Properties

Label 8036.2.a.q.1.11
Level 8036
Weight 2
Character 8036.1
Self dual Yes
Analytic conductor 64.168
Analytic rank 0
Dimension 15
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: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Root \(-2.11769\)
Character \(\chi\) = 8036.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.11769 q^{3} +3.93656 q^{5} +1.48461 q^{9} +O(q^{10})\) \(q+2.11769 q^{3} +3.93656 q^{5} +1.48461 q^{9} +4.13020 q^{11} +1.64438 q^{13} +8.33642 q^{15} -5.20325 q^{17} -6.58422 q^{19} +7.17263 q^{23} +10.4965 q^{25} -3.20913 q^{27} -9.38888 q^{29} +6.46362 q^{31} +8.74649 q^{33} +11.3246 q^{37} +3.48230 q^{39} -1.00000 q^{41} -0.742453 q^{43} +5.84425 q^{45} +0.264604 q^{47} -11.0189 q^{51} -0.838544 q^{53} +16.2588 q^{55} -13.9433 q^{57} -5.28576 q^{59} +2.56825 q^{61} +6.47323 q^{65} +12.9381 q^{67} +15.1894 q^{69} +5.81754 q^{71} +12.4835 q^{73} +22.2284 q^{75} +2.51028 q^{79} -11.2498 q^{81} -8.61393 q^{83} -20.4829 q^{85} -19.8827 q^{87} +1.18149 q^{89} +13.6879 q^{93} -25.9192 q^{95} +6.32575 q^{97} +6.13173 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 15q - q^{3} + 3q^{5} + 30q^{9} + O(q^{10}) \) \( 15q - q^{3} + 3q^{5} + 30q^{9} + 9q^{11} + 7q^{13} + 2q^{15} + 3q^{17} + 7q^{19} - q^{23} + 32q^{25} + 11q^{27} + 18q^{29} + 30q^{31} - 16q^{33} + 23q^{37} + 5q^{39} - 15q^{41} + 12q^{43} - 13q^{45} - 16q^{47} + 29q^{51} + 33q^{53} + 37q^{55} + 16q^{57} - 10q^{59} + q^{61} + 16q^{65} + 20q^{67} + 21q^{69} + 5q^{71} - 3q^{73} - 51q^{75} + 25q^{79} + 43q^{81} + 18q^{83} + 36q^{85} - 53q^{87} - 11q^{89} + 65q^{93} - 30q^{95} + 16q^{97} - 18q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.11769 1.22265 0.611324 0.791380i \(-0.290637\pi\)
0.611324 + 0.791380i \(0.290637\pi\)
\(4\) 0 0
\(5\) 3.93656 1.76049 0.880243 0.474524i \(-0.157380\pi\)
0.880243 + 0.474524i \(0.157380\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 1.48461 0.494869
\(10\) 0 0
\(11\) 4.13020 1.24530 0.622652 0.782499i \(-0.286055\pi\)
0.622652 + 0.782499i \(0.286055\pi\)
\(12\) 0 0
\(13\) 1.64438 0.456070 0.228035 0.973653i \(-0.426770\pi\)
0.228035 + 0.973653i \(0.426770\pi\)
\(14\) 0 0
\(15\) 8.33642 2.15245
\(16\) 0 0
\(17\) −5.20325 −1.26197 −0.630987 0.775794i \(-0.717350\pi\)
−0.630987 + 0.775794i \(0.717350\pi\)
\(18\) 0 0
\(19\) −6.58422 −1.51052 −0.755262 0.655423i \(-0.772490\pi\)
−0.755262 + 0.655423i \(0.772490\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 7.17263 1.49560 0.747798 0.663926i \(-0.231111\pi\)
0.747798 + 0.663926i \(0.231111\pi\)
\(24\) 0 0
\(25\) 10.4965 2.09931
\(26\) 0 0
\(27\) −3.20913 −0.617598
\(28\) 0 0
\(29\) −9.38888 −1.74347 −0.871736 0.489976i \(-0.837006\pi\)
−0.871736 + 0.489976i \(0.837006\pi\)
\(30\) 0 0
\(31\) 6.46362 1.16090 0.580450 0.814296i \(-0.302877\pi\)
0.580450 + 0.814296i \(0.302877\pi\)
\(32\) 0 0
\(33\) 8.74649 1.52257
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 11.3246 1.86175 0.930873 0.365343i \(-0.119048\pi\)
0.930873 + 0.365343i \(0.119048\pi\)
\(38\) 0 0
\(39\) 3.48230 0.557614
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −0.742453 −0.113223 −0.0566115 0.998396i \(-0.518030\pi\)
−0.0566115 + 0.998396i \(0.518030\pi\)
\(44\) 0 0
\(45\) 5.84425 0.871209
\(46\) 0 0
\(47\) 0.264604 0.0385964 0.0192982 0.999814i \(-0.493857\pi\)
0.0192982 + 0.999814i \(0.493857\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −11.0189 −1.54295
\(52\) 0 0
\(53\) −0.838544 −0.115183 −0.0575914 0.998340i \(-0.518342\pi\)
−0.0575914 + 0.998340i \(0.518342\pi\)
\(54\) 0 0
\(55\) 16.2588 2.19234
\(56\) 0 0
\(57\) −13.9433 −1.84684
\(58\) 0 0
\(59\) −5.28576 −0.688148 −0.344074 0.938943i \(-0.611807\pi\)
−0.344074 + 0.938943i \(0.611807\pi\)
\(60\) 0 0
\(61\) 2.56825 0.328831 0.164415 0.986391i \(-0.447426\pi\)
0.164415 + 0.986391i \(0.447426\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.47323 0.802905
\(66\) 0 0
\(67\) 12.9381 1.58064 0.790318 0.612697i \(-0.209915\pi\)
0.790318 + 0.612697i \(0.209915\pi\)
\(68\) 0 0
\(69\) 15.1894 1.82859
\(70\) 0 0
