Properties

Label 6026.2.a.h.1.11
Level 6026
Weight 2
Character 6026.1
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 24
CM No

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(24\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) = 6026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(-0.672761 q^{3}\) \(+1.00000 q^{4}\) \(-2.38352 q^{5}\) \(+0.672761 q^{6}\) \(-0.506434 q^{7}\) \(-1.00000 q^{8}\) \(-2.54739 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(-0.672761 q^{3}\) \(+1.00000 q^{4}\) \(-2.38352 q^{5}\) \(+0.672761 q^{6}\) \(-0.506434 q^{7}\) \(-1.00000 q^{8}\) \(-2.54739 q^{9}\) \(+2.38352 q^{10}\) \(+1.82292 q^{11}\) \(-0.672761 q^{12}\) \(+1.61132 q^{13}\) \(+0.506434 q^{14}\) \(+1.60354 q^{15}\) \(+1.00000 q^{16}\) \(-5.88597 q^{17}\) \(+2.54739 q^{18}\) \(-3.78727 q^{19}\) \(-2.38352 q^{20}\) \(+0.340709 q^{21}\) \(-1.82292 q^{22}\) \(-1.00000 q^{23}\) \(+0.672761 q^{24}\) \(+0.681154 q^{25}\) \(-1.61132 q^{26}\) \(+3.73207 q^{27}\) \(-0.506434 q^{28}\) \(+9.57271 q^{29}\) \(-1.60354 q^{30}\) \(+4.60370 q^{31}\) \(-1.00000 q^{32}\) \(-1.22639 q^{33}\) \(+5.88597 q^{34}\) \(+1.20709 q^{35}\) \(-2.54739 q^{36}\) \(+8.91792 q^{37}\) \(+3.78727 q^{38}\) \(-1.08403 q^{39}\) \(+2.38352 q^{40}\) \(+11.6782 q^{41}\) \(-0.340709 q^{42}\) \(-6.39686 q^{43}\) \(+1.82292 q^{44}\) \(+6.07175 q^{45}\) \(+1.00000 q^{46}\) \(-1.18292 q^{47}\) \(-0.672761 q^{48}\) \(-6.74352 q^{49}\) \(-0.681154 q^{50}\) \(+3.95985 q^{51}\) \(+1.61132 q^{52}\) \(+2.70654 q^{53}\) \(-3.73207 q^{54}\) \(-4.34495 q^{55}\) \(+0.506434 q^{56}\) \(+2.54793 q^{57}\) \(-9.57271 q^{58}\) \(+8.49714 q^{59}\) \(+1.60354 q^{60}\) \(-9.41813 q^{61}\) \(-4.60370 q^{62}\) \(+1.29009 q^{63}\) \(+1.00000 q^{64}\) \(-3.84060 q^{65}\) \(+1.22639 q^{66}\) \(+9.70644 q^{67}\) \(-5.88597 q^{68}\) \(+0.672761 q^{69}\) \(-1.20709 q^{70}\) \(-7.20117 q^{71}\) \(+2.54739 q^{72}\) \(+0.843850 q^{73}\) \(-8.91792 q^{74}\) \(-0.458254 q^{75}\) \(-3.78727 q^{76}\) \(-0.923187 q^{77}\) \(+1.08403 q^{78}\) \(-13.7873 q^{79}\) \(-2.38352 q^{80}\) \(+5.13139 q^{81}\) \(-11.6782 q^{82}\) \(+3.54948 q^{83}\) \(+0.340709 q^{84}\) \(+14.0293 q^{85}\) \(+6.39686 q^{86}\) \(-6.44014 q^{87}\) \(-1.82292 q^{88}\) \(-8.85251 q^{89}\) \(-6.07175 q^{90}\) \(-0.816026 q^{91}\) \(-1.00000 q^{92}\) \(-3.09719 q^{93}\) \(+1.18292 q^{94}\) \(+9.02703 q^{95}\) \(+0.672761 q^{96}\) \(+16.5081 q^{97}\) \(+6.74352 q^{98}\) \(-4.64368 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(24q \) \(\mathstrut -\mathstrut 24q^{2} \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut 24q^{4} \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut +\mathstrut q^{6} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 24q^{8} \) \(\mathstrut +\mathstrut 27q^{9} \) \(\mathstrut +\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut q^{12} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut +\mathstrut 7q^{14} \) \(\mathstrut -\mathstrut 6q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 5q^{17} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut -\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut q^{20} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut q^{24} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut +\mathstrut 5q^{26} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut -\mathstrut 7q^{28} \) \(\mathstrut -\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 24q^{32} \) \(\mathstrut -\mathstrut 6q^{33} \) \(\mathstrut -\mathstrut 5q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 27q^{36} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut -\mathstrut 39q^{39} \) \(\mathstrut +\mathstrut q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut -\mathstrut 44q^{43} \) \(\mathstrut -\mathstrut 4q^{44} \) \(\mathstrut -\mathstrut 13q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut -\mathstrut q^{48} \) \(\mathstrut -\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut q^{50} \) \(\mathstrut -\mathstrut 44q^{51} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 21q^{53} \) \(\mathstrut +\mathstrut q^{54} \) \(\mathstrut -\mathstrut 13q^{55} \) \(\mathstrut +\mathstrut 7q^{56} \) \(\mathstrut +\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 6q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 6q^{60} \) \(\mathstrut -\mathstrut 40q^{61} \) \(\mathstrut +\mathstrut 23q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 24q^{64} \) \(\mathstrut -\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut +\mathstrut 5q^{68} \) \(\mathstrut +\mathstrut q^{69} \) \(\mathstrut -\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut -\mathstrut 36q^{75} \) \(\mathstrut -\mathstrut 20q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 53q^{79} \) \(\mathstrut -\mathstrut q^{80} \) \(\mathstrut +\mathstrut 24q^{81} \) \(\mathstrut +\mathstrut q^{82} \) \(\mathstrut -\mathstrut 9q^{83} \) \(\mathstrut -\mathstrut 37q^{85} \) \(\mathstrut +\mathstrut 44q^{86} \) \(\mathstrut +\mathstrut 7q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut -\mathstrut 46q^{89} \) \(\mathstrut +\mathstrut 13q^{90} \) \(\mathstrut -\mathstrut 44q^{91} \) \(\mathstrut -\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 23q^{93} \) \(\mathstrut -\mathstrut 32q^{94} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 78q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.672761 −0.388419 −0.194209 0.980960i \(-0.562214\pi\)
