Properties

Label 4026.2.a.bc.1.7
Level 4026
Weight 2
Character 4026.1
Self dual Yes
Analytic conductor 32.148
Analytic rank 0
Dimension 9
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1477718538\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.09192\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.09192 q^{5}\) \(+1.00000 q^{6}\) \(-4.21340 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(+3.09192 q^{5}\) \(+1.00000 q^{6}\) \(-4.21340 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+3.09192 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(-0.518474 q^{13}\) \(-4.21340 q^{14}\) \(+3.09192 q^{15}\) \(+1.00000 q^{16}\) \(-3.01037 q^{17}\) \(+1.00000 q^{18}\) \(+8.39142 q^{19}\) \(+3.09192 q^{20}\) \(-4.21340 q^{21}\) \(+1.00000 q^{22}\) \(-0.337593 q^{23}\) \(+1.00000 q^{24}\) \(+4.55998 q^{25}\) \(-0.518474 q^{26}\) \(+1.00000 q^{27}\) \(-4.21340 q^{28}\) \(+5.57973 q^{29}\) \(+3.09192 q^{30}\) \(+4.75433 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(-3.01037 q^{34}\) \(-13.0275 q^{35}\) \(+1.00000 q^{36}\) \(+0.867362 q^{37}\) \(+8.39142 q^{38}\) \(-0.518474 q^{39}\) \(+3.09192 q^{40}\) \(+8.17976 q^{41}\) \(-4.21340 q^{42}\) \(-9.01482 q^{43}\) \(+1.00000 q^{44}\) \(+3.09192 q^{45}\) \(-0.337593 q^{46}\) \(+2.07039 q^{47}\) \(+1.00000 q^{48}\) \(+10.7527 q^{49}\) \(+4.55998 q^{50}\) \(-3.01037 q^{51}\) \(-0.518474 q^{52}\) \(+4.08394 q^{53}\) \(+1.00000 q^{54}\) \(+3.09192 q^{55}\) \(-4.21340 q^{56}\) \(+8.39142 q^{57}\) \(+5.57973 q^{58}\) \(-2.99101 q^{59}\) \(+3.09192 q^{60}\) \(-1.00000 q^{61}\) \(+4.75433 q^{62}\) \(-4.21340 q^{63}\) \(+1.00000 q^{64}\) \(-1.60308 q^{65}\) \(+1.00000 q^{66}\) \(-1.16994 q^{67}\) \(-3.01037 q^{68}\) \(-0.337593 q^{69}\) \(-13.0275 q^{70}\) \(+15.3353 q^{71}\) \(+1.00000 q^{72}\) \(+8.24649 q^{73}\) \(+0.867362 q^{74}\) \(+4.55998 q^{75}\) \(+8.39142 q^{76}\) \(-4.21340 q^{77}\) \(-0.518474 q^{78}\) \(-15.3981 q^{79}\) \(+3.09192 q^{80}\) \(+1.00000 q^{81}\) \(+8.17976 q^{82}\) \(-8.21682 q^{83}\) \(-4.21340 q^{84}\) \(-9.30782 q^{85}\) \(-9.01482 q^{86}\) \(+5.57973 q^{87}\) \(+1.00000 q^{88}\) \(+8.31023 q^{89}\) \(+3.09192 q^{90}\) \(+2.18454 q^{91}\) \(-0.337593 q^{92}\) \(+4.75433 q^{93}\) \(+2.07039 q^{94}\) \(+25.9456 q^{95}\) \(+1.00000 q^{96}\) \(-4.53172 q^{97}\) \(+10.7527 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) 3.09192 1.38275 0.691375 0.722496i \(-0.257005\pi\)
0.691375 + 0.722496i \(0.257005\pi\)
\(6\) 1.00000 0.408248
\(7\) −4.21340 −1.59251 −0.796257 0.604958i \(-0.793190\pi\)
−0.796257 + 0.604958i \(0.793190\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) 3.09192 0.977751
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −0.518474 −0.143799 −0.0718995 0.997412i \(-0.522906\pi\)
−0.0718995 + 0.997412i \(0.522906\pi\)
\(14\) −4.21340 −1.12608
\(15\) 3.09192 0.798331
\(16\) 1.00000 0.250000
\(17\) −3.01037 −0.730121 −0.365061 0.930984i \(-0.618952\pi\)
−0.365061 + 0.930984i \(0.618952\pi\)
\(18\) 1.00000 0.235702
\(19\) 8.39142 1.92512 0.962562 0.271061i \(-0.0873745\pi\)
0.962562 + 0.271061i \(0.0873745\pi\)
\(20\) 3.09192 0.691375
\(21\) −4.21340 −0.919439
\(22\) 1.00000 0.213201
\(23\) −0.337593 −0.0703930 −0.0351965 0.999380i \(-0.511206\pi\)
−0.0351965 + 0.999380i \(0.511206\pi\)
\(24\) 1.00000 0.204124
\(25\) 4.55998 0.911996
\(26\) −0.518474 −0.101681
\(27\) 1.00000 0.192450
\(28\) −4.21340 −0.796257
\(29\) 5.57973 1.03613 0.518065 0.855341i \(-0.326652\pi\)
0.518065 + 0.855341i \(0.326652\pi\)
\(30\) 3.09192 0.564505
\(31\) 4.75433 0.853903 0.426951 0.904275i \(-0.359588\pi\)
0.426951 + 0.904275i \(0.359588\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) −3.01037 −0.516274
\(35\) −13.0275 −2.20205
\(36\) 1.00000 0.166667
\(37\) 0.867362 0.142593 0.0712967 0.997455i \(-0.477286\pi\)
0.0712967 + 0.997455i \(0.477286\pi\)
\(38\) 8.39142 1.36127
\(39\) −0.518474 −0.0830223
\(40\) 3.09192 0.488876
\(41\) 8.17976 1.27746 0.638732 0.769429i \(-0.279459\pi\)
0.638732 + 0.769429i \(0.279459\pi\)
\(42\) −4.21340 −0.650141
\(43\) −9.01482 −1.37475 −0.687374 0.726304i \(-0.741236\pi\)
−0.687374 + 0.726304i \(0.741236\pi\)
\(44\) 1.00000 0.150756
\(45\) 3.09192 0.460916
\(46\) −0.337593 −0.0497753
\(47\) 2.07039 0.301998 0.150999 0.988534i \(-0.451751\pi\)
0.150999 + 0.988534i \(0.451751\pi\)
\(48\) 1.00000 0.144338
\(49\) 10.7527 1.53610
\(50\) 4.55998 0.644878
\(51\) −3.01037 −0.421536
\(52\) −0.518474 −0.0718995
\(53\) 4.08394 0.560972 0.280486 0.959858i \(-0.409504\pi\)
0.280486 + 0.959858i \(0.409504\pi\)
\(54\) 1.00000 0.136083
\(55\) 3.09192 0.416915
\(56\) −4.21340 −0.563039
\(57\) 8.39142 1.11147
\(58\) 5.57973 0.732655
\(59\) −2.99101 −0.389397 −0.194698 0.980863i \(-0.562373\pi\)
−0.194698 + 0.980863i \(0.562373\pi\)
\(60\) 3.09192 0.399165
\(61\) −1.00000 −0.128037
\(62\) 4.75433 0.603800
\(63\) −4.21340 −0.530838
\(64\) 1.00000 0.125000
\(65\) −1.60308 −0.198838
\(66\) 1.00000 0.123091
\(67\) −1.16994 −0.142930 −0.0714652 0.997443i \(-0.522767\pi\)
−0.0714652 + 0.997443i \(0.522767\pi\)
\(68\) −3.01037 −0.365061
\(69\) −0.337593 −0.0406414
