Properties

Label 4017.2.a.j.1.23
Level 4017
Weight 2
Character 4017.1
Self dual Yes
Analytic conductor 32.076
Analytic rank 0
Dimension 25
CM No

Related objects

Downloads

Learn more about

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 1.23
Character \(\chi\) = 4017.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.56785 q^{2} -1.00000 q^{3} +4.59383 q^{4} +0.753628 q^{5} -2.56785 q^{6} +4.02564 q^{7} +6.66055 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.56785 q^{2} -1.00000 q^{3} +4.59383 q^{4} +0.753628 q^{5} -2.56785 q^{6} +4.02564 q^{7} +6.66055 q^{8} +1.00000 q^{9} +1.93520 q^{10} -1.53272 q^{11} -4.59383 q^{12} +1.00000 q^{13} +10.3372 q^{14} -0.753628 q^{15} +7.91560 q^{16} +4.91511 q^{17} +2.56785 q^{18} -0.0697656 q^{19} +3.46204 q^{20} -4.02564 q^{21} -3.93579 q^{22} +6.24416 q^{23} -6.66055 q^{24} -4.43205 q^{25} +2.56785 q^{26} -1.00000 q^{27} +18.4931 q^{28} -1.50409 q^{29} -1.93520 q^{30} -5.24621 q^{31} +7.00494 q^{32} +1.53272 q^{33} +12.6213 q^{34} +3.03383 q^{35} +4.59383 q^{36} -9.76561 q^{37} -0.179147 q^{38} -1.00000 q^{39} +5.01957 q^{40} +0.427756 q^{41} -10.3372 q^{42} +8.14611 q^{43} -7.04105 q^{44} +0.753628 q^{45} +16.0340 q^{46} -4.93673 q^{47} -7.91560 q^{48} +9.20579 q^{49} -11.3808 q^{50} -4.91511 q^{51} +4.59383 q^{52} -0.860257 q^{53} -2.56785 q^{54} -1.15510 q^{55} +26.8130 q^{56} +0.0697656 q^{57} -3.86226 q^{58} -9.54775 q^{59} -3.46204 q^{60} +8.58629 q^{61} -13.4714 q^{62} +4.02564 q^{63} +2.15640 q^{64} +0.753628 q^{65} +3.93579 q^{66} +8.96869 q^{67} +22.5792 q^{68} -6.24416 q^{69} +7.79042 q^{70} +6.17201 q^{71} +6.66055 q^{72} -0.238197 q^{73} -25.0766 q^{74} +4.43205 q^{75} -0.320491 q^{76} -6.17018 q^{77} -2.56785 q^{78} -8.45410 q^{79} +5.96542 q^{80} +1.00000 q^{81} +1.09841 q^{82} -15.3727 q^{83} -18.4931 q^{84} +3.70417 q^{85} +20.9180 q^{86} +1.50409 q^{87} -10.2088 q^{88} +3.54954 q^{89} +1.93520 q^{90} +4.02564 q^{91} +28.6846 q^{92} +5.24621 q^{93} -12.6768 q^{94} -0.0525773 q^{95} -7.00494 q^{96} +9.72261 q^{97} +23.6390 q^{98} -1.53272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} + O(q^{10}) \) \( 25q + 6q^{2} - 25q^{3} + 28q^{4} + 7q^{5} - 6q^{6} + 17q^{7} + 21q^{8} + 25q^{9} - 6q^{10} + 21q^{11} - 28q^{12} + 25q^{13} + 10q^{14} - 7q^{15} + 30q^{16} + 14q^{17} + 6q^{18} + 12q^{19} + 24q^{20} - 17q^{21} + 3q^{22} + 41q^{23} - 21q^{24} + 30q^{25} + 6q^{26} - 25q^{27} + 14q^{28} + 22q^{29} + 6q^{30} + 14q^{31} + 28q^{32} - 21q^{33} - 11q^{34} + 14q^{35} + 28q^{36} - 6q^{37} + 16q^{38} - 25q^{39} - 34q^{40} + 33q^{41} - 10q^{42} + 35q^{43} + 45q^{44} + 7q^{45} + 3q^{46} + 48q^{47} - 30q^{48} - 4q^{49} + 7q^{50} - 14q^{51} + 28q^{52} + 18q^{53} - 6q^{54} + 10q^{55} + 32q^{56} - 12q^{57} + 33q^{58} + 46q^{59} - 24q^{60} - 19q^{61} + 5q^{62} + 17q^{63} + 29q^{64} + 7q^{65} - 3q^{66} + 16q^{67} + 20q^{68} - 41q^{69} - 43q^{70} + 60q^{71} + 21q^{72} - 14q^{73} - 50q^{74} - 30q^{75} + 59q^{77} - 6q^{78} + 7q^{79} + 32q^{80} + 25q^{81} + 18q^{82} + 23q^{83} - 14q^{84} - 9q^{85} - 9q^{86} - 22q^{87} + 23q^{88} + 10q^{89} - 6q^{90} + 17q^{91} + 69q^{92} - 14q^{93} - 30q^{94} + 81q^{95} - 28q^{96} - 10q^{97} + 55q^{98} + 21q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.56785 1.81574 0.907870 0.419251i \(-0.137707\pi\)
0.907870 + 0.419251i \(0.137707\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.59383 2.29691
\(5\) 0.753628 0.337032 0.168516 0.985699i \(-0.446102\pi\)
0.168516 + 0.985699i \(0.446102\pi\)
\(6\) −2.56785 −1.04832
\(7\) 4.02564 1.52155 0.760775 0.649016i \(-0.224819\pi\)
0.760775 + 0.649016i \(0.224819\pi\)
\(8\) 6.66055 2.35486
\(9\) 1.00000 0.333333
\(10\) 1.93520 0.611964
\(11\) −1.53272 −0.462133 −0.231066 0.972938i \(-0.574221\pi\)
−0.231066 + 0.972938i \(0.574221\pi\)
\(12\) −4.59383 −1.32612
\(13\) 1.00000 0.277350
\(14\) 10.3372 2.76274
\(15\) −0.753628 −0.194586
\(16\) 7.91560 1.97890
\(17\) 4.91511 1.19209 0.596045 0.802951i \(-0.296738\pi\)
0.596045 + 0.802951i \(0.296738\pi\)
\(18\) 2.56785 0.605247
\(19\) −0.0697656 −0.0160053 −0.00800267 0.999968i \(-0.502547\pi\)
−0.00800267 + 0.999968i \(0.502547\pi\)
\(20\) 3.46204 0.774135
\(21\) −4.02564 −0.878467
\(22\) −3.93579 −0.839113
\(23\) 6.24416 1.30200 0.650998 0.759079i \(-0.274351\pi\)
0.650998 + 0.759079i \(0.274351\pi\)
\(24\) −6.66055 −1.35958
\(25\) −4.43205 −0.886409
\(26\) 2.56785 0.503596
\(27\) −1.00000 −0.192450
\(28\) 18.4931 3.49487
\(29\) −1.50409 −0.279302 −0.139651 0.990201i \(-0.544598\pi\)
−0.139651 + 0.990201i \(0.544598\pi\)
\(30\) −1.93520 −0.353317
\(31\) −5.24621 −0.942246 −0.471123 0.882067i \(-0.656151\pi\)
−0.471123 + 0.882067i \(0.656151\pi\)
\(32\) 7.00494 1.23831
\(33\) 1.53272 0.266812
\(34\) 12.6213 2.16453
\(35\) 3.03383 0.512812
\(36\) 4.59383 0.765638
\(37\) −9.76561 −1.60546 −0.802728 0.596345i \(-0.796619\pi\)
−0.802728 + 0.596345i \(0.796619\pi\)
\(38\) −0.179147 −0.0290615
\(39\) −1.00000 −0.160128
\(40\) 5.01957 0.793664
\(41\) 0.427756 0.0668043 0.0334022 0.999442i \(-0.489366\pi\)
0.0334022 + 0.999442i \(0.489366\pi\)
\(42\) −10.3372 −1.59507
\(43\) 8.14611 1.24227 0.621135 0.783703i \(-0.286672\pi\)
0.621135 + 0.783703i \(0.286672\pi\)
\(44\) −7.04105 −1.06148