−0.194209 + 0.980960i \(0.562214\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.38352 −1.06594 −0.532971 0.846134i \(-0.678924\pi\)
−0.532971 + 0.846134i \(0.678924\pi\)
\(6\) 0.672761 0.274654
\(7\) −0.506434 −0.191414 −0.0957071 0.995410i \(-0.530511\pi\)
−0.0957071 + 0.995410i \(0.530511\pi\)
\(8\) −1.00000 −0.353553
\(9\) −2.54739 −0.849131
\(10\) 2.38352 0.753734
\(11\) 1.82292 0.549630 0.274815 0.961497i \(-0.411383\pi\)
0.274815 + 0.961497i \(0.411383\pi\)
\(12\) −0.672761 −0.194209
\(13\) 1.61132 0.446899 0.223449 0.974716i \(-0.428268\pi\)
0.223449 + 0.974716i \(0.428268\pi\)
\(14\) 0.506434 0.135350
\(15\) 1.60354 0.414032
\(16\) 1.00000 0.250000
\(17\) −5.88597 −1.42756 −0.713779 0.700371i \(-0.753018\pi\)
−0.713779 + 0.700371i \(0.753018\pi\)
\(18\) 2.54739 0.600426
\(19\) −3.78727 −0.868860 −0.434430 0.900706i \(-0.643050\pi\)
−0.434430 + 0.900706i \(0.643050\pi\)
\(20\) −2.38352 −0.532971
\(21\) 0.340709 0.0743488
\(22\) −1.82292 −0.388647
\(23\) −1.00000 −0.208514
\(24\) 0.672761 0.137327
\(25\) 0.681154 0.136231
\(26\) −1.61132 −0.316005
\(27\) 3.73207 0.718237
\(28\) −0.506434 −0.0957071
\(29\) 9.57271 1.77761 0.888803 0.458289i \(-0.151537\pi\)
0.888803 + 0.458289i \(0.151537\pi\)
\(30\) −1.60354 −0.292765
\(31\) 4.60370 0.826849 0.413424 0.910538i \(-0.364333\pi\)
0.413424 + 0.910538i \(0.364333\pi\)
\(32\) −1.00000 −0.176777
\(33\) −1.22639 −0.213486
\(34\) 5.88597 1.00944
\(35\) 1.20709 0.204036
\(36\) −2.54739 −0.424565
\(37\) 8.91792 1.46610 0.733048 0.680177i \(-0.238097\pi\)
0.733048 + 0.680177i \(0.238097\pi\)
\(38\) 3.78727 0.614377
\(39\) −1.08403 −0.173584
\(40\) 2.38352 0.376867
\(41\) 11.6782 1.82383 0.911917 0.410375i \(-0.134602\pi\)
0.911917 + 0.410375i \(0.134602\pi\)
\(42\) −0.340709 −0.0525726
\(43\) −6.39686 −0.975511 −0.487756 0.872980i \(-0.662184\pi\)
−0.487756 + 0.872980i \(0.662184\pi\)
\(44\) 1.82292 0.274815
\(45\) 6.07175 0.905124
\(46\) 1.00000 0.147442
\(47\) −1.18292 −0.172546 −0.0862732 0.996272i \(-0.527496\pi\)
−0.0862732 + 0.996272i \(0.527496\pi\)
\(48\) −0.672761 −0.0971047
\(49\) −6.74352 −0.963361
\(50\) −0.681154 −0.0963297
\(51\) 3.95985 0.554490
\(52\) 1.61132 0.223449
\(53\) 2.70654 0.371772 0.185886 0.982571i \(-0.440484\pi\)
0.185886 + 0.982571i \(0.440484\pi\)
\(54\) −3.73207 −0.507870
\(55\) −4.34495 −0.585873
\(56\) 0.506434 0.0676751
\(57\) 2.54793 0.337481
\(58\) −9.57271 −1.25696
\(59\) 8.49714 1.10623 0.553117 0.833104i \(-0.313438\pi\)
0.553117 + 0.833104i \(0.313438\pi\)
\(60\) 1.60354 0.207016
\(61\) −9.41813 −1.20587 −0.602934 0.797791i \(-0.706002\pi\)
−0.602934 + 0.797791i \(0.706002\pi\)
\(62\) −4.60370 −0.584670
\(63\) 1.29009 0.162536
\(64\) 1.00000 0.125000
\(65\) −3.84060 −0.476368
\(66\) 1.22639 0.150958
\(67\) 9.70644 1.18583 0.592915 0.805265i \(-0.297977\pi\)
0.592915 + 0.805265i \(0.297977\pi\)
\(68\) −5.88597 −0.713779
\(69\) 0.672761 0.0809909
\(70\) −1.20709 −0.144275
\(71\) −7.20117 −0.854621 −0.427311 0.904105i \(-0.640539\pi\)
−0.427311 + 0.904105i \(0.640539\pi\)
\(72\) 2.54739 0.300213
\(73\) 0.843850 0.0987651 0.0493826 0.998780i \(-0.484275\pi\)
0.0493826 + 0.998780i \(0.484275\pi\)
\(74\) −8.91792 −1.03669
\(75\) −0.458254 −0.0529146
\(76\) −3.78727 −0.434430
\(77\) −0.923187 −0.105207
\(78\) 1.08403 0.122742
\(79\) −13.7873 −1.55119 −0.775596 0.631229i \(-0.782551\pi\)
−0.775596 + 0.631229i \(0.782551\pi\)
\(80\) −2.38352 −0.266485
\(81\) 5.13139 0.570154
\(82\) −11.6782 −1.28964
\(83\) 3.54948 0.389606 0.194803 0.980842i \(-0.437593\pi\)
0.194803 + 0.980842i \(0.437593\pi\)
\(84\) 0.340709 0.0371744
\(85\) 14.0293 1.52169
\(86\) 6.39686 0.689791
\(87\) −6.44014 −0.690456
\(88\) −1.82292 −0.194323
\(89\) −8.85251 −0.938364 −0.469182 0.883101i \(-0.655451\pi\)
−0.469182 + 0.883101i \(0.655451\pi\)
\(90\) −6.07175 −0.640019
\(91\) −0.816026 −0.0855427
\(92\) −1.00000 −0.104257
\(93\) −3.09719 −0.321164
\(94\) 1.18292 0.122009
\(95\) 9.02703 0.926153
\(96\) 0.672761 0.0686634
\(97\) 16.5081 1.67614 0.838071 0.545561i \(-0.183683\pi\)
0.838071 + 0.545561i \(0.183683\pi\)
\(98\) 6.74352 0.681199
\(99\) −4.64368 −0.466707
\(100\) 0.681154 0.0681154
\(101\) −3.84068 −0.382162 −0.191081 0.981574i \(-0.561199\pi\)
−0.191081 + 0.981574i \(0.561199\pi\)
\(102\) −3.95985 −0.392084
\(103\) −7.33545 −0.722783 −0.361392 0.932414i \(-0.617698\pi\)
−0.361392 + 0.932414i \(0.617698\pi\)
\(104\) −1.61132 −0.158003
\(105\) −0.812086 −0.0792515
\(106\) −2.70654 −0.262883
\(107\) 12.2690 1.18609 0.593044 0.805170i \(-0.297926\pi\)
0.593044 + 0.805170i \(0.297926\pi\)
\(108\) 3.73207 0.359119
\(109\) −17.9443 −1.71876 −0.859378 0.511340i \(-0.829149\pi\)
−0.859378 + 0.511340i \(0.829149\pi\)
\(110\) 4.34495 0.414275
\(111\) −5.99963 −0.569459
\(112\) −0.506434 −0.0478535
\(113\) −5.84266 −0.549631 −0.274816 0.961497i \(-0.588617\pi\)
−0.274816 + 0.961497i \(0.588617\pi\)
\(114\) −2.54793 −0.238635
\(115\) 2.38352 0.222264
\(116\) 9.57271 0.888803
\(117\) −4.10466 −0.379476
\(118\) −8.49714 −0.782225
\(119\) 2.98086 0.273255
\(120\) −1.60354 −0.146382
\(121\) −7.67698 −0.697907
\(122\) 9.41813 0.852678
\(123\) −7.85666 −0.708411
\(124\) 4.60370 0.413424
\(125\) 10.2940 0.920727
\(126\) −1.29009 −0.114930
\(127\) 12.9448 1.14866 0.574331 0.818623i \(-0.305262\pi\)
0.574331 + 0.818623i \(0.305262\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 4.30356 0.378907
\(130\) 3.84060 0.336843
\(131\) −1.00000 −0.0873704
\(132\) −1.22639 −0.106743
\(133\) 1.91800 0.166312
\(134\) −9.70644 −0.838508
\(135\) −8.89545 −0.765599
