Properties

Label 8048.2.a.v.1.13
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.682343 q^{3}\) \(+3.69511 q^{5}\) \(+3.46637 q^{7}\) \(-2.53441 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.682343 q^{3}\) \(+3.69511 q^{5}\) \(+3.46637 q^{7}\) \(-2.53441 q^{9}\) \(-1.14497 q^{11}\) \(-0.915952 q^{13}\) \(-2.52133 q^{15}\) \(-7.09797 q^{17}\) \(+3.54009 q^{19}\) \(-2.36525 q^{21}\) \(-4.97901 q^{23}\) \(+8.65381 q^{25}\) \(+3.77636 q^{27}\) \(-4.41622 q^{29}\) \(-10.1478 q^{31}\) \(+0.781263 q^{33}\) \(+12.8086 q^{35}\) \(+2.60522 q^{37}\) \(+0.624993 q^{39}\) \(-9.41578 q^{41}\) \(-0.391661 q^{43}\) \(-9.36491 q^{45}\) \(+4.45651 q^{47}\) \(+5.01570 q^{49}\) \(+4.84325 q^{51}\) \(-1.57279 q^{53}\) \(-4.23079 q^{55}\) \(-2.41555 q^{57}\) \(+3.21174 q^{59}\) \(-5.61162 q^{61}\) \(-8.78519 q^{63}\) \(-3.38454 q^{65}\) \(+0.0216322 q^{67}\) \(+3.39739 q^{69}\) \(+1.49981 q^{71}\) \(-12.8005 q^{73}\) \(-5.90486 q^{75}\) \(-3.96889 q^{77}\) \(+6.15151 q^{79}\) \(+5.02645 q^{81}\) \(+0.0862293 q^{83}\) \(-26.2278 q^{85}\) \(+3.01338 q^{87}\) \(-16.8773 q^{89}\) \(-3.17503 q^{91}\) \(+6.92426 q^{93}\) \(+13.0810 q^{95}\) \(-10.8940 q^{97}\) \(+2.90182 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.682343 −0.393951 −0.196975 0.980408i \(-0.563112\pi\)
−0.196975 + 0.980408i \(0.563112\pi\)
\(4\) 0 0
\(5\) 3.69511 1.65250 0.826251 0.563302i \(-0.190469\pi\)
0.826251 + 0.563302i \(0.190469\pi\)
\(6\) 0 0
\(7\) 3.46637 1.31016 0.655082 0.755558i \(-0.272634\pi\)
0.655082 + 0.755558i \(0.272634\pi\)
\(8\) 0 0
\(9\) −2.53441 −0.844803
\(10\) 0 0
\(11\) −1.14497 −0.345222 −0.172611 0.984990i \(-0.555220\pi\)
−0.172611 + 0.984990i \(0.555220\pi\)
\(12\) 0 0
\(13\) −0.915952 −0.254039 −0.127020 0.991900i \(-0.540541\pi\)
−0.127020 + 0.991900i \(0.540541\pi\)
\(14\) 0 0
\(15\) −2.52133 −0.651004
\(16\) 0 0
\(17\) −7.09797 −1.72151 −0.860756 0.509018i \(-0.830009\pi\)
−0.860756 + 0.509018i \(0.830009\pi\)
\(18\) 0 0
\(19\) 3.54009 0.812152 0.406076 0.913839i \(-0.366897\pi\)
0.406076 + 0.913839i \(0.366897\pi\)
\(20\) 0 0
\(21\) −2.36525 −0.516140
\(22\) 0 0
\(23\) −4.97901 −1.03820 −0.519098 0.854715i \(-0.673732\pi\)
−0.519098 + 0.854715i \(0.673732\pi\)
\(24\) 0 0
\(25\) 8.65381 1.73076
\(26\) 0 0
\(27\) 3.77636 0.726761
\(28\) 0 0
\(29\) −4.41622 −0.820071 −0.410036 0.912069i \(-0.634484\pi\)
−0.410036 + 0.912069i \(0.634484\pi\)
\(30\) 0 0
\(31\) −10.1478 −1.82259 −0.911297 0.411749i \(-0.864918\pi\)
−0.911297 + 0.411749i \(0.864918\pi\)
\(32\) 0 0
\(33\) 0.781263 0.136000
\(34\) 0 0
\(35\) 12.8086 2.16505
\(36\) 0 0
\(37\) 2.60522 0.428296 0.214148 0.976801i \(-0.431303\pi\)
0.214148 + 0.976801i \(0.431303\pi\)
\(38\) 0 0
\(39\) 0.624993 0.100079
\(40\) 0 0
\(41\) −9.41578 −1.47050 −0.735249 0.677797i \(-0.762935\pi\)
−0.735249 + 0.677797i \(0.762935\pi\)
\(42\) 0 0
\(43\) −0.391661 −0.0597278 −0.0298639 0.999554i \(-0.509507\pi\)
−0.0298639 + 0.999554i \(0.509507\pi\)
\(44\) 0 0
\(45\) −9.36491 −1.39604
\(46\) 0 0
\(47\) 4.45651 0.650048 0.325024 0.945706i \(-0.394628\pi\)
0.325024 + 0.945706i \(0.394628\pi\)
\(48\) 0 0
\(49\) 5.01570 0.716529
\(50\) 0 0
\(51\) 4.84325 0.678191
\(52\) 0 0
\(53\) −1.57279 −0.216039 −0.108020 0.994149i \(-0.534451\pi\)
−0.108020 + 0.994149i \(0.534451\pi\)
\(54\) 0 0
\(55\) −4.23079 −0.570480
\(56\) 0 0
\(57\) −2.41555 −0.319948
\(58\) 0 0
\(59\) 3.21174 0.418133 0.209066 0.977901i \(-0.432958\pi\)
0.209066 + 0.977901i \(0.432958\pi\)
\(60\) 0 0
\(61\) −5.61162 −0.718495 −0.359247 0.933242i \(-0.616967\pi\)
−0.359247 + 0.933242i \(0.616967\pi\)
\(62\) 0 0
\(63\) −8.78519 −1.10683
\(64\) 0 0
\(65\) −3.38454 −0.419800
\(66\) 0 0
\(67\) 0.0216322 0.00264280 0.00132140 0.999999i \(-0.499579\pi\)
0.00132140 + 0.999999i \(0.499579\pi\)
\(68\) 0 0
\(69\) 3.39739 0.408998
\(70\) 0 0
\(71\) 1.49981 0.177994 0.0889972 0.996032i \(-0.471634\pi\)
0.0889972 + 0.996032i \(0.471634\pi\)
\(72\) 0 0
\(73\) −12.8005 −1.49819 −0.749095 0.662463i \(-0.769511\pi\)
−0.749095 + 0.662463i \(0.769511\pi\)
\(74\) 0 0
\(75\) −5.90486 −0.681835
\(76\) 0 0
