Properties

Label 8018.2.a.j.1.20
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
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: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-0.316697 q^{3}\) \(+1.00000 q^{4}\) \(-0.633871 q^{5}\) \(-0.316697 q^{6}\) \(+1.30218 q^{7}\) \(+1.00000 q^{8}\) \(-2.89970 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-0.316697 q^{3}\) \(+1.00000 q^{4}\) \(-0.633871 q^{5}\) \(-0.316697 q^{6}\) \(+1.30218 q^{7}\) \(+1.00000 q^{8}\) \(-2.89970 q^{9}\) \(-0.633871 q^{10}\) \(-3.28199 q^{11}\) \(-0.316697 q^{12}\) \(+2.72112 q^{13}\) \(+1.30218 q^{14}\) \(+0.200745 q^{15}\) \(+1.00000 q^{16}\) \(+7.85122 q^{17}\) \(-2.89970 q^{18}\) \(-1.00000 q^{19}\) \(-0.633871 q^{20}\) \(-0.412396 q^{21}\) \(-3.28199 q^{22}\) \(+5.94658 q^{23}\) \(-0.316697 q^{24}\) \(-4.59821 q^{25}\) \(+2.72112 q^{26}\) \(+1.86842 q^{27}\) \(+1.30218 q^{28}\) \(+4.86917 q^{29}\) \(+0.200745 q^{30}\) \(-10.3129 q^{31}\) \(+1.00000 q^{32}\) \(+1.03940 q^{33}\) \(+7.85122 q^{34}\) \(-0.825413 q^{35}\) \(-2.89970 q^{36}\) \(+6.38504 q^{37}\) \(-1.00000 q^{38}\) \(-0.861770 q^{39}\) \(-0.633871 q^{40}\) \(+6.73152 q^{41}\) \(-0.412396 q^{42}\) \(-8.64507 q^{43}\) \(-3.28199 q^{44}\) \(+1.83804 q^{45}\) \(+5.94658 q^{46}\) \(-4.92688 q^{47}\) \(-0.316697 q^{48}\) \(-5.30433 q^{49}\) \(-4.59821 q^{50}\) \(-2.48646 q^{51}\) \(+2.72112 q^{52}\) \(+6.78791 q^{53}\) \(+1.86842 q^{54}\) \(+2.08036 q^{55}\) \(+1.30218 q^{56}\) \(+0.316697 q^{57}\) \(+4.86917 q^{58}\) \(+6.46212 q^{59}\) \(+0.200745 q^{60}\) \(+8.88569 q^{61}\) \(-10.3129 q^{62}\) \(-3.77593 q^{63}\) \(+1.00000 q^{64}\) \(-1.72484 q^{65}\) \(+1.03940 q^{66}\) \(-9.62712 q^{67}\) \(+7.85122 q^{68}\) \(-1.88326 q^{69}\) \(-0.825413 q^{70}\) \(-15.4994 q^{71}\) \(-2.89970 q^{72}\) \(+11.9836 q^{73}\) \(+6.38504 q^{74}\) \(+1.45624 q^{75}\) \(-1.00000 q^{76}\) \(-4.27374 q^{77}\) \(-0.861770 q^{78}\) \(-10.1395 q^{79}\) \(-0.633871 q^{80}\) \(+8.10739 q^{81}\) \(+6.73152 q^{82}\) \(+9.02471 q^{83}\) \(-0.412396 q^{84}\) \(-4.97666 q^{85}\) \(-8.64507 q^{86}\) \(-1.54205 q^{87}\) \(-3.28199 q^{88}\) \(+1.81210 q^{89}\) \(+1.83804 q^{90}\) \(+3.54339 q^{91}\) \(+5.94658 q^{92}\) \(+3.26607 q^{93}\) \(-4.92688 q^{94}\) \(+0.633871 q^{95}\) \(-0.316697 q^{96}\) \(+11.7199 q^{97}\) \(-5.30433 q^{98}\) \(+9.51681 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.316697 −0.182845 −0.0914224 0.995812i \(-0.529141\pi\)
−0.0914224 + 0.995812i \(0.529141\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.633871 −0.283476 −0.141738 0.989904i \(-0.545269\pi\)
−0.141738 + 0.989904i \(0.545269\pi\)
\(6\) −0.316697 −0.129291
\(7\) 1.30218 0.492177 0.246089 0.969247i \(-0.420855\pi\)
0.246089 + 0.969247i \(0.420855\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.89970 −0.966568
\(10\) −0.633871 −0.200448
\(11\) −3.28199 −0.989559 −0.494779 0.869019i \(-0.664751\pi\)
−0.494779 + 0.869019i \(0.664751\pi\)
\(12\) −0.316697 −0.0914224
\(13\) 2.72112 0.754704 0.377352 0.926070i \(-0.376835\pi\)
0.377352 + 0.926070i \(0.376835\pi\)
\(14\) 1.30218 0.348022
\(15\) 0.200745 0.0518321
\(16\) 1.00000 0.250000
\(17\) 7.85122 1.90420 0.952101 0.305785i \(-0.0989187\pi\)
0.952101 + 0.305785i \(0.0989187\pi\)
\(18\) −2.89970 −0.683467
\(19\) −1.00000 −0.229416
\(20\) −0.633871 −0.141738
\(21\) −0.412396 −0.0899921
\(22\) −3.28199 −0.699724
\(23\) 5.94658 1.23995 0.619973 0.784623i \(-0.287143\pi\)
0.619973 + 0.784623i \(0.287143\pi\)
\(24\) −0.316697 −0.0646454
\(25\) −4.59821 −0.919642
\(26\) 2.72112 0.533656
\(27\) 1.86842 0.359577
\(28\) 1.30218 0.246089
\(29\) 4.86917 0.904182 0.452091 0.891972i \(-0.350678\pi\)
0.452091 + 0.891972i \(0.350678\pi\)
\(30\) 0.200745 0.0366508
\(31\) −10.3129 −1.85225 −0.926127 0.377211i \(-0.876883\pi\)
−0.926127 + 0.377211i \(0.876883\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.03940 0.180936
\(34\) 7.85122 1.34647
\(35\) −0.825413 −0.139520
\(36\) −2.89970 −0.483284
\(37\) 6.38504 1.04969 0.524847 0.851196i \(-0.324122\pi\)
0.524847 + 0.851196i \(0.324122\pi\)
\(38\) −1.00000 −0.162221
\(39\) −0.861770 −0.137994
\(40\) −0.633871 −0.100224
\(41\) 6.73152 1.05129 0.525643 0.850705i \(-0.323825\pi\)
0.525643 + 0.850705i \(0.323825\pi\)
\(42\) −0.412396 −0.0636340
\(43\) −8.64507 −1.31836 −0.659180 0.751985i \(-0.729097\pi\)
−0.659180 + 0.751985i \(0.729097\pi\)
\(44\) −3.28199 −0.494779
\(45\) 1.83804 0.273998
\(46\) 5.94658 0.876775
\(47\) −4.92688 −0.718660 −0.359330 0.933211i \(-0.616995\pi\)
−0.359330 + 0.933211i \(0.616995\pi\)
\(48\) −0.316697 −0.0457112
\(49\) −5.30433 −0.757761
\(50\) −4.59821 −0.650285
\(51\) −2.48646 −0.348173
\(52\) 2.72112 0.377352
\(53\) 6.78791 0.932391 0.466195 0.884682i \(-0.345624\pi\)
0.466195 + 0.884682i \(0.345624\pi\)
\(54\) 1.86842 0.254259
\(55\) 2.08036 0.280516
\(56\) 1.30218 0.174011
\(57\) 0.316697 0.0419475
\(58\) 4.86917 0.639353
\(59\) 6.46212 0.841297 0.420648 0.907224i \(-0.361803\pi\)
0.420648 + 0.907224i \(0.361803\pi\)
\(60\) 0.200745 0.0259160
\(61\) 8.88569 1.13770 0.568848 0.822443i \(-0.307389\pi\)
0.568848 + 0.822443i \(0.307389\pi\)
\(62\) −10.3129 −1.30974