\(71\) 5.81754 0.690415 0.345207 0.938526i \(-0.387809\pi\)
0.345207 + 0.938526i \(0.387809\pi\)
\(72\) 0 0
\(73\) 12.4835 1.46109 0.730544 0.682866i \(-0.239267\pi\)
0.730544 + 0.682866i \(0.239267\pi\)
\(74\) 0 0
\(75\) 22.2284 2.56672
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 2.51028 0.282429 0.141214 0.989979i \(-0.454899\pi\)
0.141214 + 0.989979i \(0.454899\pi\)
\(80\) 0 0
\(81\) −11.2498 −1.24997
\(82\) 0 0
\(83\) −8.61393 −0.945501 −0.472751 0.881196i \(-0.656739\pi\)
−0.472751 + 0.881196i \(0.656739\pi\)
\(84\) 0 0
\(85\) −20.4829 −2.22169
\(86\) 0 0
\(87\) −19.8827 −2.13165
\(88\) 0 0
\(89\) 1.18149 0.125238 0.0626190 0.998038i \(-0.480055\pi\)
0.0626190 + 0.998038i \(0.480055\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 13.6879 1.41937
\(94\) 0 0
\(95\) −25.9192 −2.65926
\(96\) 0 0
\(97\) 6.32575 0.642283 0.321141 0.947031i \(-0.395934\pi\)
0.321141 + 0.947031i \(0.395934\pi\)
\(98\) 0 0
\(99\) 6.13173 0.616262
\(100\) 0 0
\(101\) 13.1843 1.31189 0.655946 0.754808i \(-0.272270\pi\)
0.655946 + 0.754808i \(0.272270\pi\)
\(102\) 0 0
\(103\) 15.8507 1.56182 0.780909 0.624645i \(-0.214756\pi\)
0.780909 + 0.624645i \(0.214756\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.98270 0.771717 0.385858 0.922558i \(-0.373905\pi\)
0.385858 + 0.922558i \(0.373905\pi\)
\(108\) 0 0
\(109\) 12.0240 1.15169 0.575847 0.817557i \(-0.304672\pi\)
0.575847 + 0.817557i \(0.304672\pi\)
\(110\) 0 0
\(111\) 23.9819 2.27626
\(112\) 0 0
\(113\) −18.6408 −1.75358 −0.876788 0.480876i \(-0.840319\pi\)
−0.876788 + 0.480876i \(0.840319\pi\)
\(114\) 0 0
\(115\) 28.2355 2.63298
\(116\) 0 0
\(117\) 2.44126 0.225695
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 6.05859 0.550781
\(122\) 0 0
\(123\) −2.11769 −0.190946
\(124\) 0 0
\(125\) 21.6375 1.93532
\(126\) 0 0
\(127\) −4.15387 −0.368596 −0.184298 0.982870i \(-0.559001\pi\)
−0.184298 + 0.982870i \(0.559001\pi\)
\(128\) 0 0
\(129\) −1.57228 −0.138432
\(130\) 0 0
\(131\) −10.5045 −0.917786 −0.458893 0.888492i \(-0.651754\pi\)
−0.458893 + 0.888492i \(0.651754\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −12.6330 −1.08727
\(136\) 0 0
\(137\) 1.41888 0.121223 0.0606117 0.998161i \(-0.480695\pi\)
0.0606117 + 0.998161i \(0.480695\pi\)
\(138\) 0 0
\(139\) −10.3332 −0.876448 −0.438224 0.898866i \(-0.644392\pi\)
−0.438224 + 0.898866i \(0.644392\pi\)
\(140\) 0 0
\(141\) 0.560348 0.0471898
\(142\) 0 0
\(143\) 6.79165 0.567946
\(144\) 0 0
\(145\) −36.9599 −3.06936
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.28402 0.105191 0.0525954 0.998616i \(-0.483251\pi\)
0.0525954 + 0.998616i \(0.483251\pi\)
\(150\) 0 0
\(151\) 6.45601 0.525382 0.262691 0.964880i \(-0.415390\pi\)
0.262691 + 0.964880i \(0.415390\pi\)
\(152\) 0 0
\(153\) −7.72478 −0.624511
\(154\) 0 0
\(155\) 25.4444 2.04375
\(156\) 0 0
\(157\) −16.2843 −1.29963 −0.649815 0.760093i \(-0.725154\pi\)
−0.649815 + 0.760093i \(0.725154\pi\)
\(158\) 0 0
\(159\) −1.77577 −0.140828
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 1.33662 0.104692 0.0523459 0.998629i \(-0.483330\pi\)
0.0523459 + 0.998629i \(0.483330\pi\)
\(164\) 0 0
\(165\) 34.4311 2.68046
\(166\) 0 0
\(167\) 9.64888 0.746653 0.373326 0.927700i \(-0.378217\pi\)
0.373326 + 0.927700i \(0.378217\pi\)
\(168\) 0 0
\(169\) −10.2960 −0.792000
\(170\) 0 0
\(171\) −9.77498 −0.747511
\(172\) 0 0
\(173\) 0.394838 0.0300190 0.0150095 0.999887i \(-0.495222\pi\)
0.0150095 + 0.999887i \(0.495222\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −11.1936 −0.841362
\(178\) 0 0
\(179\) −7.95229 −0.594382 −0.297191 0.954818i \(-0.596050\pi\)
−0.297191 + 0.954818i \(0.596050\pi\)
\(180\) 0 0
\(181\) 2.47729 0.184135 0.0920677 0.995753i \(-0.470652\pi\)
0.0920677 + 0.995753i \(0.470652\pi\)
\(182\) 0 0
\(183\) 5.43875 0.402044
\(184\) 0 0
\(185\) 44.5799 3.27758
\(186\) 0 0
\(187\) −21.4905 −1.57154
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.03672 0.581517 0.290758 0.956797i \(-0.406092\pi\)
0.290758 + 0.956797i \(0.406092\pi\)
\(192\) 0 0
\(193\) −18.7700 −1.35109 −0.675547 0.737317i \(-0.736092\pi\)