\(77\) −3.96889 −0.452297
\(78\) 0 0
\(79\) 6.15151 0.692099 0.346049 0.938216i \(-0.387523\pi\)
0.346049 + 0.938216i \(0.387523\pi\)
\(80\) 0 0
\(81\) 5.02645 0.558495
\(82\) 0 0
\(83\) 0.0862293 0.00946490 0.00473245 0.999989i \(-0.498494\pi\)
0.00473245 + 0.999989i \(0.498494\pi\)
\(84\) 0 0
\(85\) −26.2278 −2.84480
\(86\) 0 0
\(87\) 3.01338 0.323068
\(88\) 0 0
\(89\) −16.8773 −1.78900 −0.894498 0.447073i \(-0.852466\pi\)
−0.894498 + 0.447073i \(0.852466\pi\)
\(90\) 0 0
\(91\) −3.17503 −0.332833
\(92\) 0 0
\(93\) 6.92426 0.718012
\(94\) 0 0
\(95\) 13.0810 1.34208
\(96\) 0 0
\(97\) −10.8940 −1.10612 −0.553059 0.833142i \(-0.686540\pi\)
−0.553059 + 0.833142i \(0.686540\pi\)
\(98\) 0 0
\(99\) 2.90182 0.291644
\(100\) 0 0
\(101\) 15.4041 1.53277 0.766384 0.642382i \(-0.222054\pi\)
0.766384 + 0.642382i \(0.222054\pi\)
\(102\) 0 0
\(103\) 7.32004 0.721265 0.360632 0.932708i \(-0.382561\pi\)
0.360632 + 0.932708i \(0.382561\pi\)
\(104\) 0 0
\(105\) −8.73985 −0.852922
\(106\) 0 0
\(107\) 0.797681 0.0771147 0.0385574 0.999256i \(-0.487724\pi\)
0.0385574 + 0.999256i \(0.487724\pi\)
\(108\) 0 0
\(109\) −16.1247 −1.54446 −0.772232 0.635341i \(-0.780860\pi\)
−0.772232 + 0.635341i \(0.780860\pi\)
\(110\) 0 0
\(111\) −1.77765 −0.168727
\(112\) 0 0
\(113\) −7.24664 −0.681707 −0.340853 0.940116i \(-0.610716\pi\)
−0.340853 + 0.940116i \(0.610716\pi\)
\(114\) 0 0
\(115\) −18.3980 −1.71562
\(116\) 0 0
\(117\) 2.32140 0.214613
\(118\) 0 0
\(119\) −24.6042 −2.25546
\(120\) 0 0
\(121\) −9.68904 −0.880822
\(122\) 0 0
\(123\) 6.42479 0.579304
\(124\) 0 0
\(125\) 13.5012 1.20758
\(126\) 0 0
\(127\) −20.1778 −1.79049 −0.895246 0.445572i \(-0.853000\pi\)
−0.895246 + 0.445572i \(0.853000\pi\)
\(128\) 0 0
\(129\) 0.267247 0.0235298
\(130\) 0 0
\(131\) 2.17787 0.190281 0.0951407 0.995464i \(-0.469670\pi\)
0.0951407 + 0.995464i \(0.469670\pi\)
\(132\) 0 0
\(133\) 12.2712 1.06405
\(134\) 0 0
\(135\) 13.9541 1.20097
\(136\) 0 0
\(137\) 9.58889 0.819235 0.409617 0.912257i \(-0.365662\pi\)
0.409617 + 0.912257i \(0.365662\pi\)
\(138\) 0 0
\(139\) −13.0832 −1.10970 −0.554851 0.831950i \(-0.687225\pi\)
−0.554851 + 0.831950i \(0.687225\pi\)
\(140\) 0 0
\(141\) −3.04086 −0.256087
\(142\) 0 0
\(143\) 1.04874 0.0876999
\(144\) 0 0
\(145\) −16.3184 −1.35517
\(146\) 0 0
\(147\) −3.42243 −0.282277
\(148\) 0 0
\(149\) −7.71463 −0.632007 −0.316004 0.948758i \(-0.602341\pi\)
−0.316004 + 0.948758i \(0.602341\pi\)
\(150\) 0 0
\(151\) 6.19163 0.503867 0.251934 0.967744i \(-0.418934\pi\)
0.251934 + 0.967744i \(0.418934\pi\)
\(152\) 0 0
\(153\) 17.9892 1.45434
\(154\) 0 0
\(155\) −37.4971 −3.01184
\(156\) 0 0
\(157\) −16.6597 −1.32959 −0.664793 0.747027i \(-0.731480\pi\)
−0.664793 + 0.747027i \(0.731480\pi\)
\(158\) 0 0
\(159\) 1.07318 0.0851088
\(160\) 0 0
\(161\) −17.2591 −1.36021
\(162\) 0 0
\(163\) −1.01575 −0.0795601 −0.0397800 0.999208i \(-0.512666\pi\)
−0.0397800 + 0.999208i \(0.512666\pi\)
\(164\) 0 0
\(165\) 2.88685 0.224741
\(166\) 0 0
\(167\) 18.5419 1.43482 0.717409 0.696652i \(-0.245328\pi\)
0.717409 + 0.696652i \(0.245328\pi\)
\(168\) 0 0
\(169\) −12.1610 −0.935464
\(170\) 0 0
\(171\) −8.97203 −0.686108
\(172\) 0 0
\(173\) 19.5050 1.48294 0.741470 0.670986i \(-0.234129\pi\)
0.741470 + 0.670986i \(0.234129\pi\)
\(174\) 0 0
\(175\) 29.9973 2.26758
\(176\) 0 0
\(177\) −2.19151 −0.164724
\(178\) 0 0
\(179\) 20.3190 1.51872 0.759358 0.650673i \(-0.225513\pi\)
0.759358 + 0.650673i \(0.225513\pi\)
\(180\) 0 0
\(181\) 11.4088 0.848011 0.424005 0.905660i \(-0.360624\pi\)
0.424005 + 0.905660i \(0.360624\pi\)
\(182\) 0 0
\(183\) 3.82905 0.283051
\(184\) 0 0
\(185\) 9.62656 0.707759
\(186\) 0 0
\(187\) 8.12697 0.594303
\(188\) 0 0
\(189\) 13.0903 0.952176
\(190\) 0 0
\(191\) −14.3105 −1.03547 −0.517734 0.855541i \(-0.673224\pi\)
−0.517734 + 0.855541i \(0.673224\pi\)
\(192\) 0 0
\(193\) 4.59672 0.330879 0.165440 0.986220i \(-0.447096\pi\)
0.165440 + 0.986220i \(0.447096\pi\)
\(194\) 0 0
\(195\) 2.30942 0.165381
\(196\) 0 0
\(197\) 18.2817 1.30251 0.651257 0.758857i \(-0.274242\pi\)
0.651257 + 0.758857i \(0.274242\pi\)
\(198\) 0 0
