Properties

Label 8002.2.a.d.1.17
Level 8002
Weight 2
Character 8002.1
Self dual Yes
Analytic conductor 63.896
Analytic rank 1
Dimension 69
CM No

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(1\)
Dimension: \(69\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 8002.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-2.01476 q^{3}\) \(+1.00000 q^{4}\) \(+2.07868 q^{5}\) \(-2.01476 q^{6}\) \(-1.64070 q^{7}\) \(+1.00000 q^{8}\) \(+1.05926 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-2.01476 q^{3}\) \(+1.00000 q^{4}\) \(+2.07868 q^{5}\) \(-2.01476 q^{6}\) \(-1.64070 q^{7}\) \(+1.00000 q^{8}\) \(+1.05926 q^{9}\) \(+2.07868 q^{10}\) \(-2.89925 q^{11}\) \(-2.01476 q^{12}\) \(-2.54576 q^{13}\) \(-1.64070 q^{14}\) \(-4.18804 q^{15}\) \(+1.00000 q^{16}\) \(+1.07742 q^{17}\) \(+1.05926 q^{18}\) \(+6.85110 q^{19}\) \(+2.07868 q^{20}\) \(+3.30563 q^{21}\) \(-2.89925 q^{22}\) \(-1.82864 q^{23}\) \(-2.01476 q^{24}\) \(-0.679103 q^{25}\) \(-2.54576 q^{26}\) \(+3.91013 q^{27}\) \(-1.64070 q^{28}\) \(-4.36452 q^{29}\) \(-4.18804 q^{30}\) \(+1.10436 q^{31}\) \(+1.00000 q^{32}\) \(+5.84129 q^{33}\) \(+1.07742 q^{34}\) \(-3.41049 q^{35}\) \(+1.05926 q^{36}\) \(-3.20421 q^{37}\) \(+6.85110 q^{38}\) \(+5.12911 q^{39}\) \(+2.07868 q^{40}\) \(+7.10776 q^{41}\) \(+3.30563 q^{42}\) \(+8.50150 q^{43}\) \(-2.89925 q^{44}\) \(+2.20186 q^{45}\) \(-1.82864 q^{46}\) \(+1.67093 q^{47}\) \(-2.01476 q^{48}\) \(-4.30809 q^{49}\) \(-0.679103 q^{50}\) \(-2.17073 q^{51}\) \(-2.54576 q^{52}\) \(+11.9804 q^{53}\) \(+3.91013 q^{54}\) \(-6.02660 q^{55}\) \(-1.64070 q^{56}\) \(-13.8033 q^{57}\) \(-4.36452 q^{58}\) \(+0.216612 q^{59}\) \(-4.18804 q^{60}\) \(-10.0683 q^{61}\) \(+1.10436 q^{62}\) \(-1.73793 q^{63}\) \(+1.00000 q^{64}\) \(-5.29182 q^{65}\) \(+5.84129 q^{66}\) \(-5.57966 q^{67}\) \(+1.07742 q^{68}\) \(+3.68427 q^{69}\) \(-3.41049 q^{70}\) \(-1.16943 q^{71}\) \(+1.05926 q^{72}\) \(-13.4122 q^{73}\) \(-3.20421 q^{74}\) \(+1.36823 q^{75}\) \(+6.85110 q^{76}\) \(+4.75681 q^{77}\) \(+5.12911 q^{78}\) \(-1.87728 q^{79}\) \(+2.07868 q^{80}\) \(-11.0557 q^{81}\) \(+7.10776 q^{82}\) \(-2.72604 q^{83}\) \(+3.30563 q^{84}\) \(+2.23960 q^{85}\) \(+8.50150 q^{86}\) \(+8.79346 q^{87}\) \(-2.89925 q^{88}\) \(+10.9186 q^{89}\) \(+2.20186 q^{90}\) \(+4.17685 q^{91}\) \(-1.82864 q^{92}\) \(-2.22502 q^{93}\) \(+1.67093 q^{94}\) \(+14.2412 q^{95}\) \(-2.01476 q^{96}\) \(+15.4145 q^{97}\) \(-4.30809 q^{98}\) \(-3.07106 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(69q \) \(\mathstrut +\mathstrut 69q^{2} \) \(\mathstrut -\mathstrut 25q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 33q^{5} \) \(\mathstrut -\mathstrut 25q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 54q^{9} \) \(\mathstrut -\mathstrut 33q^{10} \) \(\mathstrut -\mathstrut 30q^{11} \) \(\mathstrut -\mathstrut 25q^{12} \) \(\mathstrut -\mathstrut 58q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 80q^{17} \) \(\mathstrut +\mathstrut 54q^{18} \) \(\mathstrut -\mathstrut 40q^{19} \) \(\mathstrut -\mathstrut 33q^{20} \) \(\mathstrut -\mathstrut 32q^{21} \) \(\mathstrut -\mathstrut 30q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 42q^{25} \) \(\mathstrut -\mathstrut 58q^{26} \) \(\mathstrut -\mathstrut 76q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 44q^{29} \) \(\mathstrut +\mathstrut 2q^{30} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 69q^{32} \) \(\mathstrut -\mathstrut 41q^{33} \) \(\mathstrut -\mathstrut 80q^{34} \) \(\mathstrut -\mathstrut 49q^{35} \) \(\mathstrut +\mathstrut 54q^{36} \) \(\mathstrut -\mathstrut 47q^{37} \) \(\mathstrut -\mathstrut 40q^{38} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 33q^{40} \) \(\mathstrut -\mathstrut 94q^{41} \) \(\mathstrut -\mathstrut 32q^{42} \) \(\mathstrut -\mathstrut 10q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 85q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut +\mathstrut 42q^{50} \) \(\mathstrut -\mathstrut 10q^{51} \) \(\mathstrut -\mathstrut 58q^{52} \) \(\mathstrut -\mathstrut 41q^{53} \) \(\mathstrut -\mathstrut 76q^{54} \) \(\mathstrut -\mathstrut 27q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 44q^{58} \) \(\mathstrut -\mathstrut 75q^{59} \) \(\mathstrut +\mathstrut 2q^{60} \) \(\mathstrut -\mathstrut 98q^{61} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 61q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 41q^{66} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut -\mathstrut 74q^{69} \) \(\mathstrut -\mathstrut 49q^{70} \) \(\mathstrut -\mathstrut 22q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut -\mathstrut 129q^{73} \) \(\mathstrut -\mathstrut 47q^{74} \) \(\mathstrut -\mathstrut 106q^{75} \) \(\mathstrut -\mathstrut 40q^{76} \) \(\mathstrut -\mathstrut 108q^{77} \) \(\mathstrut -\mathstrut 14q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut -\mathstrut 33q^{80} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 111q^{83} \) \(\mathstrut -\mathstrut 32q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 10q^{86} \) \(\mathstrut -\mathstrut 38q^{87} \) \(\mathstrut -\mathstrut 30q^{88} \) \(\mathstrut -\mathstrut 112q^{89} \) \(\mathstrut -\mathstrut 89q^{90} \) \(\mathstrut -\mathstrut 55q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 90q^{93} \) \(\mathstrut -\mathstrut 85q^{94} \) \(\mathstrut -\mathstrut 38q^{95} \) \(\mathstrut -\mathstrut 25q^{96} \) \(\mathstrut -\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 32q^{98} \) \(\mathstrut -\mathstrut 51q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.01476 −1.16322 −0.581611 0.813467i \(-0.697577\pi\)
