Properties

Label 6027.2.a.bc.1.2
Level 6027
Weight 2
Character 6027.1
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 8
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: \(8\)
Coefficient field: 8.8.7457527933.1
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.35554\)
Character \(\chi\) = 6027.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.04183 q^{2} +1.00000 q^{3} +2.16908 q^{4} +3.68950 q^{5} -2.04183 q^{6} -0.345232 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.04183 q^{2} +1.00000 q^{3} +2.16908 q^{4} +3.68950 q^{5} -2.04183 q^{6} -0.345232 q^{8} +1.00000 q^{9} -7.53333 q^{10} +0.232219 q^{11} +2.16908 q^{12} -2.59232 q^{13} +3.68950 q^{15} -3.63325 q^{16} -4.71395 q^{17} -2.04183 q^{18} +7.74581 q^{19} +8.00281 q^{20} -0.474151 q^{22} +8.48752 q^{23} -0.345232 q^{24} +8.61238 q^{25} +5.29308 q^{26} +1.00000 q^{27} -4.10946 q^{29} -7.53333 q^{30} +10.4125 q^{31} +8.10896 q^{32} +0.232219 q^{33} +9.62509 q^{34} +2.16908 q^{36} -8.13831 q^{37} -15.8156 q^{38} -2.59232 q^{39} -1.27373 q^{40} +1.00000 q^{41} +2.59910 q^{43} +0.503701 q^{44} +3.68950 q^{45} -17.3301 q^{46} -3.41324 q^{47} -3.63325 q^{48} -17.5850 q^{50} -4.71395 q^{51} -5.62294 q^{52} -3.35153 q^{53} -2.04183 q^{54} +0.856770 q^{55} +7.74581 q^{57} +8.39082 q^{58} +8.02496 q^{59} +8.00281 q^{60} -13.1267 q^{61} -21.2607 q^{62} -9.29063 q^{64} -9.56434 q^{65} -0.474151 q^{66} +6.60562 q^{67} -10.2249 q^{68} +8.48752 q^{69} +3.23226 q^{71} -0.345232 q^{72} +6.63277 q^{73} +16.6171 q^{74} +8.61238 q^{75} +16.8013 q^{76} +5.29308 q^{78} -5.24998 q^{79} -13.4049 q^{80} +1.00000 q^{81} -2.04183 q^{82} -2.50998 q^{83} -17.3921 q^{85} -5.30693 q^{86} -4.10946 q^{87} -0.0801693 q^{88} -13.2734 q^{89} -7.53333 q^{90} +18.4101 q^{92} +10.4125 q^{93} +6.96926 q^{94} +28.5781 q^{95} +8.10896 q^{96} +7.90714 q^{97} +0.232219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + O(q^{10}) \) \( 8q + q^{2} + 8q^{3} + 13q^{4} + 7q^{5} + q^{6} + 6q^{8} + 8q^{9} + 8q^{10} + 11q^{11} + 13q^{12} + 10q^{13} + 7q^{15} - 17q^{16} + 3q^{17} + q^{18} + 6q^{19} + 11q^{20} + 15q^{22} + 14q^{23} + 6q^{24} + 25q^{25} + 24q^{26} + 8q^{27} + 2q^{29} + 8q^{30} + 16q^{31} + 3q^{32} + 11q^{33} - 4q^{34} + 13q^{36} - 20q^{37} + 10q^{38} + 10q^{39} - 3q^{40} + 8q^{41} + 7q^{43} + 7q^{45} - 5q^{46} + 14q^{47} - 17q^{48} - 5q^{50} + 3q^{51} + 23q^{52} + 7q^{53} + q^{54} + 48q^{55} + 6q^{57} - 20q^{58} + 22q^{59} + 11q^{60} - 33q^{62} - 10q^{64} - 14q^{65} + 15q^{66} + 12q^{67} - 27q^{68} + 14q^{69} - 5q^{71} + 6q^{72} + 2q^{73} + 6q^{74} + 25q^{75} + 43q^{76} + 24q^{78} - 15q^{79} - 7q^{80} + 8q^{81} + q^{82} + 15q^{83} - 43q^{85} + 31q^{86} + 2q^{87} + 17q^{88} + 29q^{89} + 8q^{90} + 19q^{92} + 16q^{93} + 20q^{94} + 14q^{95} + 3q^{96} + 19q^{97} + 11q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.04183 −1.44379 −0.721897 0.692001i \(-0.756729\pi\)
−0.721897 + 0.692001i \(0.756729\pi\)
\(3\) 1.00000 0.577350
\(4\) 2.16908 1.08454
\(5\) 3.68950 1.64999 0.824996 0.565138i \(-0.191177\pi\)
0.824996 + 0.565138i \(0.191177\pi\)
\(6\) −2.04183 −0.833575
\(7\) 0 0
\(8\) −0.345232 −0.122058
\(9\) 1.00000 0.333333
\(10\) −7.53333 −2.38225
\(11\) 0.232219 0.0700165 0.0350083 0.999387i \(-0.488854\pi\)
0.0350083 + 0.999387i \(0.488854\pi\)
\(12\) 2.16908 0.626159
\(13\) −2.59232 −0.718979 −0.359490 0.933149i \(-0.617049\pi\)
−0.359490 + 0.933149i \(0.617049\pi\)
\(14\) 0 0
\(15\) 3.68950 0.952624
\(16\) −3.63325 −0.908313
\(17\) −4.71395 −1.14330 −0.571650 0.820497i \(-0.693697\pi\)
−0.571650 + 0.820497i \(0.693697\pi\)
\(18\) −2.04183 −0.481265
\(19\) 7.74581 1.77701 0.888505 0.458866i \(-0.151744\pi\)
0.888505 + 0.458866i \(0.151744\pi\)
\(20\) 8.00281 1.78948
\(21\) 0 0
\(22\) −0.474151 −0.101089
\(23\) 8.48752 1.76977 0.884885 0.465810i \(-0.154237\pi\)
0.884885 + 0.465810i \(0.154237\pi\)
\(24\) −0.345232 −0.0704702
\(25\) 8.61238 1.72248
\(26\) 5.29308 1.03806
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.10946 −0.763107 −0.381554 0.924347i \(-0.624611\pi\)
−0.381554 + 0.924347i \(0.624611\pi\)
\(30\) −7.53333 −1.37539
\(31\) 10.4125 1.87015 0.935074 0.354454i \(-0.115333\pi\)
0.935074 + 0.354454i \(0.115333\pi\)
\(32\) 8.10896 1.43347
\(33\) 0.232219 0.0404241
\(34\) 9.62509 1.65069
\(35\) 0 0
\(36\) 2.16908 0.361513
\(37\) −8.13831 −1.33793 −0.668965 0.743294i \(-0.733262\pi\)
−0.668965 + 0.743294i \(0.733262\pi\)
\(38\) −15.8156 −2.56564
\(39\) −2.59232 −0.415103
\(40\) −1.27373 −0.201395
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 2.59910 0.396360 0.198180 0.980166i \(-0.436497\pi\)
0.198180 + 0.980166i \(0.436497\pi\)
\(44\) 0.503701 0.0759357
\(45\) 3.68950 0.549998
\(46\) −17.3301 −2.55518
\(47\) −3.41324 −0.497872 −0.248936 0.968520i \(-0.580081\pi\)
−0.248936 + 0.968520i \(0.580081\pi\)
\(48\) −3.63325 −0.524415
\(49\) 0 0
\(50\) −17.5850 −2.48690
\(51\) −4.71395 −0.660085
