Properties

Label 8008.2.a.k.1.2
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.244558277.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.50454\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.50454 q^{3}\) \(-3.40126 q^{5}\) \(+1.00000 q^{7}\) \(+3.27272 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.50454 q^{3}\) \(-3.40126 q^{5}\) \(+1.00000 q^{7}\) \(+3.27272 q^{9}\) \(-1.00000 q^{11}\) \(-1.00000 q^{13}\) \(+8.51859 q^{15}\) \(+4.74921 q^{17}\) \(+6.83057 q^{19}\) \(-2.50454 q^{21}\) \(+4.61279 q^{23}\) \(+6.56857 q^{25}\) \(-0.683051 q^{27}\) \(+5.06403 q^{29}\) \(+3.54877 q^{31}\) \(+2.50454 q^{33}\) \(-3.40126 q^{35}\) \(-6.49334 q^{37}\) \(+2.50454 q^{39}\) \(-1.94505 q^{41}\) \(-3.11733 q^{43}\) \(-11.1314 q^{45}\) \(+3.72893 q^{47}\) \(+1.00000 q^{49}\) \(-11.8946 q^{51}\) \(+2.20492 q^{53}\) \(+3.40126 q^{55}\) \(-17.1074 q^{57}\) \(-7.10214 q^{59}\) \(+3.05283 q^{61}\) \(+3.27272 q^{63}\) \(+3.40126 q^{65}\) \(-9.11450 q^{67}\) \(-11.5529 q^{69}\) \(-4.73636 q^{71}\) \(+2.08595 q^{73}\) \(-16.4513 q^{75}\) \(-1.00000 q^{77}\) \(-8.96819 q^{79}\) \(-8.10745 q^{81}\) \(+13.9901 q^{83}\) \(-16.1533 q^{85}\) \(-12.6831 q^{87}\) \(+8.62399 q^{89}\) \(-1.00000 q^{91}\) \(-8.88803 q^{93}\) \(-23.2326 q^{95}\) \(+3.09042 q^{97}\) \(-3.27272 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut +\mathstrut 29q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 42q^{81} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 46q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 55q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 41q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.50454 −1.44600 −0.722999 0.690849i \(-0.757237\pi\)
−0.722999 + 0.690849i \(0.757237\pi\)
\(4\) 0 0
\(5\) −3.40126 −1.52109 −0.760545 0.649285i \(-0.775068\pi\)
−0.760545 + 0.649285i \(0.775068\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 3.27272 1.09091
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 8.51859 2.19949
\(16\) 0 0
\(17\) 4.74921 1.15185 0.575927 0.817501i \(-0.304641\pi\)
0.575927 + 0.817501i \(0.304641\pi\)
\(18\) 0 0
\(19\) 6.83057 1.56704 0.783520 0.621366i \(-0.213422\pi\)
0.783520 + 0.621366i \(0.213422\pi\)
\(20\) 0 0
\(21\) −2.50454 −0.546536
\(22\) 0 0
\(23\) 4.61279 0.961834 0.480917 0.876766i \(-0.340304\pi\)
0.480917 + 0.876766i \(0.340304\pi\)
\(24\) 0 0
\(25\) 6.56857 1.31371
\(26\) 0 0
\(27\) −0.683051 −0.131453
\(28\) 0 0
\(29\) 5.06403 0.940367 0.470183 0.882569i \(-0.344188\pi\)
0.470183 + 0.882569i \(0.344188\pi\)
\(30\) 0 0
\(31\) 3.54877 0.637377 0.318689 0.947859i \(-0.396758\pi\)
0.318689 + 0.947859i \(0.396758\pi\)
\(32\) 0 0
\(33\) 2.50454 0.435985
\(34\) 0 0
\(35\) −3.40126 −0.574918
\(36\) 0 0
\(37\) −6.49334 −1.06750 −0.533749 0.845643i \(-0.679217\pi\)
−0.533749 + 0.845643i \(0.679217\pi\)
\(38\) 0 0
\(39\) 2.50454 0.401048
\(40\) 0 0
\(41\) −1.94505 −0.303766 −0.151883 0.988398i \(-0.548534\pi\)
−0.151883 + 0.988398i \(0.548534\pi\)
\(42\) 0 0
\(43\) −3.11733 −0.475389 −0.237695 0.971340i \(-0.576392\pi\)
−0.237695 + 0.971340i \(0.576392\pi\)
\(44\) 0 0
\(45\) −11.1314 −1.65937
\(46\) 0 0
\(47\) 3.72893 0.543921 0.271960 0.962308i \(-0.412328\pi\)
0.271960 + 0.962308i \(0.412328\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −11.8946 −1.66558
\(52\) 0 0
\(53\) 2.20492 0.302869 0.151435 0.988467i \(-0.451611\pi\)
0.151435 + 0.988467i \(0.451611\pi\)
\(54\) 0 0
\(55\) 3.40126 0.458626
\(56\) 0 0
\(57\) −17.1074 −2.26594
\(58\) 0 0
\(59\) −7.10214 −0.924620 −0.462310 0.886718i \(-0.652979\pi\)
−0.462310 + 0.886718i \(0.652979\pi\)
\(60\) 0 0
\(61\) 3.05283 0.390875 0.195437 0.980716i \(-0.437387\pi\)
0.195437 + 0.980716i \(0.437387\pi\)
\(62\) 0 0
\(63\) 3.27272 0.412325
\(64\) 0 0
\(65\) 3.40126 0.421874
\(66\) 0 0
\(67\) −9.11450 −1.11351 −0.556757 0.830676i \(-0.687954\pi\)
−0.556757 + 0.830676i \(0.687954\pi\)
\(68\) 0 0
\(69\) −11.5529 −1.39081
\(70\) 0 0
\(71\) −4.73636 −0.562102 −0.281051 0.959693i \(-0.590683\pi\)
−0.281051 + 0.959693i \(0.590683\pi\)
\(72\) 0 0
\(73\) 2.08595 0.244142 0.122071 0.992521i \(-0.461046\pi\)
