Properties

Label 4017.2.a.j.1.15
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4017 = 3 \cdot 13 \cdot 103 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4017.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0759064919\)
Analytic rank: \(0\)
Dimension: \(25\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.940078 q^{2} -1.00000 q^{3} -1.11625 q^{4} -1.95082 q^{5} -0.940078 q^{6} -0.363346 q^{7} -2.92952 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.940078 q^{2} -1.00000 q^{3} -1.11625 q^{4} -1.95082 q^{5} -0.940078 q^{6} -0.363346 q^{7} -2.92952 q^{8} +1.00000 q^{9} -1.83392 q^{10} +1.99973 q^{11} +1.11625 q^{12} +1.00000 q^{13} -0.341574 q^{14} +1.95082 q^{15} -0.521471 q^{16} -2.22976 q^{17} +0.940078 q^{18} -5.96553 q^{19} +2.17761 q^{20} +0.363346 q^{21} +1.87990 q^{22} -1.97893 q^{23} +2.92952 q^{24} -1.19429 q^{25} +0.940078 q^{26} -1.00000 q^{27} +0.405586 q^{28} -1.52189 q^{29} +1.83392 q^{30} -6.18222 q^{31} +5.36882 q^{32} -1.99973 q^{33} -2.09614 q^{34} +0.708823 q^{35} -1.11625 q^{36} +2.13653 q^{37} -5.60807 q^{38} -1.00000 q^{39} +5.71497 q^{40} -0.409818 q^{41} +0.341574 q^{42} +10.8205 q^{43} -2.23220 q^{44} -1.95082 q^{45} -1.86035 q^{46} -11.1414 q^{47} +0.521471 q^{48} -6.86798 q^{49} -1.12273 q^{50} +2.22976 q^{51} -1.11625 q^{52} +1.45789 q^{53} -0.940078 q^{54} -3.90111 q^{55} +1.06443 q^{56} +5.96553 q^{57} -1.43069 q^{58} -2.75815 q^{59} -2.17761 q^{60} -2.43812 q^{61} -5.81177 q^{62} -0.363346 q^{63} +6.09005 q^{64} -1.95082 q^{65} -1.87990 q^{66} +0.0721191 q^{67} +2.48897 q^{68} +1.97893 q^{69} +0.666349 q^{70} +11.4933 q^{71} -2.92952 q^{72} +10.7686 q^{73} +2.00851 q^{74} +1.19429 q^{75} +6.65905 q^{76} -0.726592 q^{77} -0.940078 q^{78} +8.03620 q^{79} +1.01730 q^{80} +1.00000 q^{81} -0.385261 q^{82} +10.8876 q^{83} -0.405586 q^{84} +4.34986 q^{85} +10.1721 q^{86} +1.52189 q^{87} -5.85824 q^{88} +8.54917 q^{89} -1.83392 q^{90} -0.363346 q^{91} +2.20898 q^{92} +6.18222 q^{93} -10.4738 q^{94} +11.6377 q^{95} -5.36882 q^{96} -13.4153 q^{97} -6.45644 q^{98} +1.99973 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.940078 0.664735 0.332368 0.943150i \(-0.392152\pi\)
0.332368 + 0.943150i \(0.392152\pi\)
\(3\) −1.00000 −0.577350
\(4\) −1.11625 −0.558127
\(5\) −1.95082 −0.872434 −0.436217 0.899841i \(-0.643682\pi\)
−0.436217 + 0.899841i \(0.643682\pi\)
\(6\) −0.940078 −0.383785
\(7\) −0.363346 −0.137332 −0.0686659 0.997640i \(-0.521874\pi\)
−0.0686659 + 0.997640i \(0.521874\pi\)
\(8\) −2.92952 −1.03574
\(9\) 1.00000 0.333333
\(10\) −1.83392 −0.579938
\(11\) 1.99973 0.602940 0.301470 0.953476i \(-0.402523\pi\)
0.301470 + 0.953476i \(0.402523\pi\)
\(12\) 1.11625 0.322235
\(13\) 1.00000 0.277350
\(14\) −0.341574 −0.0912894
\(15\) 1.95082 0.503700
\(16\) −0.521471 −0.130368
\(17\) −2.22976 −0.540795 −0.270398 0.962749i \(-0.587155\pi\)
−0.270398 + 0.962749i \(0.587155\pi\)
\(18\) 0.940078 0.221578
\(19\) −5.96553 −1.36859 −0.684294 0.729206i \(-0.739889\pi\)
−0.684294 + 0.729206i \(0.739889\pi\)
\(20\) 2.17761 0.486929
\(21\) 0.363346 0.0792886
\(22\) 1.87990 0.400796
\(23\) −1.97893 −0.412635 −0.206317 0.978485i \(-0.566148\pi\)
−0.206317 + 0.978485i \(0.566148\pi\)
\(24\) 2.92952 0.597986
\(25\) −1.19429 −0.238859
\(26\) 0.940078 0.184364
\(27\) −1.00000 −0.192450
\(28\) 0.405586 0.0766486
\(29\) −1.52189 −0.282607 −0.141304 0.989966i \(-0.545129\pi\)
−0.141304 + 0.989966i \(0.545129\pi\)
\(30\) 1.83392 0.334827
\(31\) −6.18222 −1.11036 −0.555180 0.831730i \(-0.687351\pi\)
−0.555180 + 0.831730i \(0.687351\pi\)
\(32\) 5.36882 0.949082
\(33\) −1.99973 −0.348108
\(34\) −2.09614 −0.359486
\(35\) 0.708823 0.119813
\(36\) −1.11625 −0.186042
\(37\) 2.13653 0.351244 0.175622 0.984458i \(-0.443806\pi\)
0.175622 + 0.984458i \(0.443806\pi\)
\(38\) −5.60807 −0.909749
\(39\) −1.00000 −0.160128
\(40\) 5.71497 0.903617
\(41\) −0.409818 −0.0640028 −0.0320014 0.999488i \(-0.510188\pi\)
−0.0320014 + 0.999488i \(0.510188\pi\)
\(42\) 0.341574 0.0527059
\(43\) 10.8205 1.65011 0.825057 0.565049i \(-0.191143\pi\)
0.825057 + 0.565049i \(0.191143\pi\)
\(44\) −2.23220 −0.336517
\(45\) −1.95082 −0.290811
\(46\) −1.86035 −0.274293
\(47\) −11.1414 −1.62514 −0.812568 0.582866i \(-0.801931\pi\)
−0.812568 + 0.582866i \(0.801931\pi\)
\(48\) 0.521471 0.0752679
\(49\) −6.86798 −0.981140
\(50\) −1.12273 −0.158778
\(51\) 2.22976 0.312228
\(52\) −1.11625 −0.154797
\(53\) 1.45789 0.200256 0.100128 0.994975i \(-0.468075\pi\)
0.100128 + 0.994975i \(0.468075\pi\)
\(54\) −0.940078 −0.127928
\(55\) −3.90111 −0.526025
\(56\) 1.06443 0.142240
\(57\) 5.96553 0.790154
\(58\) −1.43069 −0.187859
\(59\) −2.75815 −0.359081 −0.179540 0.983751i \(-0.557461\pi\)
−0.179540 + 0.983751i \(0.557461\pi\)
\(60\) −2.17761 −0.281128
\(61\) −2.43812 −0.312170 −0.156085 0.987744i \(-0.549887\pi\)
−0.156085 + 0.987744i \(0.549887\pi\)
\(62\) −5.81177 −0.738096
\(63\) −0.363346 −0.0457773
\(64\) 6.09005 0.761256
\(65\) −1.95082 −0.241970
\(66\) −1.87990 −0.231399
\(67\) 0.0721191 0.00881075 0.00440538 0.999990i \(-0.498598\pi\)
0.00440538 + 0.999990i \(0.498598\pi\)
\(68\) 2.48897 0.301832