\(136\) 5.88597 0.504718
\(137\) 11.9182 1.01824 0.509119 0.860696i \(-0.329971\pi\)
0.509119 + 0.860696i \(0.329971\pi\)
\(138\) −0.672761 −0.0572692
\(139\) 8.66538 0.734988 0.367494 0.930026i \(-0.380216\pi\)
0.367494 + 0.930026i \(0.380216\pi\)
\(140\) 1.20709 0.102018
\(141\) 0.795822 0.0670203
\(142\) 7.20117 0.604308
\(143\) 2.93729 0.245629
\(144\) −2.54739 −0.212283
\(145\) −22.8167 −1.89482
\(146\) −0.843850 −0.0698375
\(147\) 4.53678 0.374187
\(148\) 8.91792 0.733048
\(149\) 3.82877 0.313665 0.156833 0.987625i \(-0.449872\pi\)
0.156833 + 0.987625i \(0.449872\pi\)
\(150\) 0.458254 0.0374163
\(151\) 18.7863 1.52881 0.764404 0.644738i \(-0.223033\pi\)
0.764404 + 0.644738i \(0.223033\pi\)
\(152\) 3.78727 0.307188
\(153\) 14.9939 1.21218
\(154\) 0.923187 0.0743925
\(155\) −10.9730 −0.881372
\(156\) −1.08403 −0.0867919
\(157\) −24.5004 −1.95534 −0.977672 0.210137i \(-0.932609\pi\)
−0.977672 + 0.210137i \(0.932609\pi\)
\(158\) 13.7873 1.09686
\(159\) −1.82086 −0.144403
\(160\) 2.38352 0.188434
\(161\) 0.506434 0.0399126
\(162\) −5.13139 −0.403160
\(163\) 4.13777 0.324095 0.162047 0.986783i \(-0.448190\pi\)
0.162047 + 0.986783i \(0.448190\pi\)
\(164\) 11.6782 0.911917
\(165\) 2.92311 0.227564
\(166\) −3.54948 −0.275493
\(167\) 16.2307 1.25597 0.627983 0.778227i \(-0.283881\pi\)
0.627983 + 0.778227i \(0.283881\pi\)
\(168\) −0.340709 −0.0262863
\(169\) −10.4037 −0.800281
\(170\) −14.0293 −1.07600
\(171\) 9.64767 0.737775
\(172\) −6.39686 −0.487756
\(173\) 7.54592 0.573706 0.286853 0.957975i \(-0.407391\pi\)
0.286853 + 0.957975i \(0.407391\pi\)
\(174\) 6.44014 0.488226
\(175\) −0.344960 −0.0260765
\(176\) 1.82292 0.137407
\(177\) −5.71655 −0.429682
\(178\) 8.85251 0.663524
\(179\) 12.1313 0.906740 0.453370 0.891323i \(-0.350222\pi\)
0.453370 + 0.891323i \(0.350222\pi\)
\(180\) 6.07175 0.452562
\(181\) 8.61582 0.640409 0.320204 0.947348i \(-0.396248\pi\)
0.320204 + 0.947348i \(0.396248\pi\)
\(182\) 0.816026 0.0604879
\(183\) 6.33615 0.468382
\(184\) 1.00000 0.0737210
\(185\) −21.2560 −1.56277
\(186\) 3.09719 0.227097
\(187\) −10.7296 −0.784628
\(188\) −1.18292 −0.0862732
\(189\) −1.89005 −0.137481
\(190\) −9.02703 −0.654889
\(191\) −21.5763 −1.56121 −0.780605 0.625025i \(-0.785089\pi\)
−0.780605 + 0.625025i \(0.785089\pi\)
\(192\) −0.672761 −0.0485524
\(193\) −15.6581 −1.12710 −0.563549 0.826083i \(-0.690564\pi\)
−0.563549 + 0.826083i \(0.690564\pi\)
\(194\) −16.5081 −1.18521
\(195\) 2.58381 0.185030
\(196\) −6.74352 −0.481680
\(197\) 1.27537 0.0908664 0.0454332 0.998967i \(-0.485533\pi\)
0.0454332 + 0.998967i \(0.485533\pi\)
\(198\) 4.64368 0.330012
\(199\) −9.18160 −0.650866 −0.325433 0.945565i \(-0.605510\pi\)
−0.325433 + 0.945565i \(0.605510\pi\)
\(200\) −0.681154 −0.0481649
\(201\) −6.53011 −0.460599
\(202\) 3.84068 0.270229
\(203\) −4.84795 −0.340259
\(204\) 3.95985 0.277245
\(205\) −27.8353 −1.94410
\(206\) 7.33545 0.511085
\(207\) 2.54739 0.177056
\(208\) 1.61132 0.111725
\(209\) −6.90387 −0.477551
\(210\) 0.812086 0.0560393
\(211\) −12.3775 −0.852104 −0.426052 0.904699i \(-0.640096\pi\)
−0.426052 + 0.904699i \(0.640096\pi\)
\(212\) 2.70654 0.185886
\(213\) 4.84466 0.331951
\(214\) −12.2690 −0.838690
\(215\) 15.2470 1.03984
\(216\) −3.73207 −0.253935
\(217\) −2.33147 −0.158271
\(218\) 17.9443 1.21534
\(219\) −0.567709 −0.0383622
\(220\) −4.34495 −0.292936
\(221\) −9.48416 −0.637974
\(222\) 5.99963 0.402669
\(223\) 1.12783 0.0755250 0.0377625 0.999287i \(-0.487977\pi\)
0.0377625 + 0.999287i \(0.487977\pi\)
\(224\) 0.506434 0.0338376
\(225\) −1.73517 −0.115678
\(226\) 5.84266 0.388648
\(227\) −17.4568 −1.15865 −0.579323 0.815098i \(-0.696683\pi\)
−0.579323 + 0.815098i \(0.696683\pi\)
\(228\) 2.54793 0.168741
\(229\) 21.0847 1.39332 0.696659 0.717402i \(-0.254669\pi\)
0.696659 + 0.717402i \(0.254669\pi\)
\(230\) −2.38352 −0.157164
\(231\) 0.621084 0.0408643
\(232\) −9.57271 −0.628479
\(233\) −11.8051 −0.773380 −0.386690 0.922210i \(-0.626382\pi\)
−0.386690 + 0.922210i \(0.626382\pi\)
\(234\) 4.10466 0.268330
\(235\) 2.81951 0.183924
\(236\) 8.49714 0.553117
\(237\) 9.27556 0.602512
\(238\) −2.98086 −0.193220
\(239\) 4.00218 0.258879 0.129440 0.991587i \(-0.458682\pi\)
0.129440 + 0.991587i \(0.458682\pi\)
\(240\) 1.60354 0.103508
\(241\) −24.3560 −1.56891 −0.784455 0.620186i \(-0.787057\pi\)
−0.784455 + 0.620186i \(0.787057\pi\)
\(242\) 7.67698 0.493495
\(243\) −14.6484 −0.939696
\(244\) −9.41813 −0.602934
\(245\) 16.0733 1.02689
\(246\) 7.85666 0.500922
\(247\) −6.10249 −0.388292
\(248\) −4.60370 −0.292335
\(249\) −2.38795 −0.151330
\(250\) −10.2940 −0.651052
\(251\) 24.9801 1.57673 0.788364 0.615209i \(-0.210929\pi\)
0.788364 + 0.615209i \(0.210929\pi\)
\(252\) 1.29009 0.0812678
\(253\) −1.82292 −0.114606
\(254\) −12.9448 −0.812226
\(255\) −9.43837 −0.591054
\(256\) 1.00000 0.0625000
\(257\) 15.1813 0.946983 0.473491 0.880798i \(-0.342994\pi\)
0.473491 + 0.880798i \(0.342994\pi\)
\(258\) −4.30356 −0.267928
\(259\) −4.51634 −0.280632
\(260\) −3.84060 −0.238184
\(261\) −24.3854 −1.50942
\(262\) 1.00000 0.0617802
\(263\) −22.7905 −1.40532 −0.702660 0.711526i \(-0.748004\pi\)
−0.702660 + 0.711526i \(0.748004\pi\)
\(264\) 1.22639 0.0754789
\(265\) −6.45109 −0.396287
\(266\) −1.91800 −0.117600
\(267\) 5.95562 0.364478
\(268\) 9.70644 0.592915
\(269\) −31.5945 −1.92635 −0.963176 0.268870i \(-0.913350\pi\)
−0.963176 + 0.268870i \(0.913350\pi\)
\(270\) 8.89545 0.541360
\(271\) −31.6981 −1.92552 −0.962761 0.270353i \(-0.912860\pi\)
−0.962761 + 0.270353i \(0.912860\pi\)
