Properties

Label 6001.2.a.b.1.11
Level 6001
Weight 2
Character 6001.1
Self dual Yes
Analytic conductor 47.918
Analytic rank 1
Dimension 114
CM No

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.918226253\)
Analytic rank: \(1\)
Dimension: \(114\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.38632 q^{2}\) \(-0.731332 q^{3}\) \(+3.69453 q^{4}\) \(+1.80073 q^{5}\) \(+1.74519 q^{6}\) \(-2.93364 q^{7}\) \(-4.04370 q^{8}\) \(-2.46515 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.38632 q^{2}\) \(-0.731332 q^{3}\) \(+3.69453 q^{4}\) \(+1.80073 q^{5}\) \(+1.74519 q^{6}\) \(-2.93364 q^{7}\) \(-4.04370 q^{8}\) \(-2.46515 q^{9}\) \(-4.29713 q^{10}\) \(+0.347932 q^{11}\) \(-2.70193 q^{12}\) \(-1.80377 q^{13}\) \(+7.00060 q^{14}\) \(-1.31694 q^{15}\) \(+2.26050 q^{16}\) \(+1.00000 q^{17}\) \(+5.88265 q^{18}\) \(-1.44867 q^{19}\) \(+6.65287 q^{20}\) \(+2.14546 q^{21}\) \(-0.830278 q^{22}\) \(-1.89471 q^{23}\) \(+2.95729 q^{24}\) \(-1.75735 q^{25}\) \(+4.30438 q^{26}\) \(+3.99684 q^{27}\) \(-10.8384 q^{28}\) \(+1.23132 q^{29}\) \(+3.14263 q^{30}\) \(-3.19162 q^{31}\) \(+2.69312 q^{32}\) \(-0.254454 q^{33}\) \(-2.38632 q^{34}\) \(-5.28271 q^{35}\) \(-9.10758 q^{36}\) \(+7.85544 q^{37}\) \(+3.45699 q^{38}\) \(+1.31916 q^{39}\) \(-7.28162 q^{40}\) \(+10.4853 q^{41}\) \(-5.11977 q^{42}\) \(-5.61665 q^{43}\) \(+1.28545 q^{44}\) \(-4.43909 q^{45}\) \(+4.52138 q^{46}\) \(+6.76065 q^{47}\) \(-1.65317 q^{48}\) \(+1.60623 q^{49}\) \(+4.19361 q^{50}\) \(-0.731332 q^{51}\) \(-6.66410 q^{52}\) \(+4.45378 q^{53}\) \(-9.53775 q^{54}\) \(+0.626534 q^{55}\) \(+11.8627 q^{56}\) \(+1.05946 q^{57}\) \(-2.93834 q^{58}\) \(+9.13356 q^{59}\) \(-4.86546 q^{60}\) \(-4.99819 q^{61}\) \(+7.61622 q^{62}\) \(+7.23187 q^{63}\) \(-10.9476 q^{64}\) \(-3.24812 q^{65}\) \(+0.607209 q^{66}\) \(+3.64704 q^{67}\) \(+3.69453 q^{68}\) \(+1.38566 q^{69}\) \(+12.6062 q^{70}\) \(-1.83384 q^{71}\) \(+9.96833 q^{72}\) \(+11.1597 q^{73}\) \(-18.7456 q^{74}\) \(+1.28521 q^{75}\) \(-5.35216 q^{76}\) \(-1.02071 q^{77}\) \(-3.14794 q^{78}\) \(+8.20187 q^{79}\) \(+4.07056 q^{80}\) \(+4.47244 q^{81}\) \(-25.0212 q^{82}\) \(-1.21802 q^{83}\) \(+7.92648 q^{84}\) \(+1.80073 q^{85}\) \(+13.4031 q^{86}\) \(-0.900507 q^{87}\) \(-1.40693 q^{88}\) \(-2.60146 q^{89}\) \(+10.5931 q^{90}\) \(+5.29162 q^{91}\) \(-7.00005 q^{92}\) \(+2.33413 q^{93}\) \(-16.1331 q^{94}\) \(-2.60867 q^{95}\) \(-1.96957 q^{96}\) \(+15.2585 q^{97}\) \(-3.83299 q^{98}\) \(-0.857706 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(114q \) \(\mathstrut -\mathstrut 8q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 110q^{4} \) \(\mathstrut -\mathstrut 27q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 53q^{7} \) \(\mathstrut -\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 107q^{9} \) \(\mathstrut -\mathstrut 19q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 49q^{12} \) \(\mathstrut -\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 40q^{14} \) \(\mathstrut -\mathstrut 39q^{15} \) \(\mathstrut +\mathstrut 110q^{16} \) \(\mathstrut +\mathstrut 114q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 88q^{20} \) \(\mathstrut -\mathstrut 30q^{21} \) \(\mathstrut -\mathstrut 36q^{22} \) \(\mathstrut -\mathstrut 77q^{23} \) \(\mathstrut -\mathstrut 72q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 79q^{26} \) \(\mathstrut -\mathstrut 77q^{27} \) \(\mathstrut -\mathstrut 92q^{28} \) \(\mathstrut -\mathstrut 65q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 131q^{31} \) \(\mathstrut -\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 8q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 109q^{36} \) \(\mathstrut -\mathstrut 54q^{37} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 83q^{39} \) \(\mathstrut -\mathstrut 42q^{40} \) \(\mathstrut -\mathstrut 99q^{41} \) \(\mathstrut +\mathstrut 29q^{42} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 98q^{44} \) \(\mathstrut -\mathstrut 73q^{45} \) \(\mathstrut -\mathstrut 35q^{46} \) \(\mathstrut -\mathstrut 113q^{47} \) \(\mathstrut -\mathstrut 86q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 44q^{50} \) \(\mathstrut -\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut 3q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 78q^{54} \) \(\mathstrut -\mathstrut 63q^{55} \) \(\mathstrut -\mathstrut 117q^{56} \) \(\mathstrut -\mathstrut 64q^{57} \) \(\mathstrut -\mathstrut 31q^{58} \) \(\mathstrut -\mathstrut 134q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 30q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 117q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 12q^{66} \) \(\mathstrut -\mathstrut 34q^{67} \) \(\mathstrut +\mathstrut 110q^{68} \) \(\mathstrut -\mathstrut 35q^{69} \) \(\mathstrut +\mathstrut 18q^{70} \) \(\mathstrut -\mathstrut 233q^{71} \) \(\mathstrut +\mathstrut 16q^{72} \) \(\mathstrut -\mathstrut 56q^{73} \) \(\mathstrut -\mathstrut 64q^{74} \) \(\mathstrut -\mathstrut 100q^{75} \) \(\mathstrut -\mathstrut 64q^{76} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut -\mathstrut 154q^{79} \) \(\mathstrut -\mathstrut 128q^{80} \) \(\mathstrut +\mathstrut 118q^{81} \) \(\mathstrut +\mathstrut 2q^{82} \) \(\mathstrut -\mathstrut 53q^{83} \) \(\mathstrut -\mathstrut 6q^{84} \) \(\mathstrut -\mathstrut 27q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 52q^{88} \) \(\mathstrut -\mathstrut 118q^{89} \) \(\mathstrut -\mathstrut 5q^{90} \) \(\mathstrut -\mathstrut 95q^{91} \) \(\mathstrut -\mathstrut 102q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 158q^{95} \) \(\mathstrut -\mathstrut 144q^{96} \) \(\mathstrut -\mathstrut 57q^{97} \) \(\mathstrut +\mathstrut 3q^{98} \) \(\mathstrut -\mathstrut 131q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38632 −1.68738 −0.843692 0.536827i \(-0.819623\pi\)
