Properties

Label 4026.2.a.bc.1.3
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 1.3
Root \(1.60053\)
Character \(\chi\) = 4026.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-0.600528 q^{5}\) \(+1.00000 q^{6}\) \(+0.748033 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{3}\) \(+1.00000 q^{4}\) \(-0.600528 q^{5}\) \(+1.00000 q^{6}\) \(+0.748033 q^{7}\) \(+1.00000 q^{8}\) \(+1.00000 q^{9}\) \(-0.600528 q^{10}\) \(+1.00000 q^{11}\) \(+1.00000 q^{12}\) \(-3.37388 q^{13}\) \(+0.748033 q^{14}\) \(-0.600528 q^{15}\) \(+1.00000 q^{16}\) \(+1.61669 q^{17}\) \(+1.00000 q^{18}\) \(+1.26064 q^{19}\) \(-0.600528 q^{20}\) \(+0.748033 q^{21}\) \(+1.00000 q^{22}\) \(+5.33798 q^{23}\) \(+1.00000 q^{24}\) \(-4.63937 q^{25}\) \(-3.37388 q^{26}\) \(+1.00000 q^{27}\) \(+0.748033 q^{28}\) \(+3.93905 q^{29}\) \(-0.600528 q^{30}\) \(+6.73745 q^{31}\) \(+1.00000 q^{32}\) \(+1.00000 q^{33}\) \(+1.61669 q^{34}\) \(-0.449215 q^{35}\) \(+1.00000 q^{36}\) \(+0.919689 q^{37}\) \(+1.26064 q^{38}\) \(-3.37388 q^{39}\) \(-0.600528 q^{40}\) \(+10.3291 q^{41}\) \(+0.748033 q^{42}\) \(+0.371237 q^{43}\) \(+1.00000 q^{44}\) \(-0.600528 q^{45}\) \(+5.33798 q^{46}\) \(+1.78835 q^{47}\) \(+1.00000 q^{48}\) \(-6.44045 q^{49}\) \(-4.63937 q^{50}\) \(+1.61669 q^{51}\) \(-3.37388 q^{52}\) \(-8.73693 q^{53}\) \(+1.00000 q^{54}\) \(-0.600528 q^{55}\) \(+0.748033 q^{56}\) \(+1.26064 q^{57}\) \(+3.93905 q^{58}\) \(-1.55335 q^{59}\) \(-0.600528 q^{60}\) \(-1.00000 q^{61}\) \(+6.73745 q^{62}\) \(+0.748033 q^{63}\) \(+1.00000 q^{64}\) \(+2.02611 q^{65}\) \(+1.00000 q^{66}\) \(+6.96334 q^{67}\) \(+1.61669 q^{68}\) \(+5.33798 q^{69}\) \(-0.449215 q^{70}\) \(+7.20179 q^{71}\) \(+1.00000 q^{72}\) \(+11.0840 q^{73}\) \(+0.919689 q^{74}\) \(-4.63937 q^{75}\) \(+1.26064 q^{76}\) \(+0.748033 q^{77}\) \(-3.37388 q^{78}\) \(+15.8076 q^{79}\) \(-0.600528 q^{80}\) \(+1.00000 q^{81}\) \(+10.3291 q^{82}\) \(+5.44158 q^{83}\) \(+0.748033 q^{84}\) \(-0.970868 q^{85}\) \(+0.371237 q^{86}\) \(+3.93905 q^{87}\) \(+1.00000 q^{88}\) \(+10.6282 q^{89}\) \(-0.600528 q^{90}\) \(-2.52377 q^{91}\) \(+5.33798 q^{92}\) \(+6.73745 q^{93}\) \(+1.78835 q^{94}\) \(-0.757048 q^{95}\) \(+1.00000 q^{96}\) \(-17.4847 q^{97}\) \(-6.44045 q^{98}\) \(+1.00000 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut +\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 9q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 9q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut +\mathstrut 9q^{12} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 9q^{14} \) \(\mathstrut +\mathstrut 8q^{15} \) \(\mathstrut +\mathstrut 9q^{16} \) \(\mathstrut +\mathstrut q^{17} \) \(\mathstrut +\mathstrut 9q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 8q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut -\mathstrut q^{23} \) \(\mathstrut +\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 23q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut +\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 8q^{30} \) \(\mathstrut +\mathstrut 25q^{31} \) \(\mathstrut +\mathstrut 9q^{32} \) \(\mathstrut +\mathstrut 9q^{33} \) \(\mathstrut +\mathstrut q^{34} \) \(\mathstrut +\mathstrut 5q^{35} \) \(\mathstrut +\mathstrut 9q^{36} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut +\mathstrut 5q^{38} \) \(\mathstrut +\mathstrut 8q^{39} \) \(\mathstrut +\mathstrut 8q^{40} \) \(\mathstrut +\mathstrut 5q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 5q^{43} \) \(\mathstrut +\mathstrut 9q^{44} \) \(\mathstrut +\mathstrut 8q^{45} \) \(\mathstrut -\mathstrut q^{46} \) \(\mathstrut +\mathstrut 8q^{47} \) \(\mathstrut +\mathstrut 9q^{48} \) \(\mathstrut +\mathstrut 30q^{49} \) \(\mathstrut +\mathstrut 23q^{50} \) \(\mathstrut +\mathstrut q^{51} \) \(\mathstrut +\mathstrut 8q^{52} \) \(\mathstrut +\mathstrut q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut +\mathstrut 8q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut 8q^{60} \) \(\mathstrut -\mathstrut 9q^{61} \) \(\mathstrut +\mathstrut 25q^{62} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut q^{68} \) \(\mathstrut -\mathstrut q^{69} \) \(\mathstrut +\mathstrut 5q^{70} \) \(\mathstrut +\mathstrut 20q^{71} \) \(\mathstrut +\mathstrut 9q^{72} \) \(\mathstrut +\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 5q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 8q^{80} \) \(\mathstrut +\mathstrut 9q^{81} \) \(\mathstrut +\mathstrut 5q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut +\mathstrut 5q^{86} \) \(\mathstrut -\mathstrut 14q^{87} \) \(\mathstrut +\mathstrut 9q^{88} \) \(\mathstrut +\mathstrut 10q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 19q^{91} \) \(\mathstrut -\mathstrut q^{92} \) \(\mathstrut +\mathstrut 25q^{93} \) \(\mathstrut +\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 7q^{95} \) \(\mathstrut +\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut +\mathstrut 30q^{98} \) \(\mathstrut +\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) −0.600528 −0.268564 −0.134282 0.990943i \(-0.542873\pi\)
−0.134282 + 0.990943i \(0.542873\pi\)
\(6\) 1.00000 0.408248
\(7\) 0.748033 0.282730 0.141365 0.989958i \(-0.454851\pi\)
0.141365 + 0.989958i \(0.454851\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −0.600528 −0.189904
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −3.37388 −0.935745 −0.467873 0.883796i \(-0.654979\pi\)
−0.467873 + 0.883796i \(0.654979\pi\)