−0.581611 + 0.813467i \(0.697577\pi\)
\(4\) 1.00000 0.500000
\(5\) 2.07868 0.929613 0.464806 0.885412i \(-0.346124\pi\)
0.464806 + 0.885412i \(0.346124\pi\)
\(6\) −2.01476 −0.822522
\(7\) −1.64070 −0.620128 −0.310064 0.950716i \(-0.600351\pi\)
−0.310064 + 0.950716i \(0.600351\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.05926 0.353086
\(10\) 2.07868 0.657335
\(11\) −2.89925 −0.874156 −0.437078 0.899424i \(-0.643987\pi\)
−0.437078 + 0.899424i \(0.643987\pi\)
\(12\) −2.01476 −0.581611
\(13\) −2.54576 −0.706068 −0.353034 0.935610i \(-0.614850\pi\)
−0.353034 + 0.935610i \(0.614850\pi\)
\(14\) −1.64070 −0.438497
\(15\) −4.18804 −1.08135
\(16\) 1.00000 0.250000
\(17\) 1.07742 0.261312 0.130656 0.991428i \(-0.458292\pi\)
0.130656 + 0.991428i \(0.458292\pi\)
\(18\) 1.05926 0.249670
\(19\) 6.85110 1.57175 0.785875 0.618386i \(-0.212213\pi\)
0.785875 + 0.618386i \(0.212213\pi\)
\(20\) 2.07868 0.464806
\(21\) 3.30563 0.721347
\(22\) −2.89925 −0.618122
\(23\) −1.82864 −0.381298 −0.190649 0.981658i \(-0.561059\pi\)
−0.190649 + 0.981658i \(0.561059\pi\)
\(24\) −2.01476 −0.411261
\(25\) −0.679103 −0.135821
\(26\) −2.54576 −0.499265
\(27\) 3.91013 0.752504
\(28\) −1.64070 −0.310064
\(29\) −4.36452 −0.810470 −0.405235 0.914212i \(-0.632810\pi\)
−0.405235 + 0.914212i \(0.632810\pi\)
\(30\) −4.18804 −0.764627
\(31\) 1.10436 0.198349 0.0991743 0.995070i \(-0.468380\pi\)
0.0991743 + 0.995070i \(0.468380\pi\)
\(32\) 1.00000 0.176777
\(33\) 5.84129 1.01684
\(34\) 1.07742 0.184775
\(35\) −3.41049 −0.576479
\(36\) 1.05926 0.176543
\(37\) −3.20421 −0.526769 −0.263385 0.964691i \(-0.584839\pi\)
−0.263385 + 0.964691i \(0.584839\pi\)
\(38\) 6.85110 1.11139
\(39\) 5.12911 0.821314
\(40\) 2.07868 0.328668
\(41\) 7.10776 1.11005 0.555023 0.831835i \(-0.312709\pi\)
0.555023 + 0.831835i \(0.312709\pi\)
\(42\) 3.30563 0.510069
\(43\) 8.50150 1.29647 0.648234 0.761442i \(-0.275508\pi\)
0.648234 + 0.761442i \(0.275508\pi\)
\(44\) −2.89925 −0.437078
\(45\) 2.20186 0.328234
\(46\) −1.82864 −0.269618
\(47\) 1.67093 0.243730 0.121865 0.992547i \(-0.461112\pi\)
0.121865 + 0.992547i \(0.461112\pi\)
\(48\) −2.01476 −0.290806
\(49\) −4.30809 −0.615441
\(50\) −0.679103 −0.0960396
\(51\) −2.17073 −0.303964
\(52\) −2.54576 −0.353034
\(53\) 11.9804 1.64563 0.822816 0.568308i \(-0.192402\pi\)
0.822816 + 0.568308i \(0.192402\pi\)
\(54\) 3.91013 0.532101
\(55\) −6.02660 −0.812627
\(56\) −1.64070 −0.219248
\(57\) −13.8033 −1.82829
\(58\) −4.36452 −0.573089
\(59\) 0.216612 0.0282005 0.0141002 0.999901i \(-0.495512\pi\)
0.0141002 + 0.999901i \(0.495512\pi\)
\(60\) −4.18804 −0.540673
\(61\) −10.0683 −1.28912 −0.644558 0.764555i \(-0.722959\pi\)
−0.644558 + 0.764555i \(0.722959\pi\)
\(62\) 1.10436 0.140254
\(63\) −1.73793 −0.218959
\(64\) 1.00000 0.125000
\(65\) −5.29182 −0.656370
\(66\) 5.84129 0.719013
\(67\) −5.57966 −0.681664 −0.340832 0.940124i \(-0.610709\pi\)
−0.340832 + 0.940124i \(0.610709\pi\)
\(68\) 1.07742 0.130656
\(69\) 3.68427 0.443534
\(70\) −3.41049 −0.407632
\(71\) −1.16943 −0.138785 −0.0693926 0.997589i \(-0.522106\pi\)
−0.0693926 + 0.997589i \(0.522106\pi\)
\(72\) 1.05926 0.124835
\(73\) −13.4122 −1.56977 −0.784887 0.619638i \(-0.787279\pi\)
−0.784887 + 0.619638i \(0.787279\pi\)
\(74\) −3.20421 −0.372482
\(75\) 1.36823 0.157990
\(76\) 6.85110 0.785875
\(77\) 4.75681 0.542089
\(78\) 5.12911 0.580757
\(79\) −1.87728 −0.211210 −0.105605 0.994408i \(-0.533678\pi\)
−0.105605 + 0.994408i \(0.533678\pi\)
\(80\) 2.07868 0.232403
\(81\) −11.0557 −1.22842
\(82\) 7.10776 0.784921
\(83\) −2.72604 −0.299222 −0.149611 0.988745i \(-0.547802\pi\)
−0.149611 + 0.988745i \(0.547802\pi\)
\(84\) 3.30563 0.360673
\(85\) 2.23960 0.242919
\(86\) 8.50150 0.916741
\(87\) 8.79346 0.942757
\(88\) −2.89925 −0.309061
\(89\) 10.9186 1.15737 0.578684 0.815552i \(-0.303567\pi\)
0.578684 + 0.815552i \(0.303567\pi\)
\(90\) 2.20186 0.232096
\(91\) 4.17685 0.437853
\(92\) −1.82864 −0.190649
\(93\) −2.22502 −0.230723
\(94\) 1.67093 0.172343
\(95\) 14.2412 1.46112
\(96\) −2.01476 −0.205631
\(97\) 15.4145 1.56510 0.782551 0.622587i \(-0.213918\pi\)
0.782551 + 0.622587i \(0.213918\pi\)
\(98\) −4.30809 −0.435183
\(99\) −3.07106 −0.308653
\(100\) −0.679103 −0.0679103
\(101\) −16.3718 −1.62906 −0.814529 0.580124i \(-0.803004\pi\)
−0.814529 + 0.580124i \(0.803004\pi\)
\(102\) −2.17073 −0.214935
\(103\) 3.26015 0.321232 0.160616 0.987017i \(-0.448652\pi\)
0.160616 + 0.987017i \(0.448652\pi\)
\(104\) −2.54576 −0.249633
\(105\) 6.87133 0.670573
\(106\) 11.9804 1.16364
\(107\) −17.7447 −1.71544 −0.857722 0.514114i \(-0.828121\pi\)
−0.857722 + 0.514114i \(0.828121\pi\)
\(108\) 3.91013 0.376252
\(109\) −14.0053 −1.34146 −0.670732 0.741700i \(-0.734020\pi\)
−0.670732 + 0.741700i \(0.734020\pi\)
\(110\) −6.02660 −0.574614
\(111\) 6.45572 0.612750
\(112\) −1.64070 −0.155032
\(113\) −5.42204 −0.510062 −0.255031 0.966933i \(-0.582086\pi\)
−0.255031 + 0.966933i \(0.582086\pi\)
\(114\) −13.8033 −1.29280
\(115\) −3.80115 −0.354459
\(116\) −4.36452 −0.405235
\(117\) −2.69662 −0.249303
\(118\) 0.216612 0.0199407
\(119\) −1.76772 −0.162047
\(120\) −4.18804 −0.382314
\(121\) −2.59436 −0.235851
\(122\) −10.0683 −0.911543
\(123\) −14.3204 −1.29123
\(124\) 1.10436 0.0991743
\(125\) −11.8050 −1.05587
\(126\) −1.73793 −0.154827
\(127\) −20.4551 −1.81510 −0.907549 0.419947i \(-0.862049\pi\)
−0.907549 + 0.419947i \(0.862049\pi\)
\(128\) 1.00000 0.0883883
\(129\) −17.1285 −1.50808
