Properties

Label 6027.2.a.y.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 7
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.35311\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.35311 q^{2} -1.00000 q^{3} -0.169102 q^{4} -1.31916 q^{5} +1.35311 q^{6} +2.93503 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.35311 q^{2} -1.00000 q^{3} -0.169102 q^{4} -1.31916 q^{5} +1.35311 q^{6} +2.93503 q^{8} +1.00000 q^{9} +1.78497 q^{10} -4.13524 q^{11} +0.169102 q^{12} +1.21233 q^{13} +1.31916 q^{15} -3.63320 q^{16} -7.63049 q^{17} -1.35311 q^{18} -6.01351 q^{19} +0.223073 q^{20} +5.59543 q^{22} +3.53357 q^{23} -2.93503 q^{24} -3.25981 q^{25} -1.64041 q^{26} -1.00000 q^{27} -3.42745 q^{29} -1.78497 q^{30} +1.20879 q^{31} -0.953947 q^{32} +4.13524 q^{33} +10.3249 q^{34} -0.169102 q^{36} +1.76018 q^{37} +8.13692 q^{38} -1.21233 q^{39} -3.87178 q^{40} -1.00000 q^{41} -7.13254 q^{43} +0.699279 q^{44} -1.31916 q^{45} -4.78130 q^{46} -12.3718 q^{47} +3.63320 q^{48} +4.41087 q^{50} +7.63049 q^{51} -0.205007 q^{52} +9.78151 q^{53} +1.35311 q^{54} +5.45506 q^{55} +6.01351 q^{57} +4.63770 q^{58} -12.0106 q^{59} -0.223073 q^{60} +9.75390 q^{61} -1.63562 q^{62} +8.55719 q^{64} -1.59926 q^{65} -5.59543 q^{66} +3.28779 q^{67} +1.29033 q^{68} -3.53357 q^{69} -5.17222 q^{71} +2.93503 q^{72} -11.1296 q^{73} -2.38172 q^{74} +3.25981 q^{75} +1.01690 q^{76} +1.64041 q^{78} -4.53670 q^{79} +4.79278 q^{80} +1.00000 q^{81} +1.35311 q^{82} -16.9034 q^{83} +10.0659 q^{85} +9.65109 q^{86} +3.42745 q^{87} -12.1371 q^{88} +10.3639 q^{89} +1.78497 q^{90} -0.597535 q^{92} -1.20879 q^{93} +16.7404 q^{94} +7.93279 q^{95} +0.953947 q^{96} +6.82267 q^{97} -4.13524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + O(q^{10}) \) \( 7q + 4q^{2} - 7q^{3} + 8q^{4} - q^{5} - 4q^{6} + 12q^{8} + 7q^{9} + 3q^{10} + 11q^{11} - 8q^{12} + 7q^{13} + q^{15} + 6q^{16} - 11q^{17} + 4q^{18} - 4q^{19} + 7q^{20} + 6q^{22} + 7q^{23} - 12q^{24} + 2q^{25} + 13q^{26} - 7q^{27} + 4q^{29} - 3q^{30} + 7q^{31} + 18q^{32} - 11q^{33} + 20q^{34} + 8q^{36} - 4q^{38} - 7q^{39} + 9q^{40} - 7q^{41} + q^{43} + 18q^{44} - q^{45} - 17q^{46} - 14q^{47} - 6q^{48} + 19q^{50} + 11q^{51} + 27q^{52} + 23q^{53} - 4q^{54} + 30q^{55} + 4q^{57} - 3q^{58} - 8q^{59} - 7q^{60} + 3q^{61} + 16q^{62} + 6q^{64} + 15q^{65} - 6q^{66} + 3q^{67} - 7q^{69} + 7q^{71} + 12q^{72} + 11q^{73} - 13q^{74} - 2q^{75} + 40q^{76} - 13q^{78} - q^{79} + 43q^{80} + 7q^{81} - 4q^{82} - 10q^{85} - 12q^{86} - 4q^{87} + 10q^{88} - 32q^{89} + 3q^{90} - 19q^{92} - 7q^{93} - 21q^{94} - 8q^{95} - 18q^{96} + 25q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.35311 −0.956791 −0.478395 0.878145i \(-0.658781\pi\)
−0.478395 + 0.878145i \(0.658781\pi\)
\(3\) −1.00000 −0.577350
\(4\) −0.169102 −0.0845512
\(5\) −1.31916 −0.589947 −0.294974 0.955505i \(-0.595311\pi\)
−0.294974 + 0.955505i \(0.595311\pi\)
\(6\) 1.35311 0.552403
\(7\) 0 0
\(8\) 2.93503 1.03769
\(9\) 1.00000 0.333333
\(10\) 1.78497 0.564456
\(11\) −4.13524 −1.24682 −0.623412 0.781894i \(-0.714254\pi\)
−0.623412 + 0.781894i \(0.714254\pi\)
\(12\) 0.169102 0.0488156
\(13\) 1.21233 0.336239 0.168119 0.985767i \(-0.446231\pi\)
0.168119 + 0.985767i \(0.446231\pi\)
\(14\) 0 0
\(15\) 1.31916 0.340606
\(16\) −3.63320 −0.908300
\(17\) −7.63049 −1.85067 −0.925333 0.379155i \(-0.876215\pi\)
−0.925333 + 0.379155i \(0.876215\pi\)
\(18\) −1.35311 −0.318930
\(19\) −6.01351 −1.37959 −0.689797 0.724003i \(-0.742300\pi\)
−0.689797 + 0.724003i \(0.742300\pi\)
\(20\) 0.223073 0.0498807
\(21\) 0 0
\(22\) 5.59543 1.19295
\(23\) 3.53357 0.736801 0.368400 0.929667i \(-0.379906\pi\)
0.368400 + 0.929667i \(0.379906\pi\)
\(24\) −2.93503 −0.599110
\(25\) −3.25981 −0.651962
\(26\) −1.64041 −0.321710
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −3.42745 −0.636461 −0.318230 0.948013i \(-0.603089\pi\)
−0.318230 + 0.948013i \(0.603089\pi\)
\(30\) −1.78497 −0.325889
\(31\) 1.20879 0.217105 0.108552 0.994091i \(-0.465379\pi\)
0.108552 + 0.994091i \(0.465379\pi\)
\(32\) −0.953947 −0.168636
\(33\) 4.13524 0.719854
\(34\) 10.3249 1.77070
\(35\) 0 0
\(36\) −0.169102 −0.0281837
\(37\) 1.76018 0.289373 0.144686 0.989478i \(-0.453783\pi\)
0.144686 + 0.989478i \(0.453783\pi\)
\(38\) 8.13692 1.31998
\(39\) −1.21233 −0.194128
\(40\) −3.87178 −0.612182
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −7.13254 −1.08770 −0.543851 0.839182i \(-0.683034\pi\)
−0.543851 + 0.839182i \(0.683034\pi\)
\(44\) 0.699279 0.105420
\(45\) −1.31916 −0.196649
\(46\) −4.78130 −0.704964
\(47\) −12.3718 −1.80462 −0.902308 0.431092i \(-0.858129\pi\)
−0.902308 + 0.431092i \(0.858129\pi\)
\(48\) 3.63320 0.524407
\(49\) 0 0
\(50\) 4.41087 0.623792
\(51\) 7.63049 1.06848
\(52\) −0.205007 −0.0284294
\(53\) 9.78151 1.34359 0.671797 0.740735i \(-0.265523\pi\)
0.671797 + 0.740735i \(0.265523\pi\)
\(54\) 1.35311 0.184134
\(55\) 5.45506 0.735560
\(56\) 0 0