\(14\) 0.748033 0.199920
\(15\) −0.600528 −0.155056
\(16\) 1.00000 0.250000
\(17\) 1.61669 0.392105 0.196053 0.980593i \(-0.437188\pi\)
0.196053 + 0.980593i \(0.437188\pi\)
\(18\) 1.00000 0.235702
\(19\) 1.26064 0.289210 0.144605 0.989489i \(-0.453809\pi\)
0.144605 + 0.989489i \(0.453809\pi\)
\(20\) −0.600528 −0.134282
\(21\) 0.748033 0.163234
\(22\) 1.00000 0.213201
\(23\) 5.33798 1.11305 0.556523 0.830832i \(-0.312135\pi\)
0.556523 + 0.830832i \(0.312135\pi\)
\(24\) 1.00000 0.204124
\(25\) −4.63937 −0.927873
\(26\) −3.37388 −0.661672
\(27\) 1.00000 0.192450
\(28\) 0.748033 0.141365
\(29\) 3.93905 0.731463 0.365731 0.930720i \(-0.380819\pi\)
0.365731 + 0.930720i \(0.380819\pi\)
\(30\) −0.600528 −0.109641
\(31\) 6.73745 1.21008 0.605041 0.796194i \(-0.293157\pi\)
0.605041 + 0.796194i \(0.293157\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) 1.61669 0.277260
\(35\) −0.449215 −0.0759312
\(36\) 1.00000 0.166667
\(37\) 0.919689 0.151196 0.0755979 0.997138i \(-0.475913\pi\)
0.0755979 + 0.997138i \(0.475913\pi\)
\(38\) 1.26064 0.204502
\(39\) −3.37388 −0.540253
\(40\) −0.600528 −0.0949518
\(41\) 10.3291 1.61313 0.806566 0.591144i \(-0.201323\pi\)
0.806566 + 0.591144i \(0.201323\pi\)
\(42\) 0.748033 0.115424
\(43\) 0.371237 0.0566132 0.0283066 0.999599i \(-0.490989\pi\)
0.0283066 + 0.999599i \(0.490989\pi\)
\(44\) 1.00000 0.150756
\(45\) −0.600528 −0.0895214
\(46\) 5.33798 0.787042
\(47\) 1.78835 0.260857 0.130429 0.991458i \(-0.458365\pi\)
0.130429 + 0.991458i \(0.458365\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.44045 −0.920064
\(50\) −4.63937 −0.656105
\(51\) 1.61669 0.226382
\(52\) −3.37388 −0.467873
\(53\) −8.73693 −1.20011 −0.600055 0.799959i \(-0.704855\pi\)
−0.600055 + 0.799959i \(0.704855\pi\)
\(54\) 1.00000 0.136083
\(55\) −0.600528 −0.0809751
\(56\) 0.748033 0.0999602
\(57\) 1.26064 0.166976
\(58\) 3.93905 0.517222
\(59\) −1.55335 −0.202229 −0.101115 0.994875i \(-0.532241\pi\)
−0.101115 + 0.994875i \(0.532241\pi\)
\(60\) −0.600528 −0.0775278
\(61\) −1.00000 −0.128037
\(62\) 6.73745 0.855657
\(63\) 0.748033 0.0942433
\(64\) 1.00000 0.125000
\(65\) 2.02611 0.251308
\(66\) 1.00000 0.123091
\(67\) 6.96334 0.850708 0.425354 0.905027i \(-0.360150\pi\)
0.425354 + 0.905027i \(0.360150\pi\)
\(68\) 1.61669 0.196053
\(69\) 5.33798 0.642617
\(70\) −0.449215 −0.0536914
\(71\) 7.20179 0.854695 0.427348 0.904087i \(-0.359448\pi\)
0.427348 + 0.904087i \(0.359448\pi\)
\(72\) 1.00000 0.117851
\(73\) 11.0840 1.29728 0.648640 0.761095i \(-0.275338\pi\)
0.648640 + 0.761095i \(0.275338\pi\)
\(74\) 0.919689 0.106912
\(75\) −4.63937 −0.535708
\(76\) 1.26064 0.144605
\(77\) 0.748033 0.0852463
\(78\) −3.37388 −0.382016
\(79\) 15.8076 1.77849 0.889245 0.457432i \(-0.151231\pi\)
0.889245 + 0.457432i \(0.151231\pi\)
\(80\) −0.600528 −0.0671410
\(81\) 1.00000 0.111111
\(82\) 10.3291 1.14066
\(83\) 5.44158 0.597291 0.298645 0.954364i \(-0.403465\pi\)
0.298645 + 0.954364i \(0.403465\pi\)
\(84\) 0.748033 0.0816171
\(85\) −0.970868 −0.105305
\(86\) 0.371237 0.0400316
\(87\) 3.93905 0.422310
\(88\) 1.00000 0.106600
\(89\) 10.6282 1.12659 0.563295 0.826256i \(-0.309533\pi\)
0.563295 + 0.826256i \(0.309533\pi\)
\(90\) −0.600528 −0.0633012
\(91\) −2.52377 −0.264563
\(92\) 5.33798 0.556523
\(93\) 6.73745 0.698641
\(94\) 1.78835 0.184454
\(95\) −0.757048 −0.0776715
\(96\) 1.00000 0.102062
\(97\) −17.4847 −1.77531 −0.887653 0.460513i \(-0.847665\pi\)
−0.887653 + 0.460513i \(0.847665\pi\)
\(98\) −6.44045 −0.650583
\(99\) 1.00000 0.100504
\(100\) −4.63937 −0.463937
\(101\) −13.0405 −1.29758 −0.648788 0.760970i \(-0.724724\pi\)
−0.648788 + 0.760970i \(0.724724\pi\)
\(102\) 1.61669 0.160076
\(103\) 6.66201 0.656427 0.328214 0.944604i \(-0.393553\pi\)
0.328214 + 0.944604i \(0.393553\pi\)
\(104\) −3.37388 −0.330836
\(105\) −0.449215 −0.0438389
\(106\) −8.73693 −0.848606
\(107\) −10.7711 −1.04128 −0.520638 0.853777i \(-0.674306\pi\)
−0.520638 + 0.853777i \(0.674306\pi\)
\(108\) 1.00000 0.0962250
\(109\) 7.81214 0.748267 0.374134 0.927375i \(-0.377940\pi\)
0.374134 + 0.927375i \(0.377940\pi\)
\(110\) −0.600528 −0.0572581
\(111\) 0.919689 0.0872930
\(112\) 0.748033 0.0706825
\(113\) −15.6519 −1.47241 −0.736205 0.676758i \(-0.763384\pi\)
−0.736205 + 0.676758i \(0.763384\pi\)
\(114\) 1.26064 0.118070
\(115\) −3.20561 −0.298924
\(116\) 3.93905 0.365731
\(117\) −3.37388 −0.311915
\(118\) −1.55335 −0.142998
\(119\) 1.20934 0.110860
\(120\) −0.600528 −0.0548204
\(121\) 1.00000 0.0909091
\(122\) −1.00000 −0.0905357
\(123\) 10.3291 0.931343
\(124\) 6.73745 0.605041
\(125\) 5.78871 0.517758
\(126\) 0.748033 0.0666401
\(127\) −16.1823 −1.43595 −0.717975 0.696069i \(-0.754931\pi\)
−0.717975 + 0.696069i \(0.754931\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0.371237 0.0326856
\(130\) 2.02611 0.177701
\(131\) −19.5243 −1.70584 −0.852922 0.522038i \(-0.825172\pi\)
−0.852922 + 0.522038i \(0.825172\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0.942999 0.0817684
\(134\) 6.96334 0.601541
\(135\) −0.600528 −0.0516852
\(136\) 1.61669 0.138630
\(137\) 19.6596 1.67963 0.839815 0.542872i \(-0.182663\pi\)
0.839815 + 0.542872i \(0.182663\pi\)
\(138\) 5.33798 0.454399
\(139\) 14.9071 1.26440 0.632201 0.774804i \(-0.282152\pi\)
0.632201 + 0.774804i \(0.282152\pi\)
\(140\) −0.449215 −0.0379656
\(141\) 1.78835 0.150606
\(142\) 7.20179 0.604361
\(143\) −3.37388 −0.282138
\(144\) 1.00000 0.0833333
\(145\) −2.36551 −0.196445
\(146\) 11.0840 0.917316