−0.675547 + 0.737317i \(0.736092\pi\)
\(194\) 0 0
\(195\) 13.7083 0.981670
\(196\) 0 0
\(197\) 10.9468 0.779924 0.389962 0.920831i \(-0.372488\pi\)
0.389962 + 0.920831i \(0.372488\pi\)
\(198\) 0 0
\(199\) −20.8786 −1.48004 −0.740022 0.672583i \(-0.765185\pi\)
−0.740022 + 0.672583i \(0.765185\pi\)
\(200\) 0 0
\(201\) 27.3988 1.93256
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) −3.93656 −0.274942
\(206\) 0 0
\(207\) 10.6485 0.740124
\(208\) 0 0
\(209\) −27.1942 −1.88106
\(210\) 0 0
\(211\) 4.44265 0.305845 0.152922 0.988238i \(-0.451132\pi\)
0.152922 + 0.988238i \(0.451132\pi\)
\(212\) 0 0
\(213\) 12.3197 0.844134
\(214\) 0 0
\(215\) −2.92271 −0.199327
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 26.4362 1.78640
\(220\) 0 0
\(221\) −8.55614 −0.575549
\(222\) 0 0
\(223\) 9.49744 0.635995 0.317998 0.948091i \(-0.396990\pi\)
0.317998 + 0.948091i \(0.396990\pi\)
\(224\) 0 0
\(225\) 15.5832 1.03888
\(226\) 0 0
\(227\) −12.6954 −0.842621 −0.421311 0.906916i \(-0.638430\pi\)
−0.421311 + 0.906916i \(0.638430\pi\)
\(228\) 0 0
\(229\) −13.2558 −0.875966 −0.437983 0.898983i \(-0.644307\pi\)
−0.437983 + 0.898983i \(0.644307\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.8763 0.778042 0.389021 0.921229i \(-0.372813\pi\)
0.389021 + 0.921229i \(0.372813\pi\)
\(234\) 0 0
\(235\) 1.04163 0.0679484
\(236\) 0 0
\(237\) 5.31600 0.345311
\(238\) 0 0
\(239\) −22.4170 −1.45004 −0.725018 0.688730i \(-0.758169\pi\)
−0.725018 + 0.688730i \(0.758169\pi\)
\(240\) 0 0
\(241\) −25.0278 −1.61218 −0.806092 0.591791i \(-0.798421\pi\)
−0.806092 + 0.591791i \(0.798421\pi\)
\(242\) 0 0
\(243\) −14.1961 −0.910680
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −10.8270 −0.688905
\(248\) 0 0
\(249\) −18.2416 −1.15602
\(250\) 0 0
\(251\) −2.08571 −0.131649 −0.0658244 0.997831i \(-0.520968\pi\)
−0.0658244 + 0.997831i \(0.520968\pi\)
\(252\) 0 0
\(253\) 29.6244 1.86247
\(254\) 0 0
\(255\) −43.3765 −2.71634
\(256\) 0 0
\(257\) −18.9277 −1.18068 −0.590339 0.807156i \(-0.701006\pi\)
−0.590339 + 0.807156i \(0.701006\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −13.9388 −0.862790
\(262\) 0 0
\(263\) −5.16279 −0.318351 −0.159175 0.987250i \(-0.550884\pi\)
−0.159175 + 0.987250i \(0.550884\pi\)
\(264\) 0 0
\(265\) −3.30098 −0.202778
\(266\) 0 0
\(267\) 2.50204 0.153122
\(268\) 0 0
\(269\) 6.40064 0.390254 0.195127 0.980778i \(-0.437488\pi\)
0.195127 + 0.980778i \(0.437488\pi\)
\(270\) 0 0
\(271\) −31.9665 −1.94183 −0.970915 0.239425i \(-0.923041\pi\)
−0.970915 + 0.239425i \(0.923041\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 43.3529 2.61428
\(276\) 0 0
\(277\) 24.0243 1.44348 0.721740 0.692165i \(-0.243343\pi\)
0.721740 + 0.692165i \(0.243343\pi\)
\(278\) 0 0
\(279\) 9.59593 0.574493
\(280\) 0 0
\(281\) −13.6948 −0.816965 −0.408483 0.912766i \(-0.633942\pi\)
−0.408483 + 0.912766i \(0.633942\pi\)
\(282\) 0 0
\(283\) −14.1506 −0.841165 −0.420582 0.907254i \(-0.638174\pi\)
−0.420582 + 0.907254i \(0.638174\pi\)
\(284\) 0 0
\(285\) −54.8888 −3.25133
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 10.0738 0.592577
\(290\) 0 0
\(291\) 13.3960 0.785286
\(292\) 0 0
\(293\) 4.12691 0.241097 0.120548 0.992707i \(-0.461535\pi\)
0.120548 + 0.992707i \(0.461535\pi\)
\(294\) 0 0
\(295\) −20.8077 −1.21147
\(296\) 0 0
\(297\) −13.2544 −0.769097
\(298\) 0 0
\(299\) 11.7946 0.682097
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 27.9203 1.60398
\(304\) 0 0
\(305\) 10.1101 0.578901
\(306\) 0 0
\(307\) 5.97471 0.340995 0.170497 0.985358i \(-0.445463\pi\)
0.170497 + 0.985358i \(0.445463\pi\)
\(308\) 0 0
\(309\) 33.5669 1.90955
\(310\) 0 0
\(311\) 16.1431 0.915390 0.457695 0.889109i \(-0.348675\pi\)
0.457695 + 0.889109i \(0.348675\pi\)
\(312\) 0 0
\(313\) −7.74303 −0.437662 −0.218831 0.975763i \(-0.570224\pi\)
−0.218831 + 0.975763i \(0.570224\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −24.3917 −1.36997 −0.684987 0.728556i \(-0.740192\pi\)
−0.684987 + 0.728556i \(0.740192\pi\)
\(318\) 0 0
\(319\) −38.7780 −2.17115
\(320\) 0 0