\(69\) 1.97893 0.238235
\(70\) 0.666349 0.0796440
\(71\) 11.4933 1.36400 0.682001 0.731351i \(-0.261110\pi\)
0.682001 + 0.731351i \(0.261110\pi\)
\(72\) −2.92952 −0.345247
\(73\) 10.7686 1.26036 0.630182 0.776448i \(-0.282980\pi\)
0.630182 + 0.776448i \(0.282980\pi\)
\(74\) 2.00851 0.233484
\(75\) 1.19429 0.137905
\(76\) 6.65905 0.763845
\(77\) −0.726592 −0.0828029
\(78\) −0.940078 −0.106443
\(79\) 8.03620 0.904143 0.452072 0.891982i \(-0.350685\pi\)
0.452072 + 0.891982i \(0.350685\pi\)
\(80\) 1.01730 0.113737
\(81\) 1.00000 0.111111
\(82\) −0.385261 −0.0425449
\(83\) 10.8876 1.19507 0.597535 0.801843i \(-0.296147\pi\)
0.597535 + 0.801843i \(0.296147\pi\)
\(84\) −0.405586 −0.0442531
\(85\) 4.34986 0.471808
\(86\) 10.1721 1.09689
\(87\) 1.52189 0.163163
\(88\) −5.85824 −0.624490
\(89\) 8.54917 0.906211 0.453105 0.891457i \(-0.350316\pi\)
0.453105 + 0.891457i \(0.350316\pi\)
\(90\) −1.83392 −0.193313
\(91\) −0.363346 −0.0380890
\(92\) 2.20898 0.230302
\(93\) 6.18222 0.641067
\(94\) −10.4738 −1.08029
\(95\) 11.6377 1.19400
\(96\) −5.36882 −0.547953
\(97\) −13.4153 −1.36211 −0.681057 0.732230i \(-0.738480\pi\)
−0.681057 + 0.732230i \(0.738480\pi\)
\(98\) −6.45644 −0.652199
\(99\) 1.99973 0.200980
\(100\) 1.33313 0.133313
\(101\) −6.35586 −0.632431 −0.316216 0.948687i \(-0.602412\pi\)
−0.316216 + 0.948687i \(0.602412\pi\)
\(102\) 2.09614 0.207549
\(103\) −1.00000 −0.0985329
\(104\) −2.92952 −0.287263
\(105\) −0.708823 −0.0691741
\(106\) 1.37053 0.133117
\(107\) 3.80533 0.367875 0.183938 0.982938i \(-0.441116\pi\)
0.183938 + 0.982938i \(0.441116\pi\)
\(108\) 1.11625 0.107412
\(109\) 3.96810 0.380075 0.190038 0.981777i \(-0.439139\pi\)
0.190038 + 0.981777i \(0.439139\pi\)
\(110\) −3.66735 −0.349668
\(111\) −2.13653 −0.202791
\(112\) 0.189474 0.0179037
\(113\) −1.14996 −0.108179 −0.0540893 0.998536i \(-0.517226\pi\)
−0.0540893 + 0.998536i \(0.517226\pi\)
\(114\) 5.60807 0.525244
\(115\) 3.86053 0.359997
\(116\) 1.69881 0.157731
\(117\) 1.00000 0.0924500
\(118\) −2.59288 −0.238694
\(119\) 0.810173 0.0742684
\(120\) −5.71497 −0.521703
\(121\) −7.00110 −0.636463
\(122\) −2.29203 −0.207510
\(123\) 0.409818 0.0369520
\(124\) 6.90093 0.619722
\(125\) 12.0840 1.08082
\(126\) −0.341574 −0.0304298
\(127\) −4.69610 −0.416711 −0.208356 0.978053i \(-0.566811\pi\)
−0.208356 + 0.978053i \(0.566811\pi\)
\(128\) −5.01252 −0.443048
\(129\) −10.8205 −0.952694
\(130\) −1.83392 −0.160846
\(131\) 4.34589 0.379702 0.189851 0.981813i \(-0.439199\pi\)
0.189851 + 0.981813i \(0.439199\pi\)
\(132\) 2.23220 0.194288
\(133\) 2.16755 0.187951
\(134\) 0.0677976 0.00585682
\(135\) 1.95082 0.167900
\(136\) 6.53212 0.560124
\(137\) 20.9667 1.79131 0.895655 0.444750i \(-0.146708\pi\)
0.895655 + 0.444750i \(0.146708\pi\)
\(138\) 1.86035 0.158363
\(139\) 21.8389 1.85235 0.926174 0.377096i \(-0.123077\pi\)
0.926174 + 0.377096i \(0.123077\pi\)
\(140\) −0.791227 −0.0668708
\(141\) 11.1414 0.938273
\(142\) 10.8046 0.906700
\(143\) 1.99973 0.167225
\(144\) −0.521471 −0.0434559
\(145\) 2.96893 0.246556
\(146\) 10.1233 0.837808
\(147\) 6.86798 0.566461
\(148\) −2.38491 −0.196039
\(149\) 18.1511 1.48700 0.743498 0.668738i \(-0.233165\pi\)
0.743498 + 0.668738i \(0.233165\pi\)
\(150\) 1.12273 0.0916704
\(151\) 8.10513 0.659586 0.329793 0.944053i \(-0.393021\pi\)
0.329793 + 0.944053i \(0.393021\pi\)
\(152\) 17.4762 1.41750
\(153\) −2.22976 −0.180265
\(154\) −0.683053 −0.0550420
\(155\) 12.0604 0.968716
\(156\) 1.11625 0.0893718
\(157\) −4.49931 −0.359084 −0.179542 0.983750i \(-0.557462\pi\)
−0.179542 + 0.983750i \(0.557462\pi\)
\(158\) 7.55465 0.601016
\(159\) −1.45789 −0.115618
\(160\) −10.4736 −0.828012
\(161\) 0.719035 0.0566679
\(162\) 0.940078 0.0738595
\(163\) −13.5433 −1.06080 −0.530398 0.847749i \(-0.677958\pi\)
−0.530398 + 0.847749i \(0.677958\pi\)
\(164\) 0.457461 0.0357217
\(165\) 3.90111 0.303701
\(166\) 10.2352 0.794406
\(167\) −5.80573 −0.449261 −0.224630 0.974444i \(-0.572117\pi\)
−0.224630 + 0.974444i \(0.572117\pi\)
\(168\) −1.06443 −0.0821225
\(169\) 1.00000 0.0769231
\(170\) 4.08920 0.313628
\(171\) −5.96553 −0.456196
\(172\) −12.0784 −0.920973
\(173\) −9.85387 −0.749176 −0.374588 0.927191i \(-0.622216\pi\)
−0.374588 + 0.927191i \(0.622216\pi\)
\(174\) 1.43069 0.108460
\(175\) 0.433942 0.0328029
\(176\) −1.04280 −0.0786040
\(177\) 2.75815 0.207315
\(178\) 8.03689 0.602390
\(179\) −3.97070 −0.296784 −0.148392 0.988929i \(-0.547410\pi\)
−0.148392 + 0.988929i \(0.547410\pi\)
\(180\) 2.17761 0.162310
\(181\) 11.3750 0.845497 0.422749 0.906247i \(-0.361065\pi\)
0.422749 + 0.906247i \(0.361065\pi\)
\(182\) −0.341574 −0.0253191
\(183\) 2.43812 0.180231
\(184\) 5.79731 0.427383
\(185\) −4.16799 −0.306437
\(186\) 5.81177 0.426140
\(187\) −4.45890 −0.326067
\(188\) 12.4366 0.907032
\(189\) 0.363346 0.0264295
\(190\) 10.9403 0.793696
\(191\) 15.8544 1.14719 0.573593 0.819140i \(-0.305549\pi\)
0.573593 + 0.819140i \(0.305549\pi\)
\(192\) −6.09005 −0.439512
\(193\) −14.6916 −1.05753 −0.528763 0.848770i \(-0.677344\pi\)
−0.528763 + 0.848770i \(0.677344\pi\)
\(194\) −12.6114 −0.905446
\(195\) 1.95082 0.139701