\(147\) −6.44045 −0.531199
\(148\) 0.919689 0.0755979
\(149\) −7.06181 −0.578526 −0.289263 0.957250i \(-0.593410\pi\)
−0.289263 + 0.957250i \(0.593410\pi\)
\(150\) −4.63937 −0.378803
\(151\) 0.654495 0.0532620 0.0266310 0.999645i \(-0.491522\pi\)
0.0266310 + 0.999645i \(0.491522\pi\)
\(152\) 1.26064 0.102251
\(153\) 1.61669 0.130702
\(154\) 0.748033 0.0602782
\(155\) −4.04603 −0.324985
\(156\) −3.37388 −0.270126
\(157\) 10.3719 0.827764 0.413882 0.910330i \(-0.364173\pi\)
0.413882 + 0.910330i \(0.364173\pi\)
\(158\) 15.8076 1.25758
\(159\) −8.73693 −0.692884
\(160\) −0.600528 −0.0474759
\(161\) 3.99299 0.314692
\(162\) 1.00000 0.0785674
\(163\) 10.3180 0.808170 0.404085 0.914721i \(-0.367590\pi\)
0.404085 + 0.914721i \(0.367590\pi\)
\(164\) 10.3291 0.806566
\(165\) −0.600528 −0.0467510
\(166\) 5.44158 0.422348
\(167\) 3.01833 0.233566 0.116783 0.993157i \(-0.462742\pi\)
0.116783 + 0.993157i \(0.462742\pi\)
\(168\) 0.748033 0.0577120
\(169\) −1.61695 −0.124381
\(170\) −0.970868 −0.0744622
\(171\) 1.26064 0.0964034
\(172\) 0.371237 0.0283066
\(173\) −19.7437 −1.50109 −0.750544 0.660820i \(-0.770209\pi\)
−0.750544 + 0.660820i \(0.770209\pi\)
\(174\) 3.93905 0.298618
\(175\) −3.47040 −0.262338
\(176\) 1.00000 0.0753778
\(177\) −1.55335 −0.116757
\(178\) 10.6282 0.796620
\(179\) 10.9225 0.816385 0.408192 0.912896i \(-0.366159\pi\)
0.408192 + 0.912896i \(0.366159\pi\)
\(180\) −0.600528 −0.0447607
\(181\) −1.75742 −0.130628 −0.0653140 0.997865i \(-0.520805\pi\)
−0.0653140 + 0.997865i \(0.520805\pi\)
\(182\) −2.52377 −0.187074
\(183\) −1.00000 −0.0739221
\(184\) 5.33798 0.393521
\(185\) −0.552299 −0.0406058
\(186\) 6.73745 0.494014
\(187\) 1.61669 0.118224
\(188\) 1.78835 0.130429
\(189\) 0.748033 0.0544114
\(190\) −0.757048 −0.0549220
\(191\) −12.8261 −0.928061 −0.464030 0.885819i \(-0.653597\pi\)
−0.464030 + 0.885819i \(0.653597\pi\)
\(192\) 1.00000 0.0721688
\(193\) −2.07382 −0.149277 −0.0746384 0.997211i \(-0.523780\pi\)
−0.0746384 + 0.997211i \(0.523780\pi\)
\(194\) −17.4847 −1.25533
\(195\) 2.02611 0.145093
\(196\) −6.44045 −0.460032
\(197\) −22.2990 −1.58874 −0.794369 0.607435i \(-0.792198\pi\)
−0.794369 + 0.607435i \(0.792198\pi\)
\(198\) 1.00000 0.0710669
\(199\) 5.97125 0.423291 0.211645 0.977347i \(-0.432118\pi\)
0.211645 + 0.977347i \(0.432118\pi\)
\(200\) −4.63937 −0.328053
\(201\) 6.96334 0.491156
\(202\) −13.0405 −0.917524
\(203\) 2.94654 0.206806
\(204\) 1.61669 0.113191
\(205\) −6.20291 −0.433230
\(206\) 6.66201 0.464164
\(207\) 5.33798 0.371015
\(208\) −3.37388 −0.233936
\(209\) 1.26064 0.0872002
\(210\) −0.449215 −0.0309988
\(211\) −1.30617 −0.0899206 −0.0449603 0.998989i \(-0.514316\pi\)
−0.0449603 + 0.998989i \(0.514316\pi\)
\(212\) −8.73693 −0.600055
\(213\) 7.20179 0.493458
\(214\) −10.7711 −0.736294
\(215\) −0.222938 −0.0152043
\(216\) 1.00000 0.0680414
\(217\) 5.03984 0.342127
\(218\) 7.81214 0.529105
\(219\) 11.0840 0.748985
\(220\) −0.600528 −0.0404876
\(221\) −5.45452 −0.366911
\(222\) 0.919689 0.0617255
\(223\) 22.5370 1.50919 0.754594 0.656192i \(-0.227834\pi\)
0.754594 + 0.656192i \(0.227834\pi\)
\(224\) 0.748033 0.0499801
\(225\) −4.63937 −0.309291
\(226\) −15.6519 −1.04115
\(227\) −14.0429 −0.932063 −0.466032 0.884768i \(-0.654317\pi\)
−0.466032 + 0.884768i \(0.654317\pi\)
\(228\) 1.26064 0.0834878
\(229\) −4.21543 −0.278563 −0.139282 0.990253i \(-0.544479\pi\)
−0.139282 + 0.990253i \(0.544479\pi\)
\(230\) −3.20561 −0.211371
\(231\) 0.748033 0.0492170
\(232\) 3.93905 0.258611
\(233\) −0.537423 −0.0352077 −0.0176039 0.999845i \(-0.505604\pi\)
−0.0176039 + 0.999845i \(0.505604\pi\)
\(234\) −3.37388 −0.220557
\(235\) −1.07395 −0.0700569
\(236\) −1.55335 −0.101115
\(237\) 15.8076 1.02681
\(238\) 1.20934 0.0783898
\(239\) 12.3260 0.797302 0.398651 0.917103i \(-0.369478\pi\)
0.398651 + 0.917103i \(0.369478\pi\)
\(240\) −0.600528 −0.0387639
\(241\) −9.76663 −0.629124 −0.314562 0.949237i \(-0.601858\pi\)
−0.314562 + 0.949237i \(0.601858\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) −1.00000 −0.0640184
\(245\) 3.86767 0.247096
\(246\) 10.3291 0.658559
\(247\) −4.25324 −0.270627
\(248\) 6.73745 0.427829
\(249\) 5.44158 0.344846
\(250\) 5.78871 0.366110
\(251\) −3.61129 −0.227942 −0.113971 0.993484i \(-0.536357\pi\)
−0.113971 + 0.993484i \(0.536357\pi\)
\(252\) 0.748033 0.0471217
\(253\) 5.33798 0.335596
\(254\) −16.1823 −1.01537
\(255\) −0.970868 −0.0607981
\(256\) 1.00000 0.0625000
\(257\) −16.4909 −1.02867 −0.514336 0.857589i \(-0.671962\pi\)
−0.514336 + 0.857589i \(0.671962\pi\)
\(258\) 0.371237 0.0231122
\(259\) 0.687958 0.0427476
\(260\) 2.02611 0.125654
\(261\) 3.93905 0.243821
\(262\) −19.5243 −1.20621
\(263\) −14.5435 −0.896793 −0.448396 0.893835i \(-0.648005\pi\)
−0.448396 + 0.893835i \(0.648005\pi\)
\(264\) 1.00000 0.0615457
\(265\) 5.24677 0.322306
\(266\) 0.942999 0.0578190
\(267\) 10.6282 0.650437
\(268\) 6.96334 0.425354
\(269\) −11.1059 −0.677139 −0.338570 0.940941i \(-0.609943\pi\)
−0.338570 + 0.940941i \(0.609943\pi\)
\(270\) −0.600528 −0.0365470
\(271\) 21.2573 1.29129 0.645644 0.763639i \(-0.276589\pi\)
0.645644 + 0.763639i \(0.276589\pi\)
\(272\) 1.61669 0.0980263
\(273\) −2.52377 −0.152746
\(274\) 19.6596 1.18768
\(275\) −4.63937 −0.279764
\(276\) 5.33798 0.321309
\(277\) 9.68120 0.581687 0.290844 0.956771i \(-0.406064\pi\)
0.290844 + 0.956771i \(0.406064\pi\)
\(278\) 14.9071 0.894068
\(279\) 6.73745 0.403361
\(280\) −0.449215 −0.0268457