\(272\) −5.88597 −0.356889
\(273\) 0.548990 0.0332264
\(274\) −11.9182 −0.720003
\(275\) 1.24169 0.0748765
\(276\) 0.672761 0.0404955
\(277\) −6.76294 −0.406346 −0.203173 0.979143i \(-0.565125\pi\)
−0.203173 + 0.979143i \(0.565125\pi\)
\(278\) −8.66538 −0.519715
\(279\) −11.7274 −0.702103
\(280\) −1.20709 −0.0721377
\(281\) −9.61368 −0.573504 −0.286752 0.958005i \(-0.592576\pi\)
−0.286752 + 0.958005i \(0.592576\pi\)
\(282\) −0.795822 −0.0473905
\(283\) 1.57030 0.0933446 0.0466723 0.998910i \(-0.485138\pi\)
0.0466723 + 0.998910i \(0.485138\pi\)
\(284\) −7.20117 −0.427311
\(285\) −6.07303 −0.359735
\(286\) −2.93729 −0.173686
\(287\) −5.91426 −0.349107
\(288\) 2.54739 0.150107
\(289\) 17.6446 1.03792
\(290\) 22.8167 1.33984
\(291\) −11.1060 −0.651045
\(292\) 0.843850 0.0493826
\(293\) 12.8511 0.750771 0.375385 0.926869i \(-0.377510\pi\)
0.375385 + 0.926869i \(0.377510\pi\)
\(294\) −4.53678 −0.264590
\(295\) −20.2531 −1.17918
\(296\) −8.91792 −0.518343
\(297\) 6.80325 0.394764
\(298\) −3.82877 −0.221795
\(299\) −1.61132 −0.0931848
\(300\) −0.458254 −0.0264573
\(301\) 3.23959 0.186727
\(302\) −18.7863 −1.08103
\(303\) 2.58386 0.148439
\(304\) −3.78727 −0.217215
\(305\) 22.4483 1.28538
\(306\) −14.9939 −0.857143
\(307\) 19.7982 1.12994 0.564972 0.825110i \(-0.308887\pi\)
0.564972 + 0.825110i \(0.308887\pi\)
\(308\) −0.923187 −0.0526034
\(309\) 4.93500 0.280743
\(310\) 10.9730 0.623224
\(311\) 5.47894 0.310682 0.155341 0.987861i \(-0.450352\pi\)
0.155341 + 0.987861i \(0.450352\pi\)
\(312\) 1.08403 0.0613712
\(313\) 0.110383 0.00623924 0.00311962 0.999995i \(-0.499007\pi\)
0.00311962 + 0.999995i \(0.499007\pi\)
\(314\) 24.5004 1.38264
\(315\) −3.07494 −0.173253
\(316\) −13.7873 −0.775596
\(317\) 1.84352 0.103542 0.0517711 0.998659i \(-0.483513\pi\)
0.0517711 + 0.998659i \(0.483513\pi\)
\(318\) 1.82086 0.102109
\(319\) 17.4502 0.977025
\(320\) −2.38352 −0.133243
\(321\) −8.25409 −0.460699
\(322\) −0.506434 −0.0282225
\(323\) 22.2918 1.24035
\(324\) 5.13139 0.285077
\(325\) 1.09755 0.0608814
\(326\) −4.13777 −0.229170
\(327\) 12.0723 0.667597
\(328\) −11.6782 −0.644822
\(329\) 0.599071 0.0330278
\(330\) −2.92311 −0.160912
\(331\) −27.4908 −1.51103 −0.755515 0.655132i \(-0.772613\pi\)
−0.755515 + 0.655132i \(0.772613\pi\)
\(332\) 3.54948 0.194803
\(333\) −22.7174 −1.24491
\(334\) −16.2307 −0.888102
\(335\) −23.1355 −1.26403
\(336\) 0.340709 0.0185872
\(337\) −28.4809 −1.55145 −0.775726 0.631070i \(-0.782616\pi\)
−0.775726 + 0.631070i \(0.782616\pi\)
\(338\) 10.4037 0.565884
\(339\) 3.93072 0.213487
\(340\) 14.0293 0.760846
\(341\) 8.39215 0.454461
\(342\) −9.64767 −0.521686
\(343\) 6.96019 0.375815
\(344\) 6.39686 0.344895
\(345\) −1.60354 −0.0863316
\(346\) −7.54592 −0.405671
\(347\) 2.15208 0.115530 0.0577649 0.998330i \(-0.481603\pi\)
0.0577649 + 0.998330i \(0.481603\pi\)
\(348\) −6.44014 −0.345228
\(349\) 3.84808 0.205983 0.102992 0.994682i \(-0.467159\pi\)
0.102992 + 0.994682i \(0.467159\pi\)
\(350\) 0.344960 0.0184389
\(351\) 6.01355 0.320979
\(352\) −1.82292 −0.0971617
\(353\) −2.14133 −0.113971 −0.0569857 0.998375i \(-0.518149\pi\)
−0.0569857 + 0.998375i \(0.518149\pi\)
\(354\) 5.71655 0.303831
\(355\) 17.1641 0.910976
\(356\) −8.85251 −0.469182
\(357\) −2.00540 −0.106137
\(358\) −12.1313 −0.641162
\(359\) 7.16507 0.378158 0.189079 0.981962i \(-0.439450\pi\)
0.189079 + 0.981962i \(0.439450\pi\)
\(360\) −6.07175 −0.320010
\(361\) −4.65658 −0.245083
\(362\) −8.61582 −0.452837
\(363\) 5.16477 0.271080
\(364\) −0.816026 −0.0427714
\(365\) −2.01133 −0.105278
\(366\) −6.33615 −0.331196
\(367\) −20.6045 −1.07555 −0.537774 0.843089i \(-0.680734\pi\)
−0.537774 + 0.843089i \(0.680734\pi\)
\(368\) −1.00000 −0.0521286
\(369\) −29.7490 −1.54867
\(370\) 21.2560 1.10505
\(371\) −1.37069 −0.0711624
\(372\) −3.09719 −0.160582
\(373\) −32.3418 −1.67459 −0.837296 0.546749i \(-0.815865\pi\)
−0.837296 + 0.546749i \(0.815865\pi\)
\(374\) 10.7296 0.554816
\(375\) −6.92543 −0.357628
\(376\) 1.18292 0.0610044
\(377\) 15.4247 0.794410
\(378\) 1.89005 0.0972136
\(379\) 13.4038 0.688508 0.344254 0.938877i \(-0.388132\pi\)
0.344254 + 0.938877i \(0.388132\pi\)
\(380\) 9.02703 0.463077
\(381\) −8.70873 −0.446162
\(382\) 21.5763 1.10394
\(383\) 5.03055 0.257049 0.128525 0.991706i \(-0.458976\pi\)
0.128525 + 0.991706i \(0.458976\pi\)
\(384\) 0.672761 0.0343317
\(385\) 2.20043 0.112144
\(386\) 15.6581 0.796979
\(387\) 16.2953 0.828337
\(388\) 16.5081 0.838071
\(389\) 10.8135 0.548264 0.274132 0.961692i \(-0.411609\pi\)
0.274132 + 0.961692i \(0.411609\pi\)
\(390\) −2.58381 −0.130836
\(391\) 5.88597 0.297666
\(392\) 6.74352 0.340599
\(393\) 0.672761 0.0339363
\(394\) −1.27537 −0.0642523
\(395\) 32.8623 1.65348
\(396\) −4.64368 −0.233354
\(397\) 32.4228 1.62725 0.813627 0.581387i \(-0.197490\pi\)
0.813627 + 0.581387i \(0.197490\pi\)
\(398\) 9.18160 0.460232
\(399\) −1.29036 −0.0645987
\(400\) 0.681154 0.0340577
\(401\) −14.2130 −0.709763 −0.354881 0.934911i \(-0.615479\pi\)
−0.354881 + 0.934911i \(0.615479\pi\)
\(402\) 6.53011 0.325692
\(403\) 7.41802 0.369518
\(404\) −3.84068 −0.191081
\(405\) −12.2307 −0.607751
\(406\) 4.84795 0.240599
\(407\) 16.2566 0.805810
\(408\) −3.95985 −0.196042
\(409\) 20.0218 0.990014 0.495007 0.868889i \(-0.335165\pi\)
0.495007 + 0.868889i \(0.335165\pi\)
\(410\) 27.8353 1.37469
\(411\) −8.01808 −0.395503
\(412\) −7.33545 −0.361392
\(413\) −4.30324 −0.211749
\(414\) −2.54739 −0.125198
\(415\) −8.46024 −0.415297
\(416\) −1.61132 −0.0790013
