Properties

Label 8018.2.a.d.1.5
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
CM No

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Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(1\)
Dimension: \(30\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} -2.47683 q^{3} +1.00000 q^{4} -0.567392 q^{5} -2.47683 q^{6} -4.82108 q^{7} +1.00000 q^{8} +3.13468 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -2.47683 q^{3} +1.00000 q^{4} -0.567392 q^{5} -2.47683 q^{6} -4.82108 q^{7} +1.00000 q^{8} +3.13468 q^{9} -0.567392 q^{10} +1.83375 q^{11} -2.47683 q^{12} -5.69770 q^{13} -4.82108 q^{14} +1.40533 q^{15} +1.00000 q^{16} +4.15123 q^{17} +3.13468 q^{18} +1.00000 q^{19} -0.567392 q^{20} +11.9410 q^{21} +1.83375 q^{22} +3.32654 q^{23} -2.47683 q^{24} -4.67807 q^{25} -5.69770 q^{26} -0.333577 q^{27} -4.82108 q^{28} +0.666868 q^{29} +1.40533 q^{30} +1.19796 q^{31} +1.00000 q^{32} -4.54189 q^{33} +4.15123 q^{34} +2.73544 q^{35} +3.13468 q^{36} -1.66156 q^{37} +1.00000 q^{38} +14.1122 q^{39} -0.567392 q^{40} +12.1142 q^{41} +11.9410 q^{42} -0.920599 q^{43} +1.83375 q^{44} -1.77859 q^{45} +3.32654 q^{46} +5.33894 q^{47} -2.47683 q^{48} +16.2428 q^{49} -4.67807 q^{50} -10.2819 q^{51} -5.69770 q^{52} -6.95873 q^{53} -0.333577 q^{54} -1.04046 q^{55} -4.82108 q^{56} -2.47683 q^{57} +0.666868 q^{58} -9.75807 q^{59} +1.40533 q^{60} +3.51810 q^{61} +1.19796 q^{62} -15.1125 q^{63} +1.00000 q^{64} +3.23283 q^{65} -4.54189 q^{66} -10.6946 q^{67} +4.15123 q^{68} -8.23928 q^{69} +2.73544 q^{70} +13.2989 q^{71} +3.13468 q^{72} -0.562291 q^{73} -1.66156 q^{74} +11.5868 q^{75} +1.00000 q^{76} -8.84067 q^{77} +14.1122 q^{78} +7.21166 q^{79} -0.567392 q^{80} -8.57782 q^{81} +12.1142 q^{82} +13.7036 q^{83} +11.9410 q^{84} -2.35538 q^{85} -0.920599 q^{86} -1.65172 q^{87} +1.83375 q^{88} -8.31843 q^{89} -1.77859 q^{90} +27.4691 q^{91} +3.32654 q^{92} -2.96713 q^{93} +5.33894 q^{94} -0.567392 q^{95} -2.47683 q^{96} +6.85317 q^{97} +16.2428 q^{98} +5.74823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} + O(q^{10}) \) \( 30q + 30q^{2} - 10q^{3} + 30q^{4} - 12q^{5} - 10q^{6} - 15q^{7} + 30q^{8} + 10q^{9} - 12q^{10} - 17q^{11} - 10q^{12} - 19q^{13} - 15q^{14} - 8q^{15} + 30q^{16} - 18q^{17} + 10q^{18} + 30q^{19} - 12q^{20} - 14q^{21} - 17q^{22} - 15q^{23} - 10q^{24} - 4q^{25} - 19q^{26} - 37q^{27} - 15q^{28} - 37q^{29} - 8q^{30} - 11q^{31} + 30q^{32} + 6q^{33} - 18q^{34} - 4q^{35} + 10q^{36} - 46q^{37} + 30q^{38} - 12q^{40} - 28q^{41} - 14q^{42} - 61q^{43} - 17q^{44} - 14q^{45} - 15q^{46} - 4q^{47} - 10q^{48} - q^{49} - 4q^{50} - 8q^{51} - 19q^{52} - 19q^{53} - 37q^{54} - 17q^{55} - 15q^{56} - 10q^{57} - 37q^{58} - 6q^{59} - 8q^{60} - 32q^{61} - 11q^{62} - 24q^{63} + 30q^{64} - 24q^{65} + 6q^{66} - 44q^{67} - 18q^{68} - 2q^{69} - 4q^{70} + 10q^{71} + 10q^{72} - 58q^{73} - 46q^{74} - 42q^{75} + 30q^{76} - 32q^{77} - 42q^{79} - 12q^{80} - 38q^{81} - 28q^{82} - 25q^{83} - 14q^{84} - 48q^{85} - 61q^{86} - 15q^{87} - 17q^{88} - 39q^{89} - 14q^{90} - 21q^{91} - 15q^{92} - 45q^{93} - 4q^{94} - 12q^{95} - 10q^{96} - 33q^{97} - q^{98} - 38q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −2.47683 −1.43000 −0.714999 0.699126i \(-0.753573\pi\)
−0.714999 + 0.699126i \(0.753573\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.567392 −0.253746 −0.126873 0.991919i \(-0.540494\pi\)
−0.126873 + 0.991919i \(0.540494\pi\)
\(6\) −2.47683 −1.01116
\(7\) −4.82108 −1.82220 −0.911099 0.412188i \(-0.864765\pi\)
−0.911099 + 0.412188i \(0.864765\pi\)
\(8\) 1.00000 0.353553
\(9\) 3.13468 1.04489
\(10\) −0.567392 −0.179425
\(11\) 1.83375 0.552897 0.276449 0.961029i \(-0.410842\pi\)
0.276449 + 0.961029i \(0.410842\pi\)
\(12\) −2.47683 −0.714999
\(13\) −5.69770 −1.58026 −0.790128 0.612942i \(-0.789986\pi\)
−0.790128 + 0.612942i \(0.789986\pi\)
\(14\) −4.82108 −1.28849
\(15\) 1.40533 0.362856
\(16\) 1.00000 0.250000
\(17\) 4.15123 1.00682 0.503410 0.864047i \(-0.332078\pi\)
0.503410 + 0.864047i \(0.332078\pi\)
\(18\) 3.13468 0.738851
\(19\) 1.00000 0.229416
\(20\) −0.567392 −0.126873
\(21\) 11.9410 2.60574
\(22\) 1.83375 0.390958
\(23\) 3.32654 0.693632 0.346816 0.937933i \(-0.387263\pi\)
0.346816 + 0.937933i \(0.387263\pi\)
\(24\) −2.47683 −0.505580
\(25\) −4.67807 −0.935613
\(26\) −5.69770 −1.11741
\(27\) −0.333577 −0.0641969
\(28\) −4.82108 −0.911099
\(29\) 0.666868 0.123834 0.0619171 0.998081i \(-0.480279\pi\)
0.0619171 + 0.998081i \(0.480279\pi\)
\(30\) 1.40533 0.256578
\(31\) 1.19796 0.215159 0.107580 0.994196i \(-0.465690\pi\)
0.107580 + 0.994196i \(0.465690\pi\)
\(32\) 1.00000 0.176777
\(33\) −4.54189 −0.790642
\(34\) 4.15123 0.711930
\(35\) 2.73544 0.462375
\(36\) 3.13468 0.522447
\(37\) −1.66156 −0.273159 −0.136579 0.990629i \(-0.543611\pi\)
−0.136579 + 0.990629i \(0.543611\pi\)
\(38\) 1.00000 0.162221
\(39\) 14.1122 2.25976
\(40\) −0.567392 −0.0897126
\(41\) 12.1142 1.89193 0.945963 0.324274i \(-0.105120\pi\)
0.945963 + 0.324274i \(0.105120\pi\)
\(42\) 11.9410 1.84254
\(43\) −0.920599 −0.140390 −0.0701950 0.997533i \(-0.522362\pi\)
−0.0701950 + 0.997533i \(0.522362\pi\)
\(44\) 1.83375 0.276449
\(45\) −1.77859 −0.265137
\(46\) 3.32654 0.490472
\(47\) 5.33894 0.778764 0.389382 0.921076i \(-0.372689\pi\)