\(196\) 7.66641 0.547600
\(197\) 9.75438 0.694971 0.347485 0.937685i \(-0.387036\pi\)
0.347485 + 0.937685i \(0.387036\pi\)
\(198\) 1.87990 0.133599
\(199\) 22.2546 1.57758 0.788792 0.614660i \(-0.210707\pi\)
0.788792 + 0.614660i \(0.210707\pi\)
\(200\) 3.49871 0.247396
\(201\) −0.0721191 −0.00508689
\(202\) −5.97500 −0.420400
\(203\) 0.552971 0.0388110
\(204\) −2.48897 −0.174263
\(205\) 0.799482 0.0558382
\(206\) −0.940078 −0.0654983
\(207\) −1.97893 −0.137545
\(208\) −0.521471 −0.0361575
\(209\) −11.9294 −0.825176
\(210\) −0.666349 −0.0459825
\(211\) 15.3333 1.05559 0.527793 0.849373i \(-0.323020\pi\)
0.527793 + 0.849373i \(0.323020\pi\)
\(212\) −1.62737 −0.111768
\(213\) −11.4933 −0.787507
\(214\) 3.57731 0.244540
\(215\) −21.1089 −1.43962
\(216\) 2.92952 0.199329
\(217\) 2.24629 0.152488
\(218\) 3.73033 0.252650
\(219\) −10.7686 −0.727671
\(220\) 4.35463 0.293589
\(221\) −2.22976 −0.149990
\(222\) −2.00851 −0.134802
\(223\) 11.1131 0.744191 0.372095 0.928194i \(-0.378639\pi\)
0.372095 + 0.928194i \(0.378639\pi\)
\(224\) −1.95074 −0.130339
\(225\) −1.19429 −0.0796195
\(226\) −1.08105 −0.0719102
\(227\) 1.68257 0.111676 0.0558380 0.998440i \(-0.482217\pi\)
0.0558380 + 0.998440i \(0.482217\pi\)
\(228\) −6.65905 −0.441006
\(229\) 21.7690 1.43853 0.719267 0.694734i \(-0.244478\pi\)
0.719267 + 0.694734i \(0.244478\pi\)
\(230\) 3.62920 0.239303
\(231\) 0.726592 0.0478063
\(232\) 4.45840 0.292708
\(233\) 27.7588 1.81854 0.909270 0.416206i \(-0.136641\pi\)
0.909270 + 0.416206i \(0.136641\pi\)
\(234\) 0.940078 0.0614548
\(235\) 21.7348 1.41782
\(236\) 3.07880 0.200413
\(237\) −8.03620 −0.522007
\(238\) 0.761625 0.0493688
\(239\) −16.5132 −1.06815 −0.534076 0.845436i \(-0.679340\pi\)
−0.534076 + 0.845436i \(0.679340\pi\)
\(240\) −1.01730 −0.0656663
\(241\) −16.5745 −1.06766 −0.533828 0.845593i \(-0.679247\pi\)
−0.533828 + 0.845593i \(0.679247\pi\)
\(242\) −6.58158 −0.423080
\(243\) −1.00000 −0.0641500
\(244\) 2.72156 0.174230
\(245\) 13.3982 0.855980
\(246\) 0.385261 0.0245633
\(247\) −5.96553 −0.379578
\(248\) 18.1110 1.15005
\(249\) −10.8876 −0.689974
\(250\) 11.3599 0.718461
\(251\) −17.0792 −1.07803 −0.539014 0.842297i \(-0.681203\pi\)
−0.539014 + 0.842297i \(0.681203\pi\)
\(252\) 0.405586 0.0255495
\(253\) −3.95731 −0.248794
\(254\) −4.41470 −0.277003
\(255\) −4.34986 −0.272399
\(256\) −16.8923 −1.05577
\(257\) −14.9303 −0.931324 −0.465662 0.884963i \(-0.654184\pi\)
−0.465662 + 0.884963i \(0.654184\pi\)
\(258\) −10.1721 −0.633290
\(259\) −0.776300 −0.0482370
\(260\) 2.17761 0.135050
\(261\) −1.52189 −0.0942024
\(262\) 4.08548 0.252402
\(263\) 24.9300 1.53725 0.768626 0.639699i \(-0.220941\pi\)
0.768626 + 0.639699i \(0.220941\pi\)
\(264\) 5.85824 0.360550
\(265\) −2.84408 −0.174710
\(266\) 2.03767 0.124937
\(267\) −8.54917 −0.523201
\(268\) −0.0805032 −0.00491752
\(269\) −5.86892 −0.357834 −0.178917 0.983864i \(-0.557259\pi\)
−0.178917 + 0.983864i \(0.557259\pi\)
\(270\) 1.83392 0.111609
\(271\) 17.2185 1.04595 0.522975 0.852348i \(-0.324822\pi\)
0.522975 + 0.852348i \(0.324822\pi\)
\(272\) 1.16275 0.0705023
\(273\) 0.363346 0.0219907
\(274\) 19.7104 1.19075
\(275\) −2.38826 −0.144017
\(276\) −2.20898 −0.132965
\(277\) −10.4297 −0.626662 −0.313331 0.949644i \(-0.601445\pi\)
−0.313331 + 0.949644i \(0.601445\pi\)
\(278\) 20.5302 1.23132
\(279\) −6.18222 −0.370120
\(280\) −2.07651 −0.124095
\(281\) 19.2605 1.14898 0.574492 0.818510i \(-0.305200\pi\)
0.574492 + 0.818510i \(0.305200\pi\)
\(282\) 10.4738 0.623703
\(283\) −14.3040 −0.850287 −0.425143 0.905126i \(-0.639776\pi\)
−0.425143 + 0.905126i \(0.639776\pi\)
\(284\) −12.8294 −0.761286
\(285\) −11.6377 −0.689358
\(286\) 1.87990 0.111161
\(287\) 0.148906 0.00878962
\(288\) 5.36882 0.316361
\(289\) −12.0282 −0.707541
\(290\) 2.79102 0.163895
\(291\) 13.4153 0.786417
\(292\) −12.0204 −0.703443
\(293\) 12.3450 0.721203 0.360601 0.932720i \(-0.382571\pi\)
0.360601 + 0.932720i \(0.382571\pi\)
\(294\) 6.45644 0.376547
\(295\) 5.38066 0.313274
\(296\) −6.25902 −0.363798
\(297\) −1.99973 −0.116036
\(298\) 17.0635 0.988459
\(299\) −1.97893 −0.114444
\(300\) −1.33313 −0.0769685
\(301\) −3.93159 −0.226613
\(302\) 7.61946 0.438451
\(303\) 6.35586 0.365134
\(304\) 3.11085 0.178420
\(305\) 4.75634 0.272347
\(306\) −2.09614 −0.119829
\(307\) −27.0107 −1.54158 −0.770792 0.637087i \(-0.780139\pi\)
−0.770792 + 0.637087i \(0.780139\pi\)
\(308\) 0.811061 0.0462145
\(309\) 1.00000 0.0568880
\(310\) 11.3377 0.643940
\(311\) −30.3100 −1.71872 −0.859361 0.511369i \(-0.829139\pi\)
−0.859361 + 0.511369i \(0.829139\pi\)
\(312\) 2.92952 0.165851
\(313\) 0.581827 0.0328868 0.0164434 0.999865i \(-0.494766\pi\)
0.0164434 + 0.999865i \(0.494766\pi\)
\(314\) −4.22970 −0.238696
\(315\) 0.708823 0.0399377
\(316\) −8.97044 −0.504626
\(317\) −10.0796 −0.566128 −0.283064 0.959101i \(-0.591351\pi\)
−0.283064 + 0.959101i \(0.591351\pi\)
\(318\) −1.37053 −0.0768553
\(319\) −3.04335 −0.170395
\(320\) −11.8806 −0.664146
\(321\) −3.80533 −0.212393
\(322\) 0.675949 0.0376692
\(323\) 13.3017 0.740125
\(324\) −1.11625 −0.0620141
\(325\) −1.19429 −0.0662475
\(326\) −12.7318 −0.705149
