Properties

Label 8036.2.a.t.1.19
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 20
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1677830643\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{3} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Root \(3.09326\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+3.09326 q^{3}\) \(+2.53432 q^{5}\) \(+6.56828 q^{9}\) \(+O(q^{10})\) \(q\)\(+3.09326 q^{3}\) \(+2.53432 q^{5}\) \(+6.56828 q^{9}\) \(+2.41450 q^{11}\) \(+0.891914 q^{13}\) \(+7.83932 q^{15}\) \(-1.35119 q^{17}\) \(+7.44412 q^{19}\) \(+7.55317 q^{23}\) \(+1.42278 q^{25}\) \(+11.0376 q^{27}\) \(-9.21648 q^{29}\) \(-7.97616 q^{31}\) \(+7.46869 q^{33}\) \(-3.88292 q^{37}\) \(+2.75893 q^{39}\) \(-1.00000 q^{41}\) \(-10.1485 q^{43}\) \(+16.6461 q^{45}\) \(+11.3109 q^{47}\) \(-4.17959 q^{51}\) \(+6.76801 q^{53}\) \(+6.11912 q^{55}\) \(+23.0266 q^{57}\) \(+5.15894 q^{59}\) \(-12.0219 q^{61}\) \(+2.26040 q^{65}\) \(+10.3013 q^{67}\) \(+23.3639 q^{69}\) \(-2.32034 q^{71}\) \(-13.1459 q^{73}\) \(+4.40103 q^{75}\) \(+10.1492 q^{79}\) \(+14.4375 q^{81}\) \(+5.32036 q^{83}\) \(-3.42435 q^{85}\) \(-28.5090 q^{87}\) \(-1.69894 q^{89}\) \(-24.6724 q^{93}\) \(+18.8658 q^{95}\) \(+7.08919 q^{97}\) \(+15.8591 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(20q \) \(\mathstrut +\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 16q^{9} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 8q^{17} \) \(\mathstrut +\mathstrut 24q^{19} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 20q^{25} \) \(\mathstrut +\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 12q^{29} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 12q^{39} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut +\mathstrut 28q^{57} \) \(\mathstrut +\mathstrut 16q^{59} \) \(\mathstrut +\mathstrut 68q^{61} \) \(\mathstrut -\mathstrut 8q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 32q^{69} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 48q^{73} \) \(\mathstrut +\mathstrut 60q^{75} \) \(\mathstrut -\mathstrut 20q^{79} \) \(\mathstrut +\mathstrut 32q^{81} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 40q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 3.09326 1.78590 0.892948 0.450159i \(-0.148633\pi\)
0.892948 + 0.450159i \(0.148633\pi\)
\(4\) 0 0
\(5\) 2.53432 1.13338 0.566691 0.823930i \(-0.308223\pi\)
0.566691 + 0.823930i \(0.308223\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 6.56828 2.18943
\(10\) 0 0
\(11\) 2.41450 0.727999 0.364000 0.931399i \(-0.381411\pi\)
0.364000 + 0.931399i \(0.381411\pi\)
\(12\) 0 0
\(13\) 0.891914 0.247372 0.123686 0.992321i \(-0.460528\pi\)
0.123686 + 0.992321i \(0.460528\pi\)
\(14\) 0 0
\(15\) 7.83932 2.02410
\(16\) 0 0
\(17\) −1.35119 −0.327712 −0.163856 0.986484i \(-0.552393\pi\)
−0.163856 + 0.986484i \(0.552393\pi\)
\(18\) 0 0
\(19\) 7.44412 1.70780 0.853899 0.520439i \(-0.174232\pi\)
0.853899 + 0.520439i \(0.174232\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.55317 1.57494 0.787472 0.616350i \(-0.211389\pi\)
0.787472 + 0.616350i \(0.211389\pi\)
\(24\) 0 0
\(25\) 1.42278 0.284556
\(26\) 0 0
\(27\) 11.0376 2.12419
\(28\) 0 0
\(29\) −9.21648 −1.71146 −0.855729 0.517424i \(-0.826891\pi\)
−0.855729 + 0.517424i \(0.826891\pi\)
\(30\) 0 0
\(31\) −7.97616 −1.43256 −0.716280 0.697813i \(-0.754157\pi\)
−0.716280 + 0.697813i \(0.754157\pi\)
\(32\) 0 0
\(33\) 7.46869 1.30013
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.88292 −0.638348 −0.319174 0.947696i \(-0.603405\pi\)
−0.319174 + 0.947696i \(0.603405\pi\)
\(38\) 0 0
\(39\) 2.75893 0.441782
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −10.1485 −1.54763 −0.773817 0.633409i \(-0.781655\pi\)
−0.773817 + 0.633409i \(0.781655\pi\)
\(44\) 0 0
\(45\) 16.6461 2.48146
\(46\) 0 0
\(47\) 11.3109 1.64986 0.824929 0.565237i \(-0.191215\pi\)
0.824929 + 0.565237i \(0.191215\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −4.17959 −0.585260
\(52\) 0 0
\(53\) 6.76801 0.929658 0.464829 0.885400i \(-0.346116\pi\)
0.464829 + 0.885400i \(0.346116\pi\)
\(54\) 0 0
\(55\) 6.11912 0.825101
\(56\) 0 0