\(199\) 12.0533 0.854436 0.427218 0.904149i \(-0.359494\pi\)
0.427218 + 0.904149i \(0.359494\pi\)
\(200\) 0 0
\(201\) −0.0147606 −0.00104113
\(202\) 0 0
\(203\) −15.3082 −1.07443
\(204\) 0 0
\(205\) −34.7923 −2.43000
\(206\) 0 0
\(207\) 12.6188 0.877071
\(208\) 0 0
\(209\) −4.05330 −0.280372
\(210\) 0 0
\(211\) −24.0136 −1.65317 −0.826583 0.562815i \(-0.809718\pi\)
−0.826583 + 0.562815i \(0.809718\pi\)
\(212\) 0 0
\(213\) −1.02338 −0.0701210
\(214\) 0 0
\(215\) −1.44723 −0.0987002
\(216\) 0 0
\(217\) −35.1759 −2.38790
\(218\) 0 0
\(219\) 8.73435 0.590213
\(220\) 0 0
\(221\) 6.50140 0.437332
\(222\) 0 0
\(223\) −1.04220 −0.0697911 −0.0348955 0.999391i \(-0.511110\pi\)
−0.0348955 + 0.999391i \(0.511110\pi\)
\(224\) 0 0
\(225\) −21.9323 −1.46215
\(226\) 0 0
\(227\) −7.91737 −0.525495 −0.262747 0.964865i \(-0.584629\pi\)
−0.262747 + 0.964865i \(0.584629\pi\)
\(228\) 0 0
\(229\) 3.95775 0.261535 0.130768 0.991413i \(-0.458256\pi\)
0.130768 + 0.991413i \(0.458256\pi\)
\(230\) 0 0
\(231\) 2.70814 0.178183
\(232\) 0 0
\(233\) 16.8280 1.10244 0.551221 0.834359i \(-0.314162\pi\)
0.551221 + 0.834359i \(0.314162\pi\)
\(234\) 0 0
\(235\) 16.4673 1.07421
\(236\) 0 0
\(237\) −4.19743 −0.272653
\(238\) 0 0
\(239\) 12.8700 0.832494 0.416247 0.909252i \(-0.363345\pi\)
0.416247 + 0.909252i \(0.363345\pi\)
\(240\) 0 0
\(241\) 2.95315 0.190229 0.0951145 0.995466i \(-0.469678\pi\)
0.0951145 + 0.995466i \(0.469678\pi\)
\(242\) 0 0
\(243\) −14.7589 −0.946781
\(244\) 0 0
\(245\) 18.5336 1.18407
\(246\) 0 0
\(247\) −3.24255 −0.206318
\(248\) 0 0
\(249\) −0.0588380 −0.00372870
\(250\) 0 0
\(251\) −23.7939 −1.50186 −0.750930 0.660381i \(-0.770395\pi\)
−0.750930 + 0.660381i \(0.770395\pi\)
\(252\) 0 0
\(253\) 5.70082 0.358408
\(254\) 0 0
\(255\) 17.8963 1.12071
\(256\) 0 0
\(257\) 18.8437 1.17544 0.587718 0.809066i \(-0.300026\pi\)
0.587718 + 0.809066i \(0.300026\pi\)
\(258\) 0 0
\(259\) 9.03065 0.561137
\(260\) 0 0
\(261\) 11.1925 0.692799
\(262\) 0 0
\(263\) 14.3719 0.886209 0.443105 0.896470i \(-0.353877\pi\)
0.443105 + 0.896470i \(0.353877\pi\)
\(264\) 0 0
\(265\) −5.81162 −0.357005
\(266\) 0 0
\(267\) 11.5161 0.704776
\(268\) 0 0
\(269\) 26.5833 1.62082 0.810408 0.585867i \(-0.199246\pi\)
0.810408 + 0.585867i \(0.199246\pi\)
\(270\) 0 0
\(271\) 4.11918 0.250222 0.125111 0.992143i \(-0.460071\pi\)
0.125111 + 0.992143i \(0.460071\pi\)
\(272\) 0 0
\(273\) 2.16646 0.131120
\(274\) 0 0
\(275\) −9.90836 −0.597497
\(276\) 0 0
\(277\) −26.1074 −1.56864 −0.784320 0.620357i \(-0.786988\pi\)
−0.784320 + 0.620357i \(0.786988\pi\)
\(278\) 0 0
\(279\) 25.7186 1.53973
\(280\) 0 0
\(281\) 3.97747 0.237276 0.118638 0.992938i \(-0.462147\pi\)
0.118638 + 0.992938i \(0.462147\pi\)
\(282\) 0 0
\(283\) −10.5153 −0.625073 −0.312536 0.949906i \(-0.601179\pi\)
−0.312536 + 0.949906i \(0.601179\pi\)
\(284\) 0 0
\(285\) −8.92572 −0.528714
\(286\) 0 0
\(287\) −32.6386 −1.92659
\(288\) 0 0
\(289\) 33.3812 1.96360
\(290\) 0 0
\(291\) 7.43345 0.435756
\(292\) 0 0
\(293\) 24.9505 1.45762 0.728811 0.684715i \(-0.240073\pi\)
0.728811 + 0.684715i \(0.240073\pi\)
\(294\) 0 0
\(295\) 11.8677 0.690965
\(296\) 0 0
\(297\) −4.32383 −0.250894
\(298\) 0 0
\(299\) 4.56053 0.263743
\(300\) 0 0
\(301\) −1.35764 −0.0782532
\(302\) 0 0
\(303\) −10.5109 −0.603835
\(304\) 0 0
\(305\) −20.7355 −1.18731
\(306\) 0 0
\(307\) −0.621755 −0.0354855 −0.0177427 0.999843i \(-0.505648\pi\)
−0.0177427 + 0.999843i \(0.505648\pi\)
\(308\) 0 0
\(309\) −4.99477 −0.284143
\(310\) 0 0
\(311\) 20.8523 1.18242 0.591212 0.806516i \(-0.298650\pi\)
0.591212 + 0.806516i \(0.298650\pi\)
\(312\) 0 0
\(313\) 25.4816 1.44030 0.720152 0.693817i \(-0.244072\pi\)
0.720152 + 0.693817i \(0.244072\pi\)
\(314\) 0 0
\(315\) −32.4622 −1.82904
\(316\) 0 0
\(317\) −6.05887 −0.340300 −0.170150 0.985418i \(-0.554425\pi\)
−0.170150 + 0.985418i \(0.554425\pi\)
\(318\) 0 0
\(319\) 5.05644 0.283107
\(320\) 0 0
\(321\) −0.544292 −0.0303794
\(322\) 0 0
\(323\) −25.1274 −1.39813
\(324\) 0 0
\(325\) −7.92647 −0.439682
\(326\) 0 0
\(327\) 11.0026 0.608442
\(328\) 0 0
\(329\) 15.4479 0.851670
\(330\) 0 0