\(57\) 6.01351 0.796508
\(58\) 4.63770 0.608960
\(59\) −12.0106 −1.56364 −0.781821 0.623503i \(-0.785709\pi\)
−0.781821 + 0.623503i \(0.785709\pi\)
\(60\) −0.223073 −0.0287986
\(61\) 9.75390 1.24886 0.624430 0.781081i \(-0.285331\pi\)
0.624430 + 0.781081i \(0.285331\pi\)
\(62\) −1.63562 −0.207724
\(63\) 0 0
\(64\) 8.55719 1.06965
\(65\) −1.59926 −0.198363
\(66\) −5.59543 −0.688749
\(67\) 3.28779 0.401667 0.200834 0.979625i \(-0.435635\pi\)
0.200834 + 0.979625i \(0.435635\pi\)
\(68\) 1.29033 0.156476
\(69\) −3.53357 −0.425392
\(70\) 0 0
\(71\) −5.17222 −0.613830 −0.306915 0.951737i \(-0.599297\pi\)
−0.306915 + 0.951737i \(0.599297\pi\)
\(72\) 2.93503 0.345896
\(73\) −11.1296 −1.30262 −0.651310 0.758812i \(-0.725780\pi\)
−0.651310 + 0.758812i \(0.725780\pi\)
\(74\) −2.38172 −0.276869
\(75\) 3.25981 0.376411
\(76\) 1.01690 0.116646
\(77\) 0 0
\(78\) 1.64041 0.185740
\(79\) −4.53670 −0.510419 −0.255209 0.966886i \(-0.582144\pi\)
−0.255209 + 0.966886i \(0.582144\pi\)
\(80\) 4.79278 0.535849
\(81\) 1.00000 0.111111
\(82\) 1.35311 0.149426
\(83\) −16.9034 −1.85539 −0.927695 0.373340i \(-0.878213\pi\)
−0.927695 + 0.373340i \(0.878213\pi\)
\(84\) 0 0
\(85\) 10.0659 1.09180
\(86\) 9.65109 1.04070
\(87\) 3.42745 0.367461
\(88\) −12.1371 −1.29381
\(89\) 10.3639 1.09857 0.549284 0.835636i \(-0.314900\pi\)
0.549284 + 0.835636i \(0.314900\pi\)
\(90\) 1.78497 0.188152
\(91\) 0 0
\(92\) −0.597535 −0.0622973
\(93\) −1.20879 −0.125345
\(94\) 16.7404 1.72664
\(95\) 7.93279 0.813887
\(96\) 0.953947 0.0973618
\(97\) 6.82267 0.692738 0.346369 0.938098i \(-0.387415\pi\)
0.346369 + 0.938098i \(0.387415\pi\)
\(98\) 0 0
\(99\) −4.13524 −0.415608
\(100\) 0.551242 0.0551242
\(101\) −7.85345 −0.781447 −0.390724 0.920508i \(-0.627775\pi\)
−0.390724 + 0.920508i \(0.627775\pi\)
\(102\) −10.3249 −1.02231
\(103\) −14.8276 −1.46101 −0.730504 0.682909i \(-0.760715\pi\)
−0.730504 + 0.682909i \(0.760715\pi\)
\(104\) 3.55821 0.348911
\(105\) 0 0
\(106\) −13.2354 −1.28554
\(107\) 15.6391 1.51189 0.755945 0.654635i \(-0.227178\pi\)
0.755945 + 0.654635i \(0.227178\pi\)
\(108\) 0.169102 0.0162719
\(109\) 2.48326 0.237853 0.118926 0.992903i \(-0.462055\pi\)
0.118926 + 0.992903i \(0.462055\pi\)
\(110\) −7.38128 −0.703777
\(111\) −1.76018 −0.167069
\(112\) 0 0
\(113\) −8.27480 −0.778428 −0.389214 0.921147i \(-0.627253\pi\)
−0.389214 + 0.921147i \(0.627253\pi\)
\(114\) −8.13692 −0.762092
\(115\) −4.66135 −0.434673
\(116\) 0.579589 0.0538135
\(117\) 1.21233 0.112080
\(118\) 16.2516 1.49608
\(119\) 0 0
\(120\) 3.87178 0.353443
\(121\) 6.10025 0.554568
\(122\) −13.1981 −1.19490
\(123\) 1.00000 0.0901670
\(124\) −0.204409 −0.0183564
\(125\) 10.8960 0.974571
\(126\) 0 0
\(127\) −15.0645 −1.33676 −0.668379 0.743821i \(-0.733012\pi\)
−0.668379 + 0.743821i \(0.733012\pi\)
\(128\) −9.67090 −0.854795
\(129\) 7.13254 0.627985
\(130\) 2.16396 0.189792
\(131\) −15.2644 −1.33366 −0.666830 0.745210i \(-0.732349\pi\)
−0.666830 + 0.745210i \(0.732349\pi\)
\(132\) −0.699279 −0.0608645
\(133\) 0 0
\(134\) −4.44873 −0.384312
\(135\) 1.31916 0.113535
\(136\) −22.3957 −1.92042
\(137\) −2.70544 −0.231142 −0.115571 0.993299i \(-0.536870\pi\)
−0.115571 + 0.993299i \(0.536870\pi\)
\(138\) 4.78130 0.407011
\(139\) 12.9107 1.09507 0.547535 0.836783i \(-0.315566\pi\)
0.547535 + 0.836783i \(0.315566\pi\)
\(140\) 0 0
\(141\) 12.3718 1.04190
\(142\) 6.99857 0.587307
\(143\) −5.01327 −0.419230
\(144\) −3.63320 −0.302767
\(145\) 4.52136 0.375478
\(146\) 15.0595 1.24634
\(147\) 0 0
\(148\) −0.297651 −0.0244668
\(149\) −22.4356 −1.83800 −0.918998 0.394261i \(-0.871001\pi\)
−0.918998 + 0.394261i \(0.871001\pi\)
\(150\) −4.41087 −0.360146
\(151\) 3.55734 0.289492 0.144746 0.989469i \(-0.453763\pi\)
0.144746 + 0.989469i \(0.453763\pi\)
\(152\) −17.6498 −1.43159
\(153\) −7.63049 −0.616889
\(154\) 0 0
\(155\) −1.59459 −0.128080
\(156\) 0.205007 0.0164137
\(157\) 7.44432 0.594121 0.297061 0.954859i \(-0.403994\pi\)
0.297061 + 0.954859i \(0.403994\pi\)
\(158\) 6.13864 0.488364
\(159\) −9.78151 −0.775725
\(160\) 1.25841 0.0994861
\(161\) 0 0
\(162\) −1.35311 −0.106310
\(163\) −2.97250 −0.232824 −0.116412 0.993201i \(-0.537139\pi\)
−0.116412 + 0.993201i \(0.537139\pi\)
\(164\) 0.169102 0.0132047
\(165\) −5.45506 −0.424676
\(166\) 22.8721 1.77522
\(167\) 18.1220 1.40232 0.701162 0.713002i \(-0.252665\pi\)
0.701162 + 0.713002i \(0.252665\pi\)
\(168\) 0 0
\(169\) −11.5303 −0.886943
\(170\) −13.6202 −1.04462
\(171\) −6.01351 −0.459864
\(172\) 1.20613 0.0919665
\(173\) −21.3159 −1.62062 −0.810308 0.586004i \(-0.800700\pi\)
−0.810308 + 0.586004i \(0.800700\pi\)
\(174\) −4.63770 −0.351583
\(175\) 0 0
\(176\) 15.0242 1.13249
\(177\) 12.0106 0.902769
\(178\) −14.0234 −1.05110
\(179\) −18.4854 −1.38166 −0.690831 0.723016i \(-0.742755\pi\)
−0.690831 + 0.723016i \(0.742755\pi\)
\(180\) 0.223073 0.0166269
\(181\) −14.2517 −1.05932 −0.529662 0.848209i \(-0.677681\pi\)