\(57\) 23.0266 3.04995
\(58\) 0 0
\(59\) 5.15894 0.671637 0.335818 0.941927i \(-0.390987\pi\)
0.335818 + 0.941927i \(0.390987\pi\)
\(60\) 0 0
\(61\) −12.0219 −1.53925 −0.769626 0.638495i \(-0.779557\pi\)
−0.769626 + 0.638495i \(0.779557\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.26040 0.280368
\(66\) 0 0
\(67\) 10.3013 1.25851 0.629253 0.777201i \(-0.283361\pi\)
0.629253 + 0.777201i \(0.283361\pi\)
\(68\) 0 0
\(69\) 23.3639 2.81269
\(70\) 0 0
\(71\) −2.32034 −0.275374 −0.137687 0.990476i \(-0.543967\pi\)
−0.137687 + 0.990476i \(0.543967\pi\)
\(72\) 0 0
\(73\) −13.1459 −1.53861 −0.769307 0.638879i \(-0.779398\pi\)
−0.769307 + 0.638879i \(0.779398\pi\)
\(74\) 0 0
\(75\) 4.40103 0.508187
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 10.1492 1.14187 0.570936 0.820995i \(-0.306581\pi\)
0.570936 + 0.820995i \(0.306581\pi\)
\(80\) 0 0
\(81\) 14.4375 1.60416
\(82\) 0 0
\(83\) 5.32036 0.583986 0.291993 0.956420i \(-0.405682\pi\)
0.291993 + 0.956420i \(0.405682\pi\)
\(84\) 0 0
\(85\) −3.42435 −0.371423
\(86\) 0 0
\(87\) −28.5090 −3.05649
\(88\) 0 0
\(89\) −1.69894 −0.180087 −0.0900437 0.995938i \(-0.528701\pi\)
−0.0900437 + 0.995938i \(0.528701\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −24.6724 −2.55840
\(94\) 0 0
\(95\) 18.8658 1.93559
\(96\) 0 0
\(97\) 7.08919 0.719798 0.359899 0.932991i \(-0.382811\pi\)
0.359899 + 0.932991i \(0.382811\pi\)
\(98\) 0 0
\(99\) 15.8591 1.59390
\(100\) 0 0
\(101\) −10.7826 −1.07291 −0.536453 0.843930i \(-0.680236\pi\)
−0.536453 + 0.843930i \(0.680236\pi\)
\(102\) 0 0
\(103\) −14.5587 −1.43451 −0.717253 0.696813i \(-0.754601\pi\)
−0.717253 + 0.696813i \(0.754601\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.44009 0.912608 0.456304 0.889824i \(-0.349173\pi\)
0.456304 + 0.889824i \(0.349173\pi\)
\(108\) 0 0
\(109\) −11.6416 −1.11506 −0.557530 0.830156i \(-0.688251\pi\)
−0.557530 + 0.830156i \(0.688251\pi\)
\(110\) 0 0
\(111\) −12.0109 −1.14002
\(112\) 0 0
\(113\) 1.52290 0.143263 0.0716314 0.997431i \(-0.477179\pi\)
0.0716314 + 0.997431i \(0.477179\pi\)
\(114\) 0 0
\(115\) 19.1421 1.78501
\(116\) 0 0
\(117\) 5.85834 0.541604
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −5.17019 −0.470017
\(122\) 0 0
\(123\) −3.09326 −0.278910
\(124\) 0 0
\(125\) −9.06582 −0.810872
\(126\) 0 0
\(127\) 7.05647 0.626160 0.313080 0.949727i \(-0.398639\pi\)
0.313080 + 0.949727i \(0.398639\pi\)
\(128\) 0 0
\(129\) −31.3920 −2.76391
\(130\) 0 0
\(131\) −11.4188 −0.997661 −0.498830 0.866700i \(-0.666237\pi\)
−0.498830 + 0.866700i \(0.666237\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 27.9729 2.40752
\(136\) 0 0
\(137\) −3.77920 −0.322879 −0.161439 0.986883i \(-0.551614\pi\)
−0.161439 + 0.986883i \(0.551614\pi\)
\(138\) 0 0
\(139\) −5.31034 −0.450418 −0.225209 0.974311i \(-0.572306\pi\)
−0.225209 + 0.974311i \(0.572306\pi\)
\(140\) 0 0
\(141\) 34.9875 2.94648
\(142\) 0 0
\(143\) 2.15353 0.180087
\(144\) 0 0
\(145\) −23.3575 −1.93974
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −15.8886 −1.30165 −0.650823 0.759229i \(-0.725576\pi\)
−0.650823 + 0.759229i \(0.725576\pi\)
\(150\) 0 0
\(151\) −8.47462 −0.689655 −0.344828 0.938666i \(-0.612063\pi\)
−0.344828 + 0.938666i \(0.612063\pi\)
\(152\) 0 0
\(153\) −8.87501 −0.717502
\(154\) 0 0
\(155\) −20.2141 −1.62364
\(156\) 0 0
\(157\) 9.38861 0.749292 0.374646 0.927168i \(-0.377764\pi\)
0.374646 + 0.927168i \(0.377764\pi\)
\(158\) 0 0
\(159\) 20.9353 1.66027
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.69722 0.211263 0.105631 0.994405i \(-0.466314\pi\)
0.105631 + 0.994405i \(0.466314\pi\)
\(164\) 0 0
\(165\) 18.9280 1.47355
\(166\) 0 0
\(167\) −2.40120 −0.185811 −0.0929054 0.995675i \(-0.529615\pi\)
−0.0929054 + 0.995675i \(0.529615\pi\)
\(168\) 0 0
\(169\) −12.2045 −0.938807
\(170\) 0 0
\(171\) 48.8951 3.73910
\(172\) 0 0
\(173\) 5.05489 0.384316 0.192158 0.981364i \(-0.438451\pi\)
0.192158 + 0.981364i \(0.438451\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 15.9580 1.19947
\(178\) 0 0
\(179\) 12.5635 0.939040 0.469520 0.882922i \(-0.344427\pi\)
0.469520 + 0.882922i \(0.344427\pi\)
\(180\) 0 0