\(331\) −26.6371 −1.46411 −0.732055 0.681246i \(-0.761438\pi\)
−0.732055 + 0.681246i \(0.761438\pi\)
\(332\) 0 0
\(333\) −6.60269 −0.361825
\(334\) 0 0
\(335\) 0.0799334 0.00436723
\(336\) 0 0
\(337\) 3.62374 0.197398 0.0986988 0.995117i \(-0.468532\pi\)
0.0986988 + 0.995117i \(0.468532\pi\)
\(338\) 0 0
\(339\) 4.94469 0.268559
\(340\) 0 0
\(341\) 11.6189 0.629199
\(342\) 0 0
\(343\) −6.87830 −0.371393
\(344\) 0 0
\(345\) 12.5537 0.675870
\(346\) 0 0
\(347\) 36.0019 1.93268 0.966340 0.257267i \(-0.0828220\pi\)
0.966340 + 0.257267i \(0.0828220\pi\)
\(348\) 0 0
\(349\) 15.2420 0.815885 0.407943 0.913008i \(-0.366246\pi\)
0.407943 + 0.913008i \(0.366246\pi\)
\(350\) 0 0
\(351\) −3.45897 −0.184626
\(352\) 0 0
\(353\) −24.5906 −1.30883 −0.654414 0.756137i \(-0.727084\pi\)
−0.654414 + 0.756137i \(0.727084\pi\)
\(354\) 0 0
\(355\) 5.54195 0.294136
\(356\) 0 0
\(357\) 16.7885 0.888541
\(358\) 0 0
\(359\) 17.6695 0.932562 0.466281 0.884637i \(-0.345593\pi\)
0.466281 + 0.884637i \(0.345593\pi\)
\(360\) 0 0
\(361\) −6.46778 −0.340410
\(362\) 0 0
\(363\) 6.61125 0.347000
\(364\) 0 0
\(365\) −47.2993 −2.47576
\(366\) 0 0
\(367\) −19.1835 −1.00137 −0.500684 0.865630i \(-0.666918\pi\)
−0.500684 + 0.865630i \(0.666918\pi\)
\(368\) 0 0
\(369\) 23.8634 1.24228
\(370\) 0 0
\(371\) −5.45187 −0.283047
\(372\) 0 0
\(373\) −14.3175 −0.741330 −0.370665 0.928767i \(-0.620870\pi\)
−0.370665 + 0.928767i \(0.620870\pi\)
\(374\) 0 0
\(375\) −9.21245 −0.475729
\(376\) 0 0
\(377\) 4.04505 0.208330
\(378\) 0 0
\(379\) 30.1133 1.54681 0.773407 0.633910i \(-0.218551\pi\)
0.773407 + 0.633910i \(0.218551\pi\)
\(380\) 0 0
\(381\) 13.7682 0.705366
\(382\) 0 0
\(383\) −13.2583 −0.677466 −0.338733 0.940882i \(-0.609998\pi\)
−0.338733 + 0.940882i \(0.609998\pi\)
\(384\) 0 0
\(385\) −14.6655 −0.747422
\(386\) 0 0
\(387\) 0.992629 0.0504582
\(388\) 0 0
\(389\) 7.00355 0.355094 0.177547 0.984112i \(-0.443184\pi\)
0.177547 + 0.984112i \(0.443184\pi\)
\(390\) 0 0
\(391\) 35.3409 1.78727
\(392\) 0 0
\(393\) −1.48605 −0.0749615
\(394\) 0 0
\(395\) 22.7305 1.14369
\(396\) 0 0
\(397\) 10.4033 0.522128 0.261064 0.965321i \(-0.415927\pi\)
0.261064 + 0.965321i \(0.415927\pi\)
\(398\) 0 0
\(399\) −8.37319 −0.419184
\(400\) 0 0
\(401\) −12.4393 −0.621190 −0.310595 0.950542i \(-0.600528\pi\)
−0.310595 + 0.950542i \(0.600528\pi\)
\(402\) 0 0
\(403\) 9.29487 0.463011
\(404\) 0 0
\(405\) 18.5733 0.922913
\(406\) 0 0
\(407\) −2.98290 −0.147857
\(408\) 0 0
\(409\) 2.06701 0.102207 0.0511035 0.998693i \(-0.483726\pi\)
0.0511035 + 0.998693i \(0.483726\pi\)
\(410\) 0 0
\(411\) −6.54291 −0.322738
\(412\) 0 0
\(413\) 11.1331 0.547822
\(414\) 0 0
\(415\) 0.318627 0.0156408
\(416\) 0 0
\(417\) 8.92722 0.437168
\(418\) 0 0
\(419\) 2.23093 0.108988 0.0544940 0.998514i \(-0.482645\pi\)
0.0544940 + 0.998514i \(0.482645\pi\)
\(420\) 0 0
\(421\) −3.43410 −0.167368 −0.0836840 0.996492i \(-0.526669\pi\)
−0.0836840 + 0.996492i \(0.526669\pi\)
\(422\) 0 0
\(423\) −11.2946 −0.549163
\(424\) 0 0
\(425\) −61.4245 −2.97953
\(426\) 0 0
\(427\) −19.4519 −0.941346
\(428\) 0 0
\(429\) −0.715599 −0.0345494
\(430\) 0 0
\(431\) −28.0604 −1.35162 −0.675811 0.737075i \(-0.736207\pi\)
−0.675811 + 0.737075i \(0.736207\pi\)
\(432\) 0 0
\(433\) −10.0537 −0.483152 −0.241576 0.970382i \(-0.577664\pi\)
−0.241576 + 0.970382i \(0.577664\pi\)
\(434\) 0 0
\(435\) 11.1347 0.533870
\(436\) 0 0
\(437\) −17.6261 −0.843172
\(438\) 0 0
\(439\) −2.16976 −0.103557 −0.0517786 0.998659i \(-0.516489\pi\)
−0.0517786 + 0.998659i \(0.516489\pi\)
\(440\) 0 0
\(441\) −12.7118 −0.605326
\(442\) 0 0
\(443\) 19.8482 0.943019 0.471509 0.881861i \(-0.343709\pi\)
0.471509 + 0.881861i \(0.343709\pi\)
\(444\) 0 0
\(445\) −62.3636 −2.95632
\(446\) 0 0
\(447\) 5.26402 0.248980
\(448\) 0 0
\(449\) −37.5743 −1.77324 −0.886621 0.462497i \(-0.846954\pi\)
−0.886621 + 0.462497i \(0.846954\pi\)
\(450\) 0 0
\(451\) 10.7808 0.507648
\(452\) 0 0
\(453\) −4.22481 −0.198499
\(454\) 0 0
\(455\) −11.7321 −0.550007
\(456\) 0 0
\(457\) −16.7147 −0.781882 −0.390941 0.920416i \(-0.627850\pi\)
−0.390941 + 0.920416i \(0.627850\pi\)