\(52\) −5.62294 −0.779761
\(53\) −3.35153 −0.460368 −0.230184 0.973147i \(-0.573933\pi\)
−0.230184 + 0.973147i \(0.573933\pi\)
\(54\) −2.04183 −0.277858
\(55\) 0.856770 0.115527
\(56\) 0 0
\(57\) 7.74581 1.02596
\(58\) 8.39082 1.10177
\(59\) 8.02496 1.04476 0.522380 0.852713i \(-0.325044\pi\)
0.522380 + 0.852713i \(0.325044\pi\)
\(60\) 8.00281 1.03316
\(61\) −13.1267 −1.68070 −0.840351 0.542042i \(-0.817651\pi\)
−0.840351 + 0.542042i \(0.817651\pi\)
\(62\) −21.2607 −2.70011
\(63\) 0 0
\(64\) −9.29063 −1.16133
\(65\) −9.56434 −1.18631
\(66\) −0.474151 −0.0583640
\(67\) 6.60562 0.807005 0.403503 0.914978i \(-0.367793\pi\)
0.403503 + 0.914978i \(0.367793\pi\)
\(68\) −10.2249 −1.23996
\(69\) 8.48752 1.02178
\(70\) 0 0
\(71\) 3.23226 0.383599 0.191800 0.981434i \(-0.438568\pi\)
0.191800 + 0.981434i \(0.438568\pi\)
\(72\) −0.345232 −0.0406860
\(73\) 6.63277 0.776307 0.388153 0.921595i \(-0.373113\pi\)
0.388153 + 0.921595i \(0.373113\pi\)
\(74\) 16.6171 1.93169
\(75\) 8.61238 0.994472
\(76\) 16.8013 1.92724
\(77\) 0 0
\(78\) 5.29308 0.599323
\(79\) −5.24998 −0.590669 −0.295334 0.955394i \(-0.595431\pi\)
−0.295334 + 0.955394i \(0.595431\pi\)
\(80\) −13.4049 −1.49871
\(81\) 1.00000 0.111111
\(82\) −2.04183 −0.225483
\(83\) −2.50998 −0.275506 −0.137753 0.990467i \(-0.543988\pi\)
−0.137753 + 0.990467i \(0.543988\pi\)
\(84\) 0 0
\(85\) −17.3921 −1.88644
\(86\) −5.30693 −0.572261
\(87\) −4.10946 −0.440580
\(88\) −0.0801693 −0.00854607
\(89\) −13.2734 −1.40698 −0.703490 0.710705i \(-0.748376\pi\)
−0.703490 + 0.710705i \(0.748376\pi\)
\(90\) −7.53333 −0.794083
\(91\) 0 0
\(92\) 18.4101 1.91939
\(93\) 10.4125 1.07973
\(94\) 6.96926 0.718825
\(95\) 28.5781 2.93206
\(96\) 8.10896 0.827617
\(97\) 7.90714 0.802848 0.401424 0.915892i \(-0.368515\pi\)
0.401424 + 0.915892i \(0.368515\pi\)
\(98\) 0 0
\(99\) 0.232219 0.0233388
\(100\) 18.6809 1.86809
\(101\) 10.8529 1.07990 0.539950 0.841697i \(-0.318443\pi\)
0.539950 + 0.841697i \(0.318443\pi\)
\(102\) 9.62509 0.953026
\(103\) 5.28687 0.520931 0.260465 0.965483i \(-0.416124\pi\)
0.260465 + 0.965483i \(0.416124\pi\)
\(104\) 0.894950 0.0877571
\(105\) 0 0
\(106\) 6.84326 0.664676
\(107\) 6.23899 0.603146 0.301573 0.953443i \(-0.402488\pi\)
0.301573 + 0.953443i \(0.402488\pi\)
\(108\) 2.16908 0.208720
\(109\) 4.43703 0.424990 0.212495 0.977162i \(-0.431841\pi\)
0.212495 + 0.977162i \(0.431841\pi\)
\(110\) −1.74938 −0.166797
\(111\) −8.13831 −0.772454
\(112\) 0 0
\(113\) 19.5852 1.84243 0.921213 0.389060i \(-0.127200\pi\)
0.921213 + 0.389060i \(0.127200\pi\)
\(114\) −15.8156 −1.48127
\(115\) 31.3147 2.92011
\(116\) −8.91374 −0.827620
\(117\) −2.59232 −0.239660
\(118\) −16.3856 −1.50842
\(119\) 0 0
\(120\) −1.27373 −0.116275
\(121\) −10.9461 −0.995098
\(122\) 26.8025 2.42659
\(123\) 1.00000 0.0901670
\(124\) 22.5856 2.02825
\(125\) 13.3279 1.19208
\(126\) 0 0
\(127\) 15.3392 1.36114 0.680568 0.732685i \(-0.261733\pi\)
0.680568 + 0.732685i \(0.261733\pi\)
\(128\) 2.75199 0.243244
\(129\) 2.59910 0.228838
\(130\) 19.5288 1.71279
\(131\) −17.1723 −1.50035 −0.750176 0.661239i \(-0.770031\pi\)
−0.750176 + 0.661239i \(0.770031\pi\)
\(132\) 0.503701 0.0438415
\(133\) 0 0
\(134\) −13.4876 −1.16515
\(135\) 3.68950 0.317541
\(136\) 1.62741 0.139549
\(137\) 9.02525 0.771079 0.385540 0.922691i \(-0.374015\pi\)
0.385540 + 0.922691i \(0.374015\pi\)
\(138\) −17.3301 −1.47524
\(139\) −11.0833 −0.940071 −0.470036 0.882647i \(-0.655759\pi\)
−0.470036 + 0.882647i \(0.655759\pi\)
\(140\) 0 0
\(141\) −3.41324 −0.287447
\(142\) −6.59974 −0.553838
\(143\) −0.601984 −0.0503404
\(144\) −3.63325 −0.302771
\(145\) −15.1618 −1.25912
\(146\) −13.5430 −1.12083
\(147\) 0 0
\(148\) −17.6526 −1.45104
\(149\) 10.2152 0.836862 0.418431 0.908249i \(-0.362580\pi\)
0.418431 + 0.908249i \(0.362580\pi\)
\(150\) −17.5850 −1.43581
\(151\) −5.71699 −0.465242 −0.232621 0.972567i \(-0.574730\pi\)
−0.232621 + 0.972567i \(0.574730\pi\)
\(152\) −2.67410 −0.216898
\(153\) −4.71395 −0.381100
\(154\) 0 0
\(155\) 38.4170 3.08573
\(156\) −5.62294 −0.450195
\(157\) 5.45503 0.435359 0.217679 0.976020i \(-0.430151\pi\)
0.217679 + 0.976020i \(0.430151\pi\)
\(158\) 10.7196 0.852804
\(159\) −3.35153 −0.265794
\(160\) 29.9180 2.36522
\(161\) 0 0
\(162\) −2.04183 −0.160422
\(163\) 12.6634 0.991874 0.495937 0.868358i \(-0.334825\pi\)
0.495937 + 0.868358i \(0.334825\pi\)
\(164\) 2.16908 0.169377
\(165\) 0.856770 0.0666994
\(166\) 5.12496 0.397774
\(167\) 11.4402 0.885268 0.442634 0.896702i \(-0.354044\pi\)
0.442634 + 0.896702i \(0.354044\pi\)
\(168\) 0 0
\(169\) −6.27990 −0.483069
\(170\) 35.5118 2.72363
\(171\) 7.74581 0.592337
\(172\) 5.63766 0.429868
\(173\) 12.2561 0.931818 0.465909 0.884833i \(-0.345727\pi\)
0.465909 + 0.884833i \(0.345727\pi\)
\(174\) 8.39082 0.636107
\(175\) 0 0
\(176\) −0.843709 −0.0635970
\(177\) 8.02496 0.603193
\(178\) 27.1021 2.03139
\(179\) −6.29779 −0.470719 −0.235359 0.971908i \(-0.575627\pi\)