−0.843692 + 0.536827i \(0.819623\pi\)
\(3\) −0.731332 −0.422235 −0.211117 0.977461i \(-0.567710\pi\)
−0.211117 + 0.977461i \(0.567710\pi\)
\(4\) 3.69453 1.84727
\(5\) 1.80073 0.805313 0.402657 0.915351i \(-0.368087\pi\)
0.402657 + 0.915351i \(0.368087\pi\)
\(6\) 1.74519 0.712473
\(7\) −2.93364 −1.10881 −0.554406 0.832247i \(-0.687054\pi\)
−0.554406 + 0.832247i \(0.687054\pi\)
\(8\) −4.04370 −1.42966
\(9\) −2.46515 −0.821718
\(10\) −4.29713 −1.35887
\(11\) 0.347932 0.104906 0.0524528 0.998623i \(-0.483296\pi\)
0.0524528 + 0.998623i \(0.483296\pi\)
\(12\) −2.70193 −0.779980
\(13\) −1.80377 −0.500277 −0.250138 0.968210i \(-0.580476\pi\)
−0.250138 + 0.968210i \(0.580476\pi\)
\(14\) 7.00060 1.87099
\(15\) −1.31694 −0.340031
\(16\) 2.26050 0.565124
\(17\) 1.00000 0.242536
\(18\) 5.88265 1.38655
\(19\) −1.44867 −0.332348 −0.166174 0.986096i \(-0.553141\pi\)
−0.166174 + 0.986096i \(0.553141\pi\)
\(20\) 6.65287 1.48763
\(21\) 2.14546 0.468179
\(22\) −0.830278 −0.177016
\(23\) −1.89471 −0.395073 −0.197537 0.980295i \(-0.563294\pi\)
−0.197537 + 0.980295i \(0.563294\pi\)
\(24\) 2.95729 0.603653
\(25\) −1.75735 −0.351471
\(26\) 4.30438 0.844159
\(27\) 3.99684 0.769193
\(28\) −10.8384 −2.04827
\(29\) 1.23132 0.228651 0.114326 0.993443i \(-0.463529\pi\)
0.114326 + 0.993443i \(0.463529\pi\)
\(30\) 3.14263 0.573763
\(31\) −3.19162 −0.573231 −0.286616 0.958046i \(-0.592530\pi\)
−0.286616 + 0.958046i \(0.592530\pi\)
\(32\) 2.69312 0.476081
\(33\) −0.254454 −0.0442948
\(34\) −2.38632 −0.409251
\(35\) −5.28271 −0.892940
\(36\) −9.10758 −1.51793
\(37\) 7.85544 1.29143 0.645713 0.763580i \(-0.276560\pi\)
0.645713 + 0.763580i \(0.276560\pi\)
\(38\) 3.45699 0.560798
\(39\) 1.31916 0.211234
\(40\) −7.28162 −1.15133
\(41\) 10.4853 1.63752 0.818761 0.574134i \(-0.194661\pi\)
0.818761 + 0.574134i \(0.194661\pi\)
\(42\) −5.11977 −0.789997
\(43\) −5.61665 −0.856531 −0.428265 0.903653i \(-0.640875\pi\)
−0.428265 + 0.903653i \(0.640875\pi\)
\(44\) 1.28545 0.193788
\(45\) −4.43909 −0.661740
\(46\) 4.52138 0.666641
\(47\) 6.76065 0.986143 0.493071 0.869989i \(-0.335874\pi\)
0.493071 + 0.869989i \(0.335874\pi\)
\(48\) −1.65317 −0.238615
\(49\) 1.60623 0.229462
\(50\) 4.19361 0.593066
\(51\) −0.731332 −0.102407
\(52\) −6.66410 −0.924144
\(53\) 4.45378 0.611774 0.305887 0.952068i \(-0.401047\pi\)
0.305887 + 0.952068i \(0.401047\pi\)
\(54\) −9.53775 −1.29792
\(55\) 0.626534 0.0844818
\(56\) 11.8627 1.58523
\(57\) 1.05946 0.140329
\(58\) −2.93834 −0.385822
\(59\) 9.13356 1.18909 0.594544 0.804063i \(-0.297333\pi\)
0.594544 + 0.804063i \(0.297333\pi\)
\(60\) −4.86546 −0.628128
\(61\) −4.99819 −0.639953 −0.319977 0.947425i \(-0.603675\pi\)
−0.319977 + 0.947425i \(0.603675\pi\)
\(62\) 7.61622 0.967261
\(63\) 7.23187 0.911130
\(64\) −10.9476 −1.36846
\(65\) −3.24812 −0.402879
\(66\) 0.607209 0.0747423
\(67\) 3.64704 0.445557 0.222779 0.974869i \(-0.428487\pi\)
0.222779 + 0.974869i \(0.428487\pi\)
\(68\) 3.69453 0.448028
\(69\) 1.38566 0.166814
\(70\) 12.6062 1.50673
\(71\) −1.83384 −0.217637 −0.108818 0.994062i \(-0.534707\pi\)
−0.108818 + 0.994062i \(0.534707\pi\)
\(72\) 9.96833 1.17478
\(73\) 11.1597 1.30615 0.653073 0.757295i \(-0.273479\pi\)
0.653073 + 0.757295i \(0.273479\pi\)
\(74\) −18.7456 −2.17913
\(75\) 1.28521 0.148403
\(76\) −5.35216 −0.613935
\(77\) −1.02071 −0.116320
\(78\) −3.14794 −0.356433
\(79\) 8.20187 0.922783 0.461391 0.887197i \(-0.347350\pi\)
0.461391 + 0.887197i \(0.347350\pi\)
\(80\) 4.07056 0.455102
\(81\) 4.47244 0.496938
\(82\) −25.0212 −2.76313
\(83\) −1.21802 −0.133695 −0.0668475 0.997763i \(-0.521294\pi\)
−0.0668475 + 0.997763i \(0.521294\pi\)
\(84\) 7.92648 0.864850
\(85\) 1.80073 0.195317
\(86\) 13.4031 1.44530
\(87\) −0.900507 −0.0965445
\(88\) −1.40693 −0.149979
\(89\) −2.60146 −0.275754 −0.137877 0.990449i \(-0.544028\pi\)
−0.137877 + 0.990449i \(0.544028\pi\)
\(90\) 10.5931 1.11661
\(91\) 5.29162 0.554712
\(92\) −7.00005 −0.729805
\(93\) 2.33413 0.242038
\(94\) −16.1331 −1.66400
\(95\) −2.60867 −0.267644
\(96\) −1.96957 −0.201018
\(97\) 15.2585 1.54927 0.774635 0.632409i \(-0.217934\pi\)
0.774635 + 0.632409i \(0.217934\pi\)
\(98\) −3.83299 −0.387191
\(99\) −0.857706 −0.0862027
\(100\) −6.49260 −0.649260
\(101\) −7.31205 −0.727576 −0.363788 0.931482i \(-0.618517\pi\)
−0.363788 + 0.931482i \(0.618517\pi\)
\(102\) 1.74519 0.172800
\(103\) 2.60750 0.256924 0.128462 0.991714i \(-0.458996\pi\)
0.128462 + 0.991714i \(0.458996\pi\)
\(104\) 7.29391 0.715227
\(105\) 3.86341 0.377030
\(106\) −10.6282 −1.03230
\(107\) 2.00243 0.193582 0.0967911 0.995305i \(-0.469142\pi\)
0.0967911 + 0.995305i \(0.469142\pi\)
\(108\) 14.7665 1.42090
\(109\) −1.94507 −0.186304 −0.0931518 0.995652i \(-0.529694\pi\)
−0.0931518 + 0.995652i \(0.529694\pi\)
\(110\) −1.49511 −0.142553
\(111\) −5.74494 −0.545285
\(112\) −6.63148 −0.626616
\(113\) −14.2743 −1.34281 −0.671406 0.741090i \(-0.734309\pi\)
−0.671406 + 0.741090i \(0.734309\pi\)
\(114\) −2.52821 −0.236789
\(115\) −3.41186 −0.318158
\(116\) 4.54917 0.422379
\(117\) 4.44658 0.411086
\(118\) −21.7956 −2.00645
\(119\) −2.93364 −0.268926
\(120\) 5.32529 0.486130
\(121\) −10.8789 −0.988995
\(122\) 11.9273 1.07985
\(123\) −7.66821 −0.691419
\(124\) −11.7915 −1.05891