\(417\) −5.82973 −0.285483
\(418\) 6.90387 0.337680
\(419\) −37.3997 −1.82709 −0.913547 0.406733i \(-0.866668\pi\)
−0.913547 + 0.406733i \(0.866668\pi\)
\(420\) −0.812086 −0.0396258
\(421\) −28.0323 −1.36621 −0.683106 0.730319i \(-0.739371\pi\)
−0.683106 + 0.730319i \(0.739371\pi\)
\(422\) 12.3775 0.602528
\(423\) 3.01336 0.146515
\(424\) −2.70654 −0.131441
\(425\) −4.00925 −0.194477
\(426\) −4.84466 −0.234725
\(427\) 4.76966 0.230820
\(428\) 12.2690 0.593044
\(429\) −1.97610 −0.0954069
\(430\) −15.2470 −0.735276
\(431\) −30.4709 −1.46773 −0.733867 0.679294i \(-0.762286\pi\)
−0.733867 + 0.679294i \(0.762286\pi\)
\(432\) 3.73207 0.179559
\(433\) 8.97319 0.431224 0.215612 0.976479i \(-0.430825\pi\)
0.215612 + 0.976479i \(0.430825\pi\)
\(434\) 2.33147 0.111914
\(435\) 15.3502 0.735986
\(436\) −17.9443 −0.859378
\(437\) 3.78727 0.181170
\(438\) 0.567709 0.0271262
\(439\) −25.1764 −1.20160 −0.600802 0.799398i \(-0.705152\pi\)
−0.600802 + 0.799398i \(0.705152\pi\)
\(440\) 4.34495 0.207137
\(441\) 17.1784 0.818019
\(442\) 9.48416 0.451115
\(443\) −2.46405 −0.117071 −0.0585353 0.998285i \(-0.518643\pi\)
−0.0585353 + 0.998285i \(0.518643\pi\)
\(444\) −5.99963 −0.284730
\(445\) 21.1001 1.00024
\(446\) −1.12783 −0.0534042
\(447\) −2.57585 −0.121833
\(448\) −0.506434 −0.0239268
\(449\) 21.0293 0.992432 0.496216 0.868199i \(-0.334722\pi\)
0.496216 + 0.868199i \(0.334722\pi\)
\(450\) 1.73517 0.0817965
\(451\) 21.2884 1.00243
\(452\) −5.84266 −0.274816
\(453\) −12.6387 −0.593818
\(454\) 17.4568 0.819286
\(455\) 1.94501 0.0911835
\(456\) −2.54793 −0.119318
\(457\) −1.97969 −0.0926061 −0.0463030 0.998927i \(-0.514744\pi\)
−0.0463030 + 0.998927i \(0.514744\pi\)
\(458\) −21.0847 −0.985225
\(459\) −21.9668 −1.02532
\(460\) 2.38352 0.111132
\(461\) 6.49877 0.302678 0.151339 0.988482i \(-0.451641\pi\)
0.151339 + 0.988482i \(0.451641\pi\)
\(462\) −0.621084 −0.0288954
\(463\) −27.2991 −1.26869 −0.634347 0.773048i \(-0.718731\pi\)
−0.634347 + 0.773048i \(0.718731\pi\)
\(464\) 9.57271 0.444402
\(465\) 7.38221 0.342342
\(466\) 11.8051 0.546862
\(467\) 9.73770 0.450607 0.225303 0.974289i \(-0.427663\pi\)
0.225303 + 0.974289i \(0.427663\pi\)
\(468\) −4.10466 −0.189738
\(469\) −4.91567 −0.226985
\(470\) −2.81951 −0.130054
\(471\) 16.4829 0.759492
\(472\) −8.49714 −0.391113
\(473\) −11.6609 −0.536170
\(474\) −9.27556 −0.426041
\(475\) −2.57972 −0.118365
\(476\) 2.98086 0.136627
\(477\) −6.89462 −0.315683
\(478\) −4.00218 −0.183055
\(479\) 7.05123 0.322179 0.161090 0.986940i \(-0.448499\pi\)
0.161090 + 0.986940i \(0.448499\pi\)
\(480\) −1.60354 −0.0731911
\(481\) 14.3696 0.655197
\(482\) 24.3560 1.10939
\(483\) −0.340709 −0.0155028
\(484\) −7.67698 −0.348954
\(485\) −39.3473 −1.78667
\(486\) 14.6484 0.664465
\(487\) 10.7401 0.486680 0.243340 0.969941i \(-0.421757\pi\)
0.243340 + 0.969941i \(0.421757\pi\)
\(488\) 9.41813 0.426339
\(489\) −2.78373 −0.125885
\(490\) −16.0733 −0.726118
\(491\) −24.6316 −1.11161 −0.555805 0.831313i \(-0.687590\pi\)
−0.555805 + 0.831313i \(0.687590\pi\)
\(492\) −7.85666 −0.354206
\(493\) −56.3446 −2.53764
\(494\) 6.10249 0.274564
\(495\) 11.0683 0.497483
\(496\) 4.60370 0.206712
\(497\) 3.64692 0.163587
\(498\) 2.38795 0.107007
\(499\) −2.20103 −0.0985316 −0.0492658 0.998786i \(-0.515688\pi\)
−0.0492658 + 0.998786i \(0.515688\pi\)
\(500\) 10.2940 0.460364
\(501\) −10.9194 −0.487841
\(502\) −24.9801 −1.11491
\(503\) −3.44258 −0.153497 −0.0767486 0.997050i \(-0.524454\pi\)
−0.0767486 + 0.997050i \(0.524454\pi\)
\(504\) −1.29009 −0.0574650
\(505\) 9.15433 0.407362
\(506\) 1.82292 0.0810385
\(507\) 6.99918 0.310844
\(508\) 12.9448 0.574331
\(509\) 17.9197 0.794279 0.397139 0.917758i \(-0.370003\pi\)
0.397139 + 0.917758i \(0.370003\pi\)
\(510\) 9.43837 0.417938
\(511\) −0.427354 −0.0189050
\(512\) −1.00000 −0.0441942
\(513\) −14.1344 −0.624047
\(514\) −15.1813 −0.669618
\(515\) 17.4842 0.770444
\(516\) 4.30356 0.189453
\(517\) −2.15636 −0.0948366
\(518\) 4.51634 0.198436
\(519\) −5.07660 −0.222838
\(520\) 3.84060 0.168421
\(521\) −2.62225 −0.114883 −0.0574415 0.998349i \(-0.518294\pi\)
−0.0574415 + 0.998349i \(0.518294\pi\)
\(522\) 24.3854 1.06732
\(523\) −1.92644 −0.0842373 −0.0421186 0.999113i \(-0.513411\pi\)
−0.0421186 + 0.999113i \(0.513411\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0.232075 0.0101286
\(526\) 22.7905 0.993711
\(527\) −27.0972 −1.18037
\(528\) −1.22639 −0.0533716
\(529\) 1.00000 0.0434783
\(530\) 6.45109 0.280217
\(531\) −21.6456 −0.939337
\(532\) 1.91800 0.0831560
\(533\) 18.8173 0.815069
\(534\) −5.95562 −0.257725
\(535\) −29.2433 −1.26430
\(536\) −9.70644 −0.419254
\(537\) −8.16150 −0.352195
\(538\) 31.5945 1.36214
\(539\) −12.2929 −0.529492
\(540\) −8.89545 −0.382799
\(541\) −11.7766 −0.506317 −0.253158 0.967425i \(-0.581469\pi\)
−0.253158 + 0.967425i \(0.581469\pi\)
\(542\) 31.6981 1.36155
\(543\) −5.79639 −0.248747
\(544\) 5.88597 0.252359
\(545\) 42.7707 1.83209
\(546\) −0.548990 −0.0234946
\(547\) 21.3311 0.912052 0.456026 0.889966i \(-0.349272\pi\)
0.456026 + 0.889966i \(0.349272\pi\)
\(548\) 11.9182 0.509119
\(549\) 23.9917 1.02394
\(550\) −1.24169 −0.0529457
\(551\) −36.2544 −1.54449
\(552\) −0.672761 −0.0286346
\(553\) 6.98236 0.296920
\(554\) 6.76294 0.287330
\(555\) 14.3002 0.607010
\(556\) 8.66538 0.367494
\(557\) −45.8374 −1.94219 −0.971096 0.238689i \(-0.923282\pi\)
−0.971096 + 0.238689i \(0.923282\pi\)
\(558\) 11.7274 0.496462
\(559\) −10.3074 −0.435955
\(560\) 1.20709 0.0510091
\(561\) 7.21847 0.304764
\(562\) 9.61368 0.405529