\(281\) 22.3772 1.33491 0.667456 0.744650i \(-0.267383\pi\)
0.667456 + 0.744650i \(0.267383\pi\)
\(282\) 1.78835 0.106495
\(283\) −28.0955 −1.67011 −0.835054 0.550169i \(-0.814563\pi\)
−0.835054 + 0.550169i \(0.814563\pi\)
\(284\) 7.20179 0.427348
\(285\) −0.757048 −0.0448437
\(286\) −3.37388 −0.199502
\(287\) 7.72650 0.456081
\(288\) 1.00000 0.0589256
\(289\) −14.3863 −0.846253
\(290\) −2.36551 −0.138907
\(291\) −17.4847 −1.02497
\(292\) 11.0840 0.648640
\(293\) −14.9028 −0.870630 −0.435315 0.900278i \(-0.643363\pi\)
−0.435315 + 0.900278i \(0.643363\pi\)
\(294\) −6.44045 −0.375614
\(295\) 0.932831 0.0543115
\(296\) 0.919689 0.0534558
\(297\) 1.00000 0.0580259
\(298\) −7.06181 −0.409080
\(299\) −18.0097 −1.04153
\(300\) −4.63937 −0.267854
\(301\) 0.277698 0.0160062
\(302\) 0.654495 0.0376619
\(303\) −13.0405 −0.749155
\(304\) 1.26064 0.0723025
\(305\) 0.600528 0.0343861
\(306\) 1.61669 0.0924201
\(307\) 0.0842553 0.00480870 0.00240435 0.999997i \(-0.499235\pi\)
0.00240435 + 0.999997i \(0.499235\pi\)
\(308\) 0.748033 0.0426232
\(309\) 6.66201 0.378988
\(310\) −4.04603 −0.229799
\(311\) 9.30703 0.527753 0.263876 0.964556i \(-0.414999\pi\)
0.263876 + 0.964556i \(0.414999\pi\)
\(312\) −3.37388 −0.191008
\(313\) 16.2487 0.918432 0.459216 0.888325i \(-0.348130\pi\)
0.459216 + 0.888325i \(0.348130\pi\)
\(314\) 10.3719 0.585318
\(315\) −0.449215 −0.0253104
\(316\) 15.8076 0.889245
\(317\) 12.4700 0.700384 0.350192 0.936678i \(-0.386116\pi\)
0.350192 + 0.936678i \(0.386116\pi\)
\(318\) −8.73693 −0.489943
\(319\) 3.93905 0.220544
\(320\) −0.600528 −0.0335705
\(321\) −10.7711 −0.601182
\(322\) 3.99299 0.222521
\(323\) 2.03806 0.113401
\(324\) 1.00000 0.0555556
\(325\) 15.6527 0.868253
\(326\) 10.3180 0.571463
\(327\) 7.81214 0.432012
\(328\) 10.3291 0.570329
\(329\) 1.33774 0.0737522
\(330\) −0.600528 −0.0330580
\(331\) 5.25978 0.289104 0.144552 0.989497i \(-0.453826\pi\)
0.144552 + 0.989497i \(0.453826\pi\)
\(332\) 5.44158 0.298645
\(333\) 0.919689 0.0503986
\(334\) 3.01833 0.165156
\(335\) −4.18168 −0.228470
\(336\) 0.748033 0.0408086
\(337\) 24.1448 1.31525 0.657625 0.753346i \(-0.271561\pi\)
0.657625 + 0.753346i \(0.271561\pi\)
\(338\) −1.61695 −0.0879504
\(339\) −15.6519 −0.850097
\(340\) −0.970868 −0.0526527
\(341\) 6.73745 0.364854
\(342\) 1.26064 0.0681675
\(343\) −10.0539 −0.542860
\(344\) 0.371237 0.0200158
\(345\) −3.20561 −0.172584
\(346\) −19.7437 −1.06143
\(347\) −18.3114 −0.983008 −0.491504 0.870875i \(-0.663553\pi\)
−0.491504 + 0.870875i \(0.663553\pi\)
\(348\) 3.93905 0.211155
\(349\) −2.13066 −0.114051 −0.0570257 0.998373i \(-0.518162\pi\)
−0.0570257 + 0.998373i \(0.518162\pi\)
\(350\) −3.47040 −0.185501
\(351\) −3.37388 −0.180084
\(352\) 1.00000 0.0533002
\(353\) 4.79482 0.255203 0.127601 0.991826i \(-0.459272\pi\)
0.127601 + 0.991826i \(0.459272\pi\)
\(354\) −1.55335 −0.0825597
\(355\) −4.32487 −0.229541
\(356\) 10.6282 0.563295
\(357\) 1.20934 0.0640050
\(358\) 10.9225 0.577271
\(359\) −22.7159 −1.19890 −0.599449 0.800413i \(-0.704613\pi\)
−0.599449 + 0.800413i \(0.704613\pi\)
\(360\) −0.600528 −0.0316506
\(361\) −17.4108 −0.916357
\(362\) −1.75742 −0.0923680
\(363\) 1.00000 0.0524864
\(364\) −2.52377 −0.132282
\(365\) −6.65623 −0.348403
\(366\) −1.00000 −0.0522708
\(367\) −27.2068 −1.42018 −0.710092 0.704109i \(-0.751347\pi\)
−0.710092 + 0.704109i \(0.751347\pi\)
\(368\) 5.33798 0.278262
\(369\) 10.3291 0.537711
\(370\) −0.552299 −0.0287126
\(371\) −6.53552 −0.339307
\(372\) 6.73745 0.349321
\(373\) −4.48288 −0.232115 −0.116057 0.993243i \(-0.537026\pi\)
−0.116057 + 0.993243i \(0.537026\pi\)
\(374\) 1.61669 0.0835971
\(375\) 5.78871 0.298928
\(376\) 1.78835 0.0922270
\(377\) −13.2899 −0.684463
\(378\) 0.748033 0.0384747
\(379\) 5.01577 0.257643 0.128821 0.991668i \(-0.458881\pi\)
0.128821 + 0.991668i \(0.458881\pi\)
\(380\) −0.757048 −0.0388357
\(381\) −16.1823 −0.829046
\(382\) −12.8261 −0.656238
\(383\) 16.6703 0.851811 0.425905 0.904768i \(-0.359956\pi\)
0.425905 + 0.904768i \(0.359956\pi\)
\(384\) 1.00000 0.0510310
\(385\) −0.449215 −0.0228941
\(386\) −2.07382 −0.105555
\(387\) 0.371237 0.0188711
\(388\) −17.4847 −0.887653
\(389\) 37.5232 1.90250 0.951252 0.308415i \(-0.0997986\pi\)
0.951252 + 0.308415i \(0.0997986\pi\)
\(390\) 2.02611 0.102596
\(391\) 8.62987 0.436431
\(392\) −6.44045 −0.325292
\(393\) −19.5243 −0.984870
\(394\) −22.2990 −1.12341
\(395\) −9.49288 −0.477639
\(396\) 1.00000 0.0502519
\(397\) 26.4230 1.32613 0.663066 0.748561i \(-0.269255\pi\)
0.663066 + 0.748561i \(0.269255\pi\)
\(398\) 5.97125 0.299312
\(399\) 0.942999 0.0472090
\(400\) −4.63937 −0.231968
\(401\) −30.7558 −1.53587 −0.767937 0.640526i \(-0.778717\pi\)
−0.767937 + 0.640526i \(0.778717\pi\)
\(402\) 6.96334 0.347300
\(403\) −22.7313 −1.13233
\(404\) −13.0405 −0.648788
\(405\) −0.600528 −0.0298405
\(406\) 2.94654 0.146234
\(407\) 0.919689 0.0455873
\(408\) 1.61669 0.0800382
\(409\) −12.3234 −0.609354 −0.304677 0.952456i \(-0.598549\pi\)
−0.304677 + 0.952456i \(0.598549\pi\)
\(410\) −6.20291 −0.306340
\(411\) 19.6596 0.969735
\(412\) 6.66201 0.328214
\(413\) −1.16196 −0.0571763
\(414\) 5.33798 0.262347
\(415\) −3.26782 −0.160411
\(416\) −3.37388 −0.165418
\(417\) 14.9071 0.730003
\(418\) 1.26064 0.0616598
\(419\) 38.1766 1.86505 0.932525 0.361106i \(-0.117601\pi\)
0.932525 + 0.361106i \(0.117601\pi\)
\(420\) −0.449215 −0.0219194
\(421\) −12.7073 −0.619318 −0.309659 0.950848i \(-0.600215\pi\)
−0.309659 + 0.950848i \(0.600215\pi\)