\(125\) −12.1682 −1.08836
\(126\) −17.2576 −1.53743
\(127\) −2.58523 −0.229402 −0.114701 0.993400i \(-0.536591\pi\)
−0.114701 + 0.993400i \(0.536591\pi\)
\(128\) 20.7384 1.83303
\(129\) 4.10764 0.361657
\(130\) 7.75105 0.679812
\(131\) 7.25358 0.633748 0.316874 0.948468i \(-0.397367\pi\)
0.316874 + 0.948468i \(0.397367\pi\)
\(132\) −0.940088 −0.0818242
\(133\) 4.24988 0.368511
\(134\) −8.70302 −0.751826
\(135\) 7.19725 0.619441
\(136\) −4.04370 −0.346744
\(137\) −16.2933 −1.39203 −0.696017 0.718025i \(-0.745046\pi\)
−0.696017 + 0.718025i \(0.745046\pi\)
\(138\) −3.30663 −0.281479
\(139\) 0.813084 0.0689649 0.0344824 0.999405i \(-0.489022\pi\)
0.0344824 + 0.999405i \(0.489022\pi\)
\(140\) −19.5171 −1.64950
\(141\) −4.94428 −0.416384
\(142\) 4.37613 0.367237
\(143\) −0.627591 −0.0524818
\(144\) −5.57247 −0.464373
\(145\) 2.21729 0.184136
\(146\) −26.6307 −2.20397
\(147\) −1.17469 −0.0968869
\(148\) 29.0222 2.38561
\(149\) −5.41745 −0.443815 −0.221907 0.975068i \(-0.571228\pi\)
−0.221907 + 0.975068i \(0.571228\pi\)
\(150\) −3.06692 −0.250413
\(151\) −15.9860 −1.30093 −0.650463 0.759538i \(-0.725425\pi\)
−0.650463 + 0.759538i \(0.725425\pi\)
\(152\) 5.85798 0.475145
\(153\) −2.46515 −0.199296
\(154\) 2.43574 0.196277
\(155\) −5.74725 −0.461630
\(156\) 4.87367 0.390206
\(157\) 15.9674 1.27434 0.637170 0.770723i \(-0.280105\pi\)
0.637170 + 0.770723i \(0.280105\pi\)
\(158\) −19.5723 −1.55709
\(159\) −3.25720 −0.258312
\(160\) 4.84959 0.383394
\(161\) 5.55838 0.438062
\(162\) −10.6727 −0.838525
\(163\) −17.2121 −1.34815 −0.674077 0.738661i \(-0.735458\pi\)
−0.674077 + 0.738661i \(0.735458\pi\)
\(164\) 38.7381 3.02494
\(165\) −0.458204 −0.0356712
\(166\) 2.90659 0.225595
\(167\) −6.95504 −0.538197 −0.269099 0.963113i \(-0.586726\pi\)
−0.269099 + 0.963113i \(0.586726\pi\)
\(168\) −8.67561 −0.669338
\(169\) −9.74640 −0.749723
\(170\) −4.29713 −0.329575
\(171\) 3.57119 0.273096
\(172\) −20.7509 −1.58224
\(173\) 15.5483 1.18212 0.591059 0.806629i \(-0.298710\pi\)
0.591059 + 0.806629i \(0.298710\pi\)
\(174\) 2.14890 0.162908
\(175\) 5.15544 0.389715
\(176\) 0.786500 0.0592846
\(177\) −6.67967 −0.502075
\(178\) 6.20792 0.465303
\(179\) −16.8613 −1.26028 −0.630138 0.776483i \(-0.717002\pi\)
−0.630138 + 0.776483i \(0.717002\pi\)
\(180\) −16.4003 −1.22241
\(181\) −8.87793 −0.659892 −0.329946 0.944000i \(-0.607030\pi\)
−0.329946 + 0.944000i \(0.607030\pi\)
\(182\) −12.6275 −0.936013
\(183\) 3.65534 0.270211
\(184\) 7.66161 0.564822
\(185\) 14.1456 1.04000
\(186\) −5.56999 −0.408411
\(187\) 0.347932 0.0254433
\(188\) 24.9774 1.82167
\(189\) −11.7253 −0.852889
\(190\) 6.22513 0.451618
\(191\) −10.2305 −0.740250 −0.370125 0.928982i \(-0.620685\pi\)
−0.370125 + 0.928982i \(0.620685\pi\)
\(192\) 8.00636 0.577810
\(193\) −7.55672 −0.543945 −0.271972 0.962305i \(-0.587676\pi\)
−0.271972 + 0.962305i \(0.587676\pi\)
\(194\) −36.4118 −2.61421
\(195\) 2.37545 0.170110
\(196\) 5.93428 0.423877
\(197\) 8.75809 0.623988 0.311994 0.950084i \(-0.399003\pi\)
0.311994 + 0.950084i \(0.399003\pi\)
\(198\) 2.04676 0.145457
\(199\) −27.7511 −1.96722 −0.983611 0.180303i \(-0.942292\pi\)
−0.983611 + 0.180303i \(0.942292\pi\)
\(200\) 7.10620 0.502484
\(201\) −2.66720 −0.188130
\(202\) 17.4489 1.22770
\(203\) −3.61226 −0.253531
\(204\) −2.70193 −0.189173
\(205\) 18.8812 1.31872
\(206\) −6.22233 −0.433530
\(207\) 4.67074 0.324639
\(208\) −4.07742 −0.282718
\(209\) −0.504039 −0.0348651
\(210\) −9.21935 −0.636195
\(211\) −21.8646 −1.50522 −0.752610 0.658467i \(-0.771205\pi\)
−0.752610 + 0.658467i \(0.771205\pi\)
\(212\) 16.4546 1.13011
\(213\) 1.34115 0.0918938
\(214\) −4.77844 −0.326647
\(215\) −10.1141 −0.689775
\(216\) −16.1620 −1.09969
\(217\) 9.36305 0.635605
\(218\) 4.64155 0.314366
\(219\) −8.16146 −0.551500
\(220\) 2.31475 0.156060
\(221\) −1.80377 −0.121335
\(222\) 13.7093 0.920106
\(223\) 14.0179 0.938709 0.469354 0.883010i \(-0.344487\pi\)
0.469354 + 0.883010i \(0.344487\pi\)
\(224\) −7.90064 −0.527884
\(225\) 4.33215 0.288810
\(226\) 34.0630 2.26584
\(227\) 2.91981 0.193795 0.0968973 0.995294i \(-0.469108\pi\)
0.0968973 + 0.995294i \(0.469108\pi\)
\(228\) 3.91421 0.259225
\(229\) 14.8579 0.981835 0.490917 0.871206i \(-0.336662\pi\)
0.490917 + 0.871206i \(0.336662\pi\)
\(230\) 8.14180 0.536854
\(231\) 0.746476 0.0491145
\(232\) −4.97910 −0.326894
\(233\) 9.89756 0.648411 0.324205 0.945987i \(-0.394903\pi\)
0.324205 + 0.945987i \(0.394903\pi\)
\(234\) −10.6110 −0.693661
\(235\) 12.1741 0.794154
\(236\) 33.7442 2.19656
\(237\) −5.99829 −0.389631
\(238\) 7.00060 0.453782
\(239\) −9.07454 −0.586983 −0.293492 0.955962i \(-0.594817\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(240\) −2.97693 −0.192160
\(241\) 22.4628 1.44695 0.723477 0.690348i \(-0.242543\pi\)
0.723477 + 0.690348i \(0.242543\pi\)
\(242\) 25.9607 1.66881
\(243\) −15.2614 −0.979017
\(244\) −18.4660 −1.18216
\(245\) 2.89240 0.184789
\(246\) 18.2988 1.16669
\(247\) 2.61307 0.166266
\(248\) 12.9059 0.819527
\(249\) 0.890777 0.0564507
\(250\) 29.0372 1.83648
\(251\) 2.12835 0.134340 0.0671702 0.997742i \(-0.478603\pi\)
0.0671702 + 0.997742i \(0.478603\pi\)
\(252\) 26.7184 1.68310
\(253\) −0.659229 −0.0414454
\(254\) 6.16919 0.387090
\(255\) −1.31694 −0.0824697
\(256\) −27.5931 −1.72457
\(257\) −28.0764 −1.75136 −0.875679 0.482894i \(-0.839586\pi\)
−0.875679 + 0.482894i \(0.839586\pi\)
\(258\) −9.80214 −0.610255
\(259\) −23.0450 −1.43195
\(260\) −12.0003 −0.744225
\(261\) −3.03540 −0.187887
\(262\) −17.3094 −1.06938
\(263\) −16.3530 −1.00837 −0.504185 0.863596i \(-0.668207\pi\)