\(63\) −3.77593 −0.475723
\(64\) 1.00000 0.125000
\(65\) −1.72484 −0.213940
\(66\) 1.03940 0.127941
\(67\) −9.62712 −1.17614 −0.588070 0.808810i \(-0.700112\pi\)
−0.588070 + 0.808810i \(0.700112\pi\)
\(68\) 7.85122 0.952101
\(69\) −1.88326 −0.226718
\(70\) −0.825413 −0.0986558
\(71\) −15.4994 −1.83944 −0.919721 0.392571i \(-0.871586\pi\)
−0.919721 + 0.392571i \(0.871586\pi\)
\(72\) −2.89970 −0.341733
\(73\) 11.9836 1.40258 0.701290 0.712876i \(-0.252608\pi\)
0.701290 + 0.712876i \(0.252608\pi\)
\(74\) 6.38504 0.742246
\(75\) 1.45624 0.168152
\(76\) −1.00000 −0.114708
\(77\) −4.27374 −0.487038
\(78\) −0.861770 −0.0975762
\(79\) −10.1395 −1.14079 −0.570393 0.821372i \(-0.693209\pi\)
−0.570393 + 0.821372i \(0.693209\pi\)
\(80\) −0.633871 −0.0708689
\(81\) 8.10739 0.900821
\(82\) 6.73152 0.743372
\(83\) 9.02471 0.990590 0.495295 0.868725i \(-0.335060\pi\)
0.495295 + 0.868725i \(0.335060\pi\)
\(84\) −0.412396 −0.0449961
\(85\) −4.97666 −0.539795
\(86\) −8.64507 −0.932221
\(87\) −1.54205 −0.165325
\(88\) −3.28199 −0.349862
\(89\) 1.81210 0.192082 0.0960411 0.995377i \(-0.469382\pi\)
0.0960411 + 0.995377i \(0.469382\pi\)
\(90\) 1.83804 0.193746
\(91\) 3.54339 0.371448
\(92\) 5.94658 0.619973
\(93\) 3.26607 0.338675
\(94\) −4.92688 −0.508169
\(95\) 0.633871 0.0650338
\(96\) −0.316697 −0.0323227
\(97\) 11.7199 1.18998 0.594989 0.803734i \(-0.297156\pi\)
0.594989 + 0.803734i \(0.297156\pi\)
\(98\) −5.30433 −0.535818
\(99\) 9.51681 0.956475
\(100\) −4.59821 −0.459821
\(101\) −8.56010 −0.851761 −0.425881 0.904779i \(-0.640036\pi\)
−0.425881 + 0.904779i \(0.640036\pi\)
\(102\) −2.48646 −0.246196
\(103\) 14.5743 1.43605 0.718024 0.696018i \(-0.245047\pi\)
0.718024 + 0.696018i \(0.245047\pi\)
\(104\) 2.72112 0.266828
\(105\) 0.261406 0.0255106
\(106\) 6.78791 0.659300
\(107\) 0.0386434 0.00373580 0.00186790 0.999998i \(-0.499405\pi\)
0.00186790 + 0.999998i \(0.499405\pi\)
\(108\) 1.86842 0.179788
\(109\) −10.5277 −1.00837 −0.504187 0.863594i \(-0.668208\pi\)
−0.504187 + 0.863594i \(0.668208\pi\)
\(110\) 2.08036 0.198355
\(111\) −2.02212 −0.191931
\(112\) 1.30218 0.123044
\(113\) 9.61364 0.904375 0.452188 0.891923i \(-0.350644\pi\)
0.452188 + 0.891923i \(0.350644\pi\)
\(114\) 0.316697 0.0296613
\(115\) −3.76936 −0.351495
\(116\) 4.86917 0.452091
\(117\) −7.89045 −0.729472
\(118\) 6.46212 0.594887
\(119\) 10.2237 0.937205
\(120\) 0.200745 0.0183254
\(121\) −0.228513 −0.0207739
\(122\) 8.88569 0.804473
\(123\) −2.13185 −0.192222
\(124\) −10.3129 −0.926127
\(125\) 6.08402 0.544172
\(126\) −3.77593 −0.336387
\(127\) −1.39508 −0.123793 −0.0618967 0.998083i \(-0.519715\pi\)
−0.0618967 + 0.998083i \(0.519715\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.73786 0.241055
\(130\) −1.72484 −0.151278
\(131\) −9.10667 −0.795653 −0.397827 0.917461i \(-0.630235\pi\)
−0.397827 + 0.917461i \(0.630235\pi\)
\(132\) 1.03940 0.0904678
\(133\) −1.30218 −0.112913
\(134\) −9.62712 −0.831656
\(135\) −1.18433 −0.101931
\(136\) 7.85122 0.673237
\(137\) 22.7634 1.94481 0.972405 0.233298i \(-0.0749517\pi\)
0.972405 + 0.233298i \(0.0749517\pi\)
\(138\) −1.88326 −0.160314
\(139\) 17.9297 1.52077 0.760387 0.649470i \(-0.225009\pi\)
0.760387 + 0.649470i \(0.225009\pi\)
\(140\) −0.825413 −0.0697602
\(141\) 1.56033 0.131403
\(142\) −15.4994 −1.30068
\(143\) −8.93071 −0.746823
\(144\) −2.89970 −0.241642
\(145\) −3.08642 −0.256314
\(146\) 11.9836 0.991774
\(147\) 1.67986 0.138553
\(148\) 6.38504 0.524847
\(149\) 12.6405 1.03555 0.517775 0.855517i \(-0.326760\pi\)
0.517775 + 0.855517i \(0.326760\pi\)
\(150\) 1.45624 0.118901
\(151\) 21.7335 1.76865 0.884324 0.466875i \(-0.154620\pi\)
0.884324 + 0.466875i \(0.154620\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −22.7662 −1.84054
\(154\) −4.27374 −0.344388
\(155\) 6.53706 0.525069
\(156\) −0.861770 −0.0689968
\(157\) 6.16246 0.491818 0.245909 0.969293i \(-0.420914\pi\)
0.245909 + 0.969293i \(0.420914\pi\)
\(158\) −10.1395 −0.806658
\(159\) −2.14971 −0.170483
\(160\) −0.633871 −0.0501119
\(161\) 7.74351 0.610274
\(162\) 8.10739 0.636977
\(163\) −11.7577 −0.920934 −0.460467 0.887677i \(-0.652318\pi\)
−0.460467 + 0.887677i \(0.652318\pi\)
\(164\) 6.73152 0.525643
\(165\) −0.658843 −0.0512909
\(166\) 9.02471 0.700453
\(167\) −5.50355 −0.425877 −0.212939 0.977066i \(-0.568303\pi\)
−0.212939 + 0.977066i \(0.568303\pi\)
\(168\) −0.412396 −0.0318170
\(169\) −5.59549 −0.430423
\(170\) −4.97666 −0.381693
\(171\) 2.89970 0.221746
\(172\) −8.64507 −0.659180
\(173\) 13.2067 1.00409 0.502044 0.864842i \(-0.332582\pi\)
0.502044 + 0.864842i \(0.332582\pi\)
\(174\) −1.54205 −0.116902
\(175\) −5.98769 −0.452627
\(176\) −3.28199 −0.247390
\(177\) −2.04653 −0.153827
\(178\) 1.81210 0.135823
\(179\) 22.4263 1.67622 0.838109 0.545503i \(-0.183661\pi\)
0.838109 + 0.545503i \(0.183661\pi\)
\(180\) 1.83804 0.136999
\(181\) 12.5002 0.929134 0.464567 0.885538i \(-0.346210\pi\)
0.464567 + 0.885538i \(0.346210\pi\)
\(182\) 3.54339 0.262653
\(183\) −2.81407 −0.208022
\(184\) 5.94658 0.438387
\(185\) −4.04729 −0.297563
\(186\) 3.26607 0.239480
\(187\) −25.7677 −1.88432
\(188\) −4.92688 −0.359330
\(189\) 2.43301 0.176976