\(130\) −5.29182 −0.464123
\(131\) −7.14967 −0.624669 −0.312335 0.949972i \(-0.601111\pi\)
−0.312335 + 0.949972i \(0.601111\pi\)
\(132\) 5.84129 0.508419
\(133\) −11.2406 −0.974686
\(134\) −5.57966 −0.482009
\(135\) 8.12789 0.699537
\(136\) 1.07742 0.0923876
\(137\) 0.872289 0.0745247 0.0372624 0.999306i \(-0.488136\pi\)
0.0372624 + 0.999306i \(0.488136\pi\)
\(138\) 3.68427 0.313626
\(139\) 1.66686 0.141381 0.0706906 0.997498i \(-0.477480\pi\)
0.0706906 + 0.997498i \(0.477480\pi\)
\(140\) −3.41049 −0.288239
\(141\) −3.36652 −0.283513
\(142\) −1.16943 −0.0981360
\(143\) 7.38080 0.617214
\(144\) 1.05926 0.0882716
\(145\) −9.07242 −0.753423
\(146\) −13.4122 −1.11000
\(147\) 8.67977 0.715895
\(148\) −3.20421 −0.263385
\(149\) −6.00583 −0.492016 −0.246008 0.969268i \(-0.579119\pi\)
−0.246008 + 0.969268i \(0.579119\pi\)
\(150\) 1.36823 0.111715
\(151\) −9.22209 −0.750483 −0.375241 0.926927i \(-0.622440\pi\)
−0.375241 + 0.926927i \(0.622440\pi\)
\(152\) 6.85110 0.555697
\(153\) 1.14126 0.0922656
\(154\) 4.75681 0.383315
\(155\) 2.29560 0.184387
\(156\) 5.12911 0.410657
\(157\) 17.1910 1.37199 0.685997 0.727604i \(-0.259366\pi\)
0.685997 + 0.727604i \(0.259366\pi\)
\(158\) −1.87728 −0.149348
\(159\) −24.1376 −1.91424
\(160\) 2.07868 0.164334
\(161\) 3.00026 0.236453
\(162\) −11.0557 −0.868622
\(163\) −0.156081 −0.0122252 −0.00611260 0.999981i \(-0.501946\pi\)
−0.00611260 + 0.999981i \(0.501946\pi\)
\(164\) 7.10776 0.555023
\(165\) 12.1422 0.945265
\(166\) −2.72604 −0.211582
\(167\) −3.81756 −0.295412 −0.147706 0.989031i \(-0.547189\pi\)
−0.147706 + 0.989031i \(0.547189\pi\)
\(168\) 3.30563 0.255035
\(169\) −6.51908 −0.501468
\(170\) 2.23960 0.171769
\(171\) 7.25709 0.554964
\(172\) 8.50150 0.648234
\(173\) 3.33903 0.253862 0.126931 0.991912i \(-0.459487\pi\)
0.126931 + 0.991912i \(0.459487\pi\)
\(174\) 8.79346 0.666630
\(175\) 1.11421 0.0842261
\(176\) −2.89925 −0.218539
\(177\) −0.436421 −0.0328034
\(178\) 10.9186 0.818382
\(179\) 13.2977 0.993915 0.496958 0.867775i \(-0.334450\pi\)
0.496958 + 0.867775i \(0.334450\pi\)
\(180\) 2.20186 0.164117
\(181\) −5.73244 −0.426089 −0.213044 0.977043i \(-0.568338\pi\)
−0.213044 + 0.977043i \(0.568338\pi\)
\(182\) 4.17685 0.309609
\(183\) 20.2853 1.49953
\(184\) −1.82864 −0.134809
\(185\) −6.66052 −0.489691
\(186\) −2.22502 −0.163146
\(187\) −3.12370 −0.228427
\(188\) 1.67093 0.121865
\(189\) −6.41536 −0.466649
\(190\) 14.2412 1.03317
\(191\) −6.52684 −0.472266 −0.236133 0.971721i \(-0.575880\pi\)
−0.236133 + 0.971721i \(0.575880\pi\)
\(192\) −2.01476 −0.145403
\(193\) −0.0138109 −0.000994128 0 −0.000497064 1.00000i \(-0.500158\pi\)
−0.000497064 1.00000i \(0.500158\pi\)
\(194\) 15.4145 1.10669
\(195\) 10.6618 0.763504
\(196\) −4.30809 −0.307721
\(197\) −11.3785 −0.810687 −0.405343 0.914164i \(-0.632848\pi\)
−0.405343 + 0.914164i \(0.632848\pi\)
\(198\) −3.07106 −0.218250
\(199\) 22.1964 1.57346 0.786730 0.617297i \(-0.211772\pi\)
0.786730 + 0.617297i \(0.211772\pi\)
\(200\) −0.679103 −0.0480198
\(201\) 11.2417 0.792926
\(202\) −16.3718 −1.15192
\(203\) 7.16088 0.502595
\(204\) −2.17073 −0.151982
\(205\) 14.7747 1.03191
\(206\) 3.26015 0.227145
\(207\) −1.93700 −0.134631
\(208\) −2.54576 −0.176517
\(209\) −19.8630 −1.37395
\(210\) 6.87133 0.474167
\(211\) −6.05237 −0.416662 −0.208331 0.978058i \(-0.566803\pi\)
−0.208331 + 0.978058i \(0.566803\pi\)
\(212\) 11.9804 0.822816
\(213\) 2.35611 0.161438
\(214\) −17.7447 −1.21300
\(215\) 17.6719 1.20521
\(216\) 3.91013 0.266050
\(217\) −1.81193 −0.123001
\(218\) −14.0053 −0.948558
\(219\) 27.0223 1.82600
\(220\) −6.02660 −0.406313
\(221\) −2.74285 −0.184504
\(222\) 6.45572 0.433279
\(223\) −9.22732 −0.617907 −0.308954 0.951077i \(-0.599979\pi\)
−0.308954 + 0.951077i \(0.599979\pi\)
\(224\) −1.64070 −0.109624
\(225\) −0.719346 −0.0479564
\(226\) −5.42204 −0.360669
\(227\) 6.19976 0.411493 0.205746 0.978605i \(-0.434038\pi\)
0.205746 + 0.978605i \(0.434038\pi\)
\(228\) −13.8033 −0.914147
\(229\) 6.41997 0.424244 0.212122 0.977243i \(-0.431963\pi\)
0.212122 + 0.977243i \(0.431963\pi\)
\(230\) −3.80115 −0.250640
\(231\) −9.58383 −0.630570
\(232\) −4.36452 −0.286545
\(233\) −16.2164 −1.06237 −0.531187 0.847254i \(-0.678254\pi\)
−0.531187 + 0.847254i \(0.678254\pi\)
\(234\) −2.69662 −0.176284
\(235\) 3.47332 0.226575
\(236\) 0.216612 0.0141002
\(237\) 3.78227 0.245685
\(238\) −1.76772 −0.114584
\(239\) −5.11535 −0.330885 −0.165442 0.986219i \(-0.552905\pi\)
−0.165442 + 0.986219i \(0.552905\pi\)
\(240\) −4.18804 −0.270337
\(241\) −18.4665 −1.18953 −0.594766 0.803899i \(-0.702755\pi\)
−0.594766 + 0.803899i \(0.702755\pi\)
\(242\) −2.59436 −0.166772
\(243\) 10.5443 0.676417
\(244\) −10.0683 −0.644558
\(245\) −8.95512 −0.572122
\(246\) −14.3204 −0.913038
\(247\) −17.4413 −1.10976
\(248\) 1.10436 0.0701268
\(249\) 5.49233 0.348062
\(250\) −11.8050 −0.746615
\(251\) 23.3686 1.47502 0.737508 0.675339i \(-0.236002\pi\)
0.737508 + 0.675339i \(0.236002\pi\)
\(252\) −1.73793 −0.109479
\(253\) 5.30168 0.333314
\(254\) −20.4551 −1.28347
\(255\) −4.51226 −0.282568
\(256\) 1.00000 0.0625000
\(257\) −22.2985 −1.39094 −0.695470 0.718555i \(-0.744804\pi\)
−0.695470 + 0.718555i \(0.744804\pi\)
\(258\) −17.1285 −1.06637
\(259\) 5.25717 0.326664
\(260\) −5.29182 −0.328185
\(261\) −4.62316 −0.286166
\(262\) −7.14967 −0.441708
\(263\) −16.1755 −0.997426 −0.498713 0.866767i \(-0.666194\pi\)
−0.498713 + 0.866767i \(0.666194\pi\)
\(264\) 5.84129 0.359507
\(265\) 24.9033 1.52980
\(266\) −11.2406 −0.689207
\(267\) −21.9983 −1.34628
\(268\) −5.57966 −0.340832
