Properties

Label 182.2.a.d.1.1
Level 182
Weight 2
Character 182.1
Self dual Yes
Analytic conductor 1.453
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 182 = 2 \cdot 7 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 182.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.45327731679\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 182.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+1.00000 q^{6}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{9}\) \(-3.00000 q^{11}\) \(+1.00000 q^{12}\) \(+1.00000 q^{13}\) \(+1.00000 q^{14}\) \(+1.00000 q^{16}\) \(-2.00000 q^{18}\) \(+2.00000 q^{19}\) \(+1.00000 q^{21}\) \(-3.00000 q^{22}\) \(-3.00000 q^{23}\) \(+1.00000 q^{24}\) \(-5.00000 q^{25}\) \(+1.00000 q^{26}\) \(-5.00000 q^{27}\) \(+1.00000 q^{28}\) \(+5.00000 q^{31}\) \(+1.00000 q^{32}\) \(-3.00000 q^{33}\) \(-2.00000 q^{36}\) \(-7.00000 q^{37}\) \(+2.00000 q^{38}\) \(+1.00000 q^{39}\) \(+3.00000 q^{41}\) \(+1.00000 q^{42}\) \(+8.00000 q^{43}\) \(-3.00000 q^{44}\) \(-3.00000 q^{46}\) \(-3.00000 q^{47}\) \(+1.00000 q^{48}\) \(+1.00000 q^{49}\) \(-5.00000 q^{50}\) \(+1.00000 q^{52}\) \(-12.0000 q^{53}\) \(-5.00000 q^{54}\) \(+1.00000 q^{56}\) \(+2.00000 q^{57}\) \(+6.00000 q^{59}\) \(-1.00000 q^{61}\) \(+5.00000 q^{62}\) \(-2.00000 q^{63}\) \(+1.00000 q^{64}\) \(-3.00000 q^{66}\) \(+5.00000 q^{67}\) \(-3.00000 q^{69}\) \(+12.0000 q^{71}\) \(-2.00000 q^{72}\) \(+11.0000 q^{73}\) \(-7.00000 q^{74}\) \(-5.00000 q^{75}\) \(+2.00000 q^{76}\) \(-3.00000 q^{77}\) \(+1.00000 q^{78}\) \(-1.00000 q^{79}\) \(+1.00000 q^{81}\) \(+3.00000 q^{82}\) \(+12.0000 q^{83}\) \(+1.00000 q^{84}\) \(+8.00000 q^{86}\) \(-3.00000 q^{88}\) \(-18.0000 q^{89}\) \(+1.00000 q^{91}\) \(-3.00000 q^{92}\) \(+5.00000 q^{93}\) \(-3.00000 q^{94}\) \(+1.00000 q^{96}\) \(+17.0000 q^{97}\) \(+1.00000 q^{98}\) \(+6.00000 q^{99}\) \(+O(q^{100})\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 1.00000 0.288675
\(13\) 1.00000 0.277350
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −2.00000 −0.471405
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) −3.00000 −0.639602
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 1.00000 0.204124
\(25\) −5.00000 −1.00000
\(26\) 1.00000 0.196116
\(27\) −5.00000 −0.962250
\(28\) 1.00000 0.188982
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.00000 −0.522233
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −7.00000 −1.15079 −0.575396 0.817875i \(-0.695152\pi\)
−0.575396 + 0.817875i \(0.695152\pi\)
\(38\) 2.00000 0.324443
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 3.00000 0.468521 0.234261 0.972174i \(-0.424733\pi\)
0.234261 + 0.972174i \(0.424733\pi\)
\(42\) 1.00000 0.154303
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) −3.00000 −0.452267
\(45\) 0 0
\(46\) −3.00000 −0.442326
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 1.00000 0.144338
\(49\) 1.00000 0.142857
\(50\) −5.00000 −0.707107
\(51\) 0 0
\(52\) 1.00000 0.138675
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 2.00000 0.264906
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) −1.00000 −0.128037 −0.0640184 0.997949i \(-0.520392\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 5.00000 0.635001
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) 5.00000 0.610847 0.305424 0.952217i \(-0.401202\pi\)
0.305424 + 0.952217i \(0.401202\pi\)
\(68\) 0 0
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −2.00000 −0.235702
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) −7.00000 −0.813733
\(75\) −5.00000 −0.577350
\(76\) 2.00000 0.229416
\(77\) −3.00000 −0.341882
\(78\) 1.00000 0.113228
\(79\) −1.00000 −0.112509 −0.0562544 0.998416i \(-0.517916\pi\)
−0.0562544 + 0.998416i \(0.517916\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 3.00000 0.331295
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) 8.00000 0.862662
\(87\) 0 0
\(88\) −3.00000 −0.319801