\(190\) 0.633871 0.0459858
\(191\) 25.8064 1.86729 0.933644 0.358203i \(-0.116610\pi\)
0.933644 + 0.358203i \(0.116610\pi\)
\(192\) −0.316697 −0.0228556
\(193\) 9.81184 0.706272 0.353136 0.935572i \(-0.385115\pi\)
0.353136 + 0.935572i \(0.385115\pi\)
\(194\) 11.7199 0.841442
\(195\) 0.546251 0.0391178
\(196\) −5.30433 −0.378881
\(197\) −9.53236 −0.679152 −0.339576 0.940579i \(-0.610284\pi\)
−0.339576 + 0.940579i \(0.610284\pi\)
\(198\) 9.51681 0.676330
\(199\) 16.1514 1.14494 0.572470 0.819926i \(-0.305985\pi\)
0.572470 + 0.819926i \(0.305985\pi\)
\(200\) −4.59821 −0.325142
\(201\) 3.04887 0.215051
\(202\) −8.56010 −0.602286
\(203\) 6.34053 0.445018
\(204\) −2.48646 −0.174087
\(205\) −4.26692 −0.298014
\(206\) 14.5743 1.01544
\(207\) −17.2433 −1.19849
\(208\) 2.72112 0.188676
\(209\) 3.28199 0.227020
\(210\) 0.261406 0.0180387
\(211\) −1.00000 −0.0688428
\(212\) 6.78791 0.466195
\(213\) 4.90861 0.336333
\(214\) 0.0386434 0.00264161
\(215\) 5.47986 0.373723
\(216\) 1.86842 0.127130
\(217\) −13.4293 −0.911638
\(218\) −10.5277 −0.713029
\(219\) −3.79518 −0.256454
\(220\) 2.08036 0.140258
\(221\) 21.3641 1.43711
\(222\) −2.02212 −0.135716
\(223\) 6.01217 0.402604 0.201302 0.979529i \(-0.435483\pi\)
0.201302 + 0.979529i \(0.435483\pi\)
\(224\) 1.30218 0.0870055
\(225\) 13.3334 0.888896
\(226\) 9.61364 0.639490
\(227\) 0.456059 0.0302697 0.0151348 0.999885i \(-0.495182\pi\)
0.0151348 + 0.999885i \(0.495182\pi\)
\(228\) 0.316697 0.0209737
\(229\) 6.93276 0.458129 0.229065 0.973411i \(-0.426433\pi\)
0.229065 + 0.973411i \(0.426433\pi\)
\(230\) −3.76936 −0.248544
\(231\) 1.35348 0.0890525
\(232\) 4.86917 0.319677
\(233\) 8.39227 0.549796 0.274898 0.961473i \(-0.411356\pi\)
0.274898 + 0.961473i \(0.411356\pi\)
\(234\) −7.89045 −0.515815
\(235\) 3.12301 0.203723
\(236\) 6.46212 0.420648
\(237\) 3.21115 0.208587
\(238\) 10.2237 0.662704
\(239\) −2.25755 −0.146029 −0.0730143 0.997331i \(-0.523262\pi\)
−0.0730143 + 0.997331i \(0.523262\pi\)
\(240\) 0.200745 0.0129580
\(241\) 5.14424 0.331370 0.165685 0.986179i \(-0.447017\pi\)
0.165685 + 0.986179i \(0.447017\pi\)
\(242\) −0.228513 −0.0146894
\(243\) −8.17283 −0.524287
\(244\) 8.88569 0.568848
\(245\) 3.36226 0.214807
\(246\) −2.13185 −0.135922
\(247\) −2.72112 −0.173141
\(248\) −10.3129 −0.654871
\(249\) −2.85809 −0.181124
\(250\) 6.08402 0.384788
\(251\) 25.9841 1.64010 0.820052 0.572289i \(-0.193944\pi\)
0.820052 + 0.572289i \(0.193944\pi\)
\(252\) −3.77593 −0.237861
\(253\) −19.5166 −1.22700
\(254\) −1.39508 −0.0875352
\(255\) 1.57609 0.0986987
\(256\) 1.00000 0.0625000
\(257\) −18.5572 −1.15756 −0.578782 0.815482i \(-0.696472\pi\)
−0.578782 + 0.815482i \(0.696472\pi\)
\(258\) 2.73786 0.170452
\(259\) 8.31447 0.516636
\(260\) −1.72484 −0.106970
\(261\) −14.1191 −0.873953
\(262\) −9.10667 −0.562612
\(263\) −20.5112 −1.26477 −0.632386 0.774653i \(-0.717924\pi\)
−0.632386 + 0.774653i \(0.717924\pi\)
\(264\) 1.03940 0.0639704
\(265\) −4.30266 −0.264310
\(266\) −1.30218 −0.0798417
\(267\) −0.573886 −0.0351212
\(268\) −9.62712 −0.588070
\(269\) −11.6832 −0.712339 −0.356170 0.934421i \(-0.615917\pi\)
−0.356170 + 0.934421i \(0.615917\pi\)
\(270\) −1.18433 −0.0720763
\(271\) 16.9254 1.02814 0.514072 0.857747i \(-0.328136\pi\)
0.514072 + 0.857747i \(0.328136\pi\)
\(272\) 7.85122 0.476050
\(273\) −1.12218 −0.0679174
\(274\) 22.7634 1.37519
\(275\) 15.0913 0.910039
\(276\) −1.88326 −0.113359
\(277\) −10.7834 −0.647910 −0.323955 0.946072i \(-0.605013\pi\)
−0.323955 + 0.946072i \(0.605013\pi\)
\(278\) 17.9297 1.07535
\(279\) 29.9044 1.79033
\(280\) −0.825413 −0.0493279
\(281\) 0.140080 0.00835650 0.00417825 0.999991i \(-0.498670\pi\)
0.00417825 + 0.999991i \(0.498670\pi\)
\(282\) 1.56033 0.0929161
\(283\) 15.7665 0.937221 0.468610 0.883405i \(-0.344755\pi\)
0.468610 + 0.883405i \(0.344755\pi\)
\(284\) −15.4994 −0.919721
\(285\) −0.200745 −0.0118911
\(286\) −8.93071 −0.528084
\(287\) 8.76565 0.517420
\(288\) −2.89970 −0.170867
\(289\) 44.6417 2.62598
\(290\) −3.08642 −0.181241
\(291\) −3.71166 −0.217581
\(292\) 11.9836 0.701290
\(293\) −19.3202 −1.12870 −0.564349 0.825536i \(-0.690873\pi\)
−0.564349 + 0.825536i \(0.690873\pi\)
\(294\) 1.67986 0.0979716
\(295\) −4.09615 −0.238487
\(296\) 6.38504 0.371123
\(297\) −6.13213 −0.355822
\(298\) 12.6405 0.732245
\(299\) 16.1814 0.935792
\(300\) 1.45624 0.0840759
\(301\) −11.2574 −0.648867
\(302\) 21.7335 1.25062
\(303\) 2.71095 0.155740
\(304\) −1.00000 −0.0573539
\(305\) −5.63238 −0.322509
\(306\) −22.7662 −1.30146
\(307\) −12.9088 −0.736745 −0.368372 0.929678i \(-0.620085\pi\)
−0.368372 + 0.929678i \(0.620085\pi\)
\(308\) −4.27374 −0.243519
\(309\) −4.61563 −0.262574
\(310\) 6.53706 0.371280
\(311\) 16.1837 0.917694 0.458847 0.888515i \(-0.348263\pi\)
0.458847 + 0.888515i \(0.348263\pi\)
\(312\) −0.861770 −0.0487881
\(313\) −30.7000 −1.73526 −0.867632 0.497206i \(-0.834359\pi\)
−0.867632 + 0.497206i \(0.834359\pi\)
\(314\) 6.16246 0.347768
\(315\) 2.39345 0.134856
\(316\) −10.1395 −0.570393
\(317\) 13.8118 0.775748 0.387874 0.921712i \(-0.373210\pi\)
0.387874 + 0.921712i \(0.373210\pi\)
\(318\) −2.14971 −0.120550
\(319\) −15.9806 −0.894741