\(70\) −13.0275 −1.55708
\(71\) 15.3353 1.81997 0.909983 0.414645i \(-0.136094\pi\)
0.909983 + 0.414645i \(0.136094\pi\)
\(72\) 1.00000 0.117851
\(73\) 8.24649 0.965179 0.482590 0.875847i \(-0.339696\pi\)
0.482590 + 0.875847i \(0.339696\pi\)
\(74\) 0.867362 0.100829
\(75\) 4.55998 0.526541
\(76\) 8.39142 0.962562
\(77\) −4.21340 −0.480161
\(78\) −0.518474 −0.0587057
\(79\) −15.3981 −1.73243 −0.866213 0.499675i \(-0.833453\pi\)
−0.866213 + 0.499675i \(0.833453\pi\)
\(80\) 3.09192 0.345687
\(81\) 1.00000 0.111111
\(82\) 8.17976 0.903304
\(83\) −8.21682 −0.901913 −0.450957 0.892546i \(-0.648917\pi\)
−0.450957 + 0.892546i \(0.648917\pi\)
\(84\) −4.21340 −0.459719
\(85\) −9.30782 −1.00957
\(86\) −9.01482 −0.972093
\(87\) 5.57973 0.598210
\(88\) 1.00000 0.106600
\(89\) 8.31023 0.880882 0.440441 0.897782i \(-0.354822\pi\)
0.440441 + 0.897782i \(0.354822\pi\)
\(90\) 3.09192 0.325917
\(91\) 2.18454 0.229002
\(92\) −0.337593 −0.0351965
\(93\) 4.75433 0.493001
\(94\) 2.07039 0.213545
\(95\) 25.9456 2.66196
\(96\) 1.00000 0.102062
\(97\) −4.53172 −0.460126 −0.230063 0.973176i \(-0.573893\pi\)
−0.230063 + 0.973176i \(0.573893\pi\)
\(98\) 10.7527 1.08619
\(99\) 1.00000 0.100504
\(100\) 4.55998 0.455998
\(101\) −1.63654 −0.162842 −0.0814208 0.996680i \(-0.525946\pi\)
−0.0814208 + 0.996680i \(0.525946\pi\)
\(102\) −3.01037 −0.298071
\(103\) 7.63116 0.751920 0.375960 0.926636i \(-0.377313\pi\)
0.375960 + 0.926636i \(0.377313\pi\)
\(104\) −0.518474 −0.0508406
\(105\) −13.0275 −1.27135
\(106\) 4.08394 0.396667
\(107\) −8.45294 −0.817176 −0.408588 0.912719i \(-0.633979\pi\)
−0.408588 + 0.912719i \(0.633979\pi\)
\(108\) 1.00000 0.0962250
\(109\) −2.43637 −0.233362 −0.116681 0.993169i \(-0.537225\pi\)
−0.116681 + 0.993169i \(0.537225\pi\)
\(110\) 3.09192 0.294803
\(111\) 0.867362 0.0823264
\(112\) −4.21340 −0.398129
\(113\) 15.3057 1.43984 0.719919 0.694059i \(-0.244179\pi\)
0.719919 + 0.694059i \(0.244179\pi\)
\(114\) 8.39142 0.785929
\(115\) −1.04381 −0.0973358
\(116\) 5.57973 0.518065
\(117\) −0.518474 −0.0479330
\(118\) −2.99101 −0.275345
\(119\) 12.6839 1.16273
\(120\) 3.09192 0.282253
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) 8.17976 0.737544
\(124\) 4.75433 0.426951
\(125\) −1.36051 −0.121688
\(126\) −4.21340 −0.375359
\(127\) 15.9129 1.41204 0.706019 0.708192i \(-0.250489\pi\)
0.706019 + 0.708192i \(0.250489\pi\)
\(128\) 1.00000 0.0883883
\(129\) −9.01482 −0.793711
\(130\) −1.60308 −0.140600
\(131\) −0.798822 −0.0697934 −0.0348967 0.999391i \(-0.511110\pi\)
−0.0348967 + 0.999391i \(0.511110\pi\)
\(132\) 1.00000 0.0870388
\(133\) −35.3564 −3.06579
\(134\) −1.16994 −0.101067
\(135\) 3.09192 0.266110
\(136\) −3.01037 −0.258137
\(137\) −2.23605 −0.191038 −0.0955191 0.995428i \(-0.530451\pi\)
−0.0955191 + 0.995428i \(0.530451\pi\)
\(138\) −0.337593 −0.0287378
\(139\) −14.7025 −1.24705 −0.623526 0.781803i \(-0.714301\pi\)
−0.623526 + 0.781803i \(0.714301\pi\)
\(140\) −13.0275 −1.10102
\(141\) 2.07039 0.174359
\(142\) 15.3353 1.28691
\(143\) −0.518474 −0.0433570
\(144\) 1.00000 0.0833333
\(145\) 17.2521 1.43271
\(146\) 8.24649 0.682485
\(147\) 10.7527 0.886870
\(148\) 0.867362 0.0712967
\(149\) 2.72711 0.223413 0.111707 0.993741i \(-0.464368\pi\)
0.111707 + 0.993741i \(0.464368\pi\)
\(150\) 4.55998 0.372321
\(151\) −10.1402 −0.825195 −0.412597 0.910914i \(-0.635378\pi\)
−0.412597 + 0.910914i \(0.635378\pi\)
\(152\) 8.39142 0.680634
\(153\) −3.01037 −0.243374
\(154\) −4.21340 −0.339525
\(155\) 14.7000 1.18073
\(156\) −0.518474 −0.0415112
\(157\) −21.1790 −1.69027 −0.845135 0.534552i \(-0.820480\pi\)
−0.845135 + 0.534552i \(0.820480\pi\)
\(158\) −15.3981 −1.22501
\(159\) 4.08394 0.323877
\(160\) 3.09192 0.244438
\(161\) 1.42241 0.112102
\(162\) 1.00000 0.0785674
\(163\) 0.185111 0.0144990 0.00724951 0.999974i \(-0.497692\pi\)
0.00724951 + 0.999974i \(0.497692\pi\)
\(164\) 8.17976 0.638732
\(165\) 3.09192 0.240706
\(166\) −8.21682 −0.637749
\(167\) −17.7975 −1.37721 −0.688606 0.725136i \(-0.741777\pi\)
−0.688606 + 0.725136i \(0.741777\pi\)
\(168\) −4.21340 −0.325071
\(169\) −12.7312 −0.979322
\(170\) −9.30782 −0.713877
\(171\) 8.39142 0.641708
\(172\) −9.01482 −0.687374
\(173\) −4.92214 −0.374223 −0.187112 0.982339i \(-0.559913\pi\)
−0.187112 + 0.982339i \(0.559913\pi\)
\(174\) 5.57973 0.422999
\(175\) −19.2130 −1.45237
\(176\) 1.00000 0.0753778
\(177\) −2.99101 −0.224818
\(178\) 8.31023 0.622878
\(179\) −5.64476 −0.421909 −0.210955 0.977496i \(-0.567657\pi\)
−0.210955 + 0.977496i \(0.567657\pi\)
\(180\) 3.09192 0.230458
\(181\) −4.40261 −0.327243 −0.163622 0.986523i \(-0.552318\pi\)
−0.163622 + 0.986523i \(0.552318\pi\)
\(182\) 2.18454 0.161929
\(183\) −1.00000 −0.0739221
\(184\) −0.337593 −0.0248877
\(185\) 2.68182 0.197171
\(186\) 4.75433 0.348604
\(187\) −3.01037 −0.220140
\(188\) 2.07039 0.150999
\(189\) −4.21340 −0.306480
\(190\) 25.9456 1.88229
\(191\) 27.0598 1.95798 0.978988 0.203920i \(-0.0653681\pi\)
0.978988 + 0.203920i \(0.0653681\pi\)
\(192\) 1.00000 0.0721688
\(193\) −10.7214 −0.771743 −0.385871 0.922553i \(-0.626099\pi\)
−0.385871 + 0.922553i \(0.626099\pi\)