\(269\) −20.6911 −1.26156 −0.630780 0.775962i \(-0.717265\pi\)
−0.630780 + 0.775962i \(0.717265\pi\)
\(270\) 8.12789 0.494648
\(271\) 13.7220 0.833550 0.416775 0.909010i \(-0.363160\pi\)
0.416775 + 0.909010i \(0.363160\pi\)
\(272\) 1.07742 0.0653279
\(273\) −8.41535 −0.509320
\(274\) 0.872289 0.0526969
\(275\) 1.96889 0.118728
\(276\) 3.68427 0.221767
\(277\) 21.9010 1.31590 0.657951 0.753061i \(-0.271423\pi\)
0.657951 + 0.753061i \(0.271423\pi\)
\(278\) 1.66686 0.0999717
\(279\) 1.16980 0.0700342
\(280\) −3.41049 −0.203816
\(281\) 18.4307 1.09949 0.549743 0.835334i \(-0.314726\pi\)
0.549743 + 0.835334i \(0.314726\pi\)
\(282\) −3.36652 −0.200474
\(283\) 10.5955 0.629837 0.314919 0.949119i \(-0.398023\pi\)
0.314919 + 0.949119i \(0.398023\pi\)
\(284\) −1.16943 −0.0693926
\(285\) −28.6926 −1.69961
\(286\) 7.38080 0.436436
\(287\) −11.6617 −0.688371
\(288\) 1.05926 0.0624175
\(289\) −15.8392 −0.931716
\(290\) −9.07242 −0.532751
\(291\) −31.0564 −1.82056
\(292\) −13.4122 −0.784887
\(293\) −19.8676 −1.16068 −0.580340 0.814374i \(-0.697080\pi\)
−0.580340 + 0.814374i \(0.697080\pi\)
\(294\) 8.67977 0.506214
\(295\) 0.450266 0.0262155
\(296\) −3.20421 −0.186241
\(297\) −11.3364 −0.657806
\(298\) −6.00583 −0.347908
\(299\) 4.65528 0.269222
\(300\) 1.36823 0.0789948
\(301\) −13.9485 −0.803976
\(302\) −9.22209 −0.530671
\(303\) 32.9853 1.89496
\(304\) 6.85110 0.392937
\(305\) −20.9288 −1.19838
\(306\) 1.14126 0.0652417
\(307\) −0.768845 −0.0438803 −0.0219402 0.999759i \(-0.506984\pi\)
−0.0219402 + 0.999759i \(0.506984\pi\)
\(308\) 4.75681 0.271044
\(309\) −6.56841 −0.373664
\(310\) 2.29560 0.130381
\(311\) 7.93499 0.449952 0.224976 0.974364i \(-0.427770\pi\)
0.224976 + 0.974364i \(0.427770\pi\)
\(312\) 5.12911 0.290378
\(313\) 13.2254 0.747541 0.373771 0.927521i \(-0.378065\pi\)
0.373771 + 0.927521i \(0.378065\pi\)
\(314\) 17.1910 0.970147
\(315\) −3.61260 −0.203547
\(316\) −1.87728 −0.105605
\(317\) −13.3207 −0.748165 −0.374083 0.927395i \(-0.622042\pi\)
−0.374083 + 0.927395i \(0.622042\pi\)
\(318\) −24.1376 −1.35357
\(319\) 12.6538 0.708478
\(320\) 2.07868 0.116202
\(321\) 35.7513 1.99544
\(322\) 3.00026 0.167198
\(323\) 7.38148 0.410717
\(324\) −11.0557 −0.614208
\(325\) 1.72884 0.0958985
\(326\) −0.156081 −0.00864452
\(327\) 28.2173 1.56042
\(328\) 7.10776 0.392460
\(329\) −2.74150 −0.151144
\(330\) 12.1422 0.668404
\(331\) 9.68418 0.532291 0.266145 0.963933i \(-0.414250\pi\)
0.266145 + 0.963933i \(0.414250\pi\)
\(332\) −2.72604 −0.149611
\(333\) −3.39409 −0.185995
\(334\) −3.81756 −0.208888
\(335\) −11.5983 −0.633683
\(336\) 3.30563 0.180337
\(337\) −13.4565 −0.733022 −0.366511 0.930414i \(-0.619448\pi\)
−0.366511 + 0.930414i \(0.619448\pi\)
\(338\) −6.51908 −0.354591
\(339\) 10.9241 0.593316
\(340\) 2.23960 0.121459
\(341\) −3.20181 −0.173388
\(342\) 7.25709 0.392419
\(343\) 18.5532 1.00178
\(344\) 8.50150 0.458370
\(345\) 7.65840 0.412315
\(346\) 3.33903 0.179507
\(347\) −33.5020 −1.79848 −0.899241 0.437454i \(-0.855880\pi\)
−0.899241 + 0.437454i \(0.855880\pi\)
\(348\) 8.79346 0.471379
\(349\) 22.2490 1.19096 0.595481 0.803369i \(-0.296961\pi\)
0.595481 + 0.803369i \(0.296961\pi\)
\(350\) 1.11421 0.0595569
\(351\) −9.95426 −0.531319
\(352\) −2.89925 −0.154530
\(353\) −18.4032 −0.979504 −0.489752 0.871862i \(-0.662913\pi\)
−0.489752 + 0.871862i \(0.662913\pi\)
\(354\) −0.436421 −0.0231955
\(355\) −2.43086 −0.129017
\(356\) 10.9186 0.578684
\(357\) 3.56153 0.188496
\(358\) 13.2977 0.702804
\(359\) 17.9357 0.946612 0.473306 0.880898i \(-0.343061\pi\)
0.473306 + 0.880898i \(0.343061\pi\)
\(360\) 2.20186 0.116048
\(361\) 27.9376 1.47040
\(362\) −5.73244 −0.301290
\(363\) 5.22701 0.274347
\(364\) 4.17685 0.218926
\(365\) −27.8795 −1.45928
\(366\) 20.2853 1.06033
\(367\) −28.2557 −1.47494 −0.737468 0.675382i \(-0.763979\pi\)
−0.737468 + 0.675382i \(0.763979\pi\)
\(368\) −1.82864 −0.0953244
\(369\) 7.52896 0.391942
\(370\) −6.66052 −0.346264
\(371\) −19.6563 −1.02050
\(372\) −2.22502 −0.115362
\(373\) −13.7847 −0.713744 −0.356872 0.934153i \(-0.616157\pi\)
−0.356872 + 0.934153i \(0.616157\pi\)
\(374\) −3.12370 −0.161522
\(375\) 23.7843 1.22822
\(376\) 1.67093 0.0861717
\(377\) 11.1110 0.572247
\(378\) −6.41536 −0.329971
\(379\) −1.98047 −0.101730 −0.0508649 0.998706i \(-0.516198\pi\)
−0.0508649 + 0.998706i \(0.516198\pi\)
\(380\) 14.2412 0.730559
\(381\) 41.2121 2.11136
\(382\) −6.52684 −0.333942
\(383\) 1.36202 0.0695960 0.0347980 0.999394i \(-0.488921\pi\)
0.0347980 + 0.999394i \(0.488921\pi\)
\(384\) −2.01476 −0.102815
\(385\) 9.88787 0.503933
\(386\) −0.0138109 −0.000702955 0
\(387\) 9.00530 0.457765
\(388\) 15.4145 0.782551
\(389\) 9.24189 0.468582 0.234291 0.972166i \(-0.424723\pi\)
0.234291 + 0.972166i \(0.424723\pi\)
\(390\) 10.6618 0.539879
\(391\) −1.97020 −0.0996375
\(392\) −4.30809 −0.217591
\(393\) 14.4049 0.726630
\(394\) −11.3785 −0.573242
\(395\) −3.90225 −0.196344
\(396\) −3.07106 −0.154326
\(397\) −26.7665 −1.34337 −0.671685 0.740837i \(-0.734429\pi\)
−0.671685 + 0.740837i \(0.734429\pi\)
\(398\) 22.1964 1.11260
\(399\) 22.6472 1.13378
\(400\) −0.679103 −0.0339551
\(401\) −23.6236 −1.17971 −0.589854 0.807510i \(-0.700815\pi\)
−0.589854 + 0.807510i \(0.700815\pi\)
\(402\) 11.2417 0.560684
\(403\) −2.81143 −0.140048
\(404\) −16.3718 −0.814529
\(405\) −22.9813 −1.14195
\(406\) 7.16088 0.355389
\(407\) 9.28980 0.460479
\(408\) −2.17073 −0.107467
\(409\) −29.0054 −1.43422 −0.717112 0.696958i \(-0.754537\pi\)
−0.717112 + 0.696958i \(0.754537\pi\)
\(410\) 14.7747 0.729672
\(411\) −1.75745 −0.0866888