−0.504185 + 0.863596i \(0.668207\pi\)
\(264\) 1.02893 0.0633266
\(265\) 8.02008 0.492670
\(266\) −10.1416 −0.621820
\(267\) 1.90253 0.116433
\(268\) 13.4741 0.823063
\(269\) 24.8267 1.51371 0.756855 0.653583i \(-0.226735\pi\)
0.756855 + 0.653583i \(0.226735\pi\)
\(270\) −17.1750 −1.04524
\(271\) 21.5124 1.30678 0.653392 0.757020i \(-0.273345\pi\)
0.653392 + 0.757020i \(0.273345\pi\)
\(272\) 2.26050 0.137063
\(273\) −3.86993 −0.234219
\(274\) 38.8812 2.34890
\(275\) −0.611440 −0.0368712
\(276\) 5.11936 0.308149
\(277\) −18.1491 −1.09048 −0.545238 0.838281i \(-0.683561\pi\)
−0.545238 + 0.838281i \(0.683561\pi\)
\(278\) −1.94028 −0.116370
\(279\) 7.86782 0.471034
\(280\) 21.3617 1.27660
\(281\) 9.52494 0.568210 0.284105 0.958793i \(-0.408304\pi\)
0.284105 + 0.958793i \(0.408304\pi\)
\(282\) 11.7987 0.702600
\(283\) 28.4718 1.69247 0.846237 0.532806i \(-0.178863\pi\)
0.846237 + 0.532806i \(0.178863\pi\)
\(284\) −6.77517 −0.402033
\(285\) 1.90781 0.113009
\(286\) 1.49763 0.0885570
\(287\) −30.7600 −1.81570
\(288\) −6.63895 −0.391204
\(289\) 1.00000 0.0588235
\(290\) −5.29116 −0.310708
\(291\) −11.1591 −0.654155
\(292\) 41.2299 2.41280
\(293\) 6.76742 0.395357 0.197678 0.980267i \(-0.436660\pi\)
0.197678 + 0.980267i \(0.436660\pi\)
\(294\) 2.80319 0.163485
\(295\) 16.4471 0.957588
\(296\) −31.7650 −1.84630
\(297\) 1.39063 0.0806926
\(298\) 12.9278 0.748886
\(299\) 3.41762 0.197646
\(300\) 4.74825 0.274140
\(301\) 16.4772 0.949731
\(302\) 38.1478 2.19516
\(303\) 5.34754 0.307208
\(304\) −3.27471 −0.187818
\(305\) −9.00042 −0.515363
\(306\) 5.88265 0.336289
\(307\) 13.3185 0.760130 0.380065 0.924960i \(-0.375902\pi\)
0.380065 + 0.924960i \(0.375902\pi\)
\(308\) −3.77103 −0.214875
\(309\) −1.90695 −0.108482
\(310\) 13.7148 0.778948
\(311\) −14.9468 −0.847553 −0.423777 0.905767i \(-0.639296\pi\)
−0.423777 + 0.905767i \(0.639296\pi\)
\(312\) −5.33427 −0.301994
\(313\) 10.8435 0.612911 0.306455 0.951885i \(-0.400857\pi\)
0.306455 + 0.951885i \(0.400857\pi\)
\(314\) −38.1034 −2.15030
\(315\) 13.0227 0.733745
\(316\) 30.3021 1.70462
\(317\) 28.0955 1.57800 0.789001 0.614392i \(-0.210599\pi\)
0.789001 + 0.614392i \(0.210599\pi\)
\(318\) 7.77272 0.435872
\(319\) 0.428417 0.0239868
\(320\) −19.7138 −1.10204
\(321\) −1.46444 −0.0817371
\(322\) −13.2641 −0.739179
\(323\) −1.44867 −0.0806062
\(324\) 16.5236 0.917976
\(325\) 3.16987 0.175833
\(326\) 41.0735 2.27485
\(327\) 1.42249 0.0786638
\(328\) −42.3992 −2.34110
\(329\) −19.8333 −1.09345
\(330\) 1.09342 0.0601910
\(331\) 6.19250 0.340371 0.170185 0.985412i \(-0.445563\pi\)
0.170185 + 0.985412i \(0.445563\pi\)
\(332\) −4.50001 −0.246970
\(333\) −19.3649 −1.06119
\(334\) 16.5970 0.908145
\(335\) 6.56736 0.358813
\(336\) 4.84982 0.264579
\(337\) 27.5485 1.50066 0.750332 0.661061i \(-0.229894\pi\)
0.750332 + 0.661061i \(0.229894\pi\)
\(338\) 23.2580 1.26507
\(339\) 10.4392 0.566982
\(340\) 6.65287 0.360803
\(341\) −1.11047 −0.0601351
\(342\) −8.52202 −0.460818
\(343\) 15.8234 0.854381
\(344\) 22.7120 1.22455
\(345\) 2.49521 0.134337
\(346\) −37.1033 −1.99469
\(347\) −3.93699 −0.211349 −0.105674 0.994401i \(-0.533700\pi\)
−0.105674 + 0.994401i \(0.533700\pi\)
\(348\) −3.32695 −0.178343
\(349\) 3.06845 0.164251 0.0821253 0.996622i \(-0.473829\pi\)
0.0821253 + 0.996622i \(0.473829\pi\)
\(350\) −12.3025 −0.657598
\(351\) −7.20940 −0.384809
\(352\) 0.937023 0.0499435
\(353\) 1.00000 0.0532246
\(354\) 15.9398 0.847193
\(355\) −3.30226 −0.175266
\(356\) −9.61117 −0.509391
\(357\) 2.14546 0.113550
\(358\) 40.2366 2.12657
\(359\) −12.8218 −0.676707 −0.338354 0.941019i \(-0.609870\pi\)
−0.338354 + 0.941019i \(0.609870\pi\)
\(360\) 17.9503 0.946065
\(361\) −16.9014 −0.889545
\(362\) 21.1856 1.11349
\(363\) 7.95612 0.417588
\(364\) 19.5501 1.02470
\(365\) 20.0957 1.05186
\(366\) −8.72282 −0.455949
\(367\) −23.3278 −1.21770 −0.608849 0.793286i \(-0.708369\pi\)
−0.608849 + 0.793286i \(0.708369\pi\)
\(368\) −4.28298 −0.223266
\(369\) −25.8478 −1.34558
\(370\) −33.7559 −1.75488
\(371\) −13.0658 −0.678342
\(372\) 8.62352 0.447109
\(373\) −28.1304 −1.45654 −0.728268 0.685293i \(-0.759674\pi\)
−0.728268 + 0.685293i \(0.759674\pi\)
\(374\) −0.830278 −0.0429327
\(375\) 8.89900 0.459542
\(376\) −27.3380 −1.40985
\(377\) −2.22103 −0.114389
\(378\) 27.9803 1.43915
\(379\) −12.4012 −0.637004 −0.318502 0.947922i \(-0.603180\pi\)
−0.318502 + 0.947922i \(0.603180\pi\)
\(380\) −9.63782 −0.494410
\(381\) 1.89066 0.0968616
\(382\) 24.4132 1.24909
\(383\) −19.9183 −1.01778 −0.508888 0.860833i \(-0.669943\pi\)
−0.508888 + 0.860833i \(0.669943\pi\)
\(384\) −15.1666 −0.773969
\(385\) −1.83802 −0.0936743
\(386\) 18.0328 0.917844
\(387\) 13.8459 0.703826
\(388\) 56.3731 2.86191
\(389\) 1.68839 0.0856048 0.0428024 0.999084i \(-0.486371\pi\)
0.0428024 + 0.999084i \(0.486371\pi\)
\(390\) −5.66860 −0.287041
\(391\) −1.89471 −0.0958194
\(392\) −6.49512 −0.328053
\(393\) −5.30478 −0.267591
\(394\) −20.8996 −1.05291
\(395\) 14.7694 0.743129
\(396\) −3.16882 −0.159239
\(397\) −36.3951 −1.82662 −0.913308 0.407269i \(-0.866481\pi\)
−0.913308 + 0.407269i \(0.866481\pi\)
\(398\) 66.2230 3.31946
\(399\) −3.10807 −0.155598
\(400\) −3.97249 −0.198625
\(401\) 21.1548 1.05642 0.528210 0.849114i \(-0.322863\pi\)
0.528210 + 0.849114i \(0.322863\pi\)
\(402\) 6.36480 0.317447
\(403\) 5.75695 0.286774
\(404\) −27.0146 −1.34403
\(405\) 8.05368 0.400190
\(406\) 8.62001 0.427804
\(407\) 2.73316 0.135478
\(408\) 2.95729 0.146407
\(409\) 6.03160 0.298243 0.149122 0.988819i \(-0.452355\pi\)