−0.235359 + 0.971908i \(0.575627\pi\)
\(180\) 8.00281 0.596494
\(181\) −18.8748 −1.40296 −0.701478 0.712691i \(-0.747476\pi\)
−0.701478 + 0.712691i \(0.747476\pi\)
\(182\) 0 0
\(183\) −13.1267 −0.970354
\(184\) −2.93016 −0.216014
\(185\) −30.0263 −2.20757
\(186\) −21.2607 −1.55891
\(187\) −1.09467 −0.0800500
\(188\) −7.40359 −0.539962
\(189\) 0 0
\(190\) −58.3518 −4.23328
\(191\) 7.98832 0.578014 0.289007 0.957327i \(-0.406675\pi\)
0.289007 + 0.957327i \(0.406675\pi\)
\(192\) −9.29063 −0.670493
\(193\) −8.36539 −0.602154 −0.301077 0.953600i \(-0.597346\pi\)
−0.301077 + 0.953600i \(0.597346\pi\)
\(194\) −16.1451 −1.15915
\(195\) −9.56434 −0.684917
\(196\) 0 0
\(197\) −20.1945 −1.43880 −0.719401 0.694595i \(-0.755583\pi\)
−0.719401 + 0.694595i \(0.755583\pi\)
\(198\) −0.474151 −0.0336965
\(199\) −2.42833 −0.172140 −0.0860700 0.996289i \(-0.527431\pi\)
−0.0860700 + 0.996289i \(0.527431\pi\)
\(200\) −2.97327 −0.210242
\(201\) 6.60562 0.465925
\(202\) −22.1597 −1.55915
\(203\) 0 0
\(204\) −10.2249 −0.715888
\(205\) 3.68950 0.257686
\(206\) −10.7949 −0.752116
\(207\) 8.48752 0.589923
\(208\) 9.41854 0.653058
\(209\) 1.79872 0.124420
\(210\) 0 0
\(211\) −10.1756 −0.700514 −0.350257 0.936654i \(-0.613906\pi\)
−0.350257 + 0.936654i \(0.613906\pi\)
\(212\) −7.26973 −0.499287
\(213\) 3.23226 0.221471
\(214\) −12.7390 −0.870819
\(215\) 9.58938 0.653991
\(216\) −0.345232 −0.0234901
\(217\) 0 0
\(218\) −9.05967 −0.613598
\(219\) 6.63277 0.448201
\(220\) 1.85840 0.125293
\(221\) 12.2200 0.822009
\(222\) 16.6171 1.11526
\(223\) −18.3685 −1.23004 −0.615022 0.788510i \(-0.710853\pi\)
−0.615022 + 0.788510i \(0.710853\pi\)
\(224\) 0 0
\(225\) 8.61238 0.574159
\(226\) −39.9898 −2.66008
\(227\) −16.6244 −1.10340 −0.551700 0.834042i \(-0.686021\pi\)
−0.551700 + 0.834042i \(0.686021\pi\)
\(228\) 16.8013 1.11269
\(229\) 15.2296 1.00640 0.503200 0.864170i \(-0.332156\pi\)
0.503200 + 0.864170i \(0.332156\pi\)
\(230\) −63.9393 −4.21603
\(231\) 0 0
\(232\) 1.41872 0.0931433
\(233\) 14.7310 0.965057 0.482528 0.875880i \(-0.339719\pi\)
0.482528 + 0.875880i \(0.339719\pi\)
\(234\) 5.29308 0.346019
\(235\) −12.5931 −0.821486
\(236\) 17.4068 1.13308
\(237\) −5.24998 −0.341023
\(238\) 0 0
\(239\) 12.3660 0.799889 0.399945 0.916539i \(-0.369029\pi\)
0.399945 + 0.916539i \(0.369029\pi\)
\(240\) −13.4049 −0.865281
\(241\) −10.7234 −0.690754 −0.345377 0.938464i \(-0.612249\pi\)
−0.345377 + 0.938464i \(0.612249\pi\)
\(242\) 22.3500 1.43672
\(243\) 1.00000 0.0641500
\(244\) −28.4729 −1.82279
\(245\) 0 0
\(246\) −2.04183 −0.130182
\(247\) −20.0796 −1.27763
\(248\) −3.59474 −0.228266
\(249\) −2.50998 −0.159064
\(250\) −27.2133 −1.72112
\(251\) 10.5518 0.666026 0.333013 0.942922i \(-0.391935\pi\)
0.333013 + 0.942922i \(0.391935\pi\)
\(252\) 0 0
\(253\) 1.97096 0.123913
\(254\) −31.3201 −1.96520
\(255\) −17.3921 −1.08914
\(256\) 12.9622 0.810135
\(257\) 26.8542 1.67512 0.837561 0.546344i \(-0.183981\pi\)
0.837561 + 0.546344i \(0.183981\pi\)
\(258\) −5.30693 −0.330395
\(259\) 0 0
\(260\) −20.7458 −1.28660
\(261\) −4.10946 −0.254369
\(262\) 35.0630 2.16620
\(263\) 22.8337 1.40799 0.703993 0.710207i \(-0.251399\pi\)
0.703993 + 0.710207i \(0.251399\pi\)
\(264\) −0.0801693 −0.00493408
\(265\) −12.3655 −0.759604
\(266\) 0 0
\(267\) −13.2734 −0.812320
\(268\) 14.3281 0.875229
\(269\) 26.4506 1.61272 0.806360 0.591424i \(-0.201434\pi\)
0.806360 + 0.591424i \(0.201434\pi\)
\(270\) −7.53333 −0.458464
\(271\) −8.75300 −0.531707 −0.265854 0.964013i \(-0.585654\pi\)
−0.265854 + 0.964013i \(0.585654\pi\)
\(272\) 17.1270 1.03848
\(273\) 0 0
\(274\) −18.4280 −1.11328
\(275\) 1.99996 0.120602
\(276\) 18.4101 1.10816
\(277\) 6.44745 0.387390 0.193695 0.981062i \(-0.437953\pi\)
0.193695 + 0.981062i \(0.437953\pi\)
\(278\) 22.6302 1.35727
\(279\) 10.4125 0.623382
\(280\) 0 0
\(281\) −21.5896 −1.28793 −0.643965 0.765055i \(-0.722712\pi\)
−0.643965 + 0.765055i \(0.722712\pi\)
\(282\) 6.96926 0.415014
\(283\) −0.145666 −0.00865894 −0.00432947 0.999991i \(-0.501378\pi\)
−0.00432947 + 0.999991i \(0.501378\pi\)
\(284\) 7.01104 0.416029
\(285\) 28.5781 1.69282
\(286\) 1.22915 0.0726812
\(287\) 0 0
\(288\) 8.10896 0.477825
\(289\) 5.22132 0.307137
\(290\) 30.9579 1.81791
\(291\) 7.90714 0.463525
\(292\) 14.3870 0.841935
\(293\) 7.84054 0.458049 0.229025 0.973421i \(-0.426446\pi\)
0.229025 + 0.973421i \(0.426446\pi\)
\(294\) 0 0
\(295\) 29.6081 1.72385
\(296\) 2.80960 0.163305
\(297\) 0.232219 0.0134747
\(298\) −20.8577 −1.20826
\(299\) −22.0023 −1.27243
\(300\) 18.6809 1.07854
\(301\) 0 0
\(302\) 11.6731 0.671713
\(303\) 10.8529 0.623481
\(304\) −28.1425 −1.61408
\(305\) −48.4309 −2.77315
\(306\) 9.62509 0.550230
\(307\) 20.8939 1.19248 0.596238 0.802808i \(-0.296662\pi\)
0.596238 + 0.802808i \(0.296662\pi\)
\(308\) 0 0
\(309\) 5.28687 0.300759
\(310\) −78.4411 −4.45516
\(311\) 28.5586 1.61941 0.809706 0.586836i \(-0.199627\pi\)