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) −3.00000 −0.312772
\(93\) 5.00000 0.518476
\(94\) −3.00000 −0.309426
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 17.0000 1.72609 0.863044 0.505128i \(-0.168555\pi\)
0.863044 + 0.505128i \(0.168555\pi\)
\(98\) 1.00000 0.101015
\(99\) 6.00000 0.603023
\(100\) −5.00000 −0.500000
\(101\) −3.00000 −0.298511 −0.149256 0.988799i \(-0.547688\pi\)
−0.149256 + 0.988799i \(0.547688\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) −5.00000 −0.481125
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 1.00000 0.0944911
\(113\) 9.00000 0.846649 0.423324 0.905978i \(-0.360863\pi\)
0.423324 + 0.905978i \(0.360863\pi\)
\(114\) 2.00000 0.187317
\(115\) 0 0
\(116\) 0 0
\(117\) −2.00000 −0.184900
\(118\) 6.00000 0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) −1.00000 −0.0905357
\(123\) 3.00000 0.270501
\(124\) 5.00000 0.449013
\(125\) 0 0
\(126\) −2.00000 −0.178174
\(127\) −7.00000 −0.621150 −0.310575 0.950549i \(-0.600522\pi\)
−0.310575 + 0.950549i \(0.600522\pi\)
\(128\) 1.00000 0.0883883
\(129\) 8.00000 0.704361
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −3.00000 −0.261116
\(133\) 2.00000 0.173422
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 −0.512615 −0.256307 0.966595i \(-0.582506\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) −3.00000 −0.255377
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 12.0000 1.00702
\(143\) −3.00000 −0.250873
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 11.0000 0.910366
\(147\) 1.00000 0.0824786
\(148\) −7.00000 −0.575396
\(149\) −15.0000 −1.22885 −0.614424 0.788976i \(-0.710612\pi\)
−0.614424 + 0.788976i \(0.710612\pi\)
\(150\) −5.00000 −0.408248
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 2.00000 0.162221
\(153\) 0 0
\(154\) −3.00000 −0.241747
\(155\) 0 0
\(156\) 1.00000 0.0800641
\(157\) −13.0000 −1.03751 −0.518756 0.854922i \(-0.673605\pi\)
−0.518756 + 0.854922i \(0.673605\pi\)
\(158\) −1.00000 −0.0795557
\(159\) −12.0000 −0.951662
\(160\) 0 0
\(161\) −3.00000 −0.236433
\(162\) 1.00000 0.0785674
\(163\) 20.0000 1.56652 0.783260 0.621694i \(-0.213555\pi\)
0.783260 + 0.621694i \(0.213555\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −24.0000 −1.85718 −0.928588 0.371113i \(-0.878976\pi\)
−0.928588 + 0.371113i \(0.878976\pi\)
\(168\) 1.00000 0.0771517
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −4.00000 −0.305888
\(172\) 8.00000 0.609994
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 0 0
\(175\) −5.00000 −0.377964
\(176\) −3.00000 −0.226134
\(177\) 6.00000 0.450988
\(178\) −18.0000 −1.34916
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 1.00000 0.0741249
\(183\) −1.00000 −0.0739221
\(184\) −3.00000 −0.221163
\(185\) 0 0
\(186\) 5.00000 0.366618
\(187\) 0 0
\(188\) −3.00000 −0.218797
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 1.00000 0.0721688
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 17.0000 1.22053
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 6.00000 0.426401
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −5.00000 −0.353553
\(201\) 5.00000 0.352673
\(202\) −3.00000 −0.211079
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 14.0000 0.975426
\(207\) 6.00000 0.417029
\(208\) 1.00000 0.0693375
\(209\) −6.00000 −0.415029
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) −12.0000 −0.824163
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 5.00000 0.339422
\(218\) 2.00000 0.135457
\(219\) 11.0000 0.743311
\(220\) 0 0
\(221\) 0 0
\(222\) −7.00000 −0.469809
\(223\) −1.00000 −0.0669650 −0.0334825 0.999439i \(-0.510660\pi\)
−0.0334825 + 0.999439i \(0.510660\pi\)
\(224\) 1.00000 0.0668153
\(225\) 10.0000 0.666667
\(226\) 9.00000 0.598671
\(227\) −24.0000 −1.59294 −0.796468 0.604681i \(-0.793301\pi\)
−0.796468 + 0.604681i \(0.793301\pi\)
\(228\) 2.00000 0.132453
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 0 0
\(231\) −3.00000 −0.197386