\(45\) 0.753628 0.112344
\(46\) 16.0340 2.36409
\(47\) −4.93673 −0.720096 −0.360048 0.932934i \(-0.617240\pi\)
−0.360048 + 0.932934i \(0.617240\pi\)
\(48\) −7.91560 −1.14252
\(49\) 9.20579 1.31511
\(50\) −11.3808 −1.60949
\(51\) −4.91511 −0.688254
\(52\) 4.59383 0.637049
\(53\) −0.860257 −0.118165 −0.0590827 0.998253i \(-0.518818\pi\)
−0.0590827 + 0.998253i \(0.518818\pi\)
\(54\) −2.56785 −0.349439
\(55\) −1.15510 −0.155754
\(56\) 26.8130 3.58304
\(57\) 0.0697656 0.00924068
\(58\) −3.86226 −0.507139
\(59\) −9.54775 −1.24301 −0.621505 0.783410i \(-0.713479\pi\)
−0.621505 + 0.783410i \(0.713479\pi\)
\(60\) −3.46204 −0.446947
\(61\) 8.58629 1.09936 0.549681 0.835375i \(-0.314749\pi\)
0.549681 + 0.835375i \(0.314749\pi\)
\(62\) −13.4714 −1.71088
\(63\) 4.02564 0.507183
\(64\) 2.15640 0.269551
\(65\) 0.753628 0.0934760
\(66\) 3.93579 0.484462
\(67\) 8.96869 1.09570 0.547850 0.836577i \(-0.315446\pi\)
0.547850 + 0.836577i \(0.315446\pi\)
\(68\) 22.5792 2.73813
\(69\) −6.24416 −0.751708
\(70\) 7.79042 0.931133
\(71\) 6.17201 0.732483 0.366242 0.930520i \(-0.380644\pi\)
0.366242 + 0.930520i \(0.380644\pi\)
\(72\) 6.66055 0.784953
\(73\) −0.238197 −0.0278788 −0.0139394 0.999903i \(-0.504437\pi\)
−0.0139394 + 0.999903i \(0.504437\pi\)
\(74\) −25.0766 −2.91509
\(75\) 4.43205 0.511769
\(76\) −0.320491 −0.0367629
\(77\) −6.17018 −0.703157
\(78\) −2.56785 −0.290751
\(79\) −8.45410 −0.951161 −0.475580 0.879672i \(-0.657762\pi\)
−0.475580 + 0.879672i \(0.657762\pi\)
\(80\) 5.96542 0.666954
\(81\) 1.00000 0.111111
\(82\) 1.09841 0.121299
\(83\) −15.3727 −1.68737 −0.843686 0.536838i \(-0.819619\pi\)
−0.843686 + 0.536838i \(0.819619\pi\)
\(84\) −18.4931 −2.01776
\(85\) 3.70417 0.401773
\(86\) 20.9180 2.25564
\(87\) 1.50409 0.161255
\(88\) −10.2088 −1.08826
\(89\) 3.54954 0.376250 0.188125 0.982145i \(-0.439759\pi\)
0.188125 + 0.982145i \(0.439759\pi\)
\(90\) 1.93520 0.203988
\(91\) 4.02564 0.422002
\(92\) 28.6846 2.99057
\(93\) 5.24621 0.544006
\(94\) −12.6768 −1.30751
\(95\) −0.0525773 −0.00539432
\(96\) −7.00494 −0.714939
\(97\) 9.72261 0.987181 0.493591 0.869694i \(-0.335684\pi\)
0.493591 + 0.869694i \(0.335684\pi\)
\(98\) 23.6390 2.38790
\(99\) −1.53272 −0.154044
\(100\) −20.3601 −2.03601
\(101\) 6.78390 0.675024 0.337512 0.941321i \(-0.390415\pi\)
0.337512 + 0.941321i \(0.390415\pi\)
\(102\) −12.6213 −1.24969
\(103\) −1.00000 −0.0985329
\(104\) 6.66055 0.653121
\(105\) −3.03383 −0.296072
\(106\) −2.20901 −0.214558
\(107\) 9.45117 0.913679 0.456839 0.889549i \(-0.348981\pi\)
0.456839 + 0.889549i \(0.348981\pi\)
\(108\) −4.59383 −0.442041
\(109\) −0.157687 −0.0151036 −0.00755182 0.999971i \(-0.502404\pi\)
−0.00755182 + 0.999971i \(0.502404\pi\)
\(110\) −2.96612 −0.282808
\(111\) 9.76561 0.926910
\(112\) 31.8654 3.01100
\(113\) −11.9407 −1.12328 −0.561642 0.827381i \(-0.689830\pi\)
−0.561642 + 0.827381i \(0.689830\pi\)
\(114\) 0.179147 0.0167787
\(115\) 4.70577 0.438815
\(116\) −6.90951 −0.641532
\(117\) 1.00000 0.0924500
\(118\) −24.5171 −2.25699
\(119\) 19.7865 1.81382
\(120\) −5.01957 −0.458222
\(121\) −8.65077 −0.786434
\(122\) 22.0483 1.99616
\(123\) −0.427756 −0.0385695
\(124\) −24.1002 −2.16426
\(125\) −7.10825 −0.635781
\(126\) 10.3372 0.920913
\(127\) −22.1645 −1.96678 −0.983390 0.181506i \(-0.941903\pi\)
−0.983390 + 0.181506i \(0.941903\pi\)
\(128\) −8.47258 −0.748877
\(129\) −8.14611 −0.717225
\(130\) 1.93520 0.169728
\(131\) −12.9047 −1.12749 −0.563746 0.825948i \(-0.690640\pi\)
−0.563746 + 0.825948i \(0.690640\pi\)
\(132\) 7.04105 0.612845
\(133\) −0.280851 −0.0243529
\(134\) 23.0302 1.98951
\(135\) −0.753628 −0.0648619
\(136\) 32.7374 2.80721
\(137\) 7.45335 0.636783 0.318391 0.947959i \(-0.396857\pi\)
0.318391 + 0.947959i \(0.396857\pi\)
\(138\) −16.0340 −1.36491
\(139\) 5.95099 0.504757 0.252378 0.967629i \(-0.418787\pi\)
0.252378 + 0.967629i \(0.418787\pi\)
\(140\) 13.9369 1.17788
\(141\) 4.93673 0.415748
\(142\) 15.8488 1.33000
\(143\) −1.53272 −0.128172
\(144\) 7.91560 0.659634
\(145\) −1.13352 −0.0941337
\(146\) −0.611652 −0.0506207
\(147\) −9.20579 −0.759281
\(148\) −44.8615 −3.68759
\(149\) 3.38143 0.277017 0.138509 0.990361i \(-0.455769\pi\)
0.138509 + 0.990361i \(0.455769\pi\)
\(150\) 11.3808 0.929239
\(151\) 7.38300 0.600820 0.300410 0.953810i \(-0.402876\pi\)
0.300410 + 0.953810i \(0.402876\pi\)
\(152\) −0.464677 −0.0376903
\(153\) 4.91511 0.397363
\(154\) −15.8441 −1.27675
\(155\) −3.95369 −0.317568
\(156\) −4.59383 −0.367801
\(157\) 21.4048 1.70829 0.854144 0.520036i \(-0.174082\pi\)
0.854144 + 0.520036i \(0.174082\pi\)
\(158\) −21.7088 −1.72706
\(159\) 0.860257 0.0682228
\(160\) 5.27912 0.417351
\(161\) 25.1367 1.98105
\(162\) 2.56785 0.201749
\(163\) 13.7063 1.07356 0.536780 0.843722i \(-0.319640\pi\)
0.536780 + 0.843722i \(0.319640\pi\)
\(164\) 1.96504 0.153444
\(165\) 1.15510 0.0899244
\(166\) −39.4747 −3.06383
\(167\) 15.9327 1.23291 0.616453 0.787391i \(-0.288569\pi\)
0.616453 + 0.787391i \(0.288569\pi\)
\(168\) −26.8130 −2.06867
\(169\) 1.00000 0.0769231
\(170\) 9.51172 0.729516
\(171\) −0.0697656 −0.00533511
\(172\) 37.4218 2.85339
\(173\) −19.6800 −1.49625 −0.748123 0.663560i \(-0.769045\pi\)
−0.748123 + 0.663560i \(0.769045\pi\)
\(174\) 3.86226 0.292797