0.809706 + 0.586836i \(0.199627\pi\)
\(312\) 0.894950 0.0506666
\(313\) −29.9521 −1.69299 −0.846497 0.532394i \(-0.821293\pi\)
−0.846497 + 0.532394i \(0.821293\pi\)
\(314\) −11.1382 −0.628568
\(315\) 0 0
\(316\) −11.3876 −0.640604
\(317\) −13.5173 −0.759204 −0.379602 0.925150i \(-0.623939\pi\)
−0.379602 + 0.925150i \(0.623939\pi\)
\(318\) 6.84326 0.383751
\(319\) −0.954292 −0.0534301
\(320\) −34.2777 −1.91618
\(321\) 6.23899 0.348227
\(322\) 0 0
\(323\) −36.5134 −2.03166
\(324\) 2.16908 0.120504
\(325\) −22.3260 −1.23842
\(326\) −25.8565 −1.43206
\(327\) 4.43703 0.245368
\(328\) −0.345232 −0.0190622
\(329\) 0 0
\(330\) −1.74938 −0.0963002
\(331\) −0.476790 −0.0262068 −0.0131034 0.999914i \(-0.504171\pi\)
−0.0131034 + 0.999914i \(0.504171\pi\)
\(332\) −5.44435 −0.298797
\(333\) −8.13831 −0.445976
\(334\) −23.3589 −1.27814
\(335\) 24.3714 1.33155
\(336\) 0 0
\(337\) −20.8216 −1.13422 −0.567111 0.823641i \(-0.691939\pi\)
−0.567111 + 0.823641i \(0.691939\pi\)
\(338\) 12.8225 0.697452
\(339\) 19.5852 1.06372
\(340\) −37.7248 −2.04592
\(341\) 2.41799 0.130941
\(342\) −15.8156 −0.855212
\(343\) 0 0
\(344\) −0.897294 −0.0483788
\(345\) 31.3147 1.68592
\(346\) −25.0250 −1.34535
\(347\) 9.11769 0.489463 0.244732 0.969591i \(-0.421300\pi\)
0.244732 + 0.969591i \(0.421300\pi\)
\(348\) −8.91374 −0.477827
\(349\) 10.4817 0.561071 0.280535 0.959844i \(-0.409488\pi\)
0.280535 + 0.959844i \(0.409488\pi\)
\(350\) 0 0
\(351\) −2.59232 −0.138368
\(352\) 1.88305 0.100367
\(353\) −4.33421 −0.230687 −0.115343 0.993326i \(-0.536797\pi\)
−0.115343 + 0.993326i \(0.536797\pi\)
\(354\) −16.3856 −0.870886
\(355\) 11.9254 0.632936
\(356\) −28.7911 −1.52593
\(357\) 0 0
\(358\) 12.8590 0.679620
\(359\) 1.63625 0.0863578 0.0431789 0.999067i \(-0.486251\pi\)
0.0431789 + 0.999067i \(0.486251\pi\)
\(360\) −1.27373 −0.0671316
\(361\) 40.9976 2.15777
\(362\) 38.5393 2.02558
\(363\) −10.9461 −0.574520
\(364\) 0 0
\(365\) 24.4716 1.28090
\(366\) 26.8025 1.40099
\(367\) −19.6883 −1.02772 −0.513861 0.857873i \(-0.671785\pi\)
−0.513861 + 0.857873i \(0.671785\pi\)
\(368\) −30.8373 −1.60751
\(369\) 1.00000 0.0520579
\(370\) 61.3086 3.18728
\(371\) 0 0
\(372\) 22.5856 1.17101
\(373\) −1.93972 −0.100435 −0.0502175 0.998738i \(-0.515991\pi\)
−0.0502175 + 0.998738i \(0.515991\pi\)
\(374\) 2.23513 0.115576
\(375\) 13.3279 0.688248
\(376\) 1.17836 0.0607693
\(377\) 10.6530 0.548658
\(378\) 0 0
\(379\) −3.47525 −0.178512 −0.0892559 0.996009i \(-0.528449\pi\)
−0.0892559 + 0.996009i \(0.528449\pi\)
\(380\) 61.9883 3.17993
\(381\) 15.3392 0.785852
\(382\) −16.3108 −0.834533
\(383\) 10.0079 0.511382 0.255691 0.966759i \(-0.417697\pi\)
0.255691 + 0.966759i \(0.417697\pi\)
\(384\) 2.75199 0.140437
\(385\) 0 0
\(386\) 17.0807 0.869386
\(387\) 2.59910 0.132120
\(388\) 17.1512 0.870721
\(389\) 21.7567 1.10311 0.551553 0.834140i \(-0.314035\pi\)
0.551553 + 0.834140i \(0.314035\pi\)
\(390\) 19.5288 0.988878
\(391\) −40.0097 −2.02338
\(392\) 0 0
\(393\) −17.1723 −0.866228
\(394\) 41.2339 2.07733
\(395\) −19.3698 −0.974599
\(396\) 0.503701 0.0253119
\(397\) −23.6233 −1.18562 −0.592811 0.805342i \(-0.701982\pi\)
−0.592811 + 0.805342i \(0.701982\pi\)
\(398\) 4.95825 0.248535
\(399\) 0 0
\(400\) −31.2910 −1.56455
\(401\) −3.67183 −0.183362 −0.0916812 0.995788i \(-0.529224\pi\)
−0.0916812 + 0.995788i \(0.529224\pi\)
\(402\) −13.4876 −0.672699
\(403\) −26.9926 −1.34460
\(404\) 23.5407 1.17119
\(405\) 3.68950 0.183333
\(406\) 0 0
\(407\) −1.88987 −0.0936772
\(408\) 1.62741 0.0805686
\(409\) −18.6205 −0.920724 −0.460362 0.887731i \(-0.652280\pi\)
−0.460362 + 0.887731i \(0.652280\pi\)
\(410\) −7.53333 −0.372045
\(411\) 9.02525 0.445183
\(412\) 11.4676 0.564970
\(413\) 0 0
\(414\) −17.3301 −0.851727
\(415\) −9.26056 −0.454583
\(416\) −21.0210 −1.03064
\(417\) −11.0833 −0.542750
\(418\) −3.67269 −0.179637
\(419\) 20.3870 0.995971 0.497985 0.867185i \(-0.334073\pi\)
0.497985 + 0.867185i \(0.334073\pi\)
\(420\) 0 0
\(421\) −24.4425 −1.19125 −0.595627 0.803261i \(-0.703096\pi\)
−0.595627 + 0.803261i \(0.703096\pi\)
\(422\) 20.7768 1.01140
\(423\) −3.41324 −0.165957
\(424\) 1.15706 0.0561916
\(425\) −40.5983 −1.96931
\(426\) −6.59974 −0.319759
\(427\) 0 0
\(428\) 13.5329 0.654136
\(429\) −0.601984 −0.0290641
\(430\) −19.5799 −0.944227
\(431\) 7.83717 0.377503 0.188752 0.982025i \(-0.439556\pi\)
0.188752 + 0.982025i \(0.439556\pi\)
\(432\) −3.63325 −0.174805
\(433\) −10.6522 −0.511914 −0.255957 0.966688i \(-0.582390\pi\)
−0.255957 + 0.966688i \(0.582390\pi\)
\(434\) 0 0
\(435\) −15.1618 −0.726954
\(436\) 9.62427 0.460919
\(437\) 65.7427 3.14490
\(438\) −13.5430 −0.647110
\(439\) 24.6501 1.17649 0.588243 0.808684i \(-0.299820\pi\)
0.588243 + 0.808684i \(0.299820\pi\)
\(440\) −0.295784 −0.0141010
\(441\) 0 0
\(442\) −24.9513 −1.18681
\(443\) −0.888234 −0.0422013 −0.0211006 0.999777i \(-0.506717\pi\)
−0.0211006 + 0.999777i \(0.506717\pi\)