0.389382 + 0.921076i \(0.372689\pi\)
\(48\) −2.47683 −0.357499
\(49\) 16.2428 2.32040
\(50\) −4.67807 −0.661578
\(51\) −10.2819 −1.43975
\(52\) −5.69770 −0.790128
\(53\) −6.95873 −0.955856 −0.477928 0.878399i \(-0.658612\pi\)
−0.477928 + 0.878399i \(0.658612\pi\)
\(54\) −0.333577 −0.0453941
\(55\) −1.04046 −0.140295
\(56\) −4.82108 −0.644244
\(57\) −2.47683 −0.328064
\(58\) 0.666868 0.0875640
\(59\) −9.75807 −1.27039 −0.635196 0.772351i \(-0.719081\pi\)
−0.635196 + 0.772351i \(0.719081\pi\)
\(60\) 1.40533 0.181428
\(61\) 3.51810 0.450447 0.225223 0.974307i \(-0.427689\pi\)
0.225223 + 0.974307i \(0.427689\pi\)
\(62\) 1.19796 0.152141
\(63\) −15.1125 −1.90400
\(64\) 1.00000 0.125000
\(65\) 3.23283 0.400983
\(66\) −4.54189 −0.559068
\(67\) −10.6946 −1.30655 −0.653274 0.757122i \(-0.726605\pi\)
−0.653274 + 0.757122i \(0.726605\pi\)
\(68\) 4.15123 0.503410
\(69\) −8.23928 −0.991892
\(70\) 2.73544 0.326948
\(71\) 13.2989 1.57828 0.789142 0.614211i \(-0.210525\pi\)
0.789142 + 0.614211i \(0.210525\pi\)
\(72\) 3.13468 0.369425
\(73\) −0.562291 −0.0658111 −0.0329056 0.999458i \(-0.510476\pi\)
−0.0329056 + 0.999458i \(0.510476\pi\)
\(74\) −1.66156 −0.193152
\(75\) 11.5868 1.33792
\(76\) 1.00000 0.114708
\(77\) −8.84067 −1.00749
\(78\) 14.1122 1.59789
\(79\) 7.21166 0.811375 0.405688 0.914012i \(-0.367032\pi\)
0.405688 + 0.914012i \(0.367032\pi\)
\(80\) −0.567392 −0.0634364
\(81\) −8.57782 −0.953092
\(82\) 12.1142 1.33779
\(83\) 13.7036 1.50416 0.752081 0.659071i \(-0.229050\pi\)
0.752081 + 0.659071i \(0.229050\pi\)
\(84\) 11.9410 1.30287
\(85\) −2.35538 −0.255476
\(86\) −0.920599 −0.0992707
\(87\) −1.65172 −0.177083
\(88\) 1.83375 0.195479
\(89\) −8.31843 −0.881752 −0.440876 0.897568i \(-0.645332\pi\)
−0.440876 + 0.897568i \(0.645332\pi\)
\(90\) −1.77859 −0.187480
\(91\) 27.4691 2.87954
\(92\) 3.32654 0.346816
\(93\) −2.96713 −0.307677
\(94\) 5.33894 0.550669
\(95\) −0.567392 −0.0582132
\(96\) −2.47683 −0.252790
\(97\) 6.85317 0.695834 0.347917 0.937525i \(-0.386889\pi\)
0.347917 + 0.937525i \(0.386889\pi\)
\(98\) 16.2428 1.64077
\(99\) 5.74823 0.577719
\(100\) −4.67807 −0.467807
\(101\) −6.59279 −0.656007 −0.328004 0.944676i \(-0.606376\pi\)
−0.328004 + 0.944676i \(0.606376\pi\)
\(102\) −10.2819 −1.01806
\(103\) 12.3679 1.21864 0.609321 0.792924i \(-0.291442\pi\)
0.609321 + 0.792924i \(0.291442\pi\)
\(104\) −5.69770 −0.558705
\(105\) −6.77523 −0.661194
\(106\) −6.95873 −0.675892
\(107\) −5.73409 −0.554335 −0.277168 0.960822i \(-0.589396\pi\)
−0.277168 + 0.960822i \(0.589396\pi\)
\(108\) −0.333577 −0.0320985
\(109\) 7.07403 0.677569 0.338785 0.940864i \(-0.389984\pi\)
0.338785 + 0.940864i \(0.389984\pi\)
\(110\) −1.04046 −0.0992037
\(111\) 4.11540 0.390616
\(112\) −4.82108 −0.455549
\(113\) 2.29029 0.215452 0.107726 0.994181i \(-0.465643\pi\)
0.107726 + 0.994181i \(0.465643\pi\)
\(114\) −2.47683 −0.231976
\(115\) −1.88746 −0.176006
\(116\) 0.666868 0.0619171
\(117\) −17.8604 −1.65120
\(118\) −9.75807 −0.898303
\(119\) −20.0134 −1.83463
\(120\) 1.40533 0.128289
\(121\) −7.63735 −0.694304
\(122\) 3.51810 0.318514
\(123\) −30.0049 −2.70545
\(124\) 1.19796 0.107580
\(125\) 5.49126 0.491153
\(126\) −15.1125 −1.34633
\(127\) 4.06565 0.360768 0.180384 0.983596i \(-0.442266\pi\)
0.180384 + 0.983596i \(0.442266\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.28017 0.200757
\(130\) 3.23283 0.283538
\(131\) −22.0302 −1.92479 −0.962395 0.271655i \(-0.912429\pi\)
−0.962395 + 0.271655i \(0.912429\pi\)
\(132\) −4.54189 −0.395321
\(133\) −4.82108 −0.418041
\(134\) −10.6946 −0.923868
\(135\) 0.189269 0.0162897
\(136\) 4.15123 0.355965
\(137\) −21.1806 −1.80958 −0.904791 0.425857i \(-0.859973\pi\)
−0.904791 + 0.425857i \(0.859973\pi\)
\(138\) −8.23928 −0.701374
\(139\) 9.81593 0.832576 0.416288 0.909233i \(-0.363331\pi\)
0.416288 + 0.909233i \(0.363331\pi\)
\(140\) 2.73544 0.231187
\(141\) −13.2236 −1.11363
\(142\) 13.2989 1.11602
\(143\) −10.4482 −0.873720
\(144\) 3.13468 0.261223
\(145\) −0.378376 −0.0314224
\(146\) −0.562291 −0.0465355
\(147\) −40.2307 −3.31817
\(148\) −1.66156 −0.136579
\(149\) −9.83654 −0.805840 −0.402920 0.915235i \(-0.632005\pi\)
−0.402920 + 0.915235i \(0.632005\pi\)
\(150\) 11.5868 0.946056
\(151\) 0.426888 0.0347397 0.0173698 0.999849i \(-0.494471\pi\)
0.0173698 + 0.999849i \(0.494471\pi\)
\(152\) 1.00000 0.0811107
\(153\) 13.0128 1.05202
\(154\) −8.84067 −0.712402
\(155\) −0.679711 −0.0545957
\(156\) 14.1122 1.12988
\(157\) −8.18977 −0.653614 −0.326807 0.945091i \(-0.605973\pi\)
−0.326807 + 0.945091i \(0.605973\pi\)
\(158\) 7.21166 0.573729
\(159\) 17.2356 1.36687
\(160\) −0.567392 −0.0448563
\(161\) −16.0375 −1.26393
\(162\) −8.57782 −0.673938
\(163\) −20.4062 −1.59833 −0.799167 0.601109i \(-0.794726\pi\)
−0.799167 + 0.601109i \(0.794726\pi\)
\(164\) 12.1142 0.945963
\(165\) 2.57703 0.200622
\(166\) 13.7036 1.06360
\(167\) −2.47910 −0.191839 −0.0959194 0.995389i \(-0.530579\pi\)
−0.0959194 + 0.995389i \(0.530579\pi\)
\(168\) 11.9410 0.921268
\(169\) 19.4637 1.49721
\(170\) −2.35538 −0.180649
\(171\) 3.13468 0.239715
\(172\) −0.920599 −0.0701950
\(173\) −9.31587 −0.708273 −0.354136 0.935194i \(-0.615225\pi\)
−0.354136 + 0.935194i \(0.615225\pi\)