\(232\) 0 0
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −2.00000 −0.130744
\(235\) 0 0
\(236\) 6.00000 0.390567
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) 26.0000 1.67481 0.837404 0.546585i \(-0.184072\pi\)
0.837404 + 0.546585i \(0.184072\pi\)
\(242\) −2.00000 −0.128565
\(243\) 16.0000 1.02640
\(244\) −1.00000 −0.0640184
\(245\) 0 0
\(246\) 3.00000 0.191273
\(247\) 2.00000 0.127257
\(248\) 5.00000 0.317500
\(249\) 12.0000 0.760469
\(250\) 0 0
\(251\) −15.0000 −0.946792 −0.473396 0.880850i \(-0.656972\pi\)
−0.473396 + 0.880850i \(0.656972\pi\)
\(252\) −2.00000 −0.125988
\(253\) 9.00000 0.565825
\(254\) −7.00000 −0.439219
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 24.0000 1.49708 0.748539 0.663090i \(-0.230755\pi\)
0.748539 + 0.663090i \(0.230755\pi\)
\(258\) 8.00000 0.498058
\(259\) −7.00000 −0.434959
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 24.0000 1.47990 0.739952 0.672660i \(-0.234848\pi\)
0.739952 + 0.672660i \(0.234848\pi\)
\(264\) −3.00000 −0.184637
\(265\) 0 0
\(266\) 2.00000 0.122628
\(267\) −18.0000 −1.10158
\(268\) 5.00000 0.305424
\(269\) −9.00000 −0.548740 −0.274370 0.961624i \(-0.588469\pi\)
−0.274370 + 0.961624i \(0.588469\pi\)
\(270\) 0 0
\(271\) 11.0000 0.668202 0.334101 0.942537i \(-0.391567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(272\) 0 0
\(273\) 1.00000 0.0605228
\(274\) −6.00000 −0.362473
\(275\) 15.0000 0.904534
\(276\) −3.00000 −0.180579
\(277\) 26.0000 1.56219 0.781094 0.624413i \(-0.214662\pi\)
0.781094 + 0.624413i \(0.214662\pi\)
\(278\) −4.00000 −0.239904
\(279\) −10.0000 −0.598684
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) −3.00000 −0.178647
\(283\) −31.0000 −1.84276 −0.921379 0.388664i \(-0.872937\pi\)
−0.921379 + 0.388664i \(0.872937\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) −3.00000 −0.177394
\(287\) 3.00000 0.177084
\(288\) −2.00000 −0.117851
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 17.0000 0.996558
\(292\) 11.0000 0.643726
\(293\) 18.0000 1.05157 0.525786 0.850617i \(-0.323771\pi\)
0.525786 + 0.850617i \(0.323771\pi\)
\(294\) 1.00000 0.0583212
\(295\) 0 0
\(296\) −7.00000 −0.406867
\(297\) 15.0000 0.870388
\(298\) −15.0000 −0.868927
\(299\) −3.00000 −0.173494
\(300\) −5.00000 −0.288675
\(301\) 8.00000 0.461112
\(302\) 8.00000 0.460348
\(303\) −3.00000 −0.172345
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) −3.00000 −0.170941
\(309\) 14.0000 0.796432
\(310\) 0 0
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) 1.00000 0.0566139
\(313\) 26.0000 1.46961 0.734803 0.678280i \(-0.237274\pi\)
0.734803 + 0.678280i \(0.237274\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −1.00000 −0.0562544
\(317\) −3.00000 −0.168497 −0.0842484 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) −12.0000 −0.672927
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) −3.00000 −0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) −5.00000 −0.277350
\(326\) 20.0000 1.10770
\(327\) 2.00000 0.110600
\(328\) 3.00000 0.165647
\(329\) −3.00000 −0.165395
\(330\) 0 0
\(331\) −19.0000 −1.04433 −0.522167 0.852843i \(-0.674876\pi\)
−0.522167 + 0.852843i \(0.674876\pi\)
\(332\) 12.0000 0.658586
\(333\) 14.0000 0.767195
\(334\) −24.0000 −1.31322
\(335\) 0 0
\(336\) 1.00000 0.0545545
\(337\) −31.0000 −1.68868 −0.844339 0.535810i \(-0.820006\pi\)
−0.844339 + 0.535810i \(0.820006\pi\)
\(338\) 1.00000 0.0543928
\(339\) 9.00000 0.488813
\(340\) 0 0
\(341\) −15.0000 −0.812296
\(342\) −4.00000 −0.216295
\(343\) 1.00000 0.0539949
\(344\) 8.00000 0.431331
\(345\) 0 0
\(346\) −18.0000 −0.967686
\(347\) 24.0000 1.28839 0.644194 0.764862i \(-0.277193\pi\)
0.644194 + 0.764862i \(0.277193\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) −5.00000 −0.267261
\(351\) −5.00000 −0.266880
\(352\) −3.00000 −0.159901
\(353\) 15.0000 0.798369 0.399185 0.916871i \(-0.369293\pi\)
0.399185 + 0.916871i \(0.369293\pi\)