0.122071 + 0.992521i \(0.461046\pi\)
\(74\) 0 0
\(75\) −16.4513 −1.89963
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) −8.96819 −1.00900 −0.504500 0.863412i \(-0.668323\pi\)
−0.504500 + 0.863412i \(0.668323\pi\)
\(80\) 0 0
\(81\) −8.10745 −0.900827
\(82\) 0 0
\(83\) 13.9901 1.53561 0.767807 0.640681i \(-0.221348\pi\)
0.767807 + 0.640681i \(0.221348\pi\)
\(84\) 0 0
\(85\) −16.1533 −1.75207
\(86\) 0 0
\(87\) −12.6831 −1.35977
\(88\) 0 0
\(89\) 8.62399 0.914142 0.457071 0.889430i \(-0.348899\pi\)
0.457071 + 0.889430i \(0.348899\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −8.88803 −0.921645
\(94\) 0 0
\(95\) −23.2326 −2.38361
\(96\) 0 0
\(97\) 3.09042 0.313785 0.156892 0.987616i \(-0.449852\pi\)
0.156892 + 0.987616i \(0.449852\pi\)
\(98\) 0 0
\(99\) −3.27272 −0.328921
\(100\) 0 0
\(101\) 5.86205 0.583296 0.291648 0.956526i \(-0.405796\pi\)
0.291648 + 0.956526i \(0.405796\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) 8.51859 0.831330
\(106\) 0 0
\(107\) −4.01980 −0.388609 −0.194305 0.980941i \(-0.562245\pi\)
−0.194305 + 0.980941i \(0.562245\pi\)
\(108\) 0 0
\(109\) 5.89460 0.564600 0.282300 0.959326i \(-0.408903\pi\)
0.282300 + 0.959326i \(0.408903\pi\)
\(110\) 0 0
\(111\) 16.2628 1.54360
\(112\) 0 0
\(113\) −0.216621 −0.0203780 −0.0101890 0.999948i \(-0.503243\pi\)
−0.0101890 + 0.999948i \(0.503243\pi\)
\(114\) 0 0
\(115\) −15.6893 −1.46304
\(116\) 0 0
\(117\) −3.27272 −0.302564
\(118\) 0 0
\(119\) 4.74921 0.435360
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 4.87146 0.439245
\(124\) 0 0
\(125\) −5.33511 −0.477187
\(126\) 0 0
\(127\) −9.75255 −0.865398 −0.432699 0.901538i \(-0.642439\pi\)
−0.432699 + 0.901538i \(0.642439\pi\)
\(128\) 0 0
\(129\) 7.80749 0.687411
\(130\) 0 0
\(131\) −10.4120 −0.909701 −0.454850 0.890568i \(-0.650307\pi\)
−0.454850 + 0.890568i \(0.650307\pi\)
\(132\) 0 0
\(133\) 6.83057 0.592286
\(134\) 0 0
\(135\) 2.32323 0.199952
\(136\) 0 0
\(137\) 9.54877 0.815806 0.407903 0.913025i \(-0.366260\pi\)
0.407903 + 0.913025i \(0.366260\pi\)
\(138\) 0 0
\(139\) 3.79344 0.321755 0.160878 0.986974i \(-0.448568\pi\)
0.160878 + 0.986974i \(0.448568\pi\)
\(140\) 0 0
\(141\) −9.33926 −0.786508
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −17.2241 −1.43038
\(146\) 0 0
\(147\) −2.50454 −0.206571
\(148\) 0 0
\(149\) −11.9128 −0.975932 −0.487966 0.872863i \(-0.662261\pi\)
−0.487966 + 0.872863i \(0.662261\pi\)
\(150\) 0 0
\(151\) 2.72691 0.221913 0.110957 0.993825i \(-0.464609\pi\)
0.110957 + 0.993825i \(0.464609\pi\)
\(152\) 0 0
\(153\) 15.5429 1.25657
\(154\) 0 0
\(155\) −12.0703 −0.969508
\(156\) 0 0
\(157\) −16.6826 −1.33142 −0.665709 0.746211i \(-0.731871\pi\)
−0.665709 + 0.746211i \(0.731871\pi\)
\(158\) 0 0
\(159\) −5.52231 −0.437948
\(160\) 0 0
\(161\) 4.61279 0.363539
\(162\) 0 0
\(163\) −0.436737 −0.0342079 −0.0171039 0.999854i \(-0.505445\pi\)
−0.0171039 + 0.999854i \(0.505445\pi\)
\(164\) 0 0
\(165\) −8.51859 −0.663172
\(166\) 0 0
\(167\) 15.7177 1.21627 0.608137 0.793832i \(-0.291917\pi\)
0.608137 + 0.793832i \(0.291917\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 22.3546 1.70950
\(172\) 0 0
\(173\) 14.8487 1.12893 0.564464 0.825458i \(-0.309083\pi\)
0.564464 + 0.825458i \(0.309083\pi\)
\(174\) 0 0
\(175\) 6.56857 0.496537
\(176\) 0 0
\(177\) 17.7876 1.33700
\(178\) 0 0
\(179\) −21.9789 −1.64278 −0.821391 0.570365i \(-0.806802\pi\)
−0.821391 + 0.570365i \(0.806802\pi\)
\(180\) 0 0
\(181\) −1.68399 −0.125170 −0.0625849 0.998040i \(-0.519934\pi\)
−0.0625849 + 0.998040i \(0.519934\pi\)
\(182\) 0 0
\(183\) −7.64593 −0.565204
\(184\) 0 0
\(185\) 22.0855 1.62376
\(186\) 0 0
\(187\) −4.74921 −0.347297
\(188\) 0 0
\(189\) −0.683051 −0.0496846
\(190\) 0 0
\(191\) 22.2190 1.60771 0.803855 0.594825i \(-0.202779\pi\)
0.803855 + 0.594825i \(0.202779\pi\)
\(192\) 0 0
\(193\) −6.53425 −0.470346 −0.235173 0.971954i \(-0.575566\pi\)
−0.235173 + 0.971954i \(0.575566\pi\)
\(194\) 0 0
\(195\) −8.51859 −0.610029
\(196\) 0 0
\(197\) 3.53473 0.251839 0.125919 0.992040i \(-0.459812\pi\)
0.125919 + 0.992040i \(0.459812\pi\)