\(194\) −4.53172 −0.325358
\(195\) −1.60308 −0.114799
\(196\) 10.7527 0.768052
\(197\) 11.7458 0.836852 0.418426 0.908251i \(-0.362582\pi\)
0.418426 + 0.908251i \(0.362582\pi\)
\(198\) 1.00000 0.0710669
\(199\) −0.770322 −0.0546067 −0.0273034 0.999627i \(-0.508692\pi\)
−0.0273034 + 0.999627i \(0.508692\pi\)
\(200\) 4.55998 0.322439
\(201\) −1.16994 −0.0825209
\(202\) −1.63654 −0.115146
\(203\) −23.5096 −1.65005
\(204\) −3.01037 −0.210768
\(205\) 25.2912 1.76641
\(206\) 7.63116 0.531688
\(207\) −0.337593 −0.0234643
\(208\) −0.518474 −0.0359497
\(209\) 8.39142 0.580447
\(210\) −13.0275 −0.898983
\(211\) −3.55095 −0.244458 −0.122229 0.992502i \(-0.539004\pi\)
−0.122229 + 0.992502i \(0.539004\pi\)
\(212\) 4.08394 0.280486
\(213\) 15.3353 1.05076
\(214\) −8.45294 −0.577831
\(215\) −27.8731 −1.90093
\(216\) 1.00000 0.0680414
\(217\) −20.0319 −1.35985
\(218\) −2.43637 −0.165012
\(219\) 8.24649 0.557246
\(220\) 3.09192 0.208457
\(221\) 1.56080 0.104991
\(222\) 0.867362 0.0582135
\(223\) −25.4930 −1.70714 −0.853569 0.520980i \(-0.825566\pi\)
−0.853569 + 0.520980i \(0.825566\pi\)
\(224\) −4.21340 −0.281519
\(225\) 4.55998 0.303999
\(226\) 15.3057 1.01812
\(227\) 0.170623 0.0113247 0.00566233 0.999984i \(-0.498198\pi\)
0.00566233 + 0.999984i \(0.498198\pi\)
\(228\) 8.39142 0.555736
\(229\) 11.6894 0.772460 0.386230 0.922402i \(-0.373777\pi\)
0.386230 + 0.922402i \(0.373777\pi\)
\(230\) −1.04381 −0.0688268
\(231\) −4.21340 −0.277221
\(232\) 5.57973 0.366327
\(233\) −3.78322 −0.247847 −0.123924 0.992292i \(-0.539548\pi\)
−0.123924 + 0.992292i \(0.539548\pi\)
\(234\) −0.518474 −0.0338937
\(235\) 6.40149 0.417587
\(236\) −2.99101 −0.194698
\(237\) −15.3981 −1.00022
\(238\) 12.6839 0.822174
\(239\) −1.37684 −0.0890604 −0.0445302 0.999008i \(-0.514179\pi\)
−0.0445302 + 0.999008i \(0.514179\pi\)
\(240\) 3.09192 0.199583
\(241\) 5.21306 0.335803 0.167901 0.985804i \(-0.446301\pi\)
0.167901 + 0.985804i \(0.446301\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 33.2466 2.12405
\(246\) 8.17976 0.521523
\(247\) −4.35074 −0.276831
\(248\) 4.75433 0.301900
\(249\) −8.21682 −0.520720
\(250\) −1.36051 −0.0860464
\(251\) 8.63092 0.544779 0.272389 0.962187i \(-0.412186\pi\)
0.272389 + 0.962187i \(0.412186\pi\)
\(252\) −4.21340 −0.265419
\(253\) −0.337593 −0.0212243
\(254\) 15.9129 0.998462
\(255\) −9.30782 −0.582878
\(256\) 1.00000 0.0625000
\(257\) −28.3616 −1.76915 −0.884573 0.466401i \(-0.845550\pi\)
−0.884573 + 0.466401i \(0.845550\pi\)
\(258\) −9.01482 −0.561238
\(259\) −3.65454 −0.227082
\(260\) −1.60308 −0.0994189
\(261\) 5.57973 0.345377
\(262\) −0.798822 −0.0493514
\(263\) −29.9754 −1.84836 −0.924182 0.381953i \(-0.875252\pi\)
−0.924182 + 0.381953i \(0.875252\pi\)
\(264\) 1.00000 0.0615457
\(265\) 12.6272 0.775684
\(266\) −35.3564 −2.16784
\(267\) 8.31023 0.508578
\(268\) −1.16994 −0.0714652
\(269\) −13.1706 −0.803027 −0.401514 0.915853i \(-0.631516\pi\)
−0.401514 + 0.915853i \(0.631516\pi\)
\(270\) 3.09192 0.188168
\(271\) −7.45328 −0.452754 −0.226377 0.974040i \(-0.572688\pi\)
−0.226377 + 0.974040i \(0.572688\pi\)
\(272\) −3.01037 −0.182530
\(273\) 2.18454 0.132214
\(274\) −2.23605 −0.135084
\(275\) 4.55998 0.274977
\(276\) −0.337593 −0.0203207
\(277\) 18.2143 1.09439 0.547194 0.837006i \(-0.315696\pi\)
0.547194 + 0.837006i \(0.315696\pi\)
\(278\) −14.7025 −0.881799
\(279\) 4.75433 0.284634
\(280\) −13.0275 −0.778542
\(281\) −0.772012 −0.0460544 −0.0230272 0.999735i \(-0.507330\pi\)
−0.0230272 + 0.999735i \(0.507330\pi\)
\(282\) 2.07039 0.123290
\(283\) 18.9952 1.12915 0.564574 0.825383i \(-0.309041\pi\)
0.564574 + 0.825383i \(0.309041\pi\)
\(284\) 15.3353 0.909983
\(285\) 25.9456 1.53689
\(286\) −0.518474 −0.0306580
\(287\) −34.4646 −2.03438
\(288\) 1.00000 0.0589256
\(289\) −7.93769 −0.466923
\(290\) 17.2521 1.01308
\(291\) −4.53172 −0.265654
\(292\) 8.24649 0.482590
\(293\) 23.3929 1.36663 0.683314 0.730125i \(-0.260538\pi\)
0.683314 + 0.730125i \(0.260538\pi\)
\(294\) 10.7527 0.627112
\(295\) −9.24798 −0.538438
\(296\) 0.867362 0.0504144
\(297\) 1.00000 0.0580259
\(298\) 2.72711 0.157977
\(299\) 0.175033 0.0101224
\(300\) 4.55998 0.263270
\(301\) 37.9830 2.18931
\(302\) −10.1402 −0.583501
\(303\) −1.63654 −0.0940167
\(304\) 8.39142 0.481281
\(305\) −3.09192 −0.177043
\(306\) −3.01037 −0.172091
\(307\) −17.5170 −0.999750 −0.499875 0.866098i \(-0.666621\pi\)
−0.499875 + 0.866098i \(0.666621\pi\)
\(308\) −4.21340 −0.240081
\(309\) 7.63116 0.434121
\(310\) 14.7000 0.834904
\(311\) −19.9778 −1.13284 −0.566418 0.824118i \(-0.691671\pi\)
−0.566418 + 0.824118i \(0.691671\pi\)
\(312\) −0.518474 −0.0293528
\(313\) 7.60209 0.429696 0.214848 0.976648i \(-0.431074\pi\)
0.214848 + 0.976648i \(0.431074\pi\)
\(314\) −21.1790 −1.19520
\(315\) −13.0275 −0.734016
\(316\) −15.3981 −0.866213
\(317\) −1.61257 −0.0905709 −0.0452855 0.998974i \(-0.514420\pi\)
−0.0452855 + 0.998974i \(0.514420\pi\)
\(318\) 4.08394 0.229016
\(319\) 5.57973 0.312405
\(320\) 3.09192 0.172844
\(321\) −8.45294 −0.471797
\(322\) 1.42241 0.0792680
\(323\) −25.2613 −1.40557
\(324\) 1.00000 0.0555556
\(325\) −2.36423 −0.131144