\(354\) 6.00000 0.318896
\(355\) 0 0
\(356\) −18.0000 −0.953998
\(357\) 0 0
\(358\) −6.00000 −0.317110
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −7.00000 −0.367912
\(363\) −2.00000 −0.104973
\(364\) 1.00000 0.0524142
\(365\) 0 0
\(366\) −1.00000 −0.0522708
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) −3.00000 −0.156386
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −12.0000 −0.623009
\(372\) 5.00000 0.259238
\(373\) −4.00000 −0.207112 −0.103556 0.994624i \(-0.533022\pi\)
−0.103556 + 0.994624i \(0.533022\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −3.00000 −0.154713
\(377\) 0 0
\(378\) −5.00000 −0.257172
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −7.00000 −0.358621
\(382\) 0 0
\(383\) 3.00000 0.153293 0.0766464 0.997058i \(-0.475579\pi\)
0.0766464 + 0.997058i \(0.475579\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −4.00000 −0.203595
\(387\) −16.0000 −0.813326
\(388\) 17.0000 0.863044
\(389\) −36.0000 −1.82527 −0.912636 0.408773i \(-0.865957\pi\)
−0.912636 + 0.408773i \(0.865957\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −3.00000 −0.151138
\(395\) 0 0
\(396\) 6.00000 0.301511
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) −16.0000 −0.802008
\(399\) 2.00000 0.100125
\(400\) −5.00000 −0.250000
\(401\) 24.0000 1.19850 0.599251 0.800561i \(-0.295465\pi\)
0.599251 + 0.800561i \(0.295465\pi\)
\(402\) 5.00000 0.249377
\(403\) 5.00000 0.249068
\(404\) −3.00000 −0.149256
\(405\) 0 0
\(406\) 0 0
\(407\) 21.0000 1.04093
\(408\) 0 0
\(409\) −22.0000 −1.08783 −0.543915 0.839140i \(-0.683059\pi\)
−0.543915 + 0.839140i \(0.683059\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) 14.0000 0.689730
\(413\) 6.00000 0.295241
\(414\) 6.00000 0.294884
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) −4.00000 −0.195881
\(418\) −6.00000 −0.293470
\(419\) 21.0000 1.02592 0.512959 0.858413i \(-0.328549\pi\)
0.512959 + 0.858413i \(0.328549\pi\)
\(420\) 0 0
\(421\) −37.0000 −1.80327 −0.901635 0.432498i \(-0.857632\pi\)
−0.901635 + 0.432498i \(0.857632\pi\)
\(422\) −22.0000 −1.07094
\(423\) 6.00000 0.291730
\(424\) −12.0000 −0.582772
\(425\) 0 0
\(426\) 12.0000 0.581402
\(427\) −1.00000 −0.0483934
\(428\) 0 0
\(429\) −3.00000 −0.144841
\(430\) 0 0
\(431\) −6.00000 −0.289010 −0.144505 0.989504i \(-0.546159\pi\)
−0.144505 + 0.989504i \(0.546159\pi\)
\(432\) −5.00000 −0.240563
\(433\) 38.0000 1.82616 0.913082 0.407777i \(-0.133696\pi\)
0.913082 + 0.407777i \(0.133696\pi\)
\(434\) 5.00000 0.240008
\(435\) 0 0
\(436\) 2.00000 0.0957826
\(437\) −6.00000 −0.287019
\(438\) 11.0000 0.525600
\(439\) 26.0000 1.24091 0.620456 0.784241i \(-0.286947\pi\)
0.620456 + 0.784241i \(0.286947\pi\)
\(440\) 0 0
\(441\) −2.00000 −0.0952381
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) −7.00000 −0.332205
\(445\) 0 0
\(446\) −1.00000 −0.0473514
\(447\) −15.0000 −0.709476
\(448\) 1.00000 0.0472456
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 10.0000 0.471405
\(451\) −9.00000 −0.423793
\(452\) 9.00000 0.423324
\(453\) 8.00000 0.375873
\(454\) −24.0000 −1.12638
\(455\) 0 0
\(456\) 2.00000 0.0936586
\(457\) 26.0000 1.21623 0.608114 0.793849i \(-0.291926\pi\)
0.608114 + 0.793849i \(0.291926\pi\)
\(458\) −4.00000 −0.186908
\(459\) 0 0
\(460\) 0 0
\(461\) 24.0000 1.11779 0.558896 0.829238i \(-0.311225\pi\)
0.558896 + 0.829238i \(0.311225\pi\)
\(462\) −3.00000 −0.139573
\(463\) −40.0000 −1.85896 −0.929479 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 3.00000 0.138972
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) −2.00000 −0.0924500
\(469\) 5.00000 0.230879
\(470\) 0 0
\(471\) −13.0000 −0.599008
\(472\) 6.00000 0.276172
\(473\) −24.0000 −1.10352
\(474\) −1.00000 −0.0459315
\(475\) −10.0000 −0.458831
\(476\) 0 0
\(477\) 24.0000 1.09888
\(478\) 6.00000 0.274434
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −7.00000 −0.319173
\(482\) 26.0000 1.18427
\(483\) −3.00000 −0.136505