\(422\) −1.30617 −0.0635835
\(423\) 1.78835 0.0869524
\(424\) −8.73693 −0.424303
\(425\) −7.50043 −0.363824
\(426\) 7.20179 0.348928
\(427\) −0.748033 −0.0361999
\(428\) −10.7711 −0.520638
\(429\) −3.37388 −0.162892
\(430\) −0.222938 −0.0107510
\(431\) −14.2871 −0.688185 −0.344093 0.938936i \(-0.611813\pi\)
−0.344093 + 0.938936i \(0.611813\pi\)
\(432\) 1.00000 0.0481125
\(433\) −24.3489 −1.17013 −0.585067 0.810985i \(-0.698932\pi\)
−0.585067 + 0.810985i \(0.698932\pi\)
\(434\) 5.03984 0.241920
\(435\) −2.36551 −0.113417
\(436\) 7.81214 0.374134
\(437\) 6.72926 0.321904
\(438\) 11.0840 0.529613
\(439\) −7.93790 −0.378855 −0.189428 0.981895i \(-0.560663\pi\)
−0.189428 + 0.981895i \(0.560663\pi\)
\(440\) −0.600528 −0.0286290
\(441\) −6.44045 −0.306688
\(442\) −5.45452 −0.259445
\(443\) −28.0951 −1.33484 −0.667419 0.744682i \(-0.732601\pi\)
−0.667419 + 0.744682i \(0.732601\pi\)
\(444\) 0.919689 0.0436465
\(445\) −6.38255 −0.302562
\(446\) 22.5370 1.06716
\(447\) −7.06181 −0.334012
\(448\) 0.748033 0.0353413
\(449\) −28.7037 −1.35461 −0.677306 0.735701i \(-0.736853\pi\)
−0.677306 + 0.735701i \(0.736853\pi\)
\(450\) −4.63937 −0.218702
\(451\) 10.3291 0.486378
\(452\) −15.6519 −0.736205
\(453\) 0.654495 0.0307508
\(454\) −14.0429 −0.659068
\(455\) 1.51560 0.0710522
\(456\) 1.26064 0.0590348
\(457\) 21.8471 1.02197 0.510983 0.859591i \(-0.329282\pi\)
0.510983 + 0.859591i \(0.329282\pi\)
\(458\) −4.21543 −0.196974
\(459\) 1.61669 0.0754607
\(460\) −3.20561 −0.149462
\(461\) 34.8711 1.62411 0.812055 0.583581i \(-0.198349\pi\)
0.812055 + 0.583581i \(0.198349\pi\)
\(462\) 0.748033 0.0348017
\(463\) −31.4892 −1.46343 −0.731714 0.681612i \(-0.761279\pi\)
−0.731714 + 0.681612i \(0.761279\pi\)
\(464\) 3.93905 0.182866
\(465\) −4.04603 −0.187630
\(466\) −0.537423 −0.0248956
\(467\) −15.1010 −0.698791 −0.349395 0.936975i \(-0.613613\pi\)
−0.349395 + 0.936975i \(0.613613\pi\)
\(468\) −3.37388 −0.155958
\(469\) 5.20881 0.240521
\(470\) −1.07395 −0.0495377
\(471\) 10.3719 0.477910
\(472\) −1.55335 −0.0714988
\(473\) 0.371237 0.0170695
\(474\) 15.8076 0.726065
\(475\) −5.84856 −0.268350
\(476\) 1.20934 0.0554300
\(477\) −8.73693 −0.400037
\(478\) 12.3260 0.563778
\(479\) −6.14658 −0.280845 −0.140422 0.990092i \(-0.544846\pi\)
−0.140422 + 0.990092i \(0.544846\pi\)
\(480\) −0.600528 −0.0274102
\(481\) −3.10292 −0.141481
\(482\) −9.76663 −0.444858
\(483\) 3.99299 0.181687
\(484\) 1.00000 0.0454545
\(485\) 10.5001 0.476784
\(486\) 1.00000 0.0453609
\(487\) 31.2664 1.41682 0.708408 0.705803i \(-0.249414\pi\)
0.708408 + 0.705803i \(0.249414\pi\)
\(488\) −1.00000 −0.0452679
\(489\) 10.3180 0.466597
\(490\) 3.86767 0.174723
\(491\) 1.81636 0.0819711 0.0409855 0.999160i \(-0.486950\pi\)
0.0409855 + 0.999160i \(0.486950\pi\)
\(492\) 10.3291 0.465671
\(493\) 6.36823 0.286810
\(494\) −4.25324 −0.191362
\(495\) −0.600528 −0.0269917
\(496\) 6.73745 0.302521
\(497\) 5.38718 0.241648
\(498\) 5.44158 0.243843
\(499\) 0.0913402 0.00408895 0.00204447 0.999998i \(-0.499349\pi\)
0.00204447 + 0.999998i \(0.499349\pi\)
\(500\) 5.78871 0.258879
\(501\) 3.01833 0.134849
\(502\) −3.61129 −0.161180
\(503\) −24.9703 −1.11337 −0.556686 0.830723i \(-0.687927\pi\)
−0.556686 + 0.830723i \(0.687927\pi\)
\(504\) 0.748033 0.0333201
\(505\) 7.83116 0.348482
\(506\) 5.33798 0.237302
\(507\) −1.61695 −0.0718112
\(508\) −16.1823 −0.717975
\(509\) −25.7241 −1.14020 −0.570100 0.821575i \(-0.693095\pi\)
−0.570100 + 0.821575i \(0.693095\pi\)
\(510\) −0.970868 −0.0429908
\(511\) 8.29118 0.366780
\(512\) 1.00000 0.0441942
\(513\) 1.26064 0.0556585
\(514\) −16.4909 −0.727381
\(515\) −4.00072 −0.176293
\(516\) 0.371237 0.0163428
\(517\) 1.78835 0.0786514
\(518\) 0.687958 0.0302271
\(519\) −19.7437 −0.866654
\(520\) 2.02611 0.0888507
\(521\) −42.6430 −1.86823 −0.934113 0.356978i \(-0.883807\pi\)
−0.934113 + 0.356978i \(0.883807\pi\)
\(522\) 3.93905 0.172407
\(523\) −4.98426 −0.217946 −0.108973 0.994045i \(-0.534756\pi\)
−0.108973 + 0.994045i \(0.534756\pi\)
\(524\) −19.5243 −0.852922
\(525\) −3.47040 −0.151461
\(526\) −14.5435 −0.634128
\(527\) 10.8924 0.474480
\(528\) 1.00000 0.0435194
\(529\) 5.49405 0.238872
\(530\) 5.24677 0.227905
\(531\) −1.55335 −0.0674097
\(532\) 0.942999 0.0408842
\(533\) −34.8491 −1.50948
\(534\) 10.6282 0.459929
\(535\) 6.46832 0.279650
\(536\) 6.96334 0.300771
\(537\) 10.9225 0.471340
\(538\) −11.1059 −0.478810
\(539\) −6.44045 −0.277410
\(540\) −0.600528 −0.0258426
\(541\) −39.3180 −1.69041 −0.845206 0.534441i \(-0.820522\pi\)
−0.845206 + 0.534441i \(0.820522\pi\)
\(542\) 21.2573 0.913078
\(543\) −1.75742 −0.0754182
\(544\) 1.61669 0.0693151
\(545\) −4.69141 −0.200958
\(546\) −2.52377 −0.108008
\(547\) −42.6203 −1.82231 −0.911157 0.412059i \(-0.864810\pi\)
−0.911157 + 0.412059i \(0.864810\pi\)
\(548\) 19.6596 0.839815
\(549\) −1.00000 −0.0426790
\(550\) −4.63937 −0.197823
\(551\) 4.96571 0.211546
\(552\) 5.33798 0.227200
\(553\) 11.8246 0.502832
\(554\) 9.68120 0.411315
\(555\) −0.552299 −0.0234438
\(556\) 14.9071 0.632201
\(557\) 10.8840 0.461171 0.230586 0.973052i \(-0.425936\pi\)
0.230586 + 0.973052i \(0.425936\pi\)
\(558\) 6.73745 0.285219
\(559\) −1.25251 −0.0529755
\(560\) −0.449215 −0.0189828
\(561\) 1.61669 0.0682568
\(562\) 22.3772 0.943925
\(563\) 30.2723 1.27583 0.637913 0.770108i \(-0.279798\pi\)
0.637913 + 0.770108i \(0.279798\pi\)
\(564\) 1.78835 0.0753030
\(565\) 9.39942 0.395437
\(566\) −28.0955 −1.18094
\(567\) 0.748033 0.0314144
\(568\) 7.20179 0.302180