\(320\) −0.633871 −0.0354345
\(321\) −0.0122382 −0.000683071 0
\(322\) 7.74351 0.431529
\(323\) −7.85122 −0.436854
\(324\) 8.10739 0.450411
\(325\) −12.5123 −0.694057
\(326\) −11.7577 −0.651199
\(327\) 3.33410 0.184376
\(328\) 6.73152 0.371686
\(329\) −6.41569 −0.353708
\(330\) −0.658843 −0.0362681
\(331\) −13.2313 −0.727256 −0.363628 0.931544i \(-0.618462\pi\)
−0.363628 + 0.931544i \(0.618462\pi\)
\(332\) 9.02471 0.495295
\(333\) −18.5147 −1.01460
\(334\) −5.50355 −0.301141
\(335\) 6.10235 0.333407
\(336\) −0.412396 −0.0224980
\(337\) 20.4876 1.11603 0.558016 0.829830i \(-0.311563\pi\)
0.558016 + 0.829830i \(0.311563\pi\)
\(338\) −5.59549 −0.304355
\(339\) −3.04461 −0.165360
\(340\) −4.97666 −0.269897
\(341\) 33.8469 1.83291
\(342\) 2.89970 0.156798
\(343\) −16.0224 −0.865130
\(344\) −8.64507 −0.466111
\(345\) 1.19374 0.0642690
\(346\) 13.2067 0.709997
\(347\) −23.1980 −1.24533 −0.622667 0.782487i \(-0.713951\pi\)
−0.622667 + 0.782487i \(0.713951\pi\)
\(348\) −1.54205 −0.0826625
\(349\) −2.16227 −0.115743 −0.0578717 0.998324i \(-0.518431\pi\)
−0.0578717 + 0.998324i \(0.518431\pi\)
\(350\) −5.98769 −0.320055
\(351\) 5.08419 0.271374
\(352\) −3.28199 −0.174931
\(353\) −15.5308 −0.826623 −0.413311 0.910590i \(-0.635628\pi\)
−0.413311 + 0.910590i \(0.635628\pi\)
\(354\) −2.04653 −0.108772
\(355\) 9.82463 0.521437
\(356\) 1.81210 0.0960411
\(357\) −3.23781 −0.171363
\(358\) 22.4263 1.18526
\(359\) −21.9983 −1.16102 −0.580512 0.814252i \(-0.697148\pi\)
−0.580512 + 0.814252i \(0.697148\pi\)
\(360\) 1.83804 0.0968731
\(361\) 1.00000 0.0526316
\(362\) 12.5002 0.656997
\(363\) 0.0723694 0.00379841
\(364\) 3.54339 0.185724
\(365\) −7.59608 −0.397597
\(366\) −2.81407 −0.147094
\(367\) 25.2122 1.31607 0.658033 0.752989i \(-0.271389\pi\)
0.658033 + 0.752989i \(0.271389\pi\)
\(368\) 5.94658 0.309987
\(369\) −19.5194 −1.01614
\(370\) −4.04729 −0.210409
\(371\) 8.83907 0.458902
\(372\) 3.26607 0.169338
\(373\) 22.5197 1.16603 0.583013 0.812463i \(-0.301873\pi\)
0.583013 + 0.812463i \(0.301873\pi\)
\(374\) −25.7677 −1.33241
\(375\) −1.92679 −0.0994990
\(376\) −4.92688 −0.254085
\(377\) 13.2496 0.682389
\(378\) 2.43301 0.125141
\(379\) −18.1362 −0.931594 −0.465797 0.884892i \(-0.654232\pi\)
−0.465797 + 0.884892i \(0.654232\pi\)
\(380\) 0.633871 0.0325169
\(381\) 0.441817 0.0226350
\(382\) 25.8064 1.32037
\(383\) 18.7929 0.960271 0.480135 0.877194i \(-0.340588\pi\)
0.480135 + 0.877194i \(0.340588\pi\)
\(384\) −0.316697 −0.0161614
\(385\) 2.70900 0.138064
\(386\) 9.81184 0.499410
\(387\) 25.0681 1.27428
\(388\) 11.7199 0.594989
\(389\) 26.0243 1.31949 0.659743 0.751492i \(-0.270665\pi\)
0.659743 + 0.751492i \(0.270665\pi\)
\(390\) 0.546251 0.0276605
\(391\) 46.6879 2.36111
\(392\) −5.30433 −0.267909
\(393\) 2.88405 0.145481
\(394\) −9.53236 −0.480233
\(395\) 6.42715 0.323385
\(396\) 9.51681 0.478238
\(397\) 13.7105 0.688110 0.344055 0.938949i \(-0.388199\pi\)
0.344055 + 0.938949i \(0.388199\pi\)
\(398\) 16.1514 0.809594
\(399\) 0.412396 0.0206456
\(400\) −4.59821 −0.229910
\(401\) −37.7874 −1.88701 −0.943506 0.331355i \(-0.892494\pi\)
−0.943506 + 0.331355i \(0.892494\pi\)
\(402\) 3.04887 0.152064
\(403\) −28.0627 −1.39790
\(404\) −8.56010 −0.425881
\(405\) −5.13904 −0.255361
\(406\) 6.34053 0.314675
\(407\) −20.9557 −1.03873
\(408\) −2.48646 −0.123098
\(409\) −20.1267 −0.995199 −0.497599 0.867407i \(-0.665785\pi\)
−0.497599 + 0.867407i \(0.665785\pi\)
\(410\) −4.26692 −0.210728
\(411\) −7.20910 −0.355599
\(412\) 14.5743 0.718024
\(413\) 8.41484 0.414067
\(414\) −17.2433 −0.847462
\(415\) −5.72050 −0.280808
\(416\) 2.72112 0.133414
\(417\) −5.67826 −0.278066
\(418\) 3.28199 0.160528
\(419\) −29.3823 −1.43542 −0.717709 0.696343i \(-0.754809\pi\)
−0.717709 + 0.696343i \(0.754809\pi\)
\(420\) 0.261406 0.0127553
\(421\) 3.09990 0.151080 0.0755400 0.997143i \(-0.475932\pi\)
0.0755400 + 0.997143i \(0.475932\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 14.2865 0.694634
\(424\) 6.78791 0.329650
\(425\) −36.1016 −1.75118
\(426\) 4.90861 0.237823
\(427\) 11.5708 0.559948
\(428\) 0.0386434 0.00186790
\(429\) 2.82832 0.136553
\(430\) 5.47986 0.264262
\(431\) 1.55279 0.0747953 0.0373977 0.999300i \(-0.488093\pi\)
0.0373977 + 0.999300i \(0.488093\pi\)
\(432\) 1.86842 0.0898942
\(433\) −9.38182 −0.450862 −0.225431 0.974259i \(-0.572379\pi\)
−0.225431 + 0.974259i \(0.572379\pi\)
\(434\) −13.4293 −0.644625
\(435\) 0.977460 0.0468656
\(436\) −10.5277 −0.504187
\(437\) −5.94658 −0.284463
\(438\) −3.79518 −0.181341
\(439\) 7.35006 0.350799 0.175400 0.984497i \(-0.443878\pi\)
0.175400 + 0.984497i \(0.443878\pi\)
\(440\) 2.08036 0.0991773
\(441\) 15.3810 0.732428
\(442\) 21.3641 1.01619
\(443\) −19.9342 −0.947104 −0.473552 0.880766i \(-0.657028\pi\)
−0.473552 + 0.880766i \(0.657028\pi\)
\(444\) −2.02212 −0.0959656
\(445\) −1.14864 −0.0544507
\(446\) 6.01217 0.284684
\(447\) −4.00321 −0.189345
\(448\) 1.30218 0.0615222
\(449\) −14.5104 −0.684787 −0.342394 0.939557i \(-0.611238\pi\)
−0.342394 + 0.939557i \(0.611238\pi\)
\(450\) 13.3334 0.628544
\(451\) −22.0928 −1.04031
\(452\) 9.61364 0.452188
\(453\) −6.88292 −0.323388