\(181\) 4.30529 0.320010 0.160005 0.987116i \(-0.448849\pi\)
0.160005 + 0.987116i \(0.448849\pi\)
\(182\) 0 0
\(183\) −37.1870 −2.74894
\(184\) 0 0
\(185\) −9.84056 −0.723492
\(186\) 0 0
\(187\) −3.26245 −0.238574
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −17.6058 −1.27391 −0.636956 0.770900i \(-0.719807\pi\)
−0.636956 + 0.770900i \(0.719807\pi\)
\(192\) 0 0
\(193\) 20.3865 1.46745 0.733727 0.679445i \(-0.237779\pi\)
0.733727 + 0.679445i \(0.237779\pi\)
\(194\) 0 0
\(195\) 6.99200 0.500708
\(196\) 0 0
\(197\) 11.6477 0.829867 0.414934 0.909852i \(-0.363805\pi\)
0.414934 + 0.909852i \(0.363805\pi\)
\(198\) 0 0
\(199\) −7.84480 −0.556103 −0.278052 0.960566i \(-0.589689\pi\)
−0.278052 + 0.960566i \(0.589689\pi\)
\(200\) 0 0
\(201\) 31.8647 2.24756
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −2.53432 −0.177005
\(206\) 0 0
\(207\) 49.6113 3.44823
\(208\) 0 0
\(209\) 17.9738 1.24328
\(210\) 0 0
\(211\) 17.2163 1.18522 0.592608 0.805491i \(-0.298098\pi\)
0.592608 + 0.805491i \(0.298098\pi\)
\(212\) 0 0
\(213\) −7.17744 −0.491790
\(214\) 0 0
\(215\) −25.7196 −1.75406
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −40.6638 −2.74781
\(220\) 0 0
\(221\) −1.20515 −0.0810670
\(222\) 0 0
\(223\) −4.19556 −0.280956 −0.140478 0.990084i \(-0.544864\pi\)
−0.140478 + 0.990084i \(0.544864\pi\)
\(224\) 0 0
\(225\) 9.34521 0.623014
\(226\) 0 0
\(227\) −10.1726 −0.675179 −0.337590 0.941293i \(-0.609612\pi\)
−0.337590 + 0.941293i \(0.609612\pi\)
\(228\) 0 0
\(229\) 18.6246 1.23075 0.615373 0.788236i \(-0.289005\pi\)
0.615373 + 0.788236i \(0.289005\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.28474 −0.0841663 −0.0420832 0.999114i \(-0.513399\pi\)
−0.0420832 + 0.999114i \(0.513399\pi\)
\(234\) 0 0
\(235\) 28.6653 1.86992
\(236\) 0 0
\(237\) 31.3941 2.03926
\(238\) 0 0
\(239\) −19.7684 −1.27871 −0.639356 0.768911i \(-0.720799\pi\)
−0.639356 + 0.768911i \(0.720799\pi\)
\(240\) 0 0
\(241\) 11.5512 0.744078 0.372039 0.928217i \(-0.378659\pi\)
0.372039 + 0.928217i \(0.378659\pi\)
\(242\) 0 0
\(243\) 11.5460 0.740677
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 6.63951 0.422462
\(248\) 0 0
\(249\) 16.4573 1.04294
\(250\) 0 0
\(251\) −6.54044 −0.412829 −0.206415 0.978465i \(-0.566180\pi\)
−0.206415 + 0.978465i \(0.566180\pi\)
\(252\) 0 0
\(253\) 18.2371 1.14656
\(254\) 0 0
\(255\) −10.5924 −0.663324
\(256\) 0 0
\(257\) 0.450903 0.0281266 0.0140633 0.999901i \(-0.495523\pi\)
0.0140633 + 0.999901i \(0.495523\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −60.5364 −3.74711
\(262\) 0 0
\(263\) 18.3401 1.13090 0.565451 0.824782i \(-0.308702\pi\)
0.565451 + 0.824782i \(0.308702\pi\)
\(264\) 0 0
\(265\) 17.1523 1.05366
\(266\) 0 0
\(267\) −5.25527 −0.321618
\(268\) 0 0
\(269\) 9.51595 0.580198 0.290099 0.956997i \(-0.406312\pi\)
0.290099 + 0.956997i \(0.406312\pi\)
\(270\) 0 0
\(271\) −25.2628 −1.53460 −0.767302 0.641286i \(-0.778401\pi\)
−0.767302 + 0.641286i \(0.778401\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 3.43530 0.207156
\(276\) 0 0
\(277\) −18.3777 −1.10421 −0.552103 0.833776i \(-0.686175\pi\)
−0.552103 + 0.833776i \(0.686175\pi\)
\(278\) 0 0
\(279\) −52.3896 −3.13649
\(280\) 0 0
\(281\) −5.32543 −0.317688 −0.158844 0.987304i \(-0.550777\pi\)
−0.158844 + 0.987304i \(0.550777\pi\)
\(282\) 0 0
\(283\) −14.0777 −0.836833 −0.418417 0.908255i \(-0.637415\pi\)
−0.418417 + 0.908255i \(0.637415\pi\)
\(284\) 0 0
\(285\) 58.3568 3.45676
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −15.1743 −0.892605
\(290\) 0 0
\(291\) 21.9287 1.28548
\(292\) 0 0
\(293\) 14.1515 0.826741 0.413370 0.910563i \(-0.364352\pi\)
0.413370 + 0.910563i \(0.364352\pi\)
\(294\) 0 0
\(295\) 13.0744 0.761222
\(296\) 0 0
\(297\) 26.6504 1.54641
\(298\) 0 0
\(299\) 6.73678 0.389598
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −33.3533 −1.91610
\(304\) 0 0
\(305\) −30.4674 −1.74456
\(306\) 0 0
\(307\) −29.7727 −1.69922 −0.849608 0.527415i \(-0.823161\pi\)
−0.849608 + 0.527415i \(0.823161\pi\)
\(308\) 0 0
\(309\) −45.0337 −2.56188
\(310\) 0 0
\(311\) 22.4152 1.27105 0.635524 0.772081i \(-0.280784\pi\)