\(321\) 16.9049 0.943538
\(322\) 0 0
\(323\) 34.2594 1.90624
\(324\) 0 0
\(325\) 17.2604 0.957432
\(326\) 0 0
\(327\) 25.4632 1.40812
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −24.4302 −1.34281 −0.671403 0.741092i \(-0.734308\pi\)
−0.671403 + 0.741092i \(0.734308\pi\)
\(332\) 0 0
\(333\) 16.8125 0.921320
\(334\) 0 0
\(335\) 50.9315 2.78269
\(336\) 0 0
\(337\) 10.3432 0.563428 0.281714 0.959498i \(-0.409097\pi\)
0.281714 + 0.959498i \(0.409097\pi\)
\(338\) 0 0
\(339\) −39.4754 −2.14401
\(340\) 0 0
\(341\) 26.6961 1.44567
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 59.7940 3.21920
\(346\) 0 0
\(347\) −23.4882 −1.26091 −0.630457 0.776224i \(-0.717133\pi\)
−0.630457 + 0.776224i \(0.717133\pi\)
\(348\) 0 0
\(349\) 5.54452 0.296791 0.148396 0.988928i \(-0.452589\pi\)
0.148396 + 0.988928i \(0.452589\pi\)
\(350\) 0 0
\(351\) −5.27705 −0.281668
\(352\) 0 0
\(353\) −3.44192 −0.183195 −0.0915974 0.995796i \(-0.529197\pi\)
−0.0915974 + 0.995796i \(0.529197\pi\)
\(354\) 0 0
\(355\) 22.9011 1.21546
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −7.62296 −0.402324 −0.201162 0.979558i \(-0.564472\pi\)
−0.201162 + 0.979558i \(0.564472\pi\)
\(360\) 0 0
\(361\) 24.3520 1.28168
\(362\) 0 0
\(363\) 12.8302 0.673411
\(364\) 0 0
\(365\) 49.1422 2.57222
\(366\) 0 0
\(367\) 12.7933 0.667806 0.333903 0.942607i \(-0.391634\pi\)
0.333903 + 0.942607i \(0.391634\pi\)
\(368\) 0 0
\(369\) −1.48461 −0.0772855
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 37.4785 1.94056 0.970281 0.241979i \(-0.0777965\pi\)
0.970281 + 0.241979i \(0.0777965\pi\)
\(374\) 0 0
\(375\) 45.8215 2.36621
\(376\) 0 0
\(377\) −15.4389 −0.795146
\(378\) 0 0
\(379\) −9.08847 −0.466844 −0.233422 0.972376i \(-0.574992\pi\)
−0.233422 + 0.972376i \(0.574992\pi\)
\(380\) 0 0
\(381\) −8.79660 −0.450663
\(382\) 0 0
\(383\) 14.3554 0.733524 0.366762 0.930315i \(-0.380466\pi\)
0.366762 + 0.930315i \(0.380466\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.10225 −0.0560305
\(388\) 0 0
\(389\) −26.6068 −1.34902 −0.674510 0.738265i \(-0.735645\pi\)
−0.674510 + 0.738265i \(0.735645\pi\)
\(390\) 0 0
\(391\) −37.3210 −1.88740
\(392\) 0 0
\(393\) −22.2453 −1.12213
\(394\) 0 0
\(395\) 9.88189 0.497212
\(396\) 0 0
\(397\) 30.0384 1.50758 0.753792 0.657113i \(-0.228223\pi\)
0.753792 + 0.657113i \(0.228223\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 14.8185 0.739999 0.369999 0.929032i \(-0.379358\pi\)
0.369999 + 0.929032i \(0.379358\pi\)
\(402\) 0 0
\(403\) 10.6287 0.529452
\(404\) 0 0
\(405\) −44.2854 −2.20056
\(406\) 0 0
\(407\) 46.7727 2.31844
\(408\) 0 0
\(409\) −18.6040 −0.919908 −0.459954 0.887943i \(-0.652134\pi\)
−0.459954 + 0.887943i \(0.652134\pi\)
\(410\) 0 0
\(411\) 3.00475 0.148214
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) −33.9093 −1.66454
\(416\) 0 0
\(417\) −21.8824 −1.07159
\(418\) 0 0
\(419\) −1.89906 −0.0927751 −0.0463875 0.998924i \(-0.514771\pi\)
−0.0463875 + 0.998924i \(0.514771\pi\)
\(420\) 0 0
\(421\) 5.78259 0.281826 0.140913 0.990022i \(-0.454996\pi\)
0.140913 + 0.990022i \(0.454996\pi\)
\(422\) 0 0
\(423\) 0.392832 0.0191002
\(424\) 0 0
\(425\) −54.6161 −2.64927
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 14.3826 0.694398
\(430\) 0 0
\(431\) −27.9485 −1.34623 −0.673117 0.739536i \(-0.735045\pi\)
−0.673117 + 0.739536i \(0.735045\pi\)
\(432\) 0 0
\(433\) 12.1725 0.584975 0.292487 0.956269i \(-0.405517\pi\)
0.292487 + 0.956269i \(0.405517\pi\)
\(434\) 0 0
\(435\) −78.2697 −3.75274
\(436\) 0 0
\(437\) −47.2262 −2.25913
\(438\) 0 0
\(439\) −10.3773 −0.495284 −0.247642 0.968852i \(-0.579656\pi\)
−0.247642 + 0.968852i \(0.579656\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −38.9198 −1.84913 −0.924567 0.381020i \(-0.875573\pi\)
−0.924567 + 0.381020i \(0.875573\pi\)
\(444\) 0 0
\(445\) 4.65103 0.220480
\(446\) 0 0
\(447\) 2.71915 0.128611
\(448\) 0 0
\(449\) −10.8233 −0.510783 −0.255391 0.966838i \(-0.582204\pi\)
−0.255391 + 0.966838i \(0.582204\pi\)
\(450\) 0 0
\(451\) −4.13020 −0.194484
\(452\) 0 0
\(453\) 13.6718 0.642358