\(458\) 0 0
\(459\) −26.8045 −1.25113
\(460\) 0 0
\(461\) −36.8100 −1.71441 −0.857205 0.514975i \(-0.827801\pi\)
−0.857205 + 0.514975i \(0.827801\pi\)
\(462\) 0 0
\(463\) −5.00847 −0.232764 −0.116382 0.993205i \(-0.537130\pi\)
−0.116382 + 0.993205i \(0.537130\pi\)
\(464\) 0 0
\(465\) 25.5859 1.18652
\(466\) 0 0
\(467\) −32.7816 −1.51695 −0.758475 0.651702i \(-0.774055\pi\)
−0.758475 + 0.651702i \(0.774055\pi\)
\(468\) 0 0
\(469\) 0.0749853 0.00346250
\(470\) 0 0
\(471\) 11.3676 0.523792
\(472\) 0 0
\(473\) 0.448441 0.0206193
\(474\) 0 0
\(475\) 30.6352 1.40564
\(476\) 0 0
\(477\) 3.98609 0.182511
\(478\) 0 0
\(479\) 23.0131 1.05150 0.525748 0.850640i \(-0.323785\pi\)
0.525748 + 0.850640i \(0.323785\pi\)
\(480\) 0 0
\(481\) −2.38626 −0.108804
\(482\) 0 0
\(483\) 11.7766 0.535854
\(484\) 0 0
\(485\) −40.2545 −1.82786
\(486\) 0 0
\(487\) 11.9167 0.539999 0.270000 0.962860i \(-0.412976\pi\)
0.270000 + 0.962860i \(0.412976\pi\)
\(488\) 0 0
\(489\) 0.693093 0.0313427
\(490\) 0 0
\(491\) 5.07035 0.228822 0.114411 0.993434i \(-0.463502\pi\)
0.114411 + 0.993434i \(0.463502\pi\)
\(492\) 0 0
\(493\) 31.3462 1.41176
\(494\) 0 0
\(495\) 10.7225 0.481943
\(496\) 0 0
\(497\) 5.19888 0.233202
\(498\) 0 0
\(499\) −11.0312 −0.493822 −0.246911 0.969038i \(-0.579416\pi\)
−0.246911 + 0.969038i \(0.579416\pi\)
\(500\) 0 0
\(501\) −12.6520 −0.565248
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 56.9199 2.53290
\(506\) 0 0
\(507\) 8.29799 0.368527
\(508\) 0 0
\(509\) 1.01308 0.0449039 0.0224520 0.999748i \(-0.492853\pi\)
0.0224520 + 0.999748i \(0.492853\pi\)
\(510\) 0 0
\(511\) −44.3714 −1.96287
\(512\) 0 0
\(513\) 13.3687 0.590240
\(514\) 0 0
\(515\) 27.0483 1.19189
\(516\) 0 0
\(517\) −5.10257 −0.224411
\(518\) 0 0
\(519\) −13.3091 −0.584205
\(520\) 0 0
\(521\) 27.5158 1.20549 0.602744 0.797934i \(-0.294074\pi\)
0.602744 + 0.797934i \(0.294074\pi\)
\(522\) 0 0
\(523\) −21.7823 −0.952474 −0.476237 0.879317i \(-0.658000\pi\)
−0.476237 + 0.879317i \(0.658000\pi\)
\(524\) 0 0
\(525\) −20.4684 −0.893315
\(526\) 0 0
\(527\) 72.0286 3.13762
\(528\) 0 0
\(529\) 1.79055 0.0778501
\(530\) 0 0
\(531\) −8.13986 −0.353240
\(532\) 0 0
\(533\) 8.62440 0.373564
\(534\) 0 0
\(535\) 2.94752 0.127432
\(536\) 0 0
\(537\) −13.8646 −0.598300
\(538\) 0 0
\(539\) −5.74284 −0.247361
\(540\) 0 0
\(541\) −39.5644 −1.70101 −0.850503 0.525970i \(-0.823702\pi\)
−0.850503 + 0.525970i \(0.823702\pi\)
\(542\) 0 0
\(543\) −7.78472 −0.334074
\(544\) 0 0
\(545\) −59.5824 −2.55223
\(546\) 0 0
\(547\) 4.64052 0.198414 0.0992072 0.995067i \(-0.468369\pi\)
0.0992072 + 0.995067i \(0.468369\pi\)
\(548\) 0 0
\(549\) 14.2221 0.606986
\(550\) 0 0
\(551\) −15.6338 −0.666022
\(552\) 0 0
\(553\) 21.3234 0.906762
\(554\) 0 0
\(555\) −6.56861 −0.278822
\(556\) 0 0
\(557\) 38.9567 1.65065 0.825325 0.564658i \(-0.190992\pi\)
0.825325 + 0.564658i \(0.190992\pi\)
\(558\) 0 0
\(559\) 0.358743 0.0151732
\(560\) 0 0
\(561\) −5.54538 −0.234126
\(562\) 0 0
\(563\) 2.24123 0.0944567 0.0472284 0.998884i \(-0.484961\pi\)
0.0472284 + 0.998884i \(0.484961\pi\)
\(564\) 0 0
\(565\) −26.7771 −1.12652
\(566\) 0 0
\(567\) 17.4235 0.731720
\(568\) 0 0
\(569\) −21.7992 −0.913869 −0.456935 0.889500i \(-0.651053\pi\)
−0.456935 + 0.889500i \(0.651053\pi\)
\(570\) 0 0
\(571\) 26.8351 1.12301 0.561507 0.827472i \(-0.310222\pi\)
0.561507 + 0.827472i \(0.310222\pi\)
\(572\) 0 0
\(573\) 9.76464 0.407924
\(574\) 0 0
\(575\) −43.0874 −1.79687
\(576\) 0 0
\(577\) −7.50651 −0.312500 −0.156250 0.987718i \(-0.549941\pi\)
−0.156250 + 0.987718i \(0.549941\pi\)
\(578\) 0 0
\(579\) −3.13654 −0.130350
\(580\) 0 0
\(581\) 0.298903 0.0124006
\(582\) 0 0
\(583\) 1.80080 0.0745814
\(584\) 0 0
\(585\) 8.57781 0.354649
\(586\) 0 0
\(587\) 16.1847 0.668015 0.334008 0.942570i \(-0.391599\pi\)
0.334008 + 0.942570i \(0.391599\pi\)
\(588\) 0 0
\(589\) −35.9240 −1.48022
\(590\) 0 0
\(591\) −12.4744 −0.513126
\(592\) 0 0
\(593\) 10.1623 0.417315 0.208657 0.977989i \(-0.433091\pi\)
0.208657 + 0.977989i \(0.433091\pi\)
\(594\) 0 0
\(595\) −90.9151 −3.72715
\(596\) 0 0
\(597\) −8.22448 −0.336606