\(454\) 0.456059 0.0214039
\(455\) −2.24605 −0.105296
\(456\) 0.316697 0.0148307
\(457\) 9.65001 0.451409 0.225704 0.974196i \(-0.427532\pi\)
0.225704 + 0.974196i \(0.427532\pi\)
\(458\) 6.93276 0.323946
\(459\) 14.6693 0.684707
\(460\) −3.76936 −0.175747
\(461\) −3.51618 −0.163765 −0.0818824 0.996642i \(-0.526093\pi\)
−0.0818824 + 0.996642i \(0.526093\pi\)
\(462\) 1.35348 0.0629696
\(463\) −14.2805 −0.663672 −0.331836 0.943337i \(-0.607668\pi\)
−0.331836 + 0.943337i \(0.607668\pi\)
\(464\) 4.86917 0.226045
\(465\) −2.07026 −0.0960062
\(466\) 8.39227 0.388765
\(467\) −7.93248 −0.367071 −0.183536 0.983013i \(-0.558754\pi\)
−0.183536 + 0.983013i \(0.558754\pi\)
\(468\) −7.89045 −0.364736
\(469\) −12.5362 −0.578869
\(470\) 3.12301 0.144054
\(471\) −1.95163 −0.0899264
\(472\) 6.46212 0.297443
\(473\) 28.3731 1.30459
\(474\) 3.21115 0.147493
\(475\) 4.59821 0.210980
\(476\) 10.2237 0.468602
\(477\) −19.6829 −0.901219
\(478\) −2.25755 −0.103258
\(479\) 21.1612 0.966878 0.483439 0.875378i \(-0.339388\pi\)
0.483439 + 0.875378i \(0.339388\pi\)
\(480\) 0.200745 0.00916270
\(481\) 17.3745 0.792208
\(482\) 5.14424 0.234314
\(483\) −2.45234 −0.111585
\(484\) −0.228513 −0.0103870
\(485\) −7.42892 −0.337330
\(486\) −8.17283 −0.370727
\(487\) −17.4317 −0.789908 −0.394954 0.918701i \(-0.629239\pi\)
−0.394954 + 0.918701i \(0.629239\pi\)
\(488\) 8.88569 0.402236
\(489\) 3.72362 0.168388
\(490\) 3.36226 0.151891
\(491\) −40.2231 −1.81525 −0.907623 0.419787i \(-0.862105\pi\)
−0.907623 + 0.419787i \(0.862105\pi\)
\(492\) −2.13185 −0.0961112
\(493\) 38.2289 1.72174
\(494\) −2.72112 −0.122429
\(495\) −6.03243 −0.271138
\(496\) −10.3129 −0.463064
\(497\) −20.1830 −0.905332
\(498\) −2.85809 −0.128074
\(499\) −18.6263 −0.833828 −0.416914 0.908946i \(-0.636888\pi\)
−0.416914 + 0.908946i \(0.636888\pi\)
\(500\) 6.08402 0.272086
\(501\) 1.74296 0.0778695
\(502\) 25.9841 1.15973
\(503\) −1.00162 −0.0446601 −0.0223301 0.999751i \(-0.507108\pi\)
−0.0223301 + 0.999751i \(0.507108\pi\)
\(504\) −3.77593 −0.168193
\(505\) 5.42600 0.241454
\(506\) −19.5166 −0.867620
\(507\) 1.77207 0.0787006
\(508\) −1.39508 −0.0618967
\(509\) −9.65915 −0.428134 −0.214067 0.976819i \(-0.568671\pi\)
−0.214067 + 0.976819i \(0.568671\pi\)
\(510\) 1.57609 0.0697905
\(511\) 15.6049 0.690318
\(512\) 1.00000 0.0441942
\(513\) −1.86842 −0.0824926
\(514\) −18.5572 −0.818522
\(515\) −9.23822 −0.407085
\(516\) 2.73786 0.120528
\(517\) 16.1700 0.711156
\(518\) 8.31447 0.365317
\(519\) −4.18252 −0.183592
\(520\) −1.72484 −0.0756392
\(521\) −39.0538 −1.71098 −0.855489 0.517822i \(-0.826743\pi\)
−0.855489 + 0.517822i \(0.826743\pi\)
\(522\) −14.1191 −0.617978
\(523\) 41.0561 1.79526 0.897628 0.440754i \(-0.145289\pi\)
0.897628 + 0.440754i \(0.145289\pi\)
\(524\) −9.10667 −0.397827
\(525\) 1.89628 0.0827605
\(526\) −20.5112 −0.894329
\(527\) −80.9690 −3.52707
\(528\) 1.03940 0.0452339
\(529\) 12.3618 0.537468
\(530\) −4.30266 −0.186896
\(531\) −18.7382 −0.813170
\(532\) −1.30218 −0.0564566
\(533\) 18.3173 0.793410
\(534\) −0.573886 −0.0248345
\(535\) −0.0244949 −0.00105901
\(536\) −9.62712 −0.415828
\(537\) −7.10232 −0.306488
\(538\) −11.6832 −0.503700
\(539\) 17.4088 0.749849
\(540\) −1.18433 −0.0509656
\(541\) −0.289335 −0.0124395 −0.00621973 0.999981i \(-0.501980\pi\)
−0.00621973 + 0.999981i \(0.501980\pi\)
\(542\) 16.9254 0.727008
\(543\) −3.95878 −0.169887
\(544\) 7.85122 0.336618
\(545\) 6.67323 0.285850
\(546\) −1.12218 −0.0480248
\(547\) −7.33466 −0.313607 −0.156804 0.987630i \(-0.550119\pi\)
−0.156804 + 0.987630i \(0.550119\pi\)
\(548\) 22.7634 0.972405
\(549\) −25.7659 −1.09966
\(550\) 15.0913 0.643495
\(551\) −4.86917 −0.207434
\(552\) −1.88326 −0.0801569
\(553\) −13.2035 −0.561469
\(554\) −10.7834 −0.458142
\(555\) 1.28176 0.0544078
\(556\) 17.9297 0.760387
\(557\) 11.7624 0.498389 0.249195 0.968453i \(-0.419834\pi\)
0.249195 + 0.968453i \(0.419834\pi\)
\(558\) 29.9044 1.26595
\(559\) −23.5243 −0.994971
\(560\) −0.825413 −0.0348801
\(561\) 8.16053 0.344538
\(562\) 0.140080 0.00590894
\(563\) −16.8546 −0.710337 −0.355169 0.934802i \(-0.615577\pi\)
−0.355169 + 0.934802i \(0.615577\pi\)
\(564\) 1.56033 0.0657016
\(565\) −6.09381 −0.256368
\(566\) 15.7665 0.662715
\(567\) 10.5573 0.443364
\(568\) −15.4994 −0.650341
\(569\) −30.4909 −1.27824 −0.639122 0.769106i \(-0.720702\pi\)
−0.639122 + 0.769106i \(0.720702\pi\)
\(570\) −0.200745 −0.00840827
\(571\) −9.28553 −0.388588 −0.194294 0.980943i \(-0.562242\pi\)
−0.194294 + 0.980943i \(0.562242\pi\)
\(572\) −8.93071 −0.373412
\(573\) −8.17281 −0.341424
\(574\) 8.76565 0.365871
\(575\) −27.3436 −1.14031
\(576\) −2.89970 −0.120821
\(577\) 41.2739 1.71825 0.859127 0.511762i \(-0.171007\pi\)
0.859127 + 0.511762i \(0.171007\pi\)
\(578\) 44.6417 1.85685
\(579\) −3.10738 −0.129138
\(580\) −3.08642 −0.128157
\(581\) 11.7518 0.487546
\(582\) −3.71166 −0.153853
\(583\) −22.2779 −0.922655
\(584\) 11.9836 0.495887
\(585\) 5.00152 0.206788
\(586\) −19.3202 −0.798111
\(587\) −13.3476 −0.550915 −0.275457 0.961313i \(-0.588829\pi\)
−0.275457 + 0.961313i \(0.588829\pi\)
\(588\) 1.67986 0.0692764
\(589\) 10.3129 0.424936
\(590\) −4.09615 −0.168636