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.2417 −0.479086 −0.239543 0.970886i \(-0.576998\pi\)
−0.239543 + 0.970886i \(0.576998\pi\)
\(458\) 0 0
\(459\) 16.6979 0.779392
\(460\) 0 0
\(461\) −24.4368 −1.13814 −0.569068 0.822290i \(-0.692696\pi\)
−0.569068 + 0.822290i \(0.692696\pi\)
\(462\) 0 0
\(463\) −21.0456 −0.978072 −0.489036 0.872264i \(-0.662651\pi\)
−0.489036 + 0.872264i \(0.662651\pi\)
\(464\) 0 0
\(465\) 53.8834 2.49878
\(466\) 0 0
\(467\) −12.2601 −0.567329 −0.283664 0.958924i \(-0.591550\pi\)
−0.283664 + 0.958924i \(0.591550\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −34.4851 −1.58899
\(472\) 0 0
\(473\) −3.06648 −0.140997
\(474\) 0 0
\(475\) −69.1116 −3.17106
\(476\) 0 0
\(477\) −1.24491 −0.0570004
\(478\) 0 0
\(479\) −22.7134 −1.03780 −0.518902 0.854834i \(-0.673659\pi\)
−0.518902 + 0.854834i \(0.673659\pi\)
\(480\) 0 0
\(481\) 18.6219 0.849087
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 24.9017 1.13073
\(486\) 0 0
\(487\) −28.5514 −1.29379 −0.646893 0.762581i \(-0.723932\pi\)
−0.646893 + 0.762581i \(0.723932\pi\)
\(488\) 0 0
\(489\) 2.83054 0.128001
\(490\) 0 0
\(491\) 8.49643 0.383438 0.191719 0.981450i \(-0.438594\pi\)
0.191719 + 0.981450i \(0.438594\pi\)
\(492\) 0 0
\(493\) 48.8527 2.20021
\(494\) 0 0
\(495\) 24.1379 1.08492
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −8.05158 −0.360438 −0.180219 0.983627i \(-0.557681\pi\)
−0.180219 + 0.983627i \(0.557681\pi\)
\(500\) 0 0
\(501\) 20.4333 0.912893
\(502\) 0 0
\(503\) −31.3484 −1.39776 −0.698879 0.715240i \(-0.746317\pi\)
−0.698879 + 0.715240i \(0.746317\pi\)
\(504\) 0 0
\(505\) 51.9010 2.30957
\(506\) 0 0
\(507\) −21.8037 −0.968337
\(508\) 0 0
\(509\) 3.98621 0.176686 0.0883429 0.996090i \(-0.471843\pi\)
0.0883429 + 0.996090i \(0.471843\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 21.1296 0.932897
\(514\) 0 0
\(515\) 62.3974 2.74956
\(516\) 0 0
\(517\) 1.09287 0.0480642
\(518\) 0 0
\(519\) 0.836144 0.0367026
\(520\) 0 0
\(521\) −42.5988 −1.86629 −0.933144 0.359503i \(-0.882946\pi\)
−0.933144 + 0.359503i \(0.882946\pi\)
\(522\) 0 0
\(523\) −13.4853 −0.589673 −0.294836 0.955548i \(-0.595265\pi\)
−0.294836 + 0.955548i \(0.595265\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −33.6318 −1.46502
\(528\) 0 0
\(529\) 28.4466 1.23681
\(530\) 0 0
\(531\) −7.84728 −0.340543
\(532\) 0 0
\(533\) −1.64438 −0.0712262
\(534\) 0 0
\(535\) 31.4244 1.35860
\(536\) 0 0
\(537\) −16.8405 −0.726720
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 31.8373 1.36879 0.684395 0.729111i \(-0.260066\pi\)
0.684395 + 0.729111i \(0.260066\pi\)
\(542\) 0 0
\(543\) 5.24613 0.225133
\(544\) 0 0
\(545\) 47.3334 2.02754
\(546\) 0 0
\(547\) −29.2689 −1.25145 −0.625723 0.780045i \(-0.715196\pi\)
−0.625723 + 0.780045i \(0.715196\pi\)
\(548\) 0 0
\(549\) 3.81284 0.162728
\(550\) 0 0
\(551\) 61.8185 2.63356
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 94.4063 4.00732
\(556\) 0 0
\(557\) 7.63655 0.323571 0.161785 0.986826i \(-0.448275\pi\)
0.161785 + 0.986826i \(0.448275\pi\)
\(558\) 0 0
\(559\) −1.22088 −0.0516377
\(560\) 0 0
\(561\) −45.5102 −1.92144
\(562\) 0 0
\(563\) 1.77861 0.0749593 0.0374797 0.999297i \(-0.488067\pi\)
0.0374797 + 0.999297i \(0.488067\pi\)
\(564\) 0 0
\(565\) −73.3806 −3.08715
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.83946 0.370570 0.185285 0.982685i \(-0.440679\pi\)
0.185285 + 0.982685i \(0.440679\pi\)
\(570\) 0 0
\(571\) 6.50457 0.272208 0.136104 0.990695i \(-0.456542\pi\)
0.136104 + 0.990695i \(0.456542\pi\)
\(572\) 0 0
\(573\) 17.0193 0.710990
\(574\) 0 0
\(575\) 75.2878 3.13972
\(576\) 0 0
\(577\) −25.7240 −1.07090 −0.535452 0.844566i \(-0.679859\pi\)
−0.535452 + 0.844566i \(0.679859\pi\)
\(578\) 0 0
\(579\) −39.7490 −1.65191
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3.46336 −0.143438
\(584\) 0 0
\(585\) 9.61019 0.397333
\(586\) 0 0
\(587\) −27.1254 −1.11959 −0.559794 0.828632i \(-0.689120\pi\)
−0.559794 + 0.828632i \(0.689120\pi\)
\(588\) 0 0
\(589\) −42.5579 −1.75357
\(590\) 0 0
\(591\) 23.1818 0.953573