\(174\) −1.65172 −0.125216
\(175\) 22.5533 1.70487
\(176\) 1.83375 0.138224
\(177\) 24.1691 1.81666
\(178\) −8.31843 −0.623493
\(179\) 9.64188 0.720668 0.360334 0.932823i \(-0.382663\pi\)
0.360334 + 0.932823i \(0.382663\pi\)
\(180\) −1.77859 −0.132568
\(181\) −9.03298 −0.671416 −0.335708 0.941966i \(-0.608976\pi\)
−0.335708 + 0.941966i \(0.608976\pi\)
\(182\) 27.4691 2.03614
\(183\) −8.71373 −0.644138
\(184\) 3.32654 0.245236
\(185\) 0.942755 0.0693128
\(186\) −2.96713 −0.217561
\(187\) 7.61233 0.556669
\(188\) 5.33894 0.389382
\(189\) 1.60820 0.116979
\(190\) −0.567392 −0.0411630
\(191\) 20.8399 1.50792 0.753962 0.656918i \(-0.228140\pi\)
0.753962 + 0.656918i \(0.228140\pi\)
\(192\) −2.47683 −0.178750
\(193\) 1.05471 0.0759197 0.0379599 0.999279i \(-0.487914\pi\)
0.0379599 + 0.999279i \(0.487914\pi\)
\(194\) 6.85317 0.492029
\(195\) −8.00716 −0.573405
\(196\) 16.2428 1.16020
\(197\) −13.1104 −0.934074 −0.467037 0.884238i \(-0.654679\pi\)
−0.467037 + 0.884238i \(0.654679\pi\)
\(198\) 5.74823 0.408509
\(199\) 2.27122 0.161002 0.0805012 0.996755i \(-0.474348\pi\)
0.0805012 + 0.996755i \(0.474348\pi\)
\(200\) −4.67807 −0.330789
\(201\) 26.4886 1.86836
\(202\) −6.59279 −0.463867
\(203\) −3.21502 −0.225650
\(204\) −10.2819 −0.719876
\(205\) −6.87353 −0.480068
\(206\) 12.3679 0.861710
\(207\) 10.4276 0.724771
\(208\) −5.69770 −0.395064
\(209\) 1.83375 0.126843
\(210\) −6.77523 −0.467535
\(211\) −1.00000 −0.0688428
\(212\) −6.95873 −0.477928
\(213\) −32.9390 −2.25694
\(214\) −5.73409 −0.391974
\(215\) 0.522341 0.0356233
\(216\) −0.333577 −0.0226970
\(217\) −5.77544 −0.392063
\(218\) 7.07403 0.479114
\(219\) 1.39270 0.0941098
\(220\) −1.04046 −0.0701476
\(221\) −23.6524 −1.59103
\(222\) 4.11540 0.276207
\(223\) 17.4547 1.16885 0.584426 0.811447i \(-0.301320\pi\)
0.584426 + 0.811447i \(0.301320\pi\)
\(224\) −4.82108 −0.322122
\(225\) −14.6642 −0.977616
\(226\) 2.29029 0.152348
\(227\) −18.6335 −1.23675 −0.618374 0.785884i \(-0.712208\pi\)
−0.618374 + 0.785884i \(0.712208\pi\)
\(228\) −2.47683 −0.164032
\(229\) 9.79335 0.647162 0.323581 0.946200i \(-0.395113\pi\)
0.323581 + 0.946200i \(0.395113\pi\)
\(230\) −1.88746 −0.124455
\(231\) 21.8968 1.44071
\(232\) 0.666868 0.0437820
\(233\) −17.5426 −1.14926 −0.574628 0.818415i \(-0.694853\pi\)
−0.574628 + 0.818415i \(0.694853\pi\)
\(234\) −17.8604 −1.16757
\(235\) −3.02927 −0.197608
\(236\) −9.75807 −0.635196
\(237\) −17.8620 −1.16026
\(238\) −20.0134 −1.29728
\(239\) 4.72853 0.305863 0.152932 0.988237i \(-0.451129\pi\)
0.152932 + 0.988237i \(0.451129\pi\)
\(240\) 1.40533 0.0907139
\(241\) −3.70715 −0.238799 −0.119399 0.992846i \(-0.538097\pi\)
−0.119399 + 0.992846i \(0.538097\pi\)
\(242\) −7.63735 −0.490947
\(243\) 22.2465 1.42712
\(244\) 3.51810 0.225223
\(245\) −9.21605 −0.588792
\(246\) −30.0049 −1.91304
\(247\) −5.69770 −0.362536
\(248\) 1.19796 0.0760703
\(249\) −33.9414 −2.15095
\(250\) 5.49126 0.347298
\(251\) −16.9366 −1.06903 −0.534515 0.845159i \(-0.679506\pi\)
−0.534515 + 0.845159i \(0.679506\pi\)
\(252\) −15.1125 −0.952001
\(253\) 6.10006 0.383507
\(254\) 4.06565 0.255102
\(255\) 5.83386 0.365330
\(256\) 1.00000 0.0625000
\(257\) −6.96918 −0.434726 −0.217363 0.976091i \(-0.569745\pi\)
−0.217363 + 0.976091i \(0.569745\pi\)
\(258\) 2.28017 0.141957
\(259\) 8.01051 0.497749
\(260\) 3.23283 0.200492
\(261\) 2.09042 0.129393
\(262\) −22.0302 −1.36103
\(263\) 6.22817 0.384045 0.192023 0.981391i \(-0.438495\pi\)
0.192023 + 0.981391i \(0.438495\pi\)
\(264\) −4.54189 −0.279534
\(265\) 3.94833 0.242544
\(266\) −4.82108 −0.295599
\(267\) 20.6033 1.26090
\(268\) −10.6946 −0.653274
\(269\) 20.3744 1.24225 0.621124 0.783712i \(-0.286676\pi\)
0.621124 + 0.783712i \(0.286676\pi\)
\(270\) 0.189269 0.0115185
\(271\) −16.5363 −1.00451 −0.502254 0.864720i \(-0.667496\pi\)
−0.502254 + 0.864720i \(0.667496\pi\)
\(272\) 4.15123 0.251705
\(273\) −68.0361 −4.11773
\(274\) −21.1806 −1.27957
\(275\) −8.57842 −0.517298
\(276\) −8.23928 −0.495946
\(277\) 17.2738 1.03788 0.518940 0.854810i \(-0.326327\pi\)
0.518940 + 0.854810i \(0.326327\pi\)
\(278\) 9.81593 0.588720
\(279\) 3.75521 0.224818
\(280\) 2.73544 0.163474
\(281\) −2.67698 −0.159695 −0.0798476 0.996807i \(-0.525443\pi\)
−0.0798476 + 0.996807i \(0.525443\pi\)
\(282\) −13.2236 −0.787456
\(283\) 11.6554 0.692840 0.346420 0.938079i \(-0.387397\pi\)
0.346420 + 0.938079i \(0.387397\pi\)
\(284\) 13.2989 0.789142
\(285\) 1.40533 0.0832448
\(286\) −10.4482 −0.617813
\(287\) −58.4037 −3.44746
\(288\) 3.13468 0.184713
\(289\) 0.232697 0.0136881
\(290\) −0.378376 −0.0222190
\(291\) −16.9741 −0.995041
\(292\) −0.562291 −0.0329056
\(293\) 20.0736 1.17271 0.586357 0.810053i \(-0.300562\pi\)
0.586357 + 0.810053i \(0.300562\pi\)
\(294\) −40.2307 −2.34630
\(295\) 5.53665 0.322356
\(296\) −1.66156 −0.0965761
\(297\) −0.611698 −0.0354943
\(298\) −9.83654 −0.569815
\(299\) −18.9536 −1.09612
\(300\) 11.5868 0.668962
\(301\) 4.43828 0.255818
\(302\) 0.426888 0.0245647
\(303\) 16.3292 0.938089
\(304\) 1.00000 0.0573539
\(305\) −1.99614 −0.114299
\(306\) 13.0128 0.743890
\(307\) −4.90950 −0.280200 −0.140100 0.990137i \(-0.544742\pi\)
−0.140100 + 0.990137i \(0.544742\pi\)
\(308\) −8.84067 −0.503744
\(309\) −30.6331 −1.74266