\(598\) 0 0
\(599\) 37.0050 1.51198 0.755991 0.654582i \(-0.227155\pi\)
0.755991 + 0.654582i \(0.227155\pi\)
\(600\) 0 0
\(601\) −17.0209 −0.694295 −0.347148 0.937811i \(-0.612850\pi\)
−0.347148 + 0.937811i \(0.612850\pi\)
\(602\) 0 0
\(603\) −0.0548249 −0.00223264
\(604\) 0 0
\(605\) −35.8020 −1.45556
\(606\) 0 0
\(607\) −33.6693 −1.36659 −0.683297 0.730140i \(-0.739455\pi\)
−0.683297 + 0.730140i \(0.739455\pi\)
\(608\) 0 0
\(609\) 10.4455 0.423272
\(610\) 0 0
\(611\) −4.08195 −0.165138
\(612\) 0 0
\(613\) 13.3329 0.538510 0.269255 0.963069i \(-0.413222\pi\)
0.269255 + 0.963069i \(0.413222\pi\)
\(614\) 0 0
\(615\) 23.7403 0.957300
\(616\) 0 0
\(617\) 32.0158 1.28891 0.644454 0.764643i \(-0.277085\pi\)
0.644454 + 0.764643i \(0.277085\pi\)
\(618\) 0 0
\(619\) −32.7902 −1.31795 −0.658974 0.752166i \(-0.729009\pi\)
−0.658974 + 0.752166i \(0.729009\pi\)
\(620\) 0 0
\(621\) −18.8026 −0.754520
\(622\) 0 0
\(623\) −58.5031 −2.34388
\(624\) 0 0
\(625\) 6.61935 0.264774
\(626\) 0 0
\(627\) 2.76574 0.110453
\(628\) 0 0
\(629\) −18.4918 −0.737316
\(630\) 0 0
\(631\) −37.7022 −1.50090 −0.750450 0.660927i \(-0.770163\pi\)
−0.750450 + 0.660927i \(0.770163\pi\)
\(632\) 0 0
\(633\) 16.3855 0.651266
\(634\) 0 0
\(635\) −74.5592 −2.95879
\(636\) 0 0
\(637\) −4.59414 −0.182027
\(638\) 0 0
\(639\) −3.80113 −0.150370
\(640\) 0 0
\(641\) −28.6119 −1.13010 −0.565051 0.825056i \(-0.691144\pi\)
−0.565051 + 0.825056i \(0.691144\pi\)
\(642\) 0 0
\(643\) 20.3342 0.801904 0.400952 0.916099i \(-0.368679\pi\)
0.400952 + 0.916099i \(0.368679\pi\)
\(644\) 0 0
\(645\) 0.987506 0.0388830
\(646\) 0 0
\(647\) −49.6208 −1.95080 −0.975398 0.220452i \(-0.929247\pi\)
−0.975398 + 0.220452i \(0.929247\pi\)
\(648\) 0 0
\(649\) −3.67735 −0.144349
\(650\) 0 0
\(651\) 24.0020 0.940714
\(652\) 0 0
\(653\) −19.0540 −0.745642 −0.372821 0.927903i \(-0.621609\pi\)
−0.372821 + 0.927903i \(0.621609\pi\)
\(654\) 0 0
\(655\) 8.04746 0.314440
\(656\) 0 0
\(657\) 32.4418 1.26567
\(658\) 0 0
\(659\) −39.9543 −1.55640 −0.778198 0.628019i \(-0.783866\pi\)
−0.778198 + 0.628019i \(0.783866\pi\)
\(660\) 0 0
\(661\) 39.7928 1.54776 0.773880 0.633332i \(-0.218313\pi\)
0.773880 + 0.633332i \(0.218313\pi\)
\(662\) 0 0
\(663\) −4.43618 −0.172287
\(664\) 0 0
\(665\) 45.3435 1.75835
\(666\) 0 0
\(667\) 21.9884 0.851395
\(668\) 0 0
\(669\) 0.711140 0.0274943
\(670\) 0 0
\(671\) 6.42514 0.248040
\(672\) 0 0
\(673\) 28.7641 1.10877 0.554387 0.832259i \(-0.312953\pi\)
0.554387 + 0.832259i \(0.312953\pi\)
\(674\) 0 0
\(675\) 32.6799 1.25785
\(676\) 0 0
\(677\) −37.2623 −1.43211 −0.716053 0.698046i \(-0.754053\pi\)
−0.716053 + 0.698046i \(0.754053\pi\)
\(678\) 0 0
\(679\) −37.7626 −1.44920
\(680\) 0 0
\(681\) 5.40236 0.207019
\(682\) 0 0
\(683\) −27.9895 −1.07099 −0.535493 0.844539i \(-0.679874\pi\)
−0.535493 + 0.844539i \(0.679874\pi\)
\(684\) 0 0
\(685\) 35.4320 1.35379
\(686\) 0 0
\(687\) −2.70054 −0.103032
\(688\) 0 0
\(689\) 1.44060 0.0548825
\(690\) 0 0
\(691\) 41.2535 1.56936 0.784679 0.619902i \(-0.212828\pi\)
0.784679 + 0.619902i \(0.212828\pi\)
\(692\) 0 0
\(693\) 10.0588 0.382102
\(694\) 0 0
\(695\) −48.3438 −1.83378
\(696\) 0 0
\(697\) 66.8329 2.53148
\(698\) 0 0
\(699\) −11.4825 −0.434308
\(700\) 0 0
\(701\) 25.1272 0.949041 0.474520 0.880245i \(-0.342622\pi\)
0.474520 + 0.880245i \(0.342622\pi\)
\(702\) 0 0
\(703\) 9.22271 0.347841
\(704\) 0 0
\(705\) −11.2363 −0.423184
\(706\) 0 0
\(707\) 53.3964 2.00818
\(708\) 0 0
\(709\) −15.7683 −0.592191 −0.296096 0.955158i \(-0.595685\pi\)
−0.296096 + 0.955158i \(0.595685\pi\)
\(710\) 0 0
\(711\) −15.5904 −0.584687
\(712\) 0 0
\(713\) 50.5259 1.89221
\(714\) 0 0
\(715\) 3.87520 0.144924
\(716\) 0 0
\(717\) −8.78178 −0.327962
\(718\) 0 0
\(719\) 41.9447 1.56427 0.782137 0.623106i \(-0.214129\pi\)
0.782137 + 0.623106i \(0.214129\pi\)
\(720\) 0 0
\(721\) 25.3739 0.944975
\(722\) 0 0
\(723\) −2.01506 −0.0749409
\(724\) 0 0
\(725\) −38.2171 −1.41935
\(726\) 0 0
\(727\) −28.4589 −1.05548 −0.527742 0.849405i \(-0.676961\pi\)
−0.527742 + 0.849405i \(0.676961\pi\)
\(728\) 0 0
\(729\) −5.00877 −0.185510