\(592\) 0 0
\(593\) 25.0630 1.02921 0.514607 0.857426i \(-0.327938\pi\)
0.514607 + 0.857426i \(0.327938\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −44.2143 −1.80957
\(598\) 0 0
\(599\) 19.8368 0.810510 0.405255 0.914204i \(-0.367183\pi\)
0.405255 + 0.914204i \(0.367183\pi\)
\(600\) 0 0
\(601\) −19.3130 −0.787792 −0.393896 0.919155i \(-0.628873\pi\)
−0.393896 + 0.919155i \(0.628873\pi\)
\(602\) 0 0
\(603\) 19.2079 0.782208
\(604\) 0 0
\(605\) 23.8500 0.969641
\(606\) 0 0
\(607\) −14.9873 −0.608318 −0.304159 0.952621i \(-0.598375\pi\)
−0.304159 + 0.952621i \(0.598375\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.435110 0.0176027
\(612\) 0 0
\(613\) 11.2933 0.456131 0.228066 0.973646i \(-0.426760\pi\)
0.228066 + 0.973646i \(0.426760\pi\)
\(614\) 0 0
\(615\) −8.33642 −0.336157
\(616\) 0 0
\(617\) 46.4782 1.87114 0.935572 0.353137i \(-0.114885\pi\)
0.935572 + 0.353137i \(0.114885\pi\)
\(618\) 0 0
\(619\) −36.4425 −1.46475 −0.732374 0.680902i \(-0.761588\pi\)
−0.732374 + 0.680902i \(0.761588\pi\)
\(620\) 0 0
\(621\) −23.0179 −0.923677
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 32.6946 1.30779
\(626\) 0 0
\(627\) −57.5888 −2.29988
\(628\) 0 0
\(629\) −58.9245 −2.34947
\(630\) 0 0
\(631\) −15.2500 −0.607095 −0.303547 0.952816i \(-0.598171\pi\)
−0.303547 + 0.952816i \(0.598171\pi\)
\(632\) 0 0
\(633\) 9.40816 0.373941
\(634\) 0 0
\(635\) −16.3520 −0.648908
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 8.63675 0.341665
\(640\) 0 0
\(641\) 21.4291 0.846398 0.423199 0.906037i \(-0.360907\pi\)
0.423199 + 0.906037i \(0.360907\pi\)
\(642\) 0 0
\(643\) 26.2975 1.03707 0.518536 0.855056i \(-0.326477\pi\)
0.518536 + 0.855056i \(0.326477\pi\)
\(644\) 0 0
\(645\) −6.18940 −0.243707
\(646\) 0 0
\(647\) 16.6289 0.653749 0.326875 0.945068i \(-0.394005\pi\)
0.326875 + 0.945068i \(0.394005\pi\)
\(648\) 0 0
\(649\) −21.8313 −0.856953
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.05664 −0.276148 −0.138074 0.990422i \(-0.544091\pi\)
−0.138074 + 0.990422i \(0.544091\pi\)
\(654\) 0 0
\(655\) −41.3518 −1.61575
\(656\) 0 0
\(657\) 18.5331 0.723046
\(658\) 0 0
\(659\) 45.2945 1.76442 0.882211 0.470854i \(-0.156054\pi\)
0.882211 + 0.470854i \(0.156054\pi\)
\(660\) 0 0
\(661\) −40.1854 −1.56303 −0.781516 0.623886i \(-0.785553\pi\)
−0.781516 + 0.623886i \(0.785553\pi\)
\(662\) 0 0
\(663\) −18.1193 −0.703693
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −67.3430 −2.60753
\(668\) 0 0
\(669\) 20.1126 0.777599
\(670\) 0 0
\(671\) 10.6074 0.409494
\(672\) 0 0
\(673\) 15.5616 0.599856 0.299928 0.953962i \(-0.403037\pi\)
0.299928 + 0.953962i \(0.403037\pi\)
\(674\) 0 0
\(675\) −33.6848 −1.29653
\(676\) 0 0
\(677\) 26.4420 1.01625 0.508124 0.861284i \(-0.330339\pi\)
0.508124 + 0.861284i \(0.330339\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −26.8848 −1.03023
\(682\) 0 0
\(683\) −1.07364 −0.0410817 −0.0205408 0.999789i \(-0.506539\pi\)
−0.0205408 + 0.999789i \(0.506539\pi\)
\(684\) 0 0
\(685\) 5.58553 0.213412
\(686\) 0 0
\(687\) −28.0716 −1.07100
\(688\) 0 0
\(689\) −1.37889 −0.0525315
\(690\) 0 0
\(691\) 8.62945 0.328280 0.164140 0.986437i \(-0.447515\pi\)
0.164140 + 0.986437i \(0.447515\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −40.6772 −1.54297
\(696\) 0 0
\(697\) 5.20325 0.197087
\(698\) 0 0
\(699\) 25.1503 0.951272
\(700\) 0 0
\(701\) −44.1873 −1.66893 −0.834465 0.551061i \(-0.814223\pi\)
−0.834465 + 0.551061i \(0.814223\pi\)
\(702\) 0 0
\(703\) −74.5634 −2.81221
\(704\) 0 0
\(705\) 2.20585 0.0830770
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 16.9496 0.636554 0.318277 0.947998i \(-0.396896\pi\)
0.318277 + 0.947998i \(0.396896\pi\)
\(710\) 0 0
\(711\) 3.72678 0.139765
\(712\) 0 0
\(713\) 46.3611 1.73624
\(714\) 0 0
\(715\) 26.7358 0.999860
\(716\) 0 0
\(717\) −47.4723 −1.77288
\(718\) 0 0
\(719\) 20.8173 0.776355 0.388177 0.921585i \(-0.373105\pi\)
0.388177 + 0.921585i \(0.373105\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −53.0011 −1.97113
\(724\) 0 0
\(725\) −98.5508 −3.66008
\(726\) 0 0