\(310\) −0.679711 −0.0386050
\(311\) −27.4826 −1.55840 −0.779199 0.626777i \(-0.784374\pi\)
−0.779199 + 0.626777i \(0.784374\pi\)
\(312\) 14.1122 0.798947
\(313\) −13.3112 −0.752395 −0.376197 0.926540i \(-0.622769\pi\)
−0.376197 + 0.926540i \(0.622769\pi\)
\(314\) −8.18977 −0.462175
\(315\) 8.57474 0.483132
\(316\) 7.21166 0.405688
\(317\) −13.3881 −0.751952 −0.375976 0.926629i \(-0.622693\pi\)
−0.375976 + 0.926629i \(0.622693\pi\)
\(318\) 17.2356 0.966524
\(319\) 1.22287 0.0684676
\(320\) −0.567392 −0.0317182
\(321\) 14.2024 0.792698
\(322\) −16.0375 −0.893737
\(323\) 4.15123 0.230981
\(324\) −8.57782 −0.476546
\(325\) 26.6542 1.47851
\(326\) −20.4062 −1.13019
\(327\) −17.5212 −0.968923
\(328\) 12.1142 0.668897
\(329\) −25.7395 −1.41906
\(330\) 2.57703 0.141861
\(331\) 18.7133 1.02858 0.514288 0.857618i \(-0.328056\pi\)
0.514288 + 0.857618i \(0.328056\pi\)
\(332\) 13.7036 0.752081
\(333\) −5.20845 −0.285421
\(334\) −2.47910 −0.135650
\(335\) 6.06801 0.331531
\(336\) 11.9410 0.651434
\(337\) −26.5988 −1.44893 −0.724464 0.689312i \(-0.757913\pi\)
−0.724464 + 0.689312i \(0.757913\pi\)
\(338\) 19.4637 1.05869
\(339\) −5.67264 −0.308096
\(340\) −2.35538 −0.127738
\(341\) 2.19676 0.118961
\(342\) 3.13468 0.169504
\(343\) −44.5604 −2.40604
\(344\) −0.920599 −0.0496354
\(345\) 4.67490 0.251688
\(346\) −9.31587 −0.500824
\(347\) 11.5652 0.620851 0.310425 0.950598i \(-0.399529\pi\)
0.310425 + 0.950598i \(0.399529\pi\)
\(348\) −1.65172 −0.0885413
\(349\) −14.2528 −0.762934 −0.381467 0.924382i \(-0.624581\pi\)
−0.381467 + 0.924382i \(0.624581\pi\)
\(350\) 22.5533 1.20553
\(351\) 1.90062 0.101448
\(352\) 1.83375 0.0977394
\(353\) 9.49285 0.505253 0.252627 0.967564i \(-0.418706\pi\)
0.252627 + 0.967564i \(0.418706\pi\)
\(354\) 24.1691 1.28457
\(355\) −7.54567 −0.400483
\(356\) −8.31843 −0.440876
\(357\) 49.5698 2.62351
\(358\) 9.64188 0.509589
\(359\) −19.1533 −1.01087 −0.505436 0.862864i \(-0.668668\pi\)
−0.505436 + 0.862864i \(0.668668\pi\)
\(360\) −1.77859 −0.0937401
\(361\) 1.00000 0.0526316
\(362\) −9.03298 −0.474763
\(363\) 18.9164 0.992854
\(364\) 27.4691 1.43977
\(365\) 0.319039 0.0166993
\(366\) −8.71373 −0.455474
\(367\) −9.02112 −0.470899 −0.235449 0.971887i \(-0.575656\pi\)
−0.235449 + 0.971887i \(0.575656\pi\)
\(368\) 3.32654 0.173408
\(369\) 37.9742 1.97686
\(370\) 0.942755 0.0490115
\(371\) 33.5486 1.74176
\(372\) −2.96713 −0.153839
\(373\) −15.6364 −0.809621 −0.404811 0.914401i \(-0.632663\pi\)
−0.404811 + 0.914401i \(0.632663\pi\)
\(374\) 7.61233 0.393624
\(375\) −13.6009 −0.702348
\(376\) 5.33894 0.275335
\(377\) −3.79961 −0.195690
\(378\) 1.60820 0.0827170
\(379\) −15.7259 −0.807786 −0.403893 0.914806i \(-0.632343\pi\)
−0.403893 + 0.914806i \(0.632343\pi\)
\(380\) −0.567392 −0.0291066
\(381\) −10.0699 −0.515898
\(382\) 20.8399 1.06626
\(383\) −1.06145 −0.0542376 −0.0271188 0.999632i \(-0.508633\pi\)
−0.0271188 + 0.999632i \(0.508633\pi\)
\(384\) −2.47683 −0.126395
\(385\) 5.01613 0.255646
\(386\) 1.05471 0.0536834
\(387\) −2.88578 −0.146693
\(388\) 6.85317 0.347917
\(389\) 17.3400 0.879172 0.439586 0.898200i \(-0.355125\pi\)
0.439586 + 0.898200i \(0.355125\pi\)
\(390\) −8.00716 −0.405458
\(391\) 13.8092 0.698363
\(392\) 16.2428 0.820387
\(393\) 54.5651 2.75244
\(394\) −13.1104 −0.660490
\(395\) −4.09184 −0.205883
\(396\) 5.74823 0.288859
\(397\) −20.1357 −1.01058 −0.505291 0.862949i \(-0.668615\pi\)
−0.505291 + 0.862949i \(0.668615\pi\)
\(398\) 2.27122 0.113846
\(399\) 11.9410 0.597797
\(400\) −4.67807 −0.233903
\(401\) −26.6269 −1.32969 −0.664843 0.746983i \(-0.731502\pi\)
−0.664843 + 0.746983i \(0.731502\pi\)
\(402\) 26.4886 1.32113
\(403\) −6.82559 −0.340007
\(404\) −6.59279 −0.328004
\(405\) 4.86699 0.241843
\(406\) −3.21502 −0.159559
\(407\) −3.04689 −0.151029
\(408\) −10.2819 −0.509029
\(409\) −4.92119 −0.243337 −0.121669 0.992571i \(-0.538825\pi\)
−0.121669 + 0.992571i \(0.538825\pi\)
\(410\) −6.87353 −0.339459
\(411\) 52.4607 2.58770
\(412\) 12.3679 0.609321
\(413\) 47.0445 2.31491
\(414\) 10.4276 0.512491
\(415\) −7.77530 −0.381674
\(416\) −5.69770 −0.279353
\(417\) −24.3124 −1.19058
\(418\) 1.83375 0.0896918
\(419\) 25.3212 1.23702 0.618511 0.785776i \(-0.287736\pi\)
0.618511 + 0.785776i \(0.287736\pi\)
\(420\) −6.77523 −0.330597
\(421\) 10.0646 0.490521 0.245260 0.969457i \(-0.421127\pi\)
0.245260 + 0.969457i \(0.421127\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 16.7359 0.813725
\(424\) −6.95873 −0.337946
\(425\) −19.4197 −0.941995
\(426\) −32.9390 −1.59590
\(427\) −16.9611 −0.820803
\(428\) −5.73409 −0.277168
\(429\) 25.8783 1.24942
\(430\) 0.522341 0.0251895
\(431\) 6.56730 0.316336 0.158168 0.987412i \(-0.449441\pi\)
0.158168 + 0.987412i \(0.449441\pi\)
\(432\) −0.333577 −0.0160492
\(433\) −34.5132 −1.65860 −0.829299 0.558805i \(-0.811260\pi\)
−0.829299 + 0.558805i \(0.811260\pi\)
\(434\) −5.77544 −0.277230
\(435\) 0.937171 0.0449339
\(436\) 7.07403 0.338785
\(437\) 3.32654 0.159130
\(438\) 1.39270 0.0665456
\(439\) 8.56863 0.408958 0.204479 0.978871i \(-0.434450\pi\)
0.204479 + 0.978871i \(0.434450\pi\)
\(440\) −1.04046 −0.0496019
\(441\) 50.9160 2.42457
\(442\) −23.6524 −1.12503
\(443\) −16.3904 −0.778732 −0.389366 0.921083i \(-0.627306\pi\)