−0.529662 + 0.848209i \(0.677681\pi\)
\(182\) 0 0
\(183\) −9.75390 −0.721029
\(184\) 10.3711 0.764570
\(185\) −2.32197 −0.170715
\(186\) 1.63562 0.119929
\(187\) 31.5540 2.30745
\(188\) 2.09210 0.152582
\(189\) 0 0
\(190\) −10.7339 −0.778720
\(191\) −5.62090 −0.406714 −0.203357 0.979105i \(-0.565185\pi\)
−0.203357 + 0.979105i \(0.565185\pi\)
\(192\) −8.55719 −0.617562
\(193\) −24.1490 −1.73828 −0.869141 0.494564i \(-0.835328\pi\)
−0.869141 + 0.494564i \(0.835328\pi\)
\(194\) −9.23181 −0.662805
\(195\) 1.59926 0.114525
\(196\) 0 0
\(197\) −7.33306 −0.522459 −0.261229 0.965277i \(-0.584128\pi\)
−0.261229 + 0.965277i \(0.584128\pi\)
\(198\) 5.59543 0.397650
\(199\) 18.0592 1.28019 0.640093 0.768297i \(-0.278896\pi\)
0.640093 + 0.768297i \(0.278896\pi\)
\(200\) −9.56763 −0.676534
\(201\) −3.28779 −0.231903
\(202\) 10.6266 0.747682
\(203\) 0 0
\(204\) −1.29033 −0.0903415
\(205\) 1.31916 0.0921343
\(206\) 20.0633 1.39788
\(207\) 3.53357 0.245600
\(208\) −4.40462 −0.305406
\(209\) 24.8673 1.72011
\(210\) 0 0
\(211\) 19.4143 1.33654 0.668268 0.743920i \(-0.267036\pi\)
0.668268 + 0.743920i \(0.267036\pi\)
\(212\) −1.65408 −0.113602
\(213\) 5.17222 0.354395
\(214\) −21.1614 −1.44656
\(215\) 9.40897 0.641687
\(216\) −2.93503 −0.199703
\(217\) 0 0
\(218\) −3.36011 −0.227576
\(219\) 11.1296 0.752068
\(220\) −0.922463 −0.0621924
\(221\) −9.25065 −0.622266
\(222\) 2.38172 0.159850
\(223\) −4.73950 −0.317380 −0.158690 0.987328i \(-0.550727\pi\)
−0.158690 + 0.987328i \(0.550727\pi\)
\(224\) 0 0
\(225\) −3.25981 −0.217321
\(226\) 11.1967 0.744793
\(227\) −5.22879 −0.347047 −0.173523 0.984830i \(-0.555515\pi\)
−0.173523 + 0.984830i \(0.555515\pi\)
\(228\) −1.01690 −0.0673457
\(229\) −18.6808 −1.23446 −0.617232 0.786781i \(-0.711746\pi\)
−0.617232 + 0.786781i \(0.711746\pi\)
\(230\) 6.30731 0.415892
\(231\) 0 0
\(232\) −10.0596 −0.660448
\(233\) −22.5430 −1.47684 −0.738421 0.674340i \(-0.764428\pi\)
−0.738421 + 0.674340i \(0.764428\pi\)
\(234\) −1.64041 −0.107237
\(235\) 16.3204 1.06463
\(236\) 2.03101 0.132208
\(237\) 4.53670 0.294690
\(238\) 0 0
\(239\) −13.9984 −0.905478 −0.452739 0.891643i \(-0.649553\pi\)
−0.452739 + 0.891643i \(0.649553\pi\)
\(240\) −4.79278 −0.309373
\(241\) 11.2619 0.725441 0.362720 0.931898i \(-0.381848\pi\)
0.362720 + 0.931898i \(0.381848\pi\)
\(242\) −8.25429 −0.530606
\(243\) −1.00000 −0.0641500
\(244\) −1.64941 −0.105592
\(245\) 0 0
\(246\) −1.35311 −0.0862709
\(247\) −7.29033 −0.463873
\(248\) 3.54782 0.225287
\(249\) 16.9034 1.07121
\(250\) −14.7435 −0.932460
\(251\) 15.3946 0.971696 0.485848 0.874043i \(-0.338511\pi\)
0.485848 + 0.874043i \(0.338511\pi\)
\(252\) 0 0
\(253\) −14.6122 −0.918660
\(254\) 20.3839 1.27900
\(255\) −10.0659 −0.630348
\(256\) −4.02862 −0.251789
\(257\) 18.0611 1.12662 0.563311 0.826245i \(-0.309527\pi\)
0.563311 + 0.826245i \(0.309527\pi\)
\(258\) −9.65109 −0.600850
\(259\) 0 0
\(260\) 0.270438 0.0167718
\(261\) −3.42745 −0.212154
\(262\) 20.6544 1.27603
\(263\) −5.44028 −0.335462 −0.167731 0.985833i \(-0.553644\pi\)
−0.167731 + 0.985833i \(0.553644\pi\)
\(264\) 12.1371 0.746984
\(265\) −12.9034 −0.792650
\(266\) 0 0
\(267\) −10.3639 −0.634259
\(268\) −0.555973 −0.0339614
\(269\) −1.51928 −0.0926320 −0.0463160 0.998927i \(-0.514748\pi\)
−0.0463160 + 0.998927i \(0.514748\pi\)
\(270\) −1.78497 −0.108630
\(271\) −1.16103 −0.0705275 −0.0352638 0.999378i \(-0.511227\pi\)
−0.0352638 + 0.999378i \(0.511227\pi\)
\(272\) 27.7231 1.68096
\(273\) 0 0
\(274\) 3.66075 0.221154
\(275\) 13.4801 0.812882
\(276\) 0.597535 0.0359674
\(277\) 10.9612 0.658593 0.329297 0.944226i \(-0.393188\pi\)
0.329297 + 0.944226i \(0.393188\pi\)
\(278\) −17.4695 −1.04775
\(279\) 1.20879 0.0723682
\(280\) 0 0
\(281\) 30.1018 1.79572 0.897861 0.440280i \(-0.145121\pi\)
0.897861 + 0.440280i \(0.145121\pi\)
\(282\) −16.7404 −0.996876
\(283\) −0.416444 −0.0247550 −0.0123775 0.999923i \(-0.503940\pi\)
−0.0123775 + 0.999923i \(0.503940\pi\)
\(284\) 0.874635 0.0519000
\(285\) −7.93279 −0.469898
\(286\) 6.78348 0.401116
\(287\) 0 0
\(288\) −0.953947 −0.0562119
\(289\) 41.2244 2.42497
\(290\) −6.11788 −0.359254
\(291\) −6.82267 −0.399952
\(292\) 1.88204 0.110138
\(293\) 12.4827 0.729249 0.364625 0.931155i \(-0.381197\pi\)
0.364625 + 0.931155i \(0.381197\pi\)
\(294\) 0 0
\(295\) 15.8439 0.922466
\(296\) 5.16619 0.300279
\(297\) 4.13524 0.239951
\(298\) 30.3578 1.75858
\(299\) 4.28384 0.247741
\(300\) −0.551242 −0.0318260
\(301\) 0 0
\(302\) −4.81346 −0.276984
\(303\) 7.85345 0.451169
\(304\) 21.8483 1.25308
\(305\) −12.8670 −0.736761
\(306\) 10.3249 0.590234
\(307\) 24.2680 1.38505 0.692524 0.721395i \(-0.256499\pi\)
0.692524 + 0.721395i \(0.256499\pi\)
\(308\) 0 0
\(309\) 14.8276 0.843513
\(310\) 2.15764 0.122546
\(311\) 14.7110 0.834183 0.417091 0.908865i \(-0.363050\pi\)
0.417091 + 0.908865i \(0.363050\pi\)
\(312\) −3.55821 −0.201444
\(313\) −6.74545 −0.381275 −0.190638 0.981660i \(-0.561056\pi\)