\(327\) −3.96810 −0.219437
\(328\) 1.20057 0.0662904
\(329\) 4.04817 0.223183
\(330\) 3.66735 0.201881
\(331\) −18.8863 −1.03808 −0.519042 0.854749i \(-0.673711\pi\)
−0.519042 + 0.854749i \(0.673711\pi\)
\(332\) −12.1533 −0.667001
\(333\) 2.13653 0.117081
\(334\) −5.45783 −0.298639
\(335\) −0.140692 −0.00768680
\(336\) −0.189474 −0.0103367
\(337\) −6.62308 −0.360782 −0.180391 0.983595i \(-0.557736\pi\)
−0.180391 + 0.983595i \(0.557736\pi\)
\(338\) 0.940078 0.0511335
\(339\) 1.14996 0.0624570
\(340\) −4.85554 −0.263329
\(341\) −12.3628 −0.669481
\(342\) −5.60807 −0.303250
\(343\) 5.03887 0.272074
\(344\) −31.6990 −1.70909
\(345\) −3.86053 −0.207844
\(346\) −9.26340 −0.498004
\(347\) −12.9059 −0.692824 −0.346412 0.938083i \(-0.612600\pi\)
−0.346412 + 0.938083i \(0.612600\pi\)
\(348\) −1.69881 −0.0910658
\(349\) −7.35854 −0.393894 −0.196947 0.980414i \(-0.563103\pi\)
−0.196947 + 0.980414i \(0.563103\pi\)
\(350\) 0.407939 0.0218053
\(351\) −1.00000 −0.0533761
\(352\) 10.7362 0.572240
\(353\) 22.9517 1.22160 0.610799 0.791786i \(-0.290848\pi\)
0.610799 + 0.791786i \(0.290848\pi\)
\(354\) 2.59288 0.137810
\(355\) −22.4213 −1.19000
\(356\) −9.54304 −0.505780
\(357\) −0.810173 −0.0428789
\(358\) −3.73276 −0.197283
\(359\) 35.4244 1.86963 0.934814 0.355138i \(-0.115566\pi\)
0.934814 + 0.355138i \(0.115566\pi\)
\(360\) 5.71497 0.301206
\(361\) 16.5876 0.873032
\(362\) 10.6934 0.562032
\(363\) 7.00110 0.367462
\(364\) 0.405586 0.0212585
\(365\) −21.0075 −1.09958
\(366\) 2.29203 0.119806
\(367\) −32.6938 −1.70660 −0.853301 0.521418i \(-0.825403\pi\)
−0.853301 + 0.521418i \(0.825403\pi\)
\(368\) 1.03195 0.0537943
\(369\) −0.409818 −0.0213343
\(370\) −3.91824 −0.203700
\(371\) −0.529717 −0.0275015
\(372\) −6.90093 −0.357797
\(373\) 2.27042 0.117558 0.0587789 0.998271i \(-0.481279\pi\)
0.0587789 + 0.998271i \(0.481279\pi\)
\(374\) −4.19171 −0.216748
\(375\) −12.0840 −0.624013
\(376\) 32.6389 1.68322
\(377\) −1.52189 −0.0783811
\(378\) 0.341574 0.0175686
\(379\) 16.7685 0.861340 0.430670 0.902509i \(-0.358277\pi\)
0.430670 + 0.902509i \(0.358277\pi\)
\(380\) −12.9906 −0.666405
\(381\) 4.69610 0.240588
\(382\) 14.9044 0.762576
\(383\) −6.32751 −0.323321 −0.161660 0.986846i \(-0.551685\pi\)
−0.161660 + 0.986846i \(0.551685\pi\)
\(384\) 5.01252 0.255794
\(385\) 1.41745 0.0722401
\(386\) −13.8113 −0.702975
\(387\) 10.8205 0.550038
\(388\) 14.9748 0.760233
\(389\) 17.5492 0.889782 0.444891 0.895585i \(-0.353242\pi\)
0.444891 + 0.895585i \(0.353242\pi\)
\(390\) 1.83392 0.0928644
\(391\) 4.41252 0.223151
\(392\) 20.1199 1.01621
\(393\) −4.34589 −0.219221
\(394\) 9.16988 0.461972
\(395\) −15.6772 −0.788805
\(396\) −2.23220 −0.112172
\(397\) 12.9479 0.649836 0.324918 0.945742i \(-0.394663\pi\)
0.324918 + 0.945742i \(0.394663\pi\)
\(398\) 20.9210 1.04868
\(399\) −2.16755 −0.108513
\(400\) 0.622789 0.0311395
\(401\) −25.5064 −1.27373 −0.636864 0.770976i \(-0.719769\pi\)
−0.636864 + 0.770976i \(0.719769\pi\)
\(402\) −0.0677976 −0.00338144
\(403\) −6.18222 −0.307959
\(404\) 7.09475 0.352977
\(405\) −1.95082 −0.0969371
\(406\) 0.519836 0.0257990
\(407\) 4.27248 0.211779
\(408\) −6.53212 −0.323388
\(409\) −16.8621 −0.833776 −0.416888 0.908958i \(-0.636879\pi\)
−0.416888 + 0.908958i \(0.636879\pi\)
\(410\) 0.751575 0.0371176
\(411\) −20.9667 −1.03421
\(412\) 1.11625 0.0549939
\(413\) 1.00216 0.0493132
\(414\) −1.86035 −0.0914310
\(415\) −21.2398 −1.04262
\(416\) 5.36882 0.263228
\(417\) −21.8389 −1.06945
\(418\) −11.2146 −0.548524
\(419\) 4.01833 0.196308 0.0981542 0.995171i \(-0.468706\pi\)
0.0981542 + 0.995171i \(0.468706\pi\)
\(420\) 0.791227 0.0386079
\(421\) −15.3640 −0.748794 −0.374397 0.927268i \(-0.622150\pi\)
−0.374397 + 0.927268i \(0.622150\pi\)
\(422\) 14.4145 0.701686
\(423\) −11.1414 −0.541712
\(424\) −4.27091 −0.207414
\(425\) 2.66298 0.129174
\(426\) −10.8046 −0.523484
\(427\) 0.885882 0.0428708
\(428\) −4.24771 −0.205321
\(429\) −1.99973 −0.0965477
\(430\) −19.8440 −0.956964
\(431\) −21.3395 −1.02789 −0.513945 0.857823i \(-0.671816\pi\)
−0.513945 + 0.857823i \(0.671816\pi\)
\(432\) 0.521471 0.0250893
\(433\) −4.61830 −0.221941 −0.110971 0.993824i \(-0.535396\pi\)
−0.110971 + 0.993824i \(0.535396\pi\)
\(434\) 2.11168 0.101364
\(435\) −2.96893 −0.142349
\(436\) −4.42941 −0.212130
\(437\) 11.8054 0.564727
\(438\) −10.1233 −0.483709
\(439\) 11.8407 0.565125 0.282562 0.959249i \(-0.408816\pi\)
0.282562 + 0.959249i \(0.408816\pi\)
\(440\) 11.4284 0.544827
\(441\) −6.86798 −0.327047
\(442\) −2.09614 −0.0997034
\(443\) −11.7872 −0.560028 −0.280014 0.959996i \(-0.590339\pi\)
−0.280014 + 0.959996i \(0.590339\pi\)
\(444\) 2.38491 0.113183
\(445\) −16.6779 −0.790609
\(446\) 10.4472 0.494690
\(447\) −18.1511 −0.858518
\(448\) −2.21280 −0.104545
\(449\) 1.56138 0.0736862 0.0368431 0.999321i \(-0.488270\pi\)
0.0368431 + 0.999321i \(0.488270\pi\)
\(450\) −1.12273 −0.0529259
\(451\) −0.819523 −0.0385898
\(452\) 1.28364 0.0603774
\(453\) −8.10513 −0.380812
\(454\) 1.58175 0.0742350
\(455\) 0.708823 0.0332302
\(456\) −17.4762 −0.818396
\(457\) 8.20490 0.383809 0.191905 0.981414i \(-0.438534\pi\)