−0.389366 + 0.921083i \(0.627306\pi\)
\(444\) 4.11540 0.195308
\(445\) 4.71981 0.223741
\(446\) 17.4547 0.826503
\(447\) 24.3634 1.15235
\(448\) −4.82108 −0.227775
\(449\) −0.0363439 −0.00171518 −0.000857588 1.00000i \(-0.500273\pi\)
−0.000857588 1.00000i \(0.500273\pi\)
\(450\) −14.6642 −0.691279
\(451\) 22.2145 1.04604
\(452\) 2.29029 0.107726
\(453\) −1.05733 −0.0496777
\(454\) −18.6335 −0.874513
\(455\) −15.5857 −0.730670
\(456\) −2.47683 −0.115988
\(457\) −2.88094 −0.134765 −0.0673823 0.997727i \(-0.521465\pi\)
−0.0673823 + 0.997727i \(0.521465\pi\)
\(458\) 9.79335 0.457613
\(459\) −1.38475 −0.0646348
\(460\) −1.88746 −0.0880030
\(461\) −20.5742 −0.958238 −0.479119 0.877750i \(-0.659044\pi\)
−0.479119 + 0.877750i \(0.659044\pi\)
\(462\) 21.8968 1.01873
\(463\) 5.76886 0.268102 0.134051 0.990974i \(-0.457201\pi\)
0.134051 + 0.990974i \(0.457201\pi\)
\(464\) 0.666868 0.0309585
\(465\) 1.68353 0.0780717
\(466\) −17.5426 −0.812646
\(467\) −0.843417 −0.0390287 −0.0195143 0.999810i \(-0.506212\pi\)
−0.0195143 + 0.999810i \(0.506212\pi\)
\(468\) −17.8604 −0.825599
\(469\) 51.5593 2.38079
\(470\) −3.02927 −0.139730
\(471\) 20.2846 0.934667
\(472\) −9.75807 −0.449152
\(473\) −1.68815 −0.0776213
\(474\) −17.8620 −0.820431
\(475\) −4.67807 −0.214644
\(476\) −20.0134 −0.917313
\(477\) −21.8134 −0.998767
\(478\) 4.72853 0.216278
\(479\) −18.0326 −0.823931 −0.411965 0.911199i \(-0.635158\pi\)
−0.411965 + 0.911199i \(0.635158\pi\)
\(480\) 1.40533 0.0641444
\(481\) 9.46705 0.431660
\(482\) −3.70715 −0.168856
\(483\) 39.7222 1.80742
\(484\) −7.63735 −0.347152
\(485\) −3.88844 −0.176565
\(486\) 22.2465 1.00912
\(487\) −42.0650 −1.90615 −0.953073 0.302742i \(-0.902098\pi\)
−0.953073 + 0.302742i \(0.902098\pi\)
\(488\) 3.51810 0.159257
\(489\) 50.5426 2.28561
\(490\) −9.21605 −0.416339
\(491\) −14.2502 −0.643101 −0.321551 0.946892i \(-0.604204\pi\)
−0.321551 + 0.946892i \(0.604204\pi\)
\(492\) −30.0049 −1.35272
\(493\) 2.76832 0.124679
\(494\) −5.69770 −0.256351
\(495\) −3.26150 −0.146594
\(496\) 1.19796 0.0537898
\(497\) −64.1149 −2.87595
\(498\) −33.9414 −1.52095
\(499\) 9.56768 0.428308 0.214154 0.976800i \(-0.431301\pi\)
0.214154 + 0.976800i \(0.431301\pi\)
\(500\) 5.49126 0.245577
\(501\) 6.14031 0.274329
\(502\) −16.9366 −0.755919
\(503\) 13.1297 0.585423 0.292711 0.956201i \(-0.405442\pi\)
0.292711 + 0.956201i \(0.405442\pi\)
\(504\) −15.1125 −0.673166
\(505\) 3.74070 0.166459
\(506\) 6.10006 0.271181
\(507\) −48.2083 −2.14101
\(508\) 4.06565 0.180384
\(509\) 42.3360 1.87651 0.938256 0.345942i \(-0.112441\pi\)
0.938256 + 0.345942i \(0.112441\pi\)
\(510\) 5.83386 0.258328
\(511\) 2.71085 0.119921
\(512\) 1.00000 0.0441942
\(513\) −0.333577 −0.0147278
\(514\) −6.96918 −0.307398
\(515\) −7.01743 −0.309225
\(516\) 2.28017 0.100379
\(517\) 9.79029 0.430577
\(518\) 8.01051 0.351962
\(519\) 23.0738 1.01283
\(520\) 3.23283 0.141769
\(521\) −6.93772 −0.303947 −0.151974 0.988385i \(-0.548563\pi\)
−0.151974 + 0.988385i \(0.548563\pi\)
\(522\) 2.09042 0.0914950
\(523\) 28.9900 1.26765 0.633823 0.773478i \(-0.281485\pi\)
0.633823 + 0.773478i \(0.281485\pi\)
\(524\) −22.0302 −0.962395
\(525\) −55.8607 −2.43796
\(526\) 6.22817 0.271561
\(527\) 4.97299 0.216627
\(528\) −4.54189 −0.197660
\(529\) −11.9341 −0.518874
\(530\) 3.94833 0.171505
\(531\) −30.5884 −1.32742
\(532\) −4.82108 −0.209020
\(533\) −69.0232 −2.98973
\(534\) 20.6033 0.891593
\(535\) 3.25348 0.140660
\(536\) −10.6946 −0.461934
\(537\) −23.8813 −1.03055
\(538\) 20.3744 0.878402
\(539\) 29.7853 1.28295
\(540\) 0.189269 0.00814484
\(541\) 25.5107 1.09679 0.548395 0.836220i \(-0.315239\pi\)
0.548395 + 0.836220i \(0.315239\pi\)
\(542\) −16.5363 −0.710295
\(543\) 22.3731 0.960124
\(544\) 4.15123 0.177982
\(545\) −4.01375 −0.171930
\(546\) −68.0361 −2.91168
\(547\) −3.26142 −0.139448 −0.0697242 0.997566i \(-0.522212\pi\)
−0.0697242 + 0.997566i \(0.522212\pi\)
\(548\) −21.1806 −0.904791
\(549\) 11.0281 0.470669
\(550\) −8.57842 −0.365785
\(551\) 0.666868 0.0284095
\(552\) −8.23928 −0.350687
\(553\) −34.7680 −1.47849
\(554\) 17.2738 0.733893
\(555\) −2.33504 −0.0991171
\(556\) 9.81593 0.416288
\(557\) −11.3735 −0.481912 −0.240956 0.970536i \(-0.577461\pi\)
−0.240956 + 0.970536i \(0.577461\pi\)
\(558\) 3.75521 0.158971
\(559\) 5.24529 0.221852
\(560\) 2.73544 0.115594
\(561\) −18.8544 −0.796035
\(562\) −2.67698 −0.112922
\(563\) 15.4769 0.652275 0.326137 0.945322i \(-0.394253\pi\)
0.326137 + 0.945322i \(0.394253\pi\)
\(564\) −13.2236 −0.556815
\(565\) −1.29949 −0.0546700
\(566\) 11.6554 0.489912
\(567\) 41.3544 1.73672
\(568\) 13.2989 0.558008
\(569\) −12.4033 −0.519975 −0.259987 0.965612i \(-0.583718\pi\)
−0.259987 + 0.965612i \(0.583718\pi\)
\(570\) 1.40533 0.0588629
\(571\) −17.6149 −0.737162 −0.368581 0.929596i \(-0.620156\pi\)
−0.368581 + 0.929596i \(0.620156\pi\)
\(572\) −10.4482 −0.436860
\(573\) −51.6169 −2.15633
\(574\) −58.4037 −2.43772
\(575\) −15.5618 −0.648971
\(576\) 3.13468 0.130612
\(577\) 24.7686 1.03113 0.515565 0.856850i \(-0.327582\pi\)
0.515565 + 0.856850i \(0.327582\pi\)
\(578\) 0.232697 0.00967894
\(579\) −2.61234 −0.108565
\(580\) −0.378376 −0.0157112
\(581\) −66.0660 −2.74088
\(582\) −16.9741 −0.703600
\(583\) −12.7606 −0.528490