−0.190638 + 0.981660i \(0.561056\pi\)
\(314\) −10.0730 −0.568450
\(315\) 0 0
\(316\) 0.767166 0.0431565
\(317\) 9.54316 0.535997 0.267999 0.963419i \(-0.413638\pi\)
0.267999 + 0.963419i \(0.413638\pi\)
\(318\) 13.2354 0.742206
\(319\) 14.1733 0.793554
\(320\) −11.2883 −0.631036
\(321\) −15.6391 −0.872890
\(322\) 0 0
\(323\) 45.8860 2.55317
\(324\) −0.169102 −0.00939457
\(325\) −3.95196 −0.219215
\(326\) 4.02211 0.222764
\(327\) −2.48326 −0.137324
\(328\) −2.93503 −0.162060
\(329\) 0 0
\(330\) 7.38128 0.406326
\(331\) 21.5662 1.18538 0.592692 0.805429i \(-0.298065\pi\)
0.592692 + 0.805429i \(0.298065\pi\)
\(332\) 2.85840 0.156875
\(333\) 1.76018 0.0964575
\(334\) −24.5210 −1.34173
\(335\) −4.33713 −0.236962
\(336\) 0 0
\(337\) −18.1135 −0.986705 −0.493353 0.869829i \(-0.664229\pi\)
−0.493353 + 0.869829i \(0.664229\pi\)
\(338\) 15.6017 0.848619
\(339\) 8.27480 0.449425
\(340\) −1.70216 −0.0923126
\(341\) −4.99863 −0.270691
\(342\) 8.13692 0.439994
\(343\) 0 0
\(344\) −20.9342 −1.12870
\(345\) 4.66135 0.250959
\(346\) 28.8427 1.55059
\(347\) 5.91793 0.317691 0.158846 0.987303i \(-0.449223\pi\)
0.158846 + 0.987303i \(0.449223\pi\)
\(348\) −0.579589 −0.0310692
\(349\) 10.6866 0.572041 0.286021 0.958223i \(-0.407667\pi\)
0.286021 + 0.958223i \(0.407667\pi\)
\(350\) 0 0
\(351\) −1.21233 −0.0647092
\(352\) 3.94480 0.210259
\(353\) 10.6294 0.565747 0.282874 0.959157i \(-0.408712\pi\)
0.282874 + 0.959157i \(0.408712\pi\)
\(354\) −16.2516 −0.863761
\(355\) 6.82300 0.362127
\(356\) −1.75255 −0.0928852
\(357\) 0 0
\(358\) 25.0127 1.32196
\(359\) −8.46027 −0.446516 −0.223258 0.974759i \(-0.571669\pi\)
−0.223258 + 0.974759i \(0.571669\pi\)
\(360\) −3.87178 −0.204061
\(361\) 17.1623 0.903277
\(362\) 19.2841 1.01355
\(363\) −6.10025 −0.320180
\(364\) 0 0
\(365\) 14.6817 0.768477
\(366\) 13.1981 0.689874
\(367\) 8.70112 0.454195 0.227097 0.973872i \(-0.427076\pi\)
0.227097 + 0.973872i \(0.427076\pi\)
\(368\) −12.8382 −0.669236
\(369\) −1.00000 −0.0520579
\(370\) 3.14187 0.163338
\(371\) 0 0
\(372\) 0.204409 0.0105981
\(373\) −3.07218 −0.159071 −0.0795357 0.996832i \(-0.525344\pi\)
−0.0795357 + 0.996832i \(0.525344\pi\)
\(374\) −42.6959 −2.20775
\(375\) −10.8960 −0.562669
\(376\) −36.3116 −1.87263
\(377\) −4.15518 −0.214003
\(378\) 0 0
\(379\) −7.43781 −0.382055 −0.191027 0.981585i \(-0.561182\pi\)
−0.191027 + 0.981585i \(0.561182\pi\)
\(380\) −1.34145 −0.0688151
\(381\) 15.0645 0.771778
\(382\) 7.60568 0.389140
\(383\) 9.19067 0.469621 0.234811 0.972041i \(-0.424553\pi\)
0.234811 + 0.972041i \(0.424553\pi\)
\(384\) 9.67090 0.493516
\(385\) 0 0
\(386\) 32.6762 1.66317
\(387\) −7.13254 −0.362567
\(388\) −1.15373 −0.0585718
\(389\) −36.7201 −1.86178 −0.930891 0.365298i \(-0.880967\pi\)
−0.930891 + 0.365298i \(0.880967\pi\)
\(390\) −2.16396 −0.109577
\(391\) −26.9629 −1.36357
\(392\) 0 0
\(393\) 15.2644 0.769989
\(394\) 9.92241 0.499884
\(395\) 5.98464 0.301120
\(396\) 0.699279 0.0351401
\(397\) 31.7045 1.59120 0.795602 0.605820i \(-0.207155\pi\)
0.795602 + 0.605820i \(0.207155\pi\)
\(398\) −24.4361 −1.22487
\(399\) 0 0
\(400\) 11.8435 0.592177
\(401\) −4.51534 −0.225485 −0.112743 0.993624i \(-0.535964\pi\)
−0.112743 + 0.993624i \(0.535964\pi\)
\(402\) 4.44873 0.221882
\(403\) 1.46544 0.0729990
\(404\) 1.32804 0.0660723
\(405\) −1.31916 −0.0655497
\(406\) 0 0
\(407\) −7.27879 −0.360796
\(408\) 22.3957 1.10875
\(409\) 27.9794 1.38349 0.691746 0.722141i \(-0.256842\pi\)
0.691746 + 0.722141i \(0.256842\pi\)
\(410\) −1.78497 −0.0881532
\(411\) 2.70544 0.133450
\(412\) 2.50738 0.123530
\(413\) 0 0
\(414\) −4.78130 −0.234988
\(415\) 22.2983 1.09458
\(416\) −1.15649 −0.0567018
\(417\) −12.9107 −0.632239
\(418\) −33.6481 −1.64578
\(419\) −13.3188 −0.650664 −0.325332 0.945600i \(-0.605476\pi\)
−0.325332 + 0.945600i \(0.605476\pi\)
\(420\) 0 0
\(421\) −4.78745 −0.233326 −0.116663 0.993172i \(-0.537220\pi\)
−0.116663 + 0.993172i \(0.537220\pi\)
\(422\) −26.2696 −1.27879
\(423\) −12.3718 −0.601539
\(424\) 28.7090 1.39423
\(425\) 24.8740 1.20656
\(426\) −6.99857 −0.339082
\(427\) 0 0
\(428\) −2.64461 −0.127832
\(429\) 5.01327 0.242043
\(430\) −12.7313 −0.613960
\(431\) −18.7726 −0.904246 −0.452123 0.891956i \(-0.649333\pi\)
−0.452123 + 0.891956i \(0.649333\pi\)
\(432\) 3.63320 0.174802
\(433\) −1.21306 −0.0582958 −0.0291479 0.999575i \(-0.509279\pi\)
−0.0291479 + 0.999575i \(0.509279\pi\)
\(434\) 0 0
\(435\) −4.52136 −0.216782
\(436\) −0.419925 −0.0201107
\(437\) −21.2492 −1.01649
\(438\) −15.0595 −0.719572
\(439\) −5.68678 −0.271415 −0.135708 0.990749i \(-0.543331\pi\)
−0.135708 + 0.990749i \(0.543331\pi\)
\(440\) 16.0107 0.763282
\(441\) 0 0
\(442\) 12.5171 0.595378
\(443\) −36.0080 −1.71079 −0.855397 0.517974i \(-0.826687\pi\)
−0.855397 + 0.517974i \(0.826687\pi\)
\(444\) 0.297651 0.0141259
\(445\) −13.6716 −0.648097
\(446\) 6.41304 0.303666
\(447\) 22.4356 1.06117