0.635524 + 0.772081i \(0.280784\pi\)
\(312\) 0 0
\(313\) 25.8733 1.46244 0.731222 0.682139i \(-0.238950\pi\)
0.731222 + 0.682139i \(0.238950\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.8452 1.28311 0.641556 0.767076i \(-0.278289\pi\)
0.641556 + 0.767076i \(0.278289\pi\)
\(318\) 0 0
\(319\) −22.2532 −1.24594
\(320\) 0 0
\(321\) 29.2007 1.62982
\(322\) 0 0
\(323\) −10.0584 −0.559666
\(324\) 0 0
\(325\) 1.26900 0.0703913
\(326\) 0 0
\(327\) −36.0105 −1.99138
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −9.55666 −0.525281 −0.262641 0.964894i \(-0.584593\pi\)
−0.262641 + 0.964894i \(0.584593\pi\)
\(332\) 0 0
\(333\) −25.5041 −1.39762
\(334\) 0 0
\(335\) 26.1068 1.42637
\(336\) 0 0
\(337\) 4.53495 0.247034 0.123517 0.992342i \(-0.460583\pi\)
0.123517 + 0.992342i \(0.460583\pi\)
\(338\) 0 0
\(339\) 4.71075 0.255853
\(340\) 0 0
\(341\) −19.2584 −1.04290
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 59.2117 3.18785
\(346\) 0 0
\(347\) 26.1857 1.40572 0.702860 0.711328i \(-0.251906\pi\)
0.702860 + 0.711328i \(0.251906\pi\)
\(348\) 0 0
\(349\) 2.83829 0.151930 0.0759650 0.997110i \(-0.475796\pi\)
0.0759650 + 0.997110i \(0.475796\pi\)
\(350\) 0 0
\(351\) 9.84462 0.525467
\(352\) 0 0
\(353\) −20.5144 −1.09187 −0.545935 0.837828i \(-0.683825\pi\)
−0.545935 + 0.837828i \(0.683825\pi\)
\(354\) 0 0
\(355\) −5.88050 −0.312104
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.41431 −0.0746443 −0.0373222 0.999303i \(-0.511883\pi\)
−0.0373222 + 0.999303i \(0.511883\pi\)
\(360\) 0 0
\(361\) 36.4149 1.91657
\(362\) 0 0
\(363\) −15.9928 −0.839402
\(364\) 0 0
\(365\) −33.3160 −1.74384
\(366\) 0 0
\(367\) 30.3424 1.58386 0.791931 0.610610i \(-0.209076\pi\)
0.791931 + 0.610610i \(0.209076\pi\)
\(368\) 0 0
\(369\) −6.56828 −0.341931
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −8.60510 −0.445555 −0.222778 0.974869i \(-0.571512\pi\)
−0.222778 + 0.974869i \(0.571512\pi\)
\(374\) 0 0
\(375\) −28.0430 −1.44813
\(376\) 0 0
\(377\) −8.22031 −0.423368
\(378\) 0 0
\(379\) −7.73291 −0.397213 −0.198606 0.980079i \(-0.563642\pi\)
−0.198606 + 0.980079i \(0.563642\pi\)
\(380\) 0 0
\(381\) 21.8275 1.11826
\(382\) 0 0
\(383\) 25.4109 1.29844 0.649219 0.760602i \(-0.275096\pi\)
0.649219 + 0.760602i \(0.275096\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −66.6583 −3.38843
\(388\) 0 0
\(389\) 11.4305 0.579551 0.289775 0.957095i \(-0.406419\pi\)
0.289775 + 0.957095i \(0.406419\pi\)
\(390\) 0 0
\(391\) −10.2058 −0.516129
\(392\) 0 0
\(393\) −35.3212 −1.78172
\(394\) 0 0
\(395\) 25.7213 1.29418
\(396\) 0 0
\(397\) 7.99386 0.401200 0.200600 0.979673i \(-0.435711\pi\)
0.200600 + 0.979673i \(0.435711\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −28.0156 −1.39903 −0.699517 0.714616i \(-0.746602\pi\)
−0.699517 + 0.714616i \(0.746602\pi\)
\(402\) 0 0
\(403\) −7.11405 −0.354376
\(404\) 0 0
\(405\) 36.5892 1.81813
\(406\) 0 0
\(407\) −9.37531 −0.464717
\(408\) 0 0
\(409\) 20.5813 1.01768 0.508840 0.860861i \(-0.330075\pi\)
0.508840 + 0.860861i \(0.330075\pi\)
\(410\) 0 0
\(411\) −11.6901 −0.576628
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 13.4835 0.661879
\(416\) 0 0
\(417\) −16.4263 −0.804399
\(418\) 0 0
\(419\) −22.7420 −1.11102 −0.555509 0.831511i \(-0.687477\pi\)
−0.555509 + 0.831511i \(0.687477\pi\)
\(420\) 0 0
\(421\) −18.8504 −0.918711 −0.459355 0.888253i \(-0.651920\pi\)
−0.459355 + 0.888253i \(0.651920\pi\)
\(422\) 0 0
\(423\) 74.2929 3.61224
\(424\) 0 0
\(425\) −1.92245 −0.0932524
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 6.66143 0.321617
\(430\) 0 0
\(431\) −15.4089 −0.742218 −0.371109 0.928589i \(-0.621022\pi\)
−0.371109 + 0.928589i \(0.621022\pi\)
\(432\) 0 0
\(433\) 18.4547 0.886878 0.443439 0.896305i \(-0.353758\pi\)
0.443439 + 0.896305i \(0.353758\pi\)
\(434\) 0 0
\(435\) −72.2510 −3.46417
\(436\) 0 0
\(437\) 56.2267 2.68969
\(438\) 0 0
\(439\) 26.4328 1.26157 0.630784 0.775958i \(-0.282733\pi\)
0.630784 + 0.775958i \(0.282733\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 39.9044 1.89592 0.947959 0.318393i \(-0.103143\pi\)
0.947959 + 0.318393i \(0.103143\pi\)
\(444\) 0 0
\(445\) −4.30566 −0.204108