0.149122 + 0.988819i \(0.452355\pi\)
\(410\) −45.0565 −2.22518
\(411\) 11.9158 0.587765
\(412\) 9.63348 0.474607
\(413\) −26.7946 −1.31847
\(414\) −11.1459 −0.547790
\(415\) −2.19333 −0.107666
\(416\) −4.85778 −0.238172
\(417\) −0.594635 −0.0291194
\(418\) 1.20280 0.0588308
\(419\) −28.7800 −1.40599 −0.702996 0.711193i \(-0.748155\pi\)
−0.702996 + 0.711193i \(0.748155\pi\)
\(420\) 14.2735 0.696475
\(421\) −26.4896 −1.29102 −0.645512 0.763750i \(-0.723356\pi\)
−0.645512 + 0.763750i \(0.723356\pi\)
\(422\) 52.1759 2.53988
\(423\) −16.6660 −0.810331
\(424\) −18.0097 −0.874630
\(425\) −1.75735 −0.0852442
\(426\) −3.20040 −0.155060
\(427\) 14.6629 0.709587
\(428\) 7.39804 0.357598
\(429\) 0.458978 0.0221596
\(430\) 24.1355 1.16392
\(431\) −19.0198 −0.916154 −0.458077 0.888913i \(-0.651462\pi\)
−0.458077 + 0.888913i \(0.651462\pi\)
\(432\) 9.03485 0.434689
\(433\) 27.3321 1.31350 0.656748 0.754110i \(-0.271931\pi\)
0.656748 + 0.754110i \(0.271931\pi\)
\(434\) −22.3432 −1.07251
\(435\) −1.62157 −0.0777486
\(436\) −7.18611 −0.344152
\(437\) 2.74480 0.131302
\(438\) 19.4759 0.930593
\(439\) 8.16086 0.389497 0.194748 0.980853i \(-0.437611\pi\)
0.194748 + 0.980853i \(0.437611\pi\)
\(440\) −2.53351 −0.120780
\(441\) −3.95961 −0.188553
\(442\) 4.30438 0.204739
\(443\) −29.3754 −1.39567 −0.697835 0.716259i \(-0.745853\pi\)
−0.697835 + 0.716259i \(0.745853\pi\)
\(444\) −21.2248 −1.00729
\(445\) −4.68454 −0.222068
\(446\) −33.4512 −1.58396
\(447\) 3.96196 0.187394
\(448\) 32.1164 1.51736
\(449\) 14.1923 0.669775 0.334888 0.942258i \(-0.391302\pi\)
0.334888 + 0.942258i \(0.391302\pi\)
\(450\) −10.3379 −0.487333
\(451\) 3.64816 0.171785
\(452\) −52.7368 −2.48053
\(453\) 11.6911 0.549296
\(454\) −6.96760 −0.327006
\(455\) 9.52880 0.446717
\(456\) −4.28413 −0.200623
\(457\) −13.6666 −0.639296 −0.319648 0.947536i \(-0.603565\pi\)
−0.319648 + 0.947536i \(0.603565\pi\)
\(458\) −35.4556 −1.65673
\(459\) 3.99684 0.186557
\(460\) −12.6052 −0.587722
\(461\) −22.9365 −1.06826 −0.534129 0.845403i \(-0.679360\pi\)
−0.534129 + 0.845403i \(0.679360\pi\)
\(462\) −1.78133 −0.0828751
\(463\) −10.9090 −0.506985 −0.253492 0.967337i \(-0.581579\pi\)
−0.253492 + 0.967337i \(0.581579\pi\)
\(464\) 2.78340 0.129216
\(465\) 4.20315 0.194916
\(466\) −23.6188 −1.09412
\(467\) −15.6351 −0.723507 −0.361753 0.932274i \(-0.617822\pi\)
−0.361753 + 0.932274i \(0.617822\pi\)
\(468\) 16.4280 0.759385
\(469\) −10.6991 −0.494039
\(470\) −29.0514 −1.34004
\(471\) −11.6775 −0.538071
\(472\) −36.9333 −1.69999
\(473\) −1.95421 −0.0898548
\(474\) 14.3139 0.657457
\(475\) 2.54583 0.116811
\(476\) −10.8384 −0.496778
\(477\) −10.9793 −0.502706
\(478\) 21.6548 0.990466
\(479\) 26.1414 1.19443 0.597216 0.802080i \(-0.296273\pi\)
0.597216 + 0.802080i \(0.296273\pi\)
\(480\) −3.54666 −0.161882
\(481\) −14.1694 −0.646071
\(482\) −53.6034 −2.44157
\(483\) −4.06502 −0.184965
\(484\) −40.1926 −1.82694
\(485\) 27.4766 1.24765
\(486\) 36.4185 1.65198
\(487\) 28.9095 1.31002 0.655008 0.755622i \(-0.272665\pi\)
0.655008 + 0.755622i \(0.272665\pi\)
\(488\) 20.2112 0.914917
\(489\) 12.5877 0.569237
\(490\) −6.90220 −0.311810
\(491\) 6.07604 0.274208 0.137104 0.990557i \(-0.456221\pi\)
0.137104 + 0.990557i \(0.456221\pi\)
\(492\) −28.3304 −1.27723
\(493\) 1.23132 0.0554561
\(494\) −6.23563 −0.280554
\(495\) −1.54450 −0.0694202
\(496\) −7.21464 −0.323947
\(497\) 5.37982 0.241318
\(498\) −2.12568 −0.0952541
\(499\) 38.8961 1.74123 0.870614 0.491966i \(-0.163722\pi\)
0.870614 + 0.491966i \(0.163722\pi\)
\(500\) −44.9558 −2.01048
\(501\) 5.08645 0.227246
\(502\) −5.07893 −0.226684
\(503\) −32.4758 −1.44802 −0.724012 0.689787i \(-0.757704\pi\)
−0.724012 + 0.689787i \(0.757704\pi\)
\(504\) −29.2435 −1.30261
\(505\) −13.1671 −0.585926
\(506\) 1.57313 0.0699343
\(507\) 7.12786 0.316559
\(508\) −9.55122 −0.423767
\(509\) −24.7597 −1.09746 −0.548728 0.836001i \(-0.684888\pi\)
−0.548728 + 0.836001i \(0.684888\pi\)
\(510\) 3.14263 0.139158
\(511\) −32.7386 −1.44827
\(512\) 24.3693 1.07698
\(513\) −5.79011 −0.255640
\(514\) 66.9993 2.95521
\(515\) 4.69541 0.206905
\(516\) 15.1758 0.668077
\(517\) 2.35225 0.103452
\(518\) 54.9928 2.41625
\(519\) −11.3710 −0.499131
\(520\) 13.1344 0.575982
\(521\) −41.3687 −1.81240 −0.906198 0.422853i \(-0.861029\pi\)
−0.906198 + 0.422853i \(0.861029\pi\)
\(522\) 7.24345 0.317037
\(523\) 9.02974 0.394843 0.197422 0.980319i \(-0.436743\pi\)
0.197422 + 0.980319i \(0.436743\pi\)
\(524\) 26.7986 1.17070
\(525\) −3.77034 −0.164551
\(526\) 39.0236 1.70151
\(527\) −3.19162 −0.139029
\(528\) −0.575193 −0.0250320
\(529\) −19.4101 −0.843917
\(530\) −19.1385 −0.831323
\(531\) −22.5156 −0.977095
\(532\) 15.7013 0.680738
\(533\) −18.9130 −0.819214
\(534\) −4.54005 −0.196467
\(535\) 3.60584 0.155894
\(536\) −14.7475 −0.636996
\(537\) 12.3312 0.532132
\(538\) −59.2445 −2.55421
\(539\) 0.558861 0.0240718
\(540\) 26.5905 1.14427
\(541\) −39.1174 −1.68179 −0.840895 0.541198i \(-0.817971\pi\)
−0.840895 + 0.541198i \(0.817971\pi\)
\(542\) −51.3354 −2.20505
\(543\) 6.49272 0.278629
\(544\) 2.69312 0.115467
\(545\) −3.50255 −0.150033
\(546\) 9.23490 0.395217
\(547\) −33.1264 −1.41638 −0.708192 0.706020i \(-0.750489\pi\)
−0.708192 + 0.706020i \(0.750489\pi\)
\(548\) −60.1963 −2.57146
\(549\) 12.3213 0.525861
\(550\) 1.45909 0.0622159
\(551\) −1.78378 −0.0759917
\(552\) −5.60318 −0.238487
\(553\) −24.0613 −1.02319
\(554\) 43.3097 1.84005
\(555\) −10.3451 −0.439125
\(556\) 3.00396 0.127396
\(557\) 11.8344 0.501439 0.250719 0.968060i \(-0.419333\pi\)
0.250719 + 0.968060i \(0.419333\pi\)