\(448\) 0 0
\(449\) 18.3922 0.867983 0.433991 0.900917i \(-0.357105\pi\)
0.433991 + 0.900917i \(0.357105\pi\)
\(450\) 4.41087 0.207931
\(451\) 4.13524 0.194721
\(452\) 1.39929 0.0658170
\(453\) −3.55734 −0.167139
\(454\) 7.07511 0.332051
\(455\) 0 0
\(456\) 17.6498 0.826528
\(457\) 4.17893 0.195482 0.0977410 0.995212i \(-0.468838\pi\)
0.0977410 + 0.995212i \(0.468838\pi\)
\(458\) 25.2771 1.18112
\(459\) 7.63049 0.356161
\(460\) 0.788246 0.0367521
\(461\) −18.4750 −0.860467 −0.430233 0.902718i \(-0.641569\pi\)
−0.430233 + 0.902718i \(0.641569\pi\)
\(462\) 0 0
\(463\) 14.2999 0.664573 0.332287 0.943178i \(-0.392180\pi\)
0.332287 + 0.943178i \(0.392180\pi\)
\(464\) 12.4526 0.578097
\(465\) 1.59459 0.0739472
\(466\) 30.5031 1.41303
\(467\) −24.0941 −1.11494 −0.557471 0.830196i \(-0.688228\pi\)
−0.557471 + 0.830196i \(0.688228\pi\)
\(468\) −0.205007 −0.00947646
\(469\) 0 0
\(470\) −22.0833 −1.01863
\(471\) −7.44432 −0.343016
\(472\) −35.2513 −1.62257
\(473\) 29.4948 1.35617
\(474\) −6.13864 −0.281957
\(475\) 19.6029 0.899443
\(476\) 0 0
\(477\) 9.78151 0.447865
\(478\) 18.9413 0.866353
\(479\) −17.9242 −0.818977 −0.409489 0.912315i \(-0.634293\pi\)
−0.409489 + 0.912315i \(0.634293\pi\)
\(480\) −1.25841 −0.0574383
\(481\) 2.13392 0.0972983
\(482\) −15.2385 −0.694095
\(483\) 0 0
\(484\) −1.03157 −0.0468894
\(485\) −9.00021 −0.408679
\(486\) 1.35311 0.0613782
\(487\) 7.14141 0.323608 0.161804 0.986823i \(-0.448269\pi\)
0.161804 + 0.986823i \(0.448269\pi\)
\(488\) 28.6280 1.29593
\(489\) 2.97250 0.134421
\(490\) 0 0
\(491\) 27.0923 1.22266 0.611328 0.791377i \(-0.290636\pi\)
0.611328 + 0.791377i \(0.290636\pi\)
\(492\) −0.169102 −0.00762372
\(493\) 26.1531 1.17788
\(494\) 9.86460 0.443829
\(495\) 5.45506 0.245187
\(496\) −4.39176 −0.197196
\(497\) 0 0
\(498\) −22.8721 −1.02492
\(499\) 44.1879 1.97812 0.989061 0.147510i \(-0.0471259\pi\)
0.989061 + 0.147510i \(0.0471259\pi\)
\(500\) −1.84254 −0.0824011
\(501\) −18.1220 −0.809632
\(502\) −20.8305 −0.929710
\(503\) 1.40040 0.0624408 0.0312204 0.999513i \(-0.490061\pi\)
0.0312204 + 0.999513i \(0.490061\pi\)
\(504\) 0 0
\(505\) 10.3600 0.461013
\(506\) 19.7718 0.878966
\(507\) 11.5303 0.512077
\(508\) 2.54744 0.113024
\(509\) 8.82748 0.391271 0.195636 0.980677i \(-0.437323\pi\)
0.195636 + 0.980677i \(0.437323\pi\)
\(510\) 13.6202 0.603112
\(511\) 0 0
\(512\) 24.7930 1.09570
\(513\) 6.01351 0.265503
\(514\) −24.4386 −1.07794
\(515\) 19.5600 0.861917
\(516\) −1.20613 −0.0530969
\(517\) 51.1605 2.25004
\(518\) 0 0
\(519\) 21.3159 0.935663
\(520\) −4.69386 −0.205839
\(521\) 6.83755 0.299558 0.149779 0.988719i \(-0.452144\pi\)
0.149779 + 0.988719i \(0.452144\pi\)
\(522\) 4.63770 0.202987
\(523\) −33.9846 −1.48604 −0.743022 0.669267i \(-0.766608\pi\)
−0.743022 + 0.669267i \(0.766608\pi\)
\(524\) 2.58125 0.112763
\(525\) 0 0
\(526\) 7.36127 0.320967
\(527\) −9.22364 −0.401788
\(528\) −15.0242 −0.653843
\(529\) −10.5139 −0.457125
\(530\) 17.4597 0.758400
\(531\) −12.0106 −0.521214
\(532\) 0 0
\(533\) −1.21233 −0.0525117
\(534\) 14.0234 0.606853
\(535\) −20.6305 −0.891935
\(536\) 9.64975 0.416806
\(537\) 18.4854 0.797703
\(538\) 2.05574 0.0886294
\(539\) 0 0
\(540\) −0.223073 −0.00959955
\(541\) 24.3280 1.04594 0.522972 0.852350i \(-0.324823\pi\)
0.522972 + 0.852350i \(0.324823\pi\)
\(542\) 1.57100 0.0674801
\(543\) 14.2517 0.611601
\(544\) 7.27908 0.312088
\(545\) −3.27582 −0.140321
\(546\) 0 0
\(547\) 12.3801 0.529335 0.264668 0.964340i \(-0.414738\pi\)
0.264668 + 0.964340i \(0.414738\pi\)
\(548\) 0.457496 0.0195433
\(549\) 9.75390 0.416286
\(550\) −18.2400 −0.777758
\(551\) 20.6110 0.878057
\(552\) −10.3711 −0.441424
\(553\) 0 0
\(554\) −14.8316 −0.630136
\(555\) 2.32197 0.0985621
\(556\) −2.18323 −0.0925894
\(557\) 43.6036 1.84754 0.923772 0.382943i \(-0.125089\pi\)
0.923772 + 0.382943i \(0.125089\pi\)
\(558\) −1.63562 −0.0692412
\(559\) −8.64697 −0.365728
\(560\) 0 0
\(561\) −31.5540 −1.33221
\(562\) −40.7309 −1.71813
\(563\) −31.1035 −1.31086 −0.655429 0.755257i \(-0.727512\pi\)
−0.655429 + 0.755257i \(0.727512\pi\)
\(564\) −2.09210 −0.0880935
\(565\) 10.9158 0.459231
\(566\) 0.563494 0.0236854
\(567\) 0 0
\(568\) −15.1806 −0.636964
\(569\) −23.4948 −0.984952 −0.492476 0.870326i \(-0.663908\pi\)
−0.492476 + 0.870326i \(0.663908\pi\)
\(570\) 10.7339 0.449594
\(571\) 38.2439 1.60046 0.800229 0.599694i \(-0.204711\pi\)
0.800229 + 0.599694i \(0.204711\pi\)
\(572\) 0.847755 0.0354464
\(573\) 5.62090 0.234817
\(574\) 0 0
\(575\) −11.5188 −0.480366
\(576\) 8.55719 0.356550
\(577\) 28.1043 1.17000 0.584999 0.811034i \(-0.301095\pi\)
0.584999 + 0.811034i \(0.301095\pi\)
\(578\) −55.7810 −2.32019
\(579\) 24.1490 1.00360
\(580\) −0.764572 −0.0317471
\(581\) 0 0
\(582\) 9.23181 0.382671
\(583\) −40.4490 −1.67522
\(584\) −32.6656 −1.35171
\(585\) −1.59926 −0.0661211
\(586\) −16.8905 −0.697739
\(587\) 1.51683 0.0626061 0.0313031 0.999510i \(-0.490034\pi\)