\(326\) 0.185111 0.0102524
\(327\) −2.43637 −0.134731
\(328\) 8.17976 0.451652
\(329\) −8.72339 −0.480936
\(330\) 3.09192 0.170205
\(331\) −18.9630 −1.04230 −0.521149 0.853465i \(-0.674497\pi\)
−0.521149 + 0.853465i \(0.674497\pi\)
\(332\) −8.21682 −0.450957
\(333\) 0.867362 0.0475312
\(334\) −17.7975 −0.973836
\(335\) −3.61735 −0.197637
\(336\) −4.21340 −0.229860
\(337\) −15.7924 −0.860268 −0.430134 0.902765i \(-0.641534\pi\)
−0.430134 + 0.902765i \(0.641534\pi\)
\(338\) −12.7312 −0.692485
\(339\) 15.3057 0.831290
\(340\) −9.30782 −0.504787
\(341\) 4.75433 0.257461
\(342\) 8.39142 0.453756
\(343\) −15.8117 −0.853752
\(344\) −9.01482 −0.486047
\(345\) −1.04381 −0.0561969
\(346\) −4.92214 −0.264616
\(347\) −18.7955 −1.00900 −0.504498 0.863413i \(-0.668323\pi\)
−0.504498 + 0.863413i \(0.668323\pi\)
\(348\) 5.57973 0.299105
\(349\) −6.73963 −0.360764 −0.180382 0.983597i \(-0.557733\pi\)
−0.180382 + 0.983597i \(0.557733\pi\)
\(350\) −19.2130 −1.02698
\(351\) −0.518474 −0.0276741
\(352\) 1.00000 0.0533002
\(353\) −8.54806 −0.454967 −0.227484 0.973782i \(-0.573050\pi\)
−0.227484 + 0.973782i \(0.573050\pi\)
\(354\) −2.99101 −0.158971
\(355\) 47.4156 2.51656
\(356\) 8.31023 0.440441
\(357\) 12.6839 0.671302
\(358\) −5.64476 −0.298335
\(359\) 13.9622 0.736896 0.368448 0.929648i \(-0.379889\pi\)
0.368448 + 0.929648i \(0.379889\pi\)
\(360\) 3.09192 0.162959
\(361\) 51.4160 2.70610
\(362\) −4.40261 −0.231396
\(363\) 1.00000 0.0524864
\(364\) 2.18454 0.114501
\(365\) 25.4975 1.33460
\(366\) −1.00000 −0.0522708
\(367\) 20.4701 1.06853 0.534264 0.845318i \(-0.320589\pi\)
0.534264 + 0.845318i \(0.320589\pi\)
\(368\) −0.337593 −0.0175982
\(369\) 8.17976 0.425821
\(370\) 2.68182 0.139421
\(371\) −17.2073 −0.893356
\(372\) 4.75433 0.246500
\(373\) −12.4446 −0.644355 −0.322178 0.946679i \(-0.604415\pi\)
−0.322178 + 0.946679i \(0.604415\pi\)
\(374\) −3.01037 −0.155662
\(375\) −1.36051 −0.0702566
\(376\) 2.07039 0.106772
\(377\) −2.89295 −0.148994
\(378\) −4.21340 −0.216714
\(379\) −16.3449 −0.839579 −0.419789 0.907622i \(-0.637896\pi\)
−0.419789 + 0.907622i \(0.637896\pi\)
\(380\) 25.9456 1.33098
\(381\) 15.9129 0.815241
\(382\) 27.0598 1.38450
\(383\) 5.46817 0.279411 0.139705 0.990193i \(-0.455384\pi\)
0.139705 + 0.990193i \(0.455384\pi\)
\(384\) 1.00000 0.0510310
\(385\) −13.0275 −0.663943
\(386\) −10.7214 −0.545705
\(387\) −9.01482 −0.458249
\(388\) −4.53172 −0.230063
\(389\) 11.8690 0.601781 0.300890 0.953659i \(-0.402716\pi\)
0.300890 + 0.953659i \(0.402716\pi\)
\(390\) −1.60308 −0.0811752
\(391\) 1.01628 0.0513954
\(392\) 10.7527 0.543094
\(393\) −0.798822 −0.0402953
\(394\) 11.7458 0.591744
\(395\) −47.6098 −2.39551
\(396\) 1.00000 0.0502519
\(397\) −6.85274 −0.343929 −0.171965 0.985103i \(-0.555011\pi\)
−0.171965 + 0.985103i \(0.555011\pi\)
\(398\) −0.770322 −0.0386128
\(399\) −35.3564 −1.77003
\(400\) 4.55998 0.227999
\(401\) −32.3814 −1.61705 −0.808526 0.588461i \(-0.799734\pi\)
−0.808526 + 0.588461i \(0.799734\pi\)
\(402\) −1.16994 −0.0583511
\(403\) −2.46500 −0.122790
\(404\) −1.63654 −0.0814208
\(405\) 3.09192 0.153639
\(406\) −23.5096 −1.16676
\(407\) 0.867362 0.0429936
\(408\) −3.01037 −0.149035
\(409\) 1.99757 0.0987732 0.0493866 0.998780i \(-0.484273\pi\)
0.0493866 + 0.998780i \(0.484273\pi\)
\(410\) 25.2912 1.24904
\(411\) −2.23605 −0.110296
\(412\) 7.63116 0.375960
\(413\) 12.6023 0.620120
\(414\) −0.337593 −0.0165918
\(415\) −25.4058 −1.24712
\(416\) −0.518474 −0.0254203
\(417\) −14.7025 −0.719986
\(418\) 8.39142 0.410438
\(419\) −33.6785 −1.64530 −0.822651 0.568546i \(-0.807506\pi\)
−0.822651 + 0.568546i \(0.807506\pi\)
\(420\) −13.0275 −0.635677
\(421\) 24.8542 1.21132 0.605660 0.795723i \(-0.292909\pi\)
0.605660 + 0.795723i \(0.292909\pi\)
\(422\) −3.55095 −0.172858
\(423\) 2.07039 0.100666
\(424\) 4.08394 0.198334
\(425\) −13.7272 −0.665867
\(426\) 15.3353 0.742998
\(427\) 4.21340 0.203901
\(428\) −8.45294 −0.408588
\(429\) −0.518474 −0.0250322
\(430\) −27.8731 −1.34416
\(431\) 23.2622 1.12050 0.560250 0.828324i \(-0.310705\pi\)
0.560250 + 0.828324i \(0.310705\pi\)
\(432\) 1.00000 0.0481125
\(433\) 37.3989 1.79728 0.898638 0.438692i \(-0.144558\pi\)
0.898638 + 0.438692i \(0.144558\pi\)
\(434\) −20.0319 −0.961561
\(435\) 17.2521 0.827175
\(436\) −2.43637 −0.116681
\(437\) −2.83288 −0.135515
\(438\) 8.24649 0.394033
\(439\) −10.1292 −0.483438 −0.241719 0.970346i \(-0.577711\pi\)
−0.241719 + 0.970346i \(0.577711\pi\)
\(440\) 3.09192 0.147402
\(441\) 10.7527 0.512034
\(442\) 1.56080 0.0742396
\(443\) −24.2824 −1.15369 −0.576845 0.816853i \(-0.695716\pi\)
−0.576845 + 0.816853i \(0.695716\pi\)
\(444\) 0.867362 0.0411632
\(445\) 25.6946 1.21804
\(446\) −25.4930 −1.20713
\(447\) 2.72711 0.128988
\(448\) −4.21340 −0.199064
\(449\) 30.9258 1.45948 0.729740 0.683724i \(-0.239641\pi\)
0.729740 + 0.683724i \(0.239641\pi\)
\(450\) 4.55998 0.214959
\(451\) 8.17976 0.385170
\(452\) 15.3057 0.719919
\(453\) −10.1402 −0.476426
\(454\) 0.170623 0.00800774
\(455\) 6.75442 0.316652
\(456\) 8.39142 0.392964
\(457\) 22.6296 1.05857 0.529284 0.848445i \(-0.322461\pi\)
0.529284 + 0.848445i \(0.322461\pi\)