\(444\) −17.6526 −0.837757
\(445\) −48.9722 −2.32151
\(446\) 37.5054 1.77593
\(447\) 10.2152 0.483162
\(448\) 0 0
\(449\) −19.6747 −0.928505 −0.464252 0.885703i \(-0.653677\pi\)
−0.464252 + 0.885703i \(0.653677\pi\)
\(450\) −17.5850 −0.828967
\(451\) 0.232219 0.0109347
\(452\) 42.4820 1.99818
\(453\) −5.71699 −0.268608
\(454\) 33.9443 1.59308
\(455\) 0 0
\(456\) −2.67410 −0.125226
\(457\) −8.76520 −0.410019 −0.205009 0.978760i \(-0.565722\pi\)
−0.205009 + 0.978760i \(0.565722\pi\)
\(458\) −31.0963 −1.45303
\(459\) −4.71395 −0.220028
\(460\) 67.9240 3.16697
\(461\) −5.76370 −0.268442 −0.134221 0.990951i \(-0.542853\pi\)
−0.134221 + 0.990951i \(0.542853\pi\)
\(462\) 0 0
\(463\) 10.6187 0.493494 0.246747 0.969080i \(-0.420638\pi\)
0.246747 + 0.969080i \(0.420638\pi\)
\(464\) 14.9307 0.693140
\(465\) 38.4170 1.78155
\(466\) −30.0781 −1.39334
\(467\) −31.6308 −1.46370 −0.731849 0.681467i \(-0.761342\pi\)
−0.731849 + 0.681467i \(0.761342\pi\)
\(468\) −5.62294 −0.259920
\(469\) 0 0
\(470\) 25.7131 1.18606
\(471\) 5.45503 0.251354
\(472\) −2.77047 −0.127521
\(473\) 0.603560 0.0277517
\(474\) 10.7196 0.492366
\(475\) 66.7099 3.06086
\(476\) 0 0
\(477\) −3.35153 −0.153456
\(478\) −25.2493 −1.15487
\(479\) −39.7627 −1.81680 −0.908401 0.418100i \(-0.862696\pi\)
−0.908401 + 0.418100i \(0.862696\pi\)
\(480\) 29.9180 1.36556
\(481\) 21.0971 0.961943
\(482\) 21.8954 0.997307
\(483\) 0 0
\(484\) −23.7429 −1.07922
\(485\) 29.1734 1.32469
\(486\) −2.04183 −0.0926194
\(487\) −13.8837 −0.629132 −0.314566 0.949236i \(-0.601859\pi\)
−0.314566 + 0.949236i \(0.601859\pi\)
\(488\) 4.53176 0.205143
\(489\) 12.6634 0.572659
\(490\) 0 0
\(491\) 20.2751 0.915001 0.457501 0.889209i \(-0.348745\pi\)
0.457501 + 0.889209i \(0.348745\pi\)
\(492\) 2.16908 0.0977897
\(493\) 19.3718 0.872461
\(494\) 40.9992 1.84464
\(495\) 0.856770 0.0385089
\(496\) −37.8314 −1.69868
\(497\) 0 0
\(498\) 5.12496 0.229655
\(499\) 9.76966 0.437350 0.218675 0.975798i \(-0.429827\pi\)
0.218675 + 0.975798i \(0.429827\pi\)
\(500\) 28.9092 1.29286
\(501\) 11.4402 0.511110
\(502\) −21.5451 −0.961605
\(503\) 6.98768 0.311565 0.155783 0.987791i \(-0.450210\pi\)
0.155783 + 0.987791i \(0.450210\pi\)
\(504\) 0 0
\(505\) 40.0416 1.78183
\(506\) −4.02437 −0.178905
\(507\) −6.27990 −0.278900
\(508\) 33.2720 1.47621
\(509\) −5.64474 −0.250199 −0.125099 0.992144i \(-0.539925\pi\)
−0.125099 + 0.992144i \(0.539925\pi\)
\(510\) 35.5118 1.57249
\(511\) 0 0
\(512\) −31.9705 −1.41291
\(513\) 7.74581 0.341986
\(514\) −54.8319 −2.41853
\(515\) 19.5059 0.859532
\(516\) 5.63766 0.248184
\(517\) −0.792618 −0.0348593
\(518\) 0 0
\(519\) 12.2561 0.537985
\(520\) 3.30192 0.144799
\(521\) −18.6235 −0.815910 −0.407955 0.913002i \(-0.633758\pi\)
−0.407955 + 0.913002i \(0.633758\pi\)
\(522\) 8.39082 0.367256
\(523\) 27.5839 1.20616 0.603081 0.797680i \(-0.293940\pi\)
0.603081 + 0.797680i \(0.293940\pi\)
\(524\) −37.2481 −1.62719
\(525\) 0 0
\(526\) −46.6226 −2.03284
\(527\) −49.0842 −2.13814
\(528\) −0.843709 −0.0367177
\(529\) 49.0380 2.13208
\(530\) 25.2482 1.09671
\(531\) 8.02496 0.348254
\(532\) 0 0
\(533\) −2.59232 −0.112286
\(534\) 27.1021 1.17282
\(535\) 23.0187 0.995187
\(536\) −2.28047 −0.0985014
\(537\) −6.29779 −0.271769
\(538\) −54.0077 −2.32844
\(539\) 0 0
\(540\) 8.00281 0.344386
\(541\) −16.8601 −0.724873 −0.362437 0.932008i \(-0.618055\pi\)
−0.362437 + 0.932008i \(0.618055\pi\)
\(542\) 17.8722 0.767675
\(543\) −18.8748 −0.809997
\(544\) −38.2252 −1.63889
\(545\) 16.3704 0.701231
\(546\) 0 0
\(547\) −17.8296 −0.762338 −0.381169 0.924505i \(-0.624478\pi\)
−0.381169 + 0.924505i \(0.624478\pi\)
\(548\) 19.5765 0.836266
\(549\) −13.1267 −0.560234
\(550\) −4.08357 −0.174124
\(551\) −31.8311 −1.35605
\(552\) −2.93016 −0.124716
\(553\) 0 0
\(554\) −13.1646 −0.559311
\(555\) −30.0263 −1.27454
\(556\) −24.0405 −1.01954
\(557\) −1.21738 −0.0515820 −0.0257910 0.999667i \(-0.508210\pi\)
−0.0257910 + 0.999667i \(0.508210\pi\)
\(558\) −21.2607 −0.900036
\(559\) −6.73770 −0.284974
\(560\) 0 0
\(561\) −1.09467 −0.0462169
\(562\) 44.0824 1.85951
\(563\) 12.9116 0.544157 0.272079 0.962275i \(-0.412289\pi\)
0.272079 + 0.962275i \(0.412289\pi\)
\(564\) −7.40359 −0.311747
\(565\) 72.2597 3.03999
\(566\) 0.297425 0.0125017
\(567\) 0 0
\(568\) −1.11588 −0.0468213
\(569\) −6.13102 −0.257026 −0.128513 0.991708i \(-0.541020\pi\)
−0.128513 + 0.991708i \(0.541020\pi\)
\(570\) −58.3518 −2.44409
\(571\) −30.1505 −1.26176 −0.630879 0.775881i \(-0.717306\pi\)
−0.630879 + 0.775881i \(0.717306\pi\)
\(572\) −1.30575 −0.0545962
\(573\) 7.98832 0.333717
\(574\) 0 0
\(575\) 73.0977 3.04839
\(576\) −9.29063 −0.387109
\(577\) 21.8970 0.911582 0.455791 0.890087i \(-0.349356\pi\)
0.455791 + 0.890087i \(0.349356\pi\)
\(578\) −10.6611 −0.443442
\(579\) −8.36539 −0.347654
\(580\) −32.8872 −1.36557
\(581\) 0 0
\(582\) −16.1451 −0.669234
\(583\) −0.778287 −0.0322334
\(584\) −2.28984 −0.0947544