0.0313031 + 0.999510i \(0.490034\pi\)
\(588\) 0 0
\(589\) −7.26905 −0.299516
\(590\) −21.4385 −0.882607
\(591\) 7.33306 0.301642
\(592\) −6.39510 −0.262837
\(593\) 26.2559 1.07820 0.539100 0.842242i \(-0.318765\pi\)
0.539100 + 0.842242i \(0.318765\pi\)
\(594\) −5.59543 −0.229583
\(595\) 0 0
\(596\) 3.79391 0.155405
\(597\) −18.0592 −0.739116
\(598\) −5.79650 −0.237036
\(599\) 6.83178 0.279139 0.139569 0.990212i \(-0.455428\pi\)
0.139569 + 0.990212i \(0.455428\pi\)
\(600\) 9.56763 0.390597
\(601\) 2.08541 0.0850656 0.0425328 0.999095i \(-0.486457\pi\)
0.0425328 + 0.999095i \(0.486457\pi\)
\(602\) 0 0
\(603\) 3.28779 0.133889
\(604\) −0.601555 −0.0244769
\(605\) −8.04722 −0.327166
\(606\) −10.6266 −0.431674
\(607\) −7.94144 −0.322333 −0.161166 0.986927i \(-0.551526\pi\)
−0.161166 + 0.986927i \(0.551526\pi\)
\(608\) 5.73657 0.232648
\(609\) 0 0
\(610\) 17.4104 0.704926
\(611\) −14.9987 −0.606782
\(612\) 1.29033 0.0521587
\(613\) −20.5806 −0.831244 −0.415622 0.909537i \(-0.636436\pi\)
−0.415622 + 0.909537i \(0.636436\pi\)
\(614\) −32.8372 −1.32520
\(615\) −1.31916 −0.0531937
\(616\) 0 0
\(617\) −8.93578 −0.359741 −0.179870 0.983690i \(-0.557568\pi\)
−0.179870 + 0.983690i \(0.557568\pi\)
\(618\) −20.0633 −0.807066
\(619\) 18.3129 0.736058 0.368029 0.929814i \(-0.380033\pi\)
0.368029 + 0.929814i \(0.380033\pi\)
\(620\) 0.269648 0.0108293
\(621\) −3.53357 −0.141797
\(622\) −19.9055 −0.798138
\(623\) 0 0
\(624\) 4.40462 0.176326
\(625\) 1.92543 0.0770171
\(626\) 9.12732 0.364801
\(627\) −24.8673 −0.993105
\(628\) −1.25885 −0.0502336
\(629\) −13.4311 −0.535532
\(630\) 0 0
\(631\) −39.2195 −1.56131 −0.780653 0.624965i \(-0.785113\pi\)
−0.780653 + 0.624965i \(0.785113\pi\)
\(632\) −13.3153 −0.529656
\(633\) −19.4143 −0.771650
\(634\) −12.9129 −0.512838
\(635\) 19.8725 0.788617
\(636\) 1.65408 0.0655884
\(637\) 0 0
\(638\) −19.1780 −0.759265
\(639\) −5.17222 −0.204610
\(640\) 12.7575 0.504284
\(641\) 36.2325 1.43110 0.715548 0.698563i \(-0.246177\pi\)
0.715548 + 0.698563i \(0.246177\pi\)
\(642\) 21.1614 0.835173
\(643\) 33.0515 1.30342 0.651712 0.758467i \(-0.274051\pi\)
0.651712 + 0.758467i \(0.274051\pi\)
\(644\) 0 0
\(645\) −9.40897 −0.370478
\(646\) −62.0887 −2.44285
\(647\) −20.5881 −0.809402 −0.404701 0.914449i \(-0.632624\pi\)
−0.404701 + 0.914449i \(0.632624\pi\)
\(648\) 2.93503 0.115299
\(649\) 49.6666 1.94958
\(650\) 5.34742 0.209743
\(651\) 0 0
\(652\) 0.502656 0.0196855
\(653\) 31.6370 1.23805 0.619025 0.785371i \(-0.287528\pi\)
0.619025 + 0.785371i \(0.287528\pi\)
\(654\) 3.36011 0.131391
\(655\) 20.1363 0.786789
\(656\) 3.63320 0.141853
\(657\) −11.1296 −0.434207
\(658\) 0 0
\(659\) 2.92227 0.113836 0.0569178 0.998379i \(-0.481873\pi\)
0.0569178 + 0.998379i \(0.481873\pi\)
\(660\) 0.922463 0.0359068
\(661\) 35.9959 1.40008 0.700038 0.714105i \(-0.253166\pi\)
0.700038 + 0.714105i \(0.253166\pi\)
\(662\) −29.1813 −1.13417
\(663\) 9.25065 0.359265
\(664\) −49.6119 −1.92532
\(665\) 0 0
\(666\) −2.38172 −0.0922897
\(667\) −12.1111 −0.468945
\(668\) −3.06447 −0.118568
\(669\) 4.73950 0.183240
\(670\) 5.86859 0.226724
\(671\) −40.3348 −1.55711
\(672\) 0 0
\(673\) −12.3452 −0.475873 −0.237936 0.971281i \(-0.576471\pi\)
−0.237936 + 0.971281i \(0.576471\pi\)
\(674\) 24.5095 0.944071
\(675\) 3.25981 0.125470
\(676\) 1.94979 0.0749921
\(677\) −15.4048 −0.592056 −0.296028 0.955179i \(-0.595662\pi\)
−0.296028 + 0.955179i \(0.595662\pi\)
\(678\) −11.1967 −0.430006
\(679\) 0 0
\(680\) 29.5436 1.13294
\(681\) 5.22879 0.200368
\(682\) 6.76368 0.258995
\(683\) −11.8482 −0.453360 −0.226680 0.973969i \(-0.572787\pi\)
−0.226680 + 0.973969i \(0.572787\pi\)
\(684\) 1.01690 0.0388821
\(685\) 3.56892 0.136361
\(686\) 0 0
\(687\) 18.6808 0.712718
\(688\) 25.9139 0.987960
\(689\) 11.8584 0.451769
\(690\) −6.30731 −0.240115
\(691\) −4.45399 −0.169438 −0.0847189 0.996405i \(-0.526999\pi\)
−0.0847189 + 0.996405i \(0.526999\pi\)
\(692\) 3.60457 0.137025
\(693\) 0 0
\(694\) −8.00760 −0.303964
\(695\) −17.0313 −0.646033
\(696\) 10.0596 0.381310
\(697\) 7.63049 0.289026
\(698\) −14.4601 −0.547324
\(699\) 22.5430 0.852655
\(700\) 0 0
\(701\) −48.6204 −1.83637 −0.918183 0.396155i \(-0.870344\pi\)
−0.918183 + 0.396155i \(0.870344\pi\)
\(702\) 1.64041 0.0619132
\(703\) −10.5849 −0.399216
\(704\) −35.3861 −1.33366
\(705\) −16.3204 −0.614663
\(706\) −14.3827 −0.541302
\(707\) 0 0
\(708\) −2.03101 −0.0763302
\(709\) −18.8664 −0.708544 −0.354272 0.935143i \(-0.615271\pi\)
−0.354272 + 0.935143i \(0.615271\pi\)
\(710\) −9.23225 −0.346480
\(711\) −4.53670 −0.170140
\(712\) 30.4182 1.13997
\(713\) 4.27134 0.159963
\(714\) 0 0
\(715\) 6.61331 0.247324
\(716\) 3.12592 0.116821
\(717\) 13.9984 0.522778
\(718\) 11.4477 0.427223
\(719\) −28.7532 −1.07231 −0.536156 0.844119i \(-0.680124\pi\)
−0.536156 + 0.844119i \(0.680124\pi\)
\(720\) 4.79278 0.178616
\(721\) 0 0
\(722\) −23.2224 −0.864247