\(563\) −17.0173 −0.717196 −0.358598 0.933492i \(-0.616745\pi\)
−0.358598 + 0.933492i \(0.616745\pi\)
\(564\) 0.795822 0.0335101
\(565\) 13.9261 0.585875
\(566\) −1.57030 −0.0660046
\(567\) −2.59871 −0.109136
\(568\) 7.20117 0.302154
\(569\) 28.3751 1.18954 0.594772 0.803894i \(-0.297242\pi\)
0.594772 + 0.803894i \(0.297242\pi\)
\(570\) 6.07303 0.254371
\(571\) −21.4665 −0.898345 −0.449172 0.893445i \(-0.648281\pi\)
−0.449172 + 0.893445i \(0.648281\pi\)
\(572\) 2.93729 0.122814
\(573\) 14.5157 0.606403
\(574\) 5.91426 0.246856
\(575\) −0.681154 −0.0284061
\(576\) −2.54739 −0.106141
\(577\) 6.69544 0.278735 0.139367 0.990241i \(-0.455493\pi\)
0.139367 + 0.990241i \(0.455493\pi\)
\(578\) −17.6446 −0.733920
\(579\) 10.5342 0.437786
\(580\) −22.8167 −0.947412
\(581\) −1.79758 −0.0745761
\(582\) 11.1060 0.460358
\(583\) 4.93380 0.204337
\(584\) −0.843850 −0.0349188
\(585\) 9.78352 0.404499
\(586\) −12.8511 −0.530875
\(587\) −11.2909 −0.466026 −0.233013 0.972474i \(-0.574858\pi\)
−0.233013 + 0.972474i \(0.574858\pi\)
\(588\) 4.53678 0.187094
\(589\) −17.4355 −0.718416
\(590\) 20.2531 0.833806
\(591\) −0.858020 −0.0352942
\(592\) 8.91792 0.366524
\(593\) −20.7622 −0.852602 −0.426301 0.904581i \(-0.640184\pi\)
−0.426301 + 0.904581i \(0.640184\pi\)
\(594\) −6.80325 −0.279141
\(595\) −7.10492 −0.291273
\(596\) 3.82877 0.156833
\(597\) 6.17702 0.252809
\(598\) 1.61132 0.0658916
\(599\) −29.4352 −1.20269 −0.601345 0.798990i \(-0.705368\pi\)
−0.601345 + 0.798990i \(0.705368\pi\)
\(600\) 0.458254 0.0187081
\(601\) −25.0299 −1.02099 −0.510495 0.859881i \(-0.670538\pi\)
−0.510495 + 0.859881i \(0.670538\pi\)
\(602\) −3.23959 −0.132036
\(603\) −24.7261 −1.00692
\(604\) 18.7863 0.764404
\(605\) 18.2982 0.743928
\(606\) −2.58386 −0.104962
\(607\) −3.98260 −0.161649 −0.0808245 0.996728i \(-0.525755\pi\)
−0.0808245 + 0.996728i \(0.525755\pi\)
\(608\) 3.78727 0.153594
\(609\) 3.26151 0.132163
\(610\) −22.4483 −0.908904
\(611\) −1.90606 −0.0771108
\(612\) 14.9939 0.606091
\(613\) 8.61945 0.348136 0.174068 0.984734i \(-0.444309\pi\)
0.174068 + 0.984734i \(0.444309\pi\)
\(614\) −19.7982 −0.798991
\(615\) 18.7265 0.755125
\(616\) 0.923187 0.0371962
\(617\) 4.45564 0.179377 0.0896886 0.995970i \(-0.471413\pi\)
0.0896886 + 0.995970i \(0.471413\pi\)
\(618\) −4.93500 −0.198515
\(619\) 22.3404 0.897936 0.448968 0.893548i \(-0.351792\pi\)
0.448968 + 0.893548i \(0.351792\pi\)
\(620\) −10.9730 −0.440686
\(621\) −3.73207 −0.149763
\(622\) −5.47894 −0.219685
\(623\) 4.48321 0.179616
\(624\) −1.08403 −0.0433960
\(625\) −27.9418 −1.11767
\(626\) −0.110383 −0.00441181
\(627\) 4.64466 0.185490
\(628\) −24.5004 −0.977672
\(629\) −52.4906 −2.09294
\(630\) 3.07494 0.122509
\(631\) −23.3547 −0.929736 −0.464868 0.885380i \(-0.653898\pi\)
−0.464868 + 0.885380i \(0.653898\pi\)
\(632\) 13.7873 0.548429
\(633\) 8.32712 0.330973
\(634\) −1.84352 −0.0732154
\(635\) −30.8541 −1.22441
\(636\) −1.82086 −0.0722016
\(637\) −10.8660 −0.430525
\(638\) −17.4502 −0.690861
\(639\) 18.3442 0.725685
\(640\) 2.38352 0.0942168
\(641\) 38.1623 1.50732 0.753660 0.657265i \(-0.228287\pi\)
0.753660 + 0.657265i \(0.228287\pi\)
\(642\) 8.25409 0.325763
\(643\) −38.7678 −1.52885 −0.764426 0.644712i \(-0.776977\pi\)
−0.764426 + 0.644712i \(0.776977\pi\)
\(644\) 0.506434 0.0199563
\(645\) −10.2576 −0.403893
\(646\) −22.2918 −0.877058
\(647\) −10.6725 −0.419581 −0.209791 0.977746i \(-0.567278\pi\)
−0.209791 + 0.977746i \(0.567278\pi\)
\(648\) −5.13139 −0.201580
\(649\) 15.4896 0.608019
\(650\) −1.09755 −0.0430496
\(651\) 1.56852 0.0614753
\(652\) 4.13777 0.162047
\(653\) 37.2012 1.45580 0.727898 0.685685i \(-0.240497\pi\)
0.727898 + 0.685685i \(0.240497\pi\)
\(654\) −12.0723 −0.472063
\(655\) 2.38352 0.0931317
\(656\) 11.6782 0.455958
\(657\) −2.14962 −0.0838645
\(658\) −0.599071 −0.0233542
\(659\) −33.8271 −1.31772 −0.658858 0.752267i \(-0.728960\pi\)
−0.658858 + 0.752267i \(0.728960\pi\)
\(660\) 2.92311 0.113782
\(661\) −5.57946 −0.217016 −0.108508 0.994096i \(-0.534607\pi\)
−0.108508 + 0.994096i \(0.534607\pi\)
\(662\) 27.4908 1.06846
\(663\) 6.38057 0.247801
\(664\) −3.54948 −0.137746
\(665\) −4.57159 −0.177279
\(666\) 22.7174 0.880283
\(667\) −9.57271 −0.370657
\(668\) 16.2307 0.627983
\(669\) −0.758759 −0.0293353
\(670\) 23.1355 0.893801
\(671\) −17.1685 −0.662781
\(672\) −0.340709 −0.0131431
\(673\) 19.3252 0.744933 0.372467 0.928046i \(-0.378512\pi\)
0.372467 + 0.928046i \(0.378512\pi\)
\(674\) 28.4809 1.09704
\(675\) 2.54211 0.0978460
\(676\) −10.4037 −0.400141
\(677\) −37.3926 −1.43711 −0.718556 0.695469i \(-0.755197\pi\)
−0.718556 + 0.695469i \(0.755197\pi\)
\(678\) −3.93072 −0.150958
\(679\) −8.36026 −0.320837
\(680\) −14.0293 −0.537999
\(681\) 11.7442 0.450040
\(682\) −8.39215 −0.321352
\(683\) −46.9554 −1.79670 −0.898349 0.439283i \(-0.855232\pi\)
−0.898349 + 0.439283i \(0.855232\pi\)
\(684\) 9.64767 0.368888
\(685\) −28.4071 −1.08538
\(686\) −6.96019 −0.265741
\(687\) −14.1850 −0.541191
\(688\) −6.39686 −0.243878
\(689\) 4.36110 0.166144
\(690\) 1.60354 0.0610456
\(691\) 24.3915 0.927896 0.463948 0.885862i \(-0.346432\pi\)
0.463948 + 0.885862i \(0.346432\pi\)
\(692\) 7.54592 0.286853
\(693\) 2.35172 0.0893344
\(694\) −2.15208 −0.0816918
\(695\) −20.6541 −0.783454
\(696\) 6.44014 0.244113
\(697\) −68.7377 −2.60363
\(698\) −3.84808 −0.145652
\(699\) 7.94203 0.300395
\(700\) −0.344960 −0.0130383
\(701\) −18.8202 −0.710830 −0.355415 0.934709i \(-0.615660\pi\)
−0.355415 + 0.934709i \(0.615660\pi\)
\(702\) −6.01355 −0.226967