\(584\) −0.562291 −0.0232677
\(585\) 10.1339 0.418984
\(586\) 20.0736 0.829234
\(587\) 3.74142 0.154425 0.0772124 0.997015i \(-0.475398\pi\)
0.0772124 + 0.997015i \(0.475398\pi\)
\(588\) −40.2307 −1.65909
\(589\) 1.19796 0.0493609
\(590\) 5.53665 0.227940
\(591\) 32.4721 1.33572
\(592\) −1.66156 −0.0682896
\(593\) −39.8877 −1.63799 −0.818996 0.573799i \(-0.805469\pi\)
−0.818996 + 0.573799i \(0.805469\pi\)
\(594\) −0.611698 −0.0250983
\(595\) 11.3555 0.465528
\(596\) −9.83654 −0.402920
\(597\) −5.62541 −0.230233
\(598\) −18.9536 −0.775072
\(599\) 6.36217 0.259951 0.129976 0.991517i \(-0.458510\pi\)
0.129976 + 0.991517i \(0.458510\pi\)
\(600\) 11.5868 0.473028
\(601\) −28.0361 −1.14362 −0.571809 0.820387i \(-0.693758\pi\)
−0.571809 + 0.820387i \(0.693758\pi\)
\(602\) 4.43828 0.180891
\(603\) −33.5240 −1.36520
\(604\) 0.426888 0.0173698
\(605\) 4.33337 0.176177
\(606\) 16.3292 0.663329
\(607\) 18.3805 0.746042 0.373021 0.927823i \(-0.378322\pi\)
0.373021 + 0.927823i \(0.378322\pi\)
\(608\) 1.00000 0.0405554
\(609\) 7.96306 0.322679
\(610\) −1.99614 −0.0808215
\(611\) −30.4196 −1.23065
\(612\) 13.0128 0.526010
\(613\) −16.5269 −0.667515 −0.333757 0.942659i \(-0.608317\pi\)
−0.333757 + 0.942659i \(0.608317\pi\)
\(614\) −4.90950 −0.198131
\(615\) 17.0245 0.686496
\(616\) −8.84067 −0.356201
\(617\) 0.181132 0.00729209 0.00364605 0.999993i \(-0.498839\pi\)
0.00364605 + 0.999993i \(0.498839\pi\)
\(618\) −30.6331 −1.23224
\(619\) 25.3398 1.01849 0.509246 0.860621i \(-0.329924\pi\)
0.509246 + 0.860621i \(0.329924\pi\)
\(620\) −0.679711 −0.0272978
\(621\) −1.10966 −0.0445291
\(622\) −27.4826 −1.10195
\(623\) 40.1038 1.60673
\(624\) 14.1122 0.564941
\(625\) 20.2746 0.810985
\(626\) −13.3112 −0.532023
\(627\) −4.54189 −0.181386
\(628\) −8.18977 −0.326807
\(629\) −6.89751 −0.275022
\(630\) 8.57474 0.341626
\(631\) 18.5985 0.740395 0.370197 0.928953i \(-0.379290\pi\)
0.370197 + 0.928953i \(0.379290\pi\)
\(632\) 7.21166 0.286864
\(633\) 2.47683 0.0984451
\(634\) −13.3881 −0.531711
\(635\) −2.30682 −0.0915434
\(636\) 17.2356 0.683436
\(637\) −92.5467 −3.66683
\(638\) 1.22287 0.0484139
\(639\) 41.6877 1.64914
\(640\) −0.567392 −0.0224282
\(641\) 27.8553 1.10022 0.550109 0.835093i \(-0.314586\pi\)
0.550109 + 0.835093i \(0.314586\pi\)
\(642\) 14.2024 0.560522
\(643\) −15.2251 −0.600420 −0.300210 0.953873i \(-0.597057\pi\)
−0.300210 + 0.953873i \(0.597057\pi\)
\(644\) −16.0375 −0.631967
\(645\) −1.29375 −0.0509413
\(646\) 4.15123 0.163328
\(647\) 26.8519 1.05566 0.527828 0.849351i \(-0.323006\pi\)
0.527828 + 0.849351i \(0.323006\pi\)
\(648\) −8.57782 −0.336969
\(649\) −17.8939 −0.702397
\(650\) 26.6542 1.04546
\(651\) 14.3048 0.560648
\(652\) −20.4062 −0.799167
\(653\) −40.0131 −1.56583 −0.782917 0.622126i \(-0.786269\pi\)
−0.782917 + 0.622126i \(0.786269\pi\)
\(654\) −17.5212 −0.685132
\(655\) 12.4998 0.488407
\(656\) 12.1142 0.472982
\(657\) −1.76260 −0.0687656
\(658\) −25.7395 −1.00343
\(659\) −37.3563 −1.45519 −0.727597 0.686004i \(-0.759363\pi\)
−0.727597 + 0.686004i \(0.759363\pi\)
\(660\) 2.57703 0.100311
\(661\) 6.81868 0.265216 0.132608 0.991169i \(-0.457665\pi\)
0.132608 + 0.991169i \(0.457665\pi\)
\(662\) 18.7133 0.727312
\(663\) 58.5830 2.27518
\(664\) 13.7036 0.531801
\(665\) 2.73544 0.106076
\(666\) −5.20845 −0.201823
\(667\) 2.21836 0.0858954
\(668\) −2.47910 −0.0959194
\(669\) −43.2322 −1.67145
\(670\) 6.06801 0.234428
\(671\) 6.45133 0.249051
\(672\) 11.9410 0.460634
\(673\) 2.68173 0.103373 0.0516866 0.998663i \(-0.483540\pi\)
0.0516866 + 0.998663i \(0.483540\pi\)
\(674\) −26.5988 −1.02455
\(675\) 1.56050 0.0600635
\(676\) 19.4637 0.748605
\(677\) −40.2480 −1.54686 −0.773429 0.633883i \(-0.781460\pi\)
−0.773429 + 0.633883i \(0.781460\pi\)
\(678\) −5.67264 −0.217857
\(679\) −33.0397 −1.26795
\(680\) −2.35538 −0.0903245
\(681\) 46.1519 1.76855
\(682\) 2.19676 0.0841181
\(683\) 18.9980 0.726938 0.363469 0.931606i \(-0.381592\pi\)
0.363469 + 0.931606i \(0.381592\pi\)
\(684\) 3.13468 0.119857
\(685\) 12.0177 0.459173
\(686\) −44.5604 −1.70132
\(687\) −24.2564 −0.925441
\(688\) −0.920599 −0.0350975
\(689\) 39.6487 1.51050
\(690\) 4.67490 0.177970
\(691\) 3.89630 0.148222 0.0741111 0.997250i \(-0.476388\pi\)
0.0741111 + 0.997250i \(0.476388\pi\)
\(692\) −9.31587 −0.354136
\(693\) −27.7127 −1.05272
\(694\) 11.5652 0.439008
\(695\) −5.56948 −0.211263
\(696\) −1.65172 −0.0626082
\(697\) 50.2890 1.90483
\(698\) −14.2528 −0.539476
\(699\) 43.4501 1.64343
\(700\) 22.5533 0.852436
\(701\) 6.16398 0.232810 0.116405 0.993202i \(-0.462863\pi\)
0.116405 + 0.993202i \(0.462863\pi\)
\(702\) 1.90062 0.0717343
\(703\) −1.66156 −0.0626669
\(704\) 1.83375 0.0691122
\(705\) 7.50299 0.282579
\(706\) 9.49285 0.357268
\(707\) 31.7844 1.19538
\(708\) 24.1691 0.908329
\(709\) −47.7828 −1.79452 −0.897261 0.441500i \(-0.854446\pi\)
−0.897261 + 0.441500i \(0.854446\pi\)
\(710\) −7.54567 −0.283184
\(711\) 22.6062 0.847800
\(712\) −8.31843 −0.311746
\(713\) 3.98505 0.149241
\(714\) 49.5698 1.85510
\(715\) 5.92821 0.221702
\(716\) 9.64188 0.360334
\(717\) −11.7118 −0.437384
\(718\) −19.1533 −0.714794
\(719\) 50.2312 1.87331 0.936653 0.350257i \(-0.113906\pi\)
0.936653 + 0.350257i \(0.113906\pi\)