\(175\) −17.8418 −1.34872
\(176\) −12.1324 −0.914514
\(177\) 9.54775 0.717653
\(178\) 9.11466 0.683173
\(179\) 13.0526 0.975596 0.487798 0.872956i \(-0.337800\pi\)
0.487798 + 0.872956i \(0.337800\pi\)
\(180\) 3.46204 0.258045
\(181\) −4.70882 −0.350004 −0.175002 0.984568i \(-0.555993\pi\)
−0.175002 + 0.984568i \(0.555993\pi\)
\(182\) 10.3372 0.766246
\(183\) −8.58629 −0.634717
\(184\) 41.5895 3.06602
\(185\) −7.35963 −0.541091
\(186\) 13.4714 0.987774
\(187\) −7.53349 −0.550904
\(188\) −22.6785 −1.65400
\(189\) −4.02564 −0.292822
\(190\) −0.135010 −0.00979468
\(191\) 20.7789 1.50351 0.751755 0.659443i \(-0.229208\pi\)
0.751755 + 0.659443i \(0.229208\pi\)
\(192\) −2.15640 −0.155625
\(193\) −13.9816 −1.00641 −0.503207 0.864166i \(-0.667847\pi\)
−0.503207 + 0.864166i \(0.667847\pi\)
\(194\) 24.9662 1.79247
\(195\) −0.753628 −0.0539684
\(196\) 42.2898 3.02070
\(197\) 24.4098 1.73912 0.869562 0.493824i \(-0.164401\pi\)
0.869562 + 0.493824i \(0.164401\pi\)
\(198\) −3.93579 −0.279704
\(199\) −9.54847 −0.676873 −0.338437 0.940989i \(-0.609898\pi\)
−0.338437 + 0.940989i \(0.609898\pi\)
\(200\) −29.5199 −2.08737
\(201\) −8.96869 −0.632603
\(202\) 17.4200 1.22567
\(203\) −6.05491 −0.424971
\(204\) −22.5792 −1.58086
\(205\) 0.322369 0.0225152
\(206\) −2.56785 −0.178910
\(207\) 6.24416 0.433999
\(208\) 7.91560 0.548848
\(209\) 0.106931 0.00739658
\(210\) −7.79042 −0.537590
\(211\) −8.76259 −0.603241 −0.301621 0.953428i \(-0.597528\pi\)
−0.301621 + 0.953428i \(0.597528\pi\)
\(212\) −3.95187 −0.271416
\(213\) −6.17201 −0.422899
\(214\) 24.2691 1.65900
\(215\) 6.13914 0.418686
\(216\) −6.66055 −0.453193
\(217\) −21.1193 −1.43367
\(218\) −0.404915 −0.0274243
\(219\) 0.238197 0.0160958
\(220\) −5.30633 −0.357753
\(221\) 4.91511 0.330626
\(222\) 25.0766 1.68303
\(223\) −10.3977 −0.696281 −0.348141 0.937442i \(-0.613187\pi\)
−0.348141 + 0.937442i \(0.613187\pi\)
\(224\) 28.1994 1.88415
\(225\) −4.43205 −0.295470
\(226\) −30.6618 −2.03959
\(227\) −13.9555 −0.926259 −0.463129 0.886291i \(-0.653273\pi\)
−0.463129 + 0.886291i \(0.653273\pi\)
\(228\) 0.320491 0.0212251
\(229\) −20.1645 −1.33250 −0.666252 0.745726i \(-0.732103\pi\)
−0.666252 + 0.745726i \(0.732103\pi\)
\(230\) 12.0837 0.796774
\(231\) 6.17018 0.405968
\(232\) −10.0180 −0.657716
\(233\) −11.2654 −0.738018 −0.369009 0.929426i \(-0.620303\pi\)
−0.369009 + 0.929426i \(0.620303\pi\)
\(234\) 2.56785 0.167865
\(235\) −3.72046 −0.242696
\(236\) −43.8607 −2.85509
\(237\) 8.45410 0.549153
\(238\) 50.8086 3.29343
\(239\) 21.3460 1.38076 0.690379 0.723448i \(-0.257444\pi\)
0.690379 + 0.723448i \(0.257444\pi\)
\(240\) −5.96542 −0.385066
\(241\) −9.34196 −0.601769 −0.300884 0.953661i \(-0.597282\pi\)
−0.300884 + 0.953661i \(0.597282\pi\)
\(242\) −22.2138 −1.42796
\(243\) −1.00000 −0.0641500
\(244\) 39.4440 2.52514
\(245\) 6.93774 0.443236
\(246\) −1.09841 −0.0700322
\(247\) −0.0697656 −0.00443908
\(248\) −34.9426 −2.21886
\(249\) 15.3727 0.974204
\(250\) −18.2529 −1.15441
\(251\) −25.1478 −1.58732 −0.793658 0.608364i \(-0.791826\pi\)
−0.793658 + 0.608364i \(0.791826\pi\)
\(252\) 18.4931 1.16496
\(253\) −9.57054 −0.601695
\(254\) −56.9150 −3.57116
\(255\) −3.70417 −0.231964
\(256\) −26.0691 −1.62932
\(257\) −7.81426 −0.487440 −0.243720 0.969846i \(-0.578368\pi\)
−0.243720 + 0.969846i \(0.578368\pi\)
\(258\) −20.9180 −1.30230
\(259\) −39.3128 −2.44278
\(260\) 3.46204 0.214706
\(261\) −1.50409 −0.0931006
\(262\) −33.1374 −2.04723
\(263\) 19.9147 1.22799 0.613996 0.789309i \(-0.289561\pi\)
0.613996 + 0.789309i \(0.289561\pi\)
\(264\) 10.2088 0.628306
\(265\) −0.648313 −0.0398256
\(266\) −0.721183 −0.0442186
\(267\) −3.54954 −0.217228
\(268\) 41.2006 2.51673
\(269\) −19.9305 −1.21518 −0.607591 0.794250i \(-0.707864\pi\)
−0.607591 + 0.794250i \(0.707864\pi\)
\(270\) −1.93520 −0.117772
\(271\) 1.68019 0.102064 0.0510322 0.998697i \(-0.483749\pi\)
0.0510322 + 0.998697i \(0.483749\pi\)
\(272\) 38.9061 2.35903
\(273\) −4.02564 −0.243643
\(274\) 19.1390 1.15623
\(275\) 6.79309 0.409638
\(276\) −28.6846 −1.72661
\(277\) −15.6127 −0.938075 −0.469038 0.883178i \(-0.655399\pi\)
−0.469038 + 0.883178i \(0.655399\pi\)
\(278\) 15.2812 0.916507
\(279\) −5.24621 −0.314082
\(280\) 20.2070 1.20760
\(281\) 9.76451 0.582502 0.291251 0.956647i \(-0.405929\pi\)
0.291251 + 0.956647i \(0.405929\pi\)
\(282\) 12.6768 0.754890
\(283\) −2.35538 −0.140013 −0.0700065 0.997547i \(-0.522302\pi\)
−0.0700065 + 0.997547i \(0.522302\pi\)
\(284\) 28.3532 1.68245
\(285\) 0.0525773 0.00311441
\(286\) −3.93579 −0.232728
\(287\) 1.72199 0.101646
\(288\) 7.00494 0.412770
\(289\) 7.15834 0.421079
\(290\) −2.91070 −0.170922
\(291\) −9.72261 −0.569949
\(292\) −1.09423 −0.0640352
\(293\) 12.9252 0.755101 0.377550 0.925989i \(-0.376767\pi\)
0.377550 + 0.925989i \(0.376767\pi\)
\(294\) −23.6390 −1.37866
\(295\) −7.19545 −0.418935
\(296\) −65.0443 −3.78062
\(297\) 1.53272 0.0889374
\(298\) 8.68299 0.502992
\(299\) 6.24416 0.361109
\(300\) 20.3601 1.17549
\(301\) 32.7933 1.89018
\(302\) 18.9584 1.09093
\(303\) −6.78390 −0.389725
\(304\) −0.552237 −0.0316730
\(305\) 6.47087 0.370521
\(306\) 12.6213 0.721509
\(307\) −7.02986 −0.401215 −0.200608 0.979672i \(-0.564292\pi\)
−0.200608 + 0.979672i \(0.564292\pi\)