\(569\) −38.1958 −1.60125 −0.800625 0.599166i \(-0.795499\pi\)
−0.800625 + 0.599166i \(0.795499\pi\)
\(570\) −0.757048 −0.0317093
\(571\) −2.00867 −0.0840601 −0.0420300 0.999116i \(-0.513383\pi\)
−0.0420300 + 0.999116i \(0.513383\pi\)
\(572\) −3.37388 −0.141069
\(573\) −12.8261 −0.535816
\(574\) 7.72650 0.322498
\(575\) −24.7649 −1.03277
\(576\) 1.00000 0.0416667
\(577\) −14.8650 −0.618838 −0.309419 0.950926i \(-0.600135\pi\)
−0.309419 + 0.950926i \(0.600135\pi\)
\(578\) −14.3863 −0.598391
\(579\) −2.07382 −0.0861850
\(580\) −2.36551 −0.0982224
\(581\) 4.07048 0.168872
\(582\) −17.4847 −0.724766
\(583\) −8.73693 −0.361847
\(584\) 11.0840 0.458658
\(585\) 2.02611 0.0837692
\(586\) −14.9028 −0.615628
\(587\) 9.08738 0.375076 0.187538 0.982257i \(-0.439949\pi\)
0.187538 + 0.982257i \(0.439949\pi\)
\(588\) −6.44045 −0.265600
\(589\) 8.49349 0.349968
\(590\) 0.932831 0.0384040
\(591\) −22.2990 −0.917258
\(592\) 0.919689 0.0377990
\(593\) 38.0272 1.56159 0.780795 0.624787i \(-0.214814\pi\)
0.780795 + 0.624787i \(0.214814\pi\)
\(594\) 1.00000 0.0410305
\(595\) −0.726242 −0.0297730
\(596\) −7.06181 −0.289263
\(597\) 5.97125 0.244387
\(598\) −18.0097 −0.736471
\(599\) 36.8970 1.50757 0.753786 0.657120i \(-0.228225\pi\)
0.753786 + 0.657120i \(0.228225\pi\)
\(600\) −4.63937 −0.189401
\(601\) 17.1213 0.698392 0.349196 0.937050i \(-0.386455\pi\)
0.349196 + 0.937050i \(0.386455\pi\)
\(602\) 0.277698 0.0113181
\(603\) 6.96334 0.283569
\(604\) 0.654495 0.0266310
\(605\) −0.600528 −0.0244149
\(606\) −13.0405 −0.529733
\(607\) −9.20705 −0.373703 −0.186851 0.982388i \(-0.559828\pi\)
−0.186851 + 0.982388i \(0.559828\pi\)
\(608\) 1.26064 0.0511256
\(609\) 2.94654 0.119400
\(610\) 0.600528 0.0243147
\(611\) −6.03367 −0.244096
\(612\) 1.61669 0.0653509
\(613\) −19.8503 −0.801745 −0.400872 0.916134i \(-0.631293\pi\)
−0.400872 + 0.916134i \(0.631293\pi\)
\(614\) 0.0842553 0.00340027
\(615\) −6.20291 −0.250125
\(616\) 0.748033 0.0301391
\(617\) −42.1748 −1.69789 −0.848947 0.528477i \(-0.822763\pi\)
−0.848947 + 0.528477i \(0.822763\pi\)
\(618\) 6.66201 0.267985
\(619\) 2.09824 0.0843356 0.0421678 0.999111i \(-0.486574\pi\)
0.0421678 + 0.999111i \(0.486574\pi\)
\(620\) −4.04603 −0.162492
\(621\) 5.33798 0.214206
\(622\) 9.30703 0.373178
\(623\) 7.95027 0.318521
\(624\) −3.37388 −0.135063
\(625\) 19.7206 0.788822
\(626\) 16.2487 0.649430
\(627\) 1.26064 0.0503450
\(628\) 10.3719 0.413882
\(629\) 1.48685 0.0592847
\(630\) −0.449215 −0.0178971
\(631\) 25.3717 1.01003 0.505016 0.863110i \(-0.331486\pi\)
0.505016 + 0.863110i \(0.331486\pi\)
\(632\) 15.8076 0.628791
\(633\) −1.30617 −0.0519157
\(634\) 12.4700 0.495246
\(635\) 9.71794 0.385645
\(636\) −8.73693 −0.346442
\(637\) 21.7293 0.860945
\(638\) 3.93905 0.155948
\(639\) 7.20179 0.284898
\(640\) −0.600528 −0.0237379
\(641\) 34.8899 1.37807 0.689033 0.724730i \(-0.258035\pi\)
0.689033 + 0.724730i \(0.258035\pi\)
\(642\) −10.7711 −0.425100
\(643\) 2.14306 0.0845139 0.0422570 0.999107i \(-0.486545\pi\)
0.0422570 + 0.999107i \(0.486545\pi\)
\(644\) 3.99299 0.157346
\(645\) −0.222938 −0.00877819
\(646\) 2.03806 0.0801865
\(647\) −7.22845 −0.284179 −0.142090 0.989854i \(-0.545382\pi\)
−0.142090 + 0.989854i \(0.545382\pi\)
\(648\) 1.00000 0.0392837
\(649\) −1.55335 −0.0609744
\(650\) 15.6527 0.613948
\(651\) 5.03984 0.197527
\(652\) 10.3180 0.404085
\(653\) 5.49278 0.214949 0.107475 0.994208i \(-0.465724\pi\)
0.107475 + 0.994208i \(0.465724\pi\)
\(654\) 7.81214 0.305479
\(655\) 11.7249 0.458129
\(656\) 10.3291 0.403283
\(657\) 11.0840 0.432427
\(658\) 1.33774 0.0521507
\(659\) −27.0537 −1.05386 −0.526931 0.849908i \(-0.676658\pi\)
−0.526931 + 0.849908i \(0.676658\pi\)
\(660\) −0.600528 −0.0233755
\(661\) 24.5145 0.953504 0.476752 0.879038i \(-0.341814\pi\)
0.476752 + 0.879038i \(0.341814\pi\)
\(662\) 5.25978 0.204427
\(663\) −5.45452 −0.211836
\(664\) 5.44158 0.211174
\(665\) −0.566297 −0.0219601
\(666\) 0.919689 0.0356372
\(667\) 21.0266 0.814152
\(668\) 3.01833 0.116783
\(669\) 22.5370 0.871330
\(670\) −4.18168 −0.161552
\(671\) −1.00000 −0.0386046
\(672\) 0.748033 0.0288560
\(673\) −1.01371 −0.0390755 −0.0195378 0.999809i \(-0.506219\pi\)
−0.0195378 + 0.999809i \(0.506219\pi\)
\(674\) 24.1448 0.930022
\(675\) −4.63937 −0.178569
\(676\) −1.61695 −0.0621903
\(677\) −34.8826 −1.34065 −0.670324 0.742068i \(-0.733845\pi\)
−0.670324 + 0.742068i \(0.733845\pi\)
\(678\) −15.6519 −0.601109
\(679\) −13.0792 −0.501932
\(680\) −0.970868 −0.0372311
\(681\) −14.0429 −0.538127
\(682\) 6.73745 0.257990
\(683\) −12.8392 −0.491279 −0.245639 0.969361i \(-0.578998\pi\)
−0.245639 + 0.969361i \(0.578998\pi\)
\(684\) 1.26064 0.0482017
\(685\) −11.8061 −0.451089
\(686\) −10.0539 −0.383860
\(687\) −4.21543 −0.160829
\(688\) 0.371237 0.0141533
\(689\) 29.4773 1.12300
\(690\) −3.20561 −0.122035
\(691\) −32.5984 −1.24010 −0.620051 0.784561i \(-0.712888\pi\)
−0.620051 + 0.784561i \(0.712888\pi\)
\(692\) −19.7437 −0.750544
\(693\) 0.748033 0.0284154
\(694\) −18.3114 −0.695092
\(695\) −8.95212 −0.339573
\(696\) 3.93905 0.149309
\(697\) 16.6990 0.632518
\(698\) −2.13066 −0.0806465
\(699\) −0.537423 −0.0203272
\(700\) −3.47040 −0.131169
\(701\) 4.40381 0.166330 0.0831648 0.996536i \(-0.473497\pi\)
0.0831648 + 0.996536i \(0.473497\pi\)
\(702\) −3.37388 −0.127339
\(703\) 1.15939 0.0437274
\(704\) 1.00000 0.0376889
\(705\) −1.07395 −0.0404474
\(706\) 4.79482 0.180456
\(707\) −9.75471 −0.366863
\(708\) −1.55335 −0.0583785