\(484\) −2.00000 −0.0909091
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 20.0000 0.904431
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 3.00000 0.135250
\(493\) 0 0
\(494\) 2.00000 0.0899843
\(495\) 0 0
\(496\) 5.00000 0.224507
\(497\) 12.0000 0.538274
\(498\) 12.0000 0.537733
\(499\) 23.0000 1.02962 0.514811 0.857304i \(-0.327862\pi\)
0.514811 + 0.857304i \(0.327862\pi\)
\(500\) 0 0
\(501\) −24.0000 −1.07224
\(502\) −15.0000 −0.669483
\(503\) 12.0000 0.535054 0.267527 0.963550i \(-0.413794\pi\)
0.267527 + 0.963550i \(0.413794\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) 9.00000 0.400099
\(507\) 1.00000 0.0444116
\(508\) −7.00000 −0.310575
\(509\) −30.0000 −1.32973 −0.664863 0.746965i \(-0.731510\pi\)
−0.664863 + 0.746965i \(0.731510\pi\)
\(510\) 0 0
\(511\) 11.0000 0.486611
\(512\) 1.00000 0.0441942
\(513\) −10.0000 −0.441511
\(514\) 24.0000 1.05859
\(515\) 0 0
\(516\) 8.00000 0.352180
\(517\) 9.00000 0.395820
\(518\) −7.00000 −0.307562
\(519\) −18.0000 −0.790112
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −7.00000 −0.306089 −0.153044 0.988219i \(-0.548908\pi\)
−0.153044 + 0.988219i \(0.548908\pi\)
\(524\) 0 0
\(525\) −5.00000 −0.218218
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) −3.00000 −0.130558
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 2.00000 0.0867110
\(533\) 3.00000 0.129944
\(534\) −18.0000 −0.778936
\(535\) 0 0
\(536\) 5.00000 0.215967
\(537\) −6.00000 −0.258919
\(538\) −9.00000 −0.388018
\(539\) −3.00000 −0.129219
\(540\) 0 0
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 11.0000 0.472490
\(543\) −7.00000 −0.300399
\(544\) 0 0
\(545\) 0 0
\(546\) 1.00000 0.0427960
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −6.00000 −0.256307
\(549\) 2.00000 0.0853579
\(550\) 15.0000 0.639602
\(551\) 0 0
\(552\) −3.00000 −0.127688
\(553\) −1.00000 −0.0425243
\(554\) 26.0000 1.10463
\(555\) 0 0
\(556\) −4.00000 −0.169638
\(557\) −15.0000 −0.635570 −0.317785 0.948163i \(-0.602939\pi\)
−0.317785 + 0.948163i \(0.602939\pi\)
\(558\) −10.0000 −0.423334
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) 0 0
\(562\) 12.0000 0.506189
\(563\) −39.0000 −1.64365 −0.821827 0.569737i \(-0.807045\pi\)
−0.821827 + 0.569737i \(0.807045\pi\)
\(564\) −3.00000 −0.126323
\(565\) 0 0
\(566\) −31.0000 −1.30303
\(567\) 1.00000 0.0419961
\(568\) 12.0000 0.503509
\(569\) 21.0000 0.880366 0.440183 0.897908i \(-0.354914\pi\)
0.440183 + 0.897908i \(0.354914\pi\)
\(570\) 0 0
\(571\) −22.0000 −0.920671 −0.460336 0.887745i \(-0.652271\pi\)
−0.460336 + 0.887745i \(0.652271\pi\)
\(572\) −3.00000 −0.125436
\(573\) 0 0
\(574\) 3.00000 0.125218
\(575\) 15.0000 0.625543
\(576\) −2.00000 −0.0833333
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) −17.0000 −0.707107
\(579\) −4.00000 −0.166234
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 17.0000 0.704673
\(583\) 36.0000 1.49097
\(584\) 11.0000 0.455183
\(585\) 0 0
\(586\) 18.0000 0.743573
\(587\) 18.0000 0.742940 0.371470 0.928445i \(-0.378854\pi\)
0.371470 + 0.928445i \(0.378854\pi\)
\(588\) 1.00000 0.0412393
\(589\) 10.0000 0.412043
\(590\) 0 0
\(591\) −3.00000 −0.123404
\(592\) −7.00000 −0.287698
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) 15.0000 0.615457
\(595\) 0 0
\(596\) −15.0000 −0.614424
\(597\) −16.0000 −0.654836
\(598\) −3.00000 −0.122679
\(599\) 39.0000 1.59350 0.796748 0.604311i \(-0.206552\pi\)
0.796748 + 0.604311i \(0.206552\pi\)
\(600\) −5.00000 −0.204124
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 8.00000 0.326056
\(603\) −10.0000 −0.407231
\(604\) 8.00000 0.325515
\(605\) 0 0
\(606\) −3.00000 −0.121867
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) 2.00000 0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −3.00000 −0.121367
\(612\) 0 0
\(613\) −25.0000 −1.00974 −0.504870 0.863195i \(-0.668460\pi\)
−0.504870 + 0.863195i \(0.668460\pi\)
\(614\) −16.0000 −0.645707