\(308\) −28.3448 −1.61509
\(309\) 1.00000 0.0568880
\(310\) −10.1525 −0.576621
\(311\) 14.5830 0.826927 0.413464 0.910521i \(-0.364319\pi\)
0.413464 + 0.910521i \(0.364319\pi\)
\(312\) −6.66055 −0.377079
\(313\) 29.5782 1.67186 0.835929 0.548837i \(-0.184929\pi\)
0.835929 + 0.548837i \(0.184929\pi\)
\(314\) 54.9642 3.10181
\(315\) 3.03383 0.170937
\(316\) −38.8367 −2.18473
\(317\) 3.96422 0.222653 0.111326 0.993784i \(-0.464490\pi\)
0.111326 + 0.993784i \(0.464490\pi\)
\(318\) 2.20901 0.123875
\(319\) 2.30534 0.129074
\(320\) 1.62513 0.0908473
\(321\) −9.45117 −0.527513
\(322\) 64.5472 3.59708
\(323\) −0.342906 −0.0190798
\(324\) 4.59383 0.255213
\(325\) −4.43205 −0.245846
\(326\) 35.1957 1.94931
\(327\) 0.157687 0.00872009
\(328\) 2.84909 0.157315
\(329\) −19.8735 −1.09566
\(330\) 2.96612 0.163279
\(331\) 17.6719 0.971337 0.485668 0.874143i \(-0.338576\pi\)
0.485668 + 0.874143i \(0.338576\pi\)
\(332\) −70.6195 −3.87575
\(333\) −9.76561 −0.535152
\(334\) 40.9126 2.23864
\(335\) 6.75905 0.369286
\(336\) −31.8654 −1.73840
\(337\) −8.21093 −0.447278 −0.223639 0.974672i \(-0.571794\pi\)
−0.223639 + 0.974672i \(0.571794\pi\)
\(338\) 2.56785 0.139672
\(339\) 11.9407 0.648528
\(340\) 17.0163 0.922838
\(341\) 8.04097 0.435443
\(342\) −0.179147 −0.00968718
\(343\) 8.87972 0.479460
\(344\) 54.2576 2.92537
\(345\) −4.70577 −0.253350
\(346\) −50.5353 −2.71679
\(347\) −14.7394 −0.791250 −0.395625 0.918412i \(-0.629472\pi\)
−0.395625 + 0.918412i \(0.629472\pi\)
\(348\) 6.90951 0.370389
\(349\) −15.4725 −0.828226 −0.414113 0.910226i \(-0.635908\pi\)
−0.414113 + 0.910226i \(0.635908\pi\)
\(350\) −45.8150 −2.44892
\(351\) −1.00000 −0.0533761
\(352\) −10.7366 −0.572264
\(353\) −20.9194 −1.11343 −0.556713 0.830705i \(-0.687938\pi\)
−0.556713 + 0.830705i \(0.687938\pi\)
\(354\) 24.5171 1.30307
\(355\) 4.65140 0.246871
\(356\) 16.3060 0.864215
\(357\) −19.7865 −1.04721
\(358\) 33.5170 1.77143
\(359\) −0.351935 −0.0185744 −0.00928721 0.999957i \(-0.502956\pi\)
−0.00928721 + 0.999957i \(0.502956\pi\)
\(360\) 5.01957 0.264555
\(361\) −18.9951 −0.999744
\(362\) −12.0915 −0.635516
\(363\) 8.65077 0.454048
\(364\) 18.4931 0.969302
\(365\) −0.179512 −0.00939606
\(366\) −22.0483 −1.15248
\(367\) −29.1509 −1.52166 −0.760832 0.648949i \(-0.775209\pi\)
−0.760832 + 0.648949i \(0.775209\pi\)
\(368\) 49.4263 2.57652
\(369\) 0.427756 0.0222681
\(370\) −18.8984 −0.982481
\(371\) −3.46309 −0.179795
\(372\) 24.1002 1.24954
\(373\) −16.9152 −0.875836 −0.437918 0.899015i \(-0.644284\pi\)
−0.437918 + 0.899015i \(0.644284\pi\)
\(374\) −19.3448 −1.00030
\(375\) 7.10825 0.367068
\(376\) −32.8814 −1.69573
\(377\) −1.50409 −0.0774643
\(378\) −10.3372 −0.531689
\(379\) −0.978175 −0.0502455 −0.0251227 0.999684i \(-0.507998\pi\)
−0.0251227 + 0.999684i \(0.507998\pi\)
\(380\) −0.241531 −0.0123903
\(381\) 22.1645 1.13552
\(382\) 53.3570 2.72998
\(383\) 11.0540 0.564831 0.282416 0.959292i \(-0.408864\pi\)
0.282416 + 0.959292i \(0.408864\pi\)
\(384\) 8.47258 0.432364
\(385\) −4.65002 −0.236987
\(386\) −35.9025 −1.82739
\(387\) 8.14611 0.414090
\(388\) 44.6640 2.26747
\(389\) −4.64305 −0.235412 −0.117706 0.993048i \(-0.537554\pi\)
−0.117706 + 0.993048i \(0.537554\pi\)
\(390\) −1.93520 −0.0979926
\(391\) 30.6907 1.55210
\(392\) 61.3156 3.09691
\(393\) 12.9047 0.650958
\(394\) 62.6805 3.15780
\(395\) −6.37124 −0.320572
\(396\) −7.04105 −0.353826
\(397\) −26.8473 −1.34743 −0.673714 0.738992i \(-0.735302\pi\)
−0.673714 + 0.738992i \(0.735302\pi\)
\(398\) −24.5190 −1.22903
\(399\) 0.280851 0.0140602
\(400\) −35.0823 −1.75412
\(401\) 35.5655 1.77606 0.888029 0.459787i \(-0.152074\pi\)
0.888029 + 0.459787i \(0.152074\pi\)
\(402\) −23.0302 −1.14864
\(403\) −5.24621 −0.261332
\(404\) 31.1641 1.55047
\(405\) 0.753628 0.0374481
\(406\) −15.5481 −0.771638
\(407\) 14.9679 0.741933
\(408\) −32.7374 −1.62074
\(409\) 18.6967 0.924494 0.462247 0.886751i \(-0.347043\pi\)
0.462247 + 0.886751i \(0.347043\pi\)
\(410\) 0.827794 0.0408818
\(411\) −7.45335 −0.367647
\(412\) −4.59383 −0.226322
\(413\) −38.4358 −1.89130
\(414\) 16.0340 0.788029
\(415\) −11.5853 −0.568699
\(416\) 7.00494 0.343446
\(417\) −5.95099 −0.291421
\(418\) 0.274583 0.0134303
\(419\) −7.06660 −0.345226 −0.172613 0.984990i \(-0.555221\pi\)
−0.172613 + 0.984990i \(0.555221\pi\)
\(420\) −13.9369 −0.680052
\(421\) −5.73356 −0.279437 −0.139718 0.990191i \(-0.544620\pi\)
−0.139718 + 0.990191i \(0.544620\pi\)
\(422\) −22.5010 −1.09533
\(423\) −4.93673 −0.240032
\(424\) −5.72979 −0.278263
\(425\) −21.7840 −1.05668
\(426\) −15.8488 −0.767875
\(427\) 34.5653 1.67273
\(428\) 43.4170 2.09864
\(429\) 1.53272 0.0740004
\(430\) 15.7643 0.760224
\(431\) 28.0805 1.35259 0.676296 0.736630i \(-0.263584\pi\)
0.676296 + 0.736630i \(0.263584\pi\)
\(432\) −7.91560 −0.380840
\(433\) 1.14762 0.0551512 0.0275756 0.999620i \(-0.491221\pi\)
0.0275756 + 0.999620i \(0.491221\pi\)
\(434\) −54.2312 −2.60318
\(435\) 1.13352 0.0543481
\(436\) −0.724385 −0.0346917
\(437\) −0.435627 −0.0208389
\(438\) 0.611652 0.0292259
\(439\) −17.7511 −0.847212 −0.423606 0.905847i \(-0.639236\pi\)
−0.423606 + 0.905847i \(0.639236\pi\)
\(440\) −7.69360 −0.366778
\(441\) 9.20579 0.438371
\(442\) 12.6213 0.600332