\(709\) −13.3793 −0.502471 −0.251236 0.967926i \(-0.580837\pi\)
−0.251236 + 0.967926i \(0.580837\pi\)
\(710\) −4.32487 −0.162310
\(711\) 15.8076 0.592830
\(712\) 10.6282 0.398310
\(713\) 35.9644 1.34688
\(714\) 1.20934 0.0452584
\(715\) 2.02611 0.0757721
\(716\) 10.9225 0.408192
\(717\) 12.3260 0.460323
\(718\) −22.7159 −0.847749
\(719\) 5.46905 0.203961 0.101981 0.994786i \(-0.467482\pi\)
0.101981 + 0.994786i \(0.467482\pi\)
\(720\) −0.600528 −0.0223803
\(721\) 4.98340 0.185592
\(722\) −17.4108 −0.647963
\(723\) −9.76663 −0.363225
\(724\) −1.75742 −0.0653140
\(725\) −18.2747 −0.678705
\(726\) 1.00000 0.0371135
\(727\) −4.39354 −0.162948 −0.0814738 0.996675i \(-0.525963\pi\)
−0.0814738 + 0.996675i \(0.525963\pi\)
\(728\) −2.52377 −0.0935372
\(729\) 1.00000 0.0370370
\(730\) −6.65623 −0.246358
\(731\) 0.600176 0.0221983
\(732\) −1.00000 −0.0369611
\(733\) −18.8338 −0.695642 −0.347821 0.937561i \(-0.613078\pi\)
−0.347821 + 0.937561i \(0.613078\pi\)
\(734\) −27.2068 −1.00422
\(735\) 3.86767 0.142661
\(736\) 5.33798 0.196761
\(737\) 6.96334 0.256498
\(738\) 10.3291 0.380219
\(739\) −20.7849 −0.764586 −0.382293 0.924041i \(-0.624865\pi\)
−0.382293 + 0.924041i \(0.624865\pi\)
\(740\) −0.552299 −0.0203029
\(741\) −4.25324 −0.156247
\(742\) −6.53552 −0.239926
\(743\) 1.50202 0.0551038 0.0275519 0.999620i \(-0.491229\pi\)
0.0275519 + 0.999620i \(0.491229\pi\)
\(744\) 6.73745 0.247007
\(745\) 4.24081 0.155371
\(746\) −4.48288 −0.164130
\(747\) 5.44158 0.199097
\(748\) 1.61669 0.0591121
\(749\) −8.05711 −0.294400
\(750\) 5.78871 0.211374
\(751\) 13.0878 0.477579 0.238790 0.971071i \(-0.423249\pi\)
0.238790 + 0.971071i \(0.423249\pi\)
\(752\) 1.78835 0.0652143
\(753\) −3.61129 −0.131603
\(754\) −13.2899 −0.483988
\(755\) −0.393042 −0.0143043
\(756\) 0.748033 0.0272057
\(757\) 16.4585 0.598195 0.299097 0.954223i \(-0.403314\pi\)
0.299097 + 0.954223i \(0.403314\pi\)
\(758\) 5.01577 0.182181
\(759\) 5.33798 0.193756
\(760\) −0.757048 −0.0274610
\(761\) 29.8670 1.08268 0.541339 0.840804i \(-0.317917\pi\)
0.541339 + 0.840804i \(0.317917\pi\)
\(762\) −16.1823 −0.586224
\(763\) 5.84374 0.211558
\(764\) −12.8261 −0.464030
\(765\) −0.970868 −0.0351018
\(766\) 16.6703 0.602321
\(767\) 5.24082 0.189235
\(768\) 1.00000 0.0360844
\(769\) 1.78944 0.0645289 0.0322645 0.999479i \(-0.489728\pi\)
0.0322645 + 0.999479i \(0.489728\pi\)
\(770\) −0.449215 −0.0161886
\(771\) −16.4909 −0.593904
\(772\) −2.07382 −0.0746384
\(773\) −21.5719 −0.775888 −0.387944 0.921683i \(-0.626815\pi\)
−0.387944 + 0.921683i \(0.626815\pi\)
\(774\) 0.371237 0.0133439
\(775\) −31.2575 −1.12280
\(776\) −17.4847 −0.627665
\(777\) 0.687958 0.0246803
\(778\) 37.5232 1.34527
\(779\) 13.0212 0.466534
\(780\) 2.02611 0.0725463
\(781\) 7.20179 0.257700
\(782\) 8.62987 0.308604
\(783\) 3.93905 0.140770
\(784\) −6.44045 −0.230016
\(785\) −6.22859 −0.222308
\(786\) −19.5243 −0.696408
\(787\) 25.0599 0.893288 0.446644 0.894712i \(-0.352619\pi\)
0.446644 + 0.894712i \(0.352619\pi\)
\(788\) −22.2990 −0.794369
\(789\) −14.5435 −0.517764
\(790\) −9.49288 −0.337741
\(791\) −11.7082 −0.416295
\(792\) 1.00000 0.0355335
\(793\) 3.37388 0.119810
\(794\) 26.4230 0.937717
\(795\) 5.24677 0.186084
\(796\) 5.97125 0.211645
\(797\) −34.1523 −1.20974 −0.604868 0.796326i \(-0.706774\pi\)
−0.604868 + 0.796326i \(0.706774\pi\)
\(798\) 0.942999 0.0333818
\(799\) 2.89121 0.102284
\(800\) −4.63937 −0.164026
\(801\) 10.6282 0.375530
\(802\) −30.7558 −1.08603
\(803\) 11.0840 0.391145
\(804\) 6.96334 0.245578
\(805\) −2.39790 −0.0845149
\(806\) −22.7313 −0.800677
\(807\) −11.1059 −0.390947
\(808\) −13.0405 −0.458762
\(809\) −51.3850 −1.80660 −0.903300 0.429010i \(-0.858862\pi\)
−0.903300 + 0.429010i \(0.858862\pi\)
\(810\) −0.600528 −0.0211004
\(811\) −52.2122 −1.83342 −0.916710 0.399554i \(-0.869165\pi\)
−0.916710 + 0.399554i \(0.869165\pi\)
\(812\) 2.94654 0.103403
\(813\) 21.2573 0.745525
\(814\) 0.919689 0.0322351
\(815\) −6.19626 −0.217046
\(816\) 1.61669 0.0565955
\(817\) 0.467996 0.0163731
\(818\) −12.3234 −0.430879
\(819\) −2.52377 −0.0881878
\(820\) −6.20291 −0.216615
\(821\) −33.1972 −1.15859 −0.579295 0.815118i \(-0.696672\pi\)
−0.579295 + 0.815118i \(0.696672\pi\)
\(822\) 19.6596 0.685706
\(823\) 20.2527 0.705965 0.352982 0.935630i \(-0.385168\pi\)
0.352982 + 0.935630i \(0.385168\pi\)
\(824\) 6.66201 0.232082
\(825\) −4.63937 −0.161522
\(826\) −1.16196 −0.0404297
\(827\) 12.1521 0.422569 0.211284 0.977425i \(-0.432235\pi\)
0.211284 + 0.977425i \(0.432235\pi\)
\(828\) 5.33798 0.185508
\(829\) 7.43492 0.258225 0.129113 0.991630i \(-0.458787\pi\)
0.129113 + 0.991630i \(0.458787\pi\)
\(830\) −3.26782 −0.113428
\(831\) 9.68120 0.335837
\(832\) −3.37388 −0.116968
\(833\) −10.4122 −0.360762
\(834\) 14.9071 0.516190
\(835\) −1.81259 −0.0627273
\(836\) 1.26064 0.0436001
\(837\) 6.73745 0.232880
\(838\) 38.1766 1.31879
\(839\) 36.1001 1.24632 0.623158 0.782096i \(-0.285849\pi\)
0.623158 + 0.782096i \(0.285849\pi\)
\(840\) −0.449215 −0.0154994
\(841\) −13.4839 −0.464962
\(842\) −12.7073 −0.437924
\(843\) 22.3772 0.770711
\(844\) −1.30617 −0.0449603
\(845\) 0.971023 0.0334042
\(846\) 1.78835 0.0614846
\(847\) 0.748033 0.0257027
\(848\) −8.73693 −0.300027
\(849\) −28.0955 −0.964237
\(850\) −7.50043 −0.257262
\(851\) 4.90928 0.168288
\(852\) 7.20179 0.246729
\(853\) 50.3770 1.72488 0.862438 0.506162i \(-0.168936\pi\)
0.862438 + 0.506162i \(0.168936\pi\)
\(854\) −0.748033 −0.0255972
\(855\) −0.757048 −0.0258905