\(412\) 3.26015 0.160616
\(413\) −0.355396 −0.0174879
\(414\) −1.93700 −0.0951985
\(415\) −5.66656 −0.278161
\(416\) −2.54576 −0.124816
\(417\) −3.35832 −0.164458
\(418\) −19.8630 −0.971533
\(419\) −0.958270 −0.0468146 −0.0234073 0.999726i \(-0.507451\pi\)
−0.0234073 + 0.999726i \(0.507451\pi\)
\(420\) 6.87133 0.335287
\(421\) 12.3654 0.602651 0.301325 0.953521i \(-0.402571\pi\)
0.301325 + 0.953521i \(0.402571\pi\)
\(422\) −6.05237 −0.294625
\(423\) 1.76995 0.0860579
\(424\) 11.9804 0.581819
\(425\) −0.731676 −0.0354915
\(426\) 2.35611 0.114154
\(427\) 16.5191 0.799418
\(428\) −17.7447 −0.857722
\(429\) −14.8705 −0.717957
\(430\) 17.6719 0.852214
\(431\) 28.1431 1.35561 0.677803 0.735244i \(-0.262932\pi\)
0.677803 + 0.735244i \(0.262932\pi\)
\(432\) 3.91013 0.188126
\(433\) −31.6017 −1.51868 −0.759340 0.650694i \(-0.774478\pi\)
−0.759340 + 0.650694i \(0.774478\pi\)
\(434\) −1.81193 −0.0869752
\(435\) 18.2788 0.876399
\(436\) −14.0053 −0.670732
\(437\) −12.5282 −0.599304
\(438\) 27.0223 1.29117
\(439\) −21.9805 −1.04907 −0.524537 0.851388i \(-0.675762\pi\)
−0.524537 + 0.851388i \(0.675762\pi\)
\(440\) −6.02660 −0.287307
\(441\) −4.56338 −0.217304
\(442\) −2.74285 −0.130464
\(443\) 1.25281 0.0595226 0.0297613 0.999557i \(-0.490525\pi\)
0.0297613 + 0.999557i \(0.490525\pi\)
\(444\) 6.45572 0.306375
\(445\) 22.6962 1.07590
\(446\) −9.22732 −0.436926
\(447\) 12.1003 0.572325
\(448\) −1.64070 −0.0775160
\(449\) 10.9508 0.516799 0.258399 0.966038i \(-0.416805\pi\)
0.258399 + 0.966038i \(0.416805\pi\)
\(450\) −0.719346 −0.0339103
\(451\) −20.6072 −0.970353
\(452\) −5.42204 −0.255031
\(453\) 18.5803 0.872978
\(454\) 6.19976 0.290969
\(455\) 8.68232 0.407033
\(456\) −13.8033 −0.646400
\(457\) −23.6447 −1.10605 −0.553026 0.833164i \(-0.686527\pi\)
−0.553026 + 0.833164i \(0.686527\pi\)
\(458\) 6.41997 0.299986
\(459\) 4.21283 0.196638
\(460\) −3.80115 −0.177229
\(461\) 19.9688 0.930041 0.465020 0.885300i \(-0.346047\pi\)
0.465020 + 0.885300i \(0.346047\pi\)
\(462\) −9.58383 −0.445880
\(463\) 11.2357 0.522169 0.261084 0.965316i \(-0.415920\pi\)
0.261084 + 0.965316i \(0.415920\pi\)
\(464\) −4.36452 −0.202618
\(465\) −4.62509 −0.214483
\(466\) −16.2164 −0.751212
\(467\) 25.9897 1.20266 0.601329 0.799001i \(-0.294638\pi\)
0.601329 + 0.799001i \(0.294638\pi\)
\(468\) −2.69662 −0.124652
\(469\) 9.15457 0.422719
\(470\) 3.47332 0.160213
\(471\) −34.6358 −1.59594
\(472\) 0.216612 0.00997037
\(473\) −24.6480 −1.13331
\(474\) 3.78227 0.173725
\(475\) −4.65260 −0.213476
\(476\) −1.76772 −0.0810234
\(477\) 12.6903 0.581050
\(478\) −5.11535 −0.233971
\(479\) −16.5809 −0.757601 −0.378801 0.925478i \(-0.623663\pi\)
−0.378801 + 0.925478i \(0.623663\pi\)
\(480\) −4.18804 −0.191157
\(481\) 8.15717 0.371935
\(482\) −18.4665 −0.841126
\(483\) −6.04480 −0.275048
\(484\) −2.59436 −0.117925
\(485\) 32.0417 1.45494
\(486\) 10.5443 0.478299
\(487\) 39.0680 1.77034 0.885171 0.465266i \(-0.154041\pi\)
0.885171 + 0.465266i \(0.154041\pi\)
\(488\) −10.0683 −0.455772
\(489\) 0.314465 0.0142206
\(490\) −8.95512 −0.404551
\(491\) 16.4517 0.742454 0.371227 0.928542i \(-0.378937\pi\)
0.371227 + 0.928542i \(0.378937\pi\)
\(492\) −14.3204 −0.645615
\(493\) −4.70240 −0.211785
\(494\) −17.4413 −0.784720
\(495\) −6.38373 −0.286927
\(496\) 1.10436 0.0495871
\(497\) 1.91868 0.0860647
\(498\) 5.49233 0.246117
\(499\) −21.2789 −0.952574 −0.476287 0.879290i \(-0.658018\pi\)
−0.476287 + 0.879290i \(0.658018\pi\)
\(500\) −11.8050 −0.527937
\(501\) 7.69147 0.343630
\(502\) 23.3686 1.04299
\(503\) 30.3539 1.35341 0.676707 0.736253i \(-0.263406\pi\)
0.676707 + 0.736253i \(0.263406\pi\)
\(504\) −1.73793 −0.0774136
\(505\) −34.0317 −1.51439
\(506\) 5.30168 0.235688
\(507\) 13.1344 0.583319
\(508\) −20.4551 −0.907549
\(509\) 21.6615 0.960129 0.480064 0.877233i \(-0.340613\pi\)
0.480064 + 0.877233i \(0.340613\pi\)
\(510\) −4.51226 −0.199806
\(511\) 22.0054 0.973461
\(512\) 1.00000 0.0441942
\(513\) 26.7887 1.18275
\(514\) −22.2985 −0.983543
\(515\) 6.77679 0.298621
\(516\) −17.1285 −0.754040
\(517\) −4.84444 −0.213058
\(518\) 5.25717 0.230987
\(519\) −6.72734 −0.295297
\(520\) −5.29182 −0.232062
\(521\) −15.5545 −0.681455 −0.340728 0.940162i \(-0.610673\pi\)
−0.340728 + 0.940162i \(0.610673\pi\)
\(522\) −4.62316 −0.202350
\(523\) −22.1847 −0.970068 −0.485034 0.874495i \(-0.661193\pi\)
−0.485034 + 0.874495i \(0.661193\pi\)
\(524\) −7.14967 −0.312335
\(525\) −2.24486 −0.0979737
\(526\) −16.1755 −0.705287
\(527\) 1.18985 0.0518308
\(528\) 5.84129 0.254210
\(529\) −19.6561 −0.854612
\(530\) 24.9033 1.08173
\(531\) 0.229448 0.00995720
\(532\) −11.2406 −0.487343
\(533\) −18.0947 −0.783768
\(534\) −21.9983 −0.951961
\(535\) −36.8855 −1.59470
\(536\) −5.57966 −0.241004
\(537\) −26.7916 −1.15614
\(538\) −20.6911 −0.892057
\(539\) 12.4902 0.537992
\(540\) 8.12789 0.349769
\(541\) 37.0805 1.59422 0.797108 0.603836i \(-0.206362\pi\)
0.797108 + 0.603836i \(0.206362\pi\)
\(542\) 13.7220 0.589409
\(543\) 11.5495 0.495636
\(544\) 1.07742 0.0461938
\(545\) −29.1125 −1.24704
\(546\) −8.41535 −0.360144
\(547\) −22.6540 −0.968616 −0.484308 0.874898i \(-0.660929\pi\)
−0.484308 + 0.874898i \(0.660929\pi\)
\(548\) 0.872289 0.0372624
\(549\) −10.6650 −0.455170
\(550\) 1.96889 0.0839536
\(551\) −29.9017 −1.27386
\(552\) 3.68427 0.156813
\(553\) 3.08006 0.130977
\(554\) 21.9010 0.930483
\(555\) 13.4194 0.569620
\(556\) 1.66686 0.0706906
\(557\) −38.9272 −1.64940 −0.824700 0.565570i \(-0.808656\pi\)
−0.824700 + 0.565570i \(0.808656\pi\)
\(558\) 1.16980 0.0495216