\(446\) 0 0
\(447\) −49.1477 −2.32461
\(448\) 0 0
\(449\) 4.80415 0.226722 0.113361 0.993554i \(-0.463838\pi\)
0.113361 + 0.993554i \(0.463838\pi\)
\(450\) 0 0
\(451\) −2.41450 −0.113694
\(452\) 0 0
\(453\) −26.2142 −1.23165
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −14.6661 −0.686051 −0.343026 0.939326i \(-0.611452\pi\)
−0.343026 + 0.939326i \(0.611452\pi\)
\(458\) 0 0
\(459\) −14.9140 −0.696124
\(460\) 0 0
\(461\) 18.7184 0.871800 0.435900 0.899995i \(-0.356430\pi\)
0.435900 + 0.899995i \(0.356430\pi\)
\(462\) 0 0
\(463\) 9.63278 0.447673 0.223837 0.974627i \(-0.428142\pi\)
0.223837 + 0.974627i \(0.428142\pi\)
\(464\) 0 0
\(465\) −62.5277 −2.89965
\(466\) 0 0
\(467\) 29.7209 1.37532 0.687659 0.726034i \(-0.258638\pi\)
0.687659 + 0.726034i \(0.258638\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 29.0414 1.33816
\(472\) 0 0
\(473\) −24.5036 −1.12668
\(474\) 0 0
\(475\) 10.5913 0.485964
\(476\) 0 0
\(477\) 44.4542 2.03542
\(478\) 0 0
\(479\) −11.3588 −0.518996 −0.259498 0.965744i \(-0.583557\pi\)
−0.259498 + 0.965744i \(0.583557\pi\)
\(480\) 0 0
\(481\) −3.46323 −0.157910
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 17.9663 0.815806
\(486\) 0 0
\(487\) −39.1923 −1.77597 −0.887986 0.459870i \(-0.847896\pi\)
−0.887986 + 0.459870i \(0.847896\pi\)
\(488\) 0 0
\(489\) 8.34321 0.377293
\(490\) 0 0
\(491\) 14.9009 0.672467 0.336234 0.941779i \(-0.390847\pi\)
0.336234 + 0.941779i \(0.390847\pi\)
\(492\) 0 0
\(493\) 12.4532 0.560866
\(494\) 0 0
\(495\) 40.1921 1.80650
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 17.3001 0.774461 0.387230 0.921983i \(-0.373432\pi\)
0.387230 + 0.921983i \(0.373432\pi\)
\(500\) 0 0
\(501\) −7.42756 −0.331839
\(502\) 0 0
\(503\) 7.56980 0.337521 0.168760 0.985657i \(-0.446024\pi\)
0.168760 + 0.985657i \(0.446024\pi\)
\(504\) 0 0
\(505\) −27.3265 −1.21601
\(506\) 0 0
\(507\) −37.7517 −1.67661
\(508\) 0 0
\(509\) −36.1762 −1.60348 −0.801741 0.597672i \(-0.796093\pi\)
−0.801741 + 0.597672i \(0.796093\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 82.1655 3.62769
\(514\) 0 0
\(515\) −36.8963 −1.62584
\(516\) 0 0
\(517\) 27.3101 1.20109
\(518\) 0 0
\(519\) 15.6361 0.686349
\(520\) 0 0
\(521\) −1.34941 −0.0591188 −0.0295594 0.999563i \(-0.509410\pi\)
−0.0295594 + 0.999563i \(0.509410\pi\)
\(522\) 0 0
\(523\) 25.5118 1.11555 0.557776 0.829991i \(-0.311655\pi\)
0.557776 + 0.829991i \(0.311655\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 10.7773 0.469467
\(528\) 0 0
\(529\) 34.0503 1.48045
\(530\) 0 0
\(531\) 33.8854 1.47050
\(532\) 0 0
\(533\) −0.891914 −0.0386331
\(534\) 0 0
\(535\) 23.9242 1.03433
\(536\) 0 0
\(537\) 38.8622 1.67703
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −26.1873 −1.12588 −0.562939 0.826498i \(-0.690329\pi\)
−0.562939 + 0.826498i \(0.690329\pi\)
\(542\) 0 0
\(543\) 13.3174 0.571504
\(544\) 0 0
\(545\) −29.5035 −1.26379
\(546\) 0 0
\(547\) −12.4992 −0.534428 −0.267214 0.963637i \(-0.586103\pi\)
−0.267214 + 0.963637i \(0.586103\pi\)
\(548\) 0 0
\(549\) −78.9635 −3.37008
\(550\) 0 0
\(551\) −68.6086 −2.92282
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −30.4394 −1.29208
\(556\) 0 0
\(557\) 13.1455 0.556994 0.278497 0.960437i \(-0.410164\pi\)
0.278497 + 0.960437i \(0.410164\pi\)
\(558\) 0 0
\(559\) −9.05160 −0.382842
\(560\) 0 0
\(561\) −10.0916 −0.426069
\(562\) 0 0
\(563\) 37.8786 1.59639 0.798197 0.602397i \(-0.205788\pi\)
0.798197 + 0.602397i \(0.205788\pi\)
\(564\) 0 0
\(565\) 3.85953 0.162372
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 33.2804 1.39519 0.697593 0.716494i \(-0.254254\pi\)
0.697593 + 0.716494i \(0.254254\pi\)
\(570\) 0 0
\(571\) −36.0184 −1.50732 −0.753662 0.657262i \(-0.771714\pi\)
−0.753662 + 0.657262i \(0.771714\pi\)
\(572\) 0 0
\(573\) −54.4595 −2.27508
\(574\) 0 0
\(575\) 10.7465 0.448160
\(576\) 0 0
\(577\) 0.793094 0.0330169 0.0165085 0.999864i \(-0.494745\pi\)
0.0165085 + 0.999864i \(0.494745\pi\)
\(578\) 0 0
\(579\) 63.0609 2.62072
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 16.3414 0.676790
\(584\) 0 0
\(585\) 14.8469 0.613844
\(586\) 0 0