\(720\) −1.77859 −0.0662842
\(721\) −59.6265 −2.22061
\(722\) 1.00000 0.0372161
\(723\) 9.18198 0.341481
\(724\) −9.03298 −0.335708
\(725\) −3.11965 −0.115861
\(726\) 18.9164 0.702054
\(727\) −11.2442 −0.417024 −0.208512 0.978020i \(-0.566862\pi\)
−0.208512 + 0.978020i \(0.566862\pi\)
\(728\) 27.4691 1.01807
\(729\) −29.3674 −1.08768
\(730\) 0.319039 0.0118082
\(731\) −3.82162 −0.141348
\(732\) −8.71373 −0.322069
\(733\) 34.3250 1.26782 0.633911 0.773406i \(-0.281449\pi\)
0.633911 + 0.773406i \(0.281449\pi\)
\(734\) −9.02112 −0.332976
\(735\) 22.8266 0.841971
\(736\) 3.32654 0.122618
\(737\) −19.6112 −0.722387
\(738\) 37.9742 1.39785
\(739\) −41.8021 −1.53771 −0.768857 0.639421i \(-0.779174\pi\)
−0.768857 + 0.639421i \(0.779174\pi\)
\(740\) 0.942755 0.0346564
\(741\) 14.1122 0.518425
\(742\) 33.5486 1.23161
\(743\) −14.4206 −0.529042 −0.264521 0.964380i \(-0.585214\pi\)
−0.264521 + 0.964380i \(0.585214\pi\)
\(744\) −2.96713 −0.108780
\(745\) 5.58118 0.204478
\(746\) −15.6364 −0.572489
\(747\) 42.9563 1.57169
\(748\) 7.61233 0.278334
\(749\) 27.6445 1.01011
\(750\) −13.6009 −0.496635
\(751\) 9.10593 0.332280 0.166140 0.986102i \(-0.446870\pi\)
0.166140 + 0.986102i \(0.446870\pi\)
\(752\) 5.33894 0.194691
\(753\) 41.9491 1.52871
\(754\) −3.79961 −0.138374
\(755\) −0.242213 −0.00881504
\(756\) 1.60820 0.0584897
\(757\) −3.27757 −0.119125 −0.0595626 0.998225i \(-0.518971\pi\)
−0.0595626 + 0.998225i \(0.518971\pi\)
\(758\) −15.7259 −0.571191
\(759\) −15.1088 −0.548415
\(760\) −0.567392 −0.0205815
\(761\) 4.59832 0.166689 0.0833445 0.996521i \(-0.473440\pi\)
0.0833445 + 0.996521i \(0.473440\pi\)
\(762\) −10.0699 −0.364795
\(763\) −34.1045 −1.23467
\(764\) 20.8399 0.753962
\(765\) −7.38335 −0.266945
\(766\) −1.06145 −0.0383518
\(767\) 55.5985 2.00755
\(768\) −2.47683 −0.0893748
\(769\) 28.7812 1.03787 0.518937 0.854812i \(-0.326328\pi\)
0.518937 + 0.854812i \(0.326328\pi\)
\(770\) 5.01613 0.180769
\(771\) 17.2615 0.621657
\(772\) 1.05471 0.0379599
\(773\) 22.2648 0.800809 0.400405 0.916338i \(-0.368870\pi\)
0.400405 + 0.916338i \(0.368870\pi\)
\(774\) −2.88578 −0.103727
\(775\) −5.60412 −0.201306
\(776\) 6.85317 0.246014
\(777\) −19.8407 −0.711780
\(778\) 17.3400 0.621669
\(779\) 12.1142 0.434038
\(780\) −8.00716 −0.286702
\(781\) 24.3868 0.872629
\(782\) 13.8092 0.493817
\(783\) −0.222452 −0.00794978
\(784\) 16.2428 0.580101
\(785\) 4.64681 0.165852
\(786\) 54.5651 1.94627
\(787\) 11.8770 0.423368 0.211684 0.977338i \(-0.432105\pi\)
0.211684 + 0.977338i \(0.432105\pi\)
\(788\) −13.1104 −0.467037
\(789\) −15.4261 −0.549184
\(790\) −4.09184 −0.145581
\(791\) −11.0417 −0.392596
\(792\) 5.74823 0.204254
\(793\) −20.0451 −0.711821
\(794\) −20.1357 −0.714589
\(795\) −9.77934 −0.346837
\(796\) 2.27122 0.0805012
\(797\) −7.58194 −0.268566 −0.134283 0.990943i \(-0.542873\pi\)
−0.134283 + 0.990943i \(0.542873\pi\)
\(798\) 11.9410 0.422707
\(799\) 22.1631 0.784076
\(800\) −4.67807 −0.165395
\(801\) −26.0756 −0.921336
\(802\) −26.6269 −0.940230
\(803\) −1.03110 −0.0363868
\(804\) 26.4886 0.934180
\(805\) 9.09957 0.320718
\(806\) −6.82559 −0.240421
\(807\) −50.4639 −1.77641
\(808\) −6.59279 −0.231934
\(809\) 17.3062 0.608454 0.304227 0.952600i \(-0.401602\pi\)
0.304227 + 0.952600i \(0.401602\pi\)
\(810\) 4.86699 0.171009
\(811\) 31.7744 1.11575 0.557874 0.829925i \(-0.311617\pi\)
0.557874 + 0.829925i \(0.311617\pi\)
\(812\) −3.21502 −0.112825
\(813\) 40.9576 1.43644
\(814\) −3.04689 −0.106793
\(815\) 11.5783 0.405570
\(816\) −10.2819 −0.359938
\(817\) −0.920599 −0.0322077
\(818\) −4.92119 −0.172065
\(819\) 86.1067 3.00881
\(820\) −6.87353 −0.240034
\(821\) −36.7926 −1.28407 −0.642035 0.766675i \(-0.721910\pi\)
−0.642035 + 0.766675i \(0.721910\pi\)
\(822\) 52.4607 1.82978
\(823\) −47.3954 −1.65210 −0.826050 0.563597i \(-0.809417\pi\)
−0.826050 + 0.563597i \(0.809417\pi\)
\(824\) 12.3679 0.430855
\(825\) 21.2473 0.739735
\(826\) 47.0445 1.63689
\(827\) 23.0157 0.800334 0.400167 0.916442i \(-0.368952\pi\)
0.400167 + 0.916442i \(0.368952\pi\)
\(828\) 10.4276 0.362386
\(829\) −43.1140 −1.49741 −0.748705 0.662903i \(-0.769324\pi\)
−0.748705 + 0.662903i \(0.769324\pi\)
\(830\) −7.77530 −0.269884
\(831\) −42.7842 −1.48417
\(832\) −5.69770 −0.197532
\(833\) 67.4277 2.33623
\(834\) −24.3124 −0.841869
\(835\) 1.40662 0.0486782
\(836\) 1.83375 0.0634217
\(837\) −0.399610 −0.0138126
\(838\) 25.3212 0.874707
\(839\) 20.4668 0.706594 0.353297 0.935511i \(-0.385061\pi\)
0.353297 + 0.935511i \(0.385061\pi\)
\(840\) −6.77523 −0.233768
\(841\) −28.5553 −0.984665
\(842\) 10.0646 0.346850
\(843\) 6.63042 0.228364
\(844\) −1.00000 −0.0344214
\(845\) −11.0436 −0.379910
\(846\) 16.7359 0.575391
\(847\) 36.8203 1.26516
\(848\) −6.95873 −0.238964
\(849\) −28.8684 −0.990760
\(850\) −19.4197 −0.666091
\(851\) −5.52725 −0.189472
\(852\) −32.9390 −1.12847
\(853\) 11.2293 0.384483 0.192242 0.981348i \(-0.438424\pi\)
0.192242 + 0.981348i \(0.438424\pi\)
\(854\) −16.9611 −0.580395
\(855\) −1.77859 −0.0608266
\(856\) −5.73409 −0.195987
\(857\) 27.9813 0.955822 0.477911 0.878408i \(-0.341394\pi\)
0.477911 + 0.878408i \(0.341394\pi\)
\(858\) 25.8783 0.883471
\(859\) −0.633749 −0.0216232 −0.0108116 0.999942i \(-0.503442\pi\)