0.191905 + 0.981414i \(0.438534\pi\)
\(458\) 20.4645 0.956244
\(459\) 2.22976 0.104076
\(460\) −4.30933 −0.200924
\(461\) 11.6349 0.541890 0.270945 0.962595i \(-0.412664\pi\)
0.270945 + 0.962595i \(0.412664\pi\)
\(462\) 0.683053 0.0317785
\(463\) 30.4947 1.41721 0.708605 0.705605i \(-0.249325\pi\)
0.708605 + 0.705605i \(0.249325\pi\)
\(464\) 0.793619 0.0368429
\(465\) −12.0604 −0.559289
\(466\) 26.0955 1.20885
\(467\) −24.8221 −1.14863 −0.574315 0.818634i \(-0.694732\pi\)
−0.574315 + 0.818634i \(0.694732\pi\)
\(468\) −1.11625 −0.0515988
\(469\) −0.0262042 −0.00121000
\(470\) 20.4324 0.942478
\(471\) 4.49931 0.207317
\(472\) 8.08007 0.371915
\(473\) 21.6381 0.994920
\(474\) −7.55465 −0.346997
\(475\) 7.12460 0.326899
\(476\) −0.904358 −0.0414512
\(477\) 1.45789 0.0667520
\(478\) −15.5237 −0.710039
\(479\) 33.8138 1.54499 0.772496 0.635019i \(-0.219008\pi\)
0.772496 + 0.635019i \(0.219008\pi\)
\(480\) 10.4736 0.478053
\(481\) 2.13653 0.0974175
\(482\) −15.5813 −0.709709
\(483\) −0.719035 −0.0327172
\(484\) 7.81500 0.355227
\(485\) 26.1708 1.18836
\(486\) −0.940078 −0.0426428
\(487\) −14.2467 −0.645580 −0.322790 0.946471i \(-0.604621\pi\)
−0.322790 + 0.946471i \(0.604621\pi\)
\(488\) 7.14253 0.323327
\(489\) 13.5433 0.612451
\(490\) 12.5954 0.569000
\(491\) 14.4413 0.651727 0.325864 0.945417i \(-0.394345\pi\)
0.325864 + 0.945417i \(0.394345\pi\)
\(492\) −0.457461 −0.0206239
\(493\) 3.39343 0.152833
\(494\) −5.60807 −0.252319
\(495\) −3.90111 −0.175342
\(496\) 3.22385 0.144755
\(497\) −4.17604 −0.187321
\(498\) −10.2352 −0.458650
\(499\) −8.54587 −0.382565 −0.191283 0.981535i \(-0.561265\pi\)
−0.191283 + 0.981535i \(0.561265\pi\)
\(500\) −13.4888 −0.603236
\(501\) 5.80573 0.259381
\(502\) −16.0557 −0.716603
\(503\) 39.4044 1.75696 0.878478 0.477783i \(-0.158559\pi\)
0.878478 + 0.477783i \(0.158559\pi\)
\(504\) 1.06443 0.0474135
\(505\) 12.3991 0.551755
\(506\) −3.72018 −0.165382
\(507\) −1.00000 −0.0444116
\(508\) 5.24204 0.232578
\(509\) −37.1959 −1.64868 −0.824340 0.566096i \(-0.808453\pi\)
−0.824340 + 0.566096i \(0.808453\pi\)
\(510\) −4.08920 −0.181073
\(511\) −3.91271 −0.173088
\(512\) −5.85501 −0.258757
\(513\) 5.96553 0.263385
\(514\) −14.0356 −0.619084
\(515\) 1.95082 0.0859635
\(516\) 12.0784 0.531724
\(517\) −22.2797 −0.979860
\(518\) −0.729783 −0.0320648
\(519\) 9.85387 0.432537
\(520\) 5.71497 0.250618
\(521\) 13.2940 0.582420 0.291210 0.956659i \(-0.405942\pi\)
0.291210 + 0.956659i \(0.405942\pi\)
\(522\) −1.43069 −0.0626196
\(523\) 9.08576 0.397292 0.198646 0.980071i \(-0.436346\pi\)
0.198646 + 0.980071i \(0.436346\pi\)
\(524\) −4.85112 −0.211922
\(525\) −0.433942 −0.0189388
\(526\) 23.4362 1.02187
\(527\) 13.7848 0.600477
\(528\) 1.04280 0.0453820
\(529\) −19.0838 −0.829733
\(530\) −2.67365 −0.116136
\(531\) −2.75815 −0.119694
\(532\) −2.41954 −0.104900
\(533\) −0.409818 −0.0177512
\(534\) −8.03689 −0.347790
\(535\) −7.42352 −0.320947
\(536\) −0.211274 −0.00912567
\(537\) 3.97070 0.171348
\(538\) −5.51724 −0.237865
\(539\) −13.7341 −0.591569
\(540\) −2.17761 −0.0937095
\(541\) −1.58666 −0.0682157 −0.0341078 0.999418i \(-0.510859\pi\)
−0.0341078 + 0.999418i \(0.510859\pi\)
\(542\) 16.1867 0.695280
\(543\) −11.3750 −0.488148
\(544\) −11.9712 −0.513259
\(545\) −7.74106 −0.331591
\(546\) 0.341574 0.0146180
\(547\) −3.55748 −0.152107 −0.0760534 0.997104i \(-0.524232\pi\)
−0.0760534 + 0.997104i \(0.524232\pi\)
\(548\) −23.4042 −0.999778
\(549\) −2.43812 −0.104057
\(550\) −2.24515 −0.0957335
\(551\) 9.07886 0.386772
\(552\) −5.79731 −0.246750
\(553\) −2.91992 −0.124168
\(554\) −9.80477 −0.416565
\(555\) 4.16799 0.176922
\(556\) −24.3777 −1.03385
\(557\) 29.0416 1.23053 0.615265 0.788320i \(-0.289049\pi\)
0.615265 + 0.788320i \(0.289049\pi\)
\(558\) −5.81177 −0.246032
\(559\) 10.8205 0.457659
\(560\) −0.369631 −0.0156198
\(561\) 4.45890 0.188255
\(562\) 18.1064 0.763771
\(563\) −4.84002 −0.203983 −0.101991 0.994785i \(-0.532521\pi\)
−0.101991 + 0.994785i \(0.532521\pi\)
\(564\) −12.4366 −0.523675
\(565\) 2.24336 0.0943788
\(566\) −13.4469 −0.565216
\(567\) −0.363346 −0.0152591
\(568\) −33.6698 −1.41275
\(569\) 2.20459 0.0924213 0.0462106 0.998932i \(-0.485285\pi\)
0.0462106 + 0.998932i \(0.485285\pi\)
\(570\) −10.9403 −0.458240
\(571\) −15.0088 −0.628100 −0.314050 0.949407i \(-0.601686\pi\)
−0.314050 + 0.949407i \(0.601686\pi\)
\(572\) −2.23220 −0.0933330
\(573\) −15.8544 −0.662329
\(574\) 0.139983 0.00584277
\(575\) 2.36342 0.0985614
\(576\) 6.09005 0.253752
\(577\) 26.0752 1.08553 0.542763 0.839886i \(-0.317378\pi\)
0.542763 + 0.839886i \(0.317378\pi\)
\(578\) −11.3074 −0.470327
\(579\) 14.6916 0.610563
\(580\) −3.31408 −0.137610
\(581\) −3.95597 −0.164121
\(582\) 12.6114 0.522759
\(583\) 2.91537 0.120742
\(584\) −31.5467 −1.30541
\(585\) −1.95082 −0.0806566
\(586\) 11.6053 0.479409
\(587\) 24.5676 1.01401 0.507006 0.861943i \(-0.330752\pi\)
0.507006 + 0.861943i \(0.330752\pi\)
\(588\) −7.66641 −0.316157
\(589\) 36.8803 1.51963
\(590\) 5.05824 0.208245
\(591\) −9.75438 −0.401242
\(592\) −1.11414 −0.0457909
\(593\) 24.1549 0.991921 0.495961 0.868345i \(-0.334816\pi\)