\(587\) 6.44222 0.265899 0.132949 0.991123i \(-0.457555\pi\)
0.132949 + 0.991123i \(0.457555\pi\)
\(588\) 0 0
\(589\) −59.3755 −2.44652
\(590\) 0 0
\(591\) 36.0295 1.48206
\(592\) 0 0
\(593\) −3.73231 −0.153268 −0.0766338 0.997059i \(-0.524417\pi\)
−0.0766338 + 0.997059i \(0.524417\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −24.2661 −0.993143
\(598\) 0 0
\(599\) −38.1341 −1.55812 −0.779059 0.626951i \(-0.784303\pi\)
−0.779059 + 0.626951i \(0.784303\pi\)
\(600\) 0 0
\(601\) 41.1688 1.67931 0.839655 0.543121i \(-0.182757\pi\)
0.839655 + 0.543121i \(0.182757\pi\)
\(602\) 0 0
\(603\) 67.6619 2.75541
\(604\) 0 0
\(605\) −13.1029 −0.532709
\(606\) 0 0
\(607\) −33.1125 −1.34400 −0.671998 0.740553i \(-0.734564\pi\)
−0.671998 + 0.740553i \(0.734564\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 10.0883 0.408129
\(612\) 0 0
\(613\) −13.9028 −0.561530 −0.280765 0.959777i \(-0.590588\pi\)
−0.280765 + 0.959777i \(0.590588\pi\)
\(614\) 0 0
\(615\) −7.83932 −0.316112
\(616\) 0 0
\(617\) −35.8528 −1.44338 −0.721690 0.692216i \(-0.756635\pi\)
−0.721690 + 0.692216i \(0.756635\pi\)
\(618\) 0 0
\(619\) −40.1844 −1.61515 −0.807574 0.589766i \(-0.799220\pi\)
−0.807574 + 0.589766i \(0.799220\pi\)
\(620\) 0 0
\(621\) 83.3691 3.34549
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −30.0896 −1.20358
\(626\) 0 0
\(627\) 55.5978 2.22036
\(628\) 0 0
\(629\) 5.24657 0.209194
\(630\) 0 0
\(631\) −10.0862 −0.401523 −0.200762 0.979640i \(-0.564342\pi\)
−0.200762 + 0.979640i \(0.564342\pi\)
\(632\) 0 0
\(633\) 53.2545 2.11667
\(634\) 0 0
\(635\) 17.8833 0.709679
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −15.2407 −0.602912
\(640\) 0 0
\(641\) 4.06812 0.160681 0.0803406 0.996767i \(-0.474399\pi\)
0.0803406 + 0.996767i \(0.474399\pi\)
\(642\) 0 0
\(643\) −26.9405 −1.06243 −0.531215 0.847237i \(-0.678264\pi\)
−0.531215 + 0.847237i \(0.678264\pi\)
\(644\) 0 0
\(645\) −79.5575 −3.13257
\(646\) 0 0
\(647\) 16.6010 0.652654 0.326327 0.945257i \(-0.394189\pi\)
0.326327 + 0.945257i \(0.394189\pi\)
\(648\) 0 0
\(649\) 12.4563 0.488951
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −28.6084 −1.11953 −0.559767 0.828650i \(-0.689109\pi\)
−0.559767 + 0.828650i \(0.689109\pi\)
\(654\) 0 0
\(655\) −28.9388 −1.13073
\(656\) 0 0
\(657\) −86.3462 −3.36868
\(658\) 0 0
\(659\) 18.2029 0.709083 0.354541 0.935040i \(-0.384637\pi\)
0.354541 + 0.935040i \(0.384637\pi\)
\(660\) 0 0
\(661\) −0.933185 −0.0362967 −0.0181484 0.999835i \(-0.505777\pi\)
−0.0181484 + 0.999835i \(0.505777\pi\)
\(662\) 0 0
\(663\) −3.72784 −0.144777
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −69.6136 −2.69545
\(668\) 0 0
\(669\) −12.9780 −0.501758
\(670\) 0 0
\(671\) −29.0270 −1.12057
\(672\) 0 0
\(673\) −3.00774 −0.115940 −0.0579699 0.998318i \(-0.518463\pi\)
−0.0579699 + 0.998318i \(0.518463\pi\)
\(674\) 0 0
\(675\) 15.7041 0.604452
\(676\) 0 0
\(677\) −13.6115 −0.523134 −0.261567 0.965185i \(-0.584239\pi\)
−0.261567 + 0.965185i \(0.584239\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −31.4666 −1.20580
\(682\) 0 0
\(683\) 29.3001 1.12114 0.560570 0.828107i \(-0.310582\pi\)
0.560570 + 0.828107i \(0.310582\pi\)
\(684\) 0 0
\(685\) −9.57770 −0.365945
\(686\) 0 0
\(687\) 57.6107 2.19799
\(688\) 0 0
\(689\) 6.03649 0.229972
\(690\) 0 0
\(691\) 47.2738 1.79838 0.899190 0.437558i \(-0.144157\pi\)
0.899190 + 0.437558i \(0.144157\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −13.4581 −0.510495
\(696\) 0 0
\(697\) 1.35119 0.0511801
\(698\) 0 0
\(699\) −3.97405 −0.150312
\(700\) 0 0
\(701\) 23.0423 0.870297 0.435149 0.900359i \(-0.356696\pi\)
0.435149 + 0.900359i \(0.356696\pi\)
\(702\) 0 0
\(703\) −28.9049 −1.09017
\(704\) 0 0
\(705\) 88.6694 3.33948
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −33.2860 −1.25008 −0.625041 0.780592i \(-0.714918\pi\)
−0.625041 + 0.780592i \(0.714918\pi\)
\(710\) 0 0
\(711\) 66.6626 2.50004
\(712\) 0 0
\(713\) −60.2452 −2.25620
\(714\) 0 0
\(715\) 5.45773 0.204107
\(716\) 0 0
\(717\) −61.1489 −2.28365
\(718\) 0 0
\(719\) −36.9635 −1.37851 −0.689254 0.724520i \(-0.742062\pi\)