\(585\) −9.56434 −0.395437
\(586\) −16.0091 −0.661329
\(587\) 18.7737 0.774873 0.387436 0.921896i \(-0.373361\pi\)
0.387436 + 0.921896i \(0.373361\pi\)
\(588\) 0 0
\(589\) 80.6536 3.32327
\(590\) −60.4547 −2.48888
\(591\) −20.1945 −0.830692
\(592\) 29.5685 1.21526
\(593\) 1.40764 0.0578048 0.0289024 0.999582i \(-0.490799\pi\)
0.0289024 + 0.999582i \(0.490799\pi\)
\(594\) −0.474151 −0.0194547
\(595\) 0 0
\(596\) 22.1576 0.907610
\(597\) −2.42833 −0.0993850
\(598\) 44.9251 1.83712
\(599\) −31.7524 −1.29737 −0.648685 0.761057i \(-0.724681\pi\)
−0.648685 + 0.761057i \(0.724681\pi\)
\(600\) −2.97327 −0.121383
\(601\) −16.8874 −0.688853 −0.344427 0.938813i \(-0.611927\pi\)
−0.344427 + 0.938813i \(0.611927\pi\)
\(602\) 0 0
\(603\) 6.60562 0.269002
\(604\) −12.4006 −0.504573
\(605\) −40.3855 −1.64190
\(606\) −22.1597 −0.900177
\(607\) 11.5151 0.467382 0.233691 0.972311i \(-0.424920\pi\)
0.233691 + 0.972311i \(0.424920\pi\)
\(608\) 62.8105 2.54730
\(609\) 0 0
\(610\) 98.8878 4.00385
\(611\) 8.84820 0.357960
\(612\) −10.2249 −0.413318
\(613\) 20.5359 0.829438 0.414719 0.909949i \(-0.363880\pi\)
0.414719 + 0.909949i \(0.363880\pi\)
\(614\) −42.6618 −1.72169
\(615\) 3.68950 0.148775
\(616\) 0 0
\(617\) 1.57898 0.0635675 0.0317837 0.999495i \(-0.489881\pi\)
0.0317837 + 0.999495i \(0.489881\pi\)
\(618\) −10.7949 −0.434234
\(619\) 34.3577 1.38095 0.690476 0.723355i \(-0.257401\pi\)
0.690476 + 0.723355i \(0.257401\pi\)
\(620\) 83.3296 3.34660
\(621\) 8.48752 0.340592
\(622\) −58.3120 −2.33810
\(623\) 0 0
\(624\) 9.41854 0.377043
\(625\) 6.11122 0.244449
\(626\) 61.1572 2.44433
\(627\) 1.79872 0.0718340
\(628\) 11.8324 0.472164
\(629\) 38.3636 1.52966
\(630\) 0 0
\(631\) −19.9149 −0.792799 −0.396399 0.918078i \(-0.629740\pi\)
−0.396399 + 0.918078i \(0.629740\pi\)
\(632\) 1.81246 0.0720958
\(633\) −10.1756 −0.404442
\(634\) 27.6000 1.09613
\(635\) 56.5940 2.24586
\(636\) −7.26973 −0.288264
\(637\) 0 0
\(638\) 1.94850 0.0771420
\(639\) 3.23226 0.127866
\(640\) 10.1534 0.401350
\(641\) 24.3992 0.963712 0.481856 0.876250i \(-0.339963\pi\)
0.481856 + 0.876250i \(0.339963\pi\)
\(642\) −12.7390 −0.502767
\(643\) 42.8135 1.68840 0.844200 0.536028i \(-0.180076\pi\)
0.844200 + 0.536028i \(0.180076\pi\)
\(644\) 0 0
\(645\) 9.58938 0.377582
\(646\) 74.5542 2.93329
\(647\) 9.68055 0.380582 0.190291 0.981728i \(-0.439057\pi\)
0.190291 + 0.981728i \(0.439057\pi\)
\(648\) −0.345232 −0.0135620
\(649\) 1.86354 0.0731505
\(650\) 45.5860 1.78803
\(651\) 0 0
\(652\) 27.4679 1.07573
\(653\) −35.2294 −1.37863 −0.689317 0.724459i \(-0.742089\pi\)
−0.689317 + 0.724459i \(0.742089\pi\)
\(654\) −9.05967 −0.354261
\(655\) −63.3572 −2.47557
\(656\) −3.63325 −0.141855
\(657\) 6.63277 0.258769
\(658\) 0 0
\(659\) 12.3702 0.481875 0.240937 0.970541i \(-0.422545\pi\)
0.240937 + 0.970541i \(0.422545\pi\)
\(660\) 1.85840 0.0723382
\(661\) 43.0998 1.67639 0.838193 0.545373i \(-0.183612\pi\)
0.838193 + 0.545373i \(0.183612\pi\)
\(662\) 0.973526 0.0378372
\(663\) 12.2200 0.474587
\(664\) 0.866525 0.0336277
\(665\) 0 0
\(666\) 16.6171 0.643898
\(667\) −34.8791 −1.35052
\(668\) 24.8147 0.960109
\(669\) −18.3685 −0.710166
\(670\) −49.7624 −1.92249
\(671\) −3.04827 −0.117677
\(672\) 0 0
\(673\) −41.8091 −1.61162 −0.805811 0.592173i \(-0.798270\pi\)
−0.805811 + 0.592173i \(0.798270\pi\)
\(674\) 42.5141 1.63758
\(675\) 8.61238 0.331491
\(676\) −13.6216 −0.523908
\(677\) 14.7030 0.565081 0.282541 0.959255i \(-0.408823\pi\)
0.282541 + 0.959255i \(0.408823\pi\)
\(678\) −39.9898 −1.53580
\(679\) 0 0
\(680\) 6.00431 0.230255
\(681\) −16.6244 −0.637049
\(682\) −4.93712 −0.189052
\(683\) 25.6649 0.982040 0.491020 0.871148i \(-0.336624\pi\)
0.491020 + 0.871148i \(0.336624\pi\)
\(684\) 16.8013 0.642413
\(685\) 33.2986 1.27228
\(686\) 0 0
\(687\) 15.2296 0.581045
\(688\) −9.44320 −0.360019
\(689\) 8.68822 0.330995
\(690\) −63.9393 −2.43413
\(691\) −20.9970 −0.798763 −0.399381 0.916785i \(-0.630775\pi\)
−0.399381 + 0.916785i \(0.630775\pi\)
\(692\) 26.5846 1.01059
\(693\) 0 0
\(694\) −18.6168 −0.706684
\(695\) −40.8917 −1.55111
\(696\) 1.41872 0.0537763
\(697\) −4.71395 −0.178554
\(698\) −21.4018 −0.810070
\(699\) 14.7310 0.557176
\(700\) 0 0
\(701\) 12.6745 0.478709 0.239355 0.970932i \(-0.423064\pi\)
0.239355 + 0.970932i \(0.423064\pi\)
\(702\) 5.29308 0.199774
\(703\) −63.0378 −2.37751
\(704\) −2.15746 −0.0813122
\(705\) −12.5931 −0.474285
\(706\) 8.84974 0.333064
\(707\) 0 0
\(708\) 17.4068 0.654187
\(709\) 2.37978 0.0893745 0.0446873 0.999001i \(-0.485771\pi\)
0.0446873 + 0.999001i \(0.485771\pi\)
\(710\) −24.3497 −0.913829
\(711\) −5.24998 −0.196890
\(712\) 4.58241 0.171733
\(713\) 88.3766 3.30973
\(714\) 0 0
\(715\) −2.22102 −0.0830613
\(716\) −13.6604 −0.510513
\(717\) 12.3660 0.461816
\(718\) −3.34094 −0.124683
\(719\) 13.3645 0.498410 0.249205 0.968451i \(-0.419831\pi\)
0.249205 + 0.968451i \(0.419831\pi\)
\(720\) −13.4049 −0.499570