\(198\) 0 0
\(199\) 0.268731 0.0190498 0.00952491 0.999955i \(-0.496968\pi\)
0.00952491 + 0.999955i \(0.496968\pi\)
\(200\) 0 0
\(201\) 22.8276 1.61014
\(202\) 0 0
\(203\) 5.06403 0.355425
\(204\) 0 0
\(205\) 6.61563 0.462056
\(206\) 0 0
\(207\) 15.0964 1.04927
\(208\) 0 0
\(209\) −6.83057 −0.472481
\(210\) 0 0
\(211\) −24.7257 −1.70218 −0.851092 0.525016i \(-0.824059\pi\)
−0.851092 + 0.525016i \(0.824059\pi\)
\(212\) 0 0
\(213\) 11.8624 0.812798
\(214\) 0 0
\(215\) 10.6029 0.723109
\(216\) 0 0
\(217\) 3.54877 0.240906
\(218\) 0 0
\(219\) −5.22435 −0.353029
\(220\) 0 0
\(221\) −4.74921 −0.319467
\(222\) 0 0
\(223\) 11.2239 0.751608 0.375804 0.926699i \(-0.377367\pi\)
0.375804 + 0.926699i \(0.377367\pi\)
\(224\) 0 0
\(225\) 21.4971 1.43314
\(226\) 0 0
\(227\) 4.36710 0.289854 0.144927 0.989442i \(-0.453705\pi\)
0.144927 + 0.989442i \(0.453705\pi\)
\(228\) 0 0
\(229\) 25.3914 1.67791 0.838956 0.544199i \(-0.183166\pi\)
0.838956 + 0.544199i \(0.183166\pi\)
\(230\) 0 0
\(231\) 2.50454 0.164787
\(232\) 0 0
\(233\) 4.39913 0.288196 0.144098 0.989563i \(-0.453972\pi\)
0.144098 + 0.989563i \(0.453972\pi\)
\(234\) 0 0
\(235\) −12.6831 −0.827352
\(236\) 0 0
\(237\) 22.4612 1.45901
\(238\) 0 0
\(239\) −13.3408 −0.862945 −0.431472 0.902126i \(-0.642006\pi\)
−0.431472 + 0.902126i \(0.642006\pi\)
\(240\) 0 0
\(241\) 12.3475 0.795372 0.397686 0.917522i \(-0.369813\pi\)
0.397686 + 0.917522i \(0.369813\pi\)
\(242\) 0 0
\(243\) 22.3546 1.43405
\(244\) 0 0
\(245\) −3.40126 −0.217299
\(246\) 0 0
\(247\) −6.83057 −0.434619
\(248\) 0 0
\(249\) −35.0388 −2.22049
\(250\) 0 0
\(251\) −14.6268 −0.923238 −0.461619 0.887078i \(-0.652731\pi\)
−0.461619 + 0.887078i \(0.652731\pi\)
\(252\) 0 0
\(253\) −4.61279 −0.290004
\(254\) 0 0
\(255\) 40.4566 2.53349
\(256\) 0 0
\(257\) −14.6285 −0.912501 −0.456251 0.889851i \(-0.650808\pi\)
−0.456251 + 0.889851i \(0.650808\pi\)
\(258\) 0 0
\(259\) −6.49334 −0.403477
\(260\) 0 0
\(261\) 16.5732 1.02585
\(262\) 0 0
\(263\) 2.40458 0.148272 0.0741362 0.997248i \(-0.476380\pi\)
0.0741362 + 0.997248i \(0.476380\pi\)
\(264\) 0 0
\(265\) −7.49951 −0.460691
\(266\) 0 0
\(267\) −21.5991 −1.32185
\(268\) 0 0
\(269\) −6.60040 −0.402433 −0.201217 0.979547i \(-0.564490\pi\)
−0.201217 + 0.979547i \(0.564490\pi\)
\(270\) 0 0
\(271\) −13.1119 −0.796494 −0.398247 0.917278i \(-0.630381\pi\)
−0.398247 + 0.917278i \(0.630381\pi\)
\(272\) 0 0
\(273\) 2.50454 0.151582
\(274\) 0 0
\(275\) −6.56857 −0.396100
\(276\) 0 0
\(277\) −15.1888 −0.912607 −0.456303 0.889824i \(-0.650827\pi\)
−0.456303 + 0.889824i \(0.650827\pi\)
\(278\) 0 0
\(279\) 11.6141 0.695320
\(280\) 0 0
\(281\) 25.0642 1.49520 0.747601 0.664148i \(-0.231205\pi\)
0.747601 + 0.664148i \(0.231205\pi\)
\(282\) 0 0
\(283\) −30.5239 −1.81446 −0.907229 0.420638i \(-0.861806\pi\)
−0.907229 + 0.420638i \(0.861806\pi\)
\(284\) 0 0
\(285\) 58.1869 3.44669
\(286\) 0 0
\(287\) −1.94505 −0.114813
\(288\) 0 0
\(289\) 5.55503 0.326767
\(290\) 0 0
\(291\) −7.74009 −0.453732
\(292\) 0 0
\(293\) 21.9785 1.28399 0.641997 0.766707i \(-0.278106\pi\)
0.641997 + 0.766707i \(0.278106\pi\)
\(294\) 0 0
\(295\) 24.1562 1.40643
\(296\) 0 0
\(297\) 0.683051 0.0396346
\(298\) 0 0
\(299\) −4.61279 −0.266765
\(300\) 0 0
\(301\) −3.11733 −0.179680
\(302\) 0 0
\(303\) −14.6818 −0.843445
\(304\) 0 0
\(305\) −10.3835 −0.594555
\(306\) 0 0
\(307\) 6.13713 0.350265 0.175132 0.984545i \(-0.443965\pi\)
0.175132 + 0.984545i \(0.443965\pi\)
\(308\) 0 0
\(309\) −20.0363 −1.13983
\(310\) 0 0
\(311\) −15.4644 −0.876904 −0.438452 0.898755i \(-0.644473\pi\)
−0.438452 + 0.898755i \(0.644473\pi\)
\(312\) 0 0
\(313\) −7.61948 −0.430679 −0.215339 0.976539i \(-0.569086\pi\)
−0.215339 + 0.976539i \(0.569086\pi\)
\(314\) 0 0
\(315\) −11.1314 −0.627183
\(316\) 0 0
\(317\) 29.9807 1.68388 0.841942 0.539568i \(-0.181412\pi\)
0.841942 + 0.539568i \(0.181412\pi\)
\(318\) 0 0
\(319\) −5.06403 −0.283531
\(320\) 0 0
\(321\) 10.0678 0.561928
\(322\) 0 0
\(323\) 32.4398 1.80500
\(324\) 0 0
\(325\) −6.56857 −0.364359
\(326\) 0 0
\(327\) −14.7633 −0.816411
\(328\) 0 0
\(329\) 3.72893 0.205583