\(703\) −33.7746 −1.27383
\(704\) 1.82292 0.0687037
\(705\) −1.89685 −0.0714397
\(706\) 2.14133 0.0805900
\(707\) 1.94505 0.0731512
\(708\) −5.71655 −0.214841
\(709\) 34.8272 1.30796 0.653982 0.756510i \(-0.273097\pi\)
0.653982 + 0.756510i \(0.273097\pi\)
\(710\) −17.1641 −0.644157
\(711\) 35.1217 1.31717
\(712\) 8.85251 0.331762
\(713\) −4.60370 −0.172410
\(714\) 2.00540 0.0750504
\(715\) −7.00109 −0.261826
\(716\) 12.1313 0.453370
\(717\) −2.69251 −0.100554
\(718\) −7.16507 −0.267398
\(719\) −48.2471 −1.79931 −0.899656 0.436599i \(-0.856183\pi\)
−0.899656 + 0.436599i \(0.856183\pi\)
\(720\) 6.07175 0.226281
\(721\) 3.71492 0.138351
\(722\) 4.65658 0.173300
\(723\) 16.3858 0.609394
\(724\) 8.61582 0.320204
\(725\) 6.52049 0.242165
\(726\) −5.16477 −0.191683
\(727\) 13.0458 0.483843 0.241922 0.970296i \(-0.422222\pi\)
0.241922 + 0.970296i \(0.422222\pi\)
\(728\) 0.816026 0.0302439
\(729\) −5.53928 −0.205158
\(730\) 2.01133 0.0744427
\(731\) 37.6517 1.39260
\(732\) 6.33615 0.234191
\(733\) 22.1887 0.819559 0.409780 0.912185i \(-0.365606\pi\)
0.409780 + 0.912185i \(0.365606\pi\)
\(734\) 20.6045 0.760527
\(735\) −10.8135 −0.398862
\(736\) 1.00000 0.0368605
\(737\) 17.6940 0.651767
\(738\) 29.7490 1.09508
\(739\) 34.2684 1.26059 0.630293 0.776358i \(-0.282935\pi\)
0.630293 + 0.776358i \(0.282935\pi\)
\(740\) −21.2560 −0.781386
\(741\) 4.10552 0.150820
\(742\) 1.37069 0.0503194
\(743\) −7.69305 −0.282231 −0.141115 0.989993i \(-0.545069\pi\)
−0.141115 + 0.989993i \(0.545069\pi\)
\(744\) 3.09719 0.113548
\(745\) −9.12594 −0.334349
\(746\) 32.3418 1.18412
\(747\) −9.04191 −0.330826
\(748\) −10.7296 −0.392314
\(749\) −6.21343 −0.227034
\(750\) 6.92543 0.252881
\(751\) −0.0799624 −0.00291787 −0.00145893 0.999999i \(-0.500464\pi\)
−0.00145893 + 0.999999i \(0.500464\pi\)
\(752\) −1.18292 −0.0431366
\(753\) −16.8056 −0.612431
\(754\) −15.4247 −0.561733
\(755\) −44.7775 −1.62962
\(756\) −1.89005 −0.0687404
\(757\) 13.9771 0.508006 0.254003 0.967203i \(-0.418253\pi\)
0.254003 + 0.967203i \(0.418253\pi\)
\(758\) −13.4038 −0.486848
\(759\) 1.22639 0.0445150
\(760\) −9.02703 −0.327445
\(761\) −23.1755 −0.840113 −0.420056 0.907498i \(-0.637990\pi\)
−0.420056 + 0.907498i \(0.637990\pi\)
\(762\) 8.70873 0.315484
\(763\) 9.08763 0.328994
\(764\) −21.5763 −0.780605
\(765\) −35.7382 −1.29212
\(766\) −5.03055 −0.181761
\(767\) 13.6916 0.494374
\(768\) −0.672761 −0.0242762
\(769\) 48.1369 1.73586 0.867930 0.496686i \(-0.165450\pi\)
0.867930 + 0.496686i \(0.165450\pi\)
\(770\) −2.20043 −0.0792980
\(771\) −10.2134 −0.367826
\(772\) −15.6581 −0.563549
\(773\) −12.2053 −0.438995 −0.219498 0.975613i \(-0.570442\pi\)
−0.219498 + 0.975613i \(0.570442\pi\)
\(774\) −16.2953 −0.585722
\(775\) 3.13583 0.112642
\(776\) −16.5081 −0.592606
\(777\) 3.03842 0.109003
\(778\) −10.8135 −0.387681
\(779\) −44.2286 −1.58466
\(780\) 2.58381 0.0925151
\(781\) −13.1271 −0.469725
\(782\) −5.88597 −0.210482
\(783\) 35.7260 1.27674
\(784\) −6.74352 −0.240840
\(785\) 58.3971 2.08428
\(786\) −0.672761 −0.0239966
\(787\) 4.55518 0.162375 0.0811873 0.996699i \(-0.474129\pi\)
0.0811873 + 0.996699i \(0.474129\pi\)
\(788\) 1.27537 0.0454332
\(789\) 15.3325 0.545852
\(790\) −32.8623 −1.16919
\(791\) 2.95892 0.105207
\(792\) 4.64368 0.165006
\(793\) −15.1756 −0.538901
\(794\) −32.4228 −1.15064
\(795\) 4.34004 0.153925
\(796\) −9.18160 −0.325433
\(797\) 39.4654 1.39794 0.698968 0.715153i \(-0.253643\pi\)
0.698968 + 0.715153i \(0.253643\pi\)
\(798\) 1.29036 0.0456782
\(799\) 6.96262 0.246320
\(800\) −0.681154 −0.0240824
\(801\) 22.5508 0.796794
\(802\) 14.2130 0.501878
\(803\) 1.53827 0.0542843
\(804\) −6.53011 −0.230299
\(805\) −1.20709 −0.0425445
\(806\) −7.41802 −0.261289
\(807\) 21.2556 0.748232
\(808\) 3.84068 0.135115
\(809\) 47.6537 1.67541 0.837707 0.546121i \(-0.183896\pi\)
0.837707 + 0.546121i \(0.183896\pi\)
\(810\) 12.2307 0.429745
\(811\) −56.7207 −1.99173 −0.995867 0.0908286i \(-0.971048\pi\)
−0.995867 + 0.0908286i \(0.971048\pi\)
\(812\) −4.84795 −0.170130
\(813\) 21.3253 0.747909
\(814\) −16.2566 −0.569794
\(815\) −9.86244 −0.345466
\(816\) 3.95985 0.138623
\(817\) 24.2266 0.847582
\(818\) −20.0218 −0.700046
\(819\) 2.07874 0.0726370
\(820\) −27.8353 −0.972050
\(821\) −7.87088 −0.274696 −0.137348 0.990523i \(-0.543858\pi\)
−0.137348 + 0.990523i \(0.543858\pi\)
\(822\) 8.01808 0.279663
\(823\) −43.7404 −1.52469 −0.762347 0.647169i \(-0.775953\pi\)
−0.762347 + 0.647169i \(0.775953\pi\)
\(824\) 7.33545 0.255542
\(825\) −0.835358 −0.0290834
\(826\) 4.30324 0.149729
\(827\) −22.6754 −0.788499 −0.394250 0.919003i \(-0.628995\pi\)
−0.394250 + 0.919003i \(0.628995\pi\)
\(828\) 2.54739 0.0885280
\(829\) 18.9462 0.658030 0.329015 0.944325i \(-0.393283\pi\)
0.329015 + 0.944325i \(0.393283\pi\)
\(830\) 8.46024 0.293659
\(831\) 4.54984 0.157832
\(832\) 1.61132 0.0558623
\(833\) 39.6922 1.37525
\(834\) 5.82973 0.201867
\(835\) −38.6861 −1.33879
\(836\) −6.90387 −0.238775
\(837\) 17.1813 0.593874
\(838\) 37.3997 1.29195
\(839\) 43.6875 1.50826 0.754130 0.656725i \(-0.228059\pi\)
0.754130 + 0.656725i \(0.228059\pi\)
\(840\) 0.812086 0.0280196
\(841\) 62.6367 2.15989
\(842\) 28.0323 0.966058
\(843\) 6.46771 0.222760
\(844\) −12.3775 −0.426052
\(845\) 24.7973 0.853053
\(846\) −3.01336 −0.103601
\(847\) 3.88788 0.133589
\(848\) 2.70654 0.0929430
\(849\) −1.05644 −0.0362568
\(850\) 4.00925 0.137516
\(851\) −8.91792 −0.305702
\(852\) 4.84466 0.165975
\(853\) 3.03424 0.103890 0.0519452 0.998650i \(-0.483458\pi\)