0.495961 + 0.868345i \(0.334816\pi\)
\(594\) −1.87990 −0.0771332
\(595\) −1.58050 −0.0647943
\(596\) −20.2612 −0.829932
\(597\) −22.2546 −0.910819
\(598\) −1.86035 −0.0760752
\(599\) −19.7524 −0.807061 −0.403530 0.914966i \(-0.632217\pi\)
−0.403530 + 0.914966i \(0.632217\pi\)
\(600\) −3.49871 −0.142834
\(601\) −36.9777 −1.50835 −0.754175 0.656673i \(-0.771963\pi\)
−0.754175 + 0.656673i \(0.771963\pi\)
\(602\) −3.69601 −0.150638
\(603\) 0.0721191 0.00293692
\(604\) −9.04738 −0.368133
\(605\) 13.6579 0.555272
\(606\) 5.97500 0.242718
\(607\) 25.8702 1.05004 0.525020 0.851090i \(-0.324058\pi\)
0.525020 + 0.851090i \(0.324058\pi\)
\(608\) −32.0279 −1.29890
\(609\) −0.552971 −0.0224075
\(610\) 4.47133 0.181039
\(611\) −11.1414 −0.450732
\(612\) 2.48897 0.100611
\(613\) 4.23254 0.170951 0.0854754 0.996340i \(-0.472759\pi\)
0.0854754 + 0.996340i \(0.472759\pi\)
\(614\) −25.3922 −1.02475
\(615\) −0.799482 −0.0322382
\(616\) 2.12857 0.0857624
\(617\) −27.6785 −1.11429 −0.557147 0.830414i \(-0.688104\pi\)
−0.557147 + 0.830414i \(0.688104\pi\)
\(618\) 0.940078 0.0378155
\(619\) 14.3567 0.577044 0.288522 0.957473i \(-0.406836\pi\)
0.288522 + 0.957473i \(0.406836\pi\)
\(620\) −13.4625 −0.540666
\(621\) 1.97893 0.0794116
\(622\) −28.4938 −1.14250
\(623\) −3.10631 −0.124452
\(624\) 0.521471 0.0208756
\(625\) −17.6022 −0.704088
\(626\) 0.546963 0.0218610
\(627\) 11.9294 0.476416
\(628\) 5.02237 0.200414
\(629\) −4.76394 −0.189951
\(630\) 0.666349 0.0265480
\(631\) −3.90054 −0.155278 −0.0776391 0.996982i \(-0.524738\pi\)
−0.0776391 + 0.996982i \(0.524738\pi\)
\(632\) −23.5422 −0.936459
\(633\) −15.3333 −0.609443
\(634\) −9.47563 −0.376325
\(635\) 9.16126 0.363553
\(636\) 1.62737 0.0645295
\(637\) −6.86798 −0.272119
\(638\) −2.86099 −0.113268
\(639\) 11.4933 0.454667
\(640\) 9.77853 0.386530
\(641\) 7.88596 0.311477 0.155738 0.987798i \(-0.450224\pi\)
0.155738 + 0.987798i \(0.450224\pi\)
\(642\) −3.57731 −0.141185
\(643\) 18.0104 0.710261 0.355131 0.934817i \(-0.384436\pi\)
0.355131 + 0.934817i \(0.384436\pi\)
\(644\) −0.802625 −0.0316279
\(645\) 21.1089 0.831163
\(646\) 12.5046 0.491988
\(647\) −1.54626 −0.0607899 −0.0303950 0.999538i \(-0.509677\pi\)
−0.0303950 + 0.999538i \(0.509677\pi\)
\(648\) −2.92952 −0.115082
\(649\) −5.51555 −0.216504
\(650\) −1.12273 −0.0440370
\(651\) −2.24629 −0.0880389
\(652\) 15.1178 0.592059
\(653\) −30.6869 −1.20087 −0.600435 0.799674i \(-0.705006\pi\)
−0.600435 + 0.799674i \(0.705006\pi\)
\(654\) −3.73033 −0.145867
\(655\) −8.47807 −0.331265
\(656\) 0.213708 0.00834390
\(657\) 10.7686 0.420121
\(658\) 3.80560 0.148358
\(659\) 6.68165 0.260280 0.130140 0.991496i \(-0.458457\pi\)
0.130140 + 0.991496i \(0.458457\pi\)
\(660\) −4.35463 −0.169504
\(661\) −19.1587 −0.745185 −0.372593 0.927995i \(-0.621531\pi\)
−0.372593 + 0.927995i \(0.621531\pi\)
\(662\) −17.7546 −0.690051
\(663\) 2.22976 0.0865965
\(664\) −31.8955 −1.23778
\(665\) −4.22851 −0.163975
\(666\) 2.00851 0.0778281
\(667\) 3.01170 0.116613
\(668\) 6.48066 0.250744
\(669\) −11.1131 −0.429659
\(670\) −0.132261 −0.00510969
\(671\) −4.87558 −0.188220
\(672\) 1.95074 0.0752514
\(673\) 17.6735 0.681263 0.340632 0.940197i \(-0.389359\pi\)
0.340632 + 0.940197i \(0.389359\pi\)
\(674\) −6.22621 −0.239825
\(675\) 1.19429 0.0459684
\(676\) −1.11625 −0.0429328
\(677\) 37.0818 1.42517 0.712584 0.701587i \(-0.247525\pi\)
0.712584 + 0.701587i \(0.247525\pi\)
\(678\) 1.08105 0.0415174
\(679\) 4.87439 0.187062
\(680\) −12.7430 −0.488672
\(681\) −1.68257 −0.0644762
\(682\) −11.6220 −0.445028
\(683\) 24.9633 0.955193 0.477597 0.878579i \(-0.341508\pi\)
0.477597 + 0.878579i \(0.341508\pi\)
\(684\) 6.65905 0.254615
\(685\) −40.9024 −1.56280
\(686\) 4.73693 0.180857
\(687\) −21.7690 −0.830538
\(688\) −5.64259 −0.215122
\(689\) 1.45789 0.0555411
\(690\) −3.62920 −0.138161
\(691\) 37.2090 1.41550 0.707748 0.706465i \(-0.249711\pi\)
0.707748 + 0.706465i \(0.249711\pi\)
\(692\) 10.9994 0.418135
\(693\) −0.726592 −0.0276010
\(694\) −12.1325 −0.460544
\(695\) −42.6037 −1.61605
\(696\) −4.45840 −0.168995
\(697\) 0.913793 0.0346124
\(698\) −6.91760 −0.261835
\(699\) −27.7588 −1.04993
\(700\) −0.484389 −0.0183082
\(701\) 5.78338 0.218435 0.109218 0.994018i \(-0.465165\pi\)
0.109218 + 0.994018i \(0.465165\pi\)
\(702\) −0.940078 −0.0354810
\(703\) −12.7456 −0.480708
\(704\) 12.1784 0.458992
\(705\) −21.7348 −0.818581
\(706\) 21.5764 0.812039
\(707\) 2.30938 0.0868530
\(708\) −3.07880 −0.115708
\(709\) −35.2990 −1.32568 −0.662841 0.748760i \(-0.730649\pi\)
−0.662841 + 0.748760i \(0.730649\pi\)
\(710\) −21.0778 −0.791036
\(711\) 8.03620 0.301381
\(712\) −25.0450 −0.938600
\(713\) 12.2342 0.458173
\(714\) −0.761625 −0.0285031
\(715\) −3.90111 −0.145893
\(716\) 4.43230 0.165643
\(717\) 16.5132 0.616698
\(718\) 33.3017 1.24281
\(719\) 28.8586 1.07624 0.538121 0.842867i \(-0.319134\pi\)
0.538121 + 0.842867i \(0.319134\pi\)
\(720\) 1.01730 0.0379124
\(721\) 0.363346 0.0135317
\(722\) 15.5936 0.580335
\(723\) 16.5745 0.616412
\(724\) −12.6974 −0.471895
\(725\) 1.81758 0.0675031
\(726\) 6.58158 0.244265
\(727\) 22.4518 0.832693 0.416346 0.909206i \(-0.363310\pi\)