\(856\) −10.7711 −0.368147
\(857\) −55.0933 −1.88195 −0.940975 0.338476i \(-0.890088\pi\)
−0.940975 + 0.338476i \(0.890088\pi\)
\(858\) −3.37388 −0.115182
\(859\) 45.3208 1.54633 0.773164 0.634207i \(-0.218673\pi\)
0.773164 + 0.634207i \(0.218673\pi\)
\(860\) −0.222938 −0.00760213
\(861\) 7.72650 0.263319
\(862\) −14.2871 −0.486620
\(863\) −11.3309 −0.385707 −0.192853 0.981228i \(-0.561774\pi\)
−0.192853 + 0.981228i \(0.561774\pi\)
\(864\) 1.00000 0.0340207
\(865\) 11.8567 0.403139
\(866\) −24.3489 −0.827409
\(867\) −14.3863 −0.488585
\(868\) 5.03984 0.171063
\(869\) 15.8076 0.536235
\(870\) −2.36551 −0.0801982
\(871\) −23.4935 −0.796046
\(872\) 7.81214 0.264552
\(873\) −17.4847 −0.591769
\(874\) 6.72926 0.227621
\(875\) 4.33015 0.146386
\(876\) 11.0840 0.374493
\(877\) 16.8916 0.570388 0.285194 0.958470i \(-0.407942\pi\)
0.285194 + 0.958470i \(0.407942\pi\)
\(878\) −7.93790 −0.267891
\(879\) −14.9028 −0.502658
\(880\) −0.600528 −0.0202438
\(881\) 40.7768 1.37381 0.686903 0.726749i \(-0.258970\pi\)
0.686903 + 0.726749i \(0.258970\pi\)
\(882\) −6.44045 −0.216861
\(883\) −49.9531 −1.68106 −0.840528 0.541769i \(-0.817755\pi\)
−0.840528 + 0.541769i \(0.817755\pi\)
\(884\) −5.45452 −0.183455
\(885\) 0.932831 0.0313568
\(886\) −28.0951 −0.943873
\(887\) 27.2297 0.914284 0.457142 0.889394i \(-0.348873\pi\)
0.457142 + 0.889394i \(0.348873\pi\)
\(888\) 0.919689 0.0308627
\(889\) −12.1049 −0.405986
\(890\) −6.38255 −0.213944
\(891\) 1.00000 0.0335013
\(892\) 22.5370 0.754594
\(893\) 2.25446 0.0754426
\(894\) −7.06181 −0.236182
\(895\) −6.55926 −0.219252
\(896\) 0.748033 0.0249900
\(897\) −18.0097 −0.601326
\(898\) −28.7037 −0.957856
\(899\) 26.5392 0.885130
\(900\) −4.63937 −0.154646
\(901\) −14.1249 −0.470569
\(902\) 10.3291 0.343921
\(903\) 0.277698 0.00924121
\(904\) −15.6519 −0.520576
\(905\) 1.05538 0.0350820
\(906\) 0.654495 0.0217441
\(907\) −0.157384 −0.00522584 −0.00261292 0.999997i \(-0.500832\pi\)
−0.00261292 + 0.999997i \(0.500832\pi\)
\(908\) −14.0429 −0.466032
\(909\) −13.0405 −0.432525
\(910\) 1.51560 0.0502415
\(911\) 4.07678 0.135070 0.0675348 0.997717i \(-0.478487\pi\)
0.0675348 + 0.997717i \(0.478487\pi\)
\(912\) 1.26064 0.0417439
\(913\) 5.44158 0.180090
\(914\) 21.8471 0.722639
\(915\) 0.600528 0.0198528
\(916\) −4.21543 −0.139282
\(917\) −14.6048 −0.482293
\(918\) 1.61669 0.0533588
\(919\) 22.3245 0.736417 0.368208 0.929743i \(-0.379971\pi\)
0.368208 + 0.929743i \(0.379971\pi\)
\(920\) −3.20561 −0.105686
\(921\) 0.0842553 0.00277631
\(922\) 34.8711 1.14842
\(923\) −24.2980 −0.799777
\(924\) 0.748033 0.0246085
\(925\) −4.26677 −0.140291
\(926\) −31.4892 −1.03480
\(927\) 6.66201 0.218809
\(928\) 3.93905 0.129306
\(929\) 1.07769 0.0353577 0.0176789 0.999844i \(-0.494372\pi\)
0.0176789 + 0.999844i \(0.494372\pi\)
\(930\) −4.04603 −0.132674
\(931\) −8.11907 −0.266092
\(932\) −0.537423 −0.0176039
\(933\) 9.30703 0.304698
\(934\) −15.1010 −0.494120
\(935\) −0.970868 −0.0317508
\(936\) −3.37388 −0.110279
\(937\) 2.15606 0.0704352 0.0352176 0.999380i \(-0.488788\pi\)
0.0352176 + 0.999380i \(0.488788\pi\)
\(938\) 5.20881 0.170074
\(939\) 16.2487 0.530257
\(940\) −1.07395 −0.0350285
\(941\) 20.0132 0.652412 0.326206 0.945299i \(-0.394230\pi\)
0.326206 + 0.945299i \(0.394230\pi\)
\(942\) 10.3719 0.337933
\(943\) 55.1365 1.79549
\(944\) −1.55335 −0.0505573
\(945\) −0.449215 −0.0146130
\(946\) 0.371237 0.0120700
\(947\) −45.9800 −1.49415 −0.747075 0.664740i \(-0.768542\pi\)
−0.747075 + 0.664740i \(0.768542\pi\)
\(948\) 15.8076 0.513406
\(949\) −37.3960 −1.21392
\(950\) −5.84856 −0.189752
\(951\) 12.4700 0.404367
\(952\) 1.20934 0.0391949
\(953\) 39.6331 1.28384 0.641921 0.766771i \(-0.278138\pi\)
0.641921 + 0.766771i \(0.278138\pi\)
\(954\) −8.73693 −0.282869
\(955\) 7.70240 0.249244
\(956\) 12.3260 0.398651
\(957\) 3.93905 0.127331
\(958\) −6.14658 −0.198587
\(959\) 14.7060 0.474882
\(960\) −0.600528 −0.0193820
\(961\) 14.3933 0.464299
\(962\) −3.10292 −0.100042
\(963\) −10.7711 −0.347092
\(964\) −9.76663 −0.314562
\(965\) 1.24539 0.0400904
\(966\) 3.99299 0.128472
\(967\) −36.4860 −1.17331 −0.586655 0.809837i \(-0.699555\pi\)
−0.586655 + 0.809837i \(0.699555\pi\)
\(968\) 1.00000 0.0321412
\(969\) 2.03806 0.0654720
\(970\) 10.5001 0.337137
\(971\) −40.1208 −1.28754 −0.643769 0.765220i \(-0.722630\pi\)
−0.643769 + 0.765220i \(0.722630\pi\)
\(972\) 1.00000 0.0320750
\(973\) 11.1510 0.357485
\(974\) 31.2664 1.00184
\(975\) 15.6527 0.501286
\(976\) −1.00000 −0.0320092
\(977\) −5.41498 −0.173241 −0.0866203 0.996241i \(-0.527607\pi\)
−0.0866203 + 0.996241i \(0.527607\pi\)
\(978\) 10.3180 0.329934
\(979\) 10.6282 0.339680
\(980\) 3.86767 0.123548
\(981\) 7.81214 0.249422
\(982\) 1.81636 0.0579623
\(983\) 31.0918 0.991674 0.495837 0.868415i \(-0.334861\pi\)
0.495837 + 0.868415i \(0.334861\pi\)
\(984\) 10.3291 0.329279
\(985\) 13.3912 0.426678
\(986\) 6.36823 0.202806
\(987\) 1.33774 0.0425808
\(988\) −4.25324 −0.135314
\(989\) 1.98166 0.0630131
\(990\) −0.600528 −0.0190860
\(991\) 13.5368 0.430011 0.215006 0.976613i \(-0.431023\pi\)
0.215006 + 0.976613i \(0.431023\pi\)
\(992\) 6.73745 0.213914
\(993\) 5.25978 0.166914
\(994\) 5.38718 0.170871
\(995\) −3.58590 −0.113681
\(996\) 5.44158 0.172423
\(997\) 55.5304 1.75867 0.879333 0.476208i \(-0.157989\pi\)
0.879333 + 0.476208i \(0.157989\pi\)
\(998\) 0.0913402 0.00289132
\(999\) 0.919689 0.0290977
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 \(a_p\))