0.0519452 + 0.998650i \(0.483458\pi\)
\(854\) −4.76966 −0.163215
\(855\) −22.9954 −0.786425
\(856\) −12.2690 −0.419345
\(857\) 10.7632 0.367664 0.183832 0.982958i \(-0.441150\pi\)
0.183832 + 0.982958i \(0.441150\pi\)
\(858\) 1.97610 0.0674628
\(859\) −3.14654 −0.107359 −0.0536793 0.998558i \(-0.517095\pi\)
−0.0536793 + 0.998558i \(0.517095\pi\)
\(860\) 15.2470 0.519919
\(861\) 3.97888 0.135600
\(862\) 30.4709 1.03784
\(863\) 12.4796 0.424812 0.212406 0.977182i \(-0.431870\pi\)
0.212406 + 0.977182i \(0.431870\pi\)
\(864\) −3.73207 −0.126968
\(865\) −17.9858 −0.611537
\(866\) −8.97319 −0.304921
\(867\) −11.8706 −0.403147
\(868\) −2.33147 −0.0791353
\(869\) −25.1331 −0.852581
\(870\) −15.3502 −0.520420
\(871\) 15.6401 0.529946
\(872\) 17.9443 0.607672
\(873\) −42.0526 −1.42326
\(874\) −3.78727 −0.128106
\(875\) −5.21326 −0.176240
\(876\) −0.567709 −0.0191811
\(877\) 29.8172 1.00685 0.503427 0.864038i \(-0.332072\pi\)
0.503427 + 0.864038i \(0.332072\pi\)
\(878\) 25.1764 0.849663
\(879\) −8.64574 −0.291613
\(880\) −4.34495 −0.146468
\(881\) 4.56774 0.153891 0.0769456 0.997035i \(-0.475483\pi\)
0.0769456 + 0.997035i \(0.475483\pi\)
\(882\) −17.1784 −0.578427
\(883\) 10.7647 0.362260 0.181130 0.983459i \(-0.442024\pi\)
0.181130 + 0.983459i \(0.442024\pi\)
\(884\) −9.48416 −0.318987
\(885\) 13.6255 0.458016
\(886\) 2.46405 0.0827814
\(887\) 8.26673 0.277570 0.138785 0.990323i \(-0.455680\pi\)
0.138785 + 0.990323i \(0.455680\pi\)
\(888\) 5.99963 0.201334
\(889\) −6.55567 −0.219870
\(890\) −21.1001 −0.707277
\(891\) 9.35408 0.313374
\(892\) 1.12783 0.0377625
\(893\) 4.48003 0.149919
\(894\) 2.57585 0.0861493
\(895\) −28.9153 −0.966531
\(896\) 0.506434 0.0169188
\(897\) 1.08403 0.0361947
\(898\) −21.0293 −0.701756
\(899\) 44.0699 1.46981
\(900\) −1.73517 −0.0578389
\(901\) −15.9306 −0.530726
\(902\) −21.2884 −0.708827
\(903\) −2.17947 −0.0725281
\(904\) 5.84266 0.194324
\(905\) −20.5360 −0.682638
\(906\) 12.6387 0.419892
\(907\) −28.7898 −0.955949 −0.477975 0.878374i \(-0.658629\pi\)
−0.477975 + 0.878374i \(0.658629\pi\)
\(908\) −17.4568 −0.579323
\(909\) 9.78372 0.324506
\(910\) −1.94501 −0.0644765
\(911\) 4.02025 0.133197 0.0665985 0.997780i \(-0.478785\pi\)
0.0665985 + 0.997780i \(0.478785\pi\)
\(912\) 2.54793 0.0843704
\(913\) 6.47040 0.214139
\(914\) 1.97969 0.0654824
\(915\) −15.1023 −0.499268
\(916\) 21.0847 0.696659
\(917\) 0.506434 0.0167239
\(918\) 21.9668 0.725014
\(919\) 14.8215 0.488915 0.244458 0.969660i \(-0.421390\pi\)
0.244458 + 0.969660i \(0.421390\pi\)
\(920\) −2.38352 −0.0785822
\(921\) −13.3195 −0.438891
\(922\) −6.49877 −0.214026
\(923\) −11.6034 −0.381929
\(924\) 0.621084 0.0204322
\(925\) 6.07447 0.199727
\(926\) 27.2991 0.897103
\(927\) 18.6863 0.613737
\(928\) −9.57271 −0.314239
\(929\) −19.4765 −0.639004 −0.319502 0.947586i \(-0.603516\pi\)
−0.319502 + 0.947586i \(0.603516\pi\)
\(930\) −7.38221 −0.242072
\(931\) 25.5396 0.837025
\(932\) −11.8051 −0.386690
\(933\) −3.68602 −0.120675
\(934\) −9.73770 −0.318627
\(935\) 25.5742 0.836367
\(936\) 4.10466 0.134165
\(937\) −33.9966 −1.11062 −0.555310 0.831643i \(-0.687400\pi\)
−0.555310 + 0.831643i \(0.687400\pi\)
\(938\) 4.91567 0.160502
\(939\) −0.0742616 −0.00242344
\(940\) 2.81951 0.0919622
\(941\) 44.1517 1.43931 0.719653 0.694334i \(-0.244301\pi\)
0.719653 + 0.694334i \(0.244301\pi\)
\(942\) −16.4829 −0.537042
\(943\) −11.6782 −0.380296
\(944\) 8.49714 0.276558
\(945\) 4.50496 0.146546
\(946\) 11.6609 0.379129
\(947\) −6.86659 −0.223134 −0.111567 0.993757i \(-0.535587\pi\)
−0.111567 + 0.993757i \(0.535587\pi\)
\(948\) 9.27556 0.301256
\(949\) 1.35971 0.0441380
\(950\) 2.57972 0.0836970
\(951\) −1.24025 −0.0402178
\(952\) −2.98086 −0.0966101
\(953\) −26.9441 −0.872805 −0.436403 0.899751i \(-0.643748\pi\)
−0.436403 + 0.899751i \(0.643748\pi\)
\(954\) 6.89462 0.223222
\(955\) 51.4276 1.66416
\(956\) 4.00218 0.129440
\(957\) −11.7398 −0.379495
\(958\) −7.05123 −0.227815
\(959\) −6.03577 −0.194905
\(960\) 1.60354 0.0517540
\(961\) −9.80595 −0.316321
\(962\) −14.3696 −0.463294
\(963\) −31.2539 −1.00714
\(964\) −24.3560 −0.784455
\(965\) 37.3215 1.20142
\(966\) 0.340709 0.0109621
\(967\) 9.65533 0.310495 0.155247 0.987876i \(-0.450383\pi\)
0.155247 + 0.987876i \(0.450383\pi\)
\(968\) 7.67698 0.246747
\(969\) −14.9970 −0.481774
\(970\) 39.3473 1.26337
\(971\) 33.3561 1.07045 0.535224 0.844710i \(-0.320227\pi\)
0.535224 + 0.844710i \(0.320227\pi\)
\(972\) −14.6484 −0.469848
\(973\) −4.38844 −0.140687
\(974\) −10.7401 −0.344135
\(975\) −0.738392 −0.0236475
\(976\) −9.41813 −0.301467
\(977\) 33.4629 1.07057 0.535287 0.844671i \(-0.320204\pi\)
0.535287 + 0.844671i \(0.320204\pi\)
\(978\) 2.78373 0.0890138
\(979\) −16.1374 −0.515753
\(980\) 16.0733 0.513443
\(981\) 45.7113 1.45945
\(982\) 24.6316 0.786026
\(983\) −0.234127 −0.00746750 −0.00373375 0.999993i \(-0.501188\pi\)
−0.00373375 + 0.999993i \(0.501188\pi\)
\(984\) 7.85666 0.250461
\(985\) −3.03987 −0.0968583
\(986\) 56.3446 1.79438
\(987\) −0.403031 −0.0128286
\(988\) −6.10249 −0.194146
\(989\) 6.39686 0.203408
\(990\) −11.0683 −0.351773
\(991\) 29.2613 0.929517 0.464758 0.885438i \(-0.346141\pi\)
0.464758 + 0.885438i \(0.346141\pi\)
\(992\) −4.60370 −0.146168
\(993\) 18.4947 0.586912
\(994\) −3.64692 −0.115673
\(995\) 21.8845 0.693785
\(996\) −2.38795 −0.0756651
\(997\) 32.2678 1.02193 0.510966 0.859601i \(-0.329288\pi\)
0.510966 + 0.859601i \(0.329288\pi\)
\(998\) 2.20103 0.0696724
\(999\) 33.2823 1.05300
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 \(a_p\))