−0.689254 + 0.724520i \(0.742062\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 35.7309 1.32885
\(724\) 0 0
\(725\) −13.1130 −0.487005
\(726\) 0 0
\(727\) −34.3030 −1.27223 −0.636114 0.771595i \(-0.719459\pi\)
−0.636114 + 0.771595i \(0.719459\pi\)
\(728\) 0 0
\(729\) −7.59756 −0.281391
\(730\) 0 0
\(731\) 13.7126 0.507179
\(732\) 0 0
\(733\) −0.158131 −0.00584069 −0.00292034 0.999996i \(-0.500930\pi\)
−0.00292034 + 0.999996i \(0.500930\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.8725 0.916191
\(738\) 0 0
\(739\) −15.1280 −0.556494 −0.278247 0.960510i \(-0.589753\pi\)
−0.278247 + 0.960510i \(0.589753\pi\)
\(740\) 0 0
\(741\) 20.5378 0.754474
\(742\) 0 0
\(743\) −20.9477 −0.768497 −0.384249 0.923230i \(-0.625539\pi\)
−0.384249 + 0.923230i \(0.625539\pi\)
\(744\) 0 0
\(745\) −40.2668 −1.47526
\(746\) 0 0
\(747\) 34.9456 1.27859
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −11.3640 −0.414678 −0.207339 0.978269i \(-0.566480\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(752\) 0 0
\(753\) −20.2313 −0.737270
\(754\) 0 0
\(755\) −21.4774 −0.781643
\(756\) 0 0
\(757\) 6.23584 0.226645 0.113323 0.993558i \(-0.463851\pi\)
0.113323 + 0.993558i \(0.463851\pi\)
\(758\) 0 0
\(759\) 56.4122 2.04763
\(760\) 0 0
\(761\) 34.9397 1.26656 0.633282 0.773921i \(-0.281707\pi\)
0.633282 + 0.773921i \(0.281707\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −22.4921 −0.813204
\(766\) 0 0
\(767\) 4.60133 0.166144
\(768\) 0 0
\(769\) 26.3262 0.949347 0.474673 0.880162i \(-0.342566\pi\)
0.474673 + 0.880162i \(0.342566\pi\)
\(770\) 0 0
\(771\) 1.39476 0.0502312
\(772\) 0 0
\(773\) 2.96790 0.106748 0.0533740 0.998575i \(-0.483002\pi\)
0.0533740 + 0.998575i \(0.483002\pi\)
\(774\) 0 0
\(775\) −11.3483 −0.407643
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.44412 −0.266713
\(780\) 0 0
\(781\) −5.60247 −0.200472
\(782\) 0 0
\(783\) −101.728 −3.63547
\(784\) 0 0
\(785\) 23.7937 0.849235
\(786\) 0 0
\(787\) 42.1978 1.50419 0.752095 0.659054i \(-0.229043\pi\)
0.752095 + 0.659054i \(0.229043\pi\)
\(788\) 0 0
\(789\) 56.7309 2.01967
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −10.7225 −0.380768
\(794\) 0 0
\(795\) 53.0566 1.88173
\(796\) 0 0
\(797\) −38.7324 −1.37197 −0.685986 0.727615i \(-0.740629\pi\)
−0.685986 + 0.727615i \(0.740629\pi\)
\(798\) 0 0
\(799\) −15.2831 −0.540679
\(800\) 0 0
\(801\) −11.1591 −0.394288
\(802\) 0 0
\(803\) −31.7408 −1.12011
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 29.4353 1.03617
\(808\) 0 0
\(809\) 49.5673 1.74269 0.871347 0.490667i \(-0.163247\pi\)
0.871347 + 0.490667i \(0.163247\pi\)
\(810\) 0 0
\(811\) 0.994275 0.0349137 0.0174569 0.999848i \(-0.494443\pi\)
0.0174569 + 0.999848i \(0.494443\pi\)
\(812\) 0 0
\(813\) −78.1444 −2.74064
\(814\) 0 0
\(815\) 6.83562 0.239441
\(816\) 0 0
\(817\) −75.5467 −2.64305
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 49.8508 1.73980 0.869902 0.493224i \(-0.164182\pi\)
0.869902 + 0.493224i \(0.164182\pi\)
\(822\) 0 0
\(823\) 23.6941 0.825924 0.412962 0.910748i \(-0.364494\pi\)
0.412962 + 0.910748i \(0.364494\pi\)
\(824\) 0 0
\(825\) 10.6263 0.369960
\(826\) 0 0
\(827\) −24.2592 −0.843574 −0.421787 0.906695i \(-0.638597\pi\)
−0.421787 + 0.906695i \(0.638597\pi\)
\(828\) 0 0
\(829\) −37.0930 −1.28829 −0.644146 0.764902i \(-0.722787\pi\)
−0.644146 + 0.764902i \(0.722787\pi\)
\(830\) 0 0
\(831\) −56.8470 −1.97200
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −6.08542 −0.210595
\(836\) 0 0
\(837\) −88.0379 −3.04304
\(838\) 0 0
\(839\) 46.8392 1.61707 0.808535 0.588448i \(-0.200261\pi\)
0.808535 + 0.588448i \(0.200261\pi\)
\(840\) 0 0
\(841\) 55.9435 1.92909
\(842\) 0 0
\(843\) −16.4730 −0.567359
\(844\) 0 0
\(845\) −30.9301 −1.06403
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −43.5461 −1.49450
\(850\) 0 0
\(851\) −29.3283 −1.00536
\(852\) 0 0
\(853\) 15.0349 0.514784 0.257392 0.966307i \(-0.417137\pi\)
0.257392 + 0.966307i \(0.417137\pi\)
\(854\) 0 0
\(855\) 123.916 4.23783
\(856\) 0 0
\(857\) 32.1946 1.09975 0.549873 0.835248i \(-0.314676\pi\)
0.549873 + 0.835248i \(0.314676\pi\)
\(858\) 0 0
\(859\) 30.1032 1.02711 0.513554 0.858057i \(-0.328329\pi\)