0.416346 + 0.909206i \(0.363310\pi\)
\(728\) 1.06443 0.0394504
\(729\) 1.00000 0.0370370
\(730\) −19.7487 −0.730933
\(731\) −24.1271 −0.892374
\(732\) −2.72156 −0.100592
\(733\) 0.202654 0.00748521 0.00374261 0.999993i \(-0.498809\pi\)
0.00374261 + 0.999993i \(0.498809\pi\)
\(734\) −30.7347 −1.13444
\(735\) −13.3982 −0.494200
\(736\) −10.6245 −0.391624
\(737\) 0.144218 0.00531235
\(738\) −0.385261 −0.0141816
\(739\) −11.7675 −0.432873 −0.216437 0.976297i \(-0.569444\pi\)
−0.216437 + 0.976297i \(0.569444\pi\)
\(740\) 4.65254 0.171031
\(741\) 5.96553 0.219149
\(742\) −0.497975 −0.0182813
\(743\) 6.90155 0.253193 0.126597 0.991954i \(-0.459595\pi\)
0.126597 + 0.991954i \(0.459595\pi\)
\(744\) −18.1110 −0.663980
\(745\) −35.4096 −1.29731
\(746\) 2.13437 0.0781448
\(747\) 10.8876 0.398357
\(748\) 4.97726 0.181987
\(749\) −1.38265 −0.0505210
\(750\) −11.3599 −0.414804
\(751\) −43.7926 −1.59802 −0.799008 0.601320i \(-0.794642\pi\)
−0.799008 + 0.601320i \(0.794642\pi\)
\(752\) 5.80990 0.211865
\(753\) 17.0792 0.622399
\(754\) −1.43069 −0.0521027
\(755\) −15.8117 −0.575446
\(756\) −0.405586 −0.0147510
\(757\) 0.472591 0.0171766 0.00858830 0.999963i \(-0.497266\pi\)
0.00858830 + 0.999963i \(0.497266\pi\)
\(758\) 15.7637 0.572563
\(759\) 3.95731 0.143641
\(760\) −34.0929 −1.23668
\(761\) 31.2067 1.13124 0.565621 0.824665i \(-0.308636\pi\)
0.565621 + 0.824665i \(0.308636\pi\)
\(762\) 4.41470 0.159928
\(763\) −1.44179 −0.0521965
\(764\) −17.6976 −0.640276
\(765\) 4.34986 0.157269
\(766\) −5.94836 −0.214923
\(767\) −2.75815 −0.0995911
\(768\) 16.8923 0.609547
\(769\) 44.7549 1.61390 0.806951 0.590618i \(-0.201116\pi\)
0.806951 + 0.590618i \(0.201116\pi\)
\(770\) 1.33252 0.0480205
\(771\) 14.9303 0.537700
\(772\) 16.3996 0.590233
\(773\) 41.2095 1.48220 0.741101 0.671394i \(-0.234304\pi\)
0.741101 + 0.671394i \(0.234304\pi\)
\(774\) 10.1721 0.365630
\(775\) 7.38339 0.265219
\(776\) 39.3003 1.41080
\(777\) 0.776300 0.0278496
\(778\) 16.4977 0.591470
\(779\) 2.44478 0.0875934
\(780\) −2.17761 −0.0779710
\(781\) 22.9834 0.822411
\(782\) 4.14811 0.148336
\(783\) 1.52189 0.0543878
\(784\) 3.58145 0.127909
\(785\) 8.77735 0.313277
\(786\) −4.08548 −0.145724
\(787\) 24.8745 0.886680 0.443340 0.896354i \(-0.353794\pi\)
0.443340 + 0.896354i \(0.353794\pi\)
\(788\) −10.8884 −0.387882
\(789\) −24.9300 −0.887533
\(790\) −14.7378 −0.524347
\(791\) 0.417832 0.0148564
\(792\) −5.85824 −0.208163
\(793\) −2.43812 −0.0865803
\(794\) 12.1720 0.431969
\(795\) 2.84408 0.100869
\(796\) −24.8417 −0.880492
\(797\) −9.33618 −0.330704 −0.165352 0.986235i \(-0.552876\pi\)
−0.165352 + 0.986235i \(0.552876\pi\)
\(798\) −2.03767 −0.0721327
\(799\) 24.8425 0.878866
\(800\) −6.41194 −0.226696
\(801\) 8.54917 0.302070
\(802\) −23.9780 −0.846693
\(803\) 21.5341 0.759924
\(804\) 0.0805032 0.00283913
\(805\) −1.40271 −0.0494390
\(806\) −5.81177 −0.204711
\(807\) 5.86892 0.206596
\(808\) 18.6196 0.655036
\(809\) 37.5827 1.32134 0.660668 0.750678i \(-0.270273\pi\)
0.660668 + 0.750678i \(0.270273\pi\)
\(810\) −1.83392 −0.0644375
\(811\) −46.0354 −1.61652 −0.808260 0.588826i \(-0.799590\pi\)
−0.808260 + 0.588826i \(0.799590\pi\)
\(812\) −0.617256 −0.0216614
\(813\) −17.2185 −0.603880
\(814\) 4.01646 0.140777
\(815\) 26.4207 0.925475
\(816\) −1.16275 −0.0407045
\(817\) −64.5502 −2.25833
\(818\) −15.8517 −0.554241
\(819\) −0.363346 −0.0126963
\(820\) −0.892424 −0.0311648
\(821\) −3.55570 −0.124095 −0.0620473 0.998073i \(-0.519763\pi\)
−0.0620473 + 0.998073i \(0.519763\pi\)
\(822\) −19.7104 −0.687478
\(823\) 4.62255 0.161132 0.0805660 0.996749i \(-0.474327\pi\)
0.0805660 + 0.996749i \(0.474327\pi\)
\(824\) 2.92952 0.102055
\(825\) 2.38826 0.0831485
\(826\) 0.942112 0.0327803
\(827\) 24.9504 0.867612 0.433806 0.901006i \(-0.357170\pi\)
0.433806 + 0.901006i \(0.357170\pi\)
\(828\) 2.20898 0.0767675
\(829\) −18.3119 −0.636000 −0.318000 0.948091i \(-0.603011\pi\)
−0.318000 + 0.948091i \(0.603011\pi\)
\(830\) −19.9671 −0.693067
\(831\) 10.4297 0.361804
\(832\) 6.09005 0.211135
\(833\) 15.3139 0.530596
\(834\) −20.5302 −0.710904
\(835\) 11.3259 0.391950
\(836\) 13.3163 0.460553
\(837\) 6.18222 0.213689
\(838\) 3.77755 0.130493
\(839\) 19.2523 0.664663 0.332332 0.943163i \(-0.392165\pi\)
0.332332 + 0.943163i \(0.392165\pi\)
\(840\) 2.07651 0.0716465
\(841\) −26.6839 −0.920133
\(842\) −14.4433 −0.497750
\(843\) −19.2605 −0.663366
\(844\) −17.1158 −0.589151
\(845\) −1.95082 −0.0671103
\(846\) −10.4738 −0.360095
\(847\) 2.54382 0.0874067
\(848\) −0.760246 −0.0261069
\(849\) 14.3040 0.490913
\(850\) 2.50341 0.0858663
\(851\) −4.22804 −0.144935
\(852\) 12.8294 0.439529
\(853\) −52.3913 −1.79384 −0.896922 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(854\) 0.832798 0.0284978
\(855\) 11.6377 0.398001
\(856\) −11.1478 −0.381024
\(857\) 45.9744 1.57046 0.785228 0.619207i \(-0.212546\pi\)
0.785228 + 0.619207i \(0.212546\pi\)
\(858\) −1.87990 −0.0641787
\(859\) −13.0709 −0.445974 −0.222987 0.974821i \(-0.571581\pi\)
−0.222987 + 0.974821i \(0.571581\pi\)
\(860\) 23.5629 0.803488
\(861\) −0.148906 −0.00507469
\(862\) −20.0608 −0.683274