\(727\) 7.51361 0.278664 0.139332 0.990246i \(-0.455504\pi\)
0.139332 + 0.990246i \(0.455504\pi\)
\(728\) 0 0
\(729\) 3.68636 0.136532
\(730\) 0 0
\(731\) 3.86317 0.142884
\(732\) 0 0
\(733\) 24.7527 0.914261 0.457131 0.889400i \(-0.348877\pi\)
0.457131 + 0.889400i \(0.348877\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 53.4369 1.96837
\(738\) 0 0
\(739\) 36.3640 1.33767 0.668836 0.743410i \(-0.266793\pi\)
0.668836 + 0.743410i \(0.266793\pi\)
\(740\) 0 0
\(741\) −22.9282 −0.842289
\(742\) 0 0
\(743\) −11.7748 −0.431976 −0.215988 0.976396i \(-0.569297\pi\)
−0.215988 + 0.976396i \(0.569297\pi\)
\(744\) 0 0
\(745\) 5.05462 0.185187
\(746\) 0 0
\(747\) −12.7883 −0.467899
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −2.08643 −0.0761350 −0.0380675 0.999275i \(-0.512120\pi\)
−0.0380675 + 0.999275i \(0.512120\pi\)
\(752\) 0 0
\(753\) −4.41688 −0.160960
\(754\) 0 0
\(755\) 25.4145 0.924928
\(756\) 0 0
\(757\) −40.7156 −1.47983 −0.739917 0.672698i \(-0.765135\pi\)
−0.739917 + 0.672698i \(0.765135\pi\)
\(758\) 0 0
\(759\) 62.7353 2.27715
\(760\) 0 0
\(761\) −19.7790 −0.716989 −0.358495 0.933532i \(-0.616710\pi\)
−0.358495 + 0.933532i \(0.616710\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −30.4091 −1.09944
\(766\) 0 0
\(767\) −8.69183 −0.313844
\(768\) 0 0
\(769\) 24.9578 0.900003 0.450001 0.893028i \(-0.351423\pi\)
0.450001 + 0.893028i \(0.351423\pi\)
\(770\) 0 0
\(771\) −40.0830 −1.44355
\(772\) 0 0
\(773\) 13.6827 0.492133 0.246067 0.969253i \(-0.420862\pi\)
0.246067 + 0.969253i \(0.420862\pi\)
\(774\) 0 0
\(775\) 67.8456 2.43709
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.58422 0.235904
\(780\) 0 0
\(781\) 24.0276 0.859776
\(782\) 0 0
\(783\) 30.1302 1.07676
\(784\) 0 0
\(785\) −64.1042 −2.28798
\(786\) 0 0
\(787\) 10.7902 0.384630 0.192315 0.981333i \(-0.438401\pi\)
0.192315 + 0.981333i \(0.438401\pi\)
\(788\) 0 0
\(789\) −10.9332 −0.389231
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 4.22319 0.149970
\(794\) 0 0
\(795\) −6.99045 −0.247926
\(796\) 0 0
\(797\) −3.70563 −0.131260 −0.0656301 0.997844i \(-0.520906\pi\)
−0.0656301 + 0.997844i \(0.520906\pi\)
\(798\) 0 0
\(799\) −1.37680 −0.0487076
\(800\) 0 0
\(801\) 1.75405 0.0619764
\(802\) 0 0
\(803\) 51.5595 1.81950
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 13.5546 0.477144
\(808\) 0 0
\(809\) 21.1550 0.743769 0.371884 0.928279i \(-0.378712\pi\)
0.371884 + 0.928279i \(0.378712\pi\)
\(810\) 0 0
\(811\) 12.1506 0.426667 0.213333 0.976979i \(-0.431568\pi\)
0.213333 + 0.976979i \(0.431568\pi\)
\(812\) 0 0
\(813\) −67.6952 −2.37417
\(814\) 0 0
\(815\) 5.26167 0.184308
\(816\) 0 0
\(817\) 4.88848 0.171026
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 15.2915 0.533675 0.266838 0.963741i \(-0.414021\pi\)
0.266838 + 0.963741i \(0.414021\pi\)
\(822\) 0 0
\(823\) 57.1962 1.99373 0.996867 0.0791017i \(-0.0252052\pi\)
0.996867 + 0.0791017i \(0.0252052\pi\)
\(824\) 0 0
\(825\) 91.8079 3.19634
\(826\) 0 0
\(827\) −29.1296 −1.01294 −0.506469 0.862258i \(-0.669049\pi\)
−0.506469 + 0.862258i \(0.669049\pi\)
\(828\) 0 0
\(829\) −21.4260 −0.744155 −0.372077 0.928202i \(-0.621354\pi\)
−0.372077 + 0.928202i \(0.621354\pi\)
\(830\) 0 0
\(831\) 50.8759 1.76487
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 37.9834 1.31447
\(836\) 0 0
\(837\) −20.7426 −0.716969
\(838\) 0 0
\(839\) −13.9582 −0.481891 −0.240945 0.970539i \(-0.577457\pi\)
−0.240945 + 0.970539i \(0.577457\pi\)
\(840\) 0 0
\(841\) 59.1511 2.03969
\(842\) 0 0
\(843\) −29.0014 −0.998861
\(844\) 0 0
\(845\) −40.5309 −1.39430
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −29.9665 −1.02845
\(850\) 0 0
\(851\) 81.2269 2.78442
\(852\) 0 0
\(853\) 10.9836 0.376070 0.188035 0.982162i \(-0.439788\pi\)
0.188035 + 0.982162i \(0.439788\pi\)
\(854\) 0 0
\(855\) −38.4798 −1.31598
\(856\) 0 0
\(857\) 34.9320 1.19325 0.596627 0.802519i \(-0.296507\pi\)
0.596627 + 0.802519i \(0.296507\pi\)
\(858\) 0 0
\(859\) 4.09973 0.139881 0.0699405 0.997551i \(-0.477719\pi\)