\(458\) 11.6894 0.546212
\(459\) −3.01037 −0.140512
\(460\) −1.04381 −0.0486679
\(461\) 21.0195 0.978975 0.489488 0.872010i \(-0.337184\pi\)
0.489488 + 0.872010i \(0.337184\pi\)
\(462\) −4.21340 −0.196025
\(463\) −8.76779 −0.407474 −0.203737 0.979026i \(-0.565309\pi\)
−0.203737 + 0.979026i \(0.565309\pi\)
\(464\) 5.57973 0.259033
\(465\) 14.7000 0.681697
\(466\) −3.78322 −0.175254
\(467\) −16.6077 −0.768514 −0.384257 0.923226i \(-0.625542\pi\)
−0.384257 + 0.923226i \(0.625542\pi\)
\(468\) −0.518474 −0.0239665
\(469\) 4.92940 0.227619
\(470\) 6.40149 0.295279
\(471\) −21.1790 −0.975878
\(472\) −2.99101 −0.137673
\(473\) −9.01482 −0.414502
\(474\) −15.3981 −0.707260
\(475\) 38.2647 1.75570
\(476\) 12.6839 0.581364
\(477\) 4.08394 0.186991
\(478\) −1.37684 −0.0629752
\(479\) 8.73112 0.398935 0.199467 0.979904i \(-0.436079\pi\)
0.199467 + 0.979904i \(0.436079\pi\)
\(480\) 3.09192 0.141126
\(481\) −0.449705 −0.0205048
\(482\) 5.21306 0.237448
\(483\) 1.42241 0.0647220
\(484\) 1.00000 0.0454545
\(485\) −14.0117 −0.636239
\(486\) 1.00000 0.0453609
\(487\) 20.8409 0.944393 0.472196 0.881493i \(-0.343461\pi\)
0.472196 + 0.881493i \(0.343461\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 0.185111 0.00837101
\(490\) 33.2466 1.50193
\(491\) −12.7316 −0.574567 −0.287284 0.957846i \(-0.592752\pi\)
−0.287284 + 0.957846i \(0.592752\pi\)
\(492\) 8.17976 0.368772
\(493\) −16.7970 −0.756501
\(494\) −4.35074 −0.195749
\(495\) 3.09192 0.138972
\(496\) 4.75433 0.213476
\(497\) −64.6138 −2.89832
\(498\) −8.21682 −0.368205
\(499\) −14.9212 −0.667964 −0.333982 0.942579i \(-0.608393\pi\)
−0.333982 + 0.942579i \(0.608393\pi\)
\(500\) −1.36051 −0.0608440
\(501\) −17.7975 −0.795134
\(502\) 8.63092 0.385217
\(503\) 8.87163 0.395567 0.197783 0.980246i \(-0.436626\pi\)
0.197783 + 0.980246i \(0.436626\pi\)
\(504\) −4.21340 −0.187680
\(505\) −5.06005 −0.225169
\(506\) −0.337593 −0.0150078
\(507\) −12.7312 −0.565412
\(508\) 15.9129 0.706019
\(509\) −4.80090 −0.212796 −0.106398 0.994324i \(-0.533932\pi\)
−0.106398 + 0.994324i \(0.533932\pi\)
\(510\) −9.30782 −0.412157
\(511\) −34.7458 −1.53706
\(512\) 1.00000 0.0441942
\(513\) 8.39142 0.370490
\(514\) −28.3616 −1.25098
\(515\) 23.5949 1.03972
\(516\) −9.01482 −0.396855
\(517\) 2.07039 0.0910558
\(518\) −3.65454 −0.160571
\(519\) −4.92214 −0.216058
\(520\) −1.60308 −0.0702998
\(521\) 36.6061 1.60374 0.801870 0.597498i \(-0.203839\pi\)
0.801870 + 0.597498i \(0.203839\pi\)
\(522\) 5.57973 0.244218
\(523\) 40.8389 1.78576 0.892880 0.450296i \(-0.148681\pi\)
0.892880 + 0.450296i \(0.148681\pi\)
\(524\) −0.798822 −0.0348967
\(525\) −19.2130 −0.838524
\(526\) −29.9754 −1.30699
\(527\) −14.3123 −0.623453
\(528\) 1.00000 0.0435194
\(529\) −22.8860 −0.995045
\(530\) 12.6272 0.548491
\(531\) −2.99101 −0.129799
\(532\) −35.3564 −1.53289
\(533\) −4.24100 −0.183698
\(534\) 8.31023 0.359619
\(535\) −26.1358 −1.12995
\(536\) −1.16994 −0.0505335
\(537\) −5.64476 −0.243589
\(538\) −13.1706 −0.567826
\(539\) 10.7527 0.463153
\(540\) 3.09192 0.133055
\(541\) 32.2117 1.38489 0.692444 0.721472i \(-0.256534\pi\)
0.692444 + 0.721472i \(0.256534\pi\)
\(542\) −7.45328 −0.320146
\(543\) −4.40261 −0.188934
\(544\) −3.01037 −0.129068
\(545\) −7.53305 −0.322681
\(546\) 2.18454 0.0934896
\(547\) −17.2349 −0.736910 −0.368455 0.929646i \(-0.620113\pi\)
−0.368455 + 0.929646i \(0.620113\pi\)
\(548\) −2.23605 −0.0955191
\(549\) −1.00000 −0.0426790
\(550\) 4.55998 0.194438
\(551\) 46.8219 1.99468
\(552\) −0.337593 −0.0143689
\(553\) 64.8785 2.75891
\(554\) 18.2143 0.773850
\(555\) 2.68182 0.113837
\(556\) −14.7025 −0.623526
\(557\) −19.3746 −0.820927 −0.410463 0.911877i \(-0.634633\pi\)
−0.410463 + 0.911877i \(0.634633\pi\)
\(558\) 4.75433 0.201267
\(559\) 4.67395 0.197687
\(560\) −13.0275 −0.550512
\(561\) −3.01037 −0.127098
\(562\) −0.772012 −0.0325654
\(563\) −27.7582 −1.16987 −0.584933 0.811081i \(-0.698879\pi\)
−0.584933 + 0.811081i \(0.698879\pi\)
\(564\) 2.07039 0.0871793
\(565\) 47.3240 1.99093
\(566\) 18.9952 0.798428
\(567\) −4.21340 −0.176946
\(568\) 15.3353 0.643455
\(569\) −22.9603 −0.962546 −0.481273 0.876571i \(-0.659825\pi\)
−0.481273 + 0.876571i \(0.659825\pi\)
\(570\) 25.9456 1.08674
\(571\) −5.52471 −0.231202 −0.115601 0.993296i \(-0.536879\pi\)
−0.115601 + 0.993296i \(0.536879\pi\)
\(572\) −0.518474 −0.0216785
\(573\) 27.0598 1.13044
\(574\) −34.4646 −1.43852
\(575\) −1.53942 −0.0641981
\(576\) 1.00000 0.0416667
\(577\) 38.0739 1.58504 0.792519 0.609847i \(-0.208769\pi\)
0.792519 + 0.609847i \(0.208769\pi\)
\(578\) −7.93769 −0.330164
\(579\) −10.7214 −0.445566
\(580\) 17.2521 0.716354
\(581\) 34.6207 1.43631
\(582\) −4.53172 −0.187846
\(583\) 4.08394 0.169139
\(584\) 8.24649 0.341242
\(585\) −1.60308 −0.0662793
\(586\) 23.3929 0.966352
\(587\) −30.4377 −1.25630 −0.628149 0.778093i \(-0.716187\pi\)
−0.628149 + 0.778093i \(0.716187\pi\)
\(588\) 10.7527 0.443435
\(589\) 39.8956 1.64387
\(590\) −9.24798 −0.380733
\(591\) 11.7458 0.483157
\(592\) 0.867362 0.0356484
\(593\) −26.0646 −1.07034 −0.535172 0.844743i \(-0.679753\pi\)
−0.535172 + 0.844743i \(0.679753\pi\)