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 14.0000 0.563163
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) 15.0000 0.601929
\(622\) 30.0000 1.20289
\(623\) −18.0000 −0.721155
\(624\) 1.00000 0.0400320
\(625\) 25.0000 1.00000
\(626\) 26.0000 1.03917
\(627\) −6.00000 −0.239617
\(628\) −13.0000 −0.518756
\(629\) 0 0
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) −1.00000 −0.0397779
\(633\) −22.0000 −0.874421
\(634\) −3.00000 −0.119145
\(635\) 0 0
\(636\) −12.0000 −0.475831
\(637\) 1.00000 0.0396214
\(638\) 0 0
\(639\) −24.0000 −0.949425
\(640\) 0 0
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 0 0
\(643\) 32.0000 1.26196 0.630978 0.775800i \(-0.282654\pi\)
0.630978 + 0.775800i \(0.282654\pi\)
\(644\) −3.00000 −0.118217
\(645\) 0 0
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 1.00000 0.0392837
\(649\) −18.0000 −0.706562
\(650\) −5.00000 −0.196116
\(651\) 5.00000 0.195965
\(652\) 20.0000 0.783260
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 2.00000 0.0782062
\(655\) 0 0
\(656\) 3.00000 0.117130
\(657\) −22.0000 −0.858302
\(658\) −3.00000 −0.116952
\(659\) 42.0000 1.63609 0.818044 0.575156i \(-0.195059\pi\)
0.818044 + 0.575156i \(0.195059\pi\)
\(660\) 0 0
\(661\) 32.0000 1.24466 0.622328 0.782757i \(-0.286187\pi\)
0.622328 + 0.782757i \(0.286187\pi\)
\(662\) −19.0000 −0.738456
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 14.0000 0.542489
\(667\) 0 0
\(668\) −24.0000 −0.928588
\(669\) −1.00000 −0.0386622
\(670\) 0 0
\(671\) 3.00000 0.115814
\(672\) 1.00000 0.0385758
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) −31.0000 −1.19408
\(675\) 25.0000 0.962250
\(676\) 1.00000 0.0384615
\(677\) −39.0000 −1.49889 −0.749446 0.662066i \(-0.769680\pi\)
−0.749446 + 0.662066i \(0.769680\pi\)
\(678\) 9.00000 0.345643
\(679\) 17.0000 0.652400
\(680\) 0 0
\(681\) −24.0000 −0.919682
\(682\) −15.0000 −0.574380
\(683\) −27.0000 −1.03313 −0.516563 0.856249i \(-0.672789\pi\)
−0.516563 + 0.856249i \(0.672789\pi\)
\(684\) −4.00000 −0.152944
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) −4.00000 −0.152610
\(688\) 8.00000 0.304997
\(689\) −12.0000 −0.457164
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) −18.0000 −0.684257
\(693\) 6.00000 0.227921
\(694\) 24.0000 0.911028
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −10.0000 −0.378506
\(699\) 3.00000 0.113470
\(700\) −5.00000 −0.188982
\(701\) −36.0000 −1.35970 −0.679851 0.733351i \(-0.737955\pi\)
−0.679851 + 0.733351i \(0.737955\pi\)
\(702\) −5.00000 −0.188713
\(703\) −14.0000 −0.528020
\(704\) −3.00000 −0.113067
\(705\) 0 0
\(706\) 15.0000 0.564532
\(707\) −3.00000 −0.112827
\(708\) 6.00000 0.225494
\(709\) 35.0000 1.31445 0.657226 0.753693i \(-0.271730\pi\)
0.657226 + 0.753693i \(0.271730\pi\)
\(710\) 0 0
\(711\) 2.00000 0.0750059
\(712\) −18.0000 −0.674579
\(713\) −15.0000 −0.561754
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) 6.00000 0.224074
\(718\) −24.0000 −0.895672
\(719\) 6.00000 0.223762 0.111881 0.993722i \(-0.464312\pi\)
0.111881 + 0.993722i \(0.464312\pi\)
\(720\) 0 0
\(721\) 14.0000 0.521387
\(722\) −15.0000 −0.558242
\(723\) 26.0000 0.966950
\(724\) −7.00000 −0.260153
\(725\) 0 0
\(726\) −2.00000 −0.0742270
\(727\) 26.0000 0.964287 0.482143 0.876092i \(-0.339858\pi\)
0.482143 + 0.876092i \(0.339858\pi\)
\(728\) 1.00000 0.0370625
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) −1.00000 −0.0369611
\(733\) −4.00000 −0.147743 −0.0738717 0.997268i \(-0.523536\pi\)
−0.0738717 + 0.997268i \(0.523536\pi\)
\(734\) −28.0000 −1.03350
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) −15.0000 −0.552532
\(738\) −6.00000 −0.220863
\(739\) −16.0000 −0.588570 −0.294285 0.955718i \(-0.595081\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 0 0
\(741\) 2.00000 0.0734718
\(742\) −12.0000 −0.440534
\(743\) −24.0000 −0.880475 −0.440237 0.897881i \(-0.645106\pi\)
−0.440237 + 0.897881i \(0.645106\pi\)
\(744\) 5.00000 0.183309