\(558\) −18.7751 −0.794815
\(559\) 10.1312 0.428502
\(560\) −11.9415 −0.504622
\(561\) −0.254454 −0.0107431
\(562\) −22.7296 −0.958789
\(563\) 1.38282 0.0582788 0.0291394 0.999575i \(-0.490723\pi\)
0.0291394 + 0.999575i \(0.490723\pi\)
\(564\) −18.2668 −0.769172
\(565\) −25.7042 −1.08138
\(566\) −67.9429 −2.85585
\(567\) −13.1205 −0.551010
\(568\) 7.41548 0.311147
\(569\) 14.2588 0.597760 0.298880 0.954291i \(-0.403387\pi\)
0.298880 + 0.954291i \(0.403387\pi\)
\(570\) −4.55264 −0.190689
\(571\) −12.7902 −0.535254 −0.267627 0.963523i \(-0.586239\pi\)
−0.267627 + 0.963523i \(0.586239\pi\)
\(572\) −2.31865 −0.0969478
\(573\) 7.48187 0.312560
\(574\) 73.4032 3.06379
\(575\) 3.32967 0.138857
\(576\) 26.9876 1.12448
\(577\) −15.9144 −0.662525 −0.331262 0.943539i \(-0.607475\pi\)
−0.331262 + 0.943539i \(0.607475\pi\)
\(578\) −2.38632 −0.0992579
\(579\) 5.52648 0.229673
\(580\) 8.19184 0.340148
\(581\) 3.57323 0.148243
\(582\) 26.6291 1.10381
\(583\) 1.54961 0.0641785
\(584\) −45.1265 −1.86735
\(585\) 8.00711 0.331053
\(586\) −16.1492 −0.667119
\(587\) −23.6222 −0.974992 −0.487496 0.873125i \(-0.662090\pi\)
−0.487496 + 0.873125i \(0.662090\pi\)
\(588\) −4.33993 −0.178976
\(589\) 4.62360 0.190512
\(590\) −39.2481 −1.61582
\(591\) −6.40507 −0.263469
\(592\) 17.7572 0.729816
\(593\) 25.4016 1.04312 0.521560 0.853215i \(-0.325350\pi\)
0.521560 + 0.853215i \(0.325350\pi\)
\(594\) −3.31849 −0.136159
\(595\) −5.28271 −0.216570
\(596\) −20.0149 −0.819844
\(597\) 20.2953 0.830630
\(598\) −8.15554 −0.333505
\(599\) −19.8692 −0.811833 −0.405916 0.913910i \(-0.633048\pi\)
−0.405916 + 0.913910i \(0.633048\pi\)
\(600\) −5.19700 −0.212166
\(601\) −2.68442 −0.109500 −0.0547500 0.998500i \(-0.517436\pi\)
−0.0547500 + 0.998500i \(0.517436\pi\)
\(602\) −39.3199 −1.60256
\(603\) −8.99052 −0.366122
\(604\) −59.0609 −2.40315
\(605\) −19.5901 −0.796451
\(606\) −12.7609 −0.518378
\(607\) 48.1090 1.95268 0.976342 0.216233i \(-0.0693770\pi\)
0.976342 + 0.216233i \(0.0693770\pi\)
\(608\) −3.90144 −0.158224
\(609\) 2.64176 0.107050
\(610\) 21.4779 0.869615
\(611\) −12.1947 −0.493344
\(612\) −9.10758 −0.368152
\(613\) −8.90899 −0.359831 −0.179915 0.983682i \(-0.557582\pi\)
−0.179915 + 0.983682i \(0.557582\pi\)
\(614\) −31.7823 −1.28263
\(615\) −13.8084 −0.556809
\(616\) 4.12743 0.166299
\(617\) 16.7211 0.673165 0.336582 0.941654i \(-0.390729\pi\)
0.336582 + 0.941654i \(0.390729\pi\)
\(618\) 4.55059 0.183052
\(619\) −1.04364 −0.0419474 −0.0209737 0.999780i \(-0.506677\pi\)
−0.0209737 + 0.999780i \(0.506677\pi\)
\(620\) −21.2334 −0.852754
\(621\) −7.57284 −0.303888
\(622\) 35.6678 1.43015
\(623\) 7.63174 0.305759
\(624\) 2.98195 0.119374
\(625\) −13.1249 −0.524998
\(626\) −25.8761 −1.03422
\(627\) 0.368620 0.0147213
\(628\) 58.9922 2.35404
\(629\) 7.85544 0.313217
\(630\) −31.0763 −1.23811
\(631\) −23.6152 −0.940108 −0.470054 0.882638i \(-0.655766\pi\)
−0.470054 + 0.882638i \(0.655766\pi\)
\(632\) −33.1659 −1.31927
\(633\) 15.9903 0.635556
\(634\) −67.0450 −2.66270
\(635\) −4.65532 −0.184741
\(636\) −12.0338 −0.477172
\(637\) −2.89728 −0.114795
\(638\) −1.02234 −0.0404749
\(639\) 4.52069 0.178836
\(640\) 37.3443 1.47616
\(641\) 22.5720 0.891541 0.445770 0.895147i \(-0.352930\pi\)
0.445770 + 0.895147i \(0.352930\pi\)
\(642\) 3.49463 0.137922
\(643\) −37.5789 −1.48197 −0.740984 0.671522i \(-0.765641\pi\)
−0.740984 + 0.671522i \(0.765641\pi\)
\(644\) 20.5356 0.809216
\(645\) 7.39676 0.291247
\(646\) 3.45699 0.136014
\(647\) −7.42682 −0.291978 −0.145989 0.989286i \(-0.546636\pi\)
−0.145989 + 0.989286i \(0.546636\pi\)
\(648\) −18.0852 −0.710453
\(649\) 3.17786 0.124742
\(650\) −7.56433 −0.296697
\(651\) −6.84750 −0.268375
\(652\) −63.5905 −2.49040
\(653\) 32.5806 1.27498 0.637488 0.770460i \(-0.279973\pi\)
0.637488 + 0.770460i \(0.279973\pi\)
\(654\) −3.39452 −0.132736
\(655\) 13.0618 0.510366
\(656\) 23.7019 0.925403
\(657\) −27.5104 −1.07328
\(658\) 47.3287 1.84506
\(659\) 33.3575 1.29942 0.649712 0.760181i \(-0.274890\pi\)
0.649712 + 0.760181i \(0.274890\pi\)
\(660\) −1.69285 −0.0658941
\(661\) 13.0929 0.509256 0.254628 0.967039i \(-0.418047\pi\)
0.254628 + 0.967039i \(0.418047\pi\)
\(662\) −14.7773 −0.574336
\(663\) 1.31916 0.0512318
\(664\) 4.92530 0.191139
\(665\) 7.65290 0.296767
\(666\) 46.2108 1.79063
\(667\) −2.33300 −0.0903340
\(668\) −25.6956 −0.994193
\(669\) −10.2517 −0.396356
\(670\) −15.6718 −0.605456
\(671\) −1.73903 −0.0671346
\(672\) 5.77799 0.222891
\(673\) −13.4103 −0.516931 −0.258465 0.966020i \(-0.583217\pi\)
−0.258465 + 0.966020i \(0.583217\pi\)
\(674\) −65.7397 −2.53220
\(675\) −7.02387 −0.270349
\(676\) −36.0084 −1.38494
\(677\) −27.3196 −1.04998 −0.524989 0.851109i \(-0.675931\pi\)
−0.524989 + 0.851109i \(0.675931\pi\)
\(678\) −24.9114 −0.956717
\(679\) −44.7630 −1.71785
\(680\) −7.28162 −0.279238
\(681\) −2.13535 −0.0818268
\(682\) 2.64993 0.101471
\(683\) −3.80562 −0.145618 −0.0728089 0.997346i \(-0.523196\pi\)
−0.0728089 + 0.997346i \(0.523196\pi\)
\(684\) 13.1939 0.504481
\(685\) −29.3400 −1.12102
\(686\) −37.7596 −1.44167
\(687\) −10.8660 −0.414565
\(688\) −12.6964 −0.484046
\(689\) −8.03362 −0.306056
\(690\) −5.95436 −0.226679
\(691\) −19.2715 −0.733123 −0.366562 0.930394i \(-0.619465\pi\)
−0.366562 + 0.930394i \(0.619465\pi\)
\(692\) 57.4438 2.18368
\(693\) 2.51620 0.0955825
\(694\) 9.39493 0.356627
\(695\) 1.46415 0.0555383
\(696\) 3.64138 0.138026
\(697\) 10.4853 0.397158
\(698\) −7.32232 −0.277154
\(699\) −7.23841 −0.273782
\(700\) 19.0469 0.719906