−0.0108116 + 0.999942i \(0.503442\pi\)
\(860\) 0.522341 0.0178117
\(861\) 144.656 4.92986
\(862\) 6.56730 0.223683
\(863\) −29.6830 −1.01042 −0.505211 0.862996i \(-0.668585\pi\)
−0.505211 + 0.862996i \(0.668585\pi\)
\(864\) −0.333577 −0.0113485
\(865\) 5.28575 0.179721
\(866\) −34.5132 −1.17281
\(867\) −0.576352 −0.0195739
\(868\) −5.77544 −0.196031
\(869\) 13.2244 0.448607
\(870\) 0.937171 0.0317731
\(871\) 60.9343 2.06468
\(872\) 7.07403 0.239557
\(873\) 21.4825 0.727072
\(874\) 3.32654 0.112522
\(875\) −26.4738 −0.894978
\(876\) 1.39270 0.0470549
\(877\) −21.4846 −0.725482 −0.362741 0.931890i \(-0.618159\pi\)
−0.362741 + 0.931890i \(0.618159\pi\)
\(878\) 8.56863 0.289177
\(879\) −49.7189 −1.67698
\(880\) −1.04046 −0.0350738
\(881\) −8.74990 −0.294792 −0.147396 0.989078i \(-0.547089\pi\)
−0.147396 + 0.989078i \(0.547089\pi\)
\(882\) 50.9160 1.71443
\(883\) 17.2547 0.580666 0.290333 0.956926i \(-0.406234\pi\)
0.290333 + 0.956926i \(0.406234\pi\)
\(884\) −23.6524 −0.795517
\(885\) −13.7133 −0.460969
\(886\) −16.3904 −0.550647
\(887\) 30.3658 1.01958 0.509792 0.860298i \(-0.329722\pi\)
0.509792 + 0.860298i \(0.329722\pi\)
\(888\) 4.11540 0.138104
\(889\) −19.6008 −0.657391
\(890\) 4.71981 0.158208
\(891\) −15.7296 −0.526962
\(892\) 17.4547 0.584426
\(893\) 5.33894 0.178661
\(894\) 24.3634 0.814834
\(895\) −5.47073 −0.182866
\(896\) −4.82108 −0.161061
\(897\) 46.9449 1.56744
\(898\) −0.0363439 −0.00121281
\(899\) 0.798878 0.0266441
\(900\) −14.6642 −0.488808
\(901\) −28.8873 −0.962375
\(902\) 22.2145 0.739663
\(903\) −10.9929 −0.365820
\(904\) 2.29029 0.0761738
\(905\) 5.12524 0.170369
\(906\) −1.05733 −0.0351274
\(907\) −12.2095 −0.405410 −0.202705 0.979240i \(-0.564973\pi\)
−0.202705 + 0.979240i \(0.564973\pi\)
\(908\) −18.6335 −0.618374
\(909\) −20.6663 −0.685458
\(910\) −15.5857 −0.516662
\(911\) −33.1195 −1.09730 −0.548649 0.836053i \(-0.684858\pi\)
−0.548649 + 0.836053i \(0.684858\pi\)
\(912\) −2.47683 −0.0820160
\(913\) 25.1290 0.831647
\(914\) −2.88094 −0.0952930
\(915\) 4.94411 0.163447
\(916\) 9.79335 0.323581
\(917\) 106.209 3.50735
\(918\) −1.38475 −0.0457037
\(919\) 30.2242 0.997004 0.498502 0.866888i \(-0.333884\pi\)
0.498502 + 0.866888i \(0.333884\pi\)
\(920\) −1.88746 −0.0622276
\(921\) 12.1600 0.400685
\(922\) −20.5742 −0.677576
\(923\) −75.7729 −2.49409
\(924\) 21.8968 0.720353
\(925\) 7.77288 0.255571
\(926\) 5.76886 0.189576
\(927\) 38.7693 1.27335
\(928\) 0.666868 0.0218910
\(929\) −24.7144 −0.810854 −0.405427 0.914127i \(-0.632877\pi\)
−0.405427 + 0.914127i \(0.632877\pi\)
\(930\) 1.68353 0.0552050
\(931\) 16.2428 0.532337
\(932\) −17.5426 −0.574628
\(933\) 68.0698 2.22850
\(934\) −0.843417 −0.0275974
\(935\) −4.31918 −0.141252
\(936\) −17.8604 −0.583787
\(937\) −0.140002 −0.00457366 −0.00228683 0.999997i \(-0.500728\pi\)
−0.00228683 + 0.999997i \(0.500728\pi\)
\(938\) 51.5593 1.68347
\(939\) 32.9696 1.07592
\(940\) −3.02927 −0.0988040
\(941\) 10.5083 0.342560 0.171280 0.985222i \(-0.445210\pi\)
0.171280 + 0.985222i \(0.445210\pi\)
\(942\) 20.2846 0.660909
\(943\) 40.2985 1.31230
\(944\) −9.75807 −0.317598
\(945\) −0.912482 −0.0296830
\(946\) −1.68815 −0.0548865
\(947\) −9.12492 −0.296520 −0.148260 0.988948i \(-0.547367\pi\)
−0.148260 + 0.988948i \(0.547367\pi\)
\(948\) −17.8620 −0.580132
\(949\) 3.20376 0.103998
\(950\) −4.67807 −0.151777
\(951\) 33.1601 1.07529
\(952\) −20.0134 −0.648638
\(953\) 7.07306 0.229119 0.114559 0.993416i \(-0.463454\pi\)
0.114559 + 0.993416i \(0.463454\pi\)
\(954\) −21.8134 −0.706235
\(955\) −11.8244 −0.382629
\(956\) 4.72853 0.152932
\(957\) −3.02884 −0.0979085
\(958\) −18.0326 −0.582607
\(959\) 102.113 3.29741
\(960\) 1.40533 0.0453569
\(961\) −29.5649 −0.953707
\(962\) 9.46705 0.305230
\(963\) −17.9745 −0.579221
\(964\) −3.70715 −0.119399
\(965\) −0.598435 −0.0192643
\(966\) 39.7222 1.27804
\(967\) 20.3506 0.654430 0.327215 0.944950i \(-0.393890\pi\)
0.327215 + 0.944950i \(0.393890\pi\)
\(968\) −7.63735 −0.245474
\(969\) −10.2819 −0.330302
\(970\) −3.88844 −0.124850
\(971\) −12.1285 −0.389222 −0.194611 0.980880i \(-0.562344\pi\)
−0.194611 + 0.980880i \(0.562344\pi\)
\(972\) 22.2465 0.713558
\(973\) −47.3234 −1.51712
\(974\) −42.0650 −1.34785
\(975\) −66.0179 −2.11426
\(976\) 3.51810 0.112612
\(977\) −57.9253 −1.85319 −0.926597 0.376057i \(-0.877280\pi\)
−0.926597 + 0.376057i \(0.877280\pi\)
\(978\) 50.5426 1.61617
\(979\) −15.2539 −0.487518
\(980\) −9.21605 −0.294396
\(981\) 22.1748 0.707988
\(982\) −14.2502 −0.454741
\(983\) 17.9013 0.570962 0.285481 0.958384i \(-0.407847\pi\)
0.285481 + 0.958384i \(0.407847\pi\)
\(984\) −30.0049 −0.956521
\(985\) 7.43872 0.237017
\(986\) 2.76832 0.0881613
\(987\) 63.7522 2.02926
\(988\) −5.69770 −0.181268
\(989\) −3.06241 −0.0973790
\(990\) −3.26150 −0.103657
\(991\) 5.21954 0.165804 0.0829021 0.996558i \(-0.473581\pi\)
0.0829021 + 0.996558i \(0.473581\pi\)
\(992\) 1.19796 0.0380351
\(993\) −46.3496 −1.47086
\(994\) −64.1149 −2.03360
\(995\) −1.28867 −0.0408536
\(996\) −33.9414 −1.07547
\(997\) −13.1277 −0.415758 −0.207879 0.978155i \(-0.566656\pi\)
−0.207879 + 0.978155i \(0.566656\pi\)
\(998\) 9.56768 0.302860
\(999\) 0.554258 0.0175359
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 \(a_p\))