i \(0.340357\pi\)
\(954\) 0 0
\(955\) 41.7169 1.34993
\(956\) 0 0
\(957\) −3.26735 −0.105619
\(958\) 0 0
\(959\) 2.06042 0.0665346
\(960\) 0 0
\(961\) −12.7258 −0.410509
\(962\) 0 0
\(963\) 6.90474 0.222502
\(964\) 0 0
\(965\) 47.2625 1.52143
\(966\) 0 0
\(967\) −4.93932 −0.158838 −0.0794189 0.996841i \(-0.525306\pi\)
−0.0794189 + 0.996841i \(0.525306\pi\)
\(968\) 0 0
\(969\) −46.9907 −1.50956
\(970\) 0 0
\(971\) −13.1712 −0.422684 −0.211342 0.977412i \(-0.567783\pi\)
−0.211342 + 0.977412i \(0.567783\pi\)
\(972\) 0 0
\(973\) 1.70137 0.0545433
\(974\) 0 0
\(975\) −45.0357 −1.44230
\(976\) 0 0
\(977\) −19.5422 −0.625210 −0.312605 0.949883i \(-0.601202\pi\)
−0.312605 + 0.949883i \(0.601202\pi\)
\(978\) 0 0
\(979\) 31.8749 1.01873
\(980\) 0 0
\(981\) −5.66407 −0.180840
\(982\) 0 0
\(983\) −53.8905 −1.71884 −0.859420 0.511270i \(-0.829175\pi\)
−0.859420 + 0.511270i \(0.829175\pi\)
\(984\) 0 0
\(985\) −23.2558 −0.740992
\(986\) 0 0
\(987\) −0.517215 −0.0164631
\(988\) 0 0
\(989\) −5.88474 −0.187124
\(990\) 0 0
\(991\) 18.8625 0.599188 0.299594 0.954067i \(-0.403149\pi\)
0.299594 + 0.954067i \(0.403149\pi\)
\(992\) 0 0
\(993\) −14.7565 −0.468284
\(994\) 0 0
\(995\) −55.2557 −1.75172
\(996\) 0 0
\(997\) −32.0914 −1.01634 −0.508172 0.861256i \(-0.669678\pi\)
−0.508172 + 0.861256i \(0.669678\pi\)
\(998\) 0 0
\(999\) 20.1359 0.637073
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 \(a_p\))