\(701\) −45.4262 −1.71572 −0.857862 0.513880i \(-0.828208\pi\)
−0.857862 + 0.513880i \(0.828208\pi\)
\(702\) 17.2039 0.649321
\(703\) −11.3799 −0.429203
\(704\) −3.80904 −0.143559
\(705\) −8.90335 −0.335319
\(706\) −2.38632 −0.0898104
\(707\) 21.4509 0.806744
\(708\) −24.6782 −0.927465
\(709\) −5.02016 −0.188536 −0.0942680 0.995547i \(-0.530051\pi\)
−0.0942680 + 0.995547i \(0.530051\pi\)
\(710\) 7.88025 0.295740
\(711\) −20.2189 −0.758267
\(712\) 10.5195 0.394235
\(713\) 6.04717 0.226468
\(714\) −5.11977 −0.191603
\(715\) −1.13013 −0.0422643
\(716\) −62.2947 −2.32806
\(717\) 6.63651 0.247845
\(718\) 30.5969 1.14186
\(719\) 0.626950 0.0233813 0.0116907 0.999932i \(-0.496279\pi\)
0.0116907 + 0.999932i \(0.496279\pi\)
\(720\) −10.0345 −0.373965
\(721\) −7.64945 −0.284881
\(722\) 40.3321 1.50100
\(723\) −16.4277 −0.610955
\(724\) −32.7998 −1.21899
\(725\) −2.16387 −0.0803642
\(726\) −18.9859 −0.704632
\(727\) 8.82628 0.327349 0.163674 0.986514i \(-0.447665\pi\)
0.163674 + 0.986514i \(0.447665\pi\)
\(728\) −21.3977 −0.793051
\(729\) −2.25619 −0.0835624
\(730\) −47.9548 −1.77489
\(731\) −5.61665 −0.207739
\(732\) 13.5048 0.499151
\(733\) 41.5035 1.53297 0.766484 0.642263i \(-0.222004\pi\)
0.766484 + 0.642263i \(0.222004\pi\)
\(734\) 55.6675 2.05473
\(735\) −2.11531 −0.0780243
\(736\) −5.10267 −0.188087
\(737\) 1.26892 0.0467414
\(738\) 61.6811 2.27051
\(739\) −20.0707 −0.738312 −0.369156 0.929367i \(-0.620353\pi\)
−0.369156 + 0.929367i \(0.620353\pi\)
\(740\) 52.2612 1.92116
\(741\) −1.91103 −0.0702033
\(742\) 31.1792 1.14462
\(743\) 24.6198 0.903211 0.451606 0.892218i \(-0.350851\pi\)
0.451606 + 0.892218i \(0.350851\pi\)
\(744\) −9.43852 −0.346033
\(745\) −9.75539 −0.357410
\(746\) 67.1281 2.45774
\(747\) 3.00261 0.109860
\(748\) 1.28545 0.0470006
\(749\) −5.87440 −0.214646
\(750\) −21.2359 −0.775425
\(751\) 20.2311 0.738242 0.369121 0.929381i \(-0.379659\pi\)
0.369121 + 0.929381i \(0.379659\pi\)
\(752\) 15.2824 0.557293
\(753\) −1.55653 −0.0567232
\(754\) 5.30009 0.193018
\(755\) −28.7866 −1.04765
\(756\) −43.3195 −1.57551
\(757\) 1.00053 0.0363648 0.0181824 0.999835i \(-0.494212\pi\)
0.0181824 + 0.999835i \(0.494212\pi\)
\(758\) 29.5931 1.07487
\(759\) 0.482116 0.0174997
\(760\) 10.5487 0.382641
\(761\) −10.7841 −0.390925 −0.195462 0.980711i \(-0.562621\pi\)
−0.195462 + 0.980711i \(0.562621\pi\)
\(762\) −4.51173 −0.163443
\(763\) 5.70612 0.206575
\(764\) −37.7968 −1.36744
\(765\) −4.43909 −0.160496
\(766\) 47.5314 1.71738
\(767\) −16.4749 −0.594873
\(768\) 20.1797 0.728173
\(769\) 9.46018 0.341143 0.170571 0.985345i \(-0.445439\pi\)
0.170571 + 0.985345i \(0.445439\pi\)
\(770\) 4.38611 0.158065
\(771\) 20.5332 0.739484
\(772\) −27.9185 −1.00481
\(773\) −26.8074 −0.964196 −0.482098 0.876117i \(-0.660125\pi\)
−0.482098 + 0.876117i \(0.660125\pi\)
\(774\) −33.0408 −1.18763
\(775\) 5.60880 0.201474
\(776\) −61.7009 −2.21493
\(777\) 16.8536 0.604618
\(778\) −4.02904 −0.144448
\(779\) −15.1897 −0.544227
\(780\) 8.77619 0.314238
\(781\) −0.638051 −0.0228313
\(782\) 4.52138 0.161684
\(783\) 4.92141 0.175877
\(784\) 3.63089 0.129675
\(785\) 28.7531 1.02624
\(786\) 12.6589 0.451528
\(787\) −32.6755 −1.16476 −0.582378 0.812918i \(-0.697878\pi\)
−0.582378 + 0.812918i \(0.697878\pi\)
\(788\) 32.3570 1.15267
\(789\) 11.9595 0.425769
\(790\) −35.2445 −1.25394
\(791\) 41.8756 1.48892
\(792\) 3.46830 0.123241
\(793\) 9.01561 0.320154
\(794\) 86.8504 3.08220
\(795\) −5.86535 −0.208022
\(796\) −102.527 −3.63398
\(797\) 25.4005 0.899730 0.449865 0.893096i \(-0.351472\pi\)
0.449865 + 0.893096i \(0.351472\pi\)
\(798\) 7.41686 0.262554
\(799\) 6.76065 0.239175
\(800\) −4.73276 −0.167328
\(801\) 6.41300 0.226592
\(802\) −50.4821 −1.78259
\(803\) 3.88283 0.137022
\(804\) −9.85406 −0.347526
\(805\) 10.0092 0.352777
\(806\) −13.7379 −0.483898
\(807\) −18.1566 −0.639141
\(808\) 29.5677 1.04019
\(809\) −50.4976 −1.77540 −0.887701 0.460420i \(-0.847699\pi\)
−0.887701 + 0.460420i \(0.847699\pi\)
\(810\) −19.2187 −0.675275
\(811\) −40.3610 −1.41727 −0.708633 0.705577i \(-0.750688\pi\)
−0.708633 + 0.705577i \(0.750688\pi\)
\(812\) −13.3456 −0.468339
\(813\) −15.7327 −0.551770
\(814\) −6.52220 −0.228603
\(815\) −30.9944 −1.08569
\(816\) −1.65317 −0.0578727
\(817\) 8.13667 0.284666
\(818\) −14.3933 −0.503251
\(819\) −13.0447 −0.455817
\(820\) 69.7571 2.43602
\(821\) −11.2198 −0.391575 −0.195788 0.980646i \(-0.562726\pi\)
−0.195788 + 0.980646i \(0.562726\pi\)
\(822\) −28.4350 −0.991786
\(823\) 15.4730 0.539356 0.269678 0.962951i \(-0.413083\pi\)
0.269678 + 0.962951i \(0.413083\pi\)
\(824\) −10.5439 −0.367315
\(825\) 0.447166 0.0155683
\(826\) 63.9404 2.22477
\(827\) −54.6475 −1.90028 −0.950139 0.311826i \(-0.899059\pi\)
−0.950139 + 0.311826i \(0.899059\pi\)
\(828\) 17.2562 0.599694
\(829\) 26.8692 0.933206 0.466603 0.884467i \(-0.345478\pi\)
0.466603 + 0.884467i \(0.345478\pi\)
\(830\) 5.23399 0.181675
\(831\) 13.2730 0.460437
\(832\) 19.7471 0.684606
\(833\) 1.60623 0.0556527
\(834\) 1.41899 0.0491356
\(835\) −12.5242 −0.433417
\(836\) −1.86219 −0.0644051
\(837\) −12.7564 −0.440925
\(838\) 68.6782 2.37245
\(839\) −36.2163 −1.25033 −0.625163 0.780494i \(-0.714968\pi\)
−0.625163 + 0.780494i \(0.714968\pi\)
\(840\) −15.6225 −0.539026
\(841\) −27.4838 −0.947719
\(842\) 63.2127 2.17845
\(843\) −6.96589 −0.239918
\(844\) −80.7794 −2.78054
\(845\) −17.5507 −0.603762
\(846\) 39.7705 1.36734
\(847\) 31.9149 1.09661
\(848\) 10.0678 0.345728
\(849\) −20.8224 −0.714622
\(850\) 4.19361 0.143840
\(851\) −14.8837 −0.510208
\(852\) 4.95490 0.169752