\(559\) −21.6428 −0.915394
\(560\) −3.41049 −0.144120
\(561\) 6.29350 0.265712
\(562\) 18.4307 0.777454
\(563\) 21.7304 0.915826 0.457913 0.888997i \(-0.348597\pi\)
0.457913 + 0.888997i \(0.348597\pi\)
\(564\) −3.36652 −0.141756
\(565\) −11.2707 −0.474160
\(566\) 10.5955 0.445362
\(567\) 18.1392 0.761776
\(568\) −1.16943 −0.0490680
\(569\) −0.0195358 −0.000818983 0 −0.000409492 1.00000i \(-0.500130\pi\)
−0.000409492 1.00000i \(0.500130\pi\)
\(570\) −28.6926 −1.20180
\(571\) −33.7804 −1.41367 −0.706834 0.707380i \(-0.749877\pi\)
−0.706834 + 0.707380i \(0.749877\pi\)
\(572\) 7.38080 0.308607
\(573\) 13.1500 0.549350
\(574\) −11.6617 −0.486751
\(575\) 1.24183 0.0517880
\(576\) 1.05926 0.0441358
\(577\) 10.1027 0.420583 0.210291 0.977639i \(-0.432559\pi\)
0.210291 + 0.977639i \(0.432559\pi\)
\(578\) −15.8392 −0.658823
\(579\) 0.0278256 0.00115639
\(580\) −9.07242 −0.376712
\(581\) 4.47263 0.185556
\(582\) −31.0564 −1.28733
\(583\) −34.7341 −1.43854
\(584\) −13.4122 −0.554999
\(585\) −5.60541 −0.231755
\(586\) −19.8676 −0.820724
\(587\) 40.0622 1.65354 0.826772 0.562537i \(-0.190175\pi\)
0.826772 + 0.562537i \(0.190175\pi\)
\(588\) 8.67977 0.357947
\(589\) 7.56606 0.311754
\(590\) 0.450266 0.0185372
\(591\) 22.9250 0.943009
\(592\) −3.20421 −0.131692
\(593\) −9.83030 −0.403682 −0.201841 0.979418i \(-0.564692\pi\)
−0.201841 + 0.979418i \(0.564692\pi\)
\(594\) −11.3364 −0.465139
\(595\) −3.67452 −0.150641
\(596\) −6.00583 −0.246008
\(597\) −44.7204 −1.83029
\(598\) 4.65528 0.190369
\(599\) 38.7111 1.58169 0.790846 0.612015i \(-0.209641\pi\)
0.790846 + 0.612015i \(0.209641\pi\)
\(600\) 1.36823 0.0558577
\(601\) −37.0042 −1.50943 −0.754716 0.656051i \(-0.772225\pi\)
−0.754716 + 0.656051i \(0.772225\pi\)
\(602\) −13.9485 −0.568497
\(603\) −5.91030 −0.240686
\(604\) −9.22209 −0.375241
\(605\) −5.39284 −0.219250
\(606\) 32.9853 1.33994
\(607\) 35.7322 1.45033 0.725163 0.688577i \(-0.241764\pi\)
0.725163 + 0.688577i \(0.241764\pi\)
\(608\) 6.85110 0.277849
\(609\) −14.4275 −0.584630
\(610\) −20.9288 −0.847382
\(611\) −4.25380 −0.172090
\(612\) 1.14126 0.0461328
\(613\) −1.78866 −0.0722434 −0.0361217 0.999347i \(-0.511500\pi\)
−0.0361217 + 0.999347i \(0.511500\pi\)
\(614\) −0.768845 −0.0310281
\(615\) −29.7676 −1.20034
\(616\) 4.75681 0.191657
\(617\) −46.2330 −1.86127 −0.930635 0.365948i \(-0.880745\pi\)
−0.930635 + 0.365948i \(0.880745\pi\)
\(618\) −6.56841 −0.264220
\(619\) 4.35356 0.174984 0.0874921 0.996165i \(-0.472115\pi\)
0.0874921 + 0.996165i \(0.472115\pi\)
\(620\) 2.29560 0.0921936
\(621\) −7.15021 −0.286928
\(622\) 7.93499 0.318164
\(623\) −17.9142 −0.717716
\(624\) 5.12911 0.205329
\(625\) −21.1433 −0.845732
\(626\) 13.2254 0.528591
\(627\) 40.0193 1.59822
\(628\) 17.1910 0.685997
\(629\) −3.45227 −0.137651
\(630\) −3.61260 −0.143929
\(631\) −10.3924 −0.413716 −0.206858 0.978371i \(-0.566324\pi\)
−0.206858 + 0.978371i \(0.566324\pi\)
\(632\) −1.87728 −0.0746741
\(633\) 12.1941 0.484671
\(634\) −13.3207 −0.529033
\(635\) −42.5196 −1.68734
\(636\) −24.1376 −0.957118
\(637\) 10.9674 0.434543
\(638\) 12.6538 0.500969
\(639\) −1.23873 −0.0490032
\(640\) 2.07868 0.0821669
\(641\) 8.25885 0.326205 0.163103 0.986609i \(-0.447850\pi\)
0.163103 + 0.986609i \(0.447850\pi\)
\(642\) 35.7513 1.41099
\(643\) 10.5189 0.414826 0.207413 0.978254i \(-0.433496\pi\)
0.207413 + 0.978254i \(0.433496\pi\)
\(644\) 3.00026 0.118227
\(645\) −35.6046 −1.40193
\(646\) 7.38148 0.290421
\(647\) 0.435539 0.0171228 0.00856140 0.999963i \(-0.497275\pi\)
0.00856140 + 0.999963i \(0.497275\pi\)
\(648\) −11.0557 −0.434311
\(649\) −0.628011 −0.0246516
\(650\) 1.72884 0.0678105
\(651\) 3.65060 0.143078
\(652\) −0.156081 −0.00611260
\(653\) −12.3102 −0.481734 −0.240867 0.970558i \(-0.577432\pi\)
−0.240867 + 0.970558i \(0.577432\pi\)
\(654\) 28.2173 1.10338
\(655\) −14.8618 −0.580701
\(656\) 7.10776 0.277511
\(657\) −14.2070 −0.554266
\(658\) −2.74150 −0.106875
\(659\) −34.9670 −1.36212 −0.681060 0.732227i \(-0.738481\pi\)
−0.681060 + 0.732227i \(0.738481\pi\)
\(660\) 12.1422 0.472633
\(661\) 8.79554 0.342107 0.171054 0.985262i \(-0.445283\pi\)
0.171054 + 0.985262i \(0.445283\pi\)
\(662\) 9.68418 0.376386
\(663\) 5.52618 0.214619
\(664\) −2.72604 −0.105791
\(665\) −23.3656 −0.906081
\(666\) −3.39409 −0.131518
\(667\) 7.98112 0.309030
\(668\) −3.81756 −0.147706
\(669\) 18.5908 0.718763
\(670\) −11.5983 −0.448082
\(671\) 29.1906 1.12689
\(672\) 3.30563 0.127517
\(673\) −36.7564 −1.41686 −0.708428 0.705783i \(-0.750595\pi\)
−0.708428 + 0.705783i \(0.750595\pi\)
\(674\) −13.4565 −0.518325
\(675\) −2.65538 −0.102206
\(676\) −6.51908 −0.250734
\(677\) −34.7975 −1.33738 −0.668688 0.743543i \(-0.733144\pi\)
−0.668688 + 0.743543i \(0.733144\pi\)
\(678\) 10.9241 0.419538
\(679\) −25.2906 −0.970563
\(680\) 2.23960 0.0858847
\(681\) −12.4910 −0.478657
\(682\) −3.20181 −0.122604
\(683\) −15.8912 −0.608058 −0.304029 0.952663i \(-0.598332\pi\)
−0.304029 + 0.952663i \(0.598332\pi\)
\(684\) 7.25709 0.277482
\(685\) 1.81321 0.0692791
\(686\) 18.5532 0.708366
\(687\) −12.9347 −0.493490
\(688\) 8.50150 0.324117
\(689\) −30.4992 −1.16193
\(690\) 7.65840 0.291550
\(691\) −26.6627 −1.01430 −0.507148 0.861859i \(-0.669300\pi\)
−0.507148 + 0.861859i \(0.669300\pi\)
\(692\) 3.33903 0.126931
\(693\) 5.03870 0.191404
\(694\) −33.5020 −1.27172
\(695\) 3.46486 0.131430
\(696\) 8.79346 0.333315
\(697\) 7.65801 0.290068
\(698\) 22.2490 0.842138
\(699\) 32.6723 1.23578
\(700\) 1.11421 0.0421131
\(701\) 35.0557 1.32404 0.662018 0.749488i \(-0.269700\pi\)