\(591\) 3.01886 0.124179
\(592\) 6.38504 0.262424
\(593\) −28.3630 −1.16473 −0.582364 0.812928i \(-0.697872\pi\)
−0.582364 + 0.812928i \(0.697872\pi\)
\(594\) −6.13213 −0.251604
\(595\) −6.48051 −0.265675
\(596\) 12.6405 0.517775
\(597\) −5.11508 −0.209346
\(598\) 16.1814 0.661705
\(599\) 30.7521 1.25650 0.628248 0.778013i \(-0.283772\pi\)
0.628248 + 0.778013i \(0.283772\pi\)
\(600\) 1.45624 0.0594506
\(601\) 35.3404 1.44156 0.720782 0.693162i \(-0.243783\pi\)
0.720782 + 0.693162i \(0.243783\pi\)
\(602\) −11.2574 −0.458818
\(603\) 27.9158 1.13682
\(604\) 21.7335 0.884324
\(605\) 0.144848 0.00588891
\(606\) 2.71095 0.110125
\(607\) −30.2690 −1.22858 −0.614290 0.789080i \(-0.710557\pi\)
−0.614290 + 0.789080i \(0.710557\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −2.00802 −0.0813692
\(610\) −5.63238 −0.228048
\(611\) −13.4067 −0.542375
\(612\) −22.7662 −0.920270
\(613\) −19.8122 −0.800207 −0.400103 0.916470i \(-0.631026\pi\)
−0.400103 + 0.916470i \(0.631026\pi\)
\(614\) −12.9088 −0.520957
\(615\) 1.35132 0.0544904
\(616\) −4.27374 −0.172194
\(617\) 3.39011 0.136481 0.0682403 0.997669i \(-0.478262\pi\)
0.0682403 + 0.997669i \(0.478262\pi\)
\(618\) −4.61563 −0.185668
\(619\) 38.3541 1.54158 0.770791 0.637088i \(-0.219861\pi\)
0.770791 + 0.637088i \(0.219861\pi\)
\(620\) 6.53706 0.262535
\(621\) 11.1107 0.445856
\(622\) 16.1837 0.648908
\(623\) 2.35968 0.0945385
\(624\) −0.861770 −0.0344984
\(625\) 19.1346 0.765382
\(626\) −30.7000 −1.22702
\(627\) −1.03940 −0.0415095
\(628\) 6.16246 0.245909
\(629\) 50.1304 1.99883
\(630\) 2.39345 0.0953575
\(631\) 33.9402 1.35114 0.675569 0.737297i \(-0.263898\pi\)
0.675569 + 0.737297i \(0.263898\pi\)
\(632\) −10.1395 −0.403329
\(633\) 0.316697 0.0125876
\(634\) 13.8118 0.548537
\(635\) 0.884301 0.0350924
\(636\) −2.14971 −0.0852414
\(637\) −14.4337 −0.571885
\(638\) −15.9806 −0.632677
\(639\) 44.9437 1.77795
\(640\) −0.633871 −0.0250559
\(641\) 19.7731 0.780990 0.390495 0.920605i \(-0.372304\pi\)
0.390495 + 0.920605i \(0.372304\pi\)
\(642\) −0.0122382 −0.000483004 0
\(643\) −37.2279 −1.46813 −0.734063 0.679081i \(-0.762379\pi\)
−0.734063 + 0.679081i \(0.762379\pi\)
\(644\) 7.74351 0.305137
\(645\) −1.73545 −0.0683333
\(646\) −7.85122 −0.308902
\(647\) 39.8723 1.56754 0.783770 0.621051i \(-0.213294\pi\)
0.783770 + 0.621051i \(0.213294\pi\)
\(648\) 8.10739 0.318488
\(649\) −21.2087 −0.832513
\(650\) −12.5123 −0.490772
\(651\) 4.25300 0.166688
\(652\) −11.7577 −0.460467
\(653\) −15.0879 −0.590434 −0.295217 0.955430i \(-0.595392\pi\)
−0.295217 + 0.955430i \(0.595392\pi\)
\(654\) 3.33410 0.130374
\(655\) 5.77245 0.225548
\(656\) 6.73152 0.262822
\(657\) −34.7490 −1.35569
\(658\) −6.41569 −0.250109
\(659\) −27.2238 −1.06049 −0.530245 0.847844i \(-0.677900\pi\)
−0.530245 + 0.847844i \(0.677900\pi\)
\(660\) −0.658843 −0.0256454
\(661\) 8.89511 0.345980 0.172990 0.984924i \(-0.444657\pi\)
0.172990 + 0.984924i \(0.444657\pi\)
\(662\) −13.2313 −0.514248
\(663\) −6.76595 −0.262768
\(664\) 9.02471 0.350227
\(665\) 0.825413 0.0320082
\(666\) −18.5147 −0.717431
\(667\) 28.9549 1.12114
\(668\) −5.50355 −0.212939
\(669\) −1.90403 −0.0736141
\(670\) 6.10235 0.235754
\(671\) −29.1628 −1.12582
\(672\) −0.412396 −0.0159085
\(673\) −7.04337 −0.271502 −0.135751 0.990743i \(-0.543345\pi\)
−0.135751 + 0.990743i \(0.543345\pi\)
\(674\) 20.4876 0.789153
\(675\) −8.59136 −0.330682
\(676\) −5.59549 −0.215211
\(677\) 44.6504 1.71605 0.858027 0.513604i \(-0.171690\pi\)
0.858027 + 0.513604i \(0.171690\pi\)
\(678\) −3.04461 −0.116927
\(679\) 15.2614 0.585680
\(680\) −4.97666 −0.190846
\(681\) −0.144432 −0.00553466
\(682\) 33.8469 1.29607
\(683\) 17.4383 0.667259 0.333629 0.942704i \(-0.391727\pi\)
0.333629 + 0.942704i \(0.391727\pi\)
\(684\) 2.89970 0.110873
\(685\) −14.4291 −0.551307
\(686\) −16.0224 −0.611740
\(687\) −2.19558 −0.0837666
\(688\) −8.64507 −0.329590
\(689\) 18.4707 0.703679
\(690\) 1.19374 0.0454451
\(691\) 43.9575 1.67222 0.836110 0.548561i \(-0.184824\pi\)
0.836110 + 0.548561i \(0.184824\pi\)
\(692\) 13.2067 0.502044
\(693\) 12.3926 0.470756
\(694\) −23.1980 −0.880583
\(695\) −11.3651 −0.431103
\(696\) −1.54205 −0.0584512
\(697\) 52.8507 2.00186
\(698\) −2.16227 −0.0818430
\(699\) −2.65780 −0.100527
\(700\) −5.98769 −0.226313
\(701\) 32.3793 1.22295 0.611475 0.791264i \(-0.290576\pi\)
0.611475 + 0.791264i \(0.290576\pi\)
\(702\) 5.08419 0.191890
\(703\) −6.38504 −0.240816
\(704\) −3.28199 −0.123695
\(705\) −0.989046 −0.0372496
\(706\) −15.5308 −0.584511
\(707\) −11.1468 −0.419218
\(708\) −2.04653 −0.0769134
\(709\) −22.7288 −0.853596 −0.426798 0.904347i \(-0.640359\pi\)
−0.426798 + 0.904347i \(0.640359\pi\)
\(710\) 9.82463 0.368712
\(711\) 29.4016 1.10265
\(712\) 1.81210 0.0679113
\(713\) −61.3266 −2.29670
\(714\) −3.23781 −0.121172
\(715\) 5.66092 0.211706
\(716\) 22.4263 0.838109
\(717\) 0.714957 0.0267006
\(718\) −21.9983 −0.820968
\(719\) 21.6467 0.807284 0.403642 0.914917i \(-0.367744\pi\)
0.403642 + 0.914917i \(0.367744\pi\)
\(720\) 1.83804 0.0684996
\(721\) 18.9783 0.706791
\(722\) 1.00000 0.0372161
\(723\) −1.62916 −0.0605892
\(724\) 12.5002 0.464567
\(725\) −22.3894 −0.831523