\(721\) 0 0
\(722\) −83.7102 −3.11537
\(723\) −10.7234 −0.398807
\(724\) −40.9410 −1.52156
\(725\) −35.3922 −1.31443
\(726\) 22.3500 0.829488
\(727\) −3.33356 −0.123635 −0.0618175 0.998087i \(-0.519690\pi\)
−0.0618175 + 0.998087i \(0.519690\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −49.9668 −1.84936
\(731\) −12.2520 −0.453158
\(732\) −28.4729 −1.05239
\(733\) 40.5226 1.49674 0.748368 0.663284i \(-0.230838\pi\)
0.748368 + 0.663284i \(0.230838\pi\)
\(734\) 40.2003 1.48382
\(735\) 0 0
\(736\) 68.8249 2.53692
\(737\) 1.53395 0.0565037
\(738\) −2.04183 −0.0751609
\(739\) 0.959701 0.0353032 0.0176516 0.999844i \(-0.494381\pi\)
0.0176516 + 0.999844i \(0.494381\pi\)
\(740\) −65.1293 −2.39420
\(741\) −20.0796 −0.737642
\(742\) 0 0
\(743\) −12.4405 −0.456399 −0.228200 0.973614i \(-0.573284\pi\)
−0.228200 + 0.973614i \(0.573284\pi\)
\(744\) −3.59474 −0.131790
\(745\) 37.6889 1.38082
\(746\) 3.96059 0.145007
\(747\) −2.50998 −0.0918354
\(748\) −2.37442 −0.0868174
\(749\) 0 0
\(750\) −27.2133 −0.993689
\(751\) −46.6636 −1.70278 −0.851390 0.524534i \(-0.824240\pi\)
−0.851390 + 0.524534i \(0.824240\pi\)
\(752\) 12.4012 0.452224
\(753\) 10.5518 0.384531
\(754\) −21.7517 −0.792149
\(755\) −21.0928 −0.767646
\(756\) 0 0
\(757\) −14.4610 −0.525593 −0.262796 0.964851i \(-0.584645\pi\)
−0.262796 + 0.964851i \(0.584645\pi\)
\(758\) 7.09588 0.257734
\(759\) 1.97096 0.0715413
\(760\) −9.86609 −0.357881
\(761\) 12.7440 0.461971 0.230985 0.972957i \(-0.425805\pi\)
0.230985 + 0.972957i \(0.425805\pi\)
\(762\) −31.3201 −1.13461
\(763\) 0 0
\(764\) 17.3273 0.626880
\(765\) −17.3921 −0.628813
\(766\) −20.4345 −0.738330
\(767\) −20.8032 −0.751161
\(768\) 12.9622 0.467732
\(769\) −13.1820 −0.475354 −0.237677 0.971344i \(-0.576386\pi\)
−0.237677 + 0.971344i \(0.576386\pi\)
\(770\) 0 0
\(771\) 26.8542 0.967132
\(772\) −18.1452 −0.653060
\(773\) −7.05456 −0.253735 −0.126867 0.991920i \(-0.540492\pi\)
−0.126867 + 0.991920i \(0.540492\pi\)
\(774\) −5.30693 −0.190754
\(775\) 89.6768 3.22128
\(776\) −2.72980 −0.0979940
\(777\) 0 0
\(778\) −44.4235 −1.59266
\(779\) 7.74581 0.277522
\(780\) −20.7458 −0.742819
\(781\) 0.750592 0.0268583
\(782\) 81.6932 2.92134
\(783\) −4.10946 −0.146860
\(784\) 0 0
\(785\) 20.1263 0.718338
\(786\) 35.0630 1.25065
\(787\) 27.9275 0.995507 0.497754 0.867318i \(-0.334158\pi\)
0.497754 + 0.867318i \(0.334158\pi\)
\(788\) −43.8036 −1.56044
\(789\) 22.8337 0.812901
\(790\) 39.5498 1.40712
\(791\) 0 0
\(792\) −0.0801693 −0.00284869
\(793\) 34.0286 1.20839
\(794\) 48.2349 1.71179
\(795\) −12.3655 −0.438558
\(796\) −5.26725 −0.186693
\(797\) 35.5823 1.26039 0.630196 0.776436i \(-0.282975\pi\)
0.630196 + 0.776436i \(0.282975\pi\)
\(798\) 0 0
\(799\) 16.0898 0.569218
\(800\) 69.8374 2.46913
\(801\) −13.2734 −0.468993
\(802\) 7.49726 0.264738
\(803\) 1.54025 0.0543543
\(804\) 14.3281 0.505314
\(805\) 0 0
\(806\) 55.1144 1.94132
\(807\) 26.4506 0.931105
\(808\) −3.74675 −0.131810
\(809\) −35.9909 −1.26537 −0.632686 0.774408i \(-0.718048\pi\)
−0.632686 + 0.774408i \(0.718048\pi\)
\(810\) −7.53333 −0.264694
\(811\) 26.9511 0.946380 0.473190 0.880960i \(-0.343102\pi\)
0.473190 + 0.880960i \(0.343102\pi\)
\(812\) 0 0
\(813\) −8.75300 −0.306981
\(814\) 3.85879 0.135251
\(815\) 46.7216 1.63659
\(816\) 17.1270 0.599564
\(817\) 20.1322 0.704335
\(818\) 38.0199 1.32934
\(819\) 0 0
\(820\) 8.00281 0.279470
\(821\) 15.8769 0.554109 0.277054 0.960854i \(-0.410642\pi\)
0.277054 + 0.960854i \(0.410642\pi\)
\(822\) −18.4280 −0.642752
\(823\) 27.5922 0.961803 0.480902 0.876775i \(-0.340309\pi\)
0.480902 + 0.876775i \(0.340309\pi\)
\(824\) −1.82520 −0.0635837
\(825\) 1.99996 0.0696295
\(826\) 0 0
\(827\) −25.0669 −0.871661 −0.435831 0.900029i \(-0.643545\pi\)
−0.435831 + 0.900029i \(0.643545\pi\)
\(828\) 18.4101 0.639795
\(829\) 41.4853 1.44084 0.720422 0.693536i \(-0.243948\pi\)
0.720422 + 0.693536i \(0.243948\pi\)
\(830\) 18.9085 0.656324
\(831\) 6.44745 0.223659
\(832\) 24.0842 0.834971
\(833\) 0 0
\(834\) 22.6302 0.783619
\(835\) 42.2085 1.46069
\(836\) 3.90157 0.134939
\(837\) 10.4125 0.359910
\(838\) −41.6269 −1.43798
\(839\) 3.49825 0.120773 0.0603865 0.998175i \(-0.480767\pi\)
0.0603865 + 0.998175i \(0.480767\pi\)
\(840\) 0 0
\(841\) −12.1124 −0.417668
\(842\) 49.9075 1.71993
\(843\) −21.5896 −0.743587
\(844\) −22.0716 −0.759735
\(845\) −23.1697 −0.797060
\(846\) 6.96926 0.239608
\(847\) 0 0
\(848\) 12.1770 0.418158
\(849\) −0.145666 −0.00499924
\(850\) 82.8950 2.84328
\(851\) −69.0740 −2.36783
\(852\) 7.01104 0.240194
\(853\) −46.0844 −1.57790 −0.788950 0.614458i \(-0.789375\pi\)
−0.788950 + 0.614458i \(0.789375\pi\)
\(854\) 0 0
\(855\) 28.5781 0.977352
\(856\) −2.15390 −0.0736188
\(857\) 48.0142 1.64013 0.820067 0.572267i \(-0.193936\pi\)
0.820067 + 0.572267i \(0.193936\pi\)
\(858\) 1.22915 0.0419625
\(859\) 20.2044 0.689365 0.344682 0.938719i \(-0.387987\pi\)
0.344682 + 0.938719i \(0.387987\pi\)