0.662018 + 0.749488i \(0.269700\pi\)
\(702\) −9.95426 −0.375699
\(703\) −21.9524 −0.827949
\(704\) −2.89925 −0.109270
\(705\) −6.99792 −0.263557
\(706\) −18.4032 −0.692614
\(707\) 26.8613 1.01022
\(708\) −0.436421 −0.0164017
\(709\) 33.3012 1.25065 0.625327 0.780363i \(-0.284965\pi\)
0.625327 + 0.780363i \(0.284965\pi\)
\(710\) −2.43086 −0.0912285
\(711\) −1.98852 −0.0745755
\(712\) 10.9186 0.409191
\(713\) −2.01947 −0.0756298
\(714\) 3.56153 0.133287
\(715\) 15.3423 0.573770
\(716\) 13.2977 0.496958
\(717\) 10.3062 0.384892
\(718\) 17.9357 0.669355
\(719\) 24.7119 0.921597 0.460799 0.887505i \(-0.347563\pi\)
0.460799 + 0.887505i \(0.347563\pi\)
\(720\) 2.20186 0.0820584
\(721\) −5.34894 −0.199205
\(722\) 27.9376 1.03973
\(723\) 37.2056 1.38369
\(724\) −5.73244 −0.213044
\(725\) 2.96396 0.110079
\(726\) 5.22701 0.193993
\(727\) 2.74802 0.101919 0.0509593 0.998701i \(-0.483772\pi\)
0.0509593 + 0.998701i \(0.483772\pi\)
\(728\) 4.17685 0.154804
\(729\) 11.9230 0.441593
\(730\) −27.8795 −1.03187
\(731\) 9.15965 0.338782
\(732\) 20.2853 0.749765
\(733\) 22.8128 0.842609 0.421305 0.906919i \(-0.361572\pi\)
0.421305 + 0.906919i \(0.361572\pi\)
\(734\) −28.2557 −1.04294
\(735\) 18.0424 0.665505
\(736\) −1.82864 −0.0674045
\(737\) 16.1768 0.595880
\(738\) 7.52896 0.277145
\(739\) −48.1180 −1.77005 −0.885024 0.465545i \(-0.845858\pi\)
−0.885024 + 0.465545i \(0.845858\pi\)
\(740\) −6.66052 −0.244846
\(741\) 35.1400 1.29090
\(742\) −19.6563 −0.721604
\(743\) 21.9843 0.806525 0.403263 0.915084i \(-0.367876\pi\)
0.403263 + 0.915084i \(0.367876\pi\)
\(744\) −2.22502 −0.0815731
\(745\) −12.4842 −0.457385
\(746\) −13.7847 −0.504693
\(747\) −2.88759 −0.105651
\(748\) −3.12370 −0.114214
\(749\) 29.1138 1.06380
\(750\) 23.7843 0.868479
\(751\) −13.9298 −0.508305 −0.254152 0.967164i \(-0.581796\pi\)
−0.254152 + 0.967164i \(0.581796\pi\)
\(752\) 1.67093 0.0609326
\(753\) −47.0822 −1.71577
\(754\) 11.1110 0.404640
\(755\) −19.1697 −0.697658
\(756\) −6.41536 −0.233325
\(757\) −36.7228 −1.33471 −0.667357 0.744738i \(-0.732574\pi\)
−0.667357 + 0.744738i \(0.732574\pi\)
\(758\) −1.98047 −0.0719338
\(759\) −10.6816 −0.387718
\(760\) 14.2412 0.516583
\(761\) −15.8787 −0.575603 −0.287801 0.957690i \(-0.592924\pi\)
−0.287801 + 0.957690i \(0.592924\pi\)
\(762\) 41.2121 1.49296
\(763\) 22.9786 0.831880
\(764\) −6.52684 −0.236133
\(765\) 2.37232 0.0857713
\(766\) 1.36202 0.0492118
\(767\) −0.551443 −0.0199114
\(768\) −2.01476 −0.0727014
\(769\) −16.4751 −0.594107 −0.297053 0.954861i \(-0.596004\pi\)
−0.297053 + 0.954861i \(0.596004\pi\)
\(770\) 9.88787 0.356334
\(771\) 44.9261 1.61797
\(772\) −0.0138109 −0.000497064 0
\(773\) −42.6855 −1.53529 −0.767645 0.640875i \(-0.778572\pi\)
−0.767645 + 0.640875i \(0.778572\pi\)
\(774\) 9.00530 0.323689
\(775\) −0.749973 −0.0269398
\(776\) 15.4145 0.553347
\(777\) −10.5919 −0.379983
\(778\) 9.24189 0.331338
\(779\) 48.6960 1.74471
\(780\) 10.6618 0.381752
\(781\) 3.39046 0.121320
\(782\) −1.97020 −0.0704544
\(783\) −17.0658 −0.609882
\(784\) −4.30809 −0.153860
\(785\) 35.7346 1.27542
\(786\) 14.4049 0.513805
\(787\) −36.5012 −1.30113 −0.650564 0.759452i \(-0.725467\pi\)
−0.650564 + 0.759452i \(0.725467\pi\)
\(788\) −11.3785 −0.405343
\(789\) 32.5898 1.16023
\(790\) −3.90225 −0.138836
\(791\) 8.89596 0.316304
\(792\) −3.07106 −0.109125
\(793\) 25.6316 0.910204
\(794\) −26.7665 −0.949906
\(795\) −50.1743 −1.77950
\(796\) 22.1964 0.786730
\(797\) −17.7825 −0.629888 −0.314944 0.949110i \(-0.601986\pi\)
−0.314944 + 0.949110i \(0.601986\pi\)
\(798\) 22.6472 0.801701
\(799\) 1.80029 0.0636896
\(800\) −0.679103 −0.0240099
\(801\) 11.5656 0.408651
\(802\) −23.6236 −0.834179
\(803\) 38.8852 1.37223
\(804\) 11.2417 0.396463
\(805\) 6.23656 0.219810
\(806\) −2.81143 −0.0990286
\(807\) 41.6876 1.46747
\(808\) −16.3718 −0.575959
\(809\) 18.1265 0.637293 0.318647 0.947874i \(-0.396772\pi\)
0.318647 + 0.947874i \(0.396772\pi\)
\(810\) −22.9813 −0.807481
\(811\) 34.3911 1.20763 0.603817 0.797123i \(-0.293646\pi\)
0.603817 + 0.797123i \(0.293646\pi\)
\(812\) 7.16088 0.251298
\(813\) −27.6465 −0.969604
\(814\) 9.28980 0.325607
\(815\) −0.324442 −0.0113647
\(816\) −2.17073 −0.0759909
\(817\) 58.2446 2.03772
\(818\) −29.0054 −1.01415
\(819\) 4.42437 0.154600
\(820\) 14.7747 0.515956
\(821\) −20.6292 −0.719965 −0.359982 0.932959i \(-0.617217\pi\)
−0.359982 + 0.932959i \(0.617217\pi\)
\(822\) −1.75745 −0.0612983
\(823\) 2.44475 0.0852188 0.0426094 0.999092i \(-0.486433\pi\)
0.0426094 + 0.999092i \(0.486433\pi\)
\(824\) 3.26015 0.113573
\(825\) −3.96684 −0.138108
\(826\) −0.355396 −0.0123658
\(827\) −45.6089 −1.58598 −0.792989 0.609236i \(-0.791476\pi\)
−0.792989 + 0.609236i \(0.791476\pi\)
\(828\) −1.93700 −0.0673155
\(829\) 13.6372 0.473638 0.236819 0.971554i \(-0.423895\pi\)
0.236819 + 0.971554i \(0.423895\pi\)
\(830\) −5.66656 −0.196689
\(831\) −44.1252 −1.53069
\(832\) −2.54576 −0.0882585
\(833\) −4.64160 −0.160822
\(834\) −3.35832 −0.116289
\(835\) −7.93548 −0.274618
\(836\) −19.8630 −0.686977
\(837\) 4.31818 0.149258
\(838\) −0.958270 −0.0331029
\(839\) 42.3796 1.46311 0.731554 0.681784i \(-0.238796\pi\)
0.731554 + 0.681784i \(0.238796\pi\)
\(840\) 6.87133 0.237083
\(841\) −9.95099 −0.343138
\(842\) 12.3654 0.426139
\(843\) −37.1335 −1.27895
\(844\) −6.05237 −0.208331
\(845\) −13.5511 −0.466171
\(846\) 1.76995 0.0608521
\(847\) 4.25658 0.146258
\(848\) 11.9804 0.411408
\(849\) −21.3474 −0.732641
\(850\) −0.731676 −0.0250963
\(851\) 5.85935 0.200856
\(852\) 2.35611 0.0807191
\(853\) −46.9400 −1.60719 −0.803597 0.595173i \(-0.797083\pi\)