\(863\) −41.9159 −1.42683 −0.713417 0.700740i \(-0.752853\pi\)
−0.713417 + 0.700740i \(0.752853\pi\)
\(864\) −5.36882 −0.182651
\(865\) 19.2231 0.653606
\(866\) −4.34156 −0.147532
\(867\) 12.0282 0.408499
\(868\) −2.50743 −0.0851076
\(869\) 16.0702 0.545144
\(870\) −2.79102 −0.0946246
\(871\) 0.0721191 0.00244366
\(872\) −11.6246 −0.393660
\(873\) −13.4153 −0.454038
\(874\) 11.0980 0.375394
\(875\) −4.39066 −0.148431
\(876\) 12.0204 0.406133
\(877\) −24.9212 −0.841531 −0.420765 0.907170i \(-0.638238\pi\)
−0.420765 + 0.907170i \(0.638238\pi\)
\(878\) 11.1312 0.375659
\(879\) −12.3450 −0.416387
\(880\) 2.03432 0.0685768
\(881\) −16.9630 −0.571497 −0.285749 0.958305i \(-0.592242\pi\)
−0.285749 + 0.958305i \(0.592242\pi\)
\(882\) −6.45644 −0.217400
\(883\) −9.83390 −0.330937 −0.165469 0.986215i \(-0.552914\pi\)
−0.165469 + 0.986215i \(0.552914\pi\)
\(884\) 2.48897 0.0837132
\(885\) −5.38066 −0.180869
\(886\) −11.0809 −0.372270
\(887\) 25.0602 0.841438 0.420719 0.907191i \(-0.361778\pi\)
0.420719 + 0.907191i \(0.361778\pi\)
\(888\) 6.25902 0.210039
\(889\) 1.70631 0.0572278
\(890\) −15.6785 −0.525546
\(891\) 1.99973 0.0669933
\(892\) −12.4051 −0.415353
\(893\) 66.4642 2.22414
\(894\) −17.0635 −0.570687
\(895\) 7.74612 0.258924
\(896\) 1.82128 0.0608446
\(897\) 1.97893 0.0660744
\(898\) 1.46782 0.0489818
\(899\) 9.40864 0.313796
\(900\) 1.33313 0.0444378
\(901\) −3.25073 −0.108298
\(902\) −0.770416 −0.0256520
\(903\) 3.93159 0.130835
\(904\) 3.36882 0.112045
\(905\) −22.1906 −0.737641
\(906\) −7.61946 −0.253140
\(907\) 25.1854 0.836268 0.418134 0.908385i \(-0.362684\pi\)
0.418134 + 0.908385i \(0.362684\pi\)
\(908\) −1.87817 −0.0623294
\(909\) −6.35586 −0.210810
\(910\) 0.666349 0.0220893
\(911\) 16.1748 0.535896 0.267948 0.963433i \(-0.413655\pi\)
0.267948 + 0.963433i \(0.413655\pi\)
\(912\) −3.11085 −0.103011
\(913\) 21.7722 0.720556
\(914\) 7.71325 0.255132
\(915\) −4.75634 −0.157240
\(916\) −24.2997 −0.802884
\(917\) −1.57906 −0.0521453
\(918\) 2.09614 0.0691831
\(919\) −46.6478 −1.53877 −0.769385 0.638786i \(-0.779437\pi\)
−0.769385 + 0.638786i \(0.779437\pi\)
\(920\) −11.3095 −0.372864
\(921\) 27.0107 0.890033
\(922\) 10.9377 0.360214
\(923\) 11.4933 0.378306
\(924\) −0.811061 −0.0266820
\(925\) −2.55165 −0.0838976
\(926\) 28.6674 0.942070
\(927\) −1.00000 −0.0328443
\(928\) −8.17073 −0.268217
\(929\) −41.9061 −1.37489 −0.687447 0.726235i \(-0.741269\pi\)
−0.687447 + 0.726235i \(0.741269\pi\)
\(930\) −11.3377 −0.371779
\(931\) 40.9712 1.34278
\(932\) −30.9859 −1.01498
\(933\) 30.3100 0.992305
\(934\) −23.3347 −0.763535
\(935\) 8.69852 0.284472
\(936\) −2.92952 −0.0957544
\(937\) −19.0891 −0.623615 −0.311807 0.950145i \(-0.600934\pi\)
−0.311807 + 0.950145i \(0.600934\pi\)
\(938\) −0.0246340 −0.000804328 0
\(939\) −0.581827 −0.0189872
\(940\) −24.2616 −0.791326
\(941\) −48.5957 −1.58417 −0.792087 0.610408i \(-0.791006\pi\)
−0.792087 + 0.610408i \(0.791006\pi\)
\(942\) 4.22970 0.137811
\(943\) 0.810999 0.0264098
\(944\) 1.43830 0.0468126
\(945\) −0.708823 −0.0230580
\(946\) 20.3415 0.661359
\(947\) −24.1898 −0.786063 −0.393031 0.919525i \(-0.628574\pi\)
−0.393031 + 0.919525i \(0.628574\pi\)
\(948\) 8.97044 0.291346
\(949\) 10.7686 0.349562
\(950\) 6.69768 0.217301
\(951\) 10.0796 0.326854
\(952\) −2.37342 −0.0769229
\(953\) 22.1662 0.718033 0.359017 0.933331i \(-0.383112\pi\)
0.359017 + 0.933331i \(0.383112\pi\)
\(954\) 1.37053 0.0443724
\(955\) −30.9292 −1.00084
\(956\) 18.4330 0.596164
\(957\) 3.04335 0.0983777
\(958\) 31.7876 1.02701
\(959\) −7.61818 −0.246004
\(960\) 11.8806 0.383445
\(961\) 7.21990 0.232900
\(962\) 2.00851 0.0647569
\(963\) 3.80533 0.122625
\(964\) 18.5013 0.595888
\(965\) 28.6607 0.922622
\(966\) −0.675949 −0.0217483
\(967\) 10.2777 0.330510 0.165255 0.986251i \(-0.447155\pi\)
0.165255 + 0.986251i \(0.447155\pi\)
\(968\) 20.5099 0.659212
\(969\) −13.3017 −0.427312
\(970\) 24.6026 0.789942
\(971\) 22.4892 0.721713 0.360856 0.932621i \(-0.382484\pi\)
0.360856 + 0.932621i \(0.382484\pi\)
\(972\) 1.11625 0.0358038
\(973\) −7.93506 −0.254386
\(974\) −13.3930 −0.429140
\(975\) 1.19429 0.0382480
\(976\) 1.27141 0.0406969
\(977\) 46.0872 1.47446 0.737231 0.675641i \(-0.236133\pi\)
0.737231 + 0.675641i \(0.236133\pi\)
\(978\) 12.7318 0.407118
\(979\) 17.0960 0.546391
\(980\) −14.9558 −0.477745
\(981\) 3.96810 0.126692
\(982\) 13.5760 0.433226
\(983\) −0.0339864 −0.00108400 −0.000541999 1.00000i \(-0.500173\pi\)
−0.000541999 1.00000i \(0.500173\pi\)
\(984\) −1.20057 −0.0382728
\(985\) −19.0291 −0.606316
\(986\) 3.19009 0.101593
\(987\) −4.04817 −0.128855
\(988\) 6.65905 0.211853
\(989\) −21.4130 −0.680895
\(990\) −3.66735 −0.116556
\(991\) −23.4112 −0.743681 −0.371841 0.928297i \(-0.621273\pi\)
−0.371841 + 0.928297i \(0.621273\pi\)
\(992\) −33.1912 −1.05382
\(993\) 18.8863 0.599338
\(994\) −3.92580 −0.124519
\(995\) −43.4147 −1.37634
\(996\) 12.1533 0.385093
\(997\) 16.0225 0.507437 0.253718 0.967278i \(-0.418346\pi\)
0.253718 + 0.967278i \(0.418346\pi\)
\(998\) −8.03378 −0.254305
\(999\) −2.13653 −0.0675969
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 \(a_p\))