\(330\) 0 0
\(331\) 18.8728 1.03735 0.518673 0.854973i \(-0.326426\pi\)
0.518673 + 0.854973i \(0.326426\pi\)
\(332\) 0 0
\(333\) −21.2509 −1.16454
\(334\) 0 0
\(335\) 31.0008 1.69375
\(336\) 0 0
\(337\) 20.5367 1.11871 0.559354 0.828929i \(-0.311049\pi\)
0.559354 + 0.828929i \(0.311049\pi\)
\(338\) 0 0
\(339\) 0.542537 0.0294666
\(340\) 0 0
\(341\) −3.54877 −0.192176
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 39.2945 2.11555
\(346\) 0 0
\(347\) 13.6848 0.734636 0.367318 0.930095i \(-0.380276\pi\)
0.367318 + 0.930095i \(0.380276\pi\)
\(348\) 0 0
\(349\) −20.4422 −1.09425 −0.547123 0.837052i \(-0.684277\pi\)
−0.547123 + 0.837052i \(0.684277\pi\)
\(350\) 0 0
\(351\) 0.683051 0.0364586
\(352\) 0 0
\(353\) −21.2096 −1.12887 −0.564437 0.825476i \(-0.690907\pi\)
−0.564437 + 0.825476i \(0.690907\pi\)
\(354\) 0 0
\(355\) 16.1096 0.855008
\(356\) 0 0
\(357\) −11.8946 −0.629529
\(358\) 0 0
\(359\) 32.2260 1.70082 0.850411 0.526118i \(-0.176353\pi\)
0.850411 + 0.526118i \(0.176353\pi\)
\(360\) 0 0
\(361\) 27.6567 1.45562
\(362\) 0 0
\(363\) −2.50454 −0.131454
\(364\) 0 0
\(365\) −7.09486 −0.371362
\(366\) 0 0
\(367\) 1.03712 0.0541371 0.0270686 0.999634i \(-0.491383\pi\)
0.0270686 + 0.999634i \(0.491383\pi\)
\(368\) 0 0
\(369\) −6.36562 −0.331381
\(370\) 0 0
\(371\) 2.20492 0.114474
\(372\) 0 0
\(373\) 29.5811 1.53165 0.765826 0.643048i \(-0.222331\pi\)
0.765826 + 0.643048i \(0.222331\pi\)
\(374\) 0 0
\(375\) 13.3620 0.690011
\(376\) 0 0
\(377\) −5.06403 −0.260811
\(378\) 0 0
\(379\) −33.9666 −1.74475 −0.872373 0.488841i \(-0.837420\pi\)
−0.872373 + 0.488841i \(0.837420\pi\)
\(380\) 0 0
\(381\) 24.4256 1.25136
\(382\) 0 0
\(383\) −16.0491 −0.820071 −0.410036 0.912070i \(-0.634484\pi\)
−0.410036 + 0.912070i \(0.634484\pi\)
\(384\) 0 0
\(385\) 3.40126 0.173344
\(386\) 0 0
\(387\) −10.2022 −0.518606
\(388\) 0 0
\(389\) 27.8381 1.41145 0.705723 0.708488i \(-0.250622\pi\)
0.705723 + 0.708488i \(0.250622\pi\)
\(390\) 0 0
\(391\) 21.9071 1.10789
\(392\) 0 0
\(393\) 26.0773 1.31542
\(394\) 0 0
\(395\) 30.5031 1.53478
\(396\) 0 0
\(397\) 24.4662 1.22792 0.613961 0.789337i \(-0.289575\pi\)
0.613961 + 0.789337i \(0.289575\pi\)
\(398\) 0 0
\(399\) −17.1074 −0.856444
\(400\) 0 0
\(401\) 4.96408 0.247894 0.123947 0.992289i \(-0.460445\pi\)
0.123947 + 0.992289i \(0.460445\pi\)
\(402\) 0 0
\(403\) −3.54877 −0.176777
\(404\) 0 0
\(405\) 27.5755 1.37024
\(406\) 0 0
\(407\) 6.49334 0.321863
\(408\) 0 0
\(409\) 1.91251 0.0945674 0.0472837 0.998882i \(-0.484944\pi\)
0.0472837 + 0.998882i \(0.484944\pi\)
\(410\) 0 0
\(411\) −23.9153 −1.17965
\(412\) 0 0
\(413\) −7.10214 −0.349473
\(414\) 0 0
\(415\) −47.5840 −2.33581
\(416\) 0 0
\(417\) −9.50082 −0.465257
\(418\) 0 0
\(419\) −17.3762 −0.848882 −0.424441 0.905456i \(-0.639529\pi\)
−0.424441 + 0.905456i \(0.639529\pi\)
\(420\) 0 0
\(421\) −24.4971 −1.19391 −0.596957 0.802273i \(-0.703624\pi\)
−0.596957 + 0.802273i \(0.703624\pi\)
\(422\) 0 0
\(423\) 12.2038 0.593368
\(424\) 0 0
\(425\) 31.1955 1.51321
\(426\) 0 0
\(427\) 3.05283 0.147737
\(428\) 0 0
\(429\) −2.50454 −0.120920
\(430\) 0 0
\(431\) −27.8775 −1.34281 −0.671407 0.741089i \(-0.734310\pi\)
−0.671407 + 0.741089i \(0.734310\pi\)
\(432\) 0 0
\(433\) −32.2563 −1.55014 −0.775069 0.631877i \(-0.782285\pi\)
−0.775069 + 0.631877i \(0.782285\pi\)
\(434\) 0 0
\(435\) 43.1384 2.06833
\(436\) 0 0
\(437\) 31.5080 1.50723
\(438\) 0 0
\(439\) 16.4958 0.787301 0.393651 0.919260i \(-0.371212\pi\)
0.393651 + 0.919260i \(0.371212\pi\)
\(440\) 0 0
\(441\) 3.27272 0.155844
\(442\) 0 0
\(443\) −12.3952 −0.588912 −0.294456 0.955665i \(-0.595138\pi\)
−0.294456 + 0.955665i \(0.595138\pi\)
\(444\) 0 0
\(445\) −29.3324 −1.39049
\(446\) 0 0
\(447\) 29.8360 1.41119
\(448\) 0 0
\(449\) 26.4891 1.25010 0.625049 0.780585i \(-0.285079\pi\)
0.625049 + 0.780585i \(0.285079\pi\)
\(450\) 0 0
\(451\) 1.94505 0.0915890
\(452\) 0 0
\(453\) −6.82966 −0.320886
\(454\) 0 0
\(455\) 3.40126 0.159454
\(456\) 0 0
\(457\) −20.8706 −0.976284 −0.488142 0.872764i \(-0.662325\pi\)
−0.488142 + 0.872764i \(0.662325\pi\)
\(458\) 0 0