\(594\) 1.00000 0.0410305
\(595\) 39.2175 1.60776
\(596\) 2.72711 0.111707
\(597\) −0.770322 −0.0315272
\(598\) 0.175033 0.00715764
\(599\) 14.3108 0.584725 0.292362 0.956308i \(-0.405559\pi\)
0.292362 + 0.956308i \(0.405559\pi\)
\(600\) 4.55998 0.186160
\(601\) 12.7673 0.520790 0.260395 0.965502i \(-0.416147\pi\)
0.260395 + 0.965502i \(0.416147\pi\)
\(602\) 37.9830 1.54807
\(603\) −1.16994 −0.0476434
\(604\) −10.1402 −0.412597
\(605\) 3.09192 0.125704
\(606\) −1.63654 −0.0664798
\(607\) −19.3392 −0.784956 −0.392478 0.919761i \(-0.628382\pi\)
−0.392478 + 0.919761i \(0.628382\pi\)
\(608\) 8.39142 0.340317
\(609\) −23.5096 −0.952659
\(610\) −3.09192 −0.125188
\(611\) −1.07345 −0.0434270
\(612\) −3.01037 −0.121687
\(613\) −18.5922 −0.750931 −0.375466 0.926836i \(-0.622517\pi\)
−0.375466 + 0.926836i \(0.622517\pi\)
\(614\) −17.5170 −0.706930
\(615\) 25.2912 1.01984
\(616\) −4.21340 −0.169763
\(617\) 39.8237 1.60324 0.801621 0.597832i \(-0.203971\pi\)
0.801621 + 0.597832i \(0.203971\pi\)
\(618\) 7.63116 0.306970
\(619\) −12.4565 −0.500670 −0.250335 0.968159i \(-0.580541\pi\)
−0.250335 + 0.968159i \(0.580541\pi\)
\(620\) 14.7000 0.590367
\(621\) −0.337593 −0.0135471
\(622\) −19.9778 −0.801035
\(623\) −35.0143 −1.40282
\(624\) −0.518474 −0.0207556
\(625\) −27.0065 −1.08026
\(626\) 7.60209 0.303841
\(627\) 8.39142 0.335121
\(628\) −21.1790 −0.845135
\(629\) −2.61108 −0.104111
\(630\) −13.0275 −0.519028
\(631\) 41.6083 1.65640 0.828200 0.560433i \(-0.189365\pi\)
0.828200 + 0.560433i \(0.189365\pi\)
\(632\) −15.3981 −0.612505
\(633\) −3.55095 −0.141138
\(634\) −1.61257 −0.0640433
\(635\) 49.2013 1.95250
\(636\) 4.08394 0.161939
\(637\) −5.57501 −0.220890
\(638\) 5.57973 0.220904
\(639\) 15.3353 0.606656
\(640\) 3.09192 0.122219
\(641\) −28.3780 −1.12087 −0.560433 0.828200i \(-0.689365\pi\)
−0.560433 + 0.828200i \(0.689365\pi\)
\(642\) −8.45294 −0.333611
\(643\) 38.6590 1.52456 0.762282 0.647246i \(-0.224079\pi\)
0.762282 + 0.647246i \(0.224079\pi\)
\(644\) 1.42241 0.0560509
\(645\) −27.8731 −1.09750
\(646\) −25.2613 −0.993891
\(647\) 11.4466 0.450013 0.225006 0.974357i \(-0.427760\pi\)
0.225006 + 0.974357i \(0.427760\pi\)
\(648\) 1.00000 0.0392837
\(649\) −2.99101 −0.117408
\(650\) −2.36423 −0.0927328
\(651\) −20.0319 −0.785111
\(652\) 0.185111 0.00724951
\(653\) −1.95068 −0.0763359 −0.0381679 0.999271i \(-0.512152\pi\)
−0.0381679 + 0.999271i \(0.512152\pi\)
\(654\) −2.43637 −0.0952695
\(655\) −2.46990 −0.0965068
\(656\) 8.17976 0.319366
\(657\) 8.24649 0.321726
\(658\) −8.72339 −0.340073
\(659\) 32.5826 1.26924 0.634620 0.772825i \(-0.281157\pi\)
0.634620 + 0.772825i \(0.281157\pi\)
\(660\) 3.09192 0.120353
\(661\) 16.5972 0.645557 0.322779 0.946475i \(-0.395383\pi\)
0.322779 + 0.946475i \(0.395383\pi\)
\(662\) −18.9630 −0.737017
\(663\) 1.56080 0.0606164
\(664\) −8.21682 −0.318875
\(665\) −109.319 −4.23922
\(666\) 0.867362 0.0336096
\(667\) −1.88368 −0.0729363
\(668\) −17.7975 −0.688606
\(669\) −25.4930 −0.985616
\(670\) −3.61735 −0.139750
\(671\) −1.00000 −0.0386046
\(672\) −4.21340 −0.162535
\(673\) 8.92671 0.344099 0.172050 0.985088i \(-0.444961\pi\)
0.172050 + 0.985088i \(0.444961\pi\)
\(674\) −15.7924 −0.608301
\(675\) 4.55998 0.175514
\(676\) −12.7312 −0.489661
\(677\) −36.3408 −1.39669 −0.698345 0.715761i \(-0.746080\pi\)
−0.698345 + 0.715761i \(0.746080\pi\)
\(678\) 15.3057 0.587811
\(679\) 19.0939 0.732758
\(680\) −9.30782 −0.356939
\(681\) 0.170623 0.00653830
\(682\) 4.75433 0.182053
\(683\) 47.8386 1.83049 0.915247 0.402894i \(-0.131996\pi\)
0.915247 + 0.402894i \(0.131996\pi\)
\(684\) 8.39142 0.320854
\(685\) −6.91368 −0.264158
\(686\) −15.8117 −0.603694
\(687\) 11.6894 0.445980
\(688\) −9.01482 −0.343687
\(689\) −2.11742 −0.0806672
\(690\) −1.04381 −0.0397372
\(691\) −14.9486 −0.568670 −0.284335 0.958725i \(-0.591773\pi\)
−0.284335 + 0.958725i \(0.591773\pi\)
\(692\) −4.92214 −0.187112
\(693\) −4.21340 −0.160054
\(694\) −18.7955 −0.713468
\(695\) −45.4591 −1.72436
\(696\) 5.57973 0.211499
\(697\) −24.6241 −0.932704
\(698\) −6.73963 −0.255099
\(699\) −3.78322 −0.143095
\(700\) −19.2130 −0.726183
\(701\) −7.00137 −0.264438 −0.132219 0.991221i \(-0.542210\pi\)
−0.132219 + 0.991221i \(0.542210\pi\)
\(702\) −0.518474 −0.0195686
\(703\) 7.27840 0.274510
\(704\) 1.00000 0.0376889
\(705\) 6.40149 0.241094
\(706\) −8.54806 −0.321710
\(707\) 6.89539 0.259328
\(708\) −2.99101 −0.112409
\(709\) −2.70293 −0.101511 −0.0507554 0.998711i \(-0.516163\pi\)
−0.0507554 + 0.998711i \(0.516163\pi\)
\(710\) 47.4156 1.77948
\(711\) −15.3981 −0.577475
\(712\) 8.31023 0.311439
\(713\) −1.60503 −0.0601087
\(714\) 12.6839 0.474682
\(715\) −1.60308 −0.0599519
\(716\) −5.64476 −0.210955
\(717\) −1.37684 −0.0514190
\(718\) 13.9622 0.521064
\(719\) −25.4169 −0.947889 −0.473944 0.880555i \(-0.657170\pi\)
−0.473944 + 0.880555i \(0.657170\pi\)
\(720\) 3.09192 0.115229
\(721\) −32.1531 −1.19744
\(722\) 51.4160 1.91350
\(723\) 5.21306 0.193876
\(724\) −4.40261 −0.163622
\(725\) 25.4435 0.944946
\(726\) 1.00000 0.0371135
\(727\) −12.0829 −0.448128 −0.224064 0.974574i \(-0.571933\pi\)