\(745\) 0 0
\(746\) −4.00000 −0.146450
\(747\) −24.0000 −0.878114
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −31.0000 −1.13121 −0.565603 0.824678i \(-0.691357\pi\)
−0.565603 + 0.824678i \(0.691357\pi\)
\(752\) −3.00000 −0.109399
\(753\) −15.0000 −0.546630
\(754\) 0 0
\(755\) 0 0
\(756\) −5.00000 −0.181848
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) −16.0000 −0.581146
\(759\) 9.00000 0.326679
\(760\) 0 0
\(761\) 3.00000 0.108750 0.0543750 0.998521i \(-0.482683\pi\)
0.0543750 + 0.998521i \(0.482683\pi\)
\(762\) −7.00000 −0.253583
\(763\) 2.00000 0.0724049
\(764\) 0 0
\(765\) 0 0
\(766\) 3.00000 0.108394
\(767\) 6.00000 0.216647
\(768\) 1.00000 0.0360844
\(769\) −13.0000 −0.468792 −0.234396 0.972141i \(-0.575311\pi\)
−0.234396 + 0.972141i \(0.575311\pi\)
\(770\) 0 0
\(771\) 24.0000 0.864339
\(772\) −4.00000 −0.143963
\(773\) −54.0000 −1.94225 −0.971123 0.238581i \(-0.923318\pi\)
−0.971123 + 0.238581i \(0.923318\pi\)
\(774\) −16.0000 −0.575108
\(775\) −25.0000 −0.898027
\(776\) 17.0000 0.610264
\(777\) −7.00000 −0.251124
\(778\) −36.0000 −1.29066
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) −3.00000 −0.106871
\(789\) 24.0000 0.854423
\(790\) 0 0
\(791\) 9.00000 0.320003
\(792\) 6.00000 0.213201
\(793\) −1.00000 −0.0355110
\(794\) 20.0000 0.709773
\(795\) 0 0
\(796\) −16.0000 −0.567105
\(797\) 9.00000 0.318796 0.159398 0.987214i \(-0.449045\pi\)
0.159398 + 0.987214i \(0.449045\pi\)
\(798\) 2.00000 0.0707992
\(799\) 0 0
\(800\) −5.00000 −0.176777
\(801\) 36.0000 1.27200
\(802\) 24.0000 0.847469
\(803\) −33.0000 −1.16454
\(804\) 5.00000 0.176336
\(805\) 0 0
\(806\) 5.00000 0.176117
\(807\) −9.00000 −0.316815
\(808\) −3.00000 −0.105540
\(809\) 30.0000 1.05474 0.527372 0.849635i \(-0.323177\pi\)
0.527372 + 0.849635i \(0.323177\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 11.0000 0.385787
\(814\) 21.0000 0.736050
\(815\) 0 0
\(816\) 0 0
\(817\) 16.0000 0.559769
\(818\) −22.0000 −0.769212
\(819\) −2.00000 −0.0698857
\(820\) 0 0
\(821\) −6.00000 −0.209401 −0.104701 0.994504i \(-0.533388\pi\)
−0.104701 + 0.994504i \(0.533388\pi\)
\(822\) −6.00000 −0.209274
\(823\) 41.0000 1.42917 0.714585 0.699549i \(-0.246616\pi\)
0.714585 + 0.699549i \(0.246616\pi\)
\(824\) 14.0000 0.487713
\(825\) 15.0000 0.522233
\(826\) 6.00000 0.208767
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 6.00000 0.208514
\(829\) 38.0000 1.31979 0.659897 0.751356i \(-0.270600\pi\)
0.659897 + 0.751356i \(0.270600\pi\)
\(830\) 0 0
\(831\) 26.0000 0.901930
\(832\) 1.00000 0.0346688
\(833\) 0 0
\(834\) −4.00000 −0.138509
\(835\) 0 0
\(836\) −6.00000 −0.207514
\(837\) −25.0000 −0.864126
\(838\) 21.0000 0.725433
\(839\) −21.0000 −0.725001 −0.362500 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) −37.0000 −1.27510
\(843\) 12.0000 0.413302
\(844\) −22.0000 −0.757271
\(845\) 0 0
\(846\) 6.00000 0.206284
\(847\) −2.00000 −0.0687208
\(848\) −12.0000 −0.412082
\(849\) −31.0000 −1.06392
\(850\) 0 0
\(851\) 21.0000 0.719871
\(852\) 12.0000 0.411113
\(853\) 44.0000 1.50653 0.753266 0.657716i \(-0.228477\pi\)
0.753266 + 0.657716i \(0.228477\pi\)
\(854\) −1.00000 −0.0342193
\(855\) 0 0
\(856\) 0 0
\(857\) 54.0000 1.84460 0.922302 0.386469i \(-0.126305\pi\)
0.922302 + 0.386469i \(0.126305\pi\)
\(858\) −3.00000 −0.102418
\(859\) 23.0000 0.784750 0.392375 0.919805i \(-0.371654\pi\)
0.392375 + 0.919805i \(0.371654\pi\)
\(860\) 0 0
\(861\) 3.00000 0.102240
\(862\) −6.00000 −0.204361
\(863\) 12.0000 0.408485 0.204242 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) −5.00000 −0.170103
\(865\) 0 0
\(866\) 38.0000 1.29129
\(867\) −17.0000 −0.577350
\(868\) 5.00000 0.169711
\(869\) 3.00000 0.101768
\(870\) 0 0
\(871\) 5.00000 0.169419
\(872\) 2.00000 0.0677285
\(873\) −34.0000 −1.15073
\(874\) −6.00000 −0.202953
\(875\) 0 0
\(876\) 11.0000 0.371656
\(877\) −13.0000 −0.438979 −0.219489 0.975615i \(-0.570439\pi\)
−0.219489 + 0.975615i \(0.570439\pi\)