\(730\) 0 0
\(731\) 2.78000 0.102822
\(732\) 0 0
\(733\) −20.6873 −0.764102 −0.382051 0.924141i \(-0.624782\pi\)
−0.382051 + 0.924141i \(0.624782\pi\)
\(734\) 0 0
\(735\) −12.6462 −0.466463
\(736\) 0 0
\(737\) −0.0247683 −0.000912351 0
\(738\) 0 0
\(739\) −40.7104 −1.49756 −0.748778 0.662820i \(-0.769359\pi\)
−0.748778 + 0.662820i \(0.769359\pi\)
\(740\) 0 0
\(741\) 2.21253 0.0812793
\(742\) 0 0
\(743\) 26.9510 0.988735 0.494368 0.869253i \(-0.335400\pi\)
0.494368 + 0.869253i \(0.335400\pi\)
\(744\) 0 0
\(745\) −28.5064 −1.04439
\(746\) 0 0
\(747\) −0.218540 −0.00799597
\(748\) 0 0
\(749\) 2.76506 0.101033
\(750\) 0 0
\(751\) 19.2460 0.702298 0.351149 0.936320i \(-0.385791\pi\)
0.351149 + 0.936320i \(0.385791\pi\)
\(752\) 0 0
\(753\) 16.2356 0.591659
\(754\) 0 0
\(755\) 22.8787 0.832642
\(756\) 0 0
\(757\) −20.0449 −0.728544 −0.364272 0.931293i \(-0.618682\pi\)
−0.364272 + 0.931293i \(0.618682\pi\)
\(758\) 0 0
\(759\) −3.88991 −0.141195
\(760\) 0 0
\(761\) 11.9482 0.433120 0.216560 0.976269i \(-0.430516\pi\)
0.216560 + 0.976269i \(0.430516\pi\)
\(762\) 0 0
\(763\) −55.8940 −2.02350
\(764\) 0 0
\(765\) 66.4719 2.40330
\(766\) 0 0
\(767\) −2.94180 −0.106222
\(768\) 0 0
\(769\) −11.7469 −0.423603 −0.211802 0.977313i \(-0.567933\pi\)
−0.211802 + 0.977313i \(0.567933\pi\)
\(770\) 0 0
\(771\) −12.8578 −0.463064
\(772\) 0 0
\(773\) 29.6378 1.06600 0.532999 0.846116i \(-0.321065\pi\)
0.532999 + 0.846116i \(0.321065\pi\)
\(774\) 0 0
\(775\) −87.8169 −3.15448
\(776\) 0 0
\(777\) −6.16200 −0.221060
\(778\) 0 0
\(779\) −33.3327 −1.19427
\(780\) 0 0
\(781\) −1.71724 −0.0614475
\(782\) 0 0
\(783\) −16.6772 −0.595996
\(784\) 0 0
\(785\) −61.5593 −2.19714
\(786\) 0 0
\(787\) −5.52019 −0.196774 −0.0983868 0.995148i \(-0.531368\pi\)
−0.0983868 + 0.995148i \(0.531368\pi\)
\(788\) 0 0
\(789\) −9.80656 −0.349123
\(790\) 0 0
\(791\) −25.1195 −0.893148
\(792\) 0 0
\(793\) 5.13998 0.182526
\(794\) 0 0
\(795\) 3.96552 0.140642
\(796\) 0 0
\(797\) −7.83445 −0.277511 −0.138755 0.990327i \(-0.544310\pi\)
−0.138755 + 0.990327i \(0.544310\pi\)
\(798\) 0 0
\(799\) −31.6322 −1.11907
\(800\) 0 0
\(801\) 42.7741 1.51135
\(802\) 0 0
\(803\) 14.6562 0.517207
\(804\) 0 0
\(805\) −63.7741 −2.24774
\(806\) 0 0
\(807\) −18.1389 −0.638521
\(808\) 0 0
\(809\) 0.983806 0.0345888 0.0172944 0.999850i \(-0.494495\pi\)
0.0172944 + 0.999850i \(0.494495\pi\)
\(810\) 0 0
\(811\) 39.8528 1.39942 0.699710 0.714427i \(-0.253313\pi\)
0.699710 + 0.714427i \(0.253313\pi\)
\(812\) 0 0
\(813\) −2.81069 −0.0985752
\(814\) 0 0
\(815\) −3.75332 −0.131473
\(816\) 0 0
\(817\) −1.38651 −0.0485080
\(818\) 0 0
\(819\) 8.04681 0.281178
\(820\) 0 0
\(821\) 2.19951 0.0767634 0.0383817 0.999263i \(-0.487780\pi\)
0.0383817 + 0.999263i \(0.487780\pi\)
\(822\) 0 0
\(823\) −4.01532 −0.139965 −0.0699825 0.997548i \(-0.522294\pi\)
−0.0699825 + 0.997548i \(0.522294\pi\)
\(824\) 0 0
\(825\) 6.76090 0.235384
\(826\) 0 0
\(827\) 9.44160 0.328317 0.164158 0.986434i \(-0.447509\pi\)
0.164158 + 0.986434i \(0.447509\pi\)
\(828\) 0 0
\(829\) 43.4870 1.51036 0.755182 0.655515i \(-0.227548\pi\)
0.755182 + 0.655515i \(0.227548\pi\)
\(830\) 0 0
\(831\) 17.8142 0.617967
\(832\) 0 0
\(833\) −35.6013 −1.23351
\(834\) 0 0
\(835\) 68.5144 2.37104
\(836\) 0 0
\(837\) −38.3217 −1.32459
\(838\) 0 0
\(839\) −31.1893 −1.07677 −0.538387 0.842698i \(-0.680966\pi\)
−0.538387 + 0.842698i \(0.680966\pi\)
\(840\) 0 0
\(841\) −9.49700 −0.327483
\(842\) 0 0
\(843\) −2.71400 −0.0934751
\(844\) 0 0
\(845\) −44.9363 −1.54586
\(846\) 0 0
\(847\) −33.5858 −1.15402
\(848\) 0 0
\(849\) 7.17507 0.246248
\(850\) 0 0
\(851\) −12.9714 −0.444655
\(852\) 0 0
\(853\) −0.320054 −0.0109584 −0.00547922 0.999985i \(-0.501744\pi\)
−0.00547922 + 0.999985i \(0.501744\pi\)
\(854\) 0 0
\(855\) −33.1526 −1.13379
\(856\) 0 0
\(857\) −28.8466 −0.985381 −0.492690 0.870205i \(-0.663987\pi\)
−0.492690 + 0.870205i \(0.663987\pi\)
\(858\) 0 0
\(859\) −37.0112 −1.26281 −0.631403 0.775455i \(-0.717520\pi\)
−0.631403 + 0.775455i \(0.717520\pi\)
\(860\) 0 0
\(861\) 22.2707 0.758983
\(862\) 0 0