\(443\) 9.73512 0.462530 0.231265 0.972891i \(-0.425714\pi\)
0.231265 + 0.972891i \(0.425714\pi\)
\(444\) 44.8615 2.12903
\(445\) 2.67503 0.126809
\(446\) −26.6997 −1.26427
\(447\) −3.38143 −0.159936
\(448\) 8.68091 0.410135
\(449\) 26.9762 1.27308 0.636542 0.771242i \(-0.280364\pi\)
0.636542 + 0.771242i \(0.280364\pi\)
\(450\) −11.3808 −0.536496
\(451\) −0.655631 −0.0308724
\(452\) −54.8534 −2.58009
\(453\) −7.38300 −0.346884
\(454\) −35.8355 −1.68185
\(455\) 3.03383 0.142228
\(456\) 0.464677 0.0217605
\(457\) −15.2298 −0.712421 −0.356210 0.934406i \(-0.615931\pi\)
−0.356210 + 0.934406i \(0.615931\pi\)
\(458\) −51.7792 −2.41948
\(459\) −4.91511 −0.229418
\(460\) 21.6175 1.00792
\(461\) −26.2141 −1.22091 −0.610457 0.792049i \(-0.709014\pi\)
−0.610457 + 0.792049i \(0.709014\pi\)
\(462\) 15.8441 0.737133
\(463\) −38.6214 −1.79489 −0.897445 0.441127i \(-0.854579\pi\)
−0.897445 + 0.441127i \(0.854579\pi\)
\(464\) −11.9057 −0.552710
\(465\) 3.95369 0.183348
\(466\) −28.9277 −1.34005
\(467\) 3.88345 0.179705 0.0898523 0.995955i \(-0.471360\pi\)
0.0898523 + 0.995955i \(0.471360\pi\)
\(468\) 4.59383 0.212350
\(469\) 36.1047 1.66716
\(470\) −9.55356 −0.440673
\(471\) −21.4048 −0.986281
\(472\) −63.5932 −2.92712
\(473\) −12.4857 −0.574094
\(474\) 21.7088 0.997119
\(475\) 0.309204 0.0141873
\(476\) 90.8957 4.16620
\(477\) −0.860257 −0.0393885
\(478\) 54.8132 2.50710
\(479\) 41.5638 1.89910 0.949550 0.313616i \(-0.101540\pi\)
0.949550 + 0.313616i \(0.101540\pi\)
\(480\) −5.27912 −0.240958
\(481\) −9.76561 −0.445273
\(482\) −23.9887 −1.09266
\(483\) −25.1367 −1.14376
\(484\) −39.7401 −1.80637
\(485\) 7.32723 0.332712
\(486\) −2.56785 −0.116480
\(487\) 32.8306 1.48770 0.743848 0.668349i \(-0.232999\pi\)
0.743848 + 0.668349i \(0.232999\pi\)
\(488\) 57.1894 2.58884
\(489\) −13.7063 −0.619820
\(490\) 17.8150 0.804801
\(491\) −4.04624 −0.182604 −0.0913022 0.995823i \(-0.529103\pi\)
−0.0913022 + 0.995823i \(0.529103\pi\)
\(492\) −1.96504 −0.0885908
\(493\) −7.39275 −0.332953
\(494\) −0.179147 −0.00806022
\(495\) −1.15510 −0.0519179
\(496\) −41.5269 −1.86461
\(497\) 24.8463 1.11451
\(498\) 39.4747 1.76890
\(499\) −29.9618 −1.34127 −0.670636 0.741786i \(-0.733979\pi\)
−0.670636 + 0.741786i \(0.733979\pi\)
\(500\) −32.6541 −1.46033
\(501\) −15.9327 −0.711819
\(502\) −64.5757 −2.88215
\(503\) 5.69578 0.253962 0.126981 0.991905i \(-0.459471\pi\)
0.126981 + 0.991905i \(0.459471\pi\)
\(504\) 26.8130 1.19435
\(505\) 5.11254 0.227505
\(506\) −24.5757 −1.09252
\(507\) −1.00000 −0.0444116
\(508\) −101.820 −4.51752
\(509\) 11.1028 0.492124 0.246062 0.969254i \(-0.420863\pi\)
0.246062 + 0.969254i \(0.420863\pi\)
\(510\) −9.51172 −0.421186
\(511\) −0.958894 −0.0424190
\(512\) −49.9962 −2.20954
\(513\) 0.0697656 0.00308023
\(514\) −20.0658 −0.885065
\(515\) −0.753628 −0.0332088
\(516\) −37.4218 −1.64740
\(517\) 7.56663 0.332780
\(518\) −100.949 −4.43546
\(519\) 19.6800 0.863858
\(520\) 5.01957 0.220123
\(521\) −18.9692 −0.831055 −0.415527 0.909581i \(-0.636403\pi\)
−0.415527 + 0.909581i \(0.636403\pi\)
\(522\) −3.86226 −0.169046
\(523\) −20.5439 −0.898321 −0.449161 0.893451i \(-0.648277\pi\)
−0.449161 + 0.893451i \(0.648277\pi\)
\(524\) −59.2821 −2.58975
\(525\) 17.8418 0.778681
\(526\) 51.1379 2.22972
\(527\) −25.7857 −1.12324
\(528\) 12.1324 0.527995
\(529\) 15.9895 0.695195
\(530\) −1.66477 −0.0723129
\(531\) −9.54775 −0.414337
\(532\) −1.29018 −0.0559365
\(533\) 0.427756 0.0185282
\(534\) −9.11466 −0.394430
\(535\) 7.12266 0.307939
\(536\) 59.7364 2.58022
\(537\) −13.0526 −0.563261
\(538\) −51.1784 −2.20646
\(539\) −14.1099 −0.607756
\(540\) −3.46204 −0.148982
\(541\) −20.8922 −0.898225 −0.449112 0.893475i \(-0.648260\pi\)
−0.449112 + 0.893475i \(0.648260\pi\)
\(542\) 4.31447 0.185322
\(543\) 4.70882 0.202075
\(544\) 34.4301 1.47618
\(545\) −0.118837 −0.00509041
\(546\) −10.3372 −0.442392
\(547\) −29.6638 −1.26833 −0.634166 0.773197i \(-0.718657\pi\)
−0.634166 + 0.773197i \(0.718657\pi\)
\(548\) 34.2394 1.46264
\(549\) 8.58629 0.366454
\(550\) 17.4436 0.743797
\(551\) 0.104933 0.00447032
\(552\) −41.5895 −1.77017
\(553\) −34.0332 −1.44724
\(554\) −40.0910 −1.70330
\(555\) 7.35963 0.312399
\(556\) 27.3378 1.15938
\(557\) −8.79439 −0.372630 −0.186315 0.982490i \(-0.559655\pi\)
−0.186315 + 0.982490i \(0.559655\pi\)
\(558\) −13.4714 −0.570292
\(559\) 8.14611 0.344544
\(560\) 24.0146 1.01480
\(561\) 7.53349 0.318064
\(562\) 25.0737 1.05767
\(563\) 9.31467 0.392567 0.196283 0.980547i \(-0.437113\pi\)
0.196283 + 0.980547i \(0.437113\pi\)
\(564\) 22.6785 0.954937
\(565\) −8.99881 −0.378583
\(566\) −6.04826 −0.254227
\(567\) 4.02564 0.169061
\(568\) 41.1090 1.72489
\(569\) −8.26466 −0.346472 −0.173236 0.984880i \(-0.555422\pi\)
−0.173236 + 0.984880i \(0.555422\pi\)
\(570\) 0.135010 0.00565496
\(571\) 36.8776 1.54328 0.771640 0.636059i \(-0.219437\pi\)
0.771640 + 0.636059i \(0.219437\pi\)
\(572\) −7.04105 −0.294401
\(573\) −20.7789 −0.868051
\(574\) 4.42181 0.184563
\(575\) −27.6744 −1.15410
\(576\) 2.15640 0.0898502
\(577\) −1.41656 −0.0589723 −0.0294862 0.999565i \(-0.509387\pi\)
−0.0294862 + 0.999565i \(0.509387\pi\)
\(578\) 18.3815 0.764570
\(579\) 13.9816 0.581053
\(580\) −5.20720 −0.216217
\(581\) −61.8849 −2.56742