\(860\) 20.8001 0.709279
\(861\) 0 0
\(862\) −16.0022 −0.545037
\(863\) −15.4157 −0.524755 −0.262377 0.964965i \(-0.584507\pi\)
−0.262377 + 0.964965i \(0.584507\pi\)
\(864\) 8.10896 0.275872
\(865\) 45.2190 1.53749
\(866\) 21.7501 0.739097
\(867\) 5.22132 0.177325
\(868\) 0 0
\(869\) −1.21914 −0.0413566
\(870\) 30.9579 1.04957
\(871\) −17.1239 −0.580220
\(872\) −1.53180 −0.0518734
\(873\) 7.90714 0.267616
\(874\) −134.236 −4.54059
\(875\) 0 0
\(876\) 14.3870 0.486092
\(877\) 14.7504 0.498084 0.249042 0.968493i \(-0.419884\pi\)
0.249042 + 0.968493i \(0.419884\pi\)
\(878\) −50.3314 −1.69860
\(879\) 7.84054 0.264455
\(880\) −3.11286 −0.104935
\(881\) −33.7312 −1.13643 −0.568216 0.822879i \(-0.692366\pi\)
−0.568216 + 0.822879i \(0.692366\pi\)
\(882\) 0 0
\(883\) 16.2628 0.547286 0.273643 0.961831i \(-0.411771\pi\)
0.273643 + 0.961831i \(0.411771\pi\)
\(884\) 26.5063 0.891502
\(885\) 29.6081 0.995264
\(886\) 1.81362 0.0609299
\(887\) −32.9783 −1.10730 −0.553651 0.832749i \(-0.686766\pi\)
−0.553651 + 0.832749i \(0.686766\pi\)
\(888\) 2.80960 0.0942841
\(889\) 0 0
\(890\) 99.9931 3.35178
\(891\) 0.232219 0.00777962
\(892\) −39.8427 −1.33403
\(893\) −26.4383 −0.884724
\(894\) −20.8577 −0.697587
\(895\) −23.2357 −0.776682
\(896\) 0 0
\(897\) −22.0023 −0.734636
\(898\) 40.1724 1.34057
\(899\) −42.7899 −1.42712
\(900\) 18.6809 0.622698
\(901\) 15.7989 0.526339
\(902\) −0.474151 −0.0157875
\(903\) 0 0
\(904\) −6.76145 −0.224883
\(905\) −69.6386 −2.31487
\(906\) 11.6731 0.387814
\(907\) −14.9899 −0.497732 −0.248866 0.968538i \(-0.580058\pi\)
−0.248866 + 0.968538i \(0.580058\pi\)
\(908\) −36.0597 −1.19668
\(909\) 10.8529 0.359967
\(910\) 0 0
\(911\) 37.8616 1.25441 0.627205 0.778854i \(-0.284199\pi\)
0.627205 + 0.778854i \(0.284199\pi\)
\(912\) −28.1425 −0.931891
\(913\) −0.582864 −0.0192900
\(914\) 17.8971 0.591982
\(915\) −48.4309 −1.60108
\(916\) 33.0342 1.09148
\(917\) 0 0
\(918\) 9.62509 0.317675
\(919\) −27.0097 −0.890967 −0.445484 0.895290i \(-0.646968\pi\)
−0.445484 + 0.895290i \(0.646968\pi\)
\(920\) −10.8108 −0.356422
\(921\) 20.8939 0.688476
\(922\) 11.7685 0.387575
\(923\) −8.37905 −0.275800
\(924\) 0 0
\(925\) −70.0902 −2.30455
\(926\) −21.6817 −0.712503
\(927\) 5.28687 0.173644
\(928\) −33.3234 −1.09389
\(929\) 2.99013 0.0981030 0.0490515 0.998796i \(-0.484380\pi\)
0.0490515 + 0.998796i \(0.484380\pi\)
\(930\) −78.4411 −2.57219
\(931\) 0 0
\(932\) 31.9526 1.04664
\(933\) 28.5586 0.934968
\(934\) 64.5848 2.11328
\(935\) −4.03877 −0.132082
\(936\) 0.894950 0.0292524
\(937\) −24.0009 −0.784076 −0.392038 0.919949i \(-0.628230\pi\)
−0.392038 + 0.919949i \(0.628230\pi\)
\(938\) 0 0
\(939\) −29.9521 −0.977450
\(940\) −27.3155 −0.890934
\(941\) 3.18393 0.103793 0.0518966 0.998652i \(-0.483473\pi\)
0.0518966 + 0.998652i \(0.483473\pi\)
\(942\) −11.1382 −0.362904
\(943\) 8.48752 0.276392
\(944\) −29.1567 −0.948970
\(945\) 0 0
\(946\) −1.23237 −0.0400678
\(947\) 15.3342 0.498295 0.249147 0.968466i \(-0.419850\pi\)
0.249147 + 0.968466i \(0.419850\pi\)
\(948\) −11.3876 −0.369853
\(949\) −17.1942 −0.558148
\(950\) −136.210 −4.41925
\(951\) −13.5173 −0.438327
\(952\) 0 0
\(953\) 25.9900 0.841900 0.420950 0.907084i \(-0.361697\pi\)
0.420950 + 0.907084i \(0.361697\pi\)
\(954\) 6.84326 0.221559
\(955\) 29.4729 0.953720
\(956\) 26.8228 0.867511
\(957\) −0.954292 −0.0308479
\(958\) 81.1887 2.62309
\(959\) 0 0
\(960\) −34.2777 −1.10631
\(961\) 77.4210 2.49745
\(962\) −43.0767 −1.38885
\(963\) 6.23899 0.201049
\(964\) −23.2599 −0.749151
\(965\) −30.8641 −0.993549
\(966\) 0 0
\(967\) 5.70119 0.183338 0.0916689 0.995790i \(-0.470780\pi\)
0.0916689 + 0.995790i \(0.470780\pi\)
\(968\) 3.77893 0.121460
\(969\) −36.5134 −1.17298
\(970\) −59.5671 −1.91258
\(971\) −46.4697 −1.49128 −0.745642 0.666347i \(-0.767857\pi\)
−0.745642 + 0.666347i \(0.767857\pi\)
\(972\) 2.16908 0.0695733
\(973\) 0 0
\(974\) 28.3482 0.908336
\(975\) −22.3260 −0.715005
\(976\) 47.6926 1.52660
\(977\) 12.1107 0.387455 0.193728 0.981055i \(-0.437942\pi\)
0.193728 + 0.981055i \(0.437942\pi\)
\(978\) −25.8565 −0.826801
\(979\) −3.08233 −0.0985118
\(980\) 0 0
\(981\) 4.43703 0.141663
\(982\) −41.3983 −1.32107
\(983\) −37.1662 −1.18542 −0.592709 0.805417i \(-0.701942\pi\)
−0.592709 + 0.805417i \(0.701942\pi\)
\(984\) −0.345232 −0.0110056
\(985\) −74.5077 −2.37401
\(986\) −39.5539 −1.25965
\(987\) 0 0
\(988\) −43.5542 −1.38564
\(989\) 22.0599 0.701465
\(990\) −1.74938 −0.0555989
\(991\) −25.6087 −0.813486 −0.406743 0.913543i \(-0.633336\pi\)
−0.406743 + 0.913543i \(0.633336\pi\)
\(992\) 84.4348 2.68081
\(993\) −0.476790 −0.0151305
\(994\) 0 0
\(995\) −8.95932 −0.284030
\(996\) −5.44435 −0.172511
\(997\) −4.04117 −0.127985 −0.0639925 0.997950i \(-0.520383\pi\)
−0.0639925 + 0.997950i \(0.520383\pi\)
\(998\) −19.9480 −0.631443
\(999\) −8.13831 −0.257485
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 \(a_p\))