\(723\) −11.2619 −0.418833
\(724\) 2.41000 0.0895670
\(725\) 11.1728 0.414948
\(726\) 8.25429 0.306345
\(727\) 14.1780 0.525833 0.262917 0.964819i \(-0.415316\pi\)
0.262917 + 0.964819i \(0.415316\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −19.8660 −0.735272
\(731\) 54.4248 2.01297
\(732\) 1.64941 0.0609639
\(733\) −39.5706 −1.46157 −0.730786 0.682607i \(-0.760846\pi\)
−0.730786 + 0.682607i \(0.760846\pi\)
\(734\) −11.7735 −0.434569
\(735\) 0 0
\(736\) −3.37084 −0.124251
\(737\) −13.5958 −0.500808
\(738\) 1.35311 0.0498085
\(739\) 2.50728 0.0922319 0.0461159 0.998936i \(-0.485316\pi\)
0.0461159 + 0.998936i \(0.485316\pi\)
\(740\) 0.392650 0.0144341
\(741\) 7.29033 0.267817
\(742\) 0 0
\(743\) −6.99904 −0.256770 −0.128385 0.991724i \(-0.540979\pi\)
−0.128385 + 0.991724i \(0.540979\pi\)
\(744\) −3.54782 −0.130069
\(745\) 29.5962 1.08432
\(746\) 4.15699 0.152198
\(747\) −16.9034 −0.618463
\(748\) −5.33585 −0.195098
\(749\) 0 0
\(750\) 14.7435 0.538356
\(751\) −2.55120 −0.0930948 −0.0465474 0.998916i \(-0.514822\pi\)
−0.0465474 + 0.998916i \(0.514822\pi\)
\(752\) 44.9493 1.63913
\(753\) −15.3946 −0.561009
\(754\) 5.62241 0.204756
\(755\) −4.69271 −0.170785
\(756\) 0 0
\(757\) −2.21284 −0.0804269 −0.0402135 0.999191i \(-0.512804\pi\)
−0.0402135 + 0.999191i \(0.512804\pi\)
\(758\) 10.0642 0.365546
\(759\) 14.6122 0.530389
\(760\) 23.2830 0.844561
\(761\) −32.3515 −1.17274 −0.586370 0.810043i \(-0.699444\pi\)
−0.586370 + 0.810043i \(0.699444\pi\)
\(762\) −20.3839 −0.738430
\(763\) 0 0
\(764\) 0.950507 0.0343882
\(765\) 10.0659 0.363932
\(766\) −12.4360 −0.449329
\(767\) −14.5607 −0.525757
\(768\) 4.02862 0.145370
\(769\) −24.5951 −0.886922 −0.443461 0.896294i \(-0.646250\pi\)
−0.443461 + 0.896294i \(0.646250\pi\)
\(770\) 0 0
\(771\) −18.0611 −0.650455
\(772\) 4.08365 0.146974
\(773\) 48.9111 1.75921 0.879605 0.475704i \(-0.157807\pi\)
0.879605 + 0.475704i \(0.157807\pi\)
\(774\) 9.65109 0.346901
\(775\) −3.94042 −0.141544
\(776\) 20.0247 0.718846
\(777\) 0 0
\(778\) 49.6862 1.78134
\(779\) 6.01351 0.215456
\(780\) −0.270438 −0.00968323
\(781\) 21.3884 0.765337
\(782\) 36.4837 1.30465
\(783\) 3.42745 0.122487
\(784\) 0 0
\(785\) −9.82026 −0.350500
\(786\) −20.6544 −0.736719
\(787\) 30.3303 1.08116 0.540579 0.841293i \(-0.318205\pi\)
0.540579 + 0.841293i \(0.318205\pi\)
\(788\) 1.24004 0.0441745
\(789\) 5.44028 0.193679
\(790\) −8.09786 −0.288109
\(791\) 0 0
\(792\) −12.1371 −0.431271
\(793\) 11.8249 0.419915
\(794\) −42.8996 −1.52245
\(795\) 12.9034 0.457637
\(796\) −3.05386 −0.108241
\(797\) 34.4648 1.22081 0.610403 0.792091i \(-0.291008\pi\)
0.610403 + 0.792091i \(0.291008\pi\)
\(798\) 0 0
\(799\) 94.4031 3.33974
\(800\) 3.10969 0.109944
\(801\) 10.3639 0.366189
\(802\) 6.10974 0.215742
\(803\) 46.0236 1.62414
\(804\) 0.555973 0.0196076
\(805\) 0 0
\(806\) −1.98290 −0.0698448
\(807\) 1.51928 0.0534811
\(808\) −23.0501 −0.810899
\(809\) 1.24184 0.0436607 0.0218303 0.999762i \(-0.493051\pi\)
0.0218303 + 0.999762i \(0.493051\pi\)
\(810\) 1.78497 0.0627173
\(811\) −41.2628 −1.44893 −0.724466 0.689311i \(-0.757914\pi\)
−0.724466 + 0.689311i \(0.757914\pi\)
\(812\) 0 0
\(813\) 1.16103 0.0407191
\(814\) 9.84898 0.345207
\(815\) 3.92121 0.137354
\(816\) −27.7231 −0.970503
\(817\) 42.8916 1.50059
\(818\) −37.8591 −1.32371
\(819\) 0 0
\(820\) −0.223073 −0.00779006
\(821\) −53.2123 −1.85712 −0.928561 0.371179i \(-0.878954\pi\)
−0.928561 + 0.371179i \(0.878954\pi\)
\(822\) −3.66075 −0.127683
\(823\) 22.1657 0.772647 0.386324 0.922363i \(-0.373745\pi\)
0.386324 + 0.922363i \(0.373745\pi\)
\(824\) −43.5194 −1.51607
\(825\) −13.4801 −0.469317
\(826\) 0 0
\(827\) −9.34066 −0.324807 −0.162403 0.986724i \(-0.551925\pi\)
−0.162403 + 0.986724i \(0.551925\pi\)
\(828\) −0.597535 −0.0207658
\(829\) 39.9571 1.38777 0.693883 0.720088i \(-0.255899\pi\)
0.693883 + 0.720088i \(0.255899\pi\)
\(830\) −30.1720 −1.04729
\(831\) −10.9612 −0.380239
\(832\) 10.3741 0.359658
\(833\) 0 0
\(834\) 17.4695 0.604920
\(835\) −23.9059 −0.827297
\(836\) −4.20512 −0.145437
\(837\) −1.20879 −0.0417818
\(838\) 18.0217 0.622549
\(839\) −42.8317 −1.47871 −0.739356 0.673314i \(-0.764870\pi\)
−0.739356 + 0.673314i \(0.764870\pi\)
\(840\) 0 0
\(841\) −17.2526 −0.594918
\(842\) 6.47793 0.223244
\(843\) −30.1018 −1.03676
\(844\) −3.28301 −0.113006
\(845\) 15.2103 0.523250
\(846\) 16.7404 0.575547
\(847\) 0 0
\(848\) −35.5382 −1.22039
\(849\) 0.416444 0.0142923
\(850\) −33.6571 −1.15443
\(851\) 6.21974 0.213210
\(852\) −0.874635 −0.0299645
\(853\) 32.5731 1.11528 0.557641 0.830082i \(-0.311707\pi\)
0.557641 + 0.830082i \(0.311707\pi\)
\(854\) 0 0
\(855\) 7.93279 0.271296
\(856\) 45.9012 1.56887
\(857\) −3.19940 −0.109290 −0.0546448 0.998506i \(-0.517403\pi\)
−0.0546448 + 0.998506i \(0.517403\pi\)
\(858\) −6.78348 −0.231584
\(859\) 35.1926 1.20076 0.600379 0.799716i \(-0.295017\pi\)
0.600379 + 0.799716i \(0.295017\pi\)