0.513554 + 0.858057i \(0.328329\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 23.6664 0.805615 0.402807 0.915285i \(-0.368034\pi\)
0.402807 + 0.915285i \(0.368034\pi\)
\(864\) 0 0
\(865\) 12.8107 0.435577
\(866\) 0 0
\(867\) −46.9381 −1.59410
\(868\) 0 0
\(869\) 24.5052 0.831281
\(870\) 0 0
\(871\) 9.18788 0.311320
\(872\) 0 0
\(873\) 46.5638 1.57595
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −29.8653 −1.00848 −0.504239 0.863564i \(-0.668227\pi\)
−0.504239 + 0.863564i \(0.668227\pi\)
\(878\) 0 0
\(879\) 43.7744 1.47647
\(880\) 0 0
\(881\) −44.4129 −1.49631 −0.748154 0.663525i \(-0.769060\pi\)
−0.748154 + 0.663525i \(0.769060\pi\)
\(882\) 0 0
\(883\) 22.0274 0.741281 0.370640 0.928776i \(-0.379138\pi\)
0.370640 + 0.928776i \(0.379138\pi\)
\(884\) 0 0
\(885\) 40.4426 1.35946
\(886\) 0 0
\(887\) −23.1036 −0.775743 −0.387872 0.921713i \(-0.626790\pi\)
−0.387872 + 0.921713i \(0.626790\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 34.8593 1.16783
\(892\) 0 0
\(893\) 84.1993 2.81762
\(894\) 0 0
\(895\) 31.8399 1.06429
\(896\) 0 0
\(897\) 20.8386 0.695782
\(898\) 0 0
\(899\) 73.5121 2.45177
\(900\) 0 0
\(901\) −9.14489 −0.304660
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 10.9110 0.362693
\(906\) 0 0
\(907\) −17.1097 −0.568117 −0.284058 0.958807i \(-0.591681\pi\)
−0.284058 + 0.958807i \(0.591681\pi\)
\(908\) 0 0
\(909\) −70.8230 −2.34905
\(910\) 0 0
\(911\) −11.8392 −0.392249 −0.196124 0.980579i \(-0.562836\pi\)
−0.196124 + 0.980579i \(0.562836\pi\)
\(912\) 0 0
\(913\) 12.8460 0.425141
\(914\) 0 0
\(915\) −94.2438 −3.11560
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −33.3855 −1.10129 −0.550644 0.834740i \(-0.685618\pi\)
−0.550644 + 0.834740i \(0.685618\pi\)
\(920\) 0 0
\(921\) −92.0947 −3.03462
\(922\) 0 0
\(923\) −2.06955 −0.0681200
\(924\) 0 0
\(925\) −5.52454 −0.181646
\(926\) 0 0
\(927\) −95.6253 −3.14075
\(928\) 0 0
\(929\) 7.44181 0.244158 0.122079 0.992520i \(-0.461044\pi\)
0.122079 + 0.992520i \(0.461044\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 69.3361 2.26996
\(934\) 0 0
\(935\) −8.26810 −0.270396
\(936\) 0 0
\(937\) 13.8715 0.453163 0.226582 0.973992i \(-0.427245\pi\)
0.226582 + 0.973992i \(0.427245\pi\)
\(938\) 0 0
\(939\) 80.0329 2.61177
\(940\) 0 0
\(941\) −35.3238 −1.15152 −0.575761 0.817618i \(-0.695294\pi\)
−0.575761 + 0.817618i \(0.695294\pi\)
\(942\) 0 0
\(943\) −7.55317 −0.245965
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −57.9480 −1.88306 −0.941529 0.336933i \(-0.890611\pi\)
−0.941529 + 0.336933i \(0.890611\pi\)
\(948\) 0 0
\(949\) −11.7250 −0.380611
\(950\) 0 0
\(951\) 70.6662 2.29151
\(952\) 0 0
\(953\) −43.9224 −1.42279 −0.711394 0.702794i \(-0.751936\pi\)
−0.711394 + 0.702794i \(0.751936\pi\)
\(954\) 0 0
\(955\) −44.6188 −1.44383
\(956\) 0 0
\(957\) −68.8350 −2.22512
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 32.6191 1.05223
\(962\) 0 0
\(963\) 62.0052 1.99809
\(964\) 0 0
\(965\) 51.6660 1.66319
\(966\) 0 0
\(967\) 46.9160 1.50872 0.754358 0.656463i \(-0.227948\pi\)
0.754358 + 0.656463i \(0.227948\pi\)
\(968\) 0 0
\(969\) −31.1134 −0.999506
\(970\) 0 0
\(971\) −43.2241 −1.38713 −0.693564 0.720395i \(-0.743960\pi\)
−0.693564 + 0.720395i \(0.743960\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 3.92534 0.125712
\(976\) 0 0
\(977\) −37.7307 −1.20711 −0.603556 0.797321i \(-0.706250\pi\)
−0.603556 + 0.797321i \(0.706250\pi\)
\(978\) 0 0
\(979\) −4.10209 −0.131104
\(980\) 0 0
\(981\) −76.4652 −2.44134
\(982\) 0 0
\(983\) −26.9765 −0.860418 −0.430209 0.902729i \(-0.641560\pi\)
−0.430209 + 0.902729i \(0.641560\pi\)
\(984\) 0 0
\(985\) 29.5191 0.940557
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −76.6534 −2.43744
\(990\) 0 0
\(991\) 38.4937 1.22279 0.611396 0.791325i \(-0.290608\pi\)
0.611396 + 0.791325i \(0.290608\pi\)
\(992\) 0 0
\(993\) −29.5613 −0.938098
\(994\) 0 0
\(995\) −19.8812 −0.630278
\(996\) 0 0
\(997\) 47.0970 1.49158 0.745789 0.666183i \(-0.232073\pi\)
0.745789 + 0.666183i \(0.232073\pi\)
\(998\) 0 0
\(999\) −42.8582 −1.35597
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 \(a_p\))