\(582\) −24.9662 −1.03488
\(583\) 1.31853 0.0546081
\(584\) −1.58652 −0.0656507
\(585\) 0.753628 0.0311587
\(586\) 33.1900 1.37107
\(587\) −12.2617 −0.506093 −0.253046 0.967454i \(-0.581432\pi\)
−0.253046 + 0.967454i \(0.581432\pi\)
\(588\) −42.2898 −1.74400
\(589\) 0.366005 0.0150810
\(590\) −18.4768 −0.760677
\(591\) −24.4098 −1.00408
\(592\) −77.3007 −3.17704
\(593\) −42.0989 −1.72880 −0.864398 0.502809i \(-0.832300\pi\)
−0.864398 + 0.502809i \(0.832300\pi\)
\(594\) 3.93579 0.161487
\(595\) 14.9116 0.611318
\(596\) 15.5337 0.636285
\(597\) 9.54847 0.390793
\(598\) 16.0340 0.655680
\(599\) −12.5514 −0.512837 −0.256419 0.966566i \(-0.582543\pi\)
−0.256419 + 0.966566i \(0.582543\pi\)
\(600\) 29.5199 1.20514
\(601\) −37.6749 −1.53679 −0.768395 0.639976i \(-0.778944\pi\)
−0.768395 + 0.639976i \(0.778944\pi\)
\(602\) 84.2082 3.43207
\(603\) 8.96869 0.365233
\(604\) 33.9162 1.38003
\(605\) −6.51946 −0.265054
\(606\) −17.4200 −0.707640
\(607\) 17.4729 0.709202 0.354601 0.935018i \(-0.384617\pi\)
0.354601 + 0.935018i \(0.384617\pi\)
\(608\) −0.488704 −0.0198196
\(609\) 6.05491 0.245357
\(610\) 16.6162 0.672770
\(611\) −4.93673 −0.199719
\(612\) 22.5792 0.912710
\(613\) −35.6028 −1.43798 −0.718992 0.695019i \(-0.755396\pi\)
−0.718992 + 0.695019i \(0.755396\pi\)
\(614\) −18.0516 −0.728503
\(615\) −0.322369 −0.0129992
\(616\) −41.0968 −1.65584
\(617\) 27.1997 1.09502 0.547510 0.836799i \(-0.315576\pi\)
0.547510 + 0.836799i \(0.315576\pi\)
\(618\) 2.56785 0.103294
\(619\) 12.4081 0.498725 0.249362 0.968410i \(-0.419779\pi\)
0.249362 + 0.968410i \(0.419779\pi\)
\(620\) −18.1626 −0.729426
\(621\) −6.24416 −0.250569
\(622\) 37.4469 1.50149
\(623\) 14.2892 0.572483
\(624\) −7.91560 −0.316878
\(625\) 16.8033 0.672130
\(626\) 75.9522 3.03566
\(627\) −0.106931 −0.00427042
\(628\) 98.3299 3.92379
\(629\) −47.9991 −1.91385
\(630\) 7.79042 0.310378
\(631\) 34.9182 1.39007 0.695036 0.718975i \(-0.255388\pi\)
0.695036 + 0.718975i \(0.255388\pi\)
\(632\) −56.3090 −2.23985
\(633\) 8.76259 0.348282
\(634\) 10.1795 0.404279
\(635\) −16.7038 −0.662869
\(636\) 3.95187 0.156702
\(637\) 9.20579 0.364747
\(638\) 5.91976 0.234366
\(639\) 6.17201 0.244161
\(640\) −6.38517 −0.252396
\(641\) 20.8605 0.823941 0.411971 0.911197i \(-0.364841\pi\)
0.411971 + 0.911197i \(0.364841\pi\)
\(642\) −24.2691 −0.957826
\(643\) −8.84522 −0.348821 −0.174411 0.984673i \(-0.555802\pi\)
−0.174411 + 0.984673i \(0.555802\pi\)
\(644\) 115.474 4.55031
\(645\) −6.13914 −0.241728
\(646\) −0.880529 −0.0346440
\(647\) −8.15864 −0.320749 −0.160375 0.987056i \(-0.551270\pi\)
−0.160375 + 0.987056i \(0.551270\pi\)
\(648\) 6.66055 0.261651
\(649\) 14.6340 0.574436
\(650\) −11.3808 −0.446392
\(651\) 21.1193 0.827732
\(652\) 62.9644 2.46588
\(653\) −16.9131 −0.661862 −0.330931 0.943655i \(-0.607363\pi\)
−0.330931 + 0.943655i \(0.607363\pi\)
\(654\) 0.404915 0.0158334
\(655\) −9.72536 −0.380001
\(656\) 3.38595 0.132199
\(657\) −0.238197 −0.00929293
\(658\) −51.0321 −1.98944
\(659\) 22.7068 0.884530 0.442265 0.896884i \(-0.354175\pi\)
0.442265 + 0.896884i \(0.354175\pi\)
\(660\) 5.30633 0.206549
\(661\) 1.32046 0.0513598 0.0256799 0.999670i \(-0.491825\pi\)
0.0256799 + 0.999670i \(0.491825\pi\)
\(662\) 45.3788 1.76370
\(663\) −4.91511 −0.190887
\(664\) −102.391 −3.97352
\(665\) −0.211657 −0.00820772
\(666\) −25.0766 −0.971697
\(667\) −9.39174 −0.363650
\(668\) 73.1919 2.83188
\(669\) 10.3977 0.401998
\(670\) 17.3562 0.670528
\(671\) −13.1604 −0.508051
\(672\) −28.1994 −1.08782
\(673\) 14.1709 0.546246 0.273123 0.961979i \(-0.411943\pi\)
0.273123 + 0.961979i \(0.411943\pi\)
\(674\) −21.0844 −0.812140
\(675\) 4.43205 0.170590
\(676\) 4.59383 0.176686
\(677\) −33.5126 −1.28799 −0.643997 0.765028i \(-0.722725\pi\)
−0.643997 + 0.765028i \(0.722725\pi\)
\(678\) 30.6618 1.17756
\(679\) 39.1397 1.50205
\(680\) 24.6718 0.946119
\(681\) 13.9555 0.534776
\(682\) 20.6480 0.790651
\(683\) −16.9612 −0.649004 −0.324502 0.945885i \(-0.605197\pi\)
−0.324502 + 0.945885i \(0.605197\pi\)
\(684\) −0.320491 −0.0122543
\(685\) 5.61705 0.214616
\(686\) 22.8017 0.870575
\(687\) 20.1645 0.769322
\(688\) 64.4814 2.45833
\(689\) −0.860257 −0.0327732
\(690\) −12.0837 −0.460018
\(691\) −3.56530 −0.135631 −0.0678153 0.997698i \(-0.521603\pi\)
−0.0678153 + 0.997698i \(0.521603\pi\)
\(692\) −90.4067 −3.43675
\(693\) −6.17018 −0.234386
\(694\) −37.8484 −1.43670
\(695\) 4.48483 0.170119
\(696\) 10.0180 0.379733
\(697\) 2.10247 0.0796368
\(698\) −39.7311 −1.50384
\(699\) 11.2654 0.426095
\(700\) −81.9623 −3.09788
\(701\) 10.1457 0.383199 0.191600 0.981473i \(-0.438632\pi\)
0.191600 + 0.981473i \(0.438632\pi\)
\(702\) −2.56785 −0.0969171
\(703\) 0.681304 0.0256959
\(704\) −3.30516 −0.124568
\(705\) 3.72046 0.140121
\(706\) −53.7177 −2.02169
\(707\) 27.3096 1.02708
\(708\) 43.8607 1.64839
\(709\) 26.9164 1.01087 0.505434 0.862866i \(-0.331333\pi\)
0.505434 + 0.862866i \(0.331333\pi\)
\(710\) 11.9441 0.448253
\(711\) −8.45410 −0.317054
\(712\) 23.6419 0.886017
\(713\) −32.7581 −1.22680
\(714\) −50.8086 −1.90147
\(715\) −1.15510 −0.0431983
\(716\) 59.9613 2.24086
\(717\) −21.3460 −0.797181
\(718\) −0.903715 −0.0337263
\(719\) 34.8774 1.30071 0.650355 0.759631i \(-0.274620\pi\)