\(459\) −3.24395 −0.151415
\(460\) 0 0
\(461\) −11.7483 −0.547171 −0.273585 0.961848i \(-0.588210\pi\)
−0.273585 + 0.961848i \(0.588210\pi\)
\(462\) 0 0
\(463\) 6.97159 0.323997 0.161999 0.986791i \(-0.448206\pi\)
0.161999 + 0.986791i \(0.448206\pi\)
\(464\) 0 0
\(465\) 30.2305 1.40191
\(466\) 0 0
\(467\) −3.51362 −0.162591 −0.0812955 0.996690i \(-0.525906\pi\)
−0.0812955 + 0.996690i \(0.525906\pi\)
\(468\) 0 0
\(469\) −9.11450 −0.420868
\(470\) 0 0
\(471\) 41.7823 1.92523
\(472\) 0 0
\(473\) 3.11733 0.143335
\(474\) 0 0
\(475\) 44.8671 2.05864
\(476\) 0 0
\(477\) 7.21610 0.330402
\(478\) 0 0
\(479\) −10.8321 −0.494932 −0.247466 0.968897i \(-0.579598\pi\)
−0.247466 + 0.968897i \(0.579598\pi\)
\(480\) 0 0
\(481\) 6.49334 0.296071
\(482\) 0 0
\(483\) −11.5529 −0.525677
\(484\) 0 0
\(485\) −10.5113 −0.477295
\(486\) 0 0
\(487\) 2.96237 0.134238 0.0671188 0.997745i \(-0.478619\pi\)
0.0671188 + 0.997745i \(0.478619\pi\)
\(488\) 0 0
\(489\) 1.09383 0.0494645
\(490\) 0 0
\(491\) 35.3620 1.59586 0.797932 0.602748i \(-0.205927\pi\)
0.797932 + 0.602748i \(0.205927\pi\)
\(492\) 0 0
\(493\) 24.0502 1.08316
\(494\) 0 0
\(495\) 11.1314 0.500319
\(496\) 0 0
\(497\) −4.73636 −0.212455
\(498\) 0 0
\(499\) 7.49035 0.335314 0.167657 0.985845i \(-0.446380\pi\)
0.167657 + 0.985845i \(0.446380\pi\)
\(500\) 0 0
\(501\) −39.3657 −1.75873
\(502\) 0 0
\(503\) 18.0239 0.803645 0.401822 0.915718i \(-0.368377\pi\)
0.401822 + 0.915718i \(0.368377\pi\)
\(504\) 0 0
\(505\) −19.9384 −0.887246
\(506\) 0 0
\(507\) −2.50454 −0.111231
\(508\) 0 0
\(509\) 24.6268 1.09156 0.545782 0.837927i \(-0.316233\pi\)
0.545782 + 0.837927i \(0.316233\pi\)
\(510\) 0 0
\(511\) 2.08595 0.0922771
\(512\) 0 0
\(513\) −4.66563 −0.205992
\(514\) 0 0
\(515\) −27.2101 −1.19902
\(516\) 0 0
\(517\) −3.72893 −0.163998
\(518\) 0 0
\(519\) −37.1893 −1.63243
\(520\) 0 0
\(521\) 16.1145 0.705989 0.352995 0.935625i \(-0.385163\pi\)
0.352995 + 0.935625i \(0.385163\pi\)
\(522\) 0 0
\(523\) 17.9776 0.786106 0.393053 0.919516i \(-0.371419\pi\)
0.393053 + 0.919516i \(0.371419\pi\)
\(524\) 0 0
\(525\) −16.4513 −0.717991
\(526\) 0 0
\(527\) 16.8538 0.734165
\(528\) 0 0
\(529\) −1.72213 −0.0748754
\(530\) 0 0
\(531\) −23.2434 −1.00868
\(532\) 0 0
\(533\) 1.94505 0.0842496
\(534\) 0 0
\(535\) 13.6724 0.591109
\(536\) 0 0
\(537\) 55.0471 2.37546
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 43.1662 1.85586 0.927931 0.372753i \(-0.121586\pi\)
0.927931 + 0.372753i \(0.121586\pi\)
\(542\) 0 0
\(543\) 4.21762 0.180995
\(544\) 0 0
\(545\) −20.0491 −0.858808
\(546\) 0 0
\(547\) −8.23891 −0.352270 −0.176135 0.984366i \(-0.556360\pi\)
−0.176135 + 0.984366i \(0.556360\pi\)
\(548\) 0 0
\(549\) 9.99107 0.426408
\(550\) 0 0
\(551\) 34.5902 1.47359
\(552\) 0 0
\(553\) −8.96819 −0.381366
\(554\) 0 0
\(555\) −55.3141 −2.34795
\(556\) 0 0
\(557\) −26.7434 −1.13315 −0.566577 0.824009i \(-0.691733\pi\)
−0.566577 + 0.824009i \(0.691733\pi\)
\(558\) 0 0
\(559\) 3.11733 0.131849
\(560\) 0 0
\(561\) 11.8946 0.502190
\(562\) 0 0
\(563\) −38.9277 −1.64061 −0.820303 0.571929i \(-0.806195\pi\)
−0.820303 + 0.571929i \(0.806195\pi\)
\(564\) 0 0
\(565\) 0.736785 0.0309968
\(566\) 0 0
\(567\) −8.10745 −0.340481
\(568\) 0 0
\(569\) 8.66753 0.363362 0.181681 0.983358i \(-0.441846\pi\)
0.181681 + 0.983358i \(0.441846\pi\)
\(570\) 0 0
\(571\) 14.5391 0.608443 0.304221 0.952601i \(-0.401604\pi\)
0.304221 + 0.952601i \(0.401604\pi\)
\(572\) 0 0
\(573\) −55.6484 −2.32474
\(574\) 0 0
\(575\) 30.2995 1.26357
\(576\) 0 0
\(577\) 26.1304 1.08782 0.543912 0.839143i \(-0.316943\pi\)
0.543912 + 0.839143i \(0.316943\pi\)
\(578\) 0 0
\(579\) 16.3653 0.680118
\(580\) 0 0
\(581\) 13.9901 0.580408
\(582\) 0 0
\(583\) −2.20492 −0.0913185
\(584\) 0 0
\(585\) 11.1314 0.460226
\(586\) 0 0
\(587\) 47.8062 1.97317 0.986587 0.163238i \(-0.0521939\pi\)
0.986587 + 0.163238i \(0.0521939\pi\)
\(588\) 0 0
\(589\) 24.2401 0.998796
\(590\) 0 0
\(591\) −8.85287 −0.364158
\(592\) 0 0
\(593\) 14.7336 0.605035 0.302518 0.953144i \(-0.402173\pi\)
0.302518 + 0.953144i \(0.402173\pi\)
\(594\) 0 0
\(595\) −16.1533 −0.662221