−0.224064 + 0.974574i \(0.571933\pi\)
\(728\) 2.18454 0.0809644
\(729\) 1.00000 0.0370370
\(730\) 25.4975 0.943705
\(731\) 27.1379 1.00373
\(732\) −1.00000 −0.0369611
\(733\) 48.9537 1.80815 0.904074 0.427376i \(-0.140562\pi\)
0.904074 + 0.427376i \(0.140562\pi\)
\(734\) 20.4701 0.755564
\(735\) 33.2466 1.22632
\(736\) −0.337593 −0.0124438
\(737\) −1.16994 −0.0430951
\(738\) 8.17976 0.301101
\(739\) −21.3134 −0.784028 −0.392014 0.919959i \(-0.628222\pi\)
−0.392014 + 0.919959i \(0.628222\pi\)
\(740\) 2.68182 0.0985855
\(741\) −4.35074 −0.159828
\(742\) −17.2073 −0.631698
\(743\) −22.9101 −0.840490 −0.420245 0.907411i \(-0.638056\pi\)
−0.420245 + 0.907411i \(0.638056\pi\)
\(744\) 4.75433 0.174302
\(745\) 8.43200 0.308925
\(746\) −12.4446 −0.455628
\(747\) −8.21682 −0.300638
\(748\) −3.01037 −0.110070
\(749\) 35.6156 1.30137
\(750\) −1.36051 −0.0496789
\(751\) −15.5280 −0.566624 −0.283312 0.959028i \(-0.591433\pi\)
−0.283312 + 0.959028i \(0.591433\pi\)
\(752\) 2.07039 0.0754995
\(753\) 8.63092 0.314528
\(754\) −2.89295 −0.105355
\(755\) −31.3526 −1.14104
\(756\) −4.21340 −0.153240
\(757\) −27.9683 −1.01652 −0.508262 0.861202i \(-0.669712\pi\)
−0.508262 + 0.861202i \(0.669712\pi\)
\(758\) −16.3449 −0.593672
\(759\) −0.337593 −0.0122538
\(760\) 25.9456 0.941147
\(761\) 7.42468 0.269144 0.134572 0.990904i \(-0.457034\pi\)
0.134572 + 0.990904i \(0.457034\pi\)
\(762\) 15.9129 0.576462
\(763\) 10.2654 0.371632
\(764\) 27.0598 0.978988
\(765\) −9.30782 −0.336525
\(766\) 5.46817 0.197573
\(767\) 1.55076 0.0559948
\(768\) 1.00000 0.0360844
\(769\) −3.42766 −0.123605 −0.0618023 0.998088i \(-0.519685\pi\)
−0.0618023 + 0.998088i \(0.519685\pi\)
\(770\) −13.0275 −0.469478
\(771\) −28.3616 −1.02142
\(772\) −10.7214 −0.385871
\(773\) 43.7871 1.57491 0.787456 0.616371i \(-0.211398\pi\)
0.787456 + 0.616371i \(0.211398\pi\)
\(774\) −9.01482 −0.324031
\(775\) 21.6796 0.778755
\(776\) −4.53172 −0.162679
\(777\) −3.65454 −0.131106
\(778\) 11.8690 0.425523
\(779\) 68.6398 2.45928
\(780\) −1.60308 −0.0573995
\(781\) 15.3353 0.548741
\(782\) 1.01628 0.0363420
\(783\) 5.57973 0.199403
\(784\) 10.7527 0.384026
\(785\) −65.4839 −2.33722
\(786\) −0.798822 −0.0284931
\(787\) −32.0797 −1.14352 −0.571759 0.820422i \(-0.693739\pi\)
−0.571759 + 0.820422i \(0.693739\pi\)
\(788\) 11.7458 0.418426
\(789\) −29.9754 −1.06715
\(790\) −47.6098 −1.69388
\(791\) −64.4889 −2.29296
\(792\) 1.00000 0.0355335
\(793\) 0.518474 0.0184116
\(794\) −6.85274 −0.243195
\(795\) 12.6272 0.447841
\(796\) −0.770322 −0.0273034
\(797\) −13.5820 −0.481098 −0.240549 0.970637i \(-0.577327\pi\)
−0.240549 + 0.970637i \(0.577327\pi\)
\(798\) −35.3564 −1.25160
\(799\) −6.23264 −0.220495
\(800\) 4.55998 0.161220
\(801\) 8.31023 0.293627
\(802\) −32.3814 −1.14343
\(803\) 8.24649 0.291012
\(804\) −1.16994 −0.0412604
\(805\) 4.39799 0.155009
\(806\) −2.46500 −0.0868258
\(807\) −13.1706 −0.463628
\(808\) −1.63654 −0.0575732
\(809\) −6.04913 −0.212676 −0.106338 0.994330i \(-0.533913\pi\)
−0.106338 + 0.994330i \(0.533913\pi\)
\(810\) 3.09192 0.108639
\(811\) −33.4456 −1.17444 −0.587218 0.809429i \(-0.699777\pi\)
−0.587218 + 0.809429i \(0.699777\pi\)
\(812\) −23.5096 −0.825027
\(813\) −7.45328 −0.261398
\(814\) 0.867362 0.0304010
\(815\) 0.572349 0.0200485
\(816\) −3.01037 −0.105384
\(817\) −75.6472 −2.64656
\(818\) 1.99757 0.0698432
\(819\) 2.18454 0.0763340
\(820\) 25.2912 0.883206
\(821\) −55.1716 −1.92550 −0.962750 0.270392i \(-0.912847\pi\)
−0.962750 + 0.270392i \(0.912847\pi\)
\(822\) −2.23605 −0.0779910
\(823\) −26.8584 −0.936225 −0.468113 0.883669i \(-0.655066\pi\)
−0.468113 + 0.883669i \(0.655066\pi\)
\(824\) 7.63116 0.265844
\(825\) 4.55998 0.158758
\(826\) 12.6023 0.438491
\(827\) 22.2204 0.772678 0.386339 0.922357i \(-0.373740\pi\)
0.386339 + 0.922357i \(0.373740\pi\)
\(828\) −0.337593 −0.0117322
\(829\) 49.8459 1.73122 0.865610 0.500719i \(-0.166931\pi\)
0.865610 + 0.500719i \(0.166931\pi\)
\(830\) −25.4058 −0.881847
\(831\) 18.2143 0.631846
\(832\) −0.518474 −0.0179749
\(833\) −32.3696 −1.12154
\(834\) −14.7025 −0.509107
\(835\) −55.0285 −1.90434
\(836\) 8.39142 0.290223
\(837\) 4.75433 0.164334
\(838\) −33.6785 −1.16340
\(839\) −47.6798 −1.64609 −0.823045 0.567977i \(-0.807726\pi\)
−0.823045 + 0.567977i \(0.807726\pi\)
\(840\) −13.0275 −0.449491
\(841\) 2.13343 0.0735665
\(842\) 24.8542 0.856533
\(843\) −0.772012 −0.0265895
\(844\) −3.55095 −0.122229
\(845\) −39.3638 −1.35416
\(846\) 2.07039 0.0711816
\(847\) −4.21340 −0.144774
\(848\) 4.08394 0.140243
\(849\) 18.9952 0.651913
\(850\) −13.7272 −0.470839
\(851\) −0.292815 −0.0100376
\(852\) 15.3353 0.525379
\(853\) −49.5406 −1.69624 −0.848118 0.529807i \(-0.822264\pi\)
−0.848118 + 0.529807i \(0.822264\pi\)
\(854\) 4.21340 0.144180
\(855\) 25.9456 0.887321
\(856\) −8.45294 −0.288916
\(857\) −52.9842 −1.80991 −0.904953 0.425511i \(-0.860094\pi\)
−0.904953 + 0.425511i \(0.860094\pi\)
\(858\) −0.518474 −0.0177004
\(859\) −21.6621 −0.739102 −0.369551 0.929211i \(-0.620488\pi\)
−0.369551 + 0.929211i \(0.620488\pi\)
\(860\) −27.8731 −0.950465
\(861\) −34.4646 −1.17455
\(862\) 23.2622 0.792313