−0.803597 + 0.595173i \(0.797083\pi\)
\(854\) 16.5191 0.565274
\(855\) 15.0851 0.515901
\(856\) −17.7447 −0.606501
\(857\) −9.40426 −0.321243 −0.160622 0.987016i \(-0.551350\pi\)
−0.160622 + 0.987016i \(0.551350\pi\)
\(858\) −14.8705 −0.507672
\(859\) 48.6688 1.66056 0.830280 0.557347i \(-0.188181\pi\)
0.830280 + 0.557347i \(0.188181\pi\)
\(860\) 17.6719 0.602606
\(861\) 23.4956 0.800728
\(862\) 28.1431 0.958558
\(863\) 2.45019 0.0834055 0.0417027 0.999130i \(-0.486722\pi\)
0.0417027 + 0.999130i \(0.486722\pi\)
\(864\) 3.91013 0.133025
\(865\) 6.94076 0.235993
\(866\) −31.6017 −1.07387
\(867\) 31.9121 1.08379
\(868\) −1.81193 −0.0615007
\(869\) 5.44269 0.184631
\(870\) 18.2788 0.619708
\(871\) 14.2045 0.481301
\(872\) −14.0053 −0.474279
\(873\) 16.3279 0.552616
\(874\) −12.5282 −0.423772
\(875\) 19.3686 0.654777
\(876\) 27.0223 0.912999
\(877\) 29.3592 0.991389 0.495694 0.868497i \(-0.334914\pi\)
0.495694 + 0.868497i \(0.334914\pi\)
\(878\) −21.9805 −0.741807
\(879\) 40.0285 1.35013
\(880\) −6.02660 −0.203157
\(881\) 51.1617 1.72368 0.861841 0.507178i \(-0.169311\pi\)
0.861841 + 0.507178i \(0.169311\pi\)
\(882\) −4.56338 −0.153657
\(883\) 40.4496 1.36124 0.680619 0.732638i \(-0.261711\pi\)
0.680619 + 0.732638i \(0.261711\pi\)
\(884\) −2.74285 −0.0922519
\(885\) −0.907178 −0.0304945
\(886\) 1.25281 0.0420888
\(887\) 1.11177 0.0373297 0.0186648 0.999826i \(-0.494058\pi\)
0.0186648 + 0.999826i \(0.494058\pi\)
\(888\) 6.45572 0.216640
\(889\) 33.5608 1.12559
\(890\) 22.6962 0.760778
\(891\) 32.0534 1.07383
\(892\) −9.22732 −0.308954
\(893\) 11.4477 0.383083
\(894\) 12.1003 0.404695
\(895\) 27.6416 0.923956
\(896\) −1.64070 −0.0548121
\(897\) −9.37928 −0.313165
\(898\) 10.9508 0.365432
\(899\) −4.81999 −0.160756
\(900\) −0.719346 −0.0239782
\(901\) 12.9079 0.430023
\(902\) −20.6072 −0.686143
\(903\) 28.1028 0.935203
\(904\) −5.42204 −0.180334
\(905\) −11.9159 −0.396098
\(906\) 18.5803 0.617289
\(907\) −47.6699 −1.58285 −0.791427 0.611263i \(-0.790662\pi\)
−0.791427 + 0.611263i \(0.790662\pi\)
\(908\) 6.19976 0.205746
\(909\) −17.3420 −0.575198
\(910\) 8.68232 0.287816
\(911\) 10.2555 0.339781 0.169891 0.985463i \(-0.445659\pi\)
0.169891 + 0.985463i \(0.445659\pi\)
\(912\) −13.8033 −0.457074
\(913\) 7.90348 0.261567
\(914\) −23.6447 −0.782096
\(915\) 42.1665 1.39398
\(916\) 6.41997 0.212122
\(917\) 11.7305 0.387375
\(918\) 4.21283 0.139044
\(919\) −28.0002 −0.923642 −0.461821 0.886973i \(-0.652804\pi\)
−0.461821 + 0.886973i \(0.652804\pi\)
\(920\) −3.80115 −0.125320
\(921\) 1.54904 0.0510426
\(922\) 19.9688 0.657638
\(923\) 2.97708 0.0979919
\(924\) −9.58383 −0.315285
\(925\) 2.17599 0.0715461
\(926\) 11.2357 0.369229
\(927\) 3.45334 0.113423
\(928\) −4.36452 −0.143272
\(929\) −5.10335 −0.167435 −0.0837177 0.996490i \(-0.526679\pi\)
−0.0837177 + 0.996490i \(0.526679\pi\)
\(930\) −4.62509 −0.151663
\(931\) −29.5151 −0.967319
\(932\) −16.2164 −0.531187
\(933\) −15.9871 −0.523394
\(934\) 25.9897 0.850408
\(935\) −6.49315 −0.212349
\(936\) −2.69662 −0.0881419
\(937\) 2.82938 0.0924317 0.0462158 0.998931i \(-0.485284\pi\)
0.0462158 + 0.998931i \(0.485284\pi\)
\(938\) 9.15457 0.298907
\(939\) −26.6459 −0.869556
\(940\) 3.47332 0.113287
\(941\) 15.6158 0.509060 0.254530 0.967065i \(-0.418079\pi\)
0.254530 + 0.967065i \(0.418079\pi\)
\(942\) −34.6358 −1.12850
\(943\) −12.9975 −0.423258
\(944\) 0.216612 0.00705011
\(945\) −13.3355 −0.433803
\(946\) −24.6480 −0.801375
\(947\) 25.3784 0.824687 0.412344 0.911028i \(-0.364710\pi\)
0.412344 + 0.911028i \(0.364710\pi\)
\(948\) 3.78227 0.122842
\(949\) 34.1442 1.10837
\(950\) −4.65260 −0.150950
\(951\) 26.8380 0.870283
\(952\) −1.76772 −0.0572922
\(953\) −9.28471 −0.300761 −0.150381 0.988628i \(-0.548050\pi\)
−0.150381 + 0.988628i \(0.548050\pi\)
\(954\) 12.6903 0.410865
\(955\) −13.5672 −0.439024
\(956\) −5.11535 −0.165442
\(957\) −25.4944 −0.824117
\(958\) −16.5809 −0.535705
\(959\) −1.43117 −0.0462149
\(960\) −4.18804 −0.135168
\(961\) −29.7804 −0.960658
\(962\) 8.15717 0.262998
\(963\) −18.7962 −0.605700
\(964\) −18.4665 −0.594766
\(965\) −0.0287083 −0.000924154 0
\(966\) −6.04480 −0.194488
\(967\) 15.8865 0.510875 0.255438 0.966826i \(-0.417780\pi\)
0.255438 + 0.966826i \(0.417780\pi\)
\(968\) −2.59436 −0.0833859
\(969\) −14.8719 −0.477755
\(970\) 32.0417 1.02880
\(971\) −26.6849 −0.856361 −0.428180 0.903693i \(-0.640845\pi\)
−0.428180 + 0.903693i \(0.640845\pi\)
\(972\) 10.5443 0.338209
\(973\) −2.73483 −0.0876745
\(974\) 39.0680 1.25182
\(975\) −3.48319 −0.111551
\(976\) −10.0683 −0.322279
\(977\) 52.6438 1.68422 0.842111 0.539304i \(-0.181312\pi\)
0.842111 + 0.539304i \(0.181312\pi\)
\(978\) 0.314465 0.0100555
\(979\) −31.6557 −1.01172
\(980\) −8.95512 −0.286061
\(981\) −14.8352 −0.473653
\(982\) 16.4517 0.524994
\(983\) −21.1790 −0.675504 −0.337752 0.941235i \(-0.609667\pi\)
−0.337752 + 0.941235i \(0.609667\pi\)
\(984\) −14.3204 −0.456519
\(985\) −23.6523 −0.753625
\(986\) −4.70240 −0.149755
\(987\) 5.52347 0.175814
\(988\) −17.4413 −0.554881
\(989\) −15.5462 −0.494340
\(990\) −6.38373 −0.202888
\(991\) −25.2156 −0.800999 −0.400499 0.916297i \(-0.631163\pi\)
−0.400499 + 0.916297i \(0.631163\pi\)
\(992\) 1.10436 0.0350634
\(993\) −19.5113 −0.619172
\(994\) 1.91868 0.0608569
\(995\) 46.1391 1.46271
\(996\) 5.49233 0.174031
\(997\) 24.1344 0.764343 0.382171 0.924091i \(-0.375176\pi\)
0.382171 + 0.924091i \(0.375176\pi\)
\(998\) −21.2789 −0.673572
\(999\) −12.5289 −0.396396
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 \(a_p\))