\(863\) 8.39353 0.285719 0.142859 0.989743i \(-0.454370\pi\)
0.142859 + 0.989743i \(0.454370\pi\)
\(864\) 0 0
\(865\) 72.0732 2.45056
\(866\) 0 0
\(867\) −22.7774 −0.773562
\(868\) 0 0
\(869\) −7.04330 −0.238927
\(870\) 0 0
\(871\) −0.0198141 −0.000671375 0
\(872\) 0 0
\(873\) 27.6099 0.934452
\(874\) 0 0
\(875\) 46.8001 1.58213
\(876\) 0 0
\(877\) 29.5901 0.999186 0.499593 0.866260i \(-0.333483\pi\)
0.499593 + 0.866260i \(0.333483\pi\)
\(878\) 0 0
\(879\) −17.0248 −0.574231
\(880\) 0 0
\(881\) 17.3917 0.585943 0.292971 0.956121i \(-0.405356\pi\)
0.292971 + 0.956121i \(0.405356\pi\)
\(882\) 0 0
\(883\) 11.4133 0.384090 0.192045 0.981386i \(-0.438488\pi\)
0.192045 + 0.981386i \(0.438488\pi\)
\(884\) 0 0
\(885\) −8.09785 −0.272206
\(886\) 0 0
\(887\) −41.5424 −1.39486 −0.697428 0.716654i \(-0.745672\pi\)
−0.697428 + 0.716654i \(0.745672\pi\)
\(888\) 0 0
\(889\) −69.9438 −2.34584
\(890\) 0 0
\(891\) −5.75514 −0.192805
\(892\) 0 0
\(893\) 15.7764 0.527938
\(894\) 0 0
\(895\) 75.0810 2.50968
\(896\) 0 0
\(897\) −3.11185 −0.103902
\(898\) 0 0
\(899\) 44.8148 1.49466
\(900\) 0 0
\(901\) 11.1636 0.371914
\(902\) 0 0
\(903\) 0.926377 0.0308279
\(904\) 0 0
\(905\) 42.1568 1.40134
\(906\) 0 0
\(907\) −27.9945 −0.929542 −0.464771 0.885431i \(-0.653863\pi\)
−0.464771 + 0.885431i \(0.653863\pi\)
\(908\) 0 0
\(909\) −39.0404 −1.29489
\(910\) 0 0
\(911\) −43.1485 −1.42957 −0.714787 0.699342i \(-0.753477\pi\)
−0.714787 + 0.699342i \(0.753477\pi\)
\(912\) 0 0
\(913\) −0.0987301 −0.00326749
\(914\) 0 0
\(915\) 14.1487 0.467743
\(916\) 0 0
\(917\) 7.54930 0.249300
\(918\) 0 0
\(919\) 52.2680 1.72416 0.862082 0.506769i \(-0.169160\pi\)
0.862082 + 0.506769i \(0.169160\pi\)
\(920\) 0 0
\(921\) 0.424250 0.0139795
\(922\) 0 0
\(923\) −1.37375 −0.0452176
\(924\) 0 0
\(925\) 22.5451 0.741277
\(926\) 0 0
\(927\) −18.5520 −0.609326
\(928\) 0 0
\(929\) −30.0632 −0.986341 −0.493171 0.869933i \(-0.664162\pi\)
−0.493171 + 0.869933i \(0.664162\pi\)
\(930\) 0 0
\(931\) 17.7560 0.581930
\(932\) 0 0
\(933\) −14.2284 −0.465817
\(934\) 0 0
\(935\) 30.0300 0.982087
\(936\) 0 0
\(937\) 23.9857 0.783579 0.391789 0.920055i \(-0.371856\pi\)
0.391789 + 0.920055i \(0.371856\pi\)
\(938\) 0 0
\(939\) −17.3872 −0.567408
\(940\) 0 0
\(941\) −13.9444 −0.454573 −0.227287 0.973828i \(-0.572985\pi\)
−0.227287 + 0.973828i \(0.572985\pi\)
\(942\) 0 0
\(943\) 46.8813 1.52666
\(944\) 0 0
\(945\) 48.3699 1.57347
\(946\) 0 0
\(947\) −26.9833 −0.876840 −0.438420 0.898770i \(-0.644462\pi\)
−0.438420 + 0.898770i \(0.644462\pi\)
\(948\) 0 0
\(949\) 11.7247 0.380599
\(950\) 0 0
\(951\) 4.13422 0.134061
\(952\) 0 0
\(953\) −24.0311 −0.778444 −0.389222 0.921144i \(-0.627256\pi\)
−0.389222 + 0.921144i \(0.627256\pi\)
\(954\) 0 0
\(955\) −52.8787 −1.71111
\(956\) 0 0
\(957\) −3.45023 −0.111530
\(958\) 0 0
\(959\) 33.2386 1.07333
\(960\) 0 0
\(961\) 71.9773 2.32185
\(962\) 0 0
\(963\) −2.02165 −0.0651467
\(964\) 0 0
\(965\) 16.9854 0.546778
\(966\) 0 0
\(967\) 49.3261 1.58622 0.793110 0.609079i \(-0.208461\pi\)
0.793110 + 0.609079i \(0.208461\pi\)
\(968\) 0 0
\(969\) 17.1455 0.550794
\(970\) 0 0
\(971\) −46.6947 −1.49851 −0.749253 0.662284i \(-0.769587\pi\)
−0.749253 + 0.662284i \(0.769587\pi\)
\(972\) 0 0
\(973\) −45.3511 −1.45389
\(974\) 0 0
\(975\) 5.40857 0.173213
\(976\) 0 0
\(977\) −21.8052 −0.697610 −0.348805 0.937195i \(-0.613412\pi\)
−0.348805 + 0.937195i \(0.613412\pi\)
\(978\) 0 0
\(979\) 19.3241 0.617600
\(980\) 0 0
\(981\) 40.8665 1.30477
\(982\) 0 0
\(983\) 13.9597 0.445245 0.222623 0.974905i \(-0.428538\pi\)
0.222623 + 0.974905i \(0.428538\pi\)
\(984\) 0 0
\(985\) 67.5527 2.15241
\(986\) 0 0
\(987\) −10.5408 −0.335516
\(988\) 0 0
\(989\) 1.95009 0.0620091
\(990\) 0 0
\(991\) 42.9004 1.36278 0.681389 0.731922i \(-0.261376\pi\)
0.681389 + 0.731922i \(0.261376\pi\)
\(992\) 0 0
\(993\) 18.1756 0.576787
\(994\) 0 0
\(995\) 44.5382 1.41196
\(996\) 0 0
\(997\) −0.122631 −0.00388375 −0.00194187 0.999998i \(-0.500618\pi\)
−0.00194187 + 0.999998i \(0.500618\pi\)
\(998\) 0 0
\(999\) 9.83826 0.311269
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 \(a_p\))