0.0699405 + 0.997551i \(0.477719\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11.6514 0.396618 0.198309 0.980140i \(-0.436455\pi\)
0.198309 + 0.980140i \(0.436455\pi\)
\(864\) 0 0
\(865\) 1.55431 0.0528480
\(866\) 0 0
\(867\) 21.3332 0.724513
\(868\) 0 0
\(869\) 10.3680 0.351710
\(870\) 0 0
\(871\) 21.2752 0.720881
\(872\) 0 0
\(873\) 9.39125 0.317846
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 19.8783 0.671243 0.335621 0.941997i \(-0.391054\pi\)
0.335621 + 0.941997i \(0.391054\pi\)
\(878\) 0 0
\(879\) 8.73952 0.294777
\(880\) 0 0
\(881\) 34.3176 1.15619 0.578095 0.815970i \(-0.303796\pi\)
0.578095 + 0.815970i \(0.303796\pi\)
\(882\) 0 0
\(883\) −18.0828 −0.608535 −0.304267 0.952587i \(-0.598412\pi\)
−0.304267 + 0.952587i \(0.598412\pi\)
\(884\) 0 0
\(885\) −44.0643 −1.48121
\(886\) 0 0
\(887\) 18.8490 0.632888 0.316444 0.948611i \(-0.397511\pi\)
0.316444 + 0.948611i \(0.397511\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −46.4638 −1.55660
\(892\) 0 0
\(893\) −1.74221 −0.0583008
\(894\) 0 0
\(895\) −31.3047 −1.04640
\(896\) 0 0
\(897\) 24.9772 0.833965
\(898\) 0 0
\(899\) −60.6862 −2.02400
\(900\) 0 0
\(901\) 4.36315 0.145358
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 9.75201 0.324168
\(906\) 0 0
\(907\) 33.7374 1.12023 0.560117 0.828414i \(-0.310756\pi\)
0.560117 + 0.828414i \(0.310756\pi\)
\(908\) 0 0
\(909\) 19.5736 0.649214
\(910\) 0 0
\(911\) 42.0812 1.39421 0.697106 0.716968i \(-0.254471\pi\)
0.697106 + 0.716968i \(0.254471\pi\)
\(912\) 0 0
\(913\) −35.5773 −1.17744
\(914\) 0 0
\(915\) 21.4100 0.707793
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −22.8624 −0.754159 −0.377080 0.926181i \(-0.623072\pi\)
−0.377080 + 0.926181i \(0.623072\pi\)
\(920\) 0 0
\(921\) 12.6526 0.416917
\(922\) 0 0
\(923\) 9.56627 0.314878
\(924\) 0 0
\(925\) 118.869 3.90838
\(926\) 0 0
\(927\) 23.5321 0.772895
\(928\) 0 0
\(929\) 31.1426 1.02176 0.510878 0.859653i \(-0.329320\pi\)
0.510878 + 0.859653i \(0.329320\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 34.1860 1.11920
\(934\) 0 0
\(935\) −84.5987 −2.76667
\(936\) 0 0
\(937\) −6.94013 −0.226724 −0.113362 0.993554i \(-0.536162\pi\)
−0.113362 + 0.993554i \(0.536162\pi\)
\(938\) 0 0
\(939\) −16.3973 −0.535106
\(940\) 0 0
\(941\) −14.4228 −0.470171 −0.235086 0.971975i \(-0.575537\pi\)
−0.235086 + 0.971975i \(0.575537\pi\)
\(942\) 0 0
\(943\) −7.17263 −0.233573
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −29.9397 −0.972909 −0.486455 0.873706i \(-0.661710\pi\)
−0.486455 + 0.873706i \(0.661710\pi\)
\(948\) 0 0
\(949\) 20.5277 0.666358
\(950\) 0 0
\(951\) −51.6540 −1.67500
\(952\) 0 0
\(953\) −0.521703 −0.0168996 −0.00844981 0.999964i \(-0.502690\pi\)
−0.00844981 + 0.999964i \(0.502690\pi\)
\(954\) 0 0
\(955\) 31.6371 1.02375
\(956\) 0 0
\(957\) −82.1198 −2.65455
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 10.7784 0.347689
\(962\) 0 0
\(963\) 11.8512 0.381898
\(964\) 0 0
\(965\) −73.8893 −2.37858
\(966\) 0 0
\(967\) 29.9003 0.961529 0.480765 0.876850i \(-0.340359\pi\)
0.480765 + 0.876850i \(0.340359\pi\)
\(968\) 0 0
\(969\) 72.5507 2.33066
\(970\) 0 0
\(971\) 16.7863 0.538699 0.269349 0.963043i \(-0.413191\pi\)
0.269349 + 0.963043i \(0.413191\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 36.5521 1.17060
\(976\) 0 0
\(977\) −57.9457 −1.85385 −0.926923 0.375251i \(-0.877557\pi\)
−0.926923 + 0.375251i \(0.877557\pi\)
\(978\) 0 0
\(979\) 4.87981 0.155959
\(980\) 0 0
\(981\) 17.8510 0.569938
\(982\) 0 0
\(983\) 53.6430 1.71095 0.855473 0.517847i \(-0.173266\pi\)
0.855473 + 0.517847i \(0.173266\pi\)
\(984\) 0 0
\(985\) 43.0926 1.37304
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.32534 −0.169336
\(990\) 0 0
\(991\) 14.3369 0.455428 0.227714 0.973728i \(-0.426875\pi\)
0.227714 + 0.973728i \(0.426875\pi\)
\(992\) 0 0
\(993\) −51.7356 −1.64178
\(994\) 0 0
\(995\) −82.1899 −2.60559
\(996\) 0 0
\(997\) 25.8404 0.818373 0.409186 0.912451i \(-0.365813\pi\)
0.409186 + 0.912451i \(0.365813\pi\)
\(998\) 0 0
\(999\) −36.3420 −1.14981
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 \(a_p\))