0.650355 + 0.759631i \(0.274620\pi\)
\(720\) 5.96542 0.222318
\(721\) −4.02564 −0.149923
\(722\) −48.7766 −1.81528
\(723\) 9.34196 0.347431
\(724\) −21.6315 −0.803929
\(725\) 6.66618 0.247576
\(726\) 22.2138 0.824433
\(727\) 1.83373 0.0680094 0.0340047 0.999422i \(-0.489174\pi\)
0.0340047 + 0.999422i \(0.489174\pi\)
\(728\) 26.8130 0.993755
\(729\) 1.00000 0.0370370
\(730\) −0.460958 −0.0170608
\(731\) 40.0391 1.48090
\(732\) −39.4440 −1.45789
\(733\) −37.1021 −1.37040 −0.685199 0.728356i \(-0.740285\pi\)
−0.685199 + 0.728356i \(0.740285\pi\)
\(734\) −74.8549 −2.76295
\(735\) −6.93774 −0.255902
\(736\) 43.7400 1.61228
\(737\) −13.7465 −0.506359
\(738\) 1.09841 0.0404331
\(739\) −10.6811 −0.392912 −0.196456 0.980513i \(-0.562943\pi\)
−0.196456 + 0.980513i \(0.562943\pi\)
\(740\) −33.8089 −1.24284
\(741\) 0.0697656 0.00256290
\(742\) −8.89267 −0.326460
\(743\) 25.5886 0.938755 0.469377 0.882998i \(-0.344478\pi\)
0.469377 + 0.882998i \(0.344478\pi\)
\(744\) 34.9426 1.28106
\(745\) 2.54834 0.0933639
\(746\) −43.4356 −1.59029
\(747\) −15.3727 −0.562457
\(748\) −34.6076 −1.26538
\(749\) 38.0470 1.39021
\(750\) 18.2529 0.666501
\(751\) −27.1942 −0.992329 −0.496165 0.868228i \(-0.665259\pi\)
−0.496165 + 0.868228i \(0.665259\pi\)
\(752\) −39.0772 −1.42500
\(753\) 25.1478 0.916437
\(754\) −3.86226 −0.140655
\(755\) 5.56403 0.202496
\(756\) −18.4931 −0.672588
\(757\) 36.5157 1.32719 0.663593 0.748094i \(-0.269031\pi\)
0.663593 + 0.748094i \(0.269031\pi\)
\(758\) −2.51180 −0.0912328
\(759\) 9.57054 0.347389
\(760\) −0.350194 −0.0127029
\(761\) 19.3220 0.700421 0.350211 0.936671i \(-0.386110\pi\)
0.350211 + 0.936671i \(0.386110\pi\)
\(762\) 56.9150 2.06181
\(763\) −0.634789 −0.0229809
\(764\) 95.4548 3.45343
\(765\) 3.70417 0.133924
\(766\) 28.3849 1.02559
\(767\) −9.54775 −0.344749
\(768\) 26.0691 0.940687
\(769\) 29.2293 1.05404 0.527018 0.849854i \(-0.323310\pi\)
0.527018 + 0.849854i \(0.323310\pi\)
\(770\) −11.9405 −0.430307
\(771\) 7.81426 0.281424
\(772\) −64.2288 −2.31165
\(773\) 2.57526 0.0926257 0.0463129 0.998927i \(-0.485253\pi\)
0.0463129 + 0.998927i \(0.485253\pi\)
\(774\) 20.9180 0.751880
\(775\) 23.2514 0.835216
\(776\) 64.7579 2.32467
\(777\) 39.3128 1.41034
\(778\) −11.9226 −0.427447
\(779\) −0.0298427 −0.00106923
\(780\) −3.46204 −0.123961
\(781\) −9.45997 −0.338504
\(782\) 78.8091 2.81821
\(783\) 1.50409 0.0537516
\(784\) 72.8694 2.60248
\(785\) 16.1312 0.575749
\(786\) 33.1374 1.18197
\(787\) 13.2448 0.472126 0.236063 0.971738i \(-0.424143\pi\)
0.236063 + 0.971738i \(0.424143\pi\)
\(788\) 112.134 3.99462
\(789\) −19.9147 −0.708982
\(790\) −16.3604 −0.582076
\(791\) −48.0688 −1.70913
\(792\) −10.2088 −0.362752
\(793\) 8.58629 0.304908
\(794\) −68.9398 −2.44658
\(795\) 0.648313 0.0229933
\(796\) −43.8640 −1.55472
\(797\) 1.15649 0.0409651 0.0204826 0.999790i \(-0.493480\pi\)
0.0204826 + 0.999790i \(0.493480\pi\)
\(798\) 0.721183 0.0255296
\(799\) −24.2646 −0.858420
\(800\) −31.0462 −1.09765
\(801\) 3.54954 0.125417
\(802\) 91.3268 3.22486
\(803\) 0.365089 0.0128837
\(804\) −41.2006 −1.45303
\(805\) 18.9437 0.667679
\(806\) −13.4714 −0.474511
\(807\) 19.9305 0.701586
\(808\) 45.1845 1.58959
\(809\) −34.3868 −1.20897 −0.604487 0.796615i \(-0.706622\pi\)
−0.604487 + 0.796615i \(0.706622\pi\)
\(810\) 1.93520 0.0679960
\(811\) −36.8430 −1.29373 −0.646866 0.762604i \(-0.723921\pi\)
−0.646866 + 0.762604i \(0.723921\pi\)
\(812\) −27.8152 −0.976123
\(813\) −1.68019 −0.0589269
\(814\) 38.4354 1.34716
\(815\) 10.3294 0.361825
\(816\) −38.9061 −1.36199
\(817\) −0.568319 −0.0198830
\(818\) 48.0103 1.67864
\(819\) 4.02564 0.140667
\(820\) 1.48091 0.0517155
\(821\) 29.8368 1.04131 0.520656 0.853767i \(-0.325688\pi\)
0.520656 + 0.853767i \(0.325688\pi\)
\(822\) −19.1390 −0.667551
\(823\) −7.22794 −0.251950 −0.125975 0.992033i \(-0.540206\pi\)
−0.125975 + 0.992033i \(0.540206\pi\)
\(824\) −6.66055 −0.232031
\(825\) −6.79309 −0.236505
\(826\) −98.6972 −3.43411
\(827\) 23.2046 0.806902 0.403451 0.915001i \(-0.367811\pi\)
0.403451 + 0.915001i \(0.367811\pi\)
\(828\) 28.6846 0.996858
\(829\) 17.2545 0.599275 0.299638 0.954053i \(-0.403134\pi\)
0.299638 + 0.954053i \(0.403134\pi\)
\(830\) −29.7492 −1.03261
\(831\) 15.6127 0.541598
\(832\) 2.15640 0.0747599
\(833\) 45.2475 1.56773
\(834\) −15.2812 −0.529146
\(835\) 12.0073 0.415530
\(836\) 0.491223 0.0169893
\(837\) 5.24621 0.181335
\(838\) −18.1459 −0.626841
\(839\) −14.9565 −0.516355 −0.258178 0.966097i \(-0.583122\pi\)
−0.258178 + 0.966097i \(0.583122\pi\)
\(840\) −20.2070 −0.697208
\(841\) −26.7377 −0.921991
\(842\) −14.7229 −0.507385
\(843\) −9.76451 −0.336307
\(844\) −40.2538 −1.38559
\(845\) 0.753628 0.0259256
\(846\) −12.6768 −0.435836
\(847\) −34.8249 −1.19660
\(848\) −6.80945 −0.233838
\(849\) 2.35538 0.0808366
\(850\) −55.9380 −1.91866
\(851\) −60.9780 −2.09030
\(852\) −28.3532 −0.971363
\(853\) −0.583746 −0.0199871 −0.00999355 0.999950i \(-0.503181\pi\)
−0.00999355 + 0.999950i \(0.503181\pi\)
\(854\) 88.7584 3.03725
\(855\) −0.0525773 −0.00179811
\(856\) 62.9500 2.15159
\(857\) 29.3409 1.00227 0.501133 0.865370i \(-0.332917\pi\)
0.501133 + 0.865370i \(0.332917\pi\)
\(858\) 3.93579 0.134366
\(859\) 33.5962 1.14629 0.573144 0.819455i \(-0.305724\pi\)