\(878\) 26.0000 0.877457
\(879\) 18.0000 0.607125
\(880\) 0 0
\(881\) 6.00000 0.202145 0.101073 0.994879i \(-0.467773\pi\)
0.101073 + 0.994879i \(0.467773\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 2.00000 0.0673054 0.0336527 0.999434i \(-0.489286\pi\)
0.0336527 + 0.999434i \(0.489286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 24.0000 0.806296
\(887\) 42.0000 1.41022 0.705111 0.709097i \(-0.250897\pi\)
0.705111 + 0.709097i \(0.250897\pi\)
\(888\) −7.00000 −0.234905
\(889\) −7.00000 −0.234772
\(890\) 0 0
\(891\) −3.00000 −0.100504
\(892\) −1.00000 −0.0334825
\(893\) −6.00000 −0.200782
\(894\) −15.0000 −0.501675
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) −3.00000 −0.100167
\(898\) −6.00000 −0.200223
\(899\) 0 0
\(900\) 10.0000 0.333333
\(901\) 0 0
\(902\) −9.00000 −0.299667
\(903\) 8.00000 0.266223
\(904\) 9.00000 0.299336
\(905\) 0 0
\(906\) 8.00000 0.265782
\(907\) 26.0000 0.863316 0.431658 0.902037i \(-0.357929\pi\)
0.431658 + 0.902037i \(0.357929\pi\)
\(908\) −24.0000 −0.796468
\(909\) 6.00000 0.199007
\(910\) 0 0
\(911\) 12.0000 0.397578 0.198789 0.980042i \(-0.436299\pi\)
0.198789 + 0.980042i \(0.436299\pi\)
\(912\) 2.00000 0.0662266
\(913\) −36.0000 −1.19143
\(914\) 26.0000 0.860004
\(915\) 0 0
\(916\) −4.00000 −0.132164
\(917\) 0 0
\(918\) 0 0
\(919\) −25.0000 −0.824674 −0.412337 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) 0 0
\(921\) −16.0000 −0.527218
\(922\) 24.0000 0.790398
\(923\) 12.0000 0.394985
\(924\) −3.00000 −0.0986928
\(925\) 35.0000 1.15079
\(926\) −40.0000 −1.31448
\(927\) −28.0000 −0.919641
\(928\) 0 0
\(929\) −9.00000 −0.295280 −0.147640 0.989041i \(-0.547168\pi\)
−0.147640 + 0.989041i \(0.547168\pi\)
\(930\) 0 0
\(931\) 2.00000 0.0655474
\(932\) 3.00000 0.0982683
\(933\) 30.0000 0.982156
\(934\) 12.0000 0.392652
\(935\) 0 0
\(936\) −2.00000 −0.0653720
\(937\) −52.0000 −1.69877 −0.849383 0.527777i \(-0.823026\pi\)
−0.849383 + 0.527777i \(0.823026\pi\)
\(938\) 5.00000 0.163256
\(939\) 26.0000 0.848478
\(940\) 0 0
\(941\) 30.0000 0.977972 0.488986 0.872292i \(-0.337367\pi\)
0.488986 + 0.872292i \(0.337367\pi\)
\(942\) −13.0000 −0.423563
\(943\) −9.00000 −0.293080
\(944\) 6.00000 0.195283
\(945\) 0 0
\(946\) −24.0000 −0.780307
\(947\) 48.0000 1.55979 0.779895 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) −1.00000 −0.0324785
\(949\) 11.0000 0.357075
\(950\) −10.0000 −0.324443
\(951\) −3.00000 −0.0972817
\(952\) 0 0
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 24.0000 0.777029
\(955\) 0 0
\(956\) 6.00000 0.194054
\(957\) 0 0
\(958\) 24.0000 0.775405
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) −6.00000 −0.193548
\(962\) −7.00000 −0.225689
\(963\) 0 0
\(964\) 26.0000 0.837404
\(965\) 0 0
\(966\) −3.00000 −0.0965234
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) −2.00000 −0.0642824
\(969\) 0 0
\(970\) 0 0
\(971\) −21.0000 −0.673922 −0.336961 0.941519i \(-0.609399\pi\)
−0.336961 + 0.941519i \(0.609399\pi\)
\(972\) 16.0000 0.513200
\(973\) −4.00000 −0.128234
\(974\) 2.00000 0.0640841
\(975\) −5.00000 −0.160128
\(976\) −1.00000 −0.0320092
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 20.0000 0.639529
\(979\) 54.0000 1.72585
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) 12.0000 0.382935
\(983\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 3.00000 0.0956365
\(985\) 0 0
\(986\) 0 0
\(987\) −3.00000 −0.0954911
\(988\) 2.00000 0.0636285
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) 11.0000 0.349427 0.174713 0.984619i \(-0.444100\pi\)
0.174713 + 0.984619i \(0.444100\pi\)
\(992\) 5.00000 0.158750
\(993\) −19.0000 −0.602947
\(994\) 12.0000 0.380617
\(995\) 0 0
\(996\) 12.0000 0.380235
\(997\) −37.0000 −1.17180 −0.585901 0.810383i \(-0.699259\pi\)
−0.585901 + 0.810383i \(0.699259\pi\)
\(998\) 23.0000 0.728052
\(999\) 35.0000 1.10735
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 \(a_p\))