\(863\) 9.97990 0.339720 0.169860 0.985468i \(-0.445669\pi\)
0.169860 + 0.985468i \(0.445669\pi\)
\(864\) 1.00000 0.0340207
\(865\) −15.2189 −0.517457
\(866\) 37.3989 1.27087
\(867\) −7.93769 −0.269578
\(868\) −20.0319 −0.679926
\(869\) −15.3981 −0.522346
\(870\) 17.2521 0.584901
\(871\) 0.606581 0.0205532
\(872\) −2.43637 −0.0825058
\(873\) −4.53172 −0.153375
\(874\) −2.83288 −0.0958237
\(875\) 5.73239 0.193790
\(876\) 8.24649 0.278623
\(877\) −36.9177 −1.24662 −0.623311 0.781974i \(-0.714213\pi\)
−0.623311 + 0.781974i \(0.714213\pi\)
\(878\) −10.1292 −0.341843
\(879\) 23.3929 0.789023
\(880\) 3.09192 0.104229
\(881\) −15.2974 −0.515382 −0.257691 0.966227i \(-0.582962\pi\)
−0.257691 + 0.966227i \(0.582962\pi\)
\(882\) 10.7527 0.362063
\(883\) −27.4386 −0.923383 −0.461691 0.887041i \(-0.652757\pi\)
−0.461691 + 0.887041i \(0.652757\pi\)
\(884\) 1.56080 0.0524953
\(885\) −9.24798 −0.310867
\(886\) −24.2824 −0.815782
\(887\) −41.9719 −1.40928 −0.704640 0.709565i \(-0.748891\pi\)
−0.704640 + 0.709565i \(0.748891\pi\)
\(888\) 0.867362 0.0291068
\(889\) −67.0473 −2.24869
\(890\) 25.6946 0.861284
\(891\) 1.00000 0.0335013
\(892\) −25.4930 −0.853569
\(893\) 17.3735 0.581383
\(894\) 2.72711 0.0912081
\(895\) −17.4531 −0.583394
\(896\) −4.21340 −0.140760
\(897\) 0.175033 0.00584419
\(898\) 30.9258 1.03201
\(899\) 26.5279 0.884755
\(900\) 4.55998 0.151999
\(901\) −12.2942 −0.409578
\(902\) 8.17976 0.272356
\(903\) 37.9830 1.26400
\(904\) 15.3057 0.509059
\(905\) −13.6125 −0.452495
\(906\) −10.1402 −0.336884
\(907\) −44.2849 −1.47045 −0.735227 0.677821i \(-0.762925\pi\)
−0.735227 + 0.677821i \(0.762925\pi\)
\(908\) 0.170623 0.00566233
\(909\) −1.63654 −0.0542806
\(910\) 6.75442 0.223907
\(911\) 30.5798 1.01315 0.506576 0.862195i \(-0.330911\pi\)
0.506576 + 0.862195i \(0.330911\pi\)
\(912\) 8.39142 0.277868
\(913\) −8.21682 −0.271937
\(914\) 22.6296 0.748520
\(915\) −3.09192 −0.102216
\(916\) 11.6894 0.386230
\(917\) 3.36576 0.111147
\(918\) −3.01037 −0.0993569
\(919\) −8.45262 −0.278826 −0.139413 0.990234i \(-0.544522\pi\)
−0.139413 + 0.990234i \(0.544522\pi\)
\(920\) −1.04381 −0.0344134
\(921\) −17.5170 −0.577206
\(922\) 21.0195 0.692240
\(923\) −7.95097 −0.261709
\(924\) −4.21340 −0.138611
\(925\) 3.95515 0.130045
\(926\) −8.76779 −0.288127
\(927\) 7.63116 0.250640
\(928\) 5.57973 0.183164
\(929\) −44.0589 −1.44553 −0.722763 0.691096i \(-0.757128\pi\)
−0.722763 + 0.691096i \(0.757128\pi\)
\(930\) 14.7000 0.482032
\(931\) 90.2306 2.95719
\(932\) −3.78322 −0.123924
\(933\) −19.9778 −0.654043
\(934\) −16.6077 −0.543421
\(935\) −9.30782 −0.304398
\(936\) −0.518474 −0.0169469
\(937\) 14.8733 0.485888 0.242944 0.970040i \(-0.421887\pi\)
0.242944 + 0.970040i \(0.421887\pi\)
\(938\) 4.92940 0.160951
\(939\) 7.60209 0.248085
\(940\) 6.40149 0.208794
\(941\) 10.2978 0.335700 0.167850 0.985813i \(-0.446318\pi\)
0.167850 + 0.985813i \(0.446318\pi\)
\(942\) −21.1790 −0.690050
\(943\) −2.76143 −0.0899245
\(944\) −2.99101 −0.0973492
\(945\) −13.0275 −0.423784
\(946\) −9.01482 −0.293097
\(947\) −1.47097 −0.0478001 −0.0239000 0.999714i \(-0.507608\pi\)
−0.0239000 + 0.999714i \(0.507608\pi\)
\(948\) −15.3981 −0.500108
\(949\) −4.27560 −0.138792
\(950\) 38.2647 1.24147
\(951\) −1.61257 −0.0522912
\(952\) 12.6839 0.411087
\(953\) −33.7619 −1.09366 −0.546828 0.837245i \(-0.684165\pi\)
−0.546828 + 0.837245i \(0.684165\pi\)
\(954\) 4.08394 0.132222
\(955\) 83.6666 2.70739
\(956\) −1.37684 −0.0445302
\(957\) 5.57973 0.180367
\(958\) 8.73112 0.282090
\(959\) 9.42135 0.304231
\(960\) 3.09192 0.0997913
\(961\) −8.39636 −0.270850
\(962\) −0.449705 −0.0144991
\(963\) −8.45294 −0.272392
\(964\) 5.21306 0.167901
\(965\) −33.1497 −1.06713
\(966\) 1.42241 0.0457654
\(967\) 46.1024 1.48255 0.741276 0.671200i \(-0.234221\pi\)
0.741276 + 0.671200i \(0.234221\pi\)
\(968\) 1.00000 0.0321412
\(969\) −25.2613 −0.811509
\(970\) −14.0117 −0.449889
\(971\) −45.4790 −1.45949 −0.729745 0.683719i \(-0.760361\pi\)
−0.729745 + 0.683719i \(0.760361\pi\)
\(972\) 1.00000 0.0320750
\(973\) 61.9476 1.98595
\(974\) 20.8409 0.667786
\(975\) −2.36423 −0.0757160
\(976\) −1.00000 −0.0320092
\(977\) 36.5909 1.17065 0.585324 0.810800i \(-0.300968\pi\)
0.585324 + 0.810800i \(0.300968\pi\)
\(978\) 0.185111 0.00591920
\(979\) 8.31023 0.265596
\(980\) 33.2466 1.06202
\(981\) −2.43637 −0.0777872
\(982\) −12.7316 −0.406280
\(983\) 14.1244 0.450498 0.225249 0.974301i \(-0.427681\pi\)
0.225249 + 0.974301i \(0.427681\pi\)
\(984\) 8.17976 0.260761
\(985\) 36.3170 1.15716
\(986\) −16.7970 −0.534927
\(987\) −8.72339 −0.277669
\(988\) −4.35074 −0.138415
\(989\) 3.04334 0.0967725
\(990\) 3.09192 0.0982677
\(991\) −47.5467 −1.51037 −0.755185 0.655512i \(-0.772453\pi\)
−0.755185 + 0.655512i \(0.772453\pi\)
\(992\) 4.75433 0.150950
\(993\) −18.9630 −0.601771
\(994\) −64.6138 −2.04942
\(995\) −2.38178 −0.0755074
\(996\) −8.21682 −0.260360
\(997\) −13.1638 −0.416900 −0.208450 0.978033i \(-0.566842\pi\)
−0.208450 + 0.978033i \(0.566842\pi\)
\(998\) −14.9212 −0.472322
\(999\) 0.867362 0.0274421
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 \(a_p\))