0.573144 + 0.819455i \(0.305724\pi\)
\(860\) 28.2021 0.961685
\(861\) −1.72199 −0.0586854
\(862\) 72.1065 2.45596
\(863\) 45.7565 1.55757 0.778786 0.627290i \(-0.215836\pi\)
0.778786 + 0.627290i \(0.215836\pi\)
\(864\) −7.00494 −0.238313
\(865\) −14.8314 −0.504283
\(866\) 2.94691 0.100140
\(867\) −7.15834 −0.243110
\(868\) −97.0187 −3.29303
\(869\) 12.9578 0.439562
\(870\) 2.91070 0.0986821
\(871\) 8.96869 0.303892
\(872\) −1.05028 −0.0355669
\(873\) 9.72261 0.329060
\(874\) −1.11862 −0.0378380
\(875\) −28.6153 −0.967372
\(876\) 1.09423 0.0369707
\(877\) −54.6191 −1.84436 −0.922178 0.386766i \(-0.873592\pi\)
−0.922178 + 0.386766i \(0.873592\pi\)
\(878\) −45.5820 −1.53832
\(879\) −12.9252 −0.435958
\(880\) −9.14331 −0.308221
\(881\) 1.34888 0.0454451 0.0227225 0.999742i \(-0.492767\pi\)
0.0227225 + 0.999742i \(0.492767\pi\)
\(882\) 23.6390 0.795968
\(883\) −32.7093 −1.10075 −0.550377 0.834916i \(-0.685516\pi\)
−0.550377 + 0.834916i \(0.685516\pi\)
\(884\) 22.5792 0.759420
\(885\) 7.19545 0.241872
\(886\) 24.9983 0.839834
\(887\) −58.2866 −1.95707 −0.978537 0.206072i \(-0.933932\pi\)
−0.978537 + 0.206072i \(0.933932\pi\)
\(888\) 65.0443 2.18274
\(889\) −89.2263 −2.99255
\(890\) 6.86906 0.230251
\(891\) −1.53272 −0.0513481
\(892\) −47.7652 −1.59930
\(893\) 0.344414 0.0115254
\(894\) −8.68299 −0.290403
\(895\) 9.83679 0.328808
\(896\) −34.1076 −1.13945
\(897\) −6.24416 −0.208486
\(898\) 69.2707 2.31159
\(899\) 7.89074 0.263171
\(900\) −20.3601 −0.678669
\(901\) −4.22826 −0.140864
\(902\) −1.68356 −0.0560564
\(903\) −32.7933 −1.09129
\(904\) −79.5314 −2.64517
\(905\) −3.54870 −0.117963
\(906\) −18.9584 −0.629851
\(907\) 36.4308 1.20966 0.604832 0.796353i \(-0.293240\pi\)
0.604832 + 0.796353i \(0.293240\pi\)
\(908\) −64.1091 −2.12754
\(909\) 6.78390 0.225008
\(910\) 7.79042 0.258250
\(911\) −39.2112 −1.29913 −0.649563 0.760308i \(-0.725048\pi\)
−0.649563 + 0.760308i \(0.725048\pi\)
\(912\) 0.552237 0.0182864
\(913\) 23.5620 0.779789
\(914\) −39.1078 −1.29357
\(915\) −6.47087 −0.213920
\(916\) −92.6320 −3.06065
\(917\) −51.9498 −1.71553
\(918\) −12.6213 −0.416563
\(919\) −33.8709 −1.11730 −0.558650 0.829404i \(-0.688680\pi\)
−0.558650 + 0.829404i \(0.688680\pi\)
\(920\) 31.3430 1.03335
\(921\) 7.02986 0.231642
\(922\) −67.3138 −2.21686
\(923\) 6.17201 0.203154
\(924\) 28.3448 0.932474
\(925\) 43.2816 1.42309
\(926\) −99.1738 −3.25905
\(927\) −1.00000 −0.0328443
\(928\) −10.5360 −0.345862
\(929\) 7.69768 0.252553 0.126276 0.991995i \(-0.459697\pi\)
0.126276 + 0.991995i \(0.459697\pi\)
\(930\) 10.1525 0.332912
\(931\) −0.642248 −0.0210488
\(932\) −51.7511 −1.69516
\(933\) −14.5830 −0.477427
\(934\) 9.97210 0.326297
\(935\) −5.67745 −0.185672
\(936\) 6.66055 0.217707
\(937\) 59.7890 1.95322 0.976611 0.215013i \(-0.0689794\pi\)
0.976611 + 0.215013i \(0.0689794\pi\)
\(938\) 92.7114 3.02713
\(939\) −29.5782 −0.965248
\(940\) −17.0911 −0.557452
\(941\) −22.5376 −0.734705 −0.367353 0.930082i \(-0.619736\pi\)
−0.367353 + 0.930082i \(0.619736\pi\)
\(942\) −54.9642 −1.79083
\(943\) 2.67098 0.0869790
\(944\) −75.5762 −2.45980
\(945\) −3.03383 −0.0986906
\(946\) −32.0614 −1.04241
\(947\) −11.6363 −0.378130 −0.189065 0.981965i \(-0.560546\pi\)
−0.189065 + 0.981965i \(0.560546\pi\)
\(948\) 38.8367 1.26136
\(949\) −0.238197 −0.00773219
\(950\) 0.793989 0.0257604
\(951\) −3.96422 −0.128549
\(952\) 131.789 4.27130
\(953\) −19.1906 −0.621644 −0.310822 0.950468i \(-0.600604\pi\)
−0.310822 + 0.950468i \(0.600604\pi\)
\(954\) −2.20901 −0.0715192
\(955\) 15.6596 0.506731
\(956\) 98.0599 3.17148
\(957\) −2.30534 −0.0745211
\(958\) 106.729 3.44827
\(959\) 30.0045 0.968896
\(960\) −1.62513 −0.0524507
\(961\) −3.47732 −0.112172
\(962\) −25.0766 −0.808501
\(963\) 9.45117 0.304560
\(964\) −42.9154 −1.38221
\(965\) −10.5369 −0.339194
\(966\) −64.5472 −2.07677
\(967\) 60.8434 1.95659 0.978296 0.207210i \(-0.0664383\pi\)
0.978296 + 0.207210i \(0.0664383\pi\)
\(968\) −57.6189 −1.85194
\(969\) 0.342906 0.0110157
\(970\) 18.8152 0.604119
\(971\) 4.53003 0.145375 0.0726877 0.997355i \(-0.476842\pi\)
0.0726877 + 0.997355i \(0.476842\pi\)
\(972\) −4.59383 −0.147347
\(973\) 23.9566 0.768012
\(974\) 84.3039 2.70127
\(975\) 4.43205 0.141939
\(976\) 67.9657 2.17553
\(977\) −29.2598 −0.936105 −0.468052 0.883701i \(-0.655044\pi\)
−0.468052 + 0.883701i \(0.655044\pi\)
\(978\) −35.1957 −1.12543
\(979\) −5.44045 −0.173877
\(980\) 31.8708 1.01807
\(981\) −0.157687 −0.00503454
\(982\) −10.3901 −0.331562
\(983\) 26.5529 0.846907 0.423453 0.905918i \(-0.360818\pi\)
0.423453 + 0.905918i \(0.360818\pi\)
\(984\) −2.84909 −0.0908258
\(985\) 18.3959 0.586141
\(986\) −18.9834 −0.604556
\(987\) 19.8735 0.632581
\(988\) −0.320491 −0.0101962
\(989\) 50.8656 1.61743
\(990\) −2.96612 −0.0942694
\(991\) 23.8623 0.758010 0.379005 0.925395i \(-0.376266\pi\)
0.379005 + 0.925395i \(0.376266\pi\)
\(992\) −36.7494 −1.16679
\(993\) −17.6719 −0.560802
\(994\) 63.8015 2.02366
\(995\) −7.19599 −0.228128
\(996\) 70.6195 2.23766
\(997\) −2.34842 −0.0743753 −0.0371876 0.999308i \(-0.511840\pi\)
−0.0371876 + 0.999308i \(0.511840\pi\)
\(998\) −76.9371 −2.43540
\(999\) 9.76561 0.308970
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 \(a_p\))