\(860\) −1.59108 −0.0542554
\(861\) 0 0
\(862\) 25.4014 0.865174
\(863\) −13.2842 −0.452199 −0.226099 0.974104i \(-0.572597\pi\)
−0.226099 + 0.974104i \(0.572597\pi\)
\(864\) 0.953947 0.0324539
\(865\) 28.1191 0.956078
\(866\) 1.64140 0.0557769
\(867\) −41.2244 −1.40005
\(868\) 0 0
\(869\) 18.7604 0.636402
\(870\) 6.11788 0.207416
\(871\) 3.98587 0.135056
\(872\) 7.28843 0.246817
\(873\) 6.82267 0.230913
\(874\) 28.7524 0.972564
\(875\) 0 0
\(876\) −1.88204 −0.0635882
\(877\) 21.1466 0.714070 0.357035 0.934091i \(-0.383788\pi\)
0.357035 + 0.934091i \(0.383788\pi\)
\(878\) 7.69482 0.259688
\(879\) −12.4827 −0.421032
\(880\) −19.8193 −0.668109
\(881\) −41.0838 −1.38415 −0.692074 0.721827i \(-0.743303\pi\)
−0.692074 + 0.721827i \(0.743303\pi\)
\(882\) 0 0
\(883\) 7.09721 0.238840 0.119420 0.992844i \(-0.461896\pi\)
0.119420 + 0.992844i \(0.461896\pi\)
\(884\) 1.56431 0.0526133
\(885\) −15.8439 −0.532586
\(886\) 48.7227 1.63687
\(887\) 27.5771 0.925948 0.462974 0.886372i \(-0.346782\pi\)
0.462974 + 0.886372i \(0.346782\pi\)
\(888\) −5.16619 −0.173366
\(889\) 0 0
\(890\) 18.4992 0.620094
\(891\) −4.13524 −0.138536
\(892\) 0.801460 0.0268349
\(893\) 74.3981 2.48964
\(894\) −30.3578 −1.01532
\(895\) 24.3852 0.815107
\(896\) 0 0
\(897\) −4.28384 −0.143033
\(898\) −24.8866 −0.830478
\(899\) −4.14305 −0.138179
\(900\) 0.551242 0.0183747
\(901\) −74.6378 −2.48655
\(902\) −5.59543 −0.186307
\(903\) 0 0
\(904\) −24.2868 −0.807766
\(905\) 18.8004 0.624945
\(906\) 4.81346 0.159917
\(907\) −32.9302 −1.09343 −0.546715 0.837318i \(-0.684122\pi\)
−0.546715 + 0.837318i \(0.684122\pi\)
\(908\) 0.884200 0.0293432
\(909\) −7.85345 −0.260482
\(910\) 0 0
\(911\) 46.6376 1.54517 0.772586 0.634910i \(-0.218963\pi\)
0.772586 + 0.634910i \(0.218963\pi\)
\(912\) −21.8483 −0.723469
\(913\) 69.8997 2.31334
\(914\) −5.65454 −0.187035
\(915\) 12.8670 0.425369
\(916\) 3.15897 0.104375
\(917\) 0 0
\(918\) −10.3249 −0.340772
\(919\) 23.9661 0.790568 0.395284 0.918559i \(-0.370646\pi\)
0.395284 + 0.918559i \(0.370646\pi\)
\(920\) −13.6812 −0.451056
\(921\) −24.2680 −0.799658
\(922\) 24.9987 0.823287
\(923\) −6.27042 −0.206393
\(924\) 0 0
\(925\) −5.73787 −0.188660
\(926\) −19.3493 −0.635858
\(927\) −14.8276 −0.487002
\(928\) 3.26960 0.107330
\(929\) 20.8024 0.682505 0.341252 0.939972i \(-0.389149\pi\)
0.341252 + 0.939972i \(0.389149\pi\)
\(930\) −2.15764 −0.0707520
\(931\) 0 0
\(932\) 3.81207 0.124869
\(933\) −14.7110 −0.481616
\(934\) 32.6019 1.06677
\(935\) −41.6248 −1.36128
\(936\) 3.55821 0.116304
\(937\) −12.1738 −0.397702 −0.198851 0.980030i \(-0.563721\pi\)
−0.198851 + 0.980030i \(0.563721\pi\)
\(938\) 0 0
\(939\) 6.74545 0.220129
\(940\) −2.75982 −0.0900156
\(941\) −32.3488 −1.05454 −0.527270 0.849698i \(-0.676784\pi\)
−0.527270 + 0.849698i \(0.676784\pi\)
\(942\) 10.0730 0.328195
\(943\) −3.53357 −0.115069
\(944\) 43.6368 1.42026
\(945\) 0 0
\(946\) −39.9096 −1.29757
\(947\) −13.7273 −0.446078 −0.223039 0.974810i \(-0.571598\pi\)
−0.223039 + 0.974810i \(0.571598\pi\)
\(948\) −0.767166 −0.0249164
\(949\) −13.4927 −0.437992
\(950\) −26.5248 −0.860579
\(951\) −9.54316 −0.309458
\(952\) 0 0
\(953\) 5.34700 0.173206 0.0866031 0.996243i \(-0.472399\pi\)
0.0866031 + 0.996243i \(0.472399\pi\)
\(954\) −13.2354 −0.428513
\(955\) 7.41488 0.239940
\(956\) 2.36715 0.0765592
\(957\) −14.1733 −0.458159
\(958\) 24.2533 0.783590
\(959\) 0 0
\(960\) 11.2883 0.364329
\(961\) −29.5388 −0.952866
\(962\) −2.88742 −0.0930941
\(963\) 15.6391 0.503963
\(964\) −1.90441 −0.0613368
\(965\) 31.8564 1.02549
\(966\) 0 0
\(967\) −21.8543 −0.702786 −0.351393 0.936228i \(-0.614292\pi\)
−0.351393 + 0.936228i \(0.614292\pi\)
\(968\) 17.9044 0.575469
\(969\) −45.8860 −1.47407
\(970\) 12.1782 0.391020
\(971\) −43.0619 −1.38192 −0.690962 0.722891i \(-0.742813\pi\)
−0.690962 + 0.722891i \(0.742813\pi\)
\(972\) 0.169102 0.00542396
\(973\) 0 0
\(974\) −9.66309 −0.309626
\(975\) 3.95196 0.126564
\(976\) −35.4379 −1.13434
\(977\) 46.7460 1.49554 0.747768 0.663960i \(-0.231125\pi\)
0.747768 + 0.663960i \(0.231125\pi\)
\(978\) −4.02211 −0.128613
\(979\) −42.8571 −1.36972
\(980\) 0 0
\(981\) 2.48326 0.0792843
\(982\) −36.6587 −1.16983
\(983\) −7.90305 −0.252068 −0.126034 0.992026i \(-0.540225\pi\)
−0.126034 + 0.992026i \(0.540225\pi\)
\(984\) 2.93503 0.0935652
\(985\) 9.67349 0.308223
\(986\) −35.3879 −1.12698
\(987\) 0 0
\(988\) 1.23281 0.0392210
\(989\) −25.2033 −0.801419
\(990\) −7.38128 −0.234592
\(991\) −49.2242 −1.56366 −0.781829 0.623492i \(-0.785713\pi\)
−0.781829 + 0.623492i \(0.785713\pi\)
\(992\) −1.15312 −0.0366115
\(993\) −21.5662 −0.684382
\(994\) 0 0
\(995\) −23.8231 −0.755242
\(996\) −2.85840 −0.0905720
\(997\) −10.9194 −0.345821 −0.172910 0.984938i \(-0.555317\pi\)
−0.172910 + 0.984938i \(0.555317\pi\)
\(998\) −59.7909 −1.89265
\(999\) −1.76018 −0.0556898
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 \(a_p\))