\(596\) 0 0
\(597\) −0.673047 −0.0275460
\(598\) 0 0
\(599\) −19.3876 −0.792155 −0.396077 0.918217i \(-0.629629\pi\)
−0.396077 + 0.918217i \(0.629629\pi\)
\(600\) 0 0
\(601\) 23.0650 0.940841 0.470421 0.882442i \(-0.344102\pi\)
0.470421 + 0.882442i \(0.344102\pi\)
\(602\) 0 0
\(603\) −29.8292 −1.21474
\(604\) 0 0
\(605\) −3.40126 −0.138281
\(606\) 0 0
\(607\) 23.6912 0.961596 0.480798 0.876831i \(-0.340347\pi\)
0.480798 + 0.876831i \(0.340347\pi\)
\(608\) 0 0
\(609\) −12.6831 −0.513944
\(610\) 0 0
\(611\) −3.72893 −0.150856
\(612\) 0 0
\(613\) 11.9990 0.484637 0.242318 0.970197i \(-0.422092\pi\)
0.242318 + 0.970197i \(0.422092\pi\)
\(614\) 0 0
\(615\) −16.5691 −0.668131
\(616\) 0 0
\(617\) 12.6930 0.511001 0.255501 0.966809i \(-0.417760\pi\)
0.255501 + 0.966809i \(0.417760\pi\)
\(618\) 0 0
\(619\) −30.1566 −1.21210 −0.606048 0.795428i \(-0.707246\pi\)
−0.606048 + 0.795428i \(0.707246\pi\)
\(620\) 0 0
\(621\) −3.15077 −0.126436
\(622\) 0 0
\(623\) 8.62399 0.345513
\(624\) 0 0
\(625\) −14.6967 −0.587870
\(626\) 0 0
\(627\) 17.1074 0.683206
\(628\) 0 0
\(629\) −30.8383 −1.22960
\(630\) 0 0
\(631\) 15.5643 0.619606 0.309803 0.950801i \(-0.399737\pi\)
0.309803 + 0.950801i \(0.399737\pi\)
\(632\) 0 0
\(633\) 61.9264 2.46135
\(634\) 0 0
\(635\) 33.1709 1.31635
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) −15.5008 −0.613202
\(640\) 0 0
\(641\) 26.1761 1.03389 0.516946 0.856018i \(-0.327069\pi\)
0.516946 + 0.856018i \(0.327069\pi\)
\(642\) 0 0
\(643\) −16.8826 −0.665786 −0.332893 0.942965i \(-0.608025\pi\)
−0.332893 + 0.942965i \(0.608025\pi\)
\(644\) 0 0
\(645\) −26.5553 −1.04561
\(646\) 0 0
\(647\) 20.3352 0.799458 0.399729 0.916633i \(-0.369104\pi\)
0.399729 + 0.916633i \(0.369104\pi\)
\(648\) 0 0
\(649\) 7.10214 0.278783
\(650\) 0 0
\(651\) −8.88803 −0.348349
\(652\) 0 0
\(653\) 38.4731 1.50557 0.752784 0.658268i \(-0.228710\pi\)
0.752784 + 0.658268i \(0.228710\pi\)
\(654\) 0 0
\(655\) 35.4139 1.38374
\(656\) 0 0
\(657\) 6.82675 0.266337
\(658\) 0 0
\(659\) 37.6248 1.46566 0.732828 0.680414i \(-0.238200\pi\)
0.732828 + 0.680414i \(0.238200\pi\)
\(660\) 0 0
\(661\) 5.03341 0.195777 0.0978884 0.995197i \(-0.468791\pi\)
0.0978884 + 0.995197i \(0.468791\pi\)
\(662\) 0 0
\(663\) 11.8946 0.461948
\(664\) 0 0
\(665\) −23.2326 −0.900920
\(666\) 0 0
\(667\) 23.3593 0.904476
\(668\) 0 0
\(669\) −28.1107 −1.08682
\(670\) 0 0
\(671\) −3.05283 −0.117853
\(672\) 0 0
\(673\) −14.3284 −0.552320 −0.276160 0.961112i \(-0.589062\pi\)
−0.276160 + 0.961112i \(0.589062\pi\)
\(674\) 0 0
\(675\) −4.48667 −0.172692
\(676\) 0 0
\(677\) 15.5366 0.597119 0.298560 0.954391i \(-0.403494\pi\)
0.298560 + 0.954391i \(0.403494\pi\)
\(678\) 0 0
\(679\) 3.09042 0.118600
\(680\) 0 0
\(681\) −10.9376 −0.419129
\(682\) 0 0
\(683\) 23.8595 0.912959 0.456479 0.889734i \(-0.349110\pi\)
0.456479 + 0.889734i \(0.349110\pi\)
\(684\) 0 0
\(685\) −32.4778 −1.24091
\(686\) 0 0
\(687\) −63.5939 −2.42626
\(688\) 0 0
\(689\) −2.20492 −0.0840008
\(690\) 0 0
\(691\) −24.5720 −0.934761 −0.467381 0.884056i \(-0.654802\pi\)
−0.467381 + 0.884056i \(0.654802\pi\)
\(692\) 0 0
\(693\) −3.27272 −0.124321
\(694\) 0 0
\(695\) −12.9025 −0.489419
\(696\) 0 0
\(697\) −9.23747 −0.349894
\(698\) 0 0
\(699\) −11.0178 −0.416731
\(700\) 0 0
\(701\) 15.3814 0.580946 0.290473 0.956883i \(-0.406187\pi\)
0.290473 + 0.956883i \(0.406187\pi\)
\(702\) 0 0
\(703\) −44.3532 −1.67281
\(704\) 0 0
\(705\) 31.7653 1.19635
\(706\) 0 0
\(707\) 5.86205 0.220465
\(708\) 0 0
\(709\) −1.55709 −0.0584777 −0.0292388 0.999572i \(-0.509308\pi\)
−0.0292388 + 0.999572i \(0.509308\pi\)
\(710\) 0 0
\(711\) −29.3504 −1.10073
\(712\) 0 0
\(713\) 16.3697 0.613051
\(714\) 0 0
\(715\) −3.40126 −0.127200
\(716\) 0 0
\(717\) 33.4126 1.24782
\(718\) 0 0
\(719\) −23.0280 −0.858799 −0.429399 0.903115i \(-0.641275\pi\)
−0.429399 + 0.903115i \(0.641275\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) −30.9248 −1.15011
\(724\) 0 0
\(725\) 33.2634 1.23537
\(726\) 0 0
\(727\) −6.73851 −0.249918 −0.124959 0.992162i \(-0.539880\pi\)
−0.124959 + 0.992162i \(0.539880\pi\)