\(726\) 0.0723694 0.00268588
\(727\) 23.8204 0.883451 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(728\) 3.54339 0.131327
\(729\) −21.7339 −0.804958
\(730\) −7.59608 −0.281144
\(731\) −67.8743 −2.51042
\(732\) −2.81407 −0.104011
\(733\) 16.1370 0.596032 0.298016 0.954561i \(-0.403675\pi\)
0.298016 + 0.954561i \(0.403675\pi\)
\(734\) 25.2122 0.930599
\(735\) −1.06482 −0.0392763
\(736\) 5.94658 0.219194
\(737\) 31.5961 1.16386
\(738\) −19.5194 −0.718520
\(739\) 52.5146 1.93178 0.965889 0.258955i \(-0.0833780\pi\)
0.965889 + 0.258955i \(0.0833780\pi\)
\(740\) −4.04729 −0.148781
\(741\) 0.861770 0.0316579
\(742\) 8.83907 0.324493
\(743\) −6.84173 −0.250999 −0.125499 0.992094i \(-0.540053\pi\)
−0.125499 + 0.992094i \(0.540053\pi\)
\(744\) 3.26607 0.119740
\(745\) −8.01245 −0.293553
\(746\) 22.5197 0.824505
\(747\) −26.1690 −0.957473
\(748\) −25.7677 −0.942159
\(749\) 0.0503206 0.00183867
\(750\) −1.92679 −0.0703564
\(751\) 7.49789 0.273602 0.136801 0.990599i \(-0.456318\pi\)
0.136801 + 0.990599i \(0.456318\pi\)
\(752\) −4.92688 −0.179665
\(753\) −8.22909 −0.299885
\(754\) 13.2496 0.482522
\(755\) −13.7762 −0.501368
\(756\) 2.43301 0.0884878
\(757\) 1.81117 0.0658283 0.0329141 0.999458i \(-0.489521\pi\)
0.0329141 + 0.999458i \(0.489521\pi\)
\(758\) −18.1362 −0.658736
\(759\) 6.18085 0.224351
\(760\) 0.633871 0.0229929
\(761\) −12.4752 −0.452226 −0.226113 0.974101i \(-0.572602\pi\)
−0.226113 + 0.974101i \(0.572602\pi\)
\(762\) 0.441817 0.0160054
\(763\) −13.7090 −0.496299
\(764\) 25.8064 0.933644
\(765\) 14.4308 0.521748
\(766\) 18.7929 0.679014
\(767\) 17.5842 0.634930
\(768\) −0.316697 −0.0114278
\(769\) −4.38194 −0.158017 −0.0790084 0.996874i \(-0.525175\pi\)
−0.0790084 + 0.996874i \(0.525175\pi\)
\(770\) 2.70900 0.0976257
\(771\) 5.87699 0.211655
\(772\) 9.81184 0.353136
\(773\) 2.17024 0.0780582 0.0390291 0.999238i \(-0.487573\pi\)
0.0390291 + 0.999238i \(0.487573\pi\)
\(774\) 25.0681 0.901055
\(775\) 47.4209 1.70341
\(776\) 11.7199 0.420721
\(777\) −2.63316 −0.0944642
\(778\) 26.0243 0.933017
\(779\) −6.73152 −0.241182
\(780\) 0.546251 0.0195589
\(781\) 50.8690 1.82024
\(782\) 46.6879 1.66956
\(783\) 9.09763 0.325123
\(784\) −5.30433 −0.189440
\(785\) −3.90620 −0.139418
\(786\) 2.88405 0.102871
\(787\) 24.3865 0.869283 0.434642 0.900603i \(-0.356875\pi\)
0.434642 + 0.900603i \(0.356875\pi\)
\(788\) −9.53236 −0.339576
\(789\) 6.49581 0.231257
\(790\) 6.42715 0.228668
\(791\) 12.5187 0.445113
\(792\) 9.51681 0.338165
\(793\) 24.1790 0.858623
\(794\) 13.7105 0.486567
\(795\) 1.36264 0.0483277
\(796\) 16.1514 0.572470
\(797\) −25.2277 −0.893610 −0.446805 0.894631i \(-0.647438\pi\)
−0.446805 + 0.894631i \(0.647438\pi\)
\(798\) 0.412396 0.0145986
\(799\) −38.6821 −1.36847
\(800\) −4.59821 −0.162571
\(801\) −5.25455 −0.185661
\(802\) −37.7874 −1.33432
\(803\) −39.3303 −1.38793
\(804\) 3.04887 0.107526
\(805\) −4.90838 −0.172998
\(806\) −28.0627 −0.988467
\(807\) 3.70004 0.130248
\(808\) −8.56010 −0.301143
\(809\) −11.7622 −0.413537 −0.206768 0.978390i \(-0.566295\pi\)
−0.206768 + 0.978390i \(0.566295\pi\)
\(810\) −5.13904 −0.180567
\(811\) 46.9368 1.64817 0.824087 0.566464i \(-0.191689\pi\)
0.824087 + 0.566464i \(0.191689\pi\)
\(812\) 6.34053 0.222509
\(813\) −5.36021 −0.187991
\(814\) −20.9557 −0.734496
\(815\) 7.45286 0.261062
\(816\) −2.48646 −0.0870434
\(817\) 8.64507 0.302453
\(818\) −20.1267 −0.703712
\(819\) −10.2748 −0.359030
\(820\) −4.26692 −0.149007
\(821\) 2.44949 0.0854878 0.0427439 0.999086i \(-0.486390\pi\)
0.0427439 + 0.999086i \(0.486390\pi\)
\(822\) −7.20910 −0.251446
\(823\) −15.8230 −0.551554 −0.275777 0.961222i \(-0.588935\pi\)
−0.275777 + 0.961222i \(0.588935\pi\)
\(824\) 14.5743 0.507720
\(825\) −4.77936 −0.166396
\(826\) 8.41484 0.292790
\(827\) −29.8591 −1.03830 −0.519151 0.854683i \(-0.673752\pi\)
−0.519151 + 0.854683i \(0.673752\pi\)
\(828\) −17.2433 −0.599246
\(829\) −39.4678 −1.37078 −0.685388 0.728178i \(-0.740367\pi\)
−0.685388 + 0.728178i \(0.740367\pi\)
\(830\) −5.72050 −0.198561
\(831\) 3.41506 0.118467
\(832\) 2.72112 0.0943379
\(833\) −41.6455 −1.44293
\(834\) −5.67826 −0.196622
\(835\) 3.48854 0.120726
\(836\) 3.28199 0.113510
\(837\) −19.2688 −0.666028
\(838\) −29.3823 −1.01499
\(839\) −29.3345 −1.01274 −0.506370 0.862316i \(-0.669013\pi\)
−0.506370 + 0.862316i \(0.669013\pi\)
\(840\) 0.261406 0.00901935
\(841\) −5.29120 −0.182455
\(842\) 3.09990 0.106830
\(843\) −0.0443630 −0.00152794
\(844\) −1.00000 −0.0344214
\(845\) 3.54682 0.122014
\(846\) 14.2865 0.491180
\(847\) −0.297565 −0.0102245
\(848\) 6.78791 0.233098
\(849\) −4.99319 −0.171366
\(850\) −36.1016 −1.23827
\(851\) 37.9691 1.30157
\(852\) 4.90861 0.168166
\(853\) 20.6330 0.706461 0.353231 0.935536i \(-0.385083\pi\)
0.353231 + 0.935536i \(0.385083\pi\)
\(854\) 11.5708 0.395943
\(855\) −1.83804 −0.0628596
\(856\) 0.0386434 0.00132080
\(857\) 11.7409 0.401063 0.200531 0.979687i \(-0.435733\pi\)
0.200531 + 0.979687i \(0.435733\pi\)
\(858\) 2.82832 0.0965574
\(859\) −22.3891 −0.763906 −0.381953 0.924182i \(-0.624748\pi\)
−0.381953 + 0.924182i \(0.624748\pi\)
\(860\) 5.47986 0.186862
\(861\) −2.77605 −0.0946075