\(853\) 36.0100 1.23296 0.616480 0.787371i \(-0.288558\pi\)
0.616480 + 0.787371i \(0.288558\pi\)
\(854\) −34.9904 −1.19735
\(855\) 6.43077 0.219928
\(856\) −8.09721 −0.276757
\(857\) −22.7172 −0.776005 −0.388002 0.921658i \(-0.626835\pi\)
−0.388002 + 0.921658i \(0.626835\pi\)
\(858\) −1.09527 −0.0373918
\(859\) 37.6812 1.28567 0.642833 0.766006i \(-0.277759\pi\)
0.642833 + 0.766006i \(0.277759\pi\)
\(860\) −37.3668 −1.27420
\(861\) 22.4958 0.766653
\(862\) 45.3875 1.54590
\(863\) −0.110067 −0.00374674 −0.00187337 0.999998i \(-0.500596\pi\)
−0.00187337 + 0.999998i \(0.500596\pi\)
\(864\) 10.7640 0.366198
\(865\) 27.9984 0.951975
\(866\) −65.2232 −2.21637
\(867\) −0.731332 −0.0248373
\(868\) 34.5921 1.17413
\(869\) 2.85370 0.0968050
\(870\) 3.86960 0.131192
\(871\) −6.57844 −0.222902
\(872\) 7.86525 0.266351
\(873\) −37.6146 −1.27306
\(874\) −6.54999 −0.221557
\(875\) 35.6971 1.20678
\(876\) −30.1528 −1.01877
\(877\) 20.4861 0.691766 0.345883 0.938278i \(-0.387579\pi\)
0.345883 + 0.938278i \(0.387579\pi\)
\(878\) −19.4744 −0.657230
\(879\) −4.94923 −0.166934
\(880\) 1.41628 0.0477427
\(881\) 14.5965 0.491768 0.245884 0.969299i \(-0.420922\pi\)
0.245884 + 0.969299i \(0.420922\pi\)
\(882\) 9.44891 0.318161
\(883\) −13.8615 −0.466478 −0.233239 0.972419i \(-0.574932\pi\)
−0.233239 + 0.972419i \(0.574932\pi\)
\(884\) −6.66410 −0.224138
\(885\) −12.0283 −0.404327
\(886\) 70.0992 2.35503
\(887\) 25.1704 0.845138 0.422569 0.906331i \(-0.361128\pi\)
0.422569 + 0.906331i \(0.361128\pi\)
\(888\) 23.2308 0.779574
\(889\) 7.58413 0.254364
\(890\) 11.1788 0.374715
\(891\) 1.55611 0.0521315
\(892\) 51.7896 1.73404
\(893\) −9.79396 −0.327742
\(894\) −9.45450 −0.316206
\(895\) −30.3628 −1.01492
\(896\) −60.8388 −2.03248
\(897\) −2.49942 −0.0834531
\(898\) −33.8674 −1.13017
\(899\) −3.92991 −0.131070
\(900\) 16.0052 0.533508
\(901\) 4.45378 0.148377
\(902\) −8.70568 −0.289868
\(903\) −12.0503 −0.401009
\(904\) 57.7209 1.91977
\(905\) −15.9868 −0.531419
\(906\) −27.8987 −0.926874
\(907\) 34.5184 1.14616 0.573082 0.819498i \(-0.305748\pi\)
0.573082 + 0.819498i \(0.305748\pi\)
\(908\) 10.7873 0.357990
\(909\) 18.0253 0.597862
\(910\) −22.7388 −0.753784
\(911\) −37.5898 −1.24541 −0.622704 0.782458i \(-0.713966\pi\)
−0.622704 + 0.782458i \(0.713966\pi\)
\(912\) 2.39490 0.0793032
\(913\) −0.423788 −0.0140254
\(914\) 32.6129 1.07874
\(915\) 6.58230 0.217604
\(916\) 54.8928 1.81371
\(917\) −21.2794 −0.702707
\(918\) −9.53775 −0.314793
\(919\) 7.78236 0.256717 0.128358 0.991728i \(-0.459029\pi\)
0.128358 + 0.991728i \(0.459029\pi\)
\(920\) 13.7965 0.454858
\(921\) −9.74029 −0.320953
\(922\) 54.7338 1.80256
\(923\) 3.30783 0.108879
\(924\) 2.75788 0.0907276
\(925\) −13.8048 −0.453899
\(926\) 26.0324 0.855478
\(927\) −6.42788 −0.211119
\(928\) 3.31610 0.108856
\(929\) 20.6721 0.678231 0.339115 0.940745i \(-0.389872\pi\)
0.339115 + 0.940745i \(0.389872\pi\)
\(930\) −10.0301 −0.328899
\(931\) −2.32690 −0.0762612
\(932\) 36.5668 1.19779
\(933\) 10.9311 0.357867
\(934\) 37.3104 1.22083
\(935\) 0.626534 0.0204898
\(936\) −17.9806 −0.587715
\(937\) 49.1773 1.60655 0.803277 0.595606i \(-0.203088\pi\)
0.803277 + 0.595606i \(0.203088\pi\)
\(938\) 25.5315 0.833633
\(939\) −7.93020 −0.258792
\(940\) 44.9778 1.46701
\(941\) −32.3644 −1.05505 −0.527524 0.849540i \(-0.676880\pi\)
−0.527524 + 0.849540i \(0.676880\pi\)
\(942\) 27.8663 0.907932
\(943\) −19.8665 −0.646942
\(944\) 20.6464 0.671983
\(945\) −21.1141 −0.686843
\(946\) 4.66338 0.151620
\(947\) 36.6625 1.19137 0.595685 0.803218i \(-0.296881\pi\)
0.595685 + 0.803218i \(0.296881\pi\)
\(948\) −22.1609 −0.719752
\(949\) −20.1296 −0.653435
\(950\) −6.07516 −0.197104
\(951\) −20.5472 −0.666288
\(952\) 11.8627 0.384474
\(953\) −37.0481 −1.20011 −0.600053 0.799960i \(-0.704854\pi\)
−0.600053 + 0.799960i \(0.704854\pi\)
\(954\) 26.2000 0.848258
\(955\) −18.4224 −0.596133
\(956\) −33.5262 −1.08431
\(957\) −0.313315 −0.0101281
\(958\) −62.3818 −2.01547
\(959\) 47.7988 1.54350
\(960\) 14.4173 0.465318
\(961\) −20.8136 −0.671406
\(962\) 33.8128 1.09017
\(963\) −4.93629 −0.159070
\(964\) 82.9894 2.67291
\(965\) −13.6077 −0.438046
\(966\) 9.70045 0.312107
\(967\) 48.9858 1.57528 0.787639 0.616138i \(-0.211303\pi\)
0.787639 + 0.616138i \(0.211303\pi\)
\(968\) 43.9911 1.41393
\(969\) 1.05946 0.0340347
\(970\) −65.5679 −2.10526
\(971\) −28.5391 −0.915865 −0.457932 0.888987i \(-0.651410\pi\)
−0.457932 + 0.888987i \(0.651410\pi\)
\(972\) −56.3836 −1.80850
\(973\) −2.38529 −0.0764690
\(974\) −68.9875 −2.21050
\(975\) −2.31823 −0.0742427
\(976\) −11.2984 −0.361653
\(977\) −13.5098 −0.432216 −0.216108 0.976369i \(-0.569336\pi\)
−0.216108 + 0.976369i \(0.569336\pi\)
\(978\) −30.0384 −0.960522
\(979\) −0.905132 −0.0289281
\(980\) 10.6861 0.341354
\(981\) 4.79489 0.153089
\(982\) −14.4994 −0.462694
\(983\) 39.6418 1.26438 0.632188 0.774815i \(-0.282157\pi\)
0.632188 + 0.774815i \(0.282157\pi\)
\(984\) 31.0079 0.988496
\(985\) 15.7710 0.502506
\(986\) −2.93834 −0.0935757
\(987\) 14.5047 0.461691
\(988\) 9.65408 0.307137
\(989\) 10.6419 0.338393
\(990\) 3.68568 0.117139
\(991\) 1.60031 0.0508355 0.0254178 0.999677i \(-0.491908\pi\)
0.0254178 + 0.999677i \(0.491908\pi\)
\(992\) −8.59540 −0.272904
\(993\) −4.52878 −0.143716
\(994\) −12.8380 −0.407196
\(995\) −49.9723 −1.58423
\(996\) 3.29100 0.104279
\(997\) 30.0064 0.950313 0.475157 0.879901i \(-0.342391\pi\)
0.475157 + 0.879901i \(0.342391\pi\)
\(998\) −92.8186 −2.93812
\(999\) 31.3970 0.993356
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 \(a_p\))