\(728\) 0 0
\(729\) −31.6656 −1.17280
\(730\) 0 0
\(731\) −14.8049 −0.547579
\(732\) 0 0
\(733\) 50.3830 1.86094 0.930470 0.366368i \(-0.119399\pi\)
0.930470 + 0.366368i \(0.119399\pi\)
\(734\) 0 0
\(735\) 8.51859 0.314213
\(736\) 0 0
\(737\) 9.11450 0.335737
\(738\) 0 0
\(739\) −25.4220 −0.935162 −0.467581 0.883950i \(-0.654874\pi\)
−0.467581 + 0.883950i \(0.654874\pi\)
\(740\) 0 0
\(741\) 17.1074 0.628458
\(742\) 0 0
\(743\) −14.3196 −0.525336 −0.262668 0.964886i \(-0.584602\pi\)
−0.262668 + 0.964886i \(0.584602\pi\)
\(744\) 0 0
\(745\) 40.5184 1.48448
\(746\) 0 0
\(747\) 45.7858 1.67521
\(748\) 0 0
\(749\) −4.01980 −0.146880
\(750\) 0 0
\(751\) −39.7786 −1.45154 −0.725770 0.687937i \(-0.758517\pi\)
−0.725770 + 0.687937i \(0.758517\pi\)
\(752\) 0 0
\(753\) 36.6335 1.33500
\(754\) 0 0
\(755\) −9.27494 −0.337550
\(756\) 0 0
\(757\) −4.33088 −0.157409 −0.0787043 0.996898i \(-0.525078\pi\)
−0.0787043 + 0.996898i \(0.525078\pi\)
\(758\) 0 0
\(759\) 11.5529 0.419345
\(760\) 0 0
\(761\) 2.27636 0.0825179 0.0412590 0.999148i \(-0.486863\pi\)
0.0412590 + 0.999148i \(0.486863\pi\)
\(762\) 0 0
\(763\) 5.89460 0.213399
\(764\) 0 0
\(765\) −52.8653 −1.91135
\(766\) 0 0
\(767\) 7.10214 0.256443
\(768\) 0 0
\(769\) 34.6391 1.24912 0.624559 0.780977i \(-0.285279\pi\)
0.624559 + 0.780977i \(0.285279\pi\)
\(770\) 0 0
\(771\) 36.6377 1.31947
\(772\) 0 0
\(773\) −47.7438 −1.71723 −0.858613 0.512624i \(-0.828674\pi\)
−0.858613 + 0.512624i \(0.828674\pi\)
\(774\) 0 0
\(775\) 23.3103 0.837331
\(776\) 0 0
\(777\) 16.2628 0.583426
\(778\) 0 0
\(779\) −13.2858 −0.476014
\(780\) 0 0
\(781\) 4.73636 0.169480
\(782\) 0 0
\(783\) −3.45899 −0.123614
\(784\) 0 0
\(785\) 56.7419 2.02521
\(786\) 0 0
\(787\) −45.8931 −1.63591 −0.817956 0.575280i \(-0.804893\pi\)
−0.817956 + 0.575280i \(0.804893\pi\)
\(788\) 0 0
\(789\) −6.02236 −0.214402
\(790\) 0 0
\(791\) −0.216621 −0.00770217
\(792\) 0 0
\(793\) −3.05283 −0.108409
\(794\) 0 0
\(795\) 18.7828 0.666158
\(796\) 0 0
\(797\) −12.3065 −0.435918 −0.217959 0.975958i \(-0.569940\pi\)
−0.217959 + 0.975958i \(0.569940\pi\)
\(798\) 0 0
\(799\) 17.7095 0.626517
\(800\) 0 0
\(801\) 28.2240 0.997245
\(802\) 0 0
\(803\) −2.08595 −0.0736116
\(804\) 0 0
\(805\) −15.6893 −0.552976
\(806\) 0 0
\(807\) 16.5310 0.581917
\(808\) 0 0
\(809\) −34.8801 −1.22632 −0.613160 0.789959i \(-0.710102\pi\)
−0.613160 + 0.789959i \(0.710102\pi\)
\(810\) 0 0
\(811\) 44.9109 1.57703 0.788517 0.615013i \(-0.210849\pi\)
0.788517 + 0.615013i \(0.210849\pi\)
\(812\) 0 0
\(813\) 32.8394 1.15173
\(814\) 0 0
\(815\) 1.48546 0.0520332
\(816\) 0 0
\(817\) −21.2932 −0.744954
\(818\) 0 0
\(819\) −3.27272 −0.114358
\(820\) 0 0
\(821\) −21.4159 −0.747420 −0.373710 0.927546i \(-0.621914\pi\)
−0.373710 + 0.927546i \(0.621914\pi\)
\(822\) 0 0
\(823\) −31.2815 −1.09040 −0.545202 0.838305i \(-0.683547\pi\)
−0.545202 + 0.838305i \(0.683547\pi\)
\(824\) 0 0
\(825\) 16.4513 0.572759
\(826\) 0 0
\(827\) 42.0389 1.46183 0.730917 0.682466i \(-0.239093\pi\)
0.730917 + 0.682466i \(0.239093\pi\)
\(828\) 0 0
\(829\) 17.9982 0.625104 0.312552 0.949901i \(-0.398816\pi\)
0.312552 + 0.949901i \(0.398816\pi\)
\(830\) 0 0
\(831\) 38.0410 1.31963
\(832\) 0 0
\(833\) 4.74921 0.164551
\(834\) 0 0
\(835\) −53.4601 −1.85006
\(836\) 0 0
\(837\) −2.42399 −0.0837852
\(838\) 0 0
\(839\) −40.6970 −1.40502 −0.702509 0.711675i \(-0.747937\pi\)
−0.702509 + 0.711675i \(0.747937\pi\)
\(840\) 0 0
\(841\) −3.35561 −0.115711
\(842\) 0 0
\(843\) −62.7742 −2.16206
\(844\) 0 0
\(845\) −3.40126 −0.117007
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) 76.4484 2.62370
\(850\) 0 0
\(851\) −29.9524 −1.02676
\(852\) 0 0
\(853\) −17.1941 −0.588715 −0.294357 0.955695i \(-0.595106\pi\)
−0.294357 + 0.955695i \(0.595106\pi\)
\(854\) 0 0
\(855\) −76.0337 −2.60030
\(856\) 0 0
\(857\) 22.5654 0.770820 0.385410 0.922745i \(-0.374060\pi\)
0.385410 + 0.922745i \(0.374060\pi\)
\(858\) 0 0
\(859\) −45.9268 −1.56700 −0.783500 0.621391i \(-0.786568\pi\)
−0.783500 + 0.621391i \(0.786568\pi\)
\(860\) 0 0
\(861\) 4.87146 0.166019
\(862\) 0 0