\(862\) 1.55279 0.0528883
\(863\) −37.9279 −1.29108 −0.645540 0.763727i \(-0.723368\pi\)
−0.645540 + 0.763727i \(0.723368\pi\)
\(864\) 1.86842 0.0635648
\(865\) −8.37135 −0.284634
\(866\) −9.38182 −0.318807
\(867\) −14.1379 −0.480147
\(868\) −13.4293 −0.455819
\(869\) 33.2779 1.12887
\(870\) 0.977460 0.0331390
\(871\) −26.1966 −0.887636
\(872\) −10.5277 −0.356514
\(873\) −33.9843 −1.15019
\(874\) −5.94658 −0.201146
\(875\) 7.92249 0.267829
\(876\) −3.79518 −0.128227
\(877\) 30.0165 1.01358 0.506792 0.862068i \(-0.330831\pi\)
0.506792 + 0.862068i \(0.330831\pi\)
\(878\) 7.35006 0.248052
\(879\) 6.11864 0.206377
\(880\) 2.08036 0.0701289
\(881\) −24.7663 −0.834399 −0.417199 0.908815i \(-0.636988\pi\)
−0.417199 + 0.908815i \(0.636988\pi\)
\(882\) 15.3810 0.517905
\(883\) −13.1762 −0.443413 −0.221707 0.975113i \(-0.571163\pi\)
−0.221707 + 0.975113i \(0.571163\pi\)
\(884\) 21.3641 0.718554
\(885\) 1.29724 0.0436062
\(886\) −19.9342 −0.669703
\(887\) 16.7332 0.561846 0.280923 0.959730i \(-0.409360\pi\)
0.280923 + 0.959730i \(0.409360\pi\)
\(888\) −2.02212 −0.0678579
\(889\) −1.81665 −0.0609283
\(890\) −1.14864 −0.0385024
\(891\) −26.6084 −0.891415
\(892\) 6.01217 0.201302
\(893\) 4.92688 0.164872
\(894\) −4.00321 −0.133887
\(895\) −14.2154 −0.475167
\(896\) 1.30218 0.0435027
\(897\) −5.12458 −0.171105
\(898\) −14.5104 −0.484218
\(899\) −50.2153 −1.67478
\(900\) 13.3334 0.444448
\(901\) 53.2934 1.77546
\(902\) −22.0928 −0.735610
\(903\) 3.56519 0.118642
\(904\) 9.61364 0.319745
\(905\) −7.92353 −0.263387
\(906\) −6.88292 −0.228670
\(907\) 56.2603 1.86809 0.934047 0.357151i \(-0.116252\pi\)
0.934047 + 0.357151i \(0.116252\pi\)
\(908\) 0.456059 0.0151348
\(909\) 24.8217 0.823285
\(910\) −2.24605 −0.0744559
\(911\) 16.4810 0.546040 0.273020 0.962008i \(-0.411978\pi\)
0.273020 + 0.962008i \(0.411978\pi\)
\(912\) 0.316697 0.0104869
\(913\) −29.6190 −0.980247
\(914\) 9.65001 0.319194
\(915\) 1.78376 0.0589691
\(916\) 6.93276 0.229065
\(917\) −11.8585 −0.391603
\(918\) 14.6693 0.484161
\(919\) −23.7440 −0.783243 −0.391621 0.920126i \(-0.628086\pi\)
−0.391621 + 0.920126i \(0.628086\pi\)
\(920\) −3.76936 −0.124272
\(921\) 4.08818 0.134710
\(922\) −3.51618 −0.115799
\(923\) −42.1758 −1.38823
\(924\) 1.35348 0.0445262
\(925\) −29.3597 −0.965343
\(926\) −14.2805 −0.469287
\(927\) −42.2611 −1.38804
\(928\) 4.86917 0.159838
\(929\) 16.3866 0.537629 0.268814 0.963192i \(-0.413368\pi\)
0.268814 + 0.963192i \(0.413368\pi\)
\(930\) −2.07026 −0.0678866
\(931\) 5.30433 0.173842
\(932\) 8.39227 0.274898
\(933\) −5.12533 −0.167796
\(934\) −7.93248 −0.259559
\(935\) 16.3334 0.534159
\(936\) −7.89045 −0.257907
\(937\) −4.14264 −0.135334 −0.0676670 0.997708i \(-0.521556\pi\)
−0.0676670 + 0.997708i \(0.521556\pi\)
\(938\) −12.5362 −0.409322
\(939\) 9.72258 0.317284
\(940\) 3.12301 0.101861
\(941\) 30.2726 0.986858 0.493429 0.869786i \(-0.335743\pi\)
0.493429 + 0.869786i \(0.335743\pi\)
\(942\) −1.95163 −0.0635875
\(943\) 40.0295 1.30354
\(944\) 6.46212 0.210324
\(945\) −1.54222 −0.0501683
\(946\) 28.3731 0.922488
\(947\) −19.0803 −0.620028 −0.310014 0.950732i \(-0.600334\pi\)
−0.310014 + 0.950732i \(0.600334\pi\)
\(948\) 3.21115 0.104293
\(949\) 32.6090 1.05853
\(950\) 4.59821 0.149186
\(951\) −4.37415 −0.141841
\(952\) 10.2237 0.331352
\(953\) −9.67680 −0.313462 −0.156731 0.987641i \(-0.550096\pi\)
−0.156731 + 0.987641i \(0.550096\pi\)
\(954\) −19.6829 −0.637258
\(955\) −16.3579 −0.529331
\(956\) −2.25755 −0.0730143
\(957\) 5.06100 0.163599
\(958\) 21.1612 0.683686
\(959\) 29.6421 0.957192
\(960\) 0.200745 0.00647901
\(961\) 75.3563 2.43085
\(962\) 17.3745 0.560176
\(963\) −0.112054 −0.00361090
\(964\) 5.14424 0.165685
\(965\) −6.21944 −0.200211
\(966\) −2.45234 −0.0789028
\(967\) −1.57849 −0.0507607 −0.0253804 0.999678i \(-0.508080\pi\)
−0.0253804 + 0.999678i \(0.508080\pi\)
\(968\) −0.228513 −0.00734470
\(969\) 2.48646 0.0798765
\(970\) −7.42892 −0.238528
\(971\) −15.3795 −0.493552 −0.246776 0.969073i \(-0.579371\pi\)
−0.246776 + 0.969073i \(0.579371\pi\)
\(972\) −8.17283 −0.262144
\(973\) 23.3476 0.748491
\(974\) −17.4317 −0.558549
\(975\) 3.96260 0.126905
\(976\) 8.88569 0.284424
\(977\) −32.8029 −1.04946 −0.524729 0.851269i \(-0.675833\pi\)
−0.524729 + 0.851269i \(0.675833\pi\)
\(978\) 3.72362 0.119068
\(979\) −5.94730 −0.190077
\(980\) 3.36226 0.107403
\(981\) 30.5273 0.974663
\(982\) −40.2231 −1.28357
\(983\) 19.2148 0.612858 0.306429 0.951894i \(-0.400866\pi\)
0.306429 + 0.951894i \(0.400866\pi\)
\(984\) −2.13185 −0.0679609
\(985\) 6.04228 0.192523
\(986\) 38.2289 1.21746
\(987\) 2.03183 0.0646737
\(988\) −2.72112 −0.0865704
\(989\) −51.4085 −1.63470
\(990\) −6.03243 −0.191723
\(991\) −12.3138 −0.391160 −0.195580 0.980688i \(-0.562659\pi\)
−0.195580 + 0.980688i \(0.562659\pi\)
\(992\) −10.3129 −0.327436
\(993\) 4.19030 0.132975
\(994\) −20.1830 −0.640167
\(995\) −10.2379 −0.324563
\(996\) −2.85809 −0.0905622
\(997\) −46.7594 −1.48088 −0.740442 0.672121i \(-0.765384\pi\)
−0.740442 + 0.672121i \(0.765384\pi\)
\(998\) −18.6263 −0.589606
\(999\) 11.9299 0.377446
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 \(a_p\))