\(863\) 56.8399 1.93485 0.967426 0.253154i \(-0.0814679\pi\)
0.967426 + 0.253154i \(0.0814679\pi\)
\(864\) 0 0
\(865\) −50.5044 −1.71720
\(866\) 0 0
\(867\) −13.9128 −0.472504
\(868\) 0 0
\(869\) 8.96819 0.304225
\(870\) 0 0
\(871\) 9.11450 0.308833
\(872\) 0 0
\(873\) 10.1141 0.342311
\(874\) 0 0
\(875\) −5.33511 −0.180360
\(876\) 0 0
\(877\) −7.50993 −0.253592 −0.126796 0.991929i \(-0.540469\pi\)
−0.126796 + 0.991929i \(0.540469\pi\)
\(878\) 0 0
\(879\) −55.0459 −1.85665
\(880\) 0 0
\(881\) −28.1431 −0.948165 −0.474083 0.880480i \(-0.657220\pi\)
−0.474083 + 0.880480i \(0.657220\pi\)
\(882\) 0 0
\(883\) −50.6109 −1.70319 −0.851596 0.524199i \(-0.824365\pi\)
−0.851596 + 0.524199i \(0.824365\pi\)
\(884\) 0 0
\(885\) −60.5003 −2.03369
\(886\) 0 0
\(887\) 14.3430 0.481592 0.240796 0.970576i \(-0.422592\pi\)
0.240796 + 0.970576i \(0.422592\pi\)
\(888\) 0 0
\(889\) −9.75255 −0.327090
\(890\) 0 0
\(891\) 8.10745 0.271610
\(892\) 0 0
\(893\) 25.4707 0.852346
\(894\) 0 0
\(895\) 74.7560 2.49882
\(896\) 0 0
\(897\) 11.5529 0.385741
\(898\) 0 0
\(899\) 17.9710 0.599368
\(900\) 0 0
\(901\) 10.4716 0.348861
\(902\) 0 0
\(903\) 7.80749 0.259817
\(904\) 0 0
\(905\) 5.72768 0.190395
\(906\) 0 0
\(907\) −13.5218 −0.448982 −0.224491 0.974476i \(-0.572072\pi\)
−0.224491 + 0.974476i \(0.572072\pi\)
\(908\) 0 0
\(909\) 19.1849 0.636323
\(910\) 0 0
\(911\) −53.2557 −1.76444 −0.882221 0.470836i \(-0.843952\pi\)
−0.882221 + 0.470836i \(0.843952\pi\)
\(912\) 0 0
\(913\) −13.9901 −0.463005
\(914\) 0 0
\(915\) 26.0058 0.859725
\(916\) 0 0
\(917\) −10.4120 −0.343834
\(918\) 0 0
\(919\) −8.04948 −0.265528 −0.132764 0.991148i \(-0.542385\pi\)
−0.132764 + 0.991148i \(0.542385\pi\)
\(920\) 0 0
\(921\) −15.3707 −0.506482
\(922\) 0 0
\(923\) 4.73636 0.155899
\(924\) 0 0
\(925\) −42.6520 −1.40239
\(926\) 0 0
\(927\) 26.1818 0.859923
\(928\) 0 0
\(929\) −32.3219 −1.06045 −0.530224 0.847857i \(-0.677892\pi\)
−0.530224 + 0.847857i \(0.677892\pi\)
\(930\) 0 0
\(931\) 6.83057 0.223863
\(932\) 0 0
\(933\) 38.7311 1.26800
\(934\) 0 0
\(935\) 16.1533 0.528270
\(936\) 0 0
\(937\) −6.72242 −0.219612 −0.109806 0.993953i \(-0.535023\pi\)
−0.109806 + 0.993953i \(0.535023\pi\)
\(938\) 0 0
\(939\) 19.0833 0.622760
\(940\) 0 0
\(941\) 42.0779 1.37170 0.685850 0.727743i \(-0.259431\pi\)
0.685850 + 0.727743i \(0.259431\pi\)
\(942\) 0 0
\(943\) −8.97213 −0.292173
\(944\) 0 0
\(945\) 2.32323 0.0755748
\(946\) 0 0
\(947\) −13.2864 −0.431750 −0.215875 0.976421i \(-0.569260\pi\)
−0.215875 + 0.976421i \(0.569260\pi\)
\(948\) 0 0
\(949\) −2.08595 −0.0677129
\(950\) 0 0
\(951\) −75.0879 −2.43489
\(952\) 0 0
\(953\) −6.28886 −0.203716 −0.101858 0.994799i \(-0.532479\pi\)
−0.101858 + 0.994799i \(0.532479\pi\)
\(954\) 0 0
\(955\) −75.5726 −2.44547
\(956\) 0 0
\(957\) 12.6831 0.409985
\(958\) 0 0
\(959\) 9.54877 0.308346
\(960\) 0 0
\(961\) −18.4063 −0.593751
\(962\) 0 0
\(963\) −13.1557 −0.423937
\(964\) 0 0
\(965\) 22.2247 0.715438
\(966\) 0 0
\(967\) −54.8963 −1.76535 −0.882674 0.469987i \(-0.844259\pi\)
−0.882674 + 0.469987i \(0.844259\pi\)
\(968\) 0 0
\(969\) −81.2469 −2.61003
\(970\) 0 0
\(971\) 15.6192 0.501244 0.250622 0.968085i \(-0.419365\pi\)
0.250622 + 0.968085i \(0.419365\pi\)
\(972\) 0 0
\(973\) 3.79344 0.121612
\(974\) 0 0
\(975\) 16.4513 0.526862
\(976\) 0 0
\(977\) 56.7243 1.81477 0.907385 0.420300i \(-0.138075\pi\)
0.907385 + 0.420300i \(0.138075\pi\)
\(978\) 0 0
\(979\) −8.62399 −0.275624
\(980\) 0 0
\(981\) 19.2914 0.615927
\(982\) 0 0
\(983\) −34.1589 −1.08950 −0.544750 0.838598i \(-0.683376\pi\)
−0.544750 + 0.838598i \(0.683376\pi\)
\(984\) 0 0
\(985\) −12.0225 −0.383070
\(986\) 0 0
\(987\) −9.33926 −0.297272
\(988\) 0 0
\(989\) −14.3796 −0.457245
\(990\) 0 0
\(991\) −20.0774 −0.637779 −0.318889 0.947792i \(-0.603310\pi\)
−0.318889 + 0.947792i \(0.603310\pi\)
\(992\) 0 0
\(993\) −47.2678 −1.50000
\(994\) 0 0
\(995\) −0.914023 −0.0289765
\(996\) 0 0
\(997\) −11.6440 −0.368769 −0.184384 0.982854i \(-0.559029\pi\)
−0.184384 + 0.982854i \(0.559029\pi\)
\(998\) 0 0
\(999\) 4.43528